Subgroups — C₂×C₆₇×#3131 #30739856

Order 17152.

2222 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3131	C₂	1	16	yes	maximal, direct product factor
4	C₂×#488×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#487×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#486×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#416×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₇	C₂²	1	2	yes	—
10	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
11	#533×C₆₇	—	2	4	no	—
12	#533×C₆₇	C₂²	1	8	yes	complemented
13	#532×C₆₇	—	2	4	no	—
14	#532×C₆₇	C₂²	1	8	yes	—
15	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
17	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#125×C₆₇	C₂²	1	2	yes	—
19	C₂×#124×C₆₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
21	C₂×#121×C₆₇	—	2	2	no	—
22	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
23	C₂×C₄×D₄×C₆₇	—	2	2	no	—
24	C₂×#117×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#488×C₆₇	C₂²	1	32	yes	complemented
27	#487×C₆₇	C₂²	1	16	yes	complemented
28	#486×C₆₇	C₂²	1	16	yes	complemented
29	#416×C₆₇	C₂²	1	32	yes	complemented
30	C₂×#103×C₆₇	C₂²	1	8	yes	—
31	C₂×#102×C₆₇	C₂²	1	8	yes	—
32	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₆₇	C₂²	1	8	yes	complemented
35	C₂×#41×C₆₇	—	2	4	no	—
36	C₂×#41×C₆₇	—	2	16	no	—
37	C₂×#41×C₆₇	C₂³	1	8	yes	—
38	C₂²×Q₈×C₆₇	—	2	2	no	—
39	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
40	C₂²×D₄×C₆₇	—	2	2	no	—
41	C₂²×D₄×C₆₇	—	2	2	no	—
42	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₇	—	2	2	no	—
44	C₂³×C₄×C₆₇	D₄	1	2	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₆₇	—	2	8	no	—
47	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
48	C₂²×C₈×C₆₇	C₂³	1	8	yes	—
49	C₄⋊Q₈×C₆₇	—	2	2	no	—
50	C₄⋊Q₈×C₆₇	—	2	4	no	—
51	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
52	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
53	#127×C₆₇	—	2	2	no	—
54	#127×C₆₇	C₂³	1	4	yes	—
55	#125×C₆₇	—	2	4	no	—
56	#125×C₆₇	C₂³	1	8	yes	—
57	#124×C₆₇	—	2	4	no	—
58	#124×C₆₇	C₂³	1	8	yes	—
59	C₂²⋊Q₈×C₆₇	—	2	16	no	—
60	#121×C₆₇	—	2	16	no	—
61	C₄×Q₈×C₆₇	—	2	16	no	—
62	C₄×D₄×C₆₇	—	2	16	no	—
63	#117×C₆₇	—	2	4	no	—
64	#117×C₆₇	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
71	C₂×C₄²×C₆₇	—	2	2	no	—
72	C₂×C₄²×C₆₇	D₄	1	4	yes	—
73	C₂×C₄²×C₆₇	D₄	1	2	yes	—
74	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
77	#103×C₆₇	C₂³	1	32	yes	—
78	#102×C₆₇	C₂³	1	32	yes	—
79	C₄×C₈×C₆₇	C₂³	1	8	yes	—
80	C₄×C₈×C₆₇	C₂³	1	8	yes	—
81	C₂⁴×C₆₇	—	2	2	no	—
82	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
83	#41×C₆₇	—	2	32	no	—
84	#41×C₆₇	—	4	16	no	—
85	C₂×Q₈×C₆₇	—	2	8	no	—
86	C₂×Q₈×C₆₇	—	2	2	no	—
87	C₂×Q₈×C₆₇	—	2	8	no	—
88	C₂×Q₈×C₆₇	—	4	8	no	—
89	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
90	C₂×D₄×C₆₇	—	2	8	no	—
91	C₂×D₄×C₆₇	—	2	8	no	—
92	C₂×D₄×C₆₇	—	2	2	no	—
93	C₂×D₄×C₆₇	—	2	8	no	—
94	C₂×D₄×C₆₇	—	4	8	no	—
95	C₂×D₄×C₆₇	—	4	8	no	—
96	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₆₇	—	2	8	no	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	—	2	8	no	—
101	C₂²×C₄×C₆₇	—	4	8	no	—
102	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₇	#41	1	8	yes	—
108	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
110	C₂×C₈×C₆₇	—	2	8	no	—
111	C₂×C₈×C₆₇	—	2	16	no	—
112	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
113	C₄⋊C₄×C₆₇	—	2	8	no	—
114	C₄⋊C₄×C₆₇	—	2	16	no	—
115	C₄⋊C₄×C₆₇	—	2	8	no	—
116	C₄⋊C₄×C₆₇	—	2	4	no	—
117	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
118	C₂²⋊C₄×C₆₇	—	2	8	no	—
119	C₂²⋊C₄×C₆₇	—	2	16	no	—
120	C₄²×C₆₇	—	2	8	no	—
121	C₄²×C₆₇	C₂×D₄	1	8	yes	—
122	C₄²×C₆₇	C₂×D₄	1	2	yes	—
123	C₄²×C₆₇	C₂×D₄	1	2	yes	—
124	C₄²×C₆₇	C₂⁴	1	2	yes	—
125	C₄²×C₆₇	C₂⁴	1	2	yes	—
126	C₂³×C₆₇	—	2	4	no	—
127	C₂³×C₆₇	—	2	4	no	—
128	C₂³×C₆₇	—	4	4	no	—
129	C₂³×C₆₇	—	4	8	no	—
130	C₂³×C₆₇	#124	1	4	yes	—
131	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
132	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₆₇	—	2	8	no	—
134	Q₈×C₆₇	—	4	4	no	—
135	Q₈×C₆₇	—	4	16	no	—
136	D₄×C₆₇	—	2	8	no	—
137	D₄×C₆₇	—	4	16	no	—
138	D₄×C₆₇	—	4	4	no	—
139	D₄×C₆₇	—	4	16	no	—
140	C₂×C₄×C₆₇	—	2	4	no	—
141	C₂×C₄×C₆₇	—	2	16	no	—
142	C₂×C₄×C₆₇	—	2	8	no	—
143	C₂×C₄×C₆₇	—	2	4	no	—
144	C₂×C₄×C₆₇	—	4	4	no	—
145	C₂×C₄×C₆₇	—	4	8	no	—
146	C₂×C₄×C₆₇	—	4	16	no	—
147	C₂×C₄×C₆₇	#124	1	4	yes	—
148	C₂×C₄×C₆₇	#124	1	8	yes	—
149	C₂×C₄×C₆₇	#135	1	8	yes	—
150	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
155	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
156	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
157	C₈×C₆₇	—	2	8	no	—
158	C₂²×C₆₇	—	2	8	no	—
159	C₂²×C₆₇	—	2	4	no	—
160	C₂²×C₆₇	—	4	4	no	—
161	C₂²×C₆₇	—	4	8	no	—
162	C₂²×C₆₇	—	8	8	no	—
163	C₂²×C₆₇	C₂×#124	1	4	yes	—
164	C₂²×C₆₇	C₂×#124	1	2	yes	—
165	C₂²×C₆₇	C₂×#135	1	4	yes	—
166	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
167	C₄×C₆₇	—	2	4	no	—
168	C₄×C₆₇	—	4	4	no	—
169	C₄×C₆₇	—	4	8	no	—
170	C₄×C₆₇	C₂×#124	1	4	yes	—
171	C₄×C₆₇	C₂×#124	1	2	yes	—
172	C₄×C₆₇	C₂×#135	1	8	yes	—
173	C₄×C₆₇	C₂²×#41	1	2	yes	—
174	C₂×#3131	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₆₇	—	2	4	no	—
176	C₂×C₆₇	—	8	4	no	—
177	C₂×C₆₇	#3131	1	4	yes	direct product factor
178	C₂×C₆₇	C₂²×#124	1	1	yes	characteristic
179	C₂×C₆₇	C₂²×#135	1	2	yes	—
180	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
181	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
182	#3131	C₂×C₆₇	1	16	yes	direct product factor
183	C₂×#488	C₂×C₆₇	1	4	yes	complemented
184	C₂×#487	C₂×C₆₇	1	2	yes	complemented
185	C₂×#486	C₂×C₆₇	1	2	yes	complemented
186	C₂×#416	C₂×C₆₇	1	4	yes	complemented
187	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
188	C₆₇	C₂×#3131	1	1	yes	characteristic, direct product factor, Sylow
189	C₂²×#41	C₂²×C₆₇	1	2	yes	—
190	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
191	#533	—	2	4	no	—
192	#533	C₂²×C₆₇	1	8	yes	complemented
193	#532	—	2	4	no	—
194	#532	C₂²×C₆₇	1	8	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
197	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
198	C₂×#125	C₂²×C₆₇	1	2	yes	—
199	C₂×#124	C₂²×C₆₇	1	2	yes	—
200	C₂×C₂²⋊Q₈	—	2	2	no	—
201	C₂×#121	—	2	2	no	—
202	C₂×C₄×Q₈	—	2	2	no	—
203	C₂×C₄×D₄	—	2	2	no	—
204	C₂×#117	C₂²×C₆₇	1	2	yes	—
205	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
206	#488	C₂²×C₆₇	1	32	yes	complemented
207	#487	C₂²×C₆₇	1	16	yes	complemented
208	#486	C₂²×C₆₇	1	16	yes	complemented
209	#416	C₂²×C₆₇	1	32	yes	complemented
210	C₂×#103	C₂²×C₆₇	1	8	yes	—
211	C₂×#102	C₂²×C₆₇	1	8	yes	—
212	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₆₇	1	8	yes	complemented
215	C₂×#41	—	2	4	no	—
216	C₂×#41	—	2	16	no	—
217	C₂×#41	C₂³×C₆₇	1	8	yes	—
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
220	C₂²×D₄	—	2	2	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	D₄×C₆₇	1	2	yes	—
225	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
226	C₂²×C₈	—	2	8	no	—
227	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
228	C₂²×C₈	C₂³×C₆₇	1	8	yes	—
229	C₄⋊Q₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
232	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
233	#127	—	2	2	no	—
234	#127	C₂³×C₆₇	1	4	yes	—
235	#125	—	2	4	no	—
236	#125	C₂³×C₆₇	1	8	yes	—
237	#124	—	2	4	no	—
238	#124	C₂³×C₆₇	1	8	yes	—
239	C₂²⋊Q₈	—	2	16	no	—
240	#121	—	2	16	no	—
241	C₄×Q₈	—	2	16	no	—
242	C₄×D₄	—	2	16	no	—
243	#117	—	2	4	no	—
244	#117	C₂³×C₆₇	1	8	yes	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	D₄×C₆₇	1	2	yes	—
253	C₂×C₄²	D₄×C₆₇	1	4	yes	—
254	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
257	#103	C₂³×C₆₇	1	32	yes	—
258	#102	C₂³×C₆₇	1	32	yes	—
259	C₄×C₈	C₂³×C₆₇	1	8	yes	—
260	C₄×C₈	C₂³×C₆₇	1	8	yes	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
263	#41	—	2	32	no	—
264	#41	—	4	16	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	4	8	no	—
282	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
284	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
287	C₂²×C₄	#41×C₆₇	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
298	C₂²⋊C₄	—	2	8	no	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₄²	—	2	8	no	—
301	C₄²	C₂×D₄×C₆₇	1	8	yes	—
302	C₄²	C₂×D₄×C₆₇	1	2	yes	—
303	C₄²	C₂×D₄×C₆₇	1	2	yes	—
304	C₄²	C₂⁴×C₆₇	1	2	yes	—
305	C₄²	C₂⁴×C₆₇	1	2	yes	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	8	no	—
310	C₂³	#124×C₆₇	1	4	yes	—
311	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
312	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
313	Q₈	—	2	8	no	—
314	Q₈	—	4	4	no	—
315	Q₈	—	4	16	no	—
316	D₄	—	2	8	no	—
317	D₄	—	4	16	no	—
318	D₄	—	4	4	no	—
319	D₄	—	4	16	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	4	16	no	—
327	C₂×C₄	#124×C₆₇	1	4	yes	—
328	C₂×C₄	#124×C₆₇	1	8	yes	—
329	C₂×C₄	#135×C₆₇	1	8	yes	—
330	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
332	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
334	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
335	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
336	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	4	8	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	8	8	no	—
343	C₂²	C₂×#124×C₆₇	1	4	yes	—
344	C₂²	C₂×#124×C₆₇	1	2	yes	—
345	C₂²	C₂×#135×C₆₇	1	4	yes	—
346	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	4	8	no	—
349	C₄	—	4	4	no	—
350	C₄	C₂×#124×C₆₇	1	4	yes	—
351	C₄	C₂×#124×C₆₇	1	2	yes	—
352	C₄	C₂×#135×C₆₇	1	8	yes	—
353	C₄	C₂²×#41×C₆₇	1	2	yes	—
354	C₂	—	2	4	no	—
355	C₂	—	8	4	no	—
356	C₂	C₆₇×#3131	1	4	yes	direct product factor
357	C₂	C₂²×#124×C₆₇	1	1	yes	characteristic
358	C₂	C₂²×#135×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂²×D₄
prime radical	C₂×#532×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₆₇	C₂	semidirect
3. C₆₇×#3131	C₂	direct (N × H)
4. C₂×#488×C₆₇	C₂	semidirect
5. C₂×#487×C₆₇	C₂	semidirect
6. C₂×#486×C₆₇	C₂	semidirect
7. C₂×#416×C₆₇	C₂	semidirect
8. C₂²×C₄×C₈×C₆₇	C₂	semidirect
12. #533×C₆₇	C₂²	semidirect
26. #488×C₆₇	C₂²	semidirect
27. #487×C₆₇	C₂²	semidirect
28. #486×C₆₇	C₂²	semidirect
29. #416×C₆₇	C₂²	semidirect
34. C₂×C₄×C₈×C₆₇	C₂²	semidirect
174. C₂×#3131	C₆₇	direct (N × H)
177. C₂×C₆₇	#3131	direct (N × H)
180. C₂×#533	C₂×C₆₇	semidirect
182. #3131	C₂×C₆₇	direct (N × H)
183. C₂×#488	C₂×C₆₇	semidirect
184. C₂×#487	C₂×C₆₇	semidirect
185. C₂×#486	C₂×C₆₇	semidirect
186. C₂×#416	C₂×C₆₇	semidirect
187. C₂²×C₄×C₈	C₂×C₆₇	semidirect
188. C₆₇	C₂×#3131	direct (N × H)
192. #533	C₂²×C₆₇	semidirect
206. #488	C₂²×C₆₇	semidirect
207. #487	C₂²×C₆₇	semidirect
208. #486	C₂²×C₆₇	semidirect
209. #416	C₂²×C₆₇	semidirect
214. C₂×C₄×C₈	C₂²×C₆₇	semidirect
356. C₂	C₆₇×#3131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#533×C₆₇	2
C₂×#532×C₆₇	2
C₆₇×#3131	2
C₂×#488×C₆₇	2
C₂×#487×C₆₇	2
C₂×#486×C₆₇	2
C₂×#416×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂×#3131	67

Subgroups — C2×C67×#3131 #30739856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3131 #30739856