Finite Group Databasebeta

← C2×#24921460 #36312653

Subgroups — C2×#24921460 #36312653

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#24921460C2132yesmaximal, direct product factor
2C2×#19128427C211yesmaximal, characteristic, complemented
3C2×#19128398C213yesmaximal, complemented
4C2×#19128397C213yesmaximal, complemented
5C2×#19128371C213yesmaximal, complemented
6C2×#19128370C211yesmaximal, characteristic, complemented
7C2×#19128370C211yesmaximal, characteristic, complemented
8C2×#19128351C213yesmaximal, complemented
9C2×#19128305C213yesmaximal, complemented
10C2×#19128304C213yesmaximal, complemented
11C2×#19128246C213yesmaximal, complemented
12C2×#19128231C213yesmaximal, complemented
13C2×#19128184C211yesmaximal, characteristic, complemented
14C2×#19128183C211yesmaximal, characteristic, complemented
15C2×#41×Dic83C211yesmaximal, characteristic, complemented
16C2×#550×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050589C2216yes—
19#19128427C22116yescomplemented
20#19128398C22148yescomplemented
21#19128397C22148yescomplemented
22#19128371C22148yescomplemented
23#19128370C22116yescomplemented
24#19128370C22116yescomplemented
25#19128351C22148yescomplemented
26#19128305C22148yescomplemented
27#19128304C22148yescomplemented
28#19128246C22148yescomplemented
29C2×#14581791C2213yes—
30C2×#14581788C2213yes—
31C2×#14581788C2213yes—
32#19128231C22148yescomplemented
33C2×#14581787C2213yes—
34C2×#14581785C2213yes—
35C2×#14581784C2213yes—
36C2×#14581783C2213yes—
37C2×#14581782C2211yescharacteristic
38C2×#14581778C2213yes—
39C2×#14581776C2213yes—
40C2×#14581774C2216yes—
41C2×#14581773C2216yes—
42C2×#14581773C2213yes—
43C2×#14581769C2213yes—
44C2×#14581766C2213yes—
45C2×#14581766C2213yes—
46C2×#14581764C2213yes—
47C2×#14581764C2216yes—
48C2×#14581764C2216yes—
49C2×#14581763C2213yes—
50C2×#14581763C2213yes—
51C2×#14581763C2216yes—
52#19128184C22116yescomplemented
53#19128183C22116yescomplemented
54#41×Dic83C22116yescomplemented
55C2×Q8×Dic83C2211yescharacteristic
56C2×Q8×Dic83C2211yescharacteristic
57C2×Q8×Dic83C2211yescharacteristic
58C2×C4×Dic166C2213yes—
59C2×C4×D332C2213yes—
60C2×D4×Dic83C2213yes—
61C2×D4×Dic83C2213yes—
62C2×D4×Dic83C2213yes—
63C2×D4×Dic83C2213yes—
64C2×#14581754C2213yes—
65C2×C4×C22⋊D83C2213yes—
66C2×C4×C22⋊D83C2213yes—
67C2×(C22⋊D83)⋊C4C2216yes—
68C2×#14581751C2213yes—
69C2×#14581751C2213yes—
70C2×#14581749C2213yes—
71C22×C4⋊Dic83C2213yes—
72C2×C4⋊C4×D83C2213yes—
73C22×C4×Dic83C2213yes—
74C22×#41×C83C2211yescharacteristic
75C22×#41×C83C2211yescharacteristic
76#550×C83C22116yescomplemented
77C2×#127×C83C2213yes—
78C2×#121×C83C2213yes—
79C2×#121×C83C2213yes—
80C2×C4×Q8×C83C2211yescharacteristic
81C2×C4×D4×C83C2213yes—
82C2×#13050591—28no—
83C2×#13050591C2318yes—
84C2×#13050589—424no—
85C2×#13050589C23148yes—
86C22×Dic166C2313yes—
87C22×D332C2313yes—
88C22×C22⋊D83C2313yes—
89C22×C22⋊D83C2316yes—
90C22×C22⋊D83C2313yes—
91C22×C22⋊D83C2316yes—
92C23×Dic83C2313yes—
93C23×Dic83C2313yes—
94C23×Dic83C2316yes—
95C22×C4×D83C2313yes—
96C22×C4×D83C2316yes—
97#14581791C23124yes—
98#14581788C23124yes—
99#14581788C23124yes—
100#14581787C23124yes—
101#14581785C23124yes—
102#14581784C23124yes—
103#14581783C23124yes—
104#14581782C2318yes—
105#14581778C23124yes—
106#14581776C23124yes—
107#14581774C23148yes—
108#14581773C23148yes—
109#14581773C23124yes—
110#14581769C23124yes—
111#14581766C23124yes—
112#14581766C23124yes—
113#14581764C23124yes—
114#14581764C23148yes—
115#14581764C23148yes—
116#14581763C23124yes—
117#14581763C23124yes—
118#14581763C23148yes—
119Q8×Dic83C2318yes—
120Q8×Dic83C2318yes—
121Q8×Dic83C2318yes—
122C4×Dic166C23124yes—
123C4×D332C23124yes—
124D4×Dic83C23124yes—
125D4×Dic83C23124yes—
126D4×Dic83C23124yes—
127D4×Dic83C23124yes—
128#14581754C23124yes—
129C4×C22⋊D83C23124yes—
130C4×C22⋊D83C23124yes—
131(C22⋊D83)⋊C4C23148yes—
132#14581751C23124yes—
133#14581751C23124yes—
134#14581749C23124yes—
135C2×C4⋊Dic83C23124yes—
136C2×C4⋊Dic83C2313yes—
137C2×C4⋊Dic83C2313yes—
138C2×C4⋊Dic83C2313yes—
139C2×C4⋊Dic83C2311yescharacteristic
140C2×C4⋊Dic83C2313yes—
141C2×C4⋊Dic83C2313yes—
142C2×Dic83⋊C4C2313yes—
143C2×Dic83⋊C4C2311yescharacteristic
144C2×Dic83⋊C4C2316yes—
145C2×Dic83⋊C4C2311yescharacteristic
146C2×Dic83⋊C4C2311yescharacteristic
147C2×Dic83⋊C4C2311yescharacteristic
148C2×Dic83⋊C4C2313yes—
149C4⋊C4×D83C23124yes—
150C2×C22⋊Dic83C2313yes—
151C2×C22⋊Dic83C2316yes—
152C2×C22⋊Dic83C2313yes—
153C2×C22⋊Dic83C2313yes—
154C2×C22⋊Dic83C2313yes—
155C2×(C2×D83)⋊C4C2313yes—
156C2×(C2×D83)⋊C4C2313yes—
157C2×(C2×D83)⋊C4C2313yes—
158C2×(C2×D83)⋊C4C2313yes—
159C2×C4×Dic83C2311yescharacteristic
160C2×C4×Dic83C2313yes—
161C2×C4×Dic83C2313yes—
162C2×C4×Dic83C2313yes—
163C2×C4×Dic83C23124yes—
164C2×C4×Dic83C2313yes—
165C2×#41×C83—28no—
166C2×#41×C83—28no—
167C2×#41×C83C2318yes—
168C2×#41×C83C2318yes—
169C22×Q8×C83C2311yescharacteristic
170C22×D4×C83C2313yes—
171C22×D4×C83C2313yes—
172C22×D4×C83C2313yes—
173C22×D4×C83C2316yes—
174C23×C4×C83C2313yes—
175C23×C4×C83C2313yes—
176#127×C83C23124yes—
177#121×C83C23124yes—
178#121×C83C23124yes—
179C4×Q8×C83C2318yes—
180C4×D4×C83C23124yes—
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C4⋊C4×C83C2313yes—
183C2×C22⋊C4×C83C2313yes—
184C2×C22⋊C4×C83C2313yes—
185C2×C42×C83C2313yes—
186C23×D83C2413yes—
187#13050591—232no—
188#13050589—496no—
189C2×Dic166—212no—
190C2×Dic166C24112yes—
191C2×D332—212no—
192C2×D332C24112yes—
193C2×C22⋊D83—212no—
194C2×C22⋊D83—412no—
195C2×C22⋊D83—46no—
196C2×C22⋊D83—412no—
197C2×C22⋊D83C24112yes—
198C2×C22⋊D83C24124yes—
199C2×C22⋊D83C24112yes—
200C2×C22⋊D83C24124yes—
201C22×Dic83—212no—
202C22×Dic83—46no—
203C22×Dic83—412no—
204C22×Dic83C24112yes—
205C22×Dic83C2411yescharacteristic
206C22×Dic83C2413yes—
207C22×Dic83C2411yescharacteristic
208C22×Dic83C2413yes—
209C22×Dic83C2413yes—
210C22×Dic83C2411yescharacteristic
211C22×Dic83C24112yes—
212C22×Dic83C24124yes—
213C22×Dic83C2411yescharacteristic
214C2×C4×D83—212no—
215C2×C4×D83—412no—
216C2×C4×D83C24112yes—
217C2×C4×D83C24124yes—
218C4⋊Dic83C24112yes—
219C4⋊Dic83C24112yes—
220C4⋊Dic83C24112yes—
221C4⋊Dic83C24112yes—
222C4⋊Dic83C2414yes—
223C4⋊Dic83C24112yes—
224Dic83⋊C4C2414yes—
225Dic83⋊C4C24112yes—
226Dic83⋊C4C24124yes—
227Dic83⋊C4C2414yes—
228Dic83⋊C4C24112yes—
229Dic83⋊C4C2414yes—
230Dic83⋊C4C2414yes—
231C22⋊Dic83C24112yes—
232C22⋊Dic83C24112yes—
233C22⋊Dic83C24112yes—
234C22⋊Dic83C24124yes—
235C22⋊Dic83C24112yes—
236(C2×D83)⋊C4C24112yes—
237(C2×D83)⋊C4C24112yes—
238(C2×D83)⋊C4C24112yes—
239(C2×D83)⋊C4C24112yes—
240C4×Dic83C2414yes—
241C4×Dic83C24112yes—
242C4×Dic83C24112yes—
243C4×Dic83C24112yes—
244C4×Dic83C24112yes—
245C24×C83C2413yes—
246C24×C83C2413yes—
247#41×C83—232no—
248#41×C83—232no—
249C2×Q8×C83#4118yescomplemented
250C2×Q8×C83C2414yes—
251C2×D4×C83—212no—
252C2×D4×C83—212no—
253C2×D4×C83—412no—
254C2×D4×C83—46no—
255C2×D4×C83C24112yes—
256C2×D4×C83C24112yes—
257C2×D4×C83C24124yes—
258C2×D4×C83C24112yes—
259C22×C4×C83—212no—
260C22×C4×C83—212no—
261C22×C4×C83C24112yes—
262C22×C4×C83C24112yes—
263C22×C4×C83C2413yes—
264C22×C4×C83C2411yescharacteristic
265C22×C4×C83C2411yescharacteristic
266C22×C4×C83C2411yescharacteristic
267C22×C4×C83C2413yes—
268C4⋊C4×C83C2414yes—
269C4⋊C4×C83C24112yes—
270C22⋊C4×C83C24112yes—
271C22⋊C4×C83C24112yes—
272C42×C83C24112yes—
273C23×C83—26no—
274C23×C83—26no—
275C23×C83—26no—
276C23×C83—26no—
277C23×C83—26no—
278C23×C83—26no—
279C23×C83C2516yes—
280C23×C83C2516yes—
281C23×C83C2511yescharacteristic
282C22×D83—26no—
283C22×D83—26no—
284C22×D83—26no—
285C22×D83C2516yes—
286Q8×C83C2×#41116yescomplemented
287D4×C83—224no—
288D4×C83—224no—
289D4×C83—412no—
290D4×C83—424no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—26no—
294C2×C4×C83—22no—
295C2×C4×C83—224no—
296C2×C4×C83—224no—
297C2×C4×C83C2×#41112yes—
298C2×C4×C83C2512yes—
299C2×C4×C83C2516yes—
300C2×C4×C83C2512yes—
301C2×C4×C83C2512yes—
302C2×C4×C83C2516yes—
303C22⋊D83—224no—
304C22⋊D83—424no—
305C22⋊D83—412no—
306C22⋊D83—424no—
307C2×Dic83—22no—
308C2×Dic83—26no—
309C2×Dic83—26no—
310C2×Dic83—22no—
311C2×Dic83—26no—
312C2×Dic83—22no—
313C2×Dic83—224no—
314C2×Dic83—412no—
315C2×Dic83—424no—
316C2×Dic83H(5,𝔽2)14yes—
317C2×Dic83C2512yes—
318C2×Dic83C2512yes—
319C2×Dic83C2516yes—
320C2×Dic83C2516yes—
321C2×Dic83C2516yes—
322C2×Dic83C2512yes—
323C2×Dic83C2512yes—
324D332—224no—
325C4×D83—224no—
326C4×D83—424no—
327Dic166—224no—
328C22×C83—26no—
329C22×C83—26no—
330C22×C83—26no—
331C22×C83—26no—
332C22×C83—26no—
333C22×C83—26no—
334C22×C83—412no—
335C22×C83—412no—
336C22×C83C22×#4112yes—
337C22×C83C2×H(5,𝔽2)12yes—
338C22×C83#58512yes—
339C22×C83C2611yescharacteristic
340C2×D83—26no—
341C2×D83—26no—
342C2×D83—26no—
343C2×D83—412no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83—26no—
347C4×C83—22no—
348C4×C83C22×#41112yes—
349Dic83—22no—
350Dic83—26no—
351Dic83—26no—
352Dic83—22no—
353Dic83—26no—
354Dic83—22no—
355Dic83C2×H(5,𝔽2)14yes—
356C2×#3517—831nomaximal, Sylow
357C2×C83—46no—
358C2×C83—46no—
359C2×C83#351714yescomplemented
360C2×C83C23×#4111yescharacteristic
361C2×C83C22×H(5,𝔽2)11yescharacteristic
362C2×C83C2×#58511yescharacteristic
363D83—46no—
364#3517—8332no—
365C2×#557—831no—
366C2×#553—833no—
367C2×#553—833no—
368C2×#550—831no—
369C2×#550—831no—
370C2×#550—833no—
371C2×#550D8311yescharacteristic, complemented
372C2×#547—833no—
373C2×#540—833no—
374C2×#540—833no—
375C2×#532—833no—
376C2×#529—833no—
377C2×#520—831no—
378C2×#520—831no—
379C2×C4×#41—831no—
380C83C2×#351711yescharacteristic, complemented, Sylow
381C22×#41—831no—
382C22×#41—836no—
383C22×#41C2×D8311yescharacteristic
384C22×#41C2×D8311yescharacteristic
385#557—8316no—
386#553—8348no—
387#553—8348no—
388#550—8316no—
389#550—8316no—
390#550—8348no—
391#550C2×D83116yescomplemented
392#547—8348no—
393#540—8348no—
394#540—8348no—
395#532—8348no—
396C2×C4⋊Q8—833no—
397C2×#127—833no—
398C2×#127—833no—
399C2×#127C2×D8313yes—
400#529—8348no—
401C2×#126—833no—
402C2×#126—833no—
403C2×#125—831no—
404C2×#125—833no—
405C2×#125—833no—
406C2×#124—833no—
407C2×#123—833no—
408C2×#123—836no—
409C2×#123—833no—
410C2×#123—836no—
411C2×C22⋊Q8—833no—
412C2×#121—833no—
413C2×#121—836no—
414C2×#121—833no—
415C2×#121—836no—
416C2×#121—833no—
417C2×#121—836no—
418C2×#121—833no—
419C2×#121—833no—
420C2×#121C2×D8313yes—
421C2×#121C2×D8313yes—
422#520—8316no—
423#520—8316no—
424C4×#41—8316no—
425C2×C4×Q8—831no—
426C2×C4×Q8—831no—
427C2×C4×Q8—831no—
428C2×C4×Q8—833no—
429C2×C4×Q8C2×D8311yescharacteristic
430C2×C4×D4—833no—
431C2×C4×D4—833no—
432C2×C4×D4—833no—
433C2×C4×D4—833no—
434C2×C4×D4—833no—
435C2×C4×D4—833no—
436C2×C4×D4—833no—
437C2×C4×D4—836no—
438C2×C4×D4—833no—
439C2×C4×D4C2×D8313yes—
440C2×#117—833no—
441C2×#117—833no—
442C2×#117—833no—
443C22×C4⋊C4—833no—
444C22×C4⋊C4—833no—
445C22×C42—833no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—33224no—
449C2×#41—838no—
450C2×#41—8348no—
451C2×#41—1668no—
452C2×#41C22×D8318yes—
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×D4C22×D8313yes—
462C22×D4C22×D8313yes—
463C22×D4C22×D8313yes—
464C22×D4C22×D8316yes—
465C23×C4—836no—
466C23×C4—833no—
467C23×C4—836no—
468C23×C4—833no—
469C23×C4—833no—
470C23×C4C22×D8313yes—
471C23×C4C22×D8313yes—
472C4⋊Q8—8324no—
473#127—8324no—
474#127—8324no—
475#127C22×D83124yes—
476#126—8324no—
477#126—8324no—
478#125—838no—
479#125—8324no—
480#125—8324no—
481#124—8324no—
482#123—8324no—
483#123—8348no—
484#123—8348no—
485#123—8324no—
486C22⋊Q8—8324no—
487#121—8324no—
488#121—8348no—
489#121—8324no—
490#121—8324no—
491#121—8348no—
492#121—8348no—
493#121—8324no—
494#121—8324no—
495#121C22×D83124yes—
496#121C22×D83124yes—
497C4×Q8—838no—
498C4×Q8—838no—
499C4×Q8—838no—
500C4×Q8—8324no—
501C4×Q8C22×D8318yes—
502C4×D4—8324no—
503C4×D4—8324no—
504C4×D4—8324no—
505C4×D4—8324no—
506C4×D4—8324no—
507C4×D4—8324no—
508C4×D4—8324no—
509C4×D4—8348no—
510C4×D4—8324no—
511C4×D4C22×D83124yes—
512#117—8324no—
513#117—8324no—
514#117—8324no—
515C2×C4⋊C4—833no—
516C2×C4⋊C4—833no—
517C2×C4⋊C4—833no—
518C2×C4⋊C4—833no—
519C2×C4⋊C4—8324no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—833no—
523C2×C4⋊C4—831no—
524C2×C4⋊C4—831no—
525C2×C4⋊C4—836no—
526C2×C4⋊C4—831no—
527C2×C4⋊C4—833no—
528C2×C4⋊C4—833no—
529C2×C4⋊C4—8324no—
530C2×C4⋊C4C22×D8313yes—
531C2×C4⋊C4C22×D8311yescharacteristic
532C2×C22⋊C4—833no—
533C2×C22⋊C4—836no—
534C2×C22⋊C4—833no—
535C2×C22⋊C4—833no—
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—833no—
547C2×C42—8324no—
548C2×C42—831no—
549C2×C42C22×D8313yes—
550C24—833no—
551C24C23×D8313yes—
552C24C23×D8313yes—
553#41—232no—
554#41—232no—
555#41—33296no—
556#41—16632no—
557C2×Q8—8312no—
558C2×Q8—16612no—
559C2×Q8#1305058918yescomplemented
560C2×Q8C23×D8314yes—
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—412no—
564C2×D4—46no—
565C2×D4—33212no—
566C2×D4—33212no—
567C2×D4—3326no—
568C2×D4—8324no—
569C2×D4—8312no—
570C2×D4—8324no—
571C2×D4—8312no—
572C2×D4—8312no—
573C2×D4—16612no—
574C2×D4—16612no—
575C2×D4C23×D83112yes—
576C2×D4C23×D83112yes—
577C2×D4C23×D83112yes—
578C2×D4C23×D83124yes—
579C22×C4—212no—
580C22×C4—212no—
581C22×C4—33212no—
582C22×C4—33212no—
583C22×C4—3326no—
584C22×C4—8312no—
585C22×C4—8324no—
586C22×C4—8324no—
587C22×C4—831no—
588C22×C4—8312no—
589C22×C4—831no—
590C22×C4—831no—
591C22×C4—833no—
592C22×C4—833no—
593C22×C4—833no—
594C22×C4—831no—
595C22×C4—8312no—
596C22×C4—16612no—
597C22×C4—16612no—
598C22×C4C23×D83112yes—
599C22×C4C23×D83112yes—
600C22×C4C23×D8311yescharacteristic
601C22×C4C23×D8311yescharacteristic
602C22×C4C23×D8313yes—
603C22×C4C23×D8311yescharacteristic
604C22×C4C23×D8313yes—
605C4⋊C4—8312no—
606C4⋊C4—8312no—
607C4⋊C4—8312no—
608C4⋊C4—8312no—
609C4⋊C4—834no—
610C4⋊C4—834no—
611C4⋊C4—8312no—
612C4⋊C4—834no—
613C4⋊C4—834no—
614C4⋊C4—8324no—
615C4⋊C4—834no—
616C4⋊C4—8312no—
617C4⋊C4—8312no—
618C4⋊C4C23×D83112yes—
619C4⋊C4C23×D8314yes—
620C22⋊C4—8312no—
621C22⋊C4—8324no—
622C22⋊C4—8312no—
623C22⋊C4—8312no—
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—
635C42—8312no—
636C42C23×D83112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—26no—
643C23—836no—
644C23—1666no—
645C23—1666no—
646C23—1666no—
647C23C24×D8316yes—
648C23C24×D8316yes—
649C23C24×D8311yescharacteristic
650Q8—16624no—
651Q8C2×#13050589116yescomplemented
652D4—224no—
653D4—224no—
654D4—424no—
655D4—412no—
656D4—33224no—
657D4—33224no—
658D4—33212no—
659D4—16624no—
660D4—16624no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—26no—
664C2×C4—22no—
665C2×C4—224no—
666C2×C4—224no—
667C2×C4—33224no—
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—836no—
677C2×C4—832no—
678C2×C4—16624no—
679C2×C4—1662no—
680C2×C4—1666no—
681C2×C4—1666no—
682C2×C4—1662no—
683C2×C4—1666no—
684C2×C4—1662no—
685C2×C4—16624no—
686C2×C4C2×#13050589112yes—
687C2×C4C24×D8312yes—
688C2×C4C24×D8312yes—
689C2×C4C24×D8316yes—
690C2×C4C24×D8312yes—
691C2×C4C24×D8316yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—412no—
700C22—33212no—
701C22—1666no—
702C22—1666no—
703C22—1666no—
704C22C22×#1305058912yes—
705C22H(5,𝔽2)×D8312yes—
706C22#1912853712yes—
707C22C25×D8311yescharacteristic
708C4—22no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—834no—
713C4—1662no—
714C4—1666no—
715C4—1666no—
716C4—1662no—
717C4—1666no—
718C4—1662no—
719C4C22×#13050589112yes—
720C2—46no—
721C2—46no—
722C2—3326no—
723C2#2492146014yesdirect product factor
724C2C23×#1305058911yescharacteristic
725C2C2×H(5,𝔽2)×D8311yescharacteristic
726C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#550×C83C2
socleC23×C83C25
hypercenterC2×#550D83
hypocenterC83C2×#3517
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #24921460C2direct (N × H)
2. C2×#19128427C2semidirect
3. C2×#19128398C2semidirect
4. C2×#19128397C2semidirect
5. C2×#19128371C2semidirect
6. C2×#19128370C2semidirect
7. C2×#19128370C2semidirect
8. C2×#19128351C2semidirect
9. C2×#19128305C2semidirect
10. C2×#19128304C2semidirect
11. C2×#19128246C2semidirect
12. C2×#19128231C2semidirect
13. C2×#19128184C2semidirect
14. C2×#19128183C2semidirect
15. C2×#41×Dic83C2semidirect
16. C2×#550×C83C2semidirect
19. #19128427C22semidirect
20. #19128398C22semidirect
21. #19128397C22semidirect
22. #19128371C22semidirect
23. #19128370C22semidirect
24. #19128370C22semidirect
25. #19128351C22semidirect
26. #19128305C22semidirect
27. #19128304C22semidirect
28. #19128246C22semidirect
32. #19128231C22semidirect
52. #19128184C22semidirect
53. #19128183C22semidirect
54. #41×Dic83C22semidirect
76. #550×C83C22semidirect
249. C2×Q8×C83#41semidirect
286. Q8×C83C2×#41semidirect
359. C2×C83#3517semidirect
371. C2×#550D83semidirect
380. C83C2×#3517semidirect
391. #550C2×D83semidirect
559. C2×Q8#13050589semidirect
651. Q8C2×#13050589semidirect
723. C2#24921460direct (N × H)

Maximal subgroups

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

subgroupindex
#249214602
C2×#191284272
C2×#191283982
C2×#191283972
C2×#191283712
C2×#191283702
C2×#191283512
C2×#191283052
C2×#191283042
C2×#191282462
C2×#191282312
C2×#191281842
C2×#191281832
C2×#41×Dic832
C2×#550×C832
C2×#351783