Subgroups — C₂²×D₃×#235 #11919198

Order 1152.

13485 conjugacy classes of subgroups.

The subgroup lattice has 705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3828	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃×#67	C₂	1	2	yes	maximal, complemented
5	C₂²×#3804	C₂	1	2	yes	maximal, complemented
6	C₂×D₃×#235	C₂	1	48	yes	maximal, direct product factor
7	C₂²×D₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₃²	C₂	1	2	yes	maximal, complemented
9	C₂²×#3799	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#3798	C₂	1	2	yes	maximal, complemented
11	C₂²×#3795	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₃×#41	—	3	1	no	maximal
14	C₂³×#235	—	3	1	no	maximal
15	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
16	C₂³×D₃²	C₂²	1	2	yes	—
17	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#638	C₂²	1	2	yes	complemented
19	C₂×#3828	C₂²	1	24	yes	complemented
20	C₂²×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
22	C₂²×#634	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×#67	C₂²	1	2	yes	complemented
24	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#235	C₂²	1	24	yes	complemented
26	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₄×D₃	C₂²	1	24	yes	complemented
30	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
33	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₃×#67	C₂²	1	48	yes	complemented
35	C₂²×#627	C₂²	1	2	yes	complemented
36	C₂²×#626	C₂²	1	2	yes	complemented
37	C₂²×#626	C₂²	1	2	yes	complemented
38	C₂²×#625	C₂²	1	2	yes	complemented
39	C₂²×#624	C₂²	1	2	yes	complemented
40	C₂×#3804	C₂²	1	48	yes	complemented
41	C₂²×D₃×Dic₃	C₂²	1	2	yes	—
42	C₂²×D₃×Dic₃	C₂²	1	2	yes	complemented
43	D₃×#235	C₂²	1	256	yes	direct product factor
44	C₂×D₃×D₁₂	C₂²	1	24	yes	complemented
45	C₂×C₄×D₃²	C₂²	1	48	yes	complemented
46	C₂×#3799	C₂²	1	24	yes	complemented
47	C₂×#3798	C₂²	1	48	yes	complemented
48	C₂×#3795	C₂²	1	24	yes	complemented
49	C₂×D₃×Dic₆	C₂²	1	24	yes	complemented
50	C₂²×C₃×#41	—	3	1	no	—
51	C₂⁴×C₃×C₄	—	3	1	no	—
52	C₂³×#67	—	3	2	no	—
53	C₂×D₃×#41	—	3	48	no	—
54	C₂²×#239	—	3	1	no	—
55	C₂²×D₃×Q₈	—	3	1	no	—
56	C₂²×#237	—	3	2	no	—
57	C₂²×#237	—	3	1	no	—
58	C₂²×D₃×D₄	—	3	2	no	—
59	C₂²×D₃×D₄	—	3	1	no	—
60	C₂²×#235	—	3	1	no	—
61	C₂²×#235	—	3	1	no	—
62	C₂²×#235	—	3	2	no	—
63	C₂²×#235	—	3	48	no	—
64	C₂²×#235	—	3	1	no	—
65	C₂²×#235	—	3	2	no	—
66	C₂²×#235	—	3	2	no	—
67	C₂²×#235	—	3	1	no	—
68	C₂²×#235	—	6	1	no	—
69	C₂²×#235	D₃	1	1	yes	characteristic, direct product factor
70	C₂³×D₁₂	—	3	1	no	—
71	C₂³×C₄×D₃	—	3	2	no	—
72	C₂³×C₄×D₃	—	3	2	no	—
73	C₂³×C₄×D₃	D₃	1	1	yes	characteristic, complemented
74	C₂³×Dic₆	—	3	1	no	—
75	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
76	C₂³×C₃⋊D₃	C₂³	1	2	yes	—
77	C₂³×C₃×D₃	—	2	8	no	—
78	C₂³×C₃×D₃	C₂³	1	2	yes	—
79	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
80	C₂³×C₃×D₃	C₂³	1	12	yes	—
81	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
82	C₂²×D₃²	—	2	16	no	—
83	C₂²×D₃²	C₂³	1	24	yes	—
84	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
85	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃²×C₄	C₂³	1	12	yes	complemented
87	C₂×#638	C₂³	1	24	yes	complemented
88	C₂²×C₃⋊Dic₃	C₂³	1	2	yes	—
89	#3828	C₂³	1	64	yes	complemented
90	C₂×C₄⋊(C₃⋊D₃)	C₂³	1	12	yes	complemented
91	C₂×C₄×C₃⋊D₃	C₂³	1	24	yes	complemented
92	C₂×#634	C₂³	1	12	yes	complemented
93	C₂×C₃×#67	C₂³	1	24	yes	complemented
94	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
95	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₃×Dic₃	C₂³	1	12	yes	complemented
98	C₃×#235	C₂³	1	64	yes	complemented
99	C₂×C₃×D₁₂	C₂³	1	12	yes	complemented
100	C₂×C₃×C₄×D₃	C₂³	1	12	yes	—
101	C₂×C₃×C₄×D₃	C₂³	1	12	yes	—
102	C₂×C₃×C₄×D₃	C₂³	1	64	yes	complemented
103	C₂×C₃×C₄×D₃	C₂³	1	12	yes	complemented
104	C₂×C₃×C₄×D₃	C₂³	1	12	yes	complemented
105	C₂×C₃×C₄×D₃	C₂³	1	24	yes	complemented
106	C₂×C₃×Dic₆	C₂³	1	12	yes	complemented
107	D₃×#67	C₂³	1	128	yes	complemented
108	C₂×#627	C₂³	1	24	yes	complemented
109	C₂×#626	C₂³	1	24	yes	complemented
110	C₂×#626	C₂³	1	24	yes	complemented
111	C₂×#625	C₂³	1	24	yes	complemented
112	C₂×#624	C₂³	1	24	yes	complemented
113	#3804	C₂³	1	128	yes	complemented
114	C₂×D₃×Dic₃	C₂³	1	24	yes	—
115	C₂×D₃×Dic₃	C₂³	1	24	yes	complemented
116	D₃×D₁₂	C₂³	1	64	yes	complemented
117	C₄×D₃²	C₂³	1	128	yes	complemented
118	#3799	C₂³	1	64	yes	complemented
119	#3798	C₂³	1	128	yes	complemented
120	#3795	C₂³	1	64	yes	complemented
121	D₃×Dic₆	C₂³	1	64	yes	complemented
122	C₂³×#41	—	9	1	no	Sylow
123	C₂⁵×C₃	—	3	1	no	—
124	C₂⁴×D₃	—	3	2	no	—
125	C₂⁴×D₃	—	3	2	no	—
126	C₂⁴×D₃	C₂×D₃	1	1	yes	characteristic
127	C₂×C₃×#41	—	3	24	no	—
128	C₂²×C₃×Q₈	—	3	1	no	—
129	C₂²×C₃×D₄	—	3	2	no	—
130	C₂²×C₃×D₄	—	3	1	no	—
131	C₂³×C₃×C₄	—	2	1	no	—
132	C₂³×C₃×C₄	—	3	1	no	—
133	C₂³×C₃×C₄	—	3	1	no	—
134	C₂³×C₃×C₄	—	3	1	no	—
135	C₂³×C₃×C₄	—	3	2	no	—
136	C₂³×C₃×C₄	—	3	1	no	—
137	C₂³×C₃×C₄	—	3	1	no	—
138	C₂³×C₃×C₄	—	3	24	no	—
139	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
140	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
141	C₂²×#67	—	3	2	no	—
142	C₂²×#67	—	3	2	no	—
143	C₂²×#67	—	3	2	no	—
144	C₂²×#67	—	3	2	no	—
145	C₂²×#67	—	3	48	no	—
146	C₂²×#67	—	3	2	no	—
147	C₂²×#67	—	3	2	no	—
148	C₂²×#67	—	6	2	no	—
149	C₂²×#67	C₂×D₃	1	2	yes	complemented
150	C₂³×Dic₃	—	3	2	no	—
151	C₂³×Dic₃	—	3	2	no	—
152	C₂³×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
153	D₃×#41	—	3	256	no	—
154	C₂×#239	—	3	24	no	—
155	C₂×D₃×Q₈	—	3	24	no	—
156	C₂×#237	—	3	48	no	—
157	C₂×#237	—	3	24	no	—
158	C₂×D₃×D₄	—	3	48	no	—
159	C₂×D₃×D₄	—	3	24	no	—
160	C₂×#235	—	3	24	no	—
161	C₂×#235	—	3	24	no	—
162	C₂×#235	—	3	48	no	—
163	C₂×#235	—	3	256	no	—
164	C₂×#235	—	3	24	no	—
165	C₂×#235	—	3	48	no	—
166	C₂×#235	—	3	48	no	—
167	C₂×#235	—	3	24	no	—
168	C₂×#235	—	6	24	no	—
169	C₂×#235	C₂×D₃	1	24	yes	direct product factor
170	C₂²×D₁₂	—	3	2	no	—
171	C₂²×D₁₂	—	3	2	no	—
172	C₂²×D₁₂	—	3	1	no	—
173	C₂²×D₁₂	—	3	1	no	—
174	C₂²×D₁₂	—	3	24	no	—
175	C₂²×D₁₂	—	6	1	no	—
176	C₂²×D₁₂	C₂×D₃	1	1	yes	characteristic, complemented
177	C₂²×C₄×D₃	—	3	2	no	—
178	C₂²×C₄×D₃	—	3	2	no	—
179	C₂²×C₄×D₃	—	3	2	no	—
180	C₂²×C₄×D₃	—	3	2	no	—
181	C₂²×C₄×D₃	—	3	2	no	—
182	C₂²×C₄×D₃	—	3	2	no	—
183	C₂²×C₄×D₃	—	3	48	no	—
184	C₂²×C₄×D₃	—	3	48	no	—
185	C₂²×C₄×D₃	—	6	2	no	—
186	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
187	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
188	C₂²×C₄×D₃	C₂×D₃	1	24	yes	complemented
189	C₂²×C₄×D₃	C₂×D₃	1	2	yes	complemented
190	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic, complemented
191	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic, complemented
192	C₂²×Dic₆	—	3	1	no	—
193	C₂²×Dic₆	—	3	1	no	—
194	C₂²×Dic₆	—	3	2	no	—
195	C₂²×Dic₆	—	3	2	no	—
196	C₂²×Dic₆	—	3	24	no	—
197	C₂²×Dic₆	—	6	1	no	—
198	C₂²×Dic₆	C₂×D₃	1	1	yes	characteristic, complemented
199	C₂³×C₃²	—	2	4	no	—
200	C₂³×C₃²	C₂⁴	1	6	yes	—
201	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
202	C₂²×C₃⋊D₃	—	2	8	no	—
203	C₂²×C₃⋊D₃	C₂⁴	1	12	yes	—
204	C₂²×C₃×D₃	—	2	8	no	—
205	C₂²×C₃×D₃	—	2	4	no	—
206	C₂²×C₃×D₃	—	2	48	no	—
207	C₂²×C₃×D₃	#41	1	8	yes	complemented
208	C₂²×C₃×D₃	C₂⁴	1	12	yes	—
209	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
210	C₂²×C₃×D₃	C₂⁴	1	16	yes	—
211	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
212	C₂×D₃²	—	2	96	no	—
213	C₂×D₃²	C₂⁴	1	32	yes	—
214	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
215	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
216	C₂×C₃²×C₄	C₂⁴	1	16	yes	complemented
217	#638	C₂⁴	1	32	yes	complemented
218	C₂×C₃⋊Dic₃	C₂⁴	1	12	yes	—
219	C₄⋊(C₃⋊D₃)	C₂⁴	1	16	yes	complemented
220	C₄×C₃⋊D₃	C₂⁴	1	32	yes	complemented
221	#634	C₂⁴	1	16	yes	complemented
222	C₃×#67	C₂⁴	1	32	yes	complemented
223	C₂×C₃×Dic₃	C₂⁴	1	12	yes	—
224	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
225	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
226	C₂×C₃×Dic₃	C₂⁴	1	16	yes	complemented
227	C₃×D₁₂	C₂⁴	1	16	yes	complemented
228	C₃×C₄×D₃	C₂⁴	1	16	yes	—
229	C₃×C₄×D₃	C₂⁴	1	16	yes	—
230	C₃×C₄×D₃	C₂⁴	1	16	yes	complemented
231	C₃×C₄×D₃	C₂⁴	1	16	yes	complemented
232	C₃×C₄×D₃	C₂⁴	1	32	yes	complemented
233	C₃×Dic₆	C₂⁴	1	16	yes	complemented
234	#627	C₂⁴	1	32	yes	complemented
235	#626	C₂⁴	1	32	yes	complemented
236	#626	C₂⁴	1	32	yes	complemented
237	#625	C₂⁴	1	32	yes	complemented
238	#624	C₂⁴	1	32	yes	complemented
239	D₃×Dic₃	C₂⁴	1	32	yes	—
240	D₃×Dic₃	C₂⁴	1	32	yes	complemented
241	C₂²×#41	—	3	1	no	—
242	C₂²×#41	—	9	2	no	—
243	C₂²×#41	—	9	2	no	—
244	C₂²×#41	—	9	1	no	—
245	C₂²×#41	—	9	1	no	—
246	C₂²×#41	—	9	48	no	—
247	C₂²×#41	—	9	1	no	—
248	C₂³×Q₈	—	9	1	no	—
249	C₂³×D₄	—	9	1	no	—
250	C₂³×D₄	—	9	2	no	—
251	C₂⁴×C₄	—	3	1	no	—
252	C₂⁴×C₄	—	9	2	no	—
253	C₂⁴×C₃	—	2	1	no	—
254	C₂⁴×C₃	—	3	1	no	—
255	C₂⁴×C₃	—	3	12	no	—
256	C₂⁴×C₃	—	3	1	no	—
257	C₂⁴×C₃	—	3	2	no	—
258	C₂⁴×C₃	—	6	8	no	—
259	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
260	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
261	C₂³×D₃	—	2	8	no	—
262	C₂³×D₃	—	3	2	no	—
263	C₂³×D₃	—	3	2	no	—
264	C₂³×D₃	—	3	24	no	—
265	C₂³×D₃	—	3	24	no	—
266	C₂³×D₃	—	6	2	no	—
267	C₂³×D₃	—	6	16	no	—
268	C₂³×D₃	—	6	16	no	—
269	C₂³×D₃	C₂²×D₃	1	2	yes	—
270	C₂³×D₃	C₂²×D₃	1	1	yes	characteristic
271	C₂³×D₃	C₂²×D₃	1	12	yes	—
272	C₂³×D₃	C₂²×D₃	1	1	yes	characteristic
273	C₃×#41	—	3	64	no	—
274	C₂×C₃×Q₈	—	3	12	no	—
275	C₂×C₃×D₄	—	3	24	no	—
276	C₂×C₃×D₄	—	3	12	no	—
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	2	1	no	—
279	C₂²×C₃×C₄	—	2	12	no	—
280	C₂²×C₃×C₄	—	3	1	no	—
281	C₂²×C₃×C₄	—	3	2	no	—
282	C₂²×C₃×C₄	—	3	1	no	—
283	C₂²×C₃×C₄	—	3	12	no	—
284	C₂²×C₃×C₄	—	3	12	no	—
285	C₂²×C₃×C₄	—	3	12	no	—
286	C₂²×C₃×C₄	—	3	24	no	—
287	C₂²×C₃×C₄	—	3	12	no	—
288	C₂²×C₃×C₄	—	3	12	no	—
289	C₂²×C₃×C₄	—	3	64	no	—
290	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	complemented
295	C₂²×C₃×C₄	C₂²×D₃	1	12	yes	complemented
296	C₂×#67	—	3	24	no	—
297	C₂×#67	—	3	24	no	—
298	C₂×#67	—	3	24	no	—
299	C₂×#67	—	3	24	no	—
300	C₂×#67	—	3	128	no	—
301	C₂×#67	—	3	24	no	—
302	C₂×#67	—	3	24	no	—
303	C₂×#67	—	6	24	no	—
304	C₂×#67	C₂²×D₃	1	24	yes	complemented
305	C₂²×Dic₃	—	3	2	no	—
306	C₂²×Dic₃	—	3	2	no	—
307	C₂²×Dic₃	—	3	24	no	—
308	C₂²×Dic₃	—	3	24	no	—
309	C₂²×Dic₃	—	6	2	no	—
310	C₂²×Dic₃	C₂²×D₃	1	1	yes	characteristic
311	C₂²×Dic₃	C₂²×D₃	1	2	yes	—
312	C₂²×Dic₃	C₂²×D₃	1	1	yes	characteristic
313	C₂²×Dic₃	C₂²×D₃	1	12	yes	complemented
314	#239	—	3	64	no	—
315	D₃×Q₈	—	3	64	no	—
316	#237	—	3	128	no	—
317	#237	—	3	64	no	—
318	D₃×D₄	—	3	128	no	—
319	D₃×D₄	—	3	64	no	—
320	#235	—	3	64	no	—
321	#235	—	3	64	no	—
322	#235	—	3	128	no	—
323	#235	—	3	64	no	—
324	#235	—	3	128	no	—
325	#235	—	3	128	no	—
326	#235	—	3	64	no	—
327	#235	—	6	64	no	—
328	#235	C₂²×D₃	1	64	yes	direct product factor
329	C₂×D₁₂	—	3	24	no	—
330	C₂×D₁₂	—	3	24	no	—
331	C₂×D₁₂	—	3	12	no	—
332	C₂×D₁₂	—	3	12	no	—
333	C₂×D₁₂	—	3	64	no	—
334	C₂×D₁₂	—	6	12	no	—
335	C₂×D₁₂	C₂²×D₃	1	12	yes	complemented
336	C₂×C₄×D₃	—	3	24	no	—
337	C₂×C₄×D₃	—	3	24	no	—
338	C₂×C₄×D₃	—	3	24	no	—
339	C₂×C₄×D₃	—	3	24	no	—
340	C₂×C₄×D₃	—	3	24	no	—
341	C₂×C₄×D₃	—	3	24	no	—
342	C₂×C₄×D₃	—	3	128	no	—
343	C₂×C₄×D₃	—	3	128	no	—
344	C₂×C₄×D₃	—	6	24	no	—
345	C₂×C₄×D₃	C₂²×D₃	1	12	yes	—
346	C₂×C₄×D₃	C₂²×D₃	1	12	yes	—
347	C₂×C₄×D₃	C₂²×D₃	1	64	yes	complemented
348	C₂×C₄×D₃	C₂²×D₃	1	24	yes	complemented
349	C₂×C₄×D₃	C₂²×D₃	1	12	yes	complemented
350	C₂×C₄×D₃	C₂²×D₃	1	12	yes	complemented
351	C₂×Dic₆	—	3	12	no	—
352	C₂×Dic₆	—	3	12	no	—
353	C₂×Dic₆	—	3	24	no	—
354	C₂×Dic₆	—	3	24	no	—
355	C₂×Dic₆	—	3	64	no	—
356	C₂×Dic₆	—	6	12	no	—
357	C₂×Dic₆	C₂²×D₃	1	12	yes	complemented
358	C₂²×C₃²	—	2	12	no	—
359	C₂²×C₃²	C₂×#41	1	4	yes	complemented
360	C₂²×C₃²	C₂⁵	1	4	yes	—
361	C₂²×C₃²	C₂⁵	1	3	yes	—
362	C₂×C₃⋊D₃	—	2	24	no	—
363	C₂×C₃⋊D₃	C₂⁵	1	8	yes	—
364	C₂×C₃×D₃	—	2	24	no	—
365	C₂×C₃×D₃	—	2	12	no	—
366	C₂×C₃×D₃	—	2	32	no	—
367	C₂×C₃×D₃	C₂×#41	1	24	yes	complemented
368	C₂×C₃×D₃	C₂⁵	1	8	yes	—
369	C₂×C₃×D₃	C₂⁵	1	4	yes	—
370	C₂×C₃×D₃	C₂⁵	1	4	yes	—
371	D₃²	—	2	64	no	—
372	C₃²×C₄	C₂⁵	1	4	yes	—
373	C₃²×C₄	C₂⁵	1	4	yes	—
374	C₃⋊Dic₃	C₂⁵	1	8	yes	—
375	C₃×Dic₃	C₂⁵	1	8	yes	—
376	C₃×Dic₃	C₂⁵	1	4	yes	—
377	C₃×Dic₃	C₂⁵	1	4	yes	—
378	C₂⁵	—	3	1	no	—
379	C₂⁵	—	9	2	no	—
380	C₂×#41	—	3	24	no	—
381	C₂×#41	—	9	48	no	—
382	C₂×#41	—	9	48	no	—
383	C₂×#41	—	9	24	no	—
384	C₂×#41	—	9	24	no	—
385	C₂×#41	—	9	256	no	—
386	C₂×#41	—	9	24	no	—
387	C₂²×Q₈	—	3	1	no	—
388	C₂²×Q₈	—	9	2	no	—
389	C₂²×Q₈	—	9	24	no	—
390	C₂²×Q₈	—	9	1	no	—
391	C₂²×D₄	—	3	2	no	—
392	C₂²×D₄	—	3	1	no	—
393	C₂²×D₄	—	9	24	no	—
394	C₂²×D₄	—	9	2	no	—
395	C₂²×D₄	—	9	2	no	—
396	C₂²×D₄	—	9	48	no	—
397	C₂²×D₄	—	9	2	no	—
398	C₂²×D₄	—	9	2	no	—
399	C₂²×D₄	—	9	1	no	—
400	C₂³×C₄	—	3	1	no	—
401	C₂³×C₄	—	3	1	no	—
402	C₂³×C₄	—	3	1	no	—
403	C₂³×C₄	—	3	1	no	—
404	C₂³×C₄	—	3	1	no	—
405	C₂³×C₄	—	3	2	no	—
406	C₂³×C₄	—	3	24	no	—
407	C₂³×C₄	—	9	2	no	—
408	C₂³×C₄	—	9	48	no	—
409	C₂³×C₄	—	9	2	no	—
410	C₂³×C₄	—	9	2	no	—
411	C₂³×C₄	—	9	2	no	—
412	C₂³×C₄	D₃²	1	1	yes	characteristic, complemented
413	C₂³×C₃	—	2	4	no	—
414	C₂³×C₃	—	2	4	no	—
415	C₂³×C₃	—	2	1	no	—
416	C₂³×C₃	—	2	6	no	—
417	C₂³×C₃	—	3	8	no	—
418	C₂³×C₃	—	3	6	no	—
419	C₂³×C₃	—	3	12	no	—
420	C₂³×C₃	—	3	16	no	—
421	C₂³×C₃	—	3	6	no	—
422	C₂³×C₃	—	4	4	no	—
423	C₂³×C₃	—	6	48	no	—
424	C₂³×C₃	—	6	8	no	—
425	C₂³×C₃	—	6	4	no	—
426	C₂³×C₃	C₂³×D₃	1	6	yes	—
427	C₂³×C₃	C₂³×D₃	1	6	yes	—
428	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
429	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
430	C₂²×D₃	—	2	4	no	—
431	C₂²×D₃	—	2	8	no	—
432	C₂²×D₃	—	2	48	no	—
433	C₂²×D₃	—	3	12	no	—
434	C₂²×D₃	—	3	12	no	—
435	C₂²×D₃	—	3	32	no	—
436	C₂²×D₃	—	3	32	no	—
437	C₂²×D₃	—	6	12	no	—
438	C₂²×D₃	—	6	96	no	—
439	C₂²×D₃	—	6	8	no	—
440	C₂²×D₃	—	6	8	no	—
441	C₂²×D₃	—	6	96	no	—
442	C₂²×D₃	—	12	8	no	—
443	C₂²×D₃	#235	1	8	yes	direct product factor
444	C₂²×D₃	C₂³×D₃	1	12	yes	—
445	C₂²×D₃	C₂³×D₃	1	6	yes	—
446	C₂²×D₃	C₂³×D₃	1	16	yes	—
447	C₂²×D₃	C₂³×D₃	1	6	yes	—
448	C₃×Q₈	—	3	16	no	—
449	C₃×D₄	—	3	32	no	—
450	C₃×D₄	—	3	16	no	—
451	C₂×C₃×C₄	—	2	6	no	—
452	C₂×C₃×C₄	—	2	6	no	—
453	C₂×C₃×C₄	—	2	16	no	—
454	C₂×C₃×C₄	—	3	6	no	—
455	C₂×C₃×C₄	—	3	12	no	—
456	C₂×C₃×C₄	—	3	6	no	—
457	C₂×C₃×C₄	—	3	16	no	—
458	C₂×C₃×C₄	—	3	16	no	—
459	C₂×C₃×C₄	—	3	16	no	—
460	C₂×C₃×C₄	—	3	32	no	—
461	C₂×C₃×C₄	—	3	16	no	—
462	C₂×C₃×C₄	—	3	16	no	—
463	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
464	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
465	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
466	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
467	C₂×C₃×C₄	C₂³×D₃	1	16	yes	complemented
468	C₂×C₃×C₄	C₂³×D₃	1	16	yes	complemented
469	#67	—	3	32	no	—
470	#67	—	3	32	no	—
471	#67	—	3	32	no	—
472	#67	—	3	32	no	—
473	#67	—	3	32	no	—
474	#67	—	3	32	no	—
475	#67	—	6	32	no	—
476	#67	C₂³×D₃	1	32	yes	complemented
477	C₂×Dic₃	—	3	12	no	—
478	C₂×Dic₃	—	3	12	no	—
479	C₂×Dic₃	—	3	32	no	—
480	C₂×Dic₃	—	3	32	no	—
481	C₂×Dic₃	—	6	12	no	—
482	C₂×Dic₃	C₂³×D₃	1	6	yes	—
483	C₂×Dic₃	C₂³×D₃	1	12	yes	—
484	C₂×Dic₃	C₂³×D₃	1	6	yes	—
485	C₂×Dic₃	C₂³×D₃	1	16	yes	complemented
486	D₁₂	—	3	32	no	—
487	D₁₂	—	3	32	no	—
488	D₁₂	—	3	16	no	—
489	D₁₂	—	3	16	no	—
490	D₁₂	—	6	16	no	—
491	D₁₂	C₂³×D₃	1	16	yes	complemented
492	C₄×D₃	—	3	32	no	—
493	C₄×D₃	—	3	32	no	—
494	C₄×D₃	—	3	32	no	—
495	C₄×D₃	—	3	32	no	—
496	C₄×D₃	—	3	32	no	—
497	C₄×D₃	—	3	32	no	—
498	C₄×D₃	—	6	32	no	—
499	C₄×D₃	C₂³×D₃	1	16	yes	—
500	C₄×D₃	C₂³×D₃	1	16	yes	—
501	C₄×D₃	C₂³×D₃	1	32	yes	complemented
502	C₄×D₃	C₂³×D₃	1	16	yes	complemented
503	C₄×D₃	C₂³×D₃	1	16	yes	complemented
504	Dic₆	—	3	16	no	—
505	Dic₆	—	3	16	no	—
506	Dic₆	—	3	32	no	—
507	Dic₆	—	3	32	no	—
508	Dic₆	—	6	16	no	—
509	Dic₆	C₂³×D₃	1	16	yes	complemented
510	C₂×C₃²	—	2	4	no	—
511	C₂×C₃²	C₂²×#41	1	6	yes	complemented
512	C₂×C₃²	C₂⁶	1	1	yes	characteristic
513	C₃⋊D₃	—	2	8	no	—
514	C₃×D₃	—	2	8	no	—
515	C₃×D₃	—	2	4	no	—
516	C₃×D₃	C₂²×#41	1	8	yes	complemented
517	C₂⁴	—	3	1	no	—
518	C₂⁴	—	3	12	no	—
519	C₂⁴	—	3	1	no	—
520	C₂⁴	—	3	2	no	—
521	C₂⁴	—	6	8	no	—
522	C₂⁴	—	9	24	no	—
523	C₂⁴	—	9	2	no	—
524	C₂⁴	—	18	16	no	—
525	C₂⁴	C₂×D₃²	1	1	yes	characteristic
526	#41	—	3	64	no	—
527	#41	—	9	128	no	—
528	#41	—	9	128	no	—
529	#41	—	9	64	no	—
530	#41	—	9	64	no	—
531	#41	—	9	64	no	—
532	C₂×Q₈	—	3	12	no	—
533	C₂×Q₈	—	9	24	no	—
534	C₂×Q₈	—	9	64	no	—
535	C₂×Q₈	—	9	12	no	—
536	C₂×D₄	—	3	24	no	—
537	C₂×D₄	—	3	12	no	—
538	C₂×D₄	—	9	64	no	—
539	C₂×D₄	—	9	24	no	—
540	C₂×D₄	—	9	24	no	—
541	C₂×D₄	—	9	128	no	—
542	C₂×D₄	—	9	24	no	—
543	C₂×D₄	—	9	24	no	—
544	C₂×D₄	—	9	12	no	—
545	C₂²×C₄	—	3	1	no	—
546	C₂²×C₄	—	3	1	no	—
547	C₂²×C₄	—	3	12	no	—
548	C₂²×C₄	—	3	2	no	—
549	C₂²×C₄	—	3	12	no	—
550	C₂²×C₄	—	3	12	no	—
551	C₂²×C₄	—	3	12	no	—
552	C₂²×C₄	—	3	12	no	—
553	C₂²×C₄	—	3	24	no	—
554	C₂²×C₄	—	3	64	no	—
555	C₂²×C₄	—	9	24	no	—
556	C₂²×C₄	—	9	128	no	—
557	C₂²×C₄	—	9	24	no	—
558	C₂²×C₄	—	9	24	no	—
559	C₂²×C₄	—	9	2	no	—
560	C₂²×C₄	—	9	24	no	—
561	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₃²	1	12	yes	complemented
564	C₂²×C₃	—	2	12	no	—
565	C₂²×C₃	—	2	12	no	—
566	C₂²×C₃	—	2	4	no	—
567	C₂²×C₃	—	2	3	no	—
568	C₂²×C₃	—	2	4	no	—
569	C₂²×C₃	—	3	24	no	—
570	C₂²×C₃	—	3	4	no	—
571	C₂²×C₃	—	3	8	no	—
572	C₂²×C₃	—	3	4	no	—
573	C₂²×C₃	—	4	12	no	—
574	C₂²×C₃	—	6	32	no	—
575	C₂²×C₃	—	6	24	no	—
576	C₂²×C₃	—	6	12	no	—
577	C₂²×C₃	C₂×#235	1	4	yes	complemented
578	C₂²×C₃	D₃×#41	1	4	yes	complemented
579	C₂²×C₃	C₂⁴×D₃	1	4	yes	—
580	C₂²×C₃	C₂⁴×D₃	1	4	yes	—
581	C₂²×C₃	C₂⁴×D₃	1	3	yes	—
582	C₂²×C₃	C₂⁴×D₃	1	3	yes	—
583	C₂×D₃	—	2	12	no	—
584	C₂×D₃	—	2	24	no	—
585	C₂×D₃	—	2	32	no	—
586	C₂×D₃	—	3	8	no	—
587	C₂×D₃	—	3	8	no	—
588	C₂×D₃	—	6	8	no	—
589	C₂×D₃	—	6	64	no	—
590	C₂×D₃	—	6	24	no	—
591	C₂×D₃	—	6	24	no	—
592	C₂×D₃	—	6	64	no	—
593	C₂×D₃	—	12	24	no	—
594	C₂×D₃	C₂×#235	1	24	yes	direct product factor
595	C₂×D₃	C₂⁴×D₃	1	8	yes	—
596	C₂×D₃	C₂⁴×D₃	1	4	yes	—
597	C₂×D₃	C₂⁴×D₃	1	4	yes	—
598	C₃×C₄	—	2	4	no	—
599	C₃×C₄	—	2	4	no	—
600	C₃×C₄	—	3	4	no	—
601	C₃×C₄	—	3	8	no	—
602	C₃×C₄	—	3	4	no	—
603	C₃×C₄	C₂⁴×D₃	1	4	yes	—
604	C₃×C₄	C₂⁴×D₃	1	4	yes	—
605	C₃×C₄	C₂⁴×D₃	1	4	yes	—
606	C₃×C₄	C₂⁴×D₃	1	4	yes	—
607	Dic₃	—	3	8	no	—
608	Dic₃	—	3	8	no	—
609	Dic₃	—	6	8	no	—
610	Dic₃	C₂⁴×D₃	1	4	yes	—
611	Dic₃	C₂⁴×D₃	1	8	yes	—
612	Dic₃	C₂⁴×D₃	1	4	yes	—
613	C₃²	C₂³×#41	1	1	yes	characteristic, complemented, Sylow
614	C₂³	—	2	4	no	—
615	C₂³	—	3	8	no	—
616	C₂³	—	3	6	no	—
617	C₂³	—	3	16	no	—
618	C₂³	—	3	6	no	—
619	C₂³	—	3	12	no	—
620	C₂³	—	6	48	no	—
621	C₂³	—	6	4	no	—
622	C₂³	—	6	8	no	—
623	C₂³	—	9	32	no	—
624	C₂³	—	9	12	no	—
625	C₂³	—	18	96	no	—
626	C₂³	—	18	8	no	—
627	C₂³	C₂²×D₃²	1	6	yes	—
628	C₂³	C₂²×D₃²	1	1	yes	characteristic
629	Q₈	—	3	16	no	—
630	Q₈	—	9	32	no	—
631	Q₈	—	9	16	no	—
632	D₄	—	3	32	no	—
633	D₄	—	3	16	no	—
634	D₄	—	9	32	no	—
635	D₄	—	9	32	no	—
636	D₄	—	9	32	no	—
637	D₄	—	9	32	no	—
638	D₄	—	9	16	no	—
639	C₂×C₄	—	3	6	no	—
640	C₂×C₄	—	3	6	no	—
641	C₂×C₄	—	3	16	no	—
642	C₂×C₄	—	3	12	no	—
643	C₂×C₄	—	3	16	no	—
644	C₂×C₄	—	3	16	no	—
645	C₂×C₄	—	3	16	no	—
646	C₂×C₄	—	3	16	no	—
647	C₂×C₄	—	3	32	no	—
648	C₂×C₄	—	9	32	no	—
649	C₂×C₄	—	9	32	no	—
650	C₂×C₄	—	9	32	no	—
651	C₂×C₄	—	9	12	no	—
652	C₂×C₄	—	9	32	no	—
653	C₂×C₄	C₂²×D₃²	1	6	yes	—
654	C₂×C₄	C₂²×D₃²	1	6	yes	—
655	C₂×C₄	C₂²×D₃²	1	16	yes	complemented
656	C₂×C₃	—	2	4	no	—
657	C₂×C₃	—	2	4	no	—
658	C₂×C₃	—	2	6	no	—
659	C₂×C₃	—	2	1	no	—
660	C₂×C₃	—	3	8	no	—
661	C₂×C₃	—	4	4	no	—
662	C₂×C₃	—	6	8	no	—
663	C₂×C₃	—	6	4	no	—
664	C₂×C₃	C₂²×#235	1	6	yes	complemented
665	C₂×C₃	C₂×D₃×#41	1	6	yes	complemented
666	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
667	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
668	D₃	—	2	4	no	—
669	D₃	—	2	8	no	—
670	D₃	—	6	8	no	—
671	D₃	—	6	8	no	—
672	D₃	—	12	8	no	—
673	D₃	C₂²×#235	1	8	yes	direct product factor
674	C₂²	—	2	12	no	—
675	C₂²	—	3	24	no	—
676	C₂²	—	3	4	no	—
677	C₂²	—	3	4	no	—
678	C₂²	—	3	8	no	—
679	C₂²	—	6	32	no	—
680	C₂²	—	6	12	no	—
681	C₂²	—	6	24	no	—
682	C₂²	—	9	8	no	—
683	C₂²	—	18	64	no	—
684	C₂²	—	18	24	no	—
685	C₂²	D₃×#235	1	4	yes	direct product factor
686	C₂²	C₂³×D₃²	1	4	yes	—
687	C₂²	C₂³×D₃²	1	3	yes	—
688	C₄	—	3	4	no	—
689	C₄	—	3	4	no	—
690	C₄	—	3	8	no	—
691	C₄	—	9	8	no	—
692	C₄	C₂³×D₃²	1	4	yes	—
693	C₄	C₂³×D₃²	1	4	yes	—
694	C₃	—	2	1	no	—
695	C₃	C₂³×#235	1	1	yes	characteristic, complemented
696	C₃	C₂²×D₃×#41	1	1	yes	characteristic, complemented
697	C₂	—	2	4	no	—
698	C₂	—	3	8	no	—
699	C₂	—	6	4	no	—
700	C₂	—	6	8	no	—
701	C₂	—	18	8	no	—
702	C₂	C₂×D₃×#235	1	6	yes	direct product factor
703	C₂	C₂⁴×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂⁶
Frattini	C₂	C₂⁴×D₃²
Fitting	C₂³×C₃²×C₄	C₂²
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂³×C₄	D₃²
hypocenter	C₃²	C₂³×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#3828	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₂³×C₃×C₄×D₃	C₂	semidirect
4. C₂²×D₃×#67	C₂	semidirect
5. C₂²×#3804	C₂	semidirect
6. C₂×D₃×#235	C₂	direct (N × H)
7. C₂²×D₃×D₁₂	C₂	semidirect
8. C₂²×C₄×D₃²	C₂	semidirect
9. C₂²×#3799	C₂	semidirect
10. C₂²×#3798	C₂	semidirect
11. C₂²×#3795	C₂	semidirect
12. C₂²×D₃×Dic₆	C₂	semidirect
17. C₂³×C₃²×C₄	C₂²	semidirect
18. C₂²×#638	C₂²	semidirect
19. C₂×#3828	C₂²	semidirect
20. C₂²×C₄⋊(C₃⋊D₃)	C₂²	semidirect
21. C₂²×C₄×C₃⋊D₃	C₂²	semidirect
22. C₂²×#634	C₂²	semidirect
23. C₂²×C₃×#67	C₂²	semidirect
24. C₂³×C₃×Dic₃	C₂²	semidirect
25. C₂×C₃×#235	C₂²	semidirect
26. C₂²×C₃×D₁₂	C₂²	semidirect
29. C₂²×C₃×C₄×D₃	C₂²	semidirect
30. C₂²×C₃×C₄×D₃	C₂²	semidirect
31. C₂²×C₃×C₄×D₃	C₂²	semidirect
32. C₂²×C₃×C₄×D₃	C₂²	semidirect
33. C₂²×C₃×Dic₆	C₂²	semidirect
34. C₂×D₃×#67	C₂²	semidirect
35. C₂²×#627	C₂²	semidirect
36. C₂²×#626	C₂²	semidirect
37. C₂²×#626	C₂²	semidirect
38. C₂²×#625	C₂²	semidirect
39. C₂²×#624	C₂²	semidirect
40. C₂×#3804	C₂²	semidirect
42. C₂²×D₃×Dic₃	C₂²	semidirect
43. D₃×#235	C₂²	direct (N × H)
44. C₂×D₃×D₁₂	C₂²	semidirect
45. C₂×C₄×D₃²	C₂²	semidirect
46. C₂×#3799	C₂²	semidirect
47. C₂×#3798	C₂²	semidirect
48. C₂×#3795	C₂²	semidirect
49. C₂×D₃×Dic₆	C₂²	semidirect
69. C₂²×#235	D₃	direct (N × H)
73. C₂³×C₄×D₃	D₃	semidirect
86. C₂²×C₃²×C₄	C₂³	semidirect
87. C₂×#638	C₂³	semidirect
89. #3828	C₂³	semidirect
90. C₂×C₄⋊(C₃⋊D₃)	C₂³	semidirect
91. C₂×C₄×C₃⋊D₃	C₂³	semidirect
92. C₂×#634	C₂³	semidirect
93. C₂×C₃×#67	C₂³	semidirect
97. C₂²×C₃×Dic₃	C₂³	semidirect
98. C₃×#235	C₂³	semidirect
99. C₂×C₃×D₁₂	C₂³	semidirect
102. C₂×C₃×C₄×D₃	C₂³	semidirect
103. C₂×C₃×C₄×D₃	C₂³	semidirect
104. C₂×C₃×C₄×D₃	C₂³	semidirect
105. C₂×C₃×C₄×D₃	C₂³	semidirect
106. C₂×C₃×Dic₆	C₂³	semidirect
107. D₃×#67	C₂³	semidirect
108. C₂×#627	C₂³	semidirect
109. C₂×#626	C₂³	semidirect
110. C₂×#626	C₂³	semidirect
111. C₂×#625	C₂³	semidirect
112. C₂×#624	C₂³	semidirect
113. #3804	C₂³	semidirect
115. C₂×D₃×Dic₃	C₂³	semidirect
116. D₃×D₁₂	C₂³	semidirect
117. C₄×D₃²	C₂³	semidirect
118. #3799	C₂³	semidirect
119. #3798	C₂³	semidirect
120. #3795	C₂³	semidirect
121. D₃×Dic₆	C₂³	semidirect
139. C₂³×C₃×C₄	C₂×D₃	semidirect
140. C₂³×C₃×C₄	C₂×D₃	semidirect
149. C₂²×#67	C₂×D₃	semidirect
152. C₂³×Dic₃	C₂×D₃	semidirect
169. C₂×#235	C₂×D₃	direct (N × H)
176. C₂²×D₁₂	C₂×D₃	semidirect
188. C₂²×C₄×D₃	C₂×D₃	semidirect
189. C₂²×C₄×D₃	C₂×D₃	semidirect
190. C₂²×C₄×D₃	C₂×D₃	semidirect
191. C₂²×C₄×D₃	C₂×D₃	semidirect
198. C₂²×Dic₆	C₂×D₃	semidirect
207. C₂²×C₃×D₃	#41	semidirect
216. C₂×C₃²×C₄	C₂⁴	semidirect
217. #638	C₂⁴	semidirect
219. C₄⋊(C₃⋊D₃)	C₂⁴	semidirect
220. C₄×C₃⋊D₃	C₂⁴	semidirect
221. #634	C₂⁴	semidirect
222. C₃×#67	C₂⁴	semidirect
226. C₂×C₃×Dic₃	C₂⁴	semidirect
227. C₃×D₁₂	C₂⁴	semidirect
230. C₃×C₄×D₃	C₂⁴	semidirect
231. C₃×C₄×D₃	C₂⁴	semidirect
232. C₃×C₄×D₃	C₂⁴	semidirect
233. C₃×Dic₆	C₂⁴	semidirect
234. #627	C₂⁴	semidirect
235. #626	C₂⁴	semidirect
236. #626	C₂⁴	semidirect
237. #625	C₂⁴	semidirect
238. #624	C₂⁴	semidirect
240. D₃×Dic₃	C₂⁴	semidirect
294. C₂²×C₃×C₄	C₂²×D₃	semidirect
295. C₂²×C₃×C₄	C₂²×D₃	semidirect
304. C₂×#67	C₂²×D₃	semidirect
313. C₂²×Dic₃	C₂²×D₃	semidirect
328. #235	C₂²×D₃	direct (N × H)
335. C₂×D₁₂	C₂²×D₃	semidirect
347. C₂×C₄×D₃	C₂²×D₃	semidirect
348. C₂×C₄×D₃	C₂²×D₃	semidirect
349. C₂×C₄×D₃	C₂²×D₃	semidirect
350. C₂×C₄×D₃	C₂²×D₃	semidirect
357. C₂×Dic₆	C₂²×D₃	semidirect
359. C₂²×C₃²	C₂×#41	semidirect
367. C₂×C₃×D₃	C₂×#41	semidirect
412. C₂³×C₄	D₃²	semidirect
443. C₂²×D₃	#235	direct (N × H)
467. C₂×C₃×C₄	C₂³×D₃	semidirect
468. C₂×C₃×C₄	C₂³×D₃	semidirect
476. #67	C₂³×D₃	semidirect
485. C₂×Dic₃	C₂³×D₃	semidirect
491. D₁₂	C₂³×D₃	semidirect
501. C₄×D₃	C₂³×D₃	semidirect
502. C₄×D₃	C₂³×D₃	semidirect
503. C₄×D₃	C₂³×D₃	semidirect
509. Dic₆	C₂³×D₃	semidirect
511. C₂×C₃²	C₂²×#41	semidirect
516. C₃×D₃	C₂²×#41	semidirect
563. C₂²×C₄	C₂×D₃²	semidirect
577. C₂²×C₃	C₂×#235	semidirect
578. C₂²×C₃	D₃×#41	semidirect
594. C₂×D₃	C₂×#235	direct (N × H)
613. C₃²	C₂³×#41	semidirect
655. C₂×C₄	C₂²×D₃²	semidirect
664. C₂×C₃	C₂²×#235	semidirect
665. C₂×C₃	C₂×D₃×#41	semidirect
673. D₃	C₂²×#235	direct (N × H)
685. C₂²	D₃×#235	direct (N × H)
695. C₃	C₂³×#235	semidirect
696. C₃	C₂²×D₃×#41	semidirect
702. C₂	C₂×D₃×#235	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#3828	2
C₂²×C₃×#235	2
C₂³×C₃×C₄×D₃	2
C₂²×D₃×#67	2
C₂²×#3804	2
C₂×D₃×#235	2
C₂²×D₃×D₁₂	2
C₂²×C₄×D₃²	2
C₂²×#3799	2
C₂²×#3798	2
C₂²×#3795	2
C₂²×D₃×Dic₆	2
C₂²×D₃×#41	3
C₂³×#235	3

Subgroups — C22×D3×#235 #11919198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×#235 #11919198