Subgroups — #30867861

Order 17152.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863527	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863455	C₂	1	1	yes	maximal, characteristic
3	#22563479	C₂	1	1	yes	maximal, characteristic
4	#22560931	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560927	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560926	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560823	C₂	1	1	yes	maximal, characteristic
8	#22560820	C₂	1	1	yes	maximal, characteristic
9	#22560816	C₂	1	1	yes	maximal, characteristic
10	#22560813	C₂	1	1	yes	maximal, characteristic
11	#22560771	C₂	1	1	yes	maximal, characteristic, complemented
12	#22560764	C₂	1	1	yes	maximal, characteristic, complemented
13	#22560190	C₂	1	1	yes	maximal, characteristic
14	#22560086	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524000	C₂²	1	1	yes	characteristic
17	#16863527	—	2	4	no	—
18	#16863455	—	2	4	no	—
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×#14523954	C₂²	1	1	yes	characteristic
31	C₂×#14523954	C₂²	1	1	yes	characteristic
32	C₂×#14523953	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
35	#16863334	C₄	1	1	yes	characteristic
36	#16863331	C₄	1	1	yes	characteristic
37	#16863329	C₄	1	1	yes	characteristic
38	#16863329	C₄	1	1	yes	characteristic
39	#16863318	C₄	1	1	yes	characteristic
40	#16863318	C₄	1	1	yes	characteristic
41	#16863315	C₄	1	1	yes	characteristic
42	#16863307	C₄	1	1	yes	characteristic
43	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
46	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
48	#16863150	C₂²	1	1	yes	characteristic
49	#16863150	C₂²	1	1	yes	characteristic
50	#16863150	C₂²	1	1	yes	characteristic
51	#16863150	C₂²	1	1	yes	characteristic
52	#16863150	C₂²	1	1	yes	characteristic
53	#16863150	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
57	#336×C₆₇	C₂²	1	1	yes	characteristic
58	#336×C₆₇	C₂²	1	1	yes	characteristic
59	#336×C₆₇	C₂²	1	1	yes	characteristic
60	#336×C₆₇	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
62	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
66	#14524000	—	2	2	no	—
67	#14524000	—	2	2	no	—
68	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
84	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
85	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
86	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
87	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
88	Dic₆₇⋊C₈	—	2	2	no	—
89	Dic₆₇⋊C₈	—	2	2	no	—
90	Dic₆₇⋊C₈	—	4	1	no	—
91	Dic₆₇⋊C₈	—	4	1	no	—
92	(C₂×D₆₇)⋊C₈	—	2	2	no	—
93	(C₂×D₆₇)⋊C₈	—	2	2	no	—
94	(C₂×D₆₇)⋊C₈	—	4	1	no	—
95	(C₂×D₆₇)⋊C₈	—	4	1	no	—
96	#14523954	—	2	2	no	—
97	#14523954	D₄	1	4	yes	—
98	#14523953	—	4	1	no	—
99	C₄×C₆₇⋊C₈	—	2	2	no	—
100	C₈×Dic₆₇	—	4	1	no	—
101	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₆₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
112	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₆₇	—	2	2	no	—
117	C₄×Q₈×C₆₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₆₇	—	2	2	no	—
125	C₄×C₈×C₆₇	—	2	2	no	—
126	C₂³×D₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₆₇	—	2	1	no	—
135	C₂×C₄×D₆₇	—	2	1	no	—
136	C₂×C₄×D₆₇	—	2	1	no	—
137	C₂×C₄×D₆₇	—	2	1	no	—
138	C₂×C₄×D₆₇	—	2	1	no	—
139	C₂×C₄×D₆₇	—	2	1	no	—
140	C₂×C₆₇⋊C₈	—	2	1	no	—
141	C₂×C₆₇⋊C₈	—	2	1	no	—
142	C₂×C₆₇⋊C₈	—	2	1	no	—
143	C₂×C₆₇⋊C₈	—	2	1	no	—
144	C₂×C₆₇⋊C₈	—	2	1	no	—
145	C₂×C₆₇⋊C₈	—	2	1	no	—
146	C₂×C₆₇⋊C₈	—	2	1	no	—
147	C₂×C₆₇⋊C₈	—	2	1	no	—
148	C₂×C₆₇⋊C₈	—	2	1	no	—
149	C₂×C₆₇⋊C₈	—	2	1	no	—
150	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₄⋊Dic₆₇	—	2	2	no	—
153	C₄⋊Dic₆₇	—	4	1	no	—
154	Dic₆₇⋊C₄	—	2	2	no	—
155	Dic₆₇⋊C₄	—	2	2	no	—
156	Dic₆₇⋊C₄	—	2	2	no	—
157	Dic₆₇⋊C₄	—	2	2	no	—
158	Dic₆₇⋊C₄	—	4	1	no	—
159	Dic₆₇⋊C₄	—	4	1	no	—
160	(C₂×D₆₇)⋊C₄	—	2	2	no	—
161	(C₂×D₆₇)⋊C₄	—	2	2	no	—
162	(C₂×D₆₇)⋊C₄	—	2	2	no	—
163	(C₂×D₆₇)⋊C₄	—	2	2	no	—
164	(C₂×D₆₇)⋊C₄	—	4	1	no	—
165	(C₂×D₆₇)⋊C₄	—	4	1	no	—
166	C₄×Dic₆₇	—	2	1	no	—
167	C₄×Dic₆₇	—	2	1	no	—
168	C₄×Dic₆₇	—	2	1	no	—
169	C₄×Dic₆₇	—	2	1	no	—
170	C₄×Dic₆₇	—	2	1	no	—
171	C₄×Dic₆₇	—	2	1	no	—
172	C₂×Q₈×C₆₇	—	2	2	no	—
173	C₂×Q₈×C₆₇	—	2	2	no	—
174	C₂×Q₈×C₆₇	—	4	1	no	—
175	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
182	C₂×C₈×C₆₇	—	2	1	no	—
183	C₂×C₈×C₆₇	—	2	1	no	—
184	C₂×C₈×C₆₇	—	2	1	no	—
185	C₂×C₈×C₆₇	—	2	1	no	—
186	C₂×C₈×C₆₇	—	2	1	no	—
187	C₂×C₈×C₆₇	—	2	1	no	—
188	C₂×C₈×C₆₇	—	2	1	no	—
189	C₂×C₈×C₆₇	—	2	1	no	—
190	C₂×C₈×C₆₇	—	2	1	no	—
191	C₂×C₈×C₆₇	—	2	1	no	—
192	C₂×C₈×C₆₇	—	2	1	no	—
193	C₂×C₈×C₆₇	—	2	1	no	—
194	C₄⋊C₄×C₆₇	—	2	2	no	—
195	C₄⋊C₄×C₆₇	—	2	2	no	—
196	C₄⋊C₄×C₆₇	—	2	2	no	—
197	C₄²×C₆₇	—	2	1	no	—
198	C₄²×C₆₇	—	2	1	no	—
199	C₄²×C₆₇	—	2	1	no	—
200	C₄²×C₆₇	—	2	1	no	—
201	C₄²×C₆₇	C₂×D₄	1	2	yes	—
202	C₄²×C₆₇	#41	1	2	yes	—
203	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
204	C₂²×D₆₇	—	2	1	no	—
205	C₂²×D₆₇	—	2	1	no	—
206	C₂²×D₆₇	—	2	1	no	—
207	C₂²×D₆₇	—	2	1	no	—
208	C₂²×D₆₇	—	2	1	no	—
209	C₂²×D₆₇	—	2	1	no	—
210	C₂²×D₆₇	—	2	1	no	—
211	Q₈×C₆₇	—	4	4	no	—
212	C₂×C₄×C₆₇	—	2	1	no	—
213	C₂×C₄×C₆₇	—	2	1	no	—
214	C₂×C₄×C₆₇	—	2	1	no	—
215	C₂×C₄×C₆₇	—	2	1	no	—
216	C₂×C₄×C₆₇	—	2	1	no	—
217	C₂×C₄×C₆₇	—	2	1	no	—
218	C₂×C₄×C₆₇	—	2	1	no	—
219	C₂×C₄×C₆₇	—	2	1	no	—
220	C₂×C₄×C₆₇	—	2	1	no	—
221	C₂×C₄×C₆₇	—	2	1	no	—
222	C₂×C₄×C₆₇	—	2	1	no	—
223	C₂×C₄×C₆₇	—	2	1	no	—
224	C₂×C₄×C₆₇	—	2	1	no	—
225	C₂×C₄×C₆₇	—	2	1	no	—
226	C₂×C₄×C₆₇	—	2	1	no	—
227	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₆₇	#131	1	2	yes	—
230	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
234	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×Dic₆₇	—	2	1	no	—
237	C₂×Dic₆₇	—	2	1	no	—
238	C₂×Dic₆₇	—	2	1	no	—
239	C₂×Dic₆₇	—	2	1	no	—
240	C₂×Dic₆₇	—	2	1	no	—
241	C₂×Dic₆₇	—	2	1	no	—
242	C₂×Dic₆₇	—	2	1	no	—
243	C₂×Dic₆₇	—	2	1	no	—
244	C₂×Dic₆₇	—	2	1	no	—
245	C₂×Dic₆₇	—	2	1	no	—
246	C₂×Dic₆₇	—	2	1	no	—
247	C₂×Dic₆₇	—	2	1	no	—
248	C₂×Dic₆₇	—	2	1	no	—
249	C₂×Dic₆₇	—	2	1	no	—
250	C₂×Dic₆₇	—	2	1	no	—
251	C₂×Dic₆₇	—	2	1	no	—
252	C₂×Dic₆₇	—	2	1	no	—
253	C₂×Dic₆₇	—	2	1	no	—
254	C₂×Dic₆₇	—	2	1	no	—
255	C₂×Dic₆₇	—	2	1	no	—
256	C₂×Dic₆₇	#131	1	2	yes	—
257	C₄×D₆₇	—	4	1	no	—
258	C₄×D₆₇	—	4	1	no	—
259	C₄×D₆₇	—	4	1	no	—
260	C₄×D₆₇	—	4	1	no	—
261	C₈×C₆₇	—	4	1	no	—
262	C₈×C₆₇	—	4	1	no	—
263	C₈×C₆₇	—	4	1	no	—
264	C₈×C₆₇	—	4	1	no	—
265	C₆₇⋊C₈	—	2	2	no	—
266	C₆₇⋊C₈	—	2	2	no	—
267	C₆₇⋊C₈	—	4	1	no	—
268	C₆₇⋊C₈	—	4	1	no	—
269	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₆₇	#519	1	1	yes	characteristic
271	C₂²×C₆₇	#520	1	1	yes	characteristic
272	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
273	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
274	C₂²×C₆₇	#568	1	1	yes	characteristic
275	C₂²×C₆₇	#568	1	1	yes	characteristic
276	C₂×D₆₇	—	4	1	no	—
277	C₂×D₆₇	—	4	1	no	—
278	C₂×D₆₇	—	4	1	no	—
279	C₂×D₆₇	—	4	1	no	—
280	C₂×D₆₇	—	4	1	no	—
281	C₂×D₆₇	—	4	1	no	—
282	C₂×D₆₇	—	4	1	no	—
283	C₄×C₆₇	—	2	2	no	—
284	C₄×C₆₇	—	2	2	no	—
285	C₄×C₆₇	—	2	2	no	—
286	C₄×C₆₇	—	4	1	no	—
287	C₄×C₆₇	—	4	1	no	—
288	C₄×C₆₇	—	4	1	no	—
289	C₄×C₆₇	#536	1	1	yes	characteristic
290	C₄×C₆₇	#537	1	1	yes	characteristic
291	C₄×C₆₇	#541	1	1	yes	characteristic
292	C₄×C₆₇	#542	1	1	yes	characteristic
293	Dic₆₇	—	2	2	no	—
294	Dic₆₇	—	4	1	no	—
295	Dic₆₇	—	4	1	no	—
296	Dic₆₇	—	4	1	no	—
297	Dic₆₇	—	4	1	no	—
298	Dic₆₇	—	4	1	no	—
299	Dic₆₇	—	4	1	no	—
300	#22109	—	67	1	no	maximal, Sylow
301	C₂×C₆₇	#2323	1	1	yes	characteristic
302	C₂×C₆₇	#2933	1	1	yes	characteristic
303	C₂×C₆₇	#2935	1	1	yes	characteristic
304	C₂×C₆₇	#2986	1	1	yes	characteristic
305	C₂×C₆₇	#2987	1	1	yes	characteristic
306	C₂×C₆₇	#2992	1	1	yes	characteristic
307	C₂×C₆₇	#2993	1	1	yes	characteristic
308	D₆₇	—	8	1	no	—
309	C₂×#446	—	67	1	no	—
310	C₂×#433	—	67	1	no	—
311	#2396	—	67	1	no	—
312	#1984	D₆₇	1	1	yes	characteristic, complemented
313	#1940	—	67	1	no	—
314	#1939	—	67	1	no	—
315	#1939	—	67	1	no	—
316	#1924	—	67	1	no	—
317	#1924	—	67	1	no	—
318	#1923	—	67	1	no	—
319	#1923	—	67	1	no	—
320	#1917	—	67	1	no	—
321	#1916	—	67	1	no	—
322	#1798	—	67	1	no	—
323	#1771	—	67	1	no	—
324	C₆₇	#22109	1	1	yes	characteristic, complemented, Sylow
325	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
326	C₂×#117	—	67	1	no	—
327	#446	—	134	4	no	—
328	#433	—	134	4	no	—
329	C₂×C₄⋊C₈	—	67	1	no	—
330	C₂×C₄⋊C₈	—	67	1	no	—
331	C₂×C₄⋊C₈	—	67	1	no	—
332	C₂×C₄⋊C₈	—	67	1	no	—
333	C₂×C₄⋊C₈	—	67	1	no	—
334	C₂×C₄⋊C₈	—	67	1	no	—
335	C₂×C₄⋊C₈	—	67	1	no	—
336	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	—	67	1	no	—
338	C₂×C₂²⋊C₈	—	67	1	no	—
339	C₂×C₂²⋊C₈	—	67	1	no	—
340	C₂×C₂²⋊C₈	—	67	1	no	—
341	C₂×#97	—	67	1	no	—
342	C₂×#97	—	67	1	no	—
343	C₂×#97	—	67	1	no	—
344	C₂×C₄×C₈	—	67	1	no	—
345	C₂×C₄×C₈	—	67	1	no	—
346	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
347	#400	—	67	1	no	—
348	#399	—	67	1	no	—
349	#398	—	67	1	no	—
350	#398	—	67	1	no	—
351	#396	—	67	1	no	—
352	#396	—	67	1	no	—
353	#395	—	67	1	no	—
354	#393	—	67	1	no	—
355	C₄×C₄⋊C₄	—	67	1	no	—
356	C₄×C₄⋊C₄	—	67	1	no	—
357	C₄×C₄⋊C₄	—	67	1	no	—
358	C₄×C₂²⋊C₄	—	67	1	no	—
359	C₄×C₂²⋊C₄	—	67	1	no	—
360	#336	—	67	1	no	—
361	#336	—	67	1	no	—
362	#336	—	67	1	no	—
363	#336	—	67	1	no	—
364	#336	—	67	1	no	—
365	#336	—	67	1	no	—
366	#336	C₂×D₆₇	1	1	yes	characteristic
367	#336	C₂×D₆₇	1	1	yes	characteristic
368	#336	C₂×D₆₇	1	1	yes	characteristic
369	#336	C₂×D₆₇	1	1	yes	characteristic
370	C₂²×Q₈	C₄×D₆₇	1	1	yes	characteristic
371	C₂³×C₄	—	67	1	no	—
372	C₂²×C₈	—	67	1	no	—
373	C₂²×C₈	—	67	1	no	—
374	C₂²×C₈	—	67	1	no	—
375	C₂²×C₈	—	67	1	no	—
376	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
377	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
378	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
379	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	#117	—	134	2	no	—
383	#117	—	134	2	no	—
384	C₂×C₄⋊C₄	—	67	1	no	—
385	C₂×C₄⋊C₄	—	67	1	no	—
386	C₂×C₄⋊C₄	—	67	1	no	—
387	C₂×C₄⋊C₄	—	67	1	no	—
388	C₂×C₄⋊C₄	—	67	1	no	—
389	C₂×C₄⋊C₄	—	67	1	no	—
390	C₂×C₄⋊C₄	—	67	1	no	—
391	C₂×C₄⋊C₄	—	67	1	no	—
392	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	67	1	no	—
396	C₂×C₂²⋊C₄	—	67	1	no	—
397	C₂×C₂²⋊C₄	—	67	1	no	—
398	C₂×C₂²⋊C₄	—	67	1	no	—
399	C₂×C₂²⋊C₄	—	67	1	no	—
400	C₂×C₂²⋊C₄	—	67	1	no	—
401	C₂×C₄²	—	67	1	no	—
402	C₂×C₄²	—	67	1	no	—
403	C₂×C₄²	—	67	1	no	—
404	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
406	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
407	C₄⋊C₈	—	2	2	no	—
408	C₄⋊C₈	—	268	1	no	—
409	C₄⋊C₈	—	268	1	no	—
410	C₄⋊C₈	—	134	2	no	—
411	C₄⋊C₈	—	134	2	no	—
412	C₄⋊C₈	—	134	2	no	—
413	C₄⋊C₈	—	134	2	no	—
414	C₄⋊C₈	—	134	2	no	—
415	C₂²⋊C₈	—	268	1	no	—
416	C₂²⋊C₈	—	268	1	no	—
417	C₂²⋊C₈	—	134	2	no	—
418	C₂²⋊C₈	—	134	2	no	—
419	#97	—	268	1	no	—
420	#97	—	67	4	no	—
421	#97	—	134	2	no	—
422	C₄×C₈	—	2	2	no	—
423	C₄×C₈	—	268	1	no	—
424	C₄×C₈	—	134	2	no	—
425	#95	—	67	1	no	—
426	#95	—	67	1	no	—
427	#95	—	67	1	no	—
428	#95	—	67	1	no	—
429	#95	—	67	1	no	—
430	#95	—	67	1	no	—
431	#95	—	67	1	no	—
432	#95	—	67	1	no	—
433	#95	—	67	1	no	—
434	#95	—	67	1	no	—
435	C₂⁴	—	67	1	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂²×C₄	—	67	1	no	—
440	C₂²×C₄	—	67	1	no	—
441	C₂²×C₄	—	67	1	no	—
442	C₂²×C₄	—	67	1	no	—
443	C₂²×C₄	—	67	1	no	—
444	C₂²×C₄	—	67	1	no	—
445	C₂²×C₄	—	67	1	no	—
446	C₂²×C₄	—	134	1	no	—
447	C₂²×C₄	—	134	1	no	—
448	C₂²×C₄	—	134	1	no	—
449	C₂²×C₄	—	134	1	no	—
450	C₂²×C₄	—	134	1	no	—
451	C₂²×C₄	—	134	1	no	—
452	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
458	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	67	2	no	—
472	C₂×C₈	—	67	2	no	—
473	C₂×C₈	—	134	1	no	—
474	C₂×C₈	—	134	1	no	—
475	C₂×C₈	—	134	1	no	—
476	C₂×C₈	—	134	1	no	—
477	C₂×C₈	—	134	1	no	—
478	C₂×C₈	—	134	1	no	—
479	C₂×C₈	—	134	1	no	—
480	C₂×C₈	—	134	1	no	—
481	C₂×C₈	—	134	1	no	—
482	C₂×C₈	—	134	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	268	1	no	—
487	C₄⋊C₄	—	268	1	no	—
488	C₄⋊C₄	—	268	1	no	—
489	C₄⋊C₄	—	134	2	no	—
490	C₄⋊C₄	—	134	2	no	—
491	C₄⋊C₄	—	134	2	no	—
492	C₄⋊C₄	—	134	2	no	—
493	C₄⋊C₄	—	134	2	no	—
494	C₂²⋊C₄	—	268	1	no	—
495	C₂²⋊C₄	—	268	1	no	—
496	C₂²⋊C₄	—	134	2	no	—
497	C₂²⋊C₄	—	134	2	no	—
498	C₂²⋊C₄	—	134	2	no	—
499	C₂²⋊C₄	—	134	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	134	1	no	—
505	C₄²	—	134	1	no	—
506	C₄²	—	134	1	no	—
507	C₄²	—	134	1	no	—
508	C₄²	—	134	1	no	—
509	C₄²	—	134	1	no	—
510	C₄²	D₄×D₆₇	1	2	yes	—
511	C₄²	#11761627	1	2	yes	—
512	C₂³	—	134	1	no	—
513	C₂³	—	134	1	no	—
514	C₂³	—	134	1	no	—
515	C₂³	—	134	1	no	—
516	C₂³	—	134	1	no	—
517	C₂³	—	134	1	no	—
518	C₂³	—	134	1	no	—
519	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
520	Q₈	—	4	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	268	1	no	—
537	C₂×C₄	—	268	1	no	—
538	C₂×C₄	—	268	1	no	—
539	C₂×C₄	—	268	1	no	—
540	C₂×C₄	—	67	2	no	—
541	C₂×C₄	—	134	1	no	—
542	C₂×C₄	—	134	1	no	—
543	C₂×C₄	—	134	1	no	—
544	C₂×C₄	—	134	1	no	—
545	C₂×C₄	—	134	1	no	—
546	C₂×C₄	—	134	1	no	—
547	C₂×C₄	—	134	1	no	—
548	C₂×C₄	—	134	1	no	—
549	C₂×C₄	—	134	1	no	—
550	C₂×C₄	—	134	1	no	—
551	C₂×C₄	—	134	1	no	—
552	C₂×C₄	—	134	1	no	—
553	C₂×C₄	—	134	1	no	—
554	C₂×C₄	—	134	1	no	—
555	C₂×C₄	—	134	1	no	—
556	C₂×C₄	—	134	1	no	—
557	C₂×C₄	—	134	1	no	—
558	C₂×C₄	—	134	1	no	—
559	C₂×C₄	—	134	1	no	—
560	C₂×C₄	—	134	1	no	—
561	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	2	yes	—
562	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	2	yes	—
563	C₂×C₄	#14524049	1	2	yes	—
564	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
565	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
566	C₂×C₄	#14524089	1	1	yes	characteristic
567	C₂×C₄	#14524090	1	1	yes	characteristic
568	C₂×C₄	#14524091	1	1	yes	characteristic
569	C₂×C₄	#14524091	1	1	yes	characteristic
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	268	1	no	—
575	C₈	—	268	1	no	—
576	C₈	—	134	2	no	—
577	C₈	—	134	2	no	—
578	C₂²	—	268	1	no	—
579	C₂²	—	268	1	no	—
580	C₂²	—	268	1	no	—
581	C₂²	—	268	1	no	—
582	C₂²	—	268	1	no	—
583	C₂²	—	268	1	no	—
584	C₂²	—	268	1	no	—
585	C₂²	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
586	C₂²	#16863872	1	1	yes	characteristic
587	C₂²	#16863878	1	1	yes	characteristic
588	C₂²	#131×D₆₇	1	1	yes	characteristic
589	C₂²	C₂×#14524049	1	1	yes	characteristic
590	C₂²	#16864161	1	1	yes	characteristic
591	C₂²	#16864162	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	268	1	no	—
599	C₄	—	268	1	no	—
600	C₄	—	268	1	no	—
601	C₄	—	268	1	no	—
602	C₄	—	268	1	no	—
603	C₄	—	268	1	no	—
604	C₄	—	134	2	no	—
605	C₄	#16863969	1	1	yes	characteristic
606	C₄	#16863976	1	1	yes	characteristic
607	C₄	#16864007	1	1	yes	characteristic
608	C₄	#16864015	1	1	yes	characteristic
609	C₂	—	536	1	no	—
610	C₂	#22562894	1	1	yes	characteristic
611	C₂	#22568930	1	1	yes	characteristic
612	C₂	#22568949	1	1	yes	characteristic
613	C₂	#22569309	1	1	yes	characteristic
614	C₂	#22569312	1	1	yes	characteristic
615	C₂	#22569347	1	1	yes	characteristic
616	C₂	#22569357	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle	C₂³×C₆₇	C₂³×C₄
Fitting	C₆₇×#1984	C₂
prime radical	C₂³×D₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1984	D₆₇
hypocenter	C₆₇	#22109
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

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

N	H ≅ G/N	type
1. C₂×#16863527	C₂	semidirect
4. #22560931	C₂	semidirect
5. #22560927	C₂	semidirect
6. #22560926	C₂	semidirect
11. #22560771	C₂	semidirect
12. #22560764	C₂	semidirect
14. #22560086	C₂	semidirect
15. C₆₇×#1984	C₂	semidirect
312. #1984	D₆₇	semidirect
324. C₆₇	#22109	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863527	2
C₂×#16863455	2
#22563479	2
#22560931	2
#22560927	2
#22560926	2
#22560823	2
#22560820	2
#22560816	2
#22560813	2
#22560771	2
#22560764	2
#22560190	2
#22560086	2
C₆₇×#1984	2
#22109	67