Subgroups — C₆₇×#61649 #30740900

Order 17152.

2042 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3485	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3323	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3315	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3276	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3202	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3123	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
17	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
19	#563×C₆₇	—	2	2	no	—
20	#552×C₆₇	C₂²	1	4	yes	complemented
21	#551×C₆₇	—	2	2	no	—
22	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
23	#547×C₆₇	—	2	2	no	—
24	#547×C₆₇	C₂²	1	4	yes	—
25	#546×C₆₇	—	2	2	no	—
26	#546×C₆₇	C₂²	1	4	yes	—
27	#544×C₆₇	—	2	2	no	—
28	#541×C₆₇	C₂²	1	2	yes	complemented
29	#539×C₆₇	—	2	2	no	—
30	#536×C₆₇	C₂²	1	1	yes	characteristic
31	#536×C₆₇	C₂²	1	2	yes	—
32	#536×C₆₇	C₂²	1	1	yes	characteristic
33	#534×C₆₇	—	2	2	no	—
34	#525×C₆₇	C₂²	1	1	yes	characteristic
35	#525×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#123×C₆₇	—	2	2	no	—
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
38	#518×C₆₇	C₂²	1	1	yes	characteristic
39	#497×C₆₇	C₂²	1	2	yes	complemented
40	#494×C₆₇	C₂²	1	2	yes	complemented
41	#491×C₆₇	C₂²	1	2	yes	complemented
42	#488×C₆₇	C₂²	1	2	yes	complemented
43	#485×C₆₇	C₂²	1	4	yes	complemented
44	#485×C₆₇	C₂²	1	4	yes	complemented
45	#484×C₆₇	C₂²	1	2	yes	complemented
46	#481×C₆₇	C₂²	1	2	yes	complemented
47	#478×C₆₇	C₂²	1	4	yes	complemented
48	#470×C₆₇	C₂²	1	4	yes	complemented
49	#470×C₆₇	C₂²	1	4	yes	complemented
50	#468×C₆₇	C₂²	1	4	yes	complemented
51	#467×C₆₇	C₂²	1	4	yes	complemented
52	#464×C₆₇	C₂²	1	4	yes	complemented
53	#462×C₆₇	C₂²	1	4	yes	complemented
54	#461×C₆₇	C₂²	1	4	yes	complemented
55	#452×C₆₇	C₂²	1	4	yes	—
56	#452×C₆₇	C₂²	1	4	yes	complemented
57	#452×C₆₇	C₂²	1	4	yes	complemented
58	#452×C₆₇	C₂²	1	4	yes	complemented
59	#451×C₆₇	C₂²	1	4	yes	complemented
60	#451×C₆₇	C₂²	1	2	yes	complemented
61	#451×C₆₇	C₂²	1	4	yes	complemented
62	#450×C₆₇	C₂²	1	4	yes	—
63	#450×C₆₇	C₂²	1	4	yes	complemented
64	#448×C₆₇	C₂²	1	2	yes	complemented
65	#440×C₆₇	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
67	#436×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#433×C₆₇	C₂²	1	2	yes	complemented
70	#418×C₆₇	C₂²	1	2	yes	complemented
71	#417×C₆₇	C₂²	1	4	yes	complemented
72	#416×C₆₇	C₂²	1	2	yes	complemented
73	#408×C₆₇	C₂²	1	2	yes	—
74	#407×C₆₇	C₂²	1	2	yes	complemented
75	H(5,𝔽₂)×C₆₇	—	4	4	no	—
76	C₂×#41×C₆₇	—	2	1	no	—
77	C₂×#41×C₆₇	—	2	2	no	—
78	C₂×#41×C₆₇	—	4	4	no	—
79	C₂×#41×C₆₇	C₂³	1	4	yes	—
80	C₂×#41×C₆₇	C₂³	1	2	yes	—
81	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	—	2	1	no	—
87	C₂²×D₄×C₆₇	—	2	2	no	—
88	C₂²×D₄×C₆₇	—	2	1	no	—
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₇	—	2	1	no	—
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	#137×C₆₇	—	4	8	no	—
94	#137×C₆₇	—	4	4	no	—
95	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
96	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
97	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₆₇	—	4	4	no	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₆₇	—	2	2	no	—
106	C₄⋊Q₈×C₆₇	—	2	1	no	—
107	C₄⋊Q₈×C₆₇	—	2	4	no	—
108	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
110	#126×C₆₇	—	2	4	no	—
111	#126×C₆₇	—	2	4	no	—
112	#125×C₆₇	—	2	4	no	—
113	#125×C₆₇	—	2	4	no	—
114	#125×C₆₇	C₂³	1	2	yes	—
115	#124×C₆₇	—	2	1	no	—
116	#124×C₆₇	—	2	2	no	—
117	#124×C₆₇	C₂³	1	2	yes	—
118	#123×C₆₇	—	2	2	no	—
119	#123×C₆₇	—	2	2	no	—
120	#123×C₆₇	—	2	2	no	—
121	#123×C₆₇	—	2	4	no	—
122	#123×C₆₇	—	2	1	no	—
123	#123×C₆₇	—	2	4	no	—
124	#123×C₆₇	—	2	2	no	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	D₄	1	2	yes	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	2	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
137	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
139	#121×C₆₇	—	2	4	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	D₄	1	2	yes	—
142	#121×C₆₇	C₂³	1	2	yes	—
143	#120×C₆₇	—	2	1	no	—
144	#120×C₆₇	—	2	4	no	—
145	#120×C₆₇	D₄	1	2	yes	—
146	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
147	C₄×D₄×C₆₇	—	2	4	no	—
148	C₄×D₄×C₆₇	—	2	2	no	—
149	C₄×D₄×C₆₇	—	2	2	no	—
150	C₄×D₄×C₆₇	C₂³	1	4	yes	—
151	C₄×D₄×C₆₇	C₂³	1	4	yes	—
152	#117×C₆₇	—	2	4	no	—
153	#117×C₆₇	C₂³	1	1	yes	characteristic
154	#117×C₆₇	C₂³	1	2	yes	—
155	#117×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
157	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
161	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
162	#107×C₆₇	C₂³	1	4	yes	—
163	#106×C₆₇	C₂³	1	4	yes	—
164	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
165	#103×C₆₇	C₂³	1	4	yes	—
166	#103×C₆₇	C₂³	1	4	yes	—
167	#103×C₆₇	C₂³	1	4	yes	—
168	#103×C₆₇	C₂³	1	4	yes	—
169	#103×C₆₇	C₂³	1	4	yes	—
170	#102×C₆₇	C₂³	1	4	yes	—
171	#102×C₆₇	C₂³	1	4	yes	—
172	#102×C₆₇	C₂³	1	4	yes	—
173	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
174	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
175	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
177	#97×C₆₇	C₂³	1	2	yes	—
178	C₄×C₈×C₆₇	C₂³	1	2	yes	—
179	C₂⁴×C₆₇	—	2	1	no	—
180	C₂⁴×C₆₇	—	2	2	no	—
181	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
182	#41×C₆₇	—	2	8	no	—
183	#41×C₆₇	—	2	4	no	—
184	#41×C₆₇	—	4	2	no	—
185	#41×C₆₇	—	4	4	no	—
186	#41×C₆₇	—	4	2	no	—
187	#41×C₆₇	—	4	2	no	—
188	#41×C₆₇	—	4	8	no	—
189	#41×C₆₇	—	4	4	no	—
190	C₂×Q₈×C₆₇	—	2	1	no	—
191	C₂×Q₈×C₆₇	—	2	2	no	—
192	C₂×Q₈×C₆₇	—	2	2	no	—
193	C₂×Q₈×C₆₇	—	4	2	no	—
194	C₂×Q₈×C₆₇	—	4	2	no	—
195	C₂×Q₈×C₆₇	—	4	4	no	—
196	C₂×Q₈×C₆₇	—	4	2	no	—
197	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
198	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
199	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	1	no	—
205	C₂×D₄×C₆₇	—	2	2	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	2	1	no	—
208	C₂×D₄×C₆₇	—	2	2	no	—
209	C₂×D₄×C₆₇	—	4	2	no	—
210	C₂×D₄×C₆₇	—	4	4	no	—
211	C₂×D₄×C₆₇	—	4	4	no	—
212	C₂×D₄×C₆₇	—	4	8	no	—
213	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
214	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
217	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	1	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	2	no	—
224	C₂²×C₄×C₆₇	—	2	1	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	4	no	—
228	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
233	Q₁₆×C₆₇	—	4	4	no	—
234	Q₁₆×C₆₇	—	4	4	no	—
235	Q₁₆×C₆₇	—	4	4	no	—
236	SD₁₆×C₆₇	—	2	8	no	—
237	SD₁₆×C₆₇	—	2	8	no	—
238	SD₁₆×C₆₇	—	4	4	no	—
239	M₁₆×C₆₇	—	4	4	no	—
240	M₁₆×C₆₇	—	4	2	no	—
241	C₂×C₈×C₆₇	—	4	2	no	—
242	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
243	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
244	C₄⋊C₄×C₆₇	—	2	2	no	—
245	C₄⋊C₄×C₆₇	—	2	4	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	2	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	2	4	no	—
254	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
257	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²⋊C₄×C₆₇	—	2	1	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	2	2	no	—
263	C₂²⋊C₄×C₆₇	—	2	2	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	2	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
270	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
271	C₄²×C₆₇	—	2	2	no	—
272	C₄²×C₆₇	—	2	4	no	—
273	C₄²×C₆₇	—	2	1	no	—
274	C₄²×C₆₇	C₂⁴	1	2	yes	—
275	C₂³×C₆₇	—	2	4	no	—
276	C₂³×C₆₇	—	2	2	no	—
277	C₂³×C₆₇	—	2	1	no	—
278	C₂³×C₆₇	—	4	1	no	—
279	C₂³×C₆₇	—	4	2	no	—
280	C₂³×C₆₇	—	4	4	no	—
281	C₂³×C₆₇	—	8	2	no	—
282	C₂³×C₆₇	—	8	4	no	—
283	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
285	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
286	Q₈×C₆₇	—	2	4	no	—
287	Q₈×C₆₇	—	2	4	no	—
288	Q₈×C₆₇	—	2	4	no	—
289	Q₈×C₆₇	—	2	2	no	—
290	Q₈×C₆₇	—	4	1	no	—
291	Q₈×C₆₇	—	4	2	no	—
292	Q₈×C₆₇	—	8	2	no	—
293	Q₈×C₆₇	—	8	2	no	—
294	D₄×C₆₇	—	2	4	no	—
295	D₄×C₆₇	—	2	2	no	—
296	D₄×C₆₇	—	2	2	no	—
297	D₄×C₆₇	—	4	1	no	—
298	D₄×C₆₇	—	4	2	no	—
299	D₄×C₆₇	—	4	4	no	—
300	D₄×C₆₇	—	4	4	no	—
301	D₄×C₆₇	—	4	4	no	—
302	D₄×C₆₇	—	4	8	no	—
303	D₄×C₆₇	—	4	2	no	—
304	D₄×C₆₇	—	8	2	no	—
305	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	4	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	4	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	4	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	4	1	no	—
316	C₂×C₄×C₆₇	—	4	2	no	—
317	C₂×C₄×C₆₇	—	4	8	no	—
318	C₂×C₄×C₆₇	—	4	4	no	—
319	C₂×C₄×C₆₇	—	4	2	no	—
320	C₂×C₄×C₆₇	—	4	4	no	—
321	C₂×C₄×C₆₇	—	4	2	no	—
322	C₂×C₄×C₆₇	—	8	4	no	—
323	C₂×C₄×C₆₇	—	8	2	no	—
324	C₂×C₄×C₆₇	—	8	2	no	—
325	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
330	C₈×C₆₇	—	2	4	no	—
331	C₈×C₆₇	—	2	4	no	—
332	C₂²×C₆₇	—	2	2	no	—
333	C₂²×C₆₇	—	2	4	no	—
334	C₂²×C₆₇	—	2	2	no	—
335	C₂²×C₆₇	—	2	2	no	—
336	C₂²×C₆₇	—	2	1	no	—
337	C₂²×C₆₇	—	2	2	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	4	no	—
340	C₂²×C₆₇	—	4	4	no	—
341	C₂²×C₆₇	—	4	2	no	—
342	C₂²×C₆₇	—	4	1	no	—
343	C₂²×C₆₇	—	8	4	no	—
344	C₂²×C₆₇	—	8	2	no	—
345	C₂²×C₆₇	—	16	4	no	—
346	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
347	C₄×C₆₇	—	2	4	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	1	no	—
350	C₄×C₆₇	—	2	2	no	—
351	C₄×C₆₇	—	4	4	no	—
352	C₄×C₆₇	—	4	2	no	—
353	C₄×C₆₇	—	4	1	no	—
354	C₄×C₆₇	—	4	2	no	—
355	C₄×C₆₇	—	4	4	no	—
356	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
357	#61649	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂×C₆₇	—	4	2	no	—
359	C₂×C₆₇	—	4	1	no	—
360	C₂×C₆₇	—	4	2	no	—
361	C₂×C₆₇	—	4	4	no	—
362	C₂×C₆₇	—	8	1	no	—
363	C₂×C₆₇	#3484	1	1	yes	characteristic
364	C₂×C₆₇	#3586	1	2	yes	—
365	#3538	C₂×C₆₇	1	1	yes	characteristic, complemented
366	#3485	C₂×C₆₇	1	1	yes	characteristic
367	#3323	C₂×C₆₇	1	4	yes	complemented
368	#3315	C₂×C₆₇	1	4	yes	complemented
369	#3276	C₂×C₆₇	1	4	yes	complemented
370	#3266	C₂×C₆₇	1	4	yes	complemented
371	#3223	C₂×C₆₇	1	2	yes	complemented
372	#3202	C₂×C₆₇	1	2	yes	complemented
373	#3196	C₂×C₆₇	1	2	yes	complemented
374	#3123	C₂×C₆₇	1	2	yes	complemented
375	#3009	C₂×C₆₇	1	2	yes	complemented
376	#3007	C₂×C₆₇	1	2	yes	complemented
377	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
378	C₆₇	#61649	1	1	yes	characteristic, direct product factor, Sylow
379	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
380	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
381	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
382	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
383	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
384	#563	—	2	2	no	—
385	#552	C₂²×C₆₇	1	4	yes	complemented
386	#551	—	2	2	no	—
387	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
388	#547	—	2	2	no	—
389	#547	C₂²×C₆₇	1	4	yes	—
390	#546	—	2	2	no	—
391	#546	C₂²×C₆₇	1	4	yes	—
392	#544	—	2	2	no	—
393	#541	C₂²×C₆₇	1	2	yes	complemented
394	#539	—	2	2	no	—
395	#536	C₂²×C₆₇	1	1	yes	characteristic
396	#536	C₂²×C₆₇	1	1	yes	characteristic
397	#536	C₂²×C₆₇	1	2	yes	—
398	#534	—	2	2	no	—
399	#525	C₂²×C₆₇	1	1	yes	characteristic
400	#525	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×#123	—	2	2	no	—
402	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
403	#518	C₂²×C₆₇	1	1	yes	characteristic
404	#497	C₂²×C₆₇	1	2	yes	complemented
405	#494	C₂²×C₆₇	1	2	yes	complemented
406	#491	C₂²×C₆₇	1	2	yes	complemented
407	#488	C₂²×C₆₇	1	2	yes	complemented
408	#485	C₂²×C₆₇	1	4	yes	complemented
409	#485	C₂²×C₆₇	1	4	yes	complemented
410	#484	C₂²×C₆₇	1	2	yes	complemented
411	#481	C₂²×C₆₇	1	2	yes	complemented
412	#478	C₂²×C₆₇	1	4	yes	complemented
413	#470	C₂²×C₆₇	1	4	yes	complemented
414	#470	C₂²×C₆₇	1	4	yes	complemented
415	#468	C₂²×C₆₇	1	4	yes	complemented
416	#467	C₂²×C₆₇	1	4	yes	complemented
417	#464	C₂²×C₆₇	1	4	yes	complemented
418	#462	C₂²×C₆₇	1	4	yes	complemented
419	#461	C₂²×C₆₇	1	4	yes	complemented
420	#452	C₂²×C₆₇	1	4	yes	—
421	#452	C₂²×C₆₇	1	4	yes	complemented
422	#452	C₂²×C₆₇	1	4	yes	complemented
423	#452	C₂²×C₆₇	1	4	yes	complemented
424	#451	C₂²×C₆₇	1	2	yes	complemented
425	#451	C₂²×C₆₇	1	4	yes	complemented
426	#451	C₂²×C₆₇	1	4	yes	complemented
427	#450	C₂²×C₆₇	1	4	yes	—
428	#450	C₂²×C₆₇	1	4	yes	complemented
429	#448	C₂²×C₆₇	1	2	yes	complemented
430	#440	C₂²×C₆₇	1	4	yes	complemented
431	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
432	#436	C₂²×C₆₇	1	4	yes	complemented
433	#435	C₂²×C₆₇	1	4	yes	complemented
434	#433	C₂²×C₆₇	1	2	yes	complemented
435	#418	C₂²×C₆₇	1	2	yes	complemented
436	#417	C₂²×C₆₇	1	4	yes	complemented
437	#416	C₂²×C₆₇	1	2	yes	complemented
438	#408	C₂²×C₆₇	1	2	yes	—
439	#407	C₂²×C₆₇	1	2	yes	complemented
440	H(5,𝔽₂)	—	4	4	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	4	4	no	—
444	C₂×#41	C₂³×C₆₇	1	4	yes	—
445	C₂×#41	C₂³×C₆₇	1	2	yes	—
446	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
447	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
448	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
449	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
450	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
458	#137	—	4	8	no	—
459	#137	—	4	4	no	—
460	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
461	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
462	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
463	C₂×SD₁₆	—	4	4	no	—
464	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
465	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
466	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
467	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
468	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
469	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
470	C₄⋊Q₈	—	2	2	no	—
471	C₄⋊Q₈	—	2	1	no	—
472	C₄⋊Q₈	—	2	4	no	—
473	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
474	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
475	#126	—	2	4	no	—
476	#126	—	2	4	no	—
477	#125	—	2	4	no	—
478	#125	—	2	4	no	—
479	#125	C₂³×C₆₇	1	2	yes	—
480	#124	—	2	1	no	—
481	#124	—	2	2	no	—
482	#124	C₂³×C₆₇	1	2	yes	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	2	no	—
486	#123	—	2	4	no	—
487	#123	—	2	1	no	—
488	#123	—	2	4	no	—
489	#123	—	2	2	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	D₄×C₆₇	1	2	yes	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
499	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
501	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
502	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
503	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
504	#121	—	2	4	no	—
505	#121	—	2	4	no	—
506	#121	D₄×C₆₇	1	2	yes	—
507	#121	C₂³×C₆₇	1	2	yes	—
508	#120	—	2	1	no	—
509	#120	—	2	4	no	—
510	#120	D₄×C₆₇	1	2	yes	—
511	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	C₂³×C₆₇	1	4	yes	—
516	C₄×D₄	C₂³×C₆₇	1	4	yes	—
517	#117	—	2	4	no	—
518	#117	C₂³×C₆₇	1	1	yes	characteristic
519	#117	C₂³×C₆₇	1	2	yes	—
520	#117	C₂³×C₆₇	1	1	yes	characteristic
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	2	4	no	—
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₂²⋊C₄	—	2	2	no	—
525	C₂×C₂²⋊C₄	—	2	2	no	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	#107	C₂³×C₆₇	1	4	yes	—
528	#106	C₂³×C₆₇	1	4	yes	—
529	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
530	#103	C₂³×C₆₇	1	4	yes	—
531	#103	C₂³×C₆₇	1	4	yes	—
532	#103	C₂³×C₆₇	1	4	yes	—
533	#103	C₂³×C₆₇	1	4	yes	—
534	#103	C₂³×C₆₇	1	4	yes	—
535	#102	C₂³×C₆₇	1	4	yes	—
536	#102	C₂³×C₆₇	1	4	yes	—
537	#102	C₂³×C₆₇	1	4	yes	—
538	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
539	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
540	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
541	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
542	#97	C₂³×C₆₇	1	2	yes	—
543	C₄×C₈	C₂³×C₆₇	1	2	yes	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
547	#41	—	2	8	no	—
548	#41	—	2	4	no	—
549	#41	—	4	2	no	—
550	#41	—	4	4	no	—
551	#41	—	4	2	no	—
552	#41	—	4	2	no	—
553	#41	—	4	8	no	—
554	#41	—	4	4	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	4	2	no	—
559	C₂×Q₈	—	4	2	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
563	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
564	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
565	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	8	no	—
578	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
579	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
580	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
581	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
582	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
598	Q₁₆	—	4	4	no	—
599	Q₁₆	—	4	4	no	—
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	2	8	no	—
603	SD₁₆	—	4	4	no	—
604	M₁₆	—	4	4	no	—
605	M₁₆	—	4	2	no	—
606	C₂×C₈	—	4	2	no	—
607	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
608	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
620	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
622	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
634	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
635	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	1	no	—
639	C₄²	C₂⁴×C₆₇	1	2	yes	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	8	2	no	—
647	C₂³	—	8	4	no	—
648	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
649	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
650	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
651	Q₈	—	2	4	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	2	no	—
658	Q₈	—	8	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	2	no	—
669	D₄	—	8	2	no	—
670	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
691	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
694	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
695	C₈	—	2	4	no	—
696	C₈	—	2	4	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	8	4	no	—
709	C₂²	—	8	2	no	—
710	C₂²	—	16	4	no	—
711	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
712	C₄	—	2	4	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	4	no	—
721	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
722	C₂	—	4	1	no	—
723	C₂	—	4	2	no	—
724	C₂	—	4	2	no	—
725	C₂	—	4	4	no	—
726	C₂	—	8	1	no	—
727	C₂	C₆₇×#3484	1	1	yes	characteristic
728	C₂	C₆₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3485	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3538	C₂	semidirect
3. C₆₇×#3323	C₂	semidirect
4. C₆₇×#3315	C₂	semidirect
5. C₆₇×#3276	C₂	semidirect
6. C₆₇×#3266	C₂	semidirect
7. C₆₇×#3223	C₂	semidirect
8. C₆₇×#3202	C₂	semidirect
9. C₆₇×#3196	C₂	semidirect
10. C₆₇×#3123	C₂	semidirect
11. C₆₇×#3009	C₂	semidirect
12. C₆₇×#3007	C₂	semidirect
13. C₆₇×#2978	C₂	semidirect
16. C₂×#137×C₆₇	C₂²	semidirect
17. C₂×#137×C₆₇	C₂²	semidirect
18. C₂²×SD₁₆×C₆₇	C₂²	semidirect
20. #552×C₆₇	C₂²	semidirect
22. D₄×Q₈×C₆₇	C₂²	semidirect
28. #541×C₆₇	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
39. #497×C₆₇	C₂²	semidirect
40. #494×C₆₇	C₂²	semidirect
41. #491×C₆₇	C₂²	semidirect
42. #488×C₆₇	C₂²	semidirect
43. #485×C₆₇	C₂²	semidirect
44. #485×C₆₇	C₂²	semidirect
45. #484×C₆₇	C₂²	semidirect
46. #481×C₆₇	C₂²	semidirect
47. #478×C₆₇	C₂²	semidirect
48. #470×C₆₇	C₂²	semidirect
49. #470×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
51. #467×C₆₇	C₂²	semidirect
52. #464×C₆₇	C₂²	semidirect
53. #462×C₆₇	C₂²	semidirect
54. #461×C₆₇	C₂²	semidirect
56. #452×C₆₇	C₂²	semidirect
57. #452×C₆₇	C₂²	semidirect
58. #452×C₆₇	C₂²	semidirect
59. #451×C₆₇	C₂²	semidirect
60. #451×C₆₇	C₂²	semidirect
61. #451×C₆₇	C₂²	semidirect
63. #450×C₆₇	C₂²	semidirect
64. #448×C₆₇	C₂²	semidirect
65. #440×C₆₇	C₂²	semidirect
66. C₄×SD₁₆×C₆₇	C₂²	semidirect
67. #436×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #433×C₆₇	C₂²	semidirect
70. #418×C₆₇	C₂²	semidirect
71. #417×C₆₇	C₂²	semidirect
72. #416×C₆₇	C₂²	semidirect
74. #407×C₆₇	C₂²	semidirect
357. #61649	C₆₇	direct (N × H)
365. #3538	C₂×C₆₇	semidirect
367. #3323	C₂×C₆₇	semidirect
368. #3315	C₂×C₆₇	semidirect
369. #3276	C₂×C₆₇	semidirect
370. #3266	C₂×C₆₇	semidirect
371. #3223	C₂×C₆₇	semidirect
372. #3202	C₂×C₆₇	semidirect
373. #3196	C₂×C₆₇	semidirect
374. #3123	C₂×C₆₇	semidirect
375. #3009	C₂×C₆₇	semidirect
376. #3007	C₂×C₆₇	semidirect
377. #2978	C₂×C₆₇	semidirect
378. C₆₇	#61649	direct (N × H)
381. C₂×#137	C₂²×C₆₇	semidirect
382. C₂×#137	C₂²×C₆₇	semidirect
383. C₂²×SD₁₆	C₂²×C₆₇	semidirect
385. #552	C₂²×C₆₇	semidirect
387. D₄×Q₈	C₂²×C₆₇	semidirect
393. #541	C₂²×C₆₇	semidirect
402. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
404. #497	C₂²×C₆₇	semidirect
405. #494	C₂²×C₆₇	semidirect
406. #491	C₂²×C₆₇	semidirect
407. #488	C₂²×C₆₇	semidirect
408. #485	C₂²×C₆₇	semidirect
409. #485	C₂²×C₆₇	semidirect
410. #484	C₂²×C₆₇	semidirect
411. #481	C₂²×C₆₇	semidirect
412. #478	C₂²×C₆₇	semidirect
413. #470	C₂²×C₆₇	semidirect
414. #470	C₂²×C₆₇	semidirect
415. #468	C₂²×C₆₇	semidirect
416. #467	C₂²×C₆₇	semidirect
417. #464	C₂²×C₆₇	semidirect
418. #462	C₂²×C₆₇	semidirect
419. #461	C₂²×C₆₇	semidirect
421. #452	C₂²×C₆₇	semidirect
422. #452	C₂²×C₆₇	semidirect
423. #452	C₂²×C₆₇	semidirect
424. #451	C₂²×C₆₇	semidirect
425. #451	C₂²×C₆₇	semidirect
426. #451	C₂²×C₆₇	semidirect
428. #450	C₂²×C₆₇	semidirect
429. #448	C₂²×C₆₇	semidirect
430. #440	C₂²×C₆₇	semidirect
431. C₄×SD₁₆	C₂²×C₆₇	semidirect
432. #436	C₂²×C₆₇	semidirect
433. #435	C₂²×C₆₇	semidirect
434. #433	C₂²×C₆₇	semidirect
435. #418	C₂²×C₆₇	semidirect
436. #417	C₂²×C₆₇	semidirect
437. #416	C₂²×C₆₇	semidirect
439. #407	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3538	2
C₆₇×#3485	2
C₆₇×#3323	2
C₆₇×#3315	2
C₆₇×#3276	2
C₆₇×#3266	2
C₆₇×#3223	2
C₆₇×#3202	2
C₆₇×#3196	2
C₆₇×#3123	2
C₆₇×#3009	2
C₆₇×#3007	2
C₆₇×#2978	2
#61649	67

Subgroups — C67×#61649 #30740900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61649 #30740900