Finite Group Databasebeta

← C11×#2035 #13064873

Subgroups — C11×#2035 #13064873

Order 1408.

316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×C11×#106C211yesmaximal, characteristic, complemented
3C2×C11×#103C211yesmaximal, characteristic, complemented
4C2×C11×#103C211yesmaximal, characteristic, complemented
5C2×C11×C22⋊C8C211yesmaximal, characteristic
6C11×#380C211yesmaximal, characteristic
7C11×#340C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C23×C4×C11C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C11×C22⋊Q8—22no—
13C11×C22⋊Q8—22no—
14C2×C11×C4⋊C4—21no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4—21no—
19C2×C11×C22⋊C4—21no—
20C11×#106—22no—
21C11×#103—22no—
22C11×#103—22no—
23C11×C22⋊C8—22no—
24C11×#95—21no—
25C24×C11D411yescharacteristic
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11D412yes—
32C22×C4×C11—21no—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11—21no—
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11D411yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11D412yes—
50C11×C4⋊C4—24no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4D412yes—
57C11×C22⋊C4—24no—
58C11×C22⋊C4—42no—
59#2035C1111yesmaximal, characteristic, direct product factor, Sylow
60C23×C11—21no—
61C23×C11—21no—
62C23×C11—21no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11SD1612yes—
67C23×C11C2×D411yescharacteristic
68Q8×C11—22no—
69Q8×C11—22no—
70Q8×C11—41no—
71Q8×C11—41no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11#4111yescharacteristic
95C2×C4×C11#4111yescharacteristic
96C2×C4×C11#4111yescharacteristic
97C8×C11—22no—
98C8×C11—41no—
99C2×C22⋊Q8C2×C1111yescharacteristic
100C2×#106C2×C1111yescharacteristic, complemented
101C2×#103C2×C1111yescharacteristic, complemented
102C2×#103C2×C1111yescharacteristic, complemented
103C2×C22⋊C8C2×C1111yescharacteristic
104#380C2×C1111yescharacteristic
105#340C2×C1111yescharacteristic, complemented
106C22×C11—22no—
107C22×C11—22no—
108C22×C11—22no—
109C22×C11—41no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11#12011yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12311yescharacteristic
116C22×C11C2×SD1611yescharacteristic
117C22×C11#13511yescharacteristic
118C22×C11#13711yescharacteristic
119C22×C11#13711yescharacteristic
120C4×C11—41no—
121C4×C11—42no—
122C4×C11—42no—
123C4×C11—81no—
124C4×C11—81no—
125C4×C11#12111yescharacteristic
126C4×C11#12111yescharacteristic
127C4×C11#12311yescharacteristic
128C4×C11#12411yescharacteristic
129C22×Q8C22×C1111yescharacteristic
130C23×C4C22×C1111yescharacteristic
131C22×C8C22×C1111yescharacteristic
132C22×C8C22×C1111yescharacteristic
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C22×C1111yescharacteristic
137C2×C4⋊C4C22×C1111yescharacteristic
138C2×C4⋊C4C22×C1111yescharacteristic
139C2×C22⋊C4—21no—
140C2×C22⋊C4—21no—
141#106—22no—
142#103—22no—
143#103—22no—
144C22⋊C8—22no—
145#95—21no—
146C2×C11—42no—
147C2×C11#39411yescharacteristic
148C2×C11#44811yescharacteristic
149C2×C11#45211yescharacteristic
150C2×C11#46511yescharacteristic
151C2×C11#47011yescharacteristic
152C2×C11#48311yescharacteristic
153C2×C11#48511yescharacteristic
154C24D4×C1111yescharacteristic
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8D4×C1112yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4D4×C1111yescharacteristic
172C22×C4C23×C1111yescharacteristic
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8D4×C1112yes—
179C4⋊C4—24no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4D4×C1112yes—
186C22⋊C4—24no—
187C22⋊C4—42no—
188C11#203511yescharacteristic, direct product factor, Sylow
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23C11×SD1612yes—
196C23C2×D4×C1111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4C2×D4×C1111yescharacteristic
221C2×C4C2×D4×C1111yescharacteristic
222C2×C4C2×D4×C1111yescharacteristic
223C2×C4C11×#4111yescharacteristic
224C2×C4C11×#4111yescharacteristic
225C2×C4C11×#4111yescharacteristic
226C8—22no—
227C8—41no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22C11×#12011yescharacteristic
236C22C11×#12111yescharacteristic
237C22C11×#12311yescharacteristic
238C22C2×C11×SD1611yescharacteristic
239C22C11×#13511yescharacteristic
240C22C11×#13711yescharacteristic
241C22C11×#13711yescharacteristic
242C4—41no—
243C4—42no—
244C4—42no—
245C4—81no—
246C4—81no—
247C4C11×#12111yescharacteristic
248C4C11×#12111yescharacteristic
249C4C11×#12311yescharacteristic
250C4C11×#12411yescharacteristic
251C2—42no—
252C2C11×#39411yescharacteristic
253C2C11×#44811yescharacteristic
254C2C11×#45211yescharacteristic
255C2C11×#46511yescharacteristic
256C2C11×#47011yescharacteristic
257C2C11×#48311yescharacteristic
258C2C11×#48511yescharacteristic
subgroupG/H
center, socleC23×C11C2×D4
commutator, Frattini, cosocleC22×C4C23×C11
prime radicalC24×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#106C2semidirect
3. C2×C11×#103C2semidirect
4. C2×C11×#103C2semidirect
7. C11×#340C2semidirect
59. #2035C11direct (N × H)
100. C2×#106C2×C11semidirect
101. C2×#103C2×C11semidirect
102. C2×#103C2×C11semidirect
105. #340C2×C11semidirect
188. C11#2035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×C11×#1062
C2×C11×#1032
C2×C11×C22⋊C82
C11×#3802
C11×#3402
#203511