Finite Group Databasebeta

← C2×#24912541 #35574501

Subgroups — C2×#24912541 #35574501

Order 21248.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581782C211yesmaximal, characteristic, complemented
2C22×#14581770C211yesmaximal, characteristic
3#24912541C2116yesmaximal, direct product factor
4C2×#19127638C211yesmaximal, characteristic
5C2×#19127631C211yesmaximal, characteristic, complemented
6C2×#19127623C211yesmaximal, characteristic
7C2×#19127622C211yesmaximal, characteristic, complemented
8C2×#19127607C211yesmaximal, characteristic, complemented
9C2×#19127599C211yesmaximal, characteristic, complemented
10C2×#19127599C211yesmaximal, characteristic, complemented
11C2×#19127592C211yesmaximal, characteristic
12C2×#19127592C211yesmaximal, characteristic
13C2×#19127586C211yesmaximal, characteristic, complemented
14C2×#19127575C211yesmaximal, characteristic
15C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C2×#14581782—28no—
20C2×#14581782C2218yescomplemented
21C2×#14581770—28no—
22C2×#14581770C2218yes—
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×C4⋊Dic83C2211yescharacteristic
26C22×C4⋊Dic83C2211yescharacteristic
27C22×C4⋊Dic83C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊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#19127638C2218yes—
42#19127631C2218yescomplemented
43#19127623C2218yes—
44#19127622C2218yescomplemented
45#19127607C2218yescomplemented
46#19127599C2218yescomplemented
47#19127599C2218yescomplemented
48#19127592C2218yes—
49#19127592C2218yes—
50#19127586C2218yescomplemented
51#19127575C2218yes—
52C4×(C2×D83)⋊C4C2218yes—
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64C22×C42×C83C2211yescharacteristic
65C22×C42×C83C2211yescharacteristic
66C4×C4⋊C4×C83C2218yescomplemented
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166—42no—
73C22×Dic166C2314yes—
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C22×C4×D83—24no—
82C22×C4×D83—24no—
83C22×C4×D83—42no—
84C22×C4×D83C2314yes—
85#14581782—232no—
86#14581770—232no—
87C2×C4⋊Dic83—24no—
88C2×C4⋊Dic83—24no—
89C2×C4⋊Dic83—24no—
90C2×C4⋊Dic83—24no—
91C2×C4⋊Dic83—42no—
92C2×C4⋊Dic83C2314yes—
93C2×C4⋊Dic83C2314yes—
94C2×C4⋊Dic83C2314yes—
95C2×C4⋊Dic83C2314yes—
96C2×C4⋊Dic83C2314yes—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—24no—
102C2×Dic83⋊C4—24no—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×(C2×D83)⋊C4—24no—
110C2×(C2×D83)⋊C4—24no—
111C2×(C2×D83)⋊C4—24no—
112C2×(C2×D83)⋊C4—24no—
113C2×(C2×D83)⋊C4—42no—
114C2×(C2×D83)⋊C4Q818yescomplemented
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×C4×Dic83—24no—
122C2×C4×Dic83C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C2×C4⋊C4×C83—24no—
139C2×C4⋊C4×C83D418yes—
140C2×C4⋊C4×C83C2314yes—
141C2×C4⋊C4×C83C2314yes—
142C2×C42×C83—24no—
143C2×C42×C83—42no—
144C2×C42×C83—42no—
145C2×C42×C83C2314yes—
146C2×C42×C83C2314yes—
147C2×C42×C83C2314yes—
148#95×C83C2314yes—
149#95×C83C2314yes—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83C2×Q814yes—
157C23×D83C2412yes—
158C2×Dic166—28no—
159C2×Dic166—28no—
160C2×Dic166—44no—
161C2×Dic166—416no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
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×Dic83C2×Q814yes—
182C22×Dic83#4114yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C2×C4×D83—28no—
191C2×C4×D83—28no—
192C2×C4×D83—44no—
193C2×C4×D83—416no—
194C4⋊Dic83—28no—
195C4⋊Dic83—28no—
196C4⋊Dic83—28no—
197C4⋊Dic83—28no—
198C4⋊Dic83—44no—
199Dic83⋊C4—28no—
200Dic83⋊C4—28no—
201Dic83⋊C4—28no—
202Dic83⋊C4—28no—
203Dic83⋊C4—28no—
204Dic83⋊C4—28no—
205(C2×D83)⋊C4—28no—
206(C2×D83)⋊C4—28no—
207(C2×D83)⋊C4—28no—
208(C2×D83)⋊C4—28no—
209(C2×D83)⋊C4—44no—
210(C2×D83)⋊C4C2×Q8116yescomplemented
211C4×Dic83—28no—
212C24×C83C2411yescharacteristic
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83C2×D414yes—
229C22×C4×C83C2×D414yes—
230C22×C4×C83C2×D414yes—
231C22×C4×C83C2×Q814yes—
232C22×C4×C83#4114yes—
233C22×C4×C83#4114yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2412yes—
241C4⋊C4×C83—28no—
242C4⋊C4×C83C2×D4116yes—
243C42×C83—28no—
244C42×C83—44no—
245C42×C83—44no—
246C23×C83C22×D412yes—
247C23×C83C22×Q812yes—
248C23×C83C2×#4112yes—
249C23×C83C2×#4112yes—
250C23×C83C2×#4112yes—
251C23×C83H(5,𝔽2)12yes—
252C23×C832−1+412yes—
253C23×C83C2511yescharacteristic
254C22×D83—28no—
255C22×D83—28no—
256C22×D83—28no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—44no—
264C22×D83—44no—
265C22×D83—44no—
266C22×D83—44no—
267C22×D83C22×Q814yes—
268C2×C4×C83—28no—
269C2×C4×C83—28no—
270C2×C4×C83—28no—
271C2×C4×C83—28no—
272C2×C4×C83—28no—
273C2×C4×C83—28no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—44no—
290C2×C4×C83C22×D414yes—
291C2×C4×C83C22×D414yes—
292C2×C4×C83C22×D414yes—
293C2×C4×C83C22×Q814yes—
294C2×C4×C83C2×#4114yes—
295C2×C4×C83C2×#4114yes—
296C2×Dic83—28no—
297C2×Dic83—28no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—44no—
318C2×Dic83—44no—
319C2×Dic83—44no—
320C2×Dic83—44no—
321C2×Dic83—44no—
322C2×Dic83C22×Q814yes—
323C2×Dic83C2×#4114yes—
324C4×D83—416no—
325Dic166—416no—
326C22×C83#53214yes—
327C22×C83#53314yes—
328C22×C83#53914yes—
329C22×C83#54614yes—
330C22×C83D4×Q814yes—
331C22×C83#55214yes—
332C22×C83#55414yes—
333C22×C83C23×D411yescharacteristic
334C22×C83C23×Q811yescharacteristic
335C22×C83C22×#4111yescharacteristic
336C22×C83C22×#4111yescharacteristic
337C22×C83C22×#4111yescharacteristic
338C22×C83C2×H(5,𝔽2)11yescharacteristic
339C22×C83C2×2−1+411yescharacteristic
340C2×D83—24no—
341C2×D83—24no—
342C2×D83—24no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—42no—
346C2×D83—42no—
347C2×D83—416no—
348C4×C83—24no—
349C4×C83—24no—
350C4×C83—24no—
351C4×C83—24no—
352C4×C83—24no—
353C4×C83—24no—
354C4×C83—42no—
355Dic83—24no—
356Dic83—24no—
357Dic83—42no—
358Dic83—42no—
359Dic83—42no—
360Dic83—42no—
361Dic83—42no—
362C2×#2556—831nomaximal, Sylow
363C2×C83#255618yescomplemented
364C2×C83C2×#53211yescharacteristic
365C2×C83C2×#53311yescharacteristic
366C2×C83C2×#53911yescharacteristic
367C2×C83C2×#54611yescharacteristic
368C2×C83C2×D4×Q811yescharacteristic
369C2×C83C2×#55211yescharacteristic
370C2×C83C2×#55411yescharacteristic
371D83—44no—
372C22×#125—831no—
373C22×C22⋊Q8—831no—
374#2556—8316no—
375C2×#399—831no—
376C2×#398—831no—
377C2×#396—831no—
378C2×#395—831no—
379C2×#391—831no—
380C2×#389—831no—
381C2×#389—831no—
382C2×#388—831no—
383C2×#388—831no—
384C2×#387—831no—
385C2×#385—831no—
386C2×C4×C4⋊C4D8311yescharacteristic, complemented
387C2×C4×C22⋊C4—831no—
388C83C2×#255611yescharacteristic, complemented, Sylow
389C23×Q8—831no—
390C24×C4—831no—
391C2×#125—838no—
392C2×#125—1668no—
393C2×C22⋊Q8—838no—
394C2×C22⋊Q8—1668no—
395C22×C4⋊C4—831no—
396C22×C4⋊C4—831no—
397C22×C4⋊C4—831no—
398C22×C4⋊C4—831no—
399C22×C4⋊C4—831no—
400C22×C4⋊C4—831no—
401C22×C4⋊C4—831no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—831no—
404C22×C4⋊C4—831no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4C2×D8311yescharacteristic
407C22×C4⋊C4C2×D8311yescharacteristic
408C22×C22⋊C4—831no—
409C22×C22⋊C4—831no—
410C22×C22⋊C4—831no—
411C22×C22⋊C4—831no—
412C22×C22⋊C4—831no—
413C22×C22⋊C4—831no—
414C22×C42—831no—
415C22×C42C2×D8311yescharacteristic
416C22×C42C2×D8311yescharacteristic
417C22×C42C2×D8311yescharacteristic
418#399—838no—
419#398—838no—
420#396—838no—
421#395—838no—
422#391—838no—
423#389—838no—
424#389—838no—
425#388—838no—
426#388—838no—
427#387—838no—
428#385—838no—
429C4×C4⋊C4C2×D8318yescomplemented
430C4×C22⋊C4—838no—
431C2×#95—831no—
432C2×#95—831no—
433C2×#95—831no—
434C2×#95—831no—
435C2×#95—831no—
436C2×#95—831no—
437C2×#95—831no—
438C2×#95—831no—
439C2×#95C2×D8311yescharacteristic
440C2×#95C2×D8311yescharacteristic
441C25—831no—
442C22×Q8—3322no—
443C22×Q8—834no—
444C22×Q8—1664no—
445C22×Q8—1664no—
446C23×C4—3322no—
447C23×C4—834no—
448C23×C4—831no—
449C23×C4—831no—
450C23×C4—831no—
451C23×C4—831no—
452C23×C4—831no—
453C23×C4—831no—
454C23×C4—831no—
455C23×C4—1664no—
456C23×C4—1664no—
457C23×C4C22×D8311yescharacteristic
458C23×C4C22×D8311yescharacteristic
459C23×C4C22×D8311yescharacteristic
460C23×C4C22×D8311yescharacteristic
461C23×C4C22×D8311yescharacteristic
462C23×C4C22×D8311yescharacteristic
463C23×C4C22×D8311yescharacteristic
464#125—16632no—
465C22⋊Q8—16632no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—3322no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—834no—
478C2×C4⋊C4—834no—
479C2×C4⋊C4—1664no—
480C2×C4⋊C4—1664no—
481C2×C4⋊C4—1664no—
482C2×C4⋊C4—1664no—
483C2×C4⋊C4—1664no—
484C2×C4⋊C4—1664no—
485C2×C4⋊C4—1664no—
486C2×C4⋊C4—1664no—
487C2×C4⋊C4—1664no—
488C2×C4⋊C4—1664no—
489C2×C4⋊C4D33218yes—
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8314yes—
492C2×C22⋊C4—3322no—
493C2×C22⋊C4—834no—
494C2×C22⋊C4—838no—
495C2×C22⋊C4—834no—
496C2×C22⋊C4—834no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—1664no—
501C2×C22⋊C4—1664no—
502C2×C22⋊C4—1664no—
503C2×C22⋊C4—1664no—
504C2×C42—24no—
505C2×C42—42no—
506C2×C42—42no—
507C2×C42—834no—
508C2×C42—1664no—
509C2×C42C22×D8314yes—
510C2×C42C22×D8314yes—
511C2×C42C22×D8314yes—
512#95—834no—
513#95—834no—
514#95—834no—
515#95—834no—
516#95—834no—
517#95—834no—
518#95—834no—
519#95—834no—
520#95C22×D8314yes—
521#95C22×D8314yes—
522C24—834no—
523C24—832no—
524C24—1662no—
525C24—1662no—
526C24—1662no—
527C24—1662no—
528C24—1662no—
529C24—1662no—
530C24C23×D8311yescharacteristic
531C2×Q8—33216no—
532C2×Q8—3324no—
533C2×Q8—1668no—
534C2×Q8—1668no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—33216no—
551C22×C4—3324no—
552C22×C4—834no—
553C22×C4—834no—
554C22×C4—832no—
555C22×C4—832no—
556C22×C4—832no—
557C22×C4—832no—
558C22×C4—832no—
559C22×C4—832no—
560C22×C4—832no—
561C22×C4—1668no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1662no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1668no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1662no—
581C22×C4—1662no—
582C22×C4C2×D33214yes—
583C22×C4C2×D33214yes—
584C22×C4C2×D33214yes—
585C22×C4Q8×D8314yes—
586C22×C4#1305059014yes—
587C22×C4#1305059014yes—
588C22×C4C23×D8312yes—
589C22×C4C23×D8312yes—
590C22×C4C23×D8312yes—
591C22×C4C23×D8312yes—
592C22×C4C23×D8312yes—
593C22×C4C23×D8312yes—
594C22×C4C23×D8312yes—
595C4⋊C4—28no—
596C4⋊C4—3324no—
597C4⋊C4—1668no—
598C4⋊C4—1668no—
599C4⋊C4—1668no—
600C4⋊C4—1668no—
601C4⋊C4—1668no—
602C4⋊C4—1668no—
603C4⋊C4—1668no—
604C4⋊C4—1668no—
605C4⋊C4—1668no—
606C4⋊C4—1668no—
607C4⋊C4C2×D332116yes—
608C22⋊C4—3324no—
609C22⋊C4—8316no—
610C22⋊C4—1668no—
611C22⋊C4—1668no—
612C22⋊C4—1668no—
613C22⋊C4—1668no—
614C42—28no—
615C42—44no—
616C42—44no—
617C42—1668no—
618C23—3324no—
619C23—3324no—
620C23—3324no—
621C23—3324no—
622C23—834no—
623C23—1668no—
624C23—1668no—
625C23—1668no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23—1662no—
630C23—1662no—
631C23—1662no—
632C23C22×D33212yes—
633C23C2×Q8×D8312yes—
634C23#41×D8312yes—
635C23C2×#1305059012yes—
636C23C2×#1305059012yes—
637C23#1458183712yes—
638C23#1458183912yes—
639C23C24×D8311yescharacteristic
640Q8—33216no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—33216no—
664C2×C4—3324no—
665C2×C4—3324no—
666C2×C4—3324no—
667C2×C4—3324no—
668C2×C4—3324no—
669C2×C4—834no—
670C2×C4—834no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4—1668no—
687C2×C4—1668no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4C22×D33214yes—
693C2×C4C22×D33214yes—
694C2×C4C22×D33214yes—
695C2×C4C2×Q8×D8314yes—
696C2×C4C2×#1305059014yes—
697C2×C4C2×#1305059014yes—
698C22—3322no—
699C22—3322no—
700C22—33216no—
701C22—3322no—
702C22—3322no—
703C22—1664no—
704C22—1664no—
705C22—1664no—
706C22#1912825114yes—
707C22#1912825514yes—
708C22#1912829314yes—
709C22#1912834614yes—
710C22Q8×D33214yes—
711C22#1912838414yes—
712C22#1912840614yes—
713C22C23×D33211yescharacteristic
714C22C22×Q8×D8311yescharacteristic
715C22C2×#41×D8311yescharacteristic
716C22C22×#1305059011yescharacteristic
717C22C22×#1305059011yescharacteristic
718C22C2×#1458183711yescharacteristic
719C22C2×#1458183911yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—24no—
726C4—42no—
727C4—3322no—
728C4—3322no—
729C4—3322no—
730C4—3322no—
731C4—3322no—
732C4—1664no—
733C4—1664no—
734C2—3324no—
735C2#2491254118yesdirect product factor
736C2C2×#1912825111yescharacteristic
737C2C2×#1912825511yescharacteristic
738C2C2×#1912829311yescharacteristic
739C2C2×#1912834611yescharacteristic
740C2C2×Q8×D33211yescharacteristic
741C2C2×#1912838411yescharacteristic
742C2C2×#1912840611yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×C4×C4⋊C4×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C2×#2556
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14581782C2semidirect
3. #24912541C2direct (N × H)
5. C2×#19127631C2semidirect
7. C2×#19127622C2semidirect
8. C2×#19127607C2semidirect
9. C2×#19127599C2semidirect
10. C2×#19127599C2semidirect
13. C2×#19127586C2semidirect
16. C2×C4×C4⋊C4×C83C2semidirect
20. C2×#14581782C22semidirect
42. #19127631C22semidirect
44. #19127622C22semidirect
45. #19127607C22semidirect
46. #19127599C22semidirect
47. #19127599C22semidirect
50. #19127586C22semidirect
66. C4×C4⋊C4×C83C22semidirect
114. C2×(C2×D83)⋊C4Q8semidirect
210. (C2×D83)⋊C4C2×Q8semidirect
363. C2×C83#2556semidirect
386. C2×C4×C4⋊C4D83semidirect
388. C83C2×#2556semidirect
429. C4×C4⋊C4C2×D83semidirect
735. C2#24912541direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817822
C22×#145817702
#249125412
C2×#191276382
C2×#191276312
C2×#191276232
C2×#191276222
C2×#191276072
C2×#191275992
C2×#191275922
C2×#191275862
C2×#191275752
C2×C4×(C2×D83)⋊C42
C2×C4×C4⋊C4×C832
C2×#255683