Subgroups — C₂×#67702 #10685271

Order 768.

878 conjugacy classes of subgroups.

The subgroup lattice has 398 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	C₂×#4935	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#67702	C₂	1	4	yes	maximal, direct product factor
5	C₂×#1296	—	3	1	no	maximal, Sylow
6	C₂³×C₃×C₈	—	2	1	no	—
7	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₃	—	2	1	no	—
9	C₂²×C₄⋊Dic₃	—	2	1	no	—
10	C₂²×C₄⋊Dic₃	C₄	1	2	yes	—
11	C₂³×C₃⋊C₈	—	2	1	no	—
12	C₂×C₃×C₄⋊C₈	—	2	1	no	—
13	C₂×C₃×C₄⋊C₈	—	2	2	no	—
14	C₂×C₃×C₄⋊C₈	C₄	1	4	yes	complemented
15	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
16	#4935	—	2	1	no	—
17	#4935	—	2	1	no	—
18	#4935	C₄	1	2	yes	—
19	#4935	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₂×C₄⋊(C₃⋊C₈)	—	2	2	no	—
22	C₂×C₄⋊(C₃⋊C₈)	C₄	1	4	yes	complemented
23	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₈	—	3	1	no	—
25	C₂²×C₄⋊C₈	D₃	1	1	yes	characteristic
26	C₂×#384	—	3	1	no	—
27	#1296	—	3	4	no	—
28	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
31	C₂³×Dic₃	—	2	2	no	—
32	C₂²×C₃×C₈	—	2	4	no	—
33	C₂²×C₃×C₈	—	2	2	no	—
34	C₂²×C₃×C₈	—	4	2	no	—
35	C₂²×C₃×C₈	—	4	2	no	—
36	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
41	C₂×C₃×C₄²	D₄	1	2	yes	—
42	C₂×C₃×C₄²	Q₈	1	2	yes	—
43	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊Dic₃	—	2	2	no	—
45	C₂×C₄⋊Dic₃	—	2	2	no	—
46	C₂×C₄⋊Dic₃	—	2	2	no	—
47	C₂×C₄⋊Dic₃	—	2	2	no	—
48	C₂×C₄⋊Dic₃	—	2	2	no	—
49	C₂×C₄⋊Dic₃	—	4	2	no	—
50	C₂×C₄⋊Dic₃	—	4	2	no	—
51	C₂×C₄⋊Dic₃	—	4	2	no	—
52	C₂×C₄⋊Dic₃	—	4	2	no	—
53	C₂×C₄⋊Dic₃	—	4	4	no	—
54	C₂×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
55	C₂²×C₃⋊C₈	—	2	4	no	—
56	C₂²×C₃⋊C₈	—	2	2	no	—
57	C₂²×C₃⋊C₈	—	4	2	no	—
58	C₂²×C₃⋊C₈	—	4	2	no	—
59	C₃×C₄⋊C₈	—	2	4	no	—
60	C₃×C₄⋊C₈	—	2	2	no	—
61	C₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
62	C₄⋊(C₃⋊C₈)	—	2	4	no	—
63	C₄⋊(C₃⋊C₈)	—	2	2	no	—
64	C₄⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	complemented
65	C₂³×C₈	—	2	1	no	—
66	C₂³×C₈	—	6	1	no	—
67	C₂²×C₄⋊C₄	—	3	2	no	—
68	C₂²×C₄⋊C₄	—	6	1	no	—
69	C₂²×C₄⋊C₄	—	6	1	no	—
70	C₂²×C₄²	C₂×D₃	1	1	yes	characteristic
71	C₂×C₄⋊C₈	—	2	1	no	—
72	C₂×C₄⋊C₈	—	2	2	no	—
73	C₂×C₄⋊C₈	—	3	4	no	—
74	C₂×C₄⋊C₈	—	3	2	no	—
75	C₂×C₄⋊C₈	—	6	1	no	—
76	C₂×C₄⋊C₈	—	6	2	no	—
77	C₂×C₄⋊C₈	Dic₃	1	4	yes	complemented
78	C₂×C₄⋊C₈	C₂×D₃	1	2	yes	—
79	#384	—	3	2	no	—
80	#384	—	3	2	no	—
81	#384	—	6	1	no	—
82	#384	—	6	1	no	—
83	C₂⁴×C₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₃×C₄	—	2	2	no	—
85	C₂²×C₃×C₄	—	2	2	no	—
86	C₂²×C₃×C₄	C₄²	1	2	yes	—
87	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₃×C₄	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
93	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
94	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
95	C₂²×C₃×C₄	D₈	1	2	yes	—
96	C₂²×C₃×C₄	D₈	1	2	yes	—
97	C₂²×C₃×C₄	SD₁₆	1	2	yes	—
98	C₂²×C₃×C₄	SD₁₆	1	2	yes	—
99	C₂²×C₃×C₄	SD₁₆	1	2	yes	—
100	C₂²×C₃×C₄	SD₁₆	1	2	yes	—
101	C₂²×C₃×C₄	Q₁₆	1	2	yes	—
102	C₂²×C₃×C₄	Q₁₆	1	2	yes	—
103	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂²×Dic₃	—	2	4	no	—
107	C₂²×Dic₃	—	4	4	no	—
108	C₂²×Dic₃	—	4	4	no	—
109	C₂²×Dic₃	—	4	4	no	—
110	C₂×C₃×C₈	—	2	4	no	—
111	C₂×C₃×C₈	—	4	8	no	—
112	C₂×C₃×C₈	—	4	2	no	—
113	C₂×C₃×C₈	—	4	2	no	—
114	C₃×C₄²	C₄²	1	2	yes	—
115	C₃×C₄²	C₂²⋊C₄	1	2	yes	—
116	C₃×C₄²	C₂²⋊C₄	1	2	yes	—
117	C₃×C₄²	C₄⋊C₄	1	2	yes	—
118	C₃×C₄²	C₄⋊C₄	1	2	yes	—
119	C₃×C₄²	C₄⋊C₄	1	2	yes	—
120	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
121	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
122	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
123	C₃×C₄²	C₂×Q₈	1	1	yes	characteristic
124	C₄⋊Dic₃	—	4	4	no	—
125	C₄⋊Dic₃	—	4	4	no	—
126	C₄⋊Dic₃	—	4	4	no	—
127	C₄⋊Dic₃	—	4	2	no	—
128	C₄⋊Dic₃	—	4	2	no	—
129	C₄⋊Dic₃	—	4	2	no	—
130	C₄⋊Dic₃	—	4	2	no	—
131	C₄⋊Dic₃	—	4	4	no	—
132	C₂×C₃⋊C₈	—	2	4	no	—
133	C₂×C₃⋊C₈	—	4	8	no	—
134	C₂×C₃⋊C₈	—	4	2	no	—
135	C₂×C₃⋊C₈	—	4	2	no	—
136	C₂³×C₄	—	6	2	no	—
137	C₂³×C₄	C₄×D₃	1	1	yes	characteristic
138	C₂³×C₄	D₁₂	1	1	yes	characteristic
139	C₂³×C₄	#67	1	1	yes	characteristic
140	C₂²×C₈	—	2	4	no	—
141	C₂²×C₈	—	2	2	no	—
142	C₂²×C₈	—	4	2	no	—
143	C₂²×C₈	—	4	2	no	—
144	C₂²×C₈	—	6	4	no	—
145	C₂²×C₈	—	6	2	no	—
146	C₂²×C₈	—	12	2	no	—
147	C₂²×C₈	—	12	2	no	—
148	C₂×C₄⋊C₄	—	3	4	no	—
149	C₂×C₄⋊C₄	—	6	2	no	—
150	C₂×C₄⋊C₄	—	6	2	no	—
151	C₂×C₄⋊C₄	—	6	2	no	—
152	C₂×C₄⋊C₄	—	6	2	no	—
153	C₂×C₄⋊C₄	—	6	2	no	—
154	C₂×C₄⋊C₄	—	12	4	no	—
155	C₂×C₄⋊C₄	—	12	2	no	—
156	C₂×C₄⋊C₄	—	12	2	no	—
157	C₂×C₄⋊C₄	—	12	2	no	—
158	C₂×C₄⋊C₄	—	12	2	no	—
159	C₂×C₄²	Dic₆	1	2	yes	—
160	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
161	C₂×C₄²	C₄×D₃	1	2	yes	—
162	C₂×C₄²	D₁₂	1	1	yes	characteristic
163	C₂×C₄²	C₂×Dic₃	1	2	yes	—
164	C₂×C₄²	#67	1	1	yes	characteristic
165	C₂×C₄²	#67	1	2	yes	—
166	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
167	C₄⋊C₈	—	2	4	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	3	4	no	—
170	C₄⋊C₈	—	6	4	no	—
171	C₄⋊C₈	—	6	2	no	—
172	C₄⋊C₈	C₂×Dic₃	1	4	yes	complemented
173	C₂³×C₃	#95	1	2	yes	—
174	C₂³×C₃	#100	1	2	yes	—
175	C₂³×C₃	#101	1	2	yes	—
176	C₂³×C₃	#102	1	2	yes	—
177	C₂³×C₃	#102	1	2	yes	—
178	C₂³×C₃	#103	1	2	yes	—
179	C₂³×C₃	#103	1	2	yes	—
180	C₂³×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₃×C₄	—	2	4	no	—
182	C₂×C₃×C₄	—	2	4	no	—
183	C₂×C₃×C₄	—	2	1	no	—
184	C₂×C₃×C₄	—	2	1	no	—
185	C₂×C₃×C₄	—	2	1	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	#95	1	2	yes	—
188	C₂×C₃×C₄	#95	1	2	yes	—
189	C₂×C₃×C₄	#95	1	2	yes	—
190	C₂×C₃×C₄	#102	1	2	yes	—
191	C₂×C₃×C₄	#102	1	2	yes	—
192	C₂×C₃×C₄	#102	1	4	yes	—
193	C₂×C₃×C₄	#102	1	4	yes	—
194	C₂×C₃×C₄	#103	1	2	yes	—
195	C₂×C₃×C₄	#103	1	2	yes	—
196	C₂×C₃×C₄	#103	1	4	yes	—
197	C₂×C₃×C₄	#103	1	4	yes	—
198	C₂×C₃×C₄	#106	1	4	yes	—
199	C₂×C₃×C₄	#106	1	4	yes	—
200	C₂×C₃×C₄	#107	1	4	yes	—
201	C₂×C₃×C₄	#107	1	4	yes	—
202	C₂×C₃×C₄	C₂×C₄²	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
216	C₂×Dic₃	—	4	4	no	—
217	C₂×Dic₃	—	4	4	no	—
218	C₂×Dic₃	—	4	4	no	—
219	C₂×Dic₃	—	8	8	no	—
220	C₃×C₈	—	4	4	no	—
221	C₃⋊C₈	—	4	4	no	—
222	C₂⁴	(C₂×D₃)⋊C₄	1	1	yes	characteristic
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	6	4	no	—
226	C₂²×C₄	—	12	4	no	—
227	C₂²×C₄	—	12	4	no	—
228	C₂²×C₄	—	12	4	no	—
229	C₂²×C₄	#204	1	2	yes	—
230	C₂²×C₄	#204	1	2	yes	—
231	C₂²×C₄	D₂₄	1	2	yes	—
232	C₂²×C₄	Dic₁₂	1	2	yes	—
233	C₂²×C₄	C₄×Dic₃	1	2	yes	—
234	C₂²×C₄	Dic₃⋊C₄	1	2	yes	—
235	C₂²×C₄	Dic₃⋊C₄	1	2	yes	—
236	C₂²×C₄	C₄⋊Dic₃	1	2	yes	—
237	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
239	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
240	C₂²×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
241	C₂²×C₄	#213	1	2	yes	—
242	C₂²×C₄	#214	1	2	yes	—
243	C₂²×C₄	#215	1	2	yes	—
244	C₂²×C₄	#216	1	2	yes	—
245	C₂²×C₄	#217	1	2	yes	—
246	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂²×C₄	C₂×D₁₂	1	1	yes	characteristic
248	C₂²×C₄	C₂×#67	1	1	yes	characteristic
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	4	8	no	—
251	C₂×C₈	—	4	2	no	—
252	C₂×C₈	—	4	2	no	—
253	C₂×C₈	—	6	4	no	—
254	C₂×C₈	—	12	8	no	—
255	C₂×C₈	—	12	2	no	—
256	C₂×C₈	—	12	2	no	—
257	C₄⋊C₄	—	12	4	no	—
258	C₄⋊C₄	—	12	4	no	—
259	C₄⋊C₄	—	12	4	no	—
260	C₄⋊C₄	—	12	4	no	—
261	C₄⋊C₄	—	12	2	no	—
262	C₄⋊C₄	—	12	2	no	—
263	C₄⋊C₄	—	12	2	no	—
264	C₄⋊C₄	—	12	2	no	—
265	C₄²	C₄×Dic₃	1	2	yes	—
266	C₄²	Dic₃⋊C₄	1	2	yes	—
267	C₄²	Dic₃⋊C₄	1	2	yes	—
268	C₄²	C₄⋊Dic₃	1	2	yes	—
269	C₄²	(C₂×D₃)⋊C₄	1	2	yes	—
270	C₄²	#217	1	2	yes	—
271	C₄²	C₂×Dic₆	1	1	yes	characteristic
272	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
273	C₄²	C₂²×Dic₃	1	1	yes	characteristic
274	C₄²	C₂×#67	1	1	yes	characteristic
275	C₂²×C₃	#331	1	4	yes	—
276	C₂²×C₃	#332	1	4	yes	—
277	C₂²×C₃	#332	1	4	yes	—
278	C₂²×C₃	#333	1	4	yes	—
279	C₂²×C₃	#340	1	4	yes	—
280	C₂²×C₃	#340	1	4	yes	—
281	C₂²×C₃	#343	1	4	yes	—
282	C₂²×C₃	C₂×#95	1	1	yes	characteristic
283	C₂²×C₃	C₂×#100	1	1	yes	characteristic
284	C₂²×C₃	C₂×#101	1	1	yes	characteristic
285	C₂²×C₃	C₂×#102	1	1	yes	characteristic
286	C₂²×C₃	C₂×#102	1	1	yes	characteristic
287	C₂²×C₃	C₂×#103	1	1	yes	characteristic
288	C₂²×C₃	C₂×#103	1	1	yes	characteristic
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	#340	1	4	yes	—
293	C₃×C₄	#340	1	4	yes	—
294	C₃×C₄	C₂×#102	1	1	yes	characteristic
295	C₃×C₄	C₂×#102	1	1	yes	characteristic
296	C₃×C₄	C₂×#103	1	1	yes	characteristic
297	C₃×C₄	C₂×#103	1	1	yes	characteristic
298	C₃×C₄	C₂×#106	1	1	yes	characteristic
299	C₃×C₄	C₂×#106	1	1	yes	characteristic
300	C₃×C₄	C₂×#107	1	1	yes	characteristic
301	C₃×C₄	C₂×#107	1	1	yes	characteristic
302	Dic₃	—	8	4	no	—
303	C₂³	#809	1	2	yes	—
304	C₂³	#810	1	2	yes	—
305	C₂³	#816	1	2	yes	—
306	C₂³	#821	1	2	yes	—
307	C₂³	#823	1	2	yes	—
308	C₂³	#824	1	2	yes	—
309	C₂³	C₃⋊#95	1	2	yes	—
310	C₂³	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	12	4	no	—
318	C₂×C₄	—	12	4	no	—
319	C₂×C₄	—	12	4	no	—
320	C₂×C₄	—	24	8	no	—
321	C₂×C₄	#807	1	4	yes	—
322	C₂×C₄	#808	1	4	yes	—
323	C₂×C₄	#809	1	2	yes	—
324	C₂×C₄	#810	1	2	yes	—
325	C₂×C₄	#816	1	2	yes	—
326	C₂×C₄	#816	1	4	yes	—
327	C₂×C₄	#817	1	4	yes	—
328	C₂×C₄	#818	1	4	yes	—
329	C₂×C₄	#821	1	2	yes	—
330	C₂×C₄	#821	1	4	yes	—
331	C₂×C₄	C₃⋊#95	1	2	yes	—
332	C₂×C₄	C₃⋊#95	1	2	yes	—
333	C₂×C₄	C₃⋊#95	1	2	yes	—
334	C₂×C₄	#832	1	4	yes	—
335	C₂×C₄	#835	1	4	yes	—
336	C₂×C₄	C₂×#204	1	1	yes	characteristic
337	C₂×C₄	C₂×#204	1	1	yes	characteristic
338	C₂×C₄	C₂×D₂₄	1	1	yes	characteristic
339	C₂×C₄	C₂×Dic₁₂	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
341	C₂×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
344	C₂×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×#213	1	1	yes	characteristic
346	C₂×C₄	C₂×#214	1	1	yes	characteristic
347	C₂×C₄	C₂×#215	1	1	yes	characteristic
348	C₂×C₄	C₂×#216	1	1	yes	characteristic
349	C₂×C₄	C₂×#217	1	1	yes	characteristic
350	C₈	—	4	4	no	—
351	C₈	—	12	4	no	—
352	C₂×C₃	#1296	1	8	yes	complemented
353	C₂×C₃	C₂×#331	1	1	yes	characteristic
354	C₂×C₃	C₂×#332	1	1	yes	characteristic
355	C₂×C₃	C₂×#332	1	1	yes	characteristic
356	C₂×C₃	C₂×#333	1	1	yes	characteristic
357	C₂×C₃	C₂×#340	1	1	yes	characteristic
358	C₂×C₃	C₂×#340	1	1	yes	characteristic
359	C₂×C₃	C₂×#343	1	1	yes	characteristic
360	C₂²	#4481	1	4	yes	—
361	C₂²	#4482	1	4	yes	—
362	C₂²	#4485	1	4	yes	—
363	C₂²	#4486	1	4	yes	—
364	C₂²	#4529	1	4	yes	—
365	C₂²	#4551	1	4	yes	—
366	C₂²	#4554	1	4	yes	—
367	C₂²	C₂×#809	1	1	yes	characteristic
368	C₂²	C₂×#810	1	1	yes	characteristic
369	C₂²	C₂×#816	1	1	yes	characteristic
370	C₂²	C₂×#821	1	1	yes	characteristic
371	C₂²	C₂×#823	1	1	yes	characteristic
372	C₂²	C₂×#824	1	1	yes	characteristic
373	C₂²	C₂×C₃⋊#95	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	24	4	no	—
378	C₄	#4529	1	4	yes	—
379	C₄	#4551	1	4	yes	—
380	C₄	C₂×#807	1	1	yes	characteristic
381	C₄	C₂×#808	1	1	yes	characteristic
382	C₄	C₂×#816	1	1	yes	characteristic
383	C₄	C₂×#817	1	1	yes	characteristic
384	C₄	C₂×#818	1	1	yes	characteristic
385	C₄	C₂×#821	1	1	yes	characteristic
386	C₄	C₂×#832	1	1	yes	characteristic
387	C₄	C₂×#835	1	1	yes	characteristic
388	C₃	C₂×#1296	1	1	yes	characteristic, complemented, Sylow
389	C₂	#67702	1	8	yes	direct product factor
390	C₂	C₂×#4485	1	1	yes	characteristic
391	C₂	C₂×#4486	1	1	yes	characteristic
392	C₂	C₂×#4482	1	1	yes	characteristic
393	C₂	C₂×#4481	1	1	yes	characteristic
394	C₂	C₂×#4529	1	1	yes	characteristic
395	C₂	C₂×#4551	1	1	yes	characteristic
396	C₂	C₂×#4554	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₃
Fitting	C₂²×C₃×C₄⋊C₈	C₂
socle, prime radical	C₂⁴×C₃	C₂²⋊C₄
cosocle	C₂×C₃×C₄²	C₂³
hypercenter	C₂²×C₄⋊C₈	D₃
hypocenter	C₃	C₂×#1296
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #67702	C₂	direct (N × H)
14. C₂×C₃×C₄⋊C₈	C₄	semidirect
22. C₂×C₄⋊(C₃⋊C₈)	C₄	semidirect
61. C₃×C₄⋊C₈	C₂×C₄	semidirect
64. C₄⋊(C₃⋊C₈)	C₂×C₄	semidirect
77. C₂×C₄⋊C₈	Dic₃	semidirect
172. C₄⋊C₈	C₂×Dic₃	semidirect
352. C₂×C₃	#1296	semidirect
388. C₃	C₂×#1296	semidirect
389. C₂	#67702	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
C₂×#4935	2
C₂²×C₄⋊(C₃⋊C₈)	2
#67702	2
C₂×#1296	3

Subgroups — C2×#67702 #10685271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#67702 #10685271