Finite Group Databasebeta

← #14783687

Subgroups — #14783687

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2#13070184C214yesmaximal, complemented
3#13070179C212yesmaximal, complemented
4#13070174C212yesmaximal, complemented
5#13068332C212yesmaximal
6#13068332C212yesmaximal
7C2×#10622162C211yesmaximal, characteristic
8C11×#2296C211yesmaximal, characteristic
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#66979C2212yes—
13C23×C11⋊C8C2212yes—
14C11×#389C2212yes—
15C11×#389C2212yes—
16C11×#385—22no—
17C4×C11×C4⋊C4—22no—
18#10622825—22no—
19#10622549C2212yes—
20#10622548C2211yescharacteristic
21#10622548C2211yescharacteristic
22C4×C4⋊Dic11—22no—
23#10622167C2214yes—
24#10622167C2214yes—
25#10622167C2214yes—
26#10622167C2214yes—
27#10622162C2212yes—
28#10622162C2212yes—
29C23×C4×C11D412yes—
30C23×C4×C11C2311yescharacteristic
31C11×#117—22no—
32C11×#117—24no—
33C11×#117Q814yes—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4C2312yes—
37C2×C11×C4⋊C4C2312yes—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C42×C11—24no—
42C2×C42×C11—21no—
43C2×C42×C11D412yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47#66979—28no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52C2×C4×Dic11—22no—
53C22×C11⋊C8—24no—
54C22×C11⋊C8—24no—
55C22×C11⋊C8—24no—
56C22×C11⋊C8C2314yes—
57C11×#95—22no—
58C11×#95—22no—
59C11⋊#95—24no—
60#23744—111nomaximal, Sylow
61C24×C11C2×D411yescharacteristic
62C22×C4×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11C2×D412yes—
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×Q812yes—
71C22×C4×C11#4112yes—
72C22×C4×C11#4114yes—
73C22×C4×C11#4114yes—
74C22×C4×C11C2411yescharacteristic
75C22×Dic11—22no—
76C22×Dic11—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—44no—
80C11×C4⋊C4—44no—
81C11×C4⋊C4C2×Q814yes—
82C11×C22⋊C4—24no—
83C11×C22⋊C4—42no—
84C42×C11—24no—
85C42×C11—24no—
86C42×C11—22no—
87C42×C11—22no—
88C42×C11—42no—
89C22⋊Dic11—44no—
90C4⋊Dic11—24no—
91C4⋊Dic11—24no—
92C4⋊Dic11—44no—
93C4⋊Dic11—44no—
94C4×Dic11—44no—
95C2×C11⋊C8—24no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—48no—
99#2296D1111yescharacteristic
100#2285—111no—
101#2101—114no—
102#2100—112no—
103#2099—112no—
104#1735—112no—
105#1735—112no—
106C2×#336—111no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11C22⋊Q812yes—
110C23×C11#12312yes—
111C23×C11#12412yes—
112C23×C11C22×D411yescharacteristic
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—24no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—48no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11C22⋊Q812yes—
126C2×C4×C11#12312yes—
127C2×C4×C11#12412yes—
128C2×C4×C11#12518yes—
129C2×C4×C11#12618yes—
130C2×C4×C11#13514yes—
131C2×C4×C11C22×Q811yescharacteristic
132C2×C4×C11C2×#4111yescharacteristic
133C2×C4×C11C2×#4112yes—
134C2×C4×C11C2×#4112yes—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C11⋊C8—44no—
140C23×C8—112no—
141C2×#117—112no—
142C2×#117C2×D1111yescharacteristic
143C2×#117C2×D1111yescharacteristic
144C22×C42C2×D1111yescharacteristic
145#389C2×D1112yes—
146#389C2×D1112yes—
147#385—22no—
148#384—111no—
149#384—111no—
150#382—112no—
151#380—222no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—222no—
154#340—114no—
155#340—114no—
156#340—114no—
157#340—114no—
158#336—112no—
159#336—112no—
160C22×C11—24no—
161C22×C11—24no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11#40014yes—
165C22×C11C2×C22⋊Q811yescharacteristic
166C22×C11C2×#12311yescharacteristic
167C22×C11C2×#12411yescharacteristic
168C22×C11C2×#13512yes—
169C22×C11#57512yes—
170C4×C11—24no—
171C4×C11—44no—
172C4×C11—42no—
173C4×C11—82no—
174C4×C11#40014yes—
175C4×C11C2×#12512yes—
176C4×C11C2×#12612yes—
177Dic11—82no—
178Dic11—82no—
179C23×C4C22⋊D1112yes—
180C23×C4C22×D1111yescharacteristic
181C22×C8—114no—
182C22×C8—224no—
183C22×C8—224no—
184C22×C8—224no—
185#117—22no—
186#117—24no—
187#117—228no—
188#117Dic2214yes—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4C22×D1112yes—
196C2×C4⋊C4C22×D1112yes—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—222no—
200C2×C42—24no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—222no—
204C2×C42C22⋊D1112yes—
205C2×C42C22×D1111yescharacteristic
206C2×C42C22×D1111yescharacteristic
207#95—22no—
208#95—22no—
209#95—224no—
210C2×C11—24no—
211C2×C11C2×#40011yescharacteristic
212C2×C11#307612yes—
213C2×C11#309112yes—
214C2×C11#313111yescharacteristic
215C2×C11#313511yescharacteristic
216C24C2×C22⋊D1111yescharacteristic
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4C2×Dic2212yes—
225C22×C4#433912yes—
226C22×C4#434114yes—
227C22×C4#434314yes—
228C22×C4C2×C22⋊D1112yes—
229C22×C4C2×C22⋊D1112yes—
230C22×C4C2×C22⋊D1111yescharacteristic
231C22×C4C23×D1111yescharacteristic
232C2×C8—224no—
233C2×C8—224no—
234C2×C8—224no—
235C2×C8—448no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—44no—
239C4⋊C4—44no—
240C4⋊C4—224no—
241C4⋊C4—224no—
242C4⋊C4—444no—
243C4⋊C4—444no—
244C4⋊C4C2×Dic2214yes—
245C22⋊C4—24no—
246C22⋊C4—42no—
247C22⋊C4—444no—
248C42—24no—
249C42—24no—
250C42—22no—
251C42—22no—
252C42—42no—
253C42—444no—
254C11#2374411yescharacteristic, complemented, Sylow
255C23—22no—
256C23—22no—
257C23#6697712yes—
258C23#6698812yes—
259C23#6700012yes—
260C23C22×C22⋊D1111yescharacteristic
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—48no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—444no—
276C2×C4—444no—
277C2×C4#6694318yes—
278C2×C4#6695118yes—
279C2×C4#6697712yes—
280C2×C4#6698812yes—
281C2×C4#6700012yes—
282C2×C4#6700314yes—
283C2×C4C22×Dic2211yescharacteristic
284C2×C4C2×#433911yescharacteristic
285C2×C4C2×#434112yes—
286C2×C4C2×#434312yes—
287C8—444no—
288C22—24no—
289C22—22no—
290C22—22no—
291C22—24no—
292C22#1062259914yes—
293C22C2×#6697711yescharacteristic
294C22C2×#6698811yescharacteristic
295C22C2×#6700011yescharacteristic
296C22C2×#6700312yes—
297C22#1062335312yes—
298C4—24no—
299C4—44no—
300C4—42no—
301C4—82no—
302C4—882no—
303C4—882no—
304C4#1062259914yes—
305C4C2×#6694312yes—
306C4C2×#6695112yes—
307C2—24no—
308C2C2×#1062259911yescharacteristic
309C2#1307840412yes—
310C2#1307852512yes—
311C2#1307894111yescharacteristic
312C2#1307896411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2296C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2296D11
hypocenterC11#23744
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #13070184C2semidirect
3. #13070179C2semidirect
4. #13070174C2semidirect
254. C11#23744semidirect

Maximal subgroups

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

subgroupindex
#130710232
#130701842
#130701792
#130701742
#130683322
C2×#106221622
C11×#22962
#2374411