Finite Group Databasebeta

← #13081570

Subgroups — #13081570

Order 1408.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#554C211yesmaximal, characteristic, complemented
2#10623110C211yesmaximal, characteristic, complemented
3#10622700C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622679C211yesmaximal, characteristic, complemented
6#10622679C211yesmaximal, characteristic, complemented
7#10622678C211yesmaximal, characteristic, complemented
8#10622677C211yesmaximal, characteristic, complemented
9#10622637C211yesmaximal, characteristic, complemented
10#10622627C211yesmaximal, characteristic
11#10622627C211yesmaximal, characteristic
12C4×#4323C211yesmaximal, characteristic
13#10622622C211yesmaximal, characteristic, complemented
14#10622622C211yesmaximal, characteristic, complemented
15#10622620C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C11×#125C2211yescharacteristic
19C11×C22⋊Q8—21no—
20C11×C22⋊Q8—21no—
21C11×C22⋊Q8—21no—
22C4×Q8×C11C2211yescharacteristic
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C2×C11×C4⋊C4—21no—
27#66999—21no—
28C2×#4323C2211yescharacteristic
29#66949—21no—
30#66949—21no—
31C4⋊C4×D11—21no—
32C4×D44C2211yescharacteristic
33C4×D44C2211yescharacteristic
34C4×D44C2211yescharacteristic
35#66923C2211yescharacteristic
36#66923C2211yescharacteristic
37#66922C2211yescharacteristic
38#66896C2211yescharacteristic
39#66896C2211yescharacteristic
40#66896C2211yescharacteristic
41#66873C2211yescharacteristic
42#66873C2211yescharacteristic
43#66873C2211yescharacteristic
44#66872C2211yescharacteristic
45#66872C2211yescharacteristic
46#66872C2211yescharacteristic
47#66872C2211yescharacteristic
48#66871C2211yescharacteristic
49#66871C2211yescharacteristic
50#66871C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53C4⋊(C11⋊C8)C2211yescharacteristic
54C4⋊(C11⋊C8)C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56#66867C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11D411yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×Dic22—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4D411yescharacteristic
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C42×C11C2311yescharacteristic
85C42×C11C2311yescharacteristic
86C42×C11C2311yescharacteristic
87#4323Q814yescomplemented
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C2×C11⋊C8C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#3389—111nomaximal, Sylow
104C23×C11—21no—
105C22×D11—21no—
106Q8×C11—41no—
107Q8×C11—81no—
108D4×C11—21no—
109D4×C11C2×Q812yes—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126D44—21no—
127D44C2×Q812yes—
128C4×D11—42no—
129C4×D11—81no—
130C4×D11—81no—
131Dic22—81no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8C2×Q812yes—
136#554—111no—
137#554D1111yescharacteristic, complemented
138#501—111no—
139#501—111no—
140#499—111no—
141#478—111no—
142#478—111no—
143#478—111no—
144#478—111no—
145#474—111no—
146#474—111no—
147#446—111no—
148#442—111no—
149#442—111no—
150C4×D8—111no—
151C22×C11—22no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11C22×D411yescharacteristic
155C2×D11—22no—
156C2×D11—41no—
157C2×D11—41no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11C22×Q811yescharacteristic
168C4×C112−1+411yescharacteristic
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×D8—111no—
173C4⋊Q8—111no—
174C4⋊Q8C2×D1111yescharacteristic
175#125—111no—
176#125—111no—
177#125C2×D1111yescharacteristic
178#125C2×D1111yescharacteristic
179C22⋊Q8—21no—
180C22⋊Q8—21no—
181C22⋊Q8—21no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185C4×Q8C2×D1111yescharacteristic
186C4×D4—111no—
187C4×D4—111no—
188C4×D4—111no—
189C4×D4C2×D1111yescharacteristic
190C4×D4C2×D1111yescharacteristic
191C4×D4C2×D1111yescharacteristic
192C2×C4⋊C4—21no—
193C2×C4⋊C4—221no—
194#107—111no—
195#107—111no—
196#107—111no—
197#107—111no—
198#107—111no—
199#106—111no—
200#106—111no—
201#106—111no—
202#106—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#102—111no—
211#102—111no—
212#97—111no—
213#97—111no—
214C4×C8—111no—
215C2×C11—42no—
216C2×C11D4×Q811yescharacteristic
217C2×C11#57511yescharacteristic
218C2×C11#57611yescharacteristic
219D11—42no—
220C2×Q8—21no—
221C2×Q8—221no—
222C2×Q8C22⋊D1111yescharacteristic
223C2×D4—111no—
224C2×D4C22×D1111yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231D8—114no—
232C2×C8—111no—
233C2×C8—111no—
234C2×C8—111no—
235C2×C8—111no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—111no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4C22⋊D1111yescharacteristic
250C4⋊C4C22⋊D1111yescharacteristic
251C4⋊C4C22⋊D1111yescharacteristic
252C4⋊C4C22×D1111yescharacteristic
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42C22×D1111yescharacteristic
262C42C22×D1111yescharacteristic
263C42C22×D1111yescharacteristic
264C11#338911yescharacteristic, complemented, Sylow
265C23—21no—
266C23—221no—
267Q8—41no—
268Q8—81no—
269Q8—881no—
270D4—21no—
271D4—112no—
272D4—221no—
273D4Q8×D1112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—442no—
284C2×C4—881no—
285C2×C4—881no—
286C2×C4C2×C22⋊D1111yescharacteristic
287C2×C4C2×C22⋊D1111yescharacteristic
288C2×C4C2×C22⋊D1111yescharacteristic
289C2×C4C2×C22⋊D1111yescharacteristic
290C2×C4C2×C22⋊D1111yescharacteristic
291C2×C4C2×C22⋊D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—112no—
294C8—221no—
295C8—221no—
296C8—221no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—222no—
301C22—441no—
302C22—441no—
303C22C22×C22⋊D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4C2×Q8×D1111yescharacteristic
317C4#6704011yescharacteristic
318C2—42no—
319C2—442no—
320C2Q8×C22⋊D1111yescharacteristic
321C2#1062335311yescharacteristic
322C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#554C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#554D11
hypocenterC11#3389
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C11×#554C2semidirect
2. #10623110C2semidirect
3. #10622700C2semidirect
4. #10622693C2semidirect
5. #10622679C2semidirect
6. #10622679C2semidirect
7. #10622678C2semidirect
8. #10622677C2semidirect
9. #10622637C2semidirect
13. #10622622C2semidirect
14. #10622622C2semidirect
15. #10622620C2semidirect
87. #4323Q8semidirect
137. #554D11semidirect
264. C11#3389semidirect

Maximal subgroups

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

subgroupindex
C11×#5542
#106231102
#106227002
#106226932
#106226792
#106226782
#106226772
#106226372
#106226272
C4×#43232
#106226222
#106226202
#338911