Finite Group Databasebeta

← C2×#24920417 #36284941

Subgroups — C2×#24920417 #36284941

Order 21248.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128411C211yesmaximal, characteristic, complemented
2#24920417C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128107C211yesmaximal, characteristic, complemented
5C2×#19128100C211yesmaximal, characteristic, complemented
6C2×#19128001C211yesmaximal, characteristic, complemented
7C2×#19128001C211yesmaximal, characteristic, complemented
8C2×#19127998C211yesmaximal, characteristic, complemented
9C2×#19127998C211yesmaximal, characteristic, complemented
10C2×#19127981C211yesmaximal, characteristic, complemented
11C2×#19127978C211yesmaximal, characteristic, complemented
12C2×#19127832C211yesmaximal, characteristic, complemented
13C2×#19127811C211yesmaximal, characteristic
14C2×#19127811C211yesmaximal, characteristic
15C2×C4×#13050575C211yesmaximal, characteristic
16C2×#554×C83C211yesmaximal, characteristic, complemented
17C22×#13050575C2211yescharacteristic
18#19128411—24no—
19#19128411C2218yescomplemented
20C2×#14581792C2211yescharacteristic
21C2×#14581784C2211yescharacteristic
22C2×#14581784C2211yescharacteristic
23C2×#14581770—21no—
24C2×#14581770—21no—
25C2×#14581768—21no—
26C2×C4×D332C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×C4×D332C2211yescharacteristic
29C2×C4⋊C4×D83—21no—
30#19128111C2218yescomplemented
31#19128107C2218yescomplemented
32#19128100C2218yescomplemented
33#19128001C2218yescomplemented
34#19128001C2218yescomplemented
35#19127998C2218yescomplemented
36#19127998C2218yescomplemented
37#19127981C2218yescomplemented
38#19127978C2218yescomplemented
39#19127832C2218yescomplemented
40#19127811C2218yes—
41#19127811C2218yes—
42C4×#13050575C2218yes—
43C2×#14581725C2211yescharacteristic
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581725C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581723C2211yescharacteristic
52C2×C4⋊(C83⋊C8)C2211yescharacteristic
53C2×C4⋊(C83⋊C8)C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#554×C83—24no—
65#554×C83C2218yescomplemented
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#125×C83C2211yescharacteristic
68C2×#125×C83C2211yescharacteristic
69C2×C22⋊Q8×C83—21no—
70C2×C22⋊Q8×C83—21no—
71C2×C22⋊Q8×C83—21no—
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83C2211yescharacteristic
74C2×C4×D4×C83C2211yescharacteristic
75C2×C4×D4×C83C2211yescharacteristic
76C22×C4⋊C4×C83—21no—
77C22×Dic166—21no—
78C22×D332C2311yescharacteristic
79C22×C4×D83—21no—
80C22×C4×D83—21no—
81C22×C4×D83—21no—
82C2×#13050575Q818yescomplemented
83C2×#13050575C2314yes—
84C22×C83⋊C8C2311yescharacteristic
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2311yescharacteristic
88#14581792—22no—
89#14581792C2314yes—
90#14581784—22no—
91#14581784—22no—
92#14581784C2314yes—
93#14581784C2314yes—
94#14581770—28no—
95#14581770—28no—
96#14581768—28no—
97C4×D332—22no—
98C4×D332—22no—
99C4×D332—22no—
100C4×D332C2314yes—
101C4×D332C2314yes—
102C4×D332C2314yes—
103C2×C4⋊Dic83—21no—
104C2×C4⋊Dic83C2311yescharacteristic
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2311yescharacteristic
107C2×Dic83⋊C4—21no—
108C2×Dic83⋊C4—21no—
109C2×Dic83⋊C4—21no—
110C2×Dic83⋊C4—21no—
111C4⋊C4×D83—28no—
112C2×(C2×D83)⋊C4—21no—
113C2×(C2×D83)⋊C4—21no—
114C2×(C2×D83)⋊C4—21no—
115#14581725C2314yes—
116#14581725C2314yes—
117#14581725C2314yes—
118#14581725C2314yes—
119#14581725C2314yes—
120#14581723C2314yes—
121#14581723C2314yes—
122#14581723C2314yes—
123#14581723C2314yes—
124C4⋊(C83⋊C8)C2314yes—
125C4⋊(C83⋊C8)C2314yes—
126C4⋊(C83⋊C8)C2314yes—
127#14581713C2314yes—
128#14581713C2314yes—
129#14581713C2314yes—
130#14581712C2314yes—
131#14581712C2314yes—
132#14581712C2314yes—
133#14581703C2314yes—
134#14581703C2314yes—
135C4×C83⋊C8C2314yes—
136C22×Q8×C83—21no—
137C22×Q8×C83D411yescharacteristic
138C22×D4×C83C2311yescharacteristic
139C23×C4×C83—21no—
140C23×C4×C83—21no—
141C23×C4×C83—21no—
142C4⋊Q8×C83—22no—
143C4⋊Q8×C83C2314yes—
144#125×C83—22no—
145#125×C83—22no—
146#125×C83C2314yes—
147#125×C83C2314yes—
148C22⋊Q8×C83—28no—
149C22⋊Q8×C83—28no—
150C22⋊Q8×C83—28no—
151C4×Q8×C83D414yes—
152C4×Q8×C83C2314yes—
153C4×D4×C83—22no—
154C4×D4×C83—22no—
155C4×D4×C83—22no—
156C4×D4×C83C2314yes—
157C4×D4×C83C2314yes—
158C4×D4×C83C2314yes—
159C2×C4⋊C4×C83—21no—
160C2×C4⋊C4×C83—21no—
161C2×C4⋊C4×C83—21no—
162C2×C4⋊C4×C83—21no—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—28no—
165C2×C4⋊C4×C83D411yescharacteristic
166C2×C4⋊C4×C83D411yescharacteristic
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C22⋊C4×C83—21no—
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C42×C83C2311yescharacteristic
175C2×C42×C83C2311yescharacteristic
176C2×C42×C83C2311yescharacteristic
177C23×D83—21no—
178C2×Dic166—24no—
179C2×Dic166—82no—
180C2×D332—21no—
181C2×D332—22no—
182C2×D332C2×Q814yes—
183C2×D332C2412yes—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C2×C4×D83—24no—
188C2×C4×D83—24no—
189C2×C4×D83—24no—
190C2×C4×D83—44no—
191C2×C4×D83—82no—
192C2×C4×D83—82no—
193#13050575C2×Q8116yescomplemented
194C2×C83⋊C8—22no—
195C2×C83⋊C8—22no—
196C2×C83⋊C8—22no—
197C2×C83⋊C8C2×Q814yes—
198C2×C83⋊C8C2412yes—
199C2×C83⋊C8C2412yes—
200C2×C83⋊C8C2412yes—
201C2×C83⋊C8C2412yes—
202C4⋊Dic83—24no—
203C4⋊Dic83—21no—
204C4⋊Dic83—21no—
205C4⋊Dic83—21no—
206C4⋊Dic83C2412yes—
207C4⋊Dic83C2412yes—
208C4⋊Dic83C2412yes—
209Dic83⋊C4—24no—
210Dic83⋊C4—24no—
211Dic83⋊C4—24no—
212Dic83⋊C4—24no—
213(C2×D83)⋊C4—24no—
214(C2×D83)⋊C4—24no—
215(C2×D83)⋊C4—24no—
216C24×C83—21no—
217C2×Q8×C83—24no—
218C2×Q8×C83—42no—
219C2×Q8×C83—82no—
220C2×Q8×C83C2×D414yes—
221C2×D4×C83—21no—
222C2×D4×C83—22no—
223C2×D4×C83C2×Q814yes—
224C2×D4×C83C2412yes—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—24no—
229C22×C4×C83—24no—
230C22×C4×C83—24no—
231C22×C4×C83—44no—
232C22×C4×C83—82no—
233C22×C4×C83—82no—
234C22×C4×C83C2×D411yescharacteristic
235C22×C4×C83C2×D411yescharacteristic
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2×D411yescharacteristic
238C22×C4×C83C2×D411yescharacteristic
239C22×C4×C83C2×D411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C4⋊C4×C83—24no—
242C4⋊C4×C83—24no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—24no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83—21no—
248C4⋊C4×C83—21no—
249C4⋊C4×C83C2×D414yes—
250C4⋊C4×C83C2×D414yes—
251C4⋊C4×C83C2×D414yes—
252C4⋊C4×C83C2412yes—
253C4⋊C4×C83C2412yes—
254C4⋊C4×C83C2412yes—
255C22⋊C4×C83—24no—
256C22⋊C4×C83—24no—
257C22⋊C4×C83—24no—
258C42×C83C2×D412yes—
259C42×C83C2×D412yes—
260C42×C83C2×D412yes—
261C42×C83C2412yes—
262C42×C83C2412yes—
263C42×C83C2412yes—
264C23×C83—24no—
265C23×C83—22no—
266C23×C83—42no—
267C23×C83—42no—
268C23×C83C22×D411yescharacteristic
269C22×D83—24no—
270C22×D83—22no—
271C22×D83—42no—
272C22×D83—42no—
273Q8×C83—44no—
274Q8×C83—84no—
275D4×C83—24no—
276D4×C83—22no—
277D4×C83C22×Q814yes—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—48no—
288C2×C4×C83—42no—
289C2×C4×C83—42no—
290C2×C4×C83—42no—
291C2×C4×C83—84no—
292C2×C4×C83—84no—
293C2×C4×C83C22×D412yes—
294C2×C4×C83C22×D412yes—
295C2×C4×C83C22×D412yes—
296C2×C4×C83C22×D412yes—
297C2×C4×C83C22×D412yes—
298C2×C4×C83C22×D412yes—
299C2×C4×C83C22×D411yescharacteristic
300C2×C4×C83C22×Q812yes—
301C2×C4×C832−1+412yes—
302C2×C4×C83C2511yescharacteristic
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—42no—
307C2×Dic83—42no—
308C2×Dic83—42no—
309D332—24no—
310D332—22no—
311D332C22×Q814yes—
312C4×D83—48no—
313C4×D83—84no—
314C4×D83—84no—
315Dic166—84no—
316C83⋊C8—22no—
317C83⋊C8—22no—
318C83⋊C8—22no—
319C83⋊C8C22×Q814yes—
320C22×C83—24no—
321C22×C83—48no—
322C22×C83—42no—
323C22×C83—42no—
324C22×C83D4×Q812yes—
325C22×C83#57512yes—
326C22×C83#57612yes—
327C22×C83C23×D411yescharacteristic
328C2×D83—24no—
329C2×D83—48no—
330C2×D83—42no—
331C2×D83—42no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—22no—
335C4×C83—22no—
336C4×C83—22no—
337C4×C83—22no—
338C4×C83—42no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83D4×Q812yes—
342C4×C83C23×Q811yescharacteristic
343C4×C83C2×2−1+411yescharacteristic
344Dic83—42no—
345Dic83—42no—
346Dic83—42no—
347C2×#3389—831nomaximal, Sylow
348C2×C83—44no—
349C2×C83#338914yescomplemented
350C2×C83C2×D4×Q811yescharacteristic
351C2×C83C2×#57511yescharacteristic
352C2×C83C2×#57611yescharacteristic
353D83—44no—
354C2×#554—831no—
355C2×#554D8311yescharacteristic, complemented
356#3389—8316no—
357C2×#501—831no—
358C2×#501—831no—
359C2×#499—831no—
360C2×#478—831no—
361C2×#478—831no—
362C2×#478—831no—
363C2×#478—831no—
364C2×#474—831no—
365C2×#474—831no—
366C2×#446—831no—
367C2×#442—831no—
368C2×#442—831no—
369C2×C4×D8—831no—
370C83C2×#338911yescharacteristic, complemented, Sylow
371C22×D8—831no—
372#554—24no—
373#554—838no—
374#554—1664no—
375#554C2×D8318yescomplemented
376C2×C4⋊Q8—831no—
377C2×C4⋊Q8C2×D8311yescharacteristic
378C2×#125—831no—
379C2×#125—831no—
380C2×#125C2×D8311yescharacteristic
381C2×#125C2×D8311yescharacteristic
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—1661no—
386C2×C22⋊Q8—1661no—
387C2×C22⋊Q8—1661no—
388C2×C4×Q8C2×D8311yescharacteristic
389C2×C4×D4—831no—
390C2×C4×D4—831no—
391C2×C4×D4—831no—
392C2×C4×D4C2×D8311yescharacteristic
393C2×C4×D4C2×D8311yescharacteristic
394C2×C4×D4C2×D8311yescharacteristic
395C22×C4⋊C4—21no—
396C22×C4⋊C4—1661no—
397#501—838no—
398#501—838no—
399#499—838no—
400#478—838no—
401#478—838no—
402#478—838no—
403#478—838no—
404#474—838no—
405#474—838no—
406#446—838no—
407#442—838no—
408#442—838no—
409C4×D8—838no—
410C2×#107—831no—
411C2×#107—831no—
412C2×#107—831no—
413C2×#107—831no—
414C2×#107—831no—
415C2×#106—831no—
416C2×#106—831no—
417C2×#106—831no—
418C2×#106—831no—
419C2×C4⋊C8—831no—
420C2×C4⋊C8—831no—
421C2×C4⋊C8—831no—
422C2×#102—831no—
423C2×#102—831no—
424C2×#102—831no—
425C2×#102—831no—
426C2×#102—831no—
427C2×#102—831no—
428C2×#97—831no—
429C2×#97—831no—
430C2×C4×C8—831no—
431C22×Q8—21no—
432C22×Q8—1661no—
433C22×Q8C22⋊D8311yescharacteristic
434C22×D4—831no—
435C22×D4C22×D8311yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—1661no—
440C23×C4—1661no—
441C23×C4—1661no—
442C2×D8—838no—
443C2×D8—834no—
444C22×C8—831no—
445C22×C8—831no—
446C22×C8—831no—
447C22×C8—831no—
448C4⋊Q8—22no—
449C4⋊Q8—834no—
450C4⋊Q8—1662no—
451C4⋊Q8C22×D8314yes—
452#125—22no—
453#125—22no—
454#125—834no—
455#125—834no—
456#125—1662no—
457#125—1662no—
458#125C22×D8314yes—
459#125C22×D8314yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—1668no—
464C22⋊Q8—1668no—
465C22⋊Q8—1668no—
466C4×Q8C22⋊D8314yes—
467C4×Q8C22×D8314yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—834no—
472C4×D4—834no—
473C4×D4—834no—
474C4×D4—1662no—
475C4×D4—1662no—
476C4×D4—1662no—
477C4×D4C22×D8314yes—
478C4×D4C22×D8314yes—
479C4×D4C22×D8314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—1661no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4—1661no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1668no—
495C2×C4⋊C4C22⋊D8311yescharacteristic
496C2×C4⋊C4C22⋊D8311yescharacteristic
497C2×C4⋊C4C22⋊D8311yescharacteristic
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C4⋊C4C22×D8311yescharacteristic
500C2×C4⋊C4C22×D8311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1661no—
505C2×C22⋊C4—1661no—
506C2×C22⋊C4—1661no—
507C2×C42C22×D8311yescharacteristic
508C2×C42C22×D8311yescharacteristic
509C2×C42C22×D8311yescharacteristic
510#107—834no—
511#107—834no—
512#107—834no—
513#107—834no—
514#107—834no—
515#106—834no—
516#106—834no—
517#106—834no—
518#106—834no—
519C4⋊C8—834no—
520C4⋊C8—834no—
521C4⋊C8—834no—
522#102—834no—
523#102—834no—
524#102—834no—
525#102—834no—
526#102—834no—
527#102—834no—
528#97—834no—
529#97—834no—
530C4×C8—834no—
531C24—21no—
532C24—1661no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—6642no—
537C2×Q8—1664no—
538C2×Q8C2×C22⋊D8314yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—834no—
542C2×D4—832no—
543C2×D4—1661no—
544C2×D4—1662no—
545C2×D4Q8×D8314yes—
546C2×D4C23×D8312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—3324no—
557C22×C4—6642no—
558C22×C4—6642no—
559C22×C4—1661no—
560C22×C4—1661no—
561C22×C4—1661no—
562C22×C4—1664no—
563C22×C4—1664no—
564C22×C4—1664no—
565C22×C4C2×C22⋊D8311yescharacteristic
566C22×C4C2×C22⋊D8311yescharacteristic
567C22×C4C2×C22⋊D8311yescharacteristic
568C22×C4C2×C22⋊D8311yescharacteristic
569C22×C4C2×C22⋊D8311yescharacteristic
570C22×C4C2×C22⋊D8311yescharacteristic
571C22×C4C23×D8311yescharacteristic
572D8—8316no—
573C2×C8—834no—
574C2×C8—832no—
575C2×C8—832no—
576C2×C8—832no—
577C2×C8—832no—
578C2×C8—1662no—
579C2×C8—1662no—
580C2×C8—1662no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—832no—
590C4⋊C4—832no—
591C4⋊C4—832no—
592C4⋊C4—1661no—
593C4⋊C4—1661no—
594C4⋊C4—1661no—
595C4⋊C4—1664no—
596C4⋊C4—1664no—
597C4⋊C4—1664no—
598C4⋊C4—1664no—
599C4⋊C4—1664no—
600C4⋊C4C2×C22⋊D8314yes—
601C4⋊C4C2×C22⋊D8314yes—
602C4⋊C4C2×C22⋊D8314yes—
603C4⋊C4C23×D8312yes—
604C4⋊C4C23×D8312yes—
605C4⋊C4C23×D8312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C22⋊C4—1664no—
612C42C2×C22⋊D8312yes—
613C42C2×C22⋊D8312yes—
614C42C2×C22⋊D8312yes—
615C42C23×D8312yes—
616C42C23×D8312yes—
617C42C23×D8312yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—3322no—
623C23—3322no—
624C23—1664no—
625C23—1662no—
626C23C22×C22⋊D8311yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—6644no—
630D4—24no—
631D4—22no—
632D4—834no—
633D4—1664no—
634D4—1662no—
635D4C2×Q8×D8314yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—3328no—
652C2×C4—3322no—
653C2×C4—3322no—
654C2×C4—3322no—
655C2×C4—6644no—
656C2×C4—6644no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4C22×C22⋊D8312yes—
661C2×C4C22×C22⋊D8312yes—
662C2×C4C22×C22⋊D8312yes—
663C2×C4C22×C22⋊D8312yes—
664C2×C4C22×C22⋊D8312yes—
665C2×C4C22×C22⋊D8312yes—
666C2×C4C22×C22⋊D8311yescharacteristic
667C2×C4C2×Q8×D8312yes—
668C2×C4#1458184012yes—
669C2×C4C24×D8311yescharacteristic
670C8—834no—
671C8—1662no—
672C8—1662no—
673C8—1662no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—3322no—
679C22—3328no—
680C22—3322no—
681C22—1664no—
682C22Q8×C22⋊D8312yes—
683C22#1912849912yes—
684C22#1912850412yes—
685C22C23×C22⋊D8311yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—3322no—
696C4—3322no—
697C4—3322no—
698C4Q8×C22⋊D8312yes—
699C4C22×Q8×D8311yescharacteristic
700C4C2×#1458184011yescharacteristic
701C2—44no—
702C2—3324no—
703C2#2492041714yesdirect product factor
704C2C2×Q8×C22⋊D8311yescharacteristic
705C2C2×#1912849911yescharacteristic
706C2C2×#1912850411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#554×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050575C22
hypercenterC2×#554D83
hypocenterC83C2×#3389
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#19128411C2semidirect
2. #24920417C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128107C2semidirect
5. C2×#19128100C2semidirect
6. C2×#19128001C2semidirect
7. C2×#19128001C2semidirect
8. C2×#19127998C2semidirect
9. C2×#19127998C2semidirect
10. C2×#19127981C2semidirect
11. C2×#19127978C2semidirect
12. C2×#19127832C2semidirect
16. C2×#554×C83C2semidirect
19. #19128411C22semidirect
30. #19128111C22semidirect
31. #19128107C22semidirect
32. #19128100C22semidirect
33. #19128001C22semidirect
34. #19128001C22semidirect
35. #19127998C22semidirect
36. #19127998C22semidirect
37. #19127981C22semidirect
38. #19127978C22semidirect
39. #19127832C22semidirect
65. #554×C83C22semidirect
82. C2×#13050575Q8semidirect
193. #13050575C2×Q8semidirect
349. C2×C83#3389semidirect
355. C2×#554D83semidirect
370. C83C2×#3389semidirect
375. #554C2×D83semidirect
703. C2#24920417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284112
#249204172
C2×#191281112
C2×#191281072
C2×#191281002
C2×#191280012
C2×#191279982
C2×#191279812
C2×#191279782
C2×#191278322
C2×#191278112
C2×C4×#130505752
C2×#554×C832
C2×#338983