Finite Group Databasebeta

← C2×#23777915 #35195605

Subgroups — C2×#23777915 #35195605

Order 20224.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777915C2132yesmaximal, direct product factor
2C2×#19099309C212yesmaximal, complemented
3C2×#19099305C212yesmaximal, complemented
4C2×#19099298C211yesmaximal, characteristic, complemented
5C2×#19099296C211yesmaximal, characteristic, complemented
6C2×#19099225C211yesmaximal, characteristic, complemented
7C2×#19099223C211yesmaximal, characteristic, complemented
8C2×#19099210C211yesmaximal, characteristic, complemented
9C2×#19099206C212yesmaximal, complemented
10C2×#19099204C211yesmaximal, characteristic, complemented
11C2×#19099204C212yesmaximal, complemented
12C2×D4×D316C211yesmaximal, characteristic, complemented
13C2×#19099197C211yesmaximal, characteristic, complemented
14C2×#19099187C211yesmaximal, characteristic, complemented
15C2×#19099152C212yesmaximal, complemented
16C2×#19099152C212yesmaximal, complemented
17C2×#19099149C212yesmaximal, complemented
18C2×#19099132C211yesmaximal, characteristic, complemented
19C2×#19099131C211yesmaximal, characteristic, complemented
20C2×#19099124C212yesmaximal, complemented
21C2×#19099114C211yesmaximal, characteristic, complemented
22C2×#19099091C211yesmaximal, characteristic, complemented
23C2×#124×D79C211yesmaximal, characteristic, complemented
24C2×#542×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2212yescomplemented
26C22×#11929625C2211yescharacteristic, complemented
27C22×#11929624C2211yescharacteristic, complemented
28C22×Q8×D79C2211yescharacteristic, complemented
29C23×D316C2211yescharacteristic, complemented
30C23×D316C2212yescomplemented
31C22×D4×D79C2211yescharacteristic
32C22×D4×D79C2212yescomplemented
33C22×D4×D79C2211yescharacteristic, complemented
34#19099309C22132yescomplemented
35#19099305C22132yescomplemented
36#19099298C22116yescomplemented
37#19099296C22116yescomplemented
38#19099225C22116yescomplemented
39#19099223C22116yescomplemented
40#19099210C22116yescomplemented
41#19099206C22132yescomplemented
42#19099204C22116yescomplemented
43#19099204C22132yescomplemented
44D4×D316C22116yescomplemented
45#19099197C22116yescomplemented
46#19099187C22116yescomplemented
47#19099152C22132yescomplemented
48#19099152C22132yescomplemented
49#19099149C22132yescomplemented
50#19099132C22116yescomplemented
51#19099131C22116yescomplemented
52#19099124C22132yescomplemented
53#19099114C22116yescomplemented
54C2×#14579158C2211yescharacteristic
55C2×#14579158C2211yescharacteristic, complemented
56C2×#14579157C2211yescharacteristic
57#19099091C22116yescomplemented
58C2×#14579156C2212yescomplemented
59C2×#14579156C2211yescharacteristic, complemented
60C2×#14579154C2211yescharacteristic, complemented
61C2×#14579151C2211yescharacteristic, complemented
62C2×#14579150C2212yescomplemented
63C2×#14579150C2211yescharacteristic, complemented
64C2×#14579150C2211yescharacteristic, complemented
65C2×#14579150C2212yescomplemented
66C2×#14579149C2211yescharacteristic, complemented
67C2×#14579149C2211yescharacteristic, complemented
68C2×#14579149C2212yescomplemented
69C2×#14579149C2212yescomplemented
70C2×#14579148C2211yescharacteristic, complemented
71C2×#14579147C2212yescomplemented
72C2×#14579147C2212yescomplemented
73C2×#14579147C2212yescomplemented
74C2×#14579147C2211yescharacteristic, complemented
75C2×#14579147C2212yescomplemented
76#124×D79C22116yescomplemented
77C2×#14579146C2212yescomplemented
78C2×#14579146C2211yescharacteristic, complemented
79C2×#14579146C2212yescomplemented
80C2×#14579146C2212yescomplemented
81C2×#14579146C2212yescomplemented
82C2×#14579144C2212yescomplemented
83C2×#14579143C2211yescharacteristic, complemented
84C2×#14579143C2212yescomplemented
85C2×#14579143C2212yescomplemented
86C2×#14579141C2211yescharacteristic, complemented
87C2×#14579141C2212yescomplemented
88C2×#14579139C2212yescomplemented
89C2×#14579139C2211yescharacteristic, complemented
90C2×#14579137C2212yescomplemented
91C2×#14579136C2211yescharacteristic
92C2×#14579136C2211yescharacteristic, complemented
93C2×#14579136C2211yescharacteristic, complemented
94C2×#14579136C2212yescomplemented
95C2×#14579136C2212yescomplemented
96C2×#14579136C2212yescomplemented
97C2×#14579136C2212yescomplemented
98C2×#14579136C2212yescomplemented
99C2×#14579135C2212yescomplemented
100C2×#14579134C2211yescharacteristic
101C2×#14579134C2212yescomplemented
102C2×#14579134C2212yescomplemented
103C2×#14579134C2212yescomplemented
104C2×#14579134C2212yescomplemented
105C2×#14579132C2212yescomplemented
106C2×#14579131C2212yescomplemented
107C2×#14579131C2212yescomplemented
108C2×#14579131C2212yescomplemented
109C2×#14579131C2212yescomplemented
110C2×#14579131C2212yescomplemented
111C2×#14579131C2212yescomplemented
112C2×#14579131C2212yescomplemented
113C2×#14579131C2212yescomplemented
114C2×#14579129C2212yescomplemented
115C2×#14579129C2212yescomplemented
116C2×C4×Dic158C2211yescharacteristic, complemented
117C2×#14579126C2211yescharacteristic, complemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×C4×D316C2212yescomplemented
120C2×C4×D316C2212yescomplemented
121C2×#14579123C2211yescharacteristic, complemented
122C2×#14579123C2212yescomplemented
123C2×#14579123C2211yescharacteristic, complemented
124C2×#14579123C2211yescharacteristic, complemented
125C2×#14579123C2212yescomplemented
126C2×C4×C22⋊D79C2211yescharacteristic, complemented
127C2×C4×C22⋊D79C2211yescharacteristic, complemented
128C2×C4×C22⋊D79C2212yescomplemented
129C2×#14579118C2211yescharacteristic, complemented
130C2×C22⋊C4×D79C2212yescomplemented
131C2×C22⋊C4×D79C2212yescomplemented
132C2×C22⋊C4×D79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135#542×C79C22116yescomplemented
136C2×C4⋊Q8×C79C2211yescharacteristic, complemented
137C2×#126×C79C2212yescomplemented
138C2×#124×C79C2212yescomplemented
139C2×#124×C79C2211yescharacteristic, complemented
140C2×#123×C79C2212yescomplemented
141C2×C22⋊Q8×C79C2211yescharacteristic, complemented
142C2×C22⋊Q8×C79C2212yescomplemented
143C2×#121×C79C2211yescharacteristic
144C2×C4×Q8×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C2×#117×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C24×D79C2312yes—
150C2×#11929625—48no—
151C2×#11929625—44no—
152C2×#11929625C23116yescomplemented
153C2×#11929625C2318yescomplemented
154C2×#11929624—44no—
155C2×#11929624C2318yescomplemented
156C22×Dic158C2311yescharacteristic
157C22×Dic158C2311yescharacteristic
158C22×Dic158C2312yes—
159C2×Q8×D79—44no—
160C2×Q8×D79C2318yescomplemented
161C22×D316—48no—
162C22×D316—44no—
163C22×D316C2312yes—
164C22×D316C2311yescharacteristic
165C22×D316C2311yescharacteristic
166C22×D316C2311yescharacteristic
167C22×D316C2312yes—
168C22×D316C2311yescharacteristic
169C22×D316C2312yes—
170C22×D316C2312yes—
171C22×D316C2312yes—
172C22×D316C2312yes—
173C22×D316C2312yes—
174C22×D316C2312yes—
175C22×D316C2312yes—
176C22×D316C2318yescomplemented
177C22×D316C23116yescomplemented
178C22×C22⋊D79C2311yescharacteristic
179C22×C22⋊D79C2311yescharacteristic
180C22×C22⋊D79C2312yes—
181C22×C22⋊D79C2312yes—
182C22×C22⋊D79C2312yes—
183C22×C22⋊D79C2312yes—
184C22×C22⋊D79C2312yes—
185C2×D4×D79—44no—
186C2×D4×D79—44no—
187C2×D4×D79—48no—
188C2×D4×D79C2318yes—
189C2×D4×D79C23116yescomplemented
190C2×D4×D79C2318yescomplemented
191C22×C4×D79C2311yescharacteristic
192C22×C4×D79C2311yescharacteristic
193C22×C4×D79C2311yescharacteristic
194C22×C4×D79C2311yescharacteristic
195C22×C4×D79C2312yes—
196C22×C4×D79C2312yes—
197C22×C4×D79C2312yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2312yes—
200C22×C4×D79C2312yes—
201#14579158C2318yes—
202#14579158C2318yescomplemented
203#14579157C2318yes—
204#14579156C23116yescomplemented
205#14579156C2318yescomplemented
206#14579154C2318yescomplemented
207#14579151C2318yescomplemented
208#14579150C23116yescomplemented
209#14579150C2318yescomplemented
210#14579150C2318yescomplemented
211#14579150C23116yescomplemented
212#14579149C23116yescomplemented
213#14579149C23116yescomplemented
214#14579149C2318yescomplemented
215#14579149C2318yescomplemented
216#14579148C2318yescomplemented
217#14579147C23116yescomplemented
218#14579147C23116yescomplemented
219#14579147C23116yescomplemented
220#14579147C2318yescomplemented
221#14579147C23116yescomplemented
222#14579146C23116yescomplemented
223#14579146C23116yescomplemented
224#14579146C23116yescomplemented
225#14579146C2318yescomplemented
226#14579146C23116yescomplemented
227#14579144C23116yescomplemented
228#14579143C23116yescomplemented
229#14579143C23116yescomplemented
230#14579143C2318yescomplemented
231#14579141C23116yescomplemented
232#14579141C2318yescomplemented
233#14579139C2318yescomplemented
234#14579139C23116yescomplemented
235#14579137C23116yescomplemented
236#14579136C2318yes—
237#14579136C23116yescomplemented
238#14579136C23116yescomplemented
239#14579136C23116yescomplemented
240#14579136C2318yescomplemented
241#14579136C2318yescomplemented
242#14579136C23116yescomplemented
243#14579136C23116yescomplemented
244#14579135C23116yescomplemented
245#14579134C2318yes—
246#14579134C23116yescomplemented
247#14579134C23116yescomplemented
248#14579134C23116yescomplemented
249#14579134C23116yescomplemented
250#14579132C23116yescomplemented
251#14579131C23116yescomplemented
252#14579131C23116yescomplemented
253#14579131C23116yescomplemented
254#14579131C23116yescomplemented
255#14579131C23116yescomplemented
256#14579131C23116yescomplemented
257#14579131C23116yescomplemented
258#14579131C23116yescomplemented
259#14579129C23116yescomplemented
260#14579129C23116yescomplemented
261C4×Dic158C2318yescomplemented
262#14579126C2318yescomplemented
263C4×D316C23116yescomplemented
264C4×D316C23116yescomplemented
265C4×D316C2318yescomplemented
266#14579123C23116yescomplemented
267#14579123C23116yescomplemented
268#14579123C2318yescomplemented
269#14579123C2318yescomplemented
270#14579123C2318yescomplemented
271C4×C22⋊D79C23116yescomplemented
272C4×C22⋊D79C2318yescomplemented
273C4×C22⋊D79C2318yescomplemented
274#14579118C2318yescomplemented
275C2×C4⋊Dic79C2311yescharacteristic
276C2×C4⋊Dic79C2312yes—
277C2×C4⋊Dic79C2311yescharacteristic
278C2×Dic79⋊C4C2311yescharacteristic
279C2×Dic79⋊C4C2311yescharacteristic
280C2×Dic79⋊C4C2311yescharacteristic
281C2×Dic79⋊C4C2311yescharacteristic
282C2×Dic79⋊C4C2311yescharacteristic
283C2×Dic79⋊C4C2312yes—
284C2×Dic79⋊C4C2311yescharacteristic
285C2×C22⋊Dic79C2311yescharacteristic
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2311yescharacteristic
289C2×(C2×D79)⋊C4C2311yescharacteristic
290C2×(C2×D79)⋊C4C2312yes—
291C2×(C2×D79)⋊C4C2312yes—
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2311yescharacteristic
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2312yes—
306C2×(C2×D79)⋊C4C2311yescharacteristic
307C2×(C2×D79)⋊C4C2311yescharacteristic
308C2×(C2×D79)⋊C4C2312yes—
309C2×(C2×D79)⋊C4C2312yes—
310C22⋊C4×D79C23116yescomplemented
311C22⋊C4×D79C23116yescomplemented
312C22⋊C4×D79C23116yescomplemented
313C22⋊C4×D79C23116yescomplemented
314C2×C4×Dic79C2311yescharacteristic
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2311yescharacteristic
317C2×C4×Dic79C2311yescharacteristic
318C2×C4×Dic79C2312yes—
319C42×D79C2318yescomplemented
320C22×Q8×C79C2311yescharacteristic
321C22×Q8×C79C2312yes—
322C22×D4×C79C2311yescharacteristic
323C22×D4×C79C2312yes—
324C23×C4×C79C2311yescharacteristic
325C23×C4×C79C2312yes—
326C4⋊Q8×C79C2318yescomplemented
327#126×C79C23116yescomplemented
328#124×C79C23116yescomplemented
329#124×C79C2318yescomplemented
330#123×C79C23116yescomplemented
331C22⋊Q8×C79C2318yescomplemented
332C22⋊Q8×C79C23116yescomplemented
333#121×C79C2318yes—
334C4×Q8×C79C2318yescomplemented
335C4×D4×C79C2318yescomplemented
336#117×C79C2318yescomplemented
337C2×C4⋊C4×C79C2311yescharacteristic
338C2×C4⋊C4×C79C2311yescharacteristic
339C2×C4⋊C4×C79C2311yescharacteristic
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C4⋊C4×C79C2312yes—
342C2×C4⋊C4×C79C2312yes—
343C2×C4⋊C4×C79C2312yes—
344C2×C22⋊C4×C79C2311yescharacteristic
345C2×C22⋊C4×C79C2311yescharacteristic
346C2×C22⋊C4×C79C2312yes—
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C42×C79C2311yescharacteristic
352C2×C42×C79C2311yescharacteristic
353C2×C42×C79C2312yes—
354C23×D79—28no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79—44no—
358C23×D79—44no—
359C23×D79—44no—
360C23×D79—44no—
361C23×D79—44no—
362C23×D79—44no—
363C23×D79C2411yescharacteristic
364C23×D79C2412yes—
365C23×D79C2412yes—
366C23×D79C2412yes—
367C23×D79C2411yescharacteristic
368C23×D79C2418yes—
369C23×D79C2418yes—
370C23×D79C2418yes—
371#11929625—416no—
372#11929625—432no—
373#11929624—416no—
374C2×Dic158—24no—
375C2×Dic158—44no—
376C2×Dic158—42no—
377C2×Dic158C2414yes—
378C2×Dic158C2418yes—
379C2×Dic158C2414yes—
380Q8×D79—416no—
381C2×D316—28no—
382C2×D316—28no—
383C2×D316—24no—
384C2×D316—24no—
385C2×D316—24no—
386C2×D316—24no—
387C2×D316—44no—
388C2×D316—44no—
389C2×D316—44no—
390C2×D316—44no—
391C2×D316—44no—
392C2×D316—44no—
393C2×D316—44no—
394C2×D316—416no—
395C2×D316—432no—
396C2×D316C2414yes—
397C2×D316C2418yes—
398C2×D316C2414yes—
399C2×D316C2418yes—
400C2×D316C2414yes—
401C2×D316C2414yes—
402C2×D316C2418yes—
403C2×D316C2418yes—
404C2×D316C2418yes—
405C2×D316C2418yes—
406C2×D316C2418yes—
407C2×D316C2418yes—
408C2×D316C2418yes—
409C2×C22⋊D79—24no—
410C2×C22⋊D79—44no—
411C2×C22⋊D79—44no—
412C2×C22⋊D79—44no—
413C2×C22⋊D79—44no—
414C2×C22⋊D79—44no—
415C2×C22⋊D79—42no—
416C2×C22⋊D79C2414yes—
417C2×C22⋊D79C2418yes—
418C2×C22⋊D79C2414yes—
419C2×C22⋊D79C2418yes—
420C2×C22⋊D79C2418yes—
421C2×C22⋊D79C2418yes—
422C2×C22⋊D79C2418yes—
423D4×D79—432no—
424D4×D79—416no—
425D4×D79—416no—
426C22×Dic79C2411yescharacteristic
427C22×Dic79C2412yes—
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2411yescharacteristic
430C22×Dic79C2411yescharacteristic
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2411yescharacteristic
433C2×C4×D79—24no—
434C2×C4×D79—24no—
435C2×C4×D79—24no—
436C2×C4×D79—44no—
437C2×C4×D79—44no—
438C2×C4×D79—44no—
439C2×C4×D79—44no—
440C2×C4×D79—44no—
441C2×C4×D79—42no—
442C2×C4×D79—44no—
443C2×C4×D79C2414yes—
444C2×C4×D79C2414yes—
445C2×C4×D79C2414yes—
446C2×C4×D79C2418yes—
447C2×C4×D79C2418yes—
448C2×C4×D79C2418yes—
449C2×C4×D79C2418yes—
450C2×C4×D79C2418yes—
451C2×C4×D79C2414yes—
452C2×C4×D79C2418yes—
453C4⋊Dic79C2414yes—
454C4⋊Dic79C2418yes—
455C4⋊Dic79C2414yes—
456Dic79⋊C4C2414yes—
457Dic79⋊C4C2414yes—
458Dic79⋊C4C2414yes—
459Dic79⋊C4C2414yes—
460Dic79⋊C4C2414yes—
461Dic79⋊C4C2418yes—
462Dic79⋊C4C2414yes—
463C22⋊Dic79C2414yes—
464C22⋊Dic79C2418yes—
465C22⋊Dic79C2418yes—
466C22⋊Dic79C2414yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2418yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2414yes—
475(C2×D79)⋊C4C2414yes—
476(C2×D79)⋊C4C2414yes—
477(C2×D79)⋊C4C2418yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480(C2×D79)⋊C4C2418yes—
481(C2×D79)⋊C4C2418yes—
482(C2×D79)⋊C4C2418yes—
483(C2×D79)⋊C4C2418yes—
484(C2×D79)⋊C4C2414yes—
485(C2×D79)⋊C4C2414yes—
486(C2×D79)⋊C4C2418yes—
487(C2×D79)⋊C4C2418yes—
488C4×Dic79C2414yes—
489C4×Dic79C2414yes—
490C4×Dic79C2414yes—
491C4×Dic79C2414yes—
492C4×Dic79C2418yes—
493C24×C79C2411yescharacteristic
494C24×C79C2412yes—
495C2×Q8×C79—24no—
496C2×Q8×C79—44no—
497C2×Q8×C79C2414yes—
498C2×Q8×C79C2418yes—
499C2×D4×C79—24no—
500C2×D4×C79—44no—
501C2×D4×C79C2414yes—
502C2×D4×C79C2418yes—
503C22×C4×C79—24no—
504C22×C4×C79—44no—
505C22×C4×C79C2411yescharacteristic
506C22×C4×C79C2412yes—
507C22×C4×C79C2414yes—
508C22×C4×C79C2411yescharacteristic
509C22×C4×C79C2411yescharacteristic
510C22×C4×C79C2411yescharacteristic
511C22×C4×C79C2412yes—
512C22×C4×C79C2411yescharacteristic
513C22×C4×C79C2412yes—
514C22×C4×C79C2418yes—
515C22×C4×C79C2411yescharacteristic
516C4⋊C4×C79C2414yes—
517C4⋊C4×C79C2414yes—
518C4⋊C4×C79C2414yes—
519C4⋊C4×C79C2414yes—
520C4⋊C4×C79C2418yes—
521C4⋊C4×C79C2418yes—
522C4⋊C4×C79C2418yes—
523C22⋊C4×C79C2414yes—
524C22⋊C4×C79C2414yes—
525C22⋊C4×C79C2418yes—
526C22⋊C4×C79C2418yes—
527C22⋊C4×C79C2418yes—
528C22⋊C4×C79C2418yes—
529C22⋊C4×C79C2418yes—
530C42×C79C2414yes—
531C42×C79C2414yes—
532C42×C79C2418yes—
533C23×C79—22no—
534C23×C79—22no—
535C23×C79—24no—
536C23×C79—24no—
537C23×C79—24no—
538C23×C79—22no—
539C23×C79C2512yes—
540C23×C79C2514yes—
541C23×C79C2511yescharacteristic
542C22×D79—22no—
543C22×D79—22no—
544C22×D79—22no—
545C22×D79—24no—
546C22×D79—24no—
547C22×D79—24no—
548C22×D79—24no—
549C22×D79—24no—
550C22×D79—24no—
551C22×D79—22no—
552C22×D79—24no—
553C22×D79—22no—
554C22×D79—24no—
555C22×D79—24no—
556C22×D79—216no—
557C22×D79—48no—
558C22×D79—48no—
559C22×D79—48no—
560C22×D79—48no—
561C22×D79—48no—
562C22×D79—48no—
563C22×D79—48no—
564C22×D79—48no—
565C22×D79—816no—
566C22×D79—816no—
567C22×D79—816no—
568C22×D79H(5,𝔽2)14yes—
569C22×D79C2514yes—
570C22×D79C2512yes—
571C22×D79C2514yes—
572C22×D79C2514yes—
573C22×D79C2512yes—
574Q8×C79—28no—
575Q8×C79—48no—
576D4×C79—28no—
577D4×C79—48no—
578C2×C4×C79—22no—
579C2×C4×C79—24no—
580C2×C4×C79—22no—
581C2×C4×C79—24no—
582C2×C4×C79—24no—
583C2×C4×C79—22no—
584C2×C4×C79—22no—
585C2×C4×C79—22no—
586C2×C4×C79—28no—
587C2×C4×C79—48no—
588C2×C4×C79H(5,𝔽2)14yes—
589C2×C4×C79C2512yes—
590C2×C4×C79C2512yes—
591C2×C4×C79C2514yes—
592C2×C4×C79C2514yes—
593C2×C4×C79C2512yes—
594C2×C4×C79C2514yes—
595C2×C4×C79C2512yes—
596C2×C4×C79C2512yes—
597C2×C4×C79C2512yes—
598C22⋊D79—28no—
599C22⋊D79—48no—
600C22⋊D79—48no—
601C22⋊D79—48no—
602C22⋊D79—48no—
603C22⋊D79—44no—
604C22⋊D79—48no—
605C2×Dic79—22no—
606C2×Dic79—22no—
607C2×Dic79—22no—
608C2×Dic79—22no—
609C2×Dic79—24no—
610C2×Dic79—22no—
611C2×Dic79—22no—
612C2×Dic79C2512yes—
613C2×Dic79C2512yes—
614C2×Dic79C2512yes—
615C2×Dic79C2512yes—
616C2×Dic79C2514yes—
617C2×Dic79C2512yes—
618C2×Dic79C2512yes—
619D316—216no—
620D316—28no—
621D316—216no—
622D316—28no—
623D316—28no—
624D316—28no—
625D316—48no—
626D316—48no—
627D316—48no—
628D316—48no—
629D316—48no—
630D316—48no—
631D316—48no—
632C4×D79—28no—
633C4×D79—28no—
634C4×D79—28no—
635C4×D79—44no—
636C4×D79—48no—
637C4×D79—48no—
638C4×D79—48no—
639C4×D79—48no—
640C4×D79—48no—
641C4×D79—48no—
642Dic158—28no—
643Dic158—48no—
644Dic158—44no—
645C22×C79—22no—
646C22×C79—22no—
647C22×C79—24no—
648C22×C79—24no—
649C22×C79—24no—
650C22×C79—22no—
651C22×C79—48no—
652C22×C79—44no—
653C22×C79C2×H(5,𝔽2)12yes—
654C22×C79C2×H(5,𝔽2)12yes—
655C22×C79#58512yes—
656C22×C79C2611yescharacteristic
657C2×D79—22no—
658C2×D79—22no—
659C2×D79—28no—
660C2×D79—24no—
661C2×D79—24no—
662C2×D79—24no—
663C2×D79—24no—
664C2×D79—22no—
665C2×D79—22no—
666C2×D79—24no—
667C2×D79—24no—
668C2×D79—22no—
669C2×D79—24no—
670C2×D79—24no—
671C2×D79—24no—
672C2×D79—48no—
673C2×D79—48no—
674C2×D79—44no—
675C2×D79—48no—
676C2×D79—816no—
677C2×D79—816no—
678C2×D79—816no—
679C2×D79C2×H(5,𝔽2)14yes—
680C4×C79—22no—
681C4×C79—22no—
682C4×C79—24no—
683C4×C79—24no—
684C4×C79—24no—
685C4×C79—22no—
686C4×C79—22no—
687C4×C79—22no—
688C4×C79C2×H(5,𝔽2)14yes—
689Dic79—22no—
690Dic79—22no—
691Dic79—22no—
692Dic79—24no—
693Dic79—22no—
694Dic79—22no—
695Dic79—22no—
696C2×#3558—791nomaximal, Sylow
697C2×C79—44no—
698C2×C79—42no—
699C2×C79#355814yescomplemented
700C2×C79C22×H(5,𝔽2)11yescharacteristic
701C2×C79C22×H(5,𝔽2)11yescharacteristic
702C2×C79C2×#58511yescharacteristic
703D79—24no—
704D79—44no—
705D79—44no—
706D79—44no—
707D79—42no—
708#3558—7932no—
709C2×#562—792no—
710C2×H(3,𝔽4)—792no—
711C2×#559—791no—
712C2×#559—791no—
713C2×#548—791no—
714C2×#548—791no—
715C2×#546—792no—
716C2×#546—792no—
717C2×#546—791no—
718C2×#546—791no—
719C2×D42—791no—
720C2×D42—791no—
721C2×#542—791no—
722C2×#542D7911yescharacteristic, complemented
723C2×#538—792no—
724C2×#538—792no—
725C2×#538—792no—
726C2×#535—791no—
727C2×#535—791no—
728C2×#534—792no—
729C2×#532—791no—
730C2×#529—791no—
731C22×#124—791no—
732C79C2×#355811yescharacteristic, complemented, Sylow
733C22×#41—792no—
734C22×#41—791no—
735C22×#41—791no—
736C23×Q8—791no—
737C23×D4—791no—
738C23×D4—792no—
739C23×D4—791no—
740C23×D4—792no—
741C23×D4—791no—
742#562—7932no—
743H(3,𝔽4)—7932no—
744#559—7916no—
745#559—7916no—
746#548—7916no—
747#548—7916no—
748#546—7932no—
749#546—7932no—
750#546—7916no—
751#546—7916no—
752D42—7916no—
753D42—7916no—
754#542—7916no—
755#542C2×D79116yescomplemented
756#538—7932no—
757#538—7932no—
758#538—7932no—
759#535—7916no—
760#535—7916no—
761#534—7932no—
762#532—7916no—
763C2×C4⋊Q8C2×D7911yescharacteristic, complemented
764C2×#127—791no—
765C2×#127—791no—
766C2×#127—791no—
767#529—7916no—
768C2×#126—791no—
769C2×#126—792no—
770C2×#126—791no—
771C2×#126C2×D7912yescomplemented
772C2×#125—791no—
773C2×#124—791no—
774C2×#124—792no—
775C2×#124—791no—
776C2×#124—792no—
777C2×#124—791no—
778C2×#124—7916no—
779C2×#124—792no—
780C2×#124—792no—
781C2×#124—791no—
782C2×#124—792no—
783C2×#124—792no—
784C2×#124—791no—
785C2×#124—791no—
786C2×#124—792no—
787C2×#124—792no—
788C2×#124C2×D7911yescharacteristic, complemented
789C2×#124C2×D7912yescomplemented
790C2×#123—792no—
791C2×#123—791no—
792C2×#123—792no—
793C2×#123—792no—
794C2×#123—792no—
795C2×#123—792no—
796C2×#123—791no—
797C2×#123—792no—
798C2×#123—792no—
799C2×#123C2×D7912yescomplemented
800C2×C22⋊Q8—792no—
801C2×C22⋊Q8—791no—
802C2×C22⋊Q8—792no—
803C2×C22⋊Q8—792no—
804C2×C22⋊Q8—791no—
805C2×C22⋊Q8C2×D7911yescharacteristic, complemented
806C2×C22⋊Q8C2×D7912yescomplemented
807C2×#121—792no—
808C2×#121—792no—
809C2×#121—792no—
810C2×#121—791no—
811C2×#121—791no—
812C2×#121—792no—
813C2×#121—792no—
814C2×#121—792no—
815C2×#121—792no—
816C2×#121—791no—
817C2×#121—791no—
818C2×#121—792no—
819C2×#121—792no—
820C2×#121—792no—
821C2×#121—792no—
822C2×#121C2×D7911yescharacteristic
823C2×#120—792no—
824C2×#120—792no—
825C2×#120—792no—
826C2×#120—792no—
827C2×#120—792no—
828C2×#120—792no—
829C2×#120—792no—
830C2×#120—792no—
831C2×#120—792no—
832C2×#120—792no—
833C2×C4×Q8—791no—
834C2×C4×Q8—791no—
835C2×C4×Q8C2×D7911yescharacteristic, complemented
836C2×C4×D4—791no—
837C2×C4×D4—791no—
838C2×C4×D4—792no—
839C2×C4×D4—792no—
840C2×C4×D4—791no—
841C2×C4×D4—791no—
842C2×C4×D4—792no—
843C2×C4×D4—791no—
844C2×C4×D4—791no—
845C2×C4×D4—792no—
846C2×C4×D4—792no—
847C2×C4×D4C2×D7911yescharacteristic, complemented
848C2×#117—791no—
849C2×#117C2×D7911yescharacteristic, complemented
850C22×C22⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C22⋊C4—792no—
853C22×C22⋊C4—792no—
854C22×C42—791no—
855C25—792no—
856C25—792no—
857C25—792no—
858C2×#41—3164no—
859C2×#41—3164no—
860C2×#41—3168no—
861C2×#41—7916no—
862C2×#41—798no—
863C2×#41—798no—
864C22×Q8—3164no—
865C22×Q8—798no—
866C22×Q8—791no—
867C22×Q8—792no—
868C22×Q8—791no—
869C22×Q8C22×D7911yescharacteristic
870C22×Q8C22×D7912yes—
871C22×D4—3164no—
872C22×D4—3168no—
873C22×D4—3168no—
874C22×D4—3164no—
875C22×D4—3164no—
876C22×D4—791no—
877C22×D4—792no—
878C22×D4—792no—
879C22×D4—792no—
880C22×D4—792no—
881C22×D4—792no—
882C22×D4—798no—
883C22×D4—7916no—
884C22×D4—798no—
885C22×D4—791no—
886C22×D4—792no—
887C22×D4—792no—
888C22×D4—792no—
889C22×D4—792no—
890C22×D4—792no—
891C22×D4—792no—
892C22×D4—792no—
893C22×D4—7916no—
894C22×D4—798no—
895C22×D4—792no—
896C22×D4—792no—
897C22×D4—791no—
898C22×D4—791no—
899C22×D4—791no—
900C22×D4—791no—
901C22×D4C22×D7911yescharacteristic
902C22×D4C22×D7912yes—
903C23×C4—792no—
904C23×C4—791no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—792no—
908C23×C4—792no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4—791no—
912C23×C4—791no—
913C23×C4C22×D7911yescharacteristic
914C23×C4C22×D7912yes—
915C4⋊Q8C22×D7918yescomplemented
916#127—798no—
917#127—798no—
918#127—798no—
919#126—798no—
920#126—7916no—
921#126—798no—
922#126C22×D79116yescomplemented
923#125—798no—
924#124—798no—
925#124—7916no—
926#124—798no—
927#124—7916no—
928#124—798no—
929#124—7916no—
930#124—7916no—
931#124—798no—
932#124—7916no—
933#124—7916no—
934#124—798no—
935#124—798no—
936#124—7916no—
937#124—7916no—
938#124C22×D7918yescomplemented
939#124C22×D79116yescomplemented
940#123—7916no—
941#123—798no—
942#123—7916no—
943#123—7916no—
944#123—7916no—
945#123—7916no—
946#123—798no—
947#123—7916no—
948#123—7916no—
949#123C22×D79116yescomplemented
950C22⋊Q8—7916no—
951C22⋊Q8—798no—
952C22⋊Q8—7916no—
953C22⋊Q8—7916no—
954C22⋊Q8—798no—
955C22⋊Q8C22×D7918yescomplemented
956C22⋊Q8C22×D79116yescomplemented
957#121—7916no—
958#121—7916no—
959#121—7916no—
960#121—798no—
961#121—798no—
962#121—7916no—
963#121—7916no—
964#121—7916no—
965#121—7916no—
966#121—798no—
967#121—798no—
968#121—7916no—
969#121—7916no—
970#121—7916no—
971#121—7916no—
972#121C22×D7918yes—
973#120—7916no—
974#120—7916no—
975#120—7916no—
976#120—7916no—
977#120—7916no—
978#120—7916no—
979#120—7916no—
980#120—7916no—
981#120—7916no—
982#120—7916no—
983C4×Q8—798no—
984C4×Q8—798no—
985C4×Q8C22×D7918yescomplemented
986C4×D4—798no—
987C4×D4—798no—
988C4×D4—7916no—
989C4×D4—7916no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—7916no—
993C4×D4—798no—
994C4×D4—798no—
995C4×D4—7916no—
996C4×D4—7916no—
997C4×D4C22×D7918yescomplemented
998#117—798no—
999#117C22×D7918yescomplemented
1000C2×C4⋊C4—791no—
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—791no—
1003C2×C4⋊C4—791no—
1004C2×C4⋊C4—791no—
1005C2×C4⋊C4—791no—
1006C2×C4⋊C4—792no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—792no—
1009C2×C4⋊C4—791no—
1010C2×C4⋊C4C22×D7911yescharacteristic
1011C2×C4⋊C4C22×D7911yescharacteristic
1012C2×C4⋊C4C22×D7911yescharacteristic
1013C2×C4⋊C4C22×D7911yescharacteristic
1014C2×C4⋊C4C22×D7912yes—
1015C2×C4⋊C4C22×D7912yes—
1016C2×C4⋊C4C22×D7912yes—
1017C2×C22⋊C4—791no—
1018C2×C22⋊C4—792no—
1019C2×C22⋊C4—792no—
1020C2×C22⋊C4—791no—
1021C2×C22⋊C4—791no—
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—792no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—792no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—792no—
1028C2×C22⋊C4—791no—
1029C2×C22⋊C4—791no—
1030C2×C22⋊C4—791no—
1031C2×C22⋊C4—791no—
1032C2×C22⋊C4—792no—
1033C2×C22⋊C4—791no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—792no—
1036C2×C22⋊C4—792no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—792no—
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—792no—
1041C2×C22⋊C4—792no—
1042C2×C22⋊C4—7916no—
1043C2×C22⋊C4—7916no—
1044C2×C22⋊C4—7916no—
1045C2×C22⋊C4—7916no—
1046C2×C22⋊C4C22×D7912yes—
1047C2×C22⋊C4C22×D7912yes—
1048C2×C22⋊C4C22×D7912yes—
1049C2×C22⋊C4C22×D7912yes—
1050C2×C22⋊C4C22×D7911yescharacteristic
1051C2×C22⋊C4C22×D7911yescharacteristic
1052C2×C22⋊C4C22×D7912yes—
1053C2×C42—791no—
1054C2×C42—791no—
1055C2×C42—792no—
1056C2×C42—791no—
1057C2×C42—791no—
1058C2×C42—798no—
1059C2×C42C22×D7911yescharacteristic
1060C2×C42C22×D7911yescharacteristic
1061C2×C42C22×D7912yes—
1062C24—3164no—
1063C24—3164no—
1064C24—3164no—
1065C24—3164no—
1066C24—3164no—
1067C24—3164no—
1068C24—3164no—
1069C24—3164no—
1070C24—798no—
1071C24—798no—
1072C24—798no—
1073C24—791no—
1074C24—792no—
1075C24—791no—
1076C24—792no—
1077C24—792no—
1078C24—1588no—
1079C24C23×D7912yes—
1080C24C23×D7911yescharacteristic
1081#41—31616no—
1082#41—31616no—
1083#41—31632no—
1084C2×Q8—24no—
1085C2×Q8—44no—
1086C2×Q8—3164no—
1087C2×Q8—3162no—
1088C2×Q8—31616no—
1089C2×Q8—794no—
1090C2×Q8—798no—
1091C2×Q8—794no—
1092C2×Q8—1584no—
1093C2×Q8C23×D7914yes—
1094C2×Q8C23×D7918yes—
1095C2×D4—24no—
1096C2×D4—44no—
1097C2×D4—3164no—
1098C2×D4—3164no—
1099C2×D4—3164no—
1100C2×D4—3164no—
1101C2×D4—3164no—
1102C2×D4—3164no—
1103C2×D4—3164no—
1104C2×D4—31616no—
1105C2×D4—31632no—
1106C2×D4—31632no—
1107C2×D4—31616no—
1108C2×D4—31616no—
1109C2×D4—3164no—
1110C2×D4—3164no—
1111C2×D4—3164no—
1112C2×D4—3162no—
1113C2×D4—3164no—
1114C2×D4—3164no—
1115C2×D4—794no—
1116C2×D4—798no—
1117C2×D4—798no—
1118C2×D4—798no—
1119C2×D4—798no—
1120C2×D4—798no—
1121C2×D4—794no—
1122C2×D4—798no—
1123C2×D4—798no—
1124C2×D4—798no—
1125C2×D4—798no—
1126C2×D4—798no—
1127C2×D4—798no—
1128C2×D4—798no—
1129C2×D4—798no—
1130C2×D4—798no—
1131C2×D4—794no—
1132C2×D4—794no—
1133C2×D4—794no—
1134C2×D4—794no—
1135C2×D4—1584no—
1136C2×D4—1588no—
1137C2×D4—1588no—
1138C2×D4—1584no—
1139C2×D4—1584no—
1140C2×D4—1584no—
1141C2×D4—1584no—
1142C2×D4C23×D7914yes—
1143C2×D4C23×D7918yes—
1144C22×C4—24no—
1145C22×C4—44no—
1146C22×C4—3162no—
1147C22×C4—3164no—
1148C22×C4—3164no—
1149C22×C4—3164no—
1150C22×C4—3164no—
1151C22×C4—3164no—
1152C22×C4—3164no—
1153C22×C4—794no—
1154C22×C4—798no—
1155C22×C4—798no—
1156C22×C4—798no—
1157C22×C4—798no—
1158C22×C4—798no—
1159C22×C4—798no—
1160C22×C4—791no—
1161C22×C4—791no—
1162C22×C4—791no—
1163C22×C4—791no—
1164C22×C4—792no—
1165C22×C4—791no—
1166C22×C4—791no—
1167C22×C4—794no—
1168C22×C4—794no—
1169C22×C4—794no—
1170C22×C4—1584no—
1171C22×C4—1584no—
1172C22×C4—1584no—
1173C22×C4C23×D7914yes—
1174C22×C4C23×D7911yescharacteristic
1175C22×C4C23×D7911yescharacteristic
1176C22×C4C23×D7912yes—
1177C22×C4C23×D7911yescharacteristic
1178C22×C4C23×D7912yes—
1179C22×C4C23×D7912yes—
1180C22×C4C23×D7911yescharacteristic
1181C22×C4C23×D7911yescharacteristic
1182C22×C4C23×D7918yes—
1183C22×C4C23×D7911yescharacteristic
1184C4⋊C4—794no—
1185C4⋊C4—794no—
1186C4⋊C4—794no—
1187C4⋊C4—794no—
1188C4⋊C4—794no—
1189C4⋊C4—798no—
1190C4⋊C4—794no—
1191C4⋊C4—794no—
1192C4⋊C4—794no—
1193C4⋊C4—798no—
1194C4⋊C4C23×D7914yes—
1195C4⋊C4C23×D7914yes—
1196C4⋊C4C23×D7914yes—
1197C4⋊C4C23×D7914yes—
1198C4⋊C4C23×D7918yes—
1199C4⋊C4C23×D7918yes—
1200C4⋊C4C23×D7918yes—
1201C22⋊C4—794no—
1202C22⋊C4—798no—
1203C22⋊C4—798no—
1204C22⋊C4—794no—
1205C22⋊C4—794no—
1206C22⋊C4—798no—
1207C22⋊C4—798no—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—798no—
1211C22⋊C4—798no—
1212C22⋊C4—794no—
1213C22⋊C4—794no—
1214C22⋊C4—794no—
1215C22⋊C4—794no—
1216C22⋊C4—798no—
1217C22⋊C4—794no—
1218C22⋊C4—798no—
1219C22⋊C4—798no—
1220C22⋊C4—798no—
1221C22⋊C4—798no—
1222C22⋊C4—798no—
1223C22⋊C4—798no—
1224C22⋊C4—798no—
1225C22⋊C4—798no—
1226C22⋊C4C23×D7918yes—
1227C22⋊C4C23×D7918yes—
1228C22⋊C4C23×D7918yes—
1229C22⋊C4C23×D7918yes—
1230C22⋊C4C23×D7914yes—
1231C22⋊C4C23×D7914yes—
1232C22⋊C4C23×D7918yes—
1233C42—794no—
1234C42—794no—
1235C42—794no—
1236C42—794no—
1237C42—798no—
1238C42C23×D7914yes—
1239C42C23×D7914yes—
1240C42C23×D7918yes—
1241C23—24no—
1242C23—22no—
1243C23—22no—
1244C23—24no—
1245C23—24no—
1246C23—22no—
1247C23—3168no—
1248C23—3168no—
1249C23—3168no—
1250C23—3168no—
1251C23—3168no—
1252C23—3168no—
1253C23—3168no—
1254C23—3168no—
1255C23—794no—
1256C23—792no—
1257C23—794no—
1258C23—792no—
1259C23—794no—
1260C23—794no—
1261C23—63216no—
1262C23—63216no—
1263C23—63216no—
1264C23—15816no—
1265C23—1584no—
1266C23—1584no—
1267C23—1584no—
1268C23—1582no—
1269C23—1584no—
1270C23—1584no—
1271C23—1582no—
1272C23—1584no—
1273C23—1584no—
1274C23—1584no—
1275C23—1582no—
1276C23—1584no—
1277C23—1582no—
1278C23—1582no—
1279C23C24×D7914yes—
1280C23C24×D7912yes—
1281C23C24×D7911yescharacteristic
1282Q8—28no—
1283Q8—48no—
1284Q8—3168no—
1285Q8—3164no—
1286Q8—1588no—
1287D4—28no—
1288D4—48no—
1289D4—3168no—
1290D4—3168no—
1291D4—3168no—
1292D4—3168no—
1293D4—3168no—
1294D4—3168no—
1295D4—3168no—
1296D4—3168no—
1297D4—3168no—
1298D4—3168no—
1299D4—3164no—
1300D4—3168no—
1301D4—3168no—
1302D4—1588no—
1303D4—15816no—
1304D4—15816no—
1305D4—1588no—
1306D4—1588no—
1307D4—1588no—
1308D4—1588no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—28no—
1318C2×C4—48no—
1319C2×C4—3168no—
1320C2×C4—3168no—
1321C2×C4—3168no—
1322C2×C4—3168no—
1323C2×C4—3168no—
1324C2×C4—3168no—
1325C2×C4—3164no—
1326C2×C4—792no—
1327C2×C4—792no—
1328C2×C4—792no—
1329C2×C4—792no—
1330C2×C4—794no—
1331C2×C4—792no—
1332C2×C4—792no—
1333C2×C4—1588no—
1334C2×C4—1582no—
1335C2×C4—1582no—
1336C2×C4—1582no—
1337C2×C4—1584no—
1338C2×C4—1582no—
1339C2×C4—1582no—
1340C2×C4—1582no—
1341C2×C4—1588no—
1342C2×C4—1588no—
1343C2×C4#1457920714yes—
1344C2×C4C24×D7912yes—
1345C2×C4C24×D7912yes—
1346C2×C4C24×D7914yes—
1347C2×C4C24×D7912yes—
1348C2×C4C24×D7914yes—
1349C2×C4C24×D7914yes—
1350C2×C4C24×D7912yes—
1351C2×C4C24×D7912yes—
1352C2×C4C24×D7912yes—
1353C22—24no—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—24no—
1358C22—22no—
1359C22—48no—
1360C22—44no—
1361C22—3164no—
1362C22—3168no—
1363C22—3168no—
1364C22—3168no—
1365C22—794no—
1366C22—63216no—
1367C22—63216no—
1368C22—63216no—
1369C22—1584no—
1370C22—1584no—
1371C22—1584no—
1372C22—1582no—
1373C22—1584no—
1374C22—1584no—
1375C22—1582no—
1376C22—1584no—
1377C22—1584no—
1378C22—1584no—
1379C22—1584no—
1380C22—1582no—
1381C22—1588no—
1382C22—1582no—
1383C22—1582no—
1384C22H(5,𝔽2)×D7912yes—
1385C22C2×#1457920712yes—
1386C22#1909940012yes—
1387C22C25×D7911yescharacteristic
1388C4—22no—
1389C4—24no—
1390C4—24no—
1391C4—22no—
1392C4—22no—
1393C4—24no—
1394C4—22no—
1395C4—22no—
1396C4—1582no—
1397C4—1582no—
1398C4—1582no—
1399C4—1584no—
1400C4—1582no—
1401C4—1582no—
1402C4—1582no—
1403C4C2×#1457920714yes—
1404C2—44no—
1405C2—42no—
1406C2—3162no—
1407C2—3164no—
1408C2—3164no—
1409C2—3164no—
1410C2—1584no—
1411C2#2377791514yesdirect product factor
1412C2C2×H(5,𝔽2)×D7911yescharacteristic
1413C2C22×#1457920711yescharacteristic
1414C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#542×C79C2
socleC23×C79C25
hypercenterC2×#542D79
hypocenterC79C2×#3558
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #23777915C2direct (N × H)
2. C2×#19099309C2semidirect
3. C2×#19099305C2semidirect
4. C2×#19099298C2semidirect
5. C2×#19099296C2semidirect
6. C2×#19099225C2semidirect
7. C2×#19099223C2semidirect
8. C2×#19099210C2semidirect
9. C2×#19099206C2semidirect
10. C2×#19099204C2semidirect
11. C2×#19099204C2semidirect
12. C2×D4×D316C2semidirect
13. C2×#19099197C2semidirect
14. C2×#19099187C2semidirect
15. C2×#19099152C2semidirect
16. C2×#19099152C2semidirect
17. C2×#19099149C2semidirect
18. C2×#19099132C2semidirect
19. C2×#19099131C2semidirect
20. C2×#19099124C2semidirect
21. C2×#19099114C2semidirect
22. C2×#19099091C2semidirect
23. C2×#124×D79C2semidirect
24. C2×#542×C79C2semidirect
25. C22×#11929625C22semidirect
26. C22×#11929625C22semidirect
27. C22×#11929624C22semidirect
28. C22×Q8×D79C22semidirect
29. C23×D316C22semidirect
30. C23×D316C22semidirect
32. C22×D4×D79C22semidirect
33. C22×D4×D79C22semidirect
34. #19099309C22semidirect
35. #19099305C22semidirect
36. #19099298C22semidirect
37. #19099296C22semidirect
38. #19099225C22semidirect
39. #19099223C22semidirect
40. #19099210C22semidirect
41. #19099206C22semidirect
42. #19099204C22semidirect
43. #19099204C22semidirect
44. D4×D316C22semidirect
45. #19099197C22semidirect
46. #19099187C22semidirect
47. #19099152C22semidirect
48. #19099152C22semidirect
49. #19099149C22semidirect
50. #19099132C22semidirect
51. #19099131C22semidirect
52. #19099124C22semidirect
53. #19099114C22semidirect
55. C2×#14579158C22semidirect
57. #19099091C22semidirect
58. C2×#14579156C22semidirect
59. C2×#14579156C22semidirect
60. C2×#14579154C22semidirect
61. C2×#14579151C22semidirect
62. C2×#14579150C22semidirect
63. C2×#14579150C22semidirect
64. C2×#14579150C22semidirect
65. C2×#14579150C22semidirect
66. C2×#14579149C22semidirect
67. C2×#14579149C22semidirect
68. C2×#14579149C22semidirect
69. C2×#14579149C22semidirect
70. C2×#14579148C22semidirect
71. C2×#14579147C22semidirect
72. C2×#14579147C22semidirect
73. C2×#14579147C22semidirect
74. C2×#14579147C22semidirect
75. C2×#14579147C22semidirect
76. #124×D79C22semidirect
77. C2×#14579146C22semidirect
78. C2×#14579146C22semidirect
79. C2×#14579146C22semidirect
80. C2×#14579146C22semidirect
81. C2×#14579146C22semidirect
82. C2×#14579144C22semidirect
83. C2×#14579143C22semidirect
84. C2×#14579143C22semidirect
85. C2×#14579143C22semidirect
86. C2×#14579141C22semidirect
87. C2×#14579141C22semidirect
88. C2×#14579139C22semidirect
89. C2×#14579139C22semidirect
90. C2×#14579137C22semidirect
92. C2×#14579136C22semidirect
93. C2×#14579136C22semidirect
94. C2×#14579136C22semidirect
95. C2×#14579136C22semidirect
96. C2×#14579136C22semidirect
97. C2×#14579136C22semidirect
98. C2×#14579136C22semidirect
99. C2×#14579135C22semidirect
101. C2×#14579134C22semidirect
102. C2×#14579134C22semidirect
103. C2×#14579134C22semidirect
104. C2×#14579134C22semidirect
105. C2×#14579132C22semidirect
106. C2×#14579131C22semidirect
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×C4×Dic158C22semidirect
117. C2×#14579126C22semidirect
118. C2×C4×D316C22semidirect
119. C2×C4×D316C22semidirect
120. C2×C4×D316C22semidirect
121. C2×#14579123C22semidirect
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×#14579118C22semidirect
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. #542×C79C22semidirect
136. C2×C4⋊Q8×C79C22semidirect
137. C2×#126×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#124×C79C22semidirect
140. C2×#123×C79C22semidirect
141. C2×C22⋊Q8×C79C22semidirect
142. C2×C22⋊Q8×C79C22semidirect
144. C2×C4×Q8×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C2×#117×C79C22semidirect
152. C2×#11929625C23semidirect
153. C2×#11929625C23semidirect
155. C2×#11929624C23semidirect
160. C2×Q8×D79C23semidirect
176. C22×D316C23semidirect
177. C22×D316C23semidirect
189. C2×D4×D79C23semidirect
190. C2×D4×D79C23semidirect
202. #14579158C23semidirect
204. #14579156C23semidirect
205. #14579156C23semidirect
206. #14579154C23semidirect
207. #14579151C23semidirect
208. #14579150C23semidirect
209. #14579150C23semidirect
210. #14579150C23semidirect
211. #14579150C23semidirect
212. #14579149C23semidirect
213. #14579149C23semidirect
214. #14579149C23semidirect
215. #14579149C23semidirect
216. #14579148C23semidirect
217. #14579147C23semidirect
218. #14579147C23semidirect
219. #14579147C23semidirect
220. #14579147C23semidirect
221. #14579147C23semidirect
222. #14579146C23semidirect
223. #14579146C23semidirect
224. #14579146C23semidirect
225. #14579146C23semidirect
226. #14579146C23semidirect
227. #14579144C23semidirect
228. #14579143C23semidirect
229. #14579143C23semidirect
230. #14579143C23semidirect
231. #14579141C23semidirect
232. #14579141C23semidirect
233. #14579139C23semidirect
234. #14579139C23semidirect
235. #14579137C23semidirect
237. #14579136C23semidirect
238. #14579136C23semidirect
239. #14579136C23semidirect
240. #14579136C23semidirect
241. #14579136C23semidirect
242. #14579136C23semidirect
243. #14579136C23semidirect
244. #14579135C23semidirect
246. #14579134C23semidirect
247. #14579134C23semidirect
248. #14579134C23semidirect
249. #14579134C23semidirect
250. #14579132C23semidirect
251. #14579131C23semidirect
252. #14579131C23semidirect
253. #14579131C23semidirect
254. #14579131C23semidirect
255. #14579131C23semidirect
256. #14579131C23semidirect
257. #14579131C23semidirect
258. #14579131C23semidirect
259. #14579129C23semidirect
260. #14579129C23semidirect
261. C4×Dic158C23semidirect
262. #14579126C23semidirect
263. C4×D316C23semidirect
264. C4×D316C23semidirect
265. C4×D316C23semidirect
266. #14579123C23semidirect
267. #14579123C23semidirect
268. #14579123C23semidirect
269. #14579123C23semidirect
270. #14579123C23semidirect
271. C4×C22⋊D79C23semidirect
272. C4×C22⋊D79C23semidirect
273. C4×C22⋊D79C23semidirect
274. #14579118C23semidirect
310. C22⋊C4×D79C23semidirect
311. C22⋊C4×D79C23semidirect
312. C22⋊C4×D79C23semidirect
313. C22⋊C4×D79C23semidirect
319. C42×D79C23semidirect
326. C4⋊Q8×C79C23semidirect
327. #126×C79C23semidirect
328. #124×C79C23semidirect
329. #124×C79C23semidirect
330. #123×C79C23semidirect
331. C22⋊Q8×C79C23semidirect
332. C22⋊Q8×C79C23semidirect
334. C4×Q8×C79C23semidirect
335. C4×D4×C79C23semidirect
336. #117×C79C23semidirect
699. C2×C79#3558semidirect
722. C2×#542D79semidirect
732. C79C2×#3558semidirect
755. #542C2×D79semidirect
763. C2×C4⋊Q8C2×D79semidirect
771. C2×#126C2×D79semidirect
788. C2×#124C2×D79semidirect
789. C2×#124C2×D79semidirect
799. C2×#123C2×D79semidirect
805. C2×C22⋊Q8C2×D79semidirect
806. C2×C22⋊Q8C2×D79semidirect
835. C2×C4×Q8C2×D79semidirect
847. C2×C4×D4C2×D79semidirect
849. C2×#117C2×D79semidirect
915. C4⋊Q8C22×D79semidirect
922. #126C22×D79semidirect
938. #124C22×D79semidirect
939. #124C22×D79semidirect
949. #123C22×D79semidirect
955. C22⋊Q8C22×D79semidirect
956. C22⋊Q8C22×D79semidirect
985. C4×Q8C22×D79semidirect
997. C4×D4C22×D79semidirect
999. #117C22×D79semidirect
1411. C2#23777915direct (N × H)

Maximal subgroups

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

subgroupindex
#237779152
C2×#190993092
C2×#190993052
C2×#190992982
C2×#190992962
C2×#190992252
C2×#190992232
C2×#190992102
C2×#190992062
C2×#190992042
C2×D4×D3162
C2×#190991972
C2×#190991872
C2×#190991522
C2×#190991492
C2×#190991322
C2×#190991312
C2×#190991242
C2×#190991142
C2×#190990912
C2×#124×D792
C2×#542×C792
C2×#355879