Finite Group Databasebeta

← #14664161

Subgroups — #14664161

Order 2816.

400 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074482C211yesmaximal, characteristic
2#13068411C211yesmaximal, characteristic, complemented
3#13066938C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic
6#13066618C211yesmaximal, characteristic
7C11×#1354C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622842C411yescharacteristic
12C2×#66888—21no—
13M16×Dic11—21no—
14#10622605—21no—
15#10622604C2211yescharacteristic
16#10622603—21no—
17#10622331—21no—
18#10622286—21no—
19#10622285C411yescharacteristic
20#10622282—21no—
21#10622264C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44C2×C411yescharacteristic
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2311yescharacteristic
33#67000—41no—
34#67000—41no—
35C2×(C2×D11)⋊C4—21no—
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×Dic11⋊C4—21no—
42C2×Dic11⋊C4C2×C411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48#66940—41no—
49#66940—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66888—24no—
59#66879—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62C8×Dic11—41no—
63#11738—111nomaximal, Sylow
64C23×D11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×D44—41no—
78C2×D44—81no—
79C2×Dic22—22no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—41no—
83C11×M16—22no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—81no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
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—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—81no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2632—111no—
111C4×#101—111no—
112#1461—111no—
113#1354—111no—
114#1354D1111yescharacteristic, complemented
115#1345—111no—
116#1345—111no—
117C23×C11C2×C22⋊C411yescharacteristic
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125Q8×C11—82no—
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—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11#9911yescharacteristic
152C2×Dic11#9911yescharacteristic
153C2×Dic11#10412yes—
154D44—82no—
155Dic22—42no—
156Dic22—42no—
157C8×C11—42no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×#124—111no—
162C2×C4×Q8—111no—
163#431—221no—
164C2×#101—221no—
165C4×M16—221no—
166#399—221no—
167#395—111no—
168#395C2×D1111yescharacteristic
169#394—111no—
170#394—111no—
171#393—221no—
172#388—221no—
173#388—221no—
174#383—111no—
175#343—111no—
176#343C2×D1111yescharacteristic
177#324—111no—
178#324—221no—
179#324C2×D1111yescharacteristic
180C22×C11—21no—
181C22×C11—21no—
182C22×C11C2×#9911yescharacteristic
183C22×C11#41611yescharacteristic
184C22×C11C2×#10411yescharacteristic
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—81no—
197C4×C11—81no—
198Dic11—21no—
199Dic11—21no—
200Dic11—22no—
201Dic11—41no—
202Dic11—41no—
203Dic11—81no—
204C22×Q8—111no—
205C22×Q8C4×D1111yescharacteristic
206C22×D4—111no—
207C2×M16—21no—
208C2×M16—221no—
209#124—441no—
210#124—441no—
211C4×Q8—441no—
212C4×Q8—441no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4C22×D1111yescharacteristic
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—111no—
227C4⋊C8—441no—
228#101—224no—
229C22⋊C8—21no—
230C22⋊C8—221no—
231#97—441no—
232C4×C8—441no—
233C4×C8—441no—
234#95—21no—
235#95—111no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95C4×D1111yescharacteristic
240C2×C11—21no—
241C2×C11—21no—
242C2×C11#150111yescharacteristic
243C2×C11#212211yescharacteristic
244C2×C11#213311yescharacteristic
245D11—161no—
246C24—221no—
247C2×Q8—41no—
248C2×Q8—81no—
249C2×Q8—222no—
250C2×Q8—221no—
251C2×Q8—221no—
252C2×Q8—441no—
253C2×D4—441no—
254C2×D4—881no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4C2×C4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265M16—22no—
266M16—41no—
267M16—222no—
268M16—441no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—441no—
272C2×C8—441no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—881no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—881no—
285C22⋊C4—881no—
286C42—221no—
287C42—221no—
288C42—221no—
289C42—221no—
290C42—221no—
291C42—221no—
292C11#1173811yescharacteristic, complemented, Sylow
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23C22⋊C4×D1111yescharacteristic
301Q8—82no—
302Q8—442no—
303Q8—442no—
304D4—882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—112no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4#6696911yescharacteristic
332C2×C4#6697211yescharacteristic
333C8—42no—
334C8—81no—
335C8—442no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22—881no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22D11×#9911yescharacteristic
347C22#1062241711yescharacteristic
348C22D11×#10411yescharacteristic
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—81no—
354C4—81no—
355C4—222no—
356C4—221no—
357C4—221no—
358C4—441no—
359C4—441no—
360C4—881no—
361C2—21no—
362C2—21no—
363C2—1761no—
364C2#1306710611yescharacteristic
365C2#1307026411yescharacteristic
366C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11738
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
2. #13068411C2semidirect
3. #13066938C2semidirect
4. #13066646C2semidirect
7. C11×#1354C2semidirect
114. #1354D11semidirect
292. C11#11738semidirect

Maximal subgroups

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

subgroupindex
#130744822
#130684112
#130669382
#130666462
#130666202
#130666182
C11×#13542
#1173811