Finite Group Databasebeta

← #13078905

Subgroups — #13078905

Order 1408.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623250C211yesmaximal, characteristic
2#10623103C211yesmaximal, characteristic, complemented
3C11×#460C211yesmaximal, characteristic, complemented
4#10622783C211yesmaximal, characteristic, complemented
5#10622783C211yesmaximal, characteristic, complemented
6#10622777C211yesmaximal, characteristic, complemented
7SD16×Dic11C211yesmaximal, characteristic, complemented
8#10622688C211yesmaximal, characteristic, complemented
9#10622635C211yesmaximal, characteristic, complemented
10#10622453C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622397C211yesmaximal, characteristic, complemented
13#10622392C211yesmaximal, characteristic, complemented
14#10622371C211yesmaximal, characteristic, complemented
15#10622370C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C11×#127C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22#66992—21no—
23#66992—21no—
24#66991C2211yescharacteristic
25#66991C2211yescharacteristic
26#66988—21no—
27#66988—21no—
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32#66945—21no—
33#66945C2211yescharacteristic
34#66940—21no—
35#66940C2211yescharacteristic
36#66925—21no—
37#66925C2211yescharacteristic
38#66923C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68Q8×D11—22no—
69Q8×D11—22no—
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×Dic22C2311yescharacteristic
74C11×SD16—22no—
75C11×SD16—22no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C42×C11—21no—
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86#4324—22no—
87#4324—22no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4D411yescharacteristic
90(C2×D11)⋊C4D411yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3126—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11#4112yes—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—81no—
119D4×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—81no—
126C22⋊D11—81no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C4×D11—24no—
137C4×D11—21no—
138C4×D11—21no—
139Dic22—24no—
140Dic22—21no—
141Dic22#4112yes—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#540—111no—
147#519—111no—
148#482—111no—
149#482—111no—
150#479—111no—
151#479—111no—
152#460—111no—
153#460D1111yescharacteristic, complemented
154#448—111no—
155#448—111no—
156#440—111no—
157#440—111no—
158C4×SD16—111no—
159C4×SD16—111no—
160#433—111no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C11C2×#4111yescharacteristic
177Dic11—21no—
178Dic11—22no—
179Dic11—21no—
180Dic11—21no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184C22×Q8—111no—
185C2×SD16—111no—
186C2×SD16—111no—
187C2×SD16C2×D1111yescharacteristic
188C2×SD16C2×D1111yescharacteristic
189#127C2×D1111yescharacteristic
190#125—111no—
191#123—221no—
192#123—221no—
193#121—111no—
194#121—111no—
195#121—221no—
196#121—221no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—111no—
200C4×Q8—221no—
201C4×Q8—221no—
202C4×Q8C2×D1111yescharacteristic
203C4×D4—111no—
204C4×D4—111no—
205#117—111no—
206#117—111no—
207#117—221no—
208#117—221no—
209#107—111no—
210#107—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214C4⋊C8C2×D1111yescharacteristic
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#102—111no—
220#102—111no—
221#102C2×D1111yescharacteristic
222#102C2×D1111yescharacteristic
223C22⋊C8—111no—
224C22⋊C8—111no—
225#97—111no—
226C4×C8—111no—
227C2×C11—81no—
228C2×C11—81no—
229C2×C11#52511yescharacteristic
230C2×C11#57711yescharacteristic
231C2×C11#57711yescharacteristic
232D11—41no—
233C2×Q8—111no—
234C2×Q8—221no—
235C2×Q8—222no—
236C2×Q8—222no—
237C2×Q8C22×D1111yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4C22×D1111yescharacteristic
243C2×D4C22×D1111yescharacteristic
244C22×C4—111no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248SD16—22no—
249SD16—22no—
250SD16—222no—
251SD16—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—111no—
269C22⋊C4—111no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C42—21no—
276C42—111no—
277C42—221no—
278C42—221no—
279C42—221no—
280C42—221no—
281C42C22×D1111yescharacteristic
282C11#312611yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—111no—
286Q8—21no—
287Q8—112no—
288Q8—224no—
289Q8—221no—
290Q8#434112yes—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4—81no—
297D4—881no—
298D4—881no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—224no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4D4×D1111yescharacteristic
314C2×C4D4×D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—221no—
319C8—221no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—221no—
327C22—221no—
328C22—221no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—222no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4C2×#434111yescharacteristic
342C4#41×D1111yescharacteristic
343C2—81no—
344C2—81no—
345C2—441no—
346C2#1062313711yescharacteristic
347C2#1062329311yescharacteristic
348C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#460C2
socleC22×C11C22×D4
prime radical#10623250C2
hypercenter#460D11
hypocenterC11#3126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10623103C2semidirect
3. C11×#460C2semidirect
4. #10622783C2semidirect
5. #10622783C2semidirect
6. #10622777C2semidirect
7. SD16×Dic11C2semidirect
8. #10622688C2semidirect
9. #10622635C2semidirect
10. #10622453C2semidirect
11. #10622442C2semidirect
12. #10622397C2semidirect
13. #10622392C2semidirect
14. #10622371C2semidirect
15. #10622370C2semidirect
153. #460D11semidirect
282. C11#3126semidirect

Maximal subgroups

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

subgroupindex
#106232502
#106231032
C11×#4602
#106227832
#106227772
SD16×Dic112
#106226882
#106226352
#106224532
#106224422
#106223972
#106223922
#106223712
#106223702
#312611