Subgroups — C₂×#500×D₆₇ #31725426

Order 17152.

2398 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Q₈×D₆₇	C₂	1	2	yes	maximal
2	C₂×#16863801	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863800	C₂	1	4	yes	maximal, complemented
4	C₂×#16863799	C₂	1	2	yes	maximal, complemented
5	#500×D₆₇	C₂	1	16	yes	maximal, direct product factor
6	C₂×#107×D₆₇	C₂	1	4	yes	maximal
7	C₂×C₄×C₈×D₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#500×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×D₆₇	—	2	2	no	—
10	C₂²×C₈×D₆₇	C₂²	1	2	yes	—
11	C₂×#14524043	C₂²	1	2	yes	—
12	C₂×#14524042	—	2	2	no	—
13	C₂×#14524042	C₂²	1	4	yes	—
14	C₂×#14524041	—	2	2	no	—
15	C₄⋊Q₈×D₆₇	—	2	8	no	—
16	C₄⋊Q₈×D₆₇	C₂²	1	16	yes	—
17	C₂×C₄⋊C₄×D₆₇	—	2	2	no	—
18	C₂×C₄⋊C₄×D₆₇	C₂²	1	4	yes	—
19	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
20	#16863801	C₂²	1	8	yes	complemented
21	#16863800	C₂²	1	32	yes	complemented
22	#16863799	C₂²	1	16	yes	complemented
23	C₂×#14523977	C₂²	1	4	yes	—
24	C₂×#14523976	C₂²	1	8	yes	—
25	#107×D₆₇	C₂²	1	32	yes	—
26	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₆₇	C₂²	1	2	yes	—
28	C₄×C₈×D₆₇	C₂²	1	8	yes	—
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	#500×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#107×C₆₇	C₂²	1	4	yes	—
32	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×Dic₁₃₄	—	2	4	no	—
34	C₂²×Dic₁₃₄	—	2	2	no	—
35	C₂×Q₈×D₆₇	—	2	16	no	—
36	C₂×Q₈×D₆₇	—	4	16	no	—
37	C₂²×C₄×D₆₇	—	2	4	no	—
38	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
39	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
40	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
41	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
42	C₂×C₈×D₆₇	Q₈	1	16	yes	complemented
43	C₂×C₈×D₆₇	C₂³	1	8	yes	—
44	#14524043	—	2	4	no	—
45	#14524043	C₂³	1	8	yes	—
46	#14524042	—	2	8	no	—
47	#14524042	—	2	16	no	—
48	#14524042	C₂³	1	16	yes	—
49	#14524041	—	2	16	no	—
50	C₂×C₄⋊Dic₆₇	—	2	2	no	—
51	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
52	C₂×Dic₆₇⋊C₄	—	2	4	no	—
53	C₂×Dic₆₇⋊C₄	—	2	4	no	—
54	C₄⋊C₄×D₆₇	—	2	16	no	—
55	C₄⋊C₄×D₆₇	—	2	8	no	—
56	C₄⋊C₄×D₆₇	C₂³	1	16	yes	—
57	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
60	C₄²×D₆₇	D₄	1	4	yes	—
61	C₄²×D₆₇	C₂³	1	4	yes	—
62	#14523977	C₂³	1	16	yes	—
63	#14523976	C₂³	1	32	yes	—
64	C₄×C₆₇⋊C₈	C₂³	1	4	yes	—
65	C₈×Dic₆₇	C₂³	1	8	yes	—
66	C₂²×Q₈×C₆₇	—	2	2	no	—
67	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₆₇	—	2	4	no	—
69	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
72	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	#107×C₆₇	C₂³	1	16	yes	—
74	C₄×C₈×C₆₇	C₂³	1	4	yes	—
75	C₂³×D₆₇	C₂×D₄	1	1	yes	characteristic
76	C₂×Dic₁₃₄	—	2	8	no	—
77	C₂×Dic₁₃₄	—	2	16	no	—
78	C₂×Dic₁₃₄	—	4	8	no	—
79	C₂×Dic₁₃₄	—	4	16	no	—
80	Q₈×D₆₇	—	4	64	no	—
81	C₂²×Dic₆₇	—	2	4	no	—
82	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₆₇	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×D₆₇	—	2	16	no	—
86	C₂×C₄×D₆₇	—	4	16	no	—
87	C₂×C₄×D₆₇	D₈	1	8	yes	—
88	C₂×C₄×D₆₇	Q₁₆	1	8	yes	—
89	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
90	C₂×C₄×D₆₇	C₂×D₄	1	4	yes	—
91	C₂×C₄×D₆₇	C₂×D₄	1	4	yes	—
92	C₂×C₄×D₆₇	C₂×Q₈	1	8	yes	—
93	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
94	C₂×C₆₇⋊C₈	C₂×Q₈	1	8	yes	complemented
95	C₂×C₆₇⋊C₈	C₂⁴	1	4	yes	—
96	C₈×D₆₇	C₂×Q₈	1	32	yes	complemented
97	C₄⋊Dic₆₇	—	2	8	no	—
98	C₄⋊Dic₆₇	—	2	4	no	—
99	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
100	Dic₆₇⋊C₄	—	2	16	no	—
101	Dic₆₇⋊C₄	—	2	16	no	—
102	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
103	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
104	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
105	C₄×Dic₆₇	C₂⁴	1	2	yes	—
106	C₂×Q₈×C₆₇	—	2	8	no	—
107	C₂×Q₈×C₆₇	—	4	8	no	—
108	C₂²×C₄×C₆₇	—	2	4	no	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂×Q₈	1	8	yes	complemented
113	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
114	C₄⋊C₄×C₆₇	—	2	8	no	—
115	C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
117	C₄²×C₆₇	C₂×D₄	1	2	yes	—
118	C₄²×C₆₇	C₂⁴	1	2	yes	—
119	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
120	C₂²×D₆₇	C₄⋊Q₈	1	4	yes	—
121	C₂²×D₆₇	C₂×D₈	1	4	yes	—
122	C₂²×D₆₇	C₂×Q₁₆	1	4	yes	—
123	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
124	Q₈×C₆₇	—	4	16	no	—
125	C₂×C₄×C₆₇	—	2	8	no	—
126	C₂×C₄×C₆₇	—	4	8	no	—
127	C₂×C₄×C₆₇	C₂×D₈	1	4	yes	—
128	C₂×C₄×C₆₇	C₂×Q₁₆	1	4	yes	—
129	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
132	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
133	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
134	C₂×Dic₆₇	—	2	8	no	—
135	C₂×Dic₆₇	—	4	8	no	—
136	C₂×Dic₆₇	C₄⋊Q₈	1	4	yes	—
137	C₂×Dic₆₇	C₂×D₈	1	4	yes	—
138	C₂×Dic₆₇	C₂×Q₁₆	1	4	yes	—
139	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
140	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
141	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
142	C₄×D₆₇	—	4	32	no	—
143	C₄×D₆₇	C₄⋊Q₈	1	8	yes	—
144	C₄×D₆₇	C₂×D₈	1	16	yes	—
145	C₄×D₆₇	C₂×Q₁₆	1	16	yes	—
146	C₄×D₆₇	C₂²×Q₈	1	8	yes	—
147	Dic₁₃₄	—	4	16	no	—
148	Dic₁₃₄	—	4	32	no	—
149	C₈×C₆₇	C₂²×Q₈	1	8	yes	complemented
150	C₆₇⋊C₈	C₂²×Q₈	1	8	yes	complemented
151	C₂²×C₆₇	C₂×C₄⋊Q₈	1	2	yes	—
152	C₂²×C₆₇	C₂²×D₈	1	2	yes	—
153	C₂²×C₆₇	C₂²×Q₁₆	1	2	yes	—
154	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
155	C₂×D₆₇	#500	1	16	yes	direct product factor
156	C₂×D₆₇	C₂×C₄⋊Q₈	1	4	yes	—
157	C₂×D₆₇	C₂²×D₈	1	4	yes	—
158	C₂×D₆₇	C₂²×Q₁₆	1	4	yes	—
159	C₄×C₆₇	—	4	8	no	—
160	C₄×C₆₇	C₂×C₄⋊Q₈	1	2	yes	—
161	C₄×C₆₇	C₂²×D₈	1	4	yes	—
162	C₄×C₆₇	C₂²×Q₁₆	1	4	yes	—
163	C₄×C₆₇	C₂³×Q₈	1	2	yes	—
164	Dic₆₇	—	4	8	no	—
165	Dic₆₇	C₂×C₄⋊Q₈	1	4	yes	—
166	Dic₆₇	C₂²×D₈	1	4	yes	—
167	Dic₆₇	C₂²×Q₁₆	1	4	yes	—
168	C₂²×#500	—	67	1	no	maximal, Sylow
169	C₂×C₆₇	C₂×#500	1	4	yes	complemented
170	C₂×C₆₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
171	C₂×C₆₇	C₂³×D₈	1	1	yes	characteristic
172	C₂×C₆₇	C₂³×Q₁₆	1	1	yes	characteristic
173	D₆₇	C₂×#500	1	8	yes	direct product factor
174	C₂²×C₄⋊Q₈	—	67	2	no	—
175	C₂×#500	—	67	16	no	—
176	C₂×#500	—	67	4	no	—
177	C₂×#500	—	67	1	no	—
178	C₂×#500	—	67	2	no	—
179	C₂×#500	D₆₇	1	1	yes	characteristic, direct product factor
180	C₂²×#107	—	67	4	no	—
181	C₂²×C₄×C₈	—	67	1	no	—
182	C₆₇	C₂²×#500	1	1	yes	characteristic, complemented, Sylow
183	C₂³×Q₈	—	134	2	no	—
184	C₂³×C₈	—	67	2	no	—
185	C₂×C₄⋊Q₈	—	67	16	no	—
186	C₂×C₄⋊Q₈	—	67	4	no	—
187	C₂×C₄⋊Q₈	—	67	2	no	—
188	C₂×C₄⋊Q₈	—	134	2	no	—
189	C₂×C₄⋊Q₈	—	134	8	no	—
190	C₂×C₄⋊Q₈	—	134	2	no	—
191	C₂×C₄⋊Q₈	C₂×D₆₇	1	2	yes	—
192	C₂²×C₄⋊C₄	—	67	4	no	—
193	C₂²×C₄⋊C₄	—	134	2	no	—
194	C₂²×C₄²	—	67	1	no	—
195	#500	—	67	16	no	—
196	#500	—	67	32	no	—
197	#500	—	67	8	no	—
198	#500	C₂×D₆₇	1	8	yes	direct product factor
199	C₂×#107	—	67	4	no	—
200	C₂×#107	—	67	8	no	—
201	C₂×#107	—	67	32	no	—
202	C₂×#107	C₂×D₆₇	1	4	yes	—
203	C₂×C₄×C₈	—	67	2	no	—
204	C₂×C₄×C₈	—	67	1	no	—
205	C₂×C₄×C₈	—	67	8	no	—
206	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
207	C₂²×Q₈	—	2	2	no	—
208	C₂²×Q₈	—	268	16	no	—
209	C₂²×Q₈	—	134	4	no	—
210	C₂²×Q₈	—	134	16	no	—
211	C₂²×Q₈	—	134	2	no	—
212	C₂³×C₄	—	67	1	no	—
213	C₂³×C₄	—	67	1	no	—
214	C₂³×C₄	—	67	1	no	—
215	C₂³×C₄	—	134	4	no	—
216	C₂²×C₈	—	67	2	no	—
217	C₂²×C₈	—	67	16	no	—
218	C₂²×C₈	—	67	8	no	—
219	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
220	C₄⋊Q₈	—	2	4	no	—
221	C₄⋊Q₈	—	67	16	no	—
222	C₄⋊Q₈	—	67	8	no	—
223	C₄⋊Q₈	—	134	16	no	—
224	C₄⋊Q₈	—	134	8	no	—
225	C₄⋊Q₈	—	134	16	no	—
226	C₄⋊Q₈	—	134	4	no	—
227	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	67	4	no	—
230	C₂×C₄⋊C₄	—	67	16	no	—
231	C₂×C₄⋊C₄	—	134	8	no	—
232	C₂×C₄⋊C₄	—	134	16	no	—
233	C₂×C₄⋊C₄	—	134	4	no	—
234	C₂×C₄⋊C₄	—	134	4	no	—
235	C₂×C₄⋊C₄	—	134	2	no	—
236	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
237	C₂×C₄²	—	67	1	no	—
238	C₂×C₄²	—	67	1	no	—
239	C₂×C₄²	—	67	1	no	—
240	C₂×C₄²	—	67	4	no	—
241	C₂×C₄²	—	67	4	no	—
242	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
243	#107	—	67	16	no	—
244	#107	—	67	32	no	—
245	#107	C₂²×D₆₇	1	16	yes	—
246	C₄×C₈	—	67	8	no	—
247	C₄×C₈	—	67	4	no	—
248	C₄×C₈	C₂²×D₆₇	1	4	yes	—
249	C₂⁴	—	67	1	no	—
250	C₂×Q₈	—	2	8	no	—
251	C₂×Q₈	—	4	8	no	—
252	C₂×Q₈	—	268	16	no	—
253	C₂×Q₈	—	268	64	no	—
254	C₂×Q₈	—	268	8	no	—
255	C₂×Q₈	—	134	16	no	—
256	C₂×Q₈	—	134	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	268	16	no	—
259	C₂²×C₄	—	67	1	no	—
260	C₂²×C₄	—	67	1	no	—
261	C₂²×C₄	—	67	1	no	—
262	C₂²×C₄	—	67	8	no	—
263	C₂²×C₄	—	67	8	no	—
264	C₂²×C₄	—	67	4	no	—
265	C₂²×C₄	—	67	2	no	—
266	C₂²×C₄	—	67	4	no	—
267	C₂²×C₄	—	67	8	no	—
268	C₂²×C₄	—	67	2	no	—
269	C₂²×C₄	—	134	16	no	—
270	C₂²×C₄	—	134	4	no	—
271	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
272	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
274	C₂×C₈	—	67	8	no	—
275	C₂×C₈	—	67	4	no	—
276	C₂×C₈	—	67	32	no	—
277	C₂×C₈	Q₈×D₆₇	1	8	yes	complemented
278	C₂×C₈	C₂³×D₆₇	1	4	yes	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	67	8	no	—
282	C₄⋊C₄	—	134	16	no	—
283	C₄⋊C₄	—	134	16	no	—
284	C₄⋊C₄	—	134	4	no	—
285	C₄⋊C₄	—	134	8	no	—
286	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
287	C₄²	—	67	4	no	—
288	C₄²	—	67	4	no	—
289	C₄²	—	67	2	no	—
290	C₄²	—	67	2	no	—
291	C₄²	D₄×D₆₇	1	2	yes	—
292	C₄²	C₂³×D₆₇	1	2	yes	—
293	C₂³	—	67	4	no	—
294	C₂³	—	67	4	no	—
295	C₂³	—	67	4	no	—
296	C₂³	—	67	2	no	—
297	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
298	Q₈	—	4	16	no	—
299	Q₈	—	268	32	no	—
300	Q₈	—	268	16	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	268	32	no	—
304	C₂×C₄	—	268	8	no	—
305	C₂×C₄	—	67	4	no	—
306	C₂×C₄	—	67	4	no	—
307	C₂×C₄	—	67	4	no	—
308	C₂×C₄	—	67	2	no	—
309	C₂×C₄	—	67	2	no	—
310	C₂×C₄	—	67	2	no	—
311	C₂×C₄	—	67	16	no	—
312	C₂×C₄	—	67	16	no	—
313	C₂×C₄	—	67	8	no	—
314	C₂×C₄	—	67	8	no	—
315	C₂×C₄	—	134	8	no	—
316	C₂×C₄	D₈×D₆₇	1	4	yes	—
317	C₂×C₄	Q₁₆×D₆₇	1	4	yes	—
318	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
319	C₂×C₄	C₂×D₄×D₆₇	1	2	yes	—
320	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
321	C₂×C₄	C₂×Q₈×D₆₇	1	4	yes	—
322	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
323	C₈	—	67	8	no	—
324	C₈	C₂×Q₈×D₆₇	1	8	yes	complemented
325	C₂²	—	67	4	no	—
326	C₂²	—	67	4	no	—
327	C₂²	—	67	4	no	—
328	C₂²	—	67	16	no	—
329	C₂²	C₄⋊Q₈×D₆₇	1	2	yes	—
330	C₂²	C₂×D₈×D₆₇	1	2	yes	—
331	C₂²	C₂×Q₁₆×D₆₇	1	2	yes	—
332	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
333	C₄	—	4	8	no	—
334	C₄	—	268	8	no	—
335	C₄	—	67	4	no	—
336	C₄	—	67	4	no	—
337	C₄	—	67	4	no	—
338	C₄	C₄⋊Q₈×D₆₇	1	2	yes	—
339	C₄	C₂×D₈×D₆₇	1	4	yes	—
340	C₄	C₂×Q₁₆×D₆₇	1	4	yes	—
341	C₄	C₂²×Q₈×D₆₇	1	2	yes	—
342	C₂	—	67	8	no	—
343	C₂	#500×D₆₇	1	4	yes	direct product factor
344	C₂	C₂×C₄⋊Q₈×D₆₇	1	1	yes	characteristic
345	C₂	C₂²×D₈×D₆₇	1	1	yes	characteristic
346	C₂	C₂²×Q₁₆×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₆₇
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₂×#500×C₆₇	C₂
socle	C₂³×C₆₇	C₂²×D₄
prime radical	C₂³×D₆₇	C₂×D₄
hypercenter	C₂×#500	D₆₇
hypocenter	C₆₇	C₂²×#500
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

Complements

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

N	H ≅ G/N	type
2. C₂×#16863801	C₂	semidirect
3. C₂×#16863800	C₂	semidirect
4. C₂×#16863799	C₂	semidirect
5. #500×D₆₇	C₂	direct (N × H)
8. C₂×#500×C₆₇	C₂	semidirect
20. #16863801	C₂²	semidirect
21. #16863800	C₂²	semidirect
22. #16863799	C₂²	semidirect
30. #500×C₆₇	C₂²	semidirect
42. C₂×C₈×D₆₇	Q₈	semidirect
94. C₂×C₆₇⋊C₈	C₂×Q₈	semidirect
96. C₈×D₆₇	C₂×Q₈	semidirect
112. C₂×C₈×C₆₇	C₂×Q₈	semidirect
149. C₈×C₆₇	C₂²×Q₈	semidirect
150. C₆₇⋊C₈	C₂²×Q₈	semidirect
155. C₂×D₆₇	#500	direct (N × H)
169. C₂×C₆₇	C₂×#500	semidirect
173. D₆₇	C₂×#500	direct (N × H)
179. C₂×#500	D₆₇	direct (N × H)
182. C₆₇	C₂²×#500	semidirect
198. #500	C₂×D₆₇	direct (N × H)
277. C₂×C₈	Q₈×D₆₇	semidirect
324. C₈	C₂×Q₈×D₆₇	semidirect
343. C₂	#500×D₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Q₈×D₆₇	2
C₂×#16863801	2
C₂×#16863800	2
C₂×#16863799	2
#500×D₆₇	2
C₂×#107×D₆₇	2
C₂×C₄×C₈×D₆₇	2
C₂×#500×C₆₇	2
C₂²×#500	67

Subgroups — C2×#500×D67 #31725426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#500×D₆₇ #31725426