Finite Group Databasebeta

← C83×#11571 #35239395

Subgroups — C83×#11571 #35239395

Order 21248.

350 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C83×#2565C211yesmaximal, characteristic
2C83×#1467C211yesmaximal, characteristic
3C83×#1461C211yesmaximal, characteristic
4C83×#1325C212yesmaximal
5C83×#1324C212yesmaximal
6C2×#125×C83C411yescharacteristic
7C2×C4×Q8×C83C2211yescharacteristic
8#432×C83—21no—
9#431×C83—21no—
10#398×C83—21no—
11#398×C83—21no—
12#391×C83C411yescharacteristic
13#391×C83C411yescharacteristic
14#387×C83—21no—
15#387×C83—21no—
16#384×C83C2211yescharacteristic
17#382×C83C2211yescharacteristic
18C4×C4⋊C4×C83C411yescharacteristic
19#324×C83—21no—
20#324×C83—21no—
21#324×C83C2212yes—
22#324×C83C2212yes—
23C22×Q8×C83C2×C411yescharacteristic
24#125×C83—41no—
25#125×C83—41no—
26C4×Q8×C83—41no—
27C4×Q8×C83—41no—
28C2×C4⋊C4×C83—21no—
29C2×C4⋊C4×C83—21no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83C2×C411yescharacteristic
34C2×C4⋊C4×C83C2×C411yescharacteristic
35C2×C4⋊C4×C83D411yescharacteristic
36C2×C4⋊C4×C83D411yescharacteristic
37C2×C4⋊C4×C83C2311yescharacteristic
38C2×C42×C83C2×C411yescharacteristic
39C2×C42×C83C2×C411yescharacteristic
40C2×C42×C83C2×C411yescharacteristic
41C2×C42×C83D411yescharacteristic
42C2×C42×C83D411yescharacteristic
43C4⋊C8×C83—41no—
44C4⋊C8×C83—41no—
45C22⋊C8×C83—22no—
46C22⋊C8×C83—22no—
47#97×C83—41no—
48C4×C8×C83—41no—
49#95×C83—21no—
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83—21no—
56C2×Q8×C83—22no—
57C2×Q8×C83—22no—
58C2×Q8×C83—41no—
59C22×C4×C83—21no—
60C22×C4×C83—21no—
61C22×C4×C83—21no—
62C22×C4×C83—21no—
63C22×C4×C83C22⋊C411yescharacteristic
64C22×C4×C83C22⋊C411yescharacteristic
65C22×C4×C83C22⋊C411yescharacteristic
66C22×C4×C83C22⋊C411yescharacteristic
67C22×C4×C83C22×C411yescharacteristic
68C22×C4×C83C2×D411yescharacteristic
69C22×C4×C83C2×D411yescharacteristic
70C2×C8×C83—42no—
71C2×C8×C83—42no—
72C4⋊C4×C83—41no—
73C4⋊C4×C83—41no—
74C4⋊C4×C83—41no—
75C4⋊C4×C83—41no—
76C4⋊C4×C83—41no—
77C4⋊C4×C83—42no—
78C4⋊C4×C83—42no—
79C4⋊C4×C83—42no—
80C4⋊C4×C83—42no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—41no—
83C42×C83—21no—
84C42×C83—21no—
85C42×C83—21no—
86C42×C83—21no—
87C42×C83—21no—
88C42×C83—21no—
89C42×C83—22no—
90C42×C83—22no—
91C23×C83C2×C22⋊C411yescharacteristic
92Q8×C83—44no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—22no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
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—42no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83#9911yescharacteristic
119C2×C4×C83#9911yescharacteristic
120C2×C4×C83#10112yes—
121C2×C4×C83#13112yes—
122C8×C83—82no—
123C8×C83—82no—
124C22×C83—21no—
125C22×C83—21no—
126C22×C83#40811yescharacteristic
127C22×C83C2×#9911yescharacteristic
128C22×C83C2×#10111yescharacteristic
129C4×C83—21no—
130C4×C83—21no—
131C4×C83—22no—
132C4×C83—22no—
133C4×C83—42no—
134C4×C83—41no—
135C4×C83—41no—
136C4×C83—41no—
137C4×C83—41no—
138C4×C83—81no—
139C4×C83—81no—
140C4×C83—81no—
141#11571C8311yesmaximal, characteristic, direct product factor, Sylow
142C2×C83—21no—
143C2×C83—21no—
144C2×C83#147211yescharacteristic
145C2×C83#212611yescharacteristic
146C2×C83#213311yescharacteristic
147#2565C2×C8311yescharacteristic
148#1467C2×C8311yescharacteristic
149#1461C2×C8311yescharacteristic
150#1325C2×C8312yes—
151#1324C2×C8312yes—
152C83#1157111yescharacteristic, direct product factor, Sylow
153C2×#125C4×C8311yescharacteristic
154C2×C4×Q8C22×C8311yescharacteristic
155#432—21no—
156#431—21no—
157#398—21no—
158#398—21no—
159#391C4×C8311yescharacteristic
160#391C4×C8311yescharacteristic
161#387—21no—
162#387—21no—
163#384C22×C8311yescharacteristic
164#382C22×C8311yescharacteristic
165C4×C4⋊C4C4×C8311yescharacteristic
166#324—21no—
167#324—21no—
168#324C22×C8312yes—
169#324C22×C8312yes—
170C22×Q8C2×C4×C8311yescharacteristic
171#125—41no—
172#125—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×C4×C8311yescharacteristic
181C2×C4⋊C4C2×C4×C8311yescharacteristic
182C2×C4⋊C4D4×C8311yescharacteristic
183C2×C4⋊C4D4×C8311yescharacteristic
184C2×C4⋊C4C23×C8311yescharacteristic
185C2×C42C2×C4×C8311yescharacteristic
186C2×C42C2×C4×C8311yescharacteristic
187C2×C42C2×C4×C8311yescharacteristic
188C2×C42D4×C8311yescharacteristic
189C2×C42D4×C8311yescharacteristic
190C4⋊C8—41no—
191C4⋊C8—41no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194#97—41no—
195C4×C8—41no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22⋊C4×C8311yescharacteristic
211C22×C4C22⋊C4×C8311yescharacteristic
212C22×C4C22⋊C4×C8311yescharacteristic
213C22×C4C22⋊C4×C8311yescharacteristic
214C22×C4C22×C4×C8311yescharacteristic
215C22×C4C2×D4×C8311yescharacteristic
216C22×C4C2×D4×C8311yescharacteristic
217C2×C8—42no—
218C2×C8—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—22no—
237C42—22no—
238C23C2×C22⋊C4×C8311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#99×C8311yescharacteristic
266C2×C4#99×C8311yescharacteristic
267C2×C4#101×C8312yes—
268C2×C4#131×C8312yes—
269C8—82no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22#408×C8311yescharacteristic
274C22C2×#99×C8311yescharacteristic
275C22C2×#101×C8311yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2C83×#147211yescharacteristic
291C2C83×#212611yescharacteristic
292C2C83×#213311yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radicalC23×C83C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C22×C4×C83 ◁ C2×C4×Q8×C83 ◁ G

Complements

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

NH ≅ G/Ntype
141. #11571C83direct (N × H)
152. C83#11571direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25652
C83×#14672
C83×#14612
C83×#13252
C83×#13242
#1157183