Finite Group Databasebeta

← #25064592

Subgroups — #25064592

Order 11008.

964 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#19148567C211yesmaximal, characteristic
2#19143604C211yesmaximal, characteristic, complemented
3#19143024C211yesmaximal, characteristic, complemented
4#19133216C211yesmaximal, characteristic, complemented
5#19133214C211yesmaximal, characteristic, complemented
6#19133208C211yesmaximal, characteristic, complemented
7#19133201C211yesmaximal, characteristic, complemented
8#19133195C211yesmaximal, characteristic, complemented
9#19133188C211yesmaximal, characteristic, complemented
10#19133184C211yesmaximal, characteristic, complemented
11#19133182C211yesmaximal, characteristic, complemented
12#19133182C211yesmaximal, characteristic, complemented
13C2×#14582641C211yesmaximal, characteristic, complemented
14#330×D43C211yesmaximal, characteristic, complemented
15C43×#1528C211yesmaximal, characteristic, complemented
16C2×#13063333—21no—
17#14583626C411yescharacteristic
18#14583605C411yescharacteristic
19#14583604C411yescharacteristic
20#14583602C411yescharacteristic
21#14583597C411yescharacteristic
22#14583587C411yescharacteristic
23#14583584—21no—
24#14583584C411yescharacteristic
25#14583581—21no—
26#14583581—21no—
27#14583550—21no—
28#14583550C411yescharacteristic
29#14583508—21no—
30#14583497—21no—
31#14583496—21no—
32#14583455C2211yescharacteristic
33#14583434C2211yescharacteristic
34#14583434C2211yescharacteristic
35#14583433C2211yescharacteristic
36#125×D43C2211yescharacteristic
37#14583380—21no—
38C4×#10621898C2211yescharacteristic
39#14583028—21no—
40#14582969—21no—
41#14582967—21no—
42(C22⋊D43)⋊C8—21no—
43#14582954C2211yescharacteristic
44#14582954C2211yescharacteristic
45#14582857—21no—
46#14582853—21no—
47#14582853—21no—
48#14582851C2211yescharacteristic
49#14582851C2211yescharacteristic
50#14582851C2211yescharacteristic
51C2×#13063236C2211yescharacteristic
52C2×#13063236C2211yescharacteristic
53#97×D43C2211yescharacteristic
54#97×D43C2211yescharacteristic
55#97×D43C2211yescharacteristic
56#14582641C2211yescharacteristic
57#14582641C2211yescharacteristic
58#14582641C2211yescharacteristic
59#14582641C2211yescharacteristic
60#14582640C2211yescharacteristic
61#14582640C2211yescharacteristic
62#14582640C2211yescharacteristic
63#14582640C2211yescharacteristic
64#14582638C2211yescharacteristic
65#14582638C2211yescharacteristic
66#14582638C2211yescharacteristic
67#14582638C2211yescharacteristic
68C2×#125×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C4×M16×C43C2211yescharacteristic
71C43×#330C2211yescharacteristic
72C43×#330C2211yescharacteristic
73C43×#330C2211yescharacteristic
74C43×#330C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898D411yescharacteristic
77#13063333—28no—
78C2×#10621872—21no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C22×C43⋊C8—21no—
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86#13063324—21no—
87#13063324C2×C411yescharacteristic
88#13063324C2×C411yescharacteristic
89#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063320—21no—
94#13063320—21no—
95#13063319—21no—
96#13063317C2311yescharacteristic
97#13063316—21no—
98#13063316C2×C411yescharacteristic
99#13063316C2×C411yescharacteristic
100#13063315—21no—
101#13063315—21no—
102#13063315—21no—
103#13063315—21no—
104#13063315—21no—
105#13063315—21no—
106#13063313C2311yescharacteristic
107#13063310—21no—
108#13063310—21no—
109#13063310—21no—
110#13063310—21no—
111#13063310—21no—
112#13063310—21no—
113#13063308—21no—
114#13063308—21no—
115#13063308—21no—
116#13063305—21no—
117#13063305C2×C411yescharacteristic
118#13063305C2×C411yescharacteristic
119#13063304—21no—
120#13063304C2×C411yescharacteristic
121#13063303—21no—
122#13063303—21no—
123#13063303—21no—
124#13063303—21no—
125#13063303—21no—
126#13063303—21no—
127#13063300—21no—
128#13063300C2×C411yescharacteristic
129#13063300C2×C411yescharacteristic
130#13063299—21no—
131#13063299C2×C411yescharacteristic
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86D411yescharacteristic
135#13063290—21no—
136#13063290—21no—
137#13063290—21no—
138#13063290C2×C411yescharacteristic
139#13063290C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141C4×D172C2×C411yescharacteristic
142C4×D172D411yescharacteristic
143#13063287—21no—
144#13063287—21no—
145#13063287—21no—
146#13063287C2×C411yescharacteristic
147#13063287C2×C411yescharacteristic
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43C2×C411yescharacteristic
152C4×C22⋊D43C2×C411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155#13063284—21no—
156#13063284D411yescharacteristic
157#13063283—21no—
158#13063283—21no—
159#13063283—21no—
160#13063283C2×C411yescharacteristic
161#13063283C2×C411yescharacteristic
162#13063282—21no—
163#13063282D411yescharacteristic
164#13063282D411yescharacteristic
165C4⋊C4×D43—21no—
166C4⋊C4×D43—21no—
167C4⋊C4×D43—21no—
168C4⋊C4×D43C2×C411yescharacteristic
169C4⋊C4×D43C2×C411yescharacteristic
170C42×D43C2311yescharacteristic
171C42×D43C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176#13063236—21no—
177#13063236—21no—
178#13063236C2311yescharacteristic
179#13063236C2311yescharacteristic
180#13063236C2311yescharacteristic
181#13063236C2311yescharacteristic
182#13063235—21no—
183#13063235—21no—
184#13063235—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C8×Dic43—21no—
188C2×M16×C43—21no—
189#125×C43—21no—
190#125×C43—21no—
191#125×C43C2×C411yescharacteristic
192#125×C43C2×C411yescharacteristic
193#125×C43C2311yescharacteristic
194#125×C43C2311yescharacteristic
195C2×C4⋊C4×C43—21no—
196C2×C4⋊C4×C43—21no—
197C2×C4⋊C4×C43C2×C411yescharacteristic
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206C4×C8×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C2×C22⋊D43—21no—
213C2×C22⋊D43C22⋊C411yescharacteristic
214C2×C22⋊D43C22⋊C411yescharacteristic
215#10621898—24no—
216#10621898—44no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172C22⋊C411yescharacteristic
220C2×D172C22×C411yescharacteristic
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43C22×C411yescharacteristic
227C2×C4×D43C22×C411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C22⋊C411yescharacteristic
235C2×Dic86C22×C411yescharacteristic
236M16×C43—24no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C22×C411yescharacteristic
252C4⋊C4×C43C22×C411yescharacteristic
253C4⋊C4×C43C22×C411yescharacteristic
254C4⋊C4×C43C22×C411yescharacteristic
255C42×C43C22×C411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C42×C43C2×D411yescharacteristic
258C42×C43C2411yescharacteristic
259C22⋊Dic43—21no—
260C22⋊Dic43C22⋊C411yescharacteristic
261C22⋊Dic43C22⋊C411yescharacteristic
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275(C2×D43)⋊C4C22⋊C411yescharacteristic
276(C2×D43)⋊C4C22⋊C411yescharacteristic
277(C2×D43)⋊C4C22⋊C411yescharacteristic
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43C22⋊C411yescharacteristic
283C4⋊Dic43C22⋊C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285C4⋊Dic43C22×C411yescharacteristic
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301Dic43⋊C4C22⋊C411yescharacteristic
302C4×Dic43—21no—
303C4×Dic43—21no—
304C4×Dic43—21no—
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43C22×C411yescharacteristic
308C4×Dic43C22×C411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313C2×C43⋊C8—24no—
314C2×C43⋊C8—21no—
315C2×C43⋊C8—21no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—21no—
318C2×C43⋊C8—42no—
319#10621872—24no—
320#10621872—24no—
321#10621872—42no—
322C8×D43—24no—
323C8×D43—24no—
324C8×D43—42no—
325C23×C43C2×C22⋊C411yescharacteristic
326C22×D43—21no—
327C22×D43C2×C22⋊C411yescharacteristic
328C22×D43C2×C22⋊C411yescharacteristic
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—42no—
337C2×C4×C43—81no—
338C2×C4×C43C2×C22⋊C411yescharacteristic
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C22⋊D43—22no—
345C22⋊D43—42no—
346C22⋊D43#10414yes—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43C2×C22⋊C411yescharacteristic
355C2×Dic43C2×C22⋊C411yescharacteristic
356D172—22no—
357D172—41no—
358D172—42no—
359D172—81no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—41no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—81no—
369C4×D43—81no—
370C4×D43—81no—
371Dic86—22no—
372Dic86—42no—
373Dic86—41no—
374Dic86—81no—
375C8×C43—22no—
376C8×C43—22no—
377C8×C43—41no—
378C8×C43—41no—
379C43⋊C8—22no—
380C43⋊C8—22no—
381C43⋊C8—22no—
382C43⋊C8—41no—
383#17653—431nomaximal, Sylow
384C22×C43—21no—
385C22×C43—21no—
386C22×C43C2×#10412yes—
387C22×C43C22×C22⋊C411yescharacteristic
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—21no—
392C2×D43—21no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C2×D43C2×#10412yes—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—41no—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—41no—
413Dic43—41no—
414Dic43—41no—
415Dic43C2×#10412yes—
416#3515—431no—
417#2970—431no—
418#2875—431no—
419#1532—431no—
420#1532—431no—
421#1531—431no—
422#1529—431no—
423#1528—431no—
424#1528D4311yescharacteristic, complemented
425#1526—431no—
426#1524—431no—
427#1524—431no—
428#1524—431no—
429C2×#330—431no—
430C2×#330—431no—
431C2×C43—22no—
432C2×C43#288911yescharacteristic
433C2×C43C22×#10411yescharacteristic
434C2×C43#290111yescharacteristic
435D43—22no—
436D43—41no—
437D43—81no—
438C2×#131—861no—
439#557—431no—
440#554—431no—
441#554—431no—
442#553—431no—
443#553—431no—
444#552—431no—
445#552—431no—
446#552—861no—
447#552—861no—
448#552—861no—
449#547—431no—
450#547—861no—
451#541—861no—
452#539—861no—
453#539—861no—
454#533—431no—
455#529—431no—
456#529—431no—
457#529—431no—
458C2×#125—431no—
459C2×#125C2×D4311yescharacteristic
460#520—861no—
461C4×#41—431no—
462#446—861no—
463#435—861no—
464#435—861no—
465C8×D4—861no—
466#432—431no—
467#432—431no—
468#432C2×D4311yescharacteristic
469#405—861no—
470#405—861no—
471#405—861no—
472C4×M16—431no—
473C4×M16—431no—
474C4×M16—431no—
475C4×M16C2×D4311yescharacteristic
476C2×#97—431no—
477C2×#97—431no—
478C2×#97—431no—
479C2×#97—431no—
480C2×#97—431no—
481#330—431no—
482#330—431no—
483#330—431no—
484#330—431no—
485#330—431no—
486#330—431no—
487#330—431no—
488#330—431no—
489#330C2×D4311yescharacteristic
490#330C2×D4311yescharacteristic
491#330C2×D4311yescharacteristic
492#330C2×D4311yescharacteristic
493#329—431no—
494#329—431no—
495#329—431no—
496#329—431no—
497C43#1765311yescharacteristic, complemented, Sylow
498C2×#41—431no—
499C2×#41—861no—
500#131—868no—
501C2×M16—21no—
502C2×M16—861no—
503C2×M16—861no—
504C2×M16—861no—
505C22×C8—861no—
506C22×C8—861no—
507C22×C8—861no—
508C22×C8—861no—
509C22×C8—861no—
510C4⋊Q8—431no—
511C4⋊Q8—431no—
512C4⋊Q8—861no—
513#126—861no—
514#126—861no—
515#126—861no—
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#125—21no—
521#125—21no—
522#125—431no—
523#125—431no—
524#125—431no—
525#125—861no—
526#125—861no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125C4×D4311yescharacteristic
533#125C4×D4311yescharacteristic
534#125C22×D4311yescharacteristic
535#125C22×D4311yescharacteristic
536#124—431no—
537#123—861no—
538#123—861no—
539#123—861no—
540#123—861no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545#123—861no—
546C22⋊Q8—431no—
547C22⋊Q8—431no—
548C22⋊Q8—431no—
549C22⋊Q8—861no—
550C22⋊Q8—861no—
551C22⋊Q8—861no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557#121—431no—
558#121—431no—
559#121—431no—
560#121—861no—
561#121—861no—
562C4×Q8—431no—
563C4×Q8—431no—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8—861no—
570C4×D4—431no—
571C4×D4—431no—
572C4×D4—431no—
573C4×D4—431no—
574C4×D4—431no—
575C4×D4—431no—
576C4×D4—431no—
577C4×D4—431no—
578C4×D4—431no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585#117—431no—
586#117—431no—
587#117—431no—
588#117—431no—
589#117—431no—
590#117—861no—
591#117—861no—
592#117—861no—
593#117—861no—
594#117—861no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4C4×D4311yescharacteristic
603C2×C4⋊C4C4×D4311yescharacteristic
604C2×C42—431no—
605C2×C42—431no—
606C2×C42C22×D4311yescharacteristic
607C4⋊C8—21no—
608C4⋊C8—861no—
609C4⋊C8—861no—
610C22⋊C8—21no—
611C22⋊C8—861no—
612C22⋊C8—861no—
613#97—431no—
614#97—431no—
615#97—431no—
616#97—431no—
617#97—861no—
618#97—861no—
619#97—861no—
620#97—861no—
621#97—861no—
622#97C22×D4311yescharacteristic
623#97C22×D4311yescharacteristic
624#97C22×D4311yescharacteristic
625#97C22×D4311yescharacteristic
626C4×C8—21no—
627C4×C8—861no—
628C4×C8—861no—
629C4×C8—861no—
630#41—864no—
631#41—1724no—
632C2×Q8—431no—
633C2×Q8—431no—
634C2×Q8—861no—
635C2×Q8—861no—
636C2×D4—431no—
637C2×D4—431no—
638C2×D4—431no—
639C2×D4—431no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—431no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4C2×C4×D4311yescharacteristic
657C22×C4D4×D4311yescharacteristic
658C22×C4D4×D4311yescharacteristic
659M16—24no—
660M16—864no—
661M16—864no—
662M16—1722no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—864no—
668C2×C8—864no—
669C2×C8—864no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—1722no—
675C2×C8—1722no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—431no—
687C4⋊C4—431no—
688C4⋊C4—431no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—431no—
692C4⋊C4—431no—
693C4⋊C4—431no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4C2×C4×D4311yescharacteristic
711C4⋊C4C2×C4×D4311yescharacteristic
712C4⋊C4C2×C4×D4311yescharacteristic
713C4⋊C4C2×C4×D4311yescharacteristic
714C22⋊C4—431no—
715C22⋊C4—431no—
716C22⋊C4—431no—
717C22⋊C4—431no—
718C22⋊C4—431no—
719C22⋊C4—431no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C42—431no—
734C42—431no—
735C42—431no—
736C42—431no—
737C42—431no—
738C42—431no—
739C42—861no—
740C42—861no—
741C42—861no—
742C42—861no—
743C42—861no—
744C42C2×C4×D4311yescharacteristic
745C42D4×D4311yescharacteristic
746C42D4×D4311yescharacteristic
747C42C23×D4311yescharacteristic
748C23—431no—
749C23—431no—
750C23—861no—
751C23C22⋊C4×D4311yescharacteristic
752Q8—862no—
753Q8—3441no—
754Q8—1721no—
755Q8—1722no—
756D4—434no—
757D4—862no—
758D4—862no—
759D4—3441no—
760D4—1721no—
761D4—1722no—
762D4—1722no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—81no—
772C2×C4—431no—
773C2×C4—431no—
774C2×C4—431no—
775C2×C4—431no—
776C2×C4—431no—
777C2×C4—431no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—3441no—
784C2×C4—3441no—
785C2×C4—3441no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1722no—
791C2×C4—1722no—
792C2×C4C22⋊C4×D4311yescharacteristic
793C2×C4C22⋊C4×D4311yescharacteristic
794C2×C4C22⋊C4×D4311yescharacteristic
795C2×C4C22×C4×D4311yescharacteristic
796C2×C4C2×D4×D4311yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C8—22no—
799C8—22no—
800C8—41no—
801C8—41no—
802C8—862no—
803C8—862no—
804C8—862no—
805C8—1721no—
806C22—21no—
807C22—21no—
808C22—432no—
809C22—861no—
810C22—861no—
811C22—861no—
812C22—861no—
813C22—861no—
814C22—1721no—
815C22—1721no—
816C22—1721no—
817C22#104×D4312yes—
818C22C2×C22⋊C4×D4311yescharacteristic
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—432no—
830C4—861no—
831C4—861no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—1721no—
836C4—1721no—
837C4—1721no—
838C2—22no—
839C2—862no—
840C2—3441no—
841C2—1721no—
842C2#1914307511yescharacteristic
843C2C2×#104×D4311yescharacteristic
844C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1528C2
socleC22×C43C22×C22⋊C4
prime radical#19148567C2
cosocleC42×C43C24
hypercenter#1528D43
hypocenterC43#17653
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
2. #19143604C2semidirect
3. #19143024C2semidirect
4. #19133216C2semidirect
5. #19133214C2semidirect
6. #19133208C2semidirect
7. #19133201C2semidirect
8. #19133195C2semidirect
9. #19133188C2semidirect
10. #19133184C2semidirect
11. #19133182C2semidirect
12. #19133182C2semidirect
13. C2×#14582641C2semidirect
14. #330×D43C2semidirect
15. C43×#1528C2semidirect
424. #1528D43semidirect
497. C43#17653semidirect

Maximal subgroups

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

subgroupindex
#191485672
#191436042
#191430242
#191332162
#191332142
#191332082
#191332012
#191331952
#191331882
#191331842
#191331822
C2×#145826412
#330×D432
C43×#15282
#1765343