Subgroups — C₂×#22558116 #30746162

Order 17152.

986 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863360	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863256	C₂	1	1	yes	maximal, characteristic
3	#22558116	C₂	1	4	yes	maximal, direct product factor
4	C₂×#407×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	C₄	1	2	yes	complemented
6	C₂²×C₄⋊Dic₆₇	—	2	1	no	—
7	C₂²×C₂²⋊Dic₆₇	C₄	1	2	yes	—
8	#16863360	—	2	1	no	—
9	#16863360	—	2	1	no	—
10	#16863360	C₄	1	2	yes	complemented
11	#16863360	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
13	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
14	#16863256	—	2	1	no	—
15	#16863256	—	2	1	no	—
16	#16863256	C₄	1	2	yes	—
17	#16863256	C₂²	1	2	yes	—
18	C₂×C₆₇⋊#95	—	2	1	no	—
19	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₆₇	—	2	1	no	—
21	#407×C₆₇	—	2	1	no	—
22	#407×C₆₇	—	2	1	no	—
23	#407×C₆₇	C₄	1	2	yes	complemented
24	#407×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₇	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₆₇	C₄	1	2	yes	complemented
27	C₂³×Dic₆₇	—	2	2	no	—
28	C₂×#11761612	—	2	2	no	—
29	C₂×#11761612	—	4	4	no	—
30	C₂×#11761612	C₂×C₄	1	4	yes	complemented
31	C₂²×C₆₇⋊C₈	—	2	2	no	—
32	C₂×C₄⋊Dic₆₇	—	2	2	no	—
33	C₂×C₄⋊Dic₆₇	—	2	2	no	—
34	C₂×C₄⋊Dic₆₇	—	4	4	no	—
35	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
36	C₂×C₂²⋊Dic₆₇	—	4	4	no	—
37	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	4	yes	—
38	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
39	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
42	C₆₇⋊#95	—	2	2	no	—
43	C₆₇⋊#95	—	2	2	no	—
44	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	—	4	4	no	—
46	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
58	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
59	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₆₇	—	2	2	no	—
61	C₂×M₁₆×C₆₇	—	2	2	no	—
62	C₂×M₁₆×C₆₇	—	4	4	no	—
63	C₂²×C₈×C₆₇	—	2	2	no	—
64	C₂²⋊C₈×C₆₇	—	2	2	no	—
65	C₂²⋊C₈×C₆₇	—	2	2	no	—
66	C₂²⋊C₈×C₆₇	—	2	2	no	—
67	C₂²⋊C₈×C₆₇	C₂×C₄	1	4	yes	complemented
68	C₂²×Dic₆₇	—	2	4	no	—
69	C₂²×Dic₆₇	—	4	4	no	—
70	C₂²×Dic₆₇	—	4	4	no	—
71	C₂²×Dic₆₇	—	4	4	no	—
72	#11761612	—	4	4	no	—
73	#11761612	—	4	4	no	—
74	C₂×C₆₇⋊C₈	—	2	4	no	—
75	C₂×C₆₇⋊C₈	—	4	4	no	—
76	C₄⋊Dic₆₇	—	4	4	no	—
77	C₄⋊Dic₆₇	—	4	4	no	—
78	C₂²⋊Dic₆₇	—	4	4	no	—
79	C₂²⋊Dic₆₇	—	4	4	no	—
80	C₂⁴×C₆₇	—	2	2	no	—
81	C₂⁴×C₆₇	—	2	2	no	—
82	C₂⁴×C₆₇	—	4	2	no	—
83	C₂⁴×C₆₇	—	4	2	no	—
84	C₂⁴×C₆₇	C₄²	1	1	yes	characteristic
85	C₂⁴×C₆₇	C₄²	1	1	yes	characteristic
86	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	—	2	4	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
93	C₂²×C₄×C₆₇	—	2	4	no	—
94	C₂²×C₄×C₆₇	—	4	2	no	—
95	C₂²×C₄×C₆₇	—	4	2	no	—
96	C₂²×C₄×C₆₇	—	4	2	no	—
97	C₂²×C₄×C₆₇	—	4	2	no	—
98	C₂²×C₄×C₆₇	—	4	2	no	—
99	C₂²×C₄×C₆₇	—	4	2	no	—
100	C₂²×C₄×C₆₇	—	4	2	no	—
101	C₂²×C₄×C₆₇	—	4	2	no	—
102	C₂²×C₄×C₆₇	—	4	2	no	—
103	C₂²×C₄×C₆₇	—	4	2	no	—
104	C₂²×C₄×C₆₇	—	4	2	no	—
105	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
133	M₁₆×C₆₇	—	4	4	no	—
134	M₁₆×C₆₇	—	4	4	no	—
135	C₂×C₈×C₆₇	—	2	4	no	—
136	C₂×C₈×C₆₇	—	4	4	no	—
137	C₂³×C₆₇	—	2	2	no	—
138	C₂³×C₆₇	—	2	2	no	—
139	C₂³×C₆₇	—	2	2	no	—
140	C₂³×C₆₇	—	2	2	no	—
141	C₂³×C₆₇	—	2	2	no	—
142	C₂³×C₆₇	—	2	2	no	—
143	C₂³×C₆₇	—	2	2	no	—
144	C₂³×C₆₇	—	2	2	no	—
145	C₂³×C₆₇	—	2	2	no	—
146	C₂³×C₆₇	—	2	2	no	—
147	C₂³×C₆₇	—	2	1	no	—
148	C₂³×C₆₇	—	2	1	no	—
149	C₂³×C₆₇	—	2	1	no	—
150	C₂³×C₆₇	—	2	1	no	—
151	C₂³×C₆₇	—	4	1	no	—
152	C₂³×C₆₇	—	4	1	no	—
153	C₂³×C₆₇	—	4	1	no	—
154	C₂³×C₆₇	—	4	1	no	—
155	C₂³×C₆₇	—	4	1	no	—
156	C₂³×C₆₇	—	4	1	no	—
157	C₂³×C₆₇	—	4	1	no	—
158	C₂³×C₆₇	—	4	1	no	—
159	C₂³×C₆₇	—	4	8	no	—
160	C₂³×C₆₇	—	4	8	no	—
161	C₂³×C₆₇	#95	1	1	yes	characteristic
162	C₂³×C₆₇	#95	1	1	yes	characteristic
163	C₂³×C₆₇	#95	1	1	yes	characteristic
164	C₂³×C₆₇	#95	1	1	yes	characteristic
165	C₂³×C₆₇	#100	1	2	yes	—
166	C₂³×C₆₇	#101	1	2	yes	—
167	C₂³×C₆₇	C₂×C₄²	1	1	yes	characteristic
168	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	2	2	no	—
173	C₂×C₄×C₆₇	—	2	2	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	2	no	—
176	C₂×C₄×C₆₇	—	2	2	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	2	2	no	—
179	C₂×C₄×C₆₇	—	2	2	no	—
180	C₂×C₄×C₆₇	—	2	2	no	—
181	C₂×C₄×C₆₇	—	2	2	no	—
182	C₂×C₄×C₆₇	—	2	2	no	—
183	C₂×C₄×C₆₇	—	2	2	no	—
184	C₂×C₄×C₆₇	—	2	2	no	—
185	C₂×C₄×C₆₇	—	4	1	no	—
186	C₂×C₄×C₆₇	—	4	1	no	—
187	C₂×C₄×C₆₇	—	4	1	no	—
188	C₂×C₄×C₆₇	—	4	1	no	—
189	C₂×C₄×C₆₇	—	4	1	no	—
190	C₂×C₄×C₆₇	—	4	1	no	—
191	C₂×C₄×C₆₇	—	4	1	no	—
192	C₂×C₄×C₆₇	—	4	1	no	—
193	C₂×C₄×C₆₇	—	4	1	no	—
194	C₂×C₄×C₆₇	—	4	1	no	—
195	C₂×C₄×C₆₇	—	4	1	no	—
196	C₂×C₄×C₆₇	—	4	1	no	—
197	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
198	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
199	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
200	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
201	C₂×C₄×C₆₇	#99	1	4	yes	—
202	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×Dic₆₇	—	4	4	no	—
207	C₂×Dic₆₇	—	4	4	no	—
208	C₂×Dic₆₇	—	4	4	no	—
209	C₂×Dic₆₇	—	8	8	no	—
210	C₈×C₆₇	—	4	4	no	—
211	C₆₇⋊C₈	—	4	4	no	—
212	C₂²×C₆₇	—	2	4	no	—
213	C₂²×C₆₇	—	2	4	no	—
214	C₂²×C₆₇	—	2	1	no	—
215	C₂²×C₆₇	—	2	1	no	—
216	C₂²×C₆₇	—	2	1	no	—
217	C₂²×C₆₇	—	2	1	no	—
218	C₂²×C₆₇	—	2	1	no	—
219	C₂²×C₆₇	—	2	1	no	—
220	C₂²×C₆₇	—	2	1	no	—
221	C₂²×C₆₇	—	2	1	no	—
222	C₂²×C₆₇	—	2	1	no	—
223	C₂²×C₆₇	—	2	1	no	—
224	C₂²×C₆₇	—	2	1	no	—
225	C₂²×C₆₇	—	2	1	no	—
226	C₂²×C₆₇	—	2	1	no	—
227	C₂²×C₆₇	—	2	1	no	—
228	C₂²×C₆₇	—	2	1	no	—
229	C₂²×C₆₇	—	2	1	no	—
230	C₂²×C₆₇	—	4	2	no	—
231	C₂²×C₆₇	—	4	2	no	—
232	C₂²×C₆₇	—	4	4	no	—
233	C₂²×C₆₇	—	4	4	no	—
234	C₂²×C₆₇	—	4	2	no	—
235	C₂²×C₆₇	—	4	2	no	—
236	C₂²×C₆₇	—	4	4	no	—
237	C₂²×C₆₇	—	4	4	no	—
238	C₂²×C₆₇	#342	1	2	yes	—
239	C₂²×C₆₇	#343	1	2	yes	—
240	C₂²×C₆₇	#343	1	2	yes	—
241	C₂²×C₆₇	#344	1	2	yes	—
242	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
243	C₂²×C₆₇	C₂×#100	1	1	yes	characteristic
244	C₂²×C₆₇	C₂×#101	1	1	yes	characteristic
245	C₄×C₆₇	—	2	1	no	—
246	C₄×C₆₇	—	2	1	no	—
247	C₄×C₆₇	—	2	1	no	—
248	C₄×C₆₇	—	2	1	no	—
249	C₄×C₆₇	—	2	1	no	—
250	C₄×C₆₇	—	2	1	no	—
251	C₄×C₆₇	#342	1	2	yes	—
252	C₄×C₆₇	C₂×#99	1	2	yes	—
253	Dic₆₇	—	8	4	no	—
254	C₂×#1305	—	67	1	no	maximal, Sylow
255	C₂×C₆₇	—	2	1	no	—
256	C₂×C₆₇	—	2	2	no	—
257	C₂×C₆₇	—	2	1	no	—
258	C₂×C₆₇	—	4	1	no	—
259	C₂×C₆₇	—	4	1	no	—
260	C₂×C₆₇	—	4	1	no	—
261	C₂×C₆₇	—	4	1	no	—
262	C₂×C₆₇	#1305	1	4	yes	complemented
263	C₂×C₆₇	C₂×#342	1	1	yes	characteristic
264	C₂×C₆₇	C₂×#343	1	1	yes	characteristic
265	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
266	C₂×#407	—	67	1	no	—
267	C₂×#407	D₆₇	1	1	yes	characteristic
268	C₂×#380	—	67	1	no	—
269	#1305	—	67	4	no	—
270	C₆₇	C₂×#1305	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic
272	C₂²×M₁₆	—	2	1	no	—
273	C₂²×M₁₆	—	67	2	no	—
274	C₂²×C₄⋊C₄	—	134	1	no	—
275	C₂²×C₂²⋊C₄	—	67	2	no	—
276	#407	—	2	1	no	—
277	#407	—	2	1	no	—
278	#407	—	67	2	no	—
279	#407	—	67	2	no	—
280	#407	—	134	1	no	—
281	#407	—	134	1	no	—
282	#407	Dic₆₇	1	2	yes	complemented
283	#407	C₂×D₆₇	1	2	yes	—
284	C₂×C₂²⋊C₈	—	2	1	no	—
285	C₂×C₂²⋊C₈	—	134	1	no	—
286	C₂×C₂²⋊C₈	—	134	1	no	—
287	C₂×C₂²⋊C₈	Dic₆₇	1	2	yes	complemented
288	#380	—	67	2	no	—
289	#380	—	67	2	no	—
290	#380	—	134	1	no	—
291	#380	—	134	1	no	—
292	C₂×#95	—	134	1	no	—
293	C₂⁵	C₄×D₆₇	1	1	yes	characteristic
294	C₂³×C₄	—	4	4	no	—
295	C₂³×C₄	—	134	2	no	—
296	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
297	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
298	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
299	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
300	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
301	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
302	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
303	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
304	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
305	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
306	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
307	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
308	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
309	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	4	4	no	—
313	C₂×M₁₆	—	268	4	no	—
314	C₂×M₁₆	—	67	4	no	—
315	C₂×M₁₆	—	134	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	134	2	no	—
318	C₂×C₄⋊C₄	—	268	4	no	—
319	C₂×C₄⋊C₄	—	134	2	no	—
320	C₂×C₄⋊C₄	—	134	2	no	—
321	C₂×C₂²⋊C₄	—	268	4	no	—
322	C₂×C₂²⋊C₄	—	67	4	no	—
323	C₂×C₂²⋊C₄	—	134	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	134	2	no	—
328	C₂²⋊C₈	—	134	2	no	—
329	C₂²⋊C₈	—	134	2	no	—
330	C₂²⋊C₈	—	134	2	no	—
331	C₂²⋊C₈	C₂×Dic₆₇	1	4	yes	complemented
332	#95	—	134	2	no	—
333	#95	—	134	2	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	4	2	no	—
337	C₂⁴	—	4	2	no	—
338	C₂⁴	C₄×Dic₆₇	1	1	yes	characteristic
339	C₂⁴	C₄×Dic₆₇	1	1	yes	characteristic
340	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
341	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
342	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
343	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
344	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	268	4	no	—
360	C₂²×C₄	—	268	4	no	—
361	C₂²×C₄	—	268	4	no	—
362	C₂²×C₄	—	134	4	no	—
363	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
364	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
365	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
370	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
372	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
373	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
374	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
375	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
376	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
377	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
378	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
379	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
380	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
381	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
382	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
383	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
384	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
386	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
390	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
391	M₁₆	—	4	4	no	—
392	M₁₆	—	4	4	no	—
393	M₁₆	—	268	4	no	—
394	M₁₆	—	268	4	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	4	4	no	—
397	C₂×C₈	—	268	4	no	—
398	C₂×C₈	—	134	4	no	—
399	C₄⋊C₄	—	268	4	no	—
400	C₄⋊C₄	—	268	4	no	—
401	C₂²⋊C₄	—	268	4	no	—
402	C₂²⋊C₄	—	268	4	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	4	8	no	—
427	C₂³	C₆₇⋊#95	1	1	yes	characteristic
428	C₂³	C₆₇⋊#95	1	1	yes	characteristic
429	C₂³	C₆₇⋊#95	1	1	yes	characteristic
430	C₂³	C₆₇⋊#95	1	1	yes	characteristic
431	C₂³	#14523959	1	2	yes	—
432	C₂³	#14523961	1	2	yes	—
433	C₂³	C₂×C₄×Dic₆₇	1	1	yes	characteristic
434	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
435	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	268	4	no	—
464	C₂×C₄	—	268	4	no	—
465	C₂×C₄	—	268	4	no	—
466	C₂×C₄	—	536	8	no	—
467	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
468	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
469	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
470	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
471	C₂×C₄	#14523957	1	4	yes	—
472	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
473	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
474	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
475	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
476	C₈	—	4	4	no	—
477	C₈	—	268	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	#16863162	1	2	yes	—
505	C₂²	#16863164	1	2	yes	—
506	C₂²	#16863164	1	2	yes	—
507	C₂²	#16863167	1	2	yes	—
508	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
509	C₂²	C₂×#14523959	1	1	yes	characteristic
510	C₂²	C₂×#14523961	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	536	4	no	—
518	C₄	#16863162	1	2	yes	—
519	C₄	C₂×#14523957	1	2	yes	—
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	2	2	no	—
523	C₂	—	4	1	no	—
524	C₂	—	4	1	no	—
525	C₂	—	4	1	no	—
526	C₂	—	4	1	no	—
527	C₂	#22558116	1	4	yes	direct product factor
528	C₂	C₂×#16863162	1	1	yes	characteristic
529	C₂	C₂×#16863164	1	1	yes	characteristic
530	C₂	C₂×#16863167	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₆₇⋊#95
commutator	C₂³×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#407×C₆₇	C₂
socle	C₂³×C₆₇	#95
prime radical	C₂⁵×C₆₇	C₂×C₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#407	D₆₇
hypocenter	C₆₇	C₂×#1305
LCS	G ▷ C₂³×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #22558116	C₂	direct (N × H)
5. C₂²×#11761612	C₄	semidirect
10. #16863360	C₄	semidirect
23. #407×C₆₇	C₄	semidirect
26. C₂×C₂²⋊C₈×C₆₇	C₄	semidirect
30. C₂×#11761612	C₂×C₄	semidirect
67. C₂²⋊C₈×C₆₇	C₂×C₄	semidirect
262. C₂×C₆₇	#1305	semidirect
270. C₆₇	C₂×#1305	semidirect
282. #407	Dic₆₇	semidirect
287. C₂×C₂²⋊C₈	Dic₆₇	semidirect
331. C₂²⋊C₈	C₂×Dic₆₇	semidirect
527. C₂	#22558116	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×#16863360	2
C₂×#16863256	2
#22558116	2
C₂×#407×C₆₇	2
C₂×#1305	67

Subgroups — C2×#22558116 #30746162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22558116 #30746162