Subgroups — #10948839

Order 768.

452 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#78542	C₂	1	1	yes	maximal, characteristic
2	C₃×#2164	C₂	1	1	yes	maximal, characteristic
3	#69883	C₂	1	1	yes	maximal, characteristic
4	#69282	C₂	1	1	yes	maximal, characteristic, complemented
5	#69282	C₂	1	1	yes	maximal, characteristic, complemented
6	#69281	C₂	1	1	yes	maximal, characteristic, complemented
7	#69280	C₂	1	1	yes	maximal, characteristic, complemented
8	#69094	C₂	1	1	yes	maximal, characteristic
9	#69094	C₂	1	1	yes	maximal, characteristic
10	#69093	C₂	1	1	yes	maximal, characteristic
11	#69092	C₂	1	1	yes	maximal, characteristic
12	#69068	C₂	1	1	yes	maximal, characteristic, complemented
13	#69068	C₂	1	1	yes	maximal, characteristic, complemented
14	#69048	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₆×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#33499	—	3	1	no	maximal, Sylow
17	#5517	C₄	1	1	yes	characteristic
18	C₃×#405	C₂²	1	1	yes	characteristic
19	#5119	C₄	1	1	yes	characteristic
20	#5118	C₄	1	1	yes	characteristic
21	#5101	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₃	C₂²	1	1	yes	characteristic
23	#4999	C₄	1	1	yes	characteristic
24	#4701	C₄	1	1	yes	characteristic
25	#4701	C₄	1	1	yes	characteristic
26	#4701	C₄	1	1	yes	characteristic
27	#4701	C₄	1	1	yes	characteristic
28	C₈×Dic₆	C₂²	1	1	yes	characteristic
29	C₈×Dic₆	C₂²	1	1	yes	characteristic
30	C₈×Dic₆	C₂²	1	1	yes	characteristic
31	C₈×Dic₆	C₂²	1	1	yes	characteristic
32	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₃×#346	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₁₆	C₂²	1	1	yes	characteristic
38	#4549	C₂²	1	1	yes	characteristic
39	#4549	C₂²	1	1	yes	characteristic
40	#4502	C₂²	1	1	yes	characteristic
41	#4502	C₂²	1	1	yes	characteristic
42	#4502	C₂²	1	1	yes	characteristic
43	#4502	C₂²	1	1	yes	characteristic
44	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
45	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
46	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
47	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
48	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
49	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
50	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
51	Dic₃⋊C₁₆	C₂²	1	1	yes	characteristic
52	Dic₃×C₁₆	C₂²	1	1	yes	characteristic
53	Dic₃×C₁₆	C₂²	1	1	yes	characteristic
54	Dic₃×C₁₆	C₂²	1	1	yes	characteristic
55	Dic₃×C₁₆	C₂²	1	1	yes	characteristic
56	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
57	C₄⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
58	#4461	C₂²	1	1	yes	characteristic
59	C₄×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
60	#2960	—	3	1	no	—
61	#2183	—	3	1	no	—
62	#2183	—	3	1	no	—
63	#2183	—	3	1	no	—
64	#2183	—	3	1	no	—
65	#2183	—	3	1	no	—
66	#2183	—	3	1	no	—
67	Q₈×C₁₆	—	3	1	no	—
68	Q₈×C₁₆	—	3	1	no	—
69	#2164	—	3	1	no	—
70	#2164	—	3	1	no	—
71	#2164	—	3	1	no	—
72	#2164	D₃	1	1	yes	characteristic
73	#2163	—	3	1	no	—
74	#2162	—	3	1	no	—
75	C₂×C₃×M₁₆	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
77	C₃×#117	C₂×C₄	1	1	yes	characteristic
78	#926	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₂×#208	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
82	#890	C₈	1	1	yes	characteristic
83	#890	C₈	1	1	yes	characteristic
84	#888	C₈	1	1	yes	characteristic
85	#888	C₈	1	1	yes	characteristic
86	#878	C₈	1	1	yes	characteristic
87	#878	C₈	1	1	yes	characteristic
88	#878	C₈	1	1	yes	characteristic
89	#878	C₈	1	1	yes	characteristic
90	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
93	C₄×Dic₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₁₆	C₂³	1	1	yes	characteristic
98	C₃×#97	C₂×C₄	1	1	yes	characteristic
99	C₃×#97	C₂×C₄	1	1	yes	characteristic
100	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
101	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
102	#815	C₂×C₄	1	1	yes	characteristic
103	#815	C₂×C₄	1	1	yes	characteristic
104	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
106	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
107	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
108	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
109	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
110	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
111	Dic₃⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
113	C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₃	C₂³	1	1	yes	characteristic
115	C₈×Dic₃	C₂³	1	1	yes	characteristic
116	C₈×Dic₃	C₂³	1	1	yes	characteristic
117	C₈×Dic₃	C₂³	1	1	yes	characteristic
118	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
122	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
123	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
124	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
125	C₄⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
126	#533	—	3	1	no	—
127	#446	—	3	1	no	—
128	#446	—	3	1	no	—
129	#446	—	3	1	no	—
130	#446	—	3	1	no	—
131	C₈×Q₈	—	3	1	no	—
132	C₈×Q₈	—	3	1	no	—
133	C₈×Q₈	—	3	1	no	—
134	C₈×Q₈	—	3	1	no	—
135	#424	—	3	1	no	—
136	#424	—	3	1	no	—
137	#423	—	3	1	no	—
138	#405	—	3	1	no	—
139	#405	C₂×D₃	1	1	yes	characteristic
140	C₂×C₄×C₈	—	3	1	no	—
141	C₄⋊C₁₆	—	3	1	no	—
142	C₄⋊C₁₆	—	3	1	no	—
143	C₄⋊C₁₆	—	3	1	no	—
144	C₄⋊C₁₆	—	3	1	no	—
145	C₄⋊C₁₆	—	3	1	no	—
146	C₄⋊C₁₆	—	3	1	no	—
147	C₄⋊C₁₆	—	3	1	no	—
148	C₄⋊C₁₆	—	3	1	no	—
149	C₄⋊C₁₆	—	3	1	no	—
150	C₄⋊C₁₆	—	3	1	no	—
151	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic
152	C₄⋊C₁₆	C₂×D₃	1	1	yes	characteristic
153	C₂²⋊C₁₆	—	3	1	no	—
154	C₂²⋊C₁₆	—	3	1	no	—
155	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
156	C₂²⋊C₁₆	C₂×D₃	1	1	yes	characteristic
157	#346	—	3	1	no	—
158	#346	—	3	1	no	—
159	#346	—	3	1	no	—
160	#346	—	3	1	no	—
161	#346	—	3	1	no	—
162	#346	C₂×D₃	1	1	yes	characteristic
163	C₄×C₁₆	—	3	1	no	—
164	C₄×C₁₆	—	3	1	no	—
165	C₄×C₁₆	—	3	1	no	—
166	C₄×C₁₆	—	3	1	no	—
167	C₄×C₁₆	—	3	1	no	—
168	C₄×C₁₆	C₂×D₃	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
170	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
171	C₂²×Dic₃	C₂×C₈	1	1	yes	characteristic
172	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
173	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
174	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
175	C₂×Dic₆	C₂×C₈	1	1	yes	characteristic
176	C₃×M₁₆	—	4	1	no	—
177	C₂×C₃×C₈	—	2	1	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
186	C₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
187	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
188	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
189	#217	C₂×C₈	1	1	yes	characteristic
190	#217	C₂×C₈	1	1	yes	characteristic
191	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
192	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
193	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
194	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
195	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
196	C₄⋊Dic₃	C₂×C₈	1	1	yes	characteristic
197	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
198	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
199	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
200	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
201	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
202	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
203	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
204	Dic₃⋊C₄	C₂×C₈	1	1	yes	characteristic
205	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
206	C₄×Dic₃	C₂×C₈	1	1	yes	characteristic
207	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
208	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
209	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₃	C₂²×C₄	1	1	yes	characteristic
211	#208	—	4	1	no	—
212	C₂×C₃⋊C₈	—	4	1	no	—
213	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₃×C₁₆	—	2	1	no	—
218	C₃×C₁₆	—	2	1	no	—
219	C₃×C₁₆	—	2	1	no	—
220	C₃×C₁₆	—	2	1	no	—
221	C₃⋊C₁₆	—	2	1	no	—
222	C₃⋊C₁₆	—	2	1	no	—
223	C₃⋊C₁₆	—	2	1	no	—
224	C₃⋊C₁₆	—	2	1	no	—
225	C₂×M₁₆	—	3	1	no	—
226	C₂×M₁₆	C₄×D₃	1	1	yes	characteristic
227	C₂²×C₈	—	3	1	no	—
228	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
229	C₄⋊Q₈	—	3	1	no	—
230	C₄⋊Q₈	—	3	1	no	—
231	#125	—	3	1	no	—
232	#125	—	3	1	no	—
233	C₂²⋊Q₈	—	3	1	no	—
234	C₂²⋊Q₈	—	3	1	no	—
235	C₂²⋊Q₈	—	3	1	no	—
236	C₂²⋊Q₈	—	3	1	no	—
237	C₄×Q₈	—	3	1	no	—
238	C₄×Q₈	—	3	1	no	—
239	C₄×Q₈	—	3	1	no	—
240	C₄×Q₈	—	3	1	no	—
241	#117	—	3	1	no	—
242	#117	C₄×D₃	1	1	yes	characteristic
243	C₂×C₄²	—	3	1	no	—
244	C₂×C₁₆	—	3	1	no	—
245	C₂×C₁₆	—	3	1	no	—
246	C₂×C₁₆	—	3	1	no	—
247	C₂×C₁₆	—	3	1	no	—
248	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
249	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
250	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
251	C₂×C₁₆	C₂²×D₃	1	1	yes	characteristic
252	C₄⋊C₈	—	3	1	no	—
253	C₄⋊C₈	—	3	1	no	—
254	C₄⋊C₈	—	3	1	no	—
255	C₄⋊C₈	—	3	1	no	—
256	C₄⋊C₈	—	3	1	no	—
257	C₄⋊C₈	—	3	1	no	—
258	C₄⋊C₈	—	3	1	no	—
259	C₄⋊C₈	—	3	1	no	—
260	C₄⋊C₈	—	3	1	no	—
261	C₄⋊C₈	—	3	1	no	—
262	C₄⋊C₈	—	3	1	no	—
263	C₄⋊C₈	—	3	1	no	—
264	#97	—	3	1	no	—
265	#97	—	3	1	no	—
266	#97	C₄×D₃	1	1	yes	characteristic
267	#97	C₄×D₃	1	1	yes	characteristic
268	C₄×C₈	—	3	1	no	—
269	C₄×C₈	—	3	1	no	—
270	C₄×C₈	—	3	1	no	—
271	C₄×C₈	—	3	1	no	—
272	C₄×C₈	—	3	1	no	—
273	C₄×C₈	—	3	1	no	—
274	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
275	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
276	C₂³×C₃	C₂²×C₈	1	1	yes	characteristic
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
285	C₂×Dic₃	—	2	2	no	—
286	C₂×Dic₃	—	4	1	no	—
287	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
288	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
289	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
290	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
291	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
292	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
293	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
294	C₂×Dic₃	C₂²×C₈	1	1	yes	characteristic
295	Dic₆	—	2	2	no	—
296	Dic₆	—	2	2	no	—
297	Dic₆	—	4	1	no	—
298	Dic₆	—	4	1	no	—
299	C₃×C₈	—	2	1	no	—
300	C₃×C₈	—	2	1	no	—
301	C₃×C₈	—	2	1	no	—
302	C₃×C₈	2₋¹⁺⁴	1	1	yes	characteristic
303	C₃×C₈	2₋¹⁺⁴	1	1	yes	characteristic
304	C₃⋊C₈	—	2	1	no	—
305	C₃⋊C₈	—	2	1	no	—
306	C₃⋊C₈	—	2	1	no	—
307	C₃⋊C₈	—	2	1	no	—
308	C₂×Q₈	—	3	1	no	—
309	C₂×Q₈	—	3	1	no	—
310	C₂×Q₈	—	3	1	no	—
311	C₂×Q₈	—	3	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
315	M₁₆	—	4	1	no	—
316	M₁₆	—	12	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	3	1	no	—
320	C₂×C₈	—	3	1	no	—
321	C₂×C₈	—	3	1	no	—
322	C₂×C₈	—	3	1	no	—
323	C₂×C₈	—	12	1	no	—
324	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
326	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
327	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
328	C₄⋊C₄	—	3	1	no	—
329	C₄⋊C₄	—	3	1	no	—
330	C₄⋊C₄	—	3	1	no	—
331	C₄⋊C₄	—	3	1	no	—
332	C₄⋊C₄	—	3	1	no	—
333	C₄⋊C₄	—	3	1	no	—
334	C₄⋊C₄	—	3	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₄⋊C₄	—	3	1	no	—
337	C₄⋊C₄	—	3	1	no	—
338	C₄⋊C₄	—	3	1	no	—
339	C₄⋊C₄	—	3	1	no	—
340	C₄⋊C₄	—	3	1	no	—
341	C₄⋊C₄	—	3	1	no	—
342	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
343	C₄⋊C₄	D₃×C₈	1	1	yes	characteristic
344	C₂²⋊C₄	—	3	1	no	—
345	C₂²⋊C₄	—	3	1	no	—
346	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
347	C₂²⋊C₄	D₃×C₈	1	1	yes	characteristic
348	C₄²	—	3	1	no	—
349	C₄²	—	3	1	no	—
350	C₄²	—	3	1	no	—
351	C₄²	—	3	1	no	—
352	C₄²	—	3	1	no	—
353	C₄²	—	3	1	no	—
354	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
355	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
356	C₁₆	—	2	1	no	—
357	C₁₆	—	2	1	no	—
358	C₁₆	—	2	1	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	6	1	no	—
361	C₁₆	—	6	1	no	—
362	C₁₆	—	6	1	no	—
363	C₁₆	—	6	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	2	1	no	—
367	C₂²×C₃	C₂³×C₈	1	1	yes	characteristic
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	2	1	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	#519	1	1	yes	characteristic
374	C₃×C₄	#568	1	1	yes	characteristic
375	Dic₃	—	2	1	no	—
376	Dic₃	—	2	1	no	—
377	Dic₃	—	2	1	no	—
378	Dic₃	—	2	1	no	—
379	Dic₃	—	2	1	no	—
380	Dic₃	—	2	1	no	—
381	Dic₃	—	2	1	no	—
382	Dic₃	#504	1	2	yes	—
383	C₂³	C₂×D₃×C₈	1	1	yes	characteristic
384	Q₈	—	6	2	no	—
385	Q₈	—	6	2	no	—
386	Q₈	—	12	1	no	—
387	Q₈	—	12	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	3	1	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	3	1	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	3	1	no	—
395	C₂×C₄	—	3	1	no	—
396	C₂×C₄	—	3	1	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	12	1	no	—
400	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
401	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
402	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
403	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
404	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	6	1	no	—
410	C₈	—	6	1	no	—
411	C₈	—	6	1	no	—
412	C₈	—	6	1	no	—
413	C₈	#1010	1	1	yes	characteristic
414	C₈	#1010	1	1	yes	characteristic
415	C₂×C₃	—	4	1	no	—
416	C₂×C₃	#2982	1	1	yes	characteristic
417	C₂×C₃	C₂×#504	1	1	yes	characteristic
418	C₂×C₃	#3407	1	1	yes	characteristic
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	C₂²×D₃×C₈	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	3	2	no	—
429	C₄	—	6	1	no	—
430	C₄	—	6	1	no	—
431	C₄	—	6	1	no	—
432	C₄	—	6	1	no	—
433	C₄	—	6	1	no	—
434	C₄	—	6	1	no	—
435	C₄	—	6	1	no	—
436	C₄	#5516	1	1	yes	characteristic
437	C₄	#5745	1	1	yes	characteristic
438	C₃	#33499	1	1	yes	characteristic, complemented, Sylow
439	C₂	—	4	1	no	—
440	C₂	#79263	1	1	yes	characteristic
441	C₂	D₃×#504	1	1	yes	characteristic
442	C₂	#82012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₈
Fitting	C₃×#2164	C₂
prime radical	C₂³×C₃	C₂²×C₈
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	#2164	D₃
hypocenter	C₃	#33499
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
4. #69282	C₂	semidirect
5. #69282	C₂	semidirect
6. #69281	C₂	semidirect
7. #69280	C₂	semidirect
12. #69068	C₂	semidirect
13. #69068	C₂	semidirect
14. #69048	C₂	semidirect
15. C₁₆×Dic₆	C₂	semidirect
438. C₃	#33499	semidirect

Maximal subgroups

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

subgroup	index
#78542	2
C₃×#2164	2
#69883	2
#69282	2
#69281	2
#69280	2
#69094	2
#69093	2
#69092	2
#69068	2
#69048	2
C₁₆×Dic₆	2
#33499	3