Subgroups — C₄×#535×C₆₇ #30713339

Order 17152.

3602 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2328	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2326	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2324	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2321	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2311	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#127×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₄×#121×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₄×#120×C₆₇	C₂	1	4	yes	maximal, complemented
15	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
19	#535×C₆₇	C₄	1	16	yes	direct product factor
20	C₂×#127×C₆₇	C₂²	1	2	yes	—
21	C₂×#124×C₆₇	C₂²	1	2	yes	—
22	C₂×#121×C₆₇	C₂²	1	4	yes	—
23	C₂×#120×C₆₇	C₂²	1	4	yes	—
24	C₄×#41×C₆₇	—	2	8	no	—
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₆₇	—	2	8	no	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
41	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
45	#391×C₆₇	C₂²	1	2	yes	complemented
46	#390×C₆₇	C₂²	1	4	yes	—
47	#390×C₆₇	C₂²	1	2	yes	—
48	#390×C₆₇	C₂²	1	2	yes	—
49	#390×C₆₇	C₂²	1	2	yes	complemented
50	#390×C₆₇	C₂²	1	8	yes	complemented
51	#389×C₆₇	C₂²	1	4	yes	complemented
52	#388×C₆₇	C₂²	1	8	yes	complemented
53	#388×C₆₇	C₂²	1	8	yes	complemented
54	#386×C₆₇	C₂²	1	4	yes	—
55	#386×C₆₇	C₂²	1	8	yes	complemented
56	#386×C₆₇	C₂²	1	8	yes	complemented
57	#385×C₆₇	C₂²	1	4	yes	—
58	#385×C₆₇	C₂²	1	8	yes	complemented
59	#384×C₆₇	C₂²	1	2	yes	complemented
60	#382×C₆₇	C₂²	1	2	yes	complemented
61	#380×C₆₇	C₂²	1	4	yes	complemented
62	#379×C₆₇	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
68	#376×C₆₇	C₂²	1	2	yes	complemented
69	C₄³×C₆₇	C₂²	1	2	yes	complemented
70	C₂⁵×C₆₇	C₂³	1	2	yes	—
71	C₂×#41×C₆₇	—	2	4	no	—
72	C₂×#41×C₆₇	—	2	4	no	—
73	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
74	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₆₇	—	2	4	no	—
76	C₂²×D₄×C₆₇	—	2	4	no	—
77	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
78	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
79	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
83	C₂³×C₄×C₆₇	—	2	8	no	—
84	C₂³×C₄×C₆₇	—	4	8	no	—
85	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
87	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	#127×C₆₇	C₂×C₄	1	16	yes	complemented
95	#124×C₆₇	C₂×C₄	1	16	yes	complemented
96	#121×C₆₇	C₂×C₄	1	32	yes	complemented
97	#120×C₆₇	C₂×C₄	1	32	yes	complemented
98	C₄×Q₈×C₆₇	—	2	4	no	—
99	C₄×Q₈×C₆₇	—	2	4	no	—
100	C₄×D₄×C₆₇	—	2	8	no	—
101	C₄×D₄×C₆₇	—	2	8	no	—
102	C₄×D₄×C₆₇	—	2	8	no	—
103	C₄×D₄×C₆₇	—	2	8	no	—
104	C₄×D₄×C₆₇	—	2	8	no	—
105	C₄×D₄×C₆₇	—	2	8	no	—
106	C₄×D₄×C₆₇	—	2	4	no	—
107	C₄×D₄×C₆₇	—	2	4	no	—
108	C₄×D₄×C₆₇	—	4	16	no	—
109	#117×C₆₇	—	2	4	no	—
110	#117×C₆₇	—	2	4	no	—
111	#117×C₆₇	—	2	8	no	—
112	#117×C₆₇	C₂×C₄	1	8	yes	complemented
113	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
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	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
135	C₂×C₄²×C₆₇	—	2	8	no	—
136	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
137	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	2	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	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
148	#95×C₆₇	C₂³	1	4	yes	—
149	#95×C₆₇	C₂³	1	4	yes	—
150	#95×C₆₇	C₂³	1	8	yes	—
151	#95×C₆₇	C₂³	1	8	yes	—
152	C₂⁴×C₆₇	—	2	4	no	—
153	C₂⁴×C₆₇	—	2	4	no	—
154	C₂⁴×C₆₇	—	4	4	no	—
155	C₂⁴×C₆₇	—	4	4	no	—
156	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
157	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
158	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
159	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
160	#41×C₆₇	—	2	32	no	—
161	C₂×Q₈×C₆₇	—	2	2	no	—
162	C₂×Q₈×C₆₇	—	2	2	no	—
163	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	complemented
164	C₂×D₄×C₆₇	—	2	4	no	—
165	C₂×D₄×C₆₇	—	2	4	no	—
166	C₂×D₄×C₆₇	—	2	32	no	—
167	C₂×D₄×C₆₇	—	2	4	no	—
168	C₂×D₄×C₆₇	—	2	4	no	—
169	C₂×D₄×C₆₇	—	2	2	no	—
170	C₂×D₄×C₆₇	—	2	4	no	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	2	no	—
173	C₂×D₄×C₆₇	—	4	8	no	—
174	C₂×D₄×C₆₇	—	4	8	no	—
175	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
177	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
178	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	complemented
179	C₂×D₄×C₆₇	C₂²×C₄	1	32	yes	complemented
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	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	2	4	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	—	2	16	no	—
190	C₂²×C₄×C₆₇	—	4	8	no	—
191	C₂²×C₄×C₆₇	—	4	4	no	—
192	C₂²×C₄×C₆₇	—	4	2	no	—
193	C₂²×C₄×C₆₇	—	4	4	no	—
194	C₂²×C₄×C₆₇	—	4	32	no	—
195	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
197	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₆₇	#41	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
213	C₄⋊C₄×C₆₇	—	2	4	no	—
214	C₄⋊C₄×C₆₇	—	2	4	no	—
215	C₄⋊C₄×C₆₇	—	2	4	no	—
216	C₄⋊C₄×C₆₇	—	2	4	no	—
217	C₄⋊C₄×C₆₇	—	2	2	no	—
218	C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₄⋊C₄×C₆₇	—	2	4	no	—
220	C₄⋊C₄×C₆₇	—	4	8	no	—
221	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
222	C₂²⋊C₄×C₆₇	—	2	4	no	—
223	C₂²⋊C₄×C₆₇	—	2	4	no	—
224	C₂²⋊C₄×C₆₇	—	2	8	no	—
225	C₂²⋊C₄×C₆₇	—	2	8	no	—
226	C₂²⋊C₄×C₆₇	—	2	4	no	—
227	C₂²⋊C₄×C₆₇	—	2	4	no	—
228	C₂²⋊C₄×C₆₇	—	4	8	no	—
229	C₂²⋊C₄×C₆₇	—	4	8	no	—
230	C₂²⋊C₄×C₆₇	—	4	8	no	—
231	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₆₇	C₂²×C₄	1	32	yes	complemented
233	C₄²×C₆₇	—	2	4	no	—
234	C₄²×C₆₇	—	2	4	no	—
235	C₄²×C₆₇	—	2	4	no	—
236	C₄²×C₆₇	—	2	4	no	—
237	C₄²×C₆₇	—	2	8	no	—
238	C₄²×C₆₇	—	4	4	no	—
239	C₄²×C₆₇	C₂²×C₄	1	8	yes	complemented
240	C₄²×C₆₇	C₂×D₄	1	4	yes	—
241	C₄²×C₆₇	C₂×D₄	1	4	yes	—
242	C₄²×C₆₇	C₂×D₄	1	4	yes	—
243	C₄²×C₆₇	C₂×D₄	1	4	yes	—
244	C₂³×C₆₇	—	2	2	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	16	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	4	no	—
251	C₂³×C₆₇	—	2	4	no	—
252	C₂³×C₆₇	—	2	8	no	—
253	C₂³×C₆₇	—	2	8	no	—
254	C₂³×C₆₇	—	2	4	no	—
255	C₂³×C₆₇	—	4	16	no	—
256	C₂³×C₆₇	—	4	8	no	—
257	C₂³×C₆₇	—	4	8	no	—
258	C₂³×C₆₇	—	4	16	no	—
259	C₂³×C₆₇	C₂³×C₄	1	8	yes	—
260	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
261	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
262	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
263	C₂³×C₆₇	C₂×#41	1	2	yes	—
264	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
265	Q₈×C₆₇	—	2	8	no	—
266	D₄×C₆₇	—	2	16	no	—
267	D₄×C₆₇	—	2	16	no	—
268	D₄×C₆₇	—	2	16	no	—
269	D₄×C₆₇	—	2	8	no	—
270	D₄×C₆₇	—	4	32	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	4	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	4	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	16	no	—
279	C₂×C₄×C₆₇	—	2	8	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	4	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	8	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	4	4	no	—
290	C₂×C₄×C₆₇	—	4	8	no	—
291	C₂×C₄×C₆₇	—	4	16	no	—
292	C₂×C₄×C₆₇	—	4	8	no	—
293	C₂×C₄×C₆₇	—	4	8	no	—
294	C₂×C₄×C₆₇	—	4	16	no	—
295	C₂×C₄×C₆₇	C₄×D₄	1	16	yes	complemented
296	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
297	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
298	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₆₇	C₂²×D₄	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	H(5,𝔽₂)	1	4	yes	—
309	C₂²×C₆₇	—	2	4	no	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	2	2	no	—
312	C₂²×C₆₇	—	2	4	no	—
313	C₂²×C₆₇	—	2	4	no	—
314	C₂²×C₆₇	—	2	8	no	—
315	C₂²×C₆₇	—	2	8	no	—
316	C₂²×C₆₇	—	2	16	no	—
317	C₂²×C₆₇	—	4	32	no	—
318	C₂²×C₆₇	—	4	4	no	—
319	C₂²×C₆₇	—	4	2	no	—
320	C₂²×C₆₇	—	4	2	no	—
321	C₂²×C₆₇	—	4	4	no	—
322	C₂²×C₆₇	—	4	4	no	—
323	C₂²×C₆₇	—	4	8	no	—
324	C₂²×C₆₇	C₂×C₄×D₄	1	4	yes	—
325	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
326	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
327	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
329	C₂²×C₆₇	#585	1	2	yes	—
330	C₄×C₆₇	—	2	4	no	—
331	C₄×C₆₇	—	2	8	no	—
332	C₄×C₆₇	—	2	2	no	—
333	C₄×C₆₇	—	2	2	no	—
334	C₄×C₆₇	—	2	2	no	—
335	C₄×C₆₇	—	4	2	no	—
336	C₄×C₆₇	—	4	4	no	—
337	C₄×C₆₇	—	4	2	no	—
338	C₄×C₆₇	—	4	4	no	—
339	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
340	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
341	C₄×C₆₇	#535	1	4	yes	direct product factor
342	C₄×#535	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂×C₆₇	—	2	4	no	—
344	C₂×C₆₇	—	4	4	no	—
345	C₂×C₆₇	—	4	8	no	—
346	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
347	C₂×C₆₇	C₄×H(5,𝔽₂)	1	2	yes	—
348	C₂×C₆₇	C₂×#535	1	1	yes	characteristic
349	C₂×C₆₇	#3449	1	1	yes	characteristic
350	C₂×C₆₇	#3460	1	2	yes	—
351	C₂×#535	C₂×C₆₇	1	1	yes	characteristic
352	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
353	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
354	#2328	C₂×C₆₇	1	2	yes	complemented
355	#2326	C₂×C₆₇	1	2	yes	complemented
356	#2324	C₂×C₆₇	1	4	yes	complemented
357	#2321	C₂×C₆₇	1	4	yes	complemented
358	#2317	C₂×C₆₇	1	1	yes	characteristic, complemented
359	#2311	C₂×C₆₇	1	1	yes	characteristic, complemented
360	#2309	C₂×C₆₇	1	1	yes	characteristic, complemented
361	C₄×#127	C₂×C₆₇	1	2	yes	complemented
362	C₄×#124	C₂×C₆₇	1	2	yes	complemented
363	C₄×#121	C₂×C₆₇	1	4	yes	complemented
364	C₄×#120	C₂×C₆₇	1	4	yes	complemented
365	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
366	C₆₇	C₄×#535	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
368	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
370	#535	C₄×C₆₇	1	16	yes	direct product factor
371	C₂×#127	C₂²×C₆₇	1	2	yes	—
372	C₂×#124	C₂²×C₆₇	1	2	yes	—
373	C₂×#121	C₂²×C₆₇	1	4	yes	—
374	C₂×#120	C₂²×C₆₇	1	4	yes	—
375	C₄×#41	—	2	8	no	—
376	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
377	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
378	C₂×C₄×D₄	—	2	8	no	—
379	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
380	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
381	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
385	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
386	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
387	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
388	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
389	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
390	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
391	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
392	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
394	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
396	#391	C₂²×C₆₇	1	2	yes	complemented
397	#390	C₂²×C₆₇	1	2	yes	—
398	#390	C₂²×C₆₇	1	4	yes	—
399	#390	C₂²×C₆₇	1	2	yes	—
400	#390	C₂²×C₆₇	1	2	yes	complemented
401	#390	C₂²×C₆₇	1	8	yes	complemented
402	#389	C₂²×C₆₇	1	4	yes	complemented
403	#388	C₂²×C₆₇	1	8	yes	complemented
404	#388	C₂²×C₆₇	1	8	yes	complemented
405	#386	C₂²×C₆₇	1	4	yes	—
406	#386	C₂²×C₆₇	1	8	yes	complemented
407	#386	C₂²×C₆₇	1	8	yes	complemented
408	#385	C₂²×C₆₇	1	4	yes	—
409	#385	C₂²×C₆₇	1	8	yes	complemented
410	#384	C₂²×C₆₇	1	2	yes	complemented
411	#382	C₂²×C₆₇	1	2	yes	complemented
412	#380	C₂²×C₆₇	1	4	yes	complemented
413	#379	C₂²×C₆₇	1	4	yes	—
414	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
415	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
416	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
419	#376	C₂²×C₆₇	1	2	yes	complemented
420	C₄³	C₂²×C₆₇	1	2	yes	complemented
421	C₂⁵	C₂³×C₆₇	1	2	yes	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	—	2	4	no	—
424	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
425	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
426	C₂²×D₄	—	2	4	no	—
427	C₂²×D₄	—	2	4	no	—
428	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
429	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
430	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
431	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
432	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
433	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
434	C₂³×C₄	—	2	8	no	—
435	C₂³×C₄	—	4	8	no	—
436	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
437	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
438	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
439	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
441	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
442	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
443	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
445	#127	C₂×C₄×C₆₇	1	16	yes	complemented
446	#124	C₂×C₄×C₆₇	1	16	yes	complemented
447	#121	C₂×C₄×C₆₇	1	32	yes	complemented
448	#120	C₂×C₄×C₆₇	1	32	yes	complemented
449	C₄×Q₈	—	2	4	no	—
450	C₄×Q₈	—	2	4	no	—
451	C₄×D₄	—	2	8	no	—
452	C₄×D₄	—	2	8	no	—
453	C₄×D₄	—	2	8	no	—
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	2	8	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	—	2	4	no	—
459	C₄×D₄	—	4	16	no	—
460	#117	—	2	4	no	—
461	#117	—	2	4	no	—
462	#117	—	2	8	no	—
463	#117	C₂×C₄×C₆₇	1	8	yes	complemented
464	C₂×C₄⋊C₄	—	2	4	no	—
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
474	C₂×C₂²⋊C₄	—	2	8	no	—
475	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
486	C₂×C₄²	—	2	8	no	—
487	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
488	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
490	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
493	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
494	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
499	#95	C₂³×C₆₇	1	4	yes	—
500	#95	C₂³×C₆₇	1	4	yes	—
501	#95	C₂³×C₆₇	1	8	yes	—
502	#95	C₂³×C₆₇	1	8	yes	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	4	4	no	—
506	C₂⁴	—	4	4	no	—
507	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
508	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
509	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
510	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
511	#41	—	2	32	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	complemented
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	32	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	4	8	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
527	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
528	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
529	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	complemented
530	C₂×D₄	C₂²×C₄×C₆₇	1	32	yes	complemented
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	8	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	16	no	—
541	C₂²×C₄	—	4	8	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	32	no	—
546	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
547	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
548	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
550	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
551	C₂²×C₄	#41×C₆₇	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	4	8	no	—
572	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	4	8	no	—
580	C₂²⋊C₄	—	4	8	no	—
581	C₂²⋊C₄	—	4	8	no	—
582	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₆₇	1	32	yes	complemented
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	8	no	—
589	C₄²	—	4	4	no	—
590	C₄²	C₂²×C₄×C₆₇	1	8	yes	complemented
591	C₄²	C₂×D₄×C₆₇	1	4	yes	—
592	C₄²	C₂×D₄×C₆₇	1	4	yes	—
593	C₄²	C₂×D₄×C₆₇	1	4	yes	—
594	C₄²	C₂×D₄×C₆₇	1	4	yes	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	16	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	4	16	no	—
607	C₂³	—	4	8	no	—
608	C₂³	—	4	8	no	—
609	C₂³	—	4	16	no	—
610	C₂³	C₂³×C₄×C₆₇	1	8	yes	—
611	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
612	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
613	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
614	C₂³	C₂×#41×C₆₇	1	2	yes	—
615	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
616	Q₈	—	2	8	no	—
617	D₄	—	2	16	no	—
618	D₄	—	2	16	no	—
619	D₄	—	2	16	no	—
620	D₄	—	2	8	no	—
621	D₄	—	4	32	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	16	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	16	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	16	no	—
645	C₂×C₄	—	4	8	no	—
646	C₂×C₄	C₄×D₄×C₆₇	1	16	yes	complemented
647	C₂×C₄	C₂³×C₄×C₆₇	1	8	yes	—
648	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
649	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
650	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
654	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
657	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
658	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
659	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	2	8	no	—
667	C₂²	—	2	16	no	—
668	C₂²	—	4	32	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	8	no	—
674	C₂²	—	4	4	no	—
675	C₂²	C₂×C₄×D₄×C₆₇	1	4	yes	—
676	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
677	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
678	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
679	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
680	C₂²	#585×C₆₇	1	2	yes	—
681	C₄	—	2	4	no	—
682	C₄	—	2	8	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	4	no	—
690	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
691	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
692	C₄	#535×C₆₇	1	4	yes	direct product factor
693	C₂	—	2	4	no	—
694	C₂	—	4	8	no	—
695	C₂	—	4	4	no	—
696	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic
697	C₂	C₄×H(5,𝔽₂)×C₆₇	1	2	yes	—
698	C₂	C₂×#535×C₆₇	1	1	yes	characteristic
699	C₂	C₆₇×#3449	1	1	yes	characteristic
700	C₂	C₆₇×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#535×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₂²×C₄×D₄×C₆₇	C₂	semidirect
4. C₆₇×#2328	C₂	semidirect
5. C₆₇×#2326	C₂	semidirect
6. C₆₇×#2324	C₂	semidirect
7. C₆₇×#2321	C₂	semidirect
8. C₆₇×#2317	C₂	semidirect
9. C₆₇×#2311	C₂	semidirect
10. C₆₇×#2309	C₂	semidirect
11. C₄×#127×C₆₇	C₂	semidirect
12. C₄×#124×C₆₇	C₂	semidirect
13. C₄×#121×C₆₇	C₂	semidirect
14. C₄×#120×C₆₇	C₂	semidirect
15. C₄×#117×C₆₇	C₂	semidirect
19. #535×C₆₇	C₄	direct (N × H)
25. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
26. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×C₄×D₄×C₆₇	C₂²	semidirect
40. C₂×#117×C₆₇	C₂²	semidirect
44. C₂²×C₄²×C₆₇	C₂²	semidirect
45. #391×C₆₇	C₂²	semidirect
49. #390×C₆₇	C₂²	semidirect
50. #390×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
52. #388×C₆₇	C₂²	semidirect
53. #388×C₆₇	C₂²	semidirect
55. #386×C₆₇	C₂²	semidirect
56. #386×C₆₇	C₂²	semidirect
58. #385×C₆₇	C₂²	semidirect
59. #384×C₆₇	C₂²	semidirect
60. #382×C₆₇	C₂²	semidirect
61. #380×C₆₇	C₂²	semidirect
63. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
64. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
67. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
68. #376×C₆₇	C₂²	semidirect
69. C₄³×C₆₇	C₂²	semidirect
73. C₂×#41×C₆₇	C₂×C₄	semidirect
77. C₂²×D₄×C₆₇	C₂×C₄	semidirect
94. #127×C₆₇	C₂×C₄	semidirect
95. #124×C₆₇	C₂×C₄	semidirect
96. #121×C₆₇	C₂×C₄	semidirect
97. #120×C₆₇	C₂×C₄	semidirect
112. #117×C₆₇	C₂×C₄	semidirect
136. C₂×C₄²×C₆₇	D₄	semidirect
163. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
178. C₂×D₄×C₆₇	C₂²×C₄	semidirect
179. C₂×D₄×C₆₇	C₂²×C₄	semidirect
196. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
221. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
232. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
239. C₄²×C₆₇	C₂²×C₄	semidirect
295. C₂×C₄×C₆₇	C₄×D₄	semidirect
341. C₄×C₆₇	#535	direct (N × H)
342. C₄×#535	C₆₇	direct (N × H)
352. C₂×C₄×#41	C₂×C₆₇	semidirect
353. C₂²×C₄×D₄	C₂×C₆₇	semidirect
354. #2328	C₂×C₆₇	semidirect
355. #2326	C₂×C₆₇	semidirect
356. #2324	C₂×C₆₇	semidirect
357. #2321	C₂×C₆₇	semidirect
358. #2317	C₂×C₆₇	semidirect
359. #2311	C₂×C₆₇	semidirect
360. #2309	C₂×C₆₇	semidirect
361. C₄×#127	C₂×C₆₇	semidirect
362. C₄×#124	C₂×C₆₇	semidirect
363. C₄×#121	C₂×C₆₇	semidirect
364. C₄×#120	C₂×C₆₇	semidirect
365. C₄×#117	C₂×C₆₇	semidirect
366. C₆₇	C₄×#535	direct (N × H)
370. #535	C₄×C₆₇	direct (N × H)
376. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
377. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
385. C₂×C₄×D₄	C₂²×C₆₇	semidirect
386. C₂×C₄×D₄	C₂²×C₆₇	semidirect
387. C₂×C₄×D₄	C₂²×C₆₇	semidirect
391. C₂×#117	C₂²×C₆₇	semidirect
395. C₂²×C₄²	C₂²×C₆₇	semidirect
396. #391	C₂²×C₆₇	semidirect
400. #390	C₂²×C₆₇	semidirect
401. #390	C₂²×C₆₇	semidirect
402. #389	C₂²×C₆₇	semidirect
403. #388	C₂²×C₆₇	semidirect
404. #388	C₂²×C₆₇	semidirect
406. #386	C₂²×C₆₇	semidirect
407. #386	C₂²×C₆₇	semidirect
409. #385	C₂²×C₆₇	semidirect
410. #384	C₂²×C₆₇	semidirect
411. #382	C₂²×C₆₇	semidirect
412. #380	C₂²×C₆₇	semidirect
414. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
415. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
418. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
419. #376	C₂²×C₆₇	semidirect
420. C₄³	C₂²×C₆₇	semidirect
424. C₂×#41	C₂×C₄×C₆₇	semidirect
428. C₂²×D₄	C₂×C₄×C₆₇	semidirect
445. #127	C₂×C₄×C₆₇	semidirect
446. #124	C₂×C₄×C₆₇	semidirect
447. #121	C₂×C₄×C₆₇	semidirect
448. #120	C₂×C₄×C₆₇	semidirect
463. #117	C₂×C₄×C₆₇	semidirect
487. C₂×C₄²	D₄×C₆₇	semidirect
514. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
529. C₂×D₄	C₂²×C₄×C₆₇	semidirect
530. C₂×D₄	C₂²×C₄×C₆₇	semidirect
547. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
572. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
583. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
590. C₄²	C₂²×C₄×C₆₇	semidirect
646. C₂×C₄	C₄×D₄×C₆₇	semidirect
692. C₄	#535×C₆₇	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×#535×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2328	2
C₆₇×#2326	2
C₆₇×#2324	2
C₆₇×#2321	2
C₆₇×#2317	2
C₆₇×#2311	2
C₆₇×#2309	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
C₄×#121×C₆₇	2
C₄×#120×C₆₇	2
C₄×#117×C₆₇	2
C₄×#535	67

Subgroups — C4×#535×C67 #30713339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#535×C₆₇ #30713339