Finite Group Databasebeta

← #11788802

Subgroups — #11788802

Order 1152.

471 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 116 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#10589918C211yesmaximal, characteristic
2#10589914C211yesmaximal, characteristic, complemented
3C2×C9×#101C211yesmaximal, characteristic, complemented
4#10588819C212yesmaximal
5#10588237C212yesmaximal, complemented
6#70105—31nomaximal
7C22×Q8×C9C2211yescharacteristic
8C2×#3697C2211yescharacteristic
9C2×C9×M16C2212yes—
10#63509C412yescomplemented
11#63508—22no—
12Q8×Dic9—24no—
13#63506C412yescomplemented
14#63491—22no—
15#63488—22no—
16#63488C2211yescharacteristic
17#63488C2212yes—
18C9×#101—22no—
19#63384—24no—
20#5816—31no—
21#5812—31no—
22C2×C3×#101D311yescharacteristic
23#5139—32no—
24#4557—32no—
25C2×Q8×C9—22no—
26C2×Q8×C9—22no—
27C2×Q8×C9C2×C412yes—
28C2×Q8×C9D412yes—
29C22×C4×C9D412yes—
30C22×C4×C9C2311yescharacteristic
31C2×#611—21no—
32#3697—22no—
33#3697—22no—
34C2×D36C2×C411yescharacteristic
35C2×C4×D9—21no—
36C2×Dic18C2×C411yescharacteristic
37C9×M16—22no—
38C9×M16—22no—
39C2×C8×C9—22no—
40#3676—22no—
41#3676—21no—
42(C2×D9)⋊C4—24no—
43C4⋊Dic9—24no—
44C4⋊Dic9—22no—
45C4⋊Dic9—21no—
46Dic9⋊C4—24no—
47C4×Dic9—24no—
48C4×Dic9C2×C412yes—
49C4×Dic9D414yes—
50#1912—91noSylow
51C22×C3×Q8C2×D311yescharacteristic
52C2×#235—31no—
53C2×C3×M16C2×D312yes—
54#947—32no—
55#946—62no—
56Q8×Dic3—64no—
57#944—32no—
58#929—62no—
59#926—32no—
60#926—31no—
61#926—62no—
62C3×#101—22no—
63#825—64no—
64C23×C9C2×D411yescharacteristic
65C22×D9—21no—
66Q8×C9—24no—
67Q8×C9—24no—
68C2×C4×C9—22no—
69C2×C4×C9—22no—
70C2×C4×C9C22⋊C414yes—
71C2×C4×C9C22×C411yescharacteristic
72C2×C4×C9C2×D412yes—
73C2×C4×C9C2×D411yescharacteristic
74C2×C4×C9#4112yes—
75#611—41no—
76#611—41no—
77C2×Dic9—22no—
78C2×Dic9—21no—
79C2×Dic9—24no—
80D36—22no—
81C4×D9—42no—
82Dic18—22no—
83C8×C9—42no—
84#536—91no—
85#519—91no—
86#421—92no—
87C2×#101D911yescharacteristic, complemented
88H(3,ℤ/4)—92no—
89C2×C3×Q8—22no—
90C2×C3×Q8—22no—
91C2×C3×Q8C4×D312yes—
92C2×C3×Q8#6712yes—
93C22×C3×C4D1212yes—
94C22×C3×C4C22×D311yescharacteristic
95C2×#67—61no—
96#235—62no—
97#235—62no—
98C2×D12—31no—
99C2×C4×D3—61no—
100C2×Dic6—31no—
101C3×M16—22no—
102C3×M16—22no—
103C2×C3×C8—22no—
104#217—62no—
105#217—61no—
106(C2×D3)⋊C4—64no—
107C4⋊Dic3—64no—
108C4⋊Dic3—62no—
109C4⋊Dic3—61no—
110Dic3⋊C4—64no—
111C4×Dic3—32no—
112C4×Dic3—34no—
113C4×Dic3—64no—
114C22×C9—41no—
115C22×C9C2×C22⋊C411yescharacteristic
116C22×C9#12011yescharacteristic
117C22×C9#12311yescharacteristic
118C2×D9—42no—
119C2×D9—41no—
120C4×C9—24no—
121C4×C9C4×D412yes—
122C4×C9#12112yes—
123Dic9—44no—
124Dic9—42no—
125Dic9—41no—
126C2×#41—91no—
127C22×Q8C2×D911yescharacteristic
128C2×M16C2×D912yes—
129C4⋊Q8—92no—
130#124—92no—
131#123—182no—
132C22⋊Q8—182no—
133C4×Q8—184no—
134#117—92no—
135#117—91no—
136#117—182no—
137#104—184no—
138#101—22no—
139C23×C3C2×D1211yescharacteristic
140C22×D3—61no—
141C3×Q8—24no—
142C3×Q8—24no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4(C2×D3)⋊C414yes—
146C2×C3×C4C2×C4×D311yescharacteristic
147C2×C3×C4D3×D412yes—
148C2×C3×C4#23712yes—
149C2×C3×C4C2×#6711yescharacteristic
150#67—121no—
151#67—121no—
152C2×Dic3—64no—
153C2×Dic3—62no—
154C2×Dic3—61no—
155D12—62no—
156C4×D3—122no—
157Dic6—62no—
158C3×C8—42no—
159C2×C9—21no—
160C2×C9—21no—
161C2×C9—21no—
162C2×C9#38611yescharacteristic
163D9—81no—
164#41—182no—
165#41—182no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—91no—
169C2×Q8C4×D912yes—
170C2×Q8#61112yes—
171C2×D4—91no—
172C2×D4—181no—
173C22×C4—181no—
174C22×C4D3612yes—
175C22×C4C22×D911yescharacteristic
176M16—22no—
177M16—22no—
178C2×C8—22no—
179C4⋊C4—184no—
180C4⋊C4—184no—
181C4⋊C4—182no—
182C4⋊C4—181no—
183C22⋊C4—182no—
184C22⋊C4—181no—
185C22⋊C4—184no—
186C42—92no—
187C42—94no—
188C42—184no—
189C22×C3—41no—
190C22×C3#88211yescharacteristic
191C22×C3#88611yescharacteristic
192C22×C3C2×(C2×D3)⋊C411yescharacteristic
193C2×D3—122no—
194C2×D3—121no—
195C3×C4—24no—
196C3×C4#67⋊C412yes—
197C3×C4#93912yes—
198Dic3—124no—
199Dic3—122no—
200Dic3—121no—
201C9#191211yescharacteristic, complemented, Sylow
202C23—181no—
203C23C2×D3611yescharacteristic
204Q8—24no—
205Q8—24no—
206Q8—182no—
207D4—182no—
208D4—361no—
209D4—361no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—182no—
213C2×C4—181no—
214C2×C4—184no—
215C2×C4—362no—
216C2×C4(C2×D9)⋊C414yes—
217C2×C4C2×C4×D911yescharacteristic
218C2×C4D4×D912yes—
219C2×C4#369912yes—
220C2×C4C2×#61111yescharacteristic
221C8—42no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3#495811yescharacteristic
226D3—241no—
227C22—41no—
228C22—362no—
229C22—361no—
230C22#6344411yescharacteristic
231C22#6344811yescharacteristic
232C22C2×(C2×D9)⋊C411yescharacteristic
233C4—24no—
234C4—364no—
235C4—362no—
236C4—361no—
237C4#611⋊C412yes—
238C4#6350112yes—
239C3#7010511yescharacteristic
240C2—21no—
241C2—21no—
242C2—21no—
243C2—721no—
244C2#1058863811yescharacteristic
subgroupG/H
centerC2#10588638
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#101C2
socleC2×C3#4958
prime radicalC2×#3697C22
cosocleC22×C4×C9C23
hypercenterC2×#101D9
hypocenterC9#1912
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #10589914C2semidirect
3. C2×C9×#101C2semidirect
5. #10588237C2semidirect
10. #63509C4semidirect
13. #63506C4semidirect
87. C2×#101D9semidirect
201. C9#1912semidirect

Maximal subgroups

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

subgroupindex
#105899182
#105899142
C2×C9×#1012
#105888192
#105882372
#701053