Finite Group Databasebeta

← C2×#92304⋊C2 #14518336

Subgroups — C2×#92304⋊C2 #14518336

Order 1944.

541 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 51 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×#92306C211yesmaximal, characteristic, complemented
2C2×#92305C211yesmaximal, characteristic, complemented
3C2×#92304C211yesmaximal, characteristic, complemented
4#92304⋊C2C214yesmaximal, direct product factor
5C2×((C3⋊D3)⋊C3)⋊D3—31nomaximal
6C2×D9×C3⋊D3—31nomaximal
7C2×((C3⋊D3)⋊C9)⋊C2—31nomaximal
8C2×#6893C2211yescharacteristic, complemented
9#92306C2212yescomplemented
10#92305C2212yescomplemented
11#92304C2212yescomplemented
12C2×C3⋊#272D311yescharacteristic
13C2×C3⋊(C3⋊D9)D311yescharacteristic, complemented
14C2×C3⋊((C3⋊D3)⋊C3)—31no—
15C2×C9×C3⋊D3—31no—
16C2×C3×AGL(1,ℤ/9)—61no—
17C2×C3×(C3⋊D3)⋊C3—31no—
18C2×C32×D9—31no—
19((C3⋊D3)⋊C3)⋊D3—34no—
20D9×C3⋊D3—34no—
21C2×#4181D311yescharacteristic, complemented
22C2×#4169—31no—
23C2×#4169—61no—
24C2×(C3⋊D3)⋊C9—31no—
25C2×(C3⋊D3)⋊C9—61no—
26((C3⋊D3)⋊C9)⋊C2—34no—
27#6893C2311yescharacteristic, complemented, Sylow
28C2×#1113—91no—
29C2×D3×C3⋊D3—91no—
30C2×((C3⋊D3)⋊C3)⋊C2—93no—
31C2×D3×D9—91no—
32C2×D3×D9—93no—
33C2×C3×3−1+2—21no—
34C2×C3×H(3,𝔽3)C2×D311yescharacteristic
35C2×C32×C9C2×D311yescharacteristic, complemented
36C3⋊#272C2×D312yes—
37C3⋊(C3⋊D9)C2×D312yescomplemented
38C3⋊((C3⋊D3)⋊C3)—32no—
39C9×C3⋊D3—32no—
40C3×AGL(1,ℤ/9)—62no—
41C3×(C3⋊D3)⋊C3—32no—
42C32×D9—32no—
43C2×C32⋊C9—21no—
44C2×C32⋊C9—21no—
45C2×C32⋊C9—41no—
46C2×C32⋊C9C2×D311yescharacteristic, complemented
47#4181C2×D312yescomplemented
48#4169—32no—
49#4169—62no—
50(C3⋊D3)⋊C9—32no—
51(C3⋊D3)⋊C9—62no—
52C2×C3⋊(C3⋊D3)—31no—
53C2×C3×C3⋊D3—31no—
54C2×C3×C3⋊D3—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—61no—
57C2×C3×C3⋊D3—91no—
58C2×C32×D3—91no—
59#1113—94no—
60D3×C3⋊D3—94no—
61C2×#272—93no—
62C2×C3⋊D9—31no—
63C2×C3⋊D9—61no—
64C2×C3⋊D9—93no—
65C2×AGL(1,ℤ/9)—63no—
66C2×(C3⋊D3)⋊C3—33no—
67C2×(C3⋊D3)⋊C3—93no—
68C2×D3×C9—93no—
69C2×D3×C9—91no—
70C2×C3×D9—33no—
71C2×C3×D9—31no—
72C2×C3×D9—61no—
73((C3⋊D3)⋊C3)⋊C2—912no—
74D3×D9—94no—
75D3×D9—912no—
76C3×3−1+2—21no—
77C3×H(3,𝔽3)C22×D311yescharacteristic
78C32×C9C22×D311yescharacteristic, complemented
79C32⋊C9—21no—
80C32⋊C9—21no—
81C32⋊C9—41no—
82C32⋊C9C22×D311yescharacteristic, complemented
83C22×C3⋊D3—271no—
84C2×D32—273no—
85C2×D32—271no—
86C2×D32—271no—
87C2×D32—271no—
88C22×D9—271no—
89C2×C33—21no—
90C2×C33D3211yescharacteristic
91C2×C33D3211yescharacteristic
92C3⋊(C3⋊D3)—32no—
93C3×C3⋊D3—32no—
94C3×C3⋊D3—32no—
95C3×C3⋊D3—32no—
96C3×C3⋊D3—62no—
97C3×C3⋊D3—92no—
98C32×D3—92no—
99C2×3−1+2—63no—
100C2×H(3,𝔽3)—33no—
101C2×C3×C9—21no—
102C2×C3×C9—21no—
103C2×C3×C9—33no—
104C2×C3×C9—41no—
105C2×C3×C9D3211yescharacteristic
106#272—96no—
107C3⋊D9—32no—
108C3⋊D9—62no—
109C3⋊D9—96no—
110AGL(1,ℤ/9)—66no—
111(C3⋊D3)⋊C3—36no—
112(C3⋊D3)⋊C3—96no—
113D3×C9—96no—
114D3×C9—92no—
115C3×D9—36no—
116C3×D9—32no—
117C3×D9—62no—
118C22×C32—271no—
119C2×C3⋊D3—31no—
120C2×C3⋊D3—31no—
121C2×C3⋊D3—31no—
122C2×C3⋊D3—61no—
123C2×C3⋊D3—91no—
124C2×C3⋊D3—93no—
125C2×C3⋊D3—271no—
126C2×C3⋊D3—274no—
127C2×C3⋊D3—541no—
128C2×C3×D3—93no—
129C2×C3×D3—93no—
130C2×C3×D3—91no—
131C2×C3×D3—91no—
132C2×C3×D3—271no—
133C2×C3×D3—271no—
134C2×C3×D3—271no—
135C2×C3×D3—271no—
136C2×C3×D3—541no—
137C2×C3×D3—541no—
138D32—2712no—
139D32—274no—
140D32—274no—
141D32—274no—
142C22×C9—271no—
143C2×D9—31no—
144C2×D9—61no—
145C2×D9—271no—
146C2×D9—274no—
147C2×D9—541no—
148C33—21no—
149C33C2×D3211yescharacteristic
150C33C2×D3211yescharacteristic
1513−1+2—63no—
152H(3,𝔽3)—33no—
153C3×C9—21no—
154C3×C9—21no—
155C3×C9—33no—
156C3×C9—41no—
157C3×C9C2×D3211yescharacteristic
158C22×D3—811no—
159C22×D3—811no—
160C22×D3—813no—
161C22×D3—811no—
162C2×C32—31no—
163C2×C32—31no—
164C2×C32—31no—
165C2×C32—61no—
166C2×C32—61no—
167C2×C32—61no—
168C2×C32—61no—
169C2×C32—121no—
170C2×C32—272no—
171C2×C32((C3⋊D3)⋊C3)⋊C213yes—
172C2×C32#111311yescharacteristic
173C3⋊D3—32no—
174C3⋊D3—32no—
175C3⋊D3—32no—
176C3⋊D3—62no—
177C3⋊D3—92no—
178C3⋊D3—96no—
179C3⋊D3—272no—
180C3⋊D3—542no—
181C3×D3—96no—
182C3×D3—96no—
183C3×D3—92no—
184C3×D3—92no—
185C3×D3—272no—
186C3×D3—272no—
187C3×D3—272no—
188C3×D3—272no—
189C3×D3—542no—
190C3×D3—542no—
191C2×C9—31no—
192C2×C9—61no—
193C2×C9—61no—
194C2×C9—121no—
195C2×C9—272no—
196D9—32no—
197D9—62no—
198D9—272no—
199D9—542no—
200C22×C3—273no—
201C22×C3—271no—
202C22×C3—271no—
203C22×C3—811no—
204C2×D3—93no—
205C2×D3—91no—
206C2×D3—91no—
207C2×D3—271no—
208C2×D3—271no—
209C2×D3—271no—
210C2×D3—271no—
211C2×D3—541no—
212C2×D3—541no—
213C2×D3—813no—
214C2×D3—814no—
215C2×D3—814no—
216C2×D3—8112no—
217C2×D3—814no—
218C32—31no—
219C32—31no—
220C32—31no—
221C32—61no—
222C32—61no—
223C32—61no—
224C32—61no—
225C32—121no—
226C32C2×((C3⋊D3)⋊C3)⋊C213yes—
227C32C2×#111311yescharacteristic
228C9—31no—
229C9—61no—
230C9—61no—
231C9—121no—
232C23—2431noSylow
233C2×C3—21no—
234C2×C3—33no—
235C2×C3—91no—
236C2×C3—181no—
237C2×C3—276no—
238C2×C3—272no—
239C2×C3—272no—
240C2×C3—812no—
241C2×C3#6643211yescharacteristic
242C2×C3#4207⋊C211yescharacteristic
243D3—96no—
244D3—92no—
245D3—92no—
246D3—272no—
247D3—272no—
248D3—272no—
249D3—272no—
250D3—542no—
251D3—542no—
252D3—816no—
253C22—271no—
254C22—271no—
255C22—811no—
256C22—2434no—
257C3—21no—
258C3—33no—
259C3—91no—
260C3—181no—
261C3C2×#6643211yescharacteristic
262C3C2×#4207⋊C211yescharacteristic
263C2—272no—
264C2—272no—
265C2—812no—
266C2#92304⋊C211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#92304⋊C2
commutator, cosocle, hypocenter#6893C23
FrattiniC32C2×#1113
FittingC2×#6893C22
socleC2×C32#1113
LCSG ▷ #6893
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92306C2semidirect
2. C2×#92305C2semidirect
3. C2×#92304C2semidirect
4. #92304⋊C2C2direct (N × H)
8. C2×#6893C22semidirect
9. #92306C22semidirect
10. #92305C22semidirect
11. #92304C22semidirect
13. C2×C3⋊(C3⋊D9)D3semidirect
21. C2×#4181D3semidirect
27. #6893C23semidirect
35. C2×C32×C9C2×D3semidirect
37. C3⋊(C3⋊D9)C2×D3semidirect
46. C2×C32⋊C9C2×D3semidirect
47. #4181C2×D3semidirect
78. C32×C9C22×D3semidirect
82. C32⋊C9C22×D3semidirect
266. C2#92304⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#923062
C2×#923052
C2×#923042
#92304⋊C22
C2×((C3⋊D3)⋊C3)⋊D33
C2×D9×C3⋊D33
C2×((C3⋊D3)⋊C9)⋊C23