Finite Group Databasebeta

← C83×#9452 #35237276

Subgroups — C83×#9452 #35237276

Order 21248.

468 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2983C211yesmaximal, characteristic
2C83×#2546C211yesmaximal, characteristic
3C83×#1558C212yesmaximal
4C83×#1467C211yesmaximal, characteristic
5C83×#1285C212yesmaximal
6C2×C4⋊Q8×C83C412yes—
7C2×C4⋊Q8×C83C2211yescharacteristic
8C2×C4×Q8×C83C2211yescharacteristic
9#446×C83—24no—
10#432×C83—21no—
11#432×C83C2212yes—
12#432×C83C2212yes—
13#431×C83—21no—
14#398×C83—21no—
15#398×C83—21no—
16#391×C83C412yes—
17#389×C83—21no—
18#389×C83—21no—
19C4×C4⋊C4×C83C2211yescharacteristic
20#333×C83—24no—
21#324×C83—21no—
22#324×C83—21no—
23C22×Q8×C83C2×C412yes—
24C22×Q8×C83C2×C411yescharacteristic
25C4⋊Q8×C83—22no—
26C4⋊Q8×C83—22no—
27C4⋊Q8×C83—44no—
28C4×Q8×C83—22no—
29C4×Q8×C83—22no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—22no—
32C2×C4⋊C4×C83—22no—
33C2×C4⋊C4×C83—21no—
34C2×C4⋊C4×C83—21no—
35C2×C4⋊C4×C83C2×C411yescharacteristic
36C2×C4⋊C4×C83D411yescharacteristic
37C2×C4⋊C4×C83D411yescharacteristic
38C2×C42×C83C2×C412yes—
39C2×C42×C83D411yescharacteristic
40C2×C42×C83D411yescharacteristic
41C2×C42×C83C2311yescharacteristic
42C4⋊C8×C83—22no—
43C4⋊C8×C83—22no—
44C4⋊C8×C83—22no—
45C4⋊C8×C83D414yes—
46C22⋊C8×C83—22no—
47C22⋊C8×C83—22no—
48#97×C83—22no—
49#97×C83—22no—
50#97×C83—22no—
51C4×C8×C83—22no—
52#95×C83—22no—
53#95×C83—22no—
54#95×C83—21no—
55C2×Q8×C83—22no—
56C2×Q8×C83—22no—
57C2×Q8×C83—24no—
58C2×Q8×C83—41no—
59C2×Q8×C83—42no—
60C2×Q8×C83—42no—
61C22×C4×C83—22no—
62C22×C4×C83—22no—
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—24no—
71C2×C8×C83—42no—
72C4⋊C4×C83—24no—
73C4⋊C4×C83—22no—
74C4⋊C4×C83—22no—
75C4⋊C4×C83—22no—
76C4⋊C4×C83—44no—
77C4⋊C4×C83—44no—
78C4⋊C4×C83—41no—
79C4⋊C4×C83—42no—
80C4⋊C4×C83—41no—
81C42×C83—21no—
82C42×C83—21no—
83C42×C83—21no—
84C42×C83—21no—
85C42×C83—42no—
86C42×C83C2×D412yes—
87C42×C83#4112yes—
88C23×C83C2×C22⋊C411yescharacteristic
89Q8×C83—44no—
90Q8×C83—84no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—22no—
96C2×C4×C83—24no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—41no—
103C2×C4×C83—42no—
104C2×C4×C83—42no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—42no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83#10012yes—
111C2×C4×C83C4×D412yes—
112C2×C4×C83#12011yescharacteristic
113C2×C4×C83#12112yes—
114C2×C4×C83#12311yescharacteristic
115C8×C83—44no—
116C8×C83—82no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83#38611yescharacteristic
120C22×C83C2×#10011yescharacteristic
121C22×C83#41311yescharacteristic
122C4×C83—21no—
123C4×C83—22no—
124C4×C83—22no—
125C4×C83—22no—
126C4×C83—44no—
127C4×C83—41no—
128C4×C83—41no—
129C4×C83—41no—
130C4×C83—82no—
131C4×C83#45612yes—
132#9452C8311yesmaximal, characteristic, direct product factor, Sylow
133C2×C83—21no—
134C2×C83—21no—
135C2×C83#188611yescharacteristic
136C2×C83#190011yescharacteristic
137C2×C83#190911yescharacteristic
138#2983C2×C8311yescharacteristic
139#2546C2×C8311yescharacteristic
140#1558C2×C8312yes—
141#1467C2×C8311yescharacteristic
142#1285C2×C8312yes—
143C83#945211yescharacteristic, direct product factor, Sylow
144C2×C4⋊Q8C4×C8312yes—
145C2×C4⋊Q8C22×C8311yescharacteristic
146C2×C4×Q8C22×C8311yescharacteristic
147#446—24no—
148#432—21no—
149#432C22×C8312yes—
150#432C22×C8312yes—
151#431—21no—
152#398—21no—
153#398—21no—
154#391C4×C8312yes—
155#389—21no—
156#389—21no—
157C4×C4⋊C4C22×C8311yescharacteristic
158#333—24no—
159#324—21no—
160#324—21no—
161C22×Q8C2×C4×C8312yes—
162C22×Q8C2×C4×C8311yescharacteristic
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×C4×C8311yescharacteristic
174C2×C4⋊C4D4×C8311yescharacteristic
175C2×C4⋊C4D4×C8311yescharacteristic
176C2×C42C2×C4×C8312yes—
177C2×C42D4×C8311yescharacteristic
178C2×C42D4×C8311yescharacteristic
179C2×C42C23×C8311yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8D4×C8314yes—
184C22⋊C8—22no—
185C22⋊C8—22no—
186#97—22no—
187#97—22no—
188#97—22no—
189C4×C8—22no—
190#95—22no—
191#95—22no—
192#95—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊C4×C8311yescharacteristic
202C22×C4C22⋊C4×C8311yescharacteristic
203C22×C4C22⋊C4×C8311yescharacteristic
204C22×C4C22⋊C4×C8311yescharacteristic
205C22×C4C22×C4×C8311yescharacteristic
206C22×C4C2×D4×C8311yescharacteristic
207C22×C4C2×D4×C8311yescharacteristic
208C2×C8—24no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—44no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42C2×D4×C8312yes—
225C42#41×C8312yes—
226C23C2×C22⋊C4×C8311yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#100×C8312yes—
249C2×C4C4×D4×C8312yes—
250C2×C4#120×C8311yescharacteristic
251C2×C4#121×C8312yes—
252C2×C4#123×C8311yescharacteristic
253C8—44no—
254C8—82no—
255C22—21no—
256C22—21no—
257C22#386×C8311yescharacteristic
258C22C2×#100×C8311yescharacteristic
259C22#413×C8311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#456×C8312yes—
270C2—21no—
271C2—21no—
272C2C83×#188611yescharacteristic
273C2C83×#190011yescharacteristic
274C2C83×#190911yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC23×C83C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
132. #9452C83direct (N × H)
143. C83#9452direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29832
C83×#25462
C83×#15582
C83×#14672
C83×#12852
#945283