Subgroups — C₆₇×#34739 #30713990

Order 17152.

2598 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2442	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2441	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2440	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2439	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2438	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2437	C₂	1	4	yes	maximal
9	C₆₇×#2396	C₂	1	4	yes	maximal, complemented
10	C₄×C₂²⋊Q₈×C₆₇	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
17	#533×C₆₇	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
19	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#117×C₆₇	—	2	8	no	—
24	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₇	C₂²	1	2	yes	—
28	C₂×#117×C₆₇	C₂²	1	2	yes	—
29	C₂×#117×C₆₇	C₂²	1	2	yes	—
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	4	yes	complemented
38	#399×C₆₇	C₂²	1	4	yes	—
39	#398×C₆₇	C₂²	1	4	yes	complemented
40	#398×C₆₇	C₂²	1	4	yes	complemented
41	#396×C₆₇	C₂²	1	4	yes	—
42	#396×C₆₇	C₂²	1	4	yes	—
43	#395×C₆₇	C₂²	1	4	yes	complemented
44	#393×C₆₇	C₂²	1	4	yes	—
45	#391×C₆₇	C₂²	1	4	yes	complemented
46	#389×C₆₇	C₂²	1	2	yes	complemented
47	#389×C₆₇	C₂²	1	2	yes	complemented
48	#389×C₆₇	C₂²	1	2	yes	complemented
49	#389×C₆₇	C₂²	1	2	yes	complemented
50	#389×C₆₇	C₂²	1	4	yes	complemented
51	#387×C₆₇	C₂²	1	4	yes	complemented
52	#387×C₆₇	C₂²	1	4	yes	complemented
53	#385×C₆₇	C₂²	1	4	yes	—
54	#385×C₆₇	C₂²	1	4	yes	—
55	#385×C₆₇	C₂²	1	4	yes	—
56	#385×C₆₇	C₂²	1	4	yes	—
57	#384×C₆₇	C₂²	1	2	yes	complemented
58	#382×C₆₇	C₂²	1	2	yes	complemented
59	#381×C₆₇	C₂²	1	2	yes	—
60	#380×C₆₇	C₂²	1	2	yes	—
61	#380×C₆₇	C₂²	1	2	yes	—
62	#380×C₆₇	C₂²	1	4	yes	—
63	#380×C₆₇	C₂²	1	4	yes	—
64	#379×C₆₇	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
67	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
68	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
76	C₂×#95×C₆₇	C₂²	1	2	yes	—
77	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
79	C₂³×C₄×C₆₇	—	2	4	no	—
80	C₂³×C₄×C₆₇	—	2	4	no	—
81	C₂³×C₄×C₆₇	Q₈	1	8	yes	complemented
82	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
83	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
84	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₄⋊Q₈×C₆₇	—	2	8	no	—
92	#125×C₆₇	—	2	8	no	—
93	C₂²⋊Q₈×C₆₇	—	2	16	no	—
94	C₂²⋊Q₈×C₆₇	—	2	16	no	—
95	C₄×Q₈×C₆₇	—	2	16	no	—
96	#117×C₆₇	—	2	4	no	—
97	#117×C₆₇	—	2	4	no	—
98	#117×C₆₇	—	2	4	no	—
99	#117×C₆₇	—	2	8	no	—
100	#117×C₆₇	—	2	8	no	—
101	#117×C₆₇	—	2	8	no	—
102	#117×C₆₇	D₄	1	8	yes	—
103	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₆₇	—	2	4	no	—
132	C₂×C₄²×C₆₇	—	2	4	no	—
133	C₂×C₄²×C₆₇	—	2	8	no	—
134	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
135	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
145	#95×C₆₇	C₂³	1	2	yes	—
146	#95×C₆₇	C₂³	1	2	yes	—
147	#95×C₆₇	C₂³	1	2	yes	—
148	#95×C₆₇	C₂³	1	2	yes	—
149	#95×C₆₇	C₂³	1	4	yes	—
150	#95×C₆₇	C₂³	1	4	yes	—
151	#95×C₆₇	C₂³	1	4	yes	—
152	#95×C₆₇	C₂³	1	4	yes	—
153	#95×C₆₇	C₂³	1	4	yes	—
154	#95×C₆₇	C₂³	1	4	yes	—
155	#95×C₆₇	C₂³	1	4	yes	—
156	#95×C₆₇	C₂³	1	4	yes	—
157	C₂⁴×C₆₇	—	2	2	no	—
158	C₂⁴×C₆₇	—	2	4	no	—
159	C₂⁴×C₆₇	—	2	2	no	—
160	C₂⁴×C₆₇	—	4	2	no	—
161	C₂⁴×C₆₇	C₂×Q₈	1	4	yes	—
162	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₆₇	—	2	8	no	—
166	C₂×Q₈×C₆₇	—	2	8	no	—
167	C₂×Q₈×C₆₇	—	4	4	no	—
168	C₂²×C₄×C₆₇	—	2	2	no	—
169	C₂²×C₄×C₆₇	—	2	2	no	—
170	C₂²×C₄×C₆₇	—	2	32	no	—
171	C₂²×C₄×C₆₇	—	2	2	no	—
172	C₂²×C₄×C₆₇	—	2	2	no	—
173	C₂²×C₄×C₆₇	—	2	2	no	—
174	C₂²×C₄×C₆₇	—	2	2	no	—
175	C₂²×C₄×C₆₇	—	2	2	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	2	4	no	—
181	C₂²×C₄×C₆₇	—	2	8	no	—
182	C₂²×C₄×C₆₇	—	2	8	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	4	2	no	—
186	C₂²×C₄×C₆₇	—	4	4	no	—
187	C₂²×C₄×C₆₇	—	4	2	no	—
188	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
190	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
191	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
192	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
195	C₂²×C₄×C₆₇	#41	1	4	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₆₇	—	2	8	no	—
209	C₄⋊C₄×C₆₇	—	2	4	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	8	no	—
212	C₄⋊C₄×C₆₇	—	2	8	no	—
213	C₄⋊C₄×C₆₇	—	2	8	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	8	no	—
218	C₄⋊C₄×C₆₇	—	4	4	no	—
219	C₄⋊C₄×C₆₇	—	4	4	no	—
220	C₄⋊C₄×C₆₇	—	4	4	no	—
221	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
222	C₂²⋊C₄×C₆₇	—	2	4	no	—
223	C₂²⋊C₄×C₆₇	—	2	4	no	—
224	C₂²⋊C₄×C₆₇	—	2	4	no	—
225	C₂²⋊C₄×C₆₇	—	2	4	no	—
226	C₂²⋊C₄×C₆₇	—	2	8	no	—
227	C₂²⋊C₄×C₆₇	—	2	8	no	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	4	no	—
230	C₂²⋊C₄×C₆₇	—	4	4	no	—
231	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
232	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
233	C₄²×C₆₇	—	2	8	no	—
234	C₄²×C₆₇	—	2	4	no	—
235	C₄²×C₆₇	—	2	4	no	—
236	C₄²×C₆₇	—	2	2	no	—
237	C₄²×C₆₇	—	2	2	no	—
238	C₄²×C₆₇	—	2	4	no	—
239	C₄²×C₆₇	—	2	2	no	—
240	C₄²×C₆₇	—	2	4	no	—
241	C₄²×C₆₇	—	2	2	no	—
242	C₄²×C₆₇	—	2	4	no	—
243	C₄²×C₆₇	C₂×D₄	1	8	yes	—
244	C₂³×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	—	2	1	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	2	no	—
249	C₂³×C₆₇	—	2	8	no	—
250	C₂³×C₆₇	—	2	8	no	—
251	C₂³×C₆₇	—	2	1	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	1	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	4	4	no	—
256	C₂³×C₆₇	—	4	8	no	—
257	C₂³×C₆₇	—	4	8	no	—
258	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
259	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
260	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
261	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
262	C₂³×C₆₇	C₂×#41	1	2	yes	—
263	C₂³×C₆₇	C₂×#41	1	4	yes	—
264	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
265	Q₈×C₆₇	—	4	16	no	—
266	C₂×C₄×C₆₇	—	2	8	no	—
267	C₂×C₄×C₆₇	—	2	1	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	1	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	4	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	8	no	—
278	C₂×C₄×C₆₇	—	2	8	no	—
279	C₂×C₄×C₆₇	—	2	8	no	—
280	C₂×C₄×C₆₇	—	2	8	no	—
281	C₂×C₄×C₆₇	—	2	4	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	4	no	—
293	C₂×C₄×C₆₇	—	2	4	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	4	16	no	—
297	C₂×C₄×C₆₇	—	4	8	no	—
298	C₂×C₄×C₆₇	—	4	8	no	—
299	C₂×C₄×C₆₇	C₂²⋊Q₈	1	16	yes	complemented
300	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
301	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
304	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
305	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
306	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
308	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
309	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
310	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	2	no	—
313	C₂²×C₆₇	—	2	2	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	4	no	—
316	C₂²×C₆₇	—	2	4	no	—
317	C₂²×C₆₇	—	2	4	no	—
318	C₂²×C₆₇	—	2	4	no	—
319	C₂²×C₆₇	—	2	2	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	2	no	—
322	C₂²×C₆₇	—	4	16	no	—
323	C₂²×C₆₇	—	4	2	no	—
324	C₂²×C₆₇	—	4	2	no	—
325	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	4	yes	—
326	C₂²×C₆₇	#533	1	4	yes	complemented
327	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
328	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
329	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
330	C₂²×C₆₇	C₂²×#41	1	2	yes	—
331	C₂²×C₆₇	#585	1	2	yes	—
332	C₄×C₆₇	—	2	2	no	—
333	C₄×C₆₇	—	2	2	no	—
334	C₄×C₆₇	—	2	8	no	—
335	C₄×C₆₇	—	2	4	no	—
336	C₄×C₆₇	—	2	4	no	—
337	C₄×C₆₇	—	4	4	no	—
338	C₄×C₆₇	—	4	2	no	—
339	C₄×C₆₇	—	4	4	no	—
340	C₄×C₆₇	—	4	4	no	—
341	C₄×C₆₇	—	4	2	no	—
342	C₄×C₆₇	C₂×C₂²⋊Q₈	1	4	yes	—
343	C₄×C₆₇	C₂×C₂²⋊Q₈	1	4	yes	—
344	#34739	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₆₇	—	2	4	no	—
346	C₂×C₆₇	—	2	4	no	—
347	C₂×C₆₇	—	4	2	no	—
348	C₂×C₆₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
349	C₂×C₆₇	C₂×#533	1	1	yes	characteristic
350	C₂×C₆₇	#3458	1	1	yes	characteristic
351	C₂×C₆₇	D₄×#41	1	2	yes	—
352	C₂×C₆₇	#3475	1	2	yes	—
353	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
354	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic
355	#2442	C₂×C₆₇	1	2	yes	complemented
356	#2441	C₂×C₆₇	1	2	yes	complemented
357	#2440	C₂×C₆₇	1	2	yes	complemented
358	#2439	C₂×C₆₇	1	2	yes	complemented
359	#2438	C₂×C₆₇	1	4	yes	complemented
360	#2437	C₂×C₆₇	1	4	yes	—
361	#2396	C₂×C₆₇	1	4	yes	complemented
362	C₄×C₂²⋊Q₈	C₂×C₆₇	1	4	yes	complemented
363	#2296	C₂×C₆₇	1	1	yes	characteristic, complemented
364	#2296	C₂×C₆₇	1	1	yes	characteristic, complemented
365	#2285	C₂×C₆₇	1	1	yes	characteristic, complemented
366	#2280	C₂×C₆₇	1	1	yes	characteristic
367	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic
368	C₆₇	#34739	1	1	yes	characteristic, direct product factor, Sylow
369	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
370	#533	—	2	8	no	—
371	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
372	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
373	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
374	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
375	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
376	C₂×#117	—	2	8	no	—
377	C₂×#117	C₂²×C₆₇	1	2	yes	—
378	C₂×#117	C₂²×C₆₇	1	2	yes	—
379	C₂×#117	C₂²×C₆₇	1	2	yes	—
380	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
381	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
382	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
383	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
385	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
386	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
387	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
388	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
389	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
390	#400	C₂²×C₆₇	1	4	yes	complemented
391	#399	C₂²×C₆₇	1	4	yes	—
392	#398	C₂²×C₆₇	1	4	yes	complemented
393	#398	C₂²×C₆₇	1	4	yes	complemented
394	#396	C₂²×C₆₇	1	4	yes	—
395	#396	C₂²×C₆₇	1	4	yes	—
396	#395	C₂²×C₆₇	1	4	yes	complemented
397	#393	C₂²×C₆₇	1	4	yes	—
398	#391	C₂²×C₆₇	1	4	yes	complemented
399	#389	C₂²×C₆₇	1	4	yes	complemented
400	#389	C₂²×C₆₇	1	2	yes	complemented
401	#389	C₂²×C₆₇	1	2	yes	complemented
402	#389	C₂²×C₆₇	1	2	yes	complemented
403	#389	C₂²×C₆₇	1	2	yes	complemented
404	#387	C₂²×C₆₇	1	4	yes	complemented
405	#387	C₂²×C₆₇	1	4	yes	complemented
406	#385	C₂²×C₆₇	1	4	yes	—
407	#385	C₂²×C₆₇	1	4	yes	—
408	#385	C₂²×C₆₇	1	4	yes	—
409	#385	C₂²×C₆₇	1	4	yes	—
410	#384	C₂²×C₆₇	1	2	yes	complemented
411	#382	C₂²×C₆₇	1	2	yes	complemented
412	#381	C₂²×C₆₇	1	2	yes	—
413	#380	C₂²×C₆₇	1	4	yes	—
414	#380	C₂²×C₆₇	1	4	yes	—
415	#380	C₂²×C₆₇	1	2	yes	—
416	#380	C₂²×C₆₇	1	2	yes	—
417	#379	C₂²×C₆₇	1	2	yes	—
418	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
419	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
420	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
421	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
424	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
425	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
426	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
427	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
429	C₂×#95	C₂²×C₆₇	1	2	yes	—
430	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	2	4	no	—
434	C₂³×C₄	Q₈×C₆₇	1	8	yes	complemented
435	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
436	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
437	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
438	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
444	C₄⋊Q₈	—	2	8	no	—
445	#125	—	2	8	no	—
446	C₂²⋊Q₈	—	2	16	no	—
447	C₂²⋊Q₈	—	2	16	no	—
448	C₄×Q₈	—	2	16	no	—
449	#117	—	2	4	no	—
450	#117	—	2	4	no	—
451	#117	—	2	4	no	—
452	#117	—	2	8	no	—
453	#117	—	2	8	no	—
454	#117	—	2	8	no	—
455	#117	D₄×C₆₇	1	8	yes	—
456	C₂×C₄⋊C₄	—	2	8	no	—
457	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
471	C₂×C₂²⋊C₄	—	2	8	no	—
472	C₂×C₂²⋊C₄	—	2	8	no	—
473	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₄²	—	2	4	no	—
485	C₂×C₄²	—	2	4	no	—
486	C₂×C₄²	—	2	8	no	—
487	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
489	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
490	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
498	#95	C₂³×C₆₇	1	2	yes	—
499	#95	C₂³×C₆₇	1	2	yes	—
500	#95	C₂³×C₆₇	1	2	yes	—
501	#95	C₂³×C₆₇	1	2	yes	—
502	#95	C₂³×C₆₇	1	4	yes	—
503	#95	C₂³×C₆₇	1	4	yes	—
504	#95	C₂³×C₆₇	1	4	yes	—
505	#95	C₂³×C₆₇	1	4	yes	—
506	#95	C₂³×C₆₇	1	4	yes	—
507	#95	C₂³×C₆₇	1	4	yes	—
508	#95	C₂³×C₆₇	1	4	yes	—
509	#95	C₂³×C₆₇	1	4	yes	—
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	2	2	no	—
513	C₂⁴	—	4	2	no	—
514	C₂⁴	C₂×Q₈×C₆₇	1	4	yes	—
515	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
516	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
517	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	2	8	no	—
520	C₂×Q₈	—	4	4	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	32	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
542	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
543	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
544	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
545	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
546	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
547	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
548	C₂²×C₄	#41×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	8	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	8	no	—
569	C₄⋊C₄	—	2	8	no	—
570	C₄⋊C₄	—	2	8	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	4	no	—
574	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
585	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
586	C₄²	—	2	8	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	4	no	—
596	C₄²	C₂×D₄×C₆₇	1	8	yes	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	4	4	no	—
609	C₂³	—	4	8	no	—
610	C₂³	—	4	8	no	—
611	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
612	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
613	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
614	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
615	C₂³	C₂×#41×C₆₇	1	2	yes	—
616	C₂³	C₂×#41×C₆₇	1	4	yes	—
617	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
618	Q₈	—	4	16	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	8	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	C₂²⋊Q₈×C₆₇	1	16	yes	complemented
653	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
654	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
656	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
657	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
658	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
659	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
660	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
661	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
662	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
663	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	4	16	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	C₂×C₂²⋊Q₈×C₆₇	1	4	yes	—
679	C₂²	#533×C₆₇	1	4	yes	complemented
680	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
681	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
682	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
683	C₂²	C₂²×#41×C₆₇	1	2	yes	—
684	C₂²	#585×C₆₇	1	2	yes	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	8	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	4	no	—
695	C₄	C₂×C₂²⋊Q₈×C₆₇	1	4	yes	—
696	C₄	C₂×C₂²⋊Q₈×C₆₇	1	4	yes	—
697	C₂	—	2	4	no	—
698	C₂	—	2	4	no	—
699	C₂	—	4	2	no	—
700	C₂	C₂²×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
701	C₂	C₂×#533×C₆₇	1	1	yes	characteristic
702	C₂	C₆₇×#3458	1	1	yes	characteristic
703	C₂	D₄×#41×C₆₇	1	2	yes	—
704	C₂	C₆₇×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂⁵×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₆₇	C₂	semidirect
3. C₆₇×#2442	C₂	semidirect
4. C₆₇×#2441	C₂	semidirect
5. C₆₇×#2440	C₂	semidirect
6. C₆₇×#2439	C₂	semidirect
7. C₆₇×#2438	C₂	semidirect
9. C₆₇×#2396	C₂	semidirect
10. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
11. C₆₇×#2296	C₂	semidirect
12. C₆₇×#2296	C₂	semidirect
13. C₆₇×#2285	C₂	semidirect
18. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
19. C₂×#125×C₆₇	C₂²	semidirect
22. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
39. #398×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
43. #395×C₆₇	C₂²	semidirect
45. #391×C₆₇	C₂²	semidirect
46. #389×C₆₇	C₂²	semidirect
47. #389×C₆₇	C₂²	semidirect
48. #389×C₆₇	C₂²	semidirect
49. #389×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
51. #387×C₆₇	C₂²	semidirect
52. #387×C₆₇	C₂²	semidirect
57. #384×C₆₇	C₂²	semidirect
58. #382×C₆₇	C₂²	semidirect
65. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
66. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
67. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
81. C₂³×C₄×C₆₇	Q₈	semidirect
299. C₂×C₄×C₆₇	C₂²⋊Q₈	semidirect
326. C₂²×C₆₇	#533	semidirect
344. #34739	C₆₇	direct (N × H)
353. C₂×#533	C₂×C₆₇	semidirect
355. #2442	C₂×C₆₇	semidirect
356. #2441	C₂×C₆₇	semidirect
357. #2440	C₂×C₆₇	semidirect
358. #2439	C₂×C₆₇	semidirect
359. #2438	C₂×C₆₇	semidirect
361. #2396	C₂×C₆₇	semidirect
362. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
363. #2296	C₂×C₆₇	semidirect
364. #2296	C₂×C₆₇	semidirect
365. #2285	C₂×C₆₇	semidirect
368. C₆₇	#34739	direct (N × H)
371. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
372. C₂×#125	C₂²×C₆₇	semidirect
375. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
390. #400	C₂²×C₆₇	semidirect
392. #398	C₂²×C₆₇	semidirect
393. #398	C₂²×C₆₇	semidirect
396. #395	C₂²×C₆₇	semidirect
398. #391	C₂²×C₆₇	semidirect
399. #389	C₂²×C₆₇	semidirect
400. #389	C₂²×C₆₇	semidirect
401. #389	C₂²×C₆₇	semidirect
402. #389	C₂²×C₆₇	semidirect
403. #389	C₂²×C₆₇	semidirect
404. #387	C₂²×C₆₇	semidirect
405. #387	C₂²×C₆₇	semidirect
410. #384	C₂²×C₆₇	semidirect
411. #382	C₂²×C₆₇	semidirect
418. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
419. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
420. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
434. C₂³×C₄	Q₈×C₆₇	semidirect
652. C₂×C₄	C₂²⋊Q₈×C₆₇	semidirect
679. C₂²	#533×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₆₇	2
C₂²×#117×C₆₇	2
C₆₇×#2442	2
C₆₇×#2441	2
C₆₇×#2440	2
C₆₇×#2439	2
C₆₇×#2438	2
C₆₇×#2437	2
C₆₇×#2396	2
C₄×C₂²⋊Q₈×C₆₇	2
C₆₇×#2296	2
C₆₇×#2285	2
C₆₇×#2280	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
#34739	67

Subgroups — C67×#34739 #30713990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34739 #30713990