Finite Group Databasebeta

← C2×#11757749 #14518335

Subgroups — C2×#11757749 #14518335

Order 1944.

1038 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 57 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×#92301C211yesmaximal, characteristic, complemented
2C2×#92300C212yesmaximal, complemented
3#11757749C214yesmaximal, direct product factor
4C2×C3⋊D32—31nomaximal
5C2×((C3⋊D3)⋊C3)⋊D3—32nomaximal
6C2×C32⋊H(3,𝔽3)C2211yescharacteristic, complemented
7#92301C2212yescomplemented
8#92300C2214yescomplemented
9C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic, complemented
10C2×C32×C3⋊D3—32no—
11C3⋊D32—34no—
12C2×C3⋊#272D312yescomplemented
13C2×C3⋊((C3⋊D3)⋊C3)—32no—
14C2×C3⋊((C3⋊D3)⋊C3)—61no—
15C2×C3×(C3⋊D3)⋊C3—32no—
16C2×C3×(C3⋊D3)⋊C3—62no—
17((C3⋊D3)⋊C3)⋊D3—38no—
18C32⋊H(3,𝔽3)C2311yescharacteristic, complemented, Sylow
19C2×#1113—91no—
20C2×D3×C3⋊D3—92no—
21C2×D3×C3⋊D3—96no—
22C2×((C3⋊D3)⋊C3)⋊C2—96no—
23C2×C34C2×D311yescharacteristic, complemented
24C3⋊(C3⋊(C3⋊D3))C2×D312yescomplemented
25C32×C3⋊D3—34no—
26C2×C3×H(3,𝔽3)—22no—
27C2×C3×H(3,𝔽3)—21no—
28C2×C3×H(3,𝔽3)—41no—
29C2×C3×H(3,𝔽3)C2×D312yescomplemented
30C3⋊#272C2×D314yescomplemented
31C3⋊((C3⋊D3)⋊C3)—34no—
32C3⋊((C3⋊D3)⋊C3)—62no—
33C3×(C3⋊D3)⋊C3—34no—
34C3×(C3⋊D3)⋊C3—64no—
35C2×C3⋊(C3⋊D3)—32no—
36C2×C3⋊(C3⋊D3)—61no—
37C2×C3⋊(C3⋊D3)—96no—
38C2×C3⋊(C3⋊D3)—183no—
39C2×C3×C3⋊D3—36no—
40C2×C3×C3⋊D3—32no—
41C2×C3×C3⋊D3—32no—
42C2×C3×C3⋊D3—62no—
43C2×C3×C3⋊D3—91no—
44C2×C32×D3—96no—
45C2×C32×D3—92no—
46#1113—94no—
47D3×C3⋊D3—98no—
48D3×C3⋊D3—924no—
49C2×#272—96no—
50C2×(C3⋊D3)⋊C3—36no—
51C2×(C3⋊D3)⋊C3—66no—
52C2×(C3⋊D3)⋊C3—96no—
53C2×(C3⋊D3)⋊C3—183no—
54((C3⋊D3)⋊C3)⋊C2—924no—
55C34C22×D311yescharacteristic, complemented
56C3×H(3,𝔽3)—22no—
57C3×H(3,𝔽3)—21no—
58C3×H(3,𝔽3)—41no—
59C3×H(3,𝔽3)C22×D312yescomplemented
60C22×C3⋊D3—272no—
61C2×D32—276no—
62C2×D32—271no—
63C2×D32—279no—
64C2×D32—272no—
65C2×C33—21no—
66C2×C33—22no—
67C2×C33—36no—
68C2×C33—41no—
69C2×C33—63no—
70C2×C33D3212yes—
71C2×C33D3211yescharacteristic, complemented
72C3⋊(C3⋊D3)—34no—
73C3⋊(C3⋊D3)—62no—
74C3⋊(C3⋊D3)—912no—
75C3⋊(C3⋊D3)—186no—
76C3×C3⋊D3—312no—
77C3×C3⋊D3—34no—
78C3×C3⋊D3—34no—
79C3×C3⋊D3—64no—
80C3×C3⋊D3—92no—
81C32×D3—912no—
82C32×D3—94no—
83C2×H(3,𝔽3)—36no—
84C2×H(3,𝔽3)—63no—
85C2×H(3,𝔽3)—66no—
86C2×H(3,𝔽3)—123no—
87#272—912no—
88(C3⋊D3)⋊C3—312no—
89(C3⋊D3)⋊C3—612no—
90(C3⋊D3)⋊C3—912no—
91(C3⋊D3)⋊C3—186no—
92C22×C32—272no—
93C2×C3⋊D3—32no—
94C2×C3⋊D3—32no—
95C2×C3⋊D3—62no—
96C2×C3⋊D3—91no—
97C2×C3⋊D3—96no—
98C2×C3⋊D3—183no—
99C2×C3⋊D3—272no—
100C2×C3⋊D3—278no—
101C2×C3⋊D3—279no—
102C2×C3⋊D3—542no—
103C2×C3⋊D3—542no—
104C2×C3⋊D3—541no—
105C2×C3⋊D3—549no—
106C2×C3×D3—918no—
107C2×C3×D3—96no—
108C2×C3×D3—96no—
109C2×C3×D3—92no—
110C2×C3×D3—272no—
111C2×C3×D3—272no—
112C2×C3×D3—542no—
113C2×C3×D3—541no—
114D32—2724no—
115D32—274no—
116D32—2736no—
117D32—278no—
118C33—21no—
119C33—22no—
120C33—36no—
121C33—41no—
122C33—63no—
123C33C2×D3212yes—
124C33C2×D3211yescharacteristic, complemented
125H(3,𝔽3)—36no—
126H(3,𝔽3)—63no—
127H(3,𝔽3)—66no—
128H(3,𝔽3)—123no—
129C22×D3—812no—
130C22×D3—816no—
131C22×D3—811no—
132C2×C32—23no—
133C2×C32—32no—
134C2×C32—39no—
135C2×C32—32no—
136C2×C32—62no—
137C2×C32—61no—
138C2×C32—61no—
139C2×C32—69no—
140C2×C32—62no—
141C2×C32—62no—
142C2×C32—62no—
143C2×C32—122no—
144C2×C32—121no—
145C2×C32—121no—
146C2×C32—122no—
147C2×C32—274no—
148C2×C32((C3⋊D3)⋊C3)⋊C216yescomplemented
149C2×C32#111311yescharacteristic
150C3⋊D3—34no—
151C3⋊D3—34no—
152C3⋊D3—64no—
153C3⋊D3—92no—
154C3⋊D3—912no—
155C3⋊D3—186no—
156C3⋊D3—274no—
157C3⋊D3—2718no—
158C3⋊D3—544no—
159C3⋊D3—544no—
160C3⋊D3—542no—
161C3⋊D3—5418no—
162C3×D3—936no—
163C3×D3—912no—
164C3×D3—912no—
165C3×D3—94no—
166C3×D3—274no—
167C3×D3—274no—
168C3×D3—544no—
169C3×D3—542no—
170C22×C3—276no—
171C22×C3—272no—
172C22×C3—811no—
173C2×D3—96no—
174C2×D3—92no—
175C2×D3—272no—
176C2×D3—272no—
177C2×D3—542no—
178C2×D3—541no—
179C2×D3—816no—
180C2×D3—818no—
181C2×D3—8124no—
182C2×D3—814no—
183C2×D3—1623no—
184C32—23no—
185C32—32no—
186C32—39no—
187C32—32no—
188C32—62no—
189C32—61no—
190C32—61no—
191C32—69no—
192C32—62no—
193C32—62no—
194C32—62no—
195C32—122no—
196C32—121no—
197C32—121no—
198C32—122no—
199C32C2×((C3⋊D3)⋊C3)⋊C216yescomplemented
200C32C2×#111311yescharacteristic
201C23—2431noSylow
202C2×C3—21no—
203C2×C3—36no—
204C2×C3—63no—
205C2×C3—91no—
206C2×C3—182no—
207C2×C3—2712no—
208C2×C3—274no—
209C2×C3—361no—
210C2×C3—812no—
211C2×C3#6643212yes—
212D3—912no—
213D3—94no—
214D3—274no—
215D3—274no—
216D3—544no—
217D3—542no—
218D3—8112no—
219D3—1626no—
220C22—272no—
221C22—811no—
222C22—2434no—
223C3—21no—
224C3—36no—
225C3—63no—
226C3—91no—
227C3—182no—
228C3—361no—
229C3C2×#6643212yes—
230C2—274no—
231C2—812no—
232C2#1175774911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#11757749
commutator, cosocle, hypocenterC32⋊H(3,𝔽3)C23
FrattiniC32C2×#1113
FittingC2×C32⋊H(3,𝔽3)C22
socleC2×C32#1113
LCSG ▷ C32⋊H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92301C2semidirect
2. C2×#92300C2semidirect
3. #11757749C2direct (N × H)
6. C2×C32⋊H(3,𝔽3)C22semidirect
7. #92301C22semidirect
8. #92300C22semidirect
9. C2×C3⋊(C3⋊(C3⋊D3))D3semidirect
12. C2×C3⋊#272D3semidirect
18. C32⋊H(3,𝔽3)C23semidirect
23. C2×C34C2×D3semidirect
24. C3⋊(C3⋊(C3⋊D3))C2×D3semidirect
29. C2×C3×H(3,𝔽3)C2×D3semidirect
30. C3⋊#272C2×D3semidirect
55. C34C22×D3semidirect
59. C3×H(3,𝔽3)C22×D3semidirect
71. C2×C33D32semidirect
124. C33C2×D32semidirect
148. C2×C32((C3⋊D3)⋊C3)⋊C2semidirect
199. C32C2×((C3⋊D3)⋊C3)⋊C2semidirect
232. C2#11757749direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#923012
C2×#923002
#117577492
C2×C3⋊D323
C2×((C3⋊D3)⋊C3)⋊D33