Finite Group Databasebeta

← C2×#24912470 #35574449

Subgroups — C2×#24912470 #35574449

Order 21248.

3094 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×#14581770C211yesmaximal, characteristic
2C22×#14581770C211yesmaximal, characteristic
3#24912470C2116yesmaximal, direct product factor
4C2×#19127635C211yesmaximal, characteristic, complemented
5C2×#19127622C211yesmaximal, characteristic, complemented
6C2×#19127621C211yesmaximal, characteristic, complemented
7C2×#19127606C211yesmaximal, characteristic, complemented
8C2×#19127605C211yesmaximal, characteristic, complemented
9C2×#19127597C211yesmaximal, characteristic, complemented
10C2×#19127596C211yesmaximal, characteristic, complemented
11C2×#19127575C211yesmaximal, characteristic
12C2×#19127572C211yesmaximal, characteristic
13C2×#19127558C211yesmaximal, characteristic
14C2×#19127548C211yesmaximal, characteristic
15C2×#95×D83C211yesmaximal, characteristic
16C2×#398×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C2×#14581770—28no—
23C2×#14581770—28no—
24C2×#14581770C2218yes—
25C2×#14581770C2218yes—
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×C4×Dic83C2211yescharacteristic
39C22×C4×Dic83C2211yescharacteristic
40#19127635C2218yescomplemented
41#19127622C2218yescomplemented
42#19127621C2218yescomplemented
43#19127606C2218yescomplemented
44#19127605C2218yescomplemented
45#19127597C2218yescomplemented
46#19127596C2218yescomplemented
47#19127575C2218yes—
48#19127572C2218yes—
49#19127558C2218yes—
50#19127548C2218yes—
51C2×C83⋊#95C2211yescharacteristic
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×D83C2218yes—
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65#398×C83C2218yescomplemented
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166—24no—
73C22×Dic166—24no—
74C22×Dic166—42no—
75C22×Dic166—42no—
76C22×Dic166C2314yes—
77C22×Dic166C2314yes—
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C22×C4×D83—24no—
86C22×C4×D83—24no—
87C22×C4×D83—24no—
88C22×C4×D83—24no—
89C22×C4×D83—42no—
90C22×C4×D83—42no—
91C22×C4×D83—42no—
92C22×C4×D83—42no—
93C22×C4×D83Q818yescomplemented
94C22×C4×D83C2314yes—
95C22×C4×D83C2314yes—
96C22×C4×D83C2314yes—
97#14581770—232no—
98#14581770—232no—
99C2×C4⋊Dic83—24no—
100C2×C4⋊Dic83—42no—
101C2×C4⋊Dic83C2314yes—
102C2×C4⋊Dic83C2314yes—
103C2×Dic83⋊C4—24no—
104C2×Dic83⋊C4—24no—
105C2×Dic83⋊C4—24no—
106C2×Dic83⋊C4—24no—
107C2×Dic83⋊C4—24no—
108C2×Dic83⋊C4—42no—
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)⋊C4D418yes—
118C2×(C2×D83)⋊C4Q818yescomplemented
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×C4×Dic83—42no—
124C2×C4×Dic83—42no—
125C2×C4×Dic83C2314yes—
126C2×C4×Dic83C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C2×C4⋊C4×C83—24no—
144C2×C4⋊C4×C83—24no—
145C2×C4⋊C4×C83—42no—
146C2×C4⋊C4×C83—42no—
147C2×C4⋊C4×C83C2314yes—
148C2×C4⋊C4×C83C2314yes—
149C2×C4⋊C4×C83C2314yes—
150C2×C4⋊C4×C83C2314yes—
151#95×C83C2314yes—
152#95×C83C2314yes—
153#95×C83C2314yes—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83C2×D414yes—
159C23×D83C2×Q814yes—
160C23×D83C2×Q814yes—
161C23×D83C2412yes—
162C2×Dic166—28no—
163C2×Dic166—28no—
164C2×Dic166—28no—
165C2×Dic166—28no—
166C2×Dic166—44no—
167C2×Dic166—44no—
168C2×Dic166—416no—
169C2×Dic166—416no—
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×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83C2×D414yes—
187C22×Dic83C2×Q814yes—
188C22×Dic83C2×Q814yes—
189C22×Dic83#4114yes—
190C22×Dic83#4114yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C2×C4×D83—28no—
199C2×C4×D83—28no—
200C2×C4×D83—28no—
201C2×C4×D83—28no—
202C2×C4×D83—416no—
203C2×C4×D83—44no—
204C2×C4×D83—44no—
205C2×C4×D83—44no—
206C2×C4×D83—44no—
207C2×C4×D83—416no—
208C2×C4×D83—416no—
209C2×C4×D83C2×Q8116yescomplemented
210C4⋊Dic83—28no—
211C4⋊Dic83—44no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4—28no—
216Dic83⋊C4—28no—
217Dic83⋊C4—44no—
218(C2×D83)⋊C4—28no—
219(C2×D83)⋊C4—28no—
220(C2×D83)⋊C4C2×D4116yes—
221(C2×D83)⋊C4C2×Q8116yescomplemented
222C4×Dic83—44no—
223C4×Dic83—44no—
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×C83C2×D414yes—
244C22×C4×C83C2×Q814yes—
245C22×C4×C83C2×Q814yes—
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—
255C4⋊C4×C83—44no—
256C4⋊C4×C83—44no—
257C23×C83C22×D412yes—
258C23×C83C22×Q812yes—
259C23×C83C22×Q812yes—
260C23×C83C2×#4112yes—
261C23×C83C2×#4112yes—
262C23×C83H(5,𝔽2)12yes—
263C23×C83H(5,𝔽2)12yes—
264C23×C83C2511yescharacteristic
265C22×D83—28no—
266C22×D83—28no—
267C22×D83—28no—
268C22×D83—28no—
269C22×D83—28no—
270C22×D83—28no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83C4⋊Q8116yes—
276C22×D83C22×D414yes—
277C22×D83C22×Q814yes—
278C22×D83C22×Q814yes—
279C2×C4×C83—28no—
280C2×C4×C83—28no—
281C2×C4×C83—28no—
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—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—44no—
301C2×C4×C83—44no—
302C2×C4×C83—44no—
303C2×C4×C83—44no—
304C2×C4×C83C22×D414yes—
305C2×C4×C83C22×Q814yes—
306C2×C4×C83C22×Q814yes—
307C2×Dic83—28no—
308C2×Dic83—28no—
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—22no—
328C2×Dic83—44no—
329C2×Dic83—44no—
330C2×Dic83C22×D414yes—
331C2×Dic83C22×Q814yes—
332C2×Dic83C22×Q814yes—
333C2×Dic83C2×#4114yes—
334C2×Dic83C2×#4114yes—
335C4×D83—416no—
336C4×D83—416no—
337C4×D83—416no—
338Dic166—416no—
339Dic166—416no—
340C22×C83C2×C4⋊Q814yes—
341C22×C83#53314yes—
342C22×C83#54314yes—
343C22×C83#54614yes—
344C22×C83#54614yes—
345C22×C83#55414yes—
346C22×C83#55414yes—
347C22×C83C23×D411yescharacteristic
348C22×C83C23×Q811yescharacteristic
349C22×C83C23×Q811yescharacteristic
350C22×C83C22×#4111yescharacteristic
351C22×C83C22×#4111yescharacteristic
352C22×C83C2×H(5,𝔽2)11yescharacteristic
353C22×C83C2×H(5,𝔽2)11yescharacteristic
354C2×D83—24no—
355C2×D83—24no—
356C2×D83—24no—
357C2×D83—24no—
358C2×D83—24no—
359C2×D83—24no—
360C2×D83—232no—
361C2×D83C2×C4⋊Q818yes—
362C4×C83—24no—
363C4×C83—24no—
364C4×C83—24no—
365C4×C83—42no—
366C4×C83—42no—
367C4×C83—42no—
368C4×C83—42no—
369Dic83—24no—
370Dic83—24no—
371Dic83—24no—
372Dic83—24no—
373Dic83—24no—
374Dic83—42no—
375Dic83—42no—
376C2×#2549—831nomaximal, Sylow
377C2×C83#254918yescomplemented
378C2×C83C22×C4⋊Q811yescharacteristic
379C2×C83C2×#53311yescharacteristic
380C2×C83C2×#54311yescharacteristic
381C2×C83C2×#54611yescharacteristic
382C2×C83C2×#54611yescharacteristic
383C2×C83C2×#55411yescharacteristic
384C2×C83C2×#55411yescharacteristic
385D83—28no—
386C22×C22⋊Q8—831no—
387C22×C22⋊Q8—831no—
388#2549—8316no—
389C2×#398—831no—
390C2×#398D8311yescharacteristic, complemented
391C2×#395—831no—
392C2×#395—831no—
393C2×#391—831no—
394C2×#391—831no—
395C2×#389—831no—
396C2×#389—831no—
397C2×#385—831no—
398C2×#385—831no—
399C2×#380—831no—
400C2×C4×C22⋊C4—831no—
401C22×#95—831no—
402C83C2×#254911yescharacteristic, complemented, Sylow
403C23×Q8—831no—
404C23×Q8—831no—
405C24×C4—831no—
406C24×C4—831no—
407C24×C4—831no—
408C2×C22⋊Q8—838no—
409C2×C22⋊Q8—838no—
410C2×C22⋊Q8—1668no—
411C2×C22⋊Q8—1668no—
412C22×C4⋊C4—831no—
413C22×C4⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
421C22×C4⋊C4C2×D8311yescharacteristic
422C22×C4⋊C4C2×D8311yescharacteristic
423C22×C4⋊C4C2×D8311yescharacteristic
424C22×C22⋊C4—831no—
425C22×C22⋊C4—831no—
426C22×C22⋊C4—831no—
427C22×C22⋊C4—831no—
428C22×C42—831no—
429C22×C42—831no—
430#398—838no—
431#398C2×D8318yescomplemented
432#395—838no—
433#395—838no—
434#391—838no—
435#391—838no—
436#389—838no—
437#389—838no—
438#385—838no—
439#385—838no—
440#380—838no—
441C4×C22⋊C4—838no—
442C2×#95—831no—
443C2×#95—831no—
444C2×#95—831no—
445C2×#95—831no—
446C2×#95—831no—
447C2×#95—831no—
448C2×#95—831no—
449C2×#95—831no—
450C2×#95—831no—
451C2×#95—838no—
452C2×#95C2×D8311yescharacteristic
453C2×#95C2×D8311yescharacteristic
454C2×#95C2×D8311yescharacteristic
455C25—831no—
456C22×Q8—3322no—
457C22×Q8—3322no—
458C22×Q8—834no—
459C22×Q8—834no—
460C22×Q8—1664no—
461C22×Q8—1664no—
462C22×Q8—1664no—
463C22×Q8—1664no—
464C23×C4—3322no—
465C23×C4—3322no—
466C23×C4—3322no—
467C23×C4—3322no—
468C23×C4—838no—
469C23×C4—834no—
470C23×C4—834no—
471C23×C4—834no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—831no—
475C23×C4—831no—
476C23×C4—831no—
477C23×C4—831no—
478C23×C4—831no—
479C23×C4—1664no—
480C23×C4—1664no—
481C23×C4—1664no—
482C23×C4—1664no—
483C23×C4C22×D8311yescharacteristic
484C23×C4C22×D8311yescharacteristic
485C23×C4C22×D8311yescharacteristic
486C23×C4C22×D8311yescharacteristic
487C23×C4C22×D8311yescharacteristic
488C23×C4C22×D8311yescharacteristic
489C23×C4C22×D8311yescharacteristic
490C22⋊Q8—16632no—
491C22⋊Q8—16632no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—3322no—
497C2×C4⋊C4—3322no—
498C2×C4⋊C4—834no—
499C2×C4⋊C4—834no—
500C2×C4⋊C4—834no—
501C2×C4⋊C4—834no—
502C2×C4⋊C4—834no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—834no—
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—838no—
518C2×C22⋊C4—834no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—1664no—
523C2×C22⋊C4—1664no—
524C2×C42—3322no—
525C2×C42—3322no—
526C2×C42—834no—
527C2×C42—834no—
528#95—834no—
529#95—834no—
530#95—834no—
531#95—834no—
532#95—834no—
533#95—834no—
534#95—834no—
535#95—834no—
536#95—834no—
537#95C22×D8314yes—
538#95C22×D8314yes—
539#95C22×D8314yes—
540C24—834no—
541C24—834no—
542C24—834no—
543C24—832no—
544C24—1662no—
545C24—1662no—
546C24—1662no—
547C24—1662no—
548C24C23×D8311yescharacteristic
549C2×Q8—33216no—
550C2×Q8—3324no—
551C2×Q8—3324no—
552C2×Q8—33216no—
553C2×Q8—1668no—
554C2×Q8—1668no—
555C2×Q8—1668no—
556C2×Q8—1668no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
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—33216no—
576C22×C4—3324no—
577C22×C4—3324no—
578C22×C4—3324no—
579C22×C4—3324no—
580C22×C4—33216no—
581C22×C4—33216no—
582C22×C4—8316no—
583C22×C4—834no—
584C22×C4—834no—
585C22×C4—834no—
586C22×C4—834no—
587C22×C4—834no—
588C22×C4—832no—
589C22×C4—832no—
590C22×C4—832no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—1668no—
596C22×C4—1668no—
597C22×C4—1668no—
598C22×C4—1668no—
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×C4—1662no—
611C22×C4—1662no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4D4×D8314yes—
616C22×C4Q8×D8314yes—
617C22×C4Q8×D8314yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8312yes—
620C22×C4C23×D8312yes—
621C22×C4C23×D8312yes—
622C22×C4C23×D8312yes—
623C22×C4C23×D8312yes—
624C22×C4C23×D8312yes—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—3324no—
630C4⋊C4—3324no—
631C4⋊C4—1668no—
632C4⋊C4—1668no—
633C4⋊C4—1668no—
634C4⋊C4—1668no—
635C4⋊C4—1668no—
636C4⋊C4—1668no—
637C22⋊C4—8316no—
638C22⋊C4—8316no—
639C22⋊C4—1668no—
640C22⋊C4—1668no—
641C42—3324no—
642C42—3324no—
643C23—8316no—
644C23—834no—
645C23—834no—
646C23—834no—
647C23—1668no—
648C23—1668no—
649C23—1668no—
650C23—1668no—
651C23—1668no—
652C23—1668no—
653C23—1662no—
654C23—1662no—
655C23—1662no—
656C23—1662no—
657C23C2×D4×D8312yes—
658C23C2×Q8×D8312yes—
659C23C2×Q8×D8312yes—
660C23#41×D8312yes—
661C23#41×D8312yes—
662C23#1458183712yes—
663C23#1458183812yes—
664C23C24×D8311yescharacteristic
665Q8—33216no—
666Q8—33216no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
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—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—33216no—
693C2×C4—33216no—
694C2×C4—33216no—
695C2×C4—3324no—
696C2×C4—3324no—
697C2×C4—834no—
698C2×C4—834no—
699C2×C4—834no—
700C2×C4—834no—
701C2×C4—834no—
702C2×C4—1662no—
703C2×C4—1662no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1668no—
709C2×C4—1668no—
710C2×C4—1668no—
711C2×C4—1668no—
712C2×C4—1668no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1662no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4—1662no—
719C2×C4—1662no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4C2×D4×D8314yes—
724C2×C4C2×Q8×D8314yes—
725C2×C4C2×Q8×D8314yes—
726C22—838no—
727C22—1664no—
728C22—1664no—
729C22—1664no—
730C22—16632no—
731C22—1664no—
732C22—1664no—
733C22—1664no—
734C22C4⋊Q8×D8314yes—
735C22#1912825714yes—
736C22#1912832614yes—
737C22#1912834314yes—
738C22#1912834814yes—
739C22#1912840514yes—
740C22#1912840714yes—
741C22C22×D4×D8311yescharacteristic
742C22C22×Q8×D8311yescharacteristic
743C22C22×Q8×D8311yescharacteristic
744C22C2×#41×D8311yescharacteristic
745C22C2×#41×D8311yescharacteristic
746C22C2×#1458183711yescharacteristic
747C22C2×#1458183811yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—3322no—
756C4—3322no—
757C4—1664no—
758C4—1664no—
759C4—1664no—
760C4—1664no—
761C4—1664no—
762C2—1668no—
763C2#2491247018yesdirect product factor
764C2C2×C4⋊Q8×D8311yescharacteristic
765C2C2×#1912825711yescharacteristic
766C2C2×#1912832611yescharacteristic
767C2C2×#1912834311yescharacteristic
768C2C2×#1912834811yescharacteristic
769C2C2×#1912840511yescharacteristic
770C2C2×#1912840711yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#398×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#398D83
hypocenterC83C2×#2549
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #24912470C2direct (N × H)
4. C2×#19127635C2semidirect
5. C2×#19127622C2semidirect
6. C2×#19127621C2semidirect
7. C2×#19127606C2semidirect
8. C2×#19127605C2semidirect
9. C2×#19127597C2semidirect
10. C2×#19127596C2semidirect
16. C2×#398×C83C2semidirect
40. #19127635C22semidirect
41. #19127622C22semidirect
42. #19127621C22semidirect
43. #19127606C22semidirect
44. #19127605C22semidirect
45. #19127597C22semidirect
46. #19127596C22semidirect
65. #398×C83C22semidirect
93. C22×C4×D83Q8semidirect
118. C2×(C2×D83)⋊C4Q8semidirect
209. C2×C4×D83C2×Q8semidirect
221. (C2×D83)⋊C4C2×Q8semidirect
377. C2×C83#2549semidirect
390. C2×#398D83semidirect
402. C83C2×#2549semidirect
431. #398C2×D83semidirect
763. C2#24912470direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817702
#249124702
C2×#191276352
C2×#191276222
C2×#191276212
C2×#191276062
C2×#191276052
C2×#191275972
C2×#191275962
C2×#191275752
C2×#191275722
C2×#191275582
C2×#191275482
C2×#95×D832
C2×#398×C832
C2×#254983