Finite Group Databasebeta

← #14663259

Subgroups — #14663259

Order 2816.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071323C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic, complemented
3#13066561C212yesmaximal, complemented
4#13066547C212yesmaximal
5C11×#1467C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C411yescharacteristic
8C2×C4×D44C411yescharacteristic
9C11×#432—21no—
10#10622843C411yescharacteristic
11#10622602—21no—
12#10622602—21no—
13#10622601C2211yescharacteristic
14#10622589C2211yescharacteristic
15#10622553—21no—
16#10622553—21no—
17#10622545C411yescharacteristic
18#10622539—21no—
19C11×#324—21no—
20C11×#324C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34#67000—22no—
35#67000—22no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C4×D44—41no—
47C4×D44—41no—
48C11×C4⋊C8—41no—
49C11×C22⋊C8—22no—
50C11×#97—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11534—111nomaximal, Sylow
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×D44—21no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44M1612yes—
78C2×C4×D11—42no—
79C2×C4×D11—81no—
80C2×C4×D11—81no—
81C2×C8×C11—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91(C2×D11)⋊C4—24no—
92(C2×D11)⋊C4—24no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—81no—
96(C2×D11)⋊C4—81no—
97C4⋊Dic11—41no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—21no—
101C4×Dic11—41no—
102C4×Dic11M1612yes—
103C2×C11⋊C8—42no—
104#2326—111no—
105#1467—111no—
106#1467D1111yescharacteristic, complemented
107#1325—112no—
108#1318—112no—
109C23×C11C2×C22⋊C411yescharacteristic
110C22×D11—22no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117Q8×C11—42no—
118Q8×C11—42no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11C2×M1611yescharacteristic
137C2×C4×C11C2×M1611yescharacteristic
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147D44—42no—
148D44—42no—
149C4×D11—84no—
150C8×C11—82no—
151C11⋊C8—82no—
152C2×#124—111no—
153C2×C4×Q8C2×D1111yescharacteristic
154C2×C4×D4—111no—
155#432—21no—
156#432—221no—
157#391—111no—
158#390—111no—
159#388—221no—
160#388—221no—
161#385—221no—
162#385—221no—
163#384—111no—
164#376—111no—
165#324—21no—
166#324—112no—
167#324—221no—
168#324C2×D1112yes—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#40711yescharacteristic
172C22×C11C2×#9911yescharacteristic
173C22×C11#41311yescharacteristic
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190Dic11—42no—
191Dic11—81no—
192Dic11—81no—
193C22×Q8C4×D1111yescharacteristic
194C22×D4—111no—
195C23×C4—221no—
196#124—222no—
197#124—222no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×D4—441no—
201C4×D4—441no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4D4411yescharacteristic
206C2×C4⋊C4C22⋊D1111yescharacteristic
207C2×C4⋊C4C22×D1111yescharacteristic
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C42—111no—
214C2×C42—111no—
215C2×C42C4×D1111yescharacteristic
216C2×C42D4411yescharacteristic
217C2×C42C22⋊D1111yescharacteristic
218C4⋊C8—41no—
219C4⋊C8—441no—
220C22⋊C8—22no—
221C22⋊C8—222no—
222#97—41no—
223#97—441no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11#146511yescharacteristic
231C2×C11#212811yescharacteristic
232C2×C11#213311yescharacteristic
233D11—82no—
234C24—221no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—112no—
240C2×D4—221no—
241C2×D4—441no—
242C2×D4—441no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—442no—
247C22×C4—881no—
248C22×C4—881no—
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×D4411yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256C2×C8—42no—
257C2×C8—442no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—441no—
262C4⋊C4—881no—
263C4⋊C4—881no—
264C22⋊C4—224no—
265C22⋊C4—224no—
266C22⋊C4—441no—
267C22⋊C4—441no—
268C22⋊C4—881no—
269C22⋊C4—881no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—112no—
277C42—221no—
278C42—441no—
279C11#1153411yescharacteristic, complemented, Sylow
280C23—222no—
281C23—441no—
282C23—441no—
283C23—441no—
284C23—441no—
285C23—441no—
286C23—441no—
287C23C2×(C2×D11)⋊C411yescharacteristic
288Q8—42no—
289Q8—42no—
290D4—442no—
291D4—442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—222no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—884no—
317C2×C4#6687011yescharacteristic
318C2×C4#6687011yescharacteristic
319C2×C4M16×D1111yescharacteristic
320C2×C4M16×D1111yescharacteristic
321C8—82no—
322C8—882no—
323C22—21no—
324C22—21no—
325C22—442no—
326C22—442no—
327C22—442no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—881no—
332C22C2×#6687011yescharacteristic
333C22#1062273911yescharacteristic
334C22#1062274511yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—442no—
345C4—881no—
346C4—881no—
347C2—21no—
348C2—21no—
349C2—882no—
350C2#1306695211yescharacteristic
351C2#1307028711yescharacteristic
352C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11534
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13066960C2semidirect
3. #13066561C2semidirect
5. C11×#1467C2semidirect
106. #1467D11semidirect
279. C11#11534semidirect

Maximal subgroups

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

subgroupindex
#130713232
#130669602
#130665612
#130665472
C11×#14672
#1153411