Finite Group Databasebeta

← #13069801

Subgroups — #13069801

Order 1408.

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

normal subgroups only

This group has 368 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
1C2×#66948C211yesmaximal, characteristic
2C2×#66885C211yesmaximal, characteristic, complemented
3C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
4#10622600C211yesmaximal, characteristic, complemented
5C2×#66873C211yesmaximal, characteristic, complemented
6C2×#66871C211yesmaximal, characteristic, complemented
7C11×#340C211yesmaximal, characteristic, complemented
8C22×D44—21no—
9C22×D44C2211yescharacteristic
10C22×C4×D11C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×(C2×D11)⋊C4—21no—
15C2×(C2×D11)⋊C4—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18#66948—22no—
19#66948—22no—
20C11⋊#95—21no—
21#66885—22no—
22(C2×D11)⋊C8—22no—
23#66873—22no—
24#66871—22no—
25C23×D11—21no—
26C23×D11D411yescharacteristic
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11C2311yescharacteristic
30C22×Dic11—21no—
31C22×Dic11D411yescharacteristic
32C2×D44—24no—
33C2×D44—21no—
34C2×D44—21no—
35C2×D44—21no—
36C2×D44—21no—
37C2×D44—21no—
38C2×D44—42no—
39C2×D44—42no—
40C2×D44D412yes—
41C2×C4×D11—21no—
42C2×C4×D11—21no—
43C2×C4×D11—21no—
44C2×C4×D11—21no—
45C2×C4×D11—21no—
46C2×C4×D11—21no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4D412yes—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—42no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8D412yescomplemented
61#2033—111nomaximal, Sylow
62C23×C11C2×D411yescharacteristic
63C22×D11—21no—
64C22×D11—21no—
65C22×D11—21no—
66C22×D11—21no—
67C22×D11—21no—
68C22×D11—21no—
69C22×D11—22no—
70C22×D11—41no—
71C22×D11—41no—
72C22×D11—41no—
73C22×D11—41no—
74C22×D11—41no—
75C22×D11—41no—
76C22×D11D812yes—
77C2×C4×C11—22no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11#4111yescharacteristic
87C2×C4×C11#4111yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95D44—22no—
96D44—22no—
97D44—48no—
98D44—41no—
99D44—41no—
100C4×D11—41no—
101C4×D11—41no—
102C4×D11—41no—
103C4×D11—41no—
104C8×C11—41no—
105C11⋊C8—22no—
106C2×#121—111no—
107C2×#107—111no—
108C2×#102—111no—
109C2×#102—111no—
110C2×C22⋊C8—111no—
111#380—111no—
112#340D1111yescharacteristic, complemented
113C22×C11#12011yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12311yescharacteristic
116C22×C11C2×D811yescharacteristic
117C22×C11#13511yescharacteristic
118C22×C11AGL(1,ℤ/8)11yescharacteristic
119C22×C11#13711yescharacteristic
120C2×D11—22no—
121C2×D11—22no—
122C2×D11—22no—
123C2×D11—41no—
124C2×D11—41no—
125C2×D11—41no—
126C2×D11—41no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—81no—
131C2×D11—81no—
132C2×D11—81no—
133C2×D11—81no—
134C4×C11—42no—
135C4×C11—81no—
136C4×C11#12111yescharacteristic
137C4×C11#12111yescharacteristic
138C4×C11#12311yescharacteristic
139C4×C11#12411yescharacteristic
140Dic11—41no—
141Dic11—81no—
142C22×D4—111no—
143C22×D4—221no—
144C23×C4—111no—
145C22×C8—111no—
146C22×C8C2×D1111yescharacteristic
147#121—222no—
148#121—222no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4C2×D1111yescharacteristic
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C22⋊C4—221no—
153C2×C22⋊C4—221no—
154#107—222no—
155#102—222no—
156#102—222no—
157C22⋊C8—222no—
158#95—221no—
159C2×C11#39411yescharacteristic
160C2×C11#44711yescharacteristic
161C2×C11#45211yescharacteristic
162C2×C11#46611yescharacteristic
163C2×C11#46811yescharacteristic
164C2×C11#48011yescharacteristic
165C2×C11#48211yescharacteristic
166D11—42no—
167D11—82no—
168C24—111no—
169C24—221no—
170C2×D4—112no—
171C2×D4—224no—
172C2×D4—221no—
173C2×D4—221no—
174C2×D4—221no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—442no—
178C2×D4—442no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—111no—
182C22×C4—221no—
183C22×C4—221no—
184C22×C4—221no—
185C22×C4—221no—
186C22×C4—221no—
187C22×C4—221no—
188C22×C4—221no—
189C22×C4C22×D1111yescharacteristic
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—112no—
194C2×C8—221no—
195C2×C8—221no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4D4412yes—
202C22⋊C4—224no—
203C22⋊C4—442no—
204C11#203311yescharacteristic, complemented, Sylow
205C23—112no—
206C23—221no—
207C23—221no—
208C23—221no—
209C23—221no—
210C23—221no—
211C23—221no—
212C23—222no—
213C23—441no—
214C23—441no—
215C23—441no—
216C23—441no—
217C23—441no—
218C23—441no—
219C23D4×D1111yescharacteristic
220D4—222no—
221D4—222no—
222D4—448no—
223D4—441no—
224D4—441no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—441no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4C2×D4411yescharacteristic
242C2×C4#433911yescharacteristic
243C2×C4#433911yescharacteristic
244C2×C4D4×D1111yescharacteristic
245C2×C4D4×D1111yescharacteristic
246C2×C4#434311yescharacteristic
247C8—41no—
248C8—222no—
249C22—222no—
250C22—222no—
251C22—222no—
252C22—441no—
253C22—441no—
254C22—441no—
255C22—441no—
256C22—442no—
257C22—442no—
258C22—442no—
259C22—881no—
260C22—881no—
261C22—881no—
262C22—881no—
263C22#6693511yescharacteristic
264C22#6693711yescharacteristic
265C22#6694711yescharacteristic
266C22D8×D1111yescharacteristic
267C22#6696711yescharacteristic
268C22#6696911yescharacteristic
269C22#6697111yescharacteristic
270C4—42no—
271C4—81no—
272C4—441no—
273C4—881no—
274C4#6692811yescharacteristic
275C4#6693711yescharacteristic
276C4#6694711yescharacteristic
277C4#6694811yescharacteristic
278C2—442no—
279C2—882no—
280C2#1062228511yescharacteristic
281C2#1062238611yescharacteristic
282C2#1062238811yescharacteristic
283C2#1062242311yescharacteristic
284C2#1062242511yescharacteristic
285C2#1062247911yescharacteristic
286C2#1062249511yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socleC23×C11C2×D4
prime radicalC2×#66948C2
hypercenter#340D11
hypocenterC11#2033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#66885C2semidirect
3. C2×(C2×D11)⋊C8C2semidirect
4. #10622600C2semidirect
5. C2×#66873C2semidirect
6. C2×#66871C2semidirect
7. C11×#340C2semidirect
60. C2×C11⋊C8D4semidirect
112. #340D11semidirect
204. C11#2033semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#668852
C2×(C2×D11)⋊C82
#106226002
C2×#668732
C2×#668712
C11×#3402
#203311