Subgroups — #30823208

Order 17152.

1058 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863449	C₂	1	1	yes	maximal, characteristic
2	#22562616	C₂	1	1	yes	maximal, characteristic
3	#22558781	C₂	1	4	yes	maximal
4	#22558773	C₂	1	4	yes	maximal, complemented
5	#22558708	C₂	1	4	yes	maximal, complemented
6	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂×#14524002	—	2	1	no	—
8	#16863449	—	2	1	no	—
9	#16863449	—	2	1	no	—
10	#16863449	C₂²	1	2	yes	—
11	#16863449	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
13	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
15	#16863266	—	2	1	no	—
16	#16863262	C₂²	1	2	yes	—
17	#16863256	—	2	1	no	—
18	#16863256	C₂²	1	2	yes	—
19	C₄×C₄⋊Dic₆₇	—	2	1	no	—
20	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	—
21	#16863133	C₂²	1	16	yes	—
22	#533×C₆₇	—	2	1	no	—
23	#533×C₆₇	—	2	1	no	—
24	#533×C₆₇	—	2	1	no	—
25	#533×C₆₇	—	2	1	no	—
26	#533×C₆₇	C₄	1	2	yes	complemented
27	#533×C₆₇	C₄	1	2	yes	complemented
28	#533×C₆₇	C₂²	1	2	yes	—
29	#533×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic, complemented
31	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic, complemented
32	C₂×#125×C₆₇	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₆₇	C₄	1	2	yes	complemented
37	C₂×#117×C₆₇	—	2	1	no	—
38	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₆₇⋊C₈	—	2	2	no	—
40	#14524002	—	4	4	no	—
41	C₂×C₄⋊Dic₆₇	—	2	2	no	—
42	C₂×C₄⋊Dic₆₇	—	2	2	no	—
43	C₂×C₄⋊Dic₆₇	—	2	2	no	—
44	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
45	C₂×C₄×Dic₆₇	—	2	2	no	—
46	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
49	C₂²⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
50	C₄×C₆₇⋊C₈	—	2	2	no	—
51	C₄×C₆₇⋊C₈	—	2	2	no	—
52	C₆₇⋊#95	—	2	2	no	—
53	C₆₇⋊#95	C₂³	1	4	yes	—
54	C₂²×Q₈×C₆₇	—	2	1	no	—
55	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
56	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₆₇	—	2	1	no	—
60	C₄⋊Q₈×C₆₇	—	2	1	no	—
61	C₄⋊Q₈×C₆₇	—	2	1	no	—
62	C₄⋊Q₈×C₆₇	—	2	1	no	—
63	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
64	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
65	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
66	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
67	#125×C₆₇	—	2	2	no	—
68	#125×C₆₇	—	2	2	no	—
69	#125×C₆₇	—	2	2	no	—
70	#125×C₆₇	—	2	2	no	—
71	C₂²⋊Q₈×C₆₇	—	2	2	no	—
72	C₂²⋊Q₈×C₆₇	—	2	2	no	—
73	C₂²⋊Q₈×C₆₇	—	2	2	no	—
74	C₂²⋊Q₈×C₆₇	—	2	2	no	—
75	C₂²⋊Q₈×C₆₇	—	2	2	no	—
76	C₂²⋊Q₈×C₆₇	—	2	2	no	—
77	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
78	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
79	C₄×Q₈×C₆₇	—	2	2	no	—
80	C₄×Q₈×C₆₇	—	2	2	no	—
81	C₄×Q₈×C₆₇	—	2	2	no	—
82	C₄×Q₈×C₆₇	—	2	2	no	—
83	C₄×Q₈×C₆₇	—	2	2	no	—
84	C₄×Q₈×C₆₇	—	2	2	no	—
85	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	—
86	C₄×Q₈×C₆₇	C₂×C₄	1	4	yes	—
87	#117×C₆₇	—	2	2	no	—
88	#117×C₆₇	—	2	2	no	—
89	#117×C₆₇	—	2	2	no	—
90	#117×C₆₇	—	2	2	no	—
91	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
96	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
98	C₂×C₄²×C₆₇	—	2	2	no	—
99	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×Dic₆₇	—	2	4	no	—
112	C₂×C₆₇⋊C₈	—	2	4	no	—
113	C₂×C₆₇⋊C₈	—	4	4	no	—
114	C₄⋊Dic₆₇	—	4	4	no	—
115	C₄⋊Dic₆₇	—	4	4	no	—
116	C₄⋊Dic₆₇	—	4	4	no	—
117	C₂²⋊Dic₆₇	—	4	4	no	—
118	C₄×Dic₆₇	—	4	4	no	—
119	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₆₇	—	2	2	no	—
121	C₂×Q₈×C₆₇	—	2	2	no	—
122	C₂×Q₈×C₆₇	—	2	2	no	—
123	C₂×Q₈×C₆₇	—	4	4	no	—
124	C₂×Q₈×C₆₇	—	4	4	no	—
125	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₆₇	—	2	2	no	—
127	C₂²×C₄×C₆₇	—	2	2	no	—
128	C₂²×C₄×C₆₇	—	4	2	no	—
129	C₂²×C₄×C₆₇	—	4	2	no	—
130	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	SD₁₆	1	4	yes	—
139	C₂²×C₄×C₆₇	Q₁₆	1	4	yes	—
140	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₆₇	—	2	2	no	—
151	C₄⋊C₄×C₆₇	—	2	2	no	—
152	C₄⋊C₄×C₆₇	—	2	2	no	—
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	—	2	2	no	—
155	C₄⋊C₄×C₆₇	—	2	2	no	—
156	C₄⋊C₄×C₆₇	—	2	4	no	—
157	C₄⋊C₄×C₆₇	—	2	4	no	—
158	C₄⋊C₄×C₆₇	—	2	4	no	—
159	C₄⋊C₄×C₆₇	—	2	2	no	—
160	C₄⋊C₄×C₆₇	—	2	4	no	—
161	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
162	C₂²⋊C₄×C₆₇	—	2	4	no	—
163	C₂²⋊C₄×C₆₇	—	2	4	no	—
164	C₄²×C₆₇	—	2	4	no	—
165	C₄²×C₆₇	—	2	4	no	—
166	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
182	C₂³×C₆₇	—	4	1	no	—
183	C₂³×C₆₇	—	4	1	no	—
184	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×C₆₇	C₂×SD₁₆	1	2	yes	—
187	C₂³×C₆₇	C₂×Q₁₆	1	2	yes	—
188	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₆₇	—	4	4	no	—
190	Q₈×C₆₇	—	4	4	no	—
191	Q₈×C₆₇	—	4	4	no	—
192	Q₈×C₆₇	—	4	4	no	—
193	C₂×C₄×C₆₇	—	2	2	no	—
194	C₂×C₄×C₆₇	—	2	2	no	—
195	C₂×C₄×C₆₇	—	2	2	no	—
196	C₂×C₄×C₆₇	—	2	2	no	—
197	C₂×C₄×C₆₇	—	2	2	no	—
198	C₂×C₄×C₆₇	—	2	2	no	—
199	C₂×C₄×C₆₇	—	2	4	no	—
200	C₂×C₄×C₆₇	—	2	4	no	—
201	C₂×C₄×C₆₇	—	4	1	no	—
202	C₂×C₄×C₆₇	—	4	1	no	—
203	C₂×C₄×C₆₇	—	4	1	no	—
204	C₂×C₄×C₆₇	—	4	1	no	—
205	C₂×C₄×C₆₇	—	4	1	no	—
206	C₂×C₄×C₆₇	—	4	1	no	—
207	C₂×C₄×C₆₇	—	4	4	no	—
208	C₂×C₄×C₆₇	—	4	4	no	—
209	C₂×C₄×C₆₇	#103	1	4	yes	—
210	C₂×C₄×C₆₇	#103	1	4	yes	—
211	C₂×C₄×C₆₇	#103	1	4	yes	—
212	C₂×C₄×C₆₇	#103	1	4	yes	—
213	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
225	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
226	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
227	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×Dic₆₇	—	4	4	no	—
230	C₂×Dic₆₇	—	4	4	no	—
231	C₂×Dic₆₇	—	4	4	no	—
232	C₆₇⋊C₈	—	4	4	no	—
233	C₂²×C₆₇	—	2	1	no	—
234	C₂²×C₆₇	—	2	1	no	—
235	C₂²×C₆₇	—	2	1	no	—
236	C₂²×C₆₇	—	2	1	no	—
237	C₂²×C₆₇	—	2	1	no	—
238	C₂²×C₆₇	—	2	1	no	—
239	C₂²×C₆₇	—	4	2	no	—
240	C₂²×C₆₇	—	4	2	no	—
241	C₂²×C₆₇	C₂×#103	1	2	yes	—
242	C₂²×C₆₇	C₂×#103	1	2	yes	—
243	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
245	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
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	—	2	1	no	—
252	C₄×C₆₇	—	4	4	no	—
253	C₄×C₆₇	—	4	4	no	—
254	C₄×C₆₇	#410	1	2	yes	—
255	C₄×C₆₇	C₂×#103	1	2	yes	—
256	C₄×C₆₇	C₂×#103	1	2	yes	—
257	C₄×C₆₇	C₂×#103	1	2	yes	—
258	C₄×C₆₇	C₂×#103	1	2	yes	—
259	C₄×C₆₇	#421	1	2	yes	—
260	Dic₆₇	—	8	4	no	—
261	#17575	—	67	1	no	maximal, Sylow
262	C₂×C₆₇	—	2	1	no	—
263	C₂×C₆₇	—	2	1	no	—
264	C₂×C₆₇	—	2	2	no	—
265	C₂×C₆₇	—	2	2	no	—
266	C₂×C₆₇	C₂×#410	1	1	yes	characteristic
267	C₂×C₆₇	C₂²×#103	1	1	yes	characteristic
268	C₂×C₆₇	C₂×#421	1	1	yes	characteristic
269	C₂×#533	D₆₇	1	1	yes	characteristic
270	C₂×#431	—	67	1	no	—
271	#2285	—	67	1	no	—
272	#1520	—	67	4	no	—
273	#1518	—	67	4	no	—
274	#1503	—	67	4	no	—
275	C₆₇	#17575	1	1	yes	characteristic, complemented, Sylow
276	#533	—	2	1	no	—
277	#533	—	2	1	no	—
278	#533	—	2	1	no	—
279	#533	—	2	1	no	—
280	#533	Dic₆₇	1	2	yes	complemented
281	#533	Dic₆₇	1	2	yes	complemented
282	#533	C₂×D₆₇	1	2	yes	—
283	#533	C₂×D₆₇	1	2	yes	—
284	C₂×C₄⋊Q₈	Dic₆₇	1	1	yes	characteristic, complemented
285	C₂×C₄⋊Q₈	Dic₆₇	1	1	yes	characteristic, complemented
286	C₂×#125	—	2	1	no	—
287	C₂×C₂²⋊Q₈	—	2	1	no	—
288	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
289	C₂×C₄×Q₈	—	2	1	no	—
290	C₂×C₄×Q₈	Dic₆₇	1	2	yes	complemented
291	C₂×#117	—	2	1	no	—
292	C₂×#117	—	134	1	no	—
293	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
294	#431	—	67	2	no	—
295	#431	—	67	2	no	—
296	#431	—	134	1	no	—
297	#431	—	134	1	no	—
298	C₂×C₄⋊C₈	—	134	1	no	—
299	C₂×C₂²⋊C₈	—	67	2	no	—
300	C₂×C₄×C₈	—	134	1	no	—
301	#384	—	134	1	no	—
302	#382	—	67	2	no	—
303	#380	—	67	2	no	—
304	#380	—	134	1	no	—
305	C₄×C₄⋊C₄	—	67	2	no	—
306	C₄×C₄⋊C₄	—	134	1	no	—
307	#328	—	67	16	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	C₂×Dic₆₇	1	2	yes	—
310	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
311	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
312	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
313	C₂²×C₈	—	134	2	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
319	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
320	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
321	C₄⋊Q₈	C₂×Dic₆₇	1	2	yes	—
322	#125	—	2	2	no	—
323	#125	—	2	2	no	—
324	#125	—	2	2	no	—
325	#125	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	C₂×Dic₆₇	1	4	yes	—
333	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	C₂×Dic₆₇	1	4	yes	—
341	C₄×Q₈	C₂×Dic₆₇	1	4	yes	—
342	#117	—	2	2	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	—	268	4	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	134	2	no	—
353	C₂×C₄⋊C₄	—	134	2	no	—
354	C₂×C₄⋊C₄	—	134	2	no	—
355	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	134	2	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	134	2	no	—
360	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
361	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
362	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
363	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
364	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
365	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
366	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
367	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
368	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
369	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
370	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
371	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
372	C₄⋊C₈	—	134	2	no	—
373	C₄⋊C₈	—	134	2	no	—
374	C₂²⋊C₈	—	67	4	no	—
375	C₂²⋊C₈	—	134	2	no	—
376	C₄×C₈	—	134	2	no	—
377	C₄×C₈	—	134	2	no	—
378	#95	—	67	4	no	—
379	#95	—	134	2	no	—
380	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	—	4	4	no	—
386	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	134	4	no	—
392	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
393	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
394	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
395	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
396	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
397	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
398	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
399	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
400	C₂²×C₄	#11761615	1	4	yes	—
401	C₂²×C₄	#11761618	1	4	yes	—
402	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
403	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
411	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
412	C₂×C₈	—	268	4	no	—
413	C₂×C₈	—	134	4	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	268	4	no	—
426	C₄⋊C₄	—	268	4	no	—
427	C₄⋊C₄	—	268	4	no	—
428	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	268	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	268	4	no	—
435	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
436	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
437	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
438	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
439	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
440	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
441	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
442	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
443	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
444	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
445	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
446	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
447	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
450	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
454	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
455	C₂³	C₂×#11761615	1	2	yes	—
456	C₂³	C₂×#11761618	1	2	yes	—
457	C₂³	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
458	Q₈	—	4	4	no	—
459	Q₈	—	4	4	no	—
460	Q₈	—	4	4	no	—
461	Q₈	—	4	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	268	4	no	—
479	C₂×C₄	—	268	4	no	—
480	C₂×C₄	—	268	4	no	—
481	C₂×C₄	#14523967	1	4	yes	—
482	C₂×C₄	#14523967	1	4	yes	—
483	C₂×C₄	#14523967	1	4	yes	—
484	C₂×C₄	#14523967	1	4	yes	—
485	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
486	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
487	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
488	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
489	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
490	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
492	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
493	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
494	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
495	C₂×C₄	C₂×#11761615	1	2	yes	—
496	C₂×C₄	C₂×#11761615	1	2	yes	—
497	C₂×C₄	C₂×#11761618	1	2	yes	—
498	C₂×C₄	C₂×#11761618	1	2	yes	—
499	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
501	C₈	—	268	4	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	C₂×#14523967	1	2	yes	—
511	C₂²	C₂×#14523967	1	2	yes	—
512	C₂²	C₂²×C₂²⋊Dic₆₇	1	1	yes	characteristic
513	C₂²	C₂²×#11761615	1	1	yes	characteristic
514	C₂²	C₂²×#11761618	1	1	yes	characteristic
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	—	536	4	no	—
524	C₄	#16863370	1	2	yes	—
525	C₄	C₂×#14523967	1	2	yes	—
526	C₄	C₂×#14523967	1	2	yes	—
527	C₄	C₂×#14523967	1	2	yes	—
528	C₄	C₂×#14523967	1	2	yes	—
529	C₄	#16863413	1	2	yes	—
530	C₂	—	2	1	no	—
531	C₂	—	2	2	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	1	no	—
534	C₂	C₂×#16863370	1	1	yes	characteristic
535	C₂	C₂²×#14523967	1	1	yes	characteristic
536	C₂	C₂×#16863413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#533×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#533	D₆₇
hypocenter	C₆₇	#17575
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
4. #22558773	C₂	semidirect
5. #22558708	C₂	semidirect
26. #533×C₆₇	C₄	semidirect
27. #533×C₆₇	C₄	semidirect
30. C₂×C₄⋊Q₈×C₆₇	C₄	semidirect
31. C₂×C₄⋊Q₈×C₆₇	C₄	semidirect
36. C₂×C₄×Q₈×C₆₇	C₄	semidirect
275. C₆₇	#17575	semidirect
280. #533	Dic₆₇	semidirect
281. #533	Dic₆₇	semidirect
284. C₂×C₄⋊Q₈	Dic₆₇	semidirect
285. C₂×C₄⋊Q₈	Dic₆₇	semidirect
290. C₂×C₄×Q₈	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863449	2
#22562616	2
#22558781	2
#22558773	2
#22558708	2
C₂×#533×C₆₇	2
#17575	67