Subgroups — H(3,𝔽₃)×#547 #13154624

Order 1728.

1606 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	C₂×#41×H(3,𝔽₃)	C₂	1	2	yes	maximal, complemented
2	H(3,𝔽₃)×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	H(3,𝔽₃)×#123	C₂	1	4	yes	maximal, complemented
4	H(3,𝔽₃)×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
5	H(3,𝔽₃)×#121	C₂	1	2	yes	maximal, complemented
6	C₄×D₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×D₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₄×H(3,𝔽₃)	C₂	1	2	yes	maximal, complemented
9	C₃²×#547	C₃	1	4	yes	maximal, complemented
10	#41×H(3,𝔽₃)	—	2	8	no	—
11	C₂×Q₈×H(3,𝔽₃)	C₂²	1	2	yes	—
12	C₂×D₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
13	C₂×D₄×H(3,𝔽₃)	C₂²	1	4	yes	—
14	C₂×D₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
15	C₂²×C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
16	C₂²×C₄×H(3,𝔽₃)	C₂²	1	4	yes	—
17	C₂²×C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
18	C₄⋊C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
20	C₄⋊C₄×H(3,𝔽₃)	C₂²	1	4	yes	—
21	C₄⋊C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
23	C₂²⋊C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
24	C₂²⋊C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
25	C₂²⋊C₄×H(3,𝔽₃)	C₂²	1	4	yes	—
26	C₄²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
27	C₂×C₃²×#41	C₂×C₃	1	8	yes	complemented
28	C₃²×C₄⋊Q₈	C₂×C₃	1	4	yes	complemented
29	C₃²×#123	C₂×C₃	1	16	yes	complemented
30	C₃²×C₂²⋊Q₈	C₂×C₃	1	8	yes	complemented
31	C₃²×#121	C₂×C₃	1	8	yes	complemented
32	C₃²×C₄×D₄	C₂×C₃	1	4	yes	complemented
33	C₃²×C₄×D₄	C₂×C₃	1	4	yes	complemented
34	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	8	yes	complemented
35	C₂³×H(3,𝔽₃)	C₂³	1	2	yes	—
36	C₂³×H(3,𝔽₃)	C₂³	1	2	yes	—
37	Q₈×H(3,𝔽₃)	—	2	4	no	—
38	D₄×H(3,𝔽₃)	—	2	8	no	—
39	D₄×H(3,𝔽₃)	—	2	2	no	—
40	D₄×H(3,𝔽₃)	D₄	1	4	yes	complemented
41	C₂×C₄×H(3,𝔽₃)	—	2	8	no	—
42	C₂×C₄×H(3,𝔽₃)	—	2	4	no	—
43	C₂×C₄×H(3,𝔽₃)	—	2	4	no	—
44	C₂×C₄×H(3,𝔽₃)	C₂³	1	2	yes	—
45	C₂×C₄×H(3,𝔽₃)	C₂³	1	4	yes	—
46	C₂×C₄×H(3,𝔽₃)	C₂³	1	2	yes	—
47	C₂×C₄×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
48	C₂×C₄×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
49	C₂×C₄×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
50	C₃×#547	—	3	4	no	—
51	C₃×#547	C₃²	1	1	yes	characteristic
52	C₃²×#41	—	2	32	no	—
53	C₂×C₃²×Q₈	C₂²×C₃	1	8	yes	—
54	C₂×C₃²×D₄	C₂²×C₃	1	16	yes	—
55	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
56	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
57	C₂²×C₃²×C₄	C₂²×C₃	1	16	yes	—
58	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
59	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
60	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
61	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
62	C₃²×C₄⋊C₄	C₂²×C₃	1	16	yes	—
63	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
64	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
65	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
66	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
67	C₃²×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
68	C₃²×C₄²	C₂²×C₃	1	4	yes	—
69	C₂²×H(3,𝔽₃)	—	2	2	no	—
70	C₂²×H(3,𝔽₃)	—	2	2	no	—
71	C₂²×H(3,𝔽₃)	—	2	2	no	—
72	C₂²×H(3,𝔽₃)	—	2	2	no	—
73	C₂²×H(3,𝔽₃)	—	2	2	no	—
74	C₂²×H(3,𝔽₃)	C₂×D₄	1	4	yes	—
75	C₂²×H(3,𝔽₃)	C₂⁴	1	1	yes	characteristic
76	C₄×H(3,𝔽₃)	—	2	2	no	—
77	C₄×H(3,𝔽₃)	—	2	4	no	—
78	C₄×H(3,𝔽₃)	—	2	2	no	—
79	C₄×H(3,𝔽₃)	—	2	1	no	—
80	C₄×H(3,𝔽₃)	C₂×D₄	1	2	yes	—
81	C₄×H(3,𝔽₃)	#41	1	2	yes	complemented
82	C₂×C₃×#41	—	3	8	no	—
83	C₂×C₃×#41	C₂×C₃²	1	2	yes	—
84	C₃×C₄⋊Q₈	—	3	4	no	—
85	C₃×C₄⋊Q₈	C₂×C₃²	1	1	yes	characteristic
86	C₃×#123	—	3	16	no	—
87	C₃×#123	C₂×C₃²	1	4	yes	—
88	C₃×C₂²⋊Q₈	—	3	8	no	—
89	C₃×C₂²⋊Q₈	C₂×C₃²	1	2	yes	—
90	C₃×#121	—	3	8	no	—
91	C₃×#121	C₂×C₃²	1	2	yes	—
92	C₃×C₄×D₄	—	3	4	no	—
93	C₃×C₄×D₄	—	3	4	no	—
94	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic
95	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic
96	C₂×C₃×C₄⋊C₄	—	3	8	no	—
97	C₂×C₃×C₄⋊C₄	C₂×C₃²	1	2	yes	—
98	C₂³×C₃²	C₂³×C₃	1	8	yes	—
99	C₂³×C₃²	C₂³×C₃	1	8	yes	—
100	C₃²×Q₈	—	2	16	no	—
101	C₃²×D₄	—	2	32	no	—
102	C₃²×D₄	—	2	8	no	—
103	C₃²×D₄	C₃×D₄	1	16	yes	complemented
104	C₂×C₃²×C₄	—	2	32	no	—
105	C₂×C₃²×C₄	—	2	16	no	—
106	C₂×C₃²×C₄	—	2	16	no	—
107	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
108	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
109	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
110	C₂×C₃²×C₄	C₂³×C₃	1	16	yes	—
111	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
112	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
113	#547	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
114	C₂×H(3,𝔽₃)	—	2	4	no	—
115	C₂×H(3,𝔽₃)	—	4	2	no	—
116	C₂×H(3,𝔽₃)	C₂²×D₄	1	1	yes	characteristic
117	C₂×H(3,𝔽₃)	C₂×#41	1	1	yes	characteristic
118	C₂×H(3,𝔽₃)	2₋¹⁺⁴	1	1	yes	characteristic
119	C₃×#41	—	2	8	no	—
120	C₃×#41	—	6	32	no	—
121	C₂×C₃×Q₈	—	3	8	no	—
122	C₂×C₃×Q₈	C₂²×C₃²	1	2	yes	—
123	C₂×C₃×D₄	—	3	4	no	—
124	C₂×C₃×D₄	—	3	4	no	—
125	C₂×C₃×D₄	—	3	16	no	—
126	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
127	C₂×C₃×D₄	C₂²×C₃²	1	4	yes	—
128	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
129	C₂²×C₃×C₄	—	3	8	no	—
130	C₂²×C₃×C₄	—	3	16	no	—
131	C₂²×C₃×C₄	—	3	8	no	—
132	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
133	C₂²×C₃×C₄	C₂²×C₃²	1	4	yes	—
134	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
135	C₃×C₄⋊C₄	—	3	4	no	—
136	C₃×C₄⋊C₄	—	3	8	no	—
137	C₃×C₄⋊C₄	—	3	16	no	—
138	C₃×C₄⋊C₄	—	3	4	no	—
139	C₃×C₄⋊C₄	—	3	8	no	—
140	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
141	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
142	C₃×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
143	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
144	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
145	C₃×C₂²⋊C₄	—	3	8	no	—
146	C₃×C₂²⋊C₄	—	3	8	no	—
147	C₃×C₂²⋊C₄	—	3	16	no	—
148	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
149	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
150	C₃×C₂²⋊C₄	C₂²×C₃²	1	4	yes	—
151	C₃×C₄²	—	3	4	no	—
152	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
153	C₂²×C₃²	—	2	8	no	—
154	C₂²×C₃²	—	2	8	no	—
155	C₂²×C₃²	—	2	8	no	—
156	C₂²×C₃²	—	2	8	no	—
157	C₂²×C₃²	—	2	8	no	—
158	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	—
159	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
160	C₃²×C₄	—	2	8	no	—
161	C₃²×C₄	—	2	16	no	—
162	C₃²×C₄	—	2	8	no	—
163	C₃²×C₄	—	2	4	no	—
164	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
165	C₃²×C₄	C₃×#41	1	8	yes	complemented
166	C₂×#41	C₂×H(3,𝔽₃)	1	2	yes	complemented
167	C₄⋊Q₈	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
168	#123	C₂×H(3,𝔽₃)	1	4	yes	complemented
169	C₂²⋊Q₈	C₂×H(3,𝔽₃)	1	2	yes	complemented
170	#121	C₂×H(3,𝔽₃)	1	2	yes	complemented
171	C₄×D₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
172	C₄×D₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
173	C₂×C₄⋊C₄	C₂×H(3,𝔽₃)	1	2	yes	complemented
174	H(3,𝔽₃)	#547	1	1	yes	characteristic, direct product factor, Sylow
175	C₂³×C₃	—	3	8	no	—
176	C₂³×C₃	—	3	8	no	—
177	C₂³×C₃	C₂³×C₃²	1	2	yes	—
178	C₂³×C₃	C₂³×C₃²	1	2	yes	—
179	C₃×Q₈	—	2	4	no	—
180	C₃×Q₈	—	6	16	no	—
181	C₃×D₄	—	2	8	no	—
182	C₃×D₄	—	2	2	no	—
183	C₃×D₄	—	3	16	no	—
184	C₃×D₄	—	6	8	no	—
185	C₃×D₄	—	6	32	no	—
186	C₃×D₄	C₃²×D₄	1	4	yes	—
187	C₂×C₃×C₄	—	2	8	no	—
188	C₂×C₃×C₄	—	2	4	no	—
189	C₂×C₃×C₄	—	2	4	no	—
190	C₂×C₃×C₄	—	3	4	no	—
191	C₂×C₃×C₄	—	3	4	no	—
192	C₂×C₃×C₄	—	3	4	no	—
193	C₂×C₃×C₄	—	3	8	no	—
194	C₂×C₃×C₄	—	3	8	no	—
195	C₂×C₃×C₄	—	3	16	no	—
196	C₂×C₃×C₄	—	6	16	no	—
197	C₂×C₃×C₄	—	6	16	no	—
198	C₂×C₃×C₄	—	6	32	no	—
199	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
201	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
202	C₂×C₃×C₄	C₂³×C₃²	1	4	yes	—
203	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
205	C₂×C₃²	—	2	16	no	—
206	C₂×C₃²	—	4	8	no	—
207	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
208	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
209	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
210	#41	—	2	8	no	—
211	C₂×Q₈	C₂²×H(3,𝔽₃)	1	2	yes	—
212	C₂×D₄	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
213	C₂×D₄	C₂²×H(3,𝔽₃)	1	4	yes	—
214	C₂×D₄	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
215	C₂²×C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
216	C₂²×C₄	C₂²×H(3,𝔽₃)	1	4	yes	—
217	C₂²×C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
218	C₄⋊C₄	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
219	C₄⋊C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
220	C₄⋊C₄	C₂²×H(3,𝔽₃)	1	4	yes	—
221	C₄⋊C₄	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
222	C₄⋊C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
223	C₂²⋊C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
224	C₂²⋊C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
225	C₂²⋊C₄	C₂²×H(3,𝔽₃)	1	4	yes	—
226	C₄²	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
227	C₂²×C₃	—	2	2	no	—
228	C₂²×C₃	—	2	2	no	—
229	C₂²×C₃	—	2	2	no	—
230	C₂²×C₃	—	2	2	no	—
231	C₂²×C₃	—	2	2	no	—
232	C₂²×C₃	—	3	4	no	—
233	C₂²×C₃	—	3	16	no	—
234	C₂²×C₃	—	6	8	no	—
235	C₂²×C₃	—	6	8	no	—
236	C₂²×C₃	—	6	8	no	—
237	C₂²×C₃	—	6	8	no	—
238	C₂²×C₃	—	6	8	no	—
239	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	—
240	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
241	C₃×C₄	—	2	2	no	—
242	C₃×C₄	—	2	4	no	—
243	C₃×C₄	—	2	2	no	—
244	C₃×C₄	—	2	1	no	—
245	C₃×C₄	—	3	8	no	—
246	C₃×C₄	—	3	8	no	—
247	C₃×C₄	—	6	8	no	—
248	C₃×C₄	—	6	16	no	—
249	C₃×C₄	—	6	8	no	—
250	C₃×C₄	—	6	4	no	—
251	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
252	C₃×C₄	C₃²×#41	1	2	yes	—
253	C₃²	C₃×#547	1	4	yes	complemented
254	C₂³	C₂³×H(3,𝔽₃)	1	2	yes	—
255	C₂³	C₂³×H(3,𝔽₃)	1	2	yes	—
256	Q₈	—	2	4	no	—
257	D₄	—	2	8	no	—
258	D₄	—	2	2	no	—
259	D₄	D₄×H(3,𝔽₃)	1	4	yes	complemented
260	C₂×C₄	—	2	8	no	—
261	C₂×C₄	—	2	4	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	C₂³×H(3,𝔽₃)	1	1	yes	characteristic
264	C₂×C₄	C₂³×H(3,𝔽₃)	1	2	yes	—
265	C₂×C₄	C₂³×H(3,𝔽₃)	1	2	yes	—
266	C₂×C₄	C₂³×H(3,𝔽₃)	1	4	yes	—
267	C₂×C₄	C₂³×H(3,𝔽₃)	1	1	yes	characteristic
268	C₂×C₄	C₂³×H(3,𝔽₃)	1	1	yes	characteristic
269	C₂×C₃	—	2	4	no	—
270	C₂×C₃	—	3	4	no	—
271	C₂×C₃	—	3	4	no	—
272	C₂×C₃	—	3	4	no	—
273	C₂×C₃	—	4	2	no	—
274	C₂×C₃	—	6	16	no	—
275	C₂×C₃	—	12	8	no	—
276	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
277	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
278	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
279	C₂²	—	2	2	no	—
280	C₂²	—	2	2	no	—
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	2	2	no	—
284	C₂²	C₂×D₄×H(3,𝔽₃)	1	4	yes	—
285	C₂²	C₂⁴×H(3,𝔽₃)	1	1	yes	characteristic
286	C₄	—	2	2	no	—
287	C₄	—	2	4	no	—
288	C₄	—	2	2	no	—
289	C₄	—	2	1	no	—
290	C₄	C₂×D₄×H(3,𝔽₃)	1	2	yes	—
291	C₄	#41×H(3,𝔽₃)	1	2	yes	complemented
292	C₃	—	3	4	no	—
293	C₃	C₃²×#547	1	1	yes	characteristic
294	C₂	—	2	4	no	—
295	C₂	—	4	2	no	—
296	C₂	C₂²×D₄×H(3,𝔽₃)	1	1	yes	characteristic
297	C₂	C₂×#41×H(3,𝔽₃)	1	1	yes	characteristic
298	C₂	H(3,𝔽₃)×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²×C₃	C₂⁴×C₃²
LCS	G ▷ C₂²×C₃ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#41×H(3,𝔽₃)	C₂	semidirect
2. H(3,𝔽₃)×C₄⋊Q₈	C₂	semidirect
3. H(3,𝔽₃)×#123	C₂	semidirect
4. H(3,𝔽₃)×C₂²⋊Q₈	C₂	semidirect
5. H(3,𝔽₃)×#121	C₂	semidirect
6. C₄×D₄×H(3,𝔽₃)	C₂	semidirect
7. C₄×D₄×H(3,𝔽₃)	C₂	semidirect
8. C₂×C₄⋊C₄×H(3,𝔽₃)	C₂	semidirect
9. C₃²×#547	C₃	semidirect
27. C₂×C₃²×#41	C₂×C₃	semidirect
28. C₃²×C₄⋊Q₈	C₂×C₃	semidirect
29. C₃²×#123	C₂×C₃	semidirect
30. C₃²×C₂²⋊Q₈	C₂×C₃	semidirect
31. C₃²×#121	C₂×C₃	semidirect
32. C₃²×C₄×D₄	C₂×C₃	semidirect
33. C₃²×C₄×D₄	C₂×C₃	semidirect
34. C₂×C₃²×C₄⋊C₄	C₂×C₃	semidirect
40. D₄×H(3,𝔽₃)	D₄	semidirect
81. C₄×H(3,𝔽₃)	#41	semidirect
103. C₃²×D₄	C₃×D₄	semidirect
113. #547	H(3,𝔽₃)	direct (N × H)
165. C₃²×C₄	C₃×#41	semidirect
166. C₂×#41	C₂×H(3,𝔽₃)	semidirect
167. C₄⋊Q₈	C₂×H(3,𝔽₃)	semidirect
168. #123	C₂×H(3,𝔽₃)	semidirect
169. C₂²⋊Q₈	C₂×H(3,𝔽₃)	semidirect
170. #121	C₂×H(3,𝔽₃)	semidirect
171. C₄×D₄	C₂×H(3,𝔽₃)	semidirect
172. C₄×D₄	C₂×H(3,𝔽₃)	semidirect
173. C₂×C₄⋊C₄	C₂×H(3,𝔽₃)	semidirect
174. H(3,𝔽₃)	#547	direct (N × H)
253. C₃²	C₃×#547	semidirect
259. D₄	D₄×H(3,𝔽₃)	semidirect
291. C₄	#41×H(3,𝔽₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×H(3,𝔽₃)	2
H(3,𝔽₃)×C₄⋊Q₈	2
H(3,𝔽₃)×#123	2
H(3,𝔽₃)×C₂²⋊Q₈	2
H(3,𝔽₃)×#121	2
C₄×D₄×H(3,𝔽₃)	2
C₂×C₄⋊C₄×H(3,𝔽₃)	2
C₃²×#547	3

Subgroups — H(3,𝔽3)×#547 #13154624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — H(3,𝔽₃)×#547 #13154624