Finite Group Databasebeta

← #14667064

Subgroups — #14667064

Order 2816.

316 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070816C211yesmaximal, characteristic, complemented
2#13070799C211yesmaximal, characteristic
3#13070109C211yesmaximal, characteristic, complemented
4#13066628C211yesmaximal, characteristic, complemented
5#13066625C211yesmaximal, characteristic
6#13066556C211yesmaximal, characteristic, complemented
7C11×#3250C211yesmaximal, characteristic
8C11×#529—21no—
9C11×#479—21no—
10C11×#478—21no—
11C11×#467C2211yescharacteristic
12C11×#466C2211yescharacteristic
13C11×#465—21no—
14C11×#464—21no—
15C11×#463—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66882C2211yescharacteristic
18#10622541—21no—
19#10622202—21no—
20#10622200—21no—
21#10622189—21no—
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24C22⋊(C11⋊C16)C2211yescharacteristic
25#10622128—21no—
26#10622127—21no—
27C2×C11×Q16D411yescharacteristic
28C2×C11×SD16—21no—
29C2×C11×D8D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C11×#126—41no—
33C11×#125—21no—
34C11×#124—21no—
35C11×#123—41no—
36C11×C22⋊Q8—21no—
37C11×#121—21no—
38C4×Q8×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—41no—
41C11×#117—41no—
42C2×C42×C11D411yescharacteristic
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—41no—
46C11×#107D411yescharacteristic
47C11×#107D411yescharacteristic
48C11×#106—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#103—21no—
52C11×#103—21no—
53C11×#102—21no—
54C11×#102—21no—
55C11⋊#95—41no—
56#66882—21no—
57#66882—21no—
58C2×C11⋊C16—21no—
59C2×C11⋊C16—21no—
60#12293—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11D811yescharacteristic
66C22×C4×C11D811yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—41no—
69C22×Dic11—41no—
70C11×Q16—41no—
71C11×SD16—81no—
72C11×D8—41no—
73C2×C8×C11—21no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2×D411yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—41no—
92C4⋊Dic11—22no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—82no—
97C11⋊C16—41no—
98C11⋊C16—41no—
99#3250D1111yescharacteristic
100#2236—111no—
101#2233—111no—
102#2087—111no—
103#1348—111no—
104#1347—111no—
105#1322—111no—
106C23×C11—41no—
107C23×C11C2×D811yescharacteristic
108Q8×C11—41no—
109Q8×C11—41no—
110D4×C11—41no—
111D4×C11—41no—
112D4×C11—81no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—82no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×Dic11—42no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C8×C11—21no—
134C8×C11—21no—
135C8×C11—41no—
136#529—21no—
137#479—21no—
138#478—21no—
139#467C2×D1111yescharacteristic
140#466C2×D1111yescharacteristic
141#465—21no—
142#464—21no—
143#463—21no—
144C2×#107—111no—
145C2×C4⋊C8C2×D1111yescharacteristic
146#389—221no—
147#367—221no—
148#366—221no—
149#358—221no—
150#357—221no—
151C22⋊C16—111no—
152C22⋊C16—111no—
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—41no—
165C4×C11—41no—
166C4×C11—81no—
167C4×C11—81no—
168C4×C11—81no—
169C4×C11#45611yescharacteristic
170C4×C11#45811yescharacteristic
171Dic11—82no—
172Dic11—161no—
173C2×Q16C22⋊D1111yescharacteristic
174C2×SD16—21no—
175C2×D8C22⋊D1111yescharacteristic
176C22×C8C22⋊D1111yescharacteristic
177C22×C8C22×D1111yescharacteristic
178#126—41no—
179#125—21no—
180#124—21no—
181#123—41no—
182C22⋊Q8—21no—
183#121—21no—
184C4×Q8—21no—
185C4×D4—21no—
186C4×D4—41no—
187#117—41no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—441no—
191C2×C42C22⋊D1111yescharacteristic
192C2×C16—221no—
193C2×C16—221no—
194#107—221no—
195#107—221no—
196#107C22⋊D1111yescharacteristic
197#107C22⋊D1111yescharacteristic
198#106—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201#103—21no—
202#103—21no—
203#102—21no—
204#102—21no—
205#95—441no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11—161no—
209C2×C11#161011yescharacteristic
210C2×C11#218911yescharacteristic
211C2×C11#219011yescharacteristic
212C2×Q8—21no—
213C2×D4—21no—
214C2×D4—41no—
215C22×C4—41no—
216C22×C4—441no—
217C22×C4—441no—
218C22×C4#432311yescharacteristic
219C22×C4#432311yescharacteristic
220C22×C4C2×C22⋊D1111yescharacteristic
221Q16—41no—
222SD16—81no—
223D8—41no—
224C2×C8—21no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8C2×C22⋊D1111yescharacteristic
228C2×C8C2×C22⋊D1111yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—222no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—882no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C42—21no—
246C42—21no—
247C42—41no—
248C16—441no—
249C16—441no—
250C11#1229311yescharacteristic, complemented, Sylow
251C23—41no—
252C23C2×#432311yescharacteristic
253Q8—41no—
254Q8—41no—
255D4—41no—
256D4—41no—
257D4—81no—
258D4—81no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—82no—
270C2×C4—442no—
271C2×C4—881no—
272C2×C4—881no—
273C2×C4—881no—
274C2×C4—881no—
275C2×C4—881no—
276C2×C4#6698511yescharacteristic
277C2×C4#6700611yescharacteristic
278C8—21no—
279C8—21no—
280C8—41no—
281C22—21no—
282C22—21no—
283C22—81no—
284C22—81no—
285C22—81no—
286C22#1062280711yescharacteristic
287C22#1062280811yescharacteristic
288C22#1062283011yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—81no—
293C4—81no—
294C4—81no—
295C4—882no—
296C4—1761no—
297C4#1062285611yescharacteristic
298C4#1062285911yescharacteristic
299C2—21no—
300C2—21no—
301C2—161no—
302C2#1306761911yescharacteristic
303C2#1307055611yescharacteristic
304C2#1307056211yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#3250C2
socleC22×C11#447
prime radicalC11×#466C22
hypercenter#3250D11
hypocenterC11#12293
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3250

Complements

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

NH ≅ G/Ntype
1. #13070816C2semidirect
3. #13070109C2semidirect
4. #13066628C2semidirect
6. #13066556C2semidirect
250. C11#12293semidirect

Maximal subgroups

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

subgroupindex
#130708162
#130707992
#130701092
#130666282
#130666252
#130665562
C11×#32502
#1229311