Finite Group Databasebeta

← C2×#24918716 #36276593

Subgroups — C2×#24918716 #36276593

Order 21248.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128306C211yesmaximal, characteristic
2#24918716C2116yesmaximal, direct product factor
3C2×#19128107C211yesmaximal, characteristic, complemented
4C2×#19128100C211yesmaximal, characteristic, complemented
5C2×#19128067C211yesmaximal, characteristic, complemented
6C2×#19128049C211yesmaximal, characteristic, complemented
7C2×#19128019C211yesmaximal, characteristic, complemented
8C2×#19128025C211yesmaximal, characteristic, complemented
9C2×#19128025C211yesmaximal, characteristic, complemented
10C2×#19128014C211yesmaximal, characteristic, complemented
11C2×#19127998C211yesmaximal, characteristic, complemented
12C2×#19127998C211yesmaximal, characteristic, complemented
13C2×#19127988C211yesmaximal, characteristic, complemented
14C2×#19127978C211yesmaximal, characteristic, complemented
15C2×#19127762C211yesmaximal, characteristic, complemented
16C2×#544×C83C211yesmaximal, characteristic, complemented
17#19128306—24no—
18#19128306C2218yes—
19C2×#14581789C2211yescharacteristic
20C2×#14581784C2211yescharacteristic
21C2×#14581777—21no—
22C2×#14581777—21no—
23C2×#14581766C2211yescharacteristic
24C2×#14581766C2211yescharacteristic
25C2×#14581765—21no—
26C2×#14581765—21no—
27C2×C4×D332C2211yescharacteristic
28C2×C4×D332C2211yescharacteristic
29#19128107C2218yescomplemented
30#19128100C2218yescomplemented
31#19128067C2218yescomplemented
32#19128049C2218yescomplemented
33#19128025C2218yescomplemented
34#19128025C2218yescomplemented
35#19128019C2218yescomplemented
36#19128014C2218yescomplemented
37#19127998C2218yescomplemented
38#19127998C2218yescomplemented
39#19127988C2218yescomplemented
40#19127978C2218yescomplemented
41#19127762C2218yescomplemented
42C2×#14581725C2211yescharacteristic
43C2×#14581725C2211yescharacteristic
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×C4⋊(C83⋊C8)C2211yescharacteristic
52C2×#14581712C2211yescharacteristic
53C2×#14581712C2211yescharacteristic
54C2×#14581712C2211yescharacteristic
55C2×#14581712C2211yescharacteristic
56C2×#14581712C2211yescharacteristic
57C2×#14581712C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#544×C83—24no—
65#544×C83C2218yescomplemented
66C2×C4⋊Q8×C83—21no—
67C2×C4⋊Q8×C83C2211yescharacteristic
68C2×C4⋊Q8×C83C2211yescharacteristic
69C2×#125×C83—21no—
70C2×#125×C83C2211yescharacteristic
71C2×#125×C83C2211yescharacteristic
72C2×C22⋊Q8×C83—21no—
73C2×C22⋊Q8×C83—21no—
74C2×#117×C83C2211yescharacteristic
75C2×#117×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C22×D332—21no—
78C22×D332—21no—
79C22×D332C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C22×C4×D83—21no—
84C22×C4×D83—21no—
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89#14581789—22no—
90#14581789C2314yes—
91#14581784—22no—
92#14581784C2314yes—
93#14581777—28no—
94#14581777—28no—
95#14581766—22no—
96#14581766—22no—
97#14581766C2314yes—
98#14581766C2314yes—
99#14581765—28no—
100#14581765—28no—
101C4×D332—22no—
102C4×D332—22no—
103C4×D332C2314yes—
104C4×D332C2314yes—
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2311yescharacteristic
107C2×Dic83⋊C4—21no—
108C2×Dic83⋊C4—21no—
109C2×(C2×D83)⋊C4—21no—
110C2×(C2×D83)⋊C4—21no—
111C2×(C2×D83)⋊C4—21no—
112C2×(C2×D83)⋊C4—21no—
113#14581725C2314yes—
114#14581725C2314yes—
115#14581725C2314yes—
116#14581725C2314yes—
117#14581723C2314yes—
118#14581723C2314yes—
119#14581723C2314yes—
120#14581723C2314yes—
121C4⋊(C83⋊C8)C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123#14581712C2314yes—
124#14581712C2314yes—
125#14581712C2314yes—
126#14581712C2314yes—
127#14581712C2314yes—
128#14581712C2314yes—
129#14581712C2314yes—
130#14581712C2314yes—
131C22⋊(C83⋊C8)C2314yes—
132C22⋊(C83⋊C8)C2314yes—
133#14581703C2314yes—
134C4×C83⋊C8C2314yes—
135C22×Q8×C83—21no—
136C22×Q8×C83—21no—
137C23×C4×C83—21no—
138C23×C4×C83C2311yescharacteristic
139C4⋊Q8×C83—28no—
140C4⋊Q8×C83—22no—
141C4⋊Q8×C83—22no—
142C4⋊Q8×C83C2314yes—
143C4⋊Q8×C83C2314yes—
144#125×C83—28no—
145#125×C83—22no—
146#125×C83—22no—
147#125×C83C2314yes—
148#125×C83C2314yes—
149C22⋊Q8×C83—28no—
150C22⋊Q8×C83—28no—
151#117×C83—22no—
152#117×C83D414yes—
153#117×C83C2314yes—
154#117×C83C2314yes—
155C2×C4⋊C4×C83—21no—
156C2×C4⋊C4×C83—22no—
157C2×C4⋊C4×C83—21no—
158C2×C4⋊C4×C83—21no—
159C2×C4⋊C4×C83—21no—
160C2×C4⋊C4×C83—21no—
161C2×C4⋊C4×C83—21no—
162C2×C4⋊C4×C83—21no—
163C2×C4⋊C4×C83D411yescharacteristic
164C2×C4⋊C4×C83D411yescharacteristic
165C2×C4⋊C4×C83C2311yescharacteristic
166C2×C4⋊C4×C83C2311yescharacteristic
167C2×C4⋊C4×C83C2314yes—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C22⋊C4×C83—21no—
171C2×C22⋊C4×C83D411yescharacteristic
172C2×C22⋊C4×C83D411yescharacteristic
173C2×C42×C83—21no—
174C2×C42×C83C2311yescharacteristic
175C2×C42×C83C2311yescharacteristic
176C23×D83—21no—
177C23×D83—21no—
178C2×D332—22no—
179C2×D332—22no—
180C2×D332—22no—
181C2×D332—22no—
182C2×D332—21no—
183C2×D332—21no—
184C2×D332—24no—
185C2×D332—24no—
186C2×D332—82no—
187C2×D332—82no—
188C2×D332C2412yes—
189C2×D332C2412yes—
190C2×C22⋊D83—24no—
191C2×C22⋊D83—24no—
192C2×C22⋊D83—82no—
193C2×C22⋊D83—82no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C2×C4×D83—24no—
197C2×C4×D83—24no—
198C2×C4×D83—82no—
199C2×C4×D83—82no—
200C2×C83⋊C8—22no—
201C2×C83⋊C8—22no—
202C2×C83⋊C8—22no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C2×C83⋊C8C2412yes—
207C2×C83⋊C8C2412yes—
208C4⋊Dic83—21no—
209C4⋊Dic83—21no—
210C4⋊Dic83C2412yes—
211C4⋊Dic83C2412yes—
212Dic83⋊C4—24no—
213Dic83⋊C4—24no—
214(C2×D83)⋊C4—24no—
215(C2×D83)⋊C4—24no—
216(C2×D83)⋊C4—24no—
217(C2×D83)⋊C4—24no—
218C24×C83C2×D411yescharacteristic
219C2×Q8×C83—24no—
220C2×Q8×C83—24no—
221C2×Q8×C83—82no—
222C2×Q8×C83—82no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—24no—
230C22×C4×C83—82no—
231C22×C4×C83C2×D412yes—
232C22×C4×C83C2×D411yescharacteristic
233C22×C4×C83C2×D411yescharacteristic
234C22×C4×C83C2×D411yescharacteristic
235C22×C4×C83C2×D411yescharacteristic
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2412yes—
238C22×C4×C83C2411yescharacteristic
239C4⋊C4×C83—24no—
240C4⋊C4×C83—21no—
241C4⋊C4×C83—21no—
242C4⋊C4×C83—24no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—24no—
246C4⋊C4×C83—24no—
247C4⋊C4×C83—24no—
248C4⋊C4×C83—21no—
249C4⋊C4×C83—21no—
250C4⋊C4×C83C2×D414yes—
251C4⋊C4×C83C2×D414yes—
252C4⋊C4×C83C2412yes—
253C4⋊C4×C83C2412yes—
254C4⋊C4×C83C2412yes—
255C4⋊C4×C83C2412yes—
256C22⋊C4×C83—24no—
257C22⋊C4×C83C2×D414yes—
258C22⋊C4×C83C2×D414yes—
259C42×C83—24no—
260C42×C83C2×D412yes—
261C42×C83C2×D412yes—
262C42×C83C2412yes—
263C42×C83C2412yes—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83C22×D412yes—
268C23×C83C22×D411yescharacteristic
269C22×D83—22no—
270C22×D83—22no—
271C22×D83—42no—
272C22×D83—42no—
273C22×D83—42no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277Q8×C83—84no—
278Q8×C83—84no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—42no—
292C2×C4×C83—42no—
293C2×C4×C83—42no—
294C2×C4×C83—42no—
295C2×C4×C83—84no—
296C2×C4×C83C22×D412yes—
297C2×C4×C83C22×D412yes—
298C2×C4×C83C22×D412yes—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D412yes—
301C2×C4×C83C22×D411yescharacteristic
302C2×C4×C832−1+412yes—
303C2×C4×C832−1+412yes—
304C2×C4×C83C2511yescharacteristic
305C22⋊D83—84no—
306C22⋊D83—84no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—42no—
310C2×Dic83—42no—
311D332—22no—
312D332—22no—
313D332—22no—
314D332—22no—
315D332—42no—
316D332—42no—
317D332—84no—
318D332—84no—
319C4×D83—84no—
320C4×D83—84no—
321C83⋊C8—22no—
322C83⋊C8—22no—
323C83⋊C8—22no—
324C83⋊C8—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—44no—
329C22×C83#53612yes—
330C22×C83#57612yes—
331C22×C83#57712yes—
332C22×C83C23×D411yescharacteristic
333C2×D83—42no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—84no—
340C2×D83—84no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83—42no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83#53612yes—
351C4×C83C2×2−1+411yescharacteristic
352C4×C83C2×2−1+411yescharacteristic
353Dic83—42no—
354Dic83—42no—
355C2×#3241—831nomaximal, Sylow
356C2×C83—42no—
357C2×C83#324114yescomplemented
358C2×C83C2×#53611yescharacteristic
359C2×C83C2×#57611yescharacteristic
360C2×C83C2×#57711yescharacteristic
361D83—82no—
362D83—82no—
363C2×#544D8311yescharacteristic, complemented
364C2×#540—831no—
365#3241—8316no—
366C2×#501—831no—
367C2×#499—831no—
368C2×#490—831no—
369C2×#486—831no—
370C2×#481—831no—
371C2×#482—831no—
372C2×#482—831no—
373C2×#480—831no—
374C2×#478—831no—
375C2×#478—831no—
376C2×#476—831no—
377C2×#474—831no—
378C2×#433—831no—
379C83C2×#324111yescharacteristic, complemented, Sylow
380#544—24no—
381#544C2×D8318yescomplemented
382#540—838no—
383#540—1664no—
384C2×C4⋊Q8—21no—
385C2×C4⋊Q8C2×D8311yescharacteristic
386C2×C4⋊Q8C2×D8311yescharacteristic
387C2×#127—831no—
388C2×#125—21no—
389C2×#125—831no—
390C2×#125C2×D8311yescharacteristic
391C2×#125C2×D8311yescharacteristic
392C2×#123—1661no—
393C2×#123—1661no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×#121—831no—
397C2×#121—831no—
398C2×#121—1661no—
399C2×#121—1661no—
400C2×C4×D4—831no—
401C2×C4×D4—831no—
402C2×#117C2×D8311yescharacteristic
403C2×#117C2×D8311yescharacteristic
404C22×C4⋊C4C2×D8311yescharacteristic
405#501—838no—
406#499—838no—
407#490—838no—
408#486—838no—
409#482—838no—
410#482—838no—
411#481—838no—
412#480—838no—
413#478—838no—
414#478—838no—
415#476—838no—
416#474—838no—
417#433—838no—
418C2×#107—831no—
419C2×#107—831no—
420C2×#107—831no—
421C2×#107—831no—
422C2×#106—831no—
423C2×#106—831no—
424C2×#106—831no—
425C2×#106—831no—
426C2×C4⋊C8—831no—
427C2×C4⋊C8—831no—
428C2×#102—831no—
429C2×#102—831no—
430C2×#102—831no—
431C2×#102—831no—
432C2×#102—831no—
433C2×#102—831no—
434C2×#102—831no—
435C2×#102—831no—
436C2×C22⋊C8—831no—
437C2×C22⋊C8—831no—
438C2×#97—831no—
439C2×C4×C8—831no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×D4—831no—
443C22×D4—831no—
444C22×D4—1661no—
445C22×D4—1661no—
446C22×D4—1661no—
447C22×D4—1661no—
448C23×C4—21no—
449C23×C4—1661no—
450C23×C4—1661no—
451C23×C4C22×D8311yescharacteristic
452C22×C8—831no—
453C22×C8—831no—
454C22×C8—831no—
455C22×C8—831no—
456C4⋊Q8—28no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8C22×D8314yes—
460C4⋊Q8C22×D8314yes—
461#127—834no—
462#127—1662no—
463#125—28no—
464#125—22no—
465#125—22no—
466#125—834no—
467#125—1662no—
468#125C22×D8314yes—
469#125C22×D8314yes—
470#123—1668no—
471#123—1668no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474#121—834no—
475#121—834no—
476#121—1662no—
477#121—1662no—
478#121—1668no—
479#121—1668no—
480C4×D4—834no—
481C4×D4—834no—
482C4×D4—1662no—
483C4×D4—1662no—
484#117—22no—
485#117C22⋊D8314yes—
486#117C22×D8314yes—
487#117C22×D8314yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—831no—
497C2×C4⋊C4—831no—
498C2×C4⋊C4—1661no—
499C2×C4⋊C4—1661no—
500C2×C4⋊C4C22⋊D8311yescharacteristic
501C2×C4⋊C4C22⋊D8311yescharacteristic
502C2×C4⋊C4C22×D8311yescharacteristic
503C2×C4⋊C4C22×D8311yescharacteristic
504C2×C4⋊C4C22×D8314yes—
505C2×C4⋊C4C22×D8311yescharacteristic
506C2×C4⋊C4C22×D8311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1661no—
509C2×C22⋊C4—1661no—
510C2×C22⋊C4—1661no—
511C2×C22⋊C4—1661no—
512C2×C22⋊C4C22⋊D8311yescharacteristic
513C2×C22⋊C4C22⋊D8311yescharacteristic
514C2×C42—21no—
515C2×C42C22×D8311yescharacteristic
516C2×C42C22×D8311yescharacteristic
517#107—834no—
518#107—834no—
519#107—834no—
520#107—834no—
521#106—834no—
522#106—834no—
523#106—834no—
524#106—834no—
525C4⋊C8—834no—
526C4⋊C8—834no—
527#102—834no—
528#102—834no—
529#102—834no—
530#102—834no—
531#102—834no—
532#102—834no—
533#102—834no—
534#102—834no—
535C22⋊C8—834no—
536C22⋊C8—834no—
537#97—834no—
538C4×C8—834no—
539C24—1661no—
540C24—1661no—
541C24C2×C22⋊D8311yescharacteristic
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×D4—832no—
547C2×D4—832no—
548C2×D4—6642no—
549C2×D4—6642no—
550C2×D4—6642no—
551C2×D4—6642no—
552C2×D4—1664no—
553C2×D4—1664no—
554C2×D4—1661no—
555C2×D4—1661no—
556C2×D4—1664no—
557C2×D4—1664no—
558C2×D4—1662no—
559C2×D4—1662no—
560C2×D4—1662no—
561C2×D4—1662no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—6642no—
571C22×C4—6642no—
572C22×C4—1661no—
573C22×C4—1661no—
574C22×C4—1664no—
575C22×C4—1664no—
576C22×C4C2×C22⋊D8312yes—
577C22×C4C2×C22⋊D8311yescharacteristic
578C22×C4C2×C22⋊D8311yescharacteristic
579C22×C4C2×C22⋊D8311yescharacteristic
580C22×C4C2×C22⋊D8311yescharacteristic
581C22×C4C2×C22⋊D8311yescharacteristic
582C22×C4C23×D8312yes—
583C22×C4C23×D8311yescharacteristic
584C2×C8—832no—
585C2×C8—832no—
586C2×C8—832no—
587C2×C8—832no—
588C2×C8—1662no—
589C2×C8—1662no—
590C2×C8—1662no—
591C2×C8—1662no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—832no—
604C4⋊C4—832no—
605C4⋊C4—1661no—
606C4⋊C4—1661no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4C2×C22⋊D8314yes—
610C4⋊C4C2×C22⋊D8314yes—
611C4⋊C4C23×D8312yes—
612C4⋊C4C23×D8312yes—
613C4⋊C4C23×D8312yes—
614C4⋊C4C23×D8312yes—
615C22⋊C4—24no—
616C22⋊C4—1664no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4C2×C22⋊D8314yes—
621C22⋊C4C2×C22⋊D8314yes—
622C42—24no—
623C42C2×C22⋊D8312yes—
624C42C2×C22⋊D8312yes—
625C42C23×D8312yes—
626C42C23×D8312yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—3322no—
631C23—3322no—
632C23—3322no—
633C23—3322no—
634C23—3322no—
635C23—3322no—
636C23—1662no—
637C23—1662no—
638C23C22×C22⋊D8312yes—
639C23C22×C22⋊D8311yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—3322no—
643D4—3322no—
644D4—6644no—
645D4—6644no—
646D4—6644no—
647D4—6644no—
648D4—1662no—
649D4—1662no—
650D4—1662no—
651D4—1662no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
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—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—3322no—
670C2×C4—3322no—
671C2×C4—6644no—
672C2×C4—6644no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4C22×C22⋊D8312yes—
676C2×C4C22×C22⋊D8312yes—
677C2×C4C22×C22⋊D8312yes—
678C2×C4C22×C22⋊D8312yes—
679C2×C4C22×C22⋊D8312yes—
680C2×C4C22×C22⋊D8311yescharacteristic
681C2×C4#1458184012yes—
682C2×C4#1458184012yes—
683C2×C4C24×D8311yescharacteristic
684C8—1662no—
685C8—1662no—
686C8—1662no—
687C8—1662no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—3322no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—3322no—
697C22—3322no—
698C22—6644no—
699C22—6644no—
700C22#1912827512yes—
701C22#1912850412yes—
702C22#1912850912yes—
703C22C23×C22⋊D8311yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—3322no—
714C4—3322no—
715C4#1912827512yes—
716C4C2×#1458184011yescharacteristic
717C4C2×#1458184011yescharacteristic
718C2—42no—
719C2—6642no—
720C2—6642no—
721C2#2491871614yesdirect product factor
722C2C2×#1912827511yescharacteristic
723C2C2×#1912850411yescharacteristic
724C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#544×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128306C2
hypercenterC2×#544D83
hypocenterC83C2×#3241
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #24918716C2direct (N × H)
3. C2×#19128107C2semidirect
4. C2×#19128100C2semidirect
5. C2×#19128067C2semidirect
6. C2×#19128049C2semidirect
7. C2×#19128019C2semidirect
8. C2×#19128025C2semidirect
9. C2×#19128025C2semidirect
10. C2×#19128014C2semidirect
11. C2×#19127998C2semidirect
12. C2×#19127998C2semidirect
13. C2×#19127988C2semidirect
14. C2×#19127978C2semidirect
15. C2×#19127762C2semidirect
16. C2×#544×C83C2semidirect
29. #19128107C22semidirect
30. #19128100C22semidirect
31. #19128067C22semidirect
32. #19128049C22semidirect
33. #19128025C22semidirect
34. #19128025C22semidirect
35. #19128019C22semidirect
36. #19128014C22semidirect
37. #19127998C22semidirect
38. #19127998C22semidirect
39. #19127988C22semidirect
40. #19127978C22semidirect
41. #19127762C22semidirect
65. #544×C83C22semidirect
357. C2×C83#3241semidirect
363. C2×#544D83semidirect
379. C83C2×#3241semidirect
381. #544C2×D83semidirect
721. C2#24918716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283062
#249187162
C2×#191281072
C2×#191281002
C2×#191280672
C2×#191280492
C2×#191280192
C2×#191280252
C2×#191280142
C2×#191279982
C2×#191279882
C2×#191279782
C2×#191277622
C2×#544×C832
C2×#324183