Finite Group Databasebeta

← #35564849

Subgroups — #35564849

Order 21248.

2310 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128255C211yesmaximal, characteristic
2#24910467C212yesmaximal
3#24910465C214yesmaximal
4#24910464C212yesmaximal
5#24910422C211yesmaximal, characteristic, complemented
6#24910421C212yesmaximal, complemented
7#24910420C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic166C211yesmaximal, characteristic, complemented
9#24910375C212yesmaximal, complemented
10#24910201C214yesmaximal, complemented
11#24910084C212yesmaximal
12#24910034C212yesmaximal, complemented
13C4×#14581790C212yesmaximal, complemented
14#384×D83C211yesmaximal, characteristic
15#24909817C212yesmaximal
16C4×#14581750C211yesmaximal, characteristic
17Q8×C4⋊C4×C83C211yesmaximal, characteristic, complemented
18#19128255C4116yescomplemented
19C2×#14581791C2211yescharacteristic
20C2×#14581790C2211yescharacteristic
21C2×#14581782C2212yes—
22C2×#14581772C2211yescharacteristic
23C2×#14581770C2212yes—
24C2×#14581768C2211yescharacteristic
25C2×C4×Dic166C2212yes—
26C2×C4×Dic166C2212yes—
27C2×C4×Dic166C2211yescharacteristic
28C2×#14581757C2214yes—
29C2×#14581750C2211yescharacteristic
30C2×#14581750C2211yescharacteristic
31C2×#14581749C2212yes—
32C2×C4⋊C4×D83C2212yes—
33C2×C4⋊C4×D83C2212yes—
34C2×C4⋊C4×D83C2212yes—
35C2×C42×D83C2211yescharacteristic
36#19127608C2212yes—
37#19127606C2212yes—
38#19127605C2214yes—
39#19127599C2212yes—
40#19127598C2214yes—
41#19127597C2214yes—
42#19127596C2214yes—
43#19127596C2214yes—
44#19127596C2214yes—
45#19127596C2214yes—
46#19127587C2214yes—
47#19127585C2214yes—
48#19127584C2214yes—
49#19127582C2214yes—
50#19127572C2214yes—
51#19127572C2214yes—
52#19127571C2211yescharacteristic
53#19127570C2212yes—
54#19127570C2212yes—
55#19127570C2212yes—
56#19127570C2212yes—
57#19127567C2212yes—
58#19127566C2212yes—
59C4⋊C4×Dic83C2211yescharacteristic
60C4⋊C4×Dic83C2212yes—
61C4⋊C4×Dic83C2212yes—
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2211yescharacteristic
64C4⋊C4×Dic83C2212yes—
65C4×Dic83⋊C4C2214yes—
66C4×Dic83⋊C4C2214yes—
67C4×C4⋊Dic83C2212yes—
68C4×C4⋊Dic83C2211yescharacteristic
69#19127552C2214yes—
70C4×(C2×D83)⋊C4C2214yes—
71C4×(C2×D83)⋊C4C2212yes—
72#19127548C2212yes—
73#19127548C2214yes—
74#19127546C2212yes—
75C42×Dic83C2212yes—
76C2×C4×Q8×C83C2212yes—
77C2×C4×Q8×C83C2211yescharacteristic
78#389×C83C2214yes—
79#389×C83C2212yes—
80#384×C83C2212yes—
81#384×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×Dic166C2312yes—
85C22×Dic166C2311yescharacteristic
86C22×C4×D83C2311yescharacteristic
87C22×C4×D83C2311yescharacteristic
88C22×C4×D83C2314yes—
89C22×C4×D83C2311yescharacteristic
90#14581791C2×C418yescomplemented
91#14581790C2×C418yescomplemented
92#14581782C2×C4116yescomplemented
93#14581772C2×C418yes—
94#14581770C2×C4116yes—
95#14581768C2×C418yes—
96C4×Dic166—44no—
97C4×Dic166C2×C418yescomplemented
98C4×Dic166C2×C4116yescomplemented
99#14581757—48no—
100#14581750—24no—
101#14581750Q818yescomplemented
102#14581749C2×C4116yes—
103C2×C4⋊Dic83C2311yescharacteristic
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C2×Dic83⋊C4C2312yes—
119C2×Dic83⋊C4C2312yes—
120C4⋊C4×D83—28no—
121C4⋊C4×D83—44no—
122C4⋊C4×D83—44no—
123C2×(C2×D83)⋊C4C2312yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×C4×Dic83C2312yes—
128C2×C4×Dic83C2312yes—
129C2×C4×Dic83C2312yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2314yes—
133C2×C4×Dic83C2314yes—
134C2×C4×Dic83C2312yes—
135C2×C4×Dic83C2311yescharacteristic
136C2×C4×Dic83C2311yescharacteristic
137C2×C4×Dic83C2311yescharacteristic
138C2×C4×Dic83C2312yes—
139C42×D83C2×C418yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2314yes—
147C83⋊#95C2314yes—
148C83⋊#95C2312yes—
149C83⋊#95C2312yes—
150C22×Q8×C83C2311yescharacteristic
151C4×Q8×C83—44no—
152C4×Q8×C83C2×C418yescomplemented
153C2×C4⋊C4×C83C2312yes—
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2312yes—
157C2×C4⋊C4×C83C2314yes—
158C2×C4⋊C4×C83C2314yes—
159C2×C4⋊C4×C83C2311yescharacteristic
160C2×C4⋊C4×C83C2312yes—
161C2×C4⋊C4×C83C2311yescharacteristic
162C2×C42×C83C2312yes—
163C2×C42×C83C2314yes—
164C2×C42×C83C2312yes—
165C2×C42×C83C2311yescharacteristic
166#95×C83C2314yes—
167#95×C83C2312yes—
168C23×D83C2411yescharacteristic
169C2×Dic166—22no—
170C2×Dic166—22no—
171C2×Dic166—24no—
172C2×Dic166—24no—
173C2×Dic166C22×C418yes—
174C2×Dic166C22×C414yes—
175C22×Dic83C2414yes—
176C22×Dic83C2412yes—
177C22×Dic83C2411yescharacteristic
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2411yescharacteristic
182C22×Dic83C2411yescharacteristic
183C2×C4×D83—22no—
184C2×C4×D83—22no—
185C2×C4×D83—22no—
186C2×C4×D83—22no—
187C2×C4×D83—28no—
188C2×C4×D83—44no—
189C2×C4×D83—44no—
190C2×C4×D83C22×C414yes—
191C2×C4×D83C22×C414yes—
192C2×C4×D83C22×C414yes—
193C2×C4×D83C2×Q814yes—
194C2×C4×D83#4114yes—
195C4⋊Dic83—24no—
196C4⋊Dic83—22no—
197C4⋊Dic83—24no—
198C4⋊Dic83—42no—
199C4⋊Dic83C22×C414yes—
200C4⋊Dic83C22×C418yes—
201C4⋊Dic83C2×Q814yes—
202Dic83⋊C4—28no—
203Dic83⋊C4—28no—
204Dic83⋊C4—44no—
205Dic83⋊C4—44no—
206Dic83⋊C4—44no—
207Dic83⋊C4C22×C418yes—
208Dic83⋊C4C22×C418yes—
209Dic83⋊C4C22×C418yes—
210Dic83⋊C4C22×C418yes—
211Dic83⋊C4C22×C418yes—
212(C2×D83)⋊C4—24no—
213(C2×D83)⋊C4C22×C418yes—
214(C2×D83)⋊C4C22×C418yes—
215(C2×D83)⋊C4C2×Q818yes—
216C4×Dic83—24no—
217C4×Dic83—24no—
218C4×Dic83—24no—
219C4×Dic83—24no—
220C4×Dic83—44no—
221C4×Dic83—44no—
222C4×Dic83—44no—
223C4×Dic83C22×C414yes—
224C4×Dic83C22×C414yes—
225C4×Dic83C22×C414yes—
226C4×Dic83C22×C418yes—
227C4×Dic83C2×Q818yes—
228C2×Q8×C83—22no—
229C2×Q8×C83—22no—
230C2×Q8×C83C22×C414yes—
231C22×C4×C83C2414yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2411yescharacteristic
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2411yescharacteristic
239C4⋊C4×C83—24no—
240C4⋊C4×C83—22no—
241C4⋊C4×C83—24no—
242C4⋊C4×C83—44no—
243C4⋊C4×C83—42no—
244C4⋊C4×C83—44no—
245C4⋊C4×C83C22×C418yes—
246C4⋊C4×C83C22×C414yes—
247C4⋊C4×C83C2×Q814yes—
248C42×C83—24no—
249C42×C83—44no—
250C42×C83C22×C414yes—
251C42×C83C22×C418yes—
252C23×C83C2511yescharacteristic
253C22×D83—21no—
254C22×D83—21no—
255C22×D83—21no—
256C22×D83—21no—
257C22×D83C23×C412yes—
258C22×D83C22×Q812yes—
259C22×D83C2×#4112yes—
260Q8×C83—28no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—21no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—21no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—24no—
271C2×C4×C83—22no—
272C2×C4×C83—24no—
273C2×C4×C83—22no—
274C2×C4×C83—24no—
275C2×C4×C83C23×C412yes—
276C2×C4×C83C23×C414yes—
277C2×C4×C83C23×C414yes—
278C2×C4×C83C23×C412yes—
279C2×C4×C83C23×C412yes—
280C2×C4×C83C22×Q814yes—
281C2×C4×C83C22×Q812yes—
282C2×C4×C83C2×#4112yes—
283C2×C4×C83H(5,𝔽2)12yes—
284C2×C4×C832−1+412yes—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—21no—
289C2×Dic83—22no—
290C2×Dic83—21no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—24no—
295C2×Dic83—24no—
296C2×Dic83—24no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83C23×C412yes—
300C2×Dic83C23×C414yes—
301C2×Dic83C23×C414yes—
302C2×Dic83C23×C412yes—
303C2×Dic83C23×C412yes—
304C2×Dic83C22×Q814yes—
305C2×Dic83C22×Q812yes—
306C2×Dic83C2×#4112yes—
307C2×Dic83H(5,𝔽2)12yes—
308C2×Dic832−1+412yes—
309C4×D83—28no—
310C4×D83—28no—
311C4×D83—88no—
312C4×D83C4×Q8116yescomplemented
313Dic166—28no—
314Dic166—216no—
315C22×C83C24×C411yescharacteristic
316C22×C83C23×Q811yescharacteristic
317C22×C83C22×#4111yescharacteristic
318C22×C83C2×H(5,𝔽2)11yescharacteristic
319C22×C83C2×H(5,𝔽2)11yescharacteristic
320C22×C83C2×2−1+411yescharacteristic
321C22×C83C2×2−1+411yescharacteristic
322C2×D83—22no—
323C2×D83—22no—
324C2×D83—22no—
325C2×D83—22no—
326C2×D83—22no—
327C2×D83—22no—
328C2×D83C2×C4×Q814yes—
329C4×C83—24no—
330C4×C83—22no—
331C4×C83—24no—
332C4×C83—24no—
333C4×C83—44no—
334C4×C83—42no—
335C4×C83C2×C4×Q814yes—
336C4×C83#52014yes—
337Dic83—24no—
338Dic83—24no—
339Dic83—22no—
340Dic83—24no—
341Dic83—44no—
342Dic83—42no—
343Dic83C2×C4×Q814yes—
344Dic83#52014yes—
345#34214—831nomaximal, Sylow
346C2×C83C22×C4×Q811yescharacteristic
347C2×C83C2×#52011yescharacteristic
348C2×C83C2×#52011yescharacteristic
349C2×C83#350311yescharacteristic
350C2×C83#350311yescharacteristic
351C2×C83#350811yescharacteristic
352C2×C83#350911yescharacteristic
353D83—24no—
354C2×#533—831no—
355#2360—834no—
356#2360—832no—
357#2360—832no—
358#2355—831no—
359#2355—832no—
360#2355—831no—
361Q8×C4⋊C4—832no—
362Q8×C4⋊C4—831no—
363Q8×C4⋊C4D8311yescharacteristic, complemented
364#2330—834no—
365#2317—832no—
366C4×C4⋊Q8—832no—
367C4×C4⋊Q8—832no—
368C2×#384—831no—
369#2274—832no—
370C4×#117—831no—
371C83#3421411yescharacteristic, complemented, Sylow
372#533—8316no—
373C2×C4⋊Q8—831no—
374C2×C4⋊Q8—831no—
375C2×#125—832no—
376C2×C22⋊Q8—831no—
377C2×C22⋊Q8—832no—
378C2×C22⋊Q8—831no—
379C2×C4×Q8—834no—
380C2×C4×Q8—832no—
381C2×C4×Q8—831no—
382C2×C4×Q8—832no—
383C2×C4×Q8C2×D8312yes—
384C2×C4×Q8C2×D8311yescharacteristic
385C2×#117—831no—
386C2×#117—831no—
387C2×#117—832no—
388C22×C4⋊C4—832no—
389C22×C4⋊C4—832no—
390C22×C4⋊C4—832no—
391C22×C42—831no—
392#391—832no—
393#391—832no—
394#391—834no—
395#389—834no—
396#389—834no—
397#389—834no—
398#389—834no—
399#389—834no—
400#389—832no—
401#389—834no—
402#389C2×D8312yes—
403#389C2×D8314yes—
404#387—834no—
405#387—834no—
406#387—834no—
407#387—834no—
408#385—834no—
409#385—834no—
410#384—832no—
411#384—832no—
412#384—832no—
413#384—832no—
414#384—831no—
415#384C2×D8312yes—
416#384C2×D8311yescharacteristic
417#382—832no—
418#382—832no—
419C4×C4⋊C4—832no—
420C4×C4⋊C4—832no—
421C4×C4⋊C4—831no—
422C4×C4⋊C4—832no—
423C4×C4⋊C4—832no—
424C4×C4⋊C4—831no—
425C4×C4⋊C4—832no—
426C4×C4⋊C4—831no—
427C4×C4⋊C4—834no—
428C4×C4⋊C4—834no—
429C4×C4⋊C4—834no—
430C4×C4⋊C4C2×D8311yescharacteristic
431C4×C4⋊C4C2×D8312yes—
432C4×C22⋊C4—832no—
433C4×C22⋊C4—834no—
434C4×C22⋊C4—832no—
435C4×C22⋊C4—834no—
436#376—832no—
437C43—832no—
438C22×Q8—832no—
439C22×Q8—831no—
440C22×Q8C22×D8311yescharacteristic
441C23×C4—834no—
442C23×C4—831no—
443C23×C4—831no—
444C23×C4—831no—
445C4⋊Q8—838no—
446C4⋊Q8—838no—
447#125—8316no—
448C22⋊Q8—838no—
449C22⋊Q8—8316no—
450C22⋊Q8—838no—
451C4×Q8—44no—
452C4×Q8—3324no—
453C4×Q8—3328no—
454C4×Q8—8316no—
455C4×Q8—838no—
456C4×Q8C4×D8318yescomplemented
457#117—838no—
458#117—8316no—
459#117—1664no—
460C2×C4⋊C4—3324no—
461C2×C4⋊C4—3324no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—832no—
464C2×C4⋊C4—834no—
465C2×C4⋊C4—834no—
466C2×C4⋊C4—832no—
467C2×C4⋊C4—832no—
468C2×C4⋊C4—831no—
469C2×C4⋊C4—832no—
470C2×C4⋊C4—832no—
471C2×C4⋊C4—832no—
472C2×C4⋊C4—832no—
473C2×C4⋊C4—831no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—834no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—1668no—
480C2×C4⋊C4C22×D8312yes—
481C2×C4⋊C4C22×D8312yes—
482C2×C4⋊C4C22×D8311yescharacteristic
483C2×C4⋊C4C22×D8312yes—
484C2×C4⋊C4C22×D8314yes—
485C2×C4⋊C4C22×D8314yes—
486C2×C4⋊C4C22×D8312yes—
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C22⋊C4—832no—
490C2×C22⋊C4—832no—
491C2×C22⋊C4—832no—
492C2×C22⋊C4—832no—
493C2×C42—834no—
494C2×C42—834no—
495C2×C42—834no—
496C2×C42—832no—
497C2×C42—832no—
498C2×C42—831no—
499C2×C42—831no—
500C2×C42—831no—
501C2×C42—838no—
502C2×C42—832no—
503C2×C42—832no—
504C2×C42—832no—
505C2×C42—832no—
506C2×C42C22×D8312yes—
507C2×C42C22×D8314yes—
508C2×C42C22×D8312yes—
509C2×C42C22×D8311yescharacteristic
510#95—832no—
511#95—832no—
512#95—832no—
513#95—834no—
514#95—834no—
515#95—834no—
516#95—834no—
517#95—834no—
518#95—834no—
519#95—834no—
520#95C22×D8312yes—
521#95C22×D8314yes—
522C24—831no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—838no—
526C2×Q8—834no—
527C2×Q8—1664no—
528C2×Q8—1664no—
529C2×Q8—1662no—
530C2×Q8—1662no—
531C2×Q8C2×C4×D8314yes—
532C22×C4—3324no—
533C22×C4—3324no—
534C22×C4—831no—
535C22×C4—831no—
536C22×C4—834no—
537C22×C4—834no—
538C22×C4—834no—
539C22×C4—832no—
540C22×C4—832no—
541C22×C4—832no—
542C22×C4—831no—
543C22×C4—834no—
544C22×C4—834no—
545C22×C4—832no—
546C22×C4—834no—
547C22×C4—1662no—
548C22×C4—1662no—
549C22×C4—1668no—
550C22×C4—1662no—
551C22×C4—1662no—
552C22×C4C23×D8314yes—
553C22×C4C23×D8312yes—
554C22×C4C23×D8312yes—
555C22×C4C23×D8312yes—
556C22×C4C23×D8311yescharacteristic
557C22×C4C23×D8312yes—
558C22×C4C23×D8311yescharacteristic
559C22×C4C23×D8311yescharacteristic
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—42no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—3324no—
567C4⋊C4—3322no—
568C4⋊C4—3324no—
569C4⋊C4—3324no—
570C4⋊C4—838no—
571C4⋊C4—838no—
572C4⋊C4—838no—
573C4⋊C4—838no—
574C4⋊C4—838no—
575C4⋊C4—838no—
576C4⋊C4—834no—
577C4⋊C4—834no—
578C4⋊C4—1668no—
579C4⋊C4—1668no—
580C4⋊C4—1664no—
581C4⋊C4—1662no—
582C4⋊C4—1664no—
583C4⋊C4C2×C4×D8318yes—
584C4⋊C4C2×C4×D8314yes—
585C4⋊C4Q8×D8314yes—
586C22⋊C4—838no—
587C22⋊C4—838no—
588C22⋊C4—838no—
589C22⋊C4—1664no—
590C42—24no—
591C42—44no—
592C42—3324no—
593C42—3324no—
594C42—3324no—
595C42—834no—
596C42—834no—
597C42—834no—
598C42—838no—
599C42—838no—
600C42—1664no—
601C42—1664no—
602C42—1664no—
603C42—1664no—
604C42C2×C4×D8314yes—
605C42C2×C4×D8318yes—
606C23—832no—
607C23—832no—
608C23—832no—
609C23—1661no—
610C23—1661no—
611C23—1661no—
612C23—1661no—
613C23C24×D8311yescharacteristic
614Q8—28no—
615Q8—16616no—
616Q8—1668no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—832no—
632C2×C4—832no—
633C2×C4—832no—
634C2×C4—832no—
635C2×C4—832no—
636C2×C4—832no—
637C2×C4—8316no—
638C2×C4—832no—
639C2×C4—834no—
640C2×C4—834no—
641C2×C4—834no—
642C2×C4—6648no—
643C2×C4—1668no—
644C2×C4—1662no—
645C2×C4—1664no—
646C2×C4—1664no—
647C2×C4—1664no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1661no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1661no—
657C2×C4—1662no—
658C2×C4—1668no—
659C2×C4C22×C4×D8312yes—
660C2×C4C22×C4×D8314yes—
661C2×C4C22×C4×D8314yes—
662C2×C4C22×C4×D8312yes—
663C2×C4C22×C4×D8312yes—
664C2×C4C2×Q8×D8314yes—
665C2×C4C2×Q8×D8312yes—
666C2×C4#41×D8312yes—
667C2×C4#1458183712yes—
668C2×C4#1458184012yes—
669C22—834no—
670C22—1662no—
671C22—1662no—
672C22—1662no—
673C22—1662no—
674C22—1662no—
675C22—1662no—
676C22C23×C4×D8311yescharacteristic
677C22C22×Q8×D8311yescharacteristic
678C22C2×#41×D8311yescharacteristic
679C22H(5,𝔽2)×D8311yescharacteristic
680C22C2×#1458183711yescharacteristic
681C222−1+4×D8311yescharacteristic
682C22C2×#1458184011yescharacteristic
683C4—22no—
684C4—24no—
685C4—24no—
686C4—24no—
687C4—44no—
688C4—42no—
689C4—3322no—
690C4—3324no—
691C4—834no—
692C4—834no—
693C4—1664no—
694C4—1662no—
695C4—1664no—
696C4—1664no—
697C4C4×Q8×D8314yes—
698C4#1912818214yes—
699C2—1664no—
700C2C2×C4×Q8×D8311yescharacteristic
701C2#520×D8311yescharacteristic
702C2C2×#1912818211yescharacteristic
703C2#2492127411yescharacteristic
704C2#2492128111yescharacteristic
705C2#2492133311yescharacteristic
706C2#2492134611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingQ8×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC23×D83C24
hypercenterQ8×C4⋊C4D83
hypocenterC83#34214
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #24910422C2semidirect
6. #24910421C2semidirect
7. #24910420C2semidirect
8. C4⋊C4×Dic166C2semidirect
9. #24910375C2semidirect
10. #24910201C2semidirect
12. #24910034C2semidirect
13. C4×#14581790C2semidirect
17. Q8×C4⋊C4×C83C2semidirect
18. #19128255C4semidirect
90. #14581791C2×C4semidirect
91. #14581790C2×C4semidirect
92. #14581782C2×C4semidirect
97. C4×Dic166C2×C4semidirect
98. C4×Dic166C2×C4semidirect
101. #14581750Q8semidirect
152. C4×Q8×C83C2×C4semidirect
312. C4×D83C4×Q8semidirect
363. Q8×C4⋊C4D83semidirect
371. C83#34214semidirect
456. C4×Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282552
#249104672
#249104652
#249104642
#249104222
#249104212
#249104202
C4⋊C4×Dic1662
#249103752
#249102012
#249100842
#249100342
C4×#145817902
#384×D832
#249098172
C4×#145817502
Q8×C4⋊C4×C832
#3421483