Subgroups — C₂²×C₃×#897 #11900325

Order 1152.

3889 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
5	C₂²×C₃×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#897	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₃×C₂²⋊Q₈	—	3	1	no	maximal
8	C₂²×#897	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃²×C₄	C₂²	1	2	yes	—
11	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
13	C₂³×C₃×Dic₃	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₃	—	2	8	no	—
15	C₂²×C₃×C₄×D₃	C₂²	1	12	yes	—
16	C₂²×C₃×Dic₆	—	2	8	no	—
17	C₂²×C₃×Dic₆	C₂²	1	12	yes	complemented
18	C₂×C₃²×C₄⋊C₄	C₂²	1	12	yes	complemented
19	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	24	yes	—
20	C₂×C₃×C₄⋊Dic₃	C₂²	1	24	yes	complemented
21	C₃×#897	C₂²	1	64	yes	direct product factor
22	C₂³×C₃×Q₈	—	3	1	no	—
23	C₂⁴×C₃×C₄	—	3	1	no	—
24	C₂³×C₄×D₃	C₂×C₃	1	1	yes	characteristic
25	C₂³×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×C₂²⋊Q₈	—	3	24	no	—
27	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
28	C₂²×C₃×C₄⋊C₄	—	3	2	no	—
29	C₂²×C₃×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
30	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₂²⋊C₄	—	3	2	no	—
32	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
33	C₂²×C₄⋊Dic₃	C₂×C₃	1	2	yes	complemented
34	C₂×#897	C₂×C₃	1	24	yes	direct product factor
35	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
36	C₂³×C₃×D₃	—	2	4	no	—
37	C₂³×C₃×D₃	—	2	4	no	—
38	C₂³×C₃×D₃	Q₈	1	8	yes	complemented
39	C₂³×C₃×D₃	C₂³	1	6	yes	—
40	C₂²×C₃²×C₄	—	2	8	no	—
41	C₂²×C₃²×C₄	D₄	1	8	yes	—
42	C₂²×C₃²×C₄	C₂³	1	12	yes	—
43	C₂²×C₃²×C₄	C₂³	1	6	yes	—
44	C₂²×C₃×Dic₃	—	2	8	no	—
45	C₂²×C₃×Dic₃	—	2	4	no	—
46	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
47	C₂²×C₃×Dic₃	C₂³	1	12	yes	—
48	C₂×C₃×C₄×D₃	—	2	48	no	—
49	C₂×C₃×C₄×D₃	C₂³	1	16	yes	—
50	C₂×C₃×Dic₆	—	2	48	no	—
51	C₂×C₃×Dic₆	C₂³	1	16	yes	complemented
52	C₃²×C₄⋊C₄	C₂³	1	16	yes	complemented
53	C₃×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
54	C₃×C₄⋊Dic₃	C₂³	1	32	yes	complemented
55	C₂²×C₂²⋊Q₈	—	3	1	no	Sylow
56	C₂⁵×C₃	—	3	1	no	—
57	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₃×Q₈	—	3	12	no	—
59	C₂²×C₃×Q₈	—	6	8	no	—
60	C₂³×C₃×C₄	—	2	1	no	—
61	C₂³×C₃×C₄	—	2	2	no	—
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂³×C₃×C₄	—	3	2	no	—
64	C₂³×C₃×C₄	—	3	12	no	—
65	C₂³×C₃×C₄	—	6	8	no	—
66	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
67	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
68	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
69	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂³×Dic₃	C₂²×C₃	1	2	yes	—
71	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₄×D₃	—	2	8	no	—
73	C₂²×C₄×D₃	C₂²×C₃	1	12	yes	—
74	C₂²×Dic₆	—	2	8	no	—
75	C₂²×Dic₆	C₂²×C₃	1	12	yes	complemented
76	C₃×C₂²⋊Q₈	—	3	64	no	—
77	C₂×C₃×C₄⋊C₄	—	2	12	no	—
78	C₂×C₃×C₄⋊C₄	—	3	24	no	—
79	C₂×C₃×C₄⋊C₄	C₂×D₃	1	12	yes	complemented
80	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	12	yes	complemented
81	C₂×C₃×C₂²⋊C₄	—	3	24	no	—
82	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	24	yes	—
83	C₂×C₄⋊Dic₃	C₂²×C₃	1	24	yes	complemented
84	#897	C₂²×C₃	1	64	yes	direct product factor
85	C₂³×C₃²	C₂×D₄	1	4	yes	—
86	C₂³×C₃²	C₂×Q₈	1	4	yes	—
87	C₂³×C₃²	#41	1	4	yes	—
88	C₂³×C₃²	C₂⁴	1	3	yes	—
89	C₂²×C₃×D₃	—	2	32	no	—
90	C₂²×C₃×D₃	—	2	12	no	—
91	C₂²×C₃×D₃	—	2	12	no	—
92	C₂²×C₃×D₃	C₂×Q₈	1	24	yes	complemented
93	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
94	C₂×C₃²×C₄	—	2	24	no	—
95	C₂×C₃²×C₄	C₂×D₄	1	24	yes	—
96	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
97	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
98	C₂×C₃×Dic₃	—	2	24	no	—
99	C₂×C₃×Dic₃	—	2	12	no	—
100	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
101	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
102	C₃×C₄×D₃	—	2	32	no	—
103	C₃×Dic₆	—	2	32	no	—
104	C₂³×Q₈	—	3	1	no	—
105	C₂⁴×C₄	—	3	1	no	—
106	C₂×C₂²⋊Q₈	—	3	24	no	—
107	C₂²×C₄⋊C₄	—	3	2	no	—
108	C₂²×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic, complemented
109	C₂²×C₂²⋊C₄	—	3	2	no	—
110	C₂⁴×C₃	—	2	1	no	—
111	C₂⁴×C₃	—	3	8	no	—
112	C₂⁴×C₃	—	3	6	no	—
113	C₂⁴×C₃	—	6	4	no	—
114	C₂⁴×C₃	—	6	4	no	—
115	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
116	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
117	C₂³×D₃	—	2	4	no	—
118	C₂³×D₃	—	2	4	no	—
119	C₂³×D₃	C₃×Q₈	1	8	yes	complemented
120	C₂³×D₃	C₂³×C₃	1	6	yes	—
121	C₂×C₃×Q₈	—	3	16	no	—
122	C₂×C₃×Q₈	—	6	48	no	—
123	C₂²×C₃×C₄	—	2	8	no	—
124	C₂²×C₃×C₄	—	2	8	no	—
125	C₂²×C₃×C₄	—	2	8	no	—
126	C₂²×C₃×C₄	—	2	6	no	—
127	C₂²×C₃×C₄	—	2	12	no	—
128	C₂²×C₃×C₄	—	3	12	no	—
129	C₂²×C₃×C₄	—	3	6	no	—
130	C₂²×C₃×C₄	—	3	16	no	—
131	C₂²×C₃×C₄	—	4	8	no	—
132	C₂²×C₃×C₄	—	6	4	no	—
133	C₂²×C₃×C₄	—	6	8	no	—
134	C₂²×C₃×C₄	—	6	48	no	—
135	C₂²×C₃×C₄	D₁₂	1	8	yes	—
136	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
137	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	—
138	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
139	C₂²×C₃×C₄	C₂³×C₃	1	12	yes	—
140	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
141	C₂²×Dic₃	—	2	8	no	—
142	C₂²×Dic₃	—	2	4	no	—
143	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
144	C₂²×Dic₃	C₂³×C₃	1	12	yes	—
145	C₂×C₄×D₃	—	2	48	no	—
146	C₂×C₄×D₃	C₂³×C₃	1	16	yes	—
147	C₂×Dic₆	—	2	48	no	—
148	C₂×Dic₆	C₂³×C₃	1	16	yes	complemented
149	C₃×C₄⋊C₄	—	2	16	no	—
150	C₃×C₄⋊C₄	—	3	32	no	—
151	C₃×C₄⋊C₄	C₂²×D₃	1	16	yes	complemented
152	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	complemented
153	C₃×C₂²⋊C₄	—	3	32	no	—
154	(C₂×D₃)⋊C₄	C₂³×C₃	1	32	yes	—
155	C₄⋊Dic₃	C₂³×C₃	1	32	yes	complemented
156	C₂²×C₃²	C₂²⋊Q₈	1	16	yes	complemented
157	C₂²×C₃²	C₂²×D₄	1	6	yes	—
158	C₂²×C₃²	C₂²×Q₈	1	6	yes	—
159	C₂²×C₃²	C₂×#41	1	6	yes	—
160	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×D₃	—	2	48	no	—
162	C₂×C₃×D₃	—	2	4	no	—
163	C₂×C₃×D₃	—	2	4	no	—
164	C₂×C₃×D₃	C₂²×Q₈	1	8	yes	complemented
165	C₃²×C₄	—	2	8	no	—
166	C₃²×C₄	C₂²×D₄	1	8	yes	—
167	C₃×Dic₃	—	2	8	no	—
168	C₃×Dic₃	—	2	4	no	—
169	C₂⁵	—	3	1	no	—
170	C₂²×Q₈	—	3	12	no	—
171	C₂²×Q₈	—	6	8	no	—
172	C₂³×C₄	—	3	2	no	—
173	C₂³×C₄	—	3	1	no	—
174	C₂³×C₄	—	3	12	no	—
175	C₂³×C₄	—	6	8	no	—
176	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
177	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
178	C₂²⋊Q₈	—	3	64	no	—
179	C₂×C₄⋊C₄	—	3	24	no	—
180	C₂×C₄⋊C₄	C₂×C₃×D₃	1	12	yes	complemented
181	C₂×C₂²⋊C₄	—	3	24	no	—
182	C₂³×C₃	—	2	3	no	—
183	C₂³×C₃	—	2	4	no	—
184	C₂³×C₃	—	2	4	no	—
185	C₂³×C₃	—	2	4	no	—
186	C₂³×C₃	—	3	24	no	—
187	C₂³×C₃	—	3	4	no	—
188	C₂³×C₃	—	6	32	no	—
189	C₂³×C₃	—	6	12	no	—
190	C₂³×C₃	—	6	12	no	—
191	C₂³×C₃	C₂×D₁₂	1	4	yes	—
192	C₂³×C₃	#237	1	4	yes	—
193	C₂³×C₃	D₃×Q₈	1	4	yes	—
194	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
195	C₂³×C₃	C₂×C₃×Q₈	1	4	yes	—
196	C₂³×C₃	C₃×#41	1	4	yes	—
197	C₂³×C₃	C₂³×D₃	1	3	yes	—
198	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
199	C₂²×D₃	—	2	32	no	—
200	C₂²×D₃	—	2	12	no	—
201	C₂²×D₃	—	2	12	no	—
202	C₂²×D₃	C₂×C₃×Q₈	1	24	yes	complemented
203	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
204	C₃×Q₈	—	6	32	no	—
205	C₂×C₃×C₄	—	2	24	no	—
206	C₂×C₃×C₄	—	2	24	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	8	no	—
209	C₂×C₃×C₄	—	2	24	no	—
210	C₂×C₃×C₄	—	3	8	no	—
211	C₂×C₃×C₄	—	3	4	no	—
212	C₂×C₃×C₄	—	4	24	no	—
213	C₂×C₃×C₄	—	6	12	no	—
214	C₂×C₃×C₄	—	6	24	no	—
215	C₂×C₃×C₄	—	6	32	no	—
216	C₂×C₃×C₄	C₂×D₁₂	1	24	yes	—
217	C₂×C₃×C₄	C₂×C₃×D₄	1	24	yes	—
218	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
219	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
220	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
221	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
222	C₂×Dic₃	—	2	24	no	—
223	C₂×Dic₃	—	2	12	no	—
224	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
225	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
226	C₄×D₃	—	2	32	no	—
227	Dic₆	—	2	32	no	—
228	C₂×C₃²	C₂×C₂²⋊Q₈	1	12	yes	complemented
229	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
230	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
231	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
232	C₃×D₃	—	2	8	no	—
233	C₂⁴	—	3	6	no	—
234	C₂⁴	—	3	8	no	—
235	C₂⁴	—	6	4	no	—
236	C₂⁴	—	6	4	no	—
237	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
238	C₂×Q₈	—	3	16	no	—
239	C₂×Q₈	—	6	48	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	3	12	no	—
242	C₂²×C₄	—	3	6	no	—
243	C₂²×C₄	—	3	16	no	—
244	C₂²×C₄	—	6	4	no	—
245	C₂²×C₄	—	6	8	no	—
246	C₂²×C₄	—	6	48	no	—
247	C₂²×C₄	C₃×D₁₂	1	8	yes	—
248	C₂²×C₄	C₂²×C₃×D₃	1	12	yes	—
249	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
250	C₄⋊C₄	—	3	32	no	—
251	C₄⋊C₄	C₂²×C₃×D₃	1	16	yes	complemented
252	C₂²⋊C₄	—	3	32	no	—
253	C₂²×C₃	—	2	16	no	—
254	C₂²×C₃	—	2	6	no	—
255	C₂²×C₃	—	2	6	no	—
256	C₂²×C₃	—	2	6	no	—
257	C₂²×C₃	—	2	1	no	—
258	C₂²×C₃	—	3	8	no	—
259	C₂²×C₃	—	6	4	no	—
260	C₂²×C₃	—	6	4	no	—
261	C₂²×C₃	—	6	48	no	—
262	C₂²×C₃	#897	1	16	yes	direct product factor
263	C₂²×C₃	C₃×C₂²⋊Q₈	1	16	yes	complemented
264	C₂²×C₃	C₂²×D₁₂	1	6	yes	—
265	C₂²×C₃	C₂×#237	1	6	yes	—
266	C₂²×C₃	C₂×D₃×Q₈	1	6	yes	—
267	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
268	C₂²×C₃	C₂²×C₃×Q₈	1	6	yes	—
269	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
270	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
271	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
272	C₂×D₃	—	2	4	no	—
273	C₂×D₃	—	2	4	no	—
274	C₂×D₃	—	2	48	no	—
275	C₂×D₃	C₂²×C₃×Q₈	1	8	yes	complemented
276	C₃×C₄	—	2	8	no	—
277	C₃×C₄	—	2	8	no	—
278	C₃×C₄	—	2	8	no	—
279	C₃×C₄	—	4	8	no	—
280	C₃×C₄	—	6	4	no	—
281	C₃×C₄	—	6	8	no	—
282	C₃×C₄	C₂²×D₁₂	1	8	yes	—
283	C₃×C₄	C₂²×C₃×D₄	1	8	yes	—
284	Dic₃	—	2	8	no	—
285	Dic₃	—	2	4	no	—
286	C₃²	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	3	24	no	—
288	C₂³	—	3	4	no	—
289	C₂³	—	6	32	no	—
290	C₂³	—	6	12	no	—
291	C₂³	—	6	12	no	—
292	C₂³	C₂×C₃×D₁₂	1	4	yes	—
293	C₂³	C₃×#237	1	4	yes	—
294	C₂³	C₃×D₃×Q₈	1	4	yes	—
295	C₂³	C₂³×C₃×D₃	1	3	yes	—
296	Q₈	—	6	32	no	—
297	C₂×C₄	—	2	24	no	—
298	C₂×C₄	—	3	8	no	—
299	C₂×C₄	—	3	4	no	—
300	C₂×C₄	—	6	12	no	—
301	C₂×C₄	—	6	24	no	—
302	C₂×C₄	—	6	32	no	—
303	C₂×C₄	C₂×C₃×D₁₂	1	24	yes	—
304	C₂×C₄	C₂³×C₃×D₃	1	8	yes	—
305	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
306	C₂×C₃	—	2	12	no	—
307	C₂×C₃	—	2	1	no	—
308	C₂×C₃	—	2	1	no	—
309	C₂×C₃	—	2	1	no	—
310	C₂×C₃	—	6	8	no	—
311	C₂×C₃	C₂×#897	1	12	yes	direct product factor
312	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	12	yes	complemented
313	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
314	C₂×C₃	C₂²×#237	1	1	yes	characteristic
315	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
316	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
317	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
318	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
319	D₃	—	2	8	no	—
320	C₂²	—	3	8	no	—
321	C₂²	—	6	48	no	—
322	C₂²	—	6	4	no	—
323	C₂²	—	6	4	no	—
324	C₂²	C₃×#897	1	16	yes	direct product factor
325	C₂²	C₂²×C₃×D₁₂	1	6	yes	—
326	C₂²	C₂×C₃×#237	1	6	yes	—
327	C₂²	C₂×C₃×D₃×Q₈	1	6	yes	—
328	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
329	C₄	—	2	8	no	—
330	C₄	—	6	4	no	—
331	C₄	—	6	8	no	—
332	C₄	C₂²×C₃×D₁₂	1	8	yes	—
333	C₃	—	2	1	no	—
334	C₃	C₂²×#897	1	1	yes	characteristic, direct product factor
335	C₃	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented
336	C₂	—	6	8	no	—
337	C₂	C₂×C₃×#897	1	12	yes	direct product factor
338	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
339	C₂	C₂²×C₃×#237	1	1	yes	characteristic
340	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₆	C₂	semidirect
3. C₂²×C₃²×C₄⋊C₄	C₂	semidirect
5. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
6. C₂×C₃×#897	C₂	direct (N × H)
8. C₂²×#897	C₃	direct (N × H)
17. C₂²×C₃×Dic₆	C₂²	semidirect
18. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
20. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
21. C₃×#897	C₂²	direct (N × H)
25. C₂³×Dic₆	C₂×C₃	semidirect
29. C₂²×C₃×C₄⋊C₄	D₃	semidirect
30. C₂²×C₃×C₄⋊C₄	C₂×C₃	semidirect
33. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
34. C₂×#897	C₂×C₃	direct (N × H)
38. C₂³×C₃×D₃	Q₈	semidirect
51. C₂×C₃×Dic₆	C₂³	semidirect
52. C₃²×C₄⋊C₄	C₂³	semidirect
54. C₃×C₄⋊Dic₃	C₂³	semidirect
75. C₂²×Dic₆	C₂²×C₃	semidirect
79. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
80. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
83. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
84. #897	C₂²×C₃	direct (N × H)
92. C₂²×C₃×D₃	C₂×Q₈	semidirect
108. C₂²×C₄⋊C₄	C₃×D₃	semidirect
119. C₂³×D₃	C₃×Q₈	semidirect
148. C₂×Dic₆	C₂³×C₃	semidirect
151. C₃×C₄⋊C₄	C₂²×D₃	semidirect
152. C₃×C₄⋊C₄	C₂³×C₃	semidirect
155. C₄⋊Dic₃	C₂³×C₃	semidirect
156. C₂²×C₃²	C₂²⋊Q₈	semidirect
164. C₂×C₃×D₃	C₂²×Q₈	semidirect
180. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
202. C₂²×D₃	C₂×C₃×Q₈	semidirect
228. C₂×C₃²	C₂×C₂²⋊Q₈	semidirect
251. C₄⋊C₄	C₂²×C₃×D₃	semidirect
262. C₂²×C₃	#897	direct (N × H)
263. C₂²×C₃	C₃×C₂²⋊Q₈	semidirect
275. C₂×D₃	C₂²×C₃×Q₈	semidirect
286. C₃²	C₂²×C₂²⋊Q₈	semidirect
311. C₂×C₃	C₂×#897	direct (N × H)
312. C₂×C₃	C₂×C₃×C₂²⋊Q₈	semidirect
324. C₂²	C₃×#897	direct (N × H)
334. C₃	C₂²×#897	direct (N × H)
335. C₃	C₂²×C₃×C₂²⋊Q₈	semidirect
337. C₂	C₂×C₃×#897	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×D₃	2
C₂³×C₃×Dic₆	2
C₂²×C₃²×C₄⋊C₄	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₂²×C₃×C₄⋊Dic₃	2
C₂×C₃×#897	2
C₂²×C₃×C₂²⋊Q₈	3
C₂²×#897	3

Subgroups — C22×C3×#897 #11900325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#897 #11900325