Finite Group Databasebeta

← C2×#24919716 #36281257

Subgroups — C2×#24919716 #36281257

Order 21248.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128397C211yesmaximal, characteristic, complemented
2#24919716C2116yesmaximal, direct product factor
3C2×#19128055C211yesmaximal, characteristic, complemented
4C2×#19128022C211yesmaximal, characteristic, complemented
5C2×#19128029C211yesmaximal, characteristic, complemented
6C2×#19128008C211yesmaximal, characteristic, complemented
7C2×#19127952C211yesmaximal, characteristic, complemented
8C2×#19127949C211yesmaximal, characteristic, complemented
9C2×#19127913C211yesmaximal, characteristic, complemented
10C2×#19127846C211yesmaximal, characteristic, complemented
11C2×#19127840C211yesmaximal, characteristic, complemented
12C2×C4×#13050577C211yesmaximal, characteristic, complemented
13C2×#19127779C211yesmaximal, characteristic, complemented
14C2×#19127702C211yesmaximal, characteristic, complemented
15C2×#19127710C211yesmaximal, characteristic, complemented
16C2×#548×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19C22×#13050575C2211yescharacteristic
20C22×#13050574C2211yescharacteristic
21C22×#13050574C2211yescharacteristic
22#19128397—24no—
23#19128397C2218yescomplemented
24C2×#14581787—21no—
25C2×#14581784C2211yescharacteristic
26C2×#14581774—21no—
27C2×#14581766C2211yescharacteristic
28C2×#14581766C2211yescharacteristic
29C2×#14581764—21no—
30C2×C4×D332C2211yescharacteristic
31C2×(C22⋊D83)⋊C4—21no—
32C2×#14581751C2211yescharacteristic
33C22×C4⋊Dic83C2211yescharacteristic
34#19128055C2218yescomplemented
35#19128029C2218yescomplemented
36#19128022C2218yescomplemented
37#19128008C2218yescomplemented
38#19127952C2218yescomplemented
39#19127949C2218yescomplemented
40#19127913C2218yescomplemented
41#19127846C2218yescomplemented
42#19127840C2218yescomplemented
43C4×#13050577C2218yescomplemented
44#19127779C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49#19127710C2218yescomplemented
50#19127702C2218yescomplemented
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581716C2211yescharacteristic
54C2×#14581716C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581713C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64C22×#41×C83C2211yescharacteristic
65C23×Q8×C83C2211yescharacteristic
66#548×C83—24no—
67#548×C83C2218yescomplemented
68C2×#124×C83—21no—
69C2×#124×C83C2211yescharacteristic
70C2×C22⋊Q8×C83—21no—
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×#121×C83—21no—
73C2×#121×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×D4×C83—21no—
76C2×C4×D4×C83C2211yescharacteristic
77C22×D332C2311yescharacteristic
78C22×C22⋊D83—21no—
79C22×C22⋊D83—21no—
80C23×Dic83—21no—
81C22×C4×D83—21no—
82C2×#13050577—24no—
83C2×#13050577—42no—
84C2×#13050577C2314yes—
85C2×#13050577C2314yes—
86C2×#13050575—42no—
87C2×#13050575C2314yes—
88C2×#13050574—42no—
89C2×#13050574—42no—
90C2×#13050574C2314yes—
91C2×#13050574C2314yes—
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2311yescharacteristic
95C22×C83⋊C8C2311yescharacteristic
96#14581787—28no—
97#14581784—22no—
98#14581784C2314yes—
99#14581774—28no—
100#14581766—22no—
101#14581766—22no—
102#14581766C2314yes—
103#14581766C2314yes—
104#14581764—28no—
105C4×D332—22no—
106C4×D332C2314yes—
107(C22⋊D83)⋊C4—28no—
108#14581751—22no—
109#14581751C2314yes—
110C2×C4⋊Dic83—22no—
111C2×C4⋊Dic83—21no—
112C2×C4⋊Dic83C2314yes—
113C2×C4⋊Dic83C2311yescharacteristic
114C2×C4⋊Dic83C2311yescharacteristic
115C2×C4⋊Dic83C2311yescharacteristic
116C2×Dic83⋊C4—21no—
117C2×Dic83⋊C4—21no—
118C2×C22⋊Dic83—21no—
119C2×(C2×D83)⋊C4—21no—
120C2×(C2×D83)⋊C4—21no—
121C2×(C2×D83)⋊C4—21no—
122C2×C4×Dic83—21no—
123#14581725C2314yes—
124#14581723C2314yes—
125#14581723C2314yes—
126C4⋊(C83⋊C8)C2314yes—
127#14581716C2314yes—
128#14581716C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581716C2314yes—
133#14581713C2314yes—
134#14581713C2314yes—
135#14581713C2314yes—
136#14581712C2314yes—
137C22⋊(C83⋊C8)C2314yes—
138C22⋊(C83⋊C8)C2314yes—
139C4×C83⋊C8C2314yes—
140C2×#41×C83—22no—
141C2×#41×C83—24no—
142C2×#41×C83—42no—
143C2×#41×C83C2314yes—
144C22×Q8×C83—21no—
145C22×Q8×C83—22no—
146C22×Q8×C83—24no—
147C22×Q8×C83—42no—
148C22×Q8×C83C2311yescharacteristic
149C22×Q8×C83C2314yes—
150C22×Q8×C83C2311yescharacteristic
151C22×D4×C83—21no—
152C22×D4×C83—21no—
153C22×D4×C83D411yescharacteristic
154C22×D4×C83C2311yescharacteristic
155C23×C4×C83—21no—
156C23×C4×C83—21no—
157C23×C4×C83C2311yescharacteristic
158C23×C4×C83C2311yescharacteristic
159#124×C83—28no—
160#124×C83—22no—
161#124×C83C2314yes—
162C22⋊Q8×C83—22no—
163C22⋊Q8×C83—28no—
164C22⋊Q8×C83C2314yes—
165#121×C83—28no—
166#121×C83—22no—
167#121×C83C2314yes—
168C4×Q8×C83—22no—
169C4×Q8×C83C2314yes—
170C4×D4×C83—28no—
171C4×D4×C83D414yes—
172C4×D4×C83C2314yes—
173C2×C4⋊C4×C83—21no—
174C2×C4⋊C4×C83—21no—
175C2×C4⋊C4×C83D411yescharacteristic
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83—21no—
180C2×C22⋊C4×C83—21no—
181C2×C22⋊C4×C83D411yescharacteristic
182C2×C22⋊C4×C83D411yescharacteristic
183C2×C42×C83—21no—
184C2×C42×C83C2311yescharacteristic
185C23×D83—21no—
186C2×D332—22no—
187C2×D332—22no—
188C2×D332—21no—
189C2×D332C2412yes—
190C2×C22⋊D83—24no—
191C2×C22⋊D83—24no—
192C2×C22⋊D83—44no—
193C2×C22⋊D83—82no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—24no—
198C22×Dic83—82no—
199C2×C4×D83—24no—
200C2×C4×D83—82no—
201#13050577—28no—
202#13050577—44no—
203#13050575—44no—
204#13050574—44no—
205#13050574—44no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8—22no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83—21no—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223C22⋊Dic83—24no—
224(C2×D83)⋊C4—24no—
225(C2×D83)⋊C4—24no—
226(C2×D83)⋊C4—24no—
227C4×Dic83—24no—
228C24×C83—21no—
229C24×C83C2×D411yescharacteristic
230C24×C83C2×D411yescharacteristic
231#41×C83—28no—
232#41×C83—44no—
233#41×C83—48no—
234C2×Q8×C83—21no—
235C2×Q8×C83—24no—
236C2×Q8×C83—21no—
237C2×Q8×C83—22no—
238C2×Q8×C83—28no—
239C2×Q8×C83—22no—
240C2×Q8×C83—22no—
241C2×Q8×C83—44no—
242C2×Q8×C83—44no—
243C2×Q8×C83—48no—
244C2×Q8×C83#4114yes—
245C2×Q8×C83C2412yes—
246C2×Q8×C83C2412yes—
247C2×D4×C83—24no—
248C2×D4×C83—24no—
249C2×D4×C83—21no—
250C2×D4×C83—22no—
251C2×D4×C83—22no—
252C2×D4×C83—42no—
253C2×D4×C83—44no—
254C2×D4×C83—44no—
255C2×D4×C83C2×D414yes—
256C2×D4×C83C2412yes—
257C22×C4×C83—21no—
258C22×C4×C83—22no—
259C22×C4×C83—22no—
260C22×C4×C83—22no—
261C22×C4×C83—22no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83—24no—
265C22×C4×C83—24no—
266C22×C4×C83—44no—
267C22×C4×C83—44no—
268C22×C4×C83C2×D412yes—
269C22×C4×C83C2×D412yes—
270C22×C4×C83C2×D411yescharacteristic
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2×D411yescharacteristic
274C22×C4×C83C2412yes—
275C22×C4×C83C2412yes—
276C22×C4×C83C2411yescharacteristic
277C4⋊C4×C83—24no—
278C4⋊C4×C83—24no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83C2×D414yes—
281C4⋊C4×C83C2412yes—
282C22⋊C4×C83—24no—
283C22⋊C4×C83—24no—
284C22⋊C4×C83—24no—
285C22⋊C4×C83—24no—
286C22⋊C4×C83C2×D414yes—
287C22⋊C4×C83C2×D414yes—
288C42×C83—24no—
289C42×C83C2×D412yes—
290C42×C83C2412yes—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—42no—
299C23×C83—42no—
300C23×C83—42no—
301C23×C83C22×D412yes—
302C23×C83C22×D412yes—
303C23×C83C22×D411yescharacteristic
304C22×D83—22no—
305C22×D83—42no—
306C22×D83—42no—
307C22×D83—42no—
308Q8×C83—24no—
309Q8×C83—22no—
310Q8×C83—22no—
311Q8×C83—22no—
312Q8×C83—48no—
313Q8×C83—42no—
314Q8×C83C2×#4114yes—
315D4×C83—22no—
316D4×C83—22no—
317D4×C83—44no—
318D4×C83—48no—
319D4×C83—48no—
320D4×C83—42no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—24no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—24no—
328C2×C4×C83—24no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—48no—
336C2×C4×C83—48no—
337C2×C4×C83—42no—
338C2×C4×C83—42no—
339C2×C4×C83C22×D412yes—
340C2×C4×C83C22×D412yes—
341C2×C4×C83C22×D412yes—
342C2×C4×C83C22×D412yes—
343C2×C4×C83C22×D411yescharacteristic
344C2×C4×C83C2×#4112yes—
345C2×C4×C83H(5,𝔽2)12yes—
346C2×C4×C83C2511yescharacteristic
347C22⋊D83—48no—
348C22⋊D83—84no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—42no—
353C2×Dic83—42no—
354C2×Dic83—42no—
355C2×Dic83—84no—
356D332—22no—
357D332—22no—
358D332—42no—
359C4×D83—84no—
360C83⋊C8—22no—
361C83⋊C8—22no—
362C83⋊C8—22no—
363C83⋊C8—22no—
364C22×C83—22no—
365C22×C83—22no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—44no—
371C22×C83—44no—
372C22×C83—42no—
373C22×C83—42no—
374C22×C83—42no—
375C22×C83—84no—
376C22×C83#54612yes—
377C22×C83#57512yes—
378C22×C83#57712yes—
379C22×C83C23×D411yescharacteristic
380C2×D83—42no—
381C2×D83—42no—
382C2×D83—42no—
383C2×D83—84no—
384C4×C83—22no—
385C4×C83—22no—
386C4×C83—24no—
387C4×C83—22no—
388C4×C83—22no—
389C4×C83—42no—
390C4×C83—42no—
391C4×C83#54612yes—
392C4×C83C22×#4111yescharacteristic
393C4×C83C2×H(5,𝔽2)11yescharacteristic
394Dic83—42no—
395Dic83—42no—
396Dic83—42no—
397C2×#3326—831nomaximal, Sylow
398C2×C83—42no—
399C2×C83—42no—
400C2×C83—82no—
401C2×C83#332614yescomplemented
402C2×C83C2×#54611yescharacteristic
403C2×C83C2×#57511yescharacteristic
404C2×C83C2×#57711yescharacteristic
405D83—82no—
406C2×#553—831no—
407C2×#548D8311yescharacteristic, complemented
408#3326—8316no—
409C2×#488—831no—
410C2×#482—831no—
411C2×#483—831no—
412C2×#479—831no—
413C2×#469—831no—
414C2×#468—831no—
415C2×#463—831no—
416C2×#449—831no—
417C2×#448—831no—
418C2×C4×SD16—831no—
419C2×#436—831no—
420C2×#417—831no—
421C2×#419—831no—
422C83C2×#332611yescharacteristic, complemented, Sylow
423C22×#41C2×D8311yescharacteristic
424C23×Q8C2×D8311yescharacteristic
425C22×SD16—831no—
426C22×SD16—831no—
427C22×D8—831no—
428C22×M16—831no—
429C22×M16—831no—
430#553—838no—
431#553—1664no—
432#548—24no—
433#548C2×D8318yescomplemented
434C2×#126—1661no—
435C2×#125—831no—
436C2×#124—21no—
437C2×#124C2×D8311yescharacteristic
438C2×#123—1661no—
439C2×C22⋊Q8—21no—
440C2×C22⋊Q8C2×D8311yescharacteristic
441C2×#121—21no—
442C2×#121—831no—
443C2×#121—831no—
444C2×#121—1661no—
445C2×#121C2×D8311yescharacteristic
446C2×C4×Q8C2×D8311yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4—831no—
449C2×C4×D4—1661no—
450C2×C4×D4C2×D8311yescharacteristic
451C2×#117—831no—
452C22×C4⋊C4—831no—
453#488—838no—
454#483—838no—
455#482—838no—
456#479—838no—
457#469—838no—
458#468—838no—
459#463—838no—
460#449—838no—
461#448—838no—
462C4×SD16—838no—
463#436—838no—
464C2×#107—831no—
465C2×#106—831no—
466C2×#106—831no—
467C2×C4⋊C8—831no—
468#419—838no—
469#417—838no—
470C2×#103—831no—
471C2×#103—831no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103—831no—
475C2×#103—831no—
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×C22⋊C8—831no—
481C2×C22⋊C8—831no—
482C2×C4×C8—831no—
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D8314yes—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8C22×D8311yescharacteristic
492C22×Q8C22×D8314yes—
493C22×Q8C22×D8311yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—831no—
497C22×D4—1661no—
498C22×D4—1661no—
499C22×D4C22⋊D8311yescharacteristic
500C22×D4C22×D8311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—1661no—
504C23×C4—1661no—
505C23×C4C22×D8311yescharacteristic
506C23×C4C22×D8311yescharacteristic
507C2×SD16—3322no—
508C2×SD16—834no—
509C2×SD16—834no—
510C2×SD16—1664no—
511C2×D8—3322no—
512C2×D8—834no—
513C2×M16—3322no—
514C2×M16—3322no—
515C2×M16—834no—
516C2×M16—834no—
517C22×C8—831no—
518C22×C8—831no—
519C22×C8—831no—
520C22×C8—831no—
521#126—1668no—
522#125—834no—
523#125—1662no—
524#124—28no—
525#124—22no—
526#124C22×D8314yes—
527#123—1668no—
528C22⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8C22×D8314yes—
531#121—28no—
532#121—22no—
533#121—834no—
534#121—834no—
535#121—1668no—
536#121—1662no—
537#121—1662no—
538#121C22×D8314yes—
539C4×Q8—22no—
540C4×Q8C22×D8314yes—
541C4×D4—28no—
542C4×D4—834no—
543C4×D4—1668no—
544C4×D4—1662no—
545C4×D4C22⋊D8314yes—
546C4×D4C22×D8314yes—
547#117—834no—
548#117—1662no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—834no—
554C2×C4⋊C4—831no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1662no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4C22⋊D8311yescharacteristic
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4C22⋊D8311yescharacteristic
570C2×C22⋊C4C22⋊D8311yescharacteristic
571C2×C42—21no—
572C2×C42—1661no—
573C2×C42C22×D8311yescharacteristic
574#107—834no—
575#106—834no—
576#106—834no—
577C4⋊C8—834no—
578#103—834no—
579#103—834no—
580#103—834no—
581#103—834no—
582#103—834no—
583#103—834no—
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588C22⋊C8—834no—
589C22⋊C8—834no—
590C4×C8—834no—
591C24—21no—
592C24—1661no—
593C24C2×C22⋊D8311yescharacteristic
594C24C2×C22⋊D8311yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8#1305058914yes—
609C2×Q8C23×D8312yes—
610C2×Q8C23×D8312yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—3324no—
620C2×D4—832no—
621C2×D4—6642no—
622C2×D4—1664no—
623C2×D4—1664no—
624C2×D4—1661no—
625C2×D4—1662no—
626C2×D4—1662no—
627C2×D4C2×C22⋊D8314yes—
628C2×D4C23×D8312yes—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—6642no—
641C22×C4—6642no—
642C22×C4—1661no—
643C22×C4—1661no—
644C22×C4—1661no—
645C22×C4—1664no—
646C22×C4—1664no—
647C22×C4C2×C22⋊D8312yes—
648C22×C4C2×C22⋊D8312yes—
649C22×C4C2×C22⋊D8311yescharacteristic
650C22×C4C2×C22⋊D8311yescharacteristic
651C22×C4C2×C22⋊D8311yescharacteristic
652C22×C4C2×C22⋊D8311yescharacteristic
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656SD16—3324no—
657SD16—1668no—
658D8—3324no—
659M16—3324no—
660M16—3324no—
661C2×C8—832no—
662C2×C8—832no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8—1662no—
668C2×C8—1662no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—832no—
673C4⋊C4—832no—
674C4⋊C4—832no—
675C4⋊C4—1661no—
676C4⋊C4—1661no—
677C4⋊C4—1664no—
678C4⋊C4—1661no—
679C4⋊C4—1664no—
680C4⋊C4—1664no—
681C4⋊C4C2×C22⋊D8314yes—
682C4⋊C4C23×D8312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—1664no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4C2×C22⋊D8314yes—
692C22⋊C4C2×C22⋊D8314yes—
693C42—24no—
694C42—1664no—
695C42C2×C22⋊D8312yes—
696C42C23×D8312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—3322no—
708C23—3322no—
709C23—3322no—
710C23—1662no—
711C23C22×C22⋊D8312yes—
712C23C22×C22⋊D8312yes—
713C23C22×C22⋊D8311yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8C2×#1305058914yes—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—48no—
726D4—42no—
727D4—3328no—
728D4—3322no—
729D4—6644no—
730D4—1662no—
731D4—1662no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—3322no—
751C2×C4—3322no—
752C2×C4—3322no—
753C2×C4—6644no—
754C2×C4—6644no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4C22×C22⋊D8312yes—
759C2×C4C22×C22⋊D8312yes—
760C2×C4C22×C22⋊D8312yes—
761C2×C4C22×C22⋊D8312yes—
762C2×C4C22×C22⋊D8311yescharacteristic
763C2×C4C2×#1305058912yes—
764C2×C4#1458183712yes—
765C2×C4C24×D8311yescharacteristic
766C8—1662no—
767C8—1662no—
768C8—1662no—
769C8—1662no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—3322no—
783C22—3322no—
784C22—3322no—
785C22—6644no—
786C22#1912834512yes—
787C22#1912849912yes—
788C22#1912850912yes—
789C22C23×C22⋊D8311yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—3322no—
798C4—3322no—
799C4—3322no—
800C4#1912834512yes—
801C4C22×#1305058911yescharacteristic
802C4C2×#1458183711yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—6642no—
807C2#2491971614yesdirect product factor
808C2C2×#1912834511yescharacteristic
809C2C2×#1912849911yescharacteristic
810C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#548×C83C2
socleC23×C83C22×D4
hypercenterC2×#548D83
hypocenterC83C2×#3326
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#19128397C2semidirect
2. #24919716C2direct (N × H)
3. C2×#19128055C2semidirect
4. C2×#19128022C2semidirect
5. C2×#19128029C2semidirect
6. C2×#19128008C2semidirect
7. C2×#19127952C2semidirect
8. C2×#19127949C2semidirect
9. C2×#19127913C2semidirect
10. C2×#19127846C2semidirect
11. C2×#19127840C2semidirect
12. C2×C4×#13050577C2semidirect
13. C2×#19127779C2semidirect
14. C2×#19127702C2semidirect
15. C2×#19127710C2semidirect
16. C2×#548×C83C2semidirect
23. #19128397C22semidirect
34. #19128055C22semidirect
35. #19128029C22semidirect
36. #19128022C22semidirect
37. #19128008C22semidirect
38. #19127952C22semidirect
39. #19127949C22semidirect
40. #19127913C22semidirect
41. #19127846C22semidirect
42. #19127840C22semidirect
43. C4×#13050577C22semidirect
44. #19127779C22semidirect
49. #19127710C22semidirect
50. #19127702C22semidirect
67. #548×C83C22semidirect
401. C2×C83#3326semidirect
407. C2×#548D83semidirect
422. C83C2×#3326semidirect
433. #548C2×D83semidirect
807. C2#24919716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283972
#249197162
C2×#191280552
C2×#191280222
C2×#191280292
C2×#191280082
C2×#191279522
C2×#191279492
C2×#191279132
C2×#191278462
C2×#191278402
C2×C4×#130505772
C2×#191277792
C2×#191277022
C2×#191277102
C2×#548×C832
C2×#332683