Finite Group Databasebeta

← #13081436

Subgroups — #13081436

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623263C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#461C211yesmaximal, characteristic, complemented
4#10622778C211yesmaximal, characteristic
5#10622778C211yesmaximal, characteristic
6#10622777C211yesmaximal, characteristic, complemented
7SD16×Dic11C211yesmaximal, characteristic, complemented
8#10622695C211yesmaximal, characteristic, complemented
9#10622627C211yesmaximal, characteristic
10#10622460C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622413C211yesmaximal, characteristic, complemented
13#10622409C211yesmaximal, characteristic, complemented
14#10622408C211yesmaximal, characteristic, complemented
15#10622404C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21#67000C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24D4×Dic11C2211yescharacteristic
25D4×Dic11C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27#66977—21no—
28C2×Dic11⋊C4—21no—
29#66951—21no—
30#66951—21no—
31#66950—21no—
32#66945—21no—
33#66943C2211yescharacteristic
34#66941C2211yescharacteristic
35#66931—21no—
36#66931—21no—
37C4×D44C2211yescharacteristic
38#66923C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×Dic22—21no—
68C2×Dic22D411yescharacteristic
69C11×SD16—22no—
70C11×SD16—22no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80#4323—22no—
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—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11D411yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3376—111nomaximal, Sylow
106C23×C11—21no—
107C22×D11—21no—
108Q8×C11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—21no—
112D4×C11—21no—
113D4×C11#4112yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—81no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—42no—
125C2×Dic11—81no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130D44—21no—
131D44—21no—
132C4×D11—42no—
133Dic22—41no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#556—111no—
140#554—111no—
141#491—111no—
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#475—111no—
147#463—111no—
148#463—111no—
149#461D1111yescharacteristic, complemented
150#446—111no—
151#442—111no—
152#440—111no—
153C4×SD16—111no—
154C22×C11—22no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11C22×D411yescharacteristic
158C2×D11—41no—
159C2×D11—41no—
160C2×D11—41no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11C2×#4111yescharacteristic
167C4×C112−1+411yescharacteristic
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×SD16C2×D1111yescharacteristic
176C2×SD16C2×D1111yescharacteristic
177C2×D8—111no—
178C4⋊Q8—111no—
179C4⋊Q8C2×D1111yescharacteristic
180#126—221no—
181#126—221no—
182#125—111no—
183#125—111no—
184#124—111no—
185#124—111no—
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—111no—
193C4×D4—111no—
194C4×D4—111no—
195C4×D4—111no—
196C4×D4C2×D1111yescharacteristic
197#117—221no—
198C2×C4⋊C4—221no—
199#107—111no—
200#106—111no—
201#106—111no—
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8C2×D1111yescharacteristic
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103C2×D1111yescharacteristic
210#103C2×D1111yescharacteristic
211#102—111no—
212#102—111no—
213#102—111no—
214#102—111no—
215#97—111no—
216#97—111no—
217C4×C8—111no—
218C2×C11—42no—
219C2×C11#54811yescharacteristic
220C2×C11#57511yescharacteristic
221C2×C11#57711yescharacteristic
222D11—81no—
223C2×Q8—111no—
224C2×Q8—221no—
225C2×Q8C22×D1111yescharacteristic
226C2×Q8C22×D1111yescharacteristic
227C2×D4—111no—
228C2×D4C22×D1111yescharacteristic
229C22×C4—21no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233SD16—22no—
234SD16—22no—
235D8—222no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8C22×D1111yescharacteristic
239C2×C8C22×D1111yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C42—111no—
265C42—111no—
266C42—221no—
267C42—221no—
268C42C22×D1111yescharacteristic
269C11#337611yescharacteristic, complemented, Sylow
270C23—21no—
271C23—221no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—441no—
277Q8—881no—
278D4—21no—
279D4—221no—
280D4—221no—
281D4#434112yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—881no—
296C2×C4D4×D1111yescharacteristic
297C2×C4D4×D1111yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—221no—
302C8—221no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22C2×D4×D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—221no—
316C4—221no—
317C4—221no—
318C4—221no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4C2×#434111yescharacteristic
323C4#6704311yescharacteristic
324C2—42no—
325C2—881no—
326C2#1062312911yescharacteristic
327C2#1062329311yescharacteristic
328C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#461C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#461D11
hypocenterC11#3376
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10623263C2semidirect
2. #10623070C2semidirect
3. C11×#461C2semidirect
6. #10622777C2semidirect
7. SD16×Dic11C2semidirect
8. #10622695C2semidirect
10. #10622460C2semidirect
11. #10622441C2semidirect
12. #10622413C2semidirect
13. #10622409C2semidirect
14. #10622408C2semidirect
15. #10622404C2semidirect
149. #461D11semidirect
269. C11#3376semidirect

Maximal subgroups

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

subgroupindex
#106232632
#106230702
C11×#4612
#106227782
#106227772
SD16×Dic112
#106226952
#106226272
#106224602
#106224412
#106224132
#106224092
#106224082
#106224042
#337611