Finite Group Databasebeta

← #13081062

Subgroups — #13081062

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623173C211yesmaximal, characteristic, complemented
2#10623142C211yesmaximal, characteristic
3C11×#465C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622777C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7C2×#66882C211yesmaximal, characteristic, complemented
8#10622656C211yesmaximal, characteristic, complemented
9#10622646C211yesmaximal, characteristic, complemented
10#10622474C211yesmaximal, characteristic, complemented
11#10622469C211yesmaximal, characteristic, complemented
12#10622422C211yesmaximal, characteristic, complemented
13#10622407C211yesmaximal, characteristic, complemented
14#10622397C211yesmaximal, characteristic, complemented
15#10622379C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×SD16C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66991C2211yescharacteristic
24#66988—21no—
25D4×Dic11C2211yescharacteristic
26C4×C22⋊D11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66951—21no—
31#66945C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66943—21no—
34#66943C2211yescharacteristic
35#66941C2211yescharacteristic
36#66939—21no—
37#66936—21no—
38#66931—21no—
39#66930—21no—
40C11×#106C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66882C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68#4341—44no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×Dic22—21no—
72C11×SD16—22no—
73C2×C8×C11—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4313—22no—
106#3343—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
109C22×D11C2×D411yescharacteristic
110Q8×C11—21no—
111Q8×C11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—42no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—22no—
123C22⋊D11—42no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—42no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11#4112yescomplemented
140C11⋊C8—21no—
141C11⋊C8—21no—
142#552—111no—
143#547—111no—
144#501—111no—
145#484—111no—
146#483—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#477—111no—
151#468—111no—
152#465D1111yescharacteristic, complemented
153#440—111no—
154#435—111no—
155#428—111no—
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11AGL(1,ℤ/8)12yes—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16C2×D1111yescharacteristic
182C2×M16—111no—
183C22×C8C2×D1111yescharacteristic
184C4⋊Q8—111no—
185#126—221no—
186#125—111no—
187#125—221no—
188#123—221no—
189#123—221no—
190#123—221no—
191C22⋊Q8—111no—
192C22⋊Q8—221no—
193C22⋊Q8C2×D1111yescharacteristic
194#121—111no—
195#121C2×D1111yescharacteristic
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4—111no—
199#117—111no—
200#117—221no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#107—111no—
210#106—111no—
211#106—111no—
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103C2×D1111yescharacteristic
217#102—111no—
218#102—111no—
219#102C2×D1111yescharacteristic
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97—111no—
223C2×C11—22no—
224C2×C11—81no—
225C2×C11#54711yescharacteristic
226C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C11#57811yescharacteristic
228D11—41no—
229#41—444no—
230C2×Q8—221no—
231C2×Q8C22×D1111yescharacteristic
232C2×D4—21no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4C22×D1111yescharacteristic
236C22×C4—111no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C22×D1111yescharacteristic
242SD16—22no—
243M16—222no—
244C2×C8—22no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4C22×D1111yescharacteristic
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—111no—
268C22⋊C4—111no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C42—111no—
274C42—221no—
275C42—221no—
276C11#334311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279C23D4×D1111yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—442no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—222no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—221no—
310C8—221no—
311C8#434112yescomplemented
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—221no—
318C22—221no—
319C22—221no—
320C22#6696712yes—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—221no—
327C4—221no—
328C4—221no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4C2×#434111yescharacteristic
334C4#6704311yescharacteristic
335C2—22no—
336C2—81no—
337C2—441no—
338C2#1062314211yescharacteristic
339C2C2×#6696711yescharacteristic
340C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
prime radical#10623142C2
hypercenter#465D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10623173C2semidirect
3. C11×#465C2semidirect
4. #10622787C2semidirect
5. #10622777C2semidirect
6. #10622724C2semidirect
7. C2×#66882C2semidirect
8. #10622656C2semidirect
9. #10622646C2semidirect
10. #10622474C2semidirect
11. #10622469C2semidirect
12. #10622422C2semidirect
13. #10622407C2semidirect
14. #10622397C2semidirect
15. #10622379C2semidirect
139. C8×C11#41semidirect
152. #465D11semidirect
276. C11#3343semidirect
311. C8#4341semidirect

Maximal subgroups

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

subgroupindex
#106231732
#106231422
C11×#4652
#106227872
#106227772
#106227242
C2×#668822
#106226562
#106226462
#106224742
#106224692
#106224222
#106224072
#106223972
#106223792
#334311