Finite Group Databasebeta

← C2×#24911061 #35572422

Subgroups — C2×#24911061 #35572422

Order 21248.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581791C211yesmaximal, characteristic, complemented
2C22×#14581770C211yesmaximal, characteristic
3C22×#14581770C211yesmaximal, characteristic
4C22×C4×Dic166C211yesmaximal, characteristic, complemented
5#24911061C2116yesmaximal, direct product factor
6C2×#19127634C211yesmaximal, characteristic, complemented
7C2×#19127632C211yesmaximal, characteristic, complemented
8C2×#19127623C211yesmaximal, characteristic
9C2×#19127623C211yesmaximal, characteristic
10C2×#19127605C211yesmaximal, characteristic, complemented
11C2×#19127598C211yesmaximal, characteristic, complemented
12C2×#19127596C211yesmaximal, characteristic, complemented
13C2×#19127592C211yesmaximal, characteristic
14C2×#19127590C211yesmaximal, characteristic
15C2×#19127548C211yesmaximal, characteristic
16C2×#389×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581791—28no—
21C2×#14581791C2218yescomplemented
22C2×#14581770—28no—
23C2×#14581770—28no—
24C2×#14581770C2218yes—
25C2×#14581770C2218yes—
26C2×C4×Dic166—28no—
27C2×C4×Dic166C2218yescomplemented
28C22×C4⋊Dic83C2211yescharacteristic
29C22×C4⋊Dic83C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×Dic83⋊C4C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×Dic83⋊C4C2211yescharacteristic
37C22×Dic83⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×(C2×D83)⋊C4C2211yescharacteristic
43C22×(C2×D83)⋊C4C2211yescharacteristic
44C22×C4×Dic83C2211yescharacteristic
45C22×C4×Dic83C2211yescharacteristic
46C22×C4×Dic83C2211yescharacteristic
47#19127634C2218yescomplemented
48#19127632C2218yescomplemented
49#19127623C2218yes—
50#19127623C2218yes—
51#19127605C2218yescomplemented
52#19127598C2218yescomplemented
53#19127596C2218yescomplemented
54#19127592C2218yes—
55#19127590C2218yes—
56#19127548C2218yes—
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C2×C83⋊#95C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65C22×C4⋊C4×C83C2211yescharacteristic
66C22×C4⋊C4×C83C2211yescharacteristic
67C22×C42×C83C2211yescharacteristic
68#389×C83C2218yescomplemented
69C2×#95×C83C2211yescharacteristic
70C2×#95×C83C2211yescharacteristic
71C24×D83C2311yescharacteristic
72C22×Dic166—24no—
73C22×Dic166—24no—
74C22×Dic166—24no—
75C22×Dic166—24no—
76C22×Dic166—24no—
77C22×Dic166D418yes—
78C22×Dic166C2314yes—
79C22×Dic166C2314yes—
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C22×C4×D83—24no—
88C22×C4×D83—24no—
89C22×C4×D83—24no—
90C22×C4×D83C2314yes—
91#14581791—232no—
92#14581770—232no—
93#14581770—232no—
94C4×Dic166—232no—
95C2×C4⋊Dic83—24no—
96C2×C4⋊Dic83—24no—
97C2×C4⋊Dic83C2314yes—
98C2×C4⋊Dic83C2314yes—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—24no—
102C2×Dic83⋊C4—24no—
103C2×Dic83⋊C4—24no—
104C2×Dic83⋊C4—24no—
105C2×Dic83⋊C4—24no—
106C2×Dic83⋊C4D418yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×(C2×D83)⋊C4—24no—
116C2×(C2×D83)⋊C4—24no—
117C2×(C2×D83)⋊C4—24no—
118C2×(C2×D83)⋊C4—24no—
119C2×(C2×D83)⋊C4—24no—
120C2×(C2×D83)⋊C4Q818yescomplemented
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×C4×Dic83—24no—
128C2×C4×Dic83—24no—
129C2×C4×Dic83—24no—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C2×C4⋊C4×C83—24no—
147C2×C4⋊C4×C83—24no—
148C2×C4⋊C4×C83—24no—
149C2×C4⋊C4×C83—24no—
150C2×C4⋊C4×C83C2314yes—
151C2×C4⋊C4×C83C2314yes—
152C2×C4⋊C4×C83C2314yes—
153C2×C4⋊C4×C83C2314yes—
154C2×C42×C83—24no—
155C2×C42×C83C2314yes—
156#95×C83C2314yes—
157#95×C83C2314yes—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83C2×Q814yes—
165C23×D83C2412yes—
166C2×Dic166—232no—
167C2×Dic166—28no—
168C2×Dic166—28no—
169C2×Dic166—28no—
170C2×Dic166—28no—
171C2×Dic166—28no—
172C2×Dic166—416no—
173C2×Dic166C2×D4116yes—
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×Dic83—22no—
189C22×Dic83C2×D414yes—
190C22×Dic83C2×D414yes—
191C22×Dic83C2×D414yes—
192C22×Dic83C2×D414yes—
193C22×Dic83C2×Q814yes—
194C22×Dic83#4114yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C22×Dic83C2412yes—
199C22×Dic83C2412yes—
200C22×Dic83C2412yes—
201C22×Dic83C2412yes—
202C2×C4×D83—28no—
203C2×C4×D83—28no—
204C2×C4×D83—28no—
205C2×C4×D83—416no—
206C4⋊Dic83—28no—
207C4⋊Dic83—28no—
208Dic83⋊C4—28no—
209Dic83⋊C4—28no—
210Dic83⋊C4—28no—
211Dic83⋊C4—28no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4C2×D4116yes—
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)⋊C4C2×Q8116yescomplemented
222C4×Dic83—28no—
223C4×Dic83—28no—
224C4×Dic83—28no—
225C24×C83C2411yescharacteristic
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×C83C2×D414yes—
244C22×C4×C83C2×D414yes—
245C22×C4×C83C2×Q814yes—
246C22×C4×C83#4114yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2412yes—
251C22×C4×C83C2412yes—
252C22×C4×C83C2412yes—
253C22×C4×C83C2412yes—
254C4⋊C4×C83—28no—
255C4⋊C4×C83—28no—
256C4⋊C4×C83—28no—
257C4⋊C4×C83—28no—
258C42×C83—28no—
259C23×C83C22×D412yes—
260C23×C83C22×D412yes—
261C23×C83C22×Q812yes—
262C23×C83C2×#4112yes—
263C23×C83C2×#4112yes—
264C23×C832−1+412yes—
265C23×C832−1+412yes—
266C23×C83C2511yescharacteristic
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—44no—
277C22×D83—44no—
278C22×D83—44no—
279C22×D83—44no—
280C22×D83C22×Q814yes—
281C2×C4×C83—28no—
282C2×C4×C83—28no—
283C2×C4×C83—28no—
284C2×C4×C83—28no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
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—44no—
303C2×C4×C83—44no—
304C2×C4×C83—44no—
305C2×C4×C83C22×D414yes—
306C2×C4×C83C22×D414yes—
307C2×C4×C83C22×Q814yes—
308C2×C4×C83C2×#4114yes—
309C2×Dic83—28no—
310C2×Dic83—28no—
311C2×Dic83—28no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83—44no—
330C2×Dic83#121116yes—
331C2×Dic83C22×D414yes—
332C2×Dic83C22×D414yes—
333C2×Dic83C22×D414yes—
334C2×Dic83C22×D414yes—
335C2×Dic83C22×Q814yes—
336C2×Dic83C2×#4114yes—
337C4×D83—416no—
338Dic166—232no—
339Dic166—416no—
340C22×C83C2×#12114yes—
341C22×C83#53314yes—
342C22×C83#54114yes—
343C22×C83#54714yes—
344C22×C83#54814yes—
345C22×C83D4×Q814yes—
346C22×C83D4×Q814yes—
347C22×C83C23×D411yescharacteristic
348C22×C83C23×D411yescharacteristic
349C22×C83C23×Q811yescharacteristic
350C22×C83C22×#4111yescharacteristic
351C22×C83C22×#4111yescharacteristic
352C22×C83C2×2−1+411yescharacteristic
353C22×C83C2×2−1+411yescharacteristic
354C2×D83—24no—
355C2×D83—24no—
356C2×D83—24no—
357C2×D83—42no—
358C2×D83—416no—
359C2×D83—42no—
360C2×D83—42no—
361C2×D83—42no—
362C4×C83—24no—
363C4×C83—24no—
364C4×C83—24no—
365C4×C83—24no—
366C4×C83—42no—
367C4×C83—42no—
368C4×C83—42no—
369Dic83—24no—
370Dic83—24no—
371Dic83—24no—
372Dic83—42no—
373Dic83—42no—
374Dic83—42no—
375Dic83C2×#12118yes—
376C2×#2429—831nomaximal, Sylow
377C2×C83#242918yescomplemented
378C2×C83C22×#12111yescharacteristic
379C2×C83C2×#53311yescharacteristic
380C2×C83C2×#54111yescharacteristic
381C2×C83C2×#54711yescharacteristic
382C2×C83C2×#54811yescharacteristic
383C2×C83C2×D4×Q811yescharacteristic
384C2×C83C2×D4×Q811yescharacteristic
385D83—44no—
386C22×C4⋊Q8—831no—
387C22×C22⋊Q8—831no—
388C22×C22⋊Q8—831no—
389C22×C4×Q8—831no—
390#2429—8316no—
391C2×#398—831no—
392C2×#398—831no—
393C2×#396—831no—
394C2×#396—831no—
395C2×#391—831no—
396C2×#389—831no—
397C2×#389—831no—
398C2×#389D8311yescharacteristic, complemented
399C2×#388—831no—
400C2×#388—831no—
401C2×C4×C22⋊C4—831no—
402C83C2×#242911yescharacteristic, complemented, Sylow
403C23×Q8—831no—
404C23×Q8—831no—
405C24×C4—831no—
406C2×C4⋊Q8—838no—
407C2×C4⋊Q8—1668no—
408C2×C22⋊Q8—838no—
409C2×C22⋊Q8—838no—
410C2×C22⋊Q8—1668no—
411C2×C22⋊Q8—1668no—
412C2×C4×Q8—838no—
413C2×C4×Q8—1668no—
414C22×C4⋊C4—831no—
415C22×C4⋊C4—831no—
416C22×C4⋊C4—831no—
417C22×C4⋊C4—831no—
418C22×C4⋊C4—831no—
419C22×C4⋊C4—831no—
420C22×C4⋊C4—831no—
421C22×C4⋊C4—831no—
422C22×C4⋊C4—831no—
423C22×C4⋊C4—831no—
424C22×C4⋊C4C2×D8311yescharacteristic
425C22×C4⋊C4C2×D8311yescharacteristic
426C22×C4⋊C4C2×D8311yescharacteristic
427C22×C4⋊C4C2×D8311yescharacteristic
428C22×C22⋊C4—831no—
429C22×C22⋊C4—831no—
430C22×C22⋊C4—831no—
431C22×C22⋊C4—831no—
432C22×C22⋊C4—831no—
433C22×C22⋊C4—831no—
434C22×C42—831no—
435C22×C42—831no—
436C22×C42—831no—
437C22×C42C2×D8311yescharacteristic
438#398—838no—
439#398—838no—
440#396—838no—
441#396—838no—
442#391—838no—
443#389—838no—
444#389—838no—
445#389C2×D8318yescomplemented
446#388—838no—
447#388—838no—
448C4×C22⋊C4—838no—
449C2×#95—831no—
450C2×#95—831no—
451C2×#95—831no—
452C2×#95—831no—
453C2×#95—831no—
454C2×#95—831no—
455C2×#95C2×D8311yescharacteristic
456C2×#95C2×D8311yescharacteristic
457C25—831no—
458C22×Q8—838no—
459C22×Q8—834no—
460C22×Q8—834no—
461C22×Q8—1664no—
462C22×Q8—1664no—
463C22×Q8—1664no—
464C22×Q8—1664no—
465C22×Q8—1664no—
466C23×C4—831no—
467C23×C4—831no—
468C23×C4—831no—
469C23×C4—831no—
470C23×C4—831no—
471C23×C4—831no—
472C23×C4—831no—
473C23×C4—834no—
474C23×C4—1664no—
475C23×C4—1664no—
476C23×C4—1664no—
477C23×C4C22×D8311yescharacteristic
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C23×C4C22×D8311yescharacteristic
481C23×C4C22×D8311yescharacteristic
482C23×C4C22×D8311yescharacteristic
483C23×C4C22×D8311yescharacteristic
484C4⋊Q8—16632no—
485C22⋊Q8—16632no—
486C22⋊Q8—16632no—
487C4×Q8—16632no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—838no—
493C2×C4⋊C4—834no—
494C2×C4⋊C4—834no—
495C2×C4⋊C4—834no—
496C2×C4⋊C4—834no—
497C2×C4⋊C4—834no—
498C2×C4⋊C4—834no—
499C2×C4⋊C4—834no—
500C2×C4⋊C4—834no—
501C2×C4⋊C4—834no—
502C2×C4⋊C4—834no—
503C2×C4⋊C4—1664no—
504C2×C4⋊C4—1664no—
505C2×C4⋊C4—1664no—
506C2×C4⋊C4—1664no—
507C2×C4⋊C4—1664no—
508C2×C4⋊C4—1664no—
509C2×C4⋊C4—1664no—
510C2×C4⋊C4—1664no—
511C2×C4⋊C4—1664no—
512C2×C4⋊C4C22×D8314yes—
513C2×C4⋊C4C22×D8314yes—
514C2×C4⋊C4C22×D8314yes—
515C2×C4⋊C4C22×D8314yes—
516C2×C22⋊C4—838no—
517C2×C22⋊C4—834no—
518C2×C22⋊C4—834no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—1664no—
524C2×C22⋊C4—1664no—
525C2×C22⋊C4—1664no—
526C2×C22⋊C4—1664no—
527C2×C22⋊C4—1664no—
528C2×C42—24no—
529C2×C42—834no—
530C2×C42—834no—
531C2×C42—834no—
532C2×C42—1664no—
533C2×C42—1664no—
534C2×C42—1664no—
535C2×C42C22×D8314yes—
536#95—834no—
537#95—834no—
538#95—834no—
539#95—834no—
540#95—834no—
541#95—834no—
542#95C22×D8314yes—
543#95C22×D8314yes—
544C24—834no—
545C24—832no—
546C24—1662no—
547C24—1662no—
548C24—1662no—
549C24—1662no—
550C24—1662no—
551C24—1662no—
552C24C23×D8311yescharacteristic
553C2×Q8—33216no—
554C2×Q8—8316no—
555C2×Q8—1668no—
556C2×Q8—1668no—
557C2×Q8—1668no—
558C2×Q8—1668no—
559C2×Q8—16632no—
560C2×Q8—1668no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—33216no—
579C22×C4—834no—
580C22×C4—834no—
581C22×C4—834no—
582C22×C4—832no—
583C22×C4—834no—
584C22×C4—834no—
585C22×C4—834no—
586C22×C4—832no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—832no—
590C22×C4—832no—
591C22×C4—832no—
592C22×C4—1668no—
593C22×C4—1668no—
594C22×C4—1668no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4—1662no—
599C22×C4—1662no—
600C22×C4—1662no—
601C22×C4—1662no—
602C22×C4—1662no—
603C22×C4—1662no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4D4×D8314yes—
611C22×C4D4×D8314yes—
612C22×C4Q8×D8314yes—
613C22×C4#1305059014yes—
614C22×C4C23×D8312yes—
615C22×C4C23×D8312yes—
616C22×C4C23×D8312yes—
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8312yes—
620C22×C4C23×D8312yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—8316no—
626C4⋊C4—1668no—
627C4⋊C4—1668no—
628C4⋊C4—1668no—
629C4⋊C4—1668no—
630C4⋊C4—1668no—
631C4⋊C4—1668no—
632C4⋊C4—1668no—
633C4⋊C4—1668no—
634C4⋊C4—1668no—
635C22⋊C4—8316no—
636C22⋊C4—1668no—
637C22⋊C4—1668no—
638C22⋊C4—1668no—
639C22⋊C4—1668no—
640C22⋊C4—1668no—
641C42—28no—
642C42—1668no—
643C42—1668no—
644C42—1668no—
645C23—3324no—
646C23—3324no—
647C23—3324no—
648C23—3324no—
649C23—834no—
650C23—1668no—
651C23—1668no—
652C23—1668no—
653C23—1662no—
654C23—1662no—
655C23—1662no—
656C23—1662no—
657C23—1662no—
658C23—1662no—
659C23C2×D4×D8312yes—
660C23C2×D4×D8312yes—
661C23C2×Q8×D8312yes—
662C23#41×D8312yes—
663C23C2×#1305059012yes—
664C23#1458183912yes—
665C23#1458184012yes—
666C23C24×D8311yescharacteristic
667Q8—33216no—
668Q8—16632no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—33216no—
694C2×C4—3324no—
695C2×C4—3324no—
696C2×C4—3324no—
697C2×C4—8316no—
698C2×C4—834no—
699C2×C4—834no—
700C2×C4—834no—
701C2×C4—834no—
702C2×C4—834no—
703C2×C4—834no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4—1662no—
710C2×C4—1662no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4—1668no—
714C2×C4—1668no—
715C2×C4—1668no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4—1662no—
719C2×C4—1662no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4C2×D4×D8314yes—
723C2×C4C2×D4×D8314yes—
724C2×C4C2×Q8×D8314yes—
725C2×C4C2×#1305059014yes—
726C22—3322no—
727C22—3322no—
728C22—3322no—
729C22—33216no—
730C22—3322no—
731C22—1664no—
732C22—1664no—
733C22—1664no—
734C22#121×D8314yes—
735C22#1912825514yes—
736C22#1912831014yes—
737C22#1912835214yes—
738C22#1912836014yes—
739C22#1912836414yes—
740C22#1912836614yes—
741C22C22×D4×D8311yescharacteristic
742C22C22×D4×D8311yescharacteristic
743C22C22×Q8×D8311yescharacteristic
744C22C2×#41×D8311yescharacteristic
745C22C22×#1305059011yescharacteristic
746C22C2×#1458183911yescharacteristic
747C22C2×#1458184011yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—3322no—
756C4—3322no—
757C4—3322no—
758C4—838no—
759C4—1664no—
760C4—1664no—
761C4—1664no—
762C2—3324no—
763C2#2491106118yesdirect product factor
764C2C2×#121×D8311yescharacteristic
765C2C2×#1912825511yescharacteristic
766C2C2×#1912831011yescharacteristic
767C2C2×#1912835211yescharacteristic
768C2C2×#1912836011yescharacteristic
769C2C2×#1912836411yescharacteristic
770C2C2×#1912836611yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#389×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#389D83
hypocenterC83C2×#2429
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#14581791C2semidirect
4. C22×C4×Dic166C2semidirect
5. #24911061C2direct (N × H)
6. C2×#19127634C2semidirect
7. C2×#19127632C2semidirect
10. C2×#19127605C2semidirect
11. C2×#19127598C2semidirect
12. C2×#19127596C2semidirect
16. C2×#389×C83C2semidirect
21. C2×#14581791C22semidirect
27. C2×C4×Dic166C22semidirect
47. #19127634C22semidirect
48. #19127632C22semidirect
51. #19127605C22semidirect
52. #19127598C22semidirect
53. #19127596C22semidirect
68. #389×C83C22semidirect
120. C2×(C2×D83)⋊C4Q8semidirect
221. (C2×D83)⋊C4C2×Q8semidirect
377. C2×C83#2429semidirect
398. C2×#389D83semidirect
402. C83C2×#2429semidirect
445. #389C2×D83semidirect
763. C2#24911061direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817912
C22×#145817702
C22×C4×Dic1662
#249110612
C2×#191276342
C2×#191276322
C2×#191276232
C2×#191276052
C2×#191275982
C2×#191275962
C2×#191275922
C2×#191275902
C2×#191275482
C2×#389×C832
C2×#242983