Finite Group Databasebeta

← C2×#24918133 #36274274

Subgroups — C2×#24918133 #36274274

Order 21248.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic
2#24918133C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128093C211yesmaximal, characteristic, complemented
5C2×#19128058C211yesmaximal, characteristic, complemented
6C2×#19128051C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127949C211yesmaximal, characteristic
9C2×#19127940C211yesmaximal, characteristic, complemented
10C2×#19127932C211yesmaximal, characteristic
11C2×#19127806C211yesmaximal, characteristic, complemented
12C2×#19127799C211yesmaximal, characteristic, complemented
13C2×C4×#13050580C211yesmaximal, characteristic, complemented
14C2×C4×#13050577C211yesmaximal, characteristic, complemented
15C2×#19127657C211yesmaximal, characteristic, complemented
16C2×#541×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050580C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20C22×#13050577C2211yescharacteristic
21C22×#13050574C2211yescharacteristic
22C23×C83⋊C8C2211yescharacteristic
23#19128322—24no—
24#19128322C2218yes—
25C2×#14581792C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581780C2211yescharacteristic
28C2×#14581778—21no—
29C2×#14581774—21no—
30C2×#14581771C2211yescharacteristic
31C2×#14581770—21no—
32C2×#14581766C2211yescharacteristic
33C2×C4×Dic166C2211yescharacteristic
34C2×C4×D332C2211yescharacteristic
35#19128111C2218yescomplemented
36#19128093C2218yescomplemented
37#19128058C2218yescomplemented
38#19128051C2218yescomplemented
39#19127957C2218yescomplemented
40#19127949C2218yes—
41#19127940C2218yescomplemented
42#19127932C2218yes—
43#19127806C2218yescomplemented
44#19127799C2218yescomplemented
45C4×#13050580C2218yescomplemented
46C4×#13050577C2218yescomplemented
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581716C2211yescharacteristic
54C2×#14581716C2211yescharacteristic
55C2×#14581715C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581712C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59#19127657C2218yescomplemented
60C2×#14581703C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×C4×C83⋊C8C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#541×C83—24no—
65#541×C83C2218yescomplemented
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#126×C83—21no—
68C2×#126×C83—21no—
69C2×#125×C83—21no—
70C2×#125×C83—21no—
71C2×#125×C83C2211yescharacteristic
72C2×C22⋊Q8×C83C2211yescharacteristic
73C2×C22⋊Q8×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×Q8×C83C2211yescharacteristic
76C2×#117×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×D332C2311yescharacteristic
80C22×C22⋊D83—21no—
81C22×C4×D83—21no—
82C2×#13050580—24no—
83C2×#13050580—24no—
84C2×#13050580C2314yes—
85C2×#13050580C2314yes—
86C2×#13050577—24no—
87C2×#13050577—24no—
88C2×#13050577C2314yes—
89C2×#13050577C2314yes—
90C2×#13050574—24no—
91C2×#13050574C2314yes—
92C22×C83⋊C8—24no—
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2311yescharacteristic
95C22×C83⋊C8C2314yes—
96C22×C83⋊C8C2311yescharacteristic
97C22×C83⋊C8C2311yescharacteristic
98#14581792—22no—
99#14581792C2314yes—
100#14581787—28no—
101#14581780—22no—
102#14581780C2314yes—
103#14581778—28no—
104#14581774—28no—
105#14581771—22no—
106#14581771C2314yes—
107#14581770—28no—
108#14581766—22no—
109#14581766C2314yes—
110C4×Dic166—22no—
111C4×Dic166C2314yes—
112C4×D332—22no—
113C4×D332C2314yes—
114C2×C4⋊Dic83—21no—
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×Dic83⋊C4—21no—
118C2×Dic83⋊C4—21no—
119C2×C22⋊Dic83—21no—
120C2×(C2×D83)⋊C4—21no—
121C2×(C2×D83)⋊C4—21no—
122C2×(C2×D83)⋊C4—21no—
123C2×(C2×D83)⋊C4—21no—
124C2×C4×Dic83—21no—
125#14581725C2314yes—
126#14581725C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581716C2314yes—
133#14581715C2314yes—
134#14581715C2314yes—
135#14581712C2314yes—
136#14581712C2314yes—
137#14581703C2314yes—
138#14581703C2314yes—
139C4×C83⋊C8C2314yes—
140C4×C83⋊C8C2314yes—
141C22×Q8×C83C2311yescharacteristic
142C22×Q8×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C4⋊Q8×C83—22no—
145C4⋊Q8×C83C2314yes—
146#126×C83—28no—
147#126×C83—28no—
148#125×C83—28no—
149#125×C83—28no—
150#125×C83—22no—
151#125×C83C2314yes—
152C22⋊Q8×C83—22no—
153C22⋊Q8×C83—22no—
154C22⋊Q8×C83C2314yes—
155C22⋊Q8×C83C2314yes—
156C4×Q8×C83—22no—
157C4×Q8×C83—22no—
158C4×Q8×C83C2314yes—
159C4×Q8×C83C2314yes—
160#117×C83D414yes—
161#117×C83C2314yes—
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×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83D411yescharacteristic
171C2×C4⋊C4×C83D411yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83D411yescharacteristic
177C2×C22⋊C4×C83D411yescharacteristic
178C2×C42×C83—21no—
179C2×C42×C83—21no—
180C2×C42×C83C2311yescharacteristic
181C2×C42×C83C2311yescharacteristic
182C23×D83—21no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166—24no—
187C2×Dic166—82no—
188C2×Dic166C2412yes—
189C2×D332—22no—
190C2×D332—22no—
191C2×D332—21no—
192C2×D332C2412yes—
193C2×C22⋊D83—24no—
194C2×C22⋊D83—82no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C2×C4×D83—24no—
199C2×C4×D83—82no—
200#13050580—28no—
201#13050580—28no—
202#13050577—28no—
203#13050577—28no—
204#13050574—28no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—28no—
208C2×C83⋊C8#4114yes—
209C2×C83⋊C8#4114yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221C22⋊Dic83—24no—
222(C2×D83)⋊C4—24no—
223(C2×D83)⋊C4—24no—
224(C2×D83)⋊C4—24no—
225(C2×D83)⋊C4—24no—
226C4×Dic83—24no—
227C24×C83C2×D411yescharacteristic
228C2×Q8×C83—21no—
229C2×Q8×C83—21no—
230C2×Q8×C83—22no—
231C2×Q8×C83—22no—
232C2×Q8×C83—22no—
233C2×Q8×C83—22no—
234C2×Q8×C83C2412yes—
235C2×Q8×C83C2412yes—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83C2×D412yes—
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2412yes—
249C22×C4×C83C2411yescharacteristic
250C4⋊C4×C83—24no—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—24no—
253C4⋊C4×C83—24no—
254C4⋊C4×C83—24no—
255C4⋊C4×C83—24no—
256C4⋊C4×C83—24no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83C2×D414yes—
261C4⋊C4×C83C2×D414yes—
262C4⋊C4×C83C2412yes—
263C4⋊C4×C83C2412yes—
264C22⋊C4×C83—24no—
265C22⋊C4×C83—24no—
266C22⋊C4×C83C2×D414yes—
267C22⋊C4×C83C2×D414yes—
268C42×C83—24no—
269C42×C83—24no—
270C42×C83C2×D412yes—
271C42×C83C2×D412yes—
272C42×C83C2412yes—
273C42×C83C2412yes—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83C22×D412yes—
278C23×C83C22×D411yescharacteristic
279C22×D83—22no—
280C22×D83—42no—
281C22×D83—42no—
282C22×D83—42no—
283Q8×C83—22no—
284Q8×C83—22no—
285Q8×C83—22no—
286Q8×C83—22no—
287Q8×C83—42no—
288Q8×C83—42no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—24no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—42no—
302C2×C4×C83—42no—
303C2×C4×C83—42no—
304C2×C4×C83—42no—
305C2×C4×C83C22×D412yes—
306C2×C4×C83C22×D412yes—
307C2×C4×C83C22×D412yes—
308C2×C4×C83C22×D412yes—
309C2×C4×C83C22×D412yes—
310C2×C4×C83C22×D411yescharacteristic
311C2×C4×C83C2×#4112yes—
312C2×C4×C83C2×#4112yes—
313C2×C4×C83C2511yescharacteristic
314C22⋊D83—84no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—42no—
321D332—22no—
322D332—22no—
323D332—42no—
324C4×D83—84no—
325Dic166—22no—
326Dic166—22no—
327Dic166—42no—
328Dic166—84no—
329C83⋊C8—22no—
330C83⋊C8—22no—
331C83⋊C8C2×#4114yes—
332C83⋊C8C2×#4114yes—
333C22×C83—22no—
334C22×C83—22no—
335C22×C83—22no—
336C22×C83—44no—
337C22×C83#53212yes—
338C22×C83#57712yes—
339C22×C83#57812yes—
340C22×C83C23×D411yescharacteristic
341C2×D83—42no—
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—84no—
345C4×C83—22no—
346C4×C83—22no—
347C4×C83—22no—
348C4×C83—22no—
349C4×C83—22no—
350C4×C83—42no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354C4×C83#53212yes—
355C4×C83C22×#4111yescharacteristic
356C4×C83C22×#4111yescharacteristic
357Dic83—42no—
358Dic83—42no—
359Dic83—42no—
360C2×#3178—831nomaximal, Sylow
361C2×C83—42no—
362C2×C83#317814yescomplemented
363C2×C83C2×#53211yescharacteristic
364C2×C83C2×#57711yescharacteristic
365C2×C83C2×#57811yescharacteristic
366D83—82no—
367C2×#542—831no—
368C2×#541D8311yescharacteristic, complemented
369#3178—8316no—
370C2×#501—831no—
371C2×#497—831no—
372C2×#488—831no—
373C2×#487—831no—
374C2×#470—831no—
375C2×#468—831no—
376C2×#467—831no—
377C2×#465—831no—
378C2×#441—831no—
379C2×#440—831no—
380C2×C4×Q16—831no—
381C2×C4×SD16—831no—
382C2×#405—831no—
383C83C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—831no—
385C22×Q16—831no—
386C22×SD16—831no—
387C22×SD16—831no—
388C22×M16—831no—
389C23×C8—831no—
390#542—838no—
391#542—1664no—
392#541—24no—
393#541C2×D8318yescomplemented
394C2×C4⋊Q8—831no—
395C2×C4⋊Q8C2×D8311yescharacteristic
396C2×#126—21no—
397C2×#126—21no—
398C2×#126—1661no—
399C2×#125—21no—
400C2×#125—21no—
401C2×#125C2×D8311yescharacteristic
402C2×#124—831no—
403C2×#124—1661no—
404C2×#123—1661no—
405C2×C22⋊Q8—831no—
406C2×C22⋊Q8—1661no—
407C2×C22⋊Q8C2×D8311yescharacteristic
408C2×C22⋊Q8C2×D8311yescharacteristic
409C2×#121—831no—
410C2×C4×Q8—831no—
411C2×C4×Q8C2×D8311yescharacteristic
412C2×C4×Q8C2×D8311yescharacteristic
413C2×C4×D4—831no—
414C2×#117C2×D8311yescharacteristic
415#501—838no—
416#497—838no—
417#488—838no—
418#487—838no—
419#470—838no—
420#468—838no—
421#467—838no—
422#465—838no—
423#441—838no—
424#440—838no—
425C4×Q16—838no—
426C4×SD16—838no—
427C2×#107—831no—
428C2×#107—831no—
429C2×#106—831no—
430C2×#106—831no—
431C2×#103—831no—
432C2×#103—831no—
433C2×#103—831no—
434C2×#103—831no—
435C2×#103—831no—
436C2×#103—831no—
437C2×#102—831no—
438C2×#102—831no—
439#405—838no—
440C2×#97—831no—
441C2×#97—831no—
442C2×C4×C8—831no—
443C2×C4×C8—831no—
444C22×Q8—831no—
445C22×Q8—1661no—
446C22×Q8C22×D8311yescharacteristic
447C22×Q8C22×D8311yescharacteristic
448C22×D4—831no—
449C22×D4—1661no—
450C23×C4—1661no—
451C23×C4C22×D8311yescharacteristic
452C2×Q16—834no—
453C2×Q16—834no—
454C2×Q16—1664no—
455C2×Q16—1664no—
456C2×SD16—834no—
457C2×SD16—834no—
458C2×SD16—1664no—
459C2×SD16—1664no—
460C2×M16—834no—
461C2×M16—1664no—
462C22×C8—831no—
463C22×C8—831no—
464C22×C8—831no—
465C22×C8—834no—
466C22×C8—831no—
467C22×C8—1664no—
468C4⋊Q8—22no—
469C4⋊Q8—834no—
470C4⋊Q8—1662no—
471C4⋊Q8C22×D8314yes—
472#126—28no—
473#126—28no—
474#126—1668no—
475#125—28no—
476#125—28no—
477#125—22no—
478#125C22×D8314yes—
479#124—834no—
480#124—1668no—
481#124—1662no—
482#123—1668no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—834no—
486C22⋊Q8—1662no—
487C22⋊Q8—1668no—
488C22⋊Q8C22×D8314yes—
489C22⋊Q8C22×D8314yes—
490#121—834no—
491#121—1662no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—834no—
495C4×Q8—1662no—
496C4×Q8C22×D8314yes—
497C4×Q8C22×D8314yes—
498C4×D4—834no—
499C4×D4—1662no—
500#117C22⋊D8314yes—
501#117C22×D8314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—831no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4C22⋊D8311yescharacteristic
516C2×C4⋊C4C22⋊D8311yescharacteristic
517C2×C4⋊C4C22×D8311yescharacteristic
518C2×C4⋊C4C22×D8311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1661no—
522C2×C22⋊C4—1661no—
523C2×C22⋊C4—1661no—
524C2×C22⋊C4—1661no—
525C2×C22⋊C4—1661no—
526C2×C22⋊C4C22⋊D8311yescharacteristic
527C2×C22⋊C4C22⋊D8311yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—1661no—
531C2×C42C22×D8311yescharacteristic
532C2×C42C22×D8311yescharacteristic
533#107—834no—
534#107—834no—
535#106—834no—
536#106—834no—
537#103—834no—
538#103—834no—
539#103—834no—
540#103—834no—
541#103—834no—
542#103—834no—
543#102—834no—
544#102—834no—
545#97—834no—
546#97—834no—
547C4×C8—834no—
548C4×C8—834no—
549C24—1661no—
550C24C2×C22⋊D8311yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—832no—
558C2×Q8—6642no—
559C2×Q8—1662no—
560C2×Q8—1662no—
561C2×Q8—1661no—
562C2×Q8—1664no—
563C2×Q8C23×D8312yes—
564C2×Q8C23×D8312yes—
565C2×D4—832no—
566C2×D4—6642no—
567C2×D4—1664no—
568C2×D4—1661no—
569C2×D4—1662no—
570C2×D4—1662no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—6642no—
578C22×C4—1661no—
579C22×C4—1661no—
580C22×C4—1661no—
581C22×C4—1664no—
582C22×C4C2×C22⋊D8312yes—
583C22×C4C2×C22⋊D8311yescharacteristic
584C22×C4C2×C22⋊D8311yescharacteristic
585C22×C4C2×C22⋊D8311yescharacteristic
586C22×C4C2×C22⋊D8311yescharacteristic
587C22×C4C2×C22⋊D8311yescharacteristic
588C22×C4C23×D8312yes—
589C22×C4C23×D8311yescharacteristic
590Q16—1668no—
591Q16—1668no—
592SD16—1668no—
593SD16—1668no—
594M16—1668no—
595C2×C8—834no—
596C2×C8—834no—
597C2×C8—832no—
598C2×C8—832no—
599C2×C8—832no—
600C2×C8—832no—
601C2×C8—1668no—
602C2×C8—1662no—
603C2×C8—1662no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—832no—
615C4⋊C4—832no—
616C4⋊C4—1661no—
617C4⋊C4—1661no—
618C4⋊C4—1664no—
619C4⋊C4—1664no—
620C4⋊C4—1664no—
621C4⋊C4C2×C22⋊D8314yes—
622C4⋊C4C2×C22⋊D8314yes—
623C4⋊C4C23×D8312yes—
624C4⋊C4C23×D8312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—1664no—
628C22⋊C4—1664no—
629C22⋊C4—1664no—
630C22⋊C4—1664no—
631C22⋊C4—1664no—
632C22⋊C4C2×C22⋊D8314yes—
633C22⋊C4C2×C22⋊D8314yes—
634C42—24no—
635C42—24no—
636C42—1664no—
637C42C2×C22⋊D8312yes—
638C42C2×C22⋊D8312yes—
639C42C23×D8312yes—
640C42C23×D8312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—3322no—
645C23—3322no—
646C23—3322no—
647C23—1662no—
648C23C22×C22⋊D8312yes—
649C23C22×C22⋊D8311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—3322no—
657Q8—6644no—
658Q8—1662no—
659Q8—1662no—
660D4—3322no—
661D4—6644no—
662D4—1662no—
663D4—1662no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—3322no—
681C2×C4—3322no—
682C2×C4—3322no—
683C2×C4—6644no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4—1662no—
687C2×C4C22×C22⋊D8312yes—
688C2×C4C22×C22⋊D8312yes—
689C2×C4C22×C22⋊D8312yes—
690C2×C4C22×C22⋊D8312yes—
691C2×C4C22×C22⋊D8312yes—
692C2×C4C22×C22⋊D8311yescharacteristic
693C2×C4#41×D8312yes—
694C2×C4#41×D8312yes—
695C2×C4C24×D8311yescharacteristic
696C8—834no—
697C8—834no—
698C8—1662no—
699C8—1662no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3322no—
705C22—3322no—
706C22—3322no—
707C22—6644no—
708C22#1912824712yes—
709C22#1912850912yes—
710C22#1912851612yes—
711C22C23×C22⋊D8311yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—3322no—
722C4—3322no—
723C4—3322no—
724C4#1912824712yes—
725C4C2×#41×D8311yescharacteristic
726C4C2×#41×D8311yescharacteristic
727C2—42no—
728C2—6642no—
729C2#2491813314yesdirect product factor
730C2C2×#1912824711yescharacteristic
731C2C2×#1912850911yescharacteristic
732C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#541×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
hypercenterC2×#541D83
hypocenterC83C2×#3178
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #24918133C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128093C2semidirect
5. C2×#19128058C2semidirect
6. C2×#19128051C2semidirect
7. C2×#19127957C2semidirect
9. C2×#19127940C2semidirect
11. C2×#19127806C2semidirect
12. C2×#19127799C2semidirect
13. C2×C4×#13050580C2semidirect
14. C2×C4×#13050577C2semidirect
15. C2×#19127657C2semidirect
16. C2×#541×C83C2semidirect
35. #19128111C22semidirect
36. #19128093C22semidirect
37. #19128058C22semidirect
38. #19128051C22semidirect
39. #19127957C22semidirect
41. #19127940C22semidirect
43. #19127806C22semidirect
44. #19127799C22semidirect
45. C4×#13050580C22semidirect
46. C4×#13050577C22semidirect
59. #19127657C22semidirect
65. #541×C83C22semidirect
362. C2×C83#3178semidirect
368. C2×#541D83semidirect
383. C83C2×#3178semidirect
393. #541C2×D83semidirect
729. C2#24918133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283222
#249181332
C2×#191281112
C2×#191280932
C2×#191280582
C2×#191280512
C2×#191279572
C2×#191279492
C2×#191279402
C2×#191279322
C2×#191278062
C2×#191277992
C2×C4×#130505802
C2×C4×#130505772
C2×#191276572
C2×#541×C832
C2×#317883