Finite Group Databasebeta

← C2×#23774852 #35161224

Subgroups — C2×#23774852 #35161224

Order 20224.

1754 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099174C211yesmaximal, characteristic
2C2×#19099171C211yesmaximal, characteristic
3#23774852C2116yesmaximal, direct product factor
4C2×#19098872C211yesmaximal, characteristic, complemented
5C2×#19098871C211yesmaximal, characteristic, complemented
6C2×#19098870C211yesmaximal, characteristic, complemented
7C2×#19098868C211yesmaximal, characteristic, complemented
8C2×#19098820C211yesmaximal, characteristic
9C2×#19098818C211yesmaximal, characteristic
10C2×#19098803C211yesmaximal, characteristic
11C2×#19098801C211yesmaximal, characteristic
12C2×#19098771C211yesmaximal, characteristic, complemented
13C2×#19098771C211yesmaximal, characteristic, complemented
14C2×#19098770C211yesmaximal, characteristic, complemented
15C2×#19098588C211yesmaximal, characteristic
16C2×#462×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099174—24no—
22#19099174C2218yes—
23#19099171—24no—
24#19099171C2218yes—
25C2×#14579159C2211yescharacteristic
26C2×#14579156—21no—
27C2×#14579156—21no—
28C2×#14579156—21no—
29C2×#14579155—21no—
30C2×#14579153—21no—
31C2×#14579153C2211yescharacteristic
32C2×#14579152C2211yescharacteristic
33C2×#14579151—21no—
34C2×#14579151—21no—
35C2×#14579151—21no—
36C2×#14579141C2211yescharacteristic
37C2×#14579137C2211yescharacteristic
38C2×#14579137C2211yescharacteristic
39C2×#14579137C2211yescharacteristic
40C2×Q8×Dic79C2211yescharacteristic
41C2×Q8×Dic79C2211yescharacteristic
42C2×C4×Dic158C2211yescharacteristic
43C2×#14579118C2211yescharacteristic
44#19098872C2218yescomplemented
45#19098871C2218yescomplemented
46#19098870C2218yescomplemented
47#19098868C2218yescomplemented
48#19098820C2218yes—
49#19098818C2218yes—
50#19098803C2218yes—
51#19098801C2218yes—
52#19098771C2218yescomplemented
53#19098771C2218yescomplemented
54#19098770C2218yescomplemented
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59#19098588C2218yes—
60C2×C4⋊(C79⋊C8)C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×#14579085C2211yescharacteristic
67C2×#14579085C2211yescharacteristic
68C2×#14579085C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C2×C4⋊Q8×C79C2211yescharacteristic
72C2×C4×Q8×C79C2211yescharacteristic
73#462×C79C2218yescomplemented
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158C2311yescharacteristic
78C22×C4×D79C2311yescharacteristic
79C2×#11929614—42no—
80C2×#11929614—42no—
81C2×#11929614C2314yes—
82C2×#11929614C2314yes—
83C2×#11929607—42no—
84C2×#11929607C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87C2×C8×D79—42no—
88C2×C8×D79C2314yes—
89#14579159—22no—
90#14579159C2314yes—
91#14579156—28no—
92#14579156—28no—
93#14579156—28no—
94#14579155—28no—
95#14579153—22no—
96#14579153—28no—
97#14579153C2314yes—
98#14579152—22no—
99#14579152C2314yes—
100#14579151—28no—
101#14579151—28no—
102#14579151—28no—
103#14579141—22no—
104#14579141C2314yes—
105#14579137—22no—
106#14579137—22no—
107#14579137—22no—
108#14579137C2314yes—
109#14579137C2314yes—
110#14579137C2314yes—
111Q8×Dic79—22no—
112Q8×Dic79—22no—
113Q8×Dic79C2314yes—
114Q8×Dic79C2314yes—
115C4×Dic158—22no—
116C4×Dic158C2314yes—
117#14579118D414yes—
118#14579118C2314yes—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4D411yescharacteristic
136C2×Dic79⋊C4D411yescharacteristic
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4D411yescharacteristic
142C2×(C2×D79)⋊C4D411yescharacteristic
143C2×C4×Dic79—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79C2311yescharacteristic
147#14579095C2314yes—
148#14579094C2314yes—
149#14579093C2314yes—
150#14579092C2314yes—
151C4⋊(C79⋊C8)C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579085C2314yes—
157#14579085C2314yes—
158#14579085C2314yes—
159#14579085C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×Q8×C79C2311yescharacteristic
162C22×Q8×C79C2311yescharacteristic
163C2×Q16×C79—42no—
164C2×Q16×C79—42no—
165C2×Q16×C79C2314yes—
166C2×Q16×C79C2314yes—
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C4⋊Q8×C79—22no—
170C4⋊Q8×C79C2314yes—
171C4×Q8×C79—22no—
172C4×Q8×C79C2314yes—
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79—21no—
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C42×C79—21no—
178C2×C42×C79C2311yescharacteristic
179C4⋊C8×C79C2314yes—
180#103×C79C2314yes—
181#103×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C2×Dic158—21no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158C2412yes—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79C2×D411yescharacteristic
192C22×Dic79C2×D411yescharacteristic
193C22×Dic79C2×D411yescharacteristic
194C2×C4×D79—22no—
195C2×C4×D79—22no—
196C2×C4×D79C2×D412yes—
197C2×C4×D79C2412yes—
198#11929614—44no—
199#11929614—44no—
200#11929607—44no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C8×D79—44no—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4C2×D414yes—
226Dic79⋊C4C2×D414yes—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4C2×D414yes—
232(C2×D79)⋊C4C2×D414yes—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79C2×D412yes—
237C4×Dic79C2412yes—
238C2×Q8×C79—21no—
239C2×Q8×C79—21no—
240C2×Q8×C79—21no—
241C2×Q8×C79—22no—
242C2×Q8×C79—22no—
243C2×Q8×C79—22no—
244C2×Q8×C79—22no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79C2412yes—
248C2×Q8×C79C2412yes—
249C2×Q8×C79C2412yes—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2411yescharacteristic
257Q16×C79—44no—
258Q16×C79—44no—
259C2×C8×C79—22no—
260C2×C8×C79—22no—
261C2×C8×C79C2412yes—
262C2×C8×C79C2412yes—
263C4⋊C4×C79—24no—
264C4⋊C4×C79—24no—
265C4⋊C4×C79—24no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79C2412yes—
268C42×C79—24no—
269C42×C79C2×D412yes—
270C42×C79C2412yes—
271C23×C79C22×D411yescharacteristic
272C22×D79—22no—
273C22×D79—22no—
274C22×D79—22no—
275C22×D79C22×D412yes—
276Q8×C79—22no—
277Q8×C79—22no—
278Q8×C79—22no—
279Q8×C79—22no—
280Q8×C79—22no—
281Q8×C79—22no—
282Q8×C79—42no—
283Q8×C79—42no—
284Q8×C79—42no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D411yescharacteristic
298C2×C4×C79H(5,𝔽2)12yes—
299C2×C4×C792−1+412yes—
300C2×C4×C79C2511yescharacteristic
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—42no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79C22×D412yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315C4×D79—24no—
316C4×D79—22no—
317C4×D79—22no—
318Dic158—22no—
319Dic158—22no—
320Dic158—42no—
321C8×C79—22no—
322C8×C79—22no—
323C79⋊C8—22no—
324C79⋊C8—22no—
325C22×C79#53712yes—
326C22×C79#57812yes—
327C22×C79#57812yes—
328C22×C79C23×D411yescharacteristic
329C2×D79—22no—
330C2×D79—22no—
331C2×D79—22no—
332C2×D79—44no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—42no—
336C4×C79—42no—
337C4×C79—42no—
338C4×C79—42no—
339C4×C79#53712yes—
340C4×C79C2×H(5,𝔽2)11yescharacteristic
341C4×C79C2×2−1+411yescharacteristic
342Dic79—22no—
343Dic79—22no—
344Dic79—22no—
345Dic79—42no—
346Dic79—42no—
347Dic79—42no—
348Dic79—42no—
349C2×#3261—791nomaximal, Sylow
350C2×C79#326114yescomplemented
351C2×C79C2×#53711yescharacteristic
352C2×C79C2×#57811yescharacteristic
353C2×C79C2×#57811yescharacteristic
354D79—42no—
355C2×#541—791no—
356C2×#541—791no—
357#3261—7916no—
358C2×#479—791no—
359C2×#479—791no—
360C2×#479—791no—
361C2×#479—791no—
362C2×#470—791no—
363C2×#470—791no—
364C2×#467—791no—
365C2×#467—791no—
366C2×#462—791no—
367C2×#462—791no—
368C2×#462—791no—
369C2×#462D7911yescharacteristic, complemented
370C2×#424—791no—
371C79C2×#326111yescharacteristic, complemented, Sylow
372C22×Q16—791no—
373C22×Q16—791no—
374C22×Q16C2×D7911yescharacteristic
375C22×Q16C2×D7911yescharacteristic
376C22×M16—791no—
377C23×C8—791no—
378#541—798no—
379#541—798no—
380#541—1584no—
381#541—1584no—
382C2×C4⋊Q8—791no—
383C2×C4⋊Q8C2×D7911yescharacteristic
384C2×#126—1581no—
385C2×#126—1581no—
386C2×#126—1581no—
387C2×#126—1581no—
388C2×#125—791no—
389C2×#125—791no—
390C2×#125—1581no—
391C2×#125—1581no—
392C2×#125—1581no—
393C2×#125—1581no—
394C2×C22⋊Q8—791no—
395C2×C22⋊Q8—791no—
396C2×C22⋊Q8—791no—
397C2×C22⋊Q8—791no—
398C2×C4×Q8—791no—
399C2×C4×Q8—791no—
400C2×C4×Q8—791no—
401C2×C4×Q8C2×D7911yescharacteristic
402C2×#117—791no—
403#479—798no—
404#479—798no—
405#479—798no—
406#479—798no—
407#470—798no—
408#470—798no—
409#467—798no—
410#467—798no—
411#462—798no—
412#462—798no—
413#462—798no—
414#462C2×D7918yescomplemented
415C2×#107—791no—
416C2×#107—791no—
417C2×#106—791no—
418C2×#106—791no—
419#424—798no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8—791no—
422C2×C4⋊C8—791no—
423C2×C4⋊C8C2×D7911yescharacteristic
424C2×#103—791no—
425C2×#103—791no—
426C2×#103—791no—
427C2×#103—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103C2×D7911yescharacteristic
431C2×#103C2×D7911yescharacteristic
432C22×Q8—791no—
433C22×Q8C22×D7911yescharacteristic
434C22×Q8C22×D7911yescharacteristic
435C22×Q8C22×D7911yescharacteristic
436C23×C4—791no—
437C2×Q16—42no—
438C2×Q16—42no—
439C2×Q16—3162no—
440C2×Q16—3162no—
441C2×Q16—794no—
442C2×Q16—794no—
443C2×Q16C22×D7914yes—
444C2×Q16C22×D7914yes—
445C2×M16—3162no—
446C2×M16—794no—
447C22×C8—3162no—
448C22×C8—794no—
449C22×C8—791no—
450C22×C8—791no—
451C22×C8C22×D7911yescharacteristic
452C22×C8C22×D7911yescharacteristic
453C4⋊Q8—22no—
454C4⋊Q8—794no—
455C4⋊Q8—1582no—
456C4⋊Q8C22×D7914yes—
457#126—1588no—
458#126—1588no—
459#126—1588no—
460#126—1588no—
461#125—794no—
462#125—794no—
463#125—1588no—
464#125—1582no—
465#125—1588no—
466#125—1588no—
467#125—1588no—
468#125—1582no—
469C22⋊Q8—794no—
470C22⋊Q8—794no—
471C22⋊Q8—794no—
472C22⋊Q8—794no—
473C22⋊Q8—1582no—
474C22⋊Q8—1582no—
475C22⋊Q8—1582no—
476C22⋊Q8—1582no—
477C4×Q8—22no—
478C4×Q8—794no—
479C4×Q8—794no—
480C4×Q8—794no—
481C4×Q8—1582no—
482C4×Q8—1582no—
483C4×Q8—1582no—
484C4×Q8C22×D7914yes—
485#117—794no—
486#117—794no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—791no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—791no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C22⋊C4—791no—
510C2×C22⋊C4—791no—
511C2×C22⋊C4—1581no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C42—21no—
516C2×C42—791no—
517C2×C42—1581no—
518C2×C42—1581no—
519C2×C42—1581no—
520C2×C42C22×D7911yescharacteristic
521#107—794no—
522#107—794no—
523#106—794no—
524#106—794no—
525C4⋊C8—794no—
526C4⋊C8—794no—
527C4⋊C8—794no—
528C4⋊C8C22×D7914yes—
529#103—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103—794no—
534#103—794no—
535#103C22×D7914yes—
536#103C22×D7914yes—
537C24—791no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—792no—
548C2×Q8—1582no—
549C2×Q8—1582no—
550C2×Q8—1581no—
551C2×Q8C23×D7912yes—
552C2×Q8C23×D7912yes—
553C2×Q8C23×D7912yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—791no—
559C22×C4—791no—
560C22×C4—791no—
561C22×C4—792no—
562C22×C4—792no—
563C22×C4—1581no—
564C22×C4—1581no—
565C22×C4—1581no—
566C22×C4—1581no—
567C22×C4—1582no—
568C22×C4—1582no—
569C22×C4D4×D7911yescharacteristic
570C22×C4D4×D7911yescharacteristic
571C22×C4C23×D7911yescharacteristic
572Q16—44no—
573Q16—44no—
574Q16—3164no—
575Q16—3164no—
576M16—3164no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—3164no—
580C2×C8—792no—
581C2×C8—792no—
582C2×C8—1582no—
583C2×C8—1582no—
584C2×C8C23×D7912yes—
585C2×C8C23×D7912yes—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—794no—
591C4⋊C4—794no—
592C4⋊C4—792no—
593C4⋊C4—792no—
594C4⋊C4—792no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1584no—
601C4⋊C4—1584no—
602C4⋊C4—1584no—
603C4⋊C4—1584no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1581no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C4⋊C4C23×D7912yes—
612C22⋊C4—794no—
613C22⋊C4—794no—
614C22⋊C4—1584no—
615C22⋊C4—1584no—
616C22⋊C4—1584no—
617C22⋊C4—1584no—
618C42—24no—
619C42—792no—
620C42—792no—
621C42—1584no—
622C42—1584no—
623C42—1584no—
624C42D4×D7912yes—
625C42C23×D7912yes—
626C23—792no—
627C23—1582no—
628C23—1582no—
629C23—1582no—
630C23C2×D4×D7911yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—3162no—
641Q8—1582no—
642Q8—1582no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—3162no—
654C2×C4—3162no—
655C2×C4—3162no—
656C2×C4—3162no—
657C2×C4—792no—
658C2×C4—792no—
659C2×C4—792no—
660C2×C4—1582no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1582no—
667C2×C4—1582no—
668C2×C4—1582no—
669C2×C4—1584no—
670C2×C4C2×D4×D7912yes—
671C2×C4C2×D4×D7912yes—
672C2×C4C2×D4×D7911yescharacteristic
673C2×C4#1457920612yes—
674C2×C4#1457920812yes—
675C2×C4C24×D7911yescharacteristic
676C8—22no—
677C8—22no—
678C8—1582no—
679C8—1582no—
680C22—3164no—
681C22—1582no—
682C22—1582no—
683C22—1582no—
684C22#1909914212yes—
685C22#1909937612yes—
686C22#1909937912yes—
687C22C22×D4×D7911yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—3162no—
695C4—3162no—
696C4—3162no—
697C4—3162no—
698C4—1582no—
699C4—1582no—
700C4—1582no—
701C4#1909914212yes—
702C4C2×#1457920611yescharacteristic
703C4C2×#1457920811yescharacteristic
704C2—3162no—
705C2#2377485214yesdirect product factor
706C2C2×#1909914211yescharacteristic
707C2C2×#1909937611yescharacteristic
708C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#462×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#462D79
hypocenterC79C2×#3261
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #23774852C2direct (N × H)
4. C2×#19098872C2semidirect
5. C2×#19098871C2semidirect
6. C2×#19098870C2semidirect
7. C2×#19098868C2semidirect
12. C2×#19098771C2semidirect
13. C2×#19098771C2semidirect
14. C2×#19098770C2semidirect
16. C2×#462×C79C2semidirect
44. #19098872C22semidirect
45. #19098871C22semidirect
46. #19098870C22semidirect
47. #19098868C22semidirect
52. #19098771C22semidirect
53. #19098771C22semidirect
54. #19098770C22semidirect
73. #462×C79C22semidirect
350. C2×C79#3261semidirect
369. C2×#462D79semidirect
371. C79C2×#3261semidirect
414. #462C2×D79semidirect
705. C2#23774852direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991742
C2×#190991712
#237748522
C2×#190988722
C2×#190988712
C2×#190988702
C2×#190988682
C2×#190988202
C2×#190988182
C2×#190988032
C2×#190988012
C2×#190987712
C2×#190987702
C2×#190985882
C2×#462×C792
C2×#326179