Subgroups — C₃×#87275 #11904612

Order 1152.

3761 conjugacy classes of subgroups.

The subgroup lattice has 715 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1009	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5834	C₂	1	2	yes	maximal, complemented
4	C₃×#5833	C₂	1	3	yes	maximal, complemented
5	C₃×#5830	C₂	1	3	yes	maximal, complemented
6	C₃×#5829	C₂	1	6	yes	maximal, complemented
7	C₃×#5827	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5817	C₂	1	2	yes	maximal, complemented
9	C₃×D₄×#67	C₂	1	6	yes	maximal, complemented
10	C₃×#5791	C₂	1	3	yes	maximal, complemented
11	C₂×C₃×#930	C₂	1	3	yes	maximal, complemented
12	C₃×#3488	—	3	1	no	maximal
13	#87275	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	—	2	8	no	—
15	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
16	C₂×C₃²×#41	C₂²	1	3	yes	complemented
17	C₂×C₃²×#41	C₂²	1	3	yes	complemented
18	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃²×D₄	C₂²	1	3	yes	complemented
21	C₂³×C₃²×C₄	C₂²	1	3	yes	complemented
22	C₂²×C₃×#67	C₂²	1	6	yes	complemented
23	C₃×#1009	—	2	8	no	—
24	C₂×C₃×#239	C₂²	1	2	yes	complemented
25	C₂×C₃×D₃×D₄	C₂²	1	6	yes	complemented
26	C₂×C₃×#235	C₂²	1	3	yes	complemented
27	C₂²×C₃×D₁₂	C₂²	1	3	yes	complemented
28	C₃×#953	C₂²	1	6	yes	complemented
29	C₃×#947	C₂²	1	6	yes	complemented
30	C₃×#946	C₂²	1	6	yes	complemented
31	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
32	C₃×#940	C₂²	1	6	yes	complemented
33	C₃×#939	C₂²	1	12	yes	complemented
34	C₃×#938	C₂²	1	6	yes	complemented
35	C₃×#937	C₂²	1	12	yes	complemented
36	C₃×D₄×Dic₃	C₂²	1	6	yes	complemented
37	C₃×#930	C₂²	1	3	yes	complemented
38	C₃×#930	C₂²	1	6	yes	complemented
39	C₃×#930	C₂²	1	6	yes	complemented
40	C₃×#930	C₂²	1	6	yes	complemented
41	C₃×#930	C₂²	1	3	yes	complemented
42	C₃×#929	C₂²	1	6	yes	complemented
43	C₃×C₄×#67	C₂²	1	6	yes	complemented
44	C₃×C₄×#67	C₂²	1	6	yes	complemented
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	6	yes	complemented
46	C₃×#926	C₂²	1	3	yes	complemented
47	C₂×C₃×C₄⋊Dic₃	C₂²	1	3	yes	complemented
48	C₃×#924	C₂²	1	1	yes	characteristic, complemented
49	C₃×#924	C₂²	1	3	yes	complemented
50	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
51	C₂²×C₃×#41	—	2	1	no	—
52	C₂²×C₃×#41	D₃	1	1	yes	characteristic, complemented
53	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#1009	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#550	—	3	2	no	—
56	C₃×#548	—	3	2	no	—
57	C₃×#546	—	3	6	no	—
58	C₃×D₄²	—	3	6	no	—
59	C₃×#537	—	3	3	no	—
60	C₃×#535	—	3	3	no	—
61	C₃×#525	—	3	3	no	—
62	C₂×C₃×#121	—	3	3	no	—
63	C₃×#520	—	3	1	no	—
64	#5834	C₂×C₃	1	2	yes	complemented
65	#5833	C₂×C₃	1	3	yes	complemented
66	#5830	C₂×C₃	1	3	yes	complemented
67	#5829	C₂×C₃	1	6	yes	complemented
68	#5827	C₂×C₃	1	1	yes	characteristic, complemented
69	#5817	C₂×C₃	1	2	yes	complemented
70	D₄×#67	C₂×C₃	1	6	yes	complemented
71	#5791	C₂×C₃	1	3	yes	complemented
72	C₂×#930	C₂×C₃	1	3	yes	complemented
73	C₂⁴×C₃²	C₂³	1	3	yes	—
74	C₂³×C₃×D₃	C₂³	1	6	yes	—
75	C₃²×#41	—	2	4	no	—
76	C₃²×#41	—	2	12	no	—
77	C₃²×#41	—	2	12	no	—
78	C₃²×#41	D₄	1	8	yes	complemented
79	C₂×C₃²×Q₈	—	2	4	no	—
80	C₂×C₃²×Q₈	C₂³	1	3	yes	—
81	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃²×D₄	—	2	12	no	—
83	C₂×C₃²×D₄	C₂³	1	6	yes	—
84	C₂×C₃²×D₄	C₂³	1	3	yes	—
85	C₂×C₃²×D₄	C₂³	1	3	yes	—
86	C₂²×C₃²×C₄	—	2	12	no	—
87	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃²×C₄	C₂³	1	3	yes	—
89	C₂²×C₃²×C₄	C₂³	1	3	yes	—
90	C₂²×C₃²×C₄	C₂³	1	3	yes	—
91	C₂²×C₃²×C₄	C₂³	1	3	yes	—
92	C₂²×C₃²×C₄	C₂³	1	3	yes	—
93	C₂×C₃×#67	—	4	12	no	—
94	C₂×C₃×#67	C₂³	1	6	yes	—
95	C₂×C₃×#67	C₂³	1	6	yes	—
96	C₂×C₃×#67	C₂³	1	6	yes	—
97	C₂×C₃×#67	C₂³	1	12	yes	—
98	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
99	C₃×#239	—	2	8	no	—
100	C₃×D₃×D₄	—	2	24	no	—
101	C₃×#235	—	2	12	no	—
102	C₂×C₃×D₁₂	—	2	12	no	—
103	C₂×C₃×D₁₂	C₂³	1	3	yes	—
104	C₂×C₃×D₁₂	C₂³	1	6	yes	—
105	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
106	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
107	C₃×#217	C₂³	1	2	yes	—
108	C₃×#217	C₂³	1	6	yes	—
109	C₃×#217	C₂³	1	6	yes	—
110	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂³	1	12	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
113	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
114	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
115	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
116	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
117	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
118	C₃×C₄×Dic₃	C₂³	1	6	yes	—
119	#3488	—	3	1	no	Sylow
120	C₃×H(5,𝔽₂)	—	6	8	no	—
121	C₂×C₃×#41	—	2	16	no	—
122	C₂×C₃×#41	—	2	8	no	—
123	C₂×C₃×#41	—	2	8	no	—
124	C₂×C₃×#41	—	2	1	no	—
125	C₂×C₃×#41	—	2	3	no	—
126	C₂×C₃×#41	—	2	3	no	—
127	C₂×C₃×#41	—	2	1	no	—
128	C₂×C₃×#41	—	3	2	no	—
129	C₂×C₃×#41	—	3	3	no	—
130	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
131	C₂×C₃×#41	C₂×D₃	1	3	yes	complemented
132	C₂×C₃×#41	C₂×D₃	1	3	yes	complemented
133	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
134	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×#41	C₂²×C₃	1	3	yes	complemented
136	C₂×C₃×#41	C₂²×C₃	1	3	yes	complemented
137	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂²×C₃×Q₈	—	2	1	no	—
139	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
140	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂²×C₃×D₄	—	2	3	no	—
142	C₂²×C₃×D₄	—	3	6	no	—
143	C₂²×C₃×D₄	—	3	6	no	—
144	C₂²×C₃×D₄	—	3	3	no	—
145	C₂²×C₃×D₄	C₂×D₃	1	3	yes	complemented
146	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	complemented
147	C₂³×C₃×C₄	—	2	3	no	—
148	C₂³×C₃×C₄	C₂×D₃	1	3	yes	complemented
149	C₂³×C₃×C₄	C₂²×C₃	1	3	yes	complemented
150	C₂²×#67	C₂²×C₃	1	6	yes	complemented
151	#1009	—	2	8	no	—
152	C₂×#239	C₂²×C₃	1	2	yes	complemented
153	C₂×D₃×D₄	C₂²×C₃	1	6	yes	complemented
154	C₂×#235	C₂²×C₃	1	3	yes	complemented
155	C₂²×D₁₂	C₂²×C₃	1	3	yes	complemented
156	C₃×#127	—	3	6	no	—
157	C₃×#124	—	3	6	no	—
158	C₃×#123	—	3	6	no	—
159	C₃×C₂²⋊Q₈	—	3	6	no	—
160	C₃×C₂²⋊Q₈	—	3	1	no	—
161	C₃×C₂²⋊Q₈	—	3	3	no	—
162	C₃×#121	—	3	6	no	—
163	C₃×#121	—	3	12	no	—
164	C₃×#121	—	3	3	no	—
165	C₃×#121	—	3	6	no	—
166	C₃×#121	—	3	6	no	—
167	C₃×#121	—	3	6	no	—
168	C₃×#121	—	3	3	no	—
169	C₃×#120	—	3	6	no	—
170	C₃×#120	—	3	12	no	—
171	C₃×C₄×Q₈	—	3	2	no	—
172	C₃×C₄×D₄	—	3	6	no	—
173	C₃×C₄×D₄	—	3	6	no	—
174	C₃×C₄×D₄	—	3	6	no	—
175	C₃×#117	—	3	3	no	—
176	C₂×C₃×C₄⋊C₄	—	3	3	no	—
177	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
178	#953	C₂²×C₃	1	6	yes	complemented
179	#947	C₂²×C₃	1	6	yes	complemented
180	#946	C₂²×C₃	1	6	yes	complemented
181	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
182	#940	C₂²×C₃	1	6	yes	complemented
183	#939	C₂²×C₃	1	12	yes	complemented
184	#938	C₂²×C₃	1	6	yes	complemented
185	#937	C₂²×C₃	1	12	yes	complemented
186	D₄×Dic₃	C₂²×C₃	1	6	yes	complemented
187	#930	C₂²×C₃	1	3	yes	complemented
188	#930	C₂²×C₃	1	6	yes	complemented
189	#930	C₂²×C₃	1	6	yes	complemented
190	#930	C₂²×C₃	1	6	yes	complemented
191	#930	C₂²×C₃	1	3	yes	complemented
192	#929	C₂²×C₃	1	6	yes	complemented
193	C₄×#67	C₂²×C₃	1	6	yes	complemented
194	C₄×#67	C₂²×C₃	1	6	yes	complemented
195	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	6	yes	complemented
196	#926	C₂²×C₃	1	3	yes	complemented
197	C₂×C₄⋊Dic₃	C₂²×C₃	1	3	yes	complemented
198	#924	C₂²×C₃	1	1	yes	characteristic, complemented
199	#924	C₂²×C₃	1	3	yes	complemented
200	C₂³×C₃²	—	2	6	no	—
201	C₂³×C₃²	—	2	6	no	—
202	C₂³×C₃²	—	4	3	no	—
203	C₂³×C₃²	C₂⁴	1	3	yes	—
204	C₂³×C₃²	C₂⁴	1	3	yes	—
205	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
206	C₂²×C₃×D₃	—	2	12	no	—
207	C₂²×C₃×D₃	—	4	6	no	—
208	C₂²×C₃×D₃	—	4	6	no	—
209	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
210	C₃²×Q₈	—	2	6	no	—
211	C₃²×Q₈	C₂×D₄	1	4	yes	complemented
212	C₃²×D₄	—	2	12	no	—
213	C₃²×D₄	—	2	6	no	—
214	C₃²×D₄	C₂×D₄	1	12	yes	complemented
215	C₂×C₃²×C₄	—	2	6	no	—
216	C₂×C₃²×C₄	—	2	2	no	—
217	C₂×C₃²×C₄	—	2	6	no	—
218	C₂×C₃²×C₄	—	2	6	no	—
219	C₂×C₃²×C₄	—	2	6	no	—
220	C₂×C₃²×C₄	C₂×D₄	1	12	yes	complemented
221	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
222	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
223	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
224	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
225	C₃×#67	—	2	12	no	—
226	C₃×#67	—	2	12	no	—
227	C₃×#67	—	4	12	no	—
228	C₃×#67	—	4	6	no	—
229	C₂×C₃×Dic₃	—	4	6	no	—
230	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
231	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
232	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
233	C₃×D₁₂	—	2	6	no	—
234	C₃×D₁₂	—	2	12	no	—
235	C₃×C₄×D₃	—	2	12	no	—
236	C₃×Dic₆	—	2	2	no	—
237	C₂×H(5,𝔽₂)	—	3	1	no	—
238	C₂²×#41	C₃×D₃	1	1	yes	characteristic, complemented
239	#550	—	3	2	no	—
240	#548	—	3	2	no	—
241	#546	—	3	6	no	—
242	D₄²	—	3	6	no	—
243	#537	—	3	3	no	—
244	#535	—	3	3	no	—
245	#525	—	3	3	no	—
246	C₂×#121	—	3	3	no	—
247	#520	—	3	1	no	—
248	C₂⁴×C₃	—	2	3	no	—
249	C₂⁴×C₃	—	3	6	no	—
250	C₂⁴×C₃	C₂²×D₃	1	3	yes	—
251	C₂⁴×C₃	C₂³×C₃	1	3	yes	—
252	C₂³×D₃	C₂³×C₃	1	6	yes	—
253	C₃×#41	—	2	8	no	—
254	C₃×#41	—	2	24	no	—
255	C₃×#41	—	2	24	no	—
256	C₃×#41	—	2	4	no	—
257	C₃×#41	—	2	4	no	—
258	C₃×#41	—	2	12	no	—
259	C₃×#41	—	2	12	no	—
260	C₃×#41	—	2	12	no	—
261	C₃×#41	—	2	12	no	—
262	C₃×#41	—	2	8	no	—
263	C₃×#41	—	6	8	no	—
264	C₃×#41	—	6	12	no	—
265	C₃×#41	#67	1	8	yes	complemented
266	C₃×#41	C₃×D₄	1	8	yes	complemented
267	C₂×C₃×Q₈	—	2	8	no	—
268	C₂×C₃×Q₈	—	2	4	no	—
269	C₂×C₃×Q₈	—	2	4	no	—
270	C₂×C₃×Q₈	—	2	3	no	—
271	C₂×C₃×Q₈	—	2	1	no	—
272	C₂×C₃×Q₈	—	3	1	no	—
273	C₂×C₃×Q₈	C₂²×D₃	1	3	yes	—
274	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
275	C₂×C₃×Q₈	C₂³×C₃	1	3	yes	—
276	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₃×D₄	—	2	24	no	—
278	C₂×C₃×D₄	—	2	12	no	—
279	C₂×C₃×D₄	—	2	12	no	—
280	C₂×C₃×D₄	—	2	6	no	—
281	C₂×C₃×D₄	—	2	3	no	—
282	C₂×C₃×D₄	—	2	3	no	—
283	C₂×C₃×D₄	—	3	6	no	—
284	C₂×C₃×D₄	—	3	6	no	—
285	C₂×C₃×D₄	—	3	6	no	—
286	C₂×C₃×D₄	—	3	12	no	—
287	C₂×C₃×D₄	—	3	3	no	—
288	C₂×C₃×D₄	—	3	6	no	—
289	C₂×C₃×D₄	—	6	24	no	—
290	C₂×C₃×D₄	—	6	12	no	—
291	C₂×C₃×D₄	—	12	12	no	—
292	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
293	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
294	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
295	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
296	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
297	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
298	C₂²×C₃×C₄	—	2	24	no	—
299	C₂²×C₃×C₄	—	2	12	no	—
300	C₂²×C₃×C₄	—	2	12	no	—
301	C₂²×C₃×C₄	—	2	1	no	—
302	C₂²×C₃×C₄	—	2	3	no	—
303	C₂²×C₃×C₄	—	2	3	no	—
304	C₂²×C₃×C₄	—	2	3	no	—
305	C₂²×C₃×C₄	—	2	3	no	—
306	C₂²×C₃×C₄	—	2	3	no	—
307	C₂²×C₃×C₄	—	3	6	no	—
308	C₂²×C₃×C₄	—	3	6	no	—
309	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
310	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
311	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
312	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
314	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
315	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
317	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
318	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
319	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
320	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
321	C₂×#67	—	4	12	no	—
322	C₂×#67	C₂³×C₃	1	6	yes	—
323	C₂×#67	C₂³×C₃	1	6	yes	—
324	C₂×#67	C₂³×C₃	1	6	yes	—
325	C₂×#67	C₂³×C₃	1	12	yes	—
326	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
327	#239	—	2	8	no	—
328	D₃×D₄	—	2	24	no	—
329	#235	—	2	12	no	—
330	C₂×D₁₂	—	2	12	no	—
331	C₂×D₁₂	C₂³×C₃	1	3	yes	—
332	C₂×D₁₂	C₂³×C₃	1	6	yes	—
333	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
334	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
335	C₃×C₄⋊C₄	—	3	2	no	—
336	C₃×C₄⋊C₄	—	3	6	no	—
337	C₃×C₄⋊C₄	—	3	3	no	—
338	C₃×C₄⋊C₄	—	3	6	no	—
339	C₃×C₄⋊C₄	—	3	1	no	—
340	C₃×C₂²⋊C₄	—	3	6	no	—
341	C₃×C₂²⋊C₄	—	3	2	no	—
342	C₃×C₂²⋊C₄	—	3	6	no	—
343	C₃×C₂²⋊C₄	—	3	6	no	—
344	C₃×C₂²⋊C₄	—	3	12	no	—
345	C₃×C₂²⋊C₄	—	3	6	no	—
346	C₃×C₄²	—	3	6	no	—
347	#217	C₂³×C₃	1	2	yes	—
348	#217	C₂³×C₃	1	6	yes	—
349	#217	C₂³×C₃	1	6	yes	—
350	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
351	(C₂×D₃)⋊C₄	C₂³×C₃	1	12	yes	—
352	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
353	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
354	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
355	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
356	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
357	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
358	C₄×Dic₃	C₂³×C₃	1	6	yes	—
359	C₂²×C₃²	—	2	1	no	—
360	C₂²×C₃²	—	2	1	no	—
361	C₂²×C₃²	—	2	3	no	—
362	C₂²×C₃²	—	2	3	no	—
363	C₂²×C₃²	—	2	3	no	—
364	C₂²×C₃²	—	2	3	no	—
365	C₂²×C₃²	—	2	3	no	—
366	C₂²×C₃²	—	4	12	no	—
367	C₂²×C₃²	C₂²×D₄	1	6	yes	—
368	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	complemented
369	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
370	C₂×C₃×D₃	—	2	6	no	—
371	C₂×C₃×D₃	—	2	6	no	—
372	C₂×C₃×D₃	—	2	6	no	—
373	C₂×C₃×D₃	—	8	12	no	—
374	C₃²×C₄	—	2	1	no	—
375	C₃²×C₄	—	2	3	no	—
376	C₃²×C₄	C₂²×D₄	1	2	yes	—
377	C₃²×C₄	C₂²×D₄	1	6	yes	—
378	C₃×Dic₃	—	2	2	no	—
379	C₃×Dic₃	—	2	6	no	—
380	C₃×Dic₃	—	2	2	no	—
381	H(5,𝔽₂)	—	6	8	no	—
382	C₂×#41	—	2	8	no	—
383	C₂×#41	—	3	2	no	—
384	C₂×#41	—	3	3	no	—
385	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
386	C₂×#41	C₂×C₃×D₃	1	3	yes	complemented
387	C₂×#41	C₂×C₃×D₃	1	3	yes	complemented
388	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
389	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	3	6	no	—
391	C₂²×D₄	—	3	6	no	—
392	C₂²×D₄	—	3	3	no	—
393	C₂²×D₄	C₂×C₃×D₃	1	3	yes	complemented
394	C₂³×C₄	C₂×C₃×D₃	1	3	yes	complemented
395	#127	—	3	6	no	—
396	#124	—	3	6	no	—
397	#123	—	3	6	no	—
398	C₂²⋊Q₈	—	3	6	no	—
399	C₂²⋊Q₈	—	3	1	no	—
400	C₂²⋊Q₈	—	3	3	no	—
401	#121	—	3	12	no	—
402	#121	—	3	6	no	—
403	#121	—	3	3	no	—
404	#121	—	3	6	no	—
405	#121	—	3	6	no	—
406	#121	—	3	6	no	—
407	#121	—	3	3	no	—
408	#120	—	3	6	no	—
409	#120	—	3	12	no	—
410	C₄×Q₈	—	3	2	no	—
411	C₄×D₄	—	3	6	no	—
412	C₄×D₄	—	3	6	no	—
413	C₄×D₄	—	3	6	no	—
414	#117	—	3	3	no	—
415	C₂×C₄⋊C₄	—	3	3	no	—
416	C₂×C₂²⋊C₄	—	3	6	no	—
417	C₂³×C₃	—	2	12	no	—
418	C₂³×C₃	—	2	6	no	—
419	C₂³×C₃	—	2	6	no	—
420	C₂³×C₃	—	2	6	no	—
421	C₂³×C₃	—	2	6	no	—
422	C₂³×C₃	—	2	1	no	—
423	C₂³×C₃	—	2	3	no	—
424	C₂³×C₃	—	2	3	no	—
425	C₂³×C₃	—	3	6	no	—
426	C₂³×C₃	—	4	6	no	—
427	C₂³×C₃	—	4	3	no	—
428	C₂³×C₃	—	4	3	no	—
429	C₂³×C₃	—	4	6	no	—
430	C₂³×C₃	—	6	12	no	—
431	C₂³×C₃	—	12	6	no	—
432	C₂³×C₃	—	12	6	no	—
433	C₂³×C₃	C₂³×D₃	1	3	yes	—
434	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
435	C₂³×C₃	C₂³×D₃	1	3	yes	—
436	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
437	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
438	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
439	C₂²×D₃	—	2	12	no	—
440	C₂²×D₃	—	4	6	no	—
441	C₂²×D₃	—	4	6	no	—
442	C₂²×D₃	C₂⁴×C₃	1	6	yes	—
443	C₃×Q₈	—	2	12	no	—
444	C₃×Q₈	—	2	6	no	—
445	C₃×Q₈	—	2	6	no	—
446	C₃×Q₈	—	2	4	no	—
447	C₃×Q₈	—	6	2	no	—
448	C₃×Q₈	C₂×#67	1	4	yes	complemented
449	C₃×Q₈	C₂×C₃×D₄	1	4	yes	complemented
450	C₃×D₄	—	2	24	no	—
451	C₃×D₄	—	2	12	no	—
452	C₃×D₄	—	2	12	no	—
453	C₃×D₄	—	2	12	no	—
454	C₃×D₄	—	2	6	no	—
455	C₃×D₄	—	2	6	no	—
456	C₃×D₄	—	2	12	no	—
457	C₃×D₄	—	6	12	no	—
458	C₃×D₄	—	6	12	no	—
459	C₃×D₄	—	6	6	no	—
460	C₃×D₄	—	6	12	no	—
461	C₃×D₄	—	12	6	no	—
462	C₃×D₄	—	12	12	no	—
463	C₃×D₄	C₂×#67	1	12	yes	complemented
464	C₃×D₄	C₂×C₃×D₄	1	12	yes	complemented
465	C₂×C₃×C₄	—	2	4	no	—
466	C₂×C₃×C₄	—	2	12	no	—
467	C₂×C₃×C₄	—	2	12	no	—
468	C₂×C₃×C₄	—	2	12	no	—
469	C₂×C₃×C₄	—	2	12	no	—
470	C₂×C₃×C₄	—	2	6	no	—
471	C₂×C₃×C₄	—	2	6	no	—
472	C₂×C₃×C₄	—	2	2	no	—
473	C₂×C₃×C₄	—	2	6	no	—
474	C₂×C₃×C₄	—	2	6	no	—
475	C₂×C₃×C₄	—	2	6	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	6	no	—
478	C₂×C₃×C₄	—	2	6	no	—
479	C₂×C₃×C₄	—	2	6	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	3	no	—
483	C₂×C₃×C₄	—	2	3	no	—
484	C₂×C₃×C₄	—	2	12	no	—
485	C₂×C₃×C₄	—	3	2	no	—
486	C₂×C₃×C₄	—	3	6	no	—
487	C₂×C₃×C₄	—	3	2	no	—
488	C₂×C₃×C₄	—	6	12	no	—
489	C₂×C₃×C₄	—	12	6	no	—
490	C₂×C₃×C₄	C₂×#67	1	12	yes	complemented
491	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	complemented
492	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
494	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
495	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
497	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
498	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
499	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
500	#67	—	2	12	no	—
501	#67	—	2	12	no	—
502	#67	—	4	12	no	—
503	#67	—	4	6	no	—
504	C₂×Dic₃	—	4	6	no	—
505	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
506	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
507	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
508	D₁₂	—	2	6	no	—
509	D₁₂	—	2	12	no	—
510	C₄×D₃	—	2	12	no	—
511	Dic₆	—	2	2	no	—
512	C₂×C₃²	—	2	2	no	—
513	C₂×C₃²	—	2	6	no	—
514	C₂×C₃²	—	4	3	no	—
515	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
516	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₃²	#585	1	1	yes	characteristic
518	C₃×D₃	—	4	6	no	—
519	C₂⁴	—	3	6	no	—
520	C₂⁴	C₂²×C₃×D₃	1	3	yes	—
521	#41	—	2	4	no	—
522	#41	—	2	12	no	—
523	#41	—	2	12	no	—
524	#41	—	6	8	no	—
525	#41	—	6	12	no	—
526	#41	C₃×#67	1	8	yes	complemented
527	C₂×Q₈	—	2	4	no	—
528	C₂×Q₈	—	3	1	no	—
529	C₂×Q₈	C₂²×C₃×D₃	1	3	yes	—
530	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
531	C₂×D₄	—	2	12	no	—
532	C₂×D₄	—	3	6	no	—
533	C₂×D₄	—	3	6	no	—
534	C₂×D₄	—	3	6	no	—
535	C₂×D₄	—	3	12	no	—
536	C₂×D₄	—	3	3	no	—
537	C₂×D₄	—	3	6	no	—
538	C₂×D₄	—	6	24	no	—
539	C₂×D₄	—	6	12	no	—
540	C₂×D₄	—	12	12	no	—
541	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
542	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
543	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
544	C₂²×C₄	—	2	12	no	—
545	C₂²×C₄	—	3	6	no	—
546	C₂²×C₄	—	3	6	no	—
547	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
548	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
549	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
550	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
552	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
553	C₄⋊C₄	—	3	3	no	—
554	C₄⋊C₄	—	3	6	no	—
555	C₄⋊C₄	—	3	1	no	—
556	C₄⋊C₄	—	3	2	no	—
557	C₄⋊C₄	—	3	6	no	—
558	C₂²⋊C₄	—	3	6	no	—
559	C₂²⋊C₄	—	3	2	no	—
560	C₂²⋊C₄	—	3	6	no	—
561	C₂²⋊C₄	—	3	6	no	—
562	C₂²⋊C₄	—	3	12	no	—
563	C₂²⋊C₄	—	3	6	no	—
564	C₄²	—	3	6	no	—
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	2	2	no	—
567	C₂²×C₃	—	2	3	no	—
568	C₂²×C₃	—	2	1	no	—
569	C₂²×C₃	—	2	3	no	—
570	C₂²×C₃	—	2	1	no	—
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	3	no	—
573	C₂²×C₃	—	2	3	no	—
574	C₂²×C₃	—	2	1	no	—
575	C₂²×C₃	—	2	6	no	—
576	C₂²×C₃	—	2	3	no	—
577	C₂²×C₃	—	2	3	no	—
578	C₂²×C₃	—	2	3	no	—
579	C₂²×C₃	—	2	3	no	—
580	C₂²×C₃	—	2	3	no	—
581	C₂²×C₃	—	2	3	no	—
582	C₂²×C₃	—	2	2	no	—
583	C₂²×C₃	—	2	6	no	—
584	C₂²×C₃	—	2	1	no	—
585	C₂²×C₃	—	4	3	no	—
586	C₂²×C₃	—	4	3	no	—
587	C₂²×C₃	—	4	3	no	—
588	C₂²×C₃	—	4	3	no	—
589	C₂²×C₃	—	4	12	no	—
590	C₂²×C₃	—	4	12	no	—
591	C₂²×C₃	—	4	24	no	—
592	C₂²×C₃	—	6	6	no	—
593	C₂²×C₃	—	6	6	no	—
594	C₂²×C₃	—	6	6	no	—
595	C₂²×C₃	—	24	12	no	—
596	C₂²×C₃	#1009	1	2	yes	complemented
597	C₂²×C₃	C₂²×#67	1	6	yes	—
598	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
599	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	complemented
600	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
601	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
602	C₂×D₃	—	2	6	no	—
603	C₂×D₃	—	2	6	no	—
604	C₂×D₃	—	2	6	no	—
605	C₂×D₃	—	8	12	no	—
606	C₃×C₄	—	2	2	no	—
607	C₃×C₄	—	2	6	no	—
608	C₃×C₄	—	2	1	no	—
609	C₃×C₄	—	2	3	no	—
610	C₃×C₄	—	2	1	no	—
611	C₃×C₄	—	2	3	no	—
612	C₃×C₄	—	2	2	no	—
613	C₃×C₄	—	2	6	no	—
614	C₃×C₄	—	6	6	no	—
615	C₃×C₄	—	6	2	no	—
616	C₃×C₄	—	6	2	no	—
617	C₃×C₄	C₂²×#67	1	2	yes	—
618	C₃×C₄	C₂²×#67	1	6	yes	—
619	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
620	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
621	Dic₃	—	2	2	no	—
622	Dic₃	—	2	6	no	—
623	Dic₃	—	2	2	no	—
624	C₃²	#3488	1	1	yes	characteristic, complemented, Sylow
625	C₂³	—	2	6	no	—
626	C₂³	—	2	6	no	—
627	C₂³	—	3	6	no	—
628	C₂³	—	4	3	no	—
629	C₂³	—	6	12	no	—
630	C₂³	—	12	6	no	—
631	C₂³	—	12	6	no	—
632	C₂³	C₂³×C₃×D₃	1	3	yes	—
633	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
634	C₂³	C₂³×C₃×D₃	1	3	yes	—
635	Q₈	—	2	6	no	—
636	Q₈	—	6	2	no	—
637	Q₈	C₂×C₃×#67	1	4	yes	complemented
638	D₄	—	2	12	no	—
639	D₄	—	2	6	no	—
640	D₄	—	6	12	no	—
641	D₄	—	6	12	no	—
642	D₄	—	6	6	no	—
643	D₄	—	6	12	no	—
644	D₄	—	12	12	no	—
645	D₄	—	12	6	no	—
646	D₄	C₂×C₃×#67	1	12	yes	complemented
647	C₂×C₄	—	2	6	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	6	no	—
650	C₂×C₄	—	2	6	no	—
651	C₂×C₄	—	2	6	no	—
652	C₂×C₄	—	3	2	no	—
653	C₂×C₄	—	3	6	no	—
654	C₂×C₄	—	3	2	no	—
655	C₂×C₄	—	6	12	no	—
656	C₂×C₄	—	12	6	no	—
657	C₂×C₄	C₂×C₃×#67	1	12	yes	complemented
658	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
659	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
660	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
661	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
662	C₂×C₃	—	2	4	no	—
663	C₂×C₃	—	2	6	no	—
664	C₂×C₃	—	2	2	no	—
665	C₂×C₃	—	2	2	no	—
666	C₂×C₃	—	2	6	no	—
667	C₂×C₃	—	2	1	no	—
668	C₂×C₃	—	2	1	no	—
669	C₂×C₃	—	2	1	no	—
670	C₂×C₃	—	4	6	no	—
671	C₂×C₃	—	4	6	no	—
672	C₂×C₃	—	4	3	no	—
673	C₂×C₃	—	4	3	no	—
674	C₂×C₃	—	12	6	no	—
675	C₂×C₃	C₂×#1009	1	1	yes	characteristic
676	C₂×C₃	#5964	1	1	yes	characteristic
677	C₂×C₃	C₂³×#67	1	1	yes	characteristic
678	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
679	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂×C₃	C₃×#585	1	1	yes	characteristic
681	D₃	—	4	6	no	—
682	C₂²	—	2	3	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	3	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	3	no	—
687	C₂²	—	2	3	no	—
688	C₂²	—	2	3	no	—
689	C₂²	—	4	12	no	—
690	C₂²	—	6	6	no	—
691	C₂²	—	6	6	no	—
692	C₂²	—	6	6	no	—
693	C₂²	—	24	12	no	—
694	C₂²	C₃×#1009	1	2	yes	complemented
695	C₂²	C₂²×C₃×#67	1	6	yes	—
696	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
697	C₄	—	2	1	no	—
698	C₄	—	2	3	no	—
699	C₄	—	6	6	no	—
700	C₄	—	6	2	no	—
701	C₄	—	6	2	no	—
702	C₄	C₂²×C₃×#67	1	2	yes	—
703	C₄	C₂²×C₃×#67	1	6	yes	—
704	C₃	—	2	1	no	—
705	C₃	#87275	1	1	yes	characteristic, direct product factor
706	C₃	C₃×#3488	1	1	yes	characteristic, complemented
707	C₂	—	2	2	no	—
708	C₂	—	2	6	no	—
709	C₂	—	4	3	no	—
710	C₂	—	12	6	no	—
711	C₂	C₂×C₃×#1009	1	1	yes	characteristic
712	C₂	C₃×#5964	1	1	yes	characteristic
713	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×#41	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂²×C₃×#41	D₃
hypocenter	C₃	C₃×#3488
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×#41	C₂	semidirect
2. C₂×C₃×#1009	C₂	semidirect
3. C₃×#5834	C₂	semidirect
4. C₃×#5833	C₂	semidirect
5. C₃×#5830	C₂	semidirect
6. C₃×#5829	C₂	semidirect
7. C₃×#5827	C₂	semidirect
8. C₃×#5817	C₂	semidirect
9. C₃×D₄×#67	C₂	semidirect
10. C₃×#5791	C₂	semidirect
11. C₂×C₃×#930	C₂	semidirect
13. #87275	C₃	direct (N × H)
16. C₂×C₃²×#41	C₂²	semidirect
17. C₂×C₃²×#41	C₂²	semidirect
18. C₂×C₃²×#41	C₂²	semidirect
19. C₂²×C₃²×Q₈	C₂²	semidirect
20. C₂²×C₃²×D₄	C₂²	semidirect
21. C₂³×C₃²×C₄	C₂²	semidirect
22. C₂²×C₃×#67	C₂²	semidirect
24. C₂×C₃×#239	C₂²	semidirect
25. C₂×C₃×D₃×D₄	C₂²	semidirect
26. C₂×C₃×#235	C₂²	semidirect
27. C₂²×C₃×D₁₂	C₂²	semidirect
28. C₃×#953	C₂²	semidirect
29. C₃×#947	C₂²	semidirect
30. C₃×#946	C₂²	semidirect
31. C₃×Q₈×Dic₃	C₂²	semidirect
32. C₃×#940	C₂²	semidirect
33. C₃×#939	C₂²	semidirect
34. C₃×#938	C₂²	semidirect
35. C₃×#937	C₂²	semidirect
36. C₃×D₄×Dic₃	C₂²	semidirect
37. C₃×#930	C₂²	semidirect
38. C₃×#930	C₂²	semidirect
39. C₃×#930	C₂²	semidirect
40. C₃×#930	C₂²	semidirect
41. C₃×#930	C₂²	semidirect
42. C₃×#929	C₂²	semidirect
43. C₃×C₄×#67	C₂²	semidirect
44. C₃×C₄×#67	C₂²	semidirect
45. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
46. C₃×#926	C₂²	semidirect
47. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
48. C₃×#924	C₂²	semidirect
49. C₃×#924	C₂²	semidirect
52. C₂²×C₃×#41	D₃	semidirect
53. C₂²×C₃×#41	C₂×C₃	semidirect
54. C₂×#1009	C₂×C₃	semidirect
64. #5834	C₂×C₃	semidirect
65. #5833	C₂×C₃	semidirect
66. #5830	C₂×C₃	semidirect
67. #5829	C₂×C₃	semidirect
68. #5827	C₂×C₃	semidirect
69. #5817	C₂×C₃	semidirect
70. D₄×#67	C₂×C₃	semidirect
71. #5791	C₂×C₃	semidirect
72. C₂×#930	C₂×C₃	semidirect
78. C₃²×#41	D₄	semidirect
131. C₂×C₃×#41	C₂×D₃	semidirect
132. C₂×C₃×#41	C₂×D₃	semidirect
133. C₂×C₃×#41	C₂×D₃	semidirect
135. C₂×C₃×#41	C₂²×C₃	semidirect
136. C₂×C₃×#41	C₂²×C₃	semidirect
137. C₂×C₃×#41	C₂²×C₃	semidirect
139. C₂²×C₃×Q₈	C₂×D₃	semidirect
140. C₂²×C₃×Q₈	C₂²×C₃	semidirect
145. C₂²×C₃×D₄	C₂×D₃	semidirect
146. C₂²×C₃×D₄	C₂²×C₃	semidirect
148. C₂³×C₃×C₄	C₂×D₃	semidirect
149. C₂³×C₃×C₄	C₂²×C₃	semidirect
150. C₂²×#67	C₂²×C₃	semidirect
152. C₂×#239	C₂²×C₃	semidirect
153. C₂×D₃×D₄	C₂²×C₃	semidirect
154. C₂×#235	C₂²×C₃	semidirect
155. C₂²×D₁₂	C₂²×C₃	semidirect
178. #953	C₂²×C₃	semidirect
179. #947	C₂²×C₃	semidirect
180. #946	C₂²×C₃	semidirect
181. Q₈×Dic₃	C₂²×C₃	semidirect
182. #940	C₂²×C₃	semidirect
183. #939	C₂²×C₃	semidirect
184. #938	C₂²×C₃	semidirect
185. #937	C₂²×C₃	semidirect
186. D₄×Dic₃	C₂²×C₃	semidirect
187. #930	C₂²×C₃	semidirect
188. #930	C₂²×C₃	semidirect
189. #930	C₂²×C₃	semidirect
190. #930	C₂²×C₃	semidirect
191. #930	C₂²×C₃	semidirect
192. #929	C₂²×C₃	semidirect
193. C₄×#67	C₂²×C₃	semidirect
194. C₄×#67	C₂²×C₃	semidirect
195. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
196. #926	C₂²×C₃	semidirect
197. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
198. #924	C₂²×C₃	semidirect
199. #924	C₂²×C₃	semidirect
211. C₃²×Q₈	C₂×D₄	semidirect
214. C₃²×D₄	C₂×D₄	semidirect
220. C₂×C₃²×C₄	C₂×D₄	semidirect
238. C₂²×#41	C₃×D₃	semidirect
265. C₃×#41	#67	semidirect
266. C₃×#41	C₃×D₄	semidirect
368. C₂²×C₃²	H(5,𝔽₂)	semidirect
386. C₂×#41	C₂×C₃×D₃	semidirect
387. C₂×#41	C₂×C₃×D₃	semidirect
388. C₂×#41	C₂×C₃×D₃	semidirect
389. C₂²×Q₈	C₂×C₃×D₃	semidirect
393. C₂²×D₄	C₂×C₃×D₃	semidirect
394. C₂³×C₄	C₂×C₃×D₃	semidirect
448. C₃×Q₈	C₂×#67	semidirect
449. C₃×Q₈	C₂×C₃×D₄	semidirect
463. C₃×D₄	C₂×#67	semidirect
464. C₃×D₄	C₂×C₃×D₄	semidirect
490. C₂×C₃×C₄	C₂×#67	semidirect
491. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
526. #41	C₃×#67	semidirect
596. C₂²×C₃	#1009	semidirect
599. C₂²×C₃	C₃×H(5,𝔽₂)	semidirect
624. C₃²	#3488	semidirect
637. Q₈	C₂×C₃×#67	semidirect
646. D₄	C₂×C₃×#67	semidirect
657. C₂×C₄	C₂×C₃×#67	semidirect
694. C₂²	C₃×#1009	semidirect
705. C₃	#87275	direct (N × H)
706. C₃	C₃×#3488	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×#41	2
C₂×C₃×#1009	2
C₃×#5834	2
C₃×#5833	2
C₃×#5830	2
C₃×#5829	2
C₃×#5827	2
C₃×#5817	2
C₃×D₄×#67	2
C₃×#5791	2
C₂×C₃×#930	2
C₃×#3488	3
#87275	3

Subgroups — C3×#87275 #11904612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87275 #11904612