Subgroups — C₂×C₆₇×#1892 #30700216

Order 17152.

2094 conjugacy classes of subgroups.

The subgroup lattice has 418 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
2	C₂²×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#103×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1892	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₇	—	2	4	no	—
10	C₂³×C₈×C₆₇	—	2	8	no	—
11	C₂³×C₈×C₆₇	C₂²	1	4	yes	—
12	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
13	C₂×C₂²⋊Q₈×C₆₇	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
15	C₂×C₂²⋊Q₈×C₆₇	C₄	1	8	yes	complemented
16	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
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×#103×C₆₇	—	2	8	no	—
23	C₂×#103×C₆₇	C₂²	1	8	yes	complemented
24	#380×C₆₇	—	2	2	no	—
25	#380×C₆₇	C₂²	1	4	yes	—
26	C₂×#95×C₆₇	—	2	1	no	—
27	#340×C₆₇	C₂²	1	8	yes	complemented
28	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
29	C₂²×Q₈×C₆₇	—	2	2	no	—
30	C₂²×Q₈×C₆₇	—	2	1	no	—
31	C₂²×Q₈×C₆₇	—	2	4	no	—
32	C₂²×Q₈×C₆₇	—	2	4	no	—
33	C₂²×Q₈×C₆₇	C₂×C₄	1	4	yes	—
34	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
35	C₂³×C₄×C₆₇	—	2	4	no	—
36	C₂³×C₄×C₆₇	—	2	4	no	—
37	C₂³×C₄×C₆₇	—	2	1	no	—
38	C₂³×C₄×C₆₇	—	2	1	no	—
39	C₂³×C₄×C₆₇	—	2	2	no	—
40	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₆₇	D₄	1	2	yes	—
42	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	D₄	1	4	yes	—
44	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₆₇	—	2	32	no	—
47	C₂²×C₈×C₆₇	—	2	8	no	—
48	C₂²×C₈×C₆₇	—	2	4	no	—
49	C₂²×C₈×C₆₇	—	2	4	no	—
50	C₂²×C₈×C₆₇	—	2	16	no	—
51	C₂²×C₈×C₆₇	D₄	1	8	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
53	C₂²⋊Q₈×C₆₇	—	2	16	no	—
54	C₂²⋊Q₈×C₆₇	—	2	8	no	—
55	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
56	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
57	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
70	#103×C₆₇	—	2	16	no	—
71	#95×C₆₇	—	2	4	no	—
72	C₂⁴×C₆₇	—	2	4	no	—
73	C₂⁴×C₆₇	—	2	4	no	—
74	C₂⁴×C₆₇	C₂²⋊C₄	1	4	yes	—
75	C₂⁴×C₆₇	SD₁₆	1	4	yes	—
76	C₂⁴×C₆₇	Q₁₆	1	4	yes	—
77	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
78	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₆₇	—	2	4	no	—
80	C₂×Q₈×C₆₇	—	2	2	no	—
81	C₂×Q₈×C₆₇	—	2	16	no	—
82	C₂×Q₈×C₆₇	—	2	4	no	—
83	C₂×Q₈×C₆₇	—	2	4	no	—
84	C₂×Q₈×C₆₇	—	4	4	no	—
85	C₂×Q₈×C₆₇	—	4	4	no	—
86	C₂×Q₈×C₆₇	—	4	4	no	—
87	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₆₇	—	2	4	no	—
89	C₂²×C₄×C₆₇	—	2	16	no	—
90	C₂²×C₄×C₆₇	—	2	8	no	—
91	C₂²×C₄×C₆₇	—	2	8	no	—
92	C₂²×C₄×C₆₇	—	2	8	no	—
93	C₂²×C₄×C₆₇	—	2	4	no	—
94	C₂²×C₄×C₆₇	—	2	4	no	—
95	C₂²×C₄×C₆₇	—	2	4	no	—
96	C₂²×C₄×C₆₇	—	2	4	no	—
97	C₂²×C₄×C₆₇	—	2	2	no	—
98	C₂²×C₄×C₆₇	—	2	2	no	—
99	C₂²×C₄×C₆₇	—	2	4	no	—
100	C₂²×C₄×C₆₇	—	4	4	no	—
101	C₂²×C₄×C₆₇	—	4	4	no	—
102	C₂²×C₄×C₆₇	—	4	4	no	—
103	C₂²×C₄×C₆₇	—	4	4	no	—
104	C₂²×C₄×C₆₇	—	4	4	no	—
105	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
106	C₂²×C₄×C₆₇	C₂²⋊C₄	1	8	yes	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₆₇	#41	1	4	yes	—
115	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₆₇	—	2	32	no	—
117	C₂×C₈×C₆₇	—	2	16	no	—
118	C₂×C₈×C₆₇	—	2	4	no	—
119	C₂×C₈×C₆₇	—	2	4	no	—
120	C₂×C₈×C₆₇	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₆₇	—	2	16	no	—
122	C₄⋊C₄×C₆₇	—	2	4	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	2	4	no	—
125	C₄⋊C₄×C₆₇	—	2	4	no	—
126	C₄⋊C₄×C₆₇	—	4	4	no	—
127	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
128	C₂²⋊C₄×C₆₇	—	2	16	no	—
129	C₂²⋊C₄×C₆₇	—	4	8	no	—
130	C₂³×C₆₇	—	2	4	no	—
131	C₂³×C₆₇	—	2	4	no	—
132	C₂³×C₆₇	—	2	8	no	—
133	C₂³×C₆₇	—	2	8	no	—
134	C₂³×C₆₇	—	2	16	no	—
135	C₂³×C₆₇	—	2	16	no	—
136	C₂³×C₆₇	#103	1	16	yes	complemented
137	C₂³×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₆₇	#121	1	4	yes	—
140	C₂³×C₆₇	C₂×SD₁₆	1	4	yes	—
141	C₂³×C₆₇	C₂×SD₁₆	1	2	yes	—
142	C₂³×C₆₇	C₂×Q₁₆	1	4	yes	—
143	C₂³×C₆₇	C₂×Q₁₆	1	2	yes	—
144	C₂³×C₆₇	#135	1	4	yes	—
145	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₆₇	—	2	8	no	—
147	Q₈×C₆₇	—	4	2	no	—
148	Q₈×C₆₇	—	4	2	no	—
149	Q₈×C₆₇	—	4	8	no	—
150	C₂×C₄×C₆₇	—	2	4	no	—
151	C₂×C₄×C₆₇	—	2	8	no	—
152	C₂×C₄×C₆₇	—	2	8	no	—
153	C₂×C₄×C₆₇	—	2	4	no	—
154	C₂×C₄×C₆₇	—	2	4	no	—
155	C₂×C₄×C₆₇	—	2	16	no	—
156	C₂×C₄×C₆₇	—	2	4	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	4	4	no	—
159	C₂×C₄×C₆₇	—	4	4	no	—
160	C₂×C₄×C₆₇	—	4	8	no	—
161	C₂×C₄×C₆₇	—	4	8	no	—
162	C₂×C₄×C₆₇	—	4	4	no	—
163	C₂×C₄×C₆₇	—	4	4	no	—
164	C₂×C₄×C₆₇	—	4	4	no	—
165	C₂×C₄×C₆₇	—	8	8	no	—
166	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
169	C₂×C₄×C₆₇	#120	1	4	yes	—
170	C₂×C₄×C₆₇	#121	1	4	yes	—
171	C₂×C₄×C₆₇	#123	1	4	yes	—
172	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
176	C₈×C₆₇	—	2	8	no	—
177	C₂²×C₆₇	—	2	4	no	—
178	C₂²×C₆₇	—	2	32	no	—
179	C₂²×C₆₇	—	2	8	no	—
180	C₂²×C₆₇	—	2	8	no	—
181	C₂²×C₆₇	—	2	4	no	—
182	C₂²×C₆₇	#386	1	4	yes	—
183	C₂²×C₆₇	C₂×#103	1	4	yes	—
184	C₂²×C₆₇	C₂×#103	1	8	yes	complemented
185	C₂²×C₆₇	#416	1	4	yes	—
186	C₂²×C₆₇	#465	1	8	yes	—
187	C₂²×C₆₇	#467	1	8	yes	—
188	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₆₇	C₂×#121	1	2	yes	—
190	C₂²×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
191	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
192	C₂²×C₆₇	C₂×#135	1	2	yes	—
193	C₄×C₆₇	—	2	4	no	—
194	C₄×C₆₇	—	4	4	no	—
195	C₄×C₆₇	—	4	4	no	—
196	C₄×C₆₇	—	8	4	no	—
197	C₄×C₆₇	#386	1	4	yes	—
198	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
199	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
200	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
201	C₂×#1892	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂×C₆₇	—	2	8	no	—
203	C₂×C₆₇	#1892	1	8	yes	direct product factor
204	C₂×C₆₇	C₂×#386	1	1	yes	characteristic
205	C₂×C₆₇	C₂²×#103	1	1	yes	characteristic
206	C₂×C₆₇	C₂×#416	1	1	yes	characteristic
207	C₂×C₆₇	C₂×#465	1	2	yes	—
208	C₂×C₆₇	C₂×#467	1	2	yes	—
209	C₂⁴×C₈	C₂×C₆₇	1	1	yes	characteristic
210	C₂²×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic
211	C₂²×#103	C₂×C₆₇	1	2	yes	complemented
212	C₂×#380	C₂×C₆₇	1	1	yes	characteristic
213	#1892	C₂×C₆₇	1	8	yes	direct product factor
214	C₂×#340	C₂×C₆₇	1	2	yes	complemented
215	C₆₇	C₂×#1892	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
217	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
218	C₂³×C₈	—	2	4	no	—
219	C₂³×C₈	—	2	8	no	—
220	C₂³×C₈	C₂²×C₆₇	1	4	yes	—
221	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
222	C₂×C₂²⋊Q₈	—	2	4	no	—
223	C₂×C₂²⋊Q₈	—	2	2	no	—
224	C₂×C₂²⋊Q₈	C₄×C₆₇	1	8	yes	complemented
225	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
226	C₂²×C₄⋊C₄	—	2	1	no	—
227	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
229	C₂²×C₂²⋊C₄	—	2	1	no	—
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂×#103	—	2	8	no	—
232	C₂×#103	C₂²×C₆₇	1	8	yes	complemented
233	#380	—	2	2	no	—
234	#380	C₂²×C₆₇	1	4	yes	—
235	C₂×#95	—	2	1	no	—
236	#340	C₂²×C₆₇	1	8	yes	complemented
237	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×Q₈	—	2	4	no	—
241	C₂²×Q₈	—	2	4	no	—
242	C₂²×Q₈	C₂×C₄×C₆₇	1	4	yes	—
243	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	C₂×C₄×C₆₇	1	4	yes	—
250	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
251	C₂³×C₄	D₄×C₆₇	1	2	yes	—
252	C₂³×C₄	D₄×C₆₇	1	4	yes	—
253	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
254	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
255	C₂²×C₈	—	2	32	no	—
256	C₂²×C₈	—	2	8	no	—
257	C₂²×C₈	—	2	4	no	—
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	—	2	16	no	—
260	C₂²×C₈	D₄×C₆₇	1	8	yes	—
261	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
262	C₂²⋊Q₈	—	2	16	no	—
263	C₂²⋊Q₈	—	2	8	no	—
264	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
265	C₂×C₄⋊C₄	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₂²⋊C₄	—	4	4	no	—
279	#103	—	2	16	no	—
280	#95	—	2	4	no	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	C₂²⋊C₄×C₆₇	1	4	yes	—
284	C₂⁴	SD₁₆×C₆₇	1	4	yes	—
285	C₂⁴	Q₁₆×C₆₇	1	4	yes	—
286	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
287	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	16	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	16	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₆₇	1	8	yes	—
316	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
317	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
323	C₂²×C₄	#41×C₆₇	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
325	C₂×C₈	—	2	32	no	—
326	C₂×C₈	—	2	16	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	C₂×D₄×C₆₇	1	8	yes	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	—	4	8	no	—
339	C₂³	—	2	16	no	—
340	C₂³	—	2	16	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	8	no	—
345	C₂³	#103×C₆₇	1	16	yes	complemented
346	C₂³	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
347	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
348	C₂³	#121×C₆₇	1	4	yes	—
349	C₂³	C₂×SD₁₆×C₆₇	1	4	yes	—
350	C₂³	C₂×SD₁₆×C₆₇	1	2	yes	—
351	C₂³	C₂×Q₁₆×C₆₇	1	4	yes	—
352	C₂³	C₂×Q₁₆×C₆₇	1	2	yes	—
353	C₂³	#135×C₆₇	1	4	yes	—
354	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
355	Q₈	—	2	8	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	16	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	8	8	no	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
377	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
378	C₂×C₄	#120×C₆₇	1	4	yes	—
379	C₂×C₄	#121×C₆₇	1	4	yes	—
380	C₂×C₄	#123×C₆₇	1	4	yes	—
381	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
385	C₈	—	2	8	no	—
386	C₂²	—	2	8	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	32	no	—
391	C₂²	#386×C₆₇	1	4	yes	—
392	C₂²	C₂×#103×C₆₇	1	4	yes	—
393	C₂²	C₂×#103×C₆₇	1	8	yes	complemented
394	C₂²	#416×C₆₇	1	4	yes	—
395	C₂²	#465×C₆₇	1	8	yes	—
396	C₂²	#467×C₆₇	1	8	yes	—
397	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
398	C₂²	C₂×#121×C₆₇	1	2	yes	—
399	C₂²	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
400	C₂²	C₂²×Q₁₆×C₆₇	1	1	yes	characteristic
401	C₂²	C₂×#135×C₆₇	1	2	yes	—
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	8	4	no	—
406	C₄	#386×C₆₇	1	4	yes	—
407	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
408	C₄	C₂×#120×C₆₇	1	1	yes	characteristic
409	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
410	C₂	—	2	8	no	—
411	C₂	C₆₇×#1892	1	8	yes	direct product factor
412	C₂	C₂×#386×C₆₇	1	1	yes	characteristic
413	C₂	C₂²×#103×C₆₇	1	1	yes	characteristic
414	C₂	C₂×#416×C₆₇	1	1	yes	characteristic
415	C₂	C₂×#465×C₆₇	1	2	yes	—
416	C₂	C₂×#467×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	C₂⁵×C₆₇	D₄
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
3. C₂²×#103×C₆₇	C₂	semidirect
5. C₆₇×#1892	C₂	direct (N × H)
6. C₂×#340×C₆₇	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₆₇	C₄	semidirect
23. C₂×#103×C₆₇	C₂²	semidirect
27. #340×C₆₇	C₂²	semidirect
55. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
136. C₂³×C₆₇	#103	semidirect
184. C₂²×C₆₇	C₂×#103	semidirect
201. C₂×#1892	C₆₇	direct (N × H)
203. C₂×C₆₇	#1892	direct (N × H)
211. C₂²×#103	C₂×C₆₇	semidirect
213. #1892	C₂×C₆₇	direct (N × H)
214. C₂×#340	C₂×C₆₇	semidirect
215. C₆₇	C₂×#1892	direct (N × H)
224. C₂×C₂²⋊Q₈	C₄×C₆₇	semidirect
232. C₂×#103	C₂²×C₆₇	semidirect
236. #340	C₂²×C₆₇	semidirect
264. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
345. C₂³	#103×C₆₇	semidirect
393. C₂²	C₂×#103×C₆₇	semidirect
411. C₂	C₆₇×#1892	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×C₂²⋊Q₈×C₆₇	2
C₂²×#103×C₆₇	2
C₂×#380×C₆₇	2
C₆₇×#1892	2
C₂×#340×C₆₇	2
C₂×#1892	67

Subgroups — C2×C67×#1892 #30700216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1892 #30700216