Subgroups — C₃²×#5805 #13179182

Order 1728.

2948 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#953	C₂	1	4	yes	maximal, complemented
4	C₃²×#940	C₂	1	2	yes	maximal, complemented
5	C₃²×#938	C₂	1	4	yes	maximal, complemented
6	C₃²×#936	C₂	1	2	yes	maximal, complemented
7	C₃²×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#535	—	3	1	no	maximal
9	C₃×#5805	C₃	1	4	yes	maximal, direct product factor
10	C₂⁴×C₃³	C₂²	1	2	yes	—
11	C₂×C₃³×D₄	—	2	4	no	—
12	C₂×C₃³×D₄	C₂²	1	2	yes	—
13	C₂×C₃³×D₄	C₂²	1	2	yes	—
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃²×#67	C₂²	1	2	yes	—
16	C₂×C₃²×#67	C₂²	1	8	yes	complemented
17	C₃²×#235	—	2	4	no	—
18	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
20	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	C₃²×#217	C₂²	1	2	yes	—
22	C₃²×#217	C₂²	1	8	yes	complemented
23	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	complemented
24	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	—	3	1	no	—
26	C₂²×C₃²×D₄	—	2	4	no	—
27	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic, complemented
28	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
29	C₂×C₃×#235	C₂×C₃	1	4	yes	complemented
30	C₃²×#127	—	3	2	no	—
31	C₃²×#124	—	3	2	no	—
32	C₃²×#121	—	3	4	no	—
33	C₃²×#120	—	3	4	no	—
34	C₃²×#117	—	3	1	no	—
35	C₃×#953	C₂×C₃	1	16	yes	complemented
36	C₃×#940	C₂×C₃	1	8	yes	complemented
37	C₃×#938	C₂×C₃	1	16	yes	complemented
38	C₃×#936	C₂×C₃	1	8	yes	complemented
39	C₃×#926	C₂×C₃	1	4	yes	complemented
40	C₂³×C₃³	—	2	4	no	—
41	C₂³×C₃³	—	4	4	no	—
42	C₂³×C₃³	C₂³	1	4	yes	—
43	C₂³×C₃³	C₂³	1	1	yes	characteristic
44	C₂²×C₃²×D₃	C₂³	1	2	yes	—
45	C₃³×D₄	—	2	4	no	—
46	C₃³×D₄	—	2	4	no	—
47	C₂×C₃³×C₄	D₄	1	4	yes	complemented
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₃²×#67	—	2	4	no	—
51	C₃²×#67	—	4	8	no	—
52	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
53	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
54	C₃²×D₁₂	—	2	2	no	—
55	C₃²×C₄×D₃	—	2	4	no	—
56	C₃²×Dic₆	—	2	2	no	—
57	C₃×#535	—	3	4	no	—
58	#5805	C₃²	1	1	yes	characteristic, direct product factor
59	C₂⁴×C₃²	—	2	8	no	—
60	C₂⁴×C₃²	C₂×D₃	1	2	yes	—
61	C₂⁴×C₃²	C₂²×C₃	1	8	yes	—
62	C₃²×#41	—	6	4	no	—
63	C₂×C₃²×Q₈	—	3	1	no	—
64	C₂×C₃²×D₄	—	2	32	no	—
65	C₂×C₃²×D₄	—	2	8	no	—
66	C₂×C₃²×D₄	—	2	8	no	—
67	C₂×C₃²×D₄	—	2	4	no	—
68	C₂×C₃²×D₄	—	2	16	no	—
69	C₂×C₃²×D₄	—	3	2	no	—
70	C₂×C₃²×D₄	—	3	8	no	—
71	C₂×C₃²×D₄	—	3	1	no	—
72	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
73	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
74	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	—
75	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	—
76	C₂²×C₃²×C₄	—	2	4	no	—
77	C₂²×C₃²×C₄	—	3	2	no	—
78	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
80	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
81	C₂×C₃×#67	C₂²×C₃	1	32	yes	complemented
82	C₃×#235	—	2	16	no	—
83	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
84	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
85	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
86	C₃²×C₄⋊C₄	—	3	2	no	—
87	C₃²×C₂²⋊C₄	—	3	2	no	—
88	C₃²×C₂²⋊C₄	—	3	8	no	—
89	C₃²×C₄²	—	3	2	no	—
90	C₃×#217	C₂²×C₃	1	8	yes	—
91	C₃×#217	C₂²×C₃	1	32	yes	complemented
92	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	complemented
93	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
94	C₂²×C₃³	—	2	2	no	—
95	C₂²×C₃³	—	2	4	no	—
96	C₂²×C₃³	—	2	8	no	—
97	C₂²×C₃³	—	4	8	no	—
98	C₂²×C₃³	C₂×D₄	1	2	yes	—
99	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
100	C₂×C₃²×D₃	—	2	2	no	—
101	C₂×C₃²×D₃	—	2	4	no	—
102	C₃³×C₄	C₂×D₄	1	2	yes	—
103	C₃³×C₄	C₂×D₄	1	2	yes	—
104	C₃²×Dic₃	—	2	2	no	—
105	C₃²×Dic₃	—	2	4	no	—
106	C₂×C₃×#41	—	3	4	no	—
107	C₂²×C₃×D₄	—	2	4	no	—
108	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
109	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
110	C₂×#235	C₂×C₃²	1	1	yes	characteristic, complemented
111	C₃×#127	—	3	8	no	—
112	C₃×#124	—	3	8	no	—
113	C₃×#121	—	3	16	no	—
114	C₃×#120	—	3	16	no	—
115	C₃×#117	—	3	4	no	—
116	#953	C₂×C₃²	1	4	yes	complemented
117	#940	C₂×C₃²	1	2	yes	complemented
118	#938	C₂×C₃²	1	4	yes	complemented
119	#936	C₂×C₃²	1	2	yes	complemented
120	#926	C₂×C₃²	1	1	yes	characteristic, complemented
121	C₂³×C₃²	—	2	32	no	—
122	C₂³×C₃²	—	2	4	no	—
123	C₂³×C₃²	—	2	16	no	—
124	C₂³×C₃²	—	2	4	no	—
125	C₂³×C₃²	—	2	16	no	—
126	C₂³×C₃²	—	3	2	no	—
127	C₂³×C₃²	—	4	4	no	—
128	C₂³×C₃²	—	4	16	no	—
129	C₂³×C₃²	—	4	32	no	—
130	C₂³×C₃²	C₂²×D₃	1	4	yes	—
131	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
132	C₂³×C₃²	C₂³×C₃	1	16	yes	—
133	C₂³×C₃²	C₂³×C₃	1	4	yes	—
134	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
135	C₃²×Q₈	—	6	2	no	—
136	C₃²×D₄	—	2	32	no	—
137	C₃²×D₄	—	2	32	no	—
138	C₃²×D₄	—	2	4	no	—
139	C₃²×D₄	—	2	4	no	—
140	C₃²×D₄	—	2	16	no	—
141	C₃²×D₄	—	2	16	no	—
142	C₃²×D₄	—	6	4	no	—
143	C₃²×D₄	—	6	2	no	—
144	C₃²×D₄	—	12	8	no	—
145	C₂×C₃²×C₄	—	2	16	no	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	4	no	—
148	C₂×C₃²×C₄	—	3	4	no	—
149	C₂×C₃²×C₄	—	3	2	no	—
150	C₂×C₃²×C₄	—	6	4	no	—
151	C₂×C₃²×C₄	#67	1	4	yes	complemented
152	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
153	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
155	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
156	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
157	C₃×#67	—	2	16	no	—
158	C₃×#67	—	4	32	no	—
159	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
160	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
161	C₃×D₁₂	—	2	8	no	—
162	C₃×C₄×D₃	—	2	16	no	—
163	C₃×Dic₆	—	2	8	no	—
164	#535	—	3	1	no	Sylow
165	C₂×C₃³	—	2	2	no	—
166	C₂×C₃³	—	4	4	no	—
167	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
169	C₃²×D₃	—	4	2	no	—
170	C₂⁴×C₃	—	2	8	no	—
171	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
172	C₂⁴×C₃	C₂²×C₃²	1	2	yes	—
173	C₃×#41	—	6	16	no	—
174	C₂×C₃×Q₈	—	3	4	no	—
175	C₂×C₃×D₄	—	2	32	no	—
176	C₂×C₃×D₄	—	2	16	no	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	—	2	8	no	—
179	C₂×C₃×D₄	—	2	8	no	—
180	C₂×C₃×D₄	—	3	8	no	—
181	C₂×C₃×D₄	—	3	32	no	—
182	C₂×C₃×D₄	—	3	4	no	—
183	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
184	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
185	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	—
186	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	—
187	C₂²×C₃×C₄	—	2	4	no	—
188	C₂²×C₃×C₄	—	3	8	no	—
189	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
190	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
191	C₂×#67	C₂²×C₃²	1	2	yes	—
192	C₂×#67	C₂²×C₃²	1	8	yes	complemented
193	#235	—	2	4	no	—
194	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
195	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
196	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
197	C₃×C₄⋊C₄	—	3	8	no	—
198	C₃×C₂²⋊C₄	—	3	8	no	—
199	C₃×C₂²⋊C₄	—	3	32	no	—
200	C₃×C₄²	—	3	8	no	—
201	#217	C₂²×C₃²	1	2	yes	—
202	#217	C₂²×C₃²	1	8	yes	complemented
203	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	complemented
204	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
205	C₂²×C₃²	—	2	16	no	—
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	—	2	8	no	—
208	C₂²×C₃²	—	2	32	no	—
209	C₂²×C₃²	—	2	8	no	—
210	C₂²×C₃²	—	2	4	no	—
211	C₂²×C₃²	—	2	16	no	—
212	C₂²×C₃²	—	2	4	no	—
213	C₂²×C₃²	—	2	8	no	—
214	C₂²×C₃²	—	2	32	no	—
215	C₂²×C₃²	—	4	32	no	—
216	C₂²×C₃²	—	4	64	no	—
217	C₂²×C₃²	—	4	8	no	—
218	C₂²×C₃²	—	4	32	no	—
219	C₂²×C₃²	—	6	4	no	—
220	C₂²×C₃²	—	6	2	no	—
221	C₂²×C₃²	C₂×#67	1	2	yes	—
222	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
223	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
224	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
225	C₂×C₃×D₃	—	2	8	no	—
226	C₂×C₃×D₃	—	2	16	no	—
227	C₃²×C₄	—	2	8	no	—
228	C₃²×C₄	—	2	8	no	—
229	C₃²×C₄	—	6	4	no	—
230	C₃²×C₄	—	6	2	no	—
231	C₃²×C₄	C₂×#67	1	2	yes	—
232	C₃²×C₄	C₂×#67	1	2	yes	—
233	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
234	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
235	C₃×Dic₃	—	2	8	no	—
236	C₃×Dic₃	—	2	16	no	—
237	C₂×#41	—	3	1	no	—
238	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
239	#127	—	3	2	no	—
240	#124	—	3	2	no	—
241	#121	—	3	4	no	—
242	#120	—	3	4	no	—
243	#117	—	3	1	no	—
244	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	32	no	—
246	C₂³×C₃	—	2	16	no	—
247	C₂³×C₃	—	2	4	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	16	no	—
250	C₂³×C₃	—	3	8	no	—
251	C₂³×C₃	—	4	16	no	—
252	C₂³×C₃	—	4	4	no	—
253	C₂³×C₃	—	4	32	no	—
254	C₂³×C₃	C₂²×C₃×D₃	1	16	yes	—
255	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
256	C₂³×C₃	C₂³×C₃²	1	4	yes	—
257	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
258	C₂²×D₃	C₂³×C₃²	1	2	yes	—
259	C₃×Q₈	—	6	8	no	—
260	C₃×D₄	—	2	32	no	—
261	C₃×D₄	—	2	32	no	—
262	C₃×D₄	—	2	16	no	—
263	C₃×D₄	—	2	16	no	—
264	C₃×D₄	—	2	4	no	—
265	C₃×D₄	—	2	4	no	—
266	C₃×D₄	—	6	16	no	—
267	C₃×D₄	—	6	8	no	—
268	C₃×D₄	—	12	32	no	—
269	C₂×C₃×C₄	—	2	16	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	3	16	no	—
273	C₂×C₃×C₄	—	3	8	no	—
274	C₂×C₃×C₄	—	6	16	no	—
275	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
276	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
279	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
281	#67	—	2	4	no	—
282	#67	—	4	8	no	—
283	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
284	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
285	D₁₂	—	2	2	no	—
286	C₄×D₃	—	2	4	no	—
287	Dic₆	—	2	2	no	—
288	C₂×C₃²	—	2	16	no	—
289	C₂×C₃²	—	2	2	no	—
290	C₂×C₃²	—	2	8	no	—
291	C₂×C₃²	—	2	8	no	—
292	C₂×C₃²	—	2	4	no	—
293	C₂×C₃²	—	4	32	no	—
294	C₂×C₃²	—	4	4	no	—
295	C₂×C₃²	—	4	16	no	—
296	C₂×C₃²	—	12	2	no	—
297	C₂×C₃²	#1004	1	2	yes	—
298	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
299	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
300	C₂×C₃²	C₃×H(5,𝔽₂)	1	8	yes	—
301	C₃×D₃	—	4	8	no	—
302	C₂⁴	C₂×C₃²×D₃	1	2	yes	—
303	#41	—	6	4	no	—
304	C₂×Q₈	—	3	1	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	3	2	no	—
307	C₂×D₄	—	3	8	no	—
308	C₂×D₄	—	3	1	no	—
309	C₂×D₄	C₂×C₃²×D₃	1	2	yes	—
310	C₂×D₄	C₂×C₃²×D₃	1	2	yes	—
311	C₂²×C₄	—	3	2	no	—
312	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
313	C₄⋊C₄	—	3	2	no	—
314	C₂²⋊C₄	—	3	2	no	—
315	C₂²⋊C₄	—	3	8	no	—
316	C₄²	—	3	2	no	—
317	C₂²×C₃	—	2	16	no	—
318	C₂²×C₃	—	2	8	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	32	no	—
321	C₂²×C₃	—	2	32	no	—
322	C₂²×C₃	—	2	16	no	—
323	C₂²×C₃	—	2	4	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	—	2	8	no	—
327	C₂²×C₃	—	4	32	no	—
328	C₂²×C₃	—	4	64	no	—
329	C₂²×C₃	—	4	32	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	6	16	no	—
332	C₂²×C₃	—	6	8	no	—
333	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
334	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
335	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
336	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
337	C₂×D₃	—	2	2	no	—
338	C₂×D₃	—	2	4	no	—
339	C₃×C₄	—	2	8	no	—
340	C₃×C₄	—	2	8	no	—
341	C₃×C₄	—	6	16	no	—
342	C₃×C₄	—	6	8	no	—
343	C₃×C₄	C₂×C₃×#67	1	8	yes	—
344	C₃×C₄	C₂×C₃×#67	1	8	yes	—
345	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
346	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
347	Dic₃	—	2	2	no	—
348	Dic₃	—	2	4	no	—
349	C₃²	—	2	4	no	—
350	C₃²	#5805	1	1	yes	characteristic, direct product factor
351	C₃²	C₃×#535	1	4	yes	complemented
352	C₂³	—	2	4	no	—
353	C₂³	—	3	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	C₂²×C₃²×D₃	1	4	yes	—
356	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
357	Q₈	—	6	2	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	D₄	—	6	4	no	—
361	D₄	—	6	2	no	—
362	D₄	—	12	8	no	—
363	C₂×C₄	—	3	4	no	—
364	C₂×C₄	—	3	2	no	—
365	C₂×C₄	—	6	4	no	—
366	C₂×C₄	C₃²×#67	1	4	yes	complemented
367	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
369	C₂×C₃	—	2	16	no	—
370	C₂×C₃	—	2	8	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	8	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	—	4	32	no	—
375	C₂×C₃	—	4	16	no	—
376	C₂×C₃	—	4	4	no	—
377	C₂×C₃	—	12	8	no	—
378	C₂×C₃	C₃×#1004	1	8	yes	—
379	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
380	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
381	C₂×C₃	C₃²×H(5,𝔽₂)	1	2	yes	—
382	D₃	—	4	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	6	4	no	—
388	C₂²	—	6	2	no	—
389	C₂²	C₂×C₃²×#67	1	2	yes	—
390	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
391	C₄	—	6	4	no	—
392	C₄	—	6	2	no	—
393	C₄	C₂×C₃²×#67	1	2	yes	—
394	C₄	C₂×C₃²×#67	1	2	yes	—
395	C₃	—	2	4	no	—
396	C₃	C₃×#5805	1	4	yes	direct product factor
397	C₃	C₃²×#535	1	1	yes	characteristic, complemented
398	C₂	—	2	2	no	—
399	C₂	—	4	4	no	—
400	C₂	—	12	2	no	—
401	C₂	C₃²×#1004	1	2	yes	—
402	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₃²×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂×C₃²×#235	C₂	semidirect
3. C₃²×#953	C₂	semidirect
4. C₃²×#940	C₂	semidirect
5. C₃²×#938	C₂	semidirect
6. C₃²×#936	C₂	semidirect
7. C₃²×#926	C₂	semidirect
9. C₃×#5805	C₃	direct (N × H)
16. C₂×C₃²×#67	C₂²	semidirect
18. C₂×C₃²×D₁₂	C₂²	semidirect
19. C₂×C₃²×C₄×D₃	C₂²	semidirect
20. C₂×C₃²×Dic₆	C₂²	semidirect
22. C₃²×#217	C₂²	semidirect
23. C₃²×C₄⋊Dic₃	C₂²	semidirect
24. C₃²×C₄×Dic₃	C₂²	semidirect
27. C₂²×C₃²×D₄	D₃	semidirect
28. C₂²×C₃²×D₄	C₂×C₃	semidirect
29. C₂×C₃×#235	C₂×C₃	semidirect
35. C₃×#953	C₂×C₃	semidirect
36. C₃×#940	C₂×C₃	semidirect
37. C₃×#938	C₂×C₃	semidirect
38. C₃×#936	C₂×C₃	semidirect
39. C₃×#926	C₂×C₃	semidirect
47. C₂×C₃³×C₄	D₄	semidirect
58. #5805	C₃²	direct (N × H)
81. C₂×C₃×#67	C₂²×C₃	semidirect
83. C₂×C₃×D₁₂	C₂²×C₃	semidirect
84. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
85. C₂×C₃×Dic₆	C₂²×C₃	semidirect
91. C₃×#217	C₂²×C₃	semidirect
92. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
93. C₃×C₄×Dic₃	C₂²×C₃	semidirect
108. C₂²×C₃×D₄	C₃×D₃	semidirect
109. C₂²×C₃×D₄	C₂×C₃²	semidirect
110. C₂×#235	C₂×C₃²	semidirect
116. #953	C₂×C₃²	semidirect
117. #940	C₂×C₃²	semidirect
118. #938	C₂×C₃²	semidirect
119. #936	C₂×C₃²	semidirect
120. #926	C₂×C₃²	semidirect
151. C₂×C₃²×C₄	#67	semidirect
152. C₂×C₃²×C₄	C₃×D₄	semidirect
192. C₂×#67	C₂²×C₃²	semidirect
194. C₂×D₁₂	C₂²×C₃²	semidirect
195. C₂×C₄×D₃	C₂²×C₃²	semidirect
196. C₂×Dic₆	C₂²×C₃²	semidirect
202. #217	C₂²×C₃²	semidirect
203. C₄⋊Dic₃	C₂²×C₃²	semidirect
204. C₄×Dic₃	C₂²×C₃²	semidirect
238. C₂²×D₄	C₃²×D₃	semidirect
244. C₃³	#535	semidirect
275. C₂×C₃×C₄	C₃×#67	semidirect
276. C₂×C₃×C₄	C₃²×D₄	semidirect
350. C₃²	#5805	direct (N × H)
351. C₃²	C₃×#535	semidirect
366. C₂×C₄	C₃²×#67	semidirect
396. C₃	C₃×#5805	direct (N × H)
397. C₃	C₃²×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃³×D₄	2
C₂×C₃²×#235	2
C₃²×#953	2
C₃²×#940	2
C₃²×#938	2
C₃²×#936	2
C₃²×#926	2
C₃²×#535	3
C₃×#5805	3

Subgroups — C32×#5805 #13179182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5805 #13179182