Subgroups — D₄×#97×C₆₇ #30699747

Order 17152.

1274 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₆₇	C₂	1	2	yes	maximal
2	C₂²×#97×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1770	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1752	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₆₇	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₆₇	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
13	C₈×D₄×C₆₇	C₄	1	16	yes	complemented
14	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	—
16	C₂×#97×C₆₇	—	2	8	no	—
17	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#97×C₆₇	C₂²	1	2	yes	—
19	C₂×#97×C₆₇	C₂²	1	2	yes	—
20	C₂×#97×C₆₇	C₂²	1	4	yes	—
21	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₆₇	C₄	1	4	yes	—
26	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₄³×C₆₇	C₂²	1	1	yes	characteristic
28	#336×C₆₇	C₂²	1	4	yes	—
29	#336×C₆₇	C₂²	1	2	yes	—
30	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
33	C₂²×C₈×C₆₇	—	2	8	no	—
34	C₂²×C₈×C₆₇	—	2	8	no	—
35	C₂²×C₈×C₆₇	C₂×C₄	1	16	yes	complemented
36	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
37	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
38	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
39	C₄×D₄×C₆₇	—	2	8	no	—
40	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₆₇	—	2	4	no	—
46	C₂×C₄²×C₆₇	—	2	4	no	—
47	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
51	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₆₇	C₂×C₄	1	8	yes	complemented
55	C₂²⋊C₈×C₆₇	C₂×C₄	1	16	yes	complemented
56	#97×C₆₇	—	2	8	no	—
57	#97×C₆₇	—	2	4	no	—
58	#97×C₆₇	—	2	4	no	—
59	#97×C₆₇	—	2	2	no	—
60	#97×C₆₇	D₄	1	4	yes	direct product factor
61	C₄×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
62	#95×C₆₇	C₂×C₄	1	2	yes	—
63	#95×C₆₇	C₂×C₄	1	4	yes	—
64	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
65	C₂×D₄×C₆₇	C₄²	1	4	yes	—
66	C₂×D₄×C₆₇	M₁₆	1	8	yes	—
67	C₂²×C₄×C₆₇	—	2	2	no	—
68	C₂²×C₄×C₆₇	—	2	2	no	—
69	C₂²×C₄×C₆₇	—	2	4	no	—
70	C₂²×C₄×C₆₇	—	2	8	no	—
71	C₂²×C₄×C₆₇	—	2	8	no	—
72	C₂²×C₄×C₆₇	—	4	4	no	—
73	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₆₇	—	2	4	no	—
82	C₂×C₈×C₆₇	—	2	4	no	—
83	C₂×C₈×C₆₇	—	2	2	no	—
84	C₂×C₈×C₆₇	—	2	2	no	—
85	C₂×C₈×C₆₇	—	2	32	no	—
86	C₂×C₈×C₆₇	C₂²×C₄	1	8	yes	—
87	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
88	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₆₇	#41	1	4	yes	—
91	C₄⋊C₄×C₆₇	—	2	4	no	—
92	C₄⋊C₄×C₆₇	C₄²	1	4	yes	—
93	C₂²⋊C₄×C₆₇	—	2	8	no	—
94	C₂²⋊C₄×C₆₇	C₄²	1	8	yes	—
95	C₄²×C₆₇	—	2	8	no	—
96	C₄²×C₆₇	—	2	4	no	—
97	C₄²×C₆₇	—	2	2	no	—
98	C₄²×C₆₇	—	2	2	no	—
99	C₄²×C₆₇	—	2	2	no	—
100	C₄²×C₆₇	—	4	2	no	—
101	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
102	C₄²×C₆₇	C₂×D₄	1	2	yes	—
103	C₄²×C₆₇	#41	1	2	yes	—
104	C₂³×C₆₇	—	2	2	no	—
105	C₂³×C₆₇	—	2	2	no	—
106	C₂³×C₆₇	—	2	4	no	—
107	C₂³×C₆₇	C₂×C₄²	1	4	yes	—
108	C₂³×C₆₇	C₂×M₁₆	1	8	yes	—
109	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
110	D₄×C₆₇	#97	1	16	yes	direct product factor
111	C₂×C₄×C₆₇	—	2	2	no	—
112	C₂×C₄×C₆₇	—	2	2	no	—
113	C₂×C₄×C₆₇	—	2	2	no	—
114	C₂×C₄×C₆₇	—	2	2	no	—
115	C₂×C₄×C₆₇	—	2	2	no	—
116	C₂×C₄×C₆₇	—	2	8	no	—
117	C₂×C₄×C₆₇	—	2	8	no	—
118	C₂×C₄×C₆₇	—	2	4	no	—
119	C₂×C₄×C₆₇	—	2	2	no	—
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	2	4	no	—
122	C₂×C₄×C₆₇	—	2	2	no	—
123	C₂×C₄×C₆₇	—	2	4	no	—
124	C₂×C₄×C₆₇	—	4	16	no	—
125	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₆₇	C₂×C₄²	1	4	yes	—
127	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
129	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
130	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
133	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
134	C₈×C₆₇	—	2	8	no	—
135	C₈×C₆₇	—	2	4	no	—
136	C₈×C₆₇	C₄×D₄	1	8	yes	complemented
137	C₂²×C₆₇	—	2	4	no	—
138	C₂²×C₆₇	—	2	8	no	—
139	C₂²×C₆₇	—	2	8	no	—
140	C₂²×C₆₇	—	2	4	no	—
141	C₂²×C₆₇	C₂×#97	1	8	yes	complemented
142	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
143	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
145	C₂²×C₆₇	C₂²×M₁₆	1	2	yes	—
146	C₂²×C₆₇	#568	1	2	yes	—
147	C₄×C₆₇	—	2	2	no	—
148	C₄×C₆₇	—	2	4	no	—
149	C₄×C₆₇	—	2	4	no	—
150	C₄×C₆₇	—	4	4	no	—
151	C₄×C₆₇	—	4	2	no	—
152	C₄×C₆₇	C₂×#97	1	4	yes	complemented
153	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
154	C₄×C₆₇	C₄×#41	1	2	yes	—
155	D₄×#97	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂×C₆₇	—	2	8	no	—
157	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
158	C₂×C₆₇	C₂²×#97	1	1	yes	characteristic
159	C₂×C₆₇	#2875	1	1	yes	characteristic
160	C₂×C₆₇	D₄×M₁₆	1	2	yes	—
161	C₂×C₆₇	#2970	1	2	yes	—
162	C₂×C₈×D₄	C₂×C₆₇	1	2	yes	—
163	C₂²×#97	C₂×C₆₇	1	2	yes	complemented
164	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic
165	#1770	C₂×C₆₇	1	2	yes	complemented
166	#1767	C₂×C₆₇	1	1	yes	characteristic, complemented
167	#1752	C₂×C₆₇	1	4	yes	complemented
168	#1749	C₂×C₆₇	1	2	yes	complemented
169	C₄×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
170	C₆₇	D₄×#97	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³×C₈	C₂²×C₆₇	1	4	yes	—
172	C₂×C₄×D₄	C₄×C₆₇	1	2	yes	—
173	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
175	C₈×D₄	C₄×C₆₇	1	16	yes	complemented
176	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	—
178	C₂×#97	—	2	8	no	—
179	C₂×#97	C₂²×C₆₇	1	2	yes	—
180	C₂×#97	C₂²×C₆₇	1	4	yes	—
181	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
182	C₂×#97	C₂²×C₆₇	1	2	yes	—
183	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
185	C₄×C₄⋊C₄	C₄×C₆₇	1	2	yes	—
186	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	C₄×C₆₇	1	4	yes	—
188	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
189	C₄³	C₂²×C₆₇	1	1	yes	characteristic
190	#336	C₂²×C₆₇	1	4	yes	—
191	#336	C₂²×C₆₇	1	2	yes	—
192	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
193	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
194	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
195	C₂²×C₈	—	2	8	no	—
196	C₂²×C₈	—	2	8	no	—
197	C₂²×C₈	C₂×C₄×C₆₇	1	16	yes	complemented
198	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
199	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
200	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
201	C₄×D₄	—	2	8	no	—
202	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
203	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
204	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
205	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
206	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
210	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
211	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
212	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
214	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
216	C₄⋊C₈	C₂×C₄×C₆₇	1	8	yes	complemented
217	C₂²⋊C₈	C₂×C₄×C₆₇	1	16	yes	complemented
218	#97	—	2	8	no	—
219	#97	—	2	4	no	—
220	#97	—	2	4	no	—
221	#97	—	2	2	no	—
222	#97	D₄×C₆₇	1	4	yes	direct product factor
223	C₄×C₈	C₂×C₄×C₆₇	1	8	yes	complemented
224	#95	C₂×C₄×C₆₇	1	2	yes	—
225	#95	C₂×C₄×C₆₇	1	4	yes	—
226	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
227	C₂×D₄	C₄²×C₆₇	1	4	yes	—
228	C₂×D₄	M₁₆×C₆₇	1	8	yes	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
236	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
237	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
240	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
242	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	32	no	—
248	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
249	C₂×C₈	C₂²×C₄×C₆₇	1	8	yes	—
250	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
251	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
252	C₂×C₈	#41×C₆₇	1	4	yes	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	C₄²×C₆₇	1	4	yes	—
255	C₂²⋊C₄	—	2	8	no	—
256	C₂²⋊C₄	C₄²×C₆₇	1	8	yes	—
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	4	2	no	—
263	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
264	C₄²	C₂×D₄×C₆₇	1	2	yes	—
265	C₄²	#41×C₆₇	1	2	yes	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	4	no	—
269	C₂³	C₂×C₄²×C₆₇	1	4	yes	—
270	C₂³	C₂×M₁₆×C₆₇	1	8	yes	—
271	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
272	D₄	#97×C₆₇	1	16	yes	direct product factor
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	4	16	no	—
287	C₂×C₄	C₂×C₄²×C₆₇	1	2	yes	—
288	C₂×C₄	C₂×C₄²×C₆₇	1	4	yes	—
289	C₂×C₄	C₂×C₄²×C₆₇	1	2	yes	—
290	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
291	C₂×C₄	C₂×M₁₆×C₆₇	1	4	yes	—
292	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
294	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
295	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	—	2	4	no	—
298	C₈	C₄×D₄×C₆₇	1	8	yes	complemented
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	2	8	no	—
303	C₂²	C₂×#97×C₆₇	1	8	yes	complemented
304	C₂²	C₂²×C₄²×C₆₇	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
306	C₂²	C₄×#41×C₆₇	1	1	yes	characteristic
307	C₂²	C₂²×M₁₆×C₆₇	1	2	yes	—
308	C₂²	#568×C₆₇	1	2	yes	—
309	C₄	—	2	4	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	4	no	—
312	C₄	—	4	4	no	—
313	C₄	—	4	2	no	—
314	C₄	C₂×#97×C₆₇	1	4	yes	complemented
315	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
316	C₄	C₄×#41×C₆₇	1	2	yes	—
317	C₂	—	2	8	no	—
318	C₂	C₄²×D₄×C₆₇	1	1	yes	characteristic
319	C₂	C₂²×#97×C₆₇	1	1	yes	characteristic
320	C₂	C₆₇×#2875	1	1	yes	characteristic
321	C₂	D₄×M₁₆×C₆₇	1	2	yes	—
322	C₂	C₆₇×#2970	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂²×D₄×C₆₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#97×C₆₇	C₂	semidirect
4. C₆₇×#1770	C₂	semidirect
5. C₆₇×#1767	C₂	semidirect
6. C₆₇×#1752	C₂	semidirect
7. C₆₇×#1749	C₂	semidirect
8. C₄×#97×C₆₇	C₂	semidirect
13. C₈×D₄×C₆₇	C₄	semidirect
35. C₂²×C₈×C₆₇	C₂×C₄	semidirect
54. C₄⋊C₈×C₆₇	C₂×C₄	semidirect
55. C₂²⋊C₈×C₆₇	C₂×C₄	semidirect
60. #97×C₆₇	D₄	direct (N × H)
61. C₄×C₈×C₆₇	C₂×C₄	semidirect
110. D₄×C₆₇	#97	direct (N × H)
136. C₈×C₆₇	C₄×D₄	semidirect
141. C₂²×C₆₇	C₂×#97	semidirect
152. C₄×C₆₇	C₂×#97	semidirect
155. D₄×#97	C₆₇	direct (N × H)
163. C₂²×#97	C₂×C₆₇	semidirect
165. #1770	C₂×C₆₇	semidirect
166. #1767	C₂×C₆₇	semidirect
167. #1752	C₂×C₆₇	semidirect
168. #1749	C₂×C₆₇	semidirect
169. C₄×#97	C₂×C₆₇	semidirect
170. C₆₇	D₄×#97	direct (N × H)
175. C₈×D₄	C₄×C₆₇	semidirect
197. C₂²×C₈	C₂×C₄×C₆₇	semidirect
216. C₄⋊C₈	C₂×C₄×C₆₇	semidirect
217. C₂²⋊C₈	C₂×C₄×C₆₇	semidirect
222. #97	D₄×C₆₇	direct (N × H)
223. C₄×C₈	C₂×C₄×C₆₇	semidirect
272. D₄	#97×C₆₇	direct (N × H)
298. C₈	C₄×D₄×C₆₇	semidirect
303. C₂²	C₂×#97×C₆₇	semidirect
314. C₄	C₂×#97×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₆₇	2
C₂²×#97×C₆₇	2
C₄²×D₄×C₆₇	2
C₆₇×#1770	2
C₆₇×#1767	2
C₆₇×#1752	2
C₆₇×#1749	2
C₄×#97×C₆₇	2
D₄×#97	67

Subgroups — D4×#97×C67 #30699747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#97×C₆₇ #30699747