Subgroups — C₂×C₆₇×#3358 #30740546

Order 17152.

2402 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×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3358	C₂	1	16	yes	maximal, direct product factor
4	C₂×#486×C₆₇	C₂	1	3	yes	maximal, complemented
5	C₂×#474×C₆₇	C₂	1	3	yes	maximal, complemented
6	C₂×#459×C₆₇	C₂	1	3	yes	maximal, complemented
7	C₂×C₈×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₆₇	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₆₇	—	2	1	no	—
10	C₂³×Q₈×C₆₇	—	2	1	no	—
11	C₂²×D₈×C₆₇	C₂²	1	3	yes	—
12	#550×C₆₇	—	2	4	no	—
13	#550×C₆₇	C₂²	1	8	yes	complemented
14	D₄×Q₈×C₆₇	—	2	4	no	—
15	D₄×Q₈×C₆₇	C₂²	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₆₇	C₂²	1	3	yes	—
17	C₂×#127×C₆₇	C₂²	1	3	yes	—
18	C₂×C₂²⋊Q₈×C₆₇	—	2	3	no	—
19	C₂×#121×C₆₇	—	2	3	no	—
20	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₇	C₂²	1	3	yes	—
22	C₂×C₄×D₄×C₆₇	C₂²	1	3	yes	—
23	#486×C₆₇	C₂²	1	24	yes	complemented
24	#474×C₆₇	C₂²	1	24	yes	complemented
25	#459×C₆₇	C₂²	1	24	yes	complemented
26	C₈×Q₈×C₆₇	C₂²	1	8	yes	complemented
27	C₄×D₈×C₆₇	C₂²	1	24	yes	complemented
28	C₂×#107×C₆₇	C₂²	1	3	yes	—
29	C₂×C₄⋊C₈×C₆₇	C₂²	1	3	yes	—
30	C₂×#102×C₆₇	C₂²	1	6	yes	—
31	C₂×#102×C₆₇	C₂²	1	3	yes	—
32	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₆₇	C₂²	1	3	yes	—
34	C₂×#41×C₆₇	—	2	8	no	—
35	C₂×#41×C₆₇	—	4	8	no	—
36	C₂²×Q₈×C₆₇	—	2	8	no	—
37	C₂²×Q₈×C₆₇	—	2	3	no	—
38	C₂²×Q₈×C₆₇	—	4	8	no	—
39	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₆₇	—	2	3	no	—
41	C₂²×D₄×C₆₇	—	2	3	no	—
42	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
43	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	—	2	3	no	—
45	C₂³×C₄×C₆₇	—	2	3	no	—
46	C₂×D₈×C₆₇	—	2	12	no	—
47	C₂×D₈×C₆₇	C₂³	1	12	yes	—
48	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
49	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₆₇	—	2	6	no	—
51	C₄⋊Q₈×C₆₇	C₂³	1	12	yes	—
52	#127×C₆₇	—	2	6	no	—
53	#127×C₆₇	C₂³	1	12	yes	—
54	C₂²⋊Q₈×C₆₇	—	2	24	no	—
55	#121×C₆₇	—	2	24	no	—
56	C₄×Q₈×C₆₇	D₄	1	4	yes	—
57	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
58	C₄×D₄×C₆₇	—	2	6	no	—
59	C₄×D₄×C₆₇	—	2	6	no	—
60	C₄×D₄×C₆₇	C₂³	1	12	yes	—
61	C₄×D₄×C₆₇	C₂³	1	12	yes	—
62	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
63	C₂×C₄⋊C₄×C₆₇	D₄	1	3	yes	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
66	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
67	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
68	C₂×C₄²×C₆₇	C₂³	1	3	yes	—
69	#107×C₆₇	C₂³	1	12	yes	—
70	C₄⋊C₈×C₆₇	C₂³	1	12	yes	—
71	#102×C₆₇	C₂³	1	24	yes	—
72	#102×C₆₇	C₂³	1	12	yes	—
73	#102×C₆₇	C₂³	1	4	yes	—
74	C₄×C₈×C₆₇	C₂³	1	12	yes	—
75	C₂⁴×C₆₇	—	2	1	no	—
76	C₂⁴×C₆₇	—	2	3	no	—
77	#41×C₆₇	—	4	32	no	—
78	C₂×Q₈×C₆₇	—	2	12	no	—
79	C₂×Q₈×C₆₇	—	4	32	no	—
80	C₂×Q₈×C₆₇	—	4	12	no	—
81	C₂×Q₈×C₆₇	D₈	1	8	yes	complemented
82	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
83	C₂×D₄×C₆₇	—	2	1	no	—
84	C₂×D₄×C₆₇	—	2	3	no	—
85	C₂×D₄×C₆₇	—	2	12	no	—
86	C₂×D₄×C₆₇	—	2	12	no	—
87	C₂×D₄×C₆₇	—	2	6	no	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	6	no	—
90	C₂×D₄×C₆₇	—	4	12	no	—
91	C₂×D₄×C₆₇	—	8	6	no	—
92	C₂×D₄×C₆₇	#41	1	4	yes	complemented
93	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
94	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₆₇	—	2	1	no	—
96	C₂²×C₄×C₆₇	—	2	3	no	—
97	C₂²×C₄×C₆₇	—	2	12	no	—
98	C₂²×C₄×C₆₇	—	2	12	no	—
99	C₂²×C₄×C₆₇	—	4	12	no	—
100	C₂²×C₄×C₆₇	—	4	12	no	—
101	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
102	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
104	D₈×C₆₇	—	2	24	no	—
105	C₂×C₈×C₆₇	—	2	6	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
108	C₂×C₈×C₆₇	C₂⁴	1	6	yes	—
109	C₄⋊C₄×C₆₇	—	2	12	no	—
110	C₄⋊C₄×C₆₇	—	2	1	no	—
111	C₄⋊C₄×C₆₇	—	2	3	no	—
112	C₄⋊C₄×C₆₇	C₂×D₄	1	12	yes	—
113	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
114	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
115	C₂²⋊C₄×C₆₇	—	2	12	no	—
116	C₂²⋊C₄×C₆₇	—	2	12	no	—
117	C₄²×C₆₇	C₂×D₄	1	6	yes	—
118	C₄²×C₆₇	C₂⁴	1	6	yes	—
119	C₂³×C₆₇	—	2	4	no	—
120	C₂³×C₆₇	—	2	2	no	—
121	C₂³×C₆₇	—	2	6	no	—
122	C₂³×C₆₇	—	4	2	no	—
123	C₂³×C₆₇	—	4	2	no	—
124	C₂³×C₆₇	—	4	6	no	—
125	C₂³×C₆₇	—	4	6	no	—
126	C₂³×C₆₇	—	4	6	no	—
127	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₆₇	—	4	24	no	—
129	Q₈×C₆₇	C₂×D₈	1	16	yes	complemented
130	D₄×C₆₇	—	2	4	no	—
131	D₄×C₆₇	—	2	6	no	—
132	D₄×C₆₇	—	2	2	no	—
133	D₄×C₆₇	—	2	6	no	—
134	D₄×C₆₇	—	4	6	no	—
135	D₄×C₆₇	—	4	24	no	—
136	D₄×C₆₇	—	8	12	no	—
137	D₄×C₆₇	C₂×#41	1	4	yes	complemented
138	C₂×C₄×C₆₇	—	2	6	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	6	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	4	6	no	—
143	C₂×C₄×C₆₇	—	4	24	no	—
144	C₂×C₄×C₆₇	—	4	24	no	—
145	C₂×C₄×C₆₇	C₂×D₈	1	12	yes	—
146	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
147	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
149	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
150	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
151	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
152	C₈×C₆₇	—	2	6	no	—
153	C₈×C₆₇	—	2	2	no	—
154	C₂²×C₆₇	—	2	4	no	—
155	C₂²×C₆₇	—	4	8	no	—
156	C₂²×C₆₇	—	4	2	no	—
157	C₂²×C₆₇	—	4	2	no	—
158	C₂²×C₆₇	—	4	6	no	—
159	C₂²×C₆₇	—	4	6	no	—
160	C₂²×C₆₇	—	4	6	no	—
161	C₂²×C₆₇	—	8	12	no	—
162	C₂²×C₆₇	#548	1	2	yes	—
163	C₂²×C₆₇	C₂²×D₈	1	2	yes	—
164	C₂²×C₆₇	#577	1	2	yes	—
165	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
166	C₄×C₆₇	—	2	6	no	—
167	C₄×C₆₇	—	4	2	no	—
168	C₄×C₆₇	—	4	6	no	—
169	C₄×C₆₇	#548	1	2	yes	—
170	C₄×C₆₇	C₂²×D₈	1	12	yes	—
171	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
172	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×#3358	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₆₇	—	4	4	no	—
175	C₂×C₆₇	—	8	6	no	—
176	C₂×C₆₇	#3358	1	4	yes	direct product factor
177	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
178	C₂×C₆₇	C₂³×D₈	1	1	yes	characteristic
179	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
180	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
181	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
182	#3358	C₂×C₆₇	1	16	yes	direct product factor
183	C₂×#486	C₂×C₆₇	1	3	yes	complemented
184	C₂×#474	C₂×C₆₇	1	3	yes	complemented
185	C₂×#459	C₂×C₆₇	1	3	yes	complemented
186	C₂×C₈×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
187	C₂×C₄×D₈	C₂×C₆₇	1	3	yes	complemented
188	C₆₇	C₂×#3358	1	1	yes	characteristic, direct product factor, Sylow
189	C₂²×#41	—	2	1	no	—
190	C₂³×Q₈	—	2	1	no	—
191	C₂²×D₈	C₂²×C₆₇	1	3	yes	—
192	#550	—	2	4	no	—
193	#550	C₂²×C₆₇	1	8	yes	complemented
194	D₄×Q₈	—	2	4	no	—
195	D₄×Q₈	C₂²×C₆₇	1	8	yes	complemented
196	C₂×C₄⋊Q₈	C₂²×C₆₇	1	3	yes	—
197	C₂×#127	C₂²×C₆₇	1	3	yes	—
198	C₂×C₂²⋊Q₈	—	2	3	no	—
199	C₂×#121	—	2	3	no	—
200	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₆₇	1	3	yes	—
202	C₂×C₄×D₄	C₂²×C₆₇	1	3	yes	—
203	#486	C₂²×C₆₇	1	24	yes	complemented
204	#474	C₂²×C₆₇	1	24	yes	complemented
205	#459	C₂²×C₆₇	1	24	yes	complemented
206	C₈×Q₈	C₂²×C₆₇	1	8	yes	complemented
207	C₄×D₈	C₂²×C₆₇	1	24	yes	complemented
208	C₂×#107	C₂²×C₆₇	1	3	yes	—
209	C₂×C₄⋊C₈	C₂²×C₆₇	1	3	yes	—
210	C₂×#102	C₂²×C₆₇	1	3	yes	—
211	C₂×#102	C₂²×C₆₇	1	6	yes	—
212	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₆₇	1	3	yes	—
214	C₂×#41	—	2	8	no	—
215	C₂×#41	—	4	8	no	—
216	C₂²×Q₈	—	2	8	no	—
217	C₂²×Q₈	—	2	3	no	—
218	C₂²×Q₈	—	4	8	no	—
219	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
220	C₂²×D₄	—	2	3	no	—
221	C₂²×D₄	—	2	3	no	—
222	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
223	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
224	C₂³×C₄	—	2	3	no	—
225	C₂³×C₄	—	2	3	no	—
226	C₂×D₈	—	2	12	no	—
227	C₂×D₈	C₂³×C₆₇	1	12	yes	—
228	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
229	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
230	C₄⋊Q₈	—	2	6	no	—
231	C₄⋊Q₈	C₂³×C₆₇	1	12	yes	—
232	#127	—	2	6	no	—
233	#127	C₂³×C₆₇	1	12	yes	—
234	C₂²⋊Q₈	—	2	24	no	—
235	#121	—	2	24	no	—
236	C₄×Q₈	D₄×C₆₇	1	4	yes	—
237	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
238	C₄×D₄	—	2	6	no	—
239	C₄×D₄	—	2	6	no	—
240	C₄×D₄	C₂³×C₆₇	1	12	yes	—
241	C₄×D₄	C₂³×C₆₇	1	12	yes	—
242	C₂×C₄⋊C₄	—	2	3	no	—
243	C₂×C₄⋊C₄	D₄×C₆₇	1	3	yes	—
244	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	—
246	C₂×C₂²⋊C₄	—	2	3	no	—
247	C₂×C₂²⋊C₄	—	2	3	no	—
248	C₂×C₄²	C₂³×C₆₇	1	3	yes	—
249	#107	C₂³×C₆₇	1	12	yes	—
250	C₄⋊C₈	C₂³×C₆₇	1	12	yes	—
251	#102	C₂³×C₆₇	1	4	yes	—
252	#102	C₂³×C₆₇	1	12	yes	—
253	#102	C₂³×C₆₇	1	24	yes	—
254	C₄×C₈	C₂³×C₆₇	1	12	yes	—
255	C₂⁴	—	2	1	no	—
256	C₂⁴	—	2	3	no	—
257	#41	—	4	32	no	—
258	C₂×Q₈	—	2	12	no	—
259	C₂×Q₈	—	4	32	no	—
260	C₂×Q₈	—	4	12	no	—
261	C₂×Q₈	D₈×C₆₇	1	8	yes	complemented
262	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	3	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	12	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	6	no	—
270	C₂×D₄	—	4	12	no	—
271	C₂×D₄	—	8	6	no	—
272	C₂×D₄	#41×C₆₇	1	4	yes	complemented
273	C₂×D₄	C₂⁴×C₆₇	1	6	yes	—
274	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	12	no	—
278	C₂²×C₄	—	2	12	no	—
279	C₂²×C₄	—	4	12	no	—
280	C₂²×C₄	—	4	12	no	—
281	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
282	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
283	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
284	D₈	—	2	24	no	—
285	C₂×C₈	—	2	6	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
288	C₂×C₈	C₂⁴×C₆₇	1	6	yes	—
289	C₄⋊C₄	—	2	12	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	3	no	—
292	C₄⋊C₄	C₂×D₄×C₆₇	1	12	yes	—
293	C₄⋊C₄	C₂⁴×C₆₇	1	6	yes	—
294	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
295	C₂²⋊C₄	—	2	12	no	—
296	C₂²⋊C₄	—	2	12	no	—
297	C₄²	C₂×D₄×C₆₇	1	6	yes	—
298	C₄²	C₂⁴×C₆₇	1	6	yes	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	6	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	6	no	—
305	C₂³	—	4	6	no	—
306	C₂³	—	4	6	no	—
307	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
308	Q₈	—	4	24	no	—
309	Q₈	C₂×D₈×C₆₇	1	16	yes	complemented
310	D₄	—	2	4	no	—
311	D₄	—	2	6	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	6	no	—
314	D₄	—	4	6	no	—
315	D₄	—	4	24	no	—
316	D₄	—	8	12	no	—
317	D₄	C₂×#41×C₆₇	1	4	yes	complemented
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	6	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	6	no	—
323	C₂×C₄	—	4	24	no	—
324	C₂×C₄	—	4	24	no	—
325	C₂×C₄	C₂×D₈×C₆₇	1	12	yes	—
326	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
327	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
329	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
330	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
331	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
332	C₈	—	2	6	no	—
333	C₈	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	4	6	no	—
339	C₂²	—	4	6	no	—
340	C₂²	—	4	6	no	—
341	C₂²	—	8	12	no	—
342	C₂²	#548×C₆₇	1	2	yes	—
343	C₂²	C₂²×D₈×C₆₇	1	2	yes	—
344	C₂²	#577×C₆₇	1	2	yes	—
345	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
346	C₄	—	2	6	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	6	no	—
349	C₄	#548×C₆₇	1	2	yes	—
350	C₄	C₂²×D₈×C₆₇	1	12	yes	—
351	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
352	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
353	C₂	—	4	4	no	—
354	C₂	—	8	6	no	—
355	C₂	C₆₇×#3358	1	4	yes	direct product factor
356	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
357	C₂	C₂³×D₈×C₆₇	1	1	yes	characteristic
358	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#550×C₆₇	C₂	semidirect
2. C₂×D₄×Q₈×C₆₇	C₂	semidirect
3. C₆₇×#3358	C₂	direct (N × H)
4. C₂×#486×C₆₇	C₂	semidirect
5. C₂×#474×C₆₇	C₂	semidirect
6. C₂×#459×C₆₇	C₂	semidirect
7. C₂×C₈×Q₈×C₆₇	C₂	semidirect
8. C₂×C₄×D₈×C₆₇	C₂	semidirect
13. #550×C₆₇	C₂²	semidirect
15. D₄×Q₈×C₆₇	C₂²	semidirect
23. #486×C₆₇	C₂²	semidirect
24. #474×C₆₇	C₂²	semidirect
25. #459×C₆₇	C₂²	semidirect
26. C₈×Q₈×C₆₇	C₂²	semidirect
27. C₄×D₈×C₆₇	C₂²	semidirect
81. C₂×Q₈×C₆₇	D₈	semidirect
92. C₂×D₄×C₆₇	#41	semidirect
129. Q₈×C₆₇	C₂×D₈	semidirect
137. D₄×C₆₇	C₂×#41	semidirect
173. C₂×#3358	C₆₇	direct (N × H)
176. C₂×C₆₇	#3358	direct (N × H)
180. C₂×#550	C₂×C₆₇	semidirect
181. C₂×D₄×Q₈	C₂×C₆₇	semidirect
182. #3358	C₂×C₆₇	direct (N × H)
183. C₂×#486	C₂×C₆₇	semidirect
184. C₂×#474	C₂×C₆₇	semidirect
185. C₂×#459	C₂×C₆₇	semidirect
186. C₂×C₈×Q₈	C₂×C₆₇	semidirect
187. C₂×C₄×D₈	C₂×C₆₇	semidirect
188. C₆₇	C₂×#3358	direct (N × H)
193. #550	C₂²×C₆₇	semidirect
195. D₄×Q₈	C₂²×C₆₇	semidirect
203. #486	C₂²×C₆₇	semidirect
204. #474	C₂²×C₆₇	semidirect
205. #459	C₂²×C₆₇	semidirect
206. C₈×Q₈	C₂²×C₆₇	semidirect
207. C₄×D₈	C₂²×C₆₇	semidirect
261. C₂×Q₈	D₈×C₆₇	semidirect
272. C₂×D₄	#41×C₆₇	semidirect
309. Q₈	C₂×D₈×C₆₇	semidirect
317. D₄	C₂×#41×C₆₇	semidirect
355. C₂	C₆₇×#3358	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×#550×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₆₇×#3358	2
C₂×#486×C₆₇	2
C₂×#474×C₆₇	2
C₂×#459×C₆₇	2
C₂×C₈×Q₈×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#3358	67

Subgroups — C2×C67×#3358 #30740546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3358 #30740546