Finite Group Databasebeta

← #35567275

Subgroups — #35567275

Order 21248.

2378 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581772C211yesmaximal, characteristic
2#24910627C214yesmaximal, complemented
3#24910492C212yesmaximal, complemented
4#24910489C212yesmaximal, complemented
5#24910342C212yesmaximal, complemented
6#24910340C211yesmaximal, characteristic, complemented
7#24910338C212yesmaximal, complemented
8C22⋊C4×Dic166C211yesmaximal, characteristic, complemented
9#24910295C211yesmaximal, characteristic, complemented
10#24910215C214yesmaximal, complemented
11#24910146C212yesmaximal, complemented
12#24910143C212yesmaximal, complemented
13#24910060C212yesmaximal
14#24910058C212yesmaximal
15#24909845C211yesmaximal, characteristic
16#24909844C211yesmaximal, characteristic
17C83×#2345C211yesmaximal, characteristic, complemented
18C23×Dic166C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581772C4116yescomplemented
21C2×#14581772C2212yes—
22C2×#14581772C2211yescharacteristic
23C2×#14581772C2211yescharacteristic
24C2×#14581772C2212yes—
25C2×#14581772C2211yescharacteristic
26C2×#14581772C2211yescharacteristic
27C2×C4×Dic166C2212yescomplemented
28C2×#14581757C2212yescomplemented
29C2×#14581750C2212yes—
30C2×#14581749C2212yes—
31C22×C4⋊Dic83C2212yes—
32C22×(C2×D83)⋊C4C2212yes—
33#19127607C2212yescomplemented
34#19127606C2212yescomplemented
35#19127605C2214yescomplemented
36#19127605C2214yescomplemented
37#19127600C2212yescomplemented
38#19127599C2214yescomplemented
39#19127597C2214yescomplemented
40#19127593C2214yes—
41#19127593C2214yes—
42#19127592C2214yes—
43#19127592C2214yes—
44#19127591C2214yes—
45#19127591C2214yes—
46#19127590C2214yes—
47#19127590C2214yes—
48#19127587C2214yescomplemented
49#19127586C2214yescomplemented
50#19127586C2214yescomplemented
51#19127584C2214yescomplemented
52#19127584C2214yescomplemented
53#19127563C2212yes—
54#19127563C2212yes—
55#19127561C2212yes—
56#19127561C2211yescharacteristic
57#19127560C2212yes—
58#19127559C2211yescharacteristic
59#19127559C2212yes—
60#19127559C2211yescharacteristic
61#19127559C2212yes—
62#19127558C2212yes—
63#19127556C2211yescharacteristic
64#19127556C2211yescharacteristic
65#19127556C2212yes—
66C4⋊C4×Dic83C2212yescomplemented
67C4⋊C4×Dic83C2214yescomplemented
68C4×C4⋊Dic83C2214yescomplemented
69C22⋊C4×Dic83C2212yes—
70C22⋊C4×Dic83C2212yes—
71C22⋊C4×Dic83C2212yes—
72C4×(C2×D83)⋊C4C2212yes—
73C4×C22⋊Dic83C2212yes—
74C4×C22⋊Dic83C2211yescharacteristic
75#19127548C2212yes—
76C22×C4⋊C4×C83C2211yescharacteristic
77#389×C83C2212yescomplemented
78#387×C83C2214yescomplemented
79#380×C83C2212yes—
80#380×C83C2211yescharacteristic
81C4×C4⋊C4×C83C2212yescomplemented
82C4×C22⋊C4×C83C2212yes—
83C4×C22⋊C4×C83C2211yescharacteristic
84C24×D83C2311yescharacteristic
85C22×Dic166—44no—
86C22×Dic166C2×C418yes—
87C22×Dic166C2311yescharacteristic
88C22×Dic166C2311yescharacteristic
89C22×Dic166C2312yes—
90C23×Dic83C2312yes—
91C23×Dic83C2311yescharacteristic
92C22×C4×D83—44no—
93C22×C4×D83C2×C418yes—
94C22×C4×D83C2311yescharacteristic
95C22×C4×D83C2311yescharacteristic
96C22×C4×D83C2311yescharacteristic
97C22×C4×D83C2311yescharacteristic
98#14581772C2×C418yes—
99#14581772C2×C418yes—
100#14581772C2×C418yes—
101#14581772C2×C418yes—
102#14581772C2×C4116yes—
103#14581772C2×C4116yes—
104C4×Dic166—44no—
105#14581757—44no—
106#14581750—44no—
107#14581749—44no—
108C2×C4⋊Dic83C2×C4116yes—
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2314yes—
111C2×C4⋊Dic83C2312yes—
112C2×C4⋊Dic83C2312yes—
113C2×C4⋊Dic83C2312yes—
114C2×C4⋊Dic83C2312yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2314yes—
118C2×Dic83⋊C4C2314yes—
119C2×C22⋊Dic83C2311yescharacteristic
120C2×C22⋊Dic83C2311yescharacteristic
121C2×C22⋊Dic83C2312yes—
122C2×(C2×D83)⋊C4C2×C4116yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2312yes—
129C2×(C2×D83)⋊C4C2312yes—
130C2×(C2×D83)⋊C4C2312yes—
131C2×(C2×D83)⋊C4C2312yes—
132C2×(C2×D83)⋊C4C2312yes—
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2314yes—
136C2×C4×Dic83C2314yes—
137C2×C4×Dic83C2314yes—
138C83⋊#95C2312yes—
139C83⋊#95C2314yes—
140C83⋊#95C2312yes—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2314yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C83⋊#95C2314yes—
147C83⋊#95C2314yes—
148C83⋊#95C2314yes—
149C23×C4×C83C2311yescharacteristic
150C23×C4×C83C2312yes—
151C2×C4⋊C4×C83C2×C418yes—
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2314yes—
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2311yescharacteristic
157C2×C22⋊C4×C83C2311yescharacteristic
158C2×C22⋊C4×C83C2311yescharacteristic
159C2×C22⋊C4×C83C2312yes—
160C2×C42×C83C2312yes—
161C2×C42×C83C2314yes—
162#95×C83C2312yes—
163#95×C83C2312yes—
164#95×C83C2314yes—
165#95×C83C2314yes—
166C23×D83—22no—
167C23×D83—22no—
168C23×D83—42no—
169C23×D83—42no—
170C23×D83C22×C414yes—
171C23×D83C2411yescharacteristic
172C23×D83C2411yescharacteristic
173C2×Dic166—24no—
174C2×Dic166—24no—
175C2×Dic166—416no—
176C2×Dic166—44no—
177C2×Dic166C22×C414yes—
178C2×Dic166C22×C414yes—
179C2×Dic166C22×C418yes—
180C22×Dic83—42no—
181C22×Dic83—44no—
182C22×Dic83C22×C414yes—
183C22×Dic83C22×C418yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2414yes—
187C22×Dic83C2411yescharacteristic
188C22×Dic83C2411yescharacteristic
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C2×C4×D83—24no—
192C2×C4×D83—24no—
193C2×C4×D83—416no—
194C2×C4×D83—42no—
195C2×C4×D83—42no—
196C2×C4×D83C22×C414yes—
197C2×C4×D83C22×C414yes—
198C2×C4×D83C22×C414yes—
199C2×C4×D83C22×C414yes—
200C4⋊Dic83—24no—
201C4⋊Dic83—44no—
202C4⋊Dic83C22×C418yes—
203C4⋊Dic83C22×C418yes—
204C4⋊Dic83C22×C418yes—
205C4⋊Dic83C22×C418yes—
206Dic83⋊C4—42no—
207Dic83⋊C4—42no—
208Dic83⋊C4—44no—
209Dic83⋊C4—44no—
210C22⋊Dic83—22no—
211C22⋊Dic83—22no—
212C22⋊Dic83—24no—
213(C2×D83)⋊C4—42no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4—42no—
216(C2×D83)⋊C4—42no—
217(C2×D83)⋊C4—42no—
218(C2×D83)⋊C4—44no—
219(C2×D83)⋊C4C22×C418yes—
220(C2×D83)⋊C4C22×C418yes—
221(C2×D83)⋊C4C22×C418yes—
222(C2×D83)⋊C4C22×C418yes—
223C4×Dic83—24no—
224C4×Dic83—44no—
225C4×Dic83—44no—
226C4×Dic83—44no—
227C4×Dic83—44no—
228C24×C83C2411yescharacteristic
229C22×C4×C83—24no—
230C22×C4×C83—44no—
231C22×C4×C83C22×C414yes—
232C22×C4×C83C22×C418yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2414yes—
236C22×C4×C83C2411yescharacteristic
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2411yescharacteristic
240C4⋊C4×C83—24no—
241C4⋊C4×C83—44no—
242C4⋊C4×C83C22×C418yes—
243C4⋊C4×C83C22×C414yes—
244C4⋊C4×C83C22×C414yes—
245C22⋊C4×C83—22no—
246C22⋊C4×C83—24no—
247C22⋊C4×C83—22no—
248C42×C83—24no—
249C42×C83—44no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83C23×C412yes—
253C23×C832−1+412yes—
254C23×C832−1+412yes—
255C23×C83C2511yescharacteristic
256C22×D83—28no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—21no—
260C22×D83—21no—
261C22×D83—21no—
262C22×D83—21no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—44no—
266C22×D83—44no—
267C22×D83—48no—
268C22×D83—48no—
269C22×D83C23×C412yes—
270C22×D83C23×C412yes—
271C2×C4×C83—22no—
272C2×C4×C83—24no—
273C2×C4×C83—24no—
274C2×C4×C83—28no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—24no—
278C2×C4×C83—22no—
279C2×C4×C83—24no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83—22no—
284C2×C4×C83—48no—
285C2×C4×C83C23×C414yes—
286C2×C4×C83C23×C414yes—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C23×C412yes—
289C2×C4×C83H(5,𝔽2)14yes—
290C2×Dic83—22no—
291C2×Dic83—24no—
292C2×Dic83—24no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—24no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—24no—
300C2×Dic83—22no—
301C2×Dic83—24no—
302C2×Dic83—22no—
303C2×Dic83—44no—
304C2×Dic83—48no—
305C2×Dic83C23×C414yes—
306C2×Dic83C23×C414yes—
307C2×Dic83C23×C412yes—
308C2×Dic83C23×C412yes—
309C4×D83—28no—
310C4×D83—28no—
311C4×D83—44no—
312C4×D83—44no—
313Dic166—28no—
314Dic166—28no—
315Dic166—48no—
316C22×C83—22no—
317C22×C83—22no—
318C22×C83—24no—
319C22×C83—24no—
320C22×C83#51914yes—
321C22×C83C24×C411yescharacteristic
322C22×C83C2×H(5,𝔽2)12yes—
323C22×C83C2×2−1+411yescharacteristic
324C22×C83C2×2−1+411yescharacteristic
325C22×C83#58512yes—
326C2×D83—22no—
327C2×D83—22no—
328C2×D83—22no—
329C2×D83—22no—
330C2×D83—22no—
331C2×D83—22no—
332C2×D83—416no—
333C2×D83—42no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C4×C83—22no—
338C4×C83—24no—
339C4×C83—24no—
340C4×C83—42no—
341C4×C83—44no—
342C4×C83—42no—
343C4×C83#51814yes—
344Dic83—24no—
345Dic83—24no—
346Dic83—22no—
347Dic83—22no—
348Dic83—42no—
349Dic83—42no—
350Dic83—44no—
351#34370—831nomaximal, Sylow
352C2×C83—24no—
353C2×C83C2×#51811yescharacteristic
354C2×C83C2×#51911yescharacteristic
355C2×C83#342811yescharacteristic
356C2×C83#354112yes—
357C2×C83#354112yes—
358D83—42no—
359D83—42no—
360C22×C22⋊Q8—831no—
361#2378—834no—
362#2362—832no—
363#2362—832no—
364#2345—832no—
365#2345—832no—
366#2345—831no—
367#2345D8311yescharacteristic, complemented
368Q8×C22⋊C4—831no—
369Q8×C22⋊C4—831no—
370#2332—834no—
371#2323—832no—
372#2323—832no—
373#2312—832no—
374#2312—832no—
375#2280—831no—
376#2280—831no—
377C83#3437011yescharacteristic, complemented, Sylow
378C23×Q8—831no—
379C24×C4—831no—
380C2×C22⋊Q8—8316no—
381C2×C22⋊Q8—831no—
382C2×C22⋊Q8—831no—
383C2×C22⋊Q8—832no—
384C2×C22⋊Q8—831no—
385C2×C22⋊Q8—831no—
386C2×C22⋊Q8—832no—
387C2×C4×Q8—832no—
388C2×C4×Q8—832no—
389C2×#117—832no—
390C2×#117—832no—
391C22×C4⋊C4—832no—
392C22×C4⋊C4C2×D8311yescharacteristic
393C22×C22⋊C4—832no—
394#391—832no—
395#391—832no—
396#391—834no—
397#391—834no—
398#389—834no—
399#389—832no—
400#389—834no—
401#389C2×D8312yescomplemented
402#388—834no—
403#388—834no—
404#388—834no—
405#388—834no—
406#388—834no—
407#388—834no—
408#388—834no—
409#388—834no—
410#387—834no—
411#387—834no—
412#387—834no—
413#387—834no—
414#387—834no—
415#387C2×D8314yescomplemented
416#381—832no—
417#381—832no—
418#380—832no—
419#380—831no—
420#380—832no—
421#380—832no—
422#380—832no—
423#380—831no—
424#380—831no—
425#380—832no—
426#380C2×D8312yes—
427#380C2×D8311yescharacteristic
428#379—831no—
429#379—832no—
430#379—831no—
431C4×C4⋊C4—832no—
432C4×C4⋊C4—834no—
433C4×C4⋊C4—834no—
434C4×C4⋊C4C2×D8312yescomplemented
435C4×C22⋊C4—832no—
436C4×C22⋊C4—831no—
437C4×C22⋊C4—832no—
438C4×C22⋊C4—832no—
439C4×C22⋊C4—832no—
440C4×C22⋊C4—832no—
441C4×C22⋊C4—832no—
442C4×C22⋊C4C2×D8312yes—
443C4×C22⋊C4C2×D8311yescharacteristic
444C25—831no—
445C22×Q8—3324no—
446C22×Q8—838no—
447C22×Q8—832no—
448C22×Q8—831no—
449C22×Q8—831no—
450C23×C4—3324no—
451C23×C4—832no—
452C23×C4—831no—
453C23×C4—838no—
454C23×C4—831no—
455C23×C4—831no—
456C23×C4—831no—
457C23×C4—831no—
458C23×C4C22×D8311yescharacteristic
459C23×C4C22×D8312yes—
460C22⋊Q8—8316no—
461C22⋊Q8—8316no—
462C22⋊Q8—838no—
463C22⋊Q8—838no—
464C22⋊Q8—838no—
465C22⋊Q8—838no—
466C4×Q8—3324no—
467C4×Q8—3324no—
468#117—3324no—
469#117—3324no—
470C2×C4⋊C4—832no—
471C2×C4⋊C4—832no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—8316no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—832no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4C4×D8318yes—
482C2×C4⋊C4C22×D8312yes—
483C2×C4⋊C4C22×D8314yes—
484C2×C4⋊C4C22×D8311yescharacteristic
485C2×C4⋊C4C22×D8311yescharacteristic
486C2×C4⋊C4C22×D8312yes—
487C2×C22⋊C4—834no—
488C2×C22⋊C4—832no—
489C2×C22⋊C4—832no—
490C2×C22⋊C4—832no—
491C2×C22⋊C4—834no—
492C2×C22⋊C4—832no—
493C2×C22⋊C4—8316no—
494C2×C22⋊C4—832no—
495C2×C22⋊C4—832no—
496C2×C22⋊C4—832no—
497C2×C22⋊C4—832no—
498C2×C22⋊C4—831no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—831no—
501C2×C22⋊C4C22×D8311yescharacteristic
502C2×C22⋊C4C22×D8312yes—
503C2×C22⋊C4C22×D8311yescharacteristic
504C2×C42—834no—
505C2×C42—834no—
506C2×C42—834no—
507C2×C42—834no—
508C2×C42—832no—
509C2×C42C22×D8312yes—
510C2×C42C22×D8314yes—
511#95—832no—
512#95—832no—
513#95—834no—
514#95—832no—
515#95—832no—
516#95—834no—
517#95—834no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95C22×D8312yes—
523#95C22×D8312yes—
524#95C22×D8314yes—
525#95C22×D8314yes—
526C24—3322no—
527C24—3322no—
528C24—834no—
529C24—831no—
530C24—831no—
531C24—1662no—
532C24—1662no—
533C24C23×D8311yescharacteristic
534C2×Q8—33216no—
535C2×Q8—3324no—
536C2×Q8—838no—
537C2×Q8—834no—
538C2×Q8—834no—
539C2×Q8—1664no—
540C2×Q8—1664no—
541C22×C4—24no—
542C22×C4—44no—
543C22×C4—3322no—
544C22×C4—3322no—
545C22×C4—33216no—
546C22×C4—3322no—
547C22×C4—3324no—
548C22×C4—838no—
549C22×C4—834no—
550C22×C4—834no—
551C22×C4—834no—
552C22×C4—831no—
553C22×C4—832no—
554C22×C4—832no—
555C22×C4—831no—
556C22×C4—834no—
557C22×C4—834no—
558C22×C4—832no—
559C22×C4—834no—
560C22×C4—832no—
561C22×C4—1664no—
562C22×C4—1664no—
563C22×C4C2×C4×D8314yes—
564C22×C4C2×C4×D8318yes—
565C22×C4C23×D8312yes—
566C22×C4C23×D8314yes—
567C22×C4C23×D8312yes—
568C22×C4C23×D8311yescharacteristic
569C22×C4C23×D8312yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8311yescharacteristic
572C4⋊C4—24no—
573C4⋊C4—44no—
574C4⋊C4—3322no—
575C4⋊C4—3322no—
576C4⋊C4—3324no—
577C4⋊C4—3324no—
578C4⋊C4—3324no—
579C4⋊C4—838no—
580C4⋊C4—838no—
581C4⋊C4—838no—
582C4⋊C4—838no—
583C4⋊C4—1664no—
584C4⋊C4C2×C4×D8318yes—
585C4⋊C4C2×C4×D8314yes—
586C4⋊C4C2×C4×D8314yes—
587C22⋊C4—22no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—3322no—
591C22⋊C4—3322no—
592C22⋊C4—3324no—
593C22⋊C4—3322no—
594C22⋊C4—3324no—
595C22⋊C4—3322no—
596C22⋊C4—838no—
597C22⋊C4—838no—
598C22⋊C4—838no—
599C22⋊C4—838no—
600C22⋊C4—1662no—
601C22⋊C4—1664no—
602C22⋊C4—1662no—
603C42—24no—
604C42—44no—
605C42—3324no—
606C42—3324no—
607C42—3324no—
608C42—3324no—
609C42—1664no—
610C23—22no—
611C23—22no—
612C23—3328no—
613C23—3328no—
614C23—3324no—
615C23—3324no—
616C23—832no—
617C23—832no—
618C23—1668no—
619C23—1662no—
620C23—1662no—
621C23—1661no—
622C23—1661no—
623C23—1661no—
624C23—1661no—
625C23—1662no—
626C23—1662no—
627C23C22×C4×D8312yes—
628C23#1458183912yes—
629C23#1458184012yes—
630C23C24×D8311yescharacteristic
631Q8—3328no—
632Q8—1668no—
633Q8—1668no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—48no—
648C2×C4—3324no—
649C2×C4—3324no—
650C2×C4—3324no—
651C2×C4—3328no—
652C2×C4—834no—
653C2×C4—834no—
654C2×C4—832no—
655C2×C4—832no—
656C2×C4—1662no—
657C2×C4—1664no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1664no—
662C2×C4—1662no—
663C2×C4—1664no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1664no—
667C2×C4—1664no—
668C2×C4—1662no—
669C2×C4—1668no—
670C2×C4—1668no—
671C2×C4C22×C4×D8314yes—
672C2×C4C22×C4×D8314yes—
673C2×C4C22×C4×D8312yes—
674C2×C4C22×C4×D8312yes—
675C2×C4#1458183814yes—
676C22—22no—
677C22—22no—
678C22—24no—
679C22—24no—
680C22—33216no—
681C22—3322no—
682C22—3322no—
683C22—3322no—
684C22—3322no—
685C22—1662no—
686C22—1662no—
687C22—1662no—
688C22—1662no—
689C22—1662no—
690C22—1662no—
691C22#1912817714yes—
692C22C23×C4×D8311yescharacteristic
693C22C2×#1458183812yes—
694C22C2×#1458183911yescharacteristic
695C22C2×#1458184011yescharacteristic
696C22#1912853612yes—
697C4—22no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—44no—
702C4—42no—
703C4—3322no—
704C4—3322no—
705C4—3324no—
706C4—1662no—
707C4—1662no—
708C4—1664no—
709C4—1664no—
710C4#1912817514yes—
711C2—24no—
712C2—3322no—
713C2—3322no—
714C2C2×#1912817511yescharacteristic
715C2C2×#1912817711yescharacteristic
716C2#2492066111yescharacteristic
717C2#2492175012yes—
718C2#2492175712yes—
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2345C2
socle, cosocleC23×C83C25
prime radicalC24×D83C23
hypercenter#2345D83
hypocenterC83#34370
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #24910627C2semidirect
3. #24910492C2semidirect
4. #24910489C2semidirect
5. #24910342C2semidirect
6. #24910340C2semidirect
7. #24910338C2semidirect
8. C22⋊C4×Dic166C2semidirect
9. #24910295C2semidirect
10. #24910215C2semidirect
11. #24910146C2semidirect
12. #24910143C2semidirect
17. C83×#2345C2semidirect
20. C2×#14581772C4semidirect
27. C2×C4×Dic166C22semidirect
28. C2×#14581757C22semidirect
33. #19127607C22semidirect
34. #19127606C22semidirect
35. #19127605C22semidirect
36. #19127605C22semidirect
37. #19127600C22semidirect
38. #19127599C22semidirect
39. #19127597C22semidirect
48. #19127587C22semidirect
49. #19127586C22semidirect
50. #19127586C22semidirect
51. #19127584C22semidirect
52. #19127584C22semidirect
66. C4⋊C4×Dic83C22semidirect
67. C4⋊C4×Dic83C22semidirect
68. C4×C4⋊Dic83C22semidirect
77. #389×C83C22semidirect
78. #387×C83C22semidirect
81. C4×C4⋊C4×C83C22semidirect
367. #2345D83semidirect
377. C83#34370semidirect
401. #389C2×D83semidirect
415. #387C2×D83semidirect
434. C4×C4⋊C4C2×D83semidirect

Maximal subgroups

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

subgroupindex
C22×#145817722
#249106272
#249104922
#249104892
#249103422
#249103402
#249103382
C22⋊C4×Dic1662
#249102952
#249102152
#249101462
#249101432
#249100602
#249100582
#249098452
#249098442
C83×#23452
#3437083