Subgroups — #22574442

Order 8576.

1270 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864135	C₂	1	2	yes	maximal, complemented
2	#16864133	C₂	1	2	yes	maximal, complemented
3	#16864093	C₂	1	2	yes	maximal, complemented
4	#16864090	C₂	1	2	yes	maximal, complemented
5	#16864031	C₂	1	2	yes	maximal, complemented
6	#16864030	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊D₆₇	C₂	1	2	yes	maximal, complemented
8	#16864028	C₂	1	2	yes	maximal, complemented
9	#16863999	C₂	1	2	yes	maximal, complemented
10	#16863980	C₂	1	4	yes	maximal, complemented
11	#16863960	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863956	C₂	1	4	yes	maximal, complemented
13	#16863903	C₂	1	1	yes	maximal, characteristic, complemented
14	#121×D₆₇	C₂	1	2	yes	maximal, complemented
15	#535×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
18	C₂×D₄×D₆₇	C₂²	1	4	yes	complemented
19	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
20	C₂×D₄×D₆₇	C₂²	1	4	yes	complemented
21	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
22	#14524039	C₂²	1	2	yes	complemented
23	#14524039	C₂²	1	2	yes	complemented
24	#14524037	C₂²	1	4	yes	complemented
25	#14524036	C₂²	1	4	yes	complemented
26	#14524034	C₂²	1	2	yes	complemented
27	#14524032	C₂²	1	2	yes	complemented
28	#14524027	C₂²	1	4	yes	complemented
29	#14524025	C₂²	1	4	yes	complemented
30	#14524025	C₂²	1	4	yes	complemented
31	#14524024	C₂²	1	4	yes	complemented
32	#14524024	C₂²	1	1	yes	characteristic, complemented
33	#14524024	C₂²	1	1	yes	characteristic, complemented
34	#14524019	C₂²	1	2	yes	complemented
35	#14524018	C₂²	1	2	yes	complemented
36	#14524017	C₂²	1	2	yes	complemented
37	#14524017	C₂²	1	2	yes	complemented
38	#14524016	C₂²	1	4	yes	complemented
39	#14524016	C₂²	1	4	yes	complemented
40	#14524016	C₂²	1	4	yes	complemented
41	#14524015	C₂²	1	4	yes	complemented
42	#14524015	C₂²	1	4	yes	complemented
43	#14524015	C₂²	1	4	yes	complemented
44	#14524014	C₂²	1	2	yes	complemented
45	#14524014	C₂²	1	4	yes	complemented
46	#14524014	C₂²	1	4	yes	complemented
47	#14524014	C₂²	1	2	yes	complemented
48	#14524013	C₂²	1	4	yes	complemented
49	#14524012	C₂²	1	4	yes	complemented
50	#14524011	C₂²	1	1	yes	characteristic, complemented
51	#14524011	C₂²	1	4	yes	complemented
52	#14524011	C₂²	1	4	yes	complemented
53	#14524011	C₂²	1	1	yes	characteristic, complemented
54	#14524011	C₂²	1	2	yes	complemented
55	#14524011	C₂²	1	2	yes	complemented
56	C₄×D₂₆₈	C₂²	1	4	yes	complemented
57	D₄×Dic₆₇	C₂²	1	2	yes	complemented
58	#14524005	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
61	(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
62	#14524002	C₂²	1	1	yes	characteristic, complemented
63	#14524002	C₂²	1	1	yes	characteristic, complemented
64	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
65	C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
66	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#127×C₆₇	C₂²	1	2	yes	complemented
69	#124×C₆₇	C₂²	1	2	yes	complemented
70	#121×C₆₇	C₂²	1	2	yes	complemented
71	#121×C₆₇	C₂²	1	2	yes	complemented
72	#120×C₆₇	C₂²	1	2	yes	complemented
73	#120×C₆₇	C₂²	1	2	yes	complemented
74	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₆₇	C₂³	1	1	yes	characteristic
76	C₂³×D₆₇	C₂³	1	4	yes	—
77	C₂³×D₆₇	C₂³	1	2	yes	—
78	C₂×D₂₆₈	—	4	2	no	—
79	C₂×D₂₆₈	C₂³	1	2	yes	—
80	C₂×D₂₆₈	C₂³	1	4	yes	—
81	C₂×D₂₆₈	C₂³	1	2	yes	—
82	C₂×C₂²⋊D₆₇	—	4	8	no	—
83	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
85	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
86	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
91	D₄×D₆₇	—	4	4	no	—
92	D₄×D₆₇	—	4	8	no	—
93	D₄×D₆₇	—	4	8	no	—
94	C₂²×Dic₆₇	C₂³	1	4	yes	—
95	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₆₇	—	4	2	no	—
97	C₂×C₄×D₆₇	C₂³	1	2	yes	—
98	C₂×C₄×D₆₇	C₂³	1	2	yes	—
99	C₂×C₄×D₆₇	C₂³	1	4	yes	—
100	C₂×C₄×D₆₇	C₂³	1	4	yes	—
101	C₄⋊Dic₆₇	C₂³	1	2	yes	—
102	C₄⋊Dic₆₇	C₂³	1	2	yes	—
103	C₄⋊Dic₆₇	C₂³	1	4	yes	—
104	Dic₆₇⋊C₄	C₂³	1	4	yes	—
105	Dic₆₇⋊C₄	C₂³	1	4	yes	—
106	Dic₆₇⋊C₄	C₂³	1	2	yes	—
107	Dic₆₇⋊C₄	C₂³	1	2	yes	—
108	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
109	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
110	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
111	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
112	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
113	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
114	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
115	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
116	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
118	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
119	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
121	C₄×Dic₆₇	C₂³	1	2	yes	—
122	C₄×Dic₆₇	C₂³	1	2	yes	—
123	C₂⁴×C₆₇	C₂³	1	2	yes	—
124	#41×C₆₇	—	4	2	no	—
125	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₆₇	—	4	2	no	—
127	C₂×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₆₇	C₂³	1	4	yes	—
131	C₂×D₄×C₆₇	C₂³	1	4	yes	—
132	C₂×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₄²×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₆₇	—	4	2	no	—
143	C₂³×C₆₇	—	4	4	no	—
144	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₆₇	C₂⁴	1	4	yes	—
146	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
147	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
148	C₂²×D₆₇	—	2	4	no	—
149	C₂²×D₆₇	—	2	8	no	—
150	C₂²×D₆₇	—	4	1	no	—
151	C₂²×D₆₇	—	4	4	no	—
152	C₂²×D₆₇	—	4	4	no	—
153	C₂²×D₆₇	—	4	4	no	—
154	C₂²×D₆₇	—	4	2	no	—
155	C₂²×D₆₇	C₂⁴	1	4	yes	—
156	C₂²×D₆₇	C₂⁴	1	2	yes	—
157	Q₈×C₆₇	—	4	1	no	—
158	D₄×C₆₇	—	2	4	no	—
159	D₄×C₆₇	—	4	2	no	—
160	D₄×C₆₇	—	4	1	no	—
161	D₄×C₆₇	—	4	1	no	—
162	D₄×C₆₇	—	4	1	no	—
163	D₄×C₆₇	—	4	4	no	—
164	D₄×C₆₇	—	4	4	no	—
165	C₂×C₄×C₆₇	—	2	2	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
170	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₆₇	—	2	4	no	—
174	C₂²⋊D₆₇	—	2	8	no	—
175	C₂²⋊D₆₇	—	2	4	no	—
176	C₂²⋊D₆₇	—	4	4	no	—
177	C₂²⋊D₆₇	—	4	4	no	—
178	C₂²⋊D₆₇	—	4	4	no	—
179	C₂²⋊D₆₇	—	4	4	no	—
180	C₂²⋊D₆₇	—	4	4	no	—
181	C₂×Dic₆₇	—	4	1	no	—
182	C₂×Dic₆₇	—	4	4	no	—
183	C₂×Dic₆₇	C₂⁴	1	2	yes	—
184	C₂×Dic₆₇	C₂⁴	1	4	yes	—
185	C₂×Dic₆₇	C₂⁴	1	2	yes	—
186	C₂×Dic₆₇	C₂⁴	1	2	yes	—
187	D₂₆₈	—	2	8	no	—
188	D₂₆₈	—	2	4	no	—
189	D₂₆₈	—	4	2	no	—
190	C₄×D₆₇	—	2	4	no	—
191	C₄×D₆₇	—	4	2	no	—
192	C₄×D₆₇	—	4	4	no	—
193	C₄×D₆₇	—	4	4	no	—
194	C₂²×C₆₇	—	2	4	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	2	2	no	—
197	C₂²×C₆₇	—	2	4	no	—
198	C₂²×C₆₇	—	2	2	no	—
199	C₂²×C₆₇	—	2	2	no	—
200	C₂²×C₆₇	—	2	4	no	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	—	2	1	no	—
203	C₂²×C₆₇	—	8	4	no	—
204	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
205	C₂×D₆₇	—	2	2	no	—
206	C₂×D₆₇	—	2	2	no	—
207	C₂×D₆₇	—	2	4	no	—
208	C₂×D₆₇	—	2	4	no	—
209	C₂×D₆₇	—	2	4	no	—
210	C₂×D₆₇	—	4	4	no	—
211	C₂×D₆₇	—	8	8	no	—
212	C₂×D₆₇	—	8	4	no	—
213	C₂×D₆₇	H(5,𝔽₂)	1	4	yes	—
214	C₄×C₆₇	—	2	4	no	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	1	no	—
217	C₄×C₆₇	—	2	1	no	—
218	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
219	Dic₆₇	—	2	2	no	—
220	Dic₆₇	—	2	2	no	—
221	Dic₆₇	—	2	4	no	—
222	Dic₆₇	—	2	2	no	—
223	C₂×C₆₇	—	4	1	no	—
224	C₂×C₆₇	—	4	1	no	—
225	C₂×C₆₇	—	4	4	no	—
226	C₂×C₆₇	—	4	1	no	—
227	C₂×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
228	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	D₆₇	—	2	4	no	—
230	D₆₇	—	4	4	no	—
231	#3537	—	67	1	no	maximal, Sylow
232	C₆₇	#3537	1	1	yes	characteristic, complemented, Sylow
233	#560	—	67	2	no	—
234	#560	—	67	2	no	—
235	#553	—	67	2	no	—
236	#553	—	67	2	no	—
237	D₄²	—	67	2	no	—
238	D₄²	—	67	2	no	—
239	D₄²	—	67	2	no	—
240	D₄²	—	67	2	no	—
241	#540	—	67	2	no	—
242	#538	—	67	4	no	—
243	#535	—	67	1	no	—
244	#535	D₆₇	1	1	yes	characteristic, complemented
245	#534	—	67	4	no	—
246	#525	—	67	1	no	—
247	C₂×#121	—	67	2	no	—
248	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
249	C₂²×D₄	—	67	4	no	—
250	C₂²×D₄	—	67	4	no	—
251	C₂²×D₄	—	67	2	no	—
252	C₂²×D₄	—	67	4	no	—
253	C₂²×D₄	—	67	1	no	—
254	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
255	C₂³×C₄	—	67	1	no	—
256	#127	—	67	2	no	—
257	#127	—	67	2	no	—
258	#127	C₂×D₆₇	1	2	yes	complemented
259	#126	—	67	4	no	—
260	#126	—	67	4	no	—
261	#125	—	67	2	no	—
262	#124	—	67	2	no	—
263	#124	C₂×D₆₇	1	2	yes	complemented
264	#123	—	67	1	no	—
265	#123	—	67	1	no	—
266	#123	—	67	4	no	—
267	#123	—	67	4	no	—
268	#123	—	67	4	no	—
269	#123	—	67	4	no	—
270	C₂²⋊Q₈	—	67	2	no	—
271	#121	—	67	2	no	—
272	#121	—	67	4	no	—
273	#121	—	67	2	no	—
274	#121	—	67	4	no	—
275	#121	—	67	4	no	—
276	#121	—	67	4	no	—
277	#121	—	67	4	no	—
278	#121	—	67	2	no	—
279	#121	—	67	2	no	—
280	#121	—	67	2	no	—
281	#121	—	67	4	no	—
282	#121	—	67	4	no	—
283	#121	—	67	4	no	—
284	#121	C₂×D₆₇	1	2	yes	complemented
285	#121	C₂×D₆₇	1	2	yes	complemented
286	#120	—	67	4	no	—
287	#120	—	67	1	no	—
288	#120	—	67	1	no	—
289	#120	—	67	2	no	—
290	#120	—	67	4	no	—
291	#120	—	67	2	no	—
292	#120	—	67	4	no	—
293	#120	—	67	4	no	—
294	#120	C₂×D₆₇	1	2	yes	complemented
295	#120	C₂×D₆₇	1	2	yes	complemented
296	C₄×D₄	—	67	2	no	—
297	C₄×D₄	—	67	2	no	—
298	C₄×D₄	—	67	2	no	—
299	C₄×D₄	—	67	2	no	—
300	C₄×D₄	—	67	4	no	—
301	C₄×D₄	—	67	4	no	—
302	#117	—	67	1	no	—
303	#117	—	67	1	no	—
304	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
305	C₂×C₄⋊C₄	—	67	2	no	—
306	C₂×C₂²⋊C₄	—	67	4	no	—
307	C₂⁴	—	67	2	no	—
308	C₂⁴	—	67	4	no	—
309	C₂⁴	—	67	1	no	—
310	C₂⁴	C₂²×D₆₇	1	2	yes	—
311	#41	—	4	2	no	—
312	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	268	2	no	—
315	C₂×D₄	—	268	8	no	—
316	C₂×D₄	—	268	8	no	—
317	C₂×D₄	—	268	8	no	—
318	C₂×D₄	—	268	4	no	—
319	C₂×D₄	—	67	4	no	—
320	C₂×D₄	—	67	4	no	—
321	C₂×D₄	—	67	4	no	—
322	C₂×D₄	—	67	4	no	—
323	C₂×D₄	—	67	4	no	—
324	C₂×D₄	—	67	2	no	—
325	C₂×D₄	—	67	4	no	—
326	C₂×D₄	—	67	2	no	—
327	C₂×D₄	—	67	2	no	—
328	C₂×D₄	—	67	4	no	—
329	C₂×D₄	—	67	2	no	—
330	C₂×D₄	C₂²×D₆₇	1	2	yes	—
331	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
333	C₂×D₄	C₂²×D₆₇	1	2	yes	—
334	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
335	C₂×D₄	C₂²×D₆₇	1	4	yes	—
336	C₂×D₄	C₂²×D₆₇	1	4	yes	—
337	C₂²×C₄	—	268	2	no	—
338	C₂²×C₄	—	67	4	no	—
339	C₂²×C₄	—	67	1	no	—
340	C₂²×C₄	—	67	2	no	—
341	C₂²×C₄	—	67	4	no	—
342	C₂²×C₄	—	67	4	no	—
343	C₂²×C₄	—	67	2	no	—
344	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
347	C₄⋊C₄	—	67	2	no	—
348	C₄⋊C₄	—	67	4	no	—
349	C₄⋊C₄	—	67	2	no	—
350	C₄⋊C₄	—	67	2	no	—
351	C₄⋊C₄	—	67	2	no	—
352	C₄⋊C₄	—	67	4	no	—
353	C₄⋊C₄	—	67	4	no	—
354	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
355	C₂²⋊C₄	—	67	4	no	—
356	C₂²⋊C₄	—	67	2	no	—
357	C₂²⋊C₄	—	67	1	no	—
358	C₂²⋊C₄	—	67	1	no	—
359	C₂²⋊C₄	—	67	4	no	—
360	C₂²⋊C₄	—	67	2	no	—
361	C₂²⋊C₄	—	67	2	no	—
362	C₂²⋊C₄	—	67	4	no	—
363	C₂²⋊C₄	—	67	4	no	—
364	C₂²⋊C₄	—	67	2	no	—
365	C₂²⋊C₄	—	67	2	no	—
366	C₂²⋊C₄	—	67	4	no	—
367	C₂²⋊C₄	—	67	4	no	—
368	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
369	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
371	C₄²	—	67	2	no	—
372	C₄²	—	67	2	no	—
373	C₄²	C₂²×D₆₇	1	2	yes	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	268	1	no	—
377	C₂³	—	268	4	no	—
378	C₂³	—	268	4	no	—
379	C₂³	—	268	2	no	—
380	C₂³	—	268	4	no	—
381	C₂³	—	67	2	no	—
382	C₂³	—	67	4	no	—
383	C₂³	—	134	4	no	—
384	C₂³	—	134	8	no	—
385	C₂³	C₂³×D₆₇	1	1	yes	characteristic
386	C₂³	C₂³×D₆₇	1	4	yes	—
387	C₂³	C₂³×D₆₇	1	1	yes	characteristic
388	C₂³	C₂³×D₆₇	1	1	yes	characteristic
389	Q₈	—	4	1	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	268	2	no	—
398	D₄	—	268	4	no	—
399	D₄	—	268	4	no	—
400	D₄	—	268	4	no	—
401	D₄	—	268	4	no	—
402	D₄	—	268	4	no	—
403	D₄	—	134	8	no	—
404	D₄	—	134	4	no	—
405	D₄	—	134	8	no	—
406	D₄	—	134	4	no	—
407	D₄	—	134	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	268	2	no	—
412	C₂×C₄	—	268	4	no	—
413	C₂×C₄	—	268	4	no	—
414	C₂×C₄	—	268	1	no	—
415	C₂×C₄	—	268	4	no	—
416	C₂×C₄	—	67	2	no	—
417	C₂×C₄	—	67	2	no	—
418	C₂×C₄	—	67	4	no	—
419	C₂×C₄	—	67	2	no	—
420	C₂×C₄	—	134	4	no	—
421	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₆₇	1	4	yes	—
424	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
426	C₂²	—	2	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	268	4	no	—
437	C₂²	—	536	4	no	—
438	C₂²	—	536	8	no	—
439	C₂²	—	67	4	no	—
440	C₂²	—	134	4	no	—
441	C₂²	—	134	4	no	—
442	C₂²	—	134	4	no	—
443	C₂²	—	134	2	no	—
444	C₂²	—	134	2	no	—
445	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	134	2	no	—
451	C₄	—	134	4	no	—
452	C₄	—	134	2	no	—
453	C₄	—	134	2	no	—
454	C₄	#14524088	1	2	yes	—
455	C₂	—	4	1	no	—
456	C₂	—	4	4	no	—
457	C₂	—	4	1	no	—
458	C₂	—	4	1	no	—
459	C₂	—	268	4	no	—
460	C₂	—	134	4	no	—
461	C₂	H(5,𝔽₂)×D₆₇	1	2	yes	—
462	C₂	C₂×#14524088	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#535×C₆₇	C₂
hypercenter	#535	D₆₇
hypocenter	C₆₇	#3537
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #16864135	C₂	semidirect
2. #16864133	C₂	semidirect
3. #16864093	C₂	semidirect
4. #16864090	C₂	semidirect
5. #16864031	C₂	semidirect
6. #16864030	C₂	semidirect
7. D₄×C₂²⋊D₆₇	C₂	semidirect
8. #16864028	C₂	semidirect
9. #16863999	C₂	semidirect
10. #16863980	C₂	semidirect
11. #16863960	C₂	semidirect
12. #16863956	C₂	semidirect
13. #16863903	C₂	semidirect
14. #121×D₆₇	C₂	semidirect
15. #535×C₆₇	C₂	semidirect
16. C₂²×D₂₆₈	C₂²	semidirect
17. C₂²×C₂²⋊D₆₇	C₂²	semidirect
18. C₂×D₄×D₆₇	C₂²	semidirect
19. C₂×D₄×D₆₇	C₂²	semidirect
20. C₂×D₄×D₆₇	C₂²	semidirect
21. C₂²×C₄×D₆₇	C₂²	semidirect
22. #14524039	C₂²	semidirect
23. #14524039	C₂²	semidirect
24. #14524037	C₂²	semidirect
25. #14524036	C₂²	semidirect
26. #14524034	C₂²	semidirect
27. #14524032	C₂²	semidirect
28. #14524027	C₂²	semidirect
29. #14524025	C₂²	semidirect
30. #14524025	C₂²	semidirect
31. #14524024	C₂²	semidirect
32. #14524024	C₂²	semidirect
33. #14524024	C₂²	semidirect
34. #14524019	C₂²	semidirect
35. #14524018	C₂²	semidirect
36. #14524017	C₂²	semidirect
37. #14524017	C₂²	semidirect
38. #14524016	C₂²	semidirect
39. #14524016	C₂²	semidirect
40. #14524016	C₂²	semidirect
41. #14524015	C₂²	semidirect
42. #14524015	C₂²	semidirect
43. #14524015	C₂²	semidirect
44. #14524014	C₂²	semidirect
45. #14524014	C₂²	semidirect
46. #14524014	C₂²	semidirect
47. #14524014	C₂²	semidirect
48. #14524013	C₂²	semidirect
49. #14524012	C₂²	semidirect
50. #14524011	C₂²	semidirect
51. #14524011	C₂²	semidirect
52. #14524011	C₂²	semidirect
53. #14524011	C₂²	semidirect
54. #14524011	C₂²	semidirect
55. #14524011	C₂²	semidirect
56. C₄×D₂₆₈	C₂²	semidirect
57. D₄×Dic₆₇	C₂²	semidirect
58. #14524005	C₂²	semidirect
59. C₄×C₂²⋊D₆₇	C₂²	semidirect
60. C₄×C₂²⋊D₆₇	C₂²	semidirect
61. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
62. #14524002	C₂²	semidirect
63. #14524002	C₂²	semidirect
64. C₄⋊C₄×D₆₇	C₂²	semidirect
65. C₂²⋊C₄×D₆₇	C₂²	semidirect
66. C₂×#41×C₆₇	C₂²	semidirect
67. C₂²×D₄×C₆₇	C₂²	semidirect
68. #127×C₆₇	C₂²	semidirect
69. #124×C₆₇	C₂²	semidirect
70. #121×C₆₇	C₂²	semidirect
71. #121×C₆₇	C₂²	semidirect
72. #120×C₆₇	C₂²	semidirect
73. #120×C₆₇	C₂²	semidirect
74. #117×C₆₇	C₂²	semidirect
232. C₆₇	#3537	semidirect
244. #535	D₆₇	semidirect
248. C₂×#41	C₂×D₆₇	semidirect
254. C₂²×D₄	C₂×D₆₇	semidirect
258. #127	C₂×D₆₇	semidirect
263. #124	C₂×D₆₇	semidirect
284. #121	C₂×D₆₇	semidirect
285. #121	C₂×D₆₇	semidirect
294. #120	C₂×D₆₇	semidirect
295. #120	C₂×D₆₇	semidirect
304. #117	C₂×D₆₇	semidirect