Finite Group Databasebeta

← #35307447

Subgroups — #35307447

Order 21248.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912499C211yesmaximal, characteristic, complemented
2#24908389C211yesmaximal, characteristic
3#24908389C211yesmaximal, characteristic
4#24908268C211yesmaximal, characteristic
5#24905302C211yesmaximal, characteristic, complemented
6#24905302C211yesmaximal, characteristic, complemented
7C83×#1296C211yesmaximal, characteristic, complemented
8C2×#14581789C2211yescharacteristic
9C2×#14581783—21no—
10C2×#14581714—21no—
11C2×#14581714—21no—
12C2×#14581714—21no—
13C2×#14581714—21no—
14C2×#14581712—22no—
15C2×C4×C83⋊C8C2211yescharacteristic
16#19127634—22no—
17#19127600—21no—
18#19127597—21no—
19#19127570—21no—
20C4×C4⋊Dic83C2211yescharacteristic
21C4×C4⋊Dic83C2211yescharacteristic
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24#384×C83C2211yescharacteristic
25C22×D332—21no—
26C22×D332—21no—
27C22×D332—21no—
28C22×C83⋊C8—21no—
29#14581789—21no—
30#14581789—21no—
31#14581789—21no—
32#14581789Q812yes—
33#14581783—42no—
34#14581783—42no—
35C2×C4⋊Dic83—22no—
36C2×C4⋊Dic83D411yescharacteristic
37C2×C4⋊Dic83D411yescharacteristic
38C2×C4⋊Dic83D411yescharacteristic
39C2×C4⋊Dic83D411yescharacteristic
40C2×Dic83⋊C4—22no—
41C2×Dic83⋊C4—22no—
42C2×C4×Dic83—21no—
43C2×C4×Dic83—21no—
44#14581714—42no—
45#14581714—42no—
46#14581714—42no—
47#14581714—42no—
48#14581712—44no—
49C4×C83⋊C8—21no—
50C4×C83⋊C8—21no—
51C83⋊#95—22no—
52C83⋊#95—21no—
53C83⋊#95—21no—
54C22×C8×C83—21no—
55C22×C8×C83—21no—
56C2×C4⋊C4×C83—21no—
57C2×C4⋊C4×C83—21no—
58C2×C4⋊C4×C83D412yes—
59C2×C42×C83C2311yescharacteristic
60C4⋊C8×C83—21no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C4⋊C8×C83—21no—
64C23×D83—41no—
65C2×D332—22no—
66C2×D332—22no—
67C2×D332—22no—
68C2×D332—42no—
69C2×D332—42no—
70C2×D332—41no—
71C2×D332—41no—
72C2×D332—41no—
73C2×D332—41no—
74C2×D332—41no—
75C2×D332—41no—
76C2×D332—41no—
77C2×D332—41no—
78C2×D332—41no—
79C2×D332—41no—
80C2×D332—41no—
81C22×Dic83—21no—
82C22×Dic83—21no—
83C22×Dic83—21no—
84C22×Dic83—21no—
85C2×C83⋊C8—22no—
86C2×C83⋊C8—41no—
87C2×C83⋊C8—41no—
88C4⋊Dic83—21no—
89C4⋊Dic83—21no—
90C4⋊Dic83—21no—
91C4⋊Dic83—21no—
92C4⋊Dic83—21no—
93C4⋊Dic83—21no—
94C4⋊Dic83—44no—
95C4⋊Dic83D812yes—
96C4⋊Dic83SD1612yes—
97Dic83⋊C4—44no—
98Dic83⋊C4—82no—
99C4×Dic83—41no—
100C4×Dic83—41no—
101C4×Dic83—41no—
102C4×Dic83—41no—
103C22×C4×C83—22no—
104C22×C4×C83C2×D411yescharacteristic
105C22×C4×C83C2×D411yescharacteristic
106C22×C4×C83C2×D411yescharacteristic
107C2×C8×C83—41no—
108C2×C8×C83—41no—
109C2×C8×C83—41no—
110C2×C8×C83—41no—
111C2×C8×C83—41no—
112C2×C8×C83—41no—
113C4⋊C4×C83—42no—
114C4⋊C4×C83—41no—
115C4⋊C4×C83—41no—
116C4⋊C4×C83—41no—
117C4⋊C4×C83—41no—
118C42×C83C2×Q811yescharacteristic
119C42×C83#4111yescharacteristic
120C42×C83#4111yescharacteristic
121C42×C83#4111yescharacteristic
122C23×C83#12011yescharacteristic
123C22×D83—42no—
124C22×D83—81no—
125C22×D83—81no—
126C22×D83—81no—
127C22×D83—81no—
128C22×D83—81no—
129C22×D83—81no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—42no—
133C2×C4×C83—42no—
134C2×C4×C83—42no—
135C2×C4×C83C22⋊Q811yescharacteristic
136C2×C4×C83C22⋊Q811yescharacteristic
137C2×C4×C83C22⋊Q811yescharacteristic
138C2×C4×C83#12411yescharacteristic
139C2×C4×C83#12411yescharacteristic
140C2×C4×C83#12411yescharacteristic
141C2×C4×C83C2×D811yescharacteristic
142C2×C4×C83C2×SD1611yescharacteristic
143C2×C4×C83#13511yescharacteristic
144C2×C4×C83#13511yescharacteristic
145C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C83#13711yescharacteristic
149C2×Dic83—22no—
150C2×Dic83—22no—
151C2×Dic83—41no—
152C2×Dic83—41no—
153C2×Dic83—41no—
154C2×Dic83—41no—
155C2×Dic83—41no—
156C2×Dic83—41no—
157C2×Dic83—41no—
158C2×Dic83—41no—
159C2×Dic83—41no—
160C2×Dic83—41no—
161D332—44no—
162D332—42no—
163D332—42no—
164D332—42no—
165D332—42no—
166D332—82no—
167D332—81no—
168D332—81no—
169D332—81no—
170D332—81no—
171C8×C83—81no—
172C8×C83—81no—
173C83⋊C8—42no—
174C22×C83#39311yescharacteristic
175C22×C83#44711yescharacteristic
176C22×C83#44811yescharacteristic
177C22×C83#44911yescharacteristic
178C22×C83#44911yescharacteristic
179C22×C83#45311yescharacteristic
180C22×C83#45411yescharacteristic
181C2×D83—82no—
182C2×D83—82no—
183C2×D83—82no—
184C2×D83—161no—
185C2×D83—161no—
186C2×D83—161no—
187C2×D83—161no—
188C4×C83—21no—
189C4×C83—21no—
190C4×C83—82no—
191C4×C83#47411yescharacteristic
192C4×C83#47611yescharacteristic
193C4×C83#47811yescharacteristic
194C4×C83#47811yescharacteristic
195C4×C83#48611yescharacteristic
196C4×C83#48811yescharacteristic
197C4×C83#48911yescharacteristic
198C4×C83#49011yescharacteristic
199Dic83—42no—
200Dic83—42no—
201Dic83—81no—
202Dic83—81no—
203#10354—831nomaximal, Sylow
204C2×C83#162111yescharacteristic
205C2×C83#162211yescharacteristic
206C2×C83#162511yescharacteristic
207C2×C83#162611yescharacteristic
208C2×C83#202311yescharacteristic
209C2×C83#202511yescharacteristic
210C2×C83#202711yescharacteristic
211D83—162no—
212#2552—831no—
213#1982—831no—
214#1982—831no—
215#1957—831no—
216#1296D8311yescharacteristic, complemented
217#1279—831no—
218#1279—831no—
219C83#1035411yescharacteristic, complemented, Sylow
220C2×#127—831no—
221C2×#125—1661no—
222C2×C4⋊C8C2×D8311yescharacteristic
223C2×C4⋊C8C2×D8311yescharacteristic
224C2×#102—1661no—
225C2×#102—1661no—
226C2×#102—1661no—
227C2×#102—1661no—
228C2×#102—1662no—
229C2×C4×C8—831no—
230#398—1662no—
231#389—1661no—
232#389—1661no—
233#384—1661no—
234#384C2×D8311yescharacteristic
235C4×C4⋊C4—831no—
236C4×C4⋊C4—831no—
237C22×D4—1661no—
238C22×D4—1661no—
239C22×D4—1661no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—1661no—
243#127—832no—
244#127—1661no—
245#127—1661no—
246#127—1661no—
247#125—3322no—
248#125—3322no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—831no—
252C2×C4⋊C4—831no—
253C2×C4⋊C4—831no—
254C2×C4⋊C4—831no—
255C2×C4⋊C4—1662no—
256C2×C4⋊C4—1662no—
257C2×C4⋊C4—1662no—
258C2×C4⋊C4D33212yes—
259C2×C42—1661no—
260C2×C42—1661no—
261C2×C42C22×D8311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#102—3324no—
267#102—3322no—
268#102—3322no—
269#102—3322no—
270#102—3322no—
271C4×C8—1661no—
272C4×C8—1661no—
273#95—1662no—
274#95—1661no—
275#95—1661no—
276C24—3321no—
277C2×D4—3322no—
278C2×D4—3322no—
279C2×D4—3321no—
280C2×D4—3321no—
281C2×D4—3321no—
282C2×D4—3321no—
283C2×D4—3321no—
284C2×D4—3321no—
285C2×D4—3321no—
286C2×D4—3321no—
287C2×D4—3321no—
288C2×D4—3321no—
289C2×D4—3321no—
290C2×D4—1662no—
291C2×D4—1662no—
292C2×D4—1662no—
293C22×C4—22no—
294C22×C4—1661no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4—1661no—
298C22×C4D4×D8311yescharacteristic
299C22×C4D4×D8311yescharacteristic
300C22×C4C2×D33211yescharacteristic
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—3321no—
308C2×C8—3321no—
309C2×C8—1662no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—3324no—
316C4⋊C4—3324no—
317C4⋊C4—832no—
318C4⋊C4—832no—
319C4⋊C4—6642no—
320C4⋊C4—1661no—
321C4⋊C4—1661no—
322C4⋊C4—1661no—
323C4⋊C4—1661no—
324C4⋊C4—1661no—
325C4⋊C4—1661no—
326C42—3321no—
327C42—3321no—
328C42—3321no—
329C42—3321no—
330C42Q8×D8311yescharacteristic
331C42#1305058911yescharacteristic
332C42#1305059011yescharacteristic
333C42#1305059011yescharacteristic
334C23—3322no—
335C23—6641no—
336C23—6641no—
337C23—6641no—
338C23—6641no—
339C23—6641no—
340C23—6641no—
341C23#1458176211yescharacteristic
342D4—3324no—
343D4—3322no—
344D4—3322no—
345D4—3322no—
346D4—3322no—
347D4—6642no—
348D4—6641no—
349D4—6641no—
350D4—6641no—
351D4—6641no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—3321no—
358C2×C4—3321no—
359C2×C4—3321no—
360C2×C4—3321no—
361C2×C4—3321no—
362C2×C4—3321no—
363C2×C4—3321no—
364C2×C4—3321no—
365C2×C4—3321no—
366C2×C4—3321no—
367C2×C4—1662no—
368C2×C4—1662no—
369C2×C4#1458177011yescharacteristic
370C2×C4#1458177011yescharacteristic
371C2×C4#1458177211yescharacteristic
372C2×C4#1458177811yescharacteristic
373C2×C4#1458177811yescharacteristic
374C2×C4#1458178011yescharacteristic
375C2×C4D8×D8311yescharacteristic
376C2×C4SD16×D8311yescharacteristic
377C2×C4#1458181311yescharacteristic
378C2×C4#1458181511yescharacteristic
379C2×C4#1458181611yescharacteristic
380C2×C4#1458181911yescharacteristic
381C2×C4#1458181911yescharacteristic
382C2×C4#1458182411yescharacteristic
383C8—81no—
384C8—81no—
385C8—3322no—
386C22—13281no—
387C22—13281no—
388C22—13281no—
389C22—13281no—
390C22—6642no—
391C22—6642no—
392C22—6642no—
393C22#1912761411yescharacteristic
394C22#1912783611yescharacteristic
395C22#1912784111yescharacteristic
396C22#1912784711yescharacteristic
397C22#1912784911yescharacteristic
398C22#1912787111yescharacteristic
399C22#1912787611yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—3322no—
404C4—3322no—
405C4—6641no—
406C4—6641no—
407C4#1912798011yescharacteristic
408C4#1912799011yescharacteristic
409C4#1912800011yescharacteristic
410C4#1912800411yescharacteristic
411C4#1912804611yescharacteristic
412C4#1912805711yescharacteristic
413C4#1912806211yescharacteristic
414C4#1912806411yescharacteristic
415C2—13282no—
416C2#2490652911yescharacteristic
417C2#2490653611yescharacteristic
418C2#2490655311yescharacteristic
419C2#2490656011yescharacteristic
420C2#2490859811yescharacteristic
421C2#2490860811yescharacteristic
422C2#2490862011yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1296C2
socleC23×C83#120
prime radicalC2×#14581789C22
hypercenter#1296D83
hypocenterC83#10354
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. #24912499C2semidirect
5. #24905302C2semidirect
6. #24905302C2semidirect
7. C83×#1296C2semidirect
216. #1296D83semidirect
219. C83#10354semidirect

Maximal subgroups

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

subgroupindex
#249124992
#249083892
#249082682
#249053022
C83×#12962
#1035483