Finite Group Databasebeta

← #14647352

Subgroups — #14647352

Order 2816.

422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071533C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13066939C211yesmaximal, characteristic
4#13066518C211yesmaximal, characteristic
5#13066517C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×#66940—21no—
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66888—21no—
14#10622586—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622263C412yes—
19#10622262C412yes—
20#10622260—22no—
21#10622192—21no—
22#10622107—22no—
23C22×Dic22D411yescharacteristic
24C2×C11×M16—21no—
25C2×C11×C4⋊C4—21no—
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D411yescharacteristic
29C2×Dic11⋊C4—22no—
30C2×Dic11⋊C4—22no—
31C2×Dic11⋊C4D412yes—
32C2×C4×Dic11—21no—
33C2×C4×Dic11—22no—
34C2×C4×Dic11C2×C412yes—
35C2×#4318—21no—
36#66940—42no—
37#66940—42no—
38C4×Dic22—21no—
39C4×Dic22—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47C11×#95—21no—
48C11×#95C2×C412yes—
49C11⋊#95—22no—
50C11⋊#95C2×C411yescharacteristic
51C11⋊#95C2×C411yescharacteristic
52C22⋊(C11⋊C8)—21no—
53#66888—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4×C11⋊C8—21no—
58#8767—111nomaximal, Sylow
59C22×C4×C11—22no—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11C22⋊C412yes—
66C22×Dic11C22⋊C412yes—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22SD1612yes—
72C2×Dic22Q1612yes—
73C11×M16—41no—
74C11×M16—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—42no—
86Dic11⋊C4—22no—
87Dic11⋊C4—22no—
88Dic11⋊C4—44no—
89Dic11⋊C4—44no—
90C4×Dic11—22no—
91C4×Dic11—22no—
92C4×Dic11—44no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95#4318—41no—
96#4318—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99#2351—111no—
100#1801—111no—
101#1461—111no—
102#1303—111no—
103#1303—111no—
104#1286—111no—
105#1286D1111yescharacteristic
106C23×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11#11711yescharacteristic
113C2×C4×C11#11711yescharacteristic
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11#12311yescharacteristic
116C2×C4×C11#12311yescharacteristic
117C2×C4×C11#12311yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11C2×Q1611yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—42no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11#10314yes—
133Dic22—22no—
134Dic22—22no—
135Dic22—22no—
136Dic22—22no—
137C8×C11—81no—
138C8×C11—81no—
139C11⋊C8—81no—
140C11⋊C8—81no—
141C2×C4×Q8—111no—
142C2×C4×Q8—221no—
143#431—111no—
144#431C2×D1111yescharacteristic
145#423—111no—
146#423C2×D1111yescharacteristic
147C2×#101—221no—
148#389—222no—
149#389—221no—
150#382—112no—
151#382C2×D1111yescharacteristic
152C4×C4⋊C4—111no—
153C4×C4⋊C4—112no—
154#343—221no—
155#324—222no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11#38111yescharacteristic
159C22×C11C2×#10311yescharacteristic
160C22×C11#41811yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—82no—
166C4×C11#48111yescharacteristic
167C4×C11#48111yescharacteristic
168C4×C11#48411yescharacteristic
169C4×C11#48411yescharacteristic
170Dic11—24no—
171Dic11—42no—
172Dic11—42no—
173Dic11—81no—
174C22×Q8—111no—
175C2×M16—21no—
176C2×M16—221no—
177C4×Q8—221no—
178C4×Q8—221no—
179C4×Q8—221no—
180C4×Q8—221no—
181C4×Q8—442no—
182C4×Q8—442no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4—221no—
189C2×C42—112no—
190C2×C42—222no—
191C2×C42—221no—
192C2×C42C22×D1111yescharacteristic
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—221no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199#101—442no—
200C22⋊C8—21no—
201C22⋊C8—221no—
202C4×C8—21no—
203C4×C8—221no—
204#95—21no—
205#95—111no—
206#95—111no—
207#95—222no—
208#95C4×D1112yes—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11#182411yescharacteristic
212C2×C11#182711yescharacteristic
213C2×C11#183011yescharacteristic
214C2×Q8—112no—
215C2×Q8—112no—
216C2×Q8—221no—
217C2×Q8—221no—
218C2×Q8—221no—
219C2×Q8—221no—
220C22×C4—22no—
221C22×C4—112no—
222C22×C4—112no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4D4×D1111yescharacteristic
227C22×C4D4×D1111yescharacteristic
228M16—41no—
229M16—41no—
230M16—441no—
231M16—441no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—441no—
235C2×C8—441no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—222no—
239C4⋊C4—221no—
240C4⋊C4—222no—
241C4⋊C4—221no—
242C4⋊C4—444no—
243C4⋊C4—444no—
244C4⋊C4—442no—
245C42—222no—
246C42—222no—
247C42—444no—
248C42—441no—
249C42—441no—
250C42#433911yescharacteristic
251C42#433911yescharacteristic
252C42#434111yescharacteristic
253C42#434311yescharacteristic
254C11#876711yescharacteristic, complemented, Sylow
255C23C22⋊C4×D1111yescharacteristic
256Q8—222no—
257Q8—222no—
258Q8—222no—
259Q8—222no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—114no—
266C2×C4—222no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—442no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4#6692511yescharacteristic
277C2×C4#6693611yescharacteristic
278C2×C4#6693611yescharacteristic
279C2×C4#6694511yescharacteristic
280C2×C4#6694711yescharacteristic
281C2×C4#6694711yescharacteristic
282C2×C4#6696411yescharacteristic
283C2×C4SD16×D1111yescharacteristic
284C2×C4#6696711yescharacteristic
285C2×C4Q16×D1111yescharacteristic
286C8—81no—
287C8—81no—
288C8—881no—
289C8—881no—
290C22—21no—
291C22—21no—
292C22#1062227711yescharacteristic
293C22#1062238311yescharacteristic
294C22D11×#10311yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—82no—
300C4—224no—
301C4—442no—
302C4—442no—
303C4—881no—
304C4#1062239011yescharacteristic
305C4#1062242211yescharacteristic
306C4#1062247611yescharacteristic
307C4#1062249711yescharacteristic
308C2—21no—
309C2—21no—
310C2#1306870511yescharacteristic
311C2#1306871811yescharacteristic
312C2#1306872911yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#381
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#8767
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
254. C11#8767semidirect

Maximal subgroups

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

subgroupindex
#130715332
#130686092
#130669392
#130665182
#130665172
#130664742
C11×#12862
#876711