Finite Group Databasebeta

← #14651563

Subgroups — #14651563

Order 2816.

556 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 123 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#13077645C211yesmaximal, characteristic
2#13068706C212yesmaximal, complemented
3#13068604C211yesmaximal, characteristic
4#13066483C212yesmaximal, complemented
5C11×#2487C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#400C412yescomplemented
9C11×#399C412yescomplemented
10C11×#389—21no—
11C11×#386—21no—
12C11×#385—21no—
13C11×#380—21no—
14C11×#380C2211yescharacteristic
15C2×#66898—21no—
16#10622825C2212yes—
17#10622820—21no—
18C2×C22⋊(C11⋊C8)C2212yes—
19#10622624—24no—
20#10622539—21no—
21#10622167—24no—
22#10622164—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11—21no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C22⋊Dic11—22no—
42C2×C4⋊Dic11—22no—
43C2×#4318—22no—
44C22×C11⋊C8D414yes—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48#66898—42no—
49C11⋊#95—22no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#66867—22no—
55#9473—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—82no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4112yes—
77C22×Dic11—42no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—24no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—82no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—82no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C4⋊Dic11—44no—
94#4318—82no—
95C2×C11⋊C8—24no—
96C2×C11⋊C8—44no—
97#2973—111no—
98#2487D1111yescharacteristic
99#1824—112no—
100#1799—111no—
101#1289—112no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#12112yes—
111C23×C11AGL(1,ℤ/8)11yescharacteristic
112C23×C11#13712yes—
113C23×C11#13711yescharacteristic
114D4×C11—42no—
115D4×C11—42no—
116C2×C4×C11—24no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—81no—
135C2×C4×C11—84no—
136C2×C4×C11C4×D412yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×Dic11—82no—
140C2×Dic11—82no—
141C2×Dic11—82no—
142C11⋊C8—44no—
143C2×C4×D4C2×D1111yescharacteristic
144C22×C4⋊C4C2×D1111yescharacteristic
145#435—224no—
146#432—221no—
147C2×#99—221no—
148#407—221no—
149C2×C22⋊C8—112no—
150#400Dic1112yescomplemented
151#399Dic1112yescomplemented
152#389—21no—
153#386—21no—
154#385—21no—
155#380—21no—
156#380—112no—
157#380C2×D1111yescharacteristic
158#342—221no—
159#340—224no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—22no—
164C22×C11—41no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—81no—
172C22×C11#38611yescharacteristic
173C22×C11#41711yescharacteristic
174C22×C11#41911yescharacteristic
175C22×C11#46812yes—
176C22×C11#47012yes—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—82no—
183C4×C11—82no—
184C4×C11#45812yes—
185Dic11—162no—
186C22×D4C22⋊D1111yescharacteristic
187C23×C4—21no—
188C23×C4C22⋊D1111yescharacteristic
189C23×C4C22×D1111yescharacteristic
190C2×M16—222no—
191C22×C8—114no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4C2×Dic1112yes—
201C2×C4⋊C4C2×Dic1111yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4C2×Dic1111yescharacteristic
206C2×C22⋊C4C22⋊D1111yescharacteristic
207C2×C42C22⋊D1111yescharacteristic
208C4⋊C8—222no—
209#99—442no—
210C22⋊C8—222no—
211C22⋊C8—222no—
212C22⋊C8—222no—
213#97—222no—
214#95—22no—
215#95—22no—
216#95—222no—
217#95C2×Dic1112yes—
218C2×C11—22no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—22no—
222C2×C11—81no—
223C2×C11#189011yescharacteristic
224C2×C11#189411yescharacteristic
225C2×C11#191011yescharacteristic
226C24C22⋊Dic1111yescharacteristic
227C24C2×C22⋊D1111yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—21no—
231C2×D4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—82no—
240C22×C4—442no—
241C22×C4C22⋊Dic1111yescharacteristic
242C22×C4C22⋊Dic1111yescharacteristic
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4D4×D1112yes—
245C22×C4#434112yes—
246C22×C4C22×Dic1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248M16—882no—
249C2×C8—224no—
250C2×C8—444no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—82no—
257C4⋊C4—444no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—82no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C42—21no—
266C42—21no—
267C11#947311yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23#6699212yes—
276C23#6699512yes—
277C23#6700211yescharacteristic
278C23#6700411yescharacteristic
279C23C2×C22⋊Dic1111yescharacteristic
280D4—42no—
281D4—42no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—84no—
302C2×C4—882no—
303C2×C4—882no—
304C2×C4—882no—
305C2×C4D4×Dic1112yes—
306C2×C4#6698811yescharacteristic
307C2×C4#6699011yescharacteristic
308C8—444no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1062266212yes—
322C22#1062266512yes—
323C22#1062283311yescharacteristic
324C22#1062283811yescharacteristic
325C22#1062284511yescharacteristic
326C4—21no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—82no—
332C4—82no—
333C4—1762no—
334C4#1062266612yes—
335C2—21no—
336C2—22no—
337C2—21no—
338C2—22no—
339C2—81no—
340C2#1306903011yescharacteristic
341C2#1306905011yescharacteristic
342C2#1306914411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2487C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#2487D11
hypocenterC11#9473
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. #13068706C2semidirect
4. #13066483C2semidirect
8. C11×#400C4semidirect
9. C11×#399C4semidirect
150. #400Dic11semidirect
151. #399Dic11semidirect
267. C11#9473semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130687062
#130686042
#130664832
C11×#24872
#947311