Finite Group Databasebeta

← #14664924

Subgroups — #14664924

Order 2816.

372 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 77 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#13073979C211yesmaximal, characteristic
2#13068611C211yesmaximal, characteristic
3#13066938C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic
5#13066645C211yesmaximal, characteristic
6#13066643C211yesmaximal, characteristic
7C11×#1353C211yesmaximal, characteristic
8C2×#66940C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C2×#66888—21no—
12#10622731—21no—
13#10622595C411yescharacteristic
14#10622592C2211yescharacteristic
15#10622331—21no—
16#10622269C411yescharacteristic
17#10622267—21no—
18#10622265—21no—
19#10622263C411yescharacteristic
20#10622260—21no—
21#10622259—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Dic22C2×C411yescharacteristic
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×Dic11⋊C4—21no—
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4C2×C411yescharacteristic
37C2×Dic11⋊C4D411yescharacteristic
38C2×C4×Dic11—21no—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
43#66940—41no—
44#66940—41no—
45#66940—41no—
46#66940—41no—
47C11×C22⋊C8—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66888—42no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61Dic11⋊C8—41no—
62C8×Dic11—41no—
63#11905—111nomaximal, Sylow
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—42no—
79C2×Dic22SD1612yes—
80C2×Dic22Q1612yes—
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C4⋊Dic11—42no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—42no—
101#4318—41no—
102#4318—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2581—111no—
106#1801—111no—
107#1461—111no—
108#1354—111no—
109#1354—111no—
110#1353—111no—
111#1353D1111yescharacteristic
112C23×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11C2×SD1611yescharacteristic
125C2×C4×C11C2×Q1611yescharacteristic
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—22no—
131C2×Dic11—21no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11#9911yescharacteristic
140C2×Dic11#9911yescharacteristic
141C2×Dic11#10312yes—
142C2×Dic11#10312yes—
143Dic22—42no—
144Dic22—42no—
145Dic22—42no—
146Dic22—42no—
147C8×C11—81no—
148C8×C11—81no—
149C11⋊C8—81no—
150C11⋊C8—81no—
151C2×C4×Q8—111no—
152C2×C4×Q8—111no—
153#431—221no—
154#423—221no—
155C2×#101—221no—
156#400—111no—
157#400C2×D1111yescharacteristic
158#395—111no—
159#395—111no—
160#391—221no—
161#389—221no—
162#387—221no—
163#387—221no—
164#382—111no—
165#343—111no—
166#343C2×D1111yescharacteristic
167#324—111no—
168#324—221no—
169#324C2×D1111yescharacteristic
170C22×C11—21no—
171C22×C11—21no—
172C22×C11C2×#9911yescharacteristic
173C22×C11C2×#10311yescharacteristic
174C22×C11#42111yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—81no—
180C4×C11—81no—
181Dic11—21no—
182Dic11—21no—
183Dic11—22no—
184Dic11—22no—
185Dic11—42no—
186Dic11—41no—
187Dic11—81no—
188C22×Q8—111no—
189C22×Q8—111no—
190C2×M16—21no—
191C2×M16—221no—
192C4×Q8—441no—
193C4×Q8—441no—
194C4×Q8—441no—
195C4×Q8—441no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C4×D1111yescharacteristic
203C2×C4⋊C4C22×D1111yescharacteristic
204C2×C42—111no—
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—221no—
208C4⋊C8—441no—
209C4⋊C8—441no—
210C4⋊C8—441no—
211#101—442no—
212C22⋊C8—21no—
213C22⋊C8—221no—
214C4×C8—441no—
215#95—21no—
216#95—21no—
217#95—111no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95C4×D1111yescharacteristic
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#152011yescharacteristic
227C2×C11#212011yescharacteristic
228C2×C11#213311yescharacteristic
229C2×Q8—112no—
230C2×Q8—112no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—441no—
234C2×Q8—442no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4C2×C4×D1111yescharacteristic
244C22×C4D4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246M16—41no—
247M16—41no—
248M16—441no—
249M16—441no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—441no—
253C2×C8—441no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C4⋊C4—442no—
263C42—221no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42—221no—
268C42—221no—
269C42—442no—
270C11#1190511yescharacteristic, complemented, Sylow
271C23C22⋊C4×D1111yescharacteristic
272Q8—442no—
273Q8—442no—
274Q8—442no—
275Q8—442no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—112no—
290C2×C4—112no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—222no—
296C2×C4—221no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4SD16×D1111yescharacteristic
305C2×C4Q16×D1111yescharacteristic
306C8—81no—
307C8—81no—
308C8—881no—
309C8—881no—
310C22—21no—
311C22—21no—
312C22D11×#9911yescharacteristic
313C22D11×#10311yescharacteristic
314C22#1062243411yescharacteristic
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—81no—
320C4—81no—
321C4—222no—
322C4—222no—
323C4—221no—
324C4—221no—
325C4—442no—
326C4—441no—
327C4—881no—
328C2—21no—
329C2—21no—
330C2#1306718611yescharacteristic
331C2#1307025611yescharacteristic
332C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11905
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
270. C11#11905semidirect

Maximal subgroups

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

subgroupindex
#130739792
#130686112
#130669382
#130666472
#130666452
#130666432
C11×#13532
#1190511