Finite Group Databasebeta

← C22×C11×#356 #14610557

Subgroups — C22×C11×#356 #14610557

Order 2816.

1254 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 382 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
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C22×C11×#101C212yesmaximal
3C2×C11×#356C2112yesmaximal, direct product factor
4C23×Q8×C11C411yescharacteristic
5C23×Q8×C11C2211yescharacteristic
6C22×C11×M16—22no—
7C2×C11×C4⋊Q8—26no—
8C2×C11×C4⋊Q8C416yes—
9C2×C11×C4⋊Q8C2216yes—
10C22×C11×C4⋊C4—22no—
11C22×C42×C11C411yescharacteristic
12C2×C11×#101—26no—
13C2×C11×#101C22112yes—
14C11×#356C22116yesdirect product factor
15C22×Q8×C11—23no—
16C22×Q8×C11—43no—
17C22×Q8×C11—41no—
18C22×Q8×C11—43no—
19C22×Q8×C11—41no—
20C22×Q8×C11C2×C416yes—
21C22×Q8×C11C2×C413yes—
22C22×Q8×C11D416yes—
23C22×Q8×C11C2313yes—
24C23×C4×C11—21no—
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D412yes—
28C2×C11×M16—212no—
29C2×C11×M16—46no—
30C22×C8×C11—42no—
31C11×C4⋊Q8—212no—
32C11×C4⋊Q8—212no—
33C11×C4⋊Q8C2×C4112yes—
34C11×C4⋊Q8C2314yes—
35C2×C11×C4⋊C4—212no—
36C2×C11×C4⋊C4—212no—
37C2×C42×C11—23no—
38C2×C42×C11C2×C416yes—
39C11×#101—212no—
40C11×#101C2318yes—
41C22×#356C1111yesmaximal, characteristic, direct product factor, Sylow
42C24×C11C22⋊C411yescharacteristic
43C2×Q8×C11—26no—
44C2×Q8×C11—43no—
45C2×Q8×C11—43no—
46C2×Q8×C11—46no—
47C2×Q8×C11—46no—
48C2×Q8×C11—43no—
49C2×Q8×C11—43no—
50C2×Q8×C11—46no—
51C2×Q8×C11—46no—
52C2×Q8×C11—46no—
53C2×Q8×C11—46no—
54C2×Q8×C11C22⋊C416yes—
55C2×Q8×C11C22×C414yes—
56C2×Q8×C11C22×C413yes—
57C2×Q8×C11C2×D416yes—
58C2×Q8×C11C2411yescharacteristic
59C22×C4×C11—28no—
60C22×C4×C11—26no—
61C22×C4×C11—23no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—26no—
65C22×C4×C11—26no—
66C22×C4×C11—43no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C413yes—
69C22×C4×C11C22⋊C416yes—
70C22×C4×C11C22×C413yes—
71C22×C4×C11C2×D416yes—
72C11×M16—28no—
73C11×M16—412no—
74C2×C8×C11—412no—
75C11×C4⋊C4—224no—
76C11×C4⋊C4—28no—
77C42×C11—26no—
78C42×C11C22×C414yes—
79C22×C4⋊Q8C2×C1111yescharacteristic
80C22×#101C2×C1112yes—
81C2×#356C2×C11112yesdirect product factor
82C23×C11—24no—
83C23×C11#9913yes—
84C23×C11#9911yescharacteristic
85C23×C11C2×C22⋊C413yes—
86Q8×C11—46no—
87Q8×C11—43no—
88Q8×C11—46no—
89Q8×C11—41no—
90Q8×C11—44no—
91Q8×C11—412no—
92C2×C4×C11—224no—
93C2×C4×C11—24no—
94C2×C4×C11—26no—
95C2×C4×C11—26no—
96C2×C4×C11—26no—
97C2×C4×C11—26no—
98C2×C4×C11—23no—
99C2×C4×C11—23no—
100C2×C4×C11—23no—
101C2×C4×C11—23no—
102C2×C4×C11—24no—
103C2×C4×C11—46no—
104C2×C4×C11—46no—
105C2×C4×C11C2×C22⋊C413yes—
106C2×C4×C11C2×C22⋊C416yes—
107C2×C4×C11C23×C411yescharacteristic
108C2×C4×C11C22×D412yes—
109C8×C11—48no—
110C23×Q8C4×C1111yescharacteristic
111C23×Q8C22×C1111yescharacteristic
112C22×M16—22no—
113C2×C4⋊Q8—26no—
114C2×C4⋊Q8C4×C1116yes—
115C2×C4⋊Q8C22×C1116yes—
116C22×C4⋊C4—22no—
117C22×C42C4×C1111yescharacteristic
118C2×#101—26no—
119C2×#101C22×C11112yes—
120#356C22×C11116yesdirect product factor
121C22×C11—26no—
122C22×C11—26no—
123C22×C11#35614yesdirect product factor
124C22×C11C2×#9913yes—
125C22×C11C2×#9913yes—
126C22×C11C22×C22⋊C411yescharacteristic
127C4×C11—28no—
128C4×C11—26no—
129C4×C11—23no—
130C4×C11—21no—
131C4×C11—22no—
132C4×C11—44no—
133C22×Q8—23no—
134C22×Q8—41no—
135C22×Q8—43no—
136C22×Q8—43no—
137C22×Q8—41no—
138C22×Q8C2×C4×C1116yes—
139C22×Q8C2×C4×C1113yes—
140C22×Q8D4×C1116yes—
141C22×Q8C23×C1113yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4C2×C4×C1111yescharacteristic
145C23×C4D4×C1112yes—
146C2×M16—212no—
147C2×M16—46no—
148C22×C8—42no—
149C4⋊Q8—212no—
150C4⋊Q8—212no—
151C4⋊Q8C2×C4×C11112yes—
152C4⋊Q8C23×C1114yes—
153C2×C4⋊C4—212no—
154C2×C4⋊C4—212no—
155C2×C42—23no—
156C2×C42C2×C4×C1116yes—
157#101—212no—
158#101C23×C1118yes—
159C2×C11—21no—
160C2×C11—23no—
161C2×C11C2×#35616yesdirect product factor
162C2×C11C22×#9911yescharacteristic
163C24C11×C22⋊C411yescharacteristic
164C2×Q8—26no—
165C2×Q8—43no—
166C2×Q8—43no—
167C2×Q8—46no—
168C2×Q8—46no—
169C2×Q8—43no—
170C2×Q8—43no—
171C2×Q8—46no—
172C2×Q8—46no—
173C2×Q8—46no—
174C2×Q8—46no—
175C2×Q8C11×C22⋊C416yes—
176C2×Q8C22×C4×C1114yes—
177C2×Q8C22×C4×C1113yes—
178C2×Q8C2×D4×C1116yes—
179C2×Q8C24×C1111yescharacteristic
180C22×C4—28no—
181C22×C4—22no—
182C22×C4—26no—
183C22×C4—23no—
184C22×C4—21no—
185C22×C4—26no—
186C22×C4—26no—
187C22×C4—43no—
188C22×C4—41no—
189C22×C4C11×C22⋊C413yes—
190C22×C4C11×C22⋊C416yes—
191C22×C4C22×C4×C1113yes—
192C22×C4C2×D4×C1116yes—
193M16—28no—
194M16—412no—
195C2×C8—412no—
196C4⋊C4—224no—
197C4⋊C4—28no—
198C42—26no—
199C42C22×C4×C1114yes—
200C11C22×#35611yescharacteristic, direct product factor, Sylow
201C23—24no—
202C23C11×#9913yes—
203C23C11×#9911yescharacteristic
204C23C2×C11×C22⋊C413yes—
205Q8—46no—
206Q8—43no—
207Q8—46no—
208Q8—41no—
209Q8—44no—
210Q8—412no—
211C2×C4—224no—
212C2×C4—24no—
213C2×C4—26no—
214C2×C4—26no—
215C2×C4—26no—
216C2×C4—26no—
217C2×C4—23no—
218C2×C4—23no—
219C2×C4—23no—
220C2×C4—23no—
221C2×C4—24no—
222C2×C4—46no—
223C2×C4—46no—
224C2×C4C2×C11×C22⋊C413yes—
225C2×C4C2×C11×C22⋊C416yes—
226C2×C4C23×C4×C1111yescharacteristic
227C2×C4C22×D4×C1112yes—
228C8—48no—
229C22—26no—
230C22—26no—
231C22C11×#35614yesdirect product factor
232C22C2×C11×#9913yes—
233C22C2×C11×#9913yes—
234C22C22×C11×C22⋊C411yescharacteristic
235C4—28no—
236C4—22no—
237C4—23no—
238C4—26no—
239C4—21no—
240C4—44no—
241C2—21no—
242C2—23no—
243C2C2×C11×#35616yesdirect product factor
244C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC23×C11#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C11 ◁ C23×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#356C2direct (N × H)
14. C11×#356C22direct (N × H)
41. C22×#356C11direct (N × H)
81. C2×#356C2×C11direct (N × H)
120. #356C22×C11direct (N × H)
123. C22×C11#356direct (N × H)
161. C2×C11C2×#356direct (N × H)
200. C11C22×#356direct (N × H)
231. C22C11×#356direct (N × H)
243. C2C2×C11×#356direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×#1012
C2×C11×#3562
C22×#35611