Finite Group Databasebeta

← C2×#23773656 #35156578

Subgroups — C2×#23773656 #35156578

Order 20224.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099043C211yesmaximal, characteristic, complemented
2#23773656C2116yesmaximal, direct product factor
3C2×#19098896C211yesmaximal, characteristic, complemented
4C2×#19098874C211yesmaximal, characteristic, complemented
5C2×#19098855C211yesmaximal, characteristic, complemented
6C2×#19098840C211yesmaximal, characteristic, complemented
7C2×#19098782C211yesmaximal, characteristic, complemented
8C2×#19098775C211yesmaximal, characteristic, complemented
9C2×#19098723C211yesmaximal, characteristic, complemented
10C2×#19098706C211yesmaximal, characteristic
11C2×#19098663C211yesmaximal, characteristic, complemented
12C2×#19098661C211yesmaximal, characteristic, complemented
13C2×C4×#11929614C211yesmaximal, characteristic, complemented
14C2×C4×#11929609C211yesmaximal, characteristic, complemented
15C2×#19098624C211yesmaximal, characteristic, complemented
16C2×#542×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×#11929611C2211yescharacteristic
21C22×#11929609C2211yescharacteristic
22#19099043—24no—
23#19099043C2218yescomplemented
24C2×C4×Dic158C2211yescharacteristic
25C2×C4×Dic158C2211yescharacteristic
26C2×C4×D316C2211yescharacteristic
27C2×C4×D316C2211yescharacteristic
28C2×(C22⋊D79)⋊C4—21no—
29C2×(C22⋊D79)⋊C4—21no—
30C2×#14579119—21no—
31C22×C4⋊Dic79C2211yescharacteristic
32C2×C4⋊C4×D79—21no—
33#19098896C2218yescomplemented
34#19098874C2218yescomplemented
35#19098855C2218yescomplemented
36#19098840C2218yescomplemented
37#19098782C2218yescomplemented
38#19098775C2218yescomplemented
39#19098723C2218yescomplemented
40#19098706C2218yes—
41#19098663C2218yescomplemented
42#19098661C2218yescomplemented
43C4×#11929614C2218yescomplemented
44C4×#11929609C2218yescomplemented
45#19098624C2218yescomplemented
46C2×#14579094C2211yescharacteristic
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579094C2211yescharacteristic
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×C4⋊(C79⋊C8)C2211yescharacteristic
52C2×#14579085C2211yescharacteristic
53C2×#14579085C2211yescharacteristic
54C2×#14579084C2211yescharacteristic
55C2×#14579084C2211yescharacteristic
56C2×#14579082C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#542×C79—24no—
65#542×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#126×C79—21no—
68C2×#124×C79—21no—
69C2×#124×C79C2211yescharacteristic
70C2×#123×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C22⋊Q8×C79C2211yescharacteristic
73C2×#121×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C2×#117×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—24no—
79C2×#11929624—24no—
80C2×#11929624C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C2×#11929614—24no—
89C2×#11929614C2314yes—
90C2×#11929612—24no—
91C2×#11929612C2314yes—
92C2×#11929611—24no—
93C2×#11929611C2314yes—
94C2×#11929609—24no—
95C2×#11929609C2314yes—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98C22×C79⋊C8C2311yescharacteristic
99C22×C79⋊C8C2311yescharacteristic
100C4×Dic158—22no—
101C4×Dic158—22no—
102C4×Dic158C2314yes—
103C4×Dic158C2314yes—
104C4×D316—22no—
105C4×D316—22no—
106C4×D316C2314yes—
107C4×D316C2314yes—
108(C22⋊D79)⋊C4—28no—
109(C22⋊D79)⋊C4—28no—
110#14579119—28no—
111C2×C4⋊Dic79—21no—
112C2×C4⋊Dic79—22no—
113C2×C4⋊Dic79C2314yes—
114C2×C4⋊Dic79C2311yescharacteristic
115C2×C4⋊Dic79C2311yescharacteristic
116C2×Dic79⋊C4—21no—
117C2×Dic79⋊C4—21no—
118C4⋊C4×D79—28no—
119C2×(C2×D79)⋊C4—21no—
120C2×(C2×D79)⋊C4—21no—
121C2×C4×Dic79—21no—
122C2×C4×Dic79—21no—
123#14579094C2314yes—
124#14579094C2314yes—
125#14579094C2314yes—
126#14579094C2314yes—
127C4⋊(C79⋊C8)C2314yes—
128C4⋊(C79⋊C8)C2314yes—
129#14579085C2314yes—
130#14579085C2314yes—
131#14579084C2314yes—
132#14579084C2314yes—
133#14579082C2314yes—
134#14579082C2314yes—
135#14579081C2314yes—
136#14579081C2314yes—
137C22⋊(C79⋊C8)C2314yes—
138C22⋊(C79⋊C8)C2314yes—
139#14579072C2314yes—
140C4×C79⋊C8C2314yes—
141C22×Q8×C79—21no—
142C22×Q8×C79C2311yescharacteristic
143C22×D4×C79—21no—
144C22×D4×C79C2311yescharacteristic
145C23×C4×C79—21no—
146C23×C4×C79C2311yescharacteristic
147C4⋊Q8×C79—22no—
148C4⋊Q8×C79C2314yes—
149#126×C79—28no—
150#124×C79—28no—
151#124×C79—22no—
152#124×C79C2314yes—
153#123×C79—28no—
154C22⋊Q8×C79—22no—
155C22⋊Q8×C79—28no—
156C22⋊Q8×C79C2314yes—
157#121×C79—22no—
158#121×C79C2314yes—
159C4×Q8×C79—22no—
160C4×Q8×C79C2314yes—
161C4×D4×C79—22no—
162C4×D4×C79C2314yes—
163#117×C79D414yes—
164#117×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79D411yescharacteristic
169C2×C4⋊C4×C79D411yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79D411yescharacteristic
178C2×C22⋊C4×C79D411yescharacteristic
179C2×C42×C79—21no—
180C2×C42×C79C2311yescharacteristic
181C2×C42×C79C2311yescharacteristic
182C23×D79—21no—
183#11929624—216no—
184#11929624—28no—
185#11929624—28no—
186C2×Dic158—21no—
187C2×Dic158—22no—
188C2×Dic158#4114yes—
189C2×Dic158C2412yes—
190C2×D316—21no—
191C2×D316—22no—
192C2×D316#4114yes—
193C2×D316C2412yes—
194C2×C22⋊D79—28no—
195C2×C22⋊D79—24no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—24no—
200C22×Dic79—82no—
201C2×C4×D79—28no—
202C2×C4×D79—24no—
203C2×C4×D79—24no—
204C2×C4×D79—24no—
205C2×C4×D79—82no—
206C2×C4×D79—82no—
207#11929614—28no—
208#11929612—28no—
209#11929611—28no—
210#11929609—28no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8—22no—
215C2×C79⋊C8C2412yes—
216C2×C79⋊C8C2412yes—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C4⋊Dic79—24no—
220C4⋊Dic79—21no—
221C4⋊Dic79—21no—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C24×C79—21no—
231C24×C79C2×D411yescharacteristic
232C2×Q8×C79—21no—
233C2×Q8×C79—24no—
234C2×Q8×C79—22no—
235C2×Q8×C79—22no—
236C2×Q8×C79—82no—
237C2×Q8×C79C2412yes—
238C2×D4×C79—24no—
239C2×D4×C79—21no—
240C2×D4×C79—22no—
241C2×D4×C79—22no—
242C2×D4×C79—82no—
243C2×D4×C79C2412yes—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—24no—
250C22×C4×C79—82no—
251C22×C4×C79C2×D412yes—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2412yes—
258C22×C4×C79C2411yescharacteristic
259C4⋊C4×C79—24no—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79C2×D414yes—
265C4⋊C4×C79C2×D414yes—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C22⋊C4×C79—24no—
269C22⋊C4×C79—24no—
270C22⋊C4×C79—24no—
271C22⋊C4×C79—24no—
272C22⋊C4×C79—24no—
273C22⋊C4×C79C2×D414yes—
274C22⋊C4×C79C2×D414yes—
275C42×C79—24no—
276C42×C79C2×D412yes—
277C42×C79C2×D412yes—
278C42×C79C2412yes—
279C42×C79C2412yes—
280C23×C79—22no—
281C23×C79—22no—
282C23×C79—22no—
283C23×C79—22no—
284C23×C79—42no—
285C23×C79—42no—
286C23×C79—42no—
287C23×C79C22×D412yes—
288C23×C79C22×D411yescharacteristic
289C22×D79—24no—
290C22×D79—22no—
291C22×D79—42no—
292C22×D79—42no—
293Q8×C79—22no—
294Q8×C79—22no—
295Q8×C79—42no—
296Q8×C79—84no—
297D4×C79—22no—
298D4×C79—22no—
299D4×C79—42no—
300D4×C79—84no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—24no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—42no—
313C2×C4×C79—42no—
314C2×C4×C79—42no—
315C2×C4×C79—84no—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D412yes—
319C2×C4×C79C22×D412yes—
320C2×C4×C79C22×D412yes—
321C2×C4×C79C22×D411yescharacteristic
322C2×C4×C79C2×#4112yes—
323C2×C4×C79C2×#4112yes—
324C2×C4×C79C2511yescharacteristic
325C22⋊D79—216no—
326C2×Dic79—24no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—42no—
331C2×Dic79—42no—
332C2×Dic79—84no—
333D316—24no—
334D316—22no—
335D316C2×#4114yes—
336C4×D79—216no—
337C4×D79—84no—
338C4×D79—84no—
339Dic158—24no—
340Dic158—22no—
341Dic158C2×#4114yes—
342C79⋊C8—22no—
343C79⋊C8—22no—
344C79⋊C8—22no—
345C79⋊C8—22no—
346C22×C79—22no—
347C22×C79—22no—
348C22×C79—22no—
349C22×C79—44no—
350C22×C79—42no—
351C22×C79—42no—
352C22×C79—42no—
353C22×C79—84no—
354C22×C79#52512yes—
355C22×C79#57612yes—
356C22×C79#57812yes—
357C22×C79C23×D411yescharacteristic
358C2×D79—24no—
359C2×D79—48no—
360C2×D79—42no—
361C2×D79—42no—
362C4×C79—22no—
363C4×C79—22no—
364C4×C79—22no—
365C4×C79—22no—
366C4×C79—22no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79#52512yes—
371C4×C79C22×#4111yescharacteristic
372C4×C79C22×#4111yescharacteristic
373Dic79—24no—
374Dic79—42no—
375Dic79—42no—
376C2×#3124—791nomaximal, Sylow
377C2×C79—42no—
378C2×C79—82no—
379C2×C79#312414yescomplemented
380C2×C79C2×#52511yescharacteristic
381C2×C79C2×#57611yescharacteristic
382C2×C79C2×#57811yescharacteristic
383D79—44no—
384C2×#542D7911yescharacteristic, complemented
385C2×#520—791no—
386#3124—7916no—
387C2×#484—791no—
388C2×#480—791no—
389C2×#477—791no—
390C2×#474—791no—
391C2×#464—791no—
392C2×#463—791no—
393C2×#452—791no—
394C2×#449—791no—
395C2×#440—791no—
396C2×#440—791no—
397C2×C4×Q16—791no—
398C2×C4×D8—791no—
399C2×#433—791no—
400C79C2×#312411yescharacteristic, complemented, Sylow
401C22×#41—791no—
402C22×Q16—791no—
403C22×SD16—791no—
404C22×SD16—791no—
405C22×D8—791no—
406#542—24no—
407#542C2×D7918yescomplemented
408C2×C4⋊Q8C2×D7911yescharacteristic
409C2×#126—21no—
410C2×#124—21no—
411C2×#124C2×D7911yescharacteristic
412C2×#123—21no—
413C2×C22⋊Q8—21no—
414C2×C22⋊Q8C2×D7911yescharacteristic
415C2×#121C2×D7911yescharacteristic
416#520—798no—
417#520—1584no—
418C2×C4×Q8—791no—
419C2×C4×Q8—791no—
420C2×C4×Q8C2×D7911yescharacteristic
421C2×C4×D4—791no—
422C2×C4×D4—791no—
423C2×C4×D4—1581no—
424C2×C4×D4—1581no—
425C2×C4×D4C2×D7911yescharacteristic
426C2×#117—1581no—
427C2×#117C2×D7911yescharacteristic
428C22×C4⋊C4—791no—
429C22×C4⋊C4—1581no—
430#484—798no—
431#480—798no—
432#477—798no—
433#474—798no—
434#464—798no—
435#463—798no—
436#452—798no—
437#449—798no—
438#440—798no—
439#440—798no—
440C4×Q16—798no—
441C4×D8—798no—
442#433—798no—
443C2×#107—791no—
444C2×#107—791no—
445C2×#107—791no—
446C2×#107—791no—
447C2×C4⋊C8—791no—
448C2×C4⋊C8—791no—
449C2×#103—791no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#102—791no—
454C2×#102—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×C22⋊C8—791no—
458C2×C22⋊C8—791no—
459C2×#97—791no—
460C2×C4×C8—791no—
461C2×#41—794no—
462C2×#41—1584no—
463C2×#41—1584no—
464C2×#41—1582no—
465C22×Q8—21no—
466C22×Q8—791no—
467C22×Q8C22×D7911yescharacteristic
468C22×D4—21no—
469C22×D4—791no—
470C22×D4—1581no—
471C22×D4C22×D7911yescharacteristic
472C23×C4—21no—
473C23×C4—1581no—
474C23×C4—1581no—
475C23×C4—1581no—
476C23×C4—1581no—
477C23×C4C22×D7911yescharacteristic
478C2×Q16—794no—
479C2×Q16—1584no—
480C2×SD16—794no—
481C2×SD16—794no—
482C2×SD16—1584no—
483C2×SD16—1584no—
484C2×D8—794no—
485C2×D8—1584no—
486C22×C8—791no—
487C22×C8—791no—
488C22×C8—791no—
489C22×C8—791no—
490C4⋊Q8—22no—
491C4⋊Q8C22×D7914yes—
492#126—28no—
493#124—28no—
494#124—22no—
495#124C22×D7914yes—
496#123—28no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8C22×D7914yes—
500#121—22no—
501#121C22×D7914yes—
502C4×Q8—22no—
503C4×Q8—794no—
504C4×Q8—794no—
505C4×Q8—1582no—
506C4×Q8—1582no—
507C4×Q8C22×D7914yes—
508C4×D4—22no—
509C4×D4—794no—
510C4×D4—794no—
511C4×D4—1588no—
512C4×D4—1588no—
513C4×D4—1582no—
514C4×D4—1582no—
515C4×D4C22×D7914yes—
516#117—1588no—
517#117C22⋊D7914yes—
518#117C22×D7914yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—791no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—794no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1582no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4—1588no—
530C2×C4⋊C4C22⋊D7911yescharacteristic
531C2×C4⋊C4C22⋊D7911yescharacteristic
532C2×C4⋊C4C22×D7911yescharacteristic
533C2×C4⋊C4C22×D7911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4C22⋊D7911yescharacteristic
542C2×C22⋊C4C22⋊D7911yescharacteristic
543C2×C42—21no—
544C2×C42—1581no—
545C2×C42—1581no—
546C2×C42C22×D7911yescharacteristic
547C2×C42C22×D7911yescharacteristic
548#107—794no—
549#107—794no—
550#107—794no—
551#107—794no—
552C4⋊C8—794no—
553C4⋊C8—794no—
554#103—794no—
555#103—794no—
556#103—794no—
557#103—794no—
558#102—794no—
559#102—794no—
560#102—794no—
561#102—794no—
562C22⋊C8—794no—
563C22⋊C8—794no—
564#97—794no—
565C4×C8—794no—
566C24—21no—
567C24—1581no—
568C24C2×C22⋊D7911yescharacteristic
569#41—1588no—
570#41—1588no—
571#41—15816no—
572C2×Q8—21no—
573C2×Q8—24no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—82no—
577C2×Q8—794no—
578C2×Q8—792no—
579C2×Q8—1582no—
580C2×Q8—1581no—
581C2×Q8C23×D7912yes—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—82no—
587C2×D4—794no—
588C2×D4—792no—
589C2×D4—1588no—
590C2×D4—1584no—
591C2×D4—1582no—
592C2×D4—1581no—
593C2×D4C23×D7912yes—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—6322no—
602C22×C4—6322no—
603C22×C4—6322no—
604C22×C4—1588no—
605C22×C4—1581no—
606C22×C4—1581no—
607C22×C4—1584no—
608C22×C4—1584no—
609C22×C4—1584no—
610C22×C4—1581no—
611C22×C4—1584no—
612C22×C4C2×C22⋊D7912yes—
613C22×C4C2×C22⋊D7911yescharacteristic
614C22×C4C2×C22⋊D7911yescharacteristic
615C22×C4C2×C22⋊D7911yescharacteristic
616C22×C4C2×C22⋊D7911yescharacteristic
617C22×C4C2×C22⋊D7911yescharacteristic
618C22×C4C23×D7912yes—
619C22×C4C23×D7911yescharacteristic
620Q16—1588no—
621SD16—1588no—
622SD16—1588no—
623D8—1588no—
624C2×C8—792no—
625C2×C8—792no—
626C2×C8—792no—
627C2×C8—792no—
628C2×C8—1582no—
629C2×C8—1582no—
630C2×C8—1582no—
631C2×C8—1582no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—792no—
638C4⋊C4—792no—
639C4⋊C4—1584no—
640C4⋊C4—1584no—
641C4⋊C4—1584no—
642C4⋊C4—1581no—
643C4⋊C4—1581no—
644C4⋊C4C2×C22⋊D7914yes—
645C4⋊C4C2×C22⋊D7914yes—
646C4⋊C4C23×D7912yes—
647C4⋊C4C23×D7912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—1584no—
654C22⋊C4—1584no—
655C22⋊C4C2×C22⋊D7914yes—
656C22⋊C4C2×C22⋊D7914yes—
657C42—24no—
658C42—1584no—
659C42—1584no—
660C42C2×C22⋊D7912yes—
661C42C2×C22⋊D7912yes—
662C42C23×D7912yes—
663C42C23×D7912yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—3162no—
672C23—3162no—
673C23—1584no—
674C23—1582no—
675C23C22×C22⋊D7912yes—
676C23C22×C22⋊D7911yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—84no—
681Q8—794no—
682Q8—1584no—
683Q8—1582no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—794no—
689D4—15816no—
690D4—1584no—
691D4—1582no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—84no—
707C2×C4—3162no—
708C2×C4—3162no—
709C2×C4—6324no—
710C2×C4—6324no—
711C2×C4—6324no—
712C2×C4—15816no—
713C2×C4—1582no—
714C2×C4—1582no—
715C2×C4—1584no—
716C2×C4—1582no—
717C2×C4C22×C22⋊D7912yes—
718C2×C4C22×C22⋊D7912yes—
719C2×C4C22×C22⋊D7912yes—
720C2×C4C22×C22⋊D7912yes—
721C2×C4C22×C22⋊D7912yes—
722C2×C4C22×C22⋊D7911yescharacteristic
723C2×C4#41×D7912yes—
724C2×C4#41×D7912yes—
725C2×C4C24×D7911yescharacteristic
726C8—1582no—
727C8—1582no—
728C8—1582no—
729C8—1582no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—3162no—
739C22—3162no—
740C22—3168no—
741C22—1584no—
742C22#1909907012yes—
743C22#1909936612yes—
744C22#1909937812yes—
745C22C23×C22⋊D7911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—3162no—
755C4—3162no—
756C4—1584no—
757C4#1909907012yes—
758C4C2×#41×D7911yescharacteristic
759C4C2×#41×D7911yescharacteristic
760C2—42no—
761C2—82no—
762C2—3164no—
763C2#2377365614yesdirect product factor
764C2C2×#1909907011yescharacteristic
765C2C2×#1909936611yescharacteristic
766C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#542×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098706C2
hypercenterC2×#542D79
hypocenterC79C2×#3124
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19099043C2semidirect
2. #23773656C2direct (N × H)
3. C2×#19098896C2semidirect
4. C2×#19098874C2semidirect
5. C2×#19098855C2semidirect
6. C2×#19098840C2semidirect
7. C2×#19098782C2semidirect
8. C2×#19098775C2semidirect
9. C2×#19098723C2semidirect
11. C2×#19098663C2semidirect
12. C2×#19098661C2semidirect
13. C2×C4×#11929614C2semidirect
14. C2×C4×#11929609C2semidirect
15. C2×#19098624C2semidirect
16. C2×#542×C79C2semidirect
23. #19099043C22semidirect
33. #19098896C22semidirect
34. #19098874C22semidirect
35. #19098855C22semidirect
36. #19098840C22semidirect
37. #19098782C22semidirect
38. #19098775C22semidirect
39. #19098723C22semidirect
41. #19098663C22semidirect
42. #19098661C22semidirect
43. C4×#11929614C22semidirect
44. C4×#11929609C22semidirect
45. #19098624C22semidirect
65. #542×C79C22semidirect
379. C2×C79#3124semidirect
384. C2×#542D79semidirect
400. C79C2×#3124semidirect
407. #542C2×D79semidirect
763. C2#23773656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990432
#237736562
C2×#190988962
C2×#190988742
C2×#190988552
C2×#190988402
C2×#190987822
C2×#190987752
C2×#190987232
C2×#190987062
C2×#190986632
C2×#190986612
C2×C4×#119296142
C2×C4×#119296092
C2×#190986242
C2×#542×C792
C2×#312479