Finite Group Databasebeta

← #14658404

Subgroups — #14658404

Order 2816.

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

normal subgroups only

This group has 322 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#13069460C211yesmaximal, characteristic
2#13069391C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic
6#13066491C211yesmaximal, characteristic
7C11×#1565C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×#66888—21no—
13C2×#66888—21no—
14C2×#66886—21no—
15#10622537C2211yescharacteristic
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C11×#335—21no—
19C11×#334—21no—
20#10622196—21no—
21#10622124—21no—
22#10622124—21no—
23#10622124—22no—
24#10622096—22no—
25C22×Dic22—21no—
26C2×C11×M16D411yescharacteristic
27C2×C11×M16D411yescharacteristic
28C22×C8×C11—21no—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11Q812yes—
32C2×#4318—21no—
33C2×#4318—21no—
34C22×C11⋊C8—21no—
35#66922—21no—
36#66922—21no—
37#66922—21no—
38#66922—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8D411yescharacteristic
42C11×C4⋊C8D411yescharacteristic
43C11×C22⋊C8—21no—
44C11×#97—21no—
45C4×C8×C11—21no—
46C4×C8×C11—21no—
47#66888—42no—
48#66888—42no—
49#66886—42no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)D412yes—
56#10604—111nomaximal, Sylow
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×Q811yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—22no—
61C2×Dic22—41no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C11×M16—21no—
68C11×M16—21no—
69C11×M16—21no—
70C11×M16D812yes—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—41no—
76C2×C8×C11—81no—
77C42×C11C2×D411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C4⋊Dic11—22no—
82C4⋊Dic11—22no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85#4318—41no—
86#4318—41no—
87#4318—41no—
88#4318—41no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94#1966—111no—
95#1950—111no—
96#1571—111no—
97#1565D1111yescharacteristic
98#1546—111no—
99C2×#332—111no—
100#1292—111no—
101C23×C11C22⋊Q811yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11#12111yescharacteristic
108C2×C4×C11C22⋊Q811yescharacteristic
109C2×C4×C11C22⋊Q811yescharacteristic
110C2×C4×C11#12611yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118Dic22—81no—
119Dic22—81no—
120Dic22—81no—
121Dic22—81no—
122C8×C11—22no—
123C8×C11—41no—
124C8×C11—41no—
125C8×C11—41no—
126C8×C11—81no—
127C11⋊C8—42no—
128C11⋊C8—81no—
129C11⋊C8—81no—
130C2×C4⋊Q8—111no—
131#431C2×D1111yescharacteristic
132C2×#108—221no—
133#423—111no—
134#423—111no—
135C2×C4⋊C8—111no—
136C2×C4⋊C8C2×D1111yescharacteristic
137C2×#101—221no—
138C2×#101—221no—
139C4×M16C2×D1111yescharacteristic
140#341—221no—
141#335—21no—
142#335—222no—
143#334—21no—
144#332—222no—
145#332—221no—
146#332—221no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#39611yescharacteristic
150C22×C11#47411yescharacteristic
151C22×C11#47811yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11#45911yescharacteristic
156C4×C11#46411yescharacteristic
157C4×C11#46611yescharacteristic
158C4×C11#46811yescharacteristic
159C4×C11#47111yescharacteristic
160C4×C11#47311yescharacteristic
161Dic11—82no—
162C22×Q8—221no—
163C2×M16—221no—
164C2×M16—221no—
165C2×M16D4411yescharacteristic
166C2×M16D4411yescharacteristic
167C22×C8—21no—
168C22×C8—221no—
169C4⋊Q8—221no—
170C4⋊Q8—221no—
171C4⋊Q8—221no—
172C4⋊Q8—221no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—221no—
175C2×C42C22×D1111yescharacteristic
176#108—442no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—112no—
180C4⋊C8—221no—
181C4⋊C8—221no—
182C4⋊C8—221no—
183C4⋊C8—221no—
184C4⋊C8—221no—
185C4⋊C8C22⋊D1111yescharacteristic
186C4⋊C8C22⋊D1111yescharacteristic
187#101—442no—
188#101—442no—
189C22⋊C8—21no—
190#97—21no—
191C4×C8—21no—
192C4×C8—21no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11#206411yescharacteristic
196C2×C11#206711yescharacteristic
197C2×C11#207011yescharacteristic
198C2×Q8—441no—
199C2×Q8—441no—
200C2×Q8—441no—
201C2×Q8—441no—
202C2×Q8—441no—
203C2×Q8—441no—
204C22×C4—222no—
205C22×C4C2×D4411yescharacteristic
206C22×C4#434111yescharacteristic
207C22×C4Q8×D1111yescharacteristic
208M16—21no—
209M16—21no—
210M16—21no—
211M16—441no—
212M16—441no—
213M16—441no—
214M16—441no—
215M16D8812yes—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—81no—
222C2×C8—222no—
223C2×C8—441no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8—441no—
227C4⋊C4—222no—
228C4⋊C4—222no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C42#433911yescharacteristic
232C42D4×D1111yescharacteristic
233C42#434311yescharacteristic
234C42C2×C22⋊D1111yescharacteristic
235C11#1060411yescharacteristic, complemented, Sylow
236C23#6695011yescharacteristic
237Q8—881no—
238Q8—881no—
239Q8—881no—
240Q8—881no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4#6694811yescharacteristic
248C2×C4#6694911yescharacteristic
249C2×C4#6695111yescharacteristic
250C2×C4C2×D8811yescharacteristic
251C2×C4#6695711yescharacteristic
252C2×C4#6696111yescharacteristic
253C2×C4#6696211yescharacteristic
254C2×C4#6698311yescharacteristic
255C2×C4#6699211yescharacteristic
256C2×C4#6699911yescharacteristic
257C8—22no—
258C8—41no—
259C8—41no—
260C8—41no—
261C8—81no—
262C8—442no—
263C8—881no—
264C8—881no—
265C22—21no—
266C22—21no—
267C22#1062245911yescharacteristic
268C22#1062246011yescharacteristic
269C22#1062260711yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—882no—
274C4#1062245611yescharacteristic
275C4#1062245811yescharacteristic
276C4#1062272811yescharacteristic
277C4#1062274711yescharacteristic
278C4#1062281311yescharacteristic
279C4#1062281711yescharacteristic
280C2—21no—
281C2—21no—
282C2#1306998011yescharacteristic
283C2#1307000311yescharacteristic
284C2#1307001611yescharacteristic
subgroupG/H
centerC22#10622607
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1565C2
socleC22×C11#396
prime radicalC23×C11C22⋊Q8
hypercenter#1565D11
hypocenterC11#10604
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
235. C11#10604semidirect

Maximal subgroups

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

subgroupindex
#130694602
#130693912
#130673912
#130672872
C2×#106221242
#130664912
C11×#15652
#1060411