Subgroups — #30839278

Order 17152.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22571535	C₂	1	2	yes	maximal, complemented
2	#22570788	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559737	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559732	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559693	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559688	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559625	C₂	1	2	yes	maximal, complemented
8	#22559618	C₂	1	2	yes	maximal, complemented
9	C₂×#16863147	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558905	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863946	C₂²	1	2	yes	—
13	#16863801	C₂²	1	1	yes	characteristic
14	#16863773	C₂²	1	1	yes	characteristic
15	#16863743	C₂²	1	2	yes	—
16	#16863693	—	2	2	no	—
17	#16863691	C₂²	1	2	yes	—
18	#16863686	C₂²	1	2	yes	—
19	#16863632	—	2	1	no	—
20	#16863632	—	2	1	no	—
21	#16863630	—	2	2	no	—
22	#16863627	—	2	2	no	—
23	#16863608	—	2	2	no	—
24	#16863596	C₂²	1	2	yes	—
25	#16863591	C₂²	1	2	yes	—
26	C₄×D₅₃₆	—	2	1	no	—
27	C₄×D₅₃₆	—	2	1	no	—
28	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
29	#16863147	C₂²	1	2	yes	—
30	#16863147	C₂²	1	1	yes	characteristic
31	#16863147	C₂²	1	1	yes	characteristic
32	#16863144	C₂²	1	2	yes	—
33	#16863144	C₂²	1	2	yes	—
34	#16863139	C₂²	1	2	yes	—
35	#16863139	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	1	yes	characteristic
37	#446×C₆₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	#436×C₆₇	C₂²	1	1	yes	characteristic
40	#435×C₆₇	—	2	1	no	—
41	C₈×D₄×C₆₇	—	2	1	no	—
42	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#433×C₆₇	—	2	1	no	—
44	#432×C₆₇	C₂²	1	1	yes	characteristic
45	#405×C₆₇	—	2	1	no	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	—	2	2	no	—
48	C₂×#11761615	—	2	2	no	—
49	C₂×D₅₃₆	—	2	1	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×#11761613	—	2	2	no	—
52	C₂²×C₆₇⋊C₈	—	2	2	no	—
53	#14524043	C₂³	1	2	yes	—
54	#14524040	C₂³	1	2	yes	—
55	#14524031	—	2	2	no	—
56	#14524017	—	2	2	no	—
57	#14524017	—	2	2	no	—
58	C₄×D₂₆₈	—	2	2	no	—
59	C₄×D₂₆₈	—	2	2	no	—
60	#14523977	—	2	1	no	—
61	#14523977	—	2	1	no	—
62	#14523976	—	2	2	no	—
63	#14523974	—	2	2	no	—
64	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
67	#14523967	—	2	2	no	—
68	#14523965	—	2	2	no	—
69	#14523965	—	2	2	no	—
70	#14523964	—	2	2	no	—
71	#14523963	—	2	2	no	—
72	#14523963	—	2	2	no	—
73	C₂×M₁₆×C₆₇	—	2	1	no	—
74	C₂²×C₈×C₆₇	—	2	1	no	—
75	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
77	#126×C₆₇	—	2	1	no	—
78	#125×C₆₇	D₄	1	1	yes	characteristic
79	#124×C₆₇	D₄	1	1	yes	characteristic
80	#123×C₆₇	—	2	1	no	—
81	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
82	#121×C₆₇	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₆₇	—	2	1	no	—
85	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
86	#117×C₆₇	—	2	1	no	—
87	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	—	2	1	no	—
89	C₄⋊C₈×C₆₇	—	2	1	no	—
90	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₆₇	—	2	1	no	—
93	C₂²⋊C₈×C₆₇	—	2	1	no	—
94	C₂²⋊C₈×C₆₇	—	2	1	no	—
95	#97×C₆₇	—	2	1	no	—
96	#97×C₆₇	—	2	1	no	—
97	C₄×C₈×C₆₇	—	2	1	no	—
98	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	#11761628	—	8	4	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×D₂₆₈	—	2	2	no	—
105	C₂×D₂₆₈	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×C₂²⋊D₆₇	—	4	2	no	—
108	C₂×C₄×D₆₇	—	4	2	no	—
109	#11761615	—	8	2	no	—
110	D₅₃₆	—	4	2	no	—
111	D₅₃₆	—	4	2	no	—
112	#11761613	—	8	2	no	—
113	C₂×C₆₇⋊C₈	—	2	2	no	—
114	C₂×C₆₇⋊C₈	—	2	2	no	—
115	C₂×C₆₇⋊C₈	—	8	2	no	—
116	C₄⋊Dic₆₇	—	2	2	no	—
117	C₄⋊Dic₆₇	—	2	2	no	—
118	(C₂×D₆₇)⋊C₄	—	4	2	no	—
119	(C₂×D₆₇)⋊C₄	—	4	2	no	—
120	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₆₇	—	2	1	no	—
122	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	—	2	1	no	—
124	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
127	M₁₆×C₆₇	—	4	2	no	—
128	C₂×C₈×C₆₇	—	2	2	no	—
129	C₂×C₈×C₆₇	—	2	1	no	—
130	C₂×C₈×C₆₇	—	2	1	no	—
131	C₂×C₈×C₆₇	—	4	1	no	—
132	C₂×C₈×C₆₇	—	4	2	no	—
133	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₄⋊C₄×C₆₇	—	2	1	no	—
141	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₆₇	—	2	1	no	—
144	C₂²⋊C₄×C₆₇	—	2	1	no	—
145	C₂²⋊C₄×C₆₇	—	2	1	no	—
146	C₂²⋊C₄×C₆₇	—	2	1	no	—
147	C₂²⋊C₄×C₆₇	—	2	1	no	—
148	C₄²×C₆₇	—	2	1	no	—
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₇	#41	1	1	yes	characteristic
152	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
153	C₂³×C₆₇	—	2	1	no	—
154	C₂³×C₆₇	#121	1	1	yes	characteristic
155	C₂²×D₆₇	—	4	2	no	—
156	Q₈×C₆₇	—	2	2	no	—
157	D₄×C₆₇	—	2	2	no	—
158	D₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	2	1	no	—
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	4	1	no	—
167	C₂×C₄×C₆₇	—	4	1	no	—
168	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
170	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
174	C₂²⋊D₆₇	—	8	4	no	—
175	C₂×Dic₆₇	—	4	2	no	—
176	D₂₆₈	—	4	2	no	—
177	D₂₆₈	—	4	2	no	—
178	D₂₆₈	—	4	2	no	—
179	D₂₆₈	—	4	2	no	—
180	D₂₆₈	—	8	2	no	—
181	C₄×D₆₇	—	8	4	no	—
182	Dic₁₃₄	—	8	2	no	—
183	C₈×C₆₇	—	2	1	no	—
184	C₈×C₆₇	—	2	1	no	—
185	C₈×C₆₇	—	2	1	no	—
186	C₈×C₆₇	—	4	1	no	—
187	C₈×C₆₇	—	4	1	no	—
188	C₈×C₆₇	#135	1	2	yes	—
189	C₆₇⋊C₈	—	4	2	no	—
190	C₆₇⋊C₈	—	4	2	no	—
191	C₂²×C₆₇	—	2	1	no	—
192	C₂²×C₆₇	—	2	1	no	—
193	C₂²×C₆₇	—	4	1	no	—
194	C₂²×C₆₇	—	4	1	no	—
195	C₂²×C₆₇	—	4	1	no	—
196	C₂²×C₆₇	#472	1	2	yes	—
197	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
198	C₂×D₆₇	—	8	2	no	—
199	C₂×D₆₇	—	8	2	no	—
200	C₂×D₆₇	—	8	2	no	—
201	C₄×C₆₇	—	2	1	no	—
202	C₄×C₆₇	—	2	1	no	—
203	C₄×C₆₇	—	2	1	no	—
204	C₄×C₆₇	—	2	1	no	—
205	C₄×C₆₇	—	4	1	no	—
206	C₄×C₆₇	—	4	1	no	—
207	C₄×C₆₇	—	4	1	no	—
208	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
209	C₄×C₆₇	#575	1	1	yes	characteristic
210	C₄×C₆₇	#577	1	2	yes	—
211	Dic₆₇	—	8	2	no	—
212	#19227	—	67	1	no	maximal, Sylow
213	C₂×C₆₇	—	2	2	no	—
214	C₂×C₆₇	—	8	1	no	—
215	C₂×C₆₇	#3035	1	1	yes	characteristic
216	C₂×C₆₇	#3060	1	1	yes	characteristic
217	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
218	D₆₇	—	16	2	no	—
219	#3247	—	67	2	no	—
220	#3169	—	67	1	no	—
221	#2966	D₆₇	1	1	yes	characteristic, complemented
222	#1696	—	67	1	no	—
223	#1695	—	67	1	no	—
224	#1688	—	67	1	no	—
225	#1687	—	67	1	no	—
226	#1678	—	67	2	no	—
227	#1677	—	67	2	no	—
228	C₂×#334	—	67	1	no	—
229	#1551	—	67	2	no	—
230	C₆₇	#19227	1	1	yes	characteristic, complemented, Sylow
231	#532	—	67	2	no	—
232	#529	C₂×D₆₇	1	1	yes	characteristic
233	#500	—	67	1	no	—
234	#493	—	67	1	no	—
235	#486	—	67	2	no	—
236	#478	—	134	2	no	—
237	#477	—	67	2	no	—
238	#476	—	67	2	no	—
239	#466	—	134	1	no	—
240	#466	—	134	1	no	—
241	#466	—	134	2	no	—
242	#465	—	134	2	no	—
243	#463	—	134	2	no	—
244	#460	—	67	2	no	—
245	#459	—	67	2	no	—
246	#446	C₂×D₆₇	1	1	yes	characteristic
247	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
248	C₄×D₈	—	134	1	no	—
249	C₄×D₈	—	134	1	no	—
250	#436	C₂×D₆₇	1	1	yes	characteristic
251	#435	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
254	#433	—	2	1	no	—
255	#432	C₂×D₆₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	67	2	no	—
257	#405	—	2	1	no	—
258	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
259	#334	—	67	2	no	—
260	#334	—	67	1	no	—
261	#334	—	67	1	no	—
262	#333	—	67	2	no	—
263	#333	—	67	2	no	—
264	#331	—	67	2	no	—
265	#331	—	67	2	no	—
266	C₂×#41	—	134	2	no	—
267	C₂×SD₁₆	—	134	2	no	—
268	C₂×D₈	—	134	2	no	—
269	C₂×D₈	—	134	1	no	—
270	C₂×D₈	—	134	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	134	2	no	—
274	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
276	C₄⋊Q₈	—	67	2	no	—
277	#127	—	67	2	no	—
278	#126	—	2	1	no	—
279	#125	D₂₆₈	1	1	yes	characteristic
280	#124	—	134	2	no	—
281	#124	D₂₆₈	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	D₂₆₈	1	1	yes	characteristic
284	#121	—	134	2	no	—
285	#121	—	134	2	no	—
286	#121	D₂₆₈	1	1	yes	characteristic
287	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	134	2	no	—
290	C₄×D₄	—	134	2	no	—
291	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
294	#107	—	134	1	no	—
295	#107	—	134	1	no	—
296	#107	—	134	2	no	—
297	#106	—	134	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	67	2	no	—
301	C₄⋊C₈	—	67	2	no	—
302	C₄⋊C₈	—	134	2	no	—
303	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
304	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
305	#103	—	134	2	no	—
306	#102	—	134	2	no	—
307	#102	—	134	2	no	—
308	#102	—	134	2	no	—
309	#102	—	134	2	no	—
310	#102	—	134	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
318	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
321	#41	—	536	4	no	—
322	C₂×Q₈	—	134	2	no	—
323	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	268	2	no	—
326	C₂×D₄	—	134	2	no	—
327	C₂×D₄	—	134	2	no	—
328	C₂×D₄	—	134	2	no	—
329	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	268	2	no	—
332	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
334	C₂²×C₄	#11761628	1	1	yes	characteristic
335	SD₁₆	—	536	2	no	—
336	D₈	—	268	2	no	—
337	D₈	—	268	2	no	—
338	D₈	—	536	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	536	2	no	—
346	C₂×C₈	—	134	2	no	—
347	C₂×C₈	—	134	2	no	—
348	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	134	2	no	—
357	C₄⋊C₄	—	134	2	no	—
358	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
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	—	2	1	no	—
365	C₂²⋊C₄	—	268	2	no	—
366	C₂²⋊C₄	—	268	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
369	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
370	C₄²	#11761628	1	1	yes	characteristic
371	C₄²	C₂³×D₆₇	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	268	2	no	—
374	C₂³	#14524017	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	536	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	268	2	no	—
380	D₄	—	268	2	no	—
381	D₄	—	268	2	no	—
382	D₄	—	268	2	no	—
383	D₄	—	536	2	no	—
384	D₄	—	536	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	268	2	no	—
395	C₂×C₄	—	536	4	no	—
396	C₂×C₄	#14524017	1	1	yes	characteristic
397	C₂×C₄	#14524017	1	1	yes	characteristic
398	C₂×C₄	#14524017	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
401	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	268	2	no	—
408	C₈	—	268	2	no	—
409	C₈	#14524063	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	536	2	no	—
416	C₂²	—	536	2	no	—
417	C₂²	—	536	2	no	—
418	C₂²	#16863666	1	2	yes	—
419	C₂²	C₂×#14524017	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	536	2	no	—
428	C₄	C₂×#14524063	1	1	yes	characteristic
429	C₄	#16864194	1	1	yes	characteristic
430	C₄	#16864208	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	1072	2	no	—
434	C₂	#22569664	1	1	yes	characteristic
435	C₂	#22569871	1	1	yes	characteristic
436	C₂	C₂×#16863666	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2966	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	#2966	D₆₇
hypocenter	C₆₇	#19227
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #22571535	C₂	semidirect
2. #22570788	C₂	semidirect
3. #22559737	C₂	semidirect
4. #22559732	C₂	semidirect
5. #22559693	C₂	semidirect
6. #22559688	C₂	semidirect
7. #22559625	C₂	semidirect
8. #22559618	C₂	semidirect
9. C₂×#16863147	C₂	semidirect
10. #22558905	C₂	semidirect
11. C₆₇×#2966	C₂	semidirect
221. #2966	D₆₇	semidirect
230. C₆₇	#19227	semidirect

Maximal subgroups

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

subgroup	index
#22571535	2
#22570788	2
#22559737	2
#22559732	2
#22559693	2
#22559688	2
#22559625	2
#22559618	2
C₂×#16863147	2
#22558905	2
C₆₇×#2966	2
#19227	67