Finite Group Databasebeta

← C83×#17524 #35245348

Subgroups — C83×#17524 #35245348

Order 21248.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3482C211yesmaximal, characteristic
2C83×#2990C211yesmaximal, characteristic, complemented
3C83×#2922C211yesmaximal, characteristic, complemented
4C83×#1497C211yesmaximal, characteristic, complemented
5C83×#1495C211yesmaximal, characteristic, complemented
6C83×#1494C211yesmaximal, characteristic, complemented
7C83×#1491C211yesmaximal, characteristic, complemented
8C83×#1488C211yesmaximal, characteristic, complemented
9C83×#1487C211yesmaximal, characteristic, complemented
10C83×#1483C211yesmaximal, characteristic, complemented
11C83×#1482C211yesmaximal, characteristic, complemented
12C83×#1481C211yesmaximal, characteristic, complemented
13C83×#1479C211yesmaximal, characteristic, complemented
14C83×#1477C211yesmaximal, characteristic, complemented
15C2×Q8⋊C8×C83C211yesmaximal, characteristic, complemented
16#557×C83C411yescharacteristic
17#556×C83—21no—
18#556×C83C411yescharacteristic
19#552×C83—21no—
20#552×C83—21no—
21#552×C83C411yescharacteristic
22#552×C83C411yescharacteristic
23D4×Q8×C83C411yescharacteristic
24#548×C83C411yescharacteristic
25#548×C83C411yescharacteristic
26#547×C83—21no—
27#547×C83C411yescharacteristic
28#533×C83—21no—
29#533×C83C2211yescharacteristic
30#529×C83—21no—
31#529×C83—21no—
32#529×C83C2211yescharacteristic
33#529×C83C2211yescharacteristic
34C4×#41×C83—21no—
35C4×#41×C83C2211yescharacteristic
36C4×#41×C83C2211yescharacteristic
37C2×C4×Q8×C83C2211yescharacteristic
38C2×C4×Q8×C83C2211yescharacteristic
39#446×C83—21no—
40#435×C83—21no—
41#435×C83—21no—
42C8×D4×C83—21no—
43#433×C83—21no—
44#433×C83—21no—
45#432×C83C2211yescharacteristic
46#432×C83C2211yescharacteristic
47#431×C83C2211yescharacteristic
48#431×C83C2211yescharacteristic
49#431×C83C2211yescharacteristic
50#431×C83C2211yescharacteristic
51#431×C83C2211yescharacteristic
52#424×C83—21no—
53#423×C83C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×C4⋊C8×C83C2211yescharacteristic
56#408×C83—21no—
57C4×M16×C83C2211yescharacteristic
58C2×C4×C8×C83C2211yescharacteristic
59Q8⋊C8×C83C2211yescharacteristic
60Q8⋊C8×C83C2211yescharacteristic
61Q8⋊C8×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66Q8⋊C8×C83C2211yescharacteristic
67Q8⋊C8×C83C2211yescharacteristic
68Q8⋊C8×C83C2211yescharacteristic
69Q8⋊C8×C83C2211yescharacteristic
70Q8⋊C8×C83C2211yescharacteristic
71D4⋊C8×C83C2211yescharacteristic
72D4⋊C8×C83C2211yescharacteristic
73D4⋊C8×C83C2211yescharacteristic
74D4⋊C8×C83C2211yescharacteristic
75C2×#41×C83—21no—
76C2×#41×C83C2×C411yescharacteristic
77C2×#41×C83D411yescharacteristic
78C22×Q8×C83C2×C411yescharacteristic
79C22×Q8×C83C2×C411yescharacteristic
80C2×M16×C83—21no—
81C2×M16×C83—21no—
82C22×C8×C83—21no—
83C22×C8×C83—21no—
84C22×C8×C83—21no—
85C4⋊Q8×C83—21no—
86C4⋊Q8×C83—21no—
87C4⋊Q8×C83C2×C411yescharacteristic
88C4⋊Q8×C83C2×C411yescharacteristic
89#126×C83—21no—
90#126×C83—21no—
91#126×C83—21no—
92#126×C83—21no—
93#126×C83—21no—
94#126×C83—21no—
95#125×C83—21no—
96#125×C83—21no—
97#125×C83—21no—
98#125×C83—21no—
99#125×C83—21no—
100#125×C83C2×C411yescharacteristic
101#125×C83C2×C411yescharacteristic
102#124×C83—21no—
103#124×C83—21no—
104#124×C83C2×C411yescharacteristic
105#124×C83C2×C411yescharacteristic
106#123×C83—21no—
107#123×C83—21no—
108#123×C83—21no—
109#123×C83—21no—
110#123×C83—21no—
111#123×C83—21no—
112C22⋊Q8×C83—21no—
113C22⋊Q8×C83—21no—
114C22⋊Q8×C83—21no—
115C22⋊Q8×C83—21no—
116C22⋊Q8×C83—21no—
117C22⋊Q8×C83—21no—
118C22⋊Q8×C83—21no—
119C22⋊Q8×C83C2×C411yescharacteristic
120C22⋊Q8×C83C2×C411yescharacteristic
121C22⋊Q8×C83C2×C411yescharacteristic
122C22⋊Q8×C83C2×C411yescharacteristic
123#121×C83—21no—
124#121×C83—21no—
125#121×C83C2×C411yescharacteristic
126#121×C83C2×C411yescharacteristic
127C4×Q8×C83—21no—
128C4×Q8×C83—21no—
129C4×Q8×C83—21no—
130C4×Q8×C83—21no—
131C4×Q8×C83—21no—
132C4×Q8×C83—21no—
133C4×Q8×C83C2×C411yescharacteristic
134C4×Q8×C83C2×C411yescharacteristic
135C4×Q8×C83C2×C411yescharacteristic
136C4×Q8×C83C2×C411yescharacteristic
137C4×Q8×C83C2×C411yescharacteristic
138C4×Q8×C83C2×C411yescharacteristic
139C4×Q8×C83D411yescharacteristic
140C4×Q8×C83C2311yescharacteristic
141C4×Q8×C83C2311yescharacteristic
142C4×Q8×C83C2311yescharacteristic
143C4×D4×C83—21no—
144C4×D4×C83—21no—
145C4×D4×C83—21no—
146C4×D4×C83—21no—
147C4×D4×C83—21no—
148C4×D4×C83—21no—
149C4×D4×C83—21no—
150C4×D4×C83C2×C411yescharacteristic
151C4×D4×C83C2×C411yescharacteristic
152C4×D4×C83C2×C411yescharacteristic
153C4×D4×C83C2×C411yescharacteristic
154C4×D4×C83D411yescharacteristic
155C4×D4×C83D411yescharacteristic
156C4×D4×C83D411yescharacteristic
157C4×D4×C83C2311yescharacteristic
158#117×C83—21no—
159#117×C83—21no—
160#117×C83—21no—
161#117×C83—21no—
162#117×C83—21no—
163#117×C83—21no—
164#117×C83—21no—
165#117×C83C2×C411yescharacteristic
166#117×C83D411yescharacteristic
167#117×C83D411yescharacteristic
168#117×C83D411yescharacteristic
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83—21no—
171C2×C4⋊C4×C83C2×C411yescharacteristic
172C2×C4⋊C4×C83C2×C411yescharacteristic
173C2×C42×C83—21no—
174C2×C42×C83—21no—
175C2×C42×C83—21no—
176C2×C42×C83C2311yescharacteristic
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2311yescharacteristic
179C4⋊C8×C83—21no—
180C4⋊C8×C83—21no—
181C4⋊C8×C83—21no—
182C4⋊C8×C83—21no—
183C4⋊C8×C83—21no—
184C4⋊C8×C83—21no—
185C4⋊C8×C83—21no—
186C4⋊C8×C83C2311yescharacteristic
187C4⋊C8×C83C2311yescharacteristic
188C4⋊C8×C83C2311yescharacteristic
189C4⋊C8×C83C2311yescharacteristic
190C22⋊C8×C83—21no—
191C22⋊C8×C83—21no—
192C22⋊C8×C83—21no—
193C22⋊C8×C83—21no—
194C22⋊C8×C83—21no—
195C22⋊C8×C83—21no—
196C22⋊C8×C83—21no—
197#97×C83—21no—
198#97×C83—21no—
199#97×C83—21no—
200C4×C8×C83—21no—
201C4×C8×C83—21no—
202C4×C8×C83C2311yescharacteristic
203C4×C8×C83C2311yescharacteristic
204C4×C8×C83C2311yescharacteristic
205C4×C8×C83C2311yescharacteristic
206#41×C83—22no—
207#41×C83—42no—
208#41×C83—41no—
209#41×C83—44no—
210C2×Q8×C83—21no—
211C2×Q8×C83—21no—
212C2×Q8×C83—21no—
213C2×Q8×C83—22no—
214C2×Q8×C83—22no—
215C2×Q8×C83—41no—
216C2×Q8×C83—41no—
217C2×Q8×C83C22⋊C411yescharacteristic
218C2×Q8×C83C22×C411yescharacteristic
219C2×Q8×C83C22×C411yescharacteristic
220C2×Q8×C83C22×C411yescharacteristic
221C2×D4×C83—21no—
222C2×D4×C83—21no—
223C2×D4×C83—21no—
224C2×D4×C83C22⋊C411yescharacteristic
225C2×D4×C83C22⋊C411yescharacteristic
226C2×D4×C83C22⋊C411yescharacteristic
227C2×D4×C83C22×C411yescharacteristic
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C22×C411yescharacteristic
237C22×C4×C83C22×C411yescharacteristic
238C22×C4×C83C2×D411yescharacteristic
239C22×C4×C83C2×D411yescharacteristic
240C22×C4×C83C2×D411yescharacteristic
241C22×C4×C83C2×D411yescharacteristic
242C22×C4×C83C2×D411yescharacteristic
243C22×C4×C83C2×D411yescharacteristic
244M16×C83—42no—
245M16×C83—81no—
246C2×C8×C83—21no—
247C2×C8×C83—21no—
248C2×C8×C83—21no—
249C2×C8×C83—21no—
250C2×C8×C83—21no—
251C2×C8×C83—21no—
252C2×C8×C83—21no—
253C2×C8×C83—21no—
254C2×C8×C83—42no—
255C2×C8×C83—81no—
256C2×C8×C83—81no—
257C4⋊C4×C83—21no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83—21no—
265C4⋊C4×C83—21no—
266C4⋊C4×C83—21no—
267C4⋊C4×C83—21no—
268C4⋊C4×C83—21no—
269C4⋊C4×C83—21no—
270C4⋊C4×C83—21no—
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×C83C22⋊C411yescharacteristic
279C4⋊C4×C83C22⋊C411yescharacteristic
280C4⋊C4×C83C22⋊C411yescharacteristic
281C4⋊C4×C83C22⋊C411yescharacteristic
282C4⋊C4×C83C22⋊C411yescharacteristic
283C4⋊C4×C83C22⋊C411yescharacteristic
284C4⋊C4×C83C22×C411yescharacteristic
285C4⋊C4×C83C22×C411yescharacteristic
286C4⋊C4×C83C22×C411yescharacteristic
287C4⋊C4×C83C22×C411yescharacteristic
288C22⋊C4×C83—21no—
289C22⋊C4×C83—21no—
290C22⋊C4×C83—21no—
291C22⋊C4×C83—21no—
292C22⋊C4×C83—21no—
293C22⋊C4×C83—21no—
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×C83C22⋊C411yescharacteristic
302C22⋊C4×C83C22⋊C411yescharacteristic
303C22⋊C4×C83C22⋊C411yescharacteristic
304C22⋊C4×C83C22⋊C411yescharacteristic
305C22⋊C4×C83C22⋊C411yescharacteristic
306C22⋊C4×C83C22⋊C411yescharacteristic
307C42×C83—21no—
308C42×C83—21no—
309C42×C83—21no—
310C42×C83—21no—
311C42×C83—21no—
312C42×C83—21no—
313C42×C83—21no—
314C42×C83—21no—
315C42×C83—21no—
316C42×C83C22×C411yescharacteristic
317C42×C83C22×C411yescharacteristic
318C42×C83C22×C411yescharacteristic
319C42×C83C2×D411yescharacteristic
320C42×C83C2×D411yescharacteristic
321C42×C83C2×D411yescharacteristic
322C42×C83C2×D411yescharacteristic
323C42×C83C2×D411yescharacteristic
324C42×C83C2×D411yescharacteristic
325C42×C83C2411yescharacteristic
326C23×C83—21no—
327C23×C83C2×C22⋊C411yescharacteristic
328C23×C83C2×C22⋊C411yescharacteristic
329C23×C83C2×C22⋊C411yescharacteristic
330Q8×C83—21no—
331Q8×C83—21no—
332Q8×C83—21no—
333Q8×C83—21no—
334Q8×C83—21no—
335Q8×C83—41no—
336Q8×C83—42no—
337Q8×C83—42no—
338Q8×C83—42no—
339Q8×C83#13112yes—
340D4×C83—22no—
341D4×C83—22no—
342D4×C83—21no—
343D4×C83—21no—
344D4×C83—41no—
345D4×C83—42no—
346D4×C83—42no—
347D4×C83—42no—
348C2×C4×C83—21no—
349C2×C4×C83—22no—
350C2×C4×C83—21no—
351C2×C4×C83—21no—
352C2×C4×C83—21no—
353C2×C4×C83—21no—
354C2×C4×C83—21no—
355C2×C4×C83—21no—
356C2×C4×C83—21no—
357C2×C4×C83—21no—
358C2×C4×C83—21no—
359C2×C4×C83—21no—
360C2×C4×C83—21no—
361C2×C4×C83—21no—
362C2×C4×C83—21no—
363C2×C4×C83—21no—
364C2×C4×C83—21no—
365C2×C4×C83—21no—
366C2×C4×C83—21no—
367C2×C4×C83—21no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—42no—
371C2×C4×C83—42no—
372C2×C4×C83—42no—
373C2×C4×C83—42no—
374C2×C4×C83—42no—
375C2×C4×C83—42no—
376C2×C4×C83—41no—
377C2×C4×C83—41no—
378C2×C4×C83C2×C22⋊C411yescharacteristic
379C2×C4×C83C2×C22⋊C411yescharacteristic
380C2×C4×C83C2×C22⋊C411yescharacteristic
381C2×C4×C83C2×C22⋊C411yescharacteristic
382C2×C4×C83C2×C22⋊C411yescharacteristic
383C2×C4×C83C2×C22⋊C411yescharacteristic
384C2×C4×C83C2×C22⋊C411yescharacteristic
385C2×C4×C83C2×C22⋊C411yescharacteristic
386C2×C4×C83C2×C22⋊C411yescharacteristic
387C2×C4×C83C23×C411yescharacteristic
388C2×C4×C83C22×D411yescharacteristic
389C2×C4×C83C22×D411yescharacteristic
390C8×C83—41no—
391C8×C83—41no—
392C8×C83—41no—
393C8×C83—41no—
394C8×C83—41no—
395C8×C83—41no—
396C8×C83—41no—
397C8×C83—41no—
398C22×C83—21no—
399C22×C83—21no—
400C22×C83—21no—
401C22×C83—21no—
402C22×C83—21no—
403C22×C83—21no—
404C22×C83—21no—
405C22×C83—21no—
406C22×C83—41no—
407C22×C83—41no—
408C22×C83—41no—
409C22×C83#42112yes—
410C22×C83C22×C22⋊C411yescharacteristic
411C4×C83—21no—
412C4×C83—21no—
413C4×C83—21no—
414C4×C83—22no—
415C4×C83—21no—
416C4×C83—21no—
417C4×C83—21no—
418C4×C83—21no—
419C4×C83—21no—
420C4×C83—21no—
421C4×C83—21no—
422C4×C83—41no—
423C4×C83—41no—
424C4×C83—41no—
425C4×C83—41no—
426C4×C83—41no—
427C4×C83—41no—
428C4×C83C2×#13111yescharacteristic
429C4×C83#56811yescharacteristic
430C4×C83#57711yescharacteristic
431C4×C83#57811yescharacteristic
432#17524C8311yesmaximal, characteristic, direct product factor, Sylow
433C2×C83—22no—
434C2×C83—41no—
435C2×C83—41no—
436C2×C83—81no—
437C2×C83#288011yescharacteristic
438C2×C83#289811yescharacteristic
439C2×C83C2×#42111yescharacteristic
440#3482C2×C8311yescharacteristic
441#2990C2×C8311yescharacteristic, complemented
442#2922C2×C8311yescharacteristic, complemented
443#1497C2×C8311yescharacteristic, complemented
444#1495C2×C8311yescharacteristic, complemented
445#1494C2×C8311yescharacteristic, complemented
446#1491C2×C8311yescharacteristic, complemented
447#1488C2×C8311yescharacteristic, complemented
448#1487C2×C8311yescharacteristic, complemented
449#1483C2×C8311yescharacteristic, complemented
450#1482C2×C8311yescharacteristic, complemented
451#1481C2×C8311yescharacteristic, complemented
452#1479C2×C8311yescharacteristic, complemented
453#1477C2×C8311yescharacteristic, complemented
454C2×Q8⋊C8C2×C8311yescharacteristic, complemented
455C83#1752411yescharacteristic, direct product factor, Sylow
456#557C4×C8311yescharacteristic
457#556—21no—
458#556C4×C8311yescharacteristic
459#552—21no—
460#552—21no—
461#552C4×C8311yescharacteristic
462#552C4×C8311yescharacteristic
463D4×Q8C4×C8311yescharacteristic
464#548C4×C8311yescharacteristic
465#548C4×C8311yescharacteristic
466#547—21no—
467#547C4×C8311yescharacteristic
468#533—21no—
469#533C22×C8311yescharacteristic
470#529—21no—
471#529—21no—
472#529C22×C8311yescharacteristic
473#529C22×C8311yescharacteristic
474C4×#41—21no—
475C4×#41C22×C8311yescharacteristic
476C4×#41C22×C8311yescharacteristic
477C2×C4×Q8C22×C8311yescharacteristic
478C2×C4×Q8C22×C8311yescharacteristic
479#446—21no—
480#435—21no—
481#435—21no—
482C8×D4—21no—
483#433—21no—
484#433—21no—
485#432C22×C8311yescharacteristic
486#432C22×C8311yescharacteristic
487#431C22×C8311yescharacteristic
488#431C22×C8311yescharacteristic
489#431C22×C8311yescharacteristic
490#431C22×C8311yescharacteristic
491#431C22×C8311yescharacteristic
492#424—21no—
493#423C22×C8311yescharacteristic
494C2×C4⋊C8C22×C8311yescharacteristic
495C2×C4⋊C8C22×C8311yescharacteristic
496#408—21no—
497C4×M16C22×C8311yescharacteristic
498C2×C4×C8C22×C8311yescharacteristic
499Q8⋊C8C22×C8311yescharacteristic
500Q8⋊C8C22×C8311yescharacteristic
501Q8⋊C8C22×C8311yescharacteristic
502Q8⋊C8C22×C8311yescharacteristic
503Q8⋊C8C22×C8311yescharacteristic
504Q8⋊C8C22×C8311yescharacteristic
505Q8⋊C8C22×C8311yescharacteristic
506Q8⋊C8C22×C8311yescharacteristic
507Q8⋊C8C22×C8311yescharacteristic
508Q8⋊C8C22×C8311yescharacteristic
509Q8⋊C8C22×C8311yescharacteristic
510Q8⋊C8C22×C8311yescharacteristic
511D4⋊C8C22×C8311yescharacteristic
512D4⋊C8C22×C8311yescharacteristic
513D4⋊C8C22×C8311yescharacteristic
514D4⋊C8C22×C8311yescharacteristic
515C2×#41—21no—
516C2×#41C2×C4×C8311yescharacteristic
517C2×#41D4×C8311yescharacteristic
518C22×Q8C2×C4×C8311yescharacteristic
519C22×Q8C2×C4×C8311yescharacteristic
520C2×M16—21no—
521C2×M16—21no—
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C2×C4×C8311yescharacteristic
528C4⋊Q8C2×C4×C8311yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125C2×C4×C8311yescharacteristic
541#125C2×C4×C8311yescharacteristic
542#124—21no—
543#124—21no—
544#124C2×C4×C8311yescharacteristic
545#124C2×C4×C8311yescharacteristic
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C2×C4×C8311yescharacteristic
560C22⋊Q8C2×C4×C8311yescharacteristic
561C22⋊Q8C2×C4×C8311yescharacteristic
562C22⋊Q8C2×C4×C8311yescharacteristic
563#121—21no—
564#121—21no—
565#121C2×C4×C8311yescharacteristic
566#121C2×C4×C8311yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×C4×C8311yescharacteristic
574C4×Q8C2×C4×C8311yescharacteristic
575C4×Q8C2×C4×C8311yescharacteristic
576C4×Q8C2×C4×C8311yescharacteristic
577C4×Q8C2×C4×C8311yescharacteristic
578C4×Q8C2×C4×C8311yescharacteristic
579C4×Q8D4×C8311yescharacteristic
580C4×Q8C23×C8311yescharacteristic
581C4×Q8C23×C8311yescharacteristic
582C4×Q8C23×C8311yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4C2×C4×C8311yescharacteristic
591C4×D4C2×C4×C8311yescharacteristic
592C4×D4C2×C4×C8311yescharacteristic
593C4×D4C2×C4×C8311yescharacteristic
594C4×D4D4×C8311yescharacteristic
595C4×D4D4×C8311yescharacteristic
596C4×D4D4×C8311yescharacteristic
597C4×D4C23×C8311yescharacteristic
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C2×C4×C8311yescharacteristic
606#117D4×C8311yescharacteristic
607#117D4×C8311yescharacteristic
608#117D4×C8311yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4C2×C4×C8311yescharacteristic
612C2×C4⋊C4C2×C4×C8311yescharacteristic
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C23×C8311yescharacteristic
617C2×C42C23×C8311yescharacteristic
618C2×C42C23×C8311yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625C4⋊C8—21no—
626C4⋊C8C23×C8311yescharacteristic
627C4⋊C8C23×C8311yescharacteristic
628C4⋊C8C23×C8311yescharacteristic
629C4⋊C8C23×C8311yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637#97—21no—
638#97—21no—
639#97—21no—
640C4×C8—21no—
641C4×C8—21no—
642C4×C8C23×C8311yescharacteristic
643C4×C8C23×C8311yescharacteristic
644C4×C8C23×C8311yescharacteristic
645C4×C8C23×C8311yescharacteristic
646#41—22no—
647#41—42no—
648#41—41no—
649#41—44no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8C22⋊C4×C8311yescharacteristic
658C2×Q8C22×C4×C8311yescharacteristic
659C2×Q8C22×C4×C8311yescharacteristic
660C2×Q8C22×C4×C8311yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22⋊C4×C8311yescharacteristic
665C2×D4C22⋊C4×C8311yescharacteristic
666C2×D4C22⋊C4×C8311yescharacteristic
667C2×D4C22×C4×C8311yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4C22×C4×C8311yescharacteristic
676C22×C4C22×C4×C8311yescharacteristic
677C22×C4C22×C4×C8311yescharacteristic
678C22×C4C2×D4×C8311yescharacteristic
679C22×C4C2×D4×C8311yescharacteristic
680C22×C4C2×D4×C8311yescharacteristic
681C22×C4C2×D4×C8311yescharacteristic
682C22×C4C2×D4×C8311yescharacteristic
683C22×C4C2×D4×C8311yescharacteristic
684M16—42no—
685M16—81no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—81no—
696C2×C8—81no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C22⋊C4×C8311yescharacteristic
719C4⋊C4C22⋊C4×C8311yescharacteristic
720C4⋊C4C22⋊C4×C8311yescharacteristic
721C4⋊C4C22⋊C4×C8311yescharacteristic
722C4⋊C4C22⋊C4×C8311yescharacteristic
723C4⋊C4C22⋊C4×C8311yescharacteristic
724C4⋊C4C22×C4×C8311yescharacteristic
725C4⋊C4C22×C4×C8311yescharacteristic
726C4⋊C4C22×C4×C8311yescharacteristic
727C4⋊C4C22×C4×C8311yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4C22⋊C4×C8311yescharacteristic
742C22⋊C4C22⋊C4×C8311yescharacteristic
743C22⋊C4C22⋊C4×C8311yescharacteristic
744C22⋊C4C22⋊C4×C8311yescharacteristic
745C22⋊C4C22⋊C4×C8311yescharacteristic
746C22⋊C4C22⋊C4×C8311yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42C22×C4×C8311yescharacteristic
757C42C22×C4×C8311yescharacteristic
758C42C22×C4×C8311yescharacteristic
759C42C2×D4×C8311yescharacteristic
760C42C2×D4×C8311yescharacteristic
761C42C2×D4×C8311yescharacteristic
762C42C2×D4×C8311yescharacteristic
763C42C2×D4×C8311yescharacteristic
764C42C2×D4×C8311yescharacteristic
765C42C24×C8311yescharacteristic
766C23—21no—
767C23C2×C22⋊C4×C8311yescharacteristic
768C23C2×C22⋊C4×C8311yescharacteristic
769C23C2×C22⋊C4×C8311yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#131×C8312yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊C4×C8311yescharacteristic
819C2×C4C2×C22⋊C4×C8311yescharacteristic
820C2×C4C2×C22⋊C4×C8311yescharacteristic
821C2×C4C2×C22⋊C4×C8311yescharacteristic
822C2×C4C2×C22⋊C4×C8311yescharacteristic
823C2×C4C2×C22⋊C4×C8311yescharacteristic
824C2×C4C2×C22⋊C4×C8311yescharacteristic
825C2×C4C2×C22⋊C4×C8311yescharacteristic
826C2×C4C2×C22⋊C4×C8311yescharacteristic
827C2×C4C23×C4×C8311yescharacteristic
828C2×C4C22×D4×C8311yescharacteristic
829C2×C4C22×D4×C8311yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—41no—
837C8—41no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22#421×C8312yes—
850C22C22×C22⋊C4×C8311yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—22no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#131×C8311yescharacteristic
869C4#568×C8311yescharacteristic
870C4#577×C8311yescharacteristic
871C4#578×C8311yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2C83×#288011yescharacteristic
877C2C83×#289811yescharacteristic
878C2C2×#421×C8311yescharacteristic
subgroupG/H
centerC2×C4×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC42C24×C83
socleC22×C83C22×C22⋊C4
prime radicalC83×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C4×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2990C2semidirect
3. C83×#2922C2semidirect
4. C83×#1497C2semidirect
5. C83×#1495C2semidirect
6. C83×#1494C2semidirect
7. C83×#1491C2semidirect
8. C83×#1488C2semidirect
9. C83×#1487C2semidirect
10. C83×#1483C2semidirect
11. C83×#1482C2semidirect
12. C83×#1481C2semidirect
13. C83×#1479C2semidirect
14. C83×#1477C2semidirect
15. C2×Q8⋊C8×C83C2semidirect
432. #17524C83direct (N × H)
441. #2990C2×C83semidirect
442. #2922C2×C83semidirect
443. #1497C2×C83semidirect
444. #1495C2×C83semidirect
445. #1494C2×C83semidirect
446. #1491C2×C83semidirect
447. #1488C2×C83semidirect
448. #1487C2×C83semidirect
449. #1483C2×C83semidirect
450. #1482C2×C83semidirect
451. #1481C2×C83semidirect
452. #1479C2×C83semidirect
453. #1477C2×C83semidirect
454. C2×Q8⋊C8C2×C83semidirect
455. C83#17524direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#34822
C83×#29902
C83×#29222
C83×#14972
C83×#14952
C83×#14942
C83×#14912
C83×#14882
C83×#14872
C83×#14832
C83×#14822
C83×#14812
C83×#14792
C83×#14772
C2×Q8⋊C8×C832
#1752483