Finite Group Databasebeta

← #14725280

Subgroups — #14725280

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C212yesmaximal, complemented
2#13067530C212yesmaximal, complemented
3#13067495C214yesmaximal, complemented
4#13067435C212yesmaximal, complemented
5#13067379C211yesmaximal, characteristic, complemented
6#13067050C212yesmaximal, complemented
7#13066905C211yesmaximal, characteristic, complemented
8C4×C11×#135C211yesmaximal, characteristic
9C2×C11×#135C411yescharacteristic
10C4×C11×#41C2212yes—
11C4×C11×Q16C411yescharacteristic
12C4×C11×Q16C2211yescharacteristic
13C4×C11×SD16C412yes—
14C4×C11×SD16C2212yes—
15C4×C11×D8C411yescharacteristic
16C4×C11×D8C2211yescharacteristic
17C11×#427C411yescharacteristic
18C11×#416C412yes—
19C2×C4×C8×C11C2211yescharacteristic
20Q8×C11⋊C8C2214yes—
21#10622625—24no—
22#10622625C2214yes—
23#10622539—22no—
24#10622539C2212yes—
25#10622538C2211yescharacteristic
26C4×#4318—22no—
27C4×#4318C2211yescharacteristic
28Q8⋊(C11⋊C8)C2214yes—
29D4⋊(C11⋊C8)C2214yes—
30#10622096C2212yes—
31#10622095C2212yes—
32#10622093C2212yes—
33#10622092C2212yes—
34C2×C11×#41C2×C412yes—
35C11×#135—24no—
36C2×C11×Q16C2×C411yescharacteristic
37C2×C11×SD16C2×C412yes—
38C2×C11×D8C2×C411yescharacteristic
39C22×C8×C11C2×C411yescharacteristic
40C22×C8×C11C2×C411yescharacteristic
41C4×Q8×C11C2×C412yes—
42C4×Q8×C11C2312yes—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C4×D4×C11C2×C412yes—
46C4×D4×C11C2312yes—
47C11×#117—22no—
48C11×#117C2×C412yes—
49C2×C42×C11—22no—
50C2×C42×C11C2311yescharacteristic
51C2×#4318—24no—
52C2×#4318D412yes—
53C11×#107C2×C411yescharacteristic
54C11×#107C2×C411yescharacteristic
55C11×#106C2×C412yes—
56C11×#103C2×C412yes—
57C11×#103C2×C412yes—
58C11×#102C2×C412yes—
59C11×#102C2×C412yes—
60C4×C8×C11C2×C411yescharacteristic
61C4×C8×C11C2×C411yescharacteristic
62C4×C8×C11C2311yescharacteristic
63C4×C8×C11C2311yescharacteristic
64C22⋊(C11⋊C8)—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—24no—
69C4⋊(C11⋊C8)C2314yes—
70#66867—22no—
71#66867D412yes—
72C4×C11⋊C8—24no—
73C4×C11⋊C8C2312yes—
74C4×C11⋊C8C2312yes—
75#18043—111nomaximal, Sylow
76C11×#41—24no—
77C11×#41—42no—
78C2×Q8×C11C22×C412yes—
79C2×D4×C11—22no—
80C2×D4×C11C22×C412yes—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×Q16M1614yescomplemented
88C11×SD16—24no—
89C11×D8—22no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4C22×C412yes—
99C11×C4⋊C4C22×C412yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11C22×C411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11C2411yescharacteristic
110#4318—42no—
111#4318—48no—
112C2×C11⋊C8—24no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8C2×D414yes—
115#2971—112no—
116C4×#135D1111yescharacteristic
117#1594—112no—
118#1588—114no—
119#1579—112no—
120#1568—111no—
121#1488—112no—
122#1451—111no—
123C23×C11—22no—
124C23×C11C4×D411yescharacteristic
125Q8×C11—22no—
126Q8×C11C2×M1614yes—
127D4×C11—22no—
128D4×C11—22no—
129D4×C11—44no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11—82no—
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C23×C411yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×C4×C11C2×#4111yescharacteristic
146C8×C11—21no—
147C8×C11—21no—
148C8×C11—21no—
149C8×C11C2×M1612yes—
150C11⋊C8—24no—
151C11⋊C8—42no—
152C11⋊C8—44no—
153C2×#135Dic1111yescharacteristic
154C4×#41C2×D1112yes—
155C8×Q8—114no—
156C4×Q16Dic1111yescharacteristic
157C4×Q16C2×D1111yescharacteristic
158C4×SD16Dic1112yes—
159C4×SD16C2×D1112yes—
160C4×D8Dic1111yescharacteristic
161C4×D8C2×D1111yescharacteristic
162#436—114no—
163#436—224no—
164#432—112no—
165#432—222no—
166#431—111no—
167#427Dic1111yescharacteristic
168#416Dic1112yes—
169C4×M16—111no—
170C4×M16—222no—
171C2×C4×C8C2×D1111yescharacteristic
172#335—112no—
173#334—112no—
174Q8⋊C8—114no—
175D4⋊C8—114no—
176#322—112no—
177#322—112no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11C2×C4×D411yescharacteristic
185C4×C11—21no—
186C4×C11—24no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11C22×M1611yescharacteristic
193C4×C11#56811yescharacteristic
194C4×C11#57512yes—
195C2×#41C2×Dic1112yes—
196#135—24no—
197C2×Q16C2×Dic1111yescharacteristic
198C2×SD16C2×Dic1112yes—
199C2×D8C2×Dic1111yescharacteristic
200C2×M16—112no—
201C2×M16—224no—
202C22×C8C2×Dic1111yescharacteristic
203C22×C8C2×Dic1111yescharacteristic
204C4×Q8C2×Dic1112yes—
205C4×Q8C22×D1112yes—
206C4×D4—22no—
207C4×D4—22no—
208C4×D4C2×Dic1112yes—
209C4×D4C22×D1112yes—
210#117—22no—
211#117C2×Dic1112yes—
212C2×C42—22no—
213C2×C42C22×D1111yescharacteristic
214#107C2×Dic1111yescharacteristic
215#107C2×Dic1111yescharacteristic
216#106C2×Dic1112yes—
217C4⋊C8—114no—
218C4⋊C8—224no—
219C4⋊C8—221no—
220#103C2×Dic1112yes—
221#103C2×Dic1112yes—
222#102C2×Dic1112yes—
223#102C2×Dic1112yes—
224C22⋊C8—224no—
225C22⋊C8—222no—
226C22⋊C8—221no—
227#97—112no—
228#97—222no—
229C4×C8—112no—
230C4×C8—112no—
231C4×C8—224no—
232C4×C8C2×Dic1111yescharacteristic
233C4×C8C2×Dic1111yescharacteristic
234C4×C8C22×D1111yescharacteristic
235C4×C8C22×D1111yescharacteristic
236C2×C11—41no—
237C2×C11—82no—
238C2×C11D4×M1611yescharacteristic
239C2×C11#294311yescharacteristic
240C2×C11#295711yescharacteristic
241#41—24no—
242#41—42no—
243C2×Q8C22×Dic1112yes—
244C2×D4—22no—
245C2×D4C22×Dic1112yes—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4D4×D1111yescharacteristic
250C22×C4#434111yescharacteristic
251C22×C4C22×Dic1111yescharacteristic
252Q16#431814yescomplemented
253SD16—24no—
254D8—22no—
255M16—442no—
256M16—448no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—114no—
260C2×C8—224no—
261C2×C8—222no—
262C2×C8C22×Dic1111yescharacteristic
263C2×C8C22×Dic1111yescharacteristic
264C2×C8C22×Dic1111yescharacteristic
265C2×C8C22×Dic1111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4C22×Dic1112yes—
269C4⋊C4C22×Dic1112yes—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C42—22no—
274C42—22no—
275C42—22no—
276C42D4×D1111yescharacteristic
277C42#434111yescharacteristic
278C42C22×Dic1111yescharacteristic
279C42C23×D1111yescharacteristic
280C11#1804311yescharacteristic, complemented, Sylow
281C23—22no—
282C23D4×Dic1111yescharacteristic
283Q8—22no—
284Q8C2×#431814yes—
285D4—22no—
286D4—22no—
287D4—44no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—82no—
298C2×C4D4×Dic1111yescharacteristic
299C2×C4D4×Dic1111yescharacteristic
300C2×C4D4×Dic1111yescharacteristic
301C2×C4C2×D4×D1111yescharacteristic
302C2×C4C2×#434111yescharacteristic
303C2×C4C23×Dic1111yescharacteristic
304C8—21no—
305C8—21no—
306C8—21no—
307C8—224no—
308C8—442no—
309C8—444no—
310C8C2×#431812yes—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22C2×D4×Dic1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—24no—
322C4—21no—
323C4—42no—
324C4—42no—
325C4#1062329912yes—
326C4C22×#431811yescharacteristic
327C4#1062335011yescharacteristic
328C2—41no—
329C2—82no—
330C2D4×#431811yescharacteristic
331C2#1307741711yescharacteristic
332C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#135C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#135C4
cosocleC42×C11C24
hypercenterC4×#135D11
hypocenterC11#18043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13067530C2semidirect
3. #13067495C2semidirect
4. #13067435C2semidirect
5. #13067379C2semidirect
6. #13067050C2semidirect
7. #13066905C2semidirect
87. C11×Q16M16semidirect
252. Q16#4318semidirect
280. C11#18043semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130675302
#130674952
#130674352
#130673792
#130670502
#130669052
C4×C11×#1352
#1804311