Finite Group Databasebeta

← #25968949

Subgroups — #25968949

Order 11008.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583527C211yesmaximal, characteristic, complemented
2#19147985C211yesmaximal, characteristic
3#19145895C214yesmaximal, complemented
4#19145880C214yesmaximal, complemented
5#19145865C214yesmaximal, complemented
6#19145850C214yesmaximal, complemented
7#19145147C211yesmaximal, characteristic, complemented
8#19145141C211yesmaximal, characteristic, complemented
9#19144996C211yesmaximal, characteristic, complemented
10#19144989C211yesmaximal, characteristic, complemented
11#19144528C212yesmaximal, complemented
12#19144520C212yesmaximal, complemented
13#19144418C212yesmaximal, complemented
14#19144411C212yesmaximal, complemented
15C43×#2921C211yesmaximal, characteristic, complemented
16#14583527—22no—
17#14583527—22no—
18#14583527C2214yes—
19#14583527C2214yes—
20#14583520C2212yes—
21#14583520C2212yes—
22#14583511C2212yes—
23#14583504C2212yes—
24#14583496—21no—
25#14583496—21no—
26#14583487—21no—
27#14583487—21no—
28#14583456C2211yescharacteristic
29#14583449C2211yescharacteristic
30C2×#13063325C2211yescharacteristic
31C2×#13063325C2211yescharacteristic
32C2×#13063324—21no—
33#14583427—22no—
34#14583427—22no—
35C2×#13063317C2211yescharacteristic
36C2×#13063317C2211yescharacteristic
37C2×#13063316—21no—
38#14583410C2212yes—
39C2×#13063302—21no—
40C2×#13063302—21no—
41C4×#10621898C2212yes—
42C2×#13063284C2211yescharacteristic
43C22×C4⋊Dic43C2211yescharacteristic
44#14583308C2214yescomplemented
45#14583308C2212yescomplemented
46#14583308C2212yescomplemented
47#14583304C2212yescomplemented
48#14583301C2214yescomplemented
49#14583297C2212yescomplemented
50#14583268C2212yescomplemented
51#14583264C2212yescomplemented
52#14583259C2214yescomplemented
53#14583254C2214yescomplemented
54#14583250C2212yescomplemented
55#14583246C2212yescomplemented
56#14583241C2214yes—
57#14583241C2214yes—
58#14583235C2214yes—
59#14583230C2214yes—
60#14583224C2214yes—
61#14583224C2214yes—
62#14583218C2214yes—
63#14583213C2214yes—
64#14583207C2214yescomplemented
65#14583207C2214yescomplemented
66#14583200C2214yescomplemented
67#14583200C2214yescomplemented
68#14583195C2214yescomplemented
69#14583190C2214yescomplemented
70#14583185C2214yescomplemented
71#14583180C2214yescomplemented
72#14582941C2212yes—
73#14582941C2212yes—
74#14582941C2212yes—
75#14582941C2212yes—
76#14582901C2212yes—
77#14582901C2212yes—
78#14582901C2212yes—
79#14582901C2212yes—
80C2×#117×C43C2211yescharacteristic
81C43×#433C2214yes—
82C43×#433C2214yes—
83C43×#423C2212yes—
84C43×#407C2212yes—
85C4×M16×C43C2211yescharacteristic
86C4×M16×C43C2211yescharacteristic
87C2×#10621898C2312yes—
88C22×Dic86—21no—
89C22×Dic86—21no—
90C23×Dic43—21no—
91#13063325—22no—
92#13063325—21no—
93#13063325—21no—
94#13063325C2311yescharacteristic
95#13063325C2311yescharacteristic
96#13063325C2312yes—
97#13063325C2311yescharacteristic
98#13063325C2312yes—
99#13063325C2314yes—
100#13063324—24no—
101#13063324—24no—
102#13063322C2311yescharacteristic
103#13063320—22no—
104#13063320—22no—
105#13063318—22no—
106#13063318—22no—
107#13063317—22no—
108#13063317—21no—
109#13063317—21no—
110#13063317C2312yes—
111#13063317C2312yes—
112#13063317C2312yes—
113#13063317C2314yes—
114#13063316—24no—
115#13063316—24no—
116#13063315—22no—
117#13063315—22no—
118#13063313C2312yes—
119#13063311—22no—
120#13063311—22no—
121#13063310—22no—
122#13063310—22no—
123#13063308—22no—
124#13063307—22no—
125#13063307—22no—
126#13063304—21no—
127#13063304—21no—
128#13063304C2312yes—
129#13063304C2312yes—
130#13063303—22no—
131#13063303—22no—
132#13063302—24no—
133#13063302—24no—
134#13063302—24no—
135#13063302—24no—
136#13063299—21no—
137#13063299—21no—
138#13063299C2312yes—
139#13063299C2312yes—
140#13063298—22no—
141#13063298—22no—
142#13063294—22no—
143C4×Dic86—21no—
144C4×Dic86—21no—
145C4×Dic86C2312yes—
146C4×Dic86C2312yes—
147C4×D172—21no—
148C4×D172—21no—
149C4×D172C2312yes—
150C4×D172C2312yes—
151C4×C22⋊D43—22no—
152C4×C22⋊D43—22no—
153C4×C22⋊D43—22no—
154C4×C22⋊D43—22no—
155#13063284—22no—
156#13063284C2314yes—
157#13063284C2312yes—
158#13063282—22no—
159C2×C4⋊Dic43—21no—
160C2×C4⋊Dic43—22no—
161C2×C4⋊Dic43—21no—
162C2×C4⋊Dic43—21no—
163C2×C4⋊Dic43C2311yescharacteristic
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2314yes—
166C2×C4⋊Dic43C2311yescharacteristic
167C2×C4⋊Dic43C2311yescharacteristic
168C2×Dic43⋊C4—21no—
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×Dic43⋊C4—21no—
172C2×C22⋊Dic43—21no—
173C2×C4×Dic43—21no—
174C42×D43—22no—
175#13063259C2314yes—
176#13063259C2314yes—
177#13063259C2314yes—
178#13063259C2314yes—
179#13063257C2314yes—
180#13063257C2314yes—
181#13063257C2314yes—
182#13063257C2314yes—
183#13063250C2314yes—
184#13063250C2314yes—
185#13063250C2314yes—
186#13063250C2314yes—
187#13063247C2314yes—
188#13063247C2314yes—
189#13063247C2314yes—
190#13063247C2314yes—
191C23×C4×C43C2311yescharacteristic
192C2×M16×C43C2312yes—
193C2×M16×C43C2312yes—
194#117×C43D412yes—
195#117×C43D412yes—
196#117×C43C2312yes—
197#117×C43C2312yes—
198C2×C4⋊C4×C43D411yescharacteristic
199C2×C4⋊C4×C43D411yescharacteristic
200C2×C22⋊C4×C43D411yescharacteristic
201C2×C22⋊C4×C43D411yescharacteristic
202C2×C42×C43C2311yescharacteristic
203C2×C42×C43C2311yescharacteristic
204C4⋊C8×C43C2314yes—
205C4⋊C8×C43C2314yes—
206C22⋊C8×C43C2314yes—
207C22⋊C8×C43C2314yes—
208#97×C43C2312yes—
209#97×C43C2312yes—
210C4×C8×C43C2312yes—
211C4×C8×C43C2312yes—
212C24×C43C2×D411yescharacteristic
213C22×C4×C43—24no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2412yes—
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—22no—
223C2×C22⋊D43—22no—
224C2×C22⋊D43—22no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—24no—
230C22×Dic43—82no—
231#10621898—28no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172C2412yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—24no—
241C2×Dic86—22no—
242C2×Dic86—22no—
243C2×Dic86—82no—
244C2×Dic86—82no—
245C2×Dic86C2412yes—
246M16×C43—24no—
247M16×C43—24no—
248C2×C8×C43C2414yes—
249C2×C8×C43C2414yes—
250C4⋊C4×C43C2×D412yes—
251C4⋊C4×C43C2×D412yes—
252C4⋊C4×C43C2×D412yes—
253C4⋊C4×C43C2×D412yes—
254C22⋊C4×C43C2×D412yes—
255C22⋊C4×C43C2×D412yes—
256C22⋊C4×C43C2×D412yes—
257C22⋊C4×C43C2×D412yes—
258C42×C43C2×D412yes—
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2411yescharacteristic
262C42×C43C2411yescharacteristic
263C42×C43C2412yes—
264C22⋊Dic43—24no—
265C22⋊Dic43—22no—
266C22⋊Dic43—22no—
267C22⋊Dic43—22no—
268(C2×D43)⋊C4—22no—
269(C2×D43)⋊C4—22no—
270(C2×D43)⋊C4—22no—
271(C2×D43)⋊C4—22no—
272(C2×D43)⋊C4—22no—
273(C2×D43)⋊C4—22no—
274C4⋊Dic43—24no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—24no—
278C4⋊Dic43—22no—
279C4⋊Dic43—22no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43C2412yes—
287C4⋊Dic43C2412yes—
288C4⋊Dic43C2412yes—
289C4⋊Dic43C2412yes—
290C4⋊Dic43C2412yes—
291C4⋊Dic43C2412yes—
292Dic43⋊C4—24no—
293Dic43⋊C4—22no—
294Dic43⋊C4—22no—
295Dic43⋊C4—24no—
296Dic43⋊C4—22no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304C4×Dic43—22no—
305C4×Dic43—22no—
306C4×Dic43—22no—
307C4×Dic43—24no—
308C23×C43—22no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43C22×D412yes—
312C23×C43C22×D411yescharacteristic
313C22×D43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—24no—
316C2×C4×C43—24no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C432−1+414yes—
330C2×C4×C43C2511yescharacteristic
331C22⋊D43—44no—
332C22⋊D43—82no—
333C22⋊D43—82no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—84no—
346D172—24no—
347D172—81no—
348D172—81no—
349C4×D43—44no—
350C4×D43—82no—
351C4×D43—82no—
352Dic86—24no—
353Dic86—81no—
354Dic86—81no—
355Dic86—82no—
356Dic86—84no—
357Dic86—82no—
358C8×C43—24no—
359C8×C43—24no—
360#60867—431nomaximal, Sylow
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—44no—
367C22×C43#53612yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C4×C43—21no—
373C4×C43—22no—
374C4×C43—21no—
375C4×C43—21no—
376C4×C43—22no—
377C4×C43—21no—
378C4×C43—22no—
379C4×C43#53612yes—
380C4×C43C2×2−1+412yes—
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C2×#544—431no—
389#3455—431no—
390#3244—434no—
391#3243—434no—
392#3242—434no—
393#3241—434no—
394#3166—431no—
395#3165—431no—
396#3142—431no—
397#3141—431no—
398#3093—432no—
399#3092—432no—
400#3080—432no—
401#3079—432no—
402#2921D4311yescharacteristic, complemented
403C2×C43—22no—
404C2×C43—42no—
405C2×C43C2×#53611yescharacteristic
406C2×C43#358511yescharacteristic
407C2×C43#358611yescharacteristic
408D43—82no—
409#544—434no—
410#544—434no—
411#544—862no—
412#544—862no—
413#542—432no—
414#542—432no—
415#541—432no—
416#540—432no—
417#539—861no—
418#539—861no—
419#538—861no—
420#538—861no—
421#533—431no—
422#532—431no—
423C2×C4⋊Q8—431no—
424C2×C4⋊Q8—431no—
425C2×C4⋊Q8—861no—
426#529—862no—
427#529—862no—
428C2×#125—431no—
429C2×#125—431no—
430C2×#125—861no—
431#525—432no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C4×#41—432no—
435C2×#117—431no—
436C2×#117C2×D4311yescharacteristic
437C22×C4⋊C4—431no—
438#501—434no—
439#501—432no—
440#501—432no—
441#500—432no—
442#499—434no—
443#498—432no—
444#491—432no—
445#490—432no—
446#489—434no—
447#488—434no—
448#487—432no—
449#486—432no—
450#485—434no—
451#485—434no—
452#484—434no—
453#483—434no—
454#482—434no—
455#482—434no—
456#481—434no—
457#480—434no—
458#479—434no—
459#479—434no—
460#478—434no—
461#478—434no—
462#477—434no—
463#476—434no—
464#475—434no—
465#474—434no—
466#433C2×D4314yes—
467#433C2×D4314yes—
468#428—432no—
469#428—432no—
470#428—432no—
471#428—432no—
472#423C2×D4312yes—
473#417—432no—
474#417—432no—
475#417—432no—
476#417—432no—
477#407C2×D4312yes—
478C4×M16C2×D4311yescharacteristic
479C4×M16C2×D4311yescharacteristic
480C43#6086711yescharacteristic, complemented, Sylow
481C2×#41—432no—
482C22×Q8—861no—
483C22×Q8—861no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×M16C22×D4312yes—
487C2×M16C22×D4312yes—
488C4⋊Q8—434no—
489C4⋊Q8—432no—
490C4⋊Q8—432no—
491C4⋊Q8—431no—
492C4⋊Q8—431no—
493C4⋊Q8—431no—
494C4⋊Q8—864no—
495C4⋊Q8—864no—
496C4⋊Q8—862no—
497C4⋊Q8—861no—
498C4⋊Q8—861no—
499#127—431no—
500#126—862no—
501#126—862no—
502#126—862no—
503#126—862no—
504#125—434no—
505#125—432no—
506#125—432no—
507#125—432no—
508#125—864no—
509#125—864no—
510#125—862no—
511#125—862no—
512#125—862no—
513#125—861no—
514#125—861no—
515#124—432no—
516#124—862no—
517#124—862no—
518#123—862no—
519#123—862no—
520#123—862no—
521#123—862no—
522#123—862no—
523C22⋊Q8—432no—
524C22⋊Q8—432no—
525C22⋊Q8—861no—
526C22⋊Q8—861no—
527C22⋊Q8—862no—
528C22⋊Q8—862no—
529C22⋊Q8—864no—
530C22⋊Q8—864no—
531C22⋊Q8—864no—
532C22⋊Q8—864no—
533#121—432no—
534#121—432no—
535#121—861no—
536#121—861no—
537#121—862no—
538#121—862no—
539#120—862no—
540C4×Q8—432no—
541C4×Q8—432no—
542C4×Q8—861no—
543C4×Q8—861no—
544C4×D4—432no—
545C4×D4—432no—
546C4×D4—862no—
547C4×D4—862no—
548C4×D4—862no—
549C4×D4—862no—
550C4×D4—861no—
551C4×D4—861no—
552#117—434no—
553#117—432no—
554#117—862no—
555#117—862no—
556#117D17212yes—
557#117D17212yes—
558#117C22×D4312yes—
559#117C22×D4312yes—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—434no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4D17211yescharacteristic
574C2×C4⋊C4D17211yescharacteristic
575C2×C22⋊C4—861no—
576C2×C22⋊C4D17211yescharacteristic
577C2×C22⋊C4D17211yescharacteristic
578C2×C42—861no—
579C2×C42—862no—
580C2×C42C22×D4311yescharacteristic
581C2×C42C22×D4311yescharacteristic
582#107—434no—
583#107—434no—
584#107—434no—
585#107—434no—
586#106—434no—
587#106—434no—
588#106—434no—
589#106—434no—
590C4⋊C8C22×D4314yes—
591C4⋊C8C22×D4314yes—
592#103—434no—
593#103—434no—
594#103—434no—
595#103—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600C22⋊C8C22×D4314yes—
601C22⋊C8C22×D4314yes—
602#97C22×D4312yes—
603#97C22×D4312yes—
604C4×C8C22×D4312yes—
605C4×C8C22×D4312yes—
606C24C2×D17211yescharacteristic
607#41—868no—
608C2×Q8—432no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—864no—
612C2×Q8—862no—
613C2×Q8—862no—
614C2×Q8—3442no—
615C2×Q8—3442no—
616C2×D4—432no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—861no—
621C2×D4—861no—
622C22×C4—24no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—3442no—
632C22×C4C2×D17211yescharacteristic
633C22×C4C2×D17212yes—
634C22×C4C2×D17211yescharacteristic
635C22×C4C2×D17211yescharacteristic
636C22×C4C2×D17211yescharacteristic
637C22×C4C2×D17211yescharacteristic
638C22×C4C23×D4312yes—
639C22×C4C23×D4311yescharacteristic
640M16—24no—
641M16—24no—
642C2×C8C23×D4314yes—
643C2×C8C23×D4314yes—
644C4⋊C4—432no—
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—432no—
648C4⋊C4—432no—
649C4⋊C4—432no—
650C4⋊C4—864no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—864no—
656C4⋊C4—862no—
657C4⋊C4—862no—
658C4⋊C4—864no—
659C4⋊C4—862no—
660C4⋊C4—862no—
661C4⋊C4—864no—
662C4⋊C4—862no—
663C4⋊C4—862no—
664C4⋊C4—862no—
665C4⋊C4—862no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4—862no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4C2×D17212yes—
675C4⋊C4C2×D17212yes—
676C4⋊C4C2×D17212yes—
677C4⋊C4C2×D17212yes—
678C22⋊C4—864no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—862no—
683C22⋊C4—862no—
684C22⋊C4—862no—
685C22⋊C4—862no—
686C22⋊C4—862no—
687C22⋊C4—862no—
688C22⋊C4C2×D17212yes—
689C22⋊C4C2×D17212yes—
690C22⋊C4C2×D17212yes—
691C22⋊C4C2×D17212yes—
692C42—862no—
693C42—864no—
694C42—862no—
695C42—862no—
696C42C2×D17212yes—
697C42C2×D17211yescharacteristic
698C42C2×D17211yescharacteristic
699C42C23×D4311yescharacteristic
700C42C23×D4311yescharacteristic
701C42C23×D4312yes—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—862no—
706C23C22×D17212yes—
707C23C22×D17211yescharacteristic
708Q8—864no—
709Q8—3444no—
710Q8—3442no—
711Q8—3442no—
712Q8—3441no—
713Q8—3441no—
714D4—864no—
715D4—3441no—
716D4—3441no—
717D4—3442no—
718D4—3442no—
719D4—1724no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—3442no—
735C2×C4—3442no—
736C2×C4—3444no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1724no—
742C2×C4C22×D17212yes—
743C2×C4C22×D17212yes—
744C2×C4C22×D17212yes—
745C2×C4C22×D17211yescharacteristic
746C2×C4C22×D17211yescharacteristic
747C2×C4C22×D17211yescharacteristic
748C2×C4C22×D17211yescharacteristic
749C2×C4C22×D17211yescharacteristic
750C2×C4#1306337214yes—
751C2×C4C24×D4311yescharacteristic
752C8—24no—
753C8—24no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22#1458347512yes—
764C22C23×D17211yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—1722no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4—1722no—
778C4—1722no—
779C4#1458347512yes—
780C4C2×#1306337212yes—
781C2—22no—
782C2—42no—
783C2—3442no—
784C2C2×#1458347511yescharacteristic
785C2#1914937611yescharacteristic
786C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2921C2
socleC22×C43C23×D4
prime radical#19147985C2
hypercenter#2921D43
hypocenterC43#60867
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#14583527C2semidirect
3. #19145895C2semidirect
4. #19145880C2semidirect
5. #19145865C2semidirect
6. #19145850C2semidirect
7. #19145147C2semidirect
8. #19145141C2semidirect
9. #19144996C2semidirect
10. #19144989C2semidirect
11. #19144528C2semidirect
12. #19144520C2semidirect
13. #19144418C2semidirect
14. #19144411C2semidirect
15. C43×#2921C2semidirect
44. #14583308C22semidirect
45. #14583308C22semidirect
46. #14583308C22semidirect
47. #14583304C22semidirect
48. #14583301C22semidirect
49. #14583297C22semidirect
50. #14583268C22semidirect
51. #14583264C22semidirect
52. #14583259C22semidirect
53. #14583254C22semidirect
54. #14583250C22semidirect
55. #14583246C22semidirect
64. #14583207C22semidirect
65. #14583207C22semidirect
66. #14583200C22semidirect
67. #14583200C22semidirect
68. #14583195C22semidirect
69. #14583190C22semidirect
70. #14583185C22semidirect
71. #14583180C22semidirect
402. #2921D43semidirect
480. C43#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#145835272
#191479852
#191458952
#191458802
#191458652
#191458502
#191451472
#191451412
#191449962
#191449892
#191445282
#191445202
#191444182
#191444112
C43×#29212
#6086743