Finite Group Databasebeta

← #14651620

Subgroups — #14651620

Order 2816.

626 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 127 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#13077640C211yesmaximal, characteristic, complemented
2#13073513C211yesmaximal, characteristic
3#13067040C212yesmaximal, complemented
4#13066476C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66991—21no—
8C2×C4×D44C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×#100—21no—
11#10622826—22no—
12C2×C22⋊(C11⋊C8)—22no—
13D4×C11⋊C8—24no—
14#10622600—21no—
15#10622573C412yes—
16#10622566C412yes—
17#10622549C2211yescharacteristic
18#10622538C2212yes—
19C11×#343—21no—
20#10622121—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D412yes—
23C22×C22⋊D11—22no—
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
26C2×C11×M16—22no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2×C412yes—
31C2×C42×C11C2311yescharacteristic
32C2×C22⋊Dic11—22no—
33#66991—42no—
34#66991—42no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—22no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C22×C11⋊C8—24no—
40C4×D44—22no—
41C4×D44—22no—
42C11×C4⋊C8—22no—
43C11×C4⋊C8—22no—
44C11×#100—42no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C11⋊#95C2×C412yes—
48C22⋊(C11⋊C8)—24no—
49C22⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4×C11⋊C8D414yescomplemented
52#9485—111nomaximal, Sylow
53C24×C11C22⋊C412yes—
54C23×D11—21no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11D812yes—
58C2×D4×C11SD1612yes—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—82no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C2×C22⋊D11—44no—
67C2×C22⋊D11—44no—
68C2×C22⋊D11—82no—
69C22×Dic11—22no—
70C22×Dic11—21no—
71C2×D44—22no—
72C2×D44—42no—
73C2×C4×D11—42no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11—42no—
77C11×M16—42no—
78C11×M16—42no—
79C2×C8×C11—42no—
80C11×C4⋊C4—22no—
81C11×C22⋊C4—24no—
82C42×C11C2×D412yes—
83C42×C11#4112yes—
84C22⋊Dic11—44no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—82no—
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—84no—
93#2972—111no—
94#2535—111no—
95#1800D1111yescharacteristic, complemented
96#1486—112no—
97#1286—112no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—42no—
101C23×C11—42no—
102C23×C11#10214yes—
103C23×C11C2×C22⋊C411yescharacteristic
104C22×D11—22no—
105C22×D11—41no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111D4×C11—24no—
112D4×C11—24no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11—82no—
119C2×C4×C11C4×D412yes—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12112yes—
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11C2×D811yescharacteristic
124C2×C4×C11C2×SD1611yescharacteristic
125C2×C4×C11#13512yes—
126C22⋊D11—88no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—41no—
130C2×Dic11—42no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133D44—24no—
134D44—42no—
135C4×D11—82no—
136C4×D11—82no—
137C8×C11—82no—
138C11⋊C8—44no—
139C2×#121—221no—
140C2×C4×D4—111no—
141C2×C4×D4C2×D1111yescharacteristic
142C8×D4—224no—
143#431—112no—
144#423C2×D1112yes—
145C2×#100—21no—
146C2×C22⋊C8—222no—
147#397—112no—
148#392—112no—
149#386—222no—
150#382—111no—
151#380—221no—
152#343—21no—
153D4⋊C8—224no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—24no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—82no—
161C22×C11#38611yescharacteristic
162C22×C11C2×#10211yescharacteristic
163C22×C11#41611yescharacteristic
164C2×D11—42no—
165C2×D11—42no—
166C2×D11—42no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C2×D11—81no—
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—42no—
175C4×C11#46512yes—
176C4×C11#46612yes—
177Dic11—82no—
178Dic11—81no—
179C22×D4—111no—
180C22×D4—222no—
181C22×D4C22⋊D1111yescharacteristic
182C23×C4—221no—
183C23×C4D4412yes—
184C2×M16—22no—
185C22×C8—224no—
186#121—442no—
187#121—442no—
188C4×D4—22no—
189C4×D4—22no—
190C4×D4—222no—
191C4×D4—222no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4C22⋊D1111yescharacteristic
195C2×C22⋊C4—222no—
196C2×C22⋊C4—221no—
197C2×C22⋊C4—222no—
198C2×C22⋊C4C4×D1112yes—
199C2×C42C22×D1111yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—222no—
203#100—42no—
204C22⋊C8—224no—
205C22⋊C8—222no—
206C4×C8—114no—
207#95—112no—
208#95—222no—
209#95—221no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—44no—
213C2×C11#189111yescharacteristic
214C2×C11#189311yescharacteristic
215C2×C11#191111yescharacteristic
216D11—82no—
217C24—221no—
218C24(C2×D11)⋊C412yes—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—222no—
222C2×D4—442no—
223C2×D4—444no—
224C2×D4—444no—
225C2×D4—882no—
226C2×D4#432312yes—
227C2×D4#432512yes—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—82no—
231C22×C4—222no—
232C22×C4—221no—
233C22×C4—441no—
234C22×C4—442no—
235C22×C4—441no—
236C22×C4—442no—
237C22×C4(C2×D11)⋊C412yes—
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4C2×D4411yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—42no—
242M16—42no—
243C2×C8—42no—
244C2×C8—224no—
245C2×C8—884no—
246C4⋊C4—22no—
247C4⋊C4—222no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C22⋊C4—24no—
251C22⋊C4—444no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—882no—
255C42D4×D1112yes—
256C42#434112yes—
257C11#948511yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23—42no—
261C23—42no—
262C23—222no—
263C23—441no—
264C23—441no—
265C23—441no—
266C23—441no—
267C23—441no—
268C23—441no—
269C23#6687314yes—
270C23C2×(C2×D11)⋊C411yescharacteristic
271D4—24no—
272D4—24no—
273D4—224no—
274D4—442no—
275D4—888no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—82no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—442no—
287C2×C4—441no—
288C2×C4—882no—
289C2×C4—882no—
290C2×C4(C22⋊D11)⋊C412yes—
291C2×C4#6693511yescharacteristic
292C2×C4#6693911yescharacteristic
293C2×C4C2×#432311yescharacteristic
294C2×C4#6699212yes—
295C2×C4C2×#432511yescharacteristic
296C2×C4#6700312yes—
297C8—82no—
298C8—444no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—44no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—442no—
307C22—442no—
308C22—442no—
309C22—881no—
310C22—881no—
311C22—881no—
312C22—881no—
313C22#1062257111yescharacteristic
314C22C2×#6687311yescharacteristic
315C22#1062261511yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—42no—
320C4—882no—
321C4—881no—
322C4#1062265112yes—
323C4#1062266112yes—
324C2—21no—
325C2—21no—
326C2—44no—
327C2—882no—
328C2#1306903211yescharacteristic
329C2#1306904211yescharacteristic
330C2#1306914611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#386
prime radical#13073513C2
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#9485
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
1. #13077640C2semidirect
3. #13067040C2semidirect
4. #13066476C2semidirect
5. C11×#1800C2semidirect
51. C4×C11⋊C8D4semidirect
95. #1800D11semidirect
257. C11#9485semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130735132
#130670402
#130664762
C11×#18002
#948511