Subgroups — C₂×C₆₇×#3546 #30741998

Order 17152.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3546	C₂	1	32	yes	maximal, direct product factor
2	C₂×#560×C₆₇	C₂	1	4	yes	maximal, complemented
3	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#553×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#550×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#538×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#537×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₂×#535×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₂×#535×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
20	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
22	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
23	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
24	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
25	#560×C₆₇	C₂²	1	64	yes	complemented
26	#556×C₆₇	C₂²	1	16	yes	complemented
27	#553×C₆₇	C₂²	1	32	yes	complemented
28	#550×C₆₇	C₂²	1	32	yes	complemented
29	#550×C₆₇	C₂²	1	16	yes	complemented
30	#547×C₆₇	C₂²	1	16	yes	complemented
31	#546×C₆₇	C₂²	1	32	yes	complemented
32	#546×C₆₇	C₂²	1	32	yes	complemented
33	D₄²×C₆₇	C₂²	1	16	yes	complemented
34	#542×C₆₇	C₂²	1	32	yes	complemented
35	#538×C₆₇	C₂²	1	64	yes	complemented
36	#537×C₆₇	C₂²	1	32	yes	complemented
37	#535×C₆₇	C₂²	1	32	yes	complemented
38	#535×C₆₇	C₂²	1	32	yes	complemented
39	#532×C₆₇	C₂²	1	16	yes	complemented
40	#532×C₆₇	C₂²	1	16	yes	complemented
41	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#127×C₆₇	C₂²	1	4	yes	complemented
46	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
47	#529×C₆₇	C₂²	1	16	yes	complemented
48	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
49	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
50	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
51	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#124×C₆₇	C₂²	1	2	yes	—
54	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
55	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
56	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
57	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
58	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
59	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
60	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
65	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#121×C₆₇	C₂²	1	2	yes	—
68	C₂×#121×C₆₇	C₂²	1	2	yes	—
69	C₂×#121×C₆₇	C₂²	1	2	yes	—
70	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
71	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
72	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
73	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
75	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
76	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
77	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
79	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
80	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
81	C₂×#120×C₆₇	C₂²	1	4	yes	—
82	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
83	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
84	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
85	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
88	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
89	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
90	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
92	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
93	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
95	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
96	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
97	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
98	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₆₇	C₂³	1	4	yes	—
102	C₂×#41×C₆₇	—	4	8	no	—
103	C₂×#41×C₆₇	—	4	8	no	—
104	C₂×#41×C₆₇	—	4	8	no	—
105	C₂×#41×C₆₇	—	4	8	no	—
106	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
107	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
108	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
109	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
112	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	—	4	8	no	—
114	C₂²×D₄×C₆₇	—	4	8	no	—
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
130	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
143	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
144	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
145	#127×C₆₇	C₂³	1	8	yes	—
146	#127×C₆₇	C₂³	1	8	yes	—
147	#127×C₆₇	C₂³	1	16	yes	complemented
148	#127×C₆₇	C₂³	1	32	yes	complemented
149	#126×C₆₇	C₂³	1	16	yes	complemented
150	#126×C₆₇	C₂³	1	32	yes	complemented
151	#126×C₆₇	C₂³	1	32	yes	complemented
152	#125×C₆₇	C₂³	1	8	yes	complemented
153	#124×C₆₇	C₂³	1	8	yes	—
154	#124×C₆₇	C₂³	1	16	yes	—
155	#124×C₆₇	C₂³	1	16	yes	complemented
156	#124×C₆₇	C₂³	1	16	yes	complemented
157	#124×C₆₇	C₂³	1	32	yes	complemented
158	#123×C₆₇	C₂³	1	16	yes	complemented
159	#123×C₆₇	C₂³	1	32	yes	complemented
160	#123×C₆₇	C₂³	1	32	yes	complemented
161	#123×C₆₇	C₂³	1	32	yes	complemented
162	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
163	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
164	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
165	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
166	#121×C₆₇	C₂³	1	8	yes	—
167	#121×C₆₇	C₂³	1	8	yes	—
168	#121×C₆₇	C₂³	1	16	yes	—
169	#121×C₆₇	C₂³	1	16	yes	—
170	#121×C₆₇	C₂³	1	16	yes	—
171	#121×C₆₇	C₂³	1	16	yes	complemented
172	#121×C₆₇	C₂³	1	8	yes	complemented
173	#121×C₆₇	C₂³	1	16	yes	complemented
174	#121×C₆₇	C₂³	1	16	yes	complemented
175	#121×C₆₇	C₂³	1	32	yes	complemented
176	#121×C₆₇	C₂³	1	16	yes	complemented
177	#121×C₆₇	C₂³	1	32	yes	complemented
178	#121×C₆₇	C₂³	1	32	yes	complemented
179	#121×C₆₇	C₂³	1	32	yes	complemented
180	#121×C₆₇	C₂³	1	32	yes	complemented
181	#121×C₆₇	C₂³	1	32	yes	complemented
182	#120×C₆₇	C₂³	1	32	yes	—
183	#120×C₆₇	C₂³	1	32	yes	complemented
184	#120×C₆₇	C₂³	1	32	yes	complemented
185	#120×C₆₇	C₂³	1	32	yes	complemented
186	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
187	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
188	C₄×D₄×C₆₇	C₂³	1	8	yes	—
189	C₄×D₄×C₆₇	C₂³	1	8	yes	—
190	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
191	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
192	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
193	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
194	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
195	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
196	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
197	#117×C₆₇	C₂³	1	16	yes	complemented
198	#117×C₆₇	C₂³	1	16	yes	complemented
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
211	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
235	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
236	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
237	C₂⁴×C₆₇	—	4	8	no	—
238	C₂⁴×C₆₇	—	4	8	no	—
239	C₂⁴×C₆₇	—	4	8	no	—
240	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
241	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
242	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
243	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
245	C₂⁴×C₆₇	C₂⁴	1	16	yes	—
246	#41×C₆₇	—	4	32	no	—
247	#41×C₆₇	—	4	32	no	—
248	#41×C₆₇	—	4	32	no	—
249	#41×C₆₇	—	4	32	no	—
250	C₂×Q₈×C₆₇	—	2	4	no	—
251	C₂×Q₈×C₆₇	—	2	8	no	—
252	C₂×Q₈×C₆₇	—	4	4	no	—
253	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
255	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	8	no	—
259	C₂×D₄×C₆₇	—	2	8	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	4	32	no	—
262	C₂×D₄×C₆₇	—	4	32	no	—
263	C₂×D₄×C₆₇	—	4	8	no	—
264	C₂×D₄×C₆₇	—	4	8	no	—
265	C₂×D₄×C₆₇	—	4	4	no	—
266	C₂×D₄×C₆₇	—	4	4	no	—
267	C₂×D₄×C₆₇	—	4	4	no	—
268	C₂×D₄×C₆₇	—	4	8	no	—
269	C₂×D₄×C₆₇	—	4	4	no	—
270	C₂×D₄×C₆₇	—	4	4	no	—
271	C₂×D₄×C₆₇	—	4	4	no	—
272	C₂×D₄×C₆₇	—	4	8	no	—
273	C₂×D₄×C₆₇	—	4	8	no	—
274	C₂×D₄×C₆₇	—	4	8	no	—
275	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
276	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
277	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
278	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
279	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
280	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
281	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
282	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
283	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
284	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
285	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
286	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
287	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
288	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
289	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
290	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
291	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
292	C₂²×C₄×C₆₇	—	2	8	no	—
293	C₂²×C₄×C₆₇	—	2	8	no	—
294	C₂²×C₄×C₆₇	—	2	4	no	—
295	C₂²×C₄×C₆₇	—	2	8	no	—
296	C₂²×C₄×C₆₇	—	2	4	no	—
297	C₂²×C₄×C₆₇	—	4	2	no	—
298	C₂²×C₄×C₆₇	—	4	8	no	—
299	C₂²×C₄×C₆₇	—	4	8	no	—
300	C₂²×C₄×C₆₇	—	4	8	no	—
301	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
325	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
329	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
332	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
333	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
334	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
338	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
339	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
342	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
344	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
345	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
347	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
348	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
349	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
350	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
351	C₄²×C₆₇	C₂⁴	1	4	yes	—
352	C₄²×C₆₇	C₂⁴	1	4	yes	—
353	C₄²×C₆₇	C₂⁴	1	4	yes	—
354	C₄²×C₆₇	C₂⁴	1	4	yes	—
355	C₄²×C₆₇	C₂⁴	1	8	yes	—
356	C₄²×C₆₇	C₂⁴	1	16	yes	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	4	no	—
360	C₂³×C₆₇	—	2	4	no	—
361	C₂³×C₆₇	—	2	4	no	—
362	C₂³×C₆₇	—	2	4	no	—
363	C₂³×C₆₇	—	2	8	no	—
364	C₂³×C₆₇	—	2	8	no	—
365	C₂³×C₆₇	—	2	4	no	—
366	C₂³×C₆₇	—	2	4	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	4	no	—
369	C₂³×C₆₇	—	2	8	no	—
370	C₂³×C₆₇	—	2	4	no	—
371	C₂³×C₆₇	—	2	4	no	—
372	C₂³×C₆₇	—	4	16	no	—
373	C₂³×C₆₇	—	4	16	no	—
374	C₂³×C₆₇	—	4	16	no	—
375	C₂³×C₆₇	—	8	32	no	—
376	C₂³×C₆₇	C₂⁵	1	4	yes	—
377	C₂³×C₆₇	C₂⁵	1	4	yes	—
378	C₂³×C₆₇	C₂⁵	1	8	yes	—
379	C₂³×C₆₇	C₂⁵	1	2	yes	—
380	C₂³×C₆₇	C₂⁵	1	4	yes	—
381	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
382	Q₈×C₆₇	—	2	8	no	—
383	Q₈×C₆₇	—	2	16	no	—
384	Q₈×C₆₇	—	4	8	no	—
385	D₄×C₆₇	—	2	8	no	—
386	D₄×C₆₇	—	2	8	no	—
387	D₄×C₆₇	—	2	16	no	—
388	D₄×C₆₇	—	2	16	no	—
389	D₄×C₆₇	—	2	8	no	—
390	D₄×C₆₇	—	4	16	no	—
391	D₄×C₆₇	—	4	16	no	—
392	D₄×C₆₇	—	4	8	no	—
393	D₄×C₆₇	—	4	8	no	—
394	D₄×C₆₇	—	4	8	no	—
395	D₄×C₆₇	—	4	16	no	—
396	D₄×C₆₇	—	4	8	no	—
397	D₄×C₆₇	—	4	8	no	—
398	D₄×C₆₇	—	4	8	no	—
399	D₄×C₆₇	—	4	16	no	—
400	D₄×C₆₇	—	4	16	no	—
401	D₄×C₆₇	—	4	16	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	4	no	—
404	C₂×C₄×C₆₇	—	2	4	no	—
405	C₂×C₄×C₆₇	—	2	4	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	8	no	—
408	C₂×C₄×C₆₇	—	2	4	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	4	no	—
412	C₂×C₄×C₆₇	—	2	16	no	—
413	C₂×C₄×C₆₇	—	2	16	no	—
414	C₂×C₄×C₆₇	—	2	8	no	—
415	C₂×C₄×C₆₇	—	2	16	no	—
416	C₂×C₄×C₆₇	—	2	8	no	—
417	C₂×C₄×C₆₇	—	4	4	no	—
418	C₂×C₄×C₆₇	—	4	16	no	—
419	C₂×C₄×C₆₇	—	4	16	no	—
420	C₂×C₄×C₆₇	—	4	16	no	—
421	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
422	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
423	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
424	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
425	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
426	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
427	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
428	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
429	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
430	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
431	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
432	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
433	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
434	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	4	no	—
438	C₂²×C₆₇	—	2	4	no	—
439	C₂²×C₆₇	—	2	4	no	—
440	C₂²×C₆₇	—	2	4	no	—
441	C₂²×C₆₇	—	2	8	no	—
442	C₂²×C₆₇	—	2	8	no	—
443	C₂²×C₆₇	—	2	4	no	—
444	C₂²×C₆₇	—	2	4	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	4	no	—
447	C₂²×C₆₇	—	2	8	no	—
448	C₂²×C₆₇	—	2	4	no	—
449	C₂²×C₆₇	—	2	4	no	—
450	C₂²×C₆₇	—	4	4	no	—
451	C₂²×C₆₇	—	4	8	no	—
452	C₂²×C₆₇	—	4	16	no	—
453	C₂²×C₆₇	—	4	8	no	—
454	C₂²×C₆₇	—	4	8	no	—
455	C₂²×C₆₇	—	8	32	no	—
456	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
458	C₂²×C₆₇	#585	1	2	yes	—
459	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	4	no	—
462	C₄×C₆₇	—	2	4	no	—
463	C₄×C₆₇	—	2	4	no	—
464	C₄×C₆₇	—	2	2	no	—
465	C₄×C₆₇	—	2	8	no	—
466	C₄×C₆₇	—	2	4	no	—
467	C₄×C₆₇	—	2	2	no	—
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	4	no	—
470	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
471	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
472	C₂×#3546	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
473	C₂×C₆₇	—	4	2	no	—
474	C₂×C₆₇	—	4	4	no	—
475	C₂×C₆₇	—	4	8	no	—
476	C₂×C₆₇	—	4	4	no	—
477	C₂×C₆₇	—	4	4	no	—
478	C₂×C₆₇	#3546	1	4	yes	direct product factor
479	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
482	#3546	C₂×C₆₇	1	32	yes	direct product factor
483	C₂×#560	C₂×C₆₇	1	4	yes	complemented
484	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
485	C₂×#553	C₂×C₆₇	1	2	yes	complemented
486	C₂×#550	C₂×C₆₇	1	2	yes	complemented
487	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
488	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
489	C₂×#546	C₂×C₆₇	1	2	yes	complemented
490	C₂×#546	C₂×C₆₇	1	2	yes	complemented
491	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
492	C₂×#542	C₂×C₆₇	1	2	yes	complemented
493	C₂×#538	C₂×C₆₇	1	4	yes	complemented
494	C₂×#537	C₂×C₆₇	1	2	yes	complemented
495	C₂×#535	C₂×C₆₇	1	2	yes	complemented
496	C₂×#535	C₂×C₆₇	1	2	yes	complemented
497	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
498	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
499	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
500	C₆₇	C₂×#3546	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
502	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
503	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
504	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
505	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
506	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
507	#560	C₂²×C₆₇	1	64	yes	complemented
508	#556	C₂²×C₆₇	1	16	yes	complemented
509	#553	C₂²×C₆₇	1	32	yes	complemented
510	#550	C₂²×C₆₇	1	32	yes	complemented
511	#550	C₂²×C₆₇	1	16	yes	complemented
512	#547	C₂²×C₆₇	1	16	yes	complemented
513	#546	C₂²×C₆₇	1	32	yes	complemented
514	#546	C₂²×C₆₇	1	32	yes	complemented
515	D₄²	C₂²×C₆₇	1	16	yes	complemented
516	#542	C₂²×C₆₇	1	32	yes	complemented
517	#538	C₂²×C₆₇	1	64	yes	complemented
518	#537	C₂²×C₆₇	1	32	yes	complemented
519	#535	C₂²×C₆₇	1	32	yes	complemented
520	#535	C₂²×C₆₇	1	32	yes	complemented
521	#532	C₂²×C₆₇	1	16	yes	complemented
522	#532	C₂²×C₆₇	1	16	yes	complemented
523	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
527	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
528	C₂×#127	C₂²×C₆₇	1	4	yes	complemented
529	#529	C₂²×C₆₇	1	16	yes	complemented
530	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
531	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
532	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
533	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
535	C₂×#124	C₂²×C₆₇	1	2	yes	—
536	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
537	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
538	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
539	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
540	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
541	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
542	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
543	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
545	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
546	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
547	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
549	C₂×#121	C₂²×C₆₇	1	2	yes	—
550	C₂×#121	C₂²×C₆₇	1	2	yes	—
551	C₂×#121	C₂²×C₆₇	1	2	yes	—
552	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
553	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
555	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
556	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
557	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
558	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
559	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
560	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
561	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
562	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
563	C₂×#120	C₂²×C₆₇	1	4	yes	—
564	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
565	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
566	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
567	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
569	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
572	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
573	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
574	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
575	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
577	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
578	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
579	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
580	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
581	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
582	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
583	C₂⁵	C₂³×C₆₇	1	4	yes	—
584	C₂×#41	—	4	8	no	—
585	C₂×#41	—	4	8	no	—
586	C₂×#41	—	4	8	no	—
587	C₂×#41	—	4	8	no	—
588	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
589	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
590	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
591	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
592	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
594	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
595	C₂²×D₄	—	4	8	no	—
596	C₂²×D₄	—	4	8	no	—
597	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
600	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
601	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
603	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
604	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
605	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
606	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
607	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
608	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
609	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
610	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
611	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
612	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
613	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
614	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
615	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
616	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
617	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
618	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
619	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
622	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
623	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
624	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
626	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
627	#127	C₂³×C₆₇	1	8	yes	—
628	#127	C₂³×C₆₇	1	8	yes	—
629	#127	C₂³×C₆₇	1	16	yes	complemented
630	#127	C₂³×C₆₇	1	32	yes	complemented
631	#126	C₂³×C₆₇	1	16	yes	complemented
632	#126	C₂³×C₆₇	1	32	yes	complemented
633	#126	C₂³×C₆₇	1	32	yes	complemented
634	#125	C₂³×C₆₇	1	8	yes	complemented
635	#124	C₂³×C₆₇	1	8	yes	—
636	#124	C₂³×C₆₇	1	16	yes	—
637	#124	C₂³×C₆₇	1	16	yes	complemented
638	#124	C₂³×C₆₇	1	16	yes	complemented
639	#124	C₂³×C₆₇	1	32	yes	complemented
640	#123	C₂³×C₆₇	1	16	yes	complemented
641	#123	C₂³×C₆₇	1	32	yes	complemented
642	#123	C₂³×C₆₇	1	32	yes	complemented
643	#123	C₂³×C₆₇	1	32	yes	complemented
644	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
645	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
646	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
647	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
648	#121	C₂³×C₆₇	1	8	yes	—
649	#121	C₂³×C₆₇	1	8	yes	—
650	#121	C₂³×C₆₇	1	16	yes	—
651	#121	C₂³×C₆₇	1	16	yes	—
652	#121	C₂³×C₆₇	1	16	yes	—
653	#121	C₂³×C₆₇	1	16	yes	complemented
654	#121	C₂³×C₆₇	1	8	yes	complemented
655	#121	C₂³×C₆₇	1	16	yes	complemented
656	#121	C₂³×C₆₇	1	16	yes	complemented
657	#121	C₂³×C₆₇	1	32	yes	complemented
658	#121	C₂³×C₆₇	1	16	yes	complemented
659	#121	C₂³×C₆₇	1	32	yes	complemented
660	#121	C₂³×C₆₇	1	32	yes	complemented
661	#121	C₂³×C₆₇	1	32	yes	complemented
662	#121	C₂³×C₆₇	1	32	yes	complemented
663	#121	C₂³×C₆₇	1	32	yes	complemented
664	#120	C₂³×C₆₇	1	32	yes	—
665	#120	C₂³×C₆₇	1	32	yes	complemented
666	#120	C₂³×C₆₇	1	32	yes	complemented
667	#120	C₂³×C₆₇	1	32	yes	complemented
668	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
669	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
670	C₄×D₄	C₂³×C₆₇	1	8	yes	—
671	C₄×D₄	C₂³×C₆₇	1	8	yes	—
672	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
673	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
674	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
675	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
676	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
677	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
678	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
679	#117	C₂³×C₆₇	1	16	yes	complemented
680	#117	C₂³×C₆₇	1	16	yes	complemented
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
712	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
714	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
715	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
719	C₂⁴	—	4	8	no	—
720	C₂⁴	—	4	8	no	—
721	C₂⁴	—	4	8	no	—
722	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
723	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
724	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
725	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
727	C₂⁴	C₂⁴×C₆₇	1	16	yes	—
728	#41	—	4	32	no	—
729	#41	—	4	32	no	—
730	#41	—	4	32	no	—
731	#41	—	4	32	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	2	8	no	—
734	C₂×Q₈	—	4	4	no	—
735	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
736	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
737	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	8	no	—
741	C₂×D₄	—	2	8	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	4	32	no	—
744	C₂×D₄	—	4	32	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	8	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	4	4	no	—
749	C₂×D₄	—	4	4	no	—
750	C₂×D₄	—	4	8	no	—
751	C₂×D₄	—	4	8	no	—
752	C₂×D₄	—	4	8	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	4	no	—
755	C₂×D₄	—	4	4	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
758	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
759	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
760	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
761	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
762	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
763	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
764	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
765	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
766	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
767	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
768	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
769	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
770	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
771	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
772	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
773	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
774	C₂²×C₄	—	2	8	no	—
775	C₂²×C₄	—	2	8	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	8	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	4	8	no	—
780	C₂²×C₄	—	4	8	no	—
781	C₂²×C₄	—	4	8	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
791	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
792	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
793	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
796	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
797	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
798	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
799	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
800	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
802	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
804	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
805	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
806	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
807	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
808	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
809	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
810	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
811	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
812	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
813	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
814	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
815	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
816	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
817	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
818	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
819	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
820	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
821	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
822	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
823	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
825	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
826	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
827	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
828	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
829	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
830	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
831	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
833	C₄²	C₂⁴×C₆₇	1	4	yes	—
834	C₄²	C₂⁴×C₆₇	1	4	yes	—
835	C₄²	C₂⁴×C₆₇	1	4	yes	—
836	C₄²	C₂⁴×C₆₇	1	4	yes	—
837	C₄²	C₂⁴×C₆₇	1	8	yes	—
838	C₄²	C₂⁴×C₆₇	1	16	yes	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	8	no	—
846	C₂³	—	2	8	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	2	4	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	4	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	4	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	4	16	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	4	16	no	—
857	C₂³	—	8	32	no	—
858	C₂³	C₂⁵×C₆₇	1	4	yes	—
859	C₂³	C₂⁵×C₆₇	1	4	yes	—
860	C₂³	C₂⁵×C₆₇	1	8	yes	—
861	C₂³	C₂⁵×C₆₇	1	2	yes	—
862	C₂³	C₂⁵×C₆₇	1	4	yes	—
863	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	2	16	no	—
866	Q₈	—	4	8	no	—
867	D₄	—	2	8	no	—
868	D₄	—	2	8	no	—
869	D₄	—	2	16	no	—
870	D₄	—	2	16	no	—
871	D₄	—	2	8	no	—
872	D₄	—	4	16	no	—
873	D₄	—	4	16	no	—
874	D₄	—	4	8	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	16	no	—
878	D₄	—	4	16	no	—
879	D₄	—	4	16	no	—
880	D₄	—	4	8	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	8	no	—
883	D₄	—	4	16	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	4	no	—
894	C₂×C₄	—	2	16	no	—
895	C₂×C₄	—	2	16	no	—
896	C₂×C₄	—	2	8	no	—
897	C₂×C₄	—	2	16	no	—
898	C₂×C₄	—	2	8	no	—
899	C₂×C₄	—	4	16	no	—
900	C₂×C₄	—	4	16	no	—
901	C₂×C₄	—	4	16	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
904	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
905	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
906	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
907	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
908	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
909	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
910	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
911	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
912	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
913	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
914	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
915	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
916	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	8	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	8	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	4	8	no	—
933	C₂²	—	4	8	no	—
934	C₂²	—	4	16	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	4	8	no	—
937	C₂²	—	8	32	no	—
938	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
939	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
940	C₂²	#585×C₆₇	1	2	yes	—
941	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	8	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	4	no	—
952	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
953	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	4	no	—
956	C₂	—	4	8	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	4	no	—
959	C₂	C₆₇×#3546	1	4	yes	direct product factor
960	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
961	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
962	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
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×#3546	C₂	direct (N × H)
2. C₂×#560×C₆₇	C₂	semidirect
3. C₂×#556×C₆₇	C₂	semidirect
4. C₂×#553×C₆₇	C₂	semidirect
5. C₂×#550×C₆₇	C₂	semidirect
6. C₂×#550×C₆₇	C₂	semidirect
7. C₂×#547×C₆₇	C₂	semidirect
8. C₂×#546×C₆₇	C₂	semidirect
9. C₂×#546×C₆₇	C₂	semidirect
10. C₂×D₄²×C₆₇	C₂	semidirect
11. C₂×#542×C₆₇	C₂	semidirect
12. C₂×#538×C₆₇	C₂	semidirect
13. C₂×#537×C₆₇	C₂	semidirect
14. C₂×#535×C₆₇	C₂	semidirect
15. C₂×#535×C₆₇	C₂	semidirect
16. C₂×#532×C₆₇	C₂	semidirect
17. C₂×#532×C₆₇	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
21. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂²×#41×C₆₇	C₂²	semidirect
25. #560×C₆₇	C₂²	semidirect
26. #556×C₆₇	C₂²	semidirect
27. #553×C₆₇	C₂²	semidirect
28. #550×C₆₇	C₂²	semidirect
29. #550×C₆₇	C₂²	semidirect
30. #547×C₆₇	C₂²	semidirect
31. #546×C₆₇	C₂²	semidirect
32. #546×C₆₇	C₂²	semidirect
33. D₄²×C₆₇	C₂²	semidirect
34. #542×C₆₇	C₂²	semidirect
35. #538×C₆₇	C₂²	semidirect
36. #537×C₆₇	C₂²	semidirect
37. #535×C₆₇	C₂²	semidirect
38. #535×C₆₇	C₂²	semidirect
39. #532×C₆₇	C₂²	semidirect
40. #532×C₆₇	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
42. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
45. C₂×#127×C₆₇	C₂²	semidirect
46. C₂×#127×C₆₇	C₂²	semidirect
47. #529×C₆₇	C₂²	semidirect
48. C₂×#126×C₆₇	C₂²	semidirect
49. C₂×#126×C₆₇	C₂²	semidirect
50. C₂×#126×C₆₇	C₂²	semidirect
51. C₂×#125×C₆₇	C₂²	semidirect
54. C₂×#124×C₆₇	C₂²	semidirect
55. C₂×#124×C₆₇	C₂²	semidirect
56. C₂×#124×C₆₇	C₂²	semidirect
57. C₂×#123×C₆₇	C₂²	semidirect
58. C₂×#123×C₆₇	C₂²	semidirect
59. C₂×#123×C₆₇	C₂²	semidirect
60. C₂×#123×C₆₇	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
63. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
64. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
70. C₂×#121×C₆₇	C₂²	semidirect
71. C₂×#121×C₆₇	C₂²	semidirect
72. C₂×#121×C₆₇	C₂²	semidirect
73. C₂×#121×C₆₇	C₂²	semidirect
74. C₂×#121×C₆₇	C₂²	semidirect
75. C₂×#121×C₆₇	C₂²	semidirect
76. C₂×#121×C₆₇	C₂²	semidirect
77. C₂×#121×C₆₇	C₂²	semidirect
78. C₂×#121×C₆₇	C₂²	semidirect
79. C₂×#121×C₆₇	C₂²	semidirect
80. C₂×#121×C₆₇	C₂²	semidirect
82. C₂×#120×C₆₇	C₂²	semidirect
83. C₂×#120×C₆₇	C₂²	semidirect
84. C₂×#120×C₆₇	C₂²	semidirect
85. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
86. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
89. C₂×C₄×D₄×C₆₇	C₂²	semidirect
90. C₂×C₄×D₄×C₆₇	C₂²	semidirect
91. C₂×C₄×D₄×C₆₇	C₂²	semidirect
92. C₂×C₄×D₄×C₆₇	C₂²	semidirect
93. C₂×C₄×D₄×C₆₇	C₂²	semidirect
94. C₂×C₄×D₄×C₆₇	C₂²	semidirect
95. C₂×C₄×D₄×C₆₇	C₂²	semidirect
96. C₂×#117×C₆₇	C₂²	semidirect
97. C₂×#117×C₆₇	C₂²	semidirect
98. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
99. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
106. C₂×#41×C₆₇	C₂³	semidirect
107. C₂×#41×C₆₇	C₂³	semidirect
108. C₂×#41×C₆₇	C₂³	semidirect
109. C₂×#41×C₆₇	C₂³	semidirect
143. C₄⋊Q₈×C₆₇	C₂³	semidirect
144. C₄⋊Q₈×C₆₇	C₂³	semidirect
147. #127×C₆₇	C₂³	semidirect
148. #127×C₆₇	C₂³	semidirect
149. #126×C₆₇	C₂³	semidirect
150. #126×C₆₇	C₂³	semidirect
151. #126×C₆₇	C₂³	semidirect
152. #125×C₆₇	C₂³	semidirect
155. #124×C₆₇	C₂³	semidirect
156. #124×C₆₇	C₂³	semidirect
157. #124×C₆₇	C₂³	semidirect
158. #123×C₆₇	C₂³	semidirect
159. #123×C₆₇	C₂³	semidirect
160. #123×C₆₇	C₂³	semidirect
161. #123×C₆₇	C₂³	semidirect
162. C₂²⋊Q₈×C₆₇	C₂³	semidirect
163. C₂²⋊Q₈×C₆₇	C₂³	semidirect
164. C₂²⋊Q₈×C₆₇	C₂³	semidirect
165. C₂²⋊Q₈×C₆₇	C₂³	semidirect
171. #121×C₆₇	C₂³	semidirect
172. #121×C₆₇	C₂³	semidirect
173. #121×C₆₇	C₂³	semidirect
174. #121×C₆₇	C₂³	semidirect
175. #121×C₆₇	C₂³	semidirect
176. #121×C₆₇	C₂³	semidirect
177. #121×C₆₇	C₂³	semidirect
178. #121×C₆₇	C₂³	semidirect
179. #121×C₆₇	C₂³	semidirect
180. #121×C₆₇	C₂³	semidirect
181. #121×C₆₇	C₂³	semidirect
183. #120×C₆₇	C₂³	semidirect
184. #120×C₆₇	C₂³	semidirect
185. #120×C₆₇	C₂³	semidirect
186. C₄×Q₈×C₆₇	C₂³	semidirect
187. C₄×Q₈×C₆₇	C₂³	semidirect
190. C₄×D₄×C₆₇	C₂³	semidirect
191. C₄×D₄×C₆₇	C₂³	semidirect
192. C₄×D₄×C₆₇	C₂³	semidirect
193. C₄×D₄×C₆₇	C₂³	semidirect
194. C₄×D₄×C₆₇	C₂³	semidirect
195. C₄×D₄×C₆₇	C₂³	semidirect
196. C₄×D₄×C₆₇	C₂³	semidirect
197. #117×C₆₇	C₂³	semidirect
198. #117×C₆₇	C₂³	semidirect
212. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
229. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
236. C₂×C₄²×C₆₇	C₂³	semidirect
472. C₂×#3546	C₆₇	direct (N × H)
478. C₂×C₆₇	#3546	direct (N × H)
482. #3546	C₂×C₆₇	direct (N × H)
483. C₂×#560	C₂×C₆₇	semidirect
484. C₂×#556	C₂×C₆₇	semidirect
485. C₂×#553	C₂×C₆₇	semidirect
486. C₂×#550	C₂×C₆₇	semidirect
487. C₂×#550	C₂×C₆₇	semidirect
488. C₂×#547	C₂×C₆₇	semidirect
489. C₂×#546	C₂×C₆₇	semidirect
490. C₂×#546	C₂×C₆₇	semidirect
491. C₂×D₄²	C₂×C₆₇	semidirect
492. C₂×#542	C₂×C₆₇	semidirect
493. C₂×#538	C₂×C₆₇	semidirect
494. C₂×#537	C₂×C₆₇	semidirect
495. C₂×#535	C₂×C₆₇	semidirect
496. C₂×#535	C₂×C₆₇	semidirect
497. C₂×#532	C₂×C₆₇	semidirect
498. C₂×#532	C₂×C₆₇	semidirect
499. C₂×#529	C₂×C₆₇	semidirect
500. C₆₇	C₂×#3546	direct (N × H)
501. C₂²×#41	C₂²×C₆₇	semidirect
502. C₂²×#41	C₂²×C₆₇	semidirect
503. C₂²×#41	C₂²×C₆₇	semidirect
504. C₂²×#41	C₂²×C₆₇	semidirect
507. #560	C₂²×C₆₇	semidirect
508. #556	C₂²×C₆₇	semidirect
509. #553	C₂²×C₆₇	semidirect
510. #550	C₂²×C₆₇	semidirect
511. #550	C₂²×C₆₇	semidirect
512. #547	C₂²×C₆₇	semidirect
513. #546	C₂²×C₆₇	semidirect
514. #546	C₂²×C₆₇	semidirect
515. D₄²	C₂²×C₆₇	semidirect
516. #542	C₂²×C₆₇	semidirect
517. #538	C₂²×C₆₇	semidirect
518. #537	C₂²×C₆₇	semidirect
519. #535	C₂²×C₆₇	semidirect
520. #535	C₂²×C₆₇	semidirect
521. #532	C₂²×C₆₇	semidirect
522. #532	C₂²×C₆₇	semidirect
523. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
524. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
527. C₂×#127	C₂²×C₆₇	semidirect
528. C₂×#127	C₂²×C₆₇	semidirect
529. #529	C₂²×C₆₇	semidirect
530. C₂×#126	C₂²×C₆₇	semidirect
531. C₂×#126	C₂²×C₆₇	semidirect
532. C₂×#126	C₂²×C₆₇	semidirect
533. C₂×#125	C₂²×C₆₇	semidirect
536. C₂×#124	C₂²×C₆₇	semidirect
537. C₂×#124	C₂²×C₆₇	semidirect
538. C₂×#124	C₂²×C₆₇	semidirect
539. C₂×#123	C₂²×C₆₇	semidirect
540. C₂×#123	C₂²×C₆₇	semidirect
541. C₂×#123	C₂²×C₆₇	semidirect
542. C₂×#123	C₂²×C₆₇	semidirect
543. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
544. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
545. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
546. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
552. C₂×#121	C₂²×C₆₇	semidirect
553. C₂×#121	C₂²×C₆₇	semidirect
554. C₂×#121	C₂²×C₆₇	semidirect
555. C₂×#121	C₂²×C₆₇	semidirect
556. C₂×#121	C₂²×C₆₇	semidirect
557. C₂×#121	C₂²×C₆₇	semidirect
558. C₂×#121	C₂²×C₆₇	semidirect
559. C₂×#121	C₂²×C₆₇	semidirect
560. C₂×#121	C₂²×C₆₇	semidirect
561. C₂×#121	C₂²×C₆₇	semidirect
562. C₂×#121	C₂²×C₆₇	semidirect
564. C₂×#120	C₂²×C₆₇	semidirect
565. C₂×#120	C₂²×C₆₇	semidirect
566. C₂×#120	C₂²×C₆₇	semidirect
567. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
568. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
571. C₂×C₄×D₄	C₂²×C₆₇	semidirect
572. C₂×C₄×D₄	C₂²×C₆₇	semidirect
573. C₂×C₄×D₄	C₂²×C₆₇	semidirect
574. C₂×C₄×D₄	C₂²×C₆₇	semidirect
575. C₂×C₄×D₄	C₂²×C₆₇	semidirect
576. C₂×C₄×D₄	C₂²×C₆₇	semidirect
577. C₂×C₄×D₄	C₂²×C₆₇	semidirect
578. C₂×#117	C₂²×C₆₇	semidirect
579. C₂×#117	C₂²×C₆₇	semidirect
580. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
581. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
582. C₂²×C₄²	C₂²×C₆₇	semidirect
588. C₂×#41	C₂³×C₆₇	semidirect
589. C₂×#41	C₂³×C₆₇	semidirect
590. C₂×#41	C₂³×C₆₇	semidirect
591. C₂×#41	C₂³×C₆₇	semidirect
625. C₄⋊Q₈	C₂³×C₆₇	semidirect
626. C₄⋊Q₈	C₂³×C₆₇	semidirect
629. #127	C₂³×C₆₇	semidirect
630. #127	C₂³×C₆₇	semidirect
631. #126	C₂³×C₆₇	semidirect
632. #126	C₂³×C₆₇	semidirect
633. #126	C₂³×C₆₇	semidirect
634. #125	C₂³×C₆₇	semidirect
637. #124	C₂³×C₆₇	semidirect
638. #124	C₂³×C₆₇	semidirect
639. #124	C₂³×C₆₇	semidirect
640. #123	C₂³×C₆₇	semidirect
641. #123	C₂³×C₆₇	semidirect
642. #123	C₂³×C₆₇	semidirect
643. #123	C₂³×C₆₇	semidirect
644. C₂²⋊Q₈	C₂³×C₆₇	semidirect
645. C₂²⋊Q₈	C₂³×C₆₇	semidirect
646. C₂²⋊Q₈	C₂³×C₆₇	semidirect
647. C₂²⋊Q₈	C₂³×C₆₇	semidirect
653. #121	C₂³×C₆₇	semidirect
654. #121	C₂³×C₆₇	semidirect
655. #121	C₂³×C₆₇	semidirect
656. #121	C₂³×C₆₇	semidirect
657. #121	C₂³×C₆₇	semidirect
658. #121	C₂³×C₆₇	semidirect
659. #121	C₂³×C₆₇	semidirect
660. #121	C₂³×C₆₇	semidirect
661. #121	C₂³×C₆₇	semidirect
662. #121	C₂³×C₆₇	semidirect
663. #121	C₂³×C₆₇	semidirect
665. #120	C₂³×C₆₇	semidirect
666. #120	C₂³×C₆₇	semidirect
667. #120	C₂³×C₆₇	semidirect
668. C₄×Q₈	C₂³×C₆₇	semidirect
669. C₄×Q₈	C₂³×C₆₇	semidirect
672. C₄×D₄	C₂³×C₆₇	semidirect
673. C₄×D₄	C₂³×C₆₇	semidirect
674. C₄×D₄	C₂³×C₆₇	semidirect
675. C₄×D₄	C₂³×C₆₇	semidirect
676. C₄×D₄	C₂³×C₆₇	semidirect
677. C₄×D₄	C₂³×C₆₇	semidirect
678. C₄×D₄	C₂³×C₆₇	semidirect
679. #117	C₂³×C₆₇	semidirect
680. #117	C₂³×C₆₇	semidirect
694. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
711. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
718. C₂×C₄²	C₂³×C₆₇	semidirect
959. C₂	C₆₇×#3546	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×#3546	2
C₂×#560×C₆₇	2
C₂×#556×C₆₇	2
C₂×#553×C₆₇	2
C₂×#550×C₆₇	2
C₂×#547×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₂×#542×C₆₇	2
C₂×#538×C₆₇	2
C₂×#537×C₆₇	2
C₂×#535×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂×#3546	67

Subgroups — C2×C67×#3546 #30741998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3546 #30741998