Subgroups — C₁₁₃×#20727 #43288747

Order 28928.

1262 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	C₂²×C₄×Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2920	C₂	1	2	yes	maximal
3	C₁₁₃×#1821	C₂	1	2	yes	maximal
4	C₁₁₃×#1801	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1784	C₂	1	2	yes	maximal
6	C₄×#101×C₁₁₃	C₂	1	4	yes	maximal, complemented
7	C₂³×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₁₃	—	2	2	no	—
9	C₂×C₄×Q₈×C₁₁₃	—	2	2	no	—
10	C₂×C₄×Q₈×C₁₁₃	—	2	2	no	—
11	C₂×C₄×Q₈×C₁₁₃	—	2	2	no	—
12	C₂×C₄×Q₈×C₁₁₃	C₄	1	2	yes	—
13	C₂×C₄×Q₈×C₁₁₃	C₄	1	2	yes	—
14	C₂×C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₁₃	C₄	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₁₃	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
20	#432×C₁₁₃	—	2	2	no	—
21	#432×C₁₁₃	—	2	2	no	—
22	#431×C₁₁₃	—	2	2	no	—
23	#431×C₁₁₃	—	2	2	no	—
24	#423×C₁₁₃	C₂²	1	4	yes	—
25	C₂×#101×C₁₁₃	C₂²	1	8	yes	—
26	#407×C₁₁₃	C₂²	1	4	yes	—
27	C₄×M₁₆×C₁₁₃	C₂²	1	4	yes	—
28	#343×C₁₁₃	C₂²	1	8	yes	—
29	C₂²×Q₈×C₁₁₃	—	2	8	no	—
30	C₂²×Q₈×C₁₁₃	—	2	2	no	—
31	C₂²×Q₈×C₁₁₃	—	2	2	no	—
32	C₂²×Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
33	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₁₃	C₂³	1	8	yes	—
40	C₄×Q₈×C₁₁₃	—	2	4	no	—
41	C₄×Q₈×C₁₁₃	—	2	4	no	—
42	C₄×Q₈×C₁₁₃	—	2	4	no	—
43	C₄×Q₈×C₁₁₃	—	2	4	no	—
44	C₄×Q₈×C₁₁₃	—	2	4	no	—
45	C₄×Q₈×C₁₁₃	—	2	4	no	—
46	C₄×Q₈×C₁₁₃	—	2	4	no	—
47	C₄×Q₈×C₁₁₃	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
65	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
66	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
67	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₁₁₃	—	2	4	no	—
71	C₄⋊C₈×C₁₁₃	—	2	4	no	—
72	#101×C₁₁₃	—	2	16	no	—
73	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
74	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
75	#97×C₁₁₃	—	2	4	no	—
76	C₄×C₈×C₁₁₃	—	2	4	no	—
77	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₁₃	—	2	16	no	—
79	C₂×Q₈×C₁₁₃	—	2	16	no	—
80	C₂×Q₈×C₁₁₃	—	2	4	no	—
81	C₂×Q₈×C₁₁₃	—	2	8	no	—
82	C₂×Q₈×C₁₁₃	—	2	4	no	—
83	C₂×Q₈×C₁₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₁₃	#41	1	8	yes	—
85	C₂²×C₄×C₁₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₁₃	—	4	4	no	—
94	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₁₃	—	2	16	no	—
111	C₂×C₈×C₁₁₃	—	2	8	no	—
112	C₄⋊C₄×C₁₁₃	—	2	8	no	—
113	C₄⋊C₄×C₁₁₃	—	2	8	no	—
114	C₄⋊C₄×C₁₁₃	—	2	4	no	—
115	C₄⋊C₄×C₁₁₃	—	2	4	no	—
116	C₄²×C₁₁₃	—	2	4	no	—
117	C₄²×C₁₁₃	—	2	4	no	—
118	C₄²×C₁₁₃	—	2	4	no	—
119	C₄²×C₁₁₃	—	2	4	no	—
120	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
125	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
126	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
127	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
128	C₂³×C₁₁₃	—	2	2	no	—
129	C₂³×C₁₁₃	—	2	2	no	—
130	C₂³×C₁₁₃	—	2	2	no	—
131	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
134	Q₈×C₁₁₃	—	2	16	no	—
135	Q₈×C₁₁₃	—	2	16	no	—
136	C₂×C₄×C₁₁₃	—	2	8	no	—
137	C₂×C₄×C₁₁₃	—	2	8	no	—
138	C₂×C₄×C₁₁₃	—	2	4	no	—
139	C₂×C₄×C₁₁₃	—	2	2	no	—
140	C₂×C₄×C₁₁₃	—	2	4	no	—
141	C₂×C₄×C₁₁₃	—	2	2	no	—
142	C₂×C₄×C₁₁₃	—	2	4	no	—
143	C₂×C₄×C₁₁₃	—	2	4	no	—
144	C₂×C₄×C₁₁₃	—	2	4	no	—
145	C₂×C₄×C₁₁₃	—	2	2	no	—
146	C₂×C₄×C₁₁₃	—	2	2	no	—
147	C₂×C₄×C₁₁₃	—	2	2	no	—
148	C₂×C₄×C₁₁₃	—	2	2	no	—
149	C₂×C₄×C₁₁₃	—	2	4	no	—
150	C₂×C₄×C₁₁₃	—	4	2	no	—
151	C₂×C₄×C₁₁₃	—	4	1	no	—
152	C₂×C₄×C₁₁₃	—	4	1	no	—
153	C₂×C₄×C₁₁₃	—	4	4	no	—
154	C₂×C₄×C₁₁₃	—	4	4	no	—
155	C₂×C₄×C₁₁₃	—	4	4	no	—
156	C₂×C₄×C₁₁₃	#101	1	4	yes	complemented
157	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	#117	1	8	yes	—
165	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₁₁₃	C₂×#41	1	4	yes	—
167	C₈×C₁₁₃	—	4	8	no	—
168	C₂²×C₁₁₃	—	2	8	no	—
169	C₂²×C₁₁₃	—	2	1	no	—
170	C₂²×C₁₁₃	—	2	1	no	—
171	C₂²×C₁₁₃	—	2	1	no	—
172	C₂²×C₁₁₃	—	2	1	no	—
173	C₂²×C₁₁₃	—	2	1	no	—
174	C₂²×C₁₁₃	—	2	1	no	—
175	C₂²×C₁₁₃	C₂×#101	1	2	yes	—
176	C₂²×C₁₁₃	#413	1	2	yes	—
177	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₁₃	C₂×#117	1	2	yes	—
179	C₄×C₁₁₃	—	2	1	no	—
180	C₄×C₁₁₃	—	2	1	no	—
181	C₄×C₁₁₃	—	2	2	no	—
182	C₄×C₁₁₃	—	2	2	no	—
183	C₄×C₁₁₃	—	2	2	no	—
184	C₄×C₁₁₃	—	2	8	no	—
185	C₄×C₁₁₃	—	4	4	no	—
186	C₄×C₁₁₃	C₂×#101	1	2	yes	—
187	C₄×C₁₁₃	C₂×#101	1	2	yes	—
188	C₄×C₁₁₃	#525	1	4	yes	—
189	#20727	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₁₁₃	—	2	2	no	—
191	C₂×C₁₁₃	—	2	2	no	—
192	C₂×C₁₁₃	—	2	2	no	—
193	C₂×C₁₁₃	#2280	1	1	yes	characteristic
194	C₂×C₁₁₃	C₂²×#101	1	1	yes	characteristic
195	C₂×C₁₁₃	C₂×#413	1	1	yes	characteristic
196	C₂²×C₄×Q₈	C₂×C₁₁₃	1	1	yes	characteristic
197	#2920	C₂×C₁₁₃	1	2	yes	—
198	#1821	C₂×C₁₁₃	1	2	yes	—
199	#1801	C₂×C₁₁₃	1	4	yes	complemented
200	#1784	C₂×C₁₁₃	1	2	yes	—
201	C₄×#101	C₂×C₁₁₃	1	4	yes	complemented
202	C₁₁₃	#20727	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
204	C₂×C₄×Q₈	—	2	2	no	—
205	C₂×C₄×Q₈	—	2	2	no	—
206	C₂×C₄×Q₈	—	2	2	no	—
207	C₂×C₄×Q₈	—	2	2	no	—
208	C₂×C₄×Q₈	C₄×C₁₁₃	1	2	yes	—
209	C₂×C₄×Q₈	C₄×C₁₁₃	1	2	yes	—
210	C₂×C₄×Q₈	C₂²×C₁₁₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₁₃	1	2	yes	—
212	C₂²×C₄⋊C₄	C₄×C₁₁₃	1	2	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
214	C₂²×C₄²	C₄×C₁₁₃	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
216	#432	—	2	2	no	—
217	#432	—	2	2	no	—
218	#431	—	2	2	no	—
219	#431	—	2	2	no	—
220	#423	C₂²×C₁₁₃	1	4	yes	—
221	C₂×#101	C₂²×C₁₁₃	1	8	yes	—
222	#407	C₂²×C₁₁₃	1	4	yes	—
223	C₄×M₁₆	C₂²×C₁₁₃	1	4	yes	—
224	#343	C₂²×C₁₁₃	1	8	yes	—
225	C₂²×Q₈	—	2	8	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
229	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
230	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
231	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
232	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
233	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
235	C₂×M₁₆	C₂³×C₁₁₃	1	8	yes	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
257	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
258	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
261	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
262	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
263	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
266	C₄⋊C₈	—	2	4	no	—
267	C₄⋊C₈	—	2	4	no	—
268	#101	—	2	16	no	—
269	C₂²⋊C₈	—	2	4	no	—
270	C₂²⋊C₈	—	2	4	no	—
271	#97	—	2	4	no	—
272	C₄×C₈	—	2	4	no	—
273	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
274	C₂×Q₈	—	2	16	no	—
275	C₂×Q₈	—	2	16	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	8	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	#41×C₁₁₃	1	8	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
295	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
306	M₁₆	—	2	16	no	—
307	C₂×C₈	—	2	8	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄²	—	2	4	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	4	no	—
315	C₄²	—	2	4	no	—
316	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
317	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
318	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
319	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
320	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
321	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
322	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
323	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
328	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
329	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
330	Q₈	—	2	16	no	—
331	Q₈	—	2	16	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	#101×C₁₁₃	1	4	yes	complemented
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
360	C₂×C₄	#117×C₁₁₃	1	8	yes	—
361	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
362	C₂×C₄	C₂×#41×C₁₁₃	1	4	yes	—
363	C₈	—	4	8	no	—
364	C₂²	—	2	8	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	C₂×#101×C₁₁₃	1	2	yes	—
372	C₂²	#413×C₁₁₃	1	2	yes	—
373	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
374	C₂²	C₂×#117×C₁₁₃	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	8	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	4	no	—
382	C₄	C₂×#101×C₁₁₃	1	2	yes	—
383	C₄	C₂×#101×C₁₁₃	1	2	yes	—
384	C₄	#525×C₁₁₃	1	4	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	2	2	no	—
388	C₂	C₁₁₃×#2280	1	1	yes	characteristic
389	C₂	C₂²×#101×C₁₁₃	1	1	yes	characteristic
390	C₂	C₂×#413×C₁₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₁₃×#1801	C₂	semidirect
6. C₄×#101×C₁₁₃	C₂	semidirect
156. C₂×C₄×C₁₁₃	#101	semidirect
189. #20727	C₁₁₃	direct (N × H)
199. #1801	C₂×C₁₁₃	semidirect
201. C₄×#101	C₂×C₁₁₃	semidirect
202. C₁₁₃	#20727	direct (N × H)
352. C₂×C₄	#101×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×Q₈×C₁₁₃	2
C₁₁₃×#2920	2
C₁₁₃×#1821	2
C₁₁₃×#1801	2
C₁₁₃×#1784	2
C₄×#101×C₁₁₃	2
#20727	113

Subgroups — C113×#20727 #43288747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20727 #43288747