Subgroups — C₂×C₆₇×#3140 #30739866

Order 17152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3140	C₂	1	16	yes	maximal, direct product factor
4	C₂×#489×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#488×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#419×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#418×C₆₇	C₂	1	2	yes	maximal
8	C₂×C₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
12	#533×C₆₇	—	2	4	no	—
13	#533×C₆₇	C₂²	1	8	yes	complemented
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
15	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
16	C₂×#124×C₆₇	—	2	2	no	—
17	C₂×#124×C₆₇	—	2	4	no	—
18	C₂×#124×C₆₇	C₂²	1	2	yes	—
19	C₂×#124×C₆₇	C₂²	1	2	yes	—
20	C₂×#124×C₆₇	C₂²	1	8	yes	—
21	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
22	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
23	C₂×#117×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#489×C₆₇	C₂²	1	32	yes	complemented
27	#488×C₆₇	C₂²	1	32	yes	complemented
28	#419×C₆₇	C₂²	1	16	yes	complemented
29	#418×C₆₇	C₂²	1	16	yes	—
30	C₂×#103×C₆₇	C₂²	1	8	yes	complemented
31	C₂×#102×C₆₇	C₂²	1	8	yes	—
32	C₄×M₁₆×C₆₇	C₂²	1	8	yes	complemented
33	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
34	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
35	C₂⁵×C₆₇	—	2	1	no	—
36	C₂²×Q₈×C₆₇	—	2	2	no	—
37	C₂²×Q₈×C₆₇	—	2	2	no	—
38	C₂²×Q₈×C₆₇	—	2	1	no	—
39	C₂²×Q₈×C₆₇	—	2	8	no	—
40	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
41	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
42	C₂²×D₄×C₆₇	—	2	2	no	—
43	C₂²×D₄×C₆₇	—	2	1	no	—
44	C₂²×D₄×C₆₇	—	2	8	no	—
45	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
46	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
47	C₂³×C₄×C₆₇	—	2	1	no	—
48	C₂³×C₄×C₆₇	D₄	1	2	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₆₇	—	2	8	no	—
51	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₆₇	—	2	4	no	—
54	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
55	#125×C₆₇	—	2	4	no	—
56	#125×C₆₇	C₂³	1	8	yes	complemented
57	#124×C₆₇	—	2	16	no	—
58	#124×C₆₇	—	2	4	no	—
59	#124×C₆₇	—	2	4	no	—
60	#124×C₆₇	C₂³	1	8	yes	—
61	#124×C₆₇	C₂³	1	8	yes	—
62	C₂²⋊Q₈×C₆₇	—	2	16	no	—
63	C₄×Q₈×C₆₇	—	2	16	no	—
64	#117×C₆₇	—	2	4	no	—
65	#117×C₆₇	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	16	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
73	C₂×C₄²×C₆₇	—	2	2	no	—
74	C₂×C₄²×C₆₇	D₄	1	2	yes	—
75	C₂×C₄²×C₆₇	D₄	1	4	yes	—
76	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
79	#103×C₆₇	C₂³	1	32	yes	complemented
80	#102×C₆₇	C₂³	1	32	yes	—
81	#97×C₆₇	C₂³	1	8	yes	complemented
82	C₄×C₈×C₆₇	C₂³	1	8	yes	complemented
83	C₂⁴×C₆₇	—	2	4	no	—
84	C₂⁴×C₆₇	—	2	2	no	—
85	C₂⁴×C₆₇	—	4	8	no	—
86	C₂⁴×C₆₇	—	4	4	no	—
87	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₆₇	—	2	8	no	—
89	C₂×Q₈×C₆₇	—	2	4	no	—
90	C₂×Q₈×C₆₇	—	2	2	no	—
91	C₂×Q₈×C₆₇	—	2	8	no	—
92	C₂×Q₈×C₆₇	—	2	16	no	—
93	C₂×Q₈×C₆₇	—	4	8	no	—
94	C₂×Q₈×C₆₇	—	4	8	no	—
95	C₂×Q₈×C₆₇	—	4	4	no	—
96	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
97	C₂×D₄×C₆₇	—	2	4	no	—
98	C₂×D₄×C₆₇	—	2	2	no	—
99	C₂×D₄×C₆₇	—	2	8	no	—
100	C₂×D₄×C₆₇	—	2	16	no	—
101	C₂×D₄×C₆₇	—	4	8	no	—
102	C₂×D₄×C₆₇	—	4	4	no	—
103	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₆₇	—	2	4	no	—
105	C₂²×C₄×C₆₇	—	2	4	no	—
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	—	4	4	no	—
108	C₂²×C₄×C₆₇	—	4	4	no	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	#41	1	8	yes	—
115	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₆₇	—	2	16	no	—
118	C₂×C₈×C₆₇	—	2	8	no	—
119	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
120	C₄⋊C₄×C₆₇	—	2	16	no	—
121	C₄⋊C₄×C₆₇	—	2	8	no	—
122	C₄⋊C₄×C₆₇	—	2	4	no	—
123	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
124	C₂²⋊C₄×C₆₇	—	2	8	no	—
125	C₂²⋊C₄×C₆₇	—	2	16	no	—
126	C₂²⋊C₄×C₆₇	—	2	16	no	—
127	C₄²×C₆₇	—	2	8	no	—
128	C₄²×C₆₇	C₂×D₄	1	8	yes	—
129	C₄²×C₆₇	C₂×D₄	1	2	yes	—
130	C₄²×C₆₇	C₂×D₄	1	2	yes	—
131	C₄²×C₆₇	C₂⁴	1	2	yes	—
132	C₄²×C₆₇	C₂⁴	1	2	yes	—
133	C₂³×C₆₇	—	2	4	no	—
134	C₂³×C₆₇	—	2	4	no	—
135	C₂³×C₆₇	—	4	16	no	—
136	C₂³×C₆₇	—	4	8	no	—
137	C₂³×C₆₇	—	4	4	no	—
138	C₂³×C₆₇	—	4	8	no	—
139	C₂³×C₆₇	—	8	16	no	—
140	C₂³×C₆₇	#124	1	4	yes	—
141	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
142	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₆₇	—	2	8	no	—
144	Q₈×C₆₇	—	4	16	no	—
145	Q₈×C₆₇	—	4	8	no	—
146	Q₈×C₆₇	—	4	4	no	—
147	D₄×C₆₇	—	2	8	no	—
148	D₄×C₆₇	—	4	8	no	—
149	D₄×C₆₇	—	4	4	no	—
150	C₂×C₄×C₆₇	—	2	4	no	—
151	C₂×C₄×C₆₇	—	2	4	no	—
152	C₂×C₄×C₆₇	—	2	8	no	—
153	C₂×C₄×C₆₇	—	2	4	no	—
154	C₂×C₄×C₆₇	—	4	8	no	—
155	C₂×C₄×C₆₇	—	4	8	no	—
156	C₂×C₄×C₆₇	—	4	4	no	—
157	C₂×C₄×C₆₇	—	4	8	no	—
158	C₂×C₄×C₆₇	#124	1	8	yes	—
159	C₂×C₄×C₆₇	#124	1	4	yes	—
160	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
165	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
166	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
167	C₈×C₆₇	—	2	8	no	—
168	C₂²×C₆₇	—	2	8	no	—
169	C₂²×C₆₇	—	2	4	no	—
170	C₂²×C₆₇	—	4	4	no	—
171	C₂²×C₆₇	—	4	8	no	—
172	C₂²×C₆₇	—	8	16	no	—
173	C₂²×C₆₇	—	8	8	no	—
174	C₂²×C₆₇	C₂×#124	1	4	yes	—
175	C₂²×C₆₇	C₂×#124	1	2	yes	—
176	C₂²×C₆₇	#575	1	4	yes	—
177	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
178	C₄×C₆₇	—	2	4	no	—
179	C₄×C₆₇	—	2	4	no	—
180	C₄×C₆₇	—	4	4	no	—
181	C₄×C₆₇	—	4	8	no	—
182	C₄×C₆₇	C₂×#124	1	4	yes	—
183	C₄×C₆₇	C₂×#124	1	2	yes	—
184	C₄×C₆₇	C₂²×#41	1	2	yes	—
185	C₂×#3140	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₆₇	—	2	4	no	—
187	C₂×C₆₇	—	8	4	no	—
188	C₂×C₆₇	#3140	1	4	yes	direct product factor
189	C₂×C₆₇	C₂²×#124	1	1	yes	characteristic
190	C₂×C₆₇	C₂×#575	1	2	yes	—
191	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic
193	#3140	C₂×C₆₇	1	16	yes	direct product factor
194	C₂×#489	C₂×C₆₇	1	4	yes	complemented
195	C₂×#488	C₂×C₆₇	1	4	yes	complemented
196	C₂×#419	C₂×C₆₇	1	2	yes	complemented
197	C₂×#418	C₂×C₆₇	1	2	yes	—
198	C₂×C₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
199	C₆₇	C₂×#3140	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
201	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
202	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
203	#533	—	2	4	no	—
204	#533	C₂²×C₆₇	1	8	yes	complemented
205	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
206	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
207	C₂×#124	—	2	2	no	—
208	C₂×#124	—	2	4	no	—
209	C₂×#124	C₂²×C₆₇	1	2	yes	—
210	C₂×#124	C₂²×C₆₇	1	2	yes	—
211	C₂×#124	C₂²×C₆₇	1	8	yes	—
212	C₂×C₂²⋊Q₈	—	2	2	no	—
213	C₂×C₄×Q₈	—	2	2	no	—
214	C₂×#117	C₂²×C₆₇	1	2	yes	—
215	C₂²×C₂²⋊C₄	—	2	2	no	—
216	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
217	#489	C₂²×C₆₇	1	32	yes	complemented
218	#488	C₂²×C₆₇	1	32	yes	complemented
219	#419	C₂²×C₆₇	1	16	yes	complemented
220	#418	C₂²×C₆₇	1	16	yes	—
221	C₂×#103	C₂²×C₆₇	1	8	yes	complemented
222	C₂×#102	C₂²×C₆₇	1	8	yes	—
223	C₄×M₁₆	C₂²×C₆₇	1	8	yes	complemented
224	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
225	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
226	C₂⁵	—	2	1	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×Q₈	—	2	8	no	—
231	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
232	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	8	no	—
236	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
237	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	D₄×C₆₇	1	2	yes	—
240	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
241	C₂×M₁₆	—	2	8	no	—
242	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
243	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
246	#125	—	2	4	no	—
247	#125	C₂³×C₆₇	1	8	yes	complemented
248	#124	—	2	16	no	—
249	#124	—	2	4	no	—
250	#124	—	2	4	no	—
251	#124	C₂³×C₆₇	1	8	yes	—
252	#124	C₂³×C₆₇	1	8	yes	—
253	C₂²⋊Q₈	—	2	16	no	—
254	C₄×Q₈	—	2	16	no	—
255	#117	—	2	4	no	—
256	#117	C₂³×C₆₇	1	8	yes	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	16	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	D₄×C₆₇	1	2	yes	—
266	C₂×C₄²	D₄×C₆₇	1	4	yes	—
267	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
270	#103	C₂³×C₆₇	1	32	yes	complemented
271	#102	C₂³×C₆₇	1	32	yes	—
272	#97	C₂³×C₆₇	1	8	yes	complemented
273	C₄×C₈	C₂³×C₆₇	1	8	yes	complemented
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	4	8	no	—
277	C₂⁴	—	4	4	no	—
278	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	4	8	no	—
285	C₂×Q₈	—	4	8	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	16	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
303	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
305	C₂²×C₄	#41×C₆₇	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
308	M₁₆	—	2	16	no	—
309	C₂×C₈	—	2	8	no	—
310	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
311	C₄⋊C₄	—	2	16	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	16	no	—
317	C₂²⋊C₄	—	2	16	no	—
318	C₄²	—	2	8	no	—
319	C₄²	C₂×D₄×C₆₇	1	8	yes	—
320	C₄²	C₂×D₄×C₆₇	1	2	yes	—
321	C₄²	C₂×D₄×C₆₇	1	2	yes	—
322	C₄²	C₂⁴×C₆₇	1	2	yes	—
323	C₄²	C₂⁴×C₆₇	1	2	yes	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	—	8	16	no	—
331	C₂³	#124×C₆₇	1	4	yes	—
332	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
333	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	16	no	—
336	Q₈	—	4	8	no	—
337	Q₈	—	4	4	no	—
338	D₄	—	2	8	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	#124×C₆₇	1	8	yes	—
350	C₂×C₄	#124×C₆₇	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
352	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
356	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
357	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
358	C₈	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	4	8	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	8	16	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₂×#124×C₆₇	1	4	yes	—
366	C₂²	C₂×#124×C₆₇	1	2	yes	—
367	C₂²	#575×C₆₇	1	4	yes	—
368	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	8	no	—
372	C₄	—	4	4	no	—
373	C₄	C₂×#124×C₆₇	1	4	yes	—
374	C₄	C₂×#124×C₆₇	1	2	yes	—
375	C₄	C₂²×#41×C₆₇	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₆₇×#3140	1	4	yes	direct product factor
379	C₂	C₂²×#124×C₆₇	1	1	yes	characteristic
380	C₂	C₂×#575×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₆₇	C₂	semidirect
3. C₆₇×#3140	C₂	direct (N × H)
4. C₂×#489×C₆₇	C₂	semidirect
5. C₂×#488×C₆₇	C₂	semidirect
6. C₂×#419×C₆₇	C₂	semidirect
8. C₂×C₄×M₁₆×C₆₇	C₂	semidirect
13. #533×C₆₇	C₂²	semidirect
14. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
15. C₂×#125×C₆₇	C₂²	semidirect
26. #489×C₆₇	C₂²	semidirect
27. #488×C₆₇	C₂²	semidirect
28. #419×C₆₇	C₂²	semidirect
30. C₂×#103×C₆₇	C₂²	semidirect
32. C₄×M₁₆×C₆₇	C₂²	semidirect
33. C₂×#97×C₆₇	C₂²	semidirect
34. C₂×C₄×C₈×C₆₇	C₂²	semidirect
54. C₄⋊Q₈×C₆₇	C₂³	semidirect
56. #125×C₆₇	C₂³	semidirect
79. #103×C₆₇	C₂³	semidirect
81. #97×C₆₇	C₂³	semidirect
82. C₄×C₈×C₆₇	C₂³	semidirect
185. C₂×#3140	C₆₇	direct (N × H)
188. C₂×C₆₇	#3140	direct (N × H)
191. C₂×#533	C₂×C₆₇	semidirect
193. #3140	C₂×C₆₇	direct (N × H)
194. C₂×#489	C₂×C₆₇	semidirect
195. C₂×#488	C₂×C₆₇	semidirect
196. C₂×#419	C₂×C₆₇	semidirect
198. C₂×C₄×M₁₆	C₂×C₆₇	semidirect
199. C₆₇	C₂×#3140	direct (N × H)
204. #533	C₂²×C₆₇	semidirect
205. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
206. C₂×#125	C₂²×C₆₇	semidirect
217. #489	C₂²×C₆₇	semidirect
218. #488	C₂²×C₆₇	semidirect
219. #419	C₂²×C₆₇	semidirect
221. C₂×#103	C₂²×C₆₇	semidirect
223. C₄×M₁₆	C₂²×C₆₇	semidirect
224. C₂×#97	C₂²×C₆₇	semidirect
225. C₂×C₄×C₈	C₂²×C₆₇	semidirect
245. C₄⋊Q₈	C₂³×C₆₇	semidirect
247. #125	C₂³×C₆₇	semidirect
270. #103	C₂³×C₆₇	semidirect
272. #97	C₂³×C₆₇	semidirect
273. C₄×C₈	C₂³×C₆₇	semidirect
378. C₂	C₆₇×#3140	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×#533×C₆₇	2
C₂²×#124×C₆₇	2
C₆₇×#3140	2
C₂×#489×C₆₇	2
C₂×#488×C₆₇	2
C₂×#419×C₆₇	2
C₂×#418×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₂×#3140	67

Subgroups — C2×C67×#3140 #30739866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3140 #30739866