Subgroups — C₂×C₆₇×#3557 #30741989

Order 17152.

6554 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3557	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563×C₆₇	C₂	1	4	yes	maximal, complemented
3	C₂×#559×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#557×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#556×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#554×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#552×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#542×C₆₇	C₂	1	4	yes	maximal, complemented
10	C₂×#541×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#540×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#539×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#529×C₆₇	C₂	1	2	yes	maximal, complemented
15	#563×C₆₇	C₂²	1	64	yes	complemented
16	#559×C₆₇	C₂²	1	32	yes	complemented
17	#557×C₆₇	C₂²	1	32	yes	complemented
18	#556×C₆₇	C₂²	1	32	yes	complemented
19	#554×C₆₇	C₂²	1	32	yes	complemented
20	#552×C₆₇	C₂²	1	64	yes	complemented
21	#542×C₆₇	C₂²	1	32	yes	complemented
22	#542×C₆₇	C₂²	1	64	yes	complemented
23	#541×C₆₇	C₂²	1	16	yes	complemented
24	#540×C₆₇	C₂²	1	16	yes	—
25	#539×C₆₇	C₂²	1	64	yes	complemented
26	#533×C₆₇	C₂²	1	16	yes	complemented
27	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	4	yes	—
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
31	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
32	#529×C₆₇	C₂²	1	32	yes	complemented
33	C₂×#126×C₆₇	C₂²	1	4	yes	—
34	C₂×#126×C₆₇	C₂²	1	4	yes	—
35	C₂×#126×C₆₇	C₂²	1	4	yes	—
36	C₂×#126×C₆₇	C₂²	1	4	yes	—
37	C₂×#126×C₆₇	C₂²	1	4	yes	—
38	C₂×#125×C₆₇	C₂²	1	4	yes	—
39	C₂×#125×C₆₇	C₂²	1	4	yes	—
40	C₂×#125×C₆₇	C₂²	1	2	yes	—
41	C₂×#125×C₆₇	C₂²	1	2	yes	—
42	C₂×#125×C₆₇	C₂²	1	4	yes	—
43	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#124×C₆₇	C₂²	1	4	yes	—
46	C₂×#124×C₆₇	C₂²	1	2	yes	—
47	C₂×#124×C₆₇	C₂²	1	4	yes	—
48	C₂×#124×C₆₇	C₂²	1	2	yes	—
49	C₂×#123×C₆₇	C₂²	1	4	yes	—
50	C₂×#123×C₆₇	C₂²	1	4	yes	—
51	C₂×#123×C₆₇	C₂²	1	4	yes	—
52	C₂×#123×C₆₇	C₂²	1	4	yes	—
53	C₂×#123×C₆₇	C₂²	1	4	yes	—
54	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
60	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
62	C₂×#121×C₆₇	C₂²	1	2	yes	—
63	C₂×#121×C₆₇	C₂²	1	4	yes	—
64	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
65	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
66	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
67	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
68	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
69	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
70	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
71	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
72	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
73	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
74	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
75	C₂×#117×C₆₇	C₂²	1	4	yes	—
76	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
78	C₂×#117×C₆₇	C₂²	1	4	yes	—
79	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
80	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
81	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
82	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
83	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
87	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
91	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	—
94	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
95	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	—
96	C₄⋊Q₈×C₆₇	C₂³	1	32	yes	—
97	#127×C₆₇	C₂³	1	8	yes	—
98	#126×C₆₇	C₂³	1	32	yes	—
99	#126×C₆₇	C₂³	1	32	yes	—
100	#126×C₆₇	C₂³	1	32	yes	—
101	#126×C₆₇	C₂³	1	32	yes	—
102	#126×C₆₇	C₂³	1	32	yes	—
103	#125×C₆₇	C₂³	1	16	yes	—
104	#125×C₆₇	C₂³	1	16	yes	—
105	#125×C₆₇	C₂³	1	32	yes	—
106	#125×C₆₇	C₂³	1	32	yes	—
107	#125×C₆₇	C₂³	1	8	yes	—
108	#125×C₆₇	C₂³	1	32	yes	—
109	#125×C₆₇	C₂³	1	8	yes	—
110	#124×C₆₇	C₂³	1	16	yes	—
111	#124×C₆₇	C₂³	1	32	yes	—
112	#124×C₆₇	C₂³	1	16	yes	—
113	#124×C₆₇	C₂³	1	32	yes	—
114	#123×C₆₇	C₂³	1	32	yes	—
115	#123×C₆₇	C₂³	1	32	yes	—
116	#123×C₆₇	C₂³	1	32	yes	—
117	#123×C₆₇	C₂³	1	32	yes	—
118	#123×C₆₇	C₂³	1	32	yes	—
119	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
120	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
121	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
122	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
123	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
124	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
125	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
126	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
127	#121×C₆₇	C₂³	1	16	yes	—
128	#121×C₆₇	C₂³	1	32	yes	—
129	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
130	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
131	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
132	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
133	C₄×Q₈×C₆₇	C₂³	1	32	yes	—
134	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
135	C₄×D₄×C₆₇	C₂³	1	32	yes	—
136	C₄×D₄×C₆₇	C₂³	1	16	yes	—
137	C₄×D₄×C₆₇	C₂³	1	32	yes	—
138	C₄×D₄×C₆₇	C₂³	1	16	yes	—
139	C₄×D₄×C₆₇	C₂³	1	16	yes	—
140	#117×C₆₇	C₂³	1	32	yes	—
141	#117×C₆₇	C₂³	1	8	yes	—
142	#117×C₆₇	C₂³	1	8	yes	—
143	#117×C₆₇	C₂³	1	32	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
187	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
188	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
189	C₂×Q₈×C₆₇	—	2	8	no	—
190	C₂×Q₈×C₆₇	—	4	4	no	—
191	C₂×Q₈×C₆₇	—	4	8	no	—
192	C₂×Q₈×C₆₇	—	4	4	no	—
193	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
194	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
195	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	—
196	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
197	C₂×D₄×C₆₇	—	2	8	no	—
198	C₂×D₄×C₆₇	—	4	8	no	—
199	C₂×D₄×C₆₇	—	4	8	no	—
200	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
201	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
202	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	4	8	no	—
205	C₂²×C₄×C₆₇	—	4	4	no	—
206	C₂²×C₄×C₆₇	—	4	8	no	—
207	C₂²×C₄×C₆₇	—	4	8	no	—
208	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
225	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
226	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
227	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
228	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
229	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
230	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
231	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
232	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
233	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
234	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
235	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
236	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
237	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
238	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
239	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
240	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
241	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
242	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
243	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
244	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
245	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
246	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
247	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
248	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
249	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
250	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
251	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
252	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
253	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
254	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
255	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
256	C₄²×C₆₇	C₂⁴	1	4	yes	—
257	C₄²×C₆₇	C₂⁴	1	8	yes	—
258	C₄²×C₆₇	C₂⁴	1	4	yes	—
259	C₄²×C₆₇	C₂⁴	1	16	yes	—
260	C₄²×C₆₇	C₂⁴	1	4	yes	—
261	C₄²×C₆₇	C₂⁴	1	8	yes	—
262	C₄²×C₆₇	C₂⁴	1	4	yes	—
263	C₄²×C₆₇	C₂⁴	1	16	yes	—
264	C₄²×C₆₇	C₂⁴	1	16	yes	—
265	C₂³×C₆₇	—	2	2	no	—
266	C₂³×C₆₇	—	2	8	no	—
267	C₂³×C₆₇	—	2	8	no	—
268	C₂³×C₆₇	—	2	4	no	—
269	C₂³×C₆₇	—	2	8	no	—
270	C₂³×C₆₇	C₂⁵	1	2	yes	—
271	C₂³×C₆₇	C₂⁵	1	8	yes	—
272	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
273	Q₈×C₆₇	—	2	16	no	—
274	Q₈×C₆₇	—	4	8	no	—
275	Q₈×C₆₇	—	4	16	no	—
276	Q₈×C₆₇	—	4	8	no	—
277	D₄×C₆₇	—	2	16	no	—
278	D₄×C₆₇	—	4	16	no	—
279	D₄×C₆₇	—	4	16	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	8	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	8	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	—	2	4	no	—
290	C₂×C₄×C₆₇	—	2	8	no	—
291	C₂×C₄×C₆₇	—	4	16	no	—
292	C₂×C₄×C₆₇	—	4	8	no	—
293	C₂×C₄×C₆₇	—	4	16	no	—
294	C₂×C₄×C₆₇	—	4	16	no	—
295	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
296	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
297	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
298	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
299	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
300	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
301	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
302	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
303	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
304	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
305	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
306	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	8	no	—
309	C₂²×C₆₇	—	2	8	no	—
310	C₂²×C₆₇	—	2	4	no	—
311	C₂²×C₆₇	—	2	8	no	—
312	C₂²×C₆₇	—	4	4	no	—
313	C₂²×C₆₇	—	4	16	no	—
314	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
315	C₂²×C₆₇	#585	1	4	yes	—
316	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
317	C₄×C₆₇	—	2	2	no	—
318	C₄×C₆₇	—	2	8	no	—
319	C₄×C₆₇	—	2	4	no	—
320	C₄×C₆₇	—	2	8	no	—
321	C₄×C₆₇	—	2	4	no	—
322	C₄×C₆₇	—	2	4	no	—
323	C₄×C₆₇	—	2	8	no	—
324	C₄×C₆₇	—	2	4	no	—
325	C₄×C₆₇	—	2	4	no	—
326	C₄×C₆₇	—	2	4	no	—
327	C₄×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
328	C₂×#3557	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂×C₆₇	—	4	2	no	—
330	C₂×C₆₇	—	4	8	no	—
331	C₂×C₆₇	#3557	1	4	yes	direct product factor
332	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂×C₆₇	C₂×#585	1	2	yes	—
334	#3557	C₂×C₆₇	1	32	yes	direct product factor
335	C₂×#563	C₂×C₆₇	1	4	yes	complemented
336	C₂×#559	C₂×C₆₇	1	2	yes	complemented
337	C₂×#557	C₂×C₆₇	1	2	yes	complemented
338	C₂×#556	C₂×C₆₇	1	2	yes	complemented
339	C₂×#554	C₂×C₆₇	1	2	yes	complemented
340	C₂×#552	C₂×C₆₇	1	4	yes	complemented
341	C₂×#542	C₂×C₆₇	1	2	yes	complemented
342	C₂×#542	C₂×C₆₇	1	4	yes	complemented
343	C₂×#541	C₂×C₆₇	1	1	yes	characteristic, complemented
344	C₂×#540	C₂×C₆₇	1	1	yes	characteristic
345	C₂×#539	C₂×C₆₇	1	4	yes	complemented
346	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
347	C₂×#529	C₂×C₆₇	1	2	yes	complemented
348	C₆₇	C₂×#3557	1	1	yes	characteristic, direct product factor, Sylow
349	#563	C₂²×C₆₇	1	64	yes	complemented
350	#559	C₂²×C₆₇	1	32	yes	complemented
351	#557	C₂²×C₆₇	1	32	yes	complemented
352	#556	C₂²×C₆₇	1	32	yes	complemented
353	#554	C₂²×C₆₇	1	32	yes	complemented
354	#552	C₂²×C₆₇	1	64	yes	complemented
355	#542	C₂²×C₆₇	1	32	yes	complemented
356	#542	C₂²×C₆₇	1	64	yes	complemented
357	#541	C₂²×C₆₇	1	16	yes	complemented
358	#540	C₂²×C₆₇	1	16	yes	—
359	#539	C₂²×C₆₇	1	64	yes	complemented
360	#533	C₂²×C₆₇	1	16	yes	complemented
361	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
362	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
363	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
364	C₂×C₄⋊Q₈	C₂²×C₆₇	1	4	yes	—
365	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
366	#529	C₂²×C₆₇	1	32	yes	complemented
367	C₂×#126	C₂²×C₆₇	1	4	yes	—
368	C₂×#126	C₂²×C₆₇	1	4	yes	—
369	C₂×#126	C₂²×C₆₇	1	4	yes	—
370	C₂×#126	C₂²×C₆₇	1	4	yes	—
371	C₂×#126	C₂²×C₆₇	1	4	yes	—
372	C₂×#125	C₂²×C₆₇	1	2	yes	—
373	C₂×#125	C₂²×C₆₇	1	2	yes	—
374	C₂×#125	C₂²×C₆₇	1	4	yes	—
375	C₂×#125	C₂²×C₆₇	1	4	yes	—
376	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
377	C₂×#125	C₂²×C₆₇	1	4	yes	—
378	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
379	C₂×#124	C₂²×C₆₇	1	2	yes	—
380	C₂×#124	C₂²×C₆₇	1	4	yes	—
381	C₂×#124	C₂²×C₆₇	1	2	yes	—
382	C₂×#124	C₂²×C₆₇	1	4	yes	—
383	C₂×#123	C₂²×C₆₇	1	4	yes	—
384	C₂×#123	C₂²×C₆₇	1	4	yes	—
385	C₂×#123	C₂²×C₆₇	1	4	yes	—
386	C₂×#123	C₂²×C₆₇	1	4	yes	—
387	C₂×#123	C₂²×C₆₇	1	4	yes	—
388	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
389	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
396	C₂×#121	C₂²×C₆₇	1	2	yes	—
397	C₂×#121	C₂²×C₆₇	1	4	yes	—
398	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
399	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
400	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
401	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
403	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
405	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
407	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
409	C₂×#117	C₂²×C₆₇	1	4	yes	—
410	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
411	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×#117	C₂²×C₆₇	1	4	yes	—
413	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
414	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
416	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
417	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
418	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
419	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
420	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
421	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
422	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
424	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
425	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
426	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
427	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	—
428	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
429	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	—
430	C₄⋊Q₈	C₂³×C₆₇	1	32	yes	—
431	#127	C₂³×C₆₇	1	8	yes	—
432	#126	C₂³×C₆₇	1	32	yes	—
433	#126	C₂³×C₆₇	1	32	yes	—
434	#126	C₂³×C₆₇	1	32	yes	—
435	#126	C₂³×C₆₇	1	32	yes	—
436	#126	C₂³×C₆₇	1	32	yes	—
437	#125	C₂³×C₆₇	1	16	yes	—
438	#125	C₂³×C₆₇	1	16	yes	—
439	#125	C₂³×C₆₇	1	32	yes	—
440	#125	C₂³×C₆₇	1	32	yes	—
441	#125	C₂³×C₆₇	1	8	yes	—
442	#125	C₂³×C₆₇	1	32	yes	—
443	#125	C₂³×C₆₇	1	8	yes	—
444	#124	C₂³×C₆₇	1	16	yes	—
445	#124	C₂³×C₆₇	1	32	yes	—
446	#124	C₂³×C₆₇	1	16	yes	—
447	#124	C₂³×C₆₇	1	32	yes	—
448	#123	C₂³×C₆₇	1	32	yes	—
449	#123	C₂³×C₆₇	1	32	yes	—
450	#123	C₂³×C₆₇	1	32	yes	—
451	#123	C₂³×C₆₇	1	32	yes	—
452	#123	C₂³×C₆₇	1	32	yes	—
453	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
454	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
455	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
456	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
457	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
458	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
459	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
460	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
461	#121	C₂³×C₆₇	1	16	yes	—
462	#121	C₂³×C₆₇	1	32	yes	—
463	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
464	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
465	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
466	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
467	C₄×Q₈	C₂³×C₆₇	1	32	yes	—
468	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
469	C₄×D₄	C₂³×C₆₇	1	32	yes	—
470	C₄×D₄	C₂³×C₆₇	1	16	yes	—
471	C₄×D₄	C₂³×C₆₇	1	32	yes	—
472	C₄×D₄	C₂³×C₆₇	1	16	yes	—
473	C₄×D₄	C₂³×C₆₇	1	16	yes	—
474	#117	C₂³×C₆₇	1	32	yes	—
475	#117	C₂³×C₆₇	1	8	yes	—
476	#117	C₂³×C₆₇	1	8	yes	—
477	#117	C₂³×C₆₇	1	32	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	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	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
511	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
513	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
517	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
518	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
519	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
521	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
522	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
523	C₂×Q₈	—	2	8	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	8	no	—
526	C₂×Q₈	—	4	4	no	—
527	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
528	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
529	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	—
530	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	4	8	no	—
533	C₂×D₄	—	4	8	no	—
534	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
535	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
536	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	4	8	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	8	no	—
541	C₂²×C₄	—	4	8	no	—
542	C₂²×C₄	C₂⁴×C₆₇	1	2	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	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
555	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
556	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
557	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
558	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
559	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
560	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
561	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
562	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
563	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
564	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
565	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
566	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
567	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
568	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
569	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
570	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
571	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
572	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
573	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
574	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
575	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
576	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
577	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
578	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
579	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
580	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
581	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
582	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
583	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
584	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
585	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
586	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
587	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
588	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
589	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
590	C₄²	C₂⁴×C₆₇	1	4	yes	—
591	C₄²	C₂⁴×C₆₇	1	8	yes	—
592	C₄²	C₂⁴×C₆₇	1	4	yes	—
593	C₄²	C₂⁴×C₆₇	1	16	yes	—
594	C₄²	C₂⁴×C₆₇	1	4	yes	—
595	C₄²	C₂⁴×C₆₇	1	8	yes	—
596	C₄²	C₂⁴×C₆₇	1	4	yes	—
597	C₄²	C₂⁴×C₆₇	1	16	yes	—
598	C₄²	C₂⁴×C₆₇	1	16	yes	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	8	no	—
604	C₂³	C₂⁵×C₆₇	1	2	yes	—
605	C₂³	C₂⁵×C₆₇	1	8	yes	—
606	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
607	Q₈	—	2	16	no	—
608	Q₈	—	4	8	no	—
609	Q₈	—	4	16	no	—
610	Q₈	—	4	8	no	—
611	D₄	—	2	16	no	—
612	D₄	—	4	16	no	—
613	D₄	—	4	16	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	4	16	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	16	no	—
628	C₂×C₄	—	4	16	no	—
629	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
630	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
631	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
632	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
633	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
634	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
635	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
636	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
637	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
638	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
639	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
640	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	8	no	—
643	C₂²	—	2	8	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	16	no	—
648	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
649	C₂²	#585×C₆₇	1	4	yes	—
650	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
651	C₄	—	2	2	no	—
652	C₄	—	2	8	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	8	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	8	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	4	no	—
661	C₄	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
662	C₂	—	4	2	no	—
663	C₂	—	4	8	no	—
664	C₂	C₆₇×#3557	1	4	yes	direct product factor
665	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
666	C₂	C₂×#585×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
prime radical	C₂×#540×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3557	C₂	direct (N × H)
2. C₂×#563×C₆₇	C₂	semidirect
3. C₂×#559×C₆₇	C₂	semidirect
4. C₂×#557×C₆₇	C₂	semidirect
5. C₂×#556×C₆₇	C₂	semidirect
6. C₂×#554×C₆₇	C₂	semidirect
7. C₂×#552×C₆₇	C₂	semidirect
8. C₂×#542×C₆₇	C₂	semidirect
9. C₂×#542×C₆₇	C₂	semidirect
10. C₂×#541×C₆₇	C₂	semidirect
12. C₂×#539×C₆₇	C₂	semidirect
13. C₂×#533×C₆₇	C₂	semidirect
14. C₂×#529×C₆₇	C₂	semidirect
15. #563×C₆₇	C₂²	semidirect
16. #559×C₆₇	C₂²	semidirect
17. #557×C₆₇	C₂²	semidirect
18. #556×C₆₇	C₂²	semidirect
19. #554×C₆₇	C₂²	semidirect
20. #552×C₆₇	C₂²	semidirect
21. #542×C₆₇	C₂²	semidirect
22. #542×C₆₇	C₂²	semidirect
23. #541×C₆₇	C₂²	semidirect
25. #539×C₆₇	C₂²	semidirect
26. #533×C₆₇	C₂²	semidirect
32. #529×C₆₇	C₂²	semidirect
328. C₂×#3557	C₆₇	direct (N × H)
331. C₂×C₆₇	#3557	direct (N × H)
334. #3557	C₂×C₆₇	direct (N × H)
335. C₂×#563	C₂×C₆₇	semidirect
336. C₂×#559	C₂×C₆₇	semidirect
337. C₂×#557	C₂×C₆₇	semidirect
338. C₂×#556	C₂×C₆₇	semidirect
339. C₂×#554	C₂×C₆₇	semidirect
340. C₂×#552	C₂×C₆₇	semidirect
341. C₂×#542	C₂×C₆₇	semidirect
342. C₂×#542	C₂×C₆₇	semidirect
343. C₂×#541	C₂×C₆₇	semidirect
345. C₂×#539	C₂×C₆₇	semidirect
346. C₂×#533	C₂×C₆₇	semidirect
347. C₂×#529	C₂×C₆₇	semidirect
348. C₆₇	C₂×#3557	direct (N × H)
349. #563	C₂²×C₆₇	semidirect
350. #559	C₂²×C₆₇	semidirect
351. #557	C₂²×C₆₇	semidirect
352. #556	C₂²×C₆₇	semidirect
353. #554	C₂²×C₆₇	semidirect
354. #552	C₂²×C₆₇	semidirect
355. #542	C₂²×C₆₇	semidirect
356. #542	C₂²×C₆₇	semidirect
357. #541	C₂²×C₆₇	semidirect
359. #539	C₂²×C₆₇	semidirect
360. #533	C₂²×C₆₇	semidirect
366. #529	C₂²×C₆₇	semidirect
664. C₂	C₆₇×#3557	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×#3557	2
C₂×#563×C₆₇	2
C₂×#559×C₆₇	2
C₂×#557×C₆₇	2
C₂×#556×C₆₇	2
C₂×#554×C₆₇	2
C₂×#552×C₆₇	2
C₂×#542×C₆₇	2
C₂×#541×C₆₇	2
C₂×#540×C₆₇	2
C₂×#539×C₆₇	2
C₂×#533×C₆₇	2
C₂×#529×C₆₇	2
C₂×#3557	67

Subgroups — C2×C67×#3557 #30741989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3557 #30741989