Finite Group Databasebeta

← C2×#23776227 #35168034

Subgroups — C2×#23776227 #35168034

Order 20224.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099286C211yesmaximal, characteristic, complemented
2#23776227C2116yesmaximal, direct product factor
3C2×#19098933C211yesmaximal, characteristic, complemented
4C2×#19098925C211yesmaximal, characteristic, complemented
5C2×#19098920C211yesmaximal, characteristic, complemented
6C2×#19098867C211yesmaximal, characteristic, complemented
7C2×#19098845C211yesmaximal, characteristic, complemented
8C2×#19098860C211yesmaximal, characteristic, complemented
9C2×#19098778C211yesmaximal, characteristic
10C2×#19098778C211yesmaximal, characteristic
11C2×#19098768C211yesmaximal, characteristic, complemented
12C2×#19098694C211yesmaximal, characteristic, complemented
13C2×#19098673C211yesmaximal, characteristic
14C2×#19098663C211yesmaximal, characteristic, complemented
15C2×C4×#11929612C211yesmaximal, characteristic, complemented
16C2×#554×C79C211yesmaximal, characteristic, complemented
17C22×#11929612C2211yescharacteristic
18C22×#11929612C2211yescharacteristic
19C22×#11929609C2211yescharacteristic
20#19099286—24no—
21#19099286C2218yescomplemented
22C2×#14579161C2211yescharacteristic
23C2×#14579156—21no—
24C2×#14579156—21no—
25C2×#14579149C2211yescharacteristic
26C2×#14579149C2211yescharacteristic
27C2×#14579137—21no—
28C2×C4×Dic158C2211yescharacteristic
29C2×C4×Dic158C2211yescharacteristic
30C2×C4×D316C2211yescharacteristic
31C2×#14579119—21no—
32#19098933C2218yescomplemented
33#19098925C2218yescomplemented
34#19098920C2218yescomplemented
35#19098867C2218yescomplemented
36#19098860C2218yescomplemented
37#19098845C2218yescomplemented
38#19098778C2218yes—
39#19098778C2218yes—
40#19098768C2218yescomplemented
41#19098694C2218yescomplemented
42#19098673C2218yes—
43#19098663C2218yescomplemented
44C4×#11929612C2218yescomplemented
45C2×#14579094C2211yescharacteristic
46C2×#14579092C2211yescharacteristic
47C2×#14579092C2211yescharacteristic
48C2×C4⋊(C79⋊C8)C2211yescharacteristic
49C2×C4⋊(C79⋊C8)C2211yescharacteristic
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×#14579084C2211yescharacteristic
52C2×#14579084C2211yescharacteristic
53C2×#14579084C2211yescharacteristic
54C2×#14579084C2211yescharacteristic
55C2×#14579084C2211yescharacteristic
56C2×#14579084C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×#14579081C2211yescharacteristic
61C2×#14579072C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#554×C79—24no—
65#554×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#125×C79C2211yescharacteristic
68C2×#125×C79C2211yescharacteristic
69C2×C22⋊Q8×C79—21no—
70C2×C22⋊Q8×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C4×Q8×C79C2211yescharacteristic
73C2×C4×D4×C79C2211yescharacteristic
74C2×C4×D4×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C22×C4⋊C4×C79—21no—
77C22×Dic158C2311yescharacteristic
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C4×D79—21no—
81C2×#11929612—24no—
82C2×#11929612—24no—
83C2×#11929612C2314yes—
84C2×#11929612C2314yes—
85C2×#11929609—24no—
86C2×#11929609C2314yes—
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91#14579161—22no—
92#14579161C2314yes—
93#14579156—28no—
94#14579156—28no—
95#14579149—22no—
96#14579149—22no—
97#14579149C2314yes—
98#14579149C2314yes—
99#14579137—28no—
100C4×Dic158—22no—
101C4×Dic158—22no—
102C4×Dic158C2314yes—
103C4×Dic158C2314yes—
104C4×D316—22no—
105C4×D316C2314yes—
106#14579119—28no—
107C2×C4⋊Dic79—21no—
108C2×C4⋊Dic79—21no—
109C2×C4⋊Dic79C2311yescharacteristic
110C2×Dic79⋊C4—21no—
111C2×Dic79⋊C4—21no—
112C2×(C2×D79)⋊C4—21no—
113C2×(C2×D79)⋊C4—21no—
114C2×(C2×D79)⋊C4—21no—
115C2×(C2×D79)⋊C4—21no—
116C2×(C2×D79)⋊C4—21no—
117C2×C4×Dic79—21no—
118C2×C4×Dic79—21no—
119#14579094C2314yes—
120#14579092C2314yes—
121#14579092C2314yes—
122C4⋊(C79⋊C8)C2314yes—
123C4⋊(C79⋊C8)C2314yes—
124C4⋊(C79⋊C8)C2314yes—
125#14579084C2314yes—
126#14579084C2314yes—
127#14579084C2314yes—
128#14579084C2314yes—
129#14579084C2314yes—
130#14579084C2314yes—
131#14579082C2314yes—
132#14579081C2314yes—
133#14579081C2314yes—
134#14579081C2314yes—
135#14579072C2314yes—
136#14579072C2314yes—
137C4×C79⋊C8C2314yes—
138C22×Q8×C79—21no—
139C22×Q8×C79D411yescharacteristic
140C22×D4×C79C2311yescharacteristic
141C23×C4×C79—21no—
142C23×C4×C79—21no—
143C23×C4×C79—21no—
144C4⋊Q8×C79—22no—
145C4⋊Q8×C79C2314yes—
146#125×C79—22no—
147#125×C79—22no—
148#125×C79C2314yes—
149#125×C79C2314yes—
150C22⋊Q8×C79—28no—
151C22⋊Q8×C79—28no—
152C22⋊Q8×C79—28no—
153C4×Q8×C79D414yes—
154C4×Q8×C79C2314yes—
155C4×D4×C79—22no—
156C4×D4×C79—22no—
157C4×D4×C79—22no—
158C4×D4×C79C2314yes—
159C4×D4×C79C2314yes—
160C4×D4×C79C2314yes—
161C2×C4⋊C4×C79—21no—
162C2×C4⋊C4×C79—21no—
163C2×C4⋊C4×C79—21no—
164C2×C4⋊C4×C79—21no—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—28no—
167C2×C4⋊C4×C79D411yescharacteristic
168C2×C4⋊C4×C79D411yescharacteristic
169C2×C4⋊C4×C79D411yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C42×C79C2311yescharacteristic
177C2×C42×C79C2311yescharacteristic
178C2×C42×C79C2311yescharacteristic
179C23×D79—21no—
180C2×Dic158—21no—
181C2×Dic158—21no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158C2412yes—
187C2×Dic158C2412yes—
188C2×D316—21no—
189C2×D316—22no—
190C2×D316—22no—
191C2×D316C2412yes—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C2×C4×D79—24no—
196C2×C4×D79—44no—
197#11929612—28no—
198#11929612—28no—
199#11929609—28no—
200C2×C79⋊C8—22no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8—22no—
204C2×C79⋊C8C2412yes—
205C2×C79⋊C8C2412yes—
206C2×C79⋊C8C2412yes—
207C2×C79⋊C8C2412yes—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79C2412yes—
212Dic79⋊C4—24no—
213Dic79⋊C4—24no—
214(C2×D79)⋊C4—24no—
215(C2×D79)⋊C4—24no—
216(C2×D79)⋊C4—24no—
217(C2×D79)⋊C4—24no—
218(C2×D79)⋊C4—24no—
219C4×Dic79—24no—
220C4×Dic79—24no—
221C24×C79—21no—
222C2×Q8×C79—24no—
223C2×Q8×C79—42no—
224C2×Q8×C79—82no—
225C2×Q8×C79C2×D414yes—
226C2×D4×C79—21no—
227C2×D4×C79—22no—
228C2×D4×C79#4114yes—
229C2×D4×C79C2412yes—
230C22×C4×C79—21no—
231C22×C4×C79—21no—
232C22×C4×C79—21no—
233C22×C4×C79—24no—
234C22×C4×C79—24no—
235C22×C4×C79—24no—
236C22×C4×C79—44no—
237C22×C4×C79—82no—
238C22×C4×C79—82no—
239C22×C4×C79C2×D411yescharacteristic
240C22×C4×C79C2×D411yescharacteristic
241C22×C4×C79C2×D411yescharacteristic
242C22×C4×C79C2×D411yescharacteristic
243C22×C4×C79C2×D411yescharacteristic
244C22×C4×C79C2×D411yescharacteristic
245C22×C4×C79C2411yescharacteristic
246C4⋊C4×C79—24no—
247C4⋊C4×C79—24no—
248C4⋊C4×C79—24no—
249C4⋊C4×C79—24no—
250C4⋊C4×C79—24no—
251C4⋊C4×C79—21no—
252C4⋊C4×C79—21no—
253C4⋊C4×C79—21no—
254C4⋊C4×C79C2×D414yes—
255C4⋊C4×C79C2×D414yes—
256C4⋊C4×C79C2×D414yes—
257C4⋊C4×C79C2412yes—
258C4⋊C4×C79C2412yes—
259C4⋊C4×C79C2412yes—
260C22⋊C4×C79—24no—
261C22⋊C4×C79—24no—
262C22⋊C4×C79—24no—
263C42×C79C2×D412yes—
264C42×C79C2×D412yes—
265C42×C79C2×D412yes—
266C42×C79C2412yes—
267C42×C79C2412yes—
268C42×C79C2412yes—
269C23×C79—24no—
270C23×C79—22no—
271C23×C79—42no—
272C23×C79—42no—
273C23×C79C22×D411yescharacteristic
274C22×D79—22no—
275C22×D79—42no—
276C22×D79—42no—
277C22×D79—42no—
278Q8×C79—44no—
279Q8×C79—84no—
280D4×C79—24no—
281D4×C79—22no—
282D4×C79C2×#4114yes—
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—22no—
291C2×C4×C79—22no—
292C2×C4×C79—48no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79—42no—
296C2×C4×C79—84no—
297C2×C4×C79—84no—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D412yes—
301C2×C4×C79C22×D412yes—
302C2×C4×C79C22×D412yes—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D411yescharacteristic
305C2×C4×C79C2×#4112yes—
306C2×C4×C792−1+412yes—
307C2×C4×C79C2511yescharacteristic
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—42no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314D316—22no—
315D316—22no—
316D316—42no—
317C4×D79—48no—
318Dic158—22no—
319Dic158—22no—
320Dic158—22no—
321Dic158—22no—
322Dic158—42no—
323Dic158—42no—
324C79⋊C8—22no—
325C79⋊C8—22no—
326C79⋊C8—22no—
327C79⋊C8—22no—
328C22×C79—24no—
329C22×C79—48no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79#54812yes—
333C22×C79#57512yes—
334C22×C79#57712yes—
335C22×C79C23×D411yescharacteristic
336C2×D79—42no—
337C2×D79—42no—
338C2×D79—42no—
339C2×D79—84no—
340C4×C79—22no—
341C4×C79—22no—
342C4×C79—22no—
343C4×C79—22no—
344C4×C79—22no—
345C4×C79—22no—
346C4×C79—42no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79#54812yes—
350C4×C79C22×#4111yescharacteristic
351C4×C79C2×2−1+411yescharacteristic
352Dic79—42no—
353Dic79—42no—
354Dic79—42no—
355C2×#3376—791nomaximal, Sylow
356C2×C79—44no—
357C2×C79#337614yescomplemented
358C2×C79C2×#54811yescharacteristic
359C2×C79C2×#57511yescharacteristic
360C2×C79C2×#57711yescharacteristic
361D79—82no—
362C2×#556—791no—
363C2×#554D7911yescharacteristic, complemented
364#3376—7916no—
365C2×#491—791no—
366C2×#489—791no—
367C2×#488—791no—
368C2×#479—791no—
369C2×#475—791no—
370C2×#478—791no—
371C2×#463—791no—
372C2×#463—791no—
373C2×#461—791no—
374C2×#446—791no—
375C2×#442—791no—
376C2×#440—791no—
377C2×C4×SD16—791no—
378C79C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16—791no—
380C22×SD16—791no—
381C22×D8—791no—
382#556—798no—
383#556—1584no—
384#554—24no—
385#554C2×D7918yescomplemented
386C2×C4⋊Q8—791no—
387C2×C4⋊Q8C2×D7911yescharacteristic
388C2×#126—1581no—
389C2×#126—1581no—
390C2×#125C2×D7911yescharacteristic
391C2×#125C2×D7911yescharacteristic
392C2×#124—791no—
393C2×#124—791no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8—21no—
397C2×C22⋊Q8—1581no—
398C2×C4×Q8—791no—
399C2×C4×Q8—791no—
400C2×C4×Q8C2×D7911yescharacteristic
401C2×C4×D4—791no—
402C2×C4×D4C2×D7911yescharacteristic
403C2×C4×D4C2×D7911yescharacteristic
404C2×C4×D4C2×D7911yescharacteristic
405C2×#117—1581no—
406C22×C4⋊C4—21no—
407#491—798no—
408#489—798no—
409#488—798no—
410#479—798no—
411#478—798no—
412#475—798no—
413#463—798no—
414#463—798no—
415#461—798no—
416#446—798no—
417#442—798no—
418#440—798no—
419C4×SD16—798no—
420C2×#107—791no—
421C2×#106—791no—
422C2×#106—791no—
423C2×C4⋊C8—791no—
424C2×C4⋊C8—791no—
425C2×C4⋊C8—791no—
426C2×#103—791no—
427C2×#103—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103—791no—
431C2×#103—791no—
432C2×#102—791no—
433C2×#102—791no—
434C2×#102—791no—
435C2×#102—791no—
436C2×#97—791no—
437C2×#97—791no—
438C2×C4×C8—791no—
439C22×Q8—21no—
440C22×Q8—791no—
441C22×Q8—791no—
442C22×Q8C22⋊D7911yescharacteristic
443C22×D4—791no—
444C22×D4C22×D7911yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—1581no—
449C2×SD16—794no—
450C2×SD16—794no—
451C2×SD16—1584no—
452C2×SD16—1584no—
453C2×D8—794no—
454C2×D8—1584no—
455C22×C8—791no—
456C22×C8—791no—
457C22×C8—791no—
458C22×C8—791no—
459C4⋊Q8—22no—
460C4⋊Q8—794no—
461C4⋊Q8—1582no—
462C4⋊Q8C22×D7914yes—
463#126—1588no—
464#126—1588no—
465#125—22no—
466#125—22no—
467#125C22×D7914yes—
468#125C22×D7914yes—
469#124—794no—
470#124—794no—
471#124—1582no—
472#124—1582no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—1588no—
477C4×Q8—794no—
478C4×Q8—794no—
479C4×Q8—1582no—
480C4×Q8—1582no—
481C4×Q8C22⋊D7914yes—
482C4×Q8C22×D7914yes—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—794no—
487C4×D4—1582no—
488C4×D4C22×D7914yes—
489C4×D4C22×D7914yes—
490C4×D4C22×D7914yes—
491#117—1588no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4C22⋊D7911yescharacteristic
504C2×C4⋊C4C22⋊D7911yescharacteristic
505C2×C4⋊C4C22⋊D7911yescharacteristic
506C2×C4⋊C4C22×D7911yescharacteristic
507C2×C4⋊C4C22×D7911yescharacteristic
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C22⋊C4—1581no—
516C2×C22⋊C4—1581no—
517C2×C42—1581no—
518C2×C42—1581no—
519C2×C42C22×D7911yescharacteristic
520C2×C42C22×D7911yescharacteristic
521C2×C42C22×D7911yescharacteristic
522#107—794no—
523#106—794no—
524#106—794no—
525C4⋊C8—794no—
526C4⋊C8—794no—
527C4⋊C8—794no—
528#103—794no—
529#103—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103—794no—
534#102—794no—
535#102—794no—
536#102—794no—
537#102—794no—
538#97—794no—
539#97—794no—
540C4×C8—794no—
541C24—21no—
542C24—1581no—
543C2×Q8—24no—
544C2×Q8—42no—
545C2×Q8—82no—
546C2×Q8—792no—
547C2×Q8—792no—
548C2×Q8—1582no—
549C2×Q8—1582no—
550C2×Q8—1582no—
551C2×Q8—1582no—
552C2×Q8—1581no—
553C2×Q8—1581no—
554C2×Q8C2×C22⋊D7914yes—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—792no—
558C2×D4—1582no—
559C2×D4—1582no—
560C2×D4—1581no—
561C2×D4#1192962514yes—
562C2×D4C23×D7912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—44no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—3164no—
573C22×C4—1581no—
574C22×C4—1581no—
575C22×C4—1581no—
576C22×C4—1584no—
577C22×C4C2×C22⋊D7911yescharacteristic
578C22×C4C2×C22⋊D7911yescharacteristic
579C22×C4C2×C22⋊D7911yescharacteristic
580C22×C4C2×C22⋊D7911yescharacteristic
581C22×C4C2×C22⋊D7911yescharacteristic
582C22×C4C2×C22⋊D7911yescharacteristic
583C22×C4C23×D7911yescharacteristic
584SD16—1588no—
585SD16—1588no—
586D8—1588no—
587C2×C8—792no—
588C2×C8—792no—
589C2×C8—792no—
590C2×C8—792no—
591C2×C8—1582no—
592C2×C8—1582no—
593C2×C8—1582no—
594C2×C8—1582no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—792no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1581no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4C2×C22⋊D7914yes—
610C4⋊C4C2×C22⋊D7914yes—
611C4⋊C4C2×C22⋊D7914yes—
612C4⋊C4C23×D7912yes—
613C4⋊C4C23×D7912yes—
614C4⋊C4C23×D7912yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C22⋊C4—1584no—
623C42—1584no—
624C42—1584no—
625C42C2×C22⋊D7912yes—
626C42C2×C22⋊D7912yes—
627C42C2×C22⋊D7912yes—
628C42C23×D7912yes—
629C42C23×D7912yes—
630C42C23×D7912yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—3162no—
636C23—3162no—
637C23—3162no—
638C23—1582no—
639C23C22×C22⋊D7911yescharacteristic
640Q8—44no—
641Q8—84no—
642Q8—3162no—
643Q8—3162no—
644Q8—1582no—
645Q8—1582no—
646Q8—1582no—
647Q8—1582no—
648D4—22no—
649D4—24no—
650D4—3162no—
651D4—1582no—
652D4—1582no—
653D4C2×#1192962514yes—
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—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—3168no—
670C2×C4—3162no—
671C2×C4—3162no—
672C2×C4—3162no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4C22×C22⋊D7912yes—
677C2×C4C22×C22⋊D7912yes—
678C2×C4C22×C22⋊D7912yes—
679C2×C4C22×C22⋊D7912yes—
680C2×C4C22×C22⋊D7912yes—
681C2×C4C22×C22⋊D7912yes—
682C2×C4C22×C22⋊D7911yescharacteristic
683C2×C4C2×#1192962512yes—
684C2×C4#1457920912yes—
685C2×C4C24×D7911yescharacteristic
686C8—1582no—
687C8—1582no—
688C8—1582no—
689C8—1582no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—3162no—
695C22—3162no—
696C22—3162no—
697C22—6324no—
698C22#1909922412yes—
699C22#1909936112yes—
700C22#1909937412yes—
701C22C23×C22⋊D7911yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—3162no—
712C4—3162no—
713C4—3162no—
714C4#1909922412yes—
715C4C22×#1192962511yescharacteristic
716C4C2×#1457920911yescharacteristic
717C2—44no—
718C2—6322no—
719C2#2377622714yesdirect product factor
720C2C2×#1909922411yescharacteristic
721C2C2×#1909936111yescharacteristic
722C2C2×#1909937411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#554×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#554D79
hypocenterC79C2×#3376
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#19099286C2semidirect
2. #23776227C2direct (N × H)
3. C2×#19098933C2semidirect
4. C2×#19098925C2semidirect
5. C2×#19098920C2semidirect
6. C2×#19098867C2semidirect
7. C2×#19098845C2semidirect
8. C2×#19098860C2semidirect
11. C2×#19098768C2semidirect
12. C2×#19098694C2semidirect
14. C2×#19098663C2semidirect
15. C2×C4×#11929612C2semidirect
16. C2×#554×C79C2semidirect
21. #19099286C22semidirect
32. #19098933C22semidirect
33. #19098925C22semidirect
34. #19098920C22semidirect
35. #19098867C22semidirect
36. #19098860C22semidirect
37. #19098845C22semidirect
40. #19098768C22semidirect
41. #19098694C22semidirect
43. #19098663C22semidirect
44. C4×#11929612C22semidirect
65. #554×C79C22semidirect
357. C2×C79#3376semidirect
363. C2×#554D79semidirect
378. C79C2×#3376semidirect
385. #554C2×D79semidirect
719. C2#23776227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992862
#237762272
C2×#190989332
C2×#190989252
C2×#190989202
C2×#190988672
C2×#190988452
C2×#190988602
C2×#190987782
C2×#190987682
C2×#190986942
C2×#190986732
C2×#190986632
C2×C4×#119296122
C2×#554×C792
C2×#337679