Finite Group Databasebeta

← #35325913

Subgroups — #35325913

Order 21248.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127574C211yesmaximal, characteristic
2C2×#19127573C211yesmaximal, characteristic
3C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic83C211yesmaximal, characteristic
5C2×C22⋊C4×Dic83C211yesmaximal, characteristic
6C22×C83⋊#95C211yesmaximal, characteristic
7#24905696C211yesmaximal, characteristic, complemented
8#24905696C211yesmaximal, characteristic, complemented
9#24905694C211yesmaximal, characteristic, complemented
10#24905694C211yesmaximal, characteristic, complemented
11Dic83⋊#95C211yesmaximal, characteristic, complemented
12#24905689C211yesmaximal, characteristic, complemented
13#24905685C211yesmaximal, characteristic
14C4×C83⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C24×Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28#19127574C418yescomplemented
29#19127573C418yescomplemented
30C4×Dic83⋊C4—24no—
31C22⋊C4×Dic83—24no—
32C22⋊C4×Dic83C418yescomplemented
33C2×C83⋊#95—24no—
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
36C2×C83⋊#95C2211yescharacteristic
37C2×C83⋊#95C2211yescharacteristic
38C2×C83⋊#95C2211yescharacteristic
39C2×C83⋊#95C2211yescharacteristic
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C24×C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2211yescharacteristic
53C22×C42×C83C2211yescharacteristic
54C22×C42×C83C2211yescharacteristic
55C4×C22⋊C4×C83—24no—
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C23×Dic83—22no—
59C23×Dic83—22no—
60C23×Dic83—22no—
61C23×Dic83—22no—
62C23×Dic83—22no—
63C23×Dic83—22no—
64C23×Dic83—22no—
65C23×Dic83—22no—
66C23×Dic83—41no—
67C23×Dic83—41no—
68C23×Dic83—41no—
69C23×Dic83—41no—
70C23×Dic83C2×C414yes—
71C23×Dic83C2×C414yes—
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C2×Dic83⋊C4—22no—
81C2×Dic83⋊C4—22no—
82C2×Dic83⋊C4—22no—
83C2×Dic83⋊C4—22no—
84C2×Dic83⋊C4—41no—
85C2×Dic83⋊C4—41no—
86C2×Dic83⋊C4—41no—
87C2×Dic83⋊C4—41no—
88C2×Dic83⋊C4C2×C414yescomplemented
89C2×Dic83⋊C4C2×C414yescomplemented
90C2×Dic83⋊C4C2×C414yescomplemented
91C2×Dic83⋊C4C2×C414yescomplemented
92C2×C22⋊Dic83—22no—
93C2×C22⋊Dic83—22no—
94C2×C22⋊Dic83C2×C414yes—
95C2×C22⋊Dic83C2×C414yes—
96C2×C22⋊Dic83C2×C414yes—
97C2×C22⋊Dic83C2×C414yes—
98C2×C4×Dic83—22no—
99C2×C4×Dic83—22no—
100C2×C4×Dic83—22no—
101C2×C4×Dic83—22no—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—22no—
104C2×C4×Dic83—41no—
105C2×C4×Dic83—41no—
106C2×C4×Dic83—41no—
107C2×C4×Dic83—41no—
108C2×C4×Dic83C2×C414yescomplemented
109C2×C4×Dic83C2×C414yescomplemented
110C83⋊#95—22no—
111C83⋊#95—22no—
112C83⋊#95—22no—
113C83⋊#95—22no—
114C83⋊#95—22no—
115C83⋊#95—22no—
116C83⋊#95—22no—
117C83⋊#95—41no—
118C83⋊#95—41no—
119C83⋊#95C2×C414yescomplemented
120C83⋊#95C2×C414yescomplemented
121C83⋊#95C2×C414yescomplemented
122C83⋊#95C2×C414yescomplemented
123C83⋊#95C2×C414yescomplemented
124C83⋊#95C2×C414yescomplemented
125C83⋊#95D414yes—
126C25×C83C2311yescharacteristic
127C23×C4×C83—22no—
128C23×C4×C83—22no—
129C23×C4×C83—22no—
130C23×C4×C83—22no—
131C23×C4×C83—41no—
132C23×C4×C83—41no—
133C23×C4×C83C2×C414yes—
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C2×C22⋊C4×C83—22no—
141C2×C22⋊C4×C83—22no—
142C2×C22⋊C4×C83C2×C414yes—
143C2×C22⋊C4×C83C2×C414yes—
144C2×C22⋊C4×C83D414yes—
145C2×C22⋊C4×C83Q814yes—
146C2×C42×C83—22no—
147C2×C42×C83—22no—
148C2×C42×C83—22no—
149C2×C42×C83—22no—
150C2×C42×C83—41no—
151C2×C42×C83—41no—
152#95×C83—22no—
153#95×C83—22no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83—21no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83—21no—
165C22×Dic83—21no—
166C22×Dic83—21no—
167C22×Dic83—21no—
168C22×Dic83—21no—
169C22×Dic83—21no—
170C22×Dic83—28no—
171C22×Dic83—28no—
172C22×Dic83—21no—
173C22×Dic83—21no—
174C22×Dic83—21no—
175C22×Dic83—21no—
176C22×Dic83—21no—
177C22×Dic83—21no—
178C22×Dic83—21no—
179C22×Dic83—21no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—28no—
197C22×Dic83—28no—
198C22×Dic83—44no—
199C22×Dic83—44no—
200C22×Dic83—44no—
201C22×Dic83—44no—
202C22×Dic83—44no—
203C22×Dic83—44no—
204C22×Dic83—44no—
205C22×Dic83—44no—
206C22×Dic83—44no—
207C22×Dic83—44no—
208C22×Dic83C22×C412yes—
209C22×Dic83C22×C412yes—
210C22×Dic83C22×C412yes—
211C22×Dic83C22×C412yes—
212C22×Dic83C22×C412yes—
213C22×Dic83C22×C412yes—
214C22×Dic83C22×C412yes—
215C22×Dic83C22×C412yes—
216C22×Dic83C22×C412yes—
217C22×Dic83C22×C412yes—
218C22×Dic83C22×C412yes—
219C22×Dic83C22×C412yes—
220C22×Dic83C2×D412yes—
221C22×Dic83C2×D412yes—
222C22×Dic83#4112yes—
223C22×Dic83#4112yes—
224Dic83⋊C4—28no—
225Dic83⋊C4—28no—
226Dic83⋊C4—44no—
227Dic83⋊C4—44no—
228C22⋊Dic83—28no—
229C22⋊Dic83C42116yescomplemented
230C4×Dic83—28no—
231C4×Dic83—44no—
232C4×Dic83—44no—
233C4×Dic83—44no—
234C24×C83—21no—
235C24×C83—21no—
236C24×C83—21no—
237C24×C83—21no—
238C24×C83—21no—
239C24×C83—21no—
240C24×C83—21no—
241C24×C83—21no—
242C24×C83C22×C412yes—
243C24×C83C22×C412yes—
244C24×C83C22×C412yes—
245C24×C83C2×D412yes—
246C24×C83C2×Q812yes—
247C24×C83#4112yes—
248C24×C83#4112yes—
249C24×C83C2411yescharacteristic
250C22×C4×C83—21no—
251C22×C4×C83—21no—
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—21no—
261C22×C4×C83—21no—
262C22×C4×C83—28no—
263C22×C4×C83—21no—
264C22×C4×C83—21no—
265C22×C4×C83—21no—
266C22×C4×C83—21no—
267C22×C4×C83—21no—
268C22×C4×C83—21no—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83—21no—
276C22×C4×C83—21no—
277C22×C4×C83—21no—
278C22×C4×C83—21no—
279C22×C4×C83—21no—
280C22×C4×C83—21no—
281C22×C4×C83—28no—
282C22×C4×C83—44no—
283C22×C4×C83—44no—
284C22×C4×C83—44no—
285C22×C4×C83—44no—
286C22×C4×C83—44no—
287C22×C4×C83C22×C412yes—
288C22×C4×C83C22×C412yes—
289C22×C4×C83C22×C412yes—
290C22×C4×C83C22×C412yes—
291C22×C4×C83C22×C412yes—
292C22×C4×C83C22×C412yes—
293C22×C4×C83C2×D412yes—
294C22×C4×C83C2×D412yes—
295C22×C4×C83C2×D412yes—
296C22×C4×C83C2×Q812yes—
297C22×C4×C83C2×Q812yes—
298C22×C4×C83#4112yes—
299C22⋊C4×C83—28no—
300C22⋊C4×C83C4⋊C4116yescomplemented
301C42×C83—44no—
302C42×C83—44no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83—22no—
311C23×C83—22no—
312C23×C83—22no—
313C23×C83—22no—
314C23×C83—22no—
315C23×C83—22no—
316C23×C83—22no—
317C23×C83—22no—
318C23×C83—22no—
319C23×C83—22no—
320C23×C83—22no—
321C23×C83—22no—
322C23×C83—22no—
323C23×C83—22no—
324C23×C83—22no—
325C23×C83—22no—
326C23×C83—22no—
327C23×C83—22no—
328C23×C83—22no—
329C23×C83—22no—
330C23×C83—22no—
331C23×C83C2×C4214yes—
332C23×C83C2×C4⋊C414yes—
333C23×C83#11714yes—
334C23×C83C4×D414yes—
335C23×C83C4×D414yes—
336C23×C83C4×Q814yes—
337C23×C83C4×Q814yes—
338C23×C83C23×C411yescharacteristic
339C23×C83C23×C411yescharacteristic
340C23×C83C23×C411yescharacteristic
341C23×C83C22×D411yescharacteristic
342C23×C83C22×D411yescharacteristic
343C23×C83C22×Q811yescharacteristic
344C23×C83C2×#4111yescharacteristic
345C23×C83C2×#4111yescharacteristic
346C23×C83C2×#4111yescharacteristic
347C23×C83C2×#4111yescharacteristic
348C23×C83C2×#4111yescharacteristic
349C23×C83H(5,𝔽2)11yescharacteristic
350C23×C83H(5,𝔽2)11yescharacteristic
351C23×C83H(5,𝔽2)11yescharacteristic
352C23×C832−1+411yescharacteristic
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—22no—
373C2×C4×C83—22no—
374C2×C4×C83—22no—
375C2×C4×C83—22no—
376C2×C4×C83—22no—
377C2×C4×C83—22no—
378C2×C4×C83—22no—
379C2×C4×C83—22no—
380C2×C4×C83—416no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—41no—
384C2×C4×C83—41no—
385C2×C4×C83—41no—
386C2×C4×C83—41no—
387C2×C4×C83—41no—
388C2×C4×C83—41no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83—41no—
392C2×C4×C83—41no—
393C2×C4×C83C2×C4⋊C414yes—
394C2×C4×C83C2×C4⋊C414yes—
395C2×C4×C83C4×D414yes—
396C2×Dic83—22no—
397C2×Dic83—22no—
398C2×Dic83—22no—
399C2×Dic83—22no—
400C2×Dic83—22no—
401C2×Dic83—22no—
402C2×Dic83—22no—
403C2×Dic83—22no—
404C2×Dic83—22no—
405C2×Dic83—22no—
406C2×Dic83—22no—
407C2×Dic83—22no—
408C2×Dic83—22no—
409C2×Dic83—22no—
410C2×Dic83—22no—
411C2×Dic83—22no—
412C2×Dic83—22no—
413C2×Dic83—22no—
414C2×Dic83—22no—
415C2×Dic83—22no—
416C2×Dic83—22no—
417C2×Dic83—22no—
418C2×Dic83—22no—
419C2×Dic83—22no—
420C2×Dic83—22no—
421C2×Dic83—22no—
422C2×Dic83—22no—
423C2×Dic83—22no—
424C2×Dic83—22no—
425C2×Dic83—22no—
426C2×Dic83—22no—
427C2×Dic83—22no—
428C2×Dic83—22no—
429C2×Dic83—22no—
430C2×Dic83—22no—
431C2×Dic83—22no—
432C2×Dic83—416no—
433C2×Dic83—416no—
434C2×Dic83—41no—
435C2×Dic83—41no—
436C2×Dic83—41no—
437C2×Dic83—41no—
438C2×Dic83—41no—
439C2×Dic83—41no—
440C2×Dic83—41no—
441C2×Dic83—41no—
442C2×Dic83—41no—
443C2×Dic83—41no—
444C2×Dic83—41no—
445C2×Dic83—41no—
446C2×Dic83—41no—
447C2×Dic83—41no—
448C2×Dic83—41no—
449C2×Dic83—41no—
450C2×Dic83C2×C4214yes—
451C2×Dic83C2×C4214yes—
452C2×Dic83C4×D414yes—
453C2×Dic83C4×D414yes—
454C22×C83—24no—
455C22×C83—24no—
456C22×C83—24no—
457C22×C83—24no—
458C22×C83—24no—
459C22×C83—24no—
460C22×C83—24no—
461C22×C83—24no—
462C22×C83—24no—
463C22×C83—24no—
464C22×C83—24no—
465C22×C83—24no—
466C22×C83—24no—
467C22×C83—24no—
468C22×C83C4×C4⋊C418yescomplemented
469C22×C83C22×C4211yescharacteristic
470C22×C83C22×C4⋊C411yescharacteristic
471C22×C83C2×#11711yescharacteristic
472C22×C83C2×C4×D411yescharacteristic
473C22×C83C2×C4×D411yescharacteristic
474C22×C83C2×C4×D411yescharacteristic
475C22×C83C2×C4×D411yescharacteristic
476C22×C83C2×C4×D411yescharacteristic
477C22×C83C2×C4×Q811yescharacteristic
478C22×C83C2×C4×Q811yescharacteristic
479C22×C83C4×#4111yescharacteristic
480C22×C83C4×#4111yescharacteristic
481C22×C83C4×#4111yescharacteristic
482C22×C83#51811yescharacteristic
483C22×C83#51811yescharacteristic
484C22×C83#51811yescharacteristic
485C22×C83#52011yescharacteristic
486C22×C83#52011yescharacteristic
487C22×C83#52011yescharacteristic
488C22×C83D4211yescharacteristic
489C22×C83#54611yescharacteristic
490C22×C83#54611yescharacteristic
491C22×C83#54611yescharacteristic
492C22×C83#54611yescharacteristic
493C22×C83#54711yescharacteristic
494C22×C83D4×Q811yescharacteristic
495C22×C83#55111yescharacteristic
496C22×C83#55111yescharacteristic
497C22×C83#55111yescharacteristic
498C22×C83#55111yescharacteristic
499C22×C83#55211yescharacteristic
500C22×C83#55211yescharacteristic
501C22×C83#55411yescharacteristic
502C22×C83#55411yescharacteristic
503C22×C83#55411yescharacteristic
504C4×C83—24no—
505C4×C83—24no—
506C4×C83—24no—
507C4×C83—42no—
508C4×C83—42no—
509C4×C83—42no—
510Dic83—24no—
511Dic83—24no—
512Dic83—24no—
513Dic83—24no—
514Dic83—42no—
515Dic83—42no—
516Dic83—42no—
517Dic83—42no—
518#13814—831nomaximal, Sylow
519C2×C83—28no—
520C2×C83C2×C4×C4⋊C411yescharacteristic
521C2×C83C42×D411yescharacteristic
522C2×C83#227511yescharacteristic
523C2×C83#234211yescharacteristic
524C2×C83#234311yescharacteristic
525C2×C83D4×C4⋊C411yescharacteristic
526C2×C83#234911yescharacteristic
527C2×C83#235811yescharacteristic
528C2×C83#235811yescharacteristic
529C2×C83#235911yescharacteristic
530C2×C83#235911yescharacteristic
531C2×C83#236011yescharacteristic
532C2×C83#236011yescharacteristic
533C2×C83#236811yescharacteristic
534C2×C83#236811yescharacteristic
535C2×#385—831no—
536C2×#385—831no—
537C2×C4×C4⋊C4—831no—
538C2×C4×C22⋊C4—831no—
539C2×C4×C22⋊C4—831no—
540C2×C4×C22⋊C4D8311yescharacteristic
541C22×#95—831no—
542#1436—831no—
543#1436—831no—
544#1436—831no—
545#1436—831no—
546C4⋊#95—831no—
547#1434—831no—
548C22⋊#95—831no—
549C4×#95—831no—
550C83#1381411yescharacteristic, complemented, Sylow
551C24×C4—831no—
552C24×C4—831no—
553C24×C4C2×D8311yescharacteristic
554C22×C4⋊C4—831no—
555C22×C4⋊C4—831no—
556C22×C4⋊C4—831no—
557C22×C4⋊C4—831no—
558C22×C22⋊C4—831no—
559C22×C22⋊C4—831no—
560C22×C22⋊C4C2×D8311yescharacteristic
561C22×C22⋊C4C2×D8311yescharacteristic
562C22×C42—831no—
563C22×C42—831no—
564C22×C42—831no—
565C22×C42—831no—
566C22×C42C2×D8311yescharacteristic
567C22×C42C2×D8311yescharacteristic
568#385—838no—
569#385—838no—
570C4×C4⋊C4—1664no—
571C4×C22⋊C4—24no—
572C4×C22⋊C4—838no—
573C4×C22⋊C4—1664no—
574C2×#95—831no—
575C2×#95—831no—
576C2×#95—831no—
577C2×#95—831no—
578C2×#95—831no—
579C2×#95—831no—
580C2×#95—831no—
581C2×#95—831no—
582C2×#95—831no—
583C2×#95—831no—
584C2×#95—831no—
585C2×#95—831no—
586C2×#95—831no—
587C2×#95—831no—
588C2×#95—831no—
589C2×#95—831no—
590C2×#95—1664no—
591C2×#95C2×D8311yescharacteristic
592C2×#95C2×D8311yescharacteristic
593C25C22×D8311yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—3321no—
601C23×C4—3321no—
602C23×C4—3321no—
603C23×C4—3321no—
604C23×C4—834no—
605C23×C4—834no—
606C23×C4—831no—
607C23×C4—831no—
608C23×C4—831no—
609C23×C4—831no—
610C23×C4—831no—
611C23×C4—831no—
612C23×C4—831no—
613C23×C4—831no—
614C23×C4—1662no—
615C23×C4—1662no—
616C23×C4—1662no—
617C23×C4—1662no—
618C23×C4—1662no—
619C23×C4—1662no—
620C23×C4—1662no—
621C23×C4—1662no—
622C23×C4C4×D8314yes—
623C23×C4C22×D8311yescharacteristic
624C23×C4C22×D8311yescharacteristic
625C23×C4C22×D8311yescharacteristic
626C23×C4C22×D8311yescharacteristic
627C23×C4C22×D8311yescharacteristic
628C23×C4C22×D8311yescharacteristic
629C2×C4⋊C4—3321no—
630C2×C4⋊C4—3321no—
631C2×C4⋊C4—3321no—
632C2×C4⋊C4—3321no—
633C2×C4⋊C4—834no—
634C2×C4⋊C4—834no—
635C2×C4⋊C4—834no—
636C2×C4⋊C4—834no—
637C2×C4⋊C4—1662no—
638C2×C4⋊C4—1662no—
639C2×C4⋊C4—1662no—
640C2×C4⋊C4—1662no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—834no—
644C2×C22⋊C4—834no—
645C2×C22⋊C4—834no—
646C2×C22⋊C4—834no—
647C2×C22⋊C4—1662no—
648C2×C22⋊C4—1662no—
649C2×C22⋊C4Dic16614yes—
650C2×C22⋊C4C4×D8314yes—
651C2×C22⋊C4C4×D8314yes—
652C2×C22⋊C4C22⋊D8314yes—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42—3321no—
660C2×C42—3321no—
661C2×C42—3321no—
662C2×C42—3321no—
663C2×C42—834no—
664C2×C42—834no—
665C2×C42—1662no—
666C2×C42—1662no—
667C2×C42—1662no—
668C2×C42—1662no—
669C2×C42—1662no—
670C2×C42—1662no—
671#95—22no—
672#95—22no—
673#95—3321no—
674#95—3321no—
675#95—834no—
676#95—834no—
677#95—834no—
678#95—834no—
679#95—834no—
680#95—834no—
681#95—834no—
682#95—1662no—
683#95—1662no—
684#95—1662no—
685#95—1662no—
686#95—1662no—
687#95—1662no—
688#95—1662no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×C4×D8312yes—
698C24C2×C4×D8312yes—
699C24C2×C4×D8312yes—
700C24C2×C22⋊D8312yes—
701C24C2×Dic16612yes—
702C24#1305059012yes—
703C24#1305059012yes—
704C24C23×D8311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
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—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—3324no—
743C22×C4—3324no—
744C22×C4—3324no—
745C22×C4—3324no—
746C22×C4—3324no—
747C22×C4—3324no—
748C22×C4—3324no—
749C22×C4—3324no—
750C22×C4—3324no—
751C22×C4—3324no—
752C22×C4—832no—
753C22×C4—832no—
754C22×C4—832no—
755C22×C4—832no—
756C22×C4—832no—
757C22×C4—832no—
758C22×C4—832no—
759C22×C4—832no—
760C22×C4—832no—
761C22×C4—832no—
762C22×C4—832no—
763C22×C4—832no—
764C22×C4—832no—
765C22×C4—832no—
766C22×C4—832no—
767C22×C4—832no—
768C22×C4—1668no—
769C22×C4—1668no—
770C22×C4—1661no—
771C22×C4—1661no—
772C22×C4—1661no—
773C22×C4—1661no—
774C22×C4—1661no—
775C22×C4—1661no—
776C22×C4—1661no—
777C22×C4—1661no—
778C22×C4—1661no—
779C22×C4—1661no—
780C22×C4—1661no—
781C22×C4—1661no—
782C22×C4—1661no—
783C22×C4—1661no—
784C22×C4—1661no—
785C22×C4—1661no—
786C22×C4—1661no—
787C22×C4—1661no—
788C22×C4—1661no—
789C22×C4—1661no—
790C22×C4—1661no—
791C22×C4—1661no—
792C22×C4—1661no—
793C22×C4—1661no—
794C22×C4—1668no—
795C22×C4—1668no—
796C22×C4—1661no—
797C22×C4—1661no—
798C22×C4—1661no—
799C22×C4—1661no—
800C22×C4—1661no—
801C22×C4—1661no—
802C22×C4—1661no—
803C22×C4—1661no—
804C22×C4—1661no—
805C22×C4—1661no—
806C22×C4—1661no—
807C22×C4—1661no—
808C22×C4—1661no—
809C22×C4—1661no—
810C22×C4—1661no—
811C22×C4—1661no—
812C22×C4C2×C4×D8312yes—
813C22×C4C2×C4×D8312yes—
814C22×C4C2×C4×D8312yes—
815C22×C4C2×C4×D8312yes—
816C22×C4C2×C4×D8312yes—
817C22×C4C2×C4×D8312yes—
818C22×C4D4×D8312yes—
819C22×C4C2×C22⋊D8312yes—
820C22×C4C2×C22⋊D8312yes—
821C22×C4C2×Dic16612yes—
822C22×C4C2×Dic16612yes—
823C22×C4#1305058912yes—
824C4⋊C4—3324no—
825C4⋊C4—3324no—
826C4⋊C4—1668no—
827C4⋊C4—1668no—
828C22⋊C4—28no—
829C22⋊C4—8316no—
830C22⋊C4—1668no—
831C22⋊C4Dic83⋊C4116yescomplemented
832C42—44no—
833C42—44no—
834C42—3324no—
835C42—3324no—
836C42—3324no—
837C42—1668no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C42×D8314yes—
867C23C2×Dic83⋊C414yes—
868C23#1458174914yes—
869C23C4×C22⋊D8314yes—
870C23C4×C22⋊D8314yes—
871C23C4×Dic16614yes—
872C23C4×Dic16614yes—
873C23C22×C4×D8311yescharacteristic
874C23C22×C4×D8311yescharacteristic
875C23C22×C4×D8311yescharacteristic
876C23C2×D4×D8311yescharacteristic
877C23C22×C22⋊D8311yescharacteristic
878C23C22×Dic16611yescharacteristic
879C23#41×D8311yescharacteristic
880C23#41×D8311yescharacteristic
881C23C2×#1305058911yescharacteristic
882C23C2×#1305059011yescharacteristic
883C23C2×#1305059011yescharacteristic
884C23#1458183711yescharacteristic
885C23#1458183711yescharacteristic
886C23#1458183811yescharacteristic
887C23#1458183911yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—3321no—
929C2×C4—3321no—
930C2×C4—3321no—
931C2×C4—3321no—
932C2×C4—3321no—
933C2×C4—3321no—
934C2×C4—3321no—
935C2×C4—3321no—
936C2×C4—3321no—
937C2×C4—3321no—
938C2×C4—3321no—
939C2×C4—3321no—
940C2×C4—3321no—
941C2×C4—3321no—
942C2×C4—3321no—
943C2×C4—3321no—
944C2×C4—33216no—
945C2×C4—33216no—
946C2×C4—834no—
947C2×C4—834no—
948C2×C4—834no—
949C2×C4—834no—
950C2×C4—1662no—
951C2×C4—1662no—
952C2×C4—1662no—
953C2×C4—1662no—
954C2×C4—1662no—
955C2×C4—1662no—
956C2×C4—1662no—
957C2×C4—1662no—
958C2×C4—1662no—
959C2×C4—1662no—
960C2×C4—1662no—
961C2×C4—1662no—
962C2×C4—1662no—
963C2×C4—1662no—
964C2×C4—1662no—
965C2×C4—1662no—
966C2×C4—1662no—
967C2×C4—1662no—
968C2×C4—1662no—
969C2×C4—1662no—
970C2×C4—1662no—
971C2×C4—1662no—
972C2×C4—1662no—
973C2×C4—1662no—
974C2×C4—1662no—
975C2×C4—1662no—
976C2×C4—1662no—
977C2×C4—1662no—
978C2×C4—1662no—
979C2×C4—1662no—
980C2×C4—1662no—
981C2×C4—1662no—
982C2×C4—1662no—
983C2×C4—1662no—
984C2×C4—1662no—
985C2×C4—1662no—
986C2×C4C2×Dic83⋊C414yes—
987C2×C4C2×Dic83⋊C414yes—
988C2×C4(C22⋊D83)⋊C414yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C4×Dic83⋊C418yescomplemented
1004C22C2×C42×D8311yescharacteristic
1005C22C22×Dic83⋊C411yescharacteristic
1006C22C2×#1458174911yescharacteristic
1007C22C4×D4×D8311yescharacteristic
1008C22C4×D4×D8311yescharacteristic
1009C22C2×(C22⋊D83)⋊C411yescharacteristic
1010C22C2×C4×C22⋊D8311yescharacteristic
1011C22C2×C4×C22⋊D8311yescharacteristic
1012C22C2×C4×Dic16611yescharacteristic
1013C22C2×C4×Dic16611yescharacteristic
1014C22C4×#1305058911yescharacteristic
1015C22C4×#1305058911yescharacteristic
1016C22#1912816911yescharacteristic
1017C22#1912817311yescharacteristic
1018C22#1912817311yescharacteristic
1019C22#1912817411yescharacteristic
1020C22#1912818011yescharacteristic
1021C22#1912818011yescharacteristic
1022C22#1912818111yescharacteristic
1023C22D4×C22⋊D8311yescharacteristic
1024C22#1912833911yescharacteristic
1025C22#1912834111yescharacteristic
1026C22#1912834511yescharacteristic
1027C22#1912834711yescharacteristic
1028C22#1912835011yescharacteristic
1029C22D4×Dic16611yescharacteristic
1030C22#1912837511yescharacteristic
1031C22#1912837711yescharacteristic
1032C22#1912838011yescharacteristic
1033C22#1912838011yescharacteristic
1034C22#1912838411yescharacteristic
1035C22#1912839111yescharacteristic
1036C22#1912840811yescharacteristic
1037C22#1912841011yescharacteristic
1038C22#1912841011yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—3322no—
1046C4—3322no—
1047C4—3322no—
1048C4—3322no—
1049C4—1664no—
1050C4—1664no—
1051C4—1664no—
1052C4—1664no—
1053C2—28no—
1054C2C2×C4×Dic83⋊C411yescharacteristic
1055C2C4×(C22⋊D83)⋊C411yescharacteristic
1056C2#2490982211yescharacteristic
1057C2#2491030611yescharacteristic
1058C2#2491031711yescharacteristic
1059C2D4×Dic83⋊C411yescharacteristic
1060C2#2491036811yescharacteristic
1061C2#2491044011yescharacteristic
1062C2#2491044211yescharacteristic
1063C2#2491044911yescharacteristic
1064C2#2491045511yescharacteristic
1065C2#2491046611yescharacteristic
1066C2#2491046911yescharacteristic
1067C2#2491054111yescharacteristic
1068C2#2491054611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#13814
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic83⋊C4C2semidirect
7. #24905696C2semidirect
8. #24905696C2semidirect
9. #24905694C2semidirect
10. #24905694C2semidirect
11. Dic83⋊#95C2semidirect
12. #24905689C2semidirect
14. C4×C83⋊#95C2semidirect
28. #19127574C4semidirect
29. #19127573C4semidirect
32. C22⋊C4×Dic83C4semidirect
88. C2×Dic83⋊C4C2×C4semidirect
89. C2×Dic83⋊C4C2×C4semidirect
90. C2×Dic83⋊C4C2×C4semidirect
91. C2×Dic83⋊C4C2×C4semidirect
108. C2×C4×Dic83C2×C4semidirect
109. C2×C4×Dic83C2×C4semidirect
119. C83⋊#95C2×C4semidirect
120. C83⋊#95C2×C4semidirect
121. C83⋊#95C2×C4semidirect
122. C83⋊#95C2×C4semidirect
123. C83⋊#95C2×C4semidirect
124. C83⋊#95C2×C4semidirect
229. C22⋊Dic83C42semidirect
300. C22⋊C4×C83C4⋊C4semidirect
468. C22×C83C4×C4⋊C4semidirect
550. C83#13814semidirect
831. C22⋊C4Dic83⋊C4semidirect
1003. C22C4×Dic83⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#191275742
C2×#191275732
C2×C4×Dic83⋊C42
C2×C22⋊C4×Dic832
C22×C83⋊#952
#249056962
#249056942
Dic83⋊#952
#249056892
#249056852
C4×C83⋊#952
C2×C4×C22⋊C4×C832
#1381483