Finite Group Databasebeta

← C2×#23777319 #35196773

Subgroups — C2×#23777319 #35196773

Order 20224.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777319C2132yesmaximal, direct product factor
2C2×#19099260C214yesmaximal, complemented
3C2×#19099258C214yesmaximal, complemented
4C2×#19099256C214yesmaximal, complemented
5C2×#19099250C214yesmaximal, complemented
6C2×#19099176C211yesmaximal, characteristic, complemented
7C2×#19099175C211yesmaximal, characteristic, complemented
8C2×#19099167C211yesmaximal, characteristic, complemented
9C2×#19099142C212yesmaximal, complemented
10C2×#19099111C211yesmaximal, characteristic, complemented
11C2×#19099095C212yesmaximal, complemented
12C2×#19099094C212yesmaximal, complemented
13C2×#125×D79C211yesmaximal, characteristic, complemented
14C2×#19099042C212yesmaximal, complemented
15C2×#19099031C211yesmaximal, characteristic, complemented
16C2×#540×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929623C2212yes—
19#19099260C22164yescomplemented
20#19099258C22164yescomplemented
21#19099256C22164yescomplemented
22#19099250C22164yescomplemented
23#19099176C22116yescomplemented
24#19099175C22116yescomplemented
25#19099167C22116yescomplemented
26#19099142C22132yescomplemented
27#19099111C22116yescomplemented
28C2×#14579161C2211yescharacteristic
29#19099095C22132yescomplemented
30#19099094C22132yescomplemented
31C2×#14579156C2214yes—
32C2×#14579154C2214yes—
33C2×#14579154C2214yes—
34C2×#14579154C2214yes—
35C2×#14579153C2211yescharacteristic
36C2×#14579152C2214yes—
37C2×#14579152C2212yes—
38C2×#14579151C2214yes—
39C2×#14579151C2214yes—
40#125×D79C22116yescomplemented
41C2×#14579148C2212yes—
42C2×#14579143C2214yes—
43C2×#14579142C2214yes—
44C2×#14579142C2214yes—
45C2×#14579141C2212yes—
46C2×#14579140C2212yes—
47C2×#14579138C2214yes—
48C2×#14579134C2214yes—
49C2×#14579133C2214yes—
50C2×#14579133C2214yes—
51C2×#14579132C2214yes—
52C2×#14579132C2212yes—
53C2×#14579132C2214yes—
54#19099042C22132yescomplemented
55#19099031C22116yescomplemented
56C2×C4×Dic158C2212yes—
57C2×#14579126C2212yes—
58C2×#14579126C2212yes—
59C2×D4×Dic79C2212yes—
60C2×D4×Dic79C2214yes—
61C2×D4×Dic79C2214yes—
62C2×#14579123C2212yes—
63C2×C4×C22⋊D79C2214yes—
64C2×C4×C22⋊D79C2214yes—
65C2×(C22⋊D79)⋊C4C2212yes—
66C2×(C22⋊D79)⋊C4C2212yes—
67C2×(C22⋊D79)⋊C4C2214yes—
68C2×#14579120C2214yes—
69C2×#14579118C2211yescharacteristic
70C2×#14579118C2211yescharacteristic
71C2×#14579117C2214yes—
72C2×#14579117C2214yes—
73C22×Dic79⋊C4C2214yes—
74C2×C4⋊C4×D79C2212yes—
75C2×C4⋊C4×D79C2214yes—
76C22×C4×Dic79C2211yescharacteristic
77C2×C42×D79C2211yescharacteristic
78C2×C42×D79C2211yescharacteristic
79#540×C79C22116yescomplemented
80C2×#127×C79C2211yescharacteristic
81C2×#125×C79C2211yescharacteristic
82C2×#123×C79C2214yes—
83C2×#121×C79C2214yes—
84C2×#121×C79C2212yes—
85C2×C4×D4×C79C2212yes—
86C2×#117×C79C2211yescharacteristic
87C2×#11929624—28no—
88C2×#11929624C2318yes—
89C2×#11929623—216no—
90C2×#11929623C23116yes—
91C22×Dic158C2311yescharacteristic
92C22×Dic158C2312yes—
93C22×D316C2311yescharacteristic
94C22×C22⋊D79C2311yescharacteristic
95C22×C22⋊D79C2311yescharacteristic
96C22×C22⋊D79C2314yes—
97C22×C22⋊D79C2314yes—
98C23×Dic79C2314yes—
99C23×Dic79C2312yes—
100C23×Dic79C2314yes—
101C22×C4×D79C2311yescharacteristic
102C22×C4×D79C2312yes—
103C22×C4×D79C2312yes—
104C22×C4×D79C2314yes—
105C22×C4×D79C2311yescharacteristic
106#14579161C2318yes—
107#14579156C23132yes—
108#14579154C23132yes—
109#14579154C23132yes—
110#14579154C23132yes—
111#14579153C2318yes—
112#14579152C23132yes—
113#14579152C23116yes—
114#14579151C23132yes—
115#14579151C23132yes—
116#14579148C23116yes—
117#14579143C23132yes—
118#14579142C23132yes—
119#14579142C23132yes—
120#14579141C23116yes—
121#14579140C23116yes—
122#14579138C23132yes—
123#14579134C23132yes—
124#14579133C23132yes—
125#14579133C23132yes—
126#14579132C23116yes—
127#14579132C23132yes—
128#14579132C23132yes—
129C4×Dic158C23116yes—
130#14579126C23116yes—
131#14579126C23116yes—
132D4×Dic79C23116yes—
133D4×Dic79C23132yes—
134D4×Dic79C23132yes—
135#14579123C23116yes—
136C4×C22⋊D79C23132yes—
137C4×C22⋊D79C23132yes—
138(C22⋊D79)⋊C4C23116yes—
139(C22⋊D79)⋊C4C23132yes—
140(C22⋊D79)⋊C4C23116yes—
141#14579120C23132yes—
142#14579118C2318yes—
143#14579118C2318yes—
144#14579117C23132yes—
145#14579117C23132yes—
146C2×C4⋊Dic79C2314yes—
147C2×C4⋊Dic79C2312yes—
148C2×C4⋊Dic79C2314yes—
149C2×C4⋊Dic79C2314yes—
150C2×Dic79⋊C4C23132yes—
151C2×Dic79⋊C4C2314yes—
152C2×Dic79⋊C4C2314yes—
153C2×Dic79⋊C4C2314yes—
154C2×Dic79⋊C4C2312yes—
155C2×Dic79⋊C4C2314yes—
156C2×Dic79⋊C4C2314yes—
157C2×Dic79⋊C4C2314yes—
158C2×Dic79⋊C4C2312yes—
159C4⋊C4×D79C23116yes—
160C4⋊C4×D79C23132yes—
161C2×C22⋊Dic79C2314yes—
162C2×C22⋊Dic79C2314yes—
163C2×C22⋊Dic79C2314yes—
164C2×C22⋊Dic79C2314yes—
165C2×C22⋊Dic79C2314yes—
166C2×(C2×D79)⋊C4C2312yes—
167C2×(C2×D79)⋊C4C2312yes—
168C2×(C2×D79)⋊C4C2314yes—
169C2×C4×Dic79C2311yescharacteristic
170C2×C4×Dic79C2312yes—
171C2×C4×Dic79C2312yes—
172C2×C4×Dic79C2312yes—
173C2×C4×Dic79C2311yescharacteristic
174C2×C4×Dic79C2318yes—
175C2×C4×Dic79C2314yes—
176C2×C4×Dic79C2314yes—
177C42×D79C2318yes—
178C42×D79C2318yes—
179C22×D4×C79C2312yes—
180C22×D4×C79C2314yes—
181C22×D4×C79C2314yes—
182C23×C4×C79C2311yescharacteristic
183C23×C4×C79C2314yes—
184#127×C79C2318yes—
185#125×C79C2318yes—
186#123×C79C23132yes—
187#121×C79C23116yes—
188#121×C79C23132yes—
189C4×D4×C79C23116yes—
190#117×C79C2318yes—
191C2×C4⋊C4×C79C2312yes—
192C2×C4⋊C4×C79C2312yes—
193C2×C4⋊C4×C79C2314yes—
194C2×C22⋊C4×C79C2312yes—
195C2×C22⋊C4×C79C2314yes—
196C2×C22⋊C4×C79C2314yes—
197C2×C42×C79C2311yescharacteristic
198C2×C42×C79C2311yescharacteristic
199C23×D79C2411yescharacteristic
200C23×D79C2411yescharacteristic
201#11929624—232no—
202#11929623—264no—
203C2×Dic158—24no—
204C2×Dic158—28no—
205C2×Dic158C2418yes—
206C2×Dic158C2414yes—
207C2×D316—24no—
208C2×D316C2414yes—
209C2×C22⋊D79—24no—
210C2×C22⋊D79—216no—
211C2×C22⋊D79—24no—
212C2×C22⋊D79—48no—
213C2×C22⋊D79C24116yes—
214C2×C22⋊D79C2414yes—
215C2×C22⋊D79C2414yes—
216C2×C22⋊D79C24116yes—
217C22×Dic79—216no—
218C22×Dic79—48no—
219C22×Dic79—44no—
220C22×Dic79C2414yes—
221C22×Dic79C2411yescharacteristic
222C22×Dic79C24116yes—
223C22×Dic79C2412yes—
224C22×Dic79C2412yes—
225C22×Dic79C2414yes—
226C22×Dic79C2418yes—
227C22×Dic79C24116yes—
228C22×Dic79C2411yescharacteristic
229C2×C4×D79—24no—
230C2×C4×D79—44no—
231C2×C4×D79—48no—
232C2×C4×D79—44no—
233C2×C4×D79#4118yes—
234C2×C4×D79C2414yes—
235C2×C4×D79C2418yes—
236C2×C4×D79C2418yes—
237C2×C4×D79C24116yes—
238C2×C4×D79C2414yes—
239C4⋊Dic79C24116yes—
240C4⋊Dic79C2418yes—
241C4⋊Dic79C24116yes—
242C4⋊Dic79C24116yes—
243Dic79⋊C4C24116yes—
244Dic79⋊C4C24116yes—
245Dic79⋊C4C24116yes—
246Dic79⋊C4C2418yes—
247Dic79⋊C4C24116yes—
248Dic79⋊C4C24116yes—
249Dic79⋊C4C24116yes—
250Dic79⋊C4C2418yes—
251C22⋊Dic79C24116yes—
252C22⋊Dic79C24116yes—
253C22⋊Dic79C24116yes—
254C22⋊Dic79C24116yes—
255C22⋊Dic79C24116yes—
256(C2×D79)⋊C4C2418yes—
257(C2×D79)⋊C4C2418yes—
258(C2×D79)⋊C4C24116yes—
259C4×Dic79C2414yes—
260C4×Dic79C2418yes—
261C4×Dic79C2418yes—
262C4×Dic79C2418yes—
263C4×Dic79C2414yes—
264C4×Dic79C24116yes—
265C4×Dic79C24116yes—
266C24×C79C2414yes—
267C24×C79C2411yescharacteristic
268C2×D4×C79—28no—
269C2×D4×C79—48no—
270C2×D4×C79—48no—
271C2×D4×C79C2418yes—
272C2×D4×C79C24116yes—
273C2×D4×C79C24116yes—
274C22×C4×C79—24no—
275C22×C4×C79—48no—
276C22×C4×C79C2411yescharacteristic
277C22×C4×C79C2414yes—
278C22×C4×C79C2412yes—
279C22×C4×C79C2412yes—
280C22×C4×C79C2414yes—
281C22×C4×C79C24116yes—
282C22×C4×C79C2411yescharacteristic
283C4⋊C4×C79C2418yes—
284C4⋊C4×C79C2418yes—
285C4⋊C4×C79C24116yes—
286C22⋊C4×C79C2418yes—
287C22⋊C4×C79C24116yes—
288C22⋊C4×C79C24116yes—
289C42×C79C2414yes—
290C42×C79C2414yes—
291C23×C79—28no—
292C23×C79—22no—
293C23×C79—28no—
294C23×C79—24no—
295C23×C79—28no—
296C23×C79C2512yes—
297C23×C79C2518yes—
298C23×C79C2511yescharacteristic
299C22×D79—24no—
300C22×D79—22no—
301C22×D79—24no—
302C22×D79C2×#4114yes—
303C22×D79C2512yes—
304C22×D79C2512yes—
305D4×C79—216no—
306D4×C79—416no—
307D4×C79—416no—
308C2×C4×C79—22no—
309C2×C4×C79—24no—
310C2×C4×C79—28no—
311C2×C4×C79—24no—
312C2×C4×C79—28no—
313C2×C4×C79—416no—
314C2×C4×C79C2×#4114yes—
315C2×C4×C79C2514yes—
316C2×C4×C79C2512yes—
317C2×C4×C79C2514yes—
318C2×C4×C79C2518yes—
319C2×C4×C79C2512yes—
320C22⋊D79—232no—
321C22⋊D79—28no—
322C22⋊D79—28no—
323C22⋊D79—416no—
324C2×Dic79—22no—
325C2×Dic79—28no—
326C2×Dic79—24no—
327C2×Dic79—28no—
328C2×Dic79—24no—
329C2×Dic79—232no—
330C2×Dic79—416no—
331C2×Dic79—48no—
332C2×Dic79C2×#4114yes—
333C2×Dic79C2514yes—
334C2×Dic79C2514yes—
335C2×Dic79C2518yes—
336C2×Dic79C2512yes—
337C2×Dic79C2518yes—
338C2×Dic79C2512yes—
339D316—28no—
340C4×D79—28no—
341C4×D79—416no—
342C4×D79—48no—
343C4×D79—48no—
344C4×D79C2×#41116yes—
345Dic158—216no—
346Dic158—28no—
347C22×C79—22no—
348C22×C79—28no—
349C22×C79—28no—
350C22×C79—28no—
351C22×C79—24no—
352C22×C79—416no—
353C22×C79—44no—
354C22×C79C22×#4112yes—
355C22×C79#58514yes—
356C22×C79C2611yescharacteristic
357C2×D79—24no—
358C2×D79—28no—
359C2×D79—22no—
360C2×D79—24no—
361C2×D79—44no—
362C2×D79C22×#4114yes—
363C4×C79—22no—
364C4×C79—24no—
365C4×C79—28no—
366C4×C79—24no—
367C4×C79C22×#4114yes—
368Dic79—22no—
369Dic79—28no—
370Dic79—28no—
371Dic79—24no—
372Dic79—24no—
373Dic79C22×#4114yes—
374C2×#3512—791nomaximal, Sylow
375C2×C79—42no—
376C2×C79—48no—
377C2×C79#351214yescomplemented
378C2×C79C23×#4111yescharacteristic
379C2×C79C2×#58512yes—
380D79—24no—
381D79—42no—
382#3512—7932no—
383C2×#553—794no—
384C2×#553—794no—
385C2×#553—794no—
386C2×#552—794no—
387C2×#541—791no—
388C2×#541—791no—
389C2×#540—791no—
390C2×#540D7911yescharacteristic, complemented
391C2×#537—792no—
392C2×#532—791no—
393C2×#529—792no—
394C2×#529—792no—
395C22×#125—791no—
396C2×#520—792no—
397C2×C4×#41—791no—
398C79C2×#351211yescharacteristic, complemented, Sylow
399C22×#41—792no—
400C22×#41—791no—
401#553—7964no—
402#553—7964no—
403#553—7964no—
404#552—7964no—
405#541—7916no—
406#541—7916no—
407#540—7916no—
408#540C2×D79116yescomplemented
409#537—7932no—
410#532—7916no—
411C2×C4⋊Q8—791no—
412C2×#127C2×D7911yescharacteristic
413#529—7932no—
414#529—7932no—
415C2×#126—794no—
416C2×#126—794no—
417C2×#126—794no—
418C2×#126—794no—
419C2×#125—7916no—
420C2×#125—792no—
421C2×#125—794no—
422C2×#125—794no—
423C2×#125—794no—
424C2×#125—791no—
425C2×#125C2×D7911yescharacteristic
426C2×#124—792no—
427C2×#123—794no—
428C2×#123—794no—
429C2×#123—794no—
430C2×#123C2×D7914yes—
431C2×C22⋊Q8—792no—
432C2×C22⋊Q8—792no—
433C2×C22⋊Q8—794no—
434C2×#121—792no—
435C2×#121—794no—
436C2×#121—794no—
437C2×#121—794no—
438C2×#121—794no—
439C2×#121—794no—
440C2×#121C2×D7912yes—
441C2×#121C2×D7914yes—
442#520—7932no—
443C4×#41—7916no—
444C2×C4×Q8—792no—
445C2×C4×Q8—792no—
446C2×C4×Q8—792no—
447C2×C4×D4—792no—
448C2×C4×D4—794no—
449C2×C4×D4—794no—
450C2×C4×D4—794no—
451C2×C4×D4—794no—
452C2×C4×D4—792no—
453C2×C4×D4—792no—
454C2×C4×D4—792no—
455C2×C4×D4—794no—
456C2×C4×D4C2×D7912yes—
457C2×#117—794no—
458C2×#117—794no—
459C2×#117—794no—
460C2×#117—791no—
461C2×#117—791no—
462C2×#117C2×D7911yescharacteristic
463C22×C4⋊C4—794no—
464C22×C4⋊C4—792no—
465C22×C4⋊C4—794no—
466C22×C42—791no—
467C22×C42—791no—
468C22×C42—791no—
469C2×#41—7916no—
470C2×#41—798no—
471C2×#41—1588no—
472C2×#41—15816no—
473C22×Q8—791no—
474C22×Q8—792no—
475C22×D4—794no—
476C22×D4—791no—
477C22×D4—794no—
478C22×D4—791no—
479C22×D4—791no—
480C22×D4C22×D7912yes—
481C22×D4C22×D7914yes—
482C22×D4C22×D7914yes—
483C23×C4—794no—
484C23×C4—792no—
485C23×C4—794no—
486C23×C4—792no—
487C23×C4—792no—
488C23×C4—791no—
489C23×C4—794no—
490C23×C4—791no—
491C23×C4C22×D7911yescharacteristic
492C23×C4C22×D7914yes—
493C4⋊Q8—798no—
494#127C22×D7918yes—
495#126—7932no—
496#126—7932no—
497#126—7932no—
498#126—7932no—
499#125—7916no—
500#125—7932no—
501#125—7932no—
502#125—7932no—
503#125—798no—
504#125C22×D7918yes—
505#124—7916no—
506#123—7932no—
507#123—7932no—
508#123—7932no—
509#123C22×D79132yes—
510C22⋊Q8—7916no—
511C22⋊Q8—7916no—
512C22⋊Q8—7932no—
513#121—7916no—
514#121—7932no—
515#121—7932no—
516#121—7932no—
517#121—7932no—
518#121—7932no—
519#121C22×D79116yes—
520#121C22×D79132yes—
521C4×Q8—7916no—
522C4×Q8—7916no—
523C4×Q8—7916no—
524C4×D4—7916no—
525C4×D4—7932no—
526C4×D4—7932no—
527C4×D4—7932no—
528C4×D4—7932no—
529C4×D4—7916no—
530C4×D4—7916no—
531C4×D4—7916no—
532C4×D4—7932no—
533C4×D4C22×D79116yes—
534#117—7932no—
535#117—7932no—
536#117—7932no—
537#117—798no—
538#117—798no—
539#117C22×D7918yes—
540C2×C4⋊C4—792no—
541C2×C4⋊C4—794no—
542C2×C4⋊C4—794no—
543C2×C4⋊C4—794no—
544C2×C4⋊C4—792no—
545C2×C4⋊C4—794no—
546C2×C4⋊C4—794no—
547C2×C4⋊C4—7932no—
548C2×C4⋊C4—794no—
549C2×C4⋊C4—792no—
550C2×C4⋊C4—794no—
551C2×C4⋊C4—794no—
552C2×C4⋊C4—794no—
553C2×C4⋊C4—7916no—
554C2×C4⋊C4—7932no—
555C2×C4⋊C4C22×D7912yes—
556C2×C4⋊C4C22×D7914yes—
557C2×C4⋊C4C22×D7912yes—
558C2×C22⋊C4—794no—
559C2×C22⋊C4—794no—
560C2×C22⋊C4—794no—
561C2×C22⋊C4—794no—
562C2×C22⋊C4—794no—
563C2×C22⋊C4—792no—
564C2×C22⋊C4—792no—
565C2×C22⋊C4—794no—
566C2×C22⋊C4C22×D7914yes—
567C2×C22⋊C4C22×D7914yes—
568C2×C22⋊C4C22×D7912yes—
569C2×C42—791no—
570C2×C42—794no—
571C2×C42—794no—
572C2×C42—792no—
573C2×C42—792no—
574C2×C42—792no—
575C2×C42—798no—
576C2×C42—791no—
577C2×C42—798no—
578C2×C42—798no—
579C2×C42C22×D7911yescharacteristic
580C2×C42C22×D7911yescharacteristic
581C24—791no—
582C24—791no—
583C24C23×D7914yes—
584C24C23×D7911yescharacteristic
585#41—15832no—
586#41—15864no—
587C2×Q8—794no—
588C2×Q8—798no—
589C2×Q8—1584no—
590C2×Q8—1588no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—3168no—
595C2×D4—7916no—
596C2×D4—794no—
597C2×D4—7916no—
598C2×D4—794no—
599C2×D4—794no—
600C2×D4—1584no—
601C2×D4—1584no—
602C2×D4—1584no—
603C2×D4—15816no—
604C2×D4C23×D7918yes—
605C2×D4C23×D79116yes—
606C2×D4C23×D79116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—3164no—
610C22×C4—3168no—
611C22×C4—3164no—
612C22×C4—3164no—
613C22×C4—3168no—
614C22×C4—798no—
615C22×C4—7916no—
616C22×C4—798no—
617C22×C4—798no—
618C22×C4—7916no—
619C22×C4—791no—
620C22×C4—798no—
621C22×C4—794no—
622C22×C4—7916no—
623C22×C4—792no—
624C22×C4—792no—
625C22×C4—794no—
626C22×C4—791no—
627C22×C4—794no—
628C22×C4—794no—
629C22×C4—15816no—
630C22×C4—1584no—
631C22×C4C23×D7914yes—
632C22×C4C23×D7912yes—
633C22×C4C23×D7911yescharacteristic
634C22×C4C23×D7912yes—
635C22×C4C23×D7914yes—
636C22×C4C23×D79116yes—
637C22×C4C23×D7911yescharacteristic
638C4⋊C4—798no—
639C4⋊C4—7916no—
640C4⋊C4—7916no—
641C4⋊C4—7916no—
642C4⋊C4—7916no—
643C4⋊C4—7916no—
644C4⋊C4—798no—
645C4⋊C4—7916no—
646C4⋊C4—7916no—
647C4⋊C4—798no—
648C4⋊C4—7916no—
649C4⋊C4—7916no—
650C4⋊C4C23×D7918yes—
651C4⋊C4C23×D79116yes—
652C4⋊C4C23×D7918yes—
653C22⋊C4—7916no—
654C22⋊C4—7916no—
655C22⋊C4—7916no—
656C22⋊C4—7916no—
657C22⋊C4—7916no—
658C22⋊C4—798no—
659C22⋊C4—798no—
660C22⋊C4—7916no—
661C22⋊C4C23×D79116yes—
662C22⋊C4C23×D79116yes—
663C22⋊C4C23×D7918yes—
664C42—794no—
665C42—794no—
666C42—798no—
667C42—798no—
668C42—798no—
669C42—7916no—
670C42—7916no—
671C42C23×D7914yes—
672C42C23×D7914yes—
673C23—28no—
674C23—24no—
675C23—28no—
676C23—22no—
677C23—28no—
678C23—792no—
679C23—794no—
680C23—792no—
681C23—1584no—
682C23—1582no—
683C23—1584no—
684C23C24×D7912yes—
685C23C24×D7918yes—
686C23C24×D7911yescharacteristic
687Q8—1588no—
688Q8—15816no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—31616no—
693D4—1588no—
694D4—1588no—
695D4—1588no—
696D4—15832no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—3168no—
704C2×C4—31616no—
705C2×C4—3168no—
706C2×C4—3168no—
707C2×C4—31616no—
708C2×C4—792no—
709C2×C4—794no—
710C2×C4—7916no—
711C2×C4—794no—
712C2×C4—794no—
713C2×C4—792no—
714C2×C4—798no—
715C2×C4—798no—
716C2×C4—15832no—
717C2×C4—1584no—
718C2×C4—1584no—
719C2×C4—1588no—
720C2×C4—1588no—
721C2×C4—1582no—
722C2×C4—1588no—
723C2×C4#41×D7914yes—
724C2×C4C24×D7914yes—
725C2×C4C24×D7912yes—
726C2×C4C24×D7914yes—
727C2×C4C24×D7918yes—
728C2×C4C24×D7912yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—416no—
735C22—44no—
736C22—3164no—
737C22—794no—
738C22—1582no—
739C22—1584no—
740C22—1588no—
741C22—1584no—
742C22C2×#41×D7912yes—
743C22#1909939814yes—
744C22C25×D7911yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—794no—
750C4—1588no—
751C4—1582no—
752C4—1584no—
753C4—1584no—
754C4—1588no—
755C4C2×#41×D7914yes—
756C2—42no—
757C2—48no—
758C2—3162no—
759C2—1584no—
760C2#2377731914yesdirect product factor
761C2C22×#41×D7911yescharacteristic
762C2C2×#1909939812yes—
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#540×C79C2
socleC23×C79C25
hypercenterC2×#540D79
hypocenterC79C2×#3512
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #23777319C2direct (N × H)
2. C2×#19099260C2semidirect
3. C2×#19099258C2semidirect
4. C2×#19099256C2semidirect
5. C2×#19099250C2semidirect
6. C2×#19099176C2semidirect
7. C2×#19099175C2semidirect
8. C2×#19099167C2semidirect
9. C2×#19099142C2semidirect
10. C2×#19099111C2semidirect
11. C2×#19099095C2semidirect
12. C2×#19099094C2semidirect
13. C2×#125×D79C2semidirect
14. C2×#19099042C2semidirect
15. C2×#19099031C2semidirect
16. C2×#540×C79C2semidirect
19. #19099260C22semidirect
20. #19099258C22semidirect
21. #19099256C22semidirect
22. #19099250C22semidirect
23. #19099176C22semidirect
24. #19099175C22semidirect
25. #19099167C22semidirect
26. #19099142C22semidirect
27. #19099111C22semidirect
29. #19099095C22semidirect
30. #19099094C22semidirect
40. #125×D79C22semidirect
54. #19099042C22semidirect
55. #19099031C22semidirect
79. #540×C79C22semidirect
377. C2×C79#3512semidirect
390. C2×#540D79semidirect
398. C79C2×#3512semidirect
408. #540C2×D79semidirect
760. C2#23777319direct (N × H)

Maximal subgroups

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

subgroupindex
#237773192
C2×#190992602
C2×#190992582
C2×#190992562
C2×#190992502
C2×#190991762
C2×#190991752
C2×#190991672
C2×#190991422
C2×#190991112
C2×#190990952
C2×#190990942
C2×#125×D792
C2×#190990422
C2×#190990312
C2×#540×C792
C2×#351279