Finite Group Databasebeta

← #35564458

Subgroups — #35564458

Order 21248.

2806 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D83C211yesmaximal, characteristic
2#24910339C212yesmaximal, complemented
3#24910337C214yesmaximal, complemented
4#24910336C212yesmaximal, complemented
5#24910334C211yesmaximal, characteristic, complemented
6#24910333C212yesmaximal, complemented
7#24910332C211yesmaximal, characteristic, complemented
8#24910330C211yesmaximal, characteristic, complemented
9#24910327C212yesmaximal, complemented
10#24910078C212yesmaximal, complemented
11#24910062C214yesmaximal, complemented
12#24909845C211yesmaximal, characteristic
13#24909844C211yesmaximal, characteristic
14#24909843C212yesmaximal
15#24909842C212yesmaximal
16#24909817C212yesmaximal, complemented
17C83×#2344C211yesmaximal, characteristic, complemented
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2212yes—
20C2×#14581751C2212yes—
21C2×#14581750C2212yes—
22C2×#14581749C2212yes—
23C2×#14581748C2212yes—
24C2×#14581748C2212yes—
25C22×C4⋊Dic83C2211yescharacteristic
26C22×Dic83⋊C4C2212yes—
27C2×C4⋊C4×D83C4116yescomplemented
28C2×C4⋊C4×D83C2211yescharacteristic
29C2×C4⋊C4×D83C2212yes—
30C2×C4⋊C4×D83C2211yescharacteristic
31C2×C4⋊C4×D83C2212yes—
32C2×C4⋊C4×D83C2211yescharacteristic
33C2×C4⋊C4×D83C2211yescharacteristic
34#19127600C2212yescomplemented
35#19127599C2212yescomplemented
36#19127598C2214yescomplemented
37#19127597C2212yescomplemented
38#19127596C2214yescomplemented
39#19127588C2214yescomplemented
40#19127587C2214yescomplemented
41#19127586C2214yescomplemented
42#19127585C2214yescomplemented
43#19127584C2214yescomplemented
44#19127583C2214yescomplemented
45#19127582C2214yescomplemented
46#19127564C2212yes—
47#19127563C2212yes—
48#19127563C2212yes—
49#19127562C2212yes—
50#19127562C2212yes—
51#19127561C2211yescharacteristic
52#19127560C2214yes—
53#19127560C2212yes—
54#19127560C2214yes—
55#19127559C2211yescharacteristic
56#19127559C2211yescharacteristic
57#19127558C2212yes—
58#19127558C2214yes—
59#19127558C2214yes—
60#19127556C2211yescharacteristic
61#19127556C2212yes—
62#19127556C2211yescharacteristic
63C4⋊C4×Dic83C2212yescomplemented
64C4⋊C4×Dic83C2212yescomplemented
65C4×Dic83⋊C4C2214yescomplemented
66C4×C4⋊Dic83C2212yescomplemented
67#19127552C2214yescomplemented
68C22⋊C4×Dic83C2212yes—
69C4×(C2×D83)⋊C4C2214yes—
70C4×(C2×D83)⋊C4C2212yes—
71C4×(C2×D83)⋊C4C2214yes—
72C4×C22⋊Dic83C2211yescharacteristic
73#19127548C2212yes—
74#19127548C2214yes—
75#19127548C2214yes—
76C2×#117×C83C2212yes—
77C22×C4⋊C4×C83C2211yescharacteristic
78#389×C83C2212yescomplemented
79#387×C83C2214yescomplemented
80#381×C83C2212yes—
81#380×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2212yescomplemented
83C4×C22⋊C4×C83C2211yescharacteristic
84C24×D83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2312yes—
87C22×C4×D83—28no—
88C22×C4×D83—44no—
89C22×C4×D83—44no—
90C22×C4×D83C2×C418yes—
91C22×C4×D83C2×C4116yes—
92C22×C4×D83C2311yescharacteristic
93C22×C4×D83C2311yescharacteristic
94C22×C4×D83C2311yescharacteristic
95C22×C4×D83C2312yes—
96C22×C4×D83C2312yes—
97C22×C4×D83C2312yes—
98C22×C4×D83C2312yes—
99C22×C4×D83C2311yescharacteristic
100#14581751—44no—
101#14581750—28no—
102#14581749—28no—
103#14581748—44no—
104#14581748—44no—
105C2×C4⋊Dic83C2×C418yes—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2314yes—
108C2×C4⋊Dic83C2311yescharacteristic
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4C2×C4116yes—
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2312yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C2×Dic83⋊C4C2312yes—
119C2×Dic83⋊C4C2312yes—
120C4⋊C4×D83C2×C418yes—
121C4⋊C4×D83C2×C4116yes—
122C4⋊C4×D83C2×C418yes—
123C4⋊C4×D83C2×C4116yes—
124C4⋊C4×D83C2×C418yes—
125C4⋊C4×D83C2×C418yes—
126C2×C22⋊Dic83C2311yescharacteristic
127C2×C22⋊Dic83C2311yescharacteristic
128C2×C22⋊Dic83C2312yes—
129C2×(C2×D83)⋊C4C2314yes—
130C2×(C2×D83)⋊C4C2312yes—
131C2×(C2×D83)⋊C4C2312yes—
132C2×(C2×D83)⋊C4C2314yes—
133C2×(C2×D83)⋊C4C2312yes—
134C2×(C2×D83)⋊C4C2312yes—
135C2×C4×Dic83C2314yes—
136C2×C4×Dic83C2312yes—
137C2×C4×Dic83C2314yes—
138C2×C4×Dic83C2314yes—
139C2×C4×Dic83C2314yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2312yes—
147C83⋊#95C2312yes—
148C83⋊#95C2312yes—
149C83⋊#95C2314yes—
150C83⋊#95C2312yes—
151C23×C4×C83C2311yescharacteristic
152C23×C4×C83C2312yes—
153#117×C83—44no—
154C2×C4⋊C4×C83C2×C418yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2311yescharacteristic
158C2×C4⋊C4×C83C2312yes—
159C2×C4⋊C4×C83C2311yescharacteristic
160C2×C22⋊C4×C83C2311yescharacteristic
161C2×C22⋊C4×C83C2311yescharacteristic
162C2×C22⋊C4×C83C2312yes—
163C2×C42×C83C2312yes—
164C2×C42×C83C2314yes—
165#95×C83C2314yes—
166#95×C83C2312yes—
167#95×C83C2314yes—
168#95×C83C2312yes—
169C23×D83—22no—
170C23×D83—22no—
171C23×D83—24no—
172C23×D83—24no—
173C23×D83C22×C414yes—
174C23×D83C2411yescharacteristic
175C23×D83C2411yescharacteristic
176C22×Dic83—24no—
177C22×Dic83—24no—
178C22×Dic83—24no—
179C22×Dic83C22×C414yes—
180C22×Dic83C22×C418yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2414yes—
184C22×Dic83C2411yescharacteristic
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2411yescharacteristic
188C2×C4×D83—24no—
189C2×C4×D83—24no—
190C2×C4×D83—24no—
191C2×C4×D83—232no—
192C2×C4×D83—432no—
193C2×C4×D83—42no—
194C2×C4×D83—42no—
195C2×C4×D83—42no—
196C2×C4×D83—42no—
197C2×C4×D83—42no—
198C2×C4×D83—42no—
199C2×C4×D83—42no—
200C2×C4×D83—42no—
201C2×C4×D83C22×C414yes—
202C2×C4×D83C22×C414yes—
203C2×C4×D83C22×C414yes—
204C2×C4×D83C22×C418yes—
205C2×C4×D83C22×C418yes—
206C2×C4×D83C22×C418yes—
207C2×C4×D83C22×C418yes—
208C2×C4×D83C22×C414yes—
209C2×C4×D83#4118yes—
210C4⋊Dic83—24no—
211C4⋊Dic83—44no—
212C4⋊Dic83C22×C418yes—
213C4⋊Dic83C22×C414yes—
214C4⋊Dic83C22×C414yes—
215Dic83⋊C4—24no—
216Dic83⋊C4—24no—
217Dic83⋊C4—44no—
218Dic83⋊C4—44no—
219Dic83⋊C4C22×C418yes—
220Dic83⋊C4C22×C418yes—
221Dic83⋊C4C22×C418yes—
222Dic83⋊C4C22×C418yes—
223C22⋊Dic83—22no—
224C22⋊Dic83—24no—
225C22⋊Dic83—22no—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—28no—
229(C2×D83)⋊C4—28no—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4—24no—
232C4×Dic83—24no—
233C4×Dic83—28no—
234C4×Dic83—44no—
235C4×Dic83—44no—
236C4×Dic83—44no—
237C24×C83C2411yescharacteristic
238C22×C4×C83—24no—
239C22×C4×C83—24no—
240C22×C4×C83—24no—
241C22×C4×C83C22×C418yes—
242C22×C4×C83C22×C414yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2414yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2411yescharacteristic
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2411yescharacteristic
250C4⋊C4×C83—24no—
251C4⋊C4×C83—44no—
252C4⋊C4×C83C22×C418yes—
253C4⋊C4×C83C22×C414yes—
254C4⋊C4×C83C22×C414yes—
255C22⋊C4×C83—22no—
256C22⋊C4×C83—24no—
257C22⋊C4×C83—22no—
258C42×C83—24no—
259C42×C83—44no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83C23×C412yes—
263C23×C83H(5,𝔽2)12yes—
264C23×C83H(5,𝔽2)12yes—
265C23×C83C2511yescharacteristic
266C22×D83—216no—
267C22×D83—216no—
268C22×D83—28no—
269C22×D83—22no—
270C22×D83—21no—
271C22×D83—21no—
272C22×D83—21no—
273C22×D83—21no—
274C22×D83—22no—
275C22×D83—28no—
276C22×D83—28no—
277C22×D83C23×C412yes—
278C22×D83C23×C412yes—
279C22×D83C2×#4114yes—
280C22×D832−1+414yes—
281C2×C4×C83—216no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—28no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—24no—
291C2×C4×C83—22no—
292C2×C4×C83—24no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—24no—
296C2×C4×C83—22no—
297C2×C4×C83C23×C414yes—
298C2×C4×C83C23×C414yes—
299C2×C4×C83C23×C412yes—
300C2×C4×C83C23×C412yes—
301C2×C4×C83C2×#4114yes—
302C2×Dic83—216no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—28no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—24no—
312C2×Dic83—22no—
313C2×Dic83—24no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—24no—
318C2×Dic83C23×C412yes—
319C2×Dic83C23×C414yes—
320C2×Dic83C23×C414yes—
321C2×Dic83C23×C412yes—
322C2×Dic83C2×#4114yes—
323C4×D83—28no—
324C4×D83—28no—
325C4×D83—28no—
326C4×D83—48no—
327C4×D83—48no—
328C4×D83—48no—
329C4×D83—48no—
330C4×D83#117116yescomplemented
331C22×C83—22no—
332C22×C83—22no—
333C22×C83—24no—
334C22×C83—24no—
335C22×C83#51814yes—
336C22×C83C24×C411yescharacteristic
337C22×C83C22×#4112yes—
338C22×C83C2×H(5,𝔽2)11yescharacteristic
339C22×C83C2×H(5,𝔽2)11yescharacteristic
340C22×C83C2×2−1+412yes—
341C2×D83—232no—
342C2×D83—22no—
343C2×D83—22no—
344C2×D83—22no—
345C2×D83—22no—
346C2×D83—24no—
347C2×D83—24no—
348C2×D83—24no—
349C2×D83—24no—
350C2×D83C2×#11714yes—
351C2×D83#51914yes—
352C4×C83—22no—
353C4×C83—24no—
354C4×C83—24no—
355C4×C83—42no—
356C4×C83—42no—
357C4×C83—44no—
358C4×C83C2×#11714yes—
359Dic83—22no—
360Dic83—24no—
361Dic83—24no—
362Dic83—42no—
363Dic83—44no—
364Dic83—42no—
365Dic83C2×#11714yes—
366#34178—831nomaximal, Sylow
367C2×C83—24no—
368C2×C83C22×#11711yescharacteristic
369C2×C83C2×#51811yescharacteristic
370C2×C83C2×#51911yescharacteristic
371C2×C83#349212yes—
372C2×C83#349212yes—
373D83—24no—
374D83—24no—
375C23×C4⋊C4—831no—
376#2345—832no—
377#2345—834no—
378#2345—832no—
379#2344—832no—
380#2344—831no—
381#2344—831no—
382#2344—832no—
383#2344—831no—
384#2344D8311yescharacteristic, complemented
385#2316—832no—
386#2313—834no—
387#2280—832no—
388#2280—831no—
389#2280—831no—
390#2280—832no—
391#2274—832no—
392C83#3417811yescharacteristic, complemented, Sylow
393C24×C4—832no—
394C24×C4—831no—
395C2×#117—832no—
396C2×#117—832no—
397C2×#117—832no—
398C2×#117—832no—
399C2×#117—832no—
400C2×#117C2×D8312yes—
401C22×C4⋊C4—832no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—8316no—
404C22×C4⋊C4—832no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4—832no—
407C22×C4⋊C4—831no—
408C22×C4⋊C4—831no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4C2×D8311yescharacteristic
411#389—834no—
412#389—832no—
413#389—832no—
414#389—832no—
415#389—834no—
416#389C2×D8312yescomplemented
417#387—834no—
418#387—834no—
419#387—834no—
420#387—834no—
421#387—834no—
422#387—834no—
423#387—834no—
424#387C2×D8314yescomplemented
425#381—832no—
426#381—832no—
427#381—832no—
428#381—832no—
429#381—832no—
430#381C2×D8312yes—
431#380—831no—
432#380—834no—
433#380—834no—
434#380—832no—
435#380—831no—
436#380—831no—
437#380—834no—
438#380—834no—
439#380—832no—
440#380C2×D8311yescharacteristic
441#379—831no—
442#379—832no—
443#379—831no—
444C4×C4⋊C4—832no—
445C4×C4⋊C4—832no—
446C4×C4⋊C4—832no—
447C4×C4⋊C4—834no—
448C4×C4⋊C4—834no—
449C4×C4⋊C4C2×D8312yescomplemented
450C4×C22⋊C4—831no—
451C4×C22⋊C4—832no—
452C4×C22⋊C4—834no—
453C4×C22⋊C4—832no—
454C4×C22⋊C4—834no—
455C4×C22⋊C4—834no—
456C4×C22⋊C4—832no—
457C4×C22⋊C4—834no—
458C4×C22⋊C4C2×D8311yescharacteristic
459C25—831no—
460C23×C4—3324no—
461C23×C4—3324no—
462C23×C4—8316no—
463C23×C4—832no—
464C23×C4—832no—
465C23×C4—832no—
466C23×C4—832no—
467C23×C4—831no—
468C23×C4—832no—
469C23×C4—831no—
470C23×C4—838no—
471C23×C4—831no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—1668no—
475C23×C4C22×D8312yes—
476C23×C4C22×D8311yescharacteristic
477#117—44no—
478#117—3324no—
479#117—3324no—
480#117—3324no—
481#117—1668no—
482#117—1668no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—834no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—8316no—
487C2×C4⋊C4—838no—
488C2×C4⋊C4—832no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—832no—
491C2×C4⋊C4—832no—
492C2×C4⋊C4—832no—
493C2×C4⋊C4—832no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—838no—
496C2×C4⋊C4—838no—
497C2×C4⋊C4—8316no—
498C2×C4⋊C4—8316no—
499C2×C4⋊C4—838no—
500C2×C4⋊C4—838no—
501C2×C4⋊C4—832no—
502C2×C4⋊C4—832no—
503C2×C4⋊C4—832no—
504C2×C4⋊C4C4×D8318yes—
505C2×C4⋊C4C22×D8312yes—
506C2×C4⋊C4C22×D8314yes—
507C2×C4⋊C4C22×D8311yescharacteristic
508C2×C4⋊C4C22×D8312yes—
509C2×C4⋊C4C22×D8311yescharacteristic
510C2×C22⋊C4—831no—
511C2×C22⋊C4—831no—
512C2×C22⋊C4—832no—
513C2×C22⋊C4—832no—
514C2×C22⋊C4—834no—
515C2×C22⋊C4—832no—
516C2×C22⋊C4—832no—
517C2×C22⋊C4—834no—
518C2×C22⋊C4—832no—
519C2×C22⋊C4C22×D8311yescharacteristic
520C2×C22⋊C4C22×D8312yes—
521C2×C22⋊C4C22×D8311yescharacteristic
522C2×C42—834no—
523C2×C42—834no—
524C2×C42—834no—
525C2×C42—834no—
526C2×C42—832no—
527C2×C42C22×D8312yes—
528C2×C42C22×D8314yes—
529#95—834no—
530#95—834no—
531#95—834no—
532#95—832no—
533#95—834no—
534#95—832no—
535#95—832no—
536#95—832no—
537#95—834no—
538#95—834no—
539#95—834no—
540#95C22×D8314yes—
541#95C22×D8314yes—
542#95C22×D8312yes—
543#95C22×D8312yes—
544C24—831no—
545C24—831no—
546C24—834no—
547C24—1664no—
548C24—1664no—
549C24—1662no—
550C24—1662no—
551C24C23×D8311yescharacteristic
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—33232no—
556C22×C4—3322no—
557C22×C4—3322no—
558C22×C4—3322no—
559C22×C4—3322no—
560C22×C4—3322no—
561C22×C4—3322no—
562C22×C4—3322no—
563C22×C4—3322no—
564C22×C4—838no—
565C22×C4—838no—
566C22×C4—838no—
567C22×C4—838no—
568C22×C4—831no—
569C22×C4—834no—
570C22×C4—838no—
571C22×C4—834no—
572C22×C4—838no—
573C22×C4—831no—
574C22×C4—832no—
575C22×C4—832no—
576C22×C4—834no—
577C22×C4—834no—
578C22×C4—834no—
579C22×C4—832no—
580C22×C4—834no—
581C22×C4—832no—
582C22×C4—1664no—
583C22×C4—16632no—
584C22×C4—1664no—
585C22×C4—1664no—
586C22×C4—1664no—
587C22×C4—1664no—
588C22×C4—1664no—
589C22×C4C2×C4×D8318yes—
590C22×C4C2×C4×D8314yes—
591C22×C4C23×D8312yes—
592C22×C4C23×D8314yes—
593C22×C4C23×D8312yes—
594C22×C4C23×D8311yescharacteristic
595C22×C4C23×D8312yes—
596C22×C4C23×D8312yes—
597C22×C4C23×D8311yescharacteristic
598C4⋊C4—24no—
599C4⋊C4—44no—
600C4⋊C4—3324no—
601C4⋊C4—3324no—
602C4⋊C4—3324no—
603C4⋊C4—838no—
604C4⋊C4—838no—
605C4⋊C4—838no—
606C4⋊C4—838no—
607C4⋊C4—838no—
608C4⋊C4—834no—
609C4⋊C4—834no—
610C4⋊C4—1664no—
611C4⋊C4—1664no—
612C4⋊C4—1664no—
613C4⋊C4C2×C4×D8318yes—
614C4⋊C4C2×C4×D8314yes—
615C4⋊C4C2×C4×D8314yes—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—1664no—
620C22⋊C4—1664no—
621C22⋊C4—1668no—
622C22⋊C4—1664no—
623C22⋊C4—1664no—
624C22⋊C4—1668no—
625C22⋊C4—1662no—
626C22⋊C4—1664no—
627C22⋊C4—1662no—
628C42—24no—
629C42—44no—
630C42—3324no—
631C42—3324no—
632C42—3324no—
633C42—1668no—
634C42—1664no—
635C23—22no—
636C23—22no—
637C23—832no—
638C23—832no—
639C23—834no—
640C23—834no—
641C23—1668no—
642C23—1668no—
643C23—16616no—
644C23—16616no—
645C23—1668no—
646C23—1662no—
647C23—1661no—
648C23—1661no—
649C23—1661no—
650C23—1661no—
651C23—1662no—
652C23C22×C4×D8312yes—
653C23#1458183712yes—
654C23#1458183812yes—
655C23C24×D8311yescharacteristic
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—3328no—
673C2×C4—3328no—
674C2×C4—3328no—
675C2×C4—3328no—
676C2×C4—832no—
677C2×C4—834no—
678C2×C4—8316no—
679C2×C4—832no—
680C2×C4—834no—
681C2×C4—834no—
682C2×C4—1668no—
683C2×C4—1668no—
684C2×C4—1664no—
685C2×C4—1662no—
686C2×C4—1662no—
687C2×C4—1662no—
688C2×C4—1664no—
689C2×C4—1662no—
690C2×C4—1664no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1668no—
694C2×C4—16616no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1662no—
699C2×C4—1662no—
700C2×C4—1668no—
701C2×C4C22×C4×D8312yes—
702C2×C4C22×C4×D8314yes—
703C2×C4C22×C4×D8314yes—
704C2×C4C22×C4×D8312yes—
705C2×C4#41×D8314yes—
706C22—22no—
707C22—22no—
708C22—24no—
709C22—24no—
710C22—834no—
711C22—834no—
712C22—16632no—
713C22—1662no—
714C22—1662no—
715C22—1662no—
716C22—1662no—
717C22—1664no—
718C22—1664no—
719C22—1664no—
720C22—1664no—
721C22#1912817314yes—
722C22C23×C4×D8311yescharacteristic
723C22C2×#41×D8312yes—
724C22C2×#1458183711yescharacteristic
725C22C2×#1458183811yescharacteristic
726C222−1+4×D8312yes—
727C4—22no—
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—44no—
733C4—3324no—
734C4—3322no—
735C4—3322no—
736C4—834no—
737C4—1662no—
738C4—1664no—
739C4—1664no—
740C4#117×D8314yes—
741C2—24no—
742C2—1664no—
743C2—1664no—
744C2C2×#117×D8311yescharacteristic
745C2C2×#1912817311yescharacteristic
746C2#519×D8311yescharacteristic
747C2#2492116312yes—
748C2#2492116512yes—
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2344C2
socle, cosocleC23×C83C25
prime radicalC24×D83C23
hypercenter#2344D83
hypocenterC83#34178
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #24910339C2semidirect
3. #24910337C2semidirect
4. #24910336C2semidirect
5. #24910334C2semidirect
6. #24910333C2semidirect
7. #24910332C2semidirect
8. #24910330C2semidirect
9. #24910327C2semidirect
10. #24910078C2semidirect
11. #24910062C2semidirect
16. #24909817C2semidirect
17. C83×#2344C2semidirect
27. C2×C4⋊C4×D83C4semidirect
34. #19127600C22semidirect
35. #19127599C22semidirect
36. #19127598C22semidirect
37. #19127597C22semidirect
38. #19127596C22semidirect
39. #19127588C22semidirect
40. #19127587C22semidirect
41. #19127586C22semidirect
42. #19127585C22semidirect
43. #19127584C22semidirect
44. #19127583C22semidirect
45. #19127582C22semidirect
63. C4⋊C4×Dic83C22semidirect
64. C4⋊C4×Dic83C22semidirect
65. C4×Dic83⋊C4C22semidirect
66. C4×C4⋊Dic83C22semidirect
67. #19127552C22semidirect
78. #389×C83C22semidirect
79. #387×C83C22semidirect
82. C4×C4⋊C4×C83C22semidirect
330. C4×D83#117semidirect
384. #2344D83semidirect
392. C83#34178semidirect
416. #389C2×D83semidirect
424. #387C2×D83semidirect
449. 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×C4⋊C4×D832
#249103392
#249103372
#249103362
#249103342
#249103332
#249103322
#249103302
#249103272
#249100782
#249100622
#249098452
#249098442
#249098432
#249098422
#249098172
C83×#23442
#3417883