Subgroups — C₆₇×#35050 #30714301

Order 17152.

4146 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2846	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2626	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2617	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2561	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2539	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2534	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2482	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2411	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2404	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2321	C₂	1	4	yes	maximal, complemented
14	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
19	#525×C₆₇	—	2	8	no	—
20	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
21	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#120×C₆₇	C₂²	1	4	yes	—
27	C₂×#120×C₆₇	C₂²	1	2	yes	—
28	C₂×#120×C₆₇	C₂²	1	4	yes	—
29	C₂×#120×C₆₇	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊C₄×C₆₇	—	2	8	no	—
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
41	#399×C₆₇	C₂²	1	4	yes	complemented
42	#397×C₆₇	C₂²	1	4	yes	complemented
43	#396×C₆₇	C₂²	1	8	yes	complemented
44	#394×C₆₇	C₂²	1	8	yes	complemented
45	#393×C₆₇	C₂²	1	4	yes	complemented
46	#392×C₆₇	C₂²	1	4	yes	complemented
47	#390×C₆₇	C₂²	1	8	yes	complemented
48	#388×C₆₇	C₂²	1	8	yes	complemented
49	#388×C₆₇	C₂²	1	8	yes	complemented
50	#386×C₆₇	C₂²	1	8	yes	complemented
51	#386×C₆₇	C₂²	1	4	yes	complemented
52	#386×C₆₇	C₂²	1	4	yes	complemented
53	#385×C₆₇	C₂²	1	4	yes	complemented
54	#385×C₆₇	C₂²	1	4	yes	complemented
55	#381×C₆₇	C₂²	1	4	yes	complemented
56	#381×C₆₇	C₂²	1	2	yes	complemented
57	#380×C₆₇	C₂²	1	2	yes	complemented
58	#380×C₆₇	C₂²	1	2	yes	complemented
59	#379×C₆₇	C₂²	1	4	yes	—
60	#379×C₆₇	C₂²	1	2	yes	—
61	#379×C₆₇	C₂²	1	4	yes	—
62	#379×C₆₇	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
65	C₂⁵×C₆₇	—	2	4	no	—
66	C₂⁵×C₆₇	—	2	8	no	—
67	C₂⁵×C₆₇	—	4	4	no	—
68	C₂⁵×C₆₇	—	4	4	no	—
69	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
70	C₂⁵×C₆₇	C₂³	1	2	yes	—
71	C₂⁵×C₆₇	C₂³	1	2	yes	—
72	C₂⁵×C₆₇	C₂³	1	2	yes	—
73	C₂×#41×C₆₇	—	2	4	no	—
74	C₂×#41×C₆₇	—	4	4	no	—
75	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
76	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
78	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
79	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
81	C₂³×C₄×C₆₇	—	2	4	no	—
82	C₂³×C₄×C₆₇	—	4	4	no	—
83	C₂³×C₄×C₆₇	—	4	4	no	—
84	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
85	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	complemented
95	#123×C₆₇	—	2	8	no	—
96	#123×C₆₇	—	4	8	no	—
97	C₂²⋊Q₈×C₆₇	—	2	4	no	—
98	C₂²⋊Q₈×C₆₇	—	2	4	no	—
99	#121×C₆₇	—	2	4	no	—
100	#121×C₆₇	—	2	4	no	—
101	#120×C₆₇	—	2	8	no	—
102	#120×C₆₇	—	2	16	no	—
103	#120×C₆₇	—	4	8	no	—
104	#120×C₆₇	—	4	8	no	—
105	C₄×D₄×C₆₇	—	2	8	no	—
106	C₄×D₄×C₆₇	—	2	8	no	—
107	#117×C₆₇	—	2	4	no	—
108	#117×C₆₇	—	4	4	no	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
115	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
116	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
117	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	complemented
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	complemented
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
137	C₂×C₄²×C₆₇	C₂³	1	2	yes	complemented
138	C₂×C₄²×C₆₇	C₂³	1	4	yes	complemented
139	#95×C₆₇	C₂³	1	4	yes	complemented
140	#95×C₆₇	C₂³	1	4	yes	complemented
141	#95×C₆₇	C₂³	1	8	yes	complemented
142	#95×C₆₇	C₂³	1	8	yes	complemented
143	C₂⁴×C₆₇	—	2	4	no	—
144	C₂⁴×C₆₇	—	2	4	no	—
145	C₂⁴×C₆₇	—	2	4	no	—
146	C₂⁴×C₆₇	—	2	32	no	—
147	C₂⁴×C₆₇	—	2	4	no	—
148	C₂⁴×C₆₇	—	2	4	no	—
149	C₂⁴×C₆₇	—	2	4	no	—
150	C₂⁴×C₆₇	—	2	8	no	—
151	C₂⁴×C₆₇	—	2	8	no	—
152	C₂⁴×C₆₇	—	2	4	no	—
153	C₂⁴×C₆₇	—	2	8	no	—
154	C₂⁴×C₆₇	—	2	8	no	—
155	C₂⁴×C₆₇	—	4	4	no	—
156	C₂⁴×C₆₇	—	4	4	no	—
157	C₂⁴×C₆₇	—	4	4	no	—
158	C₂⁴×C₆₇	—	4	4	no	—
159	C₂⁴×C₆₇	—	4	64	no	—
160	C₂⁴×C₆₇	—	4	16	no	—
161	C₂⁴×C₆₇	—	4	16	no	—
162	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
163	C₂⁴×C₆₇	#41	1	8	yes	complemented
164	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
165	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
166	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
169	#41×C₆₇	—	4	16	no	—
170	C₂×Q₈×C₆₇	—	2	2	no	—
171	C₂×Q₈×C₆₇	—	4	2	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	2	8	no	—
176	C₂×D₄×C₆₇	—	2	8	no	—
177	C₂×D₄×C₆₇	—	2	8	no	—
178	C₂×D₄×C₆₇	—	2	16	no	—
179	C₂×D₄×C₆₇	—	2	2	no	—
180	C₂×D₄×C₆₇	—	4	2	no	—
181	C₂×D₄×C₆₇	—	4	8	no	—
182	C₂×D₄×C₆₇	—	4	8	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	2	4	no	—
186	C₂²×C₄×C₆₇	—	2	4	no	—
187	C₂²×C₄×C₆₇	—	2	4	no	—
188	C₂²×C₄×C₆₇	—	2	8	no	—
189	C₂²×C₄×C₆₇	—	2	4	no	—
190	C₂²×C₄×C₆₇	—	4	16	no	—
191	C₂²×C₄×C₆₇	—	4	2	no	—
192	C₂²×C₄×C₆₇	—	4	2	no	—
193	C₂²×C₄×C₆₇	—	4	2	no	—
194	C₂²×C₄×C₆₇	—	4	2	no	—
195	C₂²×C₄×C₆₇	—	4	4	no	—
196	C₂²×C₄×C₆₇	—	4	4	no	—
197	C₂²×C₄×C₆₇	—	4	4	no	—
198	C₂²×C₄×C₆₇	—	4	16	no	—
199	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	—	2	2	no	—
215	C₄⋊C₄×C₆₇	—	2	2	no	—
216	C₄⋊C₄×C₆₇	—	2	4	no	—
217	C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₄⋊C₄×C₆₇	—	4	4	no	—
219	C₄⋊C₄×C₆₇	—	4	8	no	—
220	C₂²⋊C₄×C₆₇	—	2	4	no	—
221	C₂²⋊C₄×C₆₇	—	2	4	no	—
222	C₂²⋊C₄×C₆₇	—	2	4	no	—
223	C₂²⋊C₄×C₆₇	—	2	16	no	—
224	C₂²⋊C₄×C₆₇	—	2	8	no	—
225	C₂²⋊C₄×C₆₇	—	2	8	no	—
226	C₂²⋊C₄×C₆₇	—	2	8	no	—
227	C₂²⋊C₄×C₆₇	—	2	8	no	—
228	C₂²⋊C₄×C₆₇	—	2	8	no	—
229	C₂²⋊C₄×C₆₇	—	2	8	no	—
230	C₂²⋊C₄×C₆₇	—	2	8	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	2	4	no	—
233	C₂²⋊C₄×C₆₇	—	4	8	no	—
234	C₂²⋊C₄×C₆₇	—	4	8	no	—
235	C₂²⋊C₄×C₆₇	—	4	8	no	—
236	C₄²×C₆₇	—	2	4	no	—
237	C₄²×C₆₇	—	4	4	no	—
238	C₂³×C₆₇	—	2	32	no	—
239	C₂³×C₆₇	—	2	8	no	—
240	C₂³×C₆₇	—	2	8	no	—
241	C₂³×C₆₇	—	2	8	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	2	no	—
244	C₂³×C₆₇	—	2	2	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	16	no	—
249	C₂³×C₆₇	—	2	16	no	—
250	C₂³×C₆₇	—	2	16	no	—
251	C₂³×C₆₇	—	2	4	no	—
252	C₂³×C₆₇	—	2	4	no	—
253	C₂³×C₆₇	—	2	8	no	—
254	C₂³×C₆₇	—	2	8	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	4	no	—
257	C₂³×C₆₇	—	2	4	no	—
258	C₂³×C₆₇	—	2	4	no	—
259	C₂³×C₆₇	—	4	16	no	—
260	C₂³×C₆₇	—	4	32	no	—
261	C₂³×C₆₇	—	4	32	no	—
262	C₂³×C₆₇	—	4	128	no	—
263	C₂³×C₆₇	—	4	8	no	—
264	C₂³×C₆₇	—	4	8	no	—
265	C₂³×C₆₇	—	4	8	no	—
266	C₂³×C₆₇	—	4	8	no	—
267	C₂³×C₆₇	—	4	16	no	—
268	C₂³×C₆₇	—	4	8	no	—
269	C₂³×C₆₇	—	4	8	no	—
270	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
271	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
272	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
273	C₂³×C₆₇	C₂×#41	1	8	yes	—
274	C₂³×C₆₇	C₂×#41	1	4	yes	—
275	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
276	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
277	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
278	Q₈×C₆₇	—	4	4	no	—
279	D₄×C₆₇	—	4	4	no	—
280	D₄×C₆₇	—	4	8	no	—
281	D₄×C₆₇	—	4	8	no	—
282	D₄×C₆₇	—	4	8	no	—
283	D₄×C₆₇	—	8	16	no	—
284	C₂×C₄×C₆₇	—	2	8	no	—
285	C₂×C₄×C₆₇	—	2	8	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	4	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	4	no	—
295	C₂×C₄×C₆₇	—	2	8	no	—
296	C₂×C₄×C₆₇	—	2	8	no	—
297	C₂×C₄×C₆₇	—	2	8	no	—
298	C₂×C₄×C₆₇	—	2	4	no	—
299	C₂×C₄×C₆₇	—	2	4	no	—
300	C₂×C₄×C₆₇	—	2	8	no	—
301	C₂×C₄×C₆₇	—	4	4	no	—
302	C₂×C₄×C₆₇	—	4	4	no	—
303	C₂×C₄×C₆₇	—	4	4	no	—
304	C₂×C₄×C₆₇	—	4	4	no	—
305	C₂×C₄×C₆₇	—	4	8	no	—
306	C₂×C₄×C₆₇	—	4	8	no	—
307	C₂×C₄×C₆₇	—	4	8	no	—
308	C₂×C₄×C₆₇	—	4	8	no	—
309	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
313	C₂²×C₆₇	—	2	32	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	2	no	—
317	C₂²×C₆₇	—	2	2	no	—
318	C₂²×C₆₇	—	2	2	no	—
319	C₂²×C₆₇	—	2	2	no	—
320	C₂²×C₆₇	—	2	8	no	—
321	C₂²×C₆₇	—	2	8	no	—
322	C₂²×C₆₇	—	2	8	no	—
323	C₂²×C₆₇	—	2	8	no	—
324	C₂²×C₆₇	—	2	16	no	—
325	C₂²×C₆₇	—	4	32	no	—
326	C₂²×C₆₇	—	4	32	no	—
327	C₂²×C₆₇	—	4	32	no	—
328	C₂²×C₆₇	—	4	4	no	—
329	C₂²×C₆₇	—	4	4	no	—
330	C₂²×C₆₇	—	4	8	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	8	no	—
335	C₂²×C₆₇	#525	1	4	yes	—
336	C₂²×C₆₇	#534	1	4	yes	—
337	C₂²×C₆₇	#535	1	4	yes	—
338	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
339	C₂²×C₆₇	C₂²×#41	1	2	yes	—
340	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
342	C₄×C₆₇	—	2	2	no	—
343	C₄×C₆₇	—	2	2	no	—
344	C₄×C₆₇	—	2	2	no	—
345	C₄×C₆₇	—	2	2	no	—
346	C₄×C₆₇	—	4	2	no	—
347	C₄×C₆₇	—	4	2	no	—
348	C₄×C₆₇	—	4	4	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	—	4	8	no	—
351	#35050	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂×C₆₇	—	2	4	no	—
353	C₂×C₆₇	—	2	4	no	—
354	C₂×C₆₇	—	2	4	no	—
355	C₂×C₆₇	—	4	8	no	—
356	C₂×C₆₇	—	8	2	no	—
357	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
358	C₂×C₆₇	C₂×#534	1	1	yes	characteristic
359	C₂×C₆₇	C₂×#535	1	1	yes	characteristic
360	C₂×C₆₇	#3490	1	4	yes	—
361	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
362	C₂³×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
363	#2849	C₂×C₆₇	1	2	yes	complemented
364	#2846	C₂×C₆₇	1	2	yes	complemented
365	#2626	C₂×C₆₇	1	2	yes	complemented
366	#2617	C₂×C₆₇	1	2	yes	complemented
367	#2561	C₂×C₆₇	1	2	yes	complemented
368	#2539	C₂×C₆₇	1	2	yes	complemented
369	#2534	C₂×C₆₇	1	4	yes	complemented
370	#2482	C₂×C₆₇	1	2	yes	complemented
371	#2411	C₂×C₆₇	1	4	yes	complemented
372	#2404	C₂×C₆₇	1	2	yes	complemented
373	#2321	C₂×C₆₇	1	4	yes	complemented
374	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
375	C₆₇	#35050	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁶	C₂²×C₆₇	1	1	yes	characteristic
377	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
378	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
380	#525	—	2	8	no	—
381	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
382	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
383	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
384	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
385	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
386	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
387	C₂×#120	C₂²×C₆₇	1	4	yes	—
388	C₂×#120	C₂²×C₆₇	1	2	yes	—
389	C₂×#120	C₂²×C₆₇	1	4	yes	—
390	C₂×#120	C₂²×C₆₇	1	4	yes	—
391	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
392	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
393	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
394	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
395	C₂²×C₂²⋊C₄	—	2	8	no	—
396	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
397	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
398	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
399	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
400	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
401	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
402	#399	C₂²×C₆₇	1	4	yes	complemented
403	#397	C₂²×C₆₇	1	4	yes	complemented
404	#396	C₂²×C₆₇	1	8	yes	complemented
405	#394	C₂²×C₆₇	1	8	yes	complemented
406	#393	C₂²×C₆₇	1	4	yes	complemented
407	#392	C₂²×C₆₇	1	4	yes	complemented
408	#390	C₂²×C₆₇	1	8	yes	complemented
409	#388	C₂²×C₆₇	1	8	yes	complemented
410	#388	C₂²×C₆₇	1	8	yes	complemented
411	#386	C₂²×C₆₇	1	8	yes	complemented
412	#386	C₂²×C₆₇	1	4	yes	complemented
413	#386	C₂²×C₆₇	1	4	yes	complemented
414	#385	C₂²×C₆₇	1	4	yes	complemented
415	#385	C₂²×C₆₇	1	4	yes	complemented
416	#381	C₂²×C₆₇	1	4	yes	complemented
417	#381	C₂²×C₆₇	1	2	yes	complemented
418	#380	C₂²×C₆₇	1	2	yes	complemented
419	#380	C₂²×C₆₇	1	2	yes	complemented
420	#379	C₂²×C₆₇	1	4	yes	—
421	#379	C₂²×C₆₇	1	4	yes	—
422	#379	C₂²×C₆₇	1	2	yes	—
423	#379	C₂²×C₆₇	1	4	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
425	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
426	C₂⁵	—	2	4	no	—
427	C₂⁵	—	2	8	no	—
428	C₂⁵	—	4	4	no	—
429	C₂⁵	—	4	4	no	—
430	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
431	C₂⁵	C₂³×C₆₇	1	2	yes	—
432	C₂⁵	C₂³×C₆₇	1	2	yes	—
433	C₂⁵	C₂³×C₆₇	1	2	yes	—
434	C₂×#41	—	2	4	no	—
435	C₂×#41	—	4	4	no	—
436	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
437	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
438	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
439	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
440	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
441	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
442	C₂³×C₄	—	2	4	no	—
443	C₂³×C₄	—	4	4	no	—
444	C₂³×C₄	—	4	4	no	—
445	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
446	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
447	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
450	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
451	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₆₇	1	2	yes	complemented
456	#123	—	2	8	no	—
457	#123	—	4	8	no	—
458	C₂²⋊Q₈	—	2	4	no	—
459	C₂²⋊Q₈	—	2	4	no	—
460	#121	—	2	4	no	—
461	#121	—	2	4	no	—
462	#120	—	2	8	no	—
463	#120	—	2	16	no	—
464	#120	—	4	8	no	—
465	#120	—	4	8	no	—
466	C₄×D₄	—	2	8	no	—
467	C₄×D₄	—	2	8	no	—
468	#117	—	2	4	no	—
469	#117	—	4	4	no	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
476	C₂×C₂²⋊C₄	—	2	8	no	—
477	C₂×C₂²⋊C₄	—	2	8	no	—
478	C₂×C₂²⋊C₄	—	2	8	no	—
479	C₂×C₂²⋊C₄	—	2	8	no	—
480	C₂×C₂²⋊C₄	—	2	8	no	—
481	C₂×C₂²⋊C₄	—	2	8	no	—
482	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	complemented
496	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	complemented
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
498	C₂×C₄²	C₂³×C₆₇	1	2	yes	complemented
499	C₂×C₄²	C₂³×C₆₇	1	4	yes	complemented
500	#95	C₂³×C₆₇	1	4	yes	complemented
501	#95	C₂³×C₆₇	1	4	yes	complemented
502	#95	C₂³×C₆₇	1	8	yes	complemented
503	#95	C₂³×C₆₇	1	8	yes	complemented
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	—	2	4	no	—
507	C₂⁴	—	2	32	no	—
508	C₂⁴	—	2	4	no	—
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	2	8	no	—
512	C₂⁴	—	2	8	no	—
513	C₂⁴	—	2	4	no	—
514	C₂⁴	—	2	8	no	—
515	C₂⁴	—	2	8	no	—
516	C₂⁴	—	4	4	no	—
517	C₂⁴	—	4	4	no	—
518	C₂⁴	—	4	4	no	—
519	C₂⁴	—	4	4	no	—
520	C₂⁴	—	4	64	no	—
521	C₂⁴	—	4	16	no	—
522	C₂⁴	—	4	16	no	—
523	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
524	C₂⁴	#41×C₆₇	1	8	yes	complemented
525	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
526	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
527	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
528	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
529	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
530	#41	—	4	16	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	8	no	—
539	C₂×D₄	—	2	16	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	8	no	—
543	C₂×D₄	—	4	8	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
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	—	2	4	no	—
551	C₂²×C₄	—	4	16	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	16	no	—
560	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
561	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
562	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
563	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
564	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
565	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
568	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	—	4	8	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	16	no	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	4	8	no	—
595	C₂²⋊C₄	—	4	8	no	—
596	C₂²⋊C₄	—	4	8	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	4	4	no	—
599	C₂³	—	2	32	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	16	no	—
610	C₂³	—	2	16	no	—
611	C₂³	—	2	16	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	16	no	—
621	C₂³	—	4	32	no	—
622	C₂³	—	4	32	no	—
623	C₂³	—	4	128	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	4	8	no	—
627	C₂³	—	4	8	no	—
628	C₂³	—	4	16	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	8	no	—
631	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
632	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
633	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
634	C₂³	C₂×#41×C₆₇	1	8	yes	—
635	C₂³	C₂×#41×C₆₇	1	4	yes	—
636	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
637	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
638	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
639	Q₈	—	4	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	8	no	—
644	D₄	—	8	16	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	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	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
674	C₂²	—	2	32	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	2	8	no	—
683	C₂²	—	2	8	no	—
684	C₂²	—	2	8	no	—
685	C₂²	—	2	16	no	—
686	C₂²	—	4	32	no	—
687	C₂²	—	4	32	no	—
688	C₂²	—	4	32	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	8	no	—
696	C₂²	#525×C₆₇	1	4	yes	—
697	C₂²	#534×C₆₇	1	4	yes	—
698	C₂²	#535×C₆₇	1	4	yes	—
699	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
700	C₂²	C₂²×#41×C₆₇	1	2	yes	—
701	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
702	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	8	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	8	no	—
716	C₂	—	8	2	no	—
717	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
718	C₂	C₂×#534×C₆₇	1	1	yes	characteristic
719	C₂	C₂×#535×C₆₇	1	1	yes	characteristic
720	C₂	C₆₇×#3490	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×#525×C₆₇	C₂	semidirect
2. C₂³×C₂²⋊C₄×C₆₇	C₂	semidirect
3. C₆₇×#2849	C₂	semidirect
4. C₆₇×#2846	C₂	semidirect
5. C₆₇×#2626	C₂	semidirect
6. C₆₇×#2617	C₂	semidirect
7. C₆₇×#2561	C₂	semidirect
8. C₆₇×#2539	C₂	semidirect
9. C₆₇×#2534	C₂	semidirect
10. C₆₇×#2482	C₂	semidirect
11. C₆₇×#2411	C₂	semidirect
12. C₆₇×#2404	C₂	semidirect
13. C₆₇×#2321	C₂	semidirect
14. C₆₇×#2280	C₂	semidirect
16. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂×#123×C₆₇	C₂²	semidirect
21. C₂×#123×C₆₇	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
24. C₂×#121×C₆₇	C₂²	semidirect
25. C₂×#121×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
31. C₂×C₄×D₄×C₆₇	C₂²	semidirect
32. C₂×#117×C₆₇	C₂²	semidirect
33. C₂×#117×C₆₇	C₂²	semidirect
41. #399×C₆₇	C₂²	semidirect
42. #397×C₆₇	C₂²	semidirect
43. #396×C₆₇	C₂²	semidirect
44. #394×C₆₇	C₂²	semidirect
45. #393×C₆₇	C₂²	semidirect
46. #392×C₆₇	C₂²	semidirect
47. #390×C₆₇	C₂²	semidirect
48. #388×C₆₇	C₂²	semidirect
49. #388×C₆₇	C₂²	semidirect
50. #386×C₆₇	C₂²	semidirect
51. #386×C₆₇	C₂²	semidirect
52. #386×C₆₇	C₂²	semidirect
53. #385×C₆₇	C₂²	semidirect
54. #385×C₆₇	C₂²	semidirect
55. #381×C₆₇	C₂²	semidirect
56. #381×C₆₇	C₂²	semidirect
57. #380×C₆₇	C₂²	semidirect
58. #380×C₆₇	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
75. C₂²×Q₈×C₆₇	C₂³	semidirect
80. C₂²×D₄×C₆₇	C₂³	semidirect
84. C₂³×C₄×C₆₇	D₄	semidirect
94. C₂³×C₄×C₆₇	C₂³	semidirect
109. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
110. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
111. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
112. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
113. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
114. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
134. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
135. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
136. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
137. C₂×C₄²×C₆₇	C₂³	semidirect
138. C₂×C₄²×C₆₇	C₂³	semidirect
139. #95×C₆₇	C₂³	semidirect
140. #95×C₆₇	C₂³	semidirect
141. #95×C₆₇	C₂³	semidirect
142. #95×C₆₇	C₂³	semidirect
163. C₂⁴×C₆₇	#41	semidirect
351. #35050	C₆₇	direct (N × H)
361. C₂×#525	C₂×C₆₇	semidirect
362. C₂³×C₂²⋊C₄	C₂×C₆₇	semidirect
363. #2849	C₂×C₆₇	semidirect
364. #2846	C₂×C₆₇	semidirect
365. #2626	C₂×C₆₇	semidirect
366. #2617	C₂×C₆₇	semidirect
367. #2561	C₂×C₆₇	semidirect
368. #2539	C₂×C₆₇	semidirect
369. #2534	C₂×C₆₇	semidirect
370. #2482	C₂×C₆₇	semidirect
371. #2411	C₂×C₆₇	semidirect
372. #2404	C₂×C₆₇	semidirect
373. #2321	C₂×C₆₇	semidirect
374. #2280	C₂×C₆₇	semidirect
375. C₆₇	#35050	direct (N × H)
377. C₂²×#41	C₂²×C₆₇	semidirect
381. C₂×#123	C₂²×C₆₇	semidirect
382. C₂×#123	C₂²×C₆₇	semidirect
383. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
384. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
385. C₂×#121	C₂²×C₆₇	semidirect
386. C₂×#121	C₂²×C₆₇	semidirect
391. C₂×C₄×D₄	C₂²×C₆₇	semidirect
392. C₂×C₄×D₄	C₂²×C₆₇	semidirect
393. C₂×#117	C₂²×C₆₇	semidirect
394. C₂×#117	C₂²×C₆₇	semidirect
402. #399	C₂²×C₆₇	semidirect
403. #397	C₂²×C₆₇	semidirect
404. #396	C₂²×C₆₇	semidirect
405. #394	C₂²×C₆₇	semidirect
406. #393	C₂²×C₆₇	semidirect
407. #392	C₂²×C₆₇	semidirect
408. #390	C₂²×C₆₇	semidirect
409. #388	C₂²×C₆₇	semidirect
410. #388	C₂²×C₆₇	semidirect
411. #386	C₂²×C₆₇	semidirect
412. #386	C₂²×C₆₇	semidirect
413. #386	C₂²×C₆₇	semidirect
414. #385	C₂²×C₆₇	semidirect
415. #385	C₂²×C₆₇	semidirect
416. #381	C₂²×C₆₇	semidirect
417. #381	C₂²×C₆₇	semidirect
418. #380	C₂²×C₆₇	semidirect
419. #380	C₂²×C₆₇	semidirect
424. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
425. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
436. C₂²×Q₈	C₂³×C₆₇	semidirect
441. C₂²×D₄	C₂³×C₆₇	semidirect
445. C₂³×C₄	D₄×C₆₇	semidirect
455. C₂³×C₄	C₂³×C₆₇	semidirect
470. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
471. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
472. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
473. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
474. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
475. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
495. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
496. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
497. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
498. C₂×C₄²	C₂³×C₆₇	semidirect
499. C₂×C₄²	C₂³×C₆₇	semidirect
500. #95	C₂³×C₆₇	semidirect
501. #95	C₂³×C₆₇	semidirect
502. #95	C₂³×C₆₇	semidirect
503. #95	C₂³×C₆₇	semidirect
524. C₂⁴	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₆₇	2
C₂³×C₂²⋊C₄×C₆₇	2
C₆₇×#2849	2
C₆₇×#2846	2
C₆₇×#2626	2
C₆₇×#2617	2
C₆₇×#2561	2
C₆₇×#2539	2
C₆₇×#2534	2
C₆₇×#2482	2
C₆₇×#2411	2
C₆₇×#2404	2
C₆₇×#2321	2
C₆₇×#2280	2
#35050	67

Subgroups — C67×#35050 #30714301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35050 #30714301