Finite Group Databasebeta

← #13079570

Subgroups — #13079570

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#10623363C211yesmaximal, characteristic
2#10623153C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622798C211yesmaximal, characteristic, complemented
6#10622794C211yesmaximal, characteristic, complemented
7#10622788C211yesmaximal, characteristic, complemented
8#10622779C211yesmaximal, characteristic, complemented
9#10622660C211yesmaximal, characteristic, complemented
10#10622411C211yesmaximal, characteristic, complemented
11#10622405C211yesmaximal, characteristic, complemented
12#10622380C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15#10622331C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21#67000C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66993C2211yescharacteristic
29#66992—21no—
30#66992—21no—
31#66989C2211yescharacteristic
32C2×#4324C2211yescharacteristic
33C4×C22⋊D11—21no—
34C4×C22⋊D11—21no—
35#66977C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37C2×Dic44C2211yescharacteristic
38C2×#4314C2211yescharacteristic
39#66942—21no—
40#66941C2211yescharacteristic
41#66940—21no—
42#66940C2211yescharacteristic
43#66931—21no—
44#66930—21no—
45C11×#103C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×C22⋊C8C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66885C2211yescharacteristic
52#66880C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66874C2211yescharacteristic
58#66873C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C22×Dic11D411yescharacteristic
71C22×Dic11D411yescharacteristic
72#4339—41no—
73#4339—41no—
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
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—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4326—41no—
90#4326—41no—
91#4325—41no—
92#4324—41no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11D411yescharacteristic
107C4×Dic11D411yescharacteristic
108C4×Dic11C2311yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113#4314—41no—
114#3210—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—42no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—42no—
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—21no—
146D44—21no—
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#464—111no—
167#452—111no—
168#452—111no—
169#452—111no—
170#452D1111yescharacteristic, complemented
171#431—111no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11C22×D411yescharacteristic
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11H(5,𝔽2)11yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11#13512yes—
194Dic11#13712yes—
195C2×#41—111no—
196C2×#41C2×D1111yescharacteristic
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#124—111no—
212C22⋊Q8—111no—
213C22⋊Q8—221no—
214C22⋊Q8C2×D1111yescharacteristic
215#121—221no—
216#121—221no—
217C4×Q8—111no—
218C4×Q8—111no—
219C4×Q8—221no—
220C4×D4—221no—
221C4×D4—221no—
222#117—221no—
223C2×C42—111no—
224C4⋊C8—111no—
225C4⋊C8—111no—
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⋊C8C2×D1111yescharacteristic
236C4×C8—111no—
237C4×C8—111no—
238C2×C11—41no—
239C2×C11—81no—
240C2×C11#53511yescharacteristic
241C2×C11C2×#13511yescharacteristic
242C2×C11C2×#13711yescharacteristic
243D11—81no—
244#41—41no—
245#41—41no—
246#41—441no—
247#41—441no—
248C2×Q8—111no—
249C2×Q8—111no—
250C2×Q8—221no—
251C2×Q8C22×D1111yescharacteristic
252C2×Q8C22×D1111yescharacteristic
253C2×D4—21no—
254C2×D4—111no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4C22×D1111yescharacteristic
259C22×C4—21no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—221no—
263C22×C4C22×D1111yescharacteristic
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—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C42—111no—
294C42—111no—
295C42—111no—
296C42—111no—
297C42—221no—
298C42—221no—
299C11#321011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—221no—
302C23D4×D1111yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—221no—
308Q8—221no—
309Q8—221no—
310Q8—221no—
311Q8—442no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—221no—
316D4—221no—
317D4—442no—
318D4—442no—
319D4—442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—111no—
327C2×C4—111no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—442no—
336C2×C4D4×D1111yescharacteristic
337C2×C4C23×D1111yescharacteristic
338C8—21no—
339C8—21no—
340C8—221no—
341C8—221no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—441no—
349C22—441no—
350C22—441no—
351C22C2×D4×D1111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—112no—
357C4—112no—
358C4—221no—
359C4—221no—
360C4—441no—
361C4—441no—
362C4—441no—
363C4#6703711yescharacteristic
364C4#6703711yescharacteristic
365C2—41no—
366C2—81no—
367C2—881no—
368C2#1062312311yescharacteristic
369C2D11×#13511yescharacteristic
370C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radical#10623363C2
hypercenter#452D11
hypocenterC11#3210
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10623153C2semidirect
3. C11×#452C2semidirect
4. #10622852C2semidirect
5. #10622798C2semidirect
6. #10622794C2semidirect
7. #10622788C2semidirect
8. #10622779C2semidirect
9. #10622660C2semidirect
10. #10622411C2semidirect
11. #10622405C2semidirect
12. #10622380C2semidirect
13. #10622373C2semidirect
14. #10622346C2semidirect
15. #10622331C2semidirect
170. #452D11semidirect
299. C11#3210semidirect

Maximal subgroups

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

subgroupindex
#106233632
#106231532
C11×#4522
#106228522
#106227982
#106227942
#106227882
#106227792
#106226602
#106224112
#106224052
#106223802
#106223732
#106223462
#106223312
#321011