Subgroups — C₂×C₁₁₃×#1496 #43285494

Order 28928.

1270 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#431×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1496	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄⋊C₈×C₁₁₃	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₁₃	—	2	1	no	—
7	#532×C₁₁₃	—	2	2	no	—
8	#532×C₁₁₃	—	2	2	no	—
9	#532×C₁₁₃	C₄	1	4	yes	—
10	#532×C₁₁₃	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₁₃	C₄	1	1	yes	characteristic
12	C₂×#127×C₁₁₃	C₄	1	1	yes	characteristic
13	C₂×#124×C₁₁₃	—	2	1	no	—
14	C₂×#121×C₁₁₃	—	2	1	no	—
15	C₂×#121×C₁₁₃	C₄	1	2	yes	—
16	C₂×C₄×D₄×C₁₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
19	#432×C₁₁₃	—	2	2	no	—
20	#432×C₁₁₃	C₂²	1	4	yes	complemented
21	#431×C₁₁₃	—	2	2	no	—
22	#431×C₁₁₃	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₁₁₃	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
27	C₂×#97×C₁₁₃	—	2	1	no	—
28	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
29	D₄⋊C₈×C₁₁₃	C₂²	1	16	yes	complemented
30	C₂×#41×C₁₁₃	—	2	4	no	—
31	C₂×#41×C₁₁₃	—	2	4	no	—
32	C₂×#41×C₁₁₃	—	4	8	no	—
33	C₂²×Q₈×C₁₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₁₃	—	2	2	no	—
44	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
45	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
46	#127×C₁₁₃	—	2	2	no	—
47	#127×C₁₁₃	C₂×C₄	1	4	yes	—
48	#124×C₁₁₃	—	2	4	no	—
49	#124×C₁₁₃	—	2	4	no	—
50	#121×C₁₁₃	—	2	4	no	—
51	#121×C₁₁₃	—	2	4	no	—
52	#121×C₁₁₃	—	2	4	no	—
53	#121×C₁₁₃	C₂×C₄	1	8	yes	—
54	C₄×D₄×C₁₁₃	—	2	4	no	—
55	C₄×D₄×C₁₁₃	—	2	4	no	—
56	C₄×D₄×C₁₁₃	—	2	2	no	—
57	C₄×D₄×C₁₁₃	—	2	2	no	—
58	C₄×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₁₁₃	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
69	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₁₃	—	2	4	no	—
73	C₄⋊C₈×C₁₁₃	—	2	2	no	—
74	C₄⋊C₈×C₁₁₃	C₂³	1	4	yes	—
75	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
76	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
77	#97×C₁₁₃	—	2	4	no	—
78	C₄×C₈×C₁₁₃	—	2	2	no	—
79	C₄×C₈×C₁₁₃	C₂³	1	4	yes	—
80	C₂⁴×C₁₁₃	—	2	2	no	—
81	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	#41×C₁₁₃	—	4	16	no	—
83	#41×C₁₁₃	—	4	16	no	—
84	C₂×Q₈×C₁₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₁₃	—	4	4	no	—
86	C₂×D₄×C₁₁₃	—	2	8	no	—
87	C₂×D₄×C₁₁₃	—	2	2	no	—
88	C₂×D₄×C₁₁₃	—	2	4	no	—
89	C₂×D₄×C₁₁₃	—	2	4	no	—
90	C₂×D₄×C₁₁₃	—	2	8	no	—
91	C₂×D₄×C₁₁₃	—	4	4	no	—
92	C₂×D₄×C₁₁₃	—	4	4	no	—
93	C₂×D₄×C₁₁₃	—	4	8	no	—
94	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₁₃	—	4	8	no	—
102	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₁₃	—	2	4	no	—
115	C₂×C₈×C₁₁₃	—	2	4	no	—
116	C₂×C₈×C₁₁₃	—	4	4	no	—
117	C₂×C₈×C₁₁₃	—	4	4	no	—
118	C₄⋊C₄×C₁₁₃	—	2	4	no	—
119	C₄⋊C₄×C₁₁₃	—	2	2	no	—
120	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
122	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
123	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
124	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
133	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
134	C₂³×C₁₁₃	—	2	2	no	—
135	C₂³×C₁₁₃	—	2	2	no	—
136	C₂³×C₁₁₃	—	2	2	no	—
137	C₂³×C₁₁₃	—	2	4	no	—
138	C₂³×C₁₁₃	—	4	4	no	—
139	C₂³×C₁₁₃	—	4	4	no	—
140	C₂³×C₁₁₃	—	4	4	no	—
141	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	Q₈×C₁₁₃	—	4	8	no	—
144	D₄×C₁₁₃	—	2	8	no	—
145	D₄×C₁₁₃	—	4	8	no	—
146	D₄×C₁₁₃	—	4	8	no	—
147	D₄×C₁₁₃	—	4	16	no	—
148	D₄×C₁₁₃	—	4	4	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	2	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	2	2	no	—
153	C₂×C₄×C₁₁₃	—	2	4	no	—
154	C₂×C₄×C₁₁₃	—	2	4	no	—
155	C₂×C₄×C₁₁₃	—	2	4	no	—
156	C₂×C₄×C₁₁₃	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	2	4	no	—
158	C₂×C₄×C₁₁₃	—	4	2	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	—	4	4	no	—
161	C₂×C₄×C₁₁₃	—	4	8	no	—
162	C₂×C₄×C₁₁₃	—	4	8	no	—
163	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	#131	1	4	yes	—
170	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
171	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₁₃	—	4	4	no	—
175	C₈×C₁₁₃	—	4	4	no	—
176	C₂²×C₁₁₃	—	2	2	no	—
177	C₂²×C₁₁₃	—	2	2	no	—
178	C₂²×C₁₁₃	—	2	2	no	—
179	C₂²×C₁₁₃	—	4	4	no	—
180	C₂²×C₁₁₃	—	4	4	no	—
181	C₂²×C₁₁₃	—	4	4	no	—
182	C₂²×C₁₁₃	—	4	4	no	—
183	C₂²×C₁₁₃	—	8	8	no	—
184	C₂²×C₁₁₃	#408	1	2	yes	—
185	C₂²×C₁₁₃	#418	1	2	yes	—
186	C₂²×C₁₁₃	#421	1	2	yes	—
187	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	2	1	no	—
191	C₄×C₁₁₃	—	2	1	no	—
192	C₄×C₁₁₃	—	2	2	no	—
193	C₄×C₁₁₃	—	4	4	no	—
194	C₄×C₁₁₃	#408	1	2	yes	—
195	C₄×C₁₁₃	#418	1	2	yes	—
196	C₄×C₁₁₃	C₂×#131	1	2	yes	—
197	C₄×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
198	C₂×#1496	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₁₁₃	—	4	2	no	—
200	C₂×C₁₁₃	—	8	4	no	—
201	C₂×C₁₁₃	#1496	1	4	yes	direct product factor
202	C₂×C₁₁₃	C₂×#408	1	1	yes	characteristic
203	C₂×C₁₁₃	C₂×#418	1	1	yes	characteristic
204	C₂×C₁₁₃	C₂×#421	1	1	yes	characteristic
205	C₂×#532	C₂×C₁₁₃	1	1	yes	characteristic
206	C₂×#432	C₂×C₁₁₃	1	1	yes	characteristic, complemented
207	C₂×#431	C₂×C₁₁₃	1	1	yes	characteristic, complemented
208	#1496	C₂×C₁₁₃	1	8	yes	direct product factor
209	C₂×D₄⋊C₈	C₂×C₁₁₃	1	4	yes	complemented
210	C₁₁₃	C₂×#1496	1	1	yes	characteristic, direct product factor, Sylow
211	C₂²×#41	—	2	1	no	—
212	#532	—	2	2	no	—
213	#532	—	2	2	no	—
214	#532	C₄×C₁₁₃	1	4	yes	—
215	#532	C₂²×C₁₁₃	1	4	yes	—
216	C₂×C₄⋊Q₈	C₄×C₁₁₃	1	1	yes	characteristic
217	C₂×#127	C₄×C₁₁₃	1	1	yes	characteristic
218	C₂×#124	—	2	1	no	—
219	C₂×#121	—	2	1	no	—
220	C₂×#121	C₄×C₁₁₃	1	2	yes	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
224	#432	—	2	2	no	—
225	#432	C₂²×C₁₁₃	1	4	yes	complemented
226	#431	—	2	2	no	—
227	#431	C₂²×C₁₁₃	1	4	yes	complemented
228	C₂×C₄⋊C₈	—	2	1	no	—
229	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
230	C₂×C₂²⋊C₈	—	2	1	no	—
231	C₂×C₂²⋊C₈	—	2	1	no	—
232	C₂×#97	—	2	1	no	—
233	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
234	D₄⋊C₈	C₂²×C₁₁₃	1	16	yes	complemented
235	C₂×#41	—	2	4	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	4	8	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₄⋊Q₈	—	2	2	no	—
250	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
251	#127	—	2	2	no	—
252	#127	C₂×C₄×C₁₁₃	1	4	yes	—
253	#124	—	2	4	no	—
254	#124	—	2	4	no	—
255	#121	—	2	4	no	—
256	#121	—	2	4	no	—
257	#121	—	2	4	no	—
258	#121	C₂×C₄×C₁₁₃	1	8	yes	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
264	C₄×D₄	C₂³×C₁₁₃	1	4	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
270	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
271	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
274	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
275	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
277	C₄⋊C₈	—	2	4	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	C₂³×C₁₁₃	1	4	yes	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	4	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	C₂³×C₁₁₃	1	4	yes	—
285	C₂⁴	—	2	2	no	—
286	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
287	#41	—	4	16	no	—
288	#41	—	4	16	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	8	no	—
307	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
310	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
312	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	4	4	no	—
322	C₂×C₈	—	4	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
331	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
332	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
333	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
334	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
336	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
338	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
347	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
348	Q₈	—	4	8	no	—
349	D₄	—	2	8	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	16	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
374	C₂×C₄	#131×C₁₁₃	1	4	yes	—
375	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
376	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
379	C₈	—	4	4	no	—
380	C₈	—	4	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	8	8	no	—
389	C₂²	#408×C₁₁₃	1	2	yes	—
390	C₂²	#418×C₁₁₃	1	2	yes	—
391	C₂²	#421×C₁₁₃	1	2	yes	—
392	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	4	no	—
399	C₄	#408×C₁₁₃	1	2	yes	—
400	C₄	#418×C₁₁₃	1	2	yes	—
401	C₄	C₂×#131×C₁₁₃	1	2	yes	—
402	C₄	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
403	C₂	—	4	2	no	—
404	C₂	—	8	4	no	—
405	C₂	C₁₁₃×#1496	1	4	yes	direct product factor
406	C₂	C₂×#408×C₁₁₃	1	1	yes	characteristic
407	C₂	C₂×#418×C₁₁₃	1	1	yes	characteristic
408	C₂	C₂×#421×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₁₁₃	C₂	semidirect
3. C₂×#431×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1496	C₂	direct (N × H)
5. C₂×D₄⋊C₈×C₁₁₃	C₂	semidirect
20. #432×C₁₁₃	C₂²	semidirect
22. #431×C₁₁₃	C₂²	semidirect
29. D₄⋊C₈×C₁₁₃	C₂²	semidirect
198. C₂×#1496	C₁₁₃	direct (N × H)
201. C₂×C₁₁₃	#1496	direct (N × H)
206. C₂×#432	C₂×C₁₁₃	semidirect
207. C₂×#431	C₂×C₁₁₃	semidirect
208. #1496	C₂×C₁₁₃	direct (N × H)
209. C₂×D₄⋊C₈	C₂×C₁₁₃	semidirect
210. C₁₁₃	C₂×#1496	direct (N × H)
225. #432	C₂²×C₁₁₃	semidirect
227. #431	C₂²×C₁₁₃	semidirect
234. D₄⋊C₈	C₂²×C₁₁₃	semidirect
405. C₂	C₁₁₃×#1496	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×#532×C₁₁₃	2
C₂×#432×C₁₁₃	2
C₂×#431×C₁₁₃	2
C₁₁₃×#1496	2
C₂×D₄⋊C₈×C₁₁₃	2
C₂×#1496	113

Subgroups — C2×C113×#1496 #43285494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁₃×#1496 #43285494