Subgroups — C₆₇×#34253 #30713504

Order 17152.

2426 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2353	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2352	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2347	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2345	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2344	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2320	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2319	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2311	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2295	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2293	C₂	1	2	yes	maximal, complemented
15	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2274	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	#520×C₆₇	C₄	1	16	yes	complemented
20	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
23	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₇	C₂²	1	4	yes	—
26	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₇	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#391×C₆₇	C₂²	1	1	yes	characteristic
34	#391×C₆₇	C₂²	1	2	yes	—
35	#391×C₆₇	C₂²	1	1	yes	characteristic
36	#390×C₆₇	C₂²	1	1	yes	characteristic
37	#390×C₆₇	C₂²	1	2	yes	—
38	#390×C₆₇	C₂²	1	1	yes	characteristic
39	#389×C₆₇	C₂²	1	2	yes	—
40	#389×C₆₇	C₂²	1	2	yes	—
41	#389×C₆₇	C₂²	1	2	yes	—
42	#389×C₆₇	C₂²	1	2	yes	—
43	#389×C₆₇	C₂²	1	2	yes	—
44	#389×C₆₇	C₂²	1	2	yes	—
45	#389×C₆₇	C₂²	1	2	yes	—
46	#389×C₆₇	C₂²	1	2	yes	—
47	#388×C₆₇	C₂²	1	4	yes	—
48	#388×C₆₇	C₂²	1	4	yes	—
49	#388×C₆₇	C₂²	1	4	yes	—
50	#388×C₆₇	C₂²	1	4	yes	—
51	#387×C₆₇	C₂²	1	4	yes	—
52	#387×C₆₇	C₂²	1	4	yes	—
53	#387×C₆₇	C₂²	1	4	yes	—
54	#387×C₆₇	C₂²	1	4	yes	—
55	#386×C₆₇	C₂²	1	2	yes	—
56	#386×C₆₇	C₂²	1	2	yes	—
57	#386×C₆₇	C₂²	1	4	yes	—
58	#383×C₆₇	C₂²	1	4	yes	—
59	#382×C₆₇	C₂²	1	4	yes	—
60	#381×C₆₇	C₂²	1	4	yes	—
61	#380×C₆₇	C₂²	1	2	yes	—
62	#380×C₆₇	C₂²	1	2	yes	—
63	#380×C₆₇	C₂²	1	4	yes	—
64	#380×C₆₇	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
80	#376×C₆₇	C₂²	1	2	yes	—
81	#376×C₆₇	C₂²	1	4	yes	—
82	C₂×#95×C₆₇	C₂²	1	2	yes	—
83	C₄³×C₆₇	C₂²	1	2	yes	—
84	C₂×#41×C₆₇	—	2	4	no	—
85	C₂×#41×C₆₇	—	2	4	no	—
86	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
93	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
98	C₄×D₄×C₆₇	C₂×C₄	1	32	yes	—
99	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
100	#117×C₆₇	—	2	4	no	—
101	#117×C₆₇	—	2	4	no	—
102	#117×C₆₇	—	4	8	no	—
103	#117×C₆₇	C₂×C₄	1	8	yes	—
104	#117×C₆₇	C₂×C₄	1	16	yes	complemented
105	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
106	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
107	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
108	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₄²×C₆₇	—	2	4	no	—
135	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
147	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
149	#95×C₆₇	C₂³	1	4	yes	—
150	#95×C₆₇	C₂³	1	4	yes	—
151	#95×C₆₇	C₂³	1	2	yes	—
152	#95×C₆₇	C₂³	1	2	yes	—
153	#95×C₆₇	C₂³	1	2	yes	—
154	#95×C₆₇	C₂³	1	2	yes	—
155	#95×C₆₇	C₂³	1	2	yes	—
156	#95×C₆₇	C₂³	1	4	yes	—
157	#95×C₆₇	C₂³	1	4	yes	—
158	#95×C₆₇	C₂³	1	4	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	4	yes	—
162	#95×C₆₇	C₂³	1	2	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
166	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
167	#41×C₆₇	—	2	32	no	—
168	C₂×Q₈×C₆₇	—	2	2	no	—
169	C₂×Q₈×C₆₇	—	2	2	no	—
170	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	2	no	—
174	C₂×D₄×C₆₇	—	2	2	no	—
175	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₆₇	—	2	4	no	—
178	C₂²×C₄×C₆₇	—	2	4	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	—	2	2	no	—
183	C₂²×C₄×C₆₇	—	2	2	no	—
184	C₂²×C₄×C₆₇	—	4	2	no	—
185	C₂²×C₄×C₆₇	—	4	4	no	—
186	C₂²×C₄×C₆₇	—	4	1	no	—
187	C₂²×C₄×C₆₇	—	4	1	no	—
188	C₂²×C₄×C₆₇	—	4	4	no	—
189	C₂²×C₄×C₆₇	—	4	2	no	—
190	C₂²×C₄×C₆₇	—	4	2	no	—
191	C₂²×C₄×C₆₇	—	4	2	no	—
192	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
193	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
194	C₂²×C₄×C₆₇	C₂²×C₄	1	16	yes	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₆₇	#41	1	4	yes	—
197	C₂²×C₄×C₆₇	#41	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₇	—	2	4	no	—
214	C₄⋊C₄×C₆₇	—	2	4	no	—
215	C₄⋊C₄×C₆₇	—	2	2	no	—
216	C₄⋊C₄×C₆₇	—	2	2	no	—
217	C₄⋊C₄×C₆₇	—	2	2	no	—
218	C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₄⋊C₄×C₆₇	—	2	8	no	—
220	C₄⋊C₄×C₆₇	—	4	4	no	—
221	C₄⋊C₄×C₆₇	—	4	4	no	—
222	C₄⋊C₄×C₆₇	—	4	4	no	—
223	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
224	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
225	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
226	C₄⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
227	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	4	no	—
230	C₂²⋊C₄×C₆₇	—	2	4	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	4	2	no	—
233	C₂²⋊C₄×C₆₇	—	4	4	no	—
234	C₂²⋊C₄×C₆₇	—	4	2	no	—
235	C₂²⋊C₄×C₆₇	—	4	4	no	—
236	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
237	C₂²⋊C₄×C₆₇	C₂²×C₄	1	16	yes	—
238	C₄²×C₆₇	—	2	2	no	—
239	C₄²×C₆₇	—	2	2	no	—
240	C₄²×C₆₇	—	2	2	no	—
241	C₄²×C₆₇	—	2	2	no	—
242	C₄²×C₆₇	—	2	4	no	—
243	C₄²×C₆₇	—	2	4	no	—
244	C₄²×C₆₇	—	2	4	no	—
245	C₄²×C₆₇	—	2	4	no	—
246	C₄²×C₆₇	—	4	2	no	—
247	C₄²×C₆₇	—	4	4	no	—
248	C₄²×C₆₇	—	4	2	no	—
249	C₄²×C₆₇	—	4	4	no	—
250	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
251	C₄²×C₆₇	C₂²×C₄	1	16	yes	—
252	C₂³×C₆₇	—	2	1	no	—
253	C₂³×C₆₇	—	2	1	no	—
254	C₂³×C₆₇	—	2	1	no	—
255	C₂³×C₆₇	—	2	1	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	—	2	2	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	2	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
263	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
264	C₂³×C₆₇	C₂×#41	1	2	yes	—
265	C₂³×C₆₇	C₂×#41	1	2	yes	—
266	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
267	Q₈×C₆₇	—	2	8	no	—
268	D₄×C₆₇	—	2	16	no	—
269	D₄×C₆₇	—	2	8	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	1	no	—
279	C₂×C₄×C₆₇	—	2	1	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	4	no	—
282	C₂×C₄×C₆₇	—	2	16	no	—
283	C₂×C₄×C₆₇	—	2	1	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	4	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	1	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	4	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	4	8	no	—
305	C₂×C₄×C₆₇	—	4	16	no	—
306	C₂×C₄×C₆₇	—	4	4	no	—
307	C₂×C₄×C₆₇	—	4	4	no	—
308	C₂×C₄×C₆₇	—	8	4	no	—
309	C₂×C₄×C₆₇	#117	1	16	yes	complemented
310	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
312	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
313	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
314	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
315	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
316	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
317	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
318	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
319	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
320	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
322	C₂²×C₆₇	—	2	2	no	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	2	2	no	—
325	C₂²×C₆₇	—	2	2	no	—
326	C₂²×C₆₇	—	2	2	no	—
327	C₂²×C₆₇	—	2	2	no	—
328	C₂²×C₆₇	—	2	4	no	—
329	C₂²×C₆₇	—	2	4	no	—
330	C₂²×C₆₇	—	2	4	no	—
331	C₂²×C₆₇	—	4	2	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	C₂×#117	1	4	yes	—
336	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
337	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
338	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
341	C₂²×C₆₇	#585	1	1	yes	characteristic
342	C₂²×C₆₇	#585	1	1	yes	characteristic
343	C₄×C₆₇	—	2	4	no	—
344	C₄×C₆₇	—	2	4	no	—
345	C₄×C₆₇	—	2	8	no	—
346	C₄×C₆₇	—	2	4	no	—
347	C₄×C₆₇	—	2	2	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	4	1	no	—
350	C₄×C₆₇	—	4	4	no	—
351	C₄×C₆₇	—	4	1	no	—
352	C₄×C₆₇	—	4	2	no	—
353	C₄×C₆₇	—	4	2	no	—
354	C₄×C₆₇	—	4	2	no	—
355	C₄×C₆₇	—	4	2	no	—
356	C₄×C₆₇	C₂×#117	1	4	yes	—
357	C₄×C₆₇	C₂×#117	1	4	yes	—
358	#34253	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
359	C₂×C₆₇	—	2	4	no	—
360	C₂×C₆₇	—	4	4	no	—
361	C₂×C₆₇	C₂²×#117	1	1	yes	characteristic
362	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
364	C₂×C₆₇	#3494	1	1	yes	characteristic
365	C₂×C₆₇	#3495	1	1	yes	characteristic
366	C₂×C₆₇	#3511	1	1	yes	characteristic
367	C₂×C₆₇	#3512	1	1	yes	characteristic
368	C₂×#520	C₂×C₆₇	1	1	yes	characteristic
369	#2353	C₂×C₆₇	1	4	yes	complemented
370	#2352	C₂×C₆₇	1	4	yes	complemented
371	#2347	C₂×C₆₇	1	2	yes	complemented
372	#2346	C₂×C₆₇	1	2	yes	complemented
373	#2345	C₂×C₆₇	1	2	yes	complemented
374	#2344	C₂×C₆₇	1	2	yes	complemented
375	#2320	C₂×C₆₇	1	2	yes	complemented
376	#2319	C₂×C₆₇	1	2	yes	complemented
377	#2316	C₂×C₆₇	1	1	yes	characteristic, complemented
378	#2311	C₂×C₆₇	1	1	yes	characteristic
379	#2297	C₂×C₆₇	1	1	yes	characteristic
380	#2295	C₂×C₆₇	1	2	yes	complemented
381	#2293	C₂×C₆₇	1	2	yes	complemented
382	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
383	#2274	C₂×C₆₇	1	1	yes	characteristic, complemented
384	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₆₇	#34253	1	1	yes	characteristic, direct product factor, Sylow
386	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
387	#520	C₄×C₆₇	1	16	yes	complemented
388	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
389	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
390	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
391	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
392	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
393	C₂×#117	C₂²×C₆₇	1	4	yes	—
394	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
395	C₂×#117	C₂²×C₆₇	1	2	yes	—
396	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
398	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
400	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
401	#391	C₂²×C₆₇	1	2	yes	—
402	#391	C₂²×C₆₇	1	1	yes	characteristic
403	#391	C₂²×C₆₇	1	1	yes	characteristic
404	#390	C₂²×C₆₇	1	2	yes	—
405	#390	C₂²×C₆₇	1	1	yes	characteristic
406	#390	C₂²×C₆₇	1	1	yes	characteristic
407	#389	C₂²×C₆₇	1	2	yes	—
408	#389	C₂²×C₆₇	1	2	yes	—
409	#389	C₂²×C₆₇	1	2	yes	—
410	#389	C₂²×C₆₇	1	2	yes	—
411	#389	C₂²×C₆₇	1	2	yes	—
412	#389	C₂²×C₆₇	1	2	yes	—
413	#389	C₂²×C₆₇	1	2	yes	—
414	#389	C₂²×C₆₇	1	2	yes	—
415	#388	C₂²×C₆₇	1	4	yes	—
416	#388	C₂²×C₆₇	1	4	yes	—
417	#388	C₂²×C₆₇	1	4	yes	—
418	#388	C₂²×C₆₇	1	4	yes	—
419	#387	C₂²×C₆₇	1	4	yes	—
420	#387	C₂²×C₆₇	1	4	yes	—
421	#387	C₂²×C₆₇	1	4	yes	—
422	#387	C₂²×C₆₇	1	4	yes	—
423	#386	C₂²×C₆₇	1	4	yes	—
424	#386	C₂²×C₆₇	1	2	yes	—
425	#386	C₂²×C₆₇	1	2	yes	—
426	#383	C₂²×C₆₇	1	4	yes	—
427	#382	C₂²×C₆₇	1	4	yes	—
428	#381	C₂²×C₆₇	1	4	yes	—
429	#380	C₂²×C₆₇	1	2	yes	—
430	#380	C₂²×C₆₇	1	2	yes	—
431	#380	C₂²×C₆₇	1	4	yes	—
432	#380	C₂²×C₆₇	1	4	yes	—
433	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
445	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
446	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
447	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
448	#376	C₂²×C₆₇	1	2	yes	—
449	#376	C₂²×C₆₇	1	4	yes	—
450	C₂×#95	C₂²×C₆₇	1	2	yes	—
451	C₄³	C₂²×C₆₇	1	2	yes	—
452	C₂×#41	—	2	4	no	—
453	C₂×#41	—	2	4	no	—
454	C₂×#41	C₂×C₄×C₆₇	1	8	yes	—
455	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
457	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
461	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
462	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
463	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
464	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
465	C₄×Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
466	C₄×D₄	C₂×C₄×C₆₇	1	32	yes	—
467	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
468	#117	—	2	4	no	—
469	#117	—	2	4	no	—
470	#117	—	4	8	no	—
471	#117	C₂×C₄×C₆₇	1	8	yes	—
472	#117	C₂×C₄×C₆₇	1	16	yes	complemented
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	—	4	4	no	—
475	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
476	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
502	C₂×C₄²	—	2	4	no	—
503	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
504	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
505	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
512	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
513	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
515	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
517	#95	C₂³×C₆₇	1	4	yes	—
518	#95	C₂³×C₆₇	1	4	yes	—
519	#95	C₂³×C₆₇	1	2	yes	—
520	#95	C₂³×C₆₇	1	2	yes	—
521	#95	C₂³×C₆₇	1	2	yes	—
522	#95	C₂³×C₆₇	1	2	yes	—
523	#95	C₂³×C₆₇	1	2	yes	—
524	#95	C₂³×C₆₇	1	4	yes	—
525	#95	C₂³×C₆₇	1	4	yes	—
526	#95	C₂³×C₆₇	1	4	yes	—
527	#95	C₂³×C₆₇	1	4	yes	—
528	#95	C₂³×C₆₇	1	2	yes	—
529	#95	C₂³×C₆₇	1	4	yes	—
530	#95	C₂³×C₆₇	1	2	yes	—
531	#95	C₂³×C₆₇	1	2	yes	—
532	#95	C₂³×C₆₇	1	4	yes	—
533	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
534	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
535	#41	—	2	32	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
544	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
561	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
562	C₂²×C₄	C₂²×C₄×C₆₇	1	16	yes	—
563	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
564	C₂²×C₄	#41×C₆₇	1	4	yes	—
565	C₂²×C₄	#41×C₆₇	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	—	4	4	no	—
591	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
592	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
593	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
594	C₄⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
595	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
605	C₂²⋊C₄	C₂²×C₄×C₆₇	1	16	yes	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	2	4	no	—
613	C₄²	—	2	4	no	—
614	C₄²	—	4	4	no	—
615	C₄²	—	4	2	no	—
616	C₄²	—	4	4	no	—
617	C₄²	—	4	2	no	—
618	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
619	C₄²	C₂²×C₄×C₆₇	1	16	yes	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
631	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
632	C₂³	C₂×#41×C₆₇	1	2	yes	—
633	C₂³	C₂×#41×C₆₇	1	2	yes	—
634	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
635	Q₈	—	2	8	no	—
636	D₄	—	2	16	no	—
637	D₄	—	2	8	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	16	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	4	8	no	—
673	C₂×C₄	—	4	16	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	#117×C₆₇	1	16	yes	complemented
678	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
679	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
680	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
681	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
682	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
683	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
684	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
685	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
686	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
687	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
688	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
689	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	C₂×#117×C₆₇	1	4	yes	—
704	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
705	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
706	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
707	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
708	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
709	C₂²	#585×C₆₇	1	1	yes	characteristic
710	C₂²	#585×C₆₇	1	1	yes	characteristic
711	C₄	—	2	4	no	—
712	C₄	—	2	4	no	—
713	C₄	—	2	8	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	4	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	C₂×#117×C₆₇	1	4	yes	—
725	C₄	C₂×#117×C₆₇	1	4	yes	—
726	C₂	—	2	4	no	—
727	C₂	—	4	4	no	—
728	C₂	C₂²×#117×C₆₇	1	1	yes	characteristic
729	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
730	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
731	C₂	C₆₇×#3494	1	1	yes	characteristic
732	C₂	C₆₇×#3495	1	1	yes	characteristic
733	C₂	C₆₇×#3511	1	1	yes	characteristic
734	C₂	C₆₇×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2353	C₂	semidirect
3. C₆₇×#2352	C₂	semidirect
4. C₆₇×#2347	C₂	semidirect
5. C₆₇×#2346	C₂	semidirect
6. C₆₇×#2345	C₂	semidirect
7. C₆₇×#2344	C₂	semidirect
8. C₆₇×#2320	C₂	semidirect
9. C₆₇×#2319	C₂	semidirect
10. C₆₇×#2316	C₂	semidirect
13. C₆₇×#2295	C₂	semidirect
14. C₆₇×#2293	C₂	semidirect
15. C₂×#389×C₆₇	C₂	semidirect
16. C₆₇×#2274	C₂	semidirect
17. C₄×#117×C₆₇	C₂	semidirect
19. #520×C₆₇	C₄	semidirect
97. C₄×Q₈×C₆₇	C₂×C₄	semidirect
99. C₄×D₄×C₆₇	C₂×C₄	semidirect
104. #117×C₆₇	C₂×C₄	semidirect
108. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
309. C₂×C₄×C₆₇	#117	semidirect
358. #34253	C₆₇	direct (N × H)
369. #2353	C₂×C₆₇	semidirect
370. #2352	C₂×C₆₇	semidirect
371. #2347	C₂×C₆₇	semidirect
372. #2346	C₂×C₆₇	semidirect
373. #2345	C₂×C₆₇	semidirect
374. #2344	C₂×C₆₇	semidirect
375. #2320	C₂×C₆₇	semidirect
376. #2319	C₂×C₆₇	semidirect
377. #2316	C₂×C₆₇	semidirect
380. #2295	C₂×C₆₇	semidirect
381. #2293	C₂×C₆₇	semidirect
382. C₂×#389	C₂×C₆₇	semidirect
383. #2274	C₂×C₆₇	semidirect
384. C₄×#117	C₂×C₆₇	semidirect
385. C₆₇	#34253	direct (N × H)
387. #520	C₄×C₆₇	semidirect
465. C₄×Q₈	C₂×C₄×C₆₇	semidirect
467. C₄×D₄	C₂×C₄×C₆₇	semidirect
472. #117	C₂×C₄×C₆₇	semidirect
476. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
677. C₂×C₄	#117×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#520×C₆₇	2
C₆₇×#2353	2
C₆₇×#2352	2
C₆₇×#2347	2
C₆₇×#2346	2
C₆₇×#2345	2
C₆₇×#2344	2
C₆₇×#2320	2
C₆₇×#2319	2
C₆₇×#2316	2
C₆₇×#2311	2
C₆₇×#2297	2
C₆₇×#2295	2
C₆₇×#2293	2
C₂×#389×C₆₇	2
C₆₇×#2274	2
C₄×#117×C₆₇	2
#34253	67

Subgroups — C67×#34253 #30713504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34253 #30713504