Finite Group Databasebeta

← #13079291

Subgroups — #13079291

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#10623264C211yesmaximal, characteristic
2#10623262C211yesmaximal, characteristic, complemented
3C11×#487C211yesmaximal, characteristic, complemented
4#10622699C211yesmaximal, characteristic, complemented
5#10622693C211yesmaximal, characteristic, complemented
6#10622430C211yesmaximal, characteristic, complemented
7#10622429C211yesmaximal, characteristic, complemented
8#10622426C211yesmaximal, characteristic, complemented
9#10622425C211yesmaximal, characteristic
10#10622420C211yesmaximal, characteristic
11#10622403C211yesmaximal, characteristic, complemented
12#10622402C211yesmaximal, characteristic, complemented
13#10622401C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15#10622302C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×C4⋊Q8C2211yescharacteristic
18#67000—21no—
19#66999—21no—
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66951—21no—
32#66951—21no—
33#66950C2211yescharacteristic
34#66948C2211yescharacteristic
35#66947—21no—
36#66946C2211yescharacteristic
37#66942—21no—
38#66942—21no—
39#66940C2211yescharacteristic
40#66928C2211yescharacteristic
41#66925C2211yescharacteristic
42#66923C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C4×C8×C11C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D44—21no—
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11C2311yescharacteristic
66C2×Dic22C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C42×C11C2311yescharacteristic
75#4326—22no—
76#4326—22no—
77#4325—22no—
78#4325—22no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4D411yescharacteristic
87(C2×D11)⋊C4D411yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3178—111nomaximal, Sylow
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11—81no—
116C2×C4×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
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129D44—21no—
130D44—21no—
131D44—81no—
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—81no—
135Dic22—21no—
136Dic22—21no—
137C8×C11—21no—
138C8×C11—21no—
139C11⋊C8#4112yes—
140C11⋊C8#4112yes—
141#542—111no—
142#541—111no—
143#501—111no—
144#497—111no—
145#488—111no—
146#487D1111yescharacteristic, complemented
147#470—111no—
148#468—111no—
149#467—111no—
150#465—111no—
151#441—111no—
152#440—111no—
153C4×Q16—111no—
154C4×SD16—111no—
155#405—111no—
156C22×C11C22×D411yescharacteristic
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C11C2×#4111yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×Q16—111no—
178C2×Q16—111no—
179C2×SD16—111no—
180C2×SD16—111no—
181C2×M16—111no—
182C22×C8—111no—
183C4⋊Q8C2×D1111yescharacteristic
184C4⋊Q8C2×D1111yescharacteristic
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—111no—
197C22⋊Q8—221no—
198#121—111no—
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#106—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#103C2×D1111yescharacteristic
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214#102—111no—
215#102—111no—
216#97—111no—
217#97—111no—
218C4×C8—111no—
219C4×C8C2×D1111yescharacteristic
220C2×C11#53211yescharacteristic
221C2×C11#57711yescharacteristic
222C2×C11#57811yescharacteristic
223D11—41no—
224D11—81no—
225C2×Q8—21no—
226C2×Q8—111no—
227C2×Q8C22×D1111yescharacteristic
228C2×Q8C22×D1111yescharacteristic
229C2×D4—111no—
230C2×D4—221no—
231C22×C4—111no—
232C22×C4—221no—
233Q16—222no—
234Q16—222no—
235SD16—222no—
236SD16—222no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
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—111no—
261C22⋊C4—111no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—111no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#317811yescharacteristic, complemented, Sylow
275C23—111no—
276C23—221no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—81no—
282Q8—221no—
283Q8—221no—
284D4—221no—
285D4—221no—
286D4—881no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—111no—
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—112no—
306C8—112no—
307C22—221no—
308C22—221no—
309C22—221no—
310C22—441no—
311C22—441no—
312C22—441no—
313C22C2×D4×D1111yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—221no—
321C4—221no—
322C4—221no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4#41×D1111yescharacteristic
327C4#41×D1111yescharacteristic
328C2—441no—
329C2—881no—
330C2#1062319911yescharacteristic
331C2#1062329311yescharacteristic
332C2#1062329711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#487C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#487D11
hypocenterC11#3178
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #10623262C2semidirect
3. C11×#487C2semidirect
4. #10622699C2semidirect
5. #10622693C2semidirect
6. #10622430C2semidirect
7. #10622429C2semidirect
8. #10622426C2semidirect
11. #10622403C2semidirect
12. #10622402C2semidirect
13. #10622401C2semidirect
14. #10622310C2semidirect
15. #10622302C2semidirect
146. #487D11semidirect
274. C11#3178semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106232622
C11×#4872
#106226992
#106226932
#106224302
#106224292
#106224262
#106224252
#106224202
#106224032
#106224022
#106224012
#106223102
#106223022
#317811