Finite Group Databasebeta

← C2×#24918761 #36276641

Subgroups — C2×#24918761 #36276641

Order 21248.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic
2#24918761C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128097C211yesmaximal, characteristic, complemented
5C2×#19128063C211yesmaximal, characteristic, complemented
6C2×#19128058C211yesmaximal, characteristic, complemented
7C2×#19128019C211yesmaximal, characteristic
8C2×#19128042C211yesmaximal, characteristic, complemented
9C2×#19128025C211yesmaximal, characteristic
10C2×#19128031C211yesmaximal, characteristic, complemented
11C2×#19128005C211yesmaximal, characteristic, complemented
12C2×#19127983C211yesmaximal, characteristic, complemented
13C2×#19127998C211yesmaximal, characteristic, complemented
14C2×#19127988C211yesmaximal, characteristic, complemented
15C2×#19127762C211yesmaximal, characteristic, complemented
16C2×#544×C83C211yesmaximal, characteristic, complemented
17#19128322—24no—
18#19128322C2218yes—
19C2×#14581792C2211yescharacteristic
20C2×#14581787—21no—
21C2×#14581780C2211yescharacteristic
22C2×#14581778—21no—
23C2×#14581774—21no—
24C2×#14581771C2211yescharacteristic
25C2×#14581770—21no—
26C2×#14581766C2211yescharacteristic
27C2×C4×Dic166C2211yescharacteristic
28C2×C4×D332C2211yescharacteristic
29#19128111C2218yescomplemented
30#19128097C2218yescomplemented
31#19128063C2218yescomplemented
32#19128058C2218yescomplemented
33#19128042C2218yescomplemented
34#19128031C2218yescomplemented
35#19128025C2218yes—
36#19128019C2218yes—
37#19128005C2218yescomplemented
38#19127998C2218yescomplemented
39#19127988C2218yescomplemented
40#19127983C2218yescomplemented
41#19127762C2218yescomplemented
42C2×#14581725C2211yescharacteristic
43C2×#14581725C2211yescharacteristic
44C2×#14581723C2211yescharacteristic
45C2×#14581723C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×C4⋊(C83⋊C8)C2211yescharacteristic
52C2×#14581715C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581715C2211yescharacteristic
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×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×D332C2311yescharacteristic
80C22×C22⋊D83—21no—
81C22×C4×D83—21no—
82C22×C83⋊C8C2311yescharacteristic
83C22×C83⋊C8C2311yescharacteristic
84C22×C83⋊C8C2311yescharacteristic
85C22×C83⋊C8C2311yescharacteristic
86#14581792—22no—
87#14581792C2314yes—
88#14581787—28no—
89#14581780—22no—
90#14581780C2314yes—
91#14581778—28no—
92#14581774—28no—
93#14581771—22no—
94#14581771C2314yes—
95#14581770—28no—
96#14581766—22no—
97#14581766C2314yes—
98C4×Dic166—22no—
99C4×Dic166C2314yes—
100C4×D332—22no—
101C4×D332C2314yes—
102C2×C4⋊Dic83—21no—
103C2×C4⋊Dic83C2311yescharacteristic
104C2×C4⋊Dic83C2311yescharacteristic
105C2×Dic83⋊C4—21no—
106C2×Dic83⋊C4—21no—
107C2×C22⋊Dic83—21no—
108C2×(C2×D83)⋊C4—21no—
109C2×(C2×D83)⋊C4—21no—
110C2×(C2×D83)⋊C4—21no—
111C2×(C2×D83)⋊C4—21no—
112C2×C4×Dic83—21no—
113#14581725C2314yes—
114#14581725C2314yes—
115#14581723C2314yes—
116#14581723C2314yes—
117#14581723C2314yes—
118#14581723C2314yes—
119#14581723C2314yes—
120#14581723C2314yes—
121C4⋊(C83⋊C8)C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123#14581715C2314yes—
124#14581715C2314yes—
125#14581715C2314yes—
126#14581715C2314yes—
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—
177C2×Dic166—22no—
178C2×Dic166—22no—
179C2×Dic166—21no—
180C2×Dic166—24no—
181C2×Dic166—82no—
182C2×Dic166C2412yes—
183C2×D332—22no—
184C2×D332—22no—
185C2×D332—21no—
186C2×D332C2412yes—
187C2×C22⋊D83—24no—
188C2×C22⋊D83—82no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C2×C4×D83—24no—
193C2×C4×D83—82no—
194C2×C83⋊C8—22no—
195C2×C83⋊C8—22no—
196C2×C83⋊C8—22no—
197C2×C83⋊C8—22no—
198C2×C83⋊C8C2412yes—
199C2×C83⋊C8C2412yes—
200C2×C83⋊C8C2412yes—
201C2×C83⋊C8C2412yes—
202C4⋊Dic83—21no—
203C4⋊Dic83—21no—
204C4⋊Dic83—24no—
205C4⋊Dic83C2412yes—
206C4⋊Dic83C2412yes—
207Dic83⋊C4—24no—
208Dic83⋊C4—24no—
209C22⋊Dic83—24no—
210(C2×D83)⋊C4—24no—
211(C2×D83)⋊C4—24no—
212(C2×D83)⋊C4—24no—
213(C2×D83)⋊C4—24no—
214C4×Dic83—24no—
215C24×C83C2×D411yescharacteristic
216C2×Q8×C83—24no—
217C2×Q8×C83—24no—
218C2×Q8×C83—82no—
219C2×Q8×C83—82no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—24no—
227C22×C4×C83—82no—
228C22×C4×C83C2×D412yes—
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2×D411yescharacteristic
232C22×C4×C83C2×D411yescharacteristic
233C22×C4×C83C2×D411yescharacteristic
234C22×C4×C83C2412yes—
235C22×C4×C83C2411yescharacteristic
236C4⋊C4×C83—24no—
237C4⋊C4×C83—21no—
238C4⋊C4×C83—21no—
239C4⋊C4×C83—24no—
240C4⋊C4×C83—24no—
241C4⋊C4×C83—24no—
242C4⋊C4×C83—24no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—21no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83C2×D414yes—
248C4⋊C4×C83C2×D414yes—
249C4⋊C4×C83C2412yes—
250C4⋊C4×C83C2412yes—
251C4⋊C4×C83C2412yes—
252C4⋊C4×C83C2412yes—
253C22⋊C4×C83—24no—
254C22⋊C4×C83C2×D414yes—
255C22⋊C4×C83C2×D414yes—
256C42×C83—24no—
257C42×C83C2×D412yes—
258C42×C83C2×D412yes—
259C42×C83C2412yes—
260C42×C83C2412yes—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83C22×D412yes—
265C23×C83C22×D411yescharacteristic
266C22×D83—22no—
267C22×D83—42no—
268C22×D83—42no—
269C22×D83—42no—
270Q8×C83—84no—
271Q8×C83—84no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—24no—
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—42no—
285C2×C4×C83—42no—
286C2×C4×C83—42no—
287C2×C4×C83—42no—
288C2×C4×C83—84no—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D412yes—
292C2×C4×C83C22×D412yes—
293C2×C4×C83C22×D412yes—
294C2×C4×C83C22×D411yescharacteristic
295C2×C4×C832−1+412yes—
296C2×C4×C832−1+412yes—
297C2×C4×C83C2511yescharacteristic
298C22⋊D83—84no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—42no—
303C2×Dic83—42no—
304C2×Dic83—42no—
305D332—22no—
306D332—22no—
307D332—42no—
308C4×D83—84no—
309Dic166—22no—
310Dic166—22no—
311Dic166—42no—
312Dic166—84no—
313C83⋊C8—22no—
314C83⋊C8—22no—
315C83⋊C8—22no—
316C83⋊C8—22no—
317C22×C83—22no—
318C22×C83—22no—
319C22×C83—22no—
320C22×C83—44no—
321C22×C83#53612yes—
322C22×C83#57712yes—
323C22×C83#57712yes—
324C22×C83C23×D411yescharacteristic
325C2×D83—42no—
326C2×D83—42no—
327C2×D83—42no—
328C2×D83—84no—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—42no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83—42no—
338C4×C83#53612yes—
339C4×C83C2×2−1+411yescharacteristic
340C4×C83C2×2−1+411yescharacteristic
341Dic83—42no—
342Dic83—42no—
343Dic83—42no—
344C2×#3244—831nomaximal, Sylow
345C2×C83—42no—
346C2×C83#324414yescomplemented
347C2×C83C2×#53611yescharacteristic
348C2×C83C2×#57711yescharacteristic
349C2×C83C2×#57711yescharacteristic
350D83—82no—
351C2×#544D8311yescharacteristic, complemented
352C2×#542—831no—
353#3244—8316no—
354C2×#501—831no—
355C2×#498—831no—
356C2×#489—831no—
357C2×#488—831no—
358C2×#481—831no—
359C2×#485—831no—
360C2×#482—831no—
361C2×#483—831no—
362C2×#479—831no—
363C2×#475—831no—
364C2×#478—831no—
365C2×#476—831no—
366C2×#433—831no—
367C83C2×#324411yescharacteristic, complemented, Sylow
368#544—24no—
369#544C2×D8318yescomplemented
370#542—838no—
371#542—1664no—
372C2×C4⋊Q8—21no—
373C2×C4⋊Q8—831no—
374C2×C4⋊Q8C2×D8311yescharacteristic
375C2×C4⋊Q8C2×D8311yescharacteristic
376C2×#126—1661no—
377C2×#125—21no—
378C2×#125C2×D8311yescharacteristic
379C2×#125C2×D8311yescharacteristic
380C2×#124—831no—
381C2×#124—1661no—
382C2×#123—1661no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—831no—
386C2×C22⋊Q8—1661no—
387C2×#121—831no—
388C2×C4×Q8—831no—
389C2×C4×D4—831no—
390C2×#117C2×D8311yescharacteristic
391C2×#117C2×D8311yescharacteristic
392C22×C4⋊C4C2×D8311yescharacteristic
393#501—838no—
394#498—838no—
395#489—838no—
396#488—838no—
397#485—838no—
398#483—838no—
399#482—838no—
400#481—838no—
401#479—838no—
402#478—838no—
403#476—838no—
404#475—838no—
405#433—838no—
406C2×#107—831no—
407C2×#107—831no—
408C2×#106—831no—
409C2×#106—831no—
410C2×#106—831no—
411C2×#106—831no—
412C2×#106—831no—
413C2×#106—831no—
414C2×C4⋊C8—831no—
415C2×C4⋊C8—831no—
416C2×#103—831no—
417C2×#103—831no—
418C2×#103—831no—
419C2×#103—831no—
420C2×#102—831no—
421C2×#102—831no—
422C2×#102—831no—
423C2×#102—831no—
424C2×C22⋊C8—831no—
425C2×C22⋊C8—831no—
426C2×#97—831no—
427C2×C4×C8—831no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—831no—
431C22×Q8—1661no—
432C22×D4—831no—
433C22×D4—1661no—
434C23×C4—21no—
435C23×C4—1661no—
436C23×C4C22×D8311yescharacteristic
437C22×C8—831no—
438C22×C8—831no—
439C22×C8—831no—
440C22×C8—831no—
441C4⋊Q8—28no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—834no—
445C4⋊Q8—1662no—
446C4⋊Q8C22×D8314yes—
447C4⋊Q8C22×D8314yes—
448#126—1668no—
449#125—28no—
450#125—22no—
451#125—22no—
452#125C22×D8314yes—
453#125C22×D8314yes—
454#124—834no—
455#124—1668no—
456#124—1662no—
457#123—1668no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—834no—
461C22⋊Q8—1662no—
462C22⋊Q8—1668no—
463#121—834no—
464#121—1662no—
465C4×Q8—834no—
466C4×Q8—1662no—
467C4×D4—834no—
468C4×D4—1662no—
469#117—22no—
470#117C22⋊D8314yes—
471#117C22×D8314yes—
472#117C22×D8314yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4—1661no—
485C2×C4⋊C4—1661no—
486C2×C4⋊C4C22⋊D8311yescharacteristic
487C2×C4⋊C4C22⋊D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1661no—
495C2×C22⋊C4—1661no—
496C2×C22⋊C4—1661no—
497C2×C22⋊C4—1661no—
498C2×C22⋊C4—1661no—
499C2×C22⋊C4C22⋊D8311yescharacteristic
500C2×C22⋊C4C22⋊D8311yescharacteristic
501C2×C42—21no—
502C2×C42—1661no—
503C2×C42C22×D8311yescharacteristic
504C2×C42C22×D8311yescharacteristic
505#107—834no—
506#107—834no—
507#106—834no—
508#106—834no—
509#106—834no—
510#106—834no—
511#106—834no—
512#106—834no—
513C4⋊C8—834no—
514C4⋊C8—834no—
515#103—834no—
516#103—834no—
517#103—834no—
518#103—834no—
519#102—834no—
520#102—834no—
521#102—834no—
522#102—834no—
523C22⋊C8—834no—
524C22⋊C8—834no—
525#97—834no—
526C4×C8—834no—
527C24—1661no—
528C24C2×C22⋊D8311yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—832no—
534C2×Q8—6642no—
535C2×Q8—1662no—
536C2×Q8—1662no—
537C2×Q8—1661no—
538C2×Q8—1664no—
539C2×D4—832no—
540C2×D4—6642no—
541C2×D4—1664no—
542C2×D4—1661no—
543C2×D4—1662no—
544C2×D4—1662no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—6642no—
554C22×C4—1661no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1664no—
558C22×C4C2×C22⋊D8312yes—
559C22×C4C2×C22⋊D8311yescharacteristic
560C22×C4C2×C22⋊D8311yescharacteristic
561C22×C4C2×C22⋊D8311yescharacteristic
562C22×C4C2×C22⋊D8311yescharacteristic
563C22×C4C2×C22⋊D8311yescharacteristic
564C22×C4C23×D8312yes—
565C22×C4C23×D8311yescharacteristic
566C2×C8—832no—
567C2×C8—832no—
568C2×C8—832no—
569C2×C8—832no—
570C2×C8—1662no—
571C2×C8—1662no—
572C2×C8—1662no—
573C2×C8—1662no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—832no—
586C4⋊C4—832no—
587C4⋊C4—1661no—
588C4⋊C4—1661no—
589C4⋊C4—1664no—
590C4⋊C4—1664no—
591C4⋊C4—1664no—
592C4⋊C4C2×C22⋊D8314yes—
593C4⋊C4C2×C22⋊D8314yes—
594C4⋊C4C23×D8312yes—
595C4⋊C4C23×D8312yes—
596C4⋊C4C23×D8312yes—
597C4⋊C4C23×D8312yes—
598C22⋊C4—24no—
599C22⋊C4—1664no—
600C22⋊C4—1664no—
601C22⋊C4—1664no—
602C22⋊C4—1664no—
603C22⋊C4—1664no—
604C22⋊C4C2×C22⋊D8314yes—
605C22⋊C4C2×C22⋊D8314yes—
606C42—24no—
607C42—1664no—
608C42C2×C22⋊D8312yes—
609C42C2×C22⋊D8312yes—
610C42C23×D8312yes—
611C42C23×D8312yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—3322no—
616C23—3322no—
617C23—3322no—
618C23—1662no—
619C23C22×C22⋊D8312yes—
620C23C22×C22⋊D8311yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—3322no—
624Q8—6644no—
625Q8—1662no—
626Q8—1662no—
627D4—3322no—
628D4—6644no—
629D4—1662no—
630D4—1662no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—3322no—
649C2×C4—3322no—
650C2×C4—3322no—
651C2×C4—6644no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4C22×C22⋊D8312yes—
656C2×C4C22×C22⋊D8312yes—
657C2×C4C22×C22⋊D8312yes—
658C2×C4C22×C22⋊D8312yes—
659C2×C4C22×C22⋊D8312yes—
660C2×C4C22×C22⋊D8311yescharacteristic
661C2×C4#1458184012yes—
662C2×C4#1458184012yes—
663C2×C4C24×D8311yescharacteristic
664C8—1662no—
665C8—1662no—
666C8—1662no—
667C8—1662no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—3322no—
673C22—3322no—
674C22—3322no—
675C22—6644no—
676C22#1912827512yes—
677C22#1912850912yes—
678C22#1912851212yes—
679C22C23×C22⋊D8311yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—3322no—
690C4—3322no—
691C4—3322no—
692C4#1912827512yes—
693C4C2×#1458184011yescharacteristic
694C4C2×#1458184011yescharacteristic
695C2—42no—
696C2—6642no—
697C2#2491876114yesdirect product factor
698C2C2×#1912827511yescharacteristic
699C2C2×#1912850911yescharacteristic
700C2C2×#1912851211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#544×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
hypercenterC2×#544D83
hypocenterC83C2×#3244
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. #24918761C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128097C2semidirect
5. C2×#19128063C2semidirect
6. C2×#19128058C2semidirect
8. C2×#19128042C2semidirect
10. C2×#19128031C2semidirect
11. C2×#19128005C2semidirect
12. C2×#19127983C2semidirect
13. C2×#19127998C2semidirect
14. C2×#19127988C2semidirect
15. C2×#19127762C2semidirect
16. C2×#544×C83C2semidirect
29. #19128111C22semidirect
30. #19128097C22semidirect
31. #19128063C22semidirect
32. #19128058C22semidirect
33. #19128042C22semidirect
34. #19128031C22semidirect
37. #19128005C22semidirect
38. #19127998C22semidirect
39. #19127988C22semidirect
40. #19127983C22semidirect
41. #19127762C22semidirect
65. #544×C83C22semidirect
346. C2×C83#3244semidirect
351. C2×#544D83semidirect
367. C83C2×#3244semidirect
369. #544C2×D83semidirect
697. C2#24918761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283222
#249187612
C2×#191281112
C2×#191280972
C2×#191280632
C2×#191280582
C2×#191280192
C2×#191280422
C2×#191280252
C2×#191280312
C2×#191280052
C2×#191279832
C2×#191279982
C2×#191279882
C2×#191277622
C2×#544×C832
C2×#324483