Finite Group Databasebeta

← #13081696

Subgroups — #13081696

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623099C211yesmaximal, characteristic, complemented
2#10623073C211yesmaximal, characteristic, complemented
3C11×#440C211yesmaximal, characteristic, complemented
4#10622781C211yesmaximal, characteristic
5#10622780C211yesmaximal, characteristic, complemented
6#10622644C211yesmaximal, characteristic, complemented
7#10622629C211yesmaximal, characteristic
8#10622502C211yesmaximal, characteristic, complemented
9#10622486C211yesmaximal, characteristic, complemented
10#10622411C211yesmaximal, characteristic, complemented
11#10622406C211yesmaximal, characteristic, complemented
12#10622400C211yesmaximal, characteristic
13#10622380C211yesmaximal, characteristic, complemented
14#10622328C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#67000C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66989C2211yescharacteristic
24#66989C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27#66979—21no—
28#66977—21no—
29C2×Dic44C2211yescharacteristic
30C2×Dic44C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66951—21no—
34#66949—21no—
35#66946C2211yescharacteristic
36#66940C2211yescharacteristic
37#66940C2211yescharacteristic
38#66940C2211yescharacteristic
39#66932—21no—
40#66932—21no—
41#66929—21no—
42#66928C2211yescharacteristic
43#66925—21no—
44#66922C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×#107C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49C11×#97C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×D44C2311yescharacteristic
63C2×C4×D11—21no—
64C2×Dic22D411yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×Dic22C2311yescharacteristic
67C2×Dic22C2311yescharacteristic
68C11×SD16—22no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C42×C11—21no—
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81#4326—41no—
82#4326—41no—
83#4324—41no—
84#4323—41no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11D411yescharacteristic
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
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—22no—
108Dic44—41no—
109#4314—22no—
110#4314—41no—
111#3402—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—42no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—21no—
133D44—21no—
134C4×D11—42no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—21no—
139Dic22—21no—
140Dic22—21no—
141Dic22—41no—
142C8×C11—21no—
143C8×C11#4112yes—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#556—111no—
147#556—111no—
148#497—111no—
149#497—111no—
150#495—111no—
151#464—111no—
152#464—111no—
153#463—111no—
154#463—111no—
155#462—111no—
156#462—111no—
157#446—111no—
158#440—111no—
159#440D1111yescharacteristic, complemented
160C4×Q16—111no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11C22×D411yescharacteristic
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11C2×#4111yescharacteristic
174C4×C11H(5,𝔽2)11yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×Q16—111no—
184C2×Q16—111no—
185C2×Q16—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×SD16—111no—
189C2×SD16C2×D1111yescharacteristic
190C2×D8—111no—
191C4⋊Q8—111no—
192C4⋊Q8—111no—
193#126—221no—
194#126—221no—
195#126—221no—
196#126—221no—
197#124—111no—
198#124—111no—
199#124—111no—
200#124—111no—
201C22⋊Q8—221no—
202C22⋊Q8—221no—
203C4×Q8—111no—
204C4×Q8—111no—
205C4×Q8—111no—
206C4×Q8—111no—
207C4×Q8C2×D1111yescharacteristic
208C4×D4—111no—
209C4×D4C2×D1111yescharacteristic
210#117—221no—
211#117—221no—
212#107C2×D1111yescharacteristic
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103C2×D1111yescharacteristic
220#102—111no—
221#102C2×D1111yescharacteristic
222#97—111no—
223#97C2×D1111yescharacteristic
224C4×C8—111no—
225C2×C11—81no—
226C2×C11#55011yescharacteristic
227C2×C11#57511yescharacteristic
228C2×C11#57811yescharacteristic
229D11—81no—
230C2×Q8—111no—
231C2×Q8—111no—
232C2×Q8—111no—
233C2×Q8—111no—
234C2×Q8C22×D1111yescharacteristic
235C2×D4—111no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—221no—
239Q16—222no—
240Q16—441no—
241Q16—441no—
242Q16—441no—
243SD16—22no—
244SD16—222no—
245SD16—441no—
246SD16—441no—
247D8—441no—
248C2×C8—111no—
249C2×C8—111no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
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—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C42—21no—
276C42—111no—
277C42—111no—
278C42—221no—
279C42—221no—
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#340211yescharacteristic, complemented, Sylow
283C23—21no—
284C23—221no—
285Q8—21no—
286Q8—21no—
287Q8—221no—
288Q8—221no—
289Q8—221no—
290Q8—221no—
291Q8—221no—
292Q8—221no—
293Q8—441no—
294D4—21no—
295D4—21no—
296D4—221no—
297D4—221no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—442no—
310C2×C4D4×D1111yescharacteristic
311C2×C4D4×D1111yescharacteristic
312C2×C4C23×D1111yescharacteristic
313C8—21no—
314C8—221no—
315C8—221no—
316C8#433912yes—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—441no—
321C22—441no—
322C22—441no—
323C22C2×D4×D1111yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—221no—
330C4—221no—
331C4—221no—
332C4—221no—
333C4—441no—
334C4—441no—
335C4—441no—
336C4C2×#433911yescharacteristic
337C4#6704211yescharacteristic
338C2—81no—
339C2—881no—
340C2#1062308411yescharacteristic
341C2#1062330411yescharacteristic
342C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#440D11
hypocenterC11#3402
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623099C2semidirect
2. #10623073C2semidirect
3. C11×#440C2semidirect
5. #10622780C2semidirect
6. #10622644C2semidirect
8. #10622502C2semidirect
9. #10622486C2semidirect
10. #10622411C2semidirect
11. #10622406C2semidirect
13. #10622380C2semidirect
14. #10622328C2semidirect
15. #10622314C2semidirect
159. #440D11semidirect
282. C11#3402semidirect

Maximal subgroups

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

subgroupindex
#106230992
#106230732
C11×#4402
#106227812
#106227802
#106226442
#106226292
#106225022
#106224862
#106224112
#106224062
#106224002
#106223802
#106223282
#106223142
#340211