Finite Group Databasebeta

← #14647176

Subgroups — #14647176

Order 2816.

482 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 115 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#13071014C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066498C212yesmaximal, complemented
4#13066498C212yesmaximal, complemented
5C11×#1749C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×C11×C22⋊C8—21no—
8C2×C11×#97C2212yes—
9#10622825C411yescharacteristic
10#10622825C411yescharacteristic
11#10622824—21no—
12C4×C22⋊Dic11—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622550—21no—
15#10622549C2211yescharacteristic
16#10622549C2211yescharacteristic
17C4×C4⋊Dic11C411yescharacteristic
18C4×C4⋊Dic11C411yescharacteristic
19#10622545—21no—
20C2×#66867C2212yes—
21C11×#336—21no—
22#10622162—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C8×C11—22no—
27C2×C42×C11—24no—
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×C22⋊Dic11—21no—
33C2×C22⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4×Dic11—21no—
39C2×C4×Dic11—21no—
40C22×C11⋊C8—22no—
41C11×C22⋊C8—24no—
42C11×#97—24no—
43C11⋊#95—21no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C22⋊(C11⋊C8)—24no—
52#66867—24no—
53#8720—111nomaximal, Sylow
54C24×C11C22⋊C411yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×C8×C11—24no—
75C2×C8×C11—42no—
76C2×C8×C11—42no—
77C42×C11—22no—
78C42×C11—22no—
79C42×C11—22no—
80C42×C11#4114yes—
81C22⋊Dic11—42no—
82C22⋊Dic11—42no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4×Dic11—42no—
88C4×Dic11—42no—
89C2×C11⋊C8—24no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92#2283—111no—
93#1749—111no—
94#1749D1111yescharacteristic
95#1295—112no—
96#1295—112no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11#10412yes—
104C23×C11C2×C22⋊C411yescharacteristic
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
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—44no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11#10412yes—
123C2×C4×C11#11712yes—
124C2×C4×C11#12312yes—
125C2×C4×C11#12312yes—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C8×C11—44no—
139C11⋊C8—44no—
140C22×C42C2×D1111yescharacteristic
141C2×C22⋊C8—21no—
142C2×C22⋊C8—221no—
143C2×#97—112no—
144C2×#97C2×D1112yes—
145#383—221no—
146#382—111no—
147#382—111no—
148#381—221no—
149#380—111no—
150#380—111no—
151C4×C4⋊C4—111no—
152C4×C4⋊C4—111no—
153C4×C22⋊C4—221no—
154#376—221no—
155#336—21no—
156#336—221no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11#38111yescharacteristic
165C22×C11#41311yescharacteristic
166C22×C11#41311yescharacteristic
167C22×C11C2×#10411yescharacteristic
168C22×C11C2×#10411yescharacteristic
169C22×C11#42111yescharacteristic
170C22×C11#42111yescharacteristic
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—41no—
176C4×C11—41no—
177Dic11—81no—
178Dic11—81no—
179Dic11—81no—
180Dic11—81no—
181C23×C4C4×D1111yescharacteristic
182C23×C4D4411yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C22×C8—22no—
185C22×C8—222no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C22⋊C4—221no—
191C2×C22⋊C4—221no—
192C2×C42—24no—
193C2×C42—221no—
194C2×C42—221no—
195C2×C42C4×D1111yescharacteristic
196C2×C42D4411yescharacteristic
197C2×C42C22⋊D1111yescharacteristic
198C2×C42C22×D1111yescharacteristic
199C22⋊C8—24no—
200C22⋊C8—224no—
201#97—24no—
202#97—224no—
203#95—221no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211C2×C11—42no—
212C2×C11#152411yescharacteristic
213C2×C11#152911yescharacteristic
214C2×C11#153211yescharacteristic
215C2×C11#153511yescharacteristic
216C2×C11#182211yescharacteristic
217C2×C11#182611yescharacteristic
218C2×C11#182611yescharacteristic
219C24(C2×D11)⋊C411yescharacteristic
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4C2×D4411yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239C2×C8—24no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—224no—
243C2×C8—442no—
244C2×C8—442no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C22⋊C4—442no—
250C22⋊C4—442no—
251C42—22no—
252C42—22no—
253C42—22no—
254C42—442no—
255C42—442no—
256C42#434114yes—
257C11#872011yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#6688912yes—
265C23C2×(C2×D11)⋊C411yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4#6686912yes—
296C2×C4#6693012yes—
297C2×C4#6693912yes—
298C2×C4#6698812yes—
299C8—44no—
300C8—444no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22C2×#6686911yescharacteristic
309C22#1062255611yescharacteristic
310C22#1062261811yescharacteristic
311C22#1062274511yescharacteristic
312C22#1062274511yescharacteristic
313C22C2×#6688911yescharacteristic
314C22#1062275211yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—881no—
322C4—881no—
323C4—881no—
324C4—881no—
325C2—42no—
326C2#1306720211yescharacteristic
327C2#1306722111yescharacteristic
328C2#1306723711yescharacteristic
329C2#1306724511yescharacteristic
330C2#1306869711yescharacteristic
331C2#1306871311yescharacteristic
332C2#1306871611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#8720
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #13066498C2semidirect
4. #13066498C2semidirect
257. C11#8720semidirect

Maximal subgroups

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

subgroupindex
#130710142
#130683782
#130664982
C11×#17492
#872011