Subgroups — C₃²×#3271 #11770320

Order 1152.

1464 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃²×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3271	C₃	1	4	yes	maximal, direct product factor
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
21	C₃²×#137	—	2	4	no	—
22	C₃²×#135	—	2	4	no	—
23	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
34	C₃²×#127	—	2	1	no	—
35	C₃²×#127	C₂²	1	1	yes	characteristic
36	C₃²×#124	—	2	1	no	—
37	C₃²×#124	C₂²	1	1	yes	characteristic
38	C₃²×C₂²⋊Q₈	—	2	1	no	—
39	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₃²×#121	—	2	1	no	—
41	C₃²×#121	—	2	1	no	—
42	C₃²×#121	—	2	1	no	—
43	C₃²×#121	C₂²	1	1	yes	characteristic
44	C₃²×#121	C₂²	1	1	yes	characteristic
45	C₃²×#121	C₂²	1	1	yes	characteristic
46	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
47	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
48	C₃²×C₄×D₄	—	2	1	no	—
49	C₃²×C₄×D₄	—	2	1	no	—
50	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₃²×#106	C₂²	1	1	yes	characteristic
52	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₃²×#103	C₂²	1	1	yes	characteristic
54	C₃²×#103	C₂²	1	1	yes	characteristic
55	C₃²×#103	C₂²	1	1	yes	characteristic
56	C₃²×#102	C₂²	1	1	yes	characteristic
57	C₃²×#102	C₂²	1	1	yes	characteristic
58	C₃²×#102	C₂²	1	1	yes	characteristic
59	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₃²×#97	C₂²	1	1	yes	characteristic
62	C₂×C₃×#137	C₂×C₃	1	4	yes	complemented
63	C₂×C₃×#135	C₂×C₃	1	4	yes	complemented
64	C₃×#550	C₂×C₃	1	4	yes	complemented
65	C₃×#548	C₂×C₃	1	4	yes	complemented
66	C₃×#496	C₂×C₃	1	4	yes	complemented
67	C₃×#469	C₂×C₃	1	4	yes	complemented
68	C₃×#465	C₂×C₃	1	4	yes	complemented
69	C₃×#464	C₂×C₃	1	4	yes	complemented
70	C₃×#460	C₂×C₃	1	4	yes	complemented
71	C₃×#452	C₂×C₃	1	4	yes	complemented
72	C₃×#449	C₂×C₃	1	4	yes	complemented
73	C₃×#449	C₂×C₃	1	4	yes	complemented
74	C₃×#448	C₂×C₃	1	4	yes	complemented
75	C₃×#441	C₂×C₃	1	4	yes	complemented
76	C₃×#435	C₂×C₃	1	4	yes	complemented
77	C₃²×#41	—	2	2	no	—
78	C₃²×#41	—	2	2	no	—
79	C₃²×#41	—	2	2	no	—
80	C₃²×#41	—	4	1	no	—
81	C₃²×#41	—	4	1	no	—
82	C₃²×#41	—	4	1	no	—
83	C₂×C₃²×Q₈	—	2	1	no	—
84	C₂×C₃²×Q₈	—	2	2	no	—
85	C₂×C₃²×Q₈	—	4	1	no	—
86	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
88	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
89	C₂×C₃²×D₄	—	2	1	no	—
90	C₂×C₃²×D₄	—	2	1	no	—
91	C₂×C₃²×D₄	—	2	1	no	—
92	C₂×C₃²×D₄	—	2	1	no	—
93	C₂×C₃²×D₄	—	2	1	no	—
94	C₂×C₃²×D₄	—	2	1	no	—
95	C₂×C₃²×D₄	—	2	1	no	—
96	C₂×C₃²×D₄	—	2	1	no	—
97	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
98	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
99	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
100	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
101	C₂²×C₃²×C₄	—	2	1	no	—
102	C₂²×C₃²×C₄	—	2	1	no	—
103	C₂²×C₃²×C₄	—	2	1	no	—
104	C₂²×C₃²×C₄	—	2	1	no	—
105	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
107	C₃²×Q₁₆	—	2	2	no	—
108	C₃²×Q₁₆	D₄	1	4	yes	complemented
109	C₃²×SD₁₆	—	2	2	no	—
110	C₃²×SD₁₆	—	2	2	no	—
111	C₃²×SD₁₆	—	2	2	no	—
112	C₃²×SD₁₆	—	2	2	no	—
113	C₃²×SD₁₆	—	4	1	no	—
114	C₃²×D₈	—	2	2	no	—
115	C₃²×D₈	—	4	1	no	—
116	C₃²×M₁₆	—	2	2	no	—
117	C₂×C₃²×C₈	—	2	2	no	—
118	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
120	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
121	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
122	C₃²×C₄⋊C₄	—	2	1	no	—
123	C₃²×C₄⋊C₄	—	2	1	no	—
124	C₃²×C₄⋊C₄	—	2	1	no	—
125	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
126	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃²×C₂²⋊C₄	—	2	1	no	—
129	C₃²×C₂²⋊C₄	—	2	1	no	—
130	C₃²×C₂²⋊C₄	—	2	1	no	—
131	C₃²×C₂²⋊C₄	—	2	1	no	—
132	C₃²×C₂²⋊C₄	—	2	1	no	—
133	C₃²×C₂²⋊C₄	—	2	1	no	—
134	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
135	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₃²×C₄²	—	2	1	no	—
137	C₃²×C₄²	—	2	1	no	—
138	C₃²×C₄²	C₂³	1	1	yes	characteristic
139	#3271	C₃²	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
141	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
142	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
143	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	—
144	C₃×#137	—	2	16	no	—
145	C₃×#135	—	2	16	no	—
146	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
147	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
148	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
149	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
150	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
151	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
152	C₂×C₃×SD₁₆	C₂²×C₃	1	4	yes	—
153	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
154	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
155	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
156	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
157	C₃×#127	—	2	4	no	—
158	C₃×#127	C₂²×C₃	1	4	yes	—
159	C₃×#124	—	2	4	no	—
160	C₃×#124	C₂²×C₃	1	4	yes	—
161	C₃×C₂²⋊Q₈	—	2	4	no	—
162	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
163	C₃×#121	—	2	4	no	—
164	C₃×#121	—	2	4	no	—
165	C₃×#121	—	2	4	no	—
166	C₃×#121	C₂²×C₃	1	4	yes	—
167	C₃×#121	C₂²×C₃	1	4	yes	—
168	C₃×#121	C₂²×C₃	1	4	yes	—
169	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
170	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
171	C₃×C₄×D₄	—	2	4	no	—
172	C₃×C₄×D₄	—	2	4	no	—
173	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
174	C₃×#106	C₂²×C₃	1	4	yes	—
175	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
176	C₃×#103	C₂²×C₃	1	4	yes	—
177	C₃×#103	C₂²×C₃	1	4	yes	—
178	C₃×#103	C₂²×C₃	1	4	yes	—
179	C₃×#102	C₂²×C₃	1	4	yes	—
180	C₃×#102	C₂²×C₃	1	4	yes	—
181	C₃×#102	C₂²×C₃	1	4	yes	—
182	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
183	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
184	C₃×#97	C₂²×C₃	1	4	yes	—
185	C₂³×C₃²	—	2	1	no	—
186	C₂³×C₃²	—	2	1	no	—
187	C₂³×C₃²	—	2	1	no	—
188	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
190	C₃²×Q₈	—	2	1	no	—
191	C₃²×Q₈	—	2	1	no	—
192	C₃²×Q₈	—	2	1	no	—
193	C₃²×Q₈	—	2	1	no	—
194	C₃²×Q₈	—	4	2	no	—
195	C₃²×Q₈	C₂×D₄	1	2	yes	—
196	C₃²×Q₈	C₂×D₄	1	2	yes	—
197	C₃²×D₄	—	2	1	no	—
198	C₃²×D₄	—	2	1	no	—
199	C₃²×D₄	—	2	1	no	—
200	C₃²×D₄	—	2	1	no	—
201	C₃²×D₄	—	2	1	no	—
202	C₃²×D₄	—	2	1	no	—
203	C₃²×D₄	—	4	1	no	—
204	C₃²×D₄	—	4	2	no	—
205	C₃²×D₄	—	4	2	no	—
206	C₃²×D₄	—	4	2	no	—
207	C₃²×D₄	—	4	2	no	—
208	C₃²×D₄	—	4	2	no	—
209	C₃²×D₄	—	8	1	no	—
210	C₃²×D₄	—	8	1	no	—
211	C₃²×D₄	—	8	1	no	—
212	C₂×C₃²×C₄	—	2	1	no	—
213	C₂×C₃²×C₄	—	2	1	no	—
214	C₂×C₃²×C₄	—	2	1	no	—
215	C₂×C₃²×C₄	—	2	1	no	—
216	C₂×C₃²×C₄	—	2	1	no	—
217	C₂×C₃²×C₄	—	2	1	no	—
218	C₂×C₃²×C₄	—	2	1	no	—
219	C₂×C₃²×C₄	—	2	1	no	—
220	C₂×C₃²×C₄	—	2	1	no	—
221	C₂×C₃²×C₄	—	4	2	no	—
222	C₂×C₃²×C₄	—	4	2	no	—
223	C₂×C₃²×C₄	—	4	2	no	—
224	C₂×C₃²×C₄	—	4	2	no	—
225	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
230	C₃²×C₈	—	2	1	no	—
231	C₃²×C₈	—	2	1	no	—
232	C₃²×C₈	—	2	1	no	—
233	C₃²×C₈	C₂×D₄	1	2	yes	—
234	C₂×#137	C₂×C₃²	1	1	yes	characteristic, complemented
235	C₂×#135	C₂×C₃²	1	1	yes	characteristic, complemented
236	#550	C₂×C₃²	1	1	yes	characteristic, complemented
237	#548	C₂×C₃²	1	1	yes	characteristic, complemented
238	#496	C₂×C₃²	1	1	yes	characteristic, complemented
239	#469	C₂×C₃²	1	1	yes	characteristic, complemented
240	#465	C₂×C₃²	1	1	yes	characteristic, complemented
241	#464	C₂×C₃²	1	1	yes	characteristic, complemented
242	#460	C₂×C₃²	1	1	yes	characteristic, complemented
243	#452	C₂×C₃²	1	1	yes	characteristic, complemented
244	#449	C₂×C₃²	1	1	yes	characteristic, complemented
245	#449	C₂×C₃²	1	1	yes	characteristic, complemented
246	#448	C₂×C₃²	1	1	yes	characteristic, complemented
247	#441	C₂×C₃²	1	1	yes	characteristic, complemented
248	#435	C₂×C₃²	1	1	yes	characteristic, complemented
249	C₃×#41	—	2	8	no	—
250	C₃×#41	—	2	8	no	—
251	C₃×#41	—	2	8	no	—
252	C₃×#41	—	4	4	no	—
253	C₃×#41	—	4	4	no	—
254	C₃×#41	—	4	4	no	—
255	C₂×C₃×Q₈	—	2	4	no	—
256	C₂×C₃×Q₈	—	2	8	no	—
257	C₂×C₃×Q₈	—	4	4	no	—
258	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
259	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
260	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
261	C₂×C₃×D₄	—	2	4	no	—
262	C₂×C₃×D₄	—	2	4	no	—
263	C₂×C₃×D₄	—	2	4	no	—
264	C₂×C₃×D₄	—	2	4	no	—
265	C₂×C₃×D₄	—	2	4	no	—
266	C₂×C₃×D₄	—	2	4	no	—
267	C₂×C₃×D₄	—	2	4	no	—
268	C₂×C₃×D₄	—	2	4	no	—
269	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
270	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
271	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
272	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
273	C₂²×C₃×C₄	—	2	4	no	—
274	C₂²×C₃×C₄	—	2	4	no	—
275	C₂²×C₃×C₄	—	2	4	no	—
276	C₂²×C₃×C₄	—	2	4	no	—
277	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
278	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
279	C₃×Q₁₆	—	2	8	no	—
280	C₃×Q₁₆	C₃×D₄	1	16	yes	complemented
281	C₃×SD₁₆	—	2	8	no	—
282	C₃×SD₁₆	—	2	8	no	—
283	C₃×SD₁₆	—	2	8	no	—
284	C₃×SD₁₆	—	2	8	no	—
285	C₃×SD₁₆	—	4	4	no	—
286	C₃×D₈	—	2	8	no	—
287	C₃×D₈	—	4	4	no	—
288	C₃×M₁₆	—	2	8	no	—
289	C₂×C₃×C₈	—	2	8	no	—
290	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
291	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
292	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
293	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
294	C₃×C₄⋊C₄	—	2	4	no	—
295	C₃×C₄⋊C₄	—	2	4	no	—
296	C₃×C₄⋊C₄	—	2	4	no	—
297	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
298	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
299	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
300	C₃×C₂²⋊C₄	—	2	4	no	—
301	C₃×C₂²⋊C₄	—	2	4	no	—
302	C₃×C₂²⋊C₄	—	2	4	no	—
303	C₃×C₂²⋊C₄	—	2	4	no	—
304	C₃×C₂²⋊C₄	—	2	4	no	—
305	C₃×C₂²⋊C₄	—	2	4	no	—
306	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
307	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
308	C₃×C₄²	—	2	4	no	—
309	C₃×C₄²	—	2	4	no	—
310	C₃×C₄²	C₂³×C₃	1	4	yes	—
311	C₂²×C₃²	—	2	1	no	—
312	C₂²×C₃²	—	2	1	no	—
313	C₂²×C₃²	—	2	1	no	—
314	C₂²×C₃²	—	2	1	no	—
315	C₂²×C₃²	—	2	1	no	—
316	C₂²×C₃²	—	2	1	no	—
317	C₂²×C₃²	—	4	1	no	—
318	C₂²×C₃²	—	4	1	no	—
319	C₂²×C₃²	—	4	1	no	—
320	C₂²×C₃²	—	4	1	no	—
321	C₂²×C₃²	—	4	1	no	—
322	C₂²×C₃²	—	4	1	no	—
323	C₂²×C₃²	—	4	1	no	—
324	C₂²×C₃²	—	4	1	no	—
325	C₂²×C₃²	—	4	1	no	—
326	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
327	C₃²×C₄	—	2	1	no	—
328	C₃²×C₄	—	2	1	no	—
329	C₃²×C₄	—	2	2	no	—
330	C₃²×C₄	—	2	2	no	—
331	C₃²×C₄	—	2	1	no	—
332	C₃²×C₄	—	2	1	no	—
333	C₃²×C₄	—	4	1	no	—
334	C₃²×C₄	—	4	1	no	—
335	C₃²×C₄	—	4	1	no	—
336	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
337	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
339	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
340	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
341	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic
342	#137	—	2	4	no	—
343	#135	—	2	4	no	—
344	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic
345	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic
346	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
347	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
348	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
349	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
350	C₂×SD₁₆	C₂²×C₃²	1	1	yes	characteristic
351	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
352	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
353	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
354	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
355	#127	—	2	1	no	—
356	#127	C₂²×C₃²	1	1	yes	characteristic
357	#124	—	2	1	no	—
358	#124	C₂²×C₃²	1	1	yes	characteristic
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	—	2	1	no	—
364	#121	C₂²×C₃²	1	1	yes	characteristic
365	#121	C₂²×C₃²	1	1	yes	characteristic
366	#121	C₂²×C₃²	1	1	yes	characteristic
367	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
368	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
372	#106	C₂²×C₃²	1	1	yes	characteristic
373	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
374	#103	C₂²×C₃²	1	1	yes	characteristic
375	#103	C₂²×C₃²	1	1	yes	characteristic
376	#103	C₂²×C₃²	1	1	yes	characteristic
377	#102	C₂²×C₃²	1	1	yes	characteristic
378	#102	C₂²×C₃²	1	1	yes	characteristic
379	#102	C₂²×C₃²	1	1	yes	characteristic
380	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
381	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
382	#97	C₂²×C₃²	1	1	yes	characteristic
383	C₂³×C₃	—	2	4	no	—
384	C₂³×C₃	—	2	4	no	—
385	C₂³×C₃	—	2	4	no	—
386	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
387	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
388	C₃×Q₈	—	2	4	no	—
389	C₃×Q₈	—	2	4	no	—
390	C₃×Q₈	—	2	4	no	—
391	C₃×Q₈	—	2	4	no	—
392	C₃×Q₈	—	4	8	no	—
393	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
394	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
395	C₃×D₄	—	2	4	no	—
396	C₃×D₄	—	2	4	no	—
397	C₃×D₄	—	2	4	no	—
398	C₃×D₄	—	2	4	no	—
399	C₃×D₄	—	2	4	no	—
400	C₃×D₄	—	2	4	no	—
401	C₃×D₄	—	4	4	no	—
402	C₃×D₄	—	4	8	no	—
403	C₃×D₄	—	4	8	no	—
404	C₃×D₄	—	4	8	no	—
405	C₃×D₄	—	4	8	no	—
406	C₃×D₄	—	4	8	no	—
407	C₃×D₄	—	8	4	no	—
408	C₃×D₄	—	8	4	no	—
409	C₃×D₄	—	8	4	no	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	4	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	4	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	4	no	—
417	C₂×C₃×C₄	—	2	4	no	—
418	C₂×C₃×C₄	—	2	4	no	—
419	C₂×C₃×C₄	—	4	8	no	—
420	C₂×C₃×C₄	—	4	8	no	—
421	C₂×C₃×C₄	—	4	8	no	—
422	C₂×C₃×C₄	—	4	8	no	—
423	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
424	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
425	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
426	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
427	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
428	C₃×C₈	—	2	4	no	—
429	C₃×C₈	—	2	4	no	—
430	C₃×C₈	—	2	4	no	—
431	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
432	C₂×C₃²	—	4	1	no	—
433	C₂×C₃²	—	4	1	no	—
434	C₂×C₃²	—	8	1	no	—
435	C₂×C₃²	—	8	1	no	—
436	C₂×C₃²	—	8	1	no	—
437	C₂×C₃²	D₄²	1	1	yes	characteristic
438	C₂×C₃²	#575	1	1	yes	characteristic
439	C₂×C₃²	#577	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	4	1	no	—
444	#41	—	4	1	no	—
445	#41	—	4	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	4	1	no	—
449	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
450	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
451	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
461	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
462	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
463	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
469	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
470	Q₁₆	—	2	2	no	—
471	Q₁₆	C₃²×D₄	1	4	yes	complemented
472	SD₁₆	—	2	2	no	—
473	SD₁₆	—	2	2	no	—
474	SD₁₆	—	2	2	no	—
475	SD₁₆	—	2	2	no	—
476	SD₁₆	—	4	1	no	—
477	D₈	—	2	2	no	—
478	D₈	—	4	1	no	—
479	M₁₆	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
482	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
483	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
484	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
489	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
490	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	C₃²×D₄	1	1	yes	characteristic
498	C₂²⋊C₄	C₃²×D₄	1	1	yes	characteristic
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	C₂³×C₃²	1	1	yes	characteristic
502	C₂²×C₃	—	2	4	no	—
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	4	no	—
505	C₂²×C₃	—	2	4	no	—
506	C₂²×C₃	—	2	4	no	—
507	C₂²×C₃	—	2	4	no	—
508	C₂²×C₃	—	4	4	no	—
509	C₂²×C₃	—	4	4	no	—
510	C₂²×C₃	—	4	4	no	—
511	C₂²×C₃	—	4	4	no	—
512	C₂²×C₃	—	4	4	no	—
513	C₂²×C₃	—	4	4	no	—
514	C₂²×C₃	—	4	4	no	—
515	C₂²×C₃	—	4	4	no	—
516	C₂²×C₃	—	4	4	no	—
517	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
518	C₃×C₄	—	2	4	no	—
519	C₃×C₄	—	2	4	no	—
520	C₃×C₄	—	2	4	no	—
521	C₃×C₄	—	2	4	no	—
522	C₃×C₄	—	2	8	no	—
523	C₃×C₄	—	2	8	no	—
524	C₃×C₄	—	4	4	no	—
525	C₃×C₄	—	4	4	no	—
526	C₃×C₄	—	4	4	no	—
527	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
528	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
529	C₃²	#3271	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
534	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
535	Q₈	—	2	1	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	2	1	no	—
539	Q₈	—	4	2	no	—
540	Q₈	C₂×C₃²×D₄	1	2	yes	—
541	Q₈	C₂×C₃²×D₄	1	2	yes	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	8	1	no	—
555	D₄	—	8	1	no	—
556	D₄	—	8	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
572	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	C₂×C₃²×D₄	1	2	yes	—
579	C₂×C₃	—	4	4	no	—
580	C₂×C₃	—	4	4	no	—
581	C₂×C₃	—	8	4	no	—
582	C₂×C₃	—	8	4	no	—
583	C₂×C₃	—	8	4	no	—
584	C₂×C₃	C₃×D₄²	1	4	yes	—
585	C₂×C₃	C₃×#575	1	4	yes	—
586	C₂×C₃	C₃×#577	1	4	yes	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
613	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
614	C₃	C₃×#3271	1	4	yes	direct product factor
615	C₂	—	4	1	no	—
616	C₂	—	4	1	no	—
617	C₂	—	8	1	no	—
618	C₂	—	8	1	no	—
619	C₂	—	8	1	no	—
620	C₂	C₃²×D₄²	1	1	yes	characteristic
621	C₂	C₃²×#575	1	1	yes	characteristic
622	C₂	C₃²×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#137	C₂	semidirect
2. C₂×C₃²×#135	C₂	semidirect
3. C₃²×#550	C₂	semidirect
4. C₃²×#548	C₂	semidirect
5. C₃²×#496	C₂	semidirect
6. C₃²×#469	C₂	semidirect
7. C₃²×#465	C₂	semidirect
8. C₃²×#464	C₂	semidirect
9. C₃²×#460	C₂	semidirect
10. C₃²×#452	C₂	semidirect
11. C₃²×#449	C₂	semidirect
12. C₃²×#449	C₂	semidirect
13. C₃²×#448	C₂	semidirect
14. C₃²×#441	C₂	semidirect
15. C₃²×#435	C₂	semidirect
16. C₃×#3271	C₃	direct (N × H)
62. C₂×C₃×#137	C₂×C₃	semidirect
63. C₂×C₃×#135	C₂×C₃	semidirect
64. C₃×#550	C₂×C₃	semidirect
65. C₃×#548	C₂×C₃	semidirect
66. C₃×#496	C₂×C₃	semidirect
67. C₃×#469	C₂×C₃	semidirect
68. C₃×#465	C₂×C₃	semidirect
69. C₃×#464	C₂×C₃	semidirect
70. C₃×#460	C₂×C₃	semidirect
71. C₃×#452	C₂×C₃	semidirect
72. C₃×#449	C₂×C₃	semidirect
73. C₃×#449	C₂×C₃	semidirect
74. C₃×#448	C₂×C₃	semidirect
75. C₃×#441	C₂×C₃	semidirect
76. C₃×#435	C₂×C₃	semidirect
108. C₃²×Q₁₆	D₄	semidirect
139. #3271	C₃²	direct (N × H)
234. C₂×#137	C₂×C₃²	semidirect
235. C₂×#135	C₂×C₃²	semidirect
236. #550	C₂×C₃²	semidirect
237. #548	C₂×C₃²	semidirect
238. #496	C₂×C₃²	semidirect
239. #469	C₂×C₃²	semidirect
240. #465	C₂×C₃²	semidirect
241. #464	C₂×C₃²	semidirect
242. #460	C₂×C₃²	semidirect
243. #452	C₂×C₃²	semidirect
244. #449	C₂×C₃²	semidirect
245. #449	C₂×C₃²	semidirect
246. #448	C₂×C₃²	semidirect
247. #441	C₂×C₃²	semidirect
248. #435	C₂×C₃²	semidirect
280. C₃×Q₁₆	C₃×D₄	semidirect
471. Q₁₆	C₃²×D₄	semidirect
529. C₃²	#3271	direct (N × H)
614. C₃	C₃×#3271	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#137	2
C₂×C₃²×#135	2
C₃²×#550	2
C₃²×#548	2
C₃²×#496	2
C₃²×#469	2
C₃²×#465	2
C₃²×#464	2
C₃²×#460	2
C₃²×#452	2
C₃²×#449	2
C₃²×#448	2
C₃²×#441	2
C₃²×#435	2
C₃×#3271	3

Subgroups — C32×#3271 #11770320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3271 #11770320