Finite Group Databasebeta

← C2×#23767534 #34455864

Subgroups — C2×#23767534 #34455864

Order 20224.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579151C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D79C211yesmaximal, characteristic
3#23767534C2116yesmaximal, direct product factor
4C2×#19098501C211yesmaximal, characteristic, complemented
5C2×#19098497C211yesmaximal, characteristic, complemented
6C2×#19098494C211yesmaximal, characteristic, complemented
7C2×#19098459C211yesmaximal, characteristic, complemented
8C2×#19098446C211yesmaximal, characteristic, complemented
9C2×#19098445C211yesmaximal, characteristic, complemented
10C2×#19098437C211yesmaximal, characteristic
11C2×#19098434C211yesmaximal, characteristic
12C2×#19098434C211yesmaximal, characteristic
13C2×#19098434C211yesmaximal, characteristic
14C2×#19098422C211yesmaximal, characteristic
15C2×#19098410C211yesmaximal, characteristic
16C2×#398×C79C211yesmaximal, characteristic, complemented
17C23×C4×D79C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C2×#14579151—28no—
21C2×#14579151C2218yescomplemented
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
32C2×C4⋊C4×D79—28no—
33C2×C4⋊C4×D79C2218yes—
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×(C2×D79)⋊C4C2211yescharacteristic
37C22×(C2×D79)⋊C4C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39C22×C4×Dic79C2211yescharacteristic
40#19098501C2218yescomplemented
41#19098497C2218yescomplemented
42#19098494C2218yescomplemented
43#19098459C2218yescomplemented
44#19098446C2218yescomplemented
45#19098445C2218yescomplemented
46#19098437C2218yes—
47#19098434C2218yes—
48#19098434C2218yes—
49#19098434C2218yes—
50#19098422C2218yes—
51#19098410C2218yes—
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
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×C4⋊C4×C79C2211yescharacteristic
65#398×C79C2218yescomplemented
66C2×#95×C79C2211yescharacteristic
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×D79—24no—
80C22×C4×D79—24no—
81C22×C4×D79—24no—
82C22×C4×D79—24no—
83C22×C4×D79—24no—
84C22×C4×D79—42no—
85C22×C4×D79—42no—
86C22×C4×D79C2314yes—
87C22×C4×D79C2314yes—
88C22×C4×D79C2314yes—
89#14579151—232no—
90C2×C4⋊Dic79—24no—
91C2×C4⋊Dic79D418yes—
92C2×C4⋊Dic79C2314yes—
93C2×C4⋊Dic79C2314yes—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4—24no—
96C2×Dic79⋊C4—24no—
97C2×Dic79⋊C4—24no—
98C2×Dic79⋊C4—24no—
99C2×Dic79⋊C4—24no—
100C2×Dic79⋊C4—24no—
101C2×Dic79⋊C4—42no—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2314yes—
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2314yes—
106C2×Dic79⋊C4C2314yes—
107C2×Dic79⋊C4C2314yes—
108C2×Dic79⋊C4C2314yes—
109C2×Dic79⋊C4C2314yes—
110C4⋊C4×D79—232no—
111C2×(C2×D79)⋊C4—24no—
112C2×(C2×D79)⋊C4—24no—
113C2×(C2×D79)⋊C4—24no—
114C2×(C2×D79)⋊C4Q818yes—
115C2×(C2×D79)⋊C4C2314yes—
116C2×(C2×D79)⋊C4C2314yes—
117C2×(C2×D79)⋊C4C2314yes—
118C2×(C2×D79)⋊C4C2314yes—
119C2×C4×Dic79—24no—
120C2×C4×Dic79—42no—
121C2×C4×Dic79C2314yes—
122C2×C4×Dic79C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C23×C4×C79C2311yescharacteristic
139C2×C4⋊C4×C79—24no—
140C2×C4⋊C4×C79—24no—
141C2×C4⋊C4×C79—42no—
142C2×C4⋊C4×C79—42no—
143C2×C4⋊C4×C79C2314yes—
144C2×C4⋊C4×C79C2314yes—
145C2×C4⋊C4×C79C2314yes—
146C2×C4⋊C4×C79C2314yes—
147#95×C79C2314yes—
148#95×C79C2314yes—
149#95×C79C2314yes—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79—22no—
153C23×D79—22no—
154C23×D79C2×Q814yes—
155C23×D79#4114yes—
156C23×D79#4114yes—
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×Dic79—22no—
175C22×Dic79C2×D414yes—
176C22×Dic79C2×D414yes—
177C22×Dic79C2×Q814yes—
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×D79—28no—
190C2×C4×D79—28no—
191C2×C4×D79—28no—
192C2×C4×D79—28no—
193C2×C4×D79—28no—
194C2×C4×D79—44no—
195C2×C4×D79—44no—
196C2×C4×D79—416no—
197C2×C4×D79—416no—
198C4⋊Dic79—28no—
199C4⋊Dic79C2×D4116yes—
200Dic79⋊C4—28no—
201Dic79⋊C4—28no—
202Dic79⋊C4—28no—
203Dic79⋊C4—28no—
204Dic79⋊C4—28no—
205Dic79⋊C4—28no—
206Dic79⋊C4—28no—
207Dic79⋊C4—44no—
208(C2×D79)⋊C4—28no—
209(C2×D79)⋊C4—28no—
210(C2×D79)⋊C4—28no—
211(C2×D79)⋊C4C2×Q8116yes—
212C4×Dic79—28no—
213C4×Dic79—44no—
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×C79—22no—
233C22×C4×C79—22no—
234C22×C4×C79C2×D414yes—
235C22×C4×C79C2×Q814yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22×C4×C79C2412yes—
242C22×C4×C79C2412yes—
243C4⋊C4×C79—28no—
244C4⋊C4×C79—28no—
245C4⋊C4×C79—44no—
246C4⋊C4×C79—44no—
247C23×C79C22×D412yes—
248C23×C79C22×Q812yes—
249C23×C79C2×#4112yes—
250C23×C79C2×#4112yes—
251C23×C79C2×#4112yes—
252C23×C79H(5,𝔽2)12yes—
253C23×C792−1+412yes—
254C23×C79C2511yescharacteristic
255C22×D79—28no—
256C22×D79—28no—
257C22×D79—28no—
258C22×D79—28no—
259C22×D79—28no—
260C22×D79—28no—
261C22×D79—22no—
262C22×D79—22no—
263C22×D79—22no—
264C22×D79—22no—
265C22×D79#125116yescomplemented
266C22×D79C22×Q814yes—
267C22×D79C2×#4114yes—
268C22×D79C2×#4114yes—
269C2×C4×C79—28no—
270C2×C4×C79—28no—
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—22no—
289C2×C4×C79—22no—
290C2×C4×C79—44no—
291C2×C4×C79—44no—
292C2×C4×C79—44no—
293C2×C4×C79—44no—
294C2×C4×C79—44no—
295C2×C4×C79C22×D414yes—
296C2×C4×C79C22×Q814yes—
297C2×Dic79—28no—
298C2×Dic79—28no—
299C2×Dic79—28no—
300C2×Dic79—28no—
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—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—44no—
319C2×Dic79—44no—
320C2×Dic79—44no—
321C2×Dic79C22×D414yes—
322C2×Dic79C22×D414yes—
323C2×Dic79C22×Q814yes—
324C2×Dic79C2×#4114yes—
325C4×D79—232no—
326C4×D79—416no—
327C4×D79—416no—
328C22×C79#52514yes—
329C22×C79C2×#12514yes—
330C22×C79#53914yes—
331C22×C79#54614yes—
332C22×C79D4×Q814yes—
333C22×C79#55214yes—
334C22×C79#55414yes—
335C22×C79C23×D411yescharacteristic
336C22×C79C23×Q811yescharacteristic
337C22×C79C22×#4111yescharacteristic
338C22×C79C22×#4111yescharacteristic
339C22×C79C22×#4111yescharacteristic
340C22×C79C2×H(5,𝔽2)11yescharacteristic
341C22×C79C2×2−1+411yescharacteristic
342C2×D79—24no—
343C2×D79—24no—
344C2×D79—24no—
345C2×D79—24no—
346C2×D79—24no—
347C2×D79—24no—
348C2×D79—232no—
349C2×D79C2×#12518yescomplemented
350C4×C79—24no—
351C4×C79—24no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79—42no—
356C4×C79—42no—
357Dic79—24no—
358Dic79—24no—
359Dic79—24no—
360Dic79—24no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364C2×#2473—791nomaximal, Sylow
365C2×C79#247318yescomplemented
366C2×C79C2×#52511yescharacteristic
367C2×C79C22×#12511yescharacteristic
368C2×C79C2×#53911yescharacteristic
369C2×C79C2×#54611yescharacteristic
370C2×C79C2×D4×Q811yescharacteristic
371C2×C79C2×#55211yescharacteristic
372C2×C79C2×#55411yescharacteristic
373D79—28no—
374C22×#125—791no—
375C23×C4⋊C4—791no—
376#2473—7916no—
377C2×#400—791no—
378C2×#398—791no—
379C2×#398—791no—
380C2×#398D7911yescharacteristic, complemented
381C2×#389—791no—
382C2×#387—791no—
383C2×#387—791no—
384C2×#385—791no—
385C2×#385—791no—
386C2×#385—791no—
387C2×#385—791no—
388C2×#380—791no—
389C2×C4×C22⋊C4—791no—
390C79C2×#247311yescharacteristic, complemented, Sylow
391C24×C4—791no—
392C24×C4—791no—
393C24×C4—791no—
394C2×#125—798no—
395C2×#125—1588no—
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—798no—
407C22×C4⋊C4—1588no—
408C22×C4⋊C4C2×D7911yescharacteristic
409C22×C4⋊C4C2×D7911yescharacteristic
410C22×C4⋊C4C2×D7911yescharacteristic
411C22×C4⋊C4C2×D7911yescharacteristic
412C22×C22⋊C4—791no—
413C22×C22⋊C4—791no—
414C22×C22⋊C4—791no—
415C22×C22⋊C4—791no—
416C22×C42—791no—
417C22×C42—791no—
418#400—798no—
419#398—798no—
420#398—798no—
421#398C2×D7918yescomplemented
422#389—798no—
423#387—798no—
424#387—798no—
425#385—798no—
426#385—798no—
427#385—798no—
428#385—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×#95—791no—
438C2×#95—791no—
439C2×#95—791no—
440C2×#95C2×D7911yescharacteristic
441C2×#95C2×D7911yescharacteristic
442C2×#95C2×D7911yescharacteristic
443C25—791no—
444C23×C4—3162no—
445C23×C4—3162no—
446C23×C4—794no—
447C23×C4—794no—
448C23×C4—791no—
449C23×C4—791no—
450C23×C4—791no—
451C23×C4—791no—
452C23×C4—791no—
453C23×C4—791no—
454C23×C4—791no—
455C23×C4—794no—
456C23×C4—1584no—
457C23×C4—1584no—
458C23×C4—1584no—
459C23×C4—1584no—
460C23×C4—1584no—
461C23×C4—1584no—
462C23×C4—1584no—
463C23×C4C22×D7911yescharacteristic
464C23×C4C22×D7911yescharacteristic
465C23×C4C22×D7911yescharacteristic
466C23×C4C22×D7911yescharacteristic
467C23×C4C22×D7911yescharacteristic
468C23×C4C22×D7911yescharacteristic
469C23×C4C22×D7911yescharacteristic
470#125—15832no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—3162no—
476C2×C4⋊C4—794no—
477C2×C4⋊C4—798no—
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—794no—
485C2×C4⋊C4—794no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—15832no—
488C2×C4⋊C4—1584no—
489C2×C4⋊C4—1584no—
490C2×C4⋊C4—1584no—
491C2×C4⋊C4—1584no—
492C2×C4⋊C4—1584no—
493C2×C4⋊C4—1584no—
494C2×C4⋊C4—1584no—
495C2×C4⋊C4—1584no—
496C2×C4⋊C4C22×D7914yes—
497C2×C4⋊C4C22×D7914yes—
498C2×C4⋊C4C22×D7914yes—
499C2×C4⋊C4C22×D7914yes—
500C2×C22⋊C4—798no—
501C2×C22⋊C4—794no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—794no—
505C2×C22⋊C4—1584no—
506C2×C22⋊C4—1584no—
507C2×C22⋊C4—1584no—
508C2×C42—3162no—
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#95—794no—
520#95—794no—
521#95C22×D7914yes—
522#95C22×D7914yes—
523#95C22×D7914yes—
524C24—794no—
525C24—794no—
526C24—794no—
527C24—792no—
528C24—1582no—
529C24—1582no—
530C24—1582no—
531C24—1582no—
532C24C23×D7911yescharacteristic
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—3164no—
553C22×C4—3164no—
554C22×C4—31616no—
555C22×C4—31616no—
556C22×C4—794no—
557C22×C4—794no—
558C22×C4—792no—
559C22×C4—792no—
560C22×C4—792no—
561C22×C4—792no—
562C22×C4—794no—
563C22×C4—794no—
564C22×C4—792no—
565C22×C4—792no—
566C22×C4—792no—
567C22×C4—1588no—
568C22×C4—1588no—
569C22×C4—1588no—
570C22×C4—1588no—
571C22×C4—1588no—
572C22×C4—1588no—
573C22×C4—15832no—
574C22×C4—1582no—
575C22×C4—1582no—
576C22×C4—1582no—
577C22×C4—1582no—
578C22×C4—1582no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4—1582no—
582C22×C4—1582no—
583C22×C4—1582no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4—1582no—
587C22×C4—1582no—
588C22×C4—1582no—
589C22×C4—1582no—
590C22×C4—1582no—
591C22×C4—1588no—
592C22×C4D4×D7914yes—
593C22×C4Q8×D7914yes—
594C22×C4C23×D7912yes—
595C22×C4C23×D7912yes—
596C22×C4C23×D7912yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7912yes—
599C22×C4C23×D7912yes—
600C22×C4C23×D7912yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—3164no—
606C4⋊C4—7916no—
607C4⋊C4—1588no—
608C4⋊C4—1588no—
609C4⋊C4—1588no—
610C4⋊C4—1588no—
611C4⋊C4—1588no—
612C4⋊C4—1588no—
613C4⋊C4—1588no—
614C4⋊C4—1588no—
615C22⋊C4—7916no—
616C22⋊C4—1588no—
617C22⋊C4—1588no—
618C22⋊C4—1588no—
619C42—3164no—
620C42—1588no—
621C23—7916no—
622C23—794no—
623C23—794no—
624C23—794no—
625C23—1582no—
626C23—1582no—
627C23—1588no—
628C23—1588no—
629C23—1588no—
630C23—1588no—
631C23—1588no—
632C23—1588no—
633C23—1582no—
634C23—1582no—
635C23C2×D4×D7912yes—
636C23C2×Q8×D7912yes—
637C23#41×D7912yes—
638C23#41×D7912yes—
639C23#41×D7912yes—
640C23#1457920612yes—
641C23#1457920912yes—
642C23C24×D7911yescharacteristic
643C2×C4—22no—
644C2×C4—28no—
645C2×C4—28no—
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—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—31616no—
670C2×C4—31616no—
671C2×C4—3164no—
672C2×C4—3164no—
673C2×C4—3164no—
674C2×C4—794no—
675C2×C4—794no—
676C2×C4—794no—
677C2×C4—794no—
678C2×C4—15832no—
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—1582no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1588no—
692C2×C4—1588no—
693C2×C4—1588no—
694C2×C4—1588no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4C2×D4×D7914yes—
701C2×C4C2×Q8×D7914yes—
702C22—798no—
703C22—1584no—
704C22—1584no—
705C22—1584no—
706C22—1584no—
707C22—1584no—
708C22—15832no—
709C22—1584no—
710C22#1909907114yes—
711C22#125×D7914yes—
712C22#1909915914yes—
713C22#1909921014yes—
714C22#1909922814yes—
715C22#1909924514yes—
716C22#1909926714yes—
717C22C22×D4×D7911yescharacteristic
718C22C22×Q8×D7911yescharacteristic
719C22C2×#41×D7911yescharacteristic
720C22C2×#41×D7911yescharacteristic
721C22C2×#41×D7911yescharacteristic
722C22C2×#1457920611yescharacteristic
723C22C2×#1457920911yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—3162no—
732C4—3162no—
733C4—3162no—
734C4—1584no—
735C4—1584no—
736C4—1584no—
737C4—1584no—
738C2—1588no—
739C2#2376753418yesdirect product factor
740C2C2×#1909907111yescharacteristic
741C2C2×#125×D7911yescharacteristic
742C2C2×#1909915911yescharacteristic
743C2C2×#1909921011yescharacteristic
744C2C2×#1909922811yescharacteristic
745C2C2×#1909924511yescharacteristic
746C2C2×#1909926711yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#398×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#398D79
hypocenterC79C2×#2473
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14579151C2semidirect
3. #23767534C2direct (N × H)
4. C2×#19098501C2semidirect
5. C2×#19098497C2semidirect
6. C2×#19098494C2semidirect
7. C2×#19098459C2semidirect
8. C2×#19098446C2semidirect
9. C2×#19098445C2semidirect
16. C2×#398×C79C2semidirect
21. C2×#14579151C22semidirect
40. #19098501C22semidirect
41. #19098497C22semidirect
42. #19098494C22semidirect
43. #19098459C22semidirect
44. #19098446C22semidirect
45. #19098445C22semidirect
65. #398×C79C22semidirect
265. C22×D79#125semidirect
349. C2×D79C2×#125semidirect
365. C2×C79#2473semidirect
380. C2×#398D79semidirect
390. C79C2×#2473semidirect
421. #398C2×D79semidirect
739. C2#23767534direct (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×C4⋊C4×D792
#237675342
C2×#190985012
C2×#190984972
C2×#190984942
C2×#190984592
C2×#190984462
C2×#190984452
C2×#190984372
C2×#190984342
C2×#190984222
C2×#190984102
C2×#398×C792
C2×#247379