Subgroups — C₄×#16863834 #31009153

Order 17152.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863834	C₂	1	1	yes	maximal, characteristic
2	C₄×#14524065	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₅₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562086	C₂	1	2	yes	maximal, complemented
5	#22562075	C₂	1	2	yes	maximal, complemented
6	C₄×#14523988	C₂	1	2	yes	maximal, complemented
7	C₄×D₁₀₇₂	C₂	1	2	yes	maximal, complemented
8	#22561997	C₂	1	1	yes	maximal, characteristic, complemented
9	#22561926	C₂	1	1	yes	maximal, characteristic, complemented
10	#22561922	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×M₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
14	C₄×#11761628	—	2	1	no	—
15	C₂×C₄×D₂₆₈	—	2	1	no	—
16	#16863834	C₄	1	8	yes	direct product factor
17	C₂×#14523988	C₂²	1	2	yes	—
18	C₂×D₁₀₇₂	C₂²	1	2	yes	—
19	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic, complemented
20	C₄×Dic₂₆₈	C₂²	1	1	yes	characteristic, complemented
21	C₄×#11761617	—	2	1	no	—
22	C₄×#11761617	—	2	1	no	—
23	C₄×D₅₃₆	—	2	1	no	—
24	C₄×D₅₃₆	—	2	1	no	—
25	C₄×D₅₃₆	C₂²	1	2	yes	—
26	C₄×D₅₃₆	C₂²	1	2	yes	—
27	C₄×D₅₃₆	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₅₃₆	C₂²	1	1	yes	characteristic, complemented
29	#16863434	C₂²	1	1	yes	characteristic
30	C₂×#14523977	C₂²	1	1	yes	characteristic
31	#16863393	—	2	1	no	—
32	C₂×#14523965	—	2	1	no	—
33	#16863224	C₂²	1	2	yes	complemented
34	#16863222	C₂²	1	2	yes	complemented
35	#16863201	C₂²	1	2	yes	complemented
36	#16863198	C₂²	1	2	yes	—
37	#16863198	C₂²	1	2	yes	—
38	#16863198	C₂²	1	2	yes	complemented
39	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
42	#346×C₆₇	C₂²	1	2	yes	complemented
43	C₄×C₁₆×C₆₇	C₂²	1	2	yes	complemented
44	C₂×#11761628	—	2	1	no	—
45	C₂²×D₂₆₈	—	2	1	no	—
46	C₂²×C₄×D₆₇	—	4	1	no	—
47	#14524065	—	2	2	no	—
48	#14524065	C₂×C₄	1	4	yes	complemented
49	C₂×Dic₂₆₈	C₂³	1	1	yes	characteristic
50	C₂×#11761617	—	2	1	no	—
51	C₂×D₅₃₆	—	2	1	no	—
52	C₂×D₅₃₆	—	2	2	no	—
53	C₂×D₅₃₆	C₂×C₄	1	4	yes	complemented
54	C₂×D₅₃₆	C₂³	1	2	yes	—
55	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
56	C₄×Dic₁₃₄	—	2	1	no	—
57	C₄×Dic₁₃₄	—	2	1	no	—
58	C₄×D₂₆₈	—	2	2	no	—
59	C₄×D₂₆₈	—	2	2	no	—
60	C₄×D₂₆₈	—	2	1	no	—
61	C₄×D₂₆₈	—	2	1	no	—
62	C₄×D₂₆₈	—	4	1	no	—
63	C₄×D₂₆₈	—	4	1	no	—
64	C₄×C₂²⋊D₆₇	—	4	1	no	—
65	C₄×C₂²⋊D₆₇	—	4	1	no	—
66	#14524002	—	2	1	no	—
67	#14524000	—	4	1	no	—
68	C₂×C₄⋊Dic₆₇	—	2	1	no	—
69	C₂×(C₂×D₆₇)⋊C₄	—	4	1	no	—
70	C₄²×D₆₇	—	4	1	no	—
71	#14523988	C₂×C₄	1	8	yes	complemented
72	D₁₀₇₂	C₂×C₄	1	8	yes	complemented
73	#14523977	—	2	1	no	—
74	#14523977	C₂³	1	1	yes	characteristic
75	#14523977	C₂³	1	1	yes	characteristic
76	#14523977	C₂³	1	2	yes	—
77	#14523975	—	2	1	no	—
78	#14523968	—	2	1	no	—
79	#14523968	—	2	1	no	—
80	#14523965	—	2	2	no	—
81	#14523965	—	2	2	no	—
82	#14523965	—	2	1	no	—
83	#14523965	—	2	1	no	—
84	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
87	M₃₂×C₆₇	—	2	2	no	—
88	M₃₂×C₆₇	C₂×C₄	1	4	yes	complemented
89	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
90	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
91	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
92	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂³×D₆₇	—	4	1	no	—
96	#11761628	—	2	4	no	—
97	#11761628	—	4	2	no	—
98	C₂×Dic₁₃₄	—	2	1	no	—
99	C₂×D₂₆₈	—	2	4	no	—
100	C₂×D₂₆₈	—	2	2	no	—
101	C₂×D₂₆₈	—	2	1	no	—
102	C₂×D₂₆₈	—	4	1	no	—
103	C₂×D₂₆₈	—	4	2	no	—
104	C₂×C₂²⋊D₆₇	—	4	1	no	—
105	C₂²×Dic₆₇	—	4	1	no	—
106	C₂×C₄×D₆₇	—	4	1	no	—
107	C₂×C₄×D₆₇	—	4	1	no	—
108	C₂×C₄×D₆₇	—	4	1	no	—
109	C₂×C₄×D₆₇	—	4	2	no	—
110	C₂×C₄×D₆₇	—	4	2	no	—
111	C₂×C₄×D₆₇	—	8	4	no	—
112	Dic₂₆₈	—	2	1	no	—
113	Dic₂₆₈	C₂²×C₄	1	2	yes	complemented
114	#11761617	—	2	4	no	—
115	D₅₃₆	—	2	4	no	—
116	D₅₃₆	—	2	2	no	—
117	D₅₃₆	—	2	1	no	—
118	D₅₃₆	C₂²×C₄	1	4	yes	—
119	D₅₃₆	C₂²×C₄	1	2	yes	complemented
120	C₄⋊Dic₆₇	—	2	2	no	—
121	C₄⋊Dic₆₇	—	2	1	no	—
122	C₄⋊Dic₆₇	—	2	1	no	—
123	C₄⋊Dic₆₇	—	4	1	no	—
124	Dic₆₇⋊C₄	—	4	1	no	—
125	Dic₆₇⋊C₄	—	4	1	no	—
126	C₂²⋊Dic₆₇	—	4	1	no	—
127	(C₂×D₆₇)⋊C₄	—	4	2	no	—
128	(C₂×D₆₇)⋊C₄	—	4	2	no	—
129	(C₂×D₆₇)⋊C₄	—	4	1	no	—
130	(C₂×D₆₇)⋊C₄	—	4	1	no	—
131	C₄×Dic₆₇	—	4	1	no	—
132	C₄×Dic₆₇	—	4	1	no	—
133	C₄×Dic₆₇	—	4	1	no	—
134	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	#41	1	2	yes	—
143	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
144	C₄²×C₆₇	D₈	1	1	yes	characteristic
145	C₄²×C₆₇	D₈	1	1	yes	characteristic
146	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₁₆×C₆₇	—	2	2	no	—
149	C₁₆×C₆₇	C₂²×C₄	1	4	yes	complemented
150	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
151	C₂²×D₆₇	—	4	1	no	—
152	C₂²×D₆₇	—	4	2	no	—
153	C₂²×D₆₇	—	4	4	no	—
154	C₂²×D₆₇	—	8	2	no	—
155	C₂²×D₆₇	—	8	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	4	1	no	—
158	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₇	#135	1	2	yes	—
165	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₆₇	—	4	4	no	—
167	C₂×Dic₆₇	—	4	1	no	—
168	C₂×Dic₆₇	—	4	1	no	—
169	C₂×Dic₆₇	—	4	1	no	—
170	C₂×Dic₆₇	—	4	2	no	—
171	C₂×Dic₆₇	—	8	2	no	—
172	D₂₆₈	—	2	4	no	—
173	D₂₆₈	—	2	2	no	—
174	D₂₆₈	—	4	2	no	—
175	D₂₆₈	—	4	1	no	—
176	D₂₆₈	—	4	4	no	—
177	C₄×D₆₇	—	4	4	no	—
178	C₄×D₆₇	—	8	2	no	—
179	C₄×D₆₇	—	8	4	no	—
180	C₄×D₆₇	—	8	2	no	—
181	C₄×D₆₇	—	8	4	no	—
182	Dic₁₃₄	—	2	2	no	—
183	Dic₁₃₄	—	4	1	no	—
184	C₈×C₆₇	—	2	1	no	—
185	C₈×C₆₇	—	2	1	no	—
186	C₈×C₆₇	C₄×D₄	1	2	yes	—
187	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
188	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
189	C₂²×C₆₇	—	2	1	no	—
190	C₂²×C₆₇	—	2	1	no	—
191	C₂²×C₆₇	C₄×D₈	1	2	yes	—
192	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
193	C₂×D₆₇	—	4	2	no	—
194	C₂×D₆₇	—	4	4	no	—
195	C₂×D₆₇	—	8	8	no	—
196	C₂×D₆₇	—	8	2	no	—
197	C₂×D₆₇	—	8	1	no	—
198	C₂×D₆₇	—	8	1	no	—
199	C₂×D₆₇	—	8	2	no	—
200	C₄×C₆₇	—	2	1	no	—
201	C₄×C₆₇	—	2	1	no	—
202	C₄×C₆₇	—	2	1	no	—
203	C₄×C₆₇	C₄×D₈	1	2	yes	—
204	C₄×C₆₇	#509	1	2	yes	complemented
205	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
207	Dic₆₇	—	4	2	no	—
208	Dic₆₇	—	8	2	no	—
209	Dic₆₇	—	8	1	no	—
210	Dic₆₇	—	8	1	no	—
211	C₄×#509	—	67	1	no	maximal, Sylow
212	C₂×C₆₇	—	2	2	no	—
213	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
214	C₂×C₆₇	C₂×#509	1	1	yes	characteristic
215	C₂×C₆₇	#3414	1	1	yes	characteristic
216	D₆₇	—	8	2	no	—
217	D₆₇	—	8	4	no	—
218	C₂×#509	—	67	1	no	—
219	C₄×#135	—	67	1	no	—
220	C₂×C₄×D₈	—	67	1	no	—
221	#2177	—	67	2	no	—
222	#2175	—	67	2	no	—
223	C₄×SD₃₂	—	67	2	no	—
224	C₄×D₁₆	—	67	2	no	—
225	#2159	—	67	1	no	—
226	#2140	—	67	1	no	—
227	#2139	—	67	1	no	—
228	C₄×M₃₂	D₆₇	1	1	yes	characteristic, complemented
229	C₆₇	C₄×#509	1	1	yes	characteristic, complemented, Sylow
230	C₂×#135	—	67	1	no	—
231	C₂²×D₈	—	67	1	no	—
232	C₄×#41	—	134	1	no	—
233	C₂×C₄×D₄	—	134	1	no	—
234	#509	—	67	8	no	—
235	C₂×SD₃₂	—	67	2	no	—
236	C₂×D₁₆	—	67	2	no	—
237	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
238	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
239	C₄×Q₁₆	—	67	1	no	—
240	C₄×Q₁₆	—	67	1	no	—
241	C₄×SD₁₆	—	134	1	no	—
242	C₄×SD₁₆	—	134	1	no	—
243	C₄×D₈	—	67	2	no	—
244	C₄×D₈	—	67	2	no	—
245	C₄×D₈	—	67	1	no	—
246	C₄×D₈	—	67	1	no	—
247	C₄×D₈	—	134	1	no	—
248	C₄×D₈	—	134	1	no	—
249	#427	—	67	1	no	—
250	C₂×#107	—	67	1	no	—
251	#416	—	134	1	no	—
252	C₂×#102	—	134	1	no	—
253	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
254	#367	—	67	2	no	—
255	#366	—	67	2	no	—
256	#358	—	67	2	no	—
257	#357	—	67	2	no	—
258	#357	—	67	2	no	—
259	#357	—	67	2	no	—
260	#346	C₂×D₆₇	1	2	yes	complemented
261	C₄×C₁₆	C₂×D₆₇	1	2	yes	complemented
262	C₂×#41	—	134	1	no	—
263	C₂²×D₄	—	134	1	no	—
264	C₂³×C₄	—	268	1	no	—
265	#135	—	67	4	no	—
266	#135	—	134	2	no	—
267	C₂×Q₁₆	—	67	1	no	—
268	C₂×SD₁₆	—	134	1	no	—
269	C₂×D₈	—	67	4	no	—
270	C₂×D₈	—	67	2	no	—
271	C₂×D₈	—	67	1	no	—
272	C₂×D₈	—	134	1	no	—
273	C₂×D₈	—	134	2	no	—
274	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
276	C₄×Q₈	—	134	1	no	—
277	C₄×Q₈	—	134	1	no	—
278	C₄×D₄	—	268	1	no	—
279	C₄×D₄	—	268	1	no	—
280	C₄×D₄	—	268	1	no	—
281	C₄×D₄	—	268	1	no	—
282	C₄×D₄	—	134	2	no	—
283	C₄×D₄	—	134	2	no	—
284	C₄×D₄	—	134	1	no	—
285	C₄×D₄	—	134	1	no	—
286	#117	—	268	1	no	—
287	#117	—	134	1	no	—
288	C₂×C₄⋊C₄	—	134	1	no	—
289	C₂×C₂²⋊C₄	—	268	1	no	—
290	C₂×C₄²	—	268	1	no	—
291	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
292	SD₃₂	—	67	8	no	—
293	D₁₆	—	67	8	no	—
294	M₃₂	—	2	2	no	—
295	M₃₂	C₄×D₆₇	1	4	yes	complemented
296	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
297	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
298	#107	—	67	1	no	—
299	#107	—	67	1	no	—
300	#107	—	67	2	no	—
301	#107	—	134	1	no	—
302	#106	—	134	1	no	—
303	#103	—	134	1	no	—
304	#103	—	134	1	no	—
305	#102	—	134	2	no	—
306	#102	—	134	2	no	—
307	#102	—	134	1	no	—
308	#102	—	134	1	no	—
309	C₄×C₈	D₂₆₈	1	1	yes	characteristic
310	C₄×C₈	D₂₆₈	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
313	C₂⁴	—	268	1	no	—
314	#41	—	268	2	no	—
315	#41	—	134	4	no	—
316	C₂×Q₈	—	134	1	no	—
317	C₂×D₄	—	268	1	no	—
318	C₂×D₄	—	268	1	no	—
319	C₂×D₄	—	268	2	no	—
320	C₂×D₄	—	134	4	no	—
321	C₂×D₄	—	134	2	no	—
322	C₂×D₄	—	134	1	no	—
323	C₂²×C₄	—	268	1	no	—
324	C₂²×C₄	—	268	1	no	—
325	C₂²×C₄	—	268	1	no	—
326	C₂²×C₄	—	268	2	no	—
327	C₂²×C₄	—	268	1	no	—
328	C₂²×C₄	—	268	2	no	—
329	C₂²×C₄	—	536	4	no	—
330	C₂²×C₄	D₅₃₆	1	1	yes	characteristic
331	C₂²×C₄	D₅₃₆	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
333	Q₁₆	—	67	2	no	—
334	Q₁₆	—	134	1	no	—
335	SD₁₆	—	134	4	no	—
336	D₈	—	67	2	no	—
337	D₈	—	67	4	no	—
338	D₈	—	134	4	no	—
339	D₈	—	134	2	no	—
340	D₈	—	134	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
343	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
344	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
345	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
346	C₂×C₈	#11761628	1	2	yes	—
347	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
348	C₄⋊C₄	—	268	1	no	—
349	C₄⋊C₄	—	268	1	no	—
350	C₄⋊C₄	—	268	1	no	—
351	C₄⋊C₄	—	134	2	no	—
352	C₄⋊C₄	—	134	1	no	—
353	C₄⋊C₄	—	134	1	no	—
354	C₂²⋊C₄	—	268	1	no	—
355	C₂²⋊C₄	—	268	2	no	—
356	C₂²⋊C₄	—	268	2	no	—
357	C₂²⋊C₄	—	268	1	no	—
358	C₂²⋊C₄	—	268	1	no	—
359	C₄²	—	268	1	no	—
360	C₄²	—	268	1	no	—
361	C₄²	—	268	1	no	—
362	C₄²	D₅₃₆	1	1	yes	characteristic
363	C₄²	D₅₃₆	1	1	yes	characteristic
364	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
365	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
366	C₁₆	—	2	2	no	—
367	C₁₆	C₂×C₄×D₆₇	1	4	yes	complemented
368	C₂³	—	268	1	no	—
369	C₂³	—	268	2	no	—
370	C₂³	—	268	4	no	—
371	C₂³	—	536	2	no	—
372	C₂³	—	536	2	no	—
373	C₂³	C₂×D₅₃₆	1	1	yes	characteristic
374	Q₈	—	268	1	no	—
375	Q₈	—	134	2	no	—
376	D₄	—	268	4	no	—
377	D₄	—	268	2	no	—
378	D₄	—	268	1	no	—
379	D₄	—	268	4	no	—
380	D₄	—	134	4	no	—
381	D₄	—	134	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	268	1	no	—
385	C₂×C₄	—	268	4	no	—
386	C₂×C₄	—	268	1	no	—
387	C₂×C₄	—	268	1	no	—
388	C₂×C₄	—	268	2	no	—
389	C₂×C₄	—	536	4	no	—
390	C₂×C₄	—	536	2	no	—
391	C₂×C₄	—	536	2	no	—
392	C₂×C₄	—	536	4	no	—
393	C₂×C₄	—	536	2	no	—
394	C₂×C₄	C₄×D₂₆₈	1	2	yes	—
395	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
396	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
397	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
398	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
399	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
400	C₂×C₄	#14524065	1	2	yes	—
401	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	C₄×D₂₆₈	1	2	yes	—
405	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
406	C₈	C₂×#11761628	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	268	2	no	—
410	C₂²	—	268	4	no	—
411	C₂²	—	536	8	no	—
412	C₂²	—	536	2	no	—
413	C₂²	—	536	1	no	—
414	C₂²	—	536	1	no	—
415	C₂²	—	536	2	no	—
416	C₂²	C₄×D₅₃₆	1	2	yes	—
417	C₂²	C₂²×D₅₃₆	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	268	2	no	—
422	C₄	—	536	2	no	—
423	C₄	—	536	1	no	—
424	C₄	—	536	1	no	—
425	C₄	C₄×D₅₃₆	1	2	yes	—
426	C₄	#16863834	1	2	yes	direct product factor
427	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
428	C₄	C₂×#14524065	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	536	4	no	—
431	C₂	—	536	2	no	—
432	C₂	C₂×C₄×D₅₃₆	1	1	yes	characteristic
433	C₂	C₂×#16863834	1	1	yes	characteristic
434	C₂	#22573345	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₅₃₆
commutator	C₈×C₆₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₄×M₃₂×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×D₈
prime radical	C₂×#16863834	C₂
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	C₄×M₃₂	D₆₇
hypocenter	C₆₇	C₄×#509
LCS	G ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₄×#14524065	C₂	semidirect
3. C₂×C₄×D₅₃₆	C₂	semidirect
4. #22562086	C₂	semidirect
5. #22562075	C₂	semidirect
6. C₄×#14523988	C₂	semidirect
7. C₄×D₁₀₇₂	C₂	semidirect
8. #22561997	C₂	semidirect
9. #22561926	C₂	semidirect
10. #22561922	C₂	semidirect
11. C₄×M₃₂×C₆₇	C₂	semidirect
16. #16863834	C₄	direct (N × H)
19. C₄×Dic₂₆₈	C₂²	semidirect
20. C₄×Dic₂₆₈	C₂²	semidirect
27. C₄×D₅₃₆	C₂²	semidirect
28. C₄×D₅₃₆	C₂²	semidirect
33. #16863224	C₂²	semidirect
34. #16863222	C₂²	semidirect
35. #16863201	C₂²	semidirect
38. #16863198	C₂²	semidirect
42. #346×C₆₇	C₂²	semidirect
43. C₄×C₁₆×C₆₇	C₂²	semidirect
48. #14524065	C₂×C₄	semidirect
53. C₂×D₅₃₆	C₂×C₄	semidirect
71. #14523988	C₂×C₄	semidirect
72. D₁₀₇₂	C₂×C₄	semidirect
88. M₃₂×C₆₇	C₂×C₄	semidirect
113. Dic₂₆₈	C₂²×C₄	semidirect
119. D₅₃₆	C₂²×C₄	semidirect
149. C₁₆×C₆₇	C₂²×C₄	semidirect
204. C₄×C₆₇	#509	semidirect
228. C₄×M₃₂	D₆₇	semidirect
229. C₆₇	C₄×#509	semidirect
260. #346	C₂×D₆₇	semidirect
261. C₄×C₁₆	C₂×D₆₇	semidirect
295. M₃₂	C₄×D₆₇	semidirect
367. C₁₆	C₂×C₄×D₆₇	semidirect
426. C₄	#16863834	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16863834	2
C₄×#14524065	2
C₂×C₄×D₅₃₆	2
#22562086	2
#22562075	2
C₄×#14523988	2
C₄×D₁₀₇₂	2
#22561997	2
#22561926	2
#22561922	2
C₄×M₃₂×C₆₇	2
C₄×#509	67

Subgroups — C4×#16863834 #31009153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16863834 #31009153