Subgroups — C₂×C₆₇×#2948 #30739413

Order 17152.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2948	C₂	1	16	yes	maximal, direct product factor
4	C₂×#442×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×D₈×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#427×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#418×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
10	C₂²×D₈×C₆₇	C₄	1	16	yes	complemented
11	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
12	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₇	C₂²	1	8	yes	—
14	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	#518×C₆₇	—	2	8	no	—
17	#518×C₆₇	C₂²	1	16	yes	complemented
18	C₂×C₄×D₄×C₆₇	—	2	4	no	—
19	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
20	C₂×#117×C₆₇	C₂²	1	2	yes	—
21	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₆₇	—	2	4	no	—
23	#442×C₆₇	C₂²	1	32	yes	complemented
24	C₄×D₈×C₆₇	C₂²	1	32	yes	complemented
25	#427×C₆₇	C₂²	1	8	yes	complemented
26	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
28	#418×C₆₇	C₂²	1	16	yes	complemented
29	C₂×#102×C₆₇	C₂²	1	8	yes	complemented
30	#405×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
33	C₂⁵×C₆₇	—	2	2	no	—
34	C₂²×D₄×C₆₇	—	2	2	no	—
35	C₂²×D₄×C₆₇	—	2	4	no	—
36	C₂²×D₄×C₆₇	—	2	8	no	—
37	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
38	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
39	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
40	C₂³×C₄×C₆₇	—	2	8	no	—
41	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₆₇	C₂×C₄	1	16	yes	complemented
43	C₂×D₈×C₆₇	C₂×C₄	1	16	yes	complemented
44	C₂×D₈×C₆₇	C₂×C₄	1	64	yes	complemented
45	C₂×D₈×C₆₇	C₂³	1	8	yes	—
46	C₂×D₈×C₆₇	C₂³	1	8	yes	—
47	C₂×M₁₆×C₆₇	—	2	4	no	—
48	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
49	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
50	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
54	C₄×D₄×C₆₇	—	2	32	no	—
55	C₄×D₄×C₆₇	—	2	16	no	—
56	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
57	#117×C₆₇	—	2	4	no	—
58	#117×C₆₇	D₄	1	4	yes	—
59	#117×C₆₇	C₂³	1	8	yes	—
60	#117×C₆₇	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	32	no	—
66	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
69	#107×C₆₇	C₂³	1	8	yes	complemented
70	#106×C₆₇	C₂³	1	8	yes	complemented
71	#102×C₆₇	C₂³	1	32	yes	complemented
72	#97×C₆₇	C₂³	1	8	yes	complemented
73	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
74	C₂⁴×C₆₇	—	2	4	no	—
75	C₂⁴×C₆₇	—	2	16	no	—
76	C₂⁴×C₆₇	—	2	8	no	—
77	C₂⁴×C₆₇	—	8	8	no	—
78	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₆₇	—	2	32	no	—
80	C₂×D₄×C₆₇	—	2	16	no	—
81	C₂×D₄×C₆₇	—	2	8	no	—
82	C₂×D₄×C₆₇	—	2	4	no	—
83	C₂×D₄×C₆₇	—	2	8	no	—
84	C₂×D₄×C₆₇	—	2	16	no	—
85	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
86	C₂×D₄×C₆₇	C₂²×C₄	1	32	yes	complemented
87	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₆₇	—	2	4	no	—
89	C₂²×C₄×C₆₇	—	2	32	no	—
90	C₂²×C₄×C₆₇	—	8	16	no	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	#41	1	4	yes	—
96	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	D₈×C₆₇	C₂²×C₄	1	32	yes	complemented
99	D₈×C₆₇	C₂²×C₄	1	32	yes	complemented
100	M₁₆×C₆₇	—	2	8	no	—
101	C₂×C₈×C₆₇	—	2	4	no	—
102	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
104	C₂×C₈×C₆₇	C₂²×C₄	1	16	yes	complemented
105	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
106	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
107	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
108	C₄⋊C₄×C₆₇	—	2	4	no	—
109	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
110	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
111	C₂²⋊C₄×C₆₇	—	2	8	no	—
112	C₂²⋊C₄×C₆₇	—	2	32	no	—
113	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
114	C₄²×C₆₇	—	2	8	no	—
115	C₄²×C₆₇	C₂×D₄	1	4	yes	—
116	C₄²×C₆₇	C₂⁴	1	4	yes	—
117	C₂³×C₆₇	—	2	4	no	—
118	C₂³×C₆₇	—	2	16	no	—
119	C₂³×C₆₇	—	2	8	no	—
120	C₂³×C₆₇	—	2	32	no	—
121	C₂³×C₆₇	—	4	16	no	—
122	C₂³×C₆₇	—	8	32	no	—
123	C₂³×C₆₇	—	8	16	no	—
124	C₂³×C₆₇	C₄×D₄	1	4	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
126	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
127	D₄×C₆₇	—	2	16	no	—
128	D₄×C₆₇	—	2	32	no	—
129	D₄×C₆₇	—	2	8	no	—
130	D₄×C₆₇	C₂³×C₄	1	16	yes	—
131	C₂×C₄×C₆₇	—	2	8	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	4	8	no	—
134	C₂×C₄×C₆₇	—	8	32	no	—
135	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
136	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
138	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
140	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
143	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
144	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
145	C₈×C₆₇	—	2	4	no	—
146	C₈×C₆₇	C₂³×C₄	1	4	yes	—
147	C₈×C₆₇	C₂³×C₄	1	4	yes	—
148	C₂²×C₆₇	—	2	8	no	—
149	C₂²×C₆₇	—	2	4	no	—
150	C₂²×C₆₇	—	2	16	no	—
151	C₂²×C₆₇	—	4	32	no	—
152	C₂²×C₆₇	—	4	16	no	—
153	C₂²×C₆₇	—	8	32	no	—
154	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
155	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
156	C₂²×C₆₇	#576	1	4	yes	—
157	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
158	C₄×C₆₇	—	2	8	no	—
159	C₄×C₆₇	—	4	8	no	—
160	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
161	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
162	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
163	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
164	C₂×#2948	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₆₇	—	2	4	no	—
166	C₂×C₆₇	—	4	16	no	—
167	C₂×C₆₇	#2948	1	4	yes	direct product factor
168	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
169	C₂×C₆₇	C₂×#576	1	2	yes	—
170	C₂³×D₈	C₂×C₆₇	1	1	yes	characteristic
171	C₂×#518	C₂×C₆₇	1	2	yes	complemented
172	#2948	C₂×C₆₇	1	16	yes	direct product factor
173	C₂×#442	C₂×C₆₇	1	4	yes	complemented
174	C₂×C₄×D₈	C₂×C₆₇	1	4	yes	complemented
175	C₂×#427	C₂×C₆₇	1	1	yes	characteristic, complemented
176	C₂×#418	C₂×C₆₇	1	2	yes	complemented
177	C₂×#405	C₂×C₆₇	1	1	yes	characteristic, complemented
178	C₆₇	C₂×#2948	1	1	yes	characteristic, direct product factor, Sylow
179	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
180	C₂²×D₈	C₄×C₆₇	1	16	yes	complemented
181	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
182	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
183	C₂²×D₈	C₂²×C₆₇	1	8	yes	—
184	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
185	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
186	#518	—	2	8	no	—
187	#518	C₂²×C₆₇	1	16	yes	complemented
188	C₂×C₄×D₄	—	2	4	no	—
189	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
190	C₂×#117	C₂²×C₆₇	1	2	yes	—
191	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
192	C₂²×C₂²⋊C₄	—	2	4	no	—
193	#442	C₂²×C₆₇	1	32	yes	complemented
194	C₄×D₈	C₂²×C₆₇	1	32	yes	complemented
195	#427	C₂²×C₆₇	1	8	yes	complemented
196	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
197	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
198	#418	C₂²×C₆₇	1	16	yes	complemented
199	C₂×#102	C₂²×C₆₇	1	8	yes	complemented
200	#405	C₂²×C₆₇	1	8	yes	complemented
201	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
202	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
203	C₂⁵	—	2	2	no	—
204	C₂²×D₄	—	2	2	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	8	no	—
207	C₂²×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
208	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
209	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
210	C₂³×C₄	—	2	8	no	—
211	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
212	C₂×D₈	C₂×C₄×C₆₇	1	16	yes	complemented
213	C₂×D₈	C₂×C₄×C₆₇	1	16	yes	complemented
214	C₂×D₈	C₂×C₄×C₆₇	1	64	yes	complemented
215	C₂×D₈	C₂³×C₆₇	1	8	yes	—
216	C₂×D₈	C₂³×C₆₇	1	8	yes	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
219	C₂²×C₈	C₂×C₄×C₆₇	1	8	yes	complemented
220	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
221	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
224	C₄×D₄	—	2	32	no	—
225	C₄×D₄	—	2	16	no	—
226	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
227	#117	—	2	4	no	—
228	#117	D₄×C₆₇	1	4	yes	—
229	#117	C₂³×C₆₇	1	8	yes	—
230	#117	C₂³×C₆₇	1	4	yes	—
231	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	8	no	—
235	C₂×C₂²⋊C₄	—	2	32	no	—
236	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
239	#107	C₂³×C₆₇	1	8	yes	complemented
240	#106	C₂³×C₆₇	1	8	yes	complemented
241	#102	C₂³×C₆₇	1	32	yes	complemented
242	#97	C₂³×C₆₇	1	8	yes	complemented
243	C₄×C₈	C₂³×C₆₇	1	8	yes	complemented
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	16	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	8	8	no	—
248	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
249	C₂×D₄	—	2	32	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	C₂²×C₄×C₆₇	1	16	yes	—
256	C₂×D₄	C₂²×C₄×C₆₇	1	32	yes	complemented
257	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	32	no	—
260	C₂²×C₄	—	8	16	no	—
261	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
265	C₂²×C₄	#41×C₆₇	1	4	yes	—
266	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
267	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
268	D₈	C₂²×C₄×C₆₇	1	32	yes	complemented
269	D₈	C₂²×C₄×C₆₇	1	32	yes	complemented
270	M₁₆	—	2	8	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
273	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
274	C₂×C₈	C₂²×C₄×C₆₇	1	16	yes	complemented
275	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
276	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
277	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
280	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
281	C₂²⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	2	32	no	—
283	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
284	C₄²	—	2	8	no	—
285	C₄²	C₂×D₄×C₆₇	1	4	yes	—
286	C₄²	C₂⁴×C₆₇	1	4	yes	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	16	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	32	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	8	16	no	—
293	C₂³	—	8	32	no	—
294	C₂³	C₄×D₄×C₆₇	1	4	yes	—
295	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
296	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
297	D₄	—	2	16	no	—
298	D₄	—	2	32	no	—
299	D₄	—	2	8	no	—
300	D₄	C₂³×C₄×C₆₇	1	16	yes	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	8	32	no	—
305	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
306	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
307	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
308	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
310	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
311	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
312	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
313	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
314	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
315	C₈	—	2	4	no	—
316	C₈	C₂³×C₄×C₆₇	1	4	yes	—
317	C₈	C₂³×C₄×C₆₇	1	4	yes	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	4	16	no	—
322	C₂²	—	4	32	no	—
323	C₂²	—	8	32	no	—
324	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
325	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
326	C₂²	#576×C₆₇	1	4	yes	—
327	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
328	C₄	—	2	8	no	—
329	C₄	—	4	8	no	—
330	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
331	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
332	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
333	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	4	16	no	—
336	C₂	C₆₇×#2948	1	4	yes	direct product factor
337	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
338	C₂	C₂×#576×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂³×D₈×C₆₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₆₇	C₂	semidirect
3. C₆₇×#2948	C₂	direct (N × H)
4. C₂×#442×C₆₇	C₂	semidirect
5. C₂×C₄×D₈×C₆₇	C₂	semidirect
6. C₂×#427×C₆₇	C₂	semidirect
7. C₂×#418×C₆₇	C₂	semidirect
8. C₂×#405×C₆₇	C₂	semidirect
10. C₂²×D₈×C₆₇	C₄	semidirect
17. #518×C₆₇	C₂²	semidirect
19. C₂×C₄×D₄×C₆₇	C₂²	semidirect
23. #442×C₆₇	C₂²	semidirect
24. C₄×D₈×C₆₇	C₂²	semidirect
25. #427×C₆₇	C₂²	semidirect
26. C₂×#107×C₆₇	C₂²	semidirect
27. C₂×#106×C₆₇	C₂²	semidirect
28. #418×C₆₇	C₂²	semidirect
29. C₂×#102×C₆₇	C₂²	semidirect
30. #405×C₆₇	C₂²	semidirect
31. C₂×#97×C₆₇	C₂²	semidirect
32. C₂×C₄×C₈×C₆₇	C₂²	semidirect
37. C₂²×D₄×C₆₇	C₂×C₄	semidirect
42. C₂×D₈×C₆₇	C₂×C₄	semidirect
43. C₂×D₈×C₆₇	C₂×C₄	semidirect
44. C₂×D₈×C₆₇	C₂×C₄	semidirect
49. C₂²×C₈×C₆₇	C₂×C₄	semidirect
56. C₄×D₄×C₆₇	C₂³	semidirect
69. #107×C₆₇	C₂³	semidirect
70. #106×C₆₇	C₂³	semidirect
71. #102×C₆₇	C₂³	semidirect
72. #97×C₆₇	C₂³	semidirect
73. C₄×C₈×C₆₇	C₂³	semidirect
86. C₂×D₄×C₆₇	C₂²×C₄	semidirect
98. D₈×C₆₇	C₂²×C₄	semidirect
99. D₈×C₆₇	C₂²×C₄	semidirect
104. C₂×C₈×C₆₇	C₂²×C₄	semidirect
164. C₂×#2948	C₆₇	direct (N × H)
167. C₂×C₆₇	#2948	direct (N × H)
171. C₂×#518	C₂×C₆₇	semidirect
172. #2948	C₂×C₆₇	direct (N × H)
173. C₂×#442	C₂×C₆₇	semidirect
174. C₂×C₄×D₈	C₂×C₆₇	semidirect
175. C₂×#427	C₂×C₆₇	semidirect
176. C₂×#418	C₂×C₆₇	semidirect
177. C₂×#405	C₂×C₆₇	semidirect
178. C₆₇	C₂×#2948	direct (N × H)
180. C₂²×D₈	C₄×C₆₇	semidirect
187. #518	C₂²×C₆₇	semidirect
189. C₂×C₄×D₄	C₂²×C₆₇	semidirect
193. #442	C₂²×C₆₇	semidirect
194. C₄×D₈	C₂²×C₆₇	semidirect
195. #427	C₂²×C₆₇	semidirect
196. C₂×#107	C₂²×C₆₇	semidirect
197. C₂×#106	C₂²×C₆₇	semidirect
198. #418	C₂²×C₆₇	semidirect
199. C₂×#102	C₂²×C₆₇	semidirect
200. #405	C₂²×C₆₇	semidirect
201. C₂×#97	C₂²×C₆₇	semidirect
202. C₂×C₄×C₈	C₂²×C₆₇	semidirect
207. C₂²×D₄	C₂×C₄×C₆₇	semidirect
212. C₂×D₈	C₂×C₄×C₆₇	semidirect
213. C₂×D₈	C₂×C₄×C₆₇	semidirect
214. C₂×D₈	C₂×C₄×C₆₇	semidirect
219. C₂²×C₈	C₂×C₄×C₆₇	semidirect
226. C₄×D₄	C₂³×C₆₇	semidirect
239. #107	C₂³×C₆₇	semidirect
240. #106	C₂³×C₆₇	semidirect
241. #102	C₂³×C₆₇	semidirect
242. #97	C₂³×C₆₇	semidirect
243. C₄×C₈	C₂³×C₆₇	semidirect
256. C₂×D₄	C₂²×C₄×C₆₇	semidirect
268. D₈	C₂²×C₄×C₆₇	semidirect
269. D₈	C₂²×C₄×C₆₇	semidirect
274. C₂×C₈	C₂²×C₄×C₆₇	semidirect
336. C₂	C₆₇×#2948	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₆₇	2
C₂×#518×C₆₇	2
C₆₇×#2948	2
C₂×#442×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#427×C₆₇	2
C₂×#418×C₆₇	2
C₂×#405×C₆₇	2
C₂×#2948	67

Subgroups — C2×C67×#2948 #30739413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2948 #30739413