Subgroups — #30839742

Order 17152.

716 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	#22570637	C₂	1	1	yes	maximal, characteristic, complemented
2	#22570360	C₂	1	2	yes	maximal, complemented
3	#22559579	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559574	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559569	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559564	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559557	C₂	1	2	yes	maximal, complemented
8	#22559550	C₂	1	2	yes	maximal, complemented
9	#22558972	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558912	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	—	2	1	no	—
13	C₂×#14524065	—	2	1	no	—
14	#16863946	C₂²	1	2	yes	—
15	#16863780	—	2	1	no	—
16	#16863780	—	2	1	no	—
17	#16863776	C₂²	1	1	yes	characteristic
18	#16863773	C₂²	1	1	yes	characteristic
19	#16863769	C₂²	1	2	yes	—
20	#16863720	—	2	2	no	—
21	#16863681	C₂²	1	2	yes	—
22	#16863676	C₂²	1	2	yes	—
23	#16863596	C₂²	1	2	yes	—
24	#16863591	C₂²	1	2	yes	—
25	#16863541	—	2	2	no	—
26	#16863506	—	2	2	no	—
27	#16863494	—	2	2	no	—
28	#16863453	C₂²	1	2	yes	—
29	#16863149	C₂²	1	1	yes	characteristic
30	#16863149	C₂²	1	1	yes	characteristic
31	#16863147	C₂²	1	2	yes	—
32	#16863143	C₂²	1	2	yes	—
33	#16863143	C₂²	1	2	yes	—
34	#16863139	C₂²	1	2	yes	—
35	#16863139	C₂²	1	2	yes	—
36	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₆₇	—	2	1	no	—
40	C₈×D₄×C₆₇	—	2	1	no	—
41	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#431×C₆₇	—	2	1	no	—
44	#431×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₆₇	—	2	1	no	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	—	2	2	no	—
48	#14524065	—	4	4	no	—
49	#14524065	—	4	4	no	—
50	C₂×Dic₂₆₈	—	2	1	no	—
51	C₂×Dic₂₆₈	—	2	1	no	—
52	C₂×#11761617	—	2	2	no	—
53	C₂×#11761617	—	2	2	no	—
54	C₂×#11761615	—	2	2	no	—
55	C₂×D₅₃₆	—	2	1	no	—
56	C₂×D₅₃₆	—	2	1	no	—
57	C₂×#11761613	—	2	2	no	—
58	#14524043	C₂³	1	2	yes	—
59	#14524040	C₂³	1	2	yes	—
60	#14524031	—	2	2	no	—
61	#14524017	—	2	2	no	—
62	#14524017	—	2	2	no	—
63	C₄×D₂₆₈	—	2	2	no	—
64	C₄×D₂₆₈	—	2	2	no	—
65	#14523976	—	2	2	no	—
66	#14523974	—	2	2	no	—
67	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
69	#14523967	—	2	2	no	—
70	#14523964	—	2	2	no	—
71	#14523963	—	2	2	no	—
72	#14523963	—	2	2	no	—
73	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
74	#14523954	—	2	2	no	—
75	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₆₇	—	2	1	no	—
77	C₂²×C₈×C₆₇	—	2	1	no	—
78	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₆₇	—	2	1	no	—
83	C₄×D₄×C₆₇	—	2	1	no	—
84	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
85	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
86	#117×C₆₇	—	2	1	no	—
87	#117×C₆₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₆₇	—	2	1	no	—
89	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₆₇	—	2	1	no	—
91	C₄⋊C₈×C₆₇	—	2	1	no	—
92	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₆₇	—	2	1	no	—
95	C₂²⋊C₈×C₆₇	—	2	1	no	—
96	C₂²⋊C₈×C₆₇	—	2	1	no	—
97	C₄×C₈×C₆₇	—	2	1	no	—
98	C₄×C₈×C₆₇	—	2	1	no	—
99	C₄×C₈×C₆₇	—	2	1	no	—
100	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
102	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	#11761628	—	4	4	no	—
105	#11761628	—	4	4	no	—
106	C₂×Dic₁₃₄	—	2	2	no	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×D₂₆₈	—	2	2	no	—
110	C₂×C₂²⋊D₆₇	—	4	2	no	—
111	C₂×C₄×D₆₇	—	4	2	no	—
112	Dic₂₆₈	—	4	2	no	—
113	Dic₂₆₈	—	4	2	no	—
114	#11761617	—	4	4	no	—
115	#11761617	—	4	4	no	—
116	#11761615	—	4	4	no	—
117	D₅₃₆	—	4	2	no	—
118	D₅₃₆	—	4	2	no	—
119	#11761613	—	4	4	no	—
120	C₂×C₆₇⋊C₈	—	2	2	no	—
121	C₂×C₆₇⋊C₈	—	2	2	no	—
122	C₄⋊Dic₆₇	—	2	2	no	—
123	C₄⋊Dic₆₇	—	2	2	no	—
124	(C₂×D₆₇)⋊C₄	—	4	2	no	—
125	(C₂×D₆₇)⋊C₄	—	4	2	no	—
126	#41×C₆₇	—	2	2	no	—
127	#41×C₆₇	—	2	2	no	—
128	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₆₇	—	2	1	no	—
130	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	—	2	1	no	—
132	C₂²×C₄×C₆₇	—	2	1	no	—
133	C₂²×C₄×C₆₇	—	2	1	no	—
134	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	2	1	no	—
140	C₂×C₈×C₆₇	—	2	1	no	—
141	C₂×C₈×C₆₇	—	4	2	no	—
142	C₂×C₈×C₆₇	—	4	2	no	—
143	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₆₇	—	2	1	no	—
148	C₄⋊C₄×C₆₇	—	2	1	no	—
149	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊C₄×C₆₇	—	2	1	no	—
152	C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₂²⋊C₄×C₆₇	—	2	1	no	—
154	C₄²×C₆₇	—	2	1	no	—
155	C₄²×C₆₇	—	2	1	no	—
156	C₄²×C₆₇	—	2	1	no	—
157	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₆₇	#41	1	1	yes	characteristic
160	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
161	C₂³×C₆₇	—	2	1	no	—
162	C₂³×C₆₇	#121	1	1	yes	characteristic
163	C₂²×D₆₇	—	4	2	no	—
164	Q₈×C₆₇	—	2	1	no	—
165	Q₈×C₆₇	#135	1	2	yes	complemented
166	D₄×C₆₇	—	2	4	no	—
167	D₄×C₆₇	—	2	1	no	—
168	D₄×C₆₇	#135	1	2	yes	complemented
169	C₂×C₄×C₆₇	—	2	4	no	—
170	C₂×C₄×C₆₇	—	2	1	no	—
171	C₂×C₄×C₆₇	—	2	1	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	2	1	no	—
177	C₂×C₄×C₆₇	—	4	1	no	—
178	C₂×C₄×C₆₇	—	4	2	no	—
179	C₂×C₄×C₆₇	—	4	1	no	—
180	C₂×C₄×C₆₇	—	4	1	no	—
181	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
182	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
183	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₆₇	—	8	4	no	—
188	C₂×Dic₆₇	—	4	2	no	—
189	D₂₆₈	—	4	2	no	—
190	D₂₆₈	—	4	2	no	—
191	D₂₆₈	—	4	2	no	—
192	D₂₆₈	—	4	2	no	—
193	D₂₆₈	—	8	2	no	—
194	C₄×D₆₇	—	8	4	no	—
195	Dic₁₃₄	—	4	2	no	—
196	Dic₁₃₄	—	4	2	no	—
197	C₈×C₆₇	—	2	1	no	—
198	C₈×C₆₇	—	2	1	no	—
199	C₈×C₆₇	—	4	1	no	—
200	C₈×C₆₇	—	4	1	no	—
201	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
202	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
203	C₆₇⋊C₈	—	4	2	no	—
204	C₆₇⋊C₈	—	4	2	no	—
205	C₂²×C₆₇	—	2	1	no	—
206	C₂²×C₆₇	—	2	1	no	—
207	C₂²×C₆₇	—	2	2	no	—
208	C₂²×C₆₇	—	2	1	no	—
209	C₂²×C₆₇	—	4	1	no	—
210	C₂²×C₆₇	—	4	1	no	—
211	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
212	C₂×D₆₇	—	8	2	no	—
213	C₂×D₆₇	—	8	2	no	—
214	C₂×D₆₇	—	8	2	no	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	1	no	—
217	C₄×C₆₇	—	2	2	no	—
218	C₄×C₆₇	—	2	1	no	—
219	C₄×C₆₇	—	2	1	no	—
220	C₄×C₆₇	—	4	1	no	—
221	C₄×C₆₇	—	4	1	no	—
222	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
223	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
224	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	Dic₆₇	—	8	2	no	—
227	#19269	—	67	1	no	maximal, Sylow
228	C₂×C₆₇	—	4	1	no	—
229	C₂×C₆₇	—	4	2	no	—
230	C₂×C₆₇	#3038	1	1	yes	characteristic
231	C₂×C₆₇	#3050	1	1	yes	characteristic
232	C₂×C₆₇	#3067	1	1	yes	characteristic
233	D₆₇	—	16	2	no	—
234	#3147	—	67	1	no	—
235	#3115	—	67	2	no	—
236	C₈×#41	D₆₇	1	1	yes	characteristic, complemented
237	#1670	—	67	1	no	—
238	#1669	—	67	1	no	—
239	#1668	—	67	1	no	—
240	#1667	—	67	1	no	—
241	#1666	—	67	2	no	—
242	#1665	—	67	2	no	—
243	#1568	—	67	1	no	—
244	#1553	—	67	2	no	—
245	C₆₇	#19269	1	1	yes	characteristic, complemented, Sylow
246	C₂×#135	—	134	1	no	—
247	C₂×#135	—	134	1	no	—
248	#532	—	67	2	no	—
249	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
250	#495	—	134	1	no	—
251	#495	—	134	1	no	—
252	#494	—	67	1	no	—
253	#493	—	67	1	no	—
254	#492	—	67	2	no	—
255	#482	—	134	2	no	—
256	#475	—	67	2	no	—
257	#474	—	67	2	no	—
258	#460	—	67	2	no	—
259	#459	—	67	2	no	—
260	#449	—	134	2	no	—
261	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
262	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
263	#442	—	134	2	no	—
264	#440	—	134	2	no	—
265	C₈×D₄	—	2	1	no	—
266	C₈×D₄	—	2	1	no	—
267	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
268	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
269	#432	—	67	2	no	—
270	#431	—	2	1	no	—
271	#431	C₂×D₆₇	1	1	yes	characteristic
272	C₂×C₄×C₈	—	2	1	no	—
273	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
274	#335	—	67	1	no	—
275	#335	—	67	1	no	—
276	#334	—	67	2	no	—
277	#332	—	67	2	no	—
278	#332	—	67	2	no	—
279	#331	—	67	2	no	—
280	#331	—	67	2	no	—
281	C₂×#41	—	134	2	no	—
282	C₂×#41	D₂₆₈	1	1	yes	characteristic
283	#135	—	268	4	no	—
284	#135	—	268	4	no	—
285	C₂×Q₁₆	—	134	1	no	—
286	C₂×Q₁₆	—	134	1	no	—
287	C₂×SD₁₆	—	134	2	no	—
288	C₂×SD₁₆	—	134	2	no	—
289	C₂×SD₁₆	—	134	2	no	—
290	C₂×D₈	—	134	2	no	—
291	C₂×D₈	—	134	1	no	—
292	C₂×D₈	—	134	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
297	C₄⋊Q₈	—	67	2	no	—
298	#127	—	67	2	no	—
299	#124	—	134	2	no	—
300	#121	—	134	2	no	—
301	#121	—	134	2	no	—
302	C₄×Q₈	D₂₆₈	1	1	yes	characteristic
303	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	134	2	no	—
307	C₄×D₄	—	134	2	no	—
308	C₄×D₄	D₂₆₈	1	1	yes	characteristic
309	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
310	#117	—	2	1	no	—
311	#117	D₂₆₈	1	1	yes	characteristic
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
314	#107	—	134	2	no	—
315	#106	—	134	2	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	67	2	no	—
319	C₄⋊C₈	—	67	2	no	—
320	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
321	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
322	#103	—	134	2	no	—
323	#102	—	134	2	no	—
324	#102	—	134	2	no	—
325	#102	—	134	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	134	2	no	—
330	#97	—	134	2	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
335	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	268	4	no	—
341	#41	—	268	4	no	—
342	C₂×Q₈	—	134	2	no	—
343	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	268	2	no	—
346	C₂×D₄	—	134	2	no	—
347	C₂×D₄	—	134	2	no	—
348	C₂×D₄	—	134	2	no	—
349	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	268	2	no	—
354	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
356	C₂²×C₄	#11761628	1	1	yes	characteristic
357	Q₁₆	—	268	2	no	—
358	Q₁₆	—	268	2	no	—
359	SD₁₆	—	268	4	no	—
360	SD₁₆	—	268	4	no	—
361	SD₁₆	—	268	4	no	—
362	D₈	—	268	2	no	—
363	D₈	—	268	4	no	—
364	D₈	—	268	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	134	2	no	—
372	C₂×C₈	—	134	2	no	—
373	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
376	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	134	2	no	—
380	C₄⋊C₄	—	134	2	no	—
381	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
382	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	268	2	no	—
387	C₂²⋊C₄	—	268	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
392	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
393	C₄²	#11761628	1	1	yes	characteristic
394	C₄²	C₂³×D₆₇	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	—	268	2	no	—
397	C₂³	#14524017	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	268	2	no	—
400	Q₈	—	268	2	no	—
401	Q₈	#14524065	1	2	yes	complemented
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	268	2	no	—
405	D₄	—	268	2	no	—
406	D₄	—	268	2	no	—
407	D₄	—	268	2	no	—
408	D₄	—	536	2	no	—
409	D₄	—	536	4	no	—
410	D₄	#14524065	1	2	yes	complemented
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	268	2	no	—
424	C₂×C₄	—	536	4	no	—
425	C₂×C₄	#14524017	1	1	yes	characteristic
426	C₂×C₄	#14524017	1	1	yes	characteristic
427	C₂×C₄	#14524017	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
430	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	268	2	no	—
436	C₈	—	268	2	no	—
437	C₈	#14524068	1	2	yes	—
438	C₈	#14524068	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	536	2	no	—
446	C₂²	—	536	2	no	—
447	C₂²	—	536	2	no	—
448	C₂²	C₂×#14524017	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	536	2	no	—
457	C₄	C₂×#14524065	1	1	yes	characteristic
458	C₄	C₂×#14524065	1	1	yes	characteristic
459	C₄	C₂×#14524068	1	1	yes	characteristic
460	C₄	C₂×#14524068	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	1072	2	no	—
464	C₂	#22569689	1	1	yes	characteristic
465	C₂	#22569790	1	1	yes	characteristic
466	C₂	#22569929	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×#41×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	C₈×#41	D₆₇
hypocenter	C₆₇	#19269
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #22570637	C₂	semidirect
2. #22570360	C₂	semidirect
3. #22559579	C₂	semidirect
4. #22559574	C₂	semidirect
5. #22559569	C₂	semidirect
6. #22559564	C₂	semidirect
7. #22559557	C₂	semidirect
8. #22559550	C₂	semidirect
9. #22558972	C₂	semidirect
10. #22558912	C₂	semidirect
11. C₈×#41×C₆₇	C₂	semidirect
165. Q₈×C₆₇	#135	semidirect
168. D₄×C₆₇	#135	semidirect
236. C₈×#41	D₆₇	semidirect
245. C₆₇	#19269	semidirect
401. Q₈	#14524065	semidirect
410. D₄	#14524065	semidirect

Maximal subgroups

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

subgroup	index
#22570637	2
#22570360	2
#22559579	2
#22559574	2
#22559569	2
#22559564	2
#22559557	2
#22559550	2
#22558972	2
#22558912	2
C₈×#41×C₆₇	2
#19269	67