Finite Group Databasebeta

← #13080884

Subgroups — #13080884

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
1C11×#548C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622841C211yesmaximal, characteristic, complemented
6#10622838C211yesmaximal, characteristic, complemented
7#10622669C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622665C211yesmaximal, characteristic, complemented
10#10622657C211yesmaximal, characteristic, complemented
11#10622655C211yesmaximal, characteristic, complemented
12#10622648C211yesmaximal, characteristic, complemented
13C4×#4326C211yesmaximal, characteristic, complemented
14#10622635C211yesmaximal, characteristic, complemented
15#10622625C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C11×#124—21no—
19C11×#124C2211yescharacteristic
20C11×C22⋊Q8—21no—
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121—21no—
23C11×#121C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11—21no—
26C4×D4×C11C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29#66988—21no—
30C2×#4324C2211yescharacteristic
31#66979C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33#66977C2211yescharacteristic
34#66977C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37#66942—21no—
38#66932—21no—
39#66930—21no—
40#66923C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51C22⋊(C11⋊C8)C2211yescharacteristic
52C22⋊(C11⋊C8)C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11D411yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×Dic11—21no—
75C2×Dic22C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C11×C22⋊C4D411yescharacteristic
85C11×C22⋊C4D411yescharacteristic
86C42×C11—21no—
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91#4326—22no—
92#4326—41no—
93#4324—41no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3327—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C23×C11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—42no—
119Q8×C11#4112yes—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—41no—
123D4×C11—42no—
124D4×C11—42no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2411yescharacteristic
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—42no—
144Dic22—21no—
145Dic22—21no—
146C11⋊C8—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#548D1111yescharacteristic
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×Q16—111no—
162#436—111no—
163#419—111no—
164#417—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—22no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11H(5,𝔽2)11yescharacteristic
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41C2×D1111yescharacteristic
189C22×Q8C2×D1111yescharacteristic
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—21no—
199#124C2×D1111yescharacteristic
200#123—221no—
201C22⋊Q8—21no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8C2×D1111yescharacteristic
205#121—21no—
206#121C2×D1111yescharacteristic
207C4×Q8—111no—
208C4×Q8C2×D1111yescharacteristic
209C4×D4—21no—
210C4×D4C2×D1111yescharacteristic
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#103—111no—
224#103—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228C22⋊C8—111no—
229C22⋊C8—111no—
230C4×C8—111no—
231C2×C11—41no—
232C2×C11—41no—
233C2×C11—81no—
234C2×C11#54611yescharacteristic
235C2×C11#57511yescharacteristic
236C2×C11#57811yescharacteristic
237#41—22no—
238#41—41no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—111no—
243C2×Q8C22×D1111yescharacteristic
244C2×Q8C22×D1111yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C22⋊D1111yescharacteristic
248C2×D4C22×D1111yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—221no—
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254Q16—222no—
255Q16—441no—
256SD16—441no—
257M16—441no—
258M16—441no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8—111no—
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—21no—
279C22⋊C4—21no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4C22⋊D1111yescharacteristic
284C22⋊C4C22⋊D1111yescharacteristic
285C42—21no—
286C42—221no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#332711yescharacteristic, complemented, Sylow
290C23—21no—
291C23C2×C22⋊D1111yescharacteristic
292C23C2×C22⋊D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—221no—
298Q8—221no—
299Q8#434112yes—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—442no—
319C2×C4C2×C22⋊D1111yescharacteristic
320C2×C4C2×C22⋊D1111yescharacteristic
321C2×C4C2×C22⋊D1111yescharacteristic
322C2×C4C2×C22⋊D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—221no—
325C8—221no—
326C8—221no—
327C8—221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4C2×#434111yescharacteristic
350C4#6703711yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2#1062333711yescharacteristic
355C2#1062335311yescharacteristic
356C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#548C2
socleC22×C11C22×D4
hypercenter#548D11
hypocenterC11#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. #10622852C2semidirect
4. #10622845C2semidirect
5. #10622841C2semidirect
6. #10622838C2semidirect
7. #10622669C2semidirect
8. #10622667C2semidirect
9. #10622665C2semidirect
10. #10622657C2semidirect
11. #10622655C2semidirect
12. #10622648C2semidirect
13. C4×#4326C2semidirect
14. #10622635C2semidirect
15. #10622625C2semidirect
289. C11#3327semidirect

Maximal subgroups

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

subgroupindex
C11×#5482
#106230722
#106228522
#106228452
#106228412
#106228382
#106226692
#106226672
#106226652
#106226572
#106226552
#106226482
C4×#43262
#106226352
#106226252
#332711