Subgroups — C₁₁₃×#9142 #43277162

Order 28928.

708 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#432×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#2856	C₂	1	1	yes	maximal, characteristic
3	C₁₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#331×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1296	C₂	1	2	yes	maximal, complemented
6	C₂×#127×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₂×#121×C₁₁₃	—	2	1	no	—
8	C₂×#121×C₁₁₃	—	2	1	no	—
9	C₂×#121×C₁₁₃	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
11	#432×C₁₁₃	—	2	4	no	—
12	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
14	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₁₁₃	—	2	1	no	—
16	C₂×#97×C₁₁₃	—	2	1	no	—
17	#390×C₁₁₃	—	2	1	no	—
18	#390×C₁₁₃	—	2	1	no	—
19	#390×C₁₁₃	C₄	1	2	yes	—
20	#384×C₁₁₃	C₂²	1	1	yes	characteristic
21	#336×C₁₁₃	—	2	1	no	—
22	#331×C₁₁₃	—	2	4	no	—
23	C₂²×D₄×C₁₁₃	—	2	2	no	—
24	C₂²×D₄×C₁₁₃	—	2	1	no	—
25	C₂²×D₄×C₁₁₃	—	2	1	no	—
26	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₁₃	—	2	2	no	—
32	#127×C₁₁₃	—	2	2	no	—
33	#127×C₁₁₃	—	2	2	no	—
34	#121×C₁₁₃	—	4	4	no	—
35	#121×C₁₁₃	—	4	4	no	—
36	#121×C₁₁₃	—	4	4	no	—
37	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
43	C₂×C₄²×C₁₁₃	—	2	2	no	—
44	C₂×C₄²×C₁₁₃	—	2	2	no	—
45	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₁₁₃	—	2	2	no	—
50	C₄⋊C₈×C₁₁₃	—	2	2	no	—
51	C₄⋊C₈×C₁₁₃	—	2	2	no	—
52	C₄⋊C₈×C₁₁₃	D₄	1	4	yes	complemented
53	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
54	C₂²⋊C₈×C₁₁₃	—	4	2	no	—
55	#97×C₁₁₃	—	2	4	no	—
56	C₂⁴×C₁₁₃	—	2	2	no	—
57	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×D₄×C₁₁₃	—	2	4	no	—
59	C₂×D₄×C₁₁₃	—	4	2	no	—
60	C₂×D₄×C₁₁₃	—	4	2	no	—
61	C₂×D₄×C₁₁₃	—	4	4	no	—
62	C₂×D₄×C₁₁₃	—	4	4	no	—
63	C₂×D₄×C₁₁₃	—	4	4	no	—
64	C₂×D₄×C₁₁₃	—	4	1	no	—
65	C₂×D₄×C₁₁₃	—	4	2	no	—
66	C₂×D₄×C₁₁₃	—	4	1	no	—
67	C₂×D₄×C₁₁₃	—	4	2	no	—
68	C₂×D₄×C₁₁₃	—	4	2	no	—
69	C₂×D₄×C₁₁₃	—	4	2	no	—
70	C₂×D₄×C₁₁₃	—	4	1	no	—
71	C₂×D₄×C₁₁₃	—	4	1	no	—
72	C₂²×C₄×C₁₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	4	1	no	—
84	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₁₃	—	2	4	no	—
91	C₂×C₈×C₁₁₃	—	4	2	no	—
92	C₂×C₈×C₁₁₃	—	4	2	no	—
93	C₂×C₈×C₁₁₃	—	4	2	no	—
94	C₂×C₈×C₁₁₃	—	4	2	no	—
95	C₂×C₈×C₁₁₃	—	4	2	no	—
96	C₄⋊C₄×C₁₁₃	—	4	2	no	—
97	C₄⋊C₄×C₁₁₃	—	4	2	no	—
98	C₄⋊C₄×C₁₁₃	—	4	2	no	—
99	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
100	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
101	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
102	C₄²×C₁₁₃	—	2	2	no	—
103	C₄²×C₁₁₃	—	2	1	no	—
104	C₄²×C₁₁₃	—	2	2	no	—
105	C₄²×C₁₁₃	—	2	1	no	—
106	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
107	C₄²×C₁₁₃	#41	1	2	yes	—
108	C₂³×C₁₁₃	—	2	1	no	—
109	C₂³×C₁₁₃	—	2	1	no	—
110	C₂³×C₁₁₃	—	2	1	no	—
111	C₂³×C₁₁₃	—	2	1	no	—
112	C₂³×C₁₁₃	—	2	1	no	—
113	C₂³×C₁₁₃	—	2	1	no	—
114	C₂³×C₁₁₃	—	4	2	no	—
115	C₂³×C₁₁₃	—	4	2	no	—
116	C₂³×C₁₁₃	—	4	2	no	—
117	C₂³×C₁₁₃	—	4	2	no	—
118	C₂³×C₁₁₃	—	4	2	no	—
119	C₂³×C₁₁₃	—	4	2	no	—
120	C₂³×C₁₁₃	—	4	2	no	—
121	C₂³×C₁₁₃	#100	1	2	yes	—
122	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	D₄×C₁₁₃	—	8	4	no	—
124	D₄×C₁₁₃	—	8	8	no	—
125	D₄×C₁₁₃	—	8	2	no	—
126	D₄×C₁₁₃	—	8	2	no	—
127	D₄×C₁₁₃	—	8	2	no	—
128	D₄×C₁₁₃	—	8	2	no	—
129	C₂×C₄×C₁₁₃	—	2	1	no	—
130	C₂×C₄×C₁₁₃	—	2	1	no	—
131	C₂×C₄×C₁₁₃	—	2	1	no	—
132	C₂×C₄×C₁₁₃	—	2	1	no	—
133	C₂×C₄×C₁₁₃	—	2	1	no	—
134	C₂×C₄×C₁₁₃	—	2	1	no	—
135	C₂×C₄×C₁₁₃	—	2	1	no	—
136	C₂×C₄×C₁₁₃	—	2	1	no	—
137	C₂×C₄×C₁₁₃	—	2	1	no	—
138	C₂×C₄×C₁₁₃	—	2	1	no	—
139	C₂×C₄×C₁₁₃	—	2	1	no	—
140	C₂×C₄×C₁₁₃	—	4	4	no	—
141	C₂×C₄×C₁₁₃	—	4	2	no	—
142	C₂×C₄×C₁₁₃	—	4	2	no	—
143	C₂×C₄×C₁₁₃	—	4	2	no	—
144	C₂×C₄×C₁₁₃	—	4	2	no	—
145	C₂×C₄×C₁₁₃	—	4	2	no	—
146	C₂×C₄×C₁₁₃	—	4	2	no	—
147	C₂×C₄×C₁₁₃	—	4	2	no	—
148	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
150	C₂×C₄×C₁₁₃	#121	1	2	yes	—
151	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
152	C₂×C₄×C₁₁₃	#135	1	2	yes	—
153	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₁₁₃	#137	1	1	yes	characteristic
157	C₈×C₁₁₃	—	4	4	no	—
158	C₈×C₁₁₃	—	8	2	no	—
159	C₂²×C₁₁₃	—	2	2	no	—
160	C₂²×C₁₁₃	—	2	2	no	—
161	C₂²×C₁₁₃	—	2	2	no	—
162	C₂²×C₁₁₃	—	4	1	no	—
163	C₂²×C₁₁₃	—	4	1	no	—
164	C₂²×C₁₁₃	—	4	1	no	—
165	C₂²×C₁₁₃	—	4	1	no	—
166	C₂²×C₁₁₃	—	8	2	no	—
167	C₂²×C₁₁₃	—	8	2	no	—
168	C₂²×C₁₁₃	—	8	2	no	—
169	C₂²×C₁₁₃	—	8	2	no	—
170	C₂²×C₁₁₃	—	8	2	no	—
171	C₂²×C₁₁₃	—	8	2	no	—
172	C₂²×C₁₁₃	—	8	2	no	—
173	C₂²×C₁₁₃	#386	1	1	yes	characteristic
174	C₂²×C₁₁₃	C₂×#100	1	1	yes	characteristic
175	C₂²×C₁₁₃	#413	1	1	yes	characteristic
176	C₂²×C₁₁₃	#416	1	1	yes	characteristic
177	C₂²×C₁₁₃	#417	1	1	yes	characteristic
178	C₂²×C₁₁₃	#418	1	1	yes	characteristic
179	C₂²×C₁₁₃	#418	1	1	yes	characteristic
180	C₄×C₁₁₃	—	2	2	no	—
181	C₄×C₁₁₃	—	4	1	no	—
182	C₄×C₁₁₃	—	4	1	no	—
183	C₄×C₁₁₃	—	4	1	no	—
184	C₄×C₁₁₃	—	8	2	no	—
185	C₄×C₁₁₃	#449	1	2	yes	—
186	C₄×C₁₁₃	#468	1	2	yes	—
187	C₄×C₁₁₃	#469	1	2	yes	—
188	C₄×C₁₁₃	#482	1	2	yes	—
189	#9142	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₁₁₃	—	4	2	no	—
191	C₂×C₁₁₃	—	16	2	no	—
192	C₂×C₁₁₃	#1551	1	1	yes	characteristic
193	C₂×C₁₁₃	#1553	1	1	yes	characteristic
194	C₂×C₁₁₃	#1555	1	1	yes	characteristic
195	C₂×C₁₁₃	#1557	1	1	yes	characteristic
196	C₂×C₁₁₃	#1875	1	1	yes	characteristic
197	C₂×C₁₁₃	#1895	1	1	yes	characteristic
198	C₂×C₁₁₃	#1900	1	1	yes	characteristic
199	C₂×#432	C₂×C₁₁₃	1	1	yes	characteristic, complemented
200	#2856	C₂×C₁₁₃	1	1	yes	characteristic
201	#1797	C₂×C₁₁₃	1	1	yes	characteristic, complemented
202	C₂×#331	C₂×C₁₁₃	1	2	yes	complemented
203	#1296	C₂×C₁₁₃	1	2	yes	complemented
204	C₁₁₃	#9142	1	1	yes	characteristic, direct product factor, Sylow
205	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
206	C₂×#121	—	2	1	no	—
207	C₂×#121	—	2	1	no	—
208	C₂×#121	C₄×C₁₁₃	1	2	yes	—
209	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
210	#432	—	2	4	no	—
211	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₂²⋊C₈	—	2	1	no	—
215	C₂×#97	—	2	1	no	—
216	#390	—	2	1	no	—
217	#390	—	2	1	no	—
218	#390	C₄×C₁₁₃	1	2	yes	—
219	#384	C₂²×C₁₁₃	1	1	yes	characteristic
220	#336	—	2	1	no	—
221	#331	—	2	4	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
226	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	#127	—	2	2	no	—
232	#127	—	2	2	no	—
233	#121	—	4	4	no	—
234	#121	—	4	4	no	—
235	#121	—	4	4	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	D₄×C₁₁₃	1	4	yes	complemented
252	C₂²⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	4	2	no	—
254	#97	—	2	4	no	—
255	C₂⁴	—	2	2	no	—
256	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	4	2	no	—
259	C₂×D₄	—	4	2	no	—
260	C₂×D₄	—	4	4	no	—
261	C₂×D₄	—	4	4	no	—
262	C₂×D₄	—	4	4	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	1	no	—
305	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
306	C₄²	#41×C₁₁₃	1	2	yes	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	#100×C₁₁₃	1	2	yes	—
321	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
322	D₄	—	8	4	no	—
323	D₄	—	8	8	no	—
324	D₄	—	8	2	no	—
325	D₄	—	8	2	no	—
326	D₄	—	8	2	no	—
327	D₄	—	8	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
348	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
349	C₂×C₄	#121×C₁₁₃	1	2	yes	—
350	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
351	C₂×C₄	#135×C₁₁₃	1	2	yes	—
352	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
353	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
354	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	#137×C₁₁₃	1	1	yes	characteristic
356	C₈	—	4	4	no	—
357	C₈	—	8	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	#386×C₁₁₃	1	1	yes	characteristic
373	C₂²	C₂×#100×C₁₁₃	1	1	yes	characteristic
374	C₂²	#413×C₁₁₃	1	1	yes	characteristic
375	C₂²	#416×C₁₁₃	1	1	yes	characteristic
376	C₂²	#417×C₁₁₃	1	1	yes	characteristic
377	C₂²	#418×C₁₁₃	1	1	yes	characteristic
378	C₂²	#418×C₁₁₃	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	8	2	no	—
384	C₄	#449×C₁₁₃	1	2	yes	—
385	C₄	#468×C₁₁₃	1	2	yes	—
386	C₄	#469×C₁₁₃	1	2	yes	—
387	C₄	#482×C₁₁₃	1	2	yes	—
388	C₂	—	4	2	no	—
389	C₂	—	16	2	no	—
390	C₂	C₁₁₃×#1551	1	1	yes	characteristic
391	C₂	C₁₁₃×#1553	1	1	yes	characteristic
392	C₂	C₁₁₃×#1555	1	1	yes	characteristic
393	C₂	C₁₁₃×#1557	1	1	yes	characteristic
394	C₂	C₁₁₃×#1875	1	1	yes	characteristic
395	C₂	C₁₁₃×#1895	1	1	yes	characteristic
396	C₂	C₁₁₃×#1900	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁₃
prime radical	C₁₁₃×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#432×C₁₁₃	C₂	semidirect
3. C₁₁₃×#1797	C₂	semidirect
4. C₂×#331×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1296	C₂	semidirect
52. C₄⋊C₈×C₁₁₃	D₄	semidirect
189. #9142	C₁₁₃	direct (N × H)
199. C₂×#432	C₂×C₁₁₃	semidirect
201. #1797	C₂×C₁₁₃	semidirect
202. C₂×#331	C₂×C₁₁₃	semidirect
203. #1296	C₂×C₁₁₃	semidirect
204. C₁₁₃	#9142	direct (N × H)
251. C₄⋊C₈	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×#432×C₁₁₃	2
C₁₁₃×#2856	2
C₁₁₃×#1797	2
C₂×#331×C₁₁₃	2
C₁₁₃×#1296	2
#9142	113

Subgroups — C113×#9142 #43277162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#9142 #43277162