Finite Group Databasebeta

← #14725524

Subgroups — #14725524

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077741C212yesmaximal, complemented
2#13067525C212yesmaximal, complemented
3#13067453C214yesmaximal, complemented
4#13067440C212yesmaximal, complemented
5#13067372C211yesmaximal, characteristic, complemented
6#13067055C212yesmaximal, 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
20#10622637C2214yes—
21#10622624—24no—
22D4×C11⋊C8C2214yes—
23#10622539—22no—
24#10622538C2211yescharacteristic
25#10622537C2212yes—
26C2×C4⋊(C11⋊C8)—22no—
27C4×#4318C2211yescharacteristic
28Q8⋊(C11⋊C8)C2214yes—
29D4⋊(C11⋊C8)C2214yes—
30#10622095C2212yes—
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—21no—
52C2×#4318—22no—
53C22×C11⋊C8—24no—
54C11×#107C2×C411yescharacteristic
55C11×#107C2×C411yescharacteristic
56C11×#106C2×C412yes—
57C11×#103C2×C412yes—
58C11×#103C2×C412yes—
59C11×#102C2×C412yes—
60C11×#102C2×C412yes—
61C4×C8×C11C2×C411yescharacteristic
62C4×C8×C11C2×C411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64C4×C8×C11C2311yescharacteristic
65C22⋊(C11⋊C8)—24no—
66C22⋊(C11⋊C8)D412yes—
67C4⋊(C11⋊C8)—22no—
68C4⋊(C11⋊C8)—24no—
69C4⋊(C11⋊C8)D412yes—
70C4⋊(C11⋊C8)C2314yes—
71#66867—21no—
72#66867—24no—
73C4×C11⋊C8C2312yes—
74C4×C11⋊C8C2312yes—
75#18065—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×Q16—22no—
88C11×SD16—24no—
89C11×D8M1614yescomplemented
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—82no—
112C2×C11⋊C8—24no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—84no—
115C2×C11⋊C8C2×D414yes—
116#2990—112no—
117C4×#135D1111yescharacteristic
118#1593—112no—
119#1582—114no—
120#1580—112no—
121#1566—111no—
122#1489—112no—
123#1451—111no—
124C23×C11—22no—
125C23×C11C4×D411yescharacteristic
126Q8×C11—22no—
127Q8×C11—22no—
128D4×C11—22no—
129D4×C11—44no—
130D4×C11C2×M1614yes—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—44no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—44no—
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C8×C11—21no—
149C8×C11—21no—
150C8×C11—21no—
151C8×C11C2×M1612yes—
152C11⋊C8—24no—
153C11⋊C8—42no—
154C11⋊C8—44no—
155C2×#135Dic1111yescharacteristic
156C4×#41C2×D1112yes—
157#446—114no—
158C4×Q16Dic1111yescharacteristic
159C4×Q16C2×D1111yescharacteristic
160C4×SD16Dic1112yes—
161C4×SD16C2×D1112yes—
162C4×D8Dic1111yescharacteristic
163C4×D8C2×D1111yescharacteristic
164#435—224no—
165C8×D4—114no—
166#432—222no—
167#431—111no—
168#427Dic1111yescharacteristic
169#423—112no—
170C2×C4⋊C8—222no—
171#416Dic1112yes—
172C4×M16—111no—
173C2×C4×C8C2×D1111yescharacteristic
174#334—112no—
175#334—112no—
176Q8⋊C8—114no—
177D4⋊C8—114no—
178#322—112no—
179#322—112no—
180C22×C11—21no—
181C22×C11—24no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11C2×C4×D411yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11#44412yes—
194C4×C11C22×M1611yescharacteristic
195C4×C11#56811yescharacteristic
196C4×C11#57712yes—
197C2×#41C2×Dic1112yes—
198#135—24no—
199C2×Q16C2×Dic1111yescharacteristic
200C2×SD16C2×Dic1112yes—
201C2×D8C2×Dic1111yescharacteristic
202C2×M16—221no—
203C2×M16—222no—
204C22×C8—224no—
205C22×C8C2×Dic1111yescharacteristic
206C22×C8C2×Dic1111yescharacteristic
207C4×Q8C2×Dic1112yes—
208C4×Q8C22×D1112yes—
209C4×D4—22no—
210C4×D4—22no—
211C4×D4C2×Dic1112yes—
212C4×D4C22×D1112yes—
213#117—22no—
214#117C2×Dic1112yes—
215C2×C42—22no—
216C2×C42C22×D1111yescharacteristic
217#107C2×Dic1111yescharacteristic
218#107C2×Dic1111yescharacteristic
219#106C2×Dic1112yes—
220C4⋊C8—112no—
221C4⋊C8—114no—
222C4⋊C8—224no—
223C4⋊C8—222no—
224#103C2×Dic1112yes—
225#103C2×Dic1112yes—
226#102C2×Dic1112yes—
227#102C2×Dic1112yes—
228C22⋊C8—112no—
229C22⋊C8—224no—
230#97—224no—
231#97—221no—
232C4×C8—112no—
233C4×C8—112no—
234C4×C8C2×Dic1111yescharacteristic
235C4×C8C2×Dic1111yescharacteristic
236C4×C8C22×D1111yescharacteristic
237C4×C8C22×D1111yescharacteristic
238C2×C11—41no—
239C2×C11—44no—
240C2×C11D4×M1611yescharacteristic
241C2×C11#295211yescharacteristic
242C2×C11C2×#44411yescharacteristic
243#41—24no—
244#41—42no—
245C2×Q8C22×Dic1112yes—
246C2×D4—22no—
247C2×D4C22×Dic1112yes—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434111yescharacteristic
253C22×C4C22×Dic1111yescharacteristic
254Q16—22no—
255SD16—24no—
256D8#431814yescomplemented
257M16—442no—
258M16—882no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—114no—
262C2×C8—224no—
263C2×C8—222no—
264C2×C8—884no—
265C2×C8C22×Dic1111yescharacteristic
266C2×C8C22×Dic1111yescharacteristic
267C2×C8C22×Dic1111yescharacteristic
268C2×C8C22×Dic1111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4C22×Dic1112yes—
272C4⋊C4C22×Dic1112yes—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42D4×D1111yescharacteristic
280C42#434111yescharacteristic
281C42C22×Dic1111yescharacteristic
282C42C23×D1111yescharacteristic
283C11#1806511yescharacteristic, complemented, Sylow
284C23—22no—
285C23D4×Dic1111yescharacteristic
286Q8—22no—
287Q8—22no—
288D4—22no—
289D4—44no—
290D4C2×#431814yes—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4D4×Dic1111yescharacteristic
303C2×C4D4×Dic1111yescharacteristic
304C2×C4D4×Dic1111yescharacteristic
305C2×C4C2×D4×D1111yescharacteristic
306C2×C4C2×#434111yescharacteristic
307C2×C4C23×Dic1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—224no—
312C8—442no—
313C8—444no—
314C8C2×#431812yes—
315C22—21no—
316C22—21no—
317C22—24no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22C2×D4×Dic1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—42no—
328C4#1062281012yes—
329C4#1062330112yes—
330C4C22×#431811yescharacteristic
331C4#1062335011yescharacteristic
332C2—41no—
333C2—44no—
334C2D4×#431811yescharacteristic
335C2#1307750011yescharacteristic
336C2C2×#1062281011yescharacteristic
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#18065
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. #13077741C2semidirect
2. #13067525C2semidirect
3. #13067453C2semidirect
4. #13067440C2semidirect
5. #13067372C2semidirect
6. #13067055C2semidirect
7. #13066905C2semidirect
89. C11×D8M16semidirect
256. D8#4318semidirect
283. C11#18065semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130675252
#130674532
#130674402
#130673722
#130670552
#130669052
C4×C11×#1352
#1806511