Subgroups — C₄×#11718808 #16016237

Order 3328.

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×#11718808	C₂	1	1	yes	maximal, characteristic
2	C₄×#88158	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116710	C₂	1	2	yes	maximal, complemented
4	#13116700	C₂	1	2	yes	maximal, complemented
5	C₄×#88067	C₂	1	2	yes	maximal, complemented
6	C₄×#88066	C₂	1	2	yes	maximal, complemented
7	#13116622	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116552	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88052	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	—	2	1	no	—
14	C₂×#88158	C₂²	1	1	yes	characteristic
15	C₄×#6127	—	2	1	no	—
16	C₄×C₁₃×D₈	—	2	1	no	—
17	C₄×C₁₃×D₈	—	2	1	no	—
18	C₄×C₁₃×D₈	C₂²	1	2	yes	—
19	C₄×C₁₃×D₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	—	2	1	no	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×#88067	C₂²	1	2	yes	—
24	#11718808	C₄	1	8	yes	direct product factor
25	C₂×#88066	C₂²	1	2	yes	—
26	#11718774	—	2	1	no	—
27	#11718767	C₂²	1	1	yes	characteristic
28	C₂×#88052	C₂²	1	1	yes	characteristic
29	C₂×#88052	C₂²	1	1	yes	characteristic
30	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
31	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
32	C₄×D₁₀₄	C₂²	1	1	yes	characteristic, complemented
33	C₄×D₁₀₄	C₂²	1	1	yes	characteristic, complemented
34	C₄×#6095	—	2	1	no	—
35	C₄×#6095	—	2	1	no	—
36	#11718154	C₂²	1	2	yes	—
37	#11718154	C₂²	1	2	yes	—
38	#11718084	C₂²	1	2	yes	complemented
39	#11718083	C₂²	1	2	yes	complemented
40	#11718082	C₂²	1	2	yes	complemented
41	#11718081	C₂²	1	2	yes	complemented
42	#11718053	C₂²	1	2	yes	complemented
43	C₄×#6090	C₂²	1	2	yes	complemented
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	—	4	1	no	—
46	C₂×#6127	—	2	1	no	—
47	C₂×C₁₃×D₈	—	2	1	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₁₃×D₈	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	4	1	no	—
56	C₄×D₄×C₁₃	—	4	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₃	—	4	1	no	—
61	C₄×C₂²⋊D₁₃	—	4	1	no	—
62	#88180	—	2	1	no	—
63	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
64	#88158	—	2	2	no	—
65	#88158	C₂×C₄	1	4	yes	complemented
66	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
67	C₂×#6095	—	2	1	no	—
68	C₄×D₅₂	—	2	1	no	—
69	C₄×D₅₂	—	2	1	no	—
70	#88126	—	4	1	no	—
71	C₄²×D₁₃	—	4	1	no	—
72	C₄×Dic₂₆	—	2	1	no	—
73	C₄×Dic₂₆	—	2	1	no	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	C₂³	1	2	yes	—
76	C₁₃×#102	—	2	2	no	—
77	C₁₃×#102	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#88067	C₂×C₄	1	8	yes	complemented
83	#88066	C₂×C₄	1	8	yes	complemented
84	#88061	—	2	1	no	—
85	#88061	—	2	1	no	—
86	#88058	C₂³	1	1	yes	characteristic
87	#88058	C₂³	1	1	yes	characteristic
88	#88057	—	2	1	no	—
89	#88056	—	2	1	no	—
90	#88056	—	2	1	no	—
91	#88052	—	2	2	no	—
92	#88052	C₂×C₄	1	4	yes	complemented
93	C₂×#6090	C₂³	1	2	yes	—
94	C₂×#6090	C₂³	1	2	yes	—
95	C₄×#509	—	13	1	no	maximal, Sylow
96	C₂⁴×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	—	2	4	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	—	8	4	no	—
105	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₁₃	—	4	1	no	—
109	#6127	—	2	4	no	—
110	#6127	—	4	2	no	—
111	C₂×D₅₂	—	2	1	no	—
112	C₂×C₄×D₁₃	—	4	1	no	—
113	C₂×C₄×D₁₃	—	4	1	no	—
114	C₂×C₄×D₁₃	—	4	1	no	—
115	C₂×Dic₂₆	—	2	1	no	—
116	C₁₃×D₈	—	2	4	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	C₂²×C₄	1	4	yes	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	#41	1	2	yes	—
125	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	4	1	no	—
128	C₁₃×C₂²⋊C₄	—	4	2	no	—
129	C₁₃×C₂²⋊C₄	—	4	2	no	—
130	C₄²×C₁₃	D₈	1	1	yes	characteristic
131	C₄²×C₁₃	D₈	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²⋊Dic₁₃	—	4	1	no	—
135	#6103	—	4	1	no	—
136	#6103	—	4	1	no	—
137	C₄⋊Dic₁₃	—	2	1	no	—
138	C₄⋊Dic₁₃	—	2	1	no	—
139	#6101	—	4	1	no	—
140	#6101	—	4	1	no	—
141	C₄×Dic₁₃	—	4	1	no	—
142	C₄×Dic₁₃	—	4	1	no	—
143	C₄×Dic₁₃	—	4	1	no	—
144	Dic₅₂	—	2	1	no	—
145	Dic₅₂	C₂²×C₄	1	2	yes	complemented
146	D₁₀₄	—	2	1	no	—
147	D₁₀₄	C₂²×C₄	1	2	yes	complemented
148	#6095	—	2	4	no	—
149	#6090	—	2	2	no	—
150	#6090	C₂²×C₄	1	4	yes	complemented
151	C₂×#509	—	13	1	no	—
152	C₄×#135	—	13	1	no	—
153	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic, complemented
154	#2177	—	13	2	no	—
155	#2175	—	13	2	no	—
156	C₄×SD₃₂	—	13	2	no	—
157	C₄×D₁₆	—	13	2	no	—
158	#2159	—	13	1	no	—
159	#2140	—	13	1	no	—
160	#2139	—	13	1	no	—
161	C₄×M₃₂	—	13	1	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	4	no	—
164	C₂³×C₁₃	—	8	2	no	—
165	C₂³×C₁₃	—	8	2	no	—
166	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂²×D₁₃	—	4	1	no	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	—	8	4	no	—
177	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#135	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂²⋊D₁₃	—	4	4	no	—
186	C₂×Dic₁₃	—	4	1	no	—
187	C₂×Dic₁₃	—	4	1	no	—
188	C₂×Dic₁₃	—	4	1	no	—
189	D₅₂	—	2	2	no	—
190	D₅₂	—	4	1	no	—
191	C₄×D₁₃	—	4	4	no	—
192	C₄×D₁₃	—	8	2	no	—
193	C₄×D₁₃	—	8	2	no	—
194	Dic₂₆	—	2	2	no	—
195	Dic₂₆	—	4	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	C₄×D₄	1	2	yes	—
199	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×#135	—	13	1	no	—
202	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
203	C₄×#41	—	26	1	no	—
204	C₂×C₄×D₄	—	2	1	no	—
205	#509	—	13	8	no	—
206	C₂×SD₃₂	—	13	2	no	—
207	C₂×D₁₆	—	13	2	no	—
208	C₂×M₃₂	—	13	1	no	—
209	C₂×M₃₂	—	13	1	no	—
210	C₄×Q₁₆	—	13	1	no	—
211	C₄×Q₁₆	—	13	1	no	—
212	C₄×SD₁₆	—	26	1	no	—
213	C₄×SD₁₆	—	26	1	no	—
214	C₄×D₈	—	2	1	no	—
215	C₄×D₈	—	2	1	no	—
216	C₄×D₈	—	13	1	no	—
217	C₄×D₈	—	13	1	no	—
218	C₄×D₈	C₂×D₁₃	1	2	yes	—
219	C₄×D₈	C₂×D₁₃	1	2	yes	—
220	#427	—	13	1	no	—
221	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
222	#416	—	26	1	no	—
223	C₂×#102	—	2	1	no	—
224	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
225	#367	—	13	2	no	—
226	#366	—	13	2	no	—
227	#358	—	13	2	no	—
228	#357	—	13	2	no	—
229	#357	—	13	2	no	—
230	#357	—	13	2	no	—
231	#346	—	13	2	no	—
232	C₄×C₁₆	—	13	2	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	8	8	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	C₄×D₈	1	2	yes	—
240	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
241	C₂×D₁₃	—	4	2	no	—
242	C₂×D₁₃	—	8	1	no	—
243	C₂×D₁₃	—	8	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	8	2	no	—
248	C₄×C₁₃	C₄×D₈	1	2	yes	—
249	C₄×C₁₃	#509	1	2	yes	complemented
250	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
252	Dic₁₃	—	4	2	no	—
253	Dic₁₃	—	8	1	no	—
254	Dic₁₃	—	8	1	no	—
255	C₂×#41	—	26	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂³×C₄	—	4	1	no	—
258	#135	—	13	4	no	—
259	#135	—	26	2	no	—
260	C₂×Q₁₆	—	13	1	no	—
261	C₂×SD₁₆	—	26	1	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	—	13	1	no	—
265	C₂×D₈	C₄×D₁₃	1	4	yes	complemented
266	C₂×D₈	C₂²×D₁₃	1	2	yes	—
267	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
269	C₄×Q₈	—	26	1	no	—
270	C₄×Q₈	—	26	1	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	4	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	26	1	no	—
276	C₄×D₄	—	26	1	no	—
277	C₄×D₄	—	52	1	no	—
278	C₄×D₄	—	52	1	no	—
279	#117	—	26	1	no	—
280	#117	—	52	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	4	1	no	—
283	C₂×C₄²	—	52	1	no	—
284	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
285	SD₃₂	—	13	8	no	—
286	D₁₆	—	13	8	no	—
287	M₃₂	—	13	4	no	—
288	M₃₂	—	26	2	no	—
289	C₂×C₁₆	—	13	2	no	—
290	C₂×C₁₆	—	13	2	no	—
291	#107	—	2	1	no	—
292	#107	—	13	1	no	—
293	#107	—	13	1	no	—
294	#107	C₂²×D₁₃	1	2	yes	—
295	#106	—	26	1	no	—
296	#103	—	26	1	no	—
297	#103	—	26	1	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	26	1	no	—
301	#102	—	26	1	no	—
302	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
303	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	—	8	4	no	—
308	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
310	C₂×C₁₃	#3414	1	1	yes	characteristic
311	D₁₃	—	8	2	no	—
312	C₂⁴	—	4	1	no	—
313	#41	—	26	4	no	—
314	#41	—	52	2	no	—
315	C₂×Q₈	—	26	1	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	26	1	no	—
321	C₂×D₄	—	52	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	8	4	no	—
326	C₂²×C₄	—	52	1	no	—
327	C₂²×C₄	—	52	1	no	—
328	C₂²×C₄	—	52	1	no	—
329	C₂²×C₄	#6104	1	1	yes	characteristic
330	C₂²×C₄	#6104	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
332	Q₁₆	—	13	2	no	—
333	Q₁₆	—	26	1	no	—
334	SD₁₆	—	26	4	no	—
335	D₈	—	2	4	no	—
336	D₈	—	2	2	no	—
337	D₈	—	13	2	no	—
338	D₈	—	26	1	no	—
339	D₈	C₂×C₄×D₁₃	1	4	yes	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
342	C₂×C₈	#6127	1	2	yes	—
343	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
346	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	26	1	no	—
350	C₄⋊C₄	—	26	1	no	—
351	C₄⋊C₄	—	52	1	no	—
352	C₄⋊C₄	—	52	1	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	52	1	no	—
356	C₂²⋊C₄	—	52	1	no	—
357	C₂²⋊C₄	—	52	1	no	—
358	C₄²	—	52	1	no	—
359	C₄²	—	52	1	no	—
360	C₄²	—	52	1	no	—
361	C₄²	#6104	1	1	yes	characteristic
362	C₄²	#6104	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₁₆	—	13	4	no	—
366	C₁₆	—	26	2	no	—
367	C₁₃	C₄×#509	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	4	4	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	8	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	52	1	no	—
373	C₂³	C₂×#6104	1	1	yes	characteristic
374	Q₈	—	26	2	no	—
375	Q₈	—	52	1	no	—
376	D₄	—	2	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	2	no	—
379	D₄	—	26	2	no	—
380	D₄	—	52	4	no	—
381	D₄	—	52	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	—	52	1	no	—
389	C₂×C₄	—	52	4	no	—
390	C₂×C₄	—	52	1	no	—
391	C₂×C₄	—	52	1	no	—
392	C₂×C₄	—	104	2	no	—
393	C₂×C₄	—	104	2	no	—
394	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
395	C₂×C₄	C₂×#6104	1	1	yes	characteristic
396	C₂×C₄	C₂×#6104	1	1	yes	characteristic
397	C₂×C₄	C₂×#6104	1	1	yes	characteristic
398	C₂×C₄	C₂×#6104	1	1	yes	characteristic
399	C₂×C₄	C₂×#6104	1	1	yes	characteristic
400	C₂×C₄	#88204	1	2	yes	—
401	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
405	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
406	C₈	C₂×#6127	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	8	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	52	2	no	—
414	C₂²	—	104	1	no	—
415	C₂²	—	104	1	no	—
416	C₂²	C₄×#6104	1	2	yes	—
417	C₂²	C₂²×#6104	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	52	2	no	—
423	C₄	—	104	1	no	—
424	C₄	—	104	1	no	—
425	C₄	C₄×#6104	1	2	yes	—
426	C₄	#11718808	1	2	yes	direct product factor
427	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₄	C₂×#88204	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	8	4	no	—
431	C₂	—	104	2	no	—
432	C₂	C₂×C₄×#6104	1	1	yes	characteristic
433	C₂	C₂×#11718808	1	1	yes	characteristic
434	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×#11718808	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	C₄×#509
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×#88158	C₂	semidirect
3. #13116710	C₂	semidirect
4. #13116700	C₂	semidirect
5. C₄×#88067	C₂	semidirect
6. C₄×#88066	C₂	semidirect
7. #13116622	C₂	semidirect
8. #13116552	C₂	semidirect
9. #13116546	C₂	semidirect
10. C₄×#88052	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
24. #11718808	C₄	direct (N × H)
30. C₄×Dic₅₂	C₂²	semidirect
31. C₄×Dic₅₂	C₂²	semidirect
32. C₄×D₁₀₄	C₂²	semidirect
33. C₄×D₁₀₄	C₂²	semidirect
38. #11718084	C₂²	semidirect
39. #11718083	C₂²	semidirect
40. #11718082	C₂²	semidirect
41. #11718081	C₂²	semidirect
42. #11718053	C₂²	semidirect
43. C₄×#6090	C₂²	semidirect
49. C₂×C₁₃×D₈	C₂×C₄	semidirect
65. #88158	C₂×C₄	semidirect
82. #88067	C₂×C₄	semidirect
83. #88066	C₂×C₄	semidirect
92. #88052	C₂×C₄	semidirect
145. Dic₅₂	C₂²×C₄	semidirect
147. D₁₀₄	C₂²×C₄	semidirect
150. #6090	C₂²×C₄	semidirect
153. C₂×C₄×D₈	D₁₃	semidirect
249. C₄×C₁₃	#509	semidirect
265. C₂×D₈	C₄×D₁₃	semidirect
367. C₁₃	C₄×#509	semidirect
426. C₄	#11718808	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×#11718808	2
C₄×#88158	2
#13116710	2
#13116700	2
C₄×#88067	2
C₄×#88066	2
#13116622	2
#13116552	2
#13116546	2
C₄×#88052	2
C₂×C₄×C₁₃×D₈	2
C₄×#509	13

Subgroups — C4×#11718808 #16016237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718808 #16016237