Finite Group Databasebeta

← #35372014

Subgroups — #35372014

Order 21248.

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#24916121C211yesmaximal, characteristic, complemented
2#24910323C211yesmaximal, characteristic, complemented
3#24906040C211yesmaximal, characteristic, complemented
4#24906023C211yesmaximal, characteristic, complemented
5#24906019C211yesmaximal, characteristic, complemented
6#24906010C211yesmaximal, characteristic, complemented
7#24906001C211yesmaximal, characteristic, complemented
8#24905992C211yesmaximal, characteristic, complemented
9#24905988C211yesmaximal, characteristic, complemented
10#24905971C211yesmaximal, characteristic, complemented
11#24905967C211yesmaximal, characteristic, complemented
12#24905958C211yesmaximal, characteristic, complemented
13#24905949C211yesmaximal, characteristic, complemented
14C2×#19127435C211yesmaximal, characteristic, complemented
15C83×#3494C211yesmaximal, characteristic
16#19127762—21no—
17#19127762—21no—
18#19127758C2211yescharacteristic, complemented
19#19127758C2211yescharacteristic, complemented
20#19127754C2211yescharacteristic, complemented
21#19127754C2211yescharacteristic, complemented
22#19127728—21no—
23#19127665C2211yescharacteristic
24C2×C22⋊(C83⋊C8)C2211yescharacteristic
25#19127657—21no—
26#19127587—21no—
27#19127587—21no—
28#19127576—21no—
29#19127569C2211yescharacteristic, complemented
30#19127567C2211yescharacteristic, complemented
31#19127564C2211yescharacteristic
32C4×C4⋊Dic83C2211yescharacteristic, complemented
33C22⋊C4×Dic83—21no—
34#19127547C2211yescharacteristic, complemented
35C2×C83⋊#95C2211yescharacteristic
36#19127438C2211yescharacteristic, complemented
37#19127438C2211yescharacteristic, complemented
38#19127438C2211yescharacteristic, complemented
39#19127438C2211yescharacteristic, complemented
40#19127435C2211yescharacteristic
41#19127435C2211yescharacteristic
42#19127435C2211yescharacteristic
43#19127435C2211yescharacteristic
44#19127435C2211yescharacteristic
45#19127435C2211yescharacteristic
46#19127435C2211yescharacteristic
47#19127435C2211yescharacteristic
48#19127435C2211yescharacteristic, complemented
49#19127435C2211yescharacteristic, complemented
50#19127435C2211yescharacteristic, complemented
51#19127435C2211yescharacteristic, complemented
52#555×C83—21no—
53#553×C83—21no—
54#553×C83—21no—
55#551×C83—21no—
56#551×C83—21no—
57#547×C83—21no—
58#546×C83—21no—
59#546×C83—21no—
60#544×C83C411yescharacteristic, complemented
61#542×C83C411yescharacteristic, complemented
62#542×C83C411yescharacteristic, complemented
63#540×C83C411yescharacteristic, complemented
64#540×C83C411yescharacteristic, complemented
65#535×C83C411yescharacteristic, complemented
66#532×C83C2211yescharacteristic
67#532×C83C2211yescharacteristic
68#529×C83C2211yescharacteristic
69#529×C83C2211yescharacteristic
70#525×C83C2211yescharacteristic
71C2×#121×C83C2211yescharacteristic
72#520×C83C411yescharacteristic, complemented
73#518×C83C411yescharacteristic, complemented
74C2×#117×C83C2211yescharacteristic
75C23×Dic83—21no—
76C2×#13050574—21no—
77C22×C83⋊C8—21no—
78C2×C4⋊Dic83—21no—
79C2×C4⋊Dic83—21no—
80C2×C22⋊Dic83—21no—
81C2×C4×Dic83—21no—
82C2×C4×Dic83—21no—
83C4⋊(C83⋊C8)—21no—
84C4⋊(C83⋊C8)—21no—
85C4⋊(C83⋊C8)—21no—
86C4⋊(C83⋊C8)—21no—
87C22⋊(C83⋊C8)—21no—
88C22⋊(C83⋊C8)—21no—
89C22⋊(C83⋊C8)C2311yescharacteristic
90C22⋊(C83⋊C8)C2311yescharacteristic
91C22⋊(C83⋊C8)C2311yescharacteristic
92C22⋊(C83⋊C8)C2311yescharacteristic
93#14581703—21no—
94#14581703—21no—
95C4×C83⋊C8—21no—
96C4×C83⋊C8—21no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95C2311yescharacteristic
104C83⋊#95C2311yescharacteristic
105C83⋊#95C2311yescharacteristic
106C83⋊#95C2311yescharacteristic
107C2×#41×C83—21no—
108C2×#41×C83—21no—
109C2×#41×C83C2×C411yescharacteristic
110C22×D4×C83—21no—
111C22×D4×C83C2×C411yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C4⋊Q8×C83—21no—
114C4⋊Q8×C83C2×C411yescharacteristic, complemented
115C4⋊Q8×C83C2×C411yescharacteristic, complemented
116#127×C83C2×C411yescharacteristic, complemented
117#127×C83C2×C411yescharacteristic, complemented
118#126×C83—21no—
119#126×C83—21no—
120#126×C83—21no—
121#126×C83—21no—
122#125×C83—21no—
123#125×C83C2×C411yescharacteristic, complemented
124#125×C83C2×C411yescharacteristic, complemented
125#124×C83—21no—
126#124×C83—21no—
127#124×C83—21no—
128#124×C83—21no—
129#124×C83C2×C411yescharacteristic, complemented
130#124×C83C2×C411yescharacteristic, complemented
131#123×C83—21no—
132#123×C83—21no—
133#123×C83—21no—
134#123×C83—21no—
135#123×C83—21no—
136#123×C83—21no—
137#123×C83—21no—
138#123×C83—21no—
139#123×C83—21no—
140C22⋊Q8×C83—21no—
141C22⋊Q8×C83—21no—
142C22⋊Q8×C83—21no—
143C22⋊Q8×C83—21no—
144C22⋊Q8×C83C2×C411yescharacteristic
145C22⋊Q8×C83C2311yescharacteristic
146#121×C83—21no—
147#121×C83—21no—
148#121×C83—21no—
149#121×C83—21no—
150#121×C83—21no—
151#121×C83—21no—
152#121×C83—21no—
153#121×C83—21no—
154#121×C83—21no—
155#121×C83—21no—
156#121×C83C2×C411yescharacteristic
157#121×C83C2×C411yescharacteristic
158#121×C83C2×C411yescharacteristic
159#121×C83C2311yescharacteristic
160#121×C83C2311yescharacteristic
161#121×C83C2311yescharacteristic
162#120×C83—21no—
163#120×C83—21no—
164#120×C83—21no—
165C4×Q8×C83C2×C411yescharacteristic, complemented
166C4×Q8×C83C2×C411yescharacteristic, complemented
167C4×D4×C83—21no—
168C4×D4×C83—21no—
169C4×D4×C83—21no—
170C4×D4×C83—21no—
171C4×D4×C83—21no—
172C4×D4×C83—21no—
173C4×D4×C83—21no—
174C4×D4×C83—21no—
175C4×D4×C83—21no—
176C4×D4×C83—21no—
177C4×D4×C83C2×C411yescharacteristic, complemented
178C4×D4×C83C2×C411yescharacteristic, complemented
179C4×D4×C83C2×C411yescharacteristic, complemented
180C4×D4×C83C2×C411yescharacteristic, complemented
181C4×D4×C83C2×C411yescharacteristic, complemented
182C4×D4×C83C2×C411yescharacteristic, complemented
183#117×C83—21no—
184#117×C83—21no—
185#117×C83—21no—
186#117×C83C2×C411yescharacteristic
187#117×C83C2×C411yescharacteristic
188#117×C83C2×C411yescharacteristic
189#117×C83C2×C411yescharacteristic
190#117×C83C2×C411yescharacteristic
191#117×C83D411yescharacteristic
192#117×C83D411yescharacteristic
193#117×C83D411yescharacteristic
194#117×C83D411yescharacteristic
195C2×C4⋊C4×C83—21no—
196C2×C4⋊C4×C83C2×C411yescharacteristic
197C2×C4⋊C4×C83D411yescharacteristic
198C2×C4⋊C4×C83D411yescharacteristic
199C2×C22⋊C4×C83—21no—
200C2×C22⋊C4×C83—21no—
201C2×C22⋊C4×C83—21no—
202C2×C22⋊C4×C83D411yescharacteristic
203C2×C22⋊C4×C83D411yescharacteristic
204C2×C42×C83C2311yescharacteristic
205C2×C42×C83C2311yescharacteristic
206C22×Dic83—21no—
207C22×Dic83—21no—
208C22×Dic83—21no—
209C22×Dic83—21no—
210C22×Dic83—42no—
211C22×Dic83—42no—
212C22×Dic83—81no—
213#13050574—42no—
214C2×C83⋊C8—21no—
215C2×C83⋊C8—21no—
216C2×C83⋊C8—21no—
217C2×C83⋊C8—21no—
218C2×C83⋊C8—42no—
219C4⋊Dic83—42no—
220C4⋊Dic83—81no—
221C22⋊Dic83—42no—
222C4×Dic83—42no—
223C4×Dic83—81no—
224C24×C83—21no—
225C24×C83C2×D411yescharacteristic
226#41×C83—42no—
227#41×C83—81no—
228#41×C83—81no—
229#41×C83—81no—
230#41×C83—81no—
231C2×Q8×C83—21no—
232C2×Q8×C83—21no—
233C2×Q8×C83C22×C411yescharacteristic
234C2×D4×C83—21no—
235C2×D4×C83—21no—
236C2×D4×C83—21no—
237C2×D4×C83—21no—
238C2×D4×C83—21no—
239C2×D4×C83—21no—
240C2×D4×C83—21no—
241C2×D4×C83—21no—
242C2×D4×C83—21no—
243C2×D4×C83—21no—
244C2×D4×C83—21no—
245C2×D4×C83—21no—
246C2×D4×C83—42no—
247C2×D4×C83—81no—
248C2×D4×C83—81no—
249C2×D4×C83C22×C411yescharacteristic
250C2×D4×C83C22×C411yescharacteristic
251C2×D4×C83C22×C411yescharacteristic
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—42no—
261C22×C4×C83C22×C411yescharacteristic
262C22×C4×C83C22×C411yescharacteristic
263C22×C4×C83C2×D411yescharacteristic
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D411yescharacteristic
266C22×C4×C83C2×D411yescharacteristic
267C22×C4×C83C2×D411yescharacteristic
268C22×C4×C83C2×D411yescharacteristic
269C22×C4×C83C2×D411yescharacteristic
270C22×C4×C83C2411yescharacteristic
271C4⋊C4×C83—21no—
272C4⋊C4×C83—21no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83C22⋊C411yescharacteristic
283C4⋊C4×C83C22⋊C411yescharacteristic
284C4⋊C4×C83C22⋊C411yescharacteristic
285C4⋊C4×C83C22⋊C411yescharacteristic
286C4⋊C4×C83C22⋊C411yescharacteristic
287C4⋊C4×C83C22⋊C411yescharacteristic
288C4⋊C4×C83C22⋊C411yescharacteristic
289C4⋊C4×C83C22⋊C411yescharacteristic
290C4⋊C4×C83C22×C411yescharacteristic
291C4⋊C4×C83C22×C411yescharacteristic
292C4⋊C4×C83C22×C411yescharacteristic
293C4⋊C4×C83C22×C411yescharacteristic
294C22⋊C4×C83—21no—
295C22⋊C4×C83—21no—
296C22⋊C4×C83—21no—
297C22⋊C4×C83—21no—
298C22⋊C4×C83—21no—
299C22⋊C4×C83—21no—
300C22⋊C4×C83—21no—
301C22⋊C4×C83—21no—
302C22⋊C4×C83—21no—
303C22⋊C4×C83—21no—
304C22⋊C4×C83—21no—
305C22⋊C4×C83—21no—
306C22⋊C4×C83—21no—
307C22⋊C4×C83—21no—
308C22⋊C4×C83—21no—
309C22⋊C4×C83—21no—
310C22⋊C4×C83—21no—
311C22⋊C4×C83—21no—
312C22⋊C4×C83—21no—
313C22⋊C4×C83C22⋊C411yescharacteristic
314C22⋊C4×C83C22⋊C411yescharacteristic
315C22⋊C4×C83C22⋊C411yescharacteristic
316C22⋊C4×C83C22⋊C411yescharacteristic
317C22⋊C4×C83C22⋊C411yescharacteristic
318C22⋊C4×C83C22⋊C411yescharacteristic
319C22⋊C4×C83C22⋊C411yescharacteristic
320C22⋊C4×C83C22⋊C411yescharacteristic
321C42×C83—21no—
322C42×C83—21no—
323C42×C83—21no—
324C42×C83C22×C411yescharacteristic
325C42×C83C22×C411yescharacteristic
326C42×C83C22×C411yescharacteristic
327C42×C83C22×C411yescharacteristic
328C42×C83C2×D411yescharacteristic
329C42×C83C2×D411yescharacteristic
330C42×C83C2×D411yescharacteristic
331C42×C83C2×D411yescharacteristic
332C23×C83—21no—
333C23×C83—21no—
334C23×C83—22no—
335C23×C83—21no—
336C23×C83—21no—
337C23×C83—21no—
338C23×C83—41no—
339C23×C83—42no—
340C23×C83—81no—
341C23×C83—81no—
342C23×C83C2×C22⋊C411yescharacteristic
343C23×C83C2×C22⋊C411yescharacteristic
344C23×C83C22×D411yescharacteristic
345Q8×C83—41no—
346Q8×C83—81no—
347Q8×C83—81no—
348D4×C83—41no—
349D4×C83—41no—
350D4×C83—41no—
351D4×C83—42no—
352D4×C83—41no—
353D4×C83—41no—
354D4×C83—41no—
355D4×C83—41no—
356D4×C83—41no—
357D4×C83—41no—
358D4×C83—42no—
359D4×C83—81no—
360D4×C83—81no—
361D4×C83—81no—
362D4×C83—81no—
363D4×C83—81no—
364D4×C83—81no—
365D4×C83—81no—
366C2×C4×C83—21no—
367C2×C4×C83—21no—
368C2×C4×C83—21no—
369C2×C4×C83—21no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—21no—
373C2×C4×C83—21no—
374C2×C4×C83—21no—
375C2×C4×C83—21no—
376C2×C4×C83—21no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—42no—
384C2×C4×C83—81no—
385C2×C4×C83—81no—
386C2×C4×C83—81no—
387C2×C4×C83—81no—
388C2×C4×C83—81no—
389C2×C4×C83—81no—
390C2×C4×C83—81no—
391C2×C4×C83C2×C22⋊C411yescharacteristic
392C2×C4×C83C2×C22⋊C411yescharacteristic
393C2×C4×C83C2×C22⋊C411yescharacteristic
394C2×C4×C83C2×C22⋊C411yescharacteristic
395C2×C4×C83C2×C22⋊C411yescharacteristic
396C2×C4×C83C2×C22⋊C411yescharacteristic
397C2×C4×C83C2×C22⋊C411yescharacteristic
398C2×C4×C83C2×C22⋊C411yescharacteristic
399C2×C4×C83C2×C22⋊C411yescharacteristic
400C2×C4×C83C2×C22⋊C411yescharacteristic
401C2×C4×C83C23×C411yescharacteristic
402C2×C4×C83C22×D411yescharacteristic
403C2×Dic83—22no—
404C2×Dic83—41no—
405C2×Dic83—41no—
406C2×Dic83—41no—
407C2×Dic83—41no—
408C2×Dic83—41no—
409C2×Dic83—41no—
410C2×Dic83—41no—
411C2×Dic83—41no—
412C2×Dic83—41no—
413C2×Dic83—41no—
414C2×Dic83—41no—
415C2×Dic83—84no—
416C83⋊C8—41no—
417C83⋊C8—41no—
418C83⋊C8—41no—
419C83⋊C8—41no—
420C22×C83—21no—
421C22×C83—21no—
422C22×C83—21no—
423C22×C83—21no—
424C22×C83—21no—
425C22×C83—21no—
426C22×C83—21no—
427C22×C83—42no—
428C22×C83—42no—
429C22×C83—41no—
430C22×C83—41no—
431C22×C83—41no—
432C22×C83—41no—
433C22×C83—41no—
434C22×C83—41no—
435C22×C83—41no—
436C22×C83—41no—
437C22×C83—41no—
438C22×C83—162no—
439C22×C83#41012yes—
440C22×C83C22×C22⋊C411yescharacteristic
441C22×C83#57611yescharacteristic
442C22×C83#57711yescharacteristic
443C4×C83—21no—
444C4×C83—21no—
445C4×C83—21no—
446C4×C83—21no—
447C4×C83—21no—
448C4×C83—21no—
449C4×C83—21no—
450C4×C83—21no—
451C4×C83—21no—
452C4×C83—21no—
453C4×C83—21no—
454C4×C83—21no—
455C4×C83—41no—
456C4×C83—41no—
457C4×C83—41no—
458C4×C83—41no—
459C4×C83—41no—
460Dic83—42no—
461Dic83—81no—
462Dic83—81no—
463Dic83—81no—
464#17604—831nomaximal, Sylow
465C2×C83—21no—
466C2×C83—21no—
467C2×C83—22no—
468C2×C83—41no—
469C2×C83—81no—
470C2×C83—81no—
471C2×C83—81no—
472C2×C83C2×#41011yescharacteristic
473C2×C83#289711yescharacteristic
474C2×C83#290111yescharacteristic
475#3494D8311yescharacteristic
476#2924—831no—
477#2343—831no—
478#1521—831no—
479#1517—831no—
480#1516—831no—
481#1514—831no—
482#1512—831no—
483#1510—831no—
484#1509—831no—
485#1505—831no—
486#1504—831no—
487#1502—831no—
488#1500—831no—
489C2×#327—831no—
490C83#1760411yescharacteristic, complemented, Sylow
491#555—21no—
492#553—21no—
493#553—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#546—21no—
499#544Dic8311yescharacteristic, complemented
500#542Dic8311yescharacteristic, complemented
501#542Dic8311yescharacteristic, complemented
502#540Dic8311yescharacteristic, complemented
503#540Dic8311yescharacteristic, complemented
504#535Dic8311yescharacteristic, complemented
505#532C2×D8311yescharacteristic
506#532C2×D8311yescharacteristic
507#529C2×D8311yescharacteristic
508#529C2×D8311yescharacteristic
509#525C2×D8311yescharacteristic
510C2×#121C2×D8311yescharacteristic
511#520Dic8311yescharacteristic, complemented
512#518Dic8311yescharacteristic, complemented
513C2×#117C2×D8311yescharacteristic
514#433—1661no—
515#433—1661no—
516#432—831no—
517#432—831no—
518#431—831no—
519#431—831no—
520#424—1661no—
521#407—831no—
522C2×C22⋊C8—831no—
523#405—1661no—
524#387—1661no—
525#387—1661no—
526#385—1661no—
527#383—831no—
528#382—831no—
529#381—831no—
530C4×C4⋊C4—831no—
531C4×C22⋊C4—1661no—
532#376—831no—
533C2×#95—831no—
534#328—831no—
535#328—831no—
536#328—831no—
537#328—831no—
538#327—831no—
539#327—831no—
540#327—831no—
541#327—831no—
542#327—831no—
543#327—831no—
544#327—831no—
545#327—831no—
546#327—831no—
547#327—831no—
548#327—831no—
549#327—831no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41C2×Dic8311yescharacteristic
553C22×D4—21no—
554C22×D4C2×Dic8311yescharacteristic
555C23×C4—1661no—
556C23×C4C22×D8311yescharacteristic
557C2×M16—1661no—
558C22×C8—1661no—
559C4⋊Q8—21no—
560C4⋊Q8C2×Dic8311yescharacteristic, complemented
561C4⋊Q8C2×Dic8311yescharacteristic, complemented
562#127C2×Dic8311yescharacteristic, complemented
563#127C2×Dic8311yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125C2×Dic8311yescharacteristic, complemented
570#125C2×Dic8311yescharacteristic, complemented
571#124—21no—
572#124—21no—
573#124—21no—
574#124—21no—
575#124C2×Dic8311yescharacteristic, complemented
576#124C2×Dic8311yescharacteristic, 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×Dic8311yescharacteristic
591C22⋊Q8C22×D8311yescharacteristic
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×Dic8311yescharacteristic
603#121C2×Dic8311yescharacteristic
604#121C2×Dic8311yescharacteristic
605#121C22×D8311yescharacteristic
606#121C22×D8311yescharacteristic
607#121C22×D8311yescharacteristic
608#120—21no—
609#120—21no—
610#120—21no—
611C4×Q8C2×Dic8311yescharacteristic, complemented
612C4×Q8C2×Dic8311yescharacteristic, 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×Dic8311yescharacteristic, complemented
624C4×D4C2×Dic8311yescharacteristic, complemented
625C4×D4C2×Dic8311yescharacteristic, complemented
626C4×D4C2×Dic8311yescharacteristic, complemented
627C4×D4C2×Dic8311yescharacteristic, complemented
628C4×D4C2×Dic8311yescharacteristic, complemented
629#117—21no—
630#117—21no—
631#117—21no—
632#117C2×Dic8311yescharacteristic
633#117C2×Dic8311yescharacteristic
634#117C2×Dic8311yescharacteristic
635#117C2×Dic8311yescharacteristic
636#117C2×Dic8311yescharacteristic
637#117C22⋊D8311yescharacteristic
638#117C22⋊D8311yescharacteristic
639#117C22⋊D8311yescharacteristic
640#117C22⋊D8311yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—1661no—
643C2×C4⋊C4—1661no—
644C2×C4⋊C4C2×Dic8311yescharacteristic
645C2×C4⋊C4C22⋊D8311yescharacteristic
646C2×C4⋊C4C22⋊D8311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—1661no—
651C2×C22⋊C4C22⋊D8311yescharacteristic
652C2×C22⋊C4C22⋊D8311yescharacteristic
653C2×C42—1661no—
654C2×C42—1661no—
655C2×C42C22×D8311yescharacteristic
656C2×C42C22×D8311yescharacteristic
657C4⋊C8—1661no—
658C4⋊C8—1661no—
659C4⋊C8—1661no—
660C4⋊C8—1661no—
661C22⋊C8—831no—
662C22⋊C8—831no—
663C22⋊C8—831no—
664C22⋊C8—831no—
665C22⋊C8—1661no—
666C22⋊C8—1661no—
667#97—1661no—
668#97—1661no—
669C4×C8—1661no—
670C4×C8—1661no—
671#95—831no—
672#95—831no—
673#95—831no—
674#95—831no—
675#95—1661no—
676#95—1661no—
677#95—1661no—
678#95—1661no—
679#95—1661no—
680#95—1661no—
681C24—21no—
682C24C2×C22⋊D8311yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×Dic8311yescharacteristic
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×Dic8311yescharacteristic
707C2×D4C22×Dic8311yescharacteristic
708C2×D4C22×Dic8311yescharacteristic
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—3322no—
719C22×C4—3322no—
720C22×C4—6641no—
721C22×C4—1661no—
722C22×C4—1661no—
723C22×C4—1661no—
724C22×C4—1661no—
725C22×C4C22×Dic8311yescharacteristic
726C22×C4C22×Dic8311yescharacteristic
727C22×C4C2×C22⋊D8311yescharacteristic
728C22×C4C2×C22⋊D8311yescharacteristic
729C22×C4C2×C22⋊D8311yescharacteristic
730C22×C4C2×C22⋊D8311yescharacteristic
731C22×C4C2×C22⋊D8311yescharacteristic
732C22×C4C2×C22⋊D8311yescharacteristic
733C22×C4C2×C22⋊D8311yescharacteristic
734C22×C4C23×D8311yescharacteristic
735M16—3322no—
736C2×C8—3322no—
737C2×C8—1661no—
738C2×C8—1661no—
739C2×C8—1661no—
740C2×C8—1661no—
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—3322no—
753C4⋊C4—6641no—
754C4⋊C4C22⋊Dic8311yescharacteristic
755C4⋊C4C22⋊Dic8311yescharacteristic
756C4⋊C4C22⋊Dic8311yescharacteristic
757C4⋊C4C22⋊Dic8311yescharacteristic
758C4⋊C4C22⋊Dic8311yescharacteristic
759C4⋊C4C22⋊Dic8311yescharacteristic
760C4⋊C4C22⋊Dic8311yescharacteristic
761C4⋊C4C22⋊Dic8311yescharacteristic
762C4⋊C4C22×Dic8311yescharacteristic
763C4⋊C4C22×Dic8311yescharacteristic
764C4⋊C4C22×Dic8311yescharacteristic
765C4⋊C4C22×Dic8311yescharacteristic
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—3322no—
786C22⋊C4C22⋊Dic8311yescharacteristic
787C22⋊C4C22⋊Dic8311yescharacteristic
788C22⋊C4C22⋊Dic8311yescharacteristic
789C22⋊C4C22⋊Dic8311yescharacteristic
790C22⋊C4C22⋊Dic8311yescharacteristic
791C22⋊C4C22⋊Dic8311yescharacteristic
792C22⋊C4C22⋊Dic8311yescharacteristic
793C22⋊C4C22⋊Dic8311yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—3322no—
798C42—6641no—
799C42C22×Dic8311yescharacteristic
800C42C22×Dic8311yescharacteristic
801C42C22×Dic8311yescharacteristic
802C42C22×Dic8311yescharacteristic
803C42C2×C22⋊D8311yescharacteristic
804C42C2×C22⋊D8311yescharacteristic
805C42C2×C22⋊D8311yescharacteristic
806C42C2×C22⋊D8311yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊Dic8311yescharacteristic
818C23C2×C22⋊Dic8311yescharacteristic
819C23C22×C22⋊D8311yescharacteristic
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—3321no—
867C2×C4—3321no—
868C2×C4—3321no—
869C2×C4—3321no—
870C2×C4—3321no—
871C2×C4—3321no—
872C2×C4—3321no—
873C2×C4—3321no—
874C2×C4—3321no—
875C2×C4—3321no—
876C2×C4—3321no—
877C2×C4—6644no—
878C2×C4—1662no—
879C2×C4C2×C22⋊Dic8311yescharacteristic
880C2×C4C2×C22⋊Dic8311yescharacteristic
881C2×C4C2×C22⋊Dic8311yescharacteristic
882C2×C4C2×C22⋊Dic8311yescharacteristic
883C2×C4C2×C22⋊Dic8311yescharacteristic
884C2×C4C2×C22⋊Dic8311yescharacteristic
885C2×C4C2×C22⋊Dic8311yescharacteristic
886C2×C4C2×C22⋊Dic8311yescharacteristic
887C2×C4C2×C22⋊Dic8311yescharacteristic
888C2×C4C2×C22⋊Dic8311yescharacteristic
889C2×C4C23×Dic8311yescharacteristic
890C2×C4C22×C22⋊D8311yescharacteristic
891C8—3321no—
892C8—3321no—
893C8—3321no—
894C8—3321no—
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#1912767512yes—
915C22C22×C22⋊Dic8311yescharacteristic
916C22#1912850411yescharacteristic
917C22#1912851211yescharacteristic
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—3322no—
936C4—6641no—
937C4—6641no—
938C4—6641no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×#1912767511yescharacteristic
947C2#2491598911yescharacteristic
948C2#2491601011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
Fitting, prime radicalC83×#3494C2
socleC22×C83C22×C22⋊C4
cosocleC22×C4×C83C24
hypercenter#3494D83
hypocenterC83#17604
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. #24916121C2semidirect
2. #24910323C2semidirect
3. #24906040C2semidirect
4. #24906023C2semidirect
5. #24906019C2semidirect
6. #24906010C2semidirect
7. #24906001C2semidirect
8. #24905992C2semidirect
9. #24905988C2semidirect
10. #24905971C2semidirect
11. #24905967C2semidirect
12. #24905958C2semidirect
13. #24905949C2semidirect
14. C2×#19127435C2semidirect
18. #19127758C22semidirect
19. #19127758C22semidirect
20. #19127754C22semidirect
21. #19127754C22semidirect
29. #19127569C22semidirect
30. #19127567C22semidirect
32. C4×C4⋊Dic83C22semidirect
34. #19127547C22semidirect
36. #19127438C22semidirect
37. #19127438C22semidirect
38. #19127438C22semidirect
39. #19127438C22semidirect
48. #19127435C22semidirect
49. #19127435C22semidirect
50. #19127435C22semidirect
51. #19127435C22semidirect
60. #544×C83C4semidirect
61. #542×C83C4semidirect
62. #542×C83C4semidirect
63. #540×C83C4semidirect
64. #540×C83C4semidirect
65. #535×C83C4semidirect
72. #520×C83C4semidirect
73. #518×C83C4semidirect
114. C4⋊Q8×C83C2×C4semidirect
115. C4⋊Q8×C83C2×C4semidirect
116. #127×C83C2×C4semidirect
117. #127×C83C2×C4semidirect
123. #125×C83C2×C4semidirect
124. #125×C83C2×C4semidirect
129. #124×C83C2×C4semidirect
130. #124×C83C2×C4semidirect
165. C4×Q8×C83C2×C4semidirect
166. C4×Q8×C83C2×C4semidirect
177. C4×D4×C83C2×C4semidirect
178. C4×D4×C83C2×C4semidirect
179. C4×D4×C83C2×C4semidirect
180. C4×D4×C83C2×C4semidirect
181. C4×D4×C83C2×C4semidirect
182. C4×D4×C83C2×C4semidirect
490. C83#17604semidirect
499. #544Dic83semidirect
500. #542Dic83semidirect
501. #542Dic83semidirect
502. #540Dic83semidirect
503. #540Dic83semidirect
504. #535Dic83semidirect
511. #520Dic83semidirect
512. #518Dic83semidirect
560. C4⋊Q8C2×Dic83semidirect
561. C4⋊Q8C2×Dic83semidirect
562. #127C2×Dic83semidirect
563. #127C2×Dic83semidirect
569. #125C2×Dic83semidirect
570. #125C2×Dic83semidirect
575. #124C2×Dic83semidirect
576. #124C2×Dic83semidirect
611. C4×Q8C2×Dic83semidirect
612. C4×Q8C2×Dic83semidirect
623. C4×D4C2×Dic83semidirect
624. C4×D4C2×Dic83semidirect
625. C4×D4C2×Dic83semidirect
626. C4×D4C2×Dic83semidirect
627. C4×D4C2×Dic83semidirect
628. C4×D4C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
#249161212
#249103232
#249060402
#249060232
#249060192
#249060102
#249060012
#249059922
#249059882
#249059712
#249059672
#249059582
#249059492
C2×#191274352
C83×#34942
#1760483