Finite Group Databasebeta

← C2×#24921539 #36312612

Subgroups — C2×#24921539 #36312612

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#24921539C2132yesmaximal, direct product factor
2C2×#19128433C213yesmaximal, complemented
3C2×Q8×Dic166C211yesmaximal, characteristic, complemented
4C2×#19128409C213yesmaximal, complemented
5C2×#19128370C211yesmaximal, characteristic, complemented
6C2×#19128362C211yesmaximal, characteristic, complemented
7C2×#19128355C213yesmaximal, complemented
8C2×#19128351C213yesmaximal, complemented
9C2×#19128324C213yesmaximal, complemented
10C2×#19128320C213yesmaximal, complemented
11C2×#19128246C213yesmaximal, complemented
12C2×#19128231C213yesmaximal, complemented
13C2×#19128184C211yesmaximal, characteristic, complemented
14C2×#19128183C211yesmaximal, characteristic, complemented
15C22×Q8×Dic83C211yesmaximal, characteristic, complemented
16C2×#548×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050589C2216yes—
19#19128433C22148yescomplemented
20Q8×Dic166C22116yescomplemented
21#19128409C22148yescomplemented
22#19128370C22116yescomplemented
23#19128362C22116yescomplemented
24#19128355C22148yescomplemented
25#19128351C22148yescomplemented
26#19128324C22148yescomplemented
27#19128320C22148yescomplemented
28#19128246C22148yescomplemented
29C2×#14581792C2213yes—
30C2×#14581791C2213yes—
31C2×#14581791C2213yes—
32C2×#14581788C2213yes—
33#19128231C22148yescomplemented
34C2×#14581787C2213yes—
35C2×#14581785C2213yes—
36C2×#14581782C2213yes—
37C2×#14581781C2213yes—
38C2×#14581778C2216yes—
39C2×#14581778C2213yes—
40C2×#14581776C2216yes—
41C2×#14581776C2213yes—
42C2×#14581774C2216yes—
43C2×#14581773C2213yes—
44C2×#14581772C2216yes—
45C2×#14581769C2216yes—
46C2×#14581769C2211yescharacteristic
47C2×#14581768C2213yes—
48C2×#14581766C2213yes—
49C2×#14581766C2213yes—
50C2×#14581764C2213yes—
51C2×#14581763C2213yes—
52#19128184C22116yescomplemented
53#19128183C22116yescomplemented
54C2×Q8×Dic83C2213yes—
55C2×Q8×Dic83C2211yescharacteristic
56C2×Q8×Dic83C2211yescharacteristic
57C2×Q8×Dic83C2213yes—
58C2×Q8×Dic83C2211yescharacteristic
59C2×Q8×Dic83C22116yescomplemented
60C2×C4×Dic166C2213yes—
61C2×C4×D332C2213yes—
62C2×D4×Dic83C2213yes—
63C2×D4×Dic83C2213yes—
64C2×#14581754C2213yes—
65C2×C4×C22⋊D83C2213yes—
66C2×C4×C22⋊D83C2213yes—
67C2×(C22⋊D83)⋊C4C2216yes—
68C2×#14581751C2213yes—
69C2×#14581749C2213yes—
70C22×C4⋊Dic83C2213yes—
71C22×C4⋊Dic83C2213yes—
72C2×C4⋊C4×D83C2213yes—
73C22×C4×Dic83C2213yes—
74C22×#41×C83C2211yescharacteristic
75C23×Q8×C83C2211yescharacteristic
76#548×C83C22116yescomplemented
77C2×#124×C83C2213yes—
78C2×C22⋊Q8×C83C2213yes—
79C2×#121×C83C2213yes—
80C2×C4×Q8×C83C2211yescharacteristic
81C2×C4×D4×C83C2213yes—
82C2×#13050591—28no—
83C2×#13050591C2318yes—
84C2×#13050589—424no—
85C2×#13050589C23148yes—
86C22×Dic166C2311yescharacteristic
87C22×Dic166C2316yes—
88C22×D332C2313yes—
89C22×C22⋊D83C2313yes—
90C22×C22⋊D83C2313yes—
91C22×C22⋊D83C2316yes—
92C23×Dic83C2311yescharacteristic
93C23×Dic83C2313yes—
94C23×Dic83C2316yes—
95C22×C4×D83C2313yes—
96C22×C4×D83C2316yes—
97#14581792C23124yes—
98#14581791C23124yes—
99#14581791C23124yes—
100#14581788C23124yes—
101#14581787C23124yes—
102#14581785C23124yes—
103#14581782C23124yes—
104#14581781C23124yes—
105#14581778C23148yes—
106#14581778C23124yes—
107#14581776C23148yes—
108#14581776C23124yes—
109#14581774C23148yes—
110#14581773C23124yes—
111#14581772C23148yes—
112#14581769C23148yes—
113#14581769C2318yes—
114#14581768C23124yes—
115#14581766C23124yes—
116#14581766C23124yes—
117#14581764C23124yes—
118#14581763C23124yes—
119Q8×Dic83C23124yes—
120Q8×Dic83C2318yes—
121Q8×Dic83C2318yes—
122Q8×Dic83C23124yes—
123Q8×Dic83C2318yes—
124C4×Dic166C23124yes—
125C4×D332C23124yes—
126D4×Dic83C23124yes—
127D4×Dic83C23124yes—
128#14581754C23124yes—
129C4×C22⋊D83C23124yes—
130C4×C22⋊D83C23124yes—
131(C22⋊D83)⋊C4C23148yes—
132#14581751C23124yes—
133#14581749C23124yes—
134C2×C4⋊Dic83C23124yes—
135C2×C4⋊Dic83C23124yes—
136C2×C4⋊Dic83C2313yes—
137C2×C4⋊Dic83C2313yes—
138C2×C4⋊Dic83C2313yes—
139C2×C4⋊Dic83C2313yes—
140C2×C4⋊Dic83C2316yes—
141C2×C4⋊Dic83C2311yescharacteristic
142C2×C4⋊Dic83C2313yes—
143C2×Dic83⋊C4C2313yes—
144C2×Dic83⋊C4C2311yescharacteristic
145C2×Dic83⋊C4C2313yes—
146C2×Dic83⋊C4C2311yescharacteristic
147C2×Dic83⋊C4C2313yes—
148C2×Dic83⋊C4C2313yes—
149C4⋊C4×D83C23124yes—
150C2×C22⋊Dic83C2313yes—
151C2×C22⋊Dic83C2313yes—
152C2×C22⋊Dic83C2311yescharacteristic
153C2×C22⋊Dic83C2313yes—
154C2×(C2×D83)⋊C4C2313yes—
155C2×(C2×D83)⋊C4C2313yes—
156C2×(C2×D83)⋊C4C2316yes—
157C2×(C2×D83)⋊C4C2313yes—
158C2×(C2×D83)⋊C4C2313yes—
159C2×C4×Dic83C2313yes—
160C2×C4×Dic83C2313yes—
161C2×C4×Dic83C2313yes—
162C2×C4×Dic83C2313yes—
163C2×C4×Dic83C23124yes—
164C2×C4×Dic83C2313yes—
165C2×#41×C83—28no—
166C2×#41×C83C2318yes—
167C22×Q8×C83—28no—
168C22×Q8×C83C2318yes—
169C22×Q8×C83C2313yes—
170C22×Q8×C83C2311yescharacteristic
171C22×D4×C83C2313yes—
172C22×D4×C83C2313yes—
173C23×C4×C83C2313yes—
174C23×C4×C83C2313yes—
175#124×C83C23124yes—
176C22⋊Q8×C83C23124yes—
177#121×C83C23124yes—
178C4×Q8×C83C2318yes—
179C4×D4×C83C23124yes—
180C2×C4⋊C4×C83C2313yes—
181C2×C4⋊C4×C83C2313yes—
182C2×C22⋊C4×C83C2311yescharacteristic
183C2×C22⋊C4×C83C2313yes—
184C2×C22⋊C4×C83C2316yes—
185C2×C42×C83C2313yes—
186C23×D83C2413yes—
187#13050591—232no—
188#13050589—496no—
189C2×Dic166—24no—
190C2×Dic166—412no—
191C2×Dic166C2414yes—
192C2×Dic166C24124yes—
193C2×D332—212no—
194C2×D332C24112yes—
195C2×C22⋊D83—212no—
196C2×C22⋊D83—212no—
197C2×C22⋊D83—412no—
198C2×C22⋊D83C24112yes—
199C2×C22⋊D83C24112yes—
200C2×C22⋊D83C24124yes—
201C22×Dic83—212no—
202C22×Dic83—24no—
203C22×Dic83—412no—
204C22×Dic83C2414yes—
205C22×Dic83C24112yes—
206C22×Dic83C2411yescharacteristic
207C22×Dic83C2413yes—
208C22×Dic83C2413yes—
209C22×Dic83C2413yes—
210C22×Dic83C2411yescharacteristic
211C22×Dic83C2411yescharacteristic
212C22×Dic83C24124yes—
213C22×Dic83C2411yescharacteristic
214C2×C4×D83—212no—
215C2×C4×D83—412no—
216C2×C4×D83C24112yes—
217C2×C4×D83C24124yes—
218C4⋊Dic83C24112yes—
219C4⋊Dic83C24112yes—
220C4⋊Dic83C24124yes—
221C4⋊Dic83C2414yes—
222C4⋊Dic83C24112yes—
223C4⋊Dic83C24112yes—
224C4⋊Dic83C24112yes—
225Dic83⋊C4C24112yes—
226Dic83⋊C4C24112yes—
227Dic83⋊C4C24112yes—
228Dic83⋊C4C2414yes—
229Dic83⋊C4C2414yes—
230Dic83⋊C4C24112yes—
231C22⋊Dic83C24112yes—
232C22⋊Dic83C24112yes—
233C22⋊Dic83C2414yes—
234C22⋊Dic83C24112yes—
235(C2×D83)⋊C4C24112yes—
236(C2×D83)⋊C4C24112yes—
237(C2×D83)⋊C4C24124yes—
238(C2×D83)⋊C4C24112yes—
239(C2×D83)⋊C4C24112yes—
240C4×Dic83C24112yes—
241C4×Dic83C24112yes—
242C4×Dic83C24112yes—
243C4×Dic83C24112yes—
244C4×Dic83C24112yes—
245C24×C83C2413yes—
246C24×C83C2411yescharacteristic
247#41×C83—232no—
248C2×Q8×C83—232no—
249C2×Q8×C83—212no—
250C2×Q8×C83#4118yescomplemented
251C2×Q8×C83C24112yes—
252C2×Q8×C83C2414yes—
253C2×D4×C83—212no—
254C2×D4×C83—212no—
255C2×D4×C83C24112yes—
256C2×D4×C83C24112yes—
257C22×C4×C83—212no—
258C22×C4×C83—212no—
259C22×C4×C83C24112yes—
260C22×C4×C83C24112yes—
261C22×C4×C83C2413yes—
262C22×C4×C83C2411yescharacteristic
263C22×C4×C83C2413yes—
264C22×C4×C83C2411yescharacteristic
265C22×C4×C83C2413yes—
266C4⋊C4×C83C24112yes—
267C4⋊C4×C83C24112yes—
268C22⋊C4×C83C24124yes—
269C22⋊C4×C83C2414yes—
270C22⋊C4×C83C24112yes—
271C42×C83C24112yes—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—26no—
275C23×C83—26no—
276C23×C83—26no—
277C23×C83H(5,𝔽2)14yes—
278C23×C83C2516yes—
279C23×C83C2512yes—
280C23×C83C2511yescharacteristic
281C22×D83—26no—
282C22×D83—26no—
283C22×D83—26no—
284C22×D83C2516yes—
285Q8×C83—224no—
286Q8×C83C2×#41116yescomplemented
287D4×C83—224no—
288D4×C83—224no—
289C2×C4×C83—22no—
290C2×C4×C83—26no—
291C2×C4×C83—26no—
292C2×C4×C83—22no—
293C2×C4×C83—224no—
294C2×C4×C83—224no—
295C2×C4×C83C2×#41112yes—
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—224no—
308C2×Dic83—26no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—28no—
312C2×Dic83—424no—
313C2×Dic832−1+414yes—
314C2×Dic83C2512yes—
315C2×Dic83C2512yes—
316C2×Dic83C2516yes—
317C2×Dic83C2516yes—
318C2×Dic83C2516yes—
319C2×Dic83C2512yes—
320C2×Dic83C2512yes—
321D332—224no—
322C4×D83—224no—
323C4×D83—424no—
324Dic166—28no—
325Dic166—424no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—28no—
329C22×C83—26no—
330C22×C83—26no—
331C22×C83—26no—
332C22×C83—412no—
333C22×C83C22×#4112yes—
334C22×C83C2×H(5,𝔽2)14yes—
335C22×C83C2×H(5,𝔽2)12yes—
336C22×C83C2×2−1+412yes—
337C22×C83C2611yescharacteristic
338C2×D83—26no—
339C2×D83—26no—
340C2×D83—26no—
341C2×D83—412no—
342C4×C83—22no—
343C4×C83—26no—
344C4×C83—26no—
345C4×C83—22no—
346C4×C83C22×#41112yes—
347Dic83—22no—
348Dic83—26no—
349Dic83—26no—
350Dic83—26no—
351Dic83—22no—
352Dic83—22no—
353Dic83C2×2−1+414yes—
354C2×#3522—831nomaximal, Sylow
355C2×C83—24no—
356C2×C83—46no—
357C2×C83#352214yescomplemented
358C2×C83C23×#4111yescharacteristic
359C2×C83C22×H(5,𝔽2)11yescharacteristic
360C2×C83C22×2−1+411yescharacteristic
361D83—46no—
362#3522—8332no—
363C2×#559—833no—
364C2×Q82—831no—
365C2×#554—833no—
366C2×#550—831no—
367C2×#548—831no—
368C2×#548D8311yescharacteristic, complemented
369C2×#547—833no—
370C2×#547—833no—
371C2×#542—833no—
372C2×#542—833no—
373C2×#532—833no—
374C2×#529—833no—
375C2×#520—831no—
376C2×#520—831no—
377C22×C4×Q8—831no—
378C83C2×#352211yescharacteristic, complemented, Sylow
379C22×#41—831no—
380C22×#41—836no—
381C22×#41C2×D8311yescharacteristic
382C23×Q8C2×D8311yescharacteristic
383#559—8348no—
384Q82—8316no—
385#554—8348no—
386#550—8316no—
387#548—8316no—
388#548C2×D83116yescomplemented
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×#124C2×D8313yes—
406C2×#123—833no—
407C2×#123—833no—
408C2×#123—836no—
409C2×#123—836no—
410C2×C22⋊Q8—833no—
411C2×C22⋊Q8—836no—
412C2×C22⋊Q8—831no—
413C2×C22⋊Q8—836no—
414C2×C22⋊Q8C2×D8313yes—
415C2×#121—833no—
416C2×#121—833no—
417C2×#121—833no—
418C2×#121—833no—
419C2×#121C2×D8313yes—
420#520—8316no—
421#520—8316no—
422C2×C4×Q8—831no—
423C2×C4×Q8—833no—
424C2×C4×Q8—831no—
425C2×C4×Q8—833no—
426C2×C4×Q8—8316no—
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—836no—
436C2×C4×D4—833no—
437C2×C4×D4C2×D8313yes—
438C2×#117—833no—
439C2×#117—833no—
440C22×C4⋊C4—833no—
441C22×C4⋊C4—833no—
442C22×C4⋊C4—833no—
443C22×C42—833no—
444C2×#41—28no—
445C2×#41—33224no—
446C2×#41—838no—
447C2×#41—8348no—
448C2×#41—1668no—
449C2×#41C22×D8318yes—
450C22×Q8—28no—
451C22×Q8—836no—
452C22×Q8—831no—
453C22×Q8C22×D8313yes—
454C22×Q8C22×D8318yes—
455C22×Q8C22×D8311yescharacteristic
456C22×D4—836no—
457C22×D4—833no—
458C22×D4—833no—
459C22×D4—833no—
460C22×D4C22×D8313yes—
461C22×D4C22×D8313yes—
462C23×C4—836no—
463C23×C4—836no—
464C23×C4—833no—
465C23×C4—831no—
466C23×C4—833no—
467C23×C4C22×D8313yes—
468C23×C4C22×D8313yes—
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#124C22×D83124yes—
480#123—8324no—
481#123—8348no—
482#123—8324no—
483#123—8348no—
484C22⋊Q8—8324no—
485C22⋊Q8—8348no—
486C22⋊Q8—838no—
487C22⋊Q8—8348no—
488C22⋊Q8C22×D83124yes—
489#121—8324no—
490#121—8324no—
491#121—8324no—
492#121—8324no—
493#121C22×D83124yes—
494C4×Q8—838no—
495C4×Q8—8324no—
496C4×Q8—838no—
497C4×Q8—8324no—
498C4×Q8—838no—
499C4×Q8—8324no—
500C4×Q8C22×D8318yes—
501C4×D4—8324no—
502C4×D4—8324no—
503C4×D4—8324no—
504C4×D4—8324no—
505C4×D4—8324no—
506C4×D4—8348no—
507C4×D4—8324no—
508C4×D4C22×D83124yes—
509#117—8324no—
510#117—8324no—
511C2×C4⋊C4—833no—
512C2×C4⋊C4—833no—
513C2×C4⋊C4—833no—
514C2×C4⋊C4—833no—
515C2×C4⋊C4—833no—
516C2×C4⋊C4—836no—
517C2×C4⋊C4—8324no—
518C2×C4⋊C4—8324no—
519C2×C4⋊C4—831no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—833no—
523C2×C4⋊C4—833no—
524C2×C4⋊C4—833no—
525C2×C4⋊C4—833no—
526C2×C4⋊C4—8324no—
527C2×C4⋊C4C22×D8313yes—
528C2×C4⋊C4C22×D8313yes—
529C2×C22⋊C4—833no—
530C2×C22⋊C4—833no—
531C2×C22⋊C4—831no—
532C2×C22⋊C4—833no—
533C2×C22⋊C4—833no—
534C2×C22⋊C4—833no—
535C2×C22⋊C4—833no—
536C2×C22⋊C4—836no—
537C2×C22⋊C4—833no—
538C2×C22⋊C4C22×D8316yes—
539C2×C22⋊C4C22×D8311yescharacteristic
540C2×C22⋊C4C22×D8313yes—
541C2×C42—833no—
542C2×C42—833no—
543C2×C42—833no—
544C2×C42—833no—
545C2×C42—833no—
546C2×C42—8324no—
547C2×C42C22×D8313yes—
548C24—833no—
549C24C23×D8313yes—
550C24C23×D8311yescharacteristic
551#41—232no—
552#41—33296no—
553#41—16632no—
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—33212no—
557C2×Q8—8324no—
558C2×Q8—834no—
559C2×Q8—1664no—
560C2×Q8#1305058918yescomplemented
561C2×Q8C23×D83112yes—
562C2×Q8C23×D8314yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—33212no—
566C2×D4—8324no—
567C2×D4—8312no—
568C2×D4—8312no—
569C2×D4—8312no—
570C2×D4—16612no—
571C2×D4—16612no—
572C2×D4—16612no—
573C2×D4C23×D83112yes—
574C2×D4C23×D83112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—33212no—
578C22×C4—33212no—
579C22×C4—8324no—
580C22×C4—8324no—
581C22×C4—831no—
582C22×C4—834no—
583C22×C4—8312no—
584C22×C4—831no—
585C22×C4—831no—
586C22×C4—833no—
587C22×C4—833no—
588C22×C4—833no—
589C22×C4—831no—
590C22×C4—8312no—
591C22×C4—1664no—
592C22×C4—16612no—
593C22×C4—16612no—
594C22×C4C23×D83112yes—
595C22×C4C23×D83112yes—
596C22×C4C23×D8313yes—
597C22×C4C23×D8311yescharacteristic
598C22×C4C23×D8313yes—
599C22×C4C23×D8311yescharacteristic
600C22×C4C23×D8313yes—
601C4⋊C4—8312no—
602C4⋊C4—8312no—
603C4⋊C4—8312no—
604C4⋊C4—8312no—
605C4⋊C4—8312no—
606C4⋊C4—8324no—
607C4⋊C4—834no—
608C4⋊C4—834no—
609C4⋊C4—834no—
610C4⋊C4—8312no—
611C4⋊C4—8312no—
612C4⋊C4—8312no—
613C4⋊C4—8312no—
614C4⋊C4C23×D83112yes—
615C4⋊C4C23×D83112yes—
616C22⋊C4—8312no—
617C22⋊C4—8312no—
618C22⋊C4—834no—
619C22⋊C4—8312no—
620C22⋊C4—8312no—
621C22⋊C4—8312no—
622C22⋊C4—8312no—
623C22⋊C4—8324no—
624C22⋊C4—8312no—
625C22⋊C4C23×D83124yes—
626C22⋊C4C23×D8314yes—
627C22⋊C4C23×D83112yes—
628C42—8312no—
629C42—8312no—
630C42—8312no—
631C42—8312no—
632C42—8312no—
633C42C23×D83112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—836no—
640C23—1666no—
641C23—1666no—
642C23—1666no—
643C23#1458183814yes—
644C23C24×D8316yes—
645C23C24×D8312yes—
646C23C24×D8311yescharacteristic
647Q8—224no—
648Q8—33224no—
649Q8—1668no—
650Q8C2×#13050589116yescomplemented
651D4—224no—
652D4—224no—
653D4—33224no—
654D4—16624no—
655D4—16624no—
656D4—16624no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—33224no—
664C2×C4—33224no—
665C2×C4—834no—
666C2×C4—832no—
667C2×C4—832no—
668C2×C4—832no—
669C2×C4—836no—
670C2×C4—836no—
671C2×C4—836no—
672C2×C4—832no—
673C2×C4—1668no—
674C2×C4—1662no—
675C2×C4—1666no—
676C2×C4—1666no—
677C2×C4—1666no—
678C2×C4—16624no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—16624no—
682C2×C4C2×#13050589112yes—
683C2×C4C24×D8316yes—
684C2×C4C24×D8312yes—
685C2×C4C24×D8316yes—
686C2×C4C24×D8312yes—
687C2×C4C24×D8316yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—33212no—
696C22—1666no—
697C22—1666no—
698C22—1666no—
699C22C22×#1305058912yes—
700C22C2×#1458183814yes—
701C22C2×#1458183812yes—
702C222−1+4×D8312yes—
703C22C25×D8311yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—834no—
709C4—1662no—
710C4—1666no—
711C4—1666no—
712C4—1666no—
713C4—1662no—
714C4—1662no—
715C4C22×#13050589112yes—
716C2—24no—
717C2—46no—
718C2—3326no—
719C2#2492153914yesdirect product factor
720C2C23×#1305058911yescharacteristic
721C2C22×#1458183811yescharacteristic
722C2C2×2−1+4×D8311yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#548×C83C2
socleC23×C83C25
hypercenterC2×#548D83
hypocenterC83C2×#3522
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #24921539C2direct (N × H)
2. C2×#19128433C2semidirect
3. C2×Q8×Dic166C2semidirect
4. C2×#19128409C2semidirect
5. C2×#19128370C2semidirect
6. C2×#19128362C2semidirect
7. C2×#19128355C2semidirect
8. C2×#19128351C2semidirect
9. C2×#19128324C2semidirect
10. C2×#19128320C2semidirect
11. C2×#19128246C2semidirect
12. C2×#19128231C2semidirect
13. C2×#19128184C2semidirect
14. C2×#19128183C2semidirect
15. C22×Q8×Dic83C2semidirect
16. C2×#548×C83C2semidirect
19. #19128433C22semidirect
20. Q8×Dic166C22semidirect
21. #19128409C22semidirect
22. #19128370C22semidirect
23. #19128362C22semidirect
24. #19128355C22semidirect
25. #19128351C22semidirect
26. #19128324C22semidirect
27. #19128320C22semidirect
28. #19128246C22semidirect
33. #19128231C22semidirect
52. #19128184C22semidirect
53. #19128183C22semidirect
59. C2×Q8×Dic83C22semidirect
76. #548×C83C22semidirect
250. C2×Q8×C83#41semidirect
286. Q8×C83C2×#41semidirect
357. C2×C83#3522semidirect
368. C2×#548D83semidirect
378. C83C2×#3522semidirect
388. #548C2×D83semidirect
560. C2×Q8#13050589semidirect
650. Q8C2×#13050589semidirect
719. C2#24921539direct (N × H)

Maximal subgroups

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

subgroupindex
#249215392
C2×#191284332
C2×Q8×Dic1662
C2×#191284092
C2×#191283702
C2×#191283622
C2×#191283552
C2×#191283512
C2×#191283242
C2×#191283202
C2×#191282462
C2×#191282312
C2×#191281842
C2×#191281832
C22×Q8×Dic832
C2×#548×C832
C2×#352283