Subgroups — C₄⋊C₄×Q₁₆×C₆₇ #30701935

Order 17152.

926 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₆₇	C₂	1	2	yes	maximal
2	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₆₇	C₂	1	2	yes	maximal
4	C₆₇×#1942	C₂	1	2	yes	maximal
5	C₆₇×#1863	C₂	1	4	yes	maximal
6	C₆₇×#1845	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1803	C₂	1	2	yes	maximal
8	C₈×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
11	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
12	C₄×Q₁₆×C₆₇	—	2	8	no	—
13	C₄×Q₁₆×C₆₇	C₄	1	8	yes	complemented
14	C₂×#107×C₆₇	C₂²	1	2	yes	—
15	C₂×#107×C₆₇	C₂²	1	2	yes	—
16	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×#103×C₆₇	C₂²	1	4	yes	—
19	C₂×#103×C₆₇	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
22	#389×C₆₇	—	2	4	no	—
23	#389×C₆₇	C₂²	1	4	yes	—
24	#384×C₆₇	—	2	2	no	—
25	#384×C₆₇	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
27	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	#340×C₆₇	C₂²	1	4	yes	—
29	#336×C₆₇	C₂²	1	2	yes	—
30	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
31	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	—
32	C₂×Q₁₆×C₆₇	D₄	1	4	yes	—
33	C₂×Q₁₆×C₆₇	Q₈	1	4	yes	—
34	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
35	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
37	C₄×Q₈×C₆₇	—	2	4	no	—
38	C₄×Q₈×C₆₇	—	2	8	no	—
39	C₄×Q₈×C₆₇	—	4	4	no	—
40	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
43	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
49	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
50	C₂×C₄²×C₆₇	—	2	2	no	—
51	C₂×C₄²×C₆₇	—	2	4	no	—
52	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	#107×C₆₇	—	2	4	no	—
55	#107×C₆₇	—	4	2	no	—
56	#107×C₆₇	C₂×C₄	1	4	yes	—
57	C₄⋊C₈×C₆₇	—	2	2	no	—
58	#103×C₆₇	—	2	8	no	—
59	#103×C₆₇	C₂×C₄	1	8	yes	—
60	C₄×C₈×C₆₇	—	2	4	no	—
61	C₄×C₈×C₆₇	C₂×C₄	1	4	yes	—
62	#95×C₆₇	—	2	4	no	—
63	#95×C₆₇	D₄	1	2	yes	—
64	C₂×Q₈×C₆₇	—	2	2	no	—
65	C₂×Q₈×C₆₇	—	2	2	no	—
66	C₂×Q₈×C₆₇	—	2	2	no	—
67	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
68	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
69	C₂×Q₈×C₆₇	C₂×Q₈	1	4	yes	—
70	C₂²×C₄×C₆₇	—	2	2	no	—
71	C₂²×C₄×C₆₇	—	2	2	no	—
72	C₂²×C₄×C₆₇	—	2	4	no	—
73	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
78	Q₁₆×C₆₇	C₄⋊C₄	1	16	yes	direct product factor
79	C₂×C₈×C₆₇	—	2	1	no	—
80	C₂×C₈×C₆₇	—	2	1	no	—
81	C₂×C₈×C₆₇	—	2	2	no	—
82	C₂×C₈×C₆₇	—	2	2	no	—
83	C₂×C₈×C₆₇	—	2	2	no	—
84	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
85	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
87	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
88	C₄⋊C₄×C₆₇	—	2	8	no	—
89	C₄⋊C₄×C₆₇	—	2	2	no	—
90	C₄⋊C₄×C₆₇	—	2	2	no	—
91	C₄⋊C₄×C₆₇	—	2	4	no	—
92	C₄⋊C₄×C₆₇	—	2	4	no	—
93	C₄⋊C₄×C₆₇	—	4	8	no	—
94	C₄⋊C₄×C₆₇	—	4	4	no	—
95	C₄⋊C₄×C₆₇	—	8	2	no	—
96	C₄⋊C₄×C₆₇	—	8	4	no	—
97	C₄⋊C₄×C₆₇	Q₁₆	1	4	yes	direct product factor
98	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
99	C₄²×C₆₇	—	2	8	no	—
100	C₄²×C₆₇	—	2	2	no	—
101	C₄²×C₆₇	—	2	2	no	—
102	C₄²×C₆₇	—	4	8	no	—
103	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
104	C₄²×C₆₇	#41	1	2	yes	—
105	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
106	Q₈×C₆₇	—	2	4	no	—
107	Q₈×C₆₇	—	2	4	no	—
108	Q₈×C₆₇	—	2	4	no	—
109	Q₈×C₆₇	C₂×C₄⋊C₄	1	8	yes	—
110	C₂×C₄×C₆₇	—	2	4	no	—
111	C₂×C₄×C₆₇	—	2	2	no	—
112	C₂×C₄×C₆₇	—	2	4	no	—
113	C₂×C₄×C₆₇	—	2	4	no	—
114	C₂×C₄×C₆₇	—	2	1	no	—
115	C₂×C₄×C₆₇	—	2	1	no	—
116	C₂×C₄×C₆₇	—	2	2	no	—
117	C₂×C₄×C₆₇	—	2	4	no	—
118	C₂×C₄×C₆₇	—	2	2	no	—
119	C₂×C₄×C₆₇	—	2	2	no	—
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	4	2	no	—
122	C₂×C₄×C₆₇	—	4	2	no	—
123	C₂×C₄×C₆₇	—	4	4	no	—
124	C₂×C₄×C₆₇	—	4	4	no	—
125	C₂×C₄×C₆₇	—	4	4	no	—
126	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
127	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
128	C₂×C₄×C₆₇	C₂×Q₁₆	1	4	yes	—
129	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
130	C₂×C₄×C₆₇	#135	1	2	yes	—
131	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
135	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
136	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
137	C₈×C₆₇	—	2	2	no	—
138	C₈×C₆₇	—	4	2	no	—
139	C₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
140	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
141	C₂²×C₆₇	D₄²	1	1	yes	characteristic
142	C₂²×C₆₇	D₄×Q₈	1	1	yes	characteristic
143	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
144	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
145	C₂²×C₆₇	#576	1	1	yes	characteristic
146	C₂²×C₆₇	#578	1	1	yes	characteristic
147	C₄×C₆₇	—	2	8	no	—
148	C₄×C₆₇	—	2	2	no	—
149	C₄×C₆₇	—	2	4	no	—
150	C₄×C₆₇	—	4	4	no	—
151	C₄×C₆₇	—	4	2	no	—
152	C₄×C₆₇	—	8	4	no	—
153	C₄×C₆₇	C₄×Q₁₆	1	4	yes	complemented
154	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
155	C₄×C₆₇	#520	1	1	yes	characteristic
156	C₄×C₆₇	#547	1	1	yes	characteristic
157	C₄×C₆₇	#554	1	1	yes	characteristic
158	C₄⋊C₄×Q₁₆	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₆₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
161	C₂×C₆₇	#2951	1	1	yes	characteristic
162	C₂×C₆₇	D₄×Q₁₆	1	1	yes	characteristic
163	C₂×C₆₇	#3287	1	1	yes	characteristic
164	C₂×C₆₇	Q₈×Q₁₆	1	1	yes	characteristic
165	C₂×C₆₇	#3383	1	1	yes	characteristic
166	C₂×C₄×Q₁₆	C₂×C₆₇	1	2	yes	—
167	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic
168	Q₈×C₄⋊C₄	C₂×C₆₇	1	2	yes	—
169	#1942	C₂×C₆₇	1	2	yes	—
170	#1863	C₂×C₆₇	1	4	yes	—
171	#1845	C₂×C₆₇	1	1	yes	characteristic
172	#1803	C₂×C₆₇	1	2	yes	—
173	C₈×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
174	C₆₇	C₄⋊C₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
175	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
176	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
177	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
178	C₄×Q₁₆	—	2	8	no	—
179	C₄×Q₁₆	C₄×C₆₇	1	8	yes	complemented
180	C₂×#107	C₂²×C₆₇	1	2	yes	—
181	C₂×#107	C₂²×C₆₇	1	2	yes	—
182	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
184	C₂×#103	C₂²×C₆₇	1	4	yes	—
185	C₂×#103	C₂²×C₆₇	1	2	yes	—
186	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
188	#389	—	2	4	no	—
189	#389	C₂²×C₆₇	1	4	yes	—
190	#384	—	2	2	no	—
191	#384	C₂²×C₆₇	1	2	yes	—
192	C₄×C₄⋊C₄	—	2	2	no	—
193	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
194	#340	C₂²×C₆₇	1	4	yes	—
195	#336	C₂²×C₆₇	1	2	yes	—
196	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
197	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	—
198	C₂×Q₁₆	D₄×C₆₇	1	4	yes	—
199	C₂×Q₁₆	Q₈×C₆₇	1	4	yes	—
200	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
201	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
203	C₄×Q₈	—	2	4	no	—
204	C₄×Q₈	—	2	8	no	—
205	C₄×Q₈	—	4	4	no	—
206	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	—
207	C₂×C₄⋊C₄	—	2	2	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
213	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
216	C₂×C₄²	—	2	2	no	—
217	C₂×C₄²	—	2	4	no	—
218	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
219	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
220	#107	—	2	4	no	—
221	#107	—	4	2	no	—
222	#107	C₂×C₄×C₆₇	1	4	yes	—
223	C₄⋊C₈	—	2	2	no	—
224	#103	—	2	8	no	—
225	#103	C₂×C₄×C₆₇	1	8	yes	—
226	C₄×C₈	—	2	4	no	—
227	C₄×C₈	C₂×C₄×C₆₇	1	4	yes	—
228	#95	—	2	4	no	—
229	#95	D₄×C₆₇	1	2	yes	—
230	C₂×Q₈	—	2	2	no	—
231	C₂×Q₈	—	2	2	no	—
232	C₂×Q₈	—	2	2	no	—
233	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
234	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
235	C₂×Q₈	C₂×Q₈×C₆₇	1	4	yes	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
240	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
242	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
243	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
244	Q₁₆	C₄⋊C₄×C₆₇	1	16	yes	direct product factor
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	1	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
251	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
252	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
253	C₂×C₈	C₂×Q₈×C₆₇	1	2	yes	—
254	C₄⋊C₄	—	2	8	no	—
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	4	8	no	—
260	C₄⋊C₄	—	4	4	no	—
261	C₄⋊C₄	—	8	2	no	—
262	C₄⋊C₄	—	8	4	no	—
263	C₄⋊C₄	Q₁₆×C₆₇	1	4	yes	direct product factor
264	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
265	C₄²	—	2	8	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	2	2	no	—
268	C₄²	—	4	8	no	—
269	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
270	C₄²	#41×C₆₇	1	2	yes	—
271	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
272	Q₈	—	2	4	no	—
273	Q₈	—	2	4	no	—
274	Q₈	—	2	4	no	—
275	Q₈	C₂×C₄⋊C₄×C₆₇	1	8	yes	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
293	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
294	C₂×C₄	C₂×Q₁₆×C₆₇	1	4	yes	—
295	C₂×C₄	C₂×Q₁₆×C₆₇	1	2	yes	—
296	C₂×C₄	#135×C₆₇	1	2	yes	—
297	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
298	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
299	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
300	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
301	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
302	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
303	C₈	—	2	2	no	—
304	C₈	—	4	2	no	—
305	C₈	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
306	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
307	C₂²	D₄²×C₆₇	1	1	yes	characteristic
308	C₂²	D₄×Q₈×C₆₇	1	1	yes	characteristic
309	C₂²	C₂²×Q₁₆×C₆₇	1	1	yes	characteristic
310	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
311	C₂²	#576×C₆₇	1	1	yes	characteristic
312	C₂²	#578×C₆₇	1	1	yes	characteristic
313	C₄	—	2	4	no	—
314	C₄	—	2	8	no	—
315	C₄	—	2	2	no	—
316	C₄	—	4	2	no	—
317	C₄	—	4	4	no	—
318	C₄	—	8	4	no	—
319	C₄	C₄×Q₁₆×C₆₇	1	4	yes	complemented
320	C₄	C₂²×C₄⋊C₄×C₆₇	1	1	yes	characteristic
321	C₄	#520×C₆₇	1	1	yes	characteristic
322	C₄	#547×C₆₇	1	1	yes	characteristic
323	C₄	#554×C₆₇	1	1	yes	characteristic
324	C₂	D₄×C₄⋊C₄×C₆₇	1	1	yes	characteristic
325	C₂	C₂×C₄×Q₁₆×C₆₇	1	1	yes	characteristic
326	C₂	C₆₇×#2951	1	1	yes	characteristic
327	C₂	D₄×Q₁₆×C₆₇	1	1	yes	characteristic
328	C₂	C₆₇×#3287	1	1	yes	characteristic
329	C₂	Q₈×Q₁₆×C₆₇	1	1	yes	characteristic
330	C₂	C₆₇×#3383	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. C₄×Q₁₆×C₆₇	C₄	semidirect
78. Q₁₆×C₆₇	C₄⋊C₄	direct (N × H)
97. C₄⋊C₄×C₆₇	Q₁₆	direct (N × H)
153. C₄×C₆₇	C₄×Q₁₆	semidirect
158. C₄⋊C₄×Q₁₆	C₆₇	direct (N × H)
174. C₆₇	C₄⋊C₄×Q₁₆	direct (N × H)
179. C₄×Q₁₆	C₄×C₆₇	semidirect
244. Q₁₆	C₄⋊C₄×C₆₇	direct (N × H)
263. C₄⋊C₄	Q₁₆×C₆₇	direct (N × H)
319. C₄	C₄×Q₁₆×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₆₇	2
Q₈×C₄⋊C₄×C₆₇	2
C₆₇×#1942	2
C₆₇×#1863	2
C₆₇×#1845	2
C₆₇×#1803	2
C₈×C₄⋊C₄×C₆₇	2
C₄⋊C₄×Q₁₆	67

Subgroups — C4⋊C4×Q16×C67 #30701935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×Q₁₆×C₆₇ #30701935