Finite Group Databasebeta

← #25064845

Subgroups — #25064845

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148416C211yesmaximal, characteristic
2#19143606C211yesmaximal, characteristic
3#19143604C211yesmaximal, characteristic
4#19133231C211yesmaximal, characteristic, complemented
5#19133221C211yesmaximal, characteristic, complemented
6#19133220C211yesmaximal, characteristic, complemented
7#19133210C211yesmaximal, characteristic, complemented
8#19133208C211yesmaximal, characteristic, complemented
9#19133208C211yesmaximal, characteristic, complemented
10#19133195C211yesmaximal, characteristic, complemented
11#19133195C211yesmaximal, characteristic, complemented
12#19133188C211yesmaximal, characteristic, complemented
13C2×#14582640C211yesmaximal, characteristic, complemented
14#330×D43C211yesmaximal, characteristic, complemented
15C43×#1531C211yesmaximal, characteristic, complemented
16#14583627—21no—
17#14583627—21no—
18#14583609—21no—
19#14583609—21no—
20#14583603—21no—
21#14583603—21no—
22#14583603—21no—
23#14583603—21no—
24#14583527C411yescharacteristic
25#14583527C411yescharacteristic
26#14583526C411yescharacteristic
27#14583526C411yescharacteristic
28#14583526C411yescharacteristic
29#14583526C411yescharacteristic
30#14583455C2211yescharacteristic
31#14583455C2211yescharacteristic
32C2×#13063317C2211yescharacteristic
33#125×D43C2211yescharacteristic
34#125×D43C2211yescharacteristic
35#14583379C411yescharacteristic
36#14583379C411yescharacteristic
37C4×#10621898C2211yescharacteristic
38#14583028—21no—
39#14583027—21no—
40#14582972—21no—
41#14582970—21no—
42#14582969—21no—
43#14582967—21no—
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582956C2211yescharacteristic
47#14582954C2211yescharacteristic
48#14582954C2211yescharacteristic
49#14582954C2211yescharacteristic
50#14582954C2211yescharacteristic
51#14582851C2211yescharacteristic
52#14582851C2211yescharacteristic
53C2×#13063236C2211yescharacteristic
54#97×D43C2211yescharacteristic
55#97×D43C2211yescharacteristic
56#14582641C2211yescharacteristic
57#14582641C2211yescharacteristic
58#14582641C2211yescharacteristic
59#14582641C2211yescharacteristic
60#14582640C2211yescharacteristic
61#14582640C2211yescharacteristic
62#14582640C2211yescharacteristic
63#14582640C2211yescharacteristic
64#14582640C2211yescharacteristic
65#14582640C2211yescharacteristic
66#14582640C2211yescharacteristic
67#14582640C2211yescharacteristic
68C43×#533C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C2×#97×C43C2211yescharacteristic
71C43×#330C2211yescharacteristic
72C43×#330C2211yescharacteristic
73C43×#330C2211yescharacteristic
74C43×#330C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×#10621872—21no—
77C2×#10621872—21no—
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81#13063325—21no—
82#13063325—21no—
83#13063324C2×C411yescharacteristic
84#13063324C2×C411yescharacteristic
85#13063324C2×C411yescharacteristic
86#13063324C2×C411yescharacteristic
87#13063323—21no—
88#13063323—21no—
89#13063323—21no—
90#13063323—21no—
91#13063317—21no—
92#13063317—21no—
93#13063317—21no—
94#13063317—21no—
95#13063317C2×C411yescharacteristic
96#13063317C2×C411yescharacteristic
97#13063317C2311yescharacteristic
98#13063317C2311yescharacteristic
99#13063316C2×C411yescharacteristic
100#13063316C2×C411yescharacteristic
101#13063316C2×C411yescharacteristic
102#13063316C2×C411yescharacteristic
103#13063315—21no—
104#13063315—21no—
105#13063315—21no—
106#13063315—21no—
107#13063315—21no—
108#13063315—21no—
109#13063315—21no—
110#13063315—21no—
111#13063303—21no—
112#13063303—21no—
113#13063303—21no—
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063303—21no—
118#13063303—21no—
119#13063302—21no—
120#13063302—21no—
121#13063302—21no—
122#13063302—21no—
123#13063301—21no—
124#13063301—21no—
125#13063301—21no—
126#13063301—21no—
127C4×Dic86—21no—
128C4×Dic86—21no—
129C4×Dic86D411yescharacteristic
130C4×Dic86D411yescharacteristic
131#13063290—21no—
132#13063290—21no—
133#13063290—21no—
134#13063290—21no—
135C4×D172—21no—
136C4×D172—21no—
137C4×D172D411yescharacteristic
138C4×D172D411yescharacteristic
139C4×C22⋊D43D411yescharacteristic
140C4×C22⋊D43D411yescharacteristic
141C4×C22⋊D43D411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143(C22⋊D43)⋊C4—21no—
144(C22⋊D43)⋊C4—21no—
145(C22⋊D43)⋊C4—21no—
146(C22⋊D43)⋊C4—21no—
147#13063284C2×C411yescharacteristic
148#13063283C2×C411yescharacteristic
149#13063283C2×C411yescharacteristic
150#13063283C2×C411yescharacteristic
151#13063283C2×C411yescharacteristic
152#13063282C2×C411yescharacteristic
153#13063282C2×C411yescharacteristic
154C2×C4⋊Dic43C2×C411yescharacteristic
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—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—
187C22×C8×C43—21no—
188C4⋊Q8×C43C2×C411yescharacteristic
189C4⋊Q8×C43C2×C411yescharacteristic
190#125×C43C2311yescharacteristic
191#125×C43C2311yescharacteristic
192C22⋊Q8×C43—21no—
193C22⋊Q8×C43—21no—
194C4×Q8×C43—21no—
195C4×Q8×C43—21no—
196#117×C43C2×C411yescharacteristic
197#117×C43C2×C411yescharacteristic
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201#97×C43—21no—
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206C2×Q8×C43—21no—
207C2×Q8×C43—21no—
208C22×C4×C43C22×C411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C2×C22⋊D43C22⋊C411yescharacteristic
212C2×C22⋊D43C22⋊C411yescharacteristic
213C22×Dic43—21no—
214C22×Dic43—21no—
215#10621898—24no—
216C2×D172C22⋊C411yescharacteristic
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43C22×C411yescharacteristic
222C2×C4×D43C22×C411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86C22⋊C411yescharacteristic
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—42no—
237C4⋊C4×C43—21no—
238C4⋊C4×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
245C4⋊C4×C43C22×C411yescharacteristic
246C4⋊C4×C43C22×C411yescharacteristic
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C42×C43—21no—
250C42×C43—21no—
251C42×C43C22×C411yescharacteristic
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C42×C43C2411yescharacteristic
255C22⋊Dic43C22⋊C411yescharacteristic
256C22⋊Dic43C22⋊C411yescharacteristic
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4C22⋊C411yescharacteristic
262(C2×D43)⋊C4C22⋊C411yescharacteristic
263(C2×D43)⋊C4C22⋊C411yescharacteristic
264(C2×D43)⋊C4C22⋊C411yescharacteristic
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43C22⋊C411yescharacteristic
272C4⋊Dic43C22⋊C411yescharacteristic
273C4⋊Dic43C22×C411yescharacteristic
274C4⋊Dic43C22×C411yescharacteristic
275C4⋊Dic43C22×C411yescharacteristic
276C4⋊Dic43C22×C411yescharacteristic
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
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×C43C2×C22⋊C411yescharacteristic
321C22×D43C2×C22⋊C411yescharacteristic
322C22×D43C2×C22⋊C411yescharacteristic
323Q8×C43—81no—
324Q8×C43—81no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43C2×C22⋊C411yescharacteristic
333C2×C4×C43C2×C22⋊C411yescharacteristic
334C2×C4×C43C2×C22⋊C411yescharacteristic
335C2×C4×C43C23×C411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C22⋊D43—22no—
339C22⋊D43#10114yes—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—81no—
345C2×Dic43—81no—
346C2×Dic43C2×C22⋊C411yescharacteristic
347C2×Dic43C2×C22⋊C411yescharacteristic
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352D172—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—41no—
356C4×D43—41no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—81no—
360C4×D43—81no—
361C4×D43—81no—
362C4×D43—81no—
363Dic86—22no—
364Dic86—81no—
365Dic86—81no—
366Dic86—81no—
367Dic86—81no—
368C8×C43—22no—
369C8×C43—41no—
370C8×C43—41no—
371C8×C43—41no—
372C43⋊C8—22no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375C43⋊C8—41no—
376#17689—431nomaximal, Sylow
377C22×C43—21no—
378C22×C43—21no—
379C22×C43C2×#10112yes—
380C22×C43C22×C22⋊C411yescharacteristic
381C2×D43—21no—
382C2×D43—21no—
383C2×D43—21no—
384C2×D43—21no—
385C2×D43—21no—
386C2×D43C2×#10112yes—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—41no—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—41no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406Dic43C2×#10112yes—
407#3504—431no—
408#2970—431no—
409#2970—431no—
410#1537—431no—
411#1534—431no—
412#1534—431no—
413#1531—431no—
414#1531—431no—
415#1531—431no—
416#1531D4311yescharacteristic, complemented
417#1528—431no—
418#1528—431no—
419#1526—431no—
420C2×#330—431no—
421C2×#330—431no—
422C2×C43—22no—
423C2×C43C22×#10111yescharacteristic
424C2×C43#290111yescharacteristic
425C2×C43#290111yescharacteristic
426D43—22no—
427D43—41no—
428#557—861no—
429#557—861no—
430#554—861no—
431#554—861no—
432#554—861no—
433#554—861no—
434#554—861no—
435#554—861no—
436#544—431no—
437#544—431no—
438#544—431no—
439#544—431no—
440#544—431no—
441#544—431no—
442#533—431no—
443#533—431no—
444#533C2×D4311yescharacteristic
445C2×#125—431no—
446C2×#125—431no—
447C2×#125—431no—
448#520—431no—
449#520—431no—
450C4×#41—431no—
451#446—861no—
452#446—861no—
453#435—861no—
454#435—861no—
455#435—861no—
456#435—861no—
457C8×D4—861no—
458C8×D4—861no—
459#432—431no—
460#432—431no—
461#432—431no—
462#432—431no—
463#432—431no—
464#432C2×D4311yescharacteristic
465C4×M16—431no—
466C4×M16—431no—
467C2×#97—431no—
468C2×#97—431no—
469C2×#97—431no—
470C2×#97C2×D4311yescharacteristic
471#330—431no—
472#330—431no—
473#330—431no—
474#330—431no—
475#330—431no—
476#330—431no—
477#330—431no—
478#330—431no—
479#330—431no—
480#330—431no—
481#330—431no—
482#330—431no—
483#330C2×D4311yescharacteristic
484#330C2×D4311yescharacteristic
485#330C2×D4311yescharacteristic
486#330C2×D4311yescharacteristic
487C43#1768911yescharacteristic, complemented, Sylow
488C2×#41—431no—
489C2×M16—861no—
490C2×M16—861no—
491C22×C8—21no—
492C22×C8—861no—
493C22×C8—861no—
494C22×C8—861no—
495C4⋊Q8—431no—
496C4⋊Q8—431no—
497C4⋊Q8—431no—
498C4⋊Q8—431no—
499C4⋊Q8—861no—
500C4⋊Q8—861no—
501C4⋊Q8—861no—
502C4⋊Q8—861no—
503C4⋊Q8—861no—
504C4⋊Q8—861no—
505C4⋊Q8C4×D4311yescharacteristic
506C4⋊Q8C4×D4311yescharacteristic
507#125—431no—
508#125—431no—
509#125—431no—
510#125—431no—
511#125—431no—
512#125—431no—
513#125—431no—
514#125—431no—
515#125—861no—
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#125—861no—
526#125—861no—
527#125C22×D4311yescharacteristic
528#125C22×D4311yescharacteristic
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—861no—
532C22⋊Q8—861no—
533C22⋊Q8—861no—
534C22⋊Q8—861no—
535C22⋊Q8—861no—
536C22⋊Q8—861no—
537C22⋊Q8—861no—
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⋊Q8—861no—
547C4×Q8—21no—
548C4×Q8—21no—
549C4×Q8—431no—
550C4×Q8—431no—
551C4×Q8—861no—
552C4×Q8—861no—
553C4×Q8—861no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×D4—431no—
558C4×D4—431no—
559C4×D4—431no—
560C4×D4—431no—
561C4×D4—431no—
562C4×D4—431no—
563C4×D4—861no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569#117—431no—
570#117—431no—
571#117—431no—
572#117—431no—
573#117—431no—
574#117—431no—
575#117—431no—
576#117C4×D4311yescharacteristic
577#117C4×D4311yescharacteristic
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—861no—
585C2×C4⋊C4—861no—
586C2×C4⋊C4—861no—
587C2×C4⋊C4—861no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C42—431no—
591C2×C42—431no—
592C2×C42C22×D4311yescharacteristic
593C4⋊C8—21no—
594C4⋊C8—861no—
595C4⋊C8—861no—
596C4⋊C8—861no—
597C4⋊C8—861no—
598C4⋊C8—861no—
599C22⋊C8—21no—
600C22⋊C8—861no—
601C22⋊C8—861no—
602C22⋊C8—861no—
603C22⋊C8—861no—
604C22⋊C8—861no—
605#97—21no—
606#97—431no—
607#97—431no—
608#97—431no—
609#97—431no—
610#97—861no—
611#97—861no—
612#97—861no—
613#97C22×D4311yescharacteristic
614#97C22×D4311yescharacteristic
615#97C22×D4311yescharacteristic
616#97C22×D4311yescharacteristic
617C4×C8—861no—
618C4×C8—861no—
619#41—864no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—431no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8—861no—
627C2×D4—431no—
628C2×D4—431no—
629C2×D4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4C2×C4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645M16—1722no—
646M16—1722no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—42no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—1722no—
657C2×C8—1722no—
658C2×C8—1722no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—431no—
666C4⋊C4—431no—
667C4⋊C4—431no—
668C4⋊C4—431no—
669C4⋊C4—431no—
670C4⋊C4—431no—
671C4⋊C4—431no—
672C4⋊C4—431no—
673C4⋊C4—431no—
674C4⋊C4—431no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
702C4⋊C4C2×C4×D4311yescharacteristic
703C4⋊C4C2×C4×D4311yescharacteristic
704C4⋊C4C2×C4×D4311yescharacteristic
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—431no—
708C22⋊C4—431no—
709C22⋊C4—431no—
710C22⋊C4—431no—
711C22⋊C4—431no—
712C22⋊C4—431no—
713C22⋊C4—861no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C42—21no—
718C42—21no—
719C42—431no—
720C42—431no—
721C42—431no—
722C42—431no—
723C42—431no—
724C42—431no—
725C42—861no—
726C42—861no—
727C42—861no—
728C42—861no—
729C42C2×C4×D4311yescharacteristic
730C42D4×D4311yescharacteristic
731C42D4×D4311yescharacteristic
732C42C23×D4311yescharacteristic
733C23—431no—
734C23—431no—
735C23C22⋊C4×D4311yescharacteristic
736Q8—81no—
737Q8—81no—
738Q8—862no—
739Q8—3441no—
740Q8—3441no—
741Q8—3441no—
742Q8—3441no—
743D4—434no—
744D4—862no—
745D4—862no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—431no—
754C2×C4—431no—
755C2×C4—431no—
756C2×C4—431no—
757C2×C4—431no—
758C2×C4—431no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—3441no—
766C2×C4—3441no—
767C2×C4—3441no—
768C2×C4—3441no—
769C2×C4—3441no—
770C2×C4—3441no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—862no—
786C8—1721no—
787C8—1721no—
788C8—1721no—
789C22—21no—
790C22—21no—
791C22—432no—
792C22—861no—
793C22—861no—
794C22—861no—
795C22—861no—
796C22—861no—
797C22#101×D4312yes—
798C22C2×C22⋊C4×D4311yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—432no—
810C4—861no—
811C4—861no—
812C4—861no—
813C4—861no—
814C4—861no—
815C4—1721no—
816C4—1721no—
817C4—1721no—
818C4—1721no—
819C2—22no—
820C2—862no—
821C2—1721no—
822C2C2×#101×D4311yescharacteristic
823C2#1914313911yescharacteristic
824C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1531C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898C2×C4
cosocleC42×C43C24
hypercenter#1531D43
hypocenterC43#17689
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
4. #19133231C2semidirect
5. #19133221C2semidirect
6. #19133220C2semidirect
7. #19133210C2semidirect
8. #19133208C2semidirect
9. #19133208C2semidirect
10. #19133195C2semidirect
11. #19133195C2semidirect
12. #19133188C2semidirect
13. C2×#14582640C2semidirect
14. #330×D43C2semidirect
15. C43×#1531C2semidirect
416. #1531D43semidirect
487. C43#17689semidirect

Maximal subgroups

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

subgroupindex
#191484162
#191436062
#191436042
#191332312
#191332212
#191332202
#191332102
#191332082
#191331952
#191331882
C2×#145826402
#330×D432
C43×#15312
#1768943