Finite Group Databasebeta

← C2×C3⋊#5932 #11923776

Subgroups — C2×C3⋊#5932 #11923776

Order 1152.

668 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 37 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×C3×#997C211yesmaximal, characteristic
2C3⋊#5932C212yesmaximal, direct product factor
3C2×#5932—33nomaximal
4C2×#5243—31nomaximal
5C3×#997C2211yescharacteristic
6C2×C3⋊SL(2,ℤ/4)—43nomaximal
7C2×C3×H(5,𝔽2)D311yescharacteristic
8C2×#997D313yes—
9#5932—36no—
10C2×#935—33no—
11#5243—36no—
12#5243—32no—
13C2×#834—33no—
14C22×C3×A4—43no—
15C2×C3×SL(2,𝔽3)—81no—
16C3⋊SL(2,ℤ/4)—46no—
17C2×#458—91noSylow
18C3×H(5,𝔽2)—33no—
19C3×H(5,𝔽2)—61no—
20C3×H(5,𝔽2)C2×D311yescharacteristic
21C2×C3×#41—61no—
22C22×C3×D4—33no—
23C23×Dic3—31no—
24#997C2×D313yes—
25C2×SL(2,ℤ/4)—129no—
26C2×#217—33no—
27C2×#217—63no—
28#935—36no—
29#935—36no—
30#935—63no—
31#935—63no—
32C2×Dic3⋊C4—63no—
33#834—36no—
34#834—36no—
35C2×C3×A4—46no—
36C2×C3×A4—43no—
37C2×C3⋊Dic3—161no—
38C3×SL(2,𝔽3)—81no—
39C2×H(5,𝔽2)C3⋊D311yescharacteristic
40C2×#123—93no—
41#458—96no—
42#458—92no—
43C2×#99—93no—
44C24×C3—31no—
45C24×C3S413yes—
46C22×A4—49no—
47C3×#41—61no—
48C3×#41—63no—
49C3×#41—63no—
50C3×#41—61no—
51C2×C3×Q8—21no—
52C2×C3×D4—33no—
53C2×C3×D4—33no—
54C2×C3×D4—33no—
55C2×C3×D4—33no—
56C2×C3×D4—63no—
57C2×C3×D4—66no—
58C22×C3×C4—33no—
59C22×Dic3—32no—
60C22×Dic3—63no—
61C22×Dic3—63no—
62C22×Dic3—63no—
63C2×SL(2,𝔽3)—83no—
64SL(2,ℤ/4)—1218no—
65#217—36no—
66#217—66no—
67#217—63no—
68#217—66no—
69Dic3⋊C4—66no—
70Dic3⋊C4—66no—
71C22×C32—161no—
72C3×A4—43no—
73C3⋊Dic3—162no—
74H(5,𝔽2)—33no—
75H(5,𝔽2)—61no—
76H(5,𝔽2)C2×C3⋊D311yescharacteristic
77C2×#41—61no—
78C22×D4—33no—
79C23×C4—91no—
80#123—96no—
81#123—96no—
82#123—183no—
83#123—183no—
84C2×C4⋊C4—183no—
85C2×C22⋊C4—93no—
86C2×C22⋊C4—183no—
87#99—96no—
88#99—96no—
89C23×C3—31no—
90C23×C3—33no—
91C23×C3—33no—
92C23×C3—33no—
93C23×C3—46no—
94C23×C3—122no—
95C23×C3C2×S413yes—
96C2×A4—418no—
97C2×A4—49no—
98C3×Q8—21no—
99C3×Q8—61no—
100C3×D4—63no—
101C3×D4—63no—
102C3×D4—66no—
103C2×C3×C4—33no—
104C2×C3×C4—33no—
105C2×C3×C4—63no—
106C2×C3×C4—61no—
107C2×Dic3—66no—
108C2×Dic3—66no—
109C2×Dic3—123no—
110C2×Dic3—126no—
111C2×Dic3—121no—
112C2×Dic3—483no—
113SL(2,𝔽3)—83no—
114C2×C32—162no—
115C2×C32—161no—
116C24—31no—
117C24C3⋊S413yes—
118#41—61no—
119#41—63no—
120#41—63no—
121#41—61no—
122C2×Q8—21no—
123C2×D4—33no—
124C2×D4—33no—
125C2×D4—33no—
126C2×D4—33no—
127C2×D4—63no—
128C2×D4—66no—
129C22×C4—33no—
130C22×C4—92no—
131C22×C4—183no—
132C22×C4—183no—
133C22×C4—183no—
134C4⋊C4—186no—
135C4⋊C4—186no—
136C22⋊C4—96no—
137C22⋊C4—183no—
138C22⋊C4—186no—
139C22⋊C4—186no—
140C22×C3—33no—
141C22×C3—33no—
142C22×C3—43no—
143C22×C3—66no—
144C22×C3—123no—
145C22×C3—121no—
146C22×C3—123no—
147C22×C3—163no—
148C22×C3#102011yescharacteristic
149A4—49no—
150C3×C4—61no—
151C3×C4—61no—
152Dic3—126no—
153Dic3—122no—
154Dic3—486no—
155C32—161noSylow
156C23—31no—
157C23—33no—
158C23—33no—
159C23—33no—
160C23—46no—
161C23—122no—
162C23C2×C3⋊S413yes—
163Q8—21no—
164Q8—61no—
165D4—63no—
166D4—63no—
167D4—66no—
168C2×C4—33no—
169C2×C4—33no—
170C2×C4—63no—
171C2×C4—61no—
172C2×C4—186no—
173C2×C4—186no—
174C2×C4—363no—
175C2×C4—366no—
176C2×C4—361no—
177C2×C3—63no—
178C2×C3—63no—
179C2×C3—163no—
180C2×C3—166no—
181C2×C3#593212yescomplemented
182C2×C3C2×#102011yescharacteristic
183C22—33no—
184C22—33no—
185C22—43no—
186C22—66no—
187C22—123no—
188C22—121no—
189C22—123no—
190C22C3⋊#102011yescharacteristic
191C4—61no—
192C4—61no—
193C4—366no—
194C4—362no—
195C3—163no—
196C3C2×#593211yescharacteristic, complemented
197C2—63no—
198C2—63no—
199C2C3⋊#593212yesdirect product factor
200C2C2×C3⋊#102011yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊#1020
commutator, cosocle, hypocenterC3×#997C22
FrattiniC2C2×C3⋊#1020
FittingC2×C3×H(5,𝔽2)D3
socleC22×C3#1020
prime radicalC2×C3×#997C2
LCSG ▷ C3×#997
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C3⋊#5932C2direct (N × H)
181. C2×C3#5932semidirect
196. C3C2×#5932semidirect
199. C2C3⋊#5932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9972
C3⋊#59322
C2×#59323
C2×#52433
C2×C3⋊SL(2,ℤ/4)4