Finite Group Databasebeta

← #34331990

Subgroups — #34331990

Order 20224.

958 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098901C211yesmaximal, characteristic, complemented
2C2×#19098572C211yesmaximal, characteristic, complemented
3#23766349C211yesmaximal, characteristic
4#23764943C211yesmaximal, characteristic, complemented
5#23764808C211yesmaximal, characteristic, complemented
6#23764600C211yesmaximal, characteristic, complemented
7#23764593C211yesmaximal, characteristic, complemented
8#23764038C211yesmaximal, characteristic, complemented
9#23764038C211yesmaximal, characteristic, complemented
10#23763713C211yesmaximal, characteristic, complemented
11#23763698C211yesmaximal, characteristic
12#23763597C211yesmaximal, characteristic, complemented
13#23763431C211yesmaximal, characteristic, complemented
14#23763335C211yesmaximal, characteristic, complemented
15C79×#2409C211yesmaximal, characteristic
16C22×#11929608C2211yescharacteristic
17C2×#14579120C2211yescharacteristic
18C2×#14579120C2211yescharacteristic
19#19098901—24no—
20C2×#14579094C2211yescharacteristic
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579092C2211yescharacteristic
24#19098572—24no—
25C2×#14579085C2211yescharacteristic
26C2×#14579085C2211yescharacteristic
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579085C2211yescharacteristic
31C2×#14579085C2211yescharacteristic
32C2×#14579085C2211yescharacteristic
33C2×C22⋊(C79⋊C8)C2211yescharacteristic
34C2×C22⋊(C79⋊C8)C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36#19098466—21no—
37#19098456—21no—
38#19098456—21no—
39#19098433C2211yescharacteristic
40#19098423C2211yescharacteristic
41#19098423C2211yescharacteristic
42C4⋊C4×Dic79—21no—
43C4×C4⋊Dic79C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098318C2211yescharacteristic
49#19098318C2211yescharacteristic
50C23×Q8×C79C2211yescharacteristic
51C2×C22⋊Q8×C79C2211yescharacteristic
52C2×C22⋊Q8×C79C2211yescharacteristic
53C2×C4×D4×C79C2211yescharacteristic
54#395×C79—21no—
55#393×C79—21no—
56#391×C79C2211yescharacteristic
57#391×C79C2211yescharacteristic
58#386×C79—21no—
59#385×C79—21no—
60#380×C79C2211yescharacteristic
61C2×#11929608—22no—
62C2×#11929608—22no—
63C2×#11929608—41no—
64C22×C79⋊C8C2311yescharacteristic
65C22×C79⋊C8C2311yescharacteristic
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68#14579120—22no—
69#14579120—22no—
70#14579120—41no—
71#14579120—41no—
72C2×C4⋊Dic79—21no—
73C2×C4⋊Dic79—21no—
74C2×C4⋊Dic79C2311yescharacteristic
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×C22⋊Dic79—21no—
79C2×C22⋊Dic79—21no—
80C2×C22⋊Dic79—21no—
81C2×C22⋊Dic79—21no—
82C2×C4×Dic79—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79—21no—
85#14579094—22no—
86#14579094—41no—
87#14579092—22no—
88#14579092—41no—
89#14579085—22no—
90#14579085—22no—
91#14579085—22no—
92#14579085—22no—
93#14579085—22no—
94#14579085—41no—
95#14579085—41no—
96#14579085D414yescomplemented
97C22⋊(C79⋊C8)—22no—
98C22⋊(C79⋊C8)—22no—
99C22⋊(C79⋊C8)—41no—
100C79⋊#95—21no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C22×Q8×C79—21no—
104C22×Q8×C79—22no—
105C22×Q8×C79—22no—
106C22×Q8×C79—22no—
107C22×Q8×C79—22no—
108C22×Q8×C79—41no—
109C22×Q8×C79—41no—
110C22×Q8×C79C2311yescharacteristic
111C22×Q8×C79C2311yescharacteristic
112C22×D4×C79D411yescharacteristic
113C23×C4×C79—21no—
114C23×C4×C79C2311yescharacteristic
115C23×C4×C79C2311yescharacteristic
116C22⋊Q8×C79—22no—
117C22⋊Q8×C79—22no—
118C22⋊Q8×C79—41no—
119C22⋊Q8×C79—41no—
120C4×D4×C79—22no—
121C4×D4×C79—22no—
122C2×C4⋊C4×C79—21no—
123C2×C4⋊C4×C79—21no—
124C2×C4⋊C4×C79D411yescharacteristic
125C2×C4⋊C4×C79C2311yescharacteristic
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C22⋊C4×C79—21no—
128C2×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79—21no—
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C22⋊C4×C79D411yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79—21no—
137#95×C79—21no—
138C22×Dic79—21no—
139C22×Dic79—21no—
140C22×Dic79—21no—
141C22×Dic79—21no—
142#11929608—44no—
143C2×C79⋊C8—21no—
144C2×C79⋊C8—21no—
145C2×C79⋊C8—21no—
146C2×C79⋊C8—21no—
147C2×C79⋊C8—21no—
148C2×C79⋊C8—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8C2×D412yes—
155C4⋊Dic79—21no—
156C4⋊Dic79—21no—
157C4⋊Dic79—21no—
158C4⋊Dic79—21no—
159C4⋊Dic79—21no—
160C4⋊Dic79—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—42no—
163C4⋊Dic79—81no—
164C4⋊Dic79C2×D412yes—
165C22⋊Dic79—42no—
166C22⋊Dic79—42no—
167C22⋊Dic79—81no—
168C22⋊Dic79—81no—
169C4×Dic79—42no—
170C4×Dic79—42no—
171C4×Dic79—42no—
172C24×C79C2×D411yescharacteristic
173C24×C79C2×D411yescharacteristic
174C2×Q8×C79—21no—
175C2×Q8×C79—21no—
176C2×Q8×C79—28no—
177C2×Q8×C79—21no—
178C2×Q8×C79—21no—
179C2×Q8×C79—21no—
180C2×Q8×C79—21no—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79—21no—
184C2×Q8×C79—21no—
185C2×Q8×C79—42no—
186C2×Q8×C79—42no—
187C2×Q8×C79—44no—
188C2×Q8×C79—44no—
189C2×Q8×C79—44no—
190C2×Q8×C79—42no—
191C2×Q8×C79C2×D412yes—
192C2×Q8×C79#4112yes—
193C2×D4×C79—22no—
194C2×D4×C79—22no—
195C2×D4×C79—41no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—21no—
210C22×C4×C79—42no—
211C22×C4×C79—42no—
212C22×C4×C79—42no—
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D411yescharacteristic
215C22×C4×C79C2×D411yescharacteristic
216C22×C4×C79C2×D411yescharacteristic
217C22×C4×C79#4112yes—
218C22×C4×C79#4112yes—
219C22×C4×C79C2411yescharacteristic
220C4⋊C4×C79—22no—
221C4⋊C4×C79—21no—
222C4⋊C4×C79—21no—
223C4⋊C4×C79—21no—
224C4⋊C4×C79—21no—
225C4⋊C4×C79—42no—
226C4⋊C4×C79—42no—
227C22⋊C4×C79—22no—
228C22⋊C4×C79—22no—
229C22⋊C4×C79—42no—
230C22⋊C4×C79—42no—
231C22⋊C4×C79—42no—
232C42×C79—21no—
233C42×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—21no—
238C23×C79—21no—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79—21no—
247C23×C79#12312yes—
248C23×C79C22×D411yescharacteristic
249Q8×C79—22no—
250Q8×C79—22no—
251Q8×C79—22no—
252Q8×C79—22no—
253Q8×C79—48no—
254Q8×C79—41no—
255Q8×C79—41no—
256Q8×C79—41no—
257Q8×C79—41no—
258D4×C79—44no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—21no—
268C2×C4×C79—21no—
269C2×C4×C79—21no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—48no—
276C2×C4×C79—41no—
277C2×C4×C79—41no—
278C2×C4×C79—41no—
279C2×C4×C79—41no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79—41no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79—41no—
289C2×C4×C79—41no—
290C2×C4×C79#12312yes—
291C2×C4×C79#13712yes—
292C2×C4×C79C22×D411yescharacteristic
293C2×C4×C79C2×#4111yescharacteristic
294C2×C4×C79C2×#4111yescharacteristic
295C2×C4×C79C2×#4111yescharacteristic
296C2×C4×C79H(5,𝔽2)11yescharacteristic
297C2×C4×C79H(5,𝔽2)11yescharacteristic
298C2×Dic79—22no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302C2×Dic79—41no—
303C2×Dic79—41no—
304C2×Dic79—41no—
305C2×Dic79—41no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310C79⋊C8—22no—
311C79⋊C8—41no—
312C79⋊C8—41no—
313C79⋊C8—41no—
314C22×C79—22no—
315C22×C79—22no—
316C22×C79—22no—
317C22×C79—41no—
318C22×C79—41no—
319C22×C79—41no—
320C22×C79—41no—
321C22×C79—41no—
322C22×C79—41no—
323C22×C79—41no—
324C22×C79—41no—
325C22×C79—41no—
326C22×C79—41no—
327C22×C79—41no—
328C22×C79C2×#12311yescharacteristic
329C22×C79D4211yescharacteristic
330C22×C79#54611yescharacteristic
331C22×C79C2×#13711yescharacteristic
332C22×C79#57511yescharacteristic
333C22×C79#57711yescharacteristic
334C22×C79#57811yescharacteristic
335C4×C79—22no—
336C4×C79—22no—
337C4×C79—41no—
338C4×C79—41no—
339C4×C79—42no—
340C4×C79—42no—
341C4×C79—81no—
342C4×C79—81no—
343C4×C79#52511yescharacteristic
344C4×C79#53811yescharacteristic
345C4×C79#54611yescharacteristic
346C4×C79#55111yescharacteristic
347Dic79—42no—
348Dic79—81no—
349Dic79—81no—
350Dic79—81no—
351#24892—791nomaximal, Sylow
352C2×C79—42no—
353C2×C79—81no—
354C2×C79#241811yescharacteristic
355C2×C79#309511yescharacteristic
356C2×C79#309711yescharacteristic
357C2×C79#326911yescharacteristic
358C2×C79#327811yescharacteristic
359C2×C79#332111yescharacteristic
360C2×C79#332811yescharacteristic
361C2×#485—791no—
362C2×#419—791no—
363#2409D7911yescharacteristic
364#2354—791no—
365#2096—791no—
366#2072—791no—
367#2036—791no—
368#2035—791no—
369#1928—791no—
370#1928—791no—
371#1873—791no—
372#1870—791no—
373#1854—791no—
374#1809—791no—
375#1787—791no—
376C79#2489211yescharacteristic, complemented, Sylow
377C23×Q8C2×D7911yescharacteristic
378C22×M16—791no—
379C2×C22⋊Q8C2×D7911yescharacteristic
380C2×C22⋊Q8C2×D7911yescharacteristic
381C2×C4×D4C2×D7911yescharacteristic
382C2×#117—791no—
383C2×#117—791no—
384#485—1584no—
385C2×#107—791no—
386C2×#107—791no—
387C2×#106—791no—
388C2×#106—791no—
389#419—1584no—
390C2×#103—791no—
391C2×#103—791no—
392C2×#103—791no—
393C2×#103—791no—
394C2×#103—791no—
395C2×#103—791no—
396C2×#103—791no—
397C2×#103—791no—
398C2×C22⋊C8—791no—
399C2×C22⋊C8—791no—
400C2×C22⋊C8—791no—
401#395—21no—
402#393—21no—
403#391C2×D7911yescharacteristic
404#391C2×D7911yescharacteristic
405#390—1581no—
406#388—1581no—
407#388—1581no—
408#386—21no—
409#385—21no—
410#384—791no—
411#380—791no—
412#380—791no—
413#380C2×D7911yescharacteristic
414C4×C4⋊C4—791no—
415C4×C4⋊C4—1581no—
416#340—791no—
417#340—791no—
418#340—791no—
419#340—791no—
420#336—791no—
421#336—791no—
422C22×Q8—21no—
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—41no—
428C22×Q8—41no—
429C22×Q8C22×D7911yescharacteristic
430C22×Q8C22×D7911yescharacteristic
431C22×D4C22⋊D7911yescharacteristic
432C23×C4—21no—
433C23×C4C22×D7911yescharacteristic
434C23×C4C22×D7911yescharacteristic
435C2×M16—3161no—
436C2×M16—1582no—
437C2×M16—1582no—
438C22×C8—791no—
439C22×C8—791no—
440C22×C8—791no—
441C22×C8—791no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—41no—
445C22⋊Q8—41no—
446C4×D4—22no—
447C4×D4—22no—
448#117—3161no—
449#117—3161no—
450#117—1582no—
451#117—1582no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—791no—
455C2×C4⋊C4—791no—
456C2×C4⋊C4—791no—
457C2×C4⋊C4—791no—
458C2×C4⋊C4—1581no—
459C2×C4⋊C4—1581no—
460C2×C4⋊C4C22⋊D7911yescharacteristic
461C2×C4⋊C4C22×D7911yescharacteristic
462C2×C4⋊C4C22×D7911yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1581no—
467C2×C22⋊C4—1581no—
468C2×C22⋊C4—1581no—
469C2×C22⋊C4—1581no—
470C2×C22⋊C4C22⋊D7911yescharacteristic
471C2×C22⋊C4C22⋊D7911yescharacteristic
472C2×C42—1581no—
473C2×C42—1581no—
474C2×C42—1581no—
475C2×C42C22×D7911yescharacteristic
476#107—3161no—
477#107—1582no—
478#106—3161no—
479#106—1582no—
480#103—3161no—
481#103—3161no—
482#103—794no—
483#103—1582no—
484#103—1582no—
485#103—1582no—
486#103—1582no—
487#103—1582no—
488C22⋊C8—3161no—
489C22⋊C8—1582no—
490C22⋊C8—1582no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—1581no—
497#95—1581no—
498#95—1581no—
499C24C2×C22⋊D7911yescharacteristic
500C24C2×C22⋊D7911yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—28no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—42no—
518C2×Q8D4×D7912yes—
519C2×Q8#1192962312yes—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—1581no—
541C22×C4—1581no—
542C22×C4—1581no—
543C22×C4—1581no—
544C22×C4C2×C22⋊D7911yescharacteristic
545C22×C4C2×C22⋊D7911yescharacteristic
546C22×C4C2×C22⋊D7911yescharacteristic
547C22×C4C2×C22⋊D7911yescharacteristic
548C22×C4#1192962312yes—
549C22×C4#1192962312yes—
550C22×C4C23×D7911yescharacteristic
551M16—3164no—
552C2×C8—792no—
553C2×C8—1581no—
554C2×C8—1581no—
555C2×C8—1581no—
556C2×C8—1581no—
557C2×C8—1581no—
558C2×C8—1581no—
559C2×C8—1581no—
560C2×C8—1581no—
561C2×C8—1581no—
562C2×C8—1581no—
563C2×C8—1581no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—3162no—
572C4⋊C4—792no—
573C4⋊C4—6321no—
574C4⋊C4—1581no—
575C4⋊C4—1581no—
576C4⋊C4—1581no—
577C4⋊C4—1581no—
578C4⋊C4—1581no—
579C4⋊C4—1581no—
580C4⋊C4—1581no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—3162no—
587C22⋊C4—3162no—
588C22⋊C4—6321no—
589C22⋊C4—6321no—
590C42—21no—
591C42—21no—
592C42—3162no—
593C42—3162no—
594C42—3162no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23#1457914212yes—
609C23C22×C22⋊D7911yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—48no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619D4—44no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—3161no—
652C2×C4—3161no—
653C2×C4—3161no—
654C2×C4—3161no—
655C2×C4—3161no—
656C2×C4—3161no—
657C2×C4—3161no—
658C2×C4—3161no—
659C2×C4—3161no—
660C2×C4—3161no—
661C2×C4—3161no—
662C2×C4—1582no—
663C2×C4#1457914212yes—
664C2×C4#1457919212yes—
665C2×C4C2×D4×D7911yescharacteristic
666C2×C4C2×#1192962311yescharacteristic
667C2×C4C2×#1192962311yescharacteristic
668C2×C4C2×#1192962311yescharacteristic
669C2×C4#1457920611yescharacteristic
670C2×C4#1457920611yescharacteristic
671C8—3161no—
672C8—3161no—
673C8—3161no—
674C8—1582no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22C2×#1457914211yescharacteristic
690C22D4×C22⋊D7911yescharacteristic
691C22#1909920711yescharacteristic
692C22C2×#1457919211yescharacteristic
693C22#1909936111yescharacteristic
694C22#1909937111yescharacteristic
695C22#1909937811yescharacteristic
696C4—22no—
697C4—22no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—81no—
703C4—81no—
704C4—3162no—
705C4—6321no—
706C4—6321no—
707C4—6321no—
708C4#1909906911yescharacteristic
709C4#1909914811yescharacteristic
710C4#1909920011yescharacteristic
711C4#1909924411yescharacteristic
712C2—42no—
713C2—81no—
714C2#2376685811yescharacteristic
715C2#2377334411yescharacteristic
716C2#2377336311yescharacteristic
717C2#2377495611yescharacteristic
718C2#2377506211yescharacteristic
719C2#2377558611yescharacteristic
720C2#2377568311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2409C2
socleC23×C79C22×D4
prime radicalC22×D4×C79D4
hypercenter#2409D79
hypocenterC79#24892
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C2×#19098901C2semidirect
2. C2×#19098572C2semidirect
4. #23764943C2semidirect
5. #23764808C2semidirect
6. #23764600C2semidirect
7. #23764593C2semidirect
8. #23764038C2semidirect
9. #23764038C2semidirect
10. #23763713C2semidirect
12. #23763597C2semidirect
13. #23763431C2semidirect
14. #23763335C2semidirect
96. #14579085D4semidirect
376. C79#24892semidirect

Maximal subgroups

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

subgroupindex
C2×#190989012
C2×#190985722
#237663492
#237649432
#237648082
#237646002
#237645932
#237640382
#237637132
#237636982
#237635972
#237634312
#237633352
C79×#24092
#2489279