Subgroups — C₆₇×#61832 #30741083

Order 17152.

1674 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic
2	C₂×#557×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3390	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3388	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3377	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3371	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3238	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#3232	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3117	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	#559×C₆₇	C₂²	1	2	yes	—
17	#557×C₆₇	—	2	2	no	—
18	#557×C₆₇	—	2	2	no	—
19	#557×C₆₇	C₂²	1	4	yes	—
20	#557×C₆₇	C₂²	1	4	yes	—
21	#557×C₆₇	C₂²	1	2	yes	—
22	#556×C₆₇	—	2	2	no	—
23	#556×C₆₇	C₂²	1	2	yes	—
24	#554×C₆₇	C₂²	1	2	yes	—
25	#552×C₆₇	—	2	2	no	—
26	#539×C₆₇	—	2	1	no	—
27	#539×C₆₇	—	2	1	no	—
28	#536×C₆₇	—	2	1	no	—
29	#533×C₆₇	C₂²	1	1	yes	characteristic
30	#532×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
32	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	#529×C₆₇	C₂²	1	2	yes	—
34	#529×C₆₇	C₂²	1	2	yes	—
35	C₂×#125×C₆₇	—	2	1	no	—
36	C₂×#125×C₆₇	—	2	1	no	—
37	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
39	#520×C₆₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	#501×C₆₇	C₂²	1	2	yes	—
46	#501×C₆₇	C₂²	1	4	yes	—
47	#501×C₆₇	C₂²	1	2	yes	—
48	#499×C₆₇	C₂²	1	4	yes	—
49	#491×C₆₇	C₂²	1	2	yes	—
50	#490×C₆₇	C₂²	1	2	yes	—
51	#489×C₆₇	C₂²	1	4	yes	—
52	#488×C₆₇	C₂²	1	4	yes	—
53	#484×C₆₇	C₂²	1	2	yes	—
54	#483×C₆₇	C₂²	1	2	yes	—
55	#483×C₆₇	C₂²	1	2	yes	—
56	#481×C₆₇	C₂²	1	2	yes	—
57	#480×C₆₇	C₂²	1	2	yes	—
58	#480×C₆₇	C₂²	1	2	yes	—
59	#479×C₆₇	C₂²	1	4	yes	—
60	#479×C₆₇	C₂²	1	4	yes	—
61	#479×C₆₇	C₂²	1	4	yes	—
62	#479×C₆₇	C₂²	1	4	yes	—
63	#478×C₆₇	C₂²	1	4	yes	—
64	#478×C₆₇	C₂²	1	4	yes	—
65	#477×C₆₇	C₂²	1	2	yes	—
66	#477×C₆₇	C₂²	1	4	yes	—
67	#476×C₆₇	C₂²	1	4	yes	—
68	#475×C₆₇	C₂²	1	2	yes	—
69	#464×C₆₇	C₂²	1	4	yes	—
70	#464×C₆₇	C₂²	1	4	yes	—
71	#462×C₆₇	C₂²	1	2	yes	—
72	#460×C₆₇	C₂²	1	2	yes	—
73	#451×C₆₇	C₂²	1	2	yes	—
74	#448×C₆₇	C₂²	1	2	yes	—
75	#446×C₆₇	C₂²	1	4	yes	—
76	#446×C₆₇	C₂²	1	4	yes	—
77	#441×C₆₇	C₂²	1	4	yes	—
78	#441×C₆₇	C₂²	1	4	yes	—
79	#440×C₆₇	C₂²	1	4	yes	—
80	#440×C₆₇	C₂²	1	4	yes	—
81	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	—
82	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
83	#432×C₆₇	C₂²	1	1	yes	characteristic
84	#432×C₆₇	C₂²	1	1	yes	characteristic
85	#432×C₆₇	C₂²	1	2	yes	—
86	#431×C₆₇	C₂²	1	2	yes	—
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂²×Q₈×C₆₇	—	2	1	no	—
89	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₆₇	—	2	4	no	—
94	C₄⋊Q₈×C₆₇	—	2	4	no	—
95	C₄⋊Q₈×C₆₇	—	2	2	no	—
96	C₄⋊Q₈×C₆₇	—	2	2	no	—
97	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
100	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
101	#127×C₆₇	C₂³	1	1	yes	characteristic
102	#126×C₆₇	—	2	2	no	—
103	#126×C₆₇	—	2	2	no	—
104	#126×C₆₇	—	2	2	no	—
105	#126×C₆₇	—	2	2	no	—
106	#125×C₆₇	—	2	4	no	—
107	#125×C₆₇	—	2	4	no	—
108	#125×C₆₇	—	2	4	no	—
109	#125×C₆₇	—	2	4	no	—
110	#125×C₆₇	—	2	2	no	—
111	#125×C₆₇	—	2	2	no	—
112	#125×C₆₇	—	2	2	no	—
113	#125×C₆₇	—	2	1	no	—
114	#125×C₆₇	—	2	1	no	—
115	#125×C₆₇	—	2	1	no	—
116	#125×C₆₇	C₂³	1	2	yes	—
117	#125×C₆₇	C₂³	1	4	yes	—
118	#125×C₆₇	C₂³	1	2	yes	—
119	#125×C₆₇	C₂³	1	2	yes	—
120	#125×C₆₇	C₂³	1	2	yes	—
121	#124×C₆₇	—	2	2	no	—
122	#124×C₆₇	—	2	1	no	—
123	#124×C₆₇	C₂³	1	2	yes	—
124	#124×C₆₇	C₂³	1	2	yes	—
125	#123×C₆₇	—	2	2	no	—
126	#123×C₆₇	—	2	2	no	—
127	#123×C₆₇	—	2	2	no	—
128	#123×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	2	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	#121×C₆₇	—	2	1	no	—
136	#121×C₆₇	C₂³	1	2	yes	—
137	C₄×Q₈×C₆₇	—	2	4	no	—
138	C₄×Q₈×C₆₇	—	2	4	no	—
139	C₄×Q₈×C₆₇	—	2	2	no	—
140	C₄×Q₈×C₆₇	—	2	2	no	—
141	C₄×Q₈×C₆₇	—	2	1	no	—
142	C₄×Q₈×C₆₇	—	2	1	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	—	2	1	no	—
145	C₄×Q₈×C₆₇	D₄	1	2	yes	—
146	C₄×Q₈×C₆₇	D₄	1	2	yes	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₇	C₂³	1	4	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×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×D₄×C₆₇	—	2	2	no	—
157	C₄×D₄×C₆₇	—	2	2	no	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	C₂³	1	2	yes	—
161	C₄×D₄×C₆₇	C₂³	1	2	yes	—
162	C₄×D₄×C₆₇	C₂³	1	2	yes	—
163	#117×C₆₇	—	2	1	no	—
164	#117×C₆₇	—	2	2	no	—
165	#117×C₆₇	—	2	2	no	—
166	#117×C₆₇	—	2	2	no	—
167	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
175	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
176	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₆₇	—	2	1	no	—
183	C₂×C₄²×C₆₇	—	2	1	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	#107×C₆₇	C₂³	1	4	yes	—
189	#107×C₆₇	C₂³	1	4	yes	—
190	#107×C₆₇	C₂³	1	4	yes	—
191	#106×C₆₇	C₂³	1	4	yes	—
192	#106×C₆₇	C₂³	1	4	yes	—
193	#106×C₆₇	C₂³	1	4	yes	—
194	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
208	#97×C₆₇	C₂³	1	4	yes	—
209	#97×C₆₇	C₂³	1	2	yes	—
210	#97×C₆₇	C₂³	1	2	yes	—
211	C₄×C₈×C₆₇	C₂³	1	4	yes	—
212	#41×C₆₇	—	4	4	no	—
213	C₂×Q₈×C₆₇	—	2	4	no	—
214	C₂×Q₈×C₆₇	—	2	1	no	—
215	C₂×Q₈×C₆₇	—	2	1	no	—
216	C₂×Q₈×C₆₇	—	2	4	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×Q₈×C₆₇	—	4	4	no	—
220	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	1	no	—
226	C₂×D₄×C₆₇	—	2	1	no	—
227	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₇	—	2	1	no	—
229	C₂²×C₄×C₆₇	—	2	1	no	—
230	C₂²×C₄×C₆₇	—	2	1	no	—
231	C₂²×C₄×C₆₇	—	2	1	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₆₇	—	2	8	no	—
243	SD₁₆×C₆₇	—	2	8	no	—
244	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
245	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
246	C₄⋊C₄×C₆₇	—	2	1	no	—
247	C₄⋊C₄×C₆₇	—	2	2	no	—
248	C₄⋊C₄×C₆₇	—	2	2	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	2	no	—
251	C₄⋊C₄×C₆₇	—	2	2	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	2	no	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
273	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₇	—	2	2	no	—
284	C₂²⋊C₄×C₆₇	—	2	2	no	—
285	C₂²⋊C₄×C₆₇	—	2	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₄²×C₆₇	—	2	4	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	2	2	no	—
295	C₄²×C₆₇	—	2	4	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	2	2	no	—
298	C₄²×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	C₂×D₄	1	2	yes	—
300	C₄²×C₆₇	C₂×D₄	1	2	yes	—
301	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₄²×C₆₇	C₂⁴	1	2	yes	—
305	C₄²×C₆₇	C₂⁴	1	2	yes	—
306	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₆₇	—	2	4	no	—
310	Q₈×C₆₇	—	2	2	no	—
311	Q₈×C₆₇	—	2	4	no	—
312	Q₈×C₆₇	—	4	2	no	—
313	Q₈×C₆₇	—	4	2	no	—
314	Q₈×C₆₇	—	4	8	no	—
315	Q₈×C₆₇	—	4	2	no	—
316	Q₈×C₆₇	—	8	1	no	—
317	Q₈×C₆₇	2₋¹⁺⁴	1	4	yes	—
318	D₄×C₆₇	—	2	4	no	—
319	D₄×C₆₇	—	4	2	no	—
320	D₄×C₆₇	—	4	4	no	—
321	D₄×C₆₇	—	8	1	no	—
322	C₂×C₄×C₆₇	—	2	4	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	4	1	no	—
335	C₂×C₄×C₆₇	—	4	1	no	—
336	C₂×C₄×C₆₇	—	4	1	no	—
337	C₂×C₄×C₆₇	—	4	4	no	—
338	C₂×C₄×C₆₇	—	4	2	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	—	4	2	no	—
341	C₂×C₄×C₆₇	—	8	2	no	—
342	C₂×C₄×C₆₇	—	8	2	no	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
353	C₈×C₆₇	—	2	4	no	—
354	C₈×C₆₇	—	2	4	no	—
355	C₂²×C₆₇	—	2	1	no	—
356	C₂²×C₆₇	—	2	1	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	2	no	—
360	C₂²×C₆₇	#575	1	2	yes	—
361	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	2	1	no	—
365	C₄×C₆₇	—	2	1	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	1	no	—
368	C₄×C₆₇	—	2	1	no	—
369	C₄×C₆₇	—	2	1	no	—
370	C₄×C₆₇	—	2	2	no	—
371	C₄×C₆₇	—	2	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
379	#61832	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂×C₆₇	—	2	2	no	—
381	C₂×C₆₇	—	8	2	no	—
382	C₂×C₆₇	#3486	1	1	yes	characteristic
383	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
384	C₂×C₆₇	#3586	1	1	yes	characteristic
385	#3507	C₂×C₆₇	1	1	yes	characteristic
386	C₂×#557	C₂×C₆₇	1	1	yes	characteristic, complemented
387	#3390	C₂×C₆₇	1	4	yes	complemented
388	#3388	C₂×C₆₇	1	4	yes	complemented
389	#3377	C₂×C₆₇	1	4	yes	complemented
390	#3371	C₂×C₆₇	1	4	yes	complemented
391	#3238	C₂×C₆₇	1	2	yes	complemented
392	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#3234	C₂×C₆₇	1	1	yes	characteristic
394	#3232	C₂×C₆₇	1	2	yes	complemented
395	#3117	C₂×C₆₇	1	2	yes	complemented
396	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#3112	C₂×C₆₇	1	1	yes	characteristic
398	#3108	C₂×C₆₇	1	2	yes	complemented
399	#2983	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₆₇	#61832	1	1	yes	characteristic, direct product factor, Sylow
401	#559	C₂²×C₆₇	1	2	yes	—
402	#557	—	2	2	no	—
403	#557	—	2	2	no	—
404	#557	C₂²×C₆₇	1	4	yes	—
405	#557	C₂²×C₆₇	1	4	yes	—
406	#557	C₂²×C₆₇	1	2	yes	—
407	#556	—	2	2	no	—
408	#556	C₂²×C₆₇	1	2	yes	—
409	#554	C₂²×C₆₇	1	2	yes	—
410	#552	—	2	2	no	—
411	#539	—	2	1	no	—
412	#539	—	2	1	no	—
413	#536	—	2	1	no	—
414	#533	C₂²×C₆₇	1	1	yes	characteristic
415	#532	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄⋊Q₈	—	2	1	no	—
417	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
418	#529	C₂²×C₆₇	1	2	yes	—
419	#529	C₂²×C₆₇	1	2	yes	—
420	C₂×#125	—	2	1	no	—
421	C₂×#125	—	2	1	no	—
422	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
424	#520	—	2	1	no	—
425	C₂×C₄×Q₈	—	2	1	no	—
426	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
430	#501	C₂²×C₆₇	1	2	yes	—
431	#501	C₂²×C₆₇	1	4	yes	—
432	#501	C₂²×C₆₇	1	2	yes	—
433	#499	C₂²×C₆₇	1	4	yes	—
434	#491	C₂²×C₆₇	1	2	yes	—
435	#490	C₂²×C₆₇	1	2	yes	—
436	#489	C₂²×C₆₇	1	4	yes	—
437	#488	C₂²×C₆₇	1	4	yes	—
438	#484	C₂²×C₆₇	1	2	yes	—
439	#483	C₂²×C₆₇	1	2	yes	—
440	#483	C₂²×C₆₇	1	2	yes	—
441	#481	C₂²×C₆₇	1	2	yes	—
442	#480	C₂²×C₆₇	1	2	yes	—
443	#480	C₂²×C₆₇	1	2	yes	—
444	#479	C₂²×C₆₇	1	4	yes	—
445	#479	C₂²×C₆₇	1	4	yes	—
446	#479	C₂²×C₆₇	1	4	yes	—
447	#479	C₂²×C₆₇	1	4	yes	—
448	#478	C₂²×C₆₇	1	4	yes	—
449	#478	C₂²×C₆₇	1	4	yes	—
450	#477	C₂²×C₆₇	1	2	yes	—
451	#477	C₂²×C₆₇	1	4	yes	—
452	#476	C₂²×C₆₇	1	4	yes	—
453	#475	C₂²×C₆₇	1	2	yes	—
454	#464	C₂²×C₆₇	1	4	yes	—
455	#464	C₂²×C₆₇	1	4	yes	—
456	#462	C₂²×C₆₇	1	2	yes	—
457	#460	C₂²×C₆₇	1	2	yes	—
458	#451	C₂²×C₆₇	1	2	yes	—
459	#448	C₂²×C₆₇	1	2	yes	—
460	#446	C₂²×C₆₇	1	4	yes	—
461	#446	C₂²×C₆₇	1	4	yes	—
462	#441	C₂²×C₆₇	1	4	yes	—
463	#441	C₂²×C₆₇	1	4	yes	—
464	#440	C₂²×C₆₇	1	4	yes	—
465	#440	C₂²×C₆₇	1	4	yes	—
466	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
467	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
468	#432	C₂²×C₆₇	1	1	yes	characteristic
469	#432	C₂²×C₆₇	1	1	yes	characteristic
470	#432	C₂²×C₆₇	1	2	yes	—
471	#431	C₂²×C₆₇	1	2	yes	—
472	C₂×#41	—	2	1	no	—
473	C₂²×Q₈	—	2	1	no	—
474	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
475	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
476	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
477	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
478	C₄⋊Q₈	—	2	4	no	—
479	C₄⋊Q₈	—	2	4	no	—
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
484	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
485	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
486	#127	C₂³×C₆₇	1	1	yes	characteristic
487	#126	—	2	2	no	—
488	#126	—	2	2	no	—
489	#126	—	2	2	no	—
490	#126	—	2	2	no	—
491	#125	—	2	4	no	—
492	#125	—	2	4	no	—
493	#125	—	2	4	no	—
494	#125	—	2	4	no	—
495	#125	—	2	2	no	—
496	#125	—	2	2	no	—
497	#125	—	2	2	no	—
498	#125	—	2	1	no	—
499	#125	—	2	1	no	—
500	#125	—	2	1	no	—
501	#125	C₂³×C₆₇	1	2	yes	—
502	#125	C₂³×C₆₇	1	4	yes	—
503	#125	C₂³×C₆₇	1	2	yes	—
504	#125	C₂³×C₆₇	1	2	yes	—
505	#125	C₂³×C₆₇	1	2	yes	—
506	#124	—	2	2	no	—
507	#124	—	2	1	no	—
508	#124	C₂³×C₆₇	1	2	yes	—
509	#124	C₂³×C₆₇	1	2	yes	—
510	#123	—	2	2	no	—
511	#123	—	2	2	no	—
512	#123	—	2	2	no	—
513	#123	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
520	#121	—	2	1	no	—
521	#121	C₂³×C₆₇	1	2	yes	—
522	C₄×Q₈	—	2	4	no	—
523	C₄×Q₈	—	2	4	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	D₄×C₆₇	1	2	yes	—
531	C₄×Q₈	D₄×C₆₇	1	2	yes	—
532	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
533	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
534	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
535	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
536	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
537	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
538	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
539	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
540	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	C₂³×C₆₇	1	2	yes	—
546	C₄×D₄	C₂³×C₆₇	1	2	yes	—
547	C₄×D₄	C₂³×C₆₇	1	2	yes	—
548	#117	—	2	1	no	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	2	no	—
561	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
562	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
573	#107	C₂³×C₆₇	1	4	yes	—
574	#107	C₂³×C₆₇	1	4	yes	—
575	#107	C₂³×C₆₇	1	4	yes	—
576	#106	C₂³×C₆₇	1	4	yes	—
577	#106	C₂³×C₆₇	1	4	yes	—
578	#106	C₂³×C₆₇	1	4	yes	—
579	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
580	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
581	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
582	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
583	#103	C₂³×C₆₇	1	4	yes	—
584	#103	C₂³×C₆₇	1	4	yes	—
585	#103	C₂³×C₆₇	1	4	yes	—
586	#103	C₂³×C₆₇	1	4	yes	—
587	#103	C₂³×C₆₇	1	4	yes	—
588	#102	C₂³×C₆₇	1	4	yes	—
589	#102	C₂³×C₆₇	1	4	yes	—
590	#102	C₂³×C₆₇	1	4	yes	—
591	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
592	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
593	#97	C₂³×C₆₇	1	2	yes	—
594	#97	C₂³×C₆₇	1	4	yes	—
595	#97	C₂³×C₆₇	1	2	yes	—
596	C₄×C₈	C₂³×C₆₇	1	4	yes	—
597	#41	—	4	4	no	—
598	C₂×Q₈	—	2	4	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	4	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
606	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
627	Q₁₆	—	2	8	no	—
628	SD₁₆	—	2	8	no	—
629	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
630	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
658	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
659	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	C₂×D₄×C₆₇	1	2	yes	—
685	C₄²	C₂×D₄×C₆₇	1	2	yes	—
686	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
687	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₄²	C₂⁴×C₆₇	1	2	yes	—
689	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₄²	C₂⁴×C₆₇	1	2	yes	—
691	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₂³	—	2	2	no	—
693	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
694	Q₈	—	2	4	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	4	8	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	8	1	no	—
702	Q₈	2₋¹⁺⁴×C₆₇	1	4	yes	—
703	D₄	—	2	4	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	4	no	—
706	D₄	—	8	1	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	—	8	2	no	—
728	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
737	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
738	C₈	—	2	4	no	—
739	C₈	—	2	4	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	#575×C₆₇	1	2	yes	—
746	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
764	C₂	—	2	2	no	—
765	C₂	—	8	2	no	—
766	C₂	C₆₇×#3486	1	1	yes	characteristic
767	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
768	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	#532×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#557×C₆₇	C₂	semidirect
3. C₆₇×#3390	C₂	semidirect
4. C₆₇×#3388	C₂	semidirect
5. C₆₇×#3377	C₂	semidirect
6. C₆₇×#3371	C₂	semidirect
7. C₆₇×#3238	C₂	semidirect
8. C₆₇×#3236	C₂	semidirect
10. C₆₇×#3232	C₂	semidirect
11. C₆₇×#3117	C₂	semidirect
12. C₆₇×#3113	C₂	semidirect
14. C₆₇×#3108	C₂	semidirect
15. C₆₇×#2983	C₂	semidirect
379. #61832	C₆₇	direct (N × H)
386. C₂×#557	C₂×C₆₇	semidirect
387. #3390	C₂×C₆₇	semidirect
388. #3388	C₂×C₆₇	semidirect
389. #3377	C₂×C₆₇	semidirect
390. #3371	C₂×C₆₇	semidirect
391. #3238	C₂×C₆₇	semidirect
392. #3236	C₂×C₆₇	semidirect
394. #3232	C₂×C₆₇	semidirect
395. #3117	C₂×C₆₇	semidirect
396. #3113	C₂×C₆₇	semidirect
398. #3108	C₂×C₆₇	semidirect
399. #2983	C₂×C₆₇	semidirect
400. C₆₇	#61832	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×#3507	2
C₂×#557×C₆₇	2
C₆₇×#3390	2
C₆₇×#3388	2
C₆₇×#3377	2
C₆₇×#3371	2
C₆₇×#3238	2
C₆₇×#3236	2
C₆₇×#3234	2
C₆₇×#3232	2
C₆₇×#3117	2
C₆₇×#3113	2
C₆₇×#3112	2
C₆₇×#3108	2
C₆₇×#2983	2
#61832	67

Subgroups — C67×#61832 #30741083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61832 #30741083