Subgroups — #22574777

Order 8576.

1032 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864150	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864144	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864140	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864113	C₂	1	2	yes	maximal, complemented
5	#16864073	C₂	1	2	yes	maximal, complemented
6	#16864071	C₂	1	2	yes	maximal, complemented
7	#16864061	C₂	1	2	yes	maximal, complemented
8	#16864056	C₂	1	2	yes	maximal, complemented
9	#16864038	C₂	1	2	yes	maximal, complemented
10	#16864021	C₂	1	2	yes	maximal, complemented
11	#16864020	C₂	1	2	yes	maximal, complemented
12	#16864014	C₂	1	2	yes	maximal, complemented
13	#16864012	C₂	1	2	yes	maximal, complemented
14	#16863985	C₂	1	2	yes	maximal, complemented
15	#16863969	C₂	1	2	yes	maximal, complemented
16	#16863952	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
18	#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#563×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11761628	C₂²	1	2	yes	—
21	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic
22	C₂×Q₈×D₆₇	C₂²	1	2	yes	complemented
23	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
24	#14524042	C₂²	1	1	yes	characteristic, complemented
25	#14524042	C₂²	1	2	yes	complemented
26	#14524042	C₂²	1	2	yes	complemented
27	#14524042	C₂²	1	1	yes	characteristic, complemented
28	#14524038	C₂²	1	2	yes	complemented
29	#14524038	C₂²	1	2	yes	complemented
30	#14524038	C₂²	1	2	yes	complemented
31	#14524038	C₂²	1	2	yes	complemented
32	#14524036	C₂²	1	2	yes	complemented
33	#14524035	C₂²	1	1	yes	characteristic, complemented
34	#14524032	C₂²	1	1	yes	characteristic
35	#14524032	C₂²	1	2	yes	complemented
36	#14524031	C₂²	1	1	yes	characteristic
37	#14524031	C₂²	1	2	yes	complemented
38	#14524031	C₂²	1	1	yes	characteristic, complemented
39	#14524030	C₂²	1	1	yes	characteristic
40	#14524029	C₂²	1	2	yes	—
41	#14524029	C₂²	1	2	yes	—
42	#14524029	C₂²	1	2	yes	—
43	#14524029	C₂²	1	2	yes	complemented
44	#14524029	C₂²	1	2	yes	complemented
45	#14524028	C₂²	1	2	yes	—
46	#14524028	C₂²	1	2	yes	—
47	#14524028	C₂²	1	2	yes	complemented
48	#14524028	C₂²	1	2	yes	complemented
49	#14524028	C₂²	1	2	yes	complemented
50	#14524027	C₂²	1	2	yes	complemented
51	#14524025	C₂²	1	2	yes	complemented
52	#14524025	C₂²	1	2	yes	complemented
53	#14524023	C₂²	1	1	yes	characteristic
54	#14524023	C₂²	1	2	yes	complemented
55	#14524023	C₂²	1	2	yes	complemented
56	#14524022	C₂²	1	2	yes	complemented
57	#14524021	C₂²	1	2	yes	—
58	#14524021	C₂²	1	2	yes	—
59	#14524021	C₂²	1	2	yes	—
60	#14524021	C₂²	1	2	yes	complemented
61	#14524021	C₂²	1	2	yes	complemented
62	#14524021	C₂²	1	2	yes	complemented
63	#14524021	C₂²	1	2	yes	complemented
64	#14524020	C₂²	1	2	yes	complemented
65	#14524020	C₂²	1	2	yes	complemented
66	#14524019	C₂²	1	2	yes	—
67	#14524019	C₂²	1	2	yes	complemented
68	#14524019	C₂²	1	2	yes	complemented
69	#14524018	C₂²	1	2	yes	—
70	#14524018	C₂²	1	1	yes	characteristic
71	#14524018	C₂²	1	2	yes	complemented
72	#14524016	C₂²	1	2	yes	—
73	#14524016	C₂²	1	2	yes	complemented
74	#14524015	C₂²	1	2	yes	—
75	#14524013	C₂²	1	2	yes	—
76	#14524013	C₂²	1	2	yes	—
77	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
78	#14524008	C₂²	1	2	yes	complemented
79	#14524008	C₂²	1	2	yes	complemented
80	#14524008	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₂₆₈	C₂²	1	2	yes	—
82	#14524005	C₂²	1	2	yes	—
83	#14524005	C₂²	1	2	yes	—
84	#14524005	C₂²	1	2	yes	complemented
85	#14524005	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
87	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
88	#14524001	C₂²	1	1	yes	characteristic
89	#14524001	C₂²	1	1	yes	characteristic
90	#14524001	C₂²	1	2	yes	complemented
91	#14524000	C₂²	1	2	yes	complemented
92	#14523999	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
94	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
97	C₄²×D₆₇	C₂²	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
99	#126×C₆₇	C₂²	1	2	yes	complemented
100	#126×C₆₇	C₂²	1	2	yes	complemented
101	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#124×C₆₇	C₂²	1	1	yes	characteristic
104	#123×C₆₇	C₂²	1	2	yes	—
105	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
106	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
107	C₂³×D₆₇	C₂³	1	2	yes	—
108	#11761628	—	4	4	no	—
109	C₂×Dic₁₃₄	C₂³	1	2	yes	—
110	C₂×Dic₁₃₄	C₂³	1	2	yes	—
111	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₃₄	C₂³	1	2	yes	—
113	C₂×Dic₁₃₄	C₂³	1	2	yes	—
114	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
115	Q₈×D₆₇	—	4	2	no	—
116	Q₈×D₆₇	—	4	4	no	—
117	C₂×D₂₆₈	C₂³	1	2	yes	—
118	C₂×D₂₆₈	C₂³	1	2	yes	—
119	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
120	C₂×D₂₆₈	C₂³	1	2	yes	—
121	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
125	D₄×D₆₇	—	4	2	no	—
126	C₂²×Dic₆₇	C₂³	1	2	yes	—
127	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₆₇	C₂³	1	2	yes	—
130	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₆₇	C₂³	1	2	yes	—
132	C₂×C₄×D₆₇	C₂³	1	2	yes	—
133	C₂×C₄×D₆₇	C₂³	1	2	yes	—
134	C₂×C₄×D₆₇	C₂³	1	2	yes	—
135	C₂×C₄×D₆₇	C₂³	1	2	yes	—
136	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₆₇	C₂³	1	2	yes	—
139	C₄⋊Dic₆₇	C₂³	1	2	yes	—
140	C₄⋊Dic₆₇	C₂³	1	2	yes	—
141	Dic₆₇⋊C₄	C₂³	1	2	yes	—
142	Dic₆₇⋊C₄	C₂³	1	2	yes	—
143	Dic₆₇⋊C₄	C₂³	1	2	yes	—
144	Dic₆₇⋊C₄	C₂³	1	2	yes	—
145	Dic₆₇⋊C₄	C₂³	1	2	yes	—
146	Dic₆₇⋊C₄	C₂³	1	2	yes	—
147	Dic₆₇⋊C₄	C₂³	1	2	yes	—
148	Dic₆₇⋊C₄	C₂³	1	2	yes	—
149	Dic₆₇⋊C₄	C₂³	1	2	yes	—
150	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
151	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
152	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
153	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
154	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
170	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
171	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
172	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
173	C₄×Dic₆₇	C₂³	1	2	yes	—
174	C₄×Dic₆₇	C₂³	1	2	yes	—
175	C₄×Dic₆₇	C₂³	1	2	yes	—
176	C₄×Dic₆₇	C₂³	1	2	yes	—
177	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
178	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₄²×C₆₇	C₂³	1	2	yes	—
198	C₂³×C₆₇	C₂⁴	1	2	yes	—
199	C₂²×D₆₇	—	2	4	no	—
200	C₂²×D₆₇	—	4	2	no	—
201	C₂²×D₆₇	—	4	2	no	—
202	C₂²×D₆₇	C₂⁴	1	2	yes	—
203	C₂²×D₆₇	C₂⁴	1	2	yes	—
204	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
205	Q₈×C₆₇	—	4	1	no	—
206	Q₈×C₆₇	—	4	2	no	—
207	D₄×C₆₇	—	4	1	no	—
208	C₂×C₄×C₆₇	—	4	2	no	—
209	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
210	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²⋊D₆₇	—	2	4	no	—
218	C₂²⋊D₆₇	—	4	2	no	—
219	C₂²⋊D₆₇	—	4	2	no	—
220	C₂×Dic₆₇	—	4	2	no	—
221	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
222	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₆₇	C₂⁴	1	2	yes	—
224	C₂×Dic₆₇	C₂⁴	1	2	yes	—
225	C₂×Dic₆₇	C₂⁴	1	2	yes	—
226	C₂×Dic₆₇	C₂⁴	1	2	yes	—
227	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
228	D₂₆₈	—	2	4	no	—
229	D₂₆₈	—	4	1	no	—
230	D₂₆₈	—	4	2	no	—
231	D₂₆₈	—	4	1	no	—
232	D₂₆₈	—	4	2	no	—
233	C₄×D₆₇	—	2	2	no	—
234	C₄×D₆₇	—	2	2	no	—
235	C₄×D₆₇	—	2	4	no	—
236	C₄×D₆₇	—	4	1	no	—
237	C₄×D₆₇	—	4	2	no	—
238	C₄×D₆₇	—	4	2	no	—
239	C₄×D₆₇	—	4	2	no	—
240	C₄×D₆₇	—	4	2	no	—
241	C₄×D₆₇	—	4	2	no	—
242	Dic₁₃₄	—	2	4	no	—
243	Dic₁₃₄	—	2	4	no	—
244	Dic₁₃₄	—	4	1	no	—
245	Dic₁₃₄	—	4	2	no	—
246	Dic₁₃₄	—	4	2	no	—
247	Dic₁₃₄	—	4	1	no	—
248	C₂²×C₆₇	—	2	2	no	—
249	C₂²×C₆₇	—	2	2	no	—
250	C₂²×C₆₇	—	2	2	no	—
251	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
252	C₂×D₆₇	—	2	1	no	—
253	C₂×D₆₇	—	2	1	no	—
254	C₂×D₆₇	—	2	2	no	—
255	C₂×D₆₇	—	2	2	no	—
256	C₂×D₆₇	—	2	2	no	—
257	C₂×D₆₇	—	2	2	no	—
258	C₂×D₆₇	—	2	2	no	—
259	C₂×D₆₇	—	2	2	no	—
260	C₂×D₆₇	—	8	4	no	—
261	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
262	C₄×C₆₇	—	2	2	no	—
263	C₄×C₆₇	—	2	2	no	—
264	C₄×C₆₇	—	2	2	no	—
265	C₄×C₆₇	—	2	1	no	—
266	C₄×C₆₇	—	2	1	no	—
267	C₄×C₆₇	—	2	2	no	—
268	C₄×C₆₇	—	2	2	no	—
269	C₄×C₆₇	—	2	1	no	—
270	Dic₆₇	—	2	2	no	—
271	Dic₆₇	—	2	2	no	—
272	Dic₆₇	—	2	1	no	—
273	Dic₆₇	—	2	1	no	—
274	Dic₆₇	—	2	2	no	—
275	Dic₆₇	—	2	2	no	—
276	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₆₇	—	4	2	no	—
278	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
280	C₂×C₆₇	#585	1	1	yes	characteristic
281	D₆₇	—	2	2	no	—
282	D₆₇	—	4	2	no	—
283	D₆₇	—	4	2	no	—
284	#3561	—	67	1	no	maximal, Sylow
285	C₆₇	#3561	1	1	yes	characteristic, complemented, Sylow
286	#563	—	67	1	no	—
287	#563	D₆₇	1	1	yes	characteristic, complemented
288	#562	—	67	1	no	—
289	#562	—	67	1	no	—
290	#556	—	67	2	no	—
291	#551	—	67	2	no	—
292	#551	—	67	2	no	—
293	D₄×Q₈	—	67	2	no	—
294	#548	—	67	2	no	—
295	#546	—	67	2	no	—
296	#543	—	67	2	no	—
297	#542	—	67	2	no	—
298	#542	—	67	2	no	—
299	#542	—	67	2	no	—
300	#538	—	67	2	no	—
301	#536	—	67	2	no	—
302	#533	—	67	1	no	—
303	#529	—	67	1	no	—
304	C₂×#124	—	67	1	no	—
305	C₂×#41	—	67	2	no	—
306	C₂²×Q₈	—	67	1	no	—
307	C₂²×Q₈	—	67	2	no	—
308	C₂²×D₄	—	67	1	no	—
309	C₄⋊Q₈	—	67	1	no	—
310	C₄⋊Q₈	—	67	1	no	—
311	C₄⋊Q₈	—	67	2	no	—
312	C₄⋊Q₈	—	67	2	no	—
313	C₄⋊Q₈	C₂×D₆₇	1	2	yes	complemented
314	#126	—	67	2	no	—
315	#126	—	67	2	no	—
316	#126	—	67	2	no	—
317	#126	—	67	2	no	—
318	#126	—	67	2	no	—
319	#126	C₂×D₆₇	1	2	yes	complemented
320	#126	C₂×D₆₇	1	2	yes	complemented
321	#125	—	67	1	no	—
322	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
323	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
324	#124	—	67	1	no	—
325	#124	—	67	2	no	—
326	#124	—	67	1	no	—
327	#124	—	67	2	no	—
328	#124	—	67	2	no	—
329	#124	—	67	2	no	—
330	#124	—	67	2	no	—
331	#124	—	67	2	no	—
332	#124	—	67	1	no	—
333	#124	—	67	1	no	—
334	#124	—	67	2	no	—
335	#124	C₂×D₆₇	1	1	yes	characteristic
336	#123	—	67	2	no	—
337	#123	—	67	2	no	—
338	#123	—	67	2	no	—
339	#123	—	67	2	no	—
340	#123	—	67	2	no	—
341	#123	—	67	2	no	—
342	#123	—	67	2	no	—
343	#123	—	67	2	no	—
344	#123	C₂×D₆₇	1	2	yes	—
345	C₂²⋊Q₈	—	67	2	no	—
346	C₂²⋊Q₈	—	67	2	no	—
347	C₂²⋊Q₈	—	67	2	no	—
348	C₂²⋊Q₈	—	67	2	no	—
349	C₂²⋊Q₈	—	67	1	no	—
350	C₂²⋊Q₈	—	67	2	no	—
351	C₂²⋊Q₈	—	67	2	no	—
352	C₂²⋊Q₈	—	67	2	no	—
353	C₂²⋊Q₈	—	67	2	no	—
354	C₂²⋊Q₈	—	67	2	no	—
355	C₂²⋊Q₈	—	67	2	no	—
356	C₂²⋊Q₈	—	67	2	no	—
357	C₂²⋊Q₈	—	67	2	no	—
358	C₂²⋊Q₈	—	67	2	no	—
359	C₂²⋊Q₈	—	67	2	no	—
360	C₂²⋊Q₈	—	67	2	no	—
361	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
362	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
363	#121	—	67	2	no	—
364	#121	—	67	1	no	—
365	#121	—	67	2	no	—
366	#121	—	67	2	no	—
367	#121	—	67	2	no	—
368	#121	—	67	2	no	—
369	#120	—	67	2	no	—
370	#120	—	67	2	no	—
371	C₄×Q₈	—	67	1	no	—
372	C₄×Q₈	—	67	2	no	—
373	C₄×Q₈	—	67	2	no	—
374	C₄×Q₈	—	67	2	no	—
375	C₄×D₄	—	67	2	no	—
376	C₄×D₄	—	67	2	no	—
377	C₄×D₄	—	67	1	no	—
378	C₄×D₄	—	67	2	no	—
379	C₄×D₄	—	67	2	no	—
380	C₄×D₄	—	67	2	no	—
381	C₄×D₄	—	67	2	no	—
382	#117	—	67	2	no	—
383	#117	—	67	1	no	—
384	#117	—	67	1	no	—
385	#117	—	67	2	no	—
386	#117	—	67	2	no	—
387	C₂×C₂²⋊C₄	—	67	2	no	—
388	C₂×C₂²⋊C₄	—	67	2	no	—
389	C₂×C₂²⋊C₄	—	67	2	no	—
390	C₂×C₂²⋊C₄	—	67	2	no	—
391	C₂×C₄²	—	67	1	no	—
392	C₂⁴	—	67	2	no	—
393	#41	—	268	4	no	—
394	C₂×Q₈	—	268	2	no	—
395	C₂×Q₈	—	268	4	no	—
396	C₂×Q₈	—	67	1	no	—
397	C₂×Q₈	—	67	2	no	—
398	C₂×Q₈	—	67	2	no	—
399	C₂×Q₈	—	67	1	no	—
400	C₂×Q₈	—	67	2	no	—
401	C₂×Q₈	—	67	2	no	—
402	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
403	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
404	C₂×D₄	—	268	2	no	—
405	C₂×D₄	—	67	2	no	—
406	C₂×D₄	—	67	2	no	—
407	C₂×D₄	—	67	2	no	—
408	C₂×D₄	—	67	2	no	—
409	C₂×D₄	—	67	1	no	—
410	C₂×D₄	—	67	2	no	—
411	C₂×D₄	—	67	1	no	—
412	C₂×D₄	—	67	2	no	—
413	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
414	C₂²×C₄	—	67	2	no	—
415	C₂²×C₄	—	67	1	no	—
416	C₂²×C₄	—	67	2	no	—
417	C₂²×C₄	—	67	2	no	—
418	C₂²×C₄	—	67	2	no	—
419	C₂²×C₄	—	67	2	no	—
420	C₂²×C₄	—	67	2	no	—
421	C₂²×C₄	—	67	1	no	—
422	C₂²×C₄	—	67	1	no	—
423	C₂²×C₄	—	67	2	no	—
424	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
425	C₄⋊C₄	—	67	2	no	—
426	C₄⋊C₄	—	67	2	no	—
427	C₄⋊C₄	—	67	2	no	—
428	C₄⋊C₄	—	67	2	no	—
429	C₄⋊C₄	—	67	1	no	—
430	C₄⋊C₄	—	67	1	no	—
431	C₄⋊C₄	—	67	2	no	—
432	C₄⋊C₄	—	67	2	no	—
433	C₄⋊C₄	—	67	2	no	—
434	C₄⋊C₄	—	67	2	no	—
435	C₄⋊C₄	—	67	2	no	—
436	C₄⋊C₄	—	67	2	no	—
437	C₄⋊C₄	—	67	2	no	—
438	C₄⋊C₄	—	67	2	no	—
439	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
440	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
442	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
443	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
444	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
445	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
446	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
447	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
448	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
449	C₂²⋊C₄	—	67	2	no	—
450	C₂²⋊C₄	—	67	2	no	—
451	C₂²⋊C₄	—	67	2	no	—
452	C₂²⋊C₄	—	67	2	no	—
453	C₂²⋊C₄	—	67	2	no	—
454	C₂²⋊C₄	—	67	2	no	—
455	C₂²⋊C₄	—	67	2	no	—
456	C₂²⋊C₄	—	67	2	no	—
457	C₂²⋊C₄	—	67	2	no	—
458	C₂²⋊C₄	—	67	2	no	—
459	C₂²⋊C₄	—	67	2	no	—
460	C₂²⋊C₄	—	67	2	no	—
461	C₂²⋊C₄	—	67	2	no	—
462	C₂²⋊C₄	—	67	2	no	—
463	C₂²⋊C₄	—	67	2	no	—
464	C₂²⋊C₄	—	67	2	no	—
465	C₂²⋊C₄	—	67	2	no	—
466	C₂²⋊C₄	—	67	2	no	—
467	C₂²⋊C₄	—	67	2	no	—
468	C₂²⋊C₄	—	67	2	no	—
469	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
470	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
471	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
472	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
473	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
474	C₄²	—	67	1	no	—
475	C₄²	—	67	1	no	—
476	C₄²	—	67	1	no	—
477	C₄²	—	67	2	no	—
478	C₄²	—	67	2	no	—
479	C₄²	—	67	2	no	—
480	C₄²	—	67	2	no	—
481	C₄²	C₂²×D₆₇	1	1	yes	characteristic
482	C₄²	C₂²×D₆₇	1	2	yes	—
483	C₂³	—	268	2	no	—
484	C₂³	—	268	2	no	—
485	C₂³	—	67	1	no	—
486	C₂³	—	67	2	no	—
487	C₂³	—	67	2	no	—
488	C₂³	—	134	4	no	—
489	C₂³	C₂³×D₆₇	1	2	yes	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	268	2	no	—
493	Q₈	—	268	1	no	—
494	Q₈	—	268	1	no	—
495	Q₈	—	268	2	no	—
496	Q₈	—	134	4	no	—
497	Q₈	—	134	4	no	—
498	D₄	—	4	1	no	—
499	D₄	—	268	1	no	—
500	D₄	—	268	2	no	—
501	D₄	—	268	2	no	—
502	D₄	—	268	1	no	—
503	D₄	—	268	2	no	—
504	D₄	—	268	2	no	—
505	D₄	—	134	4	no	—
506	D₄	—	134	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	268	2	no	—
509	C₂×C₄	—	268	2	no	—
510	C₂×C₄	—	268	2	no	—
511	C₂×C₄	—	268	2	no	—
512	C₂×C₄	—	268	2	no	—
513	C₂×C₄	—	268	1	no	—
514	C₂×C₄	—	268	2	no	—
515	C₂×C₄	—	67	1	no	—
516	C₂×C₄	—	67	1	no	—
517	C₂×C₄	—	67	1	no	—
518	C₂×C₄	—	67	2	no	—
519	C₂×C₄	—	67	2	no	—
520	C₂×C₄	—	67	2	no	—
521	C₂×C₄	—	67	2	no	—
522	C₂×C₄	—	134	2	no	—
523	C₂×C₄	—	134	4	no	—
524	C₂×C₄	—	134	2	no	—
525	C₂×C₄	C₂³×D₆₇	1	2	yes	—
526	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
527	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₆₇	1	2	yes	—
529	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
530	C₂×C₄	C₂³×D₆₇	1	2	yes	—
531	C₂×C₄	C₂³×D₆₇	1	2	yes	—
532	C₂×C₄	C₂³×D₆₇	1	2	yes	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	536	4	no	—
537	C₂²	—	67	2	no	—
538	C₂²	—	134	2	no	—
539	C₂²	—	134	2	no	—
540	C₂²	—	134	2	no	—
541	C₂²	—	134	2	no	—
542	C₂²	—	134	2	no	—
543	C₂²	—	134	2	no	—
544	C₂²	—	134	1	no	—
545	C₂²	—	134	1	no	—
546	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	67	2	no	—
556	C₄	—	134	2	no	—
557	C₄	—	134	2	no	—
558	C₄	—	134	1	no	—
559	C₄	—	134	2	no	—
560	C₄	—	134	2	no	—
561	C₄	—	134	1	no	—
562	C₂	—	4	2	no	—
563	C₂	—	268	2	no	—
564	C₂	—	268	2	no	—
565	C₂	—	134	2	no	—
566	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
567	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
568	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#563×C₆₇	C₂
hypercenter	#563	D₆₇
hypocenter	C₆₇	#3561
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #16864150	C₂	semidirect
2. #16864144	C₂	semidirect
3. #16864140	C₂	semidirect
4. #16864113	C₂	semidirect
5. #16864073	C₂	semidirect
6. #16864071	C₂	semidirect
7. #16864061	C₂	semidirect
8. #16864056	C₂	semidirect
9. #16864038	C₂	semidirect
10. #16864021	C₂	semidirect
11. #16864020	C₂	semidirect
12. #16864014	C₂	semidirect
13. #16864012	C₂	semidirect
14. #16863985	C₂	semidirect
15. #16863969	C₂	semidirect
16. #16863952	C₂	semidirect
17. #16863931	C₂	semidirect
18. #124×D₆₇	C₂	semidirect
19. #563×C₆₇	C₂	semidirect
22. C₂×Q₈×D₆₇	C₂²	semidirect
24. #14524042	C₂²	semidirect
25. #14524042	C₂²	semidirect
26. #14524042	C₂²	semidirect
27. #14524042	C₂²	semidirect
28. #14524038	C₂²	semidirect
29. #14524038	C₂²	semidirect
30. #14524038	C₂²	semidirect
31. #14524038	C₂²	semidirect
32. #14524036	C₂²	semidirect
33. #14524035	C₂²	semidirect
35. #14524032	C₂²	semidirect
37. #14524031	C₂²	semidirect
38. #14524031	C₂²	semidirect
43. #14524029	C₂²	semidirect
44. #14524029	C₂²	semidirect
47. #14524028	C₂²	semidirect
48. #14524028	C₂²	semidirect
49. #14524028	C₂²	semidirect
50. #14524027	C₂²	semidirect
51. #14524025	C₂²	semidirect
52. #14524025	C₂²	semidirect
54. #14524023	C₂²	semidirect
55. #14524023	C₂²	semidirect
56. #14524022	C₂²	semidirect
60. #14524021	C₂²	semidirect
61. #14524021	C₂²	semidirect
62. #14524021	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524020	C₂²	semidirect
65. #14524020	C₂²	semidirect
67. #14524019	C₂²	semidirect
68. #14524019	C₂²	semidirect
71. #14524018	C₂²	semidirect
73. #14524016	C₂²	semidirect
77. C₄×Dic₁₃₄	C₂²	semidirect
78. #14524008	C₂²	semidirect
79. #14524008	C₂²	semidirect
80. #14524008	C₂²	semidirect
84. #14524005	C₂²	semidirect
85. #14524005	C₂²	semidirect
86. C₄×C₂²⋊D₆₇	C₂²	semidirect
90. #14524001	C₂²	semidirect
91. #14524000	C₂²	semidirect
92. #14523999	C₂²	semidirect
98. C₄⋊Q₈×C₆₇	C₂²	semidirect
99. #126×C₆₇	C₂²	semidirect
100. #126×C₆₇	C₂²	semidirect
101. #125×C₆₇	C₂²	semidirect
102. #125×C₆₇	C₂²	semidirect
105. C₂²⋊Q₈×C₆₇	C₂²	semidirect
106. C₂²⋊Q₈×C₆₇	C₂²	semidirect
285. C₆₇	#3561	semidirect
287. #563	D₆₇	semidirect
313. C₄⋊Q₈	C₂×D₆₇	semidirect
319. #126	C₂×D₆₇	semidirect
320. #126	C₂×D₆₇	semidirect
322. #125	C₂×D₆₇	semidirect
323. #125	C₂×D₆₇	semidirect
361. C₂²⋊Q₈	C₂×D₆₇	semidirect
362. C₂²⋊Q₈	C₂×D₆₇	semidirect