Subgroups — #30746203

Order 17152.

942 conjugacy classes of subgroups.

The subgroup lattice has 506 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×#16863259	C₂	1	1	yes	maximal, characteristic
3	#22558118	C₂	1	4	yes	maximal, complemented
4	C₂×#407×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	—	2	1	no	—
6	C₂²×C₂²⋊Dic₆₇	C₄	1	2	yes	—
7	#16863360	—	2	1	no	—
8	#16863360	—	2	1	no	—
9	#16863360	C₄	1	2	yes	complemented
10	#16863360	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
12	C₂×C₂²⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
13	#16863259	—	2	1	no	—
14	#16863259	—	2	1	no	—
15	#16863259	C₄	1	2	yes	—
16	#16863259	C₂²	1	2	yes	—
17	C₂×C₆₇⋊#95	—	2	1	no	—
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	—	2	2	no	—
30	C₂×#11761612	—	4	4	no	—
31	C₂²×C₆₇⋊C₈	—	2	2	no	—
32	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
33	C₂×C₂²⋊Dic₆₇	—	4	4	no	—
34	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	4	yes	—
35	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
38	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	complemented
39	C₆₇⋊#95	—	2	2	no	—
40	C₆₇⋊#95	—	2	2	no	—
41	C₆₇⋊#95	—	2	2	no	—
42	C₆₇⋊#95	—	2	2	no	—
43	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	—	4	4	no	—
45	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
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	D₄	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	Q₈	1	1	yes	characteristic
57	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
58	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₆₇	—	2	2	no	—
60	C₂×M₁₆×C₆₇	—	2	2	no	—
61	C₂×M₁₆×C₆₇	—	4	4	no	—
62	C₂²×C₈×C₆₇	—	2	2	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	C₂×C₄	1	4	yes	complemented
67	C₂²×Dic₆₇	—	2	4	no	—
68	C₂²×Dic₆₇	—	4	4	no	—
69	C₂²×Dic₆₇	—	4	4	no	—
70	C₂²×Dic₆₇	—	4	4	no	—
71	#11761612	—	4	4	no	—
72	#11761612	—	4	4	no	—
73	C₂×C₆₇⋊C₈	—	2	4	no	—
74	C₂×C₆₇⋊C₈	—	4	4	no	—
75	C₂²⋊Dic₆₇	—	4	4	no	—
76	C₂²⋊Dic₆₇	—	4	4	no	—
77	C₂⁴×C₆₇	—	2	4	no	—
78	C₂⁴×C₆₇	—	4	2	no	—
79	C₂⁴×C₆₇	—	4	2	no	—
80	C₂⁴×C₆₇	C₄²	1	1	yes	characteristic
81	C₂⁴×C₆₇	C₄²	1	1	yes	characteristic
82	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	—	2	4	no	—
88	C₂²×C₄×C₆₇	—	2	4	no	—
89	C₂²×C₄×C₆₇	—	4	2	no	—
90	C₂²×C₄×C₆₇	—	4	2	no	—
91	C₂²×C₄×C₆₇	—	4	2	no	—
92	C₂²×C₄×C₆₇	—	4	2	no	—
93	C₂²×C₄×C₆₇	—	4	2	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	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
129	M₁₆×C₆₇	—	4	4	no	—
130	M₁₆×C₆₇	—	4	4	no	—
131	C₂×C₈×C₆₇	—	2	4	no	—
132	C₂×C₈×C₆₇	—	4	4	no	—
133	C₂³×C₆₇	—	2	2	no	—
134	C₂³×C₆₇	—	2	2	no	—
135	C₂³×C₆₇	—	2	2	no	—
136	C₂³×C₆₇	—	2	2	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	—	4	1	no	—
146	C₂³×C₆₇	—	4	1	no	—
147	C₂³×C₆₇	—	4	1	no	—
148	C₂³×C₆₇	—	4	1	no	—
149	C₂³×C₆₇	—	4	1	no	—
150	C₂³×C₆₇	—	4	1	no	—
151	C₂³×C₆₇	—	4	1	no	—
152	C₂³×C₆₇	—	4	1	no	—
153	C₂³×C₆₇	—	4	16	no	—
154	C₂³×C₆₇	#95	1	1	yes	characteristic
155	C₂³×C₆₇	#95	1	1	yes	characteristic
156	C₂³×C₆₇	#95	1	1	yes	characteristic
157	C₂³×C₆₇	#95	1	1	yes	characteristic
158	C₂³×C₆₇	#99	1	4	yes	—
159	C₂³×C₆₇	C₂×C₄²	1	1	yes	characteristic
160	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	2	2	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	2	2	no	—
169	C₂×C₄×C₆₇	—	2	2	no	—
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	—	4	1	no	—
175	C₂×C₄×C₆₇	—	4	1	no	—
176	C₂×C₄×C₆₇	—	4	1	no	—
177	C₂×C₄×C₆₇	—	4	1	no	—
178	C₂×C₄×C₆₇	—	4	1	no	—
179	C₂×C₄×C₆₇	—	4	1	no	—
180	C₂×C₄×C₆₇	—	4	1	no	—
181	C₂×C₄×C₆₇	—	4	1	no	—
182	C₂×C₄×C₆₇	—	4	1	no	—
183	C₂×C₄×C₆₇	—	4	1	no	—
184	C₂×C₄×C₆₇	—	4	1	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	#95	1	1	yes	characteristic
191	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
192	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
193	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
194	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₆₇	—	4	4	no	—
199	C₂×Dic₆₇	—	4	4	no	—
200	C₂×Dic₆₇	—	4	4	no	—
201	C₂×Dic₆₇	—	8	8	no	—
202	C₈×C₆₇	—	4	4	no	—
203	C₆₇⋊C₈	—	4	4	no	—
204	C₂²×C₆₇	—	2	8	no	—
205	C₂²×C₆₇	—	2	1	no	—
206	C₂²×C₆₇	—	2	1	no	—
207	C₂²×C₆₇	—	2	1	no	—
208	C₂²×C₆₇	—	2	1	no	—
209	C₂²×C₆₇	—	2	1	no	—
210	C₂²×C₆₇	—	2	1	no	—
211	C₂²×C₆₇	—	2	1	no	—
212	C₂²×C₆₇	—	2	1	no	—
213	C₂²×C₆₇	—	2	1	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	—	4	4	no	—
222	C₂²×C₆₇	—	4	4	no	—
223	C₂²×C₆₇	—	4	4	no	—
224	C₂²×C₆₇	—	4	4	no	—
225	C₂²×C₆₇	—	4	4	no	—
226	C₂²×C₆₇	—	4	4	no	—
227	C₂²×C₆₇	#342	1	2	yes	—
228	C₂²×C₆₇	#342	1	2	yes	—
229	C₂²×C₆₇	#344	1	2	yes	—
230	C₂²×C₆₇	#344	1	2	yes	—
231	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
232	C₂²×C₆₇	C₂×#99	1	2	yes	—
233	C₄×C₆₇	—	2	1	no	—
234	C₄×C₆₇	—	2	1	no	—
235	C₄×C₆₇	—	2	1	no	—
236	C₄×C₆₇	—	2	1	no	—
237	C₄×C₆₇	—	2	1	no	—
238	C₄×C₆₇	—	2	1	no	—
239	C₄×C₆₇	—	2	1	no	—
240	C₄×C₆₇	—	2	1	no	—
241	Dic₆₇	—	8	4	no	—
242	#8114	—	67	1	no	maximal, Sylow
243	C₂×C₆₇	—	2	2	no	—
244	C₂×C₆₇	—	2	2	no	—
245	C₂×C₆₇	—	2	2	no	—
246	C₂×C₆₇	—	2	2	no	—
247	C₂×C₆₇	—	2	2	no	—
248	C₂×C₆₇	—	4	1	no	—
249	C₂×C₆₇	—	4	1	no	—
250	C₂×C₆₇	C₂×#342	1	1	yes	characteristic
251	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
252	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
253	C₂×#407	—	67	1	no	—
254	C₂×#407	D₆₇	1	1	yes	characteristic
255	C₂×#381	—	67	1	no	—
256	#1306	—	67	4	no	—
257	C₆₇	#8114	1	1	yes	characteristic, complemented, Sylow
258	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic
259	C₂²×M₁₆	—	2	1	no	—
260	C₂²×M₁₆	—	134	1	no	—
261	C₂²×C₂²⋊C₄	—	67	2	no	—
262	#407	—	2	1	no	—
263	#407	—	2	1	no	—
264	#407	—	67	2	no	—
265	#407	—	67	2	no	—
266	#407	—	134	1	no	—
267	#407	—	134	1	no	—
268	#407	Dic₆₇	1	2	yes	complemented
269	#407	C₂×D₆₇	1	2	yes	—
270	C₂×C₂²⋊C₈	—	2	1	no	—
271	C₂×C₂²⋊C₈	—	67	2	no	—
272	C₂×C₂²⋊C₈	—	134	1	no	—
273	C₂×C₂²⋊C₈	Dic₆₇	1	2	yes	complemented
274	#381	—	67	2	no	—
275	#381	—	67	2	no	—
276	#381	—	134	1	no	—
277	#381	—	134	1	no	—
278	C₂×#95	—	134	1	no	—
279	C₂×#95	—	134	1	no	—
280	C₂⁵	C₄×D₆₇	1	1	yes	characteristic
281	C₂³×C₄	—	4	4	no	—
282	C₂³×C₄	—	134	2	no	—
283	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
284	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
285	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
286	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
287	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
288	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
289	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
290	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
291	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
292	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
293	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
294	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
295	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
296	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	4	4	no	—
300	C₂×M₁₆	—	268	4	no	—
301	C₂×M₁₆	—	134	2	no	—
302	C₂×M₁₆	—	134	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	134	2	no	—
305	C₂×C₂²⋊C₄	—	268	4	no	—
306	C₂×C₂²⋊C₄	—	67	4	no	—
307	C₂×C₂²⋊C₄	—	134	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	67	4	no	—
312	C₂²⋊C₈	—	134	2	no	—
313	C₂²⋊C₈	—	134	2	no	—
314	C₂²⋊C₈	—	134	2	no	—
315	C₂²⋊C₈	C₂×Dic₆₇	1	4	yes	complemented
316	#95	—	134	2	no	—
317	#95	—	134	2	no	—
318	#95	—	134	2	no	—
319	#95	—	134	2	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	4	2	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	C₄×Dic₆₇	1	1	yes	characteristic
324	C₂⁴	C₄×Dic₆₇	1	1	yes	characteristic
325	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
326	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
327	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
328	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
329	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	268	4	no	—
345	C₂²×C₄	—	268	4	no	—
346	C₂²×C₄	—	268	4	no	—
347	C₂²×C₄	—	134	4	no	—
348	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
349	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
350	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
351	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
352	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
357	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
358	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
359	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
360	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
361	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
362	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
363	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
365	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
367	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
368	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
369	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
371	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
375	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
376	M₁₆	—	4	4	no	—
377	M₁₆	—	4	4	no	—
378	M₁₆	—	268	4	no	—
379	M₁₆	—	268	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	4	4	no	—
382	C₂×C₈	—	268	4	no	—
383	C₂×C₈	—	134	4	no	—
384	C₂²⋊C₄	—	268	4	no	—
385	C₂²⋊C₄	—	268	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	16	no	—
407	C₂³	C₆₇⋊#95	1	1	yes	characteristic
408	C₂³	C₆₇⋊#95	1	1	yes	characteristic
409	C₂³	C₆₇⋊#95	1	1	yes	characteristic
410	C₂³	C₆₇⋊#95	1	1	yes	characteristic
411	C₂³	#14523957	1	4	yes	—
412	C₂³	C₂×C₄×Dic₆₇	1	1	yes	characteristic
413	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
414	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	268	4	no	—
444	C₂×C₄	—	268	4	no	—
445	C₂×C₄	—	268	4	no	—
446	C₂×C₄	—	536	8	no	—
447	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
448	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
449	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
450	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
451	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
452	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
453	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
455	C₈	—	4	4	no	—
456	C₈	—	268	4	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	#16863162	1	2	yes	—
481	C₂²	#16863162	1	2	yes	—
482	C₂²	#16863167	1	2	yes	—
483	C₂²	#16863168	1	2	yes	—
484	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
485	C₂²	C₂×#14523957	1	2	yes	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	536	4	no	—
495	C₂	—	2	2	no	—
496	C₂	—	2	2	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	2	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	1	no	—
501	C₂	—	4	1	no	—
502	C₂	C₂×#16863162	1	1	yes	characteristic
503	C₂	C₂×#16863167	1	1	yes	characteristic
504	C₂	C₂×#16863168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₆₇⋊#95
commutator	C₂³×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#407×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁵×C₆₇	C₂×C₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#407	D₆₇
hypocenter	C₆₇	#8114
LCS	G ▷ C₂³×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #22558118	C₂	semidirect
9. #16863360	C₄	semidirect
12. C₂×C₂²⋊(C₆₇⋊C₈)	C₄	semidirect
23. #407×C₆₇	C₄	semidirect
26. C₂×C₂²⋊C₈×C₆₇	C₄	semidirect
38. C₂²⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
66. C₂²⋊C₈×C₆₇	C₂×C₄	semidirect
257. C₆₇	#8114	semidirect
268. #407	Dic₆₇	semidirect
273. C₂×C₂²⋊C₈	Dic₆₇	semidirect
315. C₂²⋊C₈	C₂×Dic₆₇	semidirect

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×#16863259	2
#22558118	2
C₂×#407×C₆₇	2
#8114	67