Subgroups — C₁₁₃×#18368 #43286388

Order 28928.

1168 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#3213	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#2632	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1604	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1598	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1514	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₁₁₃	—	2	1	no	—
9	#550×C₁₁₃	—	2	2	no	—
10	D₄×Q₈×C₁₁₃	—	2	2	no	—
11	#548×C₁₁₃	—	2	4	no	—
12	#537×C₁₁₃	—	2	1	no	—
13	#537×C₁₁₃	C₂²	1	4	yes	—
14	#532×C₁₁₃	—	2	2	no	—
15	#532×C₁₁₃	C₂²	1	2	yes	—
16	C₂×#124×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
18	#496×C₁₁₃	—	2	2	no	—
19	#489×C₁₁₃	—	2	2	no	—
20	#463×C₁₁₃	—	2	4	no	—
21	#448×C₁₁₃	C₂²	1	4	yes	—
22	#447×C₁₁₃	C₂²	1	4	yes	—
23	#432×C₁₁₃	C₂²	1	2	yes	—
24	#399×C₁₁₃	—	2	1	no	—
25	#395×C₁₁₃	C₂²	1	2	yes	—
26	#394×C₁₁₃	C₂²	1	2	yes	—
27	#393×C₁₁₃	—	2	1	no	—
28	#388×C₁₁₃	—	2	2	no	—
29	#383×C₁₁₃	C₂²	1	1	yes	characteristic
30	#327×C₁₁₃	C₂²	1	8	yes	—
31	#324×C₁₁₃	C₂²	1	4	yes	—
32	2₋¹⁺⁴×C₁₁₃	—	4	8	no	—
33	C₂×#41×C₁₁₃	—	2	4	no	—
34	C₂×#41×C₁₁₃	—	2	4	no	—
35	C₂×#41×C₁₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₁₃	—	2	4	no	—
37	C₂²×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
41	C₂×D₈×C₁₁₃	—	2	4	no	—
42	C₄⋊Q₈×C₁₁₃	—	2	2	no	—
43	C₄⋊Q₈×C₁₁₃	D₄	1	2	yes	—
44	#127×C₁₁₃	—	2	2	no	—
45	#127×C₁₁₃	D₄	1	2	yes	—
46	#124×C₁₁₃	—	2	4	no	—
47	#124×C₁₁₃	—	2	2	no	—
48	#124×C₁₁₃	—	2	2	no	—
49	#124×C₁₁₃	—	2	2	no	—
50	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
51	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
52	#121×C₁₁₃	—	2	4	no	—
53	#121×C₁₁₃	—	2	8	no	—
54	#121×C₁₁₃	—	2	2	no	—
55	#121×C₁₁₃	—	2	4	no	—
56	#121×C₁₁₃	C₂³	1	4	yes	—
57	C₄×Q₈×C₁₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₁₃	—	2	2	no	—
59	C₄×D₄×C₁₁₃	—	2	4	no	—
60	C₄×D₄×C₁₁₃	—	2	4	no	—
61	C₄×D₄×C₁₁₃	—	2	2	no	—
62	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₁₃	—	2	2	no	—
73	#103×C₁₁₃	—	2	4	no	—
74	#102×C₁₁₃	—	2	4	no	—
75	C₂²⋊C₈×C₁₁₃	C₂³	1	4	yes	—
76	#97×C₁₁₃	—	2	2	no	—
77	#95×C₁₁₃	—	2	1	no	—
78	#95×C₁₁₃	—	2	1	no	—
79	#95×C₁₁₃	—	2	2	no	—
80	#95×C₁₁₃	C₂³	1	2	yes	—
81	C₂⁴×C₁₁₃	—	2	1	no	—
82	#41×C₁₁₃	—	4	8	no	—
83	#41×C₁₁₃	—	4	8	no	—
84	#41×C₁₁₃	—	4	16	no	—
85	#41×C₁₁₃	—	4	8	no	—
86	C₂×Q₈×C₁₁₃	—	2	4	no	—
87	C₂×Q₈×C₁₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₁₃	—	2	4	no	—
90	C₂×Q₈×C₁₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₁₃	—	4	16	no	—
92	C₂×Q₈×C₁₁₃	—	8	1	no	—
93	C₂×D₄×C₁₁₃	—	2	4	no	—
94	C₂×D₄×C₁₁₃	—	2	4	no	—
95	C₂×D₄×C₁₁₃	—	2	4	no	—
96	C₂×D₄×C₁₁₃	—	2	2	no	—
97	C₂×D₄×C₁₁₃	—	2	2	no	—
98	C₂×D₄×C₁₁₃	—	2	2	no	—
99	C₂×D₄×C₁₁₃	—	8	1	no	—
100	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₁₃	—	2	8	no	—
102	C₂²×C₄×C₁₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
110	SD₁₆×C₁₁₃	—	8	4	no	—
111	D₈×C₁₁₃	—	8	4	no	—
112	C₂×C₈×C₁₁₃	—	2	4	no	—
113	C₄⋊C₄×C₁₁₃	—	2	4	no	—
114	C₄⋊C₄×C₁₁₃	—	2	2	no	—
115	C₄⋊C₄×C₁₁₃	—	2	2	no	—
116	C₄⋊C₄×C₁₁₃	—	2	4	no	—
117	C₄⋊C₄×C₁₁₃	—	8	2	no	—
118	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
119	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
120	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
121	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
122	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
123	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
124	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
125	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
126	C₂²⋊C₄×C₁₁₃	—	8	2	no	—
127	C₄²×C₁₁₃	—	2	2	no	—
128	C₄²×C₁₁₃	—	2	2	no	—
129	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
130	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
131	C₂³×C₁₁₃	—	2	4	no	—
132	C₂³×C₁₁₃	—	4	2	no	—
133	C₂³×C₁₁₃	—	4	2	no	—
134	C₂³×C₁₁₃	—	4	1	no	—
135	C₂³×C₁₁₃	—	4	2	no	—
136	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₁₃	—	2	8	no	—
138	Q₈×C₁₁₃	—	4	4	no	—
139	Q₈×C₁₁₃	—	4	8	no	—
140	Q₈×C₁₁₃	—	4	4	no	—
141	D₄×C₁₁₃	—	4	4	no	—
142	D₄×C₁₁₃	—	4	4	no	—
143	D₄×C₁₁₃	—	4	4	no	—
144	D₄×C₁₁₃	—	4	8	no	—
145	D₄×C₁₁₃	—	4	4	no	—
146	D₄×C₁₁₃	—	4	8	no	—
147	D₄×C₁₁₃	—	8	4	no	—
148	C₂×C₄×C₁₁₃	—	2	2	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	2	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	2	4	no	—
153	C₂×C₄×C₁₁₃	—	4	1	no	—
154	C₂×C₄×C₁₁₃	—	4	1	no	—
155	C₂×C₄×C₁₁₃	—	4	8	no	—
156	C₂×C₄×C₁₁₃	—	4	16	no	—
157	C₂×C₄×C₁₁₃	—	4	2	no	—
158	C₂×C₄×C₁₁₃	—	4	2	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	—	4	2	no	—
161	C₂×C₄×C₁₁₃	—	4	1	no	—
162	C₂×C₄×C₁₁₃	—	4	2	no	—
163	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	#120	1	2	yes	—
166	C₂×C₄×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
167	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
168	C₈×C₁₁₃	—	4	4	no	—
169	C₂²×C₁₁₃	—	2	1	no	—
170	C₂²×C₁₁₃	—	2	1	no	—
171	C₂²×C₁₁₃	—	4	4	no	—
172	C₂²×C₁₁₃	—	4	4	no	—
173	C₂²×C₁₁₃	—	4	4	no	—
174	C₂²×C₁₁₃	—	8	4	no	—
175	C₂²×C₁₁₃	—	8	1	no	—
176	C₂²×C₁₁₃	—	8	1	no	—
177	C₂²×C₁₁₃	—	8	1	no	—
178	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
179	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
180	C₄×C₁₁₃	—	2	2	no	—
181	C₄×C₁₁₃	—	2	4	no	—
182	C₄×C₁₁₃	—	2	1	no	—
183	C₄×C₁₁₃	—	2	1	no	—
184	C₄×C₁₁₃	—	2	2	no	—
185	C₄×C₁₁₃	—	4	4	no	—
186	C₄×C₁₁₃	—	4	2	no	—
187	C₄×C₁₁₃	—	8	2	no	—
188	C₄×C₁₁₃	—	8	1	no	—
189	#18368	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₁₁₃	—	2	2	no	—
191	C₂×C₁₁₃	—	8	4	no	—
192	C₂×C₁₁₃	—	16	1	no	—
193	C₂×C₁₁₃	#3003	1	1	yes	characteristic
194	C₂×C₁₁₃	#3020	1	1	yes	characteristic
195	C₂×C₁₁₃	#3027	1	1	yes	characteristic
196	#3497	C₂×C₁₁₃	1	1	yes	characteristic, complemented
197	#3213	C₂×C₁₁₃	1	2	yes	complemented
198	#2632	C₂×C₁₁₃	1	1	yes	characteristic, complemented
199	#1604	C₂×C₁₁₃	1	4	yes	complemented
200	#1598	C₂×C₁₁₃	1	4	yes	complemented
201	#1514	C₂×C₁₁₃	1	2	yes	complemented
202	#1467	C₂×C₁₁₃	1	1	yes	characteristic, complemented
203	C₁₁₃	#18368	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×2₋¹⁺⁴	—	2	1	no	—
205	#550	—	2	2	no	—
206	D₄×Q₈	—	2	2	no	—
207	#548	—	2	4	no	—
208	#537	—	2	1	no	—
209	#537	C₂²×C₁₁₃	1	4	yes	—
210	#532	—	2	2	no	—
211	#532	C₂²×C₁₁₃	1	2	yes	—
212	C₂×#124	C₂²×C₁₁₃	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
214	#496	—	2	2	no	—
215	#489	—	2	2	no	—
216	#463	—	2	4	no	—
217	#448	C₂²×C₁₁₃	1	4	yes	—
218	#447	C₂²×C₁₁₃	1	4	yes	—
219	#432	C₂²×C₁₁₃	1	2	yes	—
220	#399	—	2	1	no	—
221	#395	C₂²×C₁₁₃	1	2	yes	—
222	#394	C₂²×C₁₁₃	1	2	yes	—
223	#393	—	2	1	no	—
224	#388	—	2	2	no	—
225	#383	C₂²×C₁₁₃	1	1	yes	characteristic
226	#327	C₂²×C₁₁₃	1	8	yes	—
227	#324	C₂²×C₁₁₃	1	4	yes	—
228	2₋¹⁺⁴	—	4	8	no	—
229	C₂×#41	—	2	4	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	2	no	—
232	C₂²×Q₈	—	2	4	no	—
233	C₂²×Q₈	D₄×C₁₁₃	1	1	yes	characteristic
234	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
235	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	4	no	—
237	C₂×D₈	—	2	4	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	D₄×C₁₁₃	1	2	yes	—
240	#127	—	2	2	no	—
241	#127	D₄×C₁₁₃	1	2	yes	—
242	#124	—	2	4	no	—
243	#124	—	2	2	no	—
244	#124	—	2	2	no	—
245	#124	—	2	2	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	8	no	—
248	#121	—	2	4	no	—
249	#121	—	2	8	no	—
250	#121	—	2	2	no	—
251	#121	—	2	4	no	—
252	#121	C₂³×C₁₁₃	1	4	yes	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	2	no	—
269	#103	—	2	4	no	—
270	#102	—	2	4	no	—
271	C₂²⋊C₈	C₂³×C₁₁₃	1	4	yes	—
272	#97	—	2	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	#95	—	2	2	no	—
276	#95	C₂³×C₁₁₃	1	2	yes	—
277	C₂⁴	—	2	1	no	—
278	#41	—	4	8	no	—
279	#41	—	4	8	no	—
280	#41	—	4	16	no	—
281	#41	—	4	8	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	16	no	—
288	C₂×Q₈	—	8	1	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	8	1	no	—
296	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
306	SD₁₆	—	8	4	no	—
307	D₈	—	8	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
326	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
333	Q₈	—	2	8	no	—
334	Q₈	—	4	4	no	—
335	Q₈	—	4	8	no	—
336	Q₈	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	8	no	—
343	D₄	—	8	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	—	4	16	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
360	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
361	C₂×C₄	#120×C₁₁₃	1	2	yes	—
362	C₂×C₄	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
363	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
364	C₈	—	4	4	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	4	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	1	no	—
373	C₂²	—	8	1	no	—
374	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
375	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
376	C₄	—	2	2	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	1	no	—
385	C₂	—	2	2	no	—
386	C₂	—	8	4	no	—
387	C₂	—	16	1	no	—
388	C₂	C₁₁₃×#3003	1	1	yes	characteristic
389	C₂	C₁₁₃×#3020	1	1	yes	characteristic
390	C₂	C₁₁₃×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
LCS	G ▷ C₂²×C₄ ▷ 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×#3497	C₂	semidirect
2. C₁₁₃×#3213	C₂	semidirect
3. C₁₁₃×#2632	C₂	semidirect
4. C₁₁₃×#1604	C₂	semidirect
5. C₁₁₃×#1598	C₂	semidirect
6. C₁₁₃×#1514	C₂	semidirect
7. C₁₁₃×#1467	C₂	semidirect
189. #18368	C₁₁₃	direct (N × H)
196. #3497	C₂×C₁₁₃	semidirect
197. #3213	C₂×C₁₁₃	semidirect
198. #2632	C₂×C₁₁₃	semidirect
199. #1604	C₂×C₁₁₃	semidirect
200. #1598	C₂×C₁₁₃	semidirect
201. #1514	C₂×C₁₁₃	semidirect
202. #1467	C₂×C₁₁₃	semidirect
203. C₁₁₃	#18368	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁₃×#3497	2
C₁₁₃×#3213	2
C₁₁₃×#2632	2
C₁₁₃×#1604	2
C₁₁₃×#1598	2
C₁₁₃×#1514	2
C₁₁₃×#1467	2
#18368	113

Subgroups — C113×#18368 #43286388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#18368 #43286388