Finite Group Databasebeta

← C2×#24919550 #36280936

Subgroups — C2×#24919550 #36280936

Order 21248.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128409C211yesmaximal, characteristic, complemented
2C2×#19128342C211yesmaximal, characteristic
3#24919550C2116yesmaximal, direct product factor
4C2×#19128062C211yesmaximal, characteristic, complemented
5C2×#19128034C211yesmaximal, characteristic, complemented
6C2×#19128016C211yesmaximal, characteristic, complemented
7C2×#19127980C211yesmaximal, characteristic, complemented
8C2×#19127950C211yesmaximal, characteristic, complemented
9C2×#19127925C211yesmaximal, characteristic, complemented
10C2×#19127862C211yesmaximal, characteristic, complemented
11C2×#19127851C211yesmaximal, characteristic, complemented
12C2×#19127804C211yesmaximal, characteristic, complemented
13C2×#19127772C211yesmaximal, characteristic, complemented
14C2×#19127701C211yesmaximal, characteristic, complemented
15C22×#14581714C211yesmaximal, characteristic, complemented
16C2×#467×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20C22×#13050577C2211yescharacteristic
21C22×#13050573C2211yescharacteristic, complemented
22#19128409—24no—
23#19128409C2218yescomplemented
24#19128342—24no—
25#19128342C2218yes—
26C2×#14581791C2211yescharacteristic, complemented
27C2×#14581782—21no—
28C2×#14581781C2211yescharacteristic
29C2×#14581777—21no—
30C2×#14581772—21no—
31C2×#14581769—21no—
32C2×#14581768C2211yescharacteristic, complemented
33C2×#14581767—21no—
34C2×#14581767C2211yescharacteristic
35C2×#14581762—21no—
36C2×Q8×Dic83C2211yescharacteristic, complemented
37C2×#14581754C2211yescharacteristic
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×(C22⋊D83)⋊C4—21no—
40C22×C4⋊Dic83C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic, complemented
42C2×C22⋊C4×D83—21no—
43#19128062C2218yescomplemented
44#19128034C2218yescomplemented
45#19128016C2218yescomplemented
46#19127980C2218yescomplemented
47#19127950C2218yescomplemented
48#19127925C2218yescomplemented
49#19127862C2218yescomplemented
50#19127851C2218yescomplemented
51#19127804C2218yescomplemented
52#19127772C2218yescomplemented
53C2×#14581725C2211yescharacteristic, complemented
54C2×#14581725C2211yescharacteristic, complemented
55C2×Dic83⋊C8C2211yescharacteristic, complemented
56#19127701C2218yescomplemented
57C2×#14581716C2211yescharacteristic, complemented
58C2×#14581716C2211yescharacteristic, complemented
59C2×#14581714C2211yescharacteristic
60C2×#14581714C2211yescharacteristic
61C2×#14581714C2211yescharacteristic
62C2×#14581714C2211yescharacteristic
63C2×#14581714C2218yescomplemented
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic, complemented
68C2×#14581702C2211yescharacteristic, complemented
69C22×Q16×C83C2211yescharacteristic, complemented
70C23×C8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C22⋊Q8×C83C2211yescharacteristic
73#467×C83C2218yescomplemented
74C2×#107×C83C2211yescharacteristic, complemented
75C2×#103×C83C2211yescharacteristic, complemented
76C2×#103×C83C2211yescharacteristic, complemented
77C24×D83—21no—
78C2×#13050591—22no—
79C2×#13050591—24no—
80C2×#13050591—42no—
81C2×#13050591C2314yes—
82C22×Dic166—21no—
83C22×D332—24no—
84C22×D332—21no—
85C22×D332—21no—
86C22×D332—22no—
87C22×D332—21no—
88C22×D332—42no—
89C22×D332C2311yescharacteristic
90C22×D332C2314yes—
91C22×D332C2311yescharacteristic
92C22×C22⋊D83D411yescharacteristic
93C23×Dic83—21no—
94C22×C4×D83—21no—
95C22×C4×D83—21no—
96C22×C4×D83—21no—
97C22×C4×D83C2311yescharacteristic
98C2×#13050577—24no—
99C2×#13050577—42no—
100C2×#13050577C2314yes—
101C2×#13050577C2314yes—
102C2×#13050573—42no—
103C2×#13050573C2314yescomplemented
104C22×C83⋊C8C2311yescharacteristic
105C22×C83⋊C8C2311yescharacteristic
106#14581791—22no—
107#14581791C2314yescomplemented
108#14581782—28no—
109#14581781—22no—
110#14581781C2314yes—
111#14581777—28no—
112#14581772—28no—
113#14581769—28no—
114#14581768—22no—
115#14581768C2314yescomplemented
116#14581767—22no—
117#14581767—28no—
118#14581767C2314yes—
119#14581762—28no—
120Q8×Dic83—22no—
121Q8×Dic83C2314yescomplemented
122#14581754—22no—
123#14581754C2314yes—
124C4×C22⋊D83D414yes—
125C4×C22⋊D83C2314yes—
126(C22⋊D83)⋊C4—28no—
127C2×C4⋊Dic83—21no—
128C2×C4⋊Dic83—22no—
129C2×C4⋊Dic83—21no—
130C2×C4⋊Dic83C2311yescharacteristic
131C2×C4⋊Dic83C2314yes—
132C2×C4⋊Dic83C2311yescharacteristic
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4D411yescharacteristic
137C4⋊C4×D83—22no—
138C4⋊C4×D83C2314yescomplemented
139C2×C22⋊Dic83D411yescharacteristic
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4D411yescharacteristic
146C22⋊C4×D83—28no—
147C2×C4×Dic83—21no—
148C2×C4×Dic83C2311yescharacteristic
149#14581725C2314yescomplemented
150#14581725C2314yescomplemented
151Dic83⋊C8C2314yescomplemented
152#14581716C2314yescomplemented
153#14581716C2314yescomplemented
154#14581714C2314yes—
155#14581714C2314yes—
156#14581714C2314yes—
157#14581714C2314yes—
158#14581712C2314yes—
159#14581712C2314yes—
160C22⋊(C83⋊C8)C2314yes—
161(C2×D83)⋊C8C2314yescomplemented
162#14581702C2314yescomplemented
163C22×Q8×C83C2311yescharacteristic
164C22×Q8×C83C2311yescharacteristic
165C23×C4×C83C2311yescharacteristic
166C2×Q16×C83—42no—
167C2×Q16×C83C2314yescomplemented
168C22×C8×C83—42no—
169C22×C8×C83C2311yescharacteristic
170C22×C8×C83C2311yescharacteristic
171C22×C8×C83C2314yes—
172C22⋊Q8×C83—22no—
173C22⋊Q8×C83—22no—
174C22⋊Q8×C83C2314yes—
175C22⋊Q8×C83C2314yes—
176C2×C4⋊C4×C83—21no—
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83C2311yescharacteristic
179C2×C4⋊C4×C83C2311yescharacteristic
180C2×C22⋊C4×C83—21no—
181C2×C22⋊C4×C83—21no—
182#107×C83C2314yescomplemented
183#103×C83C2314yescomplemented
184#103×C83C2314yescomplemented
185C23×D83—21no—
186C23×D83—21no—
187C23×D83—24no—
188C23×D83—44no—
189C23×D83—44no—
190C23×D83—82no—
191C23×D83C2×D411yescharacteristic
192#13050591—28no—
193#13050591—44no—
194#13050591—48no—
195C2×Dic166—24no—
196C2×Dic166—82no—
197C2×D332—21no—
198C2×D332—22no—
199C2×D332—22no—
200C2×D332—22no—
201C2×D332—28no—
202C2×D332—24no—
203C2×D332—24no—
204C2×D332—21no—
205C2×D332—24no—
206C2×D332—44no—
207C2×D332—48no—
208C2×D332—44no—
209C2×D332—44no—
210C2×D332—82no—
211C2×D332#4114yes—
212C2×D332C2412yes—
213C2×D332C2412yes—
214C2×C22⋊D83—24no—
215C2×C22⋊D83C2×D414yes—
216C22×Dic83—21no—
217C22×Dic83—21no—
218C22×Dic83—24no—
219C22×Dic83—82no—
220C22×Dic83C2×D411yescharacteristic
221C22×Dic83C2×D411yescharacteristic
222C22×Dic83C2×D411yescharacteristic
223C2×C4×D83—22no—
224C2×C4×D83—22no—
225C2×C4×D83—24no—
226C2×C4×D83—24no—
227C2×C4×D83—24no—
228C2×C4×D83—44no—
229C2×C4×D83—82no—
230C2×C4×D83—82no—
231C2×C4×D83C2×D412yes—
232C2×C4×D83C2412yes—
233#13050577—28no—
234#13050577—44no—
235#13050573—44no—
236C2×C83⋊C8—22no—
237C2×C83⋊C8—22no—
238C2×C83⋊C8C2412yes—
239C2×C83⋊C8C2412yes—
240C4⋊Dic83—21no—
241C4⋊Dic83—24no—
242C4⋊Dic83—21no—
243C4⋊Dic83—24no—
244C4⋊Dic83C2412yes—
245C4⋊Dic83C2412yes—
246Dic83⋊C4—24no—
247Dic83⋊C4—24no—
248Dic83⋊C4—24no—
249Dic83⋊C4C2×D414yes—
250C22⋊Dic83C2×D414yes—
251(C2×D83)⋊C4—24no—
252(C2×D83)⋊C4—24no—
253(C2×D83)⋊C4—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256(C2×D83)⋊C4C2×D414yes—
257C4×Dic83—24no—
258C4×Dic83C2×D412yes—
259C4×Dic83C2412yes—
260C24×C83C2×D411yescharacteristic
261C2×Q8×C83—21no—
262C2×Q8×C83—21no—
263C2×Q8×C83—22no—
264C2×Q8×C83—22no—
265C2×Q8×C83—22no—
266C2×Q8×C83—22no—
267C2×Q8×C83C2412yes—
268C2×Q8×C83C2412yes—
269C22×C4×C83—22no—
270C22×C4×C83—22no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83C2×D411yescharacteristic
276C22×C4×C83C2×D412yes—
277C22×C4×C83C2412yes—
278C22×C4×C83C2411yescharacteristic
279Q16×C83—44no—
280C2×C8×C83—22no—
281C2×C8×C83—22no—
282C2×C8×C83—44no—
283C2×C8×C83C2412yes—
284C2×C8×C83C2412yes—
285C4⋊C4×C83—24no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—24no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83C2412yes—
290C4⋊C4×C83C2412yes—
291C22⋊C4×C83—24no—
292C22⋊C4×C83—24no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83#13714yes—
296C23×C83C22×D412yes—
297C23×C83C22×D411yescharacteristic
298C22×D83—22no—
299C22×D83—24no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—48no—
305C22×D83—42no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—48no—
309C22×D83—42no—
310C22×D83—42no—
311C22×D83—84no—
312C22×D83—816no—
313C22×D83C22×D412yes—
314Q8×C83—22no—
315Q8×C83—22no—
316Q8×C83—22no—
317Q8×C83—22no—
318Q8×C83—42no—
319Q8×C83—42no—
320C2×C4×C83—22no—
321C2×C4×C83—24no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—42no—
329C2×C4×C83—42no—
330C2×C4×C83—42no—
331C2×C4×C83—42no—
332C2×C4×C83C22×D412yes—
333C2×C4×C83C22×D411yescharacteristic
334C2×C4×C83C2×#4112yes—
335C2×C4×C83H(5,𝔽2)12yes—
336C2×C4×C83C2511yescharacteristic
337C22⋊D83—28no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—42no—
344C2×Dic83—42no—
345C2×Dic83—84no—
346C2×Dic83C22×D412yes—
347C2×Dic83C22×D412yes—
348C2×Dic83C22×D412yes—
349D332—24no—
350D332—22no—
351D332—22no—
352D332—22no—
353D332—48no—
354D332—48no—
355D332—42no—
356D332—84no—
357D332C2×#4114yes—
358C4×D83—24no—
359C4×D83—22no—
360C4×D83—22no—
361C4×D83—48no—
362C4×D83—84no—
363C4×D83—84no—
364Dic166—84no—
365C8×C83—22no—
366C8×C83—22no—
367C83⋊C8—22no—
368C83⋊C8—22no—
369C22×C83—22no—
370C22×C83—28no—
371C22×C83—22no—
372C22×C83#54612yes—
373C22×C83C2×#13714yes—
374C22×C83C2×#13712yes—
375C22×C83#57612yes—
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—42no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—816no—
389C2×D83—84no—
390C4×C83—22no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83#54612yes—
396C4×C83C22×#4111yescharacteristic
397C4×C83C2×H(5,𝔽2)11yescharacteristic
398Dic83—22no—
399Dic83—22no—
400Dic83—22no—
401Dic83—42no—
402Dic83—42no—
403C2×#3314—831nomaximal, Sylow
404C2×C83—24no—
405C2×C83#331414yescomplemented
406C2×C83C2×#54611yescharacteristic
407C2×C83C22×#13711yescharacteristic
408C2×C83C2×#57611yescharacteristic
409D83—42no—
410D83—44no—
411D83—82no—
412C2×#554—831no—
413C2×#546—831no—
414#3314—8316no—
415C2×#489—831no—
416C2×#484—831no—
417C2×#480—831no—
418C2×#474—831no—
419C2×#468—831no—
420C2×#467D8311yescharacteristic, complemented
421C2×#464—831no—
422C2×#452—831no—
423C2×#450—831no—
424C2×#440—831no—
425C2×#435—831no—
426C2×#417—831no—
427C22×#102—831no—
428C83C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—831no—
430C23×D4—831no—
431C22×Q16C2×D8311yescharacteristic, complemented
432C22×SD16—831no—
433C22×SD16—831no—
434C22×M16—831no—
435C23×C8C2×D8311yescharacteristic
436#554—838no—
437#554—1664no—
438#546—838no—
439#546—1664no—
440C2×C4⋊Q8—831no—
441C2×#125—1661no—
442C2×#124—831no—
443C2×#123—1661no—
444C2×C22⋊Q8—831no—
445C2×C22⋊Q8—1661no—
446C2×C22⋊Q8—1661no—
447C2×C22⋊Q8C2×D8311yescharacteristic
448C2×C22⋊Q8C2×D8311yescharacteristic
449C2×#121—831no—
450C2×#121—1661no—
451C2×#120—1661no—
452C2×C4×Q8—831no—
453C2×C4×D4—831no—
454C2×C4×D4—831no—
455C2×C4×D4—1661no—
456C22×C4⋊C4—831no—
457C22×C4⋊C4—831no—
458C22×C22⋊C4—1661no—
459#489—838no—
460#484—838no—
461#480—838no—
462#474—838no—
463#468—838no—
464#467C2×D8318yescomplemented
465#464—838no—
466#452—838no—
467#450—838no—
468#440—838no—
469#435—838no—
470C2×#107—831no—
471C2×#107—831no—
472C2×#107C2×D8311yescharacteristic, complemented
473C2×C4⋊C8—831no—
474#417—838no—
475C2×#103—831no—
476C2×#103—831no—
477C2×#103C2×D8311yescharacteristic, complemented
478C2×#103C2×D8311yescharacteristic, complemented
479C2×#102—831no—
480C2×#102—831no—
481C2×#102—831no—
482C2×#102—831no—
483C2×#102—838no—
484C2×#102—831no—
485C2×#102—831no—
486C2×C22⋊C8—831no—
487C2×C22⋊C8—831no—
488C2×#97—831no—
489C25—1661no—
490C2×#41—3322no—
491C2×#41—834no—
492C2×#41—1664no—
493C2×#41—1662no—
494C22×Q8—1661no—
495C22×Q8C22×D8311yescharacteristic
496C22×Q8C22×D8311yescharacteristic
497C22×D4—3322no—
498C22×D4—831no—
499C22×D4—834no—
500C22×D4—831no—
501C22×D4—831no—
502C22×D4—1661no—
503C22×D4—1664no—
504C22×D4—1661no—
505C22×D4—1661no—
506C22×D4—1662no—
507C23×C4—831no—
508C23×C4—1661no—
509C23×C4—1661no—
510C23×C4—1661no—
511C23×C4—1661no—
512C23×C4C22×D8311yescharacteristic
513C2×Q16—42no—
514C2×Q16C22×D8314yescomplemented
515C2×SD16—3322no—
516C2×SD16—834no—
517C2×SD16—834no—
518C2×SD16—1664no—
519C2×M16—3322no—
520C2×M16—834no—
521C22×C8—42no—
522C22×C8—831no—
523C22×C8—831no—
524C22×C8C22×D8311yescharacteristic
525C22×C8C22×D8311yescharacteristic
526C22×C8C22×D8314yes—
527C4⋊Q8—834no—
528C4⋊Q8—1662no—
529#125—1668no—
530#124—834no—
531#124—1662no—
532#123—1668no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—834no—
536C22⋊Q8—1668no—
537C22⋊Q8—1668no—
538C22⋊Q8—1662no—
539C22⋊Q8C22×D8314yes—
540C22⋊Q8C22×D8314yes—
541#121—834no—
542#121—1668no—
543#121—1662no—
544#120—1668no—
545C4×Q8—834no—
546C4×Q8—1662no—
547C4×D4—834no—
548C4×D4—834no—
549C4×D4—834no—
550C4×D4—1662no—
551C4×D4—1668no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—831no—
555C2×C4⋊C4—831no—
556C2×C4⋊C4—831no—
557C2×C4⋊C4—834no—
558C2×C4⋊C4—834no—
559C2×C4⋊C4—1662no—
560C2×C4⋊C4—1661no—
561C2×C4⋊C4—1661no—
562C2×C4⋊C4—1661no—
563C2×C4⋊C4—1661no—
564C2×C4⋊C4—1661no—
565C2×C4⋊C4—1662no—
566C2×C4⋊C4C22×D8311yescharacteristic
567C2×C4⋊C4C22×D8311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—831no—
571C2×C22⋊C4—831no—
572C2×C22⋊C4—1668no—
573C2×C22⋊C4—1661no—
574C2×C22⋊C4—1661no—
575C2×C22⋊C4—1661no—
576C2×C22⋊C4—1661no—
577C2×C22⋊C4—1661no—
578C2×C42—831no—
579C2×C42—1661no—
580#107—834no—
581#107—834no—
582#107C22×D8314yescomplemented
583C4⋊C8—834no—
584#103—834no—
585#103—834no—
586#103C22×D8314yescomplemented
587#103C22×D8314yescomplemented
588#102—834no—
589#102—834no—
590#102—834no—
591#102—834no—
592#102—834no—
593#102—834no—
594C22⋊C8—834no—
595C22⋊C8—834no—
596#97—834no—
597C24—3324no—
598C24—3324no—
599C24—831no—
600C24—6642no—
601C24—1661no—
602C24—1664no—
603C24—1661no—
604C24D4×D8311yescharacteristic
605#41—3324no—
606#41—3328no—
607#41—1668no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—6642no—
615C2×Q8—1664no—
616C2×Q8C23×D8312yes—
617C2×Q8C23×D8312yes—
618C2×D4—3324no—
619C2×D4—3328no—
620C2×D4—3324no—
621C2×D4—3324no—
622C2×D4—834no—
623C2×D4—834no—
624C2×D4—832no—
625C2×D4—832no—
626C2×D4—6642no—
627C2×D4—1664no—
628C2×D4—1668no—
629C2×D4—1664no—
630C2×D4—1664no—
631C2×D4—1664no—
632C2×D4—1661no—
633C2×D4—1661no—
634C2×D4—1662no—
635C2×D4—1662no—
636C2×D4—1662no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—3324no—
644C22×C4—831no—
645C22×C4—831no—
646C22×C4—831no—
647C22×C4—832no—
648C22×C4—832no—
649C22×C4—6642no—
650C22×C4—6642no—
651C22×C4—6642no—
652C22×C4—1664no—
653C22×C4—1664no—
654C22×C4—1664no—
655C22×C4—1661no—
656C22×C4—1661no—
657C22×C4—1664no—
658C22×C4—1662no—
659C22×C4—1662no—
660C22×C4D4×D8312yes—
661C22×C4D4×D8311yescharacteristic
662C22×C4C23×D8312yes—
663C22×C4C23×D8311yescharacteristic
664Q16—44no—
665SD16—3324no—
666SD16—1668no—
667M16—3324no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—44no—
671C2×C8—832no—
672C2×C8—832no—
673C2×C8—1662no—
674C2×C8—1662no—
675C2×C8C23×D8312yes—
676C2×C8C23×D8312yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—834no—
682C4⋊C4—832no—
683C4⋊C4—832no—
684C4⋊C4—1664no—
685C4⋊C4—1664no—
686C4⋊C4—1664no—
687C4⋊C4—1664no—
688C4⋊C4—1661no—
689C4⋊C4—1664no—
690C4⋊C4—1661no—
691C4⋊C4C23×D8312yes—
692C4⋊C4C23×D8312yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—834no—
696C22⋊C4—834no—
697C22⋊C4—1664no—
698C22⋊C4—1664no—
699C22⋊C4—1664no—
700C22⋊C4—1664no—
701C22⋊C4—1664no—
702C42—832no—
703C42—832no—
704C42—1664no—
705C23—22no—
706C23—22no—
707C23—3328no—
708C23—3322no—
709C23—3322no—
710C23—3322no—
711C23—3328no—
712C23—3322no—
713C23—3322no—
714C23—832no—
715C23—6644no—
716C23—66416no—
717C23—1662no—
718C23—1664no—
719C23—1662no—
720C23—1662no—
721C23—1662no—
722C23—1662no—
723C23#1458182414yes—
724C23C2×D4×D8312yes—
725C23C2×D4×D8311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—6644no—
733D4—3328no—
734D4—3328no—
735D4—3322no—
736D4—834no—
737D4—6644no—
738D4—1668no—
739D4—1664no—
740D4—1662no—
741D4—1662no—
742D4—1662no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—3328no—
756C2×C4—3322no—
757C2×C4—3322no—
758C2×C4—832no—
759C2×C4—832no—
760C2×C4—832no—
761C2×C4—6644no—
762C2×C4—6644no—
763C2×C4—6644no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1664no—
770C2×C4—1662no—
771C2×C4—1662no—
772C2×C4C2×D4×D8312yes—
773C2×C4C2×D4×D8311yescharacteristic
774C2×C4#41×D8312yes—
775C2×C4#1458183712yes—
776C2×C4C24×D8311yescharacteristic
777C8—22no—
778C8—22no—
779C8—1662no—
780C8—1662no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—3322no—
785C22—3322no—
786C22—3328no—
787C22—3324no—
788C22—3322no—
789C22—3322no—
790C22—3322no—
791C22—66416no—
792C22—6644no—
793C22—1664no—
794C22—1662no—
795C22—1662no—
796C22—1662no—
797C22#1912834012yes—
798C22C2×#1458182414yes—
799C22C2×#1458182412yes—
800C22#1912850312yes—
801C22C22×D4×D8311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—3322no—
808C4—3322no—
809C4—1662no—
810C4—1662no—
811C4—1662no—
812C4#1912834012yes—
813C4C2×#41×D8311yescharacteristic
814C4C2×#1458183711yescharacteristic
815C2—24no—
816C2—3324no—
817C2—3322no—
818C2—6642no—
819C2#2491955014yesdirect product factor
820C2C2×#1912834011yescharacteristic
821C2C22×#1458182411yescharacteristic
822C2C2×#1912850311yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#467×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128342C2
hypercenterC2×#467D83
hypocenterC83C2×#3314
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#19128409C2semidirect
3. #24919550C2direct (N × H)
4. C2×#19128062C2semidirect
5. C2×#19128034C2semidirect
6. C2×#19128016C2semidirect
7. C2×#19127980C2semidirect
8. C2×#19127950C2semidirect
9. C2×#19127925C2semidirect
10. C2×#19127862C2semidirect
11. C2×#19127851C2semidirect
12. C2×#19127804C2semidirect
13. C2×#19127772C2semidirect
14. C2×#19127701C2semidirect
15. C22×#14581714C2semidirect
16. C2×#467×C83C2semidirect
21. C22×#13050573C22semidirect
23. #19128409C22semidirect
26. C2×#14581791C22semidirect
32. C2×#14581768C22semidirect
36. C2×Q8×Dic83C22semidirect
41. C2×C4⋊C4×D83C22semidirect
43. #19128062C22semidirect
44. #19128034C22semidirect
45. #19128016C22semidirect
46. #19127980C22semidirect
47. #19127950C22semidirect
48. #19127925C22semidirect
49. #19127862C22semidirect
50. #19127851C22semidirect
51. #19127804C22semidirect
52. #19127772C22semidirect
53. C2×#14581725C22semidirect
54. C2×#14581725C22semidirect
55. C2×Dic83⋊C8C22semidirect
56. #19127701C22semidirect
57. C2×#14581716C22semidirect
58. C2×#14581716C22semidirect
63. C2×#14581714C22semidirect
67. C2×(C2×D83)⋊C8C22semidirect
68. C2×#14581702C22semidirect
69. C22×Q16×C83C22semidirect
73. #467×C83C22semidirect
74. C2×#107×C83C22semidirect
75. C2×#103×C83C22semidirect
76. C2×#103×C83C22semidirect
103. C2×#13050573C23semidirect
107. #14581791C23semidirect
115. #14581768C23semidirect
121. Q8×Dic83C23semidirect
138. C4⋊C4×D83C23semidirect
149. #14581725C23semidirect
150. #14581725C23semidirect
151. Dic83⋊C8C23semidirect
152. #14581716C23semidirect
153. #14581716C23semidirect
161. (C2×D83)⋊C8C23semidirect
162. #14581702C23semidirect
167. C2×Q16×C83C23semidirect
182. #107×C83C23semidirect
183. #103×C83C23semidirect
184. #103×C83C23semidirect
405. C2×C83#3314semidirect
420. C2×#467D83semidirect
428. C83C2×#3314semidirect
431. C22×Q16C2×D83semidirect
464. #467C2×D83semidirect
472. C2×#107C2×D83semidirect
477. C2×#103C2×D83semidirect
478. C2×#103C2×D83semidirect
514. C2×Q16C22×D83semidirect
582. #107C22×D83semidirect
586. #103C22×D83semidirect
587. #103C22×D83semidirect
819. C2#24919550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284092
C2×#191283422
#249195502
C2×#191280622
C2×#191280342
C2×#191280162
C2×#191279802
C2×#191279502
C2×#191279252
C2×#191278622
C2×#191278512
C2×#191278042
C2×#191277722
C2×#191277012
C22×#145817142
C2×#467×C832
C2×#331483