Subgroups — C₃×#3495 #87379

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 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	2	yes	maximal, complemented
2	C₃×#554	C₂	1	2	yes	maximal, complemented
3	C₃×#552	C₂	1	2	yes	maximal, complemented
4	C₃×#552	C₂	1	4	yes	maximal, complemented
5	C₃×#552	C₂	1	2	yes	maximal, complemented
6	C₃×#551	C₂	1	4	yes	maximal, complemented
7	C₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#542	C₂	1	2	yes	maximal, complemented
9	C₃×#541	C₂	1	2	yes	maximal, complemented
10	C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#533	C₂	1	2	yes	maximal, complemented
12	C₃×#529	C₂	1	2	yes	maximal, complemented
13	C₃×#525	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	#3495	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
22	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×#126	C₂²	1	4	yes	—
26	C₃×#126	C₂²	1	4	yes	—
27	C₃×#126	C₂²	1	4	yes	complemented
28	C₃×#126	C₂²	1	4	yes	complemented
29	C₃×#125	C₂²	1	2	yes	complemented
30	C₃×#125	C₂²	1	4	yes	complemented
31	C₃×#125	C₂²	1	4	yes	complemented
32	C₃×#125	C₂²	1	4	yes	complemented
33	C₃×#125	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	4	yes	—
35	C₃×#124	C₂²	1	2	yes	complemented
36	C₃×#123	C₂²	1	2	yes	—
37	C₃×#123	C₂²	1	4	yes	—
38	C₃×#123	C₂²	1	4	yes	—
39	C₃×#123	C₂²	1	4	yes	—
40	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
49	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
50	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
51	C₃×#121	C₂²	1	1	yes	characteristic
52	C₃×#121	C₂²	1	1	yes	characteristic
53	C₃×#120	C₂²	1	2	yes	—
54	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
55	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
56	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
57	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
58	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
59	C₃×C₄×Q₈	C₂²	1	4	yes	complemented
60	C₃×C₄×D₄	C₂²	1	4	yes	—
61	C₃×C₄×D₄	C₂²	1	2	yes	—
62	C₃×C₄×D₄	C₂²	1	2	yes	—
63	C₃×C₄×D₄	C₂²	1	4	yes	—
64	C₃×C₄×D₄	C₂²	1	2	yes	complemented
65	C₃×#117	C₂²	1	1	yes	characteristic
66	C₃×#117	C₂²	1	1	yes	characteristic
67	C₃×#117	C₂²	1	2	yes	—
68	C₃×#117	C₂²	1	1	yes	characteristic
69	C₃×#117	C₂²	1	2	yes	—
70	C₃×#117	C₂²	1	1	yes	characteristic
71	C₃×#117	C₂²	1	1	yes	characteristic
72	C₃×#117	C₂²	1	4	yes	—
73	C₃×#117	C₂²	1	4	yes	—
74	C₃×#117	C₂²	1	2	yes	complemented
75	C₃×#117	C₂²	1	4	yes	complemented
76	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
80	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₂×C₃×C₄²	C₂²	1	2	yes	—
84	#556	C₂×C₃	1	2	yes	complemented
85	#554	C₂×C₃	1	2	yes	complemented
86	#552	C₂×C₃	1	2	yes	complemented
87	#552	C₂×C₃	1	4	yes	complemented
88	#552	C₂×C₃	1	2	yes	complemented
89	#551	C₂×C₃	1	4	yes	complemented
90	#544	C₂×C₃	1	1	yes	characteristic, complemented
91	#542	C₂×C₃	1	2	yes	complemented
92	#541	C₂×C₃	1	2	yes	complemented
93	#536	C₂×C₃	1	1	yes	characteristic, complemented
94	#533	C₂×C₃	1	2	yes	complemented
95	#529	C₂×C₃	1	2	yes	complemented
96	#525	C₂×C₃	1	1	yes	characteristic
97	C₂×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
98	#520	C₂×C₃	1	1	yes	characteristic, complemented
99	#519	C₂×C₃	1	1	yes	characteristic, complemented
100	C₂×#117	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂⁴×C₃	C₂³	1	1	yes	characteristic
102	C₃×#41	—	2	4	no	—
103	C₂×C₃×Q₈	—	2	4	no	—
104	C₂×C₃×Q₈	C₂³	1	2	yes	—
105	C₂×C₃×Q₈	C₂³	1	2	yes	—
106	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×Q₈	C₂³	1	4	yes	—
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	2	yes	—
112	C₂²×C₃×C₄	—	2	4	no	—
113	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂³	1	2	yes	—
115	C₂²×C₃×C₄	C₂³	1	2	yes	—
116	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₂³	1	2	yes	—
119	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₄	C₂³	1	2	yes	—
122	C₂²×C₃×C₄	C₂³	1	2	yes	—
123	C₂²×C₃×C₄	C₂³	1	4	yes	—
124	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
125	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
133	C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₃×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₃×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₃×C₄²	C₂³	1	2	yes	—
162	C₃×C₄²	C₂³	1	2	yes	—
163	C₃×C₄²	C₂³	1	2	yes	—
164	C₃×C₄²	C₂³	1	2	yes	—
165	C₃×C₄²	C₂³	1	4	yes	—
166	C₃×C₄²	C₂³	1	4	yes	—
167	C₃×C₄²	C₂³	1	4	yes	—
168	C₃×C₄²	C₂³	1	2	yes	—
169	C₂×#41	C₂²×C₃	1	1	yes	characteristic
170	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic
171	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
172	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
173	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
174	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
175	#126	C₂²×C₃	1	4	yes	—
176	#126	C₂²×C₃	1	4	yes	—
177	#126	C₂²×C₃	1	4	yes	complemented
178	#126	C₂²×C₃	1	4	yes	complemented
179	#125	C₂²×C₃	1	2	yes	complemented
180	#125	C₂²×C₃	1	4	yes	complemented
181	#125	C₂²×C₃	1	4	yes	complemented
182	#125	C₂²×C₃	1	4	yes	complemented
183	#125	C₂²×C₃	1	2	yes	complemented
184	#124	C₂²×C₃	1	4	yes	—
185	#124	C₂²×C₃	1	2	yes	complemented
186	#123	C₂²×C₃	1	2	yes	—
187	#123	C₂²×C₃	1	4	yes	—
188	#123	C₂²×C₃	1	4	yes	—
189	#123	C₂²×C₃	1	4	yes	—
190	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
191	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
192	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
193	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
194	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
195	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
196	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
197	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
198	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
199	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
200	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
201	#121	C₂²×C₃	1	1	yes	characteristic
202	#121	C₂²×C₃	1	1	yes	characteristic
203	#120	C₂²×C₃	1	2	yes	—
204	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
205	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
206	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
207	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
208	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
209	C₄×Q₈	C₂²×C₃	1	4	yes	complemented
210	C₄×D₄	C₂²×C₃	1	4	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	—
214	C₄×D₄	C₂²×C₃	1	2	yes	complemented
215	#117	C₂²×C₃	1	1	yes	characteristic
216	#117	C₂²×C₃	1	1	yes	characteristic
217	#117	C₂²×C₃	1	2	yes	—
218	#117	C₂²×C₃	1	1	yes	characteristic
219	#117	C₂²×C₃	1	2	yes	—
220	#117	C₂²×C₃	1	1	yes	characteristic
221	#117	C₂²×C₃	1	1	yes	characteristic
222	#117	C₂²×C₃	1	4	yes	—
223	#117	C₂²×C₃	1	4	yes	—
224	#117	C₂²×C₃	1	2	yes	complemented
225	#117	C₂²×C₃	1	4	yes	complemented
226	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
230	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
231	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂×C₄²	C₂²×C₃	1	2	yes	—
234	C₂³×C₃	—	2	2	no	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	4	1	no	—
237	C₂³×C₃	C₂⁴	1	1	yes	characteristic
238	C₂³×C₃	C₂⁴	1	2	yes	—
239	C₂³×C₃	C₂⁴	1	1	yes	characteristic
240	C₂³×C₃	C₂⁴	1	1	yes	characteristic
241	C₃×Q₈	—	2	4	no	—
242	C₃×Q₈	—	2	4	no	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	4	4	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	2	2	no	—
248	C₃×D₄	—	4	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	4	2	no	—
260	C₂×C₃×C₄	#41	1	4	yes	—
261	C₂×C₃×C₄	C₂⁴	1	2	yes	—
262	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂⁴	1	2	yes	—
264	C₂×C₃×C₄	C₂⁴	1	2	yes	—
265	C₂×C₃×C₄	C₂⁴	1	2	yes	—
266	C₂×C₃×C₄	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄	C₂⁴	1	4	yes	—
268	C₂×C₃×C₄	C₂⁴	1	2	yes	—
269	C₂×C₃×C₄	C₂⁴	1	2	yes	—
270	C₂×C₃×C₄	C₂⁴	1	4	yes	—
271	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
274	C₂⁴	C₂³×C₃	1	1	yes	characteristic
275	#41	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	C₂³×C₃	1	2	yes	—
278	C₂×Q₈	C₂³×C₃	1	2	yes	—
279	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
280	C₂×Q₈	C₂³×C₃	1	4	yes	—
281	C₂×D₄	C₂³×C₃	1	2	yes	—
282	C₂×D₄	C₂³×C₃	1	2	yes	—
283	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
284	C₂×D₄	C₂³×C₃	1	2	yes	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₃	1	2	yes	—
288	C₂²×C₄	C₂³×C₃	1	2	yes	—
289	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₃	1	2	yes	—
292	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₃	1	2	yes	—
295	C₂²×C₄	C₂³×C₃	1	2	yes	—
296	C₂²×C₄	C₂³×C₃	1	4	yes	—
297	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
298	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
299	C₄⋊C₄	C₂³×C₃	1	2	yes	—
300	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
301	C₄⋊C₄	C₂³×C₃	1	2	yes	—
302	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
303	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
304	C₄⋊C₄	C₂³×C₃	1	2	yes	—
305	C₄⋊C₄	C₂³×C₃	1	4	yes	—
306	C₄⋊C₄	C₂³×C₃	1	2	yes	—
307	C₄⋊C₄	C₂³×C₃	1	4	yes	—
308	C₄⋊C₄	C₂³×C₃	1	4	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	4	yes	—
312	C₄⋊C₄	C₂³×C₃	1	4	yes	—
313	C₄⋊C₄	C₂³×C₃	1	4	yes	—
314	C₄⋊C₄	C₂³×C₃	1	4	yes	—
315	C₄⋊C₄	C₂³×C₃	1	4	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	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
321	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
322	C₂²⋊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	4	yes	—
326	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
327	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
328	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
329	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
330	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
331	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
332	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
334	C₄²	C₂³×C₃	1	2	yes	—
335	C₄²	C₂³×C₃	1	2	yes	—
336	C₄²	C₂³×C₃	1	2	yes	—
337	C₄²	C₂³×C₃	1	2	yes	—
338	C₄²	C₂³×C₃	1	4	yes	—
339	C₄²	C₂³×C₃	1	4	yes	—
340	C₄²	C₂³×C₃	1	4	yes	—
341	C₄²	C₂³×C₃	1	2	yes	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	C₂×#41	1	2	yes	—
354	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
355	C₂²×C₃	C₂⁵	1	1	yes	characteristic
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	C₂×#41	1	2	yes	—
368	C₃×C₄	C₂×#41	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	C₂⁴×C₃	1	1	yes	characteristic
373	C₂³	C₂⁴×C₃	1	2	yes	—
374	C₂³	C₂⁴×C₃	1	1	yes	characteristic
375	C₂³	C₂⁴×C₃	1	1	yes	characteristic
376	Q₈	—	2	4	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	4	no	—
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	C₃×#41	1	4	yes	—
396	C₂×C₄	C₂⁴×C₃	1	2	yes	—
397	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
398	C₂×C₄	C₂⁴×C₃	1	2	yes	—
399	C₂×C₄	C₂⁴×C₃	1	2	yes	—
400	C₂×C₄	C₂⁴×C₃	1	2	yes	—
401	C₂×C₄	C₂⁴×C₃	1	2	yes	—
402	C₂×C₄	C₂⁴×C₃	1	4	yes	—
403	C₂×C₄	C₂⁴×C₃	1	2	yes	—
404	C₂×C₄	C₂⁴×C₃	1	2	yes	—
405	C₂×C₄	C₂⁴×C₃	1	4	yes	—
406	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
407	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
408	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
409	C₂×C₃	—	2	2	no	—
410	C₂×C₃	—	2	2	no	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	—	4	1	no	—
413	C₂×C₃	C₂²×#41	1	1	yes	characteristic
414	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
415	C₂×C₃	#585	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	C₂×C₃×#41	1	2	yes	—
428	C₂²	C₃×2₋¹⁺⁴	1	2	yes	—
429	C₂²	C₂⁵×C₃	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	C₂×C₃×#41	1	2	yes	—
442	C₄	C₂×C₃×#41	1	2	yes	—
443	C₃	#3495	1	1	yes	characteristic, direct product factor, Sylow
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	4	2	no	—
448	C₂	C₂²×C₃×#41	1	1	yes	characteristic
449	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
prime radical	C₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#556	C₂	semidirect
2. C₃×#554	C₂	semidirect
3. C₃×#552	C₂	semidirect
4. C₃×#552	C₂	semidirect
5. C₃×#552	C₂	semidirect
6. C₃×#551	C₂	semidirect
7. C₃×#544	C₂	semidirect
8. C₃×#542	C₂	semidirect
9. C₃×#541	C₂	semidirect
10. C₃×#536	C₂	semidirect
11. C₃×#533	C₂	semidirect
12. C₃×#529	C₂	semidirect
14. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
15. C₃×#520	C₂	semidirect
16. C₃×#519	C₂	semidirect
17. C₂×C₃×#117	C₂	semidirect
18. #3495	C₃	direct (N × H)
22. C₃×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₄⋊Q₈	C₂²	semidirect
27. C₃×#126	C₂²	semidirect
28. C₃×#126	C₂²	semidirect
29. C₃×#125	C₂²	semidirect
30. C₃×#125	C₂²	semidirect
31. C₃×#125	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
33. C₃×#125	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
48. C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₃×C₂²⋊Q₈	C₂²	semidirect
50. C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₃×C₄×Q₈	C₂²	semidirect
55. C₃×C₄×Q₈	C₂²	semidirect
56. C₃×C₄×Q₈	C₂²	semidirect
57. C₃×C₄×Q₈	C₂²	semidirect
58. C₃×C₄×Q₈	C₂²	semidirect
59. C₃×C₄×Q₈	C₂²	semidirect
64. C₃×C₄×D₄	C₂²	semidirect
74. C₃×#117	C₂²	semidirect
75. C₃×#117	C₂²	semidirect
80. C₂×C₃×C₄⋊C₄	C₂²	semidirect
84. #556	C₂×C₃	semidirect
85. #554	C₂×C₃	semidirect
86. #552	C₂×C₃	semidirect
87. #552	C₂×C₃	semidirect
88. #552	C₂×C₃	semidirect
89. #551	C₂×C₃	semidirect
90. #544	C₂×C₃	semidirect
91. #542	C₂×C₃	semidirect
92. #541	C₂×C₃	semidirect
93. #536	C₂×C₃	semidirect
94. #533	C₂×C₃	semidirect
95. #529	C₂×C₃	semidirect
97. C₂×C₂²⋊Q₈	C₂×C₃	semidirect
98. #520	C₂×C₃	semidirect
99. #519	C₂×C₃	semidirect
100. C₂×#117	C₂×C₃	semidirect
172. C₄⋊Q₈	C₂²×C₃	semidirect
173. C₄⋊Q₈	C₂²×C₃	semidirect
174. C₄⋊Q₈	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
182. #125	C₂²×C₃	semidirect
183. #125	C₂²×C₃	semidirect
185. #124	C₂²×C₃	semidirect
198. C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₂²⋊Q₈	C₂²×C₃	semidirect
200. C₂²⋊Q₈	C₂²×C₃	semidirect
204. C₄×Q₈	C₂²×C₃	semidirect
205. C₄×Q₈	C₂²×C₃	semidirect
206. C₄×Q₈	C₂²×C₃	semidirect
207. C₄×Q₈	C₂²×C₃	semidirect
208. C₄×Q₈	C₂²×C₃	semidirect
209. C₄×Q₈	C₂²×C₃	semidirect
214. C₄×D₄	C₂²×C₃	semidirect
224. #117	C₂²×C₃	semidirect
225. #117	C₂²×C₃	semidirect
230. C₂×C₄⋊C₄	C₂²×C₃	semidirect
443. C₃	#3495	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×#554	2
C₃×#552	2
C₃×#551	2
C₃×#544	2
C₃×#542	2
C₃×#541	2
C₃×#536	2
C₃×#533	2
C₃×#529	2
C₃×#525	2
C₂×C₃×C₂²⋊Q₈	2
C₃×#520	2
C₃×#519	2
C₂×C₃×#117	2
#3495	3

Subgroups — C3×#3495 #87379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3495 #87379