Finite Group Databasebeta

← #25006072

Subgroups — #25006072

Order 11008.

460 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 77 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#19132932C212yesmaximal
3#19132539C211yesmaximal, characteristic, complemented
4#19132528C212yesmaximal, complemented
5C43×#1324C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic
7C2×#13063290C411yescharacteristic
8C2×#13063287C2211yescharacteristic
9#14582861—22no—
10#14582804C2211yescharacteristic
11#14582800C411yescharacteristic
12#14582788—22no—
13#14582746—22no—
14C42×Dic43C411yescharacteristic
15#14582625C2212yes—
16#14582622—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C4×D43D412yes—
22C2×#10621872—42no—
23#13063313—22no—
24#13063313—22no—
25#13063290—41no—
26#13063290—41no—
27#13063287—41no—
28#13063287—41no—
29C2×Dic43⋊C4—21no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4D412yes—
33C2×C4×Dic43—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43C2×C411yescharacteristic
37C2×C4×Dic43C2×C411yescharacteristic
38C22⋊(C43⋊C8)—22no—
39(C2×D43)⋊C8—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×D43C22⋊C412yes—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43C22⋊C411yescharacteristic
54C22×Dic43C22⋊C411yescharacteristic
55C2×D172—21no—
56C2×D172—21no—
57C2×D172—41no—
58C2×D172—41no—
59C2×C4×D43—22no—
60C2×C4×D43—22no—
61C2×C4×D43—44no—
62C2×Dic86—21no—
63C2×Dic86—41no—
64C2×Dic86—41no—
65C2×Dic86M1612yescomplemented
66C2×C8×C43—42no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—41no—
69C42×C43—21no—
70C42×C43M1612yescomplemented
71(C2×D43)⋊C4—28no—
72(C2×D43)⋊C4—42no—
73(C2×D43)⋊C4—44no—
74Dic43⋊C4—42no—
75C4×Dic43—21no—
76C4×Dic43—21no—
77C4×Dic43—42no—
78C4×Dic43—42no—
79C4×Dic43—41no—
80C4×Dic43—41no—
81C4×Dic43—41no—
82C2×C43⋊C8—42no—
83#10621872—84no—
84C23×C43C2×C22⋊C411yescharacteristic
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—42no—
89C22×D43—42no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43C2×M1611yescharacteristic
100C2×C4×C43C2×M1611yescharacteristic
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—41no—
110C2×Dic43#9911yescharacteristic
111C2×Dic43#9911yescharacteristic
112D172—42no—
113D172—42no—
114C4×D43—44no—
115C4×D43—82no—
116Dic86—42no—
117Dic86—42no—
118C8×C43—82no—
119C43⋊C8—82no—
120#11531—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43#40711yescharacteristic
124C22×C43C2×#9911yescharacteristic
125C22×C43#41311yescharacteristic
126C2×D43—44no—
127C2×D43—42no—
128C2×D43—42no—
129C2×D43—42no—
130C2×D43—82no—
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—42no—
134C4×C43—42no—
135C4×C43—81no—
136Dic43—21no—
137Dic43—42no—
138Dic43—41no—
139Dic43—42no—
140Dic43#35412yes—
141C4×#124—431no—
142#1465—432no—
143#1324—431no—
144#1324D4311yescharacteristic, complemented
145#1319—432no—
146C2×C43—21no—
147C2×C43—21no—
148C2×C43#146511yescharacteristic
149C2×C43C2×#35411yescharacteristic
150C2×C43#213211yescharacteristic
151D43—82no—
152C2×#124—431no—
153C2×C4×Q8—431no—
154C2×C4×D4—431no—
155#407—862no—
156#391—431no—
157#390—431no—
158#388—862no—
159#382C2×D4311yescharacteristic
160C4×C22⋊C4—862no—
161C43—431no—
162#324—432no—
163#324C2×D4312yes—
164#323—862no—
165C43#1153111yescharacteristic, complemented, Sylow
166C22×Q8—431no—
167C22×D4—431no—
168C23×C4—432no—
169C2×M16—1722no—
170#124—862no—
171#124—862no—
172C4×Q8—1721no—
173C4×Q8—1721no—
174C4×D4—1721no—
175C4×D4—1721no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4C4×D4311yescharacteristic
178C2×C4⋊C4C22×D4311yescharacteristic
179C2×C22⋊C4—432no—
180C2×C22⋊C4—862no—
181C2×C22⋊C4—862no—
182C2×C42—431no—
183C2×C42—431no—
184C2×C42—861no—
185C2×C42—861no—
186C2×C42—861no—
187C2×C42C4×D4311yescharacteristic
188C22⋊C8—22no—
189C22⋊C8—862no—
190C22⋊C8—1722no—
191#95—22no—
192#95—862no—
193C24—432no—
194C2×Q8—432no—
195C2×Q8—861no—
196C2×Q8—1721no—
197C2×Q8—1721no—
198C2×D4—861no—
199C2×D4—861no—
200C2×D4—1721no—
201C2×D4—1721no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—431no—
205C22×C4—431no—
206C22×C4—862no—
207C22×C4—862no—
208C22×C4—861no—
209C22×C4—861no—
210C22×C4—1724no—
211C22×C4C2×C4×D4311yescharacteristic
212C22×C4D4×D4312yes—
213M16—3444no—
214C2×C8—42no—
215C2×C8—1722no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—1722no—
219C22⋊C4—868no—
220C22⋊C4—1722no—
221C22⋊C4—1724no—
222C42—21no—
223C42—861no—
224C42—861no—
225C42—1721no—
226C42—1721no—
227C42—1721no—
228C42—1722no—
229C42—1722no—
230C42#1062187212yescomplemented
231C23—862no—
232C23—862no—
233C23—862no—
234C23—1722no—
235C23—1722no—
236C23C22⋊C4×D4311yescharacteristic
237Q8—1722no—
238Q8—1722no—
239D4—1722no—
240D4—1722no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—431no—
251C2×C4—431no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—861no—
256C2×C4—3442no—
257C2×C4—1724no—
258C2×C4—1721no—
259C2×C4—1721no—
260C2×C4—1721no—
261C2×C4—1721no—
262C2×C4—1721no—
263C2×C4M16×D4311yescharacteristic
264C2×C4C2×#1062187211yescharacteristic
265C8—82no—
266C8—3442no—
267C22—21no—
268C22—21no—
269C22—3442no—
270C22—1724no—
271C22—1722no—
272C22—1722no—
273C22—1722no—
274C22#1458286111yescharacteristic
275C22#99×D4311yescharacteristic
276C22#1458288211yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—432no—
283C4—861no—
284C4—1722no—
285C4—1722no—
286C4—1721no—
287C2—21no—
288C2—21no—
289C2—3442no—
290C2#1913293211yescharacteristic
291C2#354×D4311yescharacteristic
292C2#1913627711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11531
LCSG ▷ C22×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
3. #19132539C2semidirect
4. #19132528C2semidirect
5. C43×#1324C2semidirect
65. C2×Dic86M16semidirect
70. C42×C43M16semidirect
144. #1324D43semidirect
165. C43#11531semidirect
230. C42#10621872semidirect

Maximal subgroups

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

subgroupindex
#191371342
#191329322
#191325392
#191325282
C43×#13242
#1153143