Subgroups — C₆₇×#35094 #30714345

Order 17152.

2434 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×#539×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2623	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2617	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2479	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2477	C₂	1	4	yes	maximal, complemented
11	C₆₇×#2475	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2471	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
17	#539×C₆₇	—	2	8	no	—
18	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
19	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
20	C₂×#123×C₆₇	C₂²	1	2	yes	—
21	C₂×#123×C₆₇	C₂²	1	2	yes	—
22	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#120×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×#117×C₆₇	—	2	8	no	—
29	C₂×#117×C₆₇	C₂²	1	4	yes	—
30	C₂×#117×C₆₇	C₂²	1	4	yes	—
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
37	#400×C₆₇	C₂²	1	4	yes	complemented
38	#399×C₆₇	C₂²	1	2	yes	—
39	#399×C₆₇	C₂²	1	4	yes	complemented
40	#398×C₆₇	C₂²	1	4	yes	complemented
41	#397×C₆₇	C₂²	1	2	yes	—
42	#397×C₆₇	C₂²	1	4	yes	complemented
43	#396×C₆₇	C₂²	1	4	yes	—
44	#394×C₆₇	C₂²	1	4	yes	—
45	#393×C₆₇	C₂²	1	2	yes	—
46	#392×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	2	yes	complemented
48	#390×C₆₇	C₂²	1	4	yes	—
49	#390×C₆₇	C₂²	1	2	yes	complemented
50	#389×C₆₇	C₂²	1	2	yes	complemented
51	#389×C₆₇	C₂²	1	2	yes	complemented
52	#388×C₆₇	C₂²	1	4	yes	—
53	#388×C₆₇	C₂²	1	4	yes	—
54	#388×C₆₇	C₂²	1	4	yes	complemented
55	#388×C₆₇	C₂²	1	4	yes	complemented
56	#387×C₆₇	C₂²	1	4	yes	complemented
57	#387×C₆₇	C₂²	1	4	yes	complemented
58	#387×C₆₇	C₂²	1	4	yes	complemented
59	#387×C₆₇	C₂²	1	4	yes	complemented
60	#386×C₆₇	C₂²	1	2	yes	—
61	#386×C₆₇	C₂²	1	2	yes	—
62	#386×C₆₇	C₂²	1	4	yes	—
63	#386×C₆₇	C₂²	1	4	yes	—
64	#386×C₆₇	C₂²	1	4	yes	—
65	#385×C₆₇	C₂²	1	2	yes	—
66	#385×C₆₇	C₂²	1	2	yes	—
67	#385×C₆₇	C₂²	1	4	yes	—
68	#385×C₆₇	C₂²	1	4	yes	—
69	#381×C₆₇	C₂²	1	2	yes	—
70	#381×C₆₇	C₂²	1	2	yes	—
71	#380×C₆₇	C₂²	1	1	yes	characteristic
72	#380×C₆₇	C₂²	1	1	yes	characteristic
73	#379×C₆₇	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
77	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₆₇	—	2	4	no	—
83	C₂³×C₄×C₆₇	—	2	4	no	—
84	C₂³×C₄×C₆₇	—	2	4	no	—
85	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	#126×C₆₇	—	2	8	no	—
94	#125×C₆₇	—	2	8	no	—
95	#123×C₆₇	—	2	8	no	—
96	#123×C₆₇	—	2	8	no	—
97	#123×C₆₇	—	2	8	no	—
98	C₂²⋊Q₈×C₆₇	—	2	4	no	—
99	C₂²⋊Q₈×C₆₇	—	2	8	no	—
100	#121×C₆₇	—	2	4	no	—
101	#120×C₆₇	—	2	8	no	—
102	C₄×D₄×C₆₇	—	2	8	no	—
103	#117×C₆₇	—	2	16	no	—
104	#117×C₆₇	—	2	16	no	—
105	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
106	C₂×C₄⋊C₄×C₆₇	D₄	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	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	4	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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	2	yes	—
128	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₆₇	—	2	4	no	—
140	C₂×C₄²×C₆₇	—	2	4	no	—
141	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
142	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
146	#95×C₆₇	C₂³	1	4	yes	—
147	#95×C₆₇	C₂³	1	4	yes	—
148	#95×C₆₇	C₂³	1	4	yes	—
149	#95×C₆₇	C₂³	1	4	yes	—
150	#95×C₆₇	C₂³	1	4	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	4	yes	—
156	#95×C₆₇	C₂³	1	4	yes	—
157	C₂⁴×C₆₇	—	2	2	no	—
158	C₂⁴×C₆₇	—	2	2	no	—
159	C₂⁴×C₆₇	—	4	2	no	—
160	C₂⁴×C₆₇	—	4	2	no	—
161	C₂⁴×C₆₇	#41	1	4	yes	—
162	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
163	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
164	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₆₇	—	2	2	no	—
166	C₂×Q₈×C₆₇	—	4	2	no	—
167	C₂×D₄×C₆₇	—	2	4	no	—
168	C₂×D₄×C₆₇	—	2	4	no	—
169	C₂×D₄×C₆₇	—	2	4	no	—
170	C₂×D₄×C₆₇	—	2	8	no	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	4	2	no	—
173	C₂×D₄×C₆₇	—	4	4	no	—
174	C₂×D₄×C₆₇	—	4	4	no	—
175	C₂²×C₄×C₆₇	—	2	32	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	8	no	—
178	C₂²×C₄×C₆₇	—	2	2	no	—
179	C₂²×C₄×C₆₇	—	2	2	no	—
180	C₂²×C₄×C₆₇	—	2	2	no	—
181	C₂²×C₄×C₆₇	—	2	8	no	—
182	C₂²×C₄×C₆₇	—	2	8	no	—
183	C₂²×C₄×C₆₇	—	2	2	no	—
184	C₂²×C₄×C₆₇	—	2	2	no	—
185	C₂²×C₄×C₆₇	—	2	4	no	—
186	C₂²×C₄×C₆₇	—	4	2	no	—
187	C₂²×C₄×C₆₇	—	4	2	no	—
188	C₂²×C₄×C₆₇	—	4	2	no	—
189	C₂²×C₄×C₆₇	—	4	2	no	—
190	C₂²×C₄×C₆₇	—	4	4	no	—
191	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₆₇	#41	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
207	C₄⋊C₄×C₆₇	—	2	8	no	—
208	C₄⋊C₄×C₆₇	—	2	4	no	—
209	C₄⋊C₄×C₆₇	—	2	2	no	—
210	C₄⋊C₄×C₆₇	—	2	4	no	—
211	C₄⋊C₄×C₆₇	—	2	4	no	—
212	C₄⋊C₄×C₆₇	—	2	2	no	—
213	C₄⋊C₄×C₆₇	—	2	4	no	—
214	C₄⋊C₄×C₆₇	—	2	8	no	—
215	C₄⋊C₄×C₆₇	—	4	2	no	—
216	C₄⋊C₄×C₆₇	—	4	2	no	—
217	C₄⋊C₄×C₆₇	—	4	4	no	—
218	C₄⋊C₄×C₆₇	—	4	4	no	—
219	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
220	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
221	C₂²⋊C₄×C₆₇	—	2	4	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	8	no	—
226	C₂²⋊C₄×C₆₇	—	2	4	no	—
227	C₂²⋊C₄×C₆₇	—	2	4	no	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	4	no	—
230	C₂²⋊C₄×C₆₇	—	2	4	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	2	8	no	—
233	C₂²⋊C₄×C₆₇	—	4	4	no	—
234	C₂²⋊C₄×C₆₇	—	4	4	no	—
235	C₂²⋊C₄×C₆₇	—	4	4	no	—
236	C₂²⋊C₄×C₆₇	—	4	4	no	—
237	C₄²×C₆₇	—	2	8	no	—
238	C₄²×C₆₇	—	2	4	no	—
239	C₄²×C₆₇	—	2	4	no	—
240	C₄²×C₆₇	—	2	4	no	—
241	C₄²×C₆₇	—	4	4	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	2	no	—
244	C₂³×C₆₇	—	2	8	no	—
245	C₂³×C₆₇	—	2	2	no	—
246	C₂³×C₆₇	—	2	2	no	—
247	C₂³×C₆₇	—	2	4	no	—
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	4	no	—
253	C₂³×C₆₇	—	2	4	no	—
254	C₂³×C₆₇	—	4	8	no	—
255	C₂³×C₆₇	—	4	8	no	—
256	C₂³×C₆₇	—	4	4	no	—
257	C₂³×C₆₇	—	4	4	no	—
258	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
259	C₂³×C₆₇	C₂×#41	1	4	yes	—
260	C₂³×C₆₇	C₂×#41	1	2	yes	—
261	C₂³×C₆₇	C₂×#41	1	2	yes	—
262	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
263	Q₈×C₆₇	—	8	2	no	—
264	D₄×C₆₇	—	4	8	no	—
265	D₄×C₆₇	—	8	2	no	—
266	D₄×C₆₇	—	8	8	no	—
267	C₂×C₄×C₆₇	—	2	32	no	—
268	C₂×C₄×C₆₇	—	2	8	no	—
269	C₂×C₄×C₆₇	—	2	8	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	2	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	4	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	4	no	—
293	C₂×C₄×C₆₇	—	2	4	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	4	4	no	—
296	C₂×C₄×C₆₇	—	4	4	no	—
297	C₂×C₄×C₆₇	—	4	4	no	—
298	C₂×C₄×C₆₇	—	4	4	no	—
299	C₂×C₄×C₆₇	—	8	4	no	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	4	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	4	yes	—
304	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
305	C₂²×C₆₇	—	2	4	no	—
306	C₂²×C₆₇	—	2	2	no	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	4	no	—
309	C₂²×C₆₇	—	2	4	no	—
310	C₂²×C₆₇	—	2	8	no	—
311	C₂²×C₆₇	—	4	16	no	—
312	C₂²×C₆₇	—	4	4	no	—
313	C₂²×C₆₇	—	4	2	no	—
314	C₂²×C₆₇	—	4	2	no	—
315	C₂²×C₆₇	—	4	2	no	—
316	C₂²×C₆₇	—	4	4	no	—
317	C₂²×C₆₇	—	4	2	no	—
318	C₂²×C₆₇	—	4	2	no	—
319	C₂²×C₆₇	—	4	4	no	—
320	C₂²×C₆₇	#525	1	4	yes	—
321	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
322	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₆₇	#585	1	2	yes	—
325	C₂²×C₆₇	#585	1	2	yes	—
326	C₄×C₆₇	—	2	4	no	—
327	C₄×C₆₇	—	2	4	no	—
328	C₄×C₆₇	—	2	4	no	—
329	C₄×C₆₇	—	2	2	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	4	2	no	—
332	C₄×C₆₇	—	4	4	no	—
333	C₄×C₆₇	—	4	2	no	—
334	C₄×C₆₇	—	4	2	no	—
335	C₄×C₆₇	—	4	2	no	—
336	C₄×C₆₇	—	4	2	no	—
337	C₄×C₆₇	—	4	4	no	—
338	#35094	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂×C₆₇	—	2	4	no	—
340	C₂×C₆₇	—	4	4	no	—
341	C₂×C₆₇	—	8	2	no	—
342	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
343	C₂×C₆₇	#3455	1	2	yes	—
344	C₂×C₆₇	#3485	1	1	yes	characteristic
345	C₂×C₆₇	#3487	1	1	yes	characteristic
346	C₂×C₆₇	#3491	1	2	yes	—
347	C₂×#539	C₂×C₆₇	1	1	yes	characteristic, complemented
348	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
349	#2855	C₂×C₆₇	1	1	yes	characteristic, complemented
350	#2854	C₂×C₆₇	1	1	yes	characteristic, complemented
351	#2849	C₂×C₆₇	1	2	yes	complemented
352	#2626	C₂×C₆₇	1	1	yes	characteristic, complemented
353	#2623	C₂×C₆₇	1	2	yes	complemented
354	#2617	C₂×C₆₇	1	1	yes	characteristic
355	#2479	C₂×C₆₇	1	4	yes	complemented
356	#2477	C₂×C₆₇	1	4	yes	complemented
357	#2475	C₂×C₆₇	1	4	yes	complemented
358	#2471	C₂×C₆₇	1	4	yes	complemented
359	#2321	C₂×C₆₇	1	2	yes	complemented
360	#2313	C₂×C₆₇	1	1	yes	characteristic, complemented
361	C₄×#123	C₂×C₆₇	1	2	yes	complemented
362	C₆₇	#35094	1	1	yes	characteristic, direct product factor, Sylow
363	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
364	#539	—	2	8	no	—
365	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
366	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
367	C₂×#123	C₂²×C₆₇	1	2	yes	—
368	C₂×#123	C₂²×C₆₇	1	2	yes	—
369	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
370	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
371	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
372	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
373	C₂×#120	C₂²×C₆₇	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
375	C₂×#117	—	2	8	no	—
376	C₂×#117	C₂²×C₆₇	1	4	yes	—
377	C₂×#117	C₂²×C₆₇	1	4	yes	—
378	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
381	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
382	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
384	#400	C₂²×C₆₇	1	4	yes	complemented
385	#399	C₂²×C₆₇	1	2	yes	—
386	#399	C₂²×C₆₇	1	4	yes	complemented
387	#398	C₂²×C₆₇	1	4	yes	complemented
388	#397	C₂²×C₆₇	1	2	yes	—
389	#397	C₂²×C₆₇	1	4	yes	complemented
390	#396	C₂²×C₆₇	1	4	yes	—
391	#394	C₂²×C₆₇	1	4	yes	—
392	#393	C₂²×C₆₇	1	2	yes	—
393	#392	C₂²×C₆₇	1	2	yes	—
394	#391	C₂²×C₆₇	1	2	yes	complemented
395	#390	C₂²×C₆₇	1	4	yes	—
396	#390	C₂²×C₆₇	1	2	yes	complemented
397	#389	C₂²×C₆₇	1	2	yes	complemented
398	#389	C₂²×C₆₇	1	2	yes	complemented
399	#388	C₂²×C₆₇	1	4	yes	—
400	#388	C₂²×C₆₇	1	4	yes	—
401	#388	C₂²×C₆₇	1	4	yes	complemented
402	#388	C₂²×C₆₇	1	4	yes	complemented
403	#387	C₂²×C₆₇	1	4	yes	complemented
404	#387	C₂²×C₆₇	1	4	yes	complemented
405	#387	C₂²×C₆₇	1	4	yes	complemented
406	#387	C₂²×C₆₇	1	4	yes	complemented
407	#386	C₂²×C₆₇	1	2	yes	—
408	#386	C₂²×C₆₇	1	4	yes	—
409	#386	C₂²×C₆₇	1	4	yes	—
410	#386	C₂²×C₆₇	1	4	yes	—
411	#386	C₂²×C₆₇	1	2	yes	—
412	#385	C₂²×C₆₇	1	2	yes	—
413	#385	C₂²×C₆₇	1	4	yes	—
414	#385	C₂²×C₆₇	1	4	yes	—
415	#385	C₂²×C₆₇	1	2	yes	—
416	#381	C₂²×C₆₇	1	2	yes	—
417	#381	C₂²×C₆₇	1	2	yes	—
418	#380	C₂²×C₆₇	1	1	yes	characteristic
419	#380	C₂²×C₆₇	1	1	yes	characteristic
420	#379	C₂²×C₆₇	1	2	yes	—
421	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
422	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
424	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
426	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
427	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
428	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
429	C₂³×C₄	—	2	4	no	—
430	C₂³×C₄	—	2	4	no	—
431	C₂³×C₄	—	2	4	no	—
432	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
433	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
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	—	2	8	no	—
441	#125	—	2	8	no	—
442	#123	—	2	8	no	—
443	#123	—	2	8	no	—
444	#123	—	2	8	no	—
445	C₂²⋊Q₈	—	2	4	no	—
446	C₂²⋊Q₈	—	2	8	no	—
447	#121	—	2	4	no	—
448	#120	—	2	8	no	—
449	C₄×D₄	—	2	8	no	—
450	#117	—	2	16	no	—
451	#117	—	2	16	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	D₄×C₆₇	1	8	yes	complemented
454	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	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	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	—	2	4	no	—
470	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	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	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	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
486	C₂×C₄²	—	2	4	no	—
487	C₂×C₄²	—	2	4	no	—
488	C₂×C₄²	C₂³×C₆₇	1	4	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	#95	C₂³×C₆₇	1	4	yes	—
494	#95	C₂³×C₆₇	1	4	yes	—
495	#95	C₂³×C₆₇	1	4	yes	—
496	#95	C₂³×C₆₇	1	4	yes	—
497	#95	C₂³×C₆₇	1	4	yes	—
498	#95	C₂³×C₆₇	1	2	yes	—
499	#95	C₂³×C₆₇	1	2	yes	—
500	#95	C₂³×C₆₇	1	4	yes	—
501	#95	C₂³×C₆₇	1	4	yes	—
502	#95	C₂³×C₆₇	1	4	yes	—
503	#95	C₂³×C₆₇	1	4	yes	—
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	4	2	no	—
507	C₂⁴	—	4	2	no	—
508	C₂⁴	#41×C₆₇	1	4	yes	—
509	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
510	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
511	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	—	4	4	no	—
522	C₂²×C₄	—	2	32	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
539	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
540	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
541	C₂²×C₄	#41×C₆₇	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	2	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	4	2	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	—	4	4	no	—
565	C₄⋊C₄	—	4	4	no	—
566	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
567	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	8	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₄²	—	2	8	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	4	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	8	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	4	no	—
605	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
606	C₂³	C₂×#41×C₆₇	1	4	yes	—
607	C₂³	C₂×#41×C₆₇	1	2	yes	—
608	C₂³	C₂×#41×C₆₇	1	2	yes	—
609	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
610	Q₈	—	8	2	no	—
611	D₄	—	4	8	no	—
612	D₄	—	8	2	no	—
613	D₄	—	8	8	no	—
614	C₂×C₄	—	2	32	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	8	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	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	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	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
651	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	4	16	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	4	no	—
667	C₂²	#525×C₆₇	1	4	yes	—
668	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
669	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
670	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
671	C₂²	#585×C₆₇	1	2	yes	—
672	C₂²	#585×C₆₇	1	2	yes	—
673	C₄	—	2	4	no	—
674	C₄	—	2	4	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	4	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	4	no	—
685	C₂	—	2	4	no	—
686	C₂	—	4	4	no	—
687	C₂	—	8	2	no	—
688	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
689	C₂	C₆₇×#3455	1	2	yes	—
690	C₂	C₆₇×#3485	1	1	yes	characteristic
691	C₂	C₆₇×#3487	1	1	yes	characteristic
692	C₂	C₆₇×#3491	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2617	C₂
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. C₂×#539×C₆₇	C₂	semidirect
2. C₂²×#117×C₆₇	C₂	semidirect
3. C₆₇×#2855	C₂	semidirect
4. C₆₇×#2854	C₂	semidirect
5. C₆₇×#2849	C₂	semidirect
6. C₆₇×#2626	C₂	semidirect
7. C₆₇×#2623	C₂	semidirect
9. C₆₇×#2479	C₂	semidirect
10. C₆₇×#2477	C₂	semidirect
11. C₆₇×#2475	C₂	semidirect
12. C₆₇×#2471	C₂	semidirect
13. C₆₇×#2321	C₂	semidirect
14. C₆₇×#2313	C₂	semidirect
15. C₄×#123×C₆₇	C₂	semidirect
18. C₂×#126×C₆₇	C₂²	semidirect
19. C₂×#125×C₆₇	C₂²	semidirect
22. C₂×#123×C₆₇	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
39. #399×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
42. #397×C₆₇	C₂²	semidirect
47. #391×C₆₇	C₂²	semidirect
49. #390×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #387×C₆₇	C₂²	semidirect
57. #387×C₆₇	C₂²	semidirect
58. #387×C₆₇	C₂²	semidirect
59. #387×C₆₇	C₂²	semidirect
74. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₂×C₄⋊C₄×C₆₇	D₄	semidirect
338. #35094	C₆₇	direct (N × H)
347. C₂×#539	C₂×C₆₇	semidirect
348. C₂²×#117	C₂×C₆₇	semidirect
349. #2855	C₂×C₆₇	semidirect
350. #2854	C₂×C₆₇	semidirect
351. #2849	C₂×C₆₇	semidirect
352. #2626	C₂×C₆₇	semidirect
353. #2623	C₂×C₆₇	semidirect
355. #2479	C₂×C₆₇	semidirect
356. #2477	C₂×C₆₇	semidirect
357. #2475	C₂×C₆₇	semidirect
358. #2471	C₂×C₆₇	semidirect
359. #2321	C₂×C₆₇	semidirect
360. #2313	C₂×C₆₇	semidirect
361. C₄×#123	C₂×C₆₇	semidirect
362. C₆₇	#35094	direct (N × H)
365. C₂×#126	C₂²×C₆₇	semidirect
366. C₂×#125	C₂²×C₆₇	semidirect
369. C₂×#123	C₂²×C₆₇	semidirect
371. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
384. #400	C₂²×C₆₇	semidirect
386. #399	C₂²×C₆₇	semidirect
387. #398	C₂²×C₆₇	semidirect
389. #397	C₂²×C₆₇	semidirect
394. #391	C₂²×C₆₇	semidirect
396. #390	C₂²×C₆₇	semidirect
397. #389	C₂²×C₆₇	semidirect
398. #389	C₂²×C₆₇	semidirect
401. #388	C₂²×C₆₇	semidirect
402. #388	C₂²×C₆₇	semidirect
403. #387	C₂²×C₆₇	semidirect
404. #387	C₂²×C₆₇	semidirect
405. #387	C₂²×C₆₇	semidirect
406. #387	C₂²×C₆₇	semidirect
421. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
423. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
453. C₂×C₄⋊C₄	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₆₇	2
C₂²×#117×C₆₇	2
C₆₇×#2855	2
C₆₇×#2854	2
C₆₇×#2849	2
C₆₇×#2626	2
C₆₇×#2623	2
C₆₇×#2617	2
C₆₇×#2479	2
C₆₇×#2477	2
C₆₇×#2475	2
C₆₇×#2471	2
C₆₇×#2321	2
C₆₇×#2313	2
C₄×#123×C₆₇	2
#35094	67

Subgroups — C67×#35094 #30714345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35094 #30714345