Subgroups — C₂×#22560255 #30855473

Order 17152.

1346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863434	C₂	1	2	yes	maximal, complemented
2	C₂×#16863370	C₂	1	2	yes	maximal
3	#22560255	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16863153	C₂	1	2	yes	maximal, complemented
5	C₂²×#131×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#14524002	C₂²	1	4	yes	—
7	#16863434	—	2	4	no	—
8	#16863434	C₂²	1	8	yes	complemented
9	C₂×#14523977	—	2	2	no	—
10	C₂×#14523975	—	2	2	no	—
11	#16863370	—	2	4	no	—
12	#16863370	C₂²	1	8	yes	—
13	C₂×#14523958	—	2	4	no	—
14	#16863153	C₂²	1	8	yes	complemented
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#131×C₆₇	—	2	2	no	—
17	C₂×#131×C₆₇	—	2	2	no	—
18	C₂×#131×C₆₇	—	2	4	no	—
19	C₂×#131×C₆₇	C₄	1	4	yes	complemented
20	C₂×#131×C₆₇	C₂²	1	4	yes	—
21	C₂²×M₁₆×C₆₇	C₄	1	2	yes	complemented
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₆₇	C₄	1	2	yes	complemented
24	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
25	#14524002	—	2	4	no	—
26	#14524002	—	2	4	no	—
27	#14524002	—	2	4	no	—
28	#14524002	C₂³	1	8	yes	—
29	C₂×C₄⋊Dic₆₇	—	2	4	no	—
30	C₂×C₂²⋊Dic₆₇	—	2	4	no	—
31	C₂×C₄×Dic₆₇	—	2	4	no	—
32	#14523977	—	2	8	no	—
33	#14523975	—	2	8	no	—
34	#14523958	—	2	16	no	—
35	C₂×#41×C₆₇	—	2	2	no	—
36	C₂×#41×C₆₇	—	2	2	no	—
37	C₂×#41×C₆₇	—	2	2	no	—
38	C₂×#41×C₆₇	—	2	2	no	—
39	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
40	C₂×#41×C₆₇	D₄	1	2	yes	—
41	C₂×#41×C₆₇	Q₈	1	2	yes	—
42	C₂×#41×C₆₇	C₂³	1	2	yes	—
43	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic
44	C₂²×D₄×C₆₇	D₄	1	2	yes	—
45	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	#131×C₆₇	—	2	8	no	—
49	#131×C₆₇	—	2	8	no	—
50	#131×C₆₇	—	2	8	no	—
51	#131×C₆₇	—	2	8	no	—
52	C₂×M₁₆×C₆₇	—	2	2	no	—
53	C₂×M₁₆×C₆₇	—	2	2	no	—
54	C₂×M₁₆×C₆₇	—	2	4	no	—
55	C₂×M₁₆×C₆₇	—	2	4	no	—
56	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
57	C₂×M₁₆×C₆₇	C₂×C₄	1	8	yes	complemented
58	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₆₇	—	2	2	no	—
60	C₂²×C₈×C₆₇	—	2	2	no	—
61	C₂²×C₈×C₆₇	—	2	4	no	—
62	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
67	C₂²×C₈×C₆₇	D₄	1	2	yes	—
68	C₂²×C₈×C₆₇	D₄	1	2	yes	—
69	C₂²×C₈×C₆₇	D₄	1	4	yes	—
70	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
71	C₂²×Dic₆₇	—	4	4	no	—
72	C₄⋊Dic₆₇	—	2	8	no	—
73	C₄⋊Dic₆₇	—	4	4	no	—
74	C₂²⋊Dic₆₇	—	2	8	no	—
75	C₂²⋊Dic₆₇	—	4	4	no	—
76	C₄×Dic₆₇	—	2	8	no	—
77	C₄×Dic₆₇	—	4	4	no	—
78	C₂⁴×C₆₇	C₄⋊C₄	1	2	yes	—
79	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
80	#41×C₆₇	—	2	4	no	—
81	#41×C₆₇	—	2	4	no	—
82	#41×C₆₇	—	2	4	no	—
83	#41×C₆₇	—	2	4	no	—
84	#41×C₆₇	—	2	4	no	—
85	#41×C₆₇	—	2	4	no	—
86	#41×C₆₇	—	2	4	no	—
87	#41×C₆₇	—	2	4	no	—
88	C₂×Q₈×C₆₇	—	2	2	no	—
89	C₂×Q₈×C₆₇	—	2	2	no	—
90	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
91	C₂×Q₈×C₆₇	C₂×Q₈	1	2	yes	—
92	C₂×D₄×C₆₇	—	2	4	no	—
93	C₂×D₄×C₆₇	—	2	4	no	—
94	C₂×D₄×C₆₇	—	2	2	no	—
95	C₂×D₄×C₆₇	—	2	2	no	—
96	C₂×D₄×C₆₇	C₄⋊C₄	1	4	yes	—
97	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
98	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₆₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₆₇	—	2	2	no	—
101	C₂²×C₄×C₆₇	—	2	2	no	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
105	C₂²×C₄×C₆₇	C₄⋊C₄	1	4	yes	—
106	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	#41	1	2	yes	—
115	C₂²×C₄×C₆₇	#41	1	2	yes	—
116	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₆₇	—	2	4	no	—
118	M₁₆×C₆₇	—	2	4	no	—
119	M₁₆×C₆₇	—	2	16	no	—
120	C₂×C₈×C₆₇	—	2	2	no	—
121	C₂×C₈×C₆₇	—	2	2	no	—
122	C₂×C₈×C₆₇	—	2	8	no	—
123	C₂×C₈×C₆₇	—	2	8	no	—
124	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
127	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
128	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
129	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
130	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
131	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
136	C₂³×C₆₇	—	2	2	no	—
137	C₂³×C₆₇	—	2	2	no	—
138	C₂³×C₆₇	—	4	2	no	—
139	C₂³×C₆₇	—	4	4	no	—
140	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂³×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
142	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₆₇	#121	1	2	yes	—
144	C₂³×C₆₇	#121	1	2	yes	—
145	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₆₇	—	2	4	no	—
147	Q₈×C₆₇	—	2	4	no	—
148	D₄×C₆₇	—	2	8	no	—
149	D₄×C₆₇	—	2	8	no	—
150	D₄×C₆₇	—	2	4	no	—
151	D₄×C₆₇	—	2	4	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	2	no	—
154	C₂×C₄×C₆₇	—	2	4	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	4	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
165	C₂×C₄×C₆₇	#117	1	2	yes	—
166	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
167	C₂×C₄×C₆₇	#121	1	2	yes	—
168	C₂×C₄×C₆₇	#121	1	2	yes	—
169	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
177	C₂×Dic₆₇	—	4	8	no	—
178	C₂×Dic₆₇	—	8	8	no	—
179	C₈×C₆₇	—	2	4	no	—
180	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
181	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
182	C₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂²×C₆₇	—	2	4	no	—
184	C₂²×C₆₇	—	2	2	no	—
185	C₂²×C₆₇	—	2	4	no	—
186	C₂²×C₆₇	—	4	1	no	—
187	C₂²×C₆₇	—	4	2	no	—
188	C₂²×C₆₇	—	4	1	no	—
189	C₂²×C₆₇	—	4	4	no	—
190	C₂²×C₆₇	—	4	4	no	—
191	C₂²×C₆₇	—	4	4	no	—
192	C₂²×C₆₇	#380	1	1	yes	characteristic
193	C₂²×C₆₇	#380	1	2	yes	—
194	C₂²×C₆₇	#380	1	1	yes	characteristic
195	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
196	C₂²×C₆₇	C₂×#121	1	2	yes	—
197	C₄×C₆₇	—	2	4	no	—
198	C₄×C₆₇	#380	1	1	yes	characteristic
199	C₄×C₆₇	#380	1	1	yes	characteristic
200	C₄×C₆₇	#380	1	2	yes	—
201	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
203	C₄×C₆₇	C₂×C₂²⋊Q₈	1	2	yes	—
204	Dic₆₇	—	8	8	no	—
205	C₂×#1812	—	67	1	no	maximal, Sylow
206	C₂×C₆₇	—	2	2	no	—
207	C₂×C₆₇	—	2	1	no	—
208	C₂×C₆₇	—	2	1	no	—
209	C₂×C₆₇	—	2	2	no	—
210	C₂×C₆₇	—	4	4	no	—
211	C₂×C₆₇	#1812	1	2	yes	complemented
212	C₂×C₆₇	C₂×#380	1	1	yes	characteristic
213	C₂²×#131	D₆₇	1	1	yes	characteristic
214	C₂×#427	—	67	2	no	—
215	C₂×#410	—	67	2	no	—
216	#1812	—	67	8	no	—
217	C₂×H(3,ℤ/4)	—	67	2	no	—
218	C₆₇	C₂×#1812	1	1	yes	characteristic, complemented, Sylow
219	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
220	C₂×#131	—	2	2	no	—
221	C₂×#131	—	2	2	no	—
222	C₂×#131	—	2	4	no	—
223	C₂×#131	Dic₆₇	1	4	yes	complemented
224	C₂×#131	C₂×D₆₇	1	4	yes	—
225	C₂²×M₁₆	Dic₆₇	1	2	yes	complemented
226	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
227	C₂³×C₈	Dic₆₇	1	2	yes	complemented
228	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
229	C₂×#117	—	67	4	no	—
230	#427	—	67	8	no	—
231	#427	—	134	4	no	—
232	C₂×#107	—	134	2	no	—
233	C₂×#106	—	134	2	no	—
234	#410	—	67	8	no	—
235	#410	—	134	4	no	—
236	C₂×#99	—	134	4	no	—
237	H(3,ℤ/4)	—	67	8	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	Dic₁₃₄	1	2	yes	—
243	C₂×#41	D₂₆₈	1	2	yes	—
244	C₂×#41	C₂×Dic₆₇	1	2	yes	—
245	C₂×#41	C₂²×D₆₇	1	2	yes	—
246	C₂²×Q₈	Dic₁₃₄	1	1	yes	characteristic
247	C₂²×D₄	Dic₁₃₄	1	1	yes	characteristic
248	C₂²×D₄	D₂₆₈	1	2	yes	—
249	C₂³×C₄	C₂×Dic₆₇	1	2	yes	—
250	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
251	#131	—	2	8	no	—
252	#131	—	2	8	no	—
253	#131	—	2	8	no	—
254	#131	—	2	8	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	4	no	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
260	C₂×M₁₆	C₂×Dic₆₇	1	8	yes	complemented
261	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
266	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
267	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
268	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
269	C₂²×C₈	C₂×Dic₆₇	1	8	yes	complemented
270	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
271	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
272	C₂²×C₈	C₂²⋊D₆₇	1	4	yes	—
273	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
274	#117	—	67	8	no	—
275	#117	—	134	4	no	—
276	#117	—	134	4	no	—
277	#117	—	134	4	no	—
278	C₂×C₄⋊C₄	—	134	4	no	—
279	C₂×C₂²⋊C₄	—	134	4	no	—
280	C₂×C₄²	—	134	4	no	—
281	#107	—	134	8	no	—
282	#106	—	134	8	no	—
283	#99	—	134	16	no	—
284	C₂⁴	C₄⋊Dic₆₇	1	2	yes	—
285	C₂⁴	C₂×D₂₆₈	1	1	yes	characteristic
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	C₄⋊Dic₆₇	1	2	yes	—
297	C₂×Q₈	C₂×Dic₁₃₄	1	2	yes	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
303	C₂×D₄	C₄⋊Dic₆₇	1	4	yes	—
304	C₂×D₄	C₂×D₂₆₈	1	4	yes	—
305	C₂×D₄	C₂×Dic₁₃₄	1	2	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	268	4	no	—
311	C₂²×C₄	C₄⋊Dic₆₇	1	2	yes	—
312	C₂²×C₄	C₄⋊Dic₆₇	1	4	yes	—
313	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
314	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
317	C₂²×C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
318	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
319	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
320	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
321	C₂²×C₄	#11761628	1	2	yes	—
322	C₂²×C₄	#11761628	1	2	yes	—
323	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	16	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	8	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
332	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
333	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
334	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
335	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
336	C₂×C₈	C₂²⋊Dic₆₇	1	4	yes	—
337	C₂×C₈	C₂²⋊Dic₆₇	1	4	yes	—
338	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
339	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
340	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₆₇	1	4	yes	—
342	C₂×C₈	C₂×C₂²⋊D₆₇	1	4	yes	—
343	C₄⋊C₄	—	268	4	no	—
344	C₄⋊C₄	—	134	8	no	—
345	C₂²⋊C₄	—	268	4	no	—
346	C₂²⋊C₄	—	134	8	no	—
347	C₄²	—	268	4	no	—
348	C₄²	—	134	8	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	4	no	—
353	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
354	C₂³	C₂×C₄⋊Dic₆₇	1	4	yes	—
355	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
356	C₂³	#14524017	1	2	yes	—
357	C₂³	#14524017	1	2	yes	—
358	C₂³	C₂²×D₂₆₈	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	8	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	268	8	no	—
372	C₂×C₄	—	536	8	no	—
373	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	2	yes	—
376	C₂×C₄	C₂×C₄⋊Dic₆₇	1	4	yes	—
377	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
379	C₂×C₄	#14524002	1	1	yes	characteristic
380	C₂×C₄	#14524002	1	2	yes	—
381	C₂×C₄	#14524002	1	1	yes	characteristic
382	C₂×C₄	#14524017	1	2	yes	—
383	C₂×C₄	#14524017	1	2	yes	—
384	C₂×C₄	#14524022	1	2	yes	—
385	C₂×C₄	#14524022	1	2	yes	—
386	C₂×C₄	#14524022	1	2	yes	—
387	C₂×C₄	#14524022	1	2	yes	—
388	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₂²⋊D₆₇	1	2	yes	—
390	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
391	C₂×C₄	C₂×#11761628	1	2	yes	—
392	C₈	—	2	4	no	—
393	C₈	C₂×C₂²⋊Dic₆₇	1	2	yes	—
394	C₈	C₂×C₂²⋊Dic₆₇	1	2	yes	—
395	C₈	C₂×C₂²⋊Dic₆₇	1	4	yes	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	#16863256	1	1	yes	characteristic
406	C₂²	#16863256	1	2	yes	—
407	C₂²	#16863256	1	1	yes	characteristic
408	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
409	C₂²	C₂×#14524017	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	536	8	no	—
412	C₄	#16863256	1	1	yes	characteristic
413	C₄	#16863256	1	1	yes	characteristic
414	C₄	#16863256	1	2	yes	—
415	C₄	C₂²×C₂²⋊Dic₆₇	1	1	yes	characteristic
416	C₄	C₂×#14524002	1	1	yes	characteristic
417	C₄	C₂×#14524022	1	2	yes	—
418	C₂	—	2	2	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	2	no	—
422	C₂	—	4	4	no	—
423	C₂	#22560255	1	2	yes	direct product factor
424	C₂	C₂×#16863256	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524002
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂²×#131×C₆₇	C₂
socle	C₂²×C₆₇	#380
prime radical	C₂²×#41×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂²×#131	D₆₇
hypocenter	C₆₇	C₂×#1812
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#16863434	C₂	semidirect
3. #22560255	C₂	direct (N × H)
4. C₂×#16863153	C₂	semidirect
8. #16863434	C₂²	semidirect
14. #16863153	C₂²	semidirect
19. C₂×#131×C₆₇	C₄	semidirect
21. C₂²×M₁₆×C₆₇	C₄	semidirect
23. C₂³×C₈×C₆₇	C₄	semidirect
57. C₂×M₁₆×C₆₇	C₂×C₄	semidirect
66. C₂²×C₈×C₆₇	C₂×C₄	semidirect
211. C₂×C₆₇	#1812	semidirect
218. C₆₇	C₂×#1812	semidirect
223. C₂×#131	Dic₆₇	semidirect
225. C₂²×M₁₆	Dic₆₇	semidirect
227. C₂³×C₈	Dic₆₇	semidirect
260. C₂×M₁₆	C₂×Dic₆₇	semidirect
269. C₂²×C₈	C₂×Dic₆₇	semidirect
423. C₂	#22560255	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16863434	2
C₂×#16863370	2
#22560255	2
C₂×#16863153	2
C₂²×#131×C₆₇	2
C₂×#1812	67

Subgroups — C2×#22560255 #30855473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560255 #30855473