Subgroups — C₆₇×#59640 #30738891

Order 17152.

2016 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2803	C₂	1	4	yes	maximal, complemented
2	C₆₇×#2592	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2548	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2544	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2541	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2500	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2491	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2459	C₂	1	4	yes	maximal, complemented
10	C₆₇×#2420	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2357	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2354	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, complemented
17	C₄×#124×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×#127×C₆₇	C₂²	1	2	yes	—
21	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₆₇	C₂²	1	2	yes	—
23	C₂×#124×C₆₇	C₂²	1	4	yes	—
24	C₂×#121×C₆₇	C₂²	1	2	yes	—
25	C₂×#121×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
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×#117×C₆₇	C₂²	1	2	yes	—
33	#397×C₆₇	C₂²	1	4	yes	—
34	#394×C₆₇	C₂²	1	4	yes	—
35	#394×C₆₇	C₂²	1	4	yes	—
36	#394×C₆₇	C₂²	1	4	yes	—
37	#394×C₆₇	C₂²	1	4	yes	—
38	#394×C₆₇	C₂²	1	4	yes	—
39	#393×C₆₇	C₂²	1	4	yes	—
40	#392×C₆₇	C₂²	1	4	yes	—
41	#391×C₆₇	C₂²	1	2	yes	—
42	#391×C₆₇	C₂²	1	1	yes	characteristic
43	#391×C₆₇	C₂²	1	2	yes	—
44	#390×C₆₇	C₂²	1	2	yes	—
45	#390×C₆₇	C₂²	1	2	yes	—
46	#390×C₆₇	C₂²	1	2	yes	—
47	#390×C₆₇	C₂²	1	2	yes	—
48	#390×C₆₇	C₂²	1	2	yes	—
49	#390×C₆₇	C₂²	1	4	yes	—
50	#390×C₆₇	C₂²	1	1	yes	characteristic
51	#390×C₆₇	C₂²	1	2	yes	—
52	#390×C₆₇	C₂²	1	2	yes	—
53	#390×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#388×C₆₇	C₂²	1	4	yes	—
58	#388×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	4	yes	—
61	#388×C₆₇	C₂²	1	4	yes	—
62	#388×C₆₇	C₂²	1	4	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#387×C₆₇	C₂²	1	4	yes	—
65	#386×C₆₇	C₂²	1	4	yes	—
66	#386×C₆₇	C₂²	1	4	yes	—
67	#384×C₆₇	C₂²	1	1	yes	characteristic
68	#384×C₆₇	C₂²	1	1	yes	characteristic
69	#382×C₆₇	C₂²	1	2	yes	—
70	#382×C₆₇	C₂²	1	1	yes	characteristic
71	#381×C₆₇	C₂²	1	4	yes	—
72	#380×C₆₇	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₂²⋊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	1	yes	characteristic
84	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
89	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
90	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₆₇	—	2	4	no	—
94	#127×C₆₇	—	2	4	no	—
95	#127×C₆₇	—	4	4	no	—
96	#124×C₆₇	—	2	4	no	—
97	#124×C₆₇	—	4	4	no	—
98	#124×C₆₇	—	4	8	no	—
99	#121×C₆₇	—	2	8	no	—
100	#121×C₆₇	—	4	4	no	—
101	C₄×Q₈×C₆₇	—	2	4	no	—
102	C₄×Q₈×C₆₇	—	4	4	no	—
103	C₄×D₄×C₆₇	—	2	8	no	—
104	C₄×D₄×C₆₇	—	2	4	no	—
105	C₄×D₄×C₆₇	—	4	4	no	—
106	C₄×D₄×C₆₇	—	4	4	no	—
107	#117×C₆₇	—	4	4	no	—
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	2	yes	—
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	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	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	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	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	4	yes	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
146	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
147	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	#95×C₆₇	C₂³	1	2	yes	—
152	#95×C₆₇	C₂³	1	2	yes	—
153	#95×C₆₇	C₂³	1	2	yes	—
154	#95×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	4	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	2	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
164	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
165	C₂×Q₈×C₆₇	—	2	2	no	—
166	C₂×Q₈×C₆₇	—	2	2	no	—
167	C₂×Q₈×C₆₇	—	2	4	no	—
168	C₂×Q₈×C₆₇	—	2	4	no	—
169	C₂×Q₈×C₆₇	—	2	2	no	—
170	C₂×Q₈×C₆₇	—	4	2	no	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	4	no	—
174	C₂×D₄×C₆₇	—	2	2	no	—
175	C₂×D₄×C₆₇	—	2	4	no	—
176	C₂×D₄×C₆₇	—	2	4	no	—
177	C₂×D₄×C₆₇	—	2	4	no	—
178	C₂×D₄×C₆₇	—	2	8	no	—
179	C₂×D₄×C₆₇	—	2	4	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	2	no	—
182	C₂×D₄×C₆₇	—	4	2	no	—
183	C₂×D₄×C₆₇	—	4	2	no	—
184	C₂×D₄×C₆₇	—	4	4	no	—
185	C₂×D₄×C₆₇	—	4	4	no	—
186	C₂×D₄×C₆₇	—	4	4	no	—
187	C₂×D₄×C₆₇	—	4	4	no	—
188	C₂×D₄×C₆₇	—	4	4	no	—
189	C₂²×C₄×C₆₇	—	2	4	no	—
190	C₂²×C₄×C₆₇	—	2	4	no	—
191	C₂²×C₄×C₆₇	—	2	4	no	—
192	C₂²×C₄×C₆₇	—	2	8	no	—
193	C₂²×C₄×C₆₇	—	4	4	no	—
194	C₂²×C₄×C₆₇	—	4	4	no	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	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	1	yes	characteristic
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	C₄⋊C₄×C₆₇	—	2	2	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	4	no	—
215	C₄⋊C₄×C₆₇	—	2	2	no	—
216	C₄⋊C₄×C₆₇	—	2	2	no	—
217	C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₄⋊C₄×C₆₇	—	4	2	no	—
220	C₄⋊C₄×C₆₇	—	4	2	no	—
221	C₄⋊C₄×C₆₇	—	4	2	no	—
222	C₄⋊C₄×C₆₇	—	4	2	no	—
223	C₄⋊C₄×C₆₇	—	4	2	no	—
224	C₄⋊C₄×C₆₇	#41	1	4	yes	—
225	C₂²⋊C₄×C₆₇	—	2	8	no	—
226	C₂²⋊C₄×C₆₇	—	2	4	no	—
227	C₂²⋊C₄×C₆₇	—	2	8	no	—
228	C₂²⋊C₄×C₆₇	—	2	4	no	—
229	C₂²⋊C₄×C₆₇	—	2	4	no	—
230	C₂²⋊C₄×C₆₇	—	2	8	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	4	2	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	C₂²⋊C₄×C₆₇	—	4	4	no	—
238	C₂²⋊C₄×C₆₇	—	4	4	no	—
239	C₂²⋊C₄×C₆₇	—	4	4	no	—
240	C₂²⋊C₄×C₆₇	—	4	4	no	—
241	C₄²×C₆₇	—	2	4	no	—
242	C₄²×C₆₇	—	2	2	no	—
243	C₄²×C₆₇	—	2	2	no	—
244	C₄²×C₆₇	—	2	2	no	—
245	C₄²×C₆₇	—	2	2	no	—
246	C₄²×C₆₇	—	2	4	no	—
247	C₄²×C₆₇	—	2	4	no	—
248	C₄²×C₆₇	—	4	1	no	—
249	C₄²×C₆₇	—	4	4	no	—
250	C₄²×C₆₇	—	4	4	no	—
251	C₄²×C₆₇	#41	1	4	yes	—
252	C₄²×C₆₇	#41	1	4	yes	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	4	no	—
256	C₂³×C₆₇	—	2	4	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	—	2	4	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	4	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	4	no	—
263	C₂³×C₆₇	—	2	4	no	—
264	C₂³×C₆₇	—	2	2	no	—
265	C₂³×C₆₇	—	2	4	no	—
266	C₂³×C₆₇	—	2	2	no	—
267	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
268	Q₈×C₆₇	—	4	8	no	—
269	Q₈×C₆₇	—	4	4	no	—
270	D₄×C₆₇	—	4	8	no	—
271	D₄×C₆₇	—	4	4	no	—
272	D₄×C₆₇	—	4	8	no	—
273	D₄×C₆₇	—	4	8	no	—
274	D₄×C₆₇	—	8	8	no	—
275	D₄×C₆₇	—	8	8	no	—
276	C₂×C₄×C₆₇	—	2	1	no	—
277	C₂×C₄×C₆₇	—	2	1	no	—
278	C₂×C₄×C₆₇	—	2	1	no	—
279	C₂×C₄×C₆₇	—	2	1	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	1	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	2	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	2	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	1	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	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	4	no	—
302	C₂×C₄×C₆₇	—	2	4	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	1	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	4	8	no	—
311	C₂×C₄×C₆₇	—	8	8	no	—
312	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
313	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
314	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
315	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
316	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
317	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
318	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
319	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
320	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
322	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₆₇	—	4	2	no	—
324	C₂²×C₆₇	—	4	4	no	—
325	C₂²×C₆₇	—	4	2	no	—
326	C₂²×C₆₇	—	4	4	no	—
327	C₂²×C₆₇	—	4	2	no	—
328	C₂²×C₆₇	—	4	4	no	—
329	C₂²×C₆₇	—	4	4	no	—
330	C₂²×C₆₇	—	4	2	no	—
331	C₂²×C₆₇	—	4	4	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	4	no	—
335	C₂²×C₆₇	—	4	2	no	—
336	C₂²×C₆₇	—	4	4	no	—
337	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
338	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₆₇	#585	1	1	yes	characteristic
344	C₄×C₆₇	—	2	2	no	—
345	C₄×C₆₇	—	2	2	no	—
346	C₄×C₆₇	—	2	2	no	—
347	C₄×C₆₇	—	2	4	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	4	2	no	—
350	C₄×C₆₇	—	4	2	no	—
351	C₄×C₆₇	—	4	2	no	—
352	C₄×C₆₇	—	4	4	no	—
353	C₄×C₆₇	—	4	2	no	—
354	C₄×C₆₇	—	4	1	no	—
355	C₄×C₆₇	—	4	2	no	—
356	C₄×C₆₇	—	4	2	no	—
357	C₄×C₆₇	#555	1	4	yes	—
358	C₄×C₆₇	#559	1	4	yes	—
359	#59640	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂×C₆₇	—	8	2	no	—
361	C₂×C₆₇	—	8	4	no	—
362	C₂×C₆₇	C₂×#555	1	1	yes	characteristic
363	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
364	C₂×C₆₇	#3480	1	1	yes	characteristic
365	C₂×C₆₇	#3506	1	1	yes	characteristic
366	C₂×C₆₇	#3508	1	1	yes	characteristic
367	C₂×C₆₇	#3519	1	1	yes	characteristic
368	C₂×C₆₇	#3546	1	1	yes	characteristic
369	#2803	C₂×C₆₇	1	4	yes	complemented
370	#2592	C₂×C₆₇	1	2	yes	complemented
371	#2548	C₂×C₆₇	1	1	yes	characteristic, complemented
372	#2548	C₂×C₆₇	1	2	yes	complemented
373	#2544	C₂×C₆₇	1	2	yes	complemented
374	#2541	C₂×C₆₇	1	1	yes	characteristic
375	#2500	C₂×C₆₇	1	2	yes	complemented
376	#2491	C₂×C₆₇	1	2	yes	complemented
377	#2459	C₂×C₆₇	1	4	yes	complemented
378	#2420	C₂×C₆₇	1	2	yes	complemented
379	#2363	C₂×C₆₇	1	2	yes	complemented
380	#2357	C₂×C₆₇	1	2	yes	complemented
381	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
382	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
383	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
384	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
386	C₆₇	#59640	1	1	yes	characteristic, direct product factor, Sylow
387	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
389	C₂×#127	C₂²×C₆₇	1	2	yes	—
390	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
391	C₂×#124	C₂²×C₆₇	1	2	yes	—
392	C₂×#124	C₂²×C₆₇	1	4	yes	—
393	C₂×#121	C₂²×C₆₇	1	2	yes	—
394	C₂×#121	C₂²×C₆₇	1	2	yes	—
395	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
401	C₂×#117	C₂²×C₆₇	1	2	yes	—
402	#397	C₂²×C₆₇	1	4	yes	—
403	#394	C₂²×C₆₇	1	4	yes	—
404	#394	C₂²×C₆₇	1	4	yes	—
405	#394	C₂²×C₆₇	1	4	yes	—
406	#394	C₂²×C₆₇	1	4	yes	—
407	#394	C₂²×C₆₇	1	4	yes	—
408	#393	C₂²×C₆₇	1	4	yes	—
409	#392	C₂²×C₆₇	1	4	yes	—
410	#391	C₂²×C₆₇	1	2	yes	—
411	#391	C₂²×C₆₇	1	1	yes	characteristic
412	#391	C₂²×C₆₇	1	2	yes	—
413	#390	C₂²×C₆₇	1	2	yes	—
414	#390	C₂²×C₆₇	1	2	yes	—
415	#390	C₂²×C₆₇	1	2	yes	—
416	#390	C₂²×C₆₇	1	2	yes	—
417	#390	C₂²×C₆₇	1	2	yes	—
418	#390	C₂²×C₆₇	1	2	yes	—
419	#390	C₂²×C₆₇	1	2	yes	—
420	#390	C₂²×C₆₇	1	4	yes	—
421	#390	C₂²×C₆₇	1	2	yes	—
422	#390	C₂²×C₆₇	1	1	yes	characteristic
423	#389	C₂²×C₆₇	1	1	yes	characteristic
424	#389	C₂²×C₆₇	1	1	yes	characteristic
425	#389	C₂²×C₆₇	1	2	yes	—
426	#388	C₂²×C₆₇	1	4	yes	—
427	#388	C₂²×C₆₇	1	4	yes	—
428	#388	C₂²×C₆₇	1	4	yes	—
429	#388	C₂²×C₆₇	1	4	yes	—
430	#388	C₂²×C₆₇	1	4	yes	—
431	#388	C₂²×C₆₇	1	2	yes	—
432	#388	C₂²×C₆₇	1	2	yes	—
433	#387	C₂²×C₆₇	1	4	yes	—
434	#386	C₂²×C₆₇	1	4	yes	—
435	#386	C₂²×C₆₇	1	4	yes	—
436	#384	C₂²×C₆₇	1	1	yes	characteristic
437	#384	C₂²×C₆₇	1	1	yes	characteristic
438	#382	C₂²×C₆₇	1	2	yes	—
439	#382	C₂²×C₆₇	1	1	yes	characteristic
440	#381	C₂²×C₆₇	1	4	yes	—
441	#380	C₂²×C₆₇	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
451	C₄³	C₂²×C₆₇	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
454	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
455	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
457	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
458	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
459	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
460	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
461	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
462	C₄⋊Q₈	—	2	4	no	—
463	#127	—	2	4	no	—
464	#127	—	4	4	no	—
465	#124	—	2	4	no	—
466	#124	—	4	4	no	—
467	#124	—	4	8	no	—
468	#121	—	2	8	no	—
469	#121	—	4	4	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×Q₈	—	4	4	no	—
472	C₄×D₄	—	2	8	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	4	4	no	—
475	C₄×D₄	—	4	4	no	—
476	#117	—	4	4	no	—
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
512	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
513	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
516	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
517	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
520	#95	C₂³×C₆₇	1	2	yes	—
521	#95	C₂³×C₆₇	1	2	yes	—
522	#95	C₂³×C₆₇	1	2	yes	—
523	#95	C₂³×C₆₇	1	2	yes	—
524	#95	C₂³×C₆₇	1	2	yes	—
525	#95	C₂³×C₆₇	1	4	yes	—
526	#95	C₂³×C₆₇	1	2	yes	—
527	#95	C₂³×C₆₇	1	4	yes	—
528	#95	C₂³×C₆₇	1	4	yes	—
529	#95	C₂³×C₆₇	1	2	yes	—
530	#95	C₂³×C₆₇	1	2	yes	—
531	#95	C₂³×C₆₇	1	4	yes	—
532	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
533	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	2	4	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	8	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	4	4	no	—
563	C₂²×C₄	—	4	4	no	—
564	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	#41×C₆₇	1	4	yes	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	—	4	4	no	—
604	C₂²⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	—	4	4	no	—
606	C₂²⋊C₄	—	4	4	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	4	2	no	—
609	C₂²⋊C₄	—	4	4	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	4	4	no	—
618	C₄²	—	4	4	no	—
619	C₄²	—	4	1	no	—
620	C₄²	#41×C₆₇	1	4	yes	—
621	C₄²	#41×C₆₇	1	4	yes	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	4	no	—
636	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
637	Q₈	—	4	8	no	—
638	Q₈	—	4	4	no	—
639	D₄	—	4	8	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	8	8	no	—
644	D₄	—	8	8	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	8	no	—
680	C₂×C₄	—	8	8	no	—
681	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
682	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
683	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
684	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
685	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
686	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
687	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
688	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
689	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
690	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
691	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
707	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
708	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
709	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
710	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
711	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
712	C₂²	#585×C₆₇	1	1	yes	characteristic
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	2	no	—
726	C₄	#555×C₆₇	1	4	yes	—
727	C₄	#559×C₆₇	1	4	yes	—
728	C₂	—	8	2	no	—
729	C₂	—	8	4	no	—
730	C₂	C₂×#555×C₆₇	1	1	yes	characteristic
731	C₂	C₂×#559×C₆₇	1	1	yes	characteristic
732	C₂	C₆₇×#3480	1	1	yes	characteristic
733	C₂	C₆₇×#3506	1	1	yes	characteristic
734	C₂	C₆₇×#3508	1	1	yes	characteristic
735	C₂	C₆₇×#3519	1	1	yes	characteristic
736	C₂	C₆₇×#3546	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2541	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. C₆₇×#2803	C₂	semidirect
2. C₆₇×#2592	C₂	semidirect
3. C₆₇×#2548	C₂	semidirect
4. C₆₇×#2548	C₂	semidirect
5. C₆₇×#2544	C₂	semidirect
7. C₆₇×#2500	C₂	semidirect
8. C₆₇×#2491	C₂	semidirect
9. C₆₇×#2459	C₂	semidirect
10. C₆₇×#2420	C₂	semidirect
11. C₆₇×#2363	C₂	semidirect
12. C₆₇×#2357	C₂	semidirect
13. C₆₇×#2355	C₂	semidirect
14. C₆₇×#2354	C₂	semidirect
15. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
16. C₄×#127×C₆₇	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
359. #59640	C₆₇	direct (N × H)
369. #2803	C₂×C₆₇	semidirect
370. #2592	C₂×C₆₇	semidirect
371. #2548	C₂×C₆₇	semidirect
372. #2548	C₂×C₆₇	semidirect
373. #2544	C₂×C₆₇	semidirect
375. #2500	C₂×C₆₇	semidirect
376. #2491	C₂×C₆₇	semidirect
377. #2459	C₂×C₆₇	semidirect
378. #2420	C₂×C₆₇	semidirect
379. #2363	C₂×C₆₇	semidirect
380. #2357	C₂×C₆₇	semidirect
381. #2355	C₂×C₆₇	semidirect
382. #2354	C₂×C₆₇	semidirect
383. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
384. C₄×#127	C₂×C₆₇	semidirect
385. C₄×#124	C₂×C₆₇	semidirect
386. C₆₇	#59640	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×#2803	2
C₆₇×#2592	2
C₆₇×#2548	2
C₆₇×#2544	2
C₆₇×#2541	2
C₆₇×#2500	2
C₆₇×#2491	2
C₆₇×#2459	2
C₆₇×#2420	2
C₆₇×#2363	2
C₆₇×#2357	2
C₆₇×#2355	2
C₆₇×#2354	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#127×C₆₇	2
C₄×#124×C₆₇	2
#59640	67

Subgroups — C67×#59640 #30738891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59640 #30738891