Finite Group Databasebeta

← #25977199

Subgroups — #25977199

Order 11008.

1782 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic
2C2×#14583629C211yesmaximal, characteristic, complemented
3#19147532C212yesmaximal, complemented
4#19147524C214yesmaximal, complemented
5#19147510C212yesmaximal, complemented
6#19147502C214yesmaximal, complemented
7#19147478C212yesmaximal, complemented
8#19147452C212yesmaximal, complemented
9#19145139C212yesmaximal, complemented
10#19144408C212yesmaximal
11#19144404C211yesmaximal, characteristic
12#19144399C212yesmaximal, complemented
13#19144396C211yesmaximal, characteristic, complemented
14M16×Dic86C211yesmaximal, characteristic, complemented
15C4×#13063358C211yesmaximal, characteristic
16#19143413C212yesmaximal
17C43×#3165C211yesmaximal, characteristic, complemented
18C2×#13063358C2211yescharacteristic
19#14583629—21no—
20#14583629—21no—
21#14583629—22no—
22#14583629C2214yes—
23#14583629C2212yes—
24#14583629C2212yes—
25#14583629C2211yescharacteristic
26#14583626C2212yes—
27#14583624C2211yescharacteristic
28#14583610C2211yescharacteristic
29#14583607—21no—
30#14583605C2212yes—
31#14583603—22no—
32#14583564C2211yescharacteristic
33#14583562—21no—
34#14583453—21no—
35#14583453—22no—
36#14583452C2212yes—
37C2×#13063324—21no—
38C2×#13063324C2212yes—
39C2×#13063323—22no—
40C4×#10621898C2211yescharacteristic
41#14583367C2212yes—
42C2×C4×Dic86C2211yescharacteristic
43C2×C4×Dic86C2211yescharacteristic
44C2×#13063290—21no—
45C2×#13063290C2212yes—
46C4×Q8×D43—21no—
47#14583307C2214yes—
48#14583306C2214yes—
49#14583303C2214yes—
50#14583296C2214yes—
51#14583209C2214yes—
52#14583205C2214yes—
53#14583203C2214yes—
54#14583193C2214yes—
55#14583193C2214yes—
56#14583191C2212yes—
57#14583191C2212yes—
58#14583188C2214yes—
59#14583186C2212yes—
60#14583183C2214yes—
61#14583183C2214yes—
62#14583181C2212yes—
63#14583181C2212yes—
64#14583178C2214yes—
65#14583176C2212yes—
66#14583029C2212yes—
67#14583027C2214yes—
68C8×Dic86C2212yes—
69#14583007C2212yes—
70#14583005C2214yes—
71#14583001C2212yes—
72#14582998C2214yes—
73C4×Dic172C2212yes—
74#14582993C2214yes—
75C4×#10621873C2212yes—
76#14582986C2214yes—
77#14582942C2212yes—
78#14582941C2211yescharacteristic
79#14582939C2212yes—
80#14582923C2211yescharacteristic
81#14582922C2212yes—
82#14582909C2211yescharacteristic
83#14582907C2212yes—
84#14582901C2211yescharacteristic
85#14582898C2212yes—
86M16×Dic43C2212yes—
87C43×#533C2211yescharacteristic
88C2×C4⋊Q8×C43C2211yescharacteristic
89C43×#501C2214yes—
90C43×#500C2212yes—
91C43×#498C2212yes—
92C43×#428C2212yes—
93C43×#428C2212yes—
94C4×M16×C43C2211yescharacteristic
95C2×#10621898C2311yescharacteristic
96C22×Dic86—22no—
97C22×Dic86D411yescharacteristic
98C22×Dic86C2311yescharacteristic
99C2×Q8×D43—21no—
100#13063358Q818yescomplemented
101C2×Dic172C2312yes—
102C2×#10621873C2312yes—
103C2×#10621877C2312yes—
104#13063324—22no—
105#13063324—21no—
106#13063324—22no—
107#13063324—22no—
108#13063324—24no—
109#13063324—22no—
110#13063324—22no—
111#13063324C2312yes—
112#13063324C2314yes—
113#13063324C2312yes—
114#13063324C2314yes—
115#13063323—21no—
116#13063323—22no—
117#13063323—24no—
118#13063323—24no—
119#13063323—24no—
120#13063323—24no—
121#13063316C2312yes—
122#13063316C2312yes—
123#13063315—22no—
124#13063315—22no—
125#13063315—22no—
126#13063305—21no—
127#13063305—22no—
128#13063303—22no—
129#13063303—22no—
130#13063303—22no—
131#13063302—22no—
132#13063302—22no—
133#13063301—21no—
134#13063301—22no—
135Q8×Dic43—21no—
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86—22no—
139C4×Dic86—22no—
140C4×Dic86D411yescharacteristic
141C4×Dic86D412yes—
142C4×Dic86D411yescharacteristic
143C4×Dic86C2312yes—
144C4×Dic86C2312yes—
145C4×Dic86C2311yescharacteristic
146C4×Dic86C2311yescharacteristic
147C4×Dic86C2311yescharacteristic
148C4×Dic86C2312yes—
149C4×Dic86C2311yescharacteristic
150#13063290—21no—
151#13063290—24no—
152#13063290—22no—
153#13063290—22no—
154#13063290—22no—
155#13063290—22no—
156#13063290—22no—
157#13063290C2314yes—
158#13063290C2314yes—
159#13063290C2312yes—
160#13063290C2312yes—
161C4×D172C2311yescharacteristic
162C4×D172C2311yescharacteristic
163#13063287C2312yes—
164#13063287C2312yes—
165C4×C22⋊D43—21no—
166C4×C22⋊D43—21no—
167(C22⋊D43)⋊C4—22no—
168(C22⋊D43)⋊C4—22no—
169#13063284C2311yescharacteristic
170#13063282—21no—
171#13063282—22no—
172C2×C4⋊Dic43D411yescharacteristic
173C2×C4⋊Dic43C2311yescharacteristic
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—22no—
176C2×Dic43⋊C4—22no—
177C2×Dic43⋊C4D412yes—
178C4⋊C4×D43—21no—
179C4⋊C4×D43—22no—
180C2×C4×Dic43—21no—
181C2×C4×Dic43—22no—
182C2×C4×Dic43C2312yes—
183C42×D43—21no—
184C42×D43—22no—
185#13063259C2312yes—
186#13063258C2314yes—
187#13063258C2314yes—
188#13063257C2312yes—
189#13063256C2314yes—
190#13063256C2314yes—
191C4⋊(C43⋊C8)C2312yes—
192C4⋊(C43⋊C8)C2312yes—
193Dic43⋊C8C2314yes—
194Dic43⋊C8C2314yes—
195#13063250C2312yes—
196#13063250C2312yes—
197#13063250C2312yes—
198#13063248C2314yes—
199#13063248C2314yes—
200#13063248C2314yes—
201#13063247C2312yes—
202#13063245C2314yes—
203#13063235C2314yes—
204C8×Dic43C2314yes—
205C22×Q8×C43—21no—
206C2×M16×C43C2311yescharacteristic
207C2×M16×C43C2311yescharacteristic
208C4⋊Q8×C43—21no—
209C4⋊Q8×C43—21no—
210C4⋊Q8×C43C2311yescharacteristic
211C4⋊Q8×C43C2312yes—
212C4⋊Q8×C43C2311yescharacteristic
213C4⋊Q8×C43C2312yes—
214#125×C43C2312yes—
215C22⋊Q8×C43—21no—
216C22⋊Q8×C43—21no—
217C4×Q8×C43—21no—
218C4×Q8×C43—21no—
219#117×C43C2312yes—
220C2×C4⋊C4×C43—21no—
221C2×C4⋊C4×C43C2312yes—
222C2×C42×C43C2311yescharacteristic
223#107×C43C2314yes—
224#107×C43C2314yes—
225#106×C43C2314yes—
226#106×C43C2314yes—
227#97×C43C2312yes—
228C4×C8×C43C2312yes—
229C2×Q8×C43—21no—
230C2×Q8×C43—21no—
231C2×Q8×C43—22no—
232C2×Q8×C43—22no—
233C2×Q8×C43—82no—
234C22×C4×C43—22no—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2411yescharacteristic
238C2×C22⋊D43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43C2×D412yes—
242C22×Dic43C2×D412yes—
243Q8×D43—44no—
244#10621898—22no—
245#10621898C2×Q814yes—
246C2×D172C2411yescharacteristic
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—22no—
250C2×C4×D43—21no—
251C2×C4×D43—22no—
252C2×Dic86—21no—
253C2×Dic86—22no—
254C2×Dic86—24no—
255C2×Dic86—22no—
256C2×Dic86—22no—
257C2×Dic86—24no—
258C2×Dic86—24no—
259C2×Dic86—84no—
260C2×Dic86C2×D412yes—
261C2×Dic86C2×D411yescharacteristic
262C2×Dic86C2×D411yescharacteristic
263C2×Dic86C2×Q814yescomplemented
264C2×Dic86C2412yes—
265C2×Dic86C2411yescharacteristic
266M16×C43—22no—
267M16×C43C2×Q814yescomplemented
268C2×C8×C43C2412yes—
269C2×C8×C43C2412yes—
270C4⋊C4×C43—22no—
271C4⋊C4×C43—22no—
272C4⋊C4×C43—22no—
273C4⋊C4×C43—22no—
274C4⋊C4×C43—22no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43C2412yes—
278C4⋊C4×C43C2414yes—
279C4⋊C4×C43C2412yes—
280C22⋊C4×C43—22no—
281C42×C43—22no—
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2411yescharacteristic
285C42×C43C2411yescharacteristic
286C22⋊Dic43—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291C4⋊Dic43—21no—
292C4⋊Dic43—22no—
293C4⋊Dic43—22no—
294C4⋊Dic43C2×D411yescharacteristic
295C4⋊Dic43C2×D411yescharacteristic
296C4⋊Dic43C2×D412yes—
297C4⋊Dic43C2412yes—
298C4⋊Dic43C2411yescharacteristic
299C4⋊Dic43C2411yescharacteristic
300Dic43⋊C4—22no—
301Dic43⋊C4—22no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—22no—
305Dic43⋊C4—22no—
306Dic43⋊C4—24no—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314Dic43⋊C4C2×D412yes—
315Dic43⋊C4C2×D412yes—
316Dic43⋊C4C2×D412yes—
317Dic43⋊C4C2×D412yes—
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—22no—
322C4×Dic43—22no—
323C4×Dic43—22no—
324C4×Dic43—22no—
325C4×Dic43—24no—
326C4×Dic43—24no—
327C4×Dic43C2×D412yes—
328C4×Dic43C2×D412yes—
329C4×Dic43C2412yes—
330C4×Dic43C2412yes—
331#10621877—24no—
332C2×C43⋊C8C2414yes—
333Dic172C2×Q818yescomplemented
334#10621873C2×Q818yescomplemented
335C23×C43C22×D411yescharacteristic
336C22×D43—21no—
337Q8×C43—42no—
338Q8×C43—81no—
339Q8×C43—82no—
340Q8×C43—82no—
341C2×C4×C43—22no—
342C2×C4×C43—24no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—41no—
346C2×C4×C43—44no—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×Q812yes—
353C2×C4×C432−1+412yes—
354C2×C4×C43C2511yescharacteristic
355C22⋊D43—24no—
356C2×Dic43—24no—
357C2×Dic43—22no—
358C2×Dic43—21no—
359C2×Dic43—24no—
360C2×Dic43—22no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—42no—
364C2×Dic43—42no—
365C2×Dic43C22×D412yes—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368C2×Dic43C22×D412yes—
369D172—21no—
370D172C22×Q812yes—
371C4×D43—24no—
372C4×D43—42no—
373C4×D43—44no—
374C4×D43—82no—
375C4×D43—81no—
376Dic86—24no—
377Dic86—22no—
378Dic86—22no—
379Dic86—21no—
380Dic86—24no—
381Dic86—44no—
382Dic86—82no—
383Dic86—84no—
384Dic86—84no—
385Dic86#13714yescomplemented
386Dic86C22×Q814yes—
387Dic86C22×Q812yes—
388C8×C43—22no—
389C8×C43C22×Q814yes—
390C43⋊C8—24no—
391Q8×#137—431nomaximal, Sylow
392C22×C43—21no—
393C22×C43—21no—
394C22×C43D4×Q812yes—
395C22×C43C23×D411yescharacteristic
396C2×D43—22no—
397C2×D43—41no—
398C2×D43—41no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—44no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43D4×Q812yes—
406C4×C43C2×#13712yes—
407C4×C43C23×Q811yescharacteristic
408C4×C43C2×2−1+411yescharacteristic
409Dic43—22no—
410Dic43—22no—
411Dic43—24no—
412Dic43—22no—
413Dic43—22no—
414Dic43—42no—
415Dic43—41no—
416Dic43—41no—
417Dic43C2×#13714yes—
418Q8×#41—431no—
419C2×Q82—431no—
420#3387—434no—
421#3387—432no—
422#3385—434no—
423#3385—432no—
424Q8×Q16—432no—
425Q8×SD16—432no—
426#3165—432no—
427#3165D4311yescharacteristic, complemented
428#3079—432no—
429#3079—431no—
430#3078—432no—
431#3078—431no—
432Q8×M16—431no—
433C4×#137—432no—
434C4×#137—431no—
435C2×C43—22no—
436C2×C43C2×D4×Q811yescharacteristic
437C2×C43C22×#13711yescharacteristic
438C2×C43#358511yescharacteristic
439D43—42no—
440C2×#137—431no—
441Q82—432no—
442Q82—431no—
443Q82—434no—
444Q82—432no—
445Q82—861no—
446Q82—862no—
447Q82—861no—
448#557—431no—
449#557—432no—
450#554—431no—
451#554—432no—
452#554—862no—
453#554—861no—
454D4×Q8—431no—
455D4×Q8—861no—
456#533—432no—
457#533—862no—
458#533—861no—
459#533C2×D4311yescharacteristic
460C2×C4⋊Q8—432no—
461C2×C4⋊Q8—861no—
462C2×C4⋊Q8—862no—
463C2×C4⋊Q8C2×D4311yescharacteristic
464C4×#41—432no—
465C4×#41—431no—
466C2×C4×Q8—431no—
467C2×C4×Q8—432no—
468C2×C4×Q8—431no—
469C2×C4×Q8—861no—
470C2×C4×Q8—861no—
471#501—434no—
472#501—434no—
473#501C2×D4314yes—
474#500—434no—
475#500C2×D4312yes—
476#498—434no—
477#498C2×D4312yes—
478#479—434no—
479#479—434no—
480#479—434no—
481#477—432no—
482#477—432no—
483#477—434no—
484#477—434no—
485#476—432no—
486#476—434no—
487#475—432no—
488#475—432no—
489#475—434no—
490#475—434no—
491#474—432no—
492#474—434no—
493#446—434no—
494#446—432no—
495C8×Q8—432no—
496#441—434no—
497#441—432no—
498#440—434no—
499#440—432no—
500C4×Q16—434no—
501C4×Q16—432no—
502C4×SD16—434no—
503C4×SD16—432no—
504#428—431no—
505#428—432no—
506#428—432no—
507#428C2×D4312yes—
508#428C2×D4312yes—
509#423—432no—
510#423—431no—
511#419—431no—
512#419—432no—
513#417—431no—
514#417—432no—
515C4×M16—432no—
516C4×M16C2×D4311yescharacteristic
517C43Q8×#13711yescharacteristic, complemented, Sylow
518C2×#41—431no—
519C22×Q8—21no—
520C22×Q8—431no—
521C22×Q8—431no—
522C22×Q8—862no—
523C22×Q8—861no—
524#137—438no—
525C2×Q16—432no—
526C2×SD16—432no—
527C2×M16—432no—
528C2×M16C22×D4311yescharacteristic
529C2×M16C22×D4311yescharacteristic
530C4⋊Q8—21no—
531C4⋊Q8—21no—
532C4⋊Q8—434no—
533C4⋊Q8—434no—
534C4⋊Q8—432no—
535C4⋊Q8—432no—
536C4⋊Q8—862no—
537C4⋊Q8—862no—
538C4⋊Q8—862no—
539C4⋊Q8—864no—
540C4⋊Q8—862no—
541C4⋊Q8—861no—
542C4⋊Q8—862no—
543C4⋊Q8—864no—
544C4⋊Q8—864no—
545C4⋊Q8—864no—
546C4⋊Q8—864no—
547C4⋊Q8—862no—
548C4⋊Q8—861no—
549C4⋊Q8C22×D4312yes—
550C4⋊Q8C22×D4312yes—
551C4⋊Q8C22×D4311yescharacteristic
552C4⋊Q8C22×D4311yescharacteristic
553#125—432no—
554#125—432no—
555#125—862no—
556#125—862no—
557#125—862no—
558#125C22×D4312yes—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—862no—
562C22⋊Q8—862no—
563C22⋊Q8—862no—
564C22⋊Q8—862no—
565C22⋊Q8—862no—
566C22⋊Q8—862no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8—862no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—431no—
573C4×Q8—432no—
574C4×Q8—431no—
575C4×Q8—431no—
576C4×Q8—432no—
577C4×Q8—431no—
578C4×Q8—434no—
579C4×Q8—434no—
580C4×Q8—432no—
581C4×Q8—432no—
582C4×Q8—432no—
583C4×Q8—432no—
584C4×Q8—431no—
585C4×Q8—431no—
586C4×Q8—862no—
587C4×Q8—862no—
588C4×Q8—862no—
589C4×Q8—862no—
590C4×Q8—862no—
591C4×Q8—861no—
592C4×Q8—862no—
593C4×Q8—864no—
594C4×Q8—862no—
595C4×Q8—861no—
596C4×Q8—861no—
597C4×Q8—861no—
598C4×D4—432no—
599C4×D4—432no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—862no—
603C4×D4—862no—
604C4×D4—861no—
605C4×D4—861no—
606#117—431no—
607#117—862no—
608#117—861no—
609#117C22×D4312yes—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—432no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—862no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—862no—
617C2×C4⋊C4—862no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4C22×D4312yes—
620C2×C42—432no—
621C2×C42—862no—
622C2×C42—862no—
623C2×C42—861no—
624C2×C42—861no—
625C2×C42C22×D4311yescharacteristic
626#107—432no—
627#107—434no—
628#107—434no—
629#107C22×D4314yes—
630#107C22×D4314yes—
631#106—432no—
632#106—434no—
633#106—434no—
634#106C22×D4314yes—
635#106C22×D4314yes—
636C4⋊C8—434no—
637C4⋊C8—434no—
638C4⋊C8—432no—
639C4⋊C8—432no—
640#103—432no—
641#103—432no—
642#103—432no—
643#103—434no—
644#103—434no—
645#103—434no—
646#102—432no—
647#102—434no—
648#97—434no—
649#97C22×D4312yes—
650C4×C8—434no—
651C4×C8C22×D4312yes—
652#41—434no—
653#41—862no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—82no—
659C2×Q8—431no—
660C2×Q8—432no—
661C2×Q8—431no—
662C2×Q8—434no—
663C2×Q8—432no—
664C2×Q8—431no—
665C2×Q8—862no—
666C2×Q8—864no—
667C2×Q8—864no—
668C2×Q8—862no—
669C2×Q8—864no—
670C2×Q8—861no—
671C2×Q8—862no—
672C2×Q8—3444no—
673C2×Q8—1724no—
674C2×D4—431no—
675C2×D4—861no—
676C22×C4—22no—
677C22×C4—432no—
678C22×C4—432no—
679C22×C4—862no—
680C22×C4—862no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4D4×D4311yescharacteristic
687C22×C4D4×D4311yescharacteristic
688C22×C4C23×D4311yescharacteristic
689Q16—438no—
690SD16—438no—
691M16—22no—
692M16—864no—
693M16Q8×D4314yescomplemented
694C2×C8—434no—
695C2×C8C23×D4312yes—
696C2×C8C23×D4312yes—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—22no—
704C4⋊C4—432no—
705C4⋊C4—431no—
706C4⋊C4—432no—
707C4⋊C4—432no—
708C4⋊C4—432no—
709C4⋊C4—432no—
710C4⋊C4—431no—
711C4⋊C4—432no—
712C4⋊C4—431no—
713C4⋊C4—431no—
714C4⋊C4—864no—
715C4⋊C4—864no—
716C4⋊C4—862no—
717C4⋊C4—862no—
718C4⋊C4—862no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4—862no—
724C4⋊C4—862no—
725C4⋊C4—862no—
726C4⋊C4—861no—
727C4⋊C4—862no—
728C4⋊C4—862no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4C23×D4314yes—
732C4⋊C4C23×D4312yes—
733C4⋊C4C23×D4312yes—
734C22⋊C4—22no—
735C22⋊C4—862no—
736C22⋊C4—862no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C42—22no—
741C42—432no—
742C42—432no—
743C42—432no—
744C42—432no—
745C42—862no—
746C42—862no—
747C42—864no—
748C42—864no—
749C42—861no—
750C42—861no—
751C42—861no—
752C42—862no—
753C42—862no—
754C42D4×D4311yescharacteristic
755C42D4×D4311yescharacteristic
756C42C23×D4311yescharacteristic
757C42C23×D4311yescharacteristic
758C23—861no—
759C23C2×D4×D4311yescharacteristic
760Q8—42no—
761Q8—82no—
762Q8—82no—
763Q8—81no—
764Q8—434no—
765Q8—434no—
766Q8—432no—
767Q8—864no—
768Q8—864no—
769Q8—862no—
770Q8—862no—
771Q8—861no—
772Q8—3444no—
773Q8—3444no—
774Q8—3442no—
775Q8—1724no—
776D4—432no—
777D4—864no—
778D4—861no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—41no—
784C2×C4—44no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—432no—
788C2×C4—432no—
789C2×C4—864no—
790C2×C4—864no—
791C2×C4—861no—
792C2×C4—862no—
793C2×C4—864no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—862no—
797C2×C4—3441no—
798C2×C4—3442no—
799C2×C4—1724no—
800C2×C4—1722no—
801C2×C4—1722no—
802C2×C4—1722no—
803C2×C4C2×D4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4C2×D4×D4311yescharacteristic
807C2×C4C2×D4×D4311yescharacteristic
808C2×C4C2×Q8×D4312yes—
809C2×C4#1306337312yes—
810C2×C4C24×D4311yescharacteristic
811C8—22no—
812C8—864no—
813C8C2×Q8×D4314yes—
814C22—21no—
815C22—21no—
816C22—862no—
817C22—1721no—
818C22—1721no—
819C22#1458356412yes—
820C22C22×D4×D4311yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4—434no—
828C4—862no—
829C4—862no—
830C4—864no—
831C4—862no—
832C4—862no—
833C4—1721no—
834C4—1721no—
835C4—1722no—
836C4#1458356412yes—
837C4#137×D4312yes—
838C4C22×Q8×D4311yescharacteristic
839C4C2×#1306337311yescharacteristic
840C2—22no—
841C2—1722no—
842C2C2×#1458356411yescharacteristic
843C2C2×#137×D4311yescharacteristic
844C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
prime radicalC2×#10621898C23
hypercenter#3165D43
hypocenterC43Q8×#137
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
2. C2×#14583629C2semidirect
3. #19147532C2semidirect
4. #19147524C2semidirect
5. #19147510C2semidirect
6. #19147502C2semidirect
7. #19147478C2semidirect
8. #19147452C2semidirect
9. #19145139C2semidirect
12. #19144399C2semidirect
13. #19144396C2semidirect
14. M16×Dic86C2semidirect
17. C43×#3165C2semidirect
100. #13063358Q8semidirect
263. C2×Dic86C2×Q8semidirect
267. M16×C43C2×Q8semidirect
333. Dic172C2×Q8semidirect
334. #10621873C2×Q8semidirect
385. Dic86#137semidirect
427. #3165D43semidirect
517. C43Q8×#137semidirect
693. M16Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191481732
C2×#145836292
#191475322
#191475242
#191475102
#191475022
#191474782
#191474522
#191451392
#191444082
#191444042
#191443992
#191443962
M16×Dic862
C4×#130633582
#191434132
C43×#31652
Q8×#13743