Finite Group Databasebeta

← C2×#11757757 #14518343

Subgroups — C2×#11757757 #14518343

Order 1944.

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

normal subgroups only

This group has 548 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×C3⋊#4179C211yesmaximal, characteristic, complemented
2C2×C3⋊#4178C211yesmaximal, characteristic, complemented
3C2×C3×#4185C211yesmaximal, characteristic, complemented
4#11757757C214yesmaximal, direct product factor
5C2×((C3⋊D3)⋊C3)⋊D3—31nomaximal
6C2×D9×C3⋊D3—31nomaximal
7C2×#4178⋊C2—31nomaximal
8C2×C3×#732C2211yescharacteristic, complemented
9C3⋊#4179C2212yescomplemented
10C3⋊#4178C2212yescomplemented
11C3×#4185C2212yescomplemented
12C2×C3⋊#272D311yescharacteristic, complemented
13C2×C3⋊(C3⋊D9)D311yescharacteristic, complemented
14C2×C3⋊((C3⋊D3)⋊C3)—31no—
15C2×C9×C3⋊D3—31no—
16C2×C3×(C3⋊D3)⋊C3—31no—
17C2×C3×(C3⋊D3)⋊C3—61no—
18C2×C32×D9—31no—
19((C3⋊D3)⋊C3)⋊D3—34no—
20D9×C3⋊D3—34no—
21C2×#4185D311yescharacteristic, complemented
22C2×#4179—31no—
23C2×#4179—61no—
24C2×#4178—31no—
25C2×#4178—61no—
26#4178⋊C2—34no—
27C3×#732C2311yescharacteristic, complemented, Sylow
28C2×#1113—91no—
29C2×D3×C3⋊D3—91no—
30C2×((C3⋊D3)⋊C3)⋊C2—91no—
31C2×((C3⋊D3)⋊C3)⋊C2—92no—
32C2×D3×D9—91no—
33C2×D3×D9—92no—
34C2×D3×D9—91no—
35C2×C3×H(3,𝔽3)—21no—
36C2×C3×H(3,𝔽3)C2×D311yescharacteristic
37C2×C32×C9C2×D311yescharacteristic, complemented
38C3⋊#272C2×D312yescomplemented
39C3⋊(C3⋊D9)C2×D312yescomplemented
40C3⋊((C3⋊D3)⋊C3)—32no—
41C9×C3⋊D3—32no—
42C3×(C3⋊D3)⋊C3—32no—
43C3×(C3⋊D3)⋊C3—62no—
44C32×D9—32no—
45C2×#732—21no—
46C2×#732—21no—
47C2×#732—41no—
48C2×#732C2×D311yescharacteristic, complemented
49#4185C2×D312yescomplemented
50#4179—32no—
51#4179—62no—
52#4178—32no—
53#4178—62no—
54C2×C3⋊(C3⋊D3)—31no—
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—31no—
57C2×C3×C3⋊D3—61no—
58C2×C3×C3⋊D3—91no—
59C2×C3×C3⋊D3—91no—
60C2×C32×D3—91no—
61#1113—94no—
62D3×C3⋊D3—94no—
63C2×#272—31no—
64C2×#272—61no—
65C2×#272—92no—
66C2×C3⋊D9—31no—
67C2×C3⋊D9—61no—
68C2×C3⋊D9—91no—
69C2×C3⋊D9—92no—
70C2×(C3⋊D3)⋊C3—32no—
71C2×(C3⋊D3)⋊C3—31no—
72C2×(C3⋊D3)⋊C3—61no—
73C2×(C3⋊D3)⋊C3—62no—
74C2×(C3⋊D3)⋊C3—92no—
75C2×(C3⋊D3)⋊C3—91no—
76C2×D3×C9—92no—
77C2×D3×C9—91no—
78C2×D3×C9—91no—
79C2×C3×D9—32no—
80C2×C3×D9—31no—
81C2×C3×D9—31no—
82((C3⋊D3)⋊C3)⋊C2—94no—
83((C3⋊D3)⋊C3)⋊C2—98no—
84D3×D9—94no—
85D3×D9—98no—
86D3×D9—94no—
87C3×H(3,𝔽3)—21no—
88C3×H(3,𝔽3)C22×D311yescharacteristic
89C32×C9C22×D311yescharacteristic, complemented
90#732—21no—
91#732—21no—
92#732—41no—
93#732C22×D311yescharacteristic, complemented
94C22×C3⋊D3—271no—
95C2×D32—272no—
96C2×D32—271no—
97C2×D32—271no—
98C2×D32—271no—
99C2×D32—271no—
100C22×D9—271no—
101C2×C33—31no—
102C2×C33—61no—
103C2×C33D3211yescharacteristic
104C3⋊(C3⋊D3)—32no—
105C3×C3⋊D3—32no—
106C3×C3⋊D3—32no—
107C3×C3⋊D3—62no—
108C3×C3⋊D3—92no—
109C3×C3⋊D3—92no—
110C32×D3—92no—
111C2×H(3,𝔽3)—21no—
112C2×H(3,𝔽3)—21no—
113C2×H(3,𝔽3)—32no—
114C2×H(3,𝔽3)—41no—
115C2×H(3,𝔽3)—62no—
116C2×H(3,𝔽3)D3211yescharacteristic
117C2×C3×C9—21no—
118C2×C3×C9—31no—
119C2×C3×C9—32no—
120C2×C3×C9D3211yescharacteristic, complemented
121#272—32no—
122#272—62no—
123#272—94no—
124C3⋊D9—32no—
125C3⋊D9—62no—
126C3⋊D9—92no—
127C3⋊D9—94no—
128(C3⋊D3)⋊C3—34no—
129(C3⋊D3)⋊C3—32no—
130(C3⋊D3)⋊C3—62no—
131(C3⋊D3)⋊C3—64no—
132(C3⋊D3)⋊C3—94no—
133(C3⋊D3)⋊C3—92no—
134D3×C9—94no—
135D3×C9—92no—
136D3×C9—92no—
137C3×D9—34no—
138C3×D9—32no—
139C3×D9—32no—
140C22×C32—271no—
141C2×C3⋊D3—31no—
142C2×C3⋊D3—31no—
143C2×C3⋊D3—61no—
144C2×C3⋊D3—91no—
145C2×C3⋊D3—91no—
146C2×C3⋊D3—92no—
147C2×C3⋊D3—91no—
148C2×C3⋊D3—271no—
149C2×C3⋊D3—274no—
150C2×C3⋊D3—541no—
151C2×C3×D3—92no—
152C2×C3×D3—91no—
153C2×C3×D3—92no—
154C2×C3×D3—91no—
155C2×C3×D3—91no—
156C2×C3×D3—91no—
157C2×C3×D3—271no—
158C2×C3×D3—271no—
159C2×C3×D3—271no—
160C2×C3×D3—271no—
161C2×C3×D3—541no—
162C2×C3×D3—541no—
163C2×C3×D3—541no—
164D32—278no—
165D32—274no—
166D32—274no—
167D32—274no—
168D32—274no—
169C22×C9—271no—
170C2×D9—31no—
171C2×D9—271no—
172C2×D9—274no—
173C2×D9—541no—
174C33—31no—
175C33—61no—
176C33C2×D3211yescharacteristic
177H(3,𝔽3)—21no—
178H(3,𝔽3)—21no—
179H(3,𝔽3)—32no—
180H(3,𝔽3)—41no—
181H(3,𝔽3)—62no—
182H(3,𝔽3)C2×D3211yescharacteristic
183C3×C9—21no—
184C3×C9—31no—
185C3×C9—32no—
186C3×C9C2×D3211yescharacteristic, complemented
187C22×D3—811no—
188C22×D3—811no—
189C22×D3—812no—
190C22×D3—811no—
191C22×D3—811no—
192C2×C32—31no—
193C2×C32—31no—
194C2×C32—61no—
195C2×C32—61no—
196C2×C32—61no—
197C2×C32—91no—
198C2×C32—121no—
199C2×C32—181no—
200C2×C32—181no—
201C2×C32—272no—
202C2×C32—361no—
203C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
204C2×C32((C3⋊D3)⋊C3)⋊C212yes—
205C2×C32#111311yescharacteristic
206C3⋊D3—32no—
207C3⋊D3—32no—
208C3⋊D3—62no—
209C3⋊D3—92no—
210C3⋊D3—92no—
211C3⋊D3—94no—
212C3⋊D3—92no—
213C3⋊D3—272no—
214C3⋊D3—542no—
215C3×D3—94no—
216C3×D3—92no—
217C3×D3—94no—
218C3×D3—92no—
219C3×D3—92no—
220C3×D3—92no—
221C3×D3—272no—
222C3×D3—272no—
223C3×D3—272no—
224C3×D3—272no—
225C3×D3—542no—
226C3×D3—542no—
227C3×D3—542no—
228C2×C9—31no—
229C2×C9—61no—
230C2×C9—272no—
231D9—32no—
232D9—272no—
233D9—542no—
234C22×C3—272no—
235C22×C3—271no—
236C22×C3—271no—
237C22×C3—271no—
238C22×C3—811no—
239C2×D3—92no—
240C2×D3—91no—
241C2×D3—91no—
242C2×D3—91no—
243C2×D3—271no—
244C2×D3—271no—
245C2×D3—271no—
246C2×D3—271no—
247C2×D3—541no—
248C2×D3—541no—
249C2×D3—541no—
250C2×D3—812no—
251C2×D3—811no—
252C2×D3—814no—
253C2×D3—814no—
254C2×D3—818no—
255C2×D3—814no—
256C2×D3—814no—
257C32—31no—
258C32—31no—
259C32—61no—
260C32—61no—
261C32—61no—
262C32—91no—
263C32—121no—
264C32—181no—
265C32—181no—
266C32—361no—
267C32C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
268C32C2×((C3⋊D3)⋊C3)⋊C212yes—
269C32C2×#111311yescharacteristic
270C9—31no—
271C9—61no—
272C23—2431noSylow
273C2×C3—21no—
274C2×C3—32no—
275C2×C3—31no—
276C2×C3—91no—
277C2×C3—181no—
278C2×C3—181no—
279C2×C3—274no—
280C2×C3—272no—
281C2×C3—272no—
282C2×C3—272no—
283C2×C3—361no—
284C2×C3—812no—
285C2×C3#4178⋊C211yescharacteristic, complemented
286C2×C3#6643211yescharacteristic
287D3—94no—
288D3—92no—
289D3—92no—
290D3—92no—
291D3—272no—
292D3—272no—
293D3—272no—
294D3—272no—
295D3—542no—
296D3—542no—
297D3—542no—
298D3—814no—
299D3—812no—
300C22—271no—
301C22—271no—
302C22—811no—
303C22—2434no—
304C3—21no—
305C3—32no—
306C3—31no—
307C3—91no—
308C3—181no—
309C3—181no—
310C3—361no—
311C3C2×#4178⋊C211yescharacteristic, complemented
312C3C2×#6643211yescharacteristic
313C2—272no—
314C2—272no—
315C2—812no—
316C2#1175775711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#11757757
commutator, cosocle, hypocenterC3×#732C23
FrattiniC32C2×#1113
FittingC2×C3×#732C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
LCSG ▷ C3×#732
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4179C2semidirect
2. C2×C3⋊#4178C2semidirect
3. C2×C3×#4185C2semidirect
4. #11757757C2direct (N × H)
8. C2×C3×#732C22semidirect
9. C3⋊#4179C22semidirect
10. C3⋊#4178C22semidirect
11. C3×#4185C22semidirect
12. C2×C3⋊#272D3semidirect
13. C2×C3⋊(C3⋊D9)D3semidirect
21. C2×#4185D3semidirect
27. C3×#732C23semidirect
37. C2×C32×C9C2×D3semidirect
38. C3⋊#272C2×D3semidirect
39. C3⋊(C3⋊D9)C2×D3semidirect
48. C2×#732C2×D3semidirect
49. #4185C2×D3semidirect
89. C32×C9C22×D3semidirect
93. #732C22×D3semidirect
120. C2×C3×C9D32semidirect
186. C3×C9C2×D32semidirect
285. C2×C3#4178⋊C2semidirect
311. C3C2×#4178⋊C2semidirect
316. C2#11757757direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3⋊#41792
C2×C3⋊#41782
C2×C3×#41852
#117577572
C2×((C3⋊D3)⋊C3)⋊D33
C2×D9×C3⋊D33
C2×#4178⋊C23