Finite Group Databasebeta

← #14653246

Subgroups — #14653246

Order 2816.

458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#10622683C211yesmaximal, characteristic
2#13068787C211yesmaximal, characteristic, complemented
3#13067302C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13067284C211yesmaximal, characteristic
6#13066909C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66896—22no—
13C2×#66886—22no—
14#10622683—21no—
15#10622683—21no—
16#10622683C414yes—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C11×#331—22no—
21#10622182—22no—
22#10622124—22no—
23#10622119—22no—
24#10622093—21no—
25#10622092—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×Dic22—21no—
30C2×C11×M16—21no—
31C11×#127—21no—
32C11×#127—21no—
33C11×#127—21no—
34C11×#127C2×C412yes—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×#4318—21no—
39C22×C11⋊C8D412yes—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49#66896—24no—
50#66896—24no—
51C22⋊(C11⋊C8)—21no—
52#66886—44no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)D412yes—
56C4×C11⋊C8—21no—
57C4×C11⋊C8C2×C412yes—
58C4×C11⋊C8D411yescharacteristic
59C4×C11⋊C8D411yescharacteristic
60#9774—111nomaximal, Sylow
61C24×C11—41no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—82no—
71C2×D4×C11—82no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—41no—
76C2×Dic22—22no—
77C2×Dic22—41no—
78C2×Dic22—82no—
79C11×M16—42no—
80C2×C8×C11—22no—
81C2×C8×C11—41no—
82C42×C11C22×C411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C4⋊Dic11—22no—
87C4⋊Dic11—22no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90#4318—42no—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8C22⋊C412yes—
96C2×C11⋊C8C22⋊C412yes—
97C2×#486—111no—
98#1848—111no—
99#1549—111no—
100#1548—111no—
101#1545—111no—
102#1545D1111yescharacteristic
103#1452—111no—
104C23×C11—42no—
105C23×C11—82no—
106C23×C11—82no—
107C23×C11—82no—
108C23×C11#12411yescharacteristic
109D4×C11—44no—
110D4×C11—82no—
111D4×C11—82no—
112D4×C11—82no—
113D4×C11—82no—
114D4×C11—81no—
115D4×C11—81no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12711yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)12yes—
125C2×C4×C11#13712yes—
126C2×Dic11—42no—
127C2×Dic11—82no—
128Dic22—82no—
129Dic22—82no—
130C8×C11—42no—
131C8×C11—81no—
132C11⋊C8—22no—
133C11⋊C8—22no—
134C11⋊C8—42no—
135C11⋊C8—81no—
136C2×C4⋊Q8—111no—
137C2×#127C2×D1111yescharacteristic
138#486—114no—
139#486—221no—
140#486—221no—
141#431—111no—
142#431C2×D1111yescharacteristic
143C2×#108—222no—
144#423—111no—
145#423C2×D1111yescharacteristic
146C2×#102—222no—
147C2×C4×C8—111no—
148#333—222no—
149#332—222no—
150#331—22no—
151#331—222no—
152#322—221no—
153#322—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11—164no—
160C22×C11#39011yescharacteristic
161C22×C11#48912yes—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11#41712yes—
165C4×C11#47112yes—
166C4×C11#47212yes—
167C4×C11#49611yescharacteristic
168C4×C11#49711yescharacteristic
169Dic11—82no—
170C22×Q8—221no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C2×M16—21no—
175C2×M16—221no—
176C22×C8—112no—
177C4⋊Q8—112no—
178C4⋊Q8—221no—
179C4⋊Q8—221no—
180C4⋊Q8—221no—
181#127—21no—
182#127—21no—
183#127—21no—
184#127C4×D1112yes—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C42C22×D1111yescharacteristic
188#108—444no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—112no—
192C4⋊C8—221no—
193C4⋊C8—221no—
194C4⋊C8C22⋊D1112yes—
195#102—224no—
196#102—224no—
197C22⋊C8—21no—
198C22⋊C8—221no—
199C4×C8—21no—
200C4×C8—112no—
201C4×C8—111no—
202C4×C8—111no—
203C4×C8—221no—
204C2×C11—22no—
205C2×C11—162no—
206C2×C11#195911yescharacteristic
207C2×C11#197711yescharacteristic
208C2×C11#197811yescharacteristic
209C24—41no—
210C2×Q8—222no—
211C2×Q8—441no—
212C2×Q8—882no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—41no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—82no—
222C2×D4—82no—
223C22×C4—441no—
224C22×C4#433911yescharacteristic
225C22×C4D4×D1111yescharacteristic
226C22×C4#434111yescharacteristic
227M16—42no—
228M16—442no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—112no—
232C2×C8—112no—
233C2×C8—222no—
234C2×C8—222no—
235C2×C8—222no—
236C2×C8—441no—
237C4⋊C4—222no—
238C4⋊C4—222no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C42C2×C4×D1111yescharacteristic
242C42D4×D1111yescharacteristic
243C42D4×D1111yescharacteristic
244C42C2×C22⋊D1111yescharacteristic
245C11#977411yescharacteristic, complemented, Sylow
246C23—42no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23#6693811yescharacteristic
251Q8—882no—
252Q8—882no—
253D4—44no—
254D4—82no—
255D4—82no—
256D4—81no—
257D4—81no—
258D4—82no—
259D4—82no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—442no—
263C2×C4—882no—
264C2×C4C22⋊C4×D1111yescharacteristic
265C2×C4(C22⋊D11)⋊C411yescharacteristic
266C2×C4#6693711yescharacteristic
267C2×C4#6696412yes—
268C2×C4#6696812yes—
269C2×C4C4×C22⋊D1111yescharacteristic
270C2×C4#6699211yescharacteristic
271C2×C4#6699311yescharacteristic
272C8—42no—
273C8—81no—
274C8—222no—
275C8—222no—
276C8—442no—
277C8—881no—
278C22—21no—
279C22—21no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—164no—
284C22#1062237812yes—
285C22#1062257011yescharacteristic
286C4—21no—
287C4—21no—
288C4—882no—
289C4#1062236212yes—
290C4#1062238412yes—
291C4#1062276711yescharacteristic
292C4#1062278011yescharacteristic
293C4#1062281312yes—
294C2—22no—
295C2—162no—
296C2#1306943111yescharacteristic
297C2#1306952211yescharacteristic
298C2#1306952311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1545C2
socleC22×C11#390
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1545D11
hypocenterC11#9774
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #13068787C2semidirect
3. #13067302C2semidirect
4. #13067296C2semidirect
6. #13066909C2semidirect
245. C11#9774semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
#130687872
#130673022
#130672962
#130672842
#130669092
C11×#15452
#977411