Subgroups — C₆₇×#60315 #30739566

Order 17152.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3529	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2981	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2978	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2969	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2968	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2935	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2929	C₂	1	2	yes	maximal, complemented
20	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#131×C₆₇	C₂²	1	2	yes	—
22	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	#563×C₆₇	C₄	1	2	yes	—
26	#563×C₆₇	C₄	1	1	yes	characteristic
27	#562×C₆₇	C₄	1	2	yes	—
28	#562×C₆₇	C₄	1	2	yes	—
29	#562×C₆₇	C₄	1	2	yes	—
30	H(3,𝔽₄)×C₆₇	C₄	1	1	yes	characteristic
31	#560×C₆₇	C₄	1	2	yes	—
32	#560×C₆₇	C₄	1	1	yes	characteristic
33	#560×C₆₇	C₄	1	2	yes	—
34	#560×C₆₇	C₄	1	1	yes	characteristic
35	#532×C₆₇	C₂²	1	1	yes	characteristic
36	#532×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	—
38	#529×C₆₇	C₂²	1	2	yes	—
39	#529×C₆₇	C₂²	1	2	yes	—
40	#525×C₆₇	C₂²	1	1	yes	characteristic
41	#525×C₆₇	C₂²	1	2	yes	—
42	#525×C₆₇	C₂²	1	1	yes	characteristic
43	#525×C₆₇	C₂²	1	2	yes	—
44	#446×C₆₇	C₂²	1	2	yes	complemented
45	#446×C₆₇	C₂²	1	2	yes	complemented
46	#446×C₆₇	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
48	#436×C₆₇	C₂²	1	2	yes	—
49	#436×C₆₇	C₂²	1	2	yes	—
50	#436×C₆₇	C₂²	1	2	yes	—
51	#436×C₆₇	C₂²	1	2	yes	complemented
52	#436×C₆₇	C₂²	1	2	yes	complemented
53	#436×C₆₇	C₂²	1	2	yes	complemented
54	#436×C₆₇	C₂²	1	2	yes	complemented
55	#436×C₆₇	C₂²	1	2	yes	complemented
56	#436×C₆₇	C₂²	1	2	yes	complemented
57	#435×C₆₇	C₂²	1	2	yes	—
58	#435×C₆₇	C₂²	1	2	yes	—
59	#435×C₆₇	C₂²	1	2	yes	—
60	#435×C₆₇	C₂²	1	2	yes	—
61	#435×C₆₇	C₂²	1	2	yes	—
62	#435×C₆₇	C₂²	1	2	yes	—
63	#435×C₆₇	C₂²	1	2	yes	complemented
64	#435×C₆₇	C₂²	1	2	yes	complemented
65	#435×C₆₇	C₂²	1	2	yes	complemented
66	#435×C₆₇	C₂²	1	2	yes	complemented
67	#435×C₆₇	C₂²	1	2	yes	complemented
68	#435×C₆₇	C₂²	1	2	yes	complemented
69	#435×C₆₇	C₂²	1	2	yes	complemented
70	#435×C₆₇	C₂²	1	2	yes	complemented
71	#435×C₆₇	C₂²	1	2	yes	complemented
72	#435×C₆₇	C₂²	1	2	yes	complemented
73	#435×C₆₇	C₂²	1	2	yes	complemented
74	#435×C₆₇	C₂²	1	2	yes	complemented
75	C₈×D₄×C₆₇	C₂²	1	2	yes	—
76	C₈×D₄×C₆₇	C₂²	1	2	yes	—
77	C₈×D₄×C₆₇	C₂²	1	2	yes	—
78	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
80	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
81	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
84	#433×C₆₇	C₂²	1	2	yes	complemented
85	#433×C₆₇	C₂²	1	2	yes	complemented
86	#433×C₆₇	C₂²	1	2	yes	complemented
87	#433×C₆₇	C₂²	1	2	yes	complemented
88	#433×C₆₇	C₂²	1	2	yes	complemented
89	#433×C₆₇	C₂²	1	2	yes	complemented
90	#432×C₆₇	C₂²	1	2	yes	complemented
91	#431×C₆₇	C₂²	1	2	yes	complemented
92	#431×C₆₇	C₂²	1	2	yes	complemented
93	#424×C₆₇	C₂²	1	2	yes	complemented
94	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#424×C₆₇	C₂²	1	2	yes	complemented
97	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
99	#408×C₆₇	C₂²	1	2	yes	—
100	#408×C₆₇	C₂²	1	1	yes	characteristic
101	#408×C₆₇	C₂²	1	1	yes	characteristic
102	#408×C₆₇	C₂²	1	1	yes	characteristic
103	#408×C₆₇	C₂²	1	2	yes	—
104	#408×C₆₇	C₂²	1	2	yes	—
105	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#408×C₆₇	C₂²	1	2	yes	complemented
107	#407×C₆₇	C₂²	1	2	yes	complemented
108	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
111	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#405×C₆₇	C₂²	1	2	yes	complemented
113	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#405×C₆₇	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
116	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×#41×C₆₇	C₂³	1	2	yes	—
119	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	#131×C₆₇	—	4	2	no	—
123	#131×C₆₇	—	4	4	no	—
124	#131×C₆₇	—	4	2	no	—
125	C₂×M₁₆×C₆₇	—	4	2	no	—
126	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
129	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
137	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₆₇	—	4	2	no	—
139	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
140	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
145	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
148	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
149	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
153	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
154	#127×C₆₇	C₂×C₄	1	2	yes	—
155	#126×C₆₇	C₂×C₄	1	2	yes	—
156	#126×C₆₇	C₂×C₄	1	2	yes	—
157	#126×C₆₇	C₂×C₄	1	2	yes	—
158	#126×C₆₇	C₂×C₄	1	2	yes	—
159	#126×C₆₇	C₂×C₄	1	2	yes	—
160	#126×C₆₇	C₂×C₄	1	2	yes	—
161	#125×C₆₇	C₂×C₄	1	2	yes	—
162	#125×C₆₇	C₂×C₄	1	2	yes	—
163	#125×C₆₇	C₂×C₄	1	2	yes	—
164	#124×C₆₇	C₂×C₄	1	2	yes	—
165	#124×C₆₇	C₂×C₄	1	2	yes	—
166	#124×C₆₇	C₂×C₄	1	2	yes	—
167	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
168	#124×C₆₇	C₂×C₄	1	2	yes	—
169	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
170	#124×C₆₇	C₂×C₄	1	2	yes	—
171	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
172	#123×C₆₇	C₂×C₄	1	2	yes	—
173	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
174	#123×C₆₇	C₂×C₄	1	2	yes	—
175	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
176	#123×C₆₇	C₂×C₄	1	2	yes	—
177	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
178	#123×C₆₇	C₂×C₄	1	2	yes	—
179	#123×C₆₇	C₂×C₄	1	2	yes	—
180	#123×C₆₇	C₂×C₄	1	2	yes	—
181	#123×C₆₇	C₂×C₄	1	2	yes	—
182	#123×C₆₇	C₂×C₄	1	2	yes	—
183	#123×C₆₇	C₂×C₄	1	2	yes	—
184	#123×C₆₇	C₂×C₄	1	2	yes	—
185	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
186	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
187	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
189	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
190	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
191	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
194	#121×C₆₇	C₂×C₄	1	2	yes	—
195	#121×C₆₇	C₂×C₄	1	2	yes	—
196	#121×C₆₇	C₂×C₄	1	2	yes	—
197	#121×C₆₇	C₂×C₄	1	2	yes	—
198	#121×C₆₇	C₂×C₄	1	2	yes	—
199	#121×C₆₇	C₂×C₄	1	2	yes	—
200	#121×C₆₇	C₂×C₄	1	2	yes	—
201	#121×C₆₇	C₂×C₄	1	2	yes	—
202	#121×C₆₇	C₂×C₄	1	2	yes	—
203	#121×C₆₇	C₂×C₄	1	2	yes	—
204	#121×C₆₇	C₂×C₄	1	2	yes	—
205	#121×C₆₇	C₂×C₄	1	2	yes	—
206	#121×C₆₇	C₂×C₄	1	2	yes	—
207	#121×C₆₇	C₂×C₄	1	2	yes	—
208	#121×C₆₇	C₂×C₄	1	2	yes	—
209	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
210	#120×C₆₇	C₂×C₄	1	2	yes	—
211	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
212	#120×C₆₇	C₂×C₄	1	2	yes	—
213	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
214	#120×C₆₇	C₂×C₄	1	2	yes	—
215	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
216	#120×C₆₇	C₂×C₄	1	2	yes	—
217	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
218	C₄×D₄×C₆₇	C₂³	1	2	yes	—
219	C₄×D₄×C₆₇	C₂³	1	2	yes	—
220	C₄×D₄×C₆₇	C₂³	1	2	yes	—
221	C₄×D₄×C₆₇	C₂³	1	2	yes	—
222	C₄×D₄×C₆₇	C₂³	1	2	yes	—
223	C₄×D₄×C₆₇	C₂³	1	2	yes	—
224	C₄×D₄×C₆₇	C₂³	1	2	yes	—
225	C₄×D₄×C₆₇	C₂³	1	2	yes	—
226	C₄×D₄×C₆₇	C₂³	1	2	yes	—
227	#117×C₆₇	C₂³	1	1	yes	characteristic
228	#117×C₆₇	C₂³	1	2	yes	—
229	#117×C₆₇	C₂³	1	1	yes	characteristic
230	#117×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
238	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
239	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
240	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
241	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
242	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
243	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
244	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
247	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
248	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
249	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
250	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
251	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
260	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
261	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
262	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
263	#97×C₆₇	C₂³	1	2	yes	—
264	#97×C₆₇	C₂³	1	2	yes	—
265	#97×C₆₇	C₂³	1	2	yes	—
266	#97×C₆₇	C₂³	1	2	yes	—
267	#97×C₆₇	C₂³	1	2	yes	—
268	#97×C₆₇	C₂³	1	2	yes	—
269	C₄×C₈×C₆₇	C₂³	1	2	yes	—
270	C₄×C₈×C₆₇	C₂³	1	2	yes	—
271	C₄×C₈×C₆₇	C₂³	1	2	yes	—
272	C₄×C₈×C₆₇	C₂³	1	2	yes	—
273	C₄×C₈×C₆₇	C₂³	1	2	yes	—
274	C₄×C₈×C₆₇	C₂³	1	2	yes	—
275	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
277	#41×C₆₇	—	4	1	no	—
278	#41×C₆₇	—	4	2	no	—
279	#41×C₆₇	—	4	1	no	—
280	#41×C₆₇	—	4	2	no	—
281	#41×C₆₇	—	4	1	no	—
282	#41×C₆₇	—	4	1	no	—
283	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
284	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
285	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
286	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
287	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
289	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
291	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
292	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
297	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
298	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
299	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
300	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
301	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
302	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
303	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	—	4	1	no	—
305	C₂²×C₄×C₆₇	—	4	1	no	—
306	C₂²×C₄×C₆₇	—	4	1	no	—
307	C₂²×C₄×C₆₇	—	4	1	no	—
308	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	M₁₆×C₆₇	—	2	4	no	—
322	M₁₆×C₆₇	—	2	4	no	—
323	M₁₆×C₆₇	—	4	2	no	—
324	M₁₆×C₆₇	—	4	2	no	—
325	M₁₆×C₆₇	—	4	1	no	—
326	M₁₆×C₆₇	—	4	2	no	—
327	M₁₆×C₆₇	—	4	1	no	—
328	M₁₆×C₆₇	—	4	1	no	—
329	M₁₆×C₆₇	—	4	1	no	—
330	M₁₆×C₆₇	—	4	1	no	—
331	M₁₆×C₆₇	—	4	2	no	—
332	M₁₆×C₆₇	—	4	1	no	—
333	C₂×C₈×C₆₇	—	2	4	no	—
334	C₂×C₈×C₆₇	—	2	2	no	—
335	C₂×C₈×C₆₇	—	2	2	no	—
336	C₂×C₈×C₆₇	—	2	2	no	—
337	C₂×C₈×C₆₇	—	4	1	no	—
338	C₂×C₈×C₆₇	—	4	2	no	—
339	C₂×C₈×C₆₇	—	4	1	no	—
340	C₂×C₈×C₆₇	—	4	2	no	—
341	C₂×C₈×C₆₇	—	4	1	no	—
342	C₂×C₈×C₆₇	—	4	2	no	—
343	C₂×C₈×C₆₇	—	4	2	no	—
344	C₂×C₈×C₆₇	—	4	2	no	—
345	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
346	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
349	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
350	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
352	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
353	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
354	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
357	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
358	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
360	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
362	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
374	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
376	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
378	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
380	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
393	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
394	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
395	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
396	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
397	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
398	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
399	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
401	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
403	C₄²×C₆₇	C₂⁴	1	2	yes	—
404	C₄²×C₆₇	C₂⁴	1	2	yes	—
405	C₄²×C₆₇	C₂⁴	1	2	yes	—
406	C₂³×C₆₇	—	4	1	no	—
407	C₂³×C₆₇	—	4	2	no	—
408	C₂³×C₆₇	—	4	1	no	—
409	C₂³×C₆₇	—	4	2	no	—
410	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
411	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
412	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
413	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
414	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
415	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
416	Q₈×C₆₇	—	4	2	no	—
417	Q₈×C₆₇	—	4	1	no	—
418	Q₈×C₆₇	—	4	2	no	—
419	Q₈×C₆₇	—	4	1	no	—
420	D₄×C₆₇	—	4	2	no	—
421	D₄×C₆₇	—	4	2	no	—
422	D₄×C₆₇	—	4	2	no	—
423	D₄×C₆₇	—	4	2	no	—
424	D₄×C₆₇	—	4	2	no	—
425	D₄×C₆₇	—	4	2	no	—
426	D₄×C₆₇	—	4	2	no	—
427	D₄×C₆₇	—	4	2	no	—
428	D₄×C₆₇	—	4	2	no	—
429	D₄×C₆₇	—	4	1	no	—
430	D₄×C₆₇	—	4	1	no	—
431	D₄×C₆₇	—	4	2	no	—
432	D₄×C₆₇	—	4	2	no	—
433	D₄×C₆₇	—	4	1	no	—
434	D₄×C₆₇	—	4	2	no	—
435	D₄×C₆₇	—	4	1	no	—
436	D₄×C₆₇	—	4	2	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	4	1	no	—
450	C₂×C₄×C₆₇	—	4	2	no	—
451	C₂×C₄×C₆₇	—	4	2	no	—
452	C₂×C₄×C₆₇	—	4	1	no	—
453	C₂×C₄×C₆₇	—	4	2	no	—
454	C₂×C₄×C₆₇	—	4	2	no	—
455	C₂×C₄×C₆₇	—	4	2	no	—
456	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
457	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
466	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
467	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
469	C₈×C₆₇	—	2	2	no	—
470	C₈×C₆₇	—	2	1	no	—
471	C₈×C₆₇	—	2	1	no	—
472	C₈×C₆₇	—	2	1	no	—
473	C₈×C₆₇	—	2	2	no	—
474	C₈×C₆₇	—	2	2	no	—
475	C₈×C₆₇	—	2	2	no	—
476	C₈×C₆₇	—	2	2	no	—
477	C₈×C₆₇	—	2	2	no	—
478	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	1	no	—
481	C₂²×C₆₇	—	2	1	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	1	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	2	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	2	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	2	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	2	no	—
494	C₂²×C₆₇	—	4	4	no	—
495	C₂²×C₆₇	—	8	2	no	—
496	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
497	C₄×C₆₇	—	2	2	no	—
498	C₄×C₆₇	—	2	1	no	—
499	C₄×C₆₇	—	2	1	no	—
500	C₄×C₆₇	—	2	2	no	—
501	C₄×C₆₇	—	2	1	no	—
502	C₄×C₆₇	—	2	2	no	—
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	2	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	—	2	2	no	—
509	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₄×C₆₇	#585	1	1	yes	characteristic
511	#60315	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
512	C₂×C₆₇	—	4	1	no	—
513	C₂×C₆₇	—	4	2	no	—
514	C₂×C₆₇	—	4	2	no	—
515	C₂×C₆₇	—	4	1	no	—
516	C₂×C₆₇	—	4	1	no	—
517	C₂×C₆₇	—	4	2	no	—
518	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₆₇	#3573	1	2	yes	—
520	#3529	C₂×C₆₇	1	1	yes	characteristic
521	#2994	C₂×C₆₇	1	2	yes	complemented
522	#2993	C₂×C₆₇	1	2	yes	complemented
523	#2992	C₂×C₆₇	1	2	yes	complemented
524	#2981	C₂×C₆₇	1	2	yes	complemented
525	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#2978	C₂×C₆₇	1	2	yes	complemented
528	#2977	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#2976	C₂×C₆₇	1	2	yes	complemented
530	#2969	C₂×C₆₇	1	2	yes	complemented
531	#2968	C₂×C₆₇	1	2	yes	complemented
532	#2967	C₂×C₆₇	1	2	yes	complemented
533	#2935	C₂×C₆₇	1	2	yes	complemented
534	#2933	C₂×C₆₇	1	2	yes	complemented
535	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#2929	C₂×C₆₇	1	2	yes	complemented
539	C₆₇	#60315	1	1	yes	characteristic, direct product factor, Sylow
540	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
541	C₂×#131	C₂²×C₆₇	1	2	yes	—
542	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
545	#563	C₄×C₆₇	1	2	yes	—
546	#563	C₄×C₆₇	1	1	yes	characteristic
547	#562	C₄×C₆₇	1	2	yes	—
548	#562	C₄×C₆₇	1	2	yes	—
549	#562	C₄×C₆₇	1	2	yes	—
550	H(3,𝔽₄)	C₄×C₆₇	1	1	yes	characteristic
551	#560	C₄×C₆₇	1	2	yes	—
552	#560	C₄×C₆₇	1	1	yes	characteristic
553	#560	C₄×C₆₇	1	2	yes	—
554	#560	C₄×C₆₇	1	1	yes	characteristic
555	#532	C₂²×C₆₇	1	1	yes	characteristic
556	#532	C₂²×C₆₇	1	2	yes	—
557	#529	C₂²×C₆₇	1	2	yes	—
558	#529	C₂²×C₆₇	1	2	yes	—
559	#529	C₂²×C₆₇	1	2	yes	—
560	#525	C₂²×C₆₇	1	1	yes	characteristic
561	#525	C₂²×C₆₇	1	2	yes	—
562	#525	C₂²×C₆₇	1	1	yes	characteristic
563	#525	C₂²×C₆₇	1	2	yes	—
564	#446	C₂²×C₆₇	1	2	yes	complemented
565	#446	C₂²×C₆₇	1	2	yes	complemented
566	#446	C₂²×C₆₇	1	2	yes	complemented
567	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
568	#436	C₂²×C₆₇	1	2	yes	—
569	#436	C₂²×C₆₇	1	2	yes	—
570	#436	C₂²×C₆₇	1	2	yes	—
571	#436	C₂²×C₆₇	1	2	yes	complemented
572	#436	C₂²×C₆₇	1	2	yes	complemented
573	#436	C₂²×C₆₇	1	2	yes	complemented
574	#436	C₂²×C₆₇	1	2	yes	complemented
575	#436	C₂²×C₆₇	1	2	yes	complemented
576	#436	C₂²×C₆₇	1	2	yes	complemented
577	#435	C₂²×C₆₇	1	2	yes	—
578	#435	C₂²×C₆₇	1	2	yes	—
579	#435	C₂²×C₆₇	1	2	yes	—
580	#435	C₂²×C₆₇	1	2	yes	—
581	#435	C₂²×C₆₇	1	2	yes	—
582	#435	C₂²×C₆₇	1	2	yes	—
583	#435	C₂²×C₆₇	1	2	yes	complemented
584	#435	C₂²×C₆₇	1	2	yes	complemented
585	#435	C₂²×C₆₇	1	2	yes	complemented
586	#435	C₂²×C₆₇	1	2	yes	complemented
587	#435	C₂²×C₆₇	1	2	yes	complemented
588	#435	C₂²×C₆₇	1	2	yes	complemented
589	#435	C₂²×C₆₇	1	2	yes	complemented
590	#435	C₂²×C₆₇	1	2	yes	complemented
591	#435	C₂²×C₆₇	1	2	yes	complemented
592	#435	C₂²×C₆₇	1	2	yes	complemented
593	#435	C₂²×C₆₇	1	2	yes	complemented
594	#435	C₂²×C₆₇	1	2	yes	complemented
595	C₈×D₄	C₂²×C₆₇	1	2	yes	—
596	C₈×D₄	C₂²×C₆₇	1	2	yes	—
597	C₈×D₄	C₂²×C₆₇	1	2	yes	—
598	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
599	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
600	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
601	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
602	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
603	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
604	#433	C₂²×C₆₇	1	2	yes	complemented
605	#433	C₂²×C₆₇	1	2	yes	complemented
606	#433	C₂²×C₆₇	1	2	yes	complemented
607	#433	C₂²×C₆₇	1	2	yes	complemented
608	#433	C₂²×C₆₇	1	2	yes	complemented
609	#433	C₂²×C₆₇	1	2	yes	complemented
610	#432	C₂²×C₆₇	1	2	yes	complemented
611	#431	C₂²×C₆₇	1	2	yes	complemented
612	#431	C₂²×C₆₇	1	2	yes	complemented
613	#424	C₂²×C₆₇	1	2	yes	complemented
614	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
615	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	#424	C₂²×C₆₇	1	2	yes	complemented
617	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
618	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
619	#408	C₂²×C₆₇	1	2	yes	—
620	#408	C₂²×C₆₇	1	1	yes	characteristic
621	#408	C₂²×C₆₇	1	1	yes	characteristic
622	#408	C₂²×C₆₇	1	1	yes	characteristic
623	#408	C₂²×C₆₇	1	2	yes	—
624	#408	C₂²×C₆₇	1	2	yes	—
625	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#408	C₂²×C₆₇	1	2	yes	complemented
627	#407	C₂²×C₆₇	1	2	yes	complemented
628	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
631	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#405	C₂²×C₆₇	1	2	yes	complemented
633	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#405	C₂²×C₆₇	1	2	yes	complemented
635	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
636	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×#41	C₂³×C₆₇	1	2	yes	—
639	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
642	#131	—	4	2	no	—
643	#131	—	4	4	no	—
644	#131	—	4	2	no	—
645	C₂×M₁₆	—	4	2	no	—
646	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
647	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
648	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
649	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
651	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
655	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
657	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
658	C₂²×C₈	—	4	2	no	—
659	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
660	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
661	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
663	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
664	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
665	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
666	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
667	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
668	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
669	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
671	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
672	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
673	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
674	#127	C₂×C₄×C₆₇	1	2	yes	—
675	#126	C₂×C₄×C₆₇	1	2	yes	—
676	#126	C₂×C₄×C₆₇	1	2	yes	—
677	#126	C₂×C₄×C₆₇	1	2	yes	—
678	#126	C₂×C₄×C₆₇	1	2	yes	—
679	#126	C₂×C₄×C₆₇	1	2	yes	—
680	#126	C₂×C₄×C₆₇	1	2	yes	—
681	#125	C₂×C₄×C₆₇	1	2	yes	—
682	#125	C₂×C₄×C₆₇	1	2	yes	—
683	#125	C₂×C₄×C₆₇	1	2	yes	—
684	#124	C₂×C₄×C₆₇	1	2	yes	—
685	#124	C₂×C₄×C₆₇	1	2	yes	—
686	#124	C₂×C₄×C₆₇	1	2	yes	—
687	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
688	#124	C₂×C₄×C₆₇	1	2	yes	—
689	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
690	#124	C₂×C₄×C₆₇	1	2	yes	—
691	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
692	#123	C₂×C₄×C₆₇	1	2	yes	—
693	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
694	#123	C₂×C₄×C₆₇	1	2	yes	—
695	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
696	#123	C₂×C₄×C₆₇	1	2	yes	—
697	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
698	#123	C₂×C₄×C₆₇	1	2	yes	—
699	#123	C₂×C₄×C₆₇	1	2	yes	—
700	#123	C₂×C₄×C₆₇	1	2	yes	—
701	#123	C₂×C₄×C₆₇	1	2	yes	—
702	#123	C₂×C₄×C₆₇	1	2	yes	—
703	#123	C₂×C₄×C₆₇	1	2	yes	—
704	#123	C₂×C₄×C₆₇	1	2	yes	—
705	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
706	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
707	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
708	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
709	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
710	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
711	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
712	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
713	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
714	#121	C₂×C₄×C₆₇	1	2	yes	—
715	#121	C₂×C₄×C₆₇	1	2	yes	—
716	#121	C₂×C₄×C₆₇	1	2	yes	—
717	#121	C₂×C₄×C₆₇	1	2	yes	—
718	#121	C₂×C₄×C₆₇	1	2	yes	—
719	#121	C₂×C₄×C₆₇	1	2	yes	—
720	#121	C₂×C₄×C₆₇	1	2	yes	—
721	#121	C₂×C₄×C₆₇	1	2	yes	—
722	#121	C₂×C₄×C₆₇	1	2	yes	—
723	#121	C₂×C₄×C₆₇	1	2	yes	—
724	#121	C₂×C₄×C₆₇	1	2	yes	—
725	#121	C₂×C₄×C₆₇	1	2	yes	—
726	#121	C₂×C₄×C₆₇	1	2	yes	—
727	#121	C₂×C₄×C₆₇	1	2	yes	—
728	#121	C₂×C₄×C₆₇	1	2	yes	—
729	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
730	#120	C₂×C₄×C₆₇	1	2	yes	—
731	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
732	#120	C₂×C₄×C₆₇	1	2	yes	—
733	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
734	#120	C₂×C₄×C₆₇	1	2	yes	—
735	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
736	#120	C₂×C₄×C₆₇	1	2	yes	—
737	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
738	C₄×D₄	C₂³×C₆₇	1	2	yes	—
739	C₄×D₄	C₂³×C₆₇	1	2	yes	—
740	C₄×D₄	C₂³×C₆₇	1	2	yes	—
741	C₄×D₄	C₂³×C₆₇	1	2	yes	—
742	C₄×D₄	C₂³×C₆₇	1	2	yes	—
743	C₄×D₄	C₂³×C₆₇	1	2	yes	—
744	C₄×D₄	C₂³×C₆₇	1	2	yes	—
745	C₄×D₄	C₂³×C₆₇	1	2	yes	—
746	C₄×D₄	C₂³×C₆₇	1	2	yes	—
747	#117	C₂³×C₆₇	1	1	yes	characteristic
748	#117	C₂³×C₆₇	1	2	yes	—
749	#117	C₂³×C₆₇	1	1	yes	characteristic
750	#117	C₂³×C₆₇	1	2	yes	—
751	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
753	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
754	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
755	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
756	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
757	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
758	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
759	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
760	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
761	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
762	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
763	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
764	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
768	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
783	#97	C₂³×C₆₇	1	2	yes	—
784	#97	C₂³×C₆₇	1	2	yes	—
785	#97	C₂³×C₆₇	1	2	yes	—
786	#97	C₂³×C₆₇	1	2	yes	—
787	#97	C₂³×C₆₇	1	2	yes	—
788	#97	C₂³×C₆₇	1	2	yes	—
789	C₄×C₈	C₂³×C₆₇	1	2	yes	—
790	C₄×C₈	C₂³×C₆₇	1	2	yes	—
791	C₄×C₈	C₂³×C₆₇	1	2	yes	—
792	C₄×C₈	C₂³×C₆₇	1	2	yes	—
793	C₄×C₈	C₂³×C₆₇	1	2	yes	—
794	C₄×C₈	C₂³×C₆₇	1	2	yes	—
795	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
796	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
797	#41	—	4	1	no	—
798	#41	—	4	2	no	—
799	#41	—	4	1	no	—
800	#41	—	4	2	no	—
801	#41	—	4	1	no	—
802	#41	—	4	1	no	—
803	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
804	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
805	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
806	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
807	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
808	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
809	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
810	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
811	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
812	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
813	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
814	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
815	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
816	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
817	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
818	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
819	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
820	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
821	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
822	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
823	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	—	4	1	no	—
825	C₂²×C₄	—	4	1	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	1	no	—
828	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
829	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
830	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
831	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
832	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
833	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
834	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
841	M₁₆	—	2	4	no	—
842	M₁₆	—	2	4	no	—
843	M₁₆	—	4	2	no	—
844	M₁₆	—	4	1	no	—
845	M₁₆	—	4	1	no	—
846	M₁₆	—	4	1	no	—
847	M₁₆	—	4	2	no	—
848	M₁₆	—	4	1	no	—
849	M₁₆	—	4	2	no	—
850	M₁₆	—	4	1	no	—
851	M₁₆	—	4	2	no	—
852	M₁₆	—	4	1	no	—
853	C₂×C₈	—	2	4	no	—
854	C₂×C₈	—	2	2	no	—
855	C₂×C₈	—	2	2	no	—
856	C₂×C₈	—	2	2	no	—
857	C₂×C₈	—	4	1	no	—
858	C₂×C₈	—	4	2	no	—
859	C₂×C₈	—	4	1	no	—
860	C₂×C₈	—	4	2	no	—
861	C₂×C₈	—	4	2	no	—
862	C₂×C₈	—	4	2	no	—
863	C₂×C₈	—	4	1	no	—
864	C₂×C₈	—	4	2	no	—
865	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
866	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
867	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
868	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
869	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
870	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
871	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
872	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
873	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
874	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
875	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
877	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
878	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
879	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
880	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
881	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
882	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
883	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
884	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
885	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
886	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
887	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
888	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
889	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
890	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
891	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
892	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
894	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
896	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
898	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
900	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
912	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
913	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
914	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
915	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
916	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
917	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
918	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
919	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
920	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
921	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
922	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
923	C₄²	C₂⁴×C₆₇	1	2	yes	—
924	C₄²	C₂⁴×C₆₇	1	2	yes	—
925	C₄²	C₂⁴×C₆₇	1	2	yes	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	4	1	no	—
929	C₂³	—	4	2	no	—
930	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
931	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
932	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
933	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
934	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
935	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
936	Q₈	—	4	1	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	4	1	no	—
939	Q₈	—	4	2	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	1	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	1	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	2	no	—
951	D₄	—	4	2	no	—
952	D₄	—	4	2	no	—
953	D₄	—	4	2	no	—
954	D₄	—	4	2	no	—
955	D₄	—	4	2	no	—
956	D₄	—	4	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	2	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
977	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
978	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
979	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
980	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
981	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
985	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
987	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
988	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
989	C₈	—	2	2	no	—
990	C₈	—	2	1	no	—
991	C₈	—	2	1	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	2	no	—
994	C₈	—	2	2	no	—
995	C₈	—	2	2	no	—
996	C₈	—	2	2	no	—
997	C₈	—	2	2	no	—
998	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	4	4	no	—
1015	C₂²	—	8	2	no	—
1016	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	2	1	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	2	no	—
1029	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1030	C₄	#585×C₆₇	1	1	yes	characteristic
1031	C₂	—	4	1	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	2	no	—
1035	C₂	—	4	1	no	—
1036	C₂	—	4	2	no	—
1037	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1038	C₂	C₆₇×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3529	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2994	C₂	semidirect
3. C₆₇×#2993	C₂	semidirect
4. C₆₇×#2992	C₂	semidirect
5. C₆₇×#2981	C₂	semidirect
6. C₆₇×#2979	C₂	semidirect
7. C₆₇×#2978	C₂	semidirect
8. C₆₇×#2978	C₂	semidirect
9. C₆₇×#2977	C₂	semidirect
10. C₆₇×#2976	C₂	semidirect
11. C₆₇×#2969	C₂	semidirect
12. C₆₇×#2968	C₂	semidirect
13. C₆₇×#2967	C₂	semidirect
14. C₆₇×#2935	C₂	semidirect
15. C₆₇×#2933	C₂	semidirect
16. C₆₇×#2932	C₂	semidirect
17. C₆₇×#2930	C₂	semidirect
18. C₆₇×#2929	C₂	semidirect
19. C₆₇×#2929	C₂	semidirect
22. C₂×#131×C₆₇	C₂²	semidirect
23. C₂²×M₁₆×C₆₇	C₂²	semidirect
24. C₂³×C₈×C₆₇	C₂²	semidirect
44. #446×C₆₇	C₂²	semidirect
45. #446×C₆₇	C₂²	semidirect
46. #446×C₆₇	C₂²	semidirect
47. C₈×Q₈×C₆₇	C₂²	semidirect
51. #436×C₆₇	C₂²	semidirect
52. #436×C₆₇	C₂²	semidirect
53. #436×C₆₇	C₂²	semidirect
54. #436×C₆₇	C₂²	semidirect
55. #436×C₆₇	C₂²	semidirect
56. #436×C₆₇	C₂²	semidirect
63. #435×C₆₇	C₂²	semidirect
64. #435×C₆₇	C₂²	semidirect
65. #435×C₆₇	C₂²	semidirect
66. #435×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #435×C₆₇	C₂²	semidirect
71. #435×C₆₇	C₂²	semidirect
72. #435×C₆₇	C₂²	semidirect
73. #435×C₆₇	C₂²	semidirect
74. #435×C₆₇	C₂²	semidirect
78. C₈×D₄×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. C₈×D₄×C₆₇	C₂²	semidirect
81. C₈×D₄×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₈×D₄×C₆₇	C₂²	semidirect
84. #433×C₆₇	C₂²	semidirect
85. #433×C₆₇	C₂²	semidirect
86. #433×C₆₇	C₂²	semidirect
87. #433×C₆₇	C₂²	semidirect
88. #433×C₆₇	C₂²	semidirect
89. #433×C₆₇	C₂²	semidirect
90. #432×C₆₇	C₂²	semidirect
91. #431×C₆₇	C₂²	semidirect
92. #431×C₆₇	C₂²	semidirect
93. #424×C₆₇	C₂²	semidirect
94. #424×C₆₇	C₂²	semidirect
95. #424×C₆₇	C₂²	semidirect
96. #424×C₆₇	C₂²	semidirect
97. #423×C₆₇	C₂²	semidirect
98. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
105. #408×C₆₇	C₂²	semidirect
106. #408×C₆₇	C₂²	semidirect
107. #407×C₆₇	C₂²	semidirect
108. #407×C₆₇	C₂²	semidirect
109. #407×C₆₇	C₂²	semidirect
110. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
111. #405×C₆₇	C₂²	semidirect
112. #405×C₆₇	C₂²	semidirect
113. #405×C₆₇	C₂²	semidirect
114. #405×C₆₇	C₂²	semidirect
115. C₄×M₁₆×C₆₇	C₂²	semidirect
116. C₂×#97×C₆₇	C₂²	semidirect
511. #60315	C₆₇	direct (N × H)
521. #2994	C₂×C₆₇	semidirect
522. #2993	C₂×C₆₇	semidirect
523. #2992	C₂×C₆₇	semidirect
524. #2981	C₂×C₆₇	semidirect
525. #2979	C₂×C₆₇	semidirect
526. #2978	C₂×C₆₇	semidirect
527. #2978	C₂×C₆₇	semidirect
528. #2977	C₂×C₆₇	semidirect
529. #2976	C₂×C₆₇	semidirect
530. #2969	C₂×C₆₇	semidirect
531. #2968	C₂×C₆₇	semidirect
532. #2967	C₂×C₆₇	semidirect
533. #2935	C₂×C₆₇	semidirect
534. #2933	C₂×C₆₇	semidirect
535. #2932	C₂×C₆₇	semidirect
536. #2930	C₂×C₆₇	semidirect
537. #2929	C₂×C₆₇	semidirect
538. #2929	C₂×C₆₇	semidirect
539. C₆₇	#60315	direct (N × H)
542. C₂×#131	C₂²×C₆₇	semidirect
543. C₂²×M₁₆	C₂²×C₆₇	semidirect
544. C₂³×C₈	C₂²×C₆₇	semidirect
564. #446	C₂²×C₆₇	semidirect
565. #446	C₂²×C₆₇	semidirect
566. #446	C₂²×C₆₇	semidirect
567. C₈×Q₈	C₂²×C₆₇	semidirect
571. #436	C₂²×C₆₇	semidirect
572. #436	C₂²×C₆₇	semidirect
573. #436	C₂²×C₆₇	semidirect
574. #436	C₂²×C₆₇	semidirect
575. #436	C₂²×C₆₇	semidirect
576. #436	C₂²×C₆₇	semidirect
583. #435	C₂²×C₆₇	semidirect
584. #435	C₂²×C₆₇	semidirect
585. #435	C₂²×C₆₇	semidirect
586. #435	C₂²×C₆₇	semidirect
587. #435	C₂²×C₆₇	semidirect
588. #435	C₂²×C₆₇	semidirect
589. #435	C₂²×C₆₇	semidirect
590. #435	C₂²×C₆₇	semidirect
591. #435	C₂²×C₆₇	semidirect
592. #435	C₂²×C₆₇	semidirect
593. #435	C₂²×C₆₇	semidirect
594. #435	C₂²×C₆₇	semidirect
598. C₈×D₄	C₂²×C₆₇	semidirect
599. C₈×D₄	C₂²×C₆₇	semidirect
600. C₈×D₄	C₂²×C₆₇	semidirect
601. C₈×D₄	C₂²×C₆₇	semidirect
602. C₈×D₄	C₂²×C₆₇	semidirect
603. C₈×D₄	C₂²×C₆₇	semidirect
604. #433	C₂²×C₆₇	semidirect
605. #433	C₂²×C₆₇	semidirect
606. #433	C₂²×C₆₇	semidirect
607. #433	C₂²×C₆₇	semidirect
608. #433	C₂²×C₆₇	semidirect
609. #433	C₂²×C₆₇	semidirect
610. #432	C₂²×C₆₇	semidirect
611. #431	C₂²×C₆₇	semidirect
612. #431	C₂²×C₆₇	semidirect
613. #424	C₂²×C₆₇	semidirect
614. #424	C₂²×C₆₇	semidirect
615. #424	C₂²×C₆₇	semidirect
616. #424	C₂²×C₆₇	semidirect
617. #423	C₂²×C₆₇	semidirect
618. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
625. #408	C₂²×C₆₇	semidirect
626. #408	C₂²×C₆₇	semidirect
627. #407	C₂²×C₆₇	semidirect
628. #407	C₂²×C₆₇	semidirect
629. #407	C₂²×C₆₇	semidirect
630. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
631. #405	C₂²×C₆₇	semidirect
632. #405	C₂²×C₆₇	semidirect
633. #405	C₂²×C₆₇	semidirect
634. #405	C₂²×C₆₇	semidirect
635. C₄×M₁₆	C₂²×C₆₇	semidirect
636. C₂×#97	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3529	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2981	2
C₆₇×#2979	2
C₆₇×#2978	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2969	2
C₆₇×#2968	2
C₆₇×#2967	2
C₆₇×#2935	2
C₆₇×#2933	2
C₆₇×#2932	2
C₆₇×#2930	2
C₆₇×#2929	2
#60315	67

Subgroups — C67×#60315 #30739566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60315 #30739566