Finite Group Databasebeta

← #14517112

Subgroups — #14517112

Order 1944.

570 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 45 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×#92300C211yesmaximal, characteristic
2#11757605C211yesmaximal, characteristic, complemented
3#11757604C211yesmaximal, characteristic, complemented
4C3⋊D3×C3⋊Dic3—31nomaximal
5#10619885—31nomaximal
6((C3⋊D3)⋊C3)⋊Dic3—31nomaximal
7C2×C32⋊H(3,𝔽3)C2211yescharacteristic
8#92300C412yescomplemented
9C2×C32×C3⋊D3—31no—
10C3⋊(C3⋊(C3⋊Dic3))D311yescharacteristic, complemented
11C32×C3⋊Dic3—31no—
12C2×C3⋊#272D311yescharacteristic
13C2×C3×(C3⋊D3)⋊C3—31no—
14C2×C3×(C3⋊D3)⋊C3—61no—
15C3⋊#1084D311yescharacteristic, complemented
16C3⋊((C3⋊Dic3)⋊C3)—31no—
17C3⋊((C3⋊Dic3)⋊C3)—31no—
18C3⋊((C3⋊Dic3)⋊C3)—61no—
19C3×(C3⋊Dic3)⋊C3—31no—
20C3×(C3⋊Dic3)⋊C3—61no—
21C32⋊H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
22#6294—91no—
23Dic3×C3⋊D3—91no—
24Dic3×C3⋊D3—93no—
25D3×C3⋊Dic3—91no—
26D3×C3⋊Dic3—93no—
27#6199—93no—
28((C3⋊D3)⋊C3)⋊C4—93no—
29C2×C34C2×D311yescharacteristic
30C32×C3⋊D3—32no—
31C2×C3×H(3,𝔽3)—21no—
32C2×C3×H(3,𝔽3)—21no—
33C2×C3×H(3,𝔽3)—21no—
34C2×C3×H(3,𝔽3)—41no—
35C2×C3×H(3,𝔽3)C2×D311yescharacteristic
36C2×C3×H(3,𝔽3)C2×D311yescharacteristic
37C3⋊#272Dic312yescomplemented
38C3×(C3⋊D3)⋊C3—32no—
39C3×(C3⋊D3)⋊C3—62no—
40C2×C3×C3⋊D3—33no—
41C2×C3×C3⋊D3—31no—
42C2×C3×C3⋊D3—31no—
43C2×C3×C3⋊D3—61no—
44C2×C32×D3—93no—
45C2×C32×D3—91no—
46C3⋊(C3⋊Dic3)—31no—
47C3⋊(C3⋊Dic3)—31no—
48C3⋊(C3⋊Dic3)—61no—
49C3⋊(C3⋊Dic3)—93no—
50C3⋊(C3⋊Dic3)—93no—
51C3⋊(C3⋊Dic3)—183no—
52C3×C3⋊Dic3—33no—
53C3×C3⋊Dic3—31no—
54C3×C3⋊Dic3—31no—
55C3×C3⋊Dic3—61no—
56C3×C3⋊Dic3—91no—
57C32×Dic3—93no—
58C32×Dic3—91no—
59C2×#272—93no—
60C2×(C3⋊D3)⋊C3—33no—
61C2×(C3⋊D3)⋊C3—63no—
62#1084—93no—
63(C3⋊Dic3)⋊C3—33no—
64(C3⋊Dic3)⋊C3—63no—
65(C3⋊Dic3)⋊C3—93no—
66(C3⋊Dic3)⋊C3—93no—
67(C3⋊Dic3)⋊C3—183no—
68C34C4×D311yescharacteristic, complemented
69C3×H(3,𝔽3)—21no—
70C3×H(3,𝔽3)—21no—
71C3×H(3,𝔽3)—21no—
72C3×H(3,𝔽3)—41no—
73C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
74C3×H(3,𝔽3)C2×Dic311yescharacteristic, complemented
75C2×C3⋊Dic3—271no—
76C4×C3⋊D3—271no—
77#624—271no—
78D3×Dic3—273no—
79D3×Dic3—273no—
80D3×Dic3—271no—
81D3×Dic3—279no—
82D3×Dic3—271no—
83C2×C33—21no—
84C2×C33—21no—
85C2×C33—21no—
86C2×C33—33no—
87C2×C33—33no—
88C2×C33—41no—
89C2×C33—63no—
90C2×C33D3211yescharacteristic
91C2×C33D3211yescharacteristic
92C2×C33D3211yescharacteristic
93C3×C3⋊D3—36no—
94C3×C3⋊D3—32no—
95C3×C3⋊D3—32no—
96C3×C3⋊D3—62no—
97C32×D3—96no—
98C32×D3—92no—
99C2×H(3,𝔽3)—33no—
100C2×H(3,𝔽3)—33no—
101C2×H(3,𝔽3)—63no—
102C2×H(3,𝔽3)—63no—
103C2×H(3,𝔽3)—63no—
104C2×H(3,𝔽3)—123no—
105#272—96no—
106(C3⋊D3)⋊C3—36no—
107(C3⋊D3)⋊C3—66no—
108C22×C32—271no—
109C2×C3⋊D3—31no—
110C2×C3⋊D3—31no—
111C2×C3⋊D3—61no—
112C2×C3×D3—99no—
113C2×C3×D3—93no—
114C2×C3×D3—93no—
115C2×C3×D3—91no—
116C2×C3×D3—271no—
117C2×C3×D3—541no—
118C32×C4—271no—
119C3⋊Dic3—31no—
120C3⋊Dic3—31no—
121C3⋊Dic3—61no—
122C3⋊Dic3—91no—
123C3⋊Dic3—93no—
124C3⋊Dic3—93no—
125C3⋊Dic3—183no—
126C3⋊Dic3—271no—
127C3⋊Dic3—271no—
128C3⋊Dic3—279no—
129C3⋊Dic3—541no—
130C3⋊Dic3—541no—
131C3⋊Dic3—541no—
132C3⋊Dic3—541no—
133C3⋊Dic3—541no—
134C3⋊Dic3—549no—
135C3×Dic3—99no—
136C3×Dic3—93no—
137C3×Dic3—93no—
138C3×Dic3—91no—
139C3×Dic3—271no—
140C3×Dic3—271no—
141C3×Dic3—271no—
142C3×Dic3—541no—
143C3×Dic3—541no—
144C33—21no—
145C33—21no—
146C33—21no—
147C33—33no—
148C33—33no—
149C33—41no—
150C33—63no—
151C33D3×Dic311yescharacteristic
152C33D3×Dic311yescharacteristic, complemented
153C33#62411yescharacteristic
154H(3,𝔽3)—33no—
155H(3,𝔽3)—33no—
156H(3,𝔽3)—63no—
157H(3,𝔽3)—63no—
158H(3,𝔽3)—63no—
159H(3,𝔽3)—123no—
160C2×Dic3—811no—
161C2×Dic3—813no—
162C4×D3—811no—
163C4×D3—811no—
164C4×D3—813no—
165C2×C32—23no—
166C2×C32—31no—
167C2×C32—31no—
168C2×C32—39no—
169C2×C32—31no—
170C2×C32—31no—
171C2×C32—61no—
172C2×C32—61no—
173C2×C32—61no—
174C2×C32—61no—
175C2×C32—69no—
176C2×C32—61no—
177C2×C32—61no—
178C2×C32—61no—
179C2×C32—61no—
180C2×C32—61no—
181C2×C32—61no—
182C2×C32—121no—
183C2×C32—121no—
184C2×C32—121no—
185C2×C32—121no—
186C2×C32—121no—
187C2×C32—121no—
188C2×C32—272no—
189C2×C32((C3⋊D3)⋊C3)⋊C213yes—
190C2×C32((C3⋊D3)⋊C3)⋊C213yes—
191C2×C32#111311yescharacteristic
192C3⋊D3—32no—
193C3⋊D3—32no—
194C3⋊D3—62no—
195C3×D3—918no—
196C3×D3—96no—
197C3×D3—96no—
198C3×D3—92no—
199C3×D3—272no—
200C3×D3—542no—
201C22×C3—273no—
202C22×C3—271no—
203C2×D3—93no—
204C2×D3—91no—
205C2×D3—271no—
206C2×D3—541no—
207C3×C4—273no—
208C3×C4—271no—
209C3×C4—811no—
210Dic3—93no—
211Dic3—91no—
212Dic3—271no—
213Dic3—271no—
214Dic3—271no—
215Dic3—541no—
216Dic3—541no—
217Dic3—813no—
218Dic3—813no—
219Dic3—1623no—
220C32—23no—
221C32—31no—
222C32—31no—
223C32—39no—
224C32—31no—
225C32—31no—
226C32—61no—
227C32—61no—
228C32—61no—
229C32—61no—
230C32—69no—
231C32—61no—
232C32—61no—
233C32—61no—
234C32—61no—
235C32—61no—
236C32—61no—
237C32—121no—
238C32—121no—
239C32—121no—
240C32—121no—
241C32—121no—
242C32—121no—
243C32((C3⋊D3)⋊C3)⋊C413yescomplemented
244C32#619913yescomplemented
245C32#629411yescharacteristic
246C2×C4—2431noSylow
247C2×C3—21no—
248C2×C3—33no—
249C2×C3—33no—
250C2×C3—63no—
251C2×C3—91no—
252C2×C3—181no—
253C2×C3—181no—
254C2×C3—276no—
255C2×C3—272no—
256C2×C3—361no—
257C2×C3#6643211yescharacteristic
258C2×C3#6643211yescharacteristic
259D3—96no—
260D3—92no—
261D3—272no—
262D3—542no—
263C22—271no—
264C4—271no—
265C4—811no—
266C3—21no—
267C3—33no—
268C3—33no—
269C3—63no—
270C3—91no—
271C3—181no—
272C3—181no—
273C3—361no—
274C3#1061990111yescharacteristic
275C3#1061990311yescharacteristic
276C2—272no—
277C2#1175774911yescharacteristic
subgroupG/H
center, hypercenterC2#11757749
commutator, hypocenterC32⋊H(3,𝔽3)C2×C4
Frattini, socleC2×C32#1113
Fitting, cosocleC2×C32⋊H(3,𝔽3)C22
prime radicalC2×#92300C2
LCSG ▷ C32⋊H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757605C2semidirect
3. #11757604C2semidirect
8. #92300C4semidirect
10. C3⋊(C3⋊(C3⋊Dic3))D3semidirect
15. C3⋊#1084D3semidirect
21. C32⋊H(3,𝔽3)C2×C4semidirect
37. C3⋊#272Dic3semidirect
68. C34C4×D3semidirect
73. C3×H(3,𝔽3)C4×D3semidirect
74. C3×H(3,𝔽3)C2×Dic3semidirect
152. C33D3×Dic3semidirect
243. C32((C3⋊D3)⋊C3)⋊C4semidirect
244. C32#6199semidirect

Maximal subgroups

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

subgroupindex
C2×#923002
#117576052
#117576042
C3⋊D3×C3⋊Dic33
#106198853
((C3⋊D3)⋊C3)⋊Dic33