Finite Group Databasebeta

← #13079950

Subgroups — #13079950

Order 1408.

354 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623211C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622801C211yesmaximal, characteristic, complemented
5#10622795C211yesmaximal, characteristic, complemented
6#10622784C211yesmaximal, characteristic
7#10622775C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622635C211yesmaximal, characteristic, complemented
10D11×C4⋊C8C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622426C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622391C211yesmaximal, characteristic
15#10622372C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66991C2211yescharacteristic
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66950C2211yescharacteristic
31#66949—21no—
32#66942—21no—
33#66941C2211yescharacteristic
34#66936—21no—
35(C22⋊D11)⋊C4—21no—
36#66932—21no—
37#66930—21no—
38#66925—21no—
39C42×D11C2211yescharacteristic
40#66923C2211yescharacteristic
41C4×Dic22—21no—
42C4×Dic22C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C2×C4×D11D411yescharacteristic
65C2×C4×D11D411yescharacteristic
66C2×C4×D11C2311yescharacteristic
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C11×Q16—41no—
70C11×SD16—41no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81#4326—41no—
82#4324—41no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C8×D11—41no—
107C8×D11—41no—
108#3248—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—42no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C4×D11—22no—
133C4×D11—21no—
134C4×D11—21no—
135C4×D11—22no—
136Dic22—21no—
137Dic22—21no—
138Dic22—42no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#533—111no—
144#529—111no—
145#479—111no—
146#479—111no—
147#475—111no—
148#474—111no—
149#467—111no—
150#467—111no—
151#465—111no—
152#465—111no—
153#464—111no—
154#464D1111yescharacteristic, complemented
155#462—111no—
156#461—111no—
157C2×C4⋊C8—111no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11C22×D411yescharacteristic
162C2×D11—21no—
163C2×D11—21no—
164C2×D11#13712yes—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11H(5,𝔽2)11yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11#13512yes—
179C2×Q16—111no—
180C2×Q16C2×D1111yescharacteristic
181C2×SD16—111no—
182C2×SD16C2×D1111yescharacteristic
183C22×C8—111no—
184C22×C8—111no—
185C4⋊Q8—111no—
186C4⋊Q8—111no—
187#126—221no—
188#125—111no—
189#125—221no—
190#124C2×D1111yescharacteristic
191#123—221no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196#121—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—221no—
200C4×Q8C2×D1111yescharacteristic
201C4×D4—111no—
202C4×D4—221no—
203#117—221no—
204#117—221no—
205C2×C42—111no—
206#107—111no—
207#107—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213C4⋊C8C2×D1111yescharacteristic
214#103—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103C2×D1111yescharacteristic
220#102—111no—
221#102C2×D1111yescharacteristic
222C2×C11—81no—
223C2×C11#53711yescharacteristic
224C2×C11C2×#13511yescharacteristic
225C2×C11C2×#13711yescharacteristic
226D11—22no—
227C2×Q8—111no—
228C2×Q8—221no—
229C2×Q8C22×D1111yescharacteristic
230C2×Q8C22×D1111yescharacteristic
231C2×D4—221no—
232C2×D4C22×D1111yescharacteristic
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—221no—
237Q16—41no—
238Q16—441no—
239SD16—41no—
240SD16—441no—
241C2×C8—111no—
242C2×C8—111no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—21no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#324811yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—221no—
284Q8—221no—
285Q8—442no—
286D4—21no—
287D4—21no—
288D4—442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—222no—
296C2×C4—222no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—442no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—112no—
315C22—221no—
316C22—221no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—112no—
324C4—221no—
325C4—221no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4#6703711yescharacteristic
331C4#6704311yescharacteristic
332C2—81no—
333C2—222no—
334C2#1062313911yescharacteristic
335C2D11×#13511yescharacteristic
336C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#464D11
hypocenterC11#3248
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. #10623109C2semidirect
3. C11×#464C2semidirect
4. #10622801C2semidirect
5. #10622795C2semidirect
7. #10622775C2semidirect
8. #10622667C2semidirect
9. #10622635C2semidirect
10. D11×C4⋊C8C2semidirect
11. #10622442C2semidirect
12. #10622426C2semidirect
13. #10622404C2semidirect
15. #10622372C2semidirect
154. #464D11semidirect
276. C11#3248semidirect

Maximal subgroups

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

subgroupindex
#106232112
#106231092
C11×#4642
#106228012
#106227952
#106227842
#106227752
#106226672
#106226352
D11×C4⋊C82
#106224422
#106224262
#106224042
#106223912
#106223722
#324811