Subgroups — C₂²×Dic₃×#67 #11899904

Order 1152.

5393 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#3757	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₃×#67	C₂	1	24	yes	maximal, direct product factor
6	C₂²×Dic₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×(C₂×D₃)⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₃²	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄×Dic₃	—	3	1	no	maximal
10	C₂²×C₄×#67	—	3	1	no	maximal
11	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
12	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
13	C₂³×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
14	C₂³×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#67	C₄	1	16	yes	complemented
16	C₂²×C₃×#67	C₂²	1	12	yes	—
17	C₂³×C₃×Dic₃	—	2	8	no	—
18	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
19	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
20	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
21	C₂³×C₃×Dic₃	C₂²	1	12	yes	complemented
22	C₂²×D₃×Dic₃	—	2	8	no	—
23	C₂²×D₃×Dic₃	C₂²	1	12	yes	complemented
24	C₂×#3757	C₂²	1	12	yes	complemented
25	Dic₃×#67	C₂²	1	64	yes	direct product factor
26	C₂×Dic₃⋊Dic₃	C₂²	1	12	yes	complemented
27	C₂×(C₂×D₃)⋊Dic₃	C₂²	1	12	yes	complemented
28	C₂×Dic₃²	C₂²	1	12	yes	complemented
29	C₂³×C₃×D₄	—	3	1	no	—
30	C₂⁴×C₃×C₄	—	3	1	no	—
31	C₂³×#67	D₃	1	1	yes	characteristic
32	C₂⁴×Dic₃	—	3	1	no	—
33	C₂⁴×Dic₃	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₄×D₃	—	3	1	no	—
35	C₂²×#217	—	3	1	no	—
36	C₂²×#217	—	3	1	no	—
37	C₂²×#217	—	3	1	no	—
38	C₂²×#217	—	6	1	no	—
39	C₂×D₄×Dic₃	—	3	24	no	—
40	C₂×C₄×#67	—	3	24	no	—
41	C₂²×(C₂×D₃)⋊C₄	—	3	1	no	—
42	C₂²×C₄⋊Dic₃	—	3	1	no	—
43	C₂²×Dic₃⋊C₄	—	3	1	no	—
44	C₂²×C₄×Dic₃	—	3	1	no	—
45	C₂²×C₄×Dic₃	—	3	1	no	—
46	C₂⁴×C₃²	—	2	4	no	—
47	C₂⁴×C₃²	—	2	4	no	—
48	C₂⁴×C₃²	C₂×C₄	1	8	yes	complemented
49	C₂⁴×C₃²	C₂³	1	6	yes	—
50	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
51	C₂³×C₃×D₃	—	2	4	no	—
52	C₂³×C₃×D₃	—	2	4	no	—
53	C₂³×C₃×D₃	C₂×C₄	1	8	yes	complemented
54	C₂³×C₃×D₃	C₂³	1	6	yes	—
55	C₂²×C₃⋊Dic₃	—	2	4	no	—
56	C₂²×C₃⋊Dic₃	—	2	4	no	—
57	C₂²×C₃⋊Dic₃	C₂³	1	6	yes	—
58	C₂²×C₃⋊Dic₃	C₂³	1	6	yes	—
59	C₂×C₃×#67	C₂×C₄	1	96	yes	complemented
60	C₂×C₃×#67	C₂³	1	16	yes	—
61	C₂²×C₃×Dic₃	—	2	4	no	—
62	C₂²×C₃×Dic₃	—	2	48	no	—
63	C₂²×C₃×Dic₃	C₂×C₄	1	8	yes	complemented
64	C₂²×C₃×Dic₃	D₄	1	8	yes	complemented
65	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
66	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
67	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
68	C₂²×C₃×Dic₃	C₂³	1	16	yes	complemented
69	C₂×D₃×Dic₃	—	2	48	no	—
70	C₂×D₃×Dic₃	C₂³	1	16	yes	complemented
71	#3757	C₂³	1	16	yes	complemented
72	Dic₃⋊Dic₃	C₂³	1	16	yes	complemented
73	(C₂×D₃)⋊Dic₃	C₂³	1	16	yes	complemented
74	Dic₃²	C₂³	1	16	yes	complemented
75	C₂²×C₄×D₄	—	9	1	no	Sylow
76	C₂⁵×C₃	—	2	1	no	—
77	C₂⁵×C₃	—	3	1	no	—
78	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
79	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
80	C₂⁴×D₃	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₃×D₄	—	3	16	no	—
82	C₂²×C₃×D₄	—	3	12	no	—
83	C₂³×C₃×C₄	—	3	1	no	—
84	C₂³×C₃×C₄	—	3	1	no	—
85	C₂³×C₃×C₄	—	3	1	no	—
86	C₂³×C₃×C₄	—	3	12	no	—
87	C₂³×C₃×C₄	—	6	8	no	—
88	C₂²×#67	Dic₃	1	16	yes	direct product factor
89	C₂²×#67	C₂×D₃	1	12	yes	—
90	C₂³×Dic₃	—	2	8	no	—
91	C₂³×Dic₃	—	3	1	no	—
92	C₂³×Dic₃	—	3	1	no	—
93	C₂³×Dic₃	—	3	1	no	—
94	C₂³×Dic₃	—	3	1	no	—
95	C₂³×Dic₃	—	3	12	no	—
96	C₂³×Dic₃	—	6	1	no	—
97	C₂³×Dic₃	—	6	1	no	—
98	C₂³×Dic₃	—	6	8	no	—
99	C₂³×Dic₃	C₂×D₃	1	1	yes	characteristic
100	C₂³×Dic₃	C₂×D₃	1	1	yes	characteristic
101	C₂³×Dic₃	C₂×D₃	1	1	yes	characteristic
102	C₂³×Dic₃	C₂×D₃	1	12	yes	complemented
103	C₂²×C₄×D₃	—	3	12	no	—
104	C₂²×C₄×D₃	—	6	8	no	—
105	C₂×#217	—	3	12	no	—
106	C₂×#217	—	3	12	no	—
107	C₂×#217	—	3	12	no	—
108	C₂×#217	—	6	12	no	—
109	D₄×Dic₃	—	3	64	no	—
110	C₄×#67	—	3	64	no	—
111	C₂×(C₂×D₃)⋊C₄	—	3	12	no	—
112	C₂×C₄⋊Dic₃	—	3	12	no	—
113	C₂×Dic₃⋊C₄	—	3	12	no	—
114	C₂×C₄×Dic₃	—	3	12	no	—
115	C₂×C₄×Dic₃	—	3	12	no	—
116	C₂³×C₃²	—	2	32	no	—
117	C₂³×C₃²	—	2	12	no	—
118	C₂³×C₃²	—	2	12	no	—
119	C₂³×C₃²	C₂²×C₄	1	4	yes	—
120	C₂³×C₃²	C₂²×C₄	1	24	yes	complemented
121	C₂³×C₃²	C₂×D₄	1	4	yes	—
122	C₂³×C₃²	#41	1	4	yes	—
123	C₂³×C₃²	C₂⁴	1	4	yes	—
124	C₂³×C₃²	C₂⁴	1	3	yes	—
125	C₂²×C₃×D₃	—	2	32	no	—
126	C₂²×C₃×D₃	—	2	12	no	—
127	C₂²×C₃×D₃	—	2	12	no	—
128	C₂²×C₃×D₃	C₂²×C₄	1	24	yes	complemented
129	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
130	C₂×C₃⋊Dic₃	—	2	12	no	—
131	C₂×C₃⋊Dic₃	—	2	12	no	—
132	C₂×C₃⋊Dic₃	C₂⁴	1	4	yes	—
133	C₂×C₃⋊Dic₃	C₂⁴	1	4	yes	—
134	C₃×#67	C₂²×C₄	1	64	yes	complemented
135	C₂×C₃×Dic₃	—	2	12	no	—
136	C₂×C₃×Dic₃	—	2	32	no	—
137	C₂×C₃×Dic₃	C₂²×C₄	1	24	yes	complemented
138	C₂×C₃×Dic₃	C₂×D₄	1	24	yes	complemented
139	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
140	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
141	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
142	D₃×Dic₃	—	2	32	no	—
143	C₂³×D₄	—	3	1	no	—
144	C₂⁴×C₄	—	3	1	no	—
145	C₂⁴×C₄	—	9	1	no	—
146	C₂×C₄×D₄	—	9	24	no	—
147	C₂²×C₄⋊C₄	—	9	1	no	—
148	C₂²×C₂²⋊C₄	—	9	1	no	—
149	C₂²×C₂²⋊C₄	—	9	1	no	—
150	C₂²×C₄²	—	9	1	no	—
151	C₂⁴×C₃	—	2	4	no	—
152	C₂⁴×C₃	—	2	4	no	—
153	C₂⁴×C₃	—	2	4	no	—
154	C₂⁴×C₃	—	2	4	no	—
155	C₂⁴×C₃	—	2	8	no	—
156	C₂⁴×C₃	—	2	6	no	—
157	C₂⁴×C₃	—	2	1	no	—
158	C₂⁴×C₃	—	3	8	no	—
159	C₂⁴×C₃	—	3	6	no	—
160	C₂⁴×C₃	—	4	4	no	—
161	C₂⁴×C₃	—	4	4	no	—
162	C₂⁴×C₃	—	6	4	no	—
163	C₂⁴×C₃	—	6	4	no	—
164	C₂⁴×C₃	C₄×D₃	1	8	yes	complemented
165	C₂⁴×C₃	C₂×Dic₃	1	8	yes	complemented
166	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
167	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
168	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
169	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
170	C₂³×D₃	—	2	4	no	—
171	C₂³×D₃	—	2	4	no	—
172	C₂³×D₃	C₂×Dic₃	1	8	yes	complemented
173	C₂³×D₃	C₂²×D₃	1	6	yes	—
174	C₂×C₃×D₄	—	3	96	no	—
175	C₂×C₃×D₄	—	3	16	no	—
176	C₂²×C₃×C₄	—	3	8	no	—
177	C₂²×C₃×C₄	—	3	8	no	—
178	C₂²×C₃×C₄	—	3	6	no	—
179	C₂²×C₃×C₄	—	3	6	no	—
180	C₂²×C₃×C₄	—	3	6	no	—
181	C₂²×C₃×C₄	—	3	16	no	—
182	C₂²×C₃×C₄	—	6	48	no	—
183	C₂²×C₃×C₄	—	6	4	no	—
184	C₂×#67	C₂×Dic₃	1	96	yes	direct product factor
185	C₂×#67	C₂²×D₃	1	16	yes	—
186	C₂²×Dic₃	—	2	4	no	—
187	C₂²×Dic₃	—	2	48	no	—
188	C₂²×Dic₃	—	3	6	no	—
189	C₂²×Dic₃	—	3	6	no	—
190	C₂²×Dic₃	—	3	6	no	—
191	C₂²×Dic₃	—	3	6	no	—
192	C₂²×Dic₃	—	3	16	no	—
193	C₂²×Dic₃	—	6	6	no	—
194	C₂²×Dic₃	—	6	6	no	—
195	C₂²×Dic₃	—	6	4	no	—
196	C₂²×Dic₃	—	6	4	no	—
197	C₂²×Dic₃	—	6	4	no	—
198	C₂²×Dic₃	—	6	4	no	—
199	C₂²×Dic₃	—	6	48	no	—
200	C₂²×Dic₃	—	12	4	no	—
201	C₂²×Dic₃	—	12	4	no	—
202	C₂²×Dic₃	C₂×Dic₃	1	8	yes	complemented
203	C₂²×Dic₃	#67	1	8	yes	direct product factor
204	C₂²×Dic₃	C₂²×D₃	1	6	yes	—
205	C₂²×Dic₃	C₂²×D₃	1	6	yes	—
206	C₂²×Dic₃	C₂²×D₃	1	6	yes	—
207	C₂²×Dic₃	C₂²×D₃	1	16	yes	complemented
208	C₂×C₄×D₃	—	3	16	no	—
209	C₂×C₄×D₃	—	6	48	no	—
210	#217	—	3	16	no	—
211	#217	—	3	16	no	—
212	#217	—	3	16	no	—
213	#217	—	6	16	no	—
214	(C₂×D₃)⋊C₄	—	3	16	no	—
215	C₄⋊Dic₃	—	3	16	no	—
216	Dic₃⋊C₄	—	3	16	no	—
217	C₄×Dic₃	—	3	16	no	—
218	C₄×Dic₃	—	3	16	no	—
219	C₂²×C₃²	—	2	48	no	—
220	C₂²×C₃²	—	2	4	no	—
221	C₂²×C₃²	—	2	4	no	—
222	C₂²×C₃²	C₄×D₄	1	16	yes	complemented
223	C₂²×C₃²	C₂³×C₄	1	6	yes	—
224	C₂²×C₃²	C₂³×C₄	1	8	yes	complemented
225	C₂²×C₃²	C₂²×D₄	1	6	yes	—
226	C₂²×C₃²	C₂×#41	1	6	yes	—
227	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
228	C₂×C₃×D₃	—	2	48	no	—
229	C₂×C₃×D₃	—	2	4	no	—
230	C₂×C₃×D₃	—	2	4	no	—
231	C₂×C₃×D₃	C₂³×C₄	1	8	yes	complemented
232	C₃⋊Dic₃	—	2	4	no	—
233	C₃⋊Dic₃	—	2	4	no	—
234	C₃×Dic₃	—	2	4	no	—
235	C₃×Dic₃	C₂³×C₄	1	8	yes	complemented
236	C₃×Dic₃	C₂²×D₄	1	8	yes	complemented
237	C₂⁵	—	3	1	no	—
238	C₂⁵	D₃²	1	1	yes	characteristic
239	C₂²×D₄	—	3	16	no	—
240	C₂²×D₄	—	3	12	no	—
241	C₂³×C₄	—	3	1	no	—
242	C₂³×C₄	—	3	1	no	—
243	C₂³×C₄	—	3	12	no	—
244	C₂³×C₄	—	3	1	no	—
245	C₂³×C₄	—	6	8	no	—
246	C₂³×C₄	—	9	12	no	—
247	C₂³×C₄	—	9	1	no	—
248	C₂³×C₄	—	9	1	no	—
249	C₂³×C₄	—	18	8	no	—
250	C₄×D₄	—	9	64	no	—
251	C₂×C₄⋊C₄	—	9	12	no	—
252	C₂×C₂²⋊C₄	—	9	12	no	—
253	C₂×C₂²⋊C₄	—	9	12	no	—
254	C₂×C₄²	—	9	12	no	—
255	C₂³×C₃	—	2	32	no	—
256	C₂³×C₃	—	2	32	no	—
257	C₂³×C₃	—	2	12	no	—
258	C₂³×C₃	—	2	12	no	—
259	C₂³×C₃	—	2	12	no	—
260	C₂³×C₃	—	2	12	no	—
261	C₂³×C₃	—	2	3	no	—
262	C₂³×C₃	—	2	4	no	—
263	C₂³×C₃	—	2	4	no	—
264	C₂³×C₃	—	2	24	no	—
265	C₂³×C₃	—	2	4	no	—
266	C₂³×C₃	—	2	4	no	—
267	C₂³×C₃	—	3	24	no	—
268	C₂³×C₃	—	3	4	no	—
269	C₂³×C₃	—	4	12	no	—
270	C₂³×C₃	—	4	12	no	—
271	C₂³×C₃	—	4	32	no	—
272	C₂³×C₃	—	6	32	no	—
273	C₂³×C₃	—	6	12	no	—
274	C₂³×C₃	—	6	12	no	—
275	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
276	C₂³×C₃	C₂×C₄×D₃	1	24	yes	complemented
277	C₂³×C₃	#235	1	4	yes	—
278	C₂³×C₃	D₃×D₄	1	4	yes	—
279	C₂³×C₃	#237	1	4	yes	—
280	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
281	C₂³×C₃	C₂²×Dic₃	1	24	yes	complemented
282	C₂³×C₃	C₂×#67	1	4	yes	—
283	C₂³×C₃	C₂³×D₃	1	4	yes	—
284	C₂³×C₃	C₂³×D₃	1	4	yes	—
285	C₂³×C₃	C₂³×D₃	1	3	yes	—
286	C₂³×C₃	C₂³×D₃	1	3	yes	—
287	C₂²×D₃	—	2	32	no	—
288	C₂²×D₃	—	2	12	no	—
289	C₂²×D₃	—	2	12	no	—
290	C₂²×D₃	C₂²×Dic₃	1	24	yes	complemented
291	C₂²×D₃	C₂³×D₃	1	4	yes	—
292	C₃×D₄	—	3	64	no	—
293	C₂×C₃×C₄	—	3	24	no	—
294	C₂×C₃×C₄	—	3	24	no	—
295	C₂×C₃×C₄	—	3	4	no	—
296	C₂×C₃×C₄	—	3	4	no	—
297	C₂×C₃×C₄	—	3	4	no	—
298	C₂×C₃×C₄	—	6	32	no	—
299	C₂×C₃×C₄	—	6	12	no	—
300	#67	C₂²×Dic₃	1	64	yes	direct product factor
301	C₂×Dic₃	—	2	12	no	—
302	C₂×Dic₃	—	2	32	no	—
303	C₂×Dic₃	—	3	4	no	—
304	C₂×Dic₃	—	3	4	no	—
305	C₂×Dic₃	—	3	4	no	—
306	C₂×Dic₃	—	3	4	no	—
307	C₂×Dic₃	—	6	4	no	—
308	C₂×Dic₃	—	6	4	no	—
309	C₂×Dic₃	—	6	12	no	—
310	C₂×Dic₃	—	6	12	no	—
311	C₂×Dic₃	—	6	12	no	—
312	C₂×Dic₃	—	6	12	no	—
313	C₂×Dic₃	—	6	32	no	—
314	C₂×Dic₃	—	12	12	no	—
315	C₂×Dic₃	—	12	12	no	—
316	C₂×Dic₃	C₂²×Dic₃	1	24	yes	complemented
317	C₂×Dic₃	C₂×#67	1	24	yes	direct product factor
318	C₂×Dic₃	C₂³×D₃	1	4	yes	—
319	C₂×Dic₃	C₂³×D₃	1	4	yes	—
320	C₂×Dic₃	C₂³×D₃	1	4	yes	—
321	C₄×D₃	—	6	32	no	—
322	C₂×C₃²	—	2	8	no	—
323	C₂×C₃²	C₂×C₄×D₄	1	12	yes	complemented
324	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
325	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
326	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
327	C₃×D₃	—	2	8	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	3	6	no	—
331	C₂⁴	—	3	8	no	—
332	C₂⁴	—	6	4	no	—
333	C₂⁴	—	6	4	no	—
334	C₂⁴	D₃×Dic₃	1	8	yes	complemented
335	C₂⁴	C₂×D₃²	1	6	yes	—
336	C₂⁴	C₂×D₃²	1	1	yes	characteristic
337	C₂×D₄	—	3	16	no	—
338	C₂×D₄	—	3	96	no	—
339	C₂²×C₄	—	3	6	no	—
340	C₂²×C₄	—	3	6	no	—
341	C₂²×C₄	—	3	8	no	—
342	C₂²×C₄	—	3	8	no	—
343	C₂²×C₄	—	3	6	no	—
344	C₂²×C₄	—	3	16	no	—
345	C₂²×C₄	—	6	48	no	—
346	C₂²×C₄	—	6	4	no	—
347	C₂²×C₄	—	9	16	no	—
348	C₂²×C₄	—	9	6	no	—
349	C₂²×C₄	—	9	6	no	—
350	C₂²×C₄	—	18	48	no	—
351	C₂²×C₄	—	18	4	no	—
352	C₂²×C₄	—	18	4	no	—
353	C₄⋊C₄	—	9	16	no	—
354	C₂²⋊C₄	—	9	16	no	—
355	C₂²⋊C₄	—	9	16	no	—
356	C₄²	—	9	16	no	—
357	C₂²×C₃	—	2	4	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	2	4	no	—
360	C₂²×C₃	—	2	4	no	—
361	C₂²×C₃	—	2	48	no	—
362	C₂²×C₃	—	2	48	no	—
363	C₂²×C₃	—	2	6	no	—
364	C₂²×C₃	—	2	8	no	—
365	C₂²×C₃	—	2	6	no	—
366	C₂²×C₃	—	2	6	no	—
367	C₂²×C₃	—	2	1	no	—
368	C₂²×C₃	—	2	16	no	—
369	C₂²×C₃	—	3	8	no	—
370	C₂²×C₃	—	4	4	no	—
371	C₂²×C₃	—	4	4	no	—
372	C₂²×C₃	—	4	48	no	—
373	C₂²×C₃	—	6	4	no	—
374	C₂²×C₃	—	6	4	no	—
375	C₂²×C₃	—	6	48	no	—
376	C₂²×C₃	C₄×#67	1	16	yes	complemented
377	C₂²×C₃	D₄×Dic₃	1	16	yes	complemented
378	C₂²×C₃	C₂²×C₄×D₃	1	6	yes	—
379	C₂²×C₃	C₂²×C₄×D₃	1	8	yes	complemented
380	C₂²×C₃	C₂×#235	1	6	yes	—
381	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
382	C₂²×C₃	C₂×#237	1	6	yes	—
383	C₂²×C₃	C₂³×Dic₃	1	6	yes	—
384	C₂²×C₃	C₂³×Dic₃	1	8	yes	complemented
385	C₂²×C₃	C₂²×#67	1	6	yes	—
386	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
387	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
388	C₂×D₃	—	2	4	no	—
389	C₂×D₃	—	2	4	no	—
390	C₂×D₃	—	2	48	no	—
391	C₂×D₃	C₂³×Dic₃	1	8	yes	complemented
392	C₃×C₄	—	3	8	no	—
393	C₃×C₄	—	3	8	no	—
394	C₃×C₄	—	6	4	no	—
395	Dic₃	—	2	4	no	—
396	Dic₃	—	6	4	no	—
397	Dic₃	—	6	4	no	—
398	Dic₃	—	6	4	no	—
399	Dic₃	—	6	4	no	—
400	Dic₃	—	12	4	no	—
401	Dic₃	—	12	4	no	—
402	Dic₃	C₂³×Dic₃	1	8	yes	complemented
403	Dic₃	C₂²×#67	1	8	yes	direct product factor
404	C₃²	C₂²×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
405	C₂³	—	2	12	no	—
406	C₂³	—	2	12	no	—
407	C₂³	—	2	32	no	—
408	C₂³	—	3	24	no	—
409	C₂³	—	3	4	no	—
410	C₂³	—	6	12	no	—
411	C₂³	—	6	12	no	—
412	C₂³	—	6	32	no	—
413	C₂³	C₂×D₃×Dic₃	1	4	yes	—
414	C₂³	C₂×D₃×Dic₃	1	24	yes	complemented
415	C₂³	#3804	1	4	yes	—
416	C₂³	D₃×#67	1	4	yes	—
417	C₂³	C₂²×D₃²	1	4	yes	—
418	C₂³	C₂²×D₃²	1	3	yes	—
419	D₄	—	3	64	no	—
420	C₂×C₄	—	3	24	no	—
421	C₂×C₄	—	3	24	no	—
422	C₂×C₄	—	3	4	no	—
423	C₂×C₄	—	3	4	no	—
424	C₂×C₄	—	3	4	no	—
425	C₂×C₄	—	6	32	no	—
426	C₂×C₄	—	6	12	no	—
427	C₂×C₄	—	9	4	no	—
428	C₂×C₄	—	9	4	no	—
429	C₂×C₄	—	18	32	no	—
430	C₂×C₄	—	18	12	no	—
431	C₂×C₄	—	18	12	no	—
432	C₂×C₃	—	2	8	no	—
433	C₂×C₃	—	2	8	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	12	no	—
438	C₂×C₃	—	4	8	no	—
439	C₂×C₃	—	6	8	no	—
440	C₂×C₃	C₂×C₄×#67	1	12	yes	complemented
441	C₂×C₃	C₂×D₄×Dic₃	1	12	yes	complemented
442	C₂×C₃	C₂³×C₄×D₃	1	1	yes	characteristic
443	C₂×C₃	C₂²×#235	1	1	yes	characteristic
444	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
445	C₂×C₃	C₂²×#237	1	1	yes	characteristic
446	C₂×C₃	C₂⁴×Dic₃	1	1	yes	characteristic
447	C₂×C₃	C₂³×#67	1	1	yes	characteristic
448	D₃	—	2	8	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	48	no	—
452	C₂²	—	3	8	no	—
453	C₂²	—	6	4	no	—
454	C₂²	—	6	4	no	—
455	C₂²	—	6	48	no	—
456	C₂²	Dic₃×#67	1	16	yes	direct product factor
457	C₂²	C₂²×D₃×Dic₃	1	6	yes	—
458	C₂²	C₂²×D₃×Dic₃	1	8	yes	complemented
459	C₂²	C₂×#3804	1	6	yes	—
460	C₂²	C₂×D₃×#67	1	6	yes	—
461	C₂²	C₂³×D₃²	1	1	yes	characteristic
462	C₄	—	3	8	no	—
463	C₄	—	3	8	no	—
464	C₄	—	6	4	no	—
465	C₄	—	18	4	no	—
466	C₄	—	18	4	no	—
467	C₃	—	2	1	no	—
468	C₃	C₂²×C₄×#67	1	1	yes	characteristic, complemented
469	C₃	C₂²×D₄×Dic₃	1	1	yes	characteristic, complemented
470	C₂	—	2	8	no	—
471	C₂	—	6	8	no	—
472	C₂	C₂×Dic₃×#67	1	12	yes	direct product factor
473	C₂	C₂³×D₃×Dic₃	1	1	yes	characteristic
474	C₂	C₂²×#3804	1	1	yes	characteristic
475	C₂	C₂²×D₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃²
commutator	C₂×C₃²	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃²
Fitting	C₂⁵×C₃²	C₂²
socle	C₂⁴×C₃²	C₂³
prime radical	C₂³×C₃×#67	C₂
cosocle	C₂²×C₃²	C₂⁵
hypercenter	C₂⁵	D₃²
hypocenter	C₃²	C₂²×C₄×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₃×Dic₃	C₂	semidirect
3. C₂³×D₃×Dic₃	C₂	semidirect
4. C₂²×#3757	C₂	semidirect
5. C₂×Dic₃×#67	C₂	direct (N × H)
6. C₂²×Dic₃⋊Dic₃	C₂	semidirect
7. C₂²×(C₂×D₃)⋊Dic₃	C₂	semidirect
8. C₂²×Dic₃²	C₂	semidirect
15. C₂²×C₃×#67	C₄	semidirect
21. C₂³×C₃×Dic₃	C₂²	semidirect
23. C₂²×D₃×Dic₃	C₂²	semidirect
24. C₂×#3757	C₂²	semidirect
25. Dic₃×#67	C₂²	direct (N × H)
26. C₂×Dic₃⋊Dic₃	C₂²	semidirect
27. C₂×(C₂×D₃)⋊Dic₃	C₂²	semidirect
28. C₂×Dic₃²	C₂²	semidirect
33. C₂⁴×Dic₃	D₃	semidirect
48. C₂⁴×C₃²	C₂×C₄	semidirect
53. C₂³×C₃×D₃	C₂×C₄	semidirect
59. C₂×C₃×#67	C₂×C₄	semidirect
63. C₂²×C₃×Dic₃	C₂×C₄	semidirect
64. C₂²×C₃×Dic₃	D₄	semidirect
68. C₂²×C₃×Dic₃	C₂³	semidirect
70. C₂×D₃×Dic₃	C₂³	semidirect
71. #3757	C₂³	semidirect
72. Dic₃⋊Dic₃	C₂³	semidirect
73. (C₂×D₃)⋊Dic₃	C₂³	semidirect
74. Dic₃²	C₂³	semidirect
88. C₂²×#67	Dic₃	direct (N × H)
102. C₂³×Dic₃	C₂×D₃	semidirect
120. C₂³×C₃²	C₂²×C₄	semidirect
128. C₂²×C₃×D₃	C₂²×C₄	semidirect
134. C₃×#67	C₂²×C₄	semidirect
137. C₂×C₃×Dic₃	C₂²×C₄	semidirect
138. C₂×C₃×Dic₃	C₂×D₄	semidirect
164. C₂⁴×C₃	C₄×D₃	semidirect
165. C₂⁴×C₃	C₂×Dic₃	semidirect
172. C₂³×D₃	C₂×Dic₃	semidirect
184. C₂×#67	C₂×Dic₃	direct (N × H)
202. C₂²×Dic₃	C₂×Dic₃	semidirect
203. C₂²×Dic₃	#67	direct (N × H)
207. C₂²×Dic₃	C₂²×D₃	semidirect
222. C₂²×C₃²	C₄×D₄	semidirect
224. C₂²×C₃²	C₂³×C₄	semidirect
231. C₂×C₃×D₃	C₂³×C₄	semidirect
235. C₃×Dic₃	C₂³×C₄	semidirect
236. C₃×Dic₃	C₂²×D₄	semidirect
276. C₂³×C₃	C₂×C₄×D₃	semidirect
281. C₂³×C₃	C₂²×Dic₃	semidirect
290. C₂²×D₃	C₂²×Dic₃	semidirect
300. #67	C₂²×Dic₃	direct (N × H)
316. C₂×Dic₃	C₂²×Dic₃	semidirect
317. C₂×Dic₃	C₂×#67	direct (N × H)
323. C₂×C₃²	C₂×C₄×D₄	semidirect
334. C₂⁴	D₃×Dic₃	semidirect
376. C₂²×C₃	C₄×#67	semidirect
377. C₂²×C₃	D₄×Dic₃	semidirect
379. C₂²×C₃	C₂²×C₄×D₃	semidirect
384. C₂²×C₃	C₂³×Dic₃	semidirect
391. C₂×D₃	C₂³×Dic₃	semidirect
402. Dic₃	C₂³×Dic₃	semidirect
403. Dic₃	C₂²×#67	direct (N × H)
404. C₃²	C₂²×C₄×D₄	semidirect
414. C₂³	C₂×D₃×Dic₃	semidirect
440. C₂×C₃	C₂×C₄×#67	semidirect
441. C₂×C₃	C₂×D₄×Dic₃	semidirect
456. C₂²	Dic₃×#67	direct (N × H)
458. C₂²	C₂²×D₃×Dic₃	semidirect
468. C₃	C₂²×C₄×#67	semidirect
469. C₃	C₂²×D₄×Dic₃	semidirect
472. C₂	C₂×Dic₃×#67	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×#67	2
C₂⁴×C₃×Dic₃	2
C₂³×D₃×Dic₃	2
C₂²×#3757	2
C₂×Dic₃×#67	2
C₂²×Dic₃⋊Dic₃	2
C₂²×(C₂×D₃)⋊Dic₃	2
C₂²×Dic₃²	2
C₂²×D₄×Dic₃	3
C₂²×C₄×#67	3

Subgroups — C22×Dic3×#67 #11899904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₃×#67 #11899904