Finite Group Databasebeta

← #13081452

Subgroups — #13081452

Order 1408.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#556C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3#10622703C211yesmaximal, characteristic, complemented
4#10622695C211yesmaximal, characteristic, complemented
5#10622669C211yesmaximal, characteristic
6#10622668C211yesmaximal, characteristic
7#10622667C211yesmaximal, characteristic
8#10622667C211yesmaximal, characteristic
9#10622643C211yesmaximal, characteristic, complemented
10C4×#4326C211yesmaximal, characteristic, complemented
11#10622637C211yesmaximal, characteristic, complemented
12#10622635C211yesmaximal, characteristic, complemented
13#10622634C211yesmaximal, characteristic, complemented
14#10622631C211yesmaximal, characteristic
15#10622622C211yesmaximal, characteristic
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#126—21no—
19C11×#124C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C11×C22⋊Q8—21no—
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C11×#117—21no—
27#66997—21no—
28C2×#4326C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31#66942—21no—
32#66942—21no—
33#66940—21no—
34#66923C2211yescharacteristic
35#66923C2211yescharacteristic
36#66922C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66874C2211yescharacteristic
50#66872C2211yescharacteristic
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×C11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×Dic22—21no—
65C2×Dic22C2311yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4D411yescharacteristic
71C11×C4⋊C4D411yescharacteristic
72C11×C4⋊C4D411yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11C2311yescharacteristic
82C42×C11C2311yescharacteristic
83C42×C11C2311yescharacteristic
84#4326—22no—
85#4326—22no—
86#4324—22no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3377—111nomaximal, Sylow
106C23×C11—21no—
107Q8×C11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—41no—
112D4×C11—21no—
113D4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129Dic22—21no—
130Dic22—42no—
131Dic22#4112yes—
132C11⋊C8—21no—
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#557—111no—
137#556D1111yescharacteristic
138#491—111no—
139#489—111no—
140#488—111no—
141#479—111no—
142#478—111no—
143#477—111no—
144#464—111no—
145#464—111no—
146#462—111no—
147#446—111no—
148#441—111no—
149#440—111no—
150C4×Q16—111no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11C22×D411yescharacteristic
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11C2×#4111yescharacteristic
165C4×C112−1+411yescharacteristic
166Dic11—22no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C2×Q16—111no—
171C2×Q16—111no—
172C2×SD16—111no—
173C4⋊Q8—111no—
174C4⋊Q8—221no—
175C4⋊Q8C2×D1111yescharacteristic
176#126—21no—
177#126—21no—
178#125—111no—
179#125—111no—
180#125—221no—
181#125—221no—
182#124C2×D1111yescharacteristic
183#124C2×D1111yescharacteristic
184C22⋊Q8—21no—
185C4×Q8—111no—
186C4×Q8—111no—
187C4×Q8—111no—
188C4×Q8—221no—
189C4×Q8C2×D1111yescharacteristic
190C4×Q8C2×D1111yescharacteristic
191C4×Q8C2×D1111yescharacteristic
192C4×D4C2×D1111yescharacteristic
193#117—21no—
194#107—111no—
195#107—111no—
196#106—111no—
197C4⋊C8—111no—
198C4⋊C8—111no—
199C4⋊C8—111no—
200#103—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#103—111no—
206#103—111no—
207#102—111no—
208#102—111no—
209#102—111no—
210#97—111no—
211#97—111no—
212C4×C8—111no—
213C2×C11—81no—
214C2×C11#54811yescharacteristic
215C2×C11#57511yescharacteristic
216C2×C11#57811yescharacteristic
217C2×Q8—111no—
218C2×Q8—221no—
219C2×Q8C22⋊D1111yescharacteristic
220C2×Q8C22×D1111yescharacteristic
221C2×Q8C22×D1111yescharacteristic
222C2×D4C22×D1111yescharacteristic
223C22×C4—21no—
224Q16—222no—
225Q16—222no—
226SD16—222no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8—111no—
230C2×C8—111no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4C22⋊D1111yescharacteristic
247C4⋊C4C22⋊D1111yescharacteristic
248C4⋊C4C22⋊D1111yescharacteristic
249C4⋊C4C22×D1111yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C42—21no—
256C42—21no—
257C42—221no—
258C42—221no—
259C42—221no—
260C42C22×D1111yescharacteristic
261C42C22×D1111yescharacteristic
262C42C22×D1111yescharacteristic
263C11#337711yescharacteristic, complemented, Sylow
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—21no—
269Q8—41no—
270Q8—112no—
271Q8—221no—
272Q8—442no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4C2×C22⋊D1111yescharacteristic
284C2×C4C2×C22⋊D1111yescharacteristic
285C2×C4C2×C22⋊D1111yescharacteristic
286C2×C4C2×C22⋊D1111yescharacteristic
287C2×C4C2×C22⋊D1111yescharacteristic
288C2×C4C2×C22⋊D1111yescharacteristic
289C2×C4C23×D1111yescharacteristic
290C8—221no—
291C8—221no—
292C8—221no—
293C8—221no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C22×C22⋊D1111yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—222no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4#41×D1111yescharacteristic
312C4#6704311yescharacteristic
313C2—81no—
314C2#1062335311yescharacteristic
315C2#1062336211yescharacteristic
316C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#556D11
hypocenterC11#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
3. #10622703C2semidirect
4. #10622695C2semidirect
9. #10622643C2semidirect
10. C4×#4326C2semidirect
11. #10622637C2semidirect
12. #10622635C2semidirect
13. #10622634C2semidirect
263. C11#3377semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106230982
#106227032
#106226952
#106226692
#106226682
#106226672
#106226432
C4×#43262
#106226372
#106226352
#106226342
#106226312
#106226222
#337711