Finite Group Databasebeta

← #13081465

Subgroups — #13081465

Order 1408.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623252C211yesmaximal, characteristic, complemented
2#10623099C211yesmaximal, characteristic
3C11×#477C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic
5#10622643C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic
7#10622502C211yesmaximal, characteristic
8#10622490C211yesmaximal, characteristic, complemented
9#10622486C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic
11#10622441C211yesmaximal, characteristic, complemented
12#10622413C211yesmaximal, characteristic
13#10622411C211yesmaximal, characteristic
14#10622410C211yesmaximal, characteristic, complemented
15#10622406C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#67000C2211yescharacteristic
19Q8×Dic11—21no—
20#66997—21no—
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×Dic44C2211yescharacteristic
24C2×#4314C2211yescharacteristic
25#66951—21no—
26#66949—21no—
27#66946C2211yescharacteristic
28#66943C2211yescharacteristic
29#66943C2211yescharacteristic
30#66942—21no—
31#66942—21no—
32#66940C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66929—21no—
36#66928C2211yescharacteristic
37#66925—21no—
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46#66885C2211yescharacteristic
47#66880C2211yescharacteristic
48#66879C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×Dic22D411yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C42×C11—21no—
74C42×C11C2311yescharacteristic
75#4326—22no—
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11D411yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85Dic11⋊C4—21no—
86Dic11⋊C4—21no—
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4D411yescharacteristic
94Dic11⋊C4D411yescharacteristic
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103Dic44—22no—
104#4314—22no—
105#3377—111nomaximal, Sylow
106C22×D11—21no—
107Q8×C11—21no—
108Q8×C11—21no—
109Q8×C11—42no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124D44—21no—
125D44—21no—
126C4×D11—42no—
127Dic22—21no—
128Dic22—21no—
129Dic22—21no—
130Dic22—41no—
131Dic22#4112yes—
132C8×C11—21no—
133C8×C11—21no—
134C11⋊C8—21no—
135C11⋊C8—21no—
136#557—111no—
137#556—111no—
138#491—111no—
139#489—111no—
140#488—111no—
141#479—111no—
142#478—111no—
143#477D1111yescharacteristic, complemented
144#464—111no—
145#464—111no—
146#462—111no—
147#446—111no—
148#441—111no—
149#440—111no—
150C4×Q16—111no—
151C22×C11C22×D411yescharacteristic
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—41no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11C2×#4111yescharacteristic
162C4×C112−1+411yescharacteristic
163Dic11—22no—
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—21no—
168Dic11—41no—
169Dic11—41no—
170C2×Q16—111no—
171C2×Q16—111no—
172C2×SD16—111no—
173C4⋊Q8—111no—
174C4⋊Q8—221no—
175C4⋊Q8C2×D1111yescharacteristic
176#126—221no—
177#126—221no—
178#125—111no—
179#125—111no—
180#125—221no—
181#125—221no—
182#124—111no—
183#124—111no—
184C22⋊Q8—221no—
185C4×Q8—111no—
186C4×Q8—111no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—221no—
191C4×Q8C2×D1111yescharacteristic
192C4×D4—111no—
193#117—221no—
194#107C2×D1111yescharacteristic
195#107C2×D1111yescharacteristic
196#106—111no—
197C4⋊C8—111no—
198C4⋊C8—111no—
199C4⋊C8C2×D1111yescharacteristic
200#103—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#103C2×D1111yescharacteristic
206#103C2×D1111yescharacteristic
207#102—111no—
208#102—111no—
209#102—111no—
210#97—111no—
211#97—111no—
212C4×C8—111no—
213C2×C11#54811yescharacteristic
214C2×C11#57511yescharacteristic
215C2×C11#57811yescharacteristic
216D11—81no—
217C2×Q8—21no—
218C2×Q8—111no—
219C2×Q8—111no—
220C2×Q8—111no—
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C22×C4—221no—
224Q16—222no—
225Q16—222no—
226SD16—222no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C4⋊C4C22×D1111yescharacteristic
250C22⋊C4—221no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C42—21no—
256C42—111no—
257C42—111no—
258C42—221no—
259C42—221no—
260C42—221no—
261C42—221no—
262C42C22×D1111yescharacteristic
263C11#337711yescharacteristic, complemented, Sylow
264C23—221no—
265Q8—21no—
266Q8—21no—
267Q8—42no—
268Q8—112no—
269Q8—221no—
270Q8—221no—
271Q8—221no—
272Q8—441no—
273D4—221no—
274D4—221no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—442no—
287C2×C4D4×D1111yescharacteristic
288C2×C4D4×D1111yescharacteristic
289C2×C4C23×D1111yescharacteristic
290C8—21no—
291C8—21no—
292C8—221no—
293C8—221no—
294C22—441no—
295C22—441no—
296C22—441no—
297C22C2×D4×D1111yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—221no—
305C4—221no—
306C4—221no—
307C4—221no—
308C4—222no—
309C4—441no—
310C4—441no—
311C4#6704011yescharacteristic
312C4#41×D1111yescharacteristic
313C2—881no—
314C2#1062316411yescharacteristic
315C2#1062329711yescharacteristic
316C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#477D11
hypocenterC11#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10623252C2semidirect
3. C11×#477C2semidirect
5. #10622643C2semidirect
8. #10622490C2semidirect
9. #10622486C2semidirect
11. #10622441C2semidirect
14. #10622410C2semidirect
15. #10622406C2semidirect
143. #477D11semidirect
263. C11#3377semidirect

Maximal subgroups

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

subgroupindex
#106232522
#106230992
C11×#4772
#106227022
#106226432
#106225042
#106225022
#106224902
#106224862
#106224582
#106224412
#106224132
#106224112
#106224102
#106224062
#337711