Subgroups — C₂×C₃×#546 #87347

Order 384.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#546	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#123	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#121	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#120	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
13	C₂×#546	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂⁵×C₃	C₂²	1	2	yes	—
15	C₂×C₃×#41	—	2	8	no	—
16	C₂×C₃×#41	C₂²	1	8	yes	complemented
17	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×D₄	—	2	8	no	—
19	C₂²×C₃×D₄	C₂²	1	2	yes	—
20	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×D₄	C₂²	1	8	yes	complemented
24	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
25	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
26	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
27	C₂³×C₃×C₄	C₂²	1	2	yes	complemented
28	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₃×C₄	C₂²	1	2	yes	complemented
30	C₃×#124	C₂²	1	8	yes	complemented
31	C₃×#123	C₂²	1	16	yes	complemented
32	C₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
33	C₃×#121	C₂²	1	8	yes	complemented
34	C₃×#121	C₂²	1	16	yes	complemented
35	C₃×#120	C₂²	1	16	yes	complemented
36	C₃×C₄×D₄	C₂²	1	8	yes	complemented
37	C₃×C₄×D₄	C₂²	1	8	yes	complemented
38	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂×C₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
44	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
46	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
47	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
49	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#41	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂³×D₄	C₂×C₃	1	1	yes	characteristic, complemented
52	#546	C₂×C₃	1	16	yes	direct product factor
53	C₂×#124	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#123	C₂×C₃	1	2	yes	complemented
55	C₂×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#121	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#121	C₂×C₃	1	2	yes	complemented
58	C₂×#120	C₂×C₃	1	2	yes	complemented
59	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂²×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
62	C₂⁴×C₃	—	2	8	no	—
63	C₂⁴×C₃	—	2	8	no	—
64	C₂⁴×C₃	—	4	4	no	—
65	C₂⁴×C₃	C₂³	1	2	yes	—
66	C₂⁴×C₃	C₂³	1	1	yes	characteristic
67	C₂⁴×C₃	C₂³	1	8	yes	—
68	C₂⁴×C₃	C₂³	1	2	yes	—
69	C₂⁴×C₃	C₂³	1	1	yes	characteristic
70	C₃×#41	—	2	32	no	—
71	C₂×C₃×Q₈	—	2	4	no	—
72	C₂×C₃×Q₈	C₂³	1	4	yes	complemented
73	C₂×C₃×D₄	—	2	8	no	—
74	C₂×C₃×D₄	—	2	8	no	—
75	C₂×C₃×D₄	—	2	4	no	—
76	C₂×C₃×D₄	—	2	32	no	—
77	C₂×C₃×D₄	—	2	4	no	—
78	C₂×C₃×D₄	—	4	4	no	—
79	C₂×C₃×D₄	D₄	1	8	yes	complemented
80	C₂×C₃×D₄	C₂³	1	4	yes	—
81	C₂×C₃×D₄	C₂³	1	8	yes	—
82	C₂×C₃×D₄	C₂³	1	4	yes	—
83	C₂×C₃×D₄	C₂³	1	4	yes	—
84	C₂×C₃×D₄	C₂³	1	8	yes	complemented
85	C₂×C₃×D₄	C₂³	1	8	yes	complemented
86	C₂²×C₃×C₄	—	2	8	no	—
87	C₂²×C₃×C₄	—	2	4	no	—
88	C₂²×C₃×C₄	—	2	4	no	—
89	C₂²×C₃×C₄	—	4	4	no	—
90	C₂²×C₃×C₄	C₂³	1	4	yes	—
91	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄	C₂³	1	2	yes	—
94	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄	C₂³	1	2	yes	—
96	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₂³	1	8	yes	complemented
99	C₂²×C₃×C₄	C₂³	1	4	yes	complemented
100	C₂²×C₃×C₄	C₂³	1	8	yes	complemented
101	C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
102	C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
103	C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
104	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
107	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
108	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
109	C₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
110	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
111	C₃×C₄²	C₂³	1	4	yes	complemented
112	C₂⁵	C₂²×C₃	1	2	yes	—
113	C₂×#41	—	2	8	no	—
114	C₂×#41	C₂²×C₃	1	8	yes	complemented
115	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₂²×D₄	—	2	8	no	—
117	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₂²×D₄	C₂²×C₃	1	2	yes	—
119	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
120	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂²×D₄	C₂²×C₃	1	8	yes	complemented
122	C₂²×D₄	C₂²×C₃	1	2	yes	complemented
123	C₂²×D₄	C₂²×C₃	1	2	yes	complemented
124	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂³×C₄	C₂²×C₃	1	2	yes	complemented
126	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂³×C₄	C₂²×C₃	1	2	yes	complemented
128	#124	C₂²×C₃	1	8	yes	complemented
129	#123	C₂²×C₃	1	16	yes	complemented
130	C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
131	#121	C₂²×C₃	1	8	yes	complemented
132	#121	C₂²×C₃	1	16	yes	complemented
133	#120	C₂²×C₃	1	16	yes	complemented
134	C₄×D₄	C₂²×C₃	1	8	yes	complemented
135	C₄×D₄	C₂²×C₃	1	8	yes	complemented
136	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
139	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
141	C₂×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
142	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
143	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
144	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
145	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
147	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₂³×C₃	—	2	2	no	—
149	C₂³×C₃	—	2	4	no	—
150	C₂³×C₃	—	2	4	no	—
151	C₂³×C₃	—	2	2	no	—
152	C₂³×C₃	—	2	2	no	—
153	C₂³×C₃	—	2	16	no	—
154	C₂³×C₃	—	2	4	no	—
155	C₂³×C₃	—	2	2	no	—
156	C₂³×C₃	—	2	4	no	—
157	C₂³×C₃	—	2	16	no	—
158	C₂³×C₃	—	2	2	no	—
159	C₂³×C₃	—	2	4	no	—
160	C₂³×C₃	—	4	8	no	—
161	C₂³×C₃	—	4	32	no	—
162	C₂³×C₃	C₂×D₄	1	8	yes	—
163	C₂³×C₃	#41	1	4	yes	complemented
164	C₂³×C₃	C₂⁴	1	4	yes	—
165	C₂³×C₃	C₂⁴	1	2	yes	—
166	C₂³×C₃	C₂⁴	1	4	yes	—
167	C₂³×C₃	C₂⁴	1	2	yes	—
168	C₂³×C₃	C₂⁴	1	1	yes	characteristic
169	C₃×Q₈	—	2	8	no	—
170	C₃×D₄	—	2	16	no	—
171	C₃×D₄	—	2	16	no	—
172	C₃×D₄	—	2	8	no	—
173	C₃×D₄	—	2	8	no	—
174	C₃×D₄	—	4	8	no	—
175	C₃×D₄	C₂×D₄	1	16	yes	complemented
176	C₂×C₃×C₄	—	2	2	no	—
177	C₂×C₃×C₄	—	2	2	no	—
178	C₂×C₃×C₄	—	2	4	no	—
179	C₂×C₃×C₄	—	2	16	no	—
180	C₂×C₃×C₄	—	2	2	no	—
181	C₂×C₃×C₄	—	2	2	no	—
182	C₂×C₃×C₄	—	2	4	no	—
183	C₂×C₃×C₄	—	2	8	no	—
184	C₂×C₃×C₄	—	2	8	no	—
185	C₂×C₃×C₄	—	4	8	no	—
186	C₂×C₃×C₄	C₂×D₄	1	4	yes	—
187	C₂×C₃×C₄	C₂⁴	1	2	yes	—
188	C₂×C₃×C₄	C₂⁴	1	2	yes	—
189	C₂×C₃×C₄	C₂⁴	1	4	yes	—
190	C₂×C₃×C₄	C₂⁴	1	2	yes	—
191	C₂×C₃×C₄	C₂⁴	1	4	yes	—
192	C₂×C₃×C₄	C₂⁴	1	2	yes	—
193	C₂×C₃×C₄	C₂⁴	1	2	yes	—
194	C₂⁴	—	2	8	no	—
195	C₂⁴	—	2	8	no	—
196	C₂⁴	—	4	4	no	—
197	C₂⁴	C₂³×C₃	1	2	yes	—
198	C₂⁴	C₂³×C₃	1	1	yes	characteristic
199	C₂⁴	C₂³×C₃	1	8	yes	—
200	C₂⁴	C₂³×C₃	1	2	yes	—
201	C₂⁴	C₂³×C₃	1	1	yes	characteristic
202	#41	—	2	32	no	—
203	C₂×Q₈	—	2	4	no	—
204	C₂×Q₈	C₂³×C₃	1	4	yes	complemented
205	C₂×D₄	—	2	8	no	—
206	C₂×D₄	—	2	8	no	—
207	C₂×D₄	—	2	4	no	—
208	C₂×D₄	—	2	32	no	—
209	C₂×D₄	—	2	4	no	—
210	C₂×D₄	—	4	4	no	—
211	C₂×D₄	C₃×D₄	1	8	yes	complemented
212	C₂×D₄	C₂³×C₃	1	4	yes	—
213	C₂×D₄	C₂³×C₃	1	8	yes	—
214	C₂×D₄	C₂³×C₃	1	4	yes	—
215	C₂×D₄	C₂³×C₃	1	4	yes	—
216	C₂×D₄	C₂³×C₃	1	8	yes	complemented
217	C₂×D₄	C₂³×C₃	1	8	yes	complemented
218	C₂²×C₄	—	2	8	no	—
219	C₂²×C₄	—	2	4	no	—
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	4	4	no	—
222	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
223	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₄	C₂³×C₃	1	2	yes	—
225	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₄	C₂³×C₃	1	2	yes	—
227	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₄	C₂³×C₃	1	4	yes	—
229	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
230	C₂²×C₄	C₂³×C₃	1	8	yes	complemented
231	C₂²×C₄	C₂³×C₃	1	4	yes	complemented
232	C₂²×C₄	C₂³×C₃	1	8	yes	complemented
233	C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
234	C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
235	C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
236	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
237	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
238	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
239	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
240	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
241	C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
242	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
243	C₄²	C₂³×C₃	1	4	yes	complemented
244	C₂²×C₃	—	2	8	no	—
245	C₂²×C₃	—	2	16	no	—
246	C₂²×C₃	—	2	2	no	—
247	C₂²×C₃	—	2	4	no	—
248	C₂²×C₃	—	2	4	no	—
249	C₂²×C₃	—	2	2	no	—
250	C₂²×C₃	—	2	2	no	—
251	C₂²×C₃	—	2	4	no	—
252	C₂²×C₃	—	2	2	no	—
253	C₂²×C₃	—	2	4	no	—
254	C₂²×C₃	—	2	2	no	—
255	C₂²×C₃	—	2	4	no	—
256	C₂²×C₃	—	4	32	no	—
257	C₂²×C₃	—	4	4	no	—
258	C₂²×C₃	—	4	8	no	—
259	C₂²×C₃	C₂²×D₄	1	8	yes	—
260	C₂²×C₃	C₂²×D₄	1	2	yes	—
261	C₂²×C₃	C₂×#41	1	2	yes	—
262	C₂²×C₃	C₂×#41	1	4	yes	complemented
263	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
264	C₂²×C₃	C₂⁵	1	1	yes	characteristic
265	C₃×C₄	—	2	2	no	—
266	C₃×C₄	—	2	2	no	—
267	C₃×C₄	—	2	4	no	—
268	C₃×C₄	—	2	2	no	—
269	C₃×C₄	—	2	2	no	—
270	C₃×C₄	—	2	4	no	—
271	C₃×C₄	C₂²×D₄	1	4	yes	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	16	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	16	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	4	8	no	—
285	C₂³	—	4	32	no	—
286	C₂³	C₂×C₃×D₄	1	8	yes	—
287	C₂³	C₃×#41	1	4	yes	complemented
288	C₂³	C₂⁴×C₃	1	4	yes	—
289	C₂³	C₂⁴×C₃	1	2	yes	—
290	C₂³	C₂⁴×C₃	1	4	yes	—
291	C₂³	C₂⁴×C₃	1	2	yes	—
292	C₂³	C₂⁴×C₃	1	1	yes	characteristic
293	Q₈	—	2	8	no	—
294	D₄	—	2	16	no	—
295	D₄	—	2	16	no	—
296	D₄	—	2	8	no	—
297	D₄	—	2	8	no	—
298	D₄	—	4	8	no	—
299	D₄	C₂×C₃×D₄	1	16	yes	complemented
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	C₂×C₃×D₄	1	4	yes	—
311	C₂×C₄	C₂⁴×C₃	1	2	yes	—
312	C₂×C₄	C₂⁴×C₃	1	2	yes	—
313	C₂×C₄	C₂⁴×C₃	1	4	yes	—
314	C₂×C₄	C₂⁴×C₃	1	2	yes	—
315	C₂×C₄	C₂⁴×C₃	1	4	yes	—
316	C₂×C₄	C₂⁴×C₃	1	2	yes	—
317	C₂×C₄	C₂⁴×C₃	1	2	yes	—
318	C₂×C₃	—	2	4	no	—
319	C₂×C₃	—	2	8	no	—
320	C₂×C₃	—	4	2	no	—
321	C₂×C₃	—	4	4	no	—
322	C₂×C₃	#546	1	4	yes	direct product factor
323	C₂×C₃	C₂³×D₄	1	1	yes	characteristic
324	C₂×C₃	C₂²×#41	1	1	yes	characteristic
325	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	8	no	—
331	C₂²	—	2	16	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	4	32	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	4	4	no	—
341	C₂²	C₂²×C₃×D₄	1	8	yes	—
342	C₂²	C₂²×C₃×D₄	1	2	yes	—
343	C₂²	C₂×C₃×#41	1	2	yes	—
344	C₂²	C₂×C₃×#41	1	4	yes	complemented
345	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
346	C₂²	C₂⁵×C₃	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	4	no	—
353	C₄	C₂²×C₃×D₄	1	4	yes	—
354	C₃	C₂×#546	1	1	yes	characteristic, direct product factor, Sylow
355	C₂	—	2	4	no	—
356	C₂	—	2	8	no	—
357	C₂	—	4	4	no	—
358	C₂	—	4	2	no	—
359	C₂	C₃×#546	1	4	yes	direct product factor
360	C₂	C₂³×C₃×D₄	1	1	yes	characteristic
361	C₂	C₂²×C₃×#41	1	1	yes	characteristic
362	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. C₂²×C₃×#41	C₂	semidirect
2. C₂³×C₃×D₄	C₂	semidirect
3. C₃×#546	C₂	direct (N × H)
4. C₂×C₃×#124	C₂	semidirect
5. C₂×C₃×#123	C₂	semidirect
6. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
7. C₂×C₃×#121	C₂	semidirect
8. C₂×C₃×#121	C₂	semidirect
9. C₂×C₃×#120	C₂	semidirect
10. C₂×C₃×C₄×D₄	C₂	semidirect
11. C₂×C₃×C₄×D₄	C₂	semidirect
12. C₂²×C₃×C₂²⋊C₄	C₂	semidirect
13. C₂×#546	C₃	direct (N × H)
16. C₂×C₃×#41	C₂²	semidirect
17. C₂²×C₃×Q₈	C₂²	semidirect
23. C₂²×C₃×D₄	C₂²	semidirect
24. C₂²×C₃×D₄	C₂²	semidirect
25. C₂²×C₃×D₄	C₂²	semidirect
27. C₂³×C₃×C₄	C₂²	semidirect
28. C₂³×C₃×C₄	C₂²	semidirect
29. C₂³×C₃×C₄	C₂²	semidirect
30. C₃×#124	C₂²	semidirect
31. C₃×#123	C₂²	semidirect
32. C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₃×#121	C₂²	semidirect
34. C₃×#121	C₂²	semidirect
35. C₃×#120	C₂²	semidirect
36. C₃×C₄×D₄	C₂²	semidirect
37. C₃×C₄×D₄	C₂²	semidirect
38. C₂×C₃×C₄⋊C₄	C₂²	semidirect
39. C₂×C₃×C₄⋊C₄	C₂²	semidirect
40. C₂×C₃×C₄⋊C₄	C₂²	semidirect
43. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
44. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
45. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
46. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
48. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₃×C₄²	C₂²	semidirect
50. C₂²×#41	C₂×C₃	semidirect
51. C₂³×D₄	C₂×C₃	semidirect
52. #546	C₂×C₃	direct (N × H)
53. C₂×#124	C₂×C₃	semidirect
54. C₂×#123	C₂×C₃	semidirect
55. C₂×C₂²⋊Q₈	C₂×C₃	semidirect
56. C₂×#121	C₂×C₃	semidirect
57. C₂×#121	C₂×C₃	semidirect
58. C₂×#120	C₂×C₃	semidirect
59. C₂×C₄×D₄	C₂×C₃	semidirect
60. C₂×C₄×D₄	C₂×C₃	semidirect
61. C₂²×C₂²⋊C₄	C₂×C₃	semidirect
72. C₂×C₃×Q₈	C₂³	semidirect
79. C₂×C₃×D₄	D₄	semidirect
84. C₂×C₃×D₄	C₂³	semidirect
85. C₂×C₃×D₄	C₂³	semidirect
98. C₂²×C₃×C₄	C₂³	semidirect
99. C₂²×C₃×C₄	C₂³	semidirect
100. C₂²×C₃×C₄	C₂³	semidirect
101. C₃×C₄⋊C₄	C₂³	semidirect
102. C₃×C₄⋊C₄	C₂³	semidirect
103. C₃×C₄⋊C₄	C₂³	semidirect
106. C₃×C₂²⋊C₄	C₂³	semidirect
107. C₃×C₂²⋊C₄	C₂³	semidirect
108. C₃×C₂²⋊C₄	C₂³	semidirect
109. C₃×C₂²⋊C₄	C₂³	semidirect
110. C₃×C₂²⋊C₄	C₂³	semidirect
111. C₃×C₄²	C₂³	semidirect
114. C₂×#41	C₂²×C₃	semidirect
115. C₂²×Q₈	C₂²×C₃	semidirect
121. C₂²×D₄	C₂²×C₃	semidirect
122. C₂²×D₄	C₂²×C₃	semidirect
123. C₂²×D₄	C₂²×C₃	semidirect
125. C₂³×C₄	C₂²×C₃	semidirect
126. C₂³×C₄	C₂²×C₃	semidirect
127. C₂³×C₄	C₂²×C₃	semidirect
128. #124	C₂²×C₃	semidirect
129. #123	C₂²×C₃	semidirect
130. C₂²⋊Q₈	C₂²×C₃	semidirect
131. #121	C₂²×C₃	semidirect
132. #121	C₂²×C₃	semidirect
133. #120	C₂²×C₃	semidirect
134. C₄×D₄	C₂²×C₃	semidirect
135. C₄×D₄	C₂²×C₃	semidirect
136. C₂×C₄⋊C₄	C₂²×C₃	semidirect
137. C₂×C₄⋊C₄	C₂²×C₃	semidirect
138. C₂×C₄⋊C₄	C₂²×C₃	semidirect
141. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
142. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
143. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
144. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
145. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
146. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
147. C₂×C₄²	C₂²×C₃	semidirect
163. C₂³×C₃	#41	semidirect
175. C₃×D₄	C₂×D₄	semidirect
204. C₂×Q₈	C₂³×C₃	semidirect
211. C₂×D₄	C₃×D₄	semidirect
216. C₂×D₄	C₂³×C₃	semidirect
217. C₂×D₄	C₂³×C₃	semidirect
230. C₂²×C₄	C₂³×C₃	semidirect
231. C₂²×C₄	C₂³×C₃	semidirect
232. C₂²×C₄	C₂³×C₃	semidirect
233. C₄⋊C₄	C₂³×C₃	semidirect
234. C₄⋊C₄	C₂³×C₃	semidirect
235. C₄⋊C₄	C₂³×C₃	semidirect
238. C₂²⋊C₄	C₂³×C₃	semidirect
239. C₂²⋊C₄	C₂³×C₃	semidirect
240. C₂²⋊C₄	C₂³×C₃	semidirect
241. C₂²⋊C₄	C₂³×C₃	semidirect
242. C₂²⋊C₄	C₂³×C₃	semidirect
243. C₄²	C₂³×C₃	semidirect
262. C₂²×C₃	C₂×#41	semidirect
287. C₂³	C₃×#41	semidirect
299. D₄	C₂×C₃×D₄	semidirect
322. C₂×C₃	#546	direct (N × H)
344. C₂²	C₂×C₃×#41	semidirect
354. C₃	C₂×#546	direct (N × H)
359. C₂	C₃×#546	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#41	2
C₂³×C₃×D₄	2
C₃×#546	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×#546	3

Subgroups — C2×C3×#546 #87347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#546 #87347