Finite Group Databasebeta

← #13069926

Subgroups — #13069926

Order 1408.

360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C11×#390C211yesmaximal, characteristic, complemented
3C2×#66896C211yesmaximal, characteristic, complemented
4C2×#66873C211yesmaximal, characteristic, complemented
5#10622552C211yesmaximal, characteristic, complemented
6C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C22⋊C4—21no—
12C2×C11×C22⋊C4—21no—
13C2×C42×C11C2211yescharacteristic
14C2×#4323—22no—
15C2×#4323—22no—
16C2×#4323—22no—
17C2×(C2×D11)⋊C4—21no—
18C2×(C2×D11)⋊C4—21no—
19C2×C4⋊Dic11C2211yescharacteristic
20C22×C11⋊C8C2211yescharacteristic
21C22×C11⋊C8C2211yescharacteristic
22#66896—22no—
23#66873—22no—
24C4⋊(C11⋊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×C11D411yescharacteristic
35C22×C4×C11D411yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11—21no—
38C2×D44—21no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44D412yes—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C22⋊C4—42no—
47C11×C22⋊C4—42no—
48C42×C11—21no—
49C42×C11—21no—
50#4323—28no—
51(C2×D11)⋊C4—42no—
52(C2×D11)⋊C4—42no—
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⋊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—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11D812yescomplemented
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11#4111yescharacteristic
94C2×C4×C11#4111yescharacteristic
95C2×C4×C11#4111yescharacteristic
96C2×Dic11—41no—
97C2×Dic11—41no—
98C2×Dic11—41no—
99D44—22no—
100D44—22no—
101D44—41no—
102D44—41no—
103C11⋊C8—22no—
104C11⋊C8—41no—
105C22×D8—111no—
106C2×C4⋊C8—111no—
107C2×#102—111no—
108C2×#102—111no—
109#390—111no—
110#390D1111yescharacteristic, complemented
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—22no—
134C4×C11—41no—
135C4×C11—81no—
136C4×C11#12011yescharacteristic
137C4×C11#12311yescharacteristic
138C4×C11#12311yescharacteristic
139C4×C11#12411yescharacteristic
140Dic11—81no—
141C22×D4—111no—
142C22×D4C2×D1111yescharacteristic
143C2×D8—222no—
144C2×D8—222no—
145C2×D8—222no—
146C22×C8—111no—
147C22×C8—111no—
148C2×C4⋊C4—111no—
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—221no—
153C2×C22⋊C4—221no—
154C2×C42C2×D1111yescharacteristic
155C4⋊C8—222no—
156#102—222no—
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×D4D4412yes—
181C22×C4—21no—
182C22×C4—221no—
183C22×C4C22⋊D1111yescharacteristic
184C22×C4C22⋊D1111yescharacteristic
185C22×C4C22×D1111yescharacteristic
186D8—228no—
187C2×C8—112no—
188C2×C8—221no—
189C2×C8—221no—
190C2×C8—221no—
191C2×C8—221no—
192C2×C8—221no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—221no—
196C4⋊C4—221no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—442no—
200C22⋊C4—442no—
201C42—21no—
202C42—21no—
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—
218C23C2×C22⋊D1111yescharacteristic
219D4—22no—
220D4—22no—
221D4—41no—
222D4—41no—
223D4—222no—
224D4—222no—
225D4—441no—
226D4—441no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4#432312yescomplemented
239C2×C4C2×D4411yescharacteristic
240C2×C4#433911yescharacteristic
241C2×C4D4×D1111yescharacteristic
242C2×C4D4×D1111yescharacteristic
243C2×C4#434111yescharacteristic
244C2×C4#434111yescharacteristic
245C8—222no—
246C8—441no—
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#6698311yescharacteristic
262C22C2×#432311yescharacteristic
263C22#6698511yescharacteristic
264C22#6699111yescharacteristic
265C22#6699211yescharacteristic
266C22#6700211yescharacteristic
267C22#6700311yescharacteristic
268C4—22no—
269C4—41no—
270C4—81no—
271C4—881no—
272C4#6693511yescharacteristic
273C4#6693611yescharacteristic
274C4#6693811yescharacteristic
275C4#6693911yescharacteristic
276C2—82no—
277C2—882no—
278C2#1062257411yescharacteristic
279C2#1062262811yescharacteristic
280C2#1062262911yescharacteristic
281C2#1062265111yescharacteristic
282C2#1062265211yescharacteristic
283C2#1062267011yescharacteristic
284C2#1062268511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#390C2
socleC23×C11C2×D4
prime radicalC22×#4323C2
hypercenter#390D11
hypocenterC11#2054
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C11×#390C2semidirect
3. C2×#66896C2semidirect
4. C2×#66873C2semidirect
5. #10622552C2semidirect
6. C2×C4⋊(C11⋊C8)C2semidirect
7. #10622167C2semidirect
89. C2×C4×C11D8semidirect
110. #390D11semidirect
203. C11#2054semidirect
238. C2×C4#4323semidirect

Maximal subgroups

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

subgroupindex
C22×#43232
C11×#3902
C2×#668962
C2×#668732
#106225522
C2×C4⋊(C11⋊C8)2
#106221672
#205411