Finite Group Databasebeta

← C2×#24920305 #36284201

Subgroups — C2×#24920305 #36284201

Order 21248.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128424C211yesmaximal, characteristic
2#24920305C2116yesmaximal, direct product factor
3C2×#19128071C211yesmaximal, characteristic, complemented
4C2×#19128063C211yesmaximal, characteristic
5C2×#19128058C211yesmaximal, characteristic
6C2×#19128005C211yesmaximal, characteristic, complemented
7C2×#19127993C211yesmaximal, characteristic, complemented
8C2×#19127998C211yesmaximal, characteristic
9C2×#19127923C211yesmaximal, characteristic
10C2×#19127923C211yesmaximal, characteristic
11C2×#19127911C211yesmaximal, characteristic, complemented
12C2×#19127832C211yesmaximal, characteristic, complemented
13C2×#19127806C211yesmaximal, characteristic, complemented
14C2×#19127799C211yesmaximal, characteristic
15C2×C4×#13050580C211yesmaximal, characteristic, complemented
16C2×#557×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050580C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20#19128424—24no—
21#19128424C2218yes—
22C2×#14581792C2211yescharacteristic
23C2×#14581787—21no—
24C2×#14581787—21no—
25C2×#14581780C2211yescharacteristic
26C2×#14581780C2211yescharacteristic
27C2×#14581768—21no—
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×Dic166C2211yescharacteristic
30C2×C4×D332C2211yescharacteristic
31C2×#14581750—21no—
32#19128071C2218yescomplemented
33#19128063C2218yes—
34#19128058C2218yes—
35#19128005C2218yescomplemented
36#19127998C2218yes—
37#19127993C2218yescomplemented
38#19127923C2218yes—
39#19127923C2218yes—
40#19127911C2218yescomplemented
41#19127832C2218yescomplemented
42#19127806C2218yescomplemented
43#19127799C2218yes—
44C4×#13050580C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49C2×C4⋊(C83⋊C8)C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581715C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581715C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581715C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#557×C83—24no—
65#557×C83C2218yescomplemented
66C2×C4⋊Q8×C83—21no—
67C2×C4⋊Q8×C83C2211yescharacteristic
68C2×#125×C83—21no—
69C2×#125×C83—21no—
70C2×#125×C83C2211yescharacteristic
71C2×#125×C83C2211yescharacteristic
72C2×C4×Q8×C83—21no—
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×Q8×C83C2211yescharacteristic
76C2×C4×Q8×C83C2211yescharacteristic
77C22×Dic166C2311yescharacteristic
78C22×Dic166C2311yescharacteristic
79C22×D332C2311yescharacteristic
80C22×C4×D83—21no—
81C2×#13050580—24no—
82C2×#13050580—24no—
83C2×#13050580C2314yes—
84C2×#13050580C2314yes—
85C2×#13050577—24no—
86C2×#13050577C2314yes—
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91#14581792—22no—
92#14581792C2314yes—
93#14581787—28no—
94#14581787—28no—
95#14581780—22no—
96#14581780—22no—
97#14581780C2314yes—
98#14581780C2314yes—
99#14581768—28no—
100C4×Dic166—22no—
101C4×Dic166—22no—
102C4×Dic166C2314yes—
103C4×Dic166C2314yes—
104C4×D332—22no—
105C4×D332C2314yes—
106#14581750—28no—
107C2×C4⋊Dic83—21no—
108C2×C4⋊Dic83—21no—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×Dic83⋊C4—21no—
111C2×Dic83⋊C4—21no—
112C2×(C2×D83)⋊C4—21no—
113C2×(C2×D83)⋊C4—21no—
114C2×(C2×D83)⋊C4—21no—
115C2×(C2×D83)⋊C4—21no—
116C2×(C2×D83)⋊C4—21no—
117C2×C4×Dic83—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581725C2314yes—
121#14581723C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123C4⋊(C83⋊C8)C2314yes—
124C4⋊(C83⋊C8)C2314yes—
125#14581716C2314yes—
126#14581715C2314yes—
127#14581715C2314yes—
128#14581715C2314yes—
129#14581715C2314yes—
130#14581715C2314yes—
131#14581715C2314yes—
132#14581712C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135#14581703C2314yes—
136#14581703C2314yes—
137C4×C83⋊C8C2314yes—
138C22×Q8×C83—21no—
139C22×Q8×C83D411yescharacteristic
140C22×Q8×C83C2311yescharacteristic
141C4⋊Q8×C83—28no—
142C4⋊Q8×C83—22no—
143C4⋊Q8×C83C2314yes—
144#125×C83—28no—
145#125×C83—28no—
146#125×C83—22no—
147#125×C83—22no—
148#125×C83C2314yes—
149#125×C83C2314yes—
150C4×Q8×C83—28no—
151C4×Q8×C83—22no—
152C4×Q8×C83—22no—
153C4×Q8×C83—22no—
154C4×Q8×C83D414yes—
155C4×Q8×C83C2314yes—
156C4×Q8×C83C2314yes—
157C4×Q8×C83C2314yes—
158C4×Q8×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—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C42×C83—21no—
174C2×C42×C83—21no—
175C2×C42×C83—21no—
176C2×C42×C83C2311yescharacteristic
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2311yescharacteristic
179C23×D83—21no—
180C2×Dic166—22no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—22no—
184C2×Dic166—21no—
185C2×Dic166—21no—
186C2×Dic166C2412yes—
187C2×Dic166C2412yes—
188C2×D332—22no—
189C2×D332—22no—
190C2×D332—21no—
191C2×D332C2412yes—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C2×C4×D83—24no—
196C2×C4×D83—44no—
197#13050580—28no—
198#13050580—28no—
199#13050577—28no—
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—24no—
209C4⋊Dic83—24no—
210C4⋊Dic83—21no—
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—
218(C2×D83)⋊C4—24no—
219C4×Dic83—24no—
220C4×Dic83—24no—
221C2×Q8×C83—21no—
222C2×Q8×C83—24no—
223C2×Q8×C83—22no—
224C2×Q8×C83—42no—
225C2×Q8×C83—44no—
226C2×Q8×C83C2×D414yes—
227C2×Q8×C83#4114yes—
228C2×Q8×C83C2412yes—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83C2×D411yescharacteristic
234C22×C4×C83C2×D411yescharacteristic
235C22×C4×C83C2×D411yescharacteristic
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2×D411yescharacteristic
238C22×C4×C83C2×D411yescharacteristic
239C22×C4×C83C2411yescharacteristic
240C4⋊C4×C83—24no—
241C4⋊C4×C83—24no—
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×C83—21no—
251C4⋊C4×C83C2×D414yes—
252C4⋊C4×C83C2×D414yes—
253C4⋊C4×C83C2×D414yes—
254C4⋊C4×C83C2412yes—
255C4⋊C4×C83C2412yes—
256C4⋊C4×C83C2412yes—
257C42×C83—24no—
258C42×C83—24no—
259C42×C83—24no—
260C42×C83C2×D412yes—
261C42×C83C2×D412yes—
262C42×C83C2×D412yes—
263C42×C83C2412yes—
264C42×C83C2412yes—
265C42×C83C2412yes—
266C23×C83C22×D411yescharacteristic
267C22×D83—22no—
268C22×D83—42no—
269C22×D83—42no—
270C22×D83—42no—
271Q8×C83—24no—
272Q8×C83—22no—
273Q8×C83—44no—
274Q8×C83—48no—
275Q8×C83C2×#4114yes—
276C2×C4×C83—24no—
277C2×C4×C83—22no—
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—42no—
288C2×C4×C83—42no—
289C2×C4×C83—42no—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D412yes—
292C2×C4×C83C22×D412yes—
293C2×C4×C83C22×D412yes—
294C2×C4×C83C22×D412yes—
295C2×C4×C83C22×D412yes—
296C2×C4×C83C22×D411yescharacteristic
297C2×C4×C83C2×#4112yes—
298C2×C4×C832−1+412yes—
299C2×C4×C83C2511yescharacteristic
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—42no—
304C2×Dic83—42no—
305C2×Dic83—42no—
306D332—22no—
307D332—22no—
308D332—42no—
309C4×D83—48no—
310Dic166—22no—
311Dic166—22no—
312Dic166—22no—
313Dic166—22no—
314Dic166—42no—
315Dic166—42no—
316C83⋊C8—22no—
317C83⋊C8—22no—
318C83⋊C8—22no—
319C83⋊C8—22no—
320C22×C83#54812yes—
321C22×C83#57512yes—
322C22×C83#57812yes—
323C22×C83C23×D411yescharacteristic
324C2×D83—42no—
325C2×D83—42no—
326C2×D83—42no—
327C2×D83—84no—
328C4×C83—24no—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—22no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83—42no—
338C4×C83#54812yes—
339C4×C83C22×#4111yescharacteristic
340C4×C83C2×2−1+411yescharacteristic
341Dic83—42no—
342Dic83—42no—
343Dic83—42no—
344C2×#3377—831nomaximal, Sylow
345C2×C83#337714yescomplemented
346C2×C83C2×#54811yescharacteristic
347C2×C83C2×#57511yescharacteristic
348C2×C83C2×#57811yescharacteristic
349D83—82no—
350C2×#557D8311yescharacteristic, complemented
351C2×#556—831no—
352#3377—8316no—
353C2×#491—831no—
354C2×#489—831no—
355C2×#488—831no—
356C2×#479—831no—
357C2×#477—831no—
358C2×#478—831no—
359C2×#464—831no—
360C2×#464—831no—
361C2×#462—831no—
362C2×#446—831no—
363C2×#441—831no—
364C2×#440—831no—
365C2×C4×Q16—831no—
366C83C2×#337711yescharacteristic, complemented, Sylow
367C22×Q16—831no—
368C22×Q16—831no—
369C22×SD16—831no—
370#557—24no—
371#557C2×D8318yescomplemented
372#556—838no—
373#556—1664no—
374C2×C4⋊Q8—21no—
375C2×C4⋊Q8—831no—
376C2×C4⋊Q8C2×D8311yescharacteristic
377C2×#126—1661no—
378C2×#126—1661no—
379C2×#125—21no—
380C2×#125—21no—
381C2×#125C2×D8311yescharacteristic
382C2×#125C2×D8311yescharacteristic
383C2×#124—831no—
384C2×#124—831no—
385C2×C22⋊Q8—1661no—
386C2×C4×Q8—21no—
387C2×C4×Q8—831no—
388C2×C4×Q8—831no—
389C2×C4×Q8C2×D8311yescharacteristic
390C2×C4×Q8C2×D8311yescharacteristic
391C2×C4×Q8C2×D8311yescharacteristic
392C2×C4×Q8C2×D8311yescharacteristic
393C2×C4×D4—831no—
394C2×#117—1661no—
395#491—838no—
396#489—838no—
397#488—838no—
398#479—838no—
399#478—838no—
400#477—838no—
401#464—838no—
402#464—838no—
403#462—838no—
404#446—838no—
405#441—838no—
406#440—838no—
407C4×Q16—838no—
408C2×#107—831no—
409C2×#107—831no—
410C2×#106—831no—
411C2×C4⋊C8—831no—
412C2×C4⋊C8—831no—
413C2×C4⋊C8—831no—
414C2×#103—831no—
415C2×#103—831no—
416C2×#103—831no—
417C2×#103—831no—
418C2×#103—831no—
419C2×#103—831no—
420C2×#103—831no—
421C2×#102—831no—
422C2×#102—831no—
423C2×#102—831no—
424C2×#97—831no—
425C2×#97—831no—
426C2×C4×C8—831no—
427C22×Q8—21no—
428C22×Q8—831no—
429C22×Q8—831no—
430C22×Q8C22⋊D8311yescharacteristic
431C22×Q8C22×D8311yescharacteristic
432C22×D4—831no—
433C23×C4—1661no—
434C2×Q16—834no—
435C2×Q16—834no—
436C2×Q16—1664no—
437C2×Q16—1664no—
438C2×SD16—834no—
439C2×SD16—1664no—
440C22×C8—831no—
441C22×C8—831no—
442C22×C8—831no—
443C22×C8—831no—
444C4⋊Q8—28no—
445C4⋊Q8—22no—
446C4⋊Q8—834no—
447C4⋊Q8—1662no—
448C4⋊Q8C22×D8314yes—
449#126—1668no—
450#126—1668no—
451#125—28no—
452#125—28no—
453#125—22no—
454#125—22no—
455#125C22×D8314yes—
456#125C22×D8314yes—
457#124—834no—
458#124—834no—
459#124—1662no—
460#124—1662no—
461C22⋊Q8—1668no—
462C4×Q8—28no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—834no—
467C4×Q8—834no—
468C4×Q8—1662no—
469C4×Q8—1662no—
470C4×Q8C22⋊D8314yes—
471C4×Q8C22×D8314yes—
472C4×Q8C22×D8314yes—
473C4×Q8C22×D8314yes—
474C4×Q8C22×D8314yes—
475C4×D4—834no—
476C4×D4—1662no—
477#117—1668no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—1661no—
488C2×C4⋊C4—1661no—
489C2×C4⋊C4—1661no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4C22⋊D8311yescharacteristic
492C2×C4⋊C4C22⋊D8311yescharacteristic
493C2×C4⋊C4C22⋊D8311yescharacteristic
494C2×C4⋊C4C22×D8311yescharacteristic
495C2×C4⋊C4C22×D8311yescharacteristic
496C2×C4⋊C4C22×D8311yescharacteristic
497C2×C22⋊C4—1661no—
498C2×C22⋊C4—1661no—
499C2×C22⋊C4—1661no—
500C2×C22⋊C4—1661no—
501C2×C22⋊C4—1661no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—1661no—
506C2×C42—1661no—
507C2×C42C22×D8311yescharacteristic
508C2×C42C22×D8311yescharacteristic
509C2×C42C22×D8311yescharacteristic
510#107—834no—
511#107—834no—
512#106—834no—
513C4⋊C8—834no—
514C4⋊C8—834no—
515C4⋊C8—834no—
516#103—834no—
517#103—834no—
518#103—834no—
519#103—834no—
520#103—834no—
521#103—834no—
522#103—834no—
523#102—834no—
524#102—834no—
525#102—834no—
526#97—834no—
527#97—834no—
528C4×C8—834no—
529C24—1661no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—832no—
536C2×Q8—832no—
537C2×Q8—1662no—
538C2×Q8—1662no—
539C2×Q8—1662no—
540C2×Q8—1662no—
541C2×Q8—1661no—
542C2×Q8—1661no—
543C2×Q8C2×C22⋊D8314yes—
544C2×Q8#1305059114yes—
545C2×Q8C23×D8312yes—
546C2×D4—832no—
547C2×D4—1661no—
548C2×D4—1662no—
549C2×D4—1662no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—3324no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1661no—
558C22×C4—1664no—
559C22×C4C2×C22⋊D8311yescharacteristic
560C22×C4C2×C22⋊D8311yescharacteristic
561C22×C4C2×C22⋊D8311yescharacteristic
562C22×C4C2×C22⋊D8311yescharacteristic
563C22×C4C2×C22⋊D8311yescharacteristic
564C22×C4C2×C22⋊D8311yescharacteristic
565C22×C4C23×D8311yescharacteristic
566Q16—1668no—
567Q16—1668no—
568SD16—1668no—
569C2×C8—832no—
570C2×C8—832no—
571C2×C8—832no—
572C2×C8—832no—
573C2×C8—1662no—
574C2×C8—1662no—
575C2×C8—1662no—
576C2×C8—1662no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—832no—
589C4⋊C4—1661no—
590C4⋊C4—1664no—
591C4⋊C4—1664no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4C2×C22⋊D8314yes—
595C4⋊C4C2×C22⋊D8314yes—
596C4⋊C4C2×C22⋊D8314yes—
597C4⋊C4C23×D8312yes—
598C4⋊C4C23×D8312yes—
599C4⋊C4C23×D8312yes—
600C22⋊C4—1664no—
601C22⋊C4—1664no—
602C22⋊C4—1664no—
603C22⋊C4—1664no—
604C22⋊C4—1664no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—1664no—
609C42—1664no—
610C42C2×C22⋊D8312yes—
611C42C2×C22⋊D8312yes—
612C42C2×C22⋊D8312yes—
613C42C23×D8312yes—
614C42C23×D8312yes—
615C42C23×D8312yes—
616C23—3322no—
617C23—3322no—
618C23—3322no—
619C23—1662no—
620C23C22×C22⋊D8311yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—44no—
624Q8—48no—
625Q8—3322no—
626Q8—3322no—
627Q8—1662no—
628Q8—1662no—
629Q8—1662no—
630Q8—1662no—
631Q8C2×#1305059114yes—
632D4—3322no—
633D4—1662no—
634D4—1662no—
635C2×C4—24no—
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—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—3328no—
650C2×C4—3322no—
651C2×C4—3322no—
652C2×C4—3322no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4C22×C22⋊D8312yes—
657C2×C4C22×C22⋊D8312yes—
658C2×C4C22×C22⋊D8312yes—
659C2×C4C22×C22⋊D8312yes—
660C2×C4C22×C22⋊D8312yes—
661C2×C4C22×C22⋊D8312yes—
662C2×C4C22×C22⋊D8311yescharacteristic
663C2×C4C2×#1305059112yes—
664C2×C4#1458184012yes—
665C2×C4C24×D8311yescharacteristic
666C8—1662no—
667C8—1662no—
668C8—1662no—
669C8—1662no—
670C22—3322no—
671C22—3322no—
672C22—3322no—
673C22—6644no—
674C22#1912836212yes—
675C22#1912849912yes—
676C22#1912851612yes—
677C22C23×C22⋊D8311yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—3322no—
689C4—3322no—
690C4—3322no—
691C4#1912836212yes—
692C4C22×#1305059111yescharacteristic
693C4C2×#1458184011yescharacteristic
694C2—6642no—
695C2#2492030514yesdirect product factor
696C2C2×#1912836211yescharacteristic
697C2C2×#1912849911yescharacteristic
698C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#557×C83C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenterC2×#557D83
hypocenterC83C2×#3377
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #24920305C2direct (N × H)
3. C2×#19128071C2semidirect
6. C2×#19128005C2semidirect
7. C2×#19127993C2semidirect
11. C2×#19127911C2semidirect
12. C2×#19127832C2semidirect
13. C2×#19127806C2semidirect
15. C2×C4×#13050580C2semidirect
16. C2×#557×C83C2semidirect
32. #19128071C22semidirect
35. #19128005C22semidirect
37. #19127993C22semidirect
40. #19127911C22semidirect
41. #19127832C22semidirect
42. #19127806C22semidirect
44. C4×#13050580C22semidirect
65. #557×C83C22semidirect
345. C2×C83#3377semidirect
350. C2×#557D83semidirect
366. C83C2×#3377semidirect
371. #557C2×D83semidirect
695. C2#24920305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284242
#249203052
C2×#191280712
C2×#191280632
C2×#191280582
C2×#191280052
C2×#191279932
C2×#191279982
C2×#191279232
C2×#191279112
C2×#191278322
C2×#191278062
C2×#191277992
C2×C4×#130505802
C2×#557×C832
C2×#337783