Finite Group Databasebeta

← C2×#24919505 #36281080

Subgroups — C2×#24919505 #36281080

Order 21248.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128422C211yesmaximal, characteristic, complemented
2C2×#19128348C211yesmaximal, characteristic
3#24919505C2116yesmaximal, direct product factor
4C2×#19128059C211yesmaximal, characteristic, complemented
5C2×#19128045C211yesmaximal, characteristic, complemented
6C2×#19128022C211yesmaximal, characteristic, complemented
7C2×#19127990C211yesmaximal, characteristic, complemented
8C2×#19127958C211yesmaximal, characteristic, complemented
9C2×#19127921C211yesmaximal, characteristic, complemented
10C2×#19127861C211yesmaximal, characteristic, complemented
11C2×#19127850C211yesmaximal, characteristic, complemented
12C2×#19127804C211yesmaximal, characteristic, complemented
13C2×#19127772C211yesmaximal, characteristic, complemented
14C2×#19127704C211yesmaximal, characteristic, complemented
15C2×#19127698C211yesmaximal, characteristic, complemented
16C2×#465×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C22×D4×D83C2211yescharacteristic
19C22×#13050580C2211yescharacteristic, complemented
20C22×#13050577C2211yescharacteristic
21C22×#13050573C2211yescharacteristic
22#19128422—24no—
23#19128422C2218yescomplemented
24#19128348—24no—
25#19128348C2218yes—
26C2×#14581791C2211yescharacteristic, complemented
27C2×#14581787—21no—
28C2×#14581785—21no—
29C2×#14581779C2211yescharacteristic
30C2×#14581778—21no—
31C2×#14581774—21no—
32C2×#14581772C2211yescharacteristic
33C2×#14581768C2211yescharacteristic
34C2×#14581763—21no—
35C2×#14581760—21no—
36C2×Q8×Dic83C2211yescharacteristic, complemented
37C2×#14581757—21no—
38C2×#14581754C2211yescharacteristic
39C2×C4×C22⋊D83C2211yescharacteristic
40C2×#14581751C2211yescharacteristic, complemented
41C2×#14581750C2211yescharacteristic
42C2×C22⋊C4×D83—21no—
43#19128059C2218yescomplemented
44#19128045C2218yescomplemented
45#19128022C2218yescomplemented
46#19127990C2218yescomplemented
47#19127958C2218yescomplemented
48#19127921C2218yescomplemented
49#19127861C2218yescomplemented
50#19127850C2218yescomplemented
51#19127804C2218yescomplemented
52#19127772C2218yescomplemented
53C2×#14581725C2211yescharacteristic, complemented
54C2×#14581723C2211yescharacteristic, complemented
55C2×Dic83⋊C8C2211yescharacteristic, complemented
56#19127704C2218yescomplemented
57#19127698C2218yescomplemented
58C2×#14581717C2211yescharacteristic, complemented
59C2×#14581717C2211yescharacteristic, complemented
60C2×#14581715C2211yescharacteristic, complemented
61C2×#14581714C2211yescharacteristic
62C2×#14581714C2211yescharacteristic
63C2×#14581713C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×#14581702C2211yescharacteristic, complemented
69C22×SD16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic, complemented
71C2×C22⋊Q8×C83C2211yescharacteristic, complemented
72C2×#121×C83C2211yescharacteristic
73#465×C83C2218yescomplemented
74C2×#106×C83C2211yescharacteristic, complemented
75C2×#103×C83C2211yescharacteristic, complemented
76C2×#102×C83C2211yescharacteristic
77C24×D83—21no—
78C2×#13050590—24no—
79C2×#13050590—22no—
80C2×#13050590—42no—
81C2×#13050590C2314yes—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C22×D332C2311yescharacteristic
85C22×C22⋊D83—21no—
86C22×C22⋊D83—21no—
87C22×C22⋊D83D411yescharacteristic
88C2×D4×D83—24no—
89C2×D4×D83—22no—
90C2×D4×D83—42no—
91C2×D4×D83C2314yes—
92C22×C4×D83—21no—
93C22×C4×D83—21no—
94C22×C4×D83C2311yescharacteristic
95C2×#13050580—42no—
96C2×#13050580C2314yescomplemented
97C2×#13050577—24no—
98C2×#13050577C2314yes—
99C2×#13050573—42no—
100C2×#13050573C2314yes—
101C22×C83⋊C8C2311yescharacteristic
102C22×C83⋊C8C2311yescharacteristic
103#14581791—22no—
104#14581791C2314yescomplemented
105#14581787—28no—
106#14581785—28no—
107#14581779—22no—
108#14581779C2314yes—
109#14581778—28no—
110#14581774—28no—
111#14581772—22no—
112#14581772C2314yes—
113#14581768—22no—
114#14581768C2314yes—
115#14581763—28no—
116#14581760—28no—
117Q8×Dic83—22no—
118Q8×Dic83C2314yescomplemented
119#14581757—28no—
120#14581754—22no—
121#14581754C2314yes—
122C4×C22⋊D83D414yes—
123C4×C22⋊D83C2314yes—
124#14581751—22no—
125#14581751C2314yescomplemented
126#14581750—22no—
127#14581750C2314yes—
128C2×C4⋊Dic83—21no—
129C2×C4⋊Dic83—21no—
130C2×C4⋊Dic83C2311yescharacteristic
131C2×C4⋊Dic83C2311yescharacteristic
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4D411yescharacteristic
135C2×C22⋊Dic83—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83D411yescharacteristic
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4D411yescharacteristic
144C22⋊C4×D83—28no—
145C2×C4×Dic83—21no—
146C2×C4×Dic83—21no—
147C2×C4×Dic83—21no—
148C2×C4×Dic83C2311yescharacteristic
149#14581725C2314yescomplemented
150#14581723C2314yescomplemented
151Dic83⋊C8C2314yescomplemented
152#14581717C2314yescomplemented
153#14581717C2314yescomplemented
154#14581715C2314yescomplemented
155#14581714C2314yes—
156#14581714C2314yes—
157#14581713C2314yes—
158#14581713C2314yes—
159#14581712C2314yes—
160C22⋊(C83⋊C8)C2314yescomplemented
161(C2×D83)⋊C8C2314yes—
162#14581702C2314yescomplemented
163C22×Q8×C83C2311yescharacteristic
164C22×D4×C83—21no—
165C22×D4×C83C2311yescharacteristic
166C23×C4×C83C2311yescharacteristic
167C2×SD16×C83—42no—
168C2×SD16×C83C2314yes—
169C22×C8×C83—42no—
170C22×C8×C83C2311yescharacteristic
171C22×C8×C83C2311yescharacteristic
172C22×C8×C83C2314yescomplemented
173C22⋊Q8×C83—22no—
174C22⋊Q8×C83C2314yescomplemented
175#121×C83—22no—
176#121×C83C2314yes—
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83C2311yescharacteristic
179C2×C4⋊C4×C83C2311yescharacteristic
180C2×C22⋊C4×C83—21no—
181C2×C22⋊C4×C83—21no—
182#106×C83C2314yescomplemented
183#103×C83C2314yescomplemented
184#102×C83C2314yes—
185C23×D83—21no—
186C23×D83—24no—
187C23×D83—44no—
188C23×D83—44no—
189C23×D83—82no—
190C23×D83C2×D411yescharacteristic
191#13050590—28no—
192#13050590—44no—
193#13050590—48no—
194C2×Dic166—22no—
195C2×Dic166—22no—
196C2×Dic166—21no—
197C2×Dic166—24no—
198C2×Dic166—44no—
199C2×Dic166C2412yes—
200C2×D332—21no—
201C2×D332—22no—
202C2×D332#4114yes—
203C2×D332C2412yes—
204C2×C22⋊D83—24no—
205C2×C22⋊D83—24no—
206C2×C22⋊D83—42no—
207C2×C22⋊D83—44no—
208C2×C22⋊D83—44no—
209C2×C22⋊D83C2×D414yes—
210D4×D83—28no—
211D4×D83—44no—
212D4×D83—48no—
213C22×Dic83—21no—
214C22×Dic83—21no—
215C22×Dic83—21no—
216C22×Dic83C2×D411yescharacteristic
217C22×Dic83C2×D411yescharacteristic
218C22×Dic83C2×D411yescharacteristic
219C2×C4×D83—22no—
220C2×C4×D83—22no—
221C2×C4×D83—24no—
222C2×C4×D83—24no—
223C2×C4×D83—44no—
224C2×C4×D83—82no—
225C2×C4×D83C2×D412yes—
226C2×C4×D83C2412yes—
227#13050580—44no—
228#13050577—28no—
229#13050573—44no—
230C2×C83⋊C8—22no—
231C2×C83⋊C8—22no—
232C2×C83⋊C8C2412yes—
233C2×C83⋊C8C2412yes—
234C4⋊Dic83—21no—
235C4⋊Dic83—21no—
236C4⋊Dic83—24no—
237C4⋊Dic83—24no—
238C4⋊Dic83C2412yes—
239C4⋊Dic83C2412yes—
240Dic83⋊C4—24no—
241Dic83⋊C4—24no—
242Dic83⋊C4C2×D414yes—
243C22⋊Dic83—24no—
244C22⋊Dic83—24no—
245C22⋊Dic83—24no—
246C22⋊Dic83C2×D414yes—
247(C2×D83)⋊C4—24no—
248(C2×D83)⋊C4—24no—
249(C2×D83)⋊C4—24no—
250(C2×D83)⋊C4—24no—
251(C2×D83)⋊C4C2×D414yes—
252C4×Dic83—24no—
253C4×Dic83—24no—
254C4×Dic83—24no—
255C4×Dic83C2×D412yes—
256C4×Dic83C2412yes—
257C24×C83—21no—
258C24×C83C2×D411yescharacteristic
259C2×Q8×C83—21no—
260C2×Q8×C83—22no—
261C2×Q8×C83—22no—
262C2×Q8×C83C2412yes—
263C2×D4×C83—24no—
264C2×D4×C83—21no—
265C2×D4×C83—22no—
266C2×D4×C83—22no—
267C2×D4×C83—82no—
268C2×D4×C83C2412yes—
269C22×C4×C83—22no—
270C22×C4×C83—22no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83C2×D411yescharacteristic
275C22×C4×C83C2×D412yes—
276C22×C4×C83C2412yes—
277C22×C4×C83C2411yescharacteristic
278SD16×C83—44no—
279C2×C8×C83—22no—
280C2×C8×C83—22no—
281C2×C8×C83—44no—
282C2×C8×C83C2412yes—
283C2×C8×C83C2412yes—
284C4⋊C4×C83—21no—
285C4⋊C4×C83—24no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83C2412yes—
288C4⋊C4×C83C2412yes—
289C22⋊C4×C83—24no—
290C22⋊C4×C83—24no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—42no—
296C23×C83—42no—
297C23×C83—42no—
298C23×C83C22×D412yes—
299C23×C83C22×D411yescharacteristic
300C22×D83—22no—
301C22×D83—24no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—48no—
306C22×D83—48no—
307C22×D83—42no—
308C22×D83—42no—
309C22×D83—84no—
310C22×D83—816no—
311C22×D83C22×D412yes—
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—42no—
315D4×C83—22no—
316D4×C83—22no—
317D4×C83—42no—
318D4×C83—84no—
319C2×C4×C83—22no—
320C2×C4×C83—24no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—42no—
327C2×C4×C83—42no—
328C2×C4×C83—42no—
329C2×C4×C83C22×D412yes—
330C2×C4×C83C22×D411yescharacteristic
331C2×C4×C83C2×#4112yes—
332C2×C4×C83H(5,𝔽2)12yes—
333C2×C4×C83C2511yescharacteristic
334C22⋊D83—44no—
335C22⋊D83—48no—
336C22⋊D83—48no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—42no—
344C2×Dic83—42no—
345C2×Dic83—42no—
346C2×Dic83C22×D412yes—
347C2×Dic83C22×D412yes—
348C2×Dic83C22×D412yes—
349D332—24no—
350D332—22no—
351D332C2×#4114yes—
352C4×D83—24no—
353C4×D83—22no—
354C4×D83—22no—
355C4×D83—48no—
356C4×D83—84no—
357Dic166—22no—
358Dic166—22no—
359Dic166—48no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C22×C83—22no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—44no—
369C22×C83—42no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—84no—
373C22×C83#54612yes—
374C22×C83#57512yes—
375C22×C83#57712yes—
376C22×C83C23×D411yescharacteristic
377C2×D83—22no—
378C2×D83—24no—
379C2×D83—22no—
380C2×D83—22no—
381C2×D83—44no—
382C2×D83—48no—
383C2×D83—42no—
384C2×D83—42no—
385C2×D83—816no—
386C4×C83—22no—
387C4×C83—42no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83#54612yes—
391C4×C83C22×#4111yescharacteristic
392C4×C83C2×H(5,𝔽2)11yescharacteristic
393Dic83—22no—
394Dic83—22no—
395Dic83—22no—
396Dic83—42no—
397Dic83—42no—
398Dic83—42no—
399C2×#3311—831nomaximal, Sylow
400C2×C83—42no—
401C2×C83—82no—
402C2×C83#331114yescomplemented
403C2×C83C2×#54611yescharacteristic
404C2×C83C2×#57511yescharacteristic
405C2×C83C2×#57711yescharacteristic
406D83—42no—
407D83—44no—
408C2×#556—831no—
409C2×#546—831no—
410#3311—8316no—
411C2×#489—831no—
412C2×#485—831no—
413C2×#482—831no—
414C2×#476—831no—
415C2×#470—831no—
416C2×#465D8311yescharacteristic, complemented
417C2×#464—831no—
418C2×#452—831no—
419C2×#450—831no—
420C2×#440—831no—
421C2×#435—831no—
422C2×#418—831no—
423C2×#416—831no—
424C83C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—831no—
426C23×D4—831no—
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16C2×D8311yescharacteristic
430C22×M16—831no—
431C23×C8C2×D8311yescharacteristic, complemented
432#556—838no—
433#556—1664no—
434#546—838no—
435#546—1664no—
436C2×C4⋊Q8—831no—
437C2×#126—1661no—
438C2×#126—1661no—
439C2×#124—831no—
440C2×#124—1661no—
441C2×#123—1661no—
442C2×C22⋊Q8—831no—
443C2×C22⋊Q8—831no—
444C2×C22⋊Q8C2×D8311yescharacteristic, complemented
445C2×#121—1661no—
446C2×#121C2×D8311yescharacteristic
447C2×#120—1661no—
448C2×C4×Q8—831no—
449C2×C4×Q8—1661no—
450C2×C4×D4—831no—
451C2×C4×D4—831no—
452C2×#117—831no—
453C2×#117—831no—
454C22×C22⋊C4—1661no—
455#489—838no—
456#485—838no—
457#482—838no—
458#476—838no—
459#470—838no—
460#465C2×D8318yescomplemented
461#464—838no—
462#452—838no—
463#450—838no—
464#440—838no—
465#435—838no—
466C2×#107—831no—
467C2×#106—831no—
468C2×#106C2×D8311yescharacteristic, complemented
469C2×C4⋊C8—831no—
470#418—838no—
471#416—838no—
472C2×#103—831no—
473C2×#103—831no—
474C2×#103—831no—
475C2×#103C2×D8311yescharacteristic, complemented
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102—831no—
481C2×#102C2×D8311yescharacteristic
482C2×C22⋊C8—831no—
483C2×C22⋊C8—831no—
484C2×#97—831no—
485C25—1661no—
486C2×#41—3322no—
487C2×#41—834no—
488C2×#41—1664no—
489C2×#41—1662no—
490C22×Q8—831no—
491C22×Q8—1661no—
492C22×Q8C22×D8311yescharacteristic
493C22×D4—21no—
494C22×D4—3322no—
495C22×D4—831no—
496C22×D4—834no—
497C22×D4—831no—
498C22×D4—1662no—
499C22×D4—1661no—
500C22×D4—1664no—
501C22×D4—1661no—
502C22×D4C22×D8311yescharacteristic
503C23×C4—831no—
504C23×C4—1661no—
505C23×C4—1661no—
506C23×C4C22×D8311yescharacteristic
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—42no—
510C2×SD16—834no—
511C2×SD16—1664no—
512C2×SD16C22×D8314yes—
513C2×M16—3322no—
514C2×M16—834no—
515C22×C8—42no—
516C22×C8—831no—
517C22×C8—831no—
518C22×C8C22×D8311yescharacteristic
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8314yescomplemented
521C4⋊Q8—834no—
522C4⋊Q8—1662no—
523#126—1668no—
524#126—1668no—
525#124—834no—
526#124—1662no—
527#124—1668no—
528#123—1668no—
529C22⋊Q8—22no—
530C22⋊Q8—834no—
531C22⋊Q8—834no—
532C22⋊Q8—1662no—
533C22⋊Q8—1662no—
534C22⋊Q8C22×D8314yescomplemented
535#121—22no—
536#121—1668no—
537#121C22×D8314yes—
538#120—1668no—
539C4×Q8—834no—
540C4×Q8—1662no—
541C4×Q8—1668no—
542C4×D4—834no—
543C4×D4—834no—
544C4×D4—834no—
545C4×D4—1662no—
546#117—834no—
547#117—834no—
548#117—1662no—
549#117—1662no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—831no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4C22×D8311yescharacteristic
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—831no—
563C2×C22⋊C4—831no—
564C2×C22⋊C4—1668no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C42—831no—
573C2×C42—1661no—
574C2×C42—1661no—
575C2×C42—1661no—
576#107—834no—
577#106—834no—
578#106C22×D8314yescomplemented
579C4⋊C8—834no—
580#103—834no—
581#103—834no—
582#103—834no—
583#103C22×D8314yescomplemented
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102—834no—
589#102C22×D8314yes—
590C22⋊C8—834no—
591C22⋊C8—834no—
592#97—834no—
593C24—21no—
594C24—3324no—
595C24—3324no—
596C24—831no—
597C24—6642no—
598C24—1664no—
599C24—1661no—
600C24D4×D8311yescharacteristic
601#41—3328no—
602#41—3324no—
603#41—1668no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—3324no—
608C2×Q8—832no—
609C2×Q8—1664no—
610C2×Q8—1662no—
611C2×Q8—1662no—
612C2×Q8—1661no—
613C2×Q8C23×D8312yes—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—82no—
619C2×D4—3324no—
620C2×D4—3324no—
621C2×D4—3328no—
622C2×D4—3322no—
623C2×D4—3324no—
624C2×D4—834no—
625C2×D4—834no—
626C2×D4—832no—
627C2×D4—1664no—
628C2×D4—1668no—
629C2×D4—1664no—
630C2×D4—1661no—
631C2×D4—1662no—
632C2×D4C23×D8312yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—3324no—
639C22×C4—831no—
640C22×C4—831no—
641C22×C4—831no—
642C22×C4—832no—
643C22×C4—832no—
644C22×C4—6642no—
645C22×C4—1664no—
646C22×C4—1661no—
647C22×C4—1661no—
648C22×C4—1661no—
649C22×C4—1664no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4D4×D8312yes—
653C22×C4D4×D8311yescharacteristic
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—44no—
658SD16—1668no—
659M16—3324no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—44no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8C23×D8312yes—
668C2×C8C23×D8312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—834no—
673C4⋊C4—832no—
674C4⋊C4—832no—
675C4⋊C4—1664no—
676C4⋊C4—1664no—
677C4⋊C4—1664no—
678C4⋊C4—1664no—
679C4⋊C4—1661no—
680C4⋊C4—1661no—
681C4⋊C4C23×D8312yes—
682C4⋊C4C23×D8312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—834no—
686C22⋊C4—834no—
687C22⋊C4—1664no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C42—832no—
695C42—832no—
696C42—1664no—
697C42—1664no—
698C42—1664no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—3328no—
707C23—3328no—
708C23—3322no—
709C23—3322no—
710C23—832no—
711C23—6644no—
712C23—66416no—
713C23—1664no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23—1662no—
718C23C2×D4×D8312yes—
719C23C2×D4×D8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—3328no—
724Q8—3322no—
725Q8—1662no—
726Q8—1662no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—3328no—
732D4—3324no—
733D4—3328no—
734D4—834no—
735D4—1664no—
736D4—1662no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—3328no—
748C2×C4—3322no—
749C2×C4—3322no—
750C2×C4—3322no—
751C2×C4—832no—
752C2×C4—832no—
753C2×C4—832no—
754C2×C4—6644no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1664no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4C2×D4×D8312yes—
765C2×C4C2×D4×D8311yescharacteristic
766C2×C4#41×D8312yes—
767C2×C4#1458183712yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1662no—
772C8—1662no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—3322no—
782C22—3322no—
783C22—3328no—
784C22—3324no—
785C22—66416no—
786C22—1664no—
787C22—1662no—
788C22—1662no—
789C22—1662no—
790C22#1912834012yes—
791C22#1912849812yes—
792C22#1912850712yes—
793C22C22×D4×D8311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—3322no—
799C4—3322no—
800C4—3322no—
801C4—1662no—
802C4—1662no—
803C4—1662no—
804C4#1912834012yes—
805C4C2×#41×D8311yescharacteristic
806C4C2×#1458183711yescharacteristic
807C2—42no—
808C2—82no—
809C2—3324no—
810C2—3322no—
811C2#2491950514yesdirect product factor
812C2C2×#1912834011yescharacteristic
813C2C2×#1912849811yescharacteristic
814C2C2×#1912850711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#465×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128348C2
hypercenterC2×#465D83
hypocenterC83C2×#3311
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#19128422C2semidirect
3. #24919505C2direct (N × H)
4. C2×#19128059C2semidirect
5. C2×#19128045C2semidirect
6. C2×#19128022C2semidirect
7. C2×#19127990C2semidirect
8. C2×#19127958C2semidirect
9. C2×#19127921C2semidirect
10. C2×#19127861C2semidirect
11. C2×#19127850C2semidirect
12. C2×#19127804C2semidirect
13. C2×#19127772C2semidirect
14. C2×#19127704C2semidirect
15. C2×#19127698C2semidirect
16. C2×#465×C83C2semidirect
19. C22×#13050580C22semidirect
23. #19128422C22semidirect
26. C2×#14581791C22semidirect
36. C2×Q8×Dic83C22semidirect
40. C2×#14581751C22semidirect
43. #19128059C22semidirect
44. #19128045C22semidirect
45. #19128022C22semidirect
46. #19127990C22semidirect
47. #19127958C22semidirect
48. #19127921C22semidirect
49. #19127861C22semidirect
50. #19127850C22semidirect
51. #19127804C22semidirect
52. #19127772C22semidirect
53. C2×#14581725C22semidirect
54. C2×#14581723C22semidirect
55. C2×Dic83⋊C8C22semidirect
56. #19127704C22semidirect
57. #19127698C22semidirect
58. C2×#14581717C22semidirect
59. C2×#14581717C22semidirect
60. C2×#14581715C22semidirect
66. C2×C22⋊(C83⋊C8)C22semidirect
68. C2×#14581702C22semidirect
70. C23×C8×C83C22semidirect
71. C2×C22⋊Q8×C83C22semidirect
73. #465×C83C22semidirect
74. C2×#106×C83C22semidirect
75. C2×#103×C83C22semidirect
96. C2×#13050580C23semidirect
104. #14581791C23semidirect
118. Q8×Dic83C23semidirect
125. #14581751C23semidirect
149. #14581725C23semidirect
150. #14581723C23semidirect
151. Dic83⋊C8C23semidirect
152. #14581717C23semidirect
153. #14581717C23semidirect
154. #14581715C23semidirect
160. C22⋊(C83⋊C8)C23semidirect
162. #14581702C23semidirect
172. C22×C8×C83C23semidirect
174. C22⋊Q8×C83C23semidirect
182. #106×C83C23semidirect
183. #103×C83C23semidirect
402. C2×C83#3311semidirect
416. C2×#465D83semidirect
424. C83C2×#3311semidirect
431. C23×C8C2×D83semidirect
444. C2×C22⋊Q8C2×D83semidirect
460. #465C2×D83semidirect
468. C2×#106C2×D83semidirect
475. C2×#103C2×D83semidirect
520. C22×C8C22×D83semidirect
534. C22⋊Q8C22×D83semidirect
578. #106C22×D83semidirect
583. #103C22×D83semidirect
811. C2#24919505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284222
C2×#191283482
#249195052
C2×#191280592
C2×#191280452
C2×#191280222
C2×#191279902
C2×#191279582
C2×#191279212
C2×#191278612
C2×#191278502
C2×#191278042
C2×#191277722
C2×#191277042
C2×#191276982
C2×#465×C832
C2×#331183