Subgroups — C₂×C₆₇×#2372 #30713398

Order 17152.

3158 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2372	C₂	1	16	yes	maximal, direct product factor
3	C₂×#391×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#388×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#386×C₆₇	C₂	1	2	yes	maximal
6	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	4	yes	maximal, complemented
7	C₂×#376×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
11	C₂×#124×C₆₇	C₄	1	16	yes	complemented
12	C₂×#124×C₆₇	C₂²	1	8	yes	—
13	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
17	C₂²×C₄²×C₆₇	C₂²	1	4	yes	—
18	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	#391×C₆₇	C₂²	1	16	yes	complemented
21	#388×C₆₇	C₂²	1	32	yes	complemented
22	#386×C₆₇	C₂²	1	16	yes	—
23	C₄×C₂²⋊C₄×C₆₇	C₂²	1	32	yes	complemented
24	#376×C₆₇	C₂²	1	16	yes	complemented
25	C₂×#95×C₆₇	C₂²	1	2	yes	—
26	C₂×#95×C₆₇	C₂²	1	4	yes	—
27	C₂×#95×C₆₇	C₂²	1	2	yes	—
28	C₂×#95×C₆₇	C₂²	1	4	yes	—
29	C₂⁵×C₆₇	C₂³	1	2	yes	—
30	C₂²×Q₈×C₆₇	—	4	2	no	—
31	C₂²×Q₈×C₆₇	—	4	2	no	—
32	C₂²×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
33	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
34	C₂²×D₄×C₆₇	—	4	2	no	—
35	C₂²×D₄×C₆₇	—	4	2	no	—
36	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
37	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
38	C₂³×C₄×C₆₇	—	2	16	no	—
39	C₂³×C₄×C₆₇	—	4	4	no	—
40	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
46	#124×C₆₇	C₂×C₄	1	64	yes	complemented
47	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
48	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
49	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
50	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
51	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	32	yes	complemented
52	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
53	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
54	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
55	C₂×C₄²×C₆₇	—	2	16	no	—
56	C₂×C₄²×C₆₇	—	4	4	no	—
57	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	complemented
58	C₂×C₄²×C₆₇	C₂³	1	16	yes	—
59	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
60	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
61	#95×C₆₇	C₂³	1	8	yes	—
62	#95×C₆₇	C₂³	1	16	yes	—
63	#95×C₆₇	C₂³	1	8	yes	—
64	#95×C₆₇	C₂³	1	16	yes	—
65	C₂⁴×C₆₇	—	2	8	no	—
66	C₂⁴×C₆₇	—	2	8	no	—
67	C₂⁴×C₆₇	—	2	4	no	—
68	C₂⁴×C₆₇	—	2	4	no	—
69	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
70	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
71	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
72	C₂×Q₈×C₆₇	—	4	16	no	—
73	C₂×Q₈×C₆₇	—	4	4	no	—
74	C₂×Q₈×C₆₇	—	4	4	no	—
75	C₂×Q₈×C₆₇	C₂²×C₄	1	16	yes	complemented
76	C₂×D₄×C₆₇	—	4	16	no	—
77	C₂×D₄×C₆₇	—	4	4	no	—
78	C₂×D₄×C₆₇	—	4	4	no	—
79	C₂×D₄×C₆₇	C₂²×C₄	1	16	yes	—
80	C₂²×C₄×C₆₇	—	2	8	no	—
81	C₂²×C₄×C₆₇	—	2	8	no	—
82	C₂²×C₄×C₆₇	—	2	8	no	—
83	C₂²×C₄×C₆₇	—	2	4	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	2	no	—
87	C₂²×C₄×C₆₇	—	2	8	no	—
88	C₂²×C₄×C₆₇	—	2	8	no	—
89	C₂²×C₄×C₆₇	—	2	8	no	—
90	C₂²×C₄×C₆₇	—	2	32	no	—
91	C₂²×C₄×C₆₇	—	4	8	no	—
92	C₂²×C₄×C₆₇	—	4	32	no	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₆₇	#41	1	16	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
102	C₄⋊C₄×C₆₇	—	4	8	no	—
103	C₂²⋊C₄×C₆₇	—	2	32	no	—
104	C₂²⋊C₄×C₆₇	—	4	8	no	—
105	C₂²⋊C₄×C₆₇	C₂²×C₄	1	64	yes	complemented
106	C₄²×C₆₇	—	2	32	no	—
107	C₄²×C₆₇	—	4	8	no	—
108	C₄²×C₆₇	C₂²×C₄	1	16	yes	complemented
109	C₂³×C₆₇	—	2	32	no	—
110	C₂³×C₆₇	—	2	16	no	—
111	C₂³×C₆₇	—	2	8	no	—
112	C₂³×C₆₇	—	2	8	no	—
113	C₂³×C₆₇	—	2	4	no	—
114	C₂³×C₆₇	—	2	4	no	—
115	C₂³×C₆₇	—	4	8	no	—
116	C₂³×C₆₇	—	4	8	no	—
117	C₂³×C₆₇	—	4	16	no	—
118	C₂³×C₆₇	C₂³×C₄	1	8	yes	—
119	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
120	C₂³×C₆₇	C₂×#41	1	8	yes	—
121	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
122	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
123	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
124	Q₈×C₆₇	—	4	16	no	—
125	D₄×C₆₇	—	4	16	no	—
126	C₂×C₄×C₆₇	—	2	16	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	—	2	16	no	—
129	C₂×C₄×C₆₇	—	2	32	no	—
130	C₂×C₄×C₆₇	—	2	8	no	—
131	C₂×C₄×C₆₇	—	2	8	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	4	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	8	no	—
138	C₂×C₄×C₆₇	—	2	8	no	—
139	C₂×C₄×C₆₇	—	2	8	no	—
140	C₂×C₄×C₆₇	—	4	32	no	—
141	C₂×C₄×C₆₇	—	4	16	no	—
142	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
143	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₆₇	C₂×#41	1	16	yes	—
146	C₂²×C₆₇	—	2	16	no	—
147	C₂²×C₆₇	—	2	8	no	—
148	C₂²×C₆₇	—	4	32	no	—
149	C₂²×C₆₇	—	4	4	no	—
150	C₂²×C₆₇	—	4	4	no	—
151	C₂²×C₆₇	—	4	8	no	—
152	C₂²×C₆₇	C₄×#41	1	8	yes	—
153	C₂²×C₆₇	#518	1	4	yes	—
154	C₂²×C₆₇	#551	1	8	yes	—
155	C₂²×C₆₇	#555	1	8	yes	—
156	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
157	C₂²×C₆₇	C₂²×#41	1	4	yes	—
158	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
159	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
160	C₄×C₆₇	—	2	8	no	—
161	C₄×C₆₇	—	2	4	no	—
162	C₄×C₆₇	—	2	8	no	—
163	C₄×C₆₇	—	2	16	no	—
164	C₄×C₆₇	—	4	8	no	—
165	C₂×#2372	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₆₇	—	4	8	no	—
167	C₂×C₆₇	#2372	1	8	yes	direct product factor
168	C₂×C₆₇	C₂×C₄×#41	1	2	yes	—
169	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
170	C₂×C₆₇	C₂×#551	1	2	yes	—
171	C₂×C₆₇	C₂×#555	1	2	yes	—
172	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic
173	#2372	C₂×C₆₇	1	16	yes	direct product factor
174	C₂×#391	C₂×C₆₇	1	2	yes	complemented
175	C₂×#388	C₂×C₆₇	1	4	yes	complemented
176	C₂×#386	C₂×C₆₇	1	2	yes	—
177	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	4	yes	complemented
178	C₂×#376	C₂×C₆₇	1	2	yes	complemented
179	C₆₇	C₂×#2372	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
181	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
182	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
183	C₂×#124	C₄×C₆₇	1	16	yes	complemented
184	C₂×#124	C₂²×C₆₇	1	8	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
186	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
189	C₂²×C₄²	C₂²×C₆₇	1	4	yes	—
190	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
191	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
192	#391	C₂²×C₆₇	1	16	yes	complemented
193	#388	C₂²×C₆₇	1	32	yes	complemented
194	#386	C₂²×C₆₇	1	16	yes	—
195	C₄×C₂²⋊C₄	C₂²×C₆₇	1	32	yes	complemented
196	#376	C₂²×C₆₇	1	16	yes	complemented
197	C₂×#95	C₂²×C₆₇	1	2	yes	—
198	C₂×#95	C₂²×C₆₇	1	4	yes	—
199	C₂×#95	C₂²×C₆₇	1	2	yes	—
200	C₂×#95	C₂²×C₆₇	1	4	yes	—
201	C₂⁵	C₂³×C₆₇	1	2	yes	—
202	C₂²×Q₈	—	4	2	no	—
203	C₂²×Q₈	—	4	2	no	—
204	C₂²×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
205	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
206	C₂²×D₄	—	4	2	no	—
207	C₂²×D₄	—	4	2	no	—
208	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	—
209	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
210	C₂³×C₄	—	2	16	no	—
211	C₂³×C₄	—	4	4	no	—
212	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
213	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
214	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
215	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
216	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
218	#124	C₂×C₄×C₆₇	1	64	yes	complemented
219	C₂×C₄⋊C₄	—	4	4	no	—
220	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
221	C₂×C₂²⋊C₄	—	2	16	no	—
222	C₂×C₂²⋊C₄	—	4	4	no	—
223	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	32	yes	complemented
224	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
227	C₂×C₄²	—	2	16	no	—
228	C₂×C₄²	—	4	4	no	—
229	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	complemented
230	C₂×C₄²	C₂³×C₆₇	1	16	yes	—
231	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
232	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
233	#95	C₂³×C₆₇	1	8	yes	—
234	#95	C₂³×C₆₇	1	16	yes	—
235	#95	C₂³×C₆₇	1	8	yes	—
236	#95	C₂³×C₆₇	1	16	yes	—
237	C₂⁴	—	2	8	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	—	2	4	no	—
241	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
242	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
243	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
244	C₂×Q₈	—	4	16	no	—
245	C₂×Q₈	—	4	4	no	—
246	C₂×Q₈	—	4	4	no	—
247	C₂×Q₈	C₂²×C₄×C₆₇	1	16	yes	complemented
248	C₂×D₄	—	4	16	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂×D₄	C₂²×C₄×C₆₇	1	16	yes	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	32	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	—	4	32	no	—
265	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
266	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
268	C₂²×C₄	#41×C₆₇	1	16	yes	—
269	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
274	C₄⋊C₄	—	4	8	no	—
275	C₂²⋊C₄	—	2	32	no	—
276	C₂²⋊C₄	—	4	8	no	—
277	C₂²⋊C₄	C₂²×C₄×C₆₇	1	64	yes	complemented
278	C₄²	—	2	32	no	—
279	C₄²	—	4	8	no	—
280	C₄²	C₂²×C₄×C₆₇	1	16	yes	complemented
281	C₂³	—	2	32	no	—
282	C₂³	—	2	16	no	—
283	C₂³	—	2	8	no	—
284	C₂³	—	2	8	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	4	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	—	4	16	no	—
290	C₂³	C₂³×C₄×C₆₇	1	8	yes	—
291	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
292	C₂³	C₂×#41×C₆₇	1	8	yes	—
293	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
294	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
295	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
296	Q₈	—	4	16	no	—
297	D₄	—	4	16	no	—
298	C₂×C₄	—	2	16	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	4	32	no	—
313	C₂×C₄	—	4	16	no	—
314	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
315	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
316	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
317	C₂×C₄	C₂×#41×C₆₇	1	16	yes	—
318	C₂²	—	2	16	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	4	32	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	8	no	—
324	C₂²	C₄×#41×C₆₇	1	8	yes	—
325	C₂²	#518×C₆₇	1	4	yes	—
326	C₂²	#551×C₆₇	1	8	yes	—
327	C₂²	#555×C₆₇	1	8	yes	—
328	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
329	C₂²	C₂²×#41×C₆₇	1	4	yes	—
330	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
331	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
332	C₄	—	2	8	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	8	no	—
335	C₄	—	2	16	no	—
336	C₄	—	4	8	no	—
337	C₂	—	4	8	no	—
338	C₂	C₆₇×#2372	1	8	yes	direct product factor
339	C₂	C₂×C₄×#41×C₆₇	1	2	yes	—
340	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
341	C₂	C₂×#551×C₆₇	1	2	yes	—
342	C₂	C₂×#555×C₆₇	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2372	C₂	direct (N × H)
3. C₂×#391×C₆₇	C₂	semidirect
4. C₂×#388×C₆₇	C₂	semidirect
6. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
7. C₂×#376×C₆₇	C₂	semidirect
11. C₂×#124×C₆₇	C₄	semidirect
20. #391×C₆₇	C₂²	semidirect
21. #388×C₆₇	C₂²	semidirect
23. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
24. #376×C₆₇	C₂²	semidirect
32. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
46. #124×C₆₇	C₂×C₄	semidirect
51. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
57. C₂×C₄²×C₆₇	C₂×C₄	semidirect
75. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
105. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
108. C₄²×C₆₇	C₂²×C₄	semidirect
165. C₂×#2372	C₆₇	direct (N × H)
167. C₂×C₆₇	#2372	direct (N × H)
173. #2372	C₂×C₆₇	direct (N × H)
174. C₂×#391	C₂×C₆₇	semidirect
175. C₂×#388	C₂×C₆₇	semidirect
177. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
178. C₂×#376	C₂×C₆₇	semidirect
179. C₆₇	C₂×#2372	direct (N × H)
183. C₂×#124	C₄×C₆₇	semidirect
192. #391	C₂²×C₆₇	semidirect
193. #388	C₂²×C₆₇	semidirect
195. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
196. #376	C₂²×C₆₇	semidirect
204. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
218. #124	C₂×C₄×C₆₇	semidirect
223. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
229. C₂×C₄²	C₂×C₄×C₆₇	semidirect
247. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
277. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
280. C₄²	C₂²×C₄×C₆₇	semidirect
338. C₂	C₆₇×#2372	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₆₇	2
C₆₇×#2372	2
C₂×#391×C₆₇	2
C₂×#388×C₆₇	2
C₂×#386×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₂×#376×C₆₇	2
C₂×#2372	67

Subgroups — C2×C67×#2372 #30713398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2372 #30713398