Subgroups — C₆₇×#60940 #30740191

Order 17152.

2362 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3245	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3226	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3205	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3186	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3169	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3100	C₂	1	8	yes	maximal, complemented
8	C₂×#431×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₇	—	2	2	no	—
10	#532×C₆₇	—	2	2	no	—
11	#532×C₆₇	—	2	2	no	—
12	#532×C₆₇	—	2	2	no	—
13	#532×C₆₇	—	2	2	no	—
14	#532×C₆₇	C₂²	1	4	yes	—
15	#532×C₆₇	C₂²	1	4	yes	—
16	#532×C₆₇	C₂²	1	4	yes	complemented
17	#532×C₆₇	C₂²	1	4	yes	complemented
18	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
19	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
20	C₂×#124×C₆₇	—	2	2	no	—
21	C₂×#121×C₆₇	—	2	2	no	—
22	C₂×#121×C₆₇	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₆₇	—	2	2	no	—
24	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	#500×C₆₇	C₂²	1	4	yes	complemented
27	#493×C₆₇	C₂²	1	4	yes	complemented
28	#486×C₆₇	C₂²	1	8	yes	complemented
29	#480×C₆₇	C₂²	1	16	yes	complemented
30	#474×C₆₇	C₂²	1	16	yes	complemented
31	#466×C₆₇	C₂²	1	16	yes	complemented
32	#459×C₆₇	C₂²	1	16	yes	complemented
33	#447×C₆₇	C₂²	1	16	yes	complemented
34	C₄×D₈×C₆₇	C₂²	1	16	yes	complemented
35	#431×C₆₇	C₂²	1	4	yes	complemented
36	#431×C₆₇	C₂²	1	4	yes	complemented
37	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	complemented
40	C₂×#41×C₆₇	—	2	4	no	—
41	C₂×#41×C₆₇	—	2	4	no	—
42	C₂×#41×C₆₇	—	2	4	no	—
43	C₂×#41×C₆₇	—	2	4	no	—
44	C₂×#41×C₆₇	—	4	16	no	—
45	C₂²×Q₈×C₆₇	—	2	2	no	—
46	C₂²×D₄×C₆₇	—	2	4	no	—
47	C₂²×D₄×C₆₇	—	2	2	no	—
48	C₂²×D₄×C₆₇	—	2	2	no	—
49	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
50	C₂³×C₄×C₆₇	—	2	4	no	—
51	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×D₈×C₆₇	C₂³	1	16	yes	—
55	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
56	C₄⋊Q₈×C₆₇	—	2	2	no	—
57	C₄⋊Q₈×C₆₇	—	2	2	no	—
58	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
60	#127×C₆₇	—	2	2	no	—
61	#127×C₆₇	—	2	2	no	—
62	#127×C₆₇	C₂³	1	4	yes	—
63	#127×C₆₇	C₂³	1	4	yes	—
64	#124×C₆₇	—	2	4	no	—
65	#124×C₆₇	—	2	4	no	—
66	#124×C₆₇	—	2	4	no	—
67	#124×C₆₇	—	2	4	no	—
68	#121×C₆₇	—	2	4	no	—
69	#121×C₆₇	—	2	4	no	—
70	#121×C₆₇	—	2	4	no	—
71	#121×C₆₇	—	2	4	no	—
72	#121×C₆₇	—	2	4	no	—
73	#121×C₆₇	—	2	4	no	—
74	#121×C₆₇	C₂³	1	8	yes	—
75	#121×C₆₇	C₂³	1	8	yes	—
76	C₄×D₄×C₆₇	—	2	4	no	—
77	C₄×D₄×C₆₇	—	2	4	no	—
78	C₄×D₄×C₆₇	—	2	4	no	—
79	C₄×D₄×C₆₇	—	2	4	no	—
80	C₄×D₄×C₆₇	—	2	4	no	—
81	C₄×D₄×C₆₇	—	2	4	no	—
82	C₄×D₄×C₆₇	C₂³	1	8	yes	—
83	C₄×D₄×C₆₇	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
88	C₂×C₄²×C₆₇	D₄	1	2	yes	—
89	C₂×C₄²×C₆₇	D₄	1	2	yes	—
90	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
94	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
96	#107×C₆₇	C₂³	1	16	yes	—
97	C₄⋊C₈×C₆₇	C₂³	1	8	yes	—
98	#102×C₆₇	C₂³	1	32	yes	—
99	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
100	C₄×C₈×C₆₇	C₂³	1	4	yes	—
101	C₄×C₈×C₆₇	C₂³	1	4	yes	—
102	C₂⁴×C₆₇	—	2	4	no	—
103	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
104	#41×C₆₇	—	4	16	no	—
105	#41×C₆₇	—	4	16	no	—
106	#41×C₆₇	—	4	16	no	—
107	#41×C₆₇	—	4	16	no	—
108	C₂×Q₈×C₆₇	—	2	4	no	—
109	C₂×Q₈×C₆₇	—	2	4	no	—
110	C₂×Q₈×C₆₇	—	4	8	no	—
111	C₂×D₄×C₆₇	—	2	8	no	—
112	C₂×D₄×C₆₇	—	2	8	no	—
113	C₂×D₄×C₆₇	—	2	4	no	—
114	C₂×D₄×C₆₇	—	2	4	no	—
115	C₂×D₄×C₆₇	—	2	4	no	—
116	C₂×D₄×C₆₇	—	2	4	no	—
117	C₂×D₄×C₆₇	—	2	4	no	—
118	C₂×D₄×C₆₇	—	4	8	no	—
119	C₂×D₄×C₆₇	—	4	8	no	—
120	C₂×D₄×C₆₇	—	4	16	no	—
121	C₂×D₄×C₆₇	—	4	8	no	—
122	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₆₇	—	2	4	no	—
124	C₂²×C₄×C₆₇	—	2	8	no	—
125	C₂²×C₄×C₆₇	—	2	8	no	—
126	C₂²×C₄×C₆₇	—	4	2	no	—
127	C₂²×C₄×C₆₇	—	4	2	no	—
128	C₂²×C₄×C₆₇	—	4	16	no	—
129	C₂²×C₄×C₆₇	D₈	1	8	yes	complemented
130	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
142	D₈×C₆₇	—	4	16	no	—
143	C₂×C₈×C₆₇	—	4	4	no	—
144	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
145	C₄⋊C₄×C₆₇	—	2	4	no	—
146	C₄⋊C₄×C₆₇	—	2	4	no	—
147	C₄⋊C₄×C₆₇	—	2	4	no	—
148	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
149	C₂²⋊C₄×C₆₇	—	2	8	no	—
150	C₂²⋊C₄×C₆₇	—	2	8	no	—
151	C₂²⋊C₄×C₆₇	—	2	8	no	—
152	C₂²⋊C₄×C₆₇	—	2	8	no	—
153	C₄²×C₆₇	C₂×D₄	1	2	yes	—
154	C₄²×C₆₇	C₂×D₄	1	2	yes	—
155	C₄²×C₆₇	C₂×D₄	1	2	yes	—
156	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₇	C₂×D₄	1	2	yes	—
158	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₆₇	C₂×D₄	1	2	yes	—
160	C₄²×C₆₇	C₂⁴	1	2	yes	—
161	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
162	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
163	C₂³×C₆₇	—	2	8	no	—
164	C₂³×C₆₇	—	4	1	no	—
165	C₂³×C₆₇	—	4	1	no	—
166	C₂³×C₆₇	—	4	8	no	—
167	C₂³×C₆₇	—	4	8	no	—
168	C₂³×C₆₇	—	4	8	no	—
169	C₂³×C₆₇	C₂×D₈	1	4	yes	—
170	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
171	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₆₇	—	4	8	no	—
173	Q₈×C₆₇	—	4	8	no	—
174	D₄×C₆₇	—	2	16	no	—
175	D₄×C₆₇	—	4	8	no	—
176	D₄×C₆₇	—	4	8	no	—
177	D₄×C₆₇	—	4	16	no	—
178	D₄×C₆₇	—	4	16	no	—
179	D₄×C₆₇	—	4	8	no	—
180	D₄×C₆₇	—	4	8	no	—
181	D₄×C₆₇	—	4	8	no	—
182	C₂×C₄×C₆₇	—	2	2	no	—
183	C₂×C₄×C₆₇	—	2	4	no	—
184	C₂×C₄×C₆₇	—	2	2	no	—
185	C₂×C₄×C₆₇	—	2	4	no	—
186	C₂×C₄×C₆₇	—	2	8	no	—
187	C₂×C₄×C₆₇	—	4	2	no	—
188	C₂×C₄×C₆₇	—	4	1	no	—
189	C₂×C₄×C₆₇	—	4	2	no	—
190	C₂×C₄×C₆₇	—	4	1	no	—
191	C₂×C₄×C₆₇	—	4	8	no	—
192	C₂×C₄×C₆₇	—	4	16	no	—
193	C₂×C₄×C₆₇	—	4	16	no	—
194	C₂×C₄×C₆₇	C₂×D₈	1	8	yes	—
195	C₂×C₄×C₆₇	C₂×D₈	1	8	yes	—
196	C₂×C₄×C₆₇	C₂×D₈	1	4	yes	—
197	C₂×C₄×C₆₇	C₂×D₈	1	4	yes	—
198	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
207	C₈×C₆₇	—	2	8	no	—
208	C₂²×C₆₇	—	2	2	no	—
209	C₂²×C₆₇	—	2	1	no	—
210	C₂²×C₆₇	—	2	2	no	—
211	C₂²×C₆₇	—	2	1	no	—
212	C₂²×C₆₇	—	4	4	no	—
213	C₂²×C₆₇	—	4	8	no	—
214	C₂²×C₆₇	—	4	8	no	—
215	C₂²×C₆₇	—	4	8	no	—
216	C₂²×C₆₇	—	8	16	no	—
217	C₂²×C₆₇	C₂²×D₈	1	4	yes	—
218	C₂²×C₆₇	C₂²×D₈	1	2	yes	—
219	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
220	C₄×C₆₇	—	2	1	no	—
221	C₄×C₆₇	—	2	2	no	—
222	C₄×C₆₇	—	2	1	no	—
223	C₄×C₆₇	—	2	2	no	—
224	C₄×C₆₇	—	4	8	no	—
225	C₄×C₆₇	C₂²×D₈	1	2	yes	—
226	C₄×C₆₇	C₂²×D₈	1	4	yes	—
227	C₄×C₆₇	C₂²×D₈	1	2	yes	—
228	C₄×C₆₇	#575	1	2	yes	—
229	C₄×C₆₇	#585	1	2	yes	—
230	#60940	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₆₇	—	2	4	no	—
232	C₂×C₆₇	—	2	2	no	—
233	C₂×C₆₇	—	8	8	no	—
234	C₂×C₆₇	#3449	1	1	yes	characteristic
235	C₂×C₆₇	C₂³×D₈	1	1	yes	characteristic
236	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
237	C₂×#532	C₂×C₆₇	1	2	yes	complemented
238	#3245	C₂×C₆₇	1	4	yes	complemented
239	#3226	C₂×C₆₇	1	4	yes	complemented
240	#3205	C₂×C₆₇	1	4	yes	complemented
241	#3186	C₂×C₆₇	1	4	yes	complemented
242	#3169	C₂×C₆₇	1	4	yes	complemented
243	#3100	C₂×C₆₇	1	8	yes	complemented
244	C₂×#431	C₂×C₆₇	1	1	yes	characteristic, complemented
245	C₆₇	#60940	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×#41	—	2	2	no	—
247	#532	—	2	2	no	—
248	#532	—	2	2	no	—
249	#532	—	2	2	no	—
250	#532	—	2	2	no	—
251	#532	C₂²×C₆₇	1	4	yes	—
252	#532	C₂²×C₆₇	1	4	yes	—
253	#532	C₂²×C₆₇	1	4	yes	complemented
254	#532	C₂²×C₆₇	1	4	yes	complemented
255	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
256	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
257	C₂×#124	—	2	2	no	—
258	C₂×#121	—	2	2	no	—
259	C₂×#121	C₂²×C₆₇	1	4	yes	—
260	C₂×C₄×D₄	—	2	2	no	—
261	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
262	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
263	#500	C₂²×C₆₇	1	4	yes	complemented
264	#493	C₂²×C₆₇	1	4	yes	complemented
265	#486	C₂²×C₆₇	1	8	yes	complemented
266	#480	C₂²×C₆₇	1	16	yes	complemented
267	#474	C₂²×C₆₇	1	16	yes	complemented
268	#466	C₂²×C₆₇	1	16	yes	complemented
269	#459	C₂²×C₆₇	1	16	yes	complemented
270	#447	C₂²×C₆₇	1	16	yes	complemented
271	C₄×D₈	C₂²×C₆₇	1	16	yes	complemented
272	#431	C₂²×C₆₇	1	4	yes	complemented
273	#431	C₂²×C₆₇	1	4	yes	complemented
274	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
275	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	complemented
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	4	no	—
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	4	16	no	—
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×D₄	—	2	4	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
289	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
291	C₂×D₈	C₂³×C₆₇	1	16	yes	—
292	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
296	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
297	#127	—	2	2	no	—
298	#127	—	2	2	no	—
299	#127	C₂³×C₆₇	1	4	yes	—
300	#127	C₂³×C₆₇	1	4	yes	—
301	#124	—	2	4	no	—
302	#124	—	2	4	no	—
303	#124	—	2	4	no	—
304	#124	—	2	4	no	—
305	#121	—	2	4	no	—
306	#121	—	2	4	no	—
307	#121	—	2	4	no	—
308	#121	—	2	4	no	—
309	#121	—	2	4	no	—
310	#121	—	2	4	no	—
311	#121	C₂³×C₆₇	1	8	yes	—
312	#121	C₂³×C₆₇	1	8	yes	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	C₂³×C₆₇	1	8	yes	—
320	C₄×D₄	C₂³×C₆₇	1	8	yes	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₄²	D₄×C₆₇	1	2	yes	—
326	C₂×C₄²	D₄×C₆₇	1	2	yes	—
327	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
330	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
331	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
333	#107	C₂³×C₆₇	1	16	yes	—
334	C₄⋊C₈	C₂³×C₆₇	1	8	yes	—
335	#102	C₂³×C₆₇	1	32	yes	—
336	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
337	C₄×C₈	C₂³×C₆₇	1	4	yes	—
338	C₄×C₈	C₂³×C₆₇	1	4	yes	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
341	#41	—	4	16	no	—
342	#41	—	4	16	no	—
343	#41	—	4	16	no	—
344	#41	—	4	16	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	4	8	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂×D₄	—	4	16	no	—
358	C₂×D₄	—	4	8	no	—
359	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	16	no	—
366	C₂²×C₄	D₈×C₆₇	1	8	yes	complemented
367	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
379	D₈	—	4	16	no	—
380	C₂×C₈	—	4	4	no	—
381	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₆₇	1	2	yes	—
392	C₄²	C₂×D₄×C₆₇	1	2	yes	—
393	C₄²	C₂×D₄×C₆₇	1	2	yes	—
394	C₄²	C₂×D₄×C₆₇	1	2	yes	—
395	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₆₇	1	2	yes	—
397	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
398	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
399	C₄²	C₂⁴×C₆₇	1	2	yes	—
400	C₂³	—	2	8	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	8	no	—
404	C₂³	—	4	8	no	—
405	C₂³	—	4	8	no	—
406	C₂³	C₂×D₈×C₆₇	1	4	yes	—
407	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
408	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
409	Q₈	—	4	8	no	—
410	Q₈	—	4	8	no	—
411	D₄	—	2	16	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	16	no	—
415	D₄	—	4	16	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	8	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	16	no	—
430	C₂×C₄	—	4	16	no	—
431	C₂×C₄	C₂×D₈×C₆₇	1	8	yes	—
432	C₂×C₄	C₂×D₈×C₆₇	1	8	yes	—
433	C₂×C₄	C₂×D₈×C₆₇	1	4	yes	—
434	C₂×C₄	C₂×D₈×C₆₇	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
443	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
444	C₈	—	2	8	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	8	16	no	—
454	C₂²	C₂²×D₈×C₆₇	1	4	yes	—
455	C₂²	C₂²×D₈×C₆₇	1	2	yes	—
456	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	8	no	—
462	C₄	C₂²×D₈×C₆₇	1	2	yes	—
463	C₄	C₂²×D₈×C₆₇	1	4	yes	—
464	C₄	C₂²×D₈×C₆₇	1	2	yes	—
465	C₄	#575×C₆₇	1	2	yes	—
466	C₄	#585×C₆₇	1	2	yes	—
467	C₂	—	2	4	no	—
468	C₂	—	2	2	no	—
469	C₂	—	8	8	no	—
470	C₂	C₆₇×#3449	1	1	yes	characteristic
471	C₂	C₂³×D₈×C₆₇	1	1	yes	characteristic
472	C₂	C₂×#575×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#532×C₆₇	C₂	semidirect
2. C₆₇×#3245	C₂	semidirect
3. C₆₇×#3226	C₂	semidirect
4. C₆₇×#3205	C₂	semidirect
5. C₆₇×#3186	C₂	semidirect
6. C₆₇×#3169	C₂	semidirect
7. C₆₇×#3100	C₂	semidirect
8. C₂×#431×C₆₇	C₂	semidirect
16. #532×C₆₇	C₂²	semidirect
17. #532×C₆₇	C₂²	semidirect
18. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
19. C₂×#127×C₆₇	C₂²	semidirect
24. C₂×C₄×D₄×C₆₇	C₂²	semidirect
26. #500×C₆₇	C₂²	semidirect
27. #493×C₆₇	C₂²	semidirect
28. #486×C₆₇	C₂²	semidirect
29. #480×C₆₇	C₂²	semidirect
30. #474×C₆₇	C₂²	semidirect
31. #466×C₆₇	C₂²	semidirect
32. #459×C₆₇	C₂²	semidirect
33. #447×C₆₇	C₂²	semidirect
34. C₄×D₈×C₆₇	C₂²	semidirect
35. #431×C₆₇	C₂²	semidirect
36. #431×C₆₇	C₂²	semidirect
37. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
39. C₂×C₄×C₈×C₆₇	C₂²	semidirect
129. C₂²×C₄×C₆₇	D₈	semidirect
230. #60940	C₆₇	direct (N × H)
237. C₂×#532	C₂×C₆₇	semidirect
238. #3245	C₂×C₆₇	semidirect
239. #3226	C₂×C₆₇	semidirect
240. #3205	C₂×C₆₇	semidirect
241. #3186	C₂×C₆₇	semidirect
242. #3169	C₂×C₆₇	semidirect
243. #3100	C₂×C₆₇	semidirect
244. C₂×#431	C₂×C₆₇	semidirect
245. C₆₇	#60940	direct (N × H)
253. #532	C₂²×C₆₇	semidirect
254. #532	C₂²×C₆₇	semidirect
255. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
256. C₂×#127	C₂²×C₆₇	semidirect
261. C₂×C₄×D₄	C₂²×C₆₇	semidirect
263. #500	C₂²×C₆₇	semidirect
264. #493	C₂²×C₆₇	semidirect
265. #486	C₂²×C₆₇	semidirect
266. #480	C₂²×C₆₇	semidirect
267. #474	C₂²×C₆₇	semidirect
268. #466	C₂²×C₆₇	semidirect
269. #459	C₂²×C₆₇	semidirect
270. #447	C₂²×C₆₇	semidirect
271. C₄×D₈	C₂²×C₆₇	semidirect
272. #431	C₂²×C₆₇	semidirect
273. #431	C₂²×C₆₇	semidirect
274. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
276. C₂×C₄×C₈	C₂²×C₆₇	semidirect
366. C₂²×C₄	D₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₆₇	2
C₆₇×#3245	2
C₆₇×#3226	2
C₆₇×#3205	2
C₆₇×#3186	2
C₆₇×#3169	2
C₆₇×#3100	2
C₂×#431×C₆₇	2
#60940	67

Subgroups — C67×#60940 #30740191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60940 #30740191