Subgroups — C₁₁₃×#20649 #43288669

Order 28928.

1510 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₁₃	C₂	1	2	yes	maximal
4	C₂×#382×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1805	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1804	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1736	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
10	C₄×#41×C₁₁₃	—	2	4	no	—
11	C₄×#41×C₁₁₃	C₄	1	8	yes	complemented
12	C₂×C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₁₃	—	2	2	no	—
14	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
15	C₂×#117×C₁₁₃	—	2	1	no	—
16	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₁₃	—	2	1	no	—
19	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
20	#423×C₁₁₃	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	4	yes	—
22	#417×C₁₁₃	—	2	8	no	—
23	C₂×#103×C₁₁₃	C₂²	1	4	yes	—
24	C₂×#102×C₁₁₃	C₂²	1	4	yes	—
25	#382×C₁₁₃	—	2	1	no	—
26	#382×C₁₁₃	—	2	1	no	—
27	#382×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#95×C₁₁₃	—	2	2	no	—
29	#340×C₁₁₃	C₂²	1	8	yes	—
30	C₂×#41×C₁₁₃	—	2	2	no	—
31	C₂×#41×C₁₁₃	—	2	2	no	—
32	C₂×#41×C₁₁₃	—	2	2	no	—
33	C₂×#41×C₁₁₃	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₁₃	D₄	1	4	yes	—
35	C₂×#41×C₁₁₃	Q₈	1	4	yes	—
36	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₁₃	—	2	1	no	—
40	C₂³×C₄×C₁₁₃	—	2	2	no	—
41	C₂³×C₄×C₁₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
43	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₁₃	—	2	4	no	—
45	C₂×M₁₆×C₁₁₃	—	2	4	no	—
46	C₂×M₁₆×C₁₁₃	—	2	4	no	—
47	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
48	C₄×Q₈×C₁₁₃	—	2	4	no	—
49	C₄×Q₈×C₁₁₃	C₂×C₄	1	8	yes	complemented
50	C₄×D₄×C₁₁₃	—	2	16	no	—
51	C₄×D₄×C₁₁₃	—	2	4	no	—
52	C₄×D₄×C₁₁₃	C₂×C₄	1	8	yes	complemented
53	#117×C₁₁₃	—	2	2	no	—
54	#117×C₁₁₃	—	2	8	no	—
55	#117×C₁₁₃	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₁₃	—	2	8	no	—
67	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₁₃	—	2	8	no	—
73	#103×C₁₁₃	—	2	8	no	—
74	#102×C₁₁₃	—	2	8	no	—
75	#95×C₁₁₃	—	2	4	no	—
76	#95×C₁₁₃	—	2	4	no	—
77	C₂⁴×C₁₁₃	—	2	1	no	—
78	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₁₃	—	2	8	no	—
80	#41×C₁₁₃	—	2	8	no	—
81	#41×C₁₁₃	—	2	8	no	—
82	#41×C₁₁₃	C₄⋊C₄	1	16	yes	—
83	C₂×Q₈×C₁₁₃	—	2	1	no	—
84	C₂×Q₈×C₁₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
87	C₂×Q₈×C₁₁₃	C₂×D₄	1	2	yes	—
88	C₂×Q₈×C₁₁₃	C₂×Q₈	1	2	yes	—
89	C₂×D₄×C₁₁₃	—	2	4	no	—
90	C₂×D₄×C₁₁₃	—	2	4	no	—
91	C₂×D₄×C₁₁₃	—	2	4	no	—
92	C₂×D₄×C₁₁₃	—	2	1	no	—
93	C₂×D₄×C₁₁₃	—	2	1	no	—
94	C₂×D₄×C₁₁₃	—	2	1	no	—
95	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₁₃	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₁₃	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₁₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₁₃	—	2	8	no	—
104	C₂²×C₄×C₁₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₁₃	—	4	8	no	—
107	C₂²×C₄×C₁₁₃	—	4	8	no	—
108	C₂²×C₄×C₁₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
110	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
118	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
119	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₁₁₃	—	4	8	no	—
121	C₂×C₈×C₁₁₃	—	2	4	no	—
122	C₂×C₈×C₁₁₃	—	2	4	no	—
123	C₂×C₈×C₁₁₃	—	2	4	no	—
124	C₄⋊C₄×C₁₁₃	—	2	8	no	—
125	C₄⋊C₄×C₁₁₃	—	2	2	no	—
126	C₄⋊C₄×C₁₁₃	—	2	4	no	—
127	C₄⋊C₄×C₁₁₃	—	2	4	no	—
128	C₄⋊C₄×C₁₁₃	—	4	4	no	—
129	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
130	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
131	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
132	C₄²×C₁₁₃	—	2	4	no	—
133	C₄²×C₁₁₃	—	2	8	no	—
134	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
135	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
136	C₄²×C₁₁₃	C₂²×C₄	1	4	yes	—
137	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
138	C₂³×C₁₁₃	—	2	4	no	—
139	C₂³×C₁₁₃	—	2	2	no	—
140	C₂³×C₁₁₃	—	2	2	no	—
141	C₂³×C₁₁₃	—	2	2	no	—
142	C₂³×C₁₁₃	—	4	4	no	—
143	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₁₁₃	#121	1	2	yes	—
145	C₂³×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
146	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₁₃	—	2	2	no	—
148	Q₈×C₁₁₃	—	2	2	no	—
149	Q₈×C₁₁₃	—	2	2	no	—
150	Q₈×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
151	D₄×C₁₁₃	—	2	16	no	—
152	D₄×C₁₁₃	—	2	2	no	—
153	D₄×C₁₁₃	—	2	2	no	—
154	D₄×C₁₁₃	—	2	2	no	—
155	D₄×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
156	C₂×C₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	2	4	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	2	16	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	4	8	no	—
164	C₂×C₄×C₁₁₃	—	4	16	no	—
165	C₂×C₄×C₁₁₃	—	4	4	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	4	8	no	—
168	C₂×C₄×C₁₁₃	—	8	8	no	—
169	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
170	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
171	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
173	C₂×C₄×C₁₁₃	#117	1	4	yes	—
174	C₂×C₄×C₁₁₃	#121	1	4	yes	—
175	C₂×C₄×C₁₁₃	#121	1	2	yes	—
176	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
177	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
184	C₈×C₁₁₃	—	4	4	no	—
185	C₂²×C₁₁₃	—	2	4	no	—
186	C₂²×C₁₁₃	—	2	4	no	—
187	C₂²×C₁₁₃	—	2	4	no	—
188	C₂²×C₁₁₃	—	2	4	no	—
189	C₂²×C₁₁₃	—	4	4	no	—
190	C₂²×C₁₁₃	—	4	4	no	—
191	C₂²×C₁₁₃	—	4	4	no	—
192	C₂²×C₁₁₃	#380	1	4	yes	—
193	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
195	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
196	C₂²×C₁₁₃	#575	1	4	yes	—
197	C₄×C₁₁₃	—	2	4	no	—
198	C₄×C₁₁₃	—	2	4	no	—
199	C₄×C₁₁₃	—	2	4	no	—
200	C₄×C₁₁₃	—	4	4	no	—
201	C₄×C₁₁₃	—	8	4	no	—
202	C₄×C₁₁₃	#380	1	4	yes	—
203	C₄×C₁₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
204	C₄×C₁₁₃	C₂×#117	1	1	yes	characteristic
205	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
206	C₄×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	#20649	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₁₁₃	—	2	4	no	—
209	C₂×C₁₁₃	—	4	4	no	—
210	C₂×C₁₁₃	C₂×#380	1	1	yes	characteristic
211	C₂×C₁₁₃	#2896	1	2	yes	—
212	C₂×C₁₁₃	#3040	1	2	yes	—
213	C₂×C₁₁₃	#3080	1	2	yes	—
214	C₂×C₄×#41	C₂×C₁₁₃	1	1	yes	characteristic
215	C₂×#423	C₂×C₁₁₃	1	1	yes	characteristic, complemented
216	C₂×#417	C₂×C₁₁₃	1	2	yes	—
217	C₂×#382	C₂×C₁₁₃	1	1	yes	characteristic, complemented
218	#1805	C₂×C₁₁₃	1	4	yes	complemented
219	#1804	C₂×C₁₁₃	1	4	yes	complemented
220	#1736	C₂×C₁₁₃	1	2	yes	complemented
221	C₁₁₃	#20649	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
223	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
224	C₄×#41	—	2	4	no	—
225	C₄×#41	C₄×C₁₁₃	1	8	yes	complemented
226	C₂×C₄×Q₈	C₂²×C₁₁₃	1	2	yes	—
227	C₂×C₄×D₄	—	2	2	no	—
228	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
229	C₂×#117	—	2	1	no	—
230	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
232	C₂²×C₄²	—	2	1	no	—
233	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
234	#423	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	4	yes	—
236	#417	—	2	8	no	—
237	C₂×#103	C₂²×C₁₁₃	1	4	yes	—
238	C₂×#102	C₂²×C₁₁₃	1	4	yes	—
239	#382	—	2	1	no	—
240	#382	—	2	1	no	—
241	#382	C₂²×C₁₁₃	1	4	yes	—
242	C₂×#95	—	2	2	no	—
243	#340	C₂²×C₁₁₃	1	8	yes	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	C₂×C₄×C₁₁₃	1	4	yes	—
248	C₂×#41	D₄×C₁₁₃	1	4	yes	—
249	C₂×#41	Q₈×C₁₁₃	1	4	yes	—
250	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	2	4	no	—
260	C₂×M₁₆	—	2	4	no	—
261	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	C₂×C₄×C₁₁₃	1	8	yes	complemented
264	C₄×D₄	—	2	16	no	—
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	C₂×C₄×C₁₁₃	1	8	yes	complemented
267	#117	—	2	2	no	—
268	#117	—	2	8	no	—
269	#117	C₂×C₄×C₁₁₃	1	4	yes	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	8	no	—
281	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
282	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₁₁₃	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
285	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
286	C₄⋊C₈	—	2	8	no	—
287	#103	—	2	8	no	—
288	#102	—	2	8	no	—
289	#95	—	2	4	no	—
290	#95	—	2	4	no	—
291	C₂⁴	—	2	1	no	—
292	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
293	#41	—	2	8	no	—
294	#41	—	2	8	no	—
295	#41	—	2	8	no	—
296	#41	C₄⋊C₄×C₁₁₃	1	16	yes	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
301	C₂×Q₈	C₂×D₄×C₁₁₃	1	2	yes	—
302	C₂×Q₈	C₂×Q₈×C₁₁₃	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
310	C₂×D₄	C₂×D₄×C₁₁₃	1	2	yes	—
311	C₂×D₄	C₂×Q₈×C₁₁₃	1	2	yes	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	—	4	8	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
331	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
332	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
334	M₁₆	—	4	8	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	2	4	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	8	no	—
348	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
349	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
350	C₄²	C₂²×C₄×C₁₁₃	1	4	yes	—
351	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	4	no	—
357	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
358	C₂³	#121×C₁₁₃	1	2	yes	—
359	C₂³	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
360	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
365	D₄	—	2	16	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	2	2	no	—
369	D₄	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	16	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	8	8	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
386	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
387	C₂×C₄	#117×C₁₁₃	1	4	yes	—
388	C₂×C₄	#121×C₁₁₃	1	4	yes	—
389	C₂×C₄	#121×C₁₁₃	1	2	yes	—
390	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
391	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	2	yes	—
392	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
398	C₈	—	4	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	#380×C₁₁₃	1	4	yes	—
407	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
408	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
409	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
410	C₂²	#575×C₁₁₃	1	4	yes	—
411	C₄	—	2	4	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	4	no	—
416	C₄	#380×C₁₁₃	1	4	yes	—
417	C₄	C₂²×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
418	C₄	C₂×#117×C₁₁₃	1	1	yes	characteristic
419	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
420	C₄	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
421	C₂	—	2	4	no	—
422	C₂	—	4	4	no	—
423	C₂	C₂×#380×C₁₁₃	1	1	yes	characteristic
424	C₂	C₁₁₃×#2896	1	2	yes	—
425	C₂	C₁₁₃×#3040	1	2	yes	—
426	C₂	C₁₁₃×#3080	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂²×#41×C₁₁₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂²×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₁₁₃	C₂	semidirect
4. C₂×#382×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1805	C₂	semidirect
6. C₁₁₃×#1804	C₂	semidirect
7. C₁₁₃×#1736	C₂	semidirect
11. C₄×#41×C₁₁₃	C₄	semidirect
49. C₄×Q₈×C₁₁₃	C₂×C₄	semidirect
52. C₄×D₄×C₁₁₃	C₂×C₄	semidirect
207. #20649	C₁₁₃	direct (N × H)
215. C₂×#423	C₂×C₁₁₃	semidirect
217. C₂×#382	C₂×C₁₁₃	semidirect
218. #1805	C₂×C₁₁₃	semidirect
219. #1804	C₂×C₁₁₃	semidirect
220. #1736	C₂×C₁₁₃	semidirect
221. C₁₁₃	#20649	direct (N × H)
225. C₄×#41	C₄×C₁₁₃	semidirect
263. C₄×Q₈	C₂×C₄×C₁₁₃	semidirect
266. C₄×D₄	C₂×C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₁₃	2
C₂×#423×C₁₁₃	2
C₂×#417×C₁₁₃	2
C₂×#382×C₁₁₃	2
C₁₁₃×#1805	2
C₁₁₃×#1804	2
C₁₁₃×#1736	2
#20649	113

Subgroups — C113×#20649 #43288669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20649 #43288669