Finite Group Databasebeta

← #13079571

Subgroups — #13079571

Order 1408.

394 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623199C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic, complemented
5#10622794C211yesmaximal, characteristic, complemented
6#10622788C211yesmaximal, characteristic, complemented
7#10622786C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622641C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622446C211yesmaximal, characteristic, complemented
12#10622423C211yesmaximal, characteristic, complemented
13#10622405C211yesmaximal, characteristic, complemented
14#10622396C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22#66999C2211yescharacteristic
23#66997C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66993C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×Dic44C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32#66950C2211yescharacteristic
33#66949—21no—
34#66942—21no—
35#66941C2211yescharacteristic
36#66937—21no—
37#66937—21no—
38(C22⋊D11)⋊C4—21no—
39(C22⋊D11)⋊C4—21no—
40#66928C2211yescharacteristic
41#66925—21no—
42C42×D11C2211yescharacteristic
43C4×Dic22—21no—
44C4×Dic22C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66880C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66#4343—41no—
67#4343—41no—
68#4341—41no—
69#4341—41no—
70C2×D44—21no—
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11D411yescharacteristic
74C2×C4×D11D411yescharacteristic
75C2×C4×D11C2311yescharacteristic
76C2×Dic22—21no—
77C2×Dic22C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×Q16—41no—
80C11×SD16—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C42×C11—21no—
88C42×C11C2311yescharacteristic
89#4326—41no—
90#4326—41no—
91#4325—41no—
92#4324—41no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11D411yescharacteristic
108C4×Dic11D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113#4314—41no—
114#3210—111nomaximal, Sylow
115C23×C11—21no—
116C22×D11—21no—
117C22×D11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—42no—
132C22⋊D11—42no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—42no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—22no—
146C4×D11—22no—
147C4×D11—42no—
148Dic22—21no—
149Dic22—21no—
150Dic22—21no—
151Dic22—21no—
152Dic22—42no—
153C8×C11—21no—
154C8×C11—21no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157#533—111no—
158#532—111no—
159#494—111no—
160#492—111no—
161#487—111no—
162#486—111no—
163#464—111no—
164#464—111no—
165#464—111no—
166#464D1111yescharacteristic, complemented
167#452—111no—
168#452—111no—
169#452—111no—
170#452—111no—
171#431—111no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11C22×D411yescharacteristic
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11H(5,𝔽2)11yescharacteristic
188C4×C11H(5,𝔽2)11yescharacteristic
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11#13512yes—
194Dic11#13712yes—
195C2×#41—111no—
196C2×#41—111no—
197C2×Q16—111no—
198C2×Q16—111no—
199C2×Q16—111no—
200C2×Q16C2×D1111yescharacteristic
201C2×SD16—111no—
202C2×SD16—111no—
203C2×SD16—111no—
204C2×SD16C2×D1111yescharacteristic
205C4⋊Q8—111no—
206C4⋊Q8—111no—
207C4⋊Q8—111no—
208#127—111no—
209#125—221no—
210#124—111no—
211#124C2×D1111yescharacteristic
212C22⋊Q8—111no—
213C22⋊Q8—111no—
214C22⋊Q8—221no—
215#121—221no—
216#121—221no—
217C4×Q8—111no—
218C4×Q8—221no—
219C4×Q8C2×D1111yescharacteristic
220C4×D4—221no—
221C4×D4—221no—
222#117—221no—
223C2×C42—111no—
224C4⋊C8—111no—
225C4⋊C8C2×D1111yescharacteristic
226#103—111no—
227#103—111no—
228#103—111no—
229#103C2×D1111yescharacteristic
230#102—111no—
231#102—111no—
232#102—111no—
233#102C2×D1111yescharacteristic
234C22⋊C8—111no—
235C22⋊C8—111no—
236C4×C8—111no—
237C4×C8—111no—
238C2×C11—81no—
239C2×C11#53511yescharacteristic
240C2×C11C2×#13511yescharacteristic
241C2×C11C2×#13711yescharacteristic
242D11—41no—
243D11—81no—
244#41—441no—
245#41—441no—
246#41—441no—
247#41—441no—
248C2×Q8—111no—
249C2×Q8—111no—
250C2×Q8—221no—
251C2×Q8C22×D1111yescharacteristic
252C2×Q8C22×D1111yescharacteristic
253C2×D4—111no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4C22×D1111yescharacteristic
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—221no—
263C22×C4—221no—
264Q16—41no—
265Q16—441no—
266Q16—441no—
267Q16—441no—
268SD16—41no—
269SD16—441no—
270SD16—441no—
271SD16—441no—
272C2×C8—111no—
273C2×C8—111no—
274C2×C8C22×D1111yescharacteristic
275C2×C8C22×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—111no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4C22×D1111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C42—21no—
294C42—111no—
295C42—111no—
296C42—111no—
297C42—221no—
298C42C22×D1111yescharacteristic
299C11#321011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—111no—
302C23—221no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—221no—
308Q8—221no—
309Q8—221no—
310Q8—221no—
311Q8—442no—
312D4—21no—
313D4—21no—
314D4—221no—
315D4—221no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4D4×D1111yescharacteristic
336C2×C4D4×D1111yescharacteristic
337C2×C4C23×D1111yescharacteristic
338C8—21no—
339C8—21no—
340C8—221no—
341C8—221no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—221no—
346C22—221no—
347C22—221no—
348C22—441no—
349C22—441no—
350C22—441no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—112no—
358C4—112no—
359C4—221no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4#6703711yescharacteristic
364C4#6704211yescharacteristic
365C2—81no—
366C2—441no—
367C2—881no—
368C2#1062313811yescharacteristic
369C2D11×#13511yescharacteristic
370C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#10623199C2
hypercenter#464D11
hypocenterC11#3210
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. #10622800C2semidirect
5. #10622794C2semidirect
6. #10622788C2semidirect
7. #10622786C2semidirect
8. #10622667C2semidirect
9. #10622641C2semidirect
10. #10622458C2semidirect
11. #10622446C2semidirect
12. #10622423C2semidirect
13. #10622405C2semidirect
14. #10622396C2semidirect
15. #10622373C2semidirect
166. #464D11semidirect
299. C11#3210semidirect

Maximal subgroups

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

subgroupindex
#106231992
#106231092
C11×#4642
#106228002
#106227942
#106227882
#106227862
#106226672
#106226412
#106224582
#106224462
#106224232
#106224052
#106223962
#106223732
#321011