Finite Group Databasebeta

← #25005752

Subgroups — #25005752

Order 11008.

462 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137001C211yesmaximal, characteristic
2#19132908C212yesmaximal
3#19132540C212yesmaximal, complemented
4#19132539C211yesmaximal, characteristic, complemented
5C43×#1324C211yesmaximal, characteristic, complemented
6C2×#13063283C411yescharacteristic
7C2×#13063283C2211yescharacteristic
8C2×C42×D43C411yescharacteristic
9#14582949—22no—
10#14582768C411yescharacteristic
11#14582768C2211yescharacteristic
12#14582765C411yescharacteristic
13#14582758—22no—
14#14582750—22no—
15#14582625C2212yes—
16#14582622—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×C4×D43—21no—
20C22×C4×D43C2×C411yescharacteristic
21#13063283—41no—
22#13063283—41no—
23#13063283—41no—
24#13063283—41no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×(C2×D43)⋊C4—21no—
30C2×(C2×D43)⋊C4D412yes—
31C2×C4×Dic43—21no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35C42×D43—22no—
36C42×D43C814yescomplemented
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×D43C22⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43C22⋊C412yes—
54C22×Dic43C22⋊C411yescharacteristic
55C2×C4×D43—21no—
56C2×C4×D43—21no—
57C2×C4×D43—22no—
58C2×C4×D43—24no—
59C2×C4×D43—42no—
60C2×C4×D43—42no—
61C2×C4×D43C2×C812yes—
62C2×C4×D43M1612yes—
63C2×C8×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C42×C43—21no—
67C42×C43C2×C812yes—
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—42no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72Dic43⋊C4—44no—
73Dic43⋊C4—44no—
74C4×Dic43—21no—
75C4×Dic43—24no—
76C4×Dic43—22no—
77C4×Dic43—22no—
78C4×Dic43—41no—
79C4×Dic43—41no—
80C4×Dic43C2×C812yes—
81C2×C43⋊C8—42no—
82C23×C43C2×C22⋊C411yescharacteristic
83C22×D43—21no—
84C22×D43—21no—
85C22×D43—41no—
86C22×D43—41no—
87C22×D43C22⋊C812yes—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—41no—
97C2×C4×C43C22×C811yescharacteristic
98C2×C4×C43C2×M1611yescharacteristic
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—41no—
106C2×Dic43C22⋊C812yes—
107C2×Dic43#9911yescharacteristic
108C2×Dic43#9911yescharacteristic
109C2×Dic43#10112yes—
110C4×D43—22no—
111C4×D43—22no—
112C4×D43—22no—
113C4×D43—22no—
114C4×D43—48no—
115C8×C43—82no—
116C43⋊C8—82no—
117#11447—431nomaximal, Sylow
118C22×C43—21no—
119C22×C43—21no—
120C22×C43C2×C22⋊C811yescharacteristic
121C22×C43C2×#9911yescharacteristic
122C22×C43C2×#10111yescharacteristic
123C2×D43—22no—
124C2×D43—42no—
125C2×D43—41no—
126C2×D43—41no—
127C2×D43—42no—
128C4×C43—21no—
129C4×C43—21no—
130C4×C43—42no—
131C4×C43—42no—
132C4×C43—81no—
133Dic43—24no—
134Dic43—42no—
135Dic43—81no—
136Dic43#32412yes—
137Dic43#32412yes—
138#2285—431no—
139#1458—432no—
140#1325—432no—
141#1324—431no—
142#1324D4311yescharacteristic, complemented
143C2×C43—21no—
144C2×C43—21no—
145C2×C43C2×#32411yescharacteristic
146C2×C43#212611yescharacteristic
147C2×C43#213211yescharacteristic
148D43—42no—
149C2×#117—431no—
150C2×#117—431no—
151C22×C42—431no—
152#431—862no—
153#384—431no—
154#384—431no—
155#382—431no—
156#382C2×D4311yescharacteristic
157#380—862no—
158C4×C4⋊C4—862no—
159#324—432no—
160#324C2×D4312yes—
161#323—862no—
162C43#1144711yescharacteristic, complemented, Sylow
163C23×C4—431no—
164C23×C4—861no—
165#117—1721no—
166#117—1721no—
167#117—1721no—
168#117—1721no—
169C2×C4⋊C4—431no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—862no—
172C2×C4⋊C4—862no—
173C2×C4⋊C4C4×D4311yescharacteristic
174C2×C4⋊C4C22×D4311yescharacteristic
175C2×C22⋊C4—432no—
176C2×C22⋊C4—861no—
177C2×C42—431no—
178C2×C42—434no—
179C2×C42—432no—
180C2×C42—862no—
181C2×C42—861no—
182C2×C42—861no—
183C2×C42C4×D4311yescharacteristic
184C4⋊C8—1722no—
185C22⋊C8—22no—
186C22⋊C8—862no—
187C4×C8—1722no—
188#95—22no—
189#95—862no—
190C24—431no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—431no—
194C22×C4—432no—
195C22×C4—432no—
196C22×C4—432no—
197C22×C4—861no—
198C22×C4—861no—
199C22×C4—862no—
200C22×C4—864no—
201C22×C4—861no—
202C22×C4—861no—
203C22×C4—1722no—
204C22×C4—1722no—
205C22×C4C2×C4×D4311yescharacteristic
206C22×C4D4×D4312yes—
207C2×C8—42no—
208C2×C8—1722no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—1721no—
212C4⋊C4—1721no—
213C4⋊C4—1724no—
214C4⋊C4—1724no—
215C22⋊C4—1722no—
216C22⋊C4—1722no—
217C42—21no—
218C42—432no—
219C42—862no—
220C42—862no—
221C42—864no—
222C42—861no—
223C42—1721no—
224C42—1721no—
225C42C8×D4312yes—
226C23—432no—
227C23—861no—
228C23—861no—
229C23—1721no—
230C23—1721no—
231C23C22⋊C4×D4311yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—432no—
242C2×C4—431no—
243C2×C4—431no—
244C2×C4—432no—
245C2×C4—862no—
246C2×C4—862no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—1728no—
254C2×C4—1722no—
255C2×C4—1721no—
256C2×C4—1722no—
257C2×C4C2×C8×D4311yescharacteristic
258C2×C4M16×D4311yescharacteristic
259C8—82no—
260C8—3442no—
261C22—21no—
262C22—21no—
263C22—862no—
264C22—1722no—
265C22—1722no—
266C22—1721no—
267C22—1721no—
268C22C22⋊C8×D4311yescharacteristic
269C22#99×D4311yescharacteristic
270C22#101×D4311yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—81no—
276C4—432no—
277C4—432no—
278C4—864no—
279C4—3441no—
280C4—1722no—
281C2—21no—
282C2—21no—
283C2—1722no—
284C2#324×D4311yescharacteristic
285C2#1913625911yescharacteristic
286C2#1913627711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11447
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
3. #19132540C2semidirect
4. #19132539C2semidirect
5. C43×#1324C2semidirect
36. C42×D43C8semidirect
142. #1324D43semidirect
162. C43#11447semidirect

Maximal subgroups

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

subgroupindex
#191370012
#191329082
#191325402
#191325392
C43×#13242
#1144743