Subgroups — C₆₇×#33891 #30713142

Order 17152.

608 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2234	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2220	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2187	C₂	1	2	yes	maximal, complemented
9	C₄×SD₃₂×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	#556×C₆₇	—	2	1	no	—
14	D₄²×C₆₇	—	2	1	no	—
15	C₂×SD₃₂×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×SD₃₂×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	#485×C₆₇	—	2	2	no	—
21	#475×C₆₇	—	2	1	no	—
22	#467×C₆₇	C₂²	1	2	yes	complemented
23	#466×C₆₇	C₂²	1	2	yes	—
24	#459×C₆₇	—	2	1	no	—
25	#447×C₆₇	—	2	2	no	—
26	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	#427×C₆₇	C₂²	1	2	yes	complemented
30	#367×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#366×C₆₇	C₂²	1	2	yes	complemented
32	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#358×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#357×C₆₇	C₂²	1	1	yes	characteristic
35	#357×C₆₇	C₂²	1	2	yes	—
36	#357×C₆₇	C₂²	1	2	yes	complemented
37	#357×C₆₇	C₂²	1	2	yes	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×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
44	C₂×D₈×C₆₇	—	2	4	no	—
45	C₂×D₈×C₆₇	—	2	2	no	—
46	C₂×D₈×C₆₇	—	2	1	no	—
47	C₂×D₈×C₆₇	—	4	2	no	—
48	C₂×D₈×C₆₇	C₂³	1	2	yes	—
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	#126×C₆₇	—	4	2	no	—
54	#124×C₆₇	—	4	1	no	—
55	C₂²⋊Q₈×C₆₇	—	2	2	no	—
56	#121×C₆₇	—	2	2	no	—
57	#121×C₆₇	—	4	1	no	—
58	#120×C₆₇	—	4	2	no	—
59	C₄×Q₈×C₆₇	—	2	1	no	—
60	C₄×Q₈×C₆₇	—	4	1	no	—
61	C₄×D₄×C₆₇	—	2	1	no	—
62	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
63	#117×C₆₇	—	2	2	no	—
64	SD₃₂×C₆₇	—	2	2	no	—
65	SD₃₂×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	#103×C₆₇	—	2	2	no	—
77	#103×C₆₇	—	2	1	no	—
78	#102×C₆₇	—	2	2	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	—	2	1	no	—
84	C₂×Q₈×C₆₇	—	4	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	1	no	—
91	C₂×D₄×C₆₇	—	4	1	no	—
92	C₂×D₄×C₆₇	—	8	2	no	—
93	C₂×D₄×C₆₇	—	8	4	no	—
94	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	—	4	1	no	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	Q₁₆×C₆₇	—	2	1	no	—
98	Q₁₆×C₆₇	—	2	1	no	—
99	D₈×C₆₇	—	2	2	no	—
100	D₈×C₆₇	—	2	1	no	—
101	D₈×C₆₇	—	2	2	no	—
102	D₈×C₆₇	—	4	4	no	—
103	D₈×C₆₇	—	8	1	no	—
104	D₈×C₆₇	#41	1	2	yes	—
105	C₂×C₈×C₆₇	—	2	2	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₆₇	—	2	1	no	—
111	C₄⋊C₄×C₆₇	—	2	1	no	—
112	C₄⋊C₄×C₆₇	—	2	2	no	—
113	C₄⋊C₄×C₆₇	—	4	1	no	—
114	C₄⋊C₄×C₆₇	—	4	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	2	no	—
121	C₂²⋊C₄×C₆₇	D₈	1	2	yes	—
122	C₄²×C₆₇	—	4	2	no	—
123	C₄²×C₆₇	—	4	1	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	2	no	—
130	C₂³×C₆₇	—	8	4	no	—
131	C₂³×C₆₇	—	8	4	no	—
132	C₂³×C₆₇	—	16	2	no	—
133	C₂³×C₆₇	C₂×D₈	1	2	yes	—
134	Q₈×C₆₇	—	4	1	no	—
135	Q₈×C₆₇	—	4	1	no	—
136	Q₈×C₆₇	—	8	2	no	—
137	D₄×C₆₇	—	2	2	no	—
138	D₄×C₆₇	—	2	2	no	—
139	D₄×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	4	1	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	8	4	no	—
143	D₄×C₆₇	—	8	4	no	—
144	D₄×C₆₇	—	8	2	no	—
145	D₄×C₆₇	—	16	1	no	—
146	C₂×C₄×C₆₇	—	2	2	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	4	1	no	—
149	C₂×C₄×C₆₇	—	4	2	no	—
150	C₂×C₄×C₆₇	—	4	1	no	—
151	C₂×C₄×C₆₇	—	4	1	no	—
152	C₂×C₄×C₆₇	—	8	2	no	—
153	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₆₇	—	2	2	no	—
158	C₈×C₆₇	—	2	1	no	—
159	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
160	C₈×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×C₆₇	—	2	2	no	—
162	C₂²×C₆₇	—	2	2	no	—
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	4	2	no	—
165	C₂²×C₆₇	—	8	1	no	—
166	C₂²×C₆₇	—	8	1	no	—
167	C₂²×C₆₇	—	8	2	no	—
168	C₂²×C₆₇	—	8	2	no	—
169	C₂²×C₆₇	—	8	2	no	—
170	C₂²×C₆₇	—	16	8	no	—
171	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	2	no	—
174	C₄×C₆₇	—	8	1	no	—
175	C₄×C₆₇	—	8	2	no	—
176	C₄×C₆₇	—	8	1	no	—
177	C₄×C₆₇	—	8	1	no	—
178	C₄×C₆₇	#509	1	2	yes	—
179	C₄×C₆₇	#546	1	1	yes	characteristic
180	C₄×C₆₇	#577	1	1	yes	characteristic
181	#33891	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₆₇	—	4	2	no	—
183	C₂×C₆₇	—	8	2	no	—
184	C₂×C₆₇	—	16	2	no	—
185	C₂×C₆₇	#3294	1	1	yes	characteristic
186	C₂×C₆₇	C₂×#509	1	1	yes	characteristic
187	C₂×C₆₇	#3416	1	1	yes	characteristic
188	#3342	C₂×C₆₇	1	1	yes	characteristic, complemented
189	D₄×D₈	C₂×C₆₇	1	1	yes	characteristic
190	#2240	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#2234	C₂×C₆₇	1	2	yes	complemented
192	#2224	C₂×C₆₇	1	1	yes	characteristic, complemented
193	#2220	C₂×C₆₇	1	2	yes	complemented
194	#2207	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#2187	C₂×C₆₇	1	2	yes	complemented
196	C₄×SD₃₂	C₂×C₆₇	1	1	yes	characteristic, complemented
197	#2169	C₂×C₆₇	1	1	yes	characteristic, complemented
198	#2140	C₂×C₆₇	1	2	yes	complemented
199	C₆₇	#33891	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
201	#556	—	2	1	no	—
202	D₄²	—	2	1	no	—
203	C₂×SD₃₂	C₂²×C₆₇	1	1	yes	characteristic
204	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	complemented
205	C₂×M₃₂	C₂²×C₆₇	1	2	yes	complemented
206	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
207	#493	C₂²×C₆₇	1	1	yes	characteristic
208	#485	—	2	2	no	—
209	#475	—	2	1	no	—
210	#467	C₂²×C₆₇	1	2	yes	complemented
211	#466	C₂²×C₆₇	1	2	yes	—
212	#459	—	2	1	no	—
213	#447	—	2	2	no	—
214	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
215	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
216	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
217	#427	C₂²×C₆₇	1	2	yes	complemented
218	#367	C₂²×C₆₇	1	1	yes	characteristic, complemented
219	#366	C₂²×C₆₇	1	2	yes	complemented
220	C₄⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
221	#358	C₂²×C₆₇	1	1	yes	characteristic, complemented
222	#357	C₂²×C₆₇	1	1	yes	characteristic
223	#357	C₂²×C₆₇	1	2	yes	—
224	#357	C₂²×C₆₇	1	2	yes	complemented
225	#357	C₂²×C₆₇	1	2	yes	complemented
226	#357	C₂²×C₆₇	1	2	yes	complemented
227	C₂²⋊C₁₆	C₂²×C₆₇	1	2	yes	complemented
228	C₄×C₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	4	1	no	—
231	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
232	C₂×D₈	—	2	4	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	4	2	no	—
236	C₂×D₈	C₂³×C₆₇	1	2	yes	—
237	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
239	C₄⋊Q₈	—	2	1	no	—
240	#127	—	2	1	no	—
241	#126	—	4	2	no	—
242	#124	—	4	1	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	#121	—	2	2	no	—
245	#121	—	4	1	no	—
246	#120	—	4	2	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	4	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
251	#117	—	2	2	no	—
252	SD₃₂	—	2	2	no	—
253	SD₃₂	—	4	2	no	—
254	M₃₂	—	4	2	no	—
255	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
258	#107	—	2	1	no	—
259	#107	C₂³×C₆₇	1	2	yes	—
260	#107	C₂³×C₆₇	1	1	yes	characteristic
261	#107	C₂³×C₆₇	1	1	yes	characteristic
262	#106	—	2	2	no	—
263	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
264	#103	—	2	1	no	—
265	#103	—	2	2	no	—
266	#102	—	2	1	no	—
267	#102	—	2	2	no	—
268	C₂²⋊C₈	D₄×C₆₇	1	2	yes	—
269	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
270	C₂⁴	—	4	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	8	2	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	D₈×C₆₇	1	1	yes	characteristic
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
285	Q₁₆	—	2	1	no	—
286	Q₁₆	—	2	1	no	—
287	D₈	—	2	2	no	—
288	D₈	—	2	1	no	—
289	D₈	—	2	2	no	—
290	D₈	—	4	4	no	—
291	D₈	—	8	1	no	—
292	D₈	#41×C₆₇	1	2	yes	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
297	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	D₈×C₆₇	1	1	yes	characteristic
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	D₈×C₆₇	1	2	yes	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	1	no	—
312	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	4	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	16	2	no	—
321	C₂³	C₂×D₈×C₆₇	1	2	yes	—
322	Q₈	—	4	1	no	—
323	Q₈	—	4	1	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	2	no	—
333	D₄	—	16	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
343	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	—	2	1	no	—
347	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
348	C₈	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	8	1	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	16	8	no	—
359	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	1	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	1	no	—
366	C₄	#509×C₆₇	1	2	yes	—
367	C₄	#546×C₆₇	1	1	yes	characteristic
368	C₄	#577×C₆₇	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	8	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₆₇×#3294	1	1	yes	characteristic
373	C₂	C₂×#509×C₆₇	1	1	yes	characteristic
374	C₂	C₆₇×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
prime radical	D₄×D₈×C₆₇	C₂
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×#3342	C₂	semidirect
3. C₆₇×#2240	C₂	semidirect
4. C₆₇×#2234	C₂	semidirect
5. C₆₇×#2224	C₂	semidirect
6. C₆₇×#2220	C₂	semidirect
7. C₆₇×#2207	C₂	semidirect
8. C₆₇×#2187	C₂	semidirect
9. C₄×SD₃₂×C₆₇	C₂	semidirect
10. C₆₇×#2169	C₂	semidirect
11. C₆₇×#2140	C₂	semidirect
16. C₂×SD₃₂×C₆₇	C₂²	semidirect
17. C₂×M₃₂×C₆₇	C₂²	semidirect
18. #500×C₆₇	C₂²	semidirect
22. #467×C₆₇	C₂²	semidirect
26. C₄×Q₁₆×C₆₇	C₂²	semidirect
29. #427×C₆₇	C₂²	semidirect
30. #367×C₆₇	C₂²	semidirect
31. #366×C₆₇	C₂²	semidirect
32. C₄⋊C₁₆×C₆₇	C₂²	semidirect
33. #358×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
181. #33891	C₆₇	direct (N × H)
188. #3342	C₂×C₆₇	semidirect
190. #2240	C₂×C₆₇	semidirect
191. #2234	C₂×C₆₇	semidirect
192. #2224	C₂×C₆₇	semidirect
193. #2220	C₂×C₆₇	semidirect
194. #2207	C₂×C₆₇	semidirect
195. #2187	C₂×C₆₇	semidirect
196. C₄×SD₃₂	C₂×C₆₇	semidirect
197. #2169	C₂×C₆₇	semidirect
198. #2140	C₂×C₆₇	semidirect
199. C₆₇	#33891	direct (N × H)
204. C₂×SD₃₂	C₂²×C₆₇	semidirect
205. C₂×M₃₂	C₂²×C₆₇	semidirect
206. #500	C₂²×C₆₇	semidirect
210. #467	C₂²×C₆₇	semidirect
214. C₄×Q₁₆	C₂²×C₆₇	semidirect
217. #427	C₂²×C₆₇	semidirect
218. #367	C₂²×C₆₇	semidirect
219. #366	C₂²×C₆₇	semidirect
220. C₄⋊C₁₆	C₂²×C₆₇	semidirect
221. #358	C₂²×C₆₇	semidirect
224. #357	C₂²×C₆₇	semidirect
225. #357	C₂²×C₆₇	semidirect
226. #357	C₂²×C₆₇	semidirect
227. C₂²⋊C₁₆	C₂²×C₆₇	semidirect
228. 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×#3342	2
D₄×D₈×C₆₇	2
C₆₇×#2240	2
C₆₇×#2234	2
C₆₇×#2224	2
C₆₇×#2220	2
C₆₇×#2207	2
C₆₇×#2187	2
C₄×SD₃₂×C₆₇	2
C₆₇×#2169	2
C₆₇×#2140	2
#33891	67

Subgroups — C67×#33891 #30713142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33891 #30713142