Finite Group Databasebeta

← #13081371

Subgroups — #13081371

Order 1408.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623116C211yesmaximal, characteristic, complemented
2#10623110C211yesmaximal, characteristic, complemented
3C11×#446C211yesmaximal, characteristic, complemented
4#10622460C211yesmaximal, characteristic, complemented
5#10622459C211yesmaximal, characteristic, complemented
6#10622457C211yesmaximal, characteristic, complemented
7#10622457C211yesmaximal, characteristic, complemented
8#10622456C211yesmaximal, characteristic
9#10622442C211yesmaximal, characteristic, complemented
10#10622327C211yesmaximal, characteristic, complemented
11#10622326C211yesmaximal, characteristic, complemented
12#10622324C211yesmaximal, characteristic, complemented
13#10622323C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15C4×D88C211yesmaximal, characteristic, complemented
16C4×Q8×C11C2211yescharacteristic
17#67000—21no—
18#66999—21no—
19C2×D88C2211yescharacteristic
20C2×D88C2211yescharacteristic
21C2×#4314C2211yescharacteristic
22#66949—21no—
23#66949—21no—
24#66947—21no—
25#66947—21no—
26#66946—21no—
27C4⋊C4×D11—21no—
28#66928C2211yescharacteristic
29#66928C2211yescharacteristic
30#66927C2211yescharacteristic
31C4×D44C2211yescharacteristic
32C4×D44C2211yescharacteristic
33C4×D44C2211yescharacteristic
34C4×D44C2211yescharacteristic
35C4×D44C2211yescharacteristic
36#66923C2211yescharacteristic
37#66923C2211yescharacteristic
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44C11×#97C2211yescharacteristic
45C4×C8×C11C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic
53#66882C2211yescharacteristic
54#66882C2211yescharacteristic
55#66881C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×Q8×C11D411yescharacteristic
60C2×D44—21no—
61C2×D44—21no—
62C2×D44C2311yescharacteristic
63C2×D44C2311yescharacteristic
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4D411yescharacteristic
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4D411yescharacteristic
79C42×C11C2311yescharacteristic
80C42×C11C2311yescharacteristic
81C42×C11C2311yescharacteristic
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102D88—22no—
103D88—22no—
104#4314—22no—
105#3370—111nomaximal, Sylow
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109Q8×C11—41no—
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122D44—21no—
123D44—21no—
124D44—21no—
125D44—21no—
126D44—21no—
127D44—42no—
128D44—81no—
129D44#4112yes—
130C4×D11—42no—
131C4×D11—81no—
132C4×D11—81no—
133C4×D11—81no—
134C4×D11—81no—
135Dic22—21no—
136Dic22—21no—
137Dic22—81no—
138C8×C11—21no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—21no—
142#559—111no—
143#554—111no—
144#490—111no—
145#489—111no—
146#488—111no—
147#479—111no—
148#478—111no—
149#474—111no—
150#463—111no—
151#463—111no—
152#459—111no—
153#446D1111yescharacteristic, complemented
154#442—111no—
155#440—111no—
156C4×D8—111no—
157C22×C11C22×D411yescharacteristic
158C2×D11—22no—
159C2×D11—41no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11C2×#4111yescharacteristic
174C4×C112−1+411yescharacteristic
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×SD16—111no—
181C2×D8—111no—
182C2×D8—111no—
183C4⋊Q8—111no—
184#127—111no—
185#125—111no—
186#125—111no—
187#124—111no—
188#124—111no—
189#124—221no—
190#123—221no—
191#123—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C22⋊Q8—221no—
195C4×Q8—111no—
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—111no—
202C4×D4—221no—
203C2×C4⋊C4—221no—
204#107—111no—
205#107—111no—
206#106—111no—
207C4⋊C8C2×D1111yescharacteristic
208C4⋊C8C2×D1111yescharacteristic
209C4⋊C8C2×D1111yescharacteristic
210#103—111no—
211#103—111no—
212#103—111no—
213#102—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#97C2×D1111yescharacteristic
221#97C2×D1111yescharacteristic
222C4×C8C2×D1111yescharacteristic
223C2×C11#54811yescharacteristic
224C2×C11#57511yescharacteristic
225C2×C11#57611yescharacteristic
226D11—42no—
227D11—81no—
228D11—81no—
229C2×Q8—111no—
230C2×Q8—221no—
231C2×Q8D4411yescharacteristic
232C2×D4—111no—
233C2×D4—111no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242SD16—222no—
243D8—222no—
244D8—222no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4D4411yescharacteristic
260C4⋊C4D4411yescharacteristic
261C4⋊C4D4411yescharacteristic
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—221no—
272C42C22×D1111yescharacteristic
273C42C22×D1111yescharacteristic
274C42C22×D1111yescharacteristic
275C11#337011yescharacteristic, complemented, Sylow
276C23—221no—
277C23—221no—
278C23—221no—
279Q8—41no—
280Q8—221no—
281Q8—221no—
282Q8—881no—
283D4—112no—
284D4—221no—
285D4—221no—
286D4—221no—
287D4—221no—
288D4—221no—
289D4—442no—
290D4—881no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—442no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×D4411yescharacteristic
302C2×C4C2×D4411yescharacteristic
303C2×C4C2×D4411yescharacteristic
304C2×C4C2×D4411yescharacteristic
305C2×C4C2×D4411yescharacteristic
306C2×C4C2×D4411yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C22—222no—
313C22—441no—
314C22—441no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22—441no—
319C22—441no—
320C22—441no—
321C22C22×D4411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4#6704011yescharacteristic
334C4#41×D1111yescharacteristic
335C2—442no—
336C2—881no—
337C2—881no—
338C2#1062310711yescharacteristic
339C2#1062327911yescharacteristic
340C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#446C2
socleC22×C11C22×D4
prime radical#10622456C2
hypercenter#446D11
hypocenterC11#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #10623116C2semidirect
2. #10623110C2semidirect
3. C11×#446C2semidirect
4. #10622460C2semidirect
5. #10622459C2semidirect
6. #10622457C2semidirect
7. #10622457C2semidirect
9. #10622442C2semidirect
10. #10622327C2semidirect
11. #10622326C2semidirect
12. #10622324C2semidirect
13. #10622323C2semidirect
14. #10622310C2semidirect
15. C4×D88C2semidirect
153. #446D11semidirect
275. C11#3370semidirect

Maximal subgroups

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

subgroupindex
#106231162
#106231102
C11×#4462
#106224602
#106224592
#106224572
#106224562
#106224422
#106223272
#106223262
#106223242
#106223232
#106223102
C4×D882
#337011