Finite Group Databasebeta

← #25072577

Subgroups — #25072577

Order 11008.

968 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic, complemented
2#19144626C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic
4#19133872C211yesmaximal, characteristic, complemented
5#19133858C211yesmaximal, characteristic, complemented
6#19133816C211yesmaximal, characteristic, complemented
7#19133802C211yesmaximal, characteristic, complemented
8#19133698C211yesmaximal, characteristic, complemented
9#19133691C211yesmaximal, characteristic, complemented
10#19133673C211yesmaximal, characteristic, complemented
11#19133667C211yesmaximal, characteristic, complemented
12#19133252C211yesmaximal, characteristic, complemented
13#19132977C211yesmaximal, characteristic, complemented
14C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15Q8×#41×C43C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583449C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583217—21no—
23#14583184C2211yescharacteristic
24#14583184C2211yescharacteristic
25#14583130—22no—
26#14583121—21no—
27#14583114—21no—
28#14583109C2211yescharacteristic
29#14583104C2211yescharacteristic
30#14583099C2211yescharacteristic
31#14583099C2211yescharacteristic
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583038—21no—
35C4×#10621884—21no—
36C4×#10621884—21no—
37C4×#10621884—22no—
38#14582952C2211yescharacteristic
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40#14582893—21no—
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582648C2211yescharacteristic
43#14582648C2211yescharacteristic
44#14582645C2211yescharacteristic
45#14582645C2211yescharacteristic
46Q8⋊(C43⋊C8)C2211yescharacteristic
47Q8⋊(C43⋊C8)C2211yescharacteristic
48Q8⋊(C43⋊C8)C2211yescharacteristic
49Q8⋊(C43⋊C8)C2211yescharacteristic
50Q8⋊(C43⋊C8)C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54Q82×C43C2211yescharacteristic
55C43×#557—21no—
56C43×#557C2211yescharacteristic
57C43×#554—22no—
58C43×#554—21no—
59C43×#554—21no—
60C43×#554C2211yescharacteristic
61D4×Q8×C43—21no—
62D4×Q8×C43C2211yescharacteristic
63C43×#533—22no—
64C43×#533—21no—
65C43×#533—21no—
66C43×#533C2211yescharacteristic
67C4×#41×C43—21no—
68C4×#41×C43C2211yescharacteristic
69C2×C4×Q8×C43—21no—
70C2×C4×Q8×C43C2211yescharacteristic
71C2×#10621898—21no—
72#13063345—44no—
73C2×#10621885—21no—
74C2×#10621883—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77C2×#10621884—21no—
78C2×#10621884—22no—
79C2×#10621882—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063313—21no—
85#13063299—21no—
86#13063299—21no—
87C4×D172—21no—
88C4×D172—21no—
89#13063256—22no—
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—22no—
98#13063249—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—22no—
107C22⋊(C43⋊C8)—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C2×#41×C43D411yescharacteristic
113C22×Q8×C43—21no—
114C22×Q8×C43D411yescharacteristic
115C4⋊Q8×C43—22no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—22no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—22no—
124#125×C43—22no—
125#125×C43—22no—
126#125×C43—21no—
127#125×C43—21no—
128#125×C43—21no—
129C22⋊Q8×C43—22no—
130C22⋊Q8×C43—22no—
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—22no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43—21no—
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43D412yes—
140C4×Q8×C43—22no—
141C4×Q8×C43—22no—
142C4×Q8×C43—22no—
143C4×Q8×C43—21no—
144C4×Q8×C43—21no—
145C4×Q8×C43—21no—
146C4×Q8×C43—21no—
147C4×Q8×C43—21no—
148C4×Q8×C43—21no—
149C4×Q8×C43—21no—
150C4×Q8×C43D411yescharacteristic
151C4×Q8×C43D411yescharacteristic
152C4×Q8×C43D411yescharacteristic
153C4×Q8×C43D412yes—
154C4×Q8×C43C2311yescharacteristic
155C4×Q8×C43C2311yescharacteristic
156C4×Q8×C43C2311yescharacteristic
157C4×D4×C43—22no—
158C4×D4×C43—22no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163C4×D4×C43D411yescharacteristic
164C4×D4×C43C2311yescharacteristic
165#117×C43—22no—
166#117×C43—21no—
167#117×C43—21no—
168#117×C43D411yescharacteristic
169C2×C4⋊C4×C43—22no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C42×C43—22no—
174C2×C42×C43—21no—
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#41×C43—22no—
178#41×C43SD1614yescomplemented
179C2×Q8×C43—22no—
180C2×Q8×C43—22no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—41no—
185C2×Q8×C43—42no—
186C2×Q8×C43—42no—
187C2×Q8×C43C2×D411yescharacteristic
188C2×Q8×C43C2×D411yescharacteristic
189C2×Q8×C43C2×D411yescharacteristic
190C2×Q8×C43C2×D412yes—
191C2×D4×C43—21no—
192C2×D4×C43C2×D411yescharacteristic
193C22×C4×C43—21no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C2×C22⋊D43—41no—
204#10621898—42no—
205#10621898—42no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×C4×D43—41no—
210C2×Dic86—21no—
211C4⋊C4×C43—22no—
212C4⋊C4×C43—22no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—22no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C2×D411yescharacteristic
232C4⋊C4×C43C2×D411yescharacteristic
233C4⋊C4×C43C2×D411yescharacteristic
234C4⋊C4×C43C2×D411yescharacteristic
235C4⋊C4×C43C2×D412yes—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—21no—
242C42×C43—22no—
243C42×C43—22no—
244C42×C43—21no—
245C42×C43—22no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43—21no—
250C42×C43—21no—
251C42×C43—21no—
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C42×C43C2×D411yescharacteristic
255C42×C43C2411yescharacteristic
256#10621885—42no—
257#10621884—44no—
258#10621884—42no—
259#10621884—42no—
260#10621884—42no—
261#10621883—42no—
262#10621882—42no—
263(C2×D43)⋊C4—41no—
264(C2×D43)⋊C4—41no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—42no—
274C2×C43⋊C8—42no—
275C23×C43—21no—
276C23×C43#12011yescharacteristic
277C22×D43—41no—
278Q8×C43—21no—
279Q8×C43—21no—
280Q8×C43—21no—
281Q8×C43—21no—
282Q8×C43—42no—
283Q8×C43—42no—
284Q8×C43—44no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—82no—
288Q8×C43C2×SD1612yes—
289Q8×C43#13512yescomplemented
290D4×C43—24no—
291D4×C43—21no—
292D4×C43C2×SD1612yes—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—24no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—41no—
306C2×C4×C43—42no—
307C2×C4×C43—44no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—81no—
311C2×C4×C43—81no—
312C2×C4×C43—82no—
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43C2×SD1612yes—
317C2×C4×C43#13712yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C22⋊D43—82no—
322C2×Dic43—41no—
323D172—42no—
324D172—41no—
325D172—41no—
326D172—41no—
327D172—41no—
328C4×D43—82no—
329Dic86—41no—
330Dic86—41no—
331C43⋊C8—22no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337#18518—431nomaximal, Sylow
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—22no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43#44812yes—
344C22×C43C2×#12011yescharacteristic
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C4×C43—22no—
349C4×C43—21no—
350C4×C43—22no—
351C4×C43—21no—
352C4×C43—21no—
353C4×C43—41no—
354C4×C43—42no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—42no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43#44812yes—
361C4×C43C22×SD1611yescharacteristic
362C4×C43C2×#13511yescharacteristic
363C4×C43C2×#13711yescharacteristic
364C4×C43#57511yescharacteristic
365Dic43—81no—
366Q8×#41D4311yescharacteristic, complemented
367#3167—431no—
368#3103—431no—
369#3035—431no—
370#1653—431no—
371#1651—431no—
372#1645—431no—
373#1643—431no—
374#1627—431no—
375#1626—431no—
376#1623—431no—
377#1622—431no—
378#1542—431no—
379#1476—431no—
380C2×Q8⋊C8—431no—
381C2×C43—22no—
382C2×C43—42no—
383C2×C43C2×#44811yescharacteristic
384C2×C43#300211yescharacteristic
385C2×C43#301811yescharacteristic
386D43—161no—
387C2×#135—861no—
388Q82C2×D4311yescharacteristic
389#557—21no—
390#557C2×D4311yescharacteristic
391#554—22no—
392#554—21no—
393#554—21no—
394#554C2×D4311yescharacteristic
395D4×Q8—21no—
396D4×Q8C2×D4311yescharacteristic
397#533—22no—
398#533—21no—
399#533—21no—
400#533C2×D4311yescharacteristic
401#532—431no—
402C4×#41—21no—
403C4×#41C2×D4311yescharacteristic
404C2×C4×Q8—21no—
405C2×C4×Q8C2×D4311yescharacteristic
406#498—431no—
407#492—431no—
408#487—431no—
409#486—431no—
410#481—861no—
411#475—431no—
412#475—431no—
413#465—862no—
414#464—861no—
415#463—861no—
416#462—431no—
417#461—431no—
418#460—431no—
419#460—431no—
420#460—431no—
421#459—431no—
422#448—861no—
423C4×SD16—861no—
424C4×SD16—861no—
425C4×SD16—862no—
426#431—431no—
427C2×C4⋊C8—431no—
428#416—861no—
429C2×C4×C8—431no—
430#333—431no—
431#333—431no—
432#332—431no—
433#332—431no—
434Q8⋊C8—431no—
435Q8⋊C8—431no—
436Q8⋊C8—431no—
437Q8⋊C8—431no—
438Q8⋊C8—431no—
439Q8⋊C8—431no—
440D4⋊C8—431no—
441D4⋊C8—431no—
442C43#1851811yescharacteristic, complemented, Sylow
443C2×#41—861no—
444C2×#41C22⋊D4311yescharacteristic
445C22×Q8—21no—
446C22×Q8C22⋊D4311yescharacteristic
447#135—1724no—
448C2×Q16—861no—
449C2×SD16—861no—
450C2×SD16—861no—
451C2×SD16—861no—
452C2×SD16—862no—
453C2×SD16—861no—
454C2×D8—861no—
455C22×C8—861no—
456C22×C8—861no—
457C4⋊Q8—22no—
458C4⋊Q8—21no—
459C4⋊Q8—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—431no—
464C4⋊Q8C22×D4311yescharacteristic
465C4⋊Q8C22×D4311yescharacteristic
466#127—431no—
467#125—22no—
468#125—22no—
469#125—22no—
470#125—21no—
471#125—21no—
472#125—21no—
473#124—861no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—22no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8C22⋊D4312yes—
485#121—861no—
486#121—861no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8C22⋊D4311yescharacteristic
498C4×Q8C22⋊D4311yescharacteristic
499C4×Q8C22⋊D4311yescharacteristic
500C4×Q8C22⋊D4312yes—
501C4×Q8C22×D4311yescharacteristic
502C4×Q8C22×D4311yescharacteristic
503C4×Q8C22×D4311yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—861no—
511C4×D4—861no—
512C4×D4C22⋊D4311yescharacteristic
513C4×D4C22×D4311yescharacteristic
514#117—22no—
515#117—21no—
516#117—21no—
517#117C22⋊D4311yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4C22⋊D4311yescharacteristic
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42C22×D4311yescharacteristic
526#106—862no—
527#106—861no—
528#106—861no—
529C4⋊C8—431no—
530C4⋊C8—431no—
531C4⋊C8—431no—
532C4⋊C8—431no—
533C4⋊C8—861no—
534#103—861no—
535#103—861no—
536#103—862no—
537#103—861no—
538#103—861no—
539#102—861no—
540#102—861no—
541#102—861no—
542#102—861no—
543#102—862no—
544C22⋊C8—861no—
545C4×C8—431no—
546C4×C8—431no—
547C4×C8—861no—
548C4×C8—861no—
549#41—22no—
550#41—1722no—
551#41—1722no—
552#41#1062188414yescomplemented
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—861no—
562C2×Q8C2×C22⋊D4311yescharacteristic
563C2×Q8C2×C22⋊D4311yescharacteristic
564C2×Q8C2×C22⋊D4311yescharacteristic
565C2×Q8C2×C22⋊D4312yes—
566C2×D4—21no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—1721no—
571C2×D4C2×C22⋊D4311yescharacteristic
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—1721no—
580C22×C4C2×C22⋊D4311yescharacteristic
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583Q16—1722no—
584SD16—1724no—
585SD16—1722no—
586SD16—1722no—
587SD16—1722no—
588SD16—1722no—
589D8—1722no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—1722no—
597C2×C8—1722no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4C2×C22⋊D4311yescharacteristic
621C4⋊C4C2×C22⋊D4311yescharacteristic
622C4⋊C4C2×C22⋊D4311yescharacteristic
623C4⋊C4C2×C22⋊D4311yescharacteristic
624C4⋊C4C2×C22⋊D4312yes—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—1721no—
632C22⋊C4—1721no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×C22⋊D4311yescharacteristic
644C42C2×C22⋊D4311yescharacteristic
645C42C2×C22⋊D4311yescharacteristic
646C42C23×D4311yescharacteristic
647C23—21no—
648C23—1721no—
649C23#1306329411yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—42no—
655Q8—42no—
656Q8—44no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8—1721no—
661Q8—1721no—
662Q8C2×#1062188412yes—
663Q8#1306334512yescomplemented
664D4—24no—
665D4—21no—
666D4—3442no—
667D4—1722no—
668D4—1721no—
669D4—1721no—
670D4—1721no—
671D4—1721no—
672D4C2×#1062188412yes—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4—3442no—
694C2×C4—1721no—
695C2×C4#1306329411yescharacteristic
696C2×C4#1306329411yescharacteristic
697C2×C4#1306329411yescharacteristic
698C2×C4C2×#1062188412yes—
699C2×C4#1306335612yes—
700C2×C4C22×C22⋊D4311yescharacteristic
701C2×C4C22×C22⋊D4311yescharacteristic
702C2×C4C22×C22⋊D4311yescharacteristic
703C8—862no—
704C8—1721no—
705C8—1721no—
706C8—1721no—
707C8—1721no—
708C8—1721no—
709C22—21no—
710C22—21no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22#1458303812yes—
718C22C2×#1306329411yescharacteristic
719C4—21no—
720C4—21no—
721C4—22no—
722C4—21no—
723C4—22no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—41no—
731C4—3441no—
732C4#1458303812yes—
733C4C22×#1062188411yescharacteristic
734C4C2×#1306334511yescharacteristic
735C4C2×#1306335611yescharacteristic
736C4#1458369711yescharacteristic
737C2—22no—
738C2—42no—
739C2—6881no—
740C2C2×#1458303811yescharacteristic
741C2#1914381311yescharacteristic
742C2#1914394411yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×#41×C43C2
socleC22×C43C2×#120
prime radical#19144050C2
hypercenterQ8×#41D43
hypocenterC43#18518
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #19145155C2semidirect
2. #19144626C2semidirect
4. #19133872C2semidirect
5. #19133858C2semidirect
6. #19133816C2semidirect
7. #19133802C2semidirect
8. #19133698C2semidirect
9. #19133691C2semidirect
10. #19133673C2semidirect
11. #19133667C2semidirect
12. #19133252C2semidirect
13. #19132977C2semidirect
14. C2×Q8⋊(C43⋊C8)C2semidirect
15. Q8×#41×C43C2semidirect
178. #41×C43SD16semidirect
289. Q8×C43#135semidirect
366. Q8×#41D43semidirect
442. C43#18518semidirect
552. #41#10621884semidirect
663. Q8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191446262
#191440502
#191338722
#191338582
#191338162
#191338022
#191336982
#191336912
#191336732
#191336672
#191332522
#191329772
C2×Q8⋊(C43⋊C8)2
Q8×#41×C432
#1851843