Finite Group Databasebeta

← #25062879

Subgroups — #25062879

Order 11008.

922 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583585C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19143682C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132961C211yesmaximal, characteristic, complemented
6#19132961C211yesmaximal, characteristic, complemented
7#19132949C211yesmaximal, characteristic, complemented
8#19132949C211yesmaximal, characteristic, complemented
9#19132934C211yesmaximal, characteristic
10#19132928C211yesmaximal, characteristic, complemented
11#19132927C211yesmaximal, characteristic, complemented
12#19132914C211yesmaximal, characteristic
13#19132908C211yesmaximal, characteristic, complemented
14#19132907C211yesmaximal, characteristic, complemented
15C43×#1473C211yesmaximal, characteristic, complemented
16#14583585—21no—
17#14583585—21no—
18#14583585—21no—
19#14583585—21no—
20#14583585—21no—
21#14583585—21no—
22#14583585—21no—
23#14583585—21no—
24C2×#13063318C2211yescharacteristic
25C2×#13063316C411yescharacteristic
26C2×#13063315C411yescharacteristic
27C2×#13063315C2211yescharacteristic
28C2×#13063307C411yescharacteristic
29C2×#13063307C411yescharacteristic
30C2×#13063303C411yescharacteristic
31C2×#13063302C411yescharacteristic
32C2×C4×Dic86C2211yescharacteristic
33C2×(C22⋊D43)⋊C4C2211yescharacteristic
34C2×#13063283C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36C2×#13063281C411yescharacteristic
37C2×C4⋊C4×D43C411yescharacteristic
38#14583029—21no—
39#14583028—21no—
40#14583028—21no—
41#14583027—21no—
42#14583027—21no—
43#14583026—21no—
44C8×Dic86—21no—
45#14583023—21no—
46#14582956C2211yescharacteristic
47#14582953C2211yescharacteristic
48#14582953C2211yescharacteristic
49#14582953C2211yescharacteristic
50#14582953C2211yescharacteristic
51#14582952C2211yescharacteristic
52#14582949C2211yescharacteristic
53#14582949C2211yescharacteristic
54#14582949C2211yescharacteristic
55#14582949C2211yescharacteristic
56#14582625C2211yescharacteristic
57#14582625C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582624C2211yescharacteristic
61#14582624C2211yescharacteristic
62#14582623C2211yescharacteristic
63#14582623C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×#126×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C22×Dic86C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C23×Dic43C2×C411yescharacteristic
78C22×C4×D43C2×C411yescharacteristic
79C22×C4×D43C2×C411yescharacteristic
80C22×C4×D43C2×C411yescharacteristic
81#13063318—21no—
82#13063318—21no—
83#13063318—21no—
84#13063318—21no—
85#13063316—21no—
86#13063316—21no—
87#13063316—21no—
88#13063316—21no—
89#13063315—21no—
90#13063315—21no—
91#13063315—21no—
92#13063315—21no—
93#13063315—21no—
94#13063315—21no—
95#13063315—21no—
96#13063315—21no—
97#13063307—21no—
98#13063307—21no—
99#13063307—21no—
100#13063307—21no—
101#13063307—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063303—21no—
106#13063303—21no—
107#13063303—21no—
108#13063303—21no—
109#13063302—21no—
110#13063302—21no—
111#13063302—21no—
112#13063302—21no—
113C4×Dic86D411yescharacteristic
114C4×Dic86D411yescharacteristic
115C4×Dic86D411yescharacteristic
116C4×Dic86D411yescharacteristic
117C4×Dic86D411yescharacteristic
118C4×Dic86D411yescharacteristic
119C4×Dic86D411yescharacteristic
120C4×Dic86D411yescharacteristic
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125#13063283—21no—
126#13063283—21no—
127#13063283—21no—
128#13063283—21no—
129#13063282—21no—
130#13063282—21no—
131#13063282—21no—
132#13063282—21no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136#13063281—21no—
137C2×C4⋊Dic43C2×C411yescharacteristic
138C2×C4⋊Dic43C2×C411yescharacteristic
139C2×C4⋊Dic43C2×C411yescharacteristic
140C2×C4⋊Dic43C2×C411yescharacteristic
141C2×Dic43⋊C4C2×C411yescharacteristic
142C2×Dic43⋊C4C2×C411yescharacteristic
143C2×Dic43⋊C4C2×C411yescharacteristic
144C2×Dic43⋊C4C2×C411yescharacteristic
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×Dic43⋊C4C2×C411yescharacteristic
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4C2311yescharacteristic
150C4⋊C4×D43—21no—
151C4⋊C4×D43—21no—
152C4⋊C4×D43—21no—
153C4⋊C4×D43—21no—
154C2×C22⋊Dic43C2×C411yescharacteristic
155C2×C22⋊Dic43C2×C411yescharacteristic
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2311yescharacteristic
159C2×C4×Dic43C2×C411yescharacteristic
160C2×C4×Dic43C2×C411yescharacteristic
161C2×C4×Dic43C2311yescharacteristic
162C2×C4×Dic43C2311yescharacteristic
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165Dic43⋊C8—21no—
166Dic43⋊C8—21no—
167Dic43⋊C8—21no—
168Dic43⋊C8—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)C2311yescharacteristic
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177#13063236—21no—
178#13063235—21no—
179#13063235—21no—
180#13063235—21no—
181#13063235—21no—
182C4×C43⋊C8—21no—
183C8×Dic43—21no—
184C8×Dic43—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187#126×C43—21no—
188#126×C43—21no—
189#126×C43—21no—
190#126×C43—21no—
191C2×C4⋊C4×C43C2×C411yescharacteristic
192C2×C4⋊C4×C43C2×C411yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2×C411yescharacteristic
195C2×C22⋊C4×C43C2×C411yescharacteristic
196C2×C22⋊C4×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205C4×C8×C43—21no—
206C24×C43C22×C411yescharacteristic
207C23×D43C22×C411yescharacteristic
208C22×C4×C43C22×C411yescharacteristic
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—22no—
217C2×C22⋊D43—41no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—42no—
221C22×Dic43C22×C411yescharacteristic
222C22×Dic43C22×C411yescharacteristic
223C22×Dic43C22×C411yescharacteristic
224C22×Dic43C22×C411yescharacteristic
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C411yescharacteristic
227C22×Dic43C22×C411yescharacteristic
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—41no—
237C2×C4×D43—41no—
238C2×C4×D43—42no—
239C2×Dic86—42no—
240C2×Dic86C22⋊C411yescharacteristic
241C2×Dic86C22⋊C411yescharacteristic
242C2×Dic86C22⋊C411yescharacteristic
243C2×Dic86C22⋊C411yescharacteristic
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2×D411yescharacteristic
263C42×C43C2×D411yescharacteristic
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267C22⋊Dic43—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—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43C22⋊C411yescharacteristic
281C4⋊Dic43C22⋊C411yescharacteristic
282C4⋊Dic43C22⋊C411yescharacteristic
283C4⋊Dic43C22⋊C411yescharacteristic
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⋊C4—21no—
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301Dic43⋊C4C22⋊C411yescharacteristic
302Dic43⋊C4C22⋊C411yescharacteristic
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313C4×Dic43C2×D411yescharacteristic
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—21no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43C23×C411yescharacteristic
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43#13112yes—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C2×C22⋊C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C22⋊D43—42no—
351C22⋊D43—42no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—22no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—41no—
363C2×Dic43—42no—
364C2×Dic43—42no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43C2×C22⋊C411yescharacteristic
368C2×Dic43C2×C22⋊C411yescharacteristic
369C2×Dic43C2×C22⋊C411yescharacteristic
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C4×D43—42no—
376C4×D43—42no—
377C4×D43—42no—
378C4×D43—42no—
379C4×D43—42no—
380C4×D43—42no—
381Dic86—22no—
382Dic86—22no—
383Dic86—41no—
384Dic86—41no—
385C8×C43—41no—
386C8×C43—41no—
387C8×C43—41no—
388C8×C43—41no—
389C43⋊C8—41no—
390C43⋊C8—41no—
391C43⋊C8—41no—
392C43⋊C8—41no—
393#17423—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43C22×C22⋊C411yescharacteristic
402C22×C43C2×#13111yescharacteristic
403C22×C43#56811yescharacteristic
404C2×D43—22no—
405C2×D43—42no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—42no—
409C4×C43—21no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—41no—
418Dic43—21no—
419Dic43—21no—
420Dic43—21no—
421Dic43—21no—
422Dic43—21no—
423Dic43—21no—
424Dic43—21no—
425Dic43—41no—
426Dic43—41no—
427Dic43—41no—
428Dic43#41312yes—
429C2×#552—431no—
430#2984—431no—
431#2984—431no—
432#1473—431no—
433#1473—431no—
434#1473—431no—
435#1473D4311yescharacteristic, complemented
436#1470—431no—
437#1470—431no—
438#1466—431no—
439#1464—431no—
440#1464—431no—
441#1460—431no—
442#1458—431no—
443#1458—431no—
444C2×C43—21no—
445C2×C43—21no—
446C2×C43—81no—
447C2×C43#288011yescharacteristic
448C2×C43#288411yescharacteristic
449C2×C43C2×#41311yescharacteristic
450D43—42no—
451#552—861no—
452#552—861no—
453#552—861no—
454#552—861no—
455#552—861no—
456#552—861no—
457#552—861no—
458#552—861no—
459C2×#126—431no—
460C2×#126C2×D4311yescharacteristic
461C2×#125—431no—
462C2×#125—431no—
463C2×#125—431no—
464C2×#123—431no—
465C2×#123—431no—
466C2×C22⋊Q8—431no—
467C2×C22⋊Q8—431no—
468C2×C4×Q8—431no—
469C2×C4×D4—431no—
470C2×#117—431no—
471C2×#117—431no—
472C2×#117—431no—
473C22×C4⋊C4—431no—
474#446—861no—
475#446—861no—
476#446—861no—
477#446—861no—
478#446—861no—
479#446—861no—
480C8×Q8—861no—
481C8×Q8—861no—
482#432—431no—
483#432—431no—
484#432—431no—
485#432—431no—
486#432—431no—
487#432C2×D4311yescharacteristic
488#431—431no—
489#431—431no—
490#431—431no—
491#431—431no—
492#431—431no—
493#431C2×D4311yescharacteristic
494#324—431no—
495#324—431no—
496#324—431no—
497#324—431no—
498#324—431no—
499#324—431no—
500#324C2×D4311yescharacteristic
501#324C2×D4311yescharacteristic
502#323—431no—
503#323—431no—
504#323—431no—
505#323—431no—
506#323—431no—
507#323—431no—
508#323C2×D4311yescharacteristic
509#323C2×D4311yescharacteristic
510C43#1742311yescharacteristic, complemented, Sylow
511C22×Q8—431no—
512C22×D4—431no—
513C23×C4—431no—
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—431no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—861no—
522#126—861no—
523#126—861no—
524#126—861no—
525#125—861no—
526#125—861no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#125—861no—
534#125—861no—
535#125—861no—
536#125—861no—
537#123—861no—
538#123—861no—
539#123—861no—
540#123—861no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545C22⋊Q8—861no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549C22⋊Q8—861no—
550C22⋊Q8—861no—
551C22⋊Q8—861no—
552C22⋊Q8—861no—
553C4×Q8—431no—
554C4×Q8—431no—
555C4×Q8—431no—
556C4×Q8—431no—
557C4×Q8—431no—
558C4×Q8—431no—
559C4×Q8—431no—
560C4×Q8—431no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4—861no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574#117—861no—
575#117—861no—
576#117—861no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—431no—
579C2×C4⋊C4—431no—
580C2×C4⋊C4—431no—
581C2×C4⋊C4—431no—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—431no—
586C2×C4⋊C4—431no—
587C2×C4⋊C4—431no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4C4×D4311yescharacteristic
595C2×C4⋊C4C4×D4311yescharacteristic
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C22⋊C4—431no—
598C2×C22⋊C4—431no—
599C2×C22⋊C4—431no—
600C2×C22⋊C4—431no—
601C2×C22⋊C4—431no—
602C2×C22⋊C4C4×D4311yescharacteristic
603C2×C22⋊C4C4×D4311yescharacteristic
604C2×C22⋊C4C22×D4311yescharacteristic
605C2×C42—431no—
606C2×C42—431no—
607C2×C42—431no—
608C2×C42—431no—
609C2×C42C22×D4311yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—861no—
613C4⋊C8—861no—
614C4⋊C8—861no—
615C4⋊C8—861no—
616C4⋊C8—861no—
617C4⋊C8—861no—
618C4⋊C8—861no—
619C4⋊C8—861no—
620C4⋊C8—861no—
621C4⋊C8—861no—
622C22⋊C8—431no—
623C22⋊C8—431no—
624C22⋊C8—431no—
625C22⋊C8—431no—
626C22⋊C8C22×D4311yescharacteristic
627C22⋊C8C22×D4311yescharacteristic
628C22⋊C8C22×D4311yescharacteristic
629C22⋊C8C22×D4311yescharacteristic
630#97—21no—
631#97—861no—
632#97—861no—
633#97—861no—
634#97—861no—
635#97—861no—
636C4×C8—21no—
637C4×C8—861no—
638C4×C8—861no—
639C4×C8—861no—
640C4×C8—861no—
641C4×C8—861no—
642C24—431no—
643C24C2×C4×D4311yescharacteristic
644C2×Q8—431no—
645C2×Q8—431no—
646C2×Q8—431no—
647C2×Q8—431no—
648C2×Q8—1722no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—862no—
652C2×D4—1721no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—1721no—
671C22×C4—1721no—
672C22×C4—1722no—
673C22×C4—1722no—
674C22×C4C2×C4×D4311yescharacteristic
675C22×C4C2×C4×D4311yescharacteristic
676C22×C4C2×C4×D4311yescharacteristic
677C22×C4C2×C4×D4311yescharacteristic
678C22×C4C2×C4×D4311yescharacteristic
679C22×C4C23×D4311yescharacteristic
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—431no—
695C4⋊C4—431no—
696C4⋊C4—431no—
697C4⋊C4—431no—
698C4⋊C4—431no—
699C4⋊C4—431no—
700C4⋊C4—431no—
701C4⋊C4—431no—
702C4⋊C4—431no—
703C4⋊C4—431no—
704C4⋊C4—431no—
705C4⋊C4—431no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—861no—
742C42—431no—
743C42—431no—
744C42—431no—
745C42—431no—
746C42—431no—
747C42—431no—
748C42—431no—
749C42—431no—
750C42—861no—
751C42—861no—
752C42—861no—
753C42—861no—
754C42D4×D4311yescharacteristic
755C42D4×D4311yescharacteristic
756C42D4×D4311yescharacteristic
757C42D4×D4311yescharacteristic
758C23—21no—
759C23—21no—
760C23—21no—
761C23—41no—
762C23—41no—
763C23—432no—
764C23—861no—
765C23—861no—
766C23—1721no—
767C23—1721no—
768C23C22×C4×D4311yescharacteristic
769Q8—862no—
770Q8—862no—
771Q8—1721no—
772Q8—1721no—
773D4—1722no—
774D4—1722no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—431no—
787C2×C4—431no—
788C2×C4—431no—
789C2×C4—431no—
790C2×C4—431no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—862no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—1722no—
805C2×C4—1722no—
806C2×C4—1722no—
807C2×C4—1722no—
808C2×C4—1722no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1721no—
812C2×C4—1722no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4C22⋊C4×D4311yescharacteristic
816C2×C4C22⋊C4×D4311yescharacteristic
817C2×C4C22⋊C4×D4311yescharacteristic
818C2×C4C22⋊C4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C2×D4×D4311yescharacteristic
821C8—41no—
822C8—41no—
823C8—41no—
824C8—41no—
825C8—1721no—
826C8—1721no—
827C8—1721no—
828C8—1721no—
829C22—21no—
830C22—21no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—81no—
835C22—81no—
836C22—862no—
837C22—1722no—
838C22—1722no—
839C22—1721no—
840C22—1721no—
841C22C2×C22⋊C4×D4311yescharacteristic
842C22#131×D4311yescharacteristic
843C22#1458366411yescharacteristic
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—432no—
854C4—861no—
855C4—861no—
856C4—861no—
857C4—861no—
858C4—861no—
859C4—861no—
860C4—861no—
861C4—1721no—
862C4—1721no—
863C4—1721no—
864C2—21no—
865C2—21no—
866C2—81no—
867C2—1722no—
868C2#1914304311yescharacteristic
869C2#1914305711yescharacteristic
870C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17423
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19143682C2semidirect
4. #19132964C2semidirect
5. #19132961C2semidirect
6. #19132961C2semidirect
7. #19132949C2semidirect
8. #19132949C2semidirect
10. #19132928C2semidirect
11. #19132927C2semidirect
13. #19132908C2semidirect
14. #19132907C2semidirect
15. C43×#1473C2semidirect
435. #1473D43semidirect
510. C43#17423semidirect

Maximal subgroups

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

subgroupindex
C2×#145835852
#191436852
#191436822
#191329642
#191329612
#191329492
#191329342
#191329282
#191329272
#191329142
#191329082
#191329072
C43×#14732
#1742343