Subgroups — C₂×C₃×#3140 #10679222

Order 768.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×#3140	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#489	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×#488	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#419	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#418	C₂	1	2	yes	maximal
8	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#3140	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
13	C₃×#533	—	2	4	no	—
14	C₃×#533	C₂²	1	8	yes	complemented
15	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
16	C₂×C₃×#125	C₂²	1	2	yes	complemented
17	C₂×C₃×#124	—	2	2	no	—
18	C₂×C₃×#124	—	2	4	no	—
19	C₂×C₃×#124	C₂²	1	2	yes	—
20	C₂×C₃×#124	C₂²	1	2	yes	—
21	C₂×C₃×#124	C₂²	1	8	yes	—
22	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
23	C₂×C₃×C₄×Q₈	—	2	2	no	—
24	C₂×C₃×#117	C₂²	1	2	yes	—
25	C₂²×C₃×C₂²⋊C₄	—	2	2	no	—
26	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
27	C₃×#489	C₂²	1	32	yes	complemented
28	C₃×#488	C₂²	1	32	yes	complemented
29	C₃×#419	C₂²	1	16	yes	complemented
30	C₃×#418	C₂²	1	16	yes	—
31	C₂×C₃×#103	C₂²	1	8	yes	complemented
32	C₂×C₃×#102	C₂²	1	8	yes	—
33	C₃×C₄×M₁₆	C₂²	1	8	yes	complemented
34	C₂×C₃×#97	C₂²	1	2	yes	complemented
35	C₂×C₃×C₄×C₈	C₂²	1	2	yes	complemented
36	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂²×#124	C₂×C₃	1	1	yes	characteristic
38	#3140	C₂×C₃	1	16	yes	direct product factor
39	C₂×#489	C₂×C₃	1	4	yes	complemented
40	C₂×#488	C₂×C₃	1	4	yes	complemented
41	C₂×#419	C₂×C₃	1	2	yes	complemented
42	C₂×#418	C₂×C₃	1	2	yes	—
43	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁵×C₃	—	2	1	no	—
45	C₂²×C₃×Q₈	—	2	2	no	—
46	C₂²×C₃×Q₈	—	2	1	no	—
47	C₂²×C₃×Q₈	—	2	2	no	—
48	C₂²×C₃×Q₈	—	2	8	no	—
49	C₂²×C₃×Q₈	C₂³	1	2	yes	—
50	C₂²×C₃×Q₈	C₂³	1	4	yes	—
51	C₂²×C₃×D₄	—	2	2	no	—
52	C₂²×C₃×D₄	—	2	1	no	—
53	C₂²×C₃×D₄	—	2	8	no	—
54	C₂²×C₃×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×D₄	C₂³	1	4	yes	—
56	C₂³×C₃×C₄	—	2	1	no	—
57	C₂³×C₃×C₄	D₄	1	2	yes	—
58	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
59	C₂×C₃×M₁₆	—	2	8	no	—
60	C₂×C₃×M₁₆	C₂³	1	8	yes	—
61	C₂²×C₃×C₈	C₂³	1	4	yes	—
62	C₃×C₄⋊Q₈	—	2	4	no	—
63	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
64	C₃×#125	—	2	4	no	—
65	C₃×#125	C₂³	1	8	yes	complemented
66	C₃×#124	—	2	16	no	—
67	C₃×#124	—	2	4	no	—
68	C₃×#124	—	2	4	no	—
69	C₃×#124	C₂³	1	8	yes	—
70	C₃×#124	C₂³	1	8	yes	—
71	C₃×C₂²⋊Q₈	—	2	16	no	—
72	C₃×C₄×Q₈	—	2	16	no	—
73	C₃×#117	—	2	4	no	—
74	C₃×#117	C₂³	1	8	yes	—
75	C₂×C₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
80	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
81	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
82	C₂×C₃×C₄²	—	2	2	no	—
83	C₂×C₃×C₄²	D₄	1	2	yes	—
84	C₂×C₃×C₄²	D₄	1	4	yes	—
85	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂³	1	4	yes	—
88	C₃×#103	C₂³	1	32	yes	complemented
89	C₃×#102	C₂³	1	32	yes	—
90	C₃×#97	C₂³	1	8	yes	complemented
91	C₃×C₄×C₈	C₂³	1	8	yes	complemented
92	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
95	#533	—	2	4	no	—
96	#533	C₂²×C₃	1	8	yes	complemented
97	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
98	C₂×#125	C₂²×C₃	1	2	yes	complemented
99	C₂×#124	—	2	2	no	—
100	C₂×#124	—	2	4	no	—
101	C₂×#124	C₂²×C₃	1	2	yes	—
102	C₂×#124	C₂²×C₃	1	2	yes	—
103	C₂×#124	C₂²×C₃	1	8	yes	—
104	C₂×C₂²⋊Q₈	—	2	2	no	—
105	C₂×C₄×Q₈	—	2	2	no	—
106	C₂×#117	C₂²×C₃	1	2	yes	—
107	C₂²×C₂²⋊C₄	—	2	2	no	—
108	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
109	#489	C₂²×C₃	1	32	yes	complemented
110	#488	C₂²×C₃	1	32	yes	complemented
111	#419	C₂²×C₃	1	16	yes	complemented
112	#418	C₂²×C₃	1	16	yes	—
113	C₂×#103	C₂²×C₃	1	8	yes	complemented
114	C₂×#102	C₂²×C₃	1	8	yes	—
115	C₄×M₁₆	C₂²×C₃	1	8	yes	complemented
116	C₂×#97	C₂²×C₃	1	2	yes	complemented
117	C₂×C₄×C₈	C₂²×C₃	1	2	yes	complemented
118	C₂⁴×C₃	—	2	4	no	—
119	C₂⁴×C₃	—	2	2	no	—
120	C₂⁴×C₃	—	4	8	no	—
121	C₂⁴×C₃	—	4	4	no	—
122	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×Q₈	—	2	8	no	—
124	C₂×C₃×Q₈	—	2	4	no	—
125	C₂×C₃×Q₈	—	2	2	no	—
126	C₂×C₃×Q₈	—	2	8	no	—
127	C₂×C₃×Q₈	—	2	16	no	—
128	C₂×C₃×Q₈	—	4	8	no	—
129	C₂×C₃×Q₈	—	4	8	no	—
130	C₂×C₃×Q₈	—	4	4	no	—
131	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
132	C₂×C₃×D₄	—	2	4	no	—
133	C₂×C₃×D₄	—	2	2	no	—
134	C₂×C₃×D₄	—	2	8	no	—
135	C₂×C₃×D₄	—	2	16	no	—
136	C₂×C₃×D₄	—	4	8	no	—
137	C₂×C₃×D₄	—	4	4	no	—
138	C₂×C₃×D₄	C₂⁴	1	4	yes	—
139	C₂²×C₃×C₄	—	2	4	no	—
140	C₂²×C₃×C₄	—	2	4	no	—
141	C₂²×C₃×C₄	—	2	2	no	—
142	C₂²×C₃×C₄	—	4	4	no	—
143	C₂²×C₃×C₄	—	4	4	no	—
144	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
145	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
146	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
147	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
148	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₃×C₄	#41	1	8	yes	—
150	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
151	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
152	C₃×M₁₆	—	2	16	no	—
153	C₂×C₃×C₈	—	2	8	no	—
154	C₂×C₃×C₈	C₂⁴	1	8	yes	—
155	C₃×C₄⋊C₄	—	2	16	no	—
156	C₃×C₄⋊C₄	—	2	8	no	—
157	C₃×C₄⋊C₄	—	2	4	no	—
158	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
159	C₃×C₂²⋊C₄	—	2	8	no	—
160	C₃×C₂²⋊C₄	—	2	16	no	—
161	C₃×C₂²⋊C₄	—	2	16	no	—
162	C₃×C₄²	—	2	8	no	—
163	C₃×C₄²	C₂×D₄	1	8	yes	—
164	C₃×C₄²	C₂×D₄	1	2	yes	—
165	C₃×C₄²	C₂×D₄	1	2	yes	—
166	C₃×C₄²	C₂⁴	1	2	yes	—
167	C₃×C₄²	C₂⁴	1	2	yes	—
168	C₂⁵	—	2	1	no	—
169	C₂²×Q₈	—	2	2	no	—
170	C₂²×Q₈	—	2	1	no	—
171	C₂²×Q₈	—	2	2	no	—
172	C₂²×Q₈	—	2	8	no	—
173	C₂²×Q₈	C₂³×C₃	1	2	yes	—
174	C₂²×Q₈	C₂³×C₃	1	4	yes	—
175	C₂²×D₄	—	2	1	no	—
176	C₂²×D₄	—	2	2	no	—
177	C₂²×D₄	—	2	8	no	—
178	C₂²×D₄	C₂³×C₃	1	2	yes	—
179	C₂²×D₄	C₂³×C₃	1	4	yes	—
180	C₂³×C₄	—	2	1	no	—
181	C₂³×C₄	C₃×D₄	1	2	yes	—
182	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂×M₁₆	—	2	8	no	—
184	C₂×M₁₆	C₂³×C₃	1	8	yes	—
185	C₂²×C₈	C₂³×C₃	1	4	yes	—
186	C₄⋊Q₈	—	2	4	no	—
187	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
188	#125	—	2	4	no	—
189	#125	C₂³×C₃	1	8	yes	complemented
190	#124	—	2	16	no	—
191	#124	—	2	4	no	—
192	#124	—	2	4	no	—
193	#124	C₂³×C₃	1	8	yes	—
194	#124	C₂³×C₃	1	8	yes	—
195	C₂²⋊Q₈	—	2	16	no	—
196	C₄×Q₈	—	2	16	no	—
197	#117	—	2	4	no	—
198	#117	C₂³×C₃	1	8	yes	—
199	C₂×C₄⋊C₄	—	2	4	no	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
202	C₂×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₂²⋊C₄	—	2	4	no	—
205	C₂×C₂²⋊C₄	—	2	16	no	—
206	C₂×C₄²	—	2	2	no	—
207	C₂×C₄²	C₃×D₄	1	2	yes	—
208	C₂×C₄²	C₃×D₄	1	4	yes	—
209	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₃	1	4	yes	—
212	#103	C₂³×C₃	1	32	yes	complemented
213	#102	C₂³×C₃	1	32	yes	—
214	#97	C₂³×C₃	1	8	yes	complemented
215	C₄×C₈	C₂³×C₃	1	8	yes	complemented
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	4	16	no	—
219	C₂³×C₃	—	4	8	no	—
220	C₂³×C₃	—	4	4	no	—
221	C₂³×C₃	—	4	8	no	—
222	C₂³×C₃	—	8	16	no	—
223	C₂³×C₃	#124	1	4	yes	—
224	C₂³×C₃	C₂²×D₄	1	2	yes	—
225	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
226	C₃×Q₈	—	2	8	no	—
227	C₃×Q₈	—	4	16	no	—
228	C₃×Q₈	—	4	8	no	—
229	C₃×Q₈	—	4	4	no	—
230	C₃×D₄	—	2	8	no	—
231	C₃×D₄	—	4	8	no	—
232	C₃×D₄	—	4	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	4	8	no	—
238	C₂×C₃×C₄	—	4	8	no	—
239	C₂×C₃×C₄	—	4	4	no	—
240	C₂×C₃×C₄	—	4	8	no	—
241	C₂×C₃×C₄	#124	1	8	yes	—
242	C₂×C₃×C₄	#124	1	4	yes	—
243	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
244	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
245	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
246	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×#41	1	4	yes	—
248	C₂×C₃×C₄	C₂×#41	1	8	yes	—
249	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
250	C₃×C₈	—	2	8	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	2	no	—
253	C₂⁴	—	4	8	no	—
254	C₂⁴	—	4	4	no	—
255	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×Q₈	—	2	8	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	8	no	—
260	C₂×Q₈	—	2	16	no	—
261	C₂×Q₈	—	4	8	no	—
262	C₂×Q₈	—	4	8	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	4	8	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	C₂⁴×C₃	1	4	yes	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
278	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
279	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
280	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
282	C₂²×C₄	C₃×#41	1	8	yes	—
283	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
285	M₁₆	—	2	16	no	—
286	C₂×C₈	—	2	8	no	—
287	C₂×C₈	C₂⁴×C₃	1	8	yes	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	—	2	16	no	—
294	C₂²⋊C₄	—	2	16	no	—
295	C₄²	—	2	8	no	—
296	C₄²	C₂×C₃×D₄	1	8	yes	—
297	C₄²	C₂×C₃×D₄	1	2	yes	—
298	C₄²	C₂×C₃×D₄	1	2	yes	—
299	C₄²	C₂⁴×C₃	1	2	yes	—
300	C₄²	C₂⁴×C₃	1	2	yes	—
301	C₂²×C₃	—	2	8	no	—
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	4	8	no	—
305	C₂²×C₃	—	8	16	no	—
306	C₂²×C₃	—	8	8	no	—
307	C₂²×C₃	C₂×#124	1	4	yes	—
308	C₂²×C₃	C₂×#124	1	2	yes	—
309	C₂²×C₃	#575	1	4	yes	—
310	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	—	4	8	no	—
315	C₃×C₄	C₂×#124	1	4	yes	—
316	C₃×C₄	C₂×#124	1	2	yes	—
317	C₃×C₄	C₂²×#41	1	2	yes	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	4	no	—
320	C₂³	—	4	16	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	8	16	no	—
325	C₂³	C₃×#124	1	4	yes	—
326	C₂³	C₂²×C₃×D₄	1	2	yes	—
327	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
328	Q₈	—	2	8	no	—
329	Q₈	—	4	16	no	—
330	Q₈	—	4	8	no	—
331	Q₈	—	4	4	no	—
332	D₄	—	2	8	no	—
333	D₄	—	4	8	no	—
334	D₄	—	4	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	C₃×#124	1	8	yes	—
344	C₂×C₄	C₃×#124	1	4	yes	—
345	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
346	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
347	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
348	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₃×#41	1	4	yes	—
350	C₂×C₄	C₂×C₃×#41	1	8	yes	—
351	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
352	C₈	—	2	8	no	—
353	C₂×C₃	—	2	4	no	—
354	C₂×C₃	—	8	4	no	—
355	C₂×C₃	#3140	1	4	yes	direct product factor
356	C₂×C₃	C₂²×#124	1	1	yes	characteristic
357	C₂×C₃	C₂×#575	1	2	yes	—
358	C₂²	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	8	no	—
362	C₂²	—	8	16	no	—
363	C₂²	—	8	8	no	—
364	C₂²	C₂×C₃×#124	1	4	yes	—
365	C₂²	C₂×C₃×#124	1	2	yes	—
366	C₂²	C₃×#575	1	4	yes	—
367	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
368	C₄	—	2	4	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	8	no	—
372	C₄	C₂×C₃×#124	1	4	yes	—
373	C₄	C₂×C₃×#124	1	2	yes	—
374	C₄	C₂²×C₃×#41	1	2	yes	—
375	C₃	C₂×#3140	1	1	yes	characteristic, direct product factor, Sylow
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₃×#3140	1	4	yes	direct product factor
379	C₂	C₂²×C₃×#124	1	1	yes	characteristic
380	C₂	C₂×C₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#533	C₂	semidirect
3. C₃×#3140	C₂	direct (N × H)
4. C₂×C₃×#489	C₂	semidirect
5. C₂×C₃×#488	C₂	semidirect
6. C₂×C₃×#419	C₂	semidirect
8. C₂×C₃×C₄×M₁₆	C₂	semidirect
9. C₂×#3140	C₃	direct (N × H)
14. C₃×#533	C₂²	semidirect
15. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₃×#125	C₂²	semidirect
27. C₃×#489	C₂²	semidirect
28. C₃×#488	C₂²	semidirect
29. C₃×#419	C₂²	semidirect
31. C₂×C₃×#103	C₂²	semidirect
33. C₃×C₄×M₁₆	C₂²	semidirect
34. C₂×C₃×#97	C₂²	semidirect
35. C₂×C₃×C₄×C₈	C₂²	semidirect
36. C₂×#533	C₂×C₃	semidirect
38. #3140	C₂×C₃	direct (N × H)
39. C₂×#489	C₂×C₃	semidirect
40. C₂×#488	C₂×C₃	semidirect
41. C₂×#419	C₂×C₃	semidirect
43. C₂×C₄×M₁₆	C₂×C₃	semidirect
63. C₃×C₄⋊Q₈	C₂³	semidirect
65. C₃×#125	C₂³	semidirect
88. C₃×#103	C₂³	semidirect
90. C₃×#97	C₂³	semidirect
91. C₃×C₄×C₈	C₂³	semidirect
96. #533	C₂²×C₃	semidirect
97. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
98. C₂×#125	C₂²×C₃	semidirect
109. #489	C₂²×C₃	semidirect
110. #488	C₂²×C₃	semidirect
111. #419	C₂²×C₃	semidirect
113. C₂×#103	C₂²×C₃	semidirect
115. C₄×M₁₆	C₂²×C₃	semidirect
116. C₂×#97	C₂²×C₃	semidirect
117. C₂×C₄×C₈	C₂²×C₃	semidirect
187. C₄⋊Q₈	C₂³×C₃	semidirect
189. #125	C₂³×C₃	semidirect
212. #103	C₂³×C₃	semidirect
214. #97	C₂³×C₃	semidirect
215. C₄×C₈	C₂³×C₃	semidirect
355. C₂×C₃	#3140	direct (N × H)
375. C₃	C₂×#3140	direct (N × H)
378. C₂	C₃×#3140	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#533	2
C₂²×C₃×#124	2
C₃×#3140	2
C₂×C₃×#489	2
C₂×C₃×#488	2
C₂×C₃×#419	2
C₂×C₃×#418	2
C₂×C₃×C₄×M₁₆	2
C₂×#3140	3

Subgroups — C2×C3×#3140 #10679222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3140 #10679222