Finite Group Databasebeta

← #13080744

Subgroups — #13080744

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623084C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622747C211yesmaximal, characteristic, complemented
5#10622746C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7#10622726C211yesmaximal, characteristic, complemented
8#10622461C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622348C211yesmaximal, characteristic, complemented
12#10622346C211yesmaximal, characteristic, complemented
13#10622346C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622326C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21#66993—21no—
22#66988—21no—
23#66983C2211yescharacteristic
24#66983C2211yescharacteristic
25#66979C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×Dic44C2211yescharacteristic
30C2×#4314C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32#66946—21no—
33#66942—21no—
34#66937—21no—
35#66937—21no—
36#66932—21no—
37#66930—21no—
38#66927C2211yescharacteristic
39#66923C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45C11×#97C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66882C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67#4339—22no—
68#4339—22no—
69#4339—41no—
70#4339—41no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44C2311yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×Dic22C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×M16—41no—
80C2×C8×C11—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4D411yescharacteristic
86C11×C22⋊C4D411yescharacteristic
87C11×C22⋊C4D411yescharacteristic
88C42×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108Dic44—22no—
109#4314—41no—
110#4314—41no—
111#3317—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116D4×C11—41no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—42no—
127C22⋊D11—42no—
128C22⋊D11—81no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137D44—21no—
138D44—21no—
139D44—21no—
140D44—21no—
141D44—42no—
142D44—81no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22#4112yes—
149C8×C11—21no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—21no—
153#552—111no—
154#550—111no—
155#490—111no—
156#482—111no—
157#481—111no—
158#479—111no—
159#468—111no—
160#465—111no—
161#460—111no—
162#452—111no—
163#452—111no—
164#441—111no—
165#435D1111yescharacteristic, complemented
166#417—111no—
167#416—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C22×D411yescharacteristic
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—22no—
188Dic11—41no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41—111no—
195C2×Q16—111no—
196C2×SD16—111no—
197C2×SD16—111no—
198C2×M16C2×D1111yescharacteristic
199C22×C8C2×D1111yescharacteristic
200#127—111no—
201#127—221no—
202#126—221no—
203#125—111no—
204#125—221no—
205#123—221no—
206C22⋊Q8—111no—
207C22⋊Q8—111no—
208#121—111no—
209#121—111no—
210#121—221no—
211#121—221no—
212C4×Q8—111no—
213C4×Q8—111no—
214C4×D4—221no—
215C4×D4C2×D1111yescharacteristic
216#117—111no—
217#117—221no—
218C2×C4⋊C4—111no—
219#107—111no—
220#106—111no—
221#106—111no—
222C4⋊C8C2×D1111yescharacteristic
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233C22⋊C8C2×D1111yescharacteristic
234C22⋊C8C2×D1111yescharacteristic
235#97C2×D1111yescharacteristic
236C2×C11—41no—
237C2×C11—41no—
238C2×C11#54611yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57711yescharacteristic
241D11—81no—
242D11—81no—
243#41—222no—
244#41—222no—
245#41—441no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8—111no—
249C2×D4—111no—
250C2×D4—111no—
251C2×D4—221no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4D4411yescharacteristic
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4C22×D1111yescharacteristic
262C22×C4C22×D1111yescharacteristic
263Q16—222no—
264SD16—441no—
265SD16—441no—
266M16—41no—
267C2×C8—41no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4D4411yescharacteristic
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4D4411yescharacteristic
290C22⋊C4D4411yescharacteristic
291C42—221no—
292C42—221no—
293C42—221no—
294C42C22×D1111yescharacteristic
295C11#331711yescharacteristic, complemented, Sylow
296C23—221no—
297C23—221no—
298C23C2×D4411yescharacteristic
299C23C2×D4411yescharacteristic
300Q8—112no—
301Q8—221no—
302Q8—221no—
303Q8—221no—
304D4—41no—
305D4—221no—
306D4—221no—
307D4—221no—
308D4—221no—
309D4—442no—
310D4—442no—
311D4—442no—
312D4—881no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4C2×D4411yescharacteristic
329C2×C4C2×D4411yescharacteristic
330C2×C4C2×D4411yescharacteristic
331C2×C4C2×D4411yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C22×D4411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—222no—
355C4—441no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4#6703711yescharacteristic
361C4#41×D1111yescharacteristic
362C2—41no—
363C2—41no—
364C2—881no—
365C2—881no—
366C2#1062308511yescharacteristic
367C2#1062327911yescharacteristic
368C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radical#10623084C2
hypercenter#435D11
hypocenterC11#3317
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. C11×#435C2semidirect
4. #10622747C2semidirect
5. #10622746C2semidirect
6. #10622727C2semidirect
7. #10622726C2semidirect
8. #10622461C2semidirect
9. #10622442C2semidirect
10. #10622350C2semidirect
11. #10622348C2semidirect
12. #10622346C2semidirect
13. #10622346C2semidirect
14. #10622329C2semidirect
15. #10622326C2semidirect
165. #435D11semidirect
295. C11#3317semidirect

Maximal subgroups

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

subgroupindex
#106230842
#106230722
C11×#4352
#106227472
#106227462
#106227272
#106227262
#106224612
#106224422
#106223502
#106223482
#106223462
#106223292
#106223262
#331711