Finite Group Databasebeta

← C2×#23777729 #35195860

Subgroups — C2×#23777729 #35195860

Order 20224.

8814 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777729C2132yesmaximal, direct product factor
2C2×#19099303C212yesmaximal, complemented
3C2×#19099301C212yesmaximal, complemented
4C2×#19099296C211yesmaximal, characteristic, complemented
5C2×#19099234C211yesmaximal, characteristic, complemented
6C2×#19099231C211yesmaximal, characteristic, complemented
7C2×#19099210C211yesmaximal, characteristic, complemented
8C2×#19099208C211yesmaximal, characteristic, complemented
9C2×#19099205C212yesmaximal, complemented
10C2×D4×D316C211yesmaximal, characteristic, complemented
11C2×#19099197C212yesmaximal, complemented
12C2×#19099197C211yesmaximal, characteristic, complemented
13C2×#19099197C211yesmaximal, characteristic, complemented
14C2×#19099169C211yesmaximal, characteristic, complemented
15C2×#19099165C212yesmaximal, complemented
16C2×#19099132C211yesmaximal, characteristic, complemented
17C2×#19099129C212yesmaximal, complemented
18C2×#19099126C211yesmaximal, characteristic, complemented
19C2×#19099124C212yesmaximal, complemented
20C2×#19099121C212yesmaximal, complemented
21C2×#127×D79C211yesmaximal, characteristic, complemented
22C2×#19099098C211yesmaximal, characteristic, complemented
23C2×#19099091C211yesmaximal, characteristic, complemented
24C2×#540×C79C211yesmaximal, characteristic, complemented
25C22×#11929624C2212yescomplemented
26C22×#11929624C2211yescharacteristic, complemented
27C22×#11929623C2211yescharacteristic, complemented
28C23×D316C2211yescharacteristic, complemented
29C23×D316C2212yescomplemented
30C22×D4×D79C2212yescomplemented
31C22×D4×D79C2212yescomplemented
32C22×D4×D79C2211yescharacteristic, complemented
33C22×D4×D79C2212yescomplemented
34C22×D4×D79C2211yescharacteristic, complemented
35C22×D4×D79C2211yescharacteristic, complemented
36C22×D4×D79C2212yescomplemented
37#19099303C22132yescomplemented
38#19099301C22132yescomplemented
39#19099296C22116yescomplemented
40#19099234C22116yescomplemented
41#19099231C22116yescomplemented
42#19099210C22116yescomplemented
43#19099208C22116yescomplemented
44#19099205C22132yescomplemented
45D4×D316C22116yescomplemented
46#19099197C22132yescomplemented
47#19099197C22116yescomplemented
48#19099197C22116yescomplemented
49#19099169C22116yescomplemented
50#19099165C22132yescomplemented
51#19099132C22116yescomplemented
52#19099129C22132yescomplemented
53#19099126C22116yescomplemented
54#19099124C22132yescomplemented
55#19099121C22132yescomplemented
56C2×#14579158C2211yescharacteristic, complemented
57C2×#14579158C2211yescharacteristic, complemented
58C2×#14579157C2211yescharacteristic
59C2×#14579157C2212yescomplemented
60C2×#14579157C2211yescharacteristic, complemented
61C2×#14579157C2211yescharacteristic, complemented
62C2×#14579157C2212yescomplemented
63C2×#14579157C2212yescomplemented
64#127×D79C22116yescomplemented
65#19099098C22116yescomplemented
66#19099091C22116yescomplemented
67C2×#14579156C2211yescharacteristic, complemented
68C2×#14579156C2212yescomplemented
69C2×#14579154C2211yescharacteristic, complemented
70C2×#14579151C2211yescharacteristic, complemented
71C2×#14579149C2211yescharacteristic, complemented
72C2×#14579149C2211yescharacteristic, complemented
73C2×#14579148C2211yescharacteristic, complemented
74C2×#14579147C2212yescomplemented
75C2×#14579147C2211yescharacteristic, complemented
76C2×#14579146C2212yescomplemented
77C2×#14579146C2211yescharacteristic, complemented
78C2×#14579146C2212yescomplemented
79C2×#14579146C2212yescomplemented
80C2×#14579145C2212yescomplemented
81C2×#14579144C2212yescomplemented
82C2×#14579143C2212yescomplemented
83C2×#14579143C2211yescharacteristic, complemented
84C2×#14579143C2212yescomplemented
85C2×#14579141C2211yescharacteristic, complemented
86C2×#14579139C2211yescharacteristic, complemented
87C2×#14579136C2211yescharacteristic
88C2×#14579136C2211yescharacteristic, complemented
89C2×#14579136C2212yescomplemented
90C2×#14579136C2211yescharacteristic, complemented
91C2×#14579136C2212yescomplemented
92C2×#14579136C2212yescomplemented
93C2×#14579136C2212yescomplemented
94C2×#14579135C2212yescomplemented
95C2×#14579135C2212yescomplemented
96C2×#14579135C2212yescomplemented
97C2×#14579134C2211yescharacteristic
98C2×#14579134C2212yescomplemented
99C2×#14579134C2212yescomplemented
100C2×#14579134C2212yescomplemented
101C2×#14579134C2212yescomplemented
102C2×#14579134C2212yescomplemented
103C2×#14579133C2212yescomplemented
104C2×#14579133C2212yescomplemented
105C2×#14579133C2212yescomplemented
106C2×#14579132C2212yescomplemented
107C2×#14579131C2212yescomplemented
108C2×#14579131C2212yescomplemented
109C2×#14579131C2212yescomplemented
110C2×#14579131C2212yescomplemented
111C2×#14579131C2212yescomplemented
112C2×#14579131C2212yescomplemented
113C2×#14579131C2212yescomplemented
114C2×#14579129C2212yescomplemented
115C2×#14579129C2212yescomplemented
116C2×#14579129C2212yescomplemented
117C2×#14579129C2212yescomplemented
118C2×#14579129C2212yescomplemented
119C2×C4×Dic158C2211yescharacteristic, complemented
120C2×#14579126C2211yescharacteristic, complemented
121C2×C4×D316C2211yescharacteristic, complemented
122C2×#14579123C2212yescomplemented
123C2×#14579123C2211yescharacteristic, complemented
124C2×#14579123C2211yescharacteristic, complemented
125C2×#14579123C2211yescharacteristic, complemented
126C2×C4×C22⋊D79C2211yescharacteristic, complemented
127C2×C4×C22⋊D79C2211yescharacteristic, complemented
128C2×C4×C22⋊D79C2212yescomplemented
129C2×(C22⋊D79)⋊C4C2212yescomplemented
130C2×#14579119C2212yescomplemented
131C2×#14579118C2211yescharacteristic, complemented
132C22×(C2×D79)⋊C4C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135#540×C79C22116yescomplemented
136C2×#127×C79C2211yescharacteristic, complemented
137C2×#125×C79C2211yescharacteristic, complemented
138C2×#123×C79C2212yescomplemented
139C2×#123×C79C2212yescomplemented
140C2×#121×C79C2211yescharacteristic, complemented
141C2×#121×C79C2211yescharacteristic, complemented
142C2×#121×C79C2212yescomplemented
143C2×#121×C79C2212yescomplemented
144C2×C4×D4×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C2×#117×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C24×D79C2312yes—
150C24×D79C2312yes—
151C2×#11929624—48no—
152C2×#11929624—44no—
153C2×#11929624C23116yescomplemented
154C2×#11929624C2318yescomplemented
155C2×#11929623—44no—
156C2×#11929623C2318yescomplemented
157C22×Dic158C2311yescharacteristic
158C22×Dic158C2311yescharacteristic
159C22×D316—48no—
160C22×D316—44no—
161C22×D316C2312yes—
162C22×D316C2311yescharacteristic
163C22×D316C2311yescharacteristic
164C22×D316C2311yescharacteristic
165C22×D316C2311yescharacteristic
166C22×D316C2312yes—
167C22×D316C2312yes—
168C22×D316C2312yes—
169C22×D316C2312yes—
170C22×D316C2312yes—
171C22×D316C2312yes—
172C22×D316C2312yes—
173C22×D316C2318yescomplemented
174C22×D316C23116yescomplemented
175C22×C22⋊D79C2312yes—
176C22×C22⋊D79C2311yescharacteristic
177C22×C22⋊D79C2311yescharacteristic
178C22×C22⋊D79C2312yes—
179C22×C22⋊D79C2312yes—
180C22×C22⋊D79C2312yes—
181C22×C22⋊D79C2312yes—
182C22×C22⋊D79C2312yes—
183C22×C22⋊D79C2312yes—
184C22×C22⋊D79C2312yes—
185C22×C22⋊D79C2312yes—
186C22×C22⋊D79C2312yes—
187C22×C22⋊D79C2312yes—
188C2×D4×D79—48no—
189C2×D4×D79—48no—
190C2×D4×D79—44no—
191C2×D4×D79—44no—
192C2×D4×D79—44no—
193C2×D4×D79—48no—
194C2×D4×D79—48no—
195C2×D4×D79C23116yescomplemented
196C2×D4×D79C23116yescomplemented
197C2×D4×D79C2318yescomplemented
198C2×D4×D79C23116yescomplemented
199C2×D4×D79C2318yescomplemented
200C2×D4×D79C2318yescomplemented
201C2×D4×D79C23116yescomplemented
202C23×Dic79C2312yes—
203C22×C4×D79C2311yescharacteristic
204C22×C4×D79C2311yescharacteristic
205C22×C4×D79C2311yescharacteristic
206C22×C4×D79C2311yescharacteristic
207C22×C4×D79C2312yes—
208C22×C4×D79C2312yes—
209C22×C4×D79C2312yes—
210C22×C4×D79C2312yes—
211#14579158C2318yescomplemented
212#14579158C2318yescomplemented
213#14579157C2318yes—
214#14579157C23116yescomplemented
215#14579157C23116yescomplemented
216#14579157C2318yescomplemented
217#14579157C2318yescomplemented
218#14579157C23116yescomplemented
219#14579156C23116yescomplemented
220#14579156C2318yescomplemented
221#14579154C2318yescomplemented
222#14579151C2318yescomplemented
223#14579149C2318yescomplemented
224#14579149C2318yescomplemented
225#14579148C2318yescomplemented
226#14579147C23116yescomplemented
227#14579147C2318yescomplemented
228#14579146C23116yescomplemented
229#14579146C23116yescomplemented
230#14579146C2318yescomplemented
231#14579146C23116yescomplemented
232#14579145C23116yescomplemented
233#14579144C23116yescomplemented
234#14579143C23116yescomplemented
235#14579143C23116yescomplemented
236#14579143C2318yescomplemented
237#14579141C2318yescomplemented
238#14579139C2318yescomplemented
239#14579136C2318yes—
240#14579136C23116yescomplemented
241#14579136C2318yescomplemented
242#14579136C23116yescomplemented
243#14579136C2318yescomplemented
244#14579136C23116yescomplemented
245#14579136C23116yescomplemented
246#14579135C23116yescomplemented
247#14579135C23116yescomplemented
248#14579135C23116yescomplemented
249#14579134C2318yes—
250#14579134C23116yescomplemented
251#14579134C23116yescomplemented
252#14579134C23116yescomplemented
253#14579134C23116yescomplemented
254#14579134C23116yescomplemented
255#14579133C23116yescomplemented
256#14579133C23116yescomplemented
257#14579133C23116yescomplemented
258#14579132C23116yescomplemented
259#14579131C23116yescomplemented
260#14579131C23116yescomplemented
261#14579131C23116yescomplemented
262#14579131C23116yescomplemented
263#14579131C23116yescomplemented
264#14579131C23116yescomplemented
265#14579131C23116yescomplemented
266#14579129C23116yescomplemented
267#14579129C23116yescomplemented
268#14579129C23116yescomplemented
269#14579129C23116yescomplemented
270#14579129C23116yescomplemented
271C4×Dic158C2318yescomplemented
272#14579126C2318yescomplemented
273C4×D316C2318yescomplemented
274#14579123C2318yescomplemented
275#14579123C2318yescomplemented
276#14579123C23116yescomplemented
277#14579123C2318yescomplemented
278C4×C22⋊D79C23116yescomplemented
279C4×C22⋊D79C2318yescomplemented
280C4×C22⋊D79C2318yescomplemented
281(C22⋊D79)⋊C4C23116yescomplemented
282#14579119C23116yescomplemented
283#14579118C2318yescomplemented
284C2×C4⋊Dic79C2312yes—
285C2×C4⋊Dic79C2311yescharacteristic
286C2×C4⋊Dic79C2311yescharacteristic
287C2×Dic79⋊C4C2311yescharacteristic
288C2×Dic79⋊C4C2311yescharacteristic
289C2×Dic79⋊C4C2311yescharacteristic
290C2×Dic79⋊C4C2311yescharacteristic
291C2×Dic79⋊C4C2311yescharacteristic
292C2×Dic79⋊C4C2312yes—
293C2×Dic79⋊C4C2311yescharacteristic
294C2×C22⋊Dic79C2312yes—
295C2×C22⋊Dic79C2311yescharacteristic
296C2×C22⋊Dic79C2311yescharacteristic
297C2×C22⋊Dic79C2312yes—
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2311yescharacteristic
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2311yescharacteristic
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2312yes—
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C2312yes—
308C2×(C2×D79)⋊C4C2311yescharacteristic
309C2×(C2×D79)⋊C4C2312yes—
310C2×(C2×D79)⋊C4C2312yes—
311C2×(C2×D79)⋊C4C2312yes—
312C2×(C2×D79)⋊C4C2312yes—
313C2×(C2×D79)⋊C4C2312yes—
314C2×(C2×D79)⋊C4C2311yescharacteristic
315C2×(C2×D79)⋊C4C23116yescomplemented
316C22⋊C4×D79C23116yescomplemented
317C2×C4×Dic79C2311yescharacteristic
318C2×C4×Dic79C2311yescharacteristic
319C2×C4×Dic79C2311yescharacteristic
320C2×C4×Dic79C2311yescharacteristic
321C2×C4×Dic79C2312yes—
322C42×D79C2318yescomplemented
323C22×D4×C79C2311yescharacteristic
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2312yes—
326C22×D4×C79C2312yes—
327C22×D4×C79C2312yes—
328C22×D4×C79C2312yes—
329C23×C4×C79C2311yescharacteristic
330C23×C4×C79C2312yes—
331C23×C4×C79C2312yes—
332#127×C79C2318yescomplemented
333#125×C79C2318yescomplemented
334#123×C79C23116yescomplemented
335#123×C79C23116yescomplemented
336#121×C79C2318yescomplemented
337#121×C79C2318yescomplemented
338#121×C79C23116yescomplemented
339#121×C79C23116yescomplemented
340C4×D4×C79C2318yescomplemented
341C4×D4×C79C2318yescomplemented
342#117×C79C2318yescomplemented
343C2×C4⋊C4×C79C2311yescharacteristic
344C2×C4⋊C4×C79C2311yescharacteristic
345C2×C4⋊C4×C79C2311yescharacteristic
346C2×C4⋊C4×C79C2311yescharacteristic
347C2×C4⋊C4×C79C2312yes—
348C2×C4⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2311yescharacteristic
350C2×C22⋊C4×C79C2311yescharacteristic
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C2312yes—
353C2×C22⋊C4×C79C2312yes—
354C2×C22⋊C4×C79C2312yes—
355C2×C42×C79C2311yescharacteristic
356C2×C42×C79C2311yescharacteristic
357C23×D79—28no—
358C23×D79—28no—
359C23×D79—44no—
360C23×D79—44no—
361C23×D79—44no—
362C23×D79—44no—
363C23×D79—44no—
364C23×D79—44no—
365C23×D79—44no—
366C23×D79—44no—
367C23×D79—44no—
368C23×D79—44no—
369C23×D79C2411yescharacteristic
370C23×D79C2412yes—
371C23×D79C2412yes—
372C23×D79C2412yes—
373C23×D79C2411yescharacteristic
374C23×D79C2418yes—
375C23×D79C2418yes—
376C23×D79C2418yes—
377C23×D79C2418yes—
378#11929624—432no—
379#11929624—416no—
380#11929623—416no—
381C2×Dic158—24no—
382C2×Dic158—24no—
383C2×Dic158C2414yes—
384C2×Dic158C2414yes—
385C2×D316—28no—
386C2×D316—24no—
387C2×D316—24no—
388C2×D316—24no—
389C2×D316—24no—
390C2×D316—44no—
391C2×D316—44no—
392C2×D316—44no—
393C2×D316—44no—
394C2×D316—44no—
395C2×D316—44no—
396C2×D316—44no—
397C2×D316—416no—
398C2×D316—432no—
399C2×D316C2414yes—
400C2×D316C2418yes—
401C2×D316C2414yes—
402C2×D316C2414yes—
403C2×D316C2414yes—
404C2×D316C2418yes—
405C2×D316C2418yes—
406C2×D316C2418yes—
407C2×D316C2418yes—
408C2×D316C2418yes—
409C2×D316C2418yes—
410C2×D316C2418yes—
411C2×C22⋊D79—28no—
412C2×C22⋊D79—24no—
413C2×C22⋊D79—28no—
414C2×C22⋊D79—24no—
415C2×C22⋊D79—44no—
416C2×C22⋊D79—44no—
417C2×C22⋊D79—44no—
418C2×C22⋊D79—44no—
419C2×C22⋊D79—44no—
420C2×C22⋊D79—44no—
421C2×C22⋊D79—44no—
422C2×C22⋊D79—44no—
423C2×C22⋊D79—44no—
424C2×C22⋊D79C2418yes—
425C2×C22⋊D79C2414yes—
426C2×C22⋊D79C2414yes—
427C2×C22⋊D79C2418yes—
428C2×C22⋊D79C2418yes—
429C2×C22⋊D79C2418yes—
430C2×C22⋊D79C2418yes—
431C2×C22⋊D79C2418yes—
432C2×C22⋊D79C2418yes—
433C2×C22⋊D79C2418yes—
434C2×C22⋊D79C2418yes—
435C2×C22⋊D79C2418yes—
436C2×C22⋊D79C2418yes—
437D4×D79—432no—
438D4×D79—432no—
439D4×D79—432no—
440D4×D79—416no—
441D4×D79—416no—
442D4×D79—416no—
443D4×D79—432no—
444C22×Dic79—44no—
445C22×Dic79C2412yes—
446C22×Dic79C2411yescharacteristic
447C22×Dic79C2411yescharacteristic
448C22×Dic79C2411yescharacteristic
449C22×Dic79C2411yescharacteristic
450C22×Dic79C2411yescharacteristic
451C22×Dic79C2418yes—
452C22×Dic79C2411yescharacteristic
453C2×C4×D79—28no—
454C2×C4×D79—24no—
455C2×C4×D79—24no—
456C2×C4×D79—24no—
457C2×C4×D79—24no—
458C2×C4×D79—44no—
459C2×C4×D79—44no—
460C2×C4×D79—44no—
461C2×C4×D79C2414yes—
462C2×C4×D79C2418yes—
463C2×C4×D79C2414yes—
464C2×C4×D79C2414yes—
465C2×C4×D79C2414yes—
466C2×C4×D79C2418yes—
467C2×C4×D79C2418yes—
468C2×C4×D79C2418yes—
469C4⋊Dic79C2418yes—
470C4⋊Dic79C2414yes—
471C4⋊Dic79C2414yes—
472Dic79⋊C4C2414yes—
473Dic79⋊C4C2414yes—
474Dic79⋊C4C2414yes—
475Dic79⋊C4C2414yes—
476Dic79⋊C4C2414yes—
477Dic79⋊C4C2418yes—
478Dic79⋊C4C2414yes—
479C22⋊Dic79C2418yes—
480C22⋊Dic79C2414yes—
481C22⋊Dic79C2414yes—
482C22⋊Dic79C2418yes—
483(C2×D79)⋊C4C2414yes—
484(C2×D79)⋊C4C2418yes—
485(C2×D79)⋊C4C2414yes—
486(C2×D79)⋊C4C2418yes—
487(C2×D79)⋊C4C2418yes—
488(C2×D79)⋊C4C2414yes—
489(C2×D79)⋊C4C2414yes—
490(C2×D79)⋊C4C2418yes—
491(C2×D79)⋊C4C2418yes—
492(C2×D79)⋊C4C2418yes—
493(C2×D79)⋊C4C2414yes—
494(C2×D79)⋊C4C2418yes—
495(C2×D79)⋊C4C2418yes—
496(C2×D79)⋊C4C2418yes—
497(C2×D79)⋊C4C2418yes—
498(C2×D79)⋊C4C2418yes—
499(C2×D79)⋊C4C2414yes—
500C4×Dic79C2414yes—
501C4×Dic79C2414yes—
502C4×Dic79C2414yes—
503C4×Dic79C2414yes—
504C4×Dic79C2418yes—
505C24×C79C2411yescharacteristic
506C24×C79C2412yes—
507C24×C79C2412yes—
508C2×D4×C79—24no—
509C2×D4×C79—24no—
510C2×D4×C79—44no—
511C2×D4×C79—44no—
512C2×D4×C79—44no—
513C2×D4×C79—44no—
514C2×D4×C79C2414yes—
515C2×D4×C79C2414yes—
516C2×D4×C79C2418yes—
517C2×D4×C79C2418yes—
518C2×D4×C79C2418yes—
519C2×D4×C79C2418yes—
520C22×C4×C79—24no—
521C22×C4×C79—44no—
522C22×C4×C79—44no—
523C22×C4×C79C2411yescharacteristic
524C22×C4×C79C2414yes—
525C22×C4×C79C2411yescharacteristic
526C22×C4×C79C2411yescharacteristic
527C22×C4×C79C2411yescharacteristic
528C22×C4×C79C2411yescharacteristic
529C22×C4×C79C2412yes—
530C22×C4×C79C2412yes—
531C22×C4×C79C2418yes—
532C22×C4×C79C2418yes—
533C22×C4×C79C2411yescharacteristic
534C4⋊C4×C79C2414yes—
535C4⋊C4×C79C2414yes—
536C4⋊C4×C79C2414yes—
537C4⋊C4×C79C2414yes—
538C4⋊C4×C79C2418yes—
539C4⋊C4×C79C2418yes—
540C22⋊C4×C79C2414yes—
541C22⋊C4×C79C2414yes—
542C22⋊C4×C79C2418yes—
543C22⋊C4×C79C2418yes—
544C22⋊C4×C79C2418yes—
545C22⋊C4×C79C2418yes—
546C42×C79C2414yes—
547C42×C79C2414yes—
548C23×C79—24no—
549C23×C79—24no—
550C23×C79—24no—
551C23×C79—22no—
552C23×C79—22no—
553C23×C79—24no—
554C23×C79—22no—
555C23×C79—24no—
556C23×C79—24no—
557C23×C79C2512yes—
558C23×C79C2514yes—
559C23×C79C2514yes—
560C23×C79C2511yescharacteristic
561C22×D79—22no—
562C22×D79—22no—
563C22×D79—22no—
564C22×D79—24no—
565C22×D79—24no—
566C22×D79—24no—
567C22×D79—24no—
568C22×D79—22no—
569C22×D79—24no—
570C22×D79—24no—
571C22×D79—24no—
572C22×D79—24no—
573C22×D79—24no—
574C22×D79—22no—
575C22×D79—216no—
576C22×D79—216no—
577C22×D79—48no—
578C22×D79—48no—
579C22×D79—48no—
580C22×D79—48no—
581C22×D79—48no—
582C22×D79—48no—
583C22×D79—48no—
584C22×D79—48no—
585C22×D79—48no—
586C22×D79—48no—
587C22×D79—816no—
588C22×D79—816no—
589C22×D79—816no—
590C22×D79—816no—
591C22×D79H(5,𝔽2)14yes—
592C22×D79C2512yes—
593C22×D79C2514yes—
594C22×D79C2514yes—
595C22×D79C2514yes—
596C22×D79C2512yes—
597D4×C79—28no—
598D4×C79—28no—
599D4×C79—48no—
600D4×C79—48no—
601D4×C79—48no—
602D4×C79—48no—
603C2×C4×C79—24no—
604C2×C4×C79—22no—
605C2×C4×C79—22no—
606C2×C4×C79—22no—
607C2×C4×C79—24no—
608C2×C4×C79—22no—
609C2×C4×C79—22no—
610C2×C4×C79—28no—
611C2×C4×C79—48no—
612C2×C4×C79—48no—
613C2×C4×C79H(5,𝔽2)14yes—
614C2×C4×C79C2512yes—
615C2×C4×C79C2512yes—
616C2×C4×C79C2514yes—
617C2×C4×C79C2514yes—
618C2×C4×C79C2512yes—
619C2×C4×C79C2512yes—
620C2×C4×C79C2512yes—
621C2×C4×C79C2512yes—
622C22⋊D79—28no—
623C22⋊D79—28no—
624C22⋊D79—216no—
625C22⋊D79—216no—
626C22⋊D79—48no—
627C22⋊D79—48no—
628C22⋊D79—48no—
629C22⋊D79—48no—
630C22⋊D79—48no—
631C22⋊D79—48no—
632C22⋊D79—48no—
633C22⋊D79—48no—
634C22⋊D79—48no—
635C2×Dic79—22no—
636C2×Dic79—22no—
637C2×Dic79—22no—
638C2×Dic79—22no—
639C2×Dic79—22no—
640C2×Dic79—24no—
641C2×Dic79—48no—
642C2×Dic79H(5,𝔽2)14yes—
643C2×Dic79C2512yes—
644C2×Dic79C2512yes—
645C2×Dic79C2514yes—
646C2×Dic79C2512yes—
647C2×Dic79C2512yes—
648C2×Dic79C2512yes—
649C2×Dic79C2512yes—
650D316—216no—
651D316—28no—
652D316—28no—
653D316—28no—
654D316—28no—
655D316—48no—
656D316—48no—
657D316—48no—
658D316—48no—
659D316—48no—
660D316—48no—
661D316—48no—
662C4×D79—28no—
663C4×D79—28no—
664C4×D79—28no—
665C4×D79—28no—
666C4×D79—216no—
667C4×D79—48no—
668C4×D79—48no—
669C4×D79—48no—
670Dic158—28no—
671Dic158—28no—
672C22×C79—24no—
673C22×C79—22no—
674C22×C79—24no—
675C22×C79—22no—
676C22×C79—22no—
677C22×C79—24no—
678C22×C79—24no—
679C22×C79—24no—
680C22×C79—24no—
681C22×C79—48no—
682C22×C79—44no—
683C22×C79—48no—
684C22×C79C2×H(5,𝔽2)12yes—
685C22×C79C2×H(5,𝔽2)12yes—
686C22×C79C2×H(5,𝔽2)12yes—
687C22×C79C2611yescharacteristic
688C2×D79—22no—
689C2×D79—22no—
690C2×D79—28no—
691C2×D79—22no—
692C2×D79—24no—
693C2×D79—24no—
694C2×D79—22no—
695C2×D79—24no—
696C2×D79—24no—
697C2×D79—24no—
698C2×D79—24no—
699C2×D79—24no—
700C2×D79—24no—
701C2×D79—24no—
702C2×D79—22no—
703C2×D79—48no—
704C2×D79—44no—
705C2×D79—48no—
706C2×D79—48no—
707C2×D79—816no—
708C2×D79—816no—
709C2×D79—816no—
710C2×D79—816no—
711C2×D79C2×H(5,𝔽2)14yes—
712C4×C79—22no—
713C4×C79—22no—
714C4×C79—22no—
715C4×C79—24no—
716C4×C79—24no—
717C4×C79—22no—
718C4×C79—22no—
719C4×C79C2×H(5,𝔽2)14yes—
720Dic79—22no—
721Dic79—22no—
722Dic79—22no—
723Dic79—22no—
724Dic79—24no—
725Dic79—22no—
726Dic79C2×H(5,𝔽2)14yes—
727C2×#3543—791nomaximal, Sylow
728C2×C79—44no—
729C2×C79—42no—
730C2×C79—44no—
731C2×C79#354314yescomplemented
732C2×C79C22×H(5,𝔽2)11yescharacteristic
733C2×C79C22×H(5,𝔽2)11yescharacteristic
734C2×C79C22×H(5,𝔽2)11yescharacteristic
735D79—24no—
736D79—44no—
737D79—42no—
738D79—44no—
739D79—44no—
740#3543—7932no—
741C2×#560—792no—
742C2×#560—792no—
743C2×#559—791no—
744C2×#550—791no—
745C2×#550—791no—
746C2×#546—792no—
747C2×#546—791no—
748C2×#546—791no—
749C2×D42—791no—
750C2×D42—791no—
751C2×D42—792no—
752C2×D42—791no—
753C2×#540—791no—
754C2×#540—792no—
755C2×#540D7911yescharacteristic, complemented
756C2×#535—791no—
757C2×#535—792no—
758C2×#535—791no—
759C2×#534—792no—
760C2×#534—792no—
761C22×#127—791no—
762C2×#529—791no—
763C2×#529—791no—
764C79C2×#354311yescharacteristic, complemented, Sylow
765C22×#41—791no—
766C22×#41—791no—
767C22×#41—792no—
768C23×D4—792no—
769C23×D4—791no—
770C23×D4—791no—
771C23×D4—792no—
772C23×D4—792no—
773C23×D4—791no—
774C23×D4—792no—
775C23×D4—792no—
776C23×D4—791no—
777#560—7932no—
778#560—7932no—
779#559—7916no—
780#550—7916no—
781#550—7916no—
782#546—7932no—
783#546—7916no—
784#546—7916no—
785D42—7916no—
786D42—7916no—
787D42—7932no—
788D42—7916no—
789#540—7916no—
790#540—7932no—
791#540C2×D79116yescomplemented
792#535—7916no—
793#535—7932no—
794#535—7916no—
795#534—7932no—
796#534—7932no—
797C2×#127—792no—
798C2×#127—791no—
799C2×#127—791no—
800C2×#127—792no—
801C2×#127—791no—
802C2×#127—792no—
803C2×#127—7916no—
804C2×#127—791no—
805C2×#127—791no—
806C2×#127C2×D7911yescharacteristic, complemented
807#529—7916no—
808#529—7916no—
809C2×#126—792no—
810C2×#126—791no—
811C2×#126—791no—
812C2×#125—791no—
813C2×#125C2×D7911yescharacteristic, complemented
814C2×#124—791no—
815C2×#124—791no—
816C2×#124—792no—
817C2×#124—791no—
818C2×#124—791no—
819C2×#123—792no—
820C2×#123—792no—
821C2×#123—791no—
822C2×#123—792no—
823C2×#123—792no—
824C2×#123—791no—
825C2×#123—792no—
826C2×#123—792no—
827C2×#123—792no—
828C2×#123C2×D7912yescomplemented
829C2×#123C2×D7912yescomplemented
830C2×C22⋊Q8—791no—
831C2×C22⋊Q8—791no—
832C2×#121—792no—
833C2×#121—792no—
834C2×#121—792no—
835C2×#121—792no—
836C2×#121—792no—
837C2×#121—792no—
838C2×#121—792no—
839C2×#121—791no—
840C2×#121—792no—
841C2×#121—792no—
842C2×#121—792no—
843C2×#121—791no—
844C2×#121—791no—
845C2×#121—792no—
846C2×#121—791no—
847C2×#121—792no—
848C2×#121—792no—
849C2×#121—792no—
850C2×#121—792no—
851C2×#121—792no—
852C2×#121C2×D7912yescomplemented
853C2×#121C2×D7911yescharacteristic, complemented
854C2×#121C2×D7911yescharacteristic, complemented
855C2×#121C2×D7912yescomplemented
856C2×#120—792no—
857C2×#120—792no—
858C2×#120—792no—
859C2×#120—792no—
860C2×#120—792no—
861C2×#120—792no—
862C2×#120—792no—
863C2×#120—792no—
864C2×#120—792no—
865C2×#120—792no—
866C2×#120—792no—
867C2×#120—792no—
868C2×C4×Q8—791no—
869C2×C4×Q8—791no—
870C2×C4×D4—791no—
871C2×C4×D4—791no—
872C2×C4×D4—792no—
873C2×C4×D4—792no—
874C2×C4×D4—791no—
875C2×C4×D4—791no—
876C2×C4×D4—791no—
877C2×C4×D4—792no—
878C2×C4×D4—791no—
879C2×C4×D4C2×D7911yescharacteristic, complemented
880C2×C4×D4C2×D7911yescharacteristic, complemented
881C2×#117—792no—
882C2×#117—791no—
883C2×#117C2×D7911yescharacteristic, complemented
884C22×C22⋊C4—792no—
885C22×C22⋊C4—792no—
886C22×C42—791no—
887C25—792no—
888C25—792no—
889C25—792no—
890C25—792no—
891C2×#41—3164no—
892C2×#41—3168no—
893C2×#41—3164no—
894C2×#41—798no—
895C2×#41—798no—
896C2×#41—7916no—
897C22×Q8—791no—
898C22×Q8—791no—
899C22×D4—3164no—
900C22×D4—3168no—
901C22×D4—3168no—
902C22×D4—3164no—
903C22×D4—3164no—
904C22×D4—3164no—
905C22×D4—3168no—
906C22×D4—3168no—
907C22×D4—3168no—
908C22×D4—792no—
909C22×D4—792no—
910C22×D4—792no—
911C22×D4—792no—
912C22×D4—792no—
913C22×D4—792no—
914C22×D4—792no—
915C22×D4—792no—
916C22×D4—792no—
917C22×D4—7916no—
918C22×D4—798no—
919C22×D4—798no—
920C22×D4—7916no—
921C22×D4—7916no—
922C22×D4—798no—
923C22×D4—7916no—
924C22×D4—791no—
925C22×D4—791no—
926C22×D4—792no—
927C22×D4—792no—
928C22×D4—792no—
929C22×D4—792no—
930C22×D4—792no—
931C22×D4—792no—
932C22×D4—792no—
933C22×D4—792no—
934C22×D4—792no—
935C22×D4—7916no—
936C22×D4—798no—
937C22×D4—792no—
938C22×D4—791no—
939C22×D4—791no—
940C22×D4—791no—
941C22×D4—791no—
942C22×D4C22×D7911yescharacteristic
943C22×D4C22×D7911yescharacteristic
944C22×D4C22×D7912yes—
945C22×D4C22×D7912yes—
946C22×D4C22×D7912yes—
947C22×D4C22×D7912yes—
948C23×C4—792no—
949C23×C4—792no—
950C23×C4—792no—
951C23×C4—792no—
952C23×C4—792no—
953C23×C4—791no—
954C23×C4—791no—
955C23×C4—791no—
956C23×C4—791no—
957C23×C4C22×D7911yescharacteristic
958C23×C4C22×D7912yes—
959C23×C4C22×D7912yes—
960#127—7916no—
961#127—798no—
962#127—798no—
963#127—7916no—
964#127—798no—
965#127—7916no—
966#127—798no—
967#127—798no—
968#127C22×D7918yescomplemented
969#126—798no—
970#126—7916no—
971#126—798no—
972#125—798no—
973#125C22×D7918yescomplemented
974#124—798no—
975#124—798no—
976#124—7916no—
977#124—798no—
978#124—798no—
979#123—7916no—
980#123—7916no—
981#123—798no—
982#123—7916no—
983#123—7916no—
984#123—798no—
985#123—7916no—
986#123—7916no—
987#123—7916no—
988#123C22×D79116yescomplemented
989#123C22×D79116yescomplemented
990C22⋊Q8—798no—
991C22⋊Q8—798no—
992#121—7916no—
993#121—7916no—
994#121—7916no—
995#121—7916no—
996#121—7916no—
997#121—7916no—
998#121—7916no—
999#121—798no—
1000#121—7916no—
1001#121—7916no—
1002#121—7916no—
1003#121—798no—
1004#121—798no—
1005#121—7916no—
1006#121—798no—
1007#121—7916no—
1008#121—7916no—
1009#121—7916no—
1010#121—7916no—
1011#121—7916no—
1012#121C22×D79116yescomplemented
1013#121C22×D7918yescomplemented
1014#121C22×D7918yescomplemented
1015#121C22×D79116yescomplemented
1016#120—7916no—
1017#120—7916no—
1018#120—7916no—
1019#120—7916no—
1020#120—7916no—
1021#120—7916no—
1022#120—7916no—
1023#120—7916no—
1024#120—7916no—
1025#120—7916no—
1026#120—7916no—
1027#120—7916no—
1028C4×Q8—798no—
1029C4×Q8—798no—
1030C4×D4—798no—
1031C4×D4—798no—
1032C4×D4—7916no—
1033C4×D4—7916no—
1034C4×D4—798no—
1035C4×D4—798no—
1036C4×D4—798no—
1037C4×D4—7916no—
1038C4×D4—798no—
1039C4×D4C22×D7918yescomplemented
1040C4×D4C22×D7918yescomplemented
1041#117—7916no—
1042#117—798no—
1043#117C22×D7918yescomplemented
1044C2×C4⋊C4—791no—
1045C2×C4⋊C4—792no—
1046C2×C4⋊C4—791no—
1047C2×C4⋊C4—791no—
1048C2×C4⋊C4—791no—
1049C2×C4⋊C4—791no—
1050C2×C4⋊C4—791no—
1051C2×C4⋊C4—792no—
1052C2×C4⋊C4—791no—
1053C2×C4⋊C4—791no—
1054C2×C4⋊C4C22×D7912yes—
1055C2×C4⋊C4C22×D7911yescharacteristic
1056C2×C4⋊C4C22×D7911yescharacteristic
1057C2×C4⋊C4C22×D7911yescharacteristic
1058C2×C4⋊C4C22×D7911yescharacteristic
1059C2×C4⋊C4C22×D7912yes—
1060C2×C22⋊C4—792no—
1061C2×C22⋊C4—791no—
1062C2×C22⋊C4—791no—
1063C2×C22⋊C4—792no—
1064C2×C22⋊C4—792no—
1065C2×C22⋊C4—791no—
1066C2×C22⋊C4—791no—
1067C2×C22⋊C4—792no—
1068C2×C22⋊C4—792no—
1069C2×C22⋊C4—7916no—
1070C2×C22⋊C4—792no—
1071C2×C22⋊C4—791no—
1072C2×C22⋊C4—792no—
1073C2×C22⋊C4—791no—
1074C2×C22⋊C4—792no—
1075C2×C22⋊C4—791no—
1076C2×C22⋊C4—791no—
1077C2×C22⋊C4—792no—
1078C2×C22⋊C4—792no—
1079C2×C22⋊C4—792no—
1080C2×C22⋊C4—792no—
1081C2×C22⋊C4—792no—
1082C2×C22⋊C4—7916no—
1083C2×C22⋊C4C22×D7912yes—
1084C2×C22⋊C4C22×D7911yescharacteristic
1085C2×C22⋊C4C22×D7911yescharacteristic
1086C2×C22⋊C4C22×D7912yes—
1087C2×C22⋊C4C22×D7912yes—
1088C2×C22⋊C4C22×D7912yes—
1089C2×C42—791no—
1090C2×C42—792no—
1091C2×C42—791no—
1092C2×C42—791no—
1093C2×C42—791no—
1094C2×C42—798no—
1095C2×C42C22×D7911yescharacteristic
1096C2×C42C22×D7911yescharacteristic
1097C24—3164no—
1098C24—3164no—
1099C24—3164no—
1100C24—3164no—
1101C24—3164no—
1102C24—3164no—
1103C24—3164no—
1104C24—3164no—
1105C24—3164no—
1106C24—3164no—
1107C24—798no—
1108C24—798no—
1109C24—798no—
1110C24—798no—
1111C24—791no—
1112C24—792no—
1113C24—792no—
1114C24—791no—
1115C24—792no—
1116C24—1588no—
1117C24—1588no—
1118C24C23×D7912yes—
1119C24C23×D7911yescharacteristic
1120C24C23×D7912yes—
1121#41—31616no—
1122#41—31632no—
1123#41—31616no—
1124C2×Q8—794no—
1125C2×Q8—794no—
1126C2×Q8—1584no—
1127C2×Q8—1584no—
1128C2×D4—24no—
1129C2×D4—24no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—3164no—
1135C2×D4—3164no—
1136C2×D4—3164no—
1137C2×D4—3164no—
1138C2×D4—3164no—
1139C2×D4—3164no—
1140C2×D4—3164no—
1141C2×D4—31616no—
1142C2×D4—31632no—
1143C2×D4—31632no—
1144C2×D4—31616no—
1145C2×D4—31616no—
1146C2×D4—31616no—
1147C2×D4—31632no—
1148C2×D4—31632no—
1149C2×D4—31632no—
1150C2×D4—3164no—
1151C2×D4—3164no—
1152C2×D4—3164no—
1153C2×D4—3164no—
1154C2×D4—3164no—
1155C2×D4—3164no—
1156C2×D4—3164no—
1157C2×D4—3164no—
1158C2×D4—3164no—
1159C2×D4—798no—
1160C2×D4—798no—
1161C2×D4—798no—
1162C2×D4—798no—
1163C2×D4—798no—
1164C2×D4—798no—
1165C2×D4—798no—
1166C2×D4—798no—
1167C2×D4—798no—
1168C2×D4—794no—
1169C2×D4—794no—
1170C2×D4—798no—
1171C2×D4—798no—
1172C2×D4—798no—
1173C2×D4—798no—
1174C2×D4—798no—
1175C2×D4—798no—
1176C2×D4—798no—
1177C2×D4—798no—
1178C2×D4—798no—
1179C2×D4—798no—
1180C2×D4—794no—
1181C2×D4—794no—
1182C2×D4—794no—
1183C2×D4—794no—
1184C2×D4—1584no—
1185C2×D4—1588no—
1186C2×D4—1584no—
1187C2×D4—1588no—
1188C2×D4—1588no—
1189C2×D4—1584no—
1190C2×D4—1584no—
1191C2×D4—1584no—
1192C2×D4—1584no—
1193C2×D4C23×D7914yes—
1194C2×D4C23×D7914yes—
1195C2×D4C23×D7918yes—
1196C2×D4C23×D7918yes—
1197C2×D4C23×D7918yes—
1198C2×D4C23×D7918yes—
1199C22×C4—24no—
1200C22×C4—44no—
1201C22×C4—44no—
1202C22×C4—3164no—
1203C22×C4—3164no—
1204C22×C4—3164no—
1205C22×C4—3164no—
1206C22×C4—798no—
1207C22×C4—798no—
1208C22×C4—798no—
1209C22×C4—798no—
1210C22×C4—791no—
1211C22×C4—791no—
1212C22×C4—791no—
1213C22×C4—791no—
1214C22×C4—792no—
1215C22×C4—791no—
1216C22×C4—791no—
1217C22×C4—794no—
1218C22×C4—794no—
1219C22×C4—794no—
1220C22×C4—798no—
1221C22×C4—794no—
1222C22×C4—1584no—
1223C22×C4—1588no—
1224C22×C4—1584no—
1225C22×C4—1584no—
1226C22×C4—1584no—
1227C22×C4C23×D7914yes—
1228C22×C4C23×D7911yescharacteristic
1229C22×C4C23×D7911yescharacteristic
1230C22×C4C23×D7912yes—
1231C22×C4C23×D7911yescharacteristic
1232C22×C4C23×D7911yescharacteristic
1233C22×C4C23×D7912yes—
1234C22×C4C23×D7911yescharacteristic
1235C22×C4C23×D7918yes—
1236C22×C4C23×D7918yes—
1237C22×C4C23×D7911yescharacteristic
1238C4⋊C4—794no—
1239C4⋊C4—794no—
1240C4⋊C4—794no—
1241C4⋊C4—794no—
1242C4⋊C4—794no—
1243C4⋊C4—798no—
1244C4⋊C4—794no—
1245C4⋊C4—798no—
1246C4⋊C4—794no—
1247C4⋊C4—794no—
1248C4⋊C4C23×D7918yes—
1249C4⋊C4C23×D7914yes—
1250C4⋊C4C23×D7914yes—
1251C4⋊C4C23×D7914yes—
1252C4⋊C4C23×D7914yes—
1253C4⋊C4C23×D7918yes—
1254C22⋊C4—798no—
1255C22⋊C4—794no—
1256C22⋊C4—794no—
1257C22⋊C4—798no—
1258C22⋊C4—798no—
1259C22⋊C4—794no—
1260C22⋊C4—794no—
1261C22⋊C4—798no—
1262C22⋊C4—798no—
1263C22⋊C4—798no—
1264C22⋊C4—794no—
1265C22⋊C4—794no—
1266C22⋊C4—798no—
1267C22⋊C4—798no—
1268C22⋊C4—794no—
1269C22⋊C4—794no—
1270C22⋊C4—798no—
1271C22⋊C4—798no—
1272C22⋊C4—798no—
1273C22⋊C4—798no—
1274C22⋊C4—798no—
1275C22⋊C4C23×D7918yes—
1276C22⋊C4C23×D7914yes—
1277C22⋊C4C23×D7914yes—
1278C22⋊C4C23×D7918yes—
1279C22⋊C4C23×D7918yes—
1280C22⋊C4C23×D7918yes—
1281C42—794no—
1282C42—794no—
1283C42—794no—
1284C42—798no—
1285C42—794no—
1286C42C23×D7914yes—
1287C42C23×D7914yes—
1288C23—24no—
1289C23—24no—
1290C23—24no—
1291C23—24no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—24no—
1296C23—24no—
1297C23—3168no—
1298C23—3168no—
1299C23—3168no—
1300C23—3168no—
1301C23—3168no—
1302C23—3168no—
1303C23—3168no—
1304C23—3168no—
1305C23—3168no—
1306C23—3168no—
1307C23—794no—
1308C23—792no—
1309C23—794no—
1310C23—794no—
1311C23—792no—
1312C23—794no—
1313C23—63216no—
1314C23—63216no—
1315C23—63216no—
1316C23—63216no—
1317C23—15816no—
1318C23—15816no—
1319C23—1584no—
1320C23—1584no—
1321C23—1584no—
1322C23—1584no—
1323C23—1582no—
1324C23—1584no—
1325C23—1584no—
1326C23—1582no—
1327C23—1584no—
1328C23—1582no—
1329C23—1584no—
1330C23—1584no—
1331C23—1582no—
1332C23—1582no—
1333C23C24×D7914yes—
1334C23C24×D7912yes—
1335C23C24×D7914yes—
1336C23C24×D7911yescharacteristic
1337Q8—1588no—
1338Q8—1588no—
1339D4—28no—
1340D4—28no—
1341D4—48no—
1342D4—48no—
1343D4—48no—
1344D4—48no—
1345D4—3168no—
1346D4—3168no—
1347D4—3168no—
1348D4—3168no—
1349D4—3168no—
1350D4—3168no—
1351D4—3168no—
1352D4—3168no—
1353D4—3168no—
1354D4—3168no—
1355D4—3168no—
1356D4—3168no—
1357D4—3168no—
1358D4—3168no—
1359D4—3168no—
1360D4—3168no—
1361D4—1588no—
1362D4—15816no—
1363D4—1588no—
1364D4—15816no—
1365D4—15816no—
1366D4—1588no—
1367D4—1588no—
1368D4—1588no—
1369D4—1588no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—28no—
1378C2×C4—48no—
1379C2×C4—48no—
1380C2×C4—3168no—
1381C2×C4—3168no—
1382C2×C4—3168no—
1383C2×C4—3168no—
1384C2×C4—794no—
1385C2×C4—792no—
1386C2×C4—792no—
1387C2×C4—792no—
1388C2×C4—792no—
1389C2×C4—794no—
1390C2×C4—792no—
1391C2×C4—792no—
1392C2×C4—1588no—
1393C2×C4—15816no—
1394C2×C4—1588no—
1395C2×C4—1582no—
1396C2×C4—1582no—
1397C2×C4—1582no—
1398C2×C4—1582no—
1399C2×C4—1584no—
1400C2×C4—1582no—
1401C2×C4—1588no—
1402C2×C4—1588no—
1403C2×C4#1457920714yes—
1404C2×C4C24×D7912yes—
1405C2×C4C24×D7912yes—
1406C2×C4C24×D7914yes—
1407C2×C4C24×D7912yes—
1408C2×C4C24×D7912yes—
1409C2×C4C24×D7914yes—
1410C2×C4C24×D7912yes—
1411C2×C4C24×D7912yes—
1412C22—24no—
1413C22—24no—
1414C22—24no—
1415C22—24no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—24no—
1420C22—24no—
1421C22—48no—
1422C22—44no—
1423C22—48no—
1424C22—3168no—
1425C22—3164no—
1426C22—3168no—
1427C22—3168no—
1428C22—794no—
1429C22—63216no—
1430C22—63216no—
1431C22—63216no—
1432C22—63216no—
1433C22—1584no—
1434C22—1584no—
1435C22—1584no—
1436C22—1584no—
1437C22—1582no—
1438C22—1584no—
1439C22—1582no—
1440C22—1584no—
1441C22—1584no—
1442C22—1582no—
1443C22—1584no—
1444C22—1584no—
1445C22—1582no—
1446C22—1582no—
1447C22—1588no—
1448C22H(5,𝔽2)×D7912yes—
1449C22H(5,𝔽2)×D7912yes—
1450C22C2×#1457920712yes—
1451C22C25×D7911yescharacteristic
1452C4—22no—
1453C4—22no—
1454C4—24no—
1455C4—24no—
1456C4—22no—
1457C4—22no—
1458C4—22no—
1459C4—794no—
1460C4—1582no—
1461C4—1582no—
1462C4—1582no—
1463C4—1582no—
1464C4—1584no—
1465C4—1582no—
1466C4C2×#1457920714yes—
1467C2—44no—
1468C2—42no—
1469C2—44no—
1470C2—3164no—
1471C2—3162no—
1472C2—3164no—
1473C2—3164no—
1474C2—1584no—
1475C2#2377772914yesdirect product factor
1476C2C2×H(5,𝔽2)×D7911yescharacteristic
1477C2C2×H(5,𝔽2)×D7911yescharacteristic
1478C2C22×#1457920711yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#540×C79C2
socleC23×C79C25
hypercenterC2×#540D79
hypocenterC79C2×#3543
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#540

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777729C2direct (N × H)
2. C2×#19099303C2semidirect
3. C2×#19099301C2semidirect
4. C2×#19099296C2semidirect
5. C2×#19099234C2semidirect
6. C2×#19099231C2semidirect
7. C2×#19099210C2semidirect
8. C2×#19099208C2semidirect
9. C2×#19099205C2semidirect
10. C2×D4×D316C2semidirect
11. C2×#19099197C2semidirect
12. C2×#19099197C2semidirect
13. C2×#19099197C2semidirect
14. C2×#19099169C2semidirect
15. C2×#19099165C2semidirect
16. C2×#19099132C2semidirect
17. C2×#19099129C2semidirect
18. C2×#19099126C2semidirect
19. C2×#19099124C2semidirect
20. C2×#19099121C2semidirect
21. C2×#127×D79C2semidirect
22. C2×#19099098C2semidirect
23. C2×#19099091C2semidirect
24. C2×#540×C79C2semidirect
25. C22×#11929624C22semidirect
26. C22×#11929624C22semidirect
27. C22×#11929623C22semidirect
28. C23×D316C22semidirect
29. C23×D316C22semidirect
30. C22×D4×D79C22semidirect
31. C22×D4×D79C22semidirect
32. C22×D4×D79C22semidirect
33. C22×D4×D79C22semidirect
34. C22×D4×D79C22semidirect
35. C22×D4×D79C22semidirect
36. C22×D4×D79C22semidirect
37. #19099303C22semidirect
38. #19099301C22semidirect
39. #19099296C22semidirect
40. #19099234C22semidirect
41. #19099231C22semidirect
42. #19099210C22semidirect
43. #19099208C22semidirect
44. #19099205C22semidirect
45. D4×D316C22semidirect
46. #19099197C22semidirect
47. #19099197C22semidirect
48. #19099197C22semidirect
49. #19099169C22semidirect
50. #19099165C22semidirect
51. #19099132C22semidirect
52. #19099129C22semidirect
53. #19099126C22semidirect
54. #19099124C22semidirect
55. #19099121C22semidirect
56. C2×#14579158C22semidirect
57. C2×#14579158C22semidirect
59. C2×#14579157C22semidirect
60. C2×#14579157C22semidirect
61. C2×#14579157C22semidirect
62. C2×#14579157C22semidirect
63. C2×#14579157C22semidirect
64. #127×D79C22semidirect
65. #19099098C22semidirect
66. #19099091C22semidirect
67. C2×#14579156C22semidirect
68. C2×#14579156C22semidirect
69. C2×#14579154C22semidirect
70. C2×#14579151C22semidirect
71. C2×#14579149C22semidirect
72. C2×#14579149C22semidirect
73. C2×#14579148C22semidirect
74. C2×#14579147C22semidirect
75. C2×#14579147C22semidirect
76. C2×#14579146C22semidirect
77. C2×#14579146C22semidirect
78. C2×#14579146C22semidirect
79. C2×#14579146C22semidirect
80. C2×#14579145C22semidirect
81. C2×#14579144C22semidirect
82. C2×#14579143C22semidirect
83. C2×#14579143C22semidirect
84. C2×#14579143C22semidirect
85. C2×#14579141C22semidirect
86. C2×#14579139C22semidirect
88. C2×#14579136C22semidirect
89. C2×#14579136C22semidirect
90. C2×#14579136C22semidirect
91. C2×#14579136C22semidirect
92. C2×#14579136C22semidirect
93. C2×#14579136C22semidirect
94. C2×#14579135C22semidirect
95. C2×#14579135C22semidirect
96. C2×#14579135C22semidirect
98. C2×#14579134C22semidirect
99. C2×#14579134C22semidirect
100. C2×#14579134C22semidirect
101. C2×#14579134C22semidirect
102. C2×#14579134C22semidirect
103. C2×#14579133C22semidirect
104. C2×#14579133C22semidirect
105. C2×#14579133C22semidirect
106. C2×#14579132C22semidirect
107. C2×#14579131C22semidirect
108. C2×#14579131C22semidirect
109. C2×#14579131C22semidirect
110. C2×#14579131C22semidirect
111. C2×#14579131C22semidirect
112. C2×#14579131C22semidirect
113. C2×#14579131C22semidirect
114. C2×#14579129C22semidirect
115. C2×#14579129C22semidirect
116. C2×#14579129C22semidirect
117. C2×#14579129C22semidirect
118. C2×#14579129C22semidirect
119. C2×C4×Dic158C22semidirect
120. C2×#14579126C22semidirect
121. C2×C4×D316C22semidirect
122. C2×#14579123C22semidirect
123. C2×#14579123C22semidirect
124. C2×#14579123C22semidirect
125. C2×#14579123C22semidirect
126. C2×C4×C22⋊D79C22semidirect
127. C2×C4×C22⋊D79C22semidirect
128. C2×C4×C22⋊D79C22semidirect
129. C2×(C22⋊D79)⋊C4C22semidirect
130. C2×#14579119C22semidirect
131. C2×#14579118C22semidirect
132. C22×(C2×D79)⋊C4C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. #540×C79C22semidirect
136. C2×#127×C79C22semidirect
137. C2×#125×C79C22semidirect
138. C2×#123×C79C22semidirect
139. C2×#123×C79C22semidirect
140. C2×#121×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#121×C79C22semidirect
144. C2×C4×D4×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C2×#117×C79C22semidirect
153. C2×#11929624C23semidirect
154. C2×#11929624C23semidirect
156. C2×#11929623C23semidirect
173. C22×D316C23semidirect
174. C22×D316C23semidirect
195. C2×D4×D79C23semidirect
196. C2×D4×D79C23semidirect
197. C2×D4×D79C23semidirect
198. C2×D4×D79C23semidirect
199. C2×D4×D79C23semidirect
200. C2×D4×D79C23semidirect
201. C2×D4×D79C23semidirect
211. #14579158C23semidirect
212. #14579158C23semidirect
214. #14579157C23semidirect
215. #14579157C23semidirect
216. #14579157C23semidirect
217. #14579157C23semidirect
218. #14579157C23semidirect
219. #14579156C23semidirect
220. #14579156C23semidirect
221. #14579154C23semidirect
222. #14579151C23semidirect
223. #14579149C23semidirect
224. #14579149C23semidirect
225. #14579148C23semidirect
226. #14579147C23semidirect
227. #14579147C23semidirect
228. #14579146C23semidirect
229. #14579146C23semidirect
230. #14579146C23semidirect
231. #14579146C23semidirect
232. #14579145C23semidirect
233. #14579144C23semidirect
234. #14579143C23semidirect
235. #14579143C23semidirect
236. #14579143C23semidirect
237. #14579141C23semidirect
238. #14579139C23semidirect
240. #14579136C23semidirect
241. #14579136C23semidirect
242. #14579136C23semidirect
243. #14579136C23semidirect
244. #14579136C23semidirect
245. #14579136C23semidirect
246. #14579135C23semidirect
247. #14579135C23semidirect
248. #14579135C23semidirect
250. #14579134C23semidirect
251. #14579134C23semidirect
252. #14579134C23semidirect
253. #14579134C23semidirect
254. #14579134C23semidirect
255. #14579133C23semidirect
256. #14579133C23semidirect
257. #14579133C23semidirect
258. #14579132C23semidirect
259. #14579131C23semidirect
260. #14579131C23semidirect
261. #14579131C23semidirect
262. #14579131C23semidirect
263. #14579131C23semidirect
264. #14579131C23semidirect
265. #14579131C23semidirect
266. #14579129C23semidirect
267. #14579129C23semidirect
268. #14579129C23semidirect
269. #14579129C23semidirect
270. #14579129C23semidirect
271. C4×Dic158C23semidirect
272. #14579126C23semidirect
273. C4×D316C23semidirect
274. #14579123C23semidirect
275. #14579123C23semidirect
276. #14579123C23semidirect
277. #14579123C23semidirect
278. C4×C22⋊D79C23semidirect
279. C4×C22⋊D79C23semidirect
280. C4×C22⋊D79C23semidirect
281. (C22⋊D79)⋊C4C23semidirect
282. #14579119C23semidirect
283. #14579118C23semidirect
315. C2×(C2×D79)⋊C4C23semidirect
316. C22⋊C4×D79C23semidirect
322. C42×D79C23semidirect
332. #127×C79C23semidirect
333. #125×C79C23semidirect
334. #123×C79C23semidirect
335. #123×C79C23semidirect
336. #121×C79C23semidirect
337. #121×C79C23semidirect
338. #121×C79C23semidirect
339. #121×C79C23semidirect
340. C4×D4×C79C23semidirect
341. C4×D4×C79C23semidirect
342. #117×C79C23semidirect
731. C2×C79#3543semidirect
755. C2×#540D79semidirect
764. C79C2×#3543semidirect
791. #540C2×D79semidirect
806. C2×#127C2×D79semidirect
813. C2×#125C2×D79semidirect
828. C2×#123C2×D79semidirect
829. C2×#123C2×D79semidirect
852. C2×#121C2×D79semidirect
853. C2×#121C2×D79semidirect
854. C2×#121C2×D79semidirect
855. C2×#121C2×D79semidirect
879. C2×C4×D4C2×D79semidirect
880. C2×C4×D4C2×D79semidirect
883. C2×#117C2×D79semidirect
968. #127C22×D79semidirect
973. #125C22×D79semidirect
988. #123C22×D79semidirect
989. #123C22×D79semidirect
1012. #121C22×D79semidirect
1013. #121C22×D79semidirect
1014. #121C22×D79semidirect
1015. #121C22×D79semidirect
1039. C4×D4C22×D79semidirect
1040. C4×D4C22×D79semidirect
1043. #117C22×D79semidirect
1475. C2#23777729direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237777292
C2×#190993032
C2×#190993012
C2×#190992962
C2×#190992342
C2×#190992312
C2×#190992102
C2×#190992082
C2×#190992052
C2×D4×D3162
C2×#190991972
C2×#190991692
C2×#190991652
C2×#190991322
C2×#190991292
C2×#190991262
C2×#190991242
C2×#190991212
C2×#127×D792
C2×#190990982
C2×#190990912
C2×#540×C792
C2×#354379