Subgroups — C₃×#10877 #10629484

Order 768.

926 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#336	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#336	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#336	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×#95	C₂	1	1	yes	maximal, characteristic
8	#10877	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄⋊C₈	—	2	2	no	—
17	C₂×C₃×C₄⋊C₈	—	2	2	no	—
18	C₂×C₃×C₄⋊C₈	C₄	1	4	yes	complemented
19	C₂×C₃×#97	—	2	2	no	—
20	C₂×C₃×#97	—	2	2	no	—
21	C₂×C₃×#97	—	2	2	no	—
22	C₂×C₃×#95	C₄	1	2	yes	—
23	C₂×C₃×#95	C₄	1	2	yes	—
24	C₃×#336	—	2	2	no	—
25	C₃×#336	—	2	2	no	—
26	C₃×#336	—	2	2	no	—
27	C₃×#336	C₄	1	4	yes	complemented
28	C₂²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
29	C₂²×#97	C₂×C₃	1	1	yes	characteristic
30	C₂×#336	C₂×C₃	1	1	yes	characteristic
31	C₂×#336	C₂×C₃	1	1	yes	characteristic
32	C₂×#336	C₂×C₃	1	1	yes	characteristic
33	C₂×#336	C₂×C₃	1	1	yes	characteristic
34	C₄×#95	C₂×C₃	1	1	yes	characteristic
35	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
37	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
38	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₈	—	2	1	no	—
41	C₂²×C₃×C₈	—	2	1	no	—
42	C₂²×C₃×C₈	—	2	1	no	—
43	C₂²×C₃×C₈	—	2	1	no	—
44	C₂²×C₃×C₈	—	2	1	no	—
45	C₂²×C₃×C₈	—	2	1	no	—
46	C₂²×C₃×C₈	—	2	1	no	—
47	C₂²×C₃×C₈	—	2	1	no	—
48	C₂²×C₃×C₈	—	2	1	no	—
49	C₂²×C₃×C₈	—	2	1	no	—
50	C₂²×C₃×C₈	—	2	1	no	—
51	C₂²×C₃×C₈	—	2	1	no	—
52	C₂²×C₃×C₈	—	2	1	no	—
53	C₂²×C₃×C₈	—	2	1	no	—
54	C₂²×C₃×C₈	—	2	1	no	—
55	C₂²×C₃×C₈	—	2	1	no	—
56	C₂²×C₃×C₈	—	2	1	no	—
57	C₂²×C₃×C₈	—	2	1	no	—
58	C₂²×C₃×C₈	—	2	1	no	—
59	C₂²×C₃×C₈	—	2	1	no	—
60	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
61	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
62	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
63	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
64	C₂²×C₃×C₈	D₄	1	2	yes	—
65	C₂²×C₃×C₈	D₄	1	2	yes	—
66	C₂²×C₃×C₈	D₄	1	2	yes	—
67	C₂²×C₃×C₈	Q₈	1	2	yes	—
68	C₂×C₃×C₄²	—	2	1	no	—
69	C₂×C₃×C₄²	—	2	1	no	—
70	C₂×C₃×C₄²	—	2	1	no	—
71	C₂×C₃×C₄²	—	2	1	no	—
72	C₂×C₃×C₄²	—	2	1	no	—
73	C₂×C₃×C₄²	—	2	1	no	—
74	C₂×C₃×C₄²	—	2	1	no	—
75	C₂×C₃×C₄²	—	2	1	no	—
76	C₂×C₃×C₄²	—	2	1	no	—
77	C₂×C₃×C₄²	—	2	1	no	—
78	C₂×C₃×C₄²	—	2	1	no	—
79	C₂×C₃×C₄²	—	2	1	no	—
80	C₂×C₃×C₄²	—	2	1	no	—
81	C₂×C₃×C₄²	—	2	1	no	—
82	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
83	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
84	C₂×C₃×C₄²	D₄	1	2	yes	—
85	C₂×C₃×C₄²	Q₈	1	2	yes	—
86	C₃×C₄⋊C₈	—	2	8	no	—
87	C₃×#97	—	2	8	no	—
88	C₃×#95	—	2	4	no	—
89	C₃×#95	—	2	4	no	—
90	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
92	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄⋊C₈	—	2	2	no	—
98	C₂×C₄⋊C₈	—	2	2	no	—
99	C₂×C₄⋊C₈	C₃×C₄	1	4	yes	complemented
100	C₂×#97	—	2	2	no	—
101	C₂×#97	—	2	2	no	—
102	C₂×#97	—	2	2	no	—
103	C₂×#95	C₃×C₄	1	2	yes	—
104	C₂×#95	C₃×C₄	1	2	yes	—
105	#336	—	2	2	no	—
106	#336	—	2	2	no	—
107	#336	—	2	2	no	—
108	#336	C₃×C₄	1	4	yes	complemented
109	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₃×C₄	—	2	1	no	—
111	C₂²×C₃×C₄	—	2	1	no	—
112	C₂²×C₃×C₄	—	2	2	no	—
113	C₂²×C₃×C₄	—	2	2	no	—
114	C₂²×C₃×C₄	—	2	1	no	—
115	C₂²×C₃×C₄	—	2	1	no	—
116	C₂²×C₃×C₄	—	2	2	no	—
117	C₂²×C₃×C₄	—	2	2	no	—
118	C₂²×C₃×C₄	—	2	2	no	—
119	C₂²×C₃×C₄	—	2	2	no	—
120	C₂²×C₃×C₄	—	2	2	no	—
121	C₂²×C₃×C₄	—	2	2	no	—
122	C₂²×C₃×C₄	—	2	2	no	—
123	C₂²×C₃×C₄	—	2	2	no	—
124	C₂²×C₃×C₄	—	2	2	no	—
125	C₂²×C₃×C₄	—	2	2	no	—
126	C₂²×C₃×C₄	—	2	2	no	—
127	C₂²×C₃×C₄	—	2	2	no	—
128	C₂²×C₃×C₄	—	2	2	no	—
129	C₂²×C₃×C₄	C₄²	1	2	yes	—
130	C₂²×C₃×C₄	C₄²	1	2	yes	—
131	C₂²×C₃×C₄	C₄⋊C₄	1	4	yes	—
132	C₂²×C₃×C₄	M₁₆	1	4	yes	—
133	C₂²×C₃×C₄	M₁₆	1	4	yes	—
134	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₃×C₄	#41	1	1	yes	characteristic
143	C₂²×C₃×C₄	#41	1	1	yes	characteristic
144	C₂²×C₃×C₄	#41	1	1	yes	characteristic
145	C₂²×C₃×C₄	#41	1	1	yes	characteristic
146	C₂²×C₃×C₄	#41	1	1	yes	characteristic
147	C₂²×C₃×C₄	#41	1	1	yes	characteristic
148	C₂×C₃×C₈	—	2	2	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	2	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	2	2	no	—
158	C₂×C₃×C₈	—	2	2	no	—
159	C₂×C₃×C₈	—	2	2	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	2	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	4	1	no	—
167	C₂×C₃×C₈	—	4	1	no	—
168	C₂×C₃×C₈	—	4	1	no	—
169	C₂×C₃×C₈	—	4	1	no	—
170	C₂×C₃×C₈	—	4	1	no	—
171	C₂×C₃×C₈	—	4	1	no	—
172	C₂×C₃×C₈	—	4	1	no	—
173	C₂×C₃×C₈	—	4	1	no	—
174	C₂×C₃×C₈	C₂²⋊C₄	1	4	yes	—
175	C₂×C₃×C₈	C₄⋊C₄	1	4	yes	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	—	2	2	no	—
178	C₃×C₄²	—	2	2	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	—	2	2	no	—
181	C₃×C₄²	—	2	2	no	—
182	C₃×C₄²	—	2	2	no	—
183	C₃×C₄²	—	2	2	no	—
184	C₃×C₄²	—	4	1	no	—
185	C₃×C₄²	—	4	1	no	—
186	C₃×C₄²	—	4	1	no	—
187	C₃×C₄²	—	4	1	no	—
188	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
189	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
190	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
191	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
192	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₈	—	2	1	no	—
194	C₂²×C₈	—	2	1	no	—
195	C₂²×C₈	—	2	1	no	—
196	C₂²×C₈	—	2	1	no	—
197	C₂²×C₈	—	2	1	no	—
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	—	2	1	no	—
200	C₂²×C₈	—	2	1	no	—
201	C₂²×C₈	—	2	1	no	—
202	C₂²×C₈	—	2	1	no	—
203	C₂²×C₈	—	2	1	no	—
204	C₂²×C₈	—	2	1	no	—
205	C₂²×C₈	—	2	1	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	—	2	1	no	—
209	C₂²×C₈	—	2	1	no	—
210	C₂²×C₈	—	2	1	no	—
211	C₂²×C₈	—	2	1	no	—
212	C₂²×C₈	—	2	1	no	—
213	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
214	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
215	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
216	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
217	C₂²×C₈	C₃×D₄	1	2	yes	—
218	C₂²×C₈	C₃×D₄	1	2	yes	—
219	C₂²×C₈	C₃×D₄	1	2	yes	—
220	C₂²×C₈	C₃×Q₈	1	2	yes	—
221	C₂×C₄²	—	2	1	no	—
222	C₂×C₄²	—	2	1	no	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	—	2	1	no	—
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	—	2	1	no	—
229	C₂×C₄²	—	2	1	no	—
230	C₂×C₄²	—	2	1	no	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
236	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
237	C₂×C₄²	C₃×D₄	1	2	yes	—
238	C₂×C₄²	C₃×Q₈	1	2	yes	—
239	C₄⋊C₈	—	2	8	no	—
240	#97	—	2	8	no	—
241	#95	—	2	4	no	—
242	#95	—	2	4	no	—
243	C₂³×C₃	C₂×C₄²	1	1	yes	characteristic
244	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂³×C₃	#117	1	1	yes	characteristic
246	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
247	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
248	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
249	C₂³×C₃	C₄×Q₈	1	1	yes	characteristic
250	C₂³×C₃	C₂×M₁₆	1	2	yes	—
251	C₂³×C₃	C₂×M₁₆	1	2	yes	—
252	C₂³×C₃	#131	1	2	yes	—
253	C₂³×C₃	#131	1	2	yes	—
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	—	2	4	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	2	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	4	2	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	4	2	no	—
276	C₂×C₃×C₄	—	4	2	no	—
277	C₂×C₃×C₄	#97	1	4	yes	complemented
278	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₃×C₄	#117	1	1	yes	characteristic
281	C₂×C₃×C₄	#117	1	1	yes	characteristic
282	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
288	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
289	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
290	C₂×C₃×C₄	#120	1	1	yes	characteristic
291	C₂×C₃×C₄	#121	1	1	yes	characteristic
292	C₂×C₃×C₄	#121	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
297	C₂×C₃×C₄	#123	1	1	yes	characteristic
298	C₂×C₃×C₄	#123	1	1	yes	characteristic
299	C₂×C₃×C₄	#123	1	1	yes	characteristic
300	C₂×C₃×C₄	#124	1	1	yes	characteristic
301	C₂×C₃×C₄	#125	1	1	yes	characteristic
302	C₂×C₃×C₄	#125	1	1	yes	characteristic
303	C₂×C₃×C₄	#126	1	1	yes	characteristic
304	C₂×C₃×C₄	#126	1	1	yes	characteristic
305	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
306	C₃×C₈	—	2	4	no	—
307	C₃×C₈	—	2	4	no	—
308	C₃×C₈	—	4	2	no	—
309	C₃×C₈	—	4	2	no	—
310	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₃×C₄²	1	2	yes	—
331	C₂²×C₄	C₃×C₄²	1	2	yes	—
332	C₂²×C₄	C₃×C₄⋊C₄	1	4	yes	—
333	C₂²×C₄	C₃×M₁₆	1	4	yes	—
334	C₂²×C₄	C₃×M₁₆	1	4	yes	—
335	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
343	C₂²×C₄	C₃×#41	1	1	yes	characteristic
344	C₂²×C₄	C₃×#41	1	1	yes	characteristic
345	C₂²×C₄	C₃×#41	1	1	yes	characteristic
346	C₂²×C₄	C₃×#41	1	1	yes	characteristic
347	C₂²×C₄	C₃×#41	1	1	yes	characteristic
348	C₂²×C₄	C₃×#41	1	1	yes	characteristic
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	C₃×C₂²⋊C₄	1	4	yes	—
376	C₂×C₈	C₃×C₄⋊C₄	1	4	yes	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₂²×C₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×C₃	C₄×C₄⋊C₄	1	1	yes	characteristic
391	C₂²×C₃	C₄×C₄⋊C₄	1	1	yes	characteristic
392	C₂²×C₃	#385	1	1	yes	characteristic
393	C₂²×C₃	#387	1	1	yes	characteristic
394	C₂²×C₃	#388	1	1	yes	characteristic
395	C₂²×C₃	#389	1	1	yes	characteristic
396	C₂²×C₃	C₂×#97	1	1	yes	characteristic
397	C₂²×C₃	C₄×M₁₆	1	1	yes	characteristic
398	C₂²×C₃	#405	1	1	yes	characteristic
399	C₂²×C₃	#405	1	1	yes	characteristic
400	C₂²×C₃	#423	1	2	yes	—
401	C₂²×C₃	#424	1	2	yes	—
402	C₂²×C₃	#432	1	2	yes	—
403	C₂²×C₃	#433	1	2	yes	—
404	C₂²×C₃	#435	1	2	yes	—
405	C₂²×C₃	#435	1	2	yes	—
406	C₂²×C₃	#435	1	2	yes	—
407	C₂²×C₃	#435	1	2	yes	—
408	C₂²×C₃	#436	1	2	yes	—
409	C₂²×C₃	#436	1	2	yes	—
410	C₂²×C₃	#446	1	2	yes	—
411	C₂²×C₃	#446	1	2	yes	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	4	4	no	—
414	C₃×C₄	—	4	4	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	#385	1	1	yes	characteristic
417	C₃×C₄	#386	1	1	yes	characteristic
418	C₃×C₄	#387	1	1	yes	characteristic
419	C₃×C₄	#387	1	1	yes	characteristic
420	C₃×C₄	#387	1	1	yes	characteristic
421	C₃×C₄	#388	1	1	yes	characteristic
422	C₃×C₄	#389	1	1	yes	characteristic
423	C₃×C₄	#391	1	1	yes	characteristic
424	C₂³	C₂×C₃×C₄²	1	1	yes	characteristic
425	C₂³	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
426	C₂³	C₃×#117	1	1	yes	characteristic
427	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
428	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
429	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
430	C₂³	C₃×C₄×Q₈	1	1	yes	characteristic
431	C₂³	C₂×C₃×M₁₆	1	2	yes	—
432	C₂³	C₂×C₃×M₁₆	1	2	yes	—
433	C₂³	C₃×#131	1	2	yes	—
434	C₂³	C₃×#131	1	2	yes	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	C₃×#97	1	4	yes	complemented
459	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₃×#117	1	1	yes	characteristic
462	C₂×C₄	C₃×#117	1	1	yes	characteristic
463	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
464	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
465	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
466	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
467	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
468	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
469	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
470	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
471	C₂×C₄	C₃×#120	1	1	yes	characteristic
472	C₂×C₄	C₃×#121	1	1	yes	characteristic
473	C₂×C₄	C₃×#121	1	1	yes	characteristic
474	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
475	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
476	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
477	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
478	C₂×C₄	C₃×#123	1	1	yes	characteristic
479	C₂×C₄	C₃×#123	1	1	yes	characteristic
480	C₂×C₄	C₃×#123	1	1	yes	characteristic
481	C₂×C₄	C₃×#124	1	1	yes	characteristic
482	C₂×C₄	C₃×#125	1	1	yes	characteristic
483	C₂×C₄	C₃×#125	1	1	yes	characteristic
484	C₂×C₄	C₃×#126	1	1	yes	characteristic
485	C₂×C₄	C₃×#126	1	1	yes	characteristic
486	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
487	C₈	—	2	4	no	—
488	C₈	—	2	4	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	2	no	—
491	C₂×C₃	#1436	1	1	yes	characteristic
492	C₂×C₃	#1752	1	1	yes	characteristic
493	C₂×C₃	#1753	1	1	yes	characteristic
494	C₂×C₃	#1767	1	1	yes	characteristic
495	C₂×C₃	#1768	1	1	yes	characteristic
496	C₂×C₃	#1770	1	1	yes	characteristic
497	C₂×C₃	#1771	1	1	yes	characteristic
498	C₂×C₃	#1851	1	2	yes	—
499	C₂×C₃	#1917	1	2	yes	—
500	C₂×C₃	#1924	1	2	yes	—
501	C₂×C₃	#1940	1	2	yes	—
502	C₂²	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
503	C₂²	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
504	C₂²	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
505	C₂²	C₃×#385	1	1	yes	characteristic
506	C₂²	C₃×#387	1	1	yes	characteristic
507	C₂²	C₃×#388	1	1	yes	characteristic
508	C₂²	C₃×#389	1	1	yes	characteristic
509	C₂²	C₂×C₃×#97	1	1	yes	characteristic
510	C₂²	C₃×C₄×M₁₆	1	1	yes	characteristic
511	C₂²	C₃×#405	1	1	yes	characteristic
512	C₂²	C₃×#405	1	1	yes	characteristic
513	C₂²	C₃×#423	1	2	yes	—
514	C₂²	C₃×#424	1	2	yes	—
515	C₂²	C₃×#432	1	2	yes	—
516	C₂²	C₃×#433	1	2	yes	—
517	C₂²	C₃×#435	1	2	yes	—
518	C₂²	C₃×#435	1	2	yes	—
519	C₂²	C₃×#435	1	2	yes	—
520	C₂²	C₃×#435	1	2	yes	—
521	C₂²	C₃×#436	1	2	yes	—
522	C₂²	C₃×#436	1	2	yes	—
523	C₂²	C₃×#446	1	2	yes	—
524	C₂²	C₃×#446	1	2	yes	—
525	C₄	—	2	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	4	no	—
529	C₄	C₃×#385	1	1	yes	characteristic
530	C₄	C₃×#386	1	1	yes	characteristic
531	C₄	C₃×#387	1	1	yes	characteristic
532	C₄	C₃×#387	1	1	yes	characteristic
533	C₄	C₃×#387	1	1	yes	characteristic
534	C₄	C₃×#388	1	1	yes	characteristic
535	C₄	C₃×#389	1	1	yes	characteristic
536	C₄	C₃×#391	1	1	yes	characteristic
537	C₃	#10877	1	1	yes	characteristic, direct product factor, Sylow
538	C₂	C₃×#1436	1	1	yes	characteristic
539	C₂	C₃×#1752	1	1	yes	characteristic
540	C₂	C₃×#1753	1	1	yes	characteristic
541	C₂	C₃×#1767	1	1	yes	characteristic
542	C₂	C₃×#1768	1	1	yes	characteristic
543	C₂	C₃×#1770	1	1	yes	characteristic
544	C₂	C₃×#1771	1	1	yes	characteristic
545	C₂	C₃×#1851	1	2	yes	—
546	C₂	C₃×#1917	1	2	yes	—
547	C₂	C₃×#1924	1	2	yes	—
548	C₂	C₃×#1940	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
8. #10877	C₃	direct (N × H)
18. C₂×C₃×C₄⋊C₈	C₄	semidirect
27. C₃×#336	C₄	semidirect
99. C₂×C₄⋊C₈	C₃×C₄	semidirect
108. #336	C₃×C₄	semidirect
277. C₂×C₃×C₄	#97	semidirect
458. C₂×C₄	C₃×#97	semidirect
537. C₃	#10877	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×C₄⋊C₈	2
C₂²×C₃×#97	2
C₂×C₃×#336	2
C₃×C₄×#95	2
#10877	3

Subgroups — C3×#10877 #10629484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10877 #10629484