Finite Group Databasebeta

← #24990009

Subgroups — #24990009

Order 11008.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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#19134358C212yesmaximal
3#19132477C212yesmaximal, complemented
4#19132476C211yesmaximal, characteristic, complemented
5C43×#1295C211yesmaximal, characteristic, complemented
6C2×#13063283C412yes—
7C2×C42×D43C2211yescharacteristic
8C2×(C2×D43)⋊C8—22no—
9C2×#13063236C2212yes—
10#14582768C412yes—
11#14582765C2211yescharacteristic
12#14582758—22no—
13#14582750—22no—
14#14582653—22no—
15C2×#97×C43C2212yes—
16C43×#382C2211yescharacteristic
17C22×C4×D43C2×C411yescharacteristic
18C22×C4×D43D412yes—
19C22×C43⋊C8—22no—
20#13063283—44no—
21C2×C4⋊Dic43C2×C412yes—
22C2×Dic43⋊C4—22no—
23C2×Dic43⋊C4—22no—
24C2×(C2×D43)⋊C4—22no—
25C2×C4×Dic43—22no—
26C2×C4×Dic43C2×C411yescharacteristic
27C2×C4×Dic43D412yes—
28C42×D43—22no—
29C42×D43—21no—
30C42×D43—21no—
31(C2×D43)⋊C8—28no—
32#13063236—22no—
33#13063236—22no—
34C43⋊#95—22no—
35C22×C8×C43—22no—
36C2×C4⋊C4×C43C2×C412yes—
37C2×C42×C43C2311yescharacteristic
38#97×C43—22no—
39#97×C43—22no—
40#95×C43—22no—
41C23×D43C22⋊C411yescharacteristic
42C22×C4×C43—22no—
43C22×C4×C43C22×C411yescharacteristic
44C22×C4×C43C2×D412yes—
45C22×Dic43—22no—
46C22×Dic43C22⋊C411yescharacteristic
47C22×Dic43C22⋊C412yes—
48C2×C4×D43—21no—
49C2×C4×D43—21no—
50C2×C4×D43—22no—
51C2×C4×D43—22no—
52C2×C4×D43—22no—
53C2×C4×D43—24no—
54C2×C4×D43—22no—
55C2×C4×D43—42no—
56C2×C8×C43—24no—
57C2×C8×C43—42no—
58C2×C8×C43—42no—
59C4⋊C4×C43—42no—
60C42×C43#4112yes—
61C42×C43#4111yescharacteristic
62C42×C43#4111yescharacteristic
63(C2×D43)⋊C4—44no—
64C4⋊Dic43—42no—
65Dic43⋊C4—44no—
66Dic43⋊C4—44no—
67C4×Dic43—21no—
68C4×Dic43—21no—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43—44no—
72C2×C43⋊C8—24no—
73C2×C43⋊C8—42no—
74C2×C43⋊C8—42no—
75C23×C43C2×C22⋊C411yescharacteristic
76C22×D43—21no—
77C22×D43—21no—
78C22×D43—22no—
79C22×D43—22no—
80C22×D43#10012yes—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43#11711yescharacteristic
89C2×C4×C43#11711yescharacteristic
90C2×C4×C43#12312yes—
91C2×C4×C43#12312yes—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43#10112yes—
100C2×Dic43#10414yes—
101C4×D43—24no—
102C4×D43—24no—
103C4×D43—44no—
104C4×D43—44no—
105C8×C43—44no—
106C43⋊C8—44no—
107#8722—431nomaximal, Sylow
108C22×C43#38111yescharacteristic
109C22×C43C2×#10011yescharacteristic
110C22×C43C2×#10111yescharacteristic
111C22×C43C2×#10412yes—
112C22×C43#42112yes—
113C2×D43—22no—
114C2×D43—24no—
115C2×D43—41no—
116C2×D43—42no—
117C2×D43—41no—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—82no—
123Dic43—22no—
124Dic43—24no—
125Dic43—82no—
126#2285—431no—
127#1749—432no—
128#1295—432no—
129#1295—431no—
130#1295D4311yescharacteristic, complemented
131C2×C43#152611yescharacteristic
132C2×C43#153012yes—
133C2×C43#153711yescharacteristic
134C2×C43#182111yescharacteristic
135C2×C43#182612yes—
136D43—42no—
137C2×#117—432no—
138C22×C42—431no—
139C2×C22⋊C8—862no—
140C2×#97—432no—
141C2×#97C2×D4312yes—
142#384—432no—
143#382—431no—
144#382C2×D4311yescharacteristic
145#380—862no—
146C4×C4⋊C4—862no—
147#336—862no—
148C43#872211yescharacteristic, complemented, Sylow
149C23×C4—431no—
150C23×C4—432no—
151C22×C8—22no—
152C22×C8—862no—
153#117—1724no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—862no—
156C2×C4⋊C4—862no—
157C2×C4⋊C4C4×D4312yes—
158C2×C22⋊C4—862no—
159C2×C42—431no—
160C2×C42—432no—
161C2×C42—862no—
162C2×C42—861no—
163C2×C42—861no—
164C2×C42—862no—
165C2×C42C22×D4311yescharacteristic
166C22⋊C8—868no—
167#97—22no—
168#97—22no—
169#97—862no—
170#97—862no—
171#95—22no—
172#95—862no—
173C24—431no—
174C22×C4—22no—
175C22×C4—431no—
176C22×C4—432no—
177C22×C4—862no—
178C22×C4—864no—
179C22×C4—862no—
180C22×C4—861no—
181C22×C4—861no—
182C22×C4—862no—
183C22×C4—862no—
184C22×C4—862no—
185C22×C4—1722no—
186C22×C4C2×C4×D4311yescharacteristic
187C22×C4D4×D4312yes—
188C2×C8—24no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—864no—
192C2×C8—1722no—
193C2×C8—1722no—
194C4⋊C4—42no—
195C4⋊C4—1722no—
196C4⋊C4—1724no—
197C4⋊C4—1724no—
198C22⋊C4—1724no—
199C42—861no—
200C42—861no—
201C42—862no—
202C42—862no—
203C42—1724no—
204C42#1062189812yes—
205C42#1062190011yescharacteristic
206C42#1062190211yescharacteristic
207C23—432no—
208C23—861no—
209C23—862no—
210C23—862no—
211C23—861no—
212C23C22⋊C4×D4311yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—432no—
221C2×C4—434no—
222C2×C4—864no—
223C2×C4—864no—
224C2×C4—861no—
225C2×C4—862no—
226C2×C4—861no—
227C2×C4—862no—
228C2×C4—1724no—
229C2×C4—1724no—
230C2×C4—1722no—
231C2×C4—1722no—
232C2×C4—1722no—
233C2×C4#1306328211yescharacteristic
234C2×C4#1306328311yescharacteristic
235C2×C4#1306330712yes—
236C2×C4#1306331012yes—
237C8—44no—
238C8—1724no—
239C22—864no—
240C22—862no—
241C22—1721no—
242C22—1721no—
243C22—1722no—
244C22#1458276111yescharacteristic
245C22#100×D4311yescharacteristic
246C22#101×D4311yescharacteristic
247C22#104×D4312yes—
248C22#1458291412yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—862no—
255C4—864no—
256C4—3442no—
257C2—1722no—
258C2#1913318811yescharacteristic
259C2#1913320412yes—
260C2#1913323111yescharacteristic
261C2#1913467411yescharacteristic
262C2#1913469312yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#8722
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #19132477C2semidirect
4. #19132476C2semidirect
5. C43×#1295C2semidirect
130. #1295D43semidirect
148. C43#8722semidirect

Maximal subgroups

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

subgroupindex
#191370012
#191343582
#191324772
#191324762
C43×#12952
#872243