Subgroups — C₂×C₆₇×#3138 #30739864

Order 17152.

2806 conjugacy classes of subgroups.

The subgroup lattice has 338 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	C₂²×#127×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3138	C₂	1	16	yes	maximal, direct product factor
4	C₂×#490×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#486×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#418×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₆₇	—	2	2	no	—
9	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
11	#533×C₆₇	—	2	4	no	—
12	#533×C₆₇	C₂²	1	8	yes	complemented
13	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
14	C₂×#127×C₆₇	—	2	2	no	—
15	C₂×#127×C₆₇	—	2	4	no	—
16	C₂×#127×C₆₇	C₂²	1	2	yes	—
17	C₂×#127×C₆₇	C₂²	1	2	yes	—
18	C₂×#127×C₆₇	C₂²	1	8	yes	—
19	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
21	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
22	C₂×#117×C₆₇	C₂²	1	2	yes	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	#490×C₆₇	C₂²	1	32	yes	complemented
25	#486×C₆₇	C₂²	1	32	yes	complemented
26	#418×C₆₇	C₂²	1	32	yes	complemented
27	C₂×#102×C₆₇	C₂²	1	16	yes	complemented
28	C₄×M₁₆×C₆₇	C₂²	1	8	yes	complemented
29	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
30	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
31	C₂⁵×C₆₇	—	2	2	no	—
32	C₂²×Q₈×C₆₇	—	2	2	no	—
33	C₂²×D₄×C₆₇	—	2	4	no	—
34	C₂²×D₄×C₆₇	—	2	2	no	—
35	C₂²×D₄×C₆₇	—	2	16	no	—
36	C₂²×D₄×C₆₇	—	2	4	no	—
37	C₂²×D₄×C₆₇	—	2	4	no	—
38	C₂²×D₄×C₆₇	—	2	16	no	—
39	C₂²×D₄×C₆₇	—	4	16	no	—
40	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
41	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
42	C₂³×C₄×C₆₇	D₄	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₆₇	—	2	8	no	—
45	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
46	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₆₇	—	2	4	no	—
48	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
49	#127×C₆₇	—	2	16	no	—
50	#127×C₆₇	—	2	4	no	—
51	#127×C₆₇	—	2	4	no	—
52	#127×C₆₇	C₂³	1	8	yes	—
53	#127×C₆₇	C₂³	1	8	yes	—
54	#125×C₆₇	—	2	4	no	—
55	#125×C₆₇	C₂³	1	8	yes	complemented
56	C₂²⋊Q₈×C₆₇	—	2	16	no	—
57	C₄×Q₈×C₆₇	—	2	16	no	—
58	#117×C₆₇	—	2	4	no	—
59	#117×C₆₇	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
64	C₂×C₄²×C₆₇	—	2	2	no	—
65	C₂×C₄²×C₆₇	D₄	1	2	yes	—
66	C₂×C₄²×C₆₇	D₄	1	4	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
70	#102×C₆₇	C₂³	1	64	yes	complemented
71	#97×C₆₇	C₂³	1	8	yes	complemented
72	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
73	C₂⁴×C₆₇	—	2	8	no	—
74	C₂⁴×C₆₇	—	2	4	no	—
75	C₂⁴×C₆₇	—	4	16	no	—
76	C₂⁴×C₆₇	—	4	8	no	—
77	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₆₇	—	2	8	no	—
79	C₂×Q₈×C₆₇	—	4	8	no	—
80	C₂×D₄×C₆₇	—	2	8	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	2	16	no	—
83	C₂×D₄×C₆₇	—	2	16	no	—
84	C₂×D₄×C₆₇	—	2	16	no	—
85	C₂×D₄×C₆₇	—	2	32	no	—
86	C₂×D₄×C₆₇	—	4	16	no	—
87	C₂×D₄×C₆₇	—	4	64	no	—
88	C₂×D₄×C₆₇	—	4	16	no	—
89	C₂×D₄×C₆₇	—	4	8	no	—
90	C₂×D₄×C₆₇	—	4	16	no	—
91	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
92	C₂²×C₄×C₆₇	—	2	8	no	—
93	C₂²×C₄×C₆₇	—	2	4	no	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₇	#41	1	8	yes	—
100	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₆₇	—	2	16	no	—
103	C₂×C₈×C₆₇	—	2	8	no	—
104	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
105	C₄⋊C₄×C₆₇	—	2	16	no	—
106	C₄⋊C₄×C₆₇	—	2	8	no	—
107	C₄⋊C₄×C₆₇	—	2	4	no	—
108	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₆₇	—	2	8	no	—
110	C₄²×C₆₇	—	2	8	no	—
111	C₄²×C₆₇	C₂×D₄	1	8	yes	—
112	C₄²×C₆₇	C₂×D₄	1	2	yes	—
113	C₄²×C₆₇	C₂×D₄	1	2	yes	—
114	C₄²×C₆₇	C₂⁴	1	2	yes	—
115	C₄²×C₆₇	C₂⁴	1	2	yes	—
116	C₂³×C₆₇	—	2	4	no	—
117	C₂³×C₆₇	—	2	8	no	—
118	C₂³×C₆₇	—	4	32	no	—
119	C₂³×C₆₇	—	4	16	no	—
120	C₂³×C₆₇	—	4	8	no	—
121	C₂³×C₆₇	—	4	16	no	—
122	C₂³×C₆₇	—	8	32	no	—
123	C₂³×C₆₇	#124	1	4	yes	—
124	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₆₇	—	4	16	no	—
127	D₄×C₆₇	—	2	16	no	—
128	D₄×C₆₇	—	4	32	no	—
129	D₄×C₆₇	—	4	16	no	—
130	D₄×C₆₇	—	4	8	no	—
131	D₄×C₆₇	—	4	32	no	—
132	C₂×C₄×C₆₇	—	2	4	no	—
133	C₂×C₄×C₆₇	—	2	16	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	4	8	no	—
136	C₂×C₄×C₆₇	#124	1	8	yes	—
137	C₂×C₄×C₆₇	#124	1	4	yes	—
138	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	8	yes	—
139	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
140	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
144	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
145	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
146	C₈×C₆₇	—	2	8	no	—
147	C₂²×C₆₇	—	2	8	no	—
148	C₂²×C₆₇	—	2	4	no	—
149	C₂²×C₆₇	—	4	8	no	—
150	C₂²×C₆₇	—	4	16	no	—
151	C₂²×C₆₇	—	8	32	no	—
152	C₂²×C₆₇	—	8	16	no	—
153	C₂²×C₆₇	C₂×#124	1	4	yes	—
154	C₂²×C₆₇	C₂×#124	1	2	yes	—
155	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
156	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
157	C₄×C₆₇	—	2	4	no	—
158	C₄×C₆₇	—	4	8	no	—
159	C₄×C₆₇	C₂×#124	1	4	yes	—
160	C₄×C₆₇	C₂×#124	1	2	yes	—
161	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	8	yes	—
162	C₄×C₆₇	C₂²×#41	1	2	yes	—
163	C₂×#3138	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂×C₆₇	—	2	4	no	—
165	C₂×C₆₇	—	8	8	no	—
166	C₂×C₆₇	#3138	1	4	yes	direct product factor
167	C₂×C₆₇	C₂²×#124	1	1	yes	characteristic
168	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	2	yes	—
169	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
170	C₂²×#127	C₂×C₆₇	1	1	yes	characteristic
171	#3138	C₂×C₆₇	1	16	yes	direct product factor
172	C₂×#490	C₂×C₆₇	1	4	yes	complemented
173	C₂×#486	C₂×C₆₇	1	4	yes	complemented
174	C₂×#418	C₂×C₆₇	1	4	yes	complemented
175	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
176	C₆₇	C₂×#3138	1	1	yes	characteristic, direct product factor, Sylow
177	C₂³×D₄	—	2	2	no	—
178	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
179	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
180	#533	—	2	4	no	—
181	#533	C₂²×C₆₇	1	8	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
183	C₂×#127	—	2	2	no	—
184	C₂×#127	—	2	4	no	—
185	C₂×#127	C₂²×C₆₇	1	2	yes	—
186	C₂×#127	C₂²×C₆₇	1	2	yes	—
187	C₂×#127	C₂²×C₆₇	1	8	yes	—
188	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
189	C₂×C₂²⋊Q₈	—	2	2	no	—
190	C₂×C₄×Q₈	—	2	2	no	—
191	C₂×#117	C₂²×C₆₇	1	2	yes	—
192	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
193	#490	C₂²×C₆₇	1	32	yes	complemented
194	#486	C₂²×C₆₇	1	32	yes	complemented
195	#418	C₂²×C₆₇	1	32	yes	complemented
196	C₂×#102	C₂²×C₆₇	1	16	yes	complemented
197	C₄×M₁₆	C₂²×C₆₇	1	8	yes	complemented
198	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
199	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
200	C₂⁵	—	2	2	no	—
201	C₂²×Q₈	—	2	2	no	—
202	C₂²×D₄	—	2	2	no	—
203	C₂²×D₄	—	2	4	no	—
204	C₂²×D₄	—	2	4	no	—
205	C₂²×D₄	—	2	16	no	—
206	C₂²×D₄	—	2	4	no	—
207	C₂²×D₄	—	2	16	no	—
208	C₂²×D₄	—	4	16	no	—
209	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
210	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
211	C₂³×C₄	D₄×C₆₇	1	2	yes	—
212	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
213	C₂×M₁₆	—	2	8	no	—
214	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
215	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
216	C₄⋊Q₈	—	2	4	no	—
217	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
218	#127	—	2	16	no	—
219	#127	—	2	4	no	—
220	#127	—	2	4	no	—
221	#127	C₂³×C₆₇	1	8	yes	—
222	#127	C₂³×C₆₇	1	8	yes	—
223	#125	—	2	4	no	—
224	#125	C₂³×C₆₇	1	8	yes	complemented
225	C₂²⋊Q₈	—	2	16	no	—
226	C₄×Q₈	—	2	16	no	—
227	#117	—	2	4	no	—
228	#117	C₂³×C₆₇	1	8	yes	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	D₄×C₆₇	1	2	yes	—
235	C₂×C₄²	D₄×C₆₇	1	4	yes	—
236	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
239	#102	C₂³×C₆₇	1	64	yes	complemented
240	#97	C₂³×C₆₇	1	8	yes	complemented
241	C₄×C₈	C₂³×C₆₇	1	8	yes	complemented
242	C₂⁴	—	2	8	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	4	16	no	—
245	C₂⁴	—	4	8	no	—
246	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
247	C₂×Q₈	—	2	8	no	—
248	C₂×Q₈	—	4	8	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	16	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	—	2	32	no	—
255	C₂×D₄	—	4	16	no	—
256	C₂×D₄	—	4	64	no	—
257	C₂×D₄	—	4	16	no	—
258	C₂×D₄	—	4	8	no	—
259	C₂×D₄	—	4	16	no	—
260	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
265	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
268	C₂²×C₄	#41×C₆₇	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
271	M₁₆	—	2	16	no	—
272	C₂×C₈	—	2	8	no	—
273	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
278	C₂²⋊C₄	—	2	8	no	—
279	C₄²	—	2	8	no	—
280	C₄²	C₂×D₄×C₆₇	1	8	yes	—
281	C₄²	C₂×D₄×C₆₇	1	2	yes	—
282	C₄²	C₂×D₄×C₆₇	1	2	yes	—
283	C₄²	C₂⁴×C₆₇	1	2	yes	—
284	C₄²	C₂⁴×C₆₇	1	2	yes	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	4	32	no	—
288	C₂³	—	4	16	no	—
289	C₂³	—	4	8	no	—
290	C₂³	—	4	16	no	—
291	C₂³	—	8	32	no	—
292	C₂³	#124×C₆₇	1	4	yes	—
293	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
294	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
295	Q₈	—	4	16	no	—
296	D₄	—	2	16	no	—
297	D₄	—	4	32	no	—
298	D₄	—	4	16	no	—
299	D₄	—	4	8	no	—
300	D₄	—	4	32	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	#124×C₆₇	1	8	yes	—
306	C₂×C₄	#124×C₆₇	1	4	yes	—
307	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
310	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
312	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
313	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
314	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
315	C₈	—	2	8	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	8	no	—
318	C₂²	—	4	16	no	—
319	C₂²	—	4	8	no	—
320	C₂²	—	8	32	no	—
321	C₂²	—	8	16	no	—
322	C₂²	C₂×#124×C₆₇	1	4	yes	—
323	C₂²	C₂×#124×C₆₇	1	2	yes	—
324	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	—
325	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	4	8	no	—
328	C₄	C₂×#124×C₆₇	1	4	yes	—
329	C₄	C₂×#124×C₆₇	1	2	yes	—
330	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	8	yes	—
331	C₄	C₂²×#41×C₆₇	1	2	yes	—
332	C₂	—	2	4	no	—
333	C₂	—	8	8	no	—
334	C₂	C₆₇×#3138	1	4	yes	direct product factor
335	C₂	C₂²×#124×C₆₇	1	1	yes	characteristic
336	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×#127×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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×#3138	C₂	direct (N × H)
4. C₂×#490×C₆₇	C₂	semidirect
5. C₂×#486×C₆₇	C₂	semidirect
6. C₂×#418×C₆₇	C₂	semidirect
7. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
12. #533×C₆₇	C₂²	semidirect
13. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
19. C₂×#125×C₆₇	C₂²	semidirect
24. #490×C₆₇	C₂²	semidirect
25. #486×C₆₇	C₂²	semidirect
26. #418×C₆₇	C₂²	semidirect
27. C₂×#102×C₆₇	C₂²	semidirect
28. C₄×M₁₆×C₆₇	C₂²	semidirect
29. C₂×#97×C₆₇	C₂²	semidirect
30. C₂×C₄×C₈×C₆₇	C₂²	semidirect
48. C₄⋊Q₈×C₆₇	C₂³	semidirect
55. #125×C₆₇	C₂³	semidirect
70. #102×C₆₇	C₂³	semidirect
71. #97×C₆₇	C₂³	semidirect
72. C₄×C₈×C₆₇	C₂³	semidirect
163. C₂×#3138	C₆₇	direct (N × H)
166. C₂×C₆₇	#3138	direct (N × H)
169. C₂×#533	C₂×C₆₇	semidirect
171. #3138	C₂×C₆₇	direct (N × H)
172. C₂×#490	C₂×C₆₇	semidirect
173. C₂×#486	C₂×C₆₇	semidirect
174. C₂×#418	C₂×C₆₇	semidirect
175. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
176. C₆₇	C₂×#3138	direct (N × H)
181. #533	C₂²×C₆₇	semidirect
182. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
188. C₂×#125	C₂²×C₆₇	semidirect
193. #490	C₂²×C₆₇	semidirect
194. #486	C₂²×C₆₇	semidirect
195. #418	C₂²×C₆₇	semidirect
196. C₂×#102	C₂²×C₆₇	semidirect
197. C₄×M₁₆	C₂²×C₆₇	semidirect
198. C₂×#97	C₂²×C₆₇	semidirect
199. C₂×C₄×C₈	C₂²×C₆₇	semidirect
217. C₄⋊Q₈	C₂³×C₆₇	semidirect
224. #125	C₂³×C₆₇	semidirect
239. #102	C₂³×C₆₇	semidirect
240. #97	C₂³×C₆₇	semidirect
241. C₄×C₈	C₂³×C₆₇	semidirect
334. C₂	C₆₇×#3138	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
C₂²×#127×C₆₇	2
C₆₇×#3138	2
C₂×#490×C₆₇	2
C₂×#486×C₆₇	2
C₂×#418×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₂×#3138	67

Subgroups — C2×C67×#3138 #30739864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3138 #30739864