Finite Group Databasebeta

← #25064207

Subgroups — #25064207

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143253C211yesmaximal, characteristic, complemented
2#19137455C211yesmaximal, characteristic, complemented
3#19133172C211yesmaximal, characteristic, complemented
4#19133155C211yesmaximal, characteristic, complemented
5#19133151C211yesmaximal, characteristic, complemented
6#19133142C211yesmaximal, characteristic, complemented
7#19133133C211yesmaximal, characteristic, complemented
8#19133124C211yesmaximal, characteristic, complemented
9#19133120C211yesmaximal, characteristic, complemented
10#19133103C211yesmaximal, characteristic, complemented
11#19133099C211yesmaximal, characteristic, complemented
12#19133090C211yesmaximal, characteristic, complemented
13#19133081C211yesmaximal, characteristic, complemented
14C2×#14582633C211yesmaximal, characteristic, complemented
15C43×#3494C211yesmaximal, characteristic
16#14582960—21no—
17#14582960—21no—
18#14582956C2211yescharacteristic, complemented
19#14582956C2211yescharacteristic, complemented
20#14582952C2211yescharacteristic, complemented
21#14582952C2211yescharacteristic, complemented
22#14582926—21no—
23#14582863C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582855—21no—
26#14582785—21no—
27#14582785—21no—
28#14582774—21no—
29#14582767C2211yescharacteristic, complemented
30#14582765C2211yescharacteristic, complemented
31#14582762C2211yescharacteristic
32C4×C4⋊Dic43C2211yescharacteristic, complemented
33C22⋊C4×Dic43—21no—
34#14582745C2211yescharacteristic, complemented
35C2×C43⋊#95C2211yescharacteristic
36#14582636C2211yescharacteristic, complemented
37#14582636C2211yescharacteristic, complemented
38#14582636C2211yescharacteristic, complemented
39#14582636C2211yescharacteristic, complemented
40#14582633C2211yescharacteristic
41#14582633C2211yescharacteristic
42#14582633C2211yescharacteristic
43#14582633C2211yescharacteristic
44#14582633C2211yescharacteristic
45#14582633C2211yescharacteristic
46#14582633C2211yescharacteristic
47#14582633C2211yescharacteristic
48#14582633C2211yescharacteristic, complemented
49#14582633C2211yescharacteristic, complemented
50#14582633C2211yescharacteristic, complemented
51#14582633C2211yescharacteristic, complemented
52C43×#555—21no—
53C43×#553—21no—
54C43×#553—21no—
55C43×#551—21no—
56C43×#551—21no—
57C43×#547—21no—
58C43×#546—21no—
59C43×#546—21no—
60C43×#544C411yescharacteristic, complemented
61C43×#542C411yescharacteristic, complemented
62C43×#542C411yescharacteristic, complemented
63C43×#540C411yescharacteristic, complemented
64C43×#540C411yescharacteristic, complemented
65C43×#535C411yescharacteristic, complemented
66C43×#532C2211yescharacteristic
67C43×#532C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#529C2211yescharacteristic
70C43×#525C2211yescharacteristic
71C2×#121×C43C2211yescharacteristic
72C43×#520C411yescharacteristic, complemented
73C43×#518C411yescharacteristic, complemented
74C2×#117×C43C2211yescharacteristic
75C23×Dic43—21no—
76C2×#10621877—21no—
77C22×C43⋊C8—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C4⋊(C43⋊C8)—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)C2311yescharacteristic
90C22⋊(C43⋊C8)C2311yescharacteristic
91C22⋊(C43⋊C8)C2311yescharacteristic
92C22⋊(C43⋊C8)C2311yescharacteristic
93#13063236—21no—
94#13063236—21no—
95C4×C43⋊C8—21no—
96C4×C43⋊C8—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95C2311yescharacteristic
104C43⋊#95C2311yescharacteristic
105C43⋊#95C2311yescharacteristic
106C43⋊#95C2311yescharacteristic
107C2×#41×C43—21no—
108C2×#41×C43—21no—
109C2×#41×C43C2×C411yescharacteristic
110C22×D4×C43—21no—
111C22×D4×C43C2×C411yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C4⋊Q8×C43—21no—
114C4⋊Q8×C43C2×C411yescharacteristic, complemented
115C4⋊Q8×C43C2×C411yescharacteristic, complemented
116#127×C43C2×C411yescharacteristic, complemented
117#127×C43C2×C411yescharacteristic, complemented
118#126×C43—21no—
119#126×C43—21no—
120#126×C43—21no—
121#126×C43—21no—
122#125×C43—21no—
123#125×C43C2×C411yescharacteristic, complemented
124#125×C43C2×C411yescharacteristic, complemented
125#124×C43—21no—
126#124×C43—21no—
127#124×C43—21no—
128#124×C43—21no—
129#124×C43C2×C411yescharacteristic, complemented
130#124×C43C2×C411yescharacteristic, complemented
131#123×C43—21no—
132#123×C43—21no—
133#123×C43—21no—
134#123×C43—21no—
135#123×C43—21no—
136#123×C43—21no—
137#123×C43—21no—
138#123×C43—21no—
139#123×C43—21no—
140C22⋊Q8×C43—21no—
141C22⋊Q8×C43—21no—
142C22⋊Q8×C43—21no—
143C22⋊Q8×C43—21no—
144C22⋊Q8×C43C2×C411yescharacteristic
145C22⋊Q8×C43C2311yescharacteristic
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—21no—
149#121×C43—21no—
150#121×C43—21no—
151#121×C43—21no—
152#121×C43—21no—
153#121×C43—21no—
154#121×C43—21no—
155#121×C43—21no—
156#121×C43C2×C411yescharacteristic
157#121×C43C2×C411yescharacteristic
158#121×C43C2×C411yescharacteristic
159#121×C43C2311yescharacteristic
160#121×C43C2311yescharacteristic
161#121×C43C2311yescharacteristic
162#120×C43—21no—
163#120×C43—21no—
164#120×C43—21no—
165C4×Q8×C43C2×C411yescharacteristic, complemented
166C4×Q8×C43C2×C411yescharacteristic, complemented
167C4×D4×C43—21no—
168C4×D4×C43—21no—
169C4×D4×C43—21no—
170C4×D4×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173C4×D4×C43—21no—
174C4×D4×C43—21no—
175C4×D4×C43—21no—
176C4×D4×C43—21no—
177C4×D4×C43C2×C411yescharacteristic, complemented
178C4×D4×C43C2×C411yescharacteristic, complemented
179C4×D4×C43C2×C411yescharacteristic, complemented
180C4×D4×C43C2×C411yescharacteristic, complemented
181C4×D4×C43C2×C411yescharacteristic, complemented
182C4×D4×C43C2×C411yescharacteristic, complemented
183#117×C43—21no—
184#117×C43—21no—
185#117×C43—21no—
186#117×C43C2×C411yescharacteristic
187#117×C43C2×C411yescharacteristic
188#117×C43C2×C411yescharacteristic
189#117×C43C2×C411yescharacteristic
190#117×C43C2×C411yescharacteristic
191#117×C43D411yescharacteristic
192#117×C43D411yescharacteristic
193#117×C43D411yescharacteristic
194#117×C43D411yescharacteristic
195C2×C4⋊C4×C43—21no—
196C2×C4⋊C4×C43C2×C411yescharacteristic
197C2×C4⋊C4×C43D411yescharacteristic
198C2×C4⋊C4×C43D411yescharacteristic
199C2×C22⋊C4×C43—21no—
200C2×C22⋊C4×C43—21no—
201C2×C22⋊C4×C43—21no—
202C2×C22⋊C4×C43D411yescharacteristic
203C2×C22⋊C4×C43D411yescharacteristic
204C2×C42×C43C2311yescharacteristic
205C2×C42×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208#41×C43—42no—
209#41×C43—81no—
210#41×C43—81no—
211#41×C43—81no—
212#41×C43—81no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43C22×C411yescharacteristic
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—42no—
229C2×D4×C43—81no—
230C2×D4×C43—81no—
231C2×D4×C43C22×C411yescharacteristic
232C2×D4×C43C22×C411yescharacteristic
233C2×D4×C43C22×C411yescharacteristic
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—42no—
243C22×C4×C43C22×C411yescharacteristic
244C22×C4×C43C22×C411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—42no—
258C22×Dic43—42no—
259C22×Dic43—81no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43C22⋊C411yescharacteristic
272C4⋊C4×C43C22⋊C411yescharacteristic
273C4⋊C4×C43C22⋊C411yescharacteristic
274C4⋊C4×C43C22⋊C411yescharacteristic
275C4⋊C4×C43C22⋊C411yescharacteristic
276C4⋊C4×C43C22⋊C411yescharacteristic
277C4⋊C4×C43C22⋊C411yescharacteristic
278C4⋊C4×C43C22⋊C411yescharacteristic
279C4⋊C4×C43C22×C411yescharacteristic
280C4⋊C4×C43C22×C411yescharacteristic
281C4⋊C4×C43C22×C411yescharacteristic
282C4⋊C4×C43C22×C411yescharacteristic
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43C22⋊C411yescharacteristic
303C22⋊C4×C43C22⋊C411yescharacteristic
304C22⋊C4×C43C22⋊C411yescharacteristic
305C22⋊C4×C43C22⋊C411yescharacteristic
306C22⋊C4×C43C22⋊C411yescharacteristic
307C22⋊C4×C43C22⋊C411yescharacteristic
308C22⋊C4×C43C22⋊C411yescharacteristic
309C22⋊C4×C43C22⋊C411yescharacteristic
310C42×C43—21no—
311C42×C43—21no—
312C42×C43—21no—
313C42×C43C22×C411yescharacteristic
314C42×C43C22×C411yescharacteristic
315C42×C43C22×C411yescharacteristic
316C42×C43C22×C411yescharacteristic
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C42×C43C2×D411yescharacteristic
320C42×C43C2×D411yescharacteristic
321C22⋊Dic43—42no—
322C4⋊Dic43—42no—
323C4⋊Dic43—81no—
324C4×Dic43—42no—
325C4×Dic43—81no—
326#10621877—42no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—42no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—22no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—41no—
339C23×C43—42no—
340C23×C43—81no—
341C23×C43—81no—
342C23×C43C2×C22⋊C411yescharacteristic
343C23×C43C2×C22⋊C411yescharacteristic
344C23×C43C22×D411yescharacteristic
345Q8×C43—41no—
346Q8×C43—81no—
347Q8×C43—81no—
348D4×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—42no—
352D4×C43—41no—
353D4×C43—41no—
354D4×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—42no—
359D4×C43—81no—
360D4×C43—81no—
361D4×C43—81no—
362D4×C43—81no—
363D4×C43—81no—
364D4×C43—81no—
365D4×C43—81no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—42no—
384C2×C4×C43—81no—
385C2×C4×C43—81no—
386C2×C4×C43—81no—
387C2×C4×C43—81no—
388C2×C4×C43—81no—
389C2×C4×C43—81no—
390C2×C4×C43—81no—
391C2×C4×C43C2×C22⋊C411yescharacteristic
392C2×C4×C43C2×C22⋊C411yescharacteristic
393C2×C4×C43C2×C22⋊C411yescharacteristic
394C2×C4×C43C2×C22⋊C411yescharacteristic
395C2×C4×C43C2×C22⋊C411yescharacteristic
396C2×C4×C43C2×C22⋊C411yescharacteristic
397C2×C4×C43C2×C22⋊C411yescharacteristic
398C2×C4×C43C2×C22⋊C411yescharacteristic
399C2×C4×C43C2×C22⋊C411yescharacteristic
400C2×C4×C43C2×C22⋊C411yescharacteristic
401C2×C4×C43C23×C411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C2×Dic43—22no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—84no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17604—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—162no—
440C22×C43#41012yes—
441C22×C43C22×C22⋊C411yescharacteristic
442C22×C43#57611yescharacteristic
443C22×C43#57711yescharacteristic
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—41no—
457C4×C43—41no—
458C4×C43—41no—
459C4×C43—41no—
460C4×C43—41no—
461Dic43—42no—
462Dic43—81no—
463Dic43—81no—
464Dic43—81no—
465#3494D4311yescharacteristic
466#2924—431no—
467#2343—431no—
468#1521—431no—
469#1517—431no—
470#1516—431no—
471#1514—431no—
472#1512—431no—
473#1510—431no—
474#1509—431no—
475#1505—431no—
476#1504—431no—
477#1502—431no—
478#1500—431no—
479C2×#327—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—22no—
483C2×C43—41no—
484C2×C43—81no—
485C2×C43—81no—
486C2×C43—81no—
487C2×C43C2×#41011yescharacteristic
488C2×C43#289711yescharacteristic
489C2×C43#290111yescharacteristic
490#555—21no—
491#553—21no—
492#553—21no—
493#551—21no—
494#551—21no—
495#547—21no—
496#546—21no—
497#546—21no—
498#544Dic4311yescharacteristic, complemented
499#542Dic4311yescharacteristic, complemented
500#542Dic4311yescharacteristic, complemented
501#540Dic4311yescharacteristic, complemented
502#540Dic4311yescharacteristic, complemented
503#535Dic4311yescharacteristic, complemented
504#532C2×D4311yescharacteristic
505#532C2×D4311yescharacteristic
506#529C2×D4311yescharacteristic
507#529C2×D4311yescharacteristic
508#525C2×D4311yescharacteristic
509C2×#121C2×D4311yescharacteristic
510#520Dic4311yescharacteristic, complemented
511#518Dic4311yescharacteristic, complemented
512C2×#117C2×D4311yescharacteristic
513#433—861no—
514#433—861no—
515#432—431no—
516#432—431no—
517#431—431no—
518#431—431no—
519#424—861no—
520#407—431no—
521C2×C22⋊C8—431no—
522#405—861no—
523#387—861no—
524#387—861no—
525#385—861no—
526#383—431no—
527#382—431no—
528#381—431no—
529C4×C4⋊C4—431no—
530C4×C22⋊C4—861no—
531#376—431no—
532C2×#95—431no—
533#328—431no—
534#328—431no—
535#328—431no—
536#328—431no—
537#327—431no—
538#327—431no—
539#327—431no—
540#327—431no—
541#327—431no—
542#327—431no—
543#327—431no—
544#327—431no—
545#327—431no—
546#327—431no—
547#327—431no—
548#327—431no—
549C43#1760411yescharacteristic, complemented, Sylow
550C2×#41—21no—
551C2×#41—21no—
552C2×#41C2×Dic4311yescharacteristic
553C22×D4—21no—
554C22×D4C2×Dic4311yescharacteristic
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×M16—861no—
558C22×C8—861no—
559C4⋊Q8—21no—
560C4⋊Q8C2×Dic4311yescharacteristic, complemented
561C4⋊Q8C2×Dic4311yescharacteristic, complemented
562#127C2×Dic4311yescharacteristic, complemented
563#127C2×Dic4311yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125C2×Dic4311yescharacteristic, complemented
570#125C2×Dic4311yescharacteristic, complemented
571#124—21no—
572#124—21no—
573#124—21no—
574#124—21no—
575#124C2×Dic4311yescharacteristic, complemented
576#124C2×Dic4311yescharacteristic, complemented
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8C2×Dic4311yescharacteristic
591C22⋊Q8C22×D4311yescharacteristic
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121C2×Dic4311yescharacteristic
603#121C2×Dic4311yescharacteristic
604#121C2×Dic4311yescharacteristic
605#121C22×D4311yescharacteristic
606#121C22×D4311yescharacteristic
607#121C22×D4311yescharacteristic
608#120—21no—
609#120—21no—
610#120—21no—
611C4×Q8C2×Dic4311yescharacteristic, complemented
612C4×Q8C2×Dic4311yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4C2×Dic4311yescharacteristic, complemented
624C4×D4C2×Dic4311yescharacteristic, complemented
625C4×D4C2×Dic4311yescharacteristic, complemented
626C4×D4C2×Dic4311yescharacteristic, complemented
627C4×D4C2×Dic4311yescharacteristic, complemented
628C4×D4C2×Dic4311yescharacteristic, complemented
629#117—21no—
630#117—21no—
631#117—21no—
632#117C2×Dic4311yescharacteristic
633#117C2×Dic4311yescharacteristic
634#117C2×Dic4311yescharacteristic
635#117C2×Dic4311yescharacteristic
636#117C2×Dic4311yescharacteristic
637#117C22⋊D4311yescharacteristic
638#117C22⋊D4311yescharacteristic
639#117C22⋊D4311yescharacteristic
640#117C22⋊D4311yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—861no—
643C2×C4⋊C4—861no—
644C2×C4⋊C4C2×Dic4311yescharacteristic
645C2×C4⋊C4C22⋊D4311yescharacteristic
646C2×C4⋊C4C22⋊D4311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4C22⋊D4311yescharacteristic
652C2×C22⋊C4C22⋊D4311yescharacteristic
653C2×C42—861no—
654C2×C42—861no—
655C2×C42C22×D4311yescharacteristic
656C2×C42C22×D4311yescharacteristic
657C4⋊C8—861no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C22⋊C8—431no—
662C22⋊C8—431no—
663C22⋊C8—431no—
664C22⋊C8—431no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667#97—861no—
668#97—861no—
669C4×C8—861no—
670C4×C8—861no—
671#95—431no—
672#95—431no—
673#95—431no—
674#95—431no—
675#95—861no—
676#95—861no—
677#95—861no—
678#95—861no—
679#95—861no—
680#95—861no—
681C24—21no—
682C24C2×C22⋊D4311yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×Dic4311yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C22×Dic4311yescharacteristic
707C2×D4C22×Dic4311yescharacteristic
708C2×D4C22×Dic4311yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—42no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—3441no—
723C22×C4—1722no—
724C22×C4—1722no—
725C22×C4C22×Dic4311yescharacteristic
726C22×C4C22×Dic4311yescharacteristic
727C22×C4C2×C22⋊D4311yescharacteristic
728C22×C4C2×C22⋊D4311yescharacteristic
729C22×C4C2×C22⋊D4311yescharacteristic
730C22×C4C2×C22⋊D4311yescharacteristic
731C22×C4C2×C22⋊D4311yescharacteristic
732C22×C4C2×C22⋊D4311yescharacteristic
733C22×C4C2×C22⋊D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—1722no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—1722no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—3441no—
753C4⋊C4—1722no—
754C4⋊C4C22⋊Dic4311yescharacteristic
755C4⋊C4C22⋊Dic4311yescharacteristic
756C4⋊C4C22⋊Dic4311yescharacteristic
757C4⋊C4C22⋊Dic4311yescharacteristic
758C4⋊C4C22⋊Dic4311yescharacteristic
759C4⋊C4C22⋊Dic4311yescharacteristic
760C4⋊C4C22⋊Dic4311yescharacteristic
761C4⋊C4C22⋊Dic4311yescharacteristic
762C4⋊C4C22×Dic4311yescharacteristic
763C4⋊C4C22×Dic4311yescharacteristic
764C4⋊C4C22×Dic4311yescharacteristic
765C4⋊C4C22×Dic4311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—1722no—
786C22⋊C4C22⋊Dic4311yescharacteristic
787C22⋊C4C22⋊Dic4311yescharacteristic
788C22⋊C4C22⋊Dic4311yescharacteristic
789C22⋊C4C22⋊Dic4311yescharacteristic
790C22⋊C4C22⋊Dic4311yescharacteristic
791C22⋊C4C22⋊Dic4311yescharacteristic
792C22⋊C4C22⋊Dic4311yescharacteristic
793C22⋊C4C22⋊Dic4311yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—3441no—
798C42—1722no—
799C42C22×Dic4311yescharacteristic
800C42C22×Dic4311yescharacteristic
801C42C22×Dic4311yescharacteristic
802C42C22×Dic4311yescharacteristic
803C42C2×C22⋊D4311yescharacteristic
804C42C2×C22⋊D4311yescharacteristic
805C42C2×C22⋊D4311yescharacteristic
806C42C2×C22⋊D4311yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊Dic4311yescharacteristic
818C23C2×C22⋊Dic4311yescharacteristic
819C23C22×C22⋊D4311yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—862no—
867C2×C4—3444no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4C2×C22⋊Dic4311yescharacteristic
880C2×C4C2×C22⋊Dic4311yescharacteristic
881C2×C4C2×C22⋊Dic4311yescharacteristic
882C2×C4C2×C22⋊Dic4311yescharacteristic
883C2×C4C2×C22⋊Dic4311yescharacteristic
884C2×C4C2×C22⋊Dic4311yescharacteristic
885C2×C4C2×C22⋊Dic4311yescharacteristic
886C2×C4C2×C22⋊Dic4311yescharacteristic
887C2×C4C2×C22⋊Dic4311yescharacteristic
888C2×C4C2×C22⋊Dic4311yescharacteristic
889C2×C4C23×Dic4311yescharacteristic
890C2×C4C22×C22⋊D4311yescharacteristic
891C8—1721no—
892C8—1721no—
893C8—1721no—
894C8—1721no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22#1458287312yes—
915C22C22×C22⋊Dic4311yescharacteristic
916C22#1458370211yescharacteristic
917C22#1458371011yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—3441no—
936C4—3441no—
937C4—3441no—
938C4—1722no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×#1458287311yescharacteristic
947C2#1914312111yescharacteristic
948C2#1914314211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3494C2
socleC22×C43C22×C22⋊C4
cosocleC22×C4×C43C24
hypercenter#3494D43
hypocenterC43#17604
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. #19143253C2semidirect
2. #19137455C2semidirect
3. #19133172C2semidirect
4. #19133155C2semidirect
5. #19133151C2semidirect
6. #19133142C2semidirect
7. #19133133C2semidirect
8. #19133124C2semidirect
9. #19133120C2semidirect
10. #19133103C2semidirect
11. #19133099C2semidirect
12. #19133090C2semidirect
13. #19133081C2semidirect
14. C2×#14582633C2semidirect
18. #14582956C22semidirect
19. #14582956C22semidirect
20. #14582952C22semidirect
21. #14582952C22semidirect
29. #14582767C22semidirect
30. #14582765C22semidirect
32. C4×C4⋊Dic43C22semidirect
34. #14582745C22semidirect
36. #14582636C22semidirect
37. #14582636C22semidirect
38. #14582636C22semidirect
39. #14582636C22semidirect
48. #14582633C22semidirect
49. #14582633C22semidirect
50. #14582633C22semidirect
51. #14582633C22semidirect
60. C43×#544C4semidirect
61. C43×#542C4semidirect
62. C43×#542C4semidirect
63. C43×#540C4semidirect
64. C43×#540C4semidirect
65. C43×#535C4semidirect
72. C43×#520C4semidirect
73. C43×#518C4semidirect
114. C4⋊Q8×C43C2×C4semidirect
115. C4⋊Q8×C43C2×C4semidirect
116. #127×C43C2×C4semidirect
117. #127×C43C2×C4semidirect
123. #125×C43C2×C4semidirect
124. #125×C43C2×C4semidirect
129. #124×C43C2×C4semidirect
130. #124×C43C2×C4semidirect
165. C4×Q8×C43C2×C4semidirect
166. C4×Q8×C43C2×C4semidirect
177. C4×D4×C43C2×C4semidirect
178. C4×D4×C43C2×C4semidirect
179. C4×D4×C43C2×C4semidirect
180. C4×D4×C43C2×C4semidirect
181. C4×D4×C43C2×C4semidirect
182. C4×D4×C43C2×C4semidirect
498. #544Dic43semidirect
499. #542Dic43semidirect
500. #542Dic43semidirect
501. #540Dic43semidirect
502. #540Dic43semidirect
503. #535Dic43semidirect
510. #520Dic43semidirect
511. #518Dic43semidirect
549. C43#17604semidirect
560. C4⋊Q8C2×Dic43semidirect
561. C4⋊Q8C2×Dic43semidirect
562. #127C2×Dic43semidirect
563. #127C2×Dic43semidirect
569. #125C2×Dic43semidirect
570. #125C2×Dic43semidirect
575. #124C2×Dic43semidirect
576. #124C2×Dic43semidirect
611. C4×Q8C2×Dic43semidirect
612. C4×Q8C2×Dic43semidirect
623. C4×D4C2×Dic43semidirect
624. C4×D4C2×Dic43semidirect
625. C4×D4C2×Dic43semidirect
626. C4×D4C2×Dic43semidirect
627. C4×D4C2×Dic43semidirect
628. C4×D4C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191432532
#191374552
#191331722
#191331552
#191331512
#191331422
#191331332
#191331242
#191331202
#191331032
#191330992
#191330902
#191330812
C2×#145826332
C43×#34942
#1760443