Finite Group Databasebeta

← #35373345

Subgroups — #35373345

Order 21248.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921349C211yesmaximal, characteristic
2#24916588C211yesmaximal, characteristic
3#24906194C211yesmaximal, characteristic, complemented
4#24906191C211yesmaximal, characteristic, complemented
5#24906188C211yesmaximal, characteristic, complemented
6#24906174C211yesmaximal, characteristic, complemented
7#24906171C211yesmaximal, characteristic, complemented
8#24906164C211yesmaximal, characteristic, complemented
9#24906161C211yesmaximal, characteristic, complemented
10#24906154C211yesmaximal, characteristic, complemented
11#24906151C211yesmaximal, characteristic, complemented
12#24906121C211yesmaximal, characteristic, complemented
13#24906118C211yesmaximal, characteristic, complemented
14C2×#19127449C211yesmaximal, characteristic, complemented
15C83×#2990C211yesmaximal, characteristic
16#19128429—21no—
17#19128429—21no—
18#19128421—21no—
19#19128421—21no—
20#19128391—21no—
21#19128391—21no—
22#19128391—21no—
23#19128391—21no—
24#19128313C412yes—
25#19128313C412yes—
26#19128272C412yes—
27#19128258C2211yescharacteristic
28#19128258C2211yescharacteristic
29#19128258C2211yescharacteristic
30#19128258C2211yescharacteristic
31#19128258C2211yescharacteristic
32C2×#14581792C2211yescharacteristic
33#19128178C412yes—
34#19127832—21no—
35#19127773—21no—
36#19127773—21no—
37D4×C83⋊C8—21no—
38#19127758C2211yescharacteristic
39#19127758C2211yescharacteristic
40#19127754C2211yescharacteristic
41#19127725C2211yescharacteristic
42C2×C4⋊(C83⋊C8)C2211yescharacteristic
43C2×C4⋊(C83⋊C8)C2211yescharacteristic
44#19127449C2211yescharacteristic
45#19127449C2211yescharacteristic
46#19127449C2211yescharacteristic
47#19127449C2211yescharacteristic
48#19127449C2211yescharacteristic
49#19127449C2211yescharacteristic
50#19127449C2211yescharacteristic
51#19127449C2211yescharacteristic
52#19127448C2211yescharacteristic
53#19127448C2211yescharacteristic
54#19127448C2211yescharacteristic
55#19127448C2211yescharacteristic
56#19127446C2211yescharacteristic
57#19127446C2211yescharacteristic
58#19127446C2211yescharacteristic
59#19127446C2211yescharacteristic
60C4×#41×C83C2211yescharacteristic
61#446×C83—21no—
62#435×C83—21no—
63#435×C83—21no—
64C8×D4×C83—21no—
65#432×C83C2211yescharacteristic
66#432×C83C2211yescharacteristic
67#431×C83C2211yescharacteristic
68#423×C83C2211yescharacteristic
69C2×C4⋊C8×C83C2211yescharacteristic
70C2×C4⋊C8×C83C2211yescharacteristic
71C22×Dic166C2×C412yes—
72C2×#13050574—21no—
73C22×C83⋊C8—21no—
74C22×C83⋊C8—21no—
75#14581792—21no—
76#14581792—21no—
77#14581792C2×C412yes—
78#14581792C2311yescharacteristic
79#14581792C2311yescharacteristic
80#14581792C2311yescharacteristic
81#14581792C2311yescharacteristic
82#14581790—22no—
83#14581785—22no—
84#14581785—22no—
85#14581785—22no—
86#14581785—22no—
87#14581784—21no—
88#14581784—21no—
89#14581784—21no—
90#14581784—21no—
91#14581784C2×C412yes—
92#14581782—22no—
93#14581782—22no—
94#14581782—22no—
95#14581782—22no—
96#14581779—22no—
97#14581773—22no—
98#14581773—22no—
99#14581771—21no—
100#14581771—21no—
101#14581771—21no—
102#14581771—21no—
103#14581771—21no—
104#14581771—21no—
105#14581771C2×C412yes—
106#14581771C2×C412yes—
107#14581771C2×C412yes—
108#14581771C2×C412yes—
109C4×Dic166—21no—
110C4×Dic166—21no—
111C4×Dic166—21no—
112C4×Dic166—21no—
113C4×Dic166—21no—
114C4×Dic166—21no—
115C4×Dic166C2×C412yes—
116C4×Dic166C2×C412yes—
117C4×Dic166C2×C412yes—
118C4×Dic166C2×C412yes—
119#14581757—22no—
120#14581757—22no—
121#14581751—21no—
122#14581751—21no—
123#14581751—21no—
124#14581751—21no—
125#14581751C2×C412yes—
126#14581748—22no—
127#14581748—22no—
128C2×C4⋊Dic83—21no—
129C2×C4⋊Dic83—21no—
130C4⋊(C83⋊C8)—21no—
131C4⋊(C83⋊C8)—21no—
132C4⋊(C83⋊C8)—21no—
133C4⋊(C83⋊C8)C2311yescharacteristic
134C4⋊(C83⋊C8)C2311yescharacteristic
135C4⋊(C83⋊C8)C2311yescharacteristic
136C4⋊(C83⋊C8)C2311yescharacteristic
137C22⋊(C83⋊C8)—21no—
138C22⋊(C83⋊C8)—21no—
139C22⋊(C83⋊C8)—21no—
140#14581703—21no—
141#14581703—21no—
142C4×C83⋊C8—21no—
143C2×#41×C83C2×C411yescharacteristic
144C2×M16×C83—21no—
145C22×C8×C83—21no—
146C22×C8×C83—21no—
147C4×Q8×C83D411yescharacteristic
148C4×Q8×C83D411yescharacteristic
149C4×D4×C83D411yescharacteristic
150C4×D4×C83D411yescharacteristic
151C4×D4×C83D411yescharacteristic
152C4×D4×C83D411yescharacteristic
153C4×D4×C83D411yescharacteristic
154C4×D4×C83D411yescharacteristic
155#117×C83C2×C411yescharacteristic
156#117×C83C2×C411yescharacteristic
157#117×C83C2×C411yescharacteristic
158C2×C42×C83C2311yescharacteristic
159C2×C42×C83C2311yescharacteristic
160C2×C42×C83C2311yescharacteristic
161C4⋊C8×C83—21no—
162C4⋊C8×C83—21no—
163C4⋊C8×C83—21no—
164C4⋊C8×C83C2311yescharacteristic
165C4⋊C8×C83C2311yescharacteristic
166C4⋊C8×C83C2311yescharacteristic
167C4⋊C8×C83C2311yescharacteristic
168C22⋊C8×C83—21no—
169C22⋊C8×C83—21no—
170C22⋊C8×C83—21no—
171#97×C83—21no—
172#97×C83—21no—
173C4×C8×C83—21no—
174C2×Dic166—22no—
175C2×Dic166—21no—
176C2×Dic166—21no—
177C2×Dic166—44no—
178C2×Dic166C22×C412yes—
179C2×Dic166C22×C412yes—
180C22×Dic83—22no—
181#13050574—81no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8—21no—
185C2×C83⋊C8—21no—
186C2×C83⋊C8—81no—
187C2×C83⋊C8—81no—
188C4⋊Dic83—22no—
189C4⋊Dic83—22no—
190C4⋊Dic83—21no—
191C4⋊Dic83—21no—
192C4⋊Dic83—21no—
193C4⋊Dic83—21no—
194C4⋊Dic83—21no—
195C4⋊Dic83—21no—
196C4⋊Dic83C22×C412yes—
197C4⋊Dic83C22×C412yes—
198Dic83⋊C4—22no—
199Dic83⋊C4—22no—
200Dic83⋊C4—22no—
201Dic83⋊C4—22no—
202Dic83⋊C4—22no—
203Dic83⋊C4—22no—
204Dic83⋊C4—22no—
205Dic83⋊C4—22no—
206Dic83⋊C4—22no—
207Dic83⋊C4—22no—
208C22⋊Dic83—22no—
209C22⋊Dic83—22no—
210C22⋊Dic83—22no—
211C22⋊Dic83—22no—
212C22⋊Dic83—22no—
213C4×Dic83—22no—
214C4×Dic83—22no—
215C4×Dic83—22no—
216C4×Dic83—22no—
217C4×Dic83—22no—
218#41×C83—42no—
219C2×Q8×C83C22⋊C411yescharacteristic
220C2×D4×C83C22⋊C411yescharacteristic
221C2×D4×C83C22⋊C411yescharacteristic
222C2×D4×C83C22⋊C411yescharacteristic
223C22×C4×C83C22×C411yescharacteristic
224C22×C4×C83C22×C411yescharacteristic
225C22×C4×C83C22×C411yescharacteristic
226C22×C4×C83C2×D411yescharacteristic
227C22×C4×C83C2×D411yescharacteristic
228C22×C4×C83C2×D411yescharacteristic
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2×D411yescharacteristic
232M16×C83—81no—
233C2×C8×C83—21no—
234C2×C8×C83—21no—
235C2×C8×C83—21no—
236C2×C8×C83—21no—
237C2×C8×C83—81no—
238C2×C8×C83—81no—
239C4⋊C4×C83C22⋊C411yescharacteristic
240C4⋊C4×C83C22⋊C411yescharacteristic
241C4⋊C4×C83C22⋊C411yescharacteristic
242C4⋊C4×C83C22⋊C411yescharacteristic
243C4⋊C4×C83C22⋊C411yescharacteristic
244C4⋊C4×C83C22⋊C411yescharacteristic
245C22⋊C4×C83C22⋊C411yescharacteristic
246C22⋊C4×C83C22⋊C411yescharacteristic
247C22⋊C4×C83C22⋊C411yescharacteristic
248C22⋊C4×C83C22⋊C411yescharacteristic
249C22⋊C4×C83C22⋊C411yescharacteristic
250C22⋊C4×C83C22⋊C411yescharacteristic
251C42×C83C22×C411yescharacteristic
252C42×C83C22×C411yescharacteristic
253C42×C83C22×C411yescharacteristic
254C42×C83C2×D411yescharacteristic
255C42×C83C2×D411yescharacteristic
256C42×C83C2×D411yescharacteristic
257C42×C83C2×D411yescharacteristic
258C42×C83C2×D411yescharacteristic
259C42×C83C2×D411yescharacteristic
260C42×C83C2411yescharacteristic
261C23×C83C2×C22⋊C411yescharacteristic
262C23×C83C2×C22⋊C411yescharacteristic
263C23×C83C2×C22⋊C411yescharacteristic
264Q8×C83—41no—
265D4×C83—22no—
266D4×C83—22no—
267D4×C83—41no—
268C2×C4×C83—22no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—21no—
277C2×C4×C83—21no—
278C2×C4×C83—21no—
279C2×C4×C83—21no—
280C2×C4×C83—21no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83C2×C22⋊C411yescharacteristic
284C2×C4×C83C2×C22⋊C411yescharacteristic
285C2×C4×C83C2×C22⋊C411yescharacteristic
286C2×C4×C83C2×C22⋊C411yescharacteristic
287C2×C4×C83C2×C22⋊C411yescharacteristic
288C2×C4×C83C2×C22⋊C411yescharacteristic
289C2×C4×C83C2×C22⋊C411yescharacteristic
290C2×C4×C83C2×C22⋊C411yescharacteristic
291C2×C4×C83C2×C22⋊C411yescharacteristic
292C2×C4×C83C23×C411yescharacteristic
293C2×C4×C83C22×D411yescharacteristic
294C2×C4×C83C22×D411yescharacteristic
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—44no—
300Dic166—44no—
301Dic166—41no—
302Dic166—41no—
303Dic166—41no—
304Dic166—41no—
305Dic166—42no—
306Dic166—42no—
307C8×C83—41no—
308C8×C83—41no—
309C8×C83—41no—
310C8×C83—41no—
311C83⋊C8—41no—
312C83⋊C8—41no—
313C83⋊C8—41no—
314C83⋊C8—41no—
315C22×C83—21no—
316C22×C83—21no—
317C22×C83—21no—
318C22×C83—21no—
319C22×C83—21no—
320C22×C83—21no—
321C22×C83—21no—
322C22×C83—21no—
323C22×C83#41312yes—
324C22×C83C22×C22⋊C411yescharacteristic
325C4×C83—21no—
326C4×C83—21no—
327C4×C83—21no—
328C4×C83—21no—
329C4×C83—21no—
330C4×C83—21no—
331C4×C83—21no—
332C4×C83—21no—
333C4×C83—21no—
334C4×C83—21no—
335C4×C83#57711yescharacteristic
336C4×C83#57711yescharacteristic
337C4×C83#57811yescharacteristic
338C4×C83#57811yescharacteristic
339Dic83—42no—
340Dic83—42no—
341Dic83—42no—
342Dic83—42no—
343#17780—831nomaximal, Sylow
344C2×C83—22no—
345C2×C83—41no—
346C2×C83—41no—
347C2×C83C2×#41311yescharacteristic
348C2×C83#289811yescharacteristic
349C2×C83#289811yescharacteristic
350#3509—831no—
351#2990—831no—
352#2990D8311yescharacteristic
353#1559—831no—
354#1559—831no—
355#1558—831no—
356#1554—831no—
357#1554—831no—
358#1552—831no—
359#1552—831no—
360#1550—831no—
361#1550—831no—
362#1542—831no—
363#1542—831no—
364C2×#333—831no—
365C83#1778011yescharacteristic, complemented, Sylow
366#557—1661no—
367#557—1661no—
368#556—1661no—
369#556—1661no—
370#552—1661no—
371#552—1661no—
372#552—1661no—
373#552—1661no—
374#541—832no—
375#541—832no—
376#536—832no—
377#533—831no—
378#533—831no—
379#533—831no—
380#533—831no—
381#533—831no—
382C2×C4⋊Q8—831no—
383#519—832no—
384C4×#41C2×D8311yescharacteristic
385#446—21no—
386#446—1661no—
387#435—21no—
388#435—21no—
389#435—1661no—
390#435—1661no—
391C8×D4—21no—
392C8×D4—1661no—
393#432—831no—
394#432—831no—
395#432C2×D8311yescharacteristic
396#432C2×D8311yescharacteristic
397#431—831no—
398#431C2×D8311yescharacteristic
399#423—831no—
400#423C2×D8311yescharacteristic
401C2×C4⋊C8—831no—
402C2×C4⋊C8—831no—
403C2×C4⋊C8C2×D8311yescharacteristic
404C2×C4⋊C8C2×D8311yescharacteristic
405#333—831no—
406#333—831no—
407#333—831no—
408#333—831no—
409#333—831no—
410#333—831no—
411#333—831no—
412#333—831no—
413#332—831no—
414#332—831no—
415#332—831no—
416#332—831no—
417#332—831no—
418#332—831no—
419#332—831no—
420#332—831no—
421C2×#41C4×D8311yescharacteristic
422C22×Q8—832no—
423C2×M16—21no—
424C2×M16—1661no—
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—1661no—
428C22×C8—1661no—
429C4⋊Q8—832no—
430C4⋊Q8—831no—
431C4⋊Q8—831no—
432C4⋊Q8—831no—
433C4⋊Q8—831no—
434C4⋊Q8—1662no—
435C4⋊Q8—1661no—
436C4⋊Q8—1661no—
437#126—1662no—
438#126—1662no—
439#126—1662no—
440#126—1662no—
441#125—832no—
442#125—1662no—
443#125—1662no—
444#125—1662no—
445#125—1662no—
446#125—1661no—
447#125—1661no—
448#125—1661no—
449#125—1661no—
450#124—1662no—
451#123—1662no—
452#123—1662no—
453C22⋊Q8—832no—
454C22⋊Q8—832no—
455C22⋊Q8—832no—
456C22⋊Q8—832no—
457C22⋊Q8—1661no—
458C22⋊Q8—1661no—
459C22⋊Q8—1661no—
460C22⋊Q8—1661no—
461C22⋊Q8—1661no—
462C22⋊Q8—1661no—
463C4×Q8—832no—
464C4×Q8—832no—
465C4×Q8—832no—
466C4×Q8—832no—
467C4×Q8—1662no—
468C4×Q8—1662no—
469C4×Q8—1661no—
470C4×Q8—1661no—
471C4×Q8—1661no—
472C4×Q8—1661no—
473C4×Q8—1661no—
474C4×Q8—1661no—
475C4×Q8D33211yescharacteristic
476C4×Q8C22⋊D8311yescharacteristic
477C4×D4D33211yescharacteristic
478C4×D4D33211yescharacteristic
479C4×D4D33211yescharacteristic
480C4×D4C22⋊D8311yescharacteristic
481C4×D4C22⋊D8311yescharacteristic
482C4×D4C22⋊D8311yescharacteristic
483#117—832no—
484#117—1661no—
485#117—1661no—
486#117—1661no—
487#117—1661no—
488#117—1662no—
489#117—1662no—
490#117C4×D8311yescharacteristic
491#117C4×D8311yescharacteristic
492#117C4×D8311yescharacteristic
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C42C22×D8311yescharacteristic
496C2×C42C22×D8311yescharacteristic
497C2×C42C22×D8311yescharacteristic
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—831no—
502C4⋊C8—831no—
503C4⋊C8—831no—
504C4⋊C8—831no—
505C4⋊C8—1661no—
506C4⋊C8—1661no—
507C4⋊C8—1661no—
508C4⋊C8C22×D8311yescharacteristic
509C4⋊C8C22×D8311yescharacteristic
510C4⋊C8C22×D8311yescharacteristic
511C4⋊C8C22×D8311yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—1661no—
516C22⋊C8—1661no—
517C22⋊C8—1661no—
518#97—21no—
519#97—21no—
520#97—1661no—
521#97—1661no—
522C4×C8—21no—
523C4×C8—1661no—
524#41—42no—
525C2×Q8—3324no—
526C2×Q8—832no—
527C2×Q8—832no—
528C2×Q8—1661no—
529C2×Q8—1661no—
530C2×Q8—1662no—
531C2×Q8(C2×D83)⋊C411yescharacteristic
532C2×D4(C2×D83)⋊C411yescharacteristic
533C2×D4(C2×D83)⋊C411yescharacteristic
534C2×D4(C2×D83)⋊C411yescharacteristic
535C22×C4—1662no—
536C22×C4C2×C4×D8311yescharacteristic
537C22×C4C2×C4×D8311yescharacteristic
538C22×C4C2×C4×D8311yescharacteristic
539C22×C4C2×C22⋊D8311yescharacteristic
540C22×C4C2×C22⋊D8311yescharacteristic
541C22×C4C2×C22⋊D8311yescharacteristic
542C22×C4C2×D33211yescharacteristic
543C22×C4C2×D33211yescharacteristic
544C22×C4C2×D33211yescharacteristic
545M16—81no—
546M16—6641no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—81no—
552C2×C8—81no—
553C2×C8—6641no—
554C2×C8—6641no—
555C2×C8—1661no—
556C2×C8—1661no—
557C2×C8—1661no—
558C2×C8—1661no—
559C4⋊C4—832no—
560C4⋊C4—832no—
561C4⋊C4—1661no—
562C4⋊C4—1661no—
563C4⋊C4—1661no—
564C4⋊C4—1661no—
565C4⋊C4—1661no—
566C4⋊C4—1661no—
567C4⋊C4—1662no—
568C4⋊C4—1662no—
569C4⋊C4—1662no—
570C4⋊C4—1662no—
571C4⋊C4—1662no—
572C4⋊C4—1662no—
573C4⋊C4—1662no—
574C4⋊C4—1662no—
575C4⋊C4—1662no—
576C4⋊C4—1662no—
577C4⋊C4—1662no—
578C4⋊C4—1662no—
579C4⋊C4(C2×D83)⋊C411yescharacteristic
580C4⋊C4(C2×D83)⋊C411yescharacteristic
581C4⋊C4(C2×D83)⋊C411yescharacteristic
582C4⋊C4(C2×D83)⋊C411yescharacteristic
583C4⋊C4(C2×D83)⋊C411yescharacteristic
584C4⋊C4(C2×D83)⋊C411yescharacteristic
585C22⋊C4—1662no—
586C22⋊C4—1662no—
587C22⋊C4—1662no—
588C22⋊C4—1662no—
589C22⋊C4—1662no—
590C22⋊C4(C2×D83)⋊C411yescharacteristic
591C22⋊C4(C2×D83)⋊C411yescharacteristic
592C22⋊C4(C2×D83)⋊C411yescharacteristic
593C22⋊C4(C2×D83)⋊C411yescharacteristic
594C22⋊C4(C2×D83)⋊C411yescharacteristic
595C22⋊C4(C2×D83)⋊C411yescharacteristic
596C42—1662no—
597C42—1662no—
598C42—1662no—
599C42—1662no—
600C42—1662no—
601C42C2×C4×D8311yescharacteristic
602C42C2×C4×D8311yescharacteristic
603C42C2×C4×D8311yescharacteristic
604C42C2×C22⋊D8311yescharacteristic
605C42C2×C22⋊D8311yescharacteristic
606C42C2×C22⋊D8311yescharacteristic
607C42C2×D33211yescharacteristic
608C42C2×D33211yescharacteristic
609C42C2×D33211yescharacteristic
610C42C23×D8311yescharacteristic
611C23C2×(C2×D83)⋊C411yescharacteristic
612C23C2×(C2×D83)⋊C411yescharacteristic
613C23C2×(C2×D83)⋊C411yescharacteristic
614Q8—41no—
615Q8—3322no—
616Q8—3322no—
617Q8—3324no—
618Q8—3321no—
619Q8—3321no—
620Q8—3321no—
621Q8—3321no—
622D4—22no—
623D4—22no—
624D4—41no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—3324no—
641C2×C4—1662no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4C2×(C2×D83)⋊C411yescharacteristic
646C2×C4C2×(C2×D83)⋊C411yescharacteristic
647C2×C4C2×(C2×D83)⋊C411yescharacteristic
648C2×C4C2×(C2×D83)⋊C411yescharacteristic
649C2×C4C2×(C2×D83)⋊C411yescharacteristic
650C2×C4C2×(C2×D83)⋊C411yescharacteristic
651C2×C4C2×(C2×D83)⋊C411yescharacteristic
652C2×C4C2×(C2×D83)⋊C411yescharacteristic
653C2×C4C2×(C2×D83)⋊C411yescharacteristic
654C2×C4C22×C4×D8311yescharacteristic
655C2×C4C22×C22⋊D8311yescharacteristic
656C2×C4C22×D33211yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C8—3321no—
662C8—3321no—
663C8—3321no—
664C8—3321no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22#1912768312yes—
674C22C22×(C2×D83)⋊C411yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—3322no—
686C4—3322no—
687C4—3322no—
688C4—3322no—
689C4#1912851211yescharacteristic
690C4#1912851311yescharacteristic
691C4#1912851611yescharacteristic
692C4#1912851811yescharacteristic
693C2—22no—
694C2—41no—
695C2—41no—
696C2C2×#1912768311yescharacteristic
697C2#2491599311yescharacteristic
698C2#2491599711yescharacteristic
subgroupG/H
centerC22C22×(C2×D83)⋊C4
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#2990C2
socleC22×C83C22×C22⋊C4
prime radicalC2×#41×C83C2×C4
cosocleC42×C83C24
hypercenter#2990D83
hypocenterC83#17780
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #24906194C2semidirect
4. #24906191C2semidirect
5. #24906188C2semidirect
6. #24906174C2semidirect
7. #24906171C2semidirect
8. #24906164C2semidirect
9. #24906161C2semidirect
10. #24906154C2semidirect
11. #24906151C2semidirect
12. #24906121C2semidirect
13. #24906118C2semidirect
14. C2×#19127449C2semidirect
365. C83#17780semidirect

Maximal subgroups

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

subgroupindex
#249213492
#249165882
#249061942
#249061912
#249061882
#249061742
#249061712
#249061642
#249061612
#249061542
#249061512
#249061212
#249061182
C2×#191274492
C83×#29902
#1778083