Subgroups — C₁₁₃×#2411 #28387207

Order 14464.

786 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#120×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#117×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#396×C₁₁₃	C₂	1	2	yes	maximal, complemented
6	#394×C₁₁₃	C₂	1	2	yes	maximal, complemented
7	#390×C₁₁₃	C₂	1	2	yes	maximal, complemented
8	#388×C₁₁₃	C₂	1	2	yes	maximal, complemented
9	#386×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#385×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#379×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁵×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	#123×C₁₁₃	—	2	4	no	—
18	#120×C₁₁₃	—	2	4	no	—
19	#117×C₁₁₃	—	2	4	no	—
20	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
21	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
25	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
36	C₂×C₄²×C₁₁₃	C₂²	1	2	yes	complemented
37	#95×C₁₁₃	C₂²	1	2	yes	complemented
38	#95×C₁₁₃	C₂²	1	2	yes	complemented
39	C₂⁴×C₁₁₃	—	2	2	no	—
40	C₂⁴×C₁₁₃	—	2	4	no	—
41	C₂⁴×C₁₁₃	—	2	2	no	—
42	C₂⁴×C₁₁₃	—	2	2	no	—
43	C₂⁴×C₁₁₃	—	4	2	no	—
44	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
45	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
46	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
47	C₂×D₄×C₁₁₃	—	2	2	no	—
48	C₂×D₄×C₁₁₃	—	2	2	no	—
49	C₂×D₄×C₁₁₃	—	2	4	no	—
50	C₂×D₄×C₁₁₃	—	2	2	no	—
51	C₂×D₄×C₁₁₃	—	2	4	no	—
52	C₂×D₄×C₁₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₁₃	—	2	2	no	—
54	C₂²×C₄×C₁₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₁₃	—	4	2	no	—
57	C₂²×C₄×C₁₁₃	D₄	1	4	yes	complemented
58	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
60	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
62	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
64	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₁₁₃	—	2	4	no	—
67	C₄⋊C₄×C₁₁₃	—	2	2	no	—
68	C₄⋊C₄×C₁₁₃	—	2	2	no	—
69	C₄⋊C₄×C₁₁₃	—	4	2	no	—
70	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
71	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
72	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
73	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
74	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
75	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
76	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
77	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
78	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
79	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
80	C₂²⋊C₄×C₁₁₃	D₄	1	4	yes	—
81	C₄²×C₁₁₃	—	2	4	no	—
82	C₂³×C₁₁₃	—	2	2	no	—
83	C₂³×C₁₁₃	—	2	2	no	—
84	C₂³×C₁₁₃	—	2	8	no	—
85	C₂³×C₁₁₃	—	2	2	no	—
86	C₂³×C₁₁₃	—	2	2	no	—
87	C₂³×C₁₁₃	—	2	2	no	—
88	C₂³×C₁₁₃	—	2	2	no	—
89	C₂³×C₁₁₃	—	2	2	no	—
90	C₂³×C₁₁₃	—	2	2	no	—
91	C₂³×C₁₁₃	—	2	1	no	—
92	C₂³×C₁₁₃	—	2	1	no	—
93	C₂³×C₁₁₃	—	2	1	no	—
94	C₂³×C₁₁₃	—	2	2	no	—
95	C₂³×C₁₁₃	—	2	2	no	—
96	C₂³×C₁₁₃	—	4	8	no	—
97	C₂³×C₁₁₃	—	4	8	no	—
98	C₂³×C₁₁₃	—	4	4	no	—
99	C₂³×C₁₁₃	—	4	4	no	—
100	C₂³×C₁₁₃	C₂×D₄	1	2	yes	—
101	C₂³×C₁₁₃	C₂×D₄	1	2	yes	—
102	C₂³×C₁₁₃	#41	1	4	yes	—
103	C₂³×C₁₁₃	#41	1	2	yes	—
104	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
105	D₄×C₁₁₃	—	4	8	no	—
106	D₄×C₁₁₃	—	4	4	no	—
107	C₂×C₄×C₁₁₃	—	2	8	no	—
108	C₂×C₄×C₁₁₃	—	2	1	no	—
109	C₂×C₄×C₁₁₃	—	2	1	no	—
110	C₂×C₄×C₁₁₃	—	2	1	no	—
111	C₂×C₄×C₁₁₃	—	2	1	no	—
112	C₂×C₄×C₁₁₃	—	2	2	no	—
113	C₂×C₄×C₁₁₃	—	2	2	no	—
114	C₂×C₄×C₁₁₃	—	2	2	no	—
115	C₂×C₄×C₁₁₃	—	2	1	no	—
116	C₂×C₄×C₁₁₃	—	2	1	no	—
117	C₂×C₄×C₁₁₃	—	2	2	no	—
118	C₂×C₄×C₁₁₃	—	2	1	no	—
119	C₂×C₄×C₁₁₃	—	2	1	no	—
120	C₂×C₄×C₁₁₃	—	2	2	no	—
121	C₂×C₄×C₁₁₃	—	2	2	no	—
122	C₂×C₄×C₁₁₃	—	2	1	no	—
123	C₂×C₄×C₁₁₃	—	2	2	no	—
124	C₂×C₄×C₁₁₃	—	2	2	no	—
125	C₂×C₄×C₁₁₃	—	2	2	no	—
126	C₂×C₄×C₁₁₃	—	2	2	no	—
127	C₂×C₄×C₁₁₃	—	4	4	no	—
128	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
129	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₁₁₃	—	2	2	no	—
132	C₂²×C₁₁₃	—	2	2	no	—
133	C₂²×C₁₁₃	—	2	4	no	—
134	C₂²×C₁₁₃	—	2	4	no	—
135	C₂²×C₁₁₃	—	2	4	no	—
136	C₂²×C₁₁₃	—	2	4	no	—
137	C₂²×C₁₁₃	—	2	4	no	—
138	C₂²×C₁₁₃	—	4	16	no	—
139	C₂²×C₁₁₃	—	4	2	no	—
140	C₂²×C₁₁₃	—	4	2	no	—
141	C₂²×C₁₁₃	—	4	2	no	—
142	C₂²×C₁₁₃	—	4	2	no	—
143	C₂²×C₁₁₃	—	4	1	no	—
144	C₂²×C₁₁₃	—	4	1	no	—
145	C₂²×C₁₁₃	—	4	1	no	—
146	C₂²×C₁₁₃	—	4	2	no	—
147	C₂²×C₁₁₃	—	4	2	no	—
148	C₂²×C₁₁₃	#121	1	4	yes	—
149	C₂²×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₂²×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
151	C₂²×C₁₁₃	C₂×#41	1	1	yes	characteristic
152	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
153	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
154	C₄×C₁₁₃	—	2	2	no	—
155	C₄×C₁₁₃	—	2	2	no	—
156	C₄×C₁₁₃	—	2	4	no	—
157	C₄×C₁₁₃	—	4	1	no	—
158	C₄×C₁₁₃	—	4	1	no	—
159	C₄×C₁₁₃	—	4	1	no	—
160	C₄×C₁₁₃	—	4	2	no	—
161	C₄×C₁₁₃	—	4	2	no	—
162	C₂×C₁₁₃	—	2	4	no	—
163	C₂×C₁₁₃	—	4	4	no	—
164	C₂×C₁₁₃	—	8	1	no	—
165	C₂×C₁₁₃	C₂×#121	1	1	yes	characteristic
166	C₂×C₁₁₃	#525	1	1	yes	characteristic
167	C₂×C₁₁₃	#535	1	1	yes	characteristic
168	C₂×C₁₁₃	#546	1	2	yes	—
169	C₂×C₁₁₃	#551	1	2	yes	—
170	#2411	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₁₁₃	#2411	1	1	yes	characteristic, direct product factor, Sylow
172	C₂×#123	C₂×C₁₁₃	1	1	yes	characteristic, complemented
173	C₂×#120	C₂×C₁₁₃	1	1	yes	characteristic
174	C₂×#117	C₂×C₁₁₃	1	1	yes	characteristic, complemented
175	C₂²×C₂²⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic, complemented
176	#396	C₂×C₁₁₃	1	2	yes	complemented
177	#394	C₂×C₁₁₃	1	2	yes	complemented
178	#390	C₂×C₁₁₃	1	2	yes	complemented
179	#388	C₂×C₁₁₃	1	2	yes	complemented
180	#386	C₂×C₁₁₃	1	1	yes	characteristic, complemented
181	#385	C₂×C₁₁₃	1	1	yes	characteristic, complemented
182	#379	C₂×C₁₁₃	1	1	yes	characteristic, complemented
183	C₂⁵	C₂²×C₁₁₃	1	1	yes	characteristic
184	C₂²×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
185	C₂²×D₄	C₂²×C₁₁₃	1	2	yes	—
186	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
187	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
188	#123	—	2	4	no	—
189	#120	—	2	4	no	—
190	#117	—	2	4	no	—
191	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
192	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
193	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
194	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
195	C₂×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
198	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
203	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
204	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
205	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
206	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
207	C₂×C₄²	C₂²×C₁₁₃	1	2	yes	complemented
208	#95	C₂²×C₁₁₃	1	2	yes	complemented
209	#95	C₂²×C₁₁₃	1	2	yes	complemented
210	C₂⁴	—	2	2	no	—
211	C₂⁴	—	2	4	no	—
212	C₂⁴	—	2	2	no	—
213	C₂⁴	—	2	2	no	—
214	C₂⁴	—	4	2	no	—
215	C₂⁴	C₂³×C₁₁₃	1	1	yes	characteristic
216	C₂⁴	C₂³×C₁₁₃	1	2	yes	—
217	C₂⁴	C₂³×C₁₁₃	1	1	yes	characteristic
218	C₂×D₄	—	2	2	no	—
219	C₂×D₄	—	2	2	no	—
220	C₂×D₄	—	2	4	no	—
221	C₂×D₄	—	2	2	no	—
222	C₂×D₄	—	2	4	no	—
223	C₂×D₄	—	4	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	D₄×C₁₁₃	1	4	yes	complemented
229	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
230	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
231	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
232	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
233	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
234	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
235	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
236	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
237	C₄⋊C₄	—	2	4	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	2	2	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₂²⋊C₄	—	2	2	no	—
242	C₂²⋊C₄	—	2	2	no	—
243	C₂²⋊C₄	—	2	4	no	—
244	C₂²⋊C₄	—	2	4	no	—
245	C₂²⋊C₄	—	2	4	no	—
246	C₂²⋊C₄	—	2	4	no	—
247	C₂²⋊C₄	—	2	2	no	—
248	C₂²⋊C₄	—	2	2	no	—
249	C₂²⋊C₄	—	4	2	no	—
250	C₂²⋊C₄	—	4	2	no	—
251	C₂²⋊C₄	D₄×C₁₁₃	1	4	yes	—
252	C₄²	—	2	4	no	—
253	C₂³	—	2	2	no	—
254	C₂³	—	2	2	no	—
255	C₂³	—	2	8	no	—
256	C₂³	—	2	2	no	—
257	C₂³	—	2	2	no	—
258	C₂³	—	2	2	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	2	no	—
262	C₂³	—	2	1	no	—
263	C₂³	—	2	1	no	—
264	C₂³	—	2	1	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	4	8	no	—
268	C₂³	—	4	8	no	—
269	C₂³	—	4	4	no	—
270	C₂³	—	4	4	no	—
271	C₂³	C₂×D₄×C₁₁₃	1	2	yes	—
272	C₂³	C₂×D₄×C₁₁₃	1	2	yes	—
273	C₂³	#41×C₁₁₃	1	4	yes	—
274	C₂³	#41×C₁₁₃	1	2	yes	—
275	C₂³	C₂⁴×C₁₁₃	1	1	yes	characteristic
276	D₄	—	4	8	no	—
277	D₄	—	4	4	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
300	C₂×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
301	C₂×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	2	4	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	4	16	no	—
310	C₂²	—	4	2	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	—	4	2	no	—
314	C₂²	—	4	1	no	—
315	C₂²	—	4	1	no	—
316	C₂²	—	4	1	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	2	no	—
319	C₂²	#121×C₁₁₃	1	4	yes	—
320	C₂²	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
321	C₂²	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
322	C₂²	C₂×#41×C₁₁₃	1	1	yes	characteristic
323	C₂²	C₂×#41×C₁₁₃	1	2	yes	—
324	C₂²	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
325	C₄	—	2	2	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	4	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	1	no	—
330	C₄	—	4	2	no	—
331	C₄	—	4	1	no	—
332	C₄	—	4	2	no	—
333	C₂	—	2	4	no	—
334	C₂	—	4	4	no	—
335	C₂	—	8	1	no	—
336	C₂	C₂×#121×C₁₁₃	1	1	yes	characteristic
337	C₂	#525×C₁₁₃	1	1	yes	characteristic
338	C₂	#535×C₁₁₃	1	1	yes	characteristic
339	C₂	#546×C₁₁₃	1	2	yes	—
340	C₂	#551×C₁₁₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁₃
prime radical	C₂×#120×C₁₁₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#123×C₁₁₃	C₂	semidirect
3. C₂×#117×C₁₁₃	C₂	semidirect
4. C₂²×C₂²⋊C₄×C₁₁₃	C₂	semidirect
5. #396×C₁₁₃	C₂	semidirect
6. #394×C₁₁₃	C₂	semidirect
7. #390×C₁₁₃	C₂	semidirect
8. #388×C₁₁₃	C₂	semidirect
9. #386×C₁₁₃	C₂	semidirect
10. #385×C₁₁₃	C₂	semidirect
11. #379×C₁₁₃	C₂	semidirect
20. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
21. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
22. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
23. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
33. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
34. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
35. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
36. C₂×C₄²×C₁₁₃	C₂²	semidirect
37. #95×C₁₁₃	C₂²	semidirect
38. #95×C₁₁₃	C₂²	semidirect
57. C₂²×C₄×C₁₁₃	D₄	semidirect
170. #2411	C₁₁₃	direct (N × H)
171. C₁₁₃	#2411	direct (N × H)
172. C₂×#123	C₂×C₁₁₃	semidirect
174. C₂×#117	C₂×C₁₁₃	semidirect
175. C₂²×C₂²⋊C₄	C₂×C₁₁₃	semidirect
176. #396	C₂×C₁₁₃	semidirect
177. #394	C₂×C₁₁₃	semidirect
178. #390	C₂×C₁₁₃	semidirect
179. #388	C₂×C₁₁₃	semidirect
180. #386	C₂×C₁₁₃	semidirect
181. #385	C₂×C₁₁₃	semidirect
182. #379	C₂×C₁₁₃	semidirect
191. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
192. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
193. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
194. C₂×C₄⋊C₄	C₂²×C₁₁₃	semidirect
204. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
205. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
206. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
207. C₂×C₄²	C₂²×C₁₁₃	semidirect
208. #95	C₂²×C₁₁₃	semidirect
209. #95	C₂²×C₁₁₃	semidirect
228. 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×#123×C₁₁₃	2
C₂×#120×C₁₁₃	2
C₂×#117×C₁₁₃	2
C₂²×C₂²⋊C₄×C₁₁₃	2
#396×C₁₁₃	2
#394×C₁₁₃	2
#390×C₁₁₃	2
#388×C₁₁₃	2
#386×C₁₁₃	2
#385×C₁₁₃	2
#379×C₁₁₃	2
#2411	113

Subgroups — C113×#2411 #28387207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#2411 #28387207