Finite Group Databasebeta

← #13080718

Subgroups — #13080718

Order 1408.

382 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#10623170C211yesmaximal, characteristic, complemented
2#10623162C211yesmaximal, characteristic
3C11×#467C211yesmaximal, characteristic, complemented
4#10622800C211yesmaximal, characteristic, complemented
5#10622795C211yesmaximal, characteristic, complemented
6#10622726C211yesmaximal, characteristic, complemented
7#10622724C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622504C211yesmaximal, characteristic, complemented
11#10622497C211yesmaximal, characteristic, complemented
12#10622430C211yesmaximal, characteristic, complemented
13#10622429C211yesmaximal, characteristic, complemented
14#10622416C211yesmaximal, characteristic, complemented
15#10622410C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24#66997C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27C4×C22⋊D11C2211yescharacteristic
28#66979C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66950C2211yescharacteristic
31#66947—21no—
32#66946C2211yescharacteristic
33#66945—21no—
34C4⋊C4×D11—21no—
35C4⋊C4×D11C2211yescharacteristic
36#66943C2211yescharacteristic
37#66942—21no—
38#66937—21no—
39#66936—21no—
40#66936—21no—
41#66932—21no—
42C11×#107C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64#4343—22no—
65#4343—41no—
66#4339—22no—
67#4339—41no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C11×Q16—41no—
77C2×C8×C11—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11D411yescharacteristic
88#4326—41no—
89#4325—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3315—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—41no—
128C22⋊D11—42no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135D44—21no—
136D44—42no—
137D44#4112yes—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—42no—
141C4×D11—42no—
142C4×D11—42no—
143C4×D11—42no—
144Dic22—21no—
145Dic22—21no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#547—111no—
152#491—111no—
153#485—111no—
154#484—111no—
155#478—111no—
156#470—111no—
157#467D1111yescharacteristic, complemented
158#462—111no—
159#452—111no—
160#452—111no—
161#440—111no—
162#435—111no—
163#417—111no—
164#416—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11C22×D411yescharacteristic
169C2×D11—22no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
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—21no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C2×#41—111no—
190C2×Q16—111no—
191C2×Q16C2×D1111yescharacteristic
192C2×SD16—111no—
193C2×M16—111no—
194C22×C8C2×D1111yescharacteristic
195C4⋊Q8—111no—
196#126—221no—
197#125—111no—
198#125—221no—
199#123—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8C2×D1111yescharacteristic
205C22⋊Q8C2×D1111yescharacteristic
206#121—221no—
207C4×Q8—111no—
208C4×D4—111no—
209C4×D4—111no—
210#117—111no—
211#117—221no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
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—
230#97—111no—
231C2×C11—41no—
232C2×C11#54611yescharacteristic
233C2×C11#57511yescharacteristic
234C2×C11#57811yescharacteristic
235D11—41no—
236D11—42no—
237#41—222no—
238#41—222no—
239#41—441no—
240#41—441no—
241C2×Q8—111no—
242C2×Q8C22×D1111yescharacteristic
243C2×Q8C22×D1111yescharacteristic
244C2×D4—111no—
245C2×D4—111no—
246C2×D4—221no—
247C2×D4—221no—
248C22×C4—111no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4C22×D1111yescharacteristic
254Q16—41no—
255Q16—441no—
256SD16—222no—
257M16—441no—
258C2×C8—41no—
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⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—111no—
281C22⋊C4—111no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C42—111no—
287C42—221no—
288C42—221no—
289C11#331511yescharacteristic, complemented, Sylow
290C23—111no—
291C23—221no—
292C23D4×D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—221no—
298Q8—221no—
299D4—112no—
300D4—221no—
301D4—442no—
302D4—441no—
303D4—442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
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×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—222no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—221no—
344C4—221no—
345C4—221no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4#6703711yescharacteristic
350C4#41×D1111yescharacteristic
351C2—41no—
352C2—441no—
353C2—442no—
354C2#1062314111yescharacteristic
355C2#1062329711yescharacteristic
356C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radical#10623162C2
hypercenter#467D11
hypocenterC11#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #10623170C2semidirect
3. C11×#467C2semidirect
4. #10622800C2semidirect
5. #10622795C2semidirect
6. #10622726C2semidirect
7. #10622724C2semidirect
8. #10622660C2semidirect
9. #10622658C2semidirect
10. #10622504C2semidirect
11. #10622497C2semidirect
12. #10622430C2semidirect
13. #10622429C2semidirect
14. #10622416C2semidirect
15. #10622410C2semidirect
157. #467D11semidirect
289. C11#3315semidirect

Maximal subgroups

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

subgroupindex
#106231702
#106231622
C11×#4672
#106228002
#106227952
#106227262
#106227242
#106226602
#106226582
#106225042
#106224972
#106224302
#106224292
#106224162
#106224102
#331511