Finite Group Databasebeta

← C2×#24910277 #35563324

Subgroups — C2×#24910277 #35563324

Order 21248.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581778C211yesmaximal, characteristic
2#24910277C2116yesmaximal, direct product factor
3C2×#19127606C211yesmaximal, characteristic, complemented
4C2×#19127605C211yesmaximal, characteristic, complemented
5C2×#19127594C211yesmaximal, characteristic, complemented
6C2×#19127591C211yesmaximal, characteristic, complemented
7C2×#19127591C211yesmaximal, characteristic, complemented
8C2×#19127589C211yesmaximal, characteristic, complemented
9C2×#19127580C211yesmaximal, characteristic
10C2×#19127577C211yesmaximal, characteristic
11C2×#19127575C211yesmaximal, characteristic, complemented
12C2×#19127568C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C2×#385×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581778C4116yescomplemented
21C2×#14581778C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×C22⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127606C2218yescomplemented
38#19127605C2218yescomplemented
39#19127594C2218yescomplemented
40#19127591C2218yescomplemented
41#19127591C2218yescomplemented
42#19127589C2218yescomplemented
43#19127580C2218yes—
44#19127577C2218yes—
45#19127575C2218yescomplemented
46#19127568C2218yescomplemented
47C4⋊C4×Dic83C2218yescomplemented
48C4×C22⋊Dic83C2218yescomplemented
49#19127548C2218yescomplemented
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C24×C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65#385×C83C2218yescomplemented
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C24×D83C2311yescharacteristic
69C22×Dic166—42no—
70C22×Dic166—42no—
71C22×Dic166C2×C418yescomplemented
72C22×Dic166C2314yes—
73C22×C22⋊D83—42no—
74C22×C22⋊D83—42no—
75C22×C22⋊D83C2×C418yes—
76C22×C22⋊D83C2314yes—
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C22×C4×D83—24no—
85C22×C4×D83—42no—
86C22×C4×D83—42no—
87C22×C4×D83C2314yes—
88#14581778C2×C4164yescomplemented
89C2×C4⋊Dic83—24no—
90C2×C4⋊Dic83C2314yes—
91C2×Dic83⋊C4—42no—
92C2×Dic83⋊C4C2314yes—
93C2×C22⋊Dic83—24no—
94C2×C22⋊Dic83—42no—
95C2×C22⋊Dic83C2×C418yescomplemented
96C2×C22⋊Dic83C2314yes—
97C2×C22⋊Dic83C2314yes—
98C2×C22⋊Dic83C2314yes—
99C2×(C2×D83)⋊C4—24no—
100C2×(C2×D83)⋊C4—42no—
101C2×(C2×D83)⋊C4—42no—
102C2×(C2×D83)⋊C4C2×C418yescomplemented
103C2×(C2×D83)⋊C4C2×C418yescomplemented
104C2×(C2×D83)⋊C4C2314yes—
105C2×(C2×D83)⋊C4C2314yes—
106C2×(C2×D83)⋊C4C2314yes—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×C4×Dic83—42no—
110C2×C4×Dic83—42no—
111C2×C4×Dic83—42no—
112C2×C4×Dic83—42no—
113C2×C4×Dic83C2×C418yescomplemented
114C2×C4×Dic83C2314yes—
115C2×C4×Dic83C2314yes—
116C2×C4×Dic83C2314yes—
117C2×C4×Dic83C2314yes—
118C2×C4×Dic83C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C25×C83C2311yescharacteristic
130C23×C4×C83—24no—
131C23×C4×C83—42no—
132C23×C4×C83—42no—
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2314yes—
140C2×C4⋊C4×C83—24no—
141C2×C4⋊C4×C83—42no—
142C2×C4⋊C4×C83C2314yes—
143C2×C4⋊C4×C83C2314yes—
144C2×C22⋊C4×C83—42no—
145C2×C22⋊C4×C83C2×C418yescomplemented
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148#95×C83C2314yes—
149#95×C83C2314yes—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83C22×C414yes—
157C23×D83C2412yes—
158C2×Dic166—416no—
159C2×Dic166—44no—
160C2×Dic166—44no—
161C2×Dic166C22×C4116yescomplemented
162C2×C22⋊D83—416no—
163C2×C22⋊D83—44no—
164C2×C22⋊D83—44no—
165C2×C22⋊D83C22×C4116yes—
166C22×Dic83—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83C22×C414yes—
184C22×Dic83C22×C414yes—
185C22×Dic83C22×C414yes—
186C22×Dic83#4114yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C2×C4×D83—28no—
195C2×C4×D83—44no—
196C2×C4×D83—44no—
197C2×C4×D83—416no—
198C4⋊Dic83—28no—
199Dic83⋊C4—44no—
200C22⋊Dic83—28no—
201C22⋊Dic83—44no—
202C22⋊Dic83C22×C4116yescomplemented
203(C2×D83)⋊C4—28no—
204(C2×D83)⋊C4—44no—
205(C2×D83)⋊C4—44no—
206(C2×D83)⋊C4C22×C4116yescomplemented
207(C2×D83)⋊C4C22×C4116yescomplemented
208C4×Dic83—44no—
209C4×Dic83—44no—
210C4×Dic83—44no—
211C4×Dic83—44no—
212C4×Dic83C22×C4116yescomplemented
213C24×C83—22no—
214C24×C83—22no—
215C24×C83—22no—
216C24×C83—22no—
217C24×C83—22no—
218C24×C83—22no—
219C24×C83C22×C414yes—
220C24×C83C2412yes—
221C24×C83C2411yescharacteristic
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—28no—
238C22×C4×C83—44no—
239C22×C4×C83—44no—
240C22×C4×C83—416no—
241C22×C4×C83C22×C414yes—
242C22×C4×C83C22×C414yes—
243C22×C4×C83#4114yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C4⋊C4×C83—28no—
251C4⋊C4×C83—44no—
252C22⋊C4×C83—44no—
253C22⋊C4×C83C22×C4116yescomplemented
254C23×C83—28no—
255C23×C83—28no—
256C23×C83—28no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—44no—
264C23×C83—44no—
265C23×C83—44no—
266C23×C83—44no—
267C23×C83C23×C414yes—
268C23×C83C23×C412yes—
269C23×C83C2×#4112yes—
270C23×C83C2×#4112yes—
271C23×C83H(5,𝔽2)12yes—
272C23×C83H(5,𝔽2)12yes—
273C23×C83H(5,𝔽2)12yes—
274C23×C832−1+412yes—
275C23×C83C2511yescharacteristic
276C22×D83—28no—
277C22×D83—28no—
278C22×D83—28no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—44no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83—44no—
289C22×D83C23×C414yes—
290C2×C4×C83—28no—
291C2×C4×C83—28no—
292C2×C4×C83—28no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—416no—
309C2×C4×C83—44no—
310C2×C4×C83—44no—
311C2×C4×C83—44no—
312C2×C4×C83C23×C414yes—
313C2×C4×C83C23×C414yes—
314C2×C4×C83C2×#4114yes—
315C22⋊D83—416no—
316C2×Dic83—28no—
317C2×Dic83—28no—
318C2×Dic83—28no—
319C2×Dic83—28no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—44no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83C23×C414yes—
341C2×Dic83C23×C414yes—
342C2×Dic83C23×C414yes—
343C2×Dic83C2×#4114yes—
344C4×D83—416no—
345Dic166—416no—
346C22×C83—24no—
347C22×C83—24no—
348C22×C83—24no—
349C22×C83—416no—
350C22×C83—42no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83C4×#4114yes—
355C22×C83#51814yes—
356C22×C83#52014yes—
357C22×C83#53814yes—
358C22×C83#53814yes—
359C22×C83#54214yes—
360C22×C83#54214yes—
361C22×C83C24×C411yescharacteristic
362C22×C83C22×#4111yescharacteristic
363C22×C83C22×#4111yescharacteristic
364C22×C83C2×H(5,𝔽2)11yescharacteristic
365C22×C83C2×H(5,𝔽2)11yescharacteristic
366C22×C83C2×H(5,𝔽2)11yescharacteristic
367C22×C83C2×2−1+411yescharacteristic
368C2×D83—24no—
369C2×D83—24no—
370C2×D83—24no—
371C2×D83—416no—
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C4×C83—24no—
377C4×C83—24no—
378C4×C83—24no—
379C4×C83—42no—
380C4×C83—42no—
381C4×C83—42no—
382Dic83—24no—
383Dic83—24no—
384Dic83—24no—
385Dic83—24no—
386Dic83—42no—
387Dic83—42no—
388Dic83—42no—
389C2×#2337—831nomaximal, Sylow
390C2×C83—44no—
391C2×C83#233718yescomplemented
392C2×C83C2×C4×#4111yescharacteristic
393C2×C83C2×#51811yescharacteristic
394C2×C83C2×#52011yescharacteristic
395C2×C83C2×#53811yescharacteristic
396C2×C83C2×#53811yescharacteristic
397C2×C83C2×#54211yescharacteristic
398C2×C83C2×#54211yescharacteristic
399D83—44no—
400C22×#124—831no—
401#2337—8316no—
402C2×#391—831no—
403C2×#391—831no—
404C2×#388—831no—
405C2×#388—831no—
406C2×#388—831no—
407C2×#388—831no—
408C2×#386—831no—
409C2×#386—831no—
410C2×#385—831no—
411C2×#385D8311yescharacteristic, complemented
412C2×#383—831no—
413C2×C4×C4⋊C4—831no—
414C2×C4×C22⋊C4—831no—
415C2×C4×C22⋊C4—831no—
416C83C2×#233711yescharacteristic, complemented, Sylow
417C23×Q8—831no—
418C23×D4—831no—
419C24×C4—831no—
420C24×C4C2×D8311yescharacteristic
421C2×#124—8316no—
422C2×#124—838no—
423C22×C4⋊C4—831no—
424C22×C4⋊C4—831no—
425C22×C4⋊C4C2×D8311yescharacteristic
426C22×C4⋊C4C2×D8311yescharacteristic
427C22×C22⋊C4—831no—
428C22×C22⋊C4—831no—
429C22×C22⋊C4—831no—
430C22×C22⋊C4—831no—
431C22×C22⋊C4—831no—
432C22×C22⋊C4—831no—
433C22×C22⋊C4—831no—
434C22×C22⋊C4—831no—
435C22×C22⋊C4C2×D8311yescharacteristic
436C22×C22⋊C4C2×D8311yescharacteristic
437C22×C42—831no—
438C22×C42—831no—
439C22×C42—831no—
440C22×C42—831no—
441C22×C42—831no—
442#391—838no—
443#391—838no—
444#388—838no—
445#388—838no—
446#388—838no—
447#388—838no—
448#386—838no—
449#386—838no—
450#385—838no—
451#385C2×D8318yescomplemented
452#383—838no—
453C4×C4⋊C4—838no—
454C4×C22⋊C4—838no—
455C4×C22⋊C4—838no—
456C2×#95—831no—
457C2×#95—831no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95C2×D8311yescharacteristic
467C2×#95C2×D8311yescharacteristic
468C25—831no—
469C25C22×D8311yescharacteristic
470C22×Q8—3322no—
471C22×Q8—3322no—
472C22×Q8—838no—
473C22×Q8—834no—
474C22×D4—3322no—
475C22×D4—3322no—
476C22×D4—838no—
477C22×D4—834no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—3322no—
482C23×C4—3322no—
483C23×C4—834no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—831no—
488C23×C4—831no—
489C23×C4—831no—
490C23×C4—831no—
491C23×C4—1664no—
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C23×C4C22×D8311yescharacteristic
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8311yescharacteristic
498C23×C4C22×D8314yes—
499#124—8364no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—3322no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—1664no—
506C2×C4⋊C4C22×D8314yes—
507C2×C4⋊C4C22×D8314yes—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—3322no—
510C2×C22⋊C4—3322no—
511C2×C22⋊C4—3322no—
512C2×C22⋊C4—834no—
513C2×C22⋊C4—834no—
514C2×C22⋊C4—834no—
515C2×C22⋊C4—838no—
516C2×C22⋊C4—834no—
517C2×C22⋊C4—838no—
518C2×C22⋊C4—838no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—1664no—
524C2×C22⋊C4—1664no—
525C2×C22⋊C4C4×D8318yescomplemented
526C2×C22⋊C4C22×D8314yes—
527C2×C22⋊C4C22×D8314yes—
528C2×C42—3322no—
529C2×C42—3322no—
530C2×C42—3322no—
531C2×C42—3322no—
532C2×C42—834no—
533C2×C42—834no—
534C2×C42—834no—
535C2×C42—834no—
536C2×C42—838no—
537C2×C42—834no—
538#95—834no—
539#95—834no—
540#95—834no—
541#95—834no—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95—834no—
548#95C22×D8314yes—
549#95C22×D8314yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—834no—
557C24—832no—
558C24—1662no—
559C24—1662no—
560C24—1662no—
561C24—1662no—
562C24—1662no—
563C24—1662no—
564C24C2×C4×D8314yes—
565C24C23×D8312yes—
566C24C23×D8311yescharacteristic
567C2×Q8—33216no—
568C2×Q8—3324no—
569C2×Q8—3324no—
570C2×Q8—8316no—
571C2×D4—33216no—
572C2×D4—3324no—
573C2×D4—3324no—
574C2×D4—8316no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—416no—
594C22×C4—3324no—
595C22×C4—3324no—
596C22×C4—33216no—
597C22×C4—834no—
598C22×C4—834no—
599C22×C4—834no—
600C22×C4—834no—
601C22×C4—832no—
602C22×C4—832no—
603C22×C4—832no—
604C22×C4—832no—
605C22×C4—832no—
606C22×C4—832no—
607C22×C4—832no—
608C22×C4—1668no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1662no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4—1662no—
617C22×C4—1662no—
618C22×C4—1662no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1662no—
622C22×C4—1662no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4—1662no—
626C22×C4C2×C4×D8314yes—
627C22×C4C2×C4×D8314yes—
628C22×C4#1305058914yes—
629C22×C4C23×D8312yes—
630C22×C4C23×D8312yes—
631C22×C4C23×D8312yes—
632C22×C4C23×D8312yes—
633C22×C4C23×D8312yes—
634C22×C4C23×D8312yes—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—3324no—
638C4⋊C4—1668no—
639C22⋊C4—44no—
640C22⋊C4—3324no—
641C22⋊C4—3324no—
642C22⋊C4—3324no—
643C22⋊C4—8316no—
644C22⋊C4—8316no—
645C22⋊C4—8316no—
646C22⋊C4—1668no—
647C22⋊C4—1668no—
648C22⋊C4C2×C4×D83116yescomplemented
649C42—3324no—
650C42—3324no—
651C42—3324no—
652C42—3324no—
653C42—8316no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—3324no—
668C23—3324no—
669C23—3324no—
670C23—3324no—
671C23—834no—
672C23—1668no—
673C23—1668no—
674C23—1668no—
675C23—1662no—
676C23—1662no—
677C23—1662no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23C22×C4×D8314yes—
682C23C22×C4×D8312yes—
683C23#41×D8312yes—
684C23C2×#1305058912yes—
685C23#1458183712yes—
686C23#1458183712yes—
687C23#1458183812yes—
688C23#1458184012yes—
689C23C24×D8311yescharacteristic
690Q8—33216no—
691D4—33216no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—33216no—
715C2×C4—3324no—
716C2×C4—3324no—
717C2×C4—3324no—
718C2×C4—834no—
719C2×C4—834no—
720C2×C4—834no—
721C2×C4—834no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1662no—
731C2×C4—1668no—
732C2×C4—1668no—
733C2×C4—1668no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1668no—
743C2×C4C22×C4×D8314yes—
744C2×C4C22×C4×D8314yes—
745C2×C4C2×#1305058914yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—416no—
752C22—42no—
753C22—42no—
754C22—3322no—
755C22—3322no—
756C22—33216no—
757C22—3322no—
758C22—3322no—
759C22—1664no—
760C22—1664no—
761C22—1664no—
762C22C4×#1305058914yes—
763C22#1912817314yes—
764C22#1912818214yes—
765C22#1912828614yes—
766C22#1912828714yes—
767C22#1912832114yes—
768C22#1912832414yes—
769C22C23×C4×D8311yescharacteristic
770C22C2×#41×D8311yescharacteristic
771C22C22×#1305058911yescharacteristic
772C22C2×#1458183711yescharacteristic
773C22C2×#1458183711yescharacteristic
774C22C2×#1458183811yescharacteristic
775C22C2×#1458184011yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—3322no—
783C4—3322no—
784C4—3322no—
785C4—1664no—
786C4—1664no—
787C4—1664no—
788C4—1664no—
789C2—44no—
790C2—3324no—
791C2#2491027718yesdirect product factor
792C2C2×C4×#1305058911yescharacteristic
793C2C2×#1912817311yescharacteristic
794C2C2×#1912818211yescharacteristic
795C2C2×#1912828611yescharacteristic
796C2C2×#1912828711yescharacteristic
797C2C2×#1912832111yescharacteristic
798C2C2×#1912832411yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
cosocleC23×C83C25
hypercenterC2×#385D83
hypocenterC83C2×#2337
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #24910277C2direct (N × H)
3. C2×#19127606C2semidirect
4. C2×#19127605C2semidirect
5. C2×#19127594C2semidirect
6. C2×#19127591C2semidirect
7. C2×#19127591C2semidirect
8. C2×#19127589C2semidirect
11. C2×#19127575C2semidirect
12. C2×#19127568C2semidirect
13. C2×C4⋊C4×Dic83C2semidirect
14. C2×C4×C22⋊Dic83C2semidirect
15. C2×#19127548C2semidirect
16. C2×#385×C83C2semidirect
20. C2×#14581778C4semidirect
37. #19127606C22semidirect
38. #19127605C22semidirect
39. #19127594C22semidirect
40. #19127591C22semidirect
41. #19127591C22semidirect
42. #19127589C22semidirect
45. #19127575C22semidirect
46. #19127568C22semidirect
47. C4⋊C4×Dic83C22semidirect
48. C4×C22⋊Dic83C22semidirect
49. #19127548C22semidirect
65. #385×C83C22semidirect
71. C22×Dic166C2×C4semidirect
88. #14581778C2×C4semidirect
95. C2×C22⋊Dic83C2×C4semidirect
102. C2×(C2×D83)⋊C4C2×C4semidirect
103. C2×(C2×D83)⋊C4C2×C4semidirect
113. C2×C4×Dic83C2×C4semidirect
145. C2×C22⋊C4×C83C2×C4semidirect
161. C2×Dic166C22×C4semidirect
202. C22⋊Dic83C22×C4semidirect
206. (C2×D83)⋊C4C22×C4semidirect
207. (C2×D83)⋊C4C22×C4semidirect
212. C4×Dic83C22×C4semidirect
253. C22⋊C4×C83C22×C4semidirect
391. C2×C83#2337semidirect
411. C2×#385D83semidirect
416. C83C2×#2337semidirect
451. #385C2×D83semidirect
525. C2×C22⋊C4C4×D83semidirect
648. C22⋊C4C2×C4×D83semidirect
791. C2#24910277direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817782
#249102772
C2×#191276062
C2×#191276052
C2×#191275942
C2×#191275912
C2×#191275892
C2×#191275802
C2×#191275772
C2×#191275752
C2×#191275682
C2×C4⋊C4×Dic832
C2×C4×C22⋊Dic832
C2×#191275482
C2×#385×C832
C2×#233783