Subgroups — C₆₇×#10836 #30690087

Order 17152.

850 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×H(3,ℤ/4)×C₆₇	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
6	C₂×#117×C₆₇	C₂²	1	2	yes	—
7	C₂×#117×C₆₇	C₂²	1	2	yes	—
8	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
9	#423×C₆₇	—	2	2	no	—
10	#423×C₆₇	—	2	1	no	—
11	#423×C₆₇	—	2	1	no	—
12	C₂×C₄⋊C₈×C₆₇	C₄	1	4	yes	complemented
13	#384×C₆₇	—	2	1	no	—
14	#382×C₆₇	—	2	1	no	—
15	#380×C₆₇	—	2	2	no	—
16	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
17	C₄×C₄⋊C₄×C₆₇	C₄	1	4	yes	complemented
18	C₄×C₂²⋊C₄×C₆₇	—	2	2	no	—
19	#376×C₆₇	C₄	1	2	yes	complemented
20	C₄³×C₆₇	C₄	1	2	yes	complemented
21	H(3,ℤ/4)×C₆₇	—	2	8	no	—
22	C₂³×C₄×C₆₇	D₄	1	2	yes	—
23	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₆₇	—	2	4	no	—
25	C₂×M₁₆×C₆₇	—	2	2	no	—
26	C₂×M₁₆×C₆₇	—	2	2	no	—
27	C₂×M₁₆×C₆₇	—	2	4	no	—
28	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
29	#117×C₆₇	—	2	2	no	—
30	#117×C₆₇	—	2	2	no	—
31	#117×C₆₇	—	2	4	no	—
32	#117×C₆₇	—	2	4	no	—
33	#117×C₆₇	D₄	1	4	yes	—
34	#117×C₆₇	Q₈	1	4	yes	—
35	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
37	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
40	C₂×C₄²×C₆₇	—	2	4	no	—
41	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₆₇	D₄	1	2	yes	—
48	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
52	C₄⋊C₈×C₆₇	—	2	4	no	—
53	C₄⋊C₈×C₆₇	—	2	4	no	—
54	#95×C₆₇	—	2	4	no	—
55	#95×C₆₇	—	2	4	no	—
56	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₆₇	—	2	4	no	—
58	C₂²×C₄×C₆₇	—	2	4	no	—
59	C₂²×C₄×C₆₇	—	4	4	no	—
60	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
74	C₂²×C₄×C₆₇	#41	1	2	yes	—
75	C₂²×C₄×C₆₇	#41	1	2	yes	—
76	M₁₆×C₆₇	—	4	4	no	—
77	M₁₆×C₆₇	—	4	2	no	—
78	M₁₆×C₆₇	—	4	2	no	—
79	C₂×C₈×C₆₇	—	2	4	no	—
80	C₂×C₈×C₆₇	—	2	8	no	—
81	C₄⋊C₄×C₆₇	—	2	4	no	—
82	C₄⋊C₄×C₆₇	—	2	4	no	—
83	C₄⋊C₄×C₆₇	—	4	8	no	—
84	C₄⋊C₄×C₆₇	—	4	2	no	—
85	C₄⋊C₄×C₆₇	—	4	2	no	—
86	C₂²⋊C₄×C₆₇	—	2	4	no	—
87	C₂²⋊C₄×C₆₇	—	2	4	no	—
88	C₂²⋊C₄×C₆₇	—	4	4	no	—
89	C₄²×C₆₇	—	2	4	no	—
90	C₄²×C₆₇	—	2	8	no	—
91	C₄²×C₆₇	—	4	8	no	—
92	C₄²×C₆₇	C₄²	1	2	yes	—
93	C₄²×C₆₇	C₄²	1	2	yes	—
94	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
100	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
101	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₇	C₄⋊C₄	1	8	yes	complemented
103	C₂³×C₆₇	—	4	2	no	—
104	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂³×C₆₇	#121	1	2	yes	—
108	C₂³×C₆₇	C₂²⋊Q₈	1	2	yes	—
109	C₂×C₄×C₆₇	—	2	4	no	—
110	C₂×C₄×C₆₇	—	2	4	no	—
111	C₂×C₄×C₆₇	—	2	4	no	—
112	C₂×C₄×C₆₇	—	2	8	no	—
113	C₂×C₄×C₆₇	—	4	2	no	—
114	C₂×C₄×C₆₇	—	4	2	no	—
115	C₂×C₄×C₆₇	—	4	2	no	—
116	C₂×C₄×C₆₇	—	4	8	no	—
117	C₂×C₄×C₆₇	—	4	8	no	—
118	C₂×C₄×C₆₇	—	4	4	no	—
119	C₂×C₄×C₆₇	#95	1	2	yes	—
120	C₂×C₄×C₆₇	#95	1	2	yes	—
121	C₂×C₄×C₆₇	#95	1	2	yes	—
122	C₂×C₄×C₆₇	#95	1	2	yes	—
123	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
124	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₆₇	#117	1	2	yes	—
129	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
133	C₂×C₄×C₆₇	#121	1	2	yes	—
134	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
135	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
136	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
137	C₂×C₄×C₆₇	#125	1	2	yes	—
138	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
139	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
140	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
141	C₈×C₆₇	—	4	4	no	—
142	C₂²×C₆₇	—	2	2	no	—
143	C₂²×C₆₇	—	2	2	no	—
144	C₂²×C₆₇	—	2	2	no	—
145	C₂²×C₆₇	—	4	2	no	—
146	C₂²×C₆₇	—	4	2	no	—
147	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
148	C₂²×C₆₇	#380	1	2	yes	—
149	C₂²×C₆₇	#389	1	2	yes	—
150	C₂²×C₆₇	#390	1	1	yes	characteristic
151	C₂²×C₆₇	#391	1	1	yes	characteristic
152	C₄×C₆₇	—	2	2	no	—
153	C₄×C₆₇	—	2	2	no	—
154	C₄×C₆₇	—	2	2	no	—
155	C₄×C₆₇	—	4	8	no	—
156	C₄×C₆₇	—	8	4	no	—
157	C₄×C₆₇	H(3,ℤ/4)	1	4	yes	complemented
158	C₄×C₆₇	C₄×C₄⋊C₄	1	2	yes	—
159	C₄×C₆₇	#382	1	1	yes	characteristic
160	C₄×C₆₇	#384	1	1	yes	characteristic
161	C₄×C₆₇	#389	1	2	yes	—
162	C₄×C₆₇	#390	1	1	yes	characteristic
163	C₄×C₆₇	#391	1	1	yes	characteristic
164	#10836	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₆₇	—	2	2	no	—
166	C₂×C₆₇	—	2	1	no	—
167	C₂×C₆₇	—	2	2	no	—
168	C₂×C₆₇	—	2	1	no	—
169	C₂×C₆₇	C₄⋊#95	1	1	yes	characteristic
170	C₂×C₆₇	C₂×H(3,ℤ/4)	1	2	yes	—
171	C₂×#423	C₂×C₆₇	1	1	yes	characteristic
172	#2285	C₂×C₆₇	1	1	yes	characteristic
173	C₄×#117	C₂×C₆₇	1	1	yes	characteristic
174	C₂×H(3,ℤ/4)	C₂×C₆₇	1	4	yes	—
175	C₆₇	#10836	1	1	yes	characteristic, direct product factor, Sylow
176	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
177	C₂×#117	C₂²×C₆₇	1	2	yes	—
178	C₂×#117	C₂²×C₆₇	1	2	yes	—
179	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
180	#423	—	2	2	no	—
181	#423	—	2	1	no	—
182	#423	—	2	1	no	—
183	C₂×C₄⋊C₈	C₄×C₆₇	1	4	yes	complemented
184	#384	—	2	1	no	—
185	#382	—	2	1	no	—
186	#380	—	2	2	no	—
187	C₄×C₄⋊C₄	—	2	2	no	—
188	C₄×C₄⋊C₄	C₄×C₆₇	1	4	yes	complemented
189	C₄×C₂²⋊C₄	—	2	2	no	—
190	#376	C₄×C₆₇	1	2	yes	complemented
191	C₄³	C₄×C₆₇	1	2	yes	complemented
192	H(3,ℤ/4)	—	2	8	no	—
193	C₂³×C₄	D₄×C₆₇	1	2	yes	—
194	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
195	C₂×M₁₆	—	2	4	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	2	4	no	—
199	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
200	#117	—	2	2	no	—
201	#117	—	2	2	no	—
202	#117	—	2	4	no	—
203	#117	—	2	4	no	—
204	#117	D₄×C₆₇	1	4	yes	—
205	#117	Q₈×C₆₇	1	4	yes	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	2	no	—
209	C₂×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₂²⋊C₄	—	2	2	no	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
213	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
214	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
215	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
218	C₂×C₄²	D₄×C₆₇	1	2	yes	—
219	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
220	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
221	C₂×C₄²	Q₈×C₆₇	1	1	yes	characteristic
222	C₂×C₄²	Q₈×C₆₇	1	1	yes	characteristic
223	C₄⋊C₈	—	2	4	no	—
224	C₄⋊C₈	—	2	4	no	—
225	#95	—	2	4	no	—
226	#95	—	2	4	no	—
227	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
232	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
233	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
234	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
235	C₂²×C₄	C₄⋊C₄×C₆₇	1	2	yes	—
236	C₂²×C₄	C₄⋊C₄×C₆₇	1	2	yes	—
237	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
241	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
243	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
244	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
245	C₂²×C₄	#41×C₆₇	1	2	yes	—
246	C₂²×C₄	#41×C₆₇	1	2	yes	—
247	M₁₆	—	4	4	no	—
248	M₁₆	—	4	2	no	—
249	M₁₆	—	4	2	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	8	no	—
252	C₄⋊C₄	—	2	4	no	—
253	C₄⋊C₄	—	2	4	no	—
254	C₄⋊C₄	—	4	8	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₂²⋊C₄	—	2	4	no	—
258	C₂²⋊C₄	—	2	4	no	—
259	C₂²⋊C₄	—	4	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	2	8	no	—
262	C₄²	—	4	8	no	—
263	C₄²	C₄²×C₆₇	1	2	yes	—
264	C₄²	C₄²×C₆₇	1	2	yes	—
265	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
266	C₄²	C₂²⋊C₄×C₆₇	1	2	yes	—
267	C₄²	C₄⋊C₄×C₆₇	1	1	yes	characteristic
268	C₄²	C₄⋊C₄×C₆₇	1	1	yes	characteristic
269	C₄²	C₄⋊C₄×C₆₇	1	1	yes	characteristic
270	C₄²	C₄⋊C₄×C₆₇	1	1	yes	characteristic
271	C₄²	C₄⋊C₄×C₆₇	1	2	yes	—
272	C₄²	C₄⋊C₄×C₆₇	1	2	yes	—
273	C₄²	C₄⋊C₄×C₆₇	1	8	yes	complemented
274	C₂³	—	4	2	no	—
275	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
276	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
277	C₂³	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
278	C₂³	#121×C₆₇	1	2	yes	—
279	C₂³	C₂²⋊Q₈×C₆₇	1	2	yes	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	8	no	—
288	C₂×C₄	—	4	8	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	#95×C₆₇	1	2	yes	—
291	C₂×C₄	#95×C₆₇	1	2	yes	—
292	C₂×C₄	#95×C₆₇	1	2	yes	—
293	C₂×C₄	#95×C₆₇	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₆₇	1	1	yes	characteristic
295	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
296	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	2	yes	—
297	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
298	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
299	C₂×C₄	#117×C₆₇	1	2	yes	—
300	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
301	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
302	C₂×C₄	C₄×Q₈×C₆₇	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₆₇	1	2	yes	—
304	C₂×C₄	#121×C₆₇	1	2	yes	—
305	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
306	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
307	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
308	C₂×C₄	#125×C₆₇	1	2	yes	—
309	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
310	C₂×C₄	C₄⋊Q₈×C₆₇	1	2	yes	—
311	C₂×C₄	C₄⋊Q₈×C₆₇	1	1	yes	characteristic
312	C₈	—	4	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	C₂×#95×C₆₇	1	1	yes	characteristic
319	C₂²	#380×C₆₇	1	2	yes	—
320	C₂²	#389×C₆₇	1	2	yes	—
321	C₂²	#390×C₆₇	1	1	yes	characteristic
322	C₂²	#391×C₆₇	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	4	8	no	—
327	C₄	—	8	4	no	—
328	C₄	H(3,ℤ/4)×C₆₇	1	4	yes	complemented
329	C₄	C₄×C₄⋊C₄×C₆₇	1	2	yes	—
330	C₄	#382×C₆₇	1	1	yes	characteristic
331	C₄	#384×C₆₇	1	1	yes	characteristic
332	C₄	#389×C₆₇	1	2	yes	—
333	C₄	#390×C₆₇	1	1	yes	characteristic
334	C₄	#391×C₆₇	1	1	yes	characteristic
335	C₂	—	2	2	no	—
336	C₂	—	2	1	no	—
337	C₂	—	2	2	no	—
338	C₂	—	2	1	no	—
339	C₂	C₆₇×C₄⋊#95	1	1	yes	characteristic
340	C₂	C₂×H(3,ℤ/4)×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₄⋊C₈×C₆₇	C₄	semidirect
17. C₄×C₄⋊C₄×C₆₇	C₄	semidirect
19. #376×C₆₇	C₄	semidirect
20. C₄³×C₆₇	C₄	semidirect
102. C₄²×C₆₇	C₄⋊C₄	semidirect
157. C₄×C₆₇	H(3,ℤ/4)	semidirect
164. #10836	C₆₇	direct (N × H)
175. C₆₇	#10836	direct (N × H)
183. C₂×C₄⋊C₈	C₄×C₆₇	semidirect
188. C₄×C₄⋊C₄	C₄×C₆₇	semidirect
190. #376	C₄×C₆₇	semidirect
191. C₄³	C₄×C₆₇	semidirect
273. C₄²	C₄⋊C₄×C₆₇	semidirect
328. C₄	H(3,ℤ/4)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#423×C₆₇	2
C₆₇×#2285	2
C₄×#117×C₆₇	2
C₂×H(3,ℤ/4)×C₆₇	2
#10836	67

Subgroups — C67×#10836 #30690087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#10836 #30690087