Finite Group Databasebeta

← #14658541

Subgroups — #14658541

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#13068770C211yesmaximal, characteristic, complemented
2#13067265C212yesmaximal
3#13066511C212yesmaximal, complemented
4#13066445C211yesmaximal, characteristic, complemented
5C11×#1963C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C2×C11×#104—21no—
9C2×C11×#104—21no—
10C11×#376C2211yescharacteristic
11#10622538C2212yes—
12C2×C4⋊(C11⋊C8)—21no—
13C2×C4⋊(C11⋊C8)—21no—
14C2×C4⋊(C11⋊C8)C2212yes—
15#10622185—22no—
16#10622182—22no—
17C2×C11×#41—21no—
18C2×C11×M16—21no—
19C11×C4⋊Q8D411yescharacteristic
20C11×#127D411yescharacteristic
21C11×#124—21no—
22C11×#121—22no—
23C4×D4×C11—22no—
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11C2311yescharacteristic
27C22×C11⋊C8—22no—
28C11×C4⋊C8—22no—
29C11×#104—42no—
30C11×#104—42no—
31C11×#95—22no—
32C22⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—22no—
34C4⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—42no—
37C4⋊(C11⋊C8)—42no—
38C4×C11⋊C8—22no—
39#10627—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—22no—
47C2×D4×C11—41no—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—41no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4112yes—
53C11×M16—41no—
54C11×M16—41no—
55C2×C8×C11—41no—
56C11×C4⋊C4—22no—
57C11×C22⋊C4—42no—
58C42×C11—21no—
59C42×C11—21no—
60C42×C11D812yes—
61C42×C11SD1612yes—
62C42×C11C2×D411yescharacteristic
63C42×C11#4111yescharacteristic
64C42×C11#4112yes—
65C2×C11⋊C8—42no—
66C2×C11⋊C8—42no—
67C2×C11⋊C8—42no—
68C2×C11⋊C8—42no—
69#1963D1111yescharacteristic
70#1843—111no—
71#1540—112no—
72#1301—112no—
73#1274—111no—
74C23×C11—41no—
75C23×C11#12311yescharacteristic
76Q8×C11—41no—
77Q8×C11—41no—
78D4×C11—41no—
79D4×C11—41no—
80D4×C11—82no—
81D4×C11—81no—
82D4×C11—81no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—41no—
89C2×C4×C11—81no—
90C2×C4×C11—81no—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11#12312yes—
93C2×C4×C11#12411yescharacteristic
94C2×C4×C11#12612yes—
95C2×C4×C11C2×D811yescharacteristic
96C2×C4×C11C2×SD1611yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C11#13711yescharacteristic
99C8×C11—81no—
100C11⋊C8—82no—
101C11⋊C8—82no—
102#532C2×D1111yescharacteristic
103#431—112no—
104#423C2×D1111yescharacteristic
105C2×C4⋊C8—112no—
106C2×C4⋊C8—221no—
107C2×C4⋊C8—221no—
108C2×#104—21no—
109C2×#104—21no—
110#376C2×D1111yescharacteristic
111#332—222no—
112#331—222no—
113C22×C11—22no—
114C22×C11—81no—
115C22×C11—82no—
116C22×C11#39711yescharacteristic
117C22×C11#48011yescharacteristic
118C22×C11#48111yescharacteristic
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—42no—
122C4×C11—42no—
123C4×C11—81no—
124C4×C11#45911yescharacteristic
125C4×C11#46111yescharacteristic
126C4×C11#48611yescharacteristic
127C4×C11#48911yescharacteristic
128C2×#41—21no—
129C2×M16—21no—
130C22×C8—222no—
131C4⋊Q8D4411yescharacteristic
132#127D4411yescharacteristic
133#124—21no—
134#121—22no—
135C4×D4—22no—
136C2×C42C22⋊D1111yescharacteristic
137C2×C42C22⋊D1111yescharacteristic
138C2×C42C22×D1111yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—222no—
141C4⋊C8—222no—
142C4⋊C8—222no—
143C4⋊C8—442no—
144C4⋊C8—442no—
145#104—42no—
146#104—42no—
147C22⋊C8—222no—
148C4×C8—222no—
149#95—22no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11—161no—
153C2×C11#207111yescharacteristic
154C2×C11#208012yes—
155#41—41no—
156#41—41no—
157#41—41no—
158#41—41no—
159C2×Q8—21no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—41no—
166C22×C4#434112yes—
167C22×C4C2×C22⋊D1111yescharacteristic
168M16—41no—
169M16—41no—
170C2×C8—41no—
171C2×C8—442no—
172C2×C8—442no—
173C2×C8—442no—
174C2×C8—442no—
175C4⋊C4—22no—
176C22⋊C4—42no—
177C42—21no—
178C42—21no—
179C42#432312yes—
180C42#432412yes—
181C42C2×D4411yescharacteristic
182C42#433911yescharacteristic
183C42#434112yes—
184C11#1062711yescharacteristic, complemented, Sylow
185C23—41no—
186C23#6698811yescharacteristic
187Q8—41no—
188Q8—41no—
189D4—41no—
190D4—41no—
191D4—82no—
192D4—81no—
193D4—81no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4#6693212yes—
203C2×C4#6693912yes—
204C2×C4#6698311yescharacteristic
205C2×C4C2×#432311yescharacteristic
206C2×C4C2×#432411yescharacteristic
207C2×C4#6698911yescharacteristic
208C2×C4#6700211yescharacteristic
209C2×C4#6700411yescharacteristic
210C8—81no—
211C8—882no—
212C8—882no—
213C22—22no—
214C22—81no—
215C22—82no—
216C22#1062256611yescharacteristic
217C22#1062264611yescharacteristic
218C22#1062264711yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—81no—
224C4#1062262811yescharacteristic
225C4#1062263211yescharacteristic
226C4#1062266811yescharacteristic
227C4#1062268311yescharacteristic
228C2—21no—
229C2—21no—
230C2—161no—
231C2#1307001911yescharacteristic
232C2#1307006612yes—
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1963C2
socleC22×C11#397
prime radicalC11×#532C22
hypercenter#1963D11
hypocenterC11#10627
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #13068770C2semidirect
3. #13066511C2semidirect
4. #13066445C2semidirect
184. C11#10627semidirect

Maximal subgroups

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

subgroupindex
#130687702
#130672652
#130665112
#130664452
C11×#19632
#1062711