Finite Group Databasebeta

← #13080889

Subgroups — #13080889

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#10623112C211yesmaximal, characteristic, complemented
2#10623107C211yesmaximal, characteristic
3C4×C11×Q16C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic, complemented
5#10622799C211yesmaximal, characteristic, complemented
6#10622641C211yesmaximal, characteristic, complemented
7#10622635C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic, complemented
9#10622497C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622425C211yesmaximal, characteristic, complemented
12#10622416C211yesmaximal, characteristic, complemented
13#10622415C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15#10622301C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21#66999C2211yescharacteristic
22#66999C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26C2×#4313C2211yescharacteristic
27#66950—21no—
28#66950C2211yescharacteristic
29#66948—21no—
30#66948C2211yescharacteristic
31#66947—21no—
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66942—21no—
35#66929—21no—
36#66928—21no—
37#66928C2211yescharacteristic
38C4×D44—21no—
39C4×D44C2211yescharacteristic
40#66925—21no—
41#66923C2211yescharacteristic
42C11×#107C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C4×C8×C11C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61#4343—22no—
62#4343—41no—
63Q8×D11—22no—
64Q8×D11—41no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44D411yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×Dic22C2311yescharacteristic
76C11×Q16—22no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86#4326—41no—
87#4325—41no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4D411yescharacteristic
96(C2×D11)⋊C4D411yescharacteristic
97C4⋊Dic11—21no—
98C4⋊Dic11D411yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4313—41no—
110#4313—41no—
111#3327—111nomaximal, Sylow
112C22×D11—21no—
113C22×D11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11#4112yes—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—21no—
132D44—21no—
133D44—41no—
134D44—42no—
135D44—42no—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—42no—
141C4×D11—42no—
142C4×D11—42no—
143Dic22—21no—
144Dic22—21no—
145Dic22—42no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#548—111no—
152#488—111no—
153#484—111no—
154#482—111no—
155#479—111no—
156#470—111no—
157#468—111no—
158#464—111no—
159#452—111no—
160#451—111no—
161C4×Q16D1111yescharacteristic, complemented
162#436—111no—
163#419—111no—
164#417—111no—
165C22×C11C22×D411yescharacteristic
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—22no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11C2×#4111yescharacteristic
182C4×C11H(5,𝔽2)11yescharacteristic
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C22×Q8—111no—
190C2×Q16—111no—
191C2×Q16C2×D1111yescharacteristic
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—111no—
204C22⋊Q8—221no—
205#121—111no—
206#121—221no—
207C4×Q8C2×D1111yescharacteristic
208C4×Q8C2×D1111yescharacteristic
209C4×D4—111no—
210C4×D4—221no—
211#117—111no—
212#117—221no—
213C2×C4⋊C4—111no—
214#107—111no—
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⋊C8—111no—
230C4×C8C2×D1111yescharacteristic
231C2×C11#54611yescharacteristic
232C2×C11#57511yescharacteristic
233C2×C11#57811yescharacteristic
234D11—41no—
235D11—41no—
236D11—81no—
237#41—222no—
238#41—441no—
239C2×Q8—111no—
240C2×Q8—221no—
241C2×Q8—222no—
242C2×Q8—441no—
243C2×Q8C22×D1111yescharacteristic
244C2×Q8C22×D1111yescharacteristic
245C2×D4—111no—
246C2×D4—111no—
247C2×D4—221no—
248C2×D4—221no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254Q16—22no—
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—111no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—111no—
277C22⋊C4—111no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—21no—
286C42—21no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#332711yescharacteristic, complemented, Sylow
290C23—111no—
291C23—111no—
292C23—221no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—221no—
297Q8—221no—
298Q8—442no—
299Q8#433912yes—
300D4—221no—
301D4—221no—
302D4—441no—
303D4—442no—
304D4—442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4D4×D1111yescharacteristic
322C2×C4D4×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—221no—
327C8—221no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—221no—
345C4—221no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4C2×#433911yescharacteristic
350C4#6704211yescharacteristic
351C2—441no—
352C2—441no—
353C2—881no—
354C2#1062308111yescharacteristic
355C2#1062329711yescharacteristic
356C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×Q16C2
socleC22×C11C22×D4
prime radical#10623107C2
hypercenterC4×Q16D11
hypocenterC11#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #10623112C2semidirect
3. C4×C11×Q16C2semidirect
4. #10622800C2semidirect
5. #10622799C2semidirect
6. #10622641C2semidirect
7. #10622635C2semidirect
8. #10622498C2semidirect
9. #10622497C2semidirect
10. #10622429C2semidirect
11. #10622425C2semidirect
12. #10622416C2semidirect
13. #10622415C2semidirect
14. #10622310C2semidirect
15. #10622301C2semidirect
161. C4×Q16D11semidirect
289. C11#3327semidirect

Maximal subgroups

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

subgroupindex
#106231122
#106231072
C4×C11×Q162
#106228002
#106227992
#106226412
#106226352
#106224982
#106224972
#106224292
#106224252
#106224162
#106224152
#106223102
#106223012
#332711