Subgroups — #30860867

Order 17152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
2	#22562607	C₂	1	1	yes	maximal, characteristic, complemented
3	#22561154	C₂	1	2	yes	maximal, complemented
4	#22561129	C₂	1	2	yes	maximal, complemented
5	#22560512	C₂	1	4	yes	maximal, complemented
6	#22560019	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11761612	C₂²	1	2	yes	—
9	C₂×#14523970	C₂²	1	8	yes	—
10	C₄×#11761612	—	2	1	no	—
11	C₄×#11761612	—	2	1	no	—
12	C₄×#11761612	C₂²	1	2	yes	—
13	C₄×#11761612	C₂²	1	2	yes	—
14	C₂×#14523954	—	2	1	no	—
15	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
16	#16863264	—	2	1	no	—
17	#16863262	—	2	1	no	—
18	#16863259	—	2	1	no	—
19	#16863256	—	2	1	no	—
20	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	—
21	C₄×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
22	#16863242	C₂²	1	2	yes	—
23	#16863155	C₂²	1	8	yes	—
24	#533×C₆₇	C₄	1	1	yes	characteristic, complemented
25	#533×C₆₇	C₄	1	1	yes	characteristic, complemented
26	#533×C₆₇	C₂²	1	1	yes	characteristic
27	#532×C₆₇	C₄	1	1	yes	characteristic, complemented
28	#532×C₆₇	C₄	1	1	yes	characteristic, complemented
29	#532×C₆₇	C₂²	1	1	yes	characteristic
30	#529×C₆₇	—	2	1	no	—
31	#529×C₆₇	—	2	1	no	—
32	#529×C₆₇	—	2	1	no	—
33	#529×C₆₇	—	2	1	no	—
34	#529×C₆₇	C₄	1	2	yes	complemented
35	#529×C₆₇	C₄	1	2	yes	complemented
36	#525×C₆₇	—	2	1	no	—
37	#525×C₆₇	—	2	1	no	—
38	#525×C₆₇	C₂²	1	2	yes	—
39	C₄×#41×C₆₇	—	2	1	no	—
40	C₄×#41×C₆₇	—	2	1	no	—
41	C₄×#41×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#11761612	—	2	8	no	—
44	C₂×#11761612	—	2	2	no	—
45	C₂×#11761612	C₂³	1	4	yes	—
46	C₂²×C₆₇⋊C₈	—	2	2	no	—
47	C₂×C₄⋊Dic₆₇	—	2	2	no	—
48	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
49	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
50	#14523970	—	2	16	no	—
51	#14523954	—	2	2	no	—
52	#14523954	—	2	2	no	—
53	C₄×C₆₇⋊C₈	—	2	2	no	—
54	C₄×C₆₇⋊C₈	—	2	2	no	—
55	C₆₇⋊#95	—	2	2	no	—
56	C₆₇⋊#95	—	2	2	no	—
57	C₆₇⋊#95	—	2	2	no	—
58	C₆₇⋊#95	—	2	2	no	—
59	C₂×#41×C₆₇	—	2	1	no	—
60	C₂×#41×C₆₇	—	2	1	no	—
61	C₂×#41×C₆₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
68	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
69	#126×C₆₇	—	2	2	no	—
70	#126×C₆₇	—	2	2	no	—
71	#125×C₆₇	—	2	1	no	—
72	#125×C₆₇	—	2	1	no	—
73	#125×C₆₇	C₂×C₄	1	2	yes	—
74	#124×C₆₇	—	2	1	no	—
75	#124×C₆₇	—	2	1	no	—
76	#124×C₆₇	C₂×C₄	1	2	yes	—
77	#123×C₆₇	—	2	2	no	—
78	#123×C₆₇	—	2	2	no	—
79	#123×C₆₇	—	2	2	no	—
80	C₂²⋊Q₈×C₆₇	—	2	1	no	—
81	C₂²⋊Q₈×C₆₇	—	2	1	no	—
82	C₂²⋊Q₈×C₆₇	—	2	1	no	—
83	C₂²⋊Q₈×C₆₇	—	2	1	no	—
84	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
85	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
86	#121×C₆₇	—	2	1	no	—
87	#121×C₆₇	—	2	1	no	—
88	#121×C₆₇	—	2	1	no	—
89	#121×C₆₇	—	2	1	no	—
90	#121×C₆₇	C₂×C₄	1	2	yes	—
91	#121×C₆₇	C₂×C₄	1	2	yes	—
92	#120×C₆₇	—	2	2	no	—
93	C₄×Q₈×C₆₇	—	2	1	no	—
94	C₄×Q₈×C₆₇	—	2	1	no	—
95	C₄×Q₈×C₆₇	—	2	1	no	—
96	C₄×Q₈×C₆₇	—	2	1	no	—
97	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
99	C₄×D₄×C₆₇	—	2	2	no	—
100	C₄×D₄×C₆₇	—	2	2	no	—
101	C₄×D₄×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	—	2	2	no	—
103	C₄×D₄×C₆₇	—	2	2	no	—
104	C₄×D₄×C₆₇	—	2	2	no	—
105	C₄×D₄×C₆₇	—	2	1	no	—
106	C₄×D₄×C₆₇	—	2	1	no	—
107	C₄×D₄×C₆₇	—	2	1	no	—
108	C₄×D₄×C₆₇	—	2	1	no	—
109	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
111	#117×C₆₇	—	2	1	no	—
112	#117×C₆₇	—	2	1	no	—
113	#117×C₆₇	—	2	2	no	—
114	#117×C₆₇	—	2	2	no	—
115	#117×C₆₇	—	2	2	no	—
116	#117×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄²×C₆₇	—	2	2	no	—
118	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×Dic₆₇	—	2	4	no	—
131	#11761612	—	2	8	no	—
132	#11761612	—	2	4	no	—
133	#11761612	#41	1	8	yes	complemented
134	C₂×C₆₇⋊C₈	—	2	8	no	—
135	C₂×C₆₇⋊C₈	—	2	4	no	—
136	C₄⋊Dic₆₇	—	4	4	no	—
137	C₂²⋊Dic₆₇	—	4	4	no	—
138	C₄×Dic₆₇	—	2	8	no	—
139	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
140	#41×C₆₇	—	2	8	no	—
141	#41×C₆₇	—	4	4	no	—
142	#41×C₆₇	—	4	4	no	—
143	C₂×Q₈×C₆₇	—	2	1	no	—
144	C₂×Q₈×C₆₇	—	2	1	no	—
145	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₆₇	—	2	2	no	—
147	C₂×D₄×C₆₇	—	2	2	no	—
148	C₂×D₄×C₆₇	—	2	2	no	—
149	C₂×D₄×C₆₇	—	2	1	no	—
150	C₂×D₄×C₆₇	—	2	1	no	—
151	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₆₇	—	2	4	no	—
153	C₂²×C₄×C₆₇	—	2	2	no	—
154	C₂²×C₄×C₆₇	—	2	2	no	—
155	C₂²×C₄×C₆₇	—	2	2	no	—
156	C₂²×C₄×C₆₇	—	4	2	no	—
157	C₂²×C₄×C₆₇	—	4	2	no	—
158	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
176	C₄⋊C₄×C₆₇	—	2	1	no	—
177	C₄⋊C₄×C₆₇	—	2	1	no	—
178	C₄⋊C₄×C₆₇	—	2	1	no	—
179	C₄⋊C₄×C₆₇	—	2	1	no	—
180	C₄⋊C₄×C₆₇	—	2	2	no	—
181	C₄⋊C₄×C₆₇	—	2	2	no	—
182	C₄⋊C₄×C₆₇	—	2	2	no	—
183	C₄⋊C₄×C₆₇	—	2	2	no	—
184	C₄⋊C₄×C₆₇	—	2	2	no	—
185	C₄⋊C₄×C₆₇	—	2	2	no	—
186	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
188	C₂²⋊C₄×C₆₇	—	2	2	no	—
189	C₂²⋊C₄×C₆₇	—	2	2	no	—
190	C₂²⋊C₄×C₆₇	—	2	2	no	—
191	C₂²⋊C₄×C₆₇	—	2	2	no	—
192	C₂²⋊C₄×C₆₇	—	2	2	no	—
193	C₂²⋊C₄×C₆₇	—	2	2	no	—
194	C₂²⋊C₄×C₆₇	—	2	2	no	—
195	C₂²⋊C₄×C₆₇	—	2	2	no	—
196	C₂²⋊C₄×C₆₇	—	2	2	no	—
197	C₄²×C₆₇	—	2	2	no	—
198	C₄²×C₆₇	—	2	2	no	—
199	C₄²×C₆₇	—	2	2	no	—
200	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂³×C₆₇	—	2	2	no	—
217	C₂³×C₆₇	—	2	2	no	—
218	C₂³×C₆₇	—	2	2	no	—
219	C₂³×C₆₇	—	4	1	no	—
220	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₆₇	—	2	4	no	—
224	Q₈×C₆₇	—	4	2	no	—
225	Q₈×C₆₇	—	4	2	no	—
226	D₄×C₆₇	—	2	4	no	—
227	D₄×C₆₇	—	4	2	no	—
228	D₄×C₆₇	—	4	4	no	—
229	D₄×C₆₇	—	4	4	no	—
230	D₄×C₆₇	—	4	4	no	—
231	D₄×C₆₇	—	4	2	no	—
232	C₂×C₄×C₆₇	—	2	2	no	—
233	C₂×C₄×C₆₇	—	2	2	no	—
234	C₂×C₄×C₆₇	—	2	2	no	—
235	C₂×C₄×C₆₇	—	2	2	no	—
236	C₂×C₄×C₆₇	—	2	2	no	—
237	C₂×C₄×C₆₇	—	2	2	no	—
238	C₂×C₄×C₆₇	—	2	2	no	—
239	C₂×C₄×C₆₇	—	2	2	no	—
240	C₂×C₄×C₆₇	—	2	2	no	—
241	C₂×C₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	—	2	2	no	—
243	C₂×C₄×C₆₇	—	2	2	no	—
244	C₂×C₄×C₆₇	—	2	2	no	—
245	C₂×C₄×C₆₇	—	4	1	no	—
246	C₂×C₄×C₆₇	—	4	1	no	—
247	C₂×C₄×C₆₇	—	4	1	no	—
248	C₂×C₄×C₆₇	—	4	1	no	—
249	C₂×C₄×C₆₇	—	4	1	no	—
250	C₂×C₄×C₆₇	—	4	1	no	—
251	C₂×C₄×C₆₇	—	4	1	no	—
252	C₂×C₄×C₆₇	—	4	4	no	—
253	C₂×C₄×C₆₇	—	4	4	no	—
254	C₂×C₄×C₆₇	—	4	4	no	—
255	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
268	C₂×Dic₆₇	—	4	4	no	—
269	C₂×Dic₆₇	—	4	4	no	—
270	C₂×Dic₆₇	—	4	4	no	—
271	C₆₇⋊C₈	—	2	8	no	—
272	C₂²×C₆₇	—	2	1	no	—
273	C₂²×C₆₇	—	2	1	no	—
274	C₂²×C₆₇	—	2	1	no	—
275	C₂²×C₆₇	—	2	1	no	—
276	C₂²×C₆₇	—	2	1	no	—
277	C₂²×C₆₇	—	2	1	no	—
278	C₂²×C₆₇	—	2	1	no	—
279	C₂²×C₆₇	—	4	4	no	—
280	C₂²×C₆₇	—	4	2	no	—
281	C₂²×C₆₇	—	4	2	no	—
282	C₂²×C₆₇	—	4	2	no	—
283	C₂²×C₆₇	#421	1	2	yes	—
284	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×C₆₇	#532	1	2	yes	—
286	C₄×C₆₇	—	2	1	no	—
287	C₄×C₆₇	—	2	1	no	—
288	C₄×C₆₇	—	2	1	no	—
289	C₄×C₆₇	—	2	1	no	—
290	C₄×C₆₇	—	2	1	no	—
291	C₄×C₆₇	—	2	1	no	—
292	C₄×C₆₇	—	2	1	no	—
293	C₄×C₆₇	—	2	1	no	—
294	C₄×C₆₇	—	2	1	no	—
295	C₄×C₆₇	—	4	2	no	—
296	C₄×C₆₇	—	4	2	no	—
297	C₄×C₆₇	—	4	2	no	—
298	C₄×C₆₇	#421	1	2	yes	—
299	C₄×C₆₇	C₄×#41	1	2	yes	—
300	C₄×C₆₇	#525	1	2	yes	—
301	Dic₆₇	—	8	4	no	—
302	#21383	—	67	1	no	maximal, Sylow
303	C₂×C₆₇	—	2	2	no	—
304	C₂×C₆₇	—	2	2	no	—
305	C₂×C₆₇	—	4	1	no	—
306	C₂×C₆₇	—	8	2	no	—
307	C₂×C₆₇	#2297	1	1	yes	characteristic
308	C₂×C₆₇	C₂×#421	1	1	yes	characteristic
309	C₂×C₆₇	C₂×#421	1	1	yes	characteristic
310	#3444	D₆₇	1	1	yes	characteristic
311	C₂×C₄×M₁₆	—	67	1	no	—
312	#2283	—	67	1	no	—
313	#1986	—	67	2	no	—
314	#1980	—	67	2	no	—
315	#1871	—	67	4	no	—
316	#1759	—	67	4	no	—
317	C₆₇	#21383	1	1	yes	characteristic, complemented, Sylow
318	C₂²×M₁₆	—	67	2	no	—
319	#533	Dic₆₇	1	1	yes	characteristic, complemented
320	#533	Dic₆₇	1	1	yes	characteristic, complemented
321	#533	C₂×D₆₇	1	1	yes	characteristic
322	#532	Dic₆₇	1	1	yes	characteristic, complemented
323	#532	Dic₆₇	1	1	yes	characteristic, complemented
324	#532	C₂×D₆₇	1	1	yes	characteristic
325	#529	—	2	1	no	—
326	#529	—	2	1	no	—
327	#529	—	2	1	no	—
328	#529	—	2	1	no	—
329	#529	Dic₆₇	1	2	yes	complemented
330	#529	Dic₆₇	1	2	yes	complemented
331	#525	—	2	1	no	—
332	#525	—	2	1	no	—
333	#525	C₂×D₆₇	1	2	yes	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	—	2	1	no	—
336	C₄×#41	C₂×D₆₇	1	2	yes	—
337	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
338	C₂×#104	—	67	8	no	—
339	C₄×M₁₆	—	67	2	no	—
340	C₄×M₁₆	—	67	2	no	—
341	C₄×M₁₆	—	134	1	no	—
342	C₄×M₁₆	—	134	1	no	—
343	C₂×#97	—	134	1	no	—
344	C₂×C₄×C₈	—	134	1	no	—
345	#383	—	134	1	no	—
346	#382	—	134	1	no	—
347	#381	—	134	1	no	—
348	#380	—	134	1	no	—
349	C₄×C₄⋊C₄	—	67	2	no	—
350	C₄×C₂²⋊C₄	—	67	2	no	—
351	#376	—	67	2	no	—
352	#339	—	67	8	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	C₂²×D₆₇	1	2	yes	—
356	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
357	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
358	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
359	C₂×M₁₆	—	67	4	no	—
360	C₂×M₁₆	—	134	8	no	—
361	C₂×M₁₆	—	134	2	no	—
362	C₂²×C₈	—	134	2	no	—
363	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
364	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
365	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
366	#127	C₂×Dic₆₇	1	1	yes	characteristic
367	#126	—	2	2	no	—
368	#126	—	2	2	no	—
369	#125	—	2	1	no	—
370	#125	—	2	1	no	—
371	#125	C₂×Dic₆₇	1	2	yes	—
372	#124	—	2	1	no	—
373	#124	—	2	1	no	—
374	#124	C₂×Dic₆₇	1	2	yes	—
375	#123	—	2	2	no	—
376	#123	—	2	2	no	—
377	#123	—	2	2	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
383	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	C₂×Dic₆₇	1	2	yes	—
389	#121	C₂×Dic₆₇	1	2	yes	—
390	#120	—	2	2	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
396	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
408	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	C₂²×D₆₇	1	2	yes	—
415	C₂×C₄⋊C₄	—	134	2	no	—
416	C₂×C₂²⋊C₄	—	134	2	no	—
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	67	4	no	—
419	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
420	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
421	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
422	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
423	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
424	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
425	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
426	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
427	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
428	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
429	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
430	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
431	#104	—	134	16	no	—
432	#97	—	134	2	no	—
433	#97	—	134	2	no	—
434	C₄×C₈	—	134	2	no	—
435	C₄×C₈	—	134	2	no	—
436	#95	—	134	2	no	—
437	#95	—	134	2	no	—
438	#95	—	134	2	no	—
439	#95	—	134	2	no	—
440	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
441	#41	—	2	8	no	—
442	#41	—	4	4	no	—
443	#41	—	4	4	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	134	4	no	—
460	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
462	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
463	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
464	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
477	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
478	M₁₆	—	67	8	no	—
479	M₁₆	—	134	8	no	—
480	M₁₆	—	134	4	no	—
481	C₂×C₈	—	134	8	no	—
482	C₂×C₈	—	134	4	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	268	4	no	—
494	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
495	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	268	4	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	134	8	no	—
510	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
511	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
512	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
513	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
514	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
515	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
516	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
517	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
518	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
519	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
520	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
521	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
522	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
523	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
524	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
525	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	1	no	—
530	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
531	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
532	C₂³	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
533	Q₈	—	2	4	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	4	2	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	268	4	no	—
566	C₂×C₄	—	268	4	no	—
567	C₂×C₄	—	268	4	no	—
568	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
571	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
572	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
573	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
574	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
575	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
576	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
577	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
578	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
579	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
580	C₂×C₄	#41×D₆₇	1	4	yes	—
581	C₈	—	134	8	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	#16863413	1	2	yes	—
594	C₂²	C₂²×C₂²⋊Dic₆₇	1	1	yes	characteristic
595	C₂²	#16863942	1	2	yes	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	536	4	no	—
609	C₄	#16863413	1	2	yes	—
610	C₄	#41×Dic₆₇	1	2	yes	—
611	C₄	#16863903	1	2	yes	—
612	C₂	—	2	2	no	—
613	C₂	—	2	2	no	—
614	C₂	—	4	1	no	—
615	C₂	—	8	2	no	—
616	C₂	#22562700	1	1	yes	characteristic
617	C₂	C₂×#16863413	1	1	yes	characteristic
618	C₂	C₂×#16863413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting, prime radical	C₆₇×#3444	C₂
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3444	D₆₇
hypocenter	C₆₇	#21383
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#11761612	C₂	semidirect
2. #22562607	C₂	semidirect
3. #22561154	C₂	semidirect
4. #22561129	C₂	semidirect
5. #22560512	C₂	semidirect
6. #22560019	C₂	semidirect
24. #533×C₆₇	C₄	semidirect
25. #533×C₆₇	C₄	semidirect
27. #532×C₆₇	C₄	semidirect
28. #532×C₆₇	C₄	semidirect
34. #529×C₆₇	C₄	semidirect
35. #529×C₆₇	C₄	semidirect
133. #11761612	#41	semidirect
317. C₆₇	#21383	semidirect
319. #533	Dic₆₇	semidirect
320. #533	Dic₆₇	semidirect
322. #532	Dic₆₇	semidirect
323. #532	Dic₆₇	semidirect
329. #529	Dic₆₇	semidirect
330. #529	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11761612	2
#22562607	2
#22561154	2
#22561129	2
#22560512	2
#22560019	2
C₆₇×#3444	2
#21383	67