Subgroups — C₆₇×#59655 #30738906

Order 17152.

2188 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2729	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2550	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2492	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2453	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2452	C₂	1	2	yes	maximal
10	C₆₇×#2440	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2429	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2429	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2367	C₂	1	2	yes	maximal
14	C₆₇×#2360	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
18	Q₈²×C₆₇	—	2	8	no	—
19	#554×C₆₇	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₆₇	C₂²	1	4	yes	—
23	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	2	yes	—
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	4	yes	—
41	#398×C₆₇	C₂²	1	4	yes	—
42	#398×C₆₇	C₂²	1	4	yes	—
43	#398×C₆₇	C₂²	1	4	yes	—
44	#396×C₆₇	C₂²	1	4	yes	—
45	#396×C₆₇	C₂²	1	4	yes	—
46	#395×C₆₇	C₂²	1	4	yes	—
47	#393×C₆₇	C₂²	1	4	yes	—
48	#391×C₆₇	C₂²	1	4	yes	—
49	#391×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	1	yes	characteristic
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	1	yes	characteristic
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	4	yes	—
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	2	yes	—
65	#389×C₆₇	C₂²	1	4	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	4	yes	—
69	#388×C₆₇	C₂²	1	4	yes	—
70	#387×C₆₇	C₂²	1	4	yes	—
71	#385×C₆₇	C₂²	1	4	yes	—
72	#385×C₆₇	C₂²	1	4	yes	—
73	#384×C₆₇	C₂²	1	1	yes	characteristic
74	#384×C₆₇	C₂²	1	1	yes	characteristic
75	#382×C₆₇	C₂²	1	1	yes	characteristic
76	#380×C₆₇	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
84	C₄³×C₆₇	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
89	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₆₇	—	2	16	no	—
94	C₄⋊Q₈×C₆₇	—	2	4	no	—
95	C₄⋊Q₈×C₆₇	—	2	8	no	—
96	C₄⋊Q₈×C₆₇	—	2	8	no	—
97	C₄⋊Q₈×C₆₇	D₄	1	8	yes	—
98	#125×C₆₇	—	2	8	no	—
99	#124×C₆₇	Q₈	1	8	yes	complemented
100	C₂²⋊Q₈×C₆₇	—	2	16	no	—
101	C₂²⋊Q₈×C₆₇	—	2	8	no	—
102	C₂²⋊Q₈×C₆₇	—	2	8	no	—
103	C₂²⋊Q₈×C₆₇	—	4	8	no	—
104	C₄×Q₈×C₆₇	—	2	8	no	—
105	C₄×Q₈×C₆₇	—	2	8	no	—
106	C₄×Q₈×C₆₇	—	2	4	no	—
107	C₄×Q₈×C₆₇	—	2	4	no	—
108	C₄×Q₈×C₆₇	—	2	4	no	—
109	C₄×Q₈×C₆₇	—	4	4	no	—
110	C₄×D₄×C₆₇	—	2	8	no	—
111	C₄×D₄×C₆₇	—	2	4	no	—
112	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
147	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
153	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	#95×C₆₇	C₂³	1	2	yes	—
157	#95×C₆₇	C₂³	1	2	yes	—
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	2	yes	—
163	#95×C₆₇	C₂³	1	4	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	#95×C₆₇	C₂³	1	2	yes	—
166	#95×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	4	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	#95×C₆₇	C₂³	1	4	yes	—
170	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
171	C₂×Q₈×C₆₇	—	2	2	no	—
172	C₂×Q₈×C₆₇	—	2	2	no	—
173	C₂×Q₈×C₆₇	—	2	2	no	—
174	C₂×Q₈×C₆₇	—	2	8	no	—
175	C₂×Q₈×C₆₇	—	2	2	no	—
176	C₂×Q₈×C₆₇	—	2	2	no	—
177	C₂×Q₈×C₆₇	—	2	2	no	—
178	C₂×Q₈×C₆₇	—	2	2	no	—
179	C₂×Q₈×C₆₇	—	4	2	no	—
180	C₂×Q₈×C₆₇	—	4	2	no	—
181	C₂×Q₈×C₆₇	—	4	4	no	—
182	C₂×Q₈×C₆₇	—	4	4	no	—
183	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
184	C₂×Q₈×C₆₇	C₂×Q₈	1	4	yes	—
185	C₂×Q₈×C₆₇	#41	1	4	yes	—
186	C₂×D₄×C₆₇	—	2	2	no	—
187	C₂×D₄×C₆₇	—	2	2	no	—
188	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
189	C₂²×C₄×C₆₇	—	2	4	no	—
190	C₂²×C₄×C₆₇	—	2	4	no	—
191	C₂²×C₄×C₆₇	—	2	4	no	—
192	C₂²×C₄×C₆₇	—	2	8	no	—
193	C₂²×C₄×C₆₇	—	4	4	no	—
194	C₂²×C₄×C₆₇	—	4	4	no	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	—	2	2	no	—
212	C₄⋊C₄×C₆₇	—	2	8	no	—
213	C₄⋊C₄×C₆₇	—	2	2	no	—
214	C₄⋊C₄×C₆₇	—	2	4	no	—
215	C₄⋊C₄×C₆₇	—	2	8	no	—
216	C₄⋊C₄×C₆₇	—	2	8	no	—
217	C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₄⋊C₄×C₆₇	—	2	4	no	—
219	C₄⋊C₄×C₆₇	—	2	2	no	—
220	C₄⋊C₄×C₆₇	—	2	2	no	—
221	C₄⋊C₄×C₆₇	—	2	8	no	—
222	C₄⋊C₄×C₆₇	—	2	4	no	—
223	C₄⋊C₄×C₆₇	—	2	8	no	—
224	C₄⋊C₄×C₆₇	—	2	4	no	—
225	C₄⋊C₄×C₆₇	—	2	4	no	—
226	C₄⋊C₄×C₆₇	—	2	8	no	—
227	C₄⋊C₄×C₆₇	—	2	4	no	—
228	C₄⋊C₄×C₆₇	—	2	4	no	—
229	C₄⋊C₄×C₆₇	—	4	2	no	—
230	C₄⋊C₄×C₆₇	—	4	2	no	—
231	C₄⋊C₄×C₆₇	—	4	4	no	—
232	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
233	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
234	C₂²⋊C₄×C₆₇	—	2	8	no	—
235	C₂²⋊C₄×C₆₇	—	2	4	no	—
236	C₂²⋊C₄×C₆₇	—	2	8	no	—
237	C₂²⋊C₄×C₆₇	—	2	4	no	—
238	C₂²⋊C₄×C₆₇	—	4	2	no	—
239	C₂²⋊C₄×C₆₇	—	4	4	no	—
240	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
241	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
242	C₄²×C₆₇	—	2	4	no	—
243	C₄²×C₆₇	—	2	8	no	—
244	C₄²×C₆₇	—	2	4	no	—
245	C₄²×C₆₇	—	2	4	no	—
246	C₄²×C₆₇	—	2	2	no	—
247	C₄²×C₆₇	—	2	2	no	—
248	C₄²×C₆₇	—	2	2	no	—
249	C₄²×C₆₇	—	2	2	no	—
250	C₄²×C₆₇	—	4	1	no	—
251	C₄²×C₆₇	—	4	4	no	—
252	C₄²×C₆₇	C₂×D₄	1	4	yes	—
253	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	—	2	2	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
261	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
262	Q₈×C₆₇	—	2	8	no	—
263	Q₈×C₆₇	—	2	8	no	—
264	Q₈×C₆₇	—	4	8	no	—
265	Q₈×C₆₇	—	4	4	no	—
266	Q₈×C₆₇	—	8	8	no	—
267	D₄×C₆₇	—	2	8	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	2	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	4	no	—
275	C₂×C₄×C₆₇	—	2	1	no	—
276	C₂×C₄×C₆₇	—	2	1	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	1	no	—
280	C₂×C₄×C₆₇	—	2	1	no	—
281	C₂×C₄×C₆₇	—	2	4	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	4	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	1	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	4	8	no	—
304	C₂×C₄×C₆₇	—	8	8	no	—
305	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
306	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
310	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
311	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
312	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
313	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
314	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
315	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
316	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
317	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
318	C₂²×C₆₇	—	2	4	no	—
319	C₂²×C₆₇	—	2	4	no	—
320	C₂²×C₆₇	—	2	4	no	—
321	C₂²×C₆₇	—	4	2	no	—
322	C₂²×C₆₇	—	4	2	no	—
323	C₂²×C₆₇	—	4	2	no	—
324	C₂²×C₆₇	—	4	2	no	—
325	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
326	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
327	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂²×C₆₇	#585	1	1	yes	characteristic
332	C₄×C₆₇	—	2	4	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	2	2	no	—
335	C₄×C₆₇	—	2	8	no	—
336	C₄×C₆₇	—	2	2	no	—
337	C₄×C₆₇	—	2	2	no	—
338	C₄×C₆₇	—	2	2	no	—
339	C₄×C₆₇	—	4	2	no	—
340	C₄×C₆₇	—	4	2	no	—
341	C₄×C₆₇	—	4	2	no	—
342	C₄×C₆₇	—	4	2	no	—
343	C₄×C₆₇	—	4	2	no	—
344	C₄×C₆₇	—	4	4	no	—
345	C₄×C₆₇	—	4	1	no	—
346	C₄×C₆₇	#548	1	4	yes	—
347	C₄×C₆₇	D₄×Q₈	1	4	yes	—
348	#59655	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂×C₆₇	—	4	4	no	—
350	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
351	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
352	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
353	C₂×C₆₇	#3496	1	1	yes	characteristic
354	C₂×C₆₇	#3503	1	1	yes	characteristic
355	C₂×C₆₇	#3522	1	1	yes	characteristic
356	C₂×C₆₇	#3555	1	1	yes	characteristic
357	C₂×Q₈²	C₂×C₆₇	1	1	yes	characteristic, complemented
358	C₂×#554	C₂×C₆₇	1	1	yes	characteristic
359	#2729	C₂×C₆₇	1	4	yes	complemented
360	#2582	C₂×C₆₇	1	1	yes	characteristic, complemented
361	#2550	C₂×C₆₇	1	2	yes	complemented
362	#2538	C₂×C₆₇	1	1	yes	characteristic
363	#2492	C₂×C₆₇	1	2	yes	complemented
364	#2453	C₂×C₆₇	1	2	yes	complemented
365	#2452	C₂×C₆₇	1	2	yes	—
366	#2440	C₂×C₆₇	1	2	yes	complemented
367	#2429	C₂×C₆₇	1	2	yes	complemented
368	#2429	C₂×C₆₇	1	4	yes	complemented
369	#2367	C₂×C₆₇	1	2	yes	—
370	#2360	C₂×C₆₇	1	2	yes	complemented
371	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
372	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
373	C₄×#124	C₂×C₆₇	1	1	yes	characteristic
374	C₆₇	#59655	1	1	yes	characteristic, direct product factor, Sylow
375	Q₈²	—	2	8	no	—
376	#554	—	2	8	no	—
377	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
378	C₂×C₄⋊Q₈	C₂²×C₆₇	1	4	yes	—
379	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
380	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
381	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
382	C₂×#125	C₂²×C₆₇	1	2	yes	—
383	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
384	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
385	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
388	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
389	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
392	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
393	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
394	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
397	#400	C₂²×C₆₇	1	4	yes	—
398	#398	C₂²×C₆₇	1	4	yes	—
399	#398	C₂²×C₆₇	1	4	yes	—
400	#398	C₂²×C₆₇	1	4	yes	—
401	#396	C₂²×C₆₇	1	4	yes	—
402	#396	C₂²×C₆₇	1	4	yes	—
403	#395	C₂²×C₆₇	1	4	yes	—
404	#393	C₂²×C₆₇	1	4	yes	—
405	#391	C₂²×C₆₇	1	1	yes	characteristic
406	#391	C₂²×C₆₇	1	2	yes	—
407	#391	C₂²×C₆₇	1	1	yes	characteristic
408	#391	C₂²×C₆₇	1	2	yes	—
409	#391	C₂²×C₆₇	1	2	yes	—
410	#391	C₂²×C₆₇	1	4	yes	—
411	#391	C₂²×C₆₇	1	1	yes	characteristic
412	#390	C₂²×C₆₇	1	2	yes	—
413	#390	C₂²×C₆₇	1	1	yes	characteristic
414	#389	C₂²×C₆₇	1	2	yes	—
415	#389	C₂²×C₆₇	1	2	yes	—
416	#389	C₂²×C₆₇	1	2	yes	—
417	#389	C₂²×C₆₇	1	2	yes	—
418	#389	C₂²×C₆₇	1	2	yes	—
419	#389	C₂²×C₆₇	1	2	yes	—
420	#389	C₂²×C₆₇	1	4	yes	—
421	#389	C₂²×C₆₇	1	4	yes	—
422	#389	C₂²×C₆₇	1	2	yes	—
423	#388	C₂²×C₆₇	1	4	yes	—
424	#388	C₂²×C₆₇	1	4	yes	—
425	#388	C₂²×C₆₇	1	2	yes	—
426	#388	C₂²×C₆₇	1	2	yes	—
427	#387	C₂²×C₆₇	1	4	yes	—
428	#385	C₂²×C₆₇	1	4	yes	—
429	#385	C₂²×C₆₇	1	4	yes	—
430	#384	C₂²×C₆₇	1	1	yes	characteristic
431	#384	C₂²×C₆₇	1	1	yes	characteristic
432	#382	C₂²×C₆₇	1	1	yes	characteristic
433	#380	C₂²×C₆₇	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
441	C₄³	C₂²×C₆₇	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
446	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
447	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
449	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
450	C₄⋊Q₈	—	2	16	no	—
451	C₄⋊Q₈	—	2	4	no	—
452	C₄⋊Q₈	—	2	8	no	—
453	C₄⋊Q₈	—	2	8	no	—
454	C₄⋊Q₈	D₄×C₆₇	1	8	yes	—
455	#125	—	2	8	no	—
456	#124	Q₈×C₆₇	1	8	yes	complemented
457	C₂²⋊Q₈	—	2	16	no	—
458	C₂²⋊Q₈	—	2	8	no	—
459	C₂²⋊Q₈	—	2	8	no	—
460	C₂²⋊Q₈	—	4	8	no	—
461	C₄×Q₈	—	2	8	no	—
462	C₄×Q₈	—	2	8	no	—
463	C₄×Q₈	—	2	4	no	—
464	C₄×Q₈	—	2	4	no	—
465	C₄×Q₈	—	2	4	no	—
466	C₄×Q₈	—	4	4	no	—
467	C₄×D₄	—	2	8	no	—
468	C₄×D₄	—	2	4	no	—
469	C₂×C₄⋊C₄	—	2	8	no	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
501	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
502	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
503	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
504	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
505	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
510	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
513	#95	C₂³×C₆₇	1	2	yes	—
514	#95	C₂³×C₆₇	1	2	yes	—
515	#95	C₂³×C₆₇	1	2	yes	—
516	#95	C₂³×C₆₇	1	4	yes	—
517	#95	C₂³×C₆₇	1	2	yes	—
518	#95	C₂³×C₆₇	1	2	yes	—
519	#95	C₂³×C₆₇	1	2	yes	—
520	#95	C₂³×C₆₇	1	4	yes	—
521	#95	C₂³×C₆₇	1	4	yes	—
522	#95	C₂³×C₆₇	1	2	yes	—
523	#95	C₂³×C₆₇	1	2	yes	—
524	#95	C₂³×C₆₇	1	4	yes	—
525	#95	C₂³×C₆₇	1	4	yes	—
526	#95	C₂³×C₆₇	1	4	yes	—
527	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	8	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	—	4	4	no	—
539	C₂×Q₈	—	4	4	no	—
540	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
541	C₂×Q₈	C₂×Q₈×C₆₇	1	4	yes	—
542	C₂×Q₈	#41×C₆₇	1	4	yes	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	8	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	8	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	4	2	no	—
587	C₄⋊C₄	—	4	4	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
590	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
598	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	8	no	—
601	C₄²	—	2	4	no	—
602	C₄²	—	2	4	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	4	4	no	—
608	C₄²	—	4	1	no	—
609	C₄²	C₂×D₄×C₆₇	1	4	yes	—
610	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
618	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
619	Q₈	—	2	8	no	—
620	Q₈	—	2	8	no	—
621	Q₈	—	4	8	no	—
622	Q₈	—	4	4	no	—
623	Q₈	—	8	8	no	—
624	D₄	—	2	8	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	8	no	—
661	C₂×C₄	—	8	8	no	—
662	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
663	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
664	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
666	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
667	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
668	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
669	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
670	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
671	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
672	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
673	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
674	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
683	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
684	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
685	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
686	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
687	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
688	C₂²	#585×C₆₇	1	1	yes	characteristic
689	C₄	—	2	2	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	8	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	#548×C₆₇	1	4	yes	—
704	C₄	D₄×Q₈×C₆₇	1	4	yes	—
705	C₂	—	4	4	no	—
706	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
707	C₂	C₂×D₄×Q₈×C₆₇	1	1	yes	characteristic
708	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
709	C₂	C₆₇×#3496	1	1	yes	characteristic
710	C₂	C₆₇×#3503	1	1	yes	characteristic
711	C₂	C₆₇×#3522	1	1	yes	characteristic
712	C₂	C₆₇×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈²×C₆₇	C₂	semidirect
3. C₆₇×#2729	C₂	semidirect
4. C₆₇×#2582	C₂	semidirect
5. C₆₇×#2550	C₂	semidirect
7. C₆₇×#2492	C₂	semidirect
8. C₆₇×#2453	C₂	semidirect
10. C₆₇×#2440	C₂	semidirect
11. C₆₇×#2429	C₂	semidirect
12. C₆₇×#2429	C₂	semidirect
14. C₆₇×#2360	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
16. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
99. #124×C₆₇	Q₈	semidirect
348. #59655	C₆₇	direct (N × H)
357. C₂×Q₈²	C₂×C₆₇	semidirect
359. #2729	C₂×C₆₇	semidirect
360. #2582	C₂×C₆₇	semidirect
361. #2550	C₂×C₆₇	semidirect
363. #2492	C₂×C₆₇	semidirect
364. #2453	C₂×C₆₇	semidirect
366. #2440	C₂×C₆₇	semidirect
367. #2429	C₂×C₆₇	semidirect
368. #2429	C₂×C₆₇	semidirect
370. #2360	C₂×C₆₇	semidirect
371. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
372. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
374. C₆₇	#59655	direct (N × H)
456. #124	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₆₇	2
C₂×#554×C₆₇	2
C₆₇×#2729	2
C₆₇×#2582	2
C₆₇×#2550	2
C₆₇×#2538	2
C₆₇×#2492	2
C₆₇×#2453	2
C₆₇×#2452	2
C₆₇×#2440	2
C₆₇×#2429	2
C₆₇×#2367	2
C₆₇×#2360	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#124×C₆₇	2
#59655	67

Subgroups — C67×#59655 #30738906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59655 #30738906