Finite Group Databasebeta

← #25112283

Subgroups — #25112283

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 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×#104×D43C211yesmaximal, characteristic, complemented
4#19137032C211yesmaximal, characteristic, complemented
5#19135512C211yesmaximal, characteristic, complemented
6#19135425C211yesmaximal, characteristic, complemented
7#19135043C211yesmaximal, characteristic, complemented
8#19135035C211yesmaximal, characteristic, complemented
9#19134897C211yesmaximal, characteristic, complemented
10#19134894C211yesmaximal, characteristic, complemented
11#19134613C211yesmaximal, characteristic, complemented
12#19134539C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134407C211yesmaximal, 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×C42×D43C2211yescharacteristic, complemented
40#14582975—21no—
41#14582970—21no—
42#14582968—21no—
43C8×C22⋊D43—21no—
44#14582922C2211yescharacteristic, complemented
45C2×#13063253C2211yescharacteristic, complemented
46C2×#13063253C2211yescharacteristic, complemented
47C2×#13063252C2211yescharacteristic
48C2×#13063252C2211yescharacteristic
49C2×#13063252C2211yescharacteristic, complemented
50C2×#13063252C2211yescharacteristic, complemented
51C2×#13063251C2211yescharacteristic, complemented
52C2×#13063251C2211yescharacteristic, complemented
53#104×D43—24no—
54#14582863C2211yescharacteristic, complemented
55#14582862C2211yescharacteristic, complemented
56M16×Dic43C2211yescharacteristic, complemented
57#14582787—21no—
58#14582780—21no—
59#14582775—21no—
60#14582770—21no—
61C4×Dic43⋊C4C2211yescharacteristic, complemented
62C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
63C4×C22⋊Dic43C2211yescharacteristic, complemented
64#14582745C2211yescharacteristic, 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×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96C2×#10621872—21no—
97M16×D43—22no—
98M16×D43—41no—
99C2×C8×D43—21no—
100#13063323—21no—
101#13063323C2×C411yescharacteristic, complemented
102#13063321—21no—
103#13063321C2×C411yescharacteristic, complemented
104#13063314—21no—
105#13063314C2×C411yescharacteristic, complemented
106#13063312—21no—
107#13063312C2×C411yescharacteristic, complemented
108#13063308—21no—
109#13063308—21no—
110#13063308—21no—
111#13063306—21no—
112#13063306—21no—
113#13063306—21no—
114#13063304—21no—
115#13063304—21no—
116#13063304C2×C411yescharacteristic, complemented
117#13063304C2×C411yescharacteristic, complemented
118#13063301—21no—
119#13063301—21no—
120#13063301C2×C411yescharacteristic
121#13063301C2×C411yescharacteristic
122#13063299—21no—
123#13063299—21no—
124#13063299C2×C411yescharacteristic, complemented
125#13063299C2×C411yescharacteristic, complemented
126#13063297—21no—
127#13063297—21no—
128#13063297—21no—
129#13063297—21no—
130#13063297—21no—
131#13063297—21no—
132#13063296—21no—
133#13063296—21no—
134#13063296C2×C411yescharacteristic
135#13063296C2×C411yescharacteristic
136#13063294—21no—
137#13063294—21no—
138#13063294—21no—
139#13063293—21no—
140#13063293—21no—
141#13063293—21no—
142Q8×Dic43C2×C411yescharacteristic, complemented
143Q8×Dic43C2×C411yescharacteristic, complemented
144D4×Dic43—21no—
145D4×Dic43—21no—
146D4×Dic43C2×C411yescharacteristic, complemented
147D4×Dic43C2×C411yescharacteristic, complemented
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⋊D43—21no—
158C4×C22⋊D43C2×C411yescharacteristic
159C4×C22⋊D43C2×C411yescharacteristic
160C4×C22⋊D43C2×C411yescharacteristic
161C4×C22⋊D43C2×C411yescharacteristic
162C4×C22⋊D43D411yescharacteristic
163C4×C22⋊D43D411yescharacteristic
164C4×C22⋊D43D411yescharacteristic
165C4×C22⋊D43D411yescharacteristic
166#13063284—21no—
167#13063284C2311yescharacteristic
168C2×Dic43⋊C4—21no—
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4D411yescharacteristic
171C2×C22⋊Dic43—21no—
172C2×C22⋊Dic43—21no—
173C2×C22⋊Dic43D411yescharacteristic
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4—21no—
176C2×(C2×D43)⋊C4D411yescharacteristic
177C2×C4×Dic43—21no—
178C2×C4×Dic43—21no—
179C2×C4×Dic43C2311yescharacteristic
180C2×C4×Dic43C2311yescharacteristic
181C2×C4×Dic43C2311yescharacteristic
182C42×D43—22no—
183C42×D43—41no—
184Dic43⋊C8—21no—
185Dic43⋊C8—21no—
186#13063253—22no—
187#13063253—41no—
188#13063252—22no—
189#13063252—22no—
190#13063252—41no—
191#13063252—41no—
192#13063251—22no—
193#13063251—41no—
194C22⋊(C43⋊C8)—21no—
195C22⋊(C43⋊C8)—21no—
196(C2×D43)⋊C8—21no—
197(C2×D43)⋊C8—21no—
198#13063235—21no—
199C8×Dic43—21no—
200C43⋊#95—21no—
201C43⋊#95—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, complemented
212C2×#41×C43C2×C411yescharacteristic, complemented
213C2×#41×C43C2311yescharacteristic
214C2×#41×C43C2311yescharacteristic
215C22×Q8×C43C2×C411yescharacteristic, complemented
216C22×D4×C43—21no—
217C22×D4×C43C2×C411yescharacteristic, complemented
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×D43—42no—
344C2×C4×D43—42no—
345C2×C4×D43—42no—
346C2×C4×D43C22×C411yescharacteristic
347C2×C4×D43C22×C411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×C4×D43C2×D411yescharacteristic
350C2×Dic86—21no—
351C2×Dic86C22×C411yescharacteristic
352M16×C43—21no—
353M16×C43—21no—
354M16×C43—21no—
355M16×C43—42no—
356M16×C43C2×D412yescomplemented
357C2×C8×C43—21no—
358C2×C8×C43—21no—
359C2×C8×C43—42no—
360C4⋊C4×C43—42no—
361C22⋊C4×C43—42no—
362C42×C43—21no—
363C42×C43—21no—
364C42×C43—21no—
365C42×C43C2×D412yescomplemented
366C22⋊Dic43—21no—
367C22⋊Dic43—21no—
368C22⋊Dic43—21no—
369C22⋊Dic43—21no—
370C22⋊Dic43—21no—
371C22⋊Dic43—21no—
372C22⋊Dic43—21no—
373C22⋊Dic43—21no—
374C22⋊Dic43—21no—
375C22⋊Dic43—42no—
376C22⋊Dic43C22⋊C411yescharacteristic
377C22⋊Dic43C22⋊C411yescharacteristic
378C22⋊Dic43C22⋊C411yescharacteristic
379C22⋊Dic43C22⋊C411yescharacteristic
380(C2×D43)⋊C4—21no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—21no—
383(C2×D43)⋊C4—21no—
384(C2×D43)⋊C4—21no—
385(C2×D43)⋊C4—21no—
386(C2×D43)⋊C4—42no—
387(C2×D43)⋊C4C22⋊C411yescharacteristic
388(C2×D43)⋊C4C22⋊C411yescharacteristic
389(C2×D43)⋊C4C22⋊C411yescharacteristic
390(C2×D43)⋊C4C22⋊C411yescharacteristic
391C4⋊Dic43—21no—
392C4⋊Dic43—21no—
393C4⋊Dic43C22×C411yescharacteristic
394C4⋊Dic43C22×C411yescharacteristic
395Dic43⋊C4—21no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401Dic43⋊C4—42no—
402Dic43⋊C4C22⋊C411yescharacteristic
403Dic43⋊C4C22⋊C411yescharacteristic
404Dic43⋊C4C22⋊C411yescharacteristic
405Dic43⋊C4C22⋊C411yescharacteristic
406C4×Dic43—21no—
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43—21no—
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—22no—
441C22×D43—21no—
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—21no—
515C2×Dic43—21no—
516C2×Dic43—21no—
517C2×Dic43—41no—
518C2×Dic43—41no—
519C2×Dic43—42no—
520C2×Dic43—42no—
521C2×Dic43—41no—
522C2×Dic43—41no—
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—48no—
547C4×D43—41no—
548C4×D43—41no—
549Dic86—21no—
550Dic86—21no—
551Dic86—42no—
552C8×C43—22no—
553C8×C43—41no—
554C43⋊C8—41no—
555C43⋊C8—41no—
556#22434—431nomaximal, Sylow
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—22no—
560C22×C43—21no—
561C22×C43—21no—
562C22×C43—21no—
563C22×C43—21no—
564C22×C43—21no—
565C22×C43—21no—
566C22×C43—41no—
567C22×C43—41no—
568C22×C43—41no—
569C22×C43—41no—
570C22×C43—41no—
571C22×C43—81no—
572C22×C43—81no—
573C22×C43—84no—
574C22×C43C22×C22⋊C411yescharacteristic
575C22×C43D4211yescharacteristic
576C22×C43#54611yescharacteristic
577C2×D43—21no—
578C2×D43—21no—
579C2×D43—21no—
580C2×D43—21no—
581C2×D43—21no—
582C2×D43—42no—
583C2×D43—42no—
584C2×D43—41no—
585C2×D43—41no—
586C2×D43—41no—
587C2×D43—84no—
588C2×D43#42112yescomplemented
589C4×C43—22no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—42no—
593C4×C43—41no—
594C4×C43—81no—
595C4×C43C2×C4×D411yescharacteristic
596C4×C43#51811yescharacteristic
597C4×C43D4211yescharacteristic
598C4×C43#54611yescharacteristic
599Dic43—21no—
600Dic43—21no—
601Dic43—21no—
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—42no—
606Dic43—41no—
607Dic43—41no—
608Dic43—41no—
609Dic43—81no—
610D4×#41—431no—
611D4×M16—431no—
612C2×#421D4311yescharacteristic, complemented
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963—431no—
617#1897—431no—
618#1896—431no—
619#1871—431no—
620#1871—431no—
621#1806—431no—
622#1789—431no—
623#1789—431no—
624#1759—431no—
625C2×C43—21no—
626C2×C43—21no—
627C2×C43—42no—
628C2×C43—41no—
629C2×C43—41no—
630C2×C43—81no—
631C2×C43D4×C22⋊C411yescharacteristic
632C2×C43C2×#42111yescharacteristic
633C2×C43#290111yescharacteristic
634D43—22no—
635D43—41no—
636D43—81no—
637C22×#41—431no—
638C22×#41C2×D4311yescharacteristic
639C22×M16—431no—
640C22×M16C2×D4311yescharacteristic, complemented
641#550—431no—
642D4×Q8—431no—
643#548—431no—
644#548—431no—
645#547—431no—
646#547—861no—
647#546—431no—
648#546—431no—
649#546—861no—
650#546—861no—
651D42—431no—
652D42—861no—
653#532—431no—
654#532—861no—
655#525—431no—
656#525—431no—
657#525—861no—
658#525—861no—
659C4×#41—431no—
660C2×C4×D4—431no—
661C2×C4×D4—861no—
662C2×#117C2×D4311yescharacteristic, complemented
663C22×C42—431no—
664#436—861no—
665#435—861no—
666#435—861no—
667C8×D4—861no—
668#423—431no—
669#421—24no—
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×#104—864no—
679C2×#104C2×D4311yescharacteristic
680C2×#104C2×D4311yescharacteristic
681C2×#104C2×D4311yescharacteristic, complemented
682C2×#104C2×D4311yescharacteristic, complemented
683#407—431no—
684#407—431no—
685C4×M16—431no—
686#388—861no—
687#387—861no—
688#386—861no—
689#385—861no—
690C4×C4⋊C4—431no—
691C4×C22⋊C4—431no—
692C4×C22⋊C4—431no—
693#376—431no—
694#339—431no—
695#339—431no—
696#339—431no—
697#339—431no—
698C43#2243411yescharacteristic, complemented, Sylow
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—22no—
702C2×#41—22no—
703C2×#41—41no—
704C2×#41—41no—
705C2×#41—431no—
706C2×#41—431no—
707C2×#41—431no—
708C2×#41—861no—
709C2×#41—861no—
710C2×#41—862no—
711C2×#41—862no—
712C2×#41—1721no—
713C2×#41—1721no—
714C2×#41C4×D4311yescharacteristic, complemented
715C2×#41C4×D4311yescharacteristic, complemented
716C2×#41C22×D4311yescharacteristic
717C2×#41C22×D4311yescharacteristic
718C22×Q8—431no—
719C22×Q8C4×D4311yescharacteristic, complemented
720C22×D4—21no—
721C22×D4—431no—
722C22×D4—431no—
723C22×D4—861no—
724C22×D4—861no—
725C22×D4C4×D4311yescharacteristic, complemented
726C23×C4—21no—
727C23×C4—431no—
728C23×C4—861no—
729C23×C4—861no—
730C23×C4C22×D4311yescharacteristic
731C2×M16—21no—
732C2×M16—22no—
733C2×M16—41no—
734C2×M16—431no—
735C2×M16—431no—
736C2×M16—861no—
737C2×M16—862no—
738C2×M16—1721no—
739C2×M16C22×D4311yescharacteristic
740C2×M16C22×D4311yescharacteristic
741C22×C8—21no—
742C22×C8—861no—
743C4⋊Q8—431no—
744C4⋊Q8—861no—
745#127—431no—
746#127—861no—
747#124—431no—
748#124—431no—
749#124—861no—
750#124—861no—
751#123—861no—
752#123—861no—
753#123—861no—
754#123—861no—
755#123—861no—
756#123—861no—
757C22⋊Q8—431no—
758C22⋊Q8—431no—
759C22⋊Q8—431no—
760C22⋊Q8—431no—
761C22⋊Q8—861no—
762C22⋊Q8—861no—
763C22⋊Q8—861no—
764C22⋊Q8—861no—
765#121—431no—
766#121—431no—
767#121—431no—
768#121—431no—
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#121—861no—
778#121—861no—
779#120—861no—
780#120—861no—
781#120—861no—
782#120—861no—
783#120—861no—
784#120—861no—
785C4×Q8—431no—
786C4×Q8—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—431no—
796C4×D4—431no—
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—
807C4×D4—861no—
808C4×D4—861no—
809#117—22no—
810#117—41no—
811#117—431no—
812#117—861no—
813C2×C4⋊C4—21no—
814C2×C4⋊C4—431no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4—861no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—431no—
819C2×C22⋊C4—431no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C42—431no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—861no—
828C2×C42—862no—
829C2×C42—861no—
830C2×C42—1721no—
831C2×C42C22×D4311yescharacteristic
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—861no—
834C4⋊C8—861no—
835#104—22no—
836#104—22no—
837#104—22no—
838#104—862no—
839#104—862no—
840#104—862no—
841#104—862no—
842#104—1721no—
843#104—1721no—
844#104—1721no—
845#104—1721no—
846#104C22⋊D4314yescomplemented
847C22⋊C8—861no—
848C22⋊C8—861no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851#97—861no—
852C4×C8—861no—
853#95—861no—
854#95—861no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—21no—
859C24—431no—
860C24—861no—
861C24D4×D4311yescharacteristic
862#41—21no—
863#41—21no—
864#41—22no—
865#41—22no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—42no—
871#41—42no—
872#41—41no—
873#41—41no—
874#41—42no—
875#41—42no—
876#41—862no—
877#41—862no—
878#41—861no—
879#41—861no—
880#41—861no—
881#41—861no—
882#41—1722no—
883#41—1722no—
884#41—1721no—
885#41—1722no—
886#41—1722no—
887#41—1721no—
888#41#1062189812yes—
889#41C2×C22⋊D4312yes—
890C2×Q8—21no—
891C2×Q8—22no—
892C2×Q8—41no—
893C2×Q8—431no—
894C2×Q8—861no—
895C2×Q8—862no—
896C2×Q8—1721no—
897C2×Q8C2×C4×D4311yescharacteristic
898C2×Q8C2×C4×D4311yescharacteristic
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—41no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—431no—
909C2×D4—431no—
910C2×D4—431no—
911C2×D4—431no—
912C2×D4—431no—
913C2×D4—861no—
914C2×D4—861no—
915C2×D4—861no—
916C2×D4—861no—
917C2×D4—862no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—861no—
923C2×D4—861no—
924C2×D4—1721no—
925C2×D4—1722no—
926C2×D4—1722no—
927C2×D4—1722no—
928C2×D4—1724no—
929C2×D4C2×C4×D4311yescharacteristic
930C2×D4C2×C4×D4311yescharacteristic
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—21no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—431no—
945C22×C4—431no—
946C22×C4—431no—
947C22×C4—431no—
948C22×C4—431no—
949C22×C4—431no—
950C22×C4—431no—
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—861no—
963C22×C4—1722no—
964C22×C4—1722no—
965C22×C4—1722no—
966C22×C4—1722no—
967C22×C4—1722no—
968C22×C4C2×C4×D4311yescharacteristic
969C22×C4C2×C4×D4311yescharacteristic
970C22×C4D4×D4311yescharacteristic
971C22×C4D4×D4311yescharacteristic
972C22×C4D4×D4311yescharacteristic
973C22×C4C23×D4311yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—42no—
978M16—861no—
979M16—861no—
980M16—861no—
981M16—861no—
982M16—1722no—
983M16C2×C22⋊D4312yescomplemented
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—42no—
987C2×C8—861no—
988C2×C8—861no—
989C2×C8—1722no—
990C4⋊C4—42no—
991C4⋊C4—431no—
992C4⋊C4—431no—
993C4⋊C4—431no—
994C4⋊C4—431no—
995C4⋊C4—431no—
996C4⋊C4—431no—
997C4⋊C4—861no—
998C4⋊C4—861no—
999C4⋊C4—861no—
1000C4⋊C4—861no—
1001C4⋊C4—861no—
1002C4⋊C4—861no—
1003C4⋊C4—861no—
1004C4⋊C4—861no—
1005C4⋊C4—1722no—
1006C22⋊C4—42no—
1007C22⋊C4—431no—
1008C22⋊C4—431no—
1009C22⋊C4—431no—
1010C22⋊C4—431no—
1011C22⋊C4—431no—
1012C22⋊C4—431no—
1013C22⋊C4—431no—
1014C22⋊C4—431no—
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—861no—
1028C22⋊C4—861no—
1029C22⋊C4—861no—
1030C22⋊C4—1722no—
1031C22⋊C4—1722no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—431no—
1036C42—431no—
1037C42—431no—
1038C42—431no—
1039C42—861no—
1040C42—861no—
1041C42—861no—
1042C42—861no—
1043C42—861no—
1044C42—861no—
1045C42—861no—
1046C42—1722no—
1047C42C2×C22⋊D4312yescomplemented
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—41no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—81no—
1057C23—431no—
1058C23—431no—
1059C23—862no—
1060C23—861no—
1061C23—861no—
1062C23—861no—
1063C23—3441no—
1064C23—1721no—
1065C23—1722no—
1066C23—1722no—
1067C23C22⋊C4×D4311yescharacteristic
1068C23C22⋊C4×D4311yescharacteristic
1069C23C2×D4×D4311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—42no—
1074Q8—861no—
1075Q8—861no—
1076Q8—1722no—
1077Q8C4×C22⋊D4312yes—
1078D4—22no—
1079D4—22no—
1080D4—21no—
1081D4—21no—
1082D4—21no—
1083D4—42no—
1084D4—42no—
1085D4—42no—
1086D4—41no—
1087D4—41no—
1088D4—862no—
1089D4—862no—
1090D4—861no—
1091D4—861no—
1092D4—3441no—
1093D4—3441no—
1094D4—3441no—
1095D4—1722no—
1096D4—1721no—
1097D4—1721no—
1098D4—1722no—
1099D4—1722no—
1100D4—1722no—
1101D4—1722no—
1102D4—1722no—
1103D4—1721no—
1104D4—1721no—
1105D4C4×C22⋊D4312yes—
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—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—431no—
1132C2×C4—431no—
1133C2×C4—431no—
1134C2×C4—431no—
1135C2×C4—431no—
1136C2×C4—431no—
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—1728no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1722no—
1158C2×C4—1722no—
1159C2×C4—1721no—
1160C2×C4—1721no—
1161C2×C4—1721no—
1162C2×C4—1721no—
1163C2×C4—1721no—
1164C2×C4—1721no—
1165C2×C4—1721no—
1166C2×C4C22⋊C4×D4311yescharacteristic
1167C2×C4C22⋊C4×D4311yescharacteristic
1168C2×C4C22×C4×D4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C22×C22⋊D4311yescharacteristic
1171C2×C4C2×#1062189811yescharacteristic
1172C2×C4#1306337011yescharacteristic
1173C2×C4#1306337011yescharacteristic
1174C8—22no—
1175C8—41no—
1176C8—1721no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—22no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—81no—
1193C22—81no—
1194C22—84no—
1195C22—432no—
1196C22—861no—
1197C22—861no—
1198C22—861no—
1199C22—861no—
1200C22—861no—
1201C22—3444no—
1202C22—1722no—
1203C22—1722no—
1204C22—1721no—
1205C22—1721no—
1206C22—1721no—
1207C22C2×C22⋊C4×D4311yescharacteristic
1208C22D4×C22⋊D4311yescharacteristic
1209C22#1458353911yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—42no—
1214C4—41no—
1215C4—81no—
1216C4—861no—
1217C4—861no—
1218C4—861no—
1219C4—861no—
1220C4—861no—
1221C4—861no—
1222C4—3441no—
1223C4—1722no—
1224C4—1721no—
1225C4—1721no—
1226C4—1721no—
1227C4C2×C4×C22⋊D4311yescharacteristic
1228C4#1458337211yescharacteristic
1229C4D4×C22⋊D4311yescharacteristic
1230C4#1458353911yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—41no—
1234C2—41no—
1235C2—42no—
1236C2—81no—
1237C2—862no—
1238C2—3441no—
1239C2—1721no—
1240C2C22⋊C4×C22⋊D4311yescharacteristic
1241C2#421×D4311yescharacteristic
1242C2#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#22434
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×#104×D43C2semidirect
4. #19137032C2semidirect
5. #19135512C2semidirect
6. #19135425C2semidirect
7. #19135043C2semidirect
8. #19135035C2semidirect
9. #19134897C2semidirect
10. #19134894C2semidirect
11. #19134613C2semidirect
12. #19134539C2semidirect
13. #19134537C2semidirect
14. #19134407C2semidirect
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×C42×D43C22semidirect
44. #14582922C22semidirect
45. C2×#13063253C22semidirect
46. C2×#13063253C22semidirect
49. C2×#13063252C22semidirect
50. C2×#13063252C22semidirect
51. C2×#13063251C22semidirect
52. C2×#13063251C22semidirect
54. #14582863C22semidirect
55. #14582862C22semidirect
56. M16×Dic43C22semidirect
61. C4×Dic43⋊C4C22semidirect
62. C4×(C2×D43)⋊C4C22semidirect
63. C4×C22⋊Dic43C22semidirect
64. #14582745C22semidirect
65. #14582660C22semidirect
66. #14582660C22semidirect
67. #14582659C22semidirect
68. #14582659C22semidirect
70. C22×M16×C43C22semidirect
71. C2×#117×C43C22semidirect
75. C2×#104×C43C22semidirect
76. C2×#104×C43C22semidirect
101. #13063323C2×C4semidirect
103. #13063321C2×C4semidirect
105. #13063314C2×C4semidirect
107. #13063312C2×C4semidirect
116. #13063304C2×C4semidirect
117. #13063304C2×C4semidirect
124. #13063299C2×C4semidirect
125. #13063299C2×C4semidirect
142. Q8×Dic43C2×C4semidirect
143. Q8×Dic43C2×C4semidirect
146. D4×Dic43C2×C4semidirect
147. D4×Dic43C2×C4semidirect
211. C2×#41×C43C2×C4semidirect
212. C2×#41×C43C2×C4semidirect
215. C22×Q8×C43C2×C4semidirect
217. C22×D4×C43C2×C4semidirect
235. #104×C43D4semidirect
356. M16×C43C2×D4semidirect
365. C42×C43C2×D4semidirect
588. C2×D43#421semidirect
612. C2×#421D43semidirect
640. C22×M16C2×D43semidirect
662. C2×#117C2×D43semidirect
681. C2×#104C2×D43semidirect
682. C2×#104C2×D43semidirect
698. C43#22434semidirect
714. C2×#41C4×D43semidirect
715. C2×#41C4×D43semidirect
719. C22×Q8C4×D43semidirect
725. C22×D4C4×D43semidirect
846. #104C22⋊D43semidirect
983. M16C2×C22⋊D43semidirect
1047. 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×#104×D432
#191370322
#191355122
#191354252
#191350432
#191350352
#191348972
#191348942
#191346132
#191345392
#191345372
#191344072
C2×C43×#4212
#2243443