Subgroups — C₆₇×#35144 #30714395

Order 17152.

2402 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2852	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2634	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2633	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2632	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2599	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2599	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2564	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2498	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2430	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×#383×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	#529×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	4	yes	—
27	C₄×#41×C₆₇	—	2	8	no	—
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	2	yes	—
39	C₂×#117×C₆₇	C₂²	1	2	yes	—
40	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	#400×C₆₇	C₂²	1	2	yes	—
43	#400×C₆₇	C₂²	1	2	yes	—
44	#399×C₆₇	C₂²	1	2	yes	—
45	#399×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#397×C₆₇	C₂²	1	2	yes	—
50	#395×C₆₇	C₂²	1	2	yes	—
51	#395×C₆₇	C₂²	1	2	yes	—
52	#394×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#393×C₆₇	C₂²	1	2	yes	—
55	#393×C₆₇	C₂²	1	2	yes	—
56	#392×C₆₇	C₂²	1	2	yes	—
57	#392×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	4	yes	—
60	#388×C₆₇	C₂²	1	4	yes	—
61	#388×C₆₇	C₂²	1	4	yes	—
62	#387×C₆₇	C₂²	1	4	yes	—
63	#387×C₆₇	C₂²	1	4	yes	—
64	#387×C₆₇	C₂²	1	4	yes	—
65	#387×C₆₇	C₂²	1	4	yes	—
66	#386×C₆₇	C₂²	1	4	yes	—
67	#386×C₆₇	C₂²	1	4	yes	—
68	#386×C₆₇	C₂²	1	4	yes	—
69	#386×C₆₇	C₂²	1	4	yes	—
70	#386×C₆₇	C₂²	1	4	yes	—
71	#386×C₆₇	C₂²	1	4	yes	—
72	#385×C₆₇	C₂²	1	4	yes	—
73	#385×C₆₇	C₂²	1	4	yes	—
74	#385×C₆₇	C₂²	1	4	yes	—
75	#385×C₆₇	C₂²	1	4	yes	—
76	#383×C₆₇	C₂²	1	2	yes	—
77	#383×C₆₇	C₂²	1	2	yes	—
78	#383×C₆₇	C₂²	1	2	yes	—
79	#383×C₆₇	C₂²	1	1	yes	characteristic
80	#383×C₆₇	C₂²	1	1	yes	characteristic
81	#380×C₆₇	C₂²	1	4	yes	—
82	C₂×#95×C₆₇	C₂²	1	2	yes	—
83	C₂×#95×C₆₇	C₂²	1	2	yes	—
84	C₂×#95×C₆₇	C₂²	1	2	yes	—
85	C₂×#41×C₆₇	—	2	8	no	—
86	C₂×#41×C₆₇	—	2	4	no	—
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
92	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
98	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	#126×C₆₇	—	2	8	no	—
103	#125×C₆₇	—	2	4	no	—
104	#124×C₆₇	—	2	4	no	—
105	#123×C₆₇	—	2	8	no	—
106	C₂²⋊Q₈×C₆₇	—	2	4	no	—
107	#121×C₆₇	—	2	16	no	—
108	#121×C₆₇	—	2	4	no	—
109	C₄×Q₈×C₆₇	—	2	4	no	—
110	C₄×Q₈×C₆₇	—	2	4	no	—
111	C₄×Q₈×C₆₇	—	2	4	no	—
112	C₄×D₄×C₆₇	—	2	8	no	—
113	C₄×D₄×C₆₇	—	2	8	no	—
114	C₄×D₄×C₆₇	—	2	8	no	—
115	C₄×D₄×C₆₇	—	2	4	no	—
116	C₄×D₄×C₆₇	—	2	4	no	—
117	C₄×D₄×C₆₇	—	2	4	no	—
118	#117×C₆₇	—	2	4	no	—
119	#117×C₆₇	—	2	8	no	—
120	#117×C₆₇	—	2	8	no	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	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	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₇	—	2	8	no	—
149	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
150	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	4	yes	—
161	#95×C₆₇	C₂³	1	4	yes	—
162	#95×C₆₇	C₂³	1	2	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	#95×C₆₇	C₂³	1	2	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	#95×C₆₇	C₂³	1	4	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
174	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
175	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
176	#41×C₆₇	—	2	32	no	—
177	C₂×Q₈×C₆₇	—	2	2	no	—
178	C₂×Q₈×C₆₇	—	2	2	no	—
179	C₂×Q₈×C₆₇	—	2	4	no	—
180	C₂×Q₈×C₆₇	—	4	2	no	—
181	C₂×D₄×C₆₇	—	2	4	no	—
182	C₂×D₄×C₆₇	—	2	4	no	—
183	C₂×D₄×C₆₇	—	2	4	no	—
184	C₂×D₄×C₆₇	—	2	4	no	—
185	C₂×D₄×C₆₇	—	2	8	no	—
186	C₂×D₄×C₆₇	—	2	8	no	—
187	C₂×D₄×C₆₇	—	2	2	no	—
188	C₂×D₄×C₆₇	—	2	2	no	—
189	C₂×D₄×C₆₇	—	4	2	no	—
190	C₂×D₄×C₆₇	—	4	4	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	#41	1	8	yes	—
193	C₂²×C₄×C₆₇	—	2	4	no	—
194	C₂²×C₄×C₆₇	—	2	4	no	—
195	C₂²×C₄×C₆₇	—	2	4	no	—
196	C₂²×C₄×C₆₇	—	2	4	no	—
197	C₂²×C₄×C₆₇	—	2	8	no	—
198	C₂²×C₄×C₆₇	—	2	4	no	—
199	C₂²×C₄×C₆₇	—	2	4	no	—
200	C₂²×C₄×C₆₇	—	2	4	no	—
201	C₂²×C₄×C₆₇	—	4	2	no	—
202	C₂²×C₄×C₆₇	—	4	2	no	—
203	C₂²×C₄×C₆₇	—	4	2	no	—
204	C₂²×C₄×C₆₇	—	4	4	no	—
205	C₂²×C₄×C₆₇	—	4	4	no	—
206	C₂²×C₄×C₆₇	—	4	2	no	—
207	C₂²×C₄×C₆₇	—	4	4	no	—
208	C₂²×C₄×C₆₇	—	4	4	no	—
209	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₄⋊C₄×C₆₇	—	2	4	no	—
227	C₄⋊C₄×C₆₇	—	2	4	no	—
228	C₄⋊C₄×C₆₇	—	2	2	no	—
229	C₄⋊C₄×C₆₇	—	2	2	no	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₄⋊C₄×C₆₇	—	2	2	no	—
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	2	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	8	no	—
237	C₄⋊C₄×C₆₇	—	4	4	no	—
238	C₄⋊C₄×C₆₇	—	4	4	no	—
239	C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	2	8	no	—
242	C₂²⋊C₄×C₆₇	—	2	4	no	—
243	C₂²⋊C₄×C₆₇	—	2	4	no	—
244	C₂²⋊C₄×C₆₇	—	2	4	no	—
245	C₂²⋊C₄×C₆₇	—	2	4	no	—
246	C₂²⋊C₄×C₆₇	—	2	4	no	—
247	C₂²⋊C₄×C₆₇	—	2	4	no	—
248	C₂²⋊C₄×C₆₇	—	2	8	no	—
249	C₂²⋊C₄×C₆₇	—	4	4	no	—
250	C₂²⋊C₄×C₆₇	—	4	4	no	—
251	C₂²⋊C₄×C₆₇	—	4	4	no	—
252	C₂²⋊C₄×C₆₇	—	4	4	no	—
253	C₄²×C₆₇	—	2	4	no	—
254	C₄²×C₆₇	—	2	4	no	—
255	C₄²×C₆₇	—	2	4	no	—
256	C₄²×C₆₇	—	2	4	no	—
257	C₄²×C₆₇	C₂×D₄	1	4	yes	—
258	C₄²×C₆₇	C₂×D₄	1	4	yes	—
259	C₄²×C₆₇	C₂×D₄	1	4	yes	—
260	C₄²×C₆₇	C₂×D₄	1	4	yes	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	2	no	—
263	C₂³×C₆₇	—	2	2	no	—
264	C₂³×C₆₇	—	2	2	no	—
265	C₂³×C₆₇	—	2	4	no	—
266	C₂³×C₆₇	—	2	4	no	—
267	C₂³×C₆₇	—	2	2	no	—
268	C₂³×C₆₇	—	2	4	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	4	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
273	C₂³×C₆₇	C₂×#41	1	4	yes	—
274	C₂³×C₆₇	C₂×#41	1	4	yes	—
275	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
276	Q₈×C₆₇	—	2	8	no	—
277	Q₈×C₆₇	—	4	4	no	—
278	D₄×C₆₇	—	2	8	no	—
279	D₄×C₆₇	—	2	16	no	—
280	D₄×C₆₇	—	4	4	no	—
281	D₄×C₆₇	—	4	8	no	—
282	D₄×C₆₇	—	8	8	no	—
283	C₂×C₄×C₆₇	—	2	16	no	—
284	C₂×C₄×C₆₇	—	2	8	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	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	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	4	no	—
299	C₂×C₄×C₆₇	—	2	4	no	—
300	C₂×C₄×C₆₇	—	2	4	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	4	no	—
303	C₂×C₄×C₆₇	—	2	4	no	—
304	C₂×C₄×C₆₇	—	2	4	no	—
305	C₂×C₄×C₆₇	—	2	4	no	—
306	C₂×C₄×C₆₇	—	2	4	no	—
307	C₂×C₄×C₆₇	—	2	4	no	—
308	C₂×C₄×C₆₇	—	2	4	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	4	4	no	—
311	C₂×C₄×C₆₇	—	4	4	no	—
312	C₂×C₄×C₆₇	—	4	8	no	—
313	C₂×C₄×C₆₇	—	4	8	no	—
314	C₂×C₄×C₆₇	—	4	8	no	—
315	C₂×C₄×C₆₇	—	8	8	no	—
316	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	2	2	no	—
325	C₂²×C₆₇	—	2	8	no	—
326	C₂²×C₆₇	—	2	4	no	—
327	C₂²×C₆₇	—	2	8	no	—
328	C₂²×C₆₇	—	4	2	no	—
329	C₂²×C₆₇	—	4	2	no	—
330	C₂²×C₆₇	—	4	4	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	4	no	—
335	C₂²×C₆₇	—	4	4	no	—
336	C₂²×C₆₇	#525	1	4	yes	—
337	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
338	C₂²×C₆₇	C₂²×#41	1	2	yes	—
339	C₂²×C₆₇	#585	1	2	yes	—
340	C₂²×C₆₇	#585	1	2	yes	—
341	C₄×C₆₇	—	2	2	no	—
342	C₄×C₆₇	—	2	2	no	—
343	C₄×C₆₇	—	2	4	no	—
344	C₄×C₆₇	—	2	2	no	—
345	C₄×C₆₇	—	2	2	no	—
346	C₄×C₆₇	—	2	2	no	—
347	C₄×C₆₇	—	2	2	no	—
348	C₄×C₆₇	—	4	2	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	—	4	2	no	—
351	C₄×C₆₇	—	4	2	no	—
352	C₄×C₆₇	—	4	2	no	—
353	C₄×C₆₇	—	4	4	no	—
354	C₄×C₆₇	—	4	4	no	—
355	#35144	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
356	C₂×C₆₇	—	2	4	no	—
357	C₂×C₆₇	—	4	4	no	—
358	C₂×C₆₇	—	8	2	no	—
359	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
360	C₂×C₆₇	#3449	1	1	yes	characteristic
361	C₂×C₆₇	#3449	1	1	yes	characteristic
362	C₂×C₆₇	#3521	1	4	yes	—
363	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
364	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
365	#2852	C₂×C₆₇	1	4	yes	complemented
366	#2634	C₂×C₆₇	1	1	yes	characteristic, complemented
367	#2633	C₂×C₆₇	1	1	yes	characteristic, complemented
368	#2632	C₂×C₆₇	1	1	yes	characteristic, complemented
369	#2631	C₂×C₆₇	1	1	yes	characteristic, complemented
370	#2599	C₂×C₆₇	1	2	yes	complemented
371	#2599	C₂×C₆₇	1	2	yes	complemented
372	#2598	C₂×C₆₇	1	2	yes	complemented
373	#2598	C₂×C₆₇	1	2	yes	complemented
374	#2564	C₂×C₆₇	1	2	yes	complemented
375	#2543	C₂×C₆₇	1	2	yes	complemented
376	#2498	C₂×C₆₇	1	2	yes	complemented
377	#2430	C₂×C₆₇	1	2	yes	complemented
378	#2325	C₂×C₆₇	1	4	yes	complemented
379	C₂×#383	C₂×C₆₇	1	1	yes	characteristic, complemented
380	C₆₇	#35144	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
382	#529	—	2	8	no	—
383	C₂×#126	C₂²×C₆₇	1	2	yes	—
384	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
385	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
386	C₂×#123	C₂²×C₆₇	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×#121	C₂²×C₆₇	1	4	yes	—
389	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
390	C₄×#41	—	2	8	no	—
391	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
393	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×#117	C₂²×C₆₇	1	2	yes	—
401	C₂×#117	C₂²×C₆₇	1	2	yes	—
402	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
403	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
404	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
405	#400	C₂²×C₆₇	1	2	yes	—
406	#400	C₂²×C₆₇	1	2	yes	—
407	#399	C₂²×C₆₇	1	2	yes	—
408	#399	C₂²×C₆₇	1	2	yes	—
409	#398	C₂²×C₆₇	1	2	yes	—
410	#398	C₂²×C₆₇	1	2	yes	—
411	#397	C₂²×C₆₇	1	2	yes	—
412	#397	C₂²×C₆₇	1	2	yes	—
413	#395	C₂²×C₆₇	1	2	yes	—
414	#395	C₂²×C₆₇	1	2	yes	—
415	#394	C₂²×C₆₇	1	2	yes	—
416	#394	C₂²×C₆₇	1	2	yes	—
417	#393	C₂²×C₆₇	1	2	yes	—
418	#393	C₂²×C₆₇	1	2	yes	—
419	#392	C₂²×C₆₇	1	2	yes	—
420	#392	C₂²×C₆₇	1	2	yes	—
421	#388	C₂²×C₆₇	1	4	yes	—
422	#388	C₂²×C₆₇	1	4	yes	—
423	#388	C₂²×C₆₇	1	4	yes	—
424	#388	C₂²×C₆₇	1	4	yes	—
425	#387	C₂²×C₆₇	1	4	yes	—
426	#387	C₂²×C₆₇	1	4	yes	—
427	#387	C₂²×C₆₇	1	4	yes	—
428	#387	C₂²×C₆₇	1	4	yes	—
429	#386	C₂²×C₆₇	1	4	yes	—
430	#386	C₂²×C₆₇	1	4	yes	—
431	#386	C₂²×C₆₇	1	4	yes	—
432	#386	C₂²×C₆₇	1	4	yes	—
433	#386	C₂²×C₆₇	1	4	yes	—
434	#386	C₂²×C₆₇	1	4	yes	—
435	#385	C₂²×C₆₇	1	4	yes	—
436	#385	C₂²×C₆₇	1	4	yes	—
437	#385	C₂²×C₆₇	1	4	yes	—
438	#385	C₂²×C₆₇	1	4	yes	—
439	#383	C₂²×C₆₇	1	2	yes	—
440	#383	C₂²×C₆₇	1	2	yes	—
441	#383	C₂²×C₆₇	1	2	yes	—
442	#383	C₂²×C₆₇	1	1	yes	characteristic
443	#383	C₂²×C₆₇	1	1	yes	characteristic
444	#380	C₂²×C₆₇	1	4	yes	—
445	C₂×#95	C₂²×C₆₇	1	2	yes	—
446	C₂×#95	C₂²×C₆₇	1	2	yes	—
447	C₂×#95	C₂²×C₆₇	1	2	yes	—
448	C₂×#41	—	2	8	no	—
449	C₂×#41	—	2	4	no	—
450	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
451	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
453	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
454	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
455	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
457	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
458	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
460	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
461	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
462	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
463	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
465	#126	—	2	8	no	—
466	#125	—	2	4	no	—
467	#124	—	2	4	no	—
468	#123	—	2	8	no	—
469	C₂²⋊Q₈	—	2	4	no	—
470	#121	—	2	16	no	—
471	#121	—	2	4	no	—
472	C₄×Q₈	—	2	4	no	—
473	C₄×Q₈	—	2	4	no	—
474	C₄×Q₈	—	2	4	no	—
475	C₄×D₄	—	2	8	no	—
476	C₄×D₄	—	2	8	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	—	2	4	no	—
481	#117	—	2	4	no	—
482	#117	—	2	8	no	—
483	#117	—	2	8	no	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	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×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
511	C₂×C₄²	—	2	8	no	—
512	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
513	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
521	#95	C₂³×C₆₇	1	2	yes	—
522	#95	C₂³×C₆₇	1	4	yes	—
523	#95	C₂³×C₆₇	1	4	yes	—
524	#95	C₂³×C₆₇	1	4	yes	—
525	#95	C₂³×C₆₇	1	2	yes	—
526	#95	C₂³×C₆₇	1	2	yes	—
527	#95	C₂³×C₆₇	1	2	yes	—
528	#95	C₂³×C₆₇	1	2	yes	—
529	#95	C₂³×C₆₇	1	2	yes	—
530	#95	C₂³×C₆₇	1	4	yes	—
531	#95	C₂³×C₆₇	1	4	yes	—
532	#95	C₂³×C₆₇	1	4	yes	—
533	#95	C₂³×C₆₇	1	4	yes	—
534	#95	C₂³×C₆₇	1	4	yes	—
535	#95	C₂³×C₆₇	1	4	yes	—
536	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
537	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
538	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
539	#41	—	2	32	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	4	2	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	#41×C₆₇	1	8	yes	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	8	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	4	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
573	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
574	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₄⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	4	no	—
619	C₄²	—	2	4	no	—
620	C₄²	C₂×D₄×C₆₇	1	4	yes	—
621	C₄²	C₂×D₄×C₆₇	1	4	yes	—
622	C₄²	C₂×D₄×C₆₇	1	4	yes	—
623	C₄²	C₂×D₄×C₆₇	1	4	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	4	no	—
634	C₂³	—	2	2	no	—
635	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
636	C₂³	C₂×#41×C₆₇	1	4	yes	—
637	C₂³	C₂×#41×C₆₇	1	4	yes	—
638	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
639	Q₈	—	2	8	no	—
640	Q₈	—	4	4	no	—
641	D₄	—	2	8	no	—
642	D₄	—	2	16	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	8	8	no	—
646	C₂×C₄	—	2	16	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	8	8	no	—
679	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
685	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
686	C₂²	—	2	8	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	8	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	#525×C₆₇	1	4	yes	—
700	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
701	C₂²	C₂²×#41×C₆₇	1	2	yes	—
702	C₂²	#585×C₆₇	1	2	yes	—
703	C₂²	#585×C₆₇	1	2	yes	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	4	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₂	—	2	4	no	—
719	C₂	—	4	4	no	—
720	C₂	—	8	2	no	—
721	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
722	C₂	C₆₇×#3449	1	1	yes	characteristic
723	C₂	C₆₇×#3449	1	1	yes	characteristic
724	C₂	C₆₇×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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×#529×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#2852	C₂	semidirect
4. C₆₇×#2634	C₂	semidirect
5. C₆₇×#2633	C₂	semidirect
6. C₆₇×#2632	C₂	semidirect
7. C₆₇×#2631	C₂	semidirect
8. C₆₇×#2599	C₂	semidirect
9. C₆₇×#2599	C₂	semidirect
10. C₆₇×#2598	C₂	semidirect
11. C₆₇×#2598	C₂	semidirect
12. C₆₇×#2564	C₂	semidirect
13. C₆₇×#2543	C₂	semidirect
14. C₆₇×#2498	C₂	semidirect
15. C₆₇×#2430	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₂×#383×C₆₇	C₂	semidirect
149. C₂×C₄²×C₆₇	D₄	semidirect
355. #35144	C₆₇	direct (N × H)
363. C₂×#529	C₂×C₆₇	semidirect
364. C₂×C₄×#41	C₂×C₆₇	semidirect
365. #2852	C₂×C₆₇	semidirect
366. #2634	C₂×C₆₇	semidirect
367. #2633	C₂×C₆₇	semidirect
368. #2632	C₂×C₆₇	semidirect
369. #2631	C₂×C₆₇	semidirect
370. #2599	C₂×C₆₇	semidirect
371. #2599	C₂×C₆₇	semidirect
372. #2598	C₂×C₆₇	semidirect
373. #2598	C₂×C₆₇	semidirect
374. #2564	C₂×C₆₇	semidirect
375. #2543	C₂×C₆₇	semidirect
376. #2498	C₂×C₆₇	semidirect
377. #2430	C₂×C₆₇	semidirect
378. #2325	C₂×C₆₇	semidirect
379. C₂×#383	C₂×C₆₇	semidirect
380. C₆₇	#35144	direct (N × H)
512. C₂×C₄²	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2852	2
C₆₇×#2634	2
C₆₇×#2633	2
C₆₇×#2632	2
C₆₇×#2631	2
C₆₇×#2599	2
C₆₇×#2598	2
C₆₇×#2564	2
C₆₇×#2543	2
C₆₇×#2498	2
C₆₇×#2430	2
C₆₇×#2325	2
C₂×#383×C₆₇	2
#35144	67

Subgroups — C67×#35144 #30714395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35144 #30714395