Subgroups — C₆₇×#17982 #30697233

Order 17152.

606 conjugacy classes of subgroups.

The subgroup lattice has 370 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	C₆₇×#2966	C₂	1	2	yes	maximal, complemented
3	C₆₇×#1588	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1587	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1586	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1585	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1494	C₂	1	2	yes	maximal, complemented
9	C₂×#322×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#529×C₆₇	C₂²	1	2	yes	—
11	#499×C₆₇	C₄	1	1	yes	characteristic
12	#495×C₆₇	C₄	1	1	yes	characteristic
13	#488×C₆₇	C₄	1	2	yes	—
14	#467×C₆₇	C₄	1	1	yes	characteristic
15	#466×C₆₇	C₄	1	1	yes	characteristic
16	#465×C₆₇	C₄	1	2	yes	—
17	#446×C₆₇	C₂²	1	2	yes	—
18	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
21	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
22	#436×C₆₇	C₂²	1	2	yes	—
23	#435×C₆₇	—	2	2	no	—
24	C₈×D₄×C₆₇	—	2	2	no	—
25	C₈×D₄×C₆₇	C₂²	1	2	yes	—
26	#433×C₆₇	—	2	2	no	—
27	#432×C₆₇	C₂²	1	2	yes	—
28	#405×C₆₇	—	2	2	no	—
29	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#335×C₆₇	C₂²	1	1	yes	characteristic
33	#335×C₆₇	C₂²	1	1	yes	characteristic
34	#334×C₆₇	C₂²	1	2	yes	—
35	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
36	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
37	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
38	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
39	#322×C₆₇	C₂²	1	2	yes	—
40	#322×C₆₇	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₆₇	—	2	2	no	—
45	C₂²×C₈×C₆₇	—	2	1	no	—
46	C₂²×C₈×C₆₇	—	2	2	no	—
47	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
51	#126×C₆₇	—	2	2	no	—
52	#125×C₆₇	C₂×C₄	1	2	yes	—
53	#124×C₆₇	C₂×C₄	1	2	yes	—
54	#123×C₆₇	—	2	2	no	—
55	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
56	#121×C₆₇	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
58	C₄×D₄×C₆₇	—	2	2	no	—
59	C₄×D₄×C₆₇	C₂³	1	2	yes	—
60	#117×C₆₇	—	2	2	no	—
61	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
62	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
63	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
64	#106×C₆₇	C₂×C₄	1	2	yes	—
65	C₄⋊C₈×C₆₇	—	2	2	no	—
66	C₄⋊C₈×C₆₇	—	2	2	no	—
67	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
68	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
69	#103×C₆₇	C₂×C₄	1	2	yes	—
70	#103×C₆₇	C₂×C₄	1	2	yes	—
71	#102×C₆₇	C₂×C₄	1	2	yes	—
72	#102×C₆₇	C₂×C₄	1	2	yes	—
73	C₂²⋊C₈×C₆₇	—	2	2	no	—
74	C₂²⋊C₈×C₆₇	—	2	2	no	—
75	C₂²⋊C₈×C₆₇	—	2	2	no	—
76	#97×C₆₇	—	2	2	no	—
77	#97×C₆₇	—	2	2	no	—
78	C₄×C₈×C₆₇	—	2	2	no	—
79	C₄×C₈×C₆₇	—	2	1	no	—
80	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₇	D₄	1	2	yes	—
83	C₄×C₈×C₆₇	C₂³	1	2	yes	—
84	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₆₇	C₂³	1	2	yes	—
87	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
94	Q₁₆×C₆₇	—	4	1	no	—
95	SD₁₆×C₆₇	—	4	2	no	—
96	D₈×C₆₇	—	4	1	no	—
97	M₁₆×C₆₇	—	4	4	no	—
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	2	2	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₂×C₈×C₆₇	—	4	1	no	—
103	C₂×C₈×C₆₇	—	4	1	no	—
104	C₂×C₈×C₆₇	—	4	1	no	—
105	C₂×C₈×C₆₇	—	4	1	no	—
106	C₂×C₈×C₆₇	—	4	4	no	—
107	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
113	C₄⋊C₄×C₆₇	—	2	2	no	—
114	C₄⋊C₄×C₆₇	—	2	2	no	—
115	C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₆₇	—	2	2	no	—
120	C₂²⋊C₄×C₆₇	—	2	2	no	—
121	C₂²⋊C₄×C₆₇	—	2	2	no	—
122	C₂²⋊C₄×C₆₇	—	2	2	no	—
123	C₂²⋊C₄×C₆₇	—	2	2	no	—
124	C₄²×C₆₇	—	2	2	no	—
125	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₇	#41	1	1	yes	characteristic
128	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
129	C₂³×C₆₇	—	2	2	no	—
130	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
131	Q₈×C₆₇	—	2	2	no	—
132	Q₈×C₆₇	—	2	2	no	—
133	D₄×C₆₇	—	2	2	no	—
134	D₄×C₆₇	—	2	2	no	—
135	D₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	2	1	no	—
139	C₂×C₄×C₆₇	—	2	1	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
152	C₈×C₆₇	—	2	4	no	—
153	C₈×C₆₇	—	2	1	no	—
154	C₈×C₆₇	—	2	1	no	—
155	C₈×C₆₇	—	2	1	no	—
156	C₈×C₆₇	—	2	1	no	—
157	C₈×C₆₇	—	2	2	no	—
158	C₈×C₆₇	—	2	2	no	—
159	C₈×C₆₇	—	4	2	no	—
160	C₈×C₆₇	—	4	2	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	—	4	2	no	—
164	C₂²×C₆₇	—	4	2	no	—
165	C₂²×C₆₇	—	4	2	no	—
166	C₂²×C₆₇	#443	1	2	yes	—
167	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	2	1	no	—
172	C₄×C₆₇	—	4	2	no	—
173	C₄×C₆₇	—	4	2	no	—
174	C₄×C₆₇	—	4	2	no	—
175	C₄×C₆₇	#568	1	1	yes	characteristic
176	C₄×C₆₇	#568	1	1	yes	characteristic
177	C₄×C₆₇	#575	1	1	yes	characteristic
178	C₄×C₆₇	#575	1	1	yes	characteristic
179	#17982	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₆₇	—	2	2	no	—
181	C₂×C₆₇	—	8	2	no	—
182	C₂×C₆₇	#2932	1	1	yes	characteristic
183	C₂×C₆₇	#2943	1	1	yes	characteristic
184	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
185	#3168	C₂×C₆₇	1	1	yes	characteristic
186	#2966	C₂×C₆₇	1	2	yes	complemented
187	#1588	C₂×C₆₇	1	2	yes	complemented
188	#1587	C₂×C₆₇	1	2	yes	complemented
189	#1586	C₂×C₆₇	1	2	yes	complemented
190	#1585	C₂×C₆₇	1	2	yes	complemented
191	#1568	C₂×C₆₇	1	1	yes	characteristic, complemented
192	#1494	C₂×C₆₇	1	2	yes	complemented
193	C₂×#322	C₂×C₆₇	1	1	yes	characteristic, complemented
194	C₆₇	#17982	1	1	yes	characteristic, direct product factor, Sylow
195	#529	C₂²×C₆₇	1	2	yes	—
196	#499	C₄×C₆₇	1	1	yes	characteristic
197	#495	C₄×C₆₇	1	1	yes	characteristic
198	#488	C₄×C₆₇	1	2	yes	—
199	#467	C₄×C₆₇	1	1	yes	characteristic
200	#466	C₄×C₆₇	1	1	yes	characteristic
201	#465	C₄×C₆₇	1	2	yes	—
202	#446	C₂²×C₆₇	1	2	yes	—
203	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
204	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
205	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
206	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
207	#436	C₂²×C₆₇	1	2	yes	—
208	#435	—	2	2	no	—
209	C₈×D₄	—	2	2	no	—
210	C₈×D₄	C₂²×C₆₇	1	2	yes	—
211	#433	—	2	2	no	—
212	#432	C₂²×C₆₇	1	2	yes	—
213	#405	—	2	2	no	—
214	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
217	#335	C₂²×C₆₇	1	1	yes	characteristic
218	#335	C₂²×C₆₇	1	1	yes	characteristic
219	#334	C₂²×C₆₇	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
221	Q₈⋊C₈	C₂²×C₆₇	1	2	yes	—
222	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
223	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
224	#322	C₂²×C₆₇	1	2	yes	—
225	#322	C₂²×C₆₇	1	2	yes	—
226	C₂×Q₁₆	C₂×C₄×C₆₇	1	1	yes	characteristic
227	C₂×SD₁₆	C₂×C₄×C₆₇	1	2	yes	—
228	C₂×D₈	C₂×C₄×C₆₇	1	1	yes	characteristic
229	C₂×M₁₆	—	2	2	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
233	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
234	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
235	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
236	#126	—	2	2	no	—
237	#125	C₂×C₄×C₆₇	1	2	yes	—
238	#124	C₂×C₄×C₆₇	1	2	yes	—
239	#123	—	2	2	no	—
240	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
241	#121	C₂×C₄×C₆₇	1	2	yes	—
242	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	C₂³×C₆₇	1	2	yes	—
245	#117	—	2	2	no	—
246	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
247	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
248	#107	C₂×C₄×C₆₇	1	1	yes	characteristic
249	#106	C₂×C₄×C₆₇	1	2	yes	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
253	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
254	#103	C₂×C₄×C₆₇	1	2	yes	—
255	#103	C₂×C₄×C₆₇	1	2	yes	—
256	#102	C₂×C₄×C₆₇	1	2	yes	—
257	#102	C₂×C₄×C₆₇	1	2	yes	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	#97	—	2	2	no	—
262	#97	—	2	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
266	C₄×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
267	C₄×C₈	D₄×C₆₇	1	2	yes	—
268	C₄×C₈	C₂³×C₆₇	1	2	yes	—
269	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₆₇	1	2	yes	—
272	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
278	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
279	Q₁₆	—	4	1	no	—
280	SD₁₆	—	4	2	no	—
281	D₈	—	4	1	no	—
282	M₁₆	—	4	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
303	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
312	C₄²	#41×C₆₇	1	1	yes	characteristic
313	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
316	Q₈	—	2	2	no	—
317	Q₈	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	#443×C₆₇	1	2	yes	—
352	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	2	no	—
360	C₄	#568×C₆₇	1	1	yes	characteristic
361	C₄	#568×C₆₇	1	1	yes	characteristic
362	C₄	#575×C₆₇	1	1	yes	characteristic
363	C₄	#575×C₆₇	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	8	2	no	—
366	C₂	C₆₇×#2932	1	1	yes	characteristic
367	C₂	C₆₇×#2943	1	1	yes	characteristic
368	C₂	C₂×#443×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₄²	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#466×C₆₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2966	C₂	semidirect
3. C₆₇×#1588	C₂	semidirect
4. C₆₇×#1587	C₂	semidirect
5. C₆₇×#1586	C₂	semidirect
6. C₆₇×#1585	C₂	semidirect
7. C₆₇×#1568	C₂	semidirect
8. C₆₇×#1494	C₂	semidirect
9. C₂×#322×C₆₇	C₂	semidirect
179. #17982	C₆₇	direct (N × H)
186. #2966	C₂×C₆₇	semidirect
187. #1588	C₂×C₆₇	semidirect
188. #1587	C₂×C₆₇	semidirect
189. #1586	C₂×C₆₇	semidirect
190. #1585	C₂×C₆₇	semidirect
191. #1568	C₂×C₆₇	semidirect
192. #1494	C₂×C₆₇	semidirect
193. C₂×#322	C₂×C₆₇	semidirect
194. C₆₇	#17982	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
C₆₇×#2966	2
C₆₇×#1588	2
C₆₇×#1587	2
C₆₇×#1586	2
C₆₇×#1585	2
C₆₇×#1568	2
C₆₇×#1494	2
C₂×#322×C₆₇	2
#17982	67

Subgroups — C67×#17982 #30697233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#17982 #30697233