Finite Group Databasebeta

← #14908827

Subgroups — #14908827

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic
2#13070813C212yesmaximal
3#13070758C212yesmaximal, complemented
4#13070666C212yesmaximal, complemented
5#13070550C212yesmaximal
6#13070485C214yesmaximal, complemented
7#13070419C211yesmaximal, characteristic
8C2×C4×C11×Q16C211yesmaximal, characteristic
9C22×C11×Q16C2211yescharacteristic
10C2×C4×Q8×C11—21no—
11#10623001—21no—
12C4×C11×Q16—21no—
13C4×C11×Q16—21no—
14C4×C11×Q16C2212yes—
15C4×C11×Q16C2212yes—
16C2×C11×#107C2211yescharacteristic
17C2×C11×#103—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66893C2214yes—
20#10622729—21no—
21#10622729C2212yes—
22#10622312C2211yescharacteristic
23C4×Dic44—21no—
24C4×Dic44C2212yes—
25#10622295C2211yescharacteristic
26#10622294—21no—
27#10622202C2214yes—
28C22⋊(C11⋊C16)C2212yes—
29#10622130C2214yes—
30#10622128C2214yes—
31C4⋊(C11⋊C16)C2212yes—
32#10622099C2212yes—
33C22×Q8×C11—21no—
34C2×C11×Q16—24no—
35C2×C11×Q16—21no—
36C2×C11×Q16C2312yes—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C4×Q8×C11—22no—
40C4×Q8×C11—22no—
41C4×Q8×C11—41no—
42C4×Q8×C11—41no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—41no—
45C2×C42×C11—41no—
46C2×C42×C11D411yescharacteristic
47#66979—41no—
48#66977—22no—
49#66977—41no—
50C2×Dic44—21no—
51C2×Dic44C2312yes—
52#66923—41no—
53#66922—21no—
54#66922—21no—
55C4×Dic22—22no—
56C4×Dic22—41no—
57C11×#107—21no—
58C11×#107C2312yes—
59C11×#103—22no—
60C11×#103—22no—
61C4×C8×C11D411yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64C4×C8×C11C2311yescharacteristic
65#66893—28no—
66#66882—21no—
67#66882C2312yes—
68#66880—22no—
69#66880—22no—
70C2×C11⋊C16C2314yes—
71#33673—111nomaximal, Sylow
72C2×Q8×C11—24no—
73C2×Q8×C11—22no—
74C2×Q8×C11—42no—
75C2×Q8×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11D811yescharacteristic
79C22×C4×C11D811yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C2×Dic22—22no—
82C2×Dic22—41no—
83C11×Q16—24no—
84C11×Q16—22no—
85C11×Q16#4114yes—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C42×C11—42no—
97C42×C11—42no—
98C42×C11D811yescharacteristic
99C42×C11D811yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—42no—
103C4⋊Dic11—22no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11—42no—
110Dic44—24no—
111Dic44—42no—
112C11⋊C16—24no—
113#3170—111no—
114C2×C4×Q16D1111yescharacteristic
115#2235—112no—
116#2225—112no—
117#2209—112no—
118#2188—112no—
119#2176—114no—
120#2163—111no—
121C23×C11C2×D811yescharacteristic
122Q8×C11—24no—
123Q8×C11—44no—
124Q8×C11—42no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—44no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—82no—
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×Dic11—42no—
140C2×Dic11—42no—
141Dic22—42no—
142Dic22—42no—
143Dic22—82no—
144C8×C11—21no—
145C8×C11—21no—
146C8×C11—21no—
147C8×C11C2×#4112yes—
148C22×Q16C2×D1111yescharacteristic
149#533—221no—
150C2×C4×Q8—21no—
151C2×Q32—114no—
152#500—111no—
153#494—111no—
154#487—221no—
155#467—112no—
156#467—221no—
157C4×Q16—21no—
158C4×Q16—21no—
159C4×Q16—112no—
160C4×Q16—221no—
161C4×Q16C2×D1112yes—
162C4×Q16C2×D1112yes—
163C2×#107C2×D1111yescharacteristic
164C2×#103—21no—
165C2×C4×C8C2×D1111yescharacteristic
166#367—114no—
167C4⋊C16—112no—
168#358—114no—
169#358—114no—
170C22⋊C16—112no—
171#346—112no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#51012yes—
175C22×C11C22×D811yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—44no—
181C4×C11—82no—
182C4×C11#51012yes—
183C4×C11#52511yescharacteristic
184C4×C11#57511yescharacteristic
185Dic11—82no—
186Dic11—82no—
187C22×Q8—21no—
188C2×Q16—24no—
189C2×Q16—21no—
190C2×Q16—112no—
191C2×Q16—221no—
192C2×Q16C22×D1112yes—
193C22×C8C22⋊D1111yescharacteristic
194C22×C8C22×D1111yescharacteristic
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197#125—441no—
198C22⋊Q8—222no—
199C22⋊Q8—441no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×Q8—41no—
203C4×Q8—41no—
204C4×Q8—222no—
205C4×Q8—441no—
206#117—441no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—41no—
209C2×C42—41no—
210C2×C42C22⋊D1111yescharacteristic
211Q32—228no—
212C2×C16—114no—
213#107—21no—
214#107—112no—
215#107—221no—
216#107C22×D1112yes—
217#103—22no—
218#103—22no—
219#103—222no—
220#103—222no—
221C4×C8C22⋊D1111yescharacteristic
222C4×C8C22⋊D1111yescharacteristic
223C4×C8C22×D1111yescharacteristic
224C4×C8C22×D1111yescharacteristic
225C2×C11—22no—
226C2×C11#310011yescharacteristic
227C2×C11C2×#51011yescharacteristic
228C2×C11C2×#51011yescharacteristic
229C2×Q8—24no—
230C2×Q8—22no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—222no—
234C2×Q8—441no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4#432311yescharacteristic
238C22×C4#432311yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240Q16—24no—
241Q16—22no—
242Q16—224no—
243Q16—442no—
244Q16#433914yes—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8C2×C22⋊D1111yescharacteristic
248C2×C8C2×C22⋊D1111yescharacteristic
249C2×C8C2×C22⋊D1111yescharacteristic
250C2×C8C23×D1111yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—222no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—442no—
259C4⋊C4—442no—
260C4⋊C4—441no—
261C22⋊C4—442no—
262C42—42no—
263C42—42no—
264C42—442no—
265C42#432311yescharacteristic
266C42#432311yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C42C2×C22⋊D1111yescharacteristic
269C16—224no—
270C11#3367311yescharacteristic, complemented, Sylow
271C23C2×#432311yescharacteristic
272Q8—24no—
273Q8—44no—
274Q8—42no—
275Q8—442no—
276Q8—442no—
277Q8—882no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—82no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4C2×#432311yescharacteristic
289C2×C4C2×#432311yescharacteristic
290C2×C4C2×#432311yescharacteristic
291C2×C4C2×#432311yescharacteristic
292C2×C4C2×#432311yescharacteristic
293C2×C4C22×C22⋊D1111yescharacteristic
294C8—21no—
295C8—21no—
296C8—21no—
297C8C2×#433912yes—
298C22—21no—
299C22—21no—
300C22#1062280812yes—
301C22C22×#432311yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—44no—
307C4—82no—
308C4—882no—
309C4—882no—
310C4#1062279212yes—
311C4#1062332211yescharacteristic
312C4#1062335311yescharacteristic
313C2—22no—
314C2#1307861611yescharacteristic
315C2C2×#1062280811yescharacteristic
316C2C2×#1062279211yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×Q16C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenterC2×C4×Q16D11
hypocenterC11#33673
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #13070758C2semidirect
4. #13070666C2semidirect
6. #13070485C2semidirect
270. C11#33673semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130708132
#130707582
#130706662
#130705502
#130704852
#130704192
C2×C4×C11×Q162
#3367311