Finite Group Databasebeta

← C2×#24921463 #36312657

Subgroups — C2×#24921463 #36312657

Order 21248.

7854 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921463C2132yesmaximal, direct product factor
2C2×#19128427C211yesmaximal, characteristic, complemented
3C2×#19128401C213yesmaximal, complemented
4C2×#19128399C213yesmaximal, complemented
5C2×#19128373C211yesmaximal, characteristic, complemented
6C2×#19128372C213yesmaximal, complemented
7C2×#19128370C211yesmaximal, characteristic, complemented
8C2×#19128370C211yesmaximal, characteristic, complemented
9C2×#19128352C213yesmaximal, complemented
10C2×#19128306C213yesmaximal, complemented
11C2×#19128302C213yesmaximal, complemented
12C2×#19128248C213yesmaximal, complemented
13C2×#19128229C213yesmaximal, complemented
14C2×#19128183C211yesmaximal, characteristic, complemented
15C2×C4×#13050591C211yesmaximal, characteristic, complemented
16C2×#520×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050591C2211yescharacteristic
19C22×#13050590C2216yes—
20#19128427C22116yescomplemented
21#19128401C22148yescomplemented
22#19128399C22148yescomplemented
23#19128373C22116yescomplemented
24#19128372C22148yescomplemented
25#19128370C22116yescomplemented
26#19128370C22116yescomplemented
27#19128352C22148yescomplemented
28#19128306C22148yescomplemented
29#19128302C22148yescomplemented
30#19128248C22148yescomplemented
31C2×#14581791C2213yes—
32C2×#14581789C2213yes—
33C2×#14581788C2213yes—
34C2×#14581788C2213yes—
35#19128229C22148yescomplemented
36C2×#14581787C2213yes—
37C2×#14581785C2213yes—
38C2×#14581784C2213yes—
39C2×#14581783C2213yes—
40C2×#14581782C2211yescharacteristic
41C2×#14581778C2213yes—
42C2×#14581777C2216yes—
43C2×#14581777C2213yes—
44C2×#14581775C2216yes—
45C2×#14581774C2213yes—
46C2×#14581770C2213yes—
47C2×#14581767C2213yes—
48C2×#14581767C2213yes—
49C2×#14581766C2213yes—
50C2×#14581766C2213yes—
51C2×#14581766C2216yes—
52C2×#14581765C2213yes—
53C2×#14581765C2216yes—
54C2×#14581765C2216yes—
55C2×#14581763C2213yes—
56C2×#14581763C2213yes—
57#19128183C22116yescomplemented
58C4×#13050591C22116yescomplemented
59C2×Q8×Dic83C2211yescharacteristic
60C2×Q8×Dic83C2211yescharacteristic
61C2×C4×Dic166C2213yes—
62C2×C4×D332C2213yes—
63C2×C4×D332C2213yes—
64C2×C4×D332C2213yes—
65C2×#14581754C2213yes—
66C2×#14581754C2213yes—
67C2×C4×C22⋊D83C2213yes—
68C2×C4×C22⋊D83C2213yes—
69C2×C4×C22⋊D83C2216yes—
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—
82C2×#13050591—28no—
83C2×#13050591—28no—
84C2×#13050591C2318yes—
85C2×#13050591C2318yes—
86C2×#13050590—424no—
87C2×#13050590C23148yes—
88C22×Dic166C2313yes—
89C22×D332C2313yes—
90C22×D332C2313yes—
91C22×D332C2313yes—
92C22×D332C2316yes—
93C22×C22⋊D83C2313yes—
94C22×C22⋊D83C2316yes—
95C22×C22⋊D83C2313yes—
96C22×C22⋊D83C2316yes—
97C22×C4×D83C2313yes—
98C22×C4×D83C2313yes—
99C22×C4×D83C2313yes—
100C22×C4×D83C2313yes—
101C22×C4×D83C2316yes—
102#14581791C23124yes—
103#14581789C23124yes—
104#14581788C23124yes—
105#14581788C23124yes—
106#14581787C23124yes—
107#14581785C23124yes—
108#14581784C23124yes—
109#14581783C23124yes—
110#14581782C2318yes—
111#14581778C23124yes—
112#14581777C23148yes—
113#14581777C23124yes—
114#14581775C23148yes—
115#14581774C23124yes—
116#14581770C23124yes—
117#14581767C23124yes—
118#14581767C23124yes—
119#14581766C23124yes—
120#14581766C23124yes—
121#14581766C23148yes—
122#14581765C23124yes—
123#14581765C23148yes—
124#14581765C23148yes—
125#14581763C23124yes—
126#14581763C23124yes—
127Q8×Dic83C2318yes—
128Q8×Dic83C2318yes—
129C4×Dic166C23124yes—
130C4×D332C23124yes—
131C4×D332C23124yes—
132C4×D332C23124yes—
133#14581754C23124yes—
134#14581754C23124yes—
135C4×C22⋊D83C23124yes—
136C4×C22⋊D83C23124yes—
137C4×C22⋊D83C23148yes—
138#14581750C23124yes—
139#14581749C23124yes—
140C2×C4⋊Dic83C2313yes—
141C2×C4⋊Dic83C2313yes—
142C2×C4⋊Dic83C2311yescharacteristic
143C2×C4⋊Dic83C2313yes—
144C2×Dic83⋊C4C2313yes—
145C2×Dic83⋊C4C2311yescharacteristic
146C2×Dic83⋊C4C2311yescharacteristic
147C2×Dic83⋊C4C2311yescharacteristic
148C2×Dic83⋊C4C2316yes—
149C2×Dic83⋊C4C2311yescharacteristic
150C2×Dic83⋊C4C2313yes—
151C4⋊C4×D83C23124yes—
152C2×C22⋊Dic83C2313yes—
153C2×C22⋊Dic83C2313yes—
154C2×(C2×D83)⋊C4C2313yes—
155C2×(C2×D83)⋊C4C2313yes—
156C2×(C2×D83)⋊C4C2316yes—
157C2×(C2×D83)⋊C4C2313yes—
158C2×(C2×D83)⋊C4C2313yes—
159C2×(C2×D83)⋊C4C2313yes—
160C2×(C2×D83)⋊C4C2313yes—
161C2×C4×Dic83C2311yescharacteristic
162C2×C4×Dic83C2313yes—
163C2×C4×Dic83C2313yes—
164C2×C4×Dic83C2313yes—
165C42×D83C23124yes—
166C2×#41×C83—28no—
167C2×#41×C83C2318yes—
168C22×Q8×C83C2311yescharacteristic
169C22×D4×C83C2313yes—
170C23×C4×C83C2313yes—
171C23×C4×C83C2316yes—
172C4×Q8×C83C2318yes—
173C4×Q8×C83C2318yes—
174C4×D4×C83C23124yes—
175C4×D4×C83C23124yes—
176#117×C83C23124yes—
177C2×C4⋊C4×C83C23124yes—
178C2×C4⋊C4×C83C2313yes—
179C2×C4⋊C4×C83C2313yes—
180C2×C4⋊C4×C83C2313yes—
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C22⋊C4×C83C2313yes—
183C2×C22⋊C4×C83C2313yes—
184C2×C42×C83C2313yes—
185C2×C42×C83C2313yes—
186C23×D83C2413yes—
187C23×D83C2413yes—
188#13050591—232no—
189#13050591—232no—
190#13050590—496no—
191C2×Dic166—212no—
192C2×Dic166C24112yes—
193C2×D332—212no—
194C2×D332—212no—
195C2×D332—46no—
196C2×D332—412no—
197C2×D332C24112yes—
198C2×D332C24112yes—
199C2×D332C24112yes—
200C2×D332C24124yes—
201C2×C22⋊D83—212no—
202C2×C22⋊D83—412no—
203C2×C22⋊D83—46no—
204C2×C22⋊D83—412no—
205C2×C22⋊D83C24112yes—
206C2×C22⋊D83C24124yes—
207C2×C22⋊D83C24124yes—
208C2×C22⋊D83C24112yes—
209C22×Dic83C2411yescharacteristic
210C22×Dic83C2411yescharacteristic
211C22×Dic83C2413yes—
212C22×Dic83C2413yes—
213C22×Dic83C2411yescharacteristic
214C22×Dic83C2411yescharacteristic
215C2×C4×D83—212no—
216C2×C4×D83—212no—
217C2×C4×D83—212no—
218C2×C4×D83—46no—
219C2×C4×D83—412no—
220C2×C4×D83C24112yes—
221C2×C4×D83C24112yes—
222C2×C4×D83C24112yes—
223C2×C4×D83C24112yes—
224C2×C4×D83C24124yes—
225C4⋊Dic83C24112yes—
226C4⋊Dic83C24112yes—
227C4⋊Dic83C24112yes—
228C4⋊Dic83C2414yes—
229Dic83⋊C4C2414yes—
230Dic83⋊C4C24112yes—
231Dic83⋊C4C24124yes—
232Dic83⋊C4C2414yes—
233Dic83⋊C4C24112yes—
234Dic83⋊C4C2414yes—
235Dic83⋊C4C2414yes—
236C22⋊Dic83C24112yes—
237C22⋊Dic83C24112yes—
238(C2×D83)⋊C4C24112yes—
239(C2×D83)⋊C4C24112yes—
240(C2×D83)⋊C4C24124yes—
241(C2×D83)⋊C4C24112yes—
242(C2×D83)⋊C4C24112yes—
243(C2×D83)⋊C4C24112yes—
244(C2×D83)⋊C4C24112yes—
245C4×Dic83C2414yes—
246C4×Dic83C24112yes—
247C4×Dic83C24112yes—
248C4×Dic83C24112yes—
249C24×C83C2413yes—
250#41×C83—232no—
251C2×Q8×C83#4118yescomplemented
252C2×Q8×C83C2414yes—
253C2×D4×C83—212no—
254C2×D4×C83C24112yes—
255C22×C4×C83—212no—
256C22×C4×C83—412no—
257C22×C4×C83C24112yes—
258C22×C4×C83C2411yescharacteristic
259C22×C4×C83C2413yes—
260C22×C4×C83C2411yescharacteristic
261C22×C4×C83C2413yes—
262C22×C4×C83C2411yescharacteristic
263C22×C4×C83C24124yes—
264C22×C4×C83C2413yes—
265C4⋊C4×C83C24112yes—
266C4⋊C4×C83C24112yes—
267C4⋊C4×C83C2414yes—
268C4⋊C4×C83C24112yes—
269C22⋊C4×C83C24112yes—
270C22⋊C4×C83C24112yes—
271C42×C83C24112yes—
272C42×C83C24112yes—
273C23×C83—26no—
274C23×C83—26no—
275C23×C83—26no—
276C23×C83C2516yes—
277C23×C83C2511yescharacteristic
278C22×D83—26no—
279C22×D83—26no—
280C22×D83—26no—
281C22×D83—26no—
282C22×D83—26no—
283C22×D83—26no—
284C22×D83C2516yes—
285C22×D83C2516yes—
286Q8×C83C2×#41116yescomplemented
287D4×C83—224no—
288C2×C4×C83—22no—
289C2×C4×C83—26no—
290C2×C4×C83—26no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—224no—
294C2×C4×C83—424no—
295C2×C4×C83C2×#41112yes—
296C2×C4×C83C2512yes—
297C2×C4×C83C2512yes—
298C2×C4×C83C2516yes—
299C2×C4×C83C2516yes—
300C2×C4×C83C2512yes—
301C2×C4×C83C2516yes—
302C22⋊D83—224no—
303C22⋊D83—424no—
304C22⋊D83—412no—
305C22⋊D83—424no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—26no—
309C2×Dic83—26no—
310C2×Dic83—22no—
311C2×Dic83H(5,𝔽2)14yes—
312C2×Dic83C2512yes—
313C2×Dic83C2512yes—
314C2×Dic83C2516yes—
315C2×Dic83C2516yes—
316C2×Dic83C2512yes—
317C2×Dic83C2512yes—
318D332—224no—
319D332—224no—
320D332—412no—
321D332—424no—
322C4×D83—224no—
323C4×D83—224no—
324C4×D83—224no—
325C4×D83—412no—
326C4×D83—424no—
327Dic166—224no—
328C22×C83—26no—
329C22×C83—26no—
330C22×C83—26no—
331C22×C83—412no—
332C22×C83C22×#4112yes—
333C22×C83C2×H(5,𝔽2)12yes—
334C22×C83#58512yes—
335C22×C83C2611yescharacteristic
336C2×D83—26no—
337C2×D83—26no—
338C2×D83—26no—
339C2×D83—26no—
340C2×D83—26no—
341C2×D83—26no—
342C2×D83—412no—
343C2×D83—412no—
344C4×C83—22no—
345C4×C83—26no—
346C4×C83—26no—
347C4×C83—22no—
348C4×C83—22no—
349C4×C83C22×#41112yes—
350Dic83—22no—
351Dic83—22no—
352Dic83—26no—
353Dic83—26no—
354Dic83—22no—
355Dic83C2×H(5,𝔽2)14yes—
356C2×#3517—831nomaximal, Sylow
357C2×C83—46no—
358C2×C83#351714yescomplemented
359C2×C83C23×#4111yescharacteristic
360C2×C83C22×H(5,𝔽2)11yescharacteristic
361C2×C83C2×#58511yescharacteristic
362D83—46no—
363D83—46no—
364#3517—8332no—
365C2×#557—831no—
366C2×#553—833no—
367C2×#553—833no—
368C2×#550—831no—
369C2×#550—831no—
370C2×#550—831no—
371C2×#550—833no—
372C2×#547—833no—
373C2×#540—833no—
374C2×#540—833no—
375C2×#532—833no—
376C2×#529—833no—
377C2×#520—831no—
378C2×#520D8311yescharacteristic, complemented
379C2×C4×#41—831no—
380C83C2×#351711yescharacteristic, complemented, Sylow
381C22×#41—831no—
382C22×#41—831no—
383C22×#41—836no—
384C22×#41C2×D8311yescharacteristic
385#557—8316no—
386#553—8348no—
387#553—8348no—
388#550—8316no—
389#550—8316no—
390#550—8316no—
391#550—8348no—
392#547—8348no—
393#540—8348no—
394#540—8348no—
395#532—8348no—
396C2×C4⋊Q8—833no—
397C2×#127—833no—
398C2×#127—833no—
399C2×#127—833no—
400#529—8348no—
401C2×#126—833no—
402C2×#126—833no—
403C2×#125—831no—
404C2×#125—833no—
405C2×#125—833no—
406C2×#124—833no—
407C2×#123—836no—
408C2×#123—833no—
409C2×#123—836no—
410C2×#123—833no—
411C2×C22⋊Q8—833no—
412C2×#121—833no—
413C2×#121—833no—
414C2×#121—833no—
415C2×#121—836no—
416C2×#121—833no—
417C2×#121—833no—
418C2×#121—833no—
419C2×#121—833no—
420C2×#121—836no—
421C2×#121—836no—
422#520—8316no—
423#520C2×D83116yescomplemented
424C4×#41—8316no—
425C2×C4×Q8—831no—
426C2×C4×Q8—831no—
427C2×C4×Q8—833no—
428C2×C4×Q8C2×D8311yescharacteristic
429C2×C4×Q8C2×D8311yescharacteristic
430C2×C4×D4—833no—
431C2×C4×D4—833no—
432C2×C4×D4—836no—
433C2×C4×D4—833no—
434C2×C4×D4—833no—
435C2×C4×D4—833no—
436C2×C4×D4—833no—
437C2×C4×D4—833no—
438C2×C4×D4C2×D8313yes—
439C2×C4×D4C2×D8313yes—
440C2×#117—833no—
441C2×#117—833no—
442C2×#117C2×D8313yes—
443C22×C4⋊C4—833no—
444C22×C4⋊C4C2×D8313yes—
445C22×C42—833no—
446C2×#41—28no—
447C2×#41—33224no—
448C2×#41—838no—
449C2×#41—838no—
450C2×#41—8348no—
451C2×#41—1668no—
452C2×#41—1668no—
453C2×#41C22×D8318yes—
454C22×Q8—833no—
455C22×Q8C22×D8311yescharacteristic
456C22×D4—836no—
457C22×D4—833no—
458C22×D4—836no—
459C22×D4—833no—
460C22×D4—833no—
461C22×D4—836no—
462C22×D4—833no—
463C22×D4—833no—
464C22×D4C22×D8313yes—
465C23×C4—836no—
466C23×C4—833no—
467C23×C4—833no—
468C23×C4—833no—
469C23×C4—833no—
470C23×C4C22×D8313yes—
471C23×C4C22×D8316yes—
472C4⋊Q8—8324no—
473#127—8324no—
474#127—8324no—
475#127—8324no—
476#126—8324no—
477#126—8324no—
478#125—838no—
479#125—8324no—
480#125—8324no—
481#124—8324no—
482#123—8348no—
483#123—8324no—
484#123—8348no—
485#123—8324no—
486C22⋊Q8—8324no—
487#121—8324no—
488#121—8324no—
489#121—8324no—
490#121—8348no—
491#121—8324no—
492#121—8324no—
493#121—8324no—
494#121—8324no—
495#121—8348no—
496#121—8348no—
497C4×Q8—838no—
498C4×Q8—838no—
499C4×Q8—8324no—
500C4×Q8C22×D8318yes—
501C4×Q8C22×D8318yes—
502C4×D4—8324no—
503C4×D4—8324no—
504C4×D4—8348no—
505C4×D4—8324no—
506C4×D4—8324no—
507C4×D4—8324no—
508C4×D4—8324no—
509C4×D4—8324no—
510C4×D4C22×D83124yes—
511C4×D4C22×D83124yes—
512#117—8324no—
513#117—8324no—
514#117C22×D83124yes—
515C2×C4⋊C4—833no—
516C2×C4⋊C4—833no—
517C2×C4⋊C4—831no—
518C2×C4⋊C4—833no—
519C2×C4⋊C4—831no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—836no—
523C2×C4⋊C4—831no—
524C2×C4⋊C4—833no—
525C2×C4⋊C4—833no—
526C2×C4⋊C4—8324no—
527C2×C4⋊C4C22×D8313yes—
528C2×C4⋊C4C22×D8313yes—
529C2×C4⋊C4C22×D8313yes—
530C2×C4⋊C4C22×D83124yes—
531C2×C4⋊C4C22×D8311yescharacteristic
532C2×C22⋊C4—833no—
533C2×C22⋊C4—833no—
534C2×C22⋊C4—833no—
535C2×C22⋊C4—836no—
536C2×C22⋊C4—833no—
537C2×C22⋊C4—833no—
538C2×C22⋊C4—833no—
539C2×C22⋊C4—833no—
540C2×C22⋊C4—833no—
541C2×C22⋊C4C22×D8313yes—
542C2×C22⋊C4C22×D8313yes—
543C2×C42—833no—
544C2×C42—833no—
545C2×C42—833no—
546C2×C42—831no—
547C2×C42—8324no—
548C2×C42C22×D8313yes—
549C2×C42C22×D8313yes—
550C24—833no—
551C24—833no—
552C24C23×D8313yes—
553#41—232no—
554#41—33296no—
555#41—16632no—
556#41—16632no—
557C2×Q8—8312no—
558C2×Q8—16612no—
559C2×Q8#1305059018yescomplemented
560C2×Q8C23×D8314yes—
561C2×D4—212no—
562C2×D4—33212no—
563C2×D4—3326no—
564C2×D4—33212no—
565C2×D4—33212no—
566C2×D4—3326no—
567C2×D4—8324no—
568C2×D4—8312no—
569C2×D4—8324no—
570C2×D4—8312no—
571C2×D4—8312no—
572C2×D4—8324no—
573C2×D4—8312no—
574C2×D4—8312no—
575C2×D4—16612no—
576C2×D4—16612no—
577C2×D4—16612no—
578C2×D4C23×D83112yes—
579C22×C4—212no—
580C22×C4—412no—
581C22×C4—33212no—
582C22×C4—3326no—
583C22×C4—8312no—
584C22×C4—8324no—
585C22×C4—831no—
586C22×C4—831no—
587C22×C4—831no—
588C22×C4—833no—
589C22×C4—833no—
590C22×C4—831no—
591C22×C4—8312no—
592C22×C4—8312no—
593C22×C4—8312no—
594C22×C4—16612no—
595C22×C4—16612no—
596C22×C4—16612no—
597C22×C4C23×D83112yes—
598C22×C4C23×D8311yescharacteristic
599C22×C4C23×D8313yes—
600C22×C4C23×D8311yescharacteristic
601C22×C4C23×D8313yes—
602C22×C4C23×D8311yescharacteristic
603C22×C4C23×D83124yes—
604C22×C4C23×D8313yes—
605C4⋊C4—8312no—
606C4⋊C4—8312no—
607C4⋊C4—834no—
608C4⋊C4—8312no—
609C4⋊C4—834no—
610C4⋊C4—834no—
611C4⋊C4—834no—
612C4⋊C4—8324no—
613C4⋊C4—834no—
614C4⋊C4—8312no—
615C4⋊C4—8312no—
616C4⋊C4C23×D83112yes—
617C4⋊C4C23×D83112yes—
618C4⋊C4C23×D83112yes—
619C4⋊C4C23×D8314yes—
620C22⋊C4—8312no—
621C22⋊C4—8312no—
622C22⋊C4—8312no—
623C22⋊C4—8324no—
624C22⋊C4—8312no—
625C22⋊C4—8312no—
626C22⋊C4—8312no—
627C22⋊C4—8312no—
628C22⋊C4—8312no—
629C22⋊C4C23×D83112yes—
630C22⋊C4C23×D83112yes—
631C42—834no—
632C42—8312no—
633C42—8312no—
634C42—8312no—
635C42C23×D83112yes—
636C42C23×D83112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—836no—
641C23—836no—
642C23—1666no—
643C23—1666no—
644C23—1666no—
645C23—1666no—
646C23—1666no—
647C23—1666no—
648C23C24×D8316yes—
649C23C24×D8311yescharacteristic
650Q8—16624no—
651Q8C2×#13050590116yescomplemented
652D4—224no—
653D4—33224no—
654D4—33212no—
655D4—33224no—
656D4—33224no—
657D4—33212no—
658D4—16624no—
659D4—16624no—
660D4—16624no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—26no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—224no—
667C2×C4—424no—
668C2×C4—33224no—
669C2×C4—33212no—
670C2×C4—834no—
671C2×C4—832no—
672C2×C4—832no—
673C2×C4—832no—
674C2×C4—836no—
675C2×C4—836no—
676C2×C4—832no—
677C2×C4—16624no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1666no—
681C2×C4—1666no—
682C2×C4—1662no—
683C2×C4—16624no—
684C2×C4—16624no—
685C2×C4C2×#13050590112yes—
686C2×C4C24×D8312yes—
687C2×C4C24×D8316yes—
688C2×C4C24×D8312yes—
689C2×C4C24×D8316yes—
690C2×C4C24×D8312yes—
691C2×C4C24×D8316yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—33212no—
697C22—33212no—
698C22—1666no—
699C22—1666no—
700C22—1666no—
701C22—1666no—
702C22—1666no—
703C22—1666no—
704C22C22×#1305059012yes—
705C22H(5,𝔽2)×D8312yes—
706C22#1912853812yes—
707C22C25×D8311yescharacteristic
708C4—22no—
709C4—26no—
710C4—26no—
711C4—22no—
712C4—22no—
713C4—834no—
714C4—1662no—
715C4—1662no—
716C4—1666no—
717C4—1666no—
718C4—1662no—
719C4C22×#13050590112yes—
720C2—46no—
721C2—3326no—
722C2—3326no—
723C2#2492146314yesdirect product factor
724C2C23×#1305059011yescharacteristic
725C2C2×H(5,𝔽2)×D8311yescharacteristic
726C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#520×C83C2
socleC23×C83C25
hypercenterC2×#520D83
hypocenterC83C2×#3517
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #24921463C2direct (N × H)
2. C2×#19128427C2semidirect
3. C2×#19128401C2semidirect
4. C2×#19128399C2semidirect
5. C2×#19128373C2semidirect
6. C2×#19128372C2semidirect
7. C2×#19128370C2semidirect
8. C2×#19128370C2semidirect
9. C2×#19128352C2semidirect
10. C2×#19128306C2semidirect
11. C2×#19128302C2semidirect
12. C2×#19128248C2semidirect
13. C2×#19128229C2semidirect
14. C2×#19128183C2semidirect
15. C2×C4×#13050591C2semidirect
16. C2×#520×C83C2semidirect
20. #19128427C22semidirect
21. #19128401C22semidirect
22. #19128399C22semidirect
23. #19128373C22semidirect
24. #19128372C22semidirect
25. #19128370C22semidirect
26. #19128370C22semidirect
27. #19128352C22semidirect
28. #19128306C22semidirect
29. #19128302C22semidirect
30. #19128248C22semidirect
35. #19128229C22semidirect
57. #19128183C22semidirect
58. C4×#13050591C22semidirect
75. #520×C83C22semidirect
251. C2×Q8×C83#41semidirect
286. Q8×C83C2×#41semidirect
358. C2×C83#3517semidirect
378. C2×#520D83semidirect
380. C83C2×#3517semidirect
423. #520C2×D83semidirect
559. C2×Q8#13050590semidirect
651. Q8C2×#13050590semidirect
723. C2#24921463direct (N × H)

Maximal subgroups

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

subgroupindex
#249214632
C2×#191284272
C2×#191284012
C2×#191283992
C2×#191283732
C2×#191283722
C2×#191283702
C2×#191283522
C2×#191283062
C2×#191283022
C2×#191282482
C2×#191282292
C2×#191281832
C2×C4×#130505912
C2×#520×C832
C2×#351783