Finite Group Databasebeta

← #14663295

Subgroups — #14663295

Order 2816.

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

normal subgroups only

This group has 460 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#13072886C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic, complemented
3#13066563C212yesmaximal, complemented
4#13066543C212yesmaximal
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C22×(C2×D11)⋊C4C411yescharacteristic
8C11×#432—21no—
9#10622824C411yescharacteristic
10#10622606—21no—
11#10622605—21no—
12#10622568C411yescharacteristic
13#10622568C2211yescharacteristic
14#10622559C411yescharacteristic
15#10622559C2211yescharacteristic
16#10622553—21no—
17#10622553—21no—
18#10622538—21no—
19C11×#324—21no—
20C11×#323C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C24×D11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×Dic11C2×C411yescharacteristic
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11C2×C411yescharacteristic
35C2×C22⋊Dic11C2×C411yescharacteristic
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×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—41no—
43C2×(C2×D11)⋊C4—41no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C11×C4⋊C8—41no—
47C11×C22⋊C8—22no—
48C11×#97—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11542—111nomaximal, Sylow
57C24×C11C22×C411yescharacteristic
58C23×D11—21no—
59C23×D11—22no—
60C23×D11—42no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11—81no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
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—41no—
78C22×Dic11—81no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C22⋊Dic11—22no—
89C22⋊Dic11—41no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—81no—
96(C2×D11)⋊C4—81no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99C2×C11⋊C8—42no—
100#2482—111no—
101#1464D1111yescharacteristic, complemented
102#1458—111no—
103#1326—112no—
104#1316—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#13112yes—
111C22×D11—22no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—42no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—42no—
120C22×D11—84no—
121C22×D11—84no—
122C22×D11—82no—
123C22×D11—82no—
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—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11#9911yescharacteristic
140C2×C4×C11#9911yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—82no—
151C8×C11—82no—
152C11⋊C8—82no—
153C2×#117C2×D1111yescharacteristic
154C22×C22⋊C4—111no—
155#432—21no—
156#431—221no—
157#399—221no—
158#397—221no—
159#388—221no—
160#388—221no—
161#385—111no—
162#385—111no—
163#381—111no—
164#379—111no—
165#379—111no—
166#324—21no—
167#324—221no—
168#323—112no—
169#323C2×D1112yes—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11#40811yescharacteristic
178C22×C11C2×#9911yescharacteristic
179C22×C11#41311yescharacteristic
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—42no—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—84no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—84no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C25—111no—
200C23×C4—111no—
201C23×C4C4×D1111yescharacteristic
202#117—41no—
203#117—41no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4D4411yescharacteristic
207C2×C4⋊C4C22⋊D1111yescharacteristic
208C2×C22⋊C4—111no—
209C2×C22⋊C4—111no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—441no—
217C2×C22⋊C4—441no—
218C2×C22⋊C4C4×D1111yescharacteristic
219C2×C22⋊C4C22×D1111yescharacteristic
220C2×C42D4411yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222C4⋊C8—41no—
223C4⋊C8—441no—
224C22⋊C8—22no—
225C22⋊C8—222no—
226#97—41no—
227C4×C8—441no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—42no—
235C2×C11#146811yescharacteristic
236C2×C11#212011yescharacteristic
237C2×C11#212211yescharacteristic
238D11—82no—
239C24—221no—
240C24—222no—
241C24—441no—
242C24—441no—
243C24—442no—
244C24—881no—
245C24C2×C4×D1111yescharacteristic
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—441no—
254C22×C4—881no—
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4C2×D4411yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C2×C8—42no—
262C2×C8—442no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—881no—
266C4⋊C4—881no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—222no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C22⋊C4—441no—
274C22⋊C4—441no—
275C22⋊C4—441no—
276C22⋊C4—881no—
277C22⋊C4—881no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—21no—
282C11#1154211yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—222no—
288C23—441no—
289C23—441no—
290C23—441no—
291C23—442no—
292C23—442no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—882no—
297C23—884no—
298C23—884no—
299C23—882no—
300C23#6696012yes—
301C23C2×(C2×D11)⋊C411yescharacteristic
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—882no—
327C2×C4#6687011yescharacteristic
328C2×C4#6687011yescharacteristic
329C8—82no—
330C8—882no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—442no—
339C22—442no—
340C22—442no—
341C22—881no—
342C22—881no—
343C22—884no—
344C22—884no—
345C22—881no—
346C22—881no—
347C22C2×#6687011yescharacteristic
348C22#1062274211yescharacteristic
349C22#1062274511yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—881no—
358C4—881no—
359C4—881no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—882no—
364C2#1306696511yescharacteristic
365C2#1307025811yescharacteristic
366C2#1307026511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×D11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1464D11
hypocenterC11#11542
LCSG ▷ C24×C11 ▷ C22×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. #13066930C2semidirect
3. #13066563C2semidirect
5. C11×#1464C2semidirect
101. #1464D11semidirect
282. C11#11542semidirect

Maximal subgroups

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

subgroupindex
#130728862
#130669302
#130665632
#130665432
C11×#14642
#1154211