Finite Group Databasebeta

← C2×#23767110 #34456754

Subgroups — C2×#23767110 #34456754

Order 20224.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579151C211yesmaximal, characteristic, complemented
2C22×#14579118C211yesmaximal, characteristic
3#23767110C2116yesmaximal, direct product factor
4C2×#19098498C211yesmaximal, characteristic
5C2×#19098498C211yesmaximal, characteristic
6C2×#19098485C211yesmaximal, characteristic
7C2×#19098485C211yesmaximal, characteristic
8C2×#19098460C211yesmaximal, characteristic, complemented
9C2×#19098458C211yesmaximal, characteristic, complemented
10C2×#19098458C211yesmaximal, characteristic, complemented
11C2×#19098450C211yesmaximal, characteristic, complemented
12C2×#19098447C211yesmaximal, characteristic, complemented
13C2×#19098432C211yesmaximal, characteristic, complemented
14C2×#19098422C211yesmaximal, characteristic
15C2×#19098410C211yesmaximal, characteristic
16C2×#389×C79C211yesmaximal, characteristic, complemented
17C23×C4×D79C2211yescharacteristic
18C2×#14579151—28no—
19C2×#14579151C2218yescomplemented
20C2×#14579118—28no—
21C2×#14579118C2218yes—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×C4⋊Dic79C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×Dic79⋊C4C2211yescharacteristic
31C22×Dic79⋊C4C2211yescharacteristic
32C22×Dic79⋊C4C2211yescharacteristic
33C22×Dic79⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×(C2×D79)⋊C4C2211yescharacteristic
39C22×(C2×D79)⋊C4C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42C22×C4×Dic79C2211yescharacteristic
43#19098498C2218yes—
44#19098498C2218yes—
45#19098485C2218yes—
46#19098485C2218yes—
47#19098460C2218yescomplemented
48#19098458C2218yescomplemented
49#19098458C2218yescomplemented
50#19098450C2218yescomplemented
51#19098447C2218yescomplemented
52#19098432C2218yescomplemented
53#19098422C2218yes—
54#19098410C2218yes—
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C2×C79⋊#95C2211yescharacteristic
60C2×C79⋊#95C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C4⋊C4×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64C22×C4⋊C4×C79C2211yescharacteristic
65C22×C42×C79C2211yescharacteristic
66#389×C79C2218yescomplemented
67C2×#95×C79C2211yescharacteristic
68C2×#95×C79C2211yescharacteristic
69C24×D79C2311yescharacteristic
70C23×Dic79C2311yescharacteristic
71C23×Dic79C2311yescharacteristic
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C22×C4×D79—24no—
78C22×C4×D79—24no—
79C22×C4×D79Q818yes—
80C22×C4×D79C2314yes—
81#14579151—232no—
82#14579118—232no—
83C2×C4⋊Dic79—24no—
84C2×C4⋊Dic79—42no—
85C2×C4⋊Dic79C2314yes—
86C2×C4⋊Dic79C2314yes—
87C2×Dic79⋊C4—24no—
88C2×Dic79⋊C4—24no—
89C2×Dic79⋊C4—24no—
90C2×Dic79⋊C4—24no—
91C2×Dic79⋊C4—24no—
92C2×Dic79⋊C4—24no—
93C2×Dic79⋊C4—24no—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4—42no—
96C2×Dic79⋊C4D418yes—
97C2×Dic79⋊C4C2314yes—
98C2×Dic79⋊C4C2314yes—
99C2×Dic79⋊C4C2314yes—
100C2×Dic79⋊C4C2314yes—
101C2×Dic79⋊C4C2314yes—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2314yes—
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2314yes—
106C2×Dic79⋊C4C2314yes—
107C2×(C2×D79)⋊C4—24no—
108C2×(C2×D79)⋊C4—24no—
109C2×(C2×D79)⋊C4—24no—
110C2×(C2×D79)⋊C4—24no—
111C2×(C2×D79)⋊C4—42no—
112C2×(C2×D79)⋊C4—42no—
113C2×(C2×D79)⋊C4C2314yes—
114C2×(C2×D79)⋊C4C2314yes—
115C2×(C2×D79)⋊C4C2314yes—
116C2×(C2×D79)⋊C4C2314yes—
117C2×(C2×D79)⋊C4C2314yes—
118C2×(C2×D79)⋊C4C2314yes—
119C2×C4×Dic79—24no—
120C2×C4×Dic79—24no—
121C2×C4×Dic79—24no—
122C2×C4×Dic79C2314yes—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C2×C4⋊C4×C79—24no—
139C2×C4⋊C4×C79—24no—
140C2×C4⋊C4×C79—42no—
141C2×C4⋊C4×C79—42no—
142C2×C4⋊C4×C79C2314yes—
143C2×C4⋊C4×C79C2314yes—
144C2×C4⋊C4×C79C2314yes—
145C2×C4⋊C4×C79C2314yes—
146C2×C42×C79—24no—
147C2×C42×C79C2314yes—
148#95×C79C2314yes—
149#95×C79C2314yes—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79—22no—
153C23×D79—22no—
154C23×D79—22no—
155C23×D79—22no—
156C23×D79C2×Q814yes—
157C23×D79C2412yes—
158C22×Dic79—22no—
159C22×Dic79—22no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79C2×D414yes—
175C22×Dic79C2×D414yes—
176C22×Dic79C2×Q814yes—
177C22×Dic79#4114yes—
178C22×Dic79#4114yes—
179C22×Dic79C2412yes—
180C22×Dic79C2412yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C2×C4×D79—232no—
187C2×C4×D79—28no—
188C2×C4×D79—28no—
189C2×C4×D79C2×Q8116yes—
190C4⋊Dic79—28no—
191C4⋊Dic79—44no—
192Dic79⋊C4—28no—
193Dic79⋊C4—28no—
194Dic79⋊C4—28no—
195Dic79⋊C4—28no—
196Dic79⋊C4—28no—
197Dic79⋊C4—28no—
198Dic79⋊C4—28no—
199Dic79⋊C4—28no—
200Dic79⋊C4—44no—
201Dic79⋊C4C2×D4116yes—
202(C2×D79)⋊C4—28no—
203(C2×D79)⋊C4—28no—
204(C2×D79)⋊C4—28no—
205(C2×D79)⋊C4—28no—
206(C2×D79)⋊C4—44no—
207(C2×D79)⋊C4—44no—
208C4×Dic79—28no—
209C4×Dic79—28no—
210C4×Dic79—28no—
211C24×C79C2411yescharacteristic
212C22×C4×C79—22no—
213C22×C4×C79—22no—
214C22×C4×C79—22no—
215C22×C4×C79—22no—
216C22×C4×C79—22no—
217C22×C4×C79—22no—
218C22×C4×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79C2×D414yes—
231C22×C4×C79C2×Q814yes—
232C22×C4×C79#4114yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C4⋊C4×C79—28no—
241C4⋊C4×C79—28no—
242C4⋊C4×C79—44no—
243C4⋊C4×C79—44no—
244C42×C79—28no—
245C23×C79C22×D412yes—
246C23×C79C22×Q812yes—
247C23×C79C2×#4112yes—
248C23×C79C2×#4112yes—
249C23×C79C2×#4112yes—
250C23×C79H(5,𝔽2)12yes—
251C23×C792−1+412yes—
252C23×C79C2511yescharacteristic
253C22×D79—28no—
254C22×D79—28no—
255C22×D79—28no—
256C22×D79—22no—
257C22×D79—22no—
258C22×D79—22no—
259C22×D79—22no—
260C22×D79—22no—
261C22×D79—22no—
262C22×D79—44no—
263C22×D79—44no—
264C22×D79—44no—
265C22×D79—44no—
266C22×D79C22×Q814yes—
267C2×C4×C79—28no—
268C2×C4×C79—28no—
269C2×C4×C79—28no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—44no—
289C2×C4×C79—44no—
290C2×C4×C79—44no—
291C2×C4×C79—44no—
292C2×C4×C79C22×D414yes—
293C2×C4×C79C22×Q814yes—
294C2×C4×C79C2×#4114yes—
295C2×Dic79—28no—
296C2×Dic79—28no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—44no—
314C2×Dic79—44no—
315C2×Dic79—44no—
316C2×Dic79—44no—
317C2×Dic79C22⋊Q8116yes—
318C2×Dic79C22×D414yes—
319C2×Dic79C22×D414yes—
320C2×Dic79C22×Q814yes—
321C2×Dic79C2×#4114yes—
322C2×Dic79C2×#4114yes—
323C4×D79—232no—
324C22×C79C2×C22⋊Q814yes—
325C22×C79#53314yes—
326C22×C79#54414yes—
327C22×C79#54714yes—
328C22×C79#55014yes—
329C22×C79#55214yes—
330C22×C79#55314yes—
331C22×C79C23×D411yescharacteristic
332C22×C79C23×Q811yescharacteristic
333C22×C79C22×#4111yescharacteristic
334C22×C79C22×#4111yescharacteristic
335C22×C79C22×#4111yescharacteristic
336C22×C79C2×H(5,𝔽2)11yescharacteristic
337C22×C79C2×2−1+411yescharacteristic
338C2×D79—24no—
339C2×D79—24no—
340C2×D79—24no—
341C2×D79—42no—
342C2×D79—416no—
343C2×D79—42no—
344C2×D79—42no—
345C2×D79—42no—
346C4×C79—24no—
347C4×C79—24no—
348C4×C79—24no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79—42no—
352C4×C79—42no—
353Dic79—24no—
354Dic79—24no—
355Dic79—42no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79C2×C22⋊Q818yes—
360C2×#2441—791nomaximal, Sylow
361C2×C79#244118yescomplemented
362C2×C79C22×C22⋊Q811yescharacteristic
363C2×C79C2×#53311yescharacteristic
364C2×C79C2×#54411yescharacteristic
365C2×C79C2×#54711yescharacteristic
366C2×C79C2×#55011yescharacteristic
367C2×C79C2×#55211yescharacteristic
368C2×C79C2×#55311yescharacteristic
369D79—44no—
370C22×#125—791no—
371C22×#117—791no—
372#2441—7916no—
373C2×#399—791no—
374C2×#399—791no—
375C2×#396—791no—
376C2×#396—791no—
377C2×#389—791no—
378C2×#389—791no—
379C2×#389—791no—
380C2×#389D7911yescharacteristic, complemented
381C2×#387—791no—
382C2×#387—791no—
383C2×#384—791no—
384C2×#380—791no—
385C2×C4×C22⋊C4—791no—
386C79C2×#244111yescharacteristic, complemented, Sylow
387C24×C4—791no—
388C2×#125—798no—
389C2×#125—1588no—
390C2×#117—798no—
391C2×#117—1588no—
392C22×C4⋊C4—791no—
393C22×C4⋊C4—791no—
394C22×C4⋊C4—791no—
395C22×C4⋊C4—791no—
396C22×C4⋊C4—791no—
397C22×C4⋊C4—791no—
398C22×C4⋊C4—791no—
399C22×C4⋊C4—791no—
400C22×C4⋊C4—791no—
401C22×C4⋊C4—791no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4—791no—
404C22×C4⋊C4C2×D7911yescharacteristic
405C22×C4⋊C4C2×D7911yescharacteristic
406C22×C4⋊C4C2×D7911yescharacteristic
407C22×C4⋊C4C2×D7911yescharacteristic
408C22×C22⋊C4—791no—
409C22×C22⋊C4—791no—
410C22×C22⋊C4—791no—
411C22×C22⋊C4—791no—
412C22×C22⋊C4—791no—
413C22×C22⋊C4—791no—
414C22×C42—791no—
415C22×C42—791no—
416C22×C42—791no—
417C22×C42C2×D7911yescharacteristic
418#399—798no—
419#399—798no—
420#396—798no—
421#396—798no—
422#389—798no—
423#389—798no—
424#389—798no—
425#389C2×D7918yescomplemented
426#387—798no—
427#387—798no—
428#384—798no—
429#380—798no—
430C4×C22⋊C4—798no—
431C2×#95—791no—
432C2×#95—791no—
433C2×#95—791no—
434C2×#95—791no—
435C2×#95—791no—
436C2×#95—791no—
437C2×#95C2×D7911yescharacteristic
438C2×#95C2×D7911yescharacteristic
439C25—791no—
440C23×C4—791no—
441C23×C4—791no—
442C23×C4—791no—
443C23×C4—798no—
444C23×C4—794no—
445C23×C4—791no—
446C23×C4—791no—
447C23×C4—791no—
448C23×C4—791no—
449C23×C4—1584no—
450C23×C4—1584no—
451C23×C4C22×D7911yescharacteristic
452C23×C4C22×D7911yescharacteristic
453C23×C4C22×D7911yescharacteristic
454C23×C4C22×D7911yescharacteristic
455C23×C4C22×D7911yescharacteristic
456C23×C4C22×D7911yescharacteristic
457C23×C4C22×D7911yescharacteristic
458#125—15832no—
459#117—15832no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—3162no—
465C2×C4⋊C4—3162no—
466C2×C4⋊C4—794no—
467C2×C4⋊C4—794no—
468C2×C4⋊C4—798no—
469C2×C4⋊C4—794no—
470C2×C4⋊C4—794no—
471C2×C4⋊C4—794no—
472C2×C4⋊C4—794no—
473C2×C4⋊C4—794no—
474C2×C4⋊C4—794no—
475C2×C4⋊C4—794no—
476C2×C4⋊C4—794no—
477C2×C4⋊C4—794no—
478C2×C4⋊C4—794no—
479C2×C4⋊C4—1584no—
480C2×C4⋊C4—1584no—
481C2×C4⋊C4—1584no—
482C2×C4⋊C4—1584no—
483C2×C4⋊C4—1584no—
484C2×C4⋊C4—1584no—
485C2×C4⋊C4—1584no—
486C2×C4⋊C4—1584no—
487C2×C4⋊C4—1584no—
488C2×C4⋊C4C22×D7914yes—
489C2×C4⋊C4C22×D7914yes—
490C2×C4⋊C4C22×D7914yes—
491C2×C4⋊C4C22×D7914yes—
492C2×C22⋊C4—3162no—
493C2×C22⋊C4—3162no—
494C2×C22⋊C4—794no—
495C2×C22⋊C4—794no—
496C2×C22⋊C4—794no—
497C2×C22⋊C4—794no—
498C2×C22⋊C4—794no—
499C2×C22⋊C4—794no—
500C2×C22⋊C4—1584no—
501C2×C22⋊C4—1584no—
502C2×C22⋊C4—1584no—
503C2×C22⋊C4—1584no—
504C2×C42—24no—
505C2×C42—794no—
506C2×C42—794no—
507C2×C42—794no—
508C2×C42—1584no—
509C2×C42—1584no—
510C2×C42—1584no—
511C2×C42C22×D7914yes—
512#95—794no—
513#95—794no—
514#95—794no—
515#95—794no—
516#95—794no—
517#95—794no—
518#95C22×D7914yes—
519#95C22×D7914yes—
520C24—794no—
521C24—792no—
522C24—1582no—
523C24—1582no—
524C24—1582no—
525C24—1582no—
526C24—1582no—
527C24—1582no—
528C24C23×D7911yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—794no—
548C22×C4—794no—
549C22×C4—792no—
550C22×C4—794no—
551C22×C4—794no—
552C22×C4—792no—
553C22×C4—792no—
554C22×C4—794no—
555C22×C4—7916no—
556C22×C4—792no—
557C22×C4—792no—
558C22×C4—792no—
559C22×C4—792no—
560C22×C4—1588no—
561C22×C4—15832no—
562C22×C4—1588no—
563C22×C4—1582no—
564C22×C4—1582no—
565C22×C4—1582no—
566C22×C4—1582no—
567C22×C4—1582no—
568C22×C4—1582no—
569C22×C4—1582no—
570C22×C4—1582no—
571C22×C4—1582no—
572C22×C4—1582no—
573C22×C4—1582no—
574C22×C4—1582no—
575C22×C4—1582no—
576C22×C4—1582no—
577C22×C4—1582no—
578C22×C4—1582no—
579C22×C4D4×D7914yes—
580C22×C4Q8×D7914yes—
581C22×C4#1192962414yes—
582C22×C4C23×D7912yes—
583C22×C4C23×D7912yes—
584C22×C4C23×D7912yes—
585C22×C4C23×D7912yes—
586C22×C4C23×D7912yes—
587C22×C4C23×D7912yes—
588C22×C4C23×D7912yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—3164no—
594C4⋊C4—3164no—
595C4⋊C4—7916no—
596C4⋊C4—1588no—
597C4⋊C4—1588no—
598C4⋊C4—1588no—
599C4⋊C4—1588no—
600C4⋊C4—1588no—
601C4⋊C4—1588no—
602C4⋊C4—1588no—
603C4⋊C4—1588no—
604C4⋊C4—1588no—
605C22⋊C4—3164no—
606C22⋊C4—3164no—
607C22⋊C4—1588no—
608C22⋊C4—1588no—
609C22⋊C4—1588no—
610C22⋊C4—1588no—
611C42—28no—
612C42—1588no—
613C42—1588no—
614C42—1588no—
615C23—3164no—
616C23—3164no—
617C23—3164no—
618C23—3164no—
619C23—794no—
620C23—1582no—
621C23—1582no—
622C23—1588no—
623C23—1588no—
624C23—1588no—
625C23—1582no—
626C23—1582no—
627C23—1582no—
628C23—1582no—
629C23C2×D4×D7912yes—
630C23C2×Q8×D7912yes—
631C23#41×D7912yes—
632C23#41×D7912yes—
633C23C2×#1192962412yes—
634C23#1457920612yes—
635C23#1457920912yes—
636C23C24×D7911yescharacteristic
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—28no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—3164no—
663C2×C4—3164no—
664C2×C4—3164no—
665C2×C4—3164no—
666C2×C4—7916no—
667C2×C4—794no—
668C2×C4—794no—
669C2×C4—794no—
670C2×C4—794no—
671C2×C4—794no—
672C2×C4—15832no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1588no—
688C2×C4—1588no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4C2×D4×D7914yes—
692C2×C4C2×Q8×D7914yes—
693C2×C4C2×#1192962414yes—
694C22—31616no—
695C22—3162no—
696C22—3162no—
697C22—3162no—
698C22—3162no—
699C22—1584no—
700C22—1584no—
701C22—1584no—
702C22C22⋊Q8×D7914yes—
703C22#1909911714yes—
704C22#1909919014yes—
705C22#1909921414yes—
706C22#1909923114yes—
707C22#1909924514yes—
708C22#1909926214yes—
709C22C22×D4×D7911yescharacteristic
710C22C22×Q8×D7911yescharacteristic
711C22C2×#41×D7911yescharacteristic
712C22C2×#41×D7911yescharacteristic
713C22C22×#1192962411yescharacteristic
714C22C2×#1457920611yescharacteristic
715C22C2×#1457920911yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—3162no—
724C4—3162no—
725C4—3162no—
726C4—3162no—
727C4—798no—
728C4—1584no—
729C4—1584no—
730C2—3164no—
731C2#2376711018yesdirect product factor
732C2C2×C22⋊Q8×D7911yescharacteristic
733C2C2×#1909911711yescharacteristic
734C2C2×#1909919011yescharacteristic
735C2C2×#1909921411yescharacteristic
736C2C2×#1909923111yescharacteristic
737C2C2×#1909924511yescharacteristic
738C2C2×#1909926211yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#389×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#389D79
hypocenterC79C2×#2441
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#14579151C2semidirect
3. #23767110C2direct (N × H)
8. C2×#19098460C2semidirect
9. C2×#19098458C2semidirect
10. C2×#19098458C2semidirect
11. C2×#19098450C2semidirect
12. C2×#19098447C2semidirect
13. C2×#19098432C2semidirect
16. C2×#389×C79C2semidirect
19. C2×#14579151C22semidirect
47. #19098460C22semidirect
48. #19098458C22semidirect
49. #19098458C22semidirect
50. #19098450C22semidirect
51. #19098447C22semidirect
52. #19098432C22semidirect
66. #389×C79C22semidirect
361. C2×C79#2441semidirect
380. C2×#389D79semidirect
386. C79C2×#2441semidirect
425. #389C2×D79semidirect
731. C2#23767110direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791512
C22×#145791182
#237671102
C2×#190984982
C2×#190984852
C2×#190984602
C2×#190984582
C2×#190984502
C2×#190984472
C2×#190984322
C2×#190984222
C2×#190984102
C2×#389×C792
C2×#244179