Finite Group Databasebeta

← C2×#23767851 #34457792

Subgroups — C2×#23767851 #34457792

Order 20224.

2702 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579139C211yesmaximal, characteristic
2C22×#14579118C211yesmaximal, characteristic
3#23767851C2116yesmaximal, direct product factor
4C2×#19098492C211yesmaximal, characteristic
5C2×#19098492C211yesmaximal, characteristic
6C2×#19098490C211yesmaximal, characteristic
7C2×#19098489C211yesmaximal, characteristic
8C2×#19098467C211yesmaximal, characteristic, complemented
9C2×#19098467C211yesmaximal, characteristic, complemented
10C2×#19098448C211yesmaximal, characteristic, complemented
11C2×#19098447C211yesmaximal, characteristic, complemented
12C2×#19098444C211yesmaximal, characteristic, complemented
13C2×#19098432C211yesmaximal, characteristic, complemented
14C2×#19098427C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic
16C2×#387×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C2×#14579139—28no—
20C2×#14579139C2218yes—
21C2×#14579118—28no—
22C2×#14579118C2218yes—
23C22×C4⋊Dic79C2211yescharacteristic
24C22×Dic79⋊C4C2211yescharacteristic
25C22×Dic79⋊C4C2211yescharacteristic
26C22×Dic79⋊C4C2211yescharacteristic
27C22×Dic79⋊C4C2211yescharacteristic
28C22×Dic79⋊C4C2211yescharacteristic
29C22×Dic79⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×(C2×D79)⋊C4C2211yescharacteristic
32C22×(C2×D79)⋊C4C2211yescharacteristic
33C22×(C2×D79)⋊C4C2211yescharacteristic
34C22×(C2×D79)⋊C4C2211yescharacteristic
35C22×(C2×D79)⋊C4C2211yescharacteristic
36C22×C4×Dic79C2211yescharacteristic
37C22×C4×Dic79C2211yescharacteristic
38C22×C4×Dic79C2211yescharacteristic
39#19098492C2218yes—
40#19098492C2218yes—
41#19098490C2218yes—
42#19098489C2218yes—
43#19098467C2218yescomplemented
44#19098467C2218yescomplemented
45#19098448C2218yescomplemented
46#19098447C2218yescomplemented
47#19098444C2218yescomplemented
48#19098432C2218yescomplemented
49#19098427C2218yescomplemented
50#19098410C2218yes—
51C2×C79⋊#95C2211yescharacteristic
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×C42×C79C2211yescharacteristic
64#387×C79C2218yescomplemented
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C2×#95×C79C2211yescharacteristic
68C2×#95×C79C2211yescharacteristic
69C24×D79C2311yescharacteristic
70C22×Dic158—24no—
71C22×Dic158—24no—
72C22×Dic158—24no—
73C22×Dic158C2314yes—
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2311yescharacteristic
81C22×C4×D79—24no—
82C22×C4×D79—24no—
83C22×C4×D79D418yes—
84C22×C4×D79C2314yes—
85#14579139—232no—
86#14579118—232no—
87C2×C4⋊Dic79—24no—
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⋊C4C2314yes—
96C2×Dic79⋊C4C2314yes—
97C2×Dic79⋊C4C2314yes—
98C2×Dic79⋊C4C2314yes—
99C2×Dic79⋊C4C2314yes—
100C2×Dic79⋊C4C2314yes—
101C2×(C2×D79)⋊C4—24no—
102C2×(C2×D79)⋊C4—24no—
103C2×(C2×D79)⋊C4—24no—
104C2×(C2×D79)⋊C4—24no—
105C2×(C2×D79)⋊C4—24no—
106C2×(C2×D79)⋊C4—24no—
107C2×(C2×D79)⋊C4C2314yes—
108C2×(C2×D79)⋊C4C2314yes—
109C2×(C2×D79)⋊C4C2314yes—
110C2×(C2×D79)⋊C4C2314yes—
111C2×(C2×D79)⋊C4C2314yes—
112C2×(C2×D79)⋊C4C2314yes—
113C2×C4×Dic79—24no—
114C2×C4×Dic79—24no—
115C2×C4×Dic79—24no—
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—
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C23×C4×C79C2311yescharacteristic
136C2×C4⋊C4×C79—24no—
137C2×C4⋊C4×C79—24no—
138C2×C4⋊C4×C79C2314yes—
139C2×C4⋊C4×C79C2314yes—
140C2×C42×C79—24no—
141C2×C42×C79C2314yes—
142#95×C79C2314yes—
143#95×C79C2314yes—
144#95×C79C2314yes—
145#95×C79C2314yes—
146C23×D79—22no—
147C23×D79—22no—
148C23×D79—22no—
149C23×D79—22no—
150C23×D79—22no—
151C23×D79—22no—
152C23×D79C2×D414yes—
153C23×D79C2412yes—
154C2×Dic158—28no—
155C2×Dic158—28no—
156C2×Dic158—28no—
157C2×Dic158—416no—
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×Dic79#4114yes—
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×D4116yes—
190C4⋊Dic79—28no—
191Dic79⋊C4—28no—
192Dic79⋊C4—28no—
193Dic79⋊C4—28no—
194Dic79⋊C4—28no—
195Dic79⋊C4—28no—
196Dic79⋊C4—28no—
197(C2×D79)⋊C4—28no—
198(C2×D79)⋊C4—28no—
199(C2×D79)⋊C4—28no—
200(C2×D79)⋊C4—28no—
201(C2×D79)⋊C4—28no—
202(C2×D79)⋊C4—28no—
203C4×Dic79—28no—
204C4×Dic79—28no—
205C4×Dic79—28no—
206C24×C79C2411yescharacteristic
207C22×C4×C79—22no—
208C22×C4×C79—22no—
209C22×C4×C79—22no—
210C22×C4×C79—22no—
211C22×C4×C79—22no—
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×C79C2×D414yes—
227C22×C4×C79#4114yes—
228C22×C4×C79C2412yes—
229C22×C4×C79C2412yes—
230C22×C4×C79C2412yes—
231C22×C4×C79C2412yes—
232C22×C4×C79C2412yes—
233C22×C4×C79C2412yes—
234C22×C4×C79C2412yes—
235C4⋊C4×C79—28no—
236C4⋊C4×C79—28no—
237C42×C79—28no—
238C23×C79C22×D412yes—
239C23×C79C2×#4112yes—
240C23×C79C2×#4112yes—
241C23×C79C2×#4112yes—
242C23×C79C2×#4112yes—
243C23×C792−1+412yes—
244C23×C792−1+412yes—
245C23×C79C2511yescharacteristic
246C22×D79—28no—
247C22×D79—28no—
248C22×D79—28no—
249C22×D79—22no—
250C22×D79—22no—
251C22×D79—22no—
252C22×D79—22no—
253C22×D79—22no—
254C22×D79—22no—
255C22×D79—44no—
256C22×D79—44no—
257C22×D79—44no—
258C22×D79—44no—
259C22×D79C22×D414yes—
260C2×C4×C79—28no—
261C2×C4×C79—28no—
262C2×C4×C79—22no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
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—44no—
282C2×C4×C79—44no—
283C2×C4×C79—44no—
284C2×C4×C79—44no—
285C2×C4×C79—44no—
286C2×C4×C79C22×D414yes—
287C2×C4×C79C2×#4114yes—
288C2×Dic79—28no—
289C2×Dic79—22no—
290C2×Dic79—22no—
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
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—44no—
307C2×Dic79—44no—
308C2×Dic79—44no—
309C2×Dic79—44no—
310C2×Dic79—44no—
311C2×Dic79#123116yes—
312C2×Dic79C22×D414yes—
313C2×Dic79C2×#4114yes—
314C2×Dic79C2×#4114yes—
315C2×Dic79C2×#4114yes—
316C4×D79—232no—
317Dic158—416no—
318C22×C79C2×#12314yes—
319C22×C79#53214yes—
320C22×C79#53614yes—
321C22×C79#55214yes—
322C22×C79#55214yes—
323C22×C79#55614yes—
324C22×C79#55614yes—
325C22×C79C23×D411yescharacteristic
326C22×C79C22×#4111yescharacteristic
327C22×C79C22×#4111yescharacteristic
328C22×C79C22×#4111yescharacteristic
329C22×C79C22×#4111yescharacteristic
330C22×C79C2×2−1+411yescharacteristic
331C22×C79C2×2−1+411yescharacteristic
332C2×D79—24no—
333C2×D79—24no—
334C2×D79—24no—
335C2×D79—42no—
336C2×D79—42no—
337C2×D79—42no—
338C2×D79—42no—
339C2×D79—416no—
340C4×C79—24no—
341C4×C79—24no—
342C4×C79—42no—
343C4×C79—42no—
344C4×C79—42no—
345C4×C79—42no—
346C4×C79—42no—
347Dic79—24no—
348Dic79—42no—
349Dic79—42no—
350Dic79—42no—
351Dic79—42no—
352Dic79—42no—
353Dic79C2×#12318yes—
354C2×#2499—791nomaximal, Sylow
355C2×C79#249918yescomplemented
356C2×C79C22×#12311yescharacteristic
357C2×C79C2×#53211yescharacteristic
358C2×C79C2×#53611yescharacteristic
359C2×C79C2×#55211yescharacteristic
360C2×C79C2×#55211yescharacteristic
361C2×C79C2×#55611yescharacteristic
362C2×C79C2×#55611yescharacteristic
363D79—44no—
364C22×C22⋊Q8—791no—
365C22×#117—791no—
366#2499—7916no—
367C2×#397—791no—
368C2×#397—791no—
369C2×#397—791no—
370C2×#397—791no—
371C2×#391—791no—
372C2×#391—791no—
373C2×#387—791no—
374C2×#387—791no—
375C2×#387—791no—
376C2×#387D7911yescharacteristic, complemented
377C2×#384—791no—
378C2×#382—791no—
379C2×C4×C22⋊C4—791no—
380C79C2×#249911yescharacteristic, complemented, Sylow
381C23×Q8—791no—
382C24×C4—791no—
383C2×C22⋊Q8—798no—
384C2×C22⋊Q8—1588no—
385C2×#117—798no—
386C2×#117—1588no—
387C22×C4⋊C4—791no—
388C22×C4⋊C4—791no—
389C22×C4⋊C4—791no—
390C22×C4⋊C4—791no—
391C22×C4⋊C4—791no—
392C22×C4⋊C4—791no—
393C22×C4⋊C4—791no—
394C22×C4⋊C4C2×D7911yescharacteristic
395C22×C4⋊C4C2×D7911yescharacteristic
396C22×C22⋊C4—791no—
397C22×C22⋊C4—791no—
398C22×C22⋊C4—791no—
399C22×C22⋊C4—791no—
400C22×C22⋊C4—791no—
401C22×C22⋊C4—791no—
402C22×C42—791no—
403C22×C42—791no—
404C22×C42—791no—
405C22×C42C2×D7911yescharacteristic
406#397—798no—
407#397—798no—
408#397—798no—
409#397—798no—
410#391—798no—
411#391—798no—
412#387—798no—
413#387—798no—
414#387—798no—
415#387C2×D7918yescomplemented
416#384—798no—
417#382—798no—
418C4×C22⋊C4—798no—
419C2×#95—791no—
420C2×#95—791no—
421C2×#95—791no—
422C2×#95—791no—
423C2×#95—791no—
424C2×#95—791no—
425C2×#95—791no—
426C2×#95—791no—
427C2×#95—791no—
428C2×#95—791no—
429C2×#95C2×D7911yescharacteristic
430C2×#95C2×D7911yescharacteristic
431C2×#95C2×D7911yescharacteristic
432C2×#95C2×D7911yescharacteristic
433C25—791no—
434C22×Q8—794no—
435C22×Q8—1584no—
436C22×Q8—1584no—
437C22×Q8—1584no—
438C23×C4—791no—
439C23×C4—791no—
440C23×C4—798no—
441C23×C4—794no—
442C23×C4—791no—
443C23×C4—791no—
444C23×C4—791no—
445C23×C4—791no—
446C23×C4—791no—
447C23×C4—1584no—
448C23×C4—1584no—
449C23×C4C22×D7911yescharacteristic
450C23×C4C22×D7911yescharacteristic
451C23×C4C22×D7911yescharacteristic
452C23×C4C22×D7911yescharacteristic
453C23×C4C22×D7911yescharacteristic
454C23×C4C22×D7911yescharacteristic
455C23×C4C22×D7911yescharacteristic
456C22⋊Q8—15832no—
457#117—15832no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—794no—
461C2×C4⋊C4—794no—
462C2×C4⋊C4—794no—
463C2×C4⋊C4—794no—
464C2×C4⋊C4—794no—
465C2×C4⋊C4—794no—
466C2×C4⋊C4—794no—
467C2×C4⋊C4—1584no—
468C2×C4⋊C4—1584no—
469C2×C4⋊C4—1584no—
470C2×C4⋊C4—1584no—
471C2×C4⋊C4—1584no—
472C2×C4⋊C4—1584no—
473C2×C4⋊C4—1584no—
474C2×C4⋊C4C22×D7914yes—
475C2×C4⋊C4C22×D7914yes—
476C2×C22⋊C4—794no—
477C2×C22⋊C4—794no—
478C2×C22⋊C4—794no—
479C2×C22⋊C4—794no—
480C2×C22⋊C4—794no—
481C2×C22⋊C4—794no—
482C2×C22⋊C4—1584no—
483C2×C22⋊C4—1584no—
484C2×C22⋊C4—1584no—
485C2×C22⋊C4—1584no—
486C2×C22⋊C4—1584no—
487C2×C22⋊C4—1584no—
488C2×C42—24no—
489C2×C42—794no—
490C2×C42—794no—
491C2×C42—794no—
492C2×C42—1584no—
493C2×C42—1584no—
494C2×C42—1584no—
495C2×C42C22×D7914yes—
496#95—794no—
497#95—794no—
498#95—794no—
499#95—794no—
500#95—794no—
501#95—794no—
502#95—794no—
503#95—794no—
504#95—794no—
505#95—794no—
506#95C22×D7914yes—
507#95C22×D7914yes—
508#95C22×D7914yes—
509#95C22×D7914yes—
510C24—792no—
511C24—794no—
512C24—1582no—
513C24—1582no—
514C24—1582no—
515C24—1582no—
516C24—1582no—
517C24—1582no—
518C24C23×D7911yescharacteristic
519C2×Q8—31616no—
520C2×Q8—1588no—
521C2×Q8—1588no—
522C2×Q8—1588no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
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—794no—
543C22×C4—794no—
544C22×C4—792no—
545C22×C4—794no—
546C22×C4—794no—
547C22×C4—792no—
548C22×C4—7916no—
549C22×C4—792no—
550C22×C4—792no—
551C22×C4—792no—
552C22×C4—792no—
553C22×C4—792no—
554C22×C4—15832no—
555C22×C4—1588no—
556C22×C4—1588no—
557C22×C4—1582no—
558C22×C4—1582no—
559C22×C4—1582no—
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×C4D4×D7914yes—
575C22×C4#1192962414yes—
576C22×C4C23×D7912yes—
577C22×C4C23×D7912yes—
578C22×C4C23×D7912yes—
579C22×C4C23×D7912yes—
580C22×C4C23×D7912yes—
581C22×C4C23×D7912yes—
582C22×C4C23×D7912yes—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—1588no—
586C4⋊C4—1588no—
587C4⋊C4—1588no—
588C4⋊C4—1588no—
589C4⋊C4—1588no—
590C4⋊C4—1588no—
591C4⋊C4—1588no—
592C22⋊C4—1588no—
593C22⋊C4—1588no—
594C22⋊C4—1588no—
595C22⋊C4—1588no—
596C22⋊C4—1588no—
597C22⋊C4—1588no—
598C42—28no—
599C42—1588no—
600C42—1588no—
601C42—1588no—
602C23—3164no—
603C23—3164no—
604C23—3164no—
605C23—3164no—
606C23—794no—
607C23—1588no—
608C23—1582no—
609C23—1582no—
610C23—1588no—
611C23—1588no—
612C23—1582no—
613C23—1582no—
614C23—1582no—
615C23—1582no—
616C23C2×D4×D7912yes—
617C23#41×D7912yes—
618C23#41×D7912yes—
619C23#41×D7912yes—
620C23C2×#1192962412yes—
621C23#1457920812yes—
622C23#1457920912yes—
623C23C24×D7911yescharacteristic
624Q8—31616no—
625C2×C4—22no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—3164no—
652C2×C4—3164no—
653C2×C4—3164no—
654C2×C4—3164no—
655C2×C4—3164no—
656C2×C4—7916no—
657C2×C4—794no—
658C2×C4—794no—
659C2×C4—794no—
660C2×C4—794no—
661C2×C4—15832no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1582no—
667C2×C4—1582no—
668C2×C4—1582no—
669C2×C4—1582no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1582no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1588no—
679C2×C4—1582no—
680C2×C4C2×D4×D7914yes—
681C2×C4C2×#1192962414yes—
682C22—31616no—
683C22—3162no—
684C22—3162no—
685C22—3162no—
686C22—3162no—
687C22—1584no—
688C22—1584no—
689C22—1584no—
690C22#123×D7914yes—
691C22#1909911014yes—
692C22#1909913614yes—
693C22#1909924514yes—
694C22#1909924614yes—
695C22#1909928014yes—
696C22#1909928514yes—
697C22C22×D4×D7911yescharacteristic
698C22C2×#41×D7911yescharacteristic
699C22C2×#41×D7911yescharacteristic
700C22C2×#41×D7911yescharacteristic
701C22C22×#1192962411yescharacteristic
702C22C2×#1457920811yescharacteristic
703C22C2×#1457920911yescharacteristic
704C4—24no—
705C4—24no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—3162no—
712C4—3162no—
713C4—3162no—
714C4—3162no—
715C4—3162no—
716C4—798no—
717C4—1584no—
718C2—3164no—
719C2#2376785118yesdirect product factor
720C2C2×#123×D7911yescharacteristic
721C2C2×#1909911011yescharacteristic
722C2C2×#1909913611yescharacteristic
723C2C2×#1909924511yescharacteristic
724C2C2×#1909924611yescharacteristic
725C2C2×#1909928011yescharacteristic
726C2C2×#1909928511yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#387×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#387D79
hypocenterC79C2×#2499
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #23767851C2direct (N × H)
8. C2×#19098467C2semidirect
9. C2×#19098467C2semidirect
10. C2×#19098448C2semidirect
11. C2×#19098447C2semidirect
12. C2×#19098444C2semidirect
13. C2×#19098432C2semidirect
14. C2×#19098427C2semidirect
16. C2×#387×C79C2semidirect
43. #19098467C22semidirect
44. #19098467C22semidirect
45. #19098448C22semidirect
46. #19098447C22semidirect
47. #19098444C22semidirect
48. #19098432C22semidirect
49. #19098427C22semidirect
64. #387×C79C22semidirect
355. C2×C79#2499semidirect
376. C2×#387D79semidirect
380. C79C2×#2499semidirect
415. #387C2×D79semidirect
719. C2#23767851direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791392
C22×#145791182
#237678512
C2×#190984922
C2×#190984902
C2×#190984892
C2×#190984672
C2×#190984482
C2×#190984472
C2×#190984442
C2×#190984322
C2×#190984272
C2×#190984102
C2×#387×C792
C2×#249979