Finite Group Databasebeta

← #13079279

Subgroups — #13079279

Order 1408.

350 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#10623156C211yesmaximal, characteristic, complemented
2#10623134C211yesmaximal, characteristic
3C11×#465C211yesmaximal, characteristic
4#10622780C211yesmaximal, characteristic, complemented
5#10622777C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7#10622714C211yesmaximal, characteristic, complemented
8#10622665C211yesmaximal, characteristic, complemented
9#10622655C211yesmaximal, characteristic
10#10622469C211yesmaximal, characteristic, complemented
11#10622466C211yesmaximal, characteristic, complemented
12#10622405C211yesmaximal, characteristic, complemented
13#10622403C211yesmaximal, characteristic, complemented
14#10622381C211yesmaximal, characteristic, complemented
15#10622371C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66989—21no—
24#66989C2211yescharacteristic
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28#66979C2211yescharacteristic
29#66977C2211yescharacteristic
30#66977C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C2×Dic44C2211yescharacteristic
33#66943—21no—
34#66943C2211yescharacteristic
35#66942—21no—
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38#66940C2211yescharacteristic
39#66932—21no—
40#66932—21no—
41#66932—21no—
42#66931—21no—
43C11×#106C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51#66879C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×Dic11—21no—
64C2×Dic22—21no—
65C2×Dic22C2311yescharacteristic
66C2×Dic22C2311yescharacteristic
67C11×SD16—22no—
68C2×C8×C11—22no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11D411yescharacteristic
82C22⋊Dic11D411yescharacteristic
83#4326—22no—
84#4324—22no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11D411yescharacteristic
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104#4318—22no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—22no—
108#3178—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—81no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132Dic22—21no—
133Dic22—21no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137C8×C11—21no—
138C8×C11#4112yes—
139C11⋊C8—21no—
140C11⋊C8#4112yes—
141#542—111no—
142#541—111no—
143#501—111no—
144#497—111no—
145#488—111no—
146#487—111no—
147#470—111no—
148#468—111no—
149#467—111no—
150#465D1111yescharacteristic
151#441—111no—
152#440—111no—
153C4×Q16—111no—
154C4×SD16—111no—
155#405—111no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C22×D411yescharacteristic
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11C2×#4111yescharacteristic
168C4×C11C2×#4111yescharacteristic
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×Q16—111no—
178C2×Q16—111no—
179C2×SD16—111no—
180C2×SD16C2×D1111yescharacteristic
181C2×M16—111no—
182C22×C8C2×D1111yescharacteristic
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—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—111no—
196C22⋊Q8—221no—
197C22⋊Q8C2×D1111yescharacteristic
198#121C2×D1111yescharacteristic
199C4×Q8—111no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×D4—111no—
203#117—111no—
204#107—111no—
205#107—111no—
206#106—111no—
207#106C2×D1111yescharacteristic
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103C2×D1111yescharacteristic
214#102—111no—
215#102C2×D1111yescharacteristic
216#97—111no—
217#97—111no—
218C4×C8—111no—
219C4×C8—111no—
220C2×C11—41no—
221C2×C11—81no—
222C2×C11#53211yescharacteristic
223C2×C11#57711yescharacteristic
224C2×C11#57811yescharacteristic
225C2×Q8—111no—
226C2×Q8—111no—
227C2×Q8—221no—
228C2×Q8C22×D1111yescharacteristic
229C2×D4—21no—
230C2×D4C22×D1111yescharacteristic
231C22×C4—221no—
232C22×C4C22×D1111yescharacteristic
233Q16—222no—
234Q16—222no—
235SD16—22no—
236SD16—222no—
237M16—222no—
238C2×C8—22no—
239C2×C8—111no—
240C2×C8—111no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—221no—
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⋊C4C22×D1111yescharacteristic
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—111no—
270C42—111no—
271C42—221no—
272C42—221no—
273C42—221no—
274C11#317811yescharacteristic, complemented, Sylow
275C23—21no—
276C23D4×D1111yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—221no—
280Q8—221no—
281Q8—221no—
282Q8—221no—
283Q8—881no—
284D4—21no—
285D4—21no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—881no—
301C2×C4D4×D1111yescharacteristic
302C2×C4C23×D1111yescharacteristic
303C8—21no—
304C8—112no—
305C8—221no—
306C8#434112yes—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22C2×D4×D1111yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—221no—
319C4—221no—
320C4—221no—
321C4—221no—
322C4—441no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4C2×#434111yescharacteristic
327C4#41×D1111yescharacteristic
328C2—41no—
329C2—81no—
330C2#1062312711yescharacteristic
331C2#1062329311yescharacteristic
332C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#465D11
hypocenterC11#3178
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. #10623156C2semidirect
4. #10622780C2semidirect
5. #10622777C2semidirect
6. #10622729C2semidirect
7. #10622714C2semidirect
8. #10622665C2semidirect
10. #10622469C2semidirect
11. #10622466C2semidirect
12. #10622405C2semidirect
13. #10622403C2semidirect
14. #10622381C2semidirect
15. #10622371C2semidirect
274. C11#3178semidirect

Maximal subgroups

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

subgroupindex
#106231562
#106231342
C11×#4652
#106227802
#106227772
#106227292
#106227142
#106226652
#106226552
#106224692
#106224662
#106224052
#106224032
#106223812
#106223712
#317811