Subgroups — C₆₇×#60047 #30739298

Order 17152.

1854 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2809	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2734	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2727	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2611	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2593	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2556	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2479	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2474	C₂	1	4	yes	maximal, complemented
9	C₆₇×#2432	C₂	1	2	yes	maximal
10	C₆₇×#2373	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2369	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2296	C₂	1	2	yes	maximal, complemented
14	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂×#126×C₆₇	C₂²	1	4	yes	—
17	C₂×#125×C₆₇	C₂²	1	2	yes	—
18	C₂×#124×C₆₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
20	C₂×#117×C₆₇	C₂²	1	2	yes	—
21	C₂×#117×C₆₇	C₂²	1	2	yes	—
22	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	#400×C₆₇	C₂²	1	2	yes	—
25	#399×C₆₇	C₂²	1	4	yes	—
26	#399×C₆₇	C₂²	1	2	yes	—
27	#398×C₆₇	C₂²	1	4	yes	—
28	#398×C₆₇	C₂²	1	2	yes	—
29	#397×C₆₇	C₂²	1	2	yes	—
30	#396×C₆₇	C₂²	1	4	yes	—
31	#395×C₆₇	C₂²	1	4	yes	—
32	#394×C₆₇	C₂²	1	4	yes	—
33	#394×C₆₇	C₂²	1	4	yes	—
34	#391×C₆₇	C₂²	1	1	yes	characteristic
35	#391×C₆₇	C₂²	1	1	yes	characteristic
36	#391×C₆₇	C₂²	1	2	yes	—
37	#391×C₆₇	C₂²	1	4	yes	—
38	#390×C₆₇	C₂²	1	1	yes	characteristic
39	#390×C₆₇	C₂²	1	1	yes	characteristic
40	#390×C₆₇	C₂²	1	2	yes	—
41	#389×C₆₇	C₂²	1	2	yes	—
42	#389×C₆₇	C₂²	1	2	yes	—
43	#389×C₆₇	C₂²	1	2	yes	—
44	#389×C₆₇	C₂²	1	2	yes	—
45	#389×C₆₇	C₂²	1	4	yes	—
46	#389×C₆₇	C₂²	1	4	yes	—
47	#388×C₆₇	C₂²	1	4	yes	—
48	#388×C₆₇	C₂²	1	4	yes	—
49	#388×C₆₇	C₂²	1	4	yes	—
50	#388×C₆₇	C₂²	1	4	yes	—
51	#388×C₆₇	C₂²	1	4	yes	—
52	#388×C₆₇	C₂²	1	4	yes	—
53	#387×C₆₇	C₂²	1	4	yes	—
54	#387×C₆₇	C₂²	1	4	yes	—
55	#387×C₆₇	C₂²	1	4	yes	—
56	#386×C₆₇	C₂²	1	4	yes	—
57	#385×C₆₇	C₂²	1	4	yes	—
58	#385×C₆₇	C₂²	1	4	yes	—
59	#385×C₆₇	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
66	#376×C₆₇	C₂²	1	2	yes	—
67	C₂×#41×C₆₇	—	2	4	no	—
68	C₂×#41×C₆₇	—	4	2	no	—
69	C₂×#41×C₆₇	—	4	2	no	—
70	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
71	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
73	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
77	C₄⋊Q₈×C₆₇	—	2	8	no	—
78	#126×C₆₇	—	2	16	no	—
79	#125×C₆₇	—	4	4	no	—
80	#124×C₆₇	—	4	4	no	—
81	C₂²⋊Q₈×C₆₇	—	4	4	no	—
82	#117×C₆₇	—	2	8	no	—
83	#117×C₆₇	—	4	2	no	—
84	#117×C₆₇	—	4	4	no	—
85	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄²×C₆₇	—	4	2	no	—
111	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
112	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
115	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
119	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
120	#95×C₆₇	C₂³	1	4	yes	—
121	#95×C₆₇	C₂³	1	2	yes	—
122	#95×C₆₇	C₂³	1	2	yes	—
123	#95×C₆₇	C₂³	1	4	yes	—
124	#95×C₆₇	C₂³	1	4	yes	—
125	#95×C₆₇	C₂³	1	4	yes	—
126	#95×C₆₇	C₂³	1	4	yes	—
127	#95×C₆₇	C₂³	1	4	yes	—
128	#95×C₆₇	C₂³	1	4	yes	—
129	#95×C₆₇	C₂³	1	4	yes	—
130	#95×C₆₇	C₂³	1	4	yes	—
131	#95×C₆₇	C₂³	1	4	yes	—
132	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
133	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
134	#41×C₆₇	—	4	16	no	—
135	C₂×Q₈×C₆₇	—	2	4	no	—
136	C₂×Q₈×C₆₇	—	4	1	no	—
137	C₂×Q₈×C₆₇	—	4	1	no	—
138	C₂×Q₈×C₆₇	—	4	2	no	—
139	C₂×Q₈×C₆₇	—	4	2	no	—
140	C₂×Q₈×C₆₇	#41	1	4	yes	—
141	C₂×D₄×C₆₇	—	2	4	no	—
142	C₂×D₄×C₆₇	—	2	4	no	—
143	C₂×D₄×C₆₇	—	2	2	no	—
144	C₂×D₄×C₆₇	—	4	1	no	—
145	C₂×D₄×C₆₇	—	4	1	no	—
146	C₂×D₄×C₆₇	—	4	2	no	—
147	C₂²×C₄×C₆₇	—	2	4	no	—
148	C₂²×C₄×C₆₇	—	2	2	no	—
149	C₂²×C₄×C₆₇	—	2	4	no	—
150	C₂²×C₄×C₆₇	—	2	2	no	—
151	C₂²×C₄×C₆₇	—	2	2	no	—
152	C₂²×C₄×C₆₇	—	2	4	no	—
153	C₂²×C₄×C₆₇	—	2	4	no	—
154	C₂²×C₄×C₆₇	—	2	4	no	—
155	C₂²×C₄×C₆₇	—	4	2	no	—
156	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₆₇	—	2	4	no	—
168	C₄⋊C₄×C₆₇	—	2	8	no	—
169	C₄⋊C₄×C₆₇	—	2	8	no	—
170	C₄⋊C₄×C₆₇	—	2	8	no	—
171	C₄⋊C₄×C₆₇	—	2	8	no	—
172	C₄⋊C₄×C₆₇	—	2	8	no	—
173	C₄⋊C₄×C₆₇	—	2	8	no	—
174	C₄⋊C₄×C₆₇	—	4	2	no	—
175	C₄⋊C₄×C₆₇	—	4	2	no	—
176	C₄⋊C₄×C₆₇	—	4	1	no	—
177	C₄⋊C₄×C₆₇	—	4	1	no	—
178	C₄⋊C₄×C₆₇	—	4	2	no	—
179	C₄⋊C₄×C₆₇	—	4	2	no	—
180	C₄⋊C₄×C₆₇	—	4	4	no	—
181	C₄⋊C₄×C₆₇	—	4	2	no	—
182	C₄⋊C₄×C₆₇	#41	1	8	yes	complemented
183	C₂²⋊C₄×C₆₇	—	2	8	no	—
184	C₂²⋊C₄×C₆₇	—	2	8	no	—
185	C₂²⋊C₄×C₆₇	—	2	8	no	—
186	C₂²⋊C₄×C₆₇	—	2	8	no	—
187	C₂²⋊C₄×C₆₇	—	2	8	no	—
188	C₂²⋊C₄×C₆₇	—	2	8	no	—
189	C₂²⋊C₄×C₆₇	—	4	2	no	—
190	C₂²⋊C₄×C₆₇	—	4	4	no	—
191	C₂²⋊C₄×C₆₇	—	4	4	no	—
192	C₄²×C₆₇	—	2	8	no	—
193	C₄²×C₆₇	—	2	8	no	—
194	C₄²×C₆₇	—	2	4	no	—
195	C₄²×C₆₇	—	2	4	no	—
196	C₄²×C₆₇	—	4	1	no	—
197	C₄²×C₆₇	—	4	2	no	—
198	C₄²×C₆₇	—	4	1	no	—
199	C₄²×C₆₇	—	4	4	no	—
200	C₄²×C₆₇	—	4	2	no	—
201	C₂³×C₆₇	—	2	2	no	—
202	C₂³×C₆₇	—	2	1	no	—
203	C₂³×C₆₇	—	2	1	no	—
204	C₂³×C₆₇	—	2	2	no	—
205	C₂³×C₆₇	—	2	4	no	—
206	C₂³×C₆₇	—	2	2	no	—
207	C₂³×C₆₇	—	2	2	no	—
208	C₂³×C₆₇	—	2	2	no	—
209	C₂³×C₆₇	—	2	4	no	—
210	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
211	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
212	Q₈×C₆₇	—	4	4	no	—
213	Q₈×C₆₇	—	8	4	no	—
214	D₄×C₆₇	—	4	8	no	—
215	D₄×C₆₇	—	4	4	no	—
216	C₂×C₄×C₆₇	—	2	16	no	—
217	C₂×C₄×C₆₇	—	2	8	no	—
218	C₂×C₄×C₆₇	—	2	2	no	—
219	C₂×C₄×C₆₇	—	2	4	no	—
220	C₂×C₄×C₆₇	—	2	1	no	—
221	C₂×C₄×C₆₇	—	2	2	no	—
222	C₂×C₄×C₆₇	—	2	2	no	—
223	C₂×C₄×C₆₇	—	2	1	no	—
224	C₂×C₄×C₆₇	—	2	1	no	—
225	C₂×C₄×C₆₇	—	2	2	no	—
226	C₂×C₄×C₆₇	—	2	1	no	—
227	C₂×C₄×C₆₇	—	2	2	no	—
228	C₂×C₄×C₆₇	—	2	4	no	—
229	C₂×C₄×C₆₇	—	2	2	no	—
230	C₂×C₄×C₆₇	—	2	4	no	—
231	C₂×C₄×C₆₇	—	2	4	no	—
232	C₂×C₄×C₆₇	—	2	4	no	—
233	C₂×C₄×C₆₇	—	2	4	no	—
234	C₂×C₄×C₆₇	—	2	4	no	—
235	C₂×C₄×C₆₇	—	2	2	no	—
236	C₂×C₄×C₆₇	—	2	2	no	—
237	C₂×C₄×C₆₇	—	2	4	no	—
238	C₂×C₄×C₆₇	—	2	4	no	—
239	C₂×C₄×C₆₇	—	2	4	no	—
240	C₂×C₄×C₆₇	—	2	4	no	—
241	C₂×C₄×C₆₇	—	2	4	no	—
242	C₂×C₄×C₆₇	—	2	4	no	—
243	C₂×C₄×C₆₇	—	4	8	no	—
244	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
245	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
246	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
247	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
248	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
249	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
250	C₂²×C₆₇	—	2	2	no	—
251	C₂²×C₆₇	—	2	4	no	—
252	C₂²×C₆₇	—	4	2	no	—
253	C₂²×C₆₇	—	4	1	no	—
254	C₂²×C₆₇	—	4	1	no	—
255	C₂²×C₆₇	—	4	4	no	—
256	C₂²×C₆₇	—	4	2	no	—
257	C₂²×C₆₇	—	4	2	no	—
258	C₂²×C₆₇	—	4	4	no	—
259	C₂²×C₆₇	—	4	2	no	—
260	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
261	C₂²×C₆₇	C₂²×#41	1	2	yes	—
262	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
265	C₄×C₆₇	—	2	8	no	—
266	C₄×C₆₇	—	2	2	no	—
267	C₄×C₆₇	—	2	2	no	—
268	C₄×C₆₇	—	2	4	no	—
269	C₄×C₆₇	—	2	4	no	—
270	C₄×C₆₇	—	2	4	no	—
271	C₄×C₆₇	—	4	2	no	—
272	C₄×C₆₇	—	4	4	no	—
273	C₄×C₆₇	—	4	4	no	—
274	C₄×C₆₇	—	4	4	no	—
275	C₄×C₆₇	—	4	2	no	—
276	#60047	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₆₇	—	4	2	no	—
278	C₂×C₆₇	—	8	2	no	—
279	C₂×C₆₇	#3482	1	2	yes	—
280	C₂×C₆₇	#3483	1	1	yes	characteristic
281	C₂×C₆₇	#3490	1	1	yes	characteristic
282	C₂×C₆₇	#3492	1	2	yes	—
283	C₂×C₆₇	#3550	1	1	yes	characteristic
284	#2809	C₂×C₆₇	1	1	yes	characteristic, complemented
285	#2734	C₂×C₆₇	1	1	yes	characteristic, complemented
286	#2727	C₂×C₆₇	1	2	yes	complemented
287	#2611	C₂×C₆₇	1	2	yes	complemented
288	#2593	C₂×C₆₇	1	2	yes	complemented
289	#2556	C₂×C₆₇	1	4	yes	complemented
290	#2479	C₂×C₆₇	1	4	yes	complemented
291	#2474	C₂×C₆₇	1	4	yes	complemented
292	#2432	C₂×C₆₇	1	2	yes	—
293	#2373	C₂×C₆₇	1	4	yes	complemented
294	#2369	C₂×C₆₇	1	2	yes	complemented
295	#2297	C₂×C₆₇	1	1	yes	characteristic
296	#2296	C₂×C₆₇	1	2	yes	complemented
297	C₆₇	#60047	1	1	yes	characteristic, direct product factor, Sylow
298	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
299	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
300	C₂×#126	C₂²×C₆₇	1	4	yes	—
301	C₂×#125	C₂²×C₆₇	1	2	yes	—
302	C₂×#124	C₂²×C₆₇	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
304	C₂×#117	C₂²×C₆₇	1	2	yes	—
305	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
306	C₂×#117	C₂²×C₆₇	1	2	yes	—
307	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
308	#400	C₂²×C₆₇	1	2	yes	—
309	#399	C₂²×C₆₇	1	2	yes	—
310	#399	C₂²×C₆₇	1	4	yes	—
311	#398	C₂²×C₆₇	1	2	yes	—
312	#398	C₂²×C₆₇	1	4	yes	—
313	#397	C₂²×C₆₇	1	2	yes	—
314	#396	C₂²×C₆₇	1	4	yes	—
315	#395	C₂²×C₆₇	1	4	yes	—
316	#394	C₂²×C₆₇	1	4	yes	—
317	#394	C₂²×C₆₇	1	4	yes	—
318	#391	C₂²×C₆₇	1	1	yes	characteristic
319	#391	C₂²×C₆₇	1	2	yes	—
320	#391	C₂²×C₆₇	1	4	yes	—
321	#391	C₂²×C₆₇	1	1	yes	characteristic
322	#390	C₂²×C₆₇	1	1	yes	characteristic
323	#390	C₂²×C₆₇	1	2	yes	—
324	#390	C₂²×C₆₇	1	1	yes	characteristic
325	#389	C₂²×C₆₇	1	4	yes	—
326	#389	C₂²×C₆₇	1	4	yes	—
327	#389	C₂²×C₆₇	1	2	yes	—
328	#389	C₂²×C₆₇	1	2	yes	—
329	#389	C₂²×C₆₇	1	2	yes	—
330	#389	C₂²×C₆₇	1	2	yes	—
331	#388	C₂²×C₆₇	1	4	yes	—
332	#388	C₂²×C₆₇	1	4	yes	—
333	#388	C₂²×C₆₇	1	4	yes	—
334	#388	C₂²×C₆₇	1	4	yes	—
335	#388	C₂²×C₆₇	1	4	yes	—
336	#388	C₂²×C₆₇	1	4	yes	—
337	#387	C₂²×C₆₇	1	4	yes	—
338	#387	C₂²×C₆₇	1	4	yes	—
339	#387	C₂²×C₆₇	1	4	yes	—
340	#386	C₂²×C₆₇	1	4	yes	—
341	#385	C₂²×C₆₇	1	4	yes	—
342	#385	C₂²×C₆₇	1	4	yes	—
343	#385	C₂²×C₆₇	1	4	yes	—
344	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
345	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
346	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
347	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
350	#376	C₂²×C₆₇	1	2	yes	—
351	C₂×#41	—	2	4	no	—
352	C₂×#41	—	4	2	no	—
353	C₂×#41	—	4	2	no	—
354	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
355	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
357	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
359	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
361	C₄⋊Q₈	—	2	8	no	—
362	#126	—	2	16	no	—
363	#125	—	4	4	no	—
364	#124	—	4	4	no	—
365	C₂²⋊Q₈	—	4	4	no	—
366	#117	—	2	8	no	—
367	#117	—	4	2	no	—
368	#117	—	4	4	no	—
369	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
394	C₂×C₄²	—	4	2	no	—
395	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
396	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
397	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
398	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
399	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
400	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
401	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
402	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
404	#95	C₂³×C₆₇	1	4	yes	—
405	#95	C₂³×C₆₇	1	2	yes	—
406	#95	C₂³×C₆₇	1	2	yes	—
407	#95	C₂³×C₆₇	1	4	yes	—
408	#95	C₂³×C₆₇	1	4	yes	—
409	#95	C₂³×C₆₇	1	4	yes	—
410	#95	C₂³×C₆₇	1	4	yes	—
411	#95	C₂³×C₆₇	1	4	yes	—
412	#95	C₂³×C₆₇	1	4	yes	—
413	#95	C₂³×C₆₇	1	4	yes	—
414	#95	C₂³×C₆₇	1	4	yes	—
415	#95	C₂³×C₆₇	1	4	yes	—
416	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
417	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
418	#41	—	4	16	no	—
419	C₂×Q₈	—	2	4	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	—	4	1	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	#41×C₆₇	1	4	yes	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	4	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	#41×C₆₇	1	8	yes	complemented
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₄²	—	2	8	no	—
477	C₄²	—	2	8	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	4	1	no	—
481	C₄²	—	4	2	no	—
482	C₄²	—	4	1	no	—
483	C₄²	—	4	4	no	—
484	C₄²	—	4	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
495	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
496	Q₈	—	4	4	no	—
497	Q₈	—	8	4	no	—
498	D₄	—	4	8	no	—
499	D₄	—	4	4	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	16	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
529	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
530	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
531	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
532	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
533	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	4	no	—
544	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
545	C₂²	C₂²×#41×C₆₇	1	2	yes	—
546	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
547	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
548	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
549	C₄	—	2	8	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	4	no	—
553	C₄	—	2	4	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	4	no	—
560	C₂	—	4	2	no	—
561	C₂	—	8	2	no	—
562	C₂	C₆₇×#3482	1	2	yes	—
563	C₂	C₆₇×#3483	1	1	yes	characteristic
564	C₂	C₆₇×#3490	1	1	yes	characteristic
565	C₂	C₆₇×#3492	1	2	yes	—
566	C₂	C₆₇×#3550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2809	C₂	semidirect
2. C₆₇×#2734	C₂	semidirect
3. C₆₇×#2727	C₂	semidirect
4. C₆₇×#2611	C₂	semidirect
5. C₆₇×#2593	C₂	semidirect
6. C₆₇×#2556	C₂	semidirect
7. C₆₇×#2479	C₂	semidirect
8. C₆₇×#2474	C₂	semidirect
10. C₆₇×#2373	C₂	semidirect
11. C₆₇×#2369	C₂	semidirect
13. C₆₇×#2296	C₂	semidirect
182. C₄⋊C₄×C₆₇	#41	semidirect
276. #60047	C₆₇	direct (N × H)
284. #2809	C₂×C₆₇	semidirect
285. #2734	C₂×C₆₇	semidirect
286. #2727	C₂×C₆₇	semidirect
287. #2611	C₂×C₆₇	semidirect
288. #2593	C₂×C₆₇	semidirect
289. #2556	C₂×C₆₇	semidirect
290. #2479	C₂×C₆₇	semidirect
291. #2474	C₂×C₆₇	semidirect
293. #2373	C₂×C₆₇	semidirect
294. #2369	C₂×C₆₇	semidirect
296. #2296	C₂×C₆₇	semidirect
297. C₆₇	#60047	direct (N × H)
466. C₄⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2809	2
C₆₇×#2734	2
C₆₇×#2727	2
C₆₇×#2611	2
C₆₇×#2593	2
C₆₇×#2556	2
C₆₇×#2479	2
C₆₇×#2474	2
C₆₇×#2432	2
C₆₇×#2373	2
C₆₇×#2369	2
C₆₇×#2297	2
C₆₇×#2296	2
#60047	67

Subgroups — C67×#60047 #30739298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60047 #30739298