Finite Group Databasebeta

← C2×#23766479 #34447898

Subgroups — C2×#23766479 #34447898

Order 20224.

3094 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×#14579137C211yesmaximal, characteristic
2#23766479C2116yesmaximal, direct product factor
3C2×#19098470C211yesmaximal, characteristic, complemented
4C2×#19098450C211yesmaximal, characteristic, complemented
5C2×#19098448C211yesmaximal, characteristic, complemented
6C2×#19098446C211yesmaximal, characteristic, complemented
7C2×#19098444C211yesmaximal, characteristic, complemented
8C2×#19098437C211yesmaximal, characteristic
9C2×#19098434C211yesmaximal, characteristic
10C2×C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
11C2×#19098414C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic
13C2×#19098410C211yesmaximal, characteristic
14C2×#19098410C211yesmaximal, characteristic
15C2×#95×D79C211yesmaximal, characteristic
16C2×#391×C79C211yesmaximal, characteristic, complemented
17C23×C4×D79C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C2×#14579137C4116yescomplemented
21C2×#14579137C2218yes—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×C4⋊Dic79C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×C4×Dic79C2211yescharacteristic
33C22×C4×Dic79C2211yescharacteristic
34C22×C4×Dic79C2211yescharacteristic
35C22×C4×Dic79C2211yescharacteristic
36C22×C4×Dic79C2211yescharacteristic
37#19098470C2218yescomplemented
38#19098450C2218yescomplemented
39#19098448C2218yescomplemented
40#19098446C2218yescomplemented
41#19098444C2218yescomplemented
42#19098437C2218yes—
43#19098434C2218yes—
44C4×Dic79⋊C4C2218yescomplemented
45#19098414C2218yescomplemented
46C4×(C2×D79)⋊C4C2218yes—
47#19098410C2218yes—
48#19098410C2218yes—
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59#95×D79C2218yes—
60C23×Q8×C79C2211yescharacteristic
61C22×C4⋊C4×C79C2211yescharacteristic
62C22×C42×C79C2211yescharacteristic
63#391×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C24×D79C2311yescharacteristic
69C23×Dic79C2311yescharacteristic
70C23×Dic79C2311yescharacteristic
71C23×Dic79C2311yescharacteristic
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C22×C4×D79—24no—
77C22×C4×D79—24no—
78C22×C4×D79—24no—
79C22×C4×D79—24no—
80C22×C4×D79—42no—
81C22×C4×D79—42no—
82C22×C4×D79—42no—
83C22×C4×D79—42no—
84C22×C4×D79C2×C418yes—
85C22×C4×D79C2314yes—
86C22×C4×D79C2314yes—
87C22×C4×D79C2314yes—
88#14579137C2×C4164yescomplemented
89C2×C4⋊Dic79—42no—
90C2×C4⋊Dic79C2×C418yescomplemented
91C2×C4⋊Dic79C2314yes—
92C2×C4⋊Dic79C2314yes—
93C2×Dic79⋊C4—24no—
94C2×Dic79⋊C4—24no—
95C2×Dic79⋊C4C2×C418yescomplemented
96C2×Dic79⋊C4C2×C418yescomplemented
97C2×Dic79⋊C4C2314yes—
98C2×Dic79⋊C4C2314yes—
99C2×Dic79⋊C4C2314yes—
100C2×Dic79⋊C4C2314yes—
101C2×(C2×D79)⋊C4—24no—
102C2×(C2×D79)⋊C4C2×C418yes—
103C2×(C2×D79)⋊C4C2×C418yes—
104C2×(C2×D79)⋊C4Q818yescomplemented
105C2×(C2×D79)⋊C4C2314yes—
106C2×(C2×D79)⋊C4C2314yes—
107C2×(C2×D79)⋊C4C2314yes—
108C2×(C2×D79)⋊C4C2314yes—
109C2×C4×Dic79—24no—
110C2×C4×Dic79—24no—
111C2×C4×Dic79—42no—
112C2×C4×Dic79—42no—
113C2×C4×Dic79—42no—
114C2×C4×Dic79C2314yes—
115C2×C4×Dic79C2314yes—
116C2×C4×Dic79C2314yes—
117C2×C4×Dic79C2314yes—
118C2×C4×Dic79C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127C79⋊#95C2314yes—
128C79⋊#95C2314yes—
129C22×Q8×C79—42no—
130C22×Q8×C79—42no—
131C22×Q8×C79C2×C418yescomplemented
132C22×Q8×C79C2314yes—
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C23×C4×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C23×C4×C79C2311yescharacteristic
139C23×C4×C79C2311yescharacteristic
140C2×C4⋊C4×C79—42no—
141C2×C4⋊C4×C79C2314yes—
142C2×C42×C79—42no—
143C2×C42×C79C2314yes—
144#95×C79C2314yes—
145#95×C79C2314yes—
146#95×C79C2314yes—
147#95×C79C2314yes—
148C23×D79—22no—
149C23×D79—22no—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79C22×C414yes—
153C23×D79C2×Q814yes—
154C23×D79#4114yes—
155C23×D79C2412yes—
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×Dic79C22×C414yes—
173C22×Dic79C22×C414yes—
174C22×Dic79C22×C414yes—
175C22×Dic79C2×Q814yes—
176C22×Dic79#4114yes—
177C22×Dic79C2412yes—
178C22×Dic79C2412yes—
179C22×Dic79C2412yes—
180C22×Dic79C2412yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C2×C4×D79—28no—
185C2×C4×D79—28no—
186C2×C4×D79—28no—
187C2×C4×D79—28no—
188C2×C4×D79—416no—
189C2×C4×D79—44no—
190C2×C4×D79—44no—
191C2×C4×D79—44no—
192C2×C4×D79—44no—
193C2×C4×D79—416no—
194C2×C4×D79—416no—
195C2×C4×D79C22×C4116yes—
196C4⋊Dic79—44no—
197C4⋊Dic79C22×C4116yescomplemented
198Dic79⋊C4—28no—
199Dic79⋊C4—28no—
200Dic79⋊C4C22×C4116yescomplemented
201Dic79⋊C4C22×C4116yescomplemented
202(C2×D79)⋊C4—28no—
203(C2×D79)⋊C4C22×C4116yes—
204(C2×D79)⋊C4C22×C4116yes—
205(C2×D79)⋊C4C2×Q8116yescomplemented
206C4×Dic79—28no—
207C4×Dic79—28no—
208C4×Dic79—44no—
209C4×Dic79—44no—
210C4×Dic79—44no—
211C24×C79C2411yescharacteristic
212C2×Q8×C79—416no—
213C2×Q8×C79—44no—
214C2×Q8×C79—44no—
215C2×Q8×C79C22×C4116yescomplemented
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×C79C22×C414yes—
233C22×C4×C79C22×C414yes—
234C22×C4×C79C22×C414yes—
235C22×C4×C79C2×Q814yes—
236C22×C4×C79#4114yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22×C4×C79C2412yes—
242C22×C4×C79C2412yes—
243C22×C4×C79C2412yes—
244C4⋊C4×C79—44no—
245C42×C79—44no—
246C23×C79C23×C412yes—
247C23×C79C22×Q812yes—
248C23×C79C2×#4112yes—
249C23×C79C2×#4112yes—
250C23×C79C2×#4112yes—
251C23×C79H(5,𝔽2)12yes—
252C23×C79H(5,𝔽2)12yes—
253C23×C79C2511yescharacteristic
254C22×D79—28no—
255C22×D79—28no—
256C22×D79—28no—
257C22×D79—28no—
258C22×D79—28no—
259C22×D79—28no—
260C22×D79—22no—
261C22×D79—22no—
262C22×D79—22no—
263C22×D79—22no—
264C22×D79C4×Q8116yes—
265C22×D79C23×C414yes—
266C22×D79C22×Q814yes—
267C22×D79C2×#4114yes—
268Q8×C79—416no—
269C2×C4×C79—28no—
270C2×C4×C79—28no—
271C2×C4×C79—28no—
272C2×C4×C79—28no—
273C2×C4×C79—28no—
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×C79C23×C414yes—
293C2×C4×C79C23×C414yes—
294C2×C4×C79C23×C414yes—
295C2×C4×C79C22×Q814yes—
296C2×C4×C79C2×#4114yes—
297C2×Dic79—28no—
298C2×Dic79—28no—
299C2×Dic79—28no—
300C2×Dic79—28no—
301C2×Dic79—28no—
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×Dic79C23×C414yes—
321C2×Dic79C23×C414yes—
322C2×Dic79C23×C414yes—
323C2×Dic79C22×Q814yes—
324C2×Dic79C2×#4114yes—
325C4×D79—416no—
326C4×D79—416no—
327C4×D79—416no—
328C22×C79C2×C4×Q814yes—
329C22×C79C4×#4114yes—
330C22×C79#51814yes—
331C22×C79#55114yes—
332C22×C79#55114yes—
333C22×C79#55414yes—
334C22×C79#55414yes—
335C22×C79C24×C411yescharacteristic
336C22×C79C23×Q811yescharacteristic
337C22×C79C22×#4111yescharacteristic
338C22×C79C22×#4111yescharacteristic
339C22×C79C22×#4111yescharacteristic
340C22×C79C2×H(5,𝔽2)11yescharacteristic
341C22×C79C2×H(5,𝔽2)11yescharacteristic
342C2×D79—232no—
343C2×D79—24no—
344C2×D79—24no—
345C2×D79—24no—
346C2×D79—24no—
347C2×D79—24no—
348C2×D79—24no—
349C2×D79C2×C4×Q818yes—
350C4×C79—24no—
351C4×C79—24no—
352C4×C79—24no—
353C4×C79—24no—
354C4×C79—24no—
355C4×C79—42no—
356C4×C79—42no—
357Dic79—24no—
358Dic79—24no—
359Dic79—24no—
360Dic79—24no—
361Dic79—24no—
362Dic79—42no—
363Dic79—42no—
364C2×#2368—791nomaximal, Sylow
365C2×C79#236818yescomplemented
366C2×C79C22×C4×Q811yescharacteristic
367C2×C79C2×C4×#4111yescharacteristic
368C2×C79C2×#51811yescharacteristic
369C2×C79C2×#55111yescharacteristic
370C2×C79C2×#55111yescharacteristic
371C2×C79C2×#55411yescharacteristic
372C2×C79C2×#55411yescharacteristic
373D79—28no—
374C22×C22⋊Q8—791no—
375#2368—7916no—
376C2×#391—791no—
377C2×#391D7911yescharacteristic, complemented
378C2×#387—791no—
379C2×#387—791no—
380C2×#387—791no—
381C2×#387—791no—
382C2×#385—791no—
383C2×#385—791no—
384C2×C4×C4⋊C4—791no—
385C2×C4×C4⋊C4—791no—
386C2×C4×C22⋊C4—791no—
387C2×C4×C22⋊C4—791no—
388C2×C4×C22⋊C4—791no—
389C22×#95—791no—
390C79C2×#236811yescharacteristic, complemented, Sylow
391C23×Q8C2×D7911yescharacteristic
392C24×C4—791no—
393C24×C4—791no—
394C24×C4—791no—
395C2×C22⋊Q8—798no—
396C2×C22⋊Q8—7916no—
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⋊C4C2×D7911yescharacteristic
404C22×C22⋊C4—791no—
405C22×C22⋊C4—791no—
406C22×C22⋊C4—791no—
407C22×C22⋊C4—791no—
408C22×C42—791no—
409C22×C42—791no—
410C22×C42—791no—
411C22×C42—791no—
412C22×C42—791no—
413C22×C42C2×D7911yescharacteristic
414#391—798no—
415#391C2×D7918yescomplemented
416#387—798no—
417#387—798no—
418#387—798no—
419#387—798no—
420#385—798no—
421#385—798no—
422C4×C4⋊C4—798no—
423C4×C4⋊C4—798no—
424C4×C22⋊C4—798no—
425C4×C22⋊C4—798no—
426C4×C22⋊C4—798no—
427C2×#95—791no—
428C2×#95—791no—
429C2×#95—791no—
430C2×#95—791no—
431C2×#95—791no—
432C2×#95—791no—
433C2×#95—791no—
434C2×#95—791no—
435C2×#95—791no—
436C2×#95—791no—
437C2×#95—798no—
438C2×#95C2×D7911yescharacteristic
439C2×#95C2×D7911yescharacteristic
440C2×#95C2×D7911yescharacteristic
441C2×#95C2×D7911yescharacteristic
442C25—791no—
443C22×Q8—42no—
444C22×Q8—42no—
445C22×Q8C4×D7918yescomplemented
446C22×Q8C22×D7914yes—
447C23×C4—3162no—
448C23×C4—3162no—
449C23×C4—3162no—
450C23×C4—3162no—
451C23×C4—798no—
452C23×C4—794no—
453C23×C4—794no—
454C23×C4—794no—
455C23×C4—791no—
456C23×C4—791no—
457C23×C4—791no—
458C23×C4—791no—
459C23×C4—791no—
460C23×C4—791no—
461C23×C4—791no—
462C23×C4—1584no—
463C23×C4—1584no—
464C23×C4—1584no—
465C23×C4—1584no—
466C23×C4C22×D7911yescharacteristic
467C23×C4C22×D7911yescharacteristic
468C23×C4C22×D7911yescharacteristic
469C23×C4C22×D7911yescharacteristic
470C23×C4C22×D7911yescharacteristic
471C23×C4C22×D7911yescharacteristic
472C23×C4C22×D7911yescharacteristic
473C22⋊Q8—7964no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—3162no—
476C2×C4⋊C4—794no—
477C2×C4⋊C4—798no—
478C2×C4⋊C4—798no—
479C2×C4⋊C4—798no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—794no—
482C2×C4⋊C4—794no—
483C2×C4⋊C4—794no—
484C2×C4⋊C4—794no—
485C2×C4⋊C4—1584no—
486C2×C4⋊C4—1584no—
487C2×C4⋊C4C22×D7914yes—
488C2×C22⋊C4—798no—
489C2×C22⋊C4—798no—
490C2×C22⋊C4—798no—
491C2×C22⋊C4—794no—
492C2×C22⋊C4—794no—
493C2×C22⋊C4—794no—
494C2×C22⋊C4—794no—
495C2×C22⋊C4—1584no—
496C2×C42—42no—
497C2×C42—3162no—
498C2×C42—3162no—
499C2×C42—3162no—
500C2×C42—794no—
501C2×C42—794no—
502C2×C42—794no—
503C2×C42—794no—
504C2×C42—794no—
505C2×C42—1584no—
506C2×C42—1584no—
507C2×C42C22×D7914yes—
508#95—794no—
509#95—794no—
510#95—794no—
511#95—794no—
512#95—794no—
513#95—794no—
514#95—794no—
515#95—794no—
516#95—794no—
517#95—794no—
518#95C22×D7914yes—
519#95C22×D7914yes—
520#95C22×D7914yes—
521#95C22×D7914yes—
522C24—794no—
523C24—794no—
524C24—792no—
525C24—794no—
526C24—1582no—
527C24—1582no—
528C24—1582no—
529C24—1582no—
530C24C23×D7911yescharacteristic
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—416no—
534C2×Q8C2×C4×D79116yescomplemented
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—31616no—
552C22×C4—3164no—
553C22×C4—3164no—
554C22×C4—3164no—
555C22×C4—31616no—
556C22×C4—3164no—
557C22×C4—31616no—
558C22×C4—7916no—
559C22×C4—794no—
560C22×C4—794no—
561C22×C4—792no—
562C22×C4—792no—
563C22×C4—792no—
564C22×C4—792no—
565C22×C4—792no—
566C22×C4—794no—
567C22×C4—794no—
568C22×C4—794no—
569C22×C4—792no—
570C22×C4—792no—
571C22×C4—1588no—
572C22×C4—1588no—
573C22×C4—1588no—
574C22×C4—1582no—
575C22×C4—1582no—
576C22×C4—1582no—
577C22×C4—1582no—
578C22×C4—1582no—
579C22×C4—1582no—
580C22×C4—1588no—
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×C4C2×C4×D7914yes—
592C22×C4C2×C4×D7914yes—
593C22×C4C2×C4×D7914yes—
594C22×C4Q8×D7914yes—
595C22×C4#1192962514yes—
596C22×C4C23×D7912yes—
597C22×C4C23×D7912yes—
598C22×C4C23×D7912yes—
599C22×C4C23×D7912yes—
600C22×C4C23×D7912yes—
601C22×C4C23×D7912yes—
602C22×C4C23×D7912yes—
603C4⋊C4—44no—
604C4⋊C4—3164no—
605C4⋊C4—7916no—
606C4⋊C4—7916no—
607C4⋊C4—7916no—
608C4⋊C4—1588no—
609C4⋊C4—1588no—
610C22⋊C4—7916no—
611C22⋊C4—7916no—
612C22⋊C4—7916no—
613C22⋊C4—1588no—
614C42—44no—
615C42—3164no—
616C42—3164no—
617C42—3164no—
618C42—1588no—
619C42—1588no—
620C23—7916no—
621C23—794no—
622C23—794no—
623C23—794no—
624C23—1582no—
625C23—1582no—
626C23—1588no—
627C23—1588no—
628C23—1588no—
629C23—1588no—
630C23—1588no—
631C23—1588no—
632C23—1582no—
633C23—1582no—
634C23C22×C4×D7912yes—
635C23C2×Q8×D7912yes—
636C23#41×D7912yes—
637C23#41×D7912yes—
638C23C2×#1192962512yes—
639C23#1457920612yes—
640C23#1457920612yes—
641C23C24×D7911yescharacteristic
642Q8—416no—
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—28no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—28no—
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—31616no—
667C2×C4—31616no—
668C2×C4—31616no—
669C2×C4—3164no—
670C2×C4—3164no—
671C2×C4—794no—
672C2×C4—794no—
673C2×C4—794no—
674C2×C4—794no—
675C2×C4—794no—
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—1588no—
687C2×C4—1588no—
688C2×C4—1588no—
689C2×C4—1588no—
690C2×C4—1588no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4C22×C4×D7914yes—
698C2×C4C22×C4×D7914yes—
699C2×C4C22×C4×D7914yes—
700C2×C4C2×Q8×D7914yes—
701C2×C4C2×#1192962514yes—
702C22—798no—
703C22—1584no—
704C22—1584no—
705C22—1584no—
706C22—1584no—
707C22—1584no—
708C22—1584no—
709C22—15832no—
710C22C4×Q8×D7914yes—
711C22C4×#1192962514yes—
712C22#1909903614yes—
713C22#1909924014yes—
714C22#1909924314yes—
715C22#1909926714yes—
716C22#1909927414yes—
717C22C23×C4×D7911yescharacteristic
718C22C22×Q8×D7911yescharacteristic
719C22C2×#41×D7911yescharacteristic
720C22C2×#41×D7911yescharacteristic
721C22C22×#1192962511yescharacteristic
722C22C2×#1457920611yescharacteristic
723C22C2×#1457920611yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—42no—
731C4—3162no—
732C4—3162no—
733C4—1584no—
734C4—1584no—
735C4—1584no—
736C4—1584no—
737C4—1584no—
738C2—1588no—
739C2#2376647918yesdirect product factor
740C2C2×C4×Q8×D7911yescharacteristic
741C2C2×C4×#1192962511yescharacteristic
742C2C2×#1909903611yescharacteristic
743C2C2×#1909924011yescharacteristic
744C2C2×#1909924311yescharacteristic
745C2C2×#1909926711yescharacteristic
746C2C2×#1909927411yescharacteristic
subgroupG/H
centerC24C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC2×#391×C79C2
socleC24×C79C24
prime radicalC24×D79C23
cosocleC23×C79C25
hypercenterC2×#391D79
hypocenterC79C2×#2368
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. #23766479C2direct (N × H)
3. C2×#19098470C2semidirect
4. C2×#19098450C2semidirect
5. C2×#19098448C2semidirect
6. C2×#19098446C2semidirect
7. C2×#19098444C2semidirect
10. C2×C4×Dic79⋊C4C2semidirect
11. C2×#19098414C2semidirect
16. C2×#391×C79C2semidirect
20. C2×#14579137C4semidirect
37. #19098470C22semidirect
38. #19098450C22semidirect
39. #19098448C22semidirect
40. #19098446C22semidirect
41. #19098444C22semidirect
44. C4×Dic79⋊C4C22semidirect
45. #19098414C22semidirect
63. #391×C79C22semidirect
88. #14579137C2×C4semidirect
90. C2×C4⋊Dic79C2×C4semidirect
95. C2×Dic79⋊C4C2×C4semidirect
96. C2×Dic79⋊C4C2×C4semidirect
104. C2×(C2×D79)⋊C4Q8semidirect
131. C22×Q8×C79C2×C4semidirect
197. C4⋊Dic79C22×C4semidirect
200. Dic79⋊C4C22×C4semidirect
201. Dic79⋊C4C22×C4semidirect
205. (C2×D79)⋊C4C2×Q8semidirect
215. C2×Q8×C79C22×C4semidirect
365. C2×C79#2368semidirect
377. C2×#391D79semidirect
390. C79C2×#2368semidirect
415. #391C2×D79semidirect
445. C22×Q8C4×D79semidirect
534. C2×Q8C2×C4×D79semidirect
739. C2#23766479direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791372
#237664792
C2×#190984702
C2×#190984502
C2×#190984482
C2×#190984462
C2×#190984442
C2×#190984372
C2×#190984342
C2×C4×Dic79⋊C42
C2×#190984142
C2×C4×(C2×D79)⋊C42
C2×#190984102
C2×#95×D792
C2×#391×C792
C2×#236879