Subgroups — C₁₁₃×#20637 #43288657

Order 28928.

1442 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₁₃	C₂	1	2	yes	maximal, complemented
3	C₂×#413×C₁₁₃	C₂	1	2	yes	maximal
4	C₁₁₃×#1801	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1800	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1742	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₁₃	C₂²	1	4	yes	—
9	C₄×#41×C₁₁₃	—	2	4	no	—
10	C₄×#41×C₁₁₃	—	2	2	no	—
11	C₄×#41×C₁₁₃	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₁₃	C₄	1	4	yes	—
14	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂×#117×C₁₁₃	C₄	1	2	yes	—
16	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₁₃	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
19	#423×C₁₁₃	—	2	2	no	—
20	#423×C₁₁₃	—	2	2	no	—
21	#423×C₁₁₃	C₂²	1	8	yes	—
22	C₂×C₄⋊C₈×C₁₁₃	—	2	4	no	—
23	#413×C₁₁₃	—	2	8	no	—
24	C₂×#101×C₁₁₃	C₂²	1	4	yes	—
25	C₂×#100×C₁₁₃	C₂²	1	4	yes	—
26	#343×C₁₁₃	C₂²	1	8	yes	—
27	C₂×#41×C₁₁₃	—	2	2	no	—
28	C₂×#41×C₁₁₃	—	2	2	no	—
29	C₂×#41×C₁₁₃	—	2	4	no	—
30	C₂×#41×C₁₁₃	D₄	1	4	yes	—
31	C₂×#41×C₁₁₃	Q₈	1	4	yes	—
32	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₁₃	—	2	4	no	—
40	C₂×M₁₆×C₁₁₃	—	2	8	no	—
41	C₂×M₁₆×C₁₁₃	—	2	8	no	—
42	C₂×M₁₆×C₁₁₃	C₂³	1	8	yes	—
43	C₂²×C₈×C₁₁₃	—	2	4	no	—
44	C₄×Q₈×C₁₁₃	—	2	4	no	—
45	C₄×Q₈×C₁₁₃	—	2	4	no	—
46	C₄×D₄×C₁₁₃	—	2	8	no	—
47	C₄×D₄×C₁₁₃	—	2	8	no	—
48	C₄×D₄×C₁₁₃	—	2	4	no	—
49	C₄×D₄×C₁₁₃	—	2	4	no	—
50	#117×C₁₁₃	—	2	2	no	—
51	#117×C₁₁₃	—	2	2	no	—
52	#117×C₁₁₃	—	2	4	no	—
53	#117×C₁₁₃	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
66	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
67	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
69	C₄⋊C₈×C₁₁₃	—	2	8	no	—
70	C₄⋊C₈×C₁₁₃	—	2	8	no	—
71	#101×C₁₁₃	—	2	8	no	—
72	#100×C₁₁₃	—	2	8	no	—
73	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₁₃	—	2	8	no	—
76	#41×C₁₁₃	—	2	8	no	—
77	#41×C₁₁₃	—	2	8	no	—
78	#41×C₁₁₃	—	2	8	no	—
79	C₂×Q₈×C₁₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
82	C₂×Q₈×C₁₁₃	C₂×Q₈	1	2	yes	—
83	C₂×D₄×C₁₁₃	—	2	4	no	—
84	C₂×D₄×C₁₁₃	—	2	4	no	—
85	C₂×D₄×C₁₁₃	—	2	2	no	—
86	C₂×D₄×C₁₁₃	—	2	2	no	—
87	C₂×D₄×C₁₁₃	C₄⋊C₄	1	8	yes	—
88	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
89	C₂×D₄×C₁₁₃	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₁₃	—	2	2	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	—	4	4	no	—
96	C₂²×C₄×C₁₁₃	—	4	8	no	—
97	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	8	yes	—
100	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
110	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₁₃	—	2	8	no	—
112	M₁₆×C₁₁₃	—	2	8	no	—
113	M₁₆×C₁₁₃	—	4	8	no	—
114	C₂×C₈×C₁₁₃	—	2	8	no	—
115	C₂×C₈×C₁₁₃	—	4	8	no	—
116	C₄⋊C₄×C₁₁₃	—	2	8	no	—
117	C₄⋊C₄×C₁₁₃	—	2	4	no	—
118	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
119	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
120	C₄²×C₁₁₃	—	2	2	no	—
121	C₄²×C₁₁₃	—	2	4	no	—
122	C₄²×C₁₁₃	—	2	4	no	—
123	C₄²×C₁₁₃	—	2	2	no	—
124	C₄²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
130	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
131	C₂³×C₁₁₃	—	2	2	no	—
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	4	2	no	—
134	C₂³×C₁₁₃	—	4	4	no	—
135	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
137	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₁₃	#117	1	2	yes	—
139	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
140	Q₈×C₁₁₃	—	2	4	no	—
141	Q₈×C₁₁₃	—	2	4	no	—
142	D₄×C₁₁₃	—	2	16	no	—
143	D₄×C₁₁₃	—	2	4	no	—
144	D₄×C₁₁₃	—	2	4	no	—
145	C₂×C₄×C₁₁₃	—	2	2	no	—
146	C₂×C₄×C₁₁₃	—	2	2	no	—
147	C₂×C₄×C₁₁₃	—	2	8	no	—
148	C₂×C₄×C₁₁₃	—	2	8	no	—
149	C₂×C₄×C₁₁₃	—	2	4	no	—
150	C₂×C₄×C₁₁₃	—	2	8	no	—
151	C₂×C₄×C₁₁₃	—	2	4	no	—
152	C₂×C₄×C₁₁₃	—	4	4	no	—
153	C₂×C₄×C₁₁₃	—	4	2	no	—
154	C₂×C₄×C₁₁₃	—	4	8	no	—
155	C₂×C₄×C₁₁₃	—	4	8	no	—
156	C₂×C₄×C₁₁₃	—	4	4	no	—
157	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
163	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₁₃	#117	1	2	yes	—
165	C₂×C₄×C₁₁₃	#121	1	4	yes	—
166	C₂×C₄×C₁₁₃	#121	1	4	yes	—
167	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
168	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
173	C₈×C₁₁₃	—	4	8	no	—
174	C₂²×C₁₁₃	—	2	2	no	—
175	C₂²×C₁₁₃	—	2	4	no	—
176	C₂²×C₁₁₃	—	2	4	no	—
177	C₂²×C₁₁₃	—	4	2	no	—
178	C₂²×C₁₁₃	—	4	2	no	—
179	C₂²×C₁₁₃	—	4	4	no	—
180	C₂²×C₁₁₃	—	4	4	no	—
181	C₂²×C₁₁₃	—	4	4	no	—
182	C₂²×C₁₁₃	#380	1	4	yes	—
183	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
186	C₄×C₁₁₃	—	2	2	no	—
187	C₄×C₁₁₃	—	2	4	no	—
188	C₄×C₁₁₃	—	2	4	no	—
189	C₄×C₁₁₃	—	4	4	no	—
190	C₄×C₁₁₃	#380	1	2	yes	—
191	C₄×C₁₁₃	#380	1	2	yes	—
192	C₄×C₁₁₃	#413	1	4	yes	complemented
193	C₄×C₁₁₃	C₂×#121	1	2	yes	—
194	C₄×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
195	#20637	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₁₁₃	—	2	1	no	—
197	C₂×C₁₁₃	—	2	1	no	—
198	C₂×C₁₁₃	—	2	4	no	—
199	C₂×C₁₁₃	—	4	4	no	—
200	C₂×C₁₁₃	C₂×#380	1	1	yes	characteristic
201	C₂×C₁₁₃	C₂×#413	1	2	yes	—
202	C₂×C₄×#41	C₂×C₁₁₃	1	1	yes	characteristic
203	C₂×#423	C₂×C₁₁₃	1	2	yes	complemented
204	C₂×#413	C₂×C₁₁₃	1	2	yes	—
205	#1801	C₂×C₁₁₃	1	4	yes	complemented
206	#1800	C₂×C₁₁₃	1	4	yes	complemented
207	#1742	C₂×C₁₁₃	1	2	yes	complemented
208	C₁₁₃	#20637	1	1	yes	characteristic, direct product factor, Sylow
209	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
210	C₂²×M₁₆	C₂²×C₁₁₃	1	4	yes	—
211	C₄×#41	—	2	4	no	—
212	C₄×#41	—	2	2	no	—
213	C₄×#41	—	2	2	no	—
214	C₂×C₄×Q₈	C₂²×C₁₁₃	1	2	yes	—
215	C₂×C₄×D₄	C₄×C₁₁₃	1	4	yes	—
216	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
217	C₂×#117	C₄×C₁₁₃	1	2	yes	—
218	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
219	C₂²×C₄²	C₄×C₁₁₃	1	2	yes	—
220	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
221	#423	—	2	2	no	—
222	#423	—	2	2	no	—
223	#423	C₂²×C₁₁₃	1	8	yes	—
224	C₂×C₄⋊C₈	—	2	4	no	—
225	#413	—	2	8	no	—
226	C₂×#101	C₂²×C₁₁₃	1	4	yes	—
227	C₂×#100	C₂²×C₁₁₃	1	4	yes	—
228	#343	C₂²×C₁₁₃	1	8	yes	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	D₄×C₁₁₃	1	4	yes	—
233	C₂×#41	Q₈×C₁₁₃	1	4	yes	—
234	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
235	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
236	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
237	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
238	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
239	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
240	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
241	C₂×M₁₆	—	2	4	no	—
242	C₂×M₁₆	—	2	8	no	—
243	C₂×M₁₆	—	2	8	no	—
244	C₂×M₁₆	C₂³×C₁₁₃	1	8	yes	—
245	C₂²×C₈	—	2	4	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×D₄	—	2	8	no	—
249	C₄×D₄	—	2	8	no	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	4	no	—
255	#117	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
264	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
265	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
268	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
269	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
271	C₄⋊C₈	—	2	8	no	—
272	C₄⋊C₈	—	2	8	no	—
273	#101	—	2	8	no	—
274	#100	—	2	8	no	—
275	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
276	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
277	#41	—	2	8	no	—
278	#41	—	2	8	no	—
279	#41	—	2	8	no	—
280	#41	—	2	8	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
284	C₂×Q₈	C₂×Q₈×C₁₁₃	1	2	yes	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₄⋊C₄×C₁₁₃	1	8	yes	—
290	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
291	C₂×D₄	C₂×Q₈×C₁₁₃	1	2	yes	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
301	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	8	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	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	2	yes	—
311	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
313	M₁₆	—	2	8	no	—
314	M₁₆	—	2	8	no	—
315	M₁₆	—	4	8	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	—	4	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
327	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
328	C₄²	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
329	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
331	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
332	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
338	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
339	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
340	C₂³	#117×C₁₁₃	1	2	yes	—
341	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	2	4	no	—
344	D₄	—	2	16	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
364	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
365	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
366	C₂×C₄	#117×C₁₁₃	1	2	yes	—
367	C₂×C₄	#121×C₁₁₃	1	4	yes	—
368	C₂×C₄	#121×C₁₁₃	1	4	yes	—
369	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
370	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
371	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
373	C₂×C₄	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
375	C₈	—	4	8	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	#380×C₁₁₃	1	4	yes	—
385	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
386	C₂²	C₂²×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
387	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	4	no	—
392	C₄	#380×C₁₁₃	1	2	yes	—
393	C₄	#380×C₁₁₃	1	2	yes	—
394	C₄	#413×C₁₁₃	1	4	yes	complemented
395	C₄	C₂×#121×C₁₁₃	1	2	yes	—
396	C₄	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	4	no	—
400	C₂	—	4	4	no	—
401	C₂	C₂×#380×C₁₁₃	1	1	yes	characteristic
402	C₂	C₂×#413×C₁₁₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1801	C₂	semidirect
5. C₁₁₃×#1800	C₂	semidirect
6. C₁₁₃×#1742	C₂	semidirect
192. C₄×C₁₁₃	#413	semidirect
195. #20637	C₁₁₃	direct (N × H)
203. C₂×#423	C₂×C₁₁₃	semidirect
205. #1801	C₂×C₁₁₃	semidirect
206. #1800	C₂×C₁₁₃	semidirect
207. #1742	C₂×C₁₁₃	semidirect
208. C₁₁₃	#20637	direct (N × H)
394. C₄	#413×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₁₃	2
C₂×#423×C₁₁₃	2
C₂×#413×C₁₁₃	2
C₁₁₃×#1801	2
C₁₁₃×#1800	2
C₁₁₃×#1742	2
#20637	113

Subgroups — C113×#20637 #43288657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20637 #43288657