Finite Group Databasebeta

← #25063671

Subgroups — #25063671

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#19148219C211yesmaximal, characteristic
2#19143722C211yesmaximal, characteristic, complemented
3#19143234C211yesmaximal, characteristic, complemented
4#19133062C211yesmaximal, characteristic, complemented
5#19133044C211yesmaximal, characteristic, complemented
6#19133031C211yesmaximal, characteristic, complemented
7#19133027C211yesmaximal, characteristic, complemented
8#19133026C211yesmaximal, characteristic, complemented
9#19133010C211yesmaximal, characteristic, complemented
10#19132994C211yesmaximal, characteristic, complemented
11#19132992C211yesmaximal, characteristic, complemented
12#19132983C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic, complemented
14#19132974C211yesmaximal, characteristic, complemented
15C43×#1496C211yesmaximal, characteristic, complemented
16#14583629C411yescharacteristic
17#14583615C411yescharacteristic
18#14583613—21no—
19#14583613C411yescharacteristic
20#14583613C411yescharacteristic
21#14583611—21no—
22#14583611—21no—
23#14583569C411yescharacteristic
24#14583569C411yescharacteristic
25#14583567—21no—
26#14583567C411yescharacteristic
27#14583567C411yescharacteristic
28#14583446—21no—
29#14583446C2211yescharacteristic
30#14583446C2211yescharacteristic
31#14583445—21no—
32#14583445—21no—
33C4×#10621898C2211yescharacteristic
34C4×#10621898C2211yescharacteristic
35C4×#10621900—21no—
36C4×#10621900C2211yescharacteristic
37C4×#10621900C2211yescharacteristic
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
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582629C2211yescharacteristic
59#14582629C2211yescharacteristic
60#14582628C2211yescharacteristic
61#14582628C2211yescharacteristic
62D4⋊(C43⋊C8)C2211yescharacteristic
63D4⋊(C43⋊C8)C2211yescharacteristic
64D4⋊(C43⋊C8)C2211yescharacteristic
65D4⋊(C43⋊C8)C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C43×#532C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×D4⋊C8C2211yescharacteristic
72C43×D4⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898D411yescharacteristic
79C2×#10621900—21no—
80C2×#10621900C2×C411yescharacteristic
81C2×#10621900C2×C411yescharacteristic
82C2×#10621872—21no—
83C2×#10621872—21no—
84C22×C43⋊C8—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063324—21no—
88#13063324C2×C411yescharacteristic
89#13063324C2×C411yescharacteristic
90#13063323—21no—
91#13063323—21no—
92#13063321—21no—
93#13063321—21no—
94#13063321—21no—
95#13063321C2×C411yescharacteristic
96#13063321C2×C411yescharacteristic
97#13063314—21no—
98#13063314—21no—
99#13063312—21no—
100#13063312—21no—
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063311—21no—
105#13063300—21no—
106#13063300C2×C411yescharacteristic
107#13063300C2×C411yescharacteristic
108#13063298—21no—
109#13063298—21no—
110#13063298—21no—
111#13063298—21no—
112#13063297—21no—
113#13063297—21no—
114#13063297—21no—
115#13063297—21no—
116#13063297—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063296—21no—
121#13063296C2×C411yescharacteristic
122#13063296C2×C411yescharacteristic
123C4×Dic86C2×C411yescharacteristic
124C4×Dic86C2×C411yescharacteristic
125C4×Dic86D411yescharacteristic
126C4×Dic86C2311yescharacteristic
127#13063290—21no—
128#13063290C2×C411yescharacteristic
129#13063290C2×C411yescharacteristic
130C4×D172C2×C411yescharacteristic
131C4×D172C2×C411yescharacteristic
132C4×D172D411yescharacteristic
133C4×D172C2311yescharacteristic
134D4×Dic43—21no—
135D4×Dic43C2×C411yescharacteristic
136D4×Dic43C2×C411yescharacteristic
137C4×C22⋊D43—21no—
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063284C2×C411yescharacteristic
152#13063284D411yescharacteristic
153#13063283—21no—
154#13063283C2×C411yescharacteristic
155#13063283C2×C411yescharacteristic
156#13063282—21no—
157#13063282D411yescharacteristic
158#13063282D411yescharacteristic
159#13063281—21no—
160#13063281—21no—
161#13063281—21no—
162#13063281—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43—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×C43—21no—
188C4⋊Q8×C43C2×C411yescharacteristic
189#127×C43C2×C411yescharacteristic
190#124×C43—21no—
191#121×C43—21no—
192#121×C43C2×C411yescharacteristic
193#121×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2311yescharacteristic
196C4×D4×C43C2311yescharacteristic
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—81no—
207#41×C43—81no—
208C2×Q8×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43C22×C411yescharacteristic
214C2×D4×C43C22×C411yescharacteristic
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43C22⋊C411yescharacteristic
230C2×C22⋊D43C22⋊C411yescharacteristic
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235#10621900—22no—
236#10621900—22no—
237#10621900—41no—
238#10621900—41no—
239#10621900—44no—
240#10621898—22no—
241#10621898—42no—
242#10621898—41no—
243#10621898—81no—
244#10621898—81no—
245#10621898—81no—
246#10621898—81no—
247C2×D172—21no—
248C2×D172—21no—
249C2×D172C22⋊C411yescharacteristic
250C2×D172C22×C411yescharacteristic
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×Dic86C22⋊C411yescharacteristic
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×C43C22×C411yescharacteristic
270C4⋊C4×C43C22×C411yescharacteristic
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C42×C43C22×C411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2411yescharacteristic
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
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)⋊C4C22⋊C411yescharacteristic
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296C4⋊Dic43C22⋊C411yescharacteristic
297C4⋊Dic43C22⋊C411yescharacteristic
298C4⋊Dic43C22×C411yescharacteristic
299C4⋊Dic43C22×C411yescharacteristic
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
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×C43—21no—
334C23×C43C2×C22⋊C411yescharacteristic
335C22×D43—21no—
336C22×D43C2×C22⋊C411yescharacteristic
337C22×D43C2×C22⋊C411yescharacteristic
338Q8×C43—81no—
339D4×C43—21no—
340D4×C43—21no—
341D4×C43—21no—
342D4×C43—21no—
343D4×C43—42no—
344D4×C43—81no—
345D4×C43—81no—
346D4×C43—81no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43C2×C22⋊C411yescharacteristic
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C23×C411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C22⋊D43—22no—
365C22⋊D43—41no—
366C22⋊D43—42no—
367C22⋊D43—42no—
368C22⋊D43—42no—
369C22⋊D43—42no—
370C22⋊D43—42no—
371C22⋊D43—81no—
372C22⋊D43—81no—
373C22⋊D43—81no—
374C22⋊D43—81no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—42no—
379C2×Dic43—42no—
380C2×Dic43—42no—
381C2×Dic43—42no—
382C2×Dic43C2×C22⋊C411yescharacteristic
383C2×Dic43C2×C22⋊C411yescharacteristic
384C2×Dic43C2×C22⋊C411yescharacteristic
385C2×Dic43C2×C22⋊C411yescharacteristic
386C2×Dic43C2×C22⋊C411yescharacteristic
387C2×Dic43C2×C22⋊C411yescharacteristic
388D172—21no—
389D172—21no—
390D172—41no—
391D172—81no—
392D172—81no—
393C4×D43—21no—
394C4×D43—21no—
395C4×D43—21no—
396C4×D43—21no—
397C4×D43—21no—
398C4×D43—21no—
399C4×D43—21no—
400C4×D43—21no—
401C4×D43—22no—
402C4×D43—41no—
403C4×D43—42no—
404C4×D43—42no—
405C4×D43—41no—
406C4×D43—41no—
407Dic86—21no—
408Dic86—22no—
409Dic86—81no—
410Dic86—81no—
411Dic86#13112yes—
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×C43—41no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43C22×C22⋊C411yescharacteristic
431C2×D43—21no—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—21no—
436C2×D43—21no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—41no—
440C4×C43—21no—
441C4×C43—21no—
442C4×C43—21no—
443C4×C43—21no—
444C4×C43—41no—
445C4×C43—41no—
446C4×C43C2×#13111yescharacteristic
447C4×C43#56811yescharacteristic
448C4×C43#57611yescharacteristic
449C4×C43#57711yescharacteristic
450Dic43—22no—
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#1496D4311yescharacteristic, complemented
464#1492—431no—
465#1489—431no—
466#1488—431no—
467#1488—431no—
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—81no—
477C2×C43#288011yescharacteristic
478C2×C43#289711yescharacteristic
479C2×C43C2×#42111yescharacteristic
480D43—41no—
481D43—41no—
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—861no—
498#532—861no—
499#532—861no—
500#532C2×D4311yescharacteristic
501C4×#41—431no—
502C4×#41—431no—
503C4×#41—431no—
504C4×#41—431no—
505C4×#41—861no—
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⋊C8—431no—
529Q8⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
539D4⋊C8C2×D4311yescharacteristic
540D4⋊C8C2×D4311yescharacteristic
541D4⋊C8C2×D4311yescharacteristic
542C43#1752611yescharacteristic, complemented, Sylow
543C2×#41—21no—
544C2×#41—431no—
545C2×#41—431no—
546C2×#41—431no—
547C2×#41—431no—
548C2×#41—861no—
549C2×#41—861no—
550C2×#41—861no—
551C2×M16—861no—
552C2×M16—861no—
553C22×C8—861no—
554C22×C8—861no—
555C22×C8—861no—
556C4⋊Q8—431no—
557C4⋊Q8—431no—
558C4⋊Q8—861no—
559C4⋊Q8—861no—
560C4⋊Q8—861no—
561C4⋊Q8C4×D4311yescharacteristic
562#127—431no—
563#127—431no—
564#127—861no—
565#127—861no—
566#127—861no—
567#127C4×D4311yescharacteristic
568#124—21no—
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—21no—
578#121—431no—
579#121—431no—
580#121—431no—
581#121—431no—
582#121—861no—
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#121C4×D4311yescharacteristic
597#121C4×D4311yescharacteristic
598C4×Q8—431no—
599C4×Q8—431no—
600C4×Q8—431no—
601C4×Q8—431no—
602C4×Q8—431no—
603C4×Q8—431no—
604C4×Q8—861no—
605C4×D4—21no—
606C4×D4—431no—
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—861no—
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×D4C22×D4311yescharacteristic
628C4×D4C22×D4311yescharacteristic
629#117—431no—
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#117—861no—
641C2×C42—431no—
642C2×C42—431no—
643C2×C42—861no—
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—81no—
675#41—81no—
676#41—862no—
677#41—862no—
678#41—862no—
679#41—3441no—
680#41—3441no—
681#41—3441no—
682#41—3441no—
683#41—1721no—
684#41—1722no—
685#41—1721no—
686#41—1721no—
687#41—1724no—
688C2×Q8—21no—
689C2×Q8—431no—
690C2×Q8—431no—
691C2×Q8—861no—
692C2×Q8—861no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—431no—
698C2×D4—431no—
699C2×D4—431no—
700C2×D4—431no—
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×D4C2×C4×D4311yescharacteristic
713C2×D4C2×C4×D4311yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—861no—
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—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—431no—
754C4⋊C4—861no—
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—21no—
766C22⋊C4—431no—
767C22⋊C4—431no—
768C22⋊C4—431no—
769C22⋊C4—431no—
770C22⋊C4—431no—
771C22⋊C4—431no—
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—431no—
784C42—431no—
785C42—431no—
786C42—431no—
787C42—431no—
788C42—431no—
789C42—861no—
790C42—861no—
791C42—861no—
792C42—861no—
793C42—861no—
794C42—861no—
795C42—861no—
796C42C2×C4×D4311yescharacteristic
797C42D4×D4311yescharacteristic
798C42D4×D4311yescharacteristic
799C42C23×D4311yescharacteristic
800C23—21no—
801C23—21no—
802C23—431no—
803C23—431no—
804C23—861no—
805C23C22⋊C4×D4311yescharacteristic
806Q8—81no—
807Q8—432no—
808Q8—862no—
809Q8—861no—
810Q8—3441no—
811Q8—3441no—
812D4—21no—
813D4—21no—
814D4—21no—
815D4—21no—
816D4—42no—
817D4—81no—
818D4—81no—
819D4—81no—
820D4—862no—
821D4—861no—
822D4—861no—
823D4—3441no—
824D4—3441no—
825D4—3441no—
826D4—3441no—
827D4—3441no—
828D4—3441no—
829D4—1721no—
830D4—1722no—
831D4—1721no—
832D4—1722no—
833D4—1722no—
834D4—1722no—
835D4—1722no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—431no—
848C2×C4—431no—
849C2×C4—431no—
850C2×C4—431no—
851C2×C4—431no—
852C2×C4—431no—
853C2×C4—862no—
854C2×C4—861no—
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—1722no—
871C2×C4—1722no—
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—41no—
895C22—41no—
896C22—41no—
897C22—861no—
898C22—861no—
899C22—861no—
900C22—861no—
901C22—861no—
902C22—861no—
903C22—1721no—
904C22—1721no—
905C22—1721no—
906C22C2×C22⋊C4×D4311yescharacteristic
907C4—21no—
908C4—21no—
909C4—21no—
910C4—21no—
911C4—41no—
912C4—41no—
913C4—432no—
914C4—861no—
915C4—861no—
916C4—862no—
917C4—861no—
918C4—861no—
919C4—861no—
920C4—1721no—
921C4—1721no—
922C4#131×D4311yescharacteristic
923C4#1458366411yescharacteristic
924C4#1458370311yescharacteristic
925C4#1458370911yescharacteristic
926C2—41no—
927C2—81no—
928C2—81no—
929C2—3441no—
930C2—1721no—
931C2—1721no—
932C2#1914304311yescharacteristic
933C2#1914312011yescharacteristic
934C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1496C2
socleC22×C43C22×C22⋊C4
prime radical#19148219C2
cosocleC42×C43C24
hypercenter#1496D43
hypocenterC43#17526
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #19143722C2semidirect
3. #19143234C2semidirect
4. #19133062C2semidirect
5. #19133044C2semidirect
6. #19133031C2semidirect
7. #19133027C2semidirect
8. #19133026C2semidirect
9. #19133010C2semidirect
10. #19132994C2semidirect
11. #19132992C2semidirect
12. #19132983C2semidirect
13. #19132979C2semidirect
14. #19132974C2semidirect
15. C43×#1496C2semidirect
463. #1496D43semidirect
542. C43#17526semidirect

Maximal subgroups

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

subgroupindex
#191482192
#191437222
#191432342
#191330622
#191330442
#191330312
#191330272
#191330262
#191330102
#191329942
#191329922
#191329832
#191329792
#191329742
C43×#14962
#1752643