Subgroups — C₆₇×#61334 #30740585

Order 17152.

1794 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3377	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3375	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3371	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3368	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3136	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3083	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3043	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
15	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₆₇	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	#559×C₆₇	C₂²	1	4	yes	—
19	Q₈²×C₆₇	—	2	1	no	—
20	Q₈²×C₆₇	C₂²	1	2	yes	complemented
21	#557×C₆₇	—	2	1	no	—
22	#557×C₆₇	—	2	2	no	—
23	#557×C₆₇	C₂²	1	4	yes	complemented
24	#557×C₆₇	C₂²	1	2	yes	complemented
25	#556×C₆₇	C₂²	1	2	yes	—
26	#555×C₆₇	—	2	1	no	—
27	#553×C₆₇	—	2	2	no	—
28	#550×C₆₇	C₂²	1	2	yes	—
29	#547×C₆₇	—	2	1	no	—
30	#544×C₆₇	—	2	2	no	—
31	#544×C₆₇	C₂²	1	2	yes	—
32	#538×C₆₇	—	2	2	no	—
33	#535×C₆₇	C₂²	1	2	yes	—
34	#533×C₆₇	—	2	2	no	—
35	#533×C₆₇	C₂²	1	1	yes	characteristic
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#532×C₆₇	C₂²	1	1	yes	characteristic
38	#525×C₆₇	—	2	2	no	—
39	#520×C₆₇	C₂²	1	2	yes	—
40	#519×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#491×C₆₇	C₂²	1	2	yes	complemented
44	#490×C₆₇	C₂²	1	4	yes	—
45	#490×C₆₇	C₂²	1	2	yes	complemented
46	#489×C₆₇	C₂²	1	4	yes	—
47	#489×C₆₇	C₂²	1	2	yes	complemented
48	#489×C₆₇	C₂²	1	2	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	—
50	#486×C₆₇	C₂²	1	4	yes	—
51	#479×C₆₇	C₂²	1	4	yes	complemented
52	#478×C₆₇	C₂²	1	4	yes	—
53	#478×C₆₇	C₂²	1	4	yes	complemented
54	#477×C₆₇	C₂²	1	4	yes	complemented
55	#476×C₆₇	C₂²	1	2	yes	—
56	#474×C₆₇	C₂²	1	2	yes	—
57	#474×C₆₇	C₂²	1	4	yes	complemented
58	#464×C₆₇	C₂²	1	4	yes	—
59	#464×C₆₇	C₂²	1	4	yes	—
60	#464×C₆₇	C₂²	1	4	yes	complemented
61	#462×C₆₇	C₂²	1	2	yes	complemented
62	#460×C₆₇	C₂²	1	4	yes	—
63	#460×C₆₇	C₂²	1	4	yes	—
64	#460×C₆₇	C₂²	1	2	yes	complemented
65	#446×C₆₇	C₂²	1	4	yes	complemented
66	#446×C₆₇	C₂²	1	4	yes	complemented
67	#441×C₆₇	C₂²	1	4	yes	complemented
68	#440×C₆₇	C₂²	1	4	yes	—
69	#440×C₆₇	C₂²	1	4	yes	—
70	#440×C₆₇	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
73	#428×C₆₇	C₂²	1	2	yes	—
74	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
75	#424×C₆₇	C₂²	1	2	yes	—
76	#423×C₆₇	C₂²	1	1	yes	characteristic
77	#418×C₆₇	C₂²	1	2	yes	—
78	#417×C₆₇	C₂²	1	2	yes	—
79	#416×C₆₇	C₂²	1	2	yes	—
80	#416×C₆₇	C₂²	1	2	yes	—
81	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
83	#405×C₆₇	C₂²	1	2	yes	—
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₇	—	2	2	no	—
86	C₂×#41×C₆₇	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	#137×C₆₇	—	2	8	no	—
91	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₇	—	2	4	no	—
93	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
95	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₇	—	2	2	no	—
99	C₄⋊Q₈×C₆₇	—	2	4	no	—
100	C₄⋊Q₈×C₆₇	—	2	2	no	—
101	C₄⋊Q₈×C₆₇	—	2	4	no	—
102	C₄⋊Q₈×C₆₇	—	2	2	no	—
103	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	#127×C₆₇	C₂³	1	4	yes	—
110	#127×C₆₇	C₂³	1	1	yes	characteristic
111	#126×C₆₇	—	2	4	no	—
112	#125×C₆₇	—	2	4	no	—
113	#125×C₆₇	—	2	4	no	—
114	#125×C₆₇	—	2	4	no	—
115	#125×C₆₇	—	2	2	no	—
116	#125×C₆₇	D₄	1	2	yes	—
117	#125×C₆₇	C₂³	1	2	yes	—
118	#125×C₆₇	C₂³	1	4	yes	—
119	#124×C₆₇	—	2	4	no	—
120	#124×C₆₇	C₂³	1	4	yes	—
121	#124×C₆₇	C₂³	1	2	yes	—
122	#123×C₆₇	—	2	4	no	—
123	#123×C₆₇	—	2	4	no	—
124	C₂²⋊Q₈×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	—	2	1	no	—
126	C₂²⋊Q₈×C₆₇	—	2	1	no	—
127	C₂²⋊Q₈×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
130	#121×C₆₇	—	2	1	no	—
131	#121×C₆₇	—	2	1	no	—
132	#121×C₆₇	—	2	2	no	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	4	no	—
136	#120×C₆₇	—	2	4	no	—
137	C₄×Q₈×C₆₇	—	2	2	no	—
138	C₄×Q₈×C₆₇	—	2	2	no	—
139	C₄×Q₈×C₆₇	—	2	2	no	—
140	C₄×Q₈×C₆₇	—	2	4	no	—
141	C₄×Q₈×C₆₇	—	2	2	no	—
142	C₄×Q₈×C₆₇	—	2	1	no	—
143	C₄×Q₈×C₆₇	—	2	1	no	—
144	C₄×Q₈×C₆₇	—	2	1	no	—
145	C₄×Q₈×C₆₇	—	2	1	no	—
146	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
150	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
151	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	4	no	—
155	C₄×D₄×C₆₇	—	2	1	no	—
156	C₄×D₄×C₆₇	—	2	1	no	—
157	C₄×D₄×C₆₇	—	2	1	no	—
158	C₄×D₄×C₆₇	—	2	1	no	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	C₄×D₄×C₆₇	C₂³	1	4	yes	—
161	C₄×D₄×C₆₇	C₂³	1	2	yes	—
162	#117×C₆₇	—	2	2	no	—
163	#117×C₆₇	—	2	2	no	—
164	#117×C₆₇	—	2	4	no	—
165	#117×C₆₇	C₂³	1	2	yes	—
166	#117×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄²×C₆₇	—	2	1	no	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	#107×C₆₇	C₂³	1	4	yes	—
175	#107×C₆₇	C₂³	1	4	yes	—
176	#106×C₆₇	C₂³	1	4	yes	—
177	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
178	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
181	#103×C₆₇	C₂³	1	4	yes	—
182	#103×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#103×C₆₇	C₂³	1	4	yes	—
187	#102×C₆₇	C₂³	1	2	yes	—
188	#102×C₆₇	C₂³	1	2	yes	—
189	#102×C₆₇	C₂³	1	4	yes	—
190	#102×C₆₇	C₂³	1	4	yes	—
191	#102×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	2	yes	—
193	#102×C₆₇	C₂³	1	4	yes	—
194	#102×C₆₇	C₂³	1	2	yes	—
195	#97×C₆₇	C₂³	1	4	yes	—
196	#97×C₆₇	C₂³	1	2	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	C₄×C₈×C₆₇	C₂³	1	4	yes	—
199	C₂⁴×C₆₇	—	2	1	no	—
200	#41×C₆₇	—	2	4	no	—
201	#41×C₆₇	—	2	4	no	—
202	#41×C₆₇	—	8	4	no	—
203	C₂×Q₈×C₆₇	—	2	1	no	—
204	C₂×Q₈×C₆₇	—	2	1	no	—
205	C₂×Q₈×C₆₇	—	2	1	no	—
206	C₂×Q₈×C₆₇	—	2	4	no	—
207	C₂×Q₈×C₆₇	—	2	2	no	—
208	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
211	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
213	C₂×D₄×C₆₇	—	2	2	no	—
214	C₂×D₄×C₆₇	—	2	1	no	—
215	C₂×D₄×C₆₇	—	2	1	no	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	1	no	—
218	C₂×D₄×C₆₇	—	2	4	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	2	no	—
221	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	—	2	1	no	—
226	C₂²×C₄×C₆₇	—	2	2	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	8	2	no	—
231	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	Q₁₆×C₆₇	—	2	8	no	—
235	SD₁₆×C₆₇	—	2	8	no	—
236	SD₁₆×C₆₇	—	2	8	no	—
237	M₁₆×C₆₇	—	2	4	no	—
238	C₂×C₈×C₆₇	—	2	2	no	—
239	C₂×C₈×C₆₇	—	2	2	no	—
240	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
241	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
242	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₆₇	—	2	1	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₄⋊C₄×C₆₇	—	2	2	no	—
247	C₄⋊C₄×C₆₇	—	2	1	no	—
248	C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	1	no	—
252	C₄⋊C₄×C₆₇	—	2	2	no	—
253	C₄⋊C₄×C₆₇	—	2	1	no	—
254	C₄⋊C₄×C₆₇	—	2	1	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	2	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
259	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₆₇	—	2	2	no	—
270	C₂²⋊C₄×C₆₇	—	2	2	no	—
271	C₂²⋊C₄×C₆₇	—	2	2	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	2	no	—
277	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
278	C₄²×C₆₇	—	2	2	no	—
279	C₄²×C₆₇	—	2	2	no	—
280	C₄²×C₆₇	—	2	4	no	—
281	C₄²×C₆₇	—	2	4	no	—
282	C₄²×C₆₇	—	2	4	no	—
283	C₄²×C₆₇	—	2	2	no	—
284	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₄²×C₆₇	C₂⁴	1	4	yes	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	—	4	2	no	—
292	C₂³×C₆₇	—	8	1	no	—
293	C₂³×C₆₇	—	8	1	no	—
294	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₆₇	—	2	4	no	—
296	Q₈×C₆₇	—	2	2	no	—
297	Q₈×C₆₇	—	2	2	no	—
298	Q₈×C₆₇	—	2	2	no	—
299	Q₈×C₆₇	—	4	2	no	—
300	Q₈×C₆₇	—	4	2	no	—
301	Q₈×C₆₇	—	4	2	no	—
302	Q₈×C₆₇	—	8	1	no	—
303	Q₈×C₆₇	—	8	4	no	—
304	Q₈×C₆₇	C₂×#41	1	4	yes	—
305	D₄×C₆₇	—	2	2	no	—
306	D₄×C₆₇	—	2	2	no	—
307	D₄×C₆₇	—	2	2	no	—
308	D₄×C₆₇	—	2	2	no	—
309	D₄×C₆₇	—	4	2	no	—
310	D₄×C₆₇	—	4	4	no	—
311	D₄×C₆₇	—	4	2	no	—
312	D₄×C₆₇	—	8	1	no	—
313	D₄×C₆₇	—	8	4	no	—
314	D₄×C₆₇	—	8	4	no	—
315	C₂×C₄×C₆₇	—	2	4	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	4	1	no	—
323	C₂×C₄×C₆₇	—	4	1	no	—
324	C₂×C₄×C₆₇	—	4	4	no	—
325	C₂×C₄×C₆₇	—	4	4	no	—
326	C₂×C₄×C₆₇	—	8	2	no	—
327	C₂×C₄×C₆₇	—	8	4	no	—
328	C₂×C₄×C₆₇	—	8	1	no	—
329	C₂×C₄×C₆₇	—	8	1	no	—
330	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
338	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
339	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
340	C₈×C₆₇	—	2	2	no	—
341	C₈×C₆₇	—	2	4	no	—
342	C₈×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	2	1	no	—
344	C₂²×C₆₇	—	2	1	no	—
345	C₂²×C₆₇	—	4	2	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	8	4	no	—
352	C₂²×C₆₇	#548	1	2	yes	—
353	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₆₇	—	2	1	no	—
355	C₄×C₆₇	—	2	1	no	—
356	C₄×C₆₇	—	2	4	no	—
357	C₄×C₆₇	—	2	1	no	—
358	C₄×C₆₇	—	2	1	no	—
359	C₄×C₆₇	—	2	4	no	—
360	C₄×C₆₇	—	2	4	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	2	no	—
363	C₄×C₆₇	—	4	2	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	2	no	—
366	C₄×C₆₇	#548	1	2	yes	—
367	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
368	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
369	#61334	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂×C₆₇	—	2	2	no	—
371	C₂×C₆₇	—	8	2	no	—
372	C₂×C₆₇	—	8	2	no	—
373	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
374	C₂×C₆₇	#3585	1	1	yes	characteristic
375	C₂×C₆₇	#3586	1	1	yes	characteristic
376	#3506	C₂×C₆₇	1	1	yes	characteristic
377	#3502	C₂×C₆₇	1	1	yes	characteristic, complemented
378	#3377	C₂×C₆₇	1	4	yes	complemented
379	#3375	C₂×C₆₇	1	4	yes	complemented
380	#3371	C₂×C₆₇	1	4	yes	complemented
381	#3368	C₂×C₆₇	1	4	yes	complemented
382	#3136	C₂×C₆₇	1	2	yes	complemented
383	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
384	#3083	C₂×C₆₇	1	2	yes	complemented
385	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
386	#3043	C₂×C₆₇	1	2	yes	complemented
387	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#2961	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#2947	C₂×C₆₇	1	2	yes	complemented
390	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₆₇	#61334	1	1	yes	characteristic, direct product factor, Sylow
392	C₂×#137	C₂²×C₆₇	1	2	yes	—
393	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
394	#559	C₂²×C₆₇	1	4	yes	—
395	Q₈²	—	2	1	no	—
396	Q₈²	C₂²×C₆₇	1	2	yes	complemented
397	#557	—	2	1	no	—
398	#557	—	2	2	no	—
399	#557	C₂²×C₆₇	1	4	yes	complemented
400	#557	C₂²×C₆₇	1	2	yes	complemented
401	#556	C₂²×C₆₇	1	2	yes	—
402	#555	—	2	1	no	—
403	#553	—	2	2	no	—
404	#550	C₂²×C₆₇	1	2	yes	—
405	#547	—	2	1	no	—
406	#544	—	2	2	no	—
407	#544	C₂²×C₆₇	1	2	yes	—
408	#538	—	2	2	no	—
409	#535	C₂²×C₆₇	1	2	yes	—
410	#533	—	2	2	no	—
411	#533	C₂²×C₆₇	1	1	yes	characteristic
412	#533	C₂²×C₆₇	1	1	yes	characteristic
413	#532	C₂²×C₆₇	1	1	yes	characteristic
414	#525	—	2	2	no	—
415	#520	C₂²×C₆₇	1	2	yes	—
416	#519	C₂²×C₆₇	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
419	#491	C₂²×C₆₇	1	2	yes	complemented
420	#490	C₂²×C₆₇	1	4	yes	—
421	#490	C₂²×C₆₇	1	2	yes	complemented
422	#489	C₂²×C₆₇	1	4	yes	—
423	#489	C₂²×C₆₇	1	2	yes	complemented
424	#489	C₂²×C₆₇	1	2	yes	complemented
425	#488	C₂²×C₆₇	1	4	yes	—
426	#486	C₂²×C₆₇	1	4	yes	—
427	#479	C₂²×C₆₇	1	4	yes	complemented
428	#478	C₂²×C₆₇	1	4	yes	—
429	#478	C₂²×C₆₇	1	4	yes	complemented
430	#477	C₂²×C₆₇	1	4	yes	complemented
431	#476	C₂²×C₆₇	1	2	yes	—
432	#474	C₂²×C₆₇	1	2	yes	—
433	#474	C₂²×C₆₇	1	4	yes	complemented
434	#464	C₂²×C₆₇	1	4	yes	—
435	#464	C₂²×C₆₇	1	4	yes	—
436	#464	C₂²×C₆₇	1	4	yes	complemented
437	#462	C₂²×C₆₇	1	2	yes	complemented
438	#460	C₂²×C₆₇	1	4	yes	—
439	#460	C₂²×C₆₇	1	4	yes	—
440	#460	C₂²×C₆₇	1	2	yes	complemented
441	#446	C₂²×C₆₇	1	4	yes	complemented
442	#446	C₂²×C₆₇	1	4	yes	complemented
443	#441	C₂²×C₆₇	1	4	yes	complemented
444	#440	C₂²×C₆₇	1	4	yes	—
445	#440	C₂²×C₆₇	1	4	yes	—
446	#440	C₂²×C₆₇	1	4	yes	complemented
447	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
448	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
449	#428	C₂²×C₆₇	1	2	yes	—
450	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
451	#424	C₂²×C₆₇	1	2	yes	—
452	#423	C₂²×C₆₇	1	1	yes	characteristic
453	#418	C₂²×C₆₇	1	2	yes	—
454	#417	C₂²×C₆₇	1	2	yes	—
455	#416	C₂²×C₆₇	1	2	yes	—
456	#416	C₂²×C₆₇	1	2	yes	—
457	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
459	#405	C₂²×C₆₇	1	2	yes	—
460	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×#41	—	2	2	no	—
462	C₂×#41	C₂³×C₆₇	1	2	yes	—
463	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
465	C₂³×C₄	—	2	1	no	—
466	#137	—	2	8	no	—
467	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
468	C₂×SD₁₆	—	2	4	no	—
469	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
471	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
472	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	—	2	4	no	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	4	no	—
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
480	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
484	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
485	#127	C₂³×C₆₇	1	1	yes	characteristic
486	#127	C₂³×C₆₇	1	4	yes	—
487	#126	—	2	4	no	—
488	#125	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	—	2	4	no	—
491	#125	—	2	2	no	—
492	#125	D₄×C₆₇	1	2	yes	—
493	#125	C₂³×C₆₇	1	2	yes	—
494	#125	C₂³×C₆₇	1	4	yes	—
495	#124	—	2	4	no	—
496	#124	C₂³×C₆₇	1	2	yes	—
497	#124	C₂³×C₆₇	1	4	yes	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
505	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	2	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	4	no	—
512	#120	—	2	4	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	4	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
523	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
524	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
525	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
526	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
527	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
528	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	C₂³×C₆₇	1	2	yes	—
536	C₄×D₄	C₂³×C₆₇	1	2	yes	—
537	C₄×D₄	C₂³×C₆₇	1	4	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	4	no	—
541	#117	C₂³×C₆₇	1	2	yes	—
542	#117	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₄²	—	2	1	no	—
549	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
550	#107	C₂³×C₆₇	1	4	yes	—
551	#107	C₂³×C₆₇	1	4	yes	—
552	#106	C₂³×C₆₇	1	4	yes	—
553	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
554	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
555	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
556	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
557	#103	C₂³×C₆₇	1	4	yes	—
558	#103	C₂³×C₆₇	1	2	yes	—
559	#103	C₂³×C₆₇	1	2	yes	—
560	#103	C₂³×C₆₇	1	2	yes	—
561	#103	C₂³×C₆₇	1	2	yes	—
562	#103	C₂³×C₆₇	1	4	yes	—
563	#102	C₂³×C₆₇	1	4	yes	—
564	#102	C₂³×C₆₇	1	2	yes	—
565	#102	C₂³×C₆₇	1	2	yes	—
566	#102	C₂³×C₆₇	1	2	yes	—
567	#102	C₂³×C₆₇	1	2	yes	—
568	#102	C₂³×C₆₇	1	4	yes	—
569	#102	C₂³×C₆₇	1	4	yes	—
570	#102	C₂³×C₆₇	1	4	yes	—
571	#97	C₂³×C₆₇	1	2	yes	—
572	#97	C₂³×C₆₇	1	2	yes	—
573	#97	C₂³×C₆₇	1	4	yes	—
574	C₄×C₈	C₂³×C₆₇	1	4	yes	—
575	C₂⁴	—	2	1	no	—
576	#41	—	2	4	no	—
577	#41	—	2	4	no	—
578	#41	—	8	4	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
585	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
586	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
587	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
588	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
598	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	8	2	no	—
607	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
610	Q₁₆	—	2	8	no	—
611	SD₁₆	—	2	8	no	—
612	SD₁₆	—	2	8	no	—
613	M₁₆	—	2	4	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
617	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
618	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
639	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
640	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
662	C₄²	C₂⁴×C₆₇	1	4	yes	—
663	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	2	no	—
678	Q₈	—	8	1	no	—
679	Q₈	—	8	4	no	—
680	Q₈	C₂×#41×C₆₇	1	4	yes	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	1	no	—
690	D₄	—	8	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	8	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
710	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
713	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
714	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
715	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	4	no	—
718	C₈	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	#548×C₆₇	1	2	yes	—
729	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	#548×C₆₇	1	2	yes	—
743	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
744	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	8	2	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
749	C₂	C₆₇×#3585	1	1	yes	characteristic
750	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×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3502	C₂	semidirect
3. C₆₇×#3377	C₂	semidirect
4. C₆₇×#3375	C₂	semidirect
5. C₆₇×#3371	C₂	semidirect
6. C₆₇×#3368	C₂	semidirect
7. C₆₇×#3136	C₂	semidirect
8. C₆₇×#3135	C₂	semidirect
9. C₆₇×#3083	C₂	semidirect
10. C₆₇×#3077	C₂	semidirect
11. C₆₇×#3043	C₂	semidirect
12. C₆₇×#3037	C₂	semidirect
13. C₆₇×#2961	C₂	semidirect
14. C₆₇×#2947	C₂	semidirect
15. C₂×#440×C₆₇	C₂	semidirect
20. Q₈²×C₆₇	C₂²	semidirect
23. #557×C₆₇	C₂²	semidirect
24. #557×C₆₇	C₂²	semidirect
43. #491×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #489×C₆₇	C₂²	semidirect
51. #479×C₆₇	C₂²	semidirect
53. #478×C₆₇	C₂²	semidirect
54. #477×C₆₇	C₂²	semidirect
57. #474×C₆₇	C₂²	semidirect
60. #464×C₆₇	C₂²	semidirect
61. #462×C₆₇	C₂²	semidirect
64. #460×C₆₇	C₂²	semidirect
65. #446×C₆₇	C₂²	semidirect
66. #446×C₆₇	C₂²	semidirect
67. #441×C₆₇	C₂²	semidirect
70. #440×C₆₇	C₂²	semidirect
71. C₄×Q₁₆×C₆₇	C₂²	semidirect
72. C₄×SD₁₆×C₆₇	C₂²	semidirect
210. C₂×Q₈×C₆₇	#41	semidirect
369. #61334	C₆₇	direct (N × H)
377. #3502	C₂×C₆₇	semidirect
378. #3377	C₂×C₆₇	semidirect
379. #3375	C₂×C₆₇	semidirect
380. #3371	C₂×C₆₇	semidirect
381. #3368	C₂×C₆₇	semidirect
382. #3136	C₂×C₆₇	semidirect
383. #3135	C₂×C₆₇	semidirect
384. #3083	C₂×C₆₇	semidirect
385. #3077	C₂×C₆₇	semidirect
386. #3043	C₂×C₆₇	semidirect
387. #3037	C₂×C₆₇	semidirect
388. #2961	C₂×C₆₇	semidirect
389. #2947	C₂×C₆₇	semidirect
390. C₂×#440	C₂×C₆₇	semidirect
391. C₆₇	#61334	direct (N × H)
396. Q₈²	C₂²×C₆₇	semidirect
399. #557	C₂²×C₆₇	semidirect
400. #557	C₂²×C₆₇	semidirect
419. #491	C₂²×C₆₇	semidirect
421. #490	C₂²×C₆₇	semidirect
423. #489	C₂²×C₆₇	semidirect
424. #489	C₂²×C₆₇	semidirect
427. #479	C₂²×C₆₇	semidirect
429. #478	C₂²×C₆₇	semidirect
430. #477	C₂²×C₆₇	semidirect
433. #474	C₂²×C₆₇	semidirect
436. #464	C₂²×C₆₇	semidirect
437. #462	C₂²×C₆₇	semidirect
440. #460	C₂²×C₆₇	semidirect
441. #446	C₂²×C₆₇	semidirect
442. #446	C₂²×C₆₇	semidirect
443. #441	C₂²×C₆₇	semidirect
446. #440	C₂²×C₆₇	semidirect
447. C₄×Q₁₆	C₂²×C₆₇	semidirect
448. C₄×SD₁₆	C₂²×C₆₇	semidirect
586. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₆₇×#3502	2
C₆₇×#3377	2
C₆₇×#3375	2
C₆₇×#3371	2
C₆₇×#3368	2
C₆₇×#3136	2
C₆₇×#3135	2
C₆₇×#3083	2
C₆₇×#3077	2
C₆₇×#3043	2
C₆₇×#3037	2
C₆₇×#2961	2
C₆₇×#2947	2
C₂×#440×C₆₇	2
#61334	67

Subgroups — C67×#61334 #30740585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61334 #30740585