Subgroups — C₂×C₃×#538 #87334

Order 384.

1336 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#538	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#124	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#123	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#121	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#120	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄×D₄	C₂	1	2	yes	maximal, complemented
10	C₂²×C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#538	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁵×C₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×D₄	C₂²	1	2	yes	—
16	C₂²×C₃×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄	C₂²	1	2	yes	complemented
21	C₃×#126	C₂²	1	16	yes	complemented
22	C₃×#124	C₂²	1	16	yes	complemented
23	C₃×#123	C₂²	1	16	yes	complemented
24	C₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
25	C₃×#121	C₂²	1	16	yes	complemented
26	C₃×#121	C₂²	1	8	yes	complemented
27	C₃×#120	C₂²	1	16	yes	complemented
28	C₃×C₄×D₄	C₂²	1	16	yes	complemented
29	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
39	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₃×C₄²	C₂²	1	2	yes	complemented
42	#538	C₂×C₃	1	16	yes	direct product factor
43	C₂×#126	C₂×C₃	1	2	yes	complemented
44	C₂×#124	C₂×C₃	1	2	yes	complemented
45	C₂×#123	C₂×C₃	1	2	yes	complemented
46	C₂×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#121	C₂×C₃	1	2	yes	complemented
48	C₂×#121	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#120	C₂×C₃	1	2	yes	complemented
50	C₂×C₄×D₄	C₂×C₃	1	2	yes	complemented
51	C₂²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃	—	2	4	no	—
53	C₂⁴×C₃	—	4	2	no	—
54	C₂⁴×C₃	—	4	2	no	—
55	C₂⁴×C₃	C₂³	1	2	yes	—
56	C₂⁴×C₃	C₂³	1	2	yes	—
57	C₂⁴×C₃	C₂³	1	1	yes	characteristic
58	C₂⁴×C₃	C₂³	1	4	yes	—
59	C₂×C₃×Q₈	—	4	2	no	—
60	C₂×C₃×Q₈	C₂³	1	4	yes	complemented
61	C₂×C₃×D₄	—	2	8	no	—
62	C₂×C₃×D₄	—	4	4	no	—
63	C₂×C₃×D₄	—	4	4	no	—
64	C₂×C₃×D₄	—	4	2	no	—
65	C₂×C₃×D₄	C₂³	1	8	yes	—
66	C₂×C₃×D₄	C₂³	1	8	yes	—
67	C₂×C₃×D₄	C₂³	1	8	yes	—
68	C₂×C₃×D₄	C₂³	1	4	yes	complemented
69	C₂²×C₃×C₄	—	4	2	no	—
70	C₂²×C₃×C₄	—	4	2	no	—
71	C₂²×C₃×C₄	—	4	4	no	—
72	C₂²×C₃×C₄	C₂³	1	2	yes	—
73	C₂²×C₃×C₄	C₂³	1	2	yes	—
74	C₂²×C₃×C₄	C₂³	1	2	yes	—
75	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₂³	1	2	yes	—
78	C₂²×C₃×C₄	C₂³	1	4	yes	—
79	C₂²×C₃×C₄	C₂³	1	4	yes	—
80	C₂²×C₃×C₄	C₂³	1	8	yes	complemented
81	C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
82	C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
83	C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
84	C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
85	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
91	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
92	C₃×C₄²	C₂³	1	8	yes	complemented
93	C₂⁵	C₂²×C₃	1	1	yes	characteristic
94	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂²×D₄	C₂²×C₃	1	2	yes	—
96	C₂²×D₄	C₂²×C₃	1	2	yes	—
97	C₂²×D₄	C₂²×C₃	1	2	yes	—
98	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂³×C₄	C₂²×C₃	1	2	yes	complemented
102	#126	C₂²×C₃	1	16	yes	complemented
103	#124	C₂²×C₃	1	16	yes	complemented
104	#123	C₂²×C₃	1	16	yes	complemented
105	C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
106	#121	C₂²×C₃	1	16	yes	complemented
107	#121	C₂²×C₃	1	8	yes	complemented
108	#120	C₂²×C₃	1	16	yes	complemented
109	C₄×D₄	C₂²×C₃	1	16	yes	complemented
110	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
111	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
112	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
116	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
117	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
119	C₂×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
120	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
121	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
122	C₂×C₄²	C₂²×C₃	1	2	yes	complemented
123	C₂³×C₃	—	2	2	no	—
124	C₂³×C₃	—	2	2	no	—
125	C₂³×C₃	—	2	4	no	—
126	C₂³×C₃	—	2	8	no	—
127	C₂³×C₃	—	2	4	no	—
128	C₂³×C₃	—	2	4	no	—
129	C₂³×C₃	—	2	4	no	—
130	C₂³×C₃	—	2	4	no	—
131	C₂³×C₃	—	2	4	no	—
132	C₂³×C₃	—	4	4	no	—
133	C₂³×C₃	—	4	4	no	—
134	C₂³×C₃	—	4	16	no	—
135	C₂³×C₃	#41	1	4	yes	—
136	C₂³×C₃	C₂⁴	1	4	yes	—
137	C₂³×C₃	C₂⁴	1	4	yes	—
138	C₂³×C₃	C₂⁴	1	2	yes	—
139	C₂³×C₃	C₂⁴	1	1	yes	characteristic
140	C₃×Q₈	—	4	4	no	—
141	C₃×D₄	—	2	16	no	—
142	C₃×D₄	—	4	8	no	—
143	C₃×D₄	—	4	8	no	—
144	C₃×D₄	—	4	4	no	—
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	—	2	4	no	—
147	C₂×C₃×C₄	—	2	2	no	—
148	C₂×C₃×C₄	—	2	4	no	—
149	C₂×C₃×C₄	—	2	2	no	—
150	C₂×C₃×C₄	—	2	4	no	—
151	C₂×C₃×C₄	—	4	4	no	—
152	C₂×C₃×C₄	—	4	4	no	—
153	C₂×C₃×C₄	—	4	8	no	—
154	C₂×C₃×C₄	C₂⁴	1	4	yes	—
155	C₂×C₃×C₄	C₂⁴	1	4	yes	—
156	C₂×C₃×C₄	C₂⁴	1	4	yes	—
157	C₂×C₃×C₄	C₂⁴	1	2	yes	—
158	C₂×C₃×C₄	C₂⁴	1	2	yes	—
159	C₂×C₃×C₄	C₂⁴	1	4	yes	—
160	C₂⁴	—	2	4	no	—
161	C₂⁴	—	4	2	no	—
162	C₂⁴	—	4	2	no	—
163	C₂⁴	C₂³×C₃	1	2	yes	—
164	C₂⁴	C₂³×C₃	1	2	yes	—
165	C₂⁴	C₂³×C₃	1	1	yes	characteristic
166	C₂⁴	C₂³×C₃	1	4	yes	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	C₂³×C₃	1	4	yes	complemented
169	C₂×D₄	—	2	8	no	—
170	C₂×D₄	—	4	4	no	—
171	C₂×D₄	—	4	4	no	—
172	C₂×D₄	—	4	2	no	—
173	C₂×D₄	C₂³×C₃	1	8	yes	—
174	C₂×D₄	C₂³×C₃	1	8	yes	—
175	C₂×D₄	C₂³×C₃	1	8	yes	—
176	C₂×D₄	C₂³×C₃	1	4	yes	complemented
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	—	4	2	no	—
179	C₂²×C₄	—	4	4	no	—
180	C₂²×C₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₄	C₂³×C₃	1	2	yes	—
182	C₂²×C₄	C₂³×C₃	1	2	yes	—
183	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄	C₂³×C₃	1	2	yes	—
186	C₂²×C₄	C₂³×C₃	1	4	yes	—
187	C₂²×C₄	C₂³×C₃	1	4	yes	—
188	C₂²×C₄	C₂³×C₃	1	8	yes	complemented
189	C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
190	C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
191	C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
192	C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
193	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
194	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
195	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
196	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
197	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
198	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
199	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
200	C₄²	C₂³×C₃	1	8	yes	complemented
201	C₂²×C₃	—	2	8	no	—
202	C₂²×C₃	—	2	2	no	—
203	C₂²×C₃	—	2	2	no	—
204	C₂²×C₃	—	2	4	no	—
205	C₂²×C₃	—	2	4	no	—
206	C₂²×C₃	—	2	4	no	—
207	C₂²×C₃	—	2	4	no	—
208	C₂²×C₃	—	2	4	no	—
209	C₂²×C₃	—	2	4	no	—
210	C₂²×C₃	—	4	16	no	—
211	C₂²×C₃	—	4	8	no	—
212	C₂²×C₃	—	4	8	no	—
213	C₂²×C₃	C₂×#41	1	4	yes	—
214	C₂²×C₃	C₂×#41	1	2	yes	—
215	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
216	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
217	C₂²×C₃	C₂⁵	1	1	yes	characteristic
218	C₃×C₄	—	2	4	no	—
219	C₃×C₄	—	2	4	no	—
220	C₃×C₄	—	2	2	no	—
221	C₃×C₄	—	2	4	no	—
222	C₃×C₄	—	2	2	no	—
223	C₃×C₄	—	2	4	no	—
224	C₂³	—	2	2	no	—
225	C₂³	—	2	2	no	—
226	C₂³	—	2	4	no	—
227	C₂³	—	2	8	no	—
228	C₂³	—	2	4	no	—
229	C₂³	—	2	4	no	—
230	C₂³	—	2	4	no	—
231	C₂³	—	2	4	no	—
232	C₂³	—	2	4	no	—
233	C₂³	—	4	4	no	—
234	C₂³	—	4	4	no	—
235	C₂³	—	4	16	no	—
236	C₂³	C₃×#41	1	4	yes	—
237	C₂³	C₂⁴×C₃	1	4	yes	—
238	C₂³	C₂⁴×C₃	1	4	yes	—
239	C₂³	C₂⁴×C₃	1	2	yes	—
240	C₂³	C₂⁴×C₃	1	1	yes	characteristic
241	Q₈	—	4	4	no	—
242	D₄	—	2	16	no	—
243	D₄	—	4	8	no	—
244	D₄	—	4	8	no	—
245	D₄	—	4	4	no	—
246	C₂×C₄	—	2	4	no	—
247	C₂×C₄	—	2	4	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	4	8	no	—
255	C₂×C₄	C₂⁴×C₃	1	4	yes	—
256	C₂×C₄	C₂⁴×C₃	1	4	yes	—
257	C₂×C₄	C₂⁴×C₃	1	4	yes	—
258	C₂×C₄	C₂⁴×C₃	1	2	yes	—
259	C₂×C₄	C₂⁴×C₃	1	2	yes	—
260	C₂×C₄	C₂⁴×C₃	1	4	yes	—
261	C₂×C₃	—	2	4	no	—
262	C₂×C₃	—	4	4	no	—
263	C₂×C₃	—	4	4	no	—
264	C₂×C₃	#538	1	4	yes	direct product factor
265	C₂×C₃	C₂²×#41	1	1	yes	characteristic
266	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
268	C₂²	—	2	2	no	—
269	C₂²	—	2	2	no	—
270	C₂²	—	2	8	no	—
271	C₂²	—	2	4	no	—
272	C₂²	—	2	4	no	—
273	C₂²	—	2	4	no	—
274	C₂²	—	2	4	no	—
275	C₂²	—	2	4	no	—
276	C₂²	—	2	4	no	—
277	C₂²	—	4	16	no	—
278	C₂²	—	4	8	no	—
279	C₂²	—	4	8	no	—
280	C₂²	C₂×C₃×#41	1	4	yes	—
281	C₂²	C₂×C₃×#41	1	2	yes	—
282	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
283	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
284	C₂²	C₂⁵×C₃	1	1	yes	characteristic
285	C₄	—	2	4	no	—
286	C₄	—	2	4	no	—
287	C₄	—	2	2	no	—
288	C₄	—	2	4	no	—
289	C₄	—	2	2	no	—
290	C₄	—	2	4	no	—
291	C₃	C₂×#538	1	1	yes	characteristic, direct product factor, Sylow
292	C₂	—	2	4	no	—
293	C₂	—	4	4	no	—
294	C₂	—	4	4	no	—
295	C₂	C₃×#538	1	4	yes	direct product factor
296	C₂	C₂²×C₃×#41	1	1	yes	characteristic
297	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#538	C₂	direct (N × H)
2. C₂×C₃×#126	C₂	semidirect
3. C₂×C₃×#124	C₂	semidirect
4. C₂×C₃×#123	C₂	semidirect
5. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
6. C₂×C₃×#121	C₂	semidirect
7. C₂×C₃×#121	C₂	semidirect
8. C₂×C₃×#120	C₂	semidirect
9. C₂×C₃×C₄×D₄	C₂	semidirect
10. C₂²×C₃×C₂²⋊C₄	C₂	semidirect
11. C₂×#538	C₃	direct (N × H)
13. C₂²×C₃×Q₈	C₂²	semidirect
17. C₂²×C₃×D₄	C₂²	semidirect
20. C₂³×C₃×C₄	C₂²	semidirect
21. C₃×#126	C₂²	semidirect
22. C₃×#124	C₂²	semidirect
23. C₃×#123	C₂²	semidirect
24. C₃×C₂²⋊Q₈	C₂²	semidirect
25. C₃×#121	C₂²	semidirect
26. C₃×#121	C₂²	semidirect
27. C₃×#120	C₂²	semidirect
28. C₃×C₄×D₄	C₂²	semidirect
29. C₂×C₃×C₄⋊C₄	C₂²	semidirect
30. C₂×C₃×C₄⋊C₄	C₂²	semidirect
31. C₂×C₃×C₄⋊C₄	C₂²	semidirect
32. C₂×C₃×C₄⋊C₄	C₂²	semidirect
38. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
39. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
41. C₂×C₃×C₄²	C₂²	semidirect
42. #538	C₂×C₃	direct (N × H)
43. C₂×#126	C₂×C₃	semidirect
44. C₂×#124	C₂×C₃	semidirect
45. C₂×#123	C₂×C₃	semidirect
46. C₂×C₂²⋊Q₈	C₂×C₃	semidirect
47. C₂×#121	C₂×C₃	semidirect
48. C₂×#121	C₂×C₃	semidirect
49. C₂×#120	C₂×C₃	semidirect
50. C₂×C₄×D₄	C₂×C₃	semidirect
51. C₂²×C₂²⋊C₄	C₂×C₃	semidirect
60. C₂×C₃×Q₈	C₂³	semidirect
68. C₂×C₃×D₄	C₂³	semidirect
80. C₂²×C₃×C₄	C₂³	semidirect
81. C₃×C₄⋊C₄	C₂³	semidirect
82. C₃×C₄⋊C₄	C₂³	semidirect
83. C₃×C₄⋊C₄	C₂³	semidirect
84. C₃×C₄⋊C₄	C₂³	semidirect
90. C₃×C₂²⋊C₄	C₂³	semidirect
91. C₃×C₂²⋊C₄	C₂³	semidirect
92. C₃×C₄²	C₂³	semidirect
94. C₂²×Q₈	C₂²×C₃	semidirect
98. C₂²×D₄	C₂²×C₃	semidirect
101. C₂³×C₄	C₂²×C₃	semidirect
102. #126	C₂²×C₃	semidirect
103. #124	C₂²×C₃	semidirect
104. #123	C₂²×C₃	semidirect
105. C₂²⋊Q₈	C₂²×C₃	semidirect
106. #121	C₂²×C₃	semidirect
107. #121	C₂²×C₃	semidirect
108. #120	C₂²×C₃	semidirect
109. C₄×D₄	C₂²×C₃	semidirect
110. C₂×C₄⋊C₄	C₂²×C₃	semidirect
111. C₂×C₄⋊C₄	C₂²×C₃	semidirect
112. C₂×C₄⋊C₄	C₂²×C₃	semidirect
113. C₂×C₄⋊C₄	C₂²×C₃	semidirect
119. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
120. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
121. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
122. C₂×C₄²	C₂²×C₃	semidirect
168. C₂×Q₈	C₂³×C₃	semidirect
176. C₂×D₄	C₂³×C₃	semidirect
188. C₂²×C₄	C₂³×C₃	semidirect
189. C₄⋊C₄	C₂³×C₃	semidirect
190. C₄⋊C₄	C₂³×C₃	semidirect
191. C₄⋊C₄	C₂³×C₃	semidirect
192. C₄⋊C₄	C₂³×C₃	semidirect
198. C₂²⋊C₄	C₂³×C₃	semidirect
199. C₂²⋊C₄	C₂³×C₃	semidirect
200. C₄²	C₂³×C₃	semidirect
264. C₂×C₃	#538	direct (N × H)
291. C₃	C₂×#538	direct (N × H)
295. C₂	C₃×#538	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#538	2
C₂×C₃×#126	2
C₂×C₃×#124	2
C₂×C₃×#123	2
C₂×C₃×C₂²⋊Q₈	2
C₂×C₃×#121	2
C₂×C₃×#120	2
C₂×C₃×C₄×D₄	2
C₂²×C₃×C₂²⋊C₄	2
C₂×#538	3

Subgroups — C2×C3×#538 #87334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#538 #87334