Subgroups — C₆₇×#21233 #30700484

Order 17152.

1790 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2309	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1972	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1970	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
9	C₂²×D₈×C₆₇	—	2	4	no	—
10	C₂²×D₈×C₆₇	—	2	4	no	—
11	C₂²×D₈×C₆₇	C₄	1	8	yes	complemented
12	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₆₇	C₂²	1	2	yes	—
17	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
18	#427×C₆₇	—	2	4	no	—
19	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
20	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
21	#418×C₆₇	—	2	8	no	—
22	C₂×#102×C₆₇	C₂²	1	8	yes	complemented
23	#405×C₆₇	—	2	4	no	—
24	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
25	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
26	#390×C₆₇	—	2	4	no	—
27	#390×C₆₇	C₂²	1	8	yes	complemented
28	#379×C₆₇	—	2	4	no	—
29	C₂⁵×C₆₇	—	2	2	no	—
30	C₂²×D₄×C₆₇	—	2	4	no	—
31	C₂²×D₄×C₆₇	—	2	4	no	—
32	C₂²×D₄×C₆₇	—	2	4	no	—
33	C₂²×D₄×C₆₇	—	2	2	no	—
34	C₂²×D₄×C₆₇	—	2	4	no	—
35	C₂²×D₄×C₆₇	—	2	4	no	—
36	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
37	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
38	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
39	C₂×D₈×C₆₇	—	2	32	no	—
40	C₂×D₈×C₆₇	—	2	4	no	—
41	C₂×D₈×C₆₇	—	2	4	no	—
42	C₂×D₈×C₆₇	—	2	4	no	—
43	C₂×D₈×C₆₇	—	2	4	no	—
44	C₂×D₈×C₆₇	C₂×C₄	1	8	yes	—
45	C₂×D₈×C₆₇	C₂×C₄	1	8	yes	—
46	C₂×M₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂×M₁₆×C₆₇	D₄	1	4	yes	—
49	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₆₇	D₄	1	4	yes	—
51	C₂²×C₈×C₆₇	D₄	1	4	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
55	#117×C₆₇	—	2	2	no	—
56	#117×C₆₇	—	2	2	no	—
57	#117×C₆₇	—	2	4	no	—
58	#117×C₆₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
63	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
64	C₂×C₄²×C₆₇	—	2	2	no	—
65	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
66	#107×C₆₇	—	2	4	no	—
67	#106×C₆₇	—	2	4	no	—
68	#102×C₆₇	—	2	16	no	—
69	#97×C₆₇	—	2	4	no	—
70	C₄×C₈×C₆₇	—	2	4	no	—
71	C₂⁴×C₆₇	—	2	4	no	—
72	C₂⁴×C₆₇	—	2	8	no	—
73	C₂⁴×C₆₇	—	4	4	no	—
74	C₂⁴×C₆₇	—	4	4	no	—
75	C₂⁴×C₆₇	—	8	8	no	—
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₆₇	—	2	16	no	—
78	C₂×D₄×C₆₇	—	2	16	no	—
79	C₂×D₄×C₆₇	—	2	8	no	—
80	C₂×D₄×C₆₇	—	2	4	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	2	4	no	—
83	C₂×D₄×C₆₇	—	2	4	no	—
84	C₂×D₄×C₆₇	—	2	4	no	—
85	C₂×D₄×C₆₇	—	4	8	no	—
86	C₂×D₄×C₆₇	—	4	4	no	—
87	C₂×D₄×C₆₇	—	4	8	no	—
88	C₂×D₄×C₆₇	—	4	4	no	—
89	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₆₇	—	2	4	no	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	#41	1	2	yes	—
98	C₂²×C₄×C₆₇	#41	1	2	yes	—
99	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
100	D₈×C₆₇	—	2	16	no	—
101	D₈×C₆₇	—	2	16	no	—
102	M₁₆×C₆₇	—	2	8	no	—
103	C₂×C₈×C₆₇	—	2	2	no	—
104	C₂×C₈×C₆₇	—	2	2	no	—
105	C₂×C₈×C₆₇	C₂²⋊C₄	1	16	yes	complemented
106	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
113	C₄⋊C₄×C₆₇	—	2	4	no	—
114	C₄⋊C₄×C₆₇	—	2	4	no	—
115	C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₂²⋊C₄×C₆₇	—	2	4	no	—
117	C₂²⋊C₄×C₆₇	—	4	4	no	—
118	C₂²⋊C₄×C₆₇	—	8	16	no	—
119	C₄²×C₆₇	—	2	2	no	—
120	C₄²×C₆₇	—	2	2	no	—
121	C₄²×C₆₇	—	4	4	no	—
122	C₂³×C₆₇	—	2	4	no	—
123	C₂³×C₆₇	—	2	8	no	—
124	C₂³×C₆₇	—	4	4	no	—
125	C₂³×C₆₇	—	4	4	no	—
126	C₂³×C₆₇	—	4	16	no	—
127	C₂³×C₆₇	—	4	16	no	—
128	C₂³×C₆₇	—	8	16	no	—
129	C₂³×C₆₇	—	8	16	no	—
130	C₂³×C₆₇	—	8	16	no	—
131	C₂³×C₆₇	C₄×D₄	1	2	yes	—
132	C₂³×C₆₇	#121	1	2	yes	—
133	C₂³×C₆₇	#127	1	2	yes	—
134	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
135	D₄×C₆₇	—	2	8	no	—
136	D₄×C₆₇	—	2	8	no	—
137	D₄×C₆₇	—	4	4	no	—
138	D₄×C₆₇	—	4	4	no	—
139	D₄×C₆₇	—	4	16	no	—
140	C₂×C₄×C₆₇	—	2	4	no	—
141	C₂×C₄×C₆₇	—	2	8	no	—
142	C₂×C₄×C₆₇	—	4	4	no	—
143	C₂×C₄×C₆₇	—	4	8	no	—
144	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
145	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₆₇	#121	1	4	yes	—
148	C₂×C₄×C₆₇	#121	1	2	yes	—
149	C₂×C₄×C₆₇	#124	1	4	yes	—
150	C₂×C₄×C₆₇	#127	1	2	yes	—
151	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
157	C₈×C₆₇	—	2	4	no	—
158	C₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
159	C₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂²×C₆₇	—	2	4	no	—
161	C₂²×C₆₇	—	2	4	no	—
162	C₂²×C₆₇	—	2	4	no	—
163	C₂²×C₆₇	—	4	16	no	—
164	C₂²×C₆₇	—	4	8	no	—
165	C₂²×C₆₇	—	8	32	no	—
166	C₂²×C₆₇	—	8	8	no	—
167	C₂²×C₆₇	—	8	8	no	—
168	C₂²×C₆₇	#390	1	4	yes	—
169	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
171	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
172	C₂²×C₆₇	#576	1	4	yes	—
173	C₄×C₆₇	—	4	4	no	—
174	C₄×C₆₇	—	8	4	no	—
175	C₄×C₆₇	#390	1	4	yes	—
176	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
178	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
179	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
180	#21233	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₆₇	—	2	4	no	—
182	C₂×C₆₇	—	8	8	no	—
183	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
184	C₂×C₆₇	#2948	1	2	yes	—
185	C₂×C₆₇	#3058	1	2	yes	—
186	C₂×C₆₇	#3155	1	2	yes	—
187	C₂³×D₈	C₂×C₆₇	1	1	yes	characteristic
188	C₂×#427	C₂×C₆₇	1	1	yes	characteristic, complemented
189	C₂×#418	C₂×C₆₇	1	2	yes	complemented
190	C₂×#405	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#2309	C₂×C₆₇	1	2	yes	complemented
192	#1972	C₂×C₆₇	1	4	yes	complemented
193	#1970	C₂×C₆₇	1	4	yes	complemented
194	C₆₇	#21233	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
196	C₂²×D₈	—	2	4	no	—
197	C₂²×D₈	—	2	4	no	—
198	C₂²×D₈	C₄×C₆₇	1	8	yes	complemented
199	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
200	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
201	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
202	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
203	C₂×#117	C₂²×C₆₇	1	2	yes	—
204	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
205	#427	—	2	4	no	—
206	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
207	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
208	#418	—	2	8	no	—
209	C₂×#102	C₂²×C₆₇	1	8	yes	complemented
210	#405	—	2	4	no	—
211	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
212	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
213	#390	—	2	4	no	—
214	#390	C₂²×C₆₇	1	8	yes	complemented
215	#379	—	2	4	no	—
216	C₂⁵	—	2	2	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	2	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	—	2	4	no	—
223	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	—
224	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
225	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
226	C₂×D₈	—	2	32	no	—
227	C₂×D₈	—	2	4	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	4	no	—
230	C₂×D₈	—	2	4	no	—
231	C₂×D₈	C₂×C₄×C₆₇	1	8	yes	—
232	C₂×D₈	C₂×C₄×C₆₇	1	8	yes	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	D₄×C₆₇	1	4	yes	—
236	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
237	C₂²×C₈	D₄×C₆₇	1	4	yes	—
238	C₂²×C₈	D₄×C₆₇	1	4	yes	—
239	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
240	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	4	no	—
245	#117	—	2	4	no	—
246	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	16	no	—
250	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
253	#107	—	2	4	no	—
254	#106	—	2	4	no	—
255	#102	—	2	16	no	—
256	#97	—	2	4	no	—
257	C₄×C₈	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	—	4	4	no	—
261	C₂⁴	—	4	4	no	—
262	C₂⁴	—	8	8	no	—
263	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
264	C₂×D₄	—	2	16	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
284	C₂²×C₄	#41×C₆₇	1	2	yes	—
285	C₂²×C₄	#41×C₆₇	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
287	D₈	—	2	16	no	—
288	D₈	—	2	16	no	—
289	M₁₆	—	2	8	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂²⋊C₄×C₆₇	1	16	yes	complemented
293	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
296	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
298	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	8	16	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	4	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	8	no	—
311	C₂³	—	4	4	no	—
312	C₂³	—	4	4	no	—
313	C₂³	—	4	16	no	—
314	C₂³	—	4	16	no	—
315	C₂³	—	8	16	no	—
316	C₂³	—	8	16	no	—
317	C₂³	—	8	16	no	—
318	C₂³	C₄×D₄×C₆₇	1	2	yes	—
319	C₂³	#121×C₆₇	1	2	yes	—
320	C₂³	#127×C₆₇	1	2	yes	—
321	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
322	D₄	—	2	8	no	—
323	D₄	—	2	8	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	16	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
332	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
333	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
334	C₂×C₄	#121×C₆₇	1	4	yes	—
335	C₂×C₄	#121×C₆₇	1	2	yes	—
336	C₂×C₄	#124×C₆₇	1	4	yes	—
337	C₂×C₄	#127×C₆₇	1	2	yes	—
338	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
346	C₈	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	16	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	8	no	—
354	C₂²	—	8	8	no	—
355	C₂²	#390×C₆₇	1	4	yes	—
356	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
357	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
358	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
359	C₂²	#576×C₆₇	1	4	yes	—
360	C₄	—	4	4	no	—
361	C₄	—	8	4	no	—
362	C₄	#390×C₆₇	1	4	yes	—
363	C₄	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
364	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
365	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
366	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	—	8	8	no	—
369	C₂	C₂×#390×C₆₇	1	1	yes	characteristic
370	C₂	C₆₇×#2948	1	2	yes	—
371	C₂	C₆₇×#3058	1	2	yes	—
372	C₂	C₆₇×#3155	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂³×D₈×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#427×C₆₇	C₂	semidirect
3. C₂×#418×C₆₇	C₂	semidirect
4. C₂×#405×C₆₇	C₂	semidirect
5. C₆₇×#2309	C₂	semidirect
6. C₆₇×#1972	C₂	semidirect
7. C₆₇×#1970	C₂	semidirect
11. C₂²×D₈×C₆₇	C₄	semidirect
19. C₂×#107×C₆₇	C₂²	semidirect
20. C₂×#106×C₆₇	C₂²	semidirect
22. C₂×#102×C₆₇	C₂²	semidirect
24. C₂×#97×C₆₇	C₂²	semidirect
25. C₂×C₄×C₈×C₆₇	C₂²	semidirect
27. #390×C₆₇	C₂²	semidirect
105. C₂×C₈×C₆₇	C₂²⋊C₄	semidirect
180. #21233	C₆₇	direct (N × H)
188. C₂×#427	C₂×C₆₇	semidirect
189. C₂×#418	C₂×C₆₇	semidirect
190. C₂×#405	C₂×C₆₇	semidirect
191. #2309	C₂×C₆₇	semidirect
192. #1972	C₂×C₆₇	semidirect
193. #1970	C₂×C₆₇	semidirect
194. C₆₇	#21233	direct (N × H)
198. C₂²×D₈	C₄×C₆₇	semidirect
206. C₂×#107	C₂²×C₆₇	semidirect
207. C₂×#106	C₂²×C₆₇	semidirect
209. C₂×#102	C₂²×C₆₇	semidirect
211. C₂×#97	C₂²×C₆₇	semidirect
212. C₂×C₄×C₈	C₂²×C₆₇	semidirect
214. #390	C₂²×C₆₇	semidirect
292. C₂×C₈	C₂²⋊C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₆₇	2
C₂×#427×C₆₇	2
C₂×#418×C₆₇	2
C₂×#405×C₆₇	2
C₆₇×#2309	2
C₆₇×#1972	2
C₆₇×#1970	2
#21233	67

Subgroups — C67×#21233 #30700484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21233 #30700484