Finite Group Databasebeta

← #14670773

Subgroups — #14670773

Order 2816.

528 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#10622719C211yesmaximal, characteristic, complemented
2C2×#10622204C212yesmaximal, complemented
3#13070227C211yesmaximal, characteristic, complemented
4#13066721C212yesmaximal, complemented
5C11×#3050C211yesmaximal, characteristic
6C2×C11×#135C2211yescharacteristic
7C23×C8×C11C2211yescharacteristic
8C11×#525—21no—
9C2×#66979—21no—
10C11×#467C412yescomplemented
11C11×#466C412yescomplemented
12C11×#465—22no—
13C11×#427C2211yescharacteristic
14C11×#416—21no—
15#10622719—24no—
16C2×#66882—21no—
17C2×#66881C2212yes—
18C2×#66876C2212yes—
19#10622204—24no—
20C22⋊(C11⋊C16)—22no—
21C2×C11×#41—21no—
22C23×C4×C11D411yescharacteristic
23C11×#135—22no—
24C11×#135—22no—
25C2×C11×Q16C2×C411yescharacteristic
26C2×C11×SD16—21no—
27C2×C11×D8C2×C411yescharacteristic
28C22×C8×C11—22no—
29C22×C8×C11—22no—
30C22×C8×C11C2×C412yes—
31C22×C8×C11D411yescharacteristic
32C22×C8×C11D412yes—
33C22×C8×C11C2311yescharacteristic
34C11×#123—41no—
35C11×C22⋊Q8—22no—
36C11×#121—22no—
37C11×#120—41no—
38C4×D4×C11—42no—
39C11×#117—21no—
40C2×C22⋊Dic11—41no—
41#66979—24no—
42#66979—42no—
43C2×C4⋊Dic11—22no—
44C2×C4×Dic11—41no—
45C11×#107C2×C412yes—
46C11×#106—21no—
47C11×#103—22no—
48C11×#102—22no—
49#66882—24no—
50#66881—22no—
51#66881D414yescomplemented
52#66876—22no—
53#66876—22no—
54C2×C11⋊C16—22no—
55#13002—111nomaximal, Sylow
56C24×C11D811yescharacteristic
57C11×#41—41no—
58C11×#41—41no—
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—42no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11C22⋊C412yes—
71C22×C4×C11D811yescharacteristic
72C22×C4×C11SD1612yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—42no—
75C11×Q16—22no—
76C11×SD16—42no—
77C11×D8—22no—
78C2×C8×C11—24no—
79C2×C8×C11—24no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11C22⋊C412yes—
83C2×C8×C11C22×C411yescharacteristic
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11C2×D412yes—
86C2×C8×C11#4112yes—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—42no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—42no—
92C42×C11—41no—
93C22⋊Dic11—44no—
94C4⋊Dic11—24no—
95C4⋊Dic11—42no—
96C4×Dic11—44no—
97C11⋊C16—42no—
98#3050D1111yescharacteristic
99C2×#427—111no—
100C2×#360—112no—
101#2112—111no—
102#1386—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—42no—
106C23×C11—41no—
107C23×C11#10212yes—
108C23×C11C2×D811yescharacteristic
109Q8×C11—41no—
110Q8×C11—41no—
111D4×C11—41no—
112D4×C11—41no—
113D4×C11—84no—
114D4×C11—81no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11#10212yes—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—44no—
134C2×Dic11—84no—
135C8×C11—22no—
136C8×C11C4×D412yes—
137C8×C11#12112yes—
138C2×#135C2×D1111yescharacteristic
139C23×C8C2×D1111yescharacteristic
140#525—21no—
141C2×#117—221no—
142C2×M32—112no—
143#467Dic1112yescomplemented
144#466Dic1112yescomplemented
145#465—22no—
146#427—224no—
147#427C2×D1111yescharacteristic
148C2×#107—221no—
149C2×#106—112no—
150#416—21no—
151#360—224no—
152C22⋊C16—222no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—81no—
160C22×C11—82no—
161C22×C11C2×#10211yescharacteristic
162C22×C11#44711yescharacteristic
163C22×C11#48011yescharacteristic
164C4×C11—22no—
165C4×C11—81no—
166C4×C11—82no—
167C4×C11#38611yescharacteristic
168C4×C11#41711yescharacteristic
169C4×C11#44811yescharacteristic
170C4×C11#48111yescharacteristic
171Dic11—84no—
172C2×#41—21no—
173C23×C4C22⋊D1111yescharacteristic
174#135—22no—
175#135—22no—
176C2×Q16C2×Dic1111yescharacteristic
177C2×SD16—21no—
178C2×D8C2×Dic1111yescharacteristic
179C22×C8—22no—
180C22×C8—22no—
181C22×C8C2×Dic1112yes—
182C22×C8C22⋊D1111yescharacteristic
183C22×C8C22⋊D1112yes—
184C22×C8C22×D1111yescharacteristic
185#123—41no—
186C22⋊Q8—22no—
187#121—22no—
188#120—41no—
189C4×D4—42no—
190#117—21no—
191#117—224no—
192#117—442no—
193C2×C4⋊C4—222no—
194C2×C22⋊C4—441no—
195C2×C42—441no—
196M32—222no—
197M32—222no—
198C2×C16—222no—
199#107—224no—
200#107C2×Dic1112yes—
201#106—21no—
202#106—114no—
203#106—222no—
204#103—22no—
205#102—22no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11—42no—
209C2×C11—161no—
210C2×C11#187411yescharacteristic
211C2×C11#214512yes—
212C24#432311yescharacteristic
213#41—41no—
214#41—41no—
215#41—41no—
216#41—41no—
217C2×Q8—21no—
218C2×D4—21no—
219C2×D4—42no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—442no—
227C22×C4#432311yescharacteristic
228C22×C4#432412yes—
229C22×C4C22⋊Dic1112yes—
230C22×C4C2×C22⋊D1111yescharacteristic
231Q16—22no—
232SD16—42no—
233D8—22no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—24no—
237C2×C8—24no—
238C2×C8C22⋊Dic1112yes—
239C2×C8D4×D1112yes—
240C2×C8#434112yes—
241C2×C8C22×Dic1111yescharacteristic
242C2×C8C2×C22⋊D1111yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—224no—
246C4⋊C4—442no—
247C22⋊C4—42no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—444no—
251C42—41no—
252C42—444no—
253C16—442no—
254C11#1300211yescharacteristic, complemented, Sylow
255C23—21no—
256C23—21no—
257C23—42no—
258C23—41no—
259C23#6689612yes—
260C23C2×#432311yescharacteristic
261Q8—41no—
262Q8—41no—
263D4—41no—
264D4—41no—
265D4—84no—
266D4—81no—
267D4—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—444no—
279C2×C4—884no—
280C2×C4#6689612yes—
281C2×C4C2×#432411yescharacteristic
282C2×C4#6698811yescharacteristic
283C2×C4#6699011yescharacteristic
284C2×C4#6700211yescharacteristic
285C2×C4#6700411yescharacteristic
286C2×C4C2×C22⋊Dic1111yescharacteristic
287C8—22no—
288C8D4×Dic1112yes—
289C8#6699212yes—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—42no—
295C22—42no—
296C22—82no—
297C22—81no—
298C22#1062264611yescharacteristic
299C22#1062264911yescharacteristic
300C22C2×#6689611yescharacteristic
301C4—22no—
302C4—82no—
303C4—81no—
304C4—884no—
305C4#1062264711yescharacteristic
306C4#1062265311yescharacteristic
307C4#1062283311yescharacteristic
308C4#1062284511yescharacteristic
309C2—21no—
310C2—21no—
311C2—42no—
312C2—161no—
313C2#1306893411yescharacteristic
314C2#1307035212yes—
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC11×#3050C2
socleC22×C11C2×#102
cosocleC22×C8×C11C23
hypercenter#3050D11
hypocenterC11#13002
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#10622719C2semidirect
2. C2×#10622204C2semidirect
3. #13070227C2semidirect
4. #13066721C2semidirect
10. C11×#467C4semidirect
11. C11×#466C4semidirect
51. #66881D4semidirect
143. #467Dic11semidirect
144. #466Dic11semidirect
254. C11#13002semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
C2×#106222042
#130702272
#130667212
C11×#30502
#1300211