Subgroups — #22574054

Order 8576.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864131	C₂	1	2	yes	maximal, complemented
2	#16864129	C₂	1	2	yes	maximal, complemented
3	#16864118	C₂	1	2	yes	maximal, complemented
4	#16864109	C₂	1	2	yes	maximal, complemented
5	#16864094	C₂	1	2	yes	maximal, complemented
6	#16864090	C₂	1	2	yes	maximal, complemented
7	#16864067	C₂	1	2	yes	maximal, complemented
8	#16864047	C₂	1	2	yes	maximal, complemented
9	#16863979	C₂	1	4	yes	maximal, complemented
10	#16863965	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863960	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863949	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863942	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863905	C₂	1	4	yes	maximal, complemented
15	#16863877	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524005	C₂	1	1	yes	maximal, characteristic, complemented
17	#520×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×D₂₆₈	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₆₇	C₂²	1	2	yes	—
22	#14524042	C₂²	1	1	yes	characteristic, complemented
23	#14524042	C₂²	1	1	yes	characteristic, complemented
24	#14524041	C₂²	1	1	yes	characteristic, complemented
25	#14524040	C₂²	1	2	yes	—
26	#14524039	C₂²	1	2	yes	—
27	#14524039	C₂²	1	1	yes	characteristic, complemented
28	#14524038	C₂²	1	4	yes	complemented
29	#14524037	C₂²	1	4	yes	complemented
30	#14524034	C₂²	1	1	yes	characteristic, complemented
31	#14524034	C₂²	1	1	yes	characteristic, complemented
32	#14524032	C₂²	1	2	yes	—
33	#14524032	C₂²	1	1	yes	characteristic, complemented
34	#14524031	C₂²	1	2	yes	—
35	#14524031	C₂²	1	4	yes	complemented
36	#14524030	C₂²	1	1	yes	characteristic, complemented
37	#14524029	C₂²	1	4	yes	complemented
38	#14524028	C₂²	1	4	yes	complemented
39	#14524028	C₂²	1	4	yes	complemented
40	#14524026	C₂²	1	4	yes	complemented
41	#14524025	C₂²	1	4	yes	complemented
42	#14524021	C₂²	1	4	yes	complemented
43	#14524020	C₂²	1	2	yes	—
44	#14524020	C₂²	1	2	yes	—
45	#14524018	C₂²	1	2	yes	—
46	#14524018	C₂²	1	2	yes	—
47	#14524017	C₂²	1	2	yes	—
48	#14524017	C₂²	1	2	yes	—
49	#14524017	C₂²	1	4	yes	complemented
50	#14524016	C₂²	1	4	yes	complemented
51	#14524016	C₂²	1	4	yes	complemented
52	#14524015	C₂²	1	2	yes	—
53	#14524015	C₂²	1	2	yes	—
54	#14524013	C₂²	1	4	yes	—
55	#14524011	C₂²	1	4	yes	—
56	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
57	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
58	#14524008	C₂²	1	2	yes	complemented
59	C₄×D₂₆₈	C₂²	1	4	yes	complemented
60	#14524005	C₂²	1	2	yes	—
61	#14524005	C₂²	1	2	yes	—
62	#14524005	C₂²	1	2	yes	—
63	#14524005	C₂²	1	2	yes	—
64	#14524005	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	—
66	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
69	#14524002	C₂²	1	1	yes	characteristic
70	#14524001	C₂²	1	2	yes	complemented
71	#14524000	C₂²	1	4	yes	complemented
72	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
74	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
75	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
77	C₄×D₄×C₆₇	C₂²	1	4	yes	—
78	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
79	#117×C₆₇	C₂²	1	1	yes	characteristic
80	#117×C₆₇	C₂²	1	2	yes	complemented
81	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂³×D₆₇	C₂³	1	2	yes	—
84	#11761628	—	2	4	no	—
85	#11761628	—	4	8	no	—
86	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₃₄	C₂³	1	2	yes	—
88	C₂×Dic₁₃₄	C₂³	1	2	yes	—
89	C₂×D₂₆₈	—	2	4	no	—
90	C₂×D₂₆₈	C₂³	1	2	yes	—
91	C₂×D₂₆₈	C₂³	1	2	yes	—
92	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
93	C₂×D₂₆₈	C₂³	1	4	yes	—
94	C₂×D₂₆₈	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₆₇	C₂³	1	4	yes	—
100	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
101	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₆₇	—	4	4	no	—
103	C₂×C₄×D₆₇	C₂³	1	2	yes	—
104	C₂×C₄×D₆₇	C₂³	1	4	yes	—
105	C₂×C₄×D₆₇	C₂³	1	4	yes	—
106	C₂×C₄×D₆₇	C₂³	1	4	yes	—
107	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₆₇	C₂³	1	2	yes	—
110	C₄⋊Dic₆₇	C₂³	1	2	yes	—
111	Dic₆₇⋊C₄	C₂³	1	4	yes	—
112	Dic₆₇⋊C₄	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	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
119	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
120	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
121	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₆₇)⋊C₄	C₂³	1	4	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	4	yes	—
130	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
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	4	yes	—
135	C₄×Dic₆₇	C₂³	1	2	yes	—
136	#41×C₆₇	—	2	4	no	—
137	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂²×C₄×C₆₇	C₂³	1	4	yes	—
143	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₄²×C₆₇	C₂³	1	2	yes	—
152	C₄²×C₆₇	C₂³	1	4	yes	—
153	C₂³×C₆₇	C₂⁴	1	2	yes	—
154	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
155	C₂²×D₆₇	—	2	4	no	—
156	C₂²×D₆₇	—	4	2	no	—
157	C₂²×D₆₇	—	4	2	no	—
158	C₂²×D₆₇	C₂⁴	1	4	yes	—
159	C₂²×D₆₇	C₂⁴	1	2	yes	—
160	Q₈×C₆₇	—	2	2	no	—
161	D₄×C₆₇	—	2	4	no	—
162	D₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	4	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	4	4	no	—
166	C₂×C₄×C₆₇	#41	1	4	yes	complemented
167	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
168	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
170	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
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	4	no	—
175	C₂²⋊D₆₇	—	4	4	no	—
176	C₂²⋊D₆₇	—	4	2	no	—
177	C₂²⋊D₆₇	—	4	4	no	—
178	C₂×Dic₆₇	—	2	2	no	—
179	C₂×Dic₆₇	—	4	1	no	—
180	C₂×Dic₆₇	C₂⁴	1	2	yes	—
181	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₆₇	C₂⁴	1	2	yes	—
183	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₆₇	C₂⁴	1	2	yes	—
186	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
187	D₂₆₈	—	2	4	no	—
188	D₂₆₈	—	2	4	no	—
189	D₂₆₈	—	2	2	no	—
190	D₂₆₈	—	4	4	no	—
191	D₂₆₈	—	4	4	no	—
192	C₄×D₆₇	—	2	4	no	—
193	C₄×D₆₇	—	2	8	no	—
194	C₄×D₆₇	—	4	4	no	—
195	C₄×D₆₇	—	4	4	no	—
196	Dic₁₃₄	—	2	2	no	—
197	Dic₁₃₄	—	2	4	no	—
198	Dic₁₃₄	—	4	2	no	—
199	C₂²×C₆₇	—	2	1	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	—	2	2	no	—
202	C₂²×C₆₇	—	2	2	no	—
203	C₂²×C₆₇	—	2	2	no	—
204	C₂²×C₆₇	C₂×#41	1	2	yes	—
205	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
206	C₂×D₆₇	—	2	2	no	—
207	C₂×D₆₇	—	2	4	no	—
208	C₂×D₆₇	—	2	4	no	—
209	C₂×D₆₇	—	2	2	no	—
210	C₂×D₆₇	—	2	2	no	—
211	C₂×D₆₇	—	2	4	no	—
212	C₂×D₆₇	—	4	8	no	—
213	C₄×C₆₇	—	2	2	no	—
214	C₄×C₆₇	—	2	2	no	—
215	C₄×C₆₇	—	2	4	no	—
216	C₄×C₆₇	—	2	2	no	—
217	C₄×C₆₇	C₂×#41	1	2	yes	—
218	C₄×C₆₇	C₂×#41	1	2	yes	—
219	Dic₆₇	—	2	2	no	—
220	Dic₆₇	—	2	2	no	—
221	Dic₆₇	—	2	1	no	—
222	Dic₆₇	—	2	1	no	—
223	Dic₆₇	—	2	2	no	—
224	Dic₆₇	—	2	1	no	—
225	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₆₇	—	2	2	no	—
227	C₂×C₆₇	—	4	2	no	—
228	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
229	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₆₇	#585	1	1	yes	characteristic
231	D₆₇	—	4	2	no	—
232	D₆₇	—	4	4	no	—
233	#3506	—	67	1	no	maximal, Sylow
234	C₆₇	#3506	1	1	yes	characteristic, complemented, Sylow
235	#559	—	67	2	no	—
236	#559	—	67	2	no	—
237	#556	—	67	2	no	—
238	#555	—	67	2	no	—
239	#553	—	67	2	no	—
240	#553	—	67	2	no	—
241	#550	—	67	2	no	—
242	#547	—	67	2	no	—
243	#538	—	67	4	no	—
244	#535	—	67	1	no	—
245	#535	—	67	1	no	—
246	#533	—	67	1	no	—
247	#532	—	67	1	no	—
248	#525	—	67	4	no	—
249	#520	—	67	1	no	—
250	#520	D₆₇	1	1	yes	characteristic, complemented
251	C₂×C₄×D₄	—	67	1	no	—
252	C₂×#41	—	67	4	no	—
253	C₂×#41	—	67	1	no	—
254	C₂×#41	C₂×D₆₇	1	1	yes	characteristic
255	C₂²×D₄	—	67	1	no	—
256	C₂³×C₄	—	67	2	no	—
257	C₄⋊Q₈	—	67	1	no	—
258	C₄⋊Q₈	—	67	1	no	—
259	C₄⋊Q₈	—	67	1	no	—
260	#127	—	67	1	no	—
261	#127	—	67	2	no	—
262	#127	—	67	2	no	—
263	#126	—	67	4	no	—
264	#126	—	67	4	no	—
265	#125	—	67	1	no	—
266	#125	—	67	1	no	—
267	#124	—	67	1	no	—
268	#124	—	67	2	no	—
269	#124	—	67	1	no	—
270	#124	—	67	4	no	—
271	#124	—	67	2	no	—
272	#124	—	67	4	no	—
273	#123	—	67	4	no	—
274	#123	—	67	4	no	—
275	#123	—	67	4	no	—
276	#123	—	67	4	no	—
277	C₂²⋊Q₈	—	67	4	no	—
278	C₂²⋊Q₈	—	67	2	no	—
279	C₂²⋊Q₈	—	67	2	no	—
280	#121	—	67	2	no	—
281	#121	—	67	2	no	—
282	#121	—	67	2	no	—
283	#121	—	67	2	no	—
284	#121	—	67	4	no	—
285	#121	—	67	2	no	—
286	#121	—	67	2	no	—
287	#121	—	67	4	no	—
288	#121	—	67	4	no	—
289	#120	—	67	4	no	—
290	#120	—	67	4	no	—
291	C₄×Q₈	—	67	2	no	—
292	C₄×Q₈	—	67	2	no	—
293	C₄×Q₈	—	67	2	no	—
294	C₄×Q₈	C₂×D₆₇	1	2	yes	complemented
295	C₄×D₄	—	67	4	no	—
296	C₄×D₄	—	67	4	no	—
297	C₄×D₄	—	67	2	no	—
298	C₄×D₄	—	67	2	no	—
299	C₄×D₄	—	67	2	no	—
300	C₄×D₄	—	67	2	no	—
301	C₄×D₄	—	67	2	no	—
302	C₄×D₄	—	67	2	no	—
303	C₄×D₄	—	67	2	no	—
304	C₄×D₄	—	67	4	no	—
305	C₄×D₄	C₂×D₆₇	1	4	yes	—
306	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
307	#117	—	67	1	no	—
308	#117	—	67	2	no	—
309	#117	—	67	4	no	—
310	#117	C₂×D₆₇	1	1	yes	characteristic
311	#117	C₂×D₆₇	1	2	yes	complemented
312	C₂×C₄⋊C₄	—	67	2	no	—
313	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂×D₆₇	1	2	yes	complemented
315	C₂×C₂²⋊C₄	—	67	2	no	—
316	C₂×C₄²	—	67	1	no	—
317	C₂⁴	—	67	2	no	—
318	#41	—	2	4	no	—
319	#41	—	268	8	no	—
320	#41	—	134	4	no	—
321	C₂×Q₈	—	67	2	no	—
322	C₂×Q₈	—	67	1	no	—
323	C₂×Q₈	—	67	2	no	—
324	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
325	C₂×D₄	—	67	4	no	—
326	C₂×D₄	—	67	2	no	—
327	C₂×D₄	—	67	4	no	—
328	C₂×D₄	—	67	2	no	—
329	C₂×D₄	—	67	2	no	—
330	C₂×D₄	—	67	4	no	—
331	C₂×D₄	—	67	4	no	—
332	C₂×D₄	—	67	2	no	—
333	C₂×D₄	—	67	2	no	—
334	C₂×D₄	—	67	1	no	—
335	C₂×D₄	—	134	4	no	—
336	C₂×D₄	C₂²×D₆₇	1	2	yes	—
337	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
338	C₂²×C₄	—	268	4	no	—
339	C₂²×C₄	—	67	1	no	—
340	C₂²×C₄	—	67	4	no	—
341	C₂²×C₄	—	67	4	no	—
342	C₂²×C₄	—	67	1	no	—
343	C₂²×C₄	—	67	2	no	—
344	C₂²×C₄	—	67	4	no	—
345	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
346	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
347	C₂²×C₄	C₂²×D₆₇	1	4	yes	—
348	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
349	C₄⋊C₄	—	67	1	no	—
350	C₄⋊C₄	—	67	4	no	—
351	C₄⋊C₄	—	67	1	no	—
352	C₄⋊C₄	—	67	2	no	—
353	C₄⋊C₄	—	67	2	no	—
354	C₄⋊C₄	—	67	2	no	—
355	C₄⋊C₄	—	67	2	no	—
356	C₄⋊C₄	—	67	2	no	—
357	C₄⋊C₄	—	67	2	no	—
358	C₄⋊C₄	—	67	2	no	—
359	C₄⋊C₄	—	67	2	no	—
360	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
361	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
362	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
364	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
365	C₂²⋊C₄	—	67	2	no	—
366	C₂²⋊C₄	—	67	2	no	—
367	C₂²⋊C₄	—	67	2	no	—
368	C₂²⋊C₄	—	67	4	no	—
369	C₂²⋊C₄	—	67	4	no	—
370	C₂²⋊C₄	—	67	4	no	—
371	C₂²⋊C₄	—	67	4	no	—
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	C₂²×D₆₇	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
379	C₄²	—	67	1	no	—
380	C₄²	—	67	1	no	—
381	C₄²	—	67	1	no	—
382	C₄²	—	67	1	no	—
383	C₄²	—	67	4	no	—
384	C₄²	—	67	2	no	—
385	C₄²	C₂²×D₆₇	1	4	yes	—
386	C₄²	C₂²×D₆₇	1	2	yes	—
387	C₂³	—	268	2	no	—
388	C₂³	—	268	2	no	—
389	C₂³	—	67	4	no	—
390	C₂³	—	67	2	no	—
391	C₂³	—	134	4	no	—
392	C₂³	C₂³×D₆₇	1	2	yes	—
393	C₂³	C₂³×D₆₇	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	268	2	no	—
396	Q₈	—	134	4	no	—
397	Q₈	—	134	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	268	4	no	—
401	D₄	—	268	4	no	—
402	D₄	—	268	4	no	—
403	D₄	—	268	2	no	—
404	D₄	—	268	4	no	—
405	D₄	—	134	4	no	—
406	D₄	—	134	4	no	—
407	D₄	—	134	4	no	—
408	D₄	—	134	4	no	—
409	D₄	—	134	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	268	4	no	—
414	C₂×C₄	—	268	4	no	—
415	C₂×C₄	—	268	1	no	—
416	C₂×C₄	—	67	1	no	—
417	C₂×C₄	—	67	2	no	—
418	C₂×C₄	—	67	1	no	—
419	C₂×C₄	—	67	2	no	—
420	C₂×C₄	—	67	1	no	—
421	C₂×C₄	—	67	1	no	—
422	C₂×C₄	—	67	2	no	—
423	C₂×C₄	—	134	8	no	—
424	C₂×C₄	—	134	2	no	—
425	C₂×C₄	—	134	4	no	—
426	C₂×C₄	#11761628	1	4	yes	complemented
427	C₂×C₄	C₂³×D₆₇	1	4	yes	—
428	C₂×C₄	C₂³×D₆₇	1	2	yes	—
429	C₂×C₄	C₂³×D₆₇	1	2	yes	—
430	C₂×C₄	C₂³×D₆₇	1	2	yes	—
431	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	268	8	no	—
439	C₂²	—	134	2	no	—
440	C₂²	—	134	4	no	—
441	C₂²	—	134	2	no	—
442	C₂²	—	134	4	no	—
443	C₂²	—	134	2	no	—
444	C₂²	—	134	4	no	—
445	C₂²	C₂×#11761628	1	2	yes	—
446	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	67	2	no	—
452	C₄	—	134	2	no	—
453	C₄	—	134	1	no	—
454	C₄	—	134	2	no	—
455	C₄	—	134	1	no	—
456	C₄	—	134	1	no	—
457	C₄	—	134	2	no	—
458	C₄	C₂×#11761628	1	2	yes	—
459	C₄	C₂×#11761628	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	—	268	4	no	—
463	C₂	—	268	2	no	—
464	C₂	C₂²×#11761628	1	1	yes	characteristic
465	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
466	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#520×C₆₇	C₂
hypercenter	#520	D₆₇
hypocenter	C₆₇	#3506
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #16864131	C₂	semidirect
2. #16864129	C₂	semidirect
3. #16864118	C₂	semidirect
4. #16864109	C₂	semidirect
5. #16864094	C₂	semidirect
6. #16864090	C₂	semidirect
7. #16864067	C₂	semidirect
8. #16864047	C₂	semidirect
9. #16863979	C₂	semidirect
10. #16863965	C₂	semidirect
11. #16863960	C₂	semidirect
12. #16863949	C₂	semidirect
13. #16863942	C₂	semidirect
14. #16863905	C₂	semidirect
15. #16863877	C₂	semidirect
16. C₂×#14524005	C₂	semidirect
17. #520×C₆₇	C₂	semidirect
19. C₂×#11761628	C₂²	semidirect
22. #14524042	C₂²	semidirect
23. #14524042	C₂²	semidirect
24. #14524041	C₂²	semidirect
27. #14524039	C₂²	semidirect
28. #14524038	C₂²	semidirect
29. #14524037	C₂²	semidirect
30. #14524034	C₂²	semidirect
31. #14524034	C₂²	semidirect
33. #14524032	C₂²	semidirect
35. #14524031	C₂²	semidirect
36. #14524030	C₂²	semidirect
37. #14524029	C₂²	semidirect
38. #14524028	C₂²	semidirect
39. #14524028	C₂²	semidirect
40. #14524026	C₂²	semidirect
41. #14524025	C₂²	semidirect
42. #14524021	C₂²	semidirect
49. #14524017	C₂²	semidirect
50. #14524016	C₂²	semidirect
51. #14524016	C₂²	semidirect
56. C₄×Dic₁₃₄	C₂²	semidirect
57. C₄×Dic₁₃₄	C₂²	semidirect
58. #14524008	C₂²	semidirect
59. C₄×D₂₆₈	C₂²	semidirect
64. #14524005	C₂²	semidirect
66. C₄×C₂²⋊D₆₇	C₂²	semidirect
67. C₄×C₂²⋊D₆₇	C₂²	semidirect
68. C₄×C₂²⋊D₆₇	C₂²	semidirect
70. #14524001	C₂²	semidirect
71. #14524000	C₂²	semidirect
72. C₄⋊C₄×D₆₇	C₂²	semidirect
76. C₄×Q₈×C₆₇	C₂²	semidirect
78. C₄×D₄×C₆₇	C₂²	semidirect
80. #117×C₆₇	C₂²	semidirect
82. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
166. C₂×C₄×C₆₇	#41	semidirect
234. C₆₇	#3506	semidirect
250. #520	D₆₇	semidirect
294. C₄×Q₈	C₂×D₆₇	semidirect
306. C₄×D₄	C₂×D₆₇	semidirect
311. #117	C₂×D₆₇	semidirect
314. C₂×C₄⋊C₄	C₂×D₆₇	semidirect
426. C₂×C₄	#11761628	semidirect