Subgroups — C₆₇×#33892 #30713143

Order 17152.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2234	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2218	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2184	C₂	1	2	yes	maximal, complemented
9	C₄×D₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2169	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2140	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
13	#555×C₆₇	—	2	1	no	—
14	D₄²×C₆₇	—	2	1	no	—
15	C₂×D₁₆×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×D₁₆×C₆₇	C₂²	1	2	yes	complemented
17	C₂×M₃₂×C₆₇	C₂²	1	2	yes	complemented
18	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
19	#493×C₆₇	C₂²	1	1	yes	characteristic
20	#482×C₆₇	—	2	2	no	—
21	#476×C₆₇	—	2	1	no	—
22	#466×C₆₇	C₂²	1	2	yes	—
23	#466×C₆₇	C₂²	1	2	yes	complemented
24	#459×C₆₇	—	2	1	no	—
25	#447×C₆₇	—	2	2	no	—
26	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	#427×C₆₇	C₂²	1	2	yes	complemented
30	#367×C₆₇	C₂²	1	2	yes	complemented
31	#366×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#357×C₆₇	C₂²	1	1	yes	characteristic
34	#357×C₆₇	C₂²	1	2	yes	—
35	#357×C₆₇	C₂²	1	2	yes	complemented
36	#357×C₆₇	C₂²	1	2	yes	complemented
37	#357×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#357×C₆₇	C₂²	1	2	yes	complemented
39	C₂²⋊C₁₆×C₆₇	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₄×C₆₇	—	2	2	no	—
42	C₂²×D₄×C₆₇	—	4	1	no	—
43	C₂×D₈×C₆₇	—	2	4	no	—
44	C₂×D₈×C₆₇	—	2	2	no	—
45	C₂×D₈×C₆₇	—	2	1	no	—
46	C₂×D₈×C₆₇	—	4	2	no	—
47	C₂×D₈×C₆₇	C₂³	1	2	yes	—
48	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₆₇	—	2	1	no	—
52	#127×C₆₇	—	2	1	no	—
53	#124×C₆₇	—	4	2	no	—
54	#121×C₆₇	—	2	2	no	—
55	#121×C₆₇	—	2	2	no	—
56	#121×C₆₇	—	4	1	no	—
57	#121×C₆₇	—	4	1	no	—
58	#120×C₆₇	—	4	2	no	—
59	C₄×D₄×C₆₇	—	2	1	no	—
60	C₄×D₄×C₆₇	—	2	1	no	—
61	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
62	#117×C₆₇	—	2	2	no	—
63	#117×C₆₇	—	4	1	no	—
64	D₁₆×C₆₇	—	2	2	no	—
65	D₁₆×C₆₇	—	4	2	no	—
66	M₃₂×C₆₇	—	4	2	no	—
67	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
69	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
70	#107×C₆₇	—	2	1	no	—
71	#107×C₆₇	C₂³	1	1	yes	characteristic
72	#107×C₆₇	C₂³	1	2	yes	—
73	#107×C₆₇	C₂³	1	1	yes	characteristic
74	#106×C₆₇	—	2	2	no	—
75	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
76	#102×C₆₇	—	2	2	no	—
77	#102×C₆₇	—	2	2	no	—
78	#102×C₆₇	—	2	1	no	—
79	#102×C₆₇	—	2	1	no	—
80	C₂²⋊C₈×C₆₇	D₄	1	2	yes	—
81	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂⁴×C₆₇	—	4	2	no	—
83	C₂×Q₈×C₆₇	—	4	1	no	—
84	C₂×D₄×C₆₇	—	2	1	no	—
85	C₂×D₄×C₆₇	—	2	1	no	—
86	C₂×D₄×C₆₇	—	2	2	no	—
87	C₂×D₄×C₆₇	—	4	4	no	—
88	C₂×D₄×C₆₇	—	4	2	no	—
89	C₂×D₄×C₆₇	—	4	2	no	—
90	C₂×D₄×C₆₇	—	4	2	no	—
91	C₂×D₄×C₆₇	—	4	1	no	—
92	C₂×D₄×C₆₇	—	4	1	no	—
93	C₂×D₄×C₆₇	—	8	2	no	—
94	C₂×D₄×C₆₇	—	8	4	no	—
95	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	—	4	1	no	—
97	C₂²×C₄×C₆₇	—	4	1	no	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
99	D₈×C₆₇	—	2	1	no	—
100	D₈×C₆₇	—	2	2	no	—
101	D₈×C₆₇	—	2	1	no	—
102	D₈×C₆₇	—	2	1	no	—
103	D₈×C₆₇	—	2	2	no	—
104	D₈×C₆₇	—	4	4	no	—
105	D₈×C₆₇	—	8	1	no	—
106	D₈×C₆₇	#41	1	2	yes	—
107	C₂×C₈×C₆₇	—	2	2	no	—
108	C₂×C₈×C₆₇	—	2	2	no	—
109	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₆₇	—	2	1	no	—
113	C₄⋊C₄×C₆₇	—	2	1	no	—
114	C₄⋊C₄×C₆₇	—	2	2	no	—
115	C₄⋊C₄×C₆₇	—	4	1	no	—
116	C₄⋊C₄×C₆₇	D₈	1	1	yes	characteristic
117	C₂²⋊C₄×C₆₇	—	4	2	no	—
118	C₂²⋊C₄×C₆₇	—	4	2	no	—
119	C₂²⋊C₄×C₆₇	—	4	1	no	—
120	C₂²⋊C₄×C₆₇	—	4	1	no	—
121	C₂²⋊C₄×C₆₇	—	4	2	no	—
122	C₂²⋊C₄×C₆₇	D₈	1	2	yes	—
123	C₄²×C₆₇	—	4	2	no	—
124	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₆₇	—	2	1	no	—
126	C₁₆×C₆₇	—	2	1	no	—
127	C₁₆×C₆₇	—	2	2	no	—
128	C₂³×C₆₇	—	4	1	no	—
129	C₂³×C₆₇	—	4	1	no	—
130	C₂³×C₆₇	—	4	2	no	—
131	C₂³×C₆₇	—	8	4	no	—
132	C₂³×C₆₇	—	8	4	no	—
133	C₂³×C₆₇	—	16	2	no	—
134	C₂³×C₆₇	C₂×D₈	1	2	yes	—
135	Q₈×C₆₇	—	16	1	no	—
136	D₄×C₆₇	—	2	2	no	—
137	D₄×C₆₇	—	2	2	no	—
138	D₄×C₆₇	—	4	2	no	—
139	D₄×C₆₇	—	4	1	no	—
140	D₄×C₆₇	—	4	1	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	4	1	no	—
143	D₄×C₆₇	—	8	4	no	—
144	D₄×C₆₇	—	8	4	no	—
145	D₄×C₆₇	—	8	2	no	—
146	D₄×C₆₇	—	16	1	no	—
147	D₄×C₆₇	—	16	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	4	1	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	1	no	—
153	C₂×C₄×C₆₇	—	8	2	no	—
154	C₂×C₄×C₆₇	—	8	2	no	—
155	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₆₇	—	2	2	no	—
160	C₈×C₆₇	—	2	1	no	—
161	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
162	C₈×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	2	2	no	—
165	C₂²×C₆₇	—	2	2	no	—
166	C₂²×C₆₇	—	4	2	no	—
167	C₂²×C₆₇	—	8	1	no	—
168	C₂²×C₆₇	—	8	1	no	—
169	C₂²×C₆₇	—	8	1	no	—
170	C₂²×C₆₇	—	8	2	no	—
171	C₂²×C₆₇	—	8	1	no	—
172	C₂²×C₆₇	—	8	2	no	—
173	C₂²×C₆₇	—	8	2	no	—
174	C₂²×C₆₇	—	8	1	no	—
175	C₂²×C₆₇	—	16	8	no	—
176	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	2	no	—
179	C₄×C₆₇	—	8	1	no	—
180	C₄×C₆₇	—	8	1	no	—
181	C₄×C₆₇	—	8	2	no	—
182	C₄×C₆₇	#509	1	2	yes	—
183	C₄×C₆₇	#546	1	1	yes	characteristic
184	C₄×C₆₇	#577	1	1	yes	characteristic
185	#33892	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₆₇	—	4	2	no	—
187	C₂×C₆₇	—	8	2	no	—
188	C₂×C₆₇	—	16	1	no	—
189	C₂×C₆₇	—	16	2	no	—
190	C₂×C₆₇	#3294	1	1	yes	characteristic
191	C₂×C₆₇	C₂×#509	1	1	yes	characteristic
192	C₂×C₆₇	#3415	1	1	yes	characteristic
193	#3341	C₂×C₆₇	1	1	yes	characteristic, complemented
194	D₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#2240	C₂×C₆₇	1	1	yes	characteristic, complemented
196	#2234	C₂×C₆₇	1	2	yes	complemented
197	#2226	C₂×C₆₇	1	1	yes	characteristic, complemented
198	#2218	C₂×C₆₇	1	2	yes	complemented
199	#2206	C₂×C₆₇	1	1	yes	characteristic, complemented
200	#2184	C₂×C₆₇	1	2	yes	complemented
201	C₄×D₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#2169	C₂×C₆₇	1	1	yes	characteristic, complemented
203	#2140	C₂×C₆₇	1	2	yes	complemented
204	C₆₇	#33892	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
206	#555	—	2	1	no	—
207	D₄²	—	2	1	no	—
208	C₂×D₁₆	C₂²×C₆₇	1	1	yes	characteristic
209	C₂×D₁₆	C₂²×C₆₇	1	2	yes	complemented
210	C₂×M₃₂	C₂²×C₆₇	1	2	yes	complemented
211	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
212	#493	C₂²×C₆₇	1	1	yes	characteristic
213	#482	—	2	2	no	—
214	#476	—	2	1	no	—
215	#466	C₂²×C₆₇	1	2	yes	—
216	#466	C₂²×C₆₇	1	2	yes	complemented
217	#459	—	2	1	no	—
218	#447	—	2	2	no	—
219	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
220	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
221	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
222	#427	C₂²×C₆₇	1	2	yes	complemented
223	#367	C₂²×C₆₇	1	2	yes	complemented
224	#366	C₂²×C₆₇	1	1	yes	characteristic, complemented
225	C₄⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
226	#357	C₂²×C₆₇	1	1	yes	characteristic
227	#357	C₂²×C₆₇	1	2	yes	—
228	#357	C₂²×C₆₇	1	2	yes	complemented
229	#357	C₂²×C₆₇	1	2	yes	complemented
230	#357	C₂²×C₆₇	1	1	yes	characteristic, complemented
231	#357	C₂²×C₆₇	1	2	yes	complemented
232	C₂²⋊C₁₆	C₂²×C₆₇	1	2	yes	complemented
233	C₄×C₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	4	1	no	—
236	C₂×D₈	—	2	4	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	1	no	—
239	C₂×D₈	—	4	2	no	—
240	C₂×D₈	C₂³×C₆₇	1	2	yes	—
241	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
242	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
244	C₄⋊Q₈	—	2	1	no	—
245	#127	—	2	1	no	—
246	#124	—	4	2	no	—
247	#121	—	2	2	no	—
248	#121	—	2	2	no	—
249	#121	—	4	1	no	—
250	#121	—	4	1	no	—
251	#120	—	4	2	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
255	#117	—	2	2	no	—
256	#117	—	4	1	no	—
257	D₁₆	—	2	2	no	—
258	D₁₆	—	4	2	no	—
259	M₃₂	—	4	2	no	—
260	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
261	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
262	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
263	#107	—	2	1	no	—
264	#107	C₂³×C₆₇	1	1	yes	characteristic
265	#107	C₂³×C₆₇	1	2	yes	—
266	#107	C₂³×C₆₇	1	1	yes	characteristic
267	#106	—	2	2	no	—
268	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
269	#102	—	2	1	no	—
270	#102	—	2	1	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
274	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
275	C₂⁴	—	4	2	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂×D₄	—	8	4	no	—
288	C₂×D₄	D₈×C₆₇	1	1	yes	characteristic
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
292	D₈	—	2	1	no	—
293	D₈	—	2	2	no	—
294	D₈	—	2	1	no	—
295	D₈	—	2	1	no	—
296	D₈	—	2	2	no	—
297	D₈	—	4	4	no	—
298	D₈	—	8	1	no	—
299	D₈	#41×C₆₇	1	2	yes	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
304	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	D₈×C₆₇	1	1	yes	characteristic
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	D₈×C₆₇	1	2	yes	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	1	no	—
320	C₁₆	—	2	2	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	8	4	no	—
325	C₂³	—	8	4	no	—
326	C₂³	—	16	2	no	—
327	C₂³	C₂×D₈×C₆₇	1	2	yes	—
328	Q₈	—	16	1	no	—
329	D₄	—	2	2	no	—
330	D₄	—	2	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	2	no	—
339	D₄	—	16	1	no	—
340	D₄	—	16	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
349	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
350	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
352	C₈	—	2	2	no	—
353	C₈	—	2	1	no	—
354	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
355	C₈	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	8	1	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	8	no	—
369	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	1	no	—
373	C₄	—	8	1	no	—
374	C₄	—	8	2	no	—
375	C₄	#509×C₆₇	1	2	yes	—
376	C₄	#546×C₆₇	1	1	yes	characteristic
377	C₄	#577×C₆₇	1	1	yes	characteristic
378	C₂	—	4	2	no	—
379	C₂	—	8	2	no	—
380	C₂	—	16	2	no	—
381	C₂	—	16	1	no	—
382	C₂	C₆₇×#3294	1	1	yes	characteristic
383	C₂	C₂×#509×C₆₇	1	1	yes	characteristic
384	C₂	C₆₇×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×D₄×C₆₇ ◁ C₈×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3341	C₂	semidirect
2. D₄×D₈×C₆₇	C₂	semidirect
3. C₆₇×#2240	C₂	semidirect
4. C₆₇×#2234	C₂	semidirect
5. C₆₇×#2226	C₂	semidirect
6. C₆₇×#2218	C₂	semidirect
7. C₆₇×#2206	C₂	semidirect
8. C₆₇×#2184	C₂	semidirect
9. C₄×D₁₆×C₆₇	C₂	semidirect
10. C₆₇×#2169	C₂	semidirect
11. C₆₇×#2140	C₂	semidirect
16. C₂×D₁₆×C₆₇	C₂²	semidirect
17. C₂×M₃₂×C₆₇	C₂²	semidirect
18. #500×C₆₇	C₂²	semidirect
23. #466×C₆₇	C₂²	semidirect
27. C₄×D₈×C₆₇	C₂²	semidirect
29. #427×C₆₇	C₂²	semidirect
30. #367×C₆₇	C₂²	semidirect
31. #366×C₆₇	C₂²	semidirect
32. C₄⋊C₁₆×C₆₇	C₂²	semidirect
35. #357×C₆₇	C₂²	semidirect
36. #357×C₆₇	C₂²	semidirect
37. #357×C₆₇	C₂²	semidirect
38. #357×C₆₇	C₂²	semidirect
39. C₂²⋊C₁₆×C₆₇	C₂²	semidirect
40. C₄×C₁₆×C₆₇	C₂²	semidirect
185. #33892	C₆₇	direct (N × H)
193. #3341	C₂×C₆₇	semidirect
194. D₄×D₈	C₂×C₆₇	semidirect
195. #2240	C₂×C₆₇	semidirect
196. #2234	C₂×C₆₇	semidirect
197. #2226	C₂×C₆₇	semidirect
198. #2218	C₂×C₆₇	semidirect
199. #2206	C₂×C₆₇	semidirect
200. #2184	C₂×C₆₇	semidirect
201. C₄×D₁₆	C₂×C₆₇	semidirect
202. #2169	C₂×C₆₇	semidirect
203. #2140	C₂×C₆₇	semidirect
204. C₆₇	#33892	direct (N × H)
209. C₂×D₁₆	C₂²×C₆₇	semidirect
210. C₂×M₃₂	C₂²×C₆₇	semidirect
211. #500	C₂²×C₆₇	semidirect
216. #466	C₂²×C₆₇	semidirect
220. C₄×D₈	C₂²×C₆₇	semidirect
222. #427	C₂²×C₆₇	semidirect
223. #367	C₂²×C₆₇	semidirect
224. #366	C₂²×C₆₇	semidirect
225. C₄⋊C₁₆	C₂²×C₆₇	semidirect
228. #357	C₂²×C₆₇	semidirect
229. #357	C₂²×C₆₇	semidirect
230. #357	C₂²×C₆₇	semidirect
231. #357	C₂²×C₆₇	semidirect
232. C₂²⋊C₁₆	C₂²×C₆₇	semidirect
233. C₄×C₁₆	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3341	2
D₄×D₈×C₆₇	2
C₆₇×#2240	2
C₆₇×#2234	2
C₆₇×#2226	2
C₆₇×#2218	2
C₆₇×#2206	2
C₆₇×#2184	2
C₄×D₁₆×C₆₇	2
C₆₇×#2169	2
C₆₇×#2140	2
#33892	67

Subgroups — C67×#33892 #30713143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33892 #30713143