Finite Group Databasebeta

← #35307598

Subgroups — #35307598

Order 21248.

352 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908406C211yesmaximal, characteristic
2#24906013C211yesmaximal, characteristic
3#24905974C211yesmaximal, characteristic
4#24905356C211yesmaximal, characteristic
5#24905327C211yesmaximal, characteristic
6#24905319C211yesmaximal, characteristic
7C83×#2606C211yesmaximal, characteristic
8#19128258C2211yescharacteristic
9#19127758C2211yescharacteristic
10#19127758C2211yescharacteristic
11C4×#13050574C2211yescharacteristic
12#19127461—21no—
13#19127461—21no—
14#19127437—21no—
15#19127437—21no—
16#19127437—21no—
17#19127437—21no—
18#398×C83—21no—
19#398×C83—21no—
20#389×C83—21no—
21#389×C83—21no—
22#387×C83—21no—
23#387×C83—21no—
24#383×C83C2211yescharacteristic
25C4×C4⋊C4×C83C2211yescharacteristic
26#376×C83C2211yescharacteristic
27C2×#13050574—21no—
28#14581792Q811yescharacteristic
29#14581792Q811yescharacteristic
30#14581784—21no—
31#14581771—21no—
32#14581771—21no—
33C4×Dic166—21no—
34C4×Dic166—21no—
35#14581751—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C22⋊(C83⋊C8)—21no—
39C22⋊(C83⋊C8)—21no—
40#14581703—21no—
41#14581703—21no—
42#14581703—21no—
43C4×C83⋊C8—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C42×C83—21no—
52C2×C42×C83D411yescharacteristic
53C2×C42×C83D411yescharacteristic
54C2×C42×C83C2311yescharacteristic
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83D411yescharacteristic
62#95×C83D411yescharacteristic
63#95×C83D411yescharacteristic
64#95×C83D411yescharacteristic
65C2×Dic166—21no—
66C2×Dic166—21no—
67#13050574—22no—
68#13050574—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C4⋊Dic83—21no—
73C4⋊Dic83—21no—
74C4⋊Dic83—21no—
75C4⋊Dic83—21no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78C22⋊Dic83—41no—
79C4×Dic83—41no—
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83C2×D411yescharacteristic
87C22×C4×C83C2×D411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C4⋊C4×C83—42no—
90C4⋊C4×C83—42no—
91C4⋊C4×C83—42no—
92C4⋊C4×C83—42no—
93C4⋊C4×C83—42no—
94C4⋊C4×C83—81no—
95C4⋊C4×C83—81no—
96C42×C83—41no—
97C42×C83—41no—
98C42×C83—42no—
99C42×C83C2×Q811yescharacteristic
100C42×C83#4111yescharacteristic
101C42×C83#4111yescharacteristic
102C42×C83#4111yescharacteristic
103C23×C83#12011yescharacteristic
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—22no—
107C2×C4×C83—22no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—41no—
125C2×C4×C83—41no—
126C2×C4×C83C22⋊Q811yescharacteristic
127C2×C4×C83C22⋊Q811yescharacteristic
128C2×C4×C83C22⋊Q811yescharacteristic
129C2×C4×C83#12411yescharacteristic
130C2×C4×C83#12411yescharacteristic
131C2×C4×C83#12411yescharacteristic
132C2×Dic83—41no—
133C2×Dic83—41no—
134Dic166—81no—
135Dic166—81no—
136C83⋊C8—42no—
137C83⋊C8—81no—
138C83⋊C8—81no—
139C22×C83—21no—
140C22×C83—21no—
141C22×C83#39311yescharacteristic
142C22×C83#45511yescharacteristic
143C22×C83#45611yescharacteristic
144C4×C83—21no—
145C4×C83—21no—
146C4×C83—21no—
147C4×C83—21no—
148C4×C83—21no—
149C4×C83—21no—
150C4×C83—42no—
151C4×C83—42no—
152C4×C83—81no—
153C4×C83—81no—
154C4×C83—81no—
155C4×C83—81no—
156Dic83—81no—
157Dic83—81no—
158#10381—831nomaximal, Sylow
159C2×C83—21no—
160C2×C83—21no—
161C2×C83#202811yescharacteristic
162C2×C83#203111yescharacteristic
163C2×C83#203111yescharacteristic
164#2606D8311yescharacteristic
165#1986—831no—
166#1515—831no—
167#1506—831no—
168#1300—831no—
169#1288—831no—
170#1285—831no—
171C83#1038111yescharacteristic, complemented, Sylow
172#533—831no—
173#432—831no—
174#432—831no—
175C4×M16—831no—
176#398—21no—
177#398—21no—
178#389—21no—
179#389—21no—
180#387—21no—
181#387—21no—
182#383C2×D8311yescharacteristic
183C4×C4⋊C4C2×D8311yescharacteristic
184#376C2×D8311yescharacteristic
185#339—1661no—
186#339—1661no—
187#328—1661no—
188#328—1661no—
189#328—1661no—
190#328—1661no—
191C2×M16—1661no—
192C4⋊Q8—831no—
193C4⋊Q8—831no—
194#125—1661no—
195C22⋊Q8—1661no—
196C22⋊Q8—1661no—
197C4×Q8—1661no—
198C4×Q8—1661no—
199#117—1661no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42C22⋊D8311yescharacteristic
209C2×C42C22⋊D8311yescharacteristic
210C2×C42C22×D8311yescharacteristic
211C4⋊C8—1661no—
212C4⋊C8—1661no—
213C22⋊C8—1661no—
214C22⋊C8—1661no—
215#97—1661no—
216#97—1661no—
217#97—1661no—
218C4×C8—1661no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C22⋊D8311yescharacteristic
226#95C22⋊D8311yescharacteristic
227#95C22⋊D8311yescharacteristic
228#95C22⋊D8311yescharacteristic
229C2×Q8—1661no—
230C2×Q8—1661no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4C2×C22⋊D8311yescharacteristic
238C22×C4C2×C22⋊D8311yescharacteristic
239C22×C4C2×C22⋊D8311yescharacteristic
240M16—3321no—
241M16—1662no—
242C2×C8—3321no—
243C2×C8—3321no—
244C2×C8—3321no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—3321no—
253C4⋊C4—3321no—
254C4⋊C4—1661no—
255C4⋊C4—1661no—
256C4⋊C4—1661no—
257C4⋊C4—1661no—
258C22⋊C4—3321no—
259C42—41no—
260C42—41no—
261C42—42no—
262C42—3321no—
263C42Q8×D8311yescharacteristic
264C42#1305059111yescharacteristic
265C42#1305059111yescharacteristic
266C42#1305059111yescharacteristic
267C23#1458176111yescharacteristic
268Q8—6641no—
269Q8—6641no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—3321no—
293C2×C4—3321no—
294C2×C4#1458176811yescharacteristic
295C2×C4#1458176811yescharacteristic
296C2×C4#1458176811yescharacteristic
297C2×C4#1458178111yescharacteristic
298C2×C4#1458178111yescharacteristic
299C2×C4#1458178111yescharacteristic
300C8—3322no—
301C8—6641no—
302C8—6641no—
303C22—21no—
304C22—21no—
305C22#1912761211yescharacteristic
306C22#1912787911yescharacteristic
307C22#1912788411yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—6641no—
321C4—6641no—
322C2—21no—
323C2—21no—
324C2#2490862111yescharacteristic
325C2#2490863211yescharacteristic
326C2#2490863211yescharacteristic
subgroupG/H
centerC22#19127612
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2606C2
socleC22×C83#393
prime radicalC23×C83#120
hypercenter#2606D83
hypocenterC83#10381
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2606

Complements

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

NH ≅ G/Ntype
171. C83#10381semidirect

Maximal subgroups

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

subgroupindex
#249084062
#249060132
#249059742
#249053562
#249053272
#249053192
C83×#26062
#1038183