Subgroups — C₂²×C₃×#924 #11900322

Order 1152.

4361 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#217	C₂	1	2	yes	maximal
4	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#924	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃×C₂²⋊Q₈	—	3	1	no	maximal
8	C₂²×#924	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
10	C₂³×C₃²×C₄	—	2	8	no	—
11	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃²×C₄	C₂²	1	12	yes	—
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
15	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
16	C₂²×C₃×Dic₆	—	2	8	no	—
17	C₂²×C₃×Dic₆	C₂²	1	12	yes	complemented
18	C₂×C₃×#217	C₂²	1	24	yes	—
19	C₂×C₃×C₄⋊Dic₃	C₂²	1	12	yes	complemented
20	C₃×#924	C₂²	1	64	yes	direct product factor
21	C₂×C₃×Dic₃⋊C₄	C₂²	1	24	yes	complemented
22	C₂³×C₃×Q₈	—	3	1	no	—
23	C₂⁴×C₃×C₄	—	2	1	no	—
24	C₂⁴×C₃×C₄	D₃	1	1	yes	characteristic
25	C₂⁴×C₃×C₄	C₂×C₃	1	1	yes	characteristic
26	C₂³×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×C₂²⋊Q₈	—	3	24	no	—
28	C₂²×C₃×C₄⋊C₄	—	3	2	no	—
29	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
30	C₂²×C₃×C₂²⋊C₄	—	3	2	no	—
31	C₂²×#217	C₂×C₃	1	2	yes	—
32	C₂²×C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#924	C₂×C₃	1	24	yes	direct product factor
34	C₂²×Dic₃⋊C₄	C₂×C₃	1	2	yes	complemented
35	C₂⁴×C₃²	—	2	4	no	—
36	C₂⁴×C₃²	—	2	4	no	—
37	C₂⁴×C₃²	Q₈	1	8	yes	complemented
38	C₂⁴×C₃²	C₂³	1	6	yes	—
39	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
40	C₂²×C₃²×C₄	—	2	4	no	—
41	C₂²×C₃²×C₄	—	2	48	no	—
42	C₂²×C₃²×C₄	D₄	1	8	yes	—
43	C₂²×C₃²×C₄	C₂³	1	6	yes	—
44	C₂²×C₃²×C₄	C₂³	1	16	yes	—
45	C₂²×C₃²×C₄	C₂³	1	6	yes	—
46	C₂²×C₃×Dic₃	—	2	8	no	—
47	C₂²×C₃×Dic₃	—	2	8	no	—
48	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
49	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
50	C₂×C₃×Dic₆	—	2	48	no	—
51	C₂×C₃×Dic₆	C₂³	1	16	yes	complemented
52	C₃×#217	C₂³	1	32	yes	—
53	C₃×C₄⋊Dic₃	C₂³	1	16	yes	complemented
54	C₃×Dic₃⋊C₄	C₂³	1	32	yes	complemented
55	C₂²×C₂²⋊Q₈	—	3	1	no	Sylow
56	C₂⁵×C₃	—	2	1	no	—
57	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
58	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
59	C₂²×C₃×Q₈	—	3	12	no	—
60	C₂²×C₃×Q₈	—	6	8	no	—
61	C₂³×C₃×C₄	—	2	16	no	—
62	C₂³×C₃×C₄	—	2	8	no	—
63	C₂³×C₃×C₄	—	2	8	no	—
64	C₂³×C₃×C₄	—	2	1	no	—
65	C₂³×C₃×C₄	—	2	12	no	—
66	C₂³×C₃×C₄	—	2	1	no	—
67	C₂³×C₃×C₄	—	3	2	no	—
68	C₂³×C₃×C₄	—	3	2	no	—
69	C₂³×C₃×C₄	C₂×D₃	1	12	yes	—
70	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
71	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
72	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
73	C₂³×C₃×C₄	C₂²×C₃	1	12	yes	—
74	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
76	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
77	C₂²×Dic₆	—	2	8	no	—
78	C₂²×Dic₆	C₂²×C₃	1	12	yes	complemented
79	C₃×C₂²⋊Q₈	—	3	64	no	—
80	C₂×C₃×C₄⋊C₄	—	3	24	no	—
81	C₂×C₃×C₄⋊C₄	—	3	12	no	—
82	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
83	C₂×#217	C₂²×C₃	1	24	yes	—
84	C₂×C₄⋊Dic₃	C₂²×C₃	1	12	yes	complemented
85	#924	C₂²×C₃	1	64	yes	direct product factor
86	C₂×Dic₃⋊C₄	C₂²×C₃	1	24	yes	complemented
87	C₂³×C₃²	—	2	32	no	—
88	C₂³×C₃²	—	2	12	no	—
89	C₂³×C₃²	—	2	12	no	—
90	C₂³×C₃²	C₂×D₄	1	4	yes	—
91	C₂³×C₃²	C₂×Q₈	1	4	yes	—
92	C₂³×C₃²	C₂×Q₈	1	24	yes	complemented
93	C₂³×C₃²	#41	1	4	yes	—
94	C₂³×C₃²	C₂⁴	1	4	yes	—
95	C₂³×C₃²	C₂⁴	1	3	yes	—
96	C₂×C₃²×C₄	—	2	12	no	—
97	C₂×C₃²×C₄	—	2	32	no	—
98	C₂×C₃²×C₄	C₂×D₄	1	24	yes	—
99	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
100	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
101	C₂×C₃×Dic₃	—	2	24	no	—
102	C₂×C₃×Dic₃	—	2	24	no	—
103	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
104	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
105	C₃×Dic₆	—	2	32	no	—
106	C₂³×Q₈	—	3	1	no	—
107	C₂⁴×C₄	C₃×D₃	1	1	yes	characteristic
108	C₂×C₂²⋊Q₈	—	3	24	no	—
109	C₂²×C₄⋊C₄	—	3	2	no	—
110	C₂²×C₄⋊C₄	—	3	1	no	—
111	C₂²×C₂²⋊C₄	—	3	2	no	—
112	C₂⁴×C₃	—	2	8	no	—
113	C₂⁴×C₃	—	2	8	no	—
114	C₂⁴×C₃	—	2	4	no	—
115	C₂⁴×C₃	—	2	4	no	—
116	C₂⁴×C₃	—	2	4	no	—
117	C₂⁴×C₃	—	2	4	no	—
118	C₂⁴×C₃	—	2	8	no	—
119	C₂⁴×C₃	—	2	6	no	—
120	C₂⁴×C₃	—	2	1	no	—
121	C₂⁴×C₃	Dic₆	1	8	yes	complemented
122	C₂⁴×C₃	C₃×Q₈	1	8	yes	complemented
123	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
124	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
125	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
126	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₃×Q₈	—	3	16	no	—
128	C₂×C₃×Q₈	—	6	48	no	—
129	C₂²×C₃×C₄	—	2	8	no	—
130	C₂²×C₃×C₄	—	2	96	no	—
131	C₂²×C₃×C₄	—	2	4	no	—
132	C₂²×C₃×C₄	—	2	4	no	—
133	C₂²×C₃×C₄	—	2	48	no	—
134	C₂²×C₃×C₄	—	2	48	no	—
135	C₂²×C₃×C₄	—	2	8	no	—
136	C₂²×C₃×C₄	—	2	6	no	—
137	C₂²×C₃×C₄	—	2	16	no	—
138	C₂²×C₃×C₄	—	2	6	no	—
139	C₂²×C₃×C₄	—	3	12	no	—
140	C₂²×C₃×C₄	—	3	12	no	—
141	C₂²×C₃×C₄	—	6	8	no	—
142	C₂²×C₃×C₄	—	6	8	no	—
143	C₂²×C₃×C₄	#67	1	8	yes	—
144	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
145	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
146	C₂²×C₃×C₄	C₂²×D₃	1	16	yes	—
147	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
148	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
149	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
150	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
151	C₂²×Dic₃	—	2	8	no	—
152	C₂²×Dic₃	—	2	8	no	—
153	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
154	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
155	C₂×Dic₆	—	2	48	no	—
156	C₂×Dic₆	C₂³×C₃	1	16	yes	complemented
157	C₃×C₄⋊C₄	—	3	32	no	—
158	C₃×C₄⋊C₄	—	3	16	no	—
159	C₃×C₂²⋊C₄	—	3	32	no	—
160	#217	C₂³×C₃	1	32	yes	—
161	C₄⋊Dic₃	C₂³×C₃	1	16	yes	complemented
162	Dic₃⋊C₄	C₂³×C₃	1	32	yes	complemented
163	C₂²×C₃²	—	2	48	no	—
164	C₂²×C₃²	—	2	4	no	—
165	C₂²×C₃²	—	2	4	no	—
166	C₂²×C₃²	C₂²⋊Q₈	1	16	yes	complemented
167	C₂²×C₃²	C₂²×D₄	1	6	yes	—
168	C₂²×C₃²	C₂²×Q₈	1	6	yes	—
169	C₂²×C₃²	C₂²×Q₈	1	8	yes	complemented
170	C₂²×C₃²	C₂×#41	1	6	yes	—
171	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
172	C₃²×C₄	—	2	4	no	—
173	C₃²×C₄	C₂²×D₄	1	8	yes	—
174	C₃×Dic₃	—	2	8	no	—
175	C₃×Dic₃	—	2	8	no	—
176	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂²×Q₈	—	3	12	no	—
178	C₂²×Q₈	—	6	8	no	—
179	C₂³×C₄	—	2	8	no	—
180	C₂³×C₄	—	3	2	no	—
181	C₂³×C₄	—	3	2	no	—
182	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂³×C₄	C₂×C₃×D₃	1	12	yes	—
184	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
185	C₂²⋊Q₈	—	3	64	no	—
186	C₂×C₄⋊C₄	—	3	24	no	—
187	C₂×C₄⋊C₄	—	3	12	no	—
188	C₂×C₂²⋊C₄	—	3	24	no	—
189	C₂³×C₃	—	2	24	no	—
190	C₂³×C₃	—	2	64	no	—
191	C₂³×C₃	—	2	24	no	—
192	C₂³×C₃	—	2	32	no	—
193	C₂³×C₃	—	2	32	no	—
194	C₂³×C₃	—	2	12	no	—
195	C₂³×C₃	—	2	12	no	—
196	C₂³×C₃	—	2	12	no	—
197	C₂³×C₃	—	2	12	no	—
198	C₂³×C₃	—	2	4	no	—
199	C₂³×C₃	—	2	3	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	—	2	24	no	—
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	—	2	4	no	—
204	C₂³×C₃	C₂×Dic₆	1	4	yes	—
205	C₂³×C₃	C₂×Dic₆	1	24	yes	complemented
206	C₂³×C₃	#235	1	4	yes	—
207	C₂³×C₃	C₂×#67	1	4	yes	—
208	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
209	C₂³×C₃	C₂×C₃×Q₈	1	4	yes	—
210	C₂³×C₃	C₂×C₃×Q₈	1	24	yes	complemented
211	C₂³×C₃	C₃×#41	1	4	yes	—
212	C₂³×C₃	C₂³×D₃	1	4	yes	—
213	C₂³×C₃	C₂³×D₃	1	3	yes	—
214	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
215	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
216	C₃×Q₈	—	6	32	no	—
217	C₂×C₃×C₄	—	2	24	no	—
218	C₂×C₃×C₄	—	2	64	no	—
219	C₂×C₃×C₄	—	2	12	no	—
220	C₂×C₃×C₄	—	2	12	no	—
221	C₂×C₃×C₄	—	2	32	no	—
222	C₂×C₃×C₄	—	2	32	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	24	no	—
226	C₂×C₃×C₄	—	3	8	no	—
227	C₂×C₃×C₄	—	3	8	no	—
228	C₂×C₃×C₄	—	6	24	no	—
229	C₂×C₃×C₄	—	6	24	no	—
230	C₂×C₃×C₄	C₂×#67	1	24	yes	—
231	C₂×C₃×C₄	C₂×C₃×D₄	1	24	yes	—
232	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
233	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
234	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
235	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
236	C₂×Dic₃	—	2	24	no	—
237	C₂×Dic₃	—	2	24	no	—
238	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
239	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
240	Dic₆	—	2	32	no	—
241	C₂×C₃²	—	2	8	no	—
242	C₂×C₃²	C₂×C₂²⋊Q₈	1	12	yes	complemented
243	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
244	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
245	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
246	C₂⁴	—	2	4	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	C₃×Dic₆	1	8	yes	complemented
249	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
250	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
251	C₂×Q₈	—	3	16	no	—
252	C₂×Q₈	—	6	48	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	48	no	—
255	C₂²×C₄	—	3	12	no	—
256	C₂²×C₄	—	3	12	no	—
257	C₂²×C₄	—	6	8	no	—
258	C₂²×C₄	—	6	8	no	—
259	C₂²×C₄	C₃×#67	1	8	yes	—
260	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
261	C₂²×C₄	C₂²×C₃×D₃	1	16	yes	—
262	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
263	C₄⋊C₄	—	3	32	no	—
264	C₄⋊C₄	—	3	16	no	—
265	C₂²⋊C₄	—	3	32	no	—
266	C₂²×C₃	—	2	8	no	—
267	C₂²×C₃	—	2	96	no	—
268	C₂²×C₃	—	2	8	no	—
269	C₂²×C₃	—	2	4	no	—
270	C₂²×C₃	—	2	4	no	—
271	C₂²×C₃	—	2	4	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	2	48	no	—
274	C₂²×C₃	—	2	48	no	—
275	C₂²×C₃	—	2	16	no	—
276	C₂²×C₃	—	2	6	no	—
277	C₂²×C₃	—	2	8	no	—
278	C₂²×C₃	—	2	6	no	—
279	C₂²×C₃	—	2	6	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	#924	1	16	yes	direct product factor
282	C₂²×C₃	C₃×C₂²⋊Q₈	1	16	yes	complemented
283	C₂²×C₃	C₂²×Dic₆	1	6	yes	—
284	C₂²×C₃	C₂²×Dic₆	1	8	yes	complemented
285	C₂²×C₃	C₂×#235	1	6	yes	—
286	C₂²×C₃	C₂²×#67	1	6	yes	—
287	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
288	C₂²×C₃	C₂²×C₃×Q₈	1	6	yes	—
289	C₂²×C₃	C₂²×C₃×Q₈	1	8	yes	complemented
290	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
291	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
292	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
293	C₃×C₄	—	2	8	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	8	no	—
297	C₃×C₄	—	6	8	no	—
298	C₃×C₄	—	6	8	no	—
299	C₃×C₄	C₂²×#67	1	8	yes	—
300	C₃×C₄	C₂²×C₃×D₄	1	8	yes	—
301	Dic₃	—	2	8	no	—
302	Dic₃	—	2	8	no	—
303	C₃²	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
304	C₂³	—	2	32	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	2	12	no	—
307	C₂³	C₂×C₃×Dic₆	1	4	yes	—
308	C₂³	C₂×C₃×Dic₆	1	24	yes	complemented
309	C₂³	C₃×#235	1	4	yes	—
310	C₂³	C₂×C₃×#67	1	4	yes	—
311	C₂³	C₂³×C₃×D₃	1	4	yes	—
312	C₂³	C₂³×C₃×D₃	1	3	yes	—
313	Q₈	—	6	32	no	—
314	C₂×C₄	—	2	12	no	—
315	C₂×C₄	—	2	32	no	—
316	C₂×C₄	—	3	8	no	—
317	C₂×C₄	—	3	8	no	—
318	C₂×C₄	—	6	24	no	—
319	C₂×C₄	—	6	24	no	—
320	C₂×C₄	C₂×C₃×#67	1	24	yes	—
321	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
322	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
323	C₂×C₃	—	2	16	no	—
324	C₂×C₃	—	2	8	no	—
325	C₂×C₃	—	2	8	no	—
326	C₂×C₃	—	2	12	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	C₂×#924	1	12	yes	direct product factor
331	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	12	yes	complemented
332	C₂×C₃	C₂³×Dic₆	1	1	yes	characteristic
333	C₂×C₃	C₂²×#235	1	1	yes	characteristic
334	C₂×C₃	C₂³×#67	1	1	yes	characteristic
335	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
336	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
337	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
338	C₂²	—	2	48	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	C₃×#924	1	16	yes	direct product factor
342	C₂²	C₂²×C₃×Dic₆	1	6	yes	—
343	C₂²	C₂²×C₃×Dic₆	1	8	yes	complemented
344	C₂²	C₂×C₃×#235	1	6	yes	—
345	C₂²	C₂²×C₃×#67	1	6	yes	—
346	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	6	8	no	—
349	C₄	—	6	8	no	—
350	C₄	C₂²×C₃×#67	1	8	yes	—
351	C₃	—	2	1	no	—
352	C₃	C₂²×#924	1	1	yes	characteristic, direct product factor
353	C₃	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented
354	C₂	—	2	8	no	—
355	C₂	C₂×C₃×#924	1	12	yes	direct product factor
356	C₂	C₂³×C₃×Dic₆	1	1	yes	characteristic
357	C₂	C₂²×C₃×#235	1	1	yes	characteristic
358	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂⁴×C₃²×C₄	C₂
socle	C₂⁴×C₃²	C₂³
prime radical	C₂⁵×C₃²	C₂²
hypercenter	C₂⁴×C₃×C₄	D₃
hypocenter	C₃	C₂²×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁴×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₆	C₂	semidirect
4. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
5. C₂×C₃×#924	C₂	direct (N × H)
6. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
8. C₂²×#924	C₃	direct (N × H)
17. C₂²×C₃×Dic₆	C₂²	semidirect
19. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
20. C₃×#924	C₂²	direct (N × H)
21. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
26. C₂³×Dic₆	C₂×C₃	semidirect
32. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
33. C₂×#924	C₂×C₃	direct (N × H)
34. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
37. C₂⁴×C₃²	Q₈	semidirect
51. C₂×C₃×Dic₆	C₂³	semidirect
53. C₃×C₄⋊Dic₃	C₂³	semidirect
54. C₃×Dic₃⋊C₄	C₂³	semidirect
78. C₂²×Dic₆	C₂²×C₃	semidirect
84. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
85. #924	C₂²×C₃	direct (N × H)
86. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
92. C₂³×C₃²	C₂×Q₈	semidirect
121. C₂⁴×C₃	Dic₆	semidirect
122. C₂⁴×C₃	C₃×Q₈	semidirect
156. C₂×Dic₆	C₂³×C₃	semidirect
161. C₄⋊Dic₃	C₂³×C₃	semidirect
162. Dic₃⋊C₄	C₂³×C₃	semidirect
166. C₂²×C₃²	C₂²⋊Q₈	semidirect
169. C₂²×C₃²	C₂²×Q₈	semidirect
205. C₂³×C₃	C₂×Dic₆	semidirect
210. C₂³×C₃	C₂×C₃×Q₈	semidirect
242. C₂×C₃²	C₂×C₂²⋊Q₈	semidirect
248. C₂⁴	C₃×Dic₆	semidirect
281. C₂²×C₃	#924	direct (N × H)
282. C₂²×C₃	C₃×C₂²⋊Q₈	semidirect
284. C₂²×C₃	C₂²×Dic₆	semidirect
289. C₂²×C₃	C₂²×C₃×Q₈	semidirect
303. C₃²	C₂²×C₂²⋊Q₈	semidirect
308. C₂³	C₂×C₃×Dic₆	semidirect
330. C₂×C₃	C₂×#924	direct (N × H)
331. C₂×C₃	C₂×C₃×C₂²⋊Q₈	semidirect
341. C₂²	C₃×#924	direct (N × H)
343. C₂²	C₂²×C₃×Dic₆	semidirect
352. C₃	C₂²×#924	direct (N × H)
353. C₃	C₂²×C₃×C₂²⋊Q₈	semidirect
355. C₂	C₂×C₃×#924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²×C₄	2
C₂³×C₃×Dic₆	2
C₂²×C₃×#217	2
C₂²×C₃×C₄⋊Dic₃	2
C₂×C₃×#924	2
C₂²×C₃×Dic₃⋊C₄	2
C₂²×C₃×C₂²⋊Q₈	3
C₂²×#924	3

Subgroups — C22×C3×#924 #11900322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#924 #11900322