Subgroups — C₃×#3475 #87359

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#553	C₂	1	2	yes	maximal, complemented
5	C₃×#552	C₂	1	2	yes	maximal, complemented
6	C₃×#552	C₂	1	2	yes	maximal, complemented
7	C₃×#551	C₂	1	4	yes	maximal, complemented
8	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#546	C₂	1	2	yes	maximal, complemented
10	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#529	C₂	1	4	yes	maximal, complemented
12	C₃×#529	C₂	1	2	yes	maximal, complemented
13	C₃×#525	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#41	C₂	1	2	yes	maximal, complemented
16	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#117	C₂	1	2	yes	maximal, complemented
18	#3475	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×#41	C₂²	1	2	yes	—
21	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂³×C₃×C₄	C₂²	1	2	yes	—
23	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×#126	C₂²	1	4	yes	complemented
26	C₃×#126	C₂²	1	4	yes	complemented
27	C₃×#126	C₂²	1	4	yes	complemented
28	C₃×#125	C₂²	1	4	yes	complemented
29	C₃×#125	C₂²	1	2	yes	complemented
30	C₃×#125	C₂²	1	2	yes	complemented
31	C₃×#124	C₂²	1	2	yes	—
32	C₃×#124	C₂²	1	4	yes	complemented
33	C₃×#123	C₂²	1	4	yes	—
34	C₃×#123	C₂²	1	4	yes	—
35	C₃×#123	C₂²	1	4	yes	complemented
36	C₃×#123	C₂²	1	4	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
42	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃×#121	C₂²	1	4	yes	—
44	C₃×#121	C₂²	1	2	yes	—
45	C₃×#121	C₂²	1	2	yes	complemented
46	C₃×#121	C₂²	1	2	yes	complemented
47	C₃×#120	C₂²	1	4	yes	—
48	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
49	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
51	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
53	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₃×C₄×D₄	C₂²	1	2	yes	—
56	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
57	C₃×C₄×D₄	C₂²	1	2	yes	—
58	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
59	C₃×C₄×D₄	C₂²	1	2	yes	—
60	C₃×C₄×D₄	C₂²	1	2	yes	—
61	C₃×C₄×D₄	C₂²	1	2	yes	—
62	C₃×C₄×D₄	C₂²	1	4	yes	complemented
63	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
64	C₃×C₄×D₄	C₂²	1	4	yes	complemented
65	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₄×D₄	C₂²	1	4	yes	complemented
67	C₃×#117	C₂²	1	1	yes	characteristic
68	C₃×#117	C₂²	1	2	yes	—
69	C₃×#117	C₂²	1	4	yes	—
70	C₃×#117	C₂²	1	4	yes	complemented
71	C₃×#117	C₂²	1	2	yes	complemented
72	C₃×#117	C₂²	1	2	yes	complemented
73	C₃×#117	C₂²	1	2	yes	complemented
74	C₃×#117	C₂²	1	4	yes	complemented
75	C₃×#117	C₂²	1	2	yes	complemented
76	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂²	1	4	yes	complemented
83	C₂×C₃×C₄²	C₂²	1	2	yes	complemented
84	#556	C₂×C₃	1	1	yes	characteristic, complemented
85	#555	C₂×C₃	1	1	yes	characteristic, complemented
86	#554	C₂×C₃	1	1	yes	characteristic, complemented
87	#553	C₂×C₃	1	2	yes	complemented
88	#552	C₂×C₃	1	2	yes	complemented
89	#552	C₂×C₃	1	2	yes	complemented
90	#551	C₂×C₃	1	4	yes	complemented
91	#547	C₂×C₃	1	1	yes	characteristic, complemented
92	#546	C₂×C₃	1	2	yes	complemented
93	#533	C₂×C₃	1	1	yes	characteristic, complemented
94	#529	C₂×C₃	1	4	yes	complemented
95	#529	C₂×C₃	1	2	yes	complemented
96	#525	C₂×C₃	1	2	yes	complemented
97	C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
98	C₄×#41	C₂×C₃	1	2	yes	complemented
99	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#117	C₂×C₃	1	2	yes	complemented
101	C₂⁴×C₃	C₂³	1	2	yes	—
102	C₃×#41	—	2	8	no	—
103	C₃×#41	—	2	4	no	—
104	C₂×C₃×Q₈	C₂³	1	2	yes	—
105	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×D₄	—	2	4	no	—
108	C₂×C₃×D₄	C₂³	1	2	yes	—
109	C₂×C₃×D₄	C₂³	1	2	yes	—
110	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
111	C₂×C₃×D₄	C₂³	1	4	yes	—
112	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
113	C₂×C₃×D₄	C₂³	1	4	yes	—
114	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₄	—	2	8	no	—
116	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂³	1	4	yes	—
118	C₂²×C₃×C₄	C₂³	1	2	yes	—
119	C₂²×C₃×C₄	C₂³	1	2	yes	—
120	C₂²×C₃×C₄	C₂³	1	2	yes	—
121	C₂²×C₃×C₄	C₂³	1	2	yes	—
122	C₂²×C₃×C₄	C₂³	1	2	yes	—
123	C₂²×C₃×C₄	C₂³	1	2	yes	—
124	C₂²×C₃×C₄	C₂³	1	2	yes	—
125	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂³	1	4	yes	—
127	C₂²×C₃×C₄	C₂³	1	2	yes	—
128	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
129	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₃×C₄²	C₂³	1	1	yes	characteristic
161	C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₃×C₄²	C₂³	1	4	yes	—
163	C₃×C₄²	C₂³	1	4	yes	—
164	C₃×C₄²	C₂³	1	2	yes	—
165	C₃×C₄²	C₂³	1	2	yes	—
166	C₃×C₄²	C₂³	1	1	yes	characteristic
167	C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₃×C₄²	C₂³	1	2	yes	—
169	C₃×C₄²	C₂³	1	4	yes	—
170	C₂×#41	C₂²×C₃	1	1	yes	characteristic
171	C₂×#41	C₂²×C₃	1	2	yes	—
172	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
173	C₂³×C₄	C₂²×C₃	1	2	yes	—
174	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
176	#126	C₂²×C₃	1	4	yes	complemented
177	#126	C₂²×C₃	1	4	yes	complemented
178	#126	C₂²×C₃	1	4	yes	complemented
179	#125	C₂²×C₃	1	4	yes	complemented
180	#125	C₂²×C₃	1	2	yes	complemented
181	#125	C₂²×C₃	1	2	yes	complemented
182	#124	C₂²×C₃	1	2	yes	—
183	#124	C₂²×C₃	1	4	yes	complemented
184	#123	C₂²×C₃	1	4	yes	—
185	#123	C₂²×C₃	1	4	yes	—
186	#123	C₂²×C₃	1	4	yes	complemented
187	#123	C₂²×C₃	1	4	yes	complemented
188	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
189	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
190	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
191	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
192	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
193	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
194	#121	C₂²×C₃	1	4	yes	—
195	#121	C₂²×C₃	1	2	yes	—
196	#121	C₂²×C₃	1	2	yes	complemented
197	#121	C₂²×C₃	1	2	yes	complemented
198	#120	C₂²×C₃	1	4	yes	—
199	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
200	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
202	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
203	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
204	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
205	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
206	C₄×D₄	C₂²×C₃	1	2	yes	—
207	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
208	C₄×D₄	C₂²×C₃	1	2	yes	—
209	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
210	C₄×D₄	C₂²×C₃	1	2	yes	—
211	C₄×D₄	C₂²×C₃	1	2	yes	—
212	C₄×D₄	C₂²×C₃	1	2	yes	—
213	C₄×D₄	C₂²×C₃	1	4	yes	complemented
214	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
215	C₄×D₄	C₂²×C₃	1	4	yes	complemented
216	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
217	C₄×D₄	C₂²×C₃	1	4	yes	complemented
218	#117	C₂²×C₃	1	1	yes	characteristic
219	#117	C₂²×C₃	1	2	yes	—
220	#117	C₂²×C₃	1	4	yes	—
221	#117	C₂²×C₃	1	4	yes	complemented
222	#117	C₂²×C₃	1	2	yes	complemented
223	#117	C₂²×C₃	1	2	yes	complemented
224	#117	C₂²×C₃	1	2	yes	complemented
225	#117	C₂²×C₃	1	4	yes	complemented
226	#117	C₂²×C₃	1	2	yes	complemented
227	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
229	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
230	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
231	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
232	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
233	C₂×C₄²	C₂²×C₃	1	4	yes	complemented
234	C₂×C₄²	C₂²×C₃	1	2	yes	complemented
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	2	4	no	—
237	C₂³×C₃	—	4	2	no	—
238	C₂³×C₃	C₂⁴	1	2	yes	—
239	C₂³×C₃	C₂⁴	1	2	yes	—
240	C₂³×C₃	C₂⁴	1	1	yes	characteristic
241	C₂³×C₃	C₂⁴	1	2	yes	—
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	2	4	no	—
244	C₃×Q₈	—	4	2	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	2	8	no	—
248	C₃×D₄	—	2	2	no	—
249	C₃×D₄	—	2	2	no	—
250	C₃×D₄	—	4	4	no	—
251	C₃×D₄	#41	1	4	yes	complemented
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	8	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	4	4	no	—
263	C₂×C₃×C₄	—	4	1	no	—
264	C₂×C₃×C₄	#41	1	4	yes	complemented
265	C₂×C₃×C₄	C₂⁴	1	2	yes	—
266	C₂×C₃×C₄	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂⁴	1	2	yes	—
269	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂⁴	1	4	yes	—
271	C₂×C₃×C₄	C₂⁴	1	2	yes	—
272	C₂×C₃×C₄	C₂⁴	1	4	yes	—
273	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂⁴	1	2	yes	—
275	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₂⁴	C₂³×C₃	1	2	yes	—
279	#41	—	2	8	no	—
280	#41	—	2	4	no	—
281	C₂×Q₈	C₂³×C₃	1	2	yes	—
282	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×Q₈	C₂³×C₃	1	2	yes	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	C₂³×C₃	1	2	yes	—
286	C₂×D₄	C₂³×C₃	1	2	yes	—
287	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
288	C₂×D₄	C₂³×C₃	1	4	yes	—
289	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
290	C₂×D₄	C₂³×C₃	1	4	yes	—
291	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₃	1	2	yes	—
295	C₂²×C₄	C₂³×C₃	1	4	yes	—
296	C₂²×C₄	C₂³×C₃	1	2	yes	—
297	C₂²×C₄	C₂³×C₃	1	2	yes	—
298	C₂²×C₄	C₂³×C₃	1	2	yes	—
299	C₂²×C₄	C₂³×C₃	1	2	yes	—
300	C₂²×C₄	C₂³×C₃	1	2	yes	—
301	C₂²×C₄	C₂³×C₃	1	2	yes	—
302	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
303	C₂²×C₄	C₂³×C₃	1	4	yes	—
304	C₂²×C₄	C₂³×C₃	1	2	yes	—
305	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
306	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
308	C₄⋊C₄	C₂³×C₃	1	2	yes	—
309	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
310	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
311	C₄⋊C₄	C₂³×C₃	1	2	yes	—
312	C₄⋊C₄	C₂³×C₃	1	2	yes	—
313	C₄⋊C₄	C₂³×C₃	1	4	yes	—
314	C₄⋊C₄	C₂³×C₃	1	4	yes	—
315	C₄⋊C₄	C₂³×C₃	1	2	yes	—
316	C₄⋊C₄	C₂³×C₃	1	2	yes	—
317	C₄⋊C₄	C₂³×C₃	1	2	yes	—
318	C₄⋊C₄	C₂³×C₃	1	4	yes	—
319	C₄⋊C₄	C₂³×C₃	1	4	yes	—
320	C₄⋊C₄	C₂³×C₃	1	4	yes	—
321	C₄⋊C₄	C₂³×C₃	1	4	yes	—
322	C₄⋊C₄	C₂³×C₃	1	2	yes	—
323	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
324	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
325	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
326	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
328	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
329	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
330	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
331	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
335	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
336	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
337	C₄²	C₂³×C₃	1	1	yes	characteristic
338	C₄²	C₂³×C₃	1	1	yes	characteristic
339	C₄²	C₂³×C₃	1	1	yes	characteristic
340	C₄²	C₂³×C₃	1	1	yes	characteristic
341	C₄²	C₂³×C₃	1	2	yes	—
342	C₄²	C₂³×C₃	1	4	yes	—
343	C₄²	C₂³×C₃	1	4	yes	—
344	C₄²	C₂³×C₃	1	4	yes	—
345	C₄²	C₂³×C₃	1	2	yes	—
346	C₄²	C₂³×C₃	1	2	yes	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	4	8	no	—
358	C₂²×C₃	C₂×#41	1	2	yes	—
359	C₂²×C₃	C₂×#41	1	4	yes	—
360	C₂²×C₃	C₂⁵	1	1	yes	characteristic
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	2	4	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	C₂×#41	1	2	yes	—
372	C₃×C₄	C₂×#41	1	2	yes	—
373	C₃×C₄	C₂×#41	1	2	yes	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₂⁴×C₃	1	2	yes	—
378	C₂³	C₂⁴×C₃	1	2	yes	—
379	C₂³	C₂⁴×C₃	1	1	yes	characteristic
380	C₂³	C₂⁴×C₃	1	2	yes	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	4	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	8	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	4	no	—
390	D₄	C₃×#41	1	4	yes	complemented
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	C₃×#41	1	4	yes	complemented
404	C₂×C₄	C₂⁴×C₃	1	2	yes	—
405	C₂×C₄	C₂⁴×C₃	1	2	yes	—
406	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
407	C₂×C₄	C₂⁴×C₃	1	2	yes	—
408	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	C₂×C₄	C₂⁴×C₃	1	4	yes	—
410	C₂×C₄	C₂⁴×C₃	1	2	yes	—
411	C₂×C₄	C₂⁴×C₃	1	4	yes	—
412	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
413	C₂×C₄	C₂⁴×C₃	1	2	yes	—
414	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
415	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
416	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
417	C₂×C₃	—	2	2	no	—
418	C₂×C₃	—	2	4	no	—
419	C₂×C₃	—	4	2	no	—
420	C₂×C₃	—	4	2	no	—
421	C₂×C₃	C₂²×#41	1	1	yes	characteristic
422	C₂×C₃	C₂²×#41	1	1	yes	characteristic
423	C₂×C₃	#585	1	1	yes	characteristic
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	C₂×C₃×#41	1	2	yes	—
436	C₂²	C₂×C₃×#41	1	4	yes	—
437	C₂²	C₂⁵×C₃	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	1	no	—
448	C₄	C₂×C₃×#41	1	2	yes	—
449	C₄	C₂×C₃×#41	1	2	yes	—
450	C₄	C₂×C₃×#41	1	2	yes	—
451	C₃	#3475	1	1	yes	characteristic, direct product factor, Sylow
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	C₂²×C₃×#41	1	1	yes	characteristic
457	C₂	C₂²×C₃×#41	1	1	yes	characteristic
458	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
socle	C₂²×C₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#556	C₂	semidirect
2. C₃×#555	C₂	semidirect
3. C₃×#554	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#552	C₂	semidirect
6. C₃×#552	C₂	semidirect
7. C₃×#551	C₂	semidirect
8. C₃×#547	C₂	semidirect
9. C₃×#546	C₂	semidirect
10. C₃×#533	C₂	semidirect
11. C₃×#529	C₂	semidirect
12. C₃×#529	C₂	semidirect
13. C₃×#525	C₂	semidirect
14. C₃×C₄×#41	C₂	semidirect
15. C₃×C₄×#41	C₂	semidirect
16. C₂×C₃×C₄×D₄	C₂	semidirect
17. C₂×C₃×#117	C₂	semidirect
18. #3475	C₃	direct (N × H)
23. C₃×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₄⋊Q₈	C₂²	semidirect
25. C₃×#126	C₂²	semidirect
26. C₃×#126	C₂²	semidirect
27. C₃×#126	C₂²	semidirect
28. C₃×#125	C₂²	semidirect
29. C₃×#125	C₂²	semidirect
30. C₃×#125	C₂²	semidirect
32. C₃×#124	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
39. C₃×C₂²⋊Q₈	C₂²	semidirect
40. C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₃×C₂²⋊Q₈	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₃×#121	C₂²	semidirect
46. C₃×#121	C₂²	semidirect
48. C₃×C₄×Q₈	C₂²	semidirect
49. C₃×C₄×Q₈	C₂²	semidirect
50. C₃×C₄×Q₈	C₂²	semidirect
51. C₃×C₄×Q₈	C₂²	semidirect
52. C₃×C₄×Q₈	C₂²	semidirect
62. C₃×C₄×D₄	C₂²	semidirect
63. C₃×C₄×D₄	C₂²	semidirect
64. C₃×C₄×D₄	C₂²	semidirect
65. C₃×C₄×D₄	C₂²	semidirect
66. C₃×C₄×D₄	C₂²	semidirect
70. C₃×#117	C₂²	semidirect
71. C₃×#117	C₂²	semidirect
72. C₃×#117	C₂²	semidirect
73. C₃×#117	C₂²	semidirect
74. C₃×#117	C₂²	semidirect
75. C₃×#117	C₂²	semidirect
77. C₂×C₃×C₄⋊C₄	C₂²	semidirect
78. C₂×C₃×C₄⋊C₄	C₂²	semidirect
82. C₂×C₃×C₄²	C₂²	semidirect
83. C₂×C₃×C₄²	C₂²	semidirect
84. #556	C₂×C₃	semidirect
85. #555	C₂×C₃	semidirect
86. #554	C₂×C₃	semidirect
87. #553	C₂×C₃	semidirect
88. #552	C₂×C₃	semidirect
89. #552	C₂×C₃	semidirect
90. #551	C₂×C₃	semidirect
91. #547	C₂×C₃	semidirect
92. #546	C₂×C₃	semidirect
93. #533	C₂×C₃	semidirect
94. #529	C₂×C₃	semidirect
95. #529	C₂×C₃	semidirect
96. #525	C₂×C₃	semidirect
97. C₄×#41	C₂×C₃	semidirect
98. C₄×#41	C₂×C₃	semidirect
99. C₂×C₄×D₄	C₂×C₃	semidirect
100. C₂×#117	C₂×C₃	semidirect
174. C₄⋊Q₈	C₂²×C₃	semidirect
175. C₄⋊Q₈	C₂²×C₃	semidirect
176. #126	C₂²×C₃	semidirect
177. #126	C₂²×C₃	semidirect
178. #126	C₂²×C₃	semidirect
179. #125	C₂²×C₃	semidirect
180. #125	C₂²×C₃	semidirect
181. #125	C₂²×C₃	semidirect
183. #124	C₂²×C₃	semidirect
186. #123	C₂²×C₃	semidirect
187. #123	C₂²×C₃	semidirect
190. C₂²⋊Q₈	C₂²×C₃	semidirect
191. C₂²⋊Q₈	C₂²×C₃	semidirect
192. C₂²⋊Q₈	C₂²×C₃	semidirect
193. C₂²⋊Q₈	C₂²×C₃	semidirect
196. #121	C₂²×C₃	semidirect
197. #121	C₂²×C₃	semidirect
199. C₄×Q₈	C₂²×C₃	semidirect
200. C₄×Q₈	C₂²×C₃	semidirect
201. C₄×Q₈	C₂²×C₃	semidirect
202. C₄×Q₈	C₂²×C₃	semidirect
203. C₄×Q₈	C₂²×C₃	semidirect
213. C₄×D₄	C₂²×C₃	semidirect
214. C₄×D₄	C₂²×C₃	semidirect
215. C₄×D₄	C₂²×C₃	semidirect
216. C₄×D₄	C₂²×C₃	semidirect
217. C₄×D₄	C₂²×C₃	semidirect
221. #117	C₂²×C₃	semidirect
222. #117	C₂²×C₃	semidirect
223. #117	C₂²×C₃	semidirect
224. #117	C₂²×C₃	semidirect
225. #117	C₂²×C₃	semidirect
226. #117	C₂²×C₃	semidirect
228. C₂×C₄⋊C₄	C₂²×C₃	semidirect
229. C₂×C₄⋊C₄	C₂²×C₃	semidirect
233. C₂×C₄²	C₂²×C₃	semidirect
234. C₂×C₄²	C₂²×C₃	semidirect
251. C₃×D₄	#41	semidirect
264. C₂×C₃×C₄	#41	semidirect
390. D₄	C₃×#41	semidirect
403. C₂×C₄	C₃×#41	semidirect
451. C₃	#3475	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#556	2
C₃×#555	2
C₃×#554	2
C₃×#553	2
C₃×#552	2
C₃×#551	2
C₃×#547	2
C₃×#546	2
C₃×#533	2
C₃×#529	2
C₃×#525	2
C₃×C₄×#41	2
C₂×C₃×C₄×D₄	2
C₂×C₃×#117	2
#3475	3

Subgroups — C3×#3475 #87359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3475 #87359