Subgroups — C₃×#3552 #87436

Order 384.

1004 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	4	yes	maximal, complemented
2	C₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#554	C₂	1	2	yes	maximal, complemented
5	C₃×#553	C₂	1	2	yes	maximal, complemented
6	C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₄×Q₈	C₂	1	2	yes	maximal, complemented
8	C₃×#548	C₂	1	2	yes	maximal, complemented
9	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#544	C₂	1	2	yes	maximal, complemented
11	C₃×#542	C₂	1	2	yes	maximal, complemented
12	C₃×#541	C₂	1	2	yes	maximal, complemented
13	C₃×#539	C₂	1	4	yes	maximal, complemented
14	C₃×#536	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	#3552	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×#41	C₂²	1	2	yes	—
20	C₂²×C₃×Q₈	C₂²	1	2	yes	—
21	C₂²×C₃×Q₈	C₂²	1	2	yes	—
22	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
29	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₃×#126	C₂²	1	2	yes	—
31	C₃×#126	C₂²	1	2	yes	—
32	C₃×#126	C₂²	1	4	yes	—
33	C₃×#126	C₂²	1	4	yes	—
34	C₃×#126	C₂²	1	4	yes	—
35	C₃×#125	C₂²	1	4	yes	—
36	C₃×#125	C₂²	1	4	yes	—
37	C₃×#125	C₂²	1	1	yes	characteristic
38	C₃×#125	C₂²	1	1	yes	characteristic
39	C₃×#125	C₂²	1	4	yes	—
40	C₃×#125	C₂²	1	2	yes	—
41	C₃×#124	C₂²	1	4	yes	—
42	C₃×#124	C₂²	1	1	yes	characteristic
43	C₃×#124	C₂²	1	1	yes	characteristic
44	C₃×#124	C₂²	1	2	yes	—
45	C₃×#123	C₂²	1	4	yes	—
46	C₃×#123	C₂²	1	4	yes	—
47	C₃×#123	C₂²	1	2	yes	—
48	C₃×#123	C₂²	1	2	yes	—
49	C₃×#123	C₂²	1	4	yes	—
50	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
51	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
52	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
54	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
57	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
58	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₃×#121	C₂²	1	1	yes	characteristic
62	C₃×#121	C₂²	1	1	yes	characteristic
63	C₃×#121	C₂²	1	4	yes	—
64	C₃×#121	C₂²	1	2	yes	—
65	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
66	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
67	C₃×C₄×Q₈	C₂²	1	2	yes	—
68	C₃×C₄×Q₈	C₂²	1	2	yes	—
69	C₃×C₄×Q₈	C₂²	1	2	yes	—
70	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
71	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
72	C₃×C₄×D₄	C₂²	1	2	yes	—
73	C₃×C₄×D₄	C₂²	1	2	yes	—
74	C₃×C₄×D₄	C₂²	1	4	yes	—
75	C₃×C₄×D₄	C₂²	1	4	yes	—
76	C₃×C₄×D₄	C₂²	1	2	yes	—
77	C₃×#117	C₂²	1	2	yes	—
78	C₃×#117	C₂²	1	2	yes	—
79	C₃×#117	C₂²	1	2	yes	—
80	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
81	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
83	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
84	#563	C₂×C₃	1	4	yes	complemented
85	#557	C₂×C₃	1	1	yes	characteristic, complemented
86	#556	C₂×C₃	1	1	yes	characteristic, complemented
87	#554	C₂×C₃	1	2	yes	complemented
88	#553	C₂×C₃	1	2	yes	complemented
89	D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
90	D₄×Q₈	C₂×C₃	1	2	yes	complemented
91	#548	C₂×C₃	1	2	yes	complemented
92	#547	C₂×C₃	1	1	yes	characteristic, complemented
93	#544	C₂×C₃	1	2	yes	complemented
94	#542	C₂×C₃	1	2	yes	complemented
95	#541	C₂×C₃	1	2	yes	complemented
96	#539	C₂×C₃	1	4	yes	complemented
97	#536	C₂×C₃	1	2	yes	complemented
98	C₂×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
99	#529	C₂×C₃	1	1	yes	characteristic, complemented
100	#529	C₂×C₃	1	1	yes	characteristic, complemented
101	C₃×#41	—	4	4	no	—
102	C₂×C₃×Q₈	—	4	4	no	—
103	C₂×C₃×Q₈	—	4	4	no	—
104	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×Q₈	C₂³	1	2	yes	—
108	C₂×C₃×Q₈	C₂³	1	4	yes	—
109	C₂×C₃×Q₈	C₂³	1	4	yes	—
110	C₂×C₃×D₄	C₂³	1	2	yes	—
111	C₂×C₃×D₄	C₂³	1	2	yes	—
112	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
113	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃×D₄	C₂³	1	4	yes	—
115	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
120	C₂²×C₃×C₄	C₂³	1	4	yes	—
121	C₂²×C₃×C₄	C₂³	1	4	yes	—
122	C₂²×C₃×C₄	C₂³	1	4	yes	—
123	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊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	2	yes	—
150	C₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
156	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₃×C₄²	C₂³	1	1	yes	characteristic
162	C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₃×C₄²	C₂³	1	1	yes	characteristic
165	C₃×C₄²	C₂³	1	2	yes	—
166	C₃×C₄²	C₂³	1	2	yes	—
167	C₃×C₄²	C₂³	1	4	yes	—
168	C₃×C₄²	C₂³	1	4	yes	—
169	C₂×#41	C₂²×C₃	1	2	yes	—
170	C₂²×Q₈	C₂²×C₃	1	2	yes	—
171	C₂²×Q₈	C₂²×C₃	1	2	yes	—
172	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
173	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
174	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
175	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
176	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
177	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
178	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
179	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
180	#126	C₂²×C₃	1	2	yes	—
181	#126	C₂²×C₃	1	2	yes	—
182	#126	C₂²×C₃	1	4	yes	—
183	#126	C₂²×C₃	1	4	yes	—
184	#126	C₂²×C₃	1	4	yes	—
185	#125	C₂²×C₃	1	1	yes	characteristic
186	#125	C₂²×C₃	1	1	yes	characteristic
187	#125	C₂²×C₃	1	4	yes	—
188	#125	C₂²×C₃	1	4	yes	—
189	#125	C₂²×C₃	1	4	yes	—
190	#125	C₂²×C₃	1	2	yes	—
191	#124	C₂²×C₃	1	1	yes	characteristic
192	#124	C₂²×C₃	1	1	yes	characteristic
193	#124	C₂²×C₃	1	2	yes	—
194	#124	C₂²×C₃	1	4	yes	—
195	#123	C₂²×C₃	1	2	yes	—
196	#123	C₂²×C₃	1	2	yes	—
197	#123	C₂²×C₃	1	4	yes	—
198	#123	C₂²×C₃	1	4	yes	—
199	#123	C₂²×C₃	1	4	yes	—
200	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
201	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
202	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
203	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
204	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
205	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
206	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
207	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
208	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
209	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
210	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
211	#121	C₂²×C₃	1	1	yes	characteristic
212	#121	C₂²×C₃	1	1	yes	characteristic
213	#121	C₂²×C₃	1	4	yes	—
214	#121	C₂²×C₃	1	2	yes	—
215	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
216	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
217	C₄×Q₈	C₂²×C₃	1	2	yes	—
218	C₄×Q₈	C₂²×C₃	1	2	yes	—
219	C₄×Q₈	C₂²×C₃	1	2	yes	—
220	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
221	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
222	C₄×D₄	C₂²×C₃	1	2	yes	—
223	C₄×D₄	C₂²×C₃	1	2	yes	—
224	C₄×D₄	C₂²×C₃	1	4	yes	—
225	C₄×D₄	C₂²×C₃	1	4	yes	—
226	C₄×D₄	C₂²×C₃	1	2	yes	—
227	#117	C₂²×C₃	1	2	yes	—
228	#117	C₂²×C₃	1	2	yes	—
229	#117	C₂²×C₃	1	2	yes	—
230	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
231	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
234	C₂³×C₃	C₂⁴	1	2	yes	—
235	C₂³×C₃	C₂⁴	1	2	yes	—
236	C₂³×C₃	C₂⁴	1	1	yes	characteristic
237	C₃×Q₈	—	2	4	no	—
238	C₃×Q₈	—	2	2	no	—
239	C₃×Q₈	—	2	4	no	—
240	C₃×Q₈	—	2	2	no	—
241	C₃×Q₈	—	4	4	no	—
242	C₃×Q₈	—	4	4	no	—
243	C₃×D₄	—	2	4	no	—
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	2	2	no	—
246	C₃×D₄	—	2	2	no	—
247	C₃×D₄	—	4	4	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	4	4	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	—	4	4	no	—
256	C₂×C₃×C₄	C₂⁴	1	2	yes	—
257	C₂×C₃×C₄	C₂⁴	1	2	yes	—
258	C₂×C₃×C₄	C₂⁴	1	2	yes	—
259	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂⁴	1	2	yes	—
263	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂⁴	1	2	yes	—
265	C₂×C₃×C₄	C₂⁴	1	4	yes	—
266	C₂×C₃×C₄	C₂⁴	1	4	yes	—
267	C₂×C₃×C₄	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
270	#41	—	4	4	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	4	no	—
273	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
275	C₂×Q₈	C₂³×C₃	1	2	yes	—
276	C₂×Q₈	C₂³×C₃	1	2	yes	—
277	C₂×Q₈	C₂³×C₃	1	4	yes	—
278	C₂×Q₈	C₂³×C₃	1	4	yes	—
279	C₂×D₄	C₂³×C₃	1	2	yes	—
280	C₂×D₄	C₂³×C₃	1	2	yes	—
281	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
282	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
283	C₂×D₄	C₂³×C₃	1	4	yes	—
284	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
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	4	yes	—
290	C₂²×C₄	C₂³×C₃	1	4	yes	—
291	C₂²×C₄	C₂³×C₃	1	4	yes	—
292	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
293	C₄⋊C₄	C₂³×C₃	1	2	yes	—
294	C₄⋊C₄	C₂³×C₃	1	2	yes	—
295	C₄⋊C₄	C₂³×C₃	1	4	yes	—
296	C₄⋊C₄	C₂³×C₃	1	2	yes	—
297	C₄⋊C₄	C₂³×C₃	1	4	yes	—
298	C₄⋊C₄	C₂³×C₃	1	4	yes	—
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	2	yes	—
303	C₄⋊C₄	C₂³×C₃	1	2	yes	—
304	C₄⋊C₄	C₂³×C₃	1	2	yes	—
305	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₄⋊C₄	C₂³×C₃	1	4	yes	—
307	C₄⋊C₄	C₂³×C₃	1	2	yes	—
308	C₄⋊C₄	C₂³×C₃	1	4	yes	—
309	C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
315	C₄⋊C₄	C₂³×C₃	1	2	yes	—
316	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
317	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
318	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
319	C₂²⋊C₄	C₂³×C₃	1	2	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	4	yes	—
324	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
325	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
326	C₂²⋊C₄	C₂³×C₃	1	2	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	C₄²	C₂³×C₃	1	1	yes	characteristic
331	C₄²	C₂³×C₃	1	1	yes	characteristic
332	C₄²	C₂³×C₃	1	1	yes	characteristic
333	C₄²	C₂³×C₃	1	1	yes	characteristic
334	C₄²	C₂³×C₃	1	2	yes	—
335	C₄²	C₂³×C₃	1	2	yes	—
336	C₄²	C₂³×C₃	1	4	yes	—
337	C₄²	C₂³×C₃	1	4	yes	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	2	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
347	C₂²×C₃	C₂⁵	1	1	yes	characteristic
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	4	no	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
361	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
362	C₂³	C₂⁴×C₃	1	2	yes	—
363	C₂³	C₂⁴×C₃	1	2	yes	—
364	C₂³	C₂⁴×C₃	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	4	no	—
370	Q₈	—	4	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	C₂⁴×C₃	1	2	yes	—
385	C₂×C₄	C₂⁴×C₃	1	2	yes	—
386	C₂×C₄	C₂⁴×C₃	1	2	yes	—
387	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
388	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
389	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
390	C₂×C₄	C₂⁴×C₃	1	2	yes	—
391	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
392	C₂×C₄	C₂⁴×C₃	1	2	yes	—
393	C₂×C₄	C₂⁴×C₃	1	4	yes	—
394	C₂×C₄	C₂⁴×C₃	1	4	yes	—
395	C₂×C₄	C₂⁴×C₃	1	2	yes	—
396	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
397	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
398	C₂×C₃	—	2	2	no	—
399	C₂×C₃	—	4	2	no	—
400	C₂×C₃	—	4	2	no	—
401	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	C₃×2₋¹⁺⁴	1	2	yes	—
413	C₂²	C₂⁵×C₃	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
427	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
428	C₃	#3552	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	4	2	no	—
432	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
434	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
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×#563	C₂	semidirect
2. C₃×#557	C₂	semidirect
3. C₃×#556	C₂	semidirect
4. C₃×#554	C₂	semidirect
5. C₃×#553	C₂	semidirect
6. C₃×D₄×Q₈	C₂	semidirect
7. C₃×D₄×Q₈	C₂	semidirect
8. C₃×#548	C₂	semidirect
9. C₃×#547	C₂	semidirect
10. C₃×#544	C₂	semidirect
11. C₃×#542	C₂	semidirect
12. C₃×#541	C₂	semidirect
13. C₃×#539	C₂	semidirect
14. C₃×#536	C₂	semidirect
15. C₂×C₃×C₄⋊Q₈	C₂	semidirect
16. C₃×#529	C₂	semidirect
17. C₃×#529	C₂	semidirect
18. #3552	C₃	direct (N × H)
84. #563	C₂×C₃	semidirect
85. #557	C₂×C₃	semidirect
86. #556	C₂×C₃	semidirect
87. #554	C₂×C₃	semidirect
88. #553	C₂×C₃	semidirect
89. D₄×Q₈	C₂×C₃	semidirect
90. D₄×Q₈	C₂×C₃	semidirect
91. #548	C₂×C₃	semidirect
92. #547	C₂×C₃	semidirect
93. #544	C₂×C₃	semidirect
94. #542	C₂×C₃	semidirect
95. #541	C₂×C₃	semidirect
96. #539	C₂×C₃	semidirect
97. #536	C₂×C₃	semidirect
98. C₂×C₄⋊Q₈	C₂×C₃	semidirect
99. #529	C₂×C₃	semidirect
100. #529	C₂×C₃	semidirect
428. C₃	#3552	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×#563	2
C₃×#557	2
C₃×#556	2
C₃×#554	2
C₃×#553	2
C₃×D₄×Q₈	2
C₃×#548	2
C₃×#547	2
C₃×#544	2
C₃×#542	2
C₃×#541	2
C₃×#539	2
C₃×#536	2
C₂×C₃×C₄⋊Q₈	2
C₃×#529	2
#3552	3

Subgroups — C3×#3552 #87436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3552 #87436