Subgroups — C₆₇×#61011 #30740262

Order 17152.

1896 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3508	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3259	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3228	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3205	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3199	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3184	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3169	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3122	C₂	1	8	yes	maximal, complemented
9	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
10	#559×C₆₇	—	2	4	no	—
11	#550×C₆₇	—	2	4	no	—
12	#546×C₆₇	—	2	4	no	—
13	#546×C₆₇	—	2	4	no	—
14	#540×C₆₇	C₂²	1	4	yes	—
15	#540×C₆₇	C₂²	1	4	yes	complemented
16	#535×C₆₇	C₂²	1	4	yes	—
17	#533×C₆₇	C₂²	1	2	yes	complemented
18	#532×C₆₇	C₂²	1	4	yes	—
19	#532×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
21	#518×C₆₇	C₂²	1	4	yes	complemented
22	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
23	#500×C₆₇	C₂²	1	2	yes	complemented
24	#498×C₆₇	C₂²	1	2	yes	complemented
25	#493×C₆₇	C₂²	1	2	yes	—
26	#493×C₆₇	C₂²	1	2	yes	—
27	#486×C₆₇	C₂²	1	4	yes	complemented
28	#486×C₆₇	C₂²	1	4	yes	complemented
29	#482×C₆₇	C₂²	1	16	yes	complemented
30	#478×C₆₇	C₂²	1	16	yes	complemented
31	#469×C₆₇	C₂²	1	8	yes	complemented
32	#466×C₆₇	C₂²	1	8	yes	complemented
33	#459×C₆₇	C₂²	1	16	yes	complemented
34	#447×C₆₇	C₂²	1	16	yes	complemented
35	#442×C₆₇	C₂²	1	8	yes	complemented
36	C₄×D₈×C₆₇	C₂²	1	8	yes	complemented
37	#433×C₆₇	C₂²	1	4	yes	complemented
38	#431×C₆₇	C₂²	1	4	yes	complemented
39	#424×C₆₇	C₂²	1	2	yes	complemented
40	#408×C₆₇	C₂²	1	2	yes	—
41	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₆₇	—	2	4	no	—
44	C₂×#41×C₆₇	—	2	4	no	—
45	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₇	—	2	4	no	—
47	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
48	C₂×D₈×C₆₇	C₂³	1	8	yes	—
49	C₂×D₈×C₆₇	C₂³	1	8	yes	—
50	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
53	#127×C₆₇	—	2	4	no	—
54	#127×C₆₇	—	2	4	no	—
55	#127×C₆₇	C₂³	1	4	yes	—
56	#127×C₆₇	C₂³	1	4	yes	—
57	#125×C₆₇	C₂³	1	4	yes	—
58	#124×C₆₇	—	2	4	no	—
59	#124×C₆₇	—	2	4	no	—
60	#124×C₆₇	—	2	4	no	—
61	#123×C₆₇	—	2	8	no	—
62	#123×C₆₇	—	2	8	no	—
63	C₂²⋊Q₈×C₆₇	—	2	4	no	—
64	#121×C₆₇	—	2	4	no	—
65	#121×C₆₇	—	2	4	no	—
66	#121×C₆₇	—	2	8	no	—
67	#121×C₆₇	—	2	8	no	—
68	#121×C₆₇	C₂³	1	8	yes	—
69	#121×C₆₇	C₂³	1	8	yes	—
70	#120×C₆₇	—	2	4	no	—
71	#120×C₆₇	—	2	4	no	—
72	C₄×Q₈×C₆₇	—	2	4	no	—
73	C₄×Q₈×C₆₇	D₄	1	2	yes	—
74	C₄×D₄×C₆₇	—	2	8	no	—
75	C₄×D₄×C₆₇	—	2	4	no	—
76	C₄×D₄×C₆₇	—	2	4	no	—
77	C₄×D₄×C₆₇	D₄	1	2	yes	—
78	C₄×D₄×C₆₇	D₄	1	4	yes	—
79	C₄×D₄×C₆₇	C₂³	1	8	yes	—
80	C₄×D₄×C₆₇	C₂³	1	8	yes	—
81	#117×C₆₇	C₂³	1	4	yes	—
82	#117×C₆₇	C₂³	1	2	yes	—
83	#117×C₆₇	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
85	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
87	#107×C₆₇	C₂³	1	8	yes	—
88	#106×C₆₇	C₂³	1	8	yes	—
89	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
90	#102×C₆₇	C₂³	1	16	yes	—
91	#102×C₆₇	C₂³	1	16	yes	—
92	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
93	#97×C₆₇	C₂³	1	2	yes	—
94	C₄×C₈×C₆₇	C₂³	1	2	yes	—
95	C₄×C₈×C₆₇	C₂³	1	2	yes	—
96	C₄×C₈×C₆₇	C₂³	1	2	yes	—
97	C₂⁴×C₆₇	—	2	4	no	—
98	#41×C₆₇	—	4	2	no	—
99	#41×C₆₇	—	8	8	no	—
100	#41×C₆₇	—	8	8	no	—
101	C₂×Q₈×C₆₇	—	2	4	no	—
102	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₆₇	—	2	8	no	—
104	C₂×D₄×C₆₇	—	2	8	no	—
105	C₂×D₄×C₆₇	—	2	4	no	—
106	C₂×D₄×C₆₇	—	2	4	no	—
107	C₂×D₄×C₆₇	—	2	4	no	—
108	C₂×D₄×C₆₇	—	2	8	no	—
109	C₂×D₄×C₆₇	—	4	8	no	—
110	C₂×D₄×C₆₇	—	8	8	no	—
111	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₆₇	—	2	8	no	—
115	C₂²×C₄×C₆₇	—	2	8	no	—
116	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
120	D₈×C₆₇	—	4	8	no	—
121	D₈×C₆₇	—	4	8	no	—
122	M₁₆×C₆₇	—	4	2	no	—
123	C₂×C₈×C₆₇	—	4	2	no	—
124	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
125	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
126	C₄⋊C₄×C₆₇	—	2	4	no	—
127	C₄⋊C₄×C₆₇	—	2	8	no	—
128	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
131	C₂²⋊C₄×C₆₇	—	2	4	no	—
132	C₂²⋊C₄×C₆₇	—	2	8	no	—
133	C₂²⋊C₄×C₆₇	—	2	8	no	—
134	C₂²⋊C₄×C₆₇	—	2	8	no	—
135	C₂²⋊C₄×C₆₇	—	2	8	no	—
136	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
138	C₄²×C₆₇	—	2	4	no	—
139	C₄²×C₆₇	C₂×D₄	1	2	yes	—
140	C₄²×C₆₇	C₂×D₄	1	4	yes	—
141	C₄²×C₆₇	C₂⁴	1	2	yes	—
142	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
143	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
144	C₂³×C₆₇	—	2	8	no	—
145	C₂³×C₆₇	—	4	8	no	—
146	C₂³×C₆₇	—	8	8	no	—
147	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
148	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₆₇	—	4	1	no	—
150	Q₈×C₆₇	—	4	8	no	—
151	D₄×C₆₇	—	2	16	no	—
152	D₄×C₆₇	—	4	2	no	—
153	D₄×C₆₇	—	4	1	no	—
154	D₄×C₆₇	—	4	8	no	—
155	D₄×C₆₇	—	4	8	no	—
156	D₄×C₆₇	—	4	8	no	—
157	D₄×C₆₇	—	8	8	no	—
158	D₄×C₆₇	—	8	8	no	—
159	D₄×C₆₇	—	8	8	no	—
160	C₂×C₄×C₆₇	—	2	8	no	—
161	C₂×C₄×C₆₇	—	2	4	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	4	no	—
164	C₂×C₄×C₆₇	—	2	8	no	—
165	C₂×C₄×C₆₇	—	8	8	no	—
166	C₂×C₄×C₆₇	—	8	8	no	—
167	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
173	C₈×C₆₇	—	2	4	no	—
174	C₈×C₆₇	—	2	4	no	—
175	C₂²×C₆₇	—	2	2	no	—
176	C₂²×C₆₇	—	2	1	no	—
177	C₂²×C₆₇	—	2	2	no	—
178	C₂²×C₆₇	—	2	4	no	—
179	C₂²×C₆₇	—	4	8	no	—
180	C₂²×C₆₇	—	4	8	no	—
181	C₂²×C₆₇	—	4	8	no	—
182	C₂²×C₆₇	—	16	8	no	—
183	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
184	C₄×C₆₇	—	2	2	no	—
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	2	no	—
187	C₄×C₆₇	—	2	4	no	—
188	C₄×C₆₇	—	4	8	no	—
189	C₄×C₆₇	#576	1	4	yes	—
190	C₄×C₆₇	#585	1	2	yes	—
191	#61011	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₆₇	—	4	1	no	—
193	C₂×C₆₇	—	4	2	no	—
194	C₂×C₆₇	—	8	8	no	—
195	C₂×C₆₇	#3449	1	1	yes	characteristic
196	C₂×C₆₇	C₂×#576	1	2	yes	—
197	#3508	C₂×C₆₇	1	2	yes	complemented
198	#3259	C₂×C₆₇	1	4	yes	complemented
199	#3228	C₂×C₆₇	1	4	yes	complemented
200	#3205	C₂×C₆₇	1	4	yes	complemented
201	#3199	C₂×C₆₇	1	4	yes	complemented
202	#3184	C₂×C₆₇	1	2	yes	complemented
203	#3169	C₂×C₆₇	1	2	yes	complemented
204	#3122	C₂×C₆₇	1	8	yes	complemented
205	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
206	C₆₇	#61011	1	1	yes	characteristic, direct product factor, Sylow
207	#559	—	2	4	no	—
208	#550	—	2	4	no	—
209	#546	—	2	4	no	—
210	#546	—	2	4	no	—
211	#540	C₂²×C₆₇	1	4	yes	—
212	#540	C₂²×C₆₇	1	4	yes	complemented
213	#535	C₂²×C₆₇	1	4	yes	—
214	#533	C₂²×C₆₇	1	2	yes	complemented
215	#532	C₂²×C₆₇	1	4	yes	—
216	#532	C₂²×C₆₇	1	4	yes	complemented
217	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
218	#518	C₂²×C₆₇	1	4	yes	complemented
219	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
220	#500	C₂²×C₆₇	1	2	yes	complemented
221	#498	C₂²×C₆₇	1	2	yes	complemented
222	#493	C₂²×C₆₇	1	2	yes	—
223	#493	C₂²×C₆₇	1	2	yes	—
224	#486	C₂²×C₆₇	1	4	yes	complemented
225	#486	C₂²×C₆₇	1	4	yes	complemented
226	#482	C₂²×C₆₇	1	16	yes	complemented
227	#478	C₂²×C₆₇	1	16	yes	complemented
228	#469	C₂²×C₆₇	1	8	yes	complemented
229	#466	C₂²×C₆₇	1	8	yes	complemented
230	#459	C₂²×C₆₇	1	16	yes	complemented
231	#447	C₂²×C₆₇	1	16	yes	complemented
232	#442	C₂²×C₆₇	1	8	yes	complemented
233	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
234	#433	C₂²×C₆₇	1	4	yes	complemented
235	#431	C₂²×C₆₇	1	4	yes	complemented
236	#424	C₂²×C₆₇	1	2	yes	complemented
237	#408	C₂²×C₆₇	1	2	yes	—
238	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
239	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
240	C₂×#41	—	2	4	no	—
241	C₂×#41	—	2	4	no	—
242	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
245	C₂×D₈	C₂³×C₆₇	1	8	yes	—
246	C₂×D₈	C₂³×C₆₇	1	8	yes	—
247	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
249	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
250	#127	—	2	4	no	—
251	#127	—	2	4	no	—
252	#127	C₂³×C₆₇	1	4	yes	—
253	#127	C₂³×C₆₇	1	4	yes	—
254	#125	C₂³×C₆₇	1	4	yes	—
255	#124	—	2	4	no	—
256	#124	—	2	4	no	—
257	#124	—	2	4	no	—
258	#123	—	2	8	no	—
259	#123	—	2	8	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	#121	—	2	4	no	—
262	#121	—	2	4	no	—
263	#121	—	2	8	no	—
264	#121	—	2	8	no	—
265	#121	C₂³×C₆₇	1	8	yes	—
266	#121	C₂³×C₆₇	1	8	yes	—
267	#120	—	2	4	no	—
268	#120	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	D₄×C₆₇	1	2	yes	—
271	C₄×D₄	—	2	8	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	D₄×C₆₇	1	2	yes	—
275	C₄×D₄	D₄×C₆₇	1	4	yes	—
276	C₄×D₄	C₂³×C₆₇	1	8	yes	—
277	C₄×D₄	C₂³×C₆₇	1	8	yes	—
278	#117	C₂³×C₆₇	1	4	yes	—
279	#117	C₂³×C₆₇	1	2	yes	—
280	#117	C₂³×C₆₇	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
283	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
284	#107	C₂³×C₆₇	1	8	yes	—
285	#106	C₂³×C₆₇	1	8	yes	—
286	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
287	#102	C₂³×C₆₇	1	16	yes	—
288	#102	C₂³×C₆₇	1	16	yes	—
289	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
290	#97	C₂³×C₆₇	1	2	yes	—
291	C₄×C₈	C₂³×C₆₇	1	2	yes	—
292	C₄×C₈	C₂³×C₆₇	1	2	yes	—
293	C₄×C₈	C₂³×C₆₇	1	2	yes	—
294	C₂⁴	—	2	4	no	—
295	#41	—	4	2	no	—
296	#41	—	8	8	no	—
297	#41	—	8	8	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	4	8	no	—
307	C₂×D₄	—	8	8	no	—
308	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
309	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
310	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
315	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
317	D₈	—	4	8	no	—
318	D₈	—	4	8	no	—
319	M₁₆	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
322	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
326	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
327	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
334	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂×D₄×C₆₇	1	2	yes	—
337	C₄²	C₂×D₄×C₆₇	1	4	yes	—
338	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
339	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
340	C₄²	C₂⁴×C₆₇	1	2	yes	—
341	C₂³	—	2	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	8	8	no	—
344	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
345	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
346	Q₈	—	4	1	no	—
347	Q₈	—	4	8	no	—
348	D₄	—	2	16	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	8	no	—
353	D₄	—	4	8	no	—
354	D₄	—	8	8	no	—
355	D₄	—	8	8	no	—
356	D₄	—	8	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	8	8	no	—
363	C₂×C₄	—	8	8	no	—
364	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
369	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	8	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	8	no	—
386	C₄	#576×C₆₇	1	4	yes	—
387	C₄	#585×C₆₇	1	2	yes	—
388	C₂	—	4	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	8	8	no	—
391	C₂	C₆₇×#3449	1	1	yes	characteristic
392	C₂	C₂×#576×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3508	C₂	semidirect
2. C₆₇×#3259	C₂	semidirect
3. C₆₇×#3228	C₂	semidirect
4. C₆₇×#3205	C₂	semidirect
5. C₆₇×#3199	C₂	semidirect
6. C₆₇×#3184	C₂	semidirect
7. C₆₇×#3169	C₂	semidirect
8. C₆₇×#3122	C₂	semidirect
9. C₆₇×#2922	C₂	semidirect
15. #540×C₆₇	C₂²	semidirect
17. #533×C₆₇	C₂²	semidirect
19. #532×C₆₇	C₂²	semidirect
20. C₂×#127×C₆₇	C₂²	semidirect
21. #518×C₆₇	C₂²	semidirect
23. #500×C₆₇	C₂²	semidirect
24. #498×C₆₇	C₂²	semidirect
27. #486×C₆₇	C₂²	semidirect
28. #486×C₆₇	C₂²	semidirect
29. #482×C₆₇	C₂²	semidirect
30. #478×C₆₇	C₂²	semidirect
31. #469×C₆₇	C₂²	semidirect
32. #466×C₆₇	C₂²	semidirect
33. #459×C₆₇	C₂²	semidirect
34. #447×C₆₇	C₂²	semidirect
35. #442×C₆₇	C₂²	semidirect
36. C₄×D₈×C₆₇	C₂²	semidirect
37. #433×C₆₇	C₂²	semidirect
38. #431×C₆₇	C₂²	semidirect
39. #424×C₆₇	C₂²	semidirect
41. C₄×M₁₆×C₆₇	C₂²	semidirect
42. C₂×C₄×C₈×C₆₇	C₂²	semidirect
191. #61011	C₆₇	direct (N × H)
197. #3508	C₂×C₆₇	semidirect
198. #3259	C₂×C₆₇	semidirect
199. #3228	C₂×C₆₇	semidirect
200. #3205	C₂×C₆₇	semidirect
201. #3199	C₂×C₆₇	semidirect
202. #3184	C₂×C₆₇	semidirect
203. #3169	C₂×C₆₇	semidirect
204. #3122	C₂×C₆₇	semidirect
205. #2922	C₂×C₆₇	semidirect
206. C₆₇	#61011	direct (N × H)
212. #540	C₂²×C₆₇	semidirect
214. #533	C₂²×C₆₇	semidirect
216. #532	C₂²×C₆₇	semidirect
217. C₂×#127	C₂²×C₆₇	semidirect
218. #518	C₂²×C₆₇	semidirect
220. #500	C₂²×C₆₇	semidirect
221. #498	C₂²×C₆₇	semidirect
224. #486	C₂²×C₆₇	semidirect
225. #486	C₂²×C₆₇	semidirect
226. #482	C₂²×C₆₇	semidirect
227. #478	C₂²×C₆₇	semidirect
228. #469	C₂²×C₆₇	semidirect
229. #466	C₂²×C₆₇	semidirect
230. #459	C₂²×C₆₇	semidirect
231. #447	C₂²×C₆₇	semidirect
232. #442	C₂²×C₆₇	semidirect
233. C₄×D₈	C₂²×C₆₇	semidirect
234. #433	C₂²×C₆₇	semidirect
235. #431	C₂²×C₆₇	semidirect
236. #424	C₂²×C₆₇	semidirect
238. C₄×M₁₆	C₂²×C₆₇	semidirect
239. C₂×C₄×C₈	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×#3508	2
C₆₇×#3259	2
C₆₇×#3228	2
C₆₇×#3205	2
C₆₇×#3199	2
C₆₇×#3184	2
C₆₇×#3169	2
C₆₇×#3122	2
C₆₇×#2922	2
#61011	67

Subgroups — C67×#61011 #30740262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61011 #30740262