Finite Group Databasebeta

← C2×#24920225 #36284179

Subgroups — C2×#24920225 #36284179

Order 21248.

1874 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
1C2×#19128429C211yesmaximal, characteristic, complemented
2#24920225C2116yesmaximal, direct product factor
3C2×#19128065C211yesmaximal, characteristic
4C2×#19128060C211yesmaximal, characteristic, complemented
5C2×#19128055C211yesmaximal, characteristic, complemented
6C2×#19128008C211yesmaximal, characteristic, complemented
7C2×#19128001C211yesmaximal, characteristic, complemented
8C2×#19127991C211yesmaximal, characteristic, complemented
9C2×#19127920C211yesmaximal, characteristic, complemented
10C2×#19127920C211yesmaximal, characteristic, complemented
11C2×#19127898C211yesmaximal, characteristic
12C2×#19127832C211yesmaximal, characteristic, complemented
13C2×#19127806C211yesmaximal, characteristic, complemented
14C2×#19127801C211yesmaximal, characteristic, complemented
15C2×C4×#13050578C211yesmaximal, characteristic, complemented
16C2×#559×C83C211yesmaximal, characteristic
17C22×#13050580C2211yescharacteristic
18C22×#13050578C2211yescharacteristic
19C22×#13050578C2211yescharacteristic
20#19128429—24no—
21#19128429C2218yescomplemented
22C2×#14581792C2211yescharacteristic
23C2×#14581790—21no—
24C2×#14581784C2211yescharacteristic
25C2×#14581784C2211yescharacteristic
26C2×#14581782—21no—
27C2×#14581782—21no—
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×Dic166C2211yescharacteristic
30C2×C4×Dic166C2211yescharacteristic
31C2×#14581757—21no—
32#19128065C2218yes—
33#19128060C2218yescomplemented
34#19128055C2218yescomplemented
35#19128008C2218yescomplemented
36#19128001C2218yescomplemented
37#19127991C2218yescomplemented
38#19127920C2218yescomplemented
39#19127920C2218yescomplemented
40#19127898C2218yes—
41#19127832C2218yescomplemented
42#19127806C2218yescomplemented
43#19127801C2218yescomplemented
44C4×#13050578C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49C2×C4⋊(C83⋊C8)C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581716C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581713C2211yescharacteristic
60C2×#14581713C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#559×C83—24no—
65#559×C83C2218yes—
66C2×#127×C83C2211yescharacteristic
67C2×#124×C83—21no—
68C2×#124×C83C2211yescharacteristic
69C2×#124×C83C2211yescharacteristic
70C2×#123×C83—21no—
71C2×#123×C83—21no—
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×D4×C83—21no—
75C2×C4×D4×C83C2211yescharacteristic
76C2×C4×D4×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C2×#13050580—24no—
80C2×#13050580C2314yes—
81C2×#13050578—24no—
82C2×#13050578—24no—
83C2×#13050578C2314yes—
84C2×#13050578C2314yes—
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89#14581792—22no—
90#14581792C2314yes—
91#14581790—28no—
92#14581784—22no—
93#14581784—22no—
94#14581784C2314yes—
95#14581784C2314yes—
96#14581782—28no—
97#14581782—28no—
98C4×Dic166—22no—
99C4×Dic166—22no—
100C4×Dic166—22no—
101C4×Dic166C2314yes—
102C4×Dic166C2314yes—
103C4×Dic166C2314yes—
104#14581757—28no—
105C2×C4⋊Dic83—21no—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2311yescharacteristic
109C2×Dic83⋊C4—21no—
110C2×Dic83⋊C4—21no—
111C2×Dic83⋊C4—21no—
112C2×Dic83⋊C4—21no—
113C2×Dic83⋊C4—21no—
114C2×Dic83⋊C4—21no—
115C2×Dic83⋊C4—21no—
116C2×C4×Dic83—21no—
117C2×C4×Dic83—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581723C2314yes—
121#14581723C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123C4⋊(C83⋊C8)C2314yes—
124C4⋊(C83⋊C8)C2314yes—
125#14581716C2314yes—
126#14581716C2314yes—
127#14581716C2314yes—
128#14581715C2314yes—
129#14581713C2314yes—
130#14581713C2314yes—
131#14581713C2314yes—
132#14581713C2314yes—
133#14581713C2314yes—
134#14581713C2314yes—
135#14581703C2314yes—
136#14581703C2314yes—
137C4×C83⋊C8C2314yes—
138C22×Q8×C83D411yescharacteristic
139C22×Q8×C83C2311yescharacteristic
140C22×D4×C83—21no—
141C22×D4×C83—21no—
142C22×D4×C83C2311yescharacteristic
143C22×D4×C83C2311yescharacteristic
144C23×C4×C83—21no—
145C23×C4×C83—21no—
146#127×C83—22no—
147#127×C83C2314yes—
148#124×C83—28no—
149#124×C83—22no—
150#124×C83—22no—
151#124×C83C2314yes—
152#124×C83C2314yes—
153#123×C83—28no—
154#123×C83—28no—
155C4×Q8×C83—22no—
156C4×Q8×C83D414yes—
157C4×Q8×C83C2314yes—
158C4×Q8×C83C2314yes—
159C4×D4×C83—28no—
160C4×D4×C83—22no—
161C4×D4×C83—22no—
162C4×D4×C83C2314yes—
163C4×D4×C83C2314yes—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83D411yescharacteristic
166C2×C4⋊C4×C83D411yescharacteristic
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C22⋊C4×C83—21no—
170C2×C22⋊C4×C83—21no—
171C2×C22⋊C4×C83—21no—
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C42×C83—21no—
176C2×C42×C83C2311yescharacteristic
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2311yescharacteristic
179C2×Dic166—21no—
180C2×Dic166—22no—
181C2×Dic166—24no—
182C2×Dic166—44no—
183C2×Dic166#4114yes—
184C2×Dic166C2412yes—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189#13050580—28no—
190#13050578—28no—
191#13050578—28no—
192C2×C83⋊C8—22no—
193C2×C83⋊C8—22no—
194C2×C83⋊C8—22no—
195C2×C83⋊C8—22no—
196C2×C83⋊C8C2412yes—
197C2×C83⋊C8C2412yes—
198C2×C83⋊C8C2412yes—
199C2×C83⋊C8C2412yes—
200C4⋊Dic83—24no—
201C4⋊Dic83—21no—
202C4⋊Dic83—21no—
203C4⋊Dic83—21no—
204C4⋊Dic83C2412yes—
205C4⋊Dic83C2412yes—
206C4⋊Dic83C2412yes—
207Dic83⋊C4—24no—
208Dic83⋊C4—24no—
209Dic83⋊C4—24no—
210Dic83⋊C4—24no—
211Dic83⋊C4—24no—
212Dic83⋊C4—24no—
213Dic83⋊C4—24no—
214C4×Dic83—24no—
215C4×Dic83—24no—
216C4×Dic83—24no—
217C24×C83—21no—
218C24×C83—21no—
219C2×Q8×C83—21no—
220C2×Q8×C83—22no—
221C2×Q8×C83—22no—
222C2×Q8×C83—42no—
223C2×Q8×C83C2×D414yes—
224C2×Q8×C83C2412yes—
225C2×D4×C83—21no—
226C2×D4×C83—21no—
227C2×D4×C83—24no—
228C2×D4×C83—24no—
229C2×D4×C83—22no—
230C2×D4×C83—22no—
231C2×D4×C83—22no—
232C2×D4×C83—22no—
233C2×D4×C83—44no—
234C2×D4×C83—82no—
235C2×D4×C83C2412yes—
236C2×D4×C83C2412yes—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—24no—
240C22×C4×C83—24no—
241C22×C4×C83—82no—
242C22×C4×C83—82no—
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2411yescharacteristic
250C4⋊C4×C83—24no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83C2×D414yes—
253C4⋊C4×C83C2×D414yes—
254C4⋊C4×C83C2×D414yes—
255C4⋊C4×C83C2412yes—
256C22⋊C4×C83—24no—
257C22⋊C4×C83—24no—
258C22⋊C4×C83—24no—
259C22⋊C4×C83—24no—
260C22⋊C4×C83—24no—
261C22⋊C4×C83—24no—
262C42×C83—24no—
263C42×C83C2×D412yes—
264C42×C83C2×D412yes—
265C42×C83C2×D412yes—
266C42×C83C2412yes—
267C42×C83C2412yes—
268C42×C83C2412yes—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—42no—
272C23×C83—42no—
273C23×C83—42no—
274C23×C83—42no—
275C23×C83—42no—
276C23×C83—42no—
277C23×C83C22×D411yescharacteristic
278Q8×C83—22no—
279Q8×C83—22no—
280Q8×C83—44no—
281Q8×C83—42no—
282D4×C83—22no—
283D4×C83—22no—
284D4×C83—22no—
285D4×C83—22no—
286D4×C83—48no—
287D4×C83—42no—
288D4×C83—42no—
289D4×C83—84no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—42no—
299C2×C4×C83—42no—
300C2×C4×C83—84no—
301C2×C4×C83—84no—
302C2×C4×C83C22×D412yes—
303C2×C4×C83C22×D412yes—
304C2×C4×C83C22×D412yes—
305C2×C4×C83C22×D412yes—
306C2×C4×C83C22×D412yes—
307C2×C4×C83C22×D412yes—
308C2×C4×C83C22×D411yescharacteristic
309C2×C4×C83C2×#4112yes—
310C2×C4×C832−1+412yes—
311C2×C4×C83C2511yescharacteristic
312C2×Dic83—24no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—42no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320Dic166—24no—
321Dic166—22no—
322Dic166—48no—
323Dic166C2×#4114yes—
324C83⋊C8—22no—
325C83⋊C8—22no—
326C83⋊C8—22no—
327C83⋊C8—22no—
328C22×C83—42no—
329C22×C83—42no—
330C22×C83—42no—
331C22×C83—42no—
332C22×C83—42no—
333C22×C83—42no—
334C22×C83—84no—
335C22×C83—84no—
336C22×C83#54812yes—
337C22×C83#57512yes—
338C22×C83#57712yes—
339C22×C83C23×D411yescharacteristic
340C4×C83—22no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83—42no—
347C4×C83—42no—
348C4×C83#54812yes—
349C4×C83C22×#4111yescharacteristic
350C4×C83C2×2−1+411yescharacteristic
351Dic83—24no—
352Dic83—42no—
353Dic83—42no—
354Dic83—42no—
355C2×#3371—831nomaximal, Sylow
356C2×C83—82no—
357C2×C83—82no—
358C2×C83#337114yescomplemented
359C2×C83C2×#54811yescharacteristic
360C2×C83C2×#57511yescharacteristic
361C2×C83C2×#57711yescharacteristic
362C2×#559D8311yescharacteristic
363C2×#557—831no—
364#3371—8316no—
365C2×#490—831no—
366C2×#489—831no—
367C2×#488—831no—
368C2×#479—831no—
369C2×#478—831no—
370C2×#476—831no—
371C2×#464—831no—
372C2×#464—831no—
373C2×#460—831no—
374C2×#446—831no—
375C2×#441—831no—
376C2×#440—831no—
377C2×C4×SD16—831no—
378C83C2×#337111yescharacteristic, complemented, Sylow
379C22×Q16—831no—
380C22×SD16—831no—
381C22×SD16—831no—
382#559—24no—
383#559C2×D8318yes—
384#557—838no—
385#557—1664no—
386C2×C4⋊Q8—831no—
387C2×C4⋊Q8—1661no—
388C2×#127C2×D8311yescharacteristic
389C2×#125—831no—
390C2×#125—831no—
391C2×#125—1661no—
392C2×#125—1661no—
393C2×#124—21no—
394C2×#124C2×D8311yescharacteristic
395C2×#124C2×D8311yescharacteristic
396C2×#123—21no—
397C2×#123—21no—
398C2×C4×Q8—831no—
399C2×C4×Q8—831no—
400C2×C4×Q8—831no—
401C2×C4×Q8—1661no—
402C2×C4×Q8C2×D8311yescharacteristic
403C2×C4×Q8C2×D8311yescharacteristic
404C2×C4×D4—21no—
405C2×C4×D4C2×D8311yescharacteristic
406C2×C4×D4C2×D8311yescharacteristic
407#490—838no—
408#489—838no—
409#488—838no—
410#479—838no—
411#478—838no—
412#476—838no—
413#464—838no—
414#464—838no—
415#460—838no—
416#446—838no—
417#441—838no—
418#440—838no—
419C4×SD16—838no—
420C2×#107—831no—
421C2×#106—831no—
422C2×#106—831no—
423C2×C4⋊C8—831no—
424C2×C4⋊C8—831no—
425C2×C4⋊C8—831no—
426C2×#103—831no—
427C2×#103—831no—
428C2×#103—831no—
429C2×#103—831no—
430C2×#102—831no—
431C2×#102—831no—
432C2×#102—831no—
433C2×#102—831no—
434C2×#102—831no—
435C2×#102—831no—
436C2×#97—831no—
437C2×#97—831no—
438C2×C4×C8—831no—
439C22×Q8—831no—
440C22×Q8—1661no—
441C22×Q8C22⋊D8311yescharacteristic
442C22×Q8C22×D8311yescharacteristic
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22×D8311yescharacteristic
446C22×D4C22×D8311yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C2×Q16—834no—
450C2×Q16—1664no—
451C2×SD16—834no—
452C2×SD16—834no—
453C2×SD16—1664no—
454C2×SD16—1664no—
455C22×C8—831no—
456C22×C8—831no—
457C22×C8—831no—
458C22×C8—831no—
459C4⋊Q8—834no—
460C4⋊Q8—1668no—
461C4⋊Q8—1662no—
462#127—22no—
463#127C22×D8314yes—
464#125—834no—
465#125—834no—
466#125—1668no—
467#125—1668no—
468#125—1662no—
469#125—1662no—
470#124—28no—
471#124—22no—
472#124—22no—
473#124C22×D8314yes—
474#124C22×D8314yes—
475#123—28no—
476#123—28no—
477C4×Q8—22no—
478C4×Q8—834no—
479C4×Q8—834no—
480C4×Q8—834no—
481C4×Q8—1668no—
482C4×Q8—1662no—
483C4×Q8—1662no—
484C4×Q8—1662no—
485C4×Q8C22⋊D8314yes—
486C4×Q8C22×D8314yes—
487C4×Q8C22×D8314yes—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4C22×D8314yes—
492C4×D4C22×D8314yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—831no—
496C2×C4⋊C4—831no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4—1661no—
499C2×C4⋊C4—1661no—
500C2×C4⋊C4—1661no—
501C2×C4⋊C4—1661no—
502C2×C4⋊C4—1661no—
503C2×C4⋊C4—1661no—
504C2×C4⋊C4—1661no—
505C2×C4⋊C4C22⋊D8311yescharacteristic
506C2×C4⋊C4C22⋊D8311yescharacteristic
507C2×C4⋊C4C22⋊D8311yescharacteristic
508C2×C4⋊C4C22×D8311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C42—21no—
516C2×C42—1661no—
517C2×C42—1661no—
518C2×C42—1661no—
519C2×C42C22×D8311yescharacteristic
520C2×C42C22×D8311yescharacteristic
521C2×C42C22×D8311yescharacteristic
522#107—834no—
523#106—834no—
524#106—834no—
525C4⋊C8—834no—
526C4⋊C8—834no—
527C4⋊C8—834no—
528#103—834no—
529#103—834no—
530#103—834no—
531#103—834no—
532#102—834no—
533#102—834no—
534#102—834no—
535#102—834no—
536#102—834no—
537#102—834no—
538#97—834no—
539#97—834no—
540C4×C8—834no—
541C24—21no—
542C24—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—3324no—
548C2×Q8—834no—
549C2×Q8—832no—
550C2×Q8—1664no—
551C2×Q8—1661no—
552C2×Q8—1662no—
553C2×Q8C2×C22⋊D8314yes—
554C2×Q8C23×D8312yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—44no—
564C2×D4—82no—
565C2×D4C23×D8312yes—
566C2×D4C23×D8312yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—1661no—
574C22×C4—1661no—
575C22×C4—1661no—
576C22×C4—1661no—
577C22×C4C2×C22⋊D8311yescharacteristic
578C22×C4C2×C22⋊D8311yescharacteristic
579C22×C4C2×C22⋊D8311yescharacteristic
580C22×C4C2×C22⋊D8311yescharacteristic
581C22×C4C2×C22⋊D8311yescharacteristic
582C22×C4C2×C22⋊D8311yescharacteristic
583C22×C4C23×D8311yescharacteristic
584Q16—1668no—
585SD16—1668no—
586SD16—1668no—
587C2×C8—832no—
588C2×C8—832no—
589C2×C8—832no—
590C2×C8—832no—
591C2×C8—1662no—
592C2×C8—1662no—
593C2×C8—1662no—
594C2×C8—1662no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—832no—
598C4⋊C4—832no—
599C4⋊C4—832no—
600C4⋊C4—1661no—
601C4⋊C4—1661no—
602C4⋊C4—1661no—
603C4⋊C4—1664no—
604C4⋊C4—1664no—
605C4⋊C4—1664no—
606C4⋊C4—1664no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4—1664no—
610C4⋊C4—1664no—
611C4⋊C4C2×C22⋊D8314yes—
612C4⋊C4C2×C22⋊D8314yes—
613C4⋊C4C2×C22⋊D8314yes—
614C4⋊C4C23×D8312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C42—24no—
622C42—1664no—
623C42—1664no—
624C42—1664no—
625C42C2×C22⋊D8312yes—
626C42C2×C22⋊D8312yes—
627C42C2×C22⋊D8312yes—
628C42C23×D8312yes—
629C42C23×D8312yes—
630C42C23×D8312yes—
631C23—22no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C22×C22⋊D8311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—44no—
643Q8—42no—
644Q8—3328no—
645Q8—834no—
646Q8—1664no—
647Q8—1662no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—42no—
654D4—42no—
655D4—84no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—3322no—
669C2×C4—3322no—
670C2×C4—3322no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1664no—
675C2×C4—1662no—
676C2×C4C22×C22⋊D8312yes—
677C2×C4C22×C22⋊D8312yes—
678C2×C4C22×C22⋊D8312yes—
679C2×C4C22×C22⋊D8312yes—
680C2×C4C22×C22⋊D8312yes—
681C2×C4C22×C22⋊D8312yes—
682C2×C4C22×C22⋊D8311yescharacteristic
683C2×C4#41×D8312yes—
684C2×C4#1458183912yes—
685C2×C4C24×D8311yescharacteristic
686C8—1662no—
687C8—1662no—
688C8—1662no—
689C8—1662no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—84no—
697C22—84no—
698C22#1912835812yes—
699C22#1912849912yes—
700C22#1912851212yes—
701C22C23×C22⋊D8311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—3322no—
711C4—3322no—
712C4—3322no—
713C4—1664no—
714C4#1912835812yes—
715C4C2×#41×D8311yescharacteristic
716C4C2×#1458183911yescharacteristic
717C2—82no—
718C2—82no—
719C2#2492022514yesdirect product factor
720C2C2×#1912835811yescharacteristic
721C2C2×#1912849911yescharacteristic
722C2C2×#1912851211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#559×C83C2
socleC23×C83C22×D4
prime radicalC2×#127×C83C22
hypercenterC2×#559D83
hypocenterC83C2×#3371
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#19128429C2semidirect
2. #24920225C2direct (N × H)
4. C2×#19128060C2semidirect
5. C2×#19128055C2semidirect
6. C2×#19128008C2semidirect
7. C2×#19128001C2semidirect
8. C2×#19127991C2semidirect
9. C2×#19127920C2semidirect
10. C2×#19127920C2semidirect
12. C2×#19127832C2semidirect
13. C2×#19127806C2semidirect
14. C2×#19127801C2semidirect
15. C2×C4×#13050578C2semidirect
21. #19128429C22semidirect
33. #19128060C22semidirect
34. #19128055C22semidirect
35. #19128008C22semidirect
36. #19128001C22semidirect
37. #19127991C22semidirect
38. #19127920C22semidirect
39. #19127920C22semidirect
41. #19127832C22semidirect
42. #19127806C22semidirect
43. #19127801C22semidirect
44. C4×#13050578C22semidirect
358. C2×C83#3371semidirect
378. C83C2×#3371semidirect
719. C2#24920225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284292
#249202252
C2×#191280652
C2×#191280602
C2×#191280552
C2×#191280082
C2×#191280012
C2×#191279912
C2×#191279202
C2×#191278982
C2×#191278322
C2×#191278062
C2×#191278012
C2×C4×#130505782
C2×#559×C832
C2×#337183