Finite Group Databasebeta

← #13080073

Subgroups — #13080073

Order 1408.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623174C211yesmaximal, characteristic, complemented
2#10623134C211yesmaximal, characteristic, complemented
3C11×#468C211yesmaximal, characteristic, complemented
4#10622779C211yesmaximal, characteristic, complemented
5#10622778C211yesmaximal, characteristic, complemented
6#10622747C211yesmaximal, characteristic, complemented
7#10622732C211yesmaximal, characteristic, complemented
8#10622664C211yesmaximal, characteristic, complemented
9#10622651C211yesmaximal, characteristic
10#10622503C211yesmaximal, characteristic, complemented
11#10622488C211yesmaximal, characteristic, complemented
12#10622411C211yesmaximal, characteristic, complemented
13#10622407C211yesmaximal, characteristic, complemented
14#10622400C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×M16C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20#67000C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66989—21no—
24#66989C2211yescharacteristic
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983C2211yescharacteristic
29#66979C2211yescharacteristic
30#66977C2211yescharacteristic
31C22×C11⋊C8C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66951—21no—
34#66950—21no—
35#66946C2211yescharacteristic
36#66941C2211yescharacteristic
37#66941C2211yescharacteristic
38#66940C2211yescharacteristic
39#66938—21no—
40#66936—21no—
41#66932—21no—
42#66931—21no—
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66882C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22C2311yescharacteristic
70C11×SD16—41no—
71C11×M16—41no—
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84C22⋊Dic11D411yescharacteristic
85#4326—41no—
86#4323—41no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11D411yescharacteristic
93C4⋊Dic11D411yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8—41no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107#4314—41no—
108#3262—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—81no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133D44—21no—
134D44—21no—
135C4×D11—81no—
136Dic22—21no—
137Dic22—21no—
138Dic22—81no—
139Dic22—81no—
140C8×C11—21no—
141C8×C11—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144#542—111no—
145#542—111no—
146#477—111no—
147#477—111no—
148#474—111no—
149#474—111no—
150#468—111no—
151#468D1111yescharacteristic, complemented
152#467—111no—
153#466—111no—
154#464—111no—
155#464—111no—
156#463—111no—
157#463—111no—
158#424—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11C22×D411yescharacteristic
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11H(5,𝔽2)11yescharacteristic
174C4×C112−1+411yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16C2×D1111yescharacteristic
185C2×D8—111no—
186C2×M16C2×D1111yescharacteristic
187C22×C8—111no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190#126—221no—
191#126—221no—
192#124—111no—
193#124—111no—
194#124—221no—
195#124—221no—
196#123—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201C22⋊Q8C2×D1111yescharacteristic
202#121—111no—
203#121C2×D1111yescharacteristic
204C4×Q8—111no—
205C4×Q8—111no—
206C4×D4—111no—
207C4×D4—111no—
208#117—111no—
209#107—111no—
210#107—111no—
211#107—111no—
212#107C2×D1111yescharacteristic
213C4⋊C8—111no—
214C4⋊C8—111no—
215C4⋊C8—111no—
216C4⋊C8—111no—
217#103—111no—
218#103—111no—
219#103—111no—
220#103C2×D1111yescharacteristic
221#102—111no—
222#102—111no—
223#102—111no—
224#102C2×D1111yescharacteristic
225C2×C11—41no—
226C2×C11—81no—
227C2×C11#53711yescharacteristic
228C2×C11#57611yescharacteristic
229C2×C11#57811yescharacteristic
230D11—81no—
231C2×Q8—111no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8C22×D1111yescharacteristic
235C2×D4—21no—
236C2×D4—111no—
237C2×D4—221no—
238C2×D4C22×D1111yescharacteristic
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C22×D1111yescharacteristic
242Q16—441no—
243SD16—41no—
244SD16—441no—
245D8—441no—
246M16—41no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—441no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—111no—
267C22⋊C4—111no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C42—111no—
277C42—111no—
278C42—221no—
279C42—221no—
280C11#326211yescharacteristic, complemented, Sylow
281C23—21no—
282C23—221no—
283C23D4×D1111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288Q8—881no—
289Q8—881no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—221no—
294D4—221no—
295D4—881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—881no—
309C2×C4—881no—
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—221no—
315C8—221no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—221no—
331C4—221no—
332C4—221no—
333C4—221no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4#6703711yescharacteristic
338C4#6704311yescharacteristic
339C2—41no—
340C2—81no—
341C2—881no—
342C2#1062312811yescharacteristic
343C2#1062330511yescharacteristic
344C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10622651C2
hypercenter#468D11
hypocenterC11#3262
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623174C2semidirect
2. #10623134C2semidirect
3. C11×#468C2semidirect
4. #10622779C2semidirect
5. #10622778C2semidirect
6. #10622747C2semidirect
7. #10622732C2semidirect
8. #10622664C2semidirect
10. #10622503C2semidirect
11. #10622488C2semidirect
12. #10622411C2semidirect
13. #10622407C2semidirect
14. #10622400C2semidirect
15. #10622372C2semidirect
151. #468D11semidirect
280. C11#3262semidirect

Maximal subgroups

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

subgroupindex
#106231742
#106231342
C11×#4682
#106227792
#106227782
#106227472
#106227322
#106226642
#106226512
#106225032
#106224882
#106224112
#106224072
#106224002
#106223722
#326211