Subgroups — C₆₇×#33702 #30712953

Order 17152.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2244	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2243	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2242	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2240	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2140	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#357×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
13	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
15	#544×C₆₇	—	2	1	no	—
16	#535×C₆₇	—	2	1	no	—
17	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	#501×C₆₇	—	2	2	no	—
20	#500×C₆₇	C₂²	1	2	yes	complemented
21	#499×C₆₇	C₂²	1	2	yes	complemented
22	#496×C₆₇	—	2	2	no	—
23	#495×C₆₇	C₂²	1	2	yes	—
24	#493×C₆₇	C₂²	1	2	yes	—
25	#428×C₆₇	—	2	1	no	—
26	#427×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
28	#405×C₆₇	C₂²	1	1	yes	characteristic
29	#358×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#358×C₆₇	C₂²	1	2	yes	complemented
31	#358×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#357×C₆₇	C₂²	1	2	yes	—
33	#357×C₆₇	C₂²	1	2	yes	—
34	#357×C₆₇	C₂²	1	2	yes	—
35	#357×C₆₇	C₂²	1	2	yes	—
36	#357×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#357×C₆₇	C₂²	1	2	yes	complemented
38	#357×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#346×C₆₇	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#41×C₆₇	—	2	1	no	—
42	C₂²×D₄×C₆₇	—	2	1	no	—
43	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
44	#135×C₆₇	—	2	2	no	—
45	#135×C₆₇	—	2	2	no	—
46	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
47	C₂×SD₁₆×C₆₇	—	2	2	no	—
48	C₂×SD₁₆×C₆₇	—	2	1	no	—
49	C₂×D₈×C₆₇	—	2	2	no	—
50	C₂×D₈×C₆₇	—	2	1	no	—
51	C₂×D₈×C₆₇	—	2	2	no	—
52	C₂×D₈×C₆₇	—	2	2	no	—
53	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₆₇	C₂³	1	2	yes	—
55	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₆₇	—	2	2	no	—
58	C₄⋊Q₈×C₆₇	—	4	1	no	—
59	#127×C₆₇	—	2	2	no	—
60	#125×C₆₇	—	2	2	no	—
61	#125×C₆₇	—	4	1	no	—
62	#124×C₆₇	—	2	2	no	—
63	C₂²⋊Q₈×C₆₇	—	4	2	no	—
64	#121×C₆₇	—	4	1	no	—
65	#121×C₆₇	—	4	1	no	—
66	#120×C₆₇	—	4	2	no	—
67	#117×C₆₇	—	2	1	no	—
68	#117×C₆₇	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
70	M₃₂×C₆₇	—	2	2	no	—
71	C₂×C₁₆×C₆₇	—	2	2	no	—
72	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
73	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
75	#107×C₆₇	—	2	2	no	—
76	#107×C₆₇	—	2	1	no	—
77	#107×C₆₇	C₂³	1	1	yes	characteristic
78	#107×C₆₇	C₂³	1	2	yes	—
79	#107×C₆₇	C₂³	1	1	yes	characteristic
80	#106×C₆₇	—	2	2	no	—
81	#106×C₆₇	—	2	1	no	—
82	#97×C₆₇	D₄	1	2	yes	—
83	C₄×C₈×C₆₇	C₂³	1	2	yes	—
84	C₂⁴×C₆₇	—	4	1	no	—
85	#41×C₆₇	—	4	2	no	—
86	#41×C₆₇	—	4	2	no	—
87	C₂×Q₈×C₆₇	—	2	1	no	—
88	C₂×Q₈×C₆₇	—	4	2	no	—
89	C₂×D₄×C₆₇	—	2	2	no	—
90	C₂×D₄×C₆₇	—	2	1	no	—
91	C₂×D₄×C₆₇	—	4	1	no	—
92	C₂×D₄×C₆₇	—	4	2	no	—
93	C₂×D₄×C₆₇	—	4	1	no	—
94	C₂×D₄×C₆₇	—	4	2	no	—
95	C₂×D₄×C₆₇	—	4	2	no	—
96	C₂×D₄×C₆₇	—	4	2	no	—
97	C₂²×C₄×C₆₇	—	4	1	no	—
98	C₂²×C₄×C₆₇	—	4	1	no	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	Q₁₆×C₆₇	—	2	1	no	—
101	Q₁₆×C₆₇	—	2	1	no	—
102	SD₁₆×C₆₇	—	4	2	no	—
103	SD₁₆×C₆₇	—	4	4	no	—
104	D₈×C₆₇	—	2	2	no	—
105	D₈×C₆₇	—	2	2	no	—
106	D₈×C₆₇	—	2	1	no	—
107	D₈×C₆₇	—	2	1	no	—
108	D₈×C₆₇	—	4	2	no	—
109	D₈×C₆₇	—	4	4	no	—
110	M₁₆×C₆₇	SD₁₆	1	4	yes	—
111	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₆₇	#41	1	2	yes	—
114	C₂×C₈×C₆₇	#41	1	2	yes	—
115	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₆₇	—	2	1	no	—
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	—	2	1	no	—
119	C₄⋊C₄×C₆₇	—	4	1	no	—
120	C₄⋊C₄×C₆₇	—	4	2	no	—
121	C₄⋊C₄×C₆₇	—	4	2	no	—
122	C₄⋊C₄×C₆₇	—	4	2	no	—
123	C₄⋊C₄×C₆₇	D₈	1	1	yes	characteristic
124	C₄⋊C₄×C₆₇	D₈	1	1	yes	characteristic
125	C₂²⋊C₄×C₆₇	—	4	1	no	—
126	C₂²⋊C₄×C₆₇	—	4	2	no	—
127	C₂²⋊C₄×C₆₇	—	4	2	no	—
128	C₂²⋊C₄×C₆₇	D₈	1	2	yes	—
129	C₄²×C₆₇	—	4	1	no	—
130	C₄²×C₆₇	C₂×D₄	1	2	yes	—
131	C₁₆×C₆₇	—	2	1	no	—
132	C₁₆×C₆₇	—	2	1	no	—
133	C₁₆×C₆₇	—	2	2	no	—
134	C₂³×C₆₇	—	4	2	no	—
135	C₂³×C₆₇	—	4	1	no	—
136	C₂³×C₆₇	—	8	2	no	—
137	C₂³×C₆₇	—	16	1	no	—
138	C₂³×C₆₇	—	16	1	no	—
139	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
140	Q₈×C₆₇	—	4	1	no	—
141	Q₈×C₆₇	—	4	1	no	—
142	Q₈×C₆₇	—	16	2	no	—
143	D₄×C₆₇	—	4	2	no	—
144	D₄×C₆₇	—	4	1	no	—
145	D₄×C₆₇	—	4	1	no	—
146	D₄×C₆₇	—	4	2	no	—
147	D₄×C₆₇	—	8	2	no	—
148	D₄×C₆₇	—	8	2	no	—
149	D₄×C₆₇	—	16	2	no	—
150	D₄×C₆₇	—	16	2	no	—
151	C₂×C₄×C₆₇	—	4	1	no	—
152	C₂×C₄×C₆₇	—	4	1	no	—
153	C₂×C₄×C₆₇	—	4	1	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	8	2	no	—
156	C₂×C₄×C₆₇	—	16	1	no	—
157	C₂×C₄×C₆₇	#124	1	2	yes	—
158	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
159	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₆₇	#124	1	2	yes	—
164	C₈×C₆₇	C₂×SD₁₆	1	4	yes	—
165	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
166	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
167	C₂²×C₆₇	—	2	1	no	—
168	C₂²×C₆₇	—	2	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	1	no	—
174	C₂²×C₆₇	—	8	2	no	—
175	C₂²×C₆₇	—	16	4	no	—
176	C₂²×C₆₇	#486	1	2	yes	—
177	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
178	C₄×C₆₇	—	2	2	no	—
179	C₄×C₆₇	—	2	2	no	—
180	C₄×C₆₇	—	8	1	no	—
181	C₄×C₆₇	—	8	2	no	—
182	C₄×C₆₇	—	8	1	no	—
183	C₄×C₆₇	—	8	1	no	—
184	C₄×C₆₇	#486	1	2	yes	—
185	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
186	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
187	#33702	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₆₇	—	2	2	no	—
189	C₂×C₆₇	—	16	1	no	—
190	C₂×C₆₇	—	16	2	no	—
191	C₂×C₆₇	C₂×#486	1	1	yes	characteristic
192	C₂×C₆₇	#3415	1	1	yes	characteristic
193	C₂×C₆₇	#3416	1	1	yes	characteristic
194	#3164	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#3155	C₂×C₆₇	1	1	yes	characteristic
196	#2244	C₂×C₆₇	1	2	yes	complemented
197	#2243	C₂×C₆₇	1	2	yes	complemented
198	#2242	C₂×C₆₇	1	2	yes	complemented
199	#2240	C₂×C₆₇	1	2	yes	complemented
200	#2140	C₂×C₆₇	1	1	yes	characteristic, complemented
201	#2139	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#2138	C₂×C₆₇	1	1	yes	characteristic, complemented
203	C₂×#357	C₂×C₆₇	1	1	yes	characteristic, complemented
204	#2108	C₂×C₆₇	1	1	yes	characteristic, complemented
205	C₆₇	#33702	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×AGL(1,ℤ/8)	—	2	1	no	—
207	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
208	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
209	#544	—	2	1	no	—
210	#535	—	2	1	no	—
211	C₂×M₃₂	C₂²×C₆₇	1	1	yes	characteristic
212	C₂²×C₁₆	C₂²×C₆₇	1	1	yes	characteristic
213	#501	—	2	2	no	—
214	#500	C₂²×C₆₇	1	2	yes	complemented
215	#499	C₂²×C₆₇	1	2	yes	complemented
216	#496	—	2	2	no	—
217	#495	C₂²×C₆₇	1	2	yes	—
218	#493	C₂²×C₆₇	1	2	yes	—
219	#428	—	2	1	no	—
220	#427	C₂²×C₆₇	1	1	yes	characteristic
221	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
222	#405	C₂²×C₆₇	1	1	yes	characteristic
223	#358	C₂²×C₆₇	1	1	yes	characteristic, complemented
224	#358	C₂²×C₆₇	1	1	yes	characteristic, complemented
225	#358	C₂²×C₆₇	1	2	yes	complemented
226	#357	C₂²×C₆₇	1	2	yes	—
227	#357	C₂²×C₆₇	1	2	yes	—
228	#357	C₂²×C₆₇	1	2	yes	—
229	#357	C₂²×C₆₇	1	2	yes	—
230	#357	C₂²×C₆₇	1	1	yes	characteristic, complemented
231	#357	C₂²×C₆₇	1	1	yes	characteristic, complemented
232	#357	C₂²×C₆₇	1	2	yes	complemented
233	#346	C₂²×C₆₇	1	2	yes	complemented
234	C₄×C₁₆	C₂²×C₆₇	1	2	yes	complemented
235	C₂×#41	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	AGL(1,ℤ/8)	—	4	4	no	—
238	#135	—	2	2	no	—
239	#135	—	2	2	no	—
240	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂×D₈	—	2	2	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×D₈	C₂³×C₆₇	1	2	yes	—
248	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
249	C₂×M₁₆	D₄×C₆₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	4	1	no	—
253	#127	—	2	2	no	—
254	#125	—	2	2	no	—
255	#125	—	4	1	no	—
256	#124	—	2	2	no	—
257	C₂²⋊Q₈	—	4	2	no	—
258	#121	—	4	1	no	—
259	#121	—	4	1	no	—
260	#120	—	4	2	no	—
261	#117	—	2	1	no	—
262	#117	D₄×C₆₇	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	1	no	—
264	M₃₂	—	2	2	no	—
265	C₂×C₁₆	—	2	2	no	—
266	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
267	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
268	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
269	#107	—	2	1	no	—
270	#107	—	2	2	no	—
271	#107	C₂³×C₆₇	1	2	yes	—
272	#107	C₂³×C₆₇	1	1	yes	characteristic
273	#107	C₂³×C₆₇	1	1	yes	characteristic
274	#106	—	2	1	no	—
275	#106	—	2	2	no	—
276	#97	D₄×C₆₇	1	2	yes	—
277	C₄×C₈	C₂³×C₆₇	1	2	yes	—
278	C₂⁴	—	4	1	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
294	Q₁₆	—	2	1	no	—
295	Q₁₆	—	2	1	no	—
296	SD₁₆	—	4	2	no	—
297	SD₁₆	—	4	4	no	—
298	D₈	—	2	2	no	—
299	D₈	—	2	2	no	—
300	D₈	—	2	1	no	—
301	D₈	—	2	1	no	—
302	D₈	—	4	2	no	—
303	D₈	—	4	4	no	—
304	M₁₆	SD₁₆×C₆₇	1	4	yes	—
305	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
307	C₂×C₈	#41×C₆₇	1	2	yes	—
308	C₂×C₈	#41×C₆₇	1	2	yes	—
309	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	D₈×C₆₇	1	1	yes	characteristic
318	C₄⋊C₄	D₈×C₆₇	1	1	yes	characteristic
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	D₈×C₆₇	1	2	yes	—
323	C₄²	—	4	1	no	—
324	C₄²	C₂×D₄×C₆₇	1	2	yes	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	2	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	8	2	no	—
331	C₂³	—	16	1	no	—
332	C₂³	—	16	1	no	—
333	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
334	Q₈	—	4	1	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	16	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	1	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	D₄	—	16	2	no	—
344	D₄	—	16	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	16	1	no	—
351	C₂×C₄	#124×C₆₇	1	2	yes	—
352	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
353	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
354	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
357	C₈	#124×C₆₇	1	2	yes	—
358	C₈	C₂×SD₁₆×C₆₇	1	4	yes	—
359	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
360	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	#486×C₆₇	1	2	yes	—
371	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	#486×C₆₇	1	2	yes	—
379	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
380	C₄	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	16	2	no	—
383	C₂	—	16	1	no	—
384	C₂	C₂×#486×C₆₇	1	1	yes	characteristic
385	C₂	C₆₇×#3415	1	1	yes	characteristic
386	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	C₆₇×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #117×C₆₇ ◁ #405×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3164	C₂	semidirect
3. C₆₇×#2244	C₂	semidirect
4. C₆₇×#2243	C₂	semidirect
5. C₆₇×#2242	C₂	semidirect
6. C₆₇×#2240	C₂	semidirect
7. C₆₇×#2140	C₂	semidirect
8. C₆₇×#2139	C₂	semidirect
9. C₆₇×#2138	C₂	semidirect
10. C₂×#357×C₆₇	C₂	semidirect
11. C₆₇×#2108	C₂	semidirect
20. #500×C₆₇	C₂²	semidirect
21. #499×C₆₇	C₂²	semidirect
29. #358×C₆₇	C₂²	semidirect
30. #358×C₆₇	C₂²	semidirect
31. #358×C₆₇	C₂²	semidirect
36. #357×C₆₇	C₂²	semidirect
37. #357×C₆₇	C₂²	semidirect
38. #357×C₆₇	C₂²	semidirect
39. #346×C₆₇	C₂²	semidirect
40. C₄×C₁₆×C₆₇	C₂²	semidirect
187. #33702	C₆₇	direct (N × H)
194. #3164	C₂×C₆₇	semidirect
196. #2244	C₂×C₆₇	semidirect
197. #2243	C₂×C₆₇	semidirect
198. #2242	C₂×C₆₇	semidirect
199. #2240	C₂×C₆₇	semidirect
200. #2140	C₂×C₆₇	semidirect
201. #2139	C₂×C₆₇	semidirect
202. #2138	C₂×C₆₇	semidirect
203. C₂×#357	C₂×C₆₇	semidirect
204. #2108	C₂×C₆₇	semidirect
205. C₆₇	#33702	direct (N × H)
214. #500	C₂²×C₆₇	semidirect
215. #499	C₂²×C₆₇	semidirect
223. #358	C₂²×C₆₇	semidirect
224. #358	C₂²×C₆₇	semidirect
225. #358	C₂²×C₆₇	semidirect
230. #357	C₂²×C₆₇	semidirect
231. #357	C₂²×C₆₇	semidirect
232. #357	C₂²×C₆₇	semidirect
233. #346	C₂²×C₆₇	semidirect
234. 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×#3164	2
C₆₇×#3155	2
C₆₇×#2244	2
C₆₇×#2243	2
C₆₇×#2242	2
C₆₇×#2240	2
C₆₇×#2140	2
C₆₇×#2139	2
C₆₇×#2138	2
C₂×#357×C₆₇	2
C₆₇×#2108	2
#33702	67

Subgroups — C67×#33702 #30712953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33702 #30712953