Finite Group Databasebeta

← #14672923

Subgroups — #14672923

Order 2816.

540 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 75 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#13076604C211yesmaximal, characteristic, complemented
2#13068575C212yesmaximal
3#13066743C211yesmaximal, characteristic, complemented
4#13066742C212yesmaximal, complemented
5C11×#1793C211yesmaximal, characteristic
6C2×C11×2−1+4C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C2×C11×#101C2211yescharacteristic
10C11×#391C2211yescharacteristic
11C2×#66901—22no—
12#10622845—22no—
13#10622843C2212yes—
14C2×#66900C2212yes—
15#10622599—21no—
16#10622541—21no—
17#10622274—22no—
18#10622268—22no—
19C11×2−1+4—21no—
20C11×2−1+4—22no—
21C11×2−1+4—42no—
22C11×2−1+4Q812yes—
23C2×C11×#41—22no—
24C2×C11×#41—21no—
25C2×C11×#41—41no—
26C22×Q8×C11—41no—
27C22×Q8×C11C2311yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D412yes—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11D412yes—
37C2×#4318—22no—
38C11×#104—42no—
39C11×#103—41no—
40C11×#102—41no—
41C11×#101—22no—
42C11×#95—22no—
43#66901—44no—
44#66900—22no—
45#66900—22no—
46#66899—42no—
47#66896—42no—
48C11⋊#95—21no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52#13379—111nomaximal, Sylow
53C11×#41—24no—
54C11×#41—22no—
55C11×#41—24no—
56C11×#41—22no—
57C11×#41—42no—
58C11×#41—41no—
59C11×#41—42no—
60C11×#41—42no—
61C11×#41—44no—
62C11×#41—42no—
63C11×#41—41no—
64C2×Q8×C11—22no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—44no—
71C2×Q8×C11C2×Q811yescharacteristic
72C2×Q8×C11#4111yescharacteristic
73C2×Q8×C11#4112yes—
74C2×D4×C11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—42no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C42×C11—41no—
90C4⋊Dic11—42no—
91C4⋊Dic11—42no—
92C4⋊Dic11—81no—
93C4⋊Dic11—81no—
94Dic11⋊C4—44no—
95C4×Dic11—42no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99#2809—111no—
100#1793—112no—
101#1793D1111yescharacteristic
102#1394—112no—
103#1394—111no—
104C23×C11—41no—
105C23×C11#12011yescharacteristic
106Q8×C11—24no—
107Q8×C11—22no—
108Q8×C11—41no—
109Q8×C11—41no—
110Q8×C11—42no—
111Q8×C11—42no—
112Q8×C11—41no—
113D4×C11—24no—
114D4×C11—22no—
115D4×C11—42no—
116D4×C11—41no—
117D4×C11—42no—
118D4×C11—42no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—44no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11C22⋊Q812yes—
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#12412yes—
136C2×C4×C11#12411yescharacteristic
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C8×C11—81no—
144C11⋊C8—82no—
145C2×2−1+4C2×D1111yescharacteristic
146C2×#104—21no—
147C2×#104—222no—
148#417—21no—
149#417—222no—
150C2×#101—112no—
151C2×#101C2×D1111yescharacteristic
152#400—221no—
153#398—222no—
154#391—112no—
155#391C2×D1111yescharacteristic
156#389—221no—
157#387—222no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—42no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11#39311yescharacteristic
164C22×C11B(4,𝔽2)11yescharacteristic
165C22×C11B(4,𝔽2)11yescharacteristic
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—22no—
169C4×C11—21no—
170C4×C11—42no—
171C4×C11—42no—
172C4×C11—81no—
173Dic11—82no—
174Dic11—82no—
1752−1+4—21no—
1762−1+4—22no—
1772−1+4—42no—
1782−1+4Dic2212yes—
179C2×#41—22no—
180C2×#41—21no—
181C2×#41—41no—
182C22×Q8—41no—
183C22×Q8C22×D1111yescharacteristic
184C2×M16—21no—
185C2×M16—222no—
186C2×C4⋊C4—112no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C42—112no—
193C2×C42C22⋊D1111yescharacteristic
194#104—42no—
195#104—444no—
196#103—41no—
197#103—442no—
198#102—41no—
199#102—442no—
200#101—22no—
201#101—222no—
202#101—222no—
203#95—22no—
204#95—221no—
205#95—222no—
206#95—222no—
207#95—222no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—82no—
211C2×C11#202911yescharacteristic
212C2×C11#220311yescharacteristic
213C2×C11#220411yescharacteristic
214#41—22no—
215#41—24no—
216#41—24no—
217#41—22no—
218#41—41no—
219#41—42no—
220#41—42no—
221#41—42no—
222#41—44no—
223#41—42no—
224#41—41no—
225C2×Q8—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—44no—
232C2×Q8C2×Dic2211yescharacteristic
233C2×Q8#433911yescharacteristic
234C2×Q8#434112yes—
235C2×D4—21no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—222no—
243C22×C4—222no—
244C22×C4D4×D1112yes—
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—41no—
247M16—41no—
248M16—442no—
249M16—442no—
250C2×C8—41no—
251C2×C8—442no—
252C4⋊C4—41no—
253C4⋊C4—442no—
254C4⋊C4—444no—
255C4⋊C4—442no—
256C4⋊C4—881no—
257C4⋊C4—881no—
258C42—41no—
259C42—442no—
260C11#1337911yescharacteristic, complemented, Sylow
261C23—41no—
262C23#6699011yescharacteristic
263Q8—24no—
264Q8—22no—
265Q8—41no—
266Q8—41no—
267Q8—42no—
268Q8—41no—
269Q8—42no—
270D4—24no—
271D4—22no—
272D4—41no—
273D4—42no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4#6693112yes—
297C2×C4#6693812yes—
298C2×C4#6697711yescharacteristic
299C2×C4#6698911yescharacteristic
300C8—81no—
301C8—882no—
302C22—21no—
303C22—21no—
304C22—42no—
305C22—81no—
306C22—81no—
307C22#1062256011yescharacteristic
308C22#1062264511yescharacteristic
309C22#1062264511yescharacteristic
310C4—21no—
311C4—22no—
312C4—22no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—882no—
318C4—882no—
319C2—21no—
320C2—21no—
321C2—82no—
322C2#1306978011yescharacteristic
323C2#1307063611yescharacteristic
324C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1793C2
socleC22×C11B(4,𝔽2)
prime radicalC2×C11×2−1+4C22
hypercenter#1793D11
hypocenterC11#13379
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1793

Complements

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

NH ≅ G/Ntype
1. #13076604C2semidirect
3. #13066743C2semidirect
4. #13066742C2semidirect
260. C11#13379semidirect

Maximal subgroups

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

subgroupindex
#130766042
#130685752
#130667432
#130667422
C11×#17932
#1337911