Finite Group Databasebeta

← #13080596

Subgroups — #13080596

Order 1408.

394 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#10623355C211yesmaximal, characteristic, complemented
2#10623145C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic, complemented
4#10622846C211yesmaximal, characteristic, complemented
5#10622787C211yesmaximal, characteristic, complemented
6#10622775C211yesmaximal, characteristic, complemented
7#10622771C211yesmaximal, characteristic, complemented
8#10622765C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic, complemented
10#10622418C211yesmaximal, characteristic, complemented
11#10622410C211yesmaximal, characteristic, complemented
12#10622384C211yesmaximal, characteristic, complemented
13#10622379C211yesmaximal, characteristic, complemented
14#10622343C211yesmaximal, characteristic, complemented
15#10622336C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#121C2211yescharacteristic
21#66999C2211yescharacteristic
22#66997C2211yescharacteristic
23#66992—21no—
24#66991—21no—
25#66991C2211yescharacteristic
26#66988—21no—
27#66988—21no—
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31#66982—21no—
32C4×C22⋊D11C2211yescharacteristic
33#66979C2211yescharacteristic
34#66977C2211yescharacteristic
35C2×Dic11⋊C4—21no—
36C22×C11⋊C8C2211yescharacteristic
37C2×#4313C2211yescharacteristic
38C4⋊C4×D11C2211yescharacteristic
39#66943C2211yescharacteristic
40(C22⋊D11)⋊C4—21no—
41#66932—21no—
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66879C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57#66874C2211yescharacteristic
58#66872C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74#4341—22no—
75#4341—41no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×SD16—41no—
80C11×D8—22no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11D411yescharacteristic
91#4324—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3307—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—42no—
122D4×C11—81no—
123D4×C11#4112yes—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—41no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—81no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—81no—
147Dic22—21no—
148Dic22—21no—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#553—111no—
154#547—111no—
155#491—111no—
156#485—111no—
157#483—111no—
158#478—111no—
159#468—111no—
160#465—111no—
161#461—111no—
162#449—111no—
163#449D1111yescharacteristic, complemented
164#442—111no—
165#435—111no—
166#417—111no—
167#416—111no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11C2×#4111yescharacteristic
185C4×C11H(5,𝔽2)11yescharacteristic
186Dic11—21no—
187Dic11—21no—
188Dic11—21no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41C2×D1111yescharacteristic
195C2×SD16—111no—
196C2×SD16C2×D1111yescharacteristic
197C2×D8C2×D1111yescharacteristic
198C2×M16—111no—
199C22×C8—111no—
200C4⋊Q8—111no—
201#126—221no—
202#125—111no—
203#123—221no—
204#123—221no—
205#123—221no—
206C22⋊Q8—111no—
207C22⋊Q8—111no—
208#121—111no—
209#121—221no—
210#121—221no—
211#121C2×D1111yescharacteristic
212C4×D4—111no—
213C4×D4—111no—
214C4×D4—111no—
215C4×D4—221no—
216#117—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219#107—111no—
220#106—111no—
221#106—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103C2×D1111yescharacteristic
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233C22⋊C8—111no—
234C22⋊C8C2×D1111yescharacteristic
235#97—111no—
236C2×C11—41no—
237C2×C11—42no—
238C2×C11—81no—
239C2×C11#54611yescharacteristic
240C2×C11#57511yescharacteristic
241C2×C11#57711yescharacteristic
242D11—41no—
243#41—22no—
244#41—41no—
245#41—222no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4C22×D1111yescharacteristic
255C2×D4C22×D1111yescharacteristic
256C22×C4—21no—
257C22×C4—111no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4C22×D1111yescharacteristic
263SD16—41no—
264SD16—441no—
265D8—22no—
266M16—441no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—441no—
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⋊C4C22×D1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—111no—
286C22⋊C4—111no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C42—111no—
294C42—221no—
295C11#330711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—111no—
299C23D4×D1111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—221no—
303Q8—221no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—81no—
309D4—441no—
310D4—442no—
311D4—442no—
312D4#434112yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—221no—
347C22—221no—
348C22—221no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—221no—
354C4—221no—
355C4—221no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#434111yescharacteristic
361C4#6703711yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—441no—
366C2#1062312211yescharacteristic
367C2#1062329911yescharacteristic
368C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3307
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623355C2semidirect
2. #10623145C2semidirect
3. C11×#449C2semidirect
4. #10622846C2semidirect
5. #10622787C2semidirect
6. #10622775C2semidirect
7. #10622771C2semidirect
8. #10622765C2semidirect
9. #10622654C2semidirect
10. #10622418C2semidirect
11. #10622410C2semidirect
12. #10622384C2semidirect
13. #10622379C2semidirect
14. #10622343C2semidirect
15. #10622336C2semidirect
163. #449D11semidirect
295. C11#3307semidirect

Maximal subgroups

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

subgroupindex
#106233552
#106231452
C11×#4492
#106228462
#106227872
#106227752
#106227712
#106227652
#106226542
#106224182
#106224102
#106223842
#106223792
#106223432
#106223362
#330711