Finite Group Databasebeta

← #13081086

Subgroups — #13081086

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
1C11×#547C211yesmaximal, characteristic, complemented
2#10623096C211yesmaximal, characteristic, complemented
3#10622697C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622652C211yesmaximal, characteristic, complemented
6#10622651C211yesmaximal, characteristic, complemented
7#10622648C211yesmaximal, characteristic, complemented
8#10622647C211yesmaximal, characteristic, complemented
9#10622627C211yesmaximal, characteristic, complemented
10#10622624C211yesmaximal, characteristic, complemented
11#10622622C211yesmaximal, characteristic, complemented
12#10622581C211yesmaximal, characteristic, complemented
13#10622580C211yesmaximal, characteristic, complemented
14#10622577C211yesmaximal, characteristic, complemented
15C2×#66872C211yesmaximal, characteristic, complemented
16C2×C11×#41—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#123—21no—
19C11×#123—21no—
20C11×C22⋊Q8—21no—
21C11×#121C2211yescharacteristic
22C11×#121C2211yescharacteristic
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27#66992—21no—
28C2×#4323C2211yescharacteristic
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31#66979C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66951—21no—
36#66936—21no—
37(C22⋊D11)⋊C4—21no—
38C4×D44C2211yescharacteristic
39#66923C2211yescharacteristic
40#66896C2211yescharacteristic
41#66896C2211yescharacteristic
42#66896C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66872C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C11×#41—44no—
60C2×Q8×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11D411yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C22×Dic11—21no—
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4D411yescharacteristic
86C11×C22⋊C4D411yescharacteristic
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89#4323—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100#4318—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#3345—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
109C23×C11C2×D411yescharacteristic
110C22×D11—21no—
111Q8×C11—42no—
112D4×C11—22no—
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—42no—
133C22⋊D11—81no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—81no—
138D44—21no—
139D44—21no—
140C4×D11—81no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144C11⋊C8#4112yescomplemented
145#553—111no—
146#547D1111yescharacteristic, complemented
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#435—111no—
158#428—111no—
159C2×#106—111no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11AGL(1,ℤ/8)12yes—
169C22×C11C22×D411yescharacteristic
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11C2×#4111yescharacteristic
181C4×C112−1+411yescharacteristic
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C2×#41—21no—
186C2×D8—111no—
187C2×M16—111no—
188C22×C8—111no—
189C4⋊Q8C2×D1111yescharacteristic
190#126—221no—
191#125—111no—
192#123—21no—
193#123—21no—
194#123—221no—
195C22⋊Q8—21no—
196#121—111no—
197#121—111no—
198#121—221no—
199#121C2×D1111yescharacteristic
200#121C2×D1111yescharacteristic
201C4×D4—111no—
202C4×D4—221no—
203C4×D4C2×D1111yescharacteristic
204C4×D4C2×D1111yescharacteristic
205#117—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4C2×D1111yescharacteristic
208C2×C4⋊C4C2×D1111yescharacteristic
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⋊C8—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102—111no—
224#102—111no—
225C22⋊C8—111no—
226C22⋊C8—111no—
227#97—111no—
228C2×C11—22no—
229C2×C11—41no—
230C2×C11—81no—
231C2×C11#54711yescharacteristic
232C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C11#57711yescharacteristic
234D11—81no—
235#41—44no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—111no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4C22⋊D1111yescharacteristic
243C2×D4C22×D1111yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251D8—222no—
252M16—222no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—222no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4C22⋊D1111yescharacteristic
268C4⋊C4C22×D1111yescharacteristic
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4C22⋊D1111yescharacteristic
279C22⋊C4C22⋊D1111yescharacteristic
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—221no—
285C23C2×C22⋊D1111yescharacteristic
286C23C2×C22⋊D1111yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—42no—
293D4—221no—
294D4—221no—
295D4—442no—
296D4—881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4C2×C22⋊D1111yescharacteristic
313C2×C4C2×C22⋊D1111yescharacteristic
314C2×C4C2×C22⋊D1111yescharacteristic
315C2×C4C2×C22⋊D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—112no—
318C8—221no—
319C8—221no—
320C8—221no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22#6698512yes—
333C22C22×C22⋊D1111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4#41×D1111yescharacteristic
345C4#6704311yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—881no—
350C2C2×#6698511yescharacteristic
351C2#1062335511yescharacteristic
352C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#547C2
socleC22×C11C22×D4
hypercenter#547D11
hypocenterC11#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C11×#547C2semidirect
2. #10623096C2semidirect
3. #10622697C2semidirect
4. #10622693C2semidirect
5. #10622652C2semidirect
6. #10622651C2semidirect
7. #10622648C2semidirect
8. #10622647C2semidirect
9. #10622627C2semidirect
10. #10622624C2semidirect
11. #10622622C2semidirect
12. #10622581C2semidirect
13. #10622580C2semidirect
14. #10622577C2semidirect
15. C2×#66872C2semidirect
144. C11⋊C8#41semidirect
146. #547D11semidirect
282. C11#3345semidirect

Maximal subgroups

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

subgroupindex
C11×#5472
#106230962
#106226972
#106226932
#106226522
#106226512
#106226482
#106226472
#106226272
#106226242
#106226222
#106225812
#106225802
#106225772
C2×#668722
#334511