Finite Group Databasebeta

← #35409677

Subgroups — #35409677

Order 21248.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127657C211yesmaximal, characteristic, complemented
2#24910072C211yesmaximal, characteristic, complemented
3#24908437C211yesmaximal, characteristic, complemented
4#24908425C211yesmaximal, characteristic, complemented
5#24908280C211yesmaximal, characteristic, complemented
6#24908275C211yesmaximal, characteristic, complemented
7#24907902C211yesmaximal, characteristic
8#24907897C211yesmaximal, characteristic, complemented
9#24907892C211yesmaximal, characteristic
10#24907887C211yesmaximal, characteristic, complemented
11#24907293C211yesmaximal, characteristic, complemented
12#24907288C211yesmaximal, characteristic, complemented
13C4×#14581716C211yesmaximal, characteristic, complemented
14C4×#14581713C211yesmaximal, characteristic, complemented
15C2×#542×C83C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18C2×#14581716C2211yescharacteristic
19C2×#14581716C2211yescharacteristic
20C2×#14581716C2211yescharacteristic
21C2×#14581716C2211yescharacteristic
22C2×#14581713C2211yescharacteristic
23C2×#14581713C2211yescharacteristic
24C2×#14581713C2211yescharacteristic
25C2×#14581713C2211yescharacteristic
26#19127657—24no—
27C2×#14581703C2211yescharacteristic
28C2×#14581703C2211yescharacteristic
29C2×C4×C83⋊C8C2211yescharacteristic
30C2×C4×C83⋊C8C2211yescharacteristic
31#19127594—21no—
32#19127594—21no—
33#19127587—21no—
34#19127587—21no—
35#19127571C2211yescharacteristic
36#19127567C2211yescharacteristic
37#19127561C2211yescharacteristic
38#19127561C2211yescharacteristic
39C4×C4⋊Dic83C2211yescharacteristic
40C4×C4⋊Dic83C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#542×C83—24no—
50#542×C83C418yescomplemented
51C2×C4⋊Q8×C83C2211yescharacteristic
52C2×#126×C83—21no—
53C2×#124×C83—21no—
54C2×#124×C83C2211yescharacteristic
55C2×#123×C83—21no—
56C2×C22⋊Q8×C83—21no—
57C2×C22⋊Q8×C83C2211yescharacteristic
58C2×#121×C83C2211yescharacteristic
59C2×C4×Q8×C83C2211yescharacteristic
60C2×C4×D4×C83C2211yescharacteristic
61C2×#117×C83C2211yescharacteristic
62C2×#13050574—22no—
63C2×#13050574—22no—
64C2×#13050574—22no—
65C22×C83⋊C8—22no—
66C22×C83⋊C8—22no—
67C22×C83⋊C8—22no—
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C2×C4⋊Dic83—21no—
73C2×C4⋊Dic83—21no—
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×C4⋊Dic83C2311yescharacteristic
78C2×C22⋊Dic83—21no—
79C2×C22⋊Dic83—21no—
80C2×C4×Dic83—21no—
81C2×C4×Dic83—21no—
82#14581716—22no—
83#14581716—22no—
84#14581716—22no—
85#14581716—22no—
86#14581713—22no—
87#14581713—22no—
88#14581713—22no—
89#14581713—22no—
90#14581703—22no—
91#14581703—22no—
92C4×C83⋊C8—22no—
93C4×C83⋊C8—22no—
94C83⋊#95—21no—
95C83⋊#95—21no—
96C83⋊#95—21no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C22×Q8×C83—21no—
101C22×Q8×C83C2311yescharacteristic
102C22×D4×C83—21no—
103C22×D4×C83C2311yescharacteristic
104C23×C4×C83—21no—
105C23×C4×C83C2311yescharacteristic
106C4⋊Q8×C83—22no—
107C4⋊Q8×C83C2×C414yes—
108#126×C83—28no—
109#124×C83—28no—
110#124×C83—22no—
111#124×C83C2×C414yes—
112#123×C83—28no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83—28no—
115C22⋊Q8×C83C2×C414yes—
116#121×C83—22no—
117#121×C83C2×C414yes—
118C4×Q8×C83—22no—
119C4×Q8×C83C2×C414yes—
120C4×D4×C83—22no—
121C4×D4×C83C2×C414yes—
122#117×C83C2×C414yes—
123#117×C83D414yes—
124C2×C4⋊C4×C83—21no—
125C2×C4⋊C4×C83—21no—
126C2×C4⋊C4×C83—21no—
127C2×C4⋊C4×C83D411yescharacteristic
128C2×C4⋊C4×C83D411yescharacteristic
129C2×C4⋊C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83C2311yescharacteristic
131C2×C22⋊C4×C83—21no—
132C2×C22⋊C4×C83—21no—
133C2×C22⋊C4×C83—21no—
134C2×C22⋊C4×C83—21no—
135C2×C22⋊C4×C83—21no—
136C2×C22⋊C4×C83D411yescharacteristic
137C2×C22⋊C4×C83D411yescharacteristic
138C2×C42×C83—21no—
139C2×C42×C83C2311yescharacteristic
140C2×C42×C83C2311yescharacteristic
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145#13050574—28no—
146C2×C83⋊C8—28no—
147C2×C83⋊C8—21no—
148C2×C83⋊C8—21no—
149C2×C83⋊C8—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8#4112yes—
156C2×C83⋊C8#4112yes—
157C2×C83⋊C8#4112yes—
158C2×C83⋊C8#4112yes—
159C4⋊Dic83—21no—
160C4⋊Dic83—21no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83—81no—
168C4⋊Dic83—81no—
169C22⋊Dic83—81no—
170C22⋊Dic83—81no—
171C4×Dic83—81no—
172C4×Dic83—81no—
173C24×C83—21no—
174C24×C83C2×D411yescharacteristic
175C2×Q8×C83—24no—
176C2×Q8×C83—21no—
177C2×Q8×C83—21no—
178C2×Q8×C83—21no—
179C2×Q8×C83—21no—
180C2×Q8×C83—21no—
181C2×Q8×C83—81no—
182C2×Q8×C83—81no—
183C2×Q8×C83C22×C412yes—
184C2×D4×C83—24no—
185C2×D4×C83—21no—
186C2×D4×C83—21no—
187C2×D4×C83—21no—
188C2×D4×C83—21no—
189C2×D4×C83—21no—
190C2×D4×C83—81no—
191C2×D4×C83—81no—
192C2×D4×C83C22×C412yes—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—24no—
201C22×C4×C83—81no—
202C22×C4×C83—81no—
203C22×C4×C83C22×C412yes—
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2×D411yescharacteristic
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83C2×D412yes—
210C22×C4×C83C2411yescharacteristic
211C4⋊C4×C83—24no—
212C4⋊C4×C83—24no—
213C4⋊C4×C83—24no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83C22⋊C414yes—
217C4⋊C4×C83C22⋊C414yes—
218C4⋊C4×C83C22×C412yes—
219C4⋊C4×C83C22×C412yes—
220C22⋊C4×C83—24no—
221C22⋊C4×C83—24no—
222C22⋊C4×C83—24no—
223C22⋊C4×C83—24no—
224C22⋊C4×C83—24no—
225C22⋊C4×C83C22⋊C414yes—
226C22⋊C4×C83C22⋊C414yes—
227C42×C83—24no—
228C42×C83C22×C412yes—
229C42×C83C22×C412yes—
230C42×C83C2×D412yes—
231C42×C83C2×D412yes—
232C23×C83—21no—
233C23×C83—21no—
234C23×C83—21no—
235C23×C83—21no—
236C23×C83—21no—
237C23×C83—21no—
238C23×C83—22no—
239C23×C83—41no—
240C23×C83—41no—
241C23×C83—41no—
242C23×C83—41no—
243C23×C83—41no—
244C23×C83—41no—
245C23×C83C2×C22⋊C412yes—
246C23×C83C22×D411yescharacteristic
247Q8×C83—22no—
248Q8×C83—22no—
249Q8×C83—41no—
250Q8×C83—41no—
251Q8×C83—84no—
252D4×C83—22no—
253D4×C83—22no—
254D4×C83—41no—
255D4×C83—41no—
256D4×C83—84no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—21no—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—21no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—41no—
278C2×C4×C83—41no—
279C2×C4×C83—41no—
280C2×C4×C83—84no—
281C2×C4×C83C2×C22⋊C412yes—
282C2×C4×C83C2×C22⋊C412yes—
283C2×C4×C83C2×C22⋊C412yes—
284C2×C4×C83C2×C22⋊C412yes—
285C2×C4×C83C2×C22⋊C412yes—
286C2×C4×C83C23×C411yescharacteristic
287C2×C4×C83C22×D411yescharacteristic
288C2×C4×C83C2×#4111yescharacteristic
289C2×C4×C83C2×#4111yescharacteristic
290C2×C4×C83C2×#4111yescharacteristic
291C2×C4×C83C2×#4111yescharacteristic
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—41no—
296C2×Dic83—41no—
297C2×Dic83—41no—
298C2×Dic83—41no—
299C2×Dic83—41no—
300C2×Dic83—41no—
301C2×Dic83—41no—
302C2×Dic83—41no—
303C2×Dic83—41no—
304C83⋊C8—22no—
305C83⋊C8—22no—
306C83⋊C8—22no—
307C83⋊C8—22no—
308C22×C83—22no—
309C22×C83—22no—
310C22×C83—22no—
311C22×C83—41no—
312C22×C83—41no—
313C22×C83—41no—
314C22×C83—41no—
315C22×C83—42no—
316C22×C83—42no—
317C22×C83—42no—
318C22×C83—81no—
319C22×C83—81no—
320C22×C83—81no—
321C22×C83—81no—
322C22×C83C22×C22⋊C411yescharacteristic
323C22×C83#53211yescharacteristic
324C22×C83#53211yescharacteristic
325C22×C83#57611yescharacteristic
326C22×C83#57711yescharacteristic
327C22×C83#57711yescharacteristic
328C22×C83#57811yescharacteristic
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—42no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83C4×#4111yescharacteristic
338C4×C83C4×#4111yescharacteristic
339C4×C83#52511yescharacteristic
340C4×C83#52511yescharacteristic
341Dic83—81no—
342Dic83—81no—
343Dic83—81no—
344Dic83—81no—
345#21412—831nomaximal, Sylow
346C2×C83—42no—
347C2×C83—82no—
348C2×C83#229711yescharacteristic
349C2×C83#289711yescharacteristic
350C2×C83#289811yescharacteristic
351C2×C83#317311yescharacteristic
352C2×C83#317511yescharacteristic
353C2×C83#317811yescharacteristic
354C2×C83#317911yescharacteristic
355C2×#542D8311yescharacteristic
356C2×#405—831no—
357#2314—831no—
358#1993—831no—
359#1990—831no—
360#1959—831no—
361#1958—831no—
362#1895—831no—
363#1894—831no—
364#1893—831no—
365#1892—831no—
366#1763—831no—
367#1762—831no—
368C4×#103—831no—
369C4×#102—831no—
370C83#2141211yescharacteristic, complemented, Sylow
371C22×M16—831no—
372C23×C8—831no—
373#542—24no—
374#542Dic8318yescomplemented
375C2×C4⋊Q8C2×D8311yescharacteristic
376C2×#126—21no—
377C2×#124—21no—
378C2×#124C2×D8311yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C2×D8311yescharacteristic
382C2×#121C2×D8311yescharacteristic
383C2×C4×Q8C2×D8311yescharacteristic
384C2×C4×D4C2×D8311yescharacteristic
385C2×#117C2×D8311yescharacteristic
386C2×#103—831no—
387C2×#103—831no—
388C2×#103—831no—
389C2×#103—831no—
390C2×#102—831no—
391C2×#102—831no—
392C2×#102—831no—
393C2×#102—831no—
394#405—1664no—
395C2×#97—831no—
396C2×#97—831no—
397C2×C4×C8—831no—
398C2×C4×C8—831no—
399#388—1661no—
400#388—1661no—
401#387—1661no—
402#387—1661no—
403#384—831no—
404#382—831no—
405#380—831no—
406#380—831no—
407C4×C4⋊C4—831no—
408C4×C4⋊C4—831no—
409#340—831no—
410#340—831no—
411#340—831no—
412#340—831no—
413#340—831no—
414#340—831no—
415#340—831no—
416#340—831no—
417C22×Q8—21no—
418C22×Q8C22×D8311yescharacteristic
419C22×D4—21no—
420C22×D4C22×D8311yescharacteristic
421C23×C4—21no—
422C23×C4C22×D8311yescharacteristic
423C2×M16—1662no—
424C2×M16—1662no—
425C2×M16—1662no—
426C22×C8—831no—
427C22×C8—831no—
428C22×C8—831no—
429C22×C8—831no—
430C22×C8—1662no—
431C22×C8—1662no—
432C22×C8—1662no—
433C4⋊Q8—22no—
434C4⋊Q8C2×Dic8314yes—
435#126—28no—
436#124—28no—
437#124—22no—
438#124C2×Dic8314yes—
439#123—28no—
440C22⋊Q8—22no—
441C22⋊Q8—28no—
442C22⋊Q8C2×Dic8314yes—
443#121—22no—
444#121C2×Dic8314yes—
445C4×Q8—22no—
446C4×Q8C2×Dic8314yes—
447C4×D4—22no—
448C4×D4C2×Dic8314yes—
449#117C2×Dic8314yes—
450#117C22⋊D8314yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—831no—
455C2×C4⋊C4—831no—
456C2×C4⋊C4—831no—
457C2×C4⋊C4—831no—
458C2×C4⋊C4—1661no—
459C2×C4⋊C4—1661no—
460C2×C4⋊C4C22⋊D8311yescharacteristic
461C2×C4⋊C4C22⋊D8311yescharacteristic
462C2×C4⋊C4C22×D8311yescharacteristic
463C2×C4⋊C4C22×D8311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—1661no—
470C2×C22⋊C4—1661no—
471C2×C22⋊C4C22⋊D8311yescharacteristic
472C2×C22⋊C4C22⋊D8311yescharacteristic
473C2×C42—21no—
474C2×C42—1661no—
475C2×C42—1661no—
476C2×C42C22×D8311yescharacteristic
477C2×C42C22×D8311yescharacteristic
478#103—1662no—
479#103—1662no—
480#103—1662no—
481#103—1662no—
482#102—1662no—
483#102—1662no—
484#102—1662no—
485#102—1662no—
486#97—1662no—
487#97—1662no—
488C4×C8—1662no—
489C4×C8—1662no—
490#95—1661no—
491#95—1661no—
492#95—1661no—
493#95—1661no—
494#95—1661no—
495#95—1661no—
496C24—21no—
497C24C2×C22⋊D8311yescharacteristic
498C2×Q8—21no—
499C2×Q8—24no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—81no—
505C2×Q8—81no—
506C2×Q8C22×Dic8312yes—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4C22×Dic8312yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—1661no—
527C22×C4—1661no—
528C22×C4—1661no—
529C22×C4—1661no—
530C22×C4C22×Dic8312yes—
531C22×C4C2×C22⋊D8312yes—
532C22×C4C2×C22⋊D8311yescharacteristic
533C22×C4C2×C22⋊D8311yescharacteristic
534C22×C4C2×C22⋊D8311yescharacteristic
535C22×C4C2×C22⋊D8311yescharacteristic
536C22×C4C2×C22⋊D8311yescharacteristic
537C22×C4C23×D8311yescharacteristic
538M16—1668no—
539C2×C8—832no—
540C2×C8—832no—
541C2×C8—832no—
542C2×C8—832no—
543C2×C8—1668no—
544C2×C8—1661no—
545C2×C8—1661no—
546C2×C8—1661no—
547C2×C8—1661no—
548C2×C8—1661no—
549C2×C8—1661no—
550C2×C8—1661no—
551C2×C8—1661no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—6641no—
558C4⋊C4—6641no—
559C4⋊C4—1661no—
560C4⋊C4—1661no—
561C4⋊C4—1661no—
562C4⋊C4—1661no—
563C4⋊C4—1661no—
564C4⋊C4—1661no—
565C4⋊C4—1661no—
566C4⋊C4—1661no—
567C4⋊C4C22⋊Dic8314yes—
568C4⋊C4C22⋊Dic8314yes—
569C4⋊C4C22×Dic8312yes—
570C4⋊C4C22×Dic8312yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—6641no—
577C22⋊C4—6641no—
578C22⋊C4C22⋊Dic8314yes—
579C22⋊C4C22⋊Dic8314yes—
580C42—24no—
581C42—6641no—
582C42—6641no—
583C42C22×Dic8312yes—
584C42C22×Dic8312yes—
585C42C2×C22⋊D8312yes—
586C42C2×C22⋊D8312yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×C22⋊Dic8312yes—
601C23C22×C22⋊D8311yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3321no—
639C2×C4—3321no—
640C2×C4—3321no—
641C2×C4—3321no—
642C2×C4—3321no—
643C2×C4—3321no—
644C2×C4—3321no—
645C2×C4—3321no—
646C2×C4—3321no—
647C2×C4—3321no—
648C2×C4C2×C22⋊Dic8312yes—
649C2×C4C2×C22⋊Dic8312yes—
650C2×C4C2×C22⋊Dic8312yes—
651C2×C4C2×C22⋊Dic8312yes—
652C2×C4C2×C22⋊Dic8312yes—
653C2×C4C23×Dic8311yescharacteristic
654C2×C4C22×C22⋊D8311yescharacteristic
655C2×C4#41×D8311yescharacteristic
656C2×C4#41×D8311yescharacteristic
657C2×C4#41×D8311yescharacteristic
658C2×C4#41×D8311yescharacteristic
659C8—1662no—
660C8—1662no—
661C8—1662no—
662C8—1662no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C22×C22⋊Dic8311yescharacteristic
678C22#1912824711yescharacteristic
679C22#1912824711yescharacteristic
680C22#1912850411yescharacteristic
681C22#1912850911yescharacteristic
682C22#1912851211yescharacteristic
683C22#1912851611yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—6641no—
693C4—6641no—
694C4—6641no—
695C4—6641no—
696C4#41×Dic8311yescharacteristic
697C4#41×Dic8311yescharacteristic
698C4#1912820811yescharacteristic
699C4#1912820811yescharacteristic
700C2—42no—
701C2—82no—
702C2#2490995411yescharacteristic
703C2#2491598911yescharacteristic
704C2#2491599611yescharacteristic
705C2#2491807411yescharacteristic
706C2#2491809611yescharacteristic
707C2#2491812511yescharacteristic
708C2#2491814011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#542×C83C2
socleC23×C83C22×D4
prime radicalC2×#121×C83C22
cosocleC22×C4×C83C24
hypercenterC2×#542D83
hypocenterC83#21412
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19127657C2semidirect
2. #24910072C2semidirect
3. #24908437C2semidirect
4. #24908425C2semidirect
5. #24908280C2semidirect
6. #24908275C2semidirect
8. #24907897C2semidirect
10. #24907887C2semidirect
11. #24907293C2semidirect
12. #24907288C2semidirect
13. C4×#14581716C2semidirect
14. C4×#14581713C2semidirect
50. #542×C83C4semidirect
370. C83#21412semidirect
374. #542Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191276572
#249100722
#249084372
#249084252
#249082802
#249082752
#249079022
#249078972
#249078922
#249078872
#249072932
#249072882
C4×#145817162
C4×#145817132
C2×#542×C832
#2141283