Finite Group Databasebeta

← #13081331

Subgroups — #13081331

Order 1408.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623258C211yesmaximal, characteristic, complemented
2#10623202C211yesmaximal, characteristic, complemented
3C11×#489C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic
6#10622431C211yesmaximal, characteristic, complemented
7#10622430C211yesmaximal, characteristic, complemented
8#10622407C211yesmaximal, characteristic, complemented
9#10622405C211yesmaximal, characteristic, complemented
10#10622400C211yesmaximal, characteristic
11#10622378C211yesmaximal, characteristic, complemented
12#10622372C211yesmaximal, characteristic, complemented
13#10622369C211yesmaximal, characteristic
14#10622323C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×Q8×D11—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#124C2211yescharacteristic
19#66999—21no—
20Q8×Dic11C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66989C2211yescharacteristic
24D4×Dic11C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27#66949—21no—
28#66949—21no—
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66941C2211yescharacteristic
32#66941C2211yescharacteristic
33#66932—21no—
34#66932—21no—
35#66931—21no—
36#66930—21no—
37C4×D44C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×Dic11—21no—
63Q8×D11—44no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×Dic22—21no—
69C2×Dic22—21no—
70C2×Dic22D411yescharacteristic
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83#4325—22no—
84#4323—22no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11D411yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4314—22no—
106#3367—111nomaximal, Sylow
107C23×C11—21no—
108C22×D11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—42no—
112D4×C11—21no—
113D4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—42no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128D44—21no—
129D44#4112yes—
130C4×D11—42no—
131C4×D11—42no—
132C4×D11—42no—
133Dic22—22no—
134Dic22—21no—
135Dic22—21no—
136Dic22—42no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142#556—111no—
143D4×Q8—111no—
144#489—111no—
145#489D1111yescharacteristic, complemented
146#487—111no—
147#477—111no—
148#477—111no—
149#474—111no—
150#463—111no—
151#463—111no—
152#461—111no—
153#446—111no—
154#440—111no—
155#440—111no—
156C4×D8—111no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C2×D11—22no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177Dic11AGL(1,ℤ/8)12yes—
178C22×Q8—221no—
179C2×SD16—111no—
180C2×SD16—111no—
181C2×D8—111no—
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184C4⋊Q8—111no—
185C4⋊Q8C2×D1111yescharacteristic
186#126—221no—
187#126—221no—
188#124—111no—
189#124C2×D1111yescharacteristic
190C22⋊Q8—221no—
191C22⋊Q8—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—111no—
201#117—221no—
202#107—111no—
203#107—111no—
204#107—111no—
205C4⋊C8—111no—
206C4⋊C8—111no—
207C4⋊C8—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214#102—111no—
215#102—111no—
216#102C2×D1111yescharacteristic
217#102C2×D1111yescharacteristic
218#97—111no—
219#97C2×D1111yescharacteristic
220C4×C8—111no—
221C2×C11—81no—
222C2×C11#54811yescharacteristic
223C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
224C2×C11#57811yescharacteristic
225D11—42no—
226C2×Q8—21no—
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—444no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—111no—
234C2×D4C22×D1111yescharacteristic
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239SD16—222no—
240SD16—222no—
241D8—222no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8C22×D1111yescharacteristic
245C2×C8C22×D1111yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—111no—
248C4⋊C4—111no—
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⋊C4—221no—
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C42—111no—
269C42—111no—
270C42—221no—
271C42—221no—
272C42C22×D1111yescharacteristic
273C11#336711yescharacteristic, complemented, Sylow
274C23—21no—
275C23—221no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—222no—
280Q8—221no—
281Q8—221no—
282Q8—442no—
283Q8—442no—
284D4—21no—
285D4—21no—
286D4—112no—
287D4—221no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4D4×D1111yescharacteristic
303C2×C4D4×D1111yescharacteristic
304C2×C4C23×D1111yescharacteristic
305C8—21no—
306C8—21no—
307C8—221no—
308C8—221no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—222no—
313C22—441no—
314C22—441no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—112no—
322C4—221no—
323C4—221no—
324C4—221no—
325C4—441no—
326C4—441no—
327C4—441no—
328C4#41×D1111yescharacteristic
329C4#6704311yescharacteristic
330C2—81no—
331C2—442no—
332C2#1062320811yescharacteristic
333C2D11×AGL(1,ℤ/8)11yescharacteristic
334C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#489C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#489D11
hypocenterC11#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10623258C2semidirect
2. #10623202C2semidirect
3. C11×#489C2semidirect
4. #10622704C2semidirect
6. #10622431C2semidirect
7. #10622430C2semidirect
8. #10622407C2semidirect
9. #10622405C2semidirect
11. #10622378C2semidirect
12. #10622372C2semidirect
14. #10622323C2semidirect
15. #10622314C2semidirect
145. #489D11semidirect
273. C11#3367semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106232022
C11×#4892
#106227042
#106226702
#106224312
#106224302
#106224072
#106224052
#106224002
#106223782
#106223722
#106223692
#106223232
#106223142
#336711