Finite Group Databasebeta

← #13081088

Subgroups — #13081088

Order 1408.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623096C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622728C211yesmaximal, characteristic, complemented
7C2×#66881C211yesmaximal, characteristic, complemented
8#10622460C211yesmaximal, characteristic, complemented
9#10622455C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622349C211yesmaximal, characteristic, complemented
12#10622348C211yesmaximal, characteristic, complemented
13#10622348C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×M16C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66992—21no—
21#66983C2211yescharacteristic
22#66983C2211yescharacteristic
23#66983C2211yescharacteristic
24#66983C2211yescharacteristic
25#66979C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×D88C2211yescharacteristic
30#66951—21no—
31#66950—21no—
32#66939—21no—
33#66939—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#66881C2211yescharacteristic
54#66881C2211yescharacteristic
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—
67C22×Dic11—21no—
68C22×Dic11—21no—
69#4341—44no—
70C2×D44C2311yescharacteristic
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×Dic22—21no—
75C11×M16—22no—
76C2×C8×C11—22no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4D411yescharacteristic
82C11×C22⋊C4D411yescharacteristic
83C11×C22⋊C4D411yescharacteristic
84C42×C11C2311yescharacteristic
85C22⋊Dic11—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)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105D88—22no—
106#3345—111nomaximal, Sylow
107C23×C11C2×D411yescharacteristic
108C23×C11C2×D411yescharacteristic
109C22×D11—21no—
110C22×D11—21no—
111D4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—42no—
122C22⋊D11—42no—
123C22⋊D11—42no—
124C22⋊D11—81no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—81no—
134D44—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138C4×D11—42no—
139C4×D11—81no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11—21no—
143C8×C11—21no—
144C8×C11#4112yescomplemented
145#553—111no—
146#547—111no—
147#501—111no—
148#482—111no—
149#481—111no—
150#481—111no—
151#480—111no—
152#478—111no—
153#476—111no—
154#469—111no—
155#466—111no—
156#442—111no—
157#435D1111yescharacteristic, complemented
158#428—111no—
159C2×#106—111no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11AGL(1,ℤ/8)12yes—
166C22×C11C22×D411yescharacteristic
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11C2×#4111yescharacteristic
178C4×C112−1+411yescharacteristic
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C2×#41—221no—
186C2×D8—111no—
187C2×M16C2×D1111yescharacteristic
188C22×C8C2×D1111yescharacteristic
189C4⋊Q8—111no—
190#126—221no—
191#125—111no—
192#123—221no—
193#123—221no—
194#123—221no—
195C22⋊Q8—221no—
196#121—111no—
197#121—111no—
198#121—111no—
199#121—111no—
200#121—221no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—221no—
204C4×D4C2×D1111yescharacteristic
205#117—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209#107—111no—
210#107—111no—
211#107—111no—
212#106—111no—
213#106—111no—
214#106—111no—
215#106—111no—
216#106—111no—
217#106—111no—
218C4⋊C8C2×D1111yescharacteristic
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225C22⋊C8C2×D1111yescharacteristic
226C22⋊C8C2×D1111yescharacteristic
227#97C2×D1111yescharacteristic
228C2×C11—22no—
229C2×C11—41no—
230C2×C11#54711yescharacteristic
231C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C2×C11#57711yescharacteristic
233D11—81no—
234D11—81no—
235#41—444no—
236C2×Q8—221no—
237C2×D4—111no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4D4411yescharacteristic
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251D8—222no—
252M16—22no—
253C2×C8—22no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4D4411yescharacteristic
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4D4411yescharacteristic
279C22⋊C4D4411yescharacteristic
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#334511yescharacteristic, complemented, Sylow
283C23—221no—
284C23—221no—
285C23C2×D4411yescharacteristic
286C23C2×D4411yescharacteristic
287Q8—442no—
288D4—22no—
289D4—221no—
290D4—221no—
291D4—221no—
292D4—221no—
293D4—442no—
294D4—442no—
295D4—442no—
296D4—881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4C2×D4411yescharacteristic
313C2×C4C2×D4411yescharacteristic
314C2×C4C2×D4411yescharacteristic
315C2×C4C2×D4411yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#434112yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22#6696112yes—
333C22C22×D4411yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4C2×#434111yescharacteristic
345C4#6704311yescharacteristic
346C2—22no—
347C2—41no—
348C2—881no—
349C2—881no—
350C2#1062308611yescharacteristic
351C2C2×#6696111yescharacteristic
352C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
hypercenter#435D11
hypocenterC11#3345
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. #10623086C2semidirect
3. C11×#435C2semidirect
4. #10622748C2semidirect
5. #10622734C2semidirect
6. #10622728C2semidirect
7. C2×#66881C2semidirect
8. #10622460C2semidirect
9. #10622455C2semidirect
10. #10622350C2semidirect
11. #10622349C2semidirect
12. #10622348C2semidirect
13. #10622348C2semidirect
14. #10622324C2semidirect
15. #10622315C2semidirect
144. C8×C11#41semidirect
157. #435D11semidirect
282. C11#3345semidirect
320. C8#4341semidirect

Maximal subgroups

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

subgroupindex
#106230962
#106230862
C11×#4352
#106227482
#106227342
#106227282
C2×#668812
#106224602
#106224552
#106223502
#106223492
#106223482
#106223242
#106223152
#334511