Finite Group Databasebeta

← #13081455

Subgroups — #13081455

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#10623202C211yesmaximal, characteristic
2#10623101C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic
4Q16×Dic11C211yesmaximal, characteristic, complemented
5#10622795C211yesmaximal, characteristic, complemented
6#10622779C211yesmaximal, characteristic
7#10622777C211yesmaximal, characteristic
8#10622668C211yesmaximal, characteristic
9#10622643C211yesmaximal, characteristic, complemented
10#10622463C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622410C211yesmaximal, characteristic, complemented
13#10622409C211yesmaximal, characteristic, complemented
14#10622381C211yesmaximal, characteristic
15#10622379C211yesmaximal, characteristic
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66989C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27#66943—21no—
28#66943—21no—
29#66943C2211yescharacteristic
30#66943C2211yescharacteristic
31#66932—21no—
32#66932—21no—
33#66931—21no—
34#66930—21no—
35#66922—21no—
36#66922C2211yescharacteristic
37C4×Dic22—21no—
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×Dic11—21no—
63C2×Dic22—21no—
64C2×Dic22D411yescharacteristic
65C2×Dic22C2311yescharacteristic
66C11×Q16—22no—
67C11×SD16—22no—
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C22⋊C4—21no—
73C11×C22⋊C4—21no—
74C42×C11—21no—
75C42×C11C2311yescharacteristic
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79#4326—22no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11D411yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4D411yescharacteristic
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3377—111nomaximal, Sylow
106C23×C11—21no—
107Q8×C11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11#4112yes—
111D4×C11—21no—
112D4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—42no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128Dic22—21no—
129Dic22—21no—
130Dic22—41no—
131Dic22—42no—
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#477—111no—
144#464—111no—
145#464D1111yescharacteristic
146#462—111no—
147#446—111no—
148#441—111no—
149#440—111no—
150C4×Q16—111no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11C22×D411yescharacteristic
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11C2×#4111yescharacteristic
161C4×C112−1+411yescharacteristic
162Dic11—21no—
163Dic11—21no—
164Dic11—21no—
165Dic11—21no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C2×Q16—111no—
171C2×Q16C2×D1111yescharacteristic
172C2×SD16C2×D1111yescharacteristic
173C4⋊Q8—111no—
174C4⋊Q8—111no—
175C4⋊Q8—221no—
176#126—221no—
177#126—221no—
178#125—111no—
179#125—111no—
180#125—221no—
181#125—221no—
182#124—111no—
183#124C2×D1111yescharacteristic
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#107—111no—
195#107—111no—
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#103—111no—
206#103C2×D1111yescharacteristic
207#102—111no—
208#102—111no—
209#102C2×D1111yescharacteristic
210#97—111no—
211#97—111no—
212C4×C8—111no—
213C2×C11—81no—
214C2×C11#54811yescharacteristic
215C2×C11#57511yescharacteristic
216C2×C11#57811yescharacteristic
217C2×Q8—111no—
218C2×Q8—111no—
219C2×Q8—221no—
220C2×Q8C22×D1111yescharacteristic
221C2×Q8C22×D1111yescharacteristic
222C2×D4C22×D1111yescharacteristic
223C22×C4—221no—
224Q16—22no—
225Q16—222no—
226SD16—22no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
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⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4C22×D1111yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
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—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—221no—
269Q8—221no—
270Q8—441no—
271Q8—442no—
272Q8#434112yes—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—221no—
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—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D1111yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—221no—
304C4—221no—
305C4—221no—
306C4—221no—
307C4—441no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4C2×#434111yescharacteristic
312C4#6704311yescharacteristic
313C2—81no—
314C2#1062312911yescharacteristic
315C2#1062330211yescharacteristic
316C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#464D11
hypocenterC11#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #10623101C2semidirect
4. Q16×Dic11C2semidirect
5. #10622795C2semidirect
9. #10622643C2semidirect
10. #10622463C2semidirect
11. #10622441C2semidirect
12. #10622410C2semidirect
13. #10622409C2semidirect
263. C11#3377semidirect

Maximal subgroups

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

subgroupindex
#106232022
#106231012
C11×#4642
Q16×Dic112
#106227952
#106227792
#106227772
#106226682
#106226432
#106224632
#106224412
#106224102
#106224092
#106223812
#106223792
#337711