Subgroups — C₂²×C₃×#832 #11857720

Order 1152.

2825 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	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#832	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₃×#102	—	3	1	no	maximal
6	C₂²×#832	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂⁵×C₃²	—	2	1	no	—
8	C₂²×C₃²×D₄	—	2	4	no	—
9	C₂²×C₃²×D₄	—	2	3	no	—
10	C₂²×C₃²×D₄	C₄	1	8	yes	complemented
11	C₂²×C₃²×D₄	C₂²	1	6	yes	—
12	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×Dic₃	—	2	1	no	—
14	C₂×C₃×C₄⋊Dic₃	—	2	3	no	—
15	C₂×C₃×C₄⋊Dic₃	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×#832	C₂²	1	16	yes	direct product factor
19	C₂³×C₃×D₄	—	2	1	no	—
20	C₂³×C₃×D₄	D₃	1	1	yes	characteristic
21	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
22	C₂³×C₃×C₈	—	3	1	no	—
23	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
24	C₂²×C₄⋊Dic₃	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×#832	C₂×C₃	1	12	yes	direct product factor
28	C₂⁴×C₃²	—	2	8	no	—
29	C₂⁴×C₃²	—	2	6	no	—
30	C₂⁴×C₃²	—	4	4	no	—
31	C₂⁴×C₃²	—	4	4	no	—
32	C₂⁴×C₃²	D₄	1	1	yes	characteristic
33	C₂×C₃²×D₄	—	2	24	no	—
34	C₂×C₃²×D₄	—	2	6	no	—
35	C₂×C₃²×D₄	—	2	12	no	—
36	C₂×C₃²×D₄	C₂×C₄	1	24	yes	complemented
37	C₂×C₃²×D₄	C₂³	1	4	yes	—
38	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
39	C₂²×C₃²×C₄	D₄	1	3	yes	—
40	C₂²×C₃²×C₄	D₄	1	4	yes	—
41	C₂²×C₃²×C₄	C₂³	1	3	yes	—
42	C₂²×C₃×Dic₃	—	2	6	no	—
43	C₂²×C₃×Dic₃	—	4	4	no	—
44	C₃×C₄⋊Dic₃	—	2	6	no	—
45	C₃×C₄⋊Dic₃	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	—	2	2	no	—
50	C₂⁵×C₃	—	2	1	no	—
51	C₂⁵×C₃	—	2	1	no	—
52	C₂²×C₃×D₄	—	2	6	no	—
53	C₂²×C₃×D₄	—	2	8	no	—
54	C₂²×C₃×D₄	—	2	3	no	—
55	C₂²×C₃×D₄	—	2	4	no	—
56	C₂²×C₃×D₄	—	2	3	no	—
57	C₂²×C₃×D₄	—	2	4	no	—
58	C₂²×C₃×D₄	—	2	8	no	—
59	C₂²×C₃×D₄	—	2	6	no	—
60	C₂²×C₃×D₄	Dic₃	1	8	yes	complemented
61	C₂²×C₃×D₄	C₃×C₄	1	8	yes	complemented
62	C₂²×C₃×D₄	C₂×D₃	1	6	yes	—
63	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
64	C₂³×C₃×C₄	—	2	1	no	—
65	C₂³×C₃×C₄	—	6	1	no	—
66	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
67	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂³×Dic₃	—	2	1	no	—
69	C₂²×C₃×C₈	—	3	6	no	—
70	C₂²×C₃×C₈	—	6	4	no	—
71	C₂×C₃×C₄⋊C₄	—	3	6	no	—
72	C₂×C₃×C₄⋊C₄	—	6	3	no	—
73	C₂×C₄⋊Dic₃	—	2	3	no	—
74	C₂×C₄⋊Dic₃	C₂²×C₃	1	6	yes	complemented
75	C₂²×C₃⋊C₈	—	2	4	no	—
76	C₂²×C₃⋊C₈	C₂²×C₃	1	6	yes	complemented
77	C₃×#102	—	3	16	no	—
78	#832	C₂²×C₃	1	16	yes	direct product factor
79	C₂³×C₃²	—	2	24	no	—
80	C₂³×C₃²	—	2	4	no	—
81	C₂³×C₃²	—	4	32	no	—
82	C₂³×C₃²	—	4	12	no	—
83	C₂³×C₃²	—	4	12	no	—
84	C₂³×C₃²	C₂²⋊C₄	1	4	yes	—
85	C₂³×C₃²	D₈	1	4	yes	—
86	C₂³×C₃²	SD₁₆	1	4	yes	—
87	C₂³×C₃²	C₂×D₄	1	3	yes	—
88	C₃²×D₄	—	2	24	no	—
89	C₃²×D₄	—	2	4	no	—
90	C₃²×D₄	C₂²×C₄	1	8	yes	complemented
91	C₂×C₃²×C₄	C₂²⋊C₄	1	12	yes	—
92	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
93	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
94	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
95	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×Dic₃	—	2	4	no	—
97	C₂×C₃×Dic₃	—	4	12	no	—
98	C₃×C₃⋊C₈	—	2	4	no	—
99	C₂³×D₄	C₃×D₃	1	1	yes	characteristic
100	C₂³×C₈	—	3	1	no	—
101	C₂²×C₄⋊C₄	—	3	1	no	—
102	C₂×#102	—	3	12	no	—
103	C₂⁴×C₃	—	2	16	no	—
104	C₂⁴×C₃	—	2	12	no	—
105	C₂⁴×C₃	—	2	8	no	—
106	C₂⁴×C₃	—	2	8	no	—
107	C₂⁴×C₃	—	2	6	no	—
108	C₂⁴×C₃	—	2	6	no	—
109	C₂⁴×C₃	—	2	1	no	—
110	C₂⁴×C₃	—	4	8	no	—
111	C₂⁴×C₃	—	4	8	no	—
112	C₂⁴×C₃	—	4	4	no	—
113	C₂⁴×C₃	—	4	4	no	—
114	C₂⁴×C₃	—	4	4	no	—
115	C₂⁴×C₃	—	4	4	no	—
116	C₂⁴×C₃	#67	1	1	yes	characteristic
117	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
118	C₂×C₃×D₄	—	2	48	no	—
119	C₂×C₃×D₄	—	2	12	no	—
120	C₂×C₃×D₄	—	2	24	no	—
121	C₂×C₃×D₄	—	2	24	no	—
122	C₂×C₃×D₄	—	2	24	no	—
123	C₂×C₃×D₄	—	2	6	no	—
124	C₂×C₃×D₄	—	2	12	no	—
125	C₂×C₃×D₄	—	2	6	no	—
126	C₂×C₃×D₄	—	2	12	no	—
127	C₂×C₃×D₄	—	2	24	no	—
128	C₂×C₃×D₄	—	2	4	no	—
129	C₂×C₃×D₄	C₂×Dic₃	1	24	yes	complemented
130	C₂×C₃×D₄	C₂×C₃×C₄	1	24	yes	complemented
131	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
132	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
133	C₂²×C₃×C₄	—	2	4	no	—
134	C₂²×C₃×C₄	—	2	3	no	—
135	C₂²×C₃×C₄	—	2	4	no	—
136	C₂²×C₃×C₄	—	2	3	no	—
137	C₂²×C₃×C₄	—	6	6	no	—
138	C₂²×C₃×C₄	—	12	4	no	—
139	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
140	C₂²×C₃×C₄	#67	1	3	yes	—
141	C₂²×C₃×C₄	#67	1	4	yes	—
142	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
143	C₂²×C₃×C₄	C₃×D₄	1	3	yes	—
144	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
145	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
146	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
147	C₂²×Dic₃	—	2	6	no	—
148	C₂²×Dic₃	—	4	4	no	—
149	C₂×C₃×C₈	—	3	4	no	—
150	C₂×C₃×C₈	—	6	12	no	—
151	C₃×C₄⋊C₄	—	3	4	no	—
152	C₃×C₄⋊C₄	—	6	6	no	—
153	C₄⋊Dic₃	—	2	6	no	—
154	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
155	C₂×C₃⋊C₈	—	2	12	no	—
156	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	complemented
157	C₂²×C₃²	—	2	8	no	—
158	C₂²×C₃²	—	4	4	no	—
159	C₂²×C₃²	—	4	4	no	—
160	C₂²×C₃²	—	4	48	no	—
161	C₂²×C₃²	#102	1	16	yes	complemented
162	C₂²×C₃²	C₂×C₂²⋊C₄	1	6	yes	—
163	C₂²×C₃²	C₂×D₈	1	6	yes	—
164	C₂²×C₃²	C₂×SD₁₆	1	6	yes	—
165	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
166	C₃²×C₄	C₂×C₂²⋊C₄	1	6	yes	—
167	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
168	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
169	C₃×Dic₃	—	4	4	no	—
170	C₂⁵	—	2	1	no	—
171	C₂²×D₄	—	2	3	no	—
172	C₂²×D₄	—	2	4	no	—
173	C₂²×D₄	C₃×Dic₃	1	8	yes	complemented
174	C₂²×D₄	C₂×C₃×D₃	1	6	yes	—
175	C₂³×C₄	—	6	1	no	—
176	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂²×C₈	—	3	6	no	—
178	C₂²×C₈	—	6	4	no	—
179	C₂×C₄⋊C₄	—	3	6	no	—
180	C₂×C₄⋊C₄	—	6	3	no	—
181	#102	—	3	16	no	—
182	C₂³×C₃	—	2	48	no	—
183	C₂³×C₃	—	2	8	no	—
184	C₂³×C₃	—	2	24	no	—
185	C₂³×C₃	—	2	24	no	—
186	C₂³×C₃	—	2	4	no	—
187	C₂³×C₃	—	2	4	no	—
188	C₂³×C₃	—	2	4	no	—
189	C₂³×C₃	—	2	4	no	—
190	C₂³×C₃	—	2	4	no	—
191	C₂³×C₃	—	2	3	no	—
192	C₂³×C₃	—	4	24	no	—
193	C₂³×C₃	—	4	24	no	—
194	C₂³×C₃	—	4	64	no	—
195	C₂³×C₃	—	4	32	no	—
196	C₂³×C₃	—	4	32	no	—
197	C₂³×C₃	—	4	12	no	—
198	C₂³×C₃	—	4	12	no	—
199	C₂³×C₃	—	4	12	no	—
200	C₂³×C₃	—	4	12	no	—
201	C₂³×C₃	#213	1	4	yes	—
202	C₂³×C₃	#214	1	4	yes	—
203	C₂³×C₃	#217	1	4	yes	—
204	C₂³×C₃	C₃×C₂²⋊C₄	1	4	yes	—
205	C₂³×C₃	C₃×D₈	1	4	yes	—
206	C₂³×C₃	C₃×SD₁₆	1	4	yes	—
207	C₂³×C₃	C₂×#67	1	3	yes	—
208	C₂³×C₃	C₂×C₃×D₄	1	3	yes	—
209	C₃×D₄	—	2	48	no	—
210	C₃×D₄	—	2	8	no	—
211	C₃×D₄	—	2	24	no	—
212	C₃×D₄	—	2	24	no	—
213	C₃×D₄	—	2	4	no	—
214	C₃×D₄	—	2	4	no	—
215	C₃×D₄	—	2	8	no	—
216	C₃×D₄	C₂²×Dic₃	1	8	yes	complemented
217	C₃×D₄	C₂²×C₃×C₄	1	8	yes	complemented
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	12	no	—
220	C₂×C₃×C₄	—	2	6	no	—
221	C₂×C₃×C₄	—	2	3	no	—
222	C₂×C₃×C₄	—	2	6	no	—
223	C₂×C₃×C₄	—	6	4	no	—
224	C₂×C₃×C₄	—	12	12	no	—
225	C₂×C₃×C₄	#217	1	12	yes	—
226	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	12	yes	—
227	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
228	C₂×C₃×C₄	C₂×#67	1	3	yes	—
229	C₂×C₃×C₄	C₂×#67	1	6	yes	—
230	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
231	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
232	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
233	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
235	C₂×Dic₃	—	2	4	no	—
236	C₂×Dic₃	—	4	12	no	—
237	C₃×C₈	—	6	4	no	—
238	C₃⋊C₈	—	2	4	no	—
239	C₂×C₃²	—	4	8	no	—
240	C₂×C₃²	C₂×#102	1	12	yes	complemented
241	C₂×C₃²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
243	C₂×C₃²	C₂²×SD₁₆	1	1	yes	characteristic
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	6	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	—	4	4	no	—
248	C₂⁴	C₃×#67	1	1	yes	characteristic
249	C₂×D₄	—	2	24	no	—
250	C₂×D₄	—	2	6	no	—
251	C₂×D₄	—	2	12	no	—
252	C₂×D₄	C₂×C₃×Dic₃	1	24	yes	complemented
253	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
254	C₂²×C₄	—	6	6	no	—
255	C₂²×C₄	—	12	4	no	—
256	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
257	C₂²×C₄	C₃×#67	1	3	yes	—
258	C₂²×C₄	C₃×#67	1	4	yes	—
259	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
260	C₂×C₈	—	3	4	no	—
261	C₂×C₈	—	6	12	no	—
262	C₄⋊C₄	—	3	4	no	—
263	C₄⋊C₄	—	6	6	no	—
264	C₂²×C₃	—	2	16	no	—
265	C₂²×C₃	—	2	8	no	—
266	C₂²×C₃	—	2	8	no	—
267	C₂²×C₃	—	2	6	no	—
268	C₂²×C₃	—	2	6	no	—
269	C₂²×C₃	—	2	6	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	16	no	—
272	C₂²×C₃	—	4	8	no	—
273	C₂²×C₃	—	4	8	no	—
274	C₂²×C₃	—	4	96	no	—
275	C₂²×C₃	—	4	4	no	—
276	C₂²×C₃	—	4	4	no	—
277	C₂²×C₃	—	4	48	no	—
278	C₂²×C₃	—	4	4	no	—
279	C₂²×C₃	—	4	4	no	—
280	C₂²×C₃	—	4	48	no	—
281	C₂²×C₃	#832	1	16	yes	direct product factor
282	C₂²×C₃	C₃×#102	1	16	yes	complemented
283	C₂²×C₃	C₂×#213	1	6	yes	—
284	C₂²×C₃	C₂×#214	1	6	yes	—
285	C₂²×C₃	C₂×#217	1	6	yes	—
286	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	6	yes	—
287	C₂²×C₃	C₂×C₃×D₈	1	6	yes	—
288	C₂²×C₃	C₂×C₃×SD₁₆	1	6	yes	—
289	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
290	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
291	C₃×C₄	—	2	6	no	—
292	C₃×C₄	—	2	1	no	—
293	C₃×C₄	—	2	1	no	—
294	C₃×C₄	—	12	4	no	—
295	C₃×C₄	C₂×#217	1	6	yes	—
296	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	6	yes	—
297	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
298	C₃×C₄	C₂²×#67	1	1	yes	characteristic
299	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
300	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
301	Dic₃	—	4	4	no	—
302	C₃²	C₂²×#102	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	2	24	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	4	12	no	—
306	C₂³	—	4	12	no	—
307	C₂³	—	4	32	no	—
308	C₂³	C₃×#213	1	4	yes	—
309	C₂³	C₃×#214	1	4	yes	—
310	C₂³	C₃×#217	1	4	yes	—
311	C₂³	C₂×C₃×#67	1	3	yes	—
312	D₄	—	2	24	no	—
313	D₄	—	2	4	no	—
314	D₄	C₂²×C₃×Dic₃	1	8	yes	complemented
315	C₂×C₄	—	6	4	no	—
316	C₂×C₄	—	12	12	no	—
317	C₂×C₄	C₃×#217	1	12	yes	—
318	C₂×C₄	C₂²×C₃×Dic₃	1	6	yes	—
319	C₂×C₄	C₂×C₃×#67	1	3	yes	—
320	C₂×C₄	C₂×C₃×#67	1	6	yes	—
321	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
322	C₈	—	6	4	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	12	no	—
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	4	16	no	—
328	C₂×C₃	—	4	8	no	—
329	C₂×C₃	—	4	8	no	—
330	C₂×C₃	C₂×#832	1	12	yes	direct product factor
331	C₂×C₃	C₂×C₃×#102	1	12	yes	complemented
332	C₂×C₃	C₂²×#213	1	1	yes	characteristic
333	C₂×C₃	C₂²×#214	1	1	yes	characteristic
334	C₂×C₃	C₂²×#217	1	1	yes	characteristic
335	C₂×C₃	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
337	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
338	C₂²	—	2	8	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	48	no	—
342	C₂²	C₃×#832	1	16	yes	direct product factor
343	C₂²	C₂×C₃×#213	1	6	yes	—
344	C₂²	C₂×C₃×#214	1	6	yes	—
345	C₂²	C₂×C₃×#217	1	6	yes	—
346	C₂²	C₂²×C₃×#67	1	1	yes	characteristic
347	C₄	—	12	4	no	—
348	C₄	C₂×C₃×#217	1	6	yes	—
349	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
350	C₄	C₂²×C₃×#67	1	1	yes	characteristic
351	C₃	—	2	1	no	—
352	C₃	C₂²×#832	1	1	yes	characteristic, direct product factor
353	C₃	C₂²×C₃×#102	1	1	yes	characteristic, complemented
354	C₂	—	4	8	no	—
355	C₂	C₂×C₃×#832	1	12	yes	direct product factor
356	C₂	C₂²×C₃×#213	1	1	yes	characteristic
357	C₂	C₂²×C₃×#214	1	1	yes	characteristic
358	C₂	C₂²×C₃×#217	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄⋊Dic₃	C₂	semidirect
3. C₂³×C₃×C₃⋊C₈	C₂	semidirect
4. C₂×C₃×#832	C₂	direct (N × H)
6. C₂²×#832	C₃	direct (N × H)
10. C₂²×C₃²×D₄	C₄	semidirect
15. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
17. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
18. C₃×#832	C₂²	direct (N × H)
24. C₂²×C₄⋊Dic₃	C₂×C₃	semidirect
25. C₂³×C₃⋊C₈	C₂×C₃	semidirect
27. C₂×#832	C₂×C₃	direct (N × H)
36. C₂×C₃²×D₄	C₂×C₄	semidirect
45. C₃×C₄⋊Dic₃	C₂³	semidirect
47. C₂×C₃×C₃⋊C₈	C₂³	semidirect
60. C₂²×C₃×D₄	Dic₃	semidirect
61. C₂²×C₃×D₄	C₃×C₄	semidirect
74. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
76. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
78. #832	C₂²×C₃	direct (N × H)
90. C₃²×D₄	C₂²×C₄	semidirect
129. C₂×C₃×D₄	C₂×Dic₃	semidirect
130. C₂×C₃×D₄	C₂×C₃×C₄	semidirect
154. C₄⋊Dic₃	C₂³×C₃	semidirect
156. C₂×C₃⋊C₈	C₂³×C₃	semidirect
161. C₂²×C₃²	#102	semidirect
173. C₂²×D₄	C₃×Dic₃	semidirect
216. C₃×D₄	C₂²×Dic₃	semidirect
217. C₃×D₄	C₂²×C₃×C₄	semidirect
240. C₂×C₃²	C₂×#102	semidirect
252. C₂×D₄	C₂×C₃×Dic₃	semidirect
281. C₂²×C₃	#832	direct (N × H)
282. C₂²×C₃	C₃×#102	semidirect
302. C₃²	C₂²×#102	semidirect
314. D₄	C₂²×C₃×Dic₃	semidirect
330. C₂×C₃	C₂×#832	direct (N × H)
331. C₂×C₃	C₂×C₃×#102	semidirect
342. C₂²	C₃×#832	direct (N × H)
352. C₃	C₂²×#832	direct (N × H)
353. C₃	C₂²×C₃×#102	semidirect
355. C₂	C₂×C₃×#832	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×C₃²×D₄	2
C₂²×C₃×C₄⋊Dic₃	2
C₂³×C₃×C₃⋊C₈	2
C₂×C₃×#832	2
C₂²×C₃×#102	3
C₂²×#832	3

Subgroups — C22×C3×#832 #11857720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#832 #11857720