Finite Group Databasebeta

← #14664465

Subgroups — #14664465

Order 2816.

472 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 79 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#13071852C211yesmaximal, characteristic
2#13068699C211yesmaximal, characteristic, complemented
3#13066623C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×C4×C22⋊D11—21no—
8C2×C4×D44C411yescharacteristic
9C11×#432—21no—
10#10622820—21no—
11#10622607—21no—
12#10622604C2211yescharacteristic
13#10622596C2211yescharacteristic
14#10622574—21no—
15#10622573C411yescharacteristic
16#10622566C411yescharacteristic
17C4×(C2×D11)⋊C4—21no—
18C4×C4⋊Dic11C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C4×C22⋊D11—44no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×#4318—22no—
46C4×D44—41no—
47C4×D44—41no—
48C11×C4⋊C8—41no—
49C11×C22⋊C8—22no—
50C11×#97—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—41no—
56C22⋊(C11⋊C8)—41no—
57#11804—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C23×D11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
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
70C2×C22⋊D11—42no—
71C2×C22⋊D11—42no—
72C2×C22⋊D11—42no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×D44—41no—
77C2×D44—42no—
78C2×C4×D11—42no—
79C2×C4×D11—42no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C8×C11—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96C4⋊Dic11—41no—
97C4⋊Dic11—42no—
98Dic11⋊C4—42no—
99C4×Dic11—42no—
100#4318—42no—
101#4318—42no—
102C2×C11⋊C8—42no—
103#2392—111no—
104#1822—111no—
105#1464D1111yescharacteristic, complemented
106#1346—112no—
107#1345—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11C2×C22⋊C411yescharacteristic
114C22×D11—22no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
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—42no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)12yes—
138C22⋊D11—48no—
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148D44—42no—
149D44—42no—
150C4×D11—82no—
151C4×D11—82no—
152C8×C11—82no—
153C11⋊C8—82no—
154C2×C4×D4—111no—
155C2×C4×D4—221no—
156C2×#117C2×D1111yescharacteristic
157#432—21no—
158#407—221no—
159#398—111no—
160#397—111no—
161#396—221no—
162#394—111no—
163#394—221no—
164#392—111no—
165C4×C4⋊C4—111no—
166C4×C22⋊C4—221no—
167#343—112no—
168#343—221no—
169#324C2×D1112yes—
170#323—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—42no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—81no—
178C22×C11C2×#9911yescharacteristic
179C22×C11#41811yescharacteristic
180C22×C11#42111yescharacteristic
181C2×D11—42no—
182C2×D11—42no—
183C2×D11—42no—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195Dic11—42no—
196Dic11—81no—
197Dic11—81no—
198C22×D4—111no—
199C22×D4—221no—
200C23×C4—221no—
201C23×C4D4411yescharacteristic
202C2×M16—222no—
203C4×D4—441no—
204C4×D4—441no—
205C4×D4—444no—
206#117—41no—
207#117—41no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4D4411yescharacteristic
212C2×C4⋊C4C22×D1111yescharacteristic
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4C4×D1111yescharacteristic
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C42—221no—
221C2×C42C4×D1111yescharacteristic
222C2×C42C22⋊D1111yescharacteristic
223C4⋊C8—41no—
224C22⋊C8—22no—
225C22⋊C8—441no—
226C22⋊C8—441no—
227#97—41no—
228#95—111no—
229#95—111no—
230#95—221no—
231#95—221no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—81no—
235C2×C11#151011yescharacteristic
236C2×C11#212011yescharacteristic
237C2×C11#213211yescharacteristic
238D11—82no—
239C24—221no—
240C24(C2×D11)⋊C411yescharacteristic
241C2×D4—441no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—442no—
245C2×D4—442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263M16—442no—
264M16—442no—
265C2×C8—42no—
266C2×C8—442no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C42—21no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—442no—
284C11#1180411yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—222no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23C2×(C2×D11)⋊C411yescharacteristic
298D4—442no—
299D4—442no—
300D4—448no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—882no—
325C2×C4—882no—
326C2×C4#6687011yescharacteristic
327C2×C4#6687011yescharacteristic
328C2×C4#6696112yes—
329C8—82no—
330C8—882no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—442no—
339C22—442no—
340C22—442no—
341C22—881no—
342C22—881no—
343C22—881no—
344C22—881no—
345C22C2×#6687011yescharacteristic
346C22#1062274411yescharacteristic
347C22#1062275211yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—442no—
356C4—881no—
357C4—881no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—882no—
362C2#1306714611yescharacteristic
363C2#1307025511yescharacteristic
364C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radical#10622573C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11804
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13068699C2semidirect
3. #13066623C2semidirect
4. #13066620C2semidirect
5. C11×#1464C2semidirect
105. #1464D11semidirect
284. C11#11804semidirect

Maximal subgroups

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

subgroupindex
#130718522
#130686992
#130666232
#130666202
C11×#14642
#1180411