Finite Group Databasebeta

← C2×#24919907 #36282939

Subgroups — C2×#24919907 #36282939

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×#19128386C211yesmaximal, characteristic, complemented
2C2×#19128351C211yesmaximal, characteristic
3#24919907C2116yesmaximal, direct product factor
4C2×#19128109C211yesmaximal, characteristic, complemented
5C2×#19128038C211yesmaximal, characteristic, complemented
6C2×#19128024C211yesmaximal, characteristic, complemented
7C2×#19128032C211yesmaximal, characteristic, complemented
8C2×#19127995C211yesmaximal, characteristic, complemented
9C2×#19128003C211yesmaximal, characteristic, complemented
10C2×#19127946C211yesmaximal, characteristic, complemented
11C2×#19127928C211yesmaximal, characteristic, complemented
12C2×#19127798C211yesmaximal, characteristic, complemented
13C2×#19127769C211yesmaximal, characteristic, complemented
14C2×#19127742C211yesmaximal, characteristic, complemented
15C22×#14581725C211yesmaximal, characteristic, complemented
16C2×#480×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×#13050578C2211yescharacteristic
19C22×#13050573C2211yescharacteristic
20C23×C83⋊C8C2211yescharacteristic
21#19128386—24no—
22#19128386C2218yescomplemented
23#19128351—24no—
24#19128351C2218yes—
25C2×#14581791C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581783C2211yescharacteristic
28C2×#14581782—21no—
29C2×#14581775—21no—
30C2×#14581774—21no—
31C2×#14581773—21no—
32C2×#14581772C2211yescharacteristic
33C2×#14581771C2211yescharacteristic
34C2×#14581769—21no—
35C2×#14581763C2211yescharacteristic
36C2×#14581757C2211yescharacteristic
37C2×D4×Dic83C2211yescharacteristic
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×#14581751—21no—
40C2×#14581750C2211yescharacteristic
41C22×C4⋊Dic83C2211yescharacteristic
42C2×C4⋊C4×D83C2211yescharacteristic
43#19128109C2218yescomplemented
44#19128038C2218yescomplemented
45#19128032C2218yescomplemented
46#19128024C2218yescomplemented
47#19128003C2218yescomplemented
48#19127995C2218yescomplemented
49#19127946C2218yescomplemented
50#19127928C2218yescomplemented
51#19127798C2218yescomplemented
52#19127769C2218yescomplemented
53#19127742C2218yescomplemented
54C2×#14581725C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×#14581725C2211yescharacteristic
57C2×#14581725C2211yescharacteristic
58C2×#14581725C2218yescomplemented
59C2×#14581724C2211yescharacteristic
60C2×#14581724C2211yescharacteristic
61C2×#14581723C2211yescharacteristic
62C2×Dic83⋊C8C2211yescharacteristic
63C2×#14581717C2211yescharacteristic
64C2×#14581717C2211yescharacteristic
65C2×#14581715C2211yescharacteristic
66C2×#14581713C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581702C2211yescharacteristic
69C2×#121×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2211yescharacteristic
71#480×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#107×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×Dic166C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83D411yescharacteristic
83C23×Dic83—21no—
84C23×Dic83—21no—
85C22×C4×D83—21no—
86C22×C4×D83C2311yescharacteristic
87C2×#13050578—24no—
88C2×#13050578C2314yes—
89C2×#13050573—24no—
90C2×#13050573C2314yes—
91C22×C83⋊C8—24no—
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2314yes—
94C22×C83⋊C8C2311yescharacteristic
95#14581791—22no—
96#14581791C2314yes—
97#14581787—28no—
98#14581783—22no—
99#14581783C2314yes—
100#14581782—28no—
101#14581775—28no—
102#14581774—28no—
103#14581773—28no—
104#14581772—22no—
105#14581772C2314yes—
106#14581771—22no—
107#14581771C2314yes—
108#14581769—28no—
109#14581763—22no—
110#14581763C2314yes—
111#14581757—22no—
112#14581757C2314yes—
113D4×Dic83—22no—
114D4×Dic83C2314yes—
115C4×C22⋊D83D414yes—
116C4×C22⋊D83C2314yes—
117#14581751—28no—
118#14581750—22no—
119#14581750C2314yes—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—22no—
123C2×C4⋊Dic83—21no—
124C2×C4⋊Dic83C2314yes—
125C2×C4⋊Dic83C2311yescharacteristic
126C2×C4⋊Dic83C2311yescharacteristic
127C2×C4⋊Dic83C2311yescharacteristic
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4D411yescharacteristic
134C4⋊C4×D83—22no—
135C4⋊C4×D83C2314yes—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83D411yescharacteristic
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4D411yescharacteristic
143C2×C4×Dic83—21no—
144C2×C4×Dic83—21no—
145C2×C4×Dic83C2311yescharacteristic
146#14581725C2314yes—
147#14581725C2314yes—
148#14581725C2314yes—
149#14581725C2314yes—
150#14581724C2314yes—
151#14581724C2314yes—
152#14581723C2314yes—
153Dic83⋊C8C2314yes—
154#14581717C2314yes—
155#14581717C2314yes—
156#14581715C2314yes—
157#14581713C2314yes—
158(C2×D83)⋊C8C2314yes—
159#14581702C2314yes—
160C22×D4×C83—21no—
161C22×D4×C83C2311yescharacteristic
162C23×C4×C83—21no—
163C23×C4×C83C2311yescharacteristic
164C22×C8×C83C2311yescharacteristic
165C22×C8×C83C2311yescharacteristic
166#121×C83—22no—
167#121×C83C2314yes—
168C2×C4⋊C4×C83—22no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83C2314yes—
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83—21no—
175#107×C83C2314yes—
176#107×C83C2314yes—
177#102×C83C2314yes—
178#102×C83C2314yes—
179C22⋊C8×C83C2314yes—
180C23×D83C2×D411yescharacteristic
181#13050589—432no—
182C2×Dic166—22no—
183C2×Dic166—22no—
184C2×Dic166—21no—
185C2×Dic166—24no—
186C2×Dic166—44no—
187C2×Dic166C2412yes—
188C2×C22⋊D83—24no—
189C2×C22⋊D83—24no—
190C2×C22⋊D83—44no—
191C2×C22⋊D83C2×D414yes—
192C22×Dic83—24no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—24no—
198C22×Dic83—44no—
199C22×Dic83—44no—
200C22×Dic83C2×D411yescharacteristic
201C22×Dic83C2×D411yescharacteristic
202C22×Dic83C2×D411yescharacteristic
203C2×C4×D83—22no—
204C2×C4×D83—22no—
205C2×C4×D83—24no—
206C2×C4×D83—44no—
207C2×C4×D83C2×D412yes—
208C2×C4×D83C2412yes—
209#13050578—28no—
210#13050573—28no—
211C2×C83⋊C8—22no—
212C2×C83⋊C8—28no—
213C2×C83⋊C8#4114yescomplemented
214C2×C83⋊C8C2412yes—
215C2×C83⋊C8C2412yes—
216C4⋊Dic83—21no—
217C4⋊Dic83—24no—
218C4⋊Dic83—21no—
219C4⋊Dic83—21no—
220C4⋊Dic83—24no—
221C4⋊Dic83—24no—
222C4⋊Dic83C2412yes—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4C2×D414yes—
231C22⋊Dic83—24no—
232C22⋊Dic83—24no—
233C22⋊Dic83—24no—
234C22⋊Dic83C2×D414yes—
235(C2×D83)⋊C4—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4C2×D414yes—
238C4×Dic83—24no—
239C4×Dic83—24no—
240C4×Dic83C2×D412yes—
241C4×Dic83C2412yes—
242C24×C83—21no—
243C24×C83C2×D411yescharacteristic
244C2×D4×C83—24no—
245C2×D4×C83—21no—
246C2×D4×C83—22no—
247C2×D4×C83—22no—
248C2×D4×C83—44no—
249C2×D4×C83C2412yes—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—24no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—44no—
257C22×C4×C83C2×D412yes—
258C22×C4×C83C2×D411yescharacteristic
259C22×C4×C83C2412yes—
260C22×C4×C83C2411yescharacteristic
261C2×C8×C83—22no—
262C2×C8×C83—22no—
263C2×C8×C83C2412yes—
264C2×C8×C83C2412yes—
265C4⋊C4×C83—21no—
266C4⋊C4×C83—24no—
267C4⋊C4×C83—21no—
268C4⋊C4×C83—21no—
269C4⋊C4×C83C2412yes—
270C4⋊C4×C83C2412yes—
271C4⋊C4×C83C2412yes—
272C22⋊C4×C83—24no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—42no—
277C23×C83—42no—
278C23×C83—42no—
279C23×C83AGL(1,ℤ/8)14yes—
280C23×C83C22×D412yes—
281C23×C83C22×D411yescharacteristic
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83C22×D412yes—
286D4×C83—22no—
287D4×C83—22no—
288D4×C83—48no—
289D4×C83—42no—
290C2×C4×C83—22no—
291C2×C4×C83—24no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—48no—
298C2×C4×C83—42no—
299C2×C4×C83—42no—
300C2×C4×C83—42no—
301C2×C4×C83C22×D412yes—
302C2×C4×C83C22×D411yescharacteristic
303C2×C4×C83C2×#4112yes—
304C2×C4×C832−1+412yes—
305C2×C4×C83C2511yescharacteristic
306C22⋊D83—28no—
307C22⋊D83—48no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—48no—
316C2×Dic83—42no—
317C2×Dic83—42no—
318C2×Dic83—42no—
319C2×Dic83—48no—
320C2×Dic83—42no—
321C2×Dic83C22×D412yes—
322C2×Dic83C22×D412yes—
323C2×Dic83C22×D412yes—
324C4×D83—24no—
325C4×D83—22no—
326C4×D83—22no—
327C4×D83—48no—
328Dic166—22no—
329Dic166—22no—
330Dic166—48no—
331Dic166—42no—
332C8×C83—22no—
333C8×C83—22no—
334C83⋊C8—22no—
335C83⋊C8C2×#4114yescomplemented
336C22×C83—28no—
337C22×C83—22no—
338C22×C83—22no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—84no—
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—22no—
349C2×D83—22no—
350C2×D83—22no—
351C2×D83—44no—
352C4×C83—22no—
353C4×C83—42no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83#54712yes—
357C4×C83C22×#4111yescharacteristic
358C4×C83C2×2−1+411yescharacteristic
359Dic83—22no—
360Dic83—22no—
361Dic83—22no—
362Dic83—42no—
363Dic83—42no—
364Dic83—42no—
365Dic83—42no—
366C2×#3343—831nomaximal, Sylow
367C2×C83—24no—
368C2×C83—82no—
369C2×C83#334314yescomplemented
370C2×C83C2×#54711yescharacteristic
371C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C83C2×#57811yescharacteristic
373D83—42no—
374C2×#552—831no—
375C2×#547—831no—
376#3343—8316no—
377C2×#501—831no—
378C2×#484—831no—
379C2×#482—831no—
380C2×#483—831no—
381C2×#480D8311yescharacteristic, complemented
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—838no—
396#552—1664no—
397#547—838no—
398#547—1664no—
399C2×C4⋊Q8—831no—
400C2×#126—1661no—
401C2×#125—831no—
402C2×#125—1661no—
403C2×#123—1661no—
404C2×#123—1661no—
405C2×#123—1661no—
406C2×C22⋊Q8—831no—
407C2×C22⋊Q8—831no—
408C2×C22⋊Q8—1661no—
409C2×#121—831no—
410C2×#121C2×D8311yescharacteristic
411C2×C4×Q8—831no—
412C2×C4×D4—831no—
413C2×C4×D4—831no—
414C2×#117—831no—
415C2×#117—1661no—
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#480C2×D8318yescomplemented
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—838no—
434C2×#107—831no—
435C2×#107—831no—
436C2×#107C2×D8311yescharacteristic
437C2×#107C2×D8311yescharacteristic
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×#102C2×D8311yescharacteristic
447C2×#102C2×D8311yescharacteristic
448C2×C22⋊C8—831no—
449C2×C22⋊C8C2×D8311yescharacteristic
450C2×#97—831no—
451C2×#41—3328no—
452C2×#41—1668no—
453C22×Q8—831no—
454C22×Q8—1661no—
455C22×D4—21no—
456C22×D4—831no—
457C22×D4—1661no—
458C22×D4C22×D8311yescharacteristic
459C23×C4—21no—
460C23×C4—831no—
461C23×C4—1661no—
462C23×C4—1661no—
463C23×C4—1661no—
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—1664no—
473C22×C8C22×D8311yescharacteristic
474C22×C8C22×D8311yescharacteristic
475C4⋊Q8—834no—
476C4⋊Q8—1662no—
477#126—1668no—
478#125—834no—
479#125—1662no—
480#125—1668no—
481#123—1668no—
482#123—1668no—
483#123—1668no—
484C22⋊Q8—834no—
485C22⋊Q8—834no—
486C22⋊Q8—1668no—
487C22⋊Q8—1662no—
488C22⋊Q8—1662no—
489#121—22no—
490#121—834no—
491#121—1662no—
492#121C22×D8314yes—
493C4×Q8—834no—
494C4×Q8—1662no—
495C4×D4—834no—
496C4×D4—834no—
497C4×D4—834no—
498C4×D4—1662no—
499#117—834no—
500#117—1668no—
501#117—1662no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—831no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—1662no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1661no—
517C2×C4⋊C4—1661no—
518C2×C4⋊C4—1662no—
519C2×C4⋊C4—1661no—
520C2×C4⋊C4C22×D8311yescharacteristic
521C2×C4⋊C4C22×D8311yescharacteristic
522C2×C4⋊C4C22×D8311yescharacteristic
523C2×C4⋊C4C22×D8314yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—831no—
526C2×C22⋊C4—831no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C22⋊C4—1661no—
531C2×C22⋊C4—1661no—
532C2×C42—831no—
533C2×C42—1661no—
534C2×C42—1661no—
535#107—834no—
536#107—834no—
537#107—834no—
538#107—834no—
539#107C22×D8314yes—
540#107C22×D8314yes—
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#102C22×D8314yes—
550#102C22×D8314yes—
551C22⋊C8—834no—
552C22⋊C8C22×D8314yes—
553#97—834no—
554C24—21no—
555C24—831no—
556C24D4×D8311yescharacteristic
557#41—33232no—
558C2×Q8—3324no—
559C2×Q8—832no—
560C2×Q8—1664no—
561C2×Q8—1662no—
562C2×Q8—1662no—
563C2×Q8—1661no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—3324no—
570C2×D4—834no—
571C2×D4—1664no—
572C2×D4—1664no—
573C2×D4C23×D8312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—44no—
581C22×C4—3324no—
582C22×C4—3324no—
583C22×C4—3324no—
584C22×C4—831no—
585C22×C4—831no—
586C22×C4—831no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—1664no—
590C22×C4—1664no—
591C22×C4—1664no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4D4×D8312yes—
599C22×C4D4×D8311yescharacteristic
600C22×C4C23×D8312yes—
601C22×C4C23×D8311yescharacteristic
602SD16—1668no—
603M16—1668no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—834no—
607C2×C8—832no—
608C2×C8—832no—
609C2×C8—1668no—
610C2×C8—1662no—
611C2×C8C23×D8312yes—
612C2×C8C23×D8312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—834no—
618C4⋊C4—832no—
619C4⋊C4—832no—
620C4⋊C4—832no—
621C4⋊C4—1664no—
622C4⋊C4—1664no—
623C4⋊C4—1664no—
624C4⋊C4—1664no—
625C4⋊C4—1664no—
626C4⋊C4—1664no—
627C4⋊C4—1661no—
628C4⋊C4—1661no—
629C4⋊C4—1664no—
630C4⋊C4—1661no—
631C4⋊C4—1664no—
632C4⋊C4C23×D8312yes—
633C4⋊C4C23×D8312yes—
634C4⋊C4C23×D8312yes—
635C22⋊C4—24no—
636C22⋊C4—834no—
637C22⋊C4—834no—
638C22⋊C4—1664no—
639C22⋊C4—1664no—
640C22⋊C4—1664no—
641C22⋊C4—1664no—
642C22⋊C4—1664no—
643C42—832no—
644C42—832no—
645C42—1664no—
646C42—1664no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—832no—
654C23—1662no—
655C23—1662no—
656C23—1662no—
657C23#1458181614yes—
658C23C2×D4×D8312yes—
659C23C2×D4×D8311yescharacteristic
660Q8—3328no—
661Q8—3322no—
662Q8—1662no—
663Q8—1662no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—3328no—
669D4—1668no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—3328no—
682C2×C4—3322no—
683C2×C4—3322no—
684C2×C4—3322no—
685C2×C4—3328no—
686C2×C4—3322no—
687C2×C4—3328no—
688C2×C4—832no—
689C2×C4—832no—
690C2×C4—832no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1664no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4C2×D4×D8312yes—
702C2×C4C2×D4×D8311yescharacteristic
703C2×C4#41×D8312yes—
704C2×C4#1458183912yes—
705C2×C4C24×D8311yescharacteristic
706C8—22no—
707C8—22no—
708C8—834no—
709C8—1662no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—3324no—
718C22—1662no—
719C22—1662no—
720C22—1662no—
721C22#1912834912yes—
722C22C2×#1458181614yes—
723C22C2×#1458181612yes—
724C22#1912851712yes—
725C22C22×D4×D8311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—3322no—
731C4—3322no—
732C4—3322no—
733C4—3322no—
734C4—1662no—
735C4—1662no—
736C4—1662no—
737C4#1912834912yes—
738C4C2×#41×D8311yescharacteristic
739C4C2×#1458183911yescharacteristic
740C2—24no—
741C2—82no—
742C2—3322no—
743C2#2491990714yesdirect product factor
744C2C2×#1912834911yescharacteristic
745C2C22×#1458181611yescharacteristic
746C2C2×#1912851711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#480×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128351C2
hypercenterC2×#480D83
hypocenterC83C2×#3343
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#19128386C2semidirect
3. #24919907C2direct (N × H)
4. C2×#19128109C2semidirect
5. C2×#19128038C2semidirect
6. C2×#19128024C2semidirect
7. C2×#19128032C2semidirect
8. C2×#19127995C2semidirect
9. C2×#19128003C2semidirect
10. C2×#19127946C2semidirect
11. C2×#19127928C2semidirect
12. C2×#19127798C2semidirect
13. C2×#19127769C2semidirect
14. C2×#19127742C2semidirect
15. C22×#14581725C2semidirect
16. C2×#480×C83C2semidirect
22. #19128386C22semidirect
43. #19128109C22semidirect
44. #19128038C22semidirect
45. #19128032C22semidirect
46. #19128024C22semidirect
47. #19128003C22semidirect
48. #19127995C22semidirect
49. #19127946C22semidirect
50. #19127928C22semidirect
51. #19127798C22semidirect
52. #19127769C22semidirect
53. #19127742C22semidirect
58. C2×#14581725C22semidirect
71. #480×C83C22semidirect
213. C2×C83⋊C8#41semidirect
335. C83⋊C8C2×#41semidirect
369. C2×C83#3343semidirect
381. C2×#480D83semidirect
390. C83C2×#3343semidirect
423. #480C2×D83semidirect
743. C2#24919907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283862
C2×#191283512
#249199072
C2×#191281092
C2×#191280382
C2×#191280242
C2×#191280322
C2×#191279952
C2×#191280032
C2×#191279462
C2×#191279282
C2×#191277982
C2×#191277692
C2×#191277422
C22×#145817252
C2×#480×C832
C2×#334383