Finite Group Databasebeta

← #14662864

Subgroups — #14662864

Order 2816.

686 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071197C211yesmaximal, characteristic
2#13066927C212yesmaximal, complemented
3#13066544C211yesmaximal, characteristic, complemented
4#13066543C212yesmaximal, complemented
5C11×#1316C211yesmaximal, characteristic, complemented
6C23×C22⋊D11C411yescharacteristic
7C2×#66930C411yescharacteristic
8C2×#66930C2211yescharacteristic
9C11×#379C2211yescharacteristic
10#10622860C411yescharacteristic
11#10622570—22no—
12#10622570—22no—
13#10622568C411yescharacteristic
14#10622568C2211yescharacteristic
15#10622331—22no—
16C11×#323C2212yes—
17#10622163C2212yes—
18#10622107—22no—
19C25×C11C2×C411yescharacteristic
20C24×D11C2×C411yescharacteristic
21C22×C22⋊D11—21no—
22C22×C22⋊D11—21no—
23C22×C22⋊D11—22no—
24C22×C22⋊D11—42no—
25C22×C22⋊D11—42no—
26C22×C22⋊D11C814yescomplemented
27C23×Dic11C2×C411yescharacteristic
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4C2311yescharacteristic
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11C2×C411yescharacteristic
33C2×C22⋊Dic11C2×C411yescharacteristic
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4D412yes—
38C2×C4×Dic11—21no—
39C2×C4×Dic11D412yes—
40#66930—42no—
41#66930—42no—
42C11×C22⋊C8—22no—
43C22⋊(C11⋊C8)—22no—
44Dic11⋊C8—42no—
45C8×Dic11—42no—
46#11427—111nomaximal, Sylow
47C24×C11—21no—
48C24×C11—21no—
49C24×C11—41no—
50C24×C11—41no—
51C24×C11—82no—
52C24×C11C2×C812yes—
53C24×C11C22×C411yescharacteristic
54C23×D11—21no—
55C23×D11—21no—
56C23×D11—41no—
57C23×D11—41no—
58C23×D11—82no—
59C23×D11C2×C812yes—
60C22×C4×C11—21no—
61C22×C4×C11C2×D412yes—
62C2×C22⋊D11—24no—
63C2×C22⋊D11—24no—
64C2×C22⋊D11—48no—
65C2×C22⋊D11—48no—
66C2×C22⋊D11—42no—
67C2×C22⋊D11—42no—
68C2×C22⋊D11—42no—
69C2×C22⋊D11—42no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C412yes—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C2×C812yes—
77C22×Dic11M1612yes—
78C2×C8×C11—42no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—82no—
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84C22⋊Dic11—82no—
85(C2×D11)⋊C4—82no—
86(C2×D11)⋊C4—82no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—42no—
92C2×C11⋊C8—42no—
93#2309—111no—
94#1458—112no—
95#1316—111no—
96#1316—112no—
97#1316D1111yescharacteristic, complemented
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—22no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—82no—
109C23×C11—82no—
110C23×C11—84no—
111C23×C11—84no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11C22×C811yescharacteristic
114C23×C11C2×M1611yescharacteristic
115C22×D11—22no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—42no—
122C22×D11—82no—
123C22×D11—82no—
124C22×D11—84no—
125C22×D11—84no—
126C2×C4×C11—22no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C22⋊D11—48no—
131C22⋊D11—48no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—24no—
135C2×Dic11—24no—
136C2×Dic11—22no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—41no—
140C2×Dic11C22⋊C812yes—
141C2×Dic11C22⋊C812yes—
142C2×Dic11#9912yes—
143C2×Dic11#10012yes—
144C8×C11—82no—
145C11⋊C8—82no—
146C23×D4—111no—
147C2×#117—111no—
148C2×#117—111no—
149#431—222no—
150#390—222no—
151#390—222no—
152#379—111no—
153#379—111no—
154#379—111no—
155#379C2×D1111yescharacteristic
156#324—222no—
157#323—112no—
158#323C2×D1112yes—
159C22×C11—22no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—82no—
170C22×C11—84no—
171C22×C11—84no—
172C22×C11—82no—
173C22×C11C2×C22⋊C811yescharacteristic
174C22×C11C2×#9911yescharacteristic
175C22×C11C2×#10011yescharacteristic
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—82no—
180C2×D11—84no—
181C2×D11—82no—
182C2×D11—84no—
183C4×C11—42no—
184C4×C11—81no—
185Dic11—22no—
186Dic11—42no—
187Dic11—81no—
188Dic11#32314yes—
189C25—111no—
190C25C4×D1111yescharacteristic
191C22×D4—114no—
192C22×D4—221no—
193C22×D4—221no—
194C22×D4—222no—
195C22×D4—442no—
196C22×D4—442no—
197C23×C4—111no—
198#117—442no—
199#117—442no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—221no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—111no—
204C2×C22⋊C4—111no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4—222no—
207C2×C22⋊C4—222no—
208C2×C22⋊C4C4×D1111yescharacteristic
209C2×C22⋊C4C22×D1111yescharacteristic
210C2×C42—112no—
211C2×C42—221no—
212C4⋊C8—442no—
213C22⋊C8—22no—
214C22⋊C8—222no—
215C4×C8—442no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11—41no—
219C2×C11—41no—
220C2×C11—82no—
221C2×C11C2×#32311yescharacteristic
222C2×C11#212212yes—
223D11—82no—
224C24—21no—
225C24—21no—
226C24—41no—
227C24—41no—
228C24—82no—
229C24—112no—
230C24—221no—
231C24—221no—
232C24—441no—
233C24—441no—
234C24—882no—
235C24C8×D1112yes—
236C24C2×C4×D1111yescharacteristic
237C2×D4—224no—
238C2×D4—224no—
239C2×D4—442no—
240C2×D4—442no—
241C2×D4—448no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—448no—
245C22×C4—21no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—112no—
249C22×C4—112no—
250C22×C4—112no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4—221no—
254C22×C4D4×D1112yes—
255C2×C8—42no—
256C2×C8—442no—
257C4⋊C4—442no—
258C4⋊C4—442no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—82no—
262C22⋊C4—441no—
263C22⋊C4—441no—
264C22⋊C4—882no—
265C22⋊C4—882no—
266C22⋊C4—882no—
267C42—222no—
268C42—222no—
269C42—442no—
270C11#1142711yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—22no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23—42no—
279C23—41no—
280C23—41no—
281C23—82no—
282C23—82no—
283C23—84no—
284C23—84no—
285C23—222no—
286C23—442no—
287C23—442no—
288C23—442no—
289C23—442no—
290C23—441no—
291C23—441no—
292C23—882no—
293C23—882no—
294C23—884no—
295C23—884no—
296C23C22⋊C4×D1111yescharacteristic
297C23C2×C8×D1111yescharacteristic
298C23M16×D1111yescharacteristic
299D4—448no—
300D4—448no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—112no—
306C2×C4—112no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—224no—
310C2×C4—224no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—222no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—441no—
317C8—82no—
318C8—882no—
319C22—22no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22—82no—
330C22—84no—
331C22—84no—
332C22—82no—
333C22—442no—
334C22—442no—
335C22—442no—
336C22—882no—
337C22—884no—
338C22—884no—
339C22—882no—
340C22D11×C22⋊C811yescharacteristic
341C22D11×#9911yescharacteristic
342C22D11×#10011yescharacteristic
343C4—42no—
344C4—81no—
345C4—114no—
346C4—222no—
347C4—442no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—41no—
352C2—41no—
353C2—82no—
354C2—882no—
355C2D11×#32311yescharacteristic
356C2#1307026412yes—
subgroupG/H
centerC22D11×#99
commutatorC23×C11C22×C8
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1316C2
socleC22×C11C2×#99
prime radicalC23×C22⋊D11C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1316D11
hypocenterC11#11427
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #13066927C2semidirect
3. #13066544C2semidirect
4. #13066543C2semidirect
5. C11×#1316C2semidirect
26. C22×C22⋊D11C8semidirect
97. #1316D11semidirect
270. C11#11427semidirect

Maximal subgroups

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

subgroupindex
#130711972
#130669272
#130665442
#130665432
C11×#13162
#1142711