Finite Group Databasebeta

← #13080887

Subgroups — #13080887

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623164C211yesmaximal, characteristic
2#10623044C211yesmaximal, characteristic, complemented
3C11×#484C211yesmaximal, characteristic, complemented
4#10622665C211yesmaximal, characteristic, complemented
5#10622579C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622498C211yesmaximal, characteristic, complemented
8#10622490C211yesmaximal, characteristic, complemented
9#10622486C211yesmaximal, characteristic, complemented
10#10622421C211yesmaximal, characteristic, complemented
11#10622415C211yesmaximal, characteristic, complemented
12#10622413C211yesmaximal, characteristic, complemented
13#10622411C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#67000C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22#66982—21no—
23C4×C22⋊D11C2211yescharacteristic
24#66979—21no—
25#66977C2211yescharacteristic
26C2×#4318C2211yescharacteristic
27C2×Dic44C2211yescharacteristic
28C2×#4314C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66949—21no—
33#66948C2211yescharacteristic
34#66946—21no—
35#66945C2211yescharacteristic
36#66943C2211yescharacteristic
37#66942—21no—
38#66940C2211yescharacteristic
39#66940C2211yescharacteristic
40#66938—21no—
41#66937—21no—
42C11×#107C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×C22⋊C8C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic
58#66872C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64Q8×D11—22no—
65Q8×D11—41no—
66#4339—22no—
67#4339—41no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×Dic22—21no—
74C2×Dic22C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11D411yescharacteristic
86#4326—41no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108Dic44—22no—
109#4314—41no—
110#4313—41no—
111#3327—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—41no—
127C22⋊D11—42no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—42no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—42no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—42no—
145Dic22#4112yes—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#548—111no—
152#488—111no—
153#484D1111yescharacteristic, complemented
154#482—111no—
155#479—111no—
156#470—111no—
157#468—111no—
158#464—111no—
159#452—111no—
160#451—111no—
161C4×Q16—111no—
162#436—111no—
163#419—111no—
164#417—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11C22×D411yescharacteristic
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11C2×#4111yescharacteristic
181C4×C11H(5,𝔽2)11yescharacteristic
182Dic11—22no—
183Dic11—21no—
184Dic11—21no—
185Dic11—21no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C22×Q8—111no—
190C2×Q16—111no—
191C2×Q16—111no—
192C2×SD16—111no—
193C2×M16—111no—
194C2×M16—111no—
195#126—221no—
196#125—111no—
197#125—221no—
198#124—111no—
199#124—221no—
200#123—221no—
201C22⋊Q8—111no—
202C22⋊Q8—111no—
203C22⋊Q8—221no—
204C22⋊Q8C2×D1111yescharacteristic
205#121—111no—
206#121—221no—
207C4×Q8—111no—
208C4×Q8—111no—
209C4×D4—111no—
210C4×D4—221no—
211#117—111no—
212#117—221no—
213C2×C4⋊C4C2×D1111yescharacteristic
214#107C2×D1111yescharacteristic
215#107C2×D1111yescharacteristic
216#106—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225#102—111no—
226#102—111no—
227#102—111no—
228C22⋊C8—111no—
229C22⋊C8C2×D1111yescharacteristic
230C4×C8—111no—
231C2×C11—41no—
232C2×C11#54611yescharacteristic
233C2×C11#57511yescharacteristic
234C2×C11#57811yescharacteristic
235D11—41no—
236D11—81no—
237#41—222no—
238#41—441no—
239C2×Q8—111no—
240C2×Q8—111no—
241C2×Q8—221no—
242C2×Q8—222no—
243C2×Q8—441no—
244C2×Q8C22×D1111yescharacteristic
245C2×D4—111no—
246C2×D4—111no—
247C2×D4—221no—
248C2×D4—221no—
249C22×C4—21no—
250C22×C4—111no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4C22×D1111yescharacteristic
254Q16—222no—
255Q16—441no—
256SD16—441no—
257M16—441no—
258M16—441no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8C22×D1111yescharacteristic
262C2×C8C22×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4C22×D1111yescharacteristic
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—111no—
278C22⋊C4—111no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—111no—
286C42—221no—
287C42—221no—
288C42—221no—
289C11#332711yescharacteristic, complemented, Sylow
290C23—111no—
291C23—221no—
292C23D4×D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—112no—
296Q8—221no—
297Q8—221no—
298Q8—221no—
299Q8—442no—
300D4—221no—
301D4—221no—
302D4—442no—
303D4—441no—
304D4—442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—111no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4D4×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—221no—
327C8—221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—221no—
344C4—221no—
345C4—221no—
346C4—222no—
347C4—441no—
348C4—441no—
349C4#41×D1111yescharacteristic
350C4#6704211yescharacteristic
351C2—41no—
352C2—441no—
353C2—881no—
354C2#1062318511yescharacteristic
355C2#1062329711yescharacteristic
356C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radical#10623164C2
hypercenter#484D11
hypocenterC11#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #10623044C2semidirect
3. C11×#484C2semidirect
4. #10622665C2semidirect
5. #10622579C2semidirect
6. #10622499C2semidirect
7. #10622498C2semidirect
8. #10622490C2semidirect
9. #10622486C2semidirect
10. #10622421C2semidirect
11. #10622415C2semidirect
12. #10622413C2semidirect
13. #10622411C2semidirect
14. #10622346C2semidirect
15. #10622342C2semidirect
153. #484D11semidirect
289. C11#3327semidirect

Maximal subgroups

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

subgroupindex
#106231642
#106230442
C11×#4842
#106226652
#106225792
#106224992
#106224982
#106224902
#106224862
#106224212
#106224152
#106224132
#106224112
#106223462
#106223422
#332711