Subgroups — C₁₁₃×#10874 #43278894

Order 28928.

1006 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#336×C₁₁₃	C₂	1	2	yes	maximal
4	C₂×#336×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#336×C₁₁₃	C₂	1	2	yes	maximal
6	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
7	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₁₃	C₄	1	2	yes	—
9	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁₃	—	2	4	no	—
13	C₂×C₄×C₈×C₁₁₃	—	2	2	no	—
14	C₄×C₄⋊C₄×C₁₁₃	—	2	2	no	—
15	C₄×C₄⋊C₄×C₁₁₃	—	2	2	no	—
16	C₂×#95×C₁₁₃	C₄	1	2	yes	—
17	#336×C₁₁₃	—	2	4	no	—
18	#336×C₁₁₃	—	2	2	no	—
19	#336×C₁₁₃	C₄	1	8	yes	complemented
20	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₁₃	—	2	2	no	—
27	C₂²×C₈×C₁₁₃	—	2	2	no	—
28	C₂²×C₈×C₁₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₁₃	—	2	2	no	—
30	C₂²×C₈×C₁₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₁₃	—	2	2	no	—
32	C₂²×C₈×C₁₁₃	—	2	2	no	—
33	C₂²×C₈×C₁₁₃	—	2	2	no	—
34	C₂²×C₈×C₁₁₃	—	2	2	no	—
35	C₂²×C₈×C₁₁₃	C₂×C₄	1	4	yes	—
36	C₂²×C₈×C₁₁₃	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₁₁₃	D₄	1	4	yes	—
38	C₂²×C₈×C₁₁₃	Q₈	1	4	yes	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₁₃	C₈	1	8	yes	complemented
42	C₂×C₄²×C₁₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₁₃	—	2	2	no	—
45	C₂×C₄²×C₁₁₃	—	2	2	no	—
46	C₂×C₄²×C₁₁₃	—	2	2	no	—
47	C₂×C₄²×C₁₁₃	—	2	2	no	—
48	C₂×C₄²×C₁₁₃	—	2	1	no	—
49	C₂×C₄²×C₁₁₃	—	2	1	no	—
50	C₂×C₄²×C₁₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
53	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
54	C₄×C₈×C₁₁₃	—	2	8	no	—
55	#95×C₁₁₃	—	2	4	no	—
56	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁₃	—	2	1	no	—
58	C₂²×C₄×C₁₁₃	—	2	1	no	—
59	C₂²×C₄×C₁₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₁₃	—	2	4	no	—
66	C₂²×C₄×C₁₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₁₃	C₄²	1	2	yes	—
70	C₂²×C₄×C₁₁₃	C₄²	1	2	yes	—
71	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
72	C₂²×C₄×C₁₁₃	C₂×C₈	1	4	yes	—
73	C₂²×C₄×C₁₁₃	C₂×C₈	1	4	yes	—
74	C₂²×C₄×C₁₁₃	C₂×C₈	1	4	yes	—
75	C₂²×C₄×C₁₁₃	M₁₆	1	4	yes	—
76	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
82	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
83	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
84	C₂×C₈×C₁₁₃	—	2	4	no	—
85	C₂×C₈×C₁₁₃	—	2	4	no	—
86	C₂×C₈×C₁₁₃	—	2	4	no	—
87	C₂×C₈×C₁₁₃	—	2	4	no	—
88	C₂×C₈×C₁₁₃	—	2	4	no	—
89	C₂×C₈×C₁₁₃	—	2	4	no	—
90	C₂×C₈×C₁₁₃	—	2	4	no	—
91	C₂×C₈×C₁₁₃	—	2	4	no	—
92	C₂×C₈×C₁₁₃	—	2	4	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	C₂×C₈×C₁₁₃	C₄⋊C₄	1	8	yes	complemented
98	C₄⋊C₄×C₁₁₃	—	2	16	no	—
99	C₄²×C₁₁₃	—	2	4	no	—
100	C₄²×C₁₁₃	—	2	4	no	—
101	C₄²×C₁₁₃	—	2	2	no	—
102	C₄²×C₁₁₃	—	2	4	no	—
103	C₄²×C₁₁₃	—	2	2	no	—
104	C₄²×C₁₁₃	—	4	1	no	—
105	C₄²×C₁₁₃	—	4	2	no	—
106	C₄²×C₁₁₃	—	4	1	no	—
107	C₂³×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
108	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×C₁₁₃	#117	1	1	yes	characteristic
110	C₂³×C₁₁₃	C₄×D₄	1	2	yes	—
111	C₂³×C₁₁₃	C₄×Q₈	1	2	yes	—
112	C₂³×C₁₁₃	C₂²×C₈	1	2	yes	—
113	C₂³×C₁₁₃	C₂×M₁₆	1	2	yes	—
114	C₂³×C₁₁₃	#131	1	4	yes	—
115	C₂×C₄×C₁₁₃	—	2	2	no	—
116	C₂×C₄×C₁₁₃	—	2	4	no	—
117	C₂×C₄×C₁₁₃	—	2	2	no	—
118	C₂×C₄×C₁₁₃	—	2	4	no	—
119	C₂×C₄×C₁₁₃	—	2	4	no	—
120	C₂×C₄×C₁₁₃	—	2	4	no	—
121	C₂×C₄×C₁₁₃	—	2	8	no	—
122	C₂×C₄×C₁₁₃	—	2	8	no	—
123	C₂×C₄×C₁₁₃	—	2	2	no	—
124	C₂×C₄×C₁₁₃	—	2	4	no	—
125	C₂×C₄×C₁₁₃	—	2	4	no	—
126	C₂×C₄×C₁₁₃	—	2	8	no	—
127	C₂×C₄×C₁₁₃	—	4	2	no	—
128	C₂×C₄×C₁₁₃	—	4	2	no	—
129	C₂×C₄×C₁₁₃	—	4	2	no	—
130	C₂×C₄×C₁₁₃	—	4	2	no	—
131	C₂×C₄×C₁₁₃	—	4	4	no	—
132	C₂×C₄×C₁₁₃	C₄×C₈	1	4	yes	complemented
133	C₂×C₄×C₁₁₃	C₂²⋊C₈	1	8	yes	—
134	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₁₁₃	#117	1	2	yes	—
136	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₁₁₃	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₁₁₃	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
141	C₂×C₄×C₁₁₃	#121	1	2	yes	—
142	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₁₁₃	#123	1	2	yes	—
145	C₂×C₄×C₁₁₃	#123	1	1	yes	characteristic
146	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
147	C₂×C₄×C₁₁₃	#125	1	2	yes	—
148	C₂×C₄×C₁₁₃	#126	1	2	yes	—
149	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
150	C₈×C₁₁₃	—	2	8	no	—
151	C₈×C₁₁₃	—	4	4	no	—
152	C₂²×C₁₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₁₁₃	C₄×C₄⋊C₄	1	2	yes	—
154	C₂²×C₁₁₃	#386	1	1	yes	characteristic
155	C₂²×C₁₁₃	#387	1	2	yes	—
156	C₂²×C₁₁₃	#391	1	1	yes	characteristic
157	C₂²×C₁₁₃	C₂×C₄×C₈	1	1	yes	characteristic
158	C₂²×C₁₁₃	C₄×M₁₆	1	1	yes	characteristic
159	C₂²×C₁₁₃	#405	1	2	yes	—
160	C₂²×C₁₁₃	C₂×C₂²⋊C₈	1	2	yes	—
161	C₂²×C₁₁₃	#408	1	2	yes	—
162	C₂²×C₁₁₃	#431	1	2	yes	—
163	C₂²×C₁₁₃	#433	1	2	yes	—
164	C₂²×C₁₁₃	C₈×D₄	1	4	yes	—
165	C₂²×C₁₁₃	#435	1	4	yes	—
166	C₂²×C₁₁₃	C₈×Q₈	1	4	yes	—
167	C₂²×C₁₁₃	#446	1	4	yes	—
168	C₄×C₁₁₃	—	2	8	no	—
169	C₄×C₁₁₃	—	2	4	no	—
170	C₄×C₁₁₃	—	4	4	no	—
171	C₄×C₁₁₃	—	4	2	no	—
172	C₄×C₁₁₃	#385	1	2	yes	—
173	C₄×C₁₁₃	#387	1	2	yes	—
174	C₄×C₁₁₃	#388	1	2	yes	—
175	C₄×C₁₁₃	#389	1	2	yes	—
176	#10874	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₁₁₃	#1436	1	1	yes	characteristic
178	C₂×C₁₁₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
179	C₂×C₁₁₃	#1750	1	1	yes	characteristic
180	C₂×C₁₁₃	C₈×C₄⋊C₄	1	2	yes	—
181	C₂×C₁₁₃	#1771	1	2	yes	—
182	C₂×C₁₁₃	#1869	1	2	yes	—
183	C₂×C₁₁₃	#1916	1	4	yes	—
184	C₂×C₁₁₃	#1984	1	2	yes	—
185	C₂²×C₄×C₈	C₂×C₁₁₃	1	1	yes	characteristic
186	C₂×C₄×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
187	C₂×#336	C₂×C₁₁₃	1	1	yes	characteristic
188	C₂×#336	C₂×C₁₁₃	1	2	yes	—
189	C₂×#336	C₂×C₁₁₃	1	2	yes	—
190	C₁₁₃	#10874	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
192	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
193	C₂²×C₄⋊C₄	C₄×C₁₁₃	1	2	yes	—
194	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
195	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
196	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
197	C₂×C₄×C₈	—	2	4	no	—
198	C₂×C₄×C₈	—	2	2	no	—
199	C₄×C₄⋊C₄	—	2	2	no	—
200	C₄×C₄⋊C₄	—	2	2	no	—
201	C₂×#95	C₄×C₁₁₃	1	2	yes	—
202	#336	—	2	4	no	—
203	#336	—	2	2	no	—
204	#336	C₄×C₁₁₃	1	8	yes	complemented
205	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
206	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
207	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
208	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
209	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
210	C₂²×C₈	—	2	2	no	—
211	C₂²×C₈	—	2	2	no	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	C₂×C₄×C₁₁₃	1	4	yes	—
221	C₂²×C₈	C₂×C₄×C₁₁₃	1	4	yes	—
222	C₂²×C₈	D₄×C₁₁₃	1	4	yes	—
223	C₂²×C₈	Q₈×C₁₁₃	1	4	yes	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	C₈×C₁₁₃	1	8	yes	complemented
227	C₂×C₄²	—	2	1	no	—
228	C₂×C₄²	—	2	1	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
237	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
238	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
239	C₄×C₈	—	2	8	no	—
240	#95	—	2	4	no	—
241	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	C₄²×C₁₁₃	1	2	yes	—
255	C₂²×C₄	C₄²×C₁₁₃	1	2	yes	—
256	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
257	C₂²×C₄	C₂×C₈×C₁₁₃	1	4	yes	—
258	C₂²×C₄	C₂×C₈×C₁₁₃	1	4	yes	—
259	C₂²×C₄	C₂×C₈×C₁₁₃	1	4	yes	—
260	C₂²×C₄	M₁₆×C₁₁₃	1	4	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
265	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
266	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
267	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
268	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	4	2	no	—
279	C₂×C₈	—	4	2	no	—
280	C₂×C₈	—	4	2	no	—
281	C₂×C₈	—	4	2	no	—
282	C₂×C₈	C₄⋊C₄×C₁₁₃	1	8	yes	complemented
283	C₄⋊C₄	—	2	16	no	—
284	C₄²	—	2	4	no	—
285	C₄²	—	2	4	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	4	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	4	1	no	—
290	C₄²	—	4	2	no	—
291	C₄²	—	4	1	no	—
292	C₂³	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
293	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
294	C₂³	#117×C₁₁₃	1	1	yes	characteristic
295	C₂³	C₄×D₄×C₁₁₃	1	2	yes	—
296	C₂³	C₄×Q₈×C₁₁₃	1	2	yes	—
297	C₂³	C₂²×C₈×C₁₁₃	1	2	yes	—
298	C₂³	C₂×M₁₆×C₁₁₃	1	2	yes	—
299	C₂³	#131×C₁₁₃	1	4	yes	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	C₄×C₈×C₁₁₃	1	4	yes	complemented
318	C₂×C₄	C₂²⋊C₈×C₁₁₃	1	8	yes	—
319	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
320	C₂×C₄	#117×C₁₁₃	1	2	yes	—
321	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
322	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
323	C₂×C₄	C₄×D₄×C₁₁₃	1	2	yes	—
324	C₂×C₄	C₄×Q₈×C₁₁₃	1	2	yes	—
325	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
326	C₂×C₄	#121×C₁₁₃	1	2	yes	—
327	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
328	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
329	C₂×C₄	#123×C₁₁₃	1	2	yes	—
330	C₂×C₄	#123×C₁₁₃	1	1	yes	characteristic
331	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
332	C₂×C₄	#125×C₁₁₃	1	2	yes	—
333	C₂×C₄	#126×C₁₁₃	1	2	yes	—
334	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
335	C₈	—	2	8	no	—
336	C₈	—	4	4	no	—
337	C₂²	C₄×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
338	C₂²	C₄×C₄⋊C₄×C₁₁₃	1	2	yes	—
339	C₂²	#386×C₁₁₃	1	1	yes	characteristic
340	C₂²	#387×C₁₁₃	1	2	yes	—
341	C₂²	#391×C₁₁₃	1	1	yes	characteristic
342	C₂²	C₂×C₄×C₈×C₁₁₃	1	1	yes	characteristic
343	C₂²	C₄×M₁₆×C₁₁₃	1	1	yes	characteristic
344	C₂²	#405×C₁₁₃	1	2	yes	—
345	C₂²	C₂×C₂²⋊C₈×C₁₁₃	1	2	yes	—
346	C₂²	#408×C₁₁₃	1	2	yes	—
347	C₂²	#431×C₁₁₃	1	2	yes	—
348	C₂²	#433×C₁₁₃	1	2	yes	—
349	C₂²	C₈×D₄×C₁₁₃	1	4	yes	—
350	C₂²	#435×C₁₁₃	1	4	yes	—
351	C₂²	C₈×Q₈×C₁₁₃	1	4	yes	—
352	C₂²	#446×C₁₁₃	1	4	yes	—
353	C₄	—	2	8	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	4	no	—
356	C₄	—	4	2	no	—
357	C₄	#385×C₁₁₃	1	2	yes	—
358	C₄	#387×C₁₁₃	1	2	yes	—
359	C₄	#388×C₁₁₃	1	2	yes	—
360	C₄	#389×C₁₁₃	1	2	yes	—
361	C₂	C₁₁₃×#1436	1	1	yes	characteristic
362	C₂	C₄×C₂²⋊C₈×C₁₁₃	1	1	yes	characteristic
363	C₂	C₁₁₃×#1750	1	1	yes	characteristic
364	C₂	C₈×C₄⋊C₄×C₁₁₃	1	2	yes	—
365	C₂	C₁₁₃×#1771	1	2	yes	—
366	C₂	C₁₁₃×#1869	1	2	yes	—
367	C₂	C₁₁₃×#1916	1	4	yes	—
368	C₂	C₁₁₃×#1984	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₁₃	C₂³
commutator	C₂²	C₂×C₄×C₈×C₁₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁₃
socle, prime radical	C₂⁴×C₁₁₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
19. #336×C₁₁₃	C₄	semidirect
41. C₂×C₄⋊C₄×C₁₁₃	C₈	semidirect
97. C₂×C₈×C₁₁₃	C₄⋊C₄	semidirect
132. C₂×C₄×C₁₁₃	C₄×C₈	semidirect
176. #10874	C₁₁₃	direct (N × H)
190. C₁₁₃	#10874	direct (N × H)
204. #336	C₄×C₁₁₃	semidirect
226. C₂×C₄⋊C₄	C₈×C₁₁₃	semidirect
282. C₂×C₈	C₄⋊C₄×C₁₁₃	semidirect
317. C₂×C₄	C₄×C₈×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈×C₁₁₃	2
C₂×C₄×C₄⋊C₄×C₁₁₃	2
C₂×#336×C₁₁₃	2
#10874	113

Subgroups — C113×#10874 #43278894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#10874 #43278894