Subgroups — C₆₇×#61552 #30740803

Order 17152.

1756 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3515	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3352	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3315	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3302	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3177	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	2	yes	—
26	#557×C₆₇	—	2	1	no	—
27	#557×C₆₇	C₂²	1	1	yes	characteristic
28	#557×C₆₇	C₂²	1	1	yes	characteristic
29	#557×C₆₇	C₂²	1	1	yes	characteristic
30	#556×C₆₇	—	2	1	no	—
31	#556×C₆₇	C₂²	1	1	yes	characteristic
32	#554×C₆₇	C₂²	1	1	yes	characteristic
33	#554×C₆₇	C₂²	1	1	yes	characteristic
34	#553×C₆₇	—	2	1	no	—
35	#552×C₆₇	—	2	2	no	—
36	#552×C₆₇	—	2	2	no	—
37	#552×C₆₇	—	2	1	no	—
38	#552×C₆₇	C₂²	1	2	yes	—
39	#552×C₆₇	C₂²	1	2	yes	—
40	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
42	#547×C₆₇	C₂²	1	1	yes	characteristic
43	#547×C₆₇	C₂²	1	2	yes	—
44	#541×C₆₇	—	2	2	no	—
45	#541×C₆₇	C₂²	1	2	yes	—
46	#541×C₆₇	C₂²	1	2	yes	—
47	#539×C₆₇	—	2	2	no	—
48	#533×C₆₇	—	2	1	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#533×C₆₇	C₂²	1	1	yes	characteristic
51	#529×C₆₇	—	2	1	no	—
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#125×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	—
56	#519×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	#499×C₆₇	C₂²	1	2	yes	—
60	#498×C₆₇	C₂²	1	1	yes	characteristic
61	#494×C₆₇	C₂²	1	2	yes	—
62	#494×C₆₇	C₂²	1	1	yes	characteristic
63	#491×C₆₇	C₂²	1	2	yes	—
64	#491×C₆₇	C₂²	1	2	yes	—
65	#487×C₆₇	C₂²	1	1	yes	characteristic
66	#487×C₆₇	C₂²	1	1	yes	characteristic
67	#485×C₆₇	C₂²	1	2	yes	—
68	#485×C₆₇	C₂²	1	2	yes	—
69	#485×C₆₇	C₂²	1	2	yes	—
70	#484×C₆₇	C₂²	1	2	yes	—
71	#484×C₆₇	C₂²	1	2	yes	—
72	#483×C₆₇	C₂²	1	2	yes	—
73	#479×C₆₇	C₂²	1	2	yes	—
74	#479×C₆₇	C₂²	1	2	yes	—
75	#479×C₆₇	C₂²	1	2	yes	—
76	#478×C₆₇	C₂²	1	2	yes	—
77	#477×C₆₇	C₂²	1	1	yes	characteristic
78	#477×C₆₇	C₂²	1	1	yes	characteristic
79	#475×C₆₇	C₂²	1	1	yes	characteristic
80	#474×C₆₇	C₂²	1	1	yes	characteristic
81	#470×C₆₇	C₂²	1	2	yes	—
82	#470×C₆₇	C₂²	1	2	yes	—
83	#470×C₆₇	C₂²	1	2	yes	—
84	#470×C₆₇	C₂²	1	2	yes	—
85	#467×C₆₇	C₂²	1	2	yes	—
86	#467×C₆₇	C₂²	1	2	yes	—
87	#462×C₆₇	C₂²	1	1	yes	characteristic
88	#462×C₆₇	C₂²	1	2	yes	—
89	#462×C₆₇	C₂²	1	1	yes	characteristic
90	#462×C₆₇	C₂²	1	1	yes	characteristic
91	#462×C₆₇	C₂²	1	2	yes	—
92	#462×C₆₇	C₂²	1	2	yes	—
93	#461×C₆₇	C₂²	1	1	yes	characteristic
94	#461×C₆₇	C₂²	1	2	yes	—
95	#452×C₆₇	C₂²	1	2	yes	—
96	#452×C₆₇	C₂²	1	2	yes	—
97	#452×C₆₇	C₂²	1	2	yes	—
98	#451×C₆₇	C₂²	1	2	yes	—
99	#451×C₆₇	C₂²	1	2	yes	—
100	#451×C₆₇	C₂²	1	2	yes	—
101	#446×C₆₇	C₂²	1	1	yes	characteristic
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
103	#441×C₆₇	C₂²	1	2	yes	—
104	#441×C₆₇	C₂²	1	2	yes	—
105	#441×C₆₇	C₂²	1	1	yes	characteristic
106	#441×C₆₇	C₂²	1	1	yes	characteristic
107	#441×C₆₇	C₂²	1	2	yes	—
108	#440×C₆₇	C₂²	1	2	yes	—
109	#440×C₆₇	C₂²	1	1	yes	characteristic
110	#440×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
113	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
116	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
121	#436×C₆₇	C₂²	1	2	yes	—
122	#436×C₆₇	C₂²	1	1	yes	characteristic
123	#435×C₆₇	C₂²	1	2	yes	—
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
125	#433×C₆₇	C₂²	1	2	yes	—
126	#431×C₆₇	C₂²	1	1	yes	characteristic
127	#428×C₆₇	C₂²	1	1	yes	characteristic
128	#428×C₆₇	C₂²	1	2	yes	—
129	#419×C₆₇	C₂²	1	1	yes	characteristic
130	#417×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	2	yes	—
132	C₂×#103×C₆₇	C₂²	1	2	yes	—
133	#405×C₆₇	C₂²	1	2	yes	—
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×#41×C₆₇	C₂³	1	2	yes	—
137	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
139	#137×C₆₇	—	2	4	no	—
140	#137×C₆₇	—	2	8	no	—
141	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₇	—	2	1	no	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	—	2	2	no	—
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	#126×C₆₇	—	2	2	no	—
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	D₄	1	2	yes	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	—	2	2	no	—
178	#125×C₆₇	—	2	2	no	—
179	#125×C₆₇	—	2	2	no	—
180	#125×C₆₇	—	2	2	no	—
181	#125×C₆₇	—	2	2	no	—
182	#125×C₆₇	—	2	2	no	—
183	#125×C₆₇	—	2	2	no	—
184	#125×C₆₇	—	2	1	no	—
185	#125×C₆₇	—	2	1	no	—
186	#125×C₆₇	D₄	1	1	yes	characteristic
187	#125×C₆₇	C₂³	1	2	yes	—
188	#125×C₆₇	C₂³	1	2	yes	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	D₄	1	1	yes	characteristic
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	D₄	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	1	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₆₇	—	2	1	no	—
216	C₄×Q₈×C₆₇	—	2	1	no	—
217	C₄×Q₈×C₆₇	—	2	2	no	—
218	C₄×Q₈×C₆₇	—	2	2	no	—
219	C₄×Q₈×C₆₇	—	2	1	no	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	—	2	1	no	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
235	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	2	yes	—
248	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
249	#117×C₆₇	—	2	1	no	—
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	2	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	2	no	—
254	#117×C₆₇	—	2	2	no	—
255	#117×C₆₇	—	2	2	no	—
256	#117×C₆₇	—	2	1	no	—
257	#117×C₆₇	C₂³	1	1	yes	characteristic
258	#117×C₆₇	C₂³	1	2	yes	—
259	#117×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₆₇	—	2	1	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	2	yes	—
273	#107×C₆₇	C₂³	1	1	yes	characteristic
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	2	yes	—
279	#106×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	1	yes	characteristic
296	#103×C₆₇	C₂³	1	1	yes	characteristic
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	#41×C₆₇	—	2	2	no	—
315	#41×C₆₇	—	2	4	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	4	1	no	—
318	C₂×Q₈×C₆₇	—	2	1	no	—
319	C₂×Q₈×C₆₇	—	2	1	no	—
320	C₂×Q₈×C₆₇	—	2	2	no	—
321	C₂×Q₈×C₆₇	—	2	1	no	—
322	C₂×Q₈×C₆₇	—	2	2	no	—
323	C₂×Q₈×C₆₇	—	2	4	no	—
324	C₂×Q₈×C₆₇	—	4	2	no	—
325	C₂×Q₈×C₆₇	—	4	1	no	—
326	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	—	2	1	no	—
338	C₂²×C₄×C₆₇	—	2	1	no	—
339	C₂²×C₄×C₆₇	—	2	2	no	—
340	C₂²×C₄×C₆₇	—	2	2	no	—
341	C₂²×C₄×C₆₇	—	2	1	no	—
342	C₂²×C₄×C₆₇	—	2	1	no	—
343	C₂²×C₄×C₆₇	—	2	2	no	—
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
350	Q₁₆×C₆₇	—	2	2	no	—
351	Q₁₆×C₆₇	—	2	4	no	—
352	Q₁₆×C₆₇	—	2	4	no	—
353	Q₁₆×C₆₇	—	2	2	no	—
354	Q₁₆×C₆₇	—	4	2	no	—
355	Q₁₆×C₆₇	—	4	2	no	—
356	Q₁₆×C₆₇	—	4	2	no	—
357	SD₁₆×C₆₇	—	2	2	no	—
358	SD₁₆×C₆₇	—	2	4	no	—
359	SD₁₆×C₆₇	#41	1	4	yes	—
360	M₁₆×C₆₇	—	2	2	no	—
361	M₁₆×C₆₇	—	2	4	no	—
362	M₁₆×C₆₇	—	4	1	no	—
363	C₂×C₈×C₆₇	—	4	2	no	—
364	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
367	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
368	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	1	no	—
372	C₄⋊C₄×C₆₇	—	2	1	no	—
373	C₄⋊C₄×C₆₇	—	2	1	no	—
374	C₄⋊C₄×C₆₇	—	2	2	no	—
375	C₄⋊C₄×C₆₇	—	2	2	no	—
376	C₄⋊C₄×C₆₇	—	2	2	no	—
377	C₄⋊C₄×C₆₇	—	2	1	no	—
378	C₄⋊C₄×C₆₇	—	2	1	no	—
379	C₄⋊C₄×C₆₇	—	2	1	no	—
380	C₄⋊C₄×C₆₇	—	2	2	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	2	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	1	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	1	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
431	C₄²×C₆₇	—	2	1	no	—
432	C₄²×C₆₇	—	2	1	no	—
433	C₄²×C₆₇	—	2	1	no	—
434	C₄²×C₆₇	—	2	1	no	—
435	C₄²×C₆₇	—	2	1	no	—
436	C₄²×C₆₇	—	2	1	no	—
437	C₄²×C₆₇	—	2	1	no	—
438	C₄²×C₆₇	—	2	2	no	—
439	C₄²×C₆₇	—	2	2	no	—
440	C₄²×C₆₇	—	2	2	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	—	2	2	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂³×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
451	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₆₇	—	2	2	no	—
453	Q₈×C₆₇	—	2	1	no	—
454	Q₈×C₆₇	—	2	1	no	—
455	Q₈×C₆₇	—	2	2	no	—
456	Q₈×C₆₇	—	2	1	no	—
457	Q₈×C₆₇	—	2	2	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	2	no	—
460	Q₈×C₆₇	—	2	1	no	—
461	Q₈×C₆₇	—	2	2	no	—
462	Q₈×C₆₇	—	4	4	no	—
463	Q₈×C₆₇	—	4	2	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	8	1	no	—
466	Q₈×C₆₇	C₂×#41	1	2	yes	—
467	D₄×C₆₇	—	2	2	no	—
468	D₄×C₆₇	—	2	1	no	—
469	D₄×C₆₇	—	4	2	no	—
470	D₄×C₆₇	—	4	4	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	C₂×#41	1	2	yes	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	1	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	4	1	no	—
490	C₂×C₄×C₆₇	—	4	2	no	—
491	C₂×C₄×C₆₇	—	4	4	no	—
492	C₂×C₄×C₆₇	—	4	2	no	—
493	C₂×C₄×C₆₇	—	4	4	no	—
494	C₂×C₄×C₆₇	—	4	2	no	—
495	C₂×C₄×C₆₇	—	4	2	no	—
496	C₂×C₄×C₆₇	—	8	1	no	—
497	C₂×C₄×C₆₇	—	8	2	no	—
498	C₂×C₄×C₆₇	—	8	2	no	—
499	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
508	C₈×C₆₇	—	2	2	no	—
509	C₈×C₆₇	—	2	1	no	—
510	C₈×C₆₇	—	2	1	no	—
511	C₈×C₆₇	—	2	2	no	—
512	C₈×C₆₇	—	2	1	no	—
513	C₈×C₆₇	C₂×#41	1	2	yes	—
514	C₂²×C₆₇	—	2	1	no	—
515	C₂²×C₆₇	—	2	2	no	—
516	C₂²×C₆₇	—	2	2	no	—
517	C₂²×C₆₇	—	2	1	no	—
518	C₂²×C₆₇	—	2	2	no	—
519	C₂²×C₆₇	—	2	1	no	—
520	C₂²×C₆₇	—	2	2	no	—
521	C₂²×C₆₇	—	4	1	no	—
522	C₂²×C₆₇	—	4	1	no	—
523	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₆₇	—	2	1	no	—
525	C₄×C₆₇	—	2	1	no	—
526	C₄×C₆₇	—	2	2	no	—
527	C₄×C₆₇	—	2	2	no	—
528	C₄×C₆₇	—	2	1	no	—
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	1	no	—
531	C₄×C₆₇	—	2	2	no	—
532	C₄×C₆₇	—	4	1	no	—
533	C₄×C₆₇	—	4	1	no	—
534	C₄×C₆₇	—	4	1	no	—
535	C₄×C₆₇	—	4	2	no	—
536	C₄×C₆₇	—	4	1	no	—
537	C₄×C₆₇	—	4	2	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	2	no	—
540	C₄×C₆₇	—	4	1	no	—
541	C₄×C₆₇	—	4	2	no	—
542	C₄×C₆₇	#578	1	2	yes	—
543	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
544	C₄×C₆₇	#585	1	1	yes	characteristic
545	#61552	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂×C₆₇	—	4	1	no	—
547	C₂×C₆₇	—	4	2	no	—
548	C₂×C₆₇	—	4	2	no	—
549	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
550	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
551	C₂×C₆₇	#3586	1	1	yes	characteristic
552	#3523	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#3515	C₂×C₆₇	1	1	yes	characteristic
554	#3395	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#3381	C₂×C₆₇	1	1	yes	characteristic, complemented
556	#3374	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#3372	C₂×C₆₇	1	1	yes	characteristic, complemented
558	#3356	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#3352	C₂×C₆₇	1	2	yes	complemented
560	#3315	C₂×C₆₇	1	2	yes	complemented
561	#3312	C₂×C₆₇	1	2	yes	complemented
562	#3302	C₂×C₆₇	1	1	yes	characteristic, complemented
563	#3299	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#3276	C₂×C₆₇	1	2	yes	complemented
566	#3185	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3177	C₂×C₆₇	1	2	yes	complemented
568	#3127	C₂×C₆₇	1	2	yes	complemented
569	#3120	C₂×C₆₇	1	2	yes	complemented
570	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2947	C₂×C₆₇	1	2	yes	complemented
574	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
575	C₆₇	#61552	1	1	yes	characteristic, direct product factor, Sylow
576	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
577	C₂×#137	C₂²×C₆₇	1	2	yes	—
578	#557	—	2	1	no	—
579	#557	C₂²×C₆₇	1	1	yes	characteristic
580	#557	C₂²×C₆₇	1	1	yes	characteristic
581	#557	C₂²×C₆₇	1	1	yes	characteristic
582	#556	—	2	1	no	—
583	#556	C₂²×C₆₇	1	1	yes	characteristic
584	#554	C₂²×C₆₇	1	1	yes	characteristic
585	#554	C₂²×C₆₇	1	1	yes	characteristic
586	#553	—	2	1	no	—
587	#552	—	2	2	no	—
588	#552	—	2	2	no	—
589	#552	—	2	1	no	—
590	#552	C₂²×C₆₇	1	2	yes	—
591	#552	C₂²×C₆₇	1	2	yes	—
592	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
593	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
594	#547	C₂²×C₆₇	1	1	yes	characteristic
595	#547	C₂²×C₆₇	1	2	yes	—
596	#541	—	2	2	no	—
597	#541	C₂²×C₆₇	1	2	yes	—
598	#541	C₂²×C₆₇	1	2	yes	—
599	#539	—	2	2	no	—
600	#533	—	2	1	no	—
601	#533	C₂²×C₆₇	1	1	yes	characteristic
602	#533	C₂²×C₆₇	1	1	yes	characteristic
603	#529	—	2	1	no	—
604	#529	—	2	1	no	—
605	#529	C₂²×C₆₇	1	1	yes	characteristic
606	C₂×#125	—	2	1	no	—
607	#520	C₂²×C₆₇	1	2	yes	—
608	#519	C₂²×C₆₇	1	2	yes	—
609	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
610	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
611	#499	C₂²×C₆₇	1	2	yes	—
612	#498	C₂²×C₆₇	1	1	yes	characteristic
613	#494	C₂²×C₆₇	1	2	yes	—
614	#494	C₂²×C₆₇	1	1	yes	characteristic
615	#491	C₂²×C₆₇	1	2	yes	—
616	#491	C₂²×C₆₇	1	2	yes	—
617	#487	C₂²×C₆₇	1	1	yes	characteristic
618	#487	C₂²×C₆₇	1	1	yes	characteristic
619	#485	C₂²×C₆₇	1	2	yes	—
620	#485	C₂²×C₆₇	1	2	yes	—
621	#485	C₂²×C₆₇	1	2	yes	—
622	#484	C₂²×C₆₇	1	2	yes	—
623	#484	C₂²×C₆₇	1	2	yes	—
624	#483	C₂²×C₆₇	1	2	yes	—
625	#479	C₂²×C₆₇	1	2	yes	—
626	#479	C₂²×C₆₇	1	2	yes	—
627	#479	C₂²×C₆₇	1	2	yes	—
628	#478	C₂²×C₆₇	1	2	yes	—
629	#477	C₂²×C₆₇	1	1	yes	characteristic
630	#477	C₂²×C₆₇	1	1	yes	characteristic
631	#475	C₂²×C₆₇	1	1	yes	characteristic
632	#474	C₂²×C₆₇	1	1	yes	characteristic
633	#470	C₂²×C₆₇	1	2	yes	—
634	#470	C₂²×C₆₇	1	2	yes	—
635	#470	C₂²×C₆₇	1	2	yes	—
636	#470	C₂²×C₆₇	1	2	yes	—
637	#467	C₂²×C₆₇	1	2	yes	—
638	#467	C₂²×C₆₇	1	2	yes	—
639	#462	C₂²×C₆₇	1	1	yes	characteristic
640	#462	C₂²×C₆₇	1	1	yes	characteristic
641	#462	C₂²×C₆₇	1	1	yes	characteristic
642	#462	C₂²×C₆₇	1	2	yes	—
643	#462	C₂²×C₆₇	1	2	yes	—
644	#462	C₂²×C₆₇	1	2	yes	—
645	#461	C₂²×C₆₇	1	1	yes	characteristic
646	#461	C₂²×C₆₇	1	2	yes	—
647	#452	C₂²×C₆₇	1	2	yes	—
648	#452	C₂²×C₆₇	1	2	yes	—
649	#452	C₂²×C₆₇	1	2	yes	—
650	#451	C₂²×C₆₇	1	2	yes	—
651	#451	C₂²×C₆₇	1	2	yes	—
652	#451	C₂²×C₆₇	1	2	yes	—
653	#446	C₂²×C₆₇	1	1	yes	characteristic
654	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
655	#441	C₂²×C₆₇	1	2	yes	—
656	#441	C₂²×C₆₇	1	2	yes	—
657	#441	C₂²×C₆₇	1	1	yes	characteristic
658	#441	C₂²×C₆₇	1	1	yes	characteristic
659	#441	C₂²×C₆₇	1	2	yes	—
660	#440	C₂²×C₆₇	1	2	yes	—
661	#440	C₂²×C₆₇	1	1	yes	characteristic
662	#440	C₂²×C₆₇	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
664	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
665	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
666	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
668	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
670	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
673	#436	C₂²×C₆₇	1	2	yes	—
674	#436	C₂²×C₆₇	1	1	yes	characteristic
675	#435	C₂²×C₆₇	1	2	yes	—
676	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
677	#433	C₂²×C₆₇	1	2	yes	—
678	#431	C₂²×C₆₇	1	1	yes	characteristic
679	#428	C₂²×C₆₇	1	1	yes	characteristic
680	#428	C₂²×C₆₇	1	2	yes	—
681	#419	C₂²×C₆₇	1	1	yes	characteristic
682	#417	C₂²×C₆₇	1	1	yes	characteristic
683	#416	C₂²×C₆₇	1	2	yes	—
684	C₂×#103	C₂²×C₆₇	1	2	yes	—
685	#405	C₂²×C₆₇	1	2	yes	—
686	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
687	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×#41	C₂³×C₆₇	1	2	yes	—
689	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
690	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
691	#137	—	2	4	no	—
692	#137	—	2	8	no	—
693	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
695	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
697	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
698	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
699	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
706	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	2	no	—
710	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	D₄×C₆₇	1	2	yes	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	1	no	—
728	#125	—	2	1	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	1	no	—
737	#125	—	2	1	no	—
738	#125	D₄×C₆₇	1	1	yes	characteristic
739	#125	C₂³×C₆₇	1	2	yes	—
740	#125	C₂³×C₆₇	1	2	yes	—
741	#124	—	2	1	no	—
742	#124	D₄×C₆₇	1	1	yes	characteristic
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	D₄×C₆₇	1	2	yes	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	D₄×C₆₇	1	1	yes	characteristic
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
784	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
785	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
786	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
787	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
788	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₆₇	1	2	yes	—
799	C₄×D₄	C₂³×C₆₇	1	2	yes	—
800	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	C₂³×C₆₇	1	1	yes	characteristic
810	#117	C₂³×C₆₇	1	2	yes	—
811	#117	C₂³×C₆₇	1	2	yes	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	2	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
819	C₂×C₄²	—	2	1	no	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
822	#107	C₂³×C₆₇	1	1	yes	characteristic
823	#107	C₂³×C₆₇	1	2	yes	—
824	#107	C₂³×C₆₇	1	1	yes	characteristic
825	#107	C₂³×C₆₇	1	2	yes	—
826	#107	C₂³×C₆₇	1	2	yes	—
827	#106	C₂³×C₆₇	1	2	yes	—
828	#106	C₂³×C₆₇	1	1	yes	characteristic
829	#106	C₂³×C₆₇	1	2	yes	—
830	#106	C₂³×C₆₇	1	1	yes	characteristic
831	#106	C₂³×C₆₇	1	2	yes	—
832	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
835	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
836	#103	C₂³×C₆₇	1	1	yes	characteristic
837	#103	C₂³×C₆₇	1	2	yes	—
838	#103	C₂³×C₆₇	1	2	yes	—
839	#103	C₂³×C₆₇	1	2	yes	—
840	#103	C₂³×C₆₇	1	2	yes	—
841	#103	C₂³×C₆₇	1	2	yes	—
842	#103	C₂³×C₆₇	1	1	yes	characteristic
843	#103	C₂³×C₆₇	1	1	yes	characteristic
844	#103	C₂³×C₆₇	1	1	yes	characteristic
845	#103	C₂³×C₆₇	1	1	yes	characteristic
846	#103	C₂³×C₆₇	1	1	yes	characteristic
847	#103	C₂³×C₆₇	1	2	yes	—
848	#103	C₂³×C₆₇	1	2	yes	—
849	#103	C₂³×C₆₇	1	2	yes	—
850	#103	C₂³×C₆₇	1	2	yes	—
851	#103	C₂³×C₆₇	1	2	yes	—
852	#103	C₂³×C₆₇	1	2	yes	—
853	#102	C₂³×C₆₇	1	1	yes	characteristic
854	#102	C₂³×C₆₇	1	2	yes	—
855	#102	C₂³×C₆₇	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
859	#97	C₂³×C₆₇	1	1	yes	characteristic
860	#97	C₂³×C₆₇	1	1	yes	characteristic
861	#97	C₂³×C₆₇	1	2	yes	—
862	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₆₇	1	2	yes	—
865	C₄×C₈	C₂³×C₆₇	1	2	yes	—
866	#41	—	2	2	no	—
867	#41	—	2	4	no	—
868	#41	—	4	2	no	—
869	#41	—	4	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	4	no	—
876	C₂×Q₈	—	4	2	no	—
877	C₂×Q₈	—	4	1	no	—
878	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
887	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
888	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
899	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
902	Q₁₆	—	2	2	no	—
903	Q₁₆	—	2	4	no	—
904	Q₁₆	—	2	2	no	—
905	Q₁₆	—	2	4	no	—
906	Q₁₆	—	4	2	no	—
907	Q₁₆	—	4	2	no	—
908	Q₁₆	—	4	2	no	—
909	SD₁₆	—	2	2	no	—
910	SD₁₆	—	2	4	no	—
911	SD₁₆	#41×C₆₇	1	4	yes	—
912	M₁₆	—	2	2	no	—
913	M₁₆	—	2	4	no	—
914	M₁₆	—	4	1	no	—
915	C₂×C₈	—	4	2	no	—
916	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
917	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
921	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
979	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
997	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
998	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
999	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₆₇	1	2	yes	—
1001	C₂³	—	2	1	no	—
1002	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1003	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1004	Q₈	—	2	2	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	4	4	no	—
1015	Q₈	—	4	2	no	—
1016	Q₈	—	4	2	no	—
1017	Q₈	—	8	1	no	—
1018	Q₈	C₂×#41×C₆₇	1	2	yes	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	4	no	—
1023	D₄	—	4	2	no	—
1024	D₄	C₂×#41×C₆₇	1	2	yes	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	8	1	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1059	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1060	C₈	—	2	1	no	—
1061	C₈	—	2	2	no	—
1062	C₈	—	2	1	no	—
1063	C₈	—	2	2	no	—
1064	C₈	—	2	1	no	—
1065	C₈	C₂×#41×C₆₇	1	2	yes	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	1	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	#578×C₆₇	1	2	yes	—
1095	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1096	C₄	#585×C₆₇	1	1	yes	characteristic
1097	C₂	—	4	1	no	—
1098	C₂	—	4	2	no	—
1099	C₂	—	4	2	no	—
1100	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1101	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1102	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3523	C₂	semidirect
3. C₆₇×#3395	C₂	semidirect
4. C₆₇×#3381	C₂	semidirect
5. C₆₇×#3374	C₂	semidirect
6. C₆₇×#3372	C₂	semidirect
7. C₆₇×#3356	C₂	semidirect
8. C₆₇×#3352	C₂	semidirect
9. C₆₇×#3315	C₂	semidirect
10. C₆₇×#3312	C₂	semidirect
11. C₆₇×#3302	C₂	semidirect
12. C₆₇×#3299	C₂	semidirect
13. C₆₇×#3276	C₂	semidirect
14. C₆₇×#3276	C₂	semidirect
15. C₆₇×#3185	C₂	semidirect
16. C₆₇×#3177	C₂	semidirect
17. C₆₇×#3127	C₂	semidirect
18. C₆₇×#3120	C₂	semidirect
19. C₆₇×#3107	C₂	semidirect
20. C₆₇×#3104	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₄×#137×C₆₇	C₂	semidirect
545. #61552	C₆₇	direct (N × H)
552. #3523	C₂×C₆₇	semidirect
554. #3395	C₂×C₆₇	semidirect
555. #3381	C₂×C₆₇	semidirect
556. #3374	C₂×C₆₇	semidirect
557. #3372	C₂×C₆₇	semidirect
558. #3356	C₂×C₆₇	semidirect
559. #3352	C₂×C₆₇	semidirect
560. #3315	C₂×C₆₇	semidirect
561. #3312	C₂×C₆₇	semidirect
562. #3302	C₂×C₆₇	semidirect
563. #3299	C₂×C₆₇	semidirect
564. #3276	C₂×C₆₇	semidirect
565. #3276	C₂×C₆₇	semidirect
566. #3185	C₂×C₆₇	semidirect
567. #3177	C₂×C₆₇	semidirect
568. #3127	C₂×C₆₇	semidirect
569. #3120	C₂×C₆₇	semidirect
570. #3107	C₂×C₆₇	semidirect
571. #3104	C₂×C₆₇	semidirect
572. #2969	C₂×C₆₇	semidirect
573. #2947	C₂×C₆₇	semidirect
574. C₄×#137	C₂×C₆₇	semidirect
575. C₆₇	#61552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3523	2
C₆₇×#3515	2
C₆₇×#3395	2
C₆₇×#3381	2
C₆₇×#3374	2
C₆₇×#3372	2
C₆₇×#3356	2
C₆₇×#3352	2
C₆₇×#3315	2
C₆₇×#3312	2
C₆₇×#3302	2
C₆₇×#3299	2
C₆₇×#3276	2
C₆₇×#3185	2
C₆₇×#3177	2
C₆₇×#3127	2
C₆₇×#3120	2
C₆₇×#3107	2
C₆₇×#3104	2
C₆₇×#2969	2
C₆₇×#2947	2
C₄×#137×C₆₇	2
#61552	67

Subgroups — C67×#61552 #30740803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61552 #30740803