Finite Group Databasebeta

← #25005870

Subgroups — #25005870

Order 11008.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#19137134C211yesmaximal, characteristic
2#19132917C212yesmaximal, complemented
3#19132539C211yesmaximal, characteristic, complemented
4#19132526C212yesmaximal
5C43×#1324C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic
7C2×#13063290C2211yescharacteristic
8C2×#13063287C411yescharacteristic
9#14582949—22no—
10#14582804C411yescharacteristic
11#14582800C2211yescharacteristic
12#14582788—22no—
13#14582746—22no—
14C42×Dic43C411yescharacteristic
15#14582625C2212yes—
16#14582624—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C4×D43—21no—
22#13063313—22no—
23#13063313C814yescomplemented
24#13063290—41no—
25#13063290—41no—
26#13063287—41no—
27#13063287—41no—
28C2×Dic43⋊C4D412yes—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—21no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43D412yes—
37Dic43⋊C8—42no—
38C22⋊(C43⋊C8)—22no—
39C8×Dic43—42no—
40C43⋊#95—22no—
41C2×C4⋊C4×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C22⋊C8×C43—22no—
45#95×C43—22no—
46C23×D43—21no—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—21no—
52C22×Dic43C22⋊C412yes—
53C22×Dic43C22⋊C411yescharacteristic
54C22×Dic43C22⋊C411yescharacteristic
55C2×D172—21no—
56C2×D172—41no—
57C2×D172—41no—
58C2×D172C2×C812yes—
59C2×C4×D43—44no—
60C2×C4×D43—41no—
61C2×C4×D43—41no—
62C2×Dic86—41no—
63C2×Dic86—41no—
64C2×Dic86C2×C812yes—
65C2×Dic86M1612yes—
66C2×C8×C43—42no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C42×C43—21no—
70C42×C43C2×C812yes—
71(C2×D43)⋊C4—28no—
72(C2×D43)⋊C4—44no—
73(C2×D43)⋊C4—42no—
74Dic43⋊C4—42no—
75C4×Dic43—22no—
76C4×Dic43—22no—
77C4×Dic43—21no—
78C4×Dic43—21no—
79C4×Dic43—42no—
80C4×Dic43—42no—
81C4×Dic43—41no—
82C2×C43⋊C8—42no—
83C23×C43C2×C22⋊C411yescharacteristic
84C22×D43—22no—
85C22×D43—42no—
86C22×D43—42no—
87C22×D43—41no—
88C22×D43—41no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—41no—
98C2×C4×C43C22×C811yescharacteristic
99C2×C4×C43C2×M1611yescharacteristic
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108C2×Dic43C22⋊C814yes—
109C2×Dic43#9911yescharacteristic
110C2×Dic43#9911yescharacteristic
111D172—42no—
112D172—42no—
113C4×D43—82no—
114C4×D43—82no—
115Dic86—42no—
116Dic86—42no—
117C8×C43—82no—
118C43⋊C8—82no—
119#11476—431nomaximal, Sylow
120C22×C43—21no—
121C22×C43—21no—
122C22×C43C2×C22⋊C811yescharacteristic
123C22×C43C2×#9911yescharacteristic
124C22×C43#41311yescharacteristic
125C2×D43—44no—
126C2×D43—42no—
127C2×D43—82no—
128C2×D43—81no—
129C2×D43—81no—
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—42no—
133C4×C43—42no—
134C4×C43—81no—
135Dic43—21no—
136Dic43—24no—
137Dic43—42no—
138Dic43—41no—
139Dic43#35512yes—
140C4×#124—431no—
141#1461—432no—
142#1324—431no—
143#1324D4311yescharacteristic, complemented
144#1318—432no—
145C2×C43—21no—
146C2×C43—21no—
147C2×C43#145911yescharacteristic
148C2×C43#212611yescharacteristic
149C2×C43C2×#35511yescharacteristic
150D43—82no—
151C2×#124—431no—
152C2×C4×Q8—431no—
153C2×C4×D4—431no—
154#431—862no—
155#391—431no—
156#390—431no—
157#388—862no—
158#382C2×D4311yescharacteristic
159C4×C22⋊C4—862no—
160C43—431no—
161#324—432no—
162#324—862no—
163#324C2×D4312yes—
164C43#1147611yescharacteristic, complemented, Sylow
165C22×Q8—431no—
166C22×D4—431no—
167C23×C4—861no—
168#124—434no—
169#124—862no—
170C4×Q8—1721no—
171C4×Q8—1721no—
172C4×D4—1721no—
173C4×D4—1721no—
174C2×C4⋊C4—432no—
175C2×C4⋊C4C4×D4311yescharacteristic
176C2×C4⋊C4C22×D4311yescharacteristic
177C2×C22⋊C4—862no—
178C2×C22⋊C4—861no—
179C2×C22⋊C4—862no—
180C2×C42—431no—
181C2×C42—432no—
182C2×C42—431no—
183C2×C42—861no—
184C2×C42—861no—
185C2×C42C4×D4311yescharacteristic
186C4⋊C8—1722no—
187C22⋊C8—22no—
188C22⋊C8—862no—
189C4×C8—1722no—
190#95—22no—
191#95—862no—
192C24—861no—
193C2×Q8—432no—
194C2×Q8—432no—
195C2×Q8—1721no—
196C2×Q8—1721no—
197C2×D4—432no—
198C2×D4—861no—
199C2×D4—1721no—
200C2×D4—1721no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—432no—
204C22×C4—431no—
205C22×C4—431no—
206C22×C4—861no—
207C22×C4—1721no—
208C22×C4—1721no—
209C22×C4—1724no—
210C22×C4C2×C4×D4311yescharacteristic
211C22×C4D4×D4312yes—
212C2×C8—42no—
213C2×C8—1722no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—1722no—
217C22⋊C4—868no—
218C22⋊C4—1722no—
219C22⋊C4—1724no—
220C42—21no—
221C42—862no—
222C42—862no—
223C42—861no—
224C42—861no—
225C42—1721no—
226C42—1722no—
227C42—1722no—
228C42C8×D4312yes—
229C23—862no—
230C23—1722no—
231C23—1722no—
232C23—1721no—
233C23—1721no—
234C23C22⋊C4×D4311yescharacteristic
235Q8—1722no—
236Q8—1722no—
237D4—1722no—
238D4—1722no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—431no—
249C2×C4—434no—
250C2×C4—431no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—861no—
256C2×C4—3442no—
257C2×C4—3442no—
258C2×C4—1721no—
259C2×C4—1721no—
260C2×C4—1721no—
261C2×C4C2×C8×D4311yescharacteristic
262C2×C4M16×D4311yescharacteristic
263C8—82no—
264C8—3442no—
265C22—21no—
266C22—21no—
267C22—3442no—
268C22—3441no—
269C22—3441no—
270C22—1724no—
271C22—1722no—
272C22C22⋊C8×D4311yescharacteristic
273C22#99×D4311yescharacteristic
274C22#1458288211yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—81no—
280C4—432no—
281C4—861no—
282C4—864no—
283C4—1722no—
284C4—1721no—
285C2—21no—
286C2—21no—
287C2—3442no—
288C2#1913291211yescharacteristic
289C2#1913625911yescharacteristic
290C2#355×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11476
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #19132917C2semidirect
3. #19132539C2semidirect
5. C43×#1324C2semidirect
23. #13063313C8semidirect
143. #1324D43semidirect
164. C43#11476semidirect

Maximal subgroups

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

subgroupindex
#191371342
#191329172
#191325392
#191325262
C43×#13242
#1147643