Finite Group Databasebeta

← C2×#23769229 #34455331

Subgroups — C2×#23769229 #34455331

Order 20224.

2614 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×#14579117C211yesmaximal, characteristic
3#23769229C2116yesmaximal, direct product factor
4C2×#19098497C211yesmaximal, characteristic, complemented
5C2×#19098496C211yesmaximal, characteristic, complemented
6C2×#19098494C211yesmaximal, characteristic, complemented
7C2×#19098493C211yesmaximal, characteristic, complemented
8C2×#19098486C211yesmaximal, characteristic
9C2×#19098486C211yesmaximal, characteristic
10C2×#19098486C211yesmaximal, characteristic
11C2×#19098460C211yesmaximal, characteristic, complemented
12C2×#19098458C211yesmaximal, characteristic, complemented
13C2×#19098432C211yesmaximal, characteristic, complemented
14C2×#19098421C211yesmaximal, characteristic
15C2×#19098421C211yesmaximal, characteristic
16C2×#396×C79C211yesmaximal, characteristic
17C24×Dic79C2211yescharacteristic
18C2×#14579151—28no—
19C2×#14579151C2218yescomplemented
20C2×#14579117—28no—
21C2×#14579117C2218yes—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×C4⋊Dic79C2211yescharacteristic
24C22×C4⋊Dic79C2211yescharacteristic
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×Dic79⋊C4C2211yescharacteristic
35C22×Dic79⋊C4C2211yescharacteristic
36C22×Dic79⋊C4C2211yescharacteristic
37C22×C22⋊Dic79C2211yescharacteristic
38C22×C22⋊Dic79C2211yescharacteristic
39C22×C22⋊Dic79C2211yescharacteristic
40C22×C4×Dic79C2211yescharacteristic
41C22×C4×Dic79C2211yescharacteristic
42#19098497C2218yescomplemented
43#19098496C2218yescomplemented
44#19098494C2218yescomplemented
45#19098493C2218yescomplemented
46#19098486C2218yes—
47#19098486C2218yes—
48#19098486C2218yes—
49#19098460C2218yescomplemented
50#19098458C2218yescomplemented
51#19098432C2218yescomplemented
52#19098421C2218yes—
53#19098421C2218yes—
54C2×C79⋊#95C2211yescharacteristic
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×C22⋊C4×C79C2211yescharacteristic
65C22×C22⋊C4×C79C2211yescharacteristic
66C22×C22⋊C4×C79C2211yescharacteristic
67#396×C79C2218yes—
68C2×#95×C79C2211yescharacteristic
69C23×Dic79—24no—
70C23×Dic79—24no—
71C23×Dic79Q818yes—
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2314yes—
80C23×Dic79C2311yescharacteristic
81#14579151—232no—
82#14579117—232no—
83C2×C4⋊Dic79—24no—
84C2×C4⋊Dic79—42no—
85C2×C4⋊Dic79—42no—
86C2×C4⋊Dic79C2314yes—
87C2×C4⋊Dic79C2314yes—
88C2×C4⋊Dic79C2314yes—
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—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4—42no—
98C2×Dic79⋊C4—42no—
99C2×Dic79⋊C4—42no—
100C2×Dic79⋊C4—42no—
101C2×Dic79⋊C4C2314yes—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2314yes—
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2314yes—
106C2×Dic79⋊C4C2314yes—
107C2×Dic79⋊C4C2314yes—
108C2×Dic79⋊C4C2314yes—
109C2×Dic79⋊C4C2314yes—
110C2×Dic79⋊C4C2314yes—
111C2×Dic79⋊C4C2314yes—
112C2×Dic79⋊C4C2314yes—
113C2×C22⋊Dic79—24no—
114C2×C22⋊Dic79—42no—
115C2×C22⋊Dic79—42no—
116C2×C22⋊Dic79C2314yes—
117C2×C22⋊Dic79C2314yes—
118C2×C22⋊Dic79C2314yes—
119C2×C4×Dic79—24no—
120C2×C4×Dic79D418yes—
121C2×C4×Dic79C2314yes—
122C2×C4×Dic79C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C25×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C2×C4⋊C4×C79—24no—
138C2×C4⋊C4×C79—42no—
139C2×C4⋊C4×C79—42no—
140C2×C4⋊C4×C79C2314yes—
141C2×C4⋊C4×C79C2314yes—
142C2×C4⋊C4×C79C2314yes—
143C2×C22⋊C4×C79—24no—
144C2×C22⋊C4×C79—42no—
145C2×C22⋊C4×C79—42no—
146C2×C22⋊C4×C79C2314yes—
147C2×C22⋊C4×C79C2314yes—
148C2×C22⋊C4×C79C2314yes—
149#95×C79C2314yes—
150C22×Dic79—232no—
151C22×Dic79—28no—
152C22×Dic79—28no—
153C22×Dic79—22no—
154C22×Dic79—22no—
155C22×Dic79—22no—
156C22×Dic79—22no—
157C22×Dic79—22no—
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×Dic79C2×D414yes—
173C22×Dic79C2×D414yes—
174C22×Dic79C2×Q8116yes—
175C22×Dic79C2×Q814yes—
176C22×Dic79C2×Q814yes—
177C22×Dic79#4114yes—
178C22×Dic79C2412yes—
179C22×Dic79C2412yes—
180C22×Dic79C2412yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C4⋊Dic79—28no—
187C4⋊Dic79—44no—
188C4⋊Dic79—44no—
189Dic79⋊C4—28no—
190Dic79⋊C4—28no—
191Dic79⋊C4—28no—
192Dic79⋊C4—28no—
193Dic79⋊C4—28no—
194Dic79⋊C4—28no—
195Dic79⋊C4—28no—
196Dic79⋊C4—28no—
197Dic79⋊C4—44no—
198Dic79⋊C4—44no—
199Dic79⋊C4—44no—
200Dic79⋊C4—44no—
201C22⋊Dic79—28no—
202C22⋊Dic79—44no—
203C22⋊Dic79—44no—
204C4×Dic79—28no—
205C4×Dic79C2×D4116yes—
206C24×C79—22no—
207C24×C79—22no—
208C24×C79—22no—
209C24×C79—22no—
210C24×C79—22no—
211C24×C79—22no—
212C24×C79C2×Q814yes—
213C24×C79C2412yes—
214C24×C79C2411yescharacteristic
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×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79C2×D414yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C4⋊C4×C79—28no—
240C4⋊C4×C79—44no—
241C4⋊C4×C79—44no—
242C22⋊C4×C79—28no—
243C22⋊C4×C79—44no—
244C22⋊C4×C79—44no—
245C23×C79—28no—
246C23×C79—28no—
247C23×C79—28no—
248C23×C79—22no—
249C23×C79—22no—
250C23×C79—22no—
251C23×C79—22no—
252C23×C79—22no—
253C23×C79—22no—
254C23×C79—44no—
255C23×C79—44no—
256C23×C79—44no—
257C23×C79—44no—
258C23×C79C22×D412yes—
259C23×C79C22×Q814yes—
260C23×C79C22×Q812yes—
261C23×C79C2×#4112yes—
262C23×C79H(5,𝔽2)12yes—
263C23×C79H(5,𝔽2)12yes—
264C23×C792−1+412yes—
265C23×C792−1+412yes—
266C23×C79C2511yescharacteristic
267C2×C4×C79—28no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
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—44no—
286C2×C4×C79—44no—
287C2×C4×C79—44no—
288C2×C4×C79—44no—
289C2×C4×C79—44no—
290C2×C4×C79C22×D414yes—
291C2×Dic79—28no—
292C2×Dic79—28no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—232no—
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×Dic79—44no—
318C2×Dic79C22⋊Q8116yes—
319C2×Dic79C22×D414yes—
320C2×Dic79C22×D414yes—
321C2×Dic79C22×Q814yes—
322C2×Dic79C22×Q814yes—
323C2×Dic79C2×#4114yes—
324C22×C79—24no—
325C22×C79—24no—
326C22×C79—24no—
327C22×C79—416no—
328C22×C79—42no—
329C22×C79—42no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79C2×C22⋊Q814yes—
333C22×C79#53714yes—
334C22×C79#53714yes—
335C22×C79#54014yes—
336C22×C79#54114yes—
337C22×C79#54414yes—
338C22×C79#54414yes—
339C22×C79C23×D411yescharacteristic
340C22×C79C23×Q811yescharacteristic
341C22×C79C22×#4111yescharacteristic
342C22×C79C2×H(5,𝔽2)11yescharacteristic
343C22×C79C2×H(5,𝔽2)11yescharacteristic
344C22×C79C2×2−1+411yescharacteristic
345C22×C79C2×2−1+411yescharacteristic
346C4×C79—24no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79—42no—
352Dic79—24no—
353Dic79—24no—
354Dic79—42no—
355Dic79—42no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79C2×C22⋊Q818yes—
360C2×#2629—791nomaximal, Sylow
361C2×C79—44no—
362C2×C79#262918yescomplemented
363C2×C79C22×C22⋊Q811yescharacteristic
364C2×C79C2×#53711yescharacteristic
365C2×C79C2×#53711yescharacteristic
366C2×C79C2×#54011yescharacteristic
367C2×C79C2×#54111yescharacteristic
368C2×C79C2×#54411yescharacteristic
369C2×C79C2×#54411yescharacteristic
370C22×#125—791no—
371C22×#117—791no—
372#2629—7916no—
373C2×#398—791no—
374C2×#398—791no—
375C2×#398—791no—
376C2×#398—791no—
377C2×#396—791no—
378C2×#396—791no—
379C2×#396—791no—
380C2×#396D7911yescharacteristic
381C2×#389—791no—
382C2×#389—791no—
383C2×#384—791no—
384C2×#380—791no—
385C2×#380—791no—
386C79C2×#262911yescharacteristic, 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⋊C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—791no—
407C22×C4⋊C4C2×D7911yescharacteristic
408C22×C4⋊C4C2×D7911yescharacteristic
409C22×C4⋊C4C2×D7911yescharacteristic
410C22×C22⋊C4—791no—
411C22×C22⋊C4—791no—
412C22×C22⋊C4—791no—
413C22×C22⋊C4C2×D7911yescharacteristic
414C22×C22⋊C4C2×D7911yescharacteristic
415C22×C22⋊C4C2×D7911yescharacteristic
416C22×C42—791no—
417C22×C42—791no—
418#398—798no—
419#398—798no—
420#398—798no—
421#398—798no—
422#396—798no—
423#396—798no—
424#396—798no—
425#396C2×D7918yes—
426#389—798no—
427#389—798no—
428#384—798no—
429#380—798no—
430#380—798no—
431C2×#95—791no—
432C2×#95—791no—
433C2×#95—791no—
434C2×#95—791no—
435C2×#95—791no—
436C2×#95—791no—
437C2×#95—791no—
438C2×#95C2×D7911yescharacteristic
439C25C22×D7911yescharacteristic
440C23×C4—791no—
441C23×C4—798no—
442C23×C4—794no—
443C23×C4—791no—
444C23×C4—791no—
445C23×C4—791no—
446C23×C4—791no—
447C23×C4—791no—
448C23×C4—791no—
449C23×C4—791no—
450C23×C4—1584no—
451C23×C4—1584no—
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—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—3162no—
464C2×C4⋊C4—3162no—
465C2×C4⋊C4—3162no—
466C2×C4⋊C4—3162no—
467C2×C4⋊C4—3162no—
468C2×C4⋊C4—3162no—
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—794no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—794no—
482C2×C4⋊C4—794no—
483C2×C4⋊C4—794no—
484C2×C4⋊C4—1584no—
485C2×C4⋊C4—1584no—
486C2×C4⋊C4—1584no—
487C2×C4⋊C4—1584no—
488C2×C4⋊C4—1584no—
489C2×C4⋊C4—1584no—
490C2×C4⋊C4—1584no—
491C2×C4⋊C4—1584no—
492C2×C4⋊C4—1584no—
493C2×C4⋊C4C22×D7914yes—
494C2×C4⋊C4C22×D7914yes—
495C2×C4⋊C4C22×D7914yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—3162no—
500C2×C22⋊C4—3162no—
501C2×C22⋊C4—794no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—1584no—
505C2×C22⋊C4C22×D7914yes—
506C2×C22⋊C4C22×D7914yes—
507C2×C22⋊C4C22×D7914yes—
508C2×C42—798no—
509C2×C42—794no—
510C2×C42—794no—
511C2×C42—1584no—
512#95—794no—
513#95—794no—
514#95—794no—
515#95—794no—
516#95—794no—
517#95—794no—
518#95—794no—
519#95C22×D7914yes—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D7914yes—
527C24C23×D7912yes—
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—794no—
547C22×C4—794no—
548C22×C4—792no—
549C22×C4—794no—
550C22×C4—7916no—
551C22×C4—794no—
552C22×C4—792no—
553C22×C4—792no—
554C22×C4—794no—
555C22×C4—792no—
556C22×C4—792no—
557C22×C4—792no—
558C22×C4—792no—
559C22×C4—792no—
560C22×C4—1582no—
561C22×C4—1582no—
562C22×C4—1582no—
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—1588no—
576C22×C4—15832no—
577C22×C4—1588no—
578C22×C4—1582no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—1582no—
582C22×C4D4×D7914yes—
583C22×C4C23×D7912yes—
584C22×C4C23×D7912yes—
585C22×C4C23×D7912yes—
586C22×C4C23×D7912yes—
587C22×C4C23×D7912yes—
588C22×C4C23×D7912yes—
589C4⋊C4—28no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—3164no—
593C4⋊C4—3164no—
594C4⋊C4—3164no—
595C4⋊C4—3164no—
596C4⋊C4—3164no—
597C4⋊C4—3164no—
598C4⋊C4—1588no—
599C4⋊C4—1588no—
600C4⋊C4—1588no—
601C4⋊C4—1588no—
602C4⋊C4—1588no—
603C4⋊C4—1588no—
604C4⋊C4—1588no—
605C4⋊C4—1588no—
606C4⋊C4—1588no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—3164no—
611C22⋊C4—3164no—
612C22⋊C4—1588no—
613C42—7916no—
614C42—1588no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—22no—
623C23—22no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D7912yes—
629C23C2×Q8×D7914yes—
630C23C2×Q8×D7912yes—
631C23#41×D7912yes—
632C23#1457920612yes—
633C23#1457920612yes—
634C23#1457920812yes—
635C23#1457920812yes—
636C23C24×D7911yescharacteristic
637C2×C4—22no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
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—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—3164no—
661C2×C4—3164no—
662C2×C4—3164no—
663C2×C4—3164no—
664C2×C4—3164no—
665C2×C4—7916no—
666C2×C4—794no—
667C2×C4—794no—
668C2×C4—794no—
669C2×C4—794no—
670C2×C4—794no—
671C2×C4—1582no—
672C2×C4—1582no—
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—15832no—
687C2×C4—1582no—
688C2×C4—1582no—
689C2×C4—1588no—
690C2×C4—1588no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4C2×D4×D7914yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22C22⋊Q8×D7914yes—
703C22#1909914014yes—
704C22#1909914214yes—
705C22#1909916314yes—
706C22#1909917014yes—
707C22#1909919214yes—
708C22#1909919214yes—
709C22C22×D4×D7911yescharacteristic
710C22C22×Q8×D7911yescharacteristic
711C22C2×#41×D7911yescharacteristic
712C22C2×#1457920611yescharacteristic
713C22C2×#1457920611yescharacteristic
714C22C2×#1457920811yescharacteristic
715C22C2×#1457920811yescharacteristic
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—3162no—
723C4—3162no—
724C4—3162no—
725C4—3162no—
726C4—3162no—
727C4—798no—
728C4—1584no—
729C4—1584no—
730C2—44no—
731C2#2376922918yesdirect product factor
732C2C2×C22⋊Q8×D7911yescharacteristic
733C2C2×#1909914011yescharacteristic
734C2C2×#1909914211yescharacteristic
735C2C2×#1909916311yescharacteristic
736C2C2×#1909917011yescharacteristic
737C2C2×#1909919211yescharacteristic
738C2C2×#1909919211yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#396×C79C2
socleC24×C79C24
prime radicalC25×C79C23
hypercenterC2×#396D79
hypocenterC79C2×#2629
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14579151C2semidirect
3. #23769229C2direct (N × H)
4. C2×#19098497C2semidirect
5. C2×#19098496C2semidirect
6. C2×#19098494C2semidirect
7. C2×#19098493C2semidirect
11. C2×#19098460C2semidirect
12. C2×#19098458C2semidirect
13. C2×#19098432C2semidirect
19. C2×#14579151C22semidirect
42. #19098497C22semidirect
43. #19098496C22semidirect
44. #19098494C22semidirect
45. #19098493C22semidirect
49. #19098460C22semidirect
50. #19098458C22semidirect
51. #19098432C22semidirect
362. C2×C79#2629semidirect
386. C79C2×#2629semidirect
731. C2#23769229direct (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×#145791172
#237692292
C2×#190984972
C2×#190984962
C2×#190984942
C2×#190984932
C2×#190984862
C2×#190984602
C2×#190984582
C2×#190984322
C2×#190984212
C2×#396×C792
C2×#262979