Subgroups — C₄×D₈×#261 #16797403

Order 3328.

1350 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×D₈×#261	C₂	1	2	yes	maximal
2	C₄×D₄×#261	C₂	1	2	yes	maximal, complemented
3	#107×#261	C₂	1	2	yes	maximal, complemented
4	C₄×#88102	C₂	1	1	yes	maximal, characteristic, complemented
5	#102×#261	C₂	1	4	yes	maximal, complemented
6	C₄×#88115	C₂	1	2	yes	maximal, complemented
7	C₄×C₈×#261	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₈×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₄×#261	C₂²	1	4	yes	—
10	C₂²×C₄×#261	—	2	2	no	—
11	C₂×D₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₄×D₄×D₁₃	C₂²	1	2	yes	—
13	C₂×#88115	C₂²	1	4	yes	—
14	C₄×C₂²⋊#261	—	2	2	no	—
15	D₈×#261	C₄	1	16	yes	direct product factor
16	C₂×#88102	C₂²	1	2	yes	—
17	C₂×C₈×#261	C₂²	1	2	yes	—
18	C₂×C₈×#261	C₂²	1	2	yes	—
19	C₄⋊C₄×#261	C₂²	1	4	yes	—
20	C₂²⋊C₄×#261	—	2	4	no	—
21	C₄×C₄⋊#261	C₂²	1	2	yes	—
22	C₄²×#261	C₂²	1	1	yes	characteristic
23	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
25	D₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
26	C₄×#6104	C₄	1	2	yes	complemented
27	D₁₃×#107	C₂²	1	1	yes	characteristic
28	#11718533	C₄	1	1	yes	characteristic, complemented
29	D₁₃×#102	C₂²	1	2	yes	—
30	#11718417	C₄	1	2	yes	complemented
31	C₄×D₁₀₄	C₄	1	1	yes	characteristic, complemented
32	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
33	#11718265	C₂²	1	2	yes	—
34	#11718246	C₂²	1	4	yes	—
35	C₂³×#261	—	2	4	no	—
36	C₂×D₄×D₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×D₁₃	—	2	2	no	—
38	C₂×C₂²⋊#261	—	2	4	no	—
39	D₄×#261	—	2	8	no	—
40	D₄×#261	C₂×C₄	1	16	yes	complemented
41	C₂×C₄⋊#261	C₂³	1	4	yes	—
42	C₂×C₄×#261	—	2	4	no	—
43	C₂×C₄×#261	—	2	2	no	—
44	C₂×C₄×#261	—	4	8	no	—
45	C₂×C₄×#261	D₄	1	2	yes	—
46	C₂×C₄×#261	D₄	1	1	yes	characteristic
47	C₂×C₄×#261	D₄	1	1	yes	characteristic
48	C₂×C₄×#261	C₂³	1	2	yes	—
49	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
50	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
51	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
52	D₄×Dic₁₃	C₂×C₄	1	2	yes	complemented
53	C₂×#6104	C₂×C₄	1	2	yes	—
54	C₄×C₂²⋊D₁₃	—	2	2	no	—
55	D₈×D₁₃	C₂×C₄	1	8	yes	—
56	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
59	#88147	C₂×C₄	1	2	yes	complemented
60	C₄⋊C₄×D₁₃	C₂³	1	2	yes	—
61	#88135	—	2	2	no	—
62	C₂²⋊C₄×D₁₃	—	2	2	no	—
63	C₄×D₅₂	C₂×C₄	1	2	yes	complemented
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	#88115	C₂×C₄	1	16	yes	complemented
66	(C₂×#261)⋊C₄	—	2	4	no	—
67	(C₂×#261)⋊C₄	—	2	2	no	—
68	C₄×#1057	—	2	1	no	—
69	C₄×#1057	—	2	1	no	—
70	#88102	C₂×C₄	1	8	yes	complemented
71	C₈×#261	—	2	4	no	—
72	C₈×#261	C₂×C₄	1	8	yes	complemented
73	C₁₃×#107	C₂×C₄	1	1	yes	characteristic, complemented
74	C₁₃×#102	C₂×C₄	1	2	yes	complemented
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
76	#88072	C₂×C₄	1	2	yes	complemented
77	#88061	C₂×C₄	1	2	yes	complemented
78	#88058	C₂×C₄	1	1	yes	characteristic, complemented
79	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
80	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
81	#88049	C₂×C₄	1	2	yes	complemented
82	#88047	C₂×C₄	1	2	yes	complemented
83	C₄×#1055	C₂×C₄	1	1	yes	characteristic, complemented
84	C₄²×D₈	—	13	1	no	maximal, Sylow
85	C₂³×D₁₃	—	2	2	no	—
86	C₂²×#261	—	2	4	no	—
87	C₂²×#261	—	2	16	no	—
88	C₂²×#261	—	4	8	no	—
89	C₂²×#261	—	4	8	no	—
90	C₂²×#261	C₂×D₄	1	2	yes	—
91	C₂²×#261	C₂×D₄	1	2	yes	—
92	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂×C₂²⋊D₁₃	—	2	2	no	—
95	C₂²×Dic₁₃	—	2	2	no	—
96	D₄×D₁₃	—	2	4	no	—
97	D₄×D₁₃	C₂²×C₄	1	8	yes	—
98	C₂×D₅₂	C₂²×C₄	1	2	yes	—
99	C₂×C₄×D₁₃	—	2	2	no	—
100	C₂×C₄×D₁₃	—	2	2	no	—
101	C₂×C₄×D₁₃	—	2	2	no	—
102	C₂×C₄×D₁₃	—	4	4	no	—
103	C₂×C₄×D₁₃	—	4	4	no	—
104	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
107	C₂²⋊#261	—	2	16	no	—
108	C₂×#1057	—	2	2	no	—
109	C₄⋊#261	—	2	4	no	—
110	C₄⋊#261	C₂²×C₄	1	8	yes	—
111	C₄×#261	—	2	4	no	—
112	C₄×#261	—	2	2	no	—
113	C₄×#261	—	4	8	no	—
114	C₄×#261	—	4	4	no	—
115	C₄×#261	D₈	1	4	yes	direct product factor
116	C₄×#261	C₂²×C₄	1	4	yes	—
117	C₄×#261	#41	1	4	yes	—
118	D₁₃⋊C₈	—	2	2	no	—
119	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
120	C₁₃×D₈	C₄²	1	4	yes	complemented
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²⋊Dic₁₃	—	2	2	no	—
127	#6104	C₄²	1	8	yes	complemented
128	#6103	—	2	2	no	—
129	#6103	—	2	2	no	—
130	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
131	#6101	—	2	2	no	—
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	#41	1	1	yes	characteristic
134	C₄×Dic₁₃	#41	1	1	yes	characteristic
135	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
136	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
137	D₁₀₄	C₄²	1	4	yes	complemented
138	C₈×D₁₃	—	2	2	no	—
139	C₈×D₁₃	C₂²×C₄	1	4	yes	—
140	C₂×C₄×D₈	—	13	2	no	—
141	C₂×C₄×D₈	—	13	1	no	—
142	C₄²×D₄	—	13	2	no	—
143	C₄×#107	—	13	1	no	—
144	C₄×#107	—	13	2	no	—
145	C₄×#102	—	13	2	no	—
146	C₄×#102	—	13	4	no	—
147	C₄²×C₈	—	13	1	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂²×D₁₃	—	2	2	no	—
150	C₂²×D₁₃	—	2	8	no	—
151	C₂²×D₁₃	—	4	2	no	—
152	C₂²×D₁₃	—	4	2	no	—
153	C₂²×D₁₃	—	4	4	no	—
154	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×#261	—	2	2	no	—
156	C₂×#261	—	2	2	no	—
157	C₂×#261	—	2	8	no	—
158	C₂×#261	—	4	4	no	—
159	C₂×#261	—	4	4	no	—
160	C₂×#261	—	4	32	no	—
161	C₂×#261	C₄×D₄	1	4	yes	—
162	C₂×#261	C₄×D₄	1	4	yes	—
163	C₂×#261	C₂×D₈	1	4	yes	—
164	C₂×#261	#135	1	4	yes	—
165	D₄×C₁₃	—	2	2	no	—
166	D₄×C₁₃	C₂×C₄²	1	4	yes	complemented
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₁₃	—	2	8	no	—
173	C₂×Dic₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	4	4	no	—
175	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
178	D₅₂	—	2	2	no	—
179	D₅₂	C₂×C₄²	1	4	yes	complemented
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	4	2	no	—
182	C₄×D₁₃	—	4	2	no	—
183	C₄×D₁₃	—	4	4	no	—
184	C₄×D₁₃	—	4	4	no	—
185	C₄×D₁₃	C₂×D₈	1	2	yes	—
186	C₄×D₁₃	#135	1	2	yes	—
187	C₄×D₁₃	C₂³×C₄	1	2	yes	—
188	C₄×D₁₃	C₂×#41	1	2	yes	—
189	#1057	—	2	4	no	—
190	C₈×C₁₃	—	2	1	no	—
191	C₈×C₁₃	C₂×C₄²	1	2	yes	complemented
192	#1055	—	2	1	no	—
193	#1055	C₂×C₄²	1	2	yes	complemented
194	C₂²×D₈	—	13	1	no	—
195	C₂×C₄×D₄	—	13	4	no	—
196	C₂×C₄×D₄	—	13	2	no	—
197	C₂²×C₄²	—	26	2	no	—
198	C₄×D₈	—	13	16	no	—
199	C₄×D₈	—	13	1	no	—
200	C₄×D₈	—	13	2	no	—
201	C₄×D₈	—	13	1	no	—
202	C₄×D₈	—	13	2	no	—
203	C₄×D₈	—	13	1	no	—
204	C₄×D₈	#261	1	1	yes	characteristic, direct product factor
205	C₂×#107	—	13	2	no	—
206	C₂×#107	—	13	1	no	—
207	C₂×#102	—	13	4	no	—
208	C₂×#102	—	13	2	no	—
209	C₂×C₄×C₈	—	13	2	no	—
210	C₂×C₄×C₈	—	13	1	no	—
211	C₂×C₄×C₈	—	13	1	no	—
212	C₂×C₄×C₈	—	13	2	no	—
213	C₄×C₄⋊C₄	—	13	2	no	—
214	C₄×C₄⋊C₄	—	13	4	no	—
215	C₄×C₂²⋊C₄	—	26	4	no	—
216	C₄×C₂²⋊C₄	—	26	2	no	—
217	C₄³	—	13	1	no	—
218	#340	—	13	4	no	—
219	#340	—	13	2	no	—
220	C₂²×C₁₃	—	2	4	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	—	4	2	no	—
223	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂×D₁₃	—	2	4	no	—
225	C₂×D₁₃	—	4	2	no	—
226	C₂×D₁₃	—	4	2	no	—
227	C₂×D₁₃	—	4	8	no	—
228	C₂×D₁₃	—	4	8	no	—
229	C₂×D₁₃	C₂×C₄×D₄	1	2	yes	—
230	C₂×D₁₃	C₂²×D₈	1	1	yes	characteristic
231	C₂×D₁₃	C₂×#135	1	2	yes	—
232	C₂×D₁₃	C₂×#135	1	1	yes	characteristic
233	#261	—	2	4	no	—
234	#261	—	4	8	no	—
235	#261	C₄×D₈	1	8	yes	direct product factor
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	C₄×D₈	1	2	yes	complemented
239	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
240	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	4	2	no	—
243	Dic₁₃	C₄×D₈	1	2	yes	complemented
244	Dic₁₃	C₄×#41	1	2	yes	—
245	C₂²×D₄	—	13	2	no	—
246	C₂³×C₄	—	26	2	no	—
247	C₂³×C₄	—	26	4	no	—
248	C₂×D₈	—	13	2	no	—
249	C₂×D₈	—	13	8	no	—
250	C₂×D₈	—	13	1	no	—
251	C₂×D₈	C₂×#261	1	1	yes	characteristic
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	2	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₄×D₄	—	13	16	no	—
256	C₄×D₄	—	13	2	no	—
257	C₄×D₄	—	13	2	no	—
258	C₄×D₄	—	13	2	no	—
259	C₄×D₄	—	26	2	no	—
260	C₄×D₄	—	26	2	no	—
261	C₄×D₄	—	26	8	no	—
262	C₄×D₄	C₂×#261	1	2	yes	complemented
263	C₂×C₄⋊C₄	—	13	4	no	—
264	C₂×C₄⋊C₄	—	13	2	no	—
265	C₂×C₂²⋊C₄	—	26	2	no	—
266	C₂×C₂²⋊C₄	—	26	4	no	—
267	C₂×C₄²	—	13	2	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	2	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	26	4	no	—
273	C₂×C₄²	—	26	2	no	—
274	C₂×C₄²	—	52	8	no	—
275	#107	—	13	8	no	—
276	#107	—	13	1	no	—
277	#107	—	13	2	no	—
278	#107	C₂×#261	1	1	yes	characteristic, complemented
279	#102	—	13	16	no	—
280	#102	—	13	2	no	—
281	#102	—	13	2	no	—
282	#102	—	13	2	no	—
283	#102	C₂×#261	1	2	yes	complemented
284	C₄×C₈	—	13	8	no	—
285	C₄×C₈	—	13	1	no	—
286	C₄×C₈	—	13	1	no	—
287	C₄×C₈	—	13	1	no	—
288	C₄×C₈	—	26	4	no	—
289	C₄×C₈	—	26	1	no	—
290	C₄×C₈	—	26	1	no	—
291	C₄×C₈	C₂×#261	1	1	yes	characteristic, complemented
292	#95	—	26	4	no	—
293	#95	—	26	2	no	—
294	C₂×C₁₃	—	4	4	no	—
295	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
296	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
297	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
298	D₁₃	—	4	4	no	—
299	D₁₃	C₂×C₄×D₈	1	2	yes	—
300	D₁₃	C₄×#135	1	2	yes	—
301	C₂⁴	—	26	2	no	—
302	C₂×D₄	—	13	8	no	—
303	C₂×D₄	—	13	2	no	—
304	C₂×D₄	—	26	4	no	—
305	C₂×D₄	—	26	2	no	—
306	C₂×D₄	C₂²×#261	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	13	2	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	2	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	26	2	no	—
314	C₂²×C₄	—	26	2	no	—
315	C₂²×C₄	—	26	2	no	—
316	C₂²×C₄	—	26	16	no	—
317	C₂²×C₄	—	26	4	no	—
318	C₂²×C₄	—	26	2	no	—
319	C₂²×C₄	—	52	4	no	—
320	C₂²×C₄	—	52	4	no	—
321	C₂²×C₄	—	52	8	no	—
322	C₂²×C₄	—	52	8	no	—
323	D₈	—	13	8	no	—
324	D₈	—	13	4	no	—
325	D₈	C₄×#261	1	4	yes	direct product factor
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	4	no	—
328	C₂×C₈	—	13	4	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	26	2	no	—
331	C₂×C₈	—	26	2	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	C₂²×#261	1	1	yes	characteristic
334	C₂×C₈	C₂²×#261	1	1	yes	characteristic
335	C₄⋊C₄	—	13	8	no	—
336	C₄⋊C₄	—	13	2	no	—
337	C₄⋊C₄	—	26	2	no	—
338	C₄⋊C₄	—	26	4	no	—
339	C₄⋊C₄	C₂²×#261	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	26	2	no	—
342	C₂²⋊C₄	—	26	2	no	—
343	C₂²⋊C₄	—	26	16	no	—
344	C₂²⋊C₄	—	26	2	no	—
345	C₄²	—	13	4	no	—
346	C₄²	—	13	4	no	—
347	C₄²	—	13	4	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	26	4	no	—
352	C₄²	—	26	2	no	—
353	C₄²	—	52	8	no	—
354	C₄²	—	52	4	no	—
355	C₄²	C₂²×#261	1	1	yes	characteristic
356	C₁₃	C₄²×D₈	1	1	yes	characteristic, complemented, Sylow
357	C₂³	—	2	2	no	—
358	C₂³	—	13	1	no	—
359	C₂³	—	26	8	no	—
360	C₂³	—	26	2	no	—
361	C₂³	—	52	2	no	—
362	C₂³	—	52	2	no	—
363	C₂³	—	52	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	13	4	no	—
366	D₄	—	26	8	no	—
367	D₄	—	26	2	no	—
368	D₄	C₂×C₄×#261	1	4	yes	complemented
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	13	4	no	—
372	C₂×C₄	—	13	4	no	—
373	C₂×C₄	—	13	4	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	2	no	—
377	C₂×C₄	—	13	2	no	—
378	C₂×C₄	—	13	2	no	—
379	C₂×C₄	—	13	2	no	—
380	C₂×C₄	—	13	4	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	8	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	52	4	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	52	2	no	—
390	C₂×C₄	—	52	4	no	—
391	C₂×C₄	—	52	32	no	—
392	C₂×C₄	—	52	4	no	—
393	C₂×C₄	—	52	4	no	—
394	C₂×C₄	—	52	4	no	—
395	C₂×C₄	D₄×#261	1	1	yes	characteristic
396	C₂×C₄	D₄×#261	1	1	yes	characteristic
397	C₂×C₄	C₂³×#261	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	13	2	no	—
400	C₈	—	26	4	no	—
401	C₈	—	26	1	no	—
402	C₈	C₂×C₄×#261	1	2	yes	complemented
403	C₂²	—	2	4	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	13	2	no	—
407	C₂²	—	13	1	no	—
408	C₂²	—	13	1	no	—
409	C₂²	—	13	2	no	—
410	C₂²	—	26	4	no	—
411	C₂²	—	52	8	no	—
412	C₂²	—	52	8	no	—
413	C₂²	—	52	2	no	—
414	C₂²	—	52	2	no	—
415	C₂²	C₂×D₄×#261	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	13	8	no	—
419	C₄	—	13	2	no	—
420	C₄	—	13	2	no	—
421	C₄	—	26	4	no	—
422	C₄	—	26	1	no	—
423	C₄	—	52	8	no	—
424	C₄	—	52	2	no	—
425	C₄	D₈×#261	1	2	yes	direct product factor
426	C₄	C₂²×C₄×#261	1	1	yes	characteristic
427	C₄	#41×#261	1	1	yes	characteristic
428	C₂	—	4	4	no	—
429	C₂	—	13	2	no	—
430	C₂	—	13	2	no	—
431	C₂	—	52	4	no	—
432	C₂	C₄×D₄×#261	1	1	yes	characteristic
433	C₂	C₂×D₈×#261	1	1	yes	characteristic
434	C₂	#135×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₄×C₁₃×D₈	C₄
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₁₃	C₂²
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₄×D₈	#261
hypocenter	C₁₃	C₄²×D₈
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₄×#261	C₂	semidirect
3. #107×#261	C₂	semidirect
4. C₄×#88102	C₂	semidirect
5. #102×#261	C₂	semidirect
6. C₄×#88115	C₂	semidirect
7. C₄×C₈×#261	C₂	semidirect
15. D₈×#261	C₄	direct (N × H)
24. C₄×C₁₃×D₈	C₄	semidirect
25. D₈×Dic₁₃	C₄	semidirect
26. C₄×#6104	C₄	semidirect
28. #11718533	C₄	semidirect
30. #11718417	C₄	semidirect
31. C₄×D₁₀₄	C₄	semidirect
40. D₄×#261	C₂×C₄	semidirect
51. C₄×D₄×C₁₃	C₂×C₄	semidirect
52. D₄×Dic₁₃	C₂×C₄	semidirect
59. #88147	C₂×C₄	semidirect
63. C₄×D₅₂	C₂×C₄	semidirect
65. #88115	C₂×C₄	semidirect
70. #88102	C₂×C₄	semidirect
72. C₈×#261	C₂×C₄	semidirect
73. C₁₃×#107	C₂×C₄	semidirect
74. C₁₃×#102	C₂×C₄	semidirect
75. C₄×C₈×C₁₃	C₂×C₄	semidirect
76. #88072	C₂×C₄	semidirect
77. #88061	C₂×C₄	semidirect
78. #88058	C₂×C₄	semidirect
79. C₈×Dic₁₃	C₂×C₄	semidirect
80. C₈×Dic₁₃	C₂×C₄	semidirect
81. #88049	C₂×C₄	semidirect
82. #88047	C₂×C₄	semidirect
83. C₄×#1055	C₂×C₄	semidirect
115. C₄×#261	D₈	direct (N × H)
120. C₁₃×D₈	C₄²	semidirect
127. #6104	C₄²	semidirect
137. D₁₀₄	C₄²	semidirect
166. D₄×C₁₃	C₂×C₄²	semidirect
179. D₅₂	C₂×C₄²	semidirect
191. C₈×C₁₃	C₂×C₄²	semidirect
193. #1055	C₂×C₄²	semidirect
204. C₄×D₈	#261	direct (N × H)
235. #261	C₄×D₈	direct (N × H)
238. C₄×C₁₃	C₄×D₈	semidirect
243. Dic₁₃	C₄×D₈	semidirect
262. C₄×D₄	C₂×#261	semidirect
278. #107	C₂×#261	semidirect
283. #102	C₂×#261	semidirect
291. C₄×C₈	C₂×#261	semidirect
325. D₈	C₄×#261	direct (N × H)
356. C₁₃	C₄²×D₈	semidirect
368. D₄	C₂×C₄×#261	semidirect
402. C₈	C₂×C₄×#261	semidirect
425. C₄	D₈×#261	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×D₈×#261	2
C₄×D₄×#261	2
#107×#261	2
C₄×#88102	2
#102×#261	2
C₄×#88115	2
C₄×C₈×#261	2
C₄×D₈×D₁₃	2
C₄²×D₈	13

Subgroups — C4×D8×#261 #16797403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₈×#261 #16797403