Finite Group Databasebeta

← #25005895

Subgroups — #25005895

Order 11008.

392 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 119 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#19132919C212yesmaximal
2#19132539C212yesmaximal
3#19132529C212yesmaximal
4C43×#2327C211yesmaximal, characteristic
5#14582952—22no—
6#14582625—22no—
7#14582625C2214yes—
8C2×C4⋊Q8×C43C411yescharacteristic
9C2×C4×Q8×C43C411yescharacteristic
10C2×C4×Q8×C43C2211yescharacteristic
11C43×#391C411yescharacteristic
12C43×#391C2211yescharacteristic
13C43×#387—22no—
14C43×#387—22no—
15C43×#382C2211yescharacteristic
16C43×#376C411yescharacteristic
17C4⋊(C43⋊C8)—42no—
18C22⋊(C43⋊C8)—24no—
19C4×C43⋊C8—42no—
20C22×Q8×C43C2×C411yescharacteristic
21C22×Q8×C43C2×C411yescharacteristic
22C4⋊Q8×C43—22no—
23C4⋊Q8×C43C814yescomplemented
24C4×Q8×C43—42no—
25C4×Q8×C43—42no—
26C2×C4⋊C4×C43—22no—
27C2×C4⋊C4×C43—21no—
28C2×C4⋊C4×C43C2×C411yescharacteristic
29C2×C4⋊C4×C43D412yes—
30C2×C4⋊C4×C43C2311yescharacteristic
31C2×C42×C43—21no—
32C2×C42×C43C2×C411yescharacteristic
33C2×C42×C43C2×C411yescharacteristic
34C2×C42×C43C2×C411yescharacteristic
35C2×C42×C43D412yes—
36#95×C43—21no—
37#95×C43—21no—
38#95×C43—22no—
39#95×C43—22no—
40#95×C43—22no—
41C2×Q8×C43—21no—
42C2×Q8×C43—41no—
43C2×Q8×C43—41no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43C2×C812yes—
47C2×Q8×C43C2×C812yes—
48C2×Q8×C43M1612yes—
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43C22⋊C412yes—
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D412yes—
58C4⋊C4×C43—28no—
59C4⋊C4×C43—42no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—42no—
63C42×C43—22no—
64C42×C43—22no—
65C42×C43—22no—
66C42×C43—21no—
67C42×C43—41no—
68C42×C43—42no—
69C42×C43C2×C812yes—
70C2×C43⋊C8—44no—
71C23×C43C2×C22⋊C411yescharacteristic
72Q8×C43—42no—
73Q8×C43—42no—
74Q8×C43—42no—
75Q8×C43—42no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43C22⋊C814yes—
97C2×C4×C43#9912yes—
98C2×C4×C43C22×C811yescharacteristic
99C2×C4×C43C2×M1611yescharacteristic
100C43⋊C8—84no—
101#11482—431nomaximal, Sylow
102C22×C43—21no—
103C22×C43—21no—
104C22×C43C2×C22⋊C811yescharacteristic
105C22×C43C2×#9911yescharacteristic
106C22×C43#41311yescharacteristic
107C4×C43—22no—
108C4×C43—24no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—42no—
112C4×C43—42no—
113C4×C43—41no—
114C4×C43—42no—
115C4×C43—81no—
116C4×C43—81no—
117#2327D4311yescharacteristic
118#1461—432no—
119#1324—432no—
120#1319—432no—
121C2×C43—21no—
122C2×C43—21no—
123C2×C43#145911yescharacteristic
124C2×C43#212911yescharacteristic
125C2×C43#213311yescharacteristic
126C2×C4⋊Q8Dic4311yescharacteristic
127C2×C4×Q8Dic4311yescharacteristic
128C2×C4×Q8C2×D4311yescharacteristic
129#431—862no—
130#391Dic4311yescharacteristic
131#391C2×D4311yescharacteristic
132#387—22no—
133#387—22no—
134#382C2×D4311yescharacteristic
135#376Dic4311yescharacteristic
136#324—434no—
137#324—862no—
138C43#1148211yescharacteristic, complemented, Sylow
139C22×Q8C2×Dic4311yescharacteristic
140C22×Q8C2×Dic4311yescharacteristic
141C4⋊Q8—22no—
142C4⋊Q8C43⋊C814yescomplemented
143C4×Q8—42no—
144C4×Q8—42no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4C2×Dic4311yescharacteristic
148C2×C4⋊C4C22⋊D4312yes—
149C2×C4⋊C4C22×D4311yescharacteristic
150C2×C42—21no—
151C2×C42C2×Dic4311yescharacteristic
152C2×C42C2×Dic4311yescharacteristic
153C2×C42C2×Dic4311yescharacteristic
154C2×C42C22⋊D4312yes—
155C4⋊C8—1722no—
156C22⋊C8—864no—
157C4×C8—1722no—
158#95—21no—
159#95—22no—
160#95—21no—
161#95—22no—
162#95—22no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8C2×C43⋊C812yes—
169C2×Q8C2×C43⋊C812yes—
170C2×Q8#1062187712yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4C22⋊Dic4312yes—
176C22×C4C22⋊Dic4311yescharacteristic
177C22×C4C22⋊Dic4311yescharacteristic
178C22×C4C22×Dic4311yescharacteristic
179C22×C4C2×C22⋊D4312yes—
180C2×C8—1724no—
181C4⋊C4—28no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C42—22no—
187C42—22no—
188C42—22no—
189C42—21no—
190C42—41no—
191C42—42no—
192C42C2×C43⋊C812yes—
193C23C2×C22⋊Dic4311yescharacteristic
194Q8—42no—
195Q8—42no—
196Q8—42no—
197Q8—42no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C22⋊(C43⋊C8)14yes—
219C2×C4#1306324012yes—
220C2×C4C22×C43⋊C811yescharacteristic
221C2×C4C2×#1062187711yescharacteristic
222C8—3444no—
223C22—21no—
224C22—21no—
225C22C2×C22⋊(C43⋊C8)11yescharacteristic
226C22C2×#1306324011yescharacteristic
227C22#1458288311yescharacteristic
228C4—22no—
229C4—24no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—42no—
234C4—41no—
235C4—42no—
236C4—81no—
237C4—81no—
238C2—21no—
239C2—21no—
240C2#1913291311yescharacteristic
241C2#1913627011yescharacteristic
242C2#1913628411yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2327C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2327D43
hypocenterC43#11482
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2327

Complements

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

NH ≅ G/Ntype
23. C4⋊Q8×C43C8semidirect
138. C43#11482semidirect
142. C4⋊Q8C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
#191329192
#191325392
#191325292
C43×#23272
#1148243