Finite Group Databasebeta

← #25968928

Subgroups — #25968928

Order 11008.

1788 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic, complemented
2C2×#14583431C211yesmaximal, characteristic
3#19145834C214yesmaximal, complemented
4#19145824C212yesmaximal, complemented
5#19145815C212yesmaximal, complemented
6#19145773C212yesmaximal, complemented
7#19145772C212yesmaximal, complemented
8#19145761C214yesmaximal, complemented
9#19145145C212yesmaximal, complemented
10#19144979C212yesmaximal, complemented
11#19144545C212yesmaximal, complemented
12#19144533C212yesmaximal
13#19144402C211yesmaximal, characteristic, complemented
14#19144396C211yesmaximal, characteristic, complemented
15#19144392C211yesmaximal, characteristic, complemented
16#19143227C211yesmaximal, characteristic, complemented
17C43×#3077C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455C2212yescomplemented
20#14583454C2211yescharacteristic, complemented
21#14583454C2211yescharacteristic, complemented
22#14583453—21no—
23#14583453—21no—
24#14583452C2212yes—
25#14583451—21no—
26#14583451—21no—
27C4⋊Q8×D43C2211yescharacteristic, complemented
28C4⋊Q8×D43C2211yescharacteristic, complemented
29#14583431—21no—
30#14583431—21no—
31#14583431—21no—
32#14583431—21no—
33#14583431C2212yes—
34#14583431C2212yes—
35#14583431C2212yes—
36#14583431C2212yes—
37C2×#13063318—21no—
38C2×#13063316C2211yescharacteristic
39#125×D43C2212yescomplemented
40C2×#13063312C2211yescharacteristic
41C2×#13063307—21no—
42C2×#13063305C2211yescharacteristic
43C22⋊Q8×D43—21no—
44C22⋊Q8×D43—21no—
45C2×#13063296C2211yescharacteristic
46C2×C4×Dic86C2211yescharacteristic
47C4×Q8×D43—21no—
48C4×Q8×D43—21no—
49C2×C4×C22⋊D43—21no—
50C2×#13063284—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583307C2214yescomplemented
54#14583306C2214yescomplemented
55#14583300C2214yescomplemented
56#14583299C2214yescomplemented
57#14583257C2214yescomplemented
58#14583257C2214yescomplemented
59#14583252C2214yescomplemented
60#14583252C2214yescomplemented
61#14583243C2214yescomplemented
62#14583242C2214yescomplemented
63#14583236C2214yescomplemented
64#14583231C2214yescomplemented
65#14583222C2214yes—
66#14583221C2214yes—
67#14583216C2214yes—
68#14583211C2214yes—
69#14583207C2214yescomplemented
70#14583203C2214yescomplemented
71#14583199C2214yescomplemented
72#14583195C2212yescomplemented
73#14583191C2212yescomplemented
74#14583189C2212yescomplemented
75#14583185C2212yescomplemented
76#14583181C2212yescomplemented
77#14583179C2212yescomplemented
78#14582955C2212yescomplemented
79#14582955C2212yescomplemented
80#14582951C2212yescomplemented
81#14582951C2212yescomplemented
82#14582942C2212yes—
83#14582941C2212yes—
84#14582939C2212yes—
85#14582923C2211yescharacteristic
86#14582909C2212yes—
87#14582907C2212yes—
88#14582904C2212yes—
89#14582862C2212yes—
90M16×Dic43C2212yes—
91C43×#533C2211yescharacteristic
92C2×C4×D4×C43C2211yescharacteristic
93C43×#478C2214yescomplemented
94C43×#476C2212yescomplemented
95C43×#474C2212yescomplemented
96C43×#428C2212yes—
97C43×#423C2211yescharacteristic
98C43×#418C2212yes—
99C22×Dic86C2311yescharacteristic
100C2×Q8×D43—21no—
101C2×Q8×D43—21no—
102C22×C22⋊D43—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×#10621877C2312yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063324—21no—
110#13063324—21no—
111#13063324C2312yes—
112#13063324C2312yes—
113#13063323—21no—
114#13063323—21no—
115#13063318—22no—
116#13063318—22no—
117#13063318—22no—
118#13063318—22no—
119#13063317C2312yes—
120#13063316—21no—
121#13063316—21no—
122#13063316C2312yes—
123#13063316C2312yes—
124#13063316C2312yes—
125#13063316C2312yes—
126#13063315—22no—
127#13063315—22no—
128#13063312—21no—
129#13063312—21no—
130#13063312C2312yes—
131#13063312C2312yes—
132#13063307—22no—
133#13063307—22no—
134#13063307—22no—
135#13063307—22no—
136#13063305—21no—
137#13063305—21no—
138#13063305—21no—
139#13063305—21no—
140#13063305C2312yes—
141#13063305C2312yes—
142#13063304—21no—
143#13063304—21no—
144#13063303—22no—
145#13063303—22no—
146#13063302—22no—
147#13063302—22no—
148#13063301—21no—
149#13063301—21no—
150#13063296—21no—
151#13063296—21no—
152#13063296C2312yes—
153#13063296C2312yes—
154Q8×Dic43—21no—
155Q8×Dic43—21no—
156C4×Dic86—21no—
157C4×Dic86—21no—
158C4×Dic86—21no—
159C4×Dic86—21no—
160C4×Dic86—22no—
161C4×Dic86—22no—
162C4×Dic86C2312yes—
163C4×Dic86C2312yes—
164#13063290—21no—
165#13063290—21no—
166#13063290—22no—
167#13063290—22no—
168C4×C22⋊D43—22no—
169C4×C22⋊D43—22no—
170C4×C22⋊D43—22no—
171C4×C22⋊D43—22no—
172#13063284—22no—
173#13063284—22no—
174#13063284—22no—
175#13063284—22no—
176#13063284C2312yes—
177#13063283C2312yes—
178#13063283C2312yes—
179#13063282—22no—
180#13063281—22no—
181C2×C4⋊Dic43—21no—
182C2×C4⋊Dic43—21no—
183C2×C4⋊Dic43C2311yescharacteristic
184C2×Dic43⋊C4—21no—
185C2×Dic43⋊C4—21no—
186C4⋊C4×D43—22no—
187C4⋊C4×D43—22no—
188C4⋊C4×D43—21no—
189C4⋊C4×D43—21no—
190C4⋊C4×D43C2312yes—
191C4⋊C4×D43C2312yes—
192C2×C22⋊Dic43—21no—
193C2×C22⋊Dic43—21no—
194C2×C22⋊Dic43—21no—
195C2×(C2×D43)⋊C4—21no—
196C22⋊C4×D43—22no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C42×D43—22no—
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063259C2314yes—
211#13063258C2314yes—
212#13063258C2314yes—
213#13063257C2314yes—
214#13063256C2314yes—
215#13063256C2314yes—
216C4⋊(C43⋊C8)C2312yes—
217C4⋊(C43⋊C8)C2312yes—
218#13063250C2314yes—
219#13063250C2314yes—
220#13063248C2314yes—
221#13063248C2314yes—
222#13063246C2314yes—
223#13063246C2314yes—
224(C2×D43)⋊C8C2314yes—
225(C2×D43)⋊C8C2314yes—
226#13063235C2314yes—
227C8×Dic43C2314yes—
228C22×D4×C43C2311yescharacteristic
229C23×C4×C43—21no—
230C2×M16×C43C2312yes—
231C4⋊Q8×C43C2311yescharacteristic
232C4⋊Q8×C43C2311yescharacteristic
233#125×C43C2312yes—
234C22⋊Q8×C43—21no—
235C22⋊Q8×C43—21no—
236C4×Q8×C43—21no—
237C4×Q8×C43—21no—
238C4×D4×C43—21no—
239C4×D4×C43—21no—
240C4×D4×C43C2312yes—
241C4×D4×C43C2312yes—
242#117×C43C2312yes—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C22⋊C4×C43—21no—
245C2×C42×C43C2311yescharacteristic
246#107×C43C2314yes—
247#106×C43C2314yes—
248C4⋊C8×C43C2312yes—
249C4⋊C8×C43C2312yes—
250#102×C43C2314yes—
251#102×C43C2314yes—
252C24×C43—21no—
253C23×D43C2×D411yescharacteristic
254C2×Q8×C43—21no—
255C2×Q8×C43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—22no—
258C2×D4×C43—22no—
259C2×D4×C43C2412yes—
260C22×C4×C43—22no—
261C22×C4×C43—22no—
262C22×C4×C43—21no—
263C22×C4×C43—44no—
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2411yescharacteristic
267C2×C22⋊D43—22no—
268C2×C22⋊D43—22no—
269C2×C22⋊D43—44no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43C2×D411yescharacteristic
273C22×Dic43C2×D411yescharacteristic
274C22×Dic43C2×D411yescharacteristic
275Q8×D43—44no—
276Q8×D43—44no—
277C2×C4×D43—22no—
278C2×C4×D43—22no—
279C2×C4×D43—22no—
280C2×C4×D43—22no—
281C2×C4×D43—42no—
282C2×C4×D43—42no—
283C2×C4×D43C2×D411yescharacteristic
284C2×C4×D43C2×D411yescharacteristic
285C2×C4×D43C2×D411yescharacteristic
286C2×C4×D43C2×D411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2×D411yescharacteristic
289C2×C4×D43C2×D411yescharacteristic
290C2×C4×D43C2×D411yescharacteristic
291C2×C4×D43C2×D411yescharacteristic
292C2×C4×D43C2×D411yescharacteristic
293C2×C4×D43C2411yescharacteristic
294C2×C4×D43C2411yescharacteristic
295C2×Dic86—22no—
296C2×Dic86—22no—
297C2×Dic86—21no—
298C2×Dic86—21no—
299C2×Dic86—21no—
300C2×Dic86—22no—
301C2×Dic86—22no—
302C2×Dic86C2412yes—
303M16×C43—24no—
304C2×C8×C43C2414yes—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—22no—
307C4⋊C4×C43—22no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43—21no—
310C4⋊C4×C43C2412yes—
311C4⋊C4×C43C2412yes—
312C4⋊C4×C43C2412yes—
313C22⋊C4×C43—22no—
314C22⋊C4×C43—22no—
315C22⋊C4×C43—22no—
316C42×C43—22no—
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C42×C43C2411yescharacteristic
320C42×C43C2411yescharacteristic
321C22⋊Dic43—22no—
322C22⋊Dic43—22no—
323C22⋊Dic43—22no—
324C22⋊Dic43—22no—
325C22⋊Dic43—22no—
326C22⋊Dic43—22no—
327C22⋊Dic43—22no—
328(C2×D43)⋊C4—22no—
329(C2×D43)⋊C4—22no—
330(C2×D43)⋊C4—22no—
331(C2×D43)⋊C4—22no—
332C4⋊Dic43—21no—
333C4⋊Dic43—21no—
334C4⋊Dic43—21no—
335C4⋊Dic43—22no—
336C4⋊Dic43—22no—
337C4⋊Dic43—22no—
338C4⋊Dic43—22no—
339C4⋊Dic43—22no—
340C4⋊Dic43—22no—
341C4⋊Dic43C2412yes—
342C4⋊Dic43C2412yes—
343C4⋊Dic43C2412yes—
344Dic43⋊C4—22no—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351Dic43⋊C4—22no—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355Dic43⋊C4—22no—
356C4×Dic43—22no—
357C4×Dic43—22no—
358C4×Dic43—22no—
359C4×Dic43—22no—
360C4×Dic43—22no—
361C4×Dic43C2×D411yescharacteristic
362C4×Dic43C2×D411yescharacteristic
363C4×Dic43C2×D411yescharacteristic
364C4×Dic43C2×D411yescharacteristic
365C4×Dic43C2×D411yescharacteristic
366C4×Dic43C2×D411yescharacteristic
367C4×Dic43C2×D411yescharacteristic
368C4×Dic43C2×D411yescharacteristic
369C4×Dic43C2×D411yescharacteristic
370C4×Dic43C2×D411yescharacteristic
371C4×Dic43C2411yescharacteristic
372C4×Dic43C2411yescharacteristic
373#10621877—24no—
374C2×C43⋊C8C2414yes—
375C23×C43—22no—
376C23×C43—42no—
377C23×C43—42no—
378C23×C43—42no—
379C23×C43C22×D411yescharacteristic
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—41no—
383C22×D43C22×D411yescharacteristic
384C22×D43C22×D411yescharacteristic
385Q8×C43—42no—
386Q8×C43—42no—
387D4×C43—22no—
388D4×C43—22no—
389D4×C43—42no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—41no—
395C2×C4×C43—44no—
396C2×C4×C43—42no—
397C2×C4×C43—44no—
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C43C22×D411yescharacteristic
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C2×C4×C432−1+412yes—
404C2×C4×C432−1+412yes—
405C2×C4×C43C2511yescharacteristic
406C22⋊D43—44no—
407C22⋊D43—44no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—42no—
416C2×Dic43—42no—
417C2×Dic43C22×D411yescharacteristic
418C2×Dic43C22×D411yescharacteristic
419C2×Dic43C22×D411yescharacteristic
420C2×Dic43C22×D411yescharacteristic
421C2×Dic43C22×D411yescharacteristic
422C2×Dic43C22×D411yescharacteristic
423C4×D43—22no—
424C4×D43—22no—
425C4×D43—22no—
426C4×D43—22no—
427C4×D43—22no—
428C4×D43—22no—
429C4×D43—21no—
430C4×D43—21no—
431C4×D43—21no—
432C4×D43—21no—
433C4×D43—41no—
434C4×D43—41no—
435C4×D43—41no—
436C4×D43—41no—
437C4×D43—44no—
438C4×D43—44no—
439Dic86—22no—
440Dic86—22no—
441Dic86—44no—
442Dic86—44no—
443Dic86—42no—
444Dic86—42no—
445Dic86—42no—
446C8×C43—24no—
447C43⋊C8—24no—
448#60866—431nomaximal, Sylow
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43—84no—
455C22×C43#53612yes—
456C22×C43C23×D411yescharacteristic
457C2×D43—21no—
458C2×D43—21no—
459C2×D43—21no—
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—44no—
463C2×D43#57512yes—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—42no—
468C4×C43—42no—
469C4×C43—42no—
470C4×C43#53612yes—
471C4×C43#57512yes—
472C4×C43C2×2−1+411yescharacteristic
473C4×C43C2×2−1+411yescharacteristic
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—21no—
479Dic43—21no—
480Dic43—42no—
481Dic43—42no—
482Dic43—42no—
483Dic43—42no—
484C2×#533—431no—
485C2×#529—431no—
486#3240—434no—
487#3239—432no—
488#3238—432no—
489#3233—432no—
490#3233—432no—
491#3232—434no—
492#3166—432no—
493#3140—432no—
494#3095—432no—
495#3094—432no—
496#3078—431no—
497#3078—431no—
498#3077—431no—
499#3077D4311yescharacteristic, complemented
500#2920—431no—
501C2×C43—22no—
502C2×C43—82no—
503C2×C43C2×#53611yescharacteristic
504C2×C43C2×#57511yescharacteristic
505C2×C43C2×#57511yescharacteristic
506D43—22no—
507D43—41no—
508#533—431no—
509#533—431no—
510#533—432no—
511#533—432no—
512#533—431no—
513#533—861no—
514#533—861no—
515#533—861no—
516#533—861no—
517#533C2×D4311yescharacteristic
518C2×C4⋊Q8—431no—
519C2×C4⋊Q8—431no—
520#529—432no—
521#529—432no—
522#529—432no—
523#529—432no—
524#529—861no—
525#529—861no—
526#529—861no—
527#529—861no—
528C2×#126—861no—
529C2×#125—432no—
530C2×#125—431no—
531C2×#124—431no—
532C2×#123—861no—
533C2×C22⋊Q8—431no—
534C2×C22⋊Q8—861no—
535C2×C22⋊Q8—861no—
536C2×#121—431no—
537C2×C4×Q8—431no—
538C2×C4×Q8—861no—
539C2×C4×Q8—861no—
540C2×C4×D4—861no—
541C2×C4×D4C2×D4311yescharacteristic
542C2×#117—432no—
543C2×#117—861no—
544C22×C42—431no—
545#501—434no—
546#501—434no—
547#499—434no—
548#499—434no—
549#489—434no—
550#489—434no—
551#488—434no—
552#488—434no—
553#485—434no—
554#485—434no—
555#484—434no—
556#483—434no—
557#482—434no—
558#482—434no—
559#481—434no—
560#480—434no—
561#479—434no—
562#479—434no—
563#478—434no—
564#478C2×D4314yescomplemented
565#477—432no—
566#477—432no—
567#476—432no—
568#476C2×D4312yescomplemented
569#475—432no—
570#475—432no—
571#474—432no—
572#474C2×D4312yescomplemented
573#432—432no—
574#432—432no—
575#431—432no—
576#431—432no—
577#428—432no—
578#428—432no—
579#428—432no—
580#428C2×D4312yes—
581#423—431no—
582#423C2×D4311yescharacteristic
583#419—432no—
584#419—432no—
585#418—432no—
586#418C2×D4312yes—
587#407—432no—
588C4×M16—432no—
589C43#6086611yescharacteristic, complemented, Sylow
590C22×Q8—431no—
591C22×Q8—861no—
592C22×Q8—861no—
593C22×D4—861no—
594C22×D4C22×D4311yescharacteristic
595C23×C4—21no—
596C23×C4—431no—
597C23×C4—431no—
598C23×C4—431no—
599C2×M16—432no—
600C2×M16C22×D4312yes—
601C4⋊Q8—432no—
602C4⋊Q8—432no—
603C4⋊Q8—431no—
604C4⋊Q8—431no—
605C4⋊Q8—861no—
606C4⋊Q8—861no—
607C4⋊Q8—861no—
608C4⋊Q8—861no—
609C4⋊Q8C22×D4311yescharacteristic
610C4⋊Q8C22×D4311yescharacteristic
611#126—862no—
612#126—862no—
613#126—862no—
614#126—862no—
615#125—432no—
616#125—432no—
617#125—432no—
618#125—432no—
619#125—432no—
620#125—861no—
621#125—861no—
622#125—862no—
623#125—862no—
624#125C22×D4312yes—
625#124—432no—
626#124—432no—
627#124—861no—
628#124—861no—
629#123—862no—
630#123—862no—
631#123—862no—
632#123—862no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8—432no—
636C22⋊Q8—432no—
637C22⋊Q8—862no—
638C22⋊Q8—862no—
639C22⋊Q8—861no—
640C22⋊Q8—861no—
641C22⋊Q8—862no—
642C22⋊Q8—862no—
643C22⋊Q8—861no—
644C22⋊Q8—861no—
645C22⋊Q8—861no—
646C22⋊Q8—861no—
647C22⋊Q8—861no—
648C22⋊Q8—861no—
649#121—432no—
650#121—432no—
651#121—861no—
652#121—861no—
653C4×Q8—21no—
654C4×Q8—21no—
655C4×Q8—432no—
656C4×Q8—432no—
657C4×Q8—862no—
658C4×Q8—862no—
659C4×Q8—862no—
660C4×Q8—861no—
661C4×Q8—862no—
662C4×Q8—861no—
663C4×Q8—861no—
664C4×Q8—861no—
665C4×Q8—861no—
666C4×Q8—861no—
667C4×Q8—861no—
668C4×Q8—861no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—862no—
672C4×D4—862no—
673C4×D4—862no—
674C4×D4—862no—
675C4×D4C22×D4312yes—
676C4×D4C22×D4312yes—
677#117—432no—
678#117—432no—
679#117—432no—
680#117—862no—
681#117—862no—
682#117—862no—
683#117—862no—
684#117—862no—
685#117—862no—
686#117C22×D4312yes—
687C2×C4⋊C4—431no—
688C2×C4⋊C4—432no—
689C2×C4⋊C4—432no—
690C2×C4⋊C4—862no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—861no—
693C2×C4⋊C4—861no—
694C2×C4⋊C4—861no—
695C2×C4⋊C4—861no—
696C2×C4⋊C4—861no—
697C2×C4⋊C4—861no—
698C2×C4⋊C4C22×D4311yescharacteristic
699C2×C22⋊C4—21no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—861no—
702C2×C22⋊C4—861no—
703C2×C22⋊C4—861no—
704C2×C22⋊C4—861no—
705C2×C42—431no—
706C2×C42—431no—
707C2×C42—431no—
708C2×C42—431no—
709C2×C42—431no—
710C2×C42—431no—
711C2×C42—431no—
712C2×C42—431no—
713C2×C42—431no—
714C2×C42—431no—
715C2×C42—431no—
716C2×C42—862no—
717C2×C42—861no—
718C2×C42C22×D4311yescharacteristic
719#107—434no—
720#107—434no—
721#107—434no—
722#107C22×D4314yes—
723#106—434no—
724#106—434no—
725#106—434no—
726#106C22×D4314yes—
727C4⋊C8—432no—
728C4⋊C8—432no—
729C4⋊C8C22×D4312yes—
730C4⋊C8C22×D4312yes—
731#103—434no—
732#103—434no—
733#103—434no—
734#103—434no—
735#102—434no—
736#102—434no—
737#102C22×D4314yes—
738#102C22×D4314yes—
739C22⋊C8—434no—
740C22⋊C8—434no—
741#97—434no—
742C4×C8—434no—
743C24—21no—
744C24—431no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—432no—
748C2×Q8—862no—
749C2×Q8—862no—
750C2×Q8—861no—
751C2×Q8—861no—
752C2×Q8—861no—
753C2×Q8—862no—
754C2×Q8—862no—
755C2×Q8—1724no—
756C2×Q8—1724no—
757C2×D4—21no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—862no—
761C2×D4—862no—
762C2×D4—1724no—
763C2×D4C23×D4312yes—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—44no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—431no—
776C22×C4—431no—
777C22×C4—431no—
778C22×C4—431no—
779C22×C4—431no—
780C22×C4—431no—
781C22×C4—431no—
782C22×C4—431no—
783C22×C4—862no—
784C22×C4—862no—
785C22×C4—862no—
786C22×C4—862no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—1722no—
790C22×C4—1722no—
791C22×C4D4×D4311yescharacteristic
792C22×C4D4×D4311yescharacteristic
793C22×C4C23×D4311yescharacteristic
794M16—24no—
795M16—864no—
796C2×C8—434no—
797C2×C8C23×D4314yes—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—432no—
804C4⋊C4—432no—
805C4⋊C4—432no—
806C4⋊C4—862no—
807C4⋊C4—862no—
808C4⋊C4—862no—
809C4⋊C4—862no—
810C4⋊C4—862no—
811C4⋊C4—862no—
812C4⋊C4—862no—
813C4⋊C4—862no—
814C4⋊C4—862no—
815C4⋊C4—862no—
816C4⋊C4—862no—
817C4⋊C4—862no—
818C4⋊C4—862no—
819C4⋊C4—862no—
820C4⋊C4—861no—
821C4⋊C4—862no—
822C4⋊C4—862no—
823C4⋊C4—862no—
824C4⋊C4—862no—
825C4⋊C4—861no—
826C4⋊C4—861no—
827C4⋊C4C23×D4312yes—
828C4⋊C4C23×D4312yes—
829C4⋊C4C23×D4312yes—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—862no—
834C22⋊C4—862no—
835C22⋊C4—862no—
836C22⋊C4—862no—
837C22⋊C4—862no—
838C22⋊C4—862no—
839C22⋊C4—862no—
840C22⋊C4—862no—
841C22⋊C4—862no—
842C22⋊C4—862no—
843C22⋊C4—862no—
844C42—22no—
845C42—431no—
846C42—431no—
847C42—431no—
848C42—431no—
849C42—431no—
850C42—431no—
851C42—431no—
852C42—431no—
853C42—431no—
854C42—431no—
855C42—431no—
856C42—431no—
857C42—862no—
858C42—862no—
859C42—862no—
860C42—862no—
861C42—862no—
862C42D4×D4311yescharacteristic
863C42D4×D4311yescharacteristic
864C42C23×D4311yescharacteristic
865C42C23×D4311yescharacteristic
866C23—22no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—431no—
871C23—431no—
872C23—862no—
873C23—862no—
874C23—1721no—
875C23C2×D4×D4311yescharacteristic
876Q8—42no—
877Q8—42no—
878Q8—862no—
879Q8—862no—
880Q8—1722no—
881Q8—1724no—
882Q8—1724no—
883Q8—1722no—
884Q8—1722no—
885D4—22no—
886D4—22no—
887D4—42no—
888D4—1724no—
889D4—1724no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—41no—
895C2×C4—44no—
896C2×C4—42no—
897C2×C4—44no—
898C2×C4—431no—
899C2×C4—431no—
900C2×C4—431no—
901C2×C4—431no—
902C2×C4—431no—
903C2×C4—431no—
904C2×C4—862no—
905C2×C4—862no—
906C2×C4—862no—
907C2×C4—862no—
908C2×C4—862no—
909C2×C4—862no—
910C2×C4—862no—
911C2×C4—861no—
912C2×C4—861no—
913C2×C4—861no—
914C2×C4—861no—
915C2×C4—862no—
916C2×C4—862no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1724no—
924C2×C4—1724no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1722no—
928C2×C4—1722no—
929C2×C4C2×D4×D4311yescharacteristic
930C2×C4C2×D4×D4311yescharacteristic
931C2×C4C2×D4×D4311yescharacteristic
932C2×C4C2×D4×D4311yescharacteristic
933C2×C4C2×D4×D4311yescharacteristic
934C2×C4#1306337212yes—
935C2×C4#1306337312yes—
936C2×C4C24×D4311yescharacteristic
937C8—24no—
938C8—864no—
939C22—21no—
940C22—21no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—84no—
945C22—432no—
946C22—861no—
947C22—861no—
948C22—861no—
949C22—861no—
950C22—861no—
951C22—1724no—
952C22#1458347212yes—
953C22C22×D4×D4311yescharacteristic
954C4—21no—
955C4—21no—
956C4—21no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—861no—
961C4—861no—
962C4—861no—
963C4—861no—
964C4—861no—
965C4—861no—
966C4—1722no—
967C4—1722no—
968C4—1722no—
969C4—1722no—
970C4#1458347212yes—
971C4#1458369512yes—
972C4C2×#1306337211yescharacteristic
973C4C2×#1306337311yescharacteristic
974C2—22no—
975C2—82no—
976C2—862no—
977C2—1721no—
978C2C2×#1458347211yescharacteristic
979C2#575×D4311yescharacteristic
980C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3077C2
socleC22×C43C23×D4
prime radicalC2×#13063296C22
hypercenter#3077D43
hypocenterC43#60866
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145834C2semidirect
4. #19145824C2semidirect
5. #19145815C2semidirect
6. #19145773C2semidirect
7. #19145772C2semidirect
8. #19145761C2semidirect
9. #19145145C2semidirect
10. #19144979C2semidirect
11. #19144545C2semidirect
13. #19144402C2semidirect
14. #19144396C2semidirect
15. #19144392C2semidirect
16. #19143227C2semidirect
17. C43×#3077C2semidirect
19. #14583455C22semidirect
20. #14583454C22semidirect
21. #14583454C22semidirect
27. C4⋊Q8×D43C22semidirect
28. C4⋊Q8×D43C22semidirect
39. #125×D43C22semidirect
53. #14583307C22semidirect
54. #14583306C22semidirect
55. #14583300C22semidirect
56. #14583299C22semidirect
57. #14583257C22semidirect
58. #14583257C22semidirect
59. #14583252C22semidirect
60. #14583252C22semidirect
61. #14583243C22semidirect
62. #14583242C22semidirect
63. #14583236C22semidirect
64. #14583231C22semidirect
69. #14583207C22semidirect
70. #14583203C22semidirect
71. #14583199C22semidirect
72. #14583195C22semidirect
73. #14583191C22semidirect
74. #14583189C22semidirect
75. #14583185C22semidirect
76. #14583181C22semidirect
77. #14583179C22semidirect
78. #14582955C22semidirect
79. #14582955C22semidirect
80. #14582951C22semidirect
81. #14582951C22semidirect
93. C43×#478C22semidirect
94. C43×#476C22semidirect
95. C43×#474C22semidirect
499. #3077D43semidirect
564. #478C2×D43semidirect
568. #476C2×D43semidirect
572. #474C2×D43semidirect
589. C43#60866semidirect

Maximal subgroups

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

subgroupindex
#533×D432
C2×#145834312
#191458342
#191458242
#191458152
#191457732
#191457722
#191457612
#191451452
#191449792
#191445452
#191445332
#191444022
#191443962
#191443922
#191432272
C43×#30772
#6086643