Finite Group Databasebeta

← #11920233

Subgroups — #11920233

Order 1152.

354 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C4×#41⋊C9C211yesmaximal, characteristic
2#10589526C212yesmaximal
3#10589493C211yesmaximal, characteristic, complemented
4#10589491C212yesmaximal, complemented
5#10589488C211yesmaximal, characteristic, complemented
6#82507—31nomaximal
7C2×#41⋊C9C2211yescharacteristic
8C4×Dic18—41nomaximal
9C4×Q8⋊C9C2211yescharacteristic
10C4×Q8⋊C9C2211yescharacteristic
11#63421C2212yes—
12#63421C2212yes—
13C3×C4×#41D311yescharacteristic
14#5470—31no—
15#5233—32no—
16#5022—32no—
17#5021—31no—
18#5020—31no—
19#5009—32no—
20#5008—31no—
21#5007—31no—
22#4998—32no—
23C2×C4⋊(C3⋊C8)—31no—
24C2×Dic18—41no—
25#41⋊C9Q812yescomplemented
26C2×Q8⋊C9C2311yescharacteristic
27C42×C9—41no—
28C4⋊Dic9—41no—
29Dic9⋊C4—42no—
30C4×Dic9—42no—
31#3076—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C3×C4×Q8C2×D311yescharacteristic
34C3×C4×Q8C2×D311yescharacteristic
35C3×C4×D4—31no—
36C3×C4×D4—31no—
37C3×#117—31no—
38C2×C3×C42—31no—
39#926—32no—
40#924—61no—
41#924—61no—
42C22×C3⋊C8—32no—
43#870—32no—
44#869—31no—
45#869—31no—
46C4×Dic6—61no—
47C4×Dic6—61no—
48#835—32no—
49#835—32no—
50#832—32no—
51#832—32no—
52#808—32no—
53#808—32no—
54#807—32no—
55#807—32no—
56C4⋊(C3⋊C8)—31no—
57C4⋊(C3⋊C8)—31no—
58C4⋊(C3⋊C8)—32no—
59C2×C4×C9—41no—
60C2×C4×C9—41no—
61C2×C4×C9—41no—
62C2×Dic9—42no—
63C2×Dic9—42no—
64Dic18—44no—
65Q8⋊C9C2×Q811yescharacteristic
66#533—91no—
67C4×#41D911yescharacteristic
68#479—92no—
69#478—92no—
70#477—91no—
71#476—91no—
72#475—91no—
73#474—91no—
74#427—92no—
75C2×C4⋊C8—91no—
76#416—92no—
77C3×#41—32no—
78C3×#41Dic612yes—
79C2×C3×Q8C22×D311yescharacteristic
80C2×C3×D4—31no—
81C22×C3×C4—31no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C2×Dic6—61no—
85C2×Dic6—61no—
86C3×C4⋊C4—31no—
87C3×C4⋊C4—31no—
88C3×C22⋊C4—61no—
89C3×C42—31no—
90C3×C42—31no—
91C3×C42—31no—
92C3×C42S411yescharacteristic
93#217—62no—
94C4⋊Dic3—32no—
95C4⋊Dic3—32no—
96C4⋊Dic3—61no—
97C4⋊Dic3—61no—
98Dic3⋊C4—62no—
99Dic3⋊C4—62no—
100C4×Dic3—62no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—64no—
104C22×C9—41no—
105C4×C9—42no—
106C4×C9—42no—
107C4×C9—81no—
108Dic9—44no—
109Dic9—82no—
110C2×#41C2×D911yescharacteristic
111C22×C8—92no—
112C4⋊Q8—91no—
113C4⋊Q8—91no—
114#125—92no—
115C22⋊Q8—181no—
116C22⋊Q8—181no—
117C4×Q8—181no—
118C4×Q8—181no—
119C4×Q8C2×D911yescharacteristic
120C4×Q8C2×D911yescharacteristic
121C4×D4—31no—
122C4×D4—31no—
123#117—31no—
124#117—92no—
125C2×C42—31no—
126#107—92no—
127#107—92no—
128#106—92no—
129#106—92no—
130C4⋊C8—91no—
131C4⋊C8—91no—
132C4⋊C8—92no—
133#103—92no—
134#103—92no—
135#102—92no—
136#102—92no—
137C23×C3—31no—
138C3×Q8—31no—
139C3×Q8C2×Dic611yescharacteristic
140C3×D4—32no—
141C3×D4—61no—
142C2×C3×C4—31no—
143C2×C3×C4—32no—
144C2×C3×C4—32no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—62no—
148C2×C3×C4—121no—
149C2×C3×C4C2×S411yescharacteristic
150C2×C3×C4C2×S411yescharacteristic
151C2×C3×C4C2×S411yescharacteristic
152C2×Dic3—62no—
153C2×Dic3—62no—
154Dic6—122no—
155Dic6—122no—
156C3⋊C8—62no—
157C3⋊C8—62no—
158C2×C9—41no—
159C2×C9—41no—
160C2×C9—41no—
161#41—32no—
162#41Dic1812yescomplemented
163C2×Q8—181no—
164C2×Q8—181no—
165C2×Q8C22×D911yescharacteristic
166C2×D4—31no—
167C22×C4—31no—
168C22×C4—31no—
169C22×C4—31no—
170C2×C8—92no—
171C2×C8—92no—
172C2×C8—184no—
173C4⋊C4—31no—
174C4⋊C4—31no—
175C4⋊C4—92no—
176C4⋊C4—92no—
177C4⋊C4—182no—
178C4⋊C4—181no—
179C4⋊C4—182no—
180C4⋊C4—181no—
181C22⋊C4—61no—
182C22⋊C4—182no—
183C42—31no—
184C42—31no—
185C42—31no—
186C42—182no—
187C42(C22⋊C9)⋊C211yescharacteristic
188C22×C3—32no—
189C22×C3—61no—
190C22×C3—61no—
191C22×C3C22×S411yescharacteristic
192C3×C4—21no—
193C3×C4—31no—
194C3×C4—31no—
195C3×C4—61no—
196C3×C4—61no—
197C3×C4A4⋊Q812yes—
198C3×C4#98512yes—
199Dic3—122no—
200Dic3—122no—
201C9—41noSylow
202C23—31no—
203Q8—31no—
204Q8—362no—
205Q8—362no—
206Q8C2×Dic1811yescharacteristic
207D4—32no—
208D4—61no—
209C2×C4—31no—
210C2×C4—32no—
211C2×C4—32no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—62no—
215C2×C4—121no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
219C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
220C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
221C8—182no—
222C8—182no—
223C2×C3—62no—
224C2×C3C2×A4⋊Q811yescharacteristic
225C2×C3C2×#98511yescharacteristic
226C2×C3#592311yescharacteristic
227C22—32no—
228C22—61no—
229C22—61no—
230C22C22×(C22⋊C9)⋊C211yescharacteristic
231C4—21no—
232C4—31no—
233C4—31no—
234C4—61no—
235C4—61no—
236C4—362no—
237C4—362no—
238C4(C22⋊C9)⋊Q812yes—
239C4#6369112yes—
240C3#8533411yescharacteristic
241C2—62no—
242C2C2×(C22⋊C9)⋊Q811yescharacteristic
243C2C2×#6369111yescharacteristic
244C2#1059309811yescharacteristic
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
prime radicalC2×C3×#41C2×D3
hypercenterC42(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×Q8
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10589493C2semidirect
4. #10589491C2semidirect
5. #10589488C2semidirect
25. #41⋊C9Q8semidirect
162. #41Dic18semidirect

Maximal subgroups

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

subgroupindex
C4×#41⋊C92
#105895262
#105894932
#105894912
#105894882
#825073
C4×Dic184