Finite Group Databasebeta

← #13069802

Subgroups — #13069802

Order 1408.

368 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 91 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×#121C211yesmaximal, characteristic
2C2×#66896C211yesmaximal, characteristic, complemented
3C2×#66896C211yesmaximal, characteristic, complemented
4#10622825C211yesmaximal, characteristic, complemented
5C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C2×#66872C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11—21no—
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C11×#121—22no—
12C11×#121—22no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4—21no—
15C2×C22⋊Dic11—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20#66896—22no—
21#66896—22no—
22C11⋊#95—21no—
23C22⋊(C11⋊C8)—22no—
24#66872—22no—
25C24×C11—21no—
26C24×C11D411yescharacteristic
27C2×D4×C11—24no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—42no—
34C2×D4×C11—42no—
35C2×D4×C11D412yes—
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×C11—21no—
43C22×C4×C11D411yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—21no—
46C22×Dic11—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4D412yes—
49C11×C22⋊C4—24no—
50C22⋊Dic11—42no—
51C4⋊Dic11—21no—
52C4⋊Dic11—21no—
53C4⋊Dic11—21no—
54C4⋊Dic11—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8D412yescomplemented
61#2034—111nomaximal, Sylow
62C23×C11—21no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11—22no—
69C23×C11—41no—
70C23×C11—41no—
71C23×C11—41no—
72C23×C11—41no—
73C23×C11—41no—
74C23×C11—41no—
75C23×C11SD1612yes—
76C23×C11C2×D411yescharacteristic
77D4×C11—22no—
78D4×C11—22no—
79D4×C11—48no—
80D4×C11—41no—
81D4×C11—41no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11#4111yescharacteristic
96C2×C4×C11#4111yescharacteristic
97C2×C4×C11#4111yescharacteristic
98C2×Dic11—41no—
99C2×Dic11—41no—
100C2×Dic11—41no—
101C2×Dic11—41no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C11⋊C8—22no—
105C11⋊C8—41no—
106C2×#121D1111yescharacteristic
107C2×#106—111no—
108C2×#102—111no—
109C2×#102—111no—
110C2×C22⋊C8—111no—
111#380—111no—
112#340—111no—
113C22×C11—22no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—81no—
124C22×C11—81no—
125C22×C11—81no—
126C22×C11—81no—
127C22×C11#12011yescharacteristic
128C22×C11#12111yescharacteristic
129C22×C11#12311yescharacteristic
130C22×C11C2×SD1611yescharacteristic
131C22×C11#13511yescharacteristic
132C22×C11AGL(1,ℤ/8)11yescharacteristic
133C22×C11AGL(1,ℤ/8)11yescharacteristic
134C4×C11—41no—
135C4×C11—42no—
136C4×C11#12111yescharacteristic
137C4×C11#12111yescharacteristic
138C4×C11#12311yescharacteristic
139C4×C11#12411yescharacteristic
140Dic11—81no—
141Dic11—81no—
142C22×D4—21no—
143C22×D4C2×D1111yescharacteristic
144C23×C4C2×D1111yescharacteristic
145C22×C8—111no—
146C22×C8—111no—
147#121—22no—
148#121—22no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C22⋊C4—21no—
153C2×C22⋊C4—221no—
154#106—222no—
155#102—222no—
156#102—222no—
157C22⋊C8—222no—
158#95—221no—
159C2×C11—42no—
160C2×C11—82no—
161C2×C11#39411yescharacteristic
162C2×C11#44911yescharacteristic
163C2×C11#45011yescharacteristic
164C2×C11#46511yescharacteristic
165C2×C11#46911yescharacteristic
166C2×C11#48111yescharacteristic
167C2×C11#48211yescharacteristic
168C24—21no—
169C24C22⋊D1111yescharacteristic
170C2×D4—24no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4C22⋊D1112yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—221no—
187C22×C4—221no—
188C22×C4C22⋊D1111yescharacteristic
189C22×C4C22×D1111yescharacteristic
190C2×C8—112no—
191C2×C8—221no—
192C2×C8—221no—
193C2×C8—221no—
194C2×C8—221no—
195C2×C8—221no—
196C4⋊C4—21no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4C22⋊D1112yes—
202C22⋊C4—24no—
203C22⋊C4—442no—
204C11#203411yescharacteristic, complemented, Sylow
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23#432412yes—
219C23C2×C22⋊D1111yescharacteristic
220D4—22no—
221D4—22no—
222D4—48no—
223D4—41no—
224D4—41no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4D4×D1111yescharacteristic
242C2×C4#434111yescharacteristic
243C2×C4#434111yescharacteristic
244C2×C4#434111yescharacteristic
245C2×C4C2×C22⋊D1111yescharacteristic
246C2×C4C2×C22⋊D1111yescharacteristic
247C8—222no—
248C8—441no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22#6698511yescharacteristic
264C22C2×#432411yescharacteristic
265C22#6698811yescharacteristic
266C22#6699211yescharacteristic
267C22#6700211yescharacteristic
268C22#6700311yescharacteristic
269C22#6700611yescharacteristic
270C4—42no—
271C4—41no—
272C4—881no—
273C4—881no—
274C4#6698811yescharacteristic
275C4#6698911yescharacteristic
276C4#6699111yescharacteristic
277C4#6699211yescharacteristic
278C2—42no—
279C2—82no—
280C2#1062264711yescharacteristic
281C2#1062264811yescharacteristic
282C2#1062265211yescharacteristic
283C2#1062265411yescharacteristic
284C2#1062283111yescharacteristic
285C2#1062283511yescharacteristic
286C2#1062285111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC2×C11×#121C2
socleC23×C11C2×D4
hypercenterC2×#121D11
hypocenterC11#2034
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66896C2semidirect
3. C2×#66896C2semidirect
4. #10622825C2semidirect
5. C2×C22⋊(C11⋊C8)C2semidirect
6. C2×#66872C2semidirect
7. #10622167C2semidirect
60. C2×C11⋊C8D4semidirect
204. C11#2034semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#668962
#106228252
C2×C22⋊(C11⋊C8)2
C2×#668722
#106221672
#203411