Subgroups — C₁₁₃×#19190 #43287210

Order 28928.

746 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3245	C₂	1	2	yes	maximal, complemented
2	C₁₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1685	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1669	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1667	C₂	1	2	yes	maximal, complemented
7	C₂×#335×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁₃×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₁₁₃	—	2	1	no	—
10	C₂×#135×C₁₁₃	—	2	1	no	—
11	C₂×#131×C₁₁₃	—	2	1	no	—
12	#532×C₁₁₃	C₂²	1	2	yes	—
13	#532×C₁₁₃	C₂²	1	1	yes	characteristic
14	#495×C₁₁₃	—	2	1	no	—
15	#495×C₁₁₃	—	2	1	no	—
16	#494×C₁₁₃	C₂²	1	1	yes	characteristic
17	#493×C₁₁₃	C₂²	1	1	yes	characteristic
18	#492×C₁₁₃	C₂²	1	2	yes	—
19	#474×C₁₁₃	—	2	2	no	—
20	#474×C₁₁₃	C₂²	1	4	yes	—
21	#466×C₁₁₃	—	2	4	no	—
22	#459×C₁₁₃	—	2	2	no	—
23	#459×C₁₁₃	C₂²	1	4	yes	—
24	#436×C₁₁₃	—	2	1	no	—
25	#436×C₁₁₃	C₂²	1	2	yes	—
26	C₈×D₄×C₁₁₃	—	2	1	no	—
27	C₈×D₄×C₁₁₃	C₂²	1	2	yes	—
28	#423×C₁₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
30	#408×C₁₁₃	—	2	1	no	—
31	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
32	#335×C₁₁₃	C₂²	1	2	yes	—
33	#335×C₁₁₃	C₂²	1	2	yes	—
34	#332×C₁₁₃	C₂²	1	4	yes	—
35	#331×C₁₁₃	C₂²	1	4	yes	—
36	C₂×#41×C₁₁₃	—	2	1	no	—
37	C₂×#41×C₁₁₃	—	2	2	no	—
38	#135×C₁₁₃	—	4	4	no	—
39	#135×C₁₁₃	—	4	4	no	—
40	C₂×Q₁₆×C₁₁₃	—	2	1	no	—
41	C₂×Q₁₆×C₁₁₃	—	2	1	no	—
42	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
43	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
44	C₂×D₈×C₁₁₃	—	2	4	no	—
45	C₂×D₈×C₁₁₃	—	2	1	no	—
46	C₂×D₈×C₁₁₃	—	2	1	no	—
47	#131×C₁₁₃	—	4	4	no	—
48	C₂×M₁₆×C₁₁₃	—	2	1	no	—
49	C₂×M₁₆×C₁₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₁₃	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₁₃	C₂³	1	2	yes	—
56	#127×C₁₁₃	D₄	1	1	yes	characteristic
57	#127×C₁₁₃	C₂³	1	2	yes	—
58	#124×C₁₁₃	—	2	2	no	—
59	#124×C₁₁₃	—	2	1	no	—
60	#121×C₁₁₃	—	2	1	no	—
61	#121×C₁₁₃	—	2	2	no	—
62	#121×C₁₁₃	—	2	2	no	—
63	#121×C₁₁₃	D₄	1	2	yes	—
64	C₄×D₄×C₁₁₃	—	2	1	no	—
65	C₄×D₄×C₁₁₃	—	2	2	no	—
66	C₄×D₄×C₁₁₃	—	2	2	no	—
67	C₄×D₄×C₁₁₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
69	#107×C₁₁₃	—	2	4	no	—
70	C₄⋊C₈×C₁₁₃	—	2	2	no	—
71	C₄⋊C₈×C₁₁₃	—	2	1	no	—
72	C₄⋊C₈×C₁₁₃	C₂³	1	2	yes	—
73	C₄⋊C₈×C₁₁₃	C₂³	1	4	yes	—
74	#102×C₁₁₃	—	2	4	no	—
75	#102×C₁₁₃	—	2	4	no	—
76	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
77	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
78	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
82	#41×C₁₁₃	—	4	2	no	—
83	#41×C₁₁₃	—	4	2	no	—
84	#41×C₁₁₃	—	4	4	no	—
85	#41×C₁₁₃	—	4	4	no	—
86	C₂×Q₈×C₁₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₁₃	—	2	2	no	—
88	C₂×D₄×C₁₁₃	—	2	2	no	—
89	C₂×D₄×C₁₁₃	—	2	1	no	—
90	C₂×D₄×C₁₁₃	—	2	1	no	—
91	C₂×D₄×C₁₁₃	—	2	2	no	—
92	C₂×D₄×C₁₁₃	—	2	2	no	—
93	C₂×D₄×C₁₁₃	—	2	2	no	—
94	C₂×D₄×C₁₁₃	—	4	2	no	—
95	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
101	Q₁₆×C₁₁₃	—	4	2	no	—
102	Q₁₆×C₁₁₃	—	4	2	no	—
103	SD₁₆×C₁₁₃	—	4	4	no	—
104	SD₁₆×C₁₁₃	—	4	4	no	—
105	D₈×C₁₁₃	—	4	2	no	—
106	D₈×C₁₁₃	—	4	2	no	—
107	D₈×C₁₁₃	—	8	4	no	—
108	M₁₆×C₁₁₃	—	4	2	no	—
109	M₁₆×C₁₁₃	—	4	4	no	—
110	C₂×C₈×C₁₁₃	—	2	2	no	—
111	C₂×C₈×C₁₁₃	—	2	2	no	—
112	C₂×C₈×C₁₁₃	—	2	4	no	—
113	C₂×C₈×C₁₁₃	—	4	4	no	—
114	C₂×C₈×C₁₁₃	—	8	2	no	—
115	C₂×C₈×C₁₁₃	D₈	1	4	yes	complemented
116	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₁₁₃	—	2	1	no	—
121	C₄⋊C₄×C₁₁₃	—	2	2	no	—
122	C₄⋊C₄×C₁₁₃	—	2	2	no	—
123	C₄⋊C₄×C₁₁₃	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
125	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
126	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
127	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
128	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₁₃	#41	1	1	yes	characteristic
131	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	4	2	no	—
134	C₂³×C₁₁₃	#121	1	1	yes	characteristic
135	Q₈×C₁₁₃	—	4	2	no	—
136	Q₈×C₁₁₃	—	4	2	no	—
137	Q₈×C₁₁₃	—	4	2	no	—
138	D₄×C₁₁₃	—	2	2	no	—
139	D₄×C₁₁₃	—	2	2	no	—
140	D₄×C₁₁₃	—	4	2	no	—
141	D₄×C₁₁₃	—	4	4	no	—
142	D₄×C₁₁₃	—	4	2	no	—
143	D₄×C₁₁₃	—	4	2	no	—
144	D₄×C₁₁₃	—	4	2	no	—
145	D₄×C₁₁₃	—	4	2	no	—
146	D₄×C₁₁₃	—	4	2	no	—
147	D₄×C₁₁₃	—	8	2	no	—
148	D₄×C₁₁₃	—	8	4	no	—
149	C₂×C₄×C₁₁₃	—	2	1	no	—
150	C₂×C₄×C₁₁₃	—	2	1	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	4	1	no	—
153	C₂×C₄×C₁₁₃	—	4	2	no	—
154	C₂×C₄×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	8	4	no	—
157	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₁₃	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
165	C₈×C₁₁₃	—	2	1	no	—
166	C₈×C₁₁₃	—	2	1	no	—
167	C₈×C₁₁₃	—	4	2	no	—
168	C₈×C₁₁₃	—	4	4	no	—
169	C₈×C₁₁₃	C₂×D₈	1	2	yes	—
170	C₈×C₁₁₃	C₂×D₈	1	2	yes	—
171	C₂²×C₁₁₃	—	2	1	no	—
172	C₂²×C₁₁₃	—	2	1	no	—
173	C₂²×C₁₁₃	—	4	2	no	—
174	C₂²×C₁₁₃	—	4	2	no	—
175	C₂²×C₁₁₃	—	4	2	no	—
176	C₂²×C₁₁₃	—	8	2	no	—
177	C₂²×C₁₁₃	—	8	2	no	—
178	C₂²×C₁₁₃	—	8	2	no	—
179	C₂²×C₁₁₃	#459	1	2	yes	—
180	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
181	C₄×C₁₁₃	—	2	1	no	—
182	C₄×C₁₁₃	—	2	1	no	—
183	C₄×C₁₁₃	—	2	1	no	—
184	C₄×C₁₁₃	—	4	2	no	—
185	C₄×C₁₁₃	—	8	2	no	—
186	C₄×C₁₁₃	#459	1	2	yes	—
187	C₄×C₁₁₃	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₄×C₁₁₃	#576	1	1	yes	characteristic
190	C₄×C₁₁₃	#578	1	1	yes	characteristic
191	#19190	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₁₁₃	—	2	2	no	—
193	C₂×C₁₁₃	—	8	2	no	—
194	C₂×C₁₁₃	—	16	2	no	—
195	C₂×C₁₁₃	C₂×#459	1	1	yes	characteristic
196	C₂×C₁₁₃	#3061	1	1	yes	characteristic
197	C₂×C₁₁₃	#3067	1	1	yes	characteristic
198	#3245	C₂×C₁₁₃	1	2	yes	complemented
199	#3147	C₂×C₁₁₃	1	1	yes	characteristic, complemented
200	#2931	C₂×C₁₁₃	1	1	yes	characteristic, complemented
201	#1685	C₂×C₁₁₃	1	4	yes	complemented
202	#1669	C₂×C₁₁₃	1	2	yes	complemented
203	#1667	C₂×C₁₁₃	1	2	yes	complemented
204	C₂×#335	C₂×C₁₁₃	1	1	yes	characteristic, complemented
205	#1547	C₂×C₁₁₃	1	2	yes	complemented
206	C₁₁₃	#19190	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#135	—	2	1	no	—
208	C₂×#135	—	2	1	no	—
209	C₂×#131	—	2	1	no	—
210	#532	C₂²×C₁₁₃	1	2	yes	—
211	#532	C₂²×C₁₁₃	1	1	yes	characteristic
212	#495	—	2	1	no	—
213	#495	—	2	1	no	—
214	#494	C₂²×C₁₁₃	1	1	yes	characteristic
215	#493	C₂²×C₁₁₃	1	1	yes	characteristic
216	#492	C₂²×C₁₁₃	1	2	yes	—
217	#474	—	2	2	no	—
218	#474	C₂²×C₁₁₃	1	4	yes	—
219	#466	—	2	4	no	—
220	#459	—	2	2	no	—
221	#459	C₂²×C₁₁₃	1	4	yes	—
222	#436	—	2	1	no	—
223	#436	C₂²×C₁₁₃	1	2	yes	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	C₂²×C₁₁₃	1	2	yes	—
226	#423	C₂²×C₁₁₃	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
228	#408	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
230	#335	C₂²×C₁₁₃	1	2	yes	—
231	#335	C₂²×C₁₁₃	1	2	yes	—
232	#332	C₂²×C₁₁₃	1	4	yes	—
233	#331	C₂²×C₁₁₃	1	4	yes	—
234	C₂×#41	—	2	1	no	—
235	C₂×#41	—	2	2	no	—
236	#135	—	4	4	no	—
237	#135	—	4	4	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	—	2	4	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	#131	—	4	4	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
252	C₄⋊Q₈	D₄×C₁₁₃	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³×C₁₁₃	1	2	yes	—
254	#127	D₄×C₁₁₃	1	1	yes	characteristic
255	#127	C₂³×C₁₁₃	1	2	yes	—
256	#124	—	2	2	no	—
257	#124	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	2	no	—
260	#121	—	2	2	no	—
261	#121	D₄×C₁₁₃	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	C₂³×C₁₁₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
267	#107	—	2	4	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₂³×C₁₁₃	1	2	yes	—
271	C₄⋊C₈	C₂³×C₁₁₃	1	4	yes	—
272	#102	—	2	4	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
277	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	#41	—	4	4	no	—
283	#41	—	4	4	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
298	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	SD₁₆	—	4	4	no	—
302	SD₁₆	—	4	4	no	—
303	D₈	—	4	2	no	—
304	D₈	—	4	2	no	—
305	D₈	—	8	4	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	4	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	—	8	2	no	—
313	C₂×C₈	D₈×C₁₁₃	1	4	yes	complemented
314	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	C₂×D₄×C₁₁₃	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
328	C₄²	#41×C₁₁₃	1	1	yes	characteristic
329	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
330	C₂³	—	2	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	#121×C₁₁₃	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	8	2	no	—
346	D₄	—	8	4	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
356	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
357	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂×D₈×C₁₁₃	1	2	yes	—
359	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	4	no	—
367	C₈	C₂×D₈×C₁₁₃	1	2	yes	—
368	C₈	C₂×D₈×C₁₁₃	1	2	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	#459×C₁₁₃	1	2	yes	—
378	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	#459×C₁₁₃	1	2	yes	—
385	C₄	C₂²×D₈×C₁₁₃	1	1	yes	characteristic
386	C₄	C₂×AGL(1,ℤ/8)×C₁₁₃	1	1	yes	characteristic
387	C₄	#576×C₁₁₃	1	1	yes	characteristic
388	C₄	#578×C₁₁₃	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	8	2	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×#459×C₁₁₃	1	1	yes	characteristic
393	C₂	C₁₁₃×#3061	1	1	yes	characteristic
394	C₂	C₁₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁₃×#3245	C₂	semidirect
2. C₁₁₃×#3147	C₂	semidirect
3. C₁₁₃×#2931	C₂	semidirect
4. C₁₁₃×#1685	C₂	semidirect
5. C₁₁₃×#1669	C₂	semidirect
6. C₁₁₃×#1667	C₂	semidirect
7. C₂×#335×C₁₁₃	C₂	semidirect
8. C₁₁₃×#1547	C₂	semidirect
115. C₂×C₈×C₁₁₃	D₈	semidirect
191. #19190	C₁₁₃	direct (N × H)
198. #3245	C₂×C₁₁₃	semidirect
199. #3147	C₂×C₁₁₃	semidirect
200. #2931	C₂×C₁₁₃	semidirect
201. #1685	C₂×C₁₁₃	semidirect
202. #1669	C₂×C₁₁₃	semidirect
203. #1667	C₂×C₁₁₃	semidirect
204. C₂×#335	C₂×C₁₁₃	semidirect
205. #1547	C₂×C₁₁₃	semidirect
206. C₁₁₃	#19190	direct (N × H)
313. C₂×C₈	D₈×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁₃×#3245	2
C₁₁₃×#3147	2
C₁₁₃×#2931	2
C₁₁₃×#1685	2
C₁₁₃×#1669	2
C₁₁₃×#1667	2
C₂×#335×C₁₁₃	2
C₁₁₃×#1547	2
#19190	113

Subgroups — C113×#19190 #43287210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#19190 #43287210