Subgroups — C₁₁₃×#16607 #43284627

Order 28928.

1426 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#398×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×#389×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1444	C₂	1	4	yes	maximal
5	C₁₁₃×#1444	C₂	1	2	yes	maximal
6	C₁₁₃×#1442	C₂	1	2	yes	maximal
7	C₁₁₃×#1441	C₂	1	2	yes	maximal
8	C₁₁₃×#1434	C₂	1	1	yes	maximal, characteristic
9	C₂×#125×C₁₁₃	—	2	8	no	—
10	C₂×#125×C₁₁₃	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
19	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
20	#398×C₁₁₃	—	2	8	no	—
21	#389×C₁₁₃	—	2	4	no	—
22	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
23	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
24	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
25	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
26	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
27	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
29	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
37	#125×C₁₁₃	—	2	32	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
54	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
55	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
56	C₂×C₄⋊C₄×C₁₁₃	D₄	1	8	yes	—
57	C₂×C₄²×C₁₁₃	—	2	4	no	—
58	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
59	#95×C₁₁₃	—	2	4	no	—
60	#95×C₁₁₃	—	2	4	no	—
61	#95×C₁₁₃	—	2	8	no	—
62	#95×C₁₁₃	—	2	8	no	—
63	#95×C₁₁₃	—	4	2	no	—
64	#95×C₁₁₃	—	4	4	no	—
65	#95×C₁₁₃	Q₈	1	8	yes	—
66	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
67	C₂²×C₄×C₁₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₁₃	—	2	4	no	—
80	C₂²×C₄×C₁₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁₃	C₂×Q₈	1	8	yes	—
107	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
109	C₄⋊C₄×C₁₁₃	—	2	8	no	—
110	C₄⋊C₄×C₁₁₃	—	2	8	no	—
111	C₄⋊C₄×C₁₁₃	—	2	8	no	—
112	C₄⋊C₄×C₁₁₃	—	2	16	no	—
113	C₄⋊C₄×C₁₁₃	—	2	16	no	—
114	C₄⋊C₄×C₁₁₃	—	4	8	no	—
115	C₄⋊C₄×C₁₁₃	—	4	16	no	—
116	C₄⋊C₄×C₁₁₃	—	4	4	no	—
117	C₄²×C₁₁₃	—	2	8	no	—
118	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
119	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
120	C₂³×C₁₁₃	C₂²×Q₈	1	2	yes	—
121	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
122	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
123	C₂³×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
124	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
125	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
126	C₂³×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
127	C₂×C₄×C₁₁₃	—	2	2	no	—
128	C₂×C₄×C₁₁₃	—	2	2	no	—
129	C₂×C₄×C₁₁₃	—	2	2	no	—
130	C₂×C₄×C₁₁₃	—	2	2	no	—
131	C₂×C₄×C₁₁₃	—	2	8	no	—
132	C₂×C₄×C₁₁₃	—	2	8	no	—
133	C₂×C₄×C₁₁₃	—	2	2	no	—
134	C₂×C₄×C₁₁₃	—	2	4	no	—
135	C₂×C₄×C₁₁₃	—	2	4	no	—
136	C₂×C₄×C₁₁₃	—	2	4	no	—
137	C₂×C₄×C₁₁₃	—	2	2	no	—
138	C₂×C₄×C₁₁₃	—	2	4	no	—
139	C₂×C₄×C₁₁₃	—	2	2	no	—
140	C₂×C₄×C₁₁₃	—	2	4	no	—
141	C₂×C₄×C₁₁₃	—	2	8	no	—
142	C₂×C₄×C₁₁₃	—	2	8	no	—
143	C₂×C₄×C₁₁₃	—	2	8	no	—
144	C₂×C₄×C₁₁₃	—	2	8	no	—
145	C₂×C₄×C₁₁₃	—	2	8	no	—
146	C₂×C₄×C₁₁₃	—	4	2	no	—
147	C₂×C₄×C₁₁₃	—	4	2	no	—
148	C₂×C₄×C₁₁₃	—	4	4	no	—
149	C₂×C₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	4	2	no	—
151	C₂×C₄×C₁₁₃	—	4	2	no	—
152	C₂×C₄×C₁₁₃	—	4	2	no	—
153	C₂×C₄×C₁₁₃	—	4	2	no	—
154	C₂×C₄×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	4	4	no	—
158	C₂×C₄×C₁₁₃	—	4	4	no	—
159	C₂×C₄×C₁₁₃	—	4	4	no	—
160	C₂×C₄×C₁₁₃	—	4	4	no	—
161	C₂×C₄×C₁₁₃	—	4	4	no	—
162	C₂×C₄×C₁₁₃	—	4	2	no	—
163	C₂×C₄×C₁₁₃	—	4	2	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	2	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	#120	1	4	yes	—
168	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	4	yes	—
169	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
170	C₂²×C₁₁₃	#525	1	1	yes	characteristic
171	C₂²×C₁₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
172	C₂²×C₁₁₃	#535	1	1	yes	characteristic
173	C₂²×C₁₁₃	#535	1	2	yes	—
174	C₂²×C₁₁₃	#536	1	1	yes	characteristic
175	C₂²×C₁₁₃	#536	1	1	yes	characteristic
176	C₂²×C₁₁₃	#537	1	1	yes	characteristic
177	C₂²×C₁₁₃	#537	1	2	yes	—
178	C₂²×C₁₁₃	#539	1	4	yes	—
179	C₂²×C₁₁₃	#544	1	4	yes	—
180	C₂²×C₁₁₃	#547	1	4	yes	—
181	C₂²×C₁₁₃	D₄×Q₈	1	4	yes	—
182	C₂²×C₁₁₃	#554	1	2	yes	—
183	C₂²×C₁₁₃	#557	1	2	yes	—
184	C₂²×C₁₁₃	#563	1	2	yes	—
185	C₂²×C₁₁₃	#564	1	2	yes	—
186	C₄×C₁₁₃	—	2	4	no	—
187	C₄×C₁₁₃	—	2	4	no	—
188	C₄×C₁₁₃	—	4	2	no	—
189	C₄×C₁₁₃	—	4	4	no	—
190	C₄×C₁₁₃	—	4	4	no	—
191	C₄×C₁₁₃	—	4	4	no	—
192	C₄×C₁₁₃	—	4	8	no	—
193	C₄×C₁₁₃	—	8	2	no	—
194	#16607	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₁₁₃	#2406	1	1	yes	characteristic
196	C₂×C₁₁₃	#2434	1	1	yes	characteristic
197	C₂×C₁₁₃	#2584	1	1	yes	characteristic
198	C₂×C₁₁₃	#2615	1	1	yes	characteristic
199	C₂×C₁₁₃	#2633	1	1	yes	characteristic
200	C₂×C₁₁₃	#2660	1	1	yes	characteristic
201	C₂×C₁₁₃	#2720	1	4	yes	—
202	C₂×C₁₁₃	#2726	1	4	yes	—
203	C₂×C₁₁₃	#2822	1	1	yes	characteristic
204	C₂²×#125	C₂×C₁₁₃	1	1	yes	characteristic
205	C₂×#398	C₂×C₁₁₃	1	2	yes	—
206	C₂×#389	C₂×C₁₁₃	1	1	yes	characteristic
207	#1444	C₂×C₁₁₃	1	2	yes	—
208	#1444	C₂×C₁₁₃	1	4	yes	—
209	#1442	C₂×C₁₁₃	1	2	yes	—
210	#1441	C₂×C₁₁₃	1	2	yes	—
211	#1434	C₂×C₁₁₃	1	1	yes	characteristic
212	C₁₁₃	#16607	1	1	yes	characteristic, direct product factor, Sylow
213	C₂×#125	—	2	8	no	—
214	C₂×#125	—	2	4	no	—
215	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
219	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
224	#398	—	2	8	no	—
225	#389	—	2	4	no	—
226	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
227	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
228	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
229	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
230	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
231	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
232	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
237	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
238	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
241	#125	—	2	32	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	8	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	4	4	no	—
258	C₂×C₄⋊C₄	—	4	4	no	—
259	C₂×C₄⋊C₄	—	4	4	no	—
260	C₂×C₄⋊C₄	D₄×C₁₁₃	1	8	yes	—
261	C₂×C₄²	—	2	4	no	—
262	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
263	#95	—	2	4	no	—
264	#95	—	2	4	no	—
265	#95	—	2	8	no	—
266	#95	—	2	8	no	—
267	#95	—	4	2	no	—
268	#95	—	4	4	no	—
269	#95	Q₈×C₁₁₃	1	8	yes	—
270	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
307	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
308	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₁₁₃	1	8	yes	—
311	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
312	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	16	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	16	no	—
318	C₄⋊C₄	—	4	8	no	—
319	C₄⋊C₄	—	4	16	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄²	—	2	8	no	—
322	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
323	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
324	C₂³	C₂²×Q₈×C₁₁₃	1	2	yes	—
325	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
326	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
327	C₂³	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
328	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
329	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
330	C₂³	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	#120×C₁₁₃	1	4	yes	—
372	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	4	yes	—
373	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
374	C₂²	#525×C₁₁₃	1	1	yes	characteristic
375	C₂²	C₂×C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
376	C₂²	#535×C₁₁₃	1	1	yes	characteristic
377	C₂²	#535×C₁₁₃	1	2	yes	—
378	C₂²	#536×C₁₁₃	1	1	yes	characteristic
379	C₂²	#536×C₁₁₃	1	1	yes	characteristic
380	C₂²	#537×C₁₁₃	1	1	yes	characteristic
381	C₂²	#537×C₁₁₃	1	2	yes	—
382	C₂²	#539×C₁₁₃	1	4	yes	—
383	C₂²	#544×C₁₁₃	1	4	yes	—
384	C₂²	#547×C₁₁₃	1	4	yes	—
385	C₂²	D₄×Q₈×C₁₁₃	1	4	yes	—
386	C₂²	#554×C₁₁₃	1	2	yes	—
387	C₂²	#557×C₁₁₃	1	2	yes	—
388	C₂²	#563×C₁₁₃	1	2	yes	—
389	C₂²	#564×C₁₁₃	1	2	yes	—
390	C₄	—	2	4	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	8	no	—
397	C₄	—	8	2	no	—
398	C₂	C₁₁₃×#2406	1	1	yes	characteristic
399	C₂	C₁₁₃×#2434	1	1	yes	characteristic
400	C₂	C₁₁₃×#2584	1	1	yes	characteristic
401	C₂	C₁₁₃×#2615	1	1	yes	characteristic
402	C₂	C₁₁₃×#2633	1	1	yes	characteristic
403	C₂	C₁₁₃×#2660	1	1	yes	characteristic
404	C₂	C₁₁₃×#2720	1	4	yes	—
405	C₂	C₁₁₃×#2726	1	4	yes	—
406	C₂	C₁₁₃×#2822	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
194. #16607	C₁₁₃	direct (N × H)
212. C₁₁₃	#16607	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#125×C₁₁₃	2
C₂×#398×C₁₁₃	2
C₂×#389×C₁₁₃	2
C₁₁₃×#1444	2
C₁₁₃×#1442	2
C₁₁₃×#1441	2
C₁₁₃×#1434	2
#16607	113

Subgroups — C113×#16607 #43284627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#16607 #43284627