Finite Group Databasebeta

← #13081118

Subgroups — #13081118

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#10623096C211yesmaximal, characteristic, complemented
2#10623094C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622728C211yesmaximal, characteristic, complemented
7#10622719C211yesmaximal, characteristic, complemented
8#10622460C211yesmaximal, characteristic, complemented
9#10622459C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622350C211yesmaximal, characteristic, complemented
12#10622350C211yesmaximal, characteristic, complemented
13#10622349C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66992—21no—
20#66991—21no—
21#66983C2211yescharacteristic
22#66983C2211yescharacteristic
23#66983C2211yescharacteristic
24#66983C2211yescharacteristic
25#66979C2211yescharacteristic
26#66979C2211yescharacteristic
27#66979C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×D88C2211yescharacteristic
30#66951—21no—
31#66945—21no—
32#66938—21no—
33#66938—21no—
34#66936—21no—
35(C22⋊D11)⋊C4—21no—
36C4×D44C2211yescharacteristic
37C4×D44C2211yescharacteristic
38#66923C2211yescharacteristic
39#66922C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×C22⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66882C2211yescharacteristic
53#66882C2211yescharacteristic
54#66882C2211yescharacteristic
55#66881C2211yescharacteristic
56#66881C2211yescharacteristic
57#66881C2211yescharacteristic
58#66881C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×Dic22—21no—
72C11×M16—22no—
73C2×C8×C11—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4D411yescharacteristic
79C11×C22⋊C4D411yescharacteristic
80C11×C22⋊C4D411yescharacteristic
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—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—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104D88—22no—
105#3347—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109C22×D11—21no—
110D4×C11—41no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C22⋊D11—81no—
122C22⋊D11—81no—
123C22⋊D11—81no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—81no—
131D44—21no—
132D44—21no—
133D44—21no—
134D44—21no—
135C4×D11—42no—
136C4×D11—81no—
137Dic22—81no—
138C8×C11—21no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11#4112yes—
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#435D1111yescharacteristic, complemented
155#428—111no—
156#427—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11C22×D411yescharacteristic
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11C2×#4111yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×D8—111no—
183C2×M16C2×D1111yescharacteristic
184C22×C8C2×D1111yescharacteristic
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—221no—
200C4×D4C2×D1111yescharacteristic
201#117—111no—
202#117—111no—
203#117—111no—
204#117—221no—
205C2×C4⋊C4—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#107—111no—
210#107—111no—
211#106—111no—
212#106—111no—
213#106—111no—
214#106—111no—
215C4⋊C8C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222C22⋊C8C2×D1111yescharacteristic
223C22⋊C8C2×D1111yescharacteristic
224#97C2×D1111yescharacteristic
225C2×C11—41no—
226C2×C11—41no—
227C2×C11#54711yescharacteristic
228C2×C11#57511yescharacteristic
229C2×C11#57611yescharacteristic
230D11—81no—
231D11—81no—
232C2×Q8—221no—
233C2×D4—111no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4D4411yescharacteristic
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1111yescharacteristic
245D8—222no—
246M16—22no—
247C2×C8—22no—
248C2×C8C22×D1111yescharacteristic
249C2×C8C22×D1111yescharacteristic
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4D4411yescharacteristic
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4D4411yescharacteristic
273C22⋊C4D4411yescharacteristic
274C42—221no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#334711yescharacteristic, complemented, Sylow
279C23—221no—
280C23—221no—
281C23C2×D4411yescharacteristic
282C23C2×D4411yescharacteristic
283Q8—881no—
284D4—41no—
285D4—221no—
286D4—221no—
287D4—221no—
288D4—221no—
289D4—442no—
290D4—881no—
291D4—881no—
292D4—881no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—442no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4C2×D4411yescharacteristic
307C2×C4C2×D4411yescharacteristic
308C2×C4C2×D4411yescharacteristic
309C2×C4C2×D4411yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8#434112yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—441no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C22×D4411yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—441no—
333C4—441no—
334C4—441no—
335C4—441no—
336C4—441no—
337C4—441no—
338C4C2×#434111yescharacteristic
339C4#6704311yescharacteristic
340C2—41no—
341C2—41no—
342C2—881no—
343C2—881no—
344C2#1062308611yescharacteristic
345C2#1062327911yescharacteristic
346C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
hypercenter#435D11
hypocenterC11#3347
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #10623096C2semidirect
2. #10623094C2semidirect
3. C11×#435C2semidirect
4. #10622748C2semidirect
5. #10622734C2semidirect
6. #10622728C2semidirect
7. #10622719C2semidirect
8. #10622460C2semidirect
9. #10622459C2semidirect
10. #10622350C2semidirect
11. #10622350C2semidirect
12. #10622350C2semidirect
13. #10622349C2semidirect
14. #10622324C2semidirect
15. #10622315C2semidirect
154. #435D11semidirect
278. C11#3347semidirect

Maximal subgroups

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

subgroupindex
#106230962
#106230942
C11×#4352
#106227482
#106227342
#106227282
#106227192
#106224602
#106224592
#106223502
#106223492
#106223242
#106223152
#334711