Finite Group Databasebeta

← #23776883

Subgroups — #23776883

Order 10112.

1648 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11929624C211yesmaximal, characteristic, complemented
2C2×#41×D79C211yesmaximal, characteristic, complemented
3#19099231C211yesmaximal, characteristic, complemented
4#19099226C211yesmaximal, characteristic, complemented
5#19099223C211yesmaximal, characteristic, complemented
6#19099219C211yesmaximal, characteristic, complemented
7#19099215C211yesmaximal, characteristic, complemented
8#19099211C212yesmaximal, complemented
9#19099210C211yesmaximal, characteristic, complemented
10#19099205C212yesmaximal, complemented
11#19099204C211yesmaximal, characteristic, complemented
12#19099200C212yesmaximal, complemented
13#19099197C211yesmaximal, characteristic, complemented
14#19099195C212yesmaximal, complemented
15#19099110C212yesmaximal, complemented
16#19099109C211yesmaximal, characteristic, complemented
17#19099075C211yesmaximal, characteristic, complemented
18#19099072C212yesmaximal, complemented
19#19099072C212yesmaximal, complemented
20#19099031C211yesmaximal, characteristic, complemented
21C2×C4×C22⋊D79C211yesmaximal, characteristic, complemented
22C4×D4×D79C212yesmaximal, complemented
23#525×C79C211yesmaximal, characteristic, complemented
24C2×#11929625C2211yescharacteristic, complemented
25C2×#11929624—28no—
26C2×#11929624C2211yescharacteristic
27C2×#11929624C2212yescomplemented
28C2×#11929624C2211yescharacteristic, complemented
29C2×#11929624C2211yescharacteristic, complemented
30C2×#11929624C2212yescomplemented
31C2×#11929624C2212yescomplemented
32C2×#11929624C2211yescharacteristic, complemented
33C2×#11929623C2212yescomplemented
34C2×#11929623C2211yescharacteristic, complemented
35#41×D79—28no—
36C22×Dic158C2211yescharacteristic, complemented
37C2×Q8×D79C2211yescharacteristic, complemented
38C22×D316C2211yescharacteristic, complemented
39C22×C22⋊D79C2211yescharacteristic
40C22×C22⋊D79C2212yescomplemented
41C2×D4×D79C2212yes—
42C2×D4×D79C2212yescomplemented
43C2×D4×D79C2211yescharacteristic, complemented
44C22×C4×D79C2212yescomplemented
45C22×C4×D79C2212yescomplemented
46C22×C4×D79C2211yescharacteristic, complemented
47#14579160C2212yescomplemented
48#14579159C2211yescharacteristic, complemented
49#14579157C2212yescomplemented
50#14579157C2211yescharacteristic, complemented
51#14579150C2211yescharacteristic, complemented
52#14579148C2211yescharacteristic, complemented
53#14579147C2212yescomplemented
54#14579147C2212yescomplemented
55#14579146C2212yescomplemented
56#14579146C2212yescomplemented
57#14579145C2212yescomplemented
58#14579143C2212yescomplemented
59#14579143C2212yescomplemented
60#14579141C2211yescharacteristic, complemented
61#14579141C2211yescharacteristic, complemented
62#14579139C2212yescomplemented
63#14579139C2212yescomplemented
64#14579138C2212yescomplemented
65#14579138C2212yescomplemented
66#14579136C2211yescharacteristic, complemented
67#14579136C2212yescomplemented
68#14579136C2211yescharacteristic, complemented
69#14579134C2212yescomplemented
70#14579134C2212yescomplemented
71#14579134C2212yescomplemented
72#14579134C2212yescomplemented
73#14579133C2212yescomplemented
74#14579133C2212yescomplemented
75#14579133C2212yescomplemented
76#14579133C2212yescomplemented
77#14579132C2212yescomplemented
78#14579131C2212yescomplemented
79#14579131C2212yescomplemented
80#14579131C2212yescomplemented
81#14579129C2212yescomplemented
82#14579129C2212yescomplemented
83#14579126C2211yescharacteristic, complemented
84#14579126C2211yescharacteristic, complemented
85C4×D316C2212yescomplemented
86C4×D316C2212yescomplemented
87D4×Dic79C2212yescomplemented
88#14579123C2211yescharacteristic, complemented
89#14579123C2211yescharacteristic, complemented
90#14579123C2212yescomplemented
91C4×C22⋊D79C2211yescharacteristic
92C4×C22⋊D79C2211yescharacteristic
93C4×C22⋊D79C2211yescharacteristic, complemented
94C4×C22⋊D79C2211yescharacteristic, complemented
95C4×C22⋊D79C2211yescharacteristic, complemented
96C4×C22⋊D79C2212yescomplemented
97C4×C22⋊D79C2211yescharacteristic, complemented
98C4×C22⋊D79C2211yescharacteristic, complemented
99C4×C22⋊D79C2211yescharacteristic, complemented
100C4×C22⋊D79C2212yescomplemented
101(C22⋊D79)⋊C4C2212yes—
102(C22⋊D79)⋊C4C2212yescomplemented
103(C22⋊D79)⋊C4C2212yescomplemented
104(C22⋊D79)⋊C4C2212yescomplemented
105#14579118C2212yescomplemented
106C2×Dic79⋊C4C2211yescharacteristic, complemented
107C4⋊C4×D79C2212yescomplemented
108C2×C22⋊Dic79C2211yescharacteristic, complemented
109C2×(C2×D79)⋊C4C2211yescharacteristic, complemented
110C22⋊C4×D79C2212yescomplemented
111C22⋊C4×D79C2212yescomplemented
112C2×C4×Dic79C2211yescharacteristic, complemented
113C42×D79C2212yescomplemented
114C2×#41×C79C2211yescharacteristic, complemented
115C23×C4×C79C2211yescharacteristic, complemented
116#123×C79C2212yescomplemented
117C22⋊Q8×C79C2211yescharacteristic, complemented
118C22⋊Q8×C79C2211yescharacteristic, complemented
119#121×C79C2211yescharacteristic, complemented
120#121×C79C2211yescharacteristic, complemented
121#120×C79C2212yescomplemented
122C4×D4×C79C2212yescomplemented
123C4×D4×C79C2212yescomplemented
124#117×C79C2211yescharacteristic, complemented
125C23×D79C2312yes—
126C23×D79C2312yes—
127C23×D79C2311yescharacteristic
128#11929625—24no—
129#11929624—24no—
130#11929624—28no—
131#11929624—28no—
132#11929624—24no—
133#11929624—24no—
134#11929624—28no—
135#11929624D418yescomplemented
136#11929623—24no—
137#11929623—28no—
138C2×Dic158—24no—
139C2×Dic158C2312yes—
140C2×Dic158C2312yes—
141C2×Dic158C2311yescharacteristic
142C2×Dic158C2311yescharacteristic
143Q8×D79—24no—
144C2×D316—24no—
145C2×D316C2312yes—
146C2×D316C2311yescharacteristic
147C2×D316C2312yes—
148C2×D316C2312yes—
149C2×D316C2312yes—
150C2×D316C2311yescharacteristic
151C2×C22⋊D79—28no—
152C2×C22⋊D79—24no—
153C2×C22⋊D79C2312yes—
154C2×C22⋊D79C2312yes—
155C2×C22⋊D79C2312yes—
156C2×C22⋊D79C2312yes—
157C2×C22⋊D79C2312yes—
158C2×C22⋊D79C2312yes—
159C2×C22⋊D79C2311yescharacteristic
160C2×C22⋊D79C2311yescharacteristic
161C2×C22⋊D79C2311yescharacteristic
162C2×C22⋊D79C2312yes—
163C2×C22⋊D79C2312yes—
164C2×C22⋊D79C2311yescharacteristic
165D4×D79—24no—
166D4×D79—28no—
167D4×D79—28no—
168C22×Dic79C2312yes—
169C22×Dic79C2311yescharacteristic
170C22×Dic79C2312yes—
171C22×Dic79C2311yescharacteristic
172C22×Dic79C2311yescharacteristic
173C2×C4×D79—28no—
174C2×C4×D79—28no—
175C2×C4×D79—24no—
176C2×C4×D79C2312yes—
177C2×C4×D79C2311yescharacteristic
178C2×C4×D79C2312yes—
179C2×C4×D79C2311yescharacteristic
180C2×C4×D79C2312yes—
181C2×C4×D79C2312yes—
182C2×C4×D79C2311yescharacteristic
183C2×C4×D79C2312yes—
184C2×C4×D79C2312yes—
185C2×C4×D79C2311yescharacteristic
186C2×C4×D79C2312yes—
187C2×C4×D79C2312yes—
188C4⋊Dic79C2312yes—
189C4⋊Dic79C2312yes—
190Dic79⋊C4C2311yescharacteristic
191Dic79⋊C4C2312yes—
192Dic79⋊C4C2311yescharacteristic
193Dic79⋊C4C2311yescharacteristic
194Dic79⋊C4C2311yescharacteristic
195Dic79⋊C4C2312yes—
196Dic79⋊C4C2312yes—
197Dic79⋊C4C2312yes—
198C22⋊Dic79C2311yescharacteristic
199C22⋊Dic79C2312yes—
200C22⋊Dic79C2311yescharacteristic
201C22⋊Dic79C2311yescharacteristic
202C22⋊Dic79C2311yescharacteristic
203C22⋊Dic79C2312yes—
204(C2×D79)⋊C4C2311yescharacteristic
205(C2×D79)⋊C4C2312yes—
206(C2×D79)⋊C4C2312yes—
207(C2×D79)⋊C4C2312yes—
208(C2×D79)⋊C4C2311yescharacteristic
209(C2×D79)⋊C4C2311yescharacteristic
210(C2×D79)⋊C4C2311yescharacteristic
211(C2×D79)⋊C4C2312yes—
212(C2×D79)⋊C4C2312yes—
213(C2×D79)⋊C4C2312yes—
214(C2×D79)⋊C4C2312yes—
215(C2×D79)⋊C4C2312yes—
216C4×Dic79C2311yescharacteristic
217C4×Dic79C2312yes—
218C4×Dic79C2312yes—
219C4×Dic79C2311yescharacteristic
220C4×Dic79C2311yescharacteristic
221C4×Dic79C2311yescharacteristic
222C24×C79C2311yescharacteristic
223#41×C79—24no—
224C2×Q8×C79C2311yescharacteristic
225C2×D4×C79C2312yes—
226C2×D4×C79C2311yescharacteristic
227C2×D4×C79C2312yes—
228C2×D4×C79C2312yes—
229C22×C4×C79—24no—
230C22×C4×C79C2311yescharacteristic
231C22×C4×C79C2311yescharacteristic
232C22×C4×C79C2311yescharacteristic
233C22×C4×C79C2311yescharacteristic
234C22×C4×C79C2312yes—
235C22×C4×C79C2311yescharacteristic
236C22×C4×C79C2311yescharacteristic
237C4⋊C4×C79C2311yescharacteristic
238C4⋊C4×C79C2311yescharacteristic
239C4⋊C4×C79C2312yes—
240C4⋊C4×C79C2312yes—
241C22⋊C4×C79C2312yes—
242C22⋊C4×C79C2312yes—
243C22⋊C4×C79C2312yes—
244C22⋊C4×C79C2312yes—
245C22⋊C4×C79C2312yes—
246C42×C79C2312yes—
247C23×C79—22no—
248C23×C79—22no—
249C23×C79—41no—
250C23×C79C2412yes—
251C23×C79C2411yescharacteristic
252C23×C79C2411yescharacteristic
253C23×C79C2411yescharacteristic
254C22×D79—22no—
255C22×D79—24no—
256C22×D79—24no—
257C22×D79—24no—
258C22×D79—24no—
259C22×D79—22no—
260C22×D79—42no—
261C22×D79—41no—
262C22×D79—42no—
263C22×D79C2411yescharacteristic
264C22×D79C2412yes—
265C22×D79C2412yes—
266C22×D79C2411yescharacteristic
267Q8×C79—22no—
268D4×C79—24no—
269D4×C79—24no—
270D4×C79—22no—
271D4×C79—42no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—24no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79C2×D414yescomplemented
279C2×C4×C79C2412yes—
280C2×C4×C79C2412yes—
281C2×C4×C79C2411yescharacteristic
282C2×C4×C79C2412yes—
283C2×C4×C79C2411yescharacteristic
284C2×C4×C79C2411yescharacteristic
285C2×C4×C79C2411yescharacteristic
286C22⋊D79—24no—
287C22⋊D79—22no—
288C22⋊D79—24no—
289C22⋊D79—24no—
290C22⋊D79—22no—
291C22⋊D79—24no—
292C22⋊D79—24no—
293C22⋊D79—24no—
294C22⋊D79—22no—
295C22⋊D79—42no—
296C22⋊D79C2×D418yescomplemented
297C22⋊D79#4114yescomplemented
298C2×Dic79—22no—
299C2×Dic79—24no—
300C2×Dic79—24no—
301C2×Dic79—22no—
302C2×Dic79—41no—
303C2×Dic79C2411yescharacteristic
304C2×Dic79C2411yescharacteristic
305C2×Dic79C2411yescharacteristic
306C2×Dic79C2411yescharacteristic
307C2×Dic79C2412yes—
308C2×Dic79C2411yescharacteristic
309C2×Dic79C2412yes—
310C2×Dic79C2411yescharacteristic
311D316—24no—
312D316—24no—
313D316—24no—
314D316—22no—
315D316—42no—
316D316C2×D414yescomplemented
317C4×D79—24no—
318C4×D79—24no—
319C4×D79—22no—
320C4×D79—22no—
321C4×D79—22no—
322C4×D79—24no—
323C4×D79—22no—
324C4×D79—24no—
325C4×D79—24no—
326C4×D79—24no—
327C4×D79—42no—
328C4×D79C2×D418yescomplemented
329Dic158—22no—
330Dic158—24no—
331Dic158—24no—
332Dic158C2×D414yescomplemented
333C22×C79—21no—
334C22×C79—21no—
335C22×C79—21no—
336C22×C79—21no—
337C22×C79—21no—
338C22×C79—22no—
339C22×C79—21no—
340C22×C79—22no—
341C22×C79—22no—
342C22×C79—21no—
343C22×C79—44no—
344C22×C79C22×D412yes—
345C22×C79C2×#4112yescomplemented
346C22×C79C2511yescharacteristic
347C2×D79—21no—
348C2×D79—22no—
349C2×D79—21no—
350C2×D79—22no—
351C2×D79—22no—
352C2×D79—21no—
353C2×D79—21no—
354C2×D79—22no—
355C2×D79—22no—
356C2×D79—21no—
357C2×D79—48no—
358C2×D79—44no—
359C2×D79—48no—
360C2×D79C22×D414yes—
361C2×D79C2×#4112yescomplemented
362C4×C79—21no—
363C4×C79—21no—
364C4×C79—22no—
365C4×C79—22no—
366C4×C79—22no—
367C4×C79C22×D412yes—
368C4×C79C22×D412yes—
369Dic79—22no—
370Dic79—21no—
371Dic79—21no—
372Dic79—21no—
373Dic79—21no—
374Dic79—21no—
375Dic79C22×D414yes—
376Dic79C2×#4112yescomplemented
377C2×C79—22no—
378C2×C79—22no—
379C2×C79—42no—
380C2×C79—41no—
381C2×C79C23×D411yescharacteristic
382C2×C79C22×#4111yescharacteristic
383C2×C79#58511yescharacteristic
384D79—22no—
385D79—24no—
386D79—41no—
387D79—42no—
388D4×#41—791nomaximal, Sylow
389C79D4×#4111yescharacteristic, complemented, Sylow
390C22×#41—791no—
391C22×#41—791no—
392#550—791no—
393D4×Q8—791no—
394#548—791no—
395#548—791no—
396#547—792no—
397#547—791no—
398#546—792no—
399#546—791no—
400#546—791no—
401#546—792no—
402D42—791no—
403D42—792no—
404#532—791no—
405#532—792no—
406#525—792no—
407#525—792no—
408#525—791no—
409#525D7911yescharacteristic, complemented
410C4×#41—791no—
411C2×C4×D4—791no—
412C2×C4×D4—792no—
413C2×#41—791no—
414C2×#41—792no—
415C2×#41—791no—
416C2×#41—791no—
417C2×#41—792no—
418C2×#41—792no—
419C2×#41—791no—
420C2×#41—791no—
421C2×#41—792no—
422C2×#41—791no—
423C2×#41—1588no—
424C2×#41—1588no—
425C2×#41C2×D7911yescharacteristic, complemented
426C22×Q8—791no—
427C22×Q8—791no—
428C22×D4—791no—
429C22×D4—792no—
430C22×D4—792no—
431C22×D4—792no—
432C22×D4—791no—
433C22×D4—791no—
434C23×C4—792no—
435C23×C4—792no—
436C23×C4—791no—
437C23×C4C2×D7911yescharacteristic, complemented
438C4⋊Q8—791no—
439C4⋊Q8—792no—
440#127—791no—
441#127—792no—
442#124—791no—
443#124—791no—
444#124—792no—
445#124—792no—
446#123—792no—
447#123—792no—
448#123—792no—
449#123—792no—
450#123—792no—
451#123C2×D7912yescomplemented
452C22⋊Q8—792no—
453C22⋊Q8—791no—
454C22⋊Q8—792no—
455C22⋊Q8—791no—
456C22⋊Q8—792no—
457C22⋊Q8—792no—
458C22⋊Q8C2×D7911yescharacteristic, complemented
459C22⋊Q8C2×D7911yescharacteristic, complemented
460#121—792no—
461#121—792no—
462#121—792no—
463#121—792no—
464#121—792no—
465#121—791no—
466#121—791no—
467#121—792no—
468#121—792no—
469#121—792no—
470#121—792no—
471#121—792no—
472#121C2×D7911yescharacteristic, complemented
473#121C2×D7911yescharacteristic, complemented
474#120—792no—
475#120—792no—
476#120—792no—
477#120—792no—
478#120—792no—
479#120C2×D7912yescomplemented
480C4×Q8—791no—
481C4×Q8—791no—
482C4×D4—792no—
483C4×D4—791no—
484C4×D4—791no—
485C4×D4—791no—
486C4×D4—792no—
487C4×D4—791no—
488C4×D4—791no—
489C4×D4—791no—
490C4×D4—791no—
491C4×D4—791no—
492C4×D4—792no—
493C4×D4—792no—
494C4×D4—791no—
495C4×D4—791no—
496C4×D4—792no—
497C4×D4—792no—
498C4×D4—792no—
499C4×D4—792no—
500C4×D4—792no—
501C4×D4—792no—
502C4×D4C2×D7912yescomplemented
503C4×D4C2×D7912yescomplemented
504#117—792no—
505#117C2×D7911yescharacteristic, complemented
506C2×C4⋊C4—791no—
507C2×C4⋊C4—792no—
508C2×C22⋊C4—791no—
509C2×C22⋊C4—791no—
510C2×C22⋊C4—792no—
511C2×C22⋊C4—792no—
512C2×C42—791no—
513C2×C42—792no—
514C24—792no—
515C24—791no—
516C24—792no—
517C24C22×D7911yescharacteristic
518#41—24no—
519#41—798no—
520#41—1588no—
521#41—1588no—
522#41—1588no—
523#41—1584no—
524#41—1584no—
525#41—1588no—
526#41—1584no—
527#41—1584no—
528#41—1584no—
529C2×Q8—791no—
530C2×Q8—792no—
531C2×Q8—792no—
532C2×Q8—791no—
533C2×Q8—1584no—
534C2×Q8—1584no—
535C2×Q8C22×D7911yescharacteristic
536C2×D4—792no—
537C2×D4—791no—
538C2×D4—792no—
539C2×D4—791no—
540C2×D4—791no—
541C2×D4—792no—
542C2×D4—791no—
543C2×D4—792no—
544C2×D4—792no—
545C2×D4—792no—
546C2×D4—792no—
547C2×D4—792no—
548C2×D4—792no—
549C2×D4—791no—
550C2×D4—792no—
551C2×D4—792no—
552C2×D4—792no—
553C2×D4—791no—
554C2×D4—1584no—
555C2×D4—1588no—
556C2×D4—1588no—
557C2×D4—1584no—
558C2×D4—1584no—
559C2×D4—1588no—
560C2×D4C22×D7912yes—
561C2×D4C22×D7912yes—
562C2×D4C22×D7911yescharacteristic
563C2×D4C22×D7912yes—
564C22×C4—24no—
565C22×C4—791no—
566C22×C4—792no—
567C22×C4—792no—
568C22×C4—791no—
569C22×C4—791no—
570C22×C4—792no—
571C22×C4—792no—
572C22×C4—792no—
573C22×C4—792no—
574C22×C4—792no—
575C22×C4—792no—
576C22×C4—791no—
577C22×C4—792no—
578C22×C4—791no—
579C22×C4—791no—
580C22×C4—791no—
581C22×C4—792no—
582C22×C4—1588no—
583C22×C4—1588no—
584C22×C4—1584no—
585C22×C4C22×D7911yescharacteristic
586C22×C4C22×D7911yescharacteristic
587C22×C4C22×D7911yescharacteristic
588C22×C4C22×D7911yescharacteristic
589C22×C4C22×D7912yes—
590C22×C4C22×D7911yescharacteristic
591C22×C4C22×D7911yescharacteristic
592C4⋊C4—791no—
593C4⋊C4—792no—
594C4⋊C4—791no—
595C4⋊C4—791no—
596C4⋊C4—791no—
597C4⋊C4—792no—
598C4⋊C4—792no—
599C4⋊C4—792no—
600C4⋊C4—792no—
601C4⋊C4—792no—
602C4⋊C4C22×D7912yes—
603C4⋊C4C22×D7911yescharacteristic
604C4⋊C4C22×D7911yescharacteristic
605C4⋊C4C22×D7912yes—
606C22⋊C4—791no—
607C22⋊C4—791no—
608C22⋊C4—791no—
609C22⋊C4—792no—
610C22⋊C4—791no—
611C22⋊C4—792no—
612C22⋊C4—791no—
613C22⋊C4—791no—
614C22⋊C4—792no—
615C22⋊C4—791no—
616C22⋊C4—792no—
617C22⋊C4—792no—
618C22⋊C4—791no—
619C22⋊C4—792no—
620C22⋊C4—792no—
621C22⋊C4—792no—
622C22⋊C4—792no—
623C22⋊C4—792no—
624C22⋊C4C22×D7912yes—
625C22⋊C4C22×D7912yes—
626C22⋊C4C22×D7912yes—
627C22⋊C4C22×D7912yes—
628C22⋊C4C22×D7912yes—
629C42—792no—
630C42—791no—
631C42—792no—
632C42—791no—
633C42—791no—
634C42—791no—
635C42C22×D7912yes—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—3161no—
640C23—3162no—
641C23—3162no—
642C23—791no—
643C23—792no—
644C23—792no—
645C23—791no—
646C23—1584no—
647C23—1584no—
648C23—1582no—
649C23—1584no—
650C23—1584no—
651C23—1582no—
652C23C23×D7912yes—
653C23C23×D7911yescharacteristic
654C23C23×D7911yescharacteristic
655C23C23×D7911yescharacteristic
656Q8—22no—
657Q8—794no—
658Q8—1584no—
659Q8—1584no—
660Q8—1582no—
661D4—24no—
662D4—24no—
663D4—22no—
664D4—42no—
665D4—3162no—
666D4—3162no—
667D4—794no—
668D4—798no—
669D4—794no—
670D4—1584no—
671D4—1584no—
672D4—1584no—
673D4—1584no—
674D4—1582no—
675D4—1584no—
676D4—1584no—
677D4—1582no—
678D4—1584no—
679D4—1584no—
680D4—1582no—
681D4—1584no—
682D4—1582no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—3162no—
690C2×C4—3161no—
691C2×C4—791no—
692C2×C4—792no—
693C2×C4—798no—
694C2×C4—791no—
695C2×C4—791no—
696C2×C4—791no—
697C2×C4—791no—
698C2×C4—791no—
699C2×C4—792no—
700C2×C4—1584no—
701C2×C4—1584no—
702C2×C4—1584no—
703C2×C4—1584no—
704C2×C4—1584no—
705C2×C4—1584no—
706C2×C4—1584no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1584no—
713C2×C4—1582no—
714C2×C4D4×D7914yescomplemented
715C2×C4C23×D7912yes—
716C2×C4C23×D7912yes—
717C2×C4C23×D7911yescharacteristic
718C2×C4C23×D7912yes—
719C2×C4C23×D7911yescharacteristic
720C2×C4C23×D7911yescharacteristic
721C2×C4C23×D7911yescharacteristic
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—22no—
728C22—21no—
729C22—22no—
730C22—22no—
731C22—21no—
732C22—44no—
733C22—3168no—
734C22—3164no—
735C22—3168no—
736C22—794no—
737C22—792no—
738C22—1581no—
739C22—1582no—
740C22—1582no—
741C22—1581no—
742C22—1582no—
743C22—1581no—
744C22—1582no—
745C22—1581no—
746C22—1581no—
747C22—1582no—
748C22C2×D4×D7912yes—
749C22#41×D7912yescomplemented
750C22C24×D7911yescharacteristic
751C4—22no—
752C4—21no—
753C4—21no—
754C4—22no—
755C4—22no—
756C4—794no—
757C4—792no—
758C4—1581no—
759C4—1581no—
760C4—1581no—
761C4—1582no—
762C4—1581no—
763C4—1581no—
764C4C2×D4×D7912yes—
765C4C2×D4×D7912yes—
766C2—22no—
767C2—22no—
768C2—41no—
769C2—42no—
770C2—3162no—
771C2—3161no—
772C2—1582no—
773C2—1584no—
774C2C22×D4×D7911yescharacteristic
775C2C2×#41×D7911yescharacteristic
776C2#1909939911yescharacteristic
subgroupG/H
centerC2×C4C23×D79
commutator, socle, cosocleC22×C79C25
FrattiniC22C24×D79
Fitting#525×C79C2
hypercenter#525D79
hypocenterC79D4×#41
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#11929624C2semidirect
2. C2×#41×D79C2semidirect
3. #19099231C2semidirect
4. #19099226C2semidirect
5. #19099223C2semidirect
6. #19099219C2semidirect
7. #19099215C2semidirect
8. #19099211C2semidirect
9. #19099210C2semidirect
10. #19099205C2semidirect
11. #19099204C2semidirect
12. #19099200C2semidirect
13. #19099197C2semidirect
14. #19099195C2semidirect
15. #19099110C2semidirect
16. #19099109C2semidirect
17. #19099075C2semidirect
18. #19099072C2semidirect
19. #19099072C2semidirect
20. #19099031C2semidirect
21. C2×C4×C22⋊D79C2semidirect
22. C4×D4×D79C2semidirect
23. #525×C79C2semidirect
24. C2×#11929625C22semidirect
27. C2×#11929624C22semidirect
28. C2×#11929624C22semidirect
29. C2×#11929624C22semidirect
30. C2×#11929624C22semidirect
31. C2×#11929624C22semidirect
32. C2×#11929624C22semidirect
33. C2×#11929623C22semidirect
34. C2×#11929623C22semidirect
36. C22×Dic158C22semidirect
37. C2×Q8×D79C22semidirect
38. C22×D316C22semidirect
40. C22×C22⋊D79C22semidirect
42. C2×D4×D79C22semidirect
43. C2×D4×D79C22semidirect
44. C22×C4×D79C22semidirect
45. C22×C4×D79C22semidirect
46. C22×C4×D79C22semidirect
47. #14579160C22semidirect
48. #14579159C22semidirect
49. #14579157C22semidirect
50. #14579157C22semidirect
51. #14579150C22semidirect
52. #14579148C22semidirect
53. #14579147C22semidirect
54. #14579147C22semidirect
55. #14579146C22semidirect
56. #14579146C22semidirect
57. #14579145C22semidirect
58. #14579143C22semidirect
59. #14579143C22semidirect
60. #14579141C22semidirect
61. #14579141C22semidirect
62. #14579139C22semidirect
63. #14579139C22semidirect
64. #14579138C22semidirect
65. #14579138C22semidirect
66. #14579136C22semidirect
67. #14579136C22semidirect
68. #14579136C22semidirect
69. #14579134C22semidirect
70. #14579134C22semidirect
71. #14579134C22semidirect
72. #14579134C22semidirect
73. #14579133C22semidirect
74. #14579133C22semidirect
75. #14579133C22semidirect
76. #14579133C22semidirect
77. #14579132C22semidirect
78. #14579131C22semidirect
79. #14579131C22semidirect
80. #14579131C22semidirect
81. #14579129C22semidirect
82. #14579129C22semidirect
83. #14579126C22semidirect
84. #14579126C22semidirect
85. C4×D316C22semidirect
86. C4×D316C22semidirect
87. D4×Dic79C22semidirect
88. #14579123C22semidirect
89. #14579123C22semidirect
90. #14579123C22semidirect
93. C4×C22⋊D79C22semidirect
94. C4×C22⋊D79C22semidirect
95. C4×C22⋊D79C22semidirect
96. C4×C22⋊D79C22semidirect
97. C4×C22⋊D79C22semidirect
98. C4×C22⋊D79C22semidirect
99. C4×C22⋊D79C22semidirect
100. C4×C22⋊D79C22semidirect
102. (C22⋊D79)⋊C4C22semidirect
103. (C22⋊D79)⋊C4C22semidirect
104. (C22⋊D79)⋊C4C22semidirect
105. #14579118C22semidirect
106. C2×Dic79⋊C4C22semidirect
107. C4⋊C4×D79C22semidirect
108. C2×C22⋊Dic79C22semidirect
109. C2×(C2×D79)⋊C4C22semidirect
110. C22⋊C4×D79C22semidirect
111. C22⋊C4×D79C22semidirect
112. C2×C4×Dic79C22semidirect
113. C42×D79C22semidirect
114. C2×#41×C79C22semidirect
115. C23×C4×C79C22semidirect
116. #123×C79C22semidirect
117. C22⋊Q8×C79C22semidirect
118. C22⋊Q8×C79C22semidirect
119. #121×C79C22semidirect
120. #121×C79C22semidirect
121. #120×C79C22semidirect
122. C4×D4×C79C22semidirect
123. C4×D4×C79C22semidirect
124. #117×C79C22semidirect
135. #11929624D4semidirect
278. C2×C4×C79C2×D4semidirect
296. C22⋊D79C2×D4semidirect
297. C22⋊D79#41semidirect
316. D316C2×D4semidirect
328. C4×D79C2×D4semidirect
332. Dic158C2×D4semidirect
345. C22×C79C2×#41semidirect
361. C2×D79C2×#41semidirect
376. Dic79C2×#41semidirect
389. C79D4×#41semidirect
409. #525D79semidirect
425. C2×#41C2×D79semidirect
437. C23×C4C2×D79semidirect
451. #123C2×D79semidirect
458. C22⋊Q8C2×D79semidirect
459. C22⋊Q8C2×D79semidirect
472. #121C2×D79semidirect
473. #121C2×D79semidirect
479. #120C2×D79semidirect
502. C4×D4C2×D79semidirect
503. C4×D4C2×D79semidirect
505. #117C2×D79semidirect
714. C2×C4D4×D79semidirect
749. C22#41×D79semidirect