Finite Group Databasebeta

← #14664707

Subgroups — #14664707

Order 2816.

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

normal subgroups only

This group has 412 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#13073996C211yesmaximal, characteristic
2#13068696C211yesmaximal, characteristic
3#13066647C212yesmaximal, complemented
4#13066623C212yesmaximal, complemented
5C2×C11×#324C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C2×C11×C22⋊C8—21no—
9#10622823—21no—
10#10622823—21no—
11C4×C22⋊Dic11C411yescharacteristic
12#10622820—21no—
13#10622596C411yescharacteristic
14#10622596C2211yescharacteristic
15#10622592C411yescharacteristic
16#10622592C2211yescharacteristic
17#10622585—21no—
18#10622585—21no—
19C11×#324—21no—
20C11×#324C2212yes—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C22×C8×C11—41no—
28C2×C11×C4⋊C4—41no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37#66977—41no—
38#66977—41no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×#4318—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11854—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—41no—
66C22×C4×C11—81no—
67C22×C4×C11—81no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×Dic22—41no—
79C2×Dic22—81no—
80C2×C8×C11—42no—
81C2×C8×C11—82no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C22⋊Dic11—24no—
87C22⋊Dic11—41no—
88C22⋊Dic11—41no—
89C4⋊Dic11—41no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—81no—
94Dic11⋊C4—81no—
95C4×Dic11—81no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99#2583—111no—
100#1821—111no—
101C2×#324D1111yescharacteristic
102#1354—112no—
103#1346—112no—
104C23×C11—22no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11#9911yescharacteristic
109C23×C11#9911yescharacteristic
110C23×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
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—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#13512yes—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143Dic22—82no—
144C8×C11—82no—
145C11⋊C8—82no—
146C2×C22⋊Q8—111no—
147C22×C4⋊C4C2×D1111yescharacteristic
148#407—221no—
149C2×C22⋊C8—21no—
150#398—111no—
151#398—111no—
152#395—111no—
153#395—111no—
154#389—221no—
155#389—221no—
156#385—221no—
157#385—221no—
158C4×C22⋊C4—111no—
159#343—112no—
160#343—221no—
161#324—21no—
162#324C2×D1112yes—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11#35612yes—
173C22×C11C2×#9911yescharacteristic
174C22×C11#41611yescharacteristic
175C22×C11#42111yescharacteristic
176C4×C11—22no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182Dic11—42no—
183Dic11—42no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—111no—
187C23×C4C4×D1111yescharacteristic
188C23×C4D4411yescharacteristic
189C23×C4C22⋊D1111yescharacteristic
190C2×M16—222no—
191C22×C8—41no—
192C22⋊Q8—441no—
193C22⋊Q8—441no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C4×D1111yescharacteristic
203C2×C4⋊C4D4411yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C4⋊C4C22×D1111yescharacteristic
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C42—221no—
209C22⋊C8—22no—
210C22⋊C8—41no—
211C22⋊C8—441no—
212C22⋊C8—441no—
213#95—111no—
214#95—111no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—22no—
222C2×C11—41no—
223C2×C11#151611yescharacteristic
224C2×C11#212111yescharacteristic
225C2×C11C2×#35611yescharacteristic
226C24(C2×D11)⋊C411yescharacteristic
227C2×Q8—441no—
228C2×Q8—881no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—41no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4C2×D4411yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249M16—442no—
250M16—442no—
251C2×C8—42no—
252C2×C8—82no—
253C2×C8—442no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C4⋊C4—881no—
263C4⋊C4—881no—
264C22⋊C4—224no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42—881no—
268C11#1185411yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—22no—
272C23—41no—
273C23#6687011yescharacteristic
274C23#6687011yescharacteristic
275C23C2×(C2×D11)⋊C411yescharacteristic
276Q8—882no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—222no—
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#6695712yes—
309C8—82no—
310C8—882no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22#1062211612yes—
321C22C2×#6687011yescharacteristic
322C22#1062272611yescharacteristic
323C22#1062275211yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—442no—
331C4—442no—
332C4—881no—
333C4—881no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2#1306717311yescharacteristic
339C2#1307026011yescharacteristic
340C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC2×C11×#324C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC2×#324D11
hypocenterC11#11854
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
4. #13066623C2semidirect
268. C11#11854semidirect

Maximal subgroups

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

subgroupindex
#130739962
#130686962
#130666472
#130666232
C2×C11×#3242
#1185411