Finite Group Databasebeta

← #13078850

Subgroups — #13078850

Order 1408.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623264C211yesmaximal, characteristic
2#10623103C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622707C211yesmaximal, characteristic, complemented
5#10622641C211yesmaximal, characteristic, complemented
6#10622502C211yesmaximal, characteristic, complemented
7#10622501C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic
9#10622486C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic
14#10622402C211yesmaximal, characteristic, complemented
15#10622401C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C11×C4⋊Q8C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19#67000—21no—
20#66999—21no—
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24C2×Dic44C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26#66951—21no—
27#66950C2211yescharacteristic
28#66948C2211yescharacteristic
29#66947—21no—
30#66946C2211yescharacteristic
31#66945—21no—
32#66945C2211yescharacteristic
33#66940—21no—
34#66940C2211yescharacteristic
35#66940C2211yescharacteristic
36#66928C2211yescharacteristic
37#66925—21no—
38#66925C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46#66885C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61Q8×D11—22no—
62Q8×D11—22no—
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11C2311yescharacteristic
68C2×Dic22—21no—
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C42×C11—21no—
79C42×C11C2311yescharacteristic
80#4326—22no—
81#4325—22no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4D411yescharacteristic
89(C2×D11)⋊C4D411yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107#4314—22no—
108#3121—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—81no—
113Q8×C11#4112yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—81no—
130C4×D11—24no—
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—81no—
134Dic22—24no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22#4112yes—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#542—111no—
144#519—111no—
145#485—111no—
146#482—111no—
147#477D1111yescharacteristic, complemented
148#475—111no—
149#464—111no—
150#464—111no—
151#451—111no—
152#448—111no—
153#441—111no—
154#440—111no—
155C4×Q16—111no—
156C4×SD16—111no—
157#433—111no—
158C22×C11C22×D411yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C4×C11—22no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C11C2×#4111yescharacteristic
173Dic11—21no—
174Dic11—22no—
175Dic11—21no—
176Dic11—21no—
177Dic11—41no—
178Dic11—41no—
179C22×Q8—111no—
180C2×Q16—111no—
181C2×Q16—111no—
182C2×SD16—111no—
183C2×SD16—111no—
184C4⋊Q8C2×D1111yescharacteristic
185#126—221no—
186#124—111no—
187#124—221no—
188#123—221no—
189C22⋊Q8—111no—
190C22⋊Q8—221no—
191#121—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—221no—
197C4×Q8—221no—
198C4×Q8C2×D1111yescharacteristic
199C4×D4—111no—
200#117—111no—
201#117—111no—
202#117—221no—
203#117—221no—
204#107C2×D1111yescharacteristic
205#107C2×D1111yescharacteristic
206#106—111no—
207#106—111no—
208C4⋊C8—111no—
209C4⋊C8C2×D1111yescharacteristic
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103C2×D1111yescharacteristic
215#103C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218C22⋊C8—111no—
219C22⋊C8—111no—
220#97—111no—
221C4×C8—111no—
222C2×C11#52511yescharacteristic
223C2×C11#57711yescharacteristic
224C2×C11#57811yescharacteristic
225D11—41no—
226D11—81no—
227C2×Q8—21no—
228C2×Q8—111no—
229C2×Q8—111no—
230C2×Q8—221no—
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8C22×D1111yescharacteristic
234C2×D4—111no—
235C2×D4—221no—
236C22×C4—111no—
237C22×C4—221no—
238C22×C4—221no—
239Q16—222no—
240Q16—222no—
241SD16—222no—
242SD16—222no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—111no—
261C22⋊C4—111no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C42—21no—
269C42—111no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#312111yescharacteristic, complemented, Sylow
277C23—111no—
278C23—221no—
279Q8—21no—
280Q8—81no—
281Q8—112no—
282Q8—224no—
283Q8—221no—
284Q8—221no—
285Q8—221no—
286Q8#434312yes—
287D4—221no—
288D4—221no—
289D4—881no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—224no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—881no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—221no—
312C22—221no—
313C22—221no—
314C22—441no—
315C22—441no—
316C22—441no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—221no—
325C4—221no—
326C4—221no—
327C4—222no—
328C4—441no—
329C4—441no—
330C4C2×#434311yescharacteristic
331C4#41×D1111yescharacteristic
332C2—441no—
333C2—881no—
334C2#1062315811yescharacteristic
335C2#1062329711yescharacteristic
336C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#477D11
hypocenterC11#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #10623103C2semidirect
3. C11×#477C2semidirect
4. #10622707C2semidirect
5. #10622641C2semidirect
6. #10622502C2semidirect
7. #10622501C2semidirect
9. #10622486C2semidirect
10. #10622458C2semidirect
11. #10622453C2semidirect
12. #10622421C2semidirect
14. #10622402C2semidirect
15. #10622401C2semidirect
147. #477D11semidirect
276. C11#3121semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106231032
C11×#4772
#106227072
#106226412
#106225022
#106225012
#106224982
#106224862
#106224582
#106224532
#106224212
#106224192
#106224022
#106224012
#312111