Subgroups — C₂×C₆₇×#2388 #30713786

Order 17152.

6238 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	3	yes	maximal, complemented
3	C₆₇×#2388	C₂	1	16	yes	maximal, direct product factor
4	C₂×#395×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#394×C₆₇	C₂	1	3	yes	maximal, complemented
6	C₂×#393×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#392×C₆₇	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₆₇	—	2	24	no	—
10	C₂²×#41×C₆₇	C₂²	1	8	yes	complemented
11	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₆₇	C₂²	1	3	yes	—
13	C₂³×D₄×C₆₇	C₂²	1	3	yes	—
14	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₆₇	C₂²	1	3	yes	—
16	C₂×C₄×D₄×C₆₇	—	2	24	no	—
17	C₂×C₄×D₄×C₆₇	C₂²	1	24	yes	complemented
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	3	yes	—
19	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	6	yes	—
20	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	3	yes	—
21	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	3	yes	—
22	C₂²×C₄²×C₆₇	C₂²	1	3	yes	—
23	#395×C₆₇	C₂²	1	8	yes	complemented
24	#394×C₆₇	C₂²	1	24	yes	complemented
25	#393×C₆₇	C₂²	1	8	yes	complemented
26	#392×C₆₇	C₂²	1	24	yes	complemented
27	C₄×C₂²⋊C₄×C₆₇	C₂²	1	24	yes	complemented
28	C₂×#95×C₆₇	C₂²	1	3	yes	—
29	C₂×#95×C₆₇	C₂²	1	3	yes	—
30	C₂⁵×C₆₇	C₂³	1	3	yes	—
31	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
32	C₂×#41×C₆₇	—	2	128	no	—
33	C₂×#41×C₆₇	—	2	96	no	—
34	C₂²×Q₈×C₆₇	—	2	12	no	—
35	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
36	C₂²×D₄×C₆₇	—	2	12	no	—
37	C₂²×D₄×C₆₇	—	2	24	no	—
38	C₂²×D₄×C₆₇	—	2	12	no	—
39	C₂²×D₄×C₆₇	—	2	12	no	—
40	C₂²×D₄×C₆₇	—	2	12	no	—
41	C₂²×D₄×C₆₇	C₂³	1	12	yes	—
42	C₂²×D₄×C₆₇	C₂³	1	12	yes	—
43	C₂³×C₄×C₆₇	—	2	24	no	—
44	C₂³×C₄×C₆₇	—	2	12	no	—
45	C₂³×C₄×C₆₇	D₄	1	24	yes	complemented
46	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
50	C₂³×C₄×C₆₇	C₂³	1	12	yes	—
51	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
52	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₆₇	—	2	96	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	12	no	—
55	C₂×C₄⋊C₄×C₆₇	C₂³	1	12	yes	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	12	no	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	12	no	—
58	C₂×C₂²⋊C₄×C₆₇	—	2	24	no	—
59	C₂×C₂²⋊C₄×C₆₇	C₂³	1	12	yes	—
60	C₂×C₂²⋊C₄×C₆₇	C₂³	1	12	yes	—
61	C₂×C₂²⋊C₄×C₆₇	C₂³	1	24	yes	—
62	C₂×C₄²×C₆₇	—	2	12	no	—
63	C₂×C₄²×C₆₇	C₂³	1	12	yes	—
64	#95×C₆₇	C₂³	1	12	yes	—
65	#95×C₆₇	C₂³	1	12	yes	—
66	C₂⁴×C₆₇	—	2	6	no	—
67	C₂⁴×C₆₇	—	2	12	no	—
68	C₂⁴×C₆₇	—	2	12	no	—
69	C₂⁴×C₆₇	—	2	6	no	—
70	C₂⁴×C₆₇	—	2	6	no	—
71	C₂⁴×C₆₇	—	2	6	no	—
72	C₂⁴×C₆₇	C₂×D₄	1	12	yes	—
73	C₂⁴×C₆₇	#41	1	4	yes	complemented
74	C₂⁴×C₆₇	C₂⁴	1	6	yes	—
75	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
76	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
77	#41×C₆₇	—	2	256	no	—
78	C₂×Q₈×C₆₇	—	2	32	no	—
79	C₂×Q₈×C₆₇	—	2	24	no	—
80	C₂×D₄×C₆₇	—	2	96	no	—
81	C₂×D₄×C₆₇	—	2	96	no	—
82	C₂×D₄×C₆₇	—	2	24	no	—
83	C₂×D₄×C₆₇	—	2	48	no	—
84	C₂×D₄×C₆₇	—	2	24	no	—
85	C₂×D₄×C₆₇	—	2	24	no	—
86	C₂×D₄×C₆₇	—	2	24	no	—
87	C₂²×C₄×C₆₇	—	2	6	no	—
88	C₂²×C₄×C₆₇	—	2	12	no	—
89	C₂²×C₄×C₆₇	—	2	6	no	—
90	C₂²×C₄×C₆₇	—	2	96	no	—
91	C₂²×C₄×C₆₇	—	2	48	no	—
92	C₂²×C₄×C₆₇	—	2	6	no	—
93	C₂²×C₄×C₆₇	—	2	6	no	—
94	C₂²×C₄×C₆₇	—	2	12	no	—
95	C₂²×C₄×C₆₇	—	2	24	no	—
96	C₂²×C₄×C₆₇	—	4	16	no	—
97	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	48	yes	complemented
100	C₂²×C₄×C₆₇	#41	1	12	yes	complemented
101	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
102	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
104	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
105	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
106	C₄⋊C₄×C₆₇	—	2	24	no	—
107	C₂²⋊C₄×C₆₇	—	2	24	no	—
108	C₂²⋊C₄×C₆₇	—	2	24	no	—
109	C₂²⋊C₄×C₆₇	—	2	48	no	—
110	C₄²×C₆₇	—	2	24	no	—
111	C₂³×C₆₇	—	2	24	no	—
112	C₂³×C₆₇	—	2	24	no	—
113	C₂³×C₆₇	—	2	24	no	—
114	C₂³×C₆₇	—	2	24	no	—
115	C₂³×C₆₇	—	2	6	no	—
116	C₂³×C₆₇	—	2	12	no	—
117	C₂³×C₆₇	—	2	12	no	—
118	C₂³×C₆₇	—	2	6	no	—
119	C₂³×C₆₇	—	2	6	no	—
120	C₂³×C₆₇	—	2	6	no	—
121	C₂³×C₆₇	—	4	4	no	—
122	C₂³×C₆₇	—	4	24	no	—
123	C₂³×C₆₇	—	4	12	no	—
124	C₂³×C₆₇	—	4	24	no	—
125	C₂³×C₆₇	C₂²×D₄	1	12	yes	—
126	C₂³×C₆₇	C₂²×D₄	1	6	yes	—
127	C₂³×C₆₇	C₂×#41	1	2	yes	—
128	C₂³×C₆₇	C₂×#41	1	6	yes	—
129	C₂³×C₆₇	C₂×#41	1	4	yes	complemented
130	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
131	Q₈×C₆₇	—	2	32	no	—
132	D₄×C₆₇	—	2	96	no	—
133	D₄×C₆₇	—	2	96	no	—
134	C₂×C₄×C₆₇	—	2	24	no	—
135	C₂×C₄×C₆₇	—	2	24	no	—
136	C₂×C₄×C₆₇	—	2	6	no	—
137	C₂×C₄×C₆₇	—	2	12	no	—
138	C₂×C₄×C₆₇	—	2	6	no	—
139	C₂×C₄×C₆₇	—	2	96	no	—
140	C₂×C₄×C₆₇	—	2	6	no	—
141	C₂×C₄×C₆₇	—	2	6	no	—
142	C₂×C₄×C₆₇	—	2	12	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	—	4	12	no	—
145	C₂×C₄×C₆₇	—	4	16	no	—
146	C₂×C₄×C₆₇	#120	1	16	yes	—
147	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
148	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
149	C₂×C₄×C₆₇	C₂×#41	1	12	yes	complemented
150	C₂²×C₆₇	—	2	12	no	—
151	C₂²×C₆₇	—	2	12	no	—
152	C₂²×C₆₇	—	2	12	no	—
153	C₂²×C₆₇	—	2	12	no	—
154	C₂²×C₆₇	—	4	48	no	—
155	C₂²×C₆₇	—	4	16	no	—
156	C₂²×C₆₇	—	4	2	no	—
157	C₂²×C₆₇	—	4	12	no	—
158	C₂²×C₆₇	—	4	6	no	—
159	C₂²×C₆₇	—	4	12	no	—
160	C₂²×C₆₇	C₂×#120	1	4	yes	—
161	C₂²×C₆₇	#525	1	12	yes	—
162	C₂²×C₆₇	#532	1	12	yes	—
163	C₂²×C₆₇	C₂³×D₄	1	3	yes	—
164	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
165	C₂²×C₆₇	C₂²×#41	1	3	yes	—
166	C₄×C₆₇	—	2	12	no	—
167	C₄×C₆₇	—	2	12	no	—
168	C₄×C₆₇	—	4	2	no	—
169	C₄×C₆₇	—	4	6	no	—
170	C₄×C₆₇	C₂×#120	1	8	yes	—
171	C₂×#2388	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₆₇	—	4	12	no	—
173	C₂×C₆₇	—	4	4	no	—
174	C₂×C₆₇	#2388	1	8	yes	direct product factor
175	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
176	C₂×C₆₇	C₂×#525	1	3	yes	—
177	C₂×C₆₇	C₂×#532	1	3	yes	—
178	C₂³×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
179	C₂²×C₄×D₄	C₂×C₆₇	1	3	yes	complemented
180	#2388	C₂×C₆₇	1	16	yes	direct product factor
181	C₂×#395	C₂×C₆₇	1	1	yes	characteristic, complemented
182	C₂×#394	C₂×C₆₇	1	3	yes	complemented
183	C₂×#393	C₂×C₆₇	1	1	yes	characteristic, complemented
184	C₂×#392	C₂×C₆₇	1	3	yes	complemented
185	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	3	yes	complemented
186	C₆₇	C₂×#2388	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²×#41	—	2	24	no	—
188	C₂²×#41	C₂²×C₆₇	1	8	yes	complemented
189	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
190	C₂³×D₄	C₂²×C₆₇	1	3	yes	—
191	C₂³×D₄	C₂²×C₆₇	1	3	yes	—
192	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
193	C₂⁴×C₄	C₂²×C₆₇	1	3	yes	—
194	C₂×C₄×D₄	—	2	24	no	—
195	C₂×C₄×D₄	C₂²×C₆₇	1	24	yes	complemented
196	C₂²×C₄⋊C₄	C₂²×C₆₇	1	3	yes	—
197	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	3	yes	—
198	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	6	yes	—
199	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	3	yes	—
200	C₂²×C₄²	C₂²×C₆₇	1	3	yes	—
201	#395	C₂²×C₆₇	1	8	yes	complemented
202	#394	C₂²×C₆₇	1	24	yes	complemented
203	#393	C₂²×C₆₇	1	8	yes	complemented
204	#392	C₂²×C₆₇	1	24	yes	complemented
205	C₄×C₂²⋊C₄	C₂²×C₆₇	1	24	yes	complemented
206	C₂×#95	C₂²×C₆₇	1	3	yes	—
207	C₂×#95	C₂²×C₆₇	1	3	yes	—
208	C₂⁵	C₂³×C₆₇	1	3	yes	—
209	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
210	C₂×#41	—	2	128	no	—
211	C₂×#41	—	2	96	no	—
212	C₂²×Q₈	—	2	12	no	—
213	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
214	C₂²×D₄	—	2	12	no	—
215	C₂²×D₄	—	2	24	no	—
216	C₂²×D₄	—	2	12	no	—
217	C₂²×D₄	—	2	12	no	—
218	C₂²×D₄	—	2	12	no	—
219	C₂²×D₄	C₂³×C₆₇	1	12	yes	—
220	C₂²×D₄	C₂³×C₆₇	1	12	yes	—
221	C₂³×C₄	—	2	24	no	—
222	C₂³×C₄	—	2	12	no	—
223	C₂³×C₄	D₄×C₆₇	1	24	yes	complemented
224	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
225	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
227	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
228	C₂³×C₄	C₂³×C₆₇	1	12	yes	—
229	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
230	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
231	C₄×D₄	—	2	96	no	—
232	C₂×C₄⋊C₄	—	2	12	no	—
233	C₂×C₄⋊C₄	C₂³×C₆₇	1	12	yes	—
234	C₂×C₂²⋊C₄	—	2	12	no	—
235	C₂×C₂²⋊C₄	—	2	12	no	—
236	C₂×C₂²⋊C₄	—	2	24	no	—
237	C₂×C₂²⋊C₄	C₂³×C₆₇	1	12	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₆₇	1	12	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₆₇	1	24	yes	—
240	C₂×C₄²	—	2	12	no	—
241	C₂×C₄²	C₂³×C₆₇	1	12	yes	—
242	#95	C₂³×C₆₇	1	12	yes	—
243	#95	C₂³×C₆₇	1	12	yes	—
244	C₂⁴	—	2	6	no	—
245	C₂⁴	—	2	12	no	—
246	C₂⁴	—	2	12	no	—
247	C₂⁴	—	2	6	no	—
248	C₂⁴	—	2	6	no	—
249	C₂⁴	—	2	6	no	—
250	C₂⁴	C₂×D₄×C₆₇	1	12	yes	—
251	C₂⁴	#41×C₆₇	1	4	yes	complemented
252	C₂⁴	C₂⁴×C₆₇	1	6	yes	—
253	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
254	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
255	#41	—	2	256	no	—
256	C₂×Q₈	—	2	32	no	—
257	C₂×Q₈	—	2	24	no	—
258	C₂×D₄	—	2	96	no	—
259	C₂×D₄	—	2	96	no	—
260	C₂×D₄	—	2	24	no	—
261	C₂×D₄	—	2	48	no	—
262	C₂×D₄	—	2	24	no	—
263	C₂×D₄	—	2	24	no	—
264	C₂×D₄	—	2	24	no	—
265	C₂²×C₄	—	2	6	no	—
266	C₂²×C₄	—	2	12	no	—
267	C₂²×C₄	—	2	6	no	—
268	C₂²×C₄	—	2	96	no	—
269	C₂²×C₄	—	2	48	no	—
270	C₂²×C₄	—	2	6	no	—
271	C₂²×C₄	—	2	6	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	24	no	—
274	C₂²×C₄	—	4	16	no	—
275	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
276	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
277	C₂²×C₄	C₂×D₄×C₆₇	1	48	yes	complemented
278	C₂²×C₄	#41×C₆₇	1	12	yes	complemented
279	C₂²×C₄	C₂⁴×C₆₇	1	6	yes	—
280	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₆₇	1	6	yes	—
282	C₂²×C₄	C₂⁴×C₆₇	1	6	yes	—
283	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
284	C₄⋊C₄	—	2	24	no	—
285	C₂²⋊C₄	—	2	24	no	—
286	C₂²⋊C₄	—	2	24	no	—
287	C₂²⋊C₄	—	2	48	no	—
288	C₄²	—	2	24	no	—
289	C₂³	—	2	24	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	2	24	no	—
293	C₂³	—	2	6	no	—
294	C₂³	—	2	12	no	—
295	C₂³	—	2	12	no	—
296	C₂³	—	2	6	no	—
297	C₂³	—	2	6	no	—
298	C₂³	—	2	6	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	24	no	—
301	C₂³	—	4	12	no	—
302	C₂³	—	4	24	no	—
303	C₂³	C₂²×D₄×C₆₇	1	12	yes	—
304	C₂³	C₂²×D₄×C₆₇	1	6	yes	—
305	C₂³	C₂×#41×C₆₇	1	2	yes	—
306	C₂³	C₂×#41×C₆₇	1	6	yes	—
307	C₂³	C₂×#41×C₆₇	1	4	yes	complemented
308	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
309	Q₈	—	2	32	no	—
310	D₄	—	2	96	no	—
311	D₄	—	2	96	no	—
312	C₂×C₄	—	2	24	no	—
313	C₂×C₄	—	2	24	no	—
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	12	no	—
316	C₂×C₄	—	2	6	no	—
317	C₂×C₄	—	2	96	no	—
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	6	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	12	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	#120×C₆₇	1	16	yes	—
325	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
326	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
327	C₂×C₄	C₂×#41×C₆₇	1	12	yes	complemented
328	C₂²	—	2	12	no	—
329	C₂²	—	2	12	no	—
330	C₂²	—	2	12	no	—
331	C₂²	—	2	12	no	—
332	C₂²	—	4	48	no	—
333	C₂²	—	4	16	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	12	no	—
336	C₂²	—	4	6	no	—
337	C₂²	—	4	12	no	—
338	C₂²	C₂×#120×C₆₇	1	4	yes	—
339	C₂²	#525×C₆₇	1	12	yes	—
340	C₂²	#532×C₆₇	1	12	yes	—
341	C₂²	C₂³×D₄×C₆₇	1	3	yes	—
342	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
343	C₂²	C₂²×#41×C₆₇	1	3	yes	—
344	C₄	—	2	12	no	—
345	C₄	—	2	12	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	6	no	—
348	C₄	C₂×#120×C₆₇	1	8	yes	—
349	C₂	—	4	12	no	—
350	C₂	—	4	4	no	—
351	C₂	C₆₇×#2388	1	8	yes	direct product factor
352	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
353	C₂	C₂×#525×C₆₇	1	3	yes	—
354	C₂	C₂×#532×C₆₇	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2388	C₂	direct (N × H)
4. C₂×#395×C₆₇	C₂	semidirect
5. C₂×#394×C₆₇	C₂	semidirect
6. C₂×#393×C₆₇	C₂	semidirect
7. C₂×#392×C₆₇	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
10. C₂²×#41×C₆₇	C₂²	semidirect
17. C₂×C₄×D₄×C₆₇	C₂²	semidirect
23. #395×C₆₇	C₂²	semidirect
24. #394×C₆₇	C₂²	semidirect
25. #393×C₆₇	C₂²	semidirect
26. #392×C₆₇	C₂²	semidirect
27. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
45. C₂³×C₄×C₆₇	D₄	semidirect
73. C₂⁴×C₆₇	#41	semidirect
99. C₂²×C₄×C₆₇	C₂×D₄	semidirect
100. C₂²×C₄×C₆₇	#41	semidirect
129. C₂³×C₆₇	C₂×#41	semidirect
149. C₂×C₄×C₆₇	C₂×#41	semidirect
171. C₂×#2388	C₆₇	direct (N × H)
174. C₂×C₆₇	#2388	direct (N × H)
178. C₂³×#41	C₂×C₆₇	semidirect
179. C₂²×C₄×D₄	C₂×C₆₇	semidirect
180. #2388	C₂×C₆₇	direct (N × H)
181. C₂×#395	C₂×C₆₇	semidirect
182. C₂×#394	C₂×C₆₇	semidirect
183. C₂×#393	C₂×C₆₇	semidirect
184. C₂×#392	C₂×C₆₇	semidirect
185. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
186. C₆₇	C₂×#2388	direct (N × H)
188. C₂²×#41	C₂²×C₆₇	semidirect
195. C₂×C₄×D₄	C₂²×C₆₇	semidirect
201. #395	C₂²×C₆₇	semidirect
202. #394	C₂²×C₆₇	semidirect
203. #393	C₂²×C₆₇	semidirect
204. #392	C₂²×C₆₇	semidirect
205. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
223. C₂³×C₄	D₄×C₆₇	semidirect
251. C₂⁴	#41×C₆₇	semidirect
277. C₂²×C₄	C₂×D₄×C₆₇	semidirect
278. C₂²×C₄	#41×C₆₇	semidirect
307. C₂³	C₂×#41×C₆₇	semidirect
327. C₂×C₄	C₂×#41×C₆₇	semidirect
351. C₂	C₆₇×#2388	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×#41×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2388	2
C₂×#395×C₆₇	2
C₂×#394×C₆₇	2
C₂×#393×C₆₇	2
C₂×#392×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₂×#2388	67

Subgroups — C2×C67×#2388 #30713786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2388 #30713786