Subgroups — #30869047

Order 17152.

806 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569818	C₂	1	1	yes	maximal, characteristic
2	#22568908	C₂	1	2	yes	maximal, complemented
3	#22560856	C₂	1	2	yes	maximal, complemented
4	#22560807	C₂	1	2	yes	maximal, complemented
5	#22560650	C₂	1	2	yes	maximal, complemented
6	#22560537	C₂	1	2	yes	maximal, complemented
7	#22560481	C₂	1	2	yes	maximal, complemented
8	#22559902	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14524065	C₂²	1	1	yes	characteristic
11	C₂×#14524051	C₂²	1	2	yes	—
12	C₂²×#11761612	C₂²	1	1	yes	characteristic
13	#16863907	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
15	#16863654	C₄	1	1	yes	characteristic, complemented
16	#16863654	C₄	1	1	yes	characteristic, complemented
17	#16863649	C₄	1	1	yes	characteristic, complemented
18	#16863649	C₄	1	1	yes	characteristic, complemented
19	#16863642	C₄	1	2	yes	complemented
20	#16863642	C₄	1	2	yes	complemented
21	#16863471	—	2	2	no	—
22	#16863471	—	2	2	no	—
23	#16863470	—	2	2	no	—
24	#16863470	—	2	2	no	—
25	#16863434	C₂²	1	1	yes	characteristic
26	#16863424	C₂²	1	2	yes	—
27	C₂×#14523969	C₂²	1	2	yes	—
28	C₂×#14523969	C₂²	1	2	yes	—
29	#16863393	C₂²	1	2	yes	—
30	#16863364	C₂²	1	2	yes	—
31	#16863354	C₂²	1	2	yes	—
32	#16863157	C₂²	1	2	yes	—
33	#16863157	C₂²	1	2	yes	—
34	#16863150	C₂²	1	2	yes	—
35	#16863150	C₂²	1	2	yes	—
36	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
39	#407×C₆₇	C₂²	1	2	yes	—
40	#341×C₆₇	C₂²	1	2	yes	—
41	C₂×#11761628	C₂³	1	2	yes	—
42	C₂³×Dic₆₇	—	2	1	no	—
43	#14524065	—	4	1	no	—
44	#14524065	—	4	1	no	—
45	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×#11761617	C₂×C₄	1	2	yes	complemented
47	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
48	#14524051	—	4	2	no	—
49	#14524051	—	4	2	no	—
50	C₂×#11761612	—	4	1	no	—
51	C₂×#11761612	—	4	1	no	—
52	C₂×#11761612	D₄	1	1	yes	characteristic
53	C₂×#11761612	D₄	1	2	yes	—
54	C₂×#11761612	D₄	1	1	yes	characteristic
55	C₂×#11761611	—	2	2	no	—
56	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
57	C₂×C₈×D₆₇	—	2	2	no	—
58	#14524026	—	2	2	no	—
59	#14524022	C₂×C₄	1	2	yes	—
60	#14524022	C₂×C₄	1	2	yes	—
61	#14524017	C₂×C₄	1	2	yes	—
62	#14524017	C₂×C₄	1	2	yes	—
63	#14524012	—	2	2	no	—
64	C₄×C₂²⋊D₆₇	—	2	2	no	—
65	C₄×C₂²⋊D₆₇	—	2	2	no	—
66	#14524002	C₂³	1	2	yes	—
67	C₂×C₄×Dic₆₇	—	2	1	no	—
68	C₂×C₄×Dic₆₇	—	4	1	no	—
69	C₂×C₄×Dic₆₇	—	4	1	no	—
70	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
71	#14523977	C₂×C₄	1	2	yes	complemented
72	#14523975	C₂×C₄	1	1	yes	characteristic, complemented
73	#14523975	C₂×C₄	1	1	yes	characteristic, complemented
74	Dic₆₇⋊C₈	—	2	2	no	—
75	Dic₆₇⋊C₈	—	2	2	no	—
76	#14523969	—	4	2	no	—
77	#14523969	—	4	2	no	—
78	#14523968	C₂×C₄	1	2	yes	complemented
79	#14523968	C₂×C₄	1	2	yes	complemented
80	#14523965	C₂×C₄	1	2	yes	complemented
81	#14523965	C₂×C₄	1	2	yes	complemented
82	(C₂×D₆₇)⋊C₈	—	2	2	no	—
83	(C₂×D₆₇)⋊C₈	—	2	2	no	—
84	#14523953	—	2	2	no	—
85	C₈×Dic₆₇	—	2	2	no	—
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₆₇	—	4	1	no	—
88	C₂×M₁₆×C₆₇	—	4	1	no	—
89	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
90	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
91	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
92	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	#108×C₆₇	—	4	1	no	—
98	#108×C₆₇	—	4	1	no	—
99	C₂²⋊C₈×C₆₇	—	2	2	no	—
100	C₂²⋊C₈×C₆₇	—	2	2	no	—
101	#11761628	—	2	2	no	—
102	#11761628	—	2	2	no	—
103	#11761628	—	2	2	no	—
104	#11761628	—	2	2	no	—
105	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
106	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
107	C₂×C₂²⋊D₆₇	—	2	2	no	—
108	C₂×C₂²⋊D₆₇	—	2	2	no	—
109	C₂×C₂²⋊D₆₇	—	2	2	no	—
110	C₂²×Dic₆₇	—	2	2	no	—
111	C₂²×Dic₆₇	—	4	4	no	—
112	C₂²×Dic₆₇	—	4	2	no	—
113	C₂×C₄×D₆₇	—	2	2	no	—
114	Dic₂₆₈	—	4	1	no	—
115	#11761617	—	4	2	no	—
116	D₅₃₆	—	4	1	no	—
117	#11761612	—	4	1	no	—
118	#11761612	—	4	2	no	—
119	#11761612	—	4	1	no	—
120	#11761611	—	4	4	no	—
121	C₂×C₆₇⋊C₈	—	2	2	no	—
122	C₂×C₆₇⋊C₈	—	2	2	no	—
123	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
124	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
125	C₈×D₆₇	—	4	4	no	—
126	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
127	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
128	Dic₆₇⋊C₄	—	2	2	no	—
129	Dic₆₇⋊C₄	—	2	2	no	—
130	C₂²⋊Dic₆₇	—	2	2	no	—
131	C₂²⋊Dic₆₇	—	2	2	no	—
132	C₂²⋊Dic₆₇	—	2	2	no	—
133	(C₂×D₆₇)⋊C₄	—	2	2	no	—
134	(C₂×D₆₇)⋊C₄	—	2	2	no	—
135	C₄×Dic₆₇	—	2	2	no	—
136	C₄×Dic₆₇	—	2	2	no	—
137	C₄×Dic₆₇	—	2	2	no	—
138	C₄×Dic₆₇	—	4	2	no	—
139	C₂⁴×C₆₇	#41	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	—	2	1	no	—
141	C₂²×C₄×C₆₇	—	2	1	no	—
142	C₂²×C₄×C₆₇	—	2	1	no	—
143	C₂²×C₄×C₆₇	—	2	1	no	—
144	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₆₇	—	2	2	no	—
151	M₁₆×C₆₇	—	2	2	no	—
152	M₁₆×C₆₇	—	2	2	no	—
153	M₁₆×C₆₇	—	2	2	no	—
154	M₁₆×C₆₇	—	4	1	no	—
155	M₁₆×C₆₇	—	4	1	no	—
156	M₁₆×C₆₇	—	4	1	no	—
157	M₁₆×C₆₇	—	4	1	no	—
158	C₂×C₈×C₆₇	—	2	1	no	—
159	C₂×C₈×C₆₇	—	2	1	no	—
160	C₂×C₈×C₆₇	—	2	1	no	—
161	C₂×C₈×C₆₇	—	2	1	no	—
162	C₂×C₈×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	—	2	2	no	—
164	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₂³×C₆₇	—	2	1	no	—
169	C₂³×C₆₇	—	2	1	no	—
170	C₂³×C₆₇	—	4	2	no	—
171	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
174	C₂²×D₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	2	1	no	—
177	C₂×C₄×C₆₇	—	2	1	no	—
178	C₂×C₄×C₆₇	—	2	1	no	—
179	C₂×C₄×C₆₇	—	2	1	no	—
180	C₂×C₄×C₆₇	—	2	1	no	—
181	C₂×C₄×C₆₇	—	2	1	no	—
182	C₂×C₄×C₆₇	—	2	1	no	—
183	C₂×C₄×C₆₇	—	2	1	no	—
184	C₂×C₄×C₆₇	—	2	1	no	—
185	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
193	C₂²⋊D₆₇	—	4	2	no	—
194	C₂²⋊D₆₇	—	4	2	no	—
195	C₂²⋊D₆₇	—	8	2	no	—
196	C₂²⋊D₆₇	—	8	2	no	—
197	C₂×Dic₆₇	—	2	4	no	—
198	C₂×Dic₆₇	—	2	2	no	—
199	C₂×Dic₆₇	—	2	2	no	—
200	C₂×Dic₆₇	—	2	2	no	—
201	C₂×Dic₆₇	—	4	2	no	—
202	C₂×Dic₆₇	—	4	8	no	—
203	C₂×Dic₆₇	—	4	2	no	—
204	D₂₆₈	—	2	2	no	—
205	D₂₆₈	—	2	2	no	—
206	C₄×D₆₇	—	4	2	no	—
207	C₄×D₆₇	—	4	2	no	—
208	Dic₁₃₄	—	2	2	no	—
209	Dic₁₃₄	—	2	2	no	—
210	C₈×C₆₇	—	2	1	no	—
211	C₈×C₆₇	—	2	1	no	—
212	C₈×C₆₇	—	2	1	no	—
213	C₈×C₆₇	—	2	1	no	—
214	C₈×C₆₇	—	4	2	no	—
215	C₈×C₆₇	—	4	2	no	—
216	C₆₇⋊C₈	—	2	2	no	—
217	C₆₇⋊C₈	—	2	2	no	—
218	C₂²×C₆₇	—	2	2	no	—
219	C₂²×C₆₇	—	2	1	no	—
220	C₂²×C₆₇	—	2	1	no	—
221	C₂²×C₆₇	—	2	2	no	—
222	C₂²×C₆₇	—	2	2	no	—
223	C₂²×C₆₇	—	4	2	no	—
224	C₂²×C₆₇	—	4	2	no	—
225	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
226	C₂²×C₆₇	#538	1	1	yes	characteristic
227	C₂²×C₆₇	#539	1	1	yes	characteristic
228	C₂×D₆₇	—	4	2	no	—
229	C₂×D₆₇	—	4	2	no	—
230	C₂×D₆₇	—	4	2	no	—
231	C₄×C₆₇	—	2	1	no	—
232	C₄×C₆₇	—	2	1	no	—
233	C₄×C₆₇	#518	1	1	yes	characteristic
234	C₄×C₆₇	#520	1	1	yes	characteristic
235	C₄×C₆₇	#534	1	1	yes	characteristic
236	C₄×C₆₇	#537	1	1	yes	characteristic
237	Dic₆₇	—	4	4	no	—
238	Dic₆₇	—	4	2	no	—
239	Dic₆₇	—	4	2	no	—
240	Dic₆₇	—	4	2	no	—
241	#22207	—	67	1	no	maximal, Sylow
242	C₂×C₆₇	—	2	1	no	—
243	C₂×C₆₇	—	2	1	no	—
244	C₂×C₆₇	—	4	1	no	—
245	C₂×C₆₇	—	4	1	no	—
246	C₂×C₆₇	#2325	1	1	yes	characteristic
247	C₂×C₆₇	#2956	1	2	yes	—
248	D₆₇	—	8	2	no	—
249	#3054	—	67	1	no	—
250	#2930	—	67	2	no	—
251	#1929	—	67	2	no	—
252	#1922	—	67	2	no	—
253	#1896	—	67	2	no	—
254	#1876	—	67	2	no	—
255	#1866	—	67	2	no	—
256	#1811	D₆₇	1	1	yes	characteristic, complemented
257	#1728	—	67	1	no	—
258	C₆₇	#22207	1	1	yes	characteristic, complemented, Sylow
259	C₂×#135	—	67	1	no	—
260	C₂×#131	—	67	2	no	—
261	C₂²×M₁₆	—	67	1	no	—
262	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
263	#525	—	67	2	no	—
264	C₂²×C₄²	—	67	1	no	—
265	#470	—	67	1	no	—
266	#470	—	67	1	no	—
267	#469	—	67	1	no	—
268	#469	—	67	1	no	—
269	#468	—	67	2	no	—
270	#468	—	67	2	no	—
271	#436	—	134	2	no	—
272	#436	—	134	2	no	—
273	#435	—	134	2	no	—
274	#435	—	134	2	no	—
275	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
276	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
277	#427	—	67	1	no	—
278	#424	—	67	2	no	—
279	C₂×#104	—	67	2	no	—
280	C₂×#104	—	67	2	no	—
281	#416	—	67	2	no	—
282	#408	—	67	2	no	—
283	#407	C₂×D₆₇	1	2	yes	—
284	#405	—	67	2	no	—
285	#341	C₂×D₆₇	1	2	yes	—
286	#339	—	67	2	no	—
287	#339	—	67	2	no	—
288	#336	—	67	2	no	—
289	#336	—	67	2	no	—
290	C₂×#41	—	67	2	no	—
291	C₂³×C₄	—	134	1	no	—
292	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
293	#135	—	268	1	no	—
294	#135	—	268	1	no	—
295	C₂×Q₁₆	—	67	1	no	—
296	C₂×SD₁₆	—	67	2	no	—
297	C₂×D₈	—	67	1	no	—
298	#131	—	268	2	no	—
299	#131	—	268	2	no	—
300	C₂×M₁₆	—	4	1	no	—
301	C₂×M₁₆	—	4	1	no	—
302	C₂×M₁₆	—	268	1	no	—
303	C₂×M₁₆	—	268	1	no	—
304	C₂×M₁₆	—	67	1	no	—
305	C₂×M₁₆	—	67	2	no	—
306	C₂×M₁₆	—	67	1	no	—
307	C₂×M₁₆	—	134	2	no	—
308	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
309	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
310	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
311	C₂×M₁₆	C₄×D₆₇	1	1	yes	characteristic
312	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
313	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
314	C₂²×C₈	—	67	2	no	—
315	C₂²×C₈	—	134	2	no	—
316	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
318	#123	—	134	2	no	—
319	C₂²⋊Q₈	—	67	2	no	—
320	C₂²⋊Q₈	—	67	2	no	—
321	#121	—	67	2	no	—
322	#121	—	67	2	no	—
323	#120	—	134	2	no	—
324	C₄×D₄	—	134	2	no	—
325	C₄×D₄	—	134	2	no	—
326	#117	—	67	2	no	—
327	C₂×C₄²	—	268	1	no	—
328	C₂×C₄²	—	268	1	no	—
329	C₂×C₄²	—	67	2	no	—
330	C₂×C₄²	—	134	1	no	—
331	#108	—	4	1	no	—
332	#108	—	4	1	no	—
333	#107	—	67	2	no	—
334	#106	—	67	1	no	—
335	#106	—	67	1	no	—
336	C₄⋊C₈	—	134	2	no	—
337	C₄⋊C₈	—	134	2	no	—
338	#104	—	268	2	no	—
339	#104	—	268	2	no	—
340	#103	—	67	2	no	—
341	#103	—	67	2	no	—
342	#102	—	67	2	no	—
343	#102	—	67	2	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	134	2	no	—
347	C₂²⋊C₈	—	134	2	no	—
348	#97	—	134	2	no	—
349	C₄×C₈	—	134	2	no	—
350	C₂⁴	#11761629	1	1	yes	characteristic
351	#41	—	134	2	no	—
352	#41	—	134	2	no	—
353	#41	—	134	2	no	—
354	#41	—	134	2	no	—
355	C₂×Q₈	—	67	2	no	—
356	C₂×D₄	—	67	2	no	—
357	C₂×D₄	—	134	2	no	—
358	C₂×D₄	—	134	2	no	—
359	C₂×D₄	—	134	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	268	2	no	—
365	C₂²×C₄	—	268	4	no	—
366	C₂²×C₄	—	134	2	no	—
367	C₂²×C₄	—	134	2	no	—
368	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
372	C₂²×C₄	#11761629	1	1	yes	characteristic
373	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
374	Q₁₆	—	268	1	no	—
375	SD₁₆	—	268	2	no	—
376	D₈	—	268	1	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	4	1	no	—
382	M₁₆	—	4	1	no	—
383	M₁₆	—	4	1	no	—
384	M₁₆	—	4	1	no	—
385	M₁₆	—	268	4	no	—
386	M₁₆	—	268	1	no	—
387	M₁₆	—	268	2	no	—
388	M₁₆	—	268	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	268	4	no	—
396	C₂×C₈	—	67	2	no	—
397	C₂×C₈	—	67	2	no	—
398	C₂×C₈	—	134	2	no	—
399	C₂×C₈	—	134	2	no	—
400	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
401	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
402	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
403	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
404	C₄⋊C₄	—	67	2	no	—
405	C₄⋊C₄	—	67	2	no	—
406	C₄⋊C₄	—	134	2	no	—
407	C₄⋊C₄	—	134	2	no	—
408	C₂²⋊C₄	—	134	2	no	—
409	C₂²⋊C₄	—	134	2	no	—
410	C₂²⋊C₄	—	134	2	no	—
411	C₂²⋊C₄	—	134	2	no	—
412	C₂²⋊C₄	—	134	2	no	—
413	C₄²	—	268	2	no	—
414	C₄²	—	134	2	no	—
415	C₄²	—	134	2	no	—
416	C₄²	—	134	2	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	134	2	no	—
421	C₂³	#14524005	1	1	yes	characteristic
422	C₂³	#14524005	1	1	yes	characteristic
423	C₂³	C₂×#11761629	1	1	yes	characteristic
424	Q₈	—	134	2	no	—
425	Q₈	—	134	2	no	—
426	D₄	—	268	2	no	—
427	D₄	—	268	2	no	—
428	D₄	—	536	2	no	—
429	D₄	—	536	2	no	—
430	D₄	—	134	2	no	—
431	D₄	—	134	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	268	2	no	—
443	C₂×C₄	—	268	8	no	—
444	C₂×C₄	—	268	2	no	—
445	C₂×C₄	—	268	2	no	—
446	C₂×C₄	—	268	2	no	—
447	C₂×C₄	—	134	4	no	—
448	C₂×C₄	—	134	2	no	—
449	C₂×C₄	—	134	2	no	—
450	C₂×C₄	—	134	2	no	—
451	C₂×C₄	#14524005	1	1	yes	characteristic
452	C₂×C₄	#14524005	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
454	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
455	C₂×C₄	#14524088	1	1	yes	characteristic
456	C₂×C₄	#14524088	1	1	yes	characteristic
457	C₂×C₄	#14524089	1	1	yes	characteristic
458	C₂×C₄	#14524090	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₈	—	134	2	no	—
466	C₈	—	134	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	268	2	no	—
475	C₂²	—	268	2	no	—
476	C₂²	—	268	2	no	—
477	C₂²	C₂×#14524005	1	1	yes	characteristic
478	C₂²	#16863986	1	1	yes	characteristic
479	C₂²	#16863995	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	268	4	no	—
483	C₄	—	268	2	no	—
484	C₄	—	268	2	no	—
485	C₄	—	268	2	no	—
486	C₄	#16863869	1	1	yes	characteristic
487	C₄	#16863876	1	1	yes	characteristic
488	C₄	#16863954	1	1	yes	characteristic
489	C₄	#16863973	1	1	yes	characteristic
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	1	no	—
493	C₂	—	4	1	no	—
494	C₂	—	536	2	no	—
495	C₂	#22562909	1	1	yes	characteristic
496	C₂	#22569118	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1811	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#22569818	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1811	D₆₇
hypocenter	C₆₇	#22207
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1811

Complements

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

N	H ≅ G/N	type
2. #22568908	C₂	semidirect
3. #22560856	C₂	semidirect
4. #22560807	C₂	semidirect
5. #22560650	C₂	semidirect
6. #22560537	C₂	semidirect
7. #22560481	C₂	semidirect
8. #22559902	C₂	semidirect
9. C₆₇×#1811	C₂	semidirect
15. #16863654	C₄	semidirect
16. #16863654	C₄	semidirect
17. #16863649	C₄	semidirect
18. #16863649	C₄	semidirect
19. #16863642	C₄	semidirect
20. #16863642	C₄	semidirect
45. C₂×Dic₂₆₈	C₂×C₄	semidirect
46. C₂×#11761617	C₂×C₄	semidirect
47. C₂×D₅₃₆	C₂×C₄	semidirect
71. #14523977	C₂×C₄	semidirect
72. #14523975	C₂×C₄	semidirect
73. #14523975	C₂×C₄	semidirect
78. #14523968	C₂×C₄	semidirect
79. #14523968	C₂×C₄	semidirect
80. #14523965	C₂×C₄	semidirect
81. #14523965	C₂×C₄	semidirect
256. #1811	D₆₇	semidirect
258. C₆₇	#22207	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22569818	2
#22568908	2
#22560856	2
#22560807	2
#22560650	2
#22560537	2
#22560481	2
#22559902	2
C₆₇×#1811	2
#22207	67