Finite Group Databasebeta

← #13070002

Subgroups — #13070002

Order 1408.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#102C211yesmaximal, characteristic
2#10622834C211yesmaximal, characteristic
3C2×#66896C211yesmaximal, characteristic
4C2×#66882C211yesmaximal, characteristic, complemented
5C2×Dic11⋊C8C211yesmaximal, characteristic, complemented
6#10622586C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C22⋊Dic11—21no—
12C2×C22⋊Dic11—21no—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4—21no—
16C2×C4×Dic11C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18C11×#102—22no—
19#66896—22no—
20C11⋊#95—21no—
21#66882—22no—
22Dic11⋊C8—22no—
23C24×C11—21no—
24C2×D4×C11—21no—
25C2×D4×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11Q812yes—
30C22×C4×C11—21no—
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—21no—
33C22×Dic11—21no—
34C22×Dic11D411yescharacteristic
35C22×Dic11D411yescharacteristic
36C2×C8×C11—21no—
37C2×C8×C11—21no—
38C2×C8×C11D412yes—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41C22⋊Dic11—42no—
42C22⋊Dic11—42no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4⋊Dic11—21no—
46C4⋊Dic11D412yes—
47Dic11⋊C4—42no—
48C4×Dic11—21no—
49C4×Dic11—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—21no—
52C2×C11⋊C8—21no—
53#2067—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—41no—
56C23×C11—41no—
57C23×C11—41no—
58C23×C11—41no—
59C23×C11—41no—
60C23×C11—41no—
61C23×C11C2×D411yescharacteristic
62D4×C11—22no—
63D4×C11—22no—
64D4×C11—41no—
65D4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×Q811yescharacteristic
72C2×C4×C11#4111yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—21no—
78C2×Dic11—22no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83C2×Dic11—41no—
84C2×Dic11—41no—
85C2×Dic11—41no—
86C2×Dic11D812yes—
87C8×C11—22no—
88C11⋊C8—41no—
89C2×#107—111no—
90C2×C4⋊C8—111no—
91C2×#102—111no—
92C2×#102D1111yescharacteristic
93#390—111no—
94#389—111no—
95#340—111no—
96C22×C11—42no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11—81no—
100C22×C11—81no—
101C22×C11—81no—
102C22×C11—81no—
103C22×C11#12111yescharacteristic
104C22×C11#12111yescharacteristic
105C22×C11C22⋊Q811yescharacteristic
106C22×C11C2×D811yescharacteristic
107C22×C11#13511yescharacteristic
108C22×C11AGL(1,ℤ/8)11yescharacteristic
109C22×C11#13711yescharacteristic
110C4×C11—81no—
111C4×C11#12111yescharacteristic
112C4×C11C22⋊Q811yescharacteristic
113C4×C11C22⋊Q811yescharacteristic
114C4×C11#12611yescharacteristic
115Dic11—22no—
116Dic11—42no—
117Dic11—41no—
118Dic11—81no—
119C22×D4C2×D1111yescharacteristic
120C22×C8—111no—
121C22×C8C2×D1111yescharacteristic
122C2×C4⋊C4—111no—
123C2×C4⋊C4—111no—
124C2×C4⋊C4—221no—
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4—221no—
127C2×C22⋊C4—221no—
128C2×C42—111no—
129#107—222no—
130C4⋊C8—222no—
131#102—22no—
132#102—222no—
133#95—221no—
134C2×C11—82no—
135C2×C11#39611yescharacteristic
136C2×C11#45911yescharacteristic
137C2×C11#46411yescharacteristic
138C2×C11#46611yescharacteristic
139C2×C11#46811yescharacteristic
140C2×C11#47411yescharacteristic
141C2×C11#47811yescharacteristic
142C24—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4Dic2212yes—
149C22×C4—21no—
150C22×C4—111no—
151C22×C4—111no—
152C22×C4—221no—
153C22×C4—221no—
154C22×C4C22×D1111yescharacteristic
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—221no—
158C2×C8—221no—
159C2×C8—221no—
160C2×C8C22⋊D1112yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—112no—
164C4⋊C4—221no—
165C4⋊C4—221no—
166C4⋊C4—221no—
167C4⋊C4—442no—
168C22⋊C4—442no—
169C22⋊C4—442no—
170C42—221no—
171C42—221no—
172C11#206711yescharacteristic, complemented, Sylow
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23D4×D1111yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—112no—
189C2×C4—221no—
190C2×C4—221no—
191C2×C4—222no—
192C2×C4—221no—
193C2×C4—221no—
194C2×C4—221no—
195C2×C4—441no—
196C2×C4—441no—
197C2×C4—441no—
198C2×C4—441no—
199C2×C4—441no—
200C2×C4C2×Dic2211yescharacteristic
201C2×C4#433911yescharacteristic
202C2×C4D4×D1111yescharacteristic
203C2×C4#434111yescharacteristic
204C2×C4#434111yescharacteristic
205C2×C4C2×C22⋊D1111yescharacteristic
206C8—22no—
207C8—441no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#6693111yescharacteristic
216C22#6693711yescharacteristic
217C22D8×D1111yescharacteristic
218C22#6696511yescharacteristic
219C22#6696711yescharacteristic
220C22#6696811yescharacteristic
221C22#6699111yescharacteristic
222C4—81no—
223C4—222no—
224C4—441no—
225C4—442no—
226C4—881no—
227C4#6693111yescharacteristic
228C4#6693211yescharacteristic
229C4#6697711yescharacteristic
230C4#6699211yescharacteristic
231C2—82no—
232C2#1062237211yescharacteristic
233C2#1062237911yescharacteristic
234C2#1062238011yescharacteristic
235C2#1062239911yescharacteristic
236C2#1062256111yescharacteristic
237C2#1062277011yescharacteristic
238C2#1062278711yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
hypercenterC2×#102D11
hypocenterC11#2067
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
4. C2×#66882C2semidirect
5. C2×Dic11⋊C8C2semidirect
6. #10622586C2semidirect
7. #10622167C2semidirect
172. C11#2067semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1022
#106228342
C2×#668962
C2×#668822
C2×Dic11⋊C82
#106225862
#106221672
#206711