Subgroups — #22573934

Order 8576.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864111	C₂	1	2	yes	maximal, complemented
2	#16864096	C₂	1	2	yes	maximal, complemented
3	#16864096	C₂	1	2	yes	maximal, complemented
4	#16864072	C₂	1	4	yes	maximal, complemented
5	#16864051	C₂	1	2	yes	maximal, complemented
6	#16864036	C₂	1	4	yes	maximal, complemented
7	#16864024	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864011	C₂	1	2	yes	maximal, complemented
9	#16863997	C₂	1	2	yes	maximal, complemented
10	#16863963	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863943	C₂	1	2	yes	maximal, complemented
12	#16863928	C₂	1	2	yes	maximal, complemented
13	#16863908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14524014	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863876	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11761628	C₂²	1	1	yes	characteristic
19	C₂×#11761628	C₂²	1	4	yes	complemented
20	C₂²×C₂²⋊D₆₇	C₂²	1	2	yes	—
21	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
22	#14524043	C₂²	1	2	yes	complemented
23	#14524042	C₂²	1	2	yes	complemented
24	#14524039	C₂²	1	2	yes	complemented
25	#14524036	C₂²	1	4	yes	complemented
26	#14524036	C₂²	1	4	yes	complemented
27	#14524035	C₂²	1	2	yes	complemented
28	#14524034	C₂²	1	2	yes	complemented
29	#14524030	C₂²	1	2	yes	complemented
30	#14524029	C₂²	1	4	yes	complemented
31	#14524029	C₂²	1	4	yes	complemented
32	#14524027	C₂²	1	2	yes	—
33	#14524026	C₂²	1	4	yes	complemented
34	#14524026	C₂²	1	4	yes	complemented
35	#14524025	C₂²	1	4	yes	complemented
36	#14524025	C₂²	1	4	yes	complemented
37	#14524023	C₂²	1	1	yes	characteristic, complemented
38	#14524023	C₂²	1	1	yes	characteristic, complemented
39	#14524022	C₂²	1	4	yes	complemented
40	#14524020	C₂²	1	4	yes	—
41	#14524018	C₂²	1	1	yes	characteristic, complemented
42	#14524018	C₂²	1	1	yes	characteristic, complemented
43	#14524017	C₂²	1	4	yes	complemented
44	#14524016	C₂²	1	4	yes	complemented
45	#14524016	C₂²	1	4	yes	complemented
46	#14524014	C₂²	1	2	yes	—
47	#14524014	C₂²	1	2	yes	—
48	#14524014	C₂²	1	2	yes	—
49	#14524014	C₂²	1	2	yes	—
50	#14524014	C₂²	1	2	yes	complemented
51	#14524014	C₂²	1	2	yes	complemented
52	#14524013	C₂²	1	2	yes	—
53	#14524012	C₂²	1	4	yes	—
54	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
55	C₄×D₂₆₈	C₂²	1	2	yes	complemented
56	C₄×D₂₆₈	C₂²	1	2	yes	complemented
57	C₄×D₂₆₈	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
60	(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	—
61	#14524002	C₂²	1	1	yes	characteristic
62	#14524002	C₂²	1	4	yes	complemented
63	#14524001	C₂²	1	1	yes	characteristic, complemented
64	#14524001	C₂²	1	2	yes	complemented
65	#14524001	C₂²	1	1	yes	characteristic, complemented
66	#14524000	C₂²	1	2	yes	complemented
67	#14523999	C₂²	1	2	yes	—
68	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
70	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
74	C₄²×D₆₇	C₂²	1	2	yes	complemented
75	C₂²×D₄×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
77	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
78	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
79	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
80	#117×C₆₇	C₂²	1	1	yes	characteristic
81	#117×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
83	C₂³×D₆₇	C₂³	1	1	yes	characteristic
84	#11761628	—	2	4	no	—
85	#11761628	—	4	8	no	—
86	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₃₄	C₂³	1	4	yes	—
88	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
89	C₂×D₂₆₈	C₂³	1	2	yes	—
90	C₂×D₂₆₈	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₆₇	—	4	4	no	—
92	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₆₇	C₂³	1	4	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	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
98	C₂²×Dic₆₇	C₂³	1	2	yes	—
99	C₂×C₄×D₆₇	—	2	4	no	—
100	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₆₇	C₂³	1	2	yes	—
102	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₆₇	C₂³	1	2	yes	—
104	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₆₇	C₂³	1	2	yes	—
107	C₂×C₄×D₆₇	C₂³	1	4	yes	—
108	C₄⋊Dic₆₇	C₂³	1	2	yes	—
109	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₆₇	C₂³	1	2	yes	—
112	C₄⋊Dic₆₇	C₂³	1	2	yes	—
113	C₄⋊Dic₆₇	C₂³	1	4	yes	—
114	C₄⋊Dic₆₇	C₂³	1	2	yes	—
115	Dic₆₇⋊C₄	C₂³	1	2	yes	—
116	Dic₆₇⋊C₄	C₂³	1	2	yes	—
117	Dic₆₇⋊C₄	C₂³	1	4	yes	—
118	Dic₆₇⋊C₄	C₂³	1	4	yes	—
119	Dic₆₇⋊C₄	C₂³	1	4	yes	—
120	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
121	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
122	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
124	C₂²⋊Dic₆₇	C₂³	1	4	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	2	yes	—
129	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
132	C₄×Dic₆₇	C₂³	1	2	yes	—
133	C₄×Dic₆₇	C₂³	1	2	yes	—
134	C₄×Dic₆₇	C₂³	1	2	yes	—
135	C₄×Dic₆₇	C₂³	1	4	yes	—
136	C₂⁴×C₆₇	C₂³	1	2	yes	—
137	C₂×D₄×C₆₇	—	2	4	no	—
138	C₂×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂×D₄×C₆₇	C₂³	1	2	yes	—
140	C₂²×C₄×C₆₇	C₂³	1	4	yes	—
141	C₂²×C₄×C₆₇	C₂³	1	4	yes	—
142	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₄²×C₆₇	C₂³	1	2	yes	—
152	C₄²×C₆₇	C₂³	1	2	yes	—
153	C₂³×C₆₇	—	2	4	no	—
154	C₂³×C₆₇	—	4	2	no	—
155	C₂³×C₆₇	—	4	2	no	—
156	C₂³×C₆₇	C₂⁴	1	4	yes	—
157	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
158	C₂²×D₆₇	—	2	2	no	—
159	C₂²×D₆₇	—	2	2	no	—
160	C₂²×D₆₇	—	4	1	no	—
161	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
162	C₂²×D₆₇	C₂⁴	1	2	yes	—
163	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
164	D₄×C₆₇	—	2	4	no	—
165	D₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	4	4	no	—
167	C₂×C₄×C₆₇	—	4	4	no	—
168	C₂×C₄×C₆₇	#41	1	4	yes	complemented
169	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
171	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
172	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
173	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
175	C₂²⋊D₆₇	—	2	4	no	—
176	C₂²⋊D₆₇	—	2	8	no	—
177	C₂²⋊D₆₇	—	4	4	no	—
178	C₂²⋊D₆₇	—	4	4	no	—
179	C₂²⋊D₆₇	—	4	4	no	—
180	C₂×Dic₆₇	—	2	2	no	—
181	C₂×Dic₆₇	—	4	2	no	—
182	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₆₇	C₂⁴	1	2	yes	—
184	C₂×Dic₆₇	C₂⁴	1	2	yes	—
185	C₂×Dic₆₇	C₂⁴	1	2	yes	—
186	C₂×Dic₆₇	C₂⁴	1	4	yes	—
187	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
188	D₂₆₈	—	2	4	no	—
189	D₂₆₈	—	2	2	no	—
190	D₂₆₈	—	4	2	no	—
191	C₄×D₆₇	—	2	4	no	—
192	C₄×D₆₇	—	2	2	no	—
193	C₄×D₆₇	—	2	2	no	—
194	C₄×D₆₇	—	2	2	no	—
195	C₄×D₆₇	—	2	2	no	—
196	C₄×D₆₇	—	2	4	no	—
197	C₄×D₆₇	—	4	2	no	—
198	C₄×D₆₇	—	4	4	no	—
199	Dic₁₃₄	—	2	2	no	—
200	Dic₁₃₄	—	4	4	no	—
201	C₂²×C₆₇	—	2	1	no	—
202	C₂²×C₆₇	—	2	1	no	—
203	C₂²×C₆₇	—	2	4	no	—
204	C₂²×C₆₇	—	2	4	no	—
205	C₂²×C₆₇	—	2	4	no	—
206	C₂²×C₆₇	—	8	4	no	—
207	C₂²×C₆₇	C₂×#41	1	2	yes	—
208	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
209	C₂×D₆₇	—	2	1	no	—
210	C₂×D₆₇	—	2	1	no	—
211	C₂×D₆₇	—	2	1	no	—
212	C₂×D₆₇	—	2	2	no	—
213	C₂×D₆₇	—	2	2	no	—
214	C₂×D₆₇	—	2	1	no	—
215	C₂×D₆₇	—	2	1	no	—
216	C₂×D₆₇	—	2	2	no	—
217	C₂×D₆₇	—	4	4	no	—
218	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
219	C₄×C₆₇	—	2	2	no	—
220	C₄×C₆₇	—	2	2	no	—
221	C₄×C₆₇	—	2	2	no	—
222	C₄×C₆₇	—	2	2	no	—
223	C₄×C₆₇	C₂×#41	1	2	yes	—
224	C₄×C₆₇	C₂×#41	1	2	yes	—
225	Dic₆₇	—	2	2	no	—
226	Dic₆₇	—	2	1	no	—
227	Dic₆₇	—	2	1	no	—
228	Dic₆₇	—	2	2	no	—
229	Dic₆₇	—	2	4	no	—
230	Dic₆₇	—	2	2	no	—
231	C₂×C₆₇	—	2	2	no	—
232	C₂×C₆₇	—	4	4	no	—
233	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
234	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₆₇	#585	1	1	yes	characteristic
236	D₆₇	—	2	2	no	—
237	D₆₇	—	4	2	no	—
238	D₆₇	—	4	1	no	—
239	#3494	—	67	1	no	maximal, Sylow
240	C₆₇	#3494	1	1	yes	characteristic, complemented, Sylow
241	#555	—	67	2	no	—
242	#553	—	67	2	no	—
243	#553	—	67	2	no	—
244	#551	—	67	4	no	—
245	#547	—	67	2	no	—
246	#546	—	67	4	no	—
247	#544	—	67	1	no	—
248	#542	—	67	2	no	—
249	#540	—	67	2	no	—
250	#535	—	67	1	no	—
251	#532	—	67	2	no	—
252	#529	—	67	2	no	—
253	#525	—	67	1	no	—
254	C₂×#121	—	67	1	no	—
255	#520	—	67	1	no	—
256	#518	D₆₇	1	1	yes	characteristic, complemented
257	C₂×#117	—	67	1	no	—
258	C₂×#41	—	67	4	no	—
259	C₂×#41	—	67	1	no	—
260	C₂²×D₄	—	67	2	no	—
261	C₂²×D₄	C₂×D₆₇	1	1	yes	characteristic
262	C₂³×C₄	—	67	1	no	—
263	C₄⋊Q₈	—	67	2	no	—
264	C₄⋊Q₈	—	67	2	no	—
265	#127	—	67	2	no	—
266	#126	—	67	4	no	—
267	#126	—	67	4	no	—
268	#125	—	67	2	no	—
269	#125	—	67	2	no	—
270	#124	—	67	2	no	—
271	#124	—	67	4	no	—
272	#124	—	67	4	no	—
273	#123	—	67	4	no	—
274	#123	—	67	4	no	—
275	#123	—	67	2	no	—
276	#123	—	67	4	no	—
277	#123	—	67	4	no	—
278	C₂²⋊Q₈	—	67	4	no	—
279	C₂²⋊Q₈	—	67	1	no	—
280	C₂²⋊Q₈	—	67	1	no	—
281	C₂²⋊Q₈	—	67	4	no	—
282	#121	—	67	2	no	—
283	#121	—	67	2	no	—
284	#121	—	67	2	no	—
285	#121	—	67	2	no	—
286	#121	—	67	2	no	—
287	#121	—	67	2	no	—
288	#121	—	67	4	no	—
289	#121	—	67	1	no	—
290	#121	—	67	1	no	—
291	#121	—	67	4	no	—
292	#121	—	67	4	no	—
293	#120	—	67	4	no	—
294	#120	—	67	2	no	—
295	C₄×Q₈	—	67	2	no	—
296	C₄×D₄	—	67	4	no	—
297	C₄×D₄	—	67	4	no	—
298	C₄×D₄	—	67	4	no	—
299	C₄×D₄	—	67	2	no	—
300	C₄×D₄	—	67	2	no	—
301	C₄×D₄	—	67	2	no	—
302	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
303	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
304	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
305	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
306	#117	—	67	1	no	—
307	#117	—	67	4	no	—
308	#117	—	67	1	no	—
309	#117	—	67	1	no	—
310	#117	—	67	2	no	—
311	#117	—	67	2	no	—
312	#117	—	67	2	no	—
313	#117	C₂×D₆₇	1	1	yes	characteristic
314	#117	C₂×D₆₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	67	1	no	—
316	C₂×C₄⋊C₄	—	67	1	no	—
317	C₂×C₄⋊C₄	—	67	1	no	—
318	C₂×C₄⋊C₄	—	67	2	no	—
319	C₂×C₂²⋊C₄	—	67	2	no	—
320	C₂×C₂²⋊C₄	—	67	2	no	—
321	C₂×C₂²⋊C₄	C₂×D₆₇	1	4	yes	—
322	C₂×C₄²	—	67	2	no	—
323	C₂⁴	—	67	1	no	—
324	C₂⁴	C₂²×D₆₇	1	2	yes	—
325	#41	—	268	8	no	—
326	#41	—	134	4	no	—
327	C₂×Q₈	—	67	4	no	—
328	C₂×Q₈	—	67	1	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	268	4	no	—
331	C₂×D₄	—	67	4	no	—
332	C₂×D₄	—	67	4	no	—
333	C₂×D₄	—	67	4	no	—
334	C₂×D₄	—	67	2	no	—
335	C₂×D₄	—	67	4	no	—
336	C₂×D₄	—	67	2	no	—
337	C₂×D₄	—	67	1	no	—
338	C₂×D₄	—	67	2	no	—
339	C₂×D₄	C₂²×D₆₇	1	2	yes	—
340	C₂×D₄	C₂²×D₆₇	1	2	yes	—
341	C₂²×C₄	—	67	2	no	—
342	C₂²×C₄	—	67	2	no	—
343	C₂²×C₄	—	67	4	no	—
344	C₂²×C₄	—	67	1	no	—
345	C₂²×C₄	—	67	1	no	—
346	C₂²×C₄	—	67	2	no	—
347	C₂²×C₄	—	67	1	no	—
348	C₂²×C₄	—	67	2	no	—
349	C₂²×C₄	—	67	1	no	—
350	C₂²×C₄	—	67	1	no	—
351	C₂²×C₄	—	134	4	no	—
352	C₂²×C₄	C₂²×D₆₇	1	4	yes	—
353	C₂²×C₄	C₂²×D₆₇	1	4	yes	—
354	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
355	C₄⋊C₄	—	67	2	no	—
356	C₄⋊C₄	—	67	1	no	—
357	C₄⋊C₄	—	67	1	no	—
358	C₄⋊C₄	—	67	2	no	—
359	C₄⋊C₄	—	67	2	no	—
360	C₄⋊C₄	—	67	2	no	—
361	C₄⋊C₄	—	67	4	no	—
362	C₄⋊C₄	—	67	2	no	—
363	C₄⋊C₄	—	67	4	no	—
364	C₄⋊C₄	—	67	4	no	—
365	C₄⋊C₄	—	67	4	no	—
366	C₄⋊C₄	—	67	2	no	—
367	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
371	C₂²⋊C₄	—	67	2	no	—
372	C₂²⋊C₄	—	67	4	no	—
373	C₂²⋊C₄	—	67	4	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	4	no	—
379	C₂²⋊C₄	—	67	2	no	—
380	C₂²⋊C₄	—	67	2	no	—
381	C₂²⋊C₄	—	67	2	no	—
382	C₂²⋊C₄	—	67	2	no	—
383	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
384	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
386	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
387	C₄²	—	67	2	no	—
388	C₄²	—	67	2	no	—
389	C₄²	—	67	2	no	—
390	C₄²	—	67	4	no	—
391	C₄²	C₂²×D₆₇	1	2	yes	—
392	C₄²	C₂²×D₆₇	1	2	yes	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	268	1	no	—
397	C₂³	—	67	1	no	—
398	C₂³	—	67	1	no	—
399	C₂³	—	67	2	no	—
400	C₂³	—	134	2	no	—
401	C₂³	—	134	2	no	—
402	C₂³	C₂³×D₆₇	1	4	yes	—
403	C₂³	C₂³×D₆₇	1	1	yes	characteristic
404	Q₈	—	268	4	no	—
405	Q₈	—	134	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	268	2	no	—
409	D₄	—	268	4	no	—
410	D₄	—	268	4	no	—
411	D₄	—	268	4	no	—
412	D₄	—	134	4	no	—
413	D₄	—	134	8	no	—
414	D₄	—	134	4	no	—
415	D₄	—	134	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	268	4	no	—
419	C₂×C₄	—	268	2	no	—
420	C₂×C₄	—	268	2	no	—
421	C₂×C₄	—	67	1	no	—
422	C₂×C₄	—	67	2	no	—
423	C₂×C₄	—	67	2	no	—
424	C₂×C₄	—	67	2	no	—
425	C₂×C₄	—	67	4	no	—
426	C₂×C₄	—	67	1	no	—
427	C₂×C₄	—	134	4	no	—
428	C₂×C₄	—	134	2	no	—
429	C₂×C₄	—	134	2	no	—
430	C₂×C₄	—	134	2	no	—
431	C₂×C₄	—	134	2	no	—
432	C₂×C₄	—	134	2	no	—
433	C₂×C₄	—	134	4	no	—
434	C₂×C₄	#11761628	1	4	yes	complemented
435	C₂×C₄	C₂³×D₆₇	1	2	yes	—
436	C₂×C₄	C₂³×D₆₇	1	2	yes	—
437	C₂×C₄	C₂³×D₆₇	1	2	yes	—
438	C₂×C₄	C₂³×D₆₇	1	2	yes	—
439	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	268	4	no	—
448	C₂²	—	67	2	no	—
449	C₂²	—	134	1	no	—
450	C₂²	—	134	2	no	—
451	C₂²	—	134	2	no	—
452	C₂²	—	134	1	no	—
453	C₂²	—	134	2	no	—
454	C₂²	—	134	1	no	—
455	C₂²	—	134	1	no	—
456	C₂²	—	134	1	no	—
457	C₂²	C₂×#11761628	1	2	yes	—
458	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	134	1	no	—
464	C₄	—	134	1	no	—
465	C₄	—	134	2	no	—
466	C₄	—	134	4	no	—
467	C₄	—	134	2	no	—
468	C₄	—	134	2	no	—
469	C₄	C₂×#11761628	1	2	yes	—
470	C₄	C₂×#11761628	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	—	268	1	no	—
474	C₂	—	268	2	no	—
475	C₂	—	134	2	no	—
476	C₂	C₂²×#11761628	1	1	yes	characteristic
477	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
478	C₂	#16864231	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#518×C₆₇	C₂
hypercenter	#518	D₆₇
hypocenter	C₆₇	#3494
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #16864111	C₂	semidirect
2. #16864096	C₂	semidirect
3. #16864096	C₂	semidirect
4. #16864072	C₂	semidirect
5. #16864051	C₂	semidirect
6. #16864036	C₂	semidirect
7. #16864024	C₂	semidirect
8. #16864011	C₂	semidirect
9. #16863997	C₂	semidirect
10. #16863963	C₂	semidirect
11. #16863943	C₂	semidirect
12. #16863928	C₂	semidirect
13. #16863908	C₂	semidirect
14. C₂×#14524014	C₂	semidirect
15. #16863876	C₂	semidirect
16. #117×D₆₇	C₂	semidirect
17. #518×C₆₇	C₂	semidirect
19. C₂×#11761628	C₂²	semidirect
22. #14524043	C₂²	semidirect
23. #14524042	C₂²	semidirect
24. #14524039	C₂²	semidirect
25. #14524036	C₂²	semidirect
26. #14524036	C₂²	semidirect
27. #14524035	C₂²	semidirect
28. #14524034	C₂²	semidirect
29. #14524030	C₂²	semidirect
30. #14524029	C₂²	semidirect
31. #14524029	C₂²	semidirect
33. #14524026	C₂²	semidirect
34. #14524026	C₂²	semidirect
35. #14524025	C₂²	semidirect
36. #14524025	C₂²	semidirect
37. #14524023	C₂²	semidirect
38. #14524023	C₂²	semidirect
39. #14524022	C₂²	semidirect
41. #14524018	C₂²	semidirect
42. #14524018	C₂²	semidirect
43. #14524017	C₂²	semidirect
44. #14524016	C₂²	semidirect
45. #14524016	C₂²	semidirect
50. #14524014	C₂²	semidirect
51. #14524014	C₂²	semidirect
54. C₄×Dic₁₃₄	C₂²	semidirect
55. C₄×D₂₆₈	C₂²	semidirect
56. C₄×D₂₆₈	C₂²	semidirect
57. C₄×D₂₆₈	C₂²	semidirect
58. C₄×C₂²⋊D₆₇	C₂²	semidirect
59. C₄×C₂²⋊D₆₇	C₂²	semidirect
62. #14524002	C₂²	semidirect
63. #14524001	C₂²	semidirect
64. #14524001	C₂²	semidirect
65. #14524001	C₂²	semidirect
66. #14524000	C₂²	semidirect
69. C₄⋊C₄×D₆₇	C₂²	semidirect
70. C₄⋊C₄×D₆₇	C₂²	semidirect
71. C₄⋊C₄×D₆₇	C₂²	semidirect
74. C₄²×D₆₇	C₂²	semidirect
76. C₄×D₄×C₆₇	C₂²	semidirect
77. C₄×D₄×C₆₇	C₂²	semidirect
78. C₄×D₄×C₆₇	C₂²	semidirect
79. C₄×D₄×C₆₇	C₂²	semidirect
168. C₂×C₄×C₆₇	#41	semidirect
240. C₆₇	#3494	semidirect
256. #518	D₆₇	semidirect
302. C₄×D₄	C₂×D₆₇	semidirect
303. C₄×D₄	C₂×D₆₇	semidirect
304. C₄×D₄	C₂×D₆₇	semidirect
305. C₄×D₄	C₂×D₆₇	semidirect
434. C₂×C₄	#11761628	semidirect