Finite Group Databasebeta

← #35327611

Subgroups — #35327611

Order 21248.

2106 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×#19127598C211yesmaximal, characteristic, complemented
2C2×#19127574C211yesmaximal, characteristic
3C2×#19127574C211yesmaximal, characteristic
4C2×#19127574C211yesmaximal, characteristic
5C2×#19127561C211yesmaximal, characteristic
6C2×C4×C22⋊Dic83C211yesmaximal, characteristic
7#24905727C211yesmaximal, characteristic, complemented
8#24905721C211yesmaximal, characteristic, complemented
9#24905717C211yesmaximal, characteristic, complemented
10#24905714C211yesmaximal, characteristic, complemented
11#24905697C211yesmaximal, characteristic, complemented
12#24905694C211yesmaximal, characteristic, complemented
13Dic83⋊#95C211yesmaximal, characteristic, complemented
14#24905686C211yesmaximal, characteristic
15C22×#95×C83C211yesmaximal, characteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×C22⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30#19127598—24no—
31#19127574—24no—
32#19127574—24no—
33#19127574C418yescomplemented
34#19127561—24no—
35C4×C22⋊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
50C24×C4×C83C2211yescharacteristic
51C24×C4×C83C2211yescharacteristic
52C24×C4×C83C2211yescharacteristic
53C2×#95×C83—24no—
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C2×C4⋊Dic83—22no—
67C2×C4⋊Dic83—22no—
68C2×C4⋊Dic83—22no—
69C2×C4⋊Dic83—22no—
70C2×C4⋊Dic83—41no—
71C2×C4⋊Dic83—41no—
72C2×Dic83⋊C4—22no—
73C2×Dic83⋊C4—22no—
74C2×Dic83⋊C4—22no—
75C2×Dic83⋊C4—22no—
76C2×Dic83⋊C4—22no—
77C2×Dic83⋊C4—22no—
78C2×Dic83⋊C4—22no—
79C2×Dic83⋊C4—22no—
80C2×Dic83⋊C4—22no—
81C2×Dic83⋊C4—22no—
82C2×Dic83⋊C4—41no—
83C2×Dic83⋊C4—41no—
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×C22⋊Dic83—22no—
91C2×C22⋊Dic83—22no—
92C2×C22⋊Dic83—22no—
93C2×C22⋊Dic83—22no—
94C2×C22⋊Dic83—22no—
95C2×C22⋊Dic83—22no—
96C2×C22⋊Dic83—22no—
97C2×C22⋊Dic83C2×C414yes—
98C2×C22⋊Dic83C2×C414yes—
99C2×C22⋊Dic83D414yes—
100C2×C22⋊Dic83D414yes—
101C2×C22⋊Dic83Q814yes—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—22no—
104C2×C4×Dic83—22no—
105C2×C4×Dic83—22no—
106C2×C4×Dic83—41no—
107C2×C4×Dic83—41no—
108C83⋊#95—22no—
109C83⋊#95—22no—
110C83⋊#95—22no—
111C83⋊#95—22no—
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×C414yescomplemented
121C83⋊#95C2×C414yescomplemented
122C25×C83C2311yescharacteristic
123C23×C4×C83—22no—
124C23×C4×C83—22no—
125C23×C4×C83—22no—
126C23×C4×C83—22no—
127C23×C4×C83—22no—
128C23×C4×C83—22no—
129C23×C4×C83—22no—
130C23×C4×C83—22no—
131C23×C4×C83—22no—
132C23×C4×C83—22no—
133C23×C4×C83—22no—
134C23×C4×C83—22no—
135C23×C4×C83—22no—
136C23×C4×C83—41no—
137C23×C4×C83—41no—
138C23×C4×C83—41no—
139C23×C4×C83—41no—
140C23×C4×C83—41no—
141C23×C4×C83—41no—
142C23×C4×C83C2×C414yes—
143C23×C4×C83Q814yes—
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2311yescharacteristic
149C23×C4×C83C2311yescharacteristic
150#95×C83—22no—
151#95×C83—22no—
152#95×C83—22no—
153#95×C83D414yes—
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—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C22×Dic83—21no—
200C22×Dic83C22×C412yes—
201C22×Dic83C22×C412yes—
202C22×Dic83C22×C412yes—
203C22×Dic83C22×C412yes—
204C22×Dic83C2×D412yes—
205C22×Dic83C2×D412yes—
206C22×Dic83C2×D412yes—
207C22×Dic83C2×D412yes—
208C22×Dic83C2×Q812yes—
209C22×Dic83C2×Q812yes—
210C4⋊Dic83—44no—
211C4⋊Dic83—44no—
212Dic83⋊C4—28no—
213Dic83⋊C4—44no—
214Dic83⋊C4—44no—
215Dic83⋊C4—44no—
216Dic83⋊C4—44no—
217Dic83⋊C4—44no—
218C22⋊Dic83—28no—
219C22⋊Dic83—28no—
220C22⋊Dic83—44no—
221C22⋊Dic83C4⋊C4116yescomplemented
222C4×Dic83—44no—
223C4×Dic83—44no—
224C24×C83—21no—
225C24×C83—21no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83—21no—
230C24×C83—21no—
231C24×C83—21no—
232C24×C83C22×C412yes—
233C24×C83C2×D412yes—
234C24×C83C2×D412yes—
235C24×C83C2×Q812yes—
236C24×C83C2×Q812yes—
237C24×C83#4112yes—
238C24×C83#4112yes—
239C24×C83C2411yescharacteristic
240C22×C4×C83—21no—
241C22×C4×C83—21no—
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—28no—
249C22×C4×C83—28no—
250C22×C4×C83—28no—
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×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83—28no—
276C22×C4×C83—28no—
277C22×C4×C83—44no—
278C22×C4×C83—44no—
279C22×C4×C83—44no—
280C22×C4×C83—44no—
281C22×C4×C83—44no—
282C22×C4×C83—44no—
283C22×C4×C83—44no—
284C22×C4×C83—44no—
285C22×C4×C83—44no—
286C22×C4×C83—44no—
287C22×C4×C83—44no—
288C22×C4×C83—44no—
289C22×C4×C83—44no—
290C22×C4×C83—44no—
291C22×C4×C83—44no—
292C22×C4×C83—44no—
293C22×C4×C83C22×C412yes—
294C22×C4×C83C22×C412yes—
295C22×C4×C83C2×D412yes—
296C22×C4×C83C2×D412yes—
297C22×C4×C83C2×D412yes—
298C22×C4×C83C2×Q812yes—
299C22×C4×C83C2×Q812yes—
300C22×C4×C83#4112yes—
301C22×C4×C83#4112yes—
302C22×C4×C83#4112yes—
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×C4⋊C414yes—
332C23×C83C4×D414yes—
333C23×C83C4×Q814yes—
334C23×C83#12114yes—
335C23×C83C22⋊Q814yes—
336C23×C83#12514yes—
337C23×C83C4⋊Q814yes—
338C23×C83C23×C411yescharacteristic
339C23×C83C22×D411yescharacteristic
340C23×C83C22×D411yescharacteristic
341C23×C83C22×D411yescharacteristic
342C23×C83C22×Q811yescharacteristic
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—416no—
378C2×C4×C83—416no—
379C2×C4×C83—416no—
380C2×C4×C83—41no—
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×C83—41no—
394C2×C4×C83—41no—
395C2×C4×C83—41no—
396C2×C4×C83C4×D414yes—
397C2×C4×C83C22⋊Q814yes—
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—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×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×Dic83—41no—
451C2×Dic83—41no—
452C2×Dic83C2×C4⋊C414yes—
453C2×Dic83C2×C4⋊C414yes—
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×C83#38918yescomplemented
469C22×C83C22×C4⋊C411yescharacteristic
470C22×C83C2×C4×D411yescharacteristic
471C22×C83C2×C4×D411yescharacteristic
472C22×C83C2×C4×Q811yescharacteristic
473C22×C83C4×#4111yescharacteristic
474C22×C83#51811yescharacteristic
475C22×C83#52011yescharacteristic
476C22×C83C2×#12111yescharacteristic
477C22×C83C2×C22⋊Q811yescharacteristic
478C22×C83C2×C22⋊Q811yescharacteristic
479C22×C83#52511yescharacteristic
480C22×C83C2×#12511yescharacteristic
481C22×C83#52911yescharacteristic
482C22×C83C2×C4⋊Q811yescharacteristic
483C22×C83#53311yescharacteristic
484C22×C83#53811yescharacteristic
485C22×C83#53911yescharacteristic
486C22×C83#54311yescharacteristic
487C22×C83#54411yescharacteristic
488C22×C83D4211yescharacteristic
489C22×C83D4211yescharacteristic
490C22×C83#54611yescharacteristic
491C22×C83#54611yescharacteristic
492C22×C83#54611yescharacteristic
493C22×C83#54611yescharacteristic
494C22×C83#54611yescharacteristic
495C22×C83#54711yescharacteristic
496C22×C83#54711yescharacteristic
497C22×C83D4×Q811yescharacteristic
498C22×C83#55111yescharacteristic
499C22×C83#55111yescharacteristic
500C22×C83#55211yescharacteristic
501C22×C83#55411yescharacteristic
502C22×C83#55411yescharacteristic
503C22×C83#55411yescharacteristic
504C4×C83—24no—
505C4×C83—24no—
506C4×C83—42no—
507C4×C83—42no—
508C4×C83—42no—
509C4×C83—42no—
510Dic83—24no—
511Dic83—24no—
512Dic83—42no—
513Dic83—42no—
514Dic83—42no—
515Dic83—42no—
516Dic83—81no—
517Dic83—81no—
518#14004—831nomaximal, Sylow
519C2×C83—28no—
520C2×C83C2×#38911yescharacteristic
521C2×C83C4×C22⋊Q811yescharacteristic
522C2×C83#232911yescharacteristic
523C2×C83D4×C4⋊C411yescharacteristic
524C2×C83#234911yescharacteristic
525C2×C83#235811yescharacteristic
526C2×C83#235911yescharacteristic
527C2×C83#242411yescharacteristic
528C2×C83#242511yescharacteristic
529C2×C83#243711yescharacteristic
530C2×C83#243811yescharacteristic
531C2×C83#244011yescharacteristic
532C2×C83#247311yescharacteristic
533C2×C83#250511yescharacteristic
534C2×C83#254911yescharacteristic
535C2×#389—831no—
536C2×#385—831no—
537C2×#385—831no—
538C2×#385—831no—
539C2×#380—831no—
540C2×C4×C22⋊C4—831no—
541C22×#95D8311yescharacteristic
542#1444—831no—
543#1442—831no—
544#1441—831no—
545#1441—831no—
546#1436—831no—
547#1436—831no—
548C4⋊#95—831no—
549C22⋊#95—831no—
550C83#1400411yescharacteristic, complemented, Sylow
551C24×C4C2×D8311yescharacteristic
552C24×C4C2×D8311yescharacteristic
553C24×C4C2×D8311yescharacteristic
554C22×C4⋊C4—831no—
555C22×C4⋊C4—831no—
556C22×C4⋊C4—831no—
557C22×C4⋊C4—831no—
558C22×C4⋊C4—831no—
559C22×C4⋊C4—831no—
560C22×C4⋊C4—831no—
561C22×C4⋊C4—831no—
562C22×C22⋊C4—831no—
563C22×C22⋊C4—831no—
564C22×C22⋊C4—831no—
565C22×C22⋊C4—831no—
566C22×C42—831no—
567C22×C42—831no—
568#389—1664no—
569#385—838no—
570#385—1664no—
571#385—1664no—
572#380—1664no—
573C4×C22⋊C4—1664no—
574C2×#95—24no—
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×#95C2×D8311yescharacteristic
590C2×#95C2×D8311yescharacteristic
591C2×#95C2×D8311yescharacteristic
592C2×#95C2×D8311yescharacteristic
593C25C22×D8311yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4—831no—
614C23×C4—831no—
615C23×C4—831no—
616C23×C4—831no—
617C23×C4—831no—
618C23×C4—831no—
619C23×C4—831no—
620C23×C4—831no—
621C23×C4Dic16614yes—
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—3321no—
634C2×C4⋊C4—3321no—
635C2×C4⋊C4—3321no—
636C2×C4⋊C4—3321no—
637C2×C4⋊C4—834no—
638C2×C4⋊C4—834no—
639C2×C4⋊C4—1662no—
640C2×C4⋊C4—1662no—
641C2×C4⋊C4—1662no—
642C2×C4⋊C4—1662no—
643C2×C4⋊C4—1662no—
644C2×C4⋊C4—1662no—
645C2×C4⋊C4—1662no—
646C2×C4⋊C4—1662no—
647C2×C4⋊C4—1662no—
648C2×C4⋊C4—1662no—
649C2×C4⋊C4—1662no—
650C2×C4⋊C4—1662no—
651C2×C4⋊C4—1662no—
652C2×C4⋊C4—1662no—
653C2×C22⋊C4—834no—
654C2×C22⋊C4—834no—
655C2×C22⋊C4—834no—
656C2×C22⋊C4—834no—
657C2×C22⋊C4—834no—
658C2×C22⋊C4—1662no—
659C2×C22⋊C4—1662no—
660C2×C22⋊C4—1662no—
661C2×C22⋊C4—1662no—
662C2×C22⋊C4—1662no—
663C2×C22⋊C4—1662no—
664C2×C22⋊C4—1662no—
665C2×C42—3321no—
666C2×C42—3321no—
667C2×C42—1662no—
668C2×C42—1662no—
669C2×C42—1662no—
670C2×C42—1662no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—3321no—
675#95—3321no—
676#95—834no—
677#95—834no—
678#95—1662no—
679#95—1662no—
680#95—1662no—
681#95—1662no—
682#95—1662no—
683#95—1662no—
684#95—1662no—
685#95—1662no—
686#95—1662no—
687#95—1662no—
688#95C22⋊D8314yes—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×C4×D8312yes—
698C24D4×D8312yes—
699C24D4×D8312yes—
700C24Q8×D8312yes—
701C24C2×Dic16612yes—
702C24#1305058912yes—
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—28no—
714C22×C4—28no—
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—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
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—1661no—
769C22×C4—1661no—
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—1661no—
795C22×C4—1661no—
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×C4—1661no—
813C22×C4—1661no—
814C22×C4C2×C4×D8312yes—
815C22×C4C2×C4×D8312yes—
816C22×C4C2×C22⋊D8312yes—
817C22×C4C2×C22⋊D8312yes—
818C22×C4C2×C22⋊D8312yes—
819C22×C4C2×Dic16612yes—
820C22×C4C2×Dic16612yes—
821C22×C4#1305059012yes—
822C22×C4#1305059012yes—
823C22×C4#1305059012yes—
824C4⋊C4—3324no—
825C4⋊C4—3324no—
826C4⋊C4—3324no—
827C4⋊C4—3324no—
828C4⋊C4—3324no—
829C4⋊C4—3324no—
830C4⋊C4—3324no—
831C4⋊C4—1668no—
832C22⋊C4—3324no—
833C22⋊C4—8316no—
834C22⋊C4—1668no—
835C22⋊C4—1668no—
836C42—3324no—
837C42—3324no—
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—
866C23C4⋊C4×D8314yes—
867C23(C22⋊D83)⋊C414yes—
868C23C4×Dic16614yes—
869C23#1458176514yes—
870C23#1458176914yes—
871C23#1458178214yes—
872C23#1458179114yes—
873C23C22×C4×D8311yescharacteristic
874C23C2×D4×D8311yescharacteristic
875C23C2×D4×D8311yescharacteristic
876C23C22×C22⋊D8311yescharacteristic
877C23C2×Q8×D8311yescharacteristic
878C23C22×Dic16611yescharacteristic
879C23C2×#1305058911yescharacteristic
880C23C2×#1305059011yescharacteristic
881C23C2×#1305059011yescharacteristic
882C23C2×#1305059011yescharacteristic
883C23C2×#1305059011yescharacteristic
884C23#1458183711yescharacteristic
885C23#1458183711yescharacteristic
886C23#1458183711yescharacteristic
887C23#1458184011yescharacteristic
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—416no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—41no—
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—41no—
929C2×C4—41no—
930C2×C4—41no—
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—3321no—
945C2×C4—3321no—
946C2×C4—3321no—
947C2×C4—3321no—
948C2×C4—3321no—
949C2×C4—3321no—
950C2×C4—3321no—
951C2×C4—3321no—
952C2×C4—3321no—
953C2×C4—3321no—
954C2×C4—3321no—
955C2×C4—3321no—
956C2×C4—3321no—
957C2×C4—3321no—
958C2×C4—3321no—
959C2×C4—3321no—
960C2×C4—3321no—
961C2×C4—834no—
962C2×C4—834no—
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×C4—1662no—
987C2×C4C4×C22⋊D8314yes—
988C2×C4#1458177114yes—
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—
1003C22#1912759818yescomplemented
1004C22C2×C4⋊C4×D8311yescharacteristic
1005C22C2×(C22⋊D83)⋊C411yescharacteristic
1006C22C2×C4×C22⋊D8311yescharacteristic
1007C22C2×C4×Dic16611yescharacteristic
1008C22C4×#1305059011yescharacteristic
1009C22#1912817411yescharacteristic
1010C22#1912818211yescharacteristic
1011C22C2×#1458176511yescharacteristic
1012C22C2×#1458176911yescharacteristic
1013C22C2×#1458177111yescharacteristic
1014C22#1912821211yescharacteristic
1015C22C2×#1458178211yescharacteristic
1016C22#1912823511yescharacteristic
1017C22C2×#1458179111yescharacteristic
1018C22#1912825811yescharacteristic
1019C22#1912828911yescharacteristic
1020C22#1912829811yescharacteristic
1021C22#1912832711yescharacteristic
1022C22#1912833211yescharacteristic
1023C22D4×C22⋊D8311yescharacteristic
1024C22D4×C22⋊D8311yescharacteristic
1025C22#1912834111yescharacteristic
1026C22#1912834111yescharacteristic
1027C22#1912834111yescharacteristic
1028C22#1912834111yescharacteristic
1029C22#1912834511yescharacteristic
1030C22#1912835211yescharacteristic
1031C22#1912835211yescharacteristic
1032C22Q8×C22⋊D8311yescharacteristic
1033C22#1912837711yescharacteristic
1034C22#1912837711yescharacteristic
1035C22#1912838611yescharacteristic
1036C22#1912840611yescharacteristic
1037C22#1912840611yescharacteristic
1038C22#1912840611yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—3322no—
1046C4—3322no—
1047C4—3322no—
1048C4—3322no—
1049C4—6641no—
1050C4—6641no—
1051C4—1664no—
1052C4—1664no—
1053C2—28no—
1054C2C2×#1912759811yescharacteristic
1055C2C4×#1458177111yescharacteristic
1056C2#2491019611yescharacteristic
1057C2C4⋊C4×C22⋊D8311yescharacteristic
1058C2#2491037011yescharacteristic
1059C2#2491044211yescharacteristic
1060C2#2491045111yescharacteristic
1061C2#2491099911yescharacteristic
1062C2#2491101411yescharacteristic
1063C2#2491112411yescharacteristic
1064C2#2491113911yescharacteristic
1065C2#2491115911yescharacteristic
1066C2#2491159811yescharacteristic
1067C2#2491196411yescharacteristic
1068C2#2491247411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC22×#95×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC22×#95D83
hypocenterC83#14004
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C2×#19127598C2semidirect
7. #24905727C2semidirect
8. #24905721C2semidirect
9. #24905717C2semidirect
10. #24905714C2semidirect
11. #24905697C2semidirect
12. #24905694C2semidirect
13. Dic83⋊#95C2semidirect
33. #19127574C4semidirect
88. C2×Dic83⋊C4C2×C4semidirect
89. C2×Dic83⋊C4C2×C4semidirect
120. C83⋊#95C2×C4semidirect
121. C83⋊#95C2×C4semidirect
221. C22⋊Dic83C4⋊C4semidirect
468. C22×C83#389semidirect
550. C83#14004semidirect
1003. C22#19127598semidirect

Maximal subgroups

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

subgroupindex
C2×#191275982
C2×#191275742
C2×#191275612
C2×C4×C22⋊Dic832
#249057272
#249057212
#249057172
#249057142
#249056972
#249056942
Dic83⋊#952
#249056862
C22×#95×C832
#1400483