Finite Group Databasebeta

← C2×#24921542 #36312611

Subgroups — C2×#24921542 #36312611

Order 21248.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921542C2132yesmaximal, direct product factor
2C2×#19128434C213yesmaximal, complemented
3C2×Q8×Dic166C211yesmaximal, characteristic, complemented
4C2×#19128406C213yesmaximal, complemented
5C2×#19128370C211yesmaximal, characteristic, complemented
6C2×#19128363C211yesmaximal, characteristic, complemented
7C2×#19128358C211yesmaximal, characteristic, complemented
8C2×#19128356C213yesmaximal, complemented
9C2×#19128352C213yesmaximal, complemented
10C2×#19128322C213yesmaximal, complemented
11C2×#19128316C213yesmaximal, complemented
12C2×#19128248C213yesmaximal, complemented
13C2×#19128229C213yesmaximal, complemented
14C2×#19128183C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
16C2×#520×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050590C2216yes—
19C22×Q8×D83C2211yescharacteristic
20#19128434C22148yescomplemented
21Q8×Dic166C22116yescomplemented
22#19128406C22148yescomplemented
23#19128370C22116yescomplemented
24#19128363C22116yescomplemented
25#19128358C22116yescomplemented
26#19128356C22148yescomplemented
27#19128352C22148yescomplemented
28#19128322C22148yescomplemented
29#19128316C22148yescomplemented
30#19128248C22148yescomplemented
31C2×#14581792C2213yes—
32C2×#14581791C2213yes—
33C2×#14581791C2213yes—
34C2×#14581788C2213yes—
35#19128229C22148yescomplemented
36C2×#14581787C2213yes—
37C2×#14581785C2213yes—
38C2×#14581782C2213yes—
39C2×#14581780C2213yes—
40C2×#14581779C2213yes—
41C2×#14581778C2216yes—
42C2×#14581778C2213yes—
43C2×#14581777C2213yes—
44C2×#14581775C2216yes—
45C2×#14581774C2216yes—
46C2×#14581774C2213yes—
47C2×#14581772C2213yes—
48C2×#14581771C2216yes—
49C2×#14581771C2213yes—
50C2×#14581770C2216yes—
51C2×#14581770C2211yescharacteristic
52C2×#14581767C2213yes—
53C2×#14581766C2213yes—
54C2×#14581765C2213yes—
55C2×#14581763C2213yes—
56C2×#14581763C2213yes—
57#19128183C22116yescomplemented
58C2×Q8×Dic83C2211yescharacteristic
59C2×Q8×Dic83C2211yescharacteristic
60C2×C4×Dic166C2213yes—
61C2×C4×Dic166C2213yes—
62C2×#14581757C2213yes—
63C4×Q8×D83C22116yescomplemented
64C2×C4×D332C2213yes—
65C2×C4×D332C2213yes—
66C2×#14581754C2213yes—
67C2×C4×C22⋊D83C2213yes—
68C2×C4×C22⋊D83C2213yes—
69C2×C4×C22⋊D83C2216yes—
70C2×#14581749C2213yes—
71C2×C4⋊C4×D83C2213yes—
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×#13050591C2318yes—
84C2×#13050590—424no—
85C2×#13050590C23148yes—
86C22×Dic166C2313yes—
87C22×Dic166C2311yescharacteristic
88C22×Dic166C2316yes—
89C2×Q8×D83—28no—
90C2×Q8×D83C2318yes—
91C22×D332C2313yes—
92C22×D332C2313yes—
93C22×C22⋊D83C2313yes—
94C22×C22⋊D83C2313yes—
95C22×C22⋊D83C2316yes—
96C22×C4×D83C2311yescharacteristic
97C22×C4×D83C2313yes—
98C22×C4×D83C2313yes—
99C22×C4×D83C2313yes—
100C22×C4×D83C2316yes—
101#14581792C23124yes—
102#14581791C23124yes—
103#14581791C23124yes—
104#14581788C23124yes—
105#14581787C23124yes—
106#14581785C23124yes—
107#14581782C23124yes—
108#14581780C23124yes—
109#14581779C23124yes—
110#14581778C23148yes—
111#14581778C23124yes—
112#14581777C23124yes—
113#14581775C23148yes—
114#14581774C23148yes—
115#14581774C23124yes—
116#14581772C23124yes—
117#14581771C23124yes—
118#14581771C23148yes—
119#14581770C23148yes—
120#14581770C2318yes—
121#14581767C23124yes—
122#14581766C23124yes—
123#14581765C23124yes—
124#14581763C23124yes—
125#14581763C23124yes—
126Q8×Dic83C2318yes—
127Q8×Dic83C2318yes—
128C4×Dic166C23124yes—
129C4×Dic166C23124yes—
130#14581757C23124yes—
131C4×D332C23124yes—
132C4×D332C23124yes—
133#14581754C23124yes—
134C4×C22⋊D83C23124yes—
135C4×C22⋊D83C23124yes—
136C4×C22⋊D83C23148yes—
137#14581749C23124yes—
138C2×C4⋊Dic83C2313yes—
139C2×C4⋊Dic83C2313yes—
140C2×C4⋊Dic83C2313yes—
141C2×C4⋊Dic83C2313yes—
142C2×Dic83⋊C4C2313yes—
143C2×Dic83⋊C4C2316yes—
144C2×Dic83⋊C4C2311yescharacteristic
145C2×Dic83⋊C4C2311yescharacteristic
146C2×Dic83⋊C4C2313yes—
147C2×Dic83⋊C4C2313yes—
148C2×Dic83⋊C4C2313yes—
149C4⋊C4×D83C23124yes—
150C4⋊C4×D83C23124yes—
151C2×C22⋊Dic83C2313yes—
152C2×C22⋊Dic83C2316yes—
153C2×C22⋊Dic83C2313yes—
154C2×(C2×D83)⋊C4C2313yes—
155C2×(C2×D83)⋊C4C2313yes—
156C2×(C2×D83)⋊C4C2311yescharacteristic
157C2×(C2×D83)⋊C4C2313yes—
158C2×(C2×D83)⋊C4C2316yes—
159C2×(C2×D83)⋊C4C2311yescharacteristic
160C2×(C2×D83)⋊C4C2313yes—
161C2×C4×Dic83C2313yes—
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×D83C2411yescharacteristic
188#13050591—232no—
189#13050590—496no—
190C2×Dic166—212no—
191C2×Dic166—24no—
192C2×Dic166—412no—
193C2×Dic166C2414yes—
194C2×Dic166C24112yes—
195C2×Dic166C24124yes—
196Q8×D83—232no—
197C2×D332—212no—
198C2×D332—212no—
199C2×D332C24112yes—
200C2×D332C24112yes—
201C2×C22⋊D83—212no—
202C2×C22⋊D83—212no—
203C2×C22⋊D83—412no—
204C2×C22⋊D83C24112yes—
205C2×C22⋊D83C24112yes—
206C2×C22⋊D83C24124yes—
207C22×Dic83C2411yescharacteristic
208C22×Dic83C2413yes—
209C22×Dic83C2413yes—
210C22×Dic83C2413yes—
211C22×Dic83C2411yescharacteristic
212C22×Dic83C2411yescharacteristic
213C2×C4×D83—212no—
214C2×C4×D83—212no—
215C2×C4×D83—212no—
216C2×C4×D83—24no—
217C2×C4×D83—412no—
218C2×C4×D83C24112yes—
219C2×C4×D83C24112yes—
220C2×C4×D83C2414yes—
221C2×C4×D83C24112yes—
222C2×C4×D83C24124yes—
223C4⋊Dic83C24112yes—
224C4⋊Dic83C24112yes—
225C4⋊Dic83C24112yes—
226C4⋊Dic83C24112yes—
227Dic83⋊C4C24112yes—
228Dic83⋊C4C24112yes—
229Dic83⋊C4C24124yes—
230Dic83⋊C4C2414yes—
231Dic83⋊C4C2414yes—
232Dic83⋊C4C24112yes—
233Dic83⋊C4C24112yes—
234C22⋊Dic83C24112yes—
235C22⋊Dic83C24124yes—
236C22⋊Dic83C24112yes—
237(C2×D83)⋊C4C24112yes—
238(C2×D83)⋊C4C24112yes—
239(C2×D83)⋊C4C24124yes—
240(C2×D83)⋊C4C2414yes—
241(C2×D83)⋊C4C2414yes—
242(C2×D83)⋊C4C24112yes—
243(C2×D83)⋊C4C24112yes—
244C4×Dic83C24112yes—
245C4×Dic83C24112yes—
246C4×Dic83C24112yes—
247C4×Dic83C24112yes—
248C24×C83C2413yes—
249#41×C83—232no—
250C2×Q8×C83#4118yescomplemented
251C2×Q8×C83C2414yes—
252C2×D4×C83—212no—
253C2×D4×C83C24112yes—
254C22×C4×C83—212no—
255C22×C4×C83—412no—
256C22×C4×C83C24112yes—
257C22×C4×C83C2413yes—
258C22×C4×C83C2411yescharacteristic
259C22×C4×C83C2413yes—
260C22×C4×C83C2411yescharacteristic
261C22×C4×C83C2411yescharacteristic
262C22×C4×C83C24124yes—
263C22×C4×C83C2413yes—
264C4⋊C4×C83C24112yes—
265C4⋊C4×C83C24112yes—
266C4⋊C4×C83C2414yes—
267C4⋊C4×C83C24112yes—
268C22⋊C4×C83C24112yes—
269C22⋊C4×C83C24112yes—
270C42×C83C24112yes—
271C42×C83C24112yes—
272C23×C83—26no—
273C23×C83—26no—
274C23×C83—26no—
275C23×C83C2516yes—
276C23×C83C2511yescharacteristic
277C22×D83—22no—
278C22×D83—22no—
279C22×D83—26no—
280C22×D83—26no—
281C22×D83—26no—
282C22×D83H(5,𝔽2)14yes—
283C22×D83C2516yes—
284C22×D83C2512yes—
285Q8×C83C2×#41116yescomplemented
286D4×C83—224no—
287C2×C4×C83—22no—
288C2×C4×C83—26no—
289C2×C4×C83—26no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—224no—
293C2×C4×C83—424no—
294C2×C4×C83C2×#41112yes—
295C2×C4×C83C2512yes—
296C2×C4×C83C2512yes—
297C2×C4×C83C2516yes—
298C2×C4×C83C2516yes—
299C2×C4×C83C2512yes—
300C2×C4×C83C2516yes—
301C22⋊D83—224no—
302C22⋊D83—224no—
303C22⋊D83—424no—
304C2×Dic83—22no—
305C2×Dic83—26no—
306C2×Dic83—26no—
307C2×Dic83—26no—
308C2×Dic83—22no—
309C2×Dic832−1+414yes—
310C2×Dic83C2512yes—
311C2×Dic83C2516yes—
312C2×Dic83C2516yes—
313C2×Dic83C2516yes—
314C2×Dic83C2512yes—
315C2×Dic83C2512yes—
316D332—224no—
317D332—224no—
318C4×D83—224no—
319C4×D83—224no—
320C4×D83—224no—
321C4×D83—28no—
322C4×D83—424no—
323Dic166—224no—
324Dic166—28no—
325Dic166—424no—
326C22×C83—26no—
327C22×C83—26no—
328C22×C83—26no—
329C22×C83—412no—
330C22×C83C22×#4112yes—
331C22×C83C2×H(5,𝔽2)12yes—
332C22×C83C2×2−1+412yes—
333C22×C83C2611yescharacteristic
334C2×D83—22no—
335C2×D83—22no—
336C2×D83—28no—
337C2×D83—26no—
338C2×D83—26no—
339C2×D83—26no—
340C2×D83—412no—
341C2×D83C2×H(5,𝔽2)14yes—
342C4×C83—22no—
343C4×C83—26no—
344C4×C83—26no—
345C4×C83—22no—
346C4×C83—22no—
347C4×C83C22×#41112yes—
348Dic83—26no—
349Dic83—22no—
350Dic83—26no—
351Dic83—26no—
352Dic83—22no—
353Dic83C2×2−1+414yes—
354C2×#3522—831nomaximal, Sylow
355C2×C83—46no—
356C2×C83#352214yescomplemented
357C2×C83C23×#4111yescharacteristic
358C2×C83C22×H(5,𝔽2)11yescharacteristic
359C2×C83C22×2−1+411yescharacteristic
360D83—24no—
361D83—46no—
362#3522—8332no—
363C2×#559—833no—
364C2×Q82—831no—
365C2×#554—833no—
366C2×#550—831no—
367C2×#548—831no—
368C2×#548—831no—
369C2×#547—833no—
370C2×#547—833no—
371C2×#542—833no—
372C2×#542—833no—
373C2×#532—833no—
374C2×#529—833no—
375C2×#520—831no—
376C2×#520D8311yescharacteristic, complemented
377C22×C4×Q8—831no—
378C83C2×#352211yescharacteristic, complemented, Sylow
379C22×#41—831no—
380C22×#41—836no—
381C22×#41C2×D8311yescharacteristic
382C23×Q8—831no—
383#559—8348no—
384Q82—8316no—
385#554—8348no—
386#550—8316no—
387#548—8316no—
388#548—8316no—
389#547—8348no—
390#547—8348no—
391#542—8348no—
392#542—8348no—
393#532—8348no—
394C2×C4⋊Q8—833no—
395C2×C4⋊Q8—833no—
396C2×C4⋊Q8—833no—
397C2×#127—833no—
398#529—8348no—
399C2×#126—833no—
400C2×#126—833no—
401C2×#125—833no—
402C2×#124—833no—
403C2×#124—833no—
404C2×#124—836no—
405C2×#124—833no—
406C2×#123—836no—
407C2×#123—833no—
408C2×#123—833no—
409C2×#123—836no—
410C2×C22⋊Q8—836no—
411C2×C22⋊Q8—833no—
412C2×C22⋊Q8—831no—
413C2×C22⋊Q8—836no—
414C2×C22⋊Q8—833no—
415C2×#121—833no—
416C2×#121—833no—
417C2×#121—833no—
418C2×#121—833no—
419C2×#121—833no—
420#520—8316no—
421#520C2×D83116yescomplemented
422C2×C4×Q8—831no—
423C2×C4×Q8—831no—
424C2×C4×Q8—8316no—
425C2×C4×Q8—833no—
426C2×C4×Q8—833no—
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×D4C2×D8313yes—
437C2×C4×D4C2×D8313yes—
438C2×#117—833no—
439C2×#117C2×D8313yes—
440C22×C4⋊C4—833no—
441C22×C4⋊C4—833no—
442C22×C4⋊C4C2×D8313yes—
443C22×C42—833no—
444C2×#41—28no—
445C2×#41—33224no—
446C2×#41—838no—
447C2×#41—8348no—
448C2×#41—1668no—
449C2×#41C22×D8318yes—
450C22×Q8—838no—
451C22×Q8—836no—
452C22×Q8—831no—
453C22×Q8—833no—
454C22×Q8—1668no—
455C22×Q8C22×D8311yescharacteristic
456C22×D4—836no—
457C22×D4—833no—
458C22×D4—833no—
459C22×D4—833no—
460C22×D4—833no—
461C22×D4C22×D8313yes—
462C23×C4—836no—
463C23×C4—833no—
464C23×C4—833no—
465C23×C4—833no—
466C23×C4—831no—
467C23×C4C22×D8313yes—
468C23×C4C22×D8316yes—
469C4⋊Q8—8324no—
470C4⋊Q8—8324no—
471C4⋊Q8—8324no—
472#127—8324no—
473#126—8324no—
474#126—8324no—
475#125—8324no—
476#124—8324no—
477#124—8324no—
478#124—8348no—
479#124—8324no—
480#123—8348no—
481#123—8324no—
482#123—8324no—
483#123—8348no—
484C22⋊Q8—8348no—
485C22⋊Q8—8324no—
486C22⋊Q8—838no—
487C22⋊Q8—8348no—
488C22⋊Q8—8324no—
489#121—8324no—
490#121—8324no—
491#121—8324no—
492#121—8324no—
493#121—8324no—
494C4×Q8—838no—
495C4×Q8—838no—
496C4×Q8—8324no—
497C4×Q8—8324no—
498C4×Q8—8324no—
499C4×Q8C22×D8318yes—
500C4×Q8C22×D8318yes—
501C4×D4—8324no—
502C4×D4—8324no—
503C4×D4—8348no—
504C4×D4—8324no—
505C4×D4—8324no—
506C4×D4—8324no—
507C4×D4C22×D83124yes—
508C4×D4C22×D83124yes—
509#117—8324no—
510#117C22×D83124yes—
511C2×C4⋊C4—833no—
512C2×C4⋊C4—833no—
513C2×C4⋊C4—833no—
514C2×C4⋊C4—836no—
515C2×C4⋊C4—831no—
516C2×C4⋊C4—831no—
517C2×C4⋊C4—833no—
518C2×C4⋊C4—833no—
519C2×C4⋊C4—833no—
520C2×C4⋊C4—833no—
521C2×C4⋊C4—833no—
522C2×C4⋊C4—8324no—
523C2×C4⋊C4—8324no—
524C2×C4⋊C4C22×D8313yes—
525C2×C4⋊C4C22×D8313yes—
526C2×C4⋊C4C22×D8313yes—
527C2×C4⋊C4C22×D83124yes—
528C2×C4⋊C4C22×D8311yescharacteristic
529C2×C22⋊C4—833no—
530C2×C22⋊C4—836no—
531C2×C22⋊C4—833no—
532C2×C22⋊C4—833no—
533C2×C22⋊C4—833no—
534C2×C22⋊C4—831no—
535C2×C22⋊C4—831no—
536C2×C22⋊C4—833no—
537C2×C22⋊C4—836no—
538C2×C22⋊C4—833no—
539C2×C22⋊C4C22×D8313yes—
540C2×C22⋊C4C22×D8313yes—
541C2×C42—833no—
542C2×C42—833no—
543C2×C42—833no—
544C2×C42—833no—
545C2×C42—8324no—
546C2×C42C22×D8313yes—
547C2×C42C22×D8313yes—
548C24—831no—
549C24—833no—
550C24C23×D8313yes—
551#41—232no—
552#41—33296no—
553#41—16632no—
554C2×Q8—33212no—
555C2×Q8—8324no—
556C2×Q8—834no—
557C2×Q8—8312no—
558C2×Q8—1664no—
559C2×Q8—16632no—
560C2×Q8—16612no—
561C2×Q8#1305059018yescomplemented
562C2×Q8C23×D8314yes—
563C2×D4—212no—
564C2×D4—33212no—
565C2×D4—8324no—
566C2×D4—8312no—
567C2×D4—8312no—
568C2×D4—8312no—
569C2×D4—8312no—
570C2×D4—16612no—
571C2×D4—16612no—
572C2×D4—16612no—
573C2×D4—16612no—
574C2×D4C23×D83112yes—
575C22×C4—212no—
576C22×C4—412no—
577C22×C4—33212no—
578C22×C4—8324no—
579C22×C4—831no—
580C22×C4—831no—
581C22×C4—833no—
582C22×C4—833no—
583C22×C4—833no—
584C22×C4—831no—
585C22×C4—834no—
586C22×C4—8312no—
587C22×C4—8312no—
588C22×C4—8312no—
589C22×C4—1664no—
590C22×C4—16612no—
591C22×C4—16612no—
592C22×C4—16612no—
593C22×C4C23×D83112yes—
594C22×C4C23×D8311yescharacteristic
595C22×C4C23×D8313yes—
596C22×C4C23×D8311yescharacteristic
597C22×C4C23×D8313yes—
598C22×C4C23×D8311yescharacteristic
599C22×C4C23×D83124yes—
600C22×C4C23×D8313yes—
601C4⋊C4—8312no—
602C4⋊C4—8312no—
603C4⋊C4—8312no—
604C4⋊C4—8324no—
605C4⋊C4—834no—
606C4⋊C4—834no—
607C4⋊C4—8312no—
608C4⋊C4—8312no—
609C4⋊C4—8312no—
610C4⋊C4—8312no—
611C4⋊C4—8312no—
612C4⋊C4C23×D83112yes—
613C4⋊C4C23×D83112yes—
614C4⋊C4C23×D83112yes—
615C4⋊C4C23×D8314yes—
616C22⋊C4—8312no—
617C22⋊C4—8324no—
618C22⋊C4—8312no—
619C22⋊C4—8312no—
620C22⋊C4—8312no—
621C22⋊C4—834no—
622C22⋊C4—834no—
623C22⋊C4—8312no—
624C22⋊C4—8324no—
625C22⋊C4—8312no—
626C22⋊C4C23×D83112yes—
627C22⋊C4C23×D83112yes—
628C42—8312no—
629C42—8312no—
630C42—8312no—
631C42—8312no—
632C42C23×D83112yes—
633C42C23×D83112yes—
634C23—26no—
635C23—26no—
636C23—26no—
637C23—834no—
638C23—832no—
639C23—836no—
640C23—1666no—
641C23—1666no—
642C23—1666no—
643C23—1662no—
644C23—1662no—
645C23C24×D8316yes—
646C23C24×D8311yescharacteristic
647Q8—33224no—
648Q8—1668no—
649Q8—16624no—
650Q8C2×#13050590116yescomplemented
651D4—224no—
652D4—33224no—
653D4—16624no—
654D4—16624no—
655D4—16624no—
656D4—16624no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—224no—
663C2×C4—424no—
664C2×C4—33224no—
665C2×C4—834no—
666C2×C4—832no—
667C2×C4—832no—
668C2×C4—836no—
669C2×C4—836no—
670C2×C4—836no—
671C2×C4—832no—
672C2×C4—1668no—
673C2×C4—16624no—
674C2×C4—1662no—
675C2×C4—1666no—
676C2×C4—1666no—
677C2×C4—1666no—
678C2×C4—1662no—
679C2×C4—16624no—
680C2×C4—16624no—
681C2×C4C2×#13050590112yes—
682C2×C4C24×D8312yes—
683C2×C4C24×D8316yes—
684C2×C4C24×D8312yes—
685C2×C4C24×D8316yes—
686C2×C4C24×D8312yes—
687C2×C4C24×D8316yes—
688C22—26no—
689C22—26no—
690C22—26no—
691C22—412no—
692C22—33212no—
693C22—834no—
694C22—1666no—
695C22—1666no—
696C22—1666no—
697C22—1662no—
698C22—1662no—
699C22—1668no—
700C22C22×#1305059012yes—
701C22H(5,𝔽2)×D8312yes—
702C222−1+4×D8312yes—
703C22C25×D8311yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—22no—
709C4—834no—
710C4—1662no—
711C4—1666no—
712C4—1666no—
713C4—1666no—
714C4—1662no—
715C4C22×#13050590112yes—
716C2—46no—
717C2—3326no—
718C2—1664no—
719C2#2492154214yesdirect product factor
720C2C23×#1305059011yescharacteristic
721C2C2×H(5,𝔽2)×D8311yescharacteristic
722C2C2×2−1+4×D8311yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#520×C83C2
socleC23×C83C25
hypercenterC2×#520D83
hypocenterC83C2×#3522
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #24921542C2direct (N × H)
2. C2×#19128434C2semidirect
3. C2×Q8×Dic166C2semidirect
4. C2×#19128406C2semidirect
5. C2×#19128370C2semidirect
6. C2×#19128363C2semidirect
7. C2×#19128358C2semidirect
8. C2×#19128356C2semidirect
9. C2×#19128352C2semidirect
10. C2×#19128322C2semidirect
11. C2×#19128316C2semidirect
12. C2×#19128248C2semidirect
13. C2×#19128229C2semidirect
14. C2×#19128183C2semidirect
15. C2×C4×Q8×D83C2semidirect
16. C2×#520×C83C2semidirect
20. #19128434C22semidirect
21. Q8×Dic166C22semidirect
22. #19128406C22semidirect
23. #19128370C22semidirect
24. #19128363C22semidirect
25. #19128358C22semidirect
26. #19128356C22semidirect
27. #19128352C22semidirect
28. #19128322C22semidirect
29. #19128316C22semidirect
30. #19128248C22semidirect
35. #19128229C22semidirect
57. #19128183C22semidirect
63. C4×Q8×D83C22semidirect
75. #520×C83C22semidirect
250. C2×Q8×C83#41semidirect
285. Q8×C83C2×#41semidirect
356. C2×C83#3522semidirect
376. C2×#520D83semidirect
378. C83C2×#3522semidirect
421. #520C2×D83semidirect
561. C2×Q8#13050590semidirect
650. Q8C2×#13050590semidirect
719. C2#24921542direct (N × H)

Maximal subgroups

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

subgroupindex
#249215422
C2×#191284342
C2×Q8×Dic1662
C2×#191284062
C2×#191283702
C2×#191283632
C2×#191283582
C2×#191283562
C2×#191283522
C2×#191283222
C2×#191283162
C2×#191282482
C2×#191282292
C2×#191281832
C2×C4×Q8×D832
C2×#520×C832
C2×#352283