Finite Group Databasebeta

← #14673583

Subgroups — #14673583

Order 2816.

330 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#13070328C212yesmaximal
2#13068776C211yesmaximal, characteristic, complemented
3#13066726C212yesmaximal, complemented
4#13066698C211yesmaximal, characteristic, complemented
5C11×#1974C211yesmaximal, characteristic
6C2×C11×#135C2211yescharacteristic
7C2×C11×#108C2211yescharacteristic
8C2×C11×#104—21no—
9C11×#408—21no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66882—21no—
12C2×#66882C2212yes—
13C2×#66876C2212yes—
14#10622548—21no—
15#10622202—22no—
16#10622200—22no—
17C2×C11×#41—21no—
18C11×#135—22no—
19C11×#135—22no—
20C2×C11×Q16D411yescharacteristic
21C2×C11×SD16—21no—
22C2×C11×D8D411yescharacteristic
23C2×C11×M16—21no—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—42no—
29C11×#108—22no—
30C11×#104—42no—
31C11×C22⋊C8—42no—
32C4×C8×C11—22no—
33#66882—22no—
34#66882—22no—
35#66882—42no—
36#66876—22no—
37#66876—22no—
38C2×C11⋊C16—22no—
39#13484—111nomaximal, Sylow
40C11×#41—41no—
41C11×#41—41no—
42C11×#41—41no—
43C11×#41—41no—
44C2×Q8×C11—21no—
45C2×D4×C11—21no—
46C2×D4×C11—41no—
47C22×C4×C11—21no—
48C22×C4×C11—41no—
49C22×C4×C11C2×D411yescharacteristic
50C22×Dic11—42no—
51C11×Q16—22no—
52C11×SD16—42no—
53C11×D8—22no—
54C11×M16—41no—
55C11×M16—41no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11—41no—
59C2×C8×C11D812yes—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11#4111yescharacteristic
62C2×C8×C11#4112yes—
63C2×C8×C11#4112yes—
64C42×C11—21no—
65C42×C11SD1612yes—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—84no—
69C11⋊C16—42no—
70#2139—112no—
71#1974D1111yescharacteristic
72#1845—111no—
73#1387—112no—
74#1376—111no—
75C23×C11—41no—
76C23×C11AGL(1,ℤ/8)11yescharacteristic
77Q8×C11—41no—
78Q8×C11—41no—
79D4×C11—41no—
80D4×C11—41no—
81D4×C11—81no—
82D4×C11—81no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—41no—
87C2×C4×C11—81no—
88C2×C4×C11—81no—
89C2×C4×C11#12111yescharacteristic
90C2×C4×C11#12311yescharacteristic
91C2×C4×C11#12411yescharacteristic
92C2×C4×C11C2×D811yescharacteristic
93C2×C4×C11C2×SD1611yescharacteristic
94C2×C4×C11#13711yescharacteristic
95C2×Dic11—84no—
96C2×Dic11—82no—
97C8×C11—22no—
98C8×C11—81no—
99C8×C11#12312yes—
100C8×C11#12612yes—
101C2×#135C2×D1111yescharacteristic
102C2×M32—112no—
103C2×#108C2×D1111yescharacteristic
104C2×#107—112no—
105C2×#107—221no—
106C2×#104—21no—
107#408—21no—
108C2×C4×C8C2×D1111yescharacteristic
109#384—221no—
110#358—222no—
111#357—222no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11—81no—
115C22×C11—81no—
116C22×C11—81no—
117C22×C11#45911yescharacteristic
118C22×C11#48111yescharacteristic
119C22×C11#48911yescharacteristic
120C4×C11—24no—
121C4×C11—81no—
122C4×C11#39711yescharacteristic
123C4×C11#46111yescharacteristic
124C4×C11#48011yescharacteristic
125C4×C11#48611yescharacteristic
126Dic11—162no—
127C2×#41—21no—
128#135—22no—
129#135—22no—
130C2×Q16D4411yescharacteristic
131C2×SD16—21no—
132C2×D8D4411yescharacteristic
133C2×M16—21no—
134C22×C8C22⋊D1111yescharacteristic
135C22×C8C22×D1111yescharacteristic
136C2×C4⋊C4—222no—
137C2×C4⋊C4—442no—
138C2×C42C22⋊D1111yescharacteristic
139M32—222no—
140M32—222no—
141C2×C16—222no—
142#108—22no—
143#107—222no—
144#107—222no—
145#107—442no—
146#104—42no—
147C22⋊C8—42no—
148C4×C8—22no—
149C2×C11—21no—
150C2×C11—21no—
151C2×C11—161no—
152C2×C11#207111yescharacteristic
153C2×C11#221311yescharacteristic
154C2×C11#221411yescharacteristic
155#41—41no—
156#41—41no—
157#41—41no—
158#41—41no—
159C2×Q8—21no—
160C2×D4—21no—
161C2×D4—41no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—442no—
165C22×C4C2×C22⋊D1111yescharacteristic
166Q16—22no—
167SD16—42no—
168D8—22no—
169M16—41no—
170M16—41no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8#432312yes—
175C2×C8C2×D4411yescharacteristic
176C2×C8#433911yescharacteristic
177C2×C8#434112yes—
178C2×C8#434112yes—
179C4⋊C4—442no—
180C4⋊C4—442no—
181C4⋊C4—884no—
182C42—21no—
183C42#432412yes—
184C16—442no—
185C11#1348411yescharacteristic, complemented, Sylow
186C23—41no—
187C23#6700211yescharacteristic
188Q8—41no—
189Q8—41no—
190D4—41no—
191D4—41no—
192D4—81no—
193D4—81no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—884no—
201C2×C4—882no—
202C2×C4#6698311yescharacteristic
203C2×C4C2×#432311yescharacteristic
204C2×C4C2×#432411yescharacteristic
205C2×C4#6698811yescharacteristic
206C2×C4#6698911yescharacteristic
207C2×C4#6700411yescharacteristic
208C8—22no—
209C8—81no—
210C8#6693212yes—
211C8#6693912yes—
212C22—21no—
213C22—21no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22#1062262811yescharacteristic
218C22#1062264711yescharacteristic
219C22#1062266811yescharacteristic
220C4—24no—
221C4—81no—
222C4—1762no—
223C4#1062256611yescharacteristic
224C4#1062263211yescharacteristic
225C4#1062264611yescharacteristic
226C4#1062268311yescharacteristic
227C2—21no—
228C2—21no—
229C2—161no—
230C2#1307001911yescharacteristic
231C2#1307069211yescharacteristic
232C2#1307069711yescharacteristic
subgroupG/H
centerC22#10622628
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1974C2
socleC22×C11#459
prime radicalC2×C11×#135C22
hypercenter#1974D11
hypocenterC11#13484
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. #13068776C2semidirect
3. #13066726C2semidirect
4. #13066698C2semidirect
185. C11#13484semidirect

Maximal subgroups

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

subgroupindex
#130703282
#130687762
#130667262
#130666982
C11×#19742
#1348411