Finite Group Databasebeta

← #14658421

Subgroups — #14658421

Order 2816.

306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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#13069391C211yesmaximal, characteristic
2#13067392C211yesmaximal, characteristic
3#13067368C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic
5C2×#10622185C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1997C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C2×#66886—21no—
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C11×#343—21no—
17C11×#343—21no—
18#10622196—21no—
19#10622185—21no—
20#10622185—21no—
21#10622185—22no—
22#10622117—22no—
23#10622096—21no—
24#10622095—21no—
25C22×Q8×C11—21no—
26C2×C11×M16—21no—
27C2×C11×M16D411yescharacteristic
28C2×C11×M16D411yescharacteristic
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4Q812yes—
35C2×C42×C11C2311yescharacteristic
36C2×#4318—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×#97—21no—
42C4×C8×C11—21no—
43C22⋊(C11⋊C8)—21no—
44#66886—42no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)D412yes—
51C4⋊(C11⋊C8)D411yescharacteristic
52C4⋊(C11⋊C8)D411yescharacteristic
53C4×C11⋊C8—21no—
54#10606—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11—81no—
58C2×Q8×C11—81no—
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×Q811yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C11×M16—21no—
64C11×M16—21no—
65C11×M16—21no—
66C11×M16—41no—
67C11×M16—41no—
68C11×M16Q1612yes—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—41no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C42×C11C2×D411yescharacteristic
77C42×C11C2×D411yescharacteristic
78C42×C11#4111yescharacteristic
79C42×C11#4111yescharacteristic
80#4318—41no—
81#4318—41no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—22no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—81no—
90#1997D1111yescharacteristic
91#1950—111no—
92#1571—111no—
93#1565—111no—
94#1549—111no—
95C2×#332—111no—
96#1292—111no—
97C23×C11C22⋊Q811yescharacteristic
98Q8×C11—82no—
99Q8×C11—81no—
100Q8×C11—81no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—82no—
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11#12111yescharacteristic
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11C22⋊Q811yescharacteristic
110C2×C4×C11C22⋊Q811yescharacteristic
111C2×C4×C11#12611yescharacteristic
112C2×C4×C11C2×Q1611yescharacteristic
113C2×C4×C11#13511yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C11#13711yescharacteristic
116C8×C11—22no—
117C8×C11—41no—
118C8×C11—81no—
119C11⋊C8—42no—
120C11⋊C8—41no—
121C11⋊C8—41no—
122C11⋊C8—81no—
123C11⋊C8—81no—
124C2×C4⋊Q8C2×D1111yescharacteristic
125#431—111no—
126C2×#108—221no—
127#423—111no—
128#423C2×D1111yescharacteristic
129C2×C4⋊C8—111no—
130C2×C4⋊C8—111no—
131C4×M16C2×D1111yescharacteristic
132#343—21no—
133#343—21no—
134#341—221no—
135#335—221no—
136#335—222no—
137#334—221no—
138#332—222no—
139#332—221no—
140#332—221no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11#39611yescharacteristic
144C22×C11#47711yescharacteristic
145C22×C11#47911yescharacteristic
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—82no—
150C4×C11#46211yescharacteristic
151C4×C11#46311yescharacteristic
152C4×C11#46711yescharacteristic
153C4×C11#46811yescharacteristic
154C4×C11#47111yescharacteristic
155C4×C11#47211yescharacteristic
156C22×Q8—21no—
157C2×M16—21no—
158C2×M16—221no—
159C2×M16C22⋊D1111yescharacteristic
160C2×M16C22⋊D1111yescharacteristic
161C22×C8—221no—
162C22×C8—221no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4Dic2212yes—
169C2×C42C22×D1111yescharacteristic
170#108—442no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—111no—
174C4⋊C8—112no—
175C4⋊C8—111no—
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181C22⋊C8—221no—
182#97—21no—
183C4×C8—21no—
184C4×C8—221no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#206311yescharacteristic
188C2×C11#206811yescharacteristic
189C2×C11#207011yescharacteristic
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—81no—
193C2×Q8—81no—
194C22×C4—22no—
195C22×C4C2×Dic2211yescharacteristic
196C22×C4#433911yescharacteristic
197C22×C4C2×C22⋊D1111yescharacteristic
198M16—21no—
199M16—21no—
200M16—21no—
201M16—41no—
202M16—41no—
203M16—441no—
204M16—441no—
205M16#432612yes—
206C2×C8—21no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—221no—
210C2×C8—221no—
211C2×C8—222no—
212C2×C8—441no—
213C2×C8—441no—
214C2×C8—441no—
215C2×C8—441no—
216C2×C8—881no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C42D4×D1111yescharacteristic
222C42D4×D1111yescharacteristic
223C42#434111yescharacteristic
224C42#434111yescharacteristic
225C11#1060611yescharacteristic, complemented, Sylow
226C23#6697711yescharacteristic
227Q8—82no—
228Q8—81no—
229Q8—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—82no—
235C2×C4#6693111yescharacteristic
236C2×C4#6693111yescharacteristic
237C2×C4#6693211yescharacteristic
238C2×C4#6693711yescharacteristic
239C2×C4#6699111yescharacteristic
240C2×C4#6699211yescharacteristic
241C2×C4#6699511yescharacteristic
242C2×C4C2×#432611yescharacteristic
243C2×C4#6700211yescharacteristic
244C2×C4#6700311yescharacteristic
245C8—22no—
246C8—41no—
247C8—81no—
248C8—441no—
249C8—441no—
250C8—442no—
251C8—881no—
252C8—881no—
253C22—21no—
254C22—21no—
255C22#1062256111yescharacteristic
256C22#1062263411yescharacteristic
257C22#1062263511yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—82no—
262C4#1062236111yescharacteristic
263C4#1062236211yescharacteristic
264C4#1062266211yescharacteristic
265C4#1062266411yescharacteristic
266C4#1062267011yescharacteristic
267C4#1062270311yescharacteristic
268C2—21no—
269C2—21no—
270C2#1306997211yescharacteristic
271C2#1307001111yescharacteristic
272C2#1307001711yescharacteristic
subgroupG/H
centerC22#10622561
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#396
prime radicalC23×C11C22⋊Q8
hypercenter#1997D11
hypocenterC11#10606
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
225. C11#10606semidirect

Maximal subgroups

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

subgroupindex
#130693912
#130673922
#130673682
#130673012
C2×#106221852
#130664902
C11×#19972
#1060611