Finite Group Databasebeta

← C2×#24910227 #35563270

Subgroups — C2×#24910227 #35563270

Order 21248.

3414 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581767C211yesmaximal, characteristic
2#24910227C2116yesmaximal, direct product factor
3C2×#19127603C211yesmaximal, characteristic, complemented
4C2×#19127602C211yesmaximal, characteristic, complemented
5C2×#19127593C211yesmaximal, characteristic, complemented
6C2×#19127591C211yesmaximal, characteristic, complemented
7C2×#19127587C211yesmaximal, characteristic, complemented
8C2×#19127579C211yesmaximal, characteristic, complemented
9C2×#19127579C211yesmaximal, characteristic, complemented
10C2×#19127579C211yesmaximal, characteristic, complemented
11C2×#19127579C211yesmaximal, characteristic, complemented
12C2×#19127563C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
14C2×#19127548C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C2×#387×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C23×D332C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C23×C4×D83C2211yescharacteristic
23C2×#14581767C4116yescomplemented
24C2×#14581767C2218yes—
25C22×C4⋊Dic83C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39C22×C4×Dic83C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41#19127603C2218yescomplemented
42#19127602C2218yescomplemented
43#19127593C2218yescomplemented
44#19127591C2218yescomplemented
45#19127587C2218yescomplemented
46#19127579C2218yescomplemented
47#19127579C2218yescomplemented
48#19127579C2218yescomplemented
49#19127579C2218yescomplemented
50#19127563C2218yescomplemented
51C4×(C2×D83)⋊C4C2218yescomplemented
52#19127548C2218yescomplemented
53#19127548C2218yescomplemented
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C42×C83C2211yescharacteristic
63#387×C83C2218yescomplemented
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C24×D83C2311yescharacteristic
69C24×D83C2311yescharacteristic
70C24×D83C2311yescharacteristic
71C22×D332—42no—
72C22×D332—42no—
73C22×D332—42no—
74C22×D332—42no—
75C22×D332—42no—
76C22×D332—42no—
77C22×D332C2×C418yes—
78C22×D332C2×C418yescomplemented
79C22×D332C2×C418yescomplemented
80C22×D332C2314yes—
81C22×D332C2314yes—
82C22×D332C2314yes—
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C23×Dic83C2311yescharacteristic
88C22×C4×D83—24no—
89C22×C4×D83—24no—
90C22×C4×D83—42no—
91C22×C4×D83—42no—
92C22×C4×D83—42no—
93C22×C4×D83—42no—
94C22×C4×D83—42no—
95C22×C4×D83—42no—
96C22×C4×D83C2×C418yescomplemented
97C22×C4×D83C2314yes—
98C22×C4×D83C2314yes—
99C22×C4×D83C2314yes—
100#14581767C2×C4164yescomplemented
101C2×C4⋊Dic83—42no—
102C2×C4⋊Dic83C2314yes—
103C2×(C2×D83)⋊C4—24no—
104C2×(C2×D83)⋊C4—24no—
105C2×(C2×D83)⋊C4—24no—
106C2×(C2×D83)⋊C4—24no—
107C2×(C2×D83)⋊C4—42no—
108C2×(C2×D83)⋊C4—42no—
109C2×(C2×D83)⋊C4—42no—
110C2×(C2×D83)⋊C4—42no—
111C2×(C2×D83)⋊C4—42no—
112C2×(C2×D83)⋊C4—42no—
113C2×(C2×D83)⋊C4C2×C418yescomplemented
114C2×(C2×D83)⋊C4C2×C418yescomplemented
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×C4×Dic83—42no—
128C2×C4×Dic83—42no—
129C2×C4×Dic83—42no—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C2×C4⋊C4×C83—42no—
147C2×C4⋊C4×C83C2×C418yescomplemented
148C2×C4⋊C4×C83C2314yes—
149C2×C4⋊C4×C83C2314yes—
150C2×C42×C83—42no—
151C2×C42×C83C2314yes—
152#95×C83C2314yes—
153#95×C83C2314yes—
154#95×C83C2314yes—
155#95×C83C2314yes—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83—22no—
165C23×D83—22no—
166C23×D83—22no—
167C23×D83—22no—
168C23×D83—22no—
169C23×D83—22no—
170C23×D83—22no—
171C23×D83—22no—
172C23×D83—22no—
173C23×D83—22no—
174C23×D83C22×C414yes—
175C23×D83C22×C414yes—
176C23×D83C22×C414yes—
177C23×D83C2412yes—
178C23×D83C2412yes—
179C23×D83C2412yes—
180C2×D332—416no—
181C2×D332—416no—
182C2×D332—416no—
183C2×D332—44no—
184C2×D332—44no—
185C2×D332—44no—
186C2×D332—44no—
187C2×D332—44no—
188C2×D332—44no—
189C2×D332C22×C4116yes—
190C2×D332C22×C4116yescomplemented
191C2×D332C22×C4116yescomplemented
192C22×Dic83—22no—
193C22×Dic83—22no—
194C22×Dic83—22no—
195C22×Dic83—22no—
196C22×Dic83—22no—
197C22×Dic83—22no—
198C22×Dic83—22no—
199C22×Dic83—22no—
200C22×Dic83—22no—
201C22×Dic83—22no—
202C22×Dic83—22no—
203C22×Dic83—22no—
204C22×Dic83—22no—
205C22×Dic83C22×C414yes—
206C22×Dic83#4114yes—
207C22×Dic83C2412yes—
208C22×Dic83C2412yes—
209C22×Dic83C2412yes—
210C22×Dic83C2412yes—
211C22×Dic83C2412yes—
212C2×C4×D83—28no—
213C2×C4×D83—28no—
214C2×C4×D83—416no—
215C2×C4×D83—44no—
216C2×C4×D83—44no—
217C2×C4×D83—44no—
218C2×C4×D83—44no—
219C2×C4×D83—44no—
220C2×C4×D83—44no—
221C2×C4×D83—416no—
222C2×C4×D83—416no—
223C2×C4×D83C22×C4116yescomplemented
224C4⋊Dic83—44no—
225(C2×D83)⋊C4—28no—
226(C2×D83)⋊C4—28no—
227(C2×D83)⋊C4—28no—
228(C2×D83)⋊C4—28no—
229(C2×D83)⋊C4—44no—
230(C2×D83)⋊C4—44no—
231(C2×D83)⋊C4—44no—
232(C2×D83)⋊C4—44no—
233(C2×D83)⋊C4—44no—
234(C2×D83)⋊C4—44no—
235(C2×D83)⋊C4C22×C4116yescomplemented
236(C2×D83)⋊C4C22×C4116yescomplemented
237C4×Dic83—44no—
238C4×Dic83—44no—
239C4×Dic83—44no—
240C24×C83C2411yescharacteristic
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—22no—
254C22×C4×C83—22no—
255C22×C4×C83—22no—
256C22×C4×C83—22no—
257C22×C4×C83—22no—
258C22×C4×C83C22×C414yes—
259C22×C4×C83C22×C414yes—
260C22×C4×C83C22×C414yes—
261C22×C4×C83#4114yes—
262C22×C4×C83C2412yes—
263C22×C4×C83C2412yes—
264C22×C4×C83C2412yes—
265C22×C4×C83C2412yes—
266C22×C4×C83C2412yes—
267C22×C4×C83C2412yes—
268C22×C4×C83C2412yes—
269C4⋊C4×C83—44no—
270C4⋊C4×C83C22×C4116yescomplemented
271C42×C83—44no—
272C23×C83C23×C412yes—
273C23×C83C2×#4112yes—
274C23×C83C2×#4112yes—
275C23×C83H(5,𝔽2)12yes—
276C23×C83H(5,𝔽2)12yes—
277C23×C83H(5,𝔽2)12yes—
278C23×C83H(5,𝔽2)12yes—
279C23×C83C2511yescharacteristic
280C22×D83—28no—
281C22×D83—28no—
282C22×D83—28no—
283C22×D83—28no—
284C22×D83—28no—
285C22×D83—28no—
286C22×D83—28no—
287C22×D83—28no—
288C22×D83—28no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—22no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—22no—
307C22×D83—44no—
308C22×D83—44no—
309C22×D83—44no—
310C22×D83—44no—
311C22×D83—44no—
312C22×D83—44no—
313C22×D83—44no—
314C22×D83—44no—
315C22×D83—44no—
316C22×D83—44no—
317C22×D83—44no—
318C22×D83—44no—
319C22×D83C23×C414yes—
320C22×D83C23×C414yes—
321C22×D83C23×C414yes—
322C2×C4×C83—28no—
323C2×C4×C83—28no—
324C2×C4×C83—28no—
325C2×C4×C83—28no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—44no—
344C2×C4×C83—44no—
345C2×C4×C83—44no—
346C2×C4×C83C23×C414yes—
347C2×C4×C83C23×C414yes—
348C2×C4×C83C23×C414yes—
349C2×C4×C83C2×#4114yes—
350C2×Dic83—28no—
351C2×Dic83—28no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
358C2×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—22no—
361C2×Dic83—22no—
362C2×Dic83—22no—
363C2×Dic83—22no—
364C2×Dic83—22no—
365C2×Dic83—44no—
366C2×Dic83—44no—
367C2×Dic83—44no—
368C2×Dic83C23×C414yes—
369C2×Dic83C2×#4114yes—
370D332—416no—
371D332—416no—
372D332—416no—
373C4×D83—416no—
374C4×D83—416no—
375C4×D83—416no—
376C22×C83C4×#4114yes—
377C22×C83#51814yes—
378C22×C83#51814yes—
379C22×C83#53814yes—
380C22×C83#53814yes—
381C22×C83#54014yes—
382C22×C83#54014yes—
383C22×C83C24×C411yescharacteristic
384C22×C83C22×#4111yescharacteristic
385C22×C83C22×#4111yescharacteristic
386C22×C83C2×H(5,𝔽2)11yescharacteristic
387C22×C83C2×H(5,𝔽2)11yescharacteristic
388C22×C83C2×H(5,𝔽2)11yescharacteristic
389C22×C83C2×H(5,𝔽2)11yescharacteristic
390C2×D83—24no—
391C2×D83—24no—
392C2×D83—24no—
393C2×D83—24no—
394C2×D83—24no—
395C2×D83—24no—
396C2×D83—24no—
397C2×D83—24no—
398C2×D83—24no—
399C2×D83—416no—
400C2×D83—416no—
401C2×D83—416no—
402C2×D83—42no—
403C2×D83—42no—
404C2×D83—42no—
405C2×D83—42no—
406C2×D83—42no—
407C2×D83—42no—
408C2×D83—42no—
409C2×D83—42no—
410C2×D83—42no—
411C2×D83—42no—
412C2×D83—42no—
413C2×D83—42no—
414C4×C83—24no—
415C4×C83—24no—
416C4×C83—24no—
417C4×C83—24no—
418C4×C83—42no—
419C4×C83—42no—
420C4×C83—42no—
421Dic83—24no—
422Dic83—24no—
423Dic83—42no—
424Dic83—42no—
425Dic83—42no—
426C2×#2333—831nomaximal, Sylow
427C2×C83#233318yescomplemented
428C2×C83C2×C4×#4111yescharacteristic
429C2×C83C2×#51811yescharacteristic
430C2×C83C2×#51811yescharacteristic
431C2×C83C2×#53811yescharacteristic
432C2×C83C2×#53811yescharacteristic
433C2×C83C2×#54011yescharacteristic
434C2×C83C2×#54011yescharacteristic
435D83—44no—
436D83—44no—
437D83—44no—
438C22×#121—831no—
439#2333—8316no—
440C2×#390—831no—
441C2×#390—831no—
442C2×#388—831no—
443C2×#388—831no—
444C2×#387—831no—
445C2×#387D8311yescharacteristic, complemented
446C2×#386—831no—
447C2×#386—831no—
448C2×#386—831no—
449C2×#386—831no—
450C2×#381—831no—
451C2×C4×C22⋊C4—831no—
452C2×C4×C22⋊C4—831no—
453C2×C4×C22⋊C4—831no—
454C83C2×#233311yescharacteristic, complemented, Sylow
455C23×D4—831no—
456C23×D4—831no—
457C23×D4—831no—
458C24×C4—831no—
459C24×C4—831no—
460C24×C4—831no—
461C2×#121—8316no—
462C2×#121—838no—
463C22×C4⋊C4—831no—
464C22×C4⋊C4C2×D8311yescharacteristic
465C22×C4⋊C4C2×D8311yescharacteristic
466C22×C22⋊C4—831no—
467C22×C22⋊C4—831no—
468C22×C22⋊C4—831no—
469C22×C22⋊C4—831no—
470C22×C22⋊C4—831no—
471C22×C22⋊C4—831no—
472C22×C22⋊C4—831no—
473C22×C22⋊C4—831no—
474C22×C22⋊C4—831no—
475C22×C22⋊C4—831no—
476C22×C22⋊C4—831no—
477C22×C22⋊C4—831no—
478C22×C42—831no—
479C22×C42—831no—
480C22×C42—831no—
481C22×C42C2×D8311yescharacteristic
482#390—838no—
483#390—838no—
484#388—838no—
485#388—838no—
486#387—838no—
487#387C2×D8318yescomplemented
488#386—838no—
489#386—838no—
490#386—838no—
491#386—838no—
492#381—838no—
493C4×C22⋊C4—838no—
494C4×C22⋊C4—838no—
495C4×C22⋊C4—838no—
496C2×#95—831no—
497C2×#95—831no—
498C2×#95—831no—
499C2×#95—831no—
500C2×#95—831no—
501C2×#95—831no—
502C2×#95C2×D8311yescharacteristic
503C2×#95C2×D8311yescharacteristic
504C2×#95C2×D8311yescharacteristic
505C2×#95C2×D8311yescharacteristic
506C25—831no—
507C25—831no—
508C25—831no—
509C22×D4—3322no—
510C22×D4—3322no—
511C22×D4—3322no—
512C22×D4—3322no—
513C22×D4—3322no—
514C22×D4—3322no—
515C22×D4—838no—
516C22×D4—838no—
517C22×D4—838no—
518C22×D4—834no—
519C22×D4—834no—
520C22×D4—834no—
521C23×C4—3322no—
522C23×C4—3322no—
523C23×C4—3322no—
524C23×C4—3322no—
525C23×C4—3322no—
526C23×C4—3322no—
527C23×C4—838no—
528C23×C4—834no—
529C23×C4—834no—
530C23×C4—834no—
531C23×C4—831no—
532C23×C4—831no—
533C23×C4—831no—
534C23×C4—831no—
535C23×C4—831no—
536C23×C4—1664no—
537C23×C4—1664no—
538C23×C4C22×D8311yescharacteristic
539C23×C4C22×D8311yescharacteristic
540C23×C4C22×D8311yescharacteristic
541C23×C4C22×D8311yescharacteristic
542C23×C4C22×D8311yescharacteristic
543C23×C4C22×D8311yescharacteristic
544C23×C4C22×D8311yescharacteristic
545#121—8364no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—3322no—
548C2×C4⋊C4—834no—
549C2×C4⋊C4C4×D8318yescomplemented
550C2×C4⋊C4C22×D8314yes—
551C2×C4⋊C4C22×D8314yes—
552C2×C22⋊C4—3322no—
553C2×C22⋊C4—3322no—
554C2×C22⋊C4—3322no—
555C2×C22⋊C4—3322no—
556C2×C22⋊C4—3322no—
557C2×C22⋊C4—3322no—
558C2×C22⋊C4—834no—
559C2×C22⋊C4—834no—
560C2×C22⋊C4—834no—
561C2×C22⋊C4—834no—
562C2×C22⋊C4—834no—
563C2×C22⋊C4—834no—
564C2×C22⋊C4—838no—
565C2×C22⋊C4—838no—
566C2×C22⋊C4—834no—
567C2×C22⋊C4—834no—
568C2×C22⋊C4—834no—
569C2×C22⋊C4—834no—
570C2×C22⋊C4—834no—
571C2×C22⋊C4—834no—
572C2×C22⋊C4—1664no—
573C2×C22⋊C4—1664no—
574C2×C22⋊C4—1664no—
575C2×C22⋊C4—1664no—
576C2×C42—42no—
577C2×C42—3322no—
578C2×C42—3322no—
579C2×C42—3322no—
580C2×C42—834no—
581C2×C42—834no—
582C2×C42—834no—
583C2×C42C22×D8314yes—
584#95—834no—
585#95—834no—
586#95—834no—
587#95—834no—
588#95—834no—
589#95—834no—
590#95C22×D8314yes—
591#95C22×D8314yes—
592#95C22×D8314yes—
593#95C22×D8314yes—
594C24—834no—
595C24—834no—
596C24—834no—
597C24—832no—
598C24—832no—
599C24—832no—
600C24—1662no—
601C24—1662no—
602C24—1662no—
603C24—1662no—
604C24—1662no—
605C24—1662no—
606C24—1662no—
607C24—1662no—
608C24—1662no—
609C24—1662no—
610C24—1662no—
611C24—1662no—
612C24—1662no—
613C24—1662no—
614C24—1662no—
615C24—1662no—
616C24—1662no—
617C24—1662no—
618C24C23×D8311yescharacteristic
619C2×D4—33216no—
620C2×D4—33216no—
621C2×D4—33216no—
622C2×D4—3324no—
623C2×D4—3324no—
624C2×D4—3324no—
625C2×D4—3324no—
626C2×D4—3324no—
627C2×D4—3324no—
628C2×D4—8316no—
629C2×D4—8316no—
630C2×D4—8316no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—33216no—
649C22×C4—33216no—
650C22×C4—3324no—
651C22×C4—3324no—
652C22×C4—3324no—
653C22×C4—3324no—
654C22×C4—3324no—
655C22×C4—3324no—
656C22×C4—33216no—
657C22×C4—8316no—
658C22×C4—834no—
659C22×C4—834no—
660C22×C4—832no—
661C22×C4—832no—
662C22×C4—832no—
663C22×C4—832no—
664C22×C4—832no—
665C22×C4—1668no—
666C22×C4—1662no—
667C22×C4—1662no—
668C22×C4—1662no—
669C22×C4—1662no—
670C22×C4—1662no—
671C22×C4—1662no—
672C22×C4—1662no—
673C22×C4—1662no—
674C22×C4—1662no—
675C22×C4—1668no—
676C22×C4—1662no—
677C22×C4—1662no—
678C22×C4—1662no—
679C22×C4—1662no—
680C22×C4C2×C4×D8314yes—
681C22×C4C2×C4×D8314yes—
682C22×C4C2×C4×D8314yes—
683C22×C4#1305059114yes—
684C22×C4C23×D8312yes—
685C22×C4C23×D8312yes—
686C22×C4C23×D8312yes—
687C22×C4C23×D8312yes—
688C22×C4C23×D8312yes—
689C22×C4C23×D8312yes—
690C22×C4C23×D8312yes—
691C4⋊C4—44no—
692C4⋊C4—3324no—
693C4⋊C4C2×C4×D83116yescomplemented
694C22⋊C4—3324no—
695C22⋊C4—3324no—
696C22⋊C4—3324no—
697C22⋊C4—3324no—
698C22⋊C4—3324no—
699C22⋊C4—3324no—
700C22⋊C4—8316no—
701C22⋊C4—8316no—
702C22⋊C4—1668no—
703C22⋊C4—1668no—
704C22⋊C4—1668no—
705C22⋊C4—1668no—
706C42—44no—
707C42—3324no—
708C42—3324no—
709C42—3324no—
710C23—3324no—
711C23—3324no—
712C23—3324no—
713C23—3324no—
714C23—3324no—
715C23—3324no—
716C23—3324no—
717C23—3324no—
718C23—3324no—
719C23—3324no—
720C23—3324no—
721C23—3324no—
722C23—834no—
723C23—834no—
724C23—834no—
725C23—1668no—
726C23—1668no—
727C23—1668no—
728C23—1668no—
729C23—1668no—
730C23—1668no—
731C23—1668no—
732C23—1668no—
733C23—1668no—
734C23—1662no—
735C23—1662no—
736C23—1662no—
737C23—1662no—
738C23—1662no—
739C23—1662no—
740C23—1662no—
741C23—1662no—
742C23—1662no—
743C23—1662no—
744C23—1662no—
745C23—1662no—
746C23—1662no—
747C23—1662no—
748C23—1662no—
749C23—1662no—
750C23—1662no—
751C23—1662no—
752C23C22×C4×D8312yes—
753C23#41×D8312yes—
754C23C2×#1305059112yes—
755C23#1458183712yes—
756C23#1458183812yes—
757C23#1458183812yes—
758C23#1458183812yes—
759C23C24×D8311yescharacteristic
760D4—33216no—
761D4—33216no—
762D4—33216no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—33216no—
788C2×C4—33216no—
789C2×C4—33216no—
790C2×C4—3324no—
791C2×C4—3324no—
792C2×C4—3324no—
793C2×C4—834no—
794C2×C4—834no—
795C2×C4—1662no—
796C2×C4—1662no—
797C2×C4—1662no—
798C2×C4—1662no—
799C2×C4—1662no—
800C2×C4—1662no—
801C2×C4—1662no—
802C2×C4—1662no—
803C2×C4—1662no—
804C2×C4—1668no—
805C2×C4—1662no—
806C2×C4—1662no—
807C2×C4—1662no—
808C2×C4—1662no—
809C2×C4—1668no—
810C2×C4C22×C4×D8314yes—
811C2×C4C22×C4×D8314yes—
812C2×C4C22×C4×D8314yes—
813C2×C4C2×#1305059114yes—
814C22—33216no—
815C22—33216no—
816C22—33216no—
817C22—3322no—
818C22—3322no—
819C22—3322no—
820C22—3322no—
821C22—3322no—
822C22—3322no—
823C22—3322no—
824C22—3322no—
825C22—3322no—
826C22—3322no—
827C22—3322no—
828C22—3322no—
829C22—1664no—
830C22—1664no—
831C22—1664no—
832C22—1664no—
833C22—1664no—
834C22—1664no—
835C22—1664no—
836C22—1664no—
837C22—1664no—
838C22C4×#1305059114yes—
839C22#1912817314yes—
840C22#1912817514yes—
841C22#1912829014yes—
842C22#1912829114yes—
843C22#1912830314yes—
844C22#1912830714yes—
845C22C23×C4×D8311yescharacteristic
846C22C2×#41×D8311yescharacteristic
847C22C22×#1305059111yescharacteristic
848C22C2×#1458183711yescharacteristic
849C22C2×#1458183811yescharacteristic
850C22C2×#1458183811yescharacteristic
851C22C2×#1458183811yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—3322no—
860C4—3322no—
861C4—3322no—
862C4—1664no—
863C4—1664no—
864C2—3324no—
865C2—3324no—
866C2—3324no—
867C2#2491022718yesdirect product factor
868C2C2×C4×#1305059111yescharacteristic
869C2C2×#1912817311yescharacteristic
870C2C2×#1912817511yescharacteristic
871C2C2×#1912829011yescharacteristic
872C2C2×#1912829111yescharacteristic
873C2C2×#1912830311yescharacteristic
874C2C2×#1912830711yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#387×C83C2
socleC24×C83C24
prime radicalC22×#14581767C2
cosocleC23×C83C25
hypercenterC2×#387D83
hypocenterC83C2×#2333
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #24910227C2direct (N × H)
3. C2×#19127603C2semidirect
4. C2×#19127602C2semidirect
5. C2×#19127593C2semidirect
6. C2×#19127591C2semidirect
7. C2×#19127587C2semidirect
8. C2×#19127579C2semidirect
9. C2×#19127579C2semidirect
10. C2×#19127579C2semidirect
11. C2×#19127579C2semidirect
12. C2×#19127563C2semidirect
13. C2×C4×(C2×D83)⋊C4C2semidirect
14. C2×#19127548C2semidirect
15. C2×#19127548C2semidirect
16. C2×#387×C83C2semidirect
23. C2×#14581767C4semidirect
41. #19127603C22semidirect
42. #19127602C22semidirect
43. #19127593C22semidirect
44. #19127591C22semidirect
45. #19127587C22semidirect
46. #19127579C22semidirect
47. #19127579C22semidirect
48. #19127579C22semidirect
49. #19127579C22semidirect
50. #19127563C22semidirect
51. C4×(C2×D83)⋊C4C22semidirect
52. #19127548C22semidirect
53. #19127548C22semidirect
63. #387×C83C22semidirect
78. C22×D332C2×C4semidirect
79. C22×D332C2×C4semidirect
96. C22×C4×D83C2×C4semidirect
100. #14581767C2×C4semidirect
113. C2×(C2×D83)⋊C4C2×C4semidirect
114. C2×(C2×D83)⋊C4C2×C4semidirect
147. C2×C4⋊C4×C83C2×C4semidirect
190. C2×D332C22×C4semidirect
191. C2×D332C22×C4semidirect
223. C2×C4×D83C22×C4semidirect
235. (C2×D83)⋊C4C22×C4semidirect
236. (C2×D83)⋊C4C22×C4semidirect
270. C4⋊C4×C83C22×C4semidirect
427. C2×C83#2333semidirect
445. C2×#387D83semidirect
454. C83C2×#2333semidirect
487. #387C2×D83semidirect
549. C2×C4⋊C4C4×D83semidirect
693. C4⋊C4C2×C4×D83semidirect
867. C2#24910227direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817672
#249102272
C2×#191276032
C2×#191276022
C2×#191275932
C2×#191275912
C2×#191275872
C2×#191275792
C2×#191275632
C2×C4×(C2×D83)⋊C42
C2×#191275482
C2×#387×C832
C2×#233383