Finite Group Databasebeta

← C2×#24921345 #36312845

Subgroups — C2×#24921345 #36312845

Order 21248.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921345C2132yesmaximal, direct product factor
2C2×#19128428C214yesmaximal, complemented
3C2×#19128418C214yesmaximal, complemented
4C2×#19128387C214yesmaximal, complemented
5C2×#19128383C214yesmaximal, complemented
6C2×#19128314C211yesmaximal, characteristic, complemented
7C2×#19128313C211yesmaximal, characteristic, complemented
8C2×#19128312C211yesmaximal, characteristic, complemented
9C2×#19128274C212yesmaximal
10C2×#19128257C211yesmaximal, characteristic, complemented
11C2×#19128255C212yesmaximal, complemented
12C2×#19128253C212yesmaximal, complemented
13C2×C4⋊Q8×D83C211yesmaximal, characteristic, complemented
14C2×#19128177C212yesmaximal, complemented
15C2×#19128169C211yesmaximal, characteristic
16C2×#541×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C22×Q8×D83C2212yes—
19#19128428C22164yescomplemented
20#19128418C22164yescomplemented
21#19128387C22164yescomplemented
22#19128383C22164yescomplemented
23#19128314C22116yescomplemented
24#19128313C22116yescomplemented
25#19128312C22116yescomplemented
26#19128274C22132yes—
27#19128257C22116yescomplemented
28#19128255C22132yescomplemented
29#19128253C22132yescomplemented
30C2×#14581792C2211yescharacteristic
31C2×#14581791C2214yes—
32C2×#14581791C2212yes—
33C2×#14581791C2214yes—
34C2×#14581790C2212yes—
35C4⋊Q8×D83C22116yescomplemented
36C2×#14581787C2214yes—
37C2×#14581787C2214yes—
38C2×#14581785C2214yes—
39C2×#14581784C2211yescharacteristic
40C2×#14581783C2214yes—
41C2×#14581782C2214yes—
42C2×#14581782C2214yes—
43C2×#14581782C2214yes—
44C2×#14581782C2214yes—
45C2×#14581778C2214yes—
46C2×#14581777C2214yes—
47C2×#14581774C2214yes—
48C2×#14581772C2212yes—
49C2×#14581771C2212yes—
50C2×#14581770C2214yes—
51C2×#14581770C2214yes—
52C2×#14581769C2214yes—
53C2×#14581768C2212yes—
54#19128177C22132yescomplemented
55#19128169C22116yes—
56C2×Q8×Dic83C2212yes—
57C2×C4×Dic166C2214yes—
58C2×C4×Dic166C2212yes—
59C2×C4×Dic166C2214yes—
60C2×#14581757C2212yes—
61C2×#14581757C2212yes—
62C2×#14581757C2214yes—
63C2×#14581757C2214yes—
64C2×#14581757C2214yes—
65C2×#14581754C2212yes—
66C2×(C22⋊D83)⋊C4C2212yes—
67C2×(C22⋊D83)⋊C4C2212yes—
68C2×#14581750C2214yes—
69C2×#14581750C2212yes—
70C2×#14581749C2211yescharacteristic
71C2×#14581749C2211yescharacteristic
72C2×#14581749C2214yes—
73C2×#14581749C2214yes—
74C2×#14581748C2214yes—
75C2×C4⋊C4×D83C2214yes—
76C22×C4×Dic83C2211yescharacteristic
77C2×C42×D83C2211yescharacteristic
78C2×C42×D83C2211yescharacteristic
79#541×C83C22116yescomplemented
80C2×C4⋊Q8×C83C2211yescharacteristic
81C2×#126×C83C2214yes—
82C2×#125×C83C2211yescharacteristic
83C2×#125×C83C2214yes—
84C2×C22⋊Q8×C83C2212yes—
85C2×C4×Q8×C83C2212yes—
86C2×#117×C83C2211yescharacteristic
87C2×#13050590—28no—
88C2×#13050590C2318yes—
89C22×Dic166C2314yes—
90C22×Dic166C2311yescharacteristic
91C22×Dic166C2312yes—
92C22×Dic166C2314yes—
93C2×Q8×D83—216no—
94C2×Q8×D83C23116yes—
95C22×D332C2311yescharacteristic
96C22×C22⋊D83C2311yescharacteristic
97C22×C22⋊D83C2311yescharacteristic
98C23×Dic83C2312yes—
99C22×C4×D83C2312yes—
100C22×C4×D83C2312yes—
101C22×C4×D83C2311yescharacteristic
102C22×C4×D83C2314yes—
103C22×C4×D83C2311yescharacteristic
104#14581792C2318yes—
105#14581791C23132yes—
106#14581791C23132yes—
107#14581791C23116yes—
108#14581790C23116yes—
109#14581787C23132yes—
110#14581787C23132yes—
111#14581785C23132yes—
112#14581784C2318yes—
113#14581783C23132yes—
114#14581782C23132yes—
115#14581782C23132yes—
116#14581782C23132yes—
117#14581782C23132yes—
118#14581778C23132yes—
119#14581777C23132yes—
120#14581774C23132yes—
121#14581772C23116yes—
122#14581771C23116yes—
123#14581770C23132yes—
124#14581770C23132yes—
125#14581769C23132yes—
126#14581768C23116yes—
127Q8×Dic83C23116yes—
128C4×Dic166C23132yes—
129C4×Dic166C23132yes—
130C4×Dic166C23116yes—
131#14581757C23132yes—
132#14581757C23132yes—
133#14581757C23132yes—
134#14581757C23116yes—
135#14581757C23116yes—
136#14581754C23116yes—
137(C22⋊D83)⋊C4C23116yes—
138(C22⋊D83)⋊C4C23116yes—
139#14581750C23132yes—
140#14581750C23116yes—
141#14581749C23132yes—
142#14581749C23132yes—
143#14581749C2318yes—
144#14581749C2318yes—
145#14581748C23132yes—
146C2×C4⋊Dic83C2314yes—
147C2×C4⋊Dic83C2312yes—
148C2×C4⋊Dic83C2314yes—
149C2×C4⋊Dic83C2314yes—
150C2×Dic83⋊C4C2314yes—
151C2×Dic83⋊C4C2314yes—
152C2×Dic83⋊C4C2314yes—
153C2×Dic83⋊C4C2312yes—
154C2×Dic83⋊C4C2312yes—
155C2×Dic83⋊C4C2314yes—
156C2×Dic83⋊C4C2314yes—
157C2×Dic83⋊C4C2314yes—
158C2×Dic83⋊C4C2314yes—
159C2×Dic83⋊C4C2314yes—
160C4⋊C4×D83C23132yes—
161C2×C22⋊Dic83C2314yes—
162C2×(C2×D83)⋊C4C2312yes—
163C2×(C2×D83)⋊C4C2314yes—
164C2×(C2×D83)⋊C4C2312yes—
165C2×(C2×D83)⋊C4C2314yes—
166C2×(C2×D83)⋊C4C2314yes—
167C2×C4×Dic83C2311yescharacteristic
168C2×C4×Dic83C2312yes—
169C2×C4×Dic83C2312yes—
170C2×C4×Dic83C2311yescharacteristic
171C2×C4×Dic83C2312yes—
172C2×C4×Dic83C2318yes—
173C2×C4×Dic83C2314yes—
174C2×C4×Dic83C2314yes—
175C2×C4×Dic83C2314yes—
176C2×C4×Dic83C2314yes—
177C42×D83C2318yes—
178C42×D83C2318yes—
179C22×Q8×C83C2312yes—
180C23×C4×C83C2311yescharacteristic
181C4⋊Q8×C83C2318yes—
182#126×C83C23132yes—
183#125×C83C23132yes—
184#125×C83C2318yes—
185C22⋊Q8×C83C23116yes—
186C4×Q8×C83C23116yes—
187#117×C83C2318yes—
188C2×C4⋊C4×C83C2312yes—
189C2×C4⋊C4×C83C2312yes—
190C2×C4⋊C4×C83C2314yes—
191C2×C4⋊C4×C83C2314yes—
192C2×C4⋊C4×C83C2314yes—
193C2×C4⋊C4×C83C2314yes—
194C2×C22⋊C4×C83C2312yes—
195C2×C22⋊C4×C83C2314yes—
196C2×C42×C83C2311yescharacteristic
197C2×C42×C83C2311yescharacteristic
198C2×C42×C83C2314yes—
199C23×D83C2411yescharacteristic
200C23×D83C2411yescharacteristic
201#13050590—232no—
202C2×Dic166—28no—
203C2×Dic166—216no—
204C2×Dic166—24no—
205C2×Dic166—216no—
206C2×Dic166C24116yes—
207C2×Dic166C2418yes—
208C2×Dic166C24116yes—
209C2×Dic166C2414yes—
210Q8×D83—264no—
211C2×D332—24no—
212C2×D332C2414yes—
213C2×C22⋊D83—24no—
214C2×C22⋊D83—24no—
215C2×C22⋊D83C2414yes—
216C2×C22⋊D83C2414yes—
217C22×Dic83—28no—
218C22×Dic83C2418yes—
219C22×Dic83C2411yescharacteristic
220C22×Dic83C2414yes—
221C22×Dic83C2412yes—
222C22×Dic83C2414yes—
223C22×Dic83C2411yescharacteristic
224C22×Dic83C2412yes—
225C2×C4×D83—216no—
226C2×C4×D83—24no—
227C2×C4×D83—28no—
228C2×C4×D83—28no—
229C2×C4×D83#4118yes—
230C2×C4×D83C2414yes—
231C2×C4×D83C2418yes—
232C2×C4×D83C2418yes—
233C2×C4×D83C24116yes—
234C2×C4×D83C2414yes—
235C4⋊Dic83C2418yes—
236C4⋊Dic83C24116yes—
237C4⋊Dic83C24116yes—
238C4⋊Dic83C24116yes—
239Dic83⋊C4C24116yes—
240Dic83⋊C4C24116yes—
241Dic83⋊C4C24116yes—
242Dic83⋊C4C24116yes—
243Dic83⋊C4C24116yes—
244Dic83⋊C4C24116yes—
245Dic83⋊C4C24116yes—
246Dic83⋊C4C24116yes—
247Dic83⋊C4C2418yes—
248Dic83⋊C4C2418yes—
249C22⋊Dic83C24116yes—
250(C2×D83)⋊C4C24116yes—
251(C2×D83)⋊C4C24116yes—
252(C2×D83)⋊C4C24116yes—
253(C2×D83)⋊C4C2418yes—
254(C2×D83)⋊C4C2418yes—
255C4×Dic83C24116yes—
256C4×Dic83C2418yes—
257C4×Dic83C2418yes—
258C4×Dic83C24116yes—
259C4×Dic83C24116yes—
260C4×Dic83C24116yes—
261C4×Dic83C2414yes—
262C4×Dic83C2418yes—
263C4×Dic83C2414yes—
264C24×C83C2411yescharacteristic
265C2×Q8×C83—28no—
266C2×Q8×C83C2418yes—
267C22×C4×C83—24no—
268C22×C4×C83C2414yes—
269C22×C4×C83C2414yes—
270C22×C4×C83C2412yes—
271C22×C4×C83C2412yes—
272C22×C4×C83C2411yescharacteristic
273C22×C4×C83C2414yes—
274C22×C4×C83C2411yescharacteristic
275C4⋊C4×C83C24116yes—
276C4⋊C4×C83C24116yes—
277C4⋊C4×C83C2418yes—
278C4⋊C4×C83C24116yes—
279C4⋊C4×C83C2418yes—
280C4⋊C4×C83C24116yes—
281C22⋊C4×C83C24116yes—
282C22⋊C4×C83C2418yes—
283C42×C83C2414yes—
284C42×C83C2414yes—
285C42×C83C24116yes—
286C23×C83—22no—
287C23×C83—24no—
288C23×C83C2512yes—
289C23×C83C2511yescharacteristic
290C22×D83—24no—
291C22×D83—22no—
292C22×D83—24no—
293C22×D83C2×#4114yes—
294C22×D83C2512yes—
295C22×D83C2512yes—
296Q8×C83—216no—
297C2×C4×C83—22no—
298C2×C4×C83—28no—
299C2×C4×C83—24no—
300C2×C4×C83—24no—
301C2×C4×C83—28no—
302C2×C4×C83—28no—
303C2×C4×C83C2×#4114yes—
304C2×C4×C83C2514yes—
305C2×C4×C83C2518yes—
306C2×C4×C83C2514yes—
307C2×C4×C83C2518yes—
308C2×C4×C83C2512yes—
309C2×C4×C83C2512yes—
310C22⋊D83—28no—
311C22⋊D83—28no—
312C2×Dic83—22no—
313C2×Dic83—28no—
314C2×Dic83—24no—
315C2×Dic83—28no—
316C2×Dic83—216no—
317C2×Dic83C2×#4114yes—
318C2×Dic832−1+418yes—
319C2×Dic83C2514yes—
320C2×Dic83C2518yes—
321C2×Dic83C2518yes—
322C2×Dic83C2512yes—
323C2×Dic83C2512yes—
324C2×Dic83C2514yes—
325D332—28no—
326C4×D83—232no—
327C4×D83—28no—
328C4×D83—216no—
329C4×D83—216no—
330C4×D83C2×#41116yes—
331Dic166—216no—
332Dic166—232no—
333Dic166—28no—
334Dic166—232no—
335C22×C83—22no—
336C22×C83—24no—
337C22×C83—44no—
338C22×C83C22×#4112yes—
339C22×C83C2×2−1+414yes—
340C22×C83C2611yescharacteristic
341C2×D83—24no—
342C2×D83—28no—
343C2×D83—22no—
344C2×D83—24no—
345C2×D83—44no—
346C2×D83C22×#4114yes—
347C4×C83—28no—
348C4×C83—22no—
349C4×C83—28no—
350C4×C83—24no—
351C4×C83—24no—
352C4×C83C22×#4114yes—
353Dic83—28no—
354Dic83—22no—
355Dic83—28no—
356Dic83—24no—
357Dic83C22×#4114yes—
358Dic83C2×2−1+418yes—
359C2×#3509—831nomaximal, Sylow
360C2×C83—42no—
361C2×C83#350914yescomplemented
362C2×C83C23×#4111yescharacteristic
363C2×C83C22×2−1+412yes—
364D83—24no—
365D83—42no—
366#3509—8332no—
367C2×#557—834no—
368C2×#556—834no—
369C2×#552—834no—
370C2×#552—834no—
371C2×#541—831no—
372C2×#541—831no—
373C2×#541—831no—
374C2×#541D8311yescharacteristic, complemented
375C2×#536—832no—
376C2×#533—831no—
377C2×#533—832no—
378C2×#533—832no—
379C22×C4⋊Q8—831no—
380C2×#519—832no—
381C2×C4×#41—831no—
382C83C2×#350911yescharacteristic, complemented, Sylow
383C22×#41—831no—
384C23×Q8—832no—
385#557—8364no—
386#556—8364no—
387#552—8364no—
388#552—8364no—
389#541—8316no—
390#541—8316no—
391#541—8316no—
392#541C2×D83116yescomplemented
393#536—8332no—
394#533—8316no—
395#533—8332no—
396#533—8332no—
397C2×C4⋊Q8—832no—
398C2×C4⋊Q8—8316no—
399C2×C4⋊Q8—834no—
400C2×C4⋊Q8—832no—
401C2×C4⋊Q8—834no—
402C2×C4⋊Q8—831no—
403C2×C4⋊Q8C2×D8311yescharacteristic
404C2×#126—834no—
405C2×#126—834no—
406C2×#126—834no—
407C2×#126C2×D8314yes—
408C2×#125—834no—
409C2×#125—834no—
410C2×#125—834no—
411C2×#125—834no—
412C2×#125—834no—
413C2×#125—831no—
414C2×#125C2×D8311yescharacteristic
415C2×#125C2×D8314yes—
416C2×#124—834no—
417C2×#123—834no—
418C2×#123—834no—
419C2×C22⋊Q8—832no—
420C2×C22⋊Q8—832no—
421C2×C22⋊Q8—832no—
422C2×C22⋊Q8—834no—
423C2×C22⋊Q8—834no—
424C2×C22⋊Q8—834no—
425C2×C22⋊Q8C2×D8312yes—
426#519—8332no—
427C4×#41—8316no—
428C2×C4×Q8—832no—
429C2×C4×Q8—832no—
430C2×C4×Q8—832no—
431C2×C4×Q8—834no—
432C2×C4×Q8—834no—
433C2×C4×Q8—834no—
434C2×C4×Q8—832no—
435C2×C4×Q8—834no—
436C2×C4×Q8—834no—
437C2×C4×Q8C2×D8312yes—
438C2×C4×D4—832no—
439C2×C4×D4—832no—
440C2×C4×D4—832no—
441C2×#117—832no—
442C2×#117—834no—
443C2×#117—834no—
444C2×#117—831no—
445C2×#117—831no—
446C2×#117—834no—
447C2×#117—834no—
448C2×#117C2×D8311yescharacteristic
449C22×C4⋊C4—834no—
450C22×C42—831no—
451C22×C42—831no—
452C22×C42—831no—
453C2×#41—838no—
454C2×#41—1668no—
455C22×Q8—8316no—
456C22×Q8—834no—
457C22×Q8—832no—
458C22×Q8—834no—
459C22×Q8—831no—
460C22×Q8—16616no—
461C22×Q8C22×D8312yes—
462C22×D4—831no—
463C22×D4—831no—
464C22×D4—831no—
465C23×C4—831no—
466C23×C4—832no—
467C23×C4—834no—
468C23×C4—832no—
469C23×C4—832no—
470C23×C4—831no—
471C23×C4C22×D8311yescharacteristic
472C4⋊Q8—8316no—
473C4⋊Q8—8332no—
474C4⋊Q8—8316no—
475C4⋊Q8—8332no—
476C4⋊Q8—838no—
477C4⋊Q8C22×D8318yes—
478#126—8332no—
479#126—8332no—
480#126—8332no—
481#126C22×D83132yes—
482#125—8332no—
483#125—8332no—
484#125—8332no—
485#125—8332no—
486#125—8332no—
487#125—838no—
488#125C22×D8318yes—
489#125C22×D83132yes—
490#124—8332no—
491#123—8332no—
492#123—8332no—
493C22⋊Q8—8316no—
494C22⋊Q8—8316no—
495C22⋊Q8—8332no—
496C22⋊Q8—8332no—
497C22⋊Q8—8316no—
498C22⋊Q8—8332no—
499C22⋊Q8C22×D83116yes—
500C4×Q8—8316no—
501C4×Q8—8316no—
502C4×Q8—8316no—
503C4×Q8—8332no—
504C4×Q8—8332no—
505C4×Q8—8332no—
506C4×Q8—8316no—
507C4×Q8—8332no—
508C4×Q8—8332no—
509C4×Q8C22×D83116yes—
510C4×D4—8316no—
511C4×D4—8316no—
512C4×D4—8316no—
513#117—8316no—
514#117—8332no—
515#117—8332no—
516#117—838no—
517#117—838no—
518#117—8332no—
519#117—8332no—
520#117C22×D8318yes—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—832no—
526C2×C4⋊C4—832no—
527C2×C4⋊C4—832no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—834no—
531C2×C4⋊C4—834no—
532C2×C4⋊C4—834no—
533C2×C4⋊C4—834no—
534C2×C4⋊C4—834no—
535C2×C4⋊C4—8332no—
536C2×C4⋊C4C22×D8314yes—
537C2×C4⋊C4C22×D8312yes—
538C2×C4⋊C4C22×D8314yes—
539C2×C4⋊C4C22×D8312yes—
540C2×C4⋊C4C22×D8314yes—
541C2×C4⋊C4C22×D8314yes—
542C2×C22⋊C4—834no—
543C2×C22⋊C4—832no—
544C2×C22⋊C4—834no—
545C2×C22⋊C4—832no—
546C2×C22⋊C4—834no—
547C2×C22⋊C4—834no—
548C2×C22⋊C4C22×D8314yes—
549C2×C22⋊C4C22×D8312yes—
550C2×C42—831no—
551C2×C42—834no—
552C2×C42—834no—
553C2×C42—834no—
554C2×C42—834no—
555C2×C42—832no—
556C2×C42—832no—
557C2×C42—832no—
558C2×C42—838no—
559C2×C42—831no—
560C2×C42—838no—
561C2×C42—838no—
562C2×C42C22×D8314yes—
563C2×C42C22×D8311yescharacteristic
564C2×C42C22×D8311yescharacteristic
565C24—831no—
566C24—831no—
567C24C23×D8311yescharacteristic
568#41—16632no—
569C2×Q8—28no—
570C2×Q8—8316no—
571C2×Q8—838no—
572C2×Q8—8316no—
573C2×Q8—834no—
574C2×Q8—16616no—
575C2×Q8—1664no—
576C2×Q8—16616no—
577C2×Q8—16664no—
578C2×Q8—1668no—
579C2×Q8C23×D8318yes—
580C2×D4—834no—
581C2×D4—834no—
582C2×D4—834no—
583C2×D4—1664no—
584C2×D4—1664no—
585C2×D4—1664no—
586C22×C4—24no—
587C22×C4—831no—
588C22×C4—832no—
589C22×C4—838no—
590C22×C4—834no—
591C22×C4—838no—
592C22×C4—832no—
593C22×C4—834no—
594C22×C4—834no—
595C22×C4—831no—
596C22×C4—838no—
597C22×C4—838no—
598C22×C4—834no—
599C22×C4—8316no—
600C22×C4—1668no—
601C22×C4—1668no—
602C22×C4—16616no—
603C22×C4—1668no—
604C22×C4—1664no—
605C22×C4C23×D8314yes—
606C22×C4C23×D8312yes—
607C22×C4C23×D8314yes—
608C22×C4C23×D8311yescharacteristic
609C22×C4C23×D8312yes—
610C22×C4C23×D8314yes—
611C22×C4C23×D8311yescharacteristic
612C4⋊C4—8316no—
613C4⋊C4—8316no—
614C4⋊C4—8316no—
615C4⋊C4—8316no—
616C4⋊C4—838no—
617C4⋊C4—838no—
618C4⋊C4—838no—
619C4⋊C4—8316no—
620C4⋊C4—8316no—
621C4⋊C4—8316no—
622C4⋊C4—8316no—
623C4⋊C4—8316no—
624C4⋊C4—8316no—
625C4⋊C4—8316no—
626C4⋊C4C23×D83116yes—
627C4⋊C4C23×D8318yes—
628C4⋊C4C23×D83116yes—
629C4⋊C4C23×D8318yes—
630C4⋊C4C23×D83116yes—
631C4⋊C4C23×D83116yes—
632C22⋊C4—8316no—
633C22⋊C4—838no—
634C22⋊C4—8316no—
635C22⋊C4—838no—
636C22⋊C4—8316no—
637C22⋊C4—8316no—
638C22⋊C4C23×D83116yes—
639C22⋊C4C23×D8318yes—
640C42—834no—
641C42—834no—
642C42—838no—
643C42—838no—
644C42—838no—
645C42—8316no—
646C42—8316no—
647C42—8316no—
648C42—8316no—
649C42C23×D8314yes—
650C42C23×D8314yes—
651C42C23×D83116yes—
652C23—22no—
653C23—24no—
654C23—834no—
655C23—832no—
656C23—832no—
657C23—1662no—
658C23—1664no—
659C23—1664no—
660C23C24×D8312yes—
661C23C24×D8311yescharacteristic
662Q8—216no—
663Q8—16632no—
664Q8—1668no—
665Q8—16632no—
666Q8—16616no—
667D4—1668no—
668D4—1668no—
669D4—1668no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—834no—
677C2×C4—838no—
678C2×C4—832no—
679C2×C4—834no—
680C2×C4—8316no—
681C2×C4—834no—
682C2×C4—838no—
683C2×C4—838no—
684C2×C4—832no—
685C2×C4—16616no—
686C2×C4—16616no—
687C2×C4—16632no—
688C2×C4—16616no—
689C2×C4—1662no—
690C2×C4—1668no—
691C2×C4—1664no—
692C2×C4—1668no—
693C2×C4—1668no—
694C2×C4#41×D8314yes—
695C2×C4C24×D8314yes—
696C2×C4C24×D8318yes—
697C2×C4C24×D8312yes—
698C2×C4C24×D8314yes—
699C2×C4C24×D8318yes—
700C2×C4C24×D8312yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—3324no—
705C22—834no—
706C22—1662no—
707C22—1664no—
708C22—1668no—
709C22—1664no—
710C22C2×#41×D8312yes—
711C222−1+4×D8314yes—
712C22C25×D8311yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—834no—
719C4—838no—
720C4—1662no—
721C4—1668no—
722C4—1664no—
723C4—1668no—
724C4C2×#41×D8314yes—
725C2—42no—
726C2—3322no—
727C2—1664no—
728C2#2492134514yesdirect product factor
729C2C22×#41×D8311yescharacteristic
730C2C2×2−1+4×D8312yes—
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#541×C83C2
socleC23×C83C25
prime radicalC22×#13050590C22
hypercenterC2×#541D83
hypocenterC83C2×#3509
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #24921345C2direct (N × H)
2. C2×#19128428C2semidirect
3. C2×#19128418C2semidirect
4. C2×#19128387C2semidirect
5. C2×#19128383C2semidirect
6. C2×#19128314C2semidirect
7. C2×#19128313C2semidirect
8. C2×#19128312C2semidirect
10. C2×#19128257C2semidirect
11. C2×#19128255C2semidirect
12. C2×#19128253C2semidirect
13. C2×C4⋊Q8×D83C2semidirect
14. C2×#19128177C2semidirect
16. C2×#541×C83C2semidirect
19. #19128428C22semidirect
20. #19128418C22semidirect
21. #19128387C22semidirect
22. #19128383C22semidirect
23. #19128314C22semidirect
24. #19128313C22semidirect
25. #19128312C22semidirect
27. #19128257C22semidirect
28. #19128255C22semidirect
29. #19128253C22semidirect
35. C4⋊Q8×D83C22semidirect
54. #19128177C22semidirect
79. #541×C83C22semidirect
361. C2×C83#3509semidirect
374. C2×#541D83semidirect
382. C83C2×#3509semidirect
392. #541C2×D83semidirect
728. C2#24921345direct (N × H)

Maximal subgroups

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

subgroupindex
#249213452
C2×#191284282
C2×#191284182
C2×#191283872
C2×#191283832
C2×#191283142
C2×#191283132
C2×#191283122
C2×#191282742
C2×#191282572
C2×#191282552
C2×#191282532
C2×C4⋊Q8×D832
C2×#191281772
C2×#191281692
C2×#541×C832
C2×#350983