Finite Group Databasebeta

← #13080883

Subgroups — #13080883

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#10623225C211yesmaximal, characteristic, complemented
2#10623208C211yesmaximal, characteristic
3C11×#488C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622667C211yesmaximal, characteristic, complemented
6#10622429C211yesmaximal, characteristic, complemented
7#10622422C211yesmaximal, characteristic, complemented
8#10622421C211yesmaximal, characteristic, complemented
9#10622415C211yesmaximal, characteristic, complemented
10#10622397C211yesmaximal, characteristic, complemented
11#10622396C211yesmaximal, characteristic, complemented
12#10622393C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14C4×Dic44C211yesmaximal, characteristic, complemented
15#10622301C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C11×#125C2211yescharacteristic
19C11×#124C2211yescharacteristic
20#66999C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22#66991C2211yescharacteristic
23C2×#4324C2211yescharacteristic
24C2×Dic44C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26C2×#4313C2211yescharacteristic
27#66951—21no—
28#66950C2211yescharacteristic
29#66950C2211yescharacteristic
30#66947—21no—
31#66945—21no—
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34#66943—21no—
35#66938—21no—
36#66937—21no—
37(C22⋊D11)⋊C4—21no—
38#66931—21no—
39C4×D44C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C4×C8×C11C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63C22×Dic11—21no—
64Q8×D11—22no—
65Q8×D11—41no—
66#4341—22no—
67#4341—41no—
68C2×D44D411yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
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×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C42×C11C2311yescharacteristic
85C22⋊Dic11—21no—
86#4326—41no—
87#4324—41no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4D411yescharacteristic
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108Dic44—22no—
109#4313—41no—
110#4313—41no—
111#3327—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—42no—
126C22⋊D11—42no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—42no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—41no—
135C4×D11—21no—
136C4×D11—21no—
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#488D1111yescharacteristic, complemented
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×Q16—111no—
162#436—111no—
163#419—111no—
164#417—111no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11C22×D411yescharacteristic
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11C2×#4111yescharacteristic
181C4×C11H(5,𝔽2)11yescharacteristic
182Dic11—22no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
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—221no—
197#125C2×D1111yescharacteristic
198#124—221no—
199#124C2×D1111yescharacteristic
200#123—221no—
201C22⋊Q8—111no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8—221no—
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⋊C4—111no—
214#107—111no—
215#107—111no—
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#102C2×D1111yescharacteristic
227#102C2×D1111yescharacteristic
228C22⋊C8—111no—
229C22⋊C8—111no—
230C4×C8C2×D1111yescharacteristic
231C2×C11—81no—
232C2×C11#54611yescharacteristic
233C2×C11#57511yescharacteristic
234C2×C11#57811yescharacteristic
235D11—41no—
236D11—41no—
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—221no—
247C2×D4—221no—
248C2×D4C22×D1111yescharacteristic
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
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—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—21no—
277C22⋊C4—21no—
278C22⋊C4—111no—
279C22⋊C4—111no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—221no—
286C42—221no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#332711yescharacteristic, complemented, Sylow
290C23—21no—
291C23—111no—
292C23—111no—
293Q8—21no—
294Q8—21no—
295Q8—112no—
296Q8—221no—
297Q8—221no—
298Q8—221no—
299Q8—442no—
300D4—21no—
301D4—21no—
302D4—441no—
303D4—442no—
304D4—442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—221no—
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—41no—
329C22—41no—
330C22—41no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—221no—
335C22—221no—
336C22—221no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—221no—
344C4—221no—
345C4—222no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4#41×D1111yescharacteristic
350C4#6704211yescharacteristic
351C2—81no—
352C2—441no—
353C2—441no—
354C2#1062320711yescharacteristic
355C2#1062329911yescharacteristic
356C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
prime radical#10623208C2
hypercenter#488D11
hypocenterC11#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623225C2semidirect
3. C11×#488C2semidirect
4. #10622676C2semidirect
5. #10622667C2semidirect
6. #10622429C2semidirect
7. #10622422C2semidirect
8. #10622421C2semidirect
9. #10622415C2semidirect
10. #10622397C2semidirect
11. #10622396C2semidirect
12. #10622393C2semidirect
13. #10622384C2semidirect
14. C4×Dic44C2semidirect
15. #10622301C2semidirect
152. #488D11semidirect
289. C11#3327semidirect

Maximal subgroups

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

subgroupindex
#106232252
#106232082
C11×#4882
#106226762
#106226672
#106224292
#106224222
#106224212
#106224152
#106223972
#106223962
#106223932
#106223842
C4×Dic442
#106223012
#332711