Finite Group Databasebeta

← C4×#92344 #14517747

Subgroups — C4×#92344 #14517747

Order 1944.

471 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 98 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×#92344C211yesmaximal, characteristic
2C4×#6908C211yesmaximal, characteristic, complemented
3#11757648C211yesmaximal, characteristic, complemented
4C4×#4207—33nomaximal
5C3×C4×C3⋊D9—31nomaximal
6C4×#733⋊C2—32nomaximal
7C4×#4185—31nomaximal
8C4×#4184—33nomaximal
9C4×#4183—33nomaximal
10C2×#6908C2211yescharacteristic
11#92344C412yesdirect product factor
12C2×#4207—33no—
13C2×C3×C3⋊D9—31no—
14C4×#737D313yescomplemented
15C32×C4×C9D311yescharacteristic, complemented
16#66409—33no—
17C3×C3⋊Dic9—31no—
18C2×#733⋊C2—32no—
19C2×#4185—31no—
20C2×#4184—33no—
21C2×#4183—33no—
22C4×#733D312yescomplemented
23C4×#732D311yescharacteristic, complemented
24C4×#731D313yescomplemented
25C4×AΣL(1,𝔽27)D313yescomplemented
26#733⋊C4—32no—
27#66332—31no—
28#66331—33no—
29#66330—33no—
30#6908C2×C411yescharacteristic, complemented, Sylow
31C3×C4×C3⋊D3—91no—
32C4×C3⋊D9—31no—
33C4×C3⋊D9—33no—
34C4×AGL(1,ℤ/9)—96no—
35C4×(C3⋊D3)⋊C3—93no—
36C3×C4×D9—91no—
37C3×C4×D9—91no—
38C3×C4×D9—91no—
39C2×#737C2×D313yes—
40C2×C32×C9C2×D311yescharacteristic
41#4207—36no—
42C3×C3⋊D9—32no—
43C2×#733C2×D312yes—
44C2×#732C2×D311yescharacteristic
45C2×#731C2×D313yes—
46C2×AΣL(1,𝔽27)C2×D313yes—
47#733⋊C2—34no—
48#4185—32no—
49#4184—36no—
50#4183—36no—
51C2×C3×C3⋊D3—91no—
52C33×C4C3⋊D311yescharacteristic
53C3×C3⋊Dic3—91no—
54C2×C3⋊D9—31no—
55C2×C3⋊D9—33no—
56C2×AGL(1,ℤ/9)—96no—
57C2×(C3⋊D3)⋊C3—93no—
58C2×C3×D9—91no—
59C2×C3×D9—91no—
60C2×C3×D9—91no—
61C4×3−1+2—63no—
62C4×3−1+2C3⋊D316yes—
63C4×H(3,𝔽3)C3⋊D313yes—
64C3×C4×C9—31no—
65C3×C4×C9—33no—
66C3×C4×C9—61no—
67C3×C4×C9C3⋊D311yescharacteristic
68C3×C4×C9C3⋊D311yescharacteristic
69C3×C4×C9C3⋊D311yescharacteristic
70C3⋊Dic9—31no—
71C3⋊Dic9—33no—
723−1+2⋊C4—96no—
73(C3⋊Dic3)⋊C3—93no—
74C3×Dic9—91no—
75C3×Dic9—91no—
76C3×Dic9—91no—
77#737C4×D313yescomplemented
78C32×C9C4×D311yescharacteristic, complemented
79#733C4×D312yescomplemented
80#732C4×D311yescharacteristic, complemented
81#731C4×D313yescomplemented
82AΣL(1,𝔽27)C4×D313yescomplemented
83C4×C3⋊D3—91no—
84C4×C3⋊D3—93no—
85C3×C4×D3—273no—
86C3×C4×D3—271no—
87C4×D9—91no—
88C4×D9—91no—
89C4×D9—96no—
90C4×D9—91no—
91C2×C33C2×C3⋊D311yescharacteristic
92C3×C3⋊D3—92no—
93C2×3−1+2—63no—
94C2×3−1+2C2×C3⋊D316yes—
95C2×H(3,𝔽3)C2×C3⋊D313yes—
96C2×C3×C9—31no—
97C2×C3×C9—33no—
98C2×C3×C9—61no—
99C2×C3×C9C2×C3⋊D311yescharacteristic
100C2×C3×C9C2×C3⋊D311yescharacteristic
101C2×C3×C9C2×C3⋊D311yescharacteristic
102C3⋊D9—32no—
103C3⋊D9—36no—
104AGL(1,ℤ/9)—912no—
105(C3⋊D3)⋊C3—96no—
106C3×D9—92no—
107C3×D9—92no—
108C3×D9—92no—
109C2×C3⋊D3—91no—
110C2×C3⋊D3—93no—
111C2×C3×D3—273no—
112C2×C3×D3—271no—
113C32×C4—31no—
114C32×C4—33no—
115C32×C4—33no—
116C32×C4C3⋊(C3⋊D3)11yescharacteristic
117C3⋊Dic3—91no—
118C3⋊Dic3—93no—
119C3×Dic3—273no—
120C3×Dic3—271no—
121C2×D9—91no—
122C2×D9—91no—
123C2×D9—96no—
124C2×D9—91no—
125C4×C9—21no—
126C4×C9—31no—
127C4×C9—31no—
128C4×C9—36no—
129C4×C9#27211yescharacteristic
130Dic9—91no—
131Dic9—91no—
132Dic9—96no—
133Dic9—91no—
134C33C4×C3⋊D311yescharacteristic
1353−1+2—63no—
1363−1+2C4×C3⋊D316yes—
137H(3,𝔽3)C4×C3⋊D313yes—
138C3×C9—31no—
139C3×C9—33no—
140C3×C9—61no—
141C3×C9C4×C3⋊D311yescharacteristic
142C3×C9C4×C3⋊D311yescharacteristic
143C3×C9C4×C3⋊D311yescharacteristic
144C2×C3×C4—811no—
145C4×D3—273no—
146C4×D3—271no—
147C4×D3—813no—
148C2×C32—31no—
149C2×C32—33no—
150C2×C32—33no—
151C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
152C3⋊D3—92no—
153C3⋊D3—96no—
154C3×D3—276no—
155C3×D3—272no—
156C2×C9—21no—
157C2×C9—31no—
158C2×C9—31no—
159C2×C9—36no—
160C2×C9C2×#27211yescharacteristic
161D9—92no—
162D9—92no—
163D9—912no—
164D9—92no—
165C22×C3—811no—
166C2×D3—273no—
167C2×D3—271no—
168C2×D3—813no—
169C3×C4—33no—
170C3×C4—31no—
171C3×C4—93no—
172C3×C4—811no—
173C3×C4C3⋊#27211yescharacteristic
174Dic3—273no—
175Dic3—271no—
176Dic3—813no—
177C32—33no—
178C32—31no—
179C32—33no—
180C32C4×C3⋊(C3⋊D3)11yescharacteristic
181C9—21no—
182C9—31no—
183C9—31no—
184C9—36no—
185C9C4×#27211yescharacteristic
186C2×C4—811noSylow
187C2×C3—33no—
188C2×C3—31no—
189C2×C3—93no—
190C2×C3—812no—
191C2×C3C2×C3⋊#27211yescharacteristic
192D3—276no—
193D3—272no—
194D3—816no—
195C22—811no—
196C4—811no—
197C4#9234411yescharacteristic, direct product factor
198C3—33no—
199C3—31no—
200C3—93no—
201C3C4×C3⋊#27211yescharacteristic
202C2—812no—
203C2C2×#9234411yescharacteristic
subgroupG/H
center, hypercenterC4#92344
commutator, hypocenter#6908C2×C4
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC4×#6908C2
socleC2×C3C2×C3⋊#272
prime radicalC2×#92344C2
cosocleC2×#6908C22
LCSG ▷ #6908
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×#6908C2semidirect
3. #11757648C2semidirect
11. #92344C4direct (N × H)
14. C4×#737D3semidirect
15. C32×C4×C9D3semidirect
22. C4×#733D3semidirect
23. C4×#732D3semidirect
24. C4×#731D3semidirect
25. C4×AΣL(1,𝔽27)D3semidirect
30. #6908C2×C4semidirect
77. #737C4×D3semidirect
78. C32×C9C4×D3semidirect
79. #733C4×D3semidirect
80. #732C4×D3semidirect
81. #731C4×D3semidirect
82. AΣL(1,𝔽27)C4×D3semidirect
197. C4#92344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#923442
C4×#69082
#117576482
C4×#42073
C3×C4×C3⋊D93
C4×#733⋊C23
C4×#41853
C4×#41843
C4×#41833