Subgroups — C₆₇×#33677 #30712928

Order 17152.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2233	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2229	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2211	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2185	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2176	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2175	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	#529×C₆₇	—	2	1	no	—
14	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
15	C₂×Q₃₂×C₆₇	C₂²	1	2	yes	—
16	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	—
17	#499×C₆₇	C₂²	1	1	yes	characteristic
18	#495×C₆₇	C₂²	1	1	yes	characteristic
19	#488×C₆₇	—	2	1	no	—
20	#467×C₆₇	C₂²	1	1	yes	characteristic
21	#466×C₆₇	C₂²	1	1	yes	characteristic
22	#465×C₆₇	—	2	1	no	—
23	C₄×Q₁₆×C₆₇	—	2	1	no	—
24	C₄×Q₁₆×C₆₇	—	2	1	no	—
25	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
26	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
27	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
28	C₄×SD₁₆×C₆₇	—	2	1	no	—
29	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₇	—	2	1	no	—
32	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	#367×C₆₇	C₂²	1	2	yes	—
34	#366×C₆₇	C₂²	1	2	yes	—
35	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
36	#358×C₆₇	C₂²	1	2	yes	—
37	#358×C₆₇	C₂²	1	2	yes	—
38	#358×C₆₇	C₂²	1	2	yes	—
39	#357×C₆₇	C₂²	1	2	yes	—
40	C₂²⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	#346×C₆₇	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₇	—	2	1	no	—
44	C₂×Q₁₆×C₆₇	—	2	4	no	—
45	C₂×Q₁₆×C₆₇	—	2	1	no	—
46	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
48	C₂×SD₁₆×C₆₇	—	2	1	no	—
49	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
52	#126×C₆₇	—	4	1	no	—
53	#125×C₆₇	—	2	1	no	—
54	#124×C₆₇	—	2	1	no	—
55	#123×C₆₇	—	4	1	no	—
56	C₂²⋊Q₈×C₆₇	—	2	1	no	—
57	#121×C₆₇	—	2	1	no	—
58	C₄×Q₈×C₆₇	—	2	2	no	—
59	C₄×Q₈×C₆₇	—	2	2	no	—
60	C₄×Q₈×C₆₇	—	2	1	no	—
61	C₄×Q₈×C₆₇	—	4	1	no	—
62	C₄×Q₈×C₆₇	—	4	1	no	—
63	C₄×D₄×C₆₇	—	2	1	no	—
64	C₄×D₄×C₆₇	—	4	1	no	—
65	#117×C₆₇	—	4	1	no	—
66	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₇	—	4	1	no	—
68	C₂×C₄²×C₆₇	—	4	1	no	—
69	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
70	Q₃₂×C₆₇	—	2	4	no	—
71	SD₃₂×C₆₇	—	2	4	no	—
72	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
73	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
74	#107×C₆₇	—	2	1	no	—
75	#107×C₆₇	C₂³	1	1	yes	characteristic
76	#107×C₆₇	C₂³	1	1	yes	characteristic
77	#107×C₆₇	C₂³	1	2	yes	—
78	#106×C₆₇	—	2	1	no	—
79	#103×C₆₇	—	2	1	no	—
80	#103×C₆₇	—	2	1	no	—
81	#103×C₆₇	—	2	2	no	—
82	#103×C₆₇	—	2	2	no	—
83	#102×C₆₇	—	2	1	no	—
84	#102×C₆₇	—	2	1	no	—
85	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
86	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
87	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₆₇	—	2	4	no	—
90	C₂×Q₈×C₆₇	—	2	2	no	—
91	C₂×Q₈×C₆₇	—	2	1	no	—
92	C₂×Q₈×C₆₇	—	4	2	no	—
93	C₂×Q₈×C₆₇	—	4	1	no	—
94	C₂×D₄×C₆₇	—	2	1	no	—
95	C₂×D₄×C₆₇	—	4	1	no	—
96	C₂²×C₄×C₆₇	—	4	1	no	—
97	C₂²×C₄×C₆₇	—	4	1	no	—
98	C₂²×C₄×C₆₇	—	4	1	no	—
99	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
102	Q₁₆×C₆₇	—	2	4	no	—
103	Q₁₆×C₆₇	—	2	2	no	—
104	Q₁₆×C₆₇	—	2	2	no	—
105	Q₁₆×C₆₇	#41	1	4	yes	—
106	SD₁₆×C₆₇	—	4	2	no	—
107	D₈×C₆₇	—	2	2	no	—
108	C₂×C₈×C₆₇	—	2	2	no	—
109	C₂×C₈×C₆₇	—	4	1	no	—
110	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₆₇	—	2	1	no	—
115	C₄⋊C₄×C₆₇	—	2	1	no	—
116	C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₄⋊C₄×C₆₇	—	4	1	no	—
118	C₄⋊C₄×C₆₇	—	4	2	no	—
119	C₄⋊C₄×C₆₇	—	4	2	no	—
120	C₄⋊C₄×C₆₇	—	4	1	no	—
121	C₄⋊C₄×C₆₇	—	4	1	no	—
122	C₄⋊C₄×C₆₇	—	4	1	no	—
123	C₄⋊C₄×C₆₇	—	4	1	no	—
124	C₂²⋊C₄×C₆₇	—	4	1	no	—
125	C₂²⋊C₄×C₆₇	—	4	1	no	—
126	C₂²⋊C₄×C₆₇	—	4	1	no	—
127	C₂²⋊C₄×C₆₇	—	4	1	no	—
128	C₂²⋊C₄×C₆₇	—	4	1	no	—
129	C₄²×C₆₇	—	4	2	no	—
130	C₄²×C₆₇	—	4	2	no	—
131	C₄²×C₆₇	—	4	1	no	—
132	C₄²×C₆₇	D₈	1	1	yes	characteristic
133	C₄²×C₆₇	D₈	1	1	yes	characteristic
134	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₆₇	—	2	2	no	—
137	C₁₆×C₆₇	—	2	2	no	—
138	C₂³×C₆₇	—	4	1	no	—
139	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
140	Q₈×C₆₇	—	2	4	no	—
141	Q₈×C₆₇	—	4	4	no	—
142	Q₈×C₆₇	—	4	2	no	—
143	Q₈×C₆₇	—	4	1	no	—
144	Q₈×C₆₇	—	4	1	no	—
145	D₄×C₆₇	—	4	1	no	—
146	D₄×C₆₇	—	4	1	no	—
147	D₄×C₆₇	—	8	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	1	no	—
150	C₂×C₄×C₆₇	—	2	1	no	—
151	C₂×C₄×C₆₇	—	4	1	no	—
152	C₂×C₄×C₆₇	—	4	4	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	4	1	no	—
156	C₂×C₄×C₆₇	—	4	1	no	—
157	C₂×C₄×C₆₇	—	4	1	no	—
158	C₂×C₄×C₆₇	—	8	2	no	—
159	C₂×C₄×C₆₇	—	8	2	no	—
160	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	1	no	—
168	C₈×C₆₇	—	2	1	no	—
169	C₈×C₆₇	C₂×#41	1	2	yes	—
170	C₂²×C₆₇	—	2	1	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	8	1	no	—
173	C₂²×C₆₇	—	8	1	no	—
174	C₂²×C₆₇	—	8	1	no	—
175	C₂²×C₆₇	#510	1	2	yes	—
176	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	4	4	no	—
183	C₄×C₆₇	—	8	1	no	—
184	C₄×C₆₇	—	8	1	no	—
185	C₄×C₆₇	—	8	2	no	—
186	C₄×C₆₇	—	8	1	no	—
187	C₄×C₆₇	#525	1	1	yes	characteristic
188	C₄×C₆₇	#575	1	1	yes	characteristic
189	#33677	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₆₇	—	2	2	no	—
191	C₂×C₆₇	—	16	1	no	—
192	C₂×C₆₇	#3100	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#510	1	1	yes	characteristic
194	C₂×C₆₇	#3414	1	1	yes	characteristic
195	#3168	C₂×C₆₇	1	1	yes	characteristic
196	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
197	#2236	C₂×C₆₇	1	1	yes	characteristic, complemented
198	#2233	C₂×C₆₇	1	1	yes	characteristic
199	#2229	C₂×C₆₇	1	2	yes	complemented
200	#2211	C₂×C₆₇	1	2	yes	complemented
201	#2188	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#2185	C₂×C₆₇	1	1	yes	characteristic
203	#2176	C₂×C₆₇	1	2	yes	complemented
204	#2175	C₂×C₆₇	1	2	yes	complemented
205	#2163	C₂×C₆₇	1	1	yes	characteristic, complemented
206	C₆₇	#33677	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
208	#529	—	2	1	no	—
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×Q₃₂	C₂²×C₆₇	1	2	yes	—
211	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	—
212	#499	C₂²×C₆₇	1	1	yes	characteristic
213	#495	C₂²×C₆₇	1	1	yes	characteristic
214	#488	—	2	1	no	—
215	#467	C₂²×C₆₇	1	1	yes	characteristic
216	#466	C₂²×C₆₇	1	1	yes	characteristic
217	#465	—	2	1	no	—
218	C₄×Q₁₆	—	2	1	no	—
219	C₄×Q₁₆	—	2	1	no	—
220	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
221	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
222	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
223	C₄×SD₁₆	—	2	1	no	—
224	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
225	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
226	C₂×#103	—	2	1	no	—
227	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
228	#367	C₂²×C₆₇	1	2	yes	—
229	#366	C₂²×C₆₇	1	2	yes	—
230	C₄⋊C₁₆	C₂²×C₆₇	1	2	yes	—
231	#358	C₂²×C₆₇	1	2	yes	—
232	#358	C₂²×C₆₇	1	2	yes	—
233	#358	C₂²×C₆₇	1	2	yes	—
234	#357	C₂²×C₆₇	1	2	yes	—
235	C₂²⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic
236	C₂²⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic
237	#346	C₂²×C₆₇	1	2	yes	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂×Q₁₆	—	2	4	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
242	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
245	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
247	#126	—	4	1	no	—
248	#125	—	2	1	no	—
249	#124	—	2	1	no	—
250	#123	—	4	1	no	—
251	C₂²⋊Q₈	—	2	1	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×Q₈	—	4	1	no	—
257	C₄×Q₈	—	4	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	4	1	no	—
260	#117	—	4	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	4	1	no	—
263	C₂×C₄²	—	4	1	no	—
264	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
265	Q₃₂	—	2	4	no	—
266	SD₃₂	—	2	4	no	—
267	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
268	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
269	#107	—	2	1	no	—
270	#107	C₂³×C₆₇	1	2	yes	—
271	#107	C₂³×C₆₇	1	1	yes	characteristic
272	#107	C₂³×C₆₇	1	1	yes	characteristic
273	#106	—	2	1	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	2	1	no	—
277	#103	—	2	1	no	—
278	#102	—	2	1	no	—
279	#102	—	2	1	no	—
280	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
281	C₄×C₈	D₄×C₆₇	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	D₈×C₆₇	1	1	yes	characteristic
295	C₂²×C₄	D₈×C₆₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
297	Q₁₆	—	2	4	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	#41×C₆₇	1	4	yes	—
301	SD₁₆	—	4	2	no	—
302	D₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
308	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	1	no	—
327	C₄²	D₈×C₆₇	1	1	yes	characteristic
328	C₄²	D₈×C₆₇	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
331	C₁₆	—	2	2	no	—
332	C₁₆	—	2	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	4	4	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
357	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	C₂×#41×C₆₇	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	#510×C₆₇	1	2	yes	—
371	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	4	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	#525×C₆₇	1	1	yes	characteristic
383	C₄	#575×C₆₇	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	16	1	no	—
386	C₂	C₆₇×#3100	1	1	yes	characteristic
387	C₂	C₂×#510×C₆₇	1	1	yes	characteristic
388	C₂	C₆₇×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
prime radical	#466×C₆₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ C₂×C₄×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₆₇	C₂	semidirect
3. C₆₇×#2236	C₂	semidirect
5. C₆₇×#2229	C₂	semidirect
6. C₆₇×#2211	C₂	semidirect
7. C₆₇×#2188	C₂	semidirect
9. C₆₇×#2176	C₂	semidirect
10. C₆₇×#2175	C₂	semidirect
11. C₆₇×#2163	C₂	semidirect
189. #33677	C₆₇	direct (N × H)
196. C₂×C₄×Q₁₆	C₂×C₆₇	semidirect
197. #2236	C₂×C₆₇	semidirect
199. #2229	C₂×C₆₇	semidirect
200. #2211	C₂×C₆₇	semidirect
201. #2188	C₂×C₆₇	semidirect
203. #2176	C₂×C₆₇	semidirect
204. #2175	C₂×C₆₇	semidirect
205. #2163	C₂×C₆₇	semidirect
206. C₆₇	#33677	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3168	2
C₂×C₄×Q₁₆×C₆₇	2
C₆₇×#2236	2
C₆₇×#2233	2
C₆₇×#2229	2
C₆₇×#2211	2
C₆₇×#2188	2
C₆₇×#2185	2
C₆₇×#2176	2
C₆₇×#2175	2
C₆₇×#2163	2
#33677	67

Subgroups — C67×#33677 #30712928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33677 #30712928