Finite Group Databasebeta

← #13078599

Subgroups — #13078599

Order 1408.

398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#10623041C211yesmaximal, characteristic
2#10623035C211yesmaximal, characteristic, complemented
3C2×C11×#107C211yesmaximal, characteristic, complemented
4#10622726C211yesmaximal, characteristic, complemented
5#10622723C211yesmaximal, characteristic, complemented
6#10622579C211yesmaximal, characteristic, complemented
7#10622577C211yesmaximal, characteristic, complemented
8#10622501C212yesmaximal, complemented
9#10622498C212yesmaximal, complemented
10#10622497C212yesmaximal, complemented
11#10622495C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×C8×C11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#66983—22no—
18C4×C22⋊D11—22no—
19#66979C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21#66950—21no—
22#66950C2212yes—
23#66948—21no—
24#66948C2212yes—
25#66946—21no—
26#66945C2212yes—
27C4⋊C4×D11C2212yes—
28#66940—21no—
29C11×#107C2212yes—
30C11×#107C2212yes—
31#66885C2211yescharacteristic
32#66885C2211yescharacteristic
33(C2×D11)⋊C8C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66880C2211yescharacteristic
36#66880C2211yescharacteristic
37#66874C2212yes—
38#66873C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—21no—
45C2×C22⋊D11D412yes—
46#4339—22no—
47#4339—22no—
48#4339—22no—
49#4339—22no—
50C2×D44—22no—
51C2×D44D411yescharacteristic
52C2×D44C2311yescharacteristic
53C2×C4×D11—22no—
54C2×C4×D11—21no—
55C2×C4×D11C2312yes—
56C2×Dic22D411yescharacteristic
57C2×Dic22C2311yescharacteristic
58C2×C8×C11—22no—
59C2×C8×C11C2311yescharacteristic
60C2×C8×C11C2311yescharacteristic
61C11×C4⋊C4—21no—
62C11×C4⋊C4—21no—
63C11×C4⋊C4C2312yes—
64C11×C4⋊C4C2312yes—
65C22⋊Dic11—21no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11C2311yescharacteristic
71C4⋊Dic11C2311yescharacteristic
72Dic11⋊C4—22no—
73C4×Dic11—22no—
74C4×Dic11—21no—
75#4318—22no—
76C2×C11⋊C8C2312yes—
77#3098—111nomaximal, Sylow
78C23×C11C2×D411yescharacteristic
79C22×D11—21no—
80C22×D11C2×D412yes—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—81no—
84C2×C4×C11—81no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11#4112yes—
87C2×C4×C11#4112yes—
88C2×C4×C11C2411yescharacteristic
89C22⋊D11—24no—
90C22⋊D11—42no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11C2×D412yes—
95D44—22no—
96D44—21no—
97D44—21no—
98D44—82no—
99C4×D11—22no—
100C4×D11—22no—
101C4×D11—42no—
102C4×D11—82no—
103Dic22—22no—
104Dic22—21no—
105Dic22—21no—
106C8×C11—21no—
107C8×C11—21no—
108C11⋊C8—22no—
109#537—111no—
110#520—111no—
111#485—112no—
112#484—112no—
113#482—112no—
114#480—112no—
115#428—111no—
116C2×#107D1111yescharacteristic, complemented
117#417—111no—
118#416—111no—
119#408—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#12312yes—
123C22×C11C22×D411yescharacteristic
124C2×D11—22no—
125C2×D11—22no—
126C2×D11—22no—
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—41no—
130C4×C11—42no—
131C4×C11—42no—
132C4×C11#12312yes—
133C4×C11C2×#4111yescharacteristic
134C4×C11C2×#4111yescharacteristic
135Dic11—22no—
136Dic11—41no—
137Dic11—41no—
138Dic11—41no—
139C2×#41—111no—
140C2×#41—111no—
141C2×M16—111no—
142C22×C8C2×D1111yescharacteristic
143C22⋊Q8—112no—
144C22⋊Q8—221no—
145#121—112no—
146#121—221no—
147#121—222no—
148C4×Q8—221no—
149C4×D4—221no—
150C4×D4—222no—
151#117—111no—
152#117—112no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4C2×D1111yescharacteristic
155C2×C4⋊C4C2×D1111yescharacteristic
156#107—112no—
157#107C2×D1112yes—
158#107C2×D1112yes—
159#106—112no—
160#103—111no—
161#103—111no—
162#103—112no—
163#102—111no—
164#102—111no—
165#102—112no—
166C22⋊C8—112no—
167C22⋊C8—112no—
168C2×C11—22no—
169C2×C11C2×#12311yescharacteristic
170C2×C11#57611yescharacteristic
171C2×C11#57811yescharacteristic
172D11—42no—
173D11—81no—
174#41—222no—
175#41—222no—
176#41—222no—
177#41—222no—
178C2×Q8—111no—
179C2×Q8—111no—
180C2×D4—112no—
181C2×D4—111no—
182C2×D4—111no—
183C2×D4—222no—
184C2×D4—221no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—112no—
188C22×C4—222no—
189C22×C4—221no—
190C22×C4C22×D1111yescharacteristic
191M16—222no—
192C2×C8—22no—
193C2×C8—112no—
194C2×C8C22×D1111yescharacteristic
195C2×C8C22×D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—111no—
199C4⋊C4—111no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4C22×D1112yes—
203C4⋊C4C22×D1112yes—
204C22⋊C4—222no—
205C22⋊C4—222no—
206C22⋊C4—222no—
207C22⋊C4—221no—
208C42—222no—
209C42—221no—
210C11#309811yescharacteristic, complemented, Sylow
211C23—112no—
212C23—221no—
213C23D4×D1111yescharacteristic
214Q8—222no—
215Q8—221no—
216Q8—221no—
217D4—224no—
218D4—222no—
219D4—221no—
220D4—221no—
221D4—442no—
222D4—882no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—112no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—442no—
234C2×C4—882no—
235C2×C4#433912yes—
236C2×C4D4×D1111yescharacteristic
237C2×C4#434312yes—
238C2×C4C23×D1111yescharacteristic
239C8—21no—
240C8—21no—
241C8—222no—
242C22—21no—
243C22—21no—
244C22—222no—
245C22—222no—
246C22—222no—
247C22—441no—
248C22—441no—
249C22—441no—
250C22#6694712yes—
251C22C2×D4×D1111yescharacteristic
252C4—42no—
253C4—42no—
254C4—222no—
255C4—441no—
256C4—441no—
257C4—441no—
258C4#6694712yes—
259C4C2×#433911yescharacteristic
260C4C2×#434311yescharacteristic
261C2—22no—
262C2—442no—
263C2—881no—
264C2C2×#6694711yescharacteristic
265C2#1062328811yescharacteristic
266C2#1062329711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#107C2
socleC22×C11C22×D4
prime radical#10623041C2
hypercenterC2×#107D11
hypocenterC11#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #10623035C2semidirect
3. C2×C11×#107C2semidirect
4. #10622726C2semidirect
5. #10622723C2semidirect
6. #10622579C2semidirect
7. #10622577C2semidirect
8. #10622501C2semidirect
9. #10622498C2semidirect
10. #10622497C2semidirect
11. #10622495C2semidirect
116. C2×#107D11semidirect
210. C11#3098semidirect

Maximal subgroups

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

subgroupindex
#106230412
#106230352
C2×C11×#1072
#106227262
#106227232
#106225792
#106225772
#106225012
#106224982
#106224972
#106224952
#309811