Subgroups — C₆₇×#22505 #30701756

Order 17152.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1986	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1896	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1871	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1826	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#104×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#339×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
13	#556×C₆₇	C₄	1	1	yes	characteristic, complemented
14	#555×C₆₇	C₄	1	1	yes	characteristic, complemented
15	#554×C₆₇	C₄	1	1	yes	characteristic, complemented
16	#553×C₆₇	C₄	1	2	yes	complemented
17	#552×C₆₇	—	2	1	no	—
18	#552×C₆₇	C₄	1	2	yes	complemented
19	#551×C₆₇	—	2	2	no	—
20	#547×C₆₇	C₄	1	1	yes	characteristic, complemented
21	#546×C₆₇	—	2	1	no	—
22	#533×C₆₇	C₂²	1	1	yes	characteristic
23	#529×C₆₇	—	2	2	no	—
24	#529×C₆₇	—	2	1	no	—
25	#525×C₆₇	C₂²	1	2	yes	—
26	C₄×#41×C₆₇	—	2	1	no	—
27	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	—	2	1	no	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
32	#436×C₆₇	—	2	1	no	—
33	#435×C₆₇	—	2	2	no	—
34	C₈×D₄×C₆₇	—	2	1	no	—
35	#423×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#104×C₆₇	C₂²	1	2	yes	—
39	#407×C₆₇	C₂²	1	2	yes	—
40	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₆₇	—	2	2	no	—
44	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
45	C₄³×C₆₇	C₂²	1	1	yes	characteristic
46	#339×C₆₇	C₂²	1	2	yes	—
47	#339×C₆₇	C₂²	1	2	yes	—
48	#339×C₆₇	C₂²	1	1	yes	characteristic
49	#339×C₆₇	C₂²	1	2	yes	—
50	#339×C₆₇	C₂²	1	2	yes	—
51	#339×C₆₇	C₂²	1	2	yes	—
52	#339×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#41×C₆₇	—	2	1	no	—
54	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₆₇	—	2	2	no	—
57	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
58	C₂×M₁₆×C₆₇	—	2	2	no	—
59	C₂×M₁₆×C₆₇	—	2	4	no	—
60	C₂×M₁₆×C₆₇	—	4	2	no	—
61	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₆₇	—	2	2	no	—
65	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
66	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
67	#126×C₆₇	—	2	2	no	—
68	#126×C₆₇	—	2	2	no	—
69	#126×C₆₇	—	2	2	no	—
70	#125×C₆₇	—	2	2	no	—
71	#125×C₆₇	—	2	1	no	—
72	#125×C₆₇	C₂×C₄	1	2	yes	complemented
73	#124×C₆₇	—	2	1	no	—
74	#124×C₆₇	—	2	2	no	—
75	#123×C₆₇	—	2	2	no	—
76	#123×C₆₇	—	2	2	no	—
77	#123×C₆₇	—	2	2	no	—
78	#123×C₆₇	—	2	2	no	—
79	C₂²⋊Q₈×C₆₇	—	2	1	no	—
80	C₂²⋊Q₈×C₆₇	—	2	1	no	—
81	C₂²⋊Q₈×C₆₇	—	2	1	no	—
82	C₂²⋊Q₈×C₆₇	—	2	2	no	—
83	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	complemented
84	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	complemented
85	#121×C₆₇	—	2	2	no	—
86	#121×C₆₇	—	2	1	no	—
87	#121×C₆₇	C₂×C₄	1	2	yes	complemented
88	#121×C₆₇	C₂×C₄	1	2	yes	complemented
89	#120×C₆₇	—	2	2	no	—
90	C₄×Q₈×C₆₇	—	2	1	no	—
91	C₄×Q₈×C₆₇	—	2	1	no	—
92	C₄×Q₈×C₆₇	—	2	1	no	—
93	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
94	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
95	C₄×D₄×C₆₇	—	2	8	no	—
96	C₄×D₄×C₆₇	—	2	1	no	—
97	C₄×D₄×C₆₇	—	2	2	no	—
98	C₄×D₄×C₆₇	—	2	1	no	—
99	C₄×D₄×C₆₇	—	2	1	no	—
100	C₄×D₄×C₆₇	—	2	2	no	—
101	C₄×D₄×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
104	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
106	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
107	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
108	C₄×D₄×C₆₇	D₄	1	2	yes	—
109	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
110	#117×C₆₇	—	2	2	no	—
111	#117×C₆₇	—	2	2	no	—
112	#117×C₆₇	—	2	1	no	—
113	#117×C₆₇	—	2	2	no	—
114	#117×C₆₇	—	2	1	no	—
115	#117×C₆₇	C₂×C₄	1	2	yes	complemented
116	#117×C₆₇	C₂×C₄	1	2	yes	complemented
117	#117×C₆₇	C₂³	1	1	yes	characteristic
118	#117×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
120	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
126	C₂×C₄²×C₆₇	—	2	2	no	—
127	C₂×C₄²×C₆₇	—	2	1	no	—
128	C₂×C₄²×C₆₇	—	2	1	no	—
129	C₂×C₄²×C₆₇	—	2	4	no	—
130	C₂×C₄²×C₆₇	—	2	2	no	—
131	C₂×C₄²×C₆₇	—	2	1	no	—
132	C₂×C₄²×C₆₇	—	4	2	no	—
133	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₆₇	—	2	1	no	—
138	C₄⋊C₈×C₆₇	—	2	1	no	—
139	#104×C₆₇	—	2	2	no	—
140	#104×C₆₇	—	2	2	no	—
141	#104×C₆₇	—	4	2	no	—
142	C₂²⋊C₈×C₆₇	—	2	2	no	—
143	C₂²⋊C₈×C₆₇	—	2	2	no	—
144	#97×C₆₇	—	2	1	no	—
145	C₄×C₈×C₆₇	—	2	1	no	—
146	#95×C₆₇	—	2	1	no	—
147	#95×C₆₇	—	2	2	no	—
148	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
149	#41×C₆₇	—	2	1	no	—
150	#41×C₆₇	—	2	1	no	—
151	#41×C₆₇	—	2	1	no	—
152	#41×C₆₇	—	2	1	no	—
153	#41×C₆₇	—	4	4	no	—
154	C₂×Q₈×C₆₇	—	2	1	no	—
155	C₂×Q₈×C₆₇	—	2	1	no	—
156	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₆₇	—	2	4	no	—
158	C₂×D₄×C₆₇	—	2	2	no	—
159	C₂×D₄×C₆₇	—	2	1	no	—
160	C₂×D₄×C₆₇	—	2	2	no	—
161	C₂×D₄×C₆₇	C₂²⋊C₄	1	2	yes	—
162	C₂×D₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×D₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	—	2	1	no	—
166	C₂²×C₄×C₆₇	—	2	2	no	—
167	C₂²×C₄×C₆₇	—	2	2	no	—
168	C₂²×C₄×C₆₇	—	2	2	no	—
169	C₂²×C₄×C₆₇	—	2	2	no	—
170	C₂²×C₄×C₆₇	—	2	8	no	—
171	C₂²×C₄×C₆₇	—	2	2	no	—
172	C₂²×C₄×C₆₇	—	2	1	no	—
173	C₂²×C₄×C₆₇	—	2	2	no	—
174	C₂²×C₄×C₆₇	—	2	2	no	—
175	C₂²×C₄×C₆₇	—	2	1	no	—
176	C₂²×C₄×C₆₇	—	2	1	no	—
177	C₂²×C₄×C₆₇	—	2	1	no	—
178	C₂²×C₄×C₆₇	—	4	4	no	—
179	C₂²×C₄×C₆₇	—	4	4	no	—
180	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
181	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
188	M₁₆×C₆₇	—	2	1	no	—
189	M₁₆×C₆₇	—	2	1	no	—
190	M₁₆×C₆₇	—	2	2	no	—
191	M₁₆×C₆₇	—	2	2	no	—
192	M₁₆×C₆₇	—	2	1	no	—
193	M₁₆×C₆₇	—	4	4	no	—
194	M₁₆×C₆₇	#41	1	2	yes	complemented
195	C₂×C₈×C₆₇	—	2	1	no	—
196	C₂×C₈×C₆₇	—	2	2	no	—
197	C₂×C₈×C₆₇	—	2	1	no	—
198	C₂×C₈×C₆₇	—	4	4	no	—
199	C₄⋊C₄×C₆₇	—	2	4	no	—
200	C₄⋊C₄×C₆₇	—	2	2	no	—
201	C₄⋊C₄×C₆₇	—	2	2	no	—
202	C₄⋊C₄×C₆₇	—	2	1	no	—
203	C₄⋊C₄×C₆₇	—	2	2	no	—
204	C₄⋊C₄×C₆₇	—	2	2	no	—
205	C₄⋊C₄×C₆₇	—	2	1	no	—
206	C₄⋊C₄×C₆₇	—	2	1	no	—
207	C₄⋊C₄×C₆₇	—	2	2	no	—
208	C₄⋊C₄×C₆₇	—	2	2	no	—
209	C₄⋊C₄×C₆₇	—	2	1	no	—
210	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
212	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
217	C₂²⋊C₄×C₆₇	—	2	8	no	—
218	C₂²⋊C₄×C₆₇	—	2	2	no	—
219	C₂²⋊C₄×C₆₇	—	2	2	no	—
220	C₂²⋊C₄×C₆₇	—	2	2	no	—
221	C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₂²⋊C₄×C₆₇	—	2	1	no	—
223	C₂²⋊C₄×C₆₇	—	2	2	no	—
224	C₂²⋊C₄×C₆₇	—	2	2	no	—
225	C₂²⋊C₄×C₆₇	—	2	1	no	—
226	C₂²⋊C₄×C₆₇	—	2	1	no	—
227	C₂²⋊C₄×C₆₇	—	2	2	no	—
228	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
229	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
230	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
231	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
232	C₄²×C₆₇	—	2	4	no	—
233	C₄²×C₆₇	—	2	2	no	—
234	C₄²×C₆₇	—	2	1	no	—
235	C₄²×C₆₇	—	2	2	no	—
236	C₄²×C₆₇	—	2	1	no	—
237	C₄²×C₆₇	—	2	1	no	—
238	C₄²×C₆₇	—	2	2	no	—
239	C₄²×C₆₇	—	2	1	no	—
240	C₄²×C₆₇	—	2	1	no	—
241	C₄²×C₆₇	—	2	2	no	—
242	C₄²×C₆₇	—	2	2	no	—
243	C₄²×C₆₇	—	2	1	no	—
244	C₄²×C₆₇	—	4	4	no	—
245	C₄²×C₆₇	—	4	2	no	—
246	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₆₇	#41	1	2	yes	complemented
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	4	no	—
254	C₂³×C₆₇	—	2	1	no	—
255	C₂³×C₆₇	—	4	2	no	—
256	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₆₇	—	2	1	no	—
260	Q₈×C₆₇	—	2	1	no	—
261	Q₈×C₆₇	—	4	2	no	—
262	Q₈×C₆₇	—	8	1	no	—
263	D₄×C₆₇	—	2	4	no	—
264	D₄×C₆₇	—	2	1	no	—
265	D₄×C₆₇	—	2	1	no	—
266	D₄×C₆₇	—	2	2	no	—
267	D₄×C₆₇	—	4	1	no	—
268	D₄×C₆₇	—	4	1	no	—
269	D₄×C₆₇	—	4	4	no	—
270	D₄×C₆₇	—	8	2	no	—
271	D₄×C₆₇	#104	1	4	yes	complemented
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	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	1	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	2	1	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	4	1	no	—
294	C₂×C₄×C₆₇	—	4	16	no	—
295	C₂×C₄×C₆₇	—	4	1	no	—
296	C₂×C₄×C₆₇	—	4	2	no	—
297	C₂×C₄×C₆₇	—	4	2	no	—
298	C₂×C₄×C₆₇	—	4	1	no	—
299	C₂×C₄×C₆₇	—	4	4	no	—
300	C₂×C₄×C₆₇	—	4	1	no	—
301	C₂×C₄×C₆₇	—	4	1	no	—
302	C₂×C₄×C₆₇	—	4	2	no	—
303	C₂×C₄×C₆₇	—	8	1	no	—
304	C₂×C₄×C₆₇	—	8	2	no	—
305	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
312	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
317	C₈×C₆₇	—	2	2	no	—
318	C₈×C₆₇	—	4	2	no	—
319	C₈×C₆₇	—	4	1	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	1	no	—
322	C₂²×C₆₇	—	2	1	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	—	4	4	no	—
328	C₂²×C₆₇	—	4	4	no	—
329	C₂²×C₆₇	—	4	1	no	—
330	C₂²×C₆₇	—	4	1	no	—
331	C₂²×C₆₇	—	4	1	no	—
332	C₂²×C₆₇	C₂×#104	1	4	yes	—
333	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
334	C₂²×C₆₇	#546	1	1	yes	characteristic
335	C₂²×C₆₇	#547	1	1	yes	characteristic
336	C₄×C₆₇	—	2	4	no	—
337	C₄×C₆₇	—	2	2	no	—
338	C₄×C₆₇	—	2	2	no	—
339	C₄×C₆₇	—	2	1	no	—
340	C₄×C₆₇	—	2	1	no	—
341	C₄×C₆₇	—	2	1	no	—
342	C₄×C₆₇	—	4	2	no	—
343	C₄×C₆₇	—	4	4	no	—
344	C₄×C₆₇	—	4	1	no	—
345	C₄×C₆₇	—	4	1	no	—
346	C₄×C₆₇	—	4	2	no	—
347	C₄×C₆₇	—	4	1	no	—
348	C₄×C₆₇	—	4	2	no	—
349	C₄×C₆₇	C₂×#104	1	2	yes	—
350	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
351	C₄×C₆₇	#520	1	1	yes	characteristic
352	C₄×C₆₇	#546	1	1	yes	characteristic
353	C₄×C₆₇	#547	1	1	yes	characteristic
354	#22505	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂×C₆₇	—	2	1	no	—
356	C₂×C₆₇	—	2	1	no	—
357	C₂×C₆₇	—	2	4	no	—
358	C₂×C₆₇	—	4	2	no	—
359	C₂×C₆₇	—	8	1	no	—
360	C₂×C₆₇	#2339	1	1	yes	characteristic
361	C₂×C₆₇	C₂²×#104	1	1	yes	characteristic
362	C₂×C₆₇	#2901	1	1	yes	characteristic
363	#3475	C₂×C₆₇	1	1	yes	characteristic
364	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
365	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
366	#1994	C₂×C₆₇	1	1	yes	characteristic, complemented
367	#1986	C₂×C₆₇	1	1	yes	characteristic, complemented
368	#1896	C₂×C₆₇	1	2	yes	complemented
369	#1871	C₂×C₆₇	1	2	yes	complemented
370	#1826	C₂×C₆₇	1	2	yes	complemented
371	#1806	C₂×C₆₇	1	1	yes	characteristic, complemented
372	C₄×#104	C₂×C₆₇	1	1	yes	characteristic, complemented
373	C₂×#339	C₂×C₆₇	1	2	yes	complemented
374	C₆₇	#22505	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
376	#556	C₄×C₆₇	1	1	yes	characteristic, complemented
377	#555	C₄×C₆₇	1	1	yes	characteristic, complemented
378	#554	C₄×C₆₇	1	1	yes	characteristic, complemented
379	#553	C₄×C₆₇	1	2	yes	complemented
380	#552	—	2	1	no	—
381	#552	C₄×C₆₇	1	2	yes	complemented
382	#551	—	2	2	no	—
383	#547	C₄×C₆₇	1	1	yes	characteristic, complemented
384	#546	—	2	1	no	—
385	#533	C₂²×C₆₇	1	1	yes	characteristic
386	#529	—	2	2	no	—
387	#529	—	2	1	no	—
388	#525	C₂²×C₆₇	1	2	yes	—
389	C₄×#41	—	2	1	no	—
390	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
391	C₂×C₄×D₄	—	2	1	no	—
392	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
393	C₂×#117	C₂²×C₆₇	1	2	yes	—
394	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
395	#436	—	2	1	no	—
396	#435	—	2	2	no	—
397	C₈×D₄	—	2	1	no	—
398	#423	C₂²×C₆₇	1	1	yes	characteristic
399	C₂×#104	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×#104	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×#104	C₂²×C₆₇	1	2	yes	—
402	#407	C₂²×C₆₇	1	2	yes	—
403	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
404	C₄×C₄⋊C₄	—	2	1	no	—
405	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
406	C₄×C₂²⋊C₄	—	2	2	no	—
407	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
408	C₄³	C₂²×C₆₇	1	1	yes	characteristic
409	#339	C₂²×C₆₇	1	2	yes	—
410	#339	C₂²×C₆₇	1	1	yes	characteristic
411	#339	C₂²×C₆₇	1	2	yes	—
412	#339	C₂²×C₆₇	1	2	yes	—
413	#339	C₂²×C₆₇	1	2	yes	—
414	#339	C₂²×C₆₇	1	2	yes	—
415	#339	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×#41	—	2	1	no	—
417	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
418	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
419	C₂³×C₄	—	2	2	no	—
420	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	2	4	no	—
423	C₂×M₁₆	—	4	2	no	—
424	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
425	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
426	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
427	C₂²×C₈	—	2	2	no	—
428	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
429	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
430	#126	—	2	2	no	—
431	#126	—	2	2	no	—
432	#126	—	2	2	no	—
433	#125	—	2	2	no	—
434	#125	—	2	1	no	—
435	#125	C₂×C₄×C₆₇	1	2	yes	complemented
436	#124	—	2	1	no	—
437	#124	—	2	2	no	—
438	#123	—	2	2	no	—
439	#123	—	2	2	no	—
440	#123	—	2	2	no	—
441	#123	—	2	2	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	—	2	1	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	complemented
447	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	complemented
448	#121	—	2	2	no	—
449	#121	—	2	1	no	—
450	#121	C₂×C₄×C₆₇	1	2	yes	complemented
451	#121	C₂×C₄×C₆₇	1	2	yes	complemented
452	#120	—	2	2	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
457	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
458	C₄×D₄	—	2	8	no	—
459	C₄×D₄	—	2	1	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
466	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
467	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
468	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
469	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
470	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
471	C₄×D₄	D₄×C₆₇	1	2	yes	—
472	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
473	#117	—	2	2	no	—
474	#117	—	2	2	no	—
475	#117	—	2	1	no	—
476	#117	—	2	2	no	—
477	#117	—	2	1	no	—
478	#117	C₂×C₄×C₆₇	1	2	yes	complemented
479	#117	C₂×C₄×C₆₇	1	2	yes	complemented
480	#117	C₂³×C₆₇	1	1	yes	characteristic
481	#117	C₂³×C₆₇	1	2	yes	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	complemented
484	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	complemented
485	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	—	2	2	no	—
487	C₂×C₂²⋊C₄	—	2	2	no	—
488	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
489	C₂×C₄²	—	2	2	no	—
490	C₂×C₄²	—	2	1	no	—
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	4	no	—
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	—	2	2	no	—
495	C₂×C₄²	—	4	2	no	—
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
498	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
500	C₄⋊C₈	—	2	1	no	—
501	C₄⋊C₈	—	2	1	no	—
502	#104	—	2	2	no	—
503	#104	—	2	2	no	—
504	#104	—	4	2	no	—
505	C₂²⋊C₈	—	2	2	no	—
506	C₂²⋊C₈	—	2	2	no	—
507	#97	—	2	1	no	—
508	C₄×C₈	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	2	no	—
511	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
512	#41	—	2	1	no	—
513	#41	—	2	1	no	—
514	#41	—	2	1	no	—
515	#41	—	2	1	no	—
516	#41	—	4	4	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	C₂²⋊C₄×C₆₇	1	2	yes	—
525	C₂×D₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
526	C₂×D₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
527	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	8	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
544	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
545	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
546	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
548	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
551	M₁₆	—	2	1	no	—
552	M₁₆	—	2	1	no	—
553	M₁₆	—	2	2	no	—
554	M₁₆	—	2	2	no	—
555	M₁₆	—	2	1	no	—
556	M₁₆	—	4	4	no	—
557	M₁₆	#41×C₆₇	1	2	yes	complemented
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	4	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
574	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
575	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
576	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
577	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
578	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
579	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	1	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
592	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
593	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
594	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
595	C₄²	—	2	4	no	—
596	C₄²	—	2	2	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	4	4	no	—
608	C₄²	—	4	2	no	—
609	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
610	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
611	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
612	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
613	C₄²	#41×C₆₇	1	2	yes	complemented
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	4	2	no	—
619	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
620	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
621	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	4	2	no	—
625	Q₈	—	8	1	no	—
626	D₄	—	2	4	no	—
627	D₄	—	2	1	no	—
628	D₄	—	2	1	no	—
629	D₄	—	2	2	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	4	no	—
633	D₄	—	8	2	no	—
634	D₄	#104×C₆₇	1	4	yes	complemented
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	16	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
669	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
670	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
671	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
672	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
673	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
674	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
675	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
676	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
677	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
678	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
679	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
680	C₈	—	2	2	no	—
681	C₈	—	4	2	no	—
682	C₈	—	4	1	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	C₂×#104×C₆₇	1	4	yes	—
696	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
697	C₂²	#546×C₆₇	1	1	yes	characteristic
698	C₂²	#547×C₆₇	1	1	yes	characteristic
699	C₄	—	2	4	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	4	4	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	2	no	—
712	C₄	C₂×#104×C₆₇	1	2	yes	—
713	C₄	C₄×#41×C₆₇	1	1	yes	characteristic
714	C₄	#520×C₆₇	1	1	yes	characteristic
715	C₄	#546×C₆₇	1	1	yes	characteristic
716	C₄	#547×C₆₇	1	1	yes	characteristic
717	C₂	—	2	1	no	—
718	C₂	—	2	1	no	—
719	C₂	—	2	4	no	—
720	C₂	—	4	2	no	—
721	C₂	—	8	1	no	—
722	C₂	C₆₇×#2339	1	1	yes	characteristic
723	C₂	C₂²×#104×C₆₇	1	1	yes	characteristic
724	C₂	C₆₇×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
prime radical	C₆₇×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₆₇	C₂	semidirect
3. C₄²×D₄×C₆₇	C₂	semidirect
4. C₆₇×#1994	C₂	semidirect
5. C₆₇×#1986	C₂	semidirect
6. C₆₇×#1896	C₂	semidirect
7. C₆₇×#1871	C₂	semidirect
8. C₆₇×#1826	C₂	semidirect
9. C₆₇×#1806	C₂	semidirect
10. C₄×#104×C₆₇	C₂	semidirect
11. C₂×#339×C₆₇	C₂	semidirect
13. #556×C₆₇	C₄	semidirect
14. #555×C₆₇	C₄	semidirect
15. #554×C₆₇	C₄	semidirect
16. #553×C₆₇	C₄	semidirect
18. #552×C₆₇	C₄	semidirect
20. #547×C₆₇	C₄	semidirect
65. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
66. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
72. #125×C₆₇	C₂×C₄	semidirect
83. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
84. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
87. #121×C₆₇	C₂×C₄	semidirect
88. #121×C₆₇	C₂×C₄	semidirect
93. C₄×Q₈×C₆₇	C₂×C₄	semidirect
94. C₄×Q₈×C₆₇	C₂×C₄	semidirect
105. C₄×D₄×C₆₇	C₂×C₄	semidirect
106. C₄×D₄×C₆₇	C₂×C₄	semidirect
115. #117×C₆₇	C₂×C₄	semidirect
116. #117×C₆₇	C₂×C₄	semidirect
120. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
121. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
194. M₁₆×C₆₇	#41	semidirect
250. C₄²×C₆₇	#41	semidirect
271. D₄×C₆₇	#104	semidirect
354. #22505	C₆₇	direct (N × H)
364. D₄×M₁₆	C₂×C₆₇	semidirect
365. C₄²×D₄	C₂×C₆₇	semidirect
366. #1994	C₂×C₆₇	semidirect
367. #1986	C₂×C₆₇	semidirect
368. #1896	C₂×C₆₇	semidirect
369. #1871	C₂×C₆₇	semidirect
370. #1826	C₂×C₆₇	semidirect
371. #1806	C₂×C₆₇	semidirect
372. C₄×#104	C₂×C₆₇	semidirect
373. C₂×#339	C₂×C₆₇	semidirect
374. C₆₇	#22505	direct (N × H)
376. #556	C₄×C₆₇	semidirect
377. #555	C₄×C₆₇	semidirect
378. #554	C₄×C₆₇	semidirect
379. #553	C₄×C₆₇	semidirect
381. #552	C₄×C₆₇	semidirect
383. #547	C₄×C₆₇	semidirect
428. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
429. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
435. #125	C₂×C₄×C₆₇	semidirect
446. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
447. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
450. #121	C₂×C₄×C₆₇	semidirect
451. #121	C₂×C₄×C₆₇	semidirect
456. C₄×Q₈	C₂×C₄×C₆₇	semidirect
457. C₄×Q₈	C₂×C₄×C₆₇	semidirect
468. C₄×D₄	C₂×C₄×C₆₇	semidirect
469. C₄×D₄	C₂×C₄×C₆₇	semidirect
478. #117	C₂×C₄×C₆₇	semidirect
479. #117	C₂×C₄×C₆₇	semidirect
483. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
484. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
557. M₁₆	#41×C₆₇	semidirect
613. C₄²	#41×C₆₇	semidirect
634. D₄	#104×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
D₄×M₁₆×C₆₇	2
C₄²×D₄×C₆₇	2
C₆₇×#1994	2
C₆₇×#1986	2
C₆₇×#1896	2
C₆₇×#1871	2
C₆₇×#1826	2
C₆₇×#1806	2
C₄×#104×C₆₇	2
C₂×#339×C₆₇	2
#22505	67

Subgroups — C67×#22505 #30701756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22505 #30701756