Subgroups — C₂²×C₃×#809 #11857717

Order 1152.

2353 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#809	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₃×#102	—	3	1	no	maximal
6	C₂²×#809	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂⁴×C₃×D₃	—	2	1	no	—
8	C₂³×C₃²×C₄	—	2	1	no	—
9	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₁₂	—	2	4	no	—
11	C₂²×C₃×D₁₂	—	2	3	no	—
12	C₂²×C₃×D₁₂	C₄	1	8	yes	complemented
13	C₂²×C₃×D₁₂	C₂²	1	6	yes	—
14	C₂×C₃²×C₄⋊C₄	—	2	3	no	—
15	C₂×C₃²×C₄⋊C₄	C₂²	1	6	yes	complemented
16	C₂²×C₃×C₃⋊C₈	—	2	4	no	—
17	C₂²×C₃×C₃⋊C₈	C₂²	1	6	yes	complemented
18	C₃×#809	C₂²	1	16	yes	direct product factor
19	C₂³×C₃×D₄	—	3	1	no	—
20	C₂³×D₁₂	C₂×C₃	1	1	yes	characteristic
21	C₂³×C₃×C₈	—	3	1	no	—
22	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
23	C₂²×C₃×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂³×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×#102	—	3	12	no	—
27	C₂×#809	C₂×C₃	1	12	yes	direct product factor
28	C₂⁴×C₃²	D₄	1	1	yes	characteristic
29	C₂³×C₃×D₃	—	2	8	no	—
30	C₂³×C₃×D₃	—	2	6	no	—
31	C₂³×C₃×D₃	—	4	4	no	—
32	C₂³×C₃×D₃	—	4	4	no	—
33	C₂²×C₃²×C₄	—	2	6	no	—
34	C₂²×C₃²×C₄	—	4	4	no	—
35	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
36	C₂²×C₃²×C₄	D₄	1	3	yes	—
37	C₂²×C₃²×C₄	D₄	1	4	yes	—
38	C₂²×C₃²×C₄	C₂³	1	3	yes	—
39	C₂×C₃×D₁₂	—	2	24	no	—
40	C₂×C₃×D₁₂	—	2	6	no	—
41	C₂×C₃×D₁₂	—	2	12	no	—
42	C₂×C₃×D₁₂	C₂×C₄	1	24	yes	complemented
43	C₂×C₃×D₁₂	C₂³	1	4	yes	—
44	C₃²×C₄⋊C₄	—	2	6	no	—
45	C₃²×C₄⋊C₄	C₂³	1	4	yes	complemented
46	C₂×C₃×C₃⋊C₈	—	2	12	no	—
47	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	complemented
48	C₂²×#102	—	3	1	no	Sylow
49	C₂⁵×C₃	—	6	1	no	—
50	C₂⁴×D₃	—	2	1	no	—
51	C₂²×C₃×D₄	—	3	8	no	—
52	C₂²×C₃×D₄	—	3	6	no	—
53	C₂²×C₃×D₄	—	6	4	no	—
54	C₂²×C₃×D₄	—	6	3	no	—
55	C₂³×C₃×C₄	—	2	2	no	—
56	C₂³×C₃×C₄	—	2	1	no	—
57	C₂³×C₃×C₄	—	2	1	no	—
58	C₂³×C₃×C₄	—	2	1	no	—
59	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
60	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
61	C₂²×D₁₂	—	2	4	no	—
62	C₂²×D₁₂	—	2	3	no	—
63	C₂²×D₁₂	C₃×C₄	1	8	yes	complemented
64	C₂²×D₁₂	C₂²×C₃	1	6	yes	—
65	C₂²×C₃×C₈	—	3	6	no	—
66	C₂²×C₃×C₈	—	6	4	no	—
67	C₂×C₃×C₄⋊C₄	—	2	6	no	—
68	C₂×C₃×C₄⋊C₄	—	2	3	no	—
69	C₂×C₃×C₄⋊C₄	—	2	3	no	—
70	C₂×C₃×C₄⋊C₄	—	2	6	no	—
71	C₂×C₃×C₄⋊C₄	C₂×D₃	1	6	yes	complemented
72	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	6	yes	complemented
73	C₂²×C₃⋊C₈	—	2	4	no	—
74	C₂²×C₃⋊C₈	C₂²×C₃	1	6	yes	complemented
75	C₃×#102	—	3	16	no	—
76	#809	C₂²×C₃	1	16	yes	direct product factor
77	C₂³×C₃²	C₂²⋊C₄	1	4	yes	—
78	C₂³×C₃²	D₈	1	4	yes	—
79	C₂³×C₃²	SD₁₆	1	4	yes	—
80	C₂³×C₃²	C₂×D₄	1	3	yes	—
81	C₂²×C₃×D₃	—	2	24	no	—
82	C₂²×C₃×D₃	—	2	4	no	—
83	C₂²×C₃×D₃	—	4	32	no	—
84	C₂²×C₃×D₃	—	4	12	no	—
85	C₂²×C₃×D₃	—	4	12	no	—
86	C₂×C₃²×C₄	—	2	4	no	—
87	C₂×C₃²×C₄	—	4	12	no	—
88	C₂×C₃²×C₄	C₂²⋊C₄	1	12	yes	—
89	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
90	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
91	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
92	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
93	C₃×D₁₂	—	2	24	no	—
94	C₃×D₁₂	—	2	4	no	—
95	C₃×D₁₂	C₂²×C₄	1	8	yes	complemented
96	C₃×C₃⋊C₈	—	2	4	no	—
97	C₂³×D₄	—	3	1	no	—
98	C₂³×C₈	—	3	1	no	—
99	C₂²×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic, complemented
100	C₂×#102	—	3	12	no	—
101	C₂⁴×C₃	—	2	1	no	—
102	C₂⁴×C₃	—	6	8	no	—
103	C₂⁴×C₃	—	6	6	no	—
104	C₂⁴×C₃	—	12	4	no	—
105	C₂⁴×C₃	—	12	4	no	—
106	C₂⁴×C₃	#67	1	1	yes	characteristic
107	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
108	C₂³×D₃	—	2	8	no	—
109	C₂³×D₃	—	2	6	no	—
110	C₂³×D₃	—	4	4	no	—
111	C₂³×D₃	—	4	4	no	—
112	C₂×C₃×D₄	—	3	24	no	—
113	C₂×C₃×D₄	—	3	4	no	—
114	C₂×C₃×D₄	—	6	24	no	—
115	C₂×C₃×D₄	—	6	12	no	—
116	C₂×C₃×D₄	—	6	6	no	—
117	C₂²×C₃×C₄	—	2	12	no	—
118	C₂²×C₃×C₄	—	2	6	no	—
119	C₂²×C₃×C₄	—	2	6	no	—
120	C₂²×C₃×C₄	—	2	4	no	—
121	C₂²×C₃×C₄	—	2	4	no	—
122	C₂²×C₃×C₄	—	2	3	no	—
123	C₂²×C₃×C₄	—	2	3	no	—
124	C₂²×C₃×C₄	—	4	8	no	—
125	C₂²×C₃×C₄	—	4	4	no	—
126	C₂²×C₃×C₄	—	4	4	no	—
127	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
128	C₂²×C₃×C₄	D₁₂	1	4	yes	—
129	C₂²×C₃×C₄	#67	1	3	yes	—
130	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
131	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
132	C₂²×C₃×C₄	C₃×D₄	1	3	yes	—
133	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
134	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
135	C₂×D₁₂	—	2	24	no	—
136	C₂×D₁₂	—	2	12	no	—
137	C₂×D₁₂	—	2	6	no	—
138	C₂×D₁₂	C₂×C₃×C₄	1	24	yes	complemented
139	C₂×D₁₂	C₂³×C₃	1	4	yes	—
140	C₂×C₃×C₈	—	3	4	no	—
141	C₂×C₃×C₈	—	6	12	no	—
142	C₃×C₄⋊C₄	—	2	12	no	—
143	C₃×C₄⋊C₄	—	2	6	no	—
144	C₃×C₄⋊C₄	—	2	6	no	—
145	C₃×C₄⋊C₄	—	2	4	no	—
146	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
147	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
148	C₂×C₃⋊C₈	—	2	12	no	—
149	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	complemented
150	C₂²×C₃²	#102	1	16	yes	complemented
151	C₂²×C₃²	C₂×C₂²⋊C₄	1	6	yes	—
152	C₂²×C₃²	C₂×D₈	1	6	yes	—
153	C₂²×C₃²	C₂×SD₁₆	1	6	yes	—
154	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₃×D₃	—	2	8	no	—
156	C₂×C₃×D₃	—	4	4	no	—
157	C₂×C₃×D₃	—	4	4	no	—
158	C₂×C₃×D₃	—	4	48	no	—
159	C₃²×C₄	—	4	4	no	—
160	C₃²×C₄	C₂×C₂²⋊C₄	1	6	yes	—
161	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
162	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
163	C₂⁵	—	6	1	no	—
164	C₂²×D₄	—	3	8	no	—
165	C₂²×D₄	—	3	6	no	—
166	C₂²×D₄	—	6	4	no	—
167	C₂²×D₄	—	6	3	no	—
168	C₂³×C₄	—	2	1	no	—
169	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
170	C₂²×C₈	—	3	6	no	—
171	C₂²×C₈	—	6	4	no	—
172	C₂×C₄⋊C₄	—	2	3	no	—
173	C₂×C₄⋊C₄	C₂×C₃×D₃	1	6	yes	complemented
174	#102	—	3	16	no	—
175	C₂³×C₃	—	2	4	no	—
176	C₂³×C₃	—	2	4	no	—
177	C₂³×C₃	—	2	4	no	—
178	C₂³×C₃	—	2	3	no	—
179	C₂³×C₃	—	6	24	no	—
180	C₂³×C₃	—	6	4	no	—
181	C₂³×C₃	—	12	32	no	—
182	C₂³×C₃	—	12	12	no	—
183	C₂³×C₃	—	12	12	no	—
184	C₂³×C₃	(C₂×D₃)⋊C₄	1	4	yes	—
185	C₂³×C₃	#213	1	4	yes	—
186	C₂³×C₃	#215	1	4	yes	—
187	C₂³×C₃	C₃×C₂²⋊C₄	1	4	yes	—
188	C₂³×C₃	C₃×D₈	1	4	yes	—
189	C₂³×C₃	C₃×SD₁₆	1	4	yes	—
190	C₂³×C₃	C₂×#67	1	3	yes	—
191	C₂³×C₃	C₂×C₃×D₄	1	3	yes	—
192	C₂²×D₃	—	2	24	no	—
193	C₂²×D₃	—	2	4	no	—
194	C₂²×D₃	—	4	32	no	—
195	C₂²×D₃	—	4	12	no	—
196	C₂²×D₃	—	4	12	no	—
197	C₃×D₄	—	3	8	no	—
198	C₃×D₄	—	6	24	no	—
199	C₃×D₄	—	6	4	no	—
200	C₂×C₃×C₄	—	2	8	no	—
201	C₂×C₃×C₄	—	2	4	no	—
202	C₂×C₃×C₄	—	2	4	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	12	no	—
205	C₂×C₃×C₄	—	2	6	no	—
206	C₂×C₃×C₄	—	2	6	no	—
207	C₂×C₃×C₄	—	2	3	no	—
208	C₂×C₃×C₄	—	4	24	no	—
209	C₂×C₃×C₄	—	4	12	no	—
210	C₂×C₃×C₄	—	4	12	no	—
211	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	12	yes	—
212	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	12	yes	—
213	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
214	C₂×C₃×C₄	C₂×D₁₂	1	6	yes	—
215	C₂×C₃×C₄	C₂×#67	1	3	yes	—
216	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
217	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
218	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
219	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
221	D₁₂	—	2	24	no	—
222	D₁₂	—	2	4	no	—
223	D₁₂	C₂²×C₃×C₄	1	8	yes	complemented
224	C₃×C₈	—	6	4	no	—
225	C₃⋊C₈	—	2	4	no	—
226	C₂×C₃²	C₂×#102	1	12	yes	complemented
227	C₂×C₃²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
229	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
230	C₃×D₃	—	4	8	no	—
231	C₂⁴	—	6	8	no	—
232	C₂⁴	—	6	6	no	—
233	C₂⁴	—	12	4	no	—
234	C₂⁴	—	12	4	no	—
235	C₂⁴	C₃×#67	1	1	yes	characteristic
236	C₂×D₄	—	3	4	no	—
237	C₂×D₄	—	3	24	no	—
238	C₂×D₄	—	6	24	no	—
239	C₂×D₄	—	6	12	no	—
240	C₂×D₄	—	6	6	no	—
241	C₂²×C₄	—	2	6	no	—
242	C₂²×C₄	—	4	4	no	—
243	C₂²×C₄	C₃×C₄×D₃	1	4	yes	—
244	C₂²×C₄	C₃×D₁₂	1	4	yes	—
245	C₂²×C₄	C₃×#67	1	3	yes	—
246	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
247	C₂×C₈	—	3	4	no	—
248	C₂×C₈	—	6	12	no	—
249	C₄⋊C₄	—	2	6	no	—
250	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	complemented
251	C₂²×C₃	—	2	6	no	—
252	C₂²×C₃	—	2	6	no	—
253	C₂²×C₃	—	2	6	no	—
254	C₂²×C₃	—	2	1	no	—
255	C₂²×C₃	—	2	16	no	—
256	C₂²×C₃	—	6	8	no	—
257	C₂²×C₃	—	12	48	no	—
258	C₂²×C₃	—	12	4	no	—
259	C₂²×C₃	—	12	4	no	—
260	C₂²×C₃	#809	1	16	yes	direct product factor
261	C₂²×C₃	C₃×#102	1	16	yes	complemented
262	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	6	yes	—
263	C₂²×C₃	C₂×#213	1	6	yes	—
264	C₂²×C₃	C₂×#215	1	6	yes	—
265	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	6	yes	—
266	C₂²×C₃	C₂×C₃×D₈	1	6	yes	—
267	C₂²×C₃	C₂×C₃×SD₁₆	1	6	yes	—
268	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
269	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
270	C₂×D₃	—	2	8	no	—
271	C₂×D₃	—	4	4	no	—
272	C₂×D₃	—	4	4	no	—
273	C₂×D₃	—	4	48	no	—
274	C₃×C₄	—	2	6	no	—
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	—	2	1	no	—
277	C₃×C₄	—	4	8	no	—
278	C₃×C₄	—	4	4	no	—
279	C₃×C₄	—	4	4	no	—
280	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	6	yes	—
281	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	6	yes	—
282	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
283	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
284	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
285	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
286	C₃²	C₂²×#102	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	6	24	no	—
288	C₂³	—	6	4	no	—
289	C₂³	—	12	12	no	—
290	C₂³	—	12	12	no	—
291	C₂³	—	12	32	no	—
292	C₂³	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
293	C₂³	C₃×#213	1	4	yes	—
294	C₂³	C₃×#215	1	4	yes	—
295	C₂³	C₂×C₃×#67	1	3	yes	—
296	D₄	—	3	8	no	—
297	D₄	—	6	24	no	—
298	D₄	—	6	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	4	12	no	—
301	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	12	yes	—
302	C₂×C₄	C₂×C₃×C₄×D₃	1	6	yes	—
303	C₂×C₄	C₂×C₃×D₁₂	1	6	yes	—
304	C₂×C₄	C₂×C₃×#67	1	3	yes	—
305	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
306	C₈	—	6	4	no	—
307	C₂×C₃	—	2	1	no	—
308	C₂×C₃	—	2	1	no	—
309	C₂×C₃	—	2	12	no	—
310	C₂×C₃	—	2	1	no	—
311	C₂×C₃	—	12	8	no	—
312	C₂×C₃	C₂×#809	1	12	yes	direct product factor
313	C₂×C₃	C₂×C₃×#102	1	12	yes	complemented
314	C₂×C₃	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
315	C₂×C₃	C₂²×#213	1	1	yes	characteristic
316	C₂×C₃	C₂²×#215	1	1	yes	characteristic
317	C₂×C₃	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
319	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
320	D₃	—	4	8	no	—
321	C₂²	—	6	8	no	—
322	C₂²	—	12	4	no	—
323	C₂²	—	12	48	no	—
324	C₂²	—	12	4	no	—
325	C₂²	C₃×#809	1	16	yes	direct product factor
326	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	6	yes	—
327	C₂²	C₂×C₃×#213	1	6	yes	—
328	C₂²	C₂×C₃×#215	1	6	yes	—
329	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
330	C₄	—	4	4	no	—
331	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	6	yes	—
332	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
333	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
334	C₃	—	2	1	no	—
335	C₃	C₂²×#809	1	1	yes	characteristic, direct product factor
336	C₃	C₂²×C₃×#102	1	1	yes	characteristic, complemented
337	C₂	—	12	8	no	—
338	C₂	C₂×C₃×#809	1	12	yes	direct product factor
339	C₂	C₂²×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
340	C₂	C₂²×C₃×#213	1	1	yes	characteristic
341	C₂	C₂²×C₃×#215	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	#67
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×C₄⋊C₄	C₂
socle	C₂⁴×C₃²	D₄
prime radical	C₂³×C₃×D₁₂	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄⋊C₄	D₃
hypocenter	C₃	C₂²×C₃×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×C₄⋊C₄	C₂	semidirect
3. C₂³×C₃×C₃⋊C₈	C₂	semidirect
4. C₂×C₃×#809	C₂	direct (N × H)
6. C₂²×#809	C₃	direct (N × H)
12. C₂²×C₃×D₁₂	C₄	semidirect
15. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
17. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
18. C₃×#809	C₂²	direct (N × H)
23. C₂²×C₃×C₄⋊C₄	D₃	semidirect
24. C₂²×C₃×C₄⋊C₄	C₂×C₃	semidirect
25. C₂³×C₃⋊C₈	C₂×C₃	semidirect
27. C₂×#809	C₂×C₃	direct (N × H)
42. C₂×C₃×D₁₂	C₂×C₄	semidirect
45. C₃²×C₄⋊C₄	C₂³	semidirect
47. C₂×C₃×C₃⋊C₈	C₂³	semidirect
63. C₂²×D₁₂	C₃×C₄	semidirect
71. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
72. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
74. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
76. #809	C₂²×C₃	direct (N × H)
95. C₃×D₁₂	C₂²×C₄	semidirect
99. C₂²×C₄⋊C₄	C₃×D₃	semidirect
138. C₂×D₁₂	C₂×C₃×C₄	semidirect
146. C₃×C₄⋊C₄	C₂²×D₃	semidirect
147. C₃×C₄⋊C₄	C₂³×C₃	semidirect
149. C₂×C₃⋊C₈	C₂³×C₃	semidirect
150. C₂²×C₃²	#102	semidirect
173. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
223. D₁₂	C₂²×C₃×C₄	semidirect
226. C₂×C₃²	C₂×#102	semidirect
250. C₄⋊C₄	C₂²×C₃×D₃	semidirect
260. C₂²×C₃	#809	direct (N × H)
261. C₂²×C₃	C₃×#102	semidirect
286. C₃²	C₂²×#102	semidirect
312. C₂×C₃	C₂×#809	direct (N × H)
313. C₂×C₃	C₂×C₃×#102	semidirect
325. C₂²	C₃×#809	direct (N × H)
335. C₃	C₂²×#809	direct (N × H)
336. C₃	C₂²×C₃×#102	semidirect
338. C₂	C₂×C₃×#809	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×D₁₂	2
C₂²×C₃²×C₄⋊C₄	2
C₂³×C₃×C₃⋊C₈	2
C₂×C₃×#809	2
C₂²×C₃×#102	3
C₂²×#809	3

Subgroups — C22×C3×#809 #11857717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#809 #11857717