Subgroups — #36338300

Order 21376.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24924020	C₂	1	1	yes	maximal, characteristic, complemented
2	#24924016	C₂	1	1	yes	maximal, characteristic, complemented
3	#24924007	C₂	1	1	yes	maximal, characteristic, complemented
4	#24924001	C₂	1	1	yes	maximal, characteristic, complemented
5	#24923966	C₂	1	1	yes	maximal, characteristic, complemented
6	#24923962	C₂	1	1	yes	maximal, characteristic, complemented
7	#24923957	C₂	1	1	yes	maximal, characteristic, complemented
8	#24923953	C₂	1	1	yes	maximal, characteristic, complemented
9	#24923946	C₂	1	1	yes	maximal, characteristic, complemented
10	#24923942	C₂	1	1	yes	maximal, characteristic, complemented
11	#24923942	C₂	1	1	yes	maximal, characteristic, complemented
12	#24923921	C₂	1	1	yes	maximal, characteristic, complemented
13	#24923917	C₂	1	1	yes	maximal, characteristic, complemented
14	#24923912	C₂	1	1	yes	maximal, characteristic, complemented
15	#24923908	C₂	1	1	yes	maximal, characteristic, complemented
16	#24923892	C₂	1	1	yes	maximal, characteristic, complemented
17	#24923883	C₂	1	1	yes	maximal, characteristic, complemented
18	#24923872	C₂	1	1	yes	maximal, characteristic, complemented
19	#24923871	C₂	1	1	yes	maximal, characteristic, complemented
20	#24923868	C₂	1	1	yes	maximal, characteristic, complemented
21	#24923867	C₂	1	1	yes	maximal, characteristic, complemented
22	#24923859	C₂	1	1	yes	maximal, characteristic, complemented
23	#24923855	C₂	1	1	yes	maximal, characteristic, complemented
24	#24923855	C₂	1	1	yes	maximal, characteristic, complemented
25	#24923853	C₂	1	1	yes	maximal, characteristic, complemented
26	#24923835	C₂	1	1	yes	maximal, characteristic, complemented
27	#24923827	C₂	1	1	yes	maximal, characteristic, complemented
28	#24923782	C₂	1	1	yes	maximal, characteristic, complemented
29	#24923779	C₂	1	1	yes	maximal, characteristic, complemented
30	#123×D₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#562×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14581951	C₂²	1	1	yes	characteristic
33	C₂×#14581950	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14581949	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₁₆₇	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₁₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₆₇	C₂²	1	1	yes	characteristic, complemented
38	#19128831	C₂²	1	1	yes	characteristic, complemented
39	#19128830	C₂²	1	1	yes	characteristic, complemented
40	#19128828	C₂²	1	1	yes	characteristic
41	#19128828	C₂²	1	1	yes	characteristic, complemented
42	#19128827	C₂²	1	1	yes	characteristic, complemented
43	#19128827	C₂²	1	1	yes	characteristic, complemented
44	#19128827	C₂²	1	1	yes	characteristic, complemented
45	#19128827	C₂²	1	1	yes	characteristic, complemented
46	#19128827	C₂²	1	1	yes	characteristic, complemented
47	#19128827	C₂²	1	1	yes	characteristic, complemented
48	#19128827	C₂²	1	1	yes	characteristic, complemented
49	#19128826	C₂²	1	1	yes	characteristic, complemented
50	#19128825	C₂²	1	1	yes	characteristic, complemented
51	#19128825	C₂²	1	1	yes	characteristic, complemented
52	#19128825	C₂²	1	1	yes	characteristic, complemented
53	#19128825	C₂²	1	1	yes	characteristic, complemented
54	#19128823	C₂²	1	1	yes	characteristic, complemented
55	#19128823	C₂²	1	1	yes	characteristic, complemented
56	#19128823	C₂²	1	1	yes	characteristic, complemented
57	#19128822	C₂²	1	1	yes	characteristic, complemented
58	#19128822	C₂²	1	1	yes	characteristic, complemented
59	#19128821	C₂²	1	1	yes	characteristic, complemented
60	#19128821	C₂²	1	1	yes	characteristic, complemented
61	#19128818	C₂²	1	1	yes	characteristic
62	#19128818	C₂²	1	1	yes	characteristic, complemented
63	#19128818	C₂²	1	1	yes	characteristic, complemented
64	#19128818	C₂²	1	1	yes	characteristic, complemented
65	#19128818	C₂²	1	1	yes	characteristic, complemented
66	#19128818	C₂²	1	1	yes	characteristic, complemented
67	#19128817	C₂²	1	1	yes	characteristic
68	#19128817	C₂²	1	1	yes	characteristic
69	#19128817	C₂²	1	1	yes	characteristic
70	#19128817	C₂²	1	1	yes	characteristic
71	#19128817	C₂²	1	1	yes	characteristic
72	#19128817	C₂²	1	1	yes	characteristic, complemented
73	#19128817	C₂²	1	1	yes	characteristic, complemented
74	#19128817	C₂²	1	1	yes	characteristic, complemented
75	#19128817	C₂²	1	1	yes	characteristic, complemented
76	#19128816	C₂²	1	1	yes	characteristic
77	#19128816	C₂²	1	1	yes	characteristic, complemented
78	#19128816	C₂²	1	1	yes	characteristic, complemented
79	#19128816	C₂²	1	1	yes	characteristic, complemented
80	#19128816	C₂²	1	1	yes	characteristic, complemented
81	#19128815	C₂²	1	1	yes	characteristic
82	#19128814	C₂²	1	1	yes	characteristic
83	#19128814	C₂²	1	1	yes	characteristic
84	#19128814	C₂²	1	1	yes	characteristic
85	#19128814	C₂²	1	1	yes	characteristic, complemented
86	#19128814	C₂²	1	1	yes	characteristic, complemented
87	#19128814	C₂²	1	1	yes	characteristic, complemented
88	#19128814	C₂²	1	1	yes	characteristic, complemented
89	#19128814	C₂²	1	1	yes	characteristic, complemented
90	#19128814	C₂²	1	1	yes	characteristic, complemented
91	#19128813	C₂²	1	1	yes	characteristic, complemented
92	#19128813	C₂²	1	1	yes	characteristic, complemented
93	#19128812	C₂²	1	1	yes	characteristic, complemented
94	#19128812	C₂²	1	1	yes	characteristic, complemented
95	#19128812	C₂²	1	1	yes	characteristic, complemented
96	#19128812	C₂²	1	1	yes	characteristic, complemented
97	#19128811	C₂²	1	1	yes	characteristic, complemented
98	#19128810	C₂²	1	1	yes	characteristic, complemented
99	#19128810	C₂²	1	1	yes	characteristic, complemented
100	#19128809	C₂²	1	1	yes	characteristic, complemented
101	#19128809	C₂²	1	1	yes	characteristic, complemented
102	#19128808	C₂²	1	1	yes	characteristic, complemented
103	#19128808	C₂²	1	1	yes	characteristic, complemented
104	#19128808	C₂²	1	1	yes	characteristic, complemented
105	#19128807	C₂²	1	1	yes	characteristic
106	#19128807	C₂²	1	1	yes	characteristic, complemented
107	#19128806	C₂²	1	1	yes	characteristic
108	#19128806	C₂²	1	1	yes	characteristic
109	#19128806	C₂²	1	1	yes	characteristic, complemented
110	#19128806	C₂²	1	1	yes	characteristic, complemented
111	#19128805	C₂²	1	1	yes	characteristic
112	#19128805	C₂²	1	1	yes	characteristic
113	#19128805	C₂²	1	1	yes	characteristic, complemented
114	#19128805	C₂²	1	1	yes	characteristic, complemented
115	#19128805	C₂²	1	1	yes	characteristic, complemented
116	#19128804	C₂²	1	1	yes	characteristic
117	#19128804	C₂²	1	1	yes	characteristic
118	#19128804	C₂²	1	1	yes	characteristic, complemented
119	#19128804	C₂²	1	1	yes	characteristic, complemented
120	#19128804	C₂²	1	1	yes	characteristic, complemented
121	#19128803	C₂²	1	1	yes	characteristic, complemented
122	#19128803	C₂²	1	1	yes	characteristic, complemented
123	#19128803	C₂²	1	1	yes	characteristic, complemented
124	#19128803	C₂²	1	1	yes	characteristic, complemented
125	#19128802	C₂²	1	1	yes	characteristic
126	#19128802	C₂²	1	1	yes	characteristic
127	#19128802	C₂²	1	1	yes	characteristic
128	#19128802	C₂²	1	1	yes	characteristic, complemented
129	#19128802	C₂²	1	1	yes	characteristic, complemented
130	#19128800	C₂²	1	1	yes	characteristic
131	#19128800	C₂²	1	1	yes	characteristic
132	#19128800	C₂²	1	1	yes	characteristic
133	#19128800	C₂²	1	1	yes	characteristic, complemented
134	#19128800	C₂²	1	1	yes	characteristic, complemented
135	Q₈×Dic₁₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₃₃₄	C₂²	1	1	yes	characteristic, complemented
137	C₄×D₆₆₈	C₂²	1	1	yes	characteristic
138	C₄×D₆₆₈	C₂²	1	1	yes	characteristic, complemented
139	D₄×Dic₁₆₇	C₂²	1	1	yes	characteristic, complemented
140	D₄×Dic₁₆₇	C₂²	1	1	yes	characteristic, complemented
141	D₄×Dic₁₆₇	C₂²	1	1	yes	characteristic, complemented
142	#19128794	C₂²	1	1	yes	characteristic, complemented
143	#19128794	C₂²	1	1	yes	characteristic, complemented
144	#19128794	C₂²	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊D₁₆₇	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₁₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₄×C₂²⋊D₁₆₇	C₂²	1	1	yes	characteristic, complemented
148	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
149	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	#19128791	C₂²	1	1	yes	characteristic, complemented
156	#19128791	C₂²	1	1	yes	characteristic, complemented
157	#19128790	C₂²	1	1	yes	characteristic, complemented
158	#19128790	C₂²	1	1	yes	characteristic, complemented
159	#19128790	C₂²	1	1	yes	characteristic, complemented
160	#19128790	C₂²	1	1	yes	characteristic, complemented
161	#19128788	C₂²	1	1	yes	characteristic, complemented
162	C₂×Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
167	C₂×(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₁₆₇	C₂²	1	1	yes	characteristic, complemented
172	#125×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
173	#124×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
174	#124×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
175	#123×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
177	#123×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
178	#123×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
183	#121×C₁₆₇	C₂²	1	1	yes	characteristic
184	#121×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
185	#121×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
186	#121×C₁₆₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₆₇	C₂³	1	1	yes	characteristic
188	C₂³×D₁₆₇	C₂³	1	1	yes	characteristic
189	C₂³×D₁₆₇	C₂³	1	1	yes	characteristic
190	#14581951	—	4	2	no	—
191	#14581950	—	4	2	no	—
192	#14581949	—	4	2	no	—
193	C₂×Dic₃₃₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₃₃₄	C₂³	1	1	yes	characteristic
195	C₂×Dic₃₃₄	C₂³	1	1	yes	characteristic
196	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
197	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
198	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
199	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
200	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
201	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
202	C₂×D₆₆₈	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₁₆₇	C₂³	1	1	yes	characteristic
217	D₄×D₁₆₇	—	4	2	no	—
218	D₄×D₁₆₇	—	4	2	no	—
219	C₂²×Dic₁₆₇	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₆₇	C₂³	1	1	yes	characteristic
221	C₂²×Dic₁₆₇	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₆₇	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₁₆₇	—	4	2	no	—
225	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₆₇	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
249	C₄⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
250	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₁₆₇⋊C₄	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₆₇	C₂³	1	1	yes	characteristic
276	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₁₆₇)⋊C₄	C₂³	1	1	yes	characteristic
304	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
305	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
307	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₆₇	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₁₆₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₁₆₇	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₁₆₇	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₆₇	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₁₆₇	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₁₆₇	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₁₆₇	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₁₆₇	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₁₆₇	C₂³	1	1	yes	characteristic
347	C₄²×C₁₆₇	C₂³	1	1	yes	characteristic
348	C₂²×D₁₆₇	—	2	2	no	—
349	C₂²×D₁₆₇	—	2	2	no	—
350	C₂²×D₁₆₇	—	4	1	no	—
351	C₂²×D₁₆₇	—	4	1	no	—
352	C₂²×D₁₆₇	—	4	1	no	—
353	C₂²×D₁₆₇	—	4	1	no	—
354	C₂²×D₁₆₇	—	4	1	no	—
355	C₂²×D₁₆₇	—	4	1	no	—
356	C₂²×D₁₆₇	—	4	1	no	—
357	C₂²×D₁₆₇	C₂⁴	1	1	yes	characteristic
358	C₂²×D₁₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×D₁₆₇	C₂⁴	1	1	yes	characteristic
361	C₂²×D₁₆₇	C₂⁴	1	1	yes	characteristic
362	Dic₃₃₄	—	4	1	no	—
363	Dic₃₃₄	—	4	1	no	—
364	Dic₃₃₄	—	4	1	no	—
365	D₆₆₈	—	2	2	no	—
366	D₆₆₈	—	2	2	no	—
367	D₆₆₈	—	4	1	no	—
368	D₆₆₈	—	4	1	no	—
369	D₆₆₈	—	4	1	no	—
370	D₆₆₈	—	4	1	no	—
371	D₆₆₈	—	4	1	no	—
372	C₂²⋊D₁₆₇	—	2	2	no	—
373	C₂²⋊D₁₆₇	—	2	2	no	—
374	C₂²⋊D₁₆₇	—	4	1	no	—
375	C₂²⋊D₁₆₇	—	4	1	no	—
376	C₂²⋊D₁₆₇	—	4	1	no	—
377	C₂²⋊D₁₆₇	—	4	1	no	—
378	C₂²⋊D₁₆₇	—	4	1	no	—
379	C₂²⋊D₁₆₇	—	4	1	no	—
380	C₂²⋊D₁₆₇	—	4	1	no	—
381	C₂²⋊D₁₆₇	—	4	1	no	—
382	C₂²⋊D₁₆₇	—	4	1	no	—
383	C₂²⋊D₁₆₇	—	4	1	no	—
384	C₂²⋊D₁₆₇	—	4	1	no	—
385	C₂²⋊D₁₆₇	—	4	1	no	—
386	C₂×Dic₁₆₇	—	4	1	no	—
387	C₂×Dic₁₆₇	—	4	1	no	—
388	C₂×Dic₁₆₇	—	4	1	no	—
389	C₂×Dic₁₆₇	—	4	1	no	—
390	C₂×Dic₁₆₇	—	4	1	no	—
391	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₆₇	C₂⁴	1	1	yes	characteristic
402	C₄×D₁₆₇	—	2	2	no	—
403	C₄×D₁₆₇	—	2	2	no	—
404	C₄×D₁₆₇	—	2	2	no	—
405	C₄×D₁₆₇	—	4	1	no	—
406	C₄×D₁₆₇	—	4	1	no	—
407	C₄×D₁₆₇	—	4	1	no	—
408	C₄×D₁₆₇	—	4	1	no	—
409	C₄×D₁₆₇	—	4	1	no	—
410	C₄×D₁₆₇	—	4	1	no	—
411	C₄×D₁₆₇	—	4	1	no	—
412	C₄×D₁₆₇	—	4	1	no	—
413	C₄×D₁₆₇	—	4	1	no	—
414	C₄×D₁₆₇	—	4	1	no	—
415	C₂³×C₁₆₇	C₂⁴	1	1	yes	characteristic
416	C₂³×C₁₆₇	C₂⁴	1	1	yes	characteristic
417	C₂³×C₁₆₇	C₂⁴	1	1	yes	characteristic
418	C₂³×C₁₆₇	C₂⁴	1	1	yes	characteristic
419	Q₈×C₁₆₇	—	4	1	no	—
420	Q₈×C₁₆₇	—	4	1	no	—
421	D₄×C₁₆₇	—	4	1	no	—
422	D₄×C₁₆₇	—	4	1	no	—
423	D₄×C₁₆₇	—	4	1	no	—
424	D₄×C₁₆₇	—	4	1	no	—
425	D₄×C₁₆₇	—	4	1	no	—
426	D₄×C₁₆₇	—	4	1	no	—
427	C₂×C₄×C₁₆₇	—	4	1	no	—
428	C₂×C₄×C₁₆₇	—	4	1	no	—
429	C₂×C₄×C₁₆₇	—	4	1	no	—
430	C₂×C₄×C₁₆₇	—	4	1	no	—
431	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
432	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
434	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
435	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
436	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
437	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
438	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
439	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
440	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
441	C₂×C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
442	C₂²×C₁₆₇	—	2	1	no	—
443	C₂²×C₁₆₇	—	2	1	no	—
444	C₂²×C₁₆₇	—	2	1	no	—
445	C₂²×C₁₆₇	—	2	1	no	—
446	C₂²×C₁₆₇	—	2	1	no	—
447	C₂²×C₁₆₇	—	2	1	no	—
448	C₂²×C₁₆₇	—	2	1	no	—
449	C₂²×C₁₆₇	—	2	1	no	—
450	C₂²×C₁₆₇	—	2	1	no	—
451	C₂²×C₁₆₇	—	2	1	no	—
452	C₂²×C₁₆₇	—	2	1	no	—
453	C₂²×C₁₆₇	—	2	1	no	—
454	C₂²×C₁₆₇	C₂⁵	1	1	yes	characteristic
455	C₂×D₁₆₇	—	2	1	no	—
456	C₂×D₁₆₇	—	2	1	no	—
457	C₂×D₁₆₇	—	2	1	no	—
458	C₂×D₁₆₇	—	2	1	no	—
459	C₂×D₁₆₇	—	2	1	no	—
460	C₂×D₁₆₇	—	2	1	no	—
461	C₂×D₁₆₇	—	2	1	no	—
462	C₂×D₁₆₇	—	2	1	no	—
463	C₂×D₁₆₇	—	2	1	no	—
464	C₂×D₁₆₇	—	2	1	no	—
465	C₂×D₁₆₇	—	2	1	no	—
466	C₂×D₁₆₇	—	2	1	no	—
467	C₂×D₁₆₇	—	2	1	no	—
468	C₂×D₁₆₇	—	2	1	no	—
469	C₂×D₁₆₇	—	4	4	no	—
470	C₂×D₁₆₇	—	8	2	no	—
471	C₂×D₁₆₇	—	8	2	no	—
472	C₂×D₁₆₇	H(5,𝔽₂)	1	2	yes	—
473	C₄×C₁₆₇	—	2	1	no	—
474	C₄×C₁₆₇	—	2	1	no	—
475	C₄×C₁₆₇	—	2	1	no	—
476	C₄×C₁₆₇	—	2	1	no	—
477	C₄×C₁₆₇	—	2	1	no	—
478	C₄×C₁₆₇	—	2	1	no	—
479	C₄×C₁₆₇	—	2	1	no	—
480	C₄×C₁₆₇	—	2	1	no	—
481	C₄×C₁₆₇	—	2	1	no	—
482	C₄×C₁₆₇	—	2	1	no	—
483	C₄×C₁₆₇	—	2	1	no	—
484	Dic₁₆₇	—	2	1	no	—
485	Dic₁₆₇	—	2	1	no	—
486	Dic₁₆₇	—	2	1	no	—
487	Dic₁₆₇	—	2	1	no	—
488	Dic₁₆₇	—	2	1	no	—
489	Dic₁₆₇	—	2	1	no	—
490	Dic₁₆₇	—	2	1	no	—
491	Dic₁₆₇	—	2	1	no	—
492	Dic₁₆₇	—	2	1	no	—
493	Dic₁₆₇	—	2	1	no	—
494	Dic₁₆₇	—	2	1	no	—
495	C₂×C₁₆₇	—	4	1	no	—
496	C₂×C₁₆₇	—	4	1	no	—
497	C₂×C₁₆₇	—	4	1	no	—
498	C₂×C₁₆₇	—	4	1	no	—
499	C₂×C₁₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂×C₁₆₇	#585	1	1	yes	characteristic
501	C₂×C₁₆₇	#585	1	1	yes	characteristic
502	D₁₆₇	—	2	2	no	—
503	D₁₆₇	—	4	1	no	—
504	D₁₆₇	—	4	1	no	—
505	D₁₆₇	—	4	1	no	—
506	D₁₆₇	—	4	1	no	—
507	C₁₆₇	#3533	1	1	yes	characteristic, complemented, Sylow
508	#3533	—	167	1	no	maximal, Sylow
509	#563	—	167	1	no	—
510	#562	—	167	1	no	—
511	#562	D₁₆₇	1	1	yes	characteristic, complemented
512	#560	—	167	1	no	—
513	#559	—	167	1	no	—
514	#553	—	167	1	no	—
515	#553	—	167	1	no	—
516	#552	—	167	1	no	—
517	#552	—	167	1	no	—
518	#551	—	167	1	no	—
519	#551	—	167	1	no	—
520	#551	—	167	1	no	—
521	#547	—	167	1	no	—
522	#547	—	167	1	no	—
523	#546	—	167	1	no	—
524	#546	—	167	1	no	—
525	#542	—	167	1	no	—
526	#542	—	167	1	no	—
527	#540	—	167	1	no	—
528	#540	—	167	1	no	—
529	#539	—	167	1	no	—
530	#539	—	167	1	no	—
531	#538	—	167	1	no	—
532	#538	—	167	1	no	—
533	#538	—	167	1	no	—
534	#538	—	167	1	no	—
535	#535	—	167	1	no	—
536	#534	—	167	1	no	—
537	#525	—	167	1	no	—
538	#525	—	167	1	no	—
539	C₂×#123	—	167	1	no	—
540	C₂×#41	—	167	1	no	—
541	C₂×#41	—	167	1	no	—
542	C₂×#41	—	167	1	no	—
543	C₂²×D₄	—	167	1	no	—
544	C₂²×D₄	—	167	1	no	—
545	C₂³×C₄	—	167	1	no	—
546	C₄⋊Q₈	—	167	1	no	—
547	C₄⋊Q₈	—	167	1	no	—
548	#127	—	167	1	no	—
549	#127	—	167	1	no	—
550	#126	—	167	1	no	—
551	#126	—	167	1	no	—
552	#126	—	167	1	no	—
553	#126	—	167	1	no	—
554	#126	—	167	1	no	—
555	#126	—	167	1	no	—
556	#126	—	167	1	no	—
557	#126	—	167	1	no	—
558	#126	—	167	1	no	—
559	#126	—	167	1	no	—
560	#126	—	167	1	no	—
561	#126	—	167	1	no	—
562	#125	—	167	1	no	—
563	#125	—	167	1	no	—
564	#125	—	167	1	no	—
565	#125	—	167	1	no	—
566	#125	—	167	1	no	—
567	#125	C₂×D₁₆₇	1	1	yes	characteristic, complemented
568	#124	—	167	1	no	—
569	#124	—	167	1	no	—
570	#124	—	167	1	no	—
571	#124	—	167	1	no	—
572	#124	—	167	1	no	—
573	#124	—	167	1	no	—
574	#124	—	167	1	no	—
575	#124	—	167	1	no	—
576	#124	C₂×D₁₆₇	1	1	yes	characteristic, complemented
577	#124	C₂×D₁₆₇	1	1	yes	characteristic, complemented
578	#123	—	167	1	no	—
579	#123	—	167	1	no	—
580	#123	—	167	1	no	—
581	#123	—	167	1	no	—
582	#123	—	167	1	no	—
583	#123	—	167	1	no	—
584	#123	—	167	1	no	—
585	#123	—	167	1	no	—
586	#123	—	167	1	no	—
587	#123	—	167	1	no	—
588	#123	—	167	1	no	—
589	#123	—	167	1	no	—
590	#123	—	167	1	no	—
591	#123	—	167	1	no	—
592	#123	—	167	1	no	—
593	#123	—	167	1	no	—
594	#123	—	167	1	no	—
595	#123	—	167	1	no	—
596	#123	—	167	1	no	—
597	#123	—	167	1	no	—
598	#123	—	167	1	no	—
599	#123	—	167	1	no	—
600	#123	—	167	1	no	—
601	#123	—	167	1	no	—
602	#123	—	167	1	no	—
603	#123	—	167	1	no	—
604	#123	C₂×D₁₆₇	1	1	yes	characteristic, complemented
605	#123	C₂×D₁₆₇	1	1	yes	characteristic, complemented
606	#123	C₂×D₁₆₇	1	1	yes	characteristic, complemented
607	#123	C₂×D₁₆₇	1	1	yes	characteristic, complemented
608	C₂²⋊Q₈	—	167	1	no	—
609	C₂²⋊Q₈	—	167	1	no	—
610	C₂²⋊Q₈	—	167	1	no	—
611	C₂²⋊Q₈	—	167	1	no	—
612	C₂²⋊Q₈	—	167	1	no	—
613	C₂²⋊Q₈	—	167	1	no	—
614	C₂²⋊Q₈	—	167	1	no	—
615	C₂²⋊Q₈	—	167	1	no	—
616	C₂²⋊Q₈	—	167	1	no	—
617	C₂²⋊Q₈	—	167	1	no	—
618	C₂²⋊Q₈	—	167	1	no	—
619	C₂²⋊Q₈	—	167	1	no	—
620	C₂²⋊Q₈	C₂×D₁₆₇	1	1	yes	characteristic, complemented
621	C₂²⋊Q₈	C₂×D₁₆₇	1	1	yes	characteristic, complemented
622	C₂²⋊Q₈	C₂×D₁₆₇	1	1	yes	characteristic, complemented
623	C₂²⋊Q₈	C₂×D₁₆₇	1	1	yes	characteristic, complemented
624	#121	—	167	1	no	—
625	#121	—	167	1	no	—
626	#121	—	167	1	no	—
627	#121	—	167	1	no	—
628	#121	—	167	1	no	—
629	#121	—	167	1	no	—
630	#121	—	167	1	no	—
631	#121	—	167	1	no	—
632	#121	—	167	1	no	—
633	#121	—	167	1	no	—
634	#121	—	167	1	no	—
635	#121	—	167	1	no	—
636	#121	—	167	1	no	—
637	#121	—	167	1	no	—
638	#121	—	167	1	no	—
639	#121	—	167	1	no	—
640	#121	—	167	1	no	—
641	#121	—	167	1	no	—
642	#121	—	167	1	no	—
643	#121	—	167	1	no	—
644	#121	C₂×D₁₆₇	1	1	yes	characteristic
645	#121	C₂×D₁₆₇	1	1	yes	characteristic, complemented
646	#121	C₂×D₁₆₇	1	1	yes	characteristic, complemented
647	#121	C₂×D₁₆₇	1	1	yes	characteristic, complemented
648	#120	—	167	1	no	—
649	#120	—	167	1	no	—
650	#120	—	167	1	no	—
651	#120	—	167	1	no	—
652	#120	—	167	1	no	—
653	#120	—	167	1	no	—
654	#120	—	167	1	no	—
655	#120	—	167	1	no	—
656	#120	—	167	1	no	—
657	#120	—	167	1	no	—
658	C₄×Q₈	—	167	1	no	—
659	C₄×Q₈	—	167	1	no	—
660	C₄×D₄	—	167	1	no	—
661	C₄×D₄	—	167	1	no	—
662	C₄×D₄	—	167	1	no	—
663	C₄×D₄	—	167	1	no	—
664	C₄×D₄	—	167	1	no	—
665	C₄×D₄	—	167	1	no	—
666	C₄×D₄	—	167	1	no	—
667	C₄×D₄	—	167	1	no	—
668	C₄×D₄	—	167	1	no	—
669	C₄×D₄	—	167	1	no	—
670	C₄×D₄	—	167	1	no	—
671	C₄×D₄	—	167	1	no	—
672	C₄×D₄	—	167	1	no	—
673	C₄×D₄	—	167	1	no	—
674	C₄×D₄	—	167	1	no	—
675	C₄×D₄	—	167	1	no	—
676	C₄×D₄	—	167	1	no	—
677	C₄×D₄	—	167	1	no	—
678	#117	—	167	1	no	—
679	#117	—	167	1	no	—
680	#117	—	167	1	no	—
681	#117	—	167	1	no	—
682	#117	—	167	1	no	—
683	#117	—	167	1	no	—
684	#117	—	167	1	no	—
685	C₂×C₄⋊C₄	—	167	1	no	—
686	C₂×C₄⋊C₄	—	167	1	no	—
687	C₂×C₄⋊C₄	—	167	1	no	—
688	C₂×C₄⋊C₄	—	167	1	no	—
689	C₂×C₂²⋊C₄	—	167	1	no	—
690	C₂×C₂²⋊C₄	—	167	1	no	—
691	C₂×C₂²⋊C₄	—	167	1	no	—
692	C₂×C₂²⋊C₄	—	167	1	no	—
693	C₂×C₂²⋊C₄	—	167	1	no	—
694	C₂×C₂²⋊C₄	—	167	1	no	—
695	C₂⁴	—	167	1	no	—
696	C₂⁴	—	167	1	no	—
697	C₂⁴	—	167	1	no	—
698	#41	—	668	2	no	—
699	#41	—	668	2	no	—
700	#41	—	668	2	no	—
701	C₂×Q₈	—	167	1	no	—
702	C₂×Q₈	—	167	1	no	—
703	C₂×Q₈	—	167	1	no	—
704	C₂×Q₈	C₂²×D₁₆₇	1	1	yes	characteristic
705	C₂×Q₈	C₂²×D₁₆₇	1	1	yes	characteristic
706	C₂×D₄	—	668	2	no	—
707	C₂×D₄	—	668	2	no	—
708	C₂×D₄	—	167	1	no	—
709	C₂×D₄	—	167	1	no	—
710	C₂×D₄	—	167	1	no	—
711	C₂×D₄	—	167	1	no	—
712	C₂×D₄	—	167	1	no	—
713	C₂×D₄	—	167	1	no	—
714	C₂×D₄	—	167	1	no	—
715	C₂×D₄	—	167	1	no	—
716	C₂×D₄	—	167	1	no	—
717	C₂×D₄	—	167	1	no	—
718	C₂×D₄	—	167	1	no	—
719	C₂×D₄	—	167	1	no	—
720	C₂×D₄	—	167	1	no	—
721	C₂×D₄	—	167	1	no	—
722	C₂×D₄	—	167	1	no	—
723	C₂×D₄	—	167	1	no	—
724	C₂×D₄	—	167	1	no	—
725	C₂×D₄	—	167	1	no	—
726	C₂×D₄	—	167	1	no	—
727	C₂×D₄	—	167	1	no	—
728	C₂×D₄	—	167	1	no	—
729	C₂×D₄	C₂²×D₁₆₇	1	1	yes	characteristic
730	C₂×D₄	C₂²×D₁₆₇	1	1	yes	characteristic
731	C₂×D₄	C₂²×D₁₆₇	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₁₆₇	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₁₆₇	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₁₆₇	1	1	yes	characteristic
735	C₂²×C₄	—	668	2	no	—
736	C₂²×C₄	—	167	1	no	—
737	C₂²×C₄	—	167	1	no	—
738	C₂²×C₄	—	167	1	no	—
739	C₂²×C₄	—	167	1	no	—
740	C₂²×C₄	—	167	1	no	—
741	C₂²×C₄	—	167	1	no	—
742	C₂²×C₄	—	167	1	no	—
743	C₂²×C₄	—	167	1	no	—
744	C₂²×C₄	—	167	1	no	—
745	C₂²×C₄	—	167	1	no	—
746	C₂²×C₄	—	167	1	no	—
747	C₂²×C₄	—	167	1	no	—
748	C₂²×C₄	—	167	1	no	—
749	C₂²×C₄	—	167	1	no	—
750	C₂²×C₄	—	167	1	no	—
751	C₂²×C₄	—	167	1	no	—
752	C₂²×C₄	—	167	1	no	—
753	C₂²×C₄	—	167	1	no	—
754	C₂²×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
758	C₄⋊C₄	—	167	1	no	—
759	C₄⋊C₄	—	167	1	no	—
760	C₄⋊C₄	—	167	1	no	—
761	C₄⋊C₄	—	167	1	no	—
762	C₄⋊C₄	—	167	1	no	—
763	C₄⋊C₄	—	167	1	no	—
764	C₄⋊C₄	—	167	1	no	—
765	C₄⋊C₄	—	167	1	no	—
766	C₄⋊C₄	—	167	1	no	—
767	C₄⋊C₄	—	167	1	no	—
768	C₄⋊C₄	—	167	1	no	—
769	C₄⋊C₄	—	167	1	no	—
770	C₄⋊C₄	—	167	1	no	—
771	C₄⋊C₄	—	167	1	no	—
772	C₄⋊C₄	—	167	1	no	—
773	C₄⋊C₄	—	167	1	no	—
774	C₄⋊C₄	—	167	1	no	—
775	C₄⋊C₄	—	167	1	no	—
776	C₄⋊C₄	—	167	1	no	—
777	C₄⋊C₄	—	167	1	no	—
778	C₄⋊C₄	—	167	1	no	—
779	C₄⋊C₄	—	167	1	no	—
780	C₄⋊C₄	—	167	1	no	—
781	C₄⋊C₄	—	167	1	no	—
782	C₄⋊C₄	—	167	1	no	—
783	C₄⋊C₄	—	167	1	no	—
784	C₄⋊C₄	—	167	1	no	—
785	C₄⋊C₄	—	167	1	no	—
786	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
796	C₂²⋊C₄	—	167	1	no	—
797	C₂²⋊C₄	—	167	1	no	—
798	C₂²⋊C₄	—	167	1	no	—
799	C₂²⋊C₄	—	167	1	no	—
800	C₂²⋊C₄	—	167	1	no	—
801	C₂²⋊C₄	—	167	1	no	—
802	C₂²⋊C₄	—	167	1	no	—
803	C₂²⋊C₄	—	167	1	no	—
804	C₂²⋊C₄	—	167	1	no	—
805	C₂²⋊C₄	—	167	1	no	—
806	C₂²⋊C₄	—	167	1	no	—
807	C₂²⋊C₄	—	167	1	no	—
808	C₂²⋊C₄	—	167	1	no	—
809	C₂²⋊C₄	—	167	1	no	—
810	C₂²⋊C₄	—	167	1	no	—
811	C₂²⋊C₄	—	167	1	no	—
812	C₂²⋊C₄	—	167	1	no	—
813	C₂²⋊C₄	—	167	1	no	—
814	C₂²⋊C₄	—	167	1	no	—
815	C₂²⋊C₄	—	167	1	no	—
816	C₂²⋊C₄	—	167	1	no	—
817	C₂²⋊C₄	—	167	1	no	—
818	C₂²⋊C₄	—	167	1	no	—
819	C₂²⋊C₄	—	167	1	no	—
820	C₂²⋊C₄	—	167	1	no	—
821	C₂²⋊C₄	—	167	1	no	—
822	C₂²⋊C₄	—	167	1	no	—
823	C₂²⋊C₄	—	167	1	no	—
824	C₂²⋊C₄	—	167	1	no	—
825	C₂²⋊C₄	—	167	1	no	—
826	C₂²⋊C₄	—	167	1	no	—
827	C₂²⋊C₄	—	167	1	no	—
828	C₂²⋊C₄	—	167	1	no	—
829	C₂²⋊C₄	—	167	1	no	—
830	C₂²⋊C₄	—	167	1	no	—
831	C₂²⋊C₄	—	167	1	no	—
832	C₂²⋊C₄	—	167	1	no	—
833	C₂²⋊C₄	—	167	1	no	—
834	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₁₆₇	1	1	yes	characteristic
846	C₄²	—	167	1	no	—
847	C₄²	—	167	1	no	—
848	C₄²	—	167	1	no	—
849	C₄²	—	167	1	no	—
850	C₄²	—	167	1	no	—
851	C₄²	—	167	1	no	—
852	C₄²	—	167	1	no	—
853	C₄²	—	167	1	no	—
854	C₄²	—	167	1	no	—
855	C₄²	C₂²×D₁₆₇	1	1	yes	characteristic
856	C₂³	—	334	2	no	—
857	C₂³	—	334	2	no	—
858	C₂³	—	668	1	no	—
859	C₂³	—	668	1	no	—
860	C₂³	—	668	1	no	—
861	C₂³	—	668	1	no	—
862	C₂³	—	668	1	no	—
863	C₂³	—	668	1	no	—
864	C₂³	—	668	1	no	—
865	C₂³	—	167	1	no	—
866	C₂³	—	167	1	no	—
867	C₂³	—	167	1	no	—
868	C₂³	—	167	1	no	—
869	C₂³	—	167	1	no	—
870	C₂³	C₂³×D₁₆₇	1	1	yes	characteristic
871	C₂³	C₂³×D₁₆₇	1	1	yes	characteristic
872	C₂³	C₂³×D₁₆₇	1	1	yes	characteristic
873	C₂³	C₂³×D₁₆₇	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	4	1	no	—
876	Q₈	—	668	1	no	—
877	Q₈	—	668	1	no	—
878	Q₈	—	668	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	1	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	334	2	no	—
886	D₄	—	334	2	no	—
887	D₄	—	334	2	no	—
888	D₄	—	334	2	no	—
889	D₄	—	668	1	no	—
890	D₄	—	668	1	no	—
891	D₄	—	668	1	no	—
892	D₄	—	668	1	no	—
893	D₄	—	668	1	no	—
894	D₄	—	668	1	no	—
895	D₄	—	668	1	no	—
896	D₄	—	668	1	no	—
897	D₄	—	668	1	no	—
898	D₄	—	668	1	no	—
899	D₄	—	668	1	no	—
900	D₄	—	668	1	no	—
901	D₄	—	668	1	no	—
902	D₄	—	668	1	no	—
903	D₄	—	668	1	no	—
904	D₄	—	668	1	no	—
905	D₄	—	668	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	334	2	no	—
911	C₂×C₄	—	334	2	no	—
912	C₂×C₄	—	334	2	no	—
913	C₂×C₄	—	668	1	no	—
914	C₂×C₄	—	668	1	no	—
915	C₂×C₄	—	668	1	no	—
916	C₂×C₄	—	668	1	no	—
917	C₂×C₄	—	668	1	no	—
918	C₂×C₄	—	668	1	no	—
919	C₂×C₄	—	668	1	no	—
920	C₂×C₄	—	668	1	no	—
921	C₂×C₄	—	668	1	no	—
922	C₂×C₄	—	668	1	no	—
923	C₂×C₄	—	668	1	no	—
924	C₂×C₄	—	668	1	no	—
925	C₂×C₄	—	668	1	no	—
926	C₂×C₄	—	668	1	no	—
927	C₂×C₄	—	668	1	no	—
928	C₂×C₄	—	167	1	no	—
929	C₂×C₄	—	167	1	no	—
930	C₂×C₄	—	167	1	no	—
931	C₂×C₄	—	167	1	no	—
932	C₂×C₄	—	167	1	no	—
933	C₂×C₄	—	167	1	no	—
934	C₂×C₄	—	167	1	no	—
935	C₂×C₄	—	167	1	no	—
936	C₂×C₄	—	167	1	no	—
937	C₂×C₄	—	167	1	no	—
938	C₂×C₄	—	167	1	no	—
939	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₁₆₇	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	1336	2	no	—
963	C₂²	—	1336	2	no	—
964	C₂²	—	334	1	no	—
965	C₂²	—	334	1	no	—
966	C₂²	—	334	1	no	—
967	C₂²	—	334	1	no	—
968	C₂²	—	334	1	no	—
969	C₂²	—	334	1	no	—
970	C₂²	—	334	1	no	—
971	C₂²	—	334	1	no	—
972	C₂²	—	334	1	no	—
973	C₂²	—	334	1	no	—
974	C₂²	—	334	1	no	—
975	C₂²	—	334	1	no	—
976	C₂²	—	334	1	no	—
977	C₂²	—	334	1	no	—
978	C₂²	—	668	4	no	—
979	C₂²	—	167	2	no	—
980	C₂²	C₂⁴×D₁₆₇	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	334	1	no	—
993	C₄	—	334	1	no	—
994	C₄	—	334	1	no	—
995	C₄	—	334	1	no	—
996	C₄	—	334	1	no	—
997	C₄	—	334	1	no	—
998	C₄	—	334	1	no	—
999	C₄	—	334	1	no	—
1000	C₄	—	334	1	no	—
1001	C₄	—	334	1	no	—
1002	C₄	—	334	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	334	2	no	—
1008	C₂	—	668	1	no	—
1009	C₂	—	668	1	no	—
1010	C₂	—	668	1	no	—
1011	C₂	—	668	1	no	—
1012	C₂	H(5,𝔽₂)×D₁₆₇	1	1	yes	characteristic
1013	C₂	#24924104	1	1	yes	characteristic
1014	C₂	#24924106	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₆₇
commutator, socle, cosocle	C₂²×C₁₆₇	C₂⁵
Fitting	#562×C₁₆₇	C₂
hypercenter	#562	D₁₆₇
hypocenter	C₁₆₇	#3533
LCS	G ▷ C₂²×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #24924020	C₂	semidirect
2. #24924016	C₂	semidirect
3. #24924007	C₂	semidirect
4. #24924001	C₂	semidirect
5. #24923966	C₂	semidirect
6. #24923962	C₂	semidirect
7. #24923957	C₂	semidirect
8. #24923953	C₂	semidirect
9. #24923946	C₂	semidirect
10. #24923942	C₂	semidirect
11. #24923942	C₂	semidirect
12. #24923921	C₂	semidirect
13. #24923917	C₂	semidirect
14. #24923912	C₂	semidirect
15. #24923908	C₂	semidirect
16. #24923892	C₂	semidirect
17. #24923883	C₂	semidirect
18. #24923872	C₂	semidirect
19. #24923871	C₂	semidirect
20. #24923868	C₂	semidirect
21. #24923867	C₂	semidirect
22. #24923859	C₂	semidirect
23. #24923855	C₂	semidirect
24. #24923855	C₂	semidirect
25. #24923853	C₂	semidirect
26. #24923835	C₂	semidirect
27. #24923827	C₂	semidirect
28. #24923782	C₂	semidirect
29. #24923779	C₂	semidirect
30. #123×D₁₆₇	C₂	semidirect
31. #562×C₁₆₇	C₂	semidirect
33. C₂×#14581950	C₂²	semidirect
37. C₂²×C₄×D₁₆₇	C₂²	semidirect
38. #19128831	C₂²	semidirect
39. #19128830	C₂²	semidirect
41. #19128828	C₂²	semidirect
42. #19128827	C₂²	semidirect
43. #19128827	C₂²	semidirect
44. #19128827	C₂²	semidirect
45. #19128827	C₂²	semidirect
46. #19128827	C₂²	semidirect
47. #19128827	C₂²	semidirect
48. #19128827	C₂²	semidirect
49. #19128826	C₂²	semidirect
50. #19128825	C₂²	semidirect
51. #19128825	C₂²	semidirect
52. #19128825	C₂²	semidirect
53. #19128825	C₂²	semidirect
54. #19128823	C₂²	semidirect
55. #19128823	C₂²	semidirect
56. #19128823	C₂²	semidirect
57. #19128822	C₂²	semidirect
58. #19128822	C₂²	semidirect
59. #19128821	C₂²	semidirect
60. #19128821	C₂²	semidirect
62. #19128818	C₂²	semidirect
63. #19128818	C₂²	semidirect
64. #19128818	C₂²	semidirect
65. #19128818	C₂²	semidirect
66. #19128818	C₂²	semidirect
72. #19128817	C₂²	semidirect
73. #19128817	C₂²	semidirect
74. #19128817	C₂²	semidirect
75. #19128817	C₂²	semidirect
77. #19128816	C₂²	semidirect
78. #19128816	C₂²	semidirect
79. #19128816	C₂²	semidirect
80. #19128816	C₂²	semidirect
85. #19128814	C₂²	semidirect
86. #19128814	C₂²	semidirect
87. #19128814	C₂²	semidirect
88. #19128814	C₂²	semidirect
89. #19128814	C₂²	semidirect
90. #19128814	C₂²	semidirect
91. #19128813	C₂²	semidirect
92. #19128813	C₂²	semidirect
93. #19128812	C₂²	semidirect
94. #19128812	C₂²	semidirect
95. #19128812	C₂²	semidirect
96. #19128812	C₂²	semidirect
97. #19128811	C₂²	semidirect
98. #19128810	C₂²	semidirect
99. #19128810	C₂²	semidirect
100. #19128809	C₂²	semidirect
101. #19128809	C₂²	semidirect
102. #19128808	C₂²	semidirect
103. #19128808	C₂²	semidirect
104. #19128808	C₂²	semidirect
106. #19128807	C₂²	semidirect
109. #19128806	C₂²	semidirect
110. #19128806	C₂²	semidirect
113. #19128805	C₂²	semidirect
114. #19128805	C₂²	semidirect
115. #19128805	C₂²	semidirect
118. #19128804	C₂²	semidirect
119. #19128804	C₂²	semidirect
120. #19128804	C₂²	semidirect
121. #19128803	C₂²	semidirect
122. #19128803	C₂²	semidirect
123. #19128803	C₂²	semidirect
124. #19128803	C₂²	semidirect
128. #19128802	C₂²	semidirect
129. #19128802	C₂²	semidirect
133. #19128800	C₂²	semidirect
134. #19128800	C₂²	semidirect
135. Q₈×Dic₁₆₇	C₂²	semidirect
136. C₄×Dic₃₃₄	C₂²	semidirect
138. C₄×D₆₆₈	C₂²	semidirect
139. D₄×Dic₁₆₇	C₂²	semidirect
140. D₄×Dic₁₆₇	C₂²	semidirect
141. D₄×Dic₁₆₇	C₂²	semidirect
142. #19128794	C₂²	semidirect
143. #19128794	C₂²	semidirect
144. #19128794	C₂²	semidirect
146. C₄×C₂²⋊D₁₆₇	C₂²	semidirect
147. C₄×C₂²⋊D₁₆₇	C₂²	semidirect
148. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
149. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
150. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
152. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
153. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
154. (C₂²⋊D₁₆₇)⋊C₄	C₂²	semidirect
155. #19128791	C₂²	semidirect
156. #19128791	C₂²	semidirect
157. #19128790	C₂²	semidirect
158. #19128790	C₂²	semidirect
159. #19128790	C₂²	semidirect
160. #19128790	C₂²	semidirect
161. #19128788	C₂²	semidirect
162. C₂×Dic₁₆₇⋊C₄	C₂²	semidirect
163. C₄⋊C₄×D₁₆₇	C₂²	semidirect
164. C₄⋊C₄×D₁₆₇	C₂²	semidirect
165. C₄⋊C₄×D₁₆₇	C₂²	semidirect
167. C₂×(C₂×D₁₆₇)⋊C₄	C₂²	semidirect
170. C₂²⋊C₄×D₁₆₇	C₂²	semidirect
171. C₂²⋊C₄×D₁₆₇	C₂²	semidirect
172. #125×C₁₆₇	C₂²	semidirect
173. #124×C₁₆₇	C₂²	semidirect
174. #124×C₁₆₇	C₂²	semidirect
175. #123×C₁₆₇	C₂²	semidirect
176. #123×C₁₆₇	C₂²	semidirect
177. #123×C₁₆₇	C₂²	semidirect
178. #123×C₁₆₇	C₂²	semidirect
179. C₂²⋊Q₈×C₁₆₇	C₂²	semidirect
180. C₂²⋊Q₈×C₁₆₇	C₂²	semidirect
181. C₂²⋊Q₈×C₁₆₇	C₂²	semidirect
182. C₂²⋊Q₈×C₁₆₇	C₂²	semidirect
184. #121×C₁₆₇	C₂²	semidirect
185. #121×C₁₆₇	C₂²	semidirect
186. #121×C₁₆₇	C₂²	semidirect
507. C₁₆₇	#3533	semidirect
511. #562	D₁₆₇	semidirect
567. #125	C₂×D₁₆₇	semidirect
576. #124	C₂×D₁₆₇	semidirect
577. #124	C₂×D₁₆₇	semidirect
604. #123	C₂×D₁₆₇	semidirect
605. #123	C₂×D₁₆₇	semidirect
606. #123	C₂×D₁₆₇	semidirect
607. #123	C₂×D₁₆₇	semidirect
620. C₂²⋊Q₈	C₂×D₁₆₇	semidirect
621. C₂²⋊Q₈	C₂×D₁₆₇	semidirect
622. C₂²⋊Q₈	C₂×D₁₆₇	semidirect
623. C₂²⋊Q₈	C₂×D₁₆₇	semidirect
645. #121	C₂×D₁₆₇	semidirect
646. #121	C₂×D₁₆₇	semidirect
647. #121	C₂×D₁₆₇	semidirect

Maximal subgroups

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

subgroup	index
#24924020	2
#24924016	2
#24924007	2
#24924001	2
#24923966	2
#24923962	2
#24923957	2
#24923953	2
#24923946	2
#24923942	2
#24923921	2
#24923917	2
#24923912	2
#24923908	2
#24923892	2
#24923883	2
#24923872	2
#24923871	2
#24923868	2
#24923867	2
#24923859	2
#24923855	2
#24923853	2
#24923835	2
#24923827	2
#24923782	2
#24923779	2
#123×D₁₆₇	2
#562×C₁₆₇	2
#3533	167