Finite Group Databasebeta

← #13081362

Subgroups — #13081362

Order 1408.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623244C211yesmaximal, characteristic, complemented
2#10623070C211yesmaximal, characteristic, complemented
3C11×#459C211yesmaximal, characteristic
4#10622766C211yesmaximal, characteristic, complemented
5#10622766C211yesmaximal, characteristic, complemented
6#10622765C211yesmaximal, characteristic, complemented
7D8×Dic11C211yesmaximal, characteristic, complemented
8#10622684C211yesmaximal, characteristic, complemented
9#10622631C211yesmaximal, characteristic, complemented
10#10622442C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622381C211yesmaximal, characteristic, complemented
13#10622378C211yesmaximal, characteristic, complemented
14#10622376C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×C11×D8C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C11×#127C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66989—21no—
21#66989C2211yescharacteristic
22#66989C2211yescharacteristic
23#66988—21no—
24#66988—21no—
25D4×Dic11—21no—
26D4×Dic11C2211yescharacteristic
27D4×Dic11C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31#66977—21no—
32C2×Dic11⋊C4—21no—
33#66943C2211yescharacteristic
34#66941C2211yescharacteristic
35#66931—21no—
36#66931—21no—
37#66923C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×Dic22—21no—
70C2×Dic22D411yescharacteristic
71C2×Dic22C2311yescharacteristic
72C11×D8—22no—
73C11×D8—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87#4324—22no—
88C4⋊Dic11—21no—
89C4⋊Dic11D411yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3370—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109D4×C11—21no—
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—42no—
115D4×C11—81no—
116D4×C11#4112yes—
117C2×C4×C11—21no—
118C2×C4×C11—81no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—42no—
127C2×Dic11—81no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134Dic22—21no—
135Dic22—21no—
136Dic22—41no—
137Dic22—81no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142#559—111no—
143#554—111no—
144#490—111no—
145#489—111no—
146#488—111no—
147#479—111no—
148#478—111no—
149#474—111no—
150#463—111no—
151#463—111no—
152#459D1111yescharacteristic
153#446—111no—
154#442—111no—
155#440—111no—
156C4×D8—111no—
157C22×C11—22no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×SD16—111no—
181C2×D8C2×D1111yescharacteristic
182C2×D8C2×D1111yescharacteristic
183C4⋊Q8—111no—
184#127C2×D1111yescharacteristic
185#125—111no—
186#125—111no—
187#124—111no—
188#124—111no—
189#124—221no—
190#123—221no—
191#123—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C22⋊Q8—221no—
195C4×Q8—111no—
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—111no—
201C4×D4—221no—
202C4×D4C2×D1111yescharacteristic
203C2×C4⋊C4—221no—
204#107—111no—
205#107—111no—
206#106—111no—
207C4⋊C8—111no—
208C4⋊C8—111no—
209C4⋊C8C2×D1111yescharacteristic
210#103—111no—
211#103—111no—
212#103—111no—
213#102—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217#102—111no—
218#102C2×D1111yescharacteristic
219#102C2×D1111yescharacteristic
220#97—111no—
221#97—111no—
222C4×C8—111no—
223C2×C11—42no—
224C2×C11—81no—
225C2×C11—81no—
226C2×C11#54811yescharacteristic
227C2×C11#57511yescharacteristic
228C2×C11#57611yescharacteristic
229C2×Q8—111no—
230C2×Q8—111no—
231C2×Q8—221no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C22×D1111yescharacteristic
235C2×D4C22×D1111yescharacteristic
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242SD16—222no—
243D8—22no—
244D8—22no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42C22×D1111yescharacteristic
275C11#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279Q8—221no—
280Q8—221no—
281Q8—441no—
282Q8—881no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—81no—
290D4#434112yes—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—442no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4D4×D1111yescharacteristic
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—221no—
311C8—221no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—221no—
326C4—221no—
327C4—221no—
328C4—221no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4C2×#434111yescharacteristic
334C4#6704311yescharacteristic
335C2—42no—
336C2—81no—
337C2—81no—
338C2#1062312911yescharacteristic
339C2#1062328811yescharacteristic
340C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#459C2
socleC22×C11C22×D4
hypercenter#459D11
hypocenterC11#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10623244C2semidirect
2. #10623070C2semidirect
4. #10622766C2semidirect
5. #10622766C2semidirect
6. #10622765C2semidirect
7. D8×Dic11C2semidirect
8. #10622684C2semidirect
9. #10622631C2semidirect
10. #10622442C2semidirect
11. #10622441C2semidirect
12. #10622381C2semidirect
13. #10622378C2semidirect
14. #10622376C2semidirect
15. #10622372C2semidirect
275. C11#3370semidirect

Maximal subgroups

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

subgroupindex
#106232442
#106230702
C11×#4592
#106227662
#106227652
D8×Dic112
#106226842
#106226312
#106224422
#106224412
#106223812
#106223782
#106223762
#106223722
#337011