Finite Group Databasebeta

← #35328209

Subgroups — #35328209

Order 21248.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581769C211yesmaximal, characteristic
2C2×#19127606C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic83C211yesmaximal, characteristic
4C22×C83⋊#95C211yesmaximal, characteristic
5#24905733C211yesmaximal, characteristic, complemented
6#24905730C211yesmaximal, characteristic, complemented
7#24905713C211yesmaximal, characteristic, complemented
8#24905713C211yesmaximal, characteristic, complemented
9#24905698C211yesmaximal, characteristic, complemented
10#24905698C211yesmaximal, characteristic, complemented
11#24905692C211yesmaximal, characteristic, complemented
12#24905686C211yesmaximal, characteristic
13#24905685C211yesmaximal, characteristic
14#24905685C211yesmaximal, characteristic
15C2×#385×C83C211yesmaximal, characteristic
16C23×Dic166C2211yescharacteristic
17C24×Dic83C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C2×#14581769—24no—
20C2×#14581769—24no—
21C2×#14581769C418yescomplemented
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×C22⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29#19127606—24no—
30C22⋊C4×Dic83—24no—
31C2×C83⋊#95—24no—
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2211yescharacteristic
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×C4⋊C4×C83C2211yescharacteristic
52C22×C4⋊C4×C83C2211yescharacteristic
53C22×C22⋊C4×C83C2211yescharacteristic
54C22×C22⋊C4×C83C2211yescharacteristic
55#385×C83—24no—
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C22×Dic166—22no—
59C22×Dic166—22no—
60C22×Dic166—22no—
61C22×Dic166—22no—
62C22×Dic166—41no—
63C22×Dic166—41no—
64C22×Dic166C2×C414yescomplemented
65C23×Dic83—22no—
66C23×Dic83—22no—
67C23×Dic83—22no—
68C23×Dic83—22no—
69C23×Dic83—22no—
70C23×Dic83—22no—
71C23×Dic83—22no—
72C23×Dic83—22no—
73C23×Dic83—41no—
74C23×Dic83—41no—
75C23×Dic83—41no—
76C23×Dic83—41no—
77C23×Dic83C2×C414yes—
78C23×Dic83Q814yescomplemented
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87#14581769—232no—
88C2×C4⋊Dic83—22no—
89C2×C4⋊Dic83—22no—
90C2×C4⋊Dic83C2×C414yescomplemented
91C2×Dic83⋊C4—22no—
92C2×Dic83⋊C4—22no—
93C2×Dic83⋊C4—22no—
94C2×Dic83⋊C4—22no—
95C2×Dic83⋊C4C2×C414yescomplemented
96C2×Dic83⋊C4C2×C414yescomplemented
97C2×C22⋊Dic83—22no—
98C2×C22⋊Dic83—22no—
99C2×C22⋊Dic83—22no—
100C2×C22⋊Dic83—22no—
101C2×C22⋊Dic83C2×C414yes—
102C2×C22⋊Dic83Q814yescomplemented
103C2×C4×Dic83—22no—
104C2×C4×Dic83—22no—
105C2×C4×Dic83—22no—
106C2×C4×Dic83—22no—
107C2×C4×Dic83—41no—
108C2×C4×Dic83—41no—
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—22no—
119C83⋊#95—22no—
120C83⋊#95—41no—
121C83⋊#95—41no—
122C83⋊#95—41no—
123C83⋊#95—41no—
124C83⋊#95—41no—
125C83⋊#95—41no—
126C83⋊#95D414yes—
127C25×C83C2311yescharacteristic
128C23×C4×C83—22no—
129C23×C4×C83—22no—
130C23×C4×C83—22no—
131C23×C4×C83—22no—
132C23×C4×C83—22no—
133C23×C4×C83—41no—
134C23×C4×C83—41no—
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C2×C4⋊C4×C83—22no—
142C2×C4⋊C4×C83—22no—
143C2×C4⋊C4×C83—22no—
144C2×C4⋊C4×C83—22no—
145C2×C4⋊C4×C83—41no—
146C2×C4⋊C4×C83—41no—
147C2×C22⋊C4×C83—22no—
148C2×C22⋊C4×C83—22no—
149C2×C22⋊C4×C83—22no—
150C2×C22⋊C4×C83C2×C414yes—
151C2×C22⋊C4×C83D414yes—
152C2×C22⋊C4×C83D414yes—
153#95×C83—22no—
154#95×C83—22no—
155C2×Dic166—28no—
156C2×Dic166—28no—
157C2×Dic166—44no—
158C2×Dic166—44no—
159C2×Dic166—44no—
160C2×Dic166—44no—
161C2×Dic166—44no—
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—21no—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83—21no—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—21no—
207C22×Dic83—21no—
208C22×Dic83—28no—
209C22×Dic83—28no—
210C22×Dic83—44no—
211C22×Dic83—44no—
212C22×Dic83—44no—
213C22×Dic83—44no—
214C22×Dic83—44no—
215C22×Dic83—44no—
216C22×Dic83—44no—
217C22×Dic83—44no—
218C22×Dic83—44no—
219C22×Dic83—44no—
220C22×Dic83C22×C412yes—
221C22×Dic83C22×C412yes—
222C22×Dic83C22×C412yes—
223C22×Dic83C22×C412yes—
224C22×Dic83C2×D412yes—
225C22×Dic83C2×D412yes—
226C22×Dic83C2×Q812yes—
227C22×Dic83C2×Q812yes—
228C22×Dic83C2×Q812yes—
229C22×Dic83C2×Q812yes—
230C22×Dic83#4112yes—
231C22×Dic83#4112yes—
232C4⋊Dic83—28no—
233Dic83⋊C4—28no—
234Dic83⋊C4—28no—
235C22⋊Dic83—28no—
236C22⋊Dic83—28no—
237C4×Dic83—44no—
238C4×Dic83—44no—
239C24×C83—21no—
240C24×C83—21no—
241C24×C83—21no—
242C24×C83—21no—
243C24×C83—21no—
244C24×C83—21no—
245C24×C83—21no—
246C24×C83—21no—
247C24×C83C22×C412yes—
248C24×C83C2×D412yes—
249C24×C83C2×D412yes—
250C24×C83C2×Q812yes—
251C24×C83C2×Q812yes—
252C24×C83#4112yes—
253C24×C83#4112yes—
254C24×C83C2411yescharacteristic
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—28no—
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—21no—
282C22×C4×C83—21no—
283C22×C4×C83—21no—
284C22×C4×C83—21no—
285C22×C4×C83—21no—
286C22×C4×C83—21no—
287C22×C4×C83—21no—
288C22×C4×C83—21no—
289C22×C4×C83—21no—
290C22×C4×C83—44no—
291C22×C4×C83—44no—
292C22×C4×C83—44no—
293C22×C4×C83—44no—
294C22×C4×C83—44no—
295C22×C4×C83—44no—
296C22×C4×C83C22×C412yes—
297C22×C4×C83C22×C412yes—
298C22×C4×C83C2×D412yes—
299C22×C4×C83C2×D412yes—
300C22×C4×C83C2×D412yes—
301C22×C4×C83C2×D412yes—
302C22×C4×C83C2×D412yes—
303C22×C4×C83#4112yes—
304C4⋊C4×C83—44no—
305C4⋊C4×C83—44no—
306C22⋊C4×C83—44no—
307C22⋊C4×C83C22⋊C4116yes—
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×C83—22no—
332C23×C83—22no—
333C23×C83—22no—
334C23×C83—22no—
335C23×C83—22no—
336C23×C83C2×C22⋊C414yes—
337C23×C83C4×Q814yes—
338C23×C83C4×Q814yes—
339C23×C83C22⋊Q814yes—
340C23×C83C22⋊Q814yes—
341C23×C83#12414yes—
342C23×C83C4⋊Q814yes—
343C23×C83C23×C411yescharacteristic
344C23×C83C22×D411yescharacteristic
345C23×C83C22×D411yescharacteristic
346C23×C83C22×D411yescharacteristic
347C23×C83C22×Q811yescharacteristic
348C23×C83C22×Q811yescharacteristic
349C23×C83C2×#4111yescharacteristic
350C23×C83C2×#4111yescharacteristic
351C23×C83C2×#4111yescharacteristic
352C23×C83C2×#4111yescharacteristic
353C23×C83C2×#4111yescharacteristic
354C23×C83H(5,𝔽2)11yescharacteristic
355C23×C83H(5,𝔽2)11yescharacteristic
356C23×C83H(5,𝔽2)11yescharacteristic
357C23×C832−1+411yescharacteristic
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—416no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
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×C83—41no—
397C2×C4×C83—41no—
398C2×C4×C83—41no—
399C2×C4×C83C2×C22⋊C414yes—
400C2×C4×C83C2×C22⋊C414yes—
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—416no—
432C2×Dic83—416no—
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×Dic83—41no—
453C2×Dic83—41no—
454C2×Dic83—41no—
455C2×Dic83—41no—
456C2×Dic83—41no—
457C2×Dic83C4×D414yes—
458C2×Dic83C22⋊Q814yescomplemented
459Dic166—416no—
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—24no—
469C22×C83—24no—
470C22×C83—24no—
471C22×C83—24no—
472C22×C83—24no—
473C22×C83—24no—
474C22×C83#39118yescomplemented
475C22×C83C22×C22⋊C411yescharacteristic
476C22×C83C2×C4×D411yescharacteristic
477C22×C83C2×C4×Q811yescharacteristic
478C22×C83C2×C4×Q811yescharacteristic
479C22×C83C4×#4111yescharacteristic
480C22×C83#51811yescharacteristic
481C22×C83#52011yescharacteristic
482C22×C83C2×C22⋊Q811yescharacteristic
483C22×C83C2×C22⋊Q811yescharacteristic
484C22×C83C2×C22⋊Q811yescharacteristic
485C22×C83#52511yescharacteristic
486C22×C83C2×#12411yescharacteristic
487C22×C83#52911yescharacteristic
488C22×C83C2×C4⋊Q811yescharacteristic
489C22×C83#53311yescharacteristic
490C22×C83#53811yescharacteristic
491C22×C83#53911yescharacteristic
492C22×C83#54311yescharacteristic
493C22×C83#54411yescharacteristic
494C22×C83D4211yescharacteristic
495C22×C83D4211yescharacteristic
496C22×C83#54611yescharacteristic
497C22×C83#54611yescharacteristic
498C22×C83#54611yescharacteristic
499C22×C83#54611yescharacteristic
500C22×C83#54611yescharacteristic
501C22×C83#54711yescharacteristic
502C22×C83#54711yescharacteristic
503C22×C83D4×Q811yescharacteristic
504C22×C83#55111yescharacteristic
505C22×C83#55111yescharacteristic
506C22×C83#55211yescharacteristic
507C22×C83#55411yescharacteristic
508C22×C83#55411yescharacteristic
509C22×C83#55411yescharacteristic
510C4×C83—24no—
511C4×C83—24no—
512C4×C83—42no—
513C4×C83—42no—
514C4×C83—81no—
515C4×C83—81no—
516Dic83—24no—
517Dic83—24no—
518Dic83—42no—
519Dic83—42no—
520Dic83—42no—
521Dic83—42no—
522Dic83—42no—
523Dic83—42no—
524#14052—831nomaximal, Sylow
525C2×C83—28no—
526C2×C83C2×#39111yescharacteristic
527C2×C83C4×C22⋊Q811yescharacteristic
528C2×C83#232911yescharacteristic
529C2×C83D4×C22⋊C411yescharacteristic
530C2×C83#233911yescharacteristic
531C2×C83#236011yescharacteristic
532C2×C83#236811yescharacteristic
533C2×C83#243711yescharacteristic
534C2×C83#243811yescharacteristic
535C2×C83#244011yescharacteristic
536C2×C83#244911yescharacteristic
537C2×C83#245011yescharacteristic
538C2×C83#247211yescharacteristic
539C2×C83#248811yescharacteristic
540C2×C83#254911yescharacteristic
541C22×C22⋊Q8—831no—
542C2×#391—831no—
543C2×#385D8311yescharacteristic
544C2×C4×C22⋊C4—831no—
545C22×#95—831no—
546#1446—831no—
547#1445—831no—
548#1441—831no—
549#1441—831no—
550#1436—831no—
551#1436—831no—
552C4⋊#95—831no—
553C22⋊#95—831no—
554C22⋊#95—831no—
555C22⋊#95—831no—
556C83#1405211yescharacteristic, complemented, Sylow
557C23×Q8—831no—
558C24×C4—831no—
559C24×C4—831no—
560C24×C4C2×D8311yescharacteristic
561C2×C22⋊Q8—838no—
562C2×C22⋊Q8—1664no—
563C2×C22⋊Q8—1664no—
564C22×C4⋊C4—831no—
565C22×C4⋊C4—831no—
566C22×C4⋊C4—831no—
567C22×C4⋊C4C2×D8311yescharacteristic
568C22×C4⋊C4C2×D8311yescharacteristic
569C22×C22⋊C4—831no—
570C22×C22⋊C4—831no—
571C22×C22⋊C4C2×D8311yescharacteristic
572C22×C22⋊C4C2×D8311yescharacteristic
573C22×C42—831no—
574C22×C42—831no—
575#391—1664no—
576#385—24no—
577C4×C22⋊C4—1664no—
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—831no—
591C2×#95—831no—
592C2×#95—831no—
593C2×#95—831no—
594C2×#95—831no—
595C2×#95—831no—
596C2×#95—1664no—
597C2×#95C2×D8311yescharacteristic
598C2×#95C2×D8311yescharacteristic
599C25C22×D8311yescharacteristic
600C22×Q8—3321no—
601C22×Q8—3321no—
602C22×Q8—834no—
603C22×Q8—1662no—
604C22×Q8—1662no—
605C22×Q8—1662no—
606C22×Q8—1662no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—41no—
613C23×C4—41no—
614C23×C4—3321no—
615C23×C4—3321no—
616C23×C4—3321no—
617C23×C4—3321no—
618C23×C4—834no—
619C23×C4—834no—
620C23×C4—831no—
621C23×C4—831no—
622C23×C4—831no—
623C23×C4—831no—
624C23×C4—831no—
625C23×C4—831no—
626C23×C4—831no—
627C23×C4—831no—
628C23×C4—1662no—
629C23×C4—1662no—
630C23×C4—1662no—
631C23×C4—1662no—
632C23×C4—1662no—
633C23×C4—1662no—
634C23×C4—1662no—
635C23×C4—1662no—
636C23×C4C22×D8311yescharacteristic
637C23×C4C22×D8311yescharacteristic
638C23×C4C22×D8311yescharacteristic
639C23×C4C22×D8311yescharacteristic
640C23×C4C22×D8311yescharacteristic
641C23×C4C22×D8311yescharacteristic
642C22⋊Q8—16632no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—834no—
650C2×C4⋊C4—834no—
651C2×C4⋊C4—834no—
652C2×C4⋊C4—1662no—
653C2×C4⋊C4—1662no—
654C2×C4⋊C4—1662no—
655C2×C4⋊C4—1662no—
656C2×C4⋊C4—1662no—
657C2×C4⋊C4—1662no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—834no—
662C2×C22⋊C4—834no—
663C2×C22⋊C4—1662no—
664C2×C22⋊C4—1662no—
665C2×C22⋊C4—1662no—
666C2×C22⋊C4—1662no—
667C2×C22⋊C4C4×D8314yes—
668C2×C22⋊C4D33214yes—
669C2×C22⋊C4C22⋊D8314yes—
670C2×C42—3321no—
671C2×C42—3321no—
672C2×C42—1662no—
673C2×C42—1662no—
674C2×C42—1662no—
675C2×C42—1662no—
676#95—22no—
677#95—22no—
678#95—3321no—
679#95—3321no—
680#95—3321no—
681#95—3321no—
682#95—3321no—
683#95—3321no—
684#95—834no—
685#95—1662no—
686#95—1662no—
687#95—1662no—
688#95—1662no—
689#95—1662no—
690#95—1662no—
691#95—1662no—
692#95—1662no—
693#95—1662no—
694#95—1662no—
695#95—1662no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C2×C4×D8312yes—
705C24C2×C22⋊D8312yes—
706C24C2×D33212yes—
707C24Q8×D8312yes—
708C24Q8×D8312yes—
709C24#1305058912yes—
710C24#1305058912yes—
711C24C23×D8311yescharacteristic
712C2×Q8—3324no—
713C2×Q8—3324no—
714C2×Q8—3324no—
715C2×Q8—3324no—
716C2×Q8—3324no—
717C2×Q8—1668no—
718C2×Q8—1668no—
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—28no—
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×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—3324no—
761C22×C4—3324no—
762C22×C4—3324no—
763C22×C4—3324no—
764C22×C4—3324no—
765C22×C4—3324no—
766C22×C4—3324no—
767C22×C4—3324no—
768C22×C4—3324no—
769C22×C4—3324no—
770C22×C4—832no—
771C22×C4—832no—
772C22×C4—832no—
773C22×C4—832no—
774C22×C4—832no—
775C22×C4—832no—
776C22×C4—832no—
777C22×C4—832no—
778C22×C4—832no—
779C22×C4—832no—
780C22×C4—832no—
781C22×C4—832no—
782C22×C4—1668no—
783C22×C4—1668no—
784C22×C4—1668no—
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×C4—1661no—
815C22×C4—1661no—
816C22×C4—1661no—
817C22×C4—1661no—
818C22×C4—1661no—
819C22×C4—1661no—
820C22×C4—1661no—
821C22×C4—1668no—
822C22×C4—1661no—
823C22×C4—1661no—
824C22×C4—1661no—
825C22×C4—1661no—
826C22×C4—1661no—
827C22×C4—1661no—
828C22×C4—1661no—
829C22×C4—1661no—
830C22×C4C2×C4×D8312yes—
831C22×C4C2×C4×D8312yes—
832C22×C4D4×D8312yes—
833C22×C4C2×C22⋊D8312yes—
834C22×C4C2×C22⋊D8312yes—
835C22×C4C2×D33212yes—
836C22×C4C2×D33212yes—
837C22×C4#1305058912yes—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—1668no—
841C4⋊C4—1668no—
842C4⋊C4—1668no—
843C22⋊C4—44no—
844C22⋊C4—1668no—
845C22⋊C4—1668no—
846C22⋊C4(C2×D83)⋊C4116yes—
847C42—3324no—
848C42—3324no—
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—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×(C2×D83)⋊C414yes—
878C23#1458175714yes—
879C23#1458175714yes—
880C23#1458177214yes—
881C23#1458177214yes—
882C23#1458177914yes—
883C23#1458179014yes—
884C23C22×C4×D8311yescharacteristic
885C23C2×D4×D8311yescharacteristic
886C23C22×C22⋊D8311yescharacteristic
887C23C22×D33211yescharacteristic
888C23C2×Q8×D8311yescharacteristic
889C23C2×Q8×D8311yescharacteristic
890C23#41×D8311yescharacteristic
891C23#41×D8311yescharacteristic
892C23C2×#1305058911yescharacteristic
893C23C2×#1305058911yescharacteristic
894C23C2×#1305058911yescharacteristic
895C23#1458183711yescharacteristic
896C23#1458183711yescharacteristic
897C23#1458183811yescharacteristic
898C23#1458183911yescharacteristic
899Q8—33216no—
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—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—416no—
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—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
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—3321no—
962C2×C4—3321no—
963C2×C4—3321no—
964C2×C4—3321no—
965C2×C4—33216no—
966C2×C4—33216no—
967C2×C4—834no—
968C2×C4—834no—
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×C4—1662no—
988C2×C4—1662no—
989C2×C4—1662no—
990C2×C4—1662no—
991C2×C4—1662no—
992C2×C4—1662no—
993C2×C4—1662no—
994C2×C4—1662no—
995C2×C4—1662no—
996C2×C4—1662no—
997C2×C4—1662no—
998C2×C4—1662no—
999C2×C4C2×(C2×D83)⋊C414yes—
1000C2×C4C2×(C2×D83)⋊C414yes—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#1912760618yescomplemented
1016C22C22×(C2×D83)⋊C411yescharacteristic
1017C22C4×D4×D8311yescharacteristic
1018C22C2×#1458175711yescharacteristic
1019C22C2×#1458175711yescharacteristic
1020C22C4×#1305058911yescharacteristic
1021C22#1912817311yescharacteristic
1022C22#1912818011yescharacteristic
1023C22C22⋊Q8×D8311yescharacteristic
1024C22C2×#1458177211yescharacteristic
1025C22C2×#1458177211yescharacteristic
1026C22#1912820711yescharacteristic
1027C22C2×#1458177911yescharacteristic
1028C22#1912822811yescharacteristic
1029C22C2×#1458179011yescharacteristic
1030C22#1912825311yescharacteristic
1031C22#1912828611yescharacteristic
1032C22#1912829511yescharacteristic
1033C22#1912832611yescharacteristic
1034C22#1912833011yescharacteristic
1035C22D4×C22⋊D8311yescharacteristic
1036C22D4×D33211yescharacteristic
1037C22#1912833811yescharacteristic
1038C22#1912833911yescharacteristic
1039C22#1912834511yescharacteristic
1040C22#1912834611yescharacteristic
1041C22#1912834611yescharacteristic
1042C22#1912835011yescharacteristic
1043C22#1912835511yescharacteristic
1044C22#1912836411yescharacteristic
1045C22#1912837411yescharacteristic
1046C22#1912838211yescharacteristic
1047C22#1912838811yescharacteristic
1048C22#1912840511yescharacteristic
1049C22#1912840511yescharacteristic
1050C22#1912840911yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—81no—
1056C4—81no—
1057C4—3322no—
1058C4—3322no—
1059C4—3322no—
1060C4—3322no—
1061C4—3322no—
1062C4—3322no—
1063C4—1664no—
1064C4—1664no—
1065C2—28no—
1066C2C2×#1912760611yescharacteristic
1067C2#2490999511yescharacteristic
1068C2#2491019411yescharacteristic
1069C2D4×(C2×D83)⋊C411yescharacteristic
1070C2#2491028811yescharacteristic
1071C2#2491046311yescharacteristic
1072C2#2491054411yescharacteristic
1073C2#2491112711yescharacteristic
1074C2#2491113711yescharacteristic
1075C2#2491116211yescharacteristic
1076C2#2491127011yescharacteristic
1077C2#2491128511yescharacteristic
1078C2#2491158811yescharacteristic
1079C2#2491179311yescharacteristic
1080C2#2491247111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#385×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83#14052
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#19127606C2semidirect
5. #24905733C2semidirect
6. #24905730C2semidirect
7. #24905713C2semidirect
8. #24905713C2semidirect
9. #24905698C2semidirect
10. #24905698C2semidirect
11. #24905692C2semidirect
21. C2×#14581769C4semidirect
64. C22×Dic166C2×C4semidirect
78. C23×Dic83Q8semidirect
90. C2×C4⋊Dic83C2×C4semidirect
95. C2×Dic83⋊C4C2×C4semidirect
96. C2×Dic83⋊C4C2×C4semidirect
102. C2×C22⋊Dic83Q8semidirect
458. C2×Dic83C22⋊Q8semidirect
474. C22×C83#391semidirect
556. C83#14052semidirect
1015. C22#19127606semidirect

Maximal subgroups

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

subgroupindex
C22×#145817692
C2×#191276062
C2×C22⋊C4×Dic832
C22×C83⋊#952
#249057332
#249057302
#249057132
#249056982
#249056922
#249056862
#249056852
C2×#385×C832
#1405283