Finite Group Databasebeta

← #13081351

Subgroups — #13081351

Order 1408.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623202C211yesmaximal, characteristic
2Q8×Dic22C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic
4#10622797C211yesmaximal, characteristic, complemented
5#10622795C211yesmaximal, characteristic, complemented
6#10622779C211yesmaximal, characteristic
7SD16×Dic11C211yesmaximal, characteristic
8#10622668C211yesmaximal, characteristic
9#10622643C211yesmaximal, characteristic, complemented
10#10622464C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622405C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622378C211yesmaximal, characteristic
15#10622374C211yesmaximal, 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#66941—21no—
28#66941—21no—
29#66941C2211yescharacteristic
30#66941C2211yescharacteristic
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#66881C2211yescharacteristic
49#66881C2211yescharacteristic
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×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22D411yescharacteristic
67C2×Dic22C2311yescharacteristic
68C11×Q16—22no—
69C11×SD16—22no—
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C42×C11—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81#4326—22no—
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#3369—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—22no—
129Dic22—21no—
130Dic22—21no—
131Dic22—81no—
132Dic22—81no—
133Dic22—81no—
134C8×C11—21no—
135C8×C11—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138Q82—111no—
139#556—111no—
140#489—111no—
141#489—111no—
142#487—111no—
143#476—111no—
144#475—111no—
145#475—111no—
146#464—111no—
147#464D1111yescharacteristic
148#462—111no—
149#446—111no—
150#441—111no—
151#441—111no—
152C4×SD16—111no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11C22×D411yescharacteristic
157C4×C11—22no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11C2×#4111yescharacteristic
163C4×C112−1+411yescharacteristic
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11#13712yes—
172C2×Q16—111no—
173C2×Q16C2×D1111yescharacteristic
174C2×SD16C2×D1111yescharacteristic
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177C4⋊Q8—111no—
178C4⋊Q8—111no—
179C4⋊Q8—221no—
180C4⋊Q8—221no—
181C4⋊Q8—221no—
182#126—221no—
183#126—221no—
184#124—111no—
185#124C2×D1111yescharacteristic
186C22⋊Q8—221no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—111no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—221no—
193C4×Q8C2×D1111yescharacteristic
194C4×D4—111no—
195#117—221no—
196#106—111no—
197#106—111no—
198#106—111no—
199C4⋊C8—111no—
200C4⋊C8—111no—
201C4⋊C8C2×D1111yescharacteristic
202#103—111no—
203#103—111no—
204#103—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103C2×D1111yescharacteristic
209#102—111no—
210#102—111no—
211#102C2×D1111yescharacteristic
212#97—111no—
213#97—111no—
214C4×C8—111no—
215C2×C11—81no—
216C2×C11#54811yescharacteristic
217C2×C11C2×#13711yescharacteristic
218C2×C11#57711yescharacteristic
219C2×Q8—111no—
220C2×Q8—111no—
221C2×Q8—221no—
222C2×Q8—221no—
223C2×Q8—221no—
224C2×Q8C22×D1111yescharacteristic
225C2×Q8C22×D1111yescharacteristic
226C2×D4C22×D1111yescharacteristic
227C22×C4—221no—
228Q16—22no—
229Q16—222no—
230SD16—22no—
231C2×C8—111no—
232C2×C8—111no—
233C2×C8C22×D1111yescharacteristic
234C2×C8C22×D1111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4C22×D1111yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—221no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C42—21no—
258C42—111no—
259C42—111no—
260C42—221no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42C22×D1111yescharacteristic
265C11#336911yescharacteristic, complemented, Sylow
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—222no—
271Q8—221no—
272Q8—221no—
273Q8—881no—
274Q8—881no—
275Q8—881no—
276Q8#434112yes—
277D4—21no—
278D4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—111no—
283C2×C4—111no—
284C2×C4—111no—
285C2×C4—111no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—442no—
291C2×C4D4×D1111yescharacteristic
292C2×C4D4×D1111yescharacteristic
293C2×C4C23×D1111yescharacteristic
294C8—21no—
295C8—21no—
296C8—221no—
297C8—221no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22C2×D4×D1111yescharacteristic
302C4—21no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—112no—
308C4—221no—
309C4—221no—
310C4—221no—
311C4—441no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4C2×#434111yescharacteristic
316C4#6704311yescharacteristic
317C2—81no—
318C2#1062312911yescharacteristic
319C2#1062330111yescharacteristic
320C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#464D11
hypocenterC11#3369
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. Q8×Dic22C2semidirect
4. #10622797C2semidirect
5. #10622795C2semidirect
9. #10622643C2semidirect
10. #10622464C2semidirect
11. #10622441C2semidirect
12. #10622405C2semidirect
13. #10622404C2semidirect
265. C11#3369semidirect

Maximal subgroups

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

subgroupindex
#106232022
Q8×Dic222
C11×#4642
#106227972
#106227952
#106227792
SD16×Dic112
#106226682
#106226432
#106224642
#106224412
#106224052
#106224042
#106223782
#106223742
#336911