Finite Group Databasebeta

← #13080361

Subgroups — #13080361

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D11C211yesmaximal, characteristic
2C22×#4326C211yesmaximal, characteristic, complemented
3C2×Q16×D11C211yesmaximal, characteristic, complemented
4#10623163C211yesmaximal, characteristic
5C11×#451C211yesmaximal, characteristic, complemented
6#10622799C211yesmaximal, characteristic, complemented
7#10622795C211yesmaximal, characteristic, complemented
8#10622794C211yesmaximal, characteristic, complemented
9#10622664C211yesmaximal, characteristic, complemented
10#10622426C211yesmaximal, characteristic, complemented
11#10622421C211yesmaximal, characteristic, complemented
12#10622406C211yesmaximal, characteristic, complemented
13#10622403C211yesmaximal, characteristic, complemented
14#10622352C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic
16C22×Q8×C11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C2×C11×Q16C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23#66999—21no—
24#66999C2211yescharacteristic
25Q8×Dic11C2211yescharacteristic
26#66997—21no—
27#66997C2211yescharacteristic
28#66997C2211yescharacteristic
29C2×#4326—24no—
30C2×#4326C2211yescharacteristic
31C2×#4326C2211yescharacteristic
32C2×#4326C2211yescharacteristic
33C2×#4326C2211yescharacteristic
34C2×#4326C2211yescharacteristic
35C4×C22⋊D11—21no—
36C4×C22⋊D11C2211yescharacteristic
37#66977—21no—
38#66977C2211yescharacteristic
39C22×C11⋊C8C2211yescharacteristic
40Q16×D11—24no—
41C2×Dic44C2211yescharacteristic
42C2×Dic44C2211yescharacteristic
43C2×C8×D11C2211yescharacteristic
44#66950C2211yescharacteristic
45#66949—21no—
46#66941—21no—
47#66940C2211yescharacteristic
48(C22⋊D11)⋊C4—21no—
49#66931—21no—
50C11×#103C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×C22⋊C8C2211yescharacteristic
53#66899C2211yescharacteristic
54(C2×D11)⋊C8C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57Dic11⋊C8C2211yescharacteristic
58C8×Dic11C2211yescharacteristic
59#66874C2211yescharacteristic
60#66871C2211yescharacteristic
61C2×Q8×C11—21no—
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11D411yescharacteristic
70C22×Dic11—21no—
71Q8×D11—22no—
72Q8×D11—22no—
73Q8×D11—41no—
74Q8×D11—41no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×Dic22—22no—
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—41no—
83C2×Dic22C2311yescharacteristic
84C2×Dic22C2311yescharacteristic
85C2×Dic22C2311yescharacteristic
86C11×Q16—22no—
87C11×Q16—41no—
88C2×C8×C11C2311yescharacteristic
89C2×C8×C11C2311yescharacteristic
90C11×C4⋊C4—21no—
91C11×C4⋊C4C2311yescharacteristic
92C11×C22⋊C4—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11D411yescharacteristic
95#4326—22no—
96#4326—22no—
97#4326—22no—
98#4326—22no—
99#4326D414yescomplemented
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4D411yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4D411yescharacteristic
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11C2311yescharacteristic
117C2×C11⋊C8—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120Dic44—22no—
121Dic44—41no—
122C8×D11—22no—
123D4×Q16—111nomaximal, Sylow
124C23×C11C2×D411yescharacteristic
125C22×D11C2×D411yescharacteristic
126Q8×C11—21no—
127Q8×C11—21no—
128Q8×C11—21no—
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11—42no—
132Q8×C11C2×D412yes—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2411yescharacteristic
142C22⋊D11Q1614yescomplemented
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—42no—
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150C2×Dic11C2×D411yescharacteristic
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—42no—
154C4×D11—42no—
155Dic22—21no—
156Dic22—21no—
157Dic22—21no—
158Dic22—21no—
159Dic22—21no—
160Dic22—42no—
161Dic22—42no—
162Dic22—42no—
163Dic22C2×D412yes—
164C8×C11—21no—
165C8×C11—21no—
166C11⋊C8—21no—
167C11⋊C8C2×D412yes—
168C22×Q16—111no—
169C22×Q16—111no—
170D4×Q8—111no—
171D4×Q8—111no—
172#494—111no—
173#467—111no—
174#467—111no—
175#462—111no—
176#462—111no—
177#451—111no—
178#451—111no—
179#451—111no—
180#451D1111yescharacteristic, complemented
181C4×Q16—111no—
182C8×D4—111no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11C2×Q1612yescomplemented
186C22×C11C22×D411yescharacteristic
187C2×D11—21no—
188C2×D11—21no—
189C2×D11C2×Q1612yescomplemented
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11C22×D411yescharacteristic
196C4×C11H(5,𝔽2)11yescharacteristic
197Dic11—22no—
198Dic11—21no—
199Dic11—21no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11C2×Q1612yescomplemented
204C22×Q8—111no—
205C22×Q8—111no—
206C22×Q8—111no—
207C22×Q8C2×D1111yescharacteristic
208C2×Q16—111no—
209C2×Q16—111no—
210C2×Q16—111no—
211C2×Q16—111no—
212C2×Q16—111no—
213C2×Q16—111no—
214C2×Q16—111no—
215C2×Q16—224no—
216C2×Q16—224no—
217C2×Q16C2×D1111yescharacteristic
218C2×Q16C2×D1111yescharacteristic
219C22×C8—111no—
220C22×C8—111no—
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C22⋊Q8—111no—
226C22⋊Q8—111no—
227C22⋊Q8—111no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232C22⋊Q8C2×D1111yescharacteristic
233C4×Q8—111no—
234C4×Q8—111no—
235C4×D4—111no—
236C4×D4—221no—
237C4×D4—221no—
238#107—111no—
239C4⋊C8—111no—
240#103—111no—
241#103—111no—
242#103—111no—
243#103—111no—
244#103C2×D1111yescharacteristic
245#103C2×D1111yescharacteristic
246C22⋊C8—111no—
247C22⋊C8C2×D1111yescharacteristic
248C4×C8—111no—
249C2×C11—22no—
250C2×C11D4211yescharacteristic
251C2×C11C22×Q1611yescharacteristic
252C2×C11#57811yescharacteristic
253D11—22no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—111no—
258C2×Q8—111no—
259C2×Q8—111no—
260C2×Q8—221no—
261C2×Q8—221no—
262C2×Q8—222no—
263C2×Q8—221no—
264C2×Q8—222no—
265C2×Q8—222no—
266C2×Q8—441no—
267C2×Q8—441no—
268C2×Q8—441no—
269C2×Q8C22×D1111yescharacteristic
270C2×Q8C22×D1111yescharacteristic
271C2×Q8C22×D1111yescharacteristic
272C2×D4—111no—
273C22×C4—21no—
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4C22×D1111yescharacteristic
279Q16—22no—
280Q16—41no—
281Q16—114no—
282Q16—222no—
283Q16—222no—
284Q16—222no—
285Q16—222no—
286Q16—222no—
287Q16—441no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8C22×D1111yescharacteristic
293C2×C8C22×D1111yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—111no—
296C4⋊C4—111no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4C22×D1111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—111no—
309C22⋊C4—111no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C42—111no—
314C42—221no—
315C42—221no—
316C11D4×Q1611yescharacteristic, complemented, Sylow
317C23—111no—
318C23D4×D1111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—112no—
326Q8—221no—
327Q8—221no—
328Q8—221no—
329Q8—221no—
330Q8—221no—
331Q8—442no—
332Q8—442no—
333Q8—442no—
334Q8D4×D1112yes—
335D4—114no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4D4×D1111yescharacteristic
356C2×C4C23×D1111yescharacteristic
357C8—21no—
358C8—21no—
359C8—112no—
360C8—221no—
361C22—21no—
362C22—21no—
363C22—112no—
364C22—221no—
365C22—221no—
366C22Q16×D1112yescomplemented
367C22C2×D4×D1111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—112no—
374C4—221no—
375C4—221no—
376C4—222no—
377C4—441no—
378C4—441no—
379C4—441no—
380C4C2×D4×D1111yescharacteristic
381C4#6703711yescharacteristic
382C2—22no—
383C2—222no—
384C2#1062312111yescharacteristic
385C2C2×Q16×D1111yescharacteristic
386C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenter#451D11
hypocenterC11D4×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C22×#4326C2semidirect
3. C2×Q16×D11C2semidirect
5. C11×#451C2semidirect
6. #10622799C2semidirect
7. #10622795C2semidirect
8. #10622794C2semidirect
9. #10622664C2semidirect
10. #10622426C2semidirect
11. #10622421C2semidirect
12. #10622406C2semidirect
13. #10622403C2semidirect
14. #10622352C2semidirect
99. #4326D4semidirect
142. C22⋊D11Q16semidirect
180. #451D11semidirect
185. C22×C11C2×Q16semidirect
189. C2×D11C2×Q16semidirect
203. Dic11C2×Q16semidirect
316. C11D4×Q16semidirect
366. C22Q16×D11semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D112
C22×#43262
C2×Q16×D112
#106231632
C11×#4512
#106227992
#106227952
#106227942
#106226642
#106224262
#106224212
#106224062
#106224032
#106223522
(C22⋊D11)⋊C82
D4×Q1611