Subgroups — C₁₁₃×#17959 #43285979

Order 28928.

630 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×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2966	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Q₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×SD₁₆×C₁₁₃	C₂	1	2	yes	maximal, complemented
8	C₈×D₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁₃×#1494	C₂	1	2	yes	maximal, complemented
11	C₂×C₈²×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#529×C₁₁₃	C₂²	1	2	yes	—
13	#499×C₁₁₃	C₄	1	1	yes	characteristic
14	#495×C₁₁₃	C₄	1	1	yes	characteristic
15	#488×C₁₁₃	C₄	1	2	yes	—
16	#467×C₁₁₃	C₄	1	1	yes	characteristic
17	#466×C₁₁₃	C₄	1	1	yes	characteristic
18	#465×C₁₁₃	C₄	1	2	yes	—
19	#446×C₁₁₃	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₁₃	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₁₁₃	C₂²	1	2	yes	—
23	C₄×D₈×C₁₁₃	C₂²	1	1	yes	characteristic
24	#436×C₁₁₃	C₂²	1	2	yes	—
25	#435×C₁₁₃	—	2	2	no	—
26	C₈×D₄×C₁₁₃	—	2	2	no	—
27	C₈×D₄×C₁₁₃	C₂²	1	2	yes	—
28	#433×C₁₁₃	—	2	2	no	—
29	#432×C₁₁₃	C₂²	1	2	yes	—
30	#405×C₁₁₃	—	2	2	no	—
31	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
34	#335×C₁₁₃	C₂²	1	1	yes	characteristic
35	#335×C₁₁₃	C₂²	1	1	yes	characteristic
36	#334×C₁₁₃	C₂²	1	2	yes	—
37	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
38	Q₈⋊C₈×C₁₁₃	C₂²	1	2	yes	—
39	D₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
40	D₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
41	C₈²×C₁₁₃	C₂²	1	1	yes	characteristic
42	C₈²×C₁₁₃	C₂²	1	1	yes	characteristic
43	C₈²×C₁₁₃	C₂²	1	1	yes	characteristic
44	C₈²×C₁₁₃	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₁₃	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₁₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
55	#126×C₁₁₃	—	2	2	no	—
56	#125×C₁₁₃	C₂×C₄	1	2	yes	—
57	#124×C₁₁₃	C₂×C₄	1	2	yes	—
58	#123×C₁₁₃	—	2	2	no	—
59	C₂²⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
60	#121×C₁₁₃	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₁₁₃	C₂³	1	2	yes	—
62	C₄×D₄×C₁₁₃	—	2	2	no	—
63	C₄×D₄×C₁₁₃	C₂³	1	2	yes	—
64	#117×C₁₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
66	#107×C₁₁₃	C₂×C₄	1	1	yes	characteristic
67	#107×C₁₁₃	C₂×C₄	1	1	yes	characteristic
68	#106×C₁₁₃	C₂×C₄	1	2	yes	—
69	C₄⋊C₈×C₁₁₃	—	2	2	no	—
70	C₄⋊C₈×C₁₁₃	—	2	2	no	—
71	C₄⋊C₈×C₁₁₃	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₁₃	C₂³	1	2	yes	—
73	#103×C₁₁₃	C₂×C₄	1	2	yes	—
74	#103×C₁₁₃	C₂×C₄	1	2	yes	—
75	#102×C₁₁₃	C₂×C₄	1	2	yes	—
76	#102×C₁₁₃	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
78	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
79	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
80	#97×C₁₁₃	—	2	2	no	—
81	#97×C₁₁₃	—	2	2	no	—
82	C₄×C₈×C₁₁₃	—	2	2	no	—
83	C₄×C₈×C₁₁₃	—	2	1	no	—
84	C₄×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₁₁₃	—	2	2	no	—
96	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₁₃	C₂²×C₄	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	—	2	2	no	—
102	SD₁₆×C₁₁₃	—	2	4	no	—
103	D₈×C₁₁₃	—	2	2	no	—
104	M₁₆×C₁₁₃	—	4	4	no	—
105	C₂×C₈×C₁₁₃	—	2	4	no	—
106	C₂×C₈×C₁₁₃	—	2	1	no	—
107	C₂×C₈×C₁₁₃	—	2	1	no	—
108	C₂×C₈×C₁₁₃	—	2	2	no	—
109	C₂×C₈×C₁₁₃	—	2	2	no	—
110	C₂×C₈×C₁₁₃	—	2	2	no	—
111	C₂×C₈×C₁₁₃	—	2	2	no	—
112	C₂×C₈×C₁₁₃	—	2	2	no	—
113	C₂×C₈×C₁₁₃	—	2	2	no	—
114	C₂×C₈×C₁₁₃	—	4	4	no	—
115	C₂×C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₁₃	—	2	2	no	—
124	C₄⋊C₄×C₁₁₃	—	2	2	no	—
125	C₄⋊C₄×C₁₁₃	—	2	2	no	—
126	C₄⋊C₄×C₁₁₃	—	2	2	no	—
127	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
129	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
130	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
131	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
132	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
133	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
134	C₄²×C₁₁₃	—	2	2	no	—
135	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₁₃	#41	1	1	yes	characteristic
138	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
139	C₂³×C₁₁₃	—	2	2	no	—
140	C₂³×C₁₁₃	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₁₁₃	—	2	2	no	—
142	Q₈×C₁₁₃	—	2	2	no	—
143	D₄×C₁₁₃	—	2	2	no	—
144	D₄×C₁₁₃	—	2	2	no	—
145	D₄×C₁₁₃	—	4	4	no	—
146	C₂×C₄×C₁₁₃	—	2	2	no	—
147	C₂×C₄×C₁₁₃	—	2	1	no	—
148	C₂×C₄×C₁₁₃	—	2	1	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	—	2	2	no	—
153	C₂×C₄×C₁₁₃	—	2	2	no	—
154	C₂×C₄×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₁₃	—	2	2	no	—
163	C₈×C₁₁₃	—	2	2	no	—
164	C₈×C₁₁₃	—	2	1	no	—
165	C₈×C₁₁₃	—	2	1	no	—
166	C₈×C₁₁₃	—	2	1	no	—
167	C₈×C₁₁₃	—	2	1	no	—
168	C₈×C₁₁₃	—	4	2	no	—
169	C₈×C₁₁₃	—	4	2	no	—
170	C₈×C₁₁₃	#131	1	2	yes	—
171	C₈×C₁₁₃	#131	1	2	yes	—
172	C₈×C₁₁₃	#135	1	2	yes	—
173	C₈×C₁₁₃	#135	1	2	yes	—
174	C₂²×C₁₁₃	—	2	1	no	—
175	C₂²×C₁₁₃	—	2	1	no	—
176	C₂²×C₁₁₃	—	4	2	no	—
177	C₂²×C₁₁₃	—	4	2	no	—
178	C₂²×C₁₁₃	—	4	2	no	—
179	C₂²×C₁₁₃	#443	1	2	yes	—
180	C₂²×C₁₁₃	C₂×C₄×D₄	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	—	2	1	no	—
185	C₄×C₁₁₃	—	4	2	no	—
186	C₄×C₁₁₃	—	4	2	no	—
187	C₄×C₁₁₃	—	4	2	no	—
188	C₄×C₁₁₃	C₂×#131	1	1	yes	characteristic
189	C₄×C₁₁₃	C₂×#131	1	1	yes	characteristic
190	C₄×C₁₁₃	C₂×#135	1	1	yes	characteristic
191	C₄×C₁₁₃	C₂×#135	1	1	yes	characteristic
192	#17959	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₁₁₃	—	2	2	no	—
194	C₂×C₁₁₃	—	8	2	no	—
195	C₂×C₁₁₃	#2931	1	1	yes	characteristic
196	C₂×C₁₁₃	C₄×#135	1	1	yes	characteristic
197	C₂×C₁₁₃	C₂×#443	1	1	yes	characteristic
198	#3168	C₂×C₁₁₃	1	1	yes	characteristic
199	#2966	C₂×C₁₁₃	1	2	yes	complemented
200	#1591	C₂×C₁₁₃	1	1	yes	characteristic, complemented
201	#1590	C₂×C₁₁₃	1	2	yes	complemented
202	#1589	C₂×C₁₁₃	1	1	yes	characteristic, complemented
203	C₈×Q₁₆	C₂×C₁₁₃	1	1	yes	characteristic, complemented
204	C₈×SD₁₆	C₂×C₁₁₃	1	2	yes	complemented
205	C₈×D₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
206	#1568	C₂×C₁₁₃	1	1	yes	characteristic, complemented
207	#1494	C₂×C₁₁₃	1	2	yes	complemented
208	C₂×C₈²	C₂×C₁₁₃	1	1	yes	characteristic, complemented
209	C₁₁₃	#17959	1	1	yes	characteristic, direct product factor, Sylow
210	#529	C₂²×C₁₁₃	1	2	yes	—
211	#499	C₄×C₁₁₃	1	1	yes	characteristic
212	#495	C₄×C₁₁₃	1	1	yes	characteristic
213	#488	C₄×C₁₁₃	1	2	yes	—
214	#467	C₄×C₁₁₃	1	1	yes	characteristic
215	#466	C₄×C₁₁₃	1	1	yes	characteristic
216	#465	C₄×C₁₁₃	1	2	yes	—
217	#446	C₂²×C₁₁₃	1	2	yes	—
218	C₈×Q₈	C₂²×C₁₁₃	1	2	yes	—
219	C₄×Q₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
220	C₄×SD₁₆	C₂²×C₁₁₃	1	2	yes	—
221	C₄×D₈	C₂²×C₁₁₃	1	1	yes	characteristic
222	#436	C₂²×C₁₁₃	1	2	yes	—
223	#435	—	2	2	no	—
224	C₈×D₄	—	2	2	no	—
225	C₈×D₄	C₂²×C₁₁₃	1	2	yes	—
226	#433	—	2	2	no	—
227	#432	C₂²×C₁₁₃	1	2	yes	—
228	#405	—	2	2	no	—
229	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
232	#335	C₂²×C₁₁₃	1	1	yes	characteristic
233	#335	C₂²×C₁₁₃	1	1	yes	characteristic
234	#334	C₂²×C₁₁₃	1	2	yes	—
235	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
236	Q₈⋊C₈	C₂²×C₁₁₃	1	2	yes	—
237	D₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
238	D₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
239	C₈²	C₂²×C₁₁₃	1	1	yes	characteristic
240	C₈²	C₂²×C₁₁₃	1	1	yes	characteristic
241	C₈²	C₂²×C₁₁₃	1	1	yes	characteristic
242	C₈²	C₂²×C₁₁₃	1	1	yes	characteristic
243	C₂×Q₁₆	C₂×C₄×C₁₁₃	1	1	yes	characteristic
244	C₂×SD₁₆	C₂×C₄×C₁₁₃	1	2	yes	—
245	C₂×D₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
246	C₂×M₁₆	—	2	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
252	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
253	#126	—	2	2	no	—
254	#125	C₂×C₄×C₁₁₃	1	2	yes	—
255	#124	C₂×C₄×C₁₁₃	1	2	yes	—
256	#123	—	2	2	no	—
257	C₂²⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
258	#121	C₂×C₄×C₁₁₃	1	2	yes	—
259	C₄×Q₈	C₂³×C₁₁₃	1	2	yes	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	C₂³×C₁₁₃	1	2	yes	—
262	#117	—	2	2	no	—
263	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
264	#107	C₂×C₄×C₁₁₃	1	1	yes	characteristic
265	#107	C₂×C₄×C₁₁₃	1	1	yes	characteristic
266	#106	C₂×C₄×C₁₁₃	1	2	yes	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	C₂³×C₁₁₃	1	2	yes	—
270	C₄⋊C₈	C₂³×C₁₁₃	1	2	yes	—
271	#103	C₂×C₄×C₁₁₃	1	2	yes	—
272	#103	C₂×C₄×C₁₁₃	1	2	yes	—
273	#102	C₂×C₄×C₁₁₃	1	2	yes	—
274	#102	C₂×C₄×C₁₁₃	1	2	yes	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	#97	—	2	2	no	—
279	#97	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
283	C₄×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
284	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
285	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
292	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂²×C₄×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	—	2	2	no	—
300	SD₁₆	—	2	4	no	—
301	D₈	—	2	2	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
314	C₂×C₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
315	C₂×C₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
316	C₂×C₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
326	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
335	C₄²	#41×C₁₁₃	1	1	yes	characteristic
336	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	C₄×D₄×C₁₁₃	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
356	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	4	2	no	—
367	C₈	—	4	2	no	—
368	C₈	#131×C₁₁₃	1	2	yes	—
369	C₈	#131×C₁₁₃	1	2	yes	—
370	C₈	#135×C₁₁₃	1	2	yes	—
371	C₈	#135×C₁₁₃	1	2	yes	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	#443×C₁₁₃	1	2	yes	—
378	C₂²	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	C₂×#131×C₁₁₃	1	1	yes	characteristic
387	C₄	C₂×#131×C₁₁₃	1	1	yes	characteristic
388	C₄	C₂×#135×C₁₁₃	1	1	yes	characteristic
389	C₄	C₂×#135×C₁₁₃	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	C₁₁₃×#2931	1	1	yes	characteristic
393	C₂	C₄×#135×C₁₁₃	1	1	yes	characteristic
394	C₂	C₂×#443×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	C₂×C₄×D₄
prime radical	#466×C₁₁₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁₃ ◁ C₂×C₄×C₈×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₃×#2966	C₂	semidirect
3. C₁₁₃×#1591	C₂	semidirect
4. C₁₁₃×#1590	C₂	semidirect
5. C₁₁₃×#1589	C₂	semidirect
6. C₈×Q₁₆×C₁₁₃	C₂	semidirect
7. C₈×SD₁₆×C₁₁₃	C₂	semidirect
8. C₈×D₈×C₁₁₃	C₂	semidirect
9. C₁₁₃×#1568	C₂	semidirect
10. C₁₁₃×#1494	C₂	semidirect
11. C₂×C₈²×C₁₁₃	C₂	semidirect
192. #17959	C₁₁₃	direct (N × H)
199. #2966	C₂×C₁₁₃	semidirect
200. #1591	C₂×C₁₁₃	semidirect
201. #1590	C₂×C₁₁₃	semidirect
202. #1589	C₂×C₁₁₃	semidirect
203. C₈×Q₁₆	C₂×C₁₁₃	semidirect
204. C₈×SD₁₆	C₂×C₁₁₃	semidirect
205. C₈×D₈	C₂×C₁₁₃	semidirect
206. #1568	C₂×C₁₁₃	semidirect
207. #1494	C₂×C₁₁₃	semidirect
208. C₂×C₈²	C₂×C₁₁₃	semidirect
209. C₁₁₃	#17959	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×#3168	2
C₁₁₃×#2966	2
C₁₁₃×#1591	2
C₁₁₃×#1590	2
C₁₁₃×#1589	2
C₈×Q₁₆×C₁₁₃	2
C₈×SD₁₆×C₁₁₃	2
C₈×D₈×C₁₁₃	2
C₁₁₃×#1568	2
C₁₁₃×#1494	2
C₂×C₈²×C₁₁₃	2
#17959	113

Subgroups — C113×#17959 #43285979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#17959 #43285979