Subgroups — C₂×C₆₇×#1937 #30700347

Order 17152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#424×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#104×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1937	C₂	1	8	yes	maximal, direct product factor
7	C₂×#341×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#339×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
16	#424×C₆₇	—	2	2	no	—
17	#424×C₆₇	C₂²	1	4	yes	complemented
18	C₂×C₄⋊C₈×C₆₇	—	2	2	no	—
19	C₂×#104×C₆₇	—	2	4	no	—
20	C₂×#104×C₆₇	C₂²	1	4	yes	—
21	#416×C₆₇	C₄	1	4	yes	complemented
22	#416×C₆₇	C₂²	1	4	yes	—
23	C₂×#103×C₆₇	C₄	1	2	yes	complemented
24	C₂×#102×C₆₇	C₄	1	2	yes	complemented
25	#408×C₆₇	—	2	2	no	—
26	#408×C₆₇	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₆₇	—	2	2	no	—
28	C₂×C₄×C₈×C₆₇	—	2	4	no	—
29	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	complemented
30	#341×C₆₇	C₂²	1	4	yes	complemented
31	#339×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#41×C₆₇	—	2	1	no	—
33	C₂×#41×C₆₇	—	2	1	no	—
34	C₂×#41×C₆₇	—	2	2	no	—
35	C₂×#41×C₆₇	—	2	2	no	—
36	C₂×#41×C₆₇	—	2	2	no	—
37	C₂×#41×C₆₇	—	2	2	no	—
38	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
39	C₂×#41×C₆₇	C₂³	1	2	yes	—
40	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₆₇	—	2	1	no	—
42	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	—	2	1	no	—
44	C₂³×C₄×C₆₇	—	2	1	no	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₆₇	—	2	1	no	—
47	C₂×M₁₆×C₆₇	—	2	1	no	—
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	2	2	no	—
50	C₂×M₁₆×C₆₇	—	2	2	no	—
51	C₂×M₁₆×C₆₇	—	2	2	no	—
52	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
53	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₇	—	2	2	no	—
55	C₂²×C₈×C₆₇	—	2	2	no	—
56	C₂²×C₈×C₆₇	—	2	2	no	—
57	C₂²×C₈×C₆₇	—	2	2	no	—
58	C₂²×C₈×C₆₇	—	2	1	no	—
59	C₂²×C₈×C₆₇	—	2	1	no	—
60	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₆₇	D₄	1	2	yes	—
63	C₂²×C₈×C₆₇	D₄	1	2	yes	—
64	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
65	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
66	#117×C₆₇	—	2	1	no	—
67	#117×C₆₇	—	2	1	no	—
68	#117×C₆₇	C₂×C₄	1	2	yes	—
69	#117×C₆₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
72	C₂×C₄²×C₆₇	—	2	1	no	—
73	C₂×C₄²×C₆₇	—	2	1	no	—
74	C₂×C₄²×C₆₇	—	2	2	no	—
75	C₂×C₄²×C₆₇	D₄	1	4	yes	—
76	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
77	C₄⋊C₈×C₆₇	—	2	8	no	—
78	#104×C₆₇	—	2	8	no	—
79	#103×C₆₇	C₂×C₄	1	8	yes	complemented
80	#102×C₆₇	C₂×C₄	1	8	yes	complemented
81	C₂²⋊C₈×C₆₇	—	2	8	no	—
82	C₄×C₈×C₆₇	—	2	8	no	—
83	C₂⁴×C₆₇	—	2	1	no	—
84	C₂⁴×C₆₇	#41	1	1	yes	characteristic
85	#41×C₆₇	—	2	4	no	—
86	#41×C₆₇	—	2	4	no	—
87	#41×C₆₇	—	2	2	no	—
88	#41×C₆₇	—	2	2	no	—
89	#41×C₆₇	—	2	2	no	—
90	#41×C₆₇	—	2	2	no	—
91	#41×C₆₇	—	4	2	no	—
92	#41×C₆₇	—	4	2	no	—
93	#41×C₆₇	—	4	2	no	—
94	#41×C₆₇	—	4	2	no	—
95	C₂×Q₈×C₆₇	—	2	1	no	—
96	C₂×Q₈×C₆₇	—	2	2	no	—
97	C₂×Q₈×C₆₇	—	2	2	no	—
98	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₆₇	—	2	2	no	—
100	C₂×D₄×C₆₇	—	2	2	no	—
101	C₂×D₄×C₆₇	—	2	2	no	—
102	C₂×D₄×C₆₇	—	2	2	no	—
103	C₂×D₄×C₆₇	—	2	1	no	—
104	C₂×D₄×C₆₇	—	4	2	no	—
105	C₂×D₄×C₆₇	—	4	2	no	—
106	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₆₇	—	2	8	no	—
108	C₂²×C₄×C₆₇	—	2	4	no	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	2	1	no	—
112	C₂²×C₄×C₆₇	—	2	2	no	—
113	C₂²×C₄×C₆₇	—	2	2	no	—
114	C₂²×C₄×C₆₇	—	4	2	no	—
115	C₂²×C₄×C₆₇	—	4	2	no	—
116	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	#41	1	2	yes	—
122	C₂²×C₄×C₆₇	#41	1	2	yes	—
123	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	#41	1	2	yes	—
125	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
126	M₁₆×C₆₇	—	2	2	no	—
127	M₁₆×C₆₇	—	2	2	no	—
128	M₁₆×C₆₇	—	2	2	no	—
129	M₁₆×C₆₇	—	2	2	no	—
130	M₁₆×C₆₇	—	4	2	no	—
131	M₁₆×C₆₇	—	4	2	no	—
132	C₂×C₈×C₆₇	—	2	4	no	—
133	C₂×C₈×C₆₇	—	2	4	no	—
134	C₂×C₈×C₆₇	—	2	4	no	—
135	C₂×C₈×C₆₇	—	2	4	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	—	2	2	no	—
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	4	2	no	—
143	C₂×C₈×C₆₇	—	4	2	no	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
145	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₆₇	—	2	2	no	—
147	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
148	C₂²⋊C₄×C₆₇	—	2	2	no	—
149	C₂²⋊C₄×C₆₇	—	2	2	no	—
150	C₄²×C₆₇	—	2	2	no	—
151	C₄²×C₆₇	—	2	4	no	—
152	C₄²×C₆₇	—	2	2	no	—
153	C₄²×C₆₇	—	2	2	no	—
154	C₄²×C₆₇	C₂×D₄	1	4	yes	—
155	C₂³×C₆₇	—	2	4	no	—
156	C₂³×C₆₇	—	2	2	no	—
157	C₂³×C₆₇	—	4	2	no	—
158	C₂³×C₆₇	—	4	4	no	—
159	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₆₇	#123	1	2	yes	—
162	C₂³×C₆₇	#126	1	2	yes	—
163	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₆₇	—	2	2	no	—
165	Q₈×C₆₇	—	2	2	no	—
166	Q₈×C₆₇	—	4	2	no	—
167	D₄×C₆₇	—	2	2	no	—
168	D₄×C₆₇	—	2	2	no	—
169	D₄×C₆₇	—	4	2	no	—
170	D₄×C₆₇	—	4	2	no	—
171	D₄×C₆₇	—	4	4	no	—
172	D₄×C₆₇	—	4	2	no	—
173	C₂×C₄×C₆₇	—	2	8	no	—
174	C₂×C₄×C₆₇	—	2	16	no	—
175	C₂×C₄×C₆₇	—	2	4	no	—
176	C₂×C₄×C₆₇	—	2	4	no	—
177	C₂×C₄×C₆₇	—	2	2	no	—
178	C₂×C₄×C₆₇	—	4	2	no	—
179	C₂×C₄×C₆₇	—	4	4	no	—
180	C₂×C₄×C₆₇	—	4	2	no	—
181	C₂×C₄×C₆₇	—	4	2	no	—
182	C₂×C₄×C₆₇	—	4	4	no	—
183	C₂×C₄×C₆₇	#117	1	2	yes	—
184	C₂×C₄×C₆₇	#117	1	2	yes	—
185	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₇	#121	1	2	yes	—
190	C₂×C₄×C₆₇	#121	1	2	yes	—
191	C₂×C₄×C₆₇	#123	1	2	yes	—
192	C₂×C₄×C₆₇	#124	1	2	yes	—
193	C₂×C₄×C₆₇	#124	1	2	yes	—
194	C₂×C₄×C₆₇	#126	1	2	yes	—
195	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
201	C₈×C₆₇	—	2	4	no	—
202	C₈×C₆₇	—	2	4	no	—
203	C₈×C₆₇	—	4	2	no	—
204	C₈×C₆₇	—	4	2	no	—
205	C₂²×C₆₇	—	2	2	no	—
206	C₂²×C₆₇	—	2	2	no	—
207	C₂²×C₆₇	—	2	4	no	—
208	C₂²×C₆₇	—	2	4	no	—
209	C₂²×C₆₇	—	4	4	no	—
210	C₂²×C₆₇	—	4	2	no	—
211	C₂²×C₆₇	—	8	4	no	—
212	C₂²×C₆₇	#388	1	2	yes	—
213	C₂²×C₆₇	#388	1	2	yes	—
214	C₂²×C₆₇	#443	1	4	yes	—
215	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
217	C₂²×C₆₇	C₂×#126	1	1	yes	characteristic
218	C₄×C₆₇	—	2	8	no	—
219	C₄×C₆₇	—	4	4	no	—
220	C₄×C₆₇	—	4	2	no	—
221	C₄×C₆₇	#388	1	2	yes	—
222	C₄×C₆₇	#388	1	2	yes	—
223	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
224	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
226	C₄×C₆₇	C₂×#124	1	1	yes	characteristic
227	C₂×#1937	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₆₇	—	2	1	no	—
229	C₂×C₆₇	—	2	1	no	—
230	C₂×C₆₇	—	2	2	no	—
231	C₂×C₆₇	—	8	2	no	—
232	C₂×C₆₇	#1937	1	4	yes	direct product factor
233	C₂×C₆₇	C₂×#388	1	1	yes	characteristic
234	C₂×C₆₇	C₂×#443	1	2	yes	—
235	C₂×#424	C₂×C₆₇	1	1	yes	characteristic, complemented
236	C₂²×#104	C₂×C₆₇	1	1	yes	characteristic
237	C₂×#416	C₂×C₆₇	1	1	yes	characteristic
238	C₂×#408	C₂×C₆₇	1	1	yes	characteristic
239	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
240	#1937	C₂×C₆₇	1	8	yes	direct product factor
241	C₂×#341	C₂×C₆₇	1	1	yes	characteristic, complemented
242	C₂×#339	C₂×C₆₇	1	1	yes	characteristic, complemented
243	C₆₇	C₂×#1937	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
245	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
247	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
249	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
250	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
251	#424	—	2	2	no	—
252	#424	C₂²×C₆₇	1	4	yes	complemented
253	C₂×C₄⋊C₈	—	2	2	no	—
254	C₂×#104	—	2	4	no	—
255	C₂×#104	C₂²×C₆₇	1	4	yes	—
256	#416	C₄×C₆₇	1	4	yes	complemented
257	#416	C₂²×C₆₇	1	4	yes	—
258	C₂×#103	C₄×C₆₇	1	2	yes	complemented
259	C₂×#102	C₄×C₆₇	1	2	yes	complemented
260	#408	—	2	2	no	—
261	#408	C₂²×C₆₇	1	4	yes	—
262	C₂×C₂²⋊C₈	—	2	2	no	—
263	C₂×C₄×C₈	—	2	4	no	—
264	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	complemented
265	#341	C₂²×C₆₇	1	4	yes	complemented
266	#339	C₂²×C₆₇	1	4	yes	complemented
267	C₂×#41	—	2	1	no	—
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
274	C₂×#41	C₂³×C₆₇	1	2	yes	—
275	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
288	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
296	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
297	C₂²×C₈	D₄×C₆₇	1	2	yes	—
298	C₂²×C₈	D₄×C₆₇	1	2	yes	—
299	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
300	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
301	#117	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	C₂×C₄×C₆₇	1	2	yes	—
304	#117	C₂³×C₆₇	1	2	yes	—
305	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	D₄×C₆₇	1	4	yes	—
311	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
312	C₄⋊C₈	—	2	8	no	—
313	#104	—	2	8	no	—
314	#103	C₂×C₄×C₆₇	1	8	yes	complemented
315	#102	C₂×C₄×C₆₇	1	8	yes	complemented
316	C₂²⋊C₈	—	2	8	no	—
317	C₄×C₈	—	2	8	no	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	#41×C₆₇	1	1	yes	characteristic
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
356	C₂²×C₄	#41×C₆₇	1	2	yes	—
357	C₂²×C₄	#41×C₆₇	1	2	yes	—
358	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
359	C₂²×C₄	#41×C₆₇	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	4	2	no	—
366	M₁₆	—	4	2	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
380	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂×D₄×C₆₇	1	4	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
395	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
396	C₂³	#123×C₆₇	1	2	yes	—
397	C₂³	#126×C₆₇	1	2	yes	—
398	C₂³	C₂×#41×C₆₇	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	4	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	#117×C₆₇	1	2	yes	—
419	C₂×C₄	#117×C₆₇	1	2	yes	—
420	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
422	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
423	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
424	C₂×C₄	#121×C₆₇	1	2	yes	—
425	C₂×C₄	#121×C₆₇	1	2	yes	—
426	C₂×C₄	#123×C₆₇	1	2	yes	—
427	C₂×C₄	#124×C₆₇	1	2	yes	—
428	C₂×C₄	#124×C₆₇	1	2	yes	—
429	C₂×C₄	#126×C₆₇	1	2	yes	—
430	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
436	C₈	—	2	4	no	—
437	C₈	—	2	4	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	4	no	—
447	C₂²	#388×C₆₇	1	2	yes	—
448	C₂²	#388×C₆₇	1	2	yes	—
449	C₂²	#443×C₆₇	1	4	yes	—
450	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
451	C₂²	C₂×#123×C₆₇	1	1	yes	characteristic
452	C₂²	C₂×#126×C₆₇	1	1	yes	characteristic
453	C₄	—	2	8	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	4	no	—
456	C₄	#388×C₆₇	1	2	yes	—
457	C₄	#388×C₆₇	1	2	yes	—
458	C₄	C₂×#117×C₆₇	1	1	yes	characteristic
459	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
460	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
461	C₄	C₂×#124×C₆₇	1	1	yes	characteristic
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	2	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₆₇×#1937	1	4	yes	direct product factor
467	C₂	C₂×#388×C₆₇	1	1	yes	characteristic
468	C₂	C₂×#443×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂³×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#424×C₆₇	C₂	semidirect
5. C₂²×C₄×C₈×C₆₇	C₂	semidirect
6. C₆₇×#1937	C₂	direct (N × H)
7. C₂×#341×C₆₇	C₂	semidirect
8. C₂×#339×C₆₇	C₂	semidirect
17. #424×C₆₇	C₂²	semidirect
21. #416×C₆₇	C₄	semidirect
23. C₂×#103×C₆₇	C₄	semidirect
24. C₂×#102×C₆₇	C₄	semidirect
29. C₂×C₄×C₈×C₆₇	C₂²	semidirect
30. #341×C₆₇	C₂²	semidirect
31. #339×C₆₇	C₂²	semidirect
79. #103×C₆₇	C₂×C₄	semidirect
80. #102×C₆₇	C₂×C₄	semidirect
227. C₂×#1937	C₆₇	direct (N × H)
232. C₂×C₆₇	#1937	direct (N × H)
235. C₂×#424	C₂×C₆₇	semidirect
239. C₂²×C₄×C₈	C₂×C₆₇	semidirect
240. #1937	C₂×C₆₇	direct (N × H)
241. C₂×#341	C₂×C₆₇	semidirect
242. C₂×#339	C₂×C₆₇	semidirect
243. C₆₇	C₂×#1937	direct (N × H)
252. #424	C₂²×C₆₇	semidirect
256. #416	C₄×C₆₇	semidirect
258. C₂×#103	C₄×C₆₇	semidirect
259. C₂×#102	C₄×C₆₇	semidirect
264. C₂×C₄×C₈	C₂²×C₆₇	semidirect
265. #341	C₂²×C₆₇	semidirect
266. #339	C₂²×C₆₇	semidirect
314. #103	C₂×C₄×C₆₇	semidirect
315. #102	C₂×C₄×C₆₇	semidirect
466. C₂	C₆₇×#1937	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×#424×C₆₇	2
C₂²×#104×C₆₇	2
C₂×#416×C₆₇	2
C₂×#408×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₆₇×#1937	2
C₂×#341×C₆₇	2
C₂×#339×C₆₇	2
C₂×#1937	67

Subgroups — C2×C67×#1937 #30700347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1937 #30700347