Subgroups — C₂×C₆₇×#2328 #30713320

Order 17152.

4430 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2328	C₂	1	16	yes	maximal, direct product factor
4	C₂×#390×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#386×C₆₇	C₂	1	8	yes	maximal, complemented
6	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#376×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
9	C₂³×D₄×C₆₇	C₂²	1	4	yes	—
10	C₂⁴×C₄×C₆₇	C₂²	1	4	yes	—
11	C₂×#127×C₆₇	C₄	1	16	yes	complemented
12	C₂×#127×C₆₇	C₂²	1	8	yes	—
13	C₂×C₄×D₄×C₆₇	—	2	16	no	—
14	C₂×C₄×D₄×C₆₇	C₂²	1	16	yes	complemented
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
18	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#390×C₆₇	C₂²	1	16	yes	complemented
22	#386×C₆₇	C₂²	1	64	yes	complemented
23	#382×C₆₇	C₂²	1	8	yes	complemented
24	#376×C₆₇	C₂²	1	8	yes	complemented
25	C₂×#95×C₆₇	C₂²	1	4	yes	—
26	C₂×#95×C₆₇	C₂²	1	4	yes	—
27	C₂⁵×C₆₇	C₂³	1	4	yes	—
28	C₂²×D₄×C₆₇	—	2	8	no	—
29	C₂²×D₄×C₆₇	—	2	8	no	—
30	C₂²×D₄×C₆₇	—	4	16	no	—
31	C₂²×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
32	C₂²×D₄×C₆₇	C₂×C₄	1	32	yes	complemented
33	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
34	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
35	C₂³×C₄×C₆₇	—	2	16	no	—
36	C₂³×C₄×C₆₇	—	4	16	no	—
37	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₆₇	C₂³	1	16	yes	—
42	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
43	#127×C₆₇	C₂×C₄	1	64	yes	complemented
44	C₄×D₄×C₆₇	—	2	64	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
46	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
47	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
48	C₂×C₂²⋊C₄×C₆₇	—	4	16	no	—
49	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
50	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	—
51	C₂×C₄²×C₆₇	—	2	4	no	—
52	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	complemented
53	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
54	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
55	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
56	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
57	#95×C₆₇	C₂³	1	16	yes	—
58	#95×C₆₇	C₂³	1	16	yes	—
59	C₂⁴×C₆₇	—	2	8	no	—
60	C₂⁴×C₆₇	—	2	8	no	—
61	C₂⁴×C₆₇	—	2	16	no	—
62	C₂⁴×C₆₇	—	2	16	no	—
63	C₂⁴×C₆₇	C₂²×C₄	1	16	yes	—
64	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
65	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
66	C₂×D₄×C₆₇	—	2	64	no	—
67	C₂×D₄×C₆₇	—	2	16	no	—
68	C₂×D₄×C₆₇	—	2	16	no	—
69	C₂×D₄×C₆₇	—	4	64	no	—
70	C₂×D₄×C₆₇	—	4	32	no	—
71	C₂×D₄×C₆₇	C₂²×C₄	1	32	yes	complemented
72	C₂×D₄×C₆₇	C₂²×C₄	1	64	yes	complemented
73	C₂²×C₄×C₆₇	—	2	8	no	—
74	C₂²×C₄×C₆₇	—	2	8	no	—
75	C₂²×C₄×C₆₇	—	2	8	no	—
76	C₂²×C₄×C₆₇	—	2	4	no	—
77	C₂²×C₄×C₆₇	—	2	8	no	—
78	C₂²×C₄×C₆₇	—	2	16	no	—
79	C₂²×C₄×C₆₇	—	2	32	no	—
80	C₂²×C₄×C₆₇	—	4	32	no	—
81	C₂²×C₄×C₆₇	—	4	64	no	—
82	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
83	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
85	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₆₇	#41	1	4	yes	—
87	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
88	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
90	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
92	C₄⋊C₄×C₆₇	—	2	16	no	—
93	C₂²⋊C₄×C₆₇	—	2	32	no	—
94	C₂²⋊C₄×C₆₇	—	4	32	no	—
95	C₄²×C₆₇	—	2	8	no	—
96	C₄²×C₆₇	C₂²×C₄	1	16	yes	complemented
97	C₄²×C₆₇	C₂×D₄	1	16	yes	complemented
98	C₂³×C₆₇	—	2	32	no	—
99	C₂³×C₆₇	—	2	64	no	—
100	C₂³×C₆₇	—	2	8	no	—
101	C₂³×C₆₇	—	2	8	no	—
102	C₂³×C₆₇	—	2	16	no	—
103	C₂³×C₆₇	—	2	16	no	—
104	C₂³×C₆₇	—	4	16	no	—
105	C₂³×C₆₇	—	4	16	no	—
106	C₂³×C₆₇	—	4	32	no	—
107	C₂³×C₆₇	C₂³×C₄	1	16	yes	—
108	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
109	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
110	C₂³×C₆₇	C₂×#41	1	2	yes	—
111	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	—
112	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
113	D₄×C₆₇	—	2	64	no	—
114	D₄×C₆₇	—	4	64	no	—
115	C₂×C₄×C₆₇	—	2	16	no	—
116	C₂×C₄×C₆₇	—	2	16	no	—
117	C₂×C₄×C₆₇	—	2	8	no	—
118	C₂×C₄×C₆₇	—	2	8	no	—
119	C₂×C₄×C₆₇	—	2	8	no	—
120	C₂×C₄×C₆₇	—	2	4	no	—
121	C₂×C₄×C₆₇	—	2	8	no	—
122	C₂×C₄×C₆₇	—	2	16	no	—
123	C₂×C₄×C₆₇	—	4	64	no	—
124	C₂×C₄×C₆₇	—	4	16	no	—
125	C₂×C₄×C₆₇	—	4	8	no	—
126	C₂×C₄×C₆₇	C₄×D₄	1	16	yes	—
127	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
128	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
129	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
130	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
131	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
132	C₂²×C₆₇	—	2	16	no	—
133	C₂²×C₆₇	—	2	32	no	—
134	C₂²×C₆₇	—	4	64	no	—
135	C₂²×C₆₇	—	4	8	no	—
136	C₂²×C₆₇	—	4	8	no	—
137	C₂²×C₆₇	—	4	16	no	—
138	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
139	C₂²×C₆₇	#518	1	8	yes	—
140	C₂²×C₆₇	#535	1	8	yes	—
141	C₂²×C₆₇	#540	1	8	yes	—
142	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
143	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
144	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
145	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
146	C₄×C₆₇	—	2	8	no	—
147	C₄×C₆₇	—	2	8	no	—
148	C₄×C₆₇	—	4	8	no	—
149	C₄×C₆₇	—	4	4	no	—
150	C₄×C₆₇	C₂×C₄×D₄	1	8	yes	—
151	C₂×#2328	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂×C₆₇	—	4	16	no	—
153	C₂×C₆₇	#2328	1	8	yes	direct product factor
154	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
155	C₂×C₆₇	C₂×#518	1	2	yes	—
156	C₂×C₆₇	C₂×#535	1	2	yes	—
157	C₂×C₆₇	C₂×#540	1	2	yes	—
158	C₂²×#127	C₂×C₆₇	1	1	yes	characteristic
159	C₂²×C₄×D₄	C₂×C₆₇	1	2	yes	complemented
160	#2328	C₂×C₆₇	1	16	yes	direct product factor
161	C₂×#390	C₂×C₆₇	1	2	yes	complemented
162	C₂×#386	C₂×C₆₇	1	8	yes	complemented
163	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
164	C₂×#376	C₂×C₆₇	1	1	yes	characteristic, complemented
165	C₆₇	C₂×#2328	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
167	C₂³×D₄	C₂²×C₆₇	1	4	yes	—
168	C₂⁴×C₄	C₂²×C₆₇	1	4	yes	—
169	C₂×#127	C₄×C₆₇	1	16	yes	complemented
170	C₂×#127	C₂²×C₆₇	1	8	yes	—
171	C₂×C₄×D₄	—	2	16	no	—
172	C₂×C₄×D₄	C₂²×C₆₇	1	16	yes	complemented
173	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
174	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
175	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
176	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
178	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
179	#390	C₂²×C₆₇	1	16	yes	complemented
180	#386	C₂²×C₆₇	1	64	yes	complemented
181	#382	C₂²×C₆₇	1	8	yes	complemented
182	#376	C₂²×C₆₇	1	8	yes	complemented
183	C₂×#95	C₂²×C₆₇	1	4	yes	—
184	C₂×#95	C₂²×C₆₇	1	4	yes	—
185	C₂⁵	C₂³×C₆₇	1	4	yes	—
186	C₂²×D₄	—	2	8	no	—
187	C₂²×D₄	—	2	8	no	—
188	C₂²×D₄	—	4	16	no	—
189	C₂²×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
190	C₂²×D₄	C₂×C₄×C₆₇	1	32	yes	complemented
191	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
192	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
193	C₂³×C₄	—	2	16	no	—
194	C₂³×C₄	—	4	16	no	—
195	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
196	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
197	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
198	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
199	C₂³×C₄	C₂³×C₆₇	1	16	yes	—
200	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
201	#127	C₂×C₄×C₆₇	1	64	yes	complemented
202	C₄×D₄	—	2	64	no	—
203	C₂×C₄⋊C₄	—	2	8	no	—
204	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
205	C₂×C₂²⋊C₄	—	2	16	no	—
206	C₂×C₂²⋊C₄	—	4	16	no	—
207	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
208	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	—
209	C₂×C₄²	—	2	4	no	—
210	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	complemented
211	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
212	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
213	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
214	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
215	#95	C₂³×C₆₇	1	16	yes	—
216	#95	C₂³×C₆₇	1	16	yes	—
217	C₂⁴	—	2	8	no	—
218	C₂⁴	—	2	8	no	—
219	C₂⁴	—	2	16	no	—
220	C₂⁴	—	2	16	no	—
221	C₂⁴	C₂²×C₄×C₆₇	1	16	yes	—
222	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
223	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
224	C₂×D₄	—	2	64	no	—
225	C₂×D₄	—	2	16	no	—
226	C₂×D₄	—	2	16	no	—
227	C₂×D₄	—	4	64	no	—
228	C₂×D₄	—	4	32	no	—
229	C₂×D₄	C₂²×C₄×C₆₇	1	32	yes	complemented
230	C₂×D₄	C₂²×C₄×C₆₇	1	64	yes	complemented
231	C₂²×C₄	—	2	8	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	8	no	—
236	C₂²×C₄	—	2	16	no	—
237	C₂²×C₄	—	2	32	no	—
238	C₂²×C₄	—	4	32	no	—
239	C₂²×C₄	—	4	64	no	—
240	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
241	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
242	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
243	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
244	C₂²×C₄	#41×C₆₇	1	4	yes	—
245	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
246	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
247	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
248	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
249	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
250	C₄⋊C₄	—	2	16	no	—
251	C₂²⋊C₄	—	2	32	no	—
252	C₂²⋊C₄	—	4	32	no	—
253	C₄²	—	2	8	no	—
254	C₄²	C₂²×C₄×C₆₇	1	16	yes	complemented
255	C₄²	C₂×D₄×C₆₇	1	16	yes	complemented
256	C₂³	—	2	32	no	—
257	C₂³	—	2	64	no	—
258	C₂³	—	2	8	no	—
259	C₂³	—	2	8	no	—
260	C₂³	—	2	16	no	—
261	C₂³	—	2	16	no	—
262	C₂³	—	4	16	no	—
263	C₂³	—	4	16	no	—
264	C₂³	—	4	32	no	—
265	C₂³	C₂³×C₄×C₆₇	1	16	yes	—
266	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
267	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
268	C₂³	C₂×#41×C₆₇	1	2	yes	—
269	C₂³	H(5,𝔽₂)×C₆₇	1	8	yes	—
270	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
271	D₄	—	2	64	no	—
272	D₄	—	4	64	no	—
273	C₂×C₄	—	2	16	no	—
274	C₂×C₄	—	2	16	no	—
275	C₂×C₄	—	2	8	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	16	no	—
281	C₂×C₄	—	4	64	no	—
282	C₂×C₄	—	4	16	no	—
283	C₂×C₄	—	4	8	no	—
284	C₂×C₄	C₄×D₄×C₆₇	1	16	yes	—
285	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
286	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
287	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
288	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
289	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
290	C₂²	—	2	16	no	—
291	C₂²	—	2	32	no	—
292	C₂²	—	4	64	no	—
293	C₂²	—	4	8	no	—
294	C₂²	—	4	8	no	—
295	C₂²	—	4	16	no	—
296	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
297	C₂²	#518×C₆₇	1	8	yes	—
298	C₂²	#535×C₆₇	1	8	yes	—
299	C₂²	#540×C₆₇	1	8	yes	—
300	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
301	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
302	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
303	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
304	C₄	—	2	8	no	—
305	C₄	—	2	8	no	—
306	C₄	—	4	8	no	—
307	C₄	—	4	4	no	—
308	C₄	C₂×C₄×D₄×C₆₇	1	8	yes	—
309	C₂	—	4	16	no	—
310	C₂	C₆₇×#2328	1	8	yes	direct product factor
311	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
312	C₂	C₂×#518×C₆₇	1	2	yes	—
313	C₂	C₂×#535×C₆₇	1	2	yes	—
314	C₂	C₂×#540×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×#127×C₆₇	C₂
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. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2328	C₂	direct (N × H)
4. C₂×#390×C₆₇	C₂	semidirect
5. C₂×#386×C₆₇	C₂	semidirect
6. C₂×#382×C₆₇	C₂	semidirect
7. C₂×#376×C₆₇	C₂	semidirect
11. C₂×#127×C₆₇	C₄	semidirect
14. C₂×C₄×D₄×C₆₇	C₂²	semidirect
21. #390×C₆₇	C₂²	semidirect
22. #386×C₆₇	C₂²	semidirect
23. #382×C₆₇	C₂²	semidirect
24. #376×C₆₇	C₂²	semidirect
31. C₂²×D₄×C₆₇	C₂×C₄	semidirect
32. C₂²×D₄×C₆₇	C₂×C₄	semidirect
43. #127×C₆₇	C₂×C₄	semidirect
52. C₂×C₄²×C₆₇	C₂×C₄	semidirect
53. C₂×C₄²×C₆₇	D₄	semidirect
71. C₂×D₄×C₆₇	C₂²×C₄	semidirect
72. C₂×D₄×C₆₇	C₂²×C₄	semidirect
96. C₄²×C₆₇	C₂²×C₄	semidirect
97. C₄²×C₆₇	C₂×D₄	semidirect
151. C₂×#2328	C₆₇	direct (N × H)
153. C₂×C₆₇	#2328	direct (N × H)
159. C₂²×C₄×D₄	C₂×C₆₇	semidirect
160. #2328	C₂×C₆₇	direct (N × H)
161. C₂×#390	C₂×C₆₇	semidirect
162. C₂×#386	C₂×C₆₇	semidirect
163. C₂×#382	C₂×C₆₇	semidirect
164. C₂×#376	C₂×C₆₇	semidirect
165. C₆₇	C₂×#2328	direct (N × H)
169. C₂×#127	C₄×C₆₇	semidirect
172. C₂×C₄×D₄	C₂²×C₆₇	semidirect
179. #390	C₂²×C₆₇	semidirect
180. #386	C₂²×C₆₇	semidirect
181. #382	C₂²×C₆₇	semidirect
182. #376	C₂²×C₆₇	semidirect
189. C₂²×D₄	C₂×C₄×C₆₇	semidirect
190. C₂²×D₄	C₂×C₄×C₆₇	semidirect
201. #127	C₂×C₄×C₆₇	semidirect
210. C₂×C₄²	C₂×C₄×C₆₇	semidirect
211. C₂×C₄²	D₄×C₆₇	semidirect
229. C₂×D₄	C₂²×C₄×C₆₇	semidirect
230. C₂×D₄	C₂²×C₄×C₆₇	semidirect
254. C₄²	C₂²×C₄×C₆₇	semidirect
255. C₄²	C₂×D₄×C₆₇	semidirect
310. C₂	C₆₇×#2328	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×#127×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2328	2
C₂×#390×C₆₇	2
C₂×#386×C₆₇	2
C₂×#382×C₆₇	2
C₂×#376×C₆₇	2
C₂×#2328	67

Subgroups — C2×C67×#2328 #30713320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2328 #30713320