Subgroups — #22574087

Order 8576.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864123	C₂	1	2	yes	maximal, complemented
2	#16864123	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864122	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864117	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864114	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864113	C₂	1	2	yes	maximal, complemented
7	#16864088	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864086	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864083	C₂	1	2	yes	maximal, complemented
10	#16864081	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864079	C₂	1	2	yes	maximal, complemented
12	#16864005	C₂	1	2	yes	maximal, complemented
13	#16864003	C₂	1	2	yes	maximal, complemented
14	#16863968	C₂	1	2	yes	maximal
15	#16863952	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863949	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863948	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863948	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14524042	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863873	C₂	1	2	yes	maximal, complemented
22	C₄×#11761627	C₂	1	1	yes	maximal, characteristic
23	#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761627	C₂²	1	1	yes	characteristic
25	C₂²×Dic₁₃₄	C₂²	1	2	yes	—
26	#14524042	C₂²	1	2	yes	—
27	#14524042	C₂²	1	2	yes	—
28	#14524042	C₂²	1	1	yes	characteristic
29	#14524042	C₂²	1	1	yes	characteristic
30	#14524042	C₂²	1	2	yes	—
31	#14524042	C₂²	1	2	yes	—
32	#14524042	C₂²	1	1	yes	characteristic
33	#14524042	C₂²	1	1	yes	characteristic
34	#14524042	C₂²	1	1	yes	characteristic
35	#14524041	C₂²	1	1	yes	characteristic
36	#14524038	C₂²	1	2	yes	—
37	#14524038	C₂²	1	2	yes	—
38	#14524038	C₂²	1	2	yes	—
39	#14524037	C₂²	1	2	yes	—
40	#14524036	C₂²	1	2	yes	—
41	#14524036	C₂²	1	2	yes	—
42	#14524036	C₂²	1	2	yes	—
43	#14524035	C₂²	1	2	yes	—
44	#14524035	C₂²	1	1	yes	characteristic
45	#14524034	C₂²	1	2	yes	—
46	#14524034	C₂²	1	2	yes	—
47	#14524034	C₂²	1	1	yes	characteristic
48	#14524034	C₂²	1	1	yes	characteristic
49	#14524033	C₂²	1	2	yes	—
50	#14524033	C₂²	1	2	yes	—
51	#14524033	C₂²	1	2	yes	—
52	#14524033	C₂²	1	2	yes	—
53	#14524033	C₂²	1	2	yes	—
54	#14524033	C₂²	1	2	yes	—
55	#14524033	C₂²	1	2	yes	—
56	#14524029	C₂²	1	2	yes	—
57	#14524029	C₂²	1	2	yes	—
58	#14524027	C₂²	1	2	yes	—
59	#14524026	C₂²	1	2	yes	—
60	#14524024	C₂²	1	2	yes	—
61	#14524023	C₂²	1	1	yes	characteristic
62	#14524022	C₂²	1	1	yes	characteristic
63	#14524022	C₂²	1	1	yes	characteristic
64	#14524021	C₂²	1	2	yes	—
65	#14524021	C₂²	1	2	yes	—
66	#14524021	C₂²	1	2	yes	—
67	#14524020	C₂²	1	2	yes	—
68	#14524020	C₂²	1	2	yes	—
69	#14524020	C₂²	1	2	yes	—
70	#14524020	C₂²	1	2	yes	—
71	#14524019	C₂²	1	1	yes	characteristic
72	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
73	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
74	C₄×Dic₁₃₄	C₂²	1	2	yes	—
75	C₄×Dic₁₃₄	C₂²	1	2	yes	—
76	C₄×Dic₁₃₄	C₂²	1	2	yes	—
77	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₃₄	C₂²	1	2	yes	—
79	C₄×Dic₁₃₄	C₂²	1	2	yes	—
80	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
81	#14524008	C₂²	1	2	yes	—
82	#14524008	C₂²	1	2	yes	—
83	#14524008	C₂²	1	1	yes	characteristic
84	#14524008	C₂²	1	2	yes	—
85	#14524008	C₂²	1	2	yes	—
86	#14524008	C₂²	1	2	yes	—
87	#14524008	C₂²	1	1	yes	characteristic
88	#14524008	C₂²	1	2	yes	—
89	#14524008	C₂²	1	1	yes	characteristic
90	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
93	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
94	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
95	#14524002	C₂²	1	2	yes	—
96	#14524002	C₂²	1	1	yes	characteristic
97	#14524001	C₂²	1	1	yes	characteristic
98	#14524001	C₂²	1	1	yes	characteristic
99	#14524001	C₂²	1	1	yes	characteristic
100	#14524000	C₂²	1	2	yes	—
101	#14523999	C₂²	1	1	yes	characteristic
102	#14523999	C₂²	1	2	yes	—
103	#14523999	C₂²	1	2	yes	—
104	#14523999	C₂²	1	2	yes	—
105	#14523999	C₂²	1	1	yes	characteristic
106	#14523999	C₂²	1	2	yes	—
107	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
108	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	—
109	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic
112	#126×C₆₇	C₂²	1	2	yes	—
113	#125×C₆₇	C₂²	1	2	yes	—
114	#125×C₆₇	C₂²	1	1	yes	characteristic
115	#123×C₆₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	#117×C₆₇	C₂²	1	2	yes	—
121	#117×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
123	#11761627	—	2	4	no	—
124	C₂×Dic₁₃₄	—	2	8	no	—
125	C₂×Dic₁₃₄	C₂³	1	2	yes	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	2	yes	—
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×Dic₁₃₄	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
134	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₆₇	C₂³	1	2	yes	—
138	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₆₇	C₂³	1	2	yes	—
145	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₆₇	C₂³	1	2	yes	—
148	C₄⋊Dic₆₇	C₂³	1	2	yes	—
149	C₄⋊Dic₆₇	C₂³	1	2	yes	—
150	C₄⋊Dic₆₇	C₂³	1	2	yes	—
151	C₄⋊Dic₆₇	C₂³	1	2	yes	—
152	Dic₆₇⋊C₄	C₂³	1	2	yes	—
153	Dic₆₇⋊C₄	C₂³	1	2	yes	—
154	Dic₆₇⋊C₄	C₂³	1	2	yes	—
155	Dic₆₇⋊C₄	C₂³	1	2	yes	—
156	Dic₆₇⋊C₄	C₂³	1	2	yes	—
157	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
158	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
159	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
166	Dic₆₇⋊C₄	C₂³	1	2	yes	—
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	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
178	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
185	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
186	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
187	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
188	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
189	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
195	C₄×Dic₆₇	C₂³	1	2	yes	—
196	C₄×Dic₆₇	C₂³	1	2	yes	—
197	C₄×Dic₆₇	C₂³	1	2	yes	—
198	C₄×Dic₆₇	C₂³	1	2	yes	—
199	C₄×Dic₆₇	C₂³	1	2	yes	—
200	C₄×Dic₆₇	C₂³	1	2	yes	—
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	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₄²×C₆₇	C₂³	1	2	yes	—
222	C₄²×C₆₇	C₂³	1	2	yes	—
223	C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
227	Q₈×C₆₇	—	2	2	no	—
228	D₄×C₆₇	—	2	2	no	—
229	C₂×C₄×C₆₇	—	2	4	no	—
230	C₂×C₄×C₆₇	—	2	2	no	—
231	C₂×C₄×C₆₇	—	2	2	no	—
232	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
237	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₆₇	—	2	2	no	—
242	C₂²⋊D₆₇	—	2	2	no	—
243	C₂×Dic₆₇	—	2	4	no	—
244	C₂×Dic₆₇	—	2	2	no	—
245	C₂×Dic₆₇	—	2	2	no	—
246	C₂×Dic₆₇	—	2	2	no	—
247	C₂×Dic₆₇	#41	1	4	yes	—
248	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₆₇	C₂⁴	1	2	yes	—
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	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
259	C₄×D₆₇	—	2	2	no	—
260	C₄×D₆₇	—	2	2	no	—
261	C₄×D₆₇	—	2	2	no	—
262	Dic₁₃₄	—	2	2	no	—
263	Dic₁₃₄	—	2	4	no	—
264	Dic₁₃₄	—	2	4	no	—
265	Dic₁₃₄	—	2	4	no	—
266	Dic₁₃₄	—	2	4	no	—
267	Dic₁₃₄	—	2	2	no	—
268	Dic₁₃₄	—	2	4	no	—
269	C₂²×C₆₇	—	2	1	no	—
270	C₂²×C₆₇	—	2	1	no	—
271	C₂²×C₆₇	—	2	1	no	—
272	C₂²×C₆₇	—	2	1	no	—
273	C₂²×C₆₇	—	2	1	no	—
274	C₂²×C₆₇	C₂×#41	1	2	yes	—
275	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
276	C₂×D₆₇	—	2	1	no	—
277	C₂×D₆₇	—	2	1	no	—
278	C₂×D₆₇	—	2	1	no	—
279	C₄×C₆₇	—	2	2	no	—
280	C₄×C₆₇	—	2	2	no	—
281	C₄×C₆₇	—	2	1	no	—
282	C₄×C₆₇	—	2	2	no	—
283	C₄×C₆₇	—	2	1	no	—
284	C₄×C₆₇	—	2	1	no	—
285	C₄×C₆₇	—	2	1	no	—
286	C₄×C₆₇	—	2	2	no	—
287	C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
288	Dic₆₇	—	2	2	no	—
289	Dic₆₇	—	2	2	no	—
290	Dic₆₇	—	2	1	no	—
291	Dic₆₇	—	2	2	no	—
292	Dic₆₇	—	2	2	no	—
293	Dic₆₇	—	2	1	no	—
294	Dic₆₇	—	2	1	no	—
295	Dic₆₇	—	2	1	no	—
296	Dic₆₇	C₂×#41	1	2	yes	—
297	Dic₆₇	C₂×#41	1	2	yes	—
298	Dic₆₇	2₋¹⁺⁴	1	2	yes	—
299	C₂×C₆₇	—	2	2	no	—
300	C₂×C₆₇	—	4	1	no	—
301	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
302	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	D₆₇	—	4	1	no	—
305	#3509	—	67	1	no	maximal, Sylow
306	C₆₇	#3509	1	1	yes	characteristic, complemented, Sylow
307	#557	—	67	2	no	—
308	#557	—	67	1	no	—
309	#557	—	67	1	no	—
310	#556	—	67	2	no	—
311	#556	—	67	1	no	—
312	#556	—	67	1	no	—
313	#552	—	67	2	no	—
314	#552	—	67	1	no	—
315	#552	—	67	1	no	—
316	#552	—	67	2	no	—
317	#552	—	67	1	no	—
318	#552	D₆₇	1	1	yes	characteristic, complemented
319	#541	—	67	2	no	—
320	#541	—	67	2	no	—
321	#536	—	67	2	no	—
322	#533	—	67	1	no	—
323	#533	—	67	1	no	—
324	#533	—	67	1	no	—
325	#533	—	67	1	no	—
326	#533	—	67	1	no	—
327	C₂×C₄⋊Q₈	—	67	1	no	—
328	#519	—	67	2	no	—
329	C₄×#41	—	67	1	no	—
330	C₂×#41	—	67	1	no	—
331	C₂²×Q₈	—	67	2	no	—
332	C₄⋊Q₈	—	67	1	no	—
333	C₄⋊Q₈	—	67	1	no	—
334	C₄⋊Q₈	—	67	1	no	—
335	C₄⋊Q₈	—	67	2	no	—
336	C₄⋊Q₈	—	67	2	no	—
337	C₄⋊Q₈	—	67	1	no	—
338	C₄⋊Q₈	—	67	1	no	—
339	C₄⋊Q₈	—	67	1	no	—
340	C₄⋊Q₈	—	67	2	no	—
341	C₄⋊Q₈	—	67	2	no	—
342	#126	—	67	2	no	—
343	#126	—	67	2	no	—
344	#126	—	67	2	no	—
345	#126	—	67	2	no	—
346	#126	—	67	2	no	—
347	#126	—	67	2	no	—
348	#126	—	67	2	no	—
349	#126	C₂×D₆₇	1	2	yes	—
350	#125	—	67	2	no	—
351	#125	—	67	2	no	—
352	#125	—	67	2	no	—
353	#125	—	67	1	no	—
354	#125	—	67	1	no	—
355	#125	—	67	2	no	—
356	#125	—	67	2	no	—
357	#125	—	67	2	no	—
358	#125	—	67	2	no	—
359	#125	—	67	2	no	—
360	#125	—	67	2	no	—
361	#125	—	67	1	no	—
362	#125	—	67	2	no	—
363	#125	C₂×D₆₇	1	1	yes	characteristic
364	#125	C₂×D₆₇	1	2	yes	—
365	#124	—	67	2	no	—
366	#124	—	67	2	no	—
367	#123	—	67	2	no	—
368	#123	—	67	2	no	—
369	#123	—	67	2	no	—
370	#123	C₂×D₆₇	1	2	yes	—
371	C₂²⋊Q₈	—	67	1	no	—
372	C₂²⋊Q₈	—	67	1	no	—
373	C₂²⋊Q₈	—	67	1	no	—
374	C₂²⋊Q₈	—	67	2	no	—
375	C₂²⋊Q₈	—	67	2	no	—
376	C₂²⋊Q₈	—	67	2	no	—
377	C₂²⋊Q₈	—	67	1	no	—
378	C₂²⋊Q₈	—	67	2	no	—
379	C₂²⋊Q₈	—	67	2	no	—
380	C₂²⋊Q₈	—	67	2	no	—
381	C₂²⋊Q₈	—	67	2	no	—
382	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
383	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
384	C₄×Q₈	—	67	1	no	—
385	C₄×Q₈	—	67	1	no	—
386	C₄×Q₈	—	67	1	no	—
387	C₄×Q₈	—	67	2	no	—
388	C₄×Q₈	—	67	2	no	—
389	C₄×Q₈	—	67	2	no	—
390	C₄×Q₈	—	67	2	no	—
391	C₄×Q₈	—	67	2	no	—
392	C₄×Q₈	—	67	1	no	—
393	C₄×Q₈	—	67	2	no	—
394	C₄×Q₈	—	67	1	no	—
395	C₄×Q₈	—	67	1	no	—
396	C₄×Q₈	—	67	2	no	—
397	C₄×Q₈	—	67	2	no	—
398	C₄×Q₈	—	67	2	no	—
399	C₄×Q₈	—	67	2	no	—
400	C₄×Q₈	—	67	2	no	—
401	C₄×Q₈	—	67	1	no	—
402	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
403	C₄×D₄	—	67	1	no	—
404	C₄×D₄	—	67	1	no	—
405	C₄×D₄	—	67	1	no	—
406	C₄×D₄	—	67	1	no	—
407	C₄×D₄	—	67	1	no	—
408	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
409	#117	—	67	2	no	—
410	#117	—	67	1	no	—
411	#117	—	67	1	no	—
412	#117	—	67	1	no	—
413	#117	—	67	1	no	—
414	#117	—	67	1	no	—
415	#117	—	67	1	no	—
416	#117	—	67	2	no	—
417	#117	—	67	2	no	—
418	#117	—	67	2	no	—
419	#117	—	67	2	no	—
420	#117	—	67	2	no	—
421	#117	C₂×D₆₇	1	2	yes	—
422	#117	C₂×D₆₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	—	67	2	no	—
424	C₂×C₄⋊C₄	—	67	1	no	—
425	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
426	C₂×C₄²	—	67	1	no	—
427	C₂×C₄²	—	67	1	no	—
428	C₂×C₄²	—	67	1	no	—
429	#41	—	134	4	no	—
430	C₂×Q₈	—	67	2	no	—
431	C₂×Q₈	—	67	1	no	—
432	C₂×Q₈	—	67	2	no	—
433	C₂×Q₈	—	67	2	no	—
434	C₂×Q₈	—	67	2	no	—
435	C₂×Q₈	—	67	2	no	—
436	C₂×Q₈	—	67	1	no	—
437	C₂×Q₈	—	134	8	no	—
438	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
439	C₂×D₄	—	67	1	no	—
440	C₂×D₄	—	67	1	no	—
441	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
442	C₂²×C₄	—	67	1	no	—
443	C₂²×C₄	—	67	1	no	—
444	C₂²×C₄	—	67	1	no	—
445	C₂²×C₄	—	67	1	no	—
446	C₂²×C₄	—	67	2	no	—
447	C₂²×C₄	—	67	1	no	—
448	C₂²×C₄	—	67	1	no	—
449	C₂²×C₄	—	67	1	no	—
450	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
453	C₄⋊C₄	—	67	2	no	—
454	C₄⋊C₄	—	67	2	no	—
455	C₄⋊C₄	—	67	1	no	—
456	C₄⋊C₄	—	67	1	no	—
457	C₄⋊C₄	—	67	2	no	—
458	C₄⋊C₄	—	67	2	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	2	no	—
468	C₄⋊C₄	—	67	2	no	—
469	C₄⋊C₄	—	67	2	no	—
470	C₄⋊C₄	—	67	2	no	—
471	C₄⋊C₄	—	67	2	no	—
472	C₄⋊C₄	—	67	2	no	—
473	C₄⋊C₄	—	67	2	no	—
474	C₄⋊C₄	—	67	2	no	—
475	C₄⋊C₄	—	67	2	no	—
476	C₄⋊C₄	—	67	2	no	—
477	C₄⋊C₄	—	67	2	no	—
478	C₄⋊C₄	—	67	2	no	—
479	C₄⋊C₄	—	67	2	no	—
480	C₄⋊C₄	—	67	2	no	—
481	C₄⋊C₄	—	67	2	no	—
482	C₄⋊C₄	—	67	2	no	—
483	C₄⋊C₄	—	67	2	no	—
484	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
492	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
493	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
494	C₂²⋊C₄	—	67	1	no	—
495	C₂²⋊C₄	—	67	2	no	—
496	C₂²⋊C₄	—	67	1	no	—
497	C₂²⋊C₄	—	67	2	no	—
498	C₂²⋊C₄	—	67	2	no	—
499	C₂²⋊C₄	—	67	1	no	—
500	C₂²⋊C₄	—	67	1	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	C₂²×D₆₇	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
510	C₄²	—	67	1	no	—
511	C₄²	—	67	1	no	—
512	C₄²	—	67	1	no	—
513	C₄²	—	67	1	no	—
514	C₄²	—	67	1	no	—
515	C₄²	—	67	1	no	—
516	C₄²	—	67	1	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	—	67	2	no	—
523	C₄²	—	67	2	no	—
524	C₄²	—	67	2	no	—
525	C₄²	—	67	2	no	—
526	C₄²	—	67	2	no	—
527	C₄²	C₂²×D₆₇	1	1	yes	characteristic
528	C₄²	C₂²×D₆₇	1	2	yes	—
529	C₄²	C₂²×D₆₇	1	2	yes	—
530	C₂³	—	67	1	no	—
531	C₂³	C₂³×D₆₇	1	1	yes	characteristic
532	C₂³	C₂³×D₆₇	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	134	4	no	—
535	Q₈	—	134	4	no	—
536	Q₈	—	134	4	no	—
537	Q₈	—	134	4	no	—
538	Q₈	—	134	2	no	—
539	Q₈	—	134	4	no	—
540	Q₈	—	134	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	134	2	no	—
543	D₄	—	134	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	67	4	no	—
548	C₂×C₄	—	67	1	no	—
549	C₂×C₄	—	67	1	no	—
550	C₂×C₄	—	67	1	no	—
551	C₂×C₄	—	67	1	no	—
552	C₂×C₄	—	67	1	no	—
553	C₂×C₄	—	67	2	no	—
554	C₂×C₄	—	67	2	no	—
555	C₂×C₄	—	67	1	no	—
556	C₂×C₄	—	67	2	no	—
557	C₂×C₄	—	67	2	no	—
558	C₂×C₄	—	67	1	no	—
559	C₂×C₄	—	134	2	no	—
560	C₂×C₄	—	134	2	no	—
561	C₂×C₄	—	134	2	no	—
562	C₂×C₄	—	134	2	no	—
563	C₂×C₄	—	134	2	no	—
564	C₂×C₄	—	134	4	no	—
565	C₂×C₄	—	134	2	no	—
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	2	yes	—
570	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₆₇	1	2	yes	—
572	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₆₇	1	2	yes	—
574	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	134	1	no	—
581	C₂²	—	134	1	no	—
582	C₂²	—	134	1	no	—
583	C₂²	#41×D₆₇	1	2	yes	—
584	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	67	2	no	—
594	C₄	—	67	2	no	—
595	C₄	—	67	2	no	—
596	C₄	—	134	1	no	—
597	C₄	—	134	2	no	—
598	C₄	—	134	2	no	—
599	C₄	—	134	1	no	—
600	C₄	—	134	1	no	—
601	C₄	—	134	2	no	—
602	C₄	—	134	1	no	—
603	C₄	—	134	2	no	—
604	C₄	#14524090	1	2	yes	—
605	C₂	—	2	2	no	—
606	C₂	—	4	1	no	—
607	C₂	—	268	1	no	—
608	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
610	C₂	C₂×#14524090	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#552×C₆₇	C₂
hypercenter	#552	D₆₇
hypocenter	C₆₇	#3509
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #16864123	C₂	semidirect
2. #16864123	C₂	semidirect
3. #16864122	C₂	semidirect
4. #16864117	C₂	semidirect
5. #16864114	C₂	semidirect
6. #16864113	C₂	semidirect
7. #16864088	C₂	semidirect
8. #16864086	C₂	semidirect
9. #16864083	C₂	semidirect
10. #16864081	C₂	semidirect
11. #16864079	C₂	semidirect
12. #16864005	C₂	semidirect
13. #16864003	C₂	semidirect
15. #16863952	C₂	semidirect
16. #16863950	C₂	semidirect
17. #16863949	C₂	semidirect
18. #16863948	C₂	semidirect
19. #16863948	C₂	semidirect
20. C₂×#14524042	C₂	semidirect
21. #16863873	C₂	semidirect
23. #552×C₆₇	C₂	semidirect
306. C₆₇	#3509	semidirect
318. #552	D₆₇	semidirect