Finite Group Databasebeta

← #25063601

Subgroups — #25063601

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148205C211yesmaximal, characteristic
2#19143717C211yesmaximal, characteristic, complemented
3#19143234C211yesmaximal, characteristic, complemented
4#19133065C211yesmaximal, characteristic, complemented
5#19133059C211yesmaximal, characteristic, complemented
6#19133054C211yesmaximal, characteristic, complemented
7#19133036C211yesmaximal, characteristic, complemented
8#19133029C211yesmaximal, characteristic, complemented
9#19133018C211yesmaximal, characteristic, complemented
10#19133007C211yesmaximal, characteristic, complemented
11#19133002C211yesmaximal, characteristic, complemented
12#19132993C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1477C211yesmaximal, characteristic, complemented
16#14583634C411yescharacteristic
17#14583609C411yescharacteristic
18#14583606C411yescharacteristic
19#14583595—21no—
20#14583593C411yescharacteristic
21#14583593C411yescharacteristic
22#14583573—21no—
23#14583573—21no—
24#14583545—21no—
25#14583537C411yescharacteristic
26#14583537C411yescharacteristic
27D4×D172C411yescharacteristic
28#14583449C2211yescharacteristic
29#14583436C2211yescharacteristic
30#14583436C2211yescharacteristic
31#14583433—21no—
32#14583408—21no—
33#14583408—21no—
34C4×#10621898C2211yescharacteristic
35C2×C4×D172—21no—
36C4×D4×D43C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38#14583028—21no—
39#14582970—21no—
40#14582969—21no—
41C8×C22⋊D43—21no—
42#14582959—21no—
43#14582957—21no—
44#14582956C2211yescharacteristic, complemented
45#14582955C2211yescharacteristic, complemented
46#14582952C2211yescharacteristic, complemented
47#14582951C2211yescharacteristic, complemented
48#14582950C2211yescharacteristic, complemented
49#14582950C2211yescharacteristic, complemented
50#14582924—21no—
51#14582921C2211yescharacteristic, complemented
52C4⋊C8×D43C2211yescharacteristic, complemented
53#14582864—21no—
54C4×#10621872C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
57Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic, complemented
60#14582628C2211yescharacteristic, complemented
61#14582628C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic
63D4⋊(C43⋊C8)C2211yescharacteristic
64#14582626C2211yescharacteristic, complemented
65#14582626C2211yescharacteristic, complemented
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C4×#41×C43C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C2×C4⋊C8×C43C2211yescharacteristic, complemented
71C43×Q8⋊C8C2211yescharacteristic, complemented
72C43×Q8⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898D411yescharacteristic
77C22×D172—21no—
78C2×D4×D43C2×C411yescharacteristic
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86#13063325C2×C411yescharacteristic
87#13063322C2×C411yescharacteristic
88#13063320—21no—
89#13063320—21no—
90#13063319—21no—
91#13063319—21no—
92#13063317—21no—
93#13063316C2×C411yescharacteristic
94#13063316C2×C411yescharacteristic
95#13063314C2×C411yescharacteristic
96#13063314C2×C411yescharacteristic
97#13063313—21no—
98#13063313—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063308—21no—
104#13063308—21no—
105#13063307—21no—
106#13063307—21no—
107#13063304—21no—
108#13063303—21no—
109#13063303—21no—
110#13063302—21no—
111#13063302—21no—
112#13063301C2×C411yescharacteristic
113#13063301C2×C411yescharacteristic
114#13063300C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
116#13063299—21no—
117#13063299—21no—
118#13063299C2×C411yescharacteristic
119#13063299C2×C411yescharacteristic
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063295—21no—
125#13063295—21no—
126#13063293—21no—
127#13063293—21no—
128C4×Dic86C2×C411yescharacteristic
129C4×Dic86D411yescharacteristic
130C4×D172—21no—
131C4×D172—21no—
132C4×D172—21no—
133C4×D172—21no—
134C4×D172—21no—
135C4×D172—21no—
136C4×D172—21no—
137C4×D172C2×C411yescharacteristic
138C4×D172D411yescharacteristic
139C4×D172C2311yescharacteristic
140C4×D172C2311yescharacteristic
141D4×Dic43C2×C411yescharacteristic
142D4×Dic43C2×C411yescharacteristic
143#13063287C2×C411yescharacteristic
144#13063287C2×C411yescharacteristic
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43C2×C411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063284D411yescharacteristic
154#13063282—21no—
155#13063282—21no—
156#13063282D411yescharacteristic
157#13063282D411yescharacteristic
158C2×C4⋊Dic43—21no—
159C4⋊C4×D43C2×C411yescharacteristic
160C4⋊C4×D43C2×C411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C42×D43C2311yescharacteristic
166C42×D43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)C2311yescharacteristic
169C4⋊(C43⋊C8)C2311yescharacteristic
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063236—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C2×#41×C43C2×C411yescharacteristic
188C22×C8×C43—21no—
189C4×Q8×C43C2×C411yescharacteristic
190C4×Q8×C43C2311yescharacteristic
191C4×D4×C43—21no—
192C4×D4×C43—21no—
193C4×D4×C43C2×C411yescharacteristic
194C4×D4×C43C2311yescharacteristic
195#117×C43—21no—
196#117×C43C2×C411yescharacteristic
197C2×C42×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C4⋊C8×C43—21no—
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C23×D43—21no—
207C23×D43—21no—
208#41×C43—22no—
209#41×C43—41no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43C22×C411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43C22⋊C411yescharacteristic
224C2×C22⋊D43C22⋊C411yescharacteristic
225C22×Dic43—21no—
226C22×Dic43—21no—
227D4×D43—22no—
228D4×D43—22no—
229D4×D43—41no—
230D4×D43—41no—
231#10621898—42no—
232#10621898—81no—
233#10621898—81no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—44no—
239C2×D172C22⋊C411yescharacteristic
240C2×D172C22×C411yescharacteristic
241C2×D172C22×C411yescharacteristic
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—81no—
249C2×C4×D43—81no—
250C2×C4×D43—81no—
251C2×C4×D43—81no—
252C2×C4×D43C22×C411yescharacteristic
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86C22⋊C411yescharacteristic
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—81no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43C22×C411yescharacteristic
268C4⋊C4×C43C22×C411yescharacteristic
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C42×C43—21no—
273C42×C43—21no—
274C42×C43—21no—
275C42×C43C22×C411yescharacteristic
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2411yescharacteristic
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43C22⋊C411yescharacteristic
282C22⋊Dic43C22⋊C411yescharacteristic
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
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)⋊C4—21no—
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C22⋊C411yescharacteristic
305C4⋊Dic43C22⋊C411yescharacteristic
306C4⋊Dic43C22×C411yescharacteristic
307C4⋊Dic43C22×C411yescharacteristic
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318C4×Dic43C22×C411yescharacteristic
319C4×Dic43C22×C411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
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×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—81no—
341C22×D43—81no—
342C22×D43C2×C22⋊C411yescharacteristic
343C22×D43C2×C22⋊C411yescharacteristic
344Q8×C43—21no—
345Q8×C43—21no—
346D4×C43—21no—
347D4×C43—42no—
348D4×C43#13112yes—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—41no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43C2×C22⋊C411yescharacteristic
362C2×C4×C43C2×C22⋊C411yescharacteristic
363C2×C4×C43C2×C22⋊C411yescharacteristic
364C2×C4×C43C23×C411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C22⋊D43—22no—
368C22⋊D43—41no—
369C22⋊D43—42no—
370C22⋊D43—42no—
371C22⋊D43—81no—
372C22⋊D43—81no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—81no—
376C2×Dic43—81no—
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C2×Dic43C2×C22⋊C411yescharacteristic
383D172—22no—
384D172—21no—
385D172—21no—
386D172—21no—
387D172—21no—
388D172—42no—
389D172—42no—
390D172—42no—
391D172—81no—
392C4×D43—22no—
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—41no—
402C4×D43—41no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—41no—
406C4×D43—81no—
407C4×D43—81no—
408C4×D43—81no—
409C4×D43—81no—
410Dic86—41no—
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#17521—431nomaximal, Sylow
421C22×C43—22no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
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—41no—
434C2×D43—41no—
435C2×D43—41no—
436C2×D43—41no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—84no—
440C2×D43—84no—
441C2×D43#42112yes—
442C4×C43—21no—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—41no—
447C4×C43—41no—
448C4×C43—41no—
449C4×C43C2×#13111yescharacteristic
450C4×C43#56811yescharacteristic
451C4×C43#57611yescharacteristic
452C4×C43#57711yescharacteristic
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—21no—
459Dic43—41no—
460Dic43—41no—
461#3481—431no—
462#2990—431no—
463#2922—431no—
464#1496—431no—
465#1495—431no—
466#1494—431no—
467#1490—431no—
468#1488—431no—
469#1486—431no—
470#1483—431no—
471#1482—431no—
472#1480—431no—
473#1478—431no—
474#1477D4311yescharacteristic, complemented
475C2×D4⋊C8—431no—
476C2×C43—42no—
477C2×C43—41no—
478C2×C43#288011yescharacteristic
479C2×C43#289711yescharacteristic
480C2×C43C2×#42111yescharacteristic
481D43—22no—
482D43—41no—
483D43—81no—
484D43—81no—
485#559—431no—
486#554—431no—
487#554—431no—
488#553—431no—
489#553—431no—
490#553—861no—
491#551—861no—
492#551—861no—
493#546—431no—
494#546—431no—
495#546—861no—
496D42—431no—
497#532—431no—
498#529—431no—
499#529—431no—
500#529—861no—
501#525—861no—
502#525—861no—
503C4×#41—431no—
504C4×#41C2×D4311yescharacteristic
505C2×C4×D4—431no—
506C2×C4×D4—431no—
507C2×C4×D4—861no—
508#446—861no—
509#435—861no—
510#435—861no—
511C8×D4—861no—
512#433—861no—
513#433—861no—
514#432—431no—
515#432—431no—
516#431—431no—
517#431—431no—
518#431—431no—
519#431—431no—
520#431C2×D4311yescharacteristic, complemented
521#424—861no—
522#423—431no—
523C2×C4⋊C8—431no—
524C2×C4⋊C8C2×D4311yescharacteristic, complemented
525#408—861no—
526C4×M16—431no—
527C2×C4×C8—431no—
528Q8⋊C8—431no—
529Q8⋊C8—431no—
530Q8⋊C8C2×D4311yescharacteristic, complemented
531Q8⋊C8C2×D4311yescharacteristic, complemented
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⋊C8—431no—
541D4⋊C8—431no—
542D4⋊C8C2×D4311yescharacteristic
543D4⋊C8C2×D4311yescharacteristic
544C43#1752111yescharacteristic, complemented, Sylow
545C2×#41—431no—
546C2×#41—861no—
547C2×#41C4×D4311yescharacteristic
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—861no—
551C23×C4—861no—
552C23×C4—861no—
553C2×M16—861no—
554C2×M16—861no—
555C22×C8—21no—
556C22×C8—861no—
557C22×C8—861no—
558C4⋊Q8—431no—
559#127—431no—
560#126—861no—
561#126—861no—
562#126—861no—
563#126—861no—
564#125—431no—
565#125—431no—
566#125—861no—
567#124—431no—
568#124—431no—
569#124—861no—
570#124—861no—
571#123—861no—
572#123—861no—
573#123—861no—
574#123—861no—
575#123—861no—
576#123—861no—
577#123—861no—
578#123—861no—
579C22⋊Q8—431no—
580C22⋊Q8—431no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8—861no—
584C22⋊Q8—861no—
585C22⋊Q8—861no—
586#121—431no—
587#121—431no—
588#121—431no—
589#121—431no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121—861no—
594#121—861no—
595#121—861no—
596#120—861no—
597#120—861no—
598#120—861no—
599#120—861no—
600C4×Q8—431no—
601C4×Q8—431no—
602C4×Q8C4×D4311yescharacteristic
603C4×Q8C22×D4311yescharacteristic
604C4×D4—21no—
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—431no—
617C4×D4—431no—
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×D4—861no—
628C4×D4—861no—
629C4×D4C4×D4311yescharacteristic
630C4×D4C22×D4311yescharacteristic
631#117—21no—
632#117—431no—
633#117—431no—
634#117—431no—
635#117—861no—
636#117—861no—
637#117C4×D4311yescharacteristic
638C2×C4⋊C4—431no—
639C2×C4⋊C4—431no—
640C2×C4⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C42—21no—
646C2×C42—431no—
647C2×C42—431no—
648C2×C42C22×D4311yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—431no—
652C4⋊C8—431no—
653C4⋊C8—861no—
654C4⋊C8—861no—
655C4⋊C8—861no—
656C4⋊C8—861no—
657C4⋊C8—861no—
658C4⋊C8C22×D4311yescharacteristic
659C4⋊C8C22×D4311yescharacteristic
660C22⋊C8—21no—
661C22⋊C8—861no—
662C22⋊C8—861no—
663C22⋊C8—861no—
664C22⋊C8—861no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667#97—861no—
668#97—861no—
669#97—861no—
670C4×C8—431no—
671C4×C8—431no—
672C4×C8—861no—
673C4×C8—861no—
674C4×C8C22×D4311yescharacteristic
675C4×C8C22×D4311yescharacteristic
676C24—861no—
677C24—861no—
678#41—22no—
679#41—41no—
680#41—3441no—
681#41—3441no—
682#41—1722no—
683C2×Q8—431no—
684C2×Q8—861no—
685C2×Q8C2×C4×D4311yescharacteristic
686C2×D4—21no—
687C2×D4—431no—
688C2×D4—431no—
689C2×D4—431no—
690C2×D4—431no—
691C2×D4—431no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—862no—
697C2×D4—862no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—1724no—
703C2×D4—1721no—
704C2×D4—1721no—
705C2×D4C2×C4×D4311yescharacteristic
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—
723C22×C4—3441no—
724C22×C4—3441no—
725C22×C4—3441no—
726C22×C4—3441no—
727C22×C4C2×C4×D4311yescharacteristic
728C22×C4D4×D4311yescharacteristic
729C22×C4D4×D4311yescharacteristic
730M16—3441no—
731M16—1722no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—81no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—3441no—
742C2×C8—1722no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4C2×C4×D4311yescharacteristic
763C4⋊C4C2×C4×D4311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—431no—
768C22⋊C4—431no—
769C22⋊C4—431no—
770C22⋊C4—431no—
771C22⋊C4—431no—
772C22⋊C4—431no—
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—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C42—21no—
790C42—21no—
791C42—21no—
792C42—431no—
793C42—431no—
794C42—431no—
795C42—431no—
796C42—431no—
797C42—431no—
798C42C2×C4×D4311yescharacteristic
799C42D4×D4311yescharacteristic
800C42D4×D4311yescharacteristic
801C42C23×D4311yescharacteristic
802C23—21no—
803C23—431no—
804C23—431no—
805C23—861no—
806C23—861no—
807C23—3441no—
808C23—3441no—
809C23—1722no—
810C23—1722no—
811C23—1722no—
812C23—1722no—
813C23C22⋊C4×D4311yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—3441no—
817Q8—1721no—
818D4—21no—
819D4—42no—
820D4—862no—
821D4—862no—
822D4—861no—
823D4—861no—
824D4—861no—
825D4—861no—
826D4—3441no—
827D4—3441no—
828D4—3441no—
829D4—1722no—
830D4—1722no—
831D4—1722no—
832D4—1721no—
833D4—1722no—
834D4—1722no—
835D4#1306333112yes—
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—3441no—
866C2×C4—3441no—
867C2×C4—3441no—
868C2×C4—3441no—
869C2×C4—3441no—
870C2×C4—3441no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4C22⋊C4×D4311yescharacteristic
877C2×C4C22⋊C4×D4311yescharacteristic
878C2×C4C22⋊C4×D4311yescharacteristic
879C2×C4C22×C4×D4311yescharacteristic
880C2×C4C2×D4×D4311yescharacteristic
881C2×C4C2×D4×D4311yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—1721no—
887C8—1721no—
888C8—1721no—
889C8—1721no—
890C22—21no—
891C22—22no—
892C22—21no—
893C22—21no—
894C22—41no—
895C22—41no—
896C22—432no—
897C22—861no—
898C22—861no—
899C22—861no—
900C22—861no—
901C22—861no—
902C22—3444no—
903C22—3444no—
904C22—1721no—
905C22—1721no—
906C22—1721no—
907C22—1721no—
908C22—1721no—
909C22—1721no—
910C22C2×C22⋊C4×D4311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—861no—
919C4—861no—
920C4—861no—
921C4—861no—
922C4—861no—
923C4—861no—
924C4—1721no—
925C4—1721no—
926C4C2×#1306333111yescharacteristic
927C4#1458366511yescharacteristic
928C4#1458370311yescharacteristic
929C4#1458370811yescharacteristic
930C2—41no—
931C2—42no—
932C2—862no—
933C2—3441no—
934C2—3441no—
935C2—1721no—
936C2#1914304111yescharacteristic
937C2#1914311911yescharacteristic
938C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1477C2
socleC22×C43C22×C22⋊C4
prime radical#19148205C2
cosocleC42×C43C24
hypercenter#1477D43
hypocenterC43#17521
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143717C2semidirect
3. #19143234C2semidirect
4. #19133065C2semidirect
5. #19133059C2semidirect
6. #19133054C2semidirect
7. #19133036C2semidirect
8. #19133029C2semidirect
9. #19133018C2semidirect
10. #19133007C2semidirect
11. #19133002C2semidirect
12. #19132993C2semidirect
13. #19132984C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1477C2semidirect
44. #14582956C22semidirect
45. #14582955C22semidirect
46. #14582952C22semidirect
47. #14582951C22semidirect
48. #14582950C22semidirect
49. #14582950C22semidirect
51. #14582921C22semidirect
52. C4⋊C8×D43C22semidirect
54. C4×#10621872C22semidirect
55. C4×C8×D43C22semidirect
56. Q8⋊(C43⋊C8)C22semidirect
57. Q8⋊(C43⋊C8)C22semidirect
58. #14582628C22semidirect
59. #14582628C22semidirect
60. #14582628C22semidirect
61. #14582628C22semidirect
64. #14582626C22semidirect
65. #14582626C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#431C22semidirect
70. C2×C4⋊C8×C43C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
474. #1477D43semidirect
520. #431C2×D43semidirect
524. C2×C4⋊C8C2×D43semidirect
530. Q8⋊C8C2×D43semidirect
531. Q8⋊C8C2×D43semidirect
544. C43#17521semidirect

Maximal subgroups

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

subgroupindex
#191482052
#191437172
#191432342
#191330652
#191330592
#191330542
#191330362
#191330292
#191330182
#191330072
#191330022
#191329932
#191329842
D4⋊C8×D432
C43×#14772
#1752143