Finite Group Databasebeta

← C2×#24919903 #36282935

Subgroups — C2×#24919903 #36282935

Order 21248.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128355C211yesmaximal, characteristic
2#24919903C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128034C211yesmaximal, characteristic, complemented
5C2×#19128025C211yesmaximal, characteristic, complemented
6C2×#19128029C211yesmaximal, characteristic, complemented
7C2×#19128014C211yesmaximal, characteristic, complemented
8C2×#19127996C211yesmaximal, characteristic, complemented
9C2×#19127998C211yesmaximal, characteristic, complemented
10C2×#19127949C211yesmaximal, characteristic, complemented
11C2×#19127932C211yesmaximal, characteristic, complemented
12C2×#19127799C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127744C211yesmaximal, characteristic, complemented
15C22×#14581725C211yesmaximal, characteristic, complemented
16C2×#552×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×#13050577C2211yescharacteristic
19C22×#13050574C2211yescharacteristic
20C23×C83⋊C8C2211yescharacteristic
21#19128355—24no—
22#19128355C2218yes—
23C2×#14581792C2211yescharacteristic
24C2×#14581776—21no—
25C2×#14581776—21no—
26C2×#14581772—21no—
27C2×#14581766C2211yescharacteristic
28C2×#14581766C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C22×C4⋊Dic83C2211yescharacteristic
31C22×C4⋊Dic83C2211yescharacteristic
32#19128111C2218yescomplemented
33#19128034C2218yescomplemented
34#19128029C2218yescomplemented
35#19128025C2218yescomplemented
36#19128014C2218yescomplemented
37#19127998C2218yescomplemented
38#19127996C2218yescomplemented
39#19127949C2218yescomplemented
40#19127932C2218yescomplemented
41#19127799C2218yescomplemented
42#19127773C2218yescomplemented
43#19127744C2218yescomplemented
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581725C2211yescharacteristic
50C2×#14581725C2218yescomplemented
51C2×#14581723C2211yescharacteristic
52C2×#14581723C2211yescharacteristic
53C2×#14581723C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64#552×C83—24no—
65#552×C83C2218yescomplemented
66C2×#126×C83—21no—
67C2×#125×C83—21no—
68C2×#125×C83C2211yescharacteristic
69C2×#123×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83C2211yescharacteristic
74C2×#117×C83—21no—
75C2×#117×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×D332C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C23×Dic83—21no—
84C23×Dic83—21no—
85C22×C4×D83—21no—
86C2×#13050577—24no—
87C2×#13050577C2314yes—
88C2×#13050574—24no—
89C2×#13050574C2314yes—
90C22×C83⋊C8—24no—
91C22×C83⋊C8C2311yescharacteristic
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2314yes—
95C22×C83⋊C8C2311yescharacteristic
96#14581792—22no—
97#14581792C2314yes—
98#14581776—28no—
99#14581776—28no—
100#14581772—28no—
101#14581766—22no—
102#14581766—22no—
103#14581766C2314yes—
104#14581766C2314yes—
105C4×D332—22no—
106C4×D332C2314yes—
107C2×C4⋊Dic83—22no—
108C2×C4⋊Dic83—22no—
109C2×C4⋊Dic83—21no—
110C2×C4⋊Dic83—21no—
111C2×C4⋊Dic83—21no—
112C2×C4⋊Dic83C2314yes—
113C2×C4⋊Dic83C2314yes—
114C2×C4⋊Dic83C2311yescharacteristic
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×(C2×D83)⋊C4—21no—
118C2×(C2×D83)⋊C4—21no—
119C2×(C2×D83)⋊C4—21no—
120#14581725C2314yes—
121#14581725C2314yes—
122#14581725C2314yes—
123#14581725C2314yes—
124#14581725C2314yes—
125#14581725C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129C4⋊(C83⋊C8)C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581716C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135#14581712C2314yes—
136C22⋊(C83⋊C8)C2314yes—
137C22⋊(C83⋊C8)C2314yes—
138#14581703C2314yes—
139C22×Q8×C83C2311yescharacteristic
140C22×D4×C83D411yescharacteristic
141C23×C4×C83—21no—
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144#126×C83—28no—
145#125×C83—28no—
146#125×C83—22no—
147#125×C83C2314yes—
148#123×C83—28no—
149C22⋊Q8×C83—22no—
150C22⋊Q8×C83—22no—
151C22⋊Q8×C83C2314yes—
152C22⋊Q8×C83C2314yes—
153C4×Q8×C83—22no—
154C4×Q8×C83C2314yes—
155C4×D4×C83D414yes—
156C4×D4×C83C2314yes—
157#117×C83—22no—
158#117×C83—28no—
159#117×C83C2314yes—
160C2×C4⋊C4×C83—21no—
161C2×C4⋊C4×C83—22no—
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×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
170C2×C4⋊C4×C83C2314yes—
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83D411yescharacteristic
176C2×C22⋊C4×C83D411yescharacteristic
177C2×C42×C83—21no—
178C2×C42×C83—21no—
179C2×C42×C83C2311yescharacteristic
180C23×D83—21no—
181#13050589—432no—
182C2×Dic166—24no—
183C2×Dic166—44no—
184C2×D332—22no—
185C2×D332—22no—
186C2×D332—21no—
187C2×D332C2412yes—
188C2×C22⋊D83—24no—
189C2×C22⋊D83—24no—
190C2×C22⋊D83—44no—
191C2×C22⋊D83—44no—
192C22×Dic83—24no—
193C22×Dic83—24no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—44no—
198C22×Dic83—44no—
199C2×C4×D83—24no—
200C2×C4×D83—44no—
201#13050577—28no—
202#13050574—28no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8—22no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—28no—
207C2×C83⋊C8#4114yescomplemented
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83—24no—
215C4⋊Dic83—24no—
216C4⋊Dic83—24no—
217C4⋊Dic83—21no—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221(C2×D83)⋊C4—24no—
222(C2×D83)⋊C4—24no—
223(C2×D83)⋊C4—24no—
224C24×C83C2×D411yescharacteristic
225C24×C83C2×D411yescharacteristic
226C2×Q8×C83—21no—
227C2×Q8×C83—22no—
228C2×Q8×C83—22no—
229C2×Q8×C83C2412yes—
230C2×D4×C83—24no—
231C2×D4×C83C2×D414yes—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—24no—
241C22×C4×C83—44no—
242C22×C4×C83C2×D412yes—
243C22×C4×C83C2×D412yes—
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2411yescharacteristic
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—24no—
254C4⋊C4×C83—24no—
255C4⋊C4×C83—24no—
256C4⋊C4×C83—24no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83C2×D414yes—
261C4⋊C4×C83C2412yes—
262C4⋊C4×C83C2412yes—
263C4⋊C4×C83C2412yes—
264C22⋊C4×C83—24no—
265C22⋊C4×C83—24no—
266C22⋊C4×C83—24no—
267C22⋊C4×C83C2×D414yes—
268C22⋊C4×C83C2×D414yes—
269C42×C83—24no—
270C42×C83—24no—
271C42×C83C2×D412yes—
272C42×C83C2412yes—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83AGL(1,ℤ/8)14yes—
279C23×C83C22×D412yes—
280C23×C83C22×D412yes—
281C23×C83C22×D411yescharacteristic
282C22×D83—22no—
283C22×D83—42no—
284C22×D83—42no—
285C22×D83—42no—
286Q8×C83—22no—
287Q8×C83—22no—
288Q8×C83—42no—
289D4×C83—28no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—24no—
295C2×C4×C83—24no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—42no—
305C2×C4×C83—48no—
306C2×C4×C83—42no—
307C2×C4×C83—42no—
308C2×C4×C83—42no—
309C2×C4×C83C22×D412yes—
310C2×C4×C83C22×D412yes—
311C2×C4×C83C22×D412yes—
312C2×C4×C83C22×D412yes—
313C2×C4×C83C22×D411yescharacteristic
314C2×C4×C83C2×#4112yes—
315C2×C4×C832−1+412yes—
316C2×C4×C83C2511yescharacteristic
317C22⋊D83—48no—
318C22⋊D83—48no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—48no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—48no—
327D332—22no—
328D332—22no—
329D332—42no—
330C4×D83—48no—
331Dic166—48no—
332C83⋊C8—22no—
333C83⋊C8—22no—
334C83⋊C8—22no—
335C83⋊C8C2×#4114yescomplemented
336C22×C83—28no—
337C22×C83—22no—
338C22×C83—22no—
339C22×C83—22no—
340C22×C83—22no—
341C22×C83—22no—
342C22×C83—44no—
343C22×C83#54712yes—
344C22×C83C2×AGL(1,ℤ/8)14yes—
345C22×C83C2×AGL(1,ℤ/8)12yes—
346C22×C83#57812yes—
347C22×C83C23×D411yescharacteristic
348C2×D83—42no—
349C2×D83—42no—
350C2×D83—42no—
351C2×D83—84no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—22no—
355C4×C83—22no—
356C4×C83—42no—
357C4×C83—42no—
358C4×C83—42no—
359C4×C83—42no—
360C4×C83#54712yes—
361C4×C83C22×#4111yescharacteristic
362C4×C83C2×2−1+411yescharacteristic
363Dic83—42no—
364Dic83—42no—
365Dic83—42no—
366C2×#3343—831nomaximal, Sylow
367C2×C83—24no—
368C2×C83—42no—
369C2×C83#334314yescomplemented
370C2×C83C2×#54711yescharacteristic
371C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C83C2×#57811yescharacteristic
373D83—82no—
374C2×#552D8311yescharacteristic, complemented
375C2×#547—831no—
376#3343—8316no—
377C2×#501—831no—
378C2×#484—831no—
379C2×#482—831no—
380C2×#483—831no—
381C2×#480—831no—
382C2×#477—831no—
383C2×#478—831no—
384C2×#468—831no—
385C2×#465—831no—
386C2×#440—831no—
387C2×#435—831no—
388C2×#428—831no—
389C22×#107—831no—
390C83C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1661no—
392C22×SD16—831no—
393C22×M16—831no—
394C23×C8—831no—
395#552—24no—
396#552C2×D8318yescomplemented
397#547—838no—
398#547—1664no—
399C2×C4⋊Q8—831no—
400C2×#126—21no—
401C2×#125—21no—
402C2×#125C2×D8311yescharacteristic
403C2×#123—21no—
404C2×#123—1661no—
405C2×#123—1661no—
406C2×C22⋊Q8—1661no—
407C2×C22⋊Q8C2×D8311yescharacteristic
408C2×C22⋊Q8C2×D8311yescharacteristic
409C2×#121—831no—
410C2×#121—831no—
411C2×C4×Q8C2×D8311yescharacteristic
412C2×C4×D4—831no—
413C2×C4×D4C2×D8311yescharacteristic
414C2×#117—21no—
415C2×#117C2×D8311yescharacteristic
416C22×C4⋊C4—831no—
417C22×C4⋊C4—831no—
418C22×C4⋊C4C2×D8311yescharacteristic
419#501—838no—
420#484—838no—
421#483—838no—
422#482—838no—
423#480—838no—
424#478—838no—
425#477—838no—
426#468—838no—
427#465—838no—
428#440—838no—
429#435—838no—
430#428—838no—
431C2×#107—831no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#107—831no—
435C2×#107—838no—
436C2×#107—831no—
437C2×#107—831no—
438C2×#106—831no—
439C2×#106—831no—
440C2×#106—831no—
441C2×C4⋊C8—831no—
442C2×#103—831no—
443C2×#103—831no—
444C2×#103—831no—
445C2×#102—831no—
446C2×#102—831no—
447C2×#102—831no—
448C2×C22⋊C8—831no—
449C2×C22⋊C8—831no—
450C2×#97—831no—
451C2×#41—3328no—
452C2×#41—1668no—
453C22×Q8—1661no—
454C22×Q8C22×D8311yescharacteristic
455C22×D4—831no—
456C22×D4—1661no—
457C22×D4—1661no—
458C22×D4C22⋊D8311yescharacteristic
459C23×C4—21no—
460C23×C4—1661no—
461C23×C4—1661no—
462C23×C4—1661no—
463C23×C4C22×D8311yescharacteristic
464C23×C4C22×D8311yescharacteristic
465C2×SD16—834no—
466C2×SD16—1664no—
467C2×M16—834no—
468C2×M16—1664no—
469C22×C8—831no—
470C22×C8—831no—
471C22×C8—834no—
472C22×C8—831no—
473C22×C8—831no—
474C22×C8—1664no—
475C4⋊Q8—834no—
476C4⋊Q8—1662no—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C22×D8314yes—
481#123—28no—
482#123—1668no—
483#123—1668no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—1668no—
487C22⋊Q8C22×D8314yes—
488C22⋊Q8C22×D8314yes—
489#121—834no—
490#121—834no—
491#121—1662no—
492#121—1662no—
493C4×Q8—22no—
494C4×Q8C22×D8314yes—
495C4×D4—834no—
496C4×D4—1662no—
497C4×D4C22⋊D8314yes—
498C4×D4C22×D8314yes—
499#117—22no—
500#117—28no—
501#117C22×D8314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—831no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—831no—
512C2×C4⋊C4—834no—
513C2×C4⋊C4—834no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1662no—
517C2×C4⋊C4—1662no—
518C2×C4⋊C4—1661no—
519C2×C4⋊C4C22⋊D8311yescharacteristic
520C2×C4⋊C4C22×D8311yescharacteristic
521C2×C4⋊C4C22×D8311yescharacteristic
522C2×C4⋊C4C22×D8314yes—
523C2×C4⋊C4C22×D8311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C22⋊C4C22⋊D8311yescharacteristic
531C2×C22⋊C4C22⋊D8311yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C22×D8311yescharacteristic
535#107—834no—
536#107—834no—
537#107—834no—
538#107—834no—
539#107—834no—
540#107—834no—
541#106—834no—
542#106—834no—
543#106—834no—
544C4⋊C8—834no—
545#103—834no—
546#103—834no—
547#103—834no—
548#102—834no—
549#102—834no—
550#102—834no—
551C22⋊C8—834no—
552C22⋊C8—834no—
553#97—834no—
554C24—1661no—
555C24C2×C22⋊D8311yescharacteristic
556C24C2×C22⋊D8311yescharacteristic
557#41—33232no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—3324no—
562C2×Q8—1664no—
563C2×Q8C23×D8312yes—
564C2×D4—24no—
565C2×D4—3324no—
566C2×D4—3324no—
567C2×D4—832no—
568C2×D4—1664no—
569C2×D4—1664no—
570C2×D4—1661no—
571C2×D4—1662no—
572C2×D4—1662no—
573C2×D4C2×C22⋊D8314yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—3324no—
585C22×C4—3324no—
586C22×C4—3324no—
587C22×C4—1664no—
588C22×C4—1664no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1664no—
593C22×C4C2×C22⋊D8312yes—
594C22×C4C2×C22⋊D8312yes—
595C22×C4C2×C22⋊D8311yescharacteristic
596C22×C4C2×C22⋊D8311yescharacteristic
597C22×C4C2×C22⋊D8311yescharacteristic
598C22×C4C2×C22⋊D8311yescharacteristic
599C22×C4C23×D8312yes—
600C22×C4C23×D8312yes—
601C22×C4C23×D8311yescharacteristic
602SD16—1668no—
603M16—1668no—
604C2×C8—834no—
605C2×C8—832no—
606C2×C8—832no—
607C2×C8—832no—
608C2×C8—832no—
609C2×C8—1668no—
610C2×C8—1662no—
611C2×C8—1662no—
612C2×C8—1662no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—832no—
623C4⋊C4—832no—
624C4⋊C4—832no—
625C4⋊C4—1661no—
626C4⋊C4—1661no—
627C4⋊C4—1661no—
628C4⋊C4—1664no—
629C4⋊C4—1664no—
630C4⋊C4—1664no—
631C4⋊C4C2×C22⋊D8314yes—
632C4⋊C4C23×D8312yes—
633C4⋊C4C23×D8312yes—
634C4⋊C4C23×D8312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1664no—
639C22⋊C4—1664no—
640C22⋊C4—1664no—
641C22⋊C4C2×C22⋊D8314yes—
642C22⋊C4C2×C22⋊D8314yes—
643C42—24no—
644C42—24no—
645C42C2×C22⋊D8312yes—
646C42C23×D8312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—3322no—
653C23—3322no—
654C23—3322no—
655C23—1662no—
656C23#1458181714yes—
657C23C22×C22⋊D8312yes—
658C23C22×C22⋊D8312yes—
659C23C22×C22⋊D8311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—3328no—
664D4—28no—
665D4—3328no—
666D4—3328no—
667D4—3322no—
668D4—1662no—
669D4—1662no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—3328no—
690C2×C4—3328no—
691C2×C4—3322no—
692C2×C4—3322no—
693C2×C4—3322no—
694C2×C4—3328no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4C22×C22⋊D8312yes—
699C2×C4C22×C22⋊D8312yes—
700C2×C4C22×C22⋊D8312yes—
701C2×C4C22×C22⋊D8312yes—
702C2×C4C22×C22⋊D8311yescharacteristic
703C2×C4#41×D8312yes—
704C2×C4#1458183912yes—
705C2×C4C24×D8311yescharacteristic
706C8—834no—
707C8—1662no—
708C8—1662no—
709C8—1662no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—3322no—
718C22—3322no—
719C22—3322no—
720C22—6644no—
721C22#1912835012yes—
722C22C2×#1458181714yes—
723C22C2×#1458181712yes—
724C22#1912851612yes—
725C22C23×C22⋊D8311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—3322no—
735C4—3322no—
736C4—3322no—
737C4#1912835012yes—
738C4C2×#41×D8311yescharacteristic
739C4C2×#1458183911yescharacteristic
740C2—24no—
741C2—42no—
742C2—6642no—
743C2#2491990314yesdirect product factor
744C2C2×#1912835011yescharacteristic
745C2C22×#1458181711yescharacteristic
746C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#552×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128355C2
hypercenterC2×#552D83
hypocenterC83C2×#3343
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #24919903C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128034C2semidirect
5. C2×#19128025C2semidirect
6. C2×#19128029C2semidirect
7. C2×#19128014C2semidirect
8. C2×#19127996C2semidirect
9. C2×#19127998C2semidirect
10. C2×#19127949C2semidirect
11. C2×#19127932C2semidirect
12. C2×#19127799C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127744C2semidirect
15. C22×#14581725C2semidirect
16. C2×#552×C83C2semidirect
32. #19128111C22semidirect
33. #19128034C22semidirect
34. #19128029C22semidirect
35. #19128025C22semidirect
36. #19128014C22semidirect
37. #19127998C22semidirect
38. #19127996C22semidirect
39. #19127949C22semidirect
40. #19127932C22semidirect
41. #19127799C22semidirect
42. #19127773C22semidirect
43. #19127744C22semidirect
50. C2×#14581725C22semidirect
65. #552×C83C22semidirect
207. C2×C83⋊C8#41semidirect
335. C83⋊C8C2×#41semidirect
369. C2×C83#3343semidirect
374. C2×#552D83semidirect
390. C83C2×#3343semidirect
396. #552C2×D83semidirect
743. C2#24919903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283552
#249199032
C2×#191281112
C2×#191280342
C2×#191280252
C2×#191280292
C2×#191280142
C2×#191279962
C2×#191279982
C2×#191279492
C2×#191279322
C2×#191277992
C2×#191277732
C2×#191277442
C22×#145817252
C2×#552×C832
C2×#334383