Subgroups — #22574712

Order 8576.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864148	C₂	1	2	yes	maximal, complemented
2	#16864147	C₂	1	2	yes	maximal, complemented
3	#16864128	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864128	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864125	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864122	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864120	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864106	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864105	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864082	C₂	1	2	yes	maximal, complemented
11	#16864079	C₂	1	2	yes	maximal, complemented
12	#16864018	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864017	C₂	1	2	yes	maximal, complemented
14	#16864015	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864012	C₂	1	2	yes	maximal, complemented
16	#16864007	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863997	C₂	1	1	yes	maximal, characteristic
18	#16863995	C₂	1	2	yes	maximal, complemented
19	#16863987	C₂	1	2	yes	maximal, complemented
20	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863933	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863925	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#14524043	C₂²	1	1	yes	characteristic
25	#14524043	C₂²	1	2	yes	—
26	#14524042	C₂²	1	2	yes	—
27	#14524042	C₂²	1	1	yes	characteristic
28	#14524042	C₂²	1	1	yes	characteristic
29	#14524041	C₂²	1	1	yes	characteristic
30	#14524039	C₂²	1	1	yes	characteristic
31	#14524038	C₂²	1	2	yes	—
32	#14524038	C₂²	1	2	yes	—
33	#14524038	C₂²	1	2	yes	—
34	#14524038	C₂²	1	2	yes	—
35	#14524038	C₂²	1	2	yes	—
36	#14524037	C₂²	1	2	yes	—
37	#14524036	C₂²	1	2	yes	—
38	#14524036	C₂²	1	2	yes	—
39	#14524035	C₂²	1	1	yes	characteristic
40	#14524035	C₂²	1	2	yes	—
41	#14524035	C₂²	1	1	yes	characteristic
42	#14524034	C₂²	1	2	yes	—
43	#14524034	C₂²	1	1	yes	characteristic
44	#14524034	C₂²	1	1	yes	characteristic
45	#14524034	C₂²	1	2	yes	—
46	#14524034	C₂²	1	2	yes	—
47	#14524033	C₂²	1	2	yes	—
48	#14524033	C₂²	1	2	yes	—
49	#14524033	C₂²	1	1	yes	characteristic
50	#14524033	C₂²	1	1	yes	characteristic
51	#14524032	C₂²	1	1	yes	characteristic
52	#14524032	C₂²	1	1	yes	characteristic
53	#14524031	C₂²	1	2	yes	—
54	#14524029	C₂²	1	2	yes	—
55	#14524029	C₂²	1	2	yes	—
56	#14524029	C₂²	1	2	yes	—
57	#14524028	C₂²	1	2	yes	—
58	#14524028	C₂²	1	2	yes	—
59	#14524027	C₂²	1	2	yes	—
60	#14524027	C₂²	1	2	yes	—
61	#14524027	C₂²	1	2	yes	—
62	#14524026	C₂²	1	2	yes	—
63	#14524025	C₂²	1	2	yes	—
64	#14524025	C₂²	1	2	yes	—
65	#14524025	C₂²	1	2	yes	—
66	#14524025	C₂²	1	2	yes	—
67	#14524023	C₂²	1	1	yes	characteristic
68	#14524023	C₂²	1	2	yes	—
69	#14524022	C₂²	1	2	yes	—
70	#14524021	C₂²	1	2	yes	—
71	#14524021	C₂²	1	1	yes	characteristic
72	#14524021	C₂²	1	2	yes	—
73	#14524021	C₂²	1	2	yes	—
74	#14524021	C₂²	1	1	yes	characteristic
75	#14524020	C₂²	1	2	yes	—
76	#14524020	C₂²	1	2	yes	—
77	#14524020	C₂²	1	2	yes	—
78	#14524019	C₂²	1	1	yes	characteristic
79	#14524019	C₂²	1	1	yes	characteristic
80	#14524019	C₂²	1	2	yes	—
81	#14524019	C₂²	1	1	yes	characteristic
82	#14524018	C₂²	1	1	yes	characteristic
83	#14524017	C₂²	1	2	yes	—
84	#14524016	C₂²	1	2	yes	—
85	#14524014	C₂²	1	1	yes	characteristic
86	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
87	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
88	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
89	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
90	C₄×Dic₁₃₄	C₂²	1	2	yes	—
91	C₄×Dic₁₃₄	C₂²	1	2	yes	—
92	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
93	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
94	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
95	C₄×D₂₆₈	C₂²	1	2	yes	—
96	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
97	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
98	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
99	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
100	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
101	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
104	#14524001	C₂²	1	2	yes	—
105	#14524000	C₂²	1	1	yes	characteristic
106	#14524000	C₂²	1	1	yes	characteristic
107	#14524000	C₂²	1	2	yes	—
108	#14523999	C₂²	1	2	yes	—
109	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	—
110	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
113	#126×C₆₇	C₂²	1	2	yes	—
114	#126×C₆₇	C₂²	1	2	yes	—
115	#124×C₆₇	C₂²	1	1	yes	characteristic
116	#124×C₆₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
122	#117×C₆₇	C₂²	1	2	yes	—
123	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
124	C₂×Dic₁₃₄	C₂³	1	2	yes	—
125	C₂×Dic₁₃₄	C₂³	1	2	yes	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
129	C₂×D₂₆₈	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
133	C₂²×Dic₆₇	C₂³	1	2	yes	—
134	C₂²×Dic₆₇	C₂³	1	2	yes	—
135	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₆₇	C₂³	1	2	yes	—
139	C₂×C₄×D₆₇	C₂³	1	2	yes	—
140	C₂×C₄×D₆₇	C₂³	1	2	yes	—
141	C₄⋊Dic₆₇	C₂³	1	2	yes	—
142	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₆₇	C₂³	1	2	yes	—
147	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₆₇	C₂³	1	2	yes	—
149	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₆₇	C₂³	1	2	yes	—
151	C₄⋊Dic₆₇	C₂³	1	2	yes	—
152	C₄⋊Dic₆₇	C₂³	1	2	yes	—
153	C₄⋊Dic₆₇	C₂³	1	2	yes	—
154	Dic₆₇⋊C₄	C₂³	1	2	yes	—
155	Dic₆₇⋊C₄	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	2	yes	—
161	Dic₆₇⋊C₄	C₂³	1	2	yes	—
162	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
176	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
190	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
191	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
192	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
193	C₄×Dic₆₇	C₂³	1	2	yes	—
194	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
195	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
196	C₄×Dic₆₇	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	2	yes	—
198	C₄×Dic₆₇	C₂³	1	2	yes	—
199	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
204	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₄²×C₆₇	C₂³	1	2	yes	—
218	C₄²×C₆₇	C₂³	1	2	yes	—
219	C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂³×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×D₆₇	C₂⁴	1	2	yes	—
225	Q₈×C₆₇	—	2	2	no	—
226	Q₈×C₆₇	—	2	2	no	—
227	Q₈×C₆₇	—	4	1	no	—
228	D₄×C₆₇	—	2	2	no	—
229	C₂×C₄×C₆₇	—	4	2	no	—
230	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
233	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂²⋊D₆₇	—	4	2	no	—
241	C₂²⋊D₆₇	—	4	2	no	—
242	C₂²⋊D₆₇	—	4	2	no	—
243	C₂×Dic₆₇	—	4	2	no	—
244	C₂×Dic₆₇	—	4	2	no	—
245	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₆₇	C₂⁴	1	2	yes	—
252	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₆₇	C₂⁴	1	2	yes	—
254	C₂×Dic₆₇	C₂⁴	1	2	yes	—
255	D₂₆₈	—	2	2	no	—
256	D₂₆₈	—	4	2	no	—
257	C₄×D₆₇	—	2	2	no	—
258	C₄×D₆₇	—	4	1	no	—
259	C₄×D₆₇	—	4	2	no	—
260	C₄×D₆₇	—	4	2	no	—
261	C₄×D₆₇	—	4	2	no	—
262	C₄×D₆₇	—	4	1	no	—
263	Dic₁₃₄	—	4	2	no	—
264	Dic₁₃₄	—	4	1	no	—
265	Dic₁₃₄	—	4	1	no	—
266	Dic₁₃₄	—	4	1	no	—
267	Dic₁₃₄	—	4	2	no	—
268	C₂²×C₆₇	—	2	2	no	—
269	C₂²×C₆₇	—	2	2	no	—
270	C₂²×C₆₇	—	2	2	no	—
271	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
272	C₂×D₆₇	—	2	1	no	—
273	C₂×D₆₇	—	2	2	no	—
274	C₂×D₆₇	—	2	2	no	—
275	C₂×D₆₇	—	2	1	no	—
276	C₂×D₆₇	—	2	2	no	—
277	C₂×D₆₇	—	2	1	no	—
278	C₄×C₆₇	—	2	2	no	—
279	C₄×C₆₇	—	2	2	no	—
280	C₄×C₆₇	—	2	1	no	—
281	C₄×C₆₇	—	2	1	no	—
282	C₄×C₆₇	—	2	1	no	—
283	C₄×C₆₇	—	2	2	no	—
284	C₄×C₆₇	—	2	1	no	—
285	C₄×C₆₇	—	2	1	no	—
286	C₄×C₆₇	—	2	1	no	—
287	C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
288	Dic₆₇	—	2	1	no	—
289	Dic₆₇	—	2	1	no	—
290	Dic₆₇	—	2	1	no	—
291	Dic₆₇	—	2	2	no	—
292	Dic₆₇	—	2	2	no	—
293	Dic₆₇	—	2	2	no	—
294	Dic₆₇	—	2	1	no	—
295	Dic₆₇	—	2	1	no	—
296	Dic₆₇	—	2	1	no	—
297	Dic₆₇	—	2	1	no	—
298	C₂×C₆₇	—	4	2	no	—
299	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
300	C₂×C₆₇	#585	1	1	yes	characteristic
301	C₂×C₆₇	#585	1	1	yes	characteristic
302	D₆₇	—	4	1	no	—
303	D₆₇	—	4	2	no	—
304	#3557	—	67	1	no	maximal, Sylow
305	C₆₇	#3557	1	1	yes	characteristic, complemented, Sylow
306	#563	—	67	2	no	—
307	#563	—	67	2	no	—
308	#559	—	67	1	no	—
309	#559	—	67	1	no	—
310	#557	—	67	1	no	—
311	#557	—	67	1	no	—
312	#556	—	67	1	no	—
313	#556	D₆₇	1	1	yes	characteristic, complemented
314	#554	—	67	1	no	—
315	#554	—	67	1	no	—
316	#552	—	67	2	no	—
317	#552	—	67	2	no	—
318	#542	—	67	2	no	—
319	#542	—	67	1	no	—
320	#542	—	67	1	no	—
321	#542	—	67	2	no	—
322	#541	—	67	1	no	—
323	#540	—	67	1	no	—
324	#539	—	67	2	no	—
325	#539	—	67	2	no	—
326	#533	—	67	1	no	—
327	#529	—	67	1	no	—
328	#529	—	67	1	no	—
329	C₄⋊Q₈	—	67	1	no	—
330	C₄⋊Q₈	—	67	1	no	—
331	C₄⋊Q₈	—	67	1	no	—
332	C₄⋊Q₈	—	67	2	no	—
333	C₄⋊Q₈	—	67	1	no	—
334	C₄⋊Q₈	—	67	2	no	—
335	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
336	#127	—	67	1	no	—
337	#126	—	67	2	no	—
338	#126	—	67	2	no	—
339	#126	—	67	2	no	—
340	#126	—	67	2	no	—
341	#126	—	67	2	no	—
342	#126	—	67	2	no	—
343	#126	—	67	2	no	—
344	#126	—	67	2	no	—
345	#126	C₂×D₆₇	1	2	yes	—
346	#126	C₂×D₆₇	1	2	yes	—
347	#125	—	67	1	no	—
348	#125	—	67	1	no	—
349	#125	—	67	1	no	—
350	#125	—	67	2	no	—
351	#125	—	67	2	no	—
352	#125	—	67	2	no	—
353	#125	—	67	1	no	—
354	#125	—	67	2	no	—
355	#125	—	67	2	no	—
356	#125	—	67	1	no	—
357	#125	—	67	2	no	—
358	#125	—	67	1	no	—
359	#124	—	67	1	no	—
360	#124	—	67	1	no	—
361	#124	—	67	2	no	—
362	#124	—	67	2	no	—
363	#124	—	67	2	no	—
364	#124	—	67	2	no	—
365	#124	C₂×D₆₇	1	1	yes	characteristic
366	#124	C₂×D₆₇	1	1	yes	characteristic
367	#123	—	67	2	no	—
368	#123	—	67	2	no	—
369	#123	—	67	2	no	—
370	#123	—	67	2	no	—
371	#123	—	67	2	no	—
372	#123	—	67	2	no	—
373	#123	—	67	2	no	—
374	#123	—	67	2	no	—
375	#123	—	67	2	no	—
376	#123	—	67	2	no	—
377	C₂²⋊Q₈	—	67	1	no	—
378	C₂²⋊Q₈	—	67	1	no	—
379	C₂²⋊Q₈	—	67	1	no	—
380	C₂²⋊Q₈	—	67	2	no	—
381	C₂²⋊Q₈	—	67	2	no	—
382	C₂²⋊Q₈	—	67	1	no	—
383	C₂²⋊Q₈	—	67	1	no	—
384	C₂²⋊Q₈	—	67	1	no	—
385	C₂²⋊Q₈	—	67	2	no	—
386	C₂²⋊Q₈	—	67	2	no	—
387	C₂²⋊Q₈	—	67	2	no	—
388	C₂²⋊Q₈	—	67	2	no	—
389	C₂²⋊Q₈	—	67	2	no	—
390	C₂²⋊Q₈	—	67	2	no	—
391	C₂²⋊Q₈	—	67	2	no	—
392	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
393	#121	—	67	1	no	—
394	#121	—	67	2	no	—
395	#121	—	67	1	no	—
396	#121	—	67	2	no	—
397	C₄×Q₈	—	67	1	no	—
398	C₄×Q₈	—	67	1	no	—
399	C₄×Q₈	—	67	1	no	—
400	C₄×Q₈	—	67	1	no	—
401	C₄×Q₈	—	67	1	no	—
402	C₄×Q₈	—	67	1	no	—
403	C₄×Q₈	—	67	1	no	—
404	C₄×Q₈	—	67	2	no	—
405	C₄×Q₈	—	67	2	no	—
406	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
408	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
409	C₄×D₄	—	67	1	no	—
410	C₄×D₄	—	67	1	no	—
411	C₄×D₄	—	67	2	no	—
412	C₄×D₄	—	67	2	no	—
413	C₄×D₄	—	67	2	no	—
414	C₄×D₄	—	67	2	no	—
415	C₄×D₄	—	67	1	no	—
416	C₄×D₄	—	67	1	no	—
417	C₄×D₄	—	67	1	no	—
418	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
419	#117	—	67	2	no	—
420	#117	—	67	2	no	—
421	#117	—	67	2	no	—
422	#117	—	67	1	no	—
423	#117	—	67	1	no	—
424	#117	C₂×D₆₇	1	2	yes	—
425	C₂×C₄⋊C₄	—	67	2	no	—
426	C₂×C₄⋊C₄	—	67	2	no	—
427	C₂×C₄²	—	67	1	no	—
428	C₂×Q₈	—	67	1	no	—
429	C₂×Q₈	—	67	2	no	—
430	C₂×Q₈	—	67	2	no	—
431	C₂×Q₈	—	67	1	no	—
432	C₂×Q₈	—	67	1	no	—
433	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
434	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
435	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
436	C₂×D₄	—	67	2	no	—
437	C₂×D₄	—	67	2	no	—
438	C₂×D₄	—	67	2	no	—
439	C₂×D₄	—	67	2	no	—
440	C₂×D₄	—	67	1	no	—
441	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
442	C₂²×C₄	—	67	2	no	—
443	C₂²×C₄	—	67	2	no	—
444	C₂²×C₄	—	67	1	no	—
445	C₂²×C₄	—	67	1	no	—
446	C₂²×C₄	—	67	2	no	—
447	C₂²×C₄	—	67	2	no	—
448	C₂²×C₄	—	67	2	no	—
449	C₂²×C₄	—	67	1	no	—
450	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
451	C₄⋊C₄	—	67	1	no	—
452	C₄⋊C₄	—	67	2	no	—
453	C₄⋊C₄	—	67	2	no	—
454	C₄⋊C₄	—	67	2	no	—
455	C₄⋊C₄	—	67	2	no	—
456	C₄⋊C₄	—	67	2	no	—
457	C₄⋊C₄	—	67	2	no	—
458	C₄⋊C₄	—	67	1	no	—
459	C₄⋊C₄	—	67	2	no	—
460	C₄⋊C₄	—	67	2	no	—
461	C₄⋊C₄	—	67	1	no	—
462	C₄⋊C₄	—	67	1	no	—
463	C₄⋊C₄	—	67	1	no	—
464	C₄⋊C₄	—	67	1	no	—
465	C₄⋊C₄	—	67	1	no	—
466	C₄⋊C₄	—	67	1	no	—
467	C₄⋊C₄	—	67	1	no	—
468	C₄⋊C₄	—	67	1	no	—
469	C₄⋊C₄	—	67	1	no	—
470	C₄⋊C₄	—	67	2	no	—
471	C₄⋊C₄	—	67	2	no	—
472	C₄⋊C₄	—	67	1	no	—
473	C₄⋊C₄	—	67	1	no	—
474	C₄⋊C₄	—	67	2	no	—
475	C₄⋊C₄	—	67	2	no	—
476	C₄⋊C₄	—	67	1	no	—
477	C₄⋊C₄	—	67	2	no	—
478	C₄⋊C₄	—	67	1	no	—
479	C₄⋊C₄	—	67	1	no	—
480	C₄⋊C₄	—	67	2	no	—
481	C₄⋊C₄	—	67	2	no	—
482	C₄⋊C₄	—	67	2	no	—
483	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
485	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
487	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
490	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
491	C₂²⋊C₄	—	67	2	no	—
492	C₂²⋊C₄	—	67	2	no	—
493	C₂²⋊C₄	—	67	2	no	—
494	C₂²⋊C₄	—	67	2	no	—
495	C₂²⋊C₄	—	67	1	no	—
496	C₂²⋊C₄	—	67	1	no	—
497	C₂²⋊C₄	—	67	2	no	—
498	C₂²⋊C₄	—	67	1	no	—
499	C₂²⋊C₄	—	67	1	no	—
500	C₂²⋊C₄	—	67	2	no	—
501	C₂²⋊C₄	—	67	2	no	—
502	C₂²⋊C₄	—	67	2	no	—
503	C₂²⋊C₄	—	67	2	no	—
504	C₂²⋊C₄	—	67	2	no	—
505	C₂²⋊C₄	—	67	2	no	—
506	C₂²⋊C₄	—	67	2	no	—
507	C₂²⋊C₄	—	67	2	no	—
508	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
513	C₄²	—	67	1	no	—
514	C₄²	—	67	1	no	—
515	C₄²	—	67	1	no	—
516	C₄²	—	67	2	no	—
517	C₄²	—	67	1	no	—
518	C₄²	—	67	1	no	—
519	C₄²	—	67	2	no	—
520	C₄²	—	67	2	no	—
521	C₄²	—	67	2	no	—
522	C₄²	C₂²×D₆₇	1	1	yes	characteristic
523	C₄²	C₂²×D₆₇	1	2	yes	—
524	C₄²	C₂²×D₆₇	1	1	yes	characteristic
525	C₄²	C₂²×D₆₇	1	1	yes	characteristic
526	C₄²	C₂²×D₆₇	1	2	yes	—
527	C₂³	—	67	1	no	—
528	C₂³	—	67	2	no	—
529	C₂³	C₂³×D₆₇	1	2	yes	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	268	2	no	—
534	Q₈	—	268	1	no	—
535	Q₈	—	268	1	no	—
536	Q₈	—	268	2	no	—
537	Q₈	—	268	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	268	2	no	—
540	D₄	—	268	2	no	—
541	D₄	—	268	2	no	—
542	D₄	—	268	2	no	—
543	D₄	—	134	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	268	2	no	—
546	C₂×C₄	—	268	1	no	—
547	C₂×C₄	—	268	2	no	—
548	C₂×C₄	—	268	1	no	—
549	C₂×C₄	—	268	2	no	—
550	C₂×C₄	—	268	2	no	—
551	C₂×C₄	—	268	2	no	—
552	C₂×C₄	—	67	1	no	—
553	C₂×C₄	—	67	1	no	—
554	C₂×C₄	—	67	1	no	—
555	C₂×C₄	—	67	1	no	—
556	C₂×C₄	—	67	1	no	—
557	C₂×C₄	—	67	1	no	—
558	C₂×C₄	—	67	2	no	—
559	C₂×C₄	—	67	2	no	—
560	C₂×C₄	—	67	1	no	—
561	C₂×C₄	—	67	2	no	—
562	C₂×C₄	—	134	2	no	—
563	C₂×C₄	C₂³×D₆₇	1	2	yes	—
564	C₂×C₄	C₂³×D₆₇	1	2	yes	—
565	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₆₇	1	2	yes	—
569	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	134	1	no	—
577	C₂²	—	134	2	no	—
578	C₂²	—	134	1	no	—
579	C₂²	—	134	2	no	—
580	C₂²	—	134	2	no	—
581	C₂²	—	134	1	no	—
582	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	134	1	no	—
593	C₄	—	134	1	no	—
594	C₄	—	134	2	no	—
595	C₄	—	134	1	no	—
596	C₄	—	134	1	no	—
597	C₄	—	134	2	no	—
598	C₄	—	134	1	no	—
599	C₄	—	134	2	no	—
600	C₄	—	134	1	no	—
601	C₄	—	134	1	no	—
602	C₄	#14524090	1	2	yes	—
603	C₂	—	4	2	no	—
604	C₂	—	268	1	no	—
605	C₂	—	268	2	no	—
606	C₂	C₂×#14524090	1	1	yes	characteristic
607	C₂	#16864232	1	1	yes	characteristic
608	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#556×C₆₇	C₂
hypercenter	#556	D₆₇
hypocenter	C₆₇	#3557
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #16864148	C₂	semidirect
2. #16864147	C₂	semidirect
3. #16864128	C₂	semidirect
4. #16864128	C₂	semidirect
5. #16864125	C₂	semidirect
6. #16864122	C₂	semidirect
7. #16864120	C₂	semidirect
8. #16864106	C₂	semidirect
9. #16864105	C₂	semidirect
10. #16864082	C₂	semidirect
11. #16864079	C₂	semidirect
12. #16864018	C₂	semidirect
13. #16864017	C₂	semidirect
14. #16864015	C₂	semidirect
15. #16864012	C₂	semidirect
16. #16864007	C₂	semidirect
18. #16863995	C₂	semidirect
19. #16863987	C₂	semidirect
20. #16863950	C₂	semidirect
21. #16863933	C₂	semidirect
22. #16863925	C₂	semidirect
23. #556×C₆₇	C₂	semidirect
305. C₆₇	#3557	semidirect
313. #556	D₆₇	semidirect