Subgroups — #22574772

Order 8576.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864147	C₂	1	2	yes	maximal, complemented
2	#16864141	C₂	1	2	yes	maximal, complemented
3	#16864118	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864115	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864076	C₂	1	2	yes	maximal, complemented
6	#16864075	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864059	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864055	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864043	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864034	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864021	C₂	1	2	yes	maximal, complemented
13	#16864019	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864013	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864011	C₂	1	2	yes	maximal, complemented
16	#16864010	C₂	1	2	yes	maximal, complemented
17	#16863978	C₂	1	2	yes	maximal, complemented
18	#16863970	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863967	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863928	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	1	yes	characteristic
25	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
28	#14524042	C₂²	1	2	yes	complemented
29	#14524042	C₂²	1	1	yes	characteristic, complemented
30	#14524041	C₂²	1	2	yes	complemented
31	#14524041	C₂²	1	1	yes	characteristic, complemented
32	#14524041	C₂²	1	1	yes	characteristic, complemented
33	#14524041	C₂²	1	1	yes	characteristic, complemented
34	#14524038	C₂²	1	2	yes	complemented
35	#14524038	C₂²	1	2	yes	complemented
36	#14524037	C₂²	1	2	yes	complemented
37	#14524036	C₂²	1	1	yes	characteristic, complemented
38	#14524036	C₂²	1	1	yes	characteristic, complemented
39	#14524036	C₂²	1	2	yes	complemented
40	#14524036	C₂²	1	2	yes	complemented
41	#14524036	C₂²	1	2	yes	complemented
42	#14524034	C₂²	1	1	yes	characteristic, complemented
43	#14524033	C₂²	1	2	yes	complemented
44	#14524032	C₂²	1	1	yes	characteristic
45	#14524032	C₂²	1	1	yes	characteristic
46	#14524031	C₂²	1	1	yes	characteristic
47	#14524030	C₂²	1	1	yes	characteristic
48	#14524030	C₂²	1	1	yes	characteristic
49	#14524030	C₂²	1	2	yes	complemented
50	#14524030	C₂²	1	1	yes	characteristic, complemented
51	#14524029	C₂²	1	2	yes	—
52	#14524029	C₂²	1	2	yes	—
53	#14524029	C₂²	1	2	yes	complemented
54	#14524029	C₂²	1	2	yes	complemented
55	#14524026	C₂²	1	2	yes	—
56	#14524026	C₂²	1	2	yes	complemented
57	#14524026	C₂²	1	2	yes	complemented
58	#14524025	C₂²	1	2	yes	—
59	#14524025	C₂²	1	1	yes	characteristic
60	#14524025	C₂²	1	1	yes	characteristic
61	#14524025	C₂²	1	2	yes	complemented
62	#14524024	C₂²	1	2	yes	complemented
63	#14524024	C₂²	1	2	yes	complemented
64	#14524024	C₂²	1	2	yes	complemented
65	#14524023	C₂²	1	1	yes	characteristic
66	#14524023	C₂²	1	1	yes	characteristic
67	#14524023	C₂²	1	2	yes	complemented
68	#14524022	C₂²	1	2	yes	complemented
69	#14524022	C₂²	1	2	yes	complemented
70	#14524022	C₂²	1	1	yes	characteristic, complemented
71	#14524022	C₂²	1	2	yes	complemented
72	#14524021	C₂²	1	2	yes	—
73	#14524021	C₂²	1	2	yes	—
74	#14524021	C₂²	1	2	yes	complemented
75	#14524021	C₂²	1	2	yes	complemented
76	#14524020	C₂²	1	2	yes	complemented
77	#14524020	C₂²	1	2	yes	complemented
78	#14524020	C₂²	1	2	yes	complemented
79	#14524019	C₂²	1	2	yes	—
80	#14524019	C₂²	1	1	yes	characteristic
81	#14524019	C₂²	1	2	yes	complemented
82	#14524019	C₂²	1	2	yes	complemented
83	#14524017	C₂²	1	1	yes	characteristic
84	#14524015	C₂²	1	2	yes	—
85	#14524015	C₂²	1	2	yes	complemented
86	#14524014	C₂²	1	2	yes	—
87	#14524014	C₂²	1	1	yes	characteristic
88	#14524011	C₂²	1	2	yes	—
89	#14524011	C₂²	1	2	yes	—
90	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
92	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
93	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
94	#14524008	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
96	#14524005	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
100	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
102	#14524002	C₂²	1	1	yes	characteristic, complemented
103	#14524002	C₂²	1	1	yes	characteristic, complemented
104	#14524000	C₂²	1	2	yes	—
105	#14524000	C₂²	1	2	yes	complemented
106	#14523999	C₂²	1	2	yes	complemented
107	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic
112	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#124×C₆₇	C₂²	1	1	yes	characteristic
115	#124×C₆₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
118	#121×C₆₇	C₂²	1	1	yes	characteristic
119	#121×C₆₇	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
122	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	#11761628	—	4	2	no	—
125	C₂×Dic₁₃₄	—	4	2	no	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	2	yes	—
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×Dic₁₃₄	C₂³	1	2	yes	—
132	Q₈×D₆₇	—	4	2	no	—
133	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
139	D₄×D₆₇	—	4	2	no	—
140	C₂²×Dic₆₇	C₂³	1	2	yes	—
141	C₂²×Dic₆₇	C₂³	1	2	yes	—
142	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	C₂³	1	2	yes	—
148	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₆₇	C₂³	1	2	yes	—
154	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₆₇	C₂³	1	2	yes	—
156	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
157	Dic₆₇⋊C₄	C₂³	1	2	yes	—
158	Dic₆₇⋊C₄	C₂³	1	2	yes	—
159	Dic₆₇⋊C₄	C₂³	1	2	yes	—
160	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₆₇⋊C₄	C₂³	1	2	yes	—
162	Dic₆₇⋊C₄	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	2	yes	—
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
183	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
196	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₆₇	C₂³	1	2	yes	—
199	C₄×Dic₆₇	C₂³	1	2	yes	—
200	C₄×Dic₆₇	C₂³	1	2	yes	—
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
203	#41×C₆₇	—	4	2	no	—
204	C₂×Q₈×C₆₇	—	4	2	no	—
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
208	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₆₇	C₂³	1	2	yes	—
210	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₆₇	C₂³	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
215	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂³×C₆₇	C₂⁴	1	2	yes	—
229	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₇	—	2	4	no	—
232	C₂²×D₆₇	—	4	2	no	—
233	C₂²×D₆₇	—	4	2	no	—
234	C₂²×D₆₇	C₂⁴	1	2	yes	—
235	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
236	Q₈×C₆₇	—	2	2	no	—
237	Q₈×C₆₇	—	2	2	no	—
238	Q₈×C₆₇	—	4	2	no	—
239	D₄×C₆₇	—	2	2	no	—
240	D₄×C₆₇	—	4	2	no	—
241	D₄×C₆₇	—	4	1	no	—
242	D₄×C₆₇	—	4	2	no	—
243	C₂×C₄×C₆₇	—	2	2	no	—
244	C₂×C₄×C₆₇	—	2	2	no	—
245	C₂×C₄×C₆₇	—	4	2	no	—
246	C₂×C₄×C₆₇	—	4	2	no	—
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₆₇	—	2	2	no	—
256	C₂²⋊D₆₇	—	2	2	no	—
257	C₂²⋊D₆₇	—	4	2	no	—
258	C₂²⋊D₆₇	—	4	2	no	—
259	C₂²⋊D₆₇	—	4	2	no	—
260	C₂×Dic₆₇	—	4	2	no	—
261	C₂×Dic₆₇	—	4	2	no	—
262	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₆₇	C₂⁴	1	2	yes	—
267	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₆₇	C₂⁴	1	2	yes	—
270	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₆₇	C₂⁴	1	2	yes	—
272	D₂₆₈	—	2	2	no	—
273	C₄×D₆₇	—	2	2	no	—
274	C₄×D₆₇	—	2	2	no	—
275	C₄×D₆₇	—	4	1	no	—
276	C₄×D₆₇	—	4	2	no	—
277	C₄×D₆₇	—	4	2	no	—
278	C₄×D₆₇	—	4	2	no	—
279	Dic₁₃₄	—	2	2	no	—
280	Dic₁₃₄	—	2	2	no	—
281	Dic₁₃₄	—	4	2	no	—
282	Dic₁₃₄	—	4	2	no	—
283	Dic₁₃₄	—	4	2	no	—
284	Dic₁₃₄	—	4	1	no	—
285	C₂²×C₆₇	—	2	1	no	—
286	C₂²×C₆₇	—	2	1	no	—
287	C₂²×C₆₇	—	2	2	no	—
288	C₂²×C₆₇	—	2	1	no	—
289	C₂²×C₆₇	—	2	1	no	—
290	C₂²×C₆₇	—	2	2	no	—
291	C₂²×C₆₇	—	2	2	no	—
292	C₂²×C₆₇	—	2	1	no	—
293	C₂²×C₆₇	—	2	1	no	—
294	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
295	C₂×D₆₇	—	2	1	no	—
296	C₂×D₆₇	—	2	1	no	—
297	C₂×D₆₇	—	2	2	no	—
298	C₂×D₆₇	—	2	2	no	—
299	C₂×D₆₇	—	2	2	no	—
300	C₂×D₆₇	—	8	4	no	—
301	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
302	C₄×C₆₇	—	2	1	no	—
303	C₄×C₆₇	—	2	2	no	—
304	C₄×C₆₇	—	2	1	no	—
305	C₄×C₆₇	—	2	2	no	—
306	C₄×C₆₇	—	2	1	no	—
307	C₄×C₆₇	—	2	2	no	—
308	C₄×C₆₇	—	2	1	no	—
309	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
310	Dic₆₇	—	2	2	no	—
311	Dic₆₇	—	2	2	no	—
312	Dic₆₇	—	2	1	no	—
313	Dic₆₇	—	2	1	no	—
314	Dic₆₇	—	2	1	no	—
315	Dic₆₇	—	2	1	no	—
316	Dic₆₇	—	2	1	no	—
317	Dic₆₇	—	2	1	no	—
318	Dic₆₇	—	2	1	no	—
319	Dic₆₇	—	2	2	no	—
320	C₂×C₆₇	—	4	2	no	—
321	C₂×C₆₇	—	4	1	no	—
322	C₂×C₆₇	—	4	1	no	—
323	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₂×C₆₇	#585	1	1	yes	characteristic
326	D₆₇	—	2	2	no	—
327	D₆₇	—	4	2	no	—
328	#3561	—	67	1	no	maximal, Sylow
329	C₆₇	#3561	1	1	yes	characteristic, complemented, Sylow
330	#563	—	67	2	no	—
331	#562	—	67	2	no	—
332	#556	—	67	1	no	—
333	#556	—	67	1	no	—
334	#551	—	67	2	no	—
335	#551	—	67	2	no	—
336	D₄×Q₈	—	67	1	no	—
337	D₄×Q₈	—	67	1	no	—
338	#548	—	67	1	no	—
339	#548	D₆₇	1	1	yes	characteristic, complemented
340	#546	—	67	1	no	—
341	#546	—	67	1	no	—
342	#543	—	67	2	no	—
343	#542	—	67	2	no	—
344	#542	—	67	1	no	—
345	#542	—	67	1	no	—
346	#542	—	67	2	no	—
347	#538	—	67	2	no	—
348	#536	—	67	1	no	—
349	#536	—	67	1	no	—
350	#533	—	67	1	no	—
351	#529	—	67	1	no	—
352	C₂×#124	—	67	1	no	—
353	C₂×#41	—	67	1	no	—
354	C₂×#41	C₂×D₆₇	1	1	yes	characteristic
355	C₂²×Q₈	—	67	1	no	—
356	C₂²×Q₈	—	67	1	no	—
357	C₂²×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
358	C₂²×D₄	—	67	1	no	—
359	C₄⋊Q₈	—	67	1	no	—
360	C₄⋊Q₈	—	67	1	no	—
361	C₄⋊Q₈	—	67	1	no	—
362	C₄⋊Q₈	—	67	2	no	—
363	C₄⋊Q₈	—	67	1	no	—
364	C₄⋊Q₈	—	67	2	no	—
365	#126	—	67	2	no	—
366	#126	—	67	2	no	—
367	#126	—	67	1	no	—
368	#126	—	67	1	no	—
369	#126	—	67	2	no	—
370	#126	—	67	2	no	—
371	#126	—	67	2	no	—
372	#126	—	67	2	no	—
373	#125	—	67	1	no	—
374	#125	—	67	2	no	—
375	#124	—	67	1	no	—
376	#124	—	67	1	no	—
377	#124	—	67	1	no	—
378	#124	—	67	1	no	—
379	#124	—	67	1	no	—
380	#124	—	67	2	no	—
381	#124	—	67	2	no	—
382	#124	—	67	2	no	—
383	#124	—	67	2	no	—
384	#124	—	67	2	no	—
385	#124	—	67	1	no	—
386	#124	C₂×D₆₇	1	1	yes	characteristic
387	#124	C₂×D₆₇	1	2	yes	complemented
388	#123	—	67	2	no	—
389	#123	—	67	2	no	—
390	#123	—	67	2	no	—
391	#123	—	67	2	no	—
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	1	no	—
395	#123	—	67	1	no	—
396	#123	—	67	2	no	—
397	#123	—	67	2	no	—
398	C₂²⋊Q₈	—	67	1	no	—
399	C₂²⋊Q₈	—	67	2	no	—
400	C₂²⋊Q₈	—	67	2	no	—
401	C₂²⋊Q₈	—	67	2	no	—
402	C₂²⋊Q₈	—	67	2	no	—
403	C₂²⋊Q₈	—	67	2	no	—
404	C₂²⋊Q₈	—	67	1	no	—
405	C₂²⋊Q₈	—	67	2	no	—
406	C₂²⋊Q₈	—	67	1	no	—
407	C₂²⋊Q₈	—	67	2	no	—
408	C₂²⋊Q₈	—	67	1	no	—
409	C₂²⋊Q₈	—	67	2	no	—
410	C₂²⋊Q₈	—	67	2	no	—
411	C₂²⋊Q₈	—	67	2	no	—
412	C₂²⋊Q₈	—	67	2	no	—
413	C₂²⋊Q₈	—	67	2	no	—
414	C₂²⋊Q₈	—	67	2	no	—
415	C₂²⋊Q₈	—	67	2	no	—
416	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
418	#121	—	67	1	no	—
419	#121	—	67	2	no	—
420	#121	—	67	2	no	—
421	#121	—	67	2	no	—
422	#121	—	67	1	no	—
423	#121	C₂×D₆₇	1	1	yes	characteristic
424	#121	C₂×D₆₇	1	2	yes	complemented
425	#120	—	67	2	no	—
426	#120	—	67	2	no	—
427	C₄×Q₈	—	67	1	no	—
428	C₄×Q₈	—	67	1	no	—
429	C₄×Q₈	—	67	1	no	—
430	C₄×Q₈	—	67	2	no	—
431	C₄×Q₈	—	67	1	no	—
432	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
433	C₄×D₄	—	67	1	no	—
434	C₄×D₄	—	67	1	no	—
435	C₄×D₄	—	67	1	no	—
436	C₄×D₄	—	67	2	no	—
437	C₄×D₄	—	67	1	no	—
438	C₄×D₄	—	67	2	no	—
439	C₄×D₄	—	67	2	no	—
440	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
441	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
442	#117	—	67	1	no	—
443	#117	—	67	1	no	—
444	#117	—	67	2	no	—
445	#117	—	67	2	no	—
446	#117	—	67	2	no	—
447	C₂×C₂²⋊C₄	—	67	2	no	—
448	C₂×C₂²⋊C₄	—	67	2	no	—
449	C₂×C₂²⋊C₄	—	67	2	no	—
450	C₂×C₂²⋊C₄	—	67	2	no	—
451	C₂×C₄²	—	67	1	no	—
452	C₂⁴	—	67	2	no	—
453	#41	—	4	2	no	—
454	#41	—	268	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	268	2	no	—
457	C₂×Q₈	—	268	2	no	—
458	C₂×Q₈	—	67	1	no	—
459	C₂×Q₈	—	67	2	no	—
460	C₂×Q₈	—	67	2	no	—
461	C₂×Q₈	—	67	2	no	—
462	C₂×Q₈	—	67	1	no	—
463	C₂×Q₈	—	67	1	no	—
464	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
465	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
467	C₂×D₄	—	268	2	no	—
468	C₂×D₄	—	67	2	no	—
469	C₂×D₄	—	67	2	no	—
470	C₂×D₄	—	67	2	no	—
471	C₂×D₄	—	67	1	no	—
472	C₂×D₄	—	67	1	no	—
473	C₂×D₄	—	67	1	no	—
474	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₆₇	1	2	yes	—
476	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₆₇	1	2	yes	—
478	C₂²×C₄	—	67	2	no	—
479	C₂²×C₄	—	67	2	no	—
480	C₂²×C₄	—	67	1	no	—
481	C₂²×C₄	—	67	2	no	—
482	C₂²×C₄	—	67	2	no	—
483	C₂²×C₄	—	67	2	no	—
484	C₂²×C₄	—	67	1	no	—
485	C₂²×C₄	—	67	1	no	—
486	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
489	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
490	C₄⋊C₄	—	67	1	no	—
491	C₄⋊C₄	—	67	1	no	—
492	C₄⋊C₄	—	67	1	no	—
493	C₄⋊C₄	—	67	1	no	—
494	C₄⋊C₄	—	67	2	no	—
495	C₄⋊C₄	—	67	2	no	—
496	C₄⋊C₄	—	67	2	no	—
497	C₄⋊C₄	—	67	1	no	—
498	C₄⋊C₄	—	67	1	no	—
499	C₄⋊C₄	—	67	2	no	—
500	C₄⋊C₄	—	67	1	no	—
501	C₄⋊C₄	—	67	2	no	—
502	C₄⋊C₄	—	67	2	no	—
503	C₄⋊C₄	—	67	2	no	—
504	C₄⋊C₄	—	67	1	no	—
505	C₄⋊C₄	—	67	1	no	—
506	C₄⋊C₄	—	67	2	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	2	no	—
509	C₄⋊C₄	—	67	1	no	—
510	C₄⋊C₄	—	67	2	no	—
511	C₄⋊C₄	—	67	2	no	—
512	C₄⋊C₄	—	67	2	no	—
513	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
517	C₂²⋊C₄	—	67	2	no	—
518	C₂²⋊C₄	—	67	2	no	—
519	C₂²⋊C₄	—	67	2	no	—
520	C₂²⋊C₄	—	67	2	no	—
521	C₂²⋊C₄	—	67	1	no	—
522	C₂²⋊C₄	—	67	1	no	—
523	C₂²⋊C₄	—	67	1	no	—
524	C₂²⋊C₄	—	67	1	no	—
525	C₂²⋊C₄	—	67	2	no	—
526	C₂²⋊C₄	—	67	1	no	—
527	C₂²⋊C₄	—	67	1	no	—
528	C₂²⋊C₄	—	67	2	no	—
529	C₂²⋊C₄	—	67	1	no	—
530	C₂²⋊C₄	—	67	1	no	—
531	C₂²⋊C₄	—	67	2	no	—
532	C₂²⋊C₄	—	67	2	no	—
533	C₂²⋊C₄	—	67	2	no	—
534	C₂²⋊C₄	—	67	2	no	—
535	C₂²⋊C₄	—	67	2	no	—
536	C₂²⋊C₄	—	67	2	no	—
537	C₂²⋊C₄	—	67	2	no	—
538	C₂²⋊C₄	—	67	2	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	2	no	—
541	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
547	C₄²	—	67	1	no	—
548	C₄²	—	67	1	no	—
549	C₄²	—	67	1	no	—
550	C₄²	—	67	2	no	—
551	C₄²	—	67	1	no	—
552	C₄²	—	67	1	no	—
553	C₄²	—	67	2	no	—
554	C₄²	—	67	2	no	—
555	C₄²	C₂²×D₆₇	1	1	yes	characteristic
556	C₄²	C₂²×D₆₇	1	2	yes	—
557	C₂³	—	268	2	no	—
558	C₂³	—	268	2	no	—
559	C₂³	—	67	1	no	—
560	C₂³	—	67	2	no	—
561	C₂³	—	134	4	no	—
562	C₂³	C₂³×D₆₇	1	2	yes	—
563	C₂³	C₂³×D₆₇	1	1	yes	characteristic
564	C₂³	C₂³×D₆₇	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	268	2	no	—
569	Q₈	—	268	2	no	—
570	Q₈	—	268	1	no	—
571	Q₈	—	268	2	no	—
572	Q₈	—	134	2	no	—
573	Q₈	—	134	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	268	2	no	—
579	D₄	—	268	2	no	—
580	D₄	—	268	2	no	—
581	D₄	—	134	2	no	—
582	D₄	—	134	2	no	—
583	D₄	—	134	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	268	2	no	—
589	C₂×C₄	—	268	2	no	—
590	C₂×C₄	—	268	2	no	—
591	C₂×C₄	—	268	1	no	—
592	C₂×C₄	—	268	2	no	—
593	C₂×C₄	—	268	2	no	—
594	C₂×C₄	—	67	1	no	—
595	C₂×C₄	—	67	1	no	—
596	C₂×C₄	—	67	1	no	—
597	C₂×C₄	—	67	1	no	—
598	C₂×C₄	—	67	2	no	—
599	C₂×C₄	—	67	1	no	—
600	C₂×C₄	—	67	1	no	—
601	C₂×C₄	—	67	1	no	—
602	C₂×C₄	—	67	2	no	—
603	C₂×C₄	—	67	2	no	—
604	C₂×C₄	—	134	2	no	—
605	C₂×C₄	—	134	2	no	—
606	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₆₇	1	2	yes	—
609	C₂×C₄	C₂³×D₆₇	1	2	yes	—
610	C₂×C₄	C₂³×D₆₇	1	2	yes	—
611	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	536	4	no	—
624	C₂²	—	67	2	no	—
625	C₂²	—	134	2	no	—
626	C₂²	—	134	2	no	—
627	C₂²	—	134	2	no	—
628	C₂²	—	134	1	no	—
629	C₂²	—	134	1	no	—
630	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	134	2	no	—
639	C₄	—	134	2	no	—
640	C₄	—	134	1	no	—
641	C₄	—	134	1	no	—
642	C₄	—	134	1	no	—
643	C₄	—	134	1	no	—
644	C₄	—	134	1	no	—
645	C₄	—	134	1	no	—
646	C₄	—	134	2	no	—
647	C₄	—	134	1	no	—
648	C₄	#14524088	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	268	2	no	—
653	C₂	—	134	2	no	—
654	C₂	C₂×#14524088	1	1	yes	characteristic
655	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
656	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#548×C₆₇	C₂
hypercenter	#548	D₆₇
hypocenter	C₆₇	#3561
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #16864147	C₂	semidirect
2. #16864141	C₂	semidirect
3. #16864118	C₂	semidirect
4. #16864115	C₂	semidirect
5. #16864076	C₂	semidirect
6. #16864075	C₂	semidirect
7. Q₈×C₂²⋊D₆₇	C₂	semidirect
8. #16864059	C₂	semidirect
9. #16864055	C₂	semidirect
10. #16864043	C₂	semidirect
11. #16864034	C₂	semidirect
12. #16864021	C₂	semidirect
13. #16864019	C₂	semidirect
14. #16864013	C₂	semidirect
15. #16864011	C₂	semidirect
16. #16864010	C₂	semidirect
17. #16863978	C₂	semidirect
18. #16863970	C₂	semidirect
19. #16863967	C₂	semidirect
20. #16863950	C₂	semidirect
21. #16863928	C₂	semidirect
22. #124×D₆₇	C₂	semidirect
23. #548×C₆₇	C₂	semidirect
25. C₂²×Dic₁₃₄	C₂²	semidirect
28. #14524042	C₂²	semidirect
29. #14524042	C₂²	semidirect
30. #14524041	C₂²	semidirect
31. #14524041	C₂²	semidirect
32. #14524041	C₂²	semidirect
33. #14524041	C₂²	semidirect
34. #14524038	C₂²	semidirect
35. #14524038	C₂²	semidirect
36. #14524037	C₂²	semidirect
37. #14524036	C₂²	semidirect
38. #14524036	C₂²	semidirect
39. #14524036	C₂²	semidirect
40. #14524036	C₂²	semidirect
41. #14524036	C₂²	semidirect
42. #14524034	C₂²	semidirect
43. #14524033	C₂²	semidirect
49. #14524030	C₂²	semidirect
50. #14524030	C₂²	semidirect
53. #14524029	C₂²	semidirect
54. #14524029	C₂²	semidirect
56. #14524026	C₂²	semidirect
57. #14524026	C₂²	semidirect
61. #14524025	C₂²	semidirect
62. #14524024	C₂²	semidirect
63. #14524024	C₂²	semidirect
64. #14524024	C₂²	semidirect
67. #14524023	C₂²	semidirect
68. #14524022	C₂²	semidirect
69. #14524022	C₂²	semidirect
70. #14524022	C₂²	semidirect
71. #14524022	C₂²	semidirect
74. #14524021	C₂²	semidirect
75. #14524021	C₂²	semidirect
76. #14524020	C₂²	semidirect
77. #14524020	C₂²	semidirect
78. #14524020	C₂²	semidirect
81. #14524019	C₂²	semidirect
82. #14524019	C₂²	semidirect
85. #14524015	C₂²	semidirect
90. Q₈×Dic₆₇	C₂²	semidirect
91. C₄×Dic₁₃₄	C₂²	semidirect
92. C₄×Dic₁₃₄	C₂²	semidirect
93. C₄×Dic₁₃₄	C₂²	semidirect
94. #14524008	C₂²	semidirect
101. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
102. #14524002	C₂²	semidirect
103. #14524002	C₂²	semidirect
105. #14524000	C₂²	semidirect
106. #14523999	C₂²	semidirect
113. C₂²×Q₈×C₆₇	C₂²	semidirect
115. #124×C₆₇	C₂²	semidirect
116. C₂²⋊Q₈×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
119. #121×C₆₇	C₂²	semidirect
120. C₄×Q₈×C₆₇	C₂²	semidirect
121. C₄×D₄×C₆₇	C₂²	semidirect
122. C₄×D₄×C₆₇	C₂²	semidirect
329. C₆₇	#3561	semidirect
339. #548	D₆₇	semidirect
357. C₂²×Q₈	C₂×D₆₇	semidirect
387. #124	C₂×D₆₇	semidirect
416. C₂²⋊Q₈	C₂×D₆₇	semidirect
417. C₂²⋊Q₈	C₂×D₆₇	semidirect
424. #121	C₂×D₆₇	semidirect
432. C₄×Q₈	C₂×D₆₇	semidirect
440. C₄×D₄	C₂×D₆₇	semidirect
441. C₄×D₄	C₂×D₆₇	semidirect