Finite Group Databasebeta

← C2×#24921448 #36312595

Subgroups — C2×#24921448 #36312595

Order 21248.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921448C2132yesmaximal, direct product factor
2C2×#19128427C211yesmaximal, characteristic, complemented
3C2×#19128421C213yesmaximal, complemented
4C2×#19128406C213yesmaximal, complemented
5C2×#19128401C213yesmaximal, complemented
6C2×#19128386C213yesmaximal, complemented
7C2×Q8×D332C211yesmaximal, characteristic, complemented
8C2×#19128358C211yesmaximal, characteristic, complemented
9C2×#19128358C211yesmaximal, characteristic, complemented
10C2×#19128316C213yesmaximal, complemented
11C2×#19128313C213yesmaximal, complemented
12C2×#19128233C213yesmaximal, complemented
13C2×#19128229C213yesmaximal, complemented
14C2×#19128177C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
16C2×#520×C83C211yesmaximal, characteristic, complemented
17C22×Q8×D83C2211yescharacteristic
18C22×Q8×D83C2211yescharacteristic
19#19128427C22116yescomplemented
20#19128421C22148yescomplemented
21#19128406C22148yescomplemented
22#19128401C22148yescomplemented
23#19128386C22148yescomplemented
24Q8×D332C22116yescomplemented
25#19128358C22116yescomplemented
26#19128358C22116yescomplemented
27#19128316C22148yescomplemented
28#19128313C22148yescomplemented
29C2×#14581792C2213yes—
30C2×#14581791C2213yes—
31#19128233C22148yescomplemented
32#19128229C22148yescomplemented
33C2×#14581787C2213yes—
34C2×#14581785C2216yes—
35C2×#14581785C2213yes—
36C2×#14581785C2216yes—
37C2×#14581784C2213yes—
38C2×#14581783C2213yes—
39C2×#14581782C2216yes—
40C2×#14581782C2213yes—
41C2×#14581779C2213yes—
42C2×#14581779C2213yes—
43C2×#14581778C2213yes—
44C2×#14581777C2211yescharacteristic
45C2×#14581775C2216yes—
46C2×#14581774C2213yes—
47C2×#14581772C2213yes—
48C2×#14581772C2213yes—
49C2×#14581771C2216yes—
50C2×#14581771C2213yes—
51C2×#14581771C2213yes—
52C2×#14581770C2213yes—
53C2×#14581765C2213yes—
54C2×#14581763C2213yes—
55C2×#14581763C2213yes—
56#19128177C22116yescomplemented
57C2×Q8×Dic83C2211yescharacteristic
58C2×Q8×Dic83C2211yescharacteristic
59C2×C4×Dic166C2213yes—
60C2×C4×Dic166C2213yes—
61C2×C4×Dic166C2213yes—
62C2×#14581757C2213yes—
63C2×#14581757C2213yes—
64C4×Q8×D83C22116yescomplemented
65C2×C4×D332C2213yes—
66C2×C4×C22⋊D83C2213yes—
67C2×C4×C22⋊D83C2213yes—
68C2×C4×C22⋊D83C2216yes—
69C2×#14581751C2216yes—
70C2×#14581750C2213yes—
71C2×#14581749C2213yes—
72C2×C4⋊C4×D83C2213yes—
73C2×C42×D83C2213yes—
74C22×#41×C83C2211yescharacteristic
75#520×C83C22116yescomplemented
76C2×C4×Q8×C83C2211yescharacteristic
77C2×C4×Q8×C83C2211yescharacteristic
78C2×C4×D4×C83C2213yes—
79C2×C4×D4×C83C2213yes—
80C2×#117×C83C2213yes—
81C22×C4⋊C4×C83C2213yes—
82C22×Dic166C2313yes—
83C22×Dic166C2313yes—
84C22×Dic166C2313yes—
85C2×Q8×D83—28no—
86C2×Q8×D83—28no—
87C2×Q8×D83C2318yes—
88C2×Q8×D83C2318yes—
89C22×D332C2311yescharacteristic
90C22×C22⋊D83C2313yes—
91C22×C22⋊D83C2313yes—
92C22×C4×D83C2311yescharacteristic
93C22×C4×D83C2313yes—
94C22×C4×D83C2313yes—
95C22×C4×D83C2313yes—
96#14581792C23124yes—
97#14581791C23124yes—
98#14581787C23124yes—
99#14581785C23148yes—
100#14581785C23124yes—
101#14581785C23148yes—
102#14581784C23124yes—
103#14581783C23124yes—
104#14581782C23148yes—
105#14581782C23124yes—
106#14581779C23124yes—
107#14581779C23124yes—
108#14581778C23124yes—
109#14581777C2318yes—
110#14581775C23148yes—
111#14581774C23124yes—
112#14581772C23124yes—
113#14581772C23124yes—
114#14581771C23124yes—
115#14581771C23124yes—
116#14581771C23148yes—
117#14581770C23124yes—
118#14581765C23124yes—
119#14581763C23124yes—
120#14581763C23124yes—
121Q8×Dic83C2318yes—
122Q8×Dic83C2318yes—
123C4×Dic166C23124yes—
124C4×Dic166C23124yes—
125C4×Dic166C23124yes—
126#14581757C23124yes—
127#14581757C23124yes—
128C4×D332C23124yes—
129C4×C22⋊D83C23124yes—
130C4×C22⋊D83C23124yes—
131C4×C22⋊D83C23148yes—
132#14581751C23148yes—
133#14581750C23124yes—
134#14581749C23124yes—
135C2×C4⋊Dic83C2313yes—
136C2×C4⋊Dic83C2313yes—
137C2×C4⋊Dic83C2313yes—
138C2×C4⋊Dic83C2316yes—
139C2×C4⋊Dic83C2313yes—
140C2×Dic83⋊C4C2316yes—
141C2×Dic83⋊C4C2313yes—
142C2×Dic83⋊C4C2313yes—
143C2×Dic83⋊C4C2313yes—
144C2×Dic83⋊C4C2313yes—
145C2×Dic83⋊C4C2316yes—
146C2×Dic83⋊C4C2311yescharacteristic
147C2×Dic83⋊C4C2313yes—
148C4⋊C4×D83C23124yes—
149C2×C22⋊Dic83C2313yes—
150C2×C22⋊Dic83C2316yes—
151C2×C22⋊Dic83C2316yes—
152C2×C22⋊Dic83C2313yes—
153C2×(C2×D83)⋊C4C2311yescharacteristic
154C2×(C2×D83)⋊C4C2313yes—
155C2×(C2×D83)⋊C4C2311yescharacteristic
156C2×(C2×D83)⋊C4C2311yescharacteristic
157C2×(C2×D83)⋊C4C2313yes—
158C2×(C2×D83)⋊C4C2313yes—
159C2×C4×Dic83C2313yes—
160C2×C4×Dic83C2313yes—
161C2×C4×Dic83C2313yes—
162C2×C4×Dic83C2313yes—
163C2×C4×Dic83C2316yes—
164C42×D83C23124yes—
165C2×#41×C83—28no—
166C2×#41×C83C2318yes—
167C22×Q8×C83C2311yescharacteristic
168C22×D4×C83C2313yes—
169C23×C4×C83C2313yes—
170C23×C4×C83C2316yes—
171C4×Q8×C83C2318yes—
172C4×Q8×C83C2318yes—
173C4×D4×C83C23124yes—
174C4×D4×C83C23124yes—
175#117×C83C23124yes—
176C2×C4⋊C4×C83C2313yes—
177C2×C4⋊C4×C83C2313yes—
178C2×C4⋊C4×C83C2313yes—
179C2×C4⋊C4×C83C23124yes—
180C2×C4⋊C4×C83C2311yescharacteristic
181C2×C22⋊C4×C83C2313yes—
182C2×C22⋊C4×C83C2313yes—
183C2×C42×C83C2313yes—
184C2×C42×C83C2313yes—
185C23×D83C2411yescharacteristic
186C23×D83C2411yescharacteristic
187C2×Dic166—212no—
188C2×Dic166—212no—
189C2×Dic166—46no—
190C2×Dic166C24112yes—
191C2×Dic166C24112yes—
192C2×Dic166C24112yes—
193Q8×D83—232no—
194Q8×D83—232no—
195C2×D332—24no—
196C2×D332C2414yes—
197C2×C22⋊D83—212no—
198C2×C22⋊D83—46no—
199C2×C22⋊D83C24112yes—
200C2×C22⋊D83C24112yes—
201C22×Dic83C2413yes—
202C22×Dic83C2413yes—
203C22×Dic83C2413yes—
204C22×Dic83C2411yescharacteristic
205C22×Dic83C2413yes—
206C22×Dic83C2411yescharacteristic
207C2×C4×D83—24no—
208C2×C4×D83—212no—
209C2×C4×D83—212no—
210C2×C4×D83—46no—
211C2×C4×D83C24112yes—
212C2×C4×D83C24112yes—
213C2×C4×D83C2414yes—
214C2×C4×D83C24112yes—
215C4⋊Dic83C24112yes—
216C4⋊Dic83C24112yes—
217C4⋊Dic83C24124yes—
218C4⋊Dic83C24112yes—
219C4⋊Dic83C24112yes—
220Dic83⋊C4C24112yes—
221Dic83⋊C4C24112yes—
222Dic83⋊C4C24112yes—
223Dic83⋊C4C24112yes—
224Dic83⋊C4C24124yes—
225Dic83⋊C4C24112yes—
226Dic83⋊C4C24124yes—
227Dic83⋊C4C2414yes—
228C22⋊Dic83C24124yes—
229C22⋊Dic83C24124yes—
230C22⋊Dic83C24112yes—
231C22⋊Dic83C24112yes—
232(C2×D83)⋊C4C24112yes—
233(C2×D83)⋊C4C2414yes—
234(C2×D83)⋊C4C24112yes—
235(C2×D83)⋊C4C24112yes—
236(C2×D83)⋊C4C2414yes—
237(C2×D83)⋊C4C2414yes—
238C4×Dic83C24112yes—
239C4×Dic83C24112yes—
240C4×Dic83C24112yes—
241C4×Dic83C24124yes—
242C4×Dic83C24112yes—
243C24×C83C2413yes—
244#41×C83—232no—
245C2×Q8×C83#4118yes—
246C2×Q8×C83C2414yes—
247C2×D4×C83—212no—
248C2×D4×C83C24112yes—
249C22×C4×C83—212no—
250C22×C4×C83—412no—
251C22×C4×C83C24112yes—
252C22×C4×C83C2411yescharacteristic
253C22×C4×C83C2413yes—
254C22×C4×C83C2411yescharacteristic
255C22×C4×C83C2413yes—
256C22×C4×C83C2411yescharacteristic
257C22×C4×C83C24124yes—
258C22×C4×C83C2413yes—
259C4⋊C4×C83C24112yes—
260C4⋊C4×C83C24112yes—
261C4⋊C4×C83C2414yes—
262C4⋊C4×C83C24112yes—
263C22⋊C4×C83C24112yes—
264C22⋊C4×C83C24112yes—
265C42×C83C24112yes—
266C42×C83C24112yes—
267C23×C83—26no—
268C23×C83—26no—
269C23×C83—26no—
270C23×C83C2516yes—
271C23×C83C2511yescharacteristic
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D832−1+414yes—
278C22×D83C2512yes—
279C22×D83C2512yes—
280Q8×C83C2×#41116yes—
281D4×C83—224no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—26no—
286C2×C4×C83—26no—
287C2×C4×C83—224no—
288C2×C4×C83—424no—
289C2×C4×C83C2×#41112yes—
290C2×C4×C83C2512yes—
291C2×C4×C83C2512yes—
292C2×C4×C83C2516yes—
293C2×C4×C83C2516yes—
294C2×C4×C83C2512yes—
295C2×C4×C83C2516yes—
296C22⋊D83—224no—
297C22⋊D83—412no—
298C2×Dic83—26no—
299C2×Dic83—26no—
300C2×Dic83—22no—
301C2×Dic83—26no—
302C2×Dic83—26no—
303C2×Dic83—22no—
304C2×Dic83C2512yes—
305C2×Dic83C2512yes—
306C2×Dic83C2516yes—
307C2×Dic83C2516yes—
308C2×Dic83C2516yes—
309C2×Dic83C2516yes—
310D332—28no—
311C4×D83—28no—
312C4×D83—224no—
313C4×D83—224no—
314C4×D83—412no—
315Dic166—224no—
316Dic166—224no—
317Dic166—412no—
318C22×C83—26no—
319C22×C83—26no—
320C22×C83—26no—
321C22×C83—412no—
322C22×C83C22×#4112yes—
323C22×C83C2×2−1+412yes—
324C22×C83#58512yes—
325C22×C83C2611yescharacteristic
326C2×D83—22no—
327C2×D83—22no—
328C2×D83—28no—
329C2×D83—22no—
330C2×D83—22no—
331C2×D83—22no—
332C2×D83—44no—
333C2×D83C2×2−1+414yes—
334C4×C83—22no—
335C4×C83—22no—
336C4×C83—22no—
337C4×C83—26no—
338C4×C83—26no—
339C4×C83C22×#41112yes—
340Dic83—26no—
341Dic83—26no—
342Dic83—22no—
343Dic83—26no—
344Dic83—22no—
345Dic83—26no—
346C2×#3516—831nomaximal, Sylow
347C2×C83—46no—
348C2×C83#351614yescomplemented
349C2×C83C23×#4111yescharacteristic
350C2×C83C22×2−1+411yescharacteristic
351C2×C83C2×#58511yescharacteristic
352D83—24no—
353D83—42no—
354#3516—8332no—
355C2×#557—831no—
356C2×#556—833no—
357C2×#554—833no—
358C2×#553—833no—
359C2×#552—833no—
360C2×D4×Q8—831no—
361C2×#548—831no—
362C2×#548—831no—
363C2×#542—833no—
364C2×#541—833no—
365C2×#529—833no—
366C2×#529—833no—
367C2×#520D8311yescharacteristic, complemented
368C2×#519—831no—
369C22×C4×Q8—831no—
370C83C2×#351611yescharacteristic, complemented, Sylow
371C22×#41C2×D8311yescharacteristic
372C23×Q8—831no—
373C23×Q8—831no—
374#557—8316no—
375#556—8348no—
376#554—8348no—
377#553—8348no—
378#552—8348no—
379D4×Q8—8316no—
380#548—8316no—
381#548—8316no—
382#542—8348no—
383#541—8348no—
384C2×C4⋊Q8—833no—
385C2×C4⋊Q8—833no—
386#529—8348no—
387#529—8348no—
388C2×#126—833no—
389C2×#126—836no—
390C2×#126—833no—
391C2×#126—836no—
392C2×#125—833no—
393C2×#125—833no—
394C2×#125—836no—
395C2×#125—833no—
396C2×#124—833no—
397C2×#124—833no—
398C2×#124—833no—
399C2×#123—836no—
400C2×#123—831no—
401C2×#123—833no—
402C2×C22⋊Q8—833no—
403C2×C22⋊Q8—833no—
404C2×C22⋊Q8—836no—
405C2×C22⋊Q8—833no—
406C2×C22⋊Q8—833no—
407C2×C22⋊Q8—833no—
408C2×#121—833no—
409C2×#121—833no—
410C2×#121—833no—
411#520C2×D83116yescomplemented
412#519—8316no—
413C2×C4×Q8—831no—
414C2×C4×Q8—831no—
415C2×C4×Q8—8316no—
416C2×C4×Q8—833no—
417C2×C4×Q8—833no—
418C2×C4×Q8—833no—
419C2×C4×Q8—833no—
420C2×C4×Q8—833no—
421C2×C4×Q8C2×D8311yescharacteristic
422C2×C4×Q8C2×D8311yescharacteristic
423C2×C4×D4—833no—
424C2×C4×D4—833no—
425C2×C4×D4—836no—
426C2×C4×D4—833no—
427C2×C4×D4C2×D8313yes—
428C2×C4×D4C2×D8313yes—
429C2×#117—836no—
430C2×#117—833no—
431C2×#117—833no—
432C2×#117C2×D8313yes—
433C22×C4⋊C4—833no—
434C22×C4⋊C4C2×D8313yes—
435C22×C42—833no—
436C2×#41—28no—
437C2×#41C22×D8318yes—
438C22×Q8—838no—
439C22×Q8—838no—
440C22×Q8—833no—
441C22×Q8—833no—
442C22×Q8—833no—
443C22×Q8—1668no—
444C22×Q8—1668no—
445C22×Q8C22×D8311yescharacteristic
446C22×D4—833no—
447C22×D4—833no—
448C22×D4—831no—
449C22×D4C22×D8313yes—
450C23×C4—833no—
451C23×C4—833no—
452C23×C4—833no—
453C23×C4—831no—
454C23×C4C22×D8313yes—
455C23×C4C22×D8316yes—
456C4⋊Q8—8324no—
457C4⋊Q8—8324no—
458#126—8324no—
459#126—8348no—
460#126—8324no—
461#126—8348no—
462#125—8324no—
463#125—8324no—
464#125—8348no—
465#125—8324no—
466#124—8324no—
467#124—8324no—
468#124—8324no—
469#123—8348no—
470#123—838no—
471#123—8324no—
472C22⋊Q8—8324no—
473C22⋊Q8—8324no—
474C22⋊Q8—8348no—
475C22⋊Q8—8324no—
476C22⋊Q8—8324no—
477C22⋊Q8—8324no—
478#121—8324no—
479#121—8324no—
480#121—8324no—
481C4×Q8—838no—
482C4×Q8—838no—
483C4×Q8—8324no—
484C4×Q8—8324no—
485C4×Q8—8324no—
486C4×Q8—8324no—
487C4×Q8—8324no—
488C4×Q8C22×D8318yes—
489C4×Q8C22×D8318yes—
490C4×D4—8324no—
491C4×D4—8324no—
492C4×D4—8348no—
493C4×D4—8324no—
494C4×D4C22×D83124yes—
495C4×D4C22×D83124yes—
496#117—8348no—
497#117—8324no—
498#117—8324no—
499#117C22×D83124yes—
500C2×C4⋊C4—833no—
501C2×C4⋊C4—836no—
502C2×C4⋊C4—833no—
503C2×C4⋊C4—833no—
504C2×C4⋊C4—833no—
505C2×C4⋊C4—833no—
506C2×C4⋊C4—836no—
507C2×C4⋊C4—833no—
508C2×C4⋊C4—833no—
509C2×C4⋊C4—836no—
510C2×C4⋊C4—833no—
511C2×C4⋊C4—831no—
512C2×C4⋊C4—833no—
513C2×C4⋊C4—8324no—
514C2×C4⋊C4C22×D8313yes—
515C2×C4⋊C4C22×D8313yes—
516C2×C4⋊C4C22×D8313yes—
517C2×C4⋊C4C22×D83124yes—
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C22⋊C4—833no—
520C2×C22⋊C4—836no—
521C2×C22⋊C4—836no—
522C2×C22⋊C4—833no—
523C2×C22⋊C4—833no—
524C2×C22⋊C4—831no—
525C2×C22⋊C4—831no—
526C2×C22⋊C4—833no—
527C2×C22⋊C4—831no—
528C2×C22⋊C4—833no—
529C2×C22⋊C4C22×D8313yes—
530C2×C22⋊C4C22×D8313yes—
531C2×C42—836no—
532C2×C42—833no—
533C2×C42—833no—
534C2×C42—833no—
535C2×C42—833no—
536C2×C42—8324no—
537C2×C42C22×D8313yes—
538C2×C42C22×D8313yes—
539C24—831no—
540C24—831no—
541C24C23×D8313yes—
542#41—232no—
543C2×Q8—3326no—
544C2×Q8—8312no—
545C2×Q8—8312no—
546C2×Q8—8312no—
547C2×Q8—16632no—
548C2×Q8—16632no—
549C2×Q8—16612no—
550C2×Q8—16612no—
551C2×Q8#1305059018yes—
552C2×Q8C23×D8314yes—
553C2×D4—212no—
554C2×D4—3326no—
555C2×D4—8312no—
556C2×D4—8312no—
557C2×D4—834no—
558C2×D4—1664no—
559C2×D4—16612no—
560C2×D4C23×D83112yes—
561C22×C4—212no—
562C22×C4—412no—
563C22×C4—3326no—
564C22×C4—8312no—
565C22×C4—831no—
566C22×C4—831no—
567C22×C4—833no—
568C22×C4—833no—
569C22×C4—833no—
570C22×C4—833no—
571C22×C4—834no—
572C22×C4—8312no—
573C22×C4—8312no—
574C22×C4—1664no—
575C22×C4—16612no—
576C22×C4—16612no—
577C22×C4C23×D83112yes—
578C22×C4C23×D8311yescharacteristic
579C22×C4C23×D8313yes—
580C22×C4C23×D8311yescharacteristic
581C22×C4C23×D8313yes—
582C22×C4C23×D8311yescharacteristic
583C22×C4C23×D83124yes—
584C22×C4C23×D8313yes—
585C4⋊C4—8312no—
586C4⋊C4—8324no—
587C4⋊C4—8312no—
588C4⋊C4—8312no—
589C4⋊C4—8312no—
590C4⋊C4—8312no—
591C4⋊C4—8324no—
592C4⋊C4—8312no—
593C4⋊C4—8312no—
594C4⋊C4—8324no—
595C4⋊C4—8312no—
596C4⋊C4—834no—
597C4⋊C4—8312no—
598C4⋊C4C23×D83112yes—
599C4⋊C4C23×D83112yes—
600C4⋊C4C23×D83112yes—
601C4⋊C4C23×D8314yes—
602C22⋊C4—8312no—
603C22⋊C4—8324no—
604C22⋊C4—8324no—
605C22⋊C4—8312no—
606C22⋊C4—8312no—
607C22⋊C4—834no—
608C22⋊C4—834no—
609C22⋊C4—8312no—
610C22⋊C4—834no—
611C22⋊C4—8312no—
612C22⋊C4C23×D83112yes—
613C22⋊C4C23×D83112yes—
614C42—8312no—
615C42—8312no—
616C42—8312no—
617C42—8324no—
618C42—8312no—
619C42C23×D83112yes—
620C42C23×D83112yes—
621C23—26no—
622C23—26no—
623C23—26no—
624C23—834no—
625C23—832no—
626C23—832no—
627C23—1662no—
628C23—1662no—
629C23—1662no—
630C23—1662no—
631C23—1662no—
632C23C24×D8316yes—
633C23C24×D8311yescharacteristic
634Q8—33212no—
635Q8—16624no—
636Q8—16624no—
637Q8C2×#13050590116yes—
638D4—224no—
639D4—33212no—
640D4—1668no—
641D4—16624no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—26no—
647C2×C4—224no—
648C2×C4—424no—
649C2×C4—33212no—
650C2×C4—832no—
651C2×C4—832no—
652C2×C4—836no—
653C2×C4—836no—
654C2×C4—836no—
655C2×C4—836no—
656C2×C4—1668no—
657C2×C4—1666no—
658C2×C4—1666no—
659C2×C4—1662no—
660C2×C4—1666no—
661C2×C4—1666no—
662C2×C4—1662no—
663C2×C4—16624no—
664C2×C4—16624no—
665C2×C4C2×#13050590112yes—
666C2×C4C24×D8312yes—
667C2×C4C24×D8316yes—
668C2×C4C24×D8312yes—
669C2×C4C24×D8316yes—
670C2×C4C24×D8312yes—
671C2×C4C24×D8316yes—
672C22—26no—
673C22—26no—
674C22—26no—
675C22—412no—
676C22—3324no—
677C22—834no—
678C22—1662no—
679C22—1662no—
680C22—1662no—
681C22—1668no—
682C22—1662no—
683C22—1662no—
684C22C22×#1305059012yes—
685C222−1+4×D8312yes—
686C22#1912853612yes—
687C22C25×D8311yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—1666no—
694C4—1666no—
695C4—1662no—
696C4—1666no—
697C4—1666no—
698C4—1662no—
699C4C22×#13050590112yes—
700C2—46no—
701C2—3322no—
702C2—1664no—
703C2#2492144814yesdirect product factor
704C2C23×#1305059011yescharacteristic
705C2C2×2−1+4×D8311yescharacteristic
706C2C2×#1912853611yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#520×C83C2
socleC23×C83C25
hypercenterC2×#520D83
hypocenterC83C2×#3516
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #24921448C2direct (N × H)
2. C2×#19128427C2semidirect
3. C2×#19128421C2semidirect
4. C2×#19128406C2semidirect
5. C2×#19128401C2semidirect
6. C2×#19128386C2semidirect
7. C2×Q8×D332C2semidirect
8. C2×#19128358C2semidirect
9. C2×#19128358C2semidirect
10. C2×#19128316C2semidirect
11. C2×#19128313C2semidirect
12. C2×#19128233C2semidirect
13. C2×#19128229C2semidirect
14. C2×#19128177C2semidirect
15. C2×C4×Q8×D83C2semidirect
16. C2×#520×C83C2semidirect
19. #19128427C22semidirect
20. #19128421C22semidirect
21. #19128406C22semidirect
22. #19128401C22semidirect
23. #19128386C22semidirect
24. Q8×D332C22semidirect
25. #19128358C22semidirect
26. #19128358C22semidirect
27. #19128316C22semidirect
28. #19128313C22semidirect
31. #19128233C22semidirect
32. #19128229C22semidirect
56. #19128177C22semidirect
64. C4×Q8×D83C22semidirect
75. #520×C83C22semidirect
348. C2×C83#3516semidirect
367. C2×#520D83semidirect
370. C83C2×#3516semidirect
411. #520C2×D83semidirect
703. C2#24921448direct (N × H)

Maximal subgroups

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

subgroupindex
#249214482
C2×#191284272
C2×#191284212
C2×#191284062
C2×#191284012
C2×#191283862
C2×Q8×D3322
C2×#191283582
C2×#191283162
C2×#191283132
C2×#191282332
C2×#191282292
C2×#191281772
C2×C4×Q8×D832
C2×#520×C832
C2×#351683