Subgroups — C₆₇×#34153 #30713404

Order 17152.

2542 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2373	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2370	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2367	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2361	C₂	1	2	yes	maximal
6	C₆₇×#2360	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2359	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2298	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2296	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2290	C₂	1	2	yes	maximal, complemented
13	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₆₇	C₄	1	16	yes	complemented
19	C₂×#126×C₆₇	C₂²	1	2	yes	—
20	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
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	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	2	yes	—
32	C₂×#117×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
38	#391×C₆₇	C₂²	1	2	yes	—
39	#390×C₆₇	C₂²	1	2	yes	—
40	#389×C₆₇	C₂²	1	2	yes	—
41	#389×C₆₇	C₂²	1	2	yes	—
42	#389×C₆₇	C₂²	1	4	yes	—
43	#389×C₆₇	C₂²	1	4	yes	—
44	#388×C₆₇	C₂²	1	4	yes	—
45	#388×C₆₇	C₂²	1	4	yes	—
46	#388×C₆₇	C₂²	1	4	yes	—
47	#388×C₆₇	C₂²	1	4	yes	—
48	#387×C₆₇	C₂²	1	4	yes	—
49	#387×C₆₇	C₂²	1	4	yes	—
50	#387×C₆₇	C₂²	1	4	yes	—
51	#387×C₆₇	C₂²	1	4	yes	—
52	#386×C₆₇	C₂²	1	4	yes	—
53	#385×C₆₇	C₂²	1	4	yes	—
54	#385×C₆₇	C₂²	1	4	yes	—
55	#385×C₆₇	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
78	#376×C₆₇	C₂²	1	2	yes	—
79	#376×C₆₇	C₂²	1	2	yes	—
80	C₂×#95×C₆₇	C₂²	1	2	yes	—
81	C₄³×C₆₇	C₂²	1	1	yes	characteristic
82	C₄³×C₆₇	C₂²	1	1	yes	characteristic
83	C₄³×C₆₇	C₂²	1	2	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
93	#126×C₆₇	C₂×C₄	1	16	yes	complemented
94	#125×C₆₇	C₂×C₄	1	8	yes	complemented
95	#124×C₆₇	C₂×C₄	1	8	yes	complemented
96	#123×C₆₇	C₂×C₄	1	16	yes	complemented
97	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
98	#121×C₆₇	C₂×C₄	1	8	yes	—
99	C₄×Q₈×C₆₇	—	2	8	no	—
100	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
101	C₄×D₄×C₆₇	—	2	8	no	—
102	C₄×D₄×C₆₇	—	2	16	no	—
103	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
104	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
105	#117×C₆₇	—	2	8	no	—
106	#117×C₆₇	—	4	4	no	—
107	#117×C₆₇	C₂×C₄	1	16	yes	complemented
108	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	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	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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	2	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄²×C₆₇	—	4	4	no	—
134	C₂×C₄²×C₆₇	—	4	4	no	—
135	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	complemented
136	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
149	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
155	#95×C₆₇	C₂³	1	2	yes	—
156	#95×C₆₇	C₂³	1	4	yes	—
157	#95×C₆₇	C₂³	1	2	yes	—
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	2	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	#95×C₆₇	C₂³	1	4	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	4	yes	—
167	#95×C₆₇	C₂³	1	4	yes	—
168	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
169	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
170	C₂×Q₈×C₆₇	—	2	4	no	—
171	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
172	C₂×D₄×C₆₇	—	2	8	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
175	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₆₇	—	2	4	no	—
177	C₂²×C₄×C₆₇	—	2	4	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	4	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	—	2	8	no	—
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	—	4	4	no	—
187	C₂²×C₄×C₆₇	—	4	4	no	—
188	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	—	2	8	no	—
208	C₄⋊C₄×C₆₇	—	2	4	no	—
209	C₄⋊C₄×C₆₇	—	2	4	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	8	no	—
212	C₄⋊C₄×C₆₇	—	2	8	no	—
213	C₄⋊C₄×C₆₇	—	4	4	no	—
214	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
216	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
217	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
218	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₆₇	#41	1	8	yes	—
221	C₂²⋊C₄×C₆₇	—	2	4	no	—
222	C₂²⋊C₄×C₆₇	—	2	8	no	—
223	C₂²⋊C₄×C₆₇	—	2	8	no	—
224	C₂²⋊C₄×C₆₇	—	4	4	no	—
225	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
231	C₄²×C₆₇	—	2	4	no	—
232	C₄²×C₆₇	—	2	4	no	—
233	C₄²×C₆₇	—	2	8	no	—
234	C₄²×C₆₇	—	2	4	no	—
235	C₄²×C₆₇	—	2	8	no	—
236	C₄²×C₆₇	—	2	4	no	—
237	C₄²×C₆₇	—	2	2	no	—
238	C₄²×C₆₇	—	2	4	no	—
239	C₄²×C₆₇	—	2	4	no	—
240	C₄²×C₆₇	—	2	2	no	—
241	C₄²×C₆₇	—	2	2	no	—
242	C₄²×C₆₇	—	2	2	no	—
243	C₄²×C₆₇	—	4	4	no	—
244	C₄²×C₆₇	—	4	4	no	—
245	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
246	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
247	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
248	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
249	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	1	no	—
252	C₂³×C₆₇	—	2	1	no	—
253	C₂³×C₆₇	—	2	4	no	—
254	C₂³×C₆₇	—	2	4	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
258	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
259	C₂³×C₆₇	C₂×#41	1	4	yes	—
260	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
261	Q₈×C₆₇	—	2	8	no	—
262	D₄×C₆₇	—	2	16	no	—
263	D₄×C₆₇	—	2	8	no	—
264	C₂×C₄×C₆₇	—	2	8	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	4	no	—
268	C₂×C₄×C₆₇	—	2	4	no	—
269	C₂×C₄×C₆₇	—	2	4	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	2	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	4	no	—
275	C₂×C₄×C₆₇	—	2	1	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	1	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	8	no	—
281	C₂×C₄×C₆₇	—	2	8	no	—
282	C₂×C₄×C₆₇	—	2	16	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	4	16	no	—
293	C₂×C₄×C₆₇	—	4	16	no	—
294	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
301	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
304	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
305	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
306	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
307	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
308	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
309	C₂²×C₆₇	—	2	2	no	—
310	C₂²×C₆₇	—	2	2	no	—
311	C₂²×C₆₇	—	2	4	no	—
312	C₂²×C₆₇	—	2	4	no	—
313	C₂²×C₆₇	—	2	4	no	—
314	C₂²×C₆₇	—	2	4	no	—
315	C₂²×C₆₇	—	2	4	no	—
316	C₂²×C₆₇	—	4	4	no	—
317	C₂²×C₆₇	—	4	4	no	—
318	C₂²×C₆₇	C₄×#41	1	4	yes	—
319	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
320	C₂²×C₆₇	C₂²×#41	1	2	yes	—
321	C₂²×C₆₇	C₂²×#41	1	2	yes	—
322	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	C₄×C₆₇	—	2	2	no	—
325	C₄×C₆₇	—	2	2	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	—	2	4	no	—
328	C₄×C₆₇	—	2	4	no	—
329	C₄×C₆₇	—	2	2	no	—
330	C₄×C₆₇	—	2	4	no	—
331	C₄×C₆₇	—	2	4	no	—
332	C₄×C₆₇	—	2	8	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	4	2	no	—
335	C₄×C₆₇	—	4	4	no	—
336	C₄×C₆₇	—	4	2	no	—
337	C₄×C₆₇	C₄×#41	1	4	yes	—
338	C₄×C₆₇	#520	1	4	yes	—
339	#34153	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂×C₆₇	—	2	4	no	—
341	C₂×C₆₇	—	4	4	no	—
342	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
343	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
344	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
345	C₂×C₆₇	#3481	1	2	yes	—
346	C₂×C₆₇	#3482	1	2	yes	—
347	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
348	#2373	C₂×C₆₇	1	4	yes	complemented
349	#2370	C₂×C₆₇	1	2	yes	complemented
350	#2367	C₂×C₆₇	1	2	yes	complemented
351	#2361	C₂×C₆₇	1	2	yes	—
352	#2360	C₂×C₆₇	1	2	yes	complemented
353	#2359	C₂×C₆₇	1	4	yes	complemented
354	#2298	C₂×C₆₇	1	2	yes	complemented
355	#2296	C₂×C₆₇	1	2	yes	complemented
356	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
357	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
358	#2290	C₂×C₆₇	1	2	yes	complemented
359	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
360	C₄²×D₄	C₂×C₆₇	1	2	yes	complemented
361	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
362	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
363	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
364	C₆₇	#34153	1	1	yes	characteristic, direct product factor, Sylow
365	#529	C₄×C₆₇	1	16	yes	complemented
366	C₂×#126	C₂²×C₆₇	1	2	yes	—
367	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
368	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
369	C₂×#123	C₂²×C₆₇	1	2	yes	—
370	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
371	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
373	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
375	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
378	C₂×#117	C₂²×C₆₇	1	2	yes	—
379	C₂×#117	C₂²×C₆₇	1	2	yes	—
380	C₂×#117	C₂²×C₆₇	1	2	yes	—
381	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
382	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
383	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
384	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
385	#391	C₂²×C₆₇	1	2	yes	—
386	#390	C₂²×C₆₇	1	2	yes	—
387	#389	C₂²×C₆₇	1	4	yes	—
388	#389	C₂²×C₆₇	1	2	yes	—
389	#389	C₂²×C₆₇	1	4	yes	—
390	#389	C₂²×C₆₇	1	2	yes	—
391	#388	C₂²×C₆₇	1	4	yes	—
392	#388	C₂²×C₆₇	1	4	yes	—
393	#388	C₂²×C₆₇	1	4	yes	—
394	#388	C₂²×C₆₇	1	4	yes	—
395	#387	C₂²×C₆₇	1	4	yes	—
396	#387	C₂²×C₆₇	1	4	yes	—
397	#387	C₂²×C₆₇	1	4	yes	—
398	#387	C₂²×C₆₇	1	4	yes	—
399	#386	C₂²×C₆₇	1	4	yes	—
400	#385	C₂²×C₆₇	1	4	yes	—
401	#385	C₂²×C₆₇	1	4	yes	—
402	#385	C₂²×C₆₇	1	4	yes	—
403	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
404	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
409	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
422	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
423	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
425	#376	C₂²×C₆₇	1	2	yes	—
426	#376	C₂²×C₆₇	1	2	yes	—
427	C₂×#95	C₂²×C₆₇	1	2	yes	—
428	C₄³	C₂²×C₆₇	1	1	yes	characteristic
429	C₄³	C₂²×C₆₇	1	1	yes	characteristic
430	C₄³	C₂²×C₆₇	1	2	yes	—
431	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
433	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
435	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
436	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
438	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
440	#126	C₂×C₄×C₆₇	1	16	yes	complemented
441	#125	C₂×C₄×C₆₇	1	8	yes	complemented
442	#124	C₂×C₄×C₆₇	1	8	yes	complemented
443	#123	C₂×C₄×C₆₇	1	16	yes	complemented
444	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
445	#121	C₂×C₄×C₆₇	1	8	yes	—
446	C₄×Q₈	—	2	8	no	—
447	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
448	C₄×D₄	—	2	8	no	—
449	C₄×D₄	—	2	16	no	—
450	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
451	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
452	#117	—	2	8	no	—
453	#117	—	4	4	no	—
454	#117	C₂×C₄×C₆₇	1	16	yes	complemented
455	C₂×C₄⋊C₄	—	2	8	no	—
456	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	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×C₄²	—	4	4	no	—
481	C₂×C₄²	—	4	4	no	—
482	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	complemented
483	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
485	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
486	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
487	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
489	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
490	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
495	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
496	C₂×C₄²	C₂³×C₆₇	1	4	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	1	yes	characteristic
502	#95	C₂³×C₆₇	1	2	yes	—
503	#95	C₂³×C₆₇	1	4	yes	—
504	#95	C₂³×C₆₇	1	2	yes	—
505	#95	C₂³×C₆₇	1	2	yes	—
506	#95	C₂³×C₆₇	1	2	yes	—
507	#95	C₂³×C₆₇	1	2	yes	—
508	#95	C₂³×C₆₇	1	2	yes	—
509	#95	C₂³×C₆₇	1	4	yes	—
510	#95	C₂³×C₆₇	1	4	yes	—
511	#95	C₂³×C₆₇	1	4	yes	—
512	#95	C₂³×C₆₇	1	4	yes	—
513	#95	C₂³×C₆₇	1	4	yes	—
514	#95	C₂³×C₆₇	1	4	yes	—
515	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
516	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
519	C₂×D₄	—	2	8	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
522	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	8	no	—
531	C₂²×C₄	—	2	8	no	—
532	C₂²×C₄	—	2	8	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
536	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
537	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
538	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
539	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	8	no	—
559	C₄⋊C₄	—	2	8	no	—
560	C₄⋊C₄	—	4	4	no	—
561	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
562	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
563	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
565	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
566	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
567	C₄⋊C₄	#41×C₆₇	1	8	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	8	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
577	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	4	no	—
580	C₄²	—	2	8	no	—
581	C₄²	—	2	4	no	—
582	C₄²	—	2	8	no	—
583	C₄²	—	2	4	no	—
584	C₄²	—	2	2	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	2	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	4	4	no	—
591	C₄²	—	4	4	no	—
592	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
593	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
594	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
595	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
596	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
605	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
606	C₂³	C₂×#41×C₆₇	1	4	yes	—
607	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
608	Q₈	—	2	8	no	—
609	D₄	—	2	16	no	—
610	D₄	—	2	8	no	—
611	C₂×C₄	—	2	8	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	16	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	16	no	—
640	C₂×C₄	—	4	16	no	—
641	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
642	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
643	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
644	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
645	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
647	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
648	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
649	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
650	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
651	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
652	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
653	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
654	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
655	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	C₄×#41×C₆₇	1	4	yes	—
666	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
667	C₂²	C₂²×#41×C₆₇	1	2	yes	—
668	C₂²	C₂²×#41×C₆₇	1	2	yes	—
669	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
670	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	4	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	8	no	—
680	C₄	—	2	4	no	—
681	C₄	—	4	4	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	C₄×#41×C₆₇	1	4	yes	—
685	C₄	#520×C₆₇	1	4	yes	—
686	C₂	—	2	4	no	—
687	C₂	—	4	4	no	—
688	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
689	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
690	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
691	C₂	C₆₇×#3481	1	2	yes	—
692	C₂	C₆₇×#3482	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×#121×C₆₇	C₂²
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. C₆₇×#2373	C₂	semidirect
3. C₆₇×#2370	C₂	semidirect
4. C₆₇×#2367	C₂	semidirect
6. C₆₇×#2360	C₂	semidirect
7. C₆₇×#2359	C₂	semidirect
8. C₆₇×#2298	C₂	semidirect
9. C₆₇×#2296	C₂	semidirect
10. C₆₇×#2295	C₂	semidirect
11. C₆₇×#2293	C₂	semidirect
12. C₆₇×#2290	C₂	semidirect
13. C₄²×Q₈×C₆₇	C₂	semidirect
14. C₄²×D₄×C₆₇	C₂	semidirect
15. C₄²×D₄×C₆₇	C₂	semidirect
16. C₄×#117×C₆₇	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
18. #529×C₆₇	C₄	semidirect
93. #126×C₆₇	C₂×C₄	semidirect
94. #125×C₆₇	C₂×C₄	semidirect
95. #124×C₆₇	C₂×C₄	semidirect
96. #123×C₆₇	C₂×C₄	semidirect
97. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
100. C₄×Q₈×C₆₇	C₂×C₄	semidirect
103. C₄×D₄×C₆₇	C₂×C₄	semidirect
104. C₄×D₄×C₆₇	C₂×C₄	semidirect
107. #117×C₆₇	C₂×C₄	semidirect
135. C₂×C₄²×C₆₇	C₂×C₄	semidirect
339. #34153	C₆₇	direct (N × H)
348. #2373	C₂×C₆₇	semidirect
349. #2370	C₂×C₆₇	semidirect
350. #2367	C₂×C₆₇	semidirect
352. #2360	C₂×C₆₇	semidirect
353. #2359	C₂×C₆₇	semidirect
354. #2298	C₂×C₆₇	semidirect
355. #2296	C₂×C₆₇	semidirect
356. #2295	C₂×C₆₇	semidirect
357. #2293	C₂×C₆₇	semidirect
358. #2290	C₂×C₆₇	semidirect
359. C₄²×Q₈	C₂×C₆₇	semidirect
360. C₄²×D₄	C₂×C₆₇	semidirect
361. C₄²×D₄	C₂×C₆₇	semidirect
362. C₄×#117	C₂×C₆₇	semidirect
363. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
364. C₆₇	#34153	direct (N × H)
365. #529	C₄×C₆₇	semidirect
440. #126	C₂×C₄×C₆₇	semidirect
441. #125	C₂×C₄×C₆₇	semidirect
442. #124	C₂×C₄×C₆₇	semidirect
443. #123	C₂×C₄×C₆₇	semidirect
444. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
447. C₄×Q₈	C₂×C₄×C₆₇	semidirect
450. C₄×D₄	C₂×C₄×C₆₇	semidirect
451. C₄×D₄	C₂×C₄×C₆₇	semidirect
454. #117	C₂×C₄×C₆₇	semidirect
482. C₂×C₄²	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₆₇×#2373	2
C₆₇×#2370	2
C₆₇×#2367	2
C₆₇×#2361	2
C₆₇×#2360	2
C₆₇×#2359	2
C₆₇×#2298	2
C₆₇×#2296	2
C₆₇×#2295	2
C₆₇×#2293	2
C₆₇×#2290	2
C₄²×Q₈×C₆₇	2
C₄²×D₄×C₆₇	2
C₄×#117×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
#34153	67

Subgroups — C67×#34153 #30713404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34153 #30713404