Subgroups — C₁₁₃×#9134 #43277154

Order 28928.

728 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#431×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	#431×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×C₄×C₈×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	2	no	—
36	#121×C₁₁₃	—	4	2	no	—
37	#121×C₁₁₃	—	4	4	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
44	C₂×C₄²×C₁₁₃	—	2	2	no	—
45	C₂×C₄²×C₁₁₃	—	2	2	no	—
46	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
50	C₄⋊C₈×C₁₁₃	—	2	2	no	—
51	C₄⋊C₈×C₁₁₃	—	2	2	no	—
52	C₄⋊C₈×C₁₁₃	—	2	2	no	—
53	C₄⋊C₈×C₁₁₃	D₄	1	4	yes	complemented
54	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
55	C₂²⋊C₈×C₁₁₃	—	4	2	no	—
56	C₄×C₈×C₁₁₃	—	2	4	no	—
57	C₂⁴×C₁₁₃	—	2	2	no	—
58	C₂⁴×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×D₄×C₁₁₃	—	2	4	no	—
60	C₂×D₄×C₁₁₃	—	4	2	no	—
61	C₂×D₄×C₁₁₃	—	4	2	no	—
62	C₂×D₄×C₁₁₃	—	4	4	no	—
63	C₂×D₄×C₁₁₃	—	4	4	no	—
64	C₂×D₄×C₁₁₃	—	4	4	no	—
65	C₂×D₄×C₁₁₃	—	4	1	no	—
66	C₂×D₄×C₁₁₃	—	4	2	no	—
67	C₂×D₄×C₁₁₃	—	4	1	no	—
68	C₂×D₄×C₁₁₃	—	4	1	no	—
69	C₂×D₄×C₁₁₃	—	4	1	no	—
70	C₂×D₄×C₁₁₃	—	4	2	no	—
71	C₂×D₄×C₁₁₃	—	4	2	no	—
72	C₂×D₄×C₁₁₃	—	4	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	1	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	2	no	—
82	C₂²×C₄×C₁₁₃	—	4	1	no	—
83	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁₃	D₈	1	2	yes	—
87	C₂²×C₄×C₁₁₃	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₈×C₁₁₃	—	2	4	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	C₂×C₈×C₁₁₃	—	4	2	no	—
97	C₄⋊C₄×C₁₁₃	—	4	2	no	—
98	C₄⋊C₄×C₁₁₃	—	4	1	no	—
99	C₄⋊C₄×C₁₁₃	—	4	1	no	—
100	C₄⋊C₄×C₁₁₃	—	4	2	no	—
101	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
102	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
103	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
104	C₄²×C₁₁₃	—	2	2	no	—
105	C₄²×C₁₁₃	—	2	1	no	—
106	C₄²×C₁₁₃	—	2	2	no	—
107	C₄²×C₁₁₃	—	2	1	no	—
108	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
109	C₄²×C₁₁₃	#41	1	2	yes	—
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	—	2	1	no	—
115	C₂³×C₁₁₃	—	2	1	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	—	4	2	no	—
122	C₂³×C₁₁₃	—	4	2	no	—
123	C₂³×C₁₁₃	#102	1	2	yes	—
124	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	D₄×C₁₁₃	—	8	4	no	—
126	D₄×C₁₁₃	—	8	8	no	—
127	D₄×C₁₁₃	—	8	2	no	—
128	D₄×C₁₁₃	—	8	2	no	—
129	D₄×C₁₁₃	—	8	2	no	—
130	D₄×C₁₁₃	—	8	2	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	4	no	—
138	C₂×C₄×C₁₁₃	—	2	4	no	—
139	C₂×C₄×C₁₁₃	—	2	1	no	—
140	C₂×C₄×C₁₁₃	—	2	1	no	—
141	C₂×C₄×C₁₁₃	—	2	1	no	—
142	C₂×C₄×C₁₁₃	—	4	4	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	#100	1	2	yes	—
149	C₂×C₄×C₁₁₃	#102	1	2	yes	—
150	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
152	C₂×C₄×C₁₁₃	#121	1	2	yes	—
153	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
154	C₂×C₄×C₁₁₃	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₁₃	#135	1	2	yes	—
157	C₂×C₄×C₁₁₃	#135	1	2	yes	—
158	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
159	C₈×C₁₁₃	—	4	4	no	—
160	C₈×C₁₁₃	—	8	2	no	—
161	C₂²×C₁₁₃	—	2	2	no	—
162	C₂²×C₁₁₃	—	2	2	no	—
163	C₂²×C₁₁₃	—	2	2	no	—
164	C₂²×C₁₁₃	—	4	1	no	—
165	C₂²×C₁₁₃	—	4	1	no	—
166	C₂²×C₁₁₃	—	4	1	no	—
167	C₂²×C₁₁₃	—	4	1	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	—	8	2	no	—
174	C₂²×C₁₁₃	—	8	2	no	—
175	C₂²×C₁₁₃	#386	1	1	yes	characteristic
176	C₂²×C₁₁₃	C₂×#100	1	1	yes	characteristic
177	C₂²×C₁₁₃	#413	1	1	yes	characteristic
178	C₂²×C₁₁₃	C₂×#102	1	1	yes	characteristic
179	C₂²×C₁₁₃	#416	1	1	yes	characteristic
180	C₂²×C₁₁₃	#416	1	1	yes	characteristic
181	C₂²×C₁₁₃	#418	1	1	yes	characteristic
182	C₄×C₁₁₃	—	2	2	no	—
183	C₄×C₁₁₃	—	2	2	no	—
184	C₄×C₁₁₃	—	2	2	no	—
185	C₄×C₁₁₃	—	4	1	no	—
186	C₄×C₁₁₃	—	8	2	no	—
187	C₄×C₁₁₃	#449	1	2	yes	—
188	C₄×C₁₁₃	#465	1	2	yes	—
189	C₄×C₁₁₃	#466	1	2	yes	—
190	C₄×C₁₁₃	#482	1	2	yes	—
191	#9134	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₁₁₃	—	4	2	no	—
193	C₂×C₁₁₃	—	16	2	no	—
194	C₂×C₁₁₃	#1540	1	1	yes	characteristic
195	C₂×C₁₁₃	#1543	1	1	yes	characteristic
196	C₂×C₁₁₃	#1545	1	1	yes	characteristic
197	C₂×C₁₁₃	#1553	1	1	yes	characteristic
198	C₂×C₁₁₃	#1875	1	1	yes	characteristic
199	C₂×C₁₁₃	#1893	1	1	yes	characteristic
200	C₂×C₁₁₃	#1900	1	1	yes	characteristic
201	C₂×#431	C₂×C₁₁₃	1	1	yes	characteristic, complemented
202	#2856	C₂×C₁₁₃	1	1	yes	characteristic
203	#1797	C₂×C₁₁₃	1	1	yes	characteristic, complemented
204	C₂×#331	C₂×C₁₁₃	1	2	yes	complemented
205	#1296	C₂×C₁₁₃	1	2	yes	complemented
206	C₁₁₃	#9134	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#127	C₂²×C₁₁₃	1	1	yes	characteristic
208	C₂×#121	—	2	1	no	—
209	C₂×#121	—	2	1	no	—
210	C₂×#121	C₄×C₁₁₃	1	2	yes	—
211	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
212	#431	—	2	4	no	—
213	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
215	C₂×C₂²⋊C₈	—	2	1	no	—
216	C₂×C₂²⋊C₈	—	2	1	no	—
217	C₂×C₄×C₈	—	2	1	no	—
218	#390	—	2	1	no	—
219	#390	—	2	1	no	—
220	#390	C₄×C₁₁₃	1	2	yes	—
221	#384	C₂²×C₁₁₃	1	1	yes	characteristic
222	#336	—	2	1	no	—
223	#331	—	2	4	no	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
228	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
230	C₂³×C₄	D₄×C₁₁₃	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	#127	—	2	2	no	—
234	#127	—	2	2	no	—
235	#121	—	4	4	no	—
236	#121	—	4	2	no	—
237	#121	—	4	2	no	—
238	#121	—	4	4	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
251	C₄⋊C₈	—	2	2	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	D₄×C₁₁₃	1	4	yes	complemented
255	C₂²⋊C₈	—	2	4	no	—
256	C₂²⋊C₈	—	4	2	no	—
257	C₄×C₈	—	2	4	no	—
258	C₂⁴	—	2	2	no	—
259	C₂⁴	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	4	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	1	no	—
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	D₈×C₁₁₃	1	2	yes	—
288	C₂²×C₄	SD₁₆×C₁₁₃	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	1	no	—
309	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
310	C₄²	#41×C₁₁₃	1	2	yes	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	#102×C₁₁₃	1	2	yes	—
325	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
326	D₄	—	8	4	no	—
327	D₄	—	8	8	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	D₄	—	8	2	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	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	#100×C₁₁₃	1	2	yes	—
350	C₂×C₄	#102×C₁₁₃	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
352	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
353	C₂×C₄	#121×C₁₁₃	1	2	yes	—
354	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×D₈×C₁₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂×SD₁₆×C₁₁₃	1	1	yes	characteristic
357	C₂×C₄	#135×C₁₁₃	1	2	yes	—
358	C₂×C₄	#135×C₁₁₃	1	2	yes	—
359	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
360	C₈	—	4	4	no	—
361	C₈	—	8	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	#386×C₁₁₃	1	1	yes	characteristic
377	C₂²	C₂×#100×C₁₁₃	1	1	yes	characteristic
378	C₂²	#413×C₁₁₃	1	1	yes	characteristic
379	C₂²	C₂×#102×C₁₁₃	1	1	yes	characteristic
380	C₂²	#416×C₁₁₃	1	1	yes	characteristic
381	C₂²	#416×C₁₁₃	1	1	yes	characteristic
382	C₂²	#418×C₁₁₃	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	8	2	no	—
388	C₄	#449×C₁₁₃	1	2	yes	—
389	C₄	#465×C₁₁₃	1	2	yes	—
390	C₄	#466×C₁₁₃	1	2	yes	—
391	C₄	#482×C₁₁₃	1	2	yes	—
392	C₂	—	4	2	no	—
393	C₂	—	16	2	no	—
394	C₂	C₁₁₃×#1540	1	1	yes	characteristic
395	C₂	C₁₁₃×#1543	1	1	yes	characteristic
396	C₂	C₁₁₃×#1545	1	1	yes	characteristic
397	C₂	C₁₁₃×#1553	1	1	yes	characteristic
398	C₂	C₁₁₃×#1875	1	1	yes	characteristic
399	C₂	C₁₁₃×#1893	1	1	yes	characteristic
400	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×#431×C₁₁₃	C₂	semidirect
3. C₁₁₃×#1797	C₂	semidirect
4. C₂×#331×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1296	C₂	semidirect
53. C₄⋊C₈×C₁₁₃	D₄	semidirect
191. #9134	C₁₁₃	direct (N × H)
201. C₂×#431	C₂×C₁₁₃	semidirect
203. #1797	C₂×C₁₁₃	semidirect
204. C₂×#331	C₂×C₁₁₃	semidirect
205. #1296	C₂×C₁₁₃	semidirect
206. C₁₁₃	#9134	direct (N × H)
254. 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×#431×C₁₁₃	2
C₁₁₃×#2856	2
C₁₁₃×#1797	2
C₂×#331×C₁₁₃	2
C₁₁₃×#1296	2
#9134	113

Subgroups — C113×#9134 #43277154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#9134 #43277154