Finite Group Databasebeta

← C2×#23775453 #35164877

Subgroups — C2×#23775453 #35164877

Order 20224.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099253C211yesmaximal, characteristic
2C2×D4×Dic158C211yesmaximal, characteristic
3#23775453C2116yesmaximal, direct product factor
4C2×#19098932C211yesmaximal, characteristic, complemented
5C2×#19098905C211yesmaximal, characteristic, complemented
6C2×#19098894C211yesmaximal, characteristic, complemented
7C2×#19098871C211yesmaximal, characteristic, complemented
8C2×#19098821C211yesmaximal, characteristic, complemented
9C2×#19098804C211yesmaximal, characteristic, complemented
10C2×#19098774C211yesmaximal, characteristic, complemented
11C2×#19098721C211yesmaximal, characteristic, complemented
12C2×#19098721C211yesmaximal, characteristic, complemented
13C2×#19098671C211yesmaximal, characteristic, complemented
14C2×#19098573C211yesmaximal, characteristic, complemented
15C22×#14579086C211yesmaximal, characteristic, complemented
16C2×#435×C79C211yesmaximal, characteristic
17C23×Dic158C2211yescharacteristic
18C23×Dic158C2211yescharacteristic
19C22×Dic316C2211yescharacteristic
20C22×Dic316C2211yescharacteristic
21C22×Dic316C2211yescharacteristic
22#19099253—24no—
23#19099253C2218yes—
24D4×Dic158—24no—
25D4×Dic158C2218yes—
26C2×#14579161C2211yescharacteristic
27C2×#14579160—21no—
28C2×#14579154—21no—
29C2×#14579153C2211yescharacteristic
30C2×#14579151—21no—
31C2×#14579142—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579140C2211yescharacteristic
34C2×#14579140C2211yescharacteristic
35C2×#14579140C2211yescharacteristic
36C2×#14579138—21no—
37C2×#14579138—21no—
38C2×C4×Dic158C2211yescharacteristic
39C2×C4×Dic158C2211yescharacteristic
40C2×D4×Dic79—21no—
41C2×#14579120C2211yescharacteristic
42C2×#14579117—21no—
43C22×C4⋊Dic79C2211yescharacteristic
44#19098932C2218yescomplemented
45#19098905C2218yescomplemented
46#19098894C2218yescomplemented
47#19098871C2218yescomplemented
48#19098821C2218yescomplemented
49#19098804C2218yescomplemented
50#19098774C2218yescomplemented
51#19098721C2218yescomplemented
52#19098721C2218yescomplemented
53#19098671C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57#19098573C2218yescomplemented
58C2×#14579086C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579086C2211yescharacteristic
66C2×#14579086C2211yescharacteristic
67C2×#14579086C2211yescharacteristic
68C2×#14579086C2218yescomplemented
69C22×M16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#435×C79C2218yes—
73C2×C4⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×C22⋊C8×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—22no—
78C22×Dic158—22no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158—24no—
82C22×Dic158—24no—
83C22×Dic158—42no—
84C22×Dic158—42no—
85C22×Dic158C2311yescharacteristic
86C22×Dic158C2311yescharacteristic
87C22×Dic158C2311yescharacteristic
88C22×Dic158C2314yes—
89C22×Dic158C2314yes—
90C22×Dic158C2311yescharacteristic
91C23×Dic79—21no—
92C23×Dic79—21no—
93C23×Dic79—21no—
94C2×Dic316—24no—
95C2×Dic316—42no—
96C2×Dic316—42no—
97C2×Dic316C2314yes—
98C2×Dic316C2314yes—
99C2×Dic316C2314yes—
100#14579161—22no—
101#14579161C2314yes—
102#14579160—28no—
103#14579154—28no—
104#14579153—22no—
105#14579153C2314yes—
106#14579151—28no—
107#14579142—28no—
108#14579140—22no—
109#14579140—22no—
110#14579140—22no—
111#14579140—22no—
112#14579140C2314yes—
113#14579140C2314yes—
114#14579140C2314yes—
115#14579140C2314yes—
116#14579138—28no—
117#14579138—28no—
118C4×Dic158—22no—
119C4×Dic158—22no—
120C4×Dic158C2314yes—
121C4×Dic158C2314yes—
122D4×Dic79—28no—
123#14579120—22no—
124#14579120C2314yes—
125#14579117—28no—
126C2×C4⋊Dic79—22no—
127C2×C4⋊Dic79—21no—
128C2×C4⋊Dic79—21no—
129C2×C4⋊Dic79—21no—
130C2×C4⋊Dic79C2314yes—
131C2×C4⋊Dic79C2311yescharacteristic
132C2×C4⋊Dic79C2311yescharacteristic
133C2×C4⋊Dic79C2311yescharacteristic
134C2×C4⋊Dic79C2311yescharacteristic
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C2×Dic79⋊C4—21no—
141C2×Dic79⋊C4—21no—
142C2×Dic79⋊C4—21no—
143C2×C22⋊Dic79—21no—
144C2×C22⋊Dic79—21no—
145C2×C22⋊Dic79—21no—
146C2×C22⋊Dic79—21no—
147C2×C22⋊Dic79—21no—
148C2×C4×Dic79—21no—
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151#14579095C2314yes—
152#14579093C2314yes—
153#14579093C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579086C2314yes—
158#14579086C2314yes—
159#14579086C2314yes—
160#14579086C2314yes—
161#14579086C2314yes—
162#14579086C2314yes—
163#14579086C2314yes—
164C22×D4×C79D411yescharacteristic
165C23×C4×C79C2311yescharacteristic
166C23×C4×C79C2311yescharacteristic
167C2×M16×C79—42no—
168C2×M16×C79C2314yes—
169C22×C8×C79—42no—
170C22×C8×C79C2311yescharacteristic
171C22×C8×C79C2311yescharacteristic
172C22×C8×C79C2311yescharacteristic
173C22×C8×C79C2311yescharacteristic
174C22×C8×C79C2314yes—
175C4×D4×C79D414yes—
176C4×D4×C79C2314yes—
177C2×C4⋊C4×C79D411yescharacteristic
178C2×C22⋊C4×C79D411yescharacteristic
179C2×C22⋊C4×C79D411yescharacteristic
180C2×C42×C79C2311yescharacteristic
181C4⋊C8×C79C2314yes—
182C22⋊C8×C79C2314yes—
183C22⋊C8×C79C2314yes—
184#97×C79C2314yes—
185C2×Dic158—28no—
186C2×Dic158—28no—
187C2×Dic158—21no—
188C2×Dic158—24no—
189C2×Dic158—24no—
190C2×Dic158—21no—
191C2×Dic158—21no—
192C2×Dic158—21no—
193C2×Dic158—22no—
194C2×Dic158—22no—
195C2×Dic158—22no—
196C2×Dic158—22no—
197C2×Dic158—22no—
198C2×Dic158—22no—
199C2×Dic158—22no—
200C2×Dic158—44no—
201C2×Dic158—44no—
202C2×Dic158—48no—
203C2×Dic158—48no—
204C2×Dic158—44no—
205C2×Dic158—44no—
206C2×Dic158#4114yes—
207C2×Dic158C2412yes—
208C2×Dic158C2412yes—
209C2×Dic158C2412yes—
210C2×Dic158C2412yes—
211C22×Dic79—21no—
212C22×Dic79—21no—
213C22×Dic79—21no—
214C22×Dic79—24no—
215C22×Dic79—24no—
216C22×Dic79—21no—
217C22×Dic79—21no—
218C22×Dic79—21no—
219C22×Dic79—21no—
220C22×Dic79—21no—
221C22×Dic79—24no—
222C22×Dic79—44no—
223C22×Dic79—44no—
224C22×Dic79—44no—
225Dic316—28no—
226Dic316—44no—
227Dic316—44no—
228C4⋊Dic79—21no—
229C4⋊Dic79—21no—
230C4⋊Dic79—24no—
231C4⋊Dic79—24no—
232C4⋊Dic79—24no—
233C4⋊Dic79—21no—
234C4⋊Dic79—21no—
235C4⋊Dic79C2412yes—
236C4⋊Dic79C2412yes—
237C4⋊Dic79C2412yes—
238C4⋊Dic79C2412yes—
239Dic79⋊C4—24no—
240Dic79⋊C4—24no—
241Dic79⋊C4—24no—
242Dic79⋊C4—24no—
243Dic79⋊C4—24no—
244Dic79⋊C4—24no—
245Dic79⋊C4—24no—
246Dic79⋊C4—24no—
247C22⋊Dic79—24no—
248C22⋊Dic79—24no—
249C22⋊Dic79—24no—
250C22⋊Dic79—24no—
251C22⋊Dic79—24no—
252C4×Dic79—24no—
253C4×Dic79—24no—
254C4×Dic79—24no—
255C24×C79C2×D411yescharacteristic
256C24×C79C2×D411yescharacteristic
257C2×D4×C79—24no—
258C2×D4×C79C2×D414yes—
259C22×C4×C79—22no—
260C22×C4×C79—22no—
261C22×C4×C79—22no—
262C22×C4×C79—22no—
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2×D411yescharacteristic
265C22×C4×C79C2×D412yes—
266C22×C4×C79C2×D412yes—
267C22×C4×C79C2×D411yescharacteristic
268C22×C4×C79C2×D411yescharacteristic
269C22×C4×C79C2412yes—
270C22×C4×C79C2412yes—
271C22×C4×C79C2411yescharacteristic
272M16×C79—44no—
273C2×C8×C79—22no—
274C2×C8×C79—22no—
275C2×C8×C79—22no—
276C2×C8×C79—22no—
277C2×C8×C79—44no—
278C2×C8×C79C2412yes—
279C2×C8×C79C2412yes—
280C2×C8×C79C2412yes—
281C2×C8×C79C2412yes—
282C4⋊C4×C79C2×D414yes—
283C22⋊C4×C79C2×D414yes—
284C22⋊C4×C79C2×D414yes—
285C42×C79C2×D412yes—
286C42×C79C2412yes—
287C23×C79—22no—
288C23×C79—22no—
289C23×C79—22no—
290C23×C79—22no—
291C23×C79—22no—
292C23×C79#13714yes—
293C23×C79C22×D412yes—
294C23×C79C22×D412yes—
295C23×C79C22×D411yescharacteristic
296D4×C79—28no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—24no—
302C2×C4×C79—24no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79C22×D412yes—
308C2×C4×C79C22×D412yes—
309C2×C4×C79C22×D412yes—
310C2×C4×C79C22×D412yes—
311C2×C4×C79C22×D411yescharacteristic
312C2×C4×C79C2×#4112yes—
313C2×C4×C79H(5,𝔽2)12yes—
314C2×C4×C79C2511yescharacteristic
315C2×Dic79—24no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—48no—
325C2×Dic79—48no—
326C2×Dic79—42no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329C2×Dic79—48no—
330C2×Dic79—42no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79—42no—
334Dic158—24no—
335Dic158—22no—
336Dic158—22no—
337Dic158—22no—
338Dic158—22no—
339Dic158—22no—
340Dic158—22no—
341Dic158—22no—
342Dic158—48no—
343Dic158—48no—
344Dic158—42no—
345Dic158—42no—
346Dic158—42no—
347Dic158C2×#4114yes—
348C8×C79—22no—
349C8×C79—22no—
350C8×C79—22no—
351C8×C79—22no—
352C22×C79—22no—
353C22×C79—28no—
354C22×C79—22no—
355C22×C79—22no—
356C22×C79—22no—
357C22×C79—22no—
358C22×C79—44no—
359C22×C79#54612yes—
360C22×C79C2×#13714yes—
361C22×C79C2×#13712yes—
362C22×C79#57812yes—
363C22×C79C23×D411yescharacteristic
364C4×C79—22no—
365C4×C79—22no—
366C4×C79—22no—
367C4×C79—22no—
368C4×C79#54612yes—
369C4×C79C22×#4111yescharacteristic
370C4×C79C2×H(5,𝔽2)11yescharacteristic
371Dic79—24no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79—42no—
379C2×#3312—791nomaximal, Sylow
380C2×C79—24no—
381C2×C79—42no—
382C2×C79#331214yescomplemented
383C2×C79C2×#54611yescharacteristic
384C2×C79C22×#13711yescharacteristic
385C2×C79C2×#57811yescharacteristic
386C2×#552—791no—
387C2×D4×Q8—791no—
388#3312—7916no—
389C2×#491—791no—
390C2×#485—791no—
391C2×#483—791no—
392C2×#479—791no—
393C2×#470—791no—
394C2×#467—791no—
395C2×#462—791no—
396C2×#451—791no—
397C2×#451—791no—
398C2×#441—791no—
399C2×#435D7911yescharacteristic
400C2×#419—791no—
401C22×#103—791no—
402C79C2×#331211yescharacteristic, complemented, Sylow
403C23×Q8—791no—
404C23×Q8—791no—
405C22×Q16—791no—
406C22×Q16—791no—
407C22×Q16—791no—
408C22×M16C2×D7911yescharacteristic
409C23×C8C2×D7911yescharacteristic
410#552—798no—
411#552—1584no—
412D4×Q8—798no—
413D4×Q8—1584no—
414C2×C4⋊Q8—791no—
415C2×C4⋊Q8—1581no—
416C2×#126—1581no—
417C2×#125—791no—
418C2×#125—1581no—
419C2×#123—1581no—
420C2×C22⋊Q8—791no—
421C2×C22⋊Q8—791no—
422C2×C22⋊Q8—791no—
423C2×C22⋊Q8—791no—
424C2×C22⋊Q8—1581no—
425C2×C22⋊Q8—1581no—
426C2×C4×Q8—791no—
427C2×C4×Q8—791no—
428C2×C4×D4—1581no—
429C2×C4×D4C2×D7911yescharacteristic
430C2×#117—791no—
431C2×#117—1581no—
432C22×C4⋊C4—791no—
433#491—798no—
434#485—798no—
435#483—798no—
436#479—798no—
437#470—798no—
438#467—798no—
439#462—798no—
440#451—798no—
441#451—798no—
442#441—798no—
443#435C2×D7918yes—
444C2×#107—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8C2×D7911yescharacteristic
448#419—798no—
449C2×#103—791no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—791no—
456C2×#103—791no—
457C2×#103—791no—
458C2×#103—798no—
459C2×#103—791no—
460C2×C22⋊C8C2×D7911yescharacteristic
461C2×C22⋊C8C2×D7911yescharacteristic
462C2×#97C2×D7911yescharacteristic
463C22×Q8—3162no—
464C22×Q8—3162no—
465C22×Q8—794no—
466C22×Q8—794no—
467C22×Q8—791no—
468C22×Q8—791no—
469C22×Q8—791no—
470C22×Q8—791no—
471C22×Q8—1584no—
472C22×Q8—1584no—
473C22×Q8—1581no—
474C22×Q8—1581no—
475C22×Q8—1582no—
476C22×Q8—1582no—
477C22×D4D31611yescharacteristic
478C23×C4—1581no—
479C23×C4—1581no—
480C23×C4—1581no—
481C23×C4C22×D7911yescharacteristic
482C23×C4C22×D7911yescharacteristic
483C2×Q16—3162no—
484C2×Q16—3162no—
485C2×Q16—794no—
486C2×Q16—794no—
487C2×Q16—794no—
488C2×Q16—1584no—
489C2×M16—42no—
490C2×M16C22×D7914yes—
491C22×C8—42no—
492C22×C8C22×D7911yescharacteristic
493C22×C8C22×D7911yescharacteristic
494C22×C8C22×D7911yescharacteristic
495C22×C8C22×D7911yescharacteristic
496C22×C8C22×D7914yes—
497C4⋊Q8—794no—
498C4⋊Q8—1588no—
499C4⋊Q8—1582no—
500#126—1588no—
501#125—794no—
502#125—1588no—
503#125—1582no—
504#123—1588no—
505C22⋊Q8—794no—
506C22⋊Q8—794no—
507C22⋊Q8—794no—
508C22⋊Q8—794no—
509C22⋊Q8—1582no—
510C22⋊Q8—1582no—
511C22⋊Q8—1582no—
512C22⋊Q8—1582no—
513C22⋊Q8—1588no—
514C22⋊Q8—1588no—
515C4×Q8—794no—
516C4×Q8—794no—
517C4×Q8—1582no—
518C4×Q8—1582no—
519C4×D4—1588no—
520C4×D4D31614yes—
521C4×D4C22×D7914yes—
522#117—794no—
523#117—1582no—
524#117—1588no—
525C2×C4⋊C4—791no—
526C2×C4⋊C4—791no—
527C2×C4⋊C4—794no—
528C2×C4⋊C4—791no—
529C2×C4⋊C4—791no—
530C2×C4⋊C4—1581no—
531C2×C4⋊C4—1582no—
532C2×C4⋊C4—1581no—
533C2×C4⋊C4—1581no—
534C2×C4⋊C4—1581no—
535C2×C4⋊C4—1581no—
536C2×C4⋊C4—1581no—
537C2×C4⋊C4—1581no—
538C2×C4⋊C4—1581no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1581no—
541C2×C4⋊C4—1581no—
542C2×C4⋊C4D31611yescharacteristic
543C2×C22⋊C4—1581no—
544C2×C22⋊C4—1581no—
545C2×C22⋊C4—1581no—
546C2×C22⋊C4—1581no—
547C2×C22⋊C4—1581no—
548C2×C22⋊C4D31611yescharacteristic
549C2×C22⋊C4D31611yescharacteristic
550C2×C42—1581no—
551C2×C42—1581no—
552C2×C42—1581no—
553C2×C42C22×D7911yescharacteristic
554#107—794no—
555#106—794no—
556#106—794no—
557C4⋊C8C22×D7914yes—
558#103—794no—
559#103—794no—
560#103—794no—
561#103—794no—
562#103—794no—
563#103—794no—
564#103—794no—
565#103—794no—
566#103—794no—
567#103—794no—
568C22⋊C8C22×D7914yes—
569C22⋊C8C22×D7914yes—
570#97C22×D7914yes—
571C24C2×D31611yescharacteristic
572C24C2×D31611yescharacteristic
573C2×Q8—3168no—
574C2×Q8—3168no—
575C2×Q8—3164no—
576C2×Q8—3164no—
577C2×Q8—3164no—
578C2×Q8—3164no—
579C2×Q8—794no—
580C2×Q8—792no—
581C2×Q8—792no—
582C2×Q8—792no—
583C2×Q8—792no—
584C2×Q8—1588no—
585C2×Q8—1588no—
586C2×Q8—1582no—
587C2×Q8—1582no—
588C2×Q8—1582no—
589C2×Q8—1582no—
590C2×Q8—1582no—
591C2×Q8—1582no—
592C2×Q8—1582no—
593C2×Q8—1581no—
594C2×Q8—1581no—
595C2×Q8—1581no—
596C2×Q8—1584no—
597C2×Q8—1584no—
598C2×Q8—1581no—
599C2×D4—24no—
600C2×D4C2×D31614yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—3164no—
606C22×C4—3164no—
607C22×C4—3164no—
608C22×C4—1584no—
609C22×C4—1584no—
610C22×C4—1584no—
611C22×C4—1581no—
612C22×C4—1581no—
613C22×C4—1581no—
614C22×C4—1581no—
615C22×C4—1581no—
616C22×C4—1581no—
617C22×C4—1581no—
618C22×C4—1581no—
619C22×C4C2×D31612yes—
620C22×C4C2×D31612yes—
621C22×C4C2×D31611yescharacteristic
622C22×C4C2×D31611yescharacteristic
623C22×C4C2×D31611yescharacteristic
624C22×C4C2×D31611yescharacteristic
625C22×C4C23×D7912yes—
626C22×C4C23×D7912yes—
627C22×C4C23×D7911yescharacteristic
628Q16—3164no—
629Q16—3164no—
630Q16—1588no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8C23×D7912yes—
638C2×C8C23×D7912yes—
639C2×C8C23×D7912yes—
640C2×C8C23×D7912yes—
641C4⋊C4—792no—
642C4⋊C4—792no—
643C4⋊C4—792no—
644C4⋊C4—792no—
645C4⋊C4—1584no—
646C4⋊C4—1584no—
647C4⋊C4—1584no—
648C4⋊C4—1584no—
649C4⋊C4—1584no—
650C4⋊C4—1584no—
651C4⋊C4—1584no—
652C4⋊C4—1584no—
653C4⋊C4—1581no—
654C4⋊C4—1581no—
655C4⋊C4—1584no—
656C4⋊C4—1581no—
657C4⋊C4—1581no—
658C4⋊C4—1584no—
659C4⋊C4—1584no—
660C4⋊C4C2×D31614yes—
661C22⋊C4—1584no—
662C22⋊C4—1584no—
663C22⋊C4—1584no—
664C22⋊C4—1584no—
665C22⋊C4—1584no—
666C22⋊C4C2×D31614yes—
667C22⋊C4C2×D31614yes—
668C42—1584no—
669C42—1584no—
670C42—1584no—
671C42C2×D31612yes—
672C42C23×D7912yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1457919414yes—
679C23C22×D31612yes—
680C23C22×D31612yes—
681C23C22×D31611yescharacteristic
682Q8—3168no—
683Q8—3168no—
684Q8—3162no—
685Q8—3162no—
686Q8—3162no—
687Q8—794no—
688Q8—1582no—
689Q8—1582no—
690Q8—1582no—
691Q8—1582no—
692Q8—1582no—
693Q8—1582no—
694Q8—1582no—
695Q8—1584no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—3162no—
708C2×C4—3162no—
709C2×C4—3162no—
710C2×C4—3168no—
711C2×C4—3162no—
712C2×C4—3162no—
713C2×C4—3162no—
714C2×C4—3162no—
715C2×C4—3168no—
716C2×C4—3168no—
717C2×C4—1582no—
718C2×C4—1582no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4—1582no—
722C2×C4—1582no—
723C2×C4—1582no—
724C2×C4—1584no—
725C2×C4—1582no—
726C2×C4C22×D31612yes—
727C2×C4C22×D31612yes—
728C2×C4C22×D31612yes—
729C2×C4C22×D31612yes—
730C2×C4C22×D31611yescharacteristic
731C2×C4#41×D7912yes—
732C2×C4#1457920612yes—
733C2×C4C24×D7911yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1909920812yes—
746C22C2×#1457919414yes—
747C22C2×#1457919412yes—
748C22#1909938012yes—
749C22C23×D31611yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4—3162no—
758C4—3162no—
759C4—3162no—
760C4—3162no—
761C4—1584no—
762C4#1909920812yes—
763C4C2×#41×D7911yescharacteristic
764C4C2×#1457920611yescharacteristic
765C2—24no—
766C2—42no—
767C2#2377545314yesdirect product factor
768C2C2×#1909920811yescharacteristic
769C2C22×#1457919411yescharacteristic
770C2C2×#1909938011yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79D4
hypercenterC2×#435D79
hypocenterC79C2×#3312
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #23775453C2direct (N × H)
4. C2×#19098932C2semidirect
5. C2×#19098905C2semidirect
6. C2×#19098894C2semidirect
7. C2×#19098871C2semidirect
8. C2×#19098821C2semidirect
9. C2×#19098804C2semidirect
10. C2×#19098774C2semidirect
11. C2×#19098721C2semidirect
12. C2×#19098721C2semidirect
13. C2×#19098671C2semidirect
14. C2×#19098573C2semidirect
15. C22×#14579086C2semidirect
44. #19098932C22semidirect
45. #19098905C22semidirect
46. #19098894C22semidirect
47. #19098871C22semidirect
48. #19098821C22semidirect
49. #19098804C22semidirect
50. #19098774C22semidirect
51. #19098721C22semidirect
52. #19098721C22semidirect
53. #19098671C22semidirect
57. #19098573C22semidirect
68. C2×#14579086C22semidirect
382. C2×C79#3312semidirect
402. C79C2×#3312semidirect
767. C2#23775453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992532
C2×D4×Dic1582
#237754532
C2×#190989322
C2×#190989052
C2×#190988942
C2×#190988712
C2×#190988212
C2×#190988042
C2×#190987742
C2×#190987212
C2×#190986712
C2×#190985732
C22×#145790862
C2×#435×C792
C2×#331279