Subgroups — C₃×#10872 #10629479

Order 768.

730 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#344	C₂	1	2	yes	maximal
5	C₃×#1733	C₂	1	2	yes	maximal
6	#10872	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×#117	C₂²	1	2	yes	—
11	C₂×C₃×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃×#108	—	2	1	no	—
13	C₂×C₃×#108	—	2	1	no	—
14	C₂×C₃×#108	—	2	2	no	—
15	C₂×C₃×#108	C₄	1	4	yes	complemented
16	C₃×#427	—	2	2	no	—
17	C₃×#427	C₄	1	4	yes	complemented
18	C₂×C₃×#107	—	2	1	no	—
19	C₂×C₃×#106	—	2	1	no	—
20	C₃×#405	—	2	1	no	—
21	C₃×#405	—	2	1	no	—
22	C₃×#405	C₄	1	2	yes	complemented
23	C₃×#405	C₄	1	2	yes	complemented
24	C₂×C₃×#97	—	2	1	no	—
25	C₂×C₃×C₄×C₈	—	2	1	no	—
26	C₃×#344	—	2	4	no	—
27	C₃×#339	—	2	4	no	—
28	C₂²×#108	C₂×C₃	1	1	yes	characteristic
29	C₂×#427	C₂×C₃	1	1	yes	characteristic
30	C₂×#405	C₂×C₃	1	1	yes	characteristic
31	C₂×#344	C₂×C₃	1	2	yes	—
32	#1733	C₂×C₃	1	2	yes	—
33	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
34	C₂×C₃×M₁₆	—	2	1	no	—
35	C₂×C₃×M₁₆	—	2	1	no	—
36	C₂×C₃×M₁₆	—	2	1	no	—
37	C₂×C₃×M₁₆	—	2	2	no	—
38	C₂×C₃×M₁₆	—	2	2	no	—
39	C₂×C₃×M₁₆	—	2	2	no	—
40	C₂×C₃×M₁₆	—	2	2	no	—
41	C₂×C₃×M₁₆	—	2	2	no	—
42	C₂×C₃×M₁₆	C₂×C₄	1	4	yes	—
43	C₂×C₃×M₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₃×M₁₆	D₄	1	2	yes	—
45	C₂×C₃×M₁₆	Q₈	1	2	yes	—
46	C₂²×C₃×C₈	—	2	1	no	—
47	C₂²×C₃×C₈	—	2	2	no	—
48	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
51	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
52	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₈	D₄	1	2	yes	—
57	C₂²×C₃×C₈	Q₈	1	2	yes	—
58	C₃×#117	—	2	1	no	—
59	C₃×#117	—	2	1	no	—
60	C₃×#117	—	2	2	no	—
61	C₃×#117	—	2	2	no	—
62	C₃×#117	—	2	2	no	—
63	C₃×#117	C₂×C₄	1	4	yes	—
64	C₃×#117	C₂×C₄	1	2	yes	—
65	C₃×#117	D₄	1	2	yes	—
66	C₂×C₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₃×C₄⋊C₄	Q₈	1	2	yes	—
68	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₃×C₄²	—	2	1	no	—
71	C₂×C₃×C₄²	—	2	2	no	—
72	C₃×#108	—	2	4	no	—
73	C₃×#108	—	2	4	no	—
74	C₃×#107	—	2	4	no	—
75	C₃×#106	—	2	4	no	—
76	C₃×#97	—	2	2	no	—
77	C₃×#97	—	2	2	no	—
78	C₃×C₄×C₈	—	2	2	no	—
79	C₃×C₄×C₈	—	2	2	no	—
80	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
81	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
82	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×#117	C₂²×C₃	1	2	yes	—
84	C₂×#117	C₂²×C₃	1	1	yes	characteristic
85	C₂×#108	—	2	1	no	—
86	C₂×#108	—	2	1	no	—
87	C₂×#108	—	2	2	no	—
88	C₂×#108	C₃×C₄	1	4	yes	complemented
89	#427	—	2	2	no	—
90	#427	C₃×C₄	1	4	yes	complemented
91	C₂×#107	—	2	1	no	—
92	C₂×#106	—	2	1	no	—
93	#405	—	2	1	no	—
94	#405	—	2	1	no	—
95	#405	C₃×C₄	1	2	yes	complemented
96	#405	C₃×C₄	1	2	yes	complemented
97	C₂×#97	—	2	1	no	—
98	C₂×C₄×C₈	—	2	1	no	—
99	#344	—	2	4	no	—
100	#339	—	2	4	no	—
101	C₂⁴×C₃	#41	1	1	yes	characteristic
102	C₂²×C₃×C₄	—	2	2	no	—
103	C₂²×C₃×C₄	—	4	2	no	—
104	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
115	C₂²×C₃×C₄	#41	1	1	yes	characteristic
116	C₂²×C₃×C₄	#41	1	1	yes	characteristic
117	C₂²×C₃×C₄	#41	1	1	yes	characteristic
118	C₃×M₁₆	—	2	2	no	—
119	C₃×M₁₆	—	2	2	no	—
120	C₃×M₁₆	—	2	2	no	—
121	C₃×M₁₆	—	2	4	no	—
122	C₃×M₁₆	—	2	4	no	—
123	C₃×M₁₆	—	4	2	no	—
124	C₃×M₁₆	—	4	2	no	—
125	C₃×M₁₆	C₄⋊C₄	1	4	yes	—
126	C₂×C₃×C₈	—	2	2	no	—
127	C₂×C₃×C₈	—	2	2	no	—
128	C₂×C₃×C₈	—	2	2	no	—
129	C₂×C₃×C₈	—	2	4	no	—
130	C₂×C₃×C₈	—	4	2	no	—
131	C₂×C₃×C₈	—	4	2	no	—
132	C₂×C₃×C₈	C₄²	1	2	yes	—
133	C₂×C₃×C₈	C₄²	1	2	yes	—
134	C₂×C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
139	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
140	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
141	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
142	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
143	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
144	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
145	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
146	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
147	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
148	C₃×C₄⋊C₄	—	2	2	no	—
149	C₃×C₄⋊C₄	—	2	4	no	—
150	C₃×C₄⋊C₄	—	4	2	no	—
151	C₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
152	C₃×C₂²⋊C₄	—	2	2	no	—
153	C₃×C₂²⋊C₄	—	2	2	no	—
154	C₃×C₂²⋊C₄	—	2	4	no	—
155	C₃×C₂²⋊C₄	—	4	2	no	—
156	C₃×C₄²	—	2	2	no	—
157	C₃×C₄²	—	2	2	no	—
158	C₃×C₄²	—	2	4	no	—
159	C₃×C₄²	—	4	2	no	—
160	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂×M₁₆	—	2	1	no	—
162	C₂×M₁₆	—	2	1	no	—
163	C₂×M₁₆	—	2	1	no	—
164	C₂×M₁₆	—	2	2	no	—
165	C₂×M₁₆	—	2	2	no	—
166	C₂×M₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	C₂×C₃×C₄	1	4	yes	—
170	C₂×M₁₆	C₂×C₃×C₄	1	2	yes	—
171	C₂×M₁₆	C₃×D₄	1	2	yes	—
172	C₂×M₁₆	C₃×Q₈	1	2	yes	—
173	C₂²×C₈	—	2	1	no	—
174	C₂²×C₈	—	2	2	no	—
175	C₂²×C₈	C₂×C₃×C₄	1	1	yes	characteristic
176	C₂²×C₈	C₂×C₃×C₄	1	1	yes	characteristic
177	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
178	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
179	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
180	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
181	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₈	C₃×D₄	1	2	yes	—
184	C₂²×C₈	C₃×Q₈	1	2	yes	—
185	#117	—	2	1	no	—
186	#117	—	2	1	no	—
187	#117	—	2	2	no	—
188	#117	—	2	2	no	—
189	#117	—	2	2	no	—
190	#117	C₂×C₃×C₄	1	4	yes	—
191	#117	C₂×C₃×C₄	1	2	yes	—
192	#117	C₃×D₄	1	2	yes	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	C₃×Q₈	1	2	yes	—
195	C₂×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₄²	—	2	1	no	—
198	C₂×C₄²	—	2	2	no	—
199	#108	—	2	4	no	—
200	#108	—	2	4	no	—
201	#107	—	2	4	no	—
202	#106	—	2	4	no	—
203	#97	—	2	2	no	—
204	#97	—	2	2	no	—
205	C₄×C₈	—	2	2	no	—
206	C₄×C₈	—	2	2	no	—
207	C₂³×C₃	—	4	2	no	—
208	C₂³×C₃	#117	1	1	yes	characteristic
209	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₃	C₄×Q₈	1	1	yes	characteristic
211	C₂³×C₃	#121	1	1	yes	characteristic
212	C₂³×C₃	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₃	#124	1	1	yes	characteristic
214	C₂³×C₃	#125	1	1	yes	characteristic
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	4	4	no	—
217	C₂×C₃×C₄	—	4	4	no	—
218	C₂×C₃×C₄	—	8	4	no	—
219	C₂×C₃×C₄	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₃×C₄	#117	1	1	yes	characteristic
229	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
233	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
234	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
235	C₂×C₃×C₄	#121	1	1	yes	characteristic
236	C₂×C₃×C₄	#121	1	1	yes	characteristic
237	C₂×C₃×C₄	#121	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₃×C₄	#124	1	1	yes	characteristic
242	C₂×C₃×C₄	#125	1	1	yes	characteristic
243	C₂×C₃×C₄	#127	1	1	yes	characteristic
244	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
245	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
246	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
247	C₃×C₈	—	2	4	no	—
248	C₃×C₈	—	4	4	no	—
249	C₃×C₈	#95	1	2	yes	—
250	C₃×C₈	#95	1	2	yes	—
251	C₃×C₈	#95	1	2	yes	—
252	C₃×C₈	#95	1	2	yes	—
253	C₂⁴	C₃×#41	1	1	yes	characteristic
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
267	C₂²×C₄	C₃×#41	1	1	yes	characteristic
268	C₂²×C₄	C₃×#41	1	1	yes	characteristic
269	C₂²×C₄	C₃×#41	1	1	yes	characteristic
270	M₁₆	—	2	2	no	—
271	M₁₆	—	2	2	no	—
272	M₁₆	—	2	2	no	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	4	no	—
275	M₁₆	—	4	2	no	—
276	M₁₆	—	4	2	no	—
277	M₁₆	C₃×C₄⋊C₄	1	4	yes	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	2	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	C₃×C₄²	1	2	yes	—
285	C₂×C₈	C₃×C₄²	1	2	yes	—
286	C₂×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
291	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
292	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
293	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
294	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
295	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
296	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
297	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
298	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
299	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	C₃×C₄⋊C₄	1	4	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	4	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	—	4	1	no	—
317	C₂²×C₃	—	4	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	C₄×C₄⋊C₄	1	1	yes	characteristic
320	C₂²×C₃	#380	1	1	yes	characteristic
321	C₂²×C₃	#382	1	1	yes	characteristic
322	C₂²×C₃	#389	1	1	yes	characteristic
323	C₂²×C₃	#389	1	1	yes	characteristic
324	C₂²×C₃	#390	1	1	yes	characteristic
325	C₂²×C₃	#391	1	1	yes	characteristic
326	C₃×C₄	—	4	4	no	—
327	C₃×C₄	—	8	4	no	—
328	C₃×C₄	C₂×#95	1	1	yes	characteristic
329	C₃×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
330	C₃×C₄	#380	1	1	yes	characteristic
331	C₃×C₄	#384	1	1	yes	characteristic
332	C₃×C₄	#389	1	1	yes	characteristic
333	C₃×C₄	#389	1	1	yes	characteristic
334	C₃×C₄	#390	1	1	yes	characteristic
335	C₃×C₄	#391	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	C₃×#117	1	1	yes	characteristic
338	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
339	C₂³	C₃×C₄×Q₈	1	1	yes	characteristic
340	C₂³	C₃×#121	1	1	yes	characteristic
341	C₂³	C₃×C₂²⋊Q₈	1	1	yes	characteristic
342	C₂³	C₃×#124	1	1	yes	characteristic
343	C₂³	C₃×#125	1	1	yes	characteristic
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
349	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₃×#117	1	1	yes	characteristic
358	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
359	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
360	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
361	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
362	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
363	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
364	C₂×C₄	C₃×#121	1	1	yes	characteristic
365	C₂×C₄	C₃×#121	1	1	yes	characteristic
366	C₂×C₄	C₃×#121	1	1	yes	characteristic
367	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
370	C₂×C₄	C₃×#124	1	1	yes	characteristic
371	C₂×C₄	C₃×#125	1	1	yes	characteristic
372	C₂×C₄	C₃×#127	1	1	yes	characteristic
373	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
374	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
375	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
376	C₈	—	2	4	no	—
377	C₈	—	4	4	no	—
378	C₈	C₃×#95	1	2	yes	—
379	C₈	C₃×#95	1	2	yes	—
380	C₈	C₃×#95	1	2	yes	—
381	C₈	C₃×#95	1	2	yes	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	C₄⋊#95	1	1	yes	characteristic
389	C₂×C₃	#1814	1	2	yes	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
398	C₂²	C₃×#380	1	1	yes	characteristic
399	C₂²	C₃×#382	1	1	yes	characteristic
400	C₂²	C₃×#389	1	1	yes	characteristic
401	C₂²	C₃×#389	1	1	yes	characteristic
402	C₂²	C₃×#390	1	1	yes	characteristic
403	C₂²	C₃×#391	1	1	yes	characteristic
404	C₄	—	4	4	no	—
405	C₄	—	8	4	no	—
406	C₄	C₂×C₃×#95	1	1	yes	characteristic
407	C₄	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
408	C₄	C₃×#380	1	1	yes	characteristic
409	C₄	C₃×#384	1	1	yes	characteristic
410	C₄	C₃×#389	1	1	yes	characteristic
411	C₄	C₃×#389	1	1	yes	characteristic
412	C₄	C₃×#390	1	1	yes	characteristic
413	C₄	C₃×#391	1	1	yes	characteristic
414	C₃	#10872	1	1	yes	characteristic, direct product factor, Sylow
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	C₃×C₄⋊#95	1	1	yes	characteristic
422	C₂	C₃×#1814	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	#121
commutator	C₂×C₄	C₂×C₃×C₄²
Frattini, cosocle	C₂³×C₄	C₂³×C₃
socle	C₂²×C₃	#380
prime radical	C₂⁴×C₃	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
6. #10872	C₃	direct (N × H)
15. C₂×C₃×#108	C₄	semidirect
17. C₃×#427	C₄	semidirect
22. C₃×#405	C₄	semidirect
23. C₃×#405	C₄	semidirect
88. C₂×#108	C₃×C₄	semidirect
90. #427	C₃×C₄	semidirect
95. #405	C₃×C₄	semidirect
96. #405	C₃×C₄	semidirect
414. C₃	#10872	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#108	2
C₂×C₃×#427	2
C₂×C₃×#405	2
C₂×C₃×#344	2
C₃×#1733	2
#10872	3

Subgroups — C3×#10872 #10629479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10872 #10629479