Finite Group Databasebeta

← #14667061

Subgroups — #14667061

Order 2816.

316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 61 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#13079962C211yesmaximal, characteristic
2#13070818C211yesmaximal, characteristic, complemented
3#13070110C211yesmaximal, characteristic, complemented
4#13066629C211yesmaximal, characteristic, complemented
5#13066625C211yesmaximal, characteristic
6#13066555C211yesmaximal, characteristic, complemented
7C11×#2233C211yesmaximal, characteristic
8#10623131—21no—
9C11×#466C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic
11#10622766—21no—
12#10622729C2211yescharacteristic
13C2×Dic11⋊C8C2211yescharacteristic
14#10622654—21no—
15#10622586—21no—
16#10622490—21no—
17#10622380—21no—
18#10622379—21no—
19C11×#367—21no—
20C11×#357—21no—
21C11×C22⋊C16C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25#10622130—21no—
26#10622127—21no—
27C2×C11×D8D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×#121—21no—
30C2×C11×C4⋊C4—21no—
31#66989—21no—
32#66988—41no—
33D4×Dic11—21no—
34D4×Dic11—41no—
35C2×#4324—21no—
36C2×C4⋊Dic11—21no—
37#66977—21no—
38C2×Dic11⋊C4—41no—
39C2×C4×Dic11D411yescharacteristic
40C22×C11⋊C8D411yescharacteristic
41C2×Dic44D411yescharacteristic
42#66943—21no—
43#66940—21no—
44#66932—41no—
45#66930—41no—
46C2×C11×C16—21no—
47C11×#107—21no—
48C11×#107—21no—
49C11×#107D411yescharacteristic
50C11×#102—21no—
51#66896—21no—
52C11⋊#95—41no—
53#66882D411yescharacteristic
54#66880—21no—
55Dic11⋊C8—21no—
56Dic11⋊C8—21no—
57C2×C11⋊C16—21no—
58#66874—21no—
59#66872—21no—
60#12293—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11D811yescharacteristic
68C22×Dic11D811yescharacteristic
69C2×Dic22—21no—
70C11×D8—41no—
71C2×C8×C11—41no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82#4324—81no—
83C4⋊Dic11—22no—
84C4⋊Dic11—21no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—82no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—41no—
96Dic44—41no—
97C11×C16—41no—
98C11⋊C16—41no—
99#3250—111no—
100#2236—111no—
101#2233D1111yescharacteristic
102#2087—111no—
103#1348—111no—
104#1347—111no—
105#1322—111no—
106C23×C11—41no—
107C23×C11C2×D811yescharacteristic
108D4×C11—41no—
109D4×C11—41no—
110D4×C11—81no—
111D4×C11—81no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—41no—
125C2×Dic11—42no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—82no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131Dic22—41no—
132Dic22—41no—
133C8×C11—21no—
134C8×C11—21no—
135C11⋊C8—41no—
136#529—221no—
137#479—221no—
138#478—221no—
139#467—111no—
140#466C2×D1111yescharacteristic
141#465—221no—
142#464—221no—
143#463—221no—
144C2×#107C2×D1111yescharacteristic
145C2×C4⋊C8—111no—
146#389—221no—
147#367—21no—
148#366—221no—
149#358—221no—
150#357—21no—
151C22⋊C16—111no—
152C22⋊C16C2×D1111yescharacteristic
153#340—111no—
154#340—221no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—81no—
158C22×C11—81no—
159C22×C11—81no—
160C22×C11#44711yescharacteristic
161C22×C11#50811yescharacteristic
162C22×C11#51011yescharacteristic
163C4×C11—21no—
164C4×C11—81no—
165C4×C11—161no—
166C4×C11#45611yescharacteristic
167C4×C11#45811yescharacteristic
168Dic11—41no—
169Dic11—41no—
170Dic11—82no—
171Dic11—81no—
172Dic11—81no—
173C2×Q16—111no—
174C2×SD16—221no—
175C2×D8C22⋊D1111yescharacteristic
176C22×C8—111no—
177C22×C8C22×D1111yescharacteristic
178#126—441no—
179#125—221no—
180#124—221no—
181#123—441no—
182C22⋊Q8—221no—
183#121—21no—
184C4×Q8—221no—
185C4×D4—221no—
186C4×D4—441no—
187#117—441no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—441no—
191C2×C42—111no—
192C2×C16—21no—
193C2×C16—221no—
194#107—21no—
195#107—21no—
196#107—111no—
197#107C22⋊D1111yescharacteristic
198#106—221no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201#103—221no—
202#103—221no—
203#102—21no—
204#102—221no—
205#95—441no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11—161no—
209C2×C11#161011yescharacteristic
210C2×C11#218911yescharacteristic
211C2×C11#219011yescharacteristic
212C2×Q8—221no—
213C2×D4—21no—
214C2×D4—41no—
215C22×C4—41no—
216C22×C4—111no—
217C22×C4—111no—
218C22×C4—441no—
219C22×C4—441no—
220C22×C4D4×D1111yescharacteristic
221Q16—441no—
222SD16—881no—
223D8—41no—
224C2×C8—41no—
225C2×C8—221no—
226C2×C8—441no—
227C2×C8D4×D1111yescharacteristic
228C2×C8C2×C22⋊D1111yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—222no—
233C4⋊C4—221no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—882no—
240C22⋊C4—41no—
241C22⋊C4—441no—
242C22⋊C4—441no—
243C22⋊C4—441no—
244C22⋊C4—441no—
245C42—221no—
246C42—221no—
247C42—441no—
248C16—41no—
249C16—441no—
250C11#1229311yescharacteristic, complemented, Sylow
251C23—41no—
252C23D8×D1111yescharacteristic
253Q8—441no—
254Q8—441no—
255D4—41no—
256D4—41no—
257D4—81no—
258D4—81no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—441no—
270C2×C4—442no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—882no—
274C2×C4—881no—
275C2×C4—881no—
276C2×C4#6696411yescharacteristic
277C2×C4#6699011yescharacteristic
278C8—21no—
279C8—21no—
280C8—441no—
281C22—21no—
282C22—21no—
283C22—81no—
284C22—81no—
285C22—81no—
286C22#1062252811yescharacteristic
287C22#1062252911yescharacteristic
288C22#1062276911yescharacteristic
289C4—21no—
290C4—81no—
291C4—161no—
292C4—441no—
293C4—441no—
294C4—882no—
295C4—881no—
296C4—881no—
297C4#1062266611yescharacteristic
298C4#1062281811yescharacteristic
299C2—21no—
300C2—21no—
301C2—161no—
302C2#1306761711yescharacteristic
303C2#1307055311yescharacteristic
304C2#1307056011yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2233C2
socleC22×C11#447
prime radicalC11×#466C22
hypercenter#2233D11
hypocenterC11#12293
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #13070818C2semidirect
3. #13070110C2semidirect
4. #13066629C2semidirect
6. #13066555C2semidirect
250. C11#12293semidirect

Maximal subgroups

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

subgroupindex
#130799622
#130708182
#130701102
#130666292
#130666252
#130665552
C11×#22332
#1229311