Finite Group Databasebeta

← C2×#24911904 #35574176

Subgroups — C2×#24911904 #35574176

Order 21248.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581777C211yesmaximal, characteristic
2C22×#14581749C211yesmaximal, characteristic, complemented
3#24911904C2116yesmaximal, direct product factor
4C2×#19127642C211yesmaximal, characteristic, complemented
5C2×#19127636C211yesmaximal, characteristic, complemented
6C2×#19127635C211yesmaximal, characteristic, complemented
7C2×#19127630C211yesmaximal, characteristic, complemented
8C2×#19127593C211yesmaximal, characteristic, complemented
9C2×#19127592C211yesmaximal, characteristic, complemented
10C2×#19127582C211yesmaximal, characteristic, complemented
11C2×#19127579C211yesmaximal, characteristic
12C2×#19127579C211yesmaximal, characteristic
13C2×#19127560C211yesmaximal, characteristic, complemented
14C2×#19127558C211yesmaximal, characteristic, complemented
15C2×#95×D83C211yesmaximal, characteristic, complemented
16C2×#387×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C2×#14581777—28no—
22C2×#14581777C2218yes—
23C2×#14581749—28no—
24C2×#14581749C2218yescomplemented
25C22×C4⋊Dic83C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41#19127642C2218yescomplemented
42#19127636C2218yescomplemented
43#19127635C2218yescomplemented
44#19127630C2218yescomplemented
45#19127593C2218yescomplemented
46#19127592C2218yescomplemented
47#19127582C2218yescomplemented
48#19127579C2218yes—
49#19127579C2218yes—
50#19127560C2218yescomplemented
51#19127558C2218yescomplemented
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60#95×D83C2218yescomplemented
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64#387×C83C2218yescomplemented
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C24×D83C2311yescharacteristic
71C22×D332—24no—
72C22×D332—24no—
73C22×D332—24no—
74C22×D332C2314yes—
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C22×C4×D83—24no—
82C22×C4×D83—24no—
83C22×C4×D83—24no—
84C22×C4×D83—24no—
85C22×C4×D83—24no—
86C22×C4×D83—24no—
87C22×C4×D83—42no—
88C22×C4×D83—42no—
89C22×C4×D83D418yes—
90C22×C4×D83C2314yes—
91C22×C4×D83C2314yes—
92C22×C4×D83C2314yes—
93#14581777—232no—
94#14581749—232no—
95C2×C4⋊Dic83—42no—
96C2×C4⋊Dic83C2314yes—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—42no—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×(C2×D83)⋊C4—24no—
108C2×(C2×D83)⋊C4—24no—
109C2×(C2×D83)⋊C4—24no—
110C2×(C2×D83)⋊C4—24no—
111C2×(C2×D83)⋊C4—24no—
112C2×(C2×D83)⋊C4—24no—
113C2×(C2×D83)⋊C4—24no—
114C2×(C2×D83)⋊C4—42no—
115C2×(C2×D83)⋊C4—42no—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×C4×Dic83—24no—
126C2×C4×Dic83C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C2×C4⋊C4×C83—24no—
143C2×C4⋊C4×C83—24no—
144C2×C4⋊C4×C83C2314yes—
145C2×C4⋊C4×C83C2314yes—
146C2×C42×C83—24no—
147C2×C42×C83C2314yes—
148#95×C83C2314yes—
149#95×C83C2314yes—
150#95×C83C2314yes—
151#95×C83C2314yes—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83C2×D414yes—
164C23×D83#4114yes—
165C23×D83#4114yes—
166C23×D83C2412yes—
167C23×D83C2412yes—
168C2×D332—28no—
169C2×D332—28no—
170C2×D332—28no—
171C2×D332—416no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83—22no—
188C22×Dic83C2×D414yes—
189C22×Dic83#4114yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C2×C4×D83—232no—
197C2×C4×D83—28no—
198C2×C4×D83—28no—
199C2×C4×D83—28no—
200C2×C4×D83—28no—
201C2×C4×D83—28no—
202C2×C4×D83—28no—
203C2×C4×D83—44no—
204C2×C4×D83—44no—
205C2×C4×D83—416no—
206C2×C4×D83—416no—
207C2×C4×D83C2×D4116yes—
208C4⋊Dic83—44no—
209Dic83⋊C4—28no—
210Dic83⋊C4—28no—
211Dic83⋊C4—28no—
212Dic83⋊C4—28no—
213Dic83⋊C4—44no—
214(C2×D83)⋊C4—28no—
215(C2×D83)⋊C4—28no—
216(C2×D83)⋊C4—28no—
217(C2×D83)⋊C4—28no—
218(C2×D83)⋊C4—28no—
219(C2×D83)⋊C4—28no—
220(C2×D83)⋊C4—28no—
221(C2×D83)⋊C4—44no—
222(C2×D83)⋊C4—44no—
223C4×Dic83—28no—
224C24×C83C2411yescharacteristic
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83C2×D414yes—
245C22×C4×C83#4114yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2412yes—
251C22×C4×C83C2412yes—
252C22×C4×C83C2412yes—
253C4⋊C4×C83—28no—
254C4⋊C4×C83—28no—
255C42×C83—28no—
256C23×C83C22×D412yes—
257C23×C83C2×#4112yes—
258C23×C83C2×#4112yes—
259C23×C83C2×#4112yes—
260C23×C83C2×#4112yes—
261C23×C83H(5,𝔽2)12yes—
262C23×C832−1+412yes—
263C23×C83C2511yescharacteristic
264C22×D83—28no—
265C22×D83—28no—
266C22×D83—28no—
267C22×D83—28no—
268C22×D83—28no—
269C22×D83—28no—
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—22no—
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—44no—
282C22×D83—44no—
283C22×D83—44no—
284C22×D83—44no—
285C22×D83—44no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83#123116yes—
289C22×D83C22×D414yes—
290C22×D83C2×#4114yes—
291C22×D83C2×#4114yes—
292C2×C4×C83—28no—
293C2×C4×C83—28no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—44no—
314C2×C4×C83—44no—
315C2×C4×C83—44no—
316C2×C4×C83—44no—
317C2×C4×C83—44no—
318C2×C4×C83C22×D414yes—
319C2×C4×C83C2×#4114yes—
320C2×Dic83—28no—
321C2×Dic83—28no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83—44no—
341C2×Dic83—44no—
342C2×Dic83C22×D414yes—
343C2×Dic83C2×#4114yes—
344D332—416no—
345C4×D83—232no—
346C4×D83—416no—
347C4×D83—416no—
348C22×C83C2×#12314yes—
349C22×C83#53214yes—
350C22×C83#53714yes—
351C22×C83#55114yes—
352C22×C83#55114yes—
353C22×C83#55214yes—
354C22×C83#55214yes—
355C22×C83C23×D411yescharacteristic
356C22×C83C22×#4111yescharacteristic
357C22×C83C22×#4111yescharacteristic
358C22×C83C22×#4111yescharacteristic
359C22×C83C22×#4111yescharacteristic
360C22×C83C2×H(5,𝔽2)11yescharacteristic
361C22×C83C2×2−1+411yescharacteristic
362C2×D83—24no—
363C2×D83—24no—
364C2×D83—24no—
365C2×D83—24no—
366C2×D83—24no—
367C2×D83—24no—
368C2×D83—232no—
369C2×D83—42no—
370C2×D83—42no—
371C2×D83—42no—
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C2×D83—88no—
377C2×D83C2×#12318yes—
378C4×C83—24no—
379C4×C83—24no—
380C4×C83—42no—
381C4×C83—42no—
382C4×C83—42no—
383C4×C83—42no—
384C4×C83—42no—
385Dic83—24no—
386Dic83—24no—
387Dic83—42no—
388Dic83—42no—
389Dic83—42no—
390Dic83—42no—
391C2×#2498—831nomaximal, Sylow
392C2×C83#249818yescomplemented
393C2×C83C22×#12311yescharacteristic
394C2×C83C2×#53211yescharacteristic
395C2×C83C2×#53711yescharacteristic
396C2×C83C2×#55111yescharacteristic
397C2×C83C2×#55111yescharacteristic
398C2×C83C2×#55211yescharacteristic
399C2×C83C2×#55211yescharacteristic
400D83—28no—
401D83—82no—
402C22×#123—831no—
403C22×#117—831no—
404#2498—8316no—
405C2×#400—831no—
406C2×#399—831no—
407C2×#398—831no—
408C2×#397—831no—
409C2×#388—831no—
410C2×#388—831no—
411C2×#387—831no—
412C2×#387D8311yescharacteristic, complemented
413C2×#386—831no—
414C2×#386—831no—
415C2×#380—831no—
416C2×#380—831no—
417C22×#95—831no—
418C83C2×#249811yescharacteristic, complemented, Sylow
419C23×D4—831no—
420C24×C4—831no—
421C24×C4—831no—
422C24×C4—831no—
423C2×#123—838no—
424C2×#123—1668no—
425C2×#117—838no—
426C2×#117—1668no—
427C22×C4⋊C4—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4—831no—
431C22×C4⋊C4—831no—
432C22×C4⋊C4—831no—
433C22×C4⋊C4C2×D8311yescharacteristic
434C22×C4⋊C4C2×D8311yescharacteristic
435C22×C22⋊C4—831no—
436C22×C22⋊C4—831no—
437C22×C22⋊C4—831no—
438C22×C22⋊C4—831no—
439C22×C22⋊C4—831no—
440C22×C22⋊C4—831no—
441C22×C22⋊C4—831no—
442C22×C22⋊C4—831no—
443C22×C22⋊C4—831no—
444C22×C42—831no—
445C22×C42C2×D8311yescharacteristic
446#400—838no—
447#399—838no—
448#398—838no—
449#397—838no—
450#388—838no—
451#388—838no—
452#387—838no—
453#387C2×D8318yescomplemented
454#386—838no—
455#386—838no—
456#380—838no—
457#380—838no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—838no—
467C2×#95C2×D8311yescharacteristic
468C2×#95C2×D8311yescharacteristic
469C2×#95C2×D8311yescharacteristic
470C2×#95C2×D8311yescharacteristic
471C25—831no—
472C25—831no—
473C22×D4—834no—
474C22×D4—1664no—
475C22×D4—1664no—
476C22×D4—1664no—
477C23×C4—3322no—
478C23×C4—3322no—
479C23×C4—834no—
480C23×C4—834no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—838no—
484C23×C4—834no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—831no—
488C23×C4—831no—
489C23×C4—1664no—
490C23×C4—1664no—
491C23×C4—1664no—
492C23×C4—1664no—
493C23×C4—1664no—
494C23×C4—1664no—
495C23×C4C22×D8311yescharacteristic
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8311yescharacteristic
498C23×C4C22×D8311yescharacteristic
499C23×C4C22×D8311yescharacteristic
500C23×C4C22×D8311yescharacteristic
501C23×C4C22×D8311yescharacteristic
502#123—16632no—
503#117—16632no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—3322no—
507C2×C4⋊C4—3322no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—834no—
511C2×C4⋊C4—834no—
512C2×C4⋊C4—834no—
513C2×C4⋊C4—834no—
514C2×C4⋊C4—1664no—
515C2×C4⋊C4—1664no—
516C2×C4⋊C4—1664no—
517C2×C4⋊C4—1664no—
518C2×C4⋊C4C22×D8314yes—
519C2×C4⋊C4C22×D8314yes—
520C2×C22⋊C4—3322no—
521C2×C22⋊C4—3322no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—834no—
525C2×C22⋊C4—834no—
526C2×C22⋊C4—834no—
527C2×C22⋊C4—834no—
528C2×C22⋊C4—834no—
529C2×C22⋊C4—834no—
530C2×C22⋊C4—834no—
531C2×C22⋊C4—1664no—
532C2×C22⋊C4—1664no—
533C2×C22⋊C4—1664no—
534C2×C22⋊C4—1664no—
535C2×C22⋊C4—1664no—
536C2×C22⋊C4—1664no—
537C2×C22⋊C4—1664no—
538C2×C42—24no—
539C2×C42—834no—
540C2×C42—1664no—
541C2×C42C22×D8314yes—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95—834no—
548#95—834no—
549#95—834no—
550#95C22×D8314yes—
551#95C22×D8314yes—
552#95C22×D8314yes—
553#95C22×D8314yes—
554C24—834no—
555C24—834no—
556C24—834no—
557C24—832no—
558C24—832no—
559C24—1662no—
560C24—1662no—
561C24—1662no—
562C24—1662no—
563C24—1662no—
564C24—1662no—
565C24—1662no—
566C24—1662no—
567C24—1662no—
568C24—1662no—
569C24—1662no—
570C24C23×D8311yescharacteristic
571C2×D4—33216no—
572C2×D4—1668no—
573C2×D4—1668no—
574C2×D4—1668no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—33216no—
595C22×C4—3324no—
596C22×C4—3324no—
597C22×C4—33216no—
598C22×C4—834no—
599C22×C4—834no—
600C22×C4—832no—
601C22×C4—832no—
602C22×C4—8316no—
603C22×C4—832no—
604C22×C4—832no—
605C22×C4—832no—
606C22×C4—832no—
607C22×C4—1668no—
608C22×C4—1668no—
609C22×C4—1668no—
610C22×C4—16632no—
611C22×C4—1668no—
612C22×C4—1668no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4—1662no—
617C22×C4—1662no—
618C22×C4—1662no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1662no—
622C22×C4—1662no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4—1668no—
626C22×C4—1662no—
627C22×C4—1662no—
628C22×C4—1662no—
629C22×C4—1662no—
630C22×C4D4×D8314yes—
631C22×C4#1305059014yes—
632C22×C4C23×D8312yes—
633C22×C4C23×D8312yes—
634C22×C4C23×D8312yes—
635C22×C4C23×D8312yes—
636C22×C4C23×D8312yes—
637C22×C4C23×D8312yes—
638C22×C4C23×D8312yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—3324no—
642C4⋊C4—3324no—
643C4⋊C4—1668no—
644C4⋊C4—1668no—
645C4⋊C4—1668no—
646C4⋊C4—1668no—
647C22⋊C4—3324no—
648C22⋊C4—3324no—
649C22⋊C4—1668no—
650C22⋊C4—1668no—
651C22⋊C4—1668no—
652C22⋊C4—1668no—
653C22⋊C4—1668no—
654C22⋊C4—1668no—
655C22⋊C4—1668no—
656C42—28no—
657C42—1668no—
658C23—3324no—
659C23—3324no—
660C23—3324no—
661C23—3324no—
662C23—3324no—
663C23—3324no—
664C23—3324no—
665C23—8316no—
666C23—834no—
667C23—834no—
668C23—834no—
669C23—1662no—
670C23—1662no—
671C23—1662no—
672C23—1662no—
673C23—1662no—
674C23—1662no—
675C23—1662no—
676C23—1668no—
677C23—1668no—
678C23—1668no—
679C23—1668no—
680C23—1668no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23—1662no—
685C23—1668no—
686C23C2×D4×D8312yes—
687C23#41×D8312yes—
688C23#41×D8312yes—
689C23#41×D8312yes—
690C23C2×#1305059012yes—
691C23#1458183812yes—
692C23#1458184012yes—
693C23C24×D8311yescharacteristic
694D4—33216no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—33216no—
722C2×C4—33216no—
723C2×C4—3324no—
724C2×C4—3324no—
725C2×C4—3324no—
726C2×C4—3324no—
727C2×C4—834no—
728C2×C4—834no—
729C2×C4—16632no—
730C2×C4—1662no—
731C2×C4—1662no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1668no—
743C2×C4—1668no—
744C2×C4—1662no—
745C2×C4—1662no—
746C2×C4—1662no—
747C2×C4—1662no—
748C2×C4C2×D4×D8314yes—
749C2×C4C2×#1305059014yes—
750C22—3322no—
751C22—3322no—
752C22—3322no—
753C22—3322no—
754C22—3322no—
755C22—3322no—
756C22—3322no—
757C22—838no—
758C22—6648no—
759C22—16632no—
760C22—1664no—
761C22—1664no—
762C22—1664no—
763C22—1664no—
764C22—1664no—
765C22—1664no—
766C22#123×D8314yes—
767C22#1912824814yes—
768C22#1912828114yes—
769C22#1912837514yes—
770C22#1912837614yes—
771C22#1912838314yes—
772C22#1912839214yes—
773C22C22×D4×D8311yescharacteristic
774C22C2×#41×D8311yescharacteristic
775C22C2×#41×D8311yescharacteristic
776C22C2×#41×D8311yescharacteristic
777C22C22×#1305059011yescharacteristic
778C22C2×#1458183811yescharacteristic
779C22C2×#1458184011yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—3322no—
788C4—3322no—
789C4—3322no—
790C4—3322no—
791C4—1664no—
792C4—1664no—
793C2—6642no—
794C2—1668no—
795C2#2491190418yesdirect product factor
796C2C2×#123×D8311yescharacteristic
797C2C2×#1912824811yescharacteristic
798C2C2×#1912828111yescharacteristic
799C2C2×#1912837511yescharacteristic
800C2C2×#1912837611yescharacteristic
801C2C2×#1912838311yescharacteristic
802C2C2×#1912839211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#387×C83C2
socleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×#387D83
hypocenterC83C2×#2498
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×#14581749C2semidirect
3. #24911904C2direct (N × H)
4. C2×#19127642C2semidirect
5. C2×#19127636C2semidirect
6. C2×#19127635C2semidirect
7. C2×#19127630C2semidirect
8. C2×#19127593C2semidirect
9. C2×#19127592C2semidirect
10. C2×#19127582C2semidirect
13. C2×#19127560C2semidirect
14. C2×#19127558C2semidirect
15. C2×#95×D83C2semidirect
16. C2×#387×C83C2semidirect
24. C2×#14581749C22semidirect
41. #19127642C22semidirect
42. #19127636C22semidirect
43. #19127635C22semidirect
44. #19127630C22semidirect
45. #19127593C22semidirect
46. #19127592C22semidirect
47. #19127582C22semidirect
50. #19127560C22semidirect
51. #19127558C22semidirect
60. #95×D83C22semidirect
64. #387×C83C22semidirect
392. C2×C83#2498semidirect
412. C2×#387D83semidirect
418. C83C2×#2498semidirect
453. #387C2×D83semidirect
795. C2#24911904direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817772
C22×#145817492
#249119042
C2×#191276422
C2×#191276362
C2×#191276352
C2×#191276302
C2×#191275932
C2×#191275922
C2×#191275822
C2×#191275792
C2×#191275602
C2×#191275582
C2×#95×D832
C2×#387×C832
C2×#249883