Subgroups — C₁₁₃×#21213 #43289233

Order 28928.

1858 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#99×C₁₁₃	C₂	1	4	yes	maximal, complemented
3	C₁₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#2273	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1964	C₂	1	8	yes	maximal, complemented
6	C₂³×D₄×C₁₁₃	C₂²	1	2	yes	—
7	#534×C₁₁₃	—	2	4	no	—
8	#534×C₁₁₃	—	2	4	no	—
9	C₂×#123×C₁₁₃	C₄	1	4	yes	complemented
10	C₂×#121×C₁₁₃	C₂²	1	4	yes	—
11	C₂×#120×C₁₁₃	C₄	1	4	yes	complemented
12	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×#99×C₁₁₃	—	2	16	no	—
16	C₂×#99×C₁₁₃	C₂²	1	16	yes	complemented
17	#385×C₁₁₃	—	2	4	no	—
18	#380×C₁₁₃	C₂²	1	4	yes	complemented
19	C₄×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
20	C₄×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	complemented
21	C₂⁵×C₁₁₃	C₂×C₄	1	2	yes	—
22	C₂⁵×C₁₁₃	C₂³	1	1	yes	characteristic
23	C₂²×D₄×C₁₁₃	—	2	4	no	—
24	C₂²×D₄×C₁₁₃	—	2	4	no	—
25	C₂²×D₄×C₁₁₃	—	2	8	no	—
26	C₂²×D₄×C₁₁₃	—	2	8	no	—
27	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
28	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	complemented
29	C₂²×D₄×C₁₁₃	C₂³	1	4	yes	—
30	C₂³×C₄×C₁₁₃	—	2	2	no	—
31	C₂³×C₄×C₁₁₃	—	2	2	no	—
32	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
34	#123×C₁₁₃	—	2	16	no	—
35	#121×C₁₁₃	—	2	8	no	—
36	#121×C₁₁₃	—	2	8	no	—
37	#120×C₁₁₃	—	2	16	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	complemented
40	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
42	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
43	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
44	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	8	yes	complemented
46	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	4	yes	—
47	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	4	yes	—
48	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	8	yes	complemented
49	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
50	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
51	C₂×C₄²×C₁₁₃	—	2	4	no	—
52	#99×C₁₁₃	—	2	32	no	—
53	#95×C₁₁₃	—	2	4	no	—
54	#95×C₁₁₃	—	2	4	no	—
55	C₂⁴×C₁₁₃	—	2	4	no	—
56	C₂⁴×C₁₁₃	—	2	8	no	—
57	C₂⁴×C₁₁₃	—	8	2	no	—
58	C₂⁴×C₁₁₃	—	8	4	no	—
59	C₂⁴×C₁₁₃	C₂²×C₄	1	4	yes	—
60	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
61	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
62	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
63	C₂⁴×C₁₁₃	C₂×D₄	1	4	yes	—
64	C₂⁴×C₁₁₃	#41	1	4	yes	—
65	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
66	C₂×D₄×C₁₁₃	—	2	8	no	—
67	C₂×D₄×C₁₁₃	—	2	16	no	—
68	C₂×D₄×C₁₁₃	—	2	8	no	—
69	C₂×D₄×C₁₁₃	—	2	4	no	—
70	C₂×D₄×C₁₁₃	—	2	4	no	—
71	C₂×D₄×C₁₁₃	—	2	8	no	—
72	C₂×D₄×C₁₁₃	—	2	8	no	—
73	C₂×D₄×C₁₁₃	—	4	8	no	—
74	C₂×D₄×C₁₁₃	—	4	8	no	—
75	C₂×D₄×C₁₁₃	—	4	8	no	—
76	C₂×D₄×C₁₁₃	—	4	8	no	—
77	C₂×D₄×C₁₁₃	—	8	4	no	—
78	C₂²×C₄×C₁₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₁₃	—	2	8	no	—
80	C₂²×C₄×C₁₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₁₃	—	2	8	no	—
82	C₂²×C₄×C₁₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₁₃	—	4	4	no	—
84	C₂²×C₄×C₁₁₃	—	8	2	no	—
85	C₂²×C₄×C₁₁₃	—	8	4	no	—
86	C₂²×C₄×C₁₁₃	—	8	4	no	—
87	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
91	C₄⋊C₄×C₁₁₃	—	2	8	no	—
92	C₄⋊C₄×C₁₁₃	—	8	4	no	—
93	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
94	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
95	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
96	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
97	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
98	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	16	yes	—
99	C₂²⋊C₄×C₁₁₃	C₂×D₄	1	8	yes	—
100	C₄²×C₁₁₃	—	8	4	no	—
101	C₂³×C₁₁₃	—	2	4	no	—
102	C₂³×C₁₁₃	—	2	8	no	—
103	C₂³×C₁₁₃	—	4	4	no	—
104	C₂³×C₁₁₃	—	4	4	no	—
105	C₂³×C₁₁₃	—	4	2	no	—
106	C₂³×C₁₁₃	—	4	4	no	—
107	C₂³×C₁₁₃	—	4	8	no	—
108	C₂³×C₁₁₃	—	4	8	no	—
109	C₂³×C₁₁₃	—	8	8	no	—
110	C₂³×C₁₁₃	—	8	4	no	—
111	C₂³×C₁₁₃	—	8	4	no	—
112	C₂³×C₁₁₃	—	8	16	no	—
113	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
114	C₂³×C₁₁₃	C₄×D₄	1	8	yes	—
115	C₂³×C₁₁₃	#121	1	4	yes	—
116	C₂³×C₁₁₃	#121	1	4	yes	—
117	C₂³×C₁₁₃	#124	1	4	yes	—
118	C₂³×C₁₁₃	#127	1	4	yes	—
119	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
120	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
121	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
122	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
123	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
124	D₄×C₁₁₃	—	4	8	no	—
125	D₄×C₁₁₃	—	4	4	no	—
126	D₄×C₁₁₃	—	4	4	no	—
127	D₄×C₁₁₃	—	4	16	no	—
128	D₄×C₁₁₃	—	8	8	no	—
129	C₂×C₄×C₁₁₃	—	2	4	no	—
130	C₂×C₄×C₁₁₃	—	2	8	no	—
131	C₂×C₄×C₁₁₃	—	2	8	no	—
132	C₂×C₄×C₁₁₃	—	4	4	no	—
133	C₂×C₄×C₁₁₃	—	4	4	no	—
134	C₂×C₄×C₁₁₃	—	4	4	no	—
135	C₂×C₄×C₁₁₃	—	4	8	no	—
136	C₂×C₄×C₁₁₃	—	4	8	no	—
137	C₂×C₄×C₁₁₃	—	4	8	no	—
138	C₂×C₄×C₁₁₃	—	4	4	no	—
139	C₂×C₄×C₁₁₃	—	8	8	no	—
140	C₂×C₄×C₁₁₃	—	8	8	no	—
141	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	—
142	C₂²×C₁₁₃	—	2	2	no	—
143	C₂²×C₁₁₃	—	2	2	no	—
144	C₂²×C₁₁₃	—	2	2	no	—
145	C₂²×C₁₁₃	—	2	8	no	—
146	C₂²×C₁₁₃	—	4	4	no	—
147	C₂²×C₁₁₃	—	4	4	no	—
148	C₂²×C₁₁₃	—	4	8	no	—
149	C₂²×C₁₁₃	—	4	4	no	—
150	C₂²×C₁₁₃	—	4	4	no	—
151	C₂²×C₁₁₃	—	4	2	no	—
152	C₂²×C₁₁₃	—	4	2	no	—
153	C₂²×C₁₁₃	—	4	8	no	—
154	C₂²×C₁₁₃	—	4	4	no	—
155	C₂²×C₁₁₃	—	8	8	no	—
156	C₂²×C₁₁₃	—	8	16	no	—
157	C₂²×C₁₁₃	#390	1	8	yes	—
158	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
160	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
161	C₂²×C₁₁₃	C₂×#124	1	1	yes	characteristic
162	C₂²×C₁₁₃	C₂×#127	1	1	yes	characteristic
163	C₄×C₁₁₃	—	2	8	no	—
164	C₄×C₁₁₃	—	4	8	no	—
165	C₄×C₁₁₃	—	4	4	no	—
166	C₄×C₁₁₃	—	8	4	no	—
167	#21213	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₁₁₃	—	2	2	no	—
169	C₂×C₁₁₃	—	2	1	no	—
170	C₂×C₁₁₃	—	2	2	no	—
171	C₂×C₁₁₃	—	2	8	no	—
172	C₂×C₁₁₃	—	2	1	no	—
173	C₂×C₁₁₃	—	8	4	no	—
174	C₂×C₁₁₃	C₂×#390	1	1	yes	characteristic
175	C₂×C₁₁₃	#2883	1	2	yes	—
176	C₂×#534	C₂×C₁₁₃	1	1	yes	characteristic
177	C₂²×#99	C₂×C₁₁₃	1	4	yes	complemented
178	#2315	C₂×C₁₁₃	1	1	yes	characteristic, complemented
179	#2273	C₂×C₁₁₃	1	1	yes	characteristic, complemented
180	#1964	C₂×C₁₁₃	1	8	yes	complemented
181	C₁₁₃	#21213	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³×D₄	C₂²×C₁₁₃	1	2	yes	—
183	#534	—	2	4	no	—
184	#534	—	2	4	no	—
185	C₂×#123	C₄×C₁₁₃	1	4	yes	complemented
186	C₂×#121	C₂²×C₁₁₃	1	4	yes	—
187	C₂×#120	C₄×C₁₁₃	1	4	yes	complemented
188	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
189	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
190	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
191	C₂×#99	—	2	16	no	—
192	C₂×#99	C₂²×C₁₁₃	1	16	yes	complemented
193	#385	—	2	4	no	—
194	#380	C₂²×C₁₁₃	1	4	yes	complemented
195	C₄×C₂²⋊C₄	—	2	4	no	—
196	C₄×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	complemented
197	C₂⁵	C₂×C₄×C₁₁₃	1	2	yes	—
198	C₂⁵	C₂³×C₁₁₃	1	1	yes	characteristic
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	—	2	4	no	—
201	C₂²×D₄	—	2	8	no	—
202	C₂²×D₄	—	2	8	no	—
203	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
204	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	complemented
205	C₂²×D₄	C₂³×C₁₁₃	1	4	yes	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	—	2	2	no	—
208	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
209	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
210	#123	—	2	16	no	—
211	#121	—	2	8	no	—
212	#121	—	2	8	no	—
213	#120	—	2	16	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	complemented
216	C₂×C₂²⋊C₄	—	2	2	no	—
217	C₂×C₂²⋊C₄	—	2	4	no	—
218	C₂×C₂²⋊C₄	—	2	8	no	—
219	C₂×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	8	yes	complemented
222	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	4	yes	—
223	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	4	yes	—
224	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	8	yes	complemented
225	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
227	C₂×C₄²	—	2	4	no	—
228	#99	—	2	32	no	—
229	#95	—	2	4	no	—
230	#95	—	2	4	no	—
231	C₂⁴	—	2	4	no	—
232	C₂⁴	—	2	8	no	—
233	C₂⁴	—	8	2	no	—
234	C₂⁴	—	8	4	no	—
235	C₂⁴	C₂²×C₄×C₁₁₃	1	4	yes	—
236	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
237	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
238	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
239	C₂⁴	C₂×D₄×C₁₁₃	1	4	yes	—
240	C₂⁴	#41×C₁₁₃	1	4	yes	—
241	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	2	16	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	8	no	—
248	C₂×D₄	—	2	8	no	—
249	C₂×D₄	—	4	8	no	—
250	C₂×D₄	—	4	8	no	—
251	C₂×D₄	—	4	8	no	—
252	C₂×D₄	—	4	8	no	—
253	C₂×D₄	—	8	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	8	2	no	—
261	C₂²×C₄	—	8	4	no	—
262	C₂²×C₄	—	8	4	no	—
263	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
265	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
266	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
267	C₄⋊C₄	—	2	8	no	—
268	C₄⋊C₄	—	8	4	no	—
269	C₂²⋊C₄	—	2	8	no	—
270	C₂²⋊C₄	—	2	4	no	—
271	C₂²⋊C₄	—	2	16	no	—
272	C₂²⋊C₄	—	2	8	no	—
273	C₂²⋊C₄	—	4	4	no	—
274	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	16	yes	—
275	C₂²⋊C₄	C₂×D₄×C₁₁₃	1	8	yes	—
276	C₄²	—	8	4	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	8	no	—
279	C₂³	—	4	4	no	—
280	C₂³	—	4	4	no	—
281	C₂³	—	4	2	no	—
282	C₂³	—	4	4	no	—
283	C₂³	—	4	8	no	—
284	C₂³	—	4	8	no	—
285	C₂³	—	8	8	no	—
286	C₂³	—	8	4	no	—
287	C₂³	—	8	4	no	—
288	C₂³	—	8	16	no	—
289	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
290	C₂³	C₄×D₄×C₁₁₃	1	8	yes	—
291	C₂³	#121×C₁₁₃	1	4	yes	—
292	C₂³	#121×C₁₁₃	1	4	yes	—
293	C₂³	#124×C₁₁₃	1	4	yes	—
294	C₂³	#127×C₁₁₃	1	4	yes	—
295	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
296	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
297	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
298	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
299	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
300	D₄	—	4	8	no	—
301	D₄	—	4	4	no	—
302	D₄	—	4	4	no	—
303	D₄	—	4	16	no	—
304	D₄	—	8	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	8	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	8	8	no	—
316	C₂×C₄	—	8	8	no	—
317	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	8	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	4	4	no	—
327	C₂²	—	4	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	4	8	no	—
331	C₂²	—	8	8	no	—
332	C₂²	—	8	16	no	—
333	C₂²	#390×C₁₁₃	1	8	yes	—
334	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
335	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
336	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
337	C₂²	C₂×#124×C₁₁₃	1	1	yes	characteristic
338	C₂²	C₂×#127×C₁₁₃	1	1	yes	characteristic
339	C₄	—	2	8	no	—
340	C₄	—	4	8	no	—
341	C₄	—	4	4	no	—
342	C₄	—	8	4	no	—
343	C₂	—	2	2	no	—
344	C₂	—	2	1	no	—
345	C₂	—	2	2	no	—
346	C₂	—	2	8	no	—
347	C₂	—	2	1	no	—
348	C₂	—	8	4	no	—
349	C₂	C₂×#390×C₁₁₃	1	1	yes	characteristic
350	C₂	C₁₁₃×#2883	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
prime radical	C₂×#534×C₁₁₃	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂²×C₂²⋊C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#99×C₁₁₃	C₂	semidirect
3. C₁₁₃×#2315	C₂	semidirect
4. C₁₁₃×#2273	C₂	semidirect
5. C₁₁₃×#1964	C₂	semidirect
9. C₂×#123×C₁₁₃	C₄	semidirect
11. C₂×#120×C₁₁₃	C₄	semidirect
16. C₂×#99×C₁₁₃	C₂²	semidirect
18. #380×C₁₁₃	C₂²	semidirect
20. C₄×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
28. C₂²×D₄×C₁₁₃	C₂×C₄	semidirect
39. C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	semidirect
45. C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	semidirect
48. C₂×C₂²⋊C₄×C₁₁₃	D₄	semidirect
167. #21213	C₁₁₃	direct (N × H)
177. C₂²×#99	C₂×C₁₁₃	semidirect
178. #2315	C₂×C₁₁₃	semidirect
179. #2273	C₂×C₁₁₃	semidirect
180. #1964	C₂×C₁₁₃	semidirect
181. C₁₁₃	#21213	direct (N × H)
185. C₂×#123	C₄×C₁₁₃	semidirect
187. C₂×#120	C₄×C₁₁₃	semidirect
192. C₂×#99	C₂²×C₁₁₃	semidirect
194. #380	C₂²×C₁₁₃	semidirect
196. C₄×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
204. C₂²×D₄	C₂×C₄×C₁₁₃	semidirect
215. C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	semidirect
221. C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	semidirect
224. C₂×C₂²⋊C₄	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₁₁₃	2
C₂²×#99×C₁₁₃	2
C₁₁₃×#2315	2
C₁₁₃×#2273	2
C₁₁₃×#1964	2
#21213	113

Subgroups — C113×#21213 #43289233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21213 #43289233