Finite Group Databasebeta

← #25064752

Subgroups — #25064752

Order 11008.

878 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
1#19148575C211yesmaximal, characteristic
2#19143604C211yesmaximal, characteristic, complemented
3#19143241C211yesmaximal, characteristic, complemented
4#19133232C211yesmaximal, characteristic, complemented
5#19133223C211yesmaximal, characteristic, complemented
6#19133220C211yesmaximal, characteristic, complemented
7#19133215C211yesmaximal, characteristic, complemented
8#19133212C211yesmaximal, characteristic, complemented
9#19133211C211yesmaximal, characteristic, complemented
10#19133199C211yesmaximal, characteristic, complemented
11#19133195C211yesmaximal, characteristic, complemented
12#19133195C211yesmaximal, characteristic, complemented
13#19133180C211yesmaximal, characteristic, complemented
14#330×D43C211yesmaximal, characteristic, complemented
15C43×#1535C211yesmaximal, characteristic, complemented
16#14583628C411yescharacteristic
17#14583609C411yescharacteristic
18#14583606C411yescharacteristic
19#14583596C411yescharacteristic
20#14583596C411yescharacteristic
21#14583589—21no—
22#14583585—21no—
23#14583585—21no—
24#14583583C411yescharacteristic
25#14583583C411yescharacteristic
26#14583554—21no—
27#14583554C411yescharacteristic
28#14583511—21no—
29#14583492—21no—
30#14583492—21no—
31#14583456C2211yescharacteristic
32#14583428C2211yescharacteristic
33#14583428C2211yescharacteristic
34#125×D43C2211yescharacteristic
35#125×D43C2211yescharacteristic
36#14583379—21no—
37C4×#10621898C2211yescharacteristic
38#14583028—21no—
39#14582969—21no—
40#14582967—21no—
41(C22⋊D43)⋊C8—21no—
42#14582959—21no—
43#14582957—21no—
44#14582956C2211yescharacteristic
45#14582954C2211yescharacteristic
46#14582954C2211yescharacteristic
47#14582954C2211yescharacteristic
48#14582954C2211yescharacteristic
49#14582924—21no—
50#14582864—21no—
51#14582851C2211yescharacteristic
52#14582851C2211yescharacteristic
53C2×#13063236C2211yescharacteristic
54#97×D43C2211yescharacteristic
55#97×D43C2211yescharacteristic
56#14582641C2211yescharacteristic
57#14582641C2211yescharacteristic
58#14582640C2211yescharacteristic
59#14582640C2211yescharacteristic
60#14582640C2211yescharacteristic
61#14582640C2211yescharacteristic
62#14582640C2211yescharacteristic
63#14582640C2211yescharacteristic
64#14582640C2211yescharacteristic
65#14582640C2211yescharacteristic
66#14582639C2211yescharacteristic
67#14582639C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#432C2211yescharacteristic
71C43×#330C2211yescharacteristic
72C43×#330C2211yescharacteristic
73C43×#329C2211yescharacteristic
74C43×#329C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898D411yescharacteristic
77C2×#10621872—21no—
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82#13063325—21no—
83#13063325C2×C411yescharacteristic
84#13063325C2×C411yescharacteristic
85#13063318—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063317—21no—
92#13063317C2311yescharacteristic
93#13063317C2311yescharacteristic
94#13063316—21no—
95#13063316—21no—
96#13063316C2×C411yescharacteristic
97#13063316C2×C411yescharacteristic
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#13063307—21no—
107#13063307—21no—
108#13063307—21no—
109#13063307—21no—
110#13063307—21no—
111#13063307—21no—
112#13063306—21no—
113#13063306—21no—
114#13063304—21no—
115#13063304—21no—
116#13063304—21no—
117#13063304—21no—
118#13063303—21no—
119#13063303—21no—
120#13063302—21no—
121#13063302—21no—
122#13063301C2×C411yescharacteristic
123#13063301C2×C411yescharacteristic
124#13063296—21no—
125#13063296—21no—
126#13063296C2×C411yescharacteristic
127#13063296C2×C411yescharacteristic
128Q8×Dic43C2×C411yescharacteristic
129Q8×Dic43C2×C411yescharacteristic
130C4×Dic86—21no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86D411yescharacteristic
135C4×D172—21no—
136C4×D172C2×C411yescharacteristic
137C4×D172D411yescharacteristic
138D4×Dic43C2×C411yescharacteristic
139D4×Dic43C2×C411yescharacteristic
140C4×C22⋊D43C2×C411yescharacteristic
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143C4×C22⋊D43D411yescharacteristic
144(C22⋊D43)⋊C4—21no—
145(C22⋊D43)⋊C4—21no—
146(C22⋊D43)⋊C4—21no—
147(C22⋊D43)⋊C4—21no—
148#13063284C2×C411yescharacteristic
149#13063284C2×C411yescharacteristic
150#13063284D411yescharacteristic
151#13063283—21no—
152#13063283—21no—
153#13063282D411yescharacteristic
154#13063282D411yescharacteristic
155#13063281—21no—
156#13063281—21no—
157C2×C4⋊Dic43—21no—
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43—21no—
162C4⋊C4×D43C2×C411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic
164C4⋊C4×D43C2×C411yescharacteristic
165C4⋊C4×D43C2×C411yescharacteristic
166C42×D43C2311yescharacteristic
167C42×D43C2311yescharacteristic
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063236—21no—
179#13063236C2311yescharacteristic
180#13063236C2311yescharacteristic
181#13063236C2311yescharacteristic
182#13063236C2311yescharacteristic
183#13063235—21no—
184#13063235—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187#126×C43—21no—
188#125×C43C2311yescharacteristic
189#124×C43C2311yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192#121×C43C2×C411yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C2×C22⋊D43—21no—
214C2×C22⋊D43—21no—
215C2×C22⋊D43C22⋊C411yescharacteristic
216C2×C22⋊D43C22⋊C411yescharacteristic
217C22×Dic43—21no—
218C22×Dic43—21no—
219#10621898—42no—
220#10621898—44no—
221C2×D172C22⋊C411yescharacteristic
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×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43C22×C411yescharacteristic
244C4⋊C4×C43C22×C411yescharacteristic
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—21no—
250C42×C43—21no—
251C42×C43C22×C411yescharacteristic
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C42×C43C2411yescharacteristic
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43C22⋊C411yescharacteristic
262C22⋊Dic43C22⋊C411yescharacteristic
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4C22⋊C411yescharacteristic
266(C2×D43)⋊C4C22⋊C411yescharacteristic
267(C2×D43)⋊C4C22⋊C411yescharacteristic
268(C2×D43)⋊C4C22⋊C411yescharacteristic
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43C22⋊C411yescharacteristic
278C4⋊Dic43C22⋊C411yescharacteristic
279C4⋊Dic43C22×C411yescharacteristic
280C4⋊Dic43C22×C411yescharacteristic
281C4⋊Dic43C22×C411yescharacteristic
282C4⋊Dic43C22×C411yescharacteristic
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301C4×Dic43—21no—
302C4×Dic43—21no—
303C4×Dic43—21no—
304C4×Dic43—21no—
305C4×Dic43C22×C411yescharacteristic
306C4×Dic43C22×C411yescharacteristic
307C4×Dic43C2×D411yescharacteristic
308C4×Dic43C2×D411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C2×C43⋊C8—21no—
312C2×C43⋊C8—21no—
313C2×C43⋊C8—21no—
314C2×C43⋊C8—21no—
315C2×C43⋊C8—42no—
316#10621872—42no—
317#10621872—42no—
318C8×D43—42no—
319C8×D43—42no—
320C23×C43—21no—
321C23×C43C2×C22⋊C411yescharacteristic
322C22×D43C2×C22⋊C411yescharacteristic
323C22×D43C2×C22⋊C411yescharacteristic
324Q8×C43—41no—
325D4×C43—41no—
326D4×C43—81no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—42no—
334C2×C4×C43C2×C22⋊C411yescharacteristic
335C2×C4×C43C2×C22⋊C411yescharacteristic
336C2×C4×C43C2×C22⋊C411yescharacteristic
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C22⋊D43—22no—
341C22⋊D43—41no—
342C22⋊D43—42no—
343C22⋊D43—42no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—81no—
349C2×Dic43—81no—
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—
357C4×D43—22no—
358C4×D43—41no—
359C4×D43—41no—
360C4×D43—41no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—81no—
366C4×D43—81no—
367Dic86—41no—
368Dic86—42no—
369Dic86—81no—
370C8×C43—41no—
371C8×C43—41no—
372C8×C43—41no—
373C8×C43—41no—
374C43⋊C8—22no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378#17680—431nomaximal, Sylow
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43C22×C22⋊C411yescharacteristic
386C2×D43—21no—
387C2×D43—21no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—21no—
391C2×D43#42112yes—
392C4×C43—21no—
393C4×C43—21no—
394C4×C43—21no—
395C4×C43—21no—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43—41no—
401Dic43—21no—
402Dic43—21no—
403Dic43—21no—
404Dic43—21no—
405Dic43—21no—
406Dic43—21no—
407Dic43—41no—
408Dic43—41no—
409Dic43—41no—
410Dic43—41no—
411#3515—431no—
412#2970—431no—
413#2923—431no—
414#1537—431no—
415#1535—431no—
416#1535D4311yescharacteristic, complemented
417#1534—431no—
418#1532—431no—
419#1532—431no—
420#1531—431no—
421#1529—431no—
422#1528—431no—
423#1528—431no—
424#1524—431no—
425C2×#330—431no—
426C2×C43—41no—
427C2×C43—81no—
428C2×C43#288911yescharacteristic
429C2×C43C2×#42111yescharacteristic
430C2×C43#290111yescharacteristic
431D43—22no—
432D43—41no—
433#557—431no—
434#554—431no—
435#554—431no—
436#553—431no—
437#553—431no—
438#552—431no—
439#552—431no—
440#552—861no—
441#552—861no—
442#552—861no—
443#547—431no—
444#547—861no—
445#541—861no—
446#539—861no—
447#539—861no—
448#533—431no—
449#529—431no—
450#529—431no—
451#529C2×D4311yescharacteristic
452C2×#125—431no—
453C2×#125—431no—
454#520—861no—
455C4×#41—431no—
456#446—861no—
457#435—861no—
458#435—861no—
459C8×D4—861no—
460#433—861no—
461#433—861no—
462#432—431no—
463#432—431no—
464#432—431no—
465#432—431no—
466#432—431no—
467#432C2×D4311yescharacteristic
468#432C2×D4311yescharacteristic
469#424—861no—
470#408—861no—
471C4×M16—431no—
472C4×M16—431no—
473C2×#97—431no—
474C2×#97—431no—
475C2×#97—431no—
476#330—431no—
477#330—431no—
478#330—431no—
479#330—431no—
480#330—431no—
481#330—431no—
482#330—431no—
483#330—431no—
484#330—431no—
485#330—431no—
486#330C2×D4311yescharacteristic
487#330C2×D4311yescharacteristic
488#329—431no—
489#329—431no—
490#329C2×D4311yescharacteristic
491#329C2×D4311yescharacteristic
492C43#1768011yescharacteristic, complemented, Sylow
493C2×#41—431no—
494C2×#41—861no—
495C2×M16—861no—
496C2×M16—861no—
497C22×C8—861no—
498C22×C8—861no—
499C22×C8—861no—
500C4⋊Q8—431no—
501C4⋊Q8—431no—
502C4⋊Q8—861no—
503#126—21no—
504#126—861no—
505#126—861no—
506#126—861no—
507#126—861no—
508#126—861no—
509#126—861no—
510#125—431no—
511#125—431no—
512#125—431no—
513#125—431no—
514#125—431no—
515#125—431no—
516#125—861no—
517#125—861no—
518#125—861no—
519#125—861no—
520#125—861no—
521#125—861no—
522#125—861no—
523#125—861no—
524#125—861no—
525#125C22×D4311yescharacteristic
526#124C22×D4311yescharacteristic
527#123—21no—
528#123—861no—
529#123—861no—
530#123—861no—
531#123—861no—
532#123—861no—
533#123—861no—
534#123—861no—
535#123—861no—
536C22⋊Q8—431no—
537C22⋊Q8—431no—
538C22⋊Q8—861no—
539C22⋊Q8—861no—
540C22⋊Q8—861no—
541C22⋊Q8—861no—
542C22⋊Q8—861no—
543C22⋊Q8—861no—
544C22⋊Q8—861no—
545C22⋊Q8—861no—
546C22⋊Q8C4×D4311yescharacteristic
547#121—431no—
548#121—431no—
549#121—861no—
550#121—861no—
551#121C4×D4311yescharacteristic
552C4×Q8—431no—
553C4×Q8—431no—
554C4×Q8—431no—
555C4×Q8—431no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×Q8—861no—
559C4×Q8C4×D4311yescharacteristic
560C4×D4—21no—
561C4×D4—431no—
562C4×D4—431no—
563C4×D4—431no—
564C4×D4—431no—
565C4×D4—431no—
566C4×D4—431no—
567C4×D4—431no—
568C4×D4—431no—
569C4×D4—861no—
570C4×D4—861no—
571C4×D4—861no—
572C4×D4—861no—
573C4×D4—861no—
574C4×D4C4×D4311yescharacteristic
575#117—21no—
576#117—431no—
577#117—431no—
578#117—431no—
579#117—431no—
580#117—431no—
581#117—861no—
582#117—861no—
583#117—861no—
584#117—861no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C42—431no—
595C2×C42—431no—
596C2×C42C22×D4311yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—21no—
599C4⋊C8—861no—
600C4⋊C8—861no—
601C4⋊C8—861no—
602C4⋊C8—861no—
603C4⋊C8—861no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—861no—
607C22⋊C8—861no—
608C22⋊C8—861no—
609C22⋊C8—861no—
610C22⋊C8—861no—
611#97—431no—
612#97—431no—
613#97—431no—
614#97—431no—
615#97—861no—
616#97—861no—
617#97—861no—
618#97C22×D4311yescharacteristic
619#97C22×D4311yescharacteristic
620#97C22×D4311yescharacteristic
621#97C22×D4311yescharacteristic
622C4×C8—861no—
623C4×C8—861no—
624#41—1722no—
625#41—1724no—
626C2×Q8—431no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×Q8C2×C4×D4311yescharacteristic
630C2×D4—21no—
631C2×D4—431no—
632C2×D4—431no—
633C2×D4—431no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4C2×C4×D4311yescharacteristic
637C22×C4—21no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4C2×C4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653M16—1722no—
654M16—1722no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—1722no—
664C2×C8—1722no—
665C2×C8—1722no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—431no—
671C4⋊C4—431no—
672C4⋊C4—431no—
673C4⋊C4—431no—
674C4⋊C4—431no—
675C4⋊C4—431no—
676C4⋊C4—431no—
677C4⋊C4—431no—
678C4⋊C4—431no—
679C4⋊C4—431no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
703C4⋊C4C2×C4×D4311yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—431no—
710C22⋊C4—431no—
711C22⋊C4—431no—
712C22⋊C4—431no—
713C22⋊C4—431no—
714C22⋊C4—431no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C42—21no—
724C42—431no—
725C42—431no—
726C42—431no—
727C42—431no—
728C42—431no—
729C42—431no—
730C42—861no—
731C42—861no—
732C42—861no—
733C42—861no—
734C42C2×C4×D4311yescharacteristic
735C42D4×D4311yescharacteristic
736C42D4×D4311yescharacteristic
737C42C23×D4311yescharacteristic
738C23—21no—
739C23—431no—
740C23—431no—
741C23C22⋊C4×D4311yescharacteristic
742Q8—41no—
743Q8—3441no—
744Q8—1721no—
745Q8—1722no—
746D4—41no—
747D4—81no—
748D4—862no—
749D4—862no—
750D4—1721no—
751D4—1722no—
752D4—1722no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—431no—
761C2×C4—431no—
762C2×C4—431no—
763C2×C4—431no—
764C2×C4—431no—
765C2×C4—431no—
766C2×C4—862no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—3441no—
772C2×C4—3441no—
773C2×C4—3441no—
774C2×C4—3441no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4C22⋊C4×D4311yescharacteristic
783C2×C4C22⋊C4×D4311yescharacteristic
784C2×C4C22⋊C4×D4311yescharacteristic
785C2×C4C22×C4×D4311yescharacteristic
786C2×C4C2×D4×D4311yescharacteristic
787C2×C4C2×D4×D4311yescharacteristic
788C8—41no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—862no—
793C8—1721no—
794C8—1721no—
795C8—1721no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—432no—
803C22—861no—
804C22—861no—
805C22—861no—
806C22—861no—
807C22—861no—
808C22C2×C22⋊C4×D4311yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—861no—
819C4—861no—
820C4—861no—
821C4—861no—
822C4—861no—
823C4—861no—
824C4—1721no—
825C4—1721no—
826C4—1721no—
827C4—1721no—
828C2—41no—
829C2—81no—
830C2—862no—
831C2—1721no—
832C2#1914307611yescharacteristic
833C2#421×D4311yescharacteristic
834C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1535C2
socleC22×C43C22×C22⋊C4
prime radical#19148575C2
cosocleC42×C43C24
hypercenter#1535D43
hypocenterC43#17680
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1535

Complements

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

NH ≅ G/Ntype
2. #19143604C2semidirect
3. #19143241C2semidirect
4. #19133232C2semidirect
5. #19133223C2semidirect
6. #19133220C2semidirect
7. #19133215C2semidirect
8. #19133212C2semidirect
9. #19133211C2semidirect
10. #19133199C2semidirect
11. #19133195C2semidirect
12. #19133195C2semidirect
13. #19133180C2semidirect
14. #330×D43C2semidirect
15. C43×#1535C2semidirect
416. #1535D43semidirect
492. C43#17680semidirect

Maximal subgroups

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

subgroupindex
#191485752
#191436042
#191432412
#191332322
#191332232
#191332202
#191332152
#191332122
#191332112
#191331992
#191331952
#191331802
#330×D432
C43×#15352
#1768043