Subgroups — C₂×C₆₇×#1893 #30700217

Order 17152.

2438 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1893	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₆₇	—	2	1	no	—
8	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₆₇	—	2	4	no	—
11	C₂³×C₈×C₆₇	—	2	8	no	—
12	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
13	C₂³×C₈×C₆₇	C₂²	1	4	yes	complemented
14	C₂×#121×C₆₇	—	2	4	no	—
15	C₂×#121×C₆₇	—	2	2	no	—
16	C₂×#121×C₆₇	C₄	1	8	yes	complemented
17	C₂×#121×C₆₇	C₂²	1	4	yes	—
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
22	C₂×#102×C₆₇	—	2	8	no	—
23	C₂×#102×C₆₇	C₂²	1	8	yes	complemented
24	#380×C₆₇	—	2	2	no	—
25	#380×C₆₇	C₂²	1	4	yes	complemented
26	C₂×#95×C₆₇	—	2	1	no	—
27	#340×C₆₇	C₂²	1	8	yes	complemented
28	C₂⁵×C₆₇	—	2	1	no	—
29	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₆₇	—	2	8	no	—
31	C₂²×D₄×C₆₇	—	2	4	no	—
32	C₂²×D₄×C₆₇	—	2	4	no	—
33	C₂²×D₄×C₆₇	—	2	1	no	—
34	C₂²×D₄×C₆₇	—	2	2	no	—
35	C₂²×D₄×C₆₇	—	2	4	no	—
36	C₂²×D₄×C₆₇	—	4	4	no	—
37	C₂²×D₄×C₆₇	—	4	4	no	—
38	C₂²×D₄×C₆₇	C₂×C₄	1	4	yes	—
39	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₆₇	—	2	4	no	—
41	C₂³×C₄×C₆₇	—	2	4	no	—
42	C₂³×C₄×C₆₇	—	2	1	no	—
43	C₂³×C₄×C₆₇	—	2	2	no	—
44	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₆₇	D₄	1	2	yes	—
46	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₇	D₄	1	4	yes	—
48	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	—	2	32	no	—
51	C₂²×C₈×C₆₇	—	2	4	no	—
52	C₂²×C₈×C₆₇	—	2	4	no	—
53	C₂²×C₈×C₆₇	—	2	8	no	—
54	C₂²×C₈×C₆₇	—	2	16	no	—
55	C₂²×C₈×C₆₇	D₄	1	8	yes	complemented
56	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
57	#121×C₆₇	—	2	16	no	—
58	#121×C₆₇	—	2	8	no	—
59	#121×C₆₇	C₂×C₄	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
72	#102×C₆₇	—	2	16	no	—
73	#95×C₆₇	—	2	4	no	—
74	C₂⁴×C₆₇	—	2	4	no	—
75	C₂⁴×C₆₇	—	2	4	no	—
76	C₂⁴×C₆₇	—	2	4	no	—
77	C₂⁴×C₆₇	—	2	2	no	—
78	C₂⁴×C₆₇	—	4	4	no	—
79	C₂⁴×C₆₇	—	4	2	no	—
80	C₂⁴×C₆₇	—	4	2	no	—
81	C₂⁴×C₆₇	—	4	4	no	—
82	C₂⁴×C₆₇	C₂²⋊C₄	1	4	yes	—
83	C₂⁴×C₆₇	D₈	1	4	yes	—
84	C₂⁴×C₆₇	SD₁₆	1	4	yes	—
85	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
86	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
87	C₂×D₄×C₆₇	—	2	16	no	—
88	C₂×D₄×C₆₇	—	2	4	no	—
89	C₂×D₄×C₆₇	—	2	16	no	—
90	C₂×D₄×C₆₇	—	2	4	no	—
91	C₂×D₄×C₆₇	—	2	2	no	—
92	C₂×D₄×C₆₇	—	2	4	no	—
93	C₂×D₄×C₆₇	—	4	32	no	—
94	C₂×D₄×C₆₇	—	4	8	no	—
95	C₂×D₄×C₆₇	—	4	8	no	—
96	C₂×D₄×C₆₇	—	4	4	no	—
97	C₂×D₄×C₆₇	—	4	4	no	—
98	C₂×D₄×C₆₇	—	4	4	no	—
99	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	2	16	no	—
102	C₂²×C₄×C₆₇	—	2	8	no	—
103	C₂²×C₄×C₆₇	—	2	8	no	—
104	C₂²×C₄×C₆₇	—	2	8	no	—
105	C₂²×C₄×C₆₇	—	2	4	no	—
106	C₂²×C₄×C₆₇	—	2	4	no	—
107	C₂²×C₄×C₆₇	—	2	4	no	—
108	C₂²×C₄×C₆₇	—	2	2	no	—
109	C₂²×C₄×C₆₇	—	2	4	no	—
110	C₂²×C₄×C₆₇	—	4	2	no	—
111	C₂²×C₄×C₆₇	—	4	2	no	—
112	C₂²×C₄×C₆₇	—	4	4	no	—
113	C₂²×C₄×C₆₇	—	4	4	no	—
114	C₂²×C₄×C₆₇	—	4	4	no	—
115	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
116	C₂²×C₄×C₆₇	C₂²⋊C₄	1	8	yes	—
117	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₆₇	#41	1	4	yes	—
125	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
126	C₂×C₈×C₆₇	—	2	32	no	—
127	C₂×C₈×C₆₇	—	2	16	no	—
128	C₂×C₈×C₆₇	—	2	4	no	—
129	C₂×C₈×C₆₇	—	2	4	no	—
130	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	complemented
131	C₄⋊C₄×C₆₇	—	2	4	no	—
132	C₄⋊C₄×C₆₇	—	2	2	no	—
133	C₄⋊C₄×C₆₇	—	2	4	no	—
134	C₄⋊C₄×C₆₇	—	2	4	no	—
135	C₄⋊C₄×C₆₇	—	4	4	no	—
136	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
137	C₂²⋊C₄×C₆₇	—	2	16	no	—
138	C₂²⋊C₄×C₆₇	—	4	8	no	—
139	C₂³×C₆₇	—	2	4	no	—
140	C₂³×C₆₇	—	2	4	no	—
141	C₂³×C₆₇	—	2	8	no	—
142	C₂³×C₆₇	—	2	8	no	—
143	C₂³×C₆₇	—	2	16	no	—
144	C₂³×C₆₇	—	2	16	no	—
145	C₂³×C₆₇	—	2	4	no	—
146	C₂³×C₆₇	—	4	4	no	—
147	C₂³×C₆₇	—	4	2	no	—
148	C₂³×C₆₇	—	4	2	no	—
149	C₂³×C₆₇	—	4	4	no	—
150	C₂³×C₆₇	—	4	8	no	—
151	C₂³×C₆₇	—	4	8	no	—
152	C₂³×C₆₇	—	4	8	no	—
153	C₂³×C₆₇	—	8	8	no	—
154	C₂³×C₆₇	—	8	8	no	—
155	C₂³×C₆₇	#102	1	16	yes	complemented
156	C₂³×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
157	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂³×C₆₇	#121	1	4	yes	—
159	C₂³×C₆₇	C₂×D₈	1	4	yes	—
160	C₂³×C₆₇	C₂×D₈	1	2	yes	—
161	C₂³×C₆₇	C₂×SD₁₆	1	4	yes	—
162	C₂³×C₆₇	C₂×SD₁₆	1	2	yes	—
163	C₂³×C₆₇	#135	1	4	yes	—
164	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	D₄×C₆₇	—	2	8	no	—
166	D₄×C₆₇	—	4	32	no	—
167	D₄×C₆₇	—	4	2	no	—
168	D₄×C₆₇	—	4	2	no	—
169	D₄×C₆₇	—	4	8	no	—
170	C₂×C₄×C₆₇	—	2	4	no	—
171	C₂×C₄×C₆₇	—	2	8	no	—
172	C₂×C₄×C₆₇	—	2	8	no	—
173	C₂×C₄×C₆₇	—	2	4	no	—
174	C₂×C₄×C₆₇	—	2	4	no	—
175	C₂×C₄×C₆₇	—	2	16	no	—
176	C₂×C₄×C₆₇	—	2	4	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	—	4	2	no	—
179	C₂×C₄×C₆₇	—	4	8	no	—
180	C₂×C₄×C₆₇	—	4	4	no	—
181	C₂×C₄×C₆₇	—	4	4	no	—
182	C₂×C₄×C₆₇	—	4	4	no	—
183	C₂×C₄×C₆₇	—	8	8	no	—
184	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
187	C₂×C₄×C₆₇	#120	1	4	yes	—
188	C₂×C₄×C₆₇	#121	1	4	yes	—
189	C₂×C₄×C₆₇	#123	1	4	yes	—
190	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
194	C₈×C₆₇	—	2	8	no	—
195	C₂²×C₆₇	—	2	4	no	—
196	C₂²×C₆₇	—	2	32	no	—
197	C₂²×C₆₇	—	2	8	no	—
198	C₂²×C₆₇	—	2	8	no	—
199	C₂²×C₆₇	—	2	4	no	—
200	C₂²×C₆₇	—	4	4	no	—
201	C₂²×C₆₇	—	4	4	no	—
202	C₂²×C₆₇	—	4	4	no	—
203	C₂²×C₆₇	—	8	16	no	—
204	C₂²×C₆₇	—	8	4	no	—
205	C₂²×C₆₇	—	8	4	no	—
206	C₂²×C₆₇	#386	1	4	yes	—
207	C₂²×C₆₇	C₂×#102	1	4	yes	—
208	C₂²×C₆₇	C₂×#102	1	8	yes	complemented
209	C₂²×C₆₇	#416	1	4	yes	—
210	C₂²×C₆₇	#465	1	8	yes	—
211	C₂²×C₆₇	#466	1	8	yes	—
212	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₆₇	C₂×#121	1	2	yes	—
214	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
215	C₂²×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂²×C₆₇	C₂×#135	1	2	yes	—
217	C₄×C₆₇	—	2	4	no	—
218	C₄×C₆₇	—	4	4	no	—
219	C₄×C₆₇	—	8	4	no	—
220	C₄×C₆₇	#386	1	4	yes	—
221	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
222	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
223	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
224	C₂×#1893	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₆₇	—	2	8	no	—
226	C₂×C₆₇	—	8	4	no	—
227	C₂×C₆₇	#1893	1	8	yes	direct product factor
228	C₂×C₆₇	C₂×#386	1	1	yes	characteristic
229	C₂×C₆₇	C₂²×#102	1	1	yes	characteristic
230	C₂×C₆₇	C₂×#416	1	1	yes	characteristic
231	C₂×C₆₇	C₂×#465	1	2	yes	—
232	C₂×C₆₇	C₂×#466	1	2	yes	—
233	C₂⁴×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
234	C₂²×#121	C₂×C₆₇	1	1	yes	characteristic
235	C₂²×#102	C₂×C₆₇	1	2	yes	complemented
236	C₂×#380	C₂×C₆₇	1	1	yes	characteristic, complemented
237	#1893	C₂×C₆₇	1	8	yes	direct product factor
238	C₂×#340	C₂×C₆₇	1	2	yes	complemented
239	C₆₇	C₂×#1893	1	1	yes	characteristic, direct product factor, Sylow
240	C₂³×D₄	—	2	1	no	—
241	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
242	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
243	C₂³×C₈	—	2	4	no	—
244	C₂³×C₈	—	2	8	no	—
245	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
246	C₂³×C₈	C₂²×C₆₇	1	4	yes	complemented
247	C₂×#121	—	2	4	no	—
248	C₂×#121	—	2	2	no	—
249	C₂×#121	C₄×C₆₇	1	8	yes	complemented
250	C₂×#121	C₂²×C₆₇	1	4	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
252	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	—	2	1	no	—
254	C₂²×C₂²⋊C₄	—	2	1	no	—
255	C₂×#102	—	2	8	no	—
256	C₂×#102	C₂²×C₆₇	1	8	yes	complemented
257	#380	—	2	2	no	—
258	#380	C₂²×C₆₇	1	4	yes	complemented
259	C₂×#95	—	2	1	no	—
260	#340	C₂²×C₆₇	1	8	yes	complemented
261	C₂⁵	—	2	1	no	—
262	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	2	4	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	4	no	—
269	C₂²×D₄	—	4	4	no	—
270	C₂²×D₄	—	4	4	no	—
271	C₂²×D₄	C₂×C₄×C₆₇	1	4	yes	—
272	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
273	C₂³×C₄	—	2	4	no	—
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
278	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
279	C₂³×C₄	D₄×C₆₇	1	2	yes	—
280	C₂³×C₄	D₄×C₆₇	1	4	yes	—
281	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
282	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
283	C₂²×C₈	—	2	32	no	—
284	C₂²×C₈	—	2	4	no	—
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	—	2	8	no	—
287	C₂²×C₈	—	2	16	no	—
288	C₂²×C₈	D₄×C₆₇	1	8	yes	complemented
289	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
290	#121	—	2	16	no	—
291	#121	—	2	8	no	—
292	#121	C₂×C₄×C₆₇	1	16	yes	complemented
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	—	4	4	no	—
305	#102	—	2	16	no	—
306	#95	—	2	4	no	—
307	C₂⁴	—	2	4	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	—	4	4	no	—
312	C₂⁴	—	4	2	no	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	4	no	—
315	C₂⁴	C₂²⋊C₄×C₆₇	1	4	yes	—
316	C₂⁴	D₈×C₆₇	1	4	yes	—
317	C₂⁴	SD₁₆×C₆₇	1	4	yes	—
318	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
319	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	16	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	4	32	no	—
327	C₂×D₄	—	4	8	no	—
328	C₂×D₄	—	4	8	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	16	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
349	C₂²×C₄	C₂²⋊C₄×C₆₇	1	8	yes	—
350	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
351	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
354	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
357	C₂²×C₄	#41×C₆₇	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
359	C₂×C₈	—	2	32	no	—
360	C₂×C₈	—	2	16	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	complemented
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	4	8	no	—
372	C₂³	—	2	16	no	—
373	C₂³	—	2	16	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	8	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	8	no	—
386	C₂³	—	8	8	no	—
387	C₂³	—	8	8	no	—
388	C₂³	#102×C₆₇	1	16	yes	complemented
389	C₂³	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
390	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
391	C₂³	#121×C₆₇	1	4	yes	—
392	C₂³	C₂×D₈×C₆₇	1	4	yes	—
393	C₂³	C₂×D₈×C₆₇	1	2	yes	—
394	C₂³	C₂×SD₁₆×C₆₇	1	4	yes	—
395	C₂³	C₂×SD₁₆×C₆₇	1	2	yes	—
396	C₂³	#135×C₆₇	1	4	yes	—
397	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
398	D₄	—	2	8	no	—
399	D₄	—	4	32	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	8	8	no	—
417	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
419	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
420	C₂×C₄	#120×C₆₇	1	4	yes	—
421	C₂×C₄	#121×C₆₇	1	4	yes	—
422	C₂×C₄	#123×C₆₇	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
427	C₈	—	2	8	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	32	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	16	no	—
439	C₂²	#386×C₆₇	1	4	yes	—
440	C₂²	C₂×#102×C₆₇	1	4	yes	—
441	C₂²	C₂×#102×C₆₇	1	8	yes	complemented
442	C₂²	#416×C₆₇	1	4	yes	—
443	C₂²	#465×C₆₇	1	8	yes	—
444	C₂²	#466×C₆₇	1	8	yes	—
445	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
446	C₂²	C₂×#121×C₆₇	1	2	yes	—
447	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
448	C₂²	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
449	C₂²	C₂×#135×C₆₇	1	2	yes	—
450	C₄	—	2	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	8	4	no	—
453	C₄	#386×C₆₇	1	4	yes	—
454	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
455	C₄	C₂×#120×C₆₇	1	1	yes	characteristic
456	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
457	C₂	—	2	8	no	—
458	C₂	—	8	4	no	—
459	C₂	C₆₇×#1893	1	8	yes	direct product factor
460	C₂	C₂×#386×C₆₇	1	1	yes	characteristic
461	C₂	C₂²×#102×C₆₇	1	1	yes	characteristic
462	C₂	C₂×#416×C₆₇	1	1	yes	characteristic
463	C₂	C₂×#465×C₆₇	1	2	yes	—
464	C₂	C₂×#466×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×#121×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₈×C₆₇	C₂	semidirect
3. C₂²×#102×C₆₇	C₂	semidirect
4. C₂×#380×C₆₇	C₂	semidirect
5. C₆₇×#1893	C₂	direct (N × H)
6. C₂×#340×C₆₇	C₂	semidirect
13. C₂³×C₈×C₆₇	C₂²	semidirect
16. C₂×#121×C₆₇	C₄	semidirect
23. C₂×#102×C₆₇	C₂²	semidirect
25. #380×C₆₇	C₂²	semidirect
27. #340×C₆₇	C₂²	semidirect
55. C₂²×C₈×C₆₇	D₄	semidirect
59. #121×C₆₇	C₂×C₄	semidirect
130. C₂×C₈×C₆₇	C₂×D₄	semidirect
155. C₂³×C₆₇	#102	semidirect
208. C₂²×C₆₇	C₂×#102	semidirect
224. C₂×#1893	C₆₇	direct (N × H)
227. C₂×C₆₇	#1893	direct (N × H)
233. C₂⁴×C₈	C₂×C₆₇	semidirect
235. C₂²×#102	C₂×C₆₇	semidirect
236. C₂×#380	C₂×C₆₇	semidirect
237. #1893	C₂×C₆₇	direct (N × H)
238. C₂×#340	C₂×C₆₇	semidirect
239. C₆₇	C₂×#1893	direct (N × H)
246. C₂³×C₈	C₂²×C₆₇	semidirect
249. C₂×#121	C₄×C₆₇	semidirect
256. C₂×#102	C₂²×C₆₇	semidirect
258. #380	C₂²×C₆₇	semidirect
260. #340	C₂²×C₆₇	semidirect
288. C₂²×C₈	D₄×C₆₇	semidirect
292. #121	C₂×C₄×C₆₇	semidirect
363. C₂×C₈	C₂×D₄×C₆₇	semidirect
388. C₂³	#102×C₆₇	semidirect
441. C₂²	C₂×#102×C₆₇	semidirect
459. C₂	C₆₇×#1893	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₈×C₆₇	2
C₂²×#121×C₆₇	2
C₂²×#102×C₆₇	2
C₂×#380×C₆₇	2
C₆₇×#1893	2
C₂×#340×C₆₇	2
C₂×#1893	67

Subgroups — C2×C67×#1893 #30700217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1893 #30700217