Finite Group Databasebeta

← #13081117

Subgroups — #13081117

Order 1408.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623063C211yesmaximal, characteristic, complemented
2#10623045C211yesmaximal, characteristic, complemented
3C11×#428C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622740C211yesmaximal, characteristic, complemented
6#10622616C211yesmaximal, characteristic, complemented
7#10622580C211yesmaximal, characteristic, complemented
8#10622503C211yesmaximal, characteristic, complemented
9#10622498C211yesmaximal, characteristic, complemented
10#10622496C211yesmaximal, characteristic, complemented
11#10622489C211yesmaximal, characteristic, complemented
12#10622484C211yesmaximal, characteristic, complemented
13#10622482C211yesmaximal, characteristic, complemented
14#10622479C211yesmaximal, characteristic, complemented
15#10622473C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C11×#117C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19#66983—21no—
20#66983C2211yescharacteristic
21#66983C2211yescharacteristic
22C4×C22⋊D11—21no—
23C4×C22⋊D11C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66951—21no—
27#66948C2211yescharacteristic
28#66948C2211yescharacteristic
29#66947—21no—
30#66946C2211yescharacteristic
31#66946C2211yescharacteristic
32#66945C2211yescharacteristic
33#66945C2211yescharacteristic
34#66943C2211yescharacteristic
35#66941C2211yescharacteristic
36#66938—21no—
37#66937—21no—
38#66928—21no—
39#66925—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66881C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51#66873C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C2×D44—21no—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×Dic22—21no—
72C11×M16—22no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C42×C11—21no—
82C22⋊Dic11D411yescharacteristic
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103D88—22no—
104C8×D11—22no—
105#3347—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C22×D11—21no—
108C22×D11—21no—
109C22×D11C2×D411yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—41no—
120C22⋊D11—42no—
121C22⋊D11—81no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—21no—
130D44—21no—
131D44—81no—
132D44—81no—
133C4×D11—21no—
134C4×D11—21no—
135C4×D11—42no—
136C4×D11—81no—
137Dic22—81no—
138C8×C11—21no—
139C8×C11#4112yes—
140C11⋊C8—21no—
141C11⋊C8—21no—
142#555—111no—
143#553—111no—
144#501—111no—
145#482—111no—
146#482—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#474—111no—
151#469—111no—
152#466—111no—
153#442—111no—
154#435—111no—
155#428D1111yescharacteristic, complemented
156#427—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11C22×D411yescharacteristic
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—21no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C112−1+411yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182C2×D8—111no—
183C2×M16C2×D1111yescharacteristic
184C22×C8—111no—
185C4⋊Q8—111no—
186#126—221no—
187#125—111no—
188#124—221no—
189#124—221no—
190#123—221no—
191#121—111no—
192#121—111no—
193#121—111no—
194#121—111no—
195#121—221no—
196#121—221no—
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—221no—
201#117—111no—
202#117—111no—
203#117—221no—
204#117C2×D1111yescharacteristic
205C2×C4⋊C4C2×D1111yescharacteristic
206#107—111no—
207#107—111no—
208#107—111no—
209#107C2×D1111yescharacteristic
210#107C2×D1111yescharacteristic
211#106—111no—
212#106—111no—
213#106C2×D1111yescharacteristic
214#106C2×D1111yescharacteristic
215C4⋊C8—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222C22⋊C8—111no—
223C22⋊C8—111no—
224#97—111no—
225C2×C11—41no—
226C2×C11#54711yescharacteristic
227C2×C11#57511yescharacteristic
228C2×C11#57611yescharacteristic
229D11—41no—
230D11—81no—
231D11—81no—
232C2×Q8—221no—
233C2×D4—111no—
234C2×D4—111no—
235C2×D4—111no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4—221no—
240C22×C4—21no—
241C22×C4—111no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4C22×D1111yescharacteristic
245D8—222no—
246M16—22no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8—222no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—111no—
265C22⋊C4—111no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—21no—
275C42—111no—
276C42—221no—
277C42—221no—
278C11#334711yescharacteristic, complemented, Sylow
279C23—111no—
280C23—221no—
281C23—221no—
282C23D4×D1111yescharacteristic
283Q8—881no—
284D4—221no—
285D4—221no—
286D4—221no—
287D4—221no—
288D4—441no—
289D4—442no—
290D4—881no—
291D4—881no—
292D4—881no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—442no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—221no—
313C8—221no—
314C8#433912yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—221no—
319C22—221no—
320C22—221no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—221no—
334C4—221no—
335C4—221no—
336C4—441no—
337C4—441no—
338C4C2×#433911yescharacteristic
339C4#6704011yescharacteristic
340C2—41no—
341C2—441no—
342C2—881no—
343C2—881no—
344C2#1062303811yescharacteristic
345C2#1062330511yescharacteristic
346C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
hypercenter#428D11
hypocenterC11#3347
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #10623063C2semidirect
2. #10623045C2semidirect
3. C11×#428C2semidirect
4. #10622748C2semidirect
5. #10622740C2semidirect
6. #10622616C2semidirect
7. #10622580C2semidirect
8. #10622503C2semidirect
9. #10622498C2semidirect
10. #10622496C2semidirect
11. #10622489C2semidirect
12. #10622484C2semidirect
13. #10622482C2semidirect
14. #10622479C2semidirect
15. #10622473C2semidirect
155. #428D11semidirect
278. C11#3347semidirect

Maximal subgroups

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

subgroupindex
#106230632
#106230452
C11×#4282
#106227482
#106227402
#106226162
#106225802
#106225032
#106224982
#106224962
#106224892
#106224842
#106224822
#106224792
#106224732
#334711