Finite Group Databasebeta

← #11921086

Subgroups — #11921086

Order 1152.

374 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#64265C211yesmaximal, characteristic
2C3×#568⋊C3C211yesmaximal, characteristic
3#10593657C211yesmaximal, characteristic
4#73130—33nomaximal
5#72022—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64265—21no—
8#64265—21no—
9C2×C3⋊#226C412yescomplemented
10C3×#131⋊C3—21no—
11C3⋊GU(2,𝔽3)—21no—
12#63651—41nomaximal
13C2×#984—33no—
14C3×#568D311yescharacteristic
15C2×#951—31no—
16#568⋊C3D313yes—
17#5423—33no—
18#5236—31no—
19C2×#824—31no—
20#5120—31no—
21C3⋊#338—31no—
22#4559—31no—
23C2×#634—41no—
24C3×#41⋊C3D411yescharacteristic
25C3×#41⋊C3D411yescharacteristic
26C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
27C3⋊#226—22no—
28C32×M16—41no—
29#3748—41no—
30#1902—91noSylow
31C2×C3×#41C2×D311yescharacteristic
32C22×Dic6—31no—
33C2×#41⋊C3C2×D313yes—
34#984—63no—
35#984—63no—
36C2×#226—36no—
37C3×#131—21no—
38C3×#131—61no—
39C2×C3×M16—31no—
40C2×C3×M16—31no—
41#951—61no—
42#951—61no—
43#951—61no—
44#951—61no—
45C2×#216—32no—
46C2×#214—32no—
47#926—31no—
48C2×#208—31no—
49C2×#208—31no—
50#131⋊C3—23no—
51GU(2,𝔽3)—63no—
52#837—61no—
53#837—61no—
54#824—61no—
55#824—61no—
56#824—123no—
57#816—62no—
58C2×C32×C4—41no—
59C2×C3⋊Dic3—42no—
60#634—81no—
61#634—81no—
62C3×SL(2,𝔽3)C22⋊C411yescharacteristic
63C32×C8—81no—
64C3⋊(C3⋊C8)—81no—
65C2×#137—91no—
66#568C3⋊D311yescharacteristic
67#421—91no—
68#419—91no—
69C2×#101—91no—
70#344—91no—
71#338—91no—
72C3×#41—31no—
73C3×#41—31no—
74C3×#41D1211yescharacteristic
75C3×#41#6711yescharacteristic
76C2×C3×Q8C4×D311yescharacteristic
77C2×C3×D4—31no—
78C22×C3×C4—31no—
79C22×Dic3—61no—
80C2×Dic6—32no—
81C2×Dic6—61no—
82C2×Dic6—61no—
83C2×Dic6—61no—
84C2×Dic6—61no—
85C2×Dic6—61no—
86C2×Dic6—123no—
87#41⋊C3D1213yes—
88#41⋊C3#6713yes—
89C2×SL(2,𝔽3)C4×D313yes—
90#226—66no—
91C3×M16—31no—
92C3×M16—43no—
93C3×M16—61no—
94C3×M16—61no—
95C3×M16S411yescharacteristic
96C2×C3×C8—32no—
97C2×C3×C8—61no—
98#217—61no—
99#216—62no—
100#216—62no—
101#214—62no—
102#214—62no—
103C4⋊Dic3—61no—
104C4×Dic3—61no—
105#208—61no—
106#208—61no—
107#208—61no—
108#208—61no—
109#208—123no—
110C2×C3⋊C8—32no—
111C2×C3⋊C8—61no—
112C22×C32—41no—
113C32×C4—41no—
114C32×C4—41no—
115C3⋊Dic3—82no—
116C2×#41C2×C3⋊D311yescharacteristic
117C22×Q8—91no—
118#137—181no—
119#137—181no—
120#137—181no—
121#137—181no—
122C2×Q16—92no—
123C2×SD16—92no—
124#131—21no—
125#131—61no—
126C2×M16—31no—
127C2×M16—31no—
128C2×M16—91no—
129C2×M16—91no—
130#117—91no—
131#104—181no—
132#104—181no—
133#103—182no—
134#101—181no—
135#101—181no—
136C23×C3—31no—
137C3×Q8—31no—
138C3×Q8(C2×D3)⋊C411yescharacteristic
139C3×D4—31no—
140C3×D4—31no—
141C3×D4—61no—
142C2×C3×C4—31no—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—43no—
148C2×C3×C4C2×S411yescharacteristic
149C2×Dic3—62no—
150C2×Dic3—126no—
151C2×Dic3—121no—
152C2×Dic3—121no—
153C2×Dic3—121no—
154Dic6—62no—
155Dic6—62no—
156Dic6—121no—
157Dic6—121no—
158Dic6—243no—
159Dic6—243no—
160SL(2,𝔽3)(C2×D3)⋊C413yes—
161C3×C8—21no—
162C3×C8—61no—
163C3×C8—83no—
164C3⋊C8—62no—
165C3⋊C8—121no—
166C3⋊C8—243no—
167C2×C32—41no—
168C2×C32—81no—
169#41—31no—
170#41—31no—
171#41C4⋊(C3⋊D3)11yescharacteristic
172#41#63811yescharacteristic
173C2×Q8—92no—
174C2×Q8—181no—
175C2×Q8—181no—
176C2×Q8—181no—
177C2×Q8—181no—
178C2×Q8—181no—
179C2×Q8C4×C3⋊D311yescharacteristic
180C2×D4—31no—
181C22×C4—31no—
182C22×C4—181no—
183Q16—182no—
184Q16—182no—
185SD16—182no—
186SD16—182no—
187M16—31no—
188M16—61no—
189M16—61no—
190M16—181no—
191M16—181no—
192M16—181no—
193M16—181no—
194M16C3⋊S411yescharacteristic
195C2×C8—32no—
196C2×C8—61no—
197C2×C8—92no—
198C2×C8—181no—
199C4⋊C4—181no—
200C22⋊C4—181no—
201C42—181no—
202C22×C3—31no—
203C22×C3—31no—
204C22×C3—43no—
205C22×C3—121no—
206C22×C3C4×S411yescharacteristic
207C3×C4—31no—
208C3×C4—31no—
209C3×C4—43no—
210C3×C4—43no—
211C3×C4C4⋊S411yescharacteristic
212C3×C4GL(2,ℤ/4)11yescharacteristic
213Dic3—122no—
214Dic3—246no—
215Dic3—241no—
216C32—41noSylow
217C23—31no—
218Q8—31no—
219Q8—182no—
220Q8—182no—
221Q8—361no—
222Q8—361no—
223Q8#375211yescharacteristic
224D4—31no—
225D4—31no—
226D4—61no—
227C2×C4—31no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—31no—
232C2×C4—182no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4C2×C3⋊S411yescharacteristic
237C8—21no—
238C8—61no—
239C8—182no—
240C8—361no—
241C2×C3—21no—
242C2×C3—43no—
243C2×C3—61no—
244C2×C3—61no—
245C2×C3—83no—
246C2×C3(C2×S4)⋊C411yescharacteristic
247C22—31no—
248C22—31no—
249C22—121no—
250C22C4×C3⋊S411yescharacteristic
251C4—31no—
252C4—31no—
253C4—362no—
254C4—721no—
255C4C4⋊(C3⋊S4)11yescharacteristic
256C4#6426911yescharacteristic
257C3—43no—
258C3#7313011yescharacteristic, complemented
259C2—21no—
260C2—61no—
261C2—61no—
262C2#1059364711yescharacteristic
subgroupG/H
centerC2#10593647
commutatorC2×C3×SL(2,𝔽3)C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC3×#568D3
socleC2×C3(C2×S4)⋊C4
prime radical, cosocleC2×C3×#41⋊C3C22
hypercenterM16C3⋊S4
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
9. C2×C3⋊#226C4semidirect
258. C3#73130semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
C3×#568⋊C32
#105936572
#731303
#720223
#636514