Finite Group Databasebeta

← #25112293

Subgroups — #25112293

Order 11008.

1472 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C22⋊D43C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4#19137054C211yesmaximal, characteristic, complemented
5#19135512C211yesmaximal, characteristic, complemented
6#19135421C211yesmaximal, characteristic, complemented
7#19135043C211yesmaximal, characteristic, complemented
8#19135040C211yesmaximal, characteristic, complemented
9#19134897C211yesmaximal, characteristic, complemented
10#19134894C211yesmaximal, characteristic, complemented
11#19134613C211yesmaximal, characteristic, complemented
12#19134539C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#104×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#421C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic, complemented
18#14583568C411yescharacteristic, complemented
19Q8×C22⋊D43C411yescharacteristic, complemented
20#14583560C411yescharacteristic, complemented
21#14583556C411yescharacteristic, complemented
22#14583548—21no—
23#14583548C411yescharacteristic, complemented
24#14583543—21no—
25#14583543C411yescharacteristic, complemented
26#14583537—21no—
27#14583537C411yescharacteristic, complemented
28D4×C22⋊D43—21no—
29D4×C22⋊D43C411yescharacteristic, complemented
30#14583445—21no—
31#14583445C2211yescharacteristic
32#14583410—21no—
33#14583410C2211yescharacteristic
34#14583406—21no—
35#14583406C2211yescharacteristic
36#41×Dic43C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×#13063282C2211yescharacteristic, complemented
40#14582975—21no—
41#14582970—21no—
42#14582968—21no—
43C8×C22⋊D43—21no—
44#14582922C2211yescharacteristic, complemented
45#14582914—24no—
46C2×#13063253C2211yescharacteristic, complemented
47C2×#13063253C2211yescharacteristic, complemented
48C2×#13063252C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063252C2211yescharacteristic, complemented
51C2×#13063252C2211yescharacteristic, complemented
52C2×#13063251C2211yescharacteristic, complemented
53C2×#13063251C2211yescharacteristic, complemented
54#14582863C2211yescharacteristic, complemented
55#14582862C2211yescharacteristic, complemented
56M16×Dic43C2211yescharacteristic, complemented
57#14582799—21no—
58#14582794—21no—
59#14582793—21no—
60#14582789—21no—
61C4×Dic43⋊C4C2211yescharacteristic, complemented
62C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
63C4×C22⋊Dic43C2211yescharacteristic, complemented
64C42×Dic43C2211yescharacteristic, complemented
65#14582660C2211yescharacteristic, complemented
66#14582660C2211yescharacteristic, complemented
67#14582659C2211yescharacteristic, complemented
68#14582659C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic, complemented
71C2×#117×C43C2211yescharacteristic, complemented
72C43×#421—24no—
73C2×#104×C43C2211yescharacteristic
74C2×#104×C43C2211yescharacteristic
75C2×#104×C43C2211yescharacteristic, complemented
76C2×#104×C43C2211yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic
78C2×#10621898—21no—
79C2×#10621898C2311yescharacteristic
80C2×#10621900—21no—
81C2×#10621900C2×C411yescharacteristic
82#41×D43—22no—
83#41×D43—22no—
84#41×D43—41no—
85#41×D43—41no—
86C2×Q8×D43C2×C411yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C2×D4×D43—21no—
90C2×D4×D43C2×C411yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93C2×#10621877C2311yescharacteristic
94C2×#10621877C2311yescharacteristic
95C2×#10621872—21no—
96M16×D43—22no—
97M16×D43—41no—
98C2×C8×D43—21no—
99#13063323—21no—
100#13063323C2×C411yescharacteristic
101#13063321—21no—
102#13063321C2×C411yescharacteristic
103#13063314—21no—
104#13063314C2×C411yescharacteristic
105#13063312—21no—
106#13063312C2×C411yescharacteristic
107#13063308—21no—
108#13063308—21no—
109#13063308—21no—
110#13063306—21no—
111#13063306—21no—
112#13063306—21no—
113#13063304—21no—
114#13063304—21no—
115#13063304C2×C411yescharacteristic
116#13063304C2×C411yescharacteristic
117#13063301—21no—
118#13063301—21no—
119#13063301C2×C411yescharacteristic
120#13063301C2×C411yescharacteristic
121#13063299—21no—
122#13063299—21no—
123#13063299C2×C411yescharacteristic
124#13063299C2×C411yescharacteristic
125#13063297—21no—
126#13063297—21no—
127#13063297—21no—
128#13063297—21no—
129#13063297—21no—
130#13063297—21no—
131#13063296—21no—
132#13063296—21no—
133#13063296C2×C411yescharacteristic
134#13063296C2×C411yescharacteristic
135#13063294—21no—
136#13063294—21no—
137#13063294—21no—
138#13063293—21no—
139#13063293—21no—
140#13063293—21no—
141Q8×Dic43C2×C411yescharacteristic
142Q8×Dic43C2×C411yescharacteristic
143D4×Dic43—21no—
144D4×Dic43—21no—
145D4×Dic43C2×C411yescharacteristic
146D4×Dic43C2×C411yescharacteristic
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152C4×C22⋊D43—21no—
153C4×C22⋊D43—21no—
154C4×C22⋊D43—21no—
155C4×C22⋊D43—21no—
156C4×C22⋊D43—21no—
157C4×C22⋊D43C2×C411yescharacteristic
158C4×C22⋊D43C2×C411yescharacteristic
159C4×C22⋊D43C2×C411yescharacteristic
160C4×C22⋊D43C2×C411yescharacteristic
161C4×C22⋊D43D411yescharacteristic
162C4×C22⋊D43D411yescharacteristic
163C4×C22⋊D43D411yescharacteristic
164C4×C22⋊D43D411yescharacteristic
165#13063284—21no—
166#13063284C2311yescharacteristic
167#13063282—22no—
168#13063282—41no—
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×Dic43⋊C4—21no—
172C2×Dic43⋊C4D411yescharacteristic
173C2×C22⋊Dic43—21no—
174C2×C22⋊Dic43—21no—
175C2×C22⋊Dic43D411yescharacteristic
176C2×(C2×D43)⋊C4—21no—
177C2×(C2×D43)⋊C4—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4D411yescharacteristic
180C2×C4×Dic43—21no—
181C2×C4×Dic43—21no—
182C2×C4×Dic43—21no—
183C2×C4×Dic43C2311yescharacteristic
184C2×C4×Dic43C2311yescharacteristic
185C2×C4×Dic43C2311yescharacteristic
186Dic43⋊C8—21no—
187Dic43⋊C8—21no—
188#13063253—22no—
189#13063253—41no—
190#13063252—22no—
191#13063252—22no—
192#13063252—41no—
193#13063252—41no—
194#13063251—22no—
195#13063251—41no—
196C22⋊(C43⋊C8)—21no—
197C22⋊(C43⋊C8)—21no—
198(C2×D43)⋊C8—21no—
199(C2×D43)⋊C8—21no—
200#13063235—21no—
201C8×Dic43—21no—
202C43⋊#95—21no—
203C43⋊#95—21no—
204C43⋊#95—21no—
205C2×#41×C43—21no—
206C2×#41×C43—21no—
207C2×#41×C43—22no—
208C2×#41×C43—22no—
209C2×#41×C43—41no—
210C2×#41×C43—41no—
211C2×#41×C43C2×C411yescharacteristic
212C2×#41×C43C2×C411yescharacteristic
213C2×#41×C43C2311yescharacteristic
214C2×#41×C43C2311yescharacteristic
215C22×Q8×C43C2×C411yescharacteristic
216C22×D4×C43—21no—
217C22×D4×C43C2×C411yescharacteristic
218C23×C4×C43—21no—
219C23×C4×C43C2311yescharacteristic
220C2×M16×C43—21no—
221C2×M16×C43—22no—
222C2×M16×C43—41no—
223C2×M16×C43C2311yescharacteristic
224C2×M16×C43C2311yescharacteristic
225C22×C8×C43—21no—
226#117×C43—22no—
227#117×C43—41no—
228C2×C4⋊C4×C43—21no—
229C2×C22⋊C4×C43—21no—
230C2×C42×C43C2311yescharacteristic
231C2×C42×C43C2311yescharacteristic
232#104×C43—22no—
233#104×C43—22no—
234#104×C43—22no—
235#104×C43D414yescomplemented
236C24×C43—21no—
237C24×C43C2×D411yescharacteristic
238C23×D43—21no—
239C23×D43C2×D411yescharacteristic
240#41×C43—21no—
241#41×C43—21no—
242#41×C43—22no—
243#41×C43—22no—
244#41×C43—21no—
245#41×C43—21no—
246#41×C43—21no—
247#41×C43—21no—
248#41×C43—42no—
249#41×C43—42no—
250#41×C43—41no—
251#41×C43—41no—
252#41×C43—42no—
253#41×C43—42no—
254#41×C43C2×D412yes—
255#41×C43#4112yes—
256C2×Q8×C43—21no—
257C2×Q8×C43—22no—
258C2×Q8×C43—41no—
259C2×Q8×C43C22×C411yescharacteristic
260C2×Q8×C43C22×C411yescharacteristic
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—22no—
267C2×D4×C43—42no—
268C2×D4×C43—42no—
269C2×D4×C43—41no—
270C2×D4×C43C22×C411yescharacteristic
271C2×D4×C43C22×C411yescharacteristic
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—21no—
280C22×C4×C43—21no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43—42no—
284C22×C4×C43—42no—
285C22×C4×C43C22×C411yescharacteristic
286C22×C4×C43C22×C411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C2×C22⋊D43—21no—
292C2×C22⋊D43—21no—
293C2×C22⋊D43—21no—
294C2×C22⋊D43—21no—
295C2×C22⋊D43—21no—
296C2×C22⋊D43—21no—
297C2×C22⋊D43—21no—
298C2×C22⋊D43—21no—
299C2×C22⋊D43—21no—
300C2×C22⋊D43—42no—
301C2×C22⋊D43—44no—
302C2×C22⋊D43C22⋊C411yescharacteristic
303C2×C22⋊D43C22⋊C411yescharacteristic
304C2×C22⋊D43C22⋊C411yescharacteristic
305C2×C22⋊D43C22⋊C411yescharacteristic
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43C2×D411yescharacteristic
312C22×Dic43C2×D411yescharacteristic
313C22×Dic43C2×D411yescharacteristic
314#10621902—22no—
315#10621902—41no—
316Q8×D43—22no—
317Q8×D43—41no—
318#10621900—22no—
319#10621900—41no—
320#10621900—42no—
321#10621900—42no—
322D4×D43—22no—
323D4×D43—42no—
324D4×D43—42no—
325D4×D43—41no—
326#10621898—21no—
327#10621898—21no—
328#10621898—21no—
329#10621898—21no—
330#10621898—42no—
331#10621898—42no—
332C2×D172—21no—
333C2×D172C22×C411yescharacteristic
334C2×C4×D43—21no—
335C2×C4×D43—21no—
336C2×C4×D43—21no—
337C2×C4×D43—21no—
338C2×C4×D43—21no—
339C2×C4×D43—21no—
340C2×C4×D43—21no—
341C2×C4×D43—42no—
342C2×C4×D43—42no—
343C2×C4×D43C22×C411yescharacteristic
344C2×C4×D43C22×C411yescharacteristic
345C2×C4×D43C2×D411yescharacteristic
346C2×C4×D43C2×D411yescharacteristic
347C2×Dic86—21no—
348C2×Dic86C22×C411yescharacteristic
349M16×C43—21no—
350M16×C43—21no—
351M16×C43—21no—
352M16×C43—42no—
353M16×C43C2×D412yescomplemented
354C2×C8×C43—21no—
355C2×C8×C43—21no—
356C2×C8×C43—42no—
357C4⋊C4×C43—42no—
358C22⋊C4×C43—42no—
359C42×C43—21no—
360C42×C43—21no—
361C42×C43—21no—
362C42×C43C2×D412yescomplemented
363C22⋊Dic43—21no—
364C22⋊Dic43—21no—
365C22⋊Dic43—21no—
366C22⋊Dic43—21no—
367C22⋊Dic43—21no—
368C22⋊Dic43—21no—
369C22⋊Dic43—21no—
370C22⋊Dic43—21no—
371C22⋊Dic43—21no—
372C22⋊Dic43—42no—
373C22⋊Dic43C22⋊C411yescharacteristic
374C22⋊Dic43C22⋊C411yescharacteristic
375C22⋊Dic43C22⋊C411yescharacteristic
376C22⋊Dic43C22⋊C411yescharacteristic
377(C2×D43)⋊C4—21no—
378(C2×D43)⋊C4—21no—
379(C2×D43)⋊C4—21no—
380(C2×D43)⋊C4—21no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—21no—
383(C2×D43)⋊C4—42no—
384(C2×D43)⋊C4—42no—
385(C2×D43)⋊C4C22⋊C411yescharacteristic
386(C2×D43)⋊C4C22⋊C411yescharacteristic
387(C2×D43)⋊C4C22⋊C411yescharacteristic
388(C2×D43)⋊C4C22⋊C411yescharacteristic
389C4⋊Dic43—21no—
390C4⋊Dic43—21no—
391C4⋊Dic43C22×C411yescharacteristic
392C4⋊Dic43C22×C411yescharacteristic
393Dic43⋊C4—21no—
394Dic43⋊C4—21no—
395Dic43⋊C4—21no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—42no—
400Dic43⋊C4—42no—
401Dic43⋊C4C22⋊C411yescharacteristic
402Dic43⋊C4C22⋊C411yescharacteristic
403Dic43⋊C4C22⋊C411yescharacteristic
404Dic43⋊C4C22⋊C411yescharacteristic
405C4×Dic43—21no—
406C4×Dic43—21no—
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—42no—
413C4×Dic43—42no—
414C4×Dic43C22×C411yescharacteristic
415C4×Dic43C22×C411yescharacteristic
416C4×Dic43C2×D411yescharacteristic
417C4×Dic43C2×D411yescharacteristic
418#10621877—21no—
419#10621877—21no—
420#10621877—21no—
421#10621877—21no—
422C2×C43⋊C8—21no—
423C2×C43⋊C8—21no—
424#10621872—42no—
425C8×D43—42no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—21no—
429C23×C43—21no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—42no—
433C23×C43—42no—
434C23×C43—81no—
435C23×C43C2×C22⋊C411yescharacteristic
436C23×C43C2×C22⋊C411yescharacteristic
437C23×C43C22×D411yescharacteristic
438C22×D43—21no—
439C22×D43—21no—
440C22×D43—21no—
441C22×D43—41no—
442C22×D43—41no—
443C22×D43—42no—
444C22×D43—42no—
445C22×D43—81no—
446C22×D43C2×C22⋊C411yescharacteristic
447C22×D43C2×C22⋊C411yescharacteristic
448Q8×C43—21no—
449Q8×C43—21no—
450Q8×C43—21no—
451Q8×C43—42no—
452Q8×C43C4×D412yes—
453D4×C43—22no—
454D4×C43—22no—
455D4×C43—21no—
456D4×C43—21no—
457D4×C43—21no—
458D4×C43—42no—
459D4×C43—42no—
460D4×C43—42no—
461D4×C43—41no—
462D4×C43—41no—
463D4×C43C4×D412yes—
464C2×C4×C43—21no—
465C2×C4×C43—21no—
466C2×C4×C43—21no—
467C2×C4×C43—21no—
468C2×C4×C43—21no—
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43—21no—
472C2×C4×C43—21no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—22no—
479C2×C4×C43—42no—
480C2×C4×C43—42no—
481C2×C4×C43—42no—
482C2×C4×C43—41no—
483C2×C4×C43—41no—
484C2×C4×C43—41no—
485C2×C4×C43—41no—
486C2×C4×C43—41no—
487C2×C4×C43—41no—
488C2×C4×C43—41no—
489C2×C4×C43C2×C22⋊C411yescharacteristic
490C2×C4×C43C2×C22⋊C411yescharacteristic
491C2×C4×C43C23×C411yescharacteristic
492C2×C4×C43C22×D411yescharacteristic
493C2×C4×C43C22×D411yescharacteristic
494C2×C4×C43C2×#4111yescharacteristic
495C2×C4×C43H(5,𝔽2)11yescharacteristic
496C2×C4×C43H(5,𝔽2)11yescharacteristic
497C22⋊D43—22no—
498C22⋊D43—22no—
499C22⋊D43—41no—
500C22⋊D43—41no—
501C22⋊D43—42no—
502C22⋊D43—42no—
503C22⋊D43—42no—
504C22⋊D43—42no—
505C22⋊D43—41no—
506C22⋊D43—41no—
507C22⋊D43—42no—
508C22⋊D43—81no—
509C22⋊D43—81no—
510C22⋊D43—81no—
511C2×Dic43—21no—
512C2×Dic43—21no—
513C2×Dic43—22no—
514C2×Dic43—22no—
515C2×Dic43—21no—
516C2×Dic43—21no—
517C2×Dic43—21no—
518C2×Dic43—41no—
519C2×Dic43—42no—
520C2×Dic43—41no—
521C2×Dic43—41no—
522C2×Dic43—42no—
523C2×Dic43—41no—
524C2×Dic43—41no—
525C2×Dic43—41no—
526C2×Dic43—81no—
527C2×Dic43C2×C22⋊C411yescharacteristic
528C2×Dic43C2×C22⋊C411yescharacteristic
529C2×Dic43C2×C22⋊C411yescharacteristic
530C2×Dic43C2×C22⋊C411yescharacteristic
531C2×Dic43C2×C22⋊C411yescharacteristic
532C2×Dic43C2×C22⋊C411yescharacteristic
533D172—21no—
534D172—21no—
535D172—42no—
536C4×D43—21no—
537C4×D43—21no—
538C4×D43—21no—
539C4×D43—21no—
540C4×D43—21no—
541C4×D43—21no—
542C4×D43—21no—
543C4×D43—21no—
544C4×D43—42no—
545C4×D43—42no—
546C4×D43—41no—
547C4×D43—41no—
548Dic86—21no—
549Dic86—21no—
550Dic86—42no—
551C8×C43—22no—
552C8×C43—41no—
553C43⋊C8—41no—
554C43⋊C8—41no—
555#22435—431nomaximal, Sylow
556C22×C43—21no—
557C22×C43—21no—
558C22×C43—22no—
559C22×C43—21no—
560C22×C43—21no—
561C22×C43—21no—
562C22×C43—21no—
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—41no—
566C22×C43—41no—
567C22×C43—41no—
568C22×C43—41no—
569C22×C43—41no—
570C22×C43—81no—
571C22×C43—81no—
572C22×C43—84no—
573C22×C43C22×C22⋊C411yescharacteristic
574C22×C43D4211yescharacteristic
575C22×C43#54611yescharacteristic
576C2×D43—21no—
577C2×D43—21no—
578C2×D43—21no—
579C2×D43—21no—
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—41no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—81no—
586C2×D43—81no—
587C2×D43—84no—
588C4×C43—22no—
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—42no—
592C4×C43—41no—
593C4×C43—81no—
594C4×C43C2×C4×D411yescharacteristic
595C4×C43#51811yescharacteristic
596C4×C43D4211yescharacteristic
597C4×C43#54611yescharacteristic
598Dic43—21no—
599Dic43—21no—
600Dic43—21no—
601Dic43—21no—
602Dic43—21no—
603Dic43—42no—
604Dic43—41no—
605Dic43—41no—
606Dic43—41no—
607Dic43—81no—
608Dic43#42112yescomplemented
609D4×#41—431no—
610D4×M16—431no—
611C2×#421—431no—
612C2×#421D4311yescharacteristic, complemented
613#2293—431no—
614#1980—431no—
615#1962—431no—
616#1897—431no—
617#1897—431no—
618#1871—431no—
619#1871—431no—
620#1806—431no—
621#1789—431no—
622#1789—431no—
623C4×#104—431no—
624C2×C43—21no—
625C2×C43—21no—
626C2×C43—42no—
627C2×C43—41no—
628C2×C43—41no—
629C2×C43—81no—
630C2×C43D4×C22⋊C411yescharacteristic
631C2×C43C2×#42111yescharacteristic
632C2×C43#290111yescharacteristic
633D43—41no—
634D43—41no—
635D43—81no—
636C22×#41—431no—
637C22×#41C2×D4311yescharacteristic
638C22×M16—431no—
639C22×M16C2×D4311yescharacteristic, complemented
640#550—431no—
641D4×Q8—431no—
642#548—431no—
643#548—431no—
644#547—431no—
645#547—861no—
646#546—431no—
647#546—431no—
648#546—861no—
649#546—861no—
650D42—431no—
651D42—861no—
652#532—431no—
653#532—861no—
654#525—431no—
655#525—431no—
656#525—861no—
657#525—861no—
658C4×#41—431no—
659C2×C4×D4—431no—
660C2×C4×D4—861no—
661C2×#117—431no—
662C2×#117C2×D4311yescharacteristic, complemented
663#436—861no—
664#435—861no—
665#435—861no—
666C8×D4—861no—
667#423—431no—
668#421—24no—
669#421—864no—
670C2×#104—431no—
671C2×#104—431no—
672C2×#104—431no—
673C2×#104—431no—
674C2×#104—431no—
675C2×#104—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104C2×D4311yescharacteristic
679C2×#104C2×D4311yescharacteristic
680C2×#104C2×D4311yescharacteristic, complemented
681C2×#104C2×D4311yescharacteristic, complemented
682#407—431no—
683#407—431no—
684C4×M16—431no—
685#390—861no—
686#389—861no—
687#388—861no—
688#388—861no—
689C4×C4⋊C4—431no—
690C4×C22⋊C4—431no—
691C4×C22⋊C4—431no—
692C43—431no—
693#339—431no—
694#339—431no—
695#339—431no—
696#339—431no—
697C43#2243511yescharacteristic, complemented, Sylow
698C2×#41—21no—
699C2×#41—21no—
700C2×#41—22no—
701C2×#41—22no—
702C2×#41—41no—
703C2×#41—41no—
704C2×#41—431no—
705C2×#41—431no—
706C2×#41—431no—
707C2×#41—861no—
708C2×#41—861no—
709C2×#41—862no—
710C2×#41—862no—
711C2×#41—1721no—
712C2×#41—1721no—
713C2×#41C4×D4311yescharacteristic
714C2×#41C4×D4311yescharacteristic
715C2×#41C22×D4311yescharacteristic
716C2×#41C22×D4311yescharacteristic
717C22×Q8—431no—
718C22×Q8C4×D4311yescharacteristic
719C22×D4—21no—
720C22×D4—431no—
721C22×D4—431no—
722C22×D4—861no—
723C22×D4—861no—
724C22×D4C4×D4311yescharacteristic
725C23×C4—21no—
726C23×C4—431no—
727C23×C4—861no—
728C23×C4C22×D4311yescharacteristic
729C2×M16—21no—
730C2×M16—22no—
731C2×M16—41no—
732C2×M16—431no—
733C2×M16—431no—
734C2×M16—861no—
735C2×M16—862no—
736C2×M16—1721no—
737C2×M16C22×D4311yescharacteristic
738C2×M16C22×D4311yescharacteristic
739C22×C8—21no—
740C22×C8—861no—
741C4⋊Q8—431no—
742C4⋊Q8—861no—
743#127—431no—
744#127—861no—
745#124—431no—
746#124—431no—
747#124—861no—
748#124—861no—
749#123—861no—
750#123—861no—
751#123—861no—
752#123—861no—
753#123—861no—
754#123—861no—
755C22⋊Q8—431no—
756C22⋊Q8—431no—
757C22⋊Q8—431no—
758C22⋊Q8—431no—
759C22⋊Q8—861no—
760C22⋊Q8—861no—
761C22⋊Q8—861no—
762C22⋊Q8—861no—
763#121—431no—
764#121—431no—
765#121—431no—
766#121—431no—
767#121—861no—
768#121—861no—
769#121—861no—
770#121—861no—
771#121—861no—
772#121—861no—
773#121—861no—
774#121—861no—
775#121—861no—
776#121—861no—
777#120—861no—
778#120—861no—
779#120—861no—
780#120—861no—
781#120—861no—
782#120—861no—
783C4×Q8—431no—
784C4×Q8—431no—
785C4×D4—431no—
786C4×D4—431no—
787C4×D4—431no—
788C4×D4—431no—
789C4×D4—431no—
790C4×D4—431no—
791C4×D4—431no—
792C4×D4—431no—
793C4×D4—431no—
794C4×D4—431no—
795C4×D4—861no—
796C4×D4—861no—
797C4×D4—861no—
798C4×D4—861no—
799C4×D4—861no—
800C4×D4—861no—
801C4×D4—861no—
802C4×D4—861no—
803C4×D4—861no—
804C4×D4—861no—
805C4×D4—861no—
806C4×D4—861no—
807#117—22no—
808#117—41no—
809#117—431no—
810#117—861no—
811#117—862no—
812#117—1721no—
813C2×C4⋊C4—21no—
814C2×C4⋊C4—431no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C4⋊C4—861no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—431no—
820C2×C22⋊C4—431no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C22⋊C4—861no—
825C2×C22⋊C4—861no—
826C2×C42—431no—
827C2×C42—431no—
828C2×C42—431no—
829C2×C42—861no—
830C2×C42—861no—
831C2×C42—861no—
832C2×C42C22×D4311yescharacteristic
833C2×C42C22×D4311yescharacteristic
834C4⋊C8—861no—
835C4⋊C8—861no—
836#104—22no—
837#104—22no—
838#104—22no—
839#104—862no—
840#104—862no—
841#104—862no—
842#104—862no—
843#104—1721no—
844#104—1721no—
845#104—1721no—
846#104—1721no—
847#104C22⋊D4314yescomplemented
848C22⋊C8—861no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851C22⋊C8—861no—
852#97—861no—
853C4×C8—861no—
854#95—861no—
855#95—861no—
856#95—861no—
857C24—21no—
858C24—431no—
859C24—861no—
860C24D4×D4311yescharacteristic
861#41—21no—
862#41—21no—
863#41—22no—
864#41—22no—
865#41—21no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—42no—
870#41—42no—
871#41—41no—
872#41—41no—
873#41—42no—
874#41—42no—
875#41—862no—
876#41—862no—
877#41—861no—
878#41—861no—
879#41—861no—
880#41—861no—
881#41—1722no—
882#41—1722no—
883#41—1721no—
884#41—1722no—
885#41—1722no—
886#41—1721no—
887#41#1062189812yes—
888#41C2×C22⋊D4312yes—
889C2×Q8—21no—
890C2×Q8—22no—
891C2×Q8—41no—
892C2×Q8—431no—
893C2×Q8—861no—
894C2×Q8—862no—
895C2×Q8—1721no—
896C2×Q8C2×C4×D4311yescharacteristic
897C2×Q8C2×C4×D4311yescharacteristic
898C2×D4—21no—
899C2×D4—22no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—431no—
908C2×D4—431no—
909C2×D4—431no—
910C2×D4—431no—
911C2×D4—431no—
912C2×D4—861no—
913C2×D4—861no—
914C2×D4—861no—
915C2×D4—861no—
916C2×D4—862no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—861no—
923C2×D4—1721no—
924C2×D4—1722no—
925C2×D4—1722no—
926C2×D4—1722no—
927C2×D4—1724no—
928C2×D4C2×C4×D4311yescharacteristic
929C2×D4C2×C4×D4311yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—431no—
944C22×C4—431no—
945C22×C4—431no—
946C22×C4—431no—
947C22×C4—431no—
948C22×C4—431no—
949C22×C4—431no—
950C22×C4—861no—
951C22×C4—861no—
952C22×C4—861no—
953C22×C4—861no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—861no—
959C22×C4—861no—
960C22×C4—861no—
961C22×C4—861no—
962C22×C4—1722no—
963C22×C4—1722no—
964C22×C4C2×C4×D4311yescharacteristic
965C22×C4C2×C4×D4311yescharacteristic
966C22×C4D4×D4311yescharacteristic
967C22×C4D4×D4311yescharacteristic
968C22×C4D4×D4311yescharacteristic
969C22×C4C23×D4311yescharacteristic
970M16—21no—
971M16—21no—
972M16—21no—
973M16—42no—
974M16—861no—
975M16—861no—
976M16—861no—
977M16—861no—
978M16—1722no—
979M16C2×C22⋊D4312yescomplemented
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—42no—
983C2×C8—861no—
984C2×C8—861no—
985C2×C8—1722no—
986C4⋊C4—42no—
987C4⋊C4—431no—
988C4⋊C4—431no—
989C4⋊C4—431no—
990C4⋊C4—431no—
991C4⋊C4—431no—
992C4⋊C4—431no—
993C4⋊C4—861no—
994C4⋊C4—861no—
995C4⋊C4—861no—
996C4⋊C4—861no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—1722no—
1002C4⋊C4—1722no—
1003C22⋊C4—42no—
1004C22⋊C4—431no—
1005C22⋊C4—431no—
1006C22⋊C4—431no—
1007C22⋊C4—431no—
1008C22⋊C4—431no—
1009C22⋊C4—431no—
1010C22⋊C4—431no—
1011C22⋊C4—431no—
1012C22⋊C4—861no—
1013C22⋊C4—861no—
1014C22⋊C4—861no—
1015C22⋊C4—861no—
1016C22⋊C4—861no—
1017C22⋊C4—861no—
1018C22⋊C4—861no—
1019C22⋊C4—861no—
1020C22⋊C4—861no—
1021C22⋊C4—861no—
1022C22⋊C4—861no—
1023C22⋊C4—861no—
1024C22⋊C4—861no—
1025C22⋊C4—861no—
1026C22⋊C4—861no—
1027C22⋊C4—1722no—
1028C22⋊C4—1722no—
1029C22⋊C4—1722no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—431no—
1034C42—431no—
1035C42—431no—
1036C42—431no—
1037C42—861no—
1038C42—861no—
1039C42—861no—
1040C42—861no—
1041C42—861no—
1042C42—861no—
1043C42—861no—
1044C42—1722no—
1045C42—1722no—
1046C42C2×C22⋊D4312yescomplemented
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—41no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—81no—
1056C23—431no—
1057C23—431no—
1058C23—861no—
1059C23—861no—
1060C23—861no—
1061C23—3441no—
1062C23—1721no—
1063C23—1721no—
1064C23—1722no—
1065C23—1722no—
1066C23C22⋊C4×D4311yescharacteristic
1067C23C22⋊C4×D4311yescharacteristic
1068C23C2×D4×D4311yescharacteristic
1069Q8—21no—
1070Q8—21no—
1071Q8—21no—
1072Q8—42no—
1073Q8—861no—
1074Q8—861no—
1075Q8—1722no—
1076Q8C4×C22⋊D4312yes—
1077D4—22no—
1078D4—22no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—42no—
1083D4—42no—
1084D4—42no—
1085D4—41no—
1086D4—41no—
1087D4—862no—
1088D4—862no—
1089D4—861no—
1090D4—861no—
1091D4—3441no—
1092D4—3441no—
1093D4—3441no—
1094D4—1722no—
1095D4—1722no—
1096D4—1721no—
1097D4—1721no—
1098D4—1722no—
1099D4—1722no—
1100D4—1722no—
1101D4—1722no—
1102D4—1721no—
1103D4—1721no—
1104D4C4×C22⋊D4312yes—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—431no—
1131C2×C4—431no—
1132C2×C4—431no—
1133C2×C4—431no—
1134C2×C4—431no—
1135C2×C4—431no—
1136C2×C4—862no—
1137C2×C4—861no—
1138C2×C4—861no—
1139C2×C4—861no—
1140C2×C4—861no—
1141C2×C4—861no—
1142C2×C4—861no—
1143C2×C4—861no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—861no—
1147C2×C4—862no—
1148C2×C4—861no—
1149C2×C4—861no—
1150C2×C4—861no—
1151C2×C4—3441no—
1152C2×C4—1722no—
1153C2×C4—1722no—
1154C2×C4—1722no—
1155C2×C4—1721no—
1156C2×C4—1722no—
1157C2×C4—1721no—
1158C2×C4—1721no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1721no—
1163C2×C4—1721no—
1164C2×C4C22⋊C4×D4311yescharacteristic
1165C2×C4C22⋊C4×D4311yescharacteristic
1166C2×C4C22×C4×D4311yescharacteristic
1167C2×C4C2×D4×D4311yescharacteristic
1168C2×C4C22×C22⋊D4311yescharacteristic
1169C2×C4C2×#1062189811yescharacteristic
1170C2×C4#1306337011yescharacteristic
1171C2×C4#1306337011yescharacteristic
1172C8—22no—
1173C8—41no—
1174C8—1721no—
1175C8—1721no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—22no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—81no—
1191C22—81no—
1192C22—84no—
1193C22—861no—
1194C22—861no—
1195C22—861no—
1196C22—861no—
1197C22—861no—
1198C22—861no—
1199C22—3441no—
1200C22—3441no—
1201C22—3444no—
1202C22—1721no—
1203C22—1721no—
1204C22—1721no—
1205C22C2×C22⋊C4×D4311yescharacteristic
1206C22D4×C22⋊D4311yescharacteristic
1207C22#1458353911yescharacteristic
1208C4—21no—
1209C4—21no—
1210C4—22no—
1211C4—42no—
1212C4—41no—
1213C4—81no—
1214C4—432no—
1215C4—861no—
1216C4—861no—
1217C4—861no—
1218C4—861no—
1219C4—861no—
1220C4—3441no—
1221C4—1722no—
1222C4—1721no—
1223C4—1721no—
1224C4—1721no—
1225C4C2×C4×C22⋊D4311yescharacteristic
1226C4#1458337211yescharacteristic
1227C4D4×C22⋊D4311yescharacteristic
1228C4#1458353911yescharacteristic
1229C2—21no—
1230C2—21no—
1231C2—41no—
1232C2—41no—
1233C2—42no—
1234C2—81no—
1235C2—3441no—
1236C2—1721no—
1237C2—1721no—
1238C2C22⋊C4×C22⋊D4311yescharacteristic
1239C2#421×D4311yescharacteristic
1240C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43C22×C22⋊C4
prime radical#41×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43#22435
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. C2×#14582914C2semidirect
4. #19137054C2semidirect
5. #19135512C2semidirect
6. #19135421C2semidirect
7. #19135043C2semidirect
8. #19135040C2semidirect
9. #19134897C2semidirect
10. #19134894C2semidirect
11. #19134613C2semidirect
12. #19134539C2semidirect
13. #19134537C2semidirect
14. #104×Dic43C2semidirect
15. C2×C43×#421C2semidirect
17. C2×M16×D43C22semidirect
18. #14583568C4semidirect
19. Q8×C22⋊D43C4semidirect
20. #14583560C4semidirect
21. #14583556C4semidirect
23. #14583548C4semidirect
25. #14583543C4semidirect
27. #14583537C4semidirect
29. D4×C22⋊D43C4semidirect
39. C2×#13063282C22semidirect
44. #14582922C22semidirect
46. C2×#13063253C22semidirect
47. C2×#13063253C22semidirect
50. C2×#13063252C22semidirect
51. C2×#13063252C22semidirect
52. C2×#13063251C22semidirect
53. C2×#13063251C22semidirect
54. #14582863C22semidirect
55. #14582862C22semidirect
56. M16×Dic43C22semidirect
61. C4×Dic43⋊C4C22semidirect
62. C4×(C2×D43)⋊C4C22semidirect
63. C4×C22⋊Dic43C22semidirect
64. C42×Dic43C22semidirect
65. #14582660C22semidirect
66. #14582660C22semidirect
67. #14582659C22semidirect
68. #14582659C22semidirect
70. C22×M16×C43C22semidirect
71. C2×#117×C43C22semidirect
75. C2×#104×C43C22semidirect
76. C2×#104×C43C22semidirect
235. #104×C43D4semidirect
353. M16×C43C2×D4semidirect
362. C42×C43C2×D4semidirect
608. Dic43#421semidirect
612. C2×#421D43semidirect
639. C22×M16C2×D43semidirect
662. C2×#117C2×D43semidirect
680. C2×#104C2×D43semidirect
681. C2×#104C2×D43semidirect
697. C43#22435semidirect
847. #104C22⋊D43semidirect
979. M16C2×C22⋊D43semidirect
1046. C42C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊D432
M16×C22⋊D432
C2×#145829142
#191370542
#191355122
#191354212
#191350432
#191350402
#191348972
#191348942
#191346132
#191345392
#191345372
#104×Dic432
C2×C43×#4212
#2243543