Finite Group Databasebeta

← #25965138

Subgroups — #25965138

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583512C211yesmaximal, characteristic, complemented
2#19147794C211yesmaximal, characteristic
3#19144897C214yesmaximal, complemented
4#19144849C214yesmaximal, complemented
5#19144816C214yesmaximal, complemented
6#19144814C214yesmaximal, complemented
7#19144545C212yesmaximal, complemented
8#19144413C211yesmaximal, characteristic, complemented
9#19144083C211yesmaximal, characteristic, complemented
10#19144082C211yesmaximal, characteristic, complemented
11#19143856C212yesmaximal
12#19143419C212yesmaximal, complemented
13#19143413C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063355C2212yes—
19#14583512—21no—
20#14583512—21no—
21#14583512—21no—
22#14583512—21no—
23#14583512C2214yes—
24#14583512C2214yescomplemented
25C2×#13063325C2211yescharacteristic, complemented
26C2×#13063320—22no—
27C2×#13063316—22no—
28C2×#13063305C2212yes—
29#14583381C2212yes—
30#14583378—22no—
31#14583378C2212yes—
32#14583375C2212yes—
33#14583371—22no—
34#14583371C2212yes—
35#41×Dic43C2211yescharacteristic
36C4×#10621898—21no—
37C4×#10621898C2211yescharacteristic
38#14583367—21no—
39#14583367C2211yescharacteristic
40C2×#13063290C2212yescomplemented
41C2×#13063282—21no—
42C2×#13063282C2211yescharacteristic
43#117×D43—21no—
44#117×D43C2211yescharacteristic
45#14583243C2214yes—
46#14583242C2214yes—
47#14583236C2214yescomplemented
48#14583231C2214yescomplemented
49#14583203C2214yescomplemented
50#14583196C2214yescomplemented
51#14583110C2214yescomplemented
52#14583109C2214yescomplemented
53#14583105C2214yescomplemented
54#14583104C2214yescomplemented
55#14583064C2214yes—
56#14583062C2214yes—
57#14583056C2214yes—
58#14583051C2214yes—
59#14583005C2214yescomplemented
60#14583003C2214yescomplemented
61#14582998C2214yescomplemented
62#14582996C2214yescomplemented
63#14582993C2214yescomplemented
64#14582991C2214yescomplemented
65#14582990C2214yescomplemented
66#14582986C2214yescomplemented
67#14582959C2214yes—
68#14582959C2214yescomplemented
69#14582939C2212yescomplemented
70#14582923C2211yescharacteristic, complemented
71#14582909C2212yescomplemented
72#14582907C2212yescomplemented
73#14582898C2212yes—
74#14582862C2212yes—
75M16×Dic43C2212yescomplemented
76C2×#125×C43C2211yescharacteristic, complemented
77C4×#41×C43C2211yescharacteristic
78C43×#479C2214yescomplemented
79C43×#478C2214yescomplemented
80C43×#428C2212yescomplemented
81C43×#423C2211yescharacteristic, complemented
82C43×#417C2212yes—
83C2×#10621902C2311yescharacteristic
84C2×#10621898—21no—
85C2×#10621898C2311yescharacteristic
86C2×#10621900—21no—
87C2×#10621900C2311yescharacteristic
88#41×D43—24no—
89#41×D43—24no—
90C22×Dic86C2312yes—
91C2×Q8×D43C2311yescharacteristic
92C2×D4×D43—21no—
93C2×D4×D43C2311yescharacteristic
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96#13063358—28no—
97#13063355—28no—
98C2×Dic172C2314yes—
99C2×#10621885C2314yes—
100C2×#10621873C2314yes—
101C2×#10621883C2314yes—
102C2×#10621877C2312yes—
103#13063325—21no—
104#13063325—21no—
105#13063325C2314yes—
106#13063320—24no—
107#13063320—24no—
108#13063320—24no—
109#13063320—24no—
110#13063316—24no—
111#13063316—24no—
112#13063316—24no—
113#13063316—24no—
114#13063305—22no—
115#13063305—22no—
116#13063305C2314yes—
117#13063305C2314yes—
118Q8×Dic43C2312yes—
119C4×Dic86—22no—
120C4×Dic86C2312yes—
121#13063290—22no—
122#13063290—22no—
123#13063290—22no—
124#13063290C2314yes—
125#13063290C2314yes—
126#13063290C2312yes—
127C4×D172—22no—
128C4×D172C2312yes—
129D4×Dic43—22no—
130D4×Dic43C2312yes—
131#13063287—22no—
132#13063287C2312yes—
133C4×C22⋊D43—22no—
134C4×C22⋊D43—22no—
135C4×C22⋊D43—22no—
136(C22⋊D43)⋊C4—22no—
137(C22⋊D43)⋊C4—22no—
138(C22⋊D43)⋊C4—22no—
139#13063284—21no—
140#13063284C2311yescharacteristic
141#13063283—22no—
142#13063283C2312yes—
143#13063282—21no—
144#13063282—21no—
145#13063282—22no—
146#13063282—22no—
147#13063282—21no—
148#13063282D411yescharacteristic
149#13063282D411yescharacteristic
150#13063282D411yescharacteristic
151#13063282D411yescharacteristic
152#13063282C2312yes—
153#13063282C2312yes—
154#13063281—21no—
155#13063281—22no—
156C2×C4⋊Dic43—22no—
157C2×C4⋊Dic43—22no—
158C2×Dic43⋊C4—22no—
159C2×Dic43⋊C4—22no—
160C2×Dic43⋊C4D412yes—
161C4⋊C4×D43—22no—
162C4⋊C4×D43C2312yes—
163C2×(C2×D43)⋊C4—22no—
164C2×(C2×D43)⋊C4—22no—
165C2×(C2×D43)⋊C4D412yes—
166C22⋊C4×D43—21no—
167C22⋊C4×D43—22no—
168C2×C4×Dic43—22no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171C42×D43—21no—
172C42×D43—21no—
173C42×D43—21no—
174#13063258C2314yes—
175#13063256C2314yes—
176C4⋊(C43⋊C8)C2314yes—
177#13063250C2314yes—
178#13063250C2314yes—
179#13063248C2314yes—
180#13063248C2314yes—
181#13063248C2314yes—
182#13063245C2314yes—
183(C2×D43)⋊C8C2314yes—
184(C2×D43)⋊C8C2314yes—
185#13063235C2314yes—
186C8×Dic43C2314yes—
187C2×#41×C43C2311yescharacteristic
188C2×M16×C43C2312yes—
189#125×C43—21no—
190#125×C43—21no—
191#125×C43C2314yes—
192C4×Q8×C43C2312yes—
193C4×D4×C43—22no—
194C4×D4×C43C2312yes—
195#117×C43—21no—
196#117×C43C2311yescharacteristic
197C2×C4⋊C4×C43—22no—
198C2×C4⋊C4×C43C2312yes—
199C2×C42×C43—21no—
200C2×C42×C43C2311yescharacteristic
201#107×C43C2314yes—
202#106×C43C2314yes—
203C4⋊C8×C43C2314yes—
204#103×C43C2314yes—
205#102×C43C2314yes—
206C23×D43—21no—
207C23×D43C2×D411yescharacteristic
208#41×C43—22no—
209#41×C43#4114yes—
210C2×Q8×C43C2411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43C2411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C22×Dic43—21no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D412yes—
226#10621902—22no—
227#10621902—22no—
228Q8×D43—22no—
229Q8×D43—22no—
230#10621900—28no—
231#10621900—22no—
232#10621900—22no—
233D4×D43—28no—
234D4×D43—22no—
235D4×D43—22no—
236#10621898—28no—
237#10621898—22no—
238#10621898#4114yes—
239C2×D172—21no—
240C2×D172C2411yescharacteristic
241C2×C4×D43—28no—
242C2×C4×D43—21no—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—21no—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—21no—
249C2×C4×D43—22no—
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2411yescharacteristic
253C2×C4×D43C2411yescharacteristic
254C2×Dic86—21no—
255C2×Dic86—24no—
256C2×Dic86—24no—
257C2×Dic86—22no—
258C2×Dic86C2414yes—
259C2×Dic86C2411yescharacteristic
260M16×C43—24no—
261C2×C8×C43C2414yes—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—24no—
264C4⋊C4×C43—22no—
265C4⋊C4×C43—22no—
266C4⋊C4×C43C2414yes—
267C4⋊C4×C43C2412yes—
268C22⋊C4×C43—22no—
269C22⋊C4×C43—21no—
270C42×C43—21no—
271C42×C43—22no—
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2412yes—
275C22⋊Dic43—22no—
276C22⋊Dic43—21no—
277#10621885—28no—
278#10621883—28no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4C2×D412yes—
285(C2×D43)⋊C4C2×D412yes—
286(C2×D43)⋊C4C2×D412yes—
287(C2×D43)⋊C4C2×D412yes—
288C4⋊Dic43—24no—
289C4⋊Dic43—24no—
290C4⋊Dic43—22no—
291C4⋊Dic43—24no—
292C4⋊Dic43—24no—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—22no—
295Dic43⋊C4—22no—
296Dic43⋊C4—22no—
297Dic43⋊C4—24no—
298Dic43⋊C4—24no—
299Dic43⋊C4C2×D412yes—
300Dic43⋊C4C2×D412yes—
301Dic43⋊C4C2×D412yes—
302Dic43⋊C4C2×D412yes—
303C4×Dic43—21no—
304C4×Dic43—22no—
305C4×Dic43—22no—
306C4×Dic43—22no—
307C4×Dic43—22no—
308C4×Dic43—24no—
309C4×Dic43—24no—
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2412yes—
313#10621877—24no—
314C2×C43⋊C8C2414yes—
315Dic172—28no—
316#10621873—28no—
317C23×C43—21no—
318C23×C43C22×D411yescharacteristic
319C22×D43—21no—
320C22×D43—24no—
321C22×D43—22no—
322C22×D43—42no—
323C22×D43—82no—
324C22×D43C22×D411yescharacteristic
325C22×D43C22×D411yescharacteristic
326Q8×C43—21no—
327Q8×C43C2×#4112yes—
328D4×C43—24no—
329D4×C43—21no—
330D4×C43C2×#4112yes—
331C2×C4×C43—21no—
332C2×C4×C43—24no—
333C2×C4×C43—24no—
334C2×C4×C43—22no—
335C2×C4×C43—42no—
336C2×C4×C43—44no—
337C2×C4×C43—82no—
338C2×C4×C43C22×D412yes—
339C2×C4×C43C22×D412yes—
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4112yes—
342C2×C4×C43C2×#4112yes—
343C2×C4×C43C2511yescharacteristic
344C22⋊D43—24no—
345C22⋊D43—24no—
346C22⋊D43—24no—
347C2×Dic43—24no—
348C2×Dic43—22no—
349C2×Dic43—21no—
350C2×Dic43—22no—
351C2×Dic43—24no—
352C2×Dic43—42no—
353C2×Dic43—44no—
354C2×Dic43—82no—
355C2×Dic43C22×D412yes—
356C2×Dic43C22×D412yes—
357C2×Dic43C22×D411yescharacteristic
358C2×Dic43C22×D411yescharacteristic
359D172—24no—
360D172—21no—
361D172C2×#4112yes—
362C4×D43—24no—
363C4×D43—24no—
364C4×D43—22no—
365C4×D43—24no—
366C4×D43—22no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—21no—
370C4×D43—21no—
371C4×D43—82no—
372C4×D43—82no—
373C4×D43—82no—
374Dic86—24no—
375Dic86—21no—
376Dic86—24no—
377Dic86—24no—
378Dic86—44no—
379Dic86C2×#4112yes—
380C8×C43—24no—
381C43⋊C8—24no—
382#60569—431nomaximal, Sylow
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—42no—
386C22×C43#52512yes—
387C22×C43C23×D411yescharacteristic
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—21no—
391C2×D43—22no—
392C2×D43—21no—
393C2×D43—42no—
394C2×D43—82no—
395C2×D43—84no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—44no—
401C4×C43#52512yes—
402C4×C43C22×#4111yescharacteristic
403C4×C43C22×#4111yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—21no—
407Dic43—22no—
408Dic43—21no—
409Dic43—42no—
410Dic43—44no—
411C2×#541—431no—
412#3428—431no—
413#3127—434no—
414#3123—434no—
415#3120—434no—
416#3120—434no—
417#3095—432no—
418#3080—431no—
419#3080D4311yescharacteristic, complemented
420#3039—431no—
421#3039—431no—
422#3007—432no—
423C4×#137—432no—
424C4×#137—432no—
425#2921—431no—
426C2×C43—22no—
427C2×C43—42no—
428C2×C43C2×#52511yescharacteristic
429C2×C43#358612yes—
430D43—41no—
431D43—41no—
432D43—42no—
433C22×#41—431no—
434C2×#137—432no—
435C2×#137—432no—
436#541—434no—
437#541—434no—
438#541—861no—
439#541—861no—
440#541—861no—
441#541—861no—
442C2×C4⋊Q8—431no—
443C2×#126—862no—
444C2×#125—862no—
445C2×#125C2×D4311yescharacteristic, complemented
446C2×C22⋊Q8—432no—
447#520—432no—
448#520—432no—
449#520—862no—
450#519—432no—
451#518—432no—
452#518—862no—
453C4×#41—431no—
454C4×#41—431no—
455C4×#41—431no—
456C4×#41—861no—
457C4×#41—861no—
458C4×#41C2×D4311yescharacteristic
459C2×C4×Q8—432no—
460C2×#117—431no—
461C2×#117—431no—
462C2×#117—861no—
463C2×#117—861no—
464#485—434no—
465#485—434no—
466#484—434no—
467#483—434no—
468#479—434no—
469#479C2×D4314yescomplemented
470#478—434no—
471#478C2×D4314yescomplemented
472#462—434no—
473#462—434no—
474#461—434no—
475#461—434no—
476#452—434no—
477#452—434no—
478#451—434no—
479#450—434no—
480#441—434no—
481#441—434no—
482#440—434no—
483#440—434no—
484C4×Q16—434no—
485C4×Q16—434no—
486C4×SD16—434no—
487C4×SD16—434no—
488#433—434no—
489#433—434no—
490#428—432no—
491#428C2×D4312yescomplemented
492#423—431no—
493#423C2×D4311yescharacteristic, complemented
494#419—432no—
495#419—432no—
496#417—432no—
497#417C2×D4312yes—
498#407—432no—
499C4×M16—432no—
500C43#6056911yescharacteristic, complemented, Sylow
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—431no—
504C2×#41—861no—
505C2×#41—861no—
506C2×#41—864no—
507C2×#41—864no—
508C2×#41C22×D4311yescharacteristic
509C22×Q8—431no—
510C22×Q8—432no—
511C22×D4—431no—
512C22×D4—861no—
513C23×C4—431no—
514C23×C4—861no—
515#137—868no—
516#137—868no—
517C2×Q16—434no—
518C2×Q16—434no—
519C2×SD16—434no—
520C2×SD16—434no—
521C2×M16—432no—
522C2×M16C22×D4312yes—
523C4⋊Q8—434no—
524C4⋊Q8—861no—
525C4⋊Q8—861no—
526#126—864no—
527#126—864no—
528#126—864no—
529#126—864no—
530#125—21no—
531#125—21no—
532#125—864no—
533#125—864no—
534#125—864no—
535#125—864no—
536#125C22×D4314yes—
537C22⋊Q8—434no—
538C22⋊Q8—434no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C4×Q8—432no—
542C4×Q8—434no—
543C4×Q8—434no—
544C4×Q8—432no—
545C4×Q8—432no—
546C4×Q8—862no—
547C4×Q8—862no—
548C4×Q8—862no—
549C4×Q8—862no—
550C4×Q8C22×D4312yes—
551C4×D4—22no—
552C4×D4—432no—
553C4×D4—432no—
554C4×D4—432no—
555C4×D4—862no—
556C4×D4—862no—
557C4×D4—862no—
558C4×D4—862no—
559C4×D4—862no—
560C4×D4—862no—
561C4×D4—862no—
562C4×D4—862no—
563C4×D4—862no—
564C4×D4C22×D4312yes—
565#117—21no—
566#117—431no—
567#117—431no—
568#117—431no—
569#117—431no—
570#117—432no—
571#117—432no—
572#117—431no—
573#117—432no—
574#117—861no—
575#117—862no—
576#117—862no—
577#117—861no—
578#117—861no—
579#117—862no—
580#117—861no—
581#117—862no—
582#117—861no—
583#117C22×D4311yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—432no—
586C2×C4⋊C4—432no—
587C2×C4⋊C4—862no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—862no—
591C2×C4⋊C4—862no—
592C2×C4⋊C4C22×D4312yes—
593C2×C22⋊C4—432no—
594C2×C22⋊C4—862no—
595C2×C22⋊C4—861no—
596C2×C22⋊C4—862no—
597C2×C22⋊C4—862no—
598C2×C42—21no—
599C2×C42—431no—
600C2×C42—861no—
601C2×C42—861no—
602C2×C42—861no—
603C2×C42—862no—
604C2×C42—861no—
605C2×C42C22×D4311yescharacteristic
606#107—434no—
607#107C22×D4314yes—
608#106—434no—
609#106C22×D4314yes—
610C4⋊C8—434no—
611C4⋊C8C22×D4314yes—
612#103—434no—
613#103—434no—
614#103—434no—
615#103—434no—
616#103—434no—
617#103C22×D4314yes—
618#102—434no—
619#102C22×D4314yes—
620C22⋊C8—434no—
621C22⋊C8—434no—
622#97—434no—
623C4×C8—434no—
624C24—431no—
625C24—861no—
626#41—22no—
627#41—434no—
628#41—868no—
629#41—862no—
630#41—868no—
631#41—862no—
632#41—862no—
633#41—862no—
634#41—862no—
635#41#1062190214yes—
636C2×Q8—431no—
637C2×Q8—434no—
638C2×Q8—861no—
639C2×Q8—862no—
640C2×Q8—862no—
641C2×Q8—862no—
642C2×Q8—864no—
643C2×Q8—864no—
644C2×Q8C23×D4311yescharacteristic
645C2×D4—21no—
646C2×D4—431no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—862no—
650C2×D4—868no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4—862no—
654C2×D4C23×D4311yescharacteristic
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—431no—
659C22×C4—432no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—861no—
665C22×C4—862no—
666C22×C4—861no—
667C22×C4—868no—
668C22×C4—862no—
669C22×C4—861no—
670C22×C4—862no—
671C22×C4—861no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4D4×D4312yes—
677C22×C4C23×D4311yescharacteristic
678Q16—868no—
679Q16—868no—
680SD16—868no—
681SD16—868no—
682M16—24no—
683M16—864no—
684C2×C8—434no—
685C2×C8C23×D4314yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—432no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—432no—
694C4⋊C4—432no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—862no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—864no—
702C4⋊C4—862no—
703C4⋊C4—864no—
704C4⋊C4—864no—
705C4⋊C4C23×D4314yes—
706C4⋊C4C23×D4312yes—
707C22⋊C4—21no—
708C22⋊C4—22no—
709C22⋊C4—432no—
710C22⋊C4—432no—
711C22⋊C4—432no—
712C22⋊C4—432no—
713C22⋊C4—862no—
714C22⋊C4—862no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—862no—
718C22⋊C4—861no—
719C22⋊C4—862no—
720C42—21no—
721C42—22no—
722C42—431no—
723C42—431no—
724C42—432no—
725C42—862no—
726C42—862no—
727C42—862no—
728C42—864no—
729C42—864no—
730C42—861no—
731C42—862no—
732C42D4×D4311yescharacteristic
733C42D4×D4311yescharacteristic
734C42C23×D4312yes—
735C23—21no—
736C23—431no—
737C23—431no—
738C23—864no—
739C23—862no—
740C23—861no—
741C23—3442no—
742C23—1722no—
743C23C2×D4×D4311yescharacteristic
744Q8—21no—
745Q8—432no—
746Q8—864no—
747Q8—861no—
748Q8—864no—
749Q8—864no—
750Q8—1724no—
751Q8C2×#1062190212yes—
752D4—24no—
753D4—21no—
754D4—432no—
755D4—864no—
756D4—864no—
757D4—864no—
758D4—864no—
759D4—861no—
760D4C2×#1062190212yes—
761C2×C4—21no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—82no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—431no—
771C2×C4—431no—
772C2×C4—864no—
773C2×C4—864no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—861no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—864no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—862no—
785C2×C4—864no—
786C2×C4—3442no—
787C2×C4—3442no—
788C2×C4—3442no—
789C2×C4—3442no—
790C2×C4—1722no—
791C2×C4—1724no—
792C2×C4C2×D4×D4312yes—
793C2×C4C2×D4×D4312yes—
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4#41×D4312yes—
796C2×C4C2×#1062190212yes—
797C2×C4C24×D4311yescharacteristic
798C8—24no—
799C8—864no—
800C22—22no—
801C22—22no—
802C22—42no—
803C22—861no—
804C22—862no—
805C22—861no—
806C22—862no—
807C22—862no—
808C22—3442no—
809C22—3444no—
810C22—1722no—
811C22#1458341212yes—
812C22C22×D4×D4311yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—44no—
817C4—42no—
818C4—861no—
819C4—861no—
820C4—862no—
821C4—862no—
822C4—862no—
823C4—1724no—
824C4—1722no—
825C4#1458341212yes—
826C4C2×#41×D4311yescharacteristic
827C4C22×#1062190211yescharacteristic
828C2—22no—
829C2—42no—
830C2—1721no—
831C2—1721no—
832C2—1722no—
833C2C2×#1458341211yescharacteristic
834C2#1914937912yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3080C2
socleC22×C43C23×D4
prime radicalC2×#41×D43C22
hypercenter#3080D43
hypocenterC43#60569
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#14583512C2semidirect
3. #19144897C2semidirect
4. #19144849C2semidirect
5. #19144816C2semidirect
6. #19144814C2semidirect
7. #19144545C2semidirect
8. #19144413C2semidirect
9. #19144083C2semidirect
10. #19144082C2semidirect
12. #19143419C2semidirect
13. #19143413C2semidirect
14. #19143232C2semidirect
15. C43×#3080C2semidirect
24. #14583512C22semidirect
25. C2×#13063325C22semidirect
40. C2×#13063290C22semidirect
47. #14583236C22semidirect
48. #14583231C22semidirect
49. #14583203C22semidirect
50. #14583196C22semidirect
51. #14583110C22semidirect
52. #14583109C22semidirect
53. #14583105C22semidirect
54. #14583104C22semidirect
59. #14583005C22semidirect
60. #14583003C22semidirect
61. #14582998C22semidirect
62. #14582996C22semidirect
63. #14582993C22semidirect
64. #14582991C22semidirect
65. #14582990C22semidirect
66. #14582986C22semidirect
68. #14582959C22semidirect
69. #14582939C22semidirect
70. #14582923C22semidirect
71. #14582909C22semidirect
72. #14582907C22semidirect
75. M16×Dic43C22semidirect
76. C2×#125×C43C22semidirect
78. C43×#479C22semidirect
79. C43×#478C22semidirect
80. C43×#428C22semidirect
81. C43×#423C22semidirect
419. #3080D43semidirect
445. C2×#125C2×D43semidirect
469. #479C2×D43semidirect
471. #478C2×D43semidirect
491. #428C2×D43semidirect
493. #423C2×D43semidirect
500. C43#60569semidirect

Maximal subgroups

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

subgroupindex
C2×#145835122
#191477942
#191448972
#191448492
#191448162
#191448142
#191445452
#191444132
#191440832
#191440822
#191438562
#191434192
#191434132
#191432322
C43×#30802
#6056943