Subgroups — C₂×#444×D₆₇ #31720124

Order 17152.

2710 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#131×D₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#16863519	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16863518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16863517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863516	C₂	1	2	yes	maximal, complemented
7	C₂×#16863515	C₂	1	2	yes	maximal, complemented
8	#444×D₆₇	C₂	1	16	yes	maximal, direct product factor
9	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#104×D₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#97×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#444×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×D₆₇	C₂²	1	2	yes	—
14	C₂×#14524066	C₄	1	1	yes	characteristic, complemented
15	C₂×#14524065	C₂²	1	1	yes	characteristic
16	C₂×#14524064	C₄	1	2	yes	complemented
17	C₂×#14524063	C₂²	1	2	yes	—
18	C₂×#14524062	C₄	1	1	yes	characteristic, complemented
19	#135×D₆₇	C₄	1	8	yes	complemented
20	#135×D₆₇	C₂²	1	8	yes	—
21	C₂×Q₁₆×D₆₇	C₄	1	1	yes	characteristic, complemented
22	C₂×SD₁₆×D₆₇	C₄	1	2	yes	complemented
23	C₂×D₈×D₆₇	C₄	1	1	yes	characteristic, complemented
24	C₂×#14524051	—	2	2	no	—
25	C₂×#14524051	C₂²	1	2	yes	complemented
26	C₂×#14524050	C₂²	1	2	yes	complemented
27	C₂×#14524049	—	2	2	no	—
28	C₂×#14524049	C₂²	1	2	yes	complemented
29	#131×D₆₇	—	2	8	no	—
30	#131×D₆₇	C₂²	1	16	yes	complemented
31	C₂×M₁₆×D₆₇	—	2	2	no	—
32	C₂×M₁₆×D₆₇	C₂²	1	2	yes	—
33	C₂²×C₈×D₆₇	—	2	2	no	—
34	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
37	#16863519	C₂²	1	8	yes	complemented
38	#16863518	C₂²	1	8	yes	complemented
39	#16863517	C₂²	1	8	yes	complemented
40	#16863516	C₂²	1	16	yes	complemented
41	#16863515	C₂²	1	16	yes	complemented
42	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14523978	C₂²	1	2	yes	complemented
44	#108×D₆₇	C₂²	1	8	yes	complemented
45	C₂×#14523971	C₂²	1	2	yes	complemented
46	C₂×#14523970	C₂²	1	2	yes	complemented
47	C₂×#14523969	C₂²	1	2	yes	complemented
48	#104×D₆₇	C₂²	1	16	yes	complemented
49	C₂×#14523954	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14523953	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14523953	C₂²	1	1	yes	characteristic, complemented
52	#97×D₆₇	C₂²	1	8	yes	complemented
53	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
55	#444×C₆₇	C₂²	1	8	yes	complemented
56	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
58	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#11761629	C₂×C₄	1	2	yes	—
60	C₂×#11761628	—	2	2	no	—
61	C₂×#11761628	C₂³	1	2	yes	—
62	C₂×#11761627	—	2	2	no	—
63	C₂×#11761627	C₂×C₄	1	2	yes	—
64	#41×D₆₇	—	2	4	no	—
65	#41×D₆₇	—	2	4	no	—
66	#41×D₆₇	C₂×C₄	1	8	yes	—
67	#41×D₆₇	C₂³	1	8	yes	—
68	C₂×Q₈×D₆₇	C₂×C₄	1	2	yes	—
69	C₂×D₄×D₆₇	—	2	2	no	—
70	C₂×D₄×D₆₇	C₂×C₄	1	2	yes	—
71	C₂²×C₄×D₆₇	—	2	2	no	—
72	C₂²×C₄×D₆₇	—	2	1	no	—
73	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
74	#14524066	C₂×C₄	1	8	yes	complemented
75	#14524065	C₂×C₄	1	4	yes	complemented
76	#14524065	C₂³	1	4	yes	—
77	#14524064	C₂×C₄	1	16	yes	complemented
78	#14524063	C₂×C₄	1	8	yes	complemented
79	#14524063	C₂³	1	8	yes	—
80	#14524062	C₂×C₄	1	8	yes	complemented
81	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×#11761618	C₂×C₄	1	2	yes	complemented
83	Q₁₆×D₆₇	C₂×C₄	1	8	yes	complemented
84	C₂×#11761617	C₂×C₄	1	2	yes	complemented
85	C₂×#11761616	C₂×C₄	1	2	yes	complemented
86	C₂×#11761615	C₂×C₄	1	2	yes	complemented
87	SD₁₆×D₆₇	C₂×C₄	1	16	yes	complemented
88	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂×#11761613	C₂×C₄	1	2	yes	complemented
90	D₈×D₆₇	C₂×C₄	1	8	yes	complemented
91	#14524051	—	2	4	no	—
92	#14524051	—	2	16	no	—
93	#14524051	C₂³	1	8	yes	complemented
94	#14524050	—	2	4	no	—
95	#14524050	C₂³	1	8	yes	complemented
96	#14524049	—	2	16	no	—
97	#14524049	—	2	4	no	—
98	#14524049	C₂³	1	8	yes	complemented
99	C₂×#11761612	—	2	2	no	—
100	C₂×#11761612	C₂³	1	2	yes	—
101	C₂×#11761611	—	2	2	no	—
102	C₂×#11761611	—	2	2	no	—
103	C₂×#11761611	—	2	2	no	—
104	M₁₆×D₆₇	—	2	4	no	—
105	M₁₆×D₆₇	—	2	16	no	—
106	M₁₆×D₆₇	C₂³	1	8	yes	—
107	C₂²×C₆₇⋊C₈	—	2	2	no	—
108	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₈×D₆₇	—	2	2	no	—
111	C₂×C₈×D₆₇	—	2	2	no	—
112	C₂×C₈×D₆₇	—	2	16	no	—
113	C₂×C₈×D₆₇	—	2	2	no	—
114	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₈×D₆₇	C₂×C₄	1	4	yes	—
117	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₈×D₆₇	D₄	1	2	yes	—
120	C₂×C₈×D₆₇	D₄	1	4	yes	—
121	C₂×C₈×D₆₇	D₄	1	2	yes	—
122	C₂×C₈×D₆₇	C₂³	1	4	yes	—
123	C₂×C₈×D₆₇	C₂³	1	4	yes	—
124	C₂×C₄×Dic₆₇	—	2	1	no	—
125	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
126	C₄²×D₆₇	—	2	2	no	—
127	C₄²×D₆₇	C₂³	1	4	yes	—
128	#14523979	C₂³	1	4	yes	complemented
129	#14523978	C₂³	1	8	yes	complemented
130	#14523971	C₂³	1	8	yes	complemented
131	#14523970	C₂³	1	8	yes	complemented
132	#14523969	C₂³	1	8	yes	complemented
133	#14523954	C₂³	1	4	yes	complemented
134	#14523953	C₂³	1	4	yes	complemented
135	#14523953	C₂³	1	4	yes	complemented
136	C₂×#41×C₆₇	C₂³	1	2	yes	—
137	#135×C₆₇	C₂×C₄	1	4	yes	complemented
138	#135×C₆₇	C₂³	1	4	yes	—
139	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
140	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
141	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
142	#131×C₆₇	—	2	4	no	—
143	#131×C₆₇	C₂³	1	8	yes	complemented
144	C₂×M₁₆×C₆₇	—	2	2	no	—
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂²×C₈×C₆₇	—	2	2	no	—
147	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
150	#108×C₆₇	C₂³	1	4	yes	complemented
151	#104×C₆₇	C₂³	1	8	yes	complemented
152	#97×C₆₇	C₂³	1	4	yes	complemented
153	C₂³×D₆₇	—	2	2	no	—
154	C₂³×D₆₇	#41	1	1	yes	characteristic
155	#11761629	—	2	4	no	—
156	#11761629	C₂²×C₄	1	8	yes	—
157	#11761628	—	2	2	no	—
158	#11761628	—	2	2	no	—
159	#11761628	—	2	8	no	—
160	#11761628	—	2	8	no	—
161	#11761628	C₂²×C₄	1	4	yes	—
162	#11761628	C₂⁴	1	4	yes	—
163	#11761627	—	2	8	no	—
164	#11761627	—	2	8	no	—
165	#11761627	—	2	4	no	—
166	#11761627	C₂²×C₄	1	8	yes	—
167	C₂×Dic₁₃₄	—	2	2	no	—
168	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
169	Q₈×D₆₇	—	2	4	no	—
170	Q₈×D₆₇	C₂²×C₄	1	8	yes	—
171	C₂×D₂₆₈	—	2	2	no	—
172	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
173	C₂×C₂²⋊D₆₇	—	2	2	no	—
174	C₂×C₂²⋊D₆₇	—	2	2	no	—
175	C₂×C₂²⋊D₆₇	—	2	2	no	—
176	D₄×D₆₇	—	2	8	no	—
177	D₄×D₆₇	—	2	8	no	—
178	D₄×D₆₇	—	2	4	no	—
179	D₄×D₆₇	C₂²×C₄	1	8	yes	—
180	C₂²×Dic₆₇	—	2	2	no	—
181	C₂²×Dic₆₇	—	2	1	no	—
182	C₂²×Dic₆₇	#41	1	1	yes	characteristic
183	C₂×C₄×D₆₇	—	2	2	no	—
184	C₂×C₄×D₆₇	—	2	2	no	—
185	C₂×C₄×D₆₇	—	2	2	no	—
186	C₂×C₄×D₆₇	—	2	8	no	—
187	C₂×C₄×D₆₇	—	2	8	no	—
188	C₂×C₄×D₆₇	—	2	4	no	—
189	C₂×C₄×D₆₇	—	4	4	no	—
190	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
192	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
195	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×D₆₇	#41	1	2	yes	—
197	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
198	Dic₂₆₈	C₂²×C₄	1	4	yes	complemented
199	#11761618	C₂²×C₄	1	8	yes	complemented
200	#11761617	C₂²×C₄	1	8	yes	complemented
201	#11761616	C₂²×C₄	1	8	yes	complemented
202	#11761615	C₂²×C₄	1	8	yes	complemented
203	D₅₃₆	C₂²×C₄	1	4	yes	complemented
204	#11761613	C₂²×C₄	1	8	yes	complemented
205	#11761612	—	2	2	no	—
206	#11761612	—	2	8	no	—
207	#11761612	C₂⁴	1	4	yes	—
208	#11761611	—	2	8	no	—
209	#11761611	—	2	8	no	—
210	#11761611	—	2	8	no	—
211	C₂×C₆₇⋊C₈	—	2	2	no	—
212	C₂×C₆₇⋊C₈	—	2	8	no	—
213	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
216	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
217	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
218	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
219	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
220	C₈×D₆₇	—	2	8	no	—
221	C₈×D₆₇	—	2	8	no	—
222	C₈×D₆₇	—	2	8	no	—
223	C₈×D₆₇	C₂²×C₄	1	4	yes	—
224	C₈×D₆₇	C₂²×C₄	1	4	yes	—
225	C₈×D₆₇	C₂²×C₄	1	4	yes	—
226	C₈×D₆₇	C₂²×C₄	1	4	yes	—
227	C₈×D₆₇	C₂×D₄	1	8	yes	—
228	C₈×D₆₇	C₂×D₄	1	8	yes	—
229	C₄×Dic₆₇	—	2	1	no	—
230	C₄×Dic₆₇	—	2	4	no	—
231	C₄×Dic₆₇	C₂⁴	1	2	yes	—
232	#41×C₆₇	—	2	2	no	—
233	#41×C₆₇	—	2	2	no	—
234	#41×C₆₇	C₂²×C₄	1	4	yes	—
235	#41×C₆₇	C₂⁴	1	4	yes	—
236	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
237	C₂×D₄×C₆₇	—	2	2	no	—
238	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₆₇	C₂²×C₄	1	4	yes	complemented
243	SD₁₆×C₆₇	C₂²×C₄	1	8	yes	complemented
244	D₈×C₆₇	C₂²×C₄	1	4	yes	complemented
245	M₁₆×C₆₇	—	2	2	no	—
246	M₁₆×C₆₇	—	2	8	no	—
247	M₁₆×C₆₇	C₂⁴	1	4	yes	—
248	C₂×C₈×C₆₇	—	2	2	no	—
249	C₂×C₈×C₆₇	—	2	8	no	—
250	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
253	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
254	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
255	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
257	C₄²×C₆₇	—	2	1	no	—
258	C₄²×C₆₇	C₂⁴	1	2	yes	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
261	C₂²×D₆₇	—	2	4	no	—
262	C₂²×D₆₇	—	2	2	no	—
263	C₂²×D₆₇	—	2	8	no	—
264	C₂²×D₆₇	—	4	8	no	—
265	C₂²×D₆₇	C₄×D₄	1	2	yes	—
266	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
267	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
268	C₂²×D₆₇	C₂×#41	1	2	yes	—
269	Q₈×C₆₇	—	2	2	no	—
270	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
271	D₄×C₆₇	—	2	4	no	—
272	D₄×C₆₇	—	2	4	no	—
273	D₄×C₆₇	—	2	2	no	—
274	D₄×C₆₇	C₂³×C₄	1	4	yes	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	4	no	—
277	C₂×C₄×C₆₇	—	2	4	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	4	2	no	—
280	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
281	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
286	C₂²⋊D₆₇	—	2	4	no	—
287	C₂²⋊D₆₇	—	2	4	no	—
288	C₂²⋊D₆₇	—	2	8	no	—
289	C₂²⋊D₆₇	—	2	8	no	—
290	C₂×Dic₆₇	—	2	2	no	—
291	C₂×Dic₆₇	—	2	8	no	—
292	C₂×Dic₆₇	—	2	2	no	—
293	C₂×Dic₆₇	—	4	2	no	—
294	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
295	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
296	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
297	C₂×Dic₆₇	C₂×#41	1	2	yes	—
298	D₂₆₈	—	2	8	no	—
299	D₂₆₈	—	2	2	no	—
300	D₂₆₈	C₂³×C₄	1	4	yes	—
301	C₄×D₆₇	—	2	8	no	—
302	C₄×D₆₇	—	2	4	no	—
303	C₄×D₆₇	—	2	4	no	—
304	C₄×D₆₇	—	2	8	no	—
305	C₄×D₆₇	—	4	8	no	—
306	C₄×D₆₇	C₄×D₄	1	2	yes	—
307	C₄×D₆₇	C₄×D₄	1	2	yes	—
308	C₄×D₆₇	C₄×D₄	1	2	yes	—
309	C₄×D₆₇	C₄×D₄	1	2	yes	—
310	C₄×D₆₇	C₂³×C₄	1	2	yes	—
311	C₄×D₆₇	C₂³×C₄	1	2	yes	—
312	C₄×D₆₇	C₂²×D₄	1	2	yes	—
313	C₄×D₆₇	C₂²×D₄	1	2	yes	—
314	Dic₁₃₄	—	2	2	no	—
315	Dic₁₃₄	—	2	8	no	—
316	Dic₁₃₄	C₂³×C₄	1	4	yes	—
317	C₈×C₆₇	—	2	4	no	—
318	C₈×C₆₇	C₂³×C₄	1	2	yes	—
319	C₈×C₆₇	C₂³×C₄	1	2	yes	—
320	C₈×C₆₇	C₂²×D₄	1	4	yes	—
321	C₆₇⋊C₈	—	2	4	no	—
322	C₆₇⋊C₈	C₂³×C₄	1	2	yes	—
323	C₆₇⋊C₈	C₂³×C₄	1	2	yes	—
324	C₆₇⋊C₈	C₂²×D₄	1	4	yes	—
325	C₂²×C₆₇	—	2	2	no	—
326	C₂²×C₆₇	—	2	4	no	—
327	C₂²×C₆₇	—	4	4	no	—
328	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
330	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
331	C₂×D₆₇	—	2	2	no	—
332	C₂×D₆₇	—	2	4	no	—
333	C₂×D₆₇	—	2	4	no	—
334	C₂×D₆₇	—	2	4	no	—
335	C₂×D₆₇	—	4	4	no	—
336	C₂×D₆₇	—	4	16	no	—
337	C₂×D₆₇	#444	1	4	yes	direct product factor
338	C₂×D₆₇	C₂×C₄×D₄	1	2	yes	—
339	C₂×D₆₇	C₂×C₄×D₄	1	2	yes	—
340	C₄×C₆₇	—	2	4	no	—
341	C₄×C₆₇	—	4	2	no	—
342	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
343	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
344	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
345	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
346	Dic₆₇	—	2	4	no	—
347	Dic₆₇	—	4	2	no	—
348	Dic₆₇	C₂×C₄×D₄	1	2	yes	—
349	Dic₆₇	C₂×C₄×D₄	1	2	yes	—
350	C₂²×#444	—	67	1	no	maximal, Sylow
351	C₂×C₆₇	—	2	1	no	—
352	C₂×C₆₇	—	2	1	no	—
353	C₂×C₆₇	—	4	4	no	—
354	C₂×C₆₇	C₂×#444	1	2	yes	complemented
355	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
356	D₆₇	—	2	2	no	—
357	D₆₇	—	4	4	no	—
358	D₆₇	C₂×#444	1	4	yes	direct product factor
359	C₂²×#135	—	67	1	no	—
360	C₂²×#131	—	67	2	no	—
361	C₂×#444	—	67	16	no	—
362	C₂×#444	—	67	1	no	—
363	C₂×#444	—	67	2	no	—
364	C₂×#444	—	67	1	no	—
365	C₂×#444	—	67	1	no	—
366	C₂×#444	—	67	2	no	—
367	C₂×#444	D₆₇	1	1	yes	characteristic, direct product factor
368	C₂²×#108	—	67	1	no	—
369	C₂²×#104	—	67	2	no	—
370	C₂²×#97	—	67	1	no	—
371	C₆₇	C₂²×#444	1	1	yes	characteristic, complemented, Sylow
372	C₂²×#41	—	67	2	no	—
373	C₂×#135	—	67	2	no	—
374	C₂×#135	—	67	8	no	—
375	C₂×#135	—	67	8	no	—
376	C₂×#135	—	67	1	no	—
377	C₂×#135	—	67	2	no	—
378	C₂×#135	—	67	1	no	—
379	C₂×#135	—	67	1	no	—
380	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
381	C₂²×Q₁₆	—	67	1	no	—
382	C₂²×SD₁₆	—	67	2	no	—
383	C₂²×D₈	—	67	1	no	—
384	C₂×#131	—	67	2	no	—
385	C₂×#131	—	67	16	no	—
386	C₂×#131	—	67	2	no	—
387	C₂×#131	—	67	2	no	—
388	C₂×#131	—	134	2	no	—
389	C₂×#131	—	134	2	no	—
390	C₂×#131	—	134	8	no	—
391	C₂×#131	C₂×D₆₇	1	2	yes	complemented
392	C₂²×M₁₆	—	67	2	no	—
393	C₂²×M₁₆	—	134	2	no	—
394	C₂³×C₈	—	67	1	no	—
395	C₂³×C₈	—	67	1	no	—
396	C₂³×C₈	—	134	2	no	—
397	C₂²×C₄²	—	67	1	no	—
398	#444	—	67	8	no	—
399	#444	—	67	16	no	—
400	#444	—	67	8	no	—
401	#444	—	67	16	no	—
402	#444	—	67	8	no	—
403	#444	C₂×D₆₇	1	8	yes	direct product factor
404	C₂×#108	—	67	2	no	—
405	C₂×#108	—	67	1	no	—
406	C₂×#108	—	67	8	no	—
407	C₂×#108	C₂×D₆₇	1	1	yes	characteristic, complemented
408	C₂×#104	—	67	2	no	—
409	C₂×#104	—	67	2	no	—
410	C₂×#104	—	67	2	no	—
411	C₂×#104	—	67	16	no	—
412	C₂×#104	C₂×D₆₇	1	2	yes	complemented
413	C₂×#97	—	67	1	no	—
414	C₂×#97	—	67	1	no	—
415	C₂×#97	—	67	1	no	—
416	C₂×#97	—	67	8	no	—
417	C₂×#97	C₂×D₆₇	1	1	yes	characteristic, complemented
418	C₂×#41	—	67	8	no	—
419	C₂×#41	—	67	8	no	—
420	C₂×#41	—	67	2	no	—
421	C₂×#41	—	67	2	no	—
422	C₂×#41	—	67	2	no	—
423	C₂×#41	—	134	2	no	—
424	C₂×#41	—	134	2	no	—
425	C₂×#41	—	134	4	no	—
426	C₂×#41	—	134	4	no	—
427	C₂×#41	C₂²×D₆₇	1	2	yes	—
428	C₂²×Q₈	—	67	2	no	—
429	C₂²×D₄	—	67	2	no	—
430	C₂²×D₄	—	134	2	no	—
431	C₂³×C₄	—	67	1	no	—
432	C₂³×C₄	—	134	1	no	—
433	C₂³×C₄	—	134	2	no	—
434	#135	—	67	8	no	—
435	#135	—	67	8	no	—
436	#135	—	67	8	no	—
437	#135	—	67	16	no	—
438	#135	—	67	8	no	—
439	#135	—	67	4	no	—
440	#135	—	67	4	no	—
441	#135	C₄×D₆₇	1	4	yes	complemented
442	#135	C₂²×D₆₇	1	4	yes	—
443	C₂×Q₁₆	—	67	2	no	—
444	C₂×Q₁₆	—	67	8	no	—
445	C₂×Q₁₆	—	67	1	no	—
446	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic, complemented
447	C₂×SD₁₆	—	67	2	no	—
448	C₂×SD₁₆	—	67	2	no	—
449	C₂×SD₁₆	—	67	16	no	—
450	C₂×SD₁₆	—	67	2	no	—
451	C₂×SD₁₆	C₄×D₆₇	1	2	yes	complemented
452	C₂×D₈	—	67	2	no	—
453	C₂×D₈	—	67	8	no	—
454	C₂×D₈	—	67	1	no	—
455	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic, complemented
456	#131	—	2	4	no	—
457	#131	—	67	8	no	—
458	#131	—	67	8	no	—
459	#131	—	67	8	no	—
460	#131	—	134	16	no	—
461	#131	—	134	4	no	—
462	#131	—	134	16	no	—
463	#131	—	134	4	no	—
464	#131	—	134	4	no	—
465	#131	C₂²×D₆₇	1	8	yes	complemented
466	C₂×M₁₆	—	2	2	no	—
467	C₂×M₁₆	—	67	2	no	—
468	C₂×M₁₆	—	67	8	no	—
469	C₂×M₁₆	—	134	2	no	—
470	C₂×M₁₆	—	134	2	no	—
471	C₂×M₁₆	—	134	16	no	—
472	C₂×M₁₆	—	134	2	no	—
473	C₂×M₁₆	—	134	4	no	—
474	C₂×M₁₆	—	134	2	no	—
475	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
476	C₂²×C₈	—	2	2	no	—
477	C₂²×C₈	—	67	1	no	—
478	C₂²×C₈	—	67	1	no	—
479	C₂²×C₈	—	67	1	no	—
480	C₂²×C₈	—	67	1	no	—
481	C₂²×C₈	—	67	1	no	—
482	C₂²×C₈	—	67	1	no	—
483	C₂²×C₈	—	67	4	no	—
484	C₂²×C₈	—	67	2	no	—
485	C₂²×C₈	—	67	4	no	—
486	C₂²×C₈	—	67	2	no	—
487	C₂²×C₈	—	67	4	no	—
488	C₂²×C₈	—	67	4	no	—
489	C₂²×C₈	—	134	2	no	—
490	C₂²×C₈	—	134	16	no	—
491	C₂²×C₈	—	134	2	no	—
492	C₂²×C₈	—	134	2	no	—
493	C₂²×C₈	—	134	2	no	—
494	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
495	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
496	C₂×C₄²	—	67	1	no	—
497	C₂×C₄²	—	67	4	no	—
498	C₂×C₄²	—	134	2	no	—
499	C₂×C₄²	—	134	1	no	—
500	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
501	#108	—	67	8	no	—
502	#108	—	67	4	no	—
503	#108	C₂²×D₆₇	1	4	yes	complemented
504	#104	—	67	8	no	—
505	#104	—	67	8	no	—
506	#104	—	67	8	no	—
507	#104	C₂²×D₆₇	1	8	yes	complemented
508	#97	—	67	4	no	—
509	#97	—	67	4	no	—
510	#97	—	67	4	no	—
511	#97	C₂²×D₆₇	1	4	yes	complemented
512	C₂⁴	—	67	1	no	—
513	C₂⁴	—	134	2	no	—
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	#41	—	67	8	no	—
517	#41	—	67	8	no	—
518	#41	—	67	4	no	—
519	#41	—	67	4	no	—
520	#41	—	134	8	no	—
521	#41	—	134	8	no	—
522	#41	—	134	8	no	—
523	#41	—	134	8	no	—
524	#41	—	134	4	no	—
525	#41	—	134	4	no	—
526	#41	—	134	2	no	—
527	#41	—	134	2	no	—
528	#41	C₂×C₄×D₆₇	1	4	yes	—
529	#41	C₂³×D₆₇	1	4	yes	—
530	C₂×Q₈	—	67	8	no	—
531	C₂×Q₈	—	67	2	no	—
532	C₂×Q₈	—	134	2	no	—
533	C₂×Q₈	—	134	4	no	—
534	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	67	8	no	—
537	C₂×D₄	—	67	2	no	—
538	C₂×D₄	—	134	2	no	—
539	C₂×D₄	—	134	4	no	—
540	C₂×D₄	—	134	2	no	—
541	C₂×D₄	—	134	8	no	—
542	C₂×D₄	—	134	8	no	—
543	C₂×D₄	—	134	2	no	—
544	C₂×D₄	—	134	2	no	—
545	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	268	4	no	—
549	C₂²×C₄	—	67	1	no	—
550	C₂²×C₄	—	67	1	no	—
551	C₂²×C₄	—	67	1	no	—
552	C₂²×C₄	—	67	2	no	—
553	C₂²×C₄	—	67	2	no	—
554	C₂²×C₄	—	67	1	no	—
555	C₂²×C₄	—	67	1	no	—
556	C₂²×C₄	—	67	2	no	—
557	C₂²×C₄	—	67	2	no	—
558	C₂²×C₄	—	134	4	no	—
559	C₂²×C₄	—	134	8	no	—
560	C₂²×C₄	—	134	2	no	—
561	C₂²×C₄	—	134	8	no	—
562	C₂²×C₄	—	134	2	no	—
563	C₂²×C₄	—	134	1	no	—
564	C₂²×C₄	—	134	2	no	—
565	C₂²×C₄	—	134	2	no	—
566	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
567	Q₁₆	—	67	8	no	—
568	Q₁₆	—	67	4	no	—
569	Q₁₆	C₂×C₄×D₆₇	1	4	yes	complemented
570	SD₁₆	—	67	8	no	—
571	SD₁₆	—	67	8	no	—
572	SD₁₆	—	67	8	no	—
573	SD₁₆	C₂×C₄×D₆₇	1	8	yes	complemented
574	D₈	—	67	8	no	—
575	D₈	—	67	4	no	—
576	D₈	C₂×C₄×D₆₇	1	4	yes	complemented
577	M₁₆	—	2	2	no	—
578	M₁₆	—	2	8	no	—
579	M₁₆	—	67	4	no	—
580	M₁₆	—	134	8	no	—
581	M₁₆	—	134	8	no	—
582	M₁₆	—	134	8	no	—
583	M₁₆	—	134	2	no	—
584	M₁₆	—	134	8	no	—
585	M₁₆	C₂³×D₆₇	1	4	yes	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	8	no	—
588	C₂×C₈	—	67	1	no	—
589	C₂×C₈	—	67	1	no	—
590	C₂×C₈	—	67	2	no	—
591	C₂×C₈	—	67	2	no	—
592	C₂×C₈	—	67	2	no	—
593	C₂×C₈	—	67	2	no	—
594	C₂×C₈	—	67	2	no	—
595	C₂×C₈	—	67	4	no	—
596	C₂×C₈	—	67	4	no	—
597	C₂×C₈	—	67	4	no	—
598	C₂×C₈	—	67	4	no	—
599	C₂×C₈	—	67	8	no	—
600	C₂×C₈	—	67	8	no	—
601	C₂×C₈	—	134	8	no	—
602	C₂×C₈	—	134	8	no	—
603	C₂×C₈	—	134	8	no	—
604	C₂×C₈	—	134	2	no	—
605	C₂×C₈	—	134	8	no	—
606	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
607	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
608	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
609	C₂×C₈	D₄×D₆₇	1	2	yes	—
610	C₂×C₈	D₄×D₆₇	1	2	yes	—
611	C₂×C₈	C₂³×D₆₇	1	2	yes	—
612	C₂×C₈	C₂³×D₆₇	1	2	yes	—
613	C₄²	—	2	1	no	—
614	C₄²	—	67	2	no	—
615	C₄²	—	134	4	no	—
616	C₄²	—	134	1	no	—
617	C₄²	C₂³×D₆₇	1	2	yes	—
618	C₂³	—	2	2	no	—
619	C₂³	—	268	8	no	—
620	C₂³	—	67	1	no	—
621	C₂³	—	67	2	no	—
622	C₂³	—	67	1	no	—
623	C₂³	—	67	2	no	—
624	C₂³	—	134	8	no	—
625	C₂³	—	134	4	no	—
626	C₂³	—	134	2	no	—
627	C₂³	#41×D₆₇	1	1	yes	characteristic
628	Q₈	—	2	2	no	—
629	Q₈	—	67	4	no	—
630	Q₈	—	134	8	no	—
631	Q₈	—	134	2	no	—
632	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
633	D₄	—	2	4	no	—
634	D₄	—	2	4	no	—
635	D₄	—	2	2	no	—
636	D₄	—	67	4	no	—
637	D₄	—	134	8	no	—
638	D₄	—	134	8	no	—
639	D₄	—	134	8	no	—
640	D₄	—	134	4	no	—
641	D₄	—	134	4	no	—
642	D₄	—	134	2	no	—
643	D₄	C₂²×C₄×D₆₇	1	4	yes	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	268	8	no	—
650	C₂×C₄	—	268	2	no	—
651	C₂×C₄	—	67	1	no	—
652	C₂×C₄	—	67	1	no	—
653	C₂×C₄	—	67	2	no	—
654	C₂×C₄	—	67	2	no	—
655	C₂×C₄	—	67	2	no	—
656	C₂×C₄	—	67	2	no	—
657	C₂×C₄	—	67	2	no	—
658	C₂×C₄	—	67	2	no	—
659	C₂×C₄	—	67	2	no	—
660	C₂×C₄	—	67	2	no	—
661	C₂×C₄	—	67	2	no	—
662	C₂×C₄	—	67	2	no	—
663	C₂×C₄	—	134	8	no	—
664	C₂×C₄	—	134	8	no	—
665	C₂×C₄	—	134	2	no	—
666	C₂×C₄	—	134	8	no	—
667	C₂×C₄	—	134	2	no	—
668	C₂×C₄	—	134	4	no	—
669	C₂×C₄	—	134	4	no	—
670	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
671	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
672	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
673	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
674	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
675	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
676	C₈	—	2	4	no	—
677	C₈	—	67	2	no	—
678	C₈	—	67	2	no	—
679	C₈	—	67	4	no	—
680	C₈	—	134	4	no	—
681	C₈	C₂²×C₄×D₆₇	1	2	yes	—
682	C₈	C₂²×C₄×D₆₇	1	2	yes	—
683	C₈	C₂×D₄×D₆₇	1	4	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	268	16	no	—
688	C₂²	—	268	4	no	—
689	C₂²	—	67	2	no	—
690	C₂²	—	67	4	no	—
691	C₂²	—	67	2	no	—
692	C₂²	—	134	4	no	—
693	C₂²	—	134	4	no	—
694	C₂²	—	134	4	no	—
695	C₂²	—	134	2	no	—
696	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
697	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
698	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
699	C₄	—	2	4	no	—
700	C₄	—	4	2	no	—
701	C₄	—	268	2	no	—
702	C₄	—	67	2	no	—
703	C₄	—	67	2	no	—
704	C₄	—	134	4	no	—
705	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
706	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
707	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
708	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
709	C₂	—	2	1	no	—
710	C₂	—	2	1	no	—
711	C₂	—	4	4	no	—
712	C₂	—	268	4	no	—
713	C₂	—	67	4	no	—
714	C₂	—	134	2	no	—
715	C₂	#444×D₆₇	1	2	yes	direct product factor
716	C₂	C₂×C₄×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₂×#444×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×D₆₇	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂×#444	D₆₇
hypocenter	C₆₇	C₂²×#444
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×#131×D₆₇	C₂	semidirect
3. C₂×#16863519	C₂	semidirect
4. C₂×#16863518	C₂	semidirect
5. C₂×#16863517	C₂	semidirect
6. C₂×#16863516	C₂	semidirect
7. C₂×#16863515	C₂	semidirect
8. #444×D₆₇	C₂	direct (N × H)
9. C₂×#108×D₆₇	C₂	semidirect
10. C₂×#104×D₆₇	C₂	semidirect
11. C₂×#97×D₆₇	C₂	semidirect
12. C₂×#444×C₆₇	C₂	semidirect
14. C₂×#14524066	C₄	semidirect
16. C₂×#14524064	C₄	semidirect
18. C₂×#14524062	C₄	semidirect
19. #135×D₆₇	C₄	semidirect
21. C₂×Q₁₆×D₆₇	C₄	semidirect
22. C₂×SD₁₆×D₆₇	C₄	semidirect
23. C₂×D₈×D₆₇	C₄	semidirect
25. C₂×#14524051	C₂²	semidirect
26. C₂×#14524050	C₂²	semidirect
28. C₂×#14524049	C₂²	semidirect
30. #131×D₆₇	C₂²	semidirect
37. #16863519	C₂²	semidirect
38. #16863518	C₂²	semidirect
39. #16863517	C₂²	semidirect
40. #16863516	C₂²	semidirect
41. #16863515	C₂²	semidirect
42. C₂×#14523979	C₂²	semidirect
43. C₂×#14523978	C₂²	semidirect
44. #108×D₆₇	C₂²	semidirect
45. C₂×#14523971	C₂²	semidirect
46. C₂×#14523970	C₂²	semidirect
47. C₂×#14523969	C₂²	semidirect
48. #104×D₆₇	C₂²	semidirect
49. C₂×#14523954	C₂²	semidirect
50. C₂×#14523953	C₂²	semidirect
51. C₂×#14523953	C₂²	semidirect
52. #97×D₆₇	C₂²	semidirect
54. C₂×#131×C₆₇	C₂²	semidirect
55. #444×C₆₇	C₂²	semidirect
56. C₂×#108×C₆₇	C₂²	semidirect
57. C₂×#104×C₆₇	C₂²	semidirect
58. C₂×#97×C₆₇	C₂²	semidirect
74. #14524066	C₂×C₄	semidirect
75. #14524065	C₂×C₄	semidirect
77. #14524064	C₂×C₄	semidirect
78. #14524063	C₂×C₄	semidirect
80. #14524062	C₂×C₄	semidirect
81. C₂×Dic₂₆₈	C₂×C₄	semidirect
82. C₂×#11761618	C₂×C₄	semidirect
83. Q₁₆×D₆₇	C₂×C₄	semidirect
84. C₂×#11761617	C₂×C₄	semidirect
85. C₂×#11761616	C₂×C₄	semidirect
86. C₂×#11761615	C₂×C₄	semidirect
87. SD₁₆×D₆₇	C₂×C₄	semidirect
88. C₂×D₅₃₆	C₂×C₄	semidirect
89. C₂×#11761613	C₂×C₄	semidirect
90. D₈×D₆₇	C₂×C₄	semidirect
93. #14524051	C₂³	semidirect
95. #14524050	C₂³	semidirect
98. #14524049	C₂³	semidirect
128. #14523979	C₂³	semidirect
129. #14523978	C₂³	semidirect
130. #14523971	C₂³	semidirect
131. #14523970	C₂³	semidirect
132. #14523969	C₂³	semidirect
133. #14523954	C₂³	semidirect
134. #14523953	C₂³	semidirect
135. #14523953	C₂³	semidirect
137. #135×C₆₇	C₂×C₄	semidirect
139. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
140. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
141. C₂×D₈×C₆₇	C₂×C₄	semidirect
143. #131×C₆₇	C₂³	semidirect
150. #108×C₆₇	C₂³	semidirect
151. #104×C₆₇	C₂³	semidirect
152. #97×C₆₇	C₂³	semidirect
198. Dic₂₆₈	C₂²×C₄	semidirect
199. #11761618	C₂²×C₄	semidirect
200. #11761617	C₂²×C₄	semidirect
201. #11761616	C₂²×C₄	semidirect
202. #11761615	C₂²×C₄	semidirect
203. D₅₃₆	C₂²×C₄	semidirect
204. #11761613	C₂²×C₄	semidirect
242. Q₁₆×C₆₇	C₂²×C₄	semidirect
243. SD₁₆×C₆₇	C₂²×C₄	semidirect
244. D₈×C₆₇	C₂²×C₄	semidirect
337. C₂×D₆₇	#444	direct (N × H)
354. C₂×C₆₇	C₂×#444	semidirect
358. D₆₇	C₂×#444	direct (N × H)
367. C₂×#444	D₆₇	direct (N × H)
371. C₆₇	C₂²×#444	semidirect
391. C₂×#131	C₂×D₆₇	semidirect
403. #444	C₂×D₆₇	direct (N × H)
407. C₂×#108	C₂×D₆₇	semidirect
412. C₂×#104	C₂×D₆₇	semidirect
417. C₂×#97	C₂×D₆₇	semidirect
441. #135	C₄×D₆₇	semidirect
446. C₂×Q₁₆	C₄×D₆₇	semidirect
451. C₂×SD₁₆	C₄×D₆₇	semidirect
455. C₂×D₈	C₄×D₆₇	semidirect
465. #131	C₂²×D₆₇	semidirect
503. #108	C₂²×D₆₇	semidirect
507. #104	C₂²×D₆₇	semidirect
511. #97	C₂²×D₆₇	semidirect
569. Q₁₆	C₂×C₄×D₆₇	semidirect
573. SD₁₆	C₂×C₄×D₆₇	semidirect
576. D₈	C₂×C₄×D₆₇	semidirect
715. C₂	#444×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×#135×D₆₇	2
C₂×#131×D₆₇	2
C₂×#16863519	2
C₂×#16863518	2
C₂×#16863517	2
C₂×#16863516	2
C₂×#16863515	2
#444×D₆₇	2
C₂×#108×D₆₇	2
C₂×#104×D₆₇	2
C₂×#97×D₆₇	2
C₂×#444×C₆₇	2
C₂²×#444	67

Subgroups — C2×#444×D67 #31720124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#444×D₆₇ #31720124