Subgroups — C₆₇×#34935 #30714186

Order 17152.

3578 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2538	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2537	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2536	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2535	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2534	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2486	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2408	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2392	C₂	1	4	yes	maximal, complemented
12	C₄×#121×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2280	C₂	1	2	yes	maximal, complemented
15	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
18	#525×C₆₇	—	2	16	no	—
19	C₂×#123×C₆₇	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
21	C₂×#121×C₆₇	C₂²	1	4	yes	—
22	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#120×C₆₇	C₂²	1	4	yes	—
24	C₄×#41×C₆₇	—	2	8	no	—
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₆₇	—	2	8	no	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	2	yes	—
39	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
44	#398×C₆₇	C₂²	1	4	yes	complemented
45	#397×C₆₇	C₂²	1	4	yes	complemented
46	#396×C₆₇	C₂²	1	8	yes	complemented
47	#394×C₆₇	C₂²	1	4	yes	—
48	#394×C₆₇	C₂²	1	8	yes	complemented
49	#392×C₆₇	C₂²	1	4	yes	—
50	#390×C₆₇	C₂²	1	4	yes	—
51	#389×C₆₇	C₂²	1	4	yes	complemented
52	#388×C₆₇	C₂²	1	8	yes	complemented
53	#386×C₆₇	C₂²	1	8	yes	complemented
54	#384×C₆₇	C₂²	1	2	yes	complemented
55	#382×C₆₇	C₂²	1	2	yes	complemented
56	#381×C₆₇	C₂²	1	4	yes	—
57	#380×C₆₇	C₂²	1	2	yes	—
58	#380×C₆₇	C₂²	1	2	yes	—
59	#380×C₆₇	C₂²	1	4	yes	complemented
60	#380×C₆₇	C₂²	1	4	yes	complemented
61	#380×C₆₇	C₂²	1	4	yes	complemented
62	#379×C₆₇	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
66	C₂⁵×C₆₇	C₂³	1	2	yes	—
67	C₂×#41×C₆₇	—	2	4	no	—
68	C₂×#41×C₆₇	—	2	4	no	—
69	C₂×#41×C₆₇	D₄	1	8	yes	complemented
70	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₇	—	2	8	no	—
72	C₂²×D₄×C₆₇	—	2	4	no	—
73	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
74	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
75	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
76	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₆₇	—	2	8	no	—
79	C₂³×C₄×C₆₇	—	2	8	no	—
80	C₂³×C₄×C₆₇	—	2	8	no	—
81	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	#123×C₆₇	—	2	16	no	—
91	C₂²⋊Q₈×C₆₇	—	2	16	no	—
92	#121×C₆₇	—	2	16	no	—
93	#121×C₆₇	—	2	16	no	—
94	#120×C₆₇	—	2	16	no	—
95	C₄×Q₈×C₆₇	—	2	4	no	—
96	C₄×Q₈×C₆₇	—	2	4	no	—
97	C₄×D₄×C₆₇	—	2	8	no	—
98	C₄×D₄×C₆₇	—	2	8	no	—
99	C₄×D₄×C₆₇	—	2	32	no	—
100	C₄×D₄×C₆₇	—	2	8	no	—
101	C₄×D₄×C₆₇	—	2	8	no	—
102	C₄×D₄×C₆₇	—	2	8	no	—
103	C₄×D₄×C₆₇	—	2	8	no	—
104	C₄×D₄×C₆₇	—	2	4	no	—
105	C₄×D₄×C₆₇	—	2	4	no	—
106	#117×C₆₇	—	2	4	no	—
107	#117×C₆₇	—	2	8	no	—
108	#117×C₆₇	—	2	8	no	—
109	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
131	C₂×C₄²×C₆₇	—	2	8	no	—
132	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
133	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	#95×C₆₇	C₂³	1	8	yes	—
142	#95×C₆₇	C₂³	1	8	yes	—
143	#95×C₆₇	C₂³	1	4	yes	—
144	#95×C₆₇	C₂³	1	4	yes	—
145	C₂⁴×C₆₇	—	2	4	no	—
146	C₂⁴×C₆₇	—	2	8	no	—
147	C₂⁴×C₆₇	—	2	4	no	—
148	C₂⁴×C₆₇	—	2	4	no	—
149	C₂⁴×C₆₇	—	4	4	no	—
150	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
151	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
152	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
153	#41×C₆₇	—	2	32	no	—
154	C₂×Q₈×C₆₇	—	2	2	no	—
155	C₂×Q₈×C₆₇	—	2	2	no	—
156	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
157	C₂×D₄×C₆₇	—	2	32	no	—
158	C₂×D₄×C₆₇	—	2	4	no	—
159	C₂×D₄×C₆₇	—	2	8	no	—
160	C₂×D₄×C₆₇	—	2	4	no	—
161	C₂×D₄×C₆₇	—	2	16	no	—
162	C₂×D₄×C₆₇	—	2	16	no	—
163	C₂×D₄×C₆₇	—	2	4	no	—
164	C₂×D₄×C₆₇	—	2	4	no	—
165	C₂×D₄×C₆₇	—	2	2	no	—
166	C₂×D₄×C₆₇	—	2	4	no	—
167	C₂×D₄×C₆₇	—	2	2	no	—
168	C₂×D₄×C₆₇	—	4	8	no	—
169	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
170	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
171	C₂×D₄×C₆₇	#41	1	8	yes	complemented
172	C₂²×C₄×C₆₇	—	2	4	no	—
173	C₂²×C₄×C₆₇	—	2	4	no	—
174	C₂²×C₄×C₆₇	—	2	4	no	—
175	C₂²×C₄×C₆₇	—	2	4	no	—
176	C₂²×C₄×C₆₇	—	2	4	no	—
177	C₂²×C₄×C₆₇	—	2	4	no	—
178	C₂²×C₄×C₆₇	—	2	4	no	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	2	8	no	—
181	C₂²×C₄×C₆₇	—	2	8	no	—
182	C₂²×C₄×C₆₇	—	2	8	no	—
183	C₂²×C₄×C₆₇	—	2	8	no	—
184	C₂²×C₄×C₆₇	—	2	8	no	—
185	C₂²×C₄×C₆₇	—	2	8	no	—
186	C₂²×C₄×C₆₇	—	2	8	no	—
187	C₂²×C₄×C₆₇	—	4	2	no	—
188	C₂²×C₄×C₆₇	—	4	4	no	—
189	C₂²×C₄×C₆₇	—	4	32	no	—
190	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	complemented
195	C₂²×C₄×C₆₇	#41	1	4	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	—	2	4	no	—
208	C₄⋊C₄×C₆₇	—	2	4	no	—
209	C₄⋊C₄×C₆₇	—	2	4	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	2	no	—
212	C₄⋊C₄×C₆₇	—	2	2	no	—
213	C₄⋊C₄×C₆₇	—	2	8	no	—
214	C₄⋊C₄×C₆₇	—	2	16	no	—
215	C₄⋊C₄×C₆₇	—	2	8	no	—
216	C₄⋊C₄×C₆₇	—	4	4	no	—
217	C₂²⋊C₄×C₆₇	—	2	4	no	—
218	C₂²⋊C₄×C₆₇	—	2	8	no	—
219	C₂²⋊C₄×C₆₇	—	2	16	no	—
220	C₂²⋊C₄×C₆₇	—	2	16	no	—
221	C₂²⋊C₄×C₆₇	—	2	8	no	—
222	C₂²⋊C₄×C₆₇	—	2	8	no	—
223	C₂²⋊C₄×C₆₇	—	2	4	no	—
224	C₂²⋊C₄×C₆₇	—	2	4	no	—
225	C₂²⋊C₄×C₆₇	—	2	16	no	—
226	C₂²⋊C₄×C₆₇	—	4	8	no	—
227	C₄²×C₆₇	—	2	4	no	—
228	C₄²×C₆₇	—	2	4	no	—
229	C₄²×C₆₇	—	2	4	no	—
230	C₄²×C₆₇	—	2	8	no	—
231	C₄²×C₆₇	C₂×D₄	1	4	yes	—
232	C₄²×C₆₇	C₂×D₄	1	4	yes	—
233	C₄²×C₆₇	C₂×D₄	1	4	yes	—
234	C₄²×C₆₇	C₂×D₄	1	4	yes	—
235	C₂³×C₆₇	—	2	2	no	—
236	C₂³×C₆₇	—	2	2	no	—
237	C₂³×C₆₇	—	2	16	no	—
238	C₂³×C₆₇	—	2	2	no	—
239	C₂³×C₆₇	—	2	4	no	—
240	C₂³×C₆₇	—	2	4	no	—
241	C₂³×C₆₇	—	2	4	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	4	no	—
244	C₂³×C₆₇	—	2	4	no	—
245	C₂³×C₆₇	—	2	4	no	—
246	C₂³×C₆₇	—	2	4	no	—
247	C₂³×C₆₇	—	2	4	no	—
248	C₂³×C₆₇	—	4	16	no	—
249	C₂³×C₆₇	—	4	16	no	—
250	C₂³×C₆₇	—	4	8	no	—
251	C₂³×C₆₇	—	4	8	no	—
252	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
253	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
254	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
255	C₂³×C₆₇	C₂×#41	1	8	yes	—
256	C₂³×C₆₇	C₂×#41	1	2	yes	—
257	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
258	Q₈×C₆₇	—	2	8	no	—
259	D₄×C₆₇	—	2	16	no	—
260	D₄×C₆₇	—	2	16	no	—
261	D₄×C₆₇	—	2	8	no	—
262	D₄×C₆₇	—	2	16	no	—
263	D₄×C₆₇	—	4	32	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	16	no	—
270	C₂×C₄×C₆₇	—	2	8	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	8	no	—
274	C₂×C₄×C₆₇	—	2	4	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	4	no	—
277	C₂×C₄×C₆₇	—	2	8	no	—
278	C₂×C₄×C₆₇	—	2	4	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	8	no	—
281	C₂×C₄×C₆₇	—	4	4	no	—
282	C₂×C₄×C₆₇	—	4	8	no	—
283	C₂×C₄×C₆₇	—	4	8	no	—
284	C₂×C₄×C₆₇	—	4	16	no	—
285	C₂×C₄×C₆₇	—	4	16	no	—
286	C₂×C₄×C₆₇	—	4	8	no	—
287	C₂×C₄×C₆₇	#121	1	16	yes	complemented
288	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
298	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
299	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
300	C₂²×C₆₇	—	2	2	no	—
301	C₂²×C₆₇	—	2	2	no	—
302	C₂²×C₆₇	—	2	4	no	—
303	C₂²×C₆₇	—	2	4	no	—
304	C₂²×C₆₇	—	2	4	no	—
305	C₂²×C₆₇	—	2	8	no	—
306	C₂²×C₆₇	—	2	8	no	—
307	C₂²×C₆₇	—	2	8	no	—
308	C₂²×C₆₇	—	2	8	no	—
309	C₂²×C₆₇	—	4	32	no	—
310	C₂²×C₆₇	—	4	4	no	—
311	C₂²×C₆₇	—	4	2	no	—
312	C₂²×C₆₇	—	4	2	no	—
313	C₂²×C₆₇	—	4	4	no	—
314	C₂²×C₆₇	—	4	4	no	—
315	C₂²×C₆₇	—	4	4	no	—
316	C₂²×C₆₇	—	4	4	no	—
317	C₂²×C₆₇	C₂×#121	1	4	yes	—
318	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
319	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
320	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₆₇	C₂²×#41	1	2	yes	—
322	C₂²×C₆₇	#585	1	2	yes	—
323	C₄×C₆₇	—	2	4	no	—
324	C₄×C₆₇	—	2	2	no	—
325	C₄×C₆₇	—	2	2	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	—	4	4	no	—
328	C₄×C₆₇	—	4	2	no	—
329	C₄×C₆₇	—	4	2	no	—
330	C₄×C₆₇	—	4	8	no	—
331	C₄×C₆₇	C₂×#121	1	4	yes	—
332	C₄×C₆₇	C₂×#121	1	4	yes	—
333	C₄×C₆₇	#525	1	4	yes	complemented
334	#34935	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂×C₆₇	—	2	4	no	—
336	C₂×C₆₇	—	4	4	no	—
337	C₂×C₆₇	—	4	8	no	—
338	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
339	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
340	C₂×C₆₇	#3449	1	1	yes	characteristic
341	C₂×C₆₇	D₄×#41	1	2	yes	—
342	C₂×C₆₇	#3475	1	2	yes	—
343	C₂×#525	C₂×C₆₇	1	2	yes	complemented
344	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
345	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
346	#2538	C₂×C₆₇	1	2	yes	complemented
347	#2537	C₂×C₆₇	1	2	yes	complemented
348	#2536	C₂×C₆₇	1	2	yes	complemented
349	#2535	C₂×C₆₇	1	2	yes	complemented
350	#2534	C₂×C₆₇	1	4	yes	complemented
351	#2486	C₂×C₆₇	1	2	yes	complemented
352	#2408	C₂×C₆₇	1	2	yes	complemented
353	#2392	C₂×C₆₇	1	4	yes	complemented
354	C₄×#121	C₂×C₆₇	1	4	yes	complemented
355	#2285	C₂×C₆₇	1	1	yes	characteristic, complemented
356	#2280	C₂×C₆₇	1	2	yes	complemented
357	C₆₇	#34935	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
359	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
360	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
361	#525	—	2	16	no	—
362	C₂×#123	C₂²×C₆₇	1	4	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
364	C₂×#121	C₂²×C₆₇	1	4	yes	—
365	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
366	C₂×#120	C₂²×C₆₇	1	4	yes	—
367	C₄×#41	—	2	8	no	—
368	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
369	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
370	C₂×C₄×D₄	—	2	8	no	—
371	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
378	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
379	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
380	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
381	C₂×#117	C₂²×C₆₇	1	2	yes	—
382	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
383	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
385	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
387	#398	C₂²×C₆₇	1	4	yes	complemented
388	#397	C₂²×C₆₇	1	4	yes	complemented
389	#396	C₂²×C₆₇	1	8	yes	complemented
390	#394	C₂²×C₆₇	1	4	yes	—
391	#394	C₂²×C₆₇	1	8	yes	complemented
392	#392	C₂²×C₆₇	1	4	yes	—
393	#390	C₂²×C₆₇	1	4	yes	—
394	#389	C₂²×C₆₇	1	4	yes	complemented
395	#388	C₂²×C₆₇	1	8	yes	complemented
396	#386	C₂²×C₆₇	1	8	yes	complemented
397	#384	C₂²×C₆₇	1	2	yes	complemented
398	#382	C₂²×C₆₇	1	2	yes	complemented
399	#381	C₂²×C₆₇	1	4	yes	—
400	#380	C₂²×C₆₇	1	2	yes	—
401	#380	C₂²×C₆₇	1	2	yes	—
402	#380	C₂²×C₆₇	1	4	yes	complemented
403	#380	C₂²×C₆₇	1	4	yes	complemented
404	#380	C₂²×C₆₇	1	4	yes	complemented
405	#379	C₂²×C₆₇	1	4	yes	—
406	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
407	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
408	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
409	C₂⁵	C₂³×C₆₇	1	2	yes	—
410	C₂×#41	—	2	4	no	—
411	C₂×#41	—	2	4	no	—
412	C₂×#41	D₄×C₆₇	1	8	yes	complemented
413	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
414	C₂²×D₄	—	2	8	no	—
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
417	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
418	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
419	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
421	C₂³×C₄	—	2	8	no	—
422	C₂³×C₄	—	2	8	no	—
423	C₂³×C₄	—	2	8	no	—
424	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
425	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
426	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
427	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
428	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
430	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
431	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
433	#123	—	2	16	no	—
434	C₂²⋊Q₈	—	2	16	no	—
435	#121	—	2	16	no	—
436	#121	—	2	16	no	—
437	#120	—	2	16	no	—
438	C₄×Q₈	—	2	4	no	—
439	C₄×Q₈	—	2	4	no	—
440	C₄×D₄	—	2	8	no	—
441	C₄×D₄	—	2	8	no	—
442	C₄×D₄	—	2	32	no	—
443	C₄×D₄	—	2	8	no	—
444	C₄×D₄	—	2	8	no	—
445	C₄×D₄	—	2	8	no	—
446	C₄×D₄	—	2	8	no	—
447	C₄×D₄	—	2	4	no	—
448	C₄×D₄	—	2	4	no	—
449	#117	—	2	4	no	—
450	#117	—	2	8	no	—
451	#117	—	2	8	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
461	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
463	C₂×C₂²⋊C₄	—	2	8	no	—
464	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
474	C₂×C₄²	—	2	8	no	—
475	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
476	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
477	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
478	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
484	#95	C₂³×C₆₇	1	8	yes	—
485	#95	C₂³×C₆₇	1	8	yes	—
486	#95	C₂³×C₆₇	1	4	yes	—
487	#95	C₂³×C₆₇	1	4	yes	—
488	C₂⁴	—	2	4	no	—
489	C₂⁴	—	2	8	no	—
490	C₂⁴	—	2	4	no	—
491	C₂⁴	—	2	4	no	—
492	C₂⁴	—	4	4	no	—
493	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
494	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
495	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
496	#41	—	2	32	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
500	C₂×D₄	—	2	32	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	8	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	16	no	—
505	C₂×D₄	—	2	16	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	4	8	no	—
512	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
513	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
514	C₂×D₄	#41×C₆₇	1	8	yes	complemented
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	2	8	no	—
526	C₂²×C₄	—	2	8	no	—
527	C₂²×C₄	—	2	8	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	32	no	—
533	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
534	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
535	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
536	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
537	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	complemented
538	C₂²×C₄	#41×C₆₇	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	—	2	16	no	—
558	C₄⋊C₄	—	2	8	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	16	no	—
563	C₂²⋊C₄	—	2	16	no	—
564	C₂²⋊C₄	—	2	8	no	—
565	C₂²⋊C₄	—	2	8	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	16	no	—
569	C₂²⋊C₄	—	4	8	no	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	4	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	8	no	—
574	C₄²	C₂×D₄×C₆₇	1	4	yes	—
575	C₄²	C₂×D₄×C₆₇	1	4	yes	—
576	C₄²	C₂×D₄×C₆₇	1	4	yes	—
577	C₄²	C₂×D₄×C₆₇	1	4	yes	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	16	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	2	4	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	4	16	no	—
592	C₂³	—	4	16	no	—
593	C₂³	—	4	8	no	—
594	C₂³	—	4	8	no	—
595	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
596	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
597	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
598	C₂³	C₂×#41×C₆₇	1	8	yes	—
599	C₂³	C₂×#41×C₆₇	1	2	yes	—
600	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
601	Q₈	—	2	8	no	—
602	D₄	—	2	16	no	—
603	D₄	—	2	16	no	—
604	D₄	—	2	8	no	—
605	D₄	—	2	16	no	—
606	D₄	—	4	32	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	16	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	8	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	16	no	—
628	C₂×C₄	—	4	16	no	—
629	C₂×C₄	—	4	8	no	—
630	C₂×C₄	#121×C₆₇	1	16	yes	complemented
631	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
632	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
634	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
635	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
636	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
637	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
638	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
640	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
641	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
642	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	8	no	—
649	C₂²	—	2	8	no	—
650	C₂²	—	2	8	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	4	32	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	4	no	—
659	C₂²	—	4	4	no	—
660	C₂²	C₂×#121×C₆₇	1	4	yes	—
661	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
662	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
663	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
664	C₂²	C₂²×#41×C₆₇	1	2	yes	—
665	C₂²	#585×C₆₇	1	2	yes	—
666	C₄	—	2	4	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	8	no	—
674	C₄	C₂×#121×C₆₇	1	4	yes	—
675	C₄	C₂×#121×C₆₇	1	4	yes	—
676	C₄	#525×C₆₇	1	4	yes	complemented
677	C₂	—	2	4	no	—
678	C₂	—	4	8	no	—
679	C₂	—	4	4	no	—
680	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
681	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
682	C₂	C₆₇×#3449	1	1	yes	characteristic
683	C₂	D₄×#41×C₆₇	1	2	yes	—
684	C₂	C₆₇×#3475	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#525×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₂²×C₄×D₄×C₆₇	C₂	semidirect
4. C₆₇×#2538	C₂	semidirect
5. C₆₇×#2537	C₂	semidirect
6. C₆₇×#2536	C₂	semidirect
7. C₆₇×#2535	C₂	semidirect
8. C₆₇×#2534	C₂	semidirect
9. C₆₇×#2486	C₂	semidirect
10. C₆₇×#2408	C₂	semidirect
11. C₆₇×#2392	C₂	semidirect
12. C₄×#121×C₆₇	C₂	semidirect
13. C₆₇×#2285	C₂	semidirect
14. C₆₇×#2280	C₂	semidirect
20. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
22. C₂×#121×C₆₇	C₂²	semidirect
25. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
26. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×C₄×D₄×C₆₇	C₂²	semidirect
39. C₂×#117×C₆₇	C₂²	semidirect
43. C₂²×C₄²×C₆₇	C₂²	semidirect
44. #398×C₆₇	C₂²	semidirect
45. #397×C₆₇	C₂²	semidirect
46. #396×C₆₇	C₂²	semidirect
48. #394×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
52. #388×C₆₇	C₂²	semidirect
53. #386×C₆₇	C₂²	semidirect
54. #384×C₆₇	C₂²	semidirect
55. #382×C₆₇	C₂²	semidirect
59. #380×C₆₇	C₂²	semidirect
60. #380×C₆₇	C₂²	semidirect
61. #380×C₆₇	C₂²	semidirect
63. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
64. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
69. C₂×#41×C₆₇	D₄	semidirect
132. C₂×C₄²×C₆₇	D₄	semidirect
156. C₂×Q₈×C₆₇	C₂×D₄	semidirect
170. C₂×D₄×C₆₇	C₂×D₄	semidirect
171. C₂×D₄×C₆₇	#41	semidirect
194. C₂²×C₄×C₆₇	C₂×D₄	semidirect
287. C₂×C₄×C₆₇	#121	semidirect
333. C₄×C₆₇	#525	semidirect
334. #34935	C₆₇	direct (N × H)
343. C₂×#525	C₂×C₆₇	semidirect
344. C₂×C₄×#41	C₂×C₆₇	semidirect
345. C₂²×C₄×D₄	C₂×C₆₇	semidirect
346. #2538	C₂×C₆₇	semidirect
347. #2537	C₂×C₆₇	semidirect
348. #2536	C₂×C₆₇	semidirect
349. #2535	C₂×C₆₇	semidirect
350. #2534	C₂×C₆₇	semidirect
351. #2486	C₂×C₆₇	semidirect
352. #2408	C₂×C₆₇	semidirect
353. #2392	C₂×C₆₇	semidirect
354. C₄×#121	C₂×C₆₇	semidirect
355. #2285	C₂×C₆₇	semidirect
356. #2280	C₂×C₆₇	semidirect
357. C₆₇	#34935	direct (N × H)
363. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
365. C₂×#121	C₂²×C₆₇	semidirect
368. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
369. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
377. C₂×C₄×D₄	C₂²×C₆₇	semidirect
378. C₂×C₄×D₄	C₂²×C₆₇	semidirect
379. C₂×C₄×D₄	C₂²×C₆₇	semidirect
382. C₂×#117	C₂²×C₆₇	semidirect
386. C₂²×C₄²	C₂²×C₆₇	semidirect
387. #398	C₂²×C₆₇	semidirect
388. #397	C₂²×C₆₇	semidirect
389. #396	C₂²×C₆₇	semidirect
391. #394	C₂²×C₆₇	semidirect
394. #389	C₂²×C₆₇	semidirect
395. #388	C₂²×C₆₇	semidirect
396. #386	C₂²×C₆₇	semidirect
397. #384	C₂²×C₆₇	semidirect
398. #382	C₂²×C₆₇	semidirect
402. #380	C₂²×C₆₇	semidirect
403. #380	C₂²×C₆₇	semidirect
404. #380	C₂²×C₆₇	semidirect
406. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
407. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
408. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
412. C₂×#41	D₄×C₆₇	semidirect
475. C₂×C₄²	D₄×C₆₇	semidirect
499. C₂×Q₈	C₂×D₄×C₆₇	semidirect
513. C₂×D₄	C₂×D₄×C₆₇	semidirect
514. C₂×D₄	#41×C₆₇	semidirect
537. C₂²×C₄	C₂×D₄×C₆₇	semidirect
630. C₂×C₄	#121×C₆₇	semidirect
676. C₄	#525×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2538	2
C₆₇×#2537	2
C₆₇×#2536	2
C₆₇×#2535	2
C₆₇×#2534	2
C₆₇×#2486	2
C₆₇×#2408	2
C₆₇×#2392	2
C₄×#121×C₆₇	2
C₆₇×#2285	2
C₆₇×#2280	2
#34935	67

Subgroups — C67×#34935 #30714186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34935 #30714186