Finite Group Databasebeta

← #25961585

Subgroups — #25961585

Order 11008.

1748 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143695C212yesmaximal, complemented
3#19143693C212yesmaximal, complemented
4#19143688C214yesmaximal, complemented
5#19143681C214yesmaximal, complemented
6#19143677C212yesmaximal, complemented
7#19143674C212yesmaximal, complemented
8#19143544C211yesmaximal, characteristic, complemented
9#19143542C211yesmaximal, characteristic, complemented
10#19143538C211yesmaximal, characteristic, complemented
11#19143528C212yesmaximal, complemented
12#19143527C212yesmaximal, complemented
13#19143252C212yesmaximal
14#19143250C212yesmaximal
15#19143226C211yesmaximal, characteristic
16C2×#14582951C211yesmaximal, characteristic
17C43×#2962C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455C412yes—
20#14583454C411yescharacteristic
21#14583454C411yescharacteristic
22#14583453C2212yes—
23#14583453C2212yes—
24#14583452C2212yes—
25#14583451C412yes—
26#14583451C412yes—
27C4⋊Q8×D43C411yescharacteristic
28C4⋊Q8×D43C411yescharacteristic
29#125×D43C412yes—
30C22⋊Q8×D43C412yes—
31C22⋊Q8×D43C412yes—
32C4×Q8×D43C2212yes—
33C4×Q8×D43C2212yes—
34#117×D43C2212yes—
35C2×C42×D43C2211yescharacteristic
36#14583030C2214yescomplemented
37#14583030C2212yescomplemented
38#14583029C2212yescomplemented
39#14583028C2214yescomplemented
40#14583028C2214yescomplemented
41#14583028C2214yescomplemented
42#14583027C2214yescomplemented
43#14583027C2214yescomplemented
44#14583027C2214yescomplemented
45#14583026C2212yescomplemented
46Q8×C43⋊C8C2212yescomplemented
47C8×Dic86C2214yescomplemented
48C8×Dic86C2214yescomplemented
49C8×Dic86C2212yescomplemented
50#14583023C2214yescomplemented
51#14583023C2214yescomplemented
52#14583023C2212yescomplemented
53#14582961C2214yes—
54#14582959C2214yes—
55#14582959C2214yes—
56#14582958C2214yes—
57#14582955C2214yes—
58#14582954C2212yes—
59#14582954C2214yes—
60#14582954C2212yes—
61#14582951C2212yes—
62#14582951C2214yes—
63#14582951C2212yes—
64#14582951C2211yescharacteristic
65#14582951C2211yescharacteristic
66#14582951C2211yescharacteristic
67#14582951C2211yescharacteristic
68#14582950C2214yes—
69#14582950C2212yes—
70#14582950C2212yes—
71#14582927C2212yes—
72#14582926C2212yes—
73#14582925C2212yes—
74#14582922C2211yescharacteristic
75#14582922C2211yescharacteristic
76C2×C4⋊(C43⋊C8)C2211yescharacteristic
77#14582862C2211yescharacteristic
78#14582862C2211yescharacteristic
79C2×(C2×D43)⋊C8C2212yes—
80#14582857C2212yes—
81#14582855C2212yes—
82#14582854C2212yes—
83C4×#10621877C2211yescharacteristic
84C2×C8×Dic43C2212yes—
85C43×#533C2211yescharacteristic
86C43×#446C2214yescomplemented
87C43×#446C2212yescomplemented
88C8×Q8×C43C2212yescomplemented
89C43×#424C2212yes—
90C2×C4⋊C8×C43C2211yescharacteristic
91C43×#405C2212yes—
92C4×M16×C43C2211yescharacteristic
93C2×Q8×D43C2×C412yes—
94C2×Q8×D43C2×C412yes—
95C22×C4×D43C2×C411yescharacteristic
96C22×C4×D43C2×C411yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621877C2311yescharacteristic
99C2×#10621877C2311yescharacteristic
100C22×C43⋊C8C2312yes—
101#13063325C2×C411yescharacteristic
102#13063325C2×C411yescharacteristic
103#13063324C2×C412yes—
104#13063324C2×C412yes—
105#13063324C2×C412yes—
106#13063324C2×C412yes—
107#13063323C2×C412yes—
108#13063323C2×C412yes—
109#13063317C2×C412yes—
110#13063316C2×C412yes—
111#13063316C2×C412yes—
112#13063315C2×C414yes—
113#13063315C2×C414yes—
114#13063305C2×C412yes—
115#13063305C2×C412yes—
116#13063304C2×C412yes—
117#13063304C2×C412yes—
118#13063303C2×C414yes—
119#13063303C2×C414yes—
120#13063302C2×C414yes—
121#13063302C2×C414yes—
122#13063301C2×C412yes—
123#13063301C2×C412yes—
124Q8×Dic43C2×C412yes—
125Q8×Dic43C2×C412yes—
126C4×Dic86C2314yes—
127C4×Dic86C2314yes—
128C4×Dic86C2312yes—
129C4×Dic86C2312yes—
130#13063290C2×C412yes—
131#13063290C2×C412yes—
132#13063290C2×C414yes—
133#13063290C2×C414yes—
134#13063284C2312yes—
135#13063283C2×C412yes—
136#13063283C2×C412yes—
137#13063282C2314yes—
138#13063281C2×C414yes—
139C4⋊C4×D43C2×C412yes—
140C4⋊C4×D43C2×C412yes—
141C4⋊C4×D43C2×C414yes—
142C4⋊C4×D43C2×C414yes—
143C4⋊C4×D43C2×C412yes—
144C4⋊C4×D43C2×C412yes—
145C22⋊C4×D43C2×C414yes—
146C2×C4×Dic43C2×C411yescharacteristic
147C2×C4×Dic43C2×C411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43C2×C411yescharacteristic
152C42×D43C2×C411yescharacteristic
153C42×D43C2311yescharacteristic
154C42×D43C2311yescharacteristic
155C42×D43C2311yescharacteristic
156C42×D43C2311yescharacteristic
157C42×D43C2314yes—
158C4⋊(C43⋊C8)C2311yescharacteristic
159C4⋊(C43⋊C8)C2312yes—
160C4⋊(C43⋊C8)C2311yescharacteristic
161C4⋊(C43⋊C8)C2314yes—
162C4⋊(C43⋊C8)C2314yes—
163Dic43⋊C8C2312yes—
164Dic43⋊C8C2312yes—
165Dic43⋊C8C2312yes—
166Dic43⋊C8C2312yes—
167Dic43⋊C8C2314yes—
168Dic43⋊C8C2314yes—
169Dic43⋊C8C2314yes—
170Dic43⋊C8C2314yes—
171(C2×D43)⋊C8C2312yes—
172(C2×D43)⋊C8C2312yes—
173(C2×D43)⋊C8C2312yes—
174(C2×D43)⋊C8C2312yes—
175(C2×D43)⋊C8C2312yes—
176(C2×D43)⋊C8C2312yes—
177(C2×D43)⋊C8C2312yes—
178(C2×D43)⋊C8C2312yes—
179#13063236C2312yes—
180#13063236C2314yes—
181#13063235C2314yes—
182#13063235C2314yes—
183C4×C43⋊C8C2312yes—
184C4×C43⋊C8C2314yes—
185C8×Dic43C2312yes—
186C8×Dic43C2312yes—
187C8×Dic43C2312yes—
188C8×Dic43C2312yes—
189C8×Dic43C2314yes—
190C8×Dic43C2314yes—
191C2×M16×C43C2311yescharacteristic
192C2×M16×C43C2311yescharacteristic
193C22×C8×C43C2312yes—
194C4⋊Q8×C43C2×C411yescharacteristic
195C4⋊Q8×C43C2×C411yescharacteristic
196#125×C43C2×C412yes—
197C22⋊Q8×C43C2×C412yes—
198C22⋊Q8×C43C2×C412yes—
199C4×Q8×C43C2312yes—
200C4×Q8×C43C2312yes—
201#117×C43C2312yes—
202C2×C42×C43C2311yescharacteristic
203C4⋊C8×C43C2311yescharacteristic
204C4⋊C8×C43C2311yescharacteristic
205C4⋊C8×C43C2312yes—
206C4⋊C8×C43C2314yes—
207C4⋊C8×C43C2314yes—
208#97×C43C2312yes—
209#97×C43C2314yes—
210C4×C8×C43C2312yes—
211C4×C8×C43C2314yes—
212C23×D43C22×C411yescharacteristic
213C2×Q8×C43C22×C412yes—
214C2×Q8×C43C22×C412yes—
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C2411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C22×Dic43C22×C411yescharacteristic
221Q8×D43—28no—
222Q8×D43—44no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—24no—
226C2×C4×D43—42no—
227C2×C4×D43C22×C411yescharacteristic
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C22×C411yescharacteristic
231C2×C4×D43C22×C411yescharacteristic
232C2×C4×D43C22×C411yescharacteristic
233C2×C4×D43C22×C411yescharacteristic
234C2×C4×D43C22×C414yes—
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C22×C411yescharacteristic
237C2×C4×D43C22×C414yes—
238C2×C4×D43C22×C411yescharacteristic
239C2×C4×D43C2411yescharacteristic
240C2×C4×D43C2411yescharacteristic
241C2×Dic86C22×C414yes—
242C2×Dic86C22×C414yes—
243C2×Dic86C22×C412yes—
244C2×Dic86C22×C412yes—
245M16×C43—22no—
246M16×C43—22no—
247C2×C8×C43—24no—
248C2×C8×C43C2412yes—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C4⋊C4×C43C22×C412yes—
253C4⋊C4×C43C22×C412yes—
254C4⋊C4×C43C22×C414yes—
255C4⋊C4×C43C22×C414yes—
256C4⋊C4×C43C22×C412yes—
257C4⋊C4×C43C22×C412yes—
258C22⋊C4×C43C22×C414yes—
259C42×C43C22×C411yescharacteristic
260C42×C43C22×C411yescharacteristic
261C42×C43C2411yescharacteristic
262C42×C43C2414yes—
263C42×C43C2411yescharacteristic
264C22⋊Dic43C22×C414yes—
265(C2×D43)⋊C4C22×C414yes—
266(C2×D43)⋊C4C22×C414yes—
267C4⋊Dic43C22×C412yes—
268C4⋊Dic43C22×C412yes—
269C4⋊Dic43C22×C412yes—
270C4⋊Dic43C22×C412yes—
271C4⋊Dic43C22×C414yes—
272C4⋊Dic43C22×C414yes—
273Dic43⋊C4C22×C414yes—
274Dic43⋊C4C22×C414yes—
275Dic43⋊C4C22×C414yes—
276Dic43⋊C4C22×C414yes—
277Dic43⋊C4C22×C414yes—
278Dic43⋊C4C22×C414yes—
279Dic43⋊C4C22×C414yes—
280Dic43⋊C4C22×C414yes—
281C4×Dic43C22×C411yescharacteristic
282C4×Dic43C22×C411yescharacteristic
283C4×Dic43C22×C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C22×C411yescharacteristic
287C4×Dic43C22×C411yescharacteristic
288C4×Dic43C22×C411yescharacteristic
289C4×Dic43C22×C411yescharacteristic
290C4×Dic43C22×C411yescharacteristic
291C4×Dic43C22×C414yes—
292C4×Dic43C22×C414yes—
293C4×Dic43C2411yescharacteristic
294C4×Dic43C2411yescharacteristic
295C4×Dic43C2414yes—
296#10621877—22no—
297#10621877—22no—
298C2×C43⋊C8—24no—
299C2×C43⋊C8C2412yes—
300C2×C43⋊C8C2412yes—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303C23×C43C23×C411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—41no—
307C22×D43C23×C411yescharacteristic
308C22×D43C23×C411yescharacteristic
309Q8×C43—24no—
310Q8×C43—42no—
311C2×C4×C43—22no—
312C2×C4×C43—41no—
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C23×C414yes—
317C2×C4×C43C23×C414yes—
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C432−1+412yes—
321C2×C4×C432−1+412yes—
322C2×C4×C43C2511yescharacteristic
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43C23×C411yescharacteristic
327C2×Dic43C23×C411yescharacteristic
328C2×Dic43C23×C411yescharacteristic
329C2×Dic43C23×C411yescharacteristic
330C2×Dic43C23×C414yes—
331C2×Dic43C23×C414yes—
332C2×Dic43C23×C411yescharacteristic
333C2×Dic43C23×C411yescharacteristic
334C4×D43—22no—
335C4×D43—28no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—21no—
340C4×D43—21no—
341C4×D43—21no—
342C4×D43—21no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—44no—
349C4×D43#13114yes—
350Dic86—24no—
351Dic86—28no—
352Dic86—28no—
353Dic86—42no—
354C8×C43—22no—
355C8×C43—22no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C43⋊C8—22no—
361C43⋊C8—22no—
362#60250—431nomaximal, Sylow
363C22×C43—21no—
364C22×C43—21no—
365C22×C43#51912yes—
366C22×C43C24×C411yescharacteristic
367C2×D43—21no—
368C2×D43—21no—
369C2×D43—21no—
370C2×D43—21no—
371C2×D43—21no—
372C2×D43—44no—
373C2×D43C2×#13112yes—
374C4×C43—24no—
375C4×C43—21no—
376C4×C43—24no—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43#51912yes—
380C4×C43C2×#13112yes—
381C4×C43C2×2−1+411yescharacteristic
382C4×C43C2×2−1+411yescharacteristic
383Dic43—21no—
384Dic43—21no—
385Dic43—24no—
386Dic43—21no—
387Dic43—24no—
388Dic43—21no—
389Dic43C2×#13112yes—
390Dic43#56812yes—
391C2×#533—431no—
392#2986—432no—
393#2986—432no—
394#2985—434no—
395#2984—434no—
396#2983—432no—
397#2982—432no—
398#2962—431no—
399#2962—431no—
400#2962—431no—
401#2962D4311yescharacteristic, complemented
402#2960—432no—
403#2960—432no—
404#2924—432no—
405#2924—432no—
406#2920—431no—
407C2×#431—431no—
408C2×C43—22no—
409C2×C43C2×#51911yescharacteristic
410C2×C43C22×#13111yescharacteristic
411C2×C43C2×#56811yescharacteristic
412D43—22no—
413D43—41no—
414#533—431no—
415#533—431no—
416#533—432no—
417#533—432no—
418#533—432no—
419#533—432no—
420#533—432no—
421#533—432no—
422#533—431no—
423#533C2×D4311yescharacteristic
424C2×C4⋊Q8—431no—
425C2×C4⋊Q8—431no—
426C2×#125—432no—
427C2×C22⋊Q8—432no—
428C2×C22⋊Q8—432no—
429C2×C4×Q8—432no—
430C2×C4×Q8—432no—
431C2×#117—432no—
432C22×C42—431no—
433#446—432no—
434#446—434no—
435#446—434no—
436#446—434no—
437#446—432no—
438#446—434no—
439#446—434no—
440#446—434no—
441#446—434no—
442#446—432no—
443#446C2×D4312yescomplemented
444#446C2×D4314yescomplemented
445C8×Q8—432no—
446C8×Q8—434no—
447C8×Q8—434no—
448C8×Q8—432no—
449C8×Q8—434no—
450C8×Q8—434no—
451C8×Q8—432no—
452C8×Q8C2×D4312yescomplemented
453#433—434no—
454#433—434no—
455#433—434no—
456#433—434no—
457#432—434no—
458#432—432no—
459#432—432no—
460#432—434no—
461#431—431no—
462#431—431no—
463#431—432no—
464#431—432no—
465#431—431no—
466#431—431no—
467#431—434no—
468#431—432no—
469#431—432no—
470#431—434no—
471#424—432no—
472#424—432no—
473#424—432no—
474#424C2×D4312yes—
475#423—431no—
476#423—431no—
477C2×C4⋊C8—431no—
478C2×C4⋊C8C2×D4311yescharacteristic
479#407—431no—
480#407—431no—
481C2×C22⋊C8—432no—
482#405—432no—
483#405—432no—
484#405—432no—
485#405C2×D4312yes—
486C4×M16—431no—
487C4×M16C2×D4311yescharacteristic
488C2×C4×C8—432no—
489C43#6025011yescharacteristic, complemented, Sylow
490C22×Q8—432no—
491C22×Q8—432no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C2×M16—431no—
496C2×M16—431no—
497C2×M16C22×D4311yescharacteristic
498C2×M16C22×D4311yescharacteristic
499C22×C8—432no—
500C22×C8C22×D4312yes—
501C4⋊Q8—432no—
502C4⋊Q8—432no—
503C4⋊Q8—432no—
504C4⋊Q8—432no—
505C4⋊Q8—432no—
506C4⋊Q8—432no—
507C4⋊Q8—431no—
508C4⋊Q8—431no—
509C4⋊Q8C4×D4311yescharacteristic
510C4⋊Q8C4×D4311yescharacteristic
511#125—434no—
512#125—434no—
513#125—432no—
514#125—432no—
515#125—432no—
516#125C4×D4312yes—
517C22⋊Q8—432no—
518C22⋊Q8—432no—
519C22⋊Q8—432no—
520C22⋊Q8—432no—
521C22⋊Q8—434no—
522C22⋊Q8—434no—
523C22⋊Q8—432no—
524C22⋊Q8—432no—
525C22⋊Q8—434no—
526C22⋊Q8—434no—
527C22⋊Q8C4×D4312yes—
528C22⋊Q8C4×D4312yes—
529C4×Q8—432no—
530C4×Q8—432no—
531C4×Q8—432no—
532C4×Q8—432no—
533C4×Q8—434no—
534C4×Q8—434no—
535C4×Q8—434no—
536C4×Q8—434no—
537C4×Q8—432no—
538C4×Q8—432no—
539C4×Q8C22×D4312yes—
540C4×Q8C22×D4312yes—
541#117—432no—
542#117—432no—
543#117—432no—
544#117—434no—
545#117—434no—
546#117C22×D4312yes—
547C2×C4⋊C4—432no—
548C2×C4⋊C4—432no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—434no—
551C2×C4⋊C4—432no—
552C2×C4⋊C4—432no—
553C2×C22⋊C4—434no—
554C2×C42—431no—
555C2×C42—431no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—434no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42C22×D4311yescharacteristic
567C4⋊C8—432no—
568C4⋊C8—432no—
569C4⋊C8—432no—
570C4⋊C8—432no—
571C4⋊C8—434no—
572C4⋊C8—434no—
573C4⋊C8—434no—
574C4⋊C8—434no—
575C4⋊C8—431no—
576C4⋊C8—431no—
577C4⋊C8—432no—
578C4⋊C8—434no—
579C4⋊C8—434no—
580C4⋊C8C22×D4311yescharacteristic
581C4⋊C8C22×D4311yescharacteristic
582C4⋊C8C22×D4312yes—
583C4⋊C8C22×D4314yes—
584C4⋊C8C22×D4314yes—
585C22⋊C8—432no—
586C22⋊C8—432no—
587C22⋊C8—432no—
588C22⋊C8—432no—
589C22⋊C8—432no—
590C22⋊C8—432no—
591C22⋊C8—432no—
592C22⋊C8—432no—
593#97—434no—
594#97—434no—
595#97—432no—
596#97—434no—
597#97C22×D4312yes—
598#97C22×D4314yes—
599C4×C8—432no—
600C4×C8—432no—
601C4×C8—432no—
602C4×C8—432no—
603C4×C8—434no—
604C4×C8—434no—
605C4×C8—432no—
606C4×C8—434no—
607C4×C8C22×D4312yes—
608C4×C8C22×D4314yes—
609C24—431no—
610C2×Q8—434no—
611C2×Q8—434no—
612C2×Q8—432no—
613C2×Q8—432no—
614C2×Q8—868no—
615C2×Q8—1724no—
616C2×Q8C2×C4×D4312yes—
617C2×Q8C2×C4×D4312yes—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—434no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—434no—
635C22×C4—864no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—1722no—
639C22×C4C2×C4×D4311yescharacteristic
640C22×C4C2×C4×D4311yescharacteristic
641C22×C4C23×D4311yescharacteristic
642M16—22no—
643M16—22no—
644M16—862no—
645M16—862no—
646C2×C8—24no—
647C2×C8—432no—
648C2×C8—432no—
649C2×C8—432no—
650C2×C8—432no—
651C2×C8—864no—
652C2×C8C23×D4312yes—
653C2×C8C23×D4312yes—
654C2×C8C23×D4312yes—
655C2×C8C23×D4312yes—
656C4⋊C4—434no—
657C4⋊C4—434no—
658C4⋊C4—432no—
659C4⋊C4—432no—
660C4⋊C4—434no—
661C4⋊C4—434no—
662C4⋊C4—434no—
663C4⋊C4—434no—
664C4⋊C4—434no—
665C4⋊C4—434no—
666C4⋊C4—434no—
667C4⋊C4—434no—
668C4⋊C4—432no—
669C4⋊C4—432no—
670C4⋊C4C2×C4×D4312yes—
671C4⋊C4C2×C4×D4312yes—
672C4⋊C4C2×C4×D4314yes—
673C4⋊C4C2×C4×D4314yes—
674C4⋊C4C2×C4×D4312yes—
675C4⋊C4C2×C4×D4312yes—
676C22⋊C4—434no—
677C22⋊C4—434no—
678C22⋊C4—434no—
679C22⋊C4C2×C4×D4314yes—
680C42—431no—
681C42—431no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—434no—
691C42—434no—
692C42—431no—
693C42—431no—
694C42—434no—
695C42C2×C4×D4311yescharacteristic
696C42C2×C4×D4311yescharacteristic
697C42C23×D4311yescharacteristic
698C42C23×D4314yes—
699C42C23×D4311yescharacteristic
700C23—431no—
701C23—431no—
702C23—862no—
703C23—862no—
704C23—1721no—
705C23C22×C4×D4311yescharacteristic
706Q8—24no—
707Q8—42no—
708Q8—868no—
709Q8—868no—
710Q8—864no—
711Q8—1722no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—431no—
715C2×C4—431no—
716C2×C4—434no—
717C2×C4—431no—
718C2×C4—431no—
719C2×C4—431no—
720C2×C4—431no—
721C2×C4—434no—
722C2×C4—434no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—868no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1724no—
741C2×C4C22×C4×D4311yescharacteristic
742C2×C4C22×C4×D4311yescharacteristic
743C2×C4C22×C4×D4311yescharacteristic
744C2×C4C22×C4×D4314yes—
745C2×C4C22×C4×D4314yes—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C22×C4×D4311yescharacteristic
748C2×C4#1306337212yes—
749C2×C4#1306337312yes—
750C2×C4C24×D4311yescharacteristic
751C8—22no—
752C8—22no—
753C8—22no—
754C8—22no—
755C8—862no—
756C8—862no—
757C8—862no—
758C8—862no—
759C22—21no—
760C22—21no—
761C22—432no—
762C22—861no—
763C22—861no—
764C22—861no—
765C22—861no—
766C22—861no—
767C22—1724no—
768C22#1458337512yes—
769C22C23×C4×D4311yescharacteristic
770C4—21no—
771C4—24no—
772C4—21no—
773C4—21no—
774C4—24no—
775C4—432no—
776C4—432no—
777C4—861no—
778C4—861no—
779C4—861no—
780C4—864no—
781C4—861no—
782C4—864no—
783C4#1458337512yes—
784C4#131×D4312yes—
785C4C2×#1306337211yescharacteristic
786C4C2×#1306337311yescharacteristic
787C2—22no—
788C2—862no—
789C2—1721no—
790C2C2×#1458337511yescharacteristic
791C2C2×#131×D4311yescharacteristic
792C2#568×D4311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2962C2
prime radicalC23×D43C22×C4
cosocleC2×C4×C43C25
hypercenter#2962D43
hypocenterC43#60250
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2962

Complements

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

NH ≅ G/Ntype
2. #19143695C2semidirect
3. #19143693C2semidirect
4. #19143688C2semidirect
5. #19143681C2semidirect
6. #19143677C2semidirect
7. #19143674C2semidirect
8. #19143544C2semidirect
9. #19143542C2semidirect
10. #19143538C2semidirect
11. #19143528C2semidirect
12. #19143527C2semidirect
17. C43×#2962C2semidirect
36. #14583030C22semidirect
37. #14583030C22semidirect
38. #14583029C22semidirect
39. #14583028C22semidirect
40. #14583028C22semidirect
41. #14583028C22semidirect
42. #14583027C22semidirect
43. #14583027C22semidirect
44. #14583027C22semidirect
45. #14583026C22semidirect
46. Q8×C43⋊C8C22semidirect
47. C8×Dic86C22semidirect
48. C8×Dic86C22semidirect
49. C8×Dic86C22semidirect
50. #14583023C22semidirect
51. #14583023C22semidirect
52. #14583023C22semidirect
86. C43×#446C22semidirect
87. C43×#446C22semidirect
88. C8×Q8×C43C22semidirect
401. #2962D43semidirect
443. #446C2×D43semidirect
444. #446C2×D43semidirect
452. C8×Q8C2×D43semidirect
489. C43#60250semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191436952
#191436932
#191436882
#191436812
#191436772
#191436742
#191435442
#191435422
#191435382
#191435282
#191435272
#191432522
#191432502
#191432262
C2×#145829512
C43×#29622
#6025043