Finite Group Databasebeta

← #13081460

Subgroups — #13081460

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
1#10623115C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C11×#446C211yesmaximal, characteristic, complemented
4#10622463C211yesmaximal, characteristic, complemented
5#10622462C211yesmaximal, characteristic, complemented
6#10622460C211yesmaximal, characteristic
7#10622458C211yesmaximal, characteristic
8#10622458C211yesmaximal, characteristic
9#10622442C211yesmaximal, characteristic, complemented
10#10622329C211yesmaximal, characteristic, complemented
11#10622327C211yesmaximal, characteristic
12#10622323C211yesmaximal, characteristic
13#10622316C211yesmaximal, characteristic, complemented
14C4×Dic44C211yesmaximal, characteristic, complemented
15#10622310C211yesmaximal, characteristic
16C4×Q8×C11C2211yescharacteristic
17#66999—21no—
18#66997—21no—
19C2×Dic44C2211yescharacteristic
20C2×Dic44C2211yescharacteristic
21C2×#4314C2211yescharacteristic
22#66951—21no—
23#66951—21no—
24#66945—21no—
25#66942—21no—
26#66942—21no—
27#66940—21no—
28#66928C2211yescharacteristic
29#66928C2211yescharacteristic
30C4×D44C2211yescharacteristic
31#66923C2211yescharacteristic
32#66923C2211yescharacteristic
33#66922C2211yescharacteristic
34#66922C2211yescharacteristic
35C4×Dic22C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44C11×#97C2211yescharacteristic
45C4×C8×C11C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×Q8×C11D411yescharacteristic
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×Dic22—21no—
63C2×Dic22C2311yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4D411yescharacteristic
71C11×C4⋊C4D411yescharacteristic
72C11×C4⋊C4D411yescharacteristic
73C42×C11C2311yescharacteristic
74C42×C11C2311yescharacteristic
75C42×C11C2311yescharacteristic
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102Dic44—22no—
103Dic44—22no—
104#4314—22no—
105#3377—111nomaximal, Sylow
106C22×D11—21no—
107Q8×C11—41no—
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2411yescharacteristic
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122D44—21no—
123D44—21no—
124C4×D11—42no—
125Dic22—21no—
126Dic22—21no—
127Dic22—21no—
128Dic22—21no—
129Dic22—21no—
130Dic22—42no—
131Dic22#4112yes—
132C8×C11—21no—
133C8×C11—21no—
134C8×C11—21no—
135C8×C11—21no—
136#557—111no—
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#446D1111yescharacteristic, complemented
148#441—111no—
149#440—111no—
150C4×Q16—111no—
151C22×C11C22×D411yescharacteristic
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—41no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11C2×#4111yescharacteristic
162C4×C112−1+411yescharacteristic
163Dic11—22no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C2×Q16—111no—
171C2×Q16—111no—
172C2×SD16—111no—
173C4⋊Q8—111no—
174C4⋊Q8—111no—
175C4⋊Q8—221no—
176#126—221no—
177#126—221no—
178#125—111no—
179#125—111no—
180#125—221no—
181#125—221no—
182#124—111no—
183#124—111no—
184C22⋊Q8—221no—
185C4×Q8—111no—
186C4×Q8—111no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—221no—
191C4×Q8C2×D1111yescharacteristic
192C4×D4—111no—
193#117—221no—
194#107—111no—
195#107—111no—
196#106—111no—
197C4⋊C8C2×D1111yescharacteristic
198C4⋊C8C2×D1111yescharacteristic
199C4⋊C8C2×D1111yescharacteristic
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#97C2×D1111yescharacteristic
211#97C2×D1111yescharacteristic
212C4×C8C2×D1111yescharacteristic
213C2×C11#54811yescharacteristic
214C2×C11#57511yescharacteristic
215C2×C11#57811yescharacteristic
216D11—81no—
217C2×Q8—111no—
218C2×Q8—111no—
219C2×Q8—111no—
220C2×Q8—221no—
221C2×Q8D4411yescharacteristic
222C2×D4—111no—
223C22×C4—221no—
224Q16—222no—
225Q16—222no—
226SD16—222no—
227C2×C8C22×D1111yescharacteristic
228C2×C8C22×D1111yescharacteristic
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
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⋊C4—221no—
247C4⋊C4D4411yescharacteristic
248C4⋊C4D4411yescharacteristic
249C4⋊C4D4411yescharacteristic
250C22⋊C4—221no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C42—221no—
256C42—221no—
257C42—221no—
258C42—221no—
259C42—221no—
260C42C22×D1111yescharacteristic
261C42C22×D1111yescharacteristic
262C42C22×D1111yescharacteristic
263C11#337711yescharacteristic, complemented, Sylow
264C23—221no—
265Q8—41no—
266Q8—112no—
267Q8—221no—
268Q8—221no—
269Q8—221no—
270Q8—221no—
271Q8—221no—
272Q8—442no—
273D4—221no—
274D4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—442no—
283C2×C4C2×D4411yescharacteristic
284C2×C4C2×D4411yescharacteristic
285C2×C4C2×D4411yescharacteristic
286C2×C4C2×D4411yescharacteristic
287C2×C4C2×D4411yescharacteristic
288C2×C4C2×D4411yescharacteristic
289C2×C4C23×D1111yescharacteristic
290C8—21no—
291C8—21no—
292C8—21no—
293C8—21no—
294C22—441no—
295C22—441no—
296C22—441no—
297C22C22×D4411yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—222no—
305C4—441no—
306C4—441no—
307C4—441no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4#6704011yescharacteristic
312C4#41×D1111yescharacteristic
313C2—881no—
314C2#1062310711yescharacteristic
315C2#1062327911yescharacteristic
316C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#446C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#446D11
hypocenterC11#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #10623098C2semidirect
3. C11×#446C2semidirect
4. #10622463C2semidirect
5. #10622462C2semidirect
9. #10622442C2semidirect
10. #10622329C2semidirect
13. #10622316C2semidirect
14. C4×Dic44C2semidirect
147. #446D11semidirect
263. C11#3377semidirect

Maximal subgroups

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

subgroupindex
#106231152
#106230982
C11×#4462
#106224632
#106224622
#106224602
#106224582
#106224422
#106223292
#106223272
#106223232
#106223162
C4×Dic442
#106223102
#337711