Finite Group Databasebeta

← #14651415

Subgroups — #14651415

Order 2816.

474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077254C211yesmaximal, characteristic
2#13073065C211yesmaximal, characteristic
3#13067148C212yesmaximal
4#13066468C212yesmaximal
5C11×#1820C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#381C2212yes—
9C4×C22⋊Dic11C2211yescharacteristic
10#10622820C2212yes—
11#10622613—24no—
12#10622590C411yescharacteristic, complemented
13#10622589C411yescharacteristic, complemented
14#10622587C411yescharacteristic, complemented
15#10622587C411yescharacteristic, complemented
16#10622565—21no—
17#10622565—21no—
18#10622546—21no—
19#10622546—21no—
20#10622537—21no—
21C4×#4318—21no—
22C11×#342—21no—
23C11×#342—21no—
24#10622090—24no—
25C23×C4×C11C2311yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C11×#117—22no—
28C11×#117—22no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—22no—
40#66977—22no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×#4318—22no—
47C11×#95—22no—
48C11×#95—22no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)D414yes—
58C4⋊(C11⋊C8)—24no—
59#66867—22no—
60C4×C11⋊C8—22no—
61#9444—111nomaximal, Sylow
62C24×C11C2×D411yescharacteristic
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11#4112yes—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×Dic22—22no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C4⋊Dic11—22no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—41no—
99C4×Dic11—41no—
100#4318—42no—
101#4318—42no—
102C2×C11⋊C8—24no—
103#2921—111no—
104#2499—111no—
105#1820D1111yescharacteristic
106#1511—112no—
107#1284—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#12112yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—82no—
129C2×C4×C11—82no—
130C2×C4×C11—82no—
131C2×C4×C11C4×D412yes—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146Dic22—82no—
147C11⋊C8—44no—
148C2×C22⋊Q8—111no—
149C2×#117C2×D1111yescharacteristic
150#433—224no—
151#423—221no—
152#407—112no—
153C4×M16—221no—
154#397—221no—
155#397—221no—
156#391—111no—
157#391—111no—
158#387—221no—
159#387—221no—
160#384—111no—
161#382—111no—
162#381C2×D1112yes—
163C4×C22⋊C4—111no—
164#342—21no—
165#342—21no—
166#328—224no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11#38611yescharacteristic
175C22×C11#41011yescharacteristic
176C22×C11#41011yescharacteristic
177C4×C11—22no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—162no—
185Dic11—42no—
186Dic11—81no—
187Dic11—81no—
188Dic11—81no—
189C22×Q8—111no—
190C23×C4C22×D1111yescharacteristic
191C2×M16—222no—
192C22⋊Q8—222no—
193C22⋊Q8—222no—
194#117—22no—
195#117—22no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4C4×D1111yescharacteristic
201C2×C4⋊C4C4×D1111yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—221no—
205C2×C22⋊C4C22⋊D1111yescharacteristic
206C2×C22⋊C4C22⋊D1111yescharacteristic
207C2×C42—111no—
208C2×C42—111no—
209C2×C42D4411yescharacteristic
210C2×C42D4411yescharacteristic
211C4⋊C8—224no—
212C22⋊C8—114no—
213C22⋊C8—222no—
214#97—222no—
215C4×C8—222no—
216#95—22no—
217#95—22no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—42no—
228C2×C11#188411yescharacteristic
229C2×C11#189911yescharacteristic
230C2×C11#190911yescharacteristic
231C24C2×C22⋊D1111yescharacteristic
232C2×Q8—222no—
233C2×Q8—441no—
234C2×Q8—441no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—42no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4C2×D4411yescharacteristic
248C22×C4D4×D1112yes—
249C22×C4#434112yes—
250M16—442no—
251M16—442no—
252C2×C8—224no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—222no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—442no—
265C22⋊C4—442no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—441no—
271C42—441no—
272C11#944411yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23C2×(C2×D11)⋊C411yescharacteristic
278C23#6699212yes—
279Q8—882no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—222no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4(C22⋊D11)⋊C412yes—
310C2×C4#6693511yescharacteristic
311C2×C4#6693911yescharacteristic
312C8—444no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22#1062257111yescharacteristic
321C22#1062261911yescharacteristic
322C22#1062261911yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—162no—
331C4—442no—
332C4—881no—
333C4—881no—
334C4—881no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1306899711yescharacteristic
339C2#1306907211yescharacteristic
340C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1820C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1820D11
hypocenterC11#9444
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
12. #10622590C4semidirect
13. #10622589C4semidirect
14. #10622587C4semidirect
15. #10622587C4semidirect
272. C11#9444semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130730652
#130671482
#130664682
C11×#18202
#944411