Finite Group Databasebeta

← #13069925

Subgroups — #13069925

Order 1408.

360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×#4323C211yesmaximal, characteristic
2C2×C11×#102C211yesmaximal, characteristic, complemented
3#10622834C211yesmaximal, characteristic, complemented
4C2×#66885C211yesmaximal, characteristic, complemented
5C2×Dic11⋊C8C211yesmaximal, characteristic, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C22⋊Dic11—21no—
13C2×C22⋊Dic11—21no—
14C2×#4323—22no—
15C2×#4323—22no—
16C2×#4323—22no—
17C2×(C2×D11)⋊C4—21no—
18C2×(C2×D11)⋊C4—21no—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4×Dic11C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22C11×#102—22no—
23#66885—22no—
24Dic11⋊C8—22no—
25C24×C11—21no—
26C23×D11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11D412yes—
33C22×C4×C11—21no—
34C22×C4×C11C2311yescharacteristic
35C22×Dic11—21no—
36C22×Dic11D411yescharacteristic
37C22×Dic11D411yescharacteristic
38C2×D44—21no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44D412yes—
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C22⋊Dic11—42no—
50C22⋊Dic11—42no—
51#4323—28no—
52(C2×D11)⋊C4—42no—
53(C2×D11)⋊C4—42no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56C4×Dic11—21no—
57C4×Dic11—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8D412yes—
61#2054—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—41no—
64C23×C11—41no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11—41no—
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11—41no—
72C22×D11—41no—
73C22×D11—41no—
74C22×D11—41no—
75C22×D11—41no—
76C22×D11—41no—
77D4×C11—22no—
78D4×C11—22no—
79D4×C11—41no—
80D4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11#4111yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—41no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98C2×Dic11D812yescomplemented
99D44—22no—
100D44—22no—
101D44—41no—
102D44—41no—
103C8×C11—41no—
104C11⋊C8—22no—
105C22×D8—111no—
106C2×C4⋊C8—111no—
107C2×#102—111no—
108C2×#102D1111yescharacteristic, complemented
109#390—111no—
110#390—111no—
111#340—111no—
112C22×C11—42no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—81no—
116C22×C11—81no—
117C22×C11—81no—
118C22×C11—81no—
119C22×C11#12111yescharacteristic
120C22×C11#12111yescharacteristic
121C22×C11#12111yescharacteristic
122C22×C11C2×D811yescharacteristic
123C22×C11#13511yescharacteristic
124C22×C11AGL(1,ℤ/8)11yescharacteristic
125C22×C11AGL(1,ℤ/8)11yescharacteristic
126C2×D11—42no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—81no—
130C2×D11—81no—
131C2×D11—81no—
132C2×D11—81no—
133C4×C11—81no—
134C4×C11#12011yescharacteristic
135C4×C11#12311yescharacteristic
136C4×C11#12311yescharacteristic
137C4×C11#12411yescharacteristic
138Dic11—22no—
139Dic11—41no—
140Dic11—81no—
141C22×D4—111no—
142C22×D4C2×D1111yescharacteristic
143C2×D8—222no—
144C2×D8—222no—
145C2×D8—222no—
146C22×C8—111no—
147C22×C8C2×D1111yescharacteristic
148C2×C4⋊C4—111no—
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C22⋊C4—221no—
151C2×C22⋊C4—221no—
152C2×C22⋊C4—221no—
153C2×C22⋊C4—221no—
154C2×C42—111no—
155C4⋊C8—222no—
156#102—22no—
157#102—222no—
158C2×C11—82no—
159C2×C11#39411yescharacteristic
160C2×C11#45911yescharacteristic
161C2×C11#45911yescharacteristic
162C2×C11#46311yescharacteristic
163C2×C11#46311yescharacteristic
164C2×C11#46611yescharacteristic
165C2×C11#46911yescharacteristic
166D11—82no—
167C24—21no—
168C24—221no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—112no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—221no—
178C2×D4—221no—
179C2×D4—221no—
180C2×D4C22⋊D1112yes—
181C22×C4—21no—
182C22×C4—111no—
183C22×C4—111no—
184C22×C4—221no—
185C22×C4C22×D1111yescharacteristic
186D8—228no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—112no—
191C2×C8—221no—
192C2×C8—221no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C22⋊C4—442no—
198C22⋊C4—442no—
199C22⋊C4—442no—
200C22⋊C4—442no—
201C42—221no—
202C42—221no—
203C11#205411yescharacteristic, complemented, Sylow
204C23—22no—
205C23—41no—
206C23—41no—
207C23—41no—
208C23—41no—
209C23—41no—
210C23—41no—
211C23—222no—
212C23—441no—
213C23—441no—
214C23—441no—
215C23—441no—
216C23—441no—
217C23—441no—
218C23D4×D1111yescharacteristic
219D4—22no—
220D4—22no—
221D4—41no—
222D4—41no—
223D4—222no—
224D4—222no—
225D4—441no—
226D4—441no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—112no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4#433911yescharacteristic
240C2×C4#433911yescharacteristic
241C2×C4D4×D1111yescharacteristic
242C2×C4D4×D1111yescharacteristic
243C2×C4#434111yescharacteristic
244C2×C4C2×C22⋊D1111yescharacteristic
245C8—41no—
246C8—222no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—81no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22—442no—
255C22—442no—
256C22—442no—
257C22—881no—
258C22—881no—
259C22—881no—
260C22—881no—
261C22#6693711yescharacteristic
262C22#6693711yescharacteristic
263C22D8×D1111yescharacteristic
264C22#6696411yescharacteristic
265C22#6696711yescharacteristic
266C22#6696911yescharacteristic
267C22#6699211yescharacteristic
268C4—81no—
269C4—222no—
270C4—441no—
271C4—881no—
272C4#6693611yescharacteristic
273C4#6693811yescharacteristic
274C4#6698211yescharacteristic
275C4#6699011yescharacteristic
276C2—82no—
277C2—882no—
278C2#1062238811yescharacteristic
279C2#1062239511yescharacteristic
280C2#1062239911yescharacteristic
281C2#1062240011yescharacteristic
282C2#1062257211yescharacteristic
283C2#1062276311yescharacteristic
284C2#1062277811yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
prime radicalC22×#4323C2
hypercenterC2×#102D11
hypocenterC11#2054
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
2. C2×C11×#102C2semidirect
3. #10622834C2semidirect
4. C2×#66885C2semidirect
5. C2×Dic11⋊C8C2semidirect
6. #10622601C2semidirect
7. #10622167C2semidirect
98. C2×Dic11D8semidirect
108. C2×#102D11semidirect
203. C11#2054semidirect

Maximal subgroups

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

subgroupindex
C22×#43232
C2×C11×#1022
#106228342
C2×#668852
C2×Dic11⋊C82
#106226012
#106221672
#205411