Finite Group Databasebeta

← #35325998

Subgroups — #35325998

Order 21248.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127594C211yesmaximal, characteristic
2C2×#19127576C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic83C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic83C211yesmaximal, characteristic
6C2×C22⋊C4×Dic83C211yesmaximal, characteristic
7#24905700C211yesmaximal, characteristic
8#24905700C211yesmaximal, characteristic
9#24905697C211yesmaximal, characteristic, complemented
10#24905697C211yesmaximal, characteristic, complemented
11#24905697C211yesmaximal, characteristic, complemented
12#24905695C211yesmaximal, characteristic, complemented
13C4×C83⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic83C211yesmaximal, characteristic, complemented
15C2×#388×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30#19127594C418yescomplemented
31#19127576C418yescomplemented
32C4⋊C4×Dic83—24no—
33C4×C4⋊Dic83—24no—
34C22⋊C4×Dic83—24no—
35C22⋊C4×Dic83—24no—
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
50C22×C4⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2211yescharacteristic
53C22×C22⋊C4×C83C2211yescharacteristic
54C22×C42×C83C2211yescharacteristic
55#388×C83C418yescomplemented
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C23×Dic83—22no—
59C23×Dic83—22no—
60C23×Dic83—22no—
61C23×Dic83—22no—
62C23×Dic83—41no—
63C23×Dic83—41no—
64C23×Dic83C2×C414yes—
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C2×C4⋊Dic83—22no—
74C2×C4⋊Dic83—22no—
75C2×C4⋊Dic83—22no—
76C2×C4⋊Dic83—22no—
77C2×C4⋊Dic83—22no—
78C2×C4⋊Dic83—22no—
79C2×C4⋊Dic83C2×C414yes—
80C2×C4⋊Dic83C2×C414yes—
81C2×C4⋊Dic83C2×C414yescomplemented
82C2×C22⋊Dic83—22no—
83C2×C22⋊Dic83—22no—
84C2×C22⋊Dic83—22no—
85C2×C22⋊Dic83—22no—
86C2×C22⋊Dic83—41no—
87C2×C22⋊Dic83—41no—
88C2×C22⋊Dic83C2×C414yes—
89C2×C22⋊Dic83C2×C414yes—
90C2×C22⋊Dic83C2×C414yes—
91C2×C4×Dic83—22no—
92C2×C4×Dic83—22no—
93C2×C4×Dic83—22no—
94C2×C4×Dic83—22no—
95C2×C4×Dic83—22no—
96C2×C4×Dic83—22no—
97C2×C4×Dic83—22no—
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—22no—
105C2×C4×Dic83—41no—
106C2×C4×Dic83—41no—
107C2×C4×Dic83—41no—
108C2×C4×Dic83—41no—
109C2×C4×Dic83—41no—
110C2×C4×Dic83—41no—
111C2×C4×Dic83C2×C414yescomplemented
112C83⋊#95—22no—
113C83⋊#95—22no—
114C83⋊#95—22no—
115C83⋊#95—22no—
116C83⋊#95—22no—
117C83⋊#95—22no—
118C83⋊#95—41no—
119C83⋊#95—41no—
120C83⋊#95C2×C414yes—
121C83⋊#95C2×C414yes—
122C83⋊#95C2×C414yescomplemented
123C83⋊#95C2×C414yescomplemented
124C83⋊#95D414yes—
125C83⋊#95D414yes—
126C25×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83—22no—
134C2×C4⋊C4×C83—22no—
135C2×C4⋊C4×C83C2×C414yescomplemented
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—22no—
138C2×C22⋊C4×C83—22no—
139C2×C22⋊C4×C83—22no—
140C2×C22⋊C4×C83C2×C414yes—
141C2×C22⋊C4×C83C2×C414yes—
142C2×C22⋊C4×C83C2×C414yes—
143C2×C22⋊C4×C83C2×C414yes—
144C2×C22⋊C4×C83C2×C414yes—
145C2×C42×C83—22no—
146C2×C42×C83—22no—
147C2×C42×C83C2×C414yescomplemented
148#95×C83C2×C414yescomplemented
149#95×C83C2×C414yescomplemented
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
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—21no—
171C22×Dic83—21no—
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—28no—
191C22×Dic83—28no—
192C22×Dic83—44no—
193C22×Dic83—44no—
194C22×Dic83—44no—
195C22×Dic83—44no—
196C22×Dic83—44no—
197C22×Dic83C22×C412yes—
198C22×Dic83C22×C412yes—
199C22×Dic83C22×C412yes—
200C22×Dic83C22×C412yes—
201C22×Dic83C22×C412yes—
202C22×Dic83C22×C412yes—
203C22×Dic83C22×C412yes—
204C22×Dic83C22×C412yes—
205C22×Dic83C2×D412yes—
206C22×Dic83C2×D412yes—
207C22×Dic83C2×D412yes—
208C22×Dic83C2×D412yes—
209C22×Dic83#4112yes—
210C22×Dic83#4112yes—
211C22×Dic83#4112yes—
212C22×Dic83#4112yes—
213C4⋊Dic83—28no—
214C4⋊Dic83—28no—
215C4⋊Dic83—28no—
216C22⋊Dic83—28no—
217C22⋊Dic83—28no—
218C22⋊Dic83—44no—
219C4×Dic83—28no—
220C4×Dic83—44no—
221C4×Dic83—44no—
222C4×Dic83—44no—
223C4×Dic83—44no—
224C4×Dic83—44no—
225C4×Dic83—44no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83—21no—
230C24×C83—21no—
231C24×C83—21no—
232C24×C83—21no—
233C24×C83—21no—
234C24×C83—21no—
235C24×C83—21no—
236C24×C83—21no—
237C24×C83—21no—
238C24×C83C22×C412yes—
239C24×C83C22×C412yes—
240C24×C83C22×C412yes—
241C24×C83C2411yescharacteristic
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
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—21no—
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×C83C22×C412yes—
271C22×C4×C83C22×C412yes—
272C22×C4×C83C22×C412yes—
273C22×C4×C83C22×C412yes—
274C22×C4×C83C22×C412yes—
275C22×C4×C83C22×C412yes—
276C22×C4×C83C22×C412yes—
277C22×C4×C83C22×C412yes—
278C22×C4×C83C22×C412yes—
279C22×C4×C83C22×C412yes—
280C22×C4×C83C2×D412yes—
281C22×C4×C83C2×D412yes—
282C22×C4×C83#4112yes—
283C22×C4×C83#4112yes—
284C4⋊C4×C83—28no—
285C22⋊C4×C83—28no—
286C22⋊C4×C83—28no—
287C22⋊C4×C83C42116yescomplemented
288C42×C83—28no—
289C23×C83—22no—
290C23×C83—22no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—22no—
300C23×C83—22no—
301C23×C83—22no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—41no—
308C23×C83—41no—
309C23×C83—41no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83—41no—
321C23×C83—41no—
322C23×C83—41no—
323C23×C83C2×C4214yes—
324C23×C83C23×C411yescharacteristic
325C23×C83C23×C411yescharacteristic
326C23×C83C23×C411yescharacteristic
327C23×C83C22×D411yescharacteristic
328C23×C83C22×D411yescharacteristic
329C23×C83C2×#4111yescharacteristic
330C23×C83C2×#4111yescharacteristic
331C23×C83C2×#4111yescharacteristic
332C23×C83C2×#4111yescharacteristic
333C23×C83C2×#4111yescharacteristic
334C23×C83C2×#4111yescharacteristic
335C23×C83H(5,𝔽2)11yescharacteristic
336C23×C83H(5,𝔽2)11yescharacteristic
337C23×C832−1+411yescharacteristic
338C23×C832−1+411yescharacteristic
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—22no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
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—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83C2×C4214yes—
378C2×C4×C83C2×C4214yes—
379C2×C4×C83C4×D414yes—
380C2×C4×C83C4×D414yes—
381C2×Dic83—22no—
382C2×Dic83—22no—
383C2×Dic83—22no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—22no—
390C2×Dic83—22no—
391C2×Dic83—22no—
392C2×Dic83—22no—
393C2×Dic83—22no—
394C2×Dic83—22no—
395C2×Dic83—22no—
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—416no—
418C2×Dic83—41no—
419C2×Dic83—41no—
420C2×Dic83—41no—
421C2×Dic83—41no—
422C2×Dic83—41no—
423C2×Dic83—41no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83—41no—
427C2×Dic83—41no—
428C2×Dic83—41no—
429C2×Dic83—41no—
430C2×Dic83—41no—
431C2×Dic83—41no—
432C2×Dic83—41no—
433C2×Dic83—41no—
434C2×Dic83C4×D414yes—
435C2×Dic83C4×D414yes—
436C2×Dic83C4×D414yes—
437C2×Dic83C4×D414yes—
438C22×C83—24no—
439C22×C83—24no—
440C22×C83—24no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83—42no—
446C22×C83—42no—
447C22×C83—42no—
448C22×C83—42no—
449C22×C83—42no—
450C22×C83—42no—
451C22×C83—42no—
452C22×C83—42no—
453C22×C83C22×C4211yescharacteristic
454C22×C83C2×C4×D411yescharacteristic
455C22×C83C2×C4×D411yescharacteristic
456C22×C83C2×C4×D411yescharacteristic
457C22×C83C2×C4×D411yescharacteristic
458C22×C83C2×C4×D411yescharacteristic
459C22×C83C2×C4×D411yescharacteristic
460C22×C83C4×#4111yescharacteristic
461C22×C83C4×#4111yescharacteristic
462C22×C83C4×#4111yescharacteristic
463C22×C83C4×#4111yescharacteristic
464C22×C83C4×#4111yescharacteristic
465C22×C83C4×#4111yescharacteristic
466C22×C83#51811yescharacteristic
467C22×C83#51911yescharacteristic
468C22×C83#52011yescharacteristic
469C22×C83#52011yescharacteristic
470C22×C83#52011yescharacteristic
471C22×C83#52011yescharacteristic
472C22×C83D4211yescharacteristic
473C22×C83#54611yescharacteristic
474C22×C83#54611yescharacteristic
475C22×C83#54711yescharacteristic
476C22×C83#54711yescharacteristic
477C22×C83#54811yescharacteristic
478C22×C83#54811yescharacteristic
479C22×C83#55111yescharacteristic
480C22×C83#55111yescharacteristic
481C22×C83#55211yescharacteristic
482C22×C83#55211yescharacteristic
483C22×C83#55311yescharacteristic
484C22×C83#55311yescharacteristic
485C22×C83#55611yescharacteristic
486C22×C83#55611yescharacteristic
487C22×C83#55911yescharacteristic
488C4×C83—24no—
489C4×C83—24no—
490C4×C83—24no—
491C4×C83—24no—
492C4×C83—42no—
493C4×C83—42no—
494Dic83—24no—
495Dic83—24no—
496Dic83—24no—
497Dic83—24no—
498Dic83—42no—
499Dic83—42no—
500Dic83—42no—
501Dic83—42no—
502#13823—831nomaximal, Sylow
503C2×C83—44no—
504C2×C83C42×D411yescharacteristic
505C2×C83C42×D411yescharacteristic
506C2×C83#227411yescharacteristic
507C2×C83#235811yescharacteristic
508C2×C83#235911yescharacteristic
509C2×C83#235911yescharacteristic
510C2×C83#236111yescharacteristic
511C2×C83#236111yescharacteristic
512C2×C83#236211yescharacteristic
513C2×C83#236211yescharacteristic
514C2×C83#236711yescharacteristic
515C2×C83#236711yescharacteristic
516C2×C83#237311yescharacteristic
517C2×C83#237311yescharacteristic
518C2×C83#237411yescharacteristic
519C2×#388—831no—
520C2×#388D8311yescharacteristic
521C2×#385—831no—
522C2×C4×C4⋊C4—831no—
523C2×C4×C4⋊C4—831no—
524C2×C4×C22⋊C4—831no—
525C2×C4×C22⋊C4—831no—
526#1437—831no—
527#1437—831no—
528#1436—831no—
529#1436—831no—
530#1436—831no—
531#1436—831no—
532C4×#95—831no—
533C4×#95—831no—
534C83#1382311yescharacteristic, complemented, Sylow
535C24×C4—831no—
536C22×C4⋊C4—831no—
537C22×C4⋊C4—831no—
538C22×C4⋊C4—831no—
539C22×C4⋊C4C2×D8311yescharacteristic
540C22×C22⋊C4—831no—
541C22×C22⋊C4—831no—
542C22×C22⋊C4—831no—
543C22×C22⋊C4C2×D8311yescharacteristic
544C22×C22⋊C4C2×D8311yescharacteristic
545C22×C22⋊C4C2×D8311yescharacteristic
546C22×C42—831no—
547C22×C42—831no—
548C22×C42—831no—
549C22×C42—831no—
550C22×C42—831no—
551C22×C42—831no—
552C22×C42—831no—
553C22×C42C2×D8311yescharacteristic
554#388—838no—
555#388Dic8318yescomplemented
556#385—838no—
557C4×C4⋊C4—1664no—
558C4×C4⋊C4—1664no—
559C4×C22⋊C4—1664no—
560C4×C22⋊C4—1664no—
561C2×#95—831no—
562C2×#95—831no—
563C2×#95—831no—
564C2×#95—831no—
565C2×#95—831no—
566C2×#95—831no—
567C2×#95—831no—
568C2×#95—831no—
569C2×#95—831no—
570C2×#95—831no—
571C2×#95—831no—
572C2×#95—831no—
573C2×#95—831no—
574C2×#95—831no—
575C2×#95C2×D8311yescharacteristic
576C2×#95C2×D8311yescharacteristic
577C25C22×D8311yescharacteristic
578C23×C4—3321no—
579C23×C4—3321no—
580C23×C4—834no—
581C23×C4—831no—
582C23×C4—831no—
583C23×C4—831no—
584C23×C4—831no—
585C23×C4—831no—
586C23×C4—831no—
587C23×C4—831no—
588C23×C4—831no—
589C23×C4—1662no—
590C23×C4—1662no—
591C23×C4—1662no—
592C23×C4—1662no—
593C23×C4C22×D8311yescharacteristic
594C23×C4C22×D8311yescharacteristic
595C23×C4C22×D8311yescharacteristic
596C23×C4C22×D8311yescharacteristic
597C23×C4C22×D8311yescharacteristic
598C23×C4C22×D8311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—834no—
602C2×C4⋊C4—834no—
603C2×C4⋊C4—834no—
604C2×C4⋊C4—1662no—
605C2×C4⋊C4—1662no—
606C2×C4⋊C4—1662no—
607C2×C4⋊C4—1662no—
608C2×C4⋊C4—1662no—
609C2×C4⋊C4—1662no—
610C2×C4⋊C4C2×Dic8314yescomplemented
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—3321no—
616C2×C22⋊C4—3321no—
617C2×C22⋊C4—834no—
618C2×C22⋊C4—834no—
619C2×C22⋊C4—834no—
620C2×C22⋊C4—1662no—
621C2×C22⋊C4—1662no—
622C2×C22⋊C4—1662no—
623C2×C22⋊C4—1662no—
624C2×C22⋊C4C4×D8314yes—
625C2×C22⋊C4C4×D8314yes—
626C2×C22⋊C4C2×Dic8314yes—
627C2×C22⋊C4C2×Dic8314yes—
628C2×C22⋊C4C2×Dic8314yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—3321no—
632C2×C42—3321no—
633C2×C42—3321no—
634C2×C42—3321no—
635C2×C42—3321no—
636C2×C42—3321no—
637C2×C42—834no—
638C2×C42—1662no—
639C2×C42—1662no—
640C2×C42—1662no—
641C2×C42—1662no—
642C2×C42—1662no—
643C2×C42—1662no—
644C2×C42—1662no—
645C2×C42—1662no—
646C2×C42—1662no—
647C2×C42—1662no—
648C2×C42—1662no—
649C2×C42—1662no—
650C2×C42—1662no—
651C2×C42—1662no—
652C2×C42C2×Dic8314yescomplemented
653#95—3321no—
654#95—3321no—
655#95—834no—
656#95—834no—
657#95—834no—
658#95—834no—
659#95—834no—
660#95—834no—
661#95—1662no—
662#95—1662no—
663#95—1662no—
664#95—1662no—
665#95—1662no—
666#95—1662no—
667#95C2×Dic8314yescomplemented
668#95C2×Dic8314yescomplemented
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D8312yes—
682C24C2×C4×D8312yes—
683C24C22×Dic8312yes—
684C24C23×D8311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
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—3324no—
714C22×C4—3324no—
715C22×C4—3324no—
716C22×C4—3324no—
717C22×C4—3324no—
718C22×C4—832no—
719C22×C4—832no—
720C22×C4—832no—
721C22×C4—832no—
722C22×C4—832no—
723C22×C4—832no—
724C22×C4—832no—
725C22×C4—832no—
726C22×C4—832no—
727C22×C4—832no—
728C22×C4—832no—
729C22×C4—832no—
730C22×C4—832no—
731C22×C4—832no—
732C22×C4—832no—
733C22×C4—832no—
734C22×C4—1668no—
735C22×C4—1668no—
736C22×C4—1661no—
737C22×C4—1661no—
738C22×C4—1661no—
739C22×C4—1661no—
740C22×C4—1661no—
741C22×C4—1661no—
742C22×C4—1661no—
743C22×C4—1661no—
744C22×C4—1661no—
745C22×C4—1661no—
746C22×C4—1661no—
747C22×C4—1661no—
748C22×C4—1661no—
749C22×C4—1661no—
750C22×C4—1661no—
751C22×C4—1661no—
752C22×C4—1661no—
753C22×C4—1661no—
754C22×C4—1661no—
755C22×C4—1661no—
756C22×C4—1661no—
757C22×C4—1661no—
758C22×C4—1661no—
759C22×C4—1661no—
760C22×C4—1661no—
761C22×C4—1661no—
762C22×C4—1661no—
763C22×C4—1661no—
764C22×C4—1661no—
765C22×C4—1661no—
766C22×C4—1661no—
767C22×C4—1661no—
768C22×C4—1661no—
769C22×C4—1661no—
770C22×C4—1661no—
771C22×C4—1661no—
772C22×C4—1661no—
773C22×C4—1661no—
774C22×C4—1661no—
775C22×C4—1661no—
776C22×C4C2×C4×D8312yes—
777C22×C4C2×C4×D8312yes—
778C22×C4C2×C4×D8312yes—
779C22×C4C2×C4×D8312yes—
780C22×C4C22×Dic8312yes—
781C22×C4C22×Dic8312yes—
782C22×C4C22×Dic8312yes—
783C22×C4C22×Dic8312yes—
784C22×C4C22×Dic8312yes—
785C22×C4C22×Dic8312yes—
786C22×C4D4×D8312yes—
787C22×C4D4×D8312yes—
788C22×C4#1305058912yes—
789C22×C4#1305058912yes—
790C4⋊C4—28no—
791C4⋊C4—1668no—
792C4⋊C4—1668no—
793C4⋊C4—1668no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—3324no—
797C22⋊C4—1668no—
798C22⋊C4—1668no—
799C22⋊C4C4×Dic83116yescomplemented
800C42—28no—
801C42—3324no—
802C42—3324no—
803C42—3324no—
804C42—3324no—
805C42—3324no—
806C42—3324no—
807C42—1668no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4×Dic8314yes—
843C23C22×C4×D8311yescharacteristic
844C23C22×C4×D8311yescharacteristic
845C23C23×Dic8311yescharacteristic
846C23C2×D4×D8311yescharacteristic
847C23C2×D4×D8311yescharacteristic
848C23#41×D8311yescharacteristic
849C23#41×D8311yescharacteristic
850C23#41×D8311yescharacteristic
851C23#41×D8311yescharacteristic
852C23C2×#1305058911yescharacteristic
853C23C2×#1305058911yescharacteristic
854C23#1458183811yescharacteristic
855C23#1458183811yescharacteristic
856C23#1458183911yescharacteristic
857C23#1458183911yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—3321no—
897C2×C4—3321no—
898C2×C4—3321no—
899C2×C4—3321no—
900C2×C4—3321no—
901C2×C4—3321no—
902C2×C4—3321no—
903C2×C4—3321no—
904C2×C4—3321no—
905C2×C4—3321no—
906C2×C4—3321no—
907C2×C4—3321no—
908C2×C4—3321no—
909C2×C4—3321no—
910C2×C4—3321no—
911C2×C4—3321no—
912C2×C4—33216no—
913C2×C4—834no—
914C2×C4—834no—
915C2×C4—834no—
916C2×C4—834no—
917C2×C4—1662no—
918C2×C4—1662no—
919C2×C4—1662no—
920C2×C4—1662no—
921C2×C4—1662no—
922C2×C4—1662no—
923C2×C4—1662no—
924C2×C4—1662no—
925C2×C4—1662no—
926C2×C4—1662no—
927C2×C4—1662no—
928C2×C4—1662no—
929C2×C4—1662no—
930C2×C4—1662no—
931C2×C4—1662no—
932C2×C4—1662no—
933C2×C4—1662no—
934C2×C4—1662no—
935C2×C4—1662no—
936C2×C4—1662no—
937C2×C4—1662no—
938C2×C4—1662no—
939C2×C4—1662no—
940C2×C4—1662no—
941C2×C4—1662no—
942C2×C4—1662no—
943C2×C4—1662no—
944C2×C4—1662no—
945C2×C4—1662no—
946C2×C4—1662no—
947C2×C4—1662no—
948C2×C4—1662no—
949C2×C4—1662no—
950C2×C4—1662no—
951C2×C4—1662no—
952C2×C4—1662no—
953C2×C4C2×C4×Dic8314yes—
954C2×C4C2×C4×Dic8314yes—
955C2×C4D4×Dic8314yes—
956C2×C4D4×Dic8314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4×Dic8311yescharacteristic
973C22C4×D4×D8311yescharacteristic
974C22C4×D4×D8311yescharacteristic
975C22C4×D4×D8311yescharacteristic
976C22C4×D4×D8311yescharacteristic
977C22C2×D4×Dic8311yescharacteristic
978C22C2×D4×Dic8311yescharacteristic
979C22C4×#1305058911yescharacteristic
980C22C4×#1305058911yescharacteristic
981C22C4×#1305058911yescharacteristic
982C22C4×#1305058911yescharacteristic
983C22#41×Dic8311yescharacteristic
984C22#41×Dic8311yescharacteristic
985C22#1912817511yescharacteristic
986C22#1912817811yescharacteristic
987C22#1912818111yescharacteristic
988C22#1912818111yescharacteristic
989C22#1912818411yescharacteristic
990C22#1912818411yescharacteristic
991C22#1912833511yescharacteristic
992C22#1912834311yescharacteristic
993C22#1912834411yescharacteristic
994C22#1912834911yescharacteristic
995C22#1912835111yescharacteristic
996C22#1912835711yescharacteristic
997C22#1912835911yescharacteristic
998C22#1912837411yescharacteristic
999C22#1912837611yescharacteristic
1000C22#1912838711yescharacteristic
1001C22#1912838811yescharacteristic
1002C22#1912840211yescharacteristic
1003C22#1912840311yescharacteristic
1004C22#1912841811yescharacteristic
1005C22#1912842011yescharacteristic
1006C22#1912843311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—3322no—
1014C4—3322no—
1015C4—3322no—
1016C4—3322no—
1017C4—1664no—
1018C4—1664no—
1019C4—1664no—
1020C4—1664no—
1021C2—44no—
1022C2C4×D4×Dic8311yescharacteristic
1023C2C4×D4×Dic8311yescharacteristic
1024C2#2490981911yescharacteristic
1025C2#2491044111yescharacteristic
1026C2#2491045411yescharacteristic
1027C2#2491045911yescharacteristic
1028C2#2491047611yescharacteristic
1029C2#2491048311yescharacteristic
1030C2#2491048711yescharacteristic
1031C2#2491049311yescharacteristic
1032C2#2491053711yescharacteristic
1033C2#2491053811yescharacteristic
1034C2#2491058711yescharacteristic
1035C2#2491059011yescharacteristic
1036C2#2491059311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#13823
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic83C2semidirect
4. C2×C4×C4⋊Dic83C2semidirect
9. #24905697C2semidirect
10. #24905697C2semidirect
11. #24905697C2semidirect
12. #24905695C2semidirect
13. C4×C83⋊#95C2semidirect
14. #95×Dic83C2semidirect
30. #19127594C4semidirect
31. #19127576C4semidirect
55. #388×C83C4semidirect
81. C2×C4⋊Dic83C2×C4semidirect
111. C2×C4×Dic83C2×C4semidirect
122. C83⋊#95C2×C4semidirect
123. C83⋊#95C2×C4semidirect
135. C2×C4⋊C4×C83C2×C4semidirect
147. C2×C42×C83C2×C4semidirect
148. #95×C83C2×C4semidirect
149. #95×C83C2×C4semidirect
287. C22⋊C4×C83C42semidirect
534. C83#13823semidirect
555. #388Dic83semidirect
610. C2×C4⋊C4C2×Dic83semidirect
652. C2×C42C2×Dic83semidirect
667. #95C2×Dic83semidirect
668. #95C2×Dic83semidirect
799. C22⋊C4C4×Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275942
C2×#191275762
C2×C4⋊C4×Dic832
C2×C4×C4⋊Dic832
C2×C22⋊C4×Dic832
#249057002
#249056972
#249056952
C4×C83⋊#952
#95×Dic832
C2×#388×C832
#1382383