Subgroups — #22574079

Order 8576.

1232 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864132	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864131	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864129	C₂	1	2	yes	maximal, complemented
4	#16864067	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864066	C₂	1	2	yes	maximal, complemented
6	#16864043	C₂	1	2	yes	maximal, complemented
7	#16864035	C₂	1	4	yes	maximal, complemented
8	#16864034	C₂	1	2	yes	maximal, complemented
9	#16863996	C₂	1	4	yes	maximal, complemented
10	#16863959	C₂	1	2	yes	maximal, complemented
11	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863942	C₂	1	2	yes	maximal, complemented
13	#16863941	C₂	1	2	yes	maximal, complemented
14	#127×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863868	C₂	1	2	yes	maximal, complemented
16	C₄×#11761627	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11761628	C₂²	1	2	yes	complemented
19	C₂×#11761627	C₂²	1	1	yes	characteristic
20	C₂×#11761627	C₂²	1	4	yes	complemented
21	C₂×D₄×D₆₇	C₂²	1	2	yes	—
22	C₂×D₄×D₆₇	C₂²	1	2	yes	—
23	C₂×D₄×D₆₇	C₂²	1	2	yes	—
24	#14524042	C₂²	1	1	yes	characteristic, complemented
25	#14524041	C₂²	1	1	yes	characteristic, complemented
26	#14524040	C₂²	1	1	yes	characteristic
27	#14524039	C₂²	1	2	yes	—
28	#14524039	C₂²	1	2	yes	—
29	#14524039	C₂²	1	2	yes	—
30	#14524039	C₂²	1	2	yes	complemented
31	#14524033	C₂²	1	2	yes	complemented
32	#14524032	C₂²	1	2	yes	complemented
33	#14524031	C₂²	1	2	yes	complemented
34	#14524030	C₂²	1	2	yes	complemented
35	#14524030	C₂²	1	2	yes	complemented
36	#14524029	C₂²	1	4	yes	complemented
37	#14524028	C₂²	1	4	yes	complemented
38	#14524026	C₂²	1	4	yes	complemented
39	#14524025	C₂²	1	4	yes	complemented
40	#14524024	C₂²	1	4	yes	complemented
41	#14524023	C₂²	1	1	yes	characteristic
42	#14524021	C₂²	1	2	yes	—
43	#14524019	C₂²	1	1	yes	characteristic
44	#14524017	C₂²	1	2	yes	complemented
45	#14524016	C₂²	1	4	yes	complemented
46	#14524015	C₂²	1	4	yes	complemented
47	#14524015	C₂²	1	4	yes	complemented
48	#14524015	C₂²	1	4	yes	complemented
49	#14524015	C₂²	1	4	yes	complemented
50	#14524014	C₂²	1	4	yes	complemented
51	#14524011	C₂²	1	4	yes	—
52	#14524011	C₂²	1	4	yes	—
53	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
54	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
56	#14524008	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₂₆₈	C₂²	1	2	yes	complemented
58	D₄×Dic₆₇	C₂²	1	2	yes	complemented
59	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
60	D₄×Dic₆₇	C₂²	1	2	yes	complemented
61	#14524005	C₂²	1	2	yes	complemented
62	#14524005	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
65	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
66	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
67	(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
68	#14524001	C₂²	1	1	yes	characteristic
69	#14524000	C₂²	1	2	yes	—
70	#14523999	C₂²	1	2	yes	complemented
71	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₆₇	C₂²	1	4	yes	—
73	C₂×C₄×Dic₆₇	C₂²	1	2	yes	complemented
74	C₄²×D₆₇	C₂²	1	1	yes	characteristic
75	C₂×#41×C₆₇	C₂²	1	2	yes	complemented
76	#127×C₆₇	C₂²	1	1	yes	characteristic
77	#127×C₆₇	C₂²	1	2	yes	complemented
78	#121×C₆₇	C₂²	1	4	yes	complemented
79	#121×C₆₇	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂³×D₆₇	C₂³	1	4	yes	—
84	#11761628	—	4	4	no	—
85	#11761627	—	2	4	no	—
86	#11761627	—	4	8	no	—
87	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
88	C₂×Dic₁₃₄	C₂³	1	2	yes	—
89	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
90	C₂×D₂₆₈	C₂³	1	2	yes	—
91	C₂×D₂₆₈	C₂³	1	2	yes	—
92	C₂×D₂₆₈	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
99	D₄×D₆₇	—	2	8	no	—
100	D₄×D₆₇	—	4	4	no	—
101	D₄×D₆₇	—	4	4	no	—
102	C₂²×Dic₆₇	C₂³	1	2	yes	—
103	C₂²×Dic₆₇	C₂³	1	2	yes	—
104	C₂²×Dic₆₇	C₂³	1	4	yes	—
105	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₆₇	C₂³	1	4	yes	—
108	C₂×C₄×D₆₇	C₂³	1	4	yes	—
109	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₆₇	C₂³	1	2	yes	—
113	Dic₆₇⋊C₄	C₂³	1	2	yes	—
114	Dic₆₇⋊C₄	C₂³	1	2	yes	—
115	Dic₆₇⋊C₄	C₂³	1	2	yes	—
116	Dic₆₇⋊C₄	C₂³	1	2	yes	—
117	Dic₆₇⋊C₄	C₂³	1	2	yes	—
118	Dic₆₇⋊C₄	C₂³	1	2	yes	—
119	Dic₆₇⋊C₄	C₂³	1	2	yes	—
120	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
121	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
124	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
131	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
132	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
133	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
134	C₄×Dic₆₇	C₂³	1	2	yes	—
135	C₄×Dic₆₇	C₂³	1	2	yes	—
136	C₄×Dic₆₇	C₂³	1	2	yes	—
137	C₄×Dic₆₇	C₂³	1	2	yes	—
138	#41×C₆₇	—	4	4	no	—
139	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₆₇	C₂³	1	2	yes	—
141	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂×D₄×C₆₇	C₂³	1	2	yes	—
144	C₂×D₄×C₆₇	C₂³	1	4	yes	—
145	C₂×D₄×C₆₇	C₂³	1	4	yes	—
146	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
147	C₂²×C₄×C₆₇	C₂³	1	4	yes	—
148	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₄²×C₆₇	C₂³	1	1	yes	characteristic
154	C₄²×C₆₇	C₂³	1	2	yes	—
155	C₂³×C₆₇	C₂⁴	1	4	yes	—
156	C₂³×C₆₇	C₂⁴	1	2	yes	—
157	C₂²×D₆₇	—	2	8	no	—
158	C₂²×D₆₇	—	4	4	no	—
159	C₂²×D₆₇	—	4	4	no	—
160	C₂²×D₆₇	C₂⁴	1	4	yes	—
161	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
162	Q₈×C₆₇	—	2	2	no	—
163	D₄×C₆₇	—	2	4	no	—
164	D₄×C₆₇	—	2	2	no	—
165	D₄×C₆₇	—	2	4	no	—
166	D₄×C₆₇	—	4	4	no	—
167	D₄×C₆₇	—	4	2	no	—
168	D₄×C₆₇	—	4	4	no	—
169	C₂×C₄×C₆₇	—	2	4	no	—
170	C₂×C₄×C₆₇	—	4	4	no	—
171	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
173	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
174	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
175	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
177	C₂²⋊D₆₇	—	2	4	no	—
178	C₂²⋊D₆₇	—	2	8	no	—
179	C₂²⋊D₆₇	—	2	8	no	—
180	C₂²⋊D₆₇	—	4	4	no	—
181	C₂²⋊D₆₇	—	4	4	no	—
182	C₂²⋊D₆₇	—	4	4	no	—
183	C₂×Dic₆₇	—	2	4	no	—
184	C₂×Dic₆₇	—	2	4	no	—
185	C₂×Dic₆₇	—	4	4	no	—
186	C₂×Dic₆₇	C₂⁴	1	2	yes	—
187	C₂×Dic₆₇	C₂⁴	1	2	yes	—
188	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₆₇	C₂⁴	1	2	yes	—
190	C₂×Dic₆₇	C₂⁴	1	2	yes	—
191	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
193	D₂₆₈	—	2	4	no	—
194	D₂₆₈	—	2	4	no	—
195	D₂₆₈	—	4	2	no	—
196	C₄×D₆₇	—	2	2	no	—
197	C₄×D₆₇	—	2	2	no	—
198	C₄×D₆₇	—	4	4	no	—
199	C₄×D₆₇	—	4	4	no	—
200	C₄×D₆₇	#41	1	4	yes	complemented
201	Dic₁₃₄	—	2	2	no	—
202	Dic₁₃₄	—	2	2	no	—
203	Dic₁₃₄	—	2	4	no	—
204	C₂²×C₆₇	—	2	2	no	—
205	C₂²×C₆₇	—	2	4	no	—
206	C₂²×C₆₇	—	2	2	no	—
207	C₂²×C₆₇	—	2	4	no	—
208	C₂²×C₆₇	—	2	2	no	—
209	C₂²×C₆₇	—	2	4	no	—
210	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
211	C₂×D₆₇	—	2	1	no	—
212	C₂×D₆₇	—	2	1	no	—
213	C₂×D₆₇	—	2	4	no	—
214	C₂×D₆₇	—	2	4	no	—
215	C₂×D₆₇	—	2	4	no	—
216	C₂×D₆₇	—	8	8	no	—
217	C₂×D₆₇	C₂×#41	1	2	yes	—
218	C₄×C₆₇	—	2	2	no	—
219	C₄×C₆₇	—	2	1	no	—
220	C₄×C₆₇	—	2	2	no	—
221	C₄×C₆₇	—	2	2	no	—
222	C₄×C₆₇	C₂×#41	1	2	yes	—
223	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
224	Dic₆₇	—	2	2	no	—
225	Dic₆₇	—	2	2	no	—
226	Dic₆₇	—	2	2	no	—
227	Dic₆₇	—	2	1	no	—
228	Dic₆₇	—	2	2	no	—
229	Dic₆₇	C₂×#41	1	2	yes	—
230	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
231	C₂×C₆₇	—	4	4	no	—
232	C₂×C₆₇	—	4	2	no	—
233	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
234	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	D₆₇	—	2	2	no	—
237	D₆₇	—	4	4	no	—
238	#3508	—	67	1	no	maximal, Sylow
239	C₆₇	#3508	1	1	yes	characteristic, complemented, Sylow
240	#559	—	67	1	no	—
241	#559	—	67	1	no	—
242	#559	—	67	2	no	—
243	#550	—	67	2	no	—
244	#550	—	67	1	no	—
245	#550	D₆₇	1	1	yes	characteristic, complemented
246	#546	—	67	2	no	—
247	#546	—	67	4	no	—
248	#546	—	67	2	no	—
249	#540	—	67	4	no	—
250	#535	—	67	2	no	—
251	#533	—	67	1	no	—
252	#532	—	67	2	no	—
253	#532	—	67	2	no	—
254	C₂×#127	—	67	1	no	—
255	#518	—	67	2	no	—
256	C₄×#41	—	67	1	no	—
257	C₂×#41	—	67	4	no	—
258	C₂×#41	—	67	1	no	—
259	C₂×#41	—	67	2	no	—
260	C₂×#41	C₂×D₆₇	1	2	yes	complemented
261	C₂²×D₄	—	67	2	no	—
262	C₂²×D₄	—	67	2	no	—
263	C₂²×D₄	—	67	2	no	—
264	C₄⋊Q₈	—	67	1	no	—
265	C₄⋊Q₈	—	67	1	no	—
266	#127	—	67	2	no	—
267	#127	—	67	2	no	—
268	#127	—	67	2	no	—
269	#127	—	67	2	no	—
270	#127	—	67	1	no	—
271	#127	C₂×D₆₇	1	1	yes	characteristic
272	#127	C₂×D₆₇	1	2	yes	complemented
273	#125	—	67	2	no	—
274	#124	—	67	2	no	—
275	#124	—	67	2	no	—
276	#124	—	67	2	no	—
277	#124	—	67	4	no	—
278	#124	—	67	2	no	—
279	#123	—	67	4	no	—
280	#123	—	67	4	no	—
281	#123	—	67	4	no	—
282	#123	—	67	4	no	—
283	C₂²⋊Q₈	—	67	1	no	—
284	C₂²⋊Q₈	—	67	2	no	—
285	C₂²⋊Q₈	—	67	1	no	—
286	#121	—	67	4	no	—
287	#121	—	67	4	no	—
288	#121	—	67	4	no	—
289	#121	—	67	4	no	—
290	#121	—	67	4	no	—
291	#121	—	67	2	no	—
292	#121	—	67	4	no	—
293	#121	C₂×D₆₇	1	2	yes	complemented
294	#121	C₂×D₆₇	1	4	yes	complemented
295	#120	—	67	4	no	—
296	#120	—	67	4	no	—
297	C₄×Q₈	—	67	1	no	—
298	C₄×Q₈	—	67	1	no	—
299	C₄×Q₈	—	67	2	no	—
300	C₄×Q₈	—	67	1	no	—
301	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
302	C₄×D₄	—	67	1	no	—
303	C₄×D₄	—	67	2	no	—
304	C₄×D₄	—	67	2	no	—
305	C₄×D₄	—	67	2	no	—
306	C₄×D₄	—	67	4	no	—
307	C₄×D₄	—	67	4	no	—
308	C₄×D₄	—	67	2	no	—
309	C₄×D₄	—	67	2	no	—
310	C₄×D₄	—	67	2	no	—
311	C₄×D₄	—	67	4	no	—
312	C₄×D₄	—	67	2	no	—
313	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
314	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
315	#117	—	67	1	no	—
316	#117	—	67	2	no	—
317	#117	—	67	2	no	—
318	C₂×C₂²⋊C₄	—	67	4	no	—
319	C₂×C₂²⋊C₄	—	67	4	no	—
320	C₂×C₄²	—	67	2	no	—
321	C₂×C₄²	—	67	1	no	—
322	C₂⁴	—	67	4	no	—
323	#41	—	4	4	no	—
324	#41	—	268	4	no	—
325	#41	—	268	8	no	—
326	#41	—	134	4	no	—
327	C₂×Q₈	—	67	1	no	—
328	C₂×Q₈	—	67	2	no	—
329	C₂×Q₈	—	67	1	no	—
330	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
331	C₂×D₄	—	268	4	no	—
332	C₂×D₄	—	268	4	no	—
333	C₂×D₄	—	67	4	no	—
334	C₂×D₄	—	67	4	no	—
335	C₂×D₄	—	67	4	no	—
336	C₂×D₄	—	67	2	no	—
337	C₂×D₄	—	67	4	no	—
338	C₂×D₄	—	67	4	no	—
339	C₂×D₄	—	67	2	no	—
340	C₂×D₄	—	67	2	no	—
341	C₂×D₄	—	67	2	no	—
342	C₂×D₄	—	134	8	no	—
343	C₂×D₄	C₂²×D₆₇	1	2	yes	—
344	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
345	C₂×D₄	C₂²×D₆₇	1	2	yes	—
346	C₂×D₄	C₂²×D₆₇	1	4	yes	—
347	C₂×D₄	C₂²×D₆₇	1	4	yes	—
348	C₂×D₄	C₂²×D₆₇	1	2	yes	—
349	C₂²×C₄	—	67	4	no	—
350	C₂²×C₄	—	67	4	no	—
351	C₂²×C₄	—	67	4	no	—
352	C₂²×C₄	—	67	1	no	—
353	C₂²×C₄	—	67	2	no	—
354	C₂²×C₄	—	67	2	no	—
355	C₂²×C₄	—	67	1	no	—
356	C₂²×C₄	—	67	1	no	—
357	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
358	C₂²×C₄	C₂²×D₆₇	1	4	yes	—
359	C₄⋊C₄	—	67	1	no	—
360	C₄⋊C₄	—	67	2	no	—
361	C₄⋊C₄	—	67	2	no	—
362	C₄⋊C₄	—	67	2	no	—
363	C₄⋊C₄	—	67	2	no	—
364	C₄⋊C₄	—	67	2	no	—
365	C₄⋊C₄	—	67	1	no	—
366	C₄⋊C₄	—	67	2	no	—
367	C₄⋊C₄	—	67	2	no	—
368	C₄⋊C₄	—	67	2	no	—
369	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
372	C₂²⋊C₄	—	67	4	no	—
373	C₂²⋊C₄	—	67	2	no	—
374	C₂²⋊C₄	—	67	4	no	—
375	C₂²⋊C₄	—	67	4	no	—
376	C₂²⋊C₄	—	67	2	no	—
377	C₂²⋊C₄	—	67	2	no	—
378	C₂²⋊C₄	—	67	2	no	—
379	C₂²⋊C₄	—	67	4	no	—
380	C₂²⋊C₄	—	67	4	no	—
381	C₂²⋊C₄	—	67	4	no	—
382	C₂²⋊C₄	—	67	4	no	—
383	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
384	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
385	C₄²	—	67	1	no	—
386	C₄²	—	67	2	no	—
387	C₄²	—	67	1	no	—
388	C₄²	—	67	2	no	—
389	C₄²	—	67	2	no	—
390	C₄²	—	67	1	no	—
391	C₄²	—	67	2	no	—
392	C₄²	C₂²×D₆₇	1	1	yes	characteristic
393	C₄²	C₂²×D₆₇	1	2	yes	—
394	C₂³	—	268	4	no	—
395	C₂³	—	268	4	no	—
396	C₂³	—	67	1	no	—
397	C₂³	—	67	4	no	—
398	C₂³	—	134	8	no	—
399	C₂³	C₂³×D₆₇	1	4	yes	—
400	C₂³	C₂³×D₆₇	1	2	yes	—
401	Q₈	—	2	2	no	—
402	Q₈	—	134	4	no	—
403	Q₈	—	134	2	no	—
404	Q₈	—	134	2	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	268	2	no	—
412	D₄	—	268	4	no	—
413	D₄	—	268	4	no	—
414	D₄	—	268	4	no	—
415	D₄	—	134	8	no	—
416	D₄	—	134	8	no	—
417	D₄	—	134	4	no	—
418	D₄	—	134	4	no	—
419	D₄	—	134	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	268	4	no	—
423	C₂×C₄	—	268	4	no	—
424	C₂×C₄	—	268	4	no	—
425	C₂×C₄	—	67	1	no	—
426	C₂×C₄	—	67	1	no	—
427	C₂×C₄	—	67	4	no	—
428	C₂×C₄	—	67	2	no	—
429	C₂×C₄	—	67	2	no	—
430	C₂×C₄	—	67	1	no	—
431	C₂×C₄	—	67	2	no	—
432	C₂×C₄	—	67	2	no	—
433	C₂×C₄	—	134	2	no	—
434	C₂×C₄	—	134	4	no	—
435	C₂×C₄	—	134	4	no	—
436	C₂×C₄	—	134	2	no	—
437	C₂×C₄	C₂³×D₆₇	1	2	yes	—
438	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₆₇	1	2	yes	—
440	C₂×C₄	C₂³×D₆₇	1	2	yes	—
441	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
442	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	536	8	no	—
450	C₂²	—	67	2	no	—
451	C₂²	—	134	4	no	—
452	C₂²	—	134	4	no	—
453	C₂²	—	134	4	no	—
454	C₂²	—	134	1	no	—
455	C₂²	—	134	1	no	—
456	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	67	2	no	—
462	C₄	—	67	2	no	—
463	C₄	—	134	2	no	—
464	C₄	—	134	2	no	—
465	C₄	—	134	2	no	—
466	C₄	—	134	2	no	—
467	C₄	—	134	1	no	—
468	C₄	#41×D₆₇	1	2	yes	—
469	C₄	#14524088	1	2	yes	—
470	C₂	—	4	4	no	—
471	C₂	—	4	2	no	—
472	C₂	—	268	4	no	—
473	C₂	—	134	2	no	—
474	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
475	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
476	C₂	C₂×#14524088	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#550×C₆₇	C₂
hypercenter	#550	D₆₇
hypocenter	C₆₇	#3508
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #16864132	C₂	semidirect
2. #16864131	C₂	semidirect
3. #16864129	C₂	semidirect
4. #16864067	C₂	semidirect
5. #16864066	C₂	semidirect
6. #16864043	C₂	semidirect
7. #16864035	C₂	semidirect
8. #16864034	C₂	semidirect
9. #16863996	C₂	semidirect
10. #16863959	C₂	semidirect
11. #16863950	C₂	semidirect
12. #16863942	C₂	semidirect
13. #16863941	C₂	semidirect
14. #127×D₆₇	C₂	semidirect
15. #16863868	C₂	semidirect
16. C₄×#11761627	C₂	semidirect
17. #550×C₆₇	C₂	semidirect
18. C₂×#11761628	C₂²	semidirect
20. C₂×#11761627	C₂²	semidirect
24. #14524042	C₂²	semidirect
25. #14524041	C₂²	semidirect
30. #14524039	C₂²	semidirect
31. #14524033	C₂²	semidirect
32. #14524032	C₂²	semidirect
33. #14524031	C₂²	semidirect
34. #14524030	C₂²	semidirect
35. #14524030	C₂²	semidirect
36. #14524029	C₂²	semidirect
37. #14524028	C₂²	semidirect
38. #14524026	C₂²	semidirect
39. #14524025	C₂²	semidirect
40. #14524024	C₂²	semidirect
44. #14524017	C₂²	semidirect
45. #14524016	C₂²	semidirect
46. #14524015	C₂²	semidirect
47. #14524015	C₂²	semidirect
48. #14524015	C₂²	semidirect
49. #14524015	C₂²	semidirect
50. #14524014	C₂²	semidirect
53. C₄×Dic₁₃₄	C₂²	semidirect
54. C₄×Dic₁₃₄	C₂²	semidirect
55. C₄×Dic₁₃₄	C₂²	semidirect
56. #14524008	C₂²	semidirect
57. C₄×D₂₆₈	C₂²	semidirect
58. D₄×Dic₆₇	C₂²	semidirect
59. D₄×Dic₆₇	C₂²	semidirect
60. D₄×Dic₆₇	C₂²	semidirect
61. #14524005	C₂²	semidirect
62. #14524005	C₂²	semidirect
64. C₄×C₂²⋊D₆₇	C₂²	semidirect
65. C₄×C₂²⋊D₆₇	C₂²	semidirect
67. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
70. #14523999	C₂²	semidirect
73. C₂×C₄×Dic₆₇	C₂²	semidirect
75. C₂×#41×C₆₇	C₂²	semidirect
77. #127×C₆₇	C₂²	semidirect
78. #121×C₆₇	C₂²	semidirect
79. #121×C₆₇	C₂²	semidirect
80. C₄×Q₈×C₆₇	C₂²	semidirect
81. C₄×D₄×C₆₇	C₂²	semidirect
82. C₄×D₄×C₆₇	C₂²	semidirect
200. C₄×D₆₇	#41	semidirect
239. C₆₇	#3508	semidirect
245. #550	D₆₇	semidirect
260. C₂×#41	C₂×D₆₇	semidirect
272. #127	C₂×D₆₇	semidirect
293. #121	C₂×D₆₇	semidirect
294. #121	C₂×D₆₇	semidirect
301. C₄×Q₈	C₂×D₆₇	semidirect
313. C₄×D₄	C₂×D₆₇	semidirect
314. C₄×D₄	C₂×D₆₇	semidirect