Finite Group Databasebeta

← #14651190

Subgroups — #14651190

Order 2816.

450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077699C211yesmaximal, characteristic
2#13073832C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic
6#13066517C211yesmaximal, characteristic
7C11×#1549C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622843—22no—
13C2×#66888—21no—
14#10622595C414yes—
15#10622590—21no—
16#10622587—21no—
17C4×C4⋊Dic11C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20#10622444—22no—
21#10622332—22no—
22#10622292—22no—
23C11×#332—22no—
24#10622192—21no—
25#10622185—22no—
26C22×Q8×C11—21no—
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4C2×C412yes—
39C2×C4×Dic11—21no—
40C2×C4×Dic11D412yes—
41C2×#4318—21no—
42C4×Dic22—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8D412yes—
49C11×C22⋊C8—21no—
50C4×C8×C11—21no—
51C11⋊#95—24no—
52C11⋊#95—24no—
53C11⋊#95C2×C412yes—
54C22⋊(C11⋊C8)—21no—
55#66888—42no—
56#66879—24no—
57Dic11⋊C8—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61C4×C11⋊C8—21no—
62#9404—111nomaximal, Sylow
63C2×Q8×C11—44no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C22×C4×C11—22no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—22no—
71C22×Dic11C22⋊C412yes—
72C22×Dic11C22⋊C412yes—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—42no—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96C4×Dic11—22no—
97C4×Dic11—22no—
98C4×Dic11—41no—
99C4×Dic11—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104#2983—111no—
105#2568—111no—
106#1801—111no—
107#1549—111no—
108#1549D1111yescharacteristic
109#1303—111no—
110#1303—111no—
111C23×C11C2×C22⋊C411yescharacteristic
112Q8×C11—82no—
113Q8×C11—82no—
114C2×C4×C11—22no—
115C2×C4×C11—41no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136Dic22—41no—
137Dic22—41no—
138Dic22—41no—
139Dic22—41no—
140C8×C11—42no—
141C8×C11—81no—
142C11⋊C8—42no—
143C11⋊C8—81no—
144C2×C4⋊Q8C2×D1111yescharacteristic
145C2×C4×Q8—111no—
146#446—222no—
147#446—222no—
148#432—222no—
149#431—111no—
150#431C2×D1111yescharacteristic
151#423—111no—
152#423C2×D1111yescharacteristic
153C2×#101—221no—
154#400—114no—
155#391—222no—
156#391—221no—
157#382—221no—
158C4×C4⋊C4—111no—
159#343—221no—
160#332—22no—
161#332—222no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11#38611yescharacteristic
165C22×C11#41711yescharacteristic
166C22×C11#41911yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11#45412yes—
172C4×C11#46811yescharacteristic
173C4×C11#46811yescharacteristic
174C4×C11#47011yescharacteristic
175C4×C11#47011yescharacteristic
176Dic11—42no—
177Dic11—42no—
178Dic11—82no—
179C22×Q8—21no—
180C22×Q8—111no—
181C2×M16—21no—
182C2×M16—221no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4×Q8—221no—
188C4×Q8—221no—
189C4×Q8—221no—
190C4×Q8—221no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4C4×D1112yes—
196C2×C42—112no—
197C2×C42—221no—
198C2×C42C22×D1111yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—112no—
202C4⋊C8—224no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8C22⋊D1112yes—
206#101—442no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209#97—224no—
210C4×C8—21no—
211C4×C8—221no—
212#95—112no—
213#95—224no—
214#95—224no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11#188811yescharacteristic
218C2×C11#189411yescharacteristic
219C2×C11#191511yescharacteristic
220C2×Q8—44no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—221no—
224C2×Q8—221no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—221no—
229C22×C4—22no—
230C22×C4—112no—
231C22×C4—112no—
232C22×C4—222no—
233C22×C4C2×C4×D1111yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4D4×D1111yescharacteristic
236M16—41no—
237M16—41no—
238M16—441no—
239M16—441no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—222no—
243C2×C8—441no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—222no—
249C4⋊C4—221no—
250C4⋊C4—222no—
251C4⋊C4—221no—
252C4⋊C4—442no—
253C42—222no—
254C42—222no—
255C42—441no—
256C42—441no—
257C42#433911yescharacteristic
258C42D4×D1111yescharacteristic
259C42#434111yescharacteristic
260C42C2×C22⋊D1111yescharacteristic
261C11#940411yescharacteristic, complemented, Sylow
262C23C22⋊C4×D1111yescharacteristic
263Q8—82no—
264Q8—82no—
265Q8—441no—
266Q8—441no—
267Q8—441no—
268Q8—441no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—42no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—222no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4(C22⋊D11)⋊C411yescharacteristic
282C2×C4#6693611yescharacteristic
283C2×C4#6693711yescharacteristic
284C2×C4#6696711yescharacteristic
285C2×C4#6696811yescharacteristic
286C2×C4#6697111yescharacteristic
287C2×C4#6697111yescharacteristic
288C2×C4C4×C22⋊D1111yescharacteristic
289C2×C4#6699011yescharacteristic
290C2×C4#6699111yescharacteristic
291C8—42no—
292C8—81no—
293C8—442no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22#1062241511yescharacteristic
298C22#1062241611yescharacteristic
299C22#1062256911yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—442no—
305C4—442no—
306C4—882no—
307C4#1062242511yescharacteristic
308C4#1062242911yescharacteristic
309C4#1062278711yescharacteristic
310C4#1062280211yescharacteristic
311C4#1062281412yes—
312C2—21no—
313C2—21no—
314C2#1306901611yescharacteristic
315C2#1306904611yescharacteristic
316C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1549D11
hypocenterC11#9404
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
261. C11#9404semidirect

Maximal subgroups

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

subgroupindex
#130776992
#130738322
#130686092
#130673012
#130665182
#130665172
C11×#15492
#940411