Finite Group Databasebeta

← C83×#9403 #35237227

Subgroups — C83×#9403 #35237227

Order 21248.

570 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2975C211yesmaximal, characteristic
2C83×#2542C211yesmaximal, characteristic
3C83×#1800C211yesmaximal, characteristic
4C83×#1549C212yesmaximal, complemented
5C83×#1303C212yesmaximal, complemented
6C2×C4⋊Q8×C83C2211yescharacteristic
7C2×C22⋊Q8×C83—22no—
8C2×C4×D4×C83C2211yescharacteristic
9#436×C83—24no—
10#431×C83C2212yes—
11#423×C83C2212yes—
12C2×#100×C83—21no—
13#407×C83—22no—
14#399×C83C414yes—
15#390×C83—21no—
16#384×C83—21no—
17C4×C4⋊C4×C83C2211yescharacteristic
18#343×C83—21no—
19#332×C83—24no—
20C22×Q8×C83—21no—
21C22×D4×C83D411yescharacteristic
22C23×C4×C83D412yes—
23C2×M16×C83—24no—
24C2×M16×C83—22no—
25C4⋊Q8×C83—22no—
26C4⋊Q8×C83—22no—
27C22⋊Q8×C83—48no—
28C4×D4×C83—22no—
29C4×D4×C83—22no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—24no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83C2×C412yes—
34C2×C4⋊C4×C83D411yescharacteristic
35C2×C22⋊C4×C83—24no—
36C2×C22⋊C4×C83C2×C412yes—
37C2×C42×C83—21no—
38C2×C42×C83C2311yescharacteristic
39C4⋊C8×C83—22no—
40C4⋊C8×C83—22no—
41C4⋊C8×C83D414yes—
42#100×C83—42no—
43C22⋊C8×C83—24no—
44C22⋊C8×C83—22no—
45C4×C8×C83—22no—
46#95×C83C2×C412yes—
47C24×C83C22⋊C412yes—
48C2×Q8×C83—44no—
49C2×Q8×C83—41no—
50C2×Q8×C83—41no—
51C2×D4×C83—22no—
52C2×D4×C83—21no—
53C2×D4×C83—22no—
54C2×D4×C83—21no—
55C22×C4×C83—22no—
56C22×C4×C83—22no—
57C22×C4×C83—22no—
58C22×C4×C83—22no—
59C22×C4×C83—44no—
60C22×C4×C83C22⋊C412yes—
61C22×C4×C83C22×C411yescharacteristic
62C22×C4×C83C2×D411yescharacteristic
63C22×C4×C83C2×D411yescharacteristic
64M16×C83—42no—
65M16×C83—42no—
66M16×C83—84no—
67C2×C8×C83—24no—
68C2×C8×C83—42no—
69C4⋊C4×C83—24no—
70C4⋊C4×C83—22no—
71C4⋊C4×C83—24no—
72C4⋊C4×C83—48no—
73C4⋊C4×C83—42no—
74C22⋊C4×C83—24no—
75C22⋊C4×C83—48no—
76C42×C83—41no—
77C42×C83—41no—
78C42×C83C2×D412yes—
79C42×C83#4112yes—
80C23×C83—22no—
81C23×C83—22no—
82C23×C83—22no—
83C23×C83—42no—
84C23×C83—42no—
85C23×C83C2×C22⋊C411yescharacteristic
86Q8×C83—82no—
87Q8×C83—82no—
88D4×C83—42no—
89D4×C83—42no—
90C2×C4×C83—22no—
91C2×C4×C83—24no—
92C2×C4×C83—22no—
93C2×C4×C83—41no—
94C2×C4×C83—42no—
95C2×C4×C83—42no—
96C2×C4×C83—44no—
97C2×C4×C83—42no—
98C2×C4×C83—44no—
99C2×C4×C83—42no—
100C2×C4×C83—82no—
101C2×C4×C83C4×D412yes—
102C2×C4×C83#12011yescharacteristic
103C2×C4×C83#12112yes—
104C2×C4×C83#12311yescharacteristic
105C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C83#13712yes—
107C2×C4×C83#13711yescharacteristic
108C8×C83—44no—
109C8×C83—82no—
110C22×C83—21no—
111C22×C83—21no—
112C22×C83—44no—
113C22×C83—42no—
114C22×C83—42no—
115C22×C83—42no—
116C22×C83—82no—
117C22×C83#38611yescharacteristic
118C22×C83#41711yescharacteristic
119C22×C83#41911yescharacteristic
120C4×C83—21no—
121C4×C83—22no—
122C4×C83—44no—
123C4×C83—42no—
124C4×C83—82no—
125C4×C83#45312yes—
126C4×C83#46812yes—
127C4×C83#47012yes—
128#9403C8311yesmaximal, characteristic, direct product factor, Sylow
129C2×C83—21no—
130C2×C83—21no—
131C2×C83—82no—
132C2×C83#188711yescharacteristic
133C2×C83#189411yescharacteristic
134C2×C83#191511yescharacteristic
135#2975C2×C8311yescharacteristic
136#2542C2×C8311yescharacteristic
137#1800C2×C8311yescharacteristic
138#1549C2×C8312yescomplemented
139#1303C2×C8312yescomplemented
140C83#940311yescharacteristic, direct product factor, Sylow
141C2×C4⋊Q8C22×C8311yescharacteristic
142C2×C22⋊Q8—22no—
143C2×C4×D4C22×C8311yescharacteristic
144#436—24no—
145#431C22×C8312yes—
146#423C22×C8312yes—
147C2×#100—21no—
148#407—22no—
149#399C4×C8314yes—
150#390—21no—
151#384—21no—
152C4×C4⋊C4C22×C8311yescharacteristic
153#343—21no—
154#332—24no—
155C22×Q8—21no—
156C22×D4D4×C8311yescharacteristic
157C23×C4D4×C8312yes—
158C2×M16—24no—
159C2×M16—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C22⋊Q8—48no—
163C4×D4—22no—
164C4×D4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C2×C4×C8312yes—
169C2×C4⋊C4D4×C8311yescharacteristic
170C2×C22⋊C4—24no—
171C2×C22⋊C4C2×C4×C8312yes—
172C2×C42—21no—
173C2×C42C23×C8311yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8D4×C8314yes—
177#100—42no—
178C22⋊C8—24no—
179C22⋊C8—22no—
180C4×C8—22no—
181#95C2×C4×C8312yes—
182C24C22⋊C4×C8312yes—
183C2×Q8—44no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4C22⋊C4×C8312yes—
196C22×C4C22×C4×C8311yescharacteristic
197C22×C4C2×D4×C8311yescharacteristic
198C22×C4C2×D4×C8311yescharacteristic
199M16—42no—
200M16—42no—
201M16—84no—
202C2×C8—24no—
203C2×C8—42no—
204C4⋊C4—24no—
205C4⋊C4—22no—
206C4⋊C4—24no—
207C4⋊C4—48no—
208C4⋊C4—42no—
209C22⋊C4—24no—
210C22⋊C4—48no—
211C42—41no—
212C42—41no—
213C42C2×D4×C8312yes—
214C42#41×C8312yes—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—42no—
219C23—42no—
220C23C2×C22⋊C4×C8311yescharacteristic
221Q8—82no—
222Q8—82no—
223D4—42no—
224D4—42no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4C4×D4×C8312yes—
237C2×C4#120×C8311yescharacteristic
238C2×C4#121×C8312yes—
239C2×C4#123×C8311yescharacteristic
240C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
241C2×C4#137×C8312yes—
242C2×C4#137×C8311yescharacteristic
243C8—44no—
244C8—82no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22#386×C8311yescharacteristic
253C22#417×C8311yescharacteristic
254C22#419×C8311yescharacteristic
255C4—21no—
256C4—22no—
257C4—44no—
258C4—42no—
259C4—82no—
260C4#453×C8312yes—
261C4#468×C8312yes—
262C4#470×C8312yes—
263C2—21no—
264C2—21no—
265C2—82no—
266C2C83×#188711yescharacteristic
267C2C83×#189411yescharacteristic
268C2C83×#191511yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC22×D4×C83D4
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
4. C83×#1549C2semidirect
5. C83×#1303C2semidirect
128. #9403C83direct (N × H)
138. #1549C2×C83semidirect
139. #1303C2×C83semidirect
140. C83#9403direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29752
C83×#25422
C83×#18002
C83×#15492
C83×#13032
#940383