Finite Group Databasebeta

← #14672920

Subgroups — #14672920

Order 2816.

540 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068574C212yesmaximal
2#13068574C211yesmaximal, characteristic
3#13066743C211yesmaximal, characteristic, complemented
4#13066743C212yesmaximal, complemented
5C11×#2809C211yesmaximal, characteristic, complemented
6C2×#67040C2211yescharacteristic
7C11×#400—21no—
8C11×#398—22no—
9C11×#391C2211yescharacteristic
10C11×#391C2212yes—
11C11×#389—21no—
12C11×#387—22no—
13C2×#66900C2212yes—
14C2×#66900C2211yescharacteristic
15#10622579—22no—
16#10622579—21no—
17C2×#66869—22no—
18C2×#66869—21no—
19C22×Q8×C11C2311yescharacteristic
20#67040—22no—
21#67040—21no—
22#67040—42no—
23#67040Q812yes—
24C2×#4343—41no—
25C2×Q8×D11—41no—
26C2×#4339—22no—
27C2×#4339—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11D412yes—
35C2×C42×C11D411yescharacteristic
36C2×#4318—22no—
37C2×#4318—21no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—22no—
43#66900—22no—
44#66900—22no—
45#66900—22no—
46#66874—42no—
47#66874—41no—
48#66873—42no—
49#66873—41no—
50#66869—42no—
51#66869—44no—
52#13379—111nomaximal, Sylow
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C2×Q8×C11C2×Q811yescharacteristic
56C2×Q8×C11#4112yes—
57C2×Q8×C11#4111yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C2×C22⋊D11—41no—
65#4343—42no—
66#4343—44no—
67#4343—42no—
68Q8×D11—42no—
69Q8×D11—44no—
70Q8×D11—42no—
71#4339—22no—
72#4339—24no—
73#4339—24no—
74#4339—22no—
75#4339—41no—
76#4339—42no—
77#4339—42no—
78#4339—41no—
79C2×D44—22no—
80C2×D44—21no—
81C2×C4×D11—42no—
82C2×C4×D11—41no—
83C2×Dic22—22no—
84C2×Dic22—21no—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—81no—
90C11×C4⋊C4—81no—
91C42×C11—41no—
92C42×C11—42no—
93#4318—41no—
94#4318—42no—
95#4318—42no—
96#4318—41no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—41no—
99#2809D1111yescharacteristic, complemented
100#1793—111no—
101#1793—112no—
102#1394—111no—
103#1394—112no—
104C23×C11#12011yescharacteristic
105C22×D11—41no—
106Q8×C11—41no—
107Q8×C11—42no—
108Q8×C11—41no—
109C2×C4×C11—22no—
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—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11C22⋊Q812yes—
125C2×C4×C11C22⋊Q811yescharacteristic
126C2×C4×C11#12412yes—
127C2×C4×C11#12411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—42no—
130C2×Dic11—41no—
131D44—24no—
132D44—22no—
133D44—42no—
134D44—41no—
135C4×D11—44no—
136C4×D11—42no—
137C4×D11—44no—
138C4×D11—42no—
139Dic22—24no—
140Dic22—22no—
141Dic22—42no—
142Dic22—41no—
143C11⋊C8—82no—
144C11⋊C8—81no—
145C2×2−1+4—111no—
146C2×#104—222no—
147C2×#104—221no—
148#417—222no—
149#417—221no—
150C2×#101—112no—
151C2×#101—111no—
152#400—21no—
153#398—22no—
154#391C2×D1111yescharacteristic
155#391C2×D1112yes—
156#389—21no—
157#387—22no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11#39311yescharacteristic
161C22×C11B(4,𝔽2)11yescharacteristic
162C22×C11B(4,𝔽2)11yescharacteristic
163C2×D11—42no—
164C2×D11—81no—
165C2×D11—81no—
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—22no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—82no—
172C4×C11—81no—
173C4×C11—82no—
174Dic11—42no—
1752−1+4—112no—
1762−1+4—222no—
1772−1+4—221no—
1782−1+4—442no—
179C2×#41—222no—
180C2×#41—221no—
181C2×#41—441no—
182C22×Q8—441no—
183C22×Q8C22×D1111yescharacteristic
184C2×M16—222no—
185C2×M16—221no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C22⋊D1112yes—
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C42C22⋊D1112yes—
193C2×C42C22⋊D1111yescharacteristic
194#104—442no—
195#104—444no—
196#103—442no—
197#103—441no—
198#102—442no—
199#102—441no—
200#101—222no—
201#101—222no—
202#101—222no—
203#95—21no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—22no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11#202911yescharacteristic
211C2×C11#220311yescharacteristic
212C2×C11#220411yescharacteristic
213D11—82no—
214#41—222no—
215#41—224no—
216#41—224no—
217#41—222no—
218#41—441no—
219#41—442no—
220#41—442no—
221#41—444no—
222#41—442no—
223#41—442no—
224#41—441no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—222no—
228C2×Q8—221no—
229C2×Q8—442no—
230C2×Q8—444no—
231C2×Q8—442no—
232C2×Q8Q8×D1111yescharacteristic
233C2×Q8#434312yes—
234C2×Q8#434311yescharacteristic
235C2×D4—222no—
236C2×D4—221no—
237C2×D4—441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—442no—
243C22×C4—441no—
244C22×C4C2×C22⋊D1112yes—
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—441no—
247M16—442no—
248M16—442no—
249M16—441no—
250C2×C8—442no—
251C2×C8—441no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C42—41no—
259C42—42no—
260C11#1337911yescharacteristic, complemented, Sylow
261C23—441no—
262C23#6700611yescharacteristic
263Q8—41no—
264Q8—42no—
265Q8—41no—
266Q8—222no—
267Q8—224no—
268Q8—441no—
269Q8—442no—
270D4—222no—
271D4—224no—
272D4—441no—
273D4—442no—
274D4—442no—
275D4—442no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—442no—
292C2×C4—444no—
293C2×C4—442no—
294C2×C4—444no—
295C2×C4—441no—
296C2×C4#6699912yes—
297C2×C4#6699911yescharacteristic
298C2×C4#6700012yes—
299C2×C4#6700011yescharacteristic
300C8—881no—
301C8—882no—
302C22—21no—
303C22—21no—
304C22—442no—
305C22—881no—
306C22—881no—
307C22#1062284411yescharacteristic
308C22#1062285711yescharacteristic
309C22#1062285711yescharacteristic
310C4—21no—
311C4—22no—
312C4—21no—
313C4—22no—
314C4—42no—
315C4—82no—
316C4—81no—
317C4—82no—
318C4—442no—
319C2—21no—
320C2—21no—
321C2—882no—
322C2#1306977911yescharacteristic
323C2#1307063711yescharacteristic
324C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#2809C2
socleC22×C11B(4,𝔽2)
prime radicalC2×#67040C22
hypercenter#2809D11
hypocenterC11#13379
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2809

Complements

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

NH ≅ G/Ntype
3. #13066743C2semidirect
4. #13066743C2semidirect
5. C11×#2809C2semidirect
99. #2809D11semidirect
260. C11#13379semidirect

Maximal subgroups

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

subgroupindex
#130685742
#130667432
C11×#28092
#1337911