Finite Group Databasebeta

← #25006086

Subgroups — #25006086

Order 11008.

440 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 75 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#19137309C211yesmaximal, characteristic
2#19132932C212yesmaximal
3#19132540C212yesmaximal, complemented
4#19132529C211yesmaximal, characteristic, complemented
5C43×#1319C211yesmaximal, characteristic, complemented
6C2×#13063314C411yescharacteristic
7C2×Q8×Dic43C411yescharacteristic
8C2×#13063287C2211yescharacteristic
9#14582861—22no—
10#14582801C411yescharacteristic
11#14582788—22no—
12#14582773—22no—
13#14582768C2211yescharacteristic
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582622—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C22×D172C2×C411yescharacteristic
20C22×C4×D43D412yes—
21C2×#10621872—42no—
22#13063314—22no—
23#13063314—22no—
24Q8×Dic43—42no—
25#13063287—42no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4D412yes—
32C2×C4×Dic43—21no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35C22⋊(C43⋊C8)—22no—
36(C2×D43)⋊C8—42no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C22×Q8×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C42×C43C2×C411yescharacteristic
42C22⋊C8×C43—22no—
43#95×C43—22no—
44C23×D43C22⋊C412yes—
45C2×Q8×C43—21no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43M1612yescomplemented
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C22×C411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—21no—
54C22×Dic43—21no—
55C22×Dic43C22⋊C411yescharacteristic
56C22×Dic43C22⋊C411yescharacteristic
57C2×D172—21no—
58C2×D172—21no—
59C2×D172—41no—
60C2×D172—41no—
61C2×C4×D43—22no—
62C2×C4×D43—22no—
63C2×C4×D43—82no—
64C2×C8×C43—42no—
65C4⋊C4×C43—41no—
66C42×C43—41no—
67(C2×D43)⋊C4—28no—
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—82no—
70C4⋊Dic43—42no—
71C4⋊Dic43—41no—
72Dic43⋊C4—82no—
73C4×Dic43—21no—
74C4×Dic43—22no—
75C4×Dic43—42no—
76C4×Dic43M1612yescomplemented
77C2×C43⋊C8—42no—
78#10621872—84no—
79C23×C43C2×C22⋊C411yescharacteristic
80C22×D43—22no—
81C22×D43—22no—
82C22×D43—22no—
83C22×D43—42no—
84C22×D43—42no—
85Q8×C43—42no—
86Q8×C43—42no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43C2×M1611yescharacteristic
98C2×C4×C43C2×M1611yescharacteristic
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105C2×Dic43—42no—
106C2×Dic43—41no—
107C2×Dic43#9912yes—
108D172—42no—
109D172—42no—
110C4×D43—44no—
111C4×D43—82no—
112C8×C43—82no—
113C43⋊C8—82no—
114#11535—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43#40711yescharacteristic
118C22×C43C2×#9911yescharacteristic
119C22×C43#41311yescharacteristic
120C2×D43—44no—
121C2×D43—42no—
122C2×D43—42no—
123C2×D43—42no—
124C2×D43—82no—
125C4×C43—21no—
126C4×C43—21no—
127C4×C43—42no—
128C4×C43—42no—
129C4×C43—81no—
130Dic43—22no—
131Dic43—42no—
132Dic43—41no—
133Dic43—81no—
134#2326—431no—
135#1465—432no—
136#1325—432no—
137#1319—431no—
138#1319D4311yescharacteristic, complemented
139C2×C43—21no—
140C2×C43—21no—
141C2×C43#146511yescharacteristic
142C2×C43#212711yescharacteristic
143C2×C43#213511yescharacteristic
144D43—82no—
145C2×#124—431no—
146C2×C4×Q8—431no—
147C2×C4×D4—431no—
148#407—862no—
149#391C2×D4311yescharacteristic
150#390—431no—
151#388—862no—
152#385—862no—
153#384—431no—
154#376—431no—
155#324—432no—
156#324C2×D4312yes—
157#323—862no—
158C43#1153511yescharacteristic, complemented, Sylow
159C22×Q8C4×D4311yescharacteristic
160C22×D4—431no—
161C23×C4—432no—
162C2×M16—1722no—
163#124—862no—
164#124—862no—
165C4×Q8—1722no—
166C4×D4—1722no—
167C2×C4⋊C4—431no—
168C2×C4⋊C4—862no—
169C2×C4⋊C4—861no—
170C2×C4⋊C4C22×D4311yescharacteristic
171C2×C22⋊C4—432no—
172C2×C22⋊C4—862no—
173C2×C22⋊C4—862no—
174C2×C42—431no—
175C2×C42—431no—
176C2×C42—861no—
177C2×C42C4×D4311yescharacteristic
178C22⋊C8—22no—
179C22⋊C8—862no—
180C22⋊C8—1722no—
181#95—22no—
182#95—861no—
183#95—861no—
184C24—432no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8#1062187212yescomplemented
189C2×D4—861no—
190C2×D4—861no—
191C2×D4—1721no—
192C2×D4—1721no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—431no—
196C22×C4—431no—
197C22×C4—862no—
198C22×C4—862no—
199C22×C4—861no—
200C22×C4—861no—
201C22×C4—3442no—
202C22×C4C2×C4×D4311yescharacteristic
203C22×C4D4×D4312yes—
204M16—3444no—
205C2×C8—42no—
206C2×C8—1722no—
207C4⋊C4—41no—
208C4⋊C4—3442no—
209C4⋊C4—1721no—
210C4⋊C4—1722no—
211C22⋊C4—868no—
212C22⋊C4—3442no—
213C22⋊C4—1722no—
214C42—41no—
215C42—432no—
216C42—862no—
217C42—861no—
218C42—1722no—
219C23—862no—
220C23—862no—
221C23—862no—
222C23—1722no—
223C23—1722no—
224C23C22⋊C4×D4311yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—1722no—
228D4—1722no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—432no—
240C2×C4—862no—
241C2×C4—861no—
242C2×C4—3442no—
243C2×C4—1724no—
244C2×C4—1721no—
245C2×C4—1722no—
246C2×C4—1721no—
247C2×C4—1721no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4M16×D4311yescharacteristic
251C2×C4C2×#1062187211yescharacteristic
252C8—82no—
253C8—3442no—
254C22—21no—
255C22—21no—
256C22—3442no—
257C22—1724no—
258C22—1722no—
259C22—1722no—
260C22—1722no—
261C22#1458286111yescharacteristic
262C22#99×D4311yescharacteristic
263C22#1458288011yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—862no—
270C4—3441no—
271C4—1722no—
272C4—1721no—
273C2—21no—
274C2—21no—
275C2—3442no—
276C2#1913293011yescharacteristic
277C2#1913626311yescharacteristic
278C2#1913628811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11535
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
4. #19132529C2semidirect
5. C43×#1319C2semidirect
48. C2×Q8×C43M16semidirect
76. C4×Dic43M16semidirect
138. #1319D43semidirect
158. C43#11535semidirect
188. C2×Q8#10621872semidirect

Maximal subgroups

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

subgroupindex
#191373092
#191329322
#191325402
#191325292
C43×#13192
#1153543