Finite Group Databasebeta

← #13081458

Subgroups — #13081458

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×#557C211yesmaximal, characteristic, complemented
2#10623115C211yesmaximal, characteristic
3#10622704C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic
5#10622682C211yesmaximal, characteristic, complemented
6#10622681C211yesmaximal, characteristic
7#10622679C211yesmaximal, characteristic
8#10622676C211yesmaximal, characteristic, complemented
9#10622644C211yesmaximal, characteristic, complemented
10#10622643C211yesmaximal, characteristic, complemented
11C4×#4326C211yesmaximal, characteristic, complemented
12#10622641C211yesmaximal, characteristic
13#10622641C211yesmaximal, characteristic
14#10622639C211yesmaximal, characteristic
15#10622637C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#125—21no—
19C11×#125—21no—
20C11×#125C2211yescharacteristic
21C11×#125C2211yescharacteristic
22C4×Q8×C11—21no—
23C4×Q8×C11C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×Q8×C11C2211yescharacteristic
26C4×Q8×C11C2211yescharacteristic
27#66999—21no—
28C2×#4326C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31#66951—21no—
32#66951—21no—
33#66945—21no—
34#66928C2211yescharacteristic
35#66928C2211yescharacteristic
36C4×D44C2211yescharacteristic
37#66922C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66899C2211yescharacteristic
41#66874C2211yescharacteristic
42#66874C2211yescharacteristic
43#66874C2211yescharacteristic
44#66874C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66873C2211yescharacteristic
48#66873C2211yescharacteristic
49#66873C2211yescharacteristic
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×C11—21no—
60C2×Q8×C11D411yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D44C2311yescharacteristic
63C2×C4×D11—21no—
64C2×Dic22C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4D411yescharacteristic
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4D411yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11C2311yescharacteristic
84C42×C11C2311yescharacteristic
85C42×C11C2311yescharacteristic
86#4326—22no—
87#4326—22no—
88#4325—22no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3377—111nomaximal, Sylow
106C22×D11—21no—
107Q8×C11—21no—
108Q8×C11—41no—
109Q8×C11—42no—
110Q8×C11#4112yes—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125D44—21no—
126D44—21no—
127C4×D11—42no—
128Dic22—21no—
129Dic22—21no—
130Dic22—21no—
131Dic22—21no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#557D1111yescharacteristic, complemented
137#556—111no—
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×C11C22×D411yescharacteristic
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—41no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11C2×#4111yescharacteristic
166C4×C112−1+411yescharacteristic
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C2×Q16—111no—
171C2×Q16—111no—
172C2×SD16—111no—
173C4⋊Q8—21no—
174C4⋊Q8—111no—
175C4⋊Q8C2×D1111yescharacteristic
176#126—221no—
177#126—221no—
178#125—21no—
179#125—21no—
180#125C2×D1111yescharacteristic
181#125C2×D1111yescharacteristic
182#124—111no—
183#124—111no—
184C22⋊Q8—221no—
185C4×Q8—21no—
186C4×Q8—111no—
187C4×Q8—111no—
188C4×Q8C2×D1111yescharacteristic
189C4×Q8C2×D1111yescharacteristic
190C4×Q8C2×D1111yescharacteristic
191C4×Q8C2×D1111yescharacteristic
192C4×D4—111no—
193#117—221no—
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#54811yescharacteristic
214C2×C11#57511yescharacteristic
215C2×C11#57811yescharacteristic
216D11—81no—
217C2×Q8—21no—
218C2×Q8—111no—
219C2×Q8—111no—
220C2×Q8C22⋊D1111yescharacteristic
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C22×C4—221no—
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—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—111no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4C22⋊D1111yescharacteristic
245C4⋊C4C22⋊D1111yescharacteristic
246C4⋊C4C22⋊D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C4⋊C4C22×D1111yescharacteristic
250C22⋊C4—221no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—221no—
259C42—221no—
260C42C22×D1111yescharacteristic
261C42C22×D1111yescharacteristic
262C42C22×D1111yescharacteristic
263C11#337711yescharacteristic, complemented, Sylow
264C23—221no—
265Q8—21no—
266Q8—41no—
267Q8—42no—
268Q8—221no—
269Q8—221no—
270Q8—221no—
271Q8—221no—
272Q8#434312yes—
273D4—221no—
274D4—221no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—442no—
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—441no—
295C22—441no—
296C22—441no—
297C22C22×C22⋊D1111yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4C2×#434311yescharacteristic
312C4#6704011yescharacteristic
313C2—881no—
314C2#1062334811yescharacteristic
315C2#1062335311yescharacteristic
316C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#557C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#557D11
hypocenterC11#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C11×#557C2semidirect
3. #10622704C2semidirect
5. #10622682C2semidirect
8. #10622676C2semidirect
9. #10622644C2semidirect
10. #10622643C2semidirect
11. C4×#4326C2semidirect
15. #10622637C2semidirect
136. #557D11semidirect
263. C11#3377semidirect

Maximal subgroups

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

subgroupindex
C11×#5572
#106231152
#106227042
#106227022
#106226822
#106226812
#106226792
#106226762
#106226442
#106226432
C4×#43262
#106226412
#106226392
#106226372
#337711