Finite Group Databasebeta

← C83×#11568 #35239392

Subgroups — C83×#11568 #35239392

Order 21248.

394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2546C211yesmaximal, characteristic
2C83×#1467C211yesmaximal, characteristic
3C83×#1461C211yesmaximal, characteristic
4C83×#1319C214yesmaximal
5C2×C4⋊Q8×C83C411yescharacteristic
6C2×C4⋊Q8×C83C412yes—
7C2×C4×Q8×C83C2211yescharacteristic
8#432×C83—21no—
9#431×C83—21no—
10#398×C83—21no—
11#398×C83—21no—
12#391×C83C2212yes—
13#389×C83—21no—
14#389×C83—21no—
15C4×C4⋊C4×C83C411yescharacteristic
16#324×C83—21no—
17#324×C83—21no—
18#324×C83C2212yes—
19#324×C83C2212yes—
20C22×Q8×C83C2×C412yes—
21C22×Q8×C83C2×C411yescharacteristic
22C4⋊Q8×C83—41no—
23C4⋊Q8×C83—41no—
24C4⋊Q8×C83—44no—
25C4×Q8×C83—41no—
26C4×Q8×C83—41no—
27C2×C4⋊C4×C83—21no—
28C2×C4⋊C4×C83—22no—
29C2×C4⋊C4×C83—22no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83D411yescharacteristic
33C2×C4⋊C4×C83D411yescharacteristic
34C2×C4⋊C4×C83C2311yescharacteristic
35C2×C42×C83C2×C411yescharacteristic
36C2×C42×C83C2×C412yes—
37C2×C42×C83D411yescharacteristic
38C2×C42×C83D411yescharacteristic
39C4⋊C8×C83—41no—
40C4⋊C8×C83—41no—
41C22⋊C8×C83—22no—
42C22⋊C8×C83—22no—
43#97×C83—41no—
44C4×C8×C83—41no—
45#95×C83—21no—
46#95×C83—22no—
47#95×C83—22no—
48C2×Q8×C83—22no—
49C2×Q8×C83—22no—
50C2×Q8×C83—24no—
51C2×Q8×C83—41no—
52C2×Q8×C83—42no—
53C2×Q8×C83—42no—
54C22×C4×C83—22no—
55C22×C4×C83—22no—
56C22×C4×C83C22⋊C411yescharacteristic
57C22×C4×C83C22⋊C411yescharacteristic
58C22×C4×C83C22⋊C411yescharacteristic
59C22×C4×C83C22⋊C411yescharacteristic
60C22×C4×C83C22×C411yescharacteristic
61C22×C4×C83C2×D411yescharacteristic
62C22×C4×C83C2×D411yescharacteristic
63C2×C8×C83—42no—
64C2×C8×C83—42no—
65C4⋊C4×C83—24no—
66C4⋊C4×C83—41no—
67C4⋊C4×C83—41no—
68C4⋊C4×C83—41no—
69C4⋊C4×C83—42no—
70C4⋊C4×C83—44no—
71C4⋊C4×C83—41no—
72C4⋊C4×C83—41no—
73C4⋊C4×C83—44no—
74C42×C83—21no—
75C42×C83—21no—
76C42×C83—21no—
77C42×C83—21no—
78C42×C83—21no—
79C42×C83—21no—
80C42×C83—42no—
81C23×C83C2×C22⋊C411yescharacteristic
82Q8×C83—44no—
83Q8×C83—84no—
84C2×C4×C83—21no—
85C2×C4×C83—21no—
86C2×C4×C83—21no—
87C2×C4×C83—21no—
88C2×C4×C83—22no—
89C2×C4×C83—24no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—42no—
97C2×C4×C83—42no—
98C2×C4×C83—41no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83—42no—
102C2×C4×C83—42no—
103C2×C4×C83—42no—
104C2×C4×C83#9911yescharacteristic
105C2×C4×C83#9911yescharacteristic
106C2×C4×C83#10012yes—
107C2×C4×C83#13112yes—
108C8×C83—82no—
109C8×C83—82no—
110C22×C83—21no—
111C22×C83—21no—
112C22×C83#40811yescharacteristic
113C22×C83C2×#9911yescharacteristic
114C22×C83C2×#10011yescharacteristic
115C4×C83—21no—
116C4×C83—22no—
117C4×C83—22no—
118C4×C83—44no—
119C4×C83—41no—
120C4×C83—41no—
121C4×C83—41no—
122C4×C83—41no—
123C4×C83—82no—
124C4×C83#35612yes—
125#11568C8311yesmaximal, characteristic, direct product factor, Sylow
126C2×C83—21no—
127C2×C83—21no—
128C2×C83#147111yescharacteristic
129C2×C83#212911yescharacteristic
130C2×C83C2×#35611yescharacteristic
131#2546C2×C8311yescharacteristic
132#1467C2×C8311yescharacteristic
133#1461C2×C8311yescharacteristic
134#1319C2×C8314yes—
135C83#1156811yescharacteristic, direct product factor, Sylow
136C2×C4⋊Q8C4×C8311yescharacteristic
137C2×C4⋊Q8C4×C8312yes—
138C2×C4×Q8C22×C8311yescharacteristic
139#432—21no—
140#431—21no—
141#398—21no—
142#398—21no—
143#391C22×C8312yes—
144#389—21no—
145#389—21no—
146C4×C4⋊C4C4×C8311yescharacteristic
147#324—21no—
148#324—21no—
149#324C22×C8312yes—
150#324C22×C8312yes—
151C22×Q8C2×C4×C8312yes—
152C22×Q8C2×C4×C8311yescharacteristic
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4⋊Q8—44no—
156C4×Q8—41no—
157C4×Q8—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4D4×C8311yescharacteristic
164C2×C4⋊C4D4×C8311yescharacteristic
165C2×C4⋊C4C23×C8311yescharacteristic
166C2×C42C2×C4×C8311yescharacteristic
167C2×C42C2×C4×C8312yes—
168C2×C42D4×C8311yescharacteristic
169C2×C42D4×C8311yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—41no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174#97—41no—
175C4×C8—41no—
176#95—21no—
177#95—22no—
178#95—22no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—24no—
182C2×Q8—41no—
183C2×Q8—42no—
184C2×Q8—42no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊C4×C8311yescharacteristic
188C22×C4C22⋊C4×C8311yescharacteristic
189C22×C4C22⋊C4×C8311yescharacteristic
190C22×C4C22⋊C4×C8311yescharacteristic
191C22×C4C22×C4×C8311yescharacteristic
192C22×C4C2×D4×C8311yescharacteristic
193C22×C4C2×D4×C8311yescharacteristic
194C2×C8—42no—
195C2×C8—42no—
196C4⋊C4—24no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—44no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—42no—
212C23C2×C22⋊C4×C8311yescharacteristic
213Q8—44no—
214Q8—84no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4#99×C8311yescharacteristic
236C2×C4#99×C8311yescharacteristic
237C2×C4#100×C8312yes—
238C2×C4#131×C8312yes—
239C8—82no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22#408×C8311yescharacteristic
244C22C2×#99×C8311yescharacteristic
245C22C2×#100×C8311yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4#356×C8312yes—
256C2—21no—
257C2—21no—
258C2C83×#147111yescharacteristic
259C2C83×#212911yescharacteristic
260C2C2×#356×C8311yescharacteristic
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
125. #11568C83direct (N × H)
135. C83#11568direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25462
C83×#14672
C83×#14612
C83×#13192
#1156883