Finite Group Databasebeta

← #14663301

Subgroups — #14663301

Order 2816.

380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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#13072900C211yesmaximal, characteristic
2#13066947C211yesmaximal, characteristic
3#13066927C211yesmaximal, characteristic
4#13066565C211yesmaximal, characteristic
5#13066563C211yesmaximal, characteristic
6#13066546C211yesmaximal, characteristic
7C11×#1317C211yesmaximal, characteristic
8C22×Dic11⋊C4C411yescharacteristic
9C2×#66930C2211yescharacteristic
10C11×#381C2211yescharacteristic
11#10622824C411yescharacteristic
12#10622563C411yescharacteristic
13#10622559C2211yescharacteristic
14#10622556C411yescharacteristic
15#10622332—21no—
16#10622331—21no—
17#10622271—21no—
18#10622270—21no—
19#10622267—21no—
20#10622265—21no—
21C11×#323C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C22⋊Dic11C2×C411yescharacteristic
33C2×C22⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—41no—
39C2×Dic11⋊C4—41no—
40C2×Dic11⋊C4D411yescharacteristic
41C2×Dic11⋊C4D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44#66930—41no—
45#66930—41no—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—41no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11544—111nomaximal, Sylow
63C24×C11C22×C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—42no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—41no—
92C4⋊Dic11—42no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2484—111no—
106#1464—111no—
107#1458—111no—
108#1326—111no—
109#1326—111no—
110#1317—111no—
111#1317D1111yescharacteristic
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11#13111yescharacteristic
118C23×C11#13111yescharacteristic
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—22no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11#9911yescharacteristic
153C2×Dic11#9911yescharacteristic
154C8×C11—81no—
155C8×C11—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158C2×#117—111no—
159C22×C4⋊C4—111no—
160#432—221no—
161#431—221no—
162#400—221no—
163#398—221no—
164#387—221no—
165#387—221no—
166#385—111no—
167#385—111no—
168#381—111no—
169#381—111no—
170#381C2×D1111yescharacteristic
171#324—221no—
172#324—221no—
173#323—111no—
174#323—111no—
175#323C2×D1111yescharacteristic
176#323C2×D1111yescharacteristic
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—42no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11#40811yescharacteristic
187C22×C11C2×#9911yescharacteristic
188C22×C11#41311yescharacteristic
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—81no—
192C4×C11—81no—
193Dic11—21no—
194Dic11—21no—
195Dic11—41no—
196Dic11—42no—
197Dic11—41no—
198Dic11—41no—
199Dic11—81no—
200C23×C4—111no—
201C23×C4—111no—
202C23×C4C4×D1111yescharacteristic
203#117—441no—
204#117—441no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—441no—
212C2×C4⋊C4—441no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4C4×D1111yescharacteristic
216C2×C22⋊C4C22×D1111yescharacteristic
217C2×C42—111no—
218C2×C42—111no—
219C4⋊C8—441no—
220C4⋊C8—441no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C22⋊C8—221no—
225#97—441no—
226C4×C8—441no—
227#95—21no—
228#95—21no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—41no—
238C2×C11—41no—
239C2×C11#146811yescharacteristic
240C2×C11#212011yescharacteristic
241C2×C11#212311yescharacteristic
242C24C2×C4×D1111yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—441no—
260C22×C4—442no—
261C22×C4—441no—
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—441no—
280C42—221no—
281C42—221no—
282C42—221no—
283C42—221no—
284C11#1154411yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23C22⋊C4×D1111yescharacteristic
290C23#6695411yescharacteristic
291C23#6696011yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—222no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C8—81no—
328C8—81no—
329C8—881no—
330C8—881no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22#1062234011yescharacteristic
341C22D11×#9911yescharacteristic
342C22#1062235811yescharacteristic
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—221no—
348C4—221no—
349C4—442no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4—881no—
354C2—21no—
355C2—21no—
356C2—41no—
357C2—41no—
358C2#1306696111yescharacteristic
359C2#1307025611yescharacteristic
360C2#1307026811yescharacteristic
subgroupG/H
centerC22D11×#99
commutator, prime radicalC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#1317D11
hypocenterC11#11544
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
284. C11#11544semidirect

Maximal subgroups

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

subgroupindex
#130729002
#130669472
#130669272
#130665652
#130665632
#130665462
C11×#13172
#1154411