Finite Group Databasebeta

← #13080039

Subgroups — #13080039

Order 1408.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623213C211yesmaximal, characteristic
2#10623114C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622802C211yesmaximal, characteristic, complemented
5#10622795C211yesmaximal, characteristic, complemented
6#10622784C211yesmaximal, characteristic
7#10622775C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622634C211yesmaximal, characteristic, complemented
10#10622464C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic, complemented
12#10622426C211yesmaximal, characteristic, complemented
13#10622412C211yesmaximal, characteristic, complemented
14#10622393C211yesmaximal, characteristic
15#10622376C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66991C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66943C2211yescharacteristic
33#66942—21no—
34#66939—21no—
35#66938—21no—
36#66932—21no—
37#66931—21no—
38#66929—21no—
39#66925C2211yescharacteristic
40#66923—21no—
41#66922C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C11×Q16—41no—
68C11×SD16—41no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C22⋊C4—21no—
74C11×C22⋊C4—21no—
75C42×C11—21no—
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79#4326—41no—
80#4324—41no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4D411yescharacteristic
85(C2×D11)⋊C4D411yescharacteristic
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—41no—
107C8×D11—41no—
108#3258—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—81no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—21no—
133C4×D11—21no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137C8×C11—21no—
138C8×C11—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141#542—111no—
142#541—111no—
143#479—111no—
144#478—111no—
145#477—111no—
146#475—111no—
147#470—111no—
148#468—111no—
149#467—111no—
150#465—111no—
151#464—111no—
152#464D1111yescharacteristic, complemented
153#462—111no—
154#461—111no—
155#424—111no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11C22×D411yescharacteristic
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11H(5,𝔽2)11yescharacteristic
169C4×C112−1+411yescharacteristic
170Dic11—21no—
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×Q16—111no—
178C2×Q16C2×D1111yescharacteristic
179C2×SD16—111no—
180C2×SD16C2×D1111yescharacteristic
181C2×M16—111no—
182C22×C8—111no—
183C4⋊Q8—111no—
184C4⋊Q8—111no—
185#126—221no—
186#126—221no—
187#126—221no—
188#125—111no—
189#125—221no—
190#125—221no—
191#124—221no—
192#124C2×D1111yescharacteristic
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—111no—
196C22⋊Q8—111no—
197C22⋊Q8—221no—
198#121—111no—
199C4×Q8—111no—
200C4×Q8—111no—
201C4×Q8C2×D1111yescharacteristic
202C4×D4—111no—
203#117—111no—
204#107—111no—
205#107—111no—
206#106—111no—
207#106—111no—
208C4⋊C8—111no—
209C4⋊C8—111no—
210C4⋊C8—111no—
211C4⋊C8C2×D1111yescharacteristic
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#103C2×D1111yescharacteristic
218#102—111no—
219#102C2×D1111yescharacteristic
220C2×C11—81no—
221C2×C11#53711yescharacteristic
222C2×C11#57711yescharacteristic
223C2×C11#57811yescharacteristic
224D11—41no—
225C2×Q8—111no—
226C2×Q8—221no—
227C2×Q8C22×D1111yescharacteristic
228C2×Q8C22×D1111yescharacteristic
229C2×D4—221no—
230C2×D4C22×D1111yescharacteristic
231C22×C4—111no—
232C22×C4—221no—
233Q16—41no—
234Q16—441no—
235SD16—41no—
236SD16—441no—
237M16—441no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—441no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—111no—
263C22⋊C4—111no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—111no—
271C42—221no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#325811yescharacteristic, complemented, Sylow
275C23—21no—
276C23—111no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—221no—
282Q8—221no—
283Q8—881no—
284D4—21no—
285D4—21no—
286D4—881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—111no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—881no—
300C2×C4D4×D1111yescharacteristic
301C2×C4D4×D1111yescharacteristic
302C2×C4C23×D1111yescharacteristic
303C8—21no—
304C8—21no—
305C8—221no—
306C8—221no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—221no—
311C22—221no—
312C22—221no—
313C22C2×D4×D1111yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—221no—
320C4—221no—
321C4—221no—
322C4—441no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4#6703711yescharacteristic
327C4#6704311yescharacteristic
328C2—81no—
329C2—441no—
330C2#1062313911yescharacteristic
331C2#1062330111yescharacteristic
332C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#464D11
hypocenterC11#3258
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #10623114C2semidirect
3. C11×#464C2semidirect
4. #10622802C2semidirect
5. #10622795C2semidirect
7. #10622775C2semidirect
8. #10622667C2semidirect
9. #10622634C2semidirect
10. #10622464C2semidirect
11. #10622452C2semidirect
12. #10622426C2semidirect
13. #10622412C2semidirect
15. #10622376C2semidirect
152. #464D11semidirect
274. C11#3258semidirect

Maximal subgroups

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

subgroupindex
#106232132
#106231142
C11×#4642
#106228022
#106227952
#106227842
#106227752
#106226672
#106226342
#106224642
#106224522
#106224262
#106224122
#106223932
#106223762
#325811