Finite Group Databasebeta

← C2×#23777430 #35196262

Subgroups — C2×#23777430 #35196262

Order 20224.

8774 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777430C2132yesmaximal, direct product factor
2C2×#19099277C211yesmaximal, characteristic, complemented
3C2×#19099269C211yesmaximal, characteristic, complemented
4C2×#19099266C211yesmaximal, characteristic, complemented
5C2×#19099260C211yesmaximal, characteristic, complemented
6C2×#19099258C212yesmaximal, complemented
7C2×#19099233C211yesmaximal, characteristic, complemented
8C2×#19099210C212yesmaximal, complemented
9C2×#19099205C212yesmaximal, complemented
10C2×#19099202C212yesmaximal, complemented
11C2×#19099198C211yesmaximal, characteristic, complemented
12C2×#19099197C211yesmaximal, characteristic, complemented
13C2×#19099197C211yesmaximal, characteristic, complemented
14C2×#19099164C211yesmaximal, characteristic, complemented
15C2×#19099149C212yesmaximal, complemented
16C2×#19099145C212yesmaximal, complemented
17C2×#19099110C211yesmaximal, characteristic, complemented
18C2×#19099091C211yesmaximal, characteristic, complemented
19C2×#19099071C212yesmaximal, complemented
20C2×#121×D79C212yesmaximal, complemented
21C2×#19099037C211yesmaximal, characteristic, complemented
22C2×#19099035C211yesmaximal, characteristic, complemented
23C2×C4×D4×D79C211yesmaximal, characteristic, complemented
24C2×#540×C79C211yesmaximal, characteristic, complemented
25C22×#11929624C2212yescomplemented
26C22×#11929623C2212yescomplemented
27C23×D316C2211yescharacteristic
28C22×D4×D79C2211yescharacteristic
29C22×D4×D79C2211yescharacteristic
30C22×D4×D79C2212yescomplemented
31C22×D4×D79C2212yescomplemented
32C22×D4×D79C2212yescomplemented
33C23×C4×D79C2212yescomplemented
34#19099277C22116yescomplemented
35#19099269C22116yescomplemented
36#19099266C22116yescomplemented
37#19099260C22116yescomplemented
38#19099258C22132yescomplemented
39#19099233C22116yescomplemented
40#19099210C22132yescomplemented
41#19099205C22132yescomplemented
42#19099202C22132yescomplemented
43#19099198C22116yescomplemented
44#19099197C22116yescomplemented
45#19099197C22116yescomplemented
46#19099164C22116yescomplemented
47#19099149C22132yescomplemented
48#19099145C22132yescomplemented
49#19099110C22116yescomplemented
50C2×#14579160C2211yescharacteristic, complemented
51C2×#14579157C2211yescharacteristic, complemented
52C2×#14579157C2211yescharacteristic, complemented
53#19099091C22116yescomplemented
54C2×#14579156C2211yescharacteristic, complemented
55C2×#14579156C2212yescomplemented
56C2×#14579154C2211yescharacteristic, complemented
57C2×#14579154C2212yescomplemented
58C2×#14579152C2211yescharacteristic, complemented
59C2×#14579151C2211yescharacteristic, complemented
60C2×#14579148C2212yescomplemented
61C2×#14579147C2211yescharacteristic, complemented
62C2×#14579147C2212yescomplemented
63C2×#14579147C2212yescomplemented
64#19099071C22132yescomplemented
65C2×#14579146C2212yescomplemented
66C2×#14579146C2211yescharacteristic, complemented
67C2×#14579144C2212yescomplemented
68C2×#14579143C2211yescharacteristic, complemented
69C2×#14579143C2212yescomplemented
70C2×#14579142C2212yescomplemented
71C2×#14579141C2212yescomplemented
72C2×#14579139C2212yescomplemented
73C2×#14579139C2212yescomplemented
74C2×#14579139C2211yescharacteristic, complemented
75C2×#14579136C2211yescharacteristic, complemented
76C2×#14579136C2211yescharacteristic, complemented
77C2×#14579136C2212yescomplemented
78C2×#14579135C2212yescomplemented
79C2×#14579134C2211yescharacteristic
80C2×#14579134C2212yescomplemented
81C2×#14579134C2212yescomplemented
82C2×#14579134C2212yescomplemented
83C2×#14579134C2212yescomplemented
84C2×#14579133C2212yescomplemented
85C2×#14579133C2212yescomplemented
86C2×#14579133C2212yescomplemented
87C2×#14579132C2212yescomplemented
88C2×#14579132C2211yescharacteristic, complemented
89C2×#14579132C2211yescharacteristic, complemented
90C2×#14579132C2212yescomplemented
91C2×#14579132C2212yescomplemented
92#121×D79C22132yescomplemented
93C2×#14579131C2212yescomplemented
94C2×#14579131C2212yescomplemented
95C2×#14579129C2212yescomplemented
96C2×#14579129C2212yescomplemented
97C2×#14579129C2212yescomplemented
98C2×#14579129C2212yescomplemented
99#19099037C22116yescomplemented
100#19099035C22116yescomplemented
101C2×C4×Dic158C2211yescharacteristic, complemented
102C2×C4×D316C2211yescharacteristic
103C2×C4×D316C2211yescharacteristic
104C2×C4×D316C2211yescharacteristic, complemented
105C2×C4×D316C2211yescharacteristic, complemented
106C2×C4×D316C2211yescharacteristic, complemented
107C2×D4×Dic79C2211yescharacteristic, complemented
108C2×D4×Dic79C2211yescharacteristic, complemented
109C2×#14579123C2211yescharacteristic
110C2×#14579123C2211yescharacteristic
111C2×#14579123C2212yescomplemented
112C2×#14579123C2212yescomplemented
113C2×#14579123C2212yescomplemented
114C2×C4×C22⋊D79C2212yescomplemented
115C2×C4×C22⋊D79C2211yescharacteristic, complemented
116C2×C4×C22⋊D79C2211yescharacteristic, complemented
117C2×C4×C22⋊D79C2212yescomplemented
118C2×C4×C22⋊D79C2212yescomplemented
119C2×(C22⋊D79)⋊C4C2212yescomplemented
120C2×(C22⋊D79)⋊C4C2212yescomplemented
121C2×(C22⋊D79)⋊C4C2212yescomplemented
122C4×D4×D79C22116yescomplemented
123C2×#14579120C2211yescharacteristic, complemented
124C2×#14579119C2211yescharacteristic, complemented
125C2×#14579118C2211yescharacteristic, complemented
126C2×#14579117C2212yescomplemented
127C2×C4⋊C4×D79C2211yescharacteristic, complemented
128C2×C4⋊C4×D79C2212yescomplemented
129C22×(C2×D79)⋊C4C2212yescomplemented
130C2×C22⋊C4×D79C2212yescomplemented
131C2×C22⋊C4×D79C2212yescomplemented
132C2×C22⋊C4×D79C2212yescomplemented
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—
150C2×#11929624—48no—
151C2×#11929624C23116yescomplemented
152C2×#11929623—48no—
153C2×#11929623C23116yescomplemented
154C22×Dic158C2311yescharacteristic
155C22×Dic158C2312yes—
156C22×D316—28no—
157C22×D316C2318yes—
158C22×D316C2312yes—
159C22×D316C2312yes—
160C22×D316C2311yescharacteristic
161C22×D316C2311yescharacteristic
162C22×D316C2312yes—
163C22×D316C2311yescharacteristic
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2312yes—
166C22×C22⋊D79C2312yes—
167C22×C22⋊D79C2311yescharacteristic
168C22×C22⋊D79C2311yescharacteristic
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2312yes—
171C22×C22⋊D79C2312yes—
172C22×C22⋊D79C2312yes—
173C22×C22⋊D79C2312yes—
174C2×D4×D79—28no—
175C2×D4×D79—28no—
176C2×D4×D79—48no—
177C2×D4×D79—48no—
178C2×D4×D79—48no—
179C2×D4×D79C2318yes—
180C2×D4×D79C2318yes—
181C2×D4×D79C23116yescomplemented
182C2×D4×D79C23116yescomplemented
183C2×D4×D79C23116yescomplemented
184C23×Dic79C2312yes—
185C23×Dic79C2312yes—
186C22×C4×D79—48no—
187C22×C4×D79C2311yescharacteristic
188C22×C4×D79C2311yescharacteristic
189C22×C4×D79C2311yescharacteristic
190C22×C4×D79C2312yes—
191C22×C4×D79C2311yescharacteristic
192C22×C4×D79C2312yes—
193C22×C4×D79C2312yes—
194C22×C4×D79C2312yes—
195C22×C4×D79C2312yes—
196C22×C4×D79C2312yes—
197C22×C4×D79C2312yes—
198C22×C4×D79C23116yescomplemented
199#14579160C2318yescomplemented
200#14579157C2318yescomplemented
201#14579157C2318yescomplemented
202#14579156C23116yescomplemented
203#14579156C2318yescomplemented
204#14579154C2318yescomplemented
205#14579154C23116yescomplemented
206#14579152C2318yescomplemented
207#14579151C2318yescomplemented
208#14579148C23116yescomplemented
209#14579147C23116yescomplemented
210#14579147C23116yescomplemented
211#14579147C2318yescomplemented
212#14579146C23116yescomplemented
213#14579146C2318yescomplemented
214#14579144C23116yescomplemented
215#14579143C23116yescomplemented
216#14579143C2318yescomplemented
217#14579142C23116yescomplemented
218#14579141C23116yescomplemented
219#14579139C23116yescomplemented
220#14579139C23116yescomplemented
221#14579139C2318yescomplemented
222#14579136C2318yescomplemented
223#14579136C2318yescomplemented
224#14579136C23116yescomplemented
225#14579135C23116yescomplemented
226#14579134C2318yes—
227#14579134C23116yescomplemented
228#14579134C23116yescomplemented
229#14579134C23116yescomplemented
230#14579134C23116yescomplemented
231#14579133C23116yescomplemented
232#14579133C23116yescomplemented
233#14579133C23116yescomplemented
234#14579132C23116yescomplemented
235#14579132C23116yescomplemented
236#14579132C2318yescomplemented
237#14579132C2318yescomplemented
238#14579132C23116yescomplemented
239#14579131C23116yescomplemented
240#14579131C23116yescomplemented
241#14579129C23116yescomplemented
242#14579129C23116yescomplemented
243#14579129C23116yescomplemented
244#14579129C23116yescomplemented
245C4×Dic158C2318yescomplemented
246C4×D316C2318yes—
247C4×D316C2318yes—
248C4×D316C2318yescomplemented
249C4×D316C2318yescomplemented
250C4×D316C2318yescomplemented
251D4×Dic79C2318yescomplemented
252D4×Dic79C2318yescomplemented
253#14579123C2318yes—
254#14579123C2318yes—
255#14579123C23116yescomplemented
256#14579123C23116yescomplemented
257#14579123C23116yescomplemented
258C4×C22⋊D79C23116yescomplemented
259C4×C22⋊D79C2318yescomplemented
260C4×C22⋊D79C2318yescomplemented
261C4×C22⋊D79C23116yescomplemented
262C4×C22⋊D79C23116yescomplemented
263(C22⋊D79)⋊C4C23116yescomplemented
264(C22⋊D79)⋊C4C23116yescomplemented
265(C22⋊D79)⋊C4C23116yescomplemented
266#14579120C2318yescomplemented
267#14579119C2318yescomplemented
268#14579118C2318yescomplemented
269#14579117C23116yescomplemented
270C2×C4⋊Dic79C2311yescharacteristic
271C2×C4⋊Dic79C2312yes—
272C2×C4⋊Dic79C2311yescharacteristic
273C2×C4⋊Dic79C2311yescharacteristic
274C2×C4⋊Dic79C2311yescharacteristic
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2312yes—
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2311yescharacteristic
279C2×Dic79⋊C4C2311yescharacteristic
280C2×Dic79⋊C4C2311yescharacteristic
281C2×Dic79⋊C4C2312yes—
282C2×Dic79⋊C4C2311yescharacteristic
283C2×Dic79⋊C4C2311yescharacteristic
284C4⋊C4×D79C23116yescomplemented
285C4⋊C4×D79C2318yescomplemented
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2311yescharacteristic
291C2×C22⋊Dic79C2311yescharacteristic
292C2×C22⋊Dic79C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2311yescharacteristic
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2312yes—
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2311yescharacteristic
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C2311yescharacteristic
308C2×(C2×D79)⋊C4C23116yescomplemented
309C22⋊C4×D79C23116yescomplemented
310C22⋊C4×D79C23116yescomplemented
311C22⋊C4×D79C23116yescomplemented
312C22⋊C4×D79C23116yescomplemented
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2311yescharacteristic
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2312yes—
317C2×C4×Dic79C2312yes—
318C2×C4×Dic79C2311yescharacteristic
319C42×D79C2318yescomplemented
320C22×D4×C79C2311yescharacteristic
321C22×D4×C79C2311yescharacteristic
322C22×D4×C79C2312yes—
323C22×D4×C79C2312yes—
324C22×D4×C79C2312yes—
325C22×D4×C79C2312yes—
326C23×C4×C79C2311yescharacteristic
327C23×C4×C79C2312yes—
328C23×C4×C79C2312yes—
329#127×C79C2318yescomplemented
330#125×C79C2318yescomplemented
331#123×C79C23116yescomplemented
332#123×C79C23116yescomplemented
333#121×C79C23116yescomplemented
334#121×C79C2318yescomplemented
335#121×C79C2318yescomplemented
336#121×C79C23116yescomplemented
337C4×D4×C79C2318yescomplemented
338C4×D4×C79C2318yescomplemented
339#117×C79C2318yescomplemented
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C4⋊C4×C79C2311yescharacteristic
342C2×C4⋊C4×C79C2311yescharacteristic
343C2×C4⋊C4×C79C2311yescharacteristic
344C2×C4⋊C4×C79C2312yes—
345C2×C4⋊C4×C79C2312yes—
346C2×C22⋊C4×C79C2311yescharacteristic
347C2×C22⋊C4×C79C2311yescharacteristic
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C22⋊C4×C79C2312yes—
352C2×C42×C79C2311yescharacteristic
353C2×C42×C79C2311yescharacteristic
354C23×D79—28no—
355C23×D79—28no—
356C23×D79—28no—
357C23×D79—28no—
358C23×D79—44no—
359C23×D79—44no—
360C23×D79—44no—
361C23×D79—44no—
362C23×D79—44no—
363C23×D79C2411yescharacteristic
364C23×D79C2412yes—
365C23×D79C2418yes—
366C23×D79C2412yes—
367C23×D79C2411yescharacteristic
368C23×D79C2418yes—
369C23×D79C2418yes—
370#11929624—432no—
371#11929623—432no—
372C2×Dic158—24no—
373C2×Dic158—44no—
374C2×Dic158C2414yes—
375C2×Dic158C2418yes—
376C2×D316—232no—
377C2×D316—28no—
378C2×D316—28no—
379C2×D316—24no—
380C2×D316—24no—
381C2×D316—44no—
382C2×D316#4118yescomplemented
383C2×D316C2418yes—
384C2×D316C2418yes—
385C2×D316C2414yes—
386C2×D316C2414yes—
387C2×D316C2418yes—
388C2×D316C2414yes—
389C2×C22⋊D79—28no—
390C2×C22⋊D79—24no—
391C2×C22⋊D79—28no—
392C2×C22⋊D79—28no—
393C2×C22⋊D79—28no—
394C2×C22⋊D79—24no—
395C2×C22⋊D79—44no—
396C2×C22⋊D79—44no—
397C2×C22⋊D79—44no—
398C2×C22⋊D79—44no—
399C2×C22⋊D79C2418yes—
400C2×C22⋊D79C2418yes—
401C2×C22⋊D79C2418yes—
402C2×C22⋊D79C2418yes—
403C2×C22⋊D79C2414yes—
404C2×C22⋊D79C2414yes—
405C2×C22⋊D79C2418yes—
406C2×C22⋊D79C2418yes—
407C2×C22⋊D79C2418yes—
408C2×C22⋊D79C2418yes—
409D4×D79—232no—
410D4×D79—232no—
411D4×D79—432no—
412D4×D79—432no—
413D4×D79—432no—
414C22×Dic79—28no—
415C22×Dic79—44no—
416C22×Dic79C2411yescharacteristic
417C22×Dic79C2411yescharacteristic
418C22×Dic79C2412yes—
419C22×Dic79C2418yes—
420C22×Dic79C2411yescharacteristic
421C22×Dic79C2411yescharacteristic
422C22×Dic79C2412yes—
423C22×Dic79C2411yescharacteristic
424C22×Dic79C2418yes—
425C22×Dic79C2411yescharacteristic
426C2×C4×D79—24no—
427C2×C4×D79—28no—
428C2×C4×D79—24no—
429C2×C4×D79—24no—
430C2×C4×D79—24no—
431C2×C4×D79—44no—
432C2×C4×D79—44no—
433C2×C4×D79—44no—
434C2×C4×D79—44no—
435C2×C4×D79—44no—
436C2×C4×D79—44no—
437C2×C4×D79—432no—
438C2×C4×D79C2414yes—
439C2×C4×D79C2414yes—
440C2×C4×D79C2414yes—
441C2×C4×D79C2418yes—
442C2×C4×D79C2414yes—
443C2×C4×D79C2418yes—
444C2×C4×D79C2418yes—
445C2×C4×D79C2418yes—
446C2×C4×D79C2418yes—
447C2×C4×D79C2418yes—
448C2×C4×D79C2418yes—
449C4⋊Dic79C2414yes—
450C4⋊Dic79C2418yes—
451C4⋊Dic79C2414yes—
452C4⋊Dic79C2414yes—
453C4⋊Dic79C2414yes—
454Dic79⋊C4C2414yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2418yes—
457Dic79⋊C4C2414yes—
458Dic79⋊C4C2414yes—
459Dic79⋊C4C2414yes—
460Dic79⋊C4C2418yes—
461Dic79⋊C4C2414yes—
462Dic79⋊C4C2414yes—
463C22⋊Dic79C2418yes—
464C22⋊Dic79C2418yes—
465C22⋊Dic79C2418yes—
466C22⋊Dic79C2418yes—
467C22⋊Dic79C2414yes—
468C22⋊Dic79C2414yes—
469C22⋊Dic79C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2418yes—
477(C2×D79)⋊C4C2414yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2414yes—
480(C2×D79)⋊C4C2418yes—
481(C2×D79)⋊C4C2414yes—
482(C2×D79)⋊C4C2414yes—
483(C2×D79)⋊C4C2418yes—
484(C2×D79)⋊C4C2414yes—
485C4×Dic79C2414yes—
486C4×Dic79C2414yes—
487C4×Dic79C2414yes—
488C4×Dic79C2418yes—
489C4×Dic79C2418yes—
490C4×Dic79C2414yes—
491C24×C79C2411yescharacteristic
492C24×C79C2412yes—
493C24×C79C2412yes—
494C2×D4×C79—24no—
495C2×D4×C79—24no—
496C2×D4×C79—44no—
497C2×D4×C79—44no—
498C2×D4×C79—44no—
499C2×D4×C79—44no—
500C2×D4×C79C2414yes—
501C2×D4×C79C2414yes—
502C2×D4×C79C2418yes—
503C2×D4×C79C2418yes—
504C2×D4×C79C2418yes—
505C2×D4×C79C2418yes—
506C22×C4×C79—24no—
507C22×C4×C79—44no—
508C22×C4×C79—44no—
509C22×C4×C79C2411yescharacteristic
510C22×C4×C79C2412yes—
511C22×C4×C79C2411yescharacteristic
512C22×C4×C79C2411yescharacteristic
513C22×C4×C79C2411yescharacteristic
514C22×C4×C79C2411yescharacteristic
515C22×C4×C79C2412yes—
516C22×C4×C79C2414yes—
517C22×C4×C79C2418yes—
518C22×C4×C79C2418yes—
519C22×C4×C79C2411yescharacteristic
520C4⋊C4×C79C2414yes—
521C4⋊C4×C79C2414yes—
522C4⋊C4×C79C2414yes—
523C4⋊C4×C79C2414yes—
524C4⋊C4×C79C2418yes—
525C4⋊C4×C79C2418yes—
526C22⋊C4×C79C2414yes—
527C22⋊C4×C79C2414yes—
528C22⋊C4×C79C2418yes—
529C22⋊C4×C79C2418yes—
530C22⋊C4×C79C2418yes—
531C22⋊C4×C79C2418yes—
532C42×C79C2414yes—
533C42×C79C2414yes—
534C23×C79—24no—
535C23×C79—24no—
536C23×C79—22no—
537C23×C79—24no—
538C23×C79—24no—
539C23×C79—24no—
540C23×C79—22no—
541C23×C79—22no—
542C23×C79—24no—
543C23×C79C2512yes—
544C23×C79C2514yes—
545C23×C79C2514yes—
546C23×C79C2511yescharacteristic
547C22×D79—22no—
548C22×D79—22no—
549C22×D79—24no—
550C22×D79—24no—
551C22×D79—22no—
552C22×D79—24no—
553C22×D79—24no—
554C22×D79—24no—
555C22×D79—22no—
556C22×D79—22no—
557C22×D79—216no—
558C22×D79—216no—
559C22×D79—216no—
560C22×D79—216no—
561C22×D79—48no—
562C22×D79—432no—
563C22×D79—48no—
564C22×D79—48no—
565C22×D79—48no—
566C22×D79—48no—
567C22×D79—816no—
568C22×D79—816no—
569C22×D79C2×#4118yes—
570C22×D79H(5,𝔽2)14yes—
571C22×D79C2512yes—
572C22×D79C2514yes—
573C22×D79C2514yes—
574C22×D79C2512yes—
575D4×C79—28no—
576D4×C79—28no—
577D4×C79—48no—
578D4×C79—48no—
579D4×C79—48no—
580D4×C79—48no—
581C2×C4×C79—22no—
582C2×C4×C79—22no—
583C2×C4×C79—22no—
584C2×C4×C79—24no—
585C2×C4×C79—22no—
586C2×C4×C79—22no—
587C2×C4×C79—24no—
588C2×C4×C79—28no—
589C2×C4×C79—48no—
590C2×C4×C79—48no—
591C2×C4×C79C2×#4114yes—
592C2×C4×C79C2512yes—
593C2×C4×C79C2512yes—
594C2×C4×C79C2512yes—
595C2×C4×C79C2514yes—
596C2×C4×C79C2512yes—
597C2×C4×C79C2512yes—
598C2×C4×C79C2514yes—
599C2×C4×C79C2512yes—
600C22⋊D79—216no—
601C22⋊D79—216no—
602C22⋊D79—28no—
603C22⋊D79—216no—
604C22⋊D79—28no—
605C22⋊D79—216no—
606C22⋊D79—48no—
607C22⋊D79—48no—
608C22⋊D79—48no—
609C22⋊D79—48no—
610C2×Dic79—22no—
611C2×Dic79—22no—
612C2×Dic79—22no—
613C2×Dic79—24no—
614C2×Dic79—22no—
615C2×Dic79—24no—
616C2×Dic79—22no—
617C2×Dic79—216no—
618C2×Dic79—48no—
619C2×Dic79H(5,𝔽2)14yes—
620C2×Dic79C2512yes—
621C2×Dic79C2512yes—
622C2×Dic79C2514yes—
623C2×Dic79C2512yes—
624C2×Dic79C2512yes—
625C2×Dic79C2514yes—
626C2×Dic79C2512yes—
627C2×Dic79C2512yes—
628D316—216no—
629D316—28no—
630D316—216no—
631D316—28no—
632D316—48no—
633D316C2×#41116yescomplemented
634C4×D79—28no—
635C4×D79—28no—
636C4×D79—28no—
637C4×D79—28no—
638C4×D79—216no—
639C4×D79—48no—
640C4×D79—48no—
641C4×D79—48no—
642C4×D79—48no—
643C4×D79—48no—
644C4×D79—48no—
645Dic158—28no—
646Dic158—48no—
647C22×C79—24no—
648C22×C79—24no—
649C22×C79—22no—
650C22×C79—24no—
651C22×C79—22no—
652C22×C79—22no—
653C22×C79—24no—
654C22×C79—24no—
655C22×C79—24no—
656C22×C79—48no—
657C22×C79—44no—
658C22×C79—48no—
659C22×C79C22×#4112yes—
660C22×C79C2×H(5,𝔽2)12yes—
661C22×C79C2×H(5,𝔽2)12yes—
662C22×C79C2611yescharacteristic
663C2×D79—22no—
664C2×D79—24no—
665C2×D79—24no—
666C2×D79—22no—
667C2×D79—28no—
668C2×D79—216no—
669C2×D79—22no—
670C2×D79—24no—
671C2×D79—24no—
672C2×D79—22no—
673C2×D79—22no—
674C2×D79—24no—
675C2×D79—432no—
676C2×D79—48no—
677C2×D79—44no—
678C2×D79—816no—
679C2×D79—816no—
680C2×D79C22×#4118yes—
681C2×D79C2×H(5,𝔽2)14yes—
682C4×C79—22no—
683C4×C79—22no—
684C4×C79—22no—
685C4×C79—24no—
686C4×C79—24no—
687C4×C79—22no—
688C4×C79—22no—
689C4×C79C22×#4114yes—
690Dic79—22no—
691Dic79—22no—
692Dic79—22no—
693Dic79—24no—
694Dic79—22no—
695Dic79—22no—
696Dic79—24no—
697Dic79C2×H(5,𝔽2)14yes—
698C2×#3519—791nomaximal, Sylow
699C2×C79—44no—
700C2×C79—42no—
701C2×C79—44no—
702C2×C79#351914yescomplemented
703C2×C79C23×#4111yescharacteristic
704C2×C79C22×H(5,𝔽2)11yescharacteristic
705C2×C79C22×H(5,𝔽2)11yescharacteristic
706D79—24no—
707D79—28no—
708D79—44no—
709D79—42no—
710#3519—7932no—
711C2×#555—791no—
712C2×#554—791no—
713C2×#553—791no—
714C2×#553—792no—
715C2×#553—791no—
716C2×#550—791no—
717C2×#546—792no—
718C2×#546—792no—
719C2×#546—792no—
720C2×D42—791no—
721C2×D42—791no—
722C2×D42—791no—
723C2×#540—791no—
724C2×#540D7911yescharacteristic, complemented
725C2×#538—792no—
726C2×#538—792no—
727C2×#532—791no—
728C2×#529—791no—
729C2×#525—792no—
730C22×#121—792no—
731C2×#518—791no—
732C2×#518—791no—
733C22×C4×D4—791no—
734C79C2×#351911yescharacteristic, complemented, Sylow
735C22×#41—792no—
736C22×#41—792no—
737C23×D4—792no—
738C23×D4—792no—
739C23×D4—792no—
740C23×D4—791no—
741C23×D4—791no—
742C23×D4—791no—
743C24×C4—792no—
744#555—7916no—
745#554—7916no—
746#553—7916no—
747#553—7932no—
748#553—7916no—
749#550—7916no—
750#546—7932no—
751#546—7932no—
752#546—7932no—
753D42—7916no—
754D42—7916no—
755D42—7916no—
756#540—7916no—
757#540C2×D79116yescomplemented
758#538—7932no—
759#538—7932no—
760#532—7916no—
761C2×C4⋊Q8—791no—
762C2×#127—791no—
763C2×#127—791no—
764C2×#127C2×D7911yescharacteristic, complemented
765#529—7916no—
766C2×#126—791no—
767C2×#126—792no—
768C2×#126—791no—
769C2×#126—792no—
770C2×#125—791no—
771C2×#125—791no—
772C2×#125C2×D7911yescharacteristic, complemented
773C2×#124—792no—
774C2×#124—791no—
775C2×#124—792no—
776C2×#124—792no—
777#525—7932no—
778C2×#123—792no—
779C2×#123—792no—
780C2×#123—791no—
781C2×#123—792no—
782C2×#123—791no—
783C2×#123—792no—
784C2×#123C2×D7912yescomplemented
785C2×#123C2×D7912yescomplemented
786C2×C22⋊Q8—791no—
787C2×C22⋊Q8—792no—
788C2×C22⋊Q8—792no—
789C2×C22⋊Q8—792no—
790C2×#121—792no—
791C2×#121—792no—
792C2×#121—792no—
793C2×#121—791no—
794C2×#121—792no—
795C2×#121—792no—
796C2×#121—792no—
797C2×#121—791no—
798C2×#121—792no—
799C2×#121—7932no—
800C2×#121—792no—
801C2×#121—791no—
802C2×#121—791no—
803C2×#121—791no—
804C2×#121—792no—
805C2×#121—792no—
806C2×#121—792no—
807C2×#121—792no—
808C2×#121C2×D7912yescomplemented
809C2×#121C2×D7911yescharacteristic, complemented
810C2×#121C2×D7911yescharacteristic, complemented
811C2×#121C2×D7912yescomplemented
812C2×#120—792no—
813C2×#120—792no—
814C2×#120—792no—
815C2×#120—792no—
816C2×#120—792no—
817C2×#120—792no—
818#518—7916no—
819#518—7916no—
820C2×C4×Q8—791no—
821C2×C4×D4—791no—
822C2×C4×D4—791no—
823C2×C4×D4—792no—
824C2×C4×D4—792no—
825C2×C4×D4—791no—
826C2×C4×D4—791no—
827C2×C4×D4—792no—
828C2×C4×D4—7916no—
829C2×C4×D4—791no—
830C2×C4×D4—792no—
831C2×C4×D4—791no—
832C2×C4×D4—792no—
833C2×C4×D4—792no—
834C2×C4×D4—792no—
835C2×C4×D4—792no—
836C2×C4×D4—792no—
837C2×C4×D4—791no—
838C2×C4×D4—791no—
839C2×C4×D4—791no—
840C2×C4×D4—791no—
841C2×C4×D4—791no—
842C2×C4×D4C2×D7911yescharacteristic, complemented
843C2×C4×D4C2×D7911yescharacteristic, complemented
844C2×#117—791no—
845C2×#117—791no—
846C2×#117—792no—
847C2×#117—791no—
848C2×#117C2×D7911yescharacteristic, complemented
849C22×C4⋊C4—791no—
850C22×C4⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C22⋊C4—792no—
853C22×C22⋊C4—792no—
854C22×C22⋊C4—792no—
855C22×C22⋊C4—792no—
856C22×C42—791no—
857C25—792no—
858C25—792no—
859C25—792no—
860C2×#41—3168no—
861C2×#41—3168no—
862C2×#41—7916no—
863C2×#41—7916no—
864C22×Q8—792no—
865C22×Q8—791no—
866C22×D4—3168no—
867C22×D4—3168no—
868C22×D4—3168no—
869C22×D4—792no—
870C22×D4—792no—
871C22×D4—792no—
872C22×D4—792no—
873C22×D4—7916no—
874C22×D4—7916no—
875C22×D4—7916no—
876C22×D4—792no—
877C22×D4—792no—
878C22×D4—792no—
879C22×D4—791no—
880C22×D4—791no—
881C22×D4—792no—
882C22×D4—798no—
883C22×D4—798no—
884C22×D4—792no—
885C22×D4—791no—
886C22×D4—792no—
887C22×D4—791no—
888C22×D4—792no—
889C22×D4—791no—
890C22×D4—798no—
891C22×D4—1588no—
892C22×D4—1588no—
893C22×D4—1588no—
894C22×D4C22×D7911yescharacteristic
895C22×D4C22×D7911yescharacteristic
896C22×D4C22×D7912yes—
897C22×D4C22×D7912yes—
898C22×D4C22×D7912yes—
899C22×D4C22×D7912yes—
900C23×C4—3168no—
901C23×C4—792no—
902C23×C4—792no—
903C23×C4—792no—
904C23×C4—792no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—792no—
908C23×C4—7916no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4—791no—
912C23×C4—792no—
913C23×C4—791no—
914C23×C4—791no—
915C23×C4C22×D7911yescharacteristic
916C23×C4C22×D7912yes—
917C23×C4C22×D7912yes—
918C4⋊Q8—798no—
919#127—798no—
920#127—798no—
921#127C22×D7918yescomplemented
922#126—798no—
923#126—7916no—
924#126—798no—
925#126—7916no—
926#125—798no—
927#125—798no—
928#125C22×D7918yescomplemented
929#124—7916no—
930#124—798no—
931#124—7916no—
932#124—7916no—
933#123—7916no—
934#123—7916no—
935#123—798no—
936#123—7916no—
937#123—798no—
938#123—7916no—
939#123C22×D79116yescomplemented
940#123C22×D79116yescomplemented
941C22⋊Q8—798no—
942C22⋊Q8—7916no—
943C22⋊Q8—7916no—
944C22⋊Q8—7916no—
945#121—7916no—
946#121—7916no—
947#121—7916no—
948#121—798no—
949#121—7916no—
950#121—7916no—
951#121—7916no—
952#121—798no—
953#121—7916no—
954#121—7916no—
955#121—798no—
956#121—798no—
957#121—798no—
958#121—7916no—
959#121—7916no—
960#121—7916no—
961#121—7916no—
962#121C22×D79116yescomplemented
963#121C22×D7918yescomplemented
964#121C22×D7918yescomplemented
965#121C22×D79116yescomplemented
966#120—7916no—
967#120—7916no—
968#120—7916no—
969#120—7916no—
970#120—7916no—
971#120—7916no—
972C4×Q8—798no—
973C4×D4—798no—
974C4×D4—798no—
975C4×D4—7916no—
976C4×D4—7916no—
977C4×D4—798no—
978C4×D4—798no—
979C4×D4—7916no—
980C4×D4—798no—
981C4×D4—7916no—
982C4×D4—798no—
983C4×D4—7916no—
984C4×D4—7916no—
985C4×D4—7916no—
986C4×D4—7916no—
987C4×D4—7916no—
988C4×D4—798no—
989C4×D4—798no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—798no—
993C4×D4C22×D7918yescomplemented
994C4×D4C22×D7918yescomplemented
995#117—798no—
996#117—798no—
997#117—7916no—
998#117—798no—
999#117C22×D7918yescomplemented
1000C2×C4⋊C4—791no—
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—792no—
1003C2×C4⋊C4—792no—
1004C2×C4⋊C4—792no—
1005C2×C4⋊C4—791no—
1006C2×C4⋊C4—791no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—791no—
1009C2×C4⋊C4—791no—
1010C2×C4⋊C4—791no—
1011C2×C4⋊C4—792no—
1012C2×C4⋊C4—791no—
1013C2×C4⋊C4—791no—
1014C2×C4⋊C4—798no—
1015C2×C4⋊C4—7916no—
1016C2×C4⋊C4C22×D7911yescharacteristic
1017C2×C4⋊C4C22×D7912yes—
1018C2×C4⋊C4C22×D7911yescharacteristic
1019C2×C4⋊C4C22×D7911yescharacteristic
1020C2×C4⋊C4C22×D7911yescharacteristic
1021C2×C4⋊C4C22×D7912yes—
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—792no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—792no—
1026C2×C22⋊C4—791no—
1027C2×C22⋊C4—791no—
1028C2×C22⋊C4—792no—
1029C2×C22⋊C4—792no—
1030C2×C22⋊C4—791no—
1031C2×C22⋊C4—792no—
1032C2×C22⋊C4—791no—
1033C2×C22⋊C4—792no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—792no—
1036C2×C22⋊C4—792no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—7916no—
1039C2×C22⋊C4—791no—
1040C2×C22⋊C4—791no—
1041C2×C22⋊C4—791no—
1042C2×C22⋊C4—791no—
1043C2×C22⋊C4—792no—
1044C2×C22⋊C4—792no—
1045C2×C22⋊C4—7916no—
1046C2×C22⋊C4—7916no—
1047C2×C22⋊C4—7916no—
1048C2×C22⋊C4—7916no—
1049C2×C22⋊C4C22×D7911yescharacteristic
1050C2×C22⋊C4C22×D7911yescharacteristic
1051C2×C22⋊C4C22×D7912yes—
1052C2×C22⋊C4C22×D7912yes—
1053C2×C22⋊C4C22×D7912yes—
1054C2×C22⋊C4C22×D7912yes—
1055C2×C42—792no—
1056C2×C42—792no—
1057C2×C42—791no—
1058C2×C42—791no—
1059C2×C42—791no—
1060C2×C42—791no—
1061C2×C42—798no—
1062C2×C42C22×D7911yescharacteristic
1063C2×C42C22×D7911yescharacteristic
1064C24—3164no—
1065C24—3164no—
1066C24—3164no—
1067C24—3164no—
1068C24—3164no—
1069C24—798no—
1070C24—798no—
1071C24—798no—
1072C24—792no—
1073C24—791no—
1074C24—791no—
1075C24—792no—
1076C24—1588no—
1077C24—1588no—
1078C24—1588no—
1079C24—1588no—
1080C24C23×D7911yescharacteristic
1081C24C23×D7912yes—
1082C24C23×D7912yes—
1083#41—31632no—
1084#41—31632no—
1085C2×Q8—3164no—
1086C2×Q8—798no—
1087C2×Q8—794no—
1088C2×Q8—1584no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—3164no—
1096C2×D4—31632no—
1097C2×D4—31632no—
1098C2×D4—31632no—
1099C2×D4—3164no—
1100C2×D4—3164no—
1101C2×D4—3164no—
1102C2×D4—3164no—
1103C2×D4—798no—
1104C2×D4—798no—
1105C2×D4—798no—
1106C2×D4—798no—
1107C2×D4—798no—
1108C2×D4—798no—
1109C2×D4—798no—
1110C2×D4—794no—
1111C2×D4—794no—
1112C2×D4—798no—
1113C2×D4—798no—
1114C2×D4—798no—
1115C2×D4—794no—
1116C2×D4—798no—
1117C2×D4—794no—
1118C2×D4—798no—
1119C2×D4—794no—
1120C2×D4—15832no—
1121C2×D4—1584no—
1122C2×D4—1588no—
1123C2×D4—1588no—
1124C2×D4—1584no—
1125C2×D4—1588no—
1126C2×D4—15832no—
1127C2×D4—15832no—
1128C2×D4—1584no—
1129C2×D4—1588no—
1130C2×D4—1588no—
1131C2×D4—1588no—
1132C2×D4—1584no—
1133C2×D4C23×D7914yes—
1134C2×D4C23×D7914yes—
1135C2×D4C23×D7918yes—
1136C2×D4C23×D7918yes—
1137C2×D4C23×D7918yes—
1138C2×D4C23×D7918yes—
1139C22×C4—24no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—3164no—
1143C22×C4—3164no—
1144C22×C4—3164no—
1145C22×C4—3164no—
1146C22×C4—3164no—
1147C22×C4—3164no—
1148C22×C4—31632no—
1149C22×C4—3164no—
1150C22×C4—798no—
1151C22×C4—798no—
1152C22×C4—798no—
1153C22×C4—798no—
1154C22×C4—798no—
1155C22×C4—798no—
1156C22×C4—798no—
1157C22×C4—791no—
1158C22×C4—798no—
1159C22×C4—791no—
1160C22×C4—791no—
1161C22×C4—792no—
1162C22×C4—791no—
1163C22×C4—791no—
1164C22×C4—792no—
1165C22×C4—791no—
1166C22×C4—794no—
1167C22×C4—794no—
1168C22×C4—794no—
1169C22×C4—798no—
1170C22×C4—794no—
1171C22×C4—1584no—
1172C22×C4—1588no—
1173C22×C4—1584no—
1174C22×C4—1588no—
1175C22×C4—1584no—
1176C22×C4—1584no—
1177C22×C4C23×D7914yes—
1178C22×C4C23×D7911yescharacteristic
1179C22×C4C23×D7911yescharacteristic
1180C22×C4C23×D7911yescharacteristic
1181C22×C4C23×D7912yes—
1182C22×C4C23×D7911yescharacteristic
1183C22×C4C23×D7911yescharacteristic
1184C22×C4C23×D7912yes—
1185C22×C4C23×D7918yes—
1186C22×C4C23×D7918yes—
1187C22×C4C23×D7911yescharacteristic
1188C4⋊C4—794no—
1189C4⋊C4—798no—
1190C4⋊C4—798no—
1191C4⋊C4—794no—
1192C4⋊C4—794no—
1193C4⋊C4—794no—
1194C4⋊C4—794no—
1195C4⋊C4—798no—
1196C4⋊C4—794no—
1197C4⋊C4—794no—
1198C4⋊C4—798no—
1199C4⋊C4—794no—
1200C4⋊C4—794no—
1201C4⋊C4—794no—
1202C4⋊C4C23×D7914yes—
1203C4⋊C4C23×D7918yes—
1204C4⋊C4C23×D7914yes—
1205C4⋊C4C23×D7914yes—
1206C4⋊C4C23×D7914yes—
1207C4⋊C4C23×D7918yes—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—798no—
1211C22⋊C4—798no—
1212C22⋊C4—794no—
1213C22⋊C4—794no—
1214C22⋊C4—798no—
1215C22⋊C4—798no—
1216C22⋊C4—794no—
1217C22⋊C4—798no—
1218C22⋊C4—794no—
1219C22⋊C4—798no—
1220C22⋊C4—798no—
1221C22⋊C4—798no—
1222C22⋊C4—798no—
1223C22⋊C4—798no—
1224C22⋊C4—794no—
1225C22⋊C4—794no—
1226C22⋊C4—794no—
1227C22⋊C4—794no—
1228C22⋊C4—798no—
1229C22⋊C4—798no—
1230C22⋊C4C23×D7914yes—
1231C22⋊C4C23×D7914yes—
1232C22⋊C4C23×D7918yes—
1233C22⋊C4C23×D7918yes—
1234C22⋊C4C23×D7918yes—
1235C22⋊C4C23×D7918yes—
1236C42—794no—
1237C42—794no—
1238C42—794no—
1239C42—798no—
1240C42—798no—
1241C42—794no—
1242C42C23×D7914yes—
1243C42C23×D7914yes—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—24no—
1252C23—24no—
1253C23—3168no—
1254C23—3168no—
1255C23—3168no—
1256C23—3168no—
1257C23—3168no—
1258C23—31632no—
1259C23—794no—
1260C23—794no—
1261C23—792no—
1262C23—798no—
1263C23—792no—
1264C23—794no—
1265C23—63216no—
1266C23—63216no—
1267C23—15816no—
1268C23—15816no—
1269C23—15816no—
1270C23—15816no—
1271C23—1584no—
1272C23—1584no—
1273C23—1582no—
1274C23—1582no—
1275C23—1582no—
1276C23—1584no—
1277C23—1582no—
1278C23—1584no—
1279C23—1584no—
1280C23—1582no—
1281C23C24×D7912yes—
1282C23C24×D7914yes—
1283C23C24×D7914yes—
1284C23C24×D7911yescharacteristic
1285Q8—3168no—
1286Q8—1588no—
1287D4—28no—
1288D4—28no—
1289D4—48no—
1290D4—48no—
1291D4—48no—
1292D4—48no—
1293D4—3168no—
1294D4—3168no—
1295D4—3168no—
1296D4—3168no—
1297D4—3168no—
1298D4—7916no—
1299D4—1588no—
1300D4—15816no—
1301D4—15816no—
1302D4—1588no—
1303D4—15816no—
1304D4—1588no—
1305D4—15816no—
1306D4—15816no—
1307D4—15816no—
1308D4—1588no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—28no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—3168no—
1320C2×C4—3168no—
1321C2×C4—3168no—
1322C2×C4—3168no—
1323C2×C4—3168no—
1324C2×C4—3168no—
1325C2×C4—3168no—
1326C2×C4—794no—
1327C2×C4—792no—
1328C2×C4—792no—
1329C2×C4—792no—
1330C2×C4—794no—
1331C2×C4—792no—
1332C2×C4—792no—
1333C2×C4—794no—
1334C2×C4—792no—
1335C2×C4—1588no—
1336C2×C4—15816no—
1337C2×C4—1588no—
1338C2×C4—15816no—
1339C2×C4—1584no—
1340C2×C4—1582no—
1341C2×C4—1582no—
1342C2×C4—1584no—
1343C2×C4—1582no—
1344C2×C4—1582no—
1345C2×C4—1582no—
1346C2×C4—1588no—
1347C2×C4—1588no—
1348C2×C4#41×D7914yes—
1349C2×C4C24×D7912yes—
1350C2×C4C24×D7912yes—
1351C2×C4C24×D7912yes—
1352C2×C4C24×D7914yes—
1353C2×C4C24×D7912yes—
1354C2×C4C24×D7912yes—
1355C2×C4C24×D7914yes—
1356C2×C4C24×D7912yes—
1357C22—22no—
1358C22—24no—
1359C22—24no—
1360C22—24no—
1361C22—24no—
1362C22—24no—
1363C22—24no—
1364C22—22no—
1365C22—22no—
1366C22—48no—
1367C22—44no—
1368C22—48no—
1369C22—31632no—
1370C22—3164no—
1371C22—3168no—
1372C22—798no—
1373C22—794no—
1374C22—63216no—
1375C22—63216no—
1376C22—1582no—
1377C22—1584no—
1378C22—1584no—
1379C22—1584no—
1380C22—1582no—
1381C22—1582no—
1382C22—1582no—
1383C22—1588no—
1384C22—15816no—
1385C22—1582no—
1386C22—1584no—
1387C22—1584no—
1388C22C2×#41×D7912yes—
1389C22H(5,𝔽2)×D7912yes—
1390C22H(5,𝔽2)×D7912yes—
1391C22C25×D7911yescharacteristic
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—24no—
1396C4—24no—
1397C4—22no—
1398C4—22no—
1399C4—794no—
1400C4—1582no—
1401C4—1582no—
1402C4—1584no—
1403C4—1582no—
1404C4—1582no—
1405C4—1584no—
1406C4—1582no—
1407C4C2×#41×D7914yes—
1408C2—44no—
1409C2—42no—
1410C2—44no—
1411C2—3162no—
1412C2—3164no—
1413C2—1584no—
1414C2—1588no—
1415C2#2377743014yesdirect product factor
1416C2C22×#41×D7911yescharacteristic
1417C2C2×H(5,𝔽2)×D7911yescharacteristic
1418C2C2×H(5,𝔽2)×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#540×C79C2
socleC23×C79C25
hypercenterC2×#540D79
hypocenterC79C2×#3519
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #23777430C2direct (N × H)
2. C2×#19099277C2semidirect
3. C2×#19099269C2semidirect
4. C2×#19099266C2semidirect
5. C2×#19099260C2semidirect
6. C2×#19099258C2semidirect
7. C2×#19099233C2semidirect
8. C2×#19099210C2semidirect
9. C2×#19099205C2semidirect
10. C2×#19099202C2semidirect
11. C2×#19099198C2semidirect
12. C2×#19099197C2semidirect
13. C2×#19099197C2semidirect
14. C2×#19099164C2semidirect
15. C2×#19099149C2semidirect
16. C2×#19099145C2semidirect
17. C2×#19099110C2semidirect
18. C2×#19099091C2semidirect
19. C2×#19099071C2semidirect
20. C2×#121×D79C2semidirect
21. C2×#19099037C2semidirect
22. C2×#19099035C2semidirect
23. C2×C4×D4×D79C2semidirect
24. C2×#540×C79C2semidirect
25. C22×#11929624C22semidirect
26. C22×#11929623C22semidirect
30. C22×D4×D79C22semidirect
31. C22×D4×D79C22semidirect
32. C22×D4×D79C22semidirect
33. C23×C4×D79C22semidirect
34. #19099277C22semidirect
35. #19099269C22semidirect
36. #19099266C22semidirect
37. #19099260C22semidirect
38. #19099258C22semidirect
39. #19099233C22semidirect
40. #19099210C22semidirect
41. #19099205C22semidirect
42. #19099202C22semidirect
43. #19099198C22semidirect
44. #19099197C22semidirect
45. #19099197C22semidirect
46. #19099164C22semidirect
47. #19099149C22semidirect
48. #19099145C22semidirect
49. #19099110C22semidirect
50. C2×#14579160C22semidirect
51. C2×#14579157C22semidirect
52. C2×#14579157C22semidirect
53. #19099091C22semidirect
54. C2×#14579156C22semidirect
55. C2×#14579156C22semidirect
56. C2×#14579154C22semidirect
57. C2×#14579154C22semidirect
58. C2×#14579152C22semidirect
59. C2×#14579151C22semidirect
60. C2×#14579148C22semidirect
61. C2×#14579147C22semidirect
62. C2×#14579147C22semidirect
63. C2×#14579147C22semidirect
64. #19099071C22semidirect
65. C2×#14579146C22semidirect
66. C2×#14579146C22semidirect
67. C2×#14579144C22semidirect
68. C2×#14579143C22semidirect
69. C2×#14579143C22semidirect
70. C2×#14579142C22semidirect
71. C2×#14579141C22semidirect
72. C2×#14579139C22semidirect
73. C2×#14579139C22semidirect
74. C2×#14579139C22semidirect
75. C2×#14579136C22semidirect
76. C2×#14579136C22semidirect
77. C2×#14579136C22semidirect
78. C2×#14579135C22semidirect
80. C2×#14579134C22semidirect
81. C2×#14579134C22semidirect
82. C2×#14579134C22semidirect
83. C2×#14579134C22semidirect
84. C2×#14579133C22semidirect
85. C2×#14579133C22semidirect
86. C2×#14579133C22semidirect
87. C2×#14579132C22semidirect
88. C2×#14579132C22semidirect
89. C2×#14579132C22semidirect
90. C2×#14579132C22semidirect
91. C2×#14579132C22semidirect
92. #121×D79C22semidirect
93. C2×#14579131C22semidirect
94. C2×#14579131C22semidirect
95. C2×#14579129C22semidirect
96. C2×#14579129C22semidirect
97. C2×#14579129C22semidirect
98. C2×#14579129C22semidirect
99. #19099037C22semidirect
100. #19099035C22semidirect
101. C2×C4×Dic158C22semidirect
104. C2×C4×D316C22semidirect
105. C2×C4×D316C22semidirect
106. C2×C4×D316C22semidirect
107. C2×D4×Dic79C22semidirect
108. C2×D4×Dic79C22semidirect
111. C2×#14579123C22semidirect
112. C2×#14579123C22semidirect
113. C2×#14579123C22semidirect
114. C2×C4×C22⋊D79C22semidirect
115. C2×C4×C22⋊D79C22semidirect
116. C2×C4×C22⋊D79C22semidirect
117. C2×C4×C22⋊D79C22semidirect
118. C2×C4×C22⋊D79C22semidirect
119. C2×(C22⋊D79)⋊C4C22semidirect
120. C2×(C22⋊D79)⋊C4C22semidirect
121. C2×(C22⋊D79)⋊C4C22semidirect
122. C4×D4×D79C22semidirect
123. C2×#14579120C22semidirect
124. C2×#14579119C22semidirect
125. C2×#14579118C22semidirect
126. C2×#14579117C22semidirect
127. C2×C4⋊C4×D79C22semidirect
128. C2×C4⋊C4×D79C22semidirect
129. C22×(C2×D79)⋊C4C22semidirect
130. C2×C22⋊C4×D79C22semidirect
131. C2×C22⋊C4×D79C22semidirect
132. C2×C22⋊C4×D79C22semidirect
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
151. C2×#11929624C23semidirect
153. C2×#11929623C23semidirect
181. C2×D4×D79C23semidirect
182. C2×D4×D79C23semidirect
183. C2×D4×D79C23semidirect
198. C22×C4×D79C23semidirect
199. #14579160C23semidirect
200. #14579157C23semidirect
201. #14579157C23semidirect
202. #14579156C23semidirect
203. #14579156C23semidirect
204. #14579154C23semidirect
205. #14579154C23semidirect
206. #14579152C23semidirect
207. #14579151C23semidirect
208. #14579148C23semidirect
209. #14579147C23semidirect
210. #14579147C23semidirect
211. #14579147C23semidirect
212. #14579146C23semidirect
213. #14579146C23semidirect
214. #14579144C23semidirect
215. #14579143C23semidirect
216. #14579143C23semidirect
217. #14579142C23semidirect
218. #14579141C23semidirect
219. #14579139C23semidirect
220. #14579139C23semidirect
221. #14579139C23semidirect
222. #14579136C23semidirect
223. #14579136C23semidirect
224. #14579136C23semidirect
225. #14579135C23semidirect
227. #14579134C23semidirect
228. #14579134C23semidirect
229. #14579134C23semidirect
230. #14579134C23semidirect
231. #14579133C23semidirect
232. #14579133C23semidirect
233. #14579133C23semidirect
234. #14579132C23semidirect
235. #14579132C23semidirect
236. #14579132C23semidirect
237. #14579132C23semidirect
238. #14579132C23semidirect
239. #14579131C23semidirect
240. #14579131C23semidirect
241. #14579129C23semidirect
242. #14579129C23semidirect
243. #14579129C23semidirect
244. #14579129C23semidirect
245. C4×Dic158C23semidirect
248. C4×D316C23semidirect
249. C4×D316C23semidirect
250. C4×D316C23semidirect
251. D4×Dic79C23semidirect
252. D4×Dic79C23semidirect
255. #14579123C23semidirect
256. #14579123C23semidirect
257. #14579123C23semidirect
258. C4×C22⋊D79C23semidirect
259. C4×C22⋊D79C23semidirect
260. C4×C22⋊D79C23semidirect
261. C4×C22⋊D79C23semidirect
262. C4×C22⋊D79C23semidirect
263. (C22⋊D79)⋊C4C23semidirect
264. (C22⋊D79)⋊C4C23semidirect
265. (C22⋊D79)⋊C4C23semidirect
266. #14579120C23semidirect
267. #14579119C23semidirect
268. #14579118C23semidirect
269. #14579117C23semidirect
284. C4⋊C4×D79C23semidirect
285. C4⋊C4×D79C23semidirect
308. C2×(C2×D79)⋊C4C23semidirect
309. C22⋊C4×D79C23semidirect
310. C22⋊C4×D79C23semidirect
311. C22⋊C4×D79C23semidirect
312. C22⋊C4×D79C23semidirect
319. C42×D79C23semidirect
329. #127×C79C23semidirect
330. #125×C79C23semidirect
331. #123×C79C23semidirect
332. #123×C79C23semidirect
333. #121×C79C23semidirect
334. #121×C79C23semidirect
335. #121×C79C23semidirect
336. #121×C79C23semidirect
337. C4×D4×C79C23semidirect
338. C4×D4×C79C23semidirect
339. #117×C79C23semidirect
382. C2×D316#41semidirect
633. D316C2×#41semidirect
702. C2×C79#3519semidirect
724. C2×#540D79semidirect
734. C79C2×#3519semidirect
757. #540C2×D79semidirect
764. C2×#127C2×D79semidirect
772. C2×#125C2×D79semidirect
784. C2×#123C2×D79semidirect
785. C2×#123C2×D79semidirect
808. C2×#121C2×D79semidirect
809. C2×#121C2×D79semidirect
810. C2×#121C2×D79semidirect
811. C2×#121C2×D79semidirect
842. C2×C4×D4C2×D79semidirect
843. C2×C4×D4C2×D79semidirect
848. C2×#117C2×D79semidirect
921. #127C22×D79semidirect
928. #125C22×D79semidirect
939. #123C22×D79semidirect
940. #123C22×D79semidirect
962. #121C22×D79semidirect
963. #121C22×D79semidirect
964. #121C22×D79semidirect
965. #121C22×D79semidirect
993. C4×D4C22×D79semidirect
994. C4×D4C22×D79semidirect
999. #117C22×D79semidirect
1415. C2#23777430direct (N × H)

Maximal subgroups

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

subgroupindex
#237774302
C2×#190992772
C2×#190992692
C2×#190992662
C2×#190992602
C2×#190992582
C2×#190992332
C2×#190992102
C2×#190992052
C2×#190992022
C2×#190991982
C2×#190991972
C2×#190991642
C2×#190991492
C2×#190991452
C2×#190991102
C2×#190990912
C2×#190990712
C2×#121×D792
C2×#190990372
C2×#190990352
C2×C4×D4×D792
C2×#540×C792
C2×#351979