Subgroups — C₆₇×#59678 #30738929

Order 17152.

1872 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2796	C₂	1	4	yes	maximal, complemented
2	C₆₇×#2597	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2562	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2544	C₂	1	2	yes	maximal
7	C₆₇×#2511	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2487	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2485	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2448	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic
17	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	2	yes	—
22	C₂×#124×C₆₇	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×#117×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
31	#400×C₆₇	C₂²	1	4	yes	—
32	#400×C₆₇	C₂²	1	4	yes	—
33	#399×C₆₇	C₂²	1	4	yes	—
34	#397×C₆₇	C₂²	1	4	yes	—
35	#397×C₆₇	C₂²	1	4	yes	—
36	#397×C₆₇	C₂²	1	4	yes	—
37	#394×C₆₇	C₂²	1	4	yes	—
38	#394×C₆₇	C₂²	1	4	yes	—
39	#391×C₆₇	C₂²	1	2	yes	—
40	#391×C₆₇	C₂²	1	2	yes	—
41	#391×C₆₇	C₂²	1	2	yes	—
42	#390×C₆₇	C₂²	1	2	yes	—
43	#390×C₆₇	C₂²	1	2	yes	—
44	#390×C₆₇	C₂²	1	2	yes	—
45	#390×C₆₇	C₂²	1	1	yes	characteristic
46	#390×C₆₇	C₂²	1	1	yes	characteristic
47	#389×C₆₇	C₂²	1	2	yes	—
48	#389×C₆₇	C₂²	1	2	yes	—
49	#389×C₆₇	C₂²	1	1	yes	characteristic
50	#389×C₆₇	C₂²	1	1	yes	characteristic
51	#389×C₆₇	C₂²	1	2	yes	—
52	#388×C₆₇	C₂²	1	4	yes	—
53	#388×C₆₇	C₂²	1	4	yes	—
54	#388×C₆₇	C₂²	1	4	yes	—
55	#388×C₆₇	C₂²	1	4	yes	—
56	#388×C₆₇	C₂²	1	4	yes	—
57	#387×C₆₇	C₂²	1	4	yes	—
58	#387×C₆₇	C₂²	1	4	yes	—
59	#387×C₆₇	C₂²	1	2	yes	—
60	#387×C₆₇	C₂²	1	2	yes	—
61	#386×C₆₇	C₂²	1	4	yes	—
62	#386×C₆₇	C₂²	1	4	yes	—
63	#385×C₆₇	C₂²	1	4	yes	—
64	#385×C₆₇	C₂²	1	4	yes	—
65	#384×C₆₇	C₂²	1	1	yes	characteristic
66	#384×C₆₇	C₂²	1	1	yes	characteristic
67	#382×C₆₇	C₂²	1	1	yes	characteristic
68	#380×C₆₇	C₂²	1	2	yes	—
69	#380×C₆₇	C₂²	1	2	yes	—
70	#380×C₆₇	C₂²	1	2	yes	—
71	#380×C₆₇	C₂²	1	2	yes	—
72	#380×C₆₇	C₂²	1	2	yes	—
73	#380×C₆₇	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
82	C₄³×C₆₇	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
91	C₄⋊Q₈×C₆₇	—	2	4	no	—
92	#127×C₆₇	—	2	4	no	—
93	#125×C₆₇	—	2	4	no	—
94	#124×C₆₇	—	2	8	no	—
95	#124×C₆₇	—	4	4	no	—
96	C₄×Q₈×C₆₇	—	4	4	no	—
97	C₄×D₄×C₆₇	—	2	8	no	—
98	C₄×D₄×C₆₇	—	2	4	no	—
99	C₄×D₄×C₆₇	—	2	4	no	—
100	C₄×D₄×C₆₇	—	4	4	no	—
101	C₄×D₄×C₆₇	—	4	4	no	—
102	#117×C₆₇	—	4	4	no	—
103	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
147	#95×C₆₇	C₂³	1	2	yes	—
148	#95×C₆₇	C₂³	1	4	yes	—
149	#95×C₆₇	C₂³	1	4	yes	—
150	#95×C₆₇	C₂³	1	2	yes	—
151	#95×C₆₇	C₂³	1	2	yes	—
152	#95×C₆₇	C₂³	1	2	yes	—
153	#95×C₆₇	C₂³	1	4	yes	—
154	#95×C₆₇	C₂³	1	4	yes	—
155	#95×C₆₇	C₂³	1	2	yes	—
156	#95×C₆₇	C₂³	1	2	yes	—
157	#95×C₆₇	C₂³	1	4	yes	—
158	#95×C₆₇	C₂³	1	4	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	4	yes	—
161	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
162	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
163	C₂×Q₈×C₆₇	—	2	4	no	—
164	C₂×Q₈×C₆₇	—	2	4	no	—
165	C₂×Q₈×C₆₇	—	2	4	no	—
166	C₂×D₄×C₆₇	—	2	4	no	—
167	C₂×D₄×C₆₇	—	2	4	no	—
168	C₂×D₄×C₆₇	—	2	2	no	—
169	C₂×D₄×C₆₇	—	2	4	no	—
170	C₂×D₄×C₆₇	—	2	2	no	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	2	2	no	—
173	C₂×D₄×C₆₇	—	2	2	no	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	4	2	no	—
176	C₂×D₄×C₆₇	—	4	2	no	—
177	C₂×D₄×C₆₇	#41	1	4	yes	—
178	C₂²×C₄×C₆₇	—	2	4	no	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	2	4	no	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	—	2	4	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	4	4	no	—
185	C₂²×C₄×C₆₇	—	4	4	no	—
186	C₂²×C₄×C₆₇	—	4	4	no	—
187	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
202	C₄⋊C₄×C₆₇	—	2	4	no	—
203	C₄⋊C₄×C₆₇	—	2	2	no	—
204	C₄⋊C₄×C₆₇	—	2	2	no	—
205	C₄⋊C₄×C₆₇	—	2	4	no	—
206	C₄⋊C₄×C₆₇	—	2	4	no	—
207	C₄⋊C₄×C₆₇	—	2	2	no	—
208	C₄⋊C₄×C₆₇	—	2	2	no	—
209	C₄⋊C₄×C₆₇	—	2	4	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	2	no	—
212	C₄⋊C₄×C₆₇	—	2	4	no	—
213	C₄⋊C₄×C₆₇	—	2	2	no	—
214	C₄⋊C₄×C₆₇	—	2	4	no	—
215	C₄⋊C₄×C₆₇	—	2	4	no	—
216	C₄⋊C₄×C₆₇	—	4	4	no	—
217	C₄⋊C₄×C₆₇	—	4	2	no	—
218	C₄⋊C₄×C₆₇	—	4	2	no	—
219	C₄⋊C₄×C₆₇	—	4	2	no	—
220	C₄⋊C₄×C₆₇	—	4	4	no	—
221	C₂²⋊C₄×C₆₇	—	2	8	no	—
222	C₂²⋊C₄×C₆₇	—	2	8	no	—
223	C₂²⋊C₄×C₆₇	—	2	4	no	—
224	C₂²⋊C₄×C₆₇	—	2	4	no	—
225	C₂²⋊C₄×C₆₇	—	2	4	no	—
226	C₂²⋊C₄×C₆₇	—	2	4	no	—
227	C₂²⋊C₄×C₆₇	—	4	4	no	—
228	C₂²⋊C₄×C₆₇	—	4	4	no	—
229	C₂²⋊C₄×C₆₇	—	4	2	no	—
230	C₂²⋊C₄×C₆₇	—	4	4	no	—
231	C₂²⋊C₄×C₆₇	—	4	2	no	—
232	C₂²⋊C₄×C₆₇	—	4	4	no	—
233	C₂²⋊C₄×C₆₇	—	4	4	no	—
234	C₄²×C₆₇	—	2	4	no	—
235	C₄²×C₆₇	—	2	2	no	—
236	C₄²×C₆₇	—	2	2	no	—
237	C₄²×C₆₇	—	2	4	no	—
238	C₄²×C₆₇	—	2	2	no	—
239	C₄²×C₆₇	—	2	2	no	—
240	C₄²×C₆₇	—	4	1	no	—
241	C₄²×C₆₇	—	4	4	no	—
242	C₄²×C₆₇	—	4	4	no	—
243	C₄²×C₆₇	#41	1	4	yes	—
244	C₄²×C₆₇	#41	1	4	yes	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	2	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	C₂×#41	1	4	yes	—
259	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
260	Q₈×C₆₇	—	4	8	no	—
261	D₄×C₆₇	—	2	8	no	—
262	D₄×C₆₇	—	4	8	no	—
263	D₄×C₆₇	—	4	8	no	—
264	D₄×C₆₇	—	4	4	no	—
265	C₂×C₄×C₆₇	—	2	1	no	—
266	C₂×C₄×C₆₇	—	2	1	no	—
267	C₂×C₄×C₆₇	—	2	1	no	—
268	C₂×C₄×C₆₇	—	2	1	no	—
269	C₂×C₄×C₆₇	—	2	1	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	4	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	4	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	4	8	no	—
301	C₂×C₄×C₆₇	—	4	8	no	—
302	C₂×C₄×C₆₇	—	8	8	no	—
303	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
304	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
305	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
306	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
307	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
308	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
309	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
310	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
311	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
313	C₂²×C₆₇	—	2	4	no	—
314	C₂²×C₆₇	—	2	4	no	—
315	C₂²×C₆₇	—	2	4	no	—
316	C₂²×C₆₇	—	4	2	no	—
317	C₂²×C₆₇	—	4	2	no	—
318	C₂²×C₆₇	—	4	2	no	—
319	C₂²×C₆₇	—	4	2	no	—
320	C₂²×C₆₇	—	4	2	no	—
321	C₂²×C₆₇	—	4	2	no	—
322	C₂²×C₆₇	—	4	2	no	—
323	C₂²×C₆₇	—	4	2	no	—
324	C₂²×C₆₇	—	4	2	no	—
325	C₂²×C₆₇	—	4	2	no	—
326	C₂²×C₆₇	—	4	2	no	—
327	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
329	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
330	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂²×C₆₇	#585	1	1	yes	characteristic
334	C₄×C₆₇	—	2	2	no	—
335	C₄×C₆₇	—	2	2	no	—
336	C₄×C₆₇	—	2	2	no	—
337	C₄×C₆₇	—	2	2	no	—
338	C₄×C₆₇	—	4	4	no	—
339	C₄×C₆₇	—	4	2	no	—
340	C₄×C₆₇	—	4	2	no	—
341	C₄×C₆₇	—	4	2	no	—
342	C₄×C₆₇	—	4	2	no	—
343	C₄×C₆₇	—	4	2	no	—
344	C₄×C₆₇	—	4	1	no	—
345	C₄×C₆₇	—	4	4	no	—
346	C₄×C₆₇	—	4	2	no	—
347	C₄×C₆₇	#553	1	4	yes	—
348	C₄×C₆₇	#559	1	4	yes	—
349	#59678	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂×C₆₇	—	4	4	no	—
351	C₂×C₆₇	—	8	2	no	—
352	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
353	C₂×C₆₇	#3475	1	1	yes	characteristic
354	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
355	C₂×C₆₇	#3507	1	1	yes	characteristic
356	C₂×C₆₇	#3511	1	1	yes	characteristic
357	C₂×C₆₇	#3520	1	1	yes	characteristic
358	C₂×C₆₇	#3546	1	1	yes	characteristic
359	#2796	C₂×C₆₇	1	4	yes	complemented
360	#2597	C₂×C₆₇	1	4	yes	complemented
361	#2562	C₂×C₆₇	1	2	yes	complemented
362	#2547	C₂×C₆₇	1	1	yes	characteristic, complemented
363	#2547	C₂×C₆₇	1	1	yes	characteristic, complemented
364	#2544	C₂×C₆₇	1	2	yes	—
365	#2511	C₂×C₆₇	1	2	yes	complemented
366	#2487	C₂×C₆₇	1	2	yes	complemented
367	#2485	C₂×C₆₇	1	2	yes	complemented
368	#2448	C₂×C₆₇	1	2	yes	complemented
369	#2367	C₂×C₆₇	1	2	yes	complemented
370	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
371	#2352	C₂×C₆₇	1	2	yes	complemented
372	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
373	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
374	C₄×#127	C₂×C₆₇	1	1	yes	characteristic
375	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
376	C₆₇	#59678	1	1	yes	characteristic, direct product factor, Sylow
377	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
378	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
379	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
380	C₂×#124	C₂²×C₆₇	1	2	yes	—
381	C₂×#124	C₂²×C₆₇	1	2	yes	—
382	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
388	C₂×#117	C₂²×C₆₇	1	2	yes	—
389	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
390	#400	C₂²×C₆₇	1	4	yes	—
391	#400	C₂²×C₆₇	1	4	yes	—
392	#399	C₂²×C₆₇	1	4	yes	—
393	#397	C₂²×C₆₇	1	4	yes	—
394	#397	C₂²×C₆₇	1	4	yes	—
395	#397	C₂²×C₆₇	1	4	yes	—
396	#394	C₂²×C₆₇	1	4	yes	—
397	#394	C₂²×C₆₇	1	4	yes	—
398	#391	C₂²×C₆₇	1	2	yes	—
399	#391	C₂²×C₆₇	1	2	yes	—
400	#391	C₂²×C₆₇	1	2	yes	—
401	#390	C₂²×C₆₇	1	2	yes	—
402	#390	C₂²×C₆₇	1	1	yes	characteristic
403	#390	C₂²×C₆₇	1	1	yes	characteristic
404	#390	C₂²×C₆₇	1	2	yes	—
405	#390	C₂²×C₆₇	1	2	yes	—
406	#389	C₂²×C₆₇	1	1	yes	characteristic
407	#389	C₂²×C₆₇	1	1	yes	characteristic
408	#389	C₂²×C₆₇	1	2	yes	—
409	#389	C₂²×C₆₇	1	2	yes	—
410	#389	C₂²×C₆₇	1	2	yes	—
411	#388	C₂²×C₆₇	1	4	yes	—
412	#388	C₂²×C₆₇	1	4	yes	—
413	#388	C₂²×C₆₇	1	4	yes	—
414	#388	C₂²×C₆₇	1	4	yes	—
415	#388	C₂²×C₆₇	1	4	yes	—
416	#387	C₂²×C₆₇	1	2	yes	—
417	#387	C₂²×C₆₇	1	2	yes	—
418	#387	C₂²×C₆₇	1	4	yes	—
419	#387	C₂²×C₆₇	1	4	yes	—
420	#386	C₂²×C₆₇	1	4	yes	—
421	#386	C₂²×C₆₇	1	4	yes	—
422	#385	C₂²×C₆₇	1	4	yes	—
423	#385	C₂²×C₆₇	1	4	yes	—
424	#384	C₂²×C₆₇	1	1	yes	characteristic
425	#384	C₂²×C₆₇	1	1	yes	characteristic
426	#382	C₂²×C₆₇	1	1	yes	characteristic
427	#380	C₂²×C₆₇	1	2	yes	—
428	#380	C₂²×C₆₇	1	2	yes	—
429	#380	C₂²×C₆₇	1	2	yes	—
430	#380	C₂²×C₆₇	1	2	yes	—
431	#380	C₂²×C₆₇	1	2	yes	—
432	#380	C₂²×C₆₇	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
441	C₄³	C₂²×C₆₇	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
443	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
445	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
446	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
448	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
449	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
450	C₄⋊Q₈	—	2	4	no	—
451	#127	—	2	4	no	—
452	#125	—	2	4	no	—
453	#124	—	2	8	no	—
454	#124	—	4	4	no	—
455	C₄×Q₈	—	4	4	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	—	2	4	no	—
459	C₄×D₄	—	4	4	no	—
460	C₄×D₄	—	4	4	no	—
461	#117	—	4	4	no	—
462	C₂×C₄⋊C₄	—	4	4	no	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
497	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
499	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
502	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
503	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
506	#95	C₂³×C₆₇	1	2	yes	—
507	#95	C₂³×C₆₇	1	4	yes	—
508	#95	C₂³×C₆₇	1	4	yes	—
509	#95	C₂³×C₆₇	1	2	yes	—
510	#95	C₂³×C₆₇	1	2	yes	—
511	#95	C₂³×C₆₇	1	2	yes	—
512	#95	C₂³×C₆₇	1	4	yes	—
513	#95	C₂³×C₆₇	1	4	yes	—
514	#95	C₂³×C₆₇	1	2	yes	—
515	#95	C₂³×C₆₇	1	2	yes	—
516	#95	C₂³×C₆₇	1	4	yes	—
517	#95	C₂³×C₆₇	1	4	yes	—
518	#95	C₂³×C₆₇	1	4	yes	—
519	#95	C₂³×C₆₇	1	4	yes	—
520	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
521	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
522	C₂×Q₈	—	2	4	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	#41×C₆₇	1	4	yes	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	4	no	—
546	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	4	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	4	4	no	—
600	C₄²	—	4	4	no	—
601	C₄²	—	4	1	no	—
602	C₄²	#41×C₆₇	1	4	yes	—
603	C₄²	#41×C₆₇	1	4	yes	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	C₂×#41×C₆₇	1	4	yes	—
618	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
619	Q₈	—	4	8	no	—
620	D₄	—	2	8	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	8	no	—
623	D₄	—	4	4	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	—	4	8	no	—
661	C₂×C₄	—	8	8	no	—
662	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
663	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
664	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
665	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
666	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
667	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
668	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
669	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
670	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
671	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
687	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
688	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
689	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
690	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
691	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
692	C₂²	#585×C₆₇	1	1	yes	characteristic
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	4	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	#553×C₆₇	1	4	yes	—
707	C₄	#559×C₆₇	1	4	yes	—
708	C₂	—	4	4	no	—
709	C₂	—	8	2	no	—
710	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
711	C₂	C₆₇×#3475	1	1	yes	characteristic
712	C₂	C₂×#559×C₆₇	1	1	yes	characteristic
713	C₂	C₆₇×#3507	1	1	yes	characteristic
714	C₂	C₆₇×#3511	1	1	yes	characteristic
715	C₂	C₆₇×#3520	1	1	yes	characteristic
716	C₂	C₆₇×#3546	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#127×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×#2796	C₂	semidirect
2. C₆₇×#2597	C₂	semidirect
3. C₆₇×#2562	C₂	semidirect
4. C₆₇×#2547	C₂	semidirect
5. C₆₇×#2547	C₂	semidirect
7. C₆₇×#2511	C₂	semidirect
8. C₆₇×#2487	C₂	semidirect
9. C₆₇×#2485	C₂	semidirect
10. C₆₇×#2448	C₂	semidirect
11. C₆₇×#2367	C₂	semidirect
12. C₆₇×#2354	C₂	semidirect
13. C₆₇×#2352	C₂	semidirect
14. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
17. C₄×#125×C₆₇	C₂	semidirect
349. #59678	C₆₇	direct (N × H)
359. #2796	C₂×C₆₇	semidirect
360. #2597	C₂×C₆₇	semidirect
361. #2562	C₂×C₆₇	semidirect
362. #2547	C₂×C₆₇	semidirect
363. #2547	C₂×C₆₇	semidirect
365. #2511	C₂×C₆₇	semidirect
366. #2487	C₂×C₆₇	semidirect
367. #2485	C₂×C₆₇	semidirect
368. #2448	C₂×C₆₇	semidirect
369. #2367	C₂×C₆₇	semidirect
370. #2354	C₂×C₆₇	semidirect
371. #2352	C₂×C₆₇	semidirect
372. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
373. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
375. C₄×#125	C₂×C₆₇	semidirect
376. C₆₇	#59678	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2796	2
C₆₇×#2597	2
C₆₇×#2562	2
C₆₇×#2547	2
C₆₇×#2544	2
C₆₇×#2511	2
C₆₇×#2487	2
C₆₇×#2485	2
C₆₇×#2448	2
C₆₇×#2367	2
C₆₇×#2354	2
C₆₇×#2352	2
D₄×C₄⋊C₄×C₆₇	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#127×C₆₇	2
C₄×#125×C₆₇	2
#59678	67

Subgroups — C67×#59678 #30738929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59678 #30738929