Finite Group Databasebeta

← #14666005

Subgroups — #14666005

Order 2816.

522 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 59 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#13074988C211yesmaximal, characteristic, complemented
2#13067585C212yesmaximal, complemented
3#13066645C212yesmaximal, complemented
4#13066548C211yesmaximal, characteristic, complemented
5C11×#2006C211yesmaximal, characteristic
6C2×C11×AGL(1,ℤ/8)—21no—
7C11×#537C2211yescharacteristic
8C2×#66931—22no—
9C2×C11×#104—21no—
10C11×#390C2211yescharacteristic
11#10622833—21no—
12#10622653—22no—
13#10622592C2212yes—
14#10622561—22no—
15#10622541—21no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×D4×C11D411yescharacteristic
21C23×Dic11—21no—
22C22×Dic22D412yes—
23C11×AGL(1,ℤ/8)—42no—
24C11×AGL(1,ℤ/8)—42no—
25C2×C11×SD16—41no—
26C2×C11×D8—41no—
27C2×C11×M16—21no—
28C11×C22⋊Q8—41no—
29C11×#121—22no—
30C11×#121—41no—
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—21no—
36C2×#4324—42no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—22no—
41#66931—48no—
42C11×#104—42no—
43C11⋊#95—22no—
44C11⋊#95D412yes—
45C22⋊(C11⋊C8)—22no—
46#66874—42no—
47#12126—111nomaximal, Sylow
48C24×C11—21no—
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C11×#41—41no—
53C2×Q8×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—22no—
56C2×D4×C11—21no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11SD1612yescomplemented
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—44no—
68C22×Dic11—81no—
69C2×Dic22—42no—
70C2×Dic22—44no—
71C11×SD16—44no—
72C11×D8—44no—
73C11×M16—22no—
74C11×M16—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—44no—
79C11×C22⋊C4—42no—
80C42×C11—41no—
81C22⋊Dic11—44no—
82C22⋊Dic11—81no—
83#4324—84no—
84C4⋊Dic11—24no—
85C4⋊Dic11—81no—
86Dic11⋊C4—44no—
87Dic11⋊C4—44no—
88C2×C11⋊C8—42no—
89#2683—111no—
90#2006D1111yescharacteristic
91#1604—112no—
92#1354—112no—
93#1318—111no—
94C23×C11—22no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11#12011yescharacteristic
101Q8×C11—41no—
102Q8×C11—41no—
103D4×C11—42no—
104D4×C11—41no—
105D4×C11—41no—
106D4×C11—81no—
107D4×C11—82no—
108D4×C11—81no—
109D4×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11#13711yescharacteristic
122C2×Dic11—24no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—84no—
129Dic22—44no—
130Dic22—82no—
131C8×C11—42no—
132C11⋊C8—82no—
133C2×AGL(1,ℤ/8)—21no—
134#537C2×D1111yescharacteristic
135C2×C22⋊Q8—222no—
136#448—222no—
137C2×#104—21no—
138#396—222no—
139#395—112no—
140#390C2×D1111yescharacteristic
141#389—221no—
142#386—221no—
143#343C2×D1111yescharacteristic
144#327—222no—
145#324—112no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—44no—
149C22×C11—42no—
150C22×C11—82no—
151C22×C11—81no—
152C22×C11—81no—
153C22×C11—81no—
154C22×C11—81no—
155C22×C11—81no—
156C22×C11#44811yescharacteristic
157C22×C11#45311yescharacteristic
158C22×C11B(4,𝔽2)11yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—42no—
162C4×C11—42no—
163C4×C11—81no—
164Dic11—44no—
165Dic11—82no—
166C2×#41—21no—
167C22×Q8—112no—
168C22×D4C22⋊D1111yescharacteristic
169C23×C4—221no—
170AGL(1,ℤ/8)—42no—
171AGL(1,ℤ/8)—42no—
172C2×SD16—41no—
173C2×SD16—442no—
174C2×D8—41no—
175C2×M16—21no—
176C22⋊Q8—41no—
177C22⋊Q8—448no—
178#121—22no—
179#121—41no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—222no—
182C2×C4⋊C4—222no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4C22×D1111yescharacteristic
185C2×C22⋊C4—22no—
186C2×C22⋊C4—222no—
187C2×C22⋊C4—221no—
188C2×C42C22⋊D1111yescharacteristic
189#104—42no—
190#103—442no—
191C22⋊C8—222no—
192#95—112no—
193#95—222no—
194C2×C11—21no—
195C2×C11—21no—
196C2×C11—82no—
197C2×C11—161no—
198C2×C11#159611yescharacteristic
199C2×C11#219611yescharacteristic
200C2×C11#220311yescharacteristic
201C24—21no—
202#41—41no—
203#41—41no—
204#41—41no—
205#41—41no—
206C2×Q8—21no—
207C2×Q8—442no—
208C2×Q8—444no—
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4#432412yescomplemented
216C22×C4—21no—
217C22×C4—41no—
218C22×C4—222no—
219C22×C4—222no—
220C22×C4—444no—
221C22×C4—881no—
222C22×C4D4×D1112yes—
223C22×C4C2×C22⋊D1111yescharacteristic
224SD16—44no—
225SD16—884no—
226D8—44no—
227M16—22no—
228M16—41no—
229C2×C8—41no—
230C2×C8—442no—
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—224no—
234C4⋊C4—444no—
235C4⋊C4—444no—
236C4⋊C4—881no—
237C22⋊C4—44no—
238C22⋊C4—42no—
239C22⋊C4—444no—
240C22⋊C4—881no—
241C42—41no—
242C11#1212611yescharacteristic, complemented, Sylow
243C23—22no—
244C23—42no—
245C23—42no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23#6699011yescharacteristic
250Q8—41no—
251Q8—41no—
252Q8—444no—
253Q8—882no—
254D4—42no—
255D4—41no—
256D4—41no—
257D4—81no—
258D4—82no—
259D4—81no—
260D4—81no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—224no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—884no—
278C2×C4C2×#432411yescharacteristic
279C2×C4#6700411yescharacteristic
280C8—42no—
281C8—882no—
282C22—21no—
283C22—21no—
284C22—44no—
285C22—42no—
286C22—82no—
287C22—81no—
288C22—81no—
289C22—81no—
290C22—81no—
291C22—81no—
292C22#1062264511yescharacteristic
293C22#1062265311yescharacteristic
294C22#1062269011yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—42no—
299C4—81no—
300C4—444no—
301C4—882no—
302C2—21no—
303C2—21no—
304C2—82no—
305C2—161no—
306C2#1306753811yescharacteristic
307C2#1307059911yescharacteristic
308C2#1307063611yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2006C2
socleC22×C11B(4,𝔽2)
hypercenter#2006D11
hypocenterC11#12126
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2006

Complements

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

NH ≅ G/Ntype
1. #13074988C2semidirect
2. #13067585C2semidirect
3. #13066645C2semidirect
4. #13066548C2semidirect
60. C2×D4×C11SD16semidirect
215. C2×D4#4324semidirect
242. C11#12126semidirect

Maximal subgroups

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

subgroupindex
#130749882
#130675852
#130666452
#130665482
C11×#20062
#1212611