Finite Group Databasebeta

← #14673588

Subgroups — #14673588

Order 2816.

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

normal subgroups only

This group has 314 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#13068780C211yesmaximal, 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×#66882C2212yes—
12C2×#66881—21no—
13C2×#66876C2212yes—
14#10622549—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—
28C11×#108—22no—
29C11×#104—42no—
30C11×C22⋊C8—42no—
31C4×C8×C11—22no—
32C11⋊#95—42no—
33#66882—22no—
34#66882—22no—
35#66881—42no—
36#66876—22no—
37#66876—22no—
38C2×C11⋊C16—22no—
39#13485—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—
68C11⋊C16—42no—
69#2139—112no—
70#1974D1111yescharacteristic
71#1846—111no—
72#1387—112no—
73#1376—111no—
74C23×C11—41no—
75C23×C11AGL(1,ℤ/8)11yescharacteristic
76Q8×C11—41no—
77Q8×C11—41no—
78D4×C11—41no—
79D4×C11—41no—
80D4×C11—81no—
81D4×C11—81no—
82C2×C4×C11—22no—
83C2×C4×C11—42no—
84C2×C4×C11—41no—
85C2×C4×C11—81no—
86C2×C4×C11—81no—
87C2×C4×C11#12111yescharacteristic
88C2×C4×C11#12311yescharacteristic
89C2×C4×C11#12411yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11C2×SD1611yescharacteristic
92C2×C4×C11#13711yescharacteristic
93C2×Dic11—84no—
94C2×Dic11—82no—
95C8×C11—22no—
96C8×C11—81no—
97C8×C11#12312yes—
98C8×C11#12612yes—
99C2×#135C2×D1111yescharacteristic
100C2×M32—112no—
101C2×#108C2×D1111yescharacteristic
102C2×#107—112no—
103C2×#106—221no—
104C2×#104—21no—
105#408—21no—
106C2×C4×C8C2×D1111yescharacteristic
107#382—221no—
108#358—222no—
109#357—222no—
110C22×C11—22no—
111C22×C11—81no—
112C22×C11—82no—
113C22×C11#45911yescharacteristic
114C22×C11#48111yescharacteristic
115C22×C11#48911yescharacteristic
116C4×C11—42no—
117C4×C11—81no—
118C4×C11#39711yescharacteristic
119C4×C11#46111yescharacteristic
120C4×C11#48011yescharacteristic
121C4×C11#48611yescharacteristic
122Dic11—162no—
123C2×#41—21no—
124#135—22no—
125#135—22no—
126C2×Q16D4411yescharacteristic
127C2×SD16—21no—
128C2×D8D4411yescharacteristic
129C2×M16—21no—
130C22×C8C22⋊D1111yescharacteristic
131C22×C8C22×D1111yescharacteristic
132C2×C4⋊C4—222no—
133C2×C42C22⋊D1111yescharacteristic
134M32—222no—
135M32—222no—
136C2×C16—222no—
137#108—22no—
138#107—222no—
139#107—222no—
140#106—442no—
141#104—42no—
142C22⋊C8—42no—
143C4×C8—22no—
144#95—442no—
145C2×C11—21no—
146C2×C11—21no—
147C2×C11—161no—
148C2×C11#207111yescharacteristic
149C2×C11#221212yes—
150#41—41no—
151#41—41no—
152#41—41no—
153#41—41no—
154C2×Q8—21no—
155C2×D4—21no—
156C2×D4—41no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—442no—
160C22×C4C2×C22⋊D1111yescharacteristic
161Q16—22no—
162SD16—42no—
163D8—22no—
164M16—41no—
165M16—41no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8#432312yes—
170C2×C8C2×D4411yescharacteristic
171C2×C8#433911yescharacteristic
172C2×C8#434112yes—
173C2×C8#434112yes—
174C4⋊C4—442no—
175C4⋊C4—442no—
176C42—21no—
177C42#432412yes—
178C16—442no—
179C11#1348511yescharacteristic, complemented, Sylow
180C23—41no—
181C23#6700211yescharacteristic
182Q8—41no—
183Q8—41no—
184D4—41no—
185D4—41no—
186D4—81no—
187D4—81no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—884no—
194C2×C4—882no—
195C2×C4#6698311yescharacteristic
196C2×C4C2×#432311yescharacteristic
197C2×C4C2×#432411yescharacteristic
198C2×C4#6698811yescharacteristic
199C2×C4#6698911yescharacteristic
200C2×C4#6700411yescharacteristic
201C8—22no—
202C8—81no—
203C8#6693212yes—
204C8#6693912yes—
205C22—22no—
206C22—82no—
207C22—81no—
208C22#1062262811yescharacteristic
209C22#1062264711yescharacteristic
210C22#1062266811yescharacteristic
211C4—42no—
212C4—81no—
213C4—1762no—
214C4#1062256611yescharacteristic
215C4#1062263211yescharacteristic
216C4#1062264611yescharacteristic
217C4#1062268311yescharacteristic
218C2—21no—
219C2—21no—
220C2—161no—
221C2#1307001911yescharacteristic
222C2#1307068512yes—
subgroupG/H
centerC22#10622628
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1974C2
socleC22×C11#459
prime radicalC2×C11×#135C22
hypercenter#1974D11
hypocenterC11#13485
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. #13068780C2semidirect
3. #13066726C2semidirect
4. #13066698C2semidirect
179. C11#13485semidirect

Maximal subgroups

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

subgroupindex
#130703282
#130687802
#130667262
#130666982
C11×#19742
#1348511