Subgroups — #30826430

Order 17152.

594 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	#22570815	C₂	1	1	yes	maximal, characteristic
2	#22569184	C₂	1	1	yes	maximal, characteristic
3	#22569143	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559119	C₂	1	2	yes	maximal, complemented
5	#22559113	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₂₆₈	C₂	1	2	yes	maximal, complemented
7	C₈×#11761617	C₂	1	2	yes	maximal, complemented
8	#22558976	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558683	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558675	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863953	C₂²	1	1	yes	characteristic
13	#16863930	C₂²	1	1	yes	characteristic
14	#16863805	C₄	1	1	yes	characteristic
15	#16863790	C₄	1	1	yes	characteristic
16	#16863765	C₄	1	1	yes	characteristic
17	#16863756	C₄	1	1	yes	characteristic
18	#16863654	C₄	1	2	yes	—
19	#16863642	C₄	1	2	yes	—
20	#16863526	—	2	1	no	—
21	#16863526	C₂²	1	2	yes	—
22	#16863526	C₂²	1	1	yes	characteristic
23	C₈×Dic₁₃₄	—	2	1	no	—
24	C₈×Dic₁₃₄	C₂²	1	2	yes	—
25	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
26	C₄×Dic₂₆₈	C₂²	1	2	yes	—
27	C₄×#11761617	C₂²	1	2	yes	—
28	#16863475	C₂²	1	1	yes	characteristic
29	#16863467	—	2	1	no	—
30	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₆₇	—	2	1	no	—
32	#16863455	—	2	1	no	—
33	#16863453	C₂²	1	1	yes	characteristic
34	#16863422	—	2	1	no	—
35	#16863420	C₂²	1	1	yes	characteristic
36	#16863351	—	2	1	no	—
37	#16863350	—	2	1	no	—
38	#16863149	C₂²	1	2	yes	—
39	#16863147	C₂²	1	2	yes	—
40	#16863128	C₂²	1	2	yes	—
41	#16863128	C₂²	1	2	yes	—
42	#16863128	C₂²	1	2	yes	—
43	#16863125	C₂²	1	2	yes	—
44	#431×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	#322×C₆₇	C₂²	1	2	yes	—
48	C₈²×C₆₇	C₂²	1	2	yes	—
49	C₂×Dic₂₆₈	C₂×C₄	1	2	yes	—
50	C₂×#11761617	C₂×C₄	1	2	yes	—
51	C₂×#11761612	—	2	1	no	—
52	C₂×#11761611	—	2	1	no	—
53	C₂×C₈×D₆₇	—	2	1	no	—
54	#14524043	C₂×C₄	1	1	yes	characteristic
55	#14524043	C₂×C₄	1	1	yes	characteristic
56	#14524037	—	2	1	no	—
57	#14524035	—	2	1	no	—
58	#14524035	C₂×C₄	1	1	yes	characteristic
59	#14524031	C₂×C₄	1	1	yes	characteristic
60	#14524026	—	2	1	no	—
61	#14524022	—	2	1	no	—
62	#14524022	C₂×C₄	1	2	yes	—
63	#14524022	C₂×C₄	1	1	yes	characteristic
64	#14524017	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₃₄	—	2	1	no	—
66	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
67	C₄×Dic₁₃₄	C₂³	1	2	yes	—
68	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₆₇	—	2	1	no	—
70	#14524002	—	2	1	no	—
71	#14524000	—	2	1	no	—
72	#14523977	C₂×C₄	1	2	yes	—
73	#14523975	C₂×C₄	1	2	yes	—
74	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
76	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₆₇⋊C₈	—	2	2	no	—
79	Dic₆₇⋊C₈	—	2	2	no	—
80	Dic₆₇⋊C₈	—	2	1	no	—
81	Dic₆₇⋊C₈	—	2	1	no	—
82	#14523968	C₂×C₄	1	2	yes	—
83	#14523968	C₂×C₄	1	2	yes	—
84	#14523968	C₂×C₄	1	2	yes	—
85	#14523965	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
87	(C₂×D₆₇)⋊C₈	—	2	1	no	—
88	(C₂×D₆₇)⋊C₈	—	2	1	no	—
89	#14523954	—	2	1	no	—
90	#14523953	—	2	2	no	—
91	#14523953	—	2	1	no	—
92	C₈×Dic₆₇	—	2	2	no	—
93	C₈×Dic₆₇	—	2	1	no	—
94	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
95	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₆₇	—	2	1	no	—
99	C₂²⋊C₈×C₆₇	—	2	1	no	—
100	#97×C₆₇	C₂×C₄	1	1	yes	characteristic
101	#97×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₆₇	C₂³	1	2	yes	—
105	C₄×C₈×C₆₇	C₂³	1	2	yes	—
106	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₃₄	—	2	1	no	—
109	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
111	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₆₇	—	2	1	no	—
113	C₂×C₄×D₆₇	—	2	1	no	—
114	Dic₂₆₈	—	2	4	no	—
115	#11761617	—	2	4	no	—
116	#11761612	—	4	2	no	—
117	#11761611	—	4	2	no	—
118	C₂×C₆₇⋊C₈	—	2	2	no	—
119	C₂×C₆₇⋊C₈	—	2	1	no	—
120	C₂×C₆₇⋊C₈	—	2	1	no	—
121	C₈×D₆₇	—	4	2	no	—
122	C₄⋊Dic₆₇	—	2	1	no	—
123	C₄⋊Dic₆₇	—	2	1	no	—
124	C₄⋊Dic₆₇	—	2	1	no	—
125	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
126	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
128	Dic₆₇⋊C₄	—	2	1	no	—
129	Dic₆₇⋊C₄	—	2	1	no	—
130	Dic₆₇⋊C₄	—	2	1	no	—
131	Dic₆₇⋊C₄	—	2	2	no	—
132	Dic₆₇⋊C₄	—	2	2	no	—
133	Dic₆₇⋊C₄	—	2	1	no	—
134	C₂²⋊Dic₆₇	—	2	2	no	—
135	C₂²⋊Dic₆₇	—	2	1	no	—
136	(C₂×D₆₇)⋊C₄	—	2	1	no	—
137	(C₂×D₆₇)⋊C₄	—	2	1	no	—
138	(C₂×D₆₇)⋊C₄	—	2	1	no	—
139	(C₂×D₆₇)⋊C₄	—	2	1	no	—
140	C₄×Dic₆₇	—	2	1	no	—
141	C₄×Dic₆₇	—	2	2	no	—
142	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
145	M₁₆×C₆₇	—	2	4	no	—
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₂×C₈×C₆₇	—	2	2	no	—
148	C₂×C₈×C₆₇	—	4	1	no	—
149	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₇	#41	1	1	yes	characteristic
158	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
159	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	1	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₆₇	—	4	2	no	—
172	C₂×Dic₆₇	—	2	1	no	—
173	C₂×Dic₆₇	—	2	1	no	—
174	C₂×Dic₆₇	—	2	2	no	—
175	C₂×Dic₆₇	—	2	2	no	—
176	C₂×Dic₆₇	—	2	1	no	—
177	D₂₆₈	—	2	2	no	—
178	C₄×D₆₇	—	4	1	no	—
179	C₄×D₆₇	—	4	1	no	—
180	Dic₁₃₄	—	2	2	no	—
181	Dic₁₃₄	—	2	2	no	—
182	Dic₁₃₄	—	2	2	no	—
183	Dic₁₃₄	—	4	2	no	—
184	C₈×C₆₇	—	2	2	no	—
185	C₈×C₆₇	—	2	1	no	—
186	C₈×C₆₇	—	2	1	no	—
187	C₈×C₆₇	—	2	1	no	—
188	C₈×C₆₇	—	4	2	no	—
189	C₈×C₆₇	#131	1	4	yes	—
190	C₈×C₆₇	#137	1	2	yes	—
191	C₆₇⋊C₈	—	4	1	no	—
192	C₆₇⋊C₈	—	4	1	no	—
193	C₆₇⋊C₈	—	4	2	no	—
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	2	1	no	—
197	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×D₆₇	—	4	1	no	—
199	C₂×D₆₇	—	4	1	no	—
200	C₂×D₆₇	—	4	1	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	C₂×#131	1	2	yes	—
206	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
207	C₄×C₆₇	#575	1	1	yes	characteristic
208	Dic₆₇	—	4	2	no	—
209	Dic₆₇	—	4	1	no	—
210	Dic₆₇	—	4	1	no	—
211	Dic₆₇	—	4	2	no	—
212	Dic₆₇	—	4	1	no	—
213	#17965	—	67	1	no	maximal, Sylow
214	C₂×C₆₇	—	4	1	no	—
215	C₂×C₆₇	#2931	1	1	yes	characteristic
216	C₂×C₆₇	C₄×#137	1	1	yes	characteristic
217	C₂×C₆₇	#2955	1	1	yes	characteristic
218	D₆₇	—	8	1	no	—
219	#3172	—	67	1	no	—
220	#2966	—	67	1	no	—
221	#2960	—	67	1	no	—
222	#1593	—	67	2	no	—
223	#1592	—	67	2	no	—
224	C₈×Q₁₆	—	67	2	no	—
225	C₈×SD₁₆	—	67	2	no	—
226	#1569	—	67	1	no	—
227	#1497	—	67	1	no	—
228	#1495	—	67	1	no	—
229	C₈×M₁₆	D₆₇	1	1	yes	characteristic, complemented
230	C₆₇	#17965	1	1	yes	characteristic, complemented, Sylow
231	#533	—	67	1	no	—
232	#529	—	67	1	no	—
233	#501	—	67	1	no	—
234	#497	—	67	1	no	—
235	#491	—	67	1	no	—
236	#489	—	67	1	no	—
237	#470	—	67	2	no	—
238	#468	—	67	2	no	—
239	#446	—	67	2	no	—
240	#446	—	67	1	no	—
241	#446	—	134	1	no	—
242	C₈×Q₈	—	67	2	no	—
243	C₈×Q₈	—	67	1	no	—
244	C₈×Q₈	—	134	1	no	—
245	C₄×Q₁₆	—	67	2	no	—
246	C₄×SD₁₆	—	67	2	no	—
247	#436	—	67	1	no	—
248	#435	—	134	1	no	—
249	C₈×D₄	—	67	1	no	—
250	C₈×D₄	—	134	1	no	—
251	#433	—	134	1	no	—
252	#432	—	67	1	no	—
253	#431	C₂×D₆₇	1	1	yes	characteristic
254	#424	—	134	1	no	—
255	#423	—	67	1	no	—
256	#405	—	134	1	no	—
257	#405	—	134	1	no	—
258	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
260	#335	—	67	2	no	—
261	#334	—	67	2	no	—
262	Q₈⋊C₈	—	67	2	no	—
263	Q₈⋊C₈	—	67	2	no	—
264	Q₈⋊C₈	—	67	2	no	—
265	D₄⋊C₈	—	67	2	no	—
266	#322	C₂×D₆₇	1	2	yes	—
267	C₈²	C₂×D₆₇	1	2	yes	—
268	C₂×Q₁₆	—	67	2	no	—
269	C₂×SD₁₆	—	67	2	no	—
270	C₂×M₁₆	—	134	1	no	—
271	C₂×M₁₆	—	134	1	no	—
272	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
273	C₂²×C₈	—	134	1	no	—
274	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
275	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
276	C₄⋊Q₈	—	67	1	no	—
277	C₄⋊Q₈	—	67	1	no	—
278	#126	—	134	1	no	—
279	#125	—	67	1	no	—
280	#125	—	134	1	no	—
281	#124	—	67	1	no	—
282	#123	—	134	1	no	—
283	C₂²⋊Q₈	—	67	1	no	—
284	C₂²⋊Q₈	—	67	2	no	—
285	C₂²⋊Q₈	—	134	1	no	—
286	#121	—	67	1	no	—
287	C₄×Q₈	—	67	1	no	—
288	C₄×Q₈	—	67	2	no	—
289	C₄×Q₈	—	134	1	no	—
290	C₄×D₄	—	67	1	no	—
291	C₄×D₄	—	134	1	no	—
292	#117	—	134	1	no	—
293	#117	—	134	1	no	—
294	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
295	#107	—	67	2	no	—
296	#106	—	67	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	67	2	no	—
299	C₄⋊C₈	—	67	1	no	—
300	C₄⋊C₈	—	67	1	no	—
301	C₄⋊C₈	—	134	2	no	—
302	C₄⋊C₈	—	134	2	no	—
303	C₄⋊C₈	—	134	1	no	—
304	C₄⋊C₈	—	134	1	no	—
305	C₄⋊C₈	—	134	1	no	—
306	#103	—	67	2	no	—
307	#103	—	67	2	no	—
308	#103	—	67	2	no	—
309	#102	—	67	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	134	1	no	—
312	C₂²⋊C₈	—	134	1	no	—
313	C₂²⋊C₈	—	134	1	no	—
314	#97	—	134	1	no	—
315	#97	—	134	2	no	—
316	#97	—	134	1	no	—
317	#97	C₄×D₆₇	1	1	yes	characteristic
318	#97	C₄×D₆₇	1	1	yes	characteristic
319	C₄×C₈	—	134	1	no	—
320	C₄×C₈	—	134	2	no	—
321	C₄×C₈	D₂₆₈	1	1	yes	characteristic
322	C₄×C₈	D₂₆₈	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₆₇	1	2	yes	—
324	C₄×C₈	C₂²×D₆₇	1	2	yes	—
325	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
327	C₂×Q₈	—	67	1	no	—
328	C₂×Q₈	—	67	2	no	—
329	C₂×Q₈	—	134	1	no	—
330	C₂×D₄	—	67	1	no	—
331	C₂×D₄	—	134	1	no	—
332	C₂²×C₄	—	134	1	no	—
333	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
335	C₂²×C₄	#11761628	1	1	yes	characteristic
336	Q₁₆	—	134	4	no	—
337	SD₁₆	—	134	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	268	2	no	—
340	M₁₆	—	268	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	268	2	no	—
345	C₂×C₈	—	134	1	no	—
346	C₂×C₈	—	134	2	no	—
347	C₂×C₈	—	134	1	no	—
348	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
349	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
350	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
351	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
352	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
353	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
354	C₄⋊C₄	—	67	2	no	—
355	C₄⋊C₄	—	67	1	no	—
356	C₄⋊C₄	—	67	1	no	—
357	C₄⋊C₄	—	134	1	no	—
358	C₄⋊C₄	—	134	1	no	—
359	C₄⋊C₄	—	134	1	no	—
360	C₄⋊C₄	—	134	1	no	—
361	C₄⋊C₄	—	134	1	no	—
362	C₄⋊C₄	—	134	2	no	—
363	C₄⋊C₄	—	134	1	no	—
364	C₄⋊C₄	—	134	2	no	—
365	C₄⋊C₄	—	134	1	no	—
366	C₂²⋊C₄	—	134	2	no	—
367	C₂²⋊C₄	—	134	1	no	—
368	C₂²⋊C₄	—	134	1	no	—
369	C₂²⋊C₄	—	134	1	no	—
370	C₂²⋊C₄	—	134	1	no	—
371	C₂²⋊C₄	—	134	1	no	—
372	C₄²	—	134	1	no	—
373	C₄²	—	134	2	no	—
374	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
376	C₄²	#11761628	1	1	yes	characteristic
377	C₄²	C₂³×D₆₇	1	1	yes	characteristic
378	C₂³	—	134	1	no	—
379	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
380	Q₈	—	268	2	no	—
381	Q₈	—	134	2	no	—
382	Q₈	—	134	2	no	—
383	Q₈	—	134	2	no	—
384	D₄	—	268	2	no	—
385	D₄	—	134	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	268	1	no	—
391	C₂×C₄	—	268	1	no	—
392	C₂×C₄	—	134	1	no	—
393	C₂×C₄	—	134	1	no	—
394	C₂×C₄	—	134	2	no	—
395	C₂×C₄	—	134	2	no	—
396	C₂×C₄	—	134	1	no	—
397	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
398	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
399	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
402	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	268	1	no	—
409	C₈	—	268	1	no	—
410	C₈	—	268	2	no	—
411	C₈	#14524049	1	4	yes	—
412	C₈	#14524076	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	268	1	no	—
417	C₂²	—	268	1	no	—
418	C₂²	—	268	1	no	—
419	C₂²	C₂×C₄×D₂₆₈	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	—	268	1	no	—
425	C₄	—	268	1	no	—
426	C₄	—	268	2	no	—
427	C₄	—	268	1	no	—
428	C₄	—	268	2	no	—
429	C₄	C₂×#14524049	1	2	yes	—
430	C₄	C₂×#14524076	1	1	yes	characteristic
431	C₄	#16864196	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	536	1	no	—
434	C₂	#22568922	1	1	yes	characteristic
435	C₂	C₄×#14524076	1	1	yes	characteristic
436	C₂	#22569113	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×M₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#14524017	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₈×M₁₆	D₆₇
hypocenter	C₆₇	#17965
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22569143	C₂	semidirect
4. #22559119	C₂	semidirect
5. #22559113	C₂	semidirect
6. C₈×Dic₂₆₈	C₂	semidirect
7. C₈×#11761617	C₂	semidirect
8. #22558976	C₂	semidirect
9. #22558683	C₂	semidirect
11. C₈×M₁₆×C₆₇	C₂	semidirect
229. C₈×M₁₆	D₆₇	semidirect
230. C₆₇	#17965	semidirect

Maximal subgroups

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

subgroup	index
#22570815	2
#22569184	2
#22569143	2
#22559119	2
#22559113	2
C₈×Dic₂₆₈	2
C₈×#11761617	2
#22558976	2
#22558683	2
#22558675	2
C₈×M₁₆×C₆₇	2
#17965	67