Finite Group Databasebeta

← #13079232

Subgroups — #13079232

Order 1408.

362 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#10623264C211yesmaximal, characteristic, complemented
2#10623213C211yesmaximal, characteristic, complemented
3C11×#489C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5#10622672C211yesmaximal, characteristic, complemented
6#10622429C211yesmaximal, characteristic, complemented
7#10622420C211yesmaximal, characteristic, complemented
8#10622402C211yesmaximal, characteristic, complemented
9#10622401C211yesmaximal, characteristic, complemented
10#10622398C211yesmaximal, characteristic, complemented
11#10622395C211yesmaximal, characteristic
12#10622391C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14#10622327C211yesmaximal, characteristic, complemented
15#10622321C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#124C2211yescharacteristic
18#67000—21no—
19#66999—21no—
20#66999C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24#66991C2211yescharacteristic
25D4×Dic11C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66946C2211yescharacteristic
35#66940C2211yescharacteristic
36#66939—21no—
37#66938—21no—
38#66932—21no—
39#66931—21no—
40#66928C2211yescharacteristic
41#66925C2211yescharacteristic
42#66922C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×#97C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64C2×D44—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11C2311yescharacteristic
68C2×Dic22—21no—
69C2×Dic22C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80#4326—22no—
81#4325—22no—
82#4324—22no—
83#4323—22no—
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)⋊C4D411yescharacteristic
91(C2×D11)⋊C4D411yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3173—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—81no—
115D4×C11—21no—
116D4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—81no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—81no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—21no—
132D44—21no—
133D44—81no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—81no—
137Dic22—21no—
138Dic22—21no—
139Dic22—81no—
140C8×C11—21no—
141C8×C11—21no—
142C11⋊C8#4112yes—
143C11⋊C8#4112yes—
144#542—111no—
145#542—111no—
146#498—111no—
147#495—111no—
148#489—111no—
149#489D1111yescharacteristic, complemented
150#470—111no—
151#469—111no—
152#465—111no—
153#465—111no—
154#442—111no—
155#441—111no—
156C4×SD16—111no—
157C4×SD16—111no—
158#405—111no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C11C2×#4111yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16—111no—
185C2×D8—111no—
186C2×M16—111no—
187C22×C8—111no—
188C4⋊Q8—111no—
189C4⋊Q8C2×D1111yescharacteristic
190#126—221no—
191#126—221no—
192#124—111no—
193#124—221no—
194#124—221no—
195#124C2×D1111yescharacteristic
196#123—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200C22⋊Q8—221no—
201C22⋊Q8—221no—
202#121—111no—
203#121—111no—
204C4×Q8—111no—
205C4×Q8—111no—
206C4×D4—111no—
207C4×D4—111no—
208#117—111no—
209#106—111no—
210#106—111no—
211#106—111no—
212#106—111no—
213#103—111no—
214#103—111no—
215#103C2×D1111yescharacteristic
216#103C2×D1111yescharacteristic
217#102—111no—
218#102—111no—
219#102C2×D1111yescharacteristic
220#102C2×D1111yescharacteristic
221#97—111no—
222#97C2×D1111yescharacteristic
223C4×C8—111no—
224C4×C8—111no—
225C2×C11—81no—
226C2×C11#53211yescharacteristic
227C2×C11#57711yescharacteristic
228C2×C11#57711yescharacteristic
229D11—41no—
230D11—81no—
231C2×Q8—21no—
232C2×Q8—111no—
233C2×Q8—221no—
234C2×Q8C22×D1111yescharacteristic
235C2×D4—111no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4C22×D1111yescharacteristic
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242Q16—222no—
243SD16—222no—
244SD16—222no—
245D8—222no—
246M16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—222no—
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—221no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#317311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—111no—
283C23—221no—
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—221no—
288Q8—221no—
289Q8—881no—
290D4—21no—
291D4—21no—
292D4—221no—
293D4—221no—
294D4—881no—
295D4—881no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—112no—
315C8—112no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—221no—
320C22—221no—
321C22—221no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—221no—
332C4—221no—
333C4—221no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4#41×D1111yescharacteristic
338C4#41×D1111yescharacteristic
339C2—81no—
340C2—441no—
341C2—881no—
342C2#1062319911yescharacteristic
343C2#1062330611yescharacteristic
344C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#489C2
socleC22×C11C22×D4
prime radical#10622395C2
hypercenter#489D11
hypocenterC11#3173
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10623264C2semidirect
2. #10623213C2semidirect
3. C11×#489C2semidirect
4. #10622692C2semidirect
5. #10622672C2semidirect
6. #10622429C2semidirect
7. #10622420C2semidirect
8. #10622402C2semidirect
9. #10622401C2semidirect
10. #10622398C2semidirect
12. #10622391C2semidirect
13. #10622371C2semidirect
14. #10622327C2semidirect
15. #10622321C2semidirect
149. #489D11semidirect
280. C11#3173semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106232132
C11×#4892
#106226922
#106226722
#106224292
#106224202
#106224022
#106224012
#106223982
#106223952
#106223912
#106223712
#106223272
#106223212
#317311