Finite Group Databasebeta

← C2×#24919574 #36280994

Subgroups — C2×#24919574 #36280994

Order 21248.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128408C211yesmaximal, characteristic, complemented
2#24919574C2116yesmaximal, direct product factor
3C2×#19128060C211yesmaximal, characteristic, complemented
4C2×#19128017C211yesmaximal, characteristic, complemented
5C2×#19128029C211yesmaximal, characteristic, complemented
6C2×#19127986C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127928C211yesmaximal, characteristic, complemented
9C2×#19127920C211yesmaximal, characteristic, complemented
10C2×#19127863C211yesmaximal, characteristic, complemented
11C2×#19127857C211yesmaximal, characteristic, complemented
12C2×#19127806C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic, complemented
14C2×#19127702C211yesmaximal, characteristic, complemented
15C22×#14581716C211yesmaximal, characteristic, complemented
16C2×#548×C83C211yesmaximal, characteristic
17C22×#13050580C2211yescharacteristic
18C22×#13050580C2211yescharacteristic
19C22×#13050578C2211yescharacteristic
20C22×#13050574C2211yescharacteristic
21C23×C83⋊C8C2211yescharacteristic
22#19128408—24no—
23#19128408C2218yescomplemented
24C2×#14581792C2211yescharacteristic
25C2×#14581783—21no—
26C2×#14581771C2211yescharacteristic
27C2×#14581771C2211yescharacteristic
28C2×#14581769—21no—
29C2×#14581769—21no—
30C2×C4×Dic166C2211yescharacteristic
31C2×D4×Dic83—21no—
32C22×C4⋊Dic83C2211yescharacteristic
33C22×C4⋊Dic83C2211yescharacteristic
34#19128060C2218yescomplemented
35#19128029C2218yescomplemented
36#19128017C2218yescomplemented
37#19127986C2218yescomplemented
38#19127957C2218yescomplemented
39#19127928C2218yescomplemented
40#19127920C2218yescomplemented
41#19127863C2218yescomplemented
42#19127857C2218yescomplemented
43#19127806C2218yescomplemented
44#19127773C2218yescomplemented
45C2×#14581723C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49#19127702C2218yescomplemented
50C2×#14581716C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581716C2211yescharacteristic
54C2×#14581716C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2218yescomplemented
57C2×#14581715C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581713C2211yescharacteristic
60C2×#14581713C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64C22×#41×C83C2211yescharacteristic
65C23×Q8×C83C2211yescharacteristic
66#548×C83—24no—
67#548×C83C2218yes—
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×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C23×Dic83—21no—
80C23×Dic83—21no—
81C2×#13050580—24no—
82C2×#13050580—42no—
83C2×#13050580C2314yes—
84C2×#13050580C2314yes—
85C2×#13050578—42no—
86C2×#13050578C2314yes—
87C2×#13050574—42no—
88C2×#13050574C2314yes—
89C22×C83⋊C8—42no—
90C22×C83⋊C8C2311yescharacteristic
91C22×C83⋊C8C2311yescharacteristic
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2314yes—
95#14581792—22no—
96#14581792C2314yes—
97#14581783—28no—
98#14581771—22no—
99#14581771—22no—
100#14581771C2314yes—
101#14581771C2314yes—
102#14581769—28no—
103#14581769—28no—
104C4×Dic166—22no—
105C4×Dic166C2314yes—
106D4×Dic83—28no—
107C2×C4⋊Dic83—22no—
108C2×C4⋊Dic83—22no—
109C2×C4⋊Dic83—21no—
110C2×C4⋊Dic83—21no—
111C2×C4⋊Dic83—21no—
112C2×C4⋊Dic83C2311yescharacteristic
113C2×C4⋊Dic83C2314yes—
114C2×C4⋊Dic83C2314yes—
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×Dic83⋊C4—21no—
118C2×Dic83⋊C4—21no—
119C2×Dic83⋊C4—21no—
120C2×C22⋊Dic83—21no—
121C2×C22⋊Dic83—21no—
122C2×C4×Dic83—21no—
123#14581723C2314yes—
124#14581723C2314yes—
125#14581723C2314yes—
126C4⋊(C83⋊C8)C2314yes—
127#14581716C2314yes—
128#14581716C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581716C2314yes—
133#14581715C2314yes—
134#14581713C2314yes—
135#14581713C2314yes—
136#14581713C2314yes—
137C22⋊(C83⋊C8)C2314yes—
138C22⋊(C83⋊C8)C2314yes—
139#14581703C2314yes—
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
185C2×Dic166—22no—
186C2×Dic166—22no—
187C2×Dic166—21no—
188C2×Dic166—24no—
189C2×Dic166—82no—
190C2×Dic166C2412yes—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—24no—
196C22×Dic83—24no—
197C22×Dic83—82no—
198C22×Dic83—82no—
199#13050580—28no—
200#13050580—44no—
201#13050578—44no—
202#13050574—44no—
203C2×C83⋊C8—22no—
204C2×C83⋊C8—22no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—44no—
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—24no—
213C4⋊Dic83—24no—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83—21no—
218C4⋊Dic83C2412yes—
219C4⋊Dic83C2412yes—
220C4⋊Dic83C2412yes—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224C22⋊Dic83—24no—
225C22⋊Dic83—24no—
226C4×Dic83—24no—
227C24×C83—21no—
228C24×C83C2×D411yescharacteristic
229C24×C83C2×D411yescharacteristic
230#41×C83—28no—
231#41×C83—44no—
232#41×C83—48no—
233C2×Q8×C83—21no—
234C2×Q8×C83—24no—
235C2×Q8×C83—21no—
236C2×Q8×C83—22no—
237C2×Q8×C83—28no—
238C2×Q8×C83—22no—
239C2×Q8×C83—22no—
240C2×Q8×C83—44no—
241C2×Q8×C83—44no—
242C2×Q8×C83—48no—
243C2×Q8×C83#4114yes—
244C2×Q8×C83C2412yes—
245C2×Q8×C83C2412yes—
246C2×D4×C83—24no—
247C2×D4×C83—24no—
248C2×D4×C83—24no—
249C2×D4×C83—21no—
250C2×D4×C83—22no—
251C2×D4×C83—22no—
252C2×D4×C83—44no—
253C2×D4×C83—44no—
254C2×D4×C83C2×D414yes—
255C2×D4×C83C2412yes—
256C22×C4×C83—21no—
257C22×C4×C83—22no—
258C22×C4×C83—22no—
259C22×C4×C83—22no—
260C22×C4×C83—22no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—24no—
264C22×C4×C83—24no—
265C22×C4×C83—44no—
266C22×C4×C83—44no—
267C22×C4×C83C2×D412yes—
268C22×C4×C83C2×D412yes—
269C22×C4×C83C2×D411yescharacteristic
270C22×C4×C83C2×D411yescharacteristic
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2×D411yescharacteristic
273C22×C4×C83C2412yes—
274C22×C4×C83C2412yes—
275C22×C4×C83C2411yescharacteristic
276C4⋊C4×C83—24no—
277C4⋊C4×C83—24no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83C2×D414yes—
280C4⋊C4×C83C2412yes—
281C22⋊C4×C83—24no—
282C22⋊C4×C83—24no—
283C22⋊C4×C83—24no—
284C22⋊C4×C83—24no—
285C22⋊C4×C83C2×D414yes—
286C22⋊C4×C83C2×D414yes—
287C42×C83—24no—
288C42×C83C2×D412yes—
289C42×C83C2412yes—
290C23×C83—22no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—42no—
297C23×C83—42no—
298C23×C83—42no—
299C23×C83#13714yes—
300C23×C83C22×D412yes—
301C23×C83C22×D412yes—
302C23×C83C22×D411yescharacteristic
303Q8×C83—24no—
304Q8×C83—22no—
305Q8×C83—22no—
306Q8×C83—22no—
307Q8×C83—48no—
308Q8×C83—42no—
309Q8×C83C2×#4114yes—
310D4×C83—28no—
311D4×C83—22no—
312D4×C83—22no—
313D4×C83—48no—
314D4×C83—48no—
315D4×C83—42no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—24no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—24no—
323C2×C4×C83—24no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—48no—
331C2×C4×C83—48no—
332C2×C4×C83—42no—
333C2×C4×C83—42no—
334C2×C4×C83C22×D412yes—
335C2×C4×C83C22×D412yes—
336C2×C4×C83C22×D412yes—
337C2×C4×C83C22×D412yes—
338C2×C4×C83C22×D411yescharacteristic
339C2×C4×C83C2×#4112yes—
340C2×C4×C83H(5,𝔽2)12yes—
341C2×C4×C83C2511yescharacteristic
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—42no—
347C2×Dic83—42no—
348C2×Dic83—42no—
349C2×Dic83—42no—
350C2×Dic83—84no—
351C2×Dic83—84no—
352Dic166—22no—
353Dic166—22no—
354Dic166—42no—
355Dic166—84no—
356C83⋊C8—22no—
357C83⋊C8—22no—
358C83⋊C8—22no—
359C83⋊C8—22no—
360C22×C83—22no—
361C22×C83—28no—
362C22×C83—22no—
363C22×C83—22no—
364C22×C83—22no—
365C22×C83—22no—
366C22×C83—44no—
367C22×C83—42no—
368C22×C83—42no—
369C22×C83—42no—
370C22×C83—84no—
371C22×C83#54612yes—
372C22×C83C2×#13714yes—
373C22×C83C2×#13712yes—
374C22×C83#57712yes—
375C22×C83C23×D411yescharacteristic
376C4×C83—22no—
377C4×C83—22no—
378C4×C83—24no—
379C4×C83—22no—
380C4×C83—22no—
381C4×C83—42no—
382C4×C83—42no—
383C4×C83#54612yes—
384C4×C83C22×#4111yescharacteristic
385C4×C83C2×H(5,𝔽2)11yescharacteristic
386Dic83—42no—
387Dic83—42no—
388Dic83—42no—
389Dic83—42no—
390C2×#3316—831nomaximal, Sylow
391C2×C83—24no—
392C2×C83—42no—
393C2×C83—82no—
394C2×C83#331614yescomplemented
395C2×C83C2×#54611yescharacteristic
396C2×C83C22×#13711yescharacteristic
397C2×C83C2×#57711yescharacteristic
398C2×#554—831no—
399C2×#548D8311yescharacteristic
400#3316—8316no—
401C2×#489—831no—
402C2×#481—831no—
403C2×#483—831no—
404C2×#475—831no—
405C2×#470—831no—
406C2×#465—831no—
407C2×#464—831no—
408C2×#452—831no—
409C2×#451—831no—
410C2×#441—831no—
411C2×#435—831no—
412C2×#417—831no—
413C22×#103—831no—
414C83C2×#331611yescharacteristic, complemented, Sylow
415C22×#41C2×D8311yescharacteristic
416C23×Q8C2×D8311yescharacteristic
417C22×Q16—831no—
418C22×Q16—831no—
419C22×SD16—831no—
420C22×M16—831no—
421C23×C8—831no—
422#554—838no—
423#554—1664no—
424#548—24no—
425#548C2×D8318yes—
426C2×C4⋊Q8—831no—
427C2×#125—1661no—
428C2×#124—21no—
429C2×#124C2×D8311yescharacteristic
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—831no—
432C2×C22⋊Q8—831no—
433C2×C22⋊Q8—1661no—
434C2×C22⋊Q8—1661no—
435C2×C22⋊Q8C2×D8311yescharacteristic
436C2×#121—21no—
437C2×#121C2×D8311yescharacteristic
438C2×C4×Q8—831no—
439C2×C4×Q8C2×D8311yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4—1661no—
442C2×C4×D4C2×D8311yescharacteristic
443C22×C4⋊C4—831no—
444C22×C4⋊C4—831no—
445#489—838no—
446#483—838no—
447#481—838no—
448#475—838no—
449#470—838no—
450#465—838no—
451#464—838no—
452#452—838no—
453#451—838no—
454#441—838no—
455#435—838no—
456C2×#106—831no—
457C2×#106—831no—
458C2×#106—831no—
459C2×C4⋊C8—831no—
460#417—838no—
461C2×#103—831no—
462C2×#103—831no—
463C2×#103—831no—
464C2×#103—831no—
465C2×#103—831no—
466C2×#103—831no—
467C2×#103—838no—
468C2×#103—831no—
469C2×#102—831no—
470C2×#102—831no—
471C2×#102—831no—
472C2×C22⋊C8—831no—
473C2×C22⋊C8—831no—
474C2×#97—831no—
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D8314yes—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—831no—
484C22×Q8—1661no—
485C22×Q8C22×D8311yescharacteristic
486C22×Q8C22×D8314yes—
487C22×Q8C22×D8311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D8311yescharacteristic
491C22×D4C22×D8311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1661no—
495C23×C4—1661no—
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8311yescharacteristic
498C2×Q16—3322no—
499C2×Q16—834no—
500C2×Q16—834no—
501C2×Q16—1664no—
502C2×SD16—3322no—
503C2×SD16—834no—
504C2×M16—3322no—
505C2×M16—834no—
506C22×C8—3322no—
507C22×C8—834no—
508C22×C8—831no—
509C22×C8—831no—
510C22×C8—831no—
511C22×C8—831no—
512C4⋊Q8—834no—
513C4⋊Q8—1662no—
514#125—1668no—
515#124—28no—
516#124—22no—
517#124C22×D8314yes—
518C22⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8—834no—
521C22⋊Q8—834no—
522C22⋊Q8—1662no—
523C22⋊Q8—1662no—
524C22⋊Q8—1668no—
525C22⋊Q8—1668no—
526C22⋊Q8C22×D8314yes—
527#121—28no—
528#121—22no—
529#121C22×D8314yes—
530C4×Q8—22no—
531C4×Q8—834no—
532C4×Q8—1662no—
533C4×Q8C22×D8314yes—
534C4×D4—28no—
535C4×D4—1668no—
536C4×D4C22⋊D8314yes—
537C4×D4C22×D8314yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—831no—
541C2×C4⋊C4—831no—
542C2×C4⋊C4—831no—
543C2×C4⋊C4—834no—
544C2×C4⋊C4—834no—
545C2×C4⋊C4—1661no—
546C2×C4⋊C4—1661no—
547C2×C4⋊C4—1662no—
548C2×C4⋊C4—1662no—
549C2×C4⋊C4—1661no—
550C2×C4⋊C4—1661no—
551C2×C4⋊C4—1661no—
552C2×C4⋊C4—1661no—
553C2×C4⋊C4C22⋊D8311yescharacteristic
554C2×C4⋊C4C22×D8311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1661no—
560C2×C22⋊C4—1661no—
561C2×C22⋊C4C22⋊D8311yescharacteristic
562C2×C22⋊C4C22⋊D8311yescharacteristic
563C2×C42—21no—
564C2×C42—1661no—
565C2×C42C22×D8311yescharacteristic
566#106—834no—
567#106—834no—
568#106—834no—
569C4⋊C8—834no—
570#103—834no—
571#103—834no—
572#103—834no—
573#103—834no—
574#103—834no—
575#103—834no—
576#103—834no—
577#102—834no—
578#102—834no—
579#102—834no—
580C22⋊C8—834no—
581C22⋊C8—834no—
582#97—834no—
583C24—21no—
584C24C2×C22⋊D8311yescharacteristic
585C24C2×C22⋊D8311yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8—832no—
600C2×Q8—6642no—
601C2×Q8—1662no—
602C2×Q8—1662no—
603C2×Q8—1661no—
604C2×Q8—1664no—
605C2×Q8#1305058914yes—
606C2×Q8C23×D8312yes—
607C2×Q8C23×D8312yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4C2×C22⋊D8314yes—
617C2×D4C23×D8312yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—6642no—
630C22×C4—6642no—
631C22×C4—1661no—
632C22×C4—1661no—
633C22×C4—1661no—
634C22×C4—1661no—
635C22×C4—1664no—
636C22×C4—1664no—
637C22×C4C2×C22⋊D8312yes—
638C22×C4C2×C22⋊D8312yes—
639C22×C4C2×C22⋊D8311yescharacteristic
640C22×C4C2×C22⋊D8311yescharacteristic
641C22×C4C2×C22⋊D8311yescharacteristic
642C22×C4C2×C22⋊D8311yescharacteristic
643C22×C4C23×D8312yes—
644C22×C4C23×D8312yes—
645C22×C4C23×D8311yescharacteristic
646Q16—3324no—
647Q16—1668no—
648SD16—3324no—
649M16—3324no—
650C2×C8—3324no—
651C2×C8—832no—
652C2×C8—832no—
653C2×C8—832no—
654C2×C8—832no—
655C2×C8—1662no—
656C2×C8—1662no—
657C2×C8—1662no—
658C2×C8—1662no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—832no—
663C4⋊C4—832no—
664C4⋊C4—832no—
665C4⋊C4—1661no—
666C4⋊C4—1664no—
667C4⋊C4—1664no—
668C4⋊C4—1661no—
669C4⋊C4—1661no—
670C4⋊C4—1664no—
671C4⋊C4—1664no—
672C4⋊C4—1664no—
673C4⋊C4—1664no—
674C4⋊C4C2×C22⋊D8314yes—
675C4⋊C4C23×D8312yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—1664no—
681C22⋊C4—1664no—
682C22⋊C4C2×C22⋊D8314yes—
683C22⋊C4C2×C22⋊D8314yes—
684C42—24no—
685C42—1664no—
686C42C2×C22⋊D8312yes—
687C42C23×D8312yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#1458182214yes—
698C23C22×C22⋊D8312yes—
699C23C22×C22⋊D8312yes—
700C23C22×C22⋊D8311yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—3322no—
708Q8—6644no—
709Q8—1662no—
710Q8—1662no—
711Q8C2×#1305058914yes—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—48no—
717D4—42no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—3322no—
737C2×C4—3322no—
738C2×C4—3322no—
739C2×C4—3322no—
740C2×C4—6644no—
741C2×C4—6644no—
742C2×C4—1662no—
743C2×C4—1662no—
744C2×C4—1662no—
745C2×C4—1662no—
746C2×C4C22×C22⋊D8312yes—
747C2×C4C22×C22⋊D8312yes—
748C2×C4C22×C22⋊D8312yes—
749C2×C4C22×C22⋊D8312yes—
750C2×C4C22×C22⋊D8311yescharacteristic
751C2×C4C2×#1305058912yes—
752C2×C4#1458183712yes—
753C2×C4C24×D8311yescharacteristic
754C8—1662no—
755C8—1662no—
756C8—1662no—
757C8—1662no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1912834512yes—
770C22C2×#1458182214yes—
771C22C2×#1458182212yes—
772C22#1912850912yes—
773C22C23×C22⋊D8311yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—3322no—
782C4—3322no—
783C4—3322no—
784C4—3322no—
785C4#1912834512yes—
786C4C22×#1305058911yescharacteristic
787C4C2×#1458183711yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#2491957414yesdirect product factor
792C2C2×#1912834511yescharacteristic
793C2C22×#1458182211yescharacteristic
794C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
Fitting, prime radicalC2×#548×C83C2
socleC23×C83C22×D4
hypercenterC2×#548D83
hypocenterC83C2×#3316
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×#19128408C2semidirect
2. #24919574C2direct (N × H)
3. C2×#19128060C2semidirect
4. C2×#19128017C2semidirect
5. C2×#19128029C2semidirect
6. C2×#19127986C2semidirect
7. C2×#19127957C2semidirect
8. C2×#19127928C2semidirect
9. C2×#19127920C2semidirect
10. C2×#19127863C2semidirect
11. C2×#19127857C2semidirect
12. C2×#19127806C2semidirect
13. C2×#19127773C2semidirect
14. C2×#19127702C2semidirect
15. C22×#14581716C2semidirect
23. #19128408C22semidirect
34. #19128060C22semidirect
35. #19128029C22semidirect
36. #19128017C22semidirect
37. #19127986C22semidirect
38. #19127957C22semidirect
39. #19127928C22semidirect
40. #19127920C22semidirect
41. #19127863C22semidirect
42. #19127857C22semidirect
43. #19127806C22semidirect
44. #19127773C22semidirect
49. #19127702C22semidirect
56. C2×#14581716C22semidirect
394. C2×C83#3316semidirect
414. C83C2×#3316semidirect
791. C2#24919574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284082
#249195742
C2×#191280602
C2×#191280172
C2×#191280292
C2×#191279862
C2×#191279572
C2×#191279282
C2×#191279202
C2×#191278632
C2×#191278572
C2×#191278062
C2×#191277732
C2×#191277022
C22×#145817162
C2×#548×C832
C2×#331683