Finite Group Databasebeta

← #25063668

Subgroups — #25063668

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148221C211yesmaximal, characteristic
2#19143722C211yesmaximal, characteristic, complemented
3#19143234C211yesmaximal, characteristic, complemented
4#19133063C211yesmaximal, characteristic, complemented
5#19133062C211yesmaximal, characteristic, complemented
6#19133044C211yesmaximal, characteristic, complemented
7#19133033C211yesmaximal, characteristic, complemented
8#19133028C211yesmaximal, characteristic, complemented
9#19133010C211yesmaximal, characteristic, complemented
10#19132995C211yesmaximal, characteristic, complemented
11#19132992C211yesmaximal, characteristic, complemented
12#19132982C211yesmaximal, characteristic, complemented
13#19132981C211yesmaximal, characteristic, complemented
14#19132976C211yesmaximal, characteristic, complemented
15C43×#1488C211yesmaximal, characteristic, complemented
16Q8×Dic86C411yescharacteristic
17#14583614—21no—
18#14583614C411yescharacteristic
19#14583612—21no—
20#14583612—21no—
21#14583612C411yescharacteristic
22#14583612C411yescharacteristic
23#14583571C411yescharacteristic
24#14583570—21no—
25#14583570C411yescharacteristic
26#14583568C411yescharacteristic
27#14583568C411yescharacteristic
28#14583449—21no—
29#14583449C2211yescharacteristic
30#14583446—21no—
31#14583446—21no—
32#14583446C2211yescharacteristic
33#14583446C2211yescharacteristic
34C4×#10621902C2211yescharacteristic
35C4×#10621902C2211yescharacteristic
36C4×#10621898—21no—
37C4×#10621898C2211yescharacteristic
38#14583027—21no—
39#14582972—21no—
40#14582967—21no—
41(C22⋊D43)⋊C8—21no—
42#14582959—21no—
43#14582957—21no—
44#14582955C2211yescharacteristic
45#14582952C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582950C2211yescharacteristic
49#14582924—21no—
50#14582921C2211yescharacteristic
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52C4⋊C8×D43C2211yescharacteristic
53#14582864—21no—
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56Q8⋊(C43⋊C8)C2211yescharacteristic
57Q8⋊(C43⋊C8)C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60#14582628C2211yescharacteristic
61#14582628C2211yescharacteristic
62D4⋊(C43⋊C8)C2211yescharacteristic
63D4⋊(C43⋊C8)C2211yescharacteristic
64#14582626C2211yescharacteristic
65#14582626C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621902C2×C411yescharacteristic
77C2×#10621898—21no—
78C2×#10621898—21no—
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898D411yescharacteristic
82C2×#10621872—21no—
83C2×#10621872—21no—
84C22×C43⋊C8—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063325—21no—
88#13063325C2×C411yescharacteristic
89#13063324—21no—
90#13063324—21no—
91#13063324C2×C411yescharacteristic
92#13063324C2×C411yescharacteristic
93#13063322—21no—
94#13063322C2×C411yescharacteristic
95#13063321—21no—
96#13063321—21no—
97#13063321C2×C411yescharacteristic
98#13063321C2×C411yescharacteristic
99#13063313—21no—
100#13063313—21no—
101#13063313—21no—
102#13063311—21no—
103#13063311—21no—
104#13063311—21no—
105#13063311—21no—
106#13063311—21no—
107#13063311—21no—
108#13063300—21no—
109#13063300—21no—
110#13063300C2×C411yescharacteristic
111#13063300C2×C411yescharacteristic
112#13063299—21no—
113#13063299—21no—
114#13063299—21no—
115#13063299—21no—
116#13063299—21no—
117#13063299C2×C411yescharacteristic
118#13063299C2×C411yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063298—21no—
124#13063298—21no—
125#13063296—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic
128#13063296C2×C411yescharacteristic
129Q8×Dic43C2×C411yescharacteristic
130Q8×Dic43C2×C411yescharacteristic
131C4×Dic86—21no—
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86D411yescharacteristic
134C4×D172—21no—
135C4×D172—21no—
136C4×D172—21no—
137C4×D172—21no—
138C4×D172C2×C411yescharacteristic
139C4×D172D411yescharacteristic
140C4×D172C2311yescharacteristic
141C4×D172C2311yescharacteristic
142#13063287—21no—
143#13063287—21no—
144#13063287C2×C411yescharacteristic
145#13063287C2×C411yescharacteristic
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43C2×C411yescharacteristic
151C4×C22⋊D43C2×C411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154#13063284—21no—
155#13063284D411yescharacteristic
156#13063283—21no—
157#13063283—21no—
158#13063283C2×C411yescharacteristic
159#13063283C2×C411yescharacteristic
160#13063282—21no—
161#13063282—21no—
162#13063282D411yescharacteristic
163#13063282D411yescharacteristic
164C42×D43—21no—
165C42×D43—21no—
166C42×D43C2311yescharacteristic
167C42×D43C2311yescharacteristic
168C4⋊(C43⋊C8)—21no—
169C4⋊(C43⋊C8)—21no—
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C2×#41×C43C2×C411yescharacteristic
188C4×Q8×C43C2×C411yescharacteristic
189C4×Q8×C43C2311yescharacteristic
190C4×D4×C43—21no—
191C4×D4×C43—21no—
192C4×D4×C43C2×C411yescharacteristic
193C4×D4×C43C2311yescharacteristic
194#117×C43—21no—
195#117×C43C2×C411yescharacteristic
196C2×C42×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#97×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206#41×C43—22no—
207#41×C43—41no—
208C2×Q8×C43C22×C411yescharacteristic
209C2×D4×C43—21no—
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43C22⋊C411yescharacteristic
226C2×C22⋊D43C22⋊C411yescharacteristic
227#10621902—22no—
228#10621902—22no—
229#10621902—41no—
230#10621902—41no—
231#10621898—42no—
232#10621898—44no—
233#10621898—81no—
234#10621898—81no—
235#10621898—81no—
236#10621898—81no—
237#10621898—81no—
238#10621898—81no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172C22⋊C411yescharacteristic
246C2×D172C22×C411yescharacteristic
247C2×D172C22×C411yescharacteristic
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43C22×C411yescharacteristic
255C2×C4×D43C22×C411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×C4×D43C2×D411yescharacteristic
260C2×Dic86—21no—
261C2×Dic86—21no—
262C2×Dic86—21no—
263C2×Dic86C22⋊C411yescharacteristic
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C22×C411yescharacteristic
271C4⋊C4×C43C22×C411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C42×C43—21no—
276C42×C43—21no—
277C42×C43—21no—
278C42×C43C22×C411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2411yescharacteristic
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43C22⋊C411yescharacteristic
304C4⋊Dic43C22⋊C411yescharacteristic
305C4⋊Dic43C22×C411yescharacteristic
306C4⋊Dic43C22×C411yescharacteristic
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43C22×C411yescharacteristic
318C4×Dic43C22×C411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—81no—
328#10621872—42no—
329#10621872—81no—
330C8×D43—42no—
331C8×D43—81no—
332C23×C43—21no—
333C23×C43C2×C22⋊C411yescharacteristic
334C22×D43—21no—
335C22×D43—21no—
336C22×D43C2×C22⋊C411yescharacteristic
337C22×D43C2×C22⋊C411yescharacteristic
338Q8×C43—21no—
339Q8×C43#13112yes—
340D4×C43—21no—
341D4×C43—21no—
342D4×C43—42no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—41no—
351C2×C4×C43—42no—
352C2×C4×C43—42no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C2×C4×C43C2×C22⋊C411yescharacteristic
358C2×C4×C43C23×C411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C22⋊D43—22no—
362C22⋊D43—41no—
363C22⋊D43—42no—
364C22⋊D43—42no—
365C22⋊D43—81no—
366C22⋊D43—81no—
367C22⋊D43—81no—
368C22⋊D43—81no—
369C22⋊D43—81no—
370C22⋊D43—81no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379D172—21no—
380D172—21no—
381D172—21no—
382D172—21no—
383D172—41no—
384D172—42no—
385D172—42no—
386D172—42no—
387D172—81no—
388D172—81no—
389D172—81no—
390C4×D43—21no—
391C4×D43—21no—
392C4×D43—21no—
393C4×D43—21no—
394C4×D43—21no—
395C4×D43—21no—
396C4×D43—21no—
397C4×D43—21no—
398C4×D43—22no—
399C4×D43—41no—
400C4×D43—42no—
401C4×D43—42no—
402C4×D43—42no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—41no—
406C4×D43—41no—
407C4×D43—42no—
408Dic86—22no—
409Dic86—81no—
410Dic86—81no—
411Dic86—81no—
412C8×C43—41no—
413C8×C43—41no—
414C8×C43—41no—
415C8×C43—41no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17526—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43C22×C22⋊C411yescharacteristic
428C2×D43—21no—
429C2×D43—21no—
430C2×D43—21no—
431C2×D43—21no—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—41no—
435C2×D43—41no—
436C2×D43—41no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—41no—
440C4×C43—22no—
441C4×C43—21no—
442C4×C43—21no—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—41no—
446C4×C43—41no—
447C4×C43C2×#13111yescharacteristic
448C4×C43#56811yescharacteristic
449C4×C43#57611yescharacteristic
450C4×C43#57711yescharacteristic
451Dic43—21no—
452Dic43—21no—
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—41no—
457Dic43—41no—
458Dic43#42112yes—
459#3483—431no—
460#2990—431no—
461#2922—431no—
462#1496—431no—
463#1496—431no—
464#1492—431no—
465#1489—431no—
466#1488—431no—
467#1488D4311yescharacteristic, complemented
468#1484—431no—
469#1480—431no—
470#1480—431no—
471#1477—431no—
472#1477—431no—
473#1476—431no—
474C2×C43—41no—
475C2×C43—81no—
476C2×C43#288011yescharacteristic
477C2×C43#289711yescharacteristic
478C2×C43C2×#42111yescharacteristic
479D43—41no—
480D43—41no—
481D43—81no—
482D43—81no—
483Q82—431no—
484#555—431no—
485#555—431no—
486#555—431no—
487#555—861no—
488#555—861no—
489#555—861no—
490#550—431no—
491#550—431no—
492#550—431no—
493#550—431no—
494#550—861no—
495#532—431no—
496#532—431no—
497#532—431no—
498#532—861no—
499#532—861no—
500#532—861no—
501C4×#41—431no—
502C4×#41—431no—
503C4×#41—431no—
504C4×#41—861no—
505C4×#41C2×D4311yescharacteristic
506#446—861no—
507#435—861no—
508#435—861no—
509C8×D4—861no—
510#433—861no—
511#433—861no—
512#432—431no—
513#432C2×D4311yescharacteristic
514#431—431no—
515#431—431no—
516#431—431no—
517#431—431no—
518#431C2×D4311yescharacteristic
519#424—861no—
520#423—431no—
521C2×C4⋊C8—431no—
522C2×C4⋊C8—431no—
523#408—861no—
524C4×M16—431no—
525C2×C4×C8—431no—
526Q8⋊C8—431no—
527Q8⋊C8—431no—
528Q8⋊C8C2×D4311yescharacteristic
529Q8⋊C8C2×D4311yescharacteristic
530D4⋊C8—431no—
531D4⋊C8—431no—
532D4⋊C8—431no—
533D4⋊C8—431no—
534D4⋊C8—431no—
535D4⋊C8—431no—
536D4⋊C8—431no—
537D4⋊C8—431no—
538D4⋊C8—431no—
539D4⋊C8—431no—
540D4⋊C8C2×D4311yescharacteristic
541D4⋊C8C2×D4311yescharacteristic
542C43#1752611yescharacteristic, complemented, Sylow
543C2×#41—431no—
544C2×#41—431no—
545C2×#41—431no—
546C2×#41—861no—
547C2×#41—861no—
548C2×#41—861no—
549C2×#41—861no—
550C2×#41C4×D4311yescharacteristic
551C2×M16—861no—
552C2×M16—861no—
553C22×C8—861no—
554C22×C8—861no—
555C22×C8—861no—
556C4⋊Q8—431no—
557C4⋊Q8—431no—
558C4⋊Q8—431no—
559C4⋊Q8—861no—
560C4⋊Q8—861no—
561C4⋊Q8—861no—
562#127—431no—
563#127—431no—
564#127—431no—
565#127—861no—
566#127—861no—
567#127—861no—
568#124—861no—
569#124—861no—
570#124—861no—
571#124—861no—
572#124—861no—
573#124—861no—
574#124—861no—
575#124—861no—
576#124—861no—
577#121—431no—
578#121—431no—
579#121—431no—
580#121—431no—
581#121—431no—
582#121—431no—
583#121—861no—
584#121—861no—
585#121—861no—
586#121—861no—
587#121—861no—
588#121—861no—
589#121—861no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121—861no—
594#121—861no—
595#121—861no—
596#121—861no—
597#121—861no—
598C4×Q8—431no—
599C4×Q8—431no—
600C4×Q8—431no—
601C4×Q8—431no—
602C4×Q8—861no—
603C4×Q8C4×D4311yescharacteristic
604C4×Q8C22×D4311yescharacteristic
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—431no—
613C4×D4—431no—
614C4×D4—431no—
615C4×D4—431no—
616C4×D4—431no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4C4×D4311yescharacteristic
628C4×D4C22×D4311yescharacteristic
629#117—21no—
630#117—431no—
631#117—431no—
632#117—431no—
633#117—431no—
634#117—431no—
635#117—861no—
636#117—861no—
637#117—861no—
638#117—861no—
639#117—861no—
640#117C4×D4311yescharacteristic
641C2×C42—21no—
642C2×C42—431no—
643C2×C42—431no—
644C2×C42—861no—
645C2×C42—861no—
646C2×C42C22×D4311yescharacteristic
647C4⋊C8—21no—
648C4⋊C8—431no—
649C4⋊C8—431no—
650C4⋊C8—861no—
651C4⋊C8—861no—
652C4⋊C8—861no—
653C4⋊C8—861no—
654C4⋊C8—861no—
655C4⋊C8—861no—
656C4⋊C8C22×D4311yescharacteristic
657C4⋊C8C22×D4311yescharacteristic
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8—861no—
661C22⋊C8—861no—
662C22⋊C8—861no—
663C22⋊C8—861no—
664C22⋊C8—861no—
665#97—21no—
666#97—861no—
667#97—861no—
668C4×C8—431no—
669C4×C8—431no—
670C4×C8—861no—
671C4×C8—861no—
672C4×C8C22×D4311yescharacteristic
673C4×C8C22×D4311yescharacteristic
674#41—22no—
675#41—41no—
676#41—862no—
677#41—862no—
678#41—3441no—
679#41—3441no—
680#41—3441no—
681#41—3441no—
682#41—3441no—
683#41—3441no—
684#41—1722no—
685#41—1724no—
686#41—1721no—
687#41—1721no—
688C2×Q8—431no—
689C2×Q8—861no—
690C2×Q8—861no—
691C2×Q8—861no—
692C2×Q8C2×C4×D4311yescharacteristic
693C2×D4—21no—
694C2×D4—431no—
695C2×D4—431no—
696C2×D4—431no—
697C2×D4—431no—
698C2×D4—431no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—861no—
706C2×D4—861no—
707C2×D4—861no—
708C2×D4—861no—
709C2×D4—861no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4C2×C4×D4311yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4C2×C4×D4311yescharacteristic
730C22×C4D4×D4311yescharacteristic
731C22×C4D4×D4311yescharacteristic
732M16—3441no—
733M16—1722no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—3441no—
743C2×C8—3441no—
744C2×C8—1722no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—431no—
754C4⋊C4—431no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4C2×C4×D4311yescharacteristic
761C4⋊C4C2×C4×D4311yescharacteristic
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—431no—
766C22⋊C4—431no—
767C22⋊C4—431no—
768C22⋊C4—431no—
769C22⋊C4—431no—
770C22⋊C4—431no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C42—21no—
784C42—21no—
785C42—21no—
786C42—431no—
787C42—431no—
788C42—431no—
789C42—431no—
790C42—431no—
791C42—431no—
792C42—861no—
793C42—861no—
794C42—861no—
795C42—861no—
796C42C2×C4×D4311yescharacteristic
797C42D4×D4311yescharacteristic
798C42D4×D4311yescharacteristic
799C42C23×D4311yescharacteristic
800C23—21no—
801C23—431no—
802C23—431no—
803C23—861no—
804C23—861no—
805C23C22⋊C4×D4311yescharacteristic
806Q8—21no—
807Q8—862no—
808Q8—3441no—
809Q8—3441no—
810Q8—3441no—
811Q8#1306333312yes—
812D4—21no—
813D4—21no—
814D4—42no—
815D4—862no—
816D4—861no—
817D4—861no—
818D4—861no—
819D4—861no—
820D4—3441no—
821D4—3441no—
822D4—3441no—
823D4—3441no—
824D4—3441no—
825D4—3441no—
826D4—3441no—
827D4—3441no—
828D4—3441no—
829D4—1721no—
830D4—1722no—
831D4—1722no—
832D4—1722no—
833D4—1722no—
834D4—1721no—
835D4—1722no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—431no—
849C2×C4—431no—
850C2×C4—431no—
851C2×C4—431no—
852C2×C4—431no—
853C2×C4—431no—
854C2×C4—862no—
855C2×C4—861no—
856C2×C4—861no—
857C2×C4—861no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—1721no—
866C2×C4—1722no—
867C2×C4—1722no—
868C2×C4—1722no—
869C2×C4—1722no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4C22⋊C4×D4311yescharacteristic
875C2×C4C22⋊C4×D4311yescharacteristic
876C2×C4C22⋊C4×D4311yescharacteristic
877C2×C4C22×C4×D4311yescharacteristic
878C2×C4C2×D4×D4311yescharacteristic
879C2×C4C2×D4×D4311yescharacteristic
880C8—41no—
881C8—41no—
882C8—41no—
883C8—41no—
884C8—1721no—
885C8—1721no—
886C8—1721no—
887C8—1721no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—861no—
895C22—861no—
896C22—861no—
897C22—861no—
898C22—861no—
899C22—861no—
900C22—1721no—
901C22—1721no—
902C22—1721no—
903C22—1721no—
904C22—1721no—
905C22—1721no—
906C22C2×C22⋊C4×D4311yescharacteristic
907C4—21no—
908C4—22no—
909C4—21no—
910C4—21no—
911C4—21no—
912C4—41no—
913C4—41no—
914C4—432no—
915C4—861no—
916C4—861no—
917C4—861no—
918C4—861no—
919C4—861no—
920C4—1721no—
921C4—1721no—
922C4C2×#1306333311yescharacteristic
923C4#1458366511yescharacteristic
924C4#1458370111yescharacteristic
925C4#1458370611yescharacteristic
926C2—41no—
927C2—81no—
928C2—3441no—
929C2—3441no—
930C2—1721no—
931C2—1721no—
932C2#1914304511yescharacteristic
933C2#1914311711yescharacteristic
934C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1488C2
socleC22×C43C22×C22⋊C4
prime radical#19148221C2
cosocleC42×C43C24
hypercenter#1488D43
hypocenterC43#17526
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #19143722C2semidirect
3. #19143234C2semidirect
4. #19133063C2semidirect
5. #19133062C2semidirect
6. #19133044C2semidirect
7. #19133033C2semidirect
8. #19133028C2semidirect
9. #19133010C2semidirect
10. #19132995C2semidirect
11. #19132992C2semidirect
12. #19132982C2semidirect
13. #19132981C2semidirect
14. #19132976C2semidirect
15. C43×#1488C2semidirect
467. #1488D43semidirect
542. C43#17526semidirect

Maximal subgroups

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

subgroupindex
#191482212
#191437222
#191432342
#191330632
#191330622
#191330442
#191330332
#191330282
#191330102
#191329952
#191329922
#191329822
#191329812
#191329762
C43×#14882
#1752643