Subgroups — C₁₁₃×#21373 #43289393

Order 28928.

1518 conjugacy classes of subgroups.

The subgroup lattice has 442 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×#431×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1984	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1954	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1869	C₂	1	4	yes	maximal, complemented
7	C₄×C₂²⋊C₈×C₁₁₃	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	C₄	1	1	yes	characteristic
9	C₂³×C₈×C₁₁₃	C₂²	1	2	yes	—
10	C₄×#41×C₁₁₃	—	2	4	no	—
11	C₄×#41×C₁₁₃	—	2	4	no	—
12	C₂×C₄×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₁₃	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₁₃	C₄	1	1	yes	characteristic
19	C₂×#117×C₁₁₃	C₄	1	2	yes	—
20	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
22	#431×C₁₁₃	—	2	4	no	—
23	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	8	yes	—
26	C₂×C₄×C₈×C₁₁₃	—	2	4	no	—
27	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
30	#336×C₁₁₃	C₂²	1	8	yes	—
31	C₂×#41×C₁₁₃	—	2	4	no	—
32	C₂×#41×C₁₁₃	—	2	4	no	—
33	C₂×#41×C₁₁₃	C₈	1	8	yes	complemented
34	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₁₃	—	2	8	no	—
45	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
46	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
47	C₄×Q₈×C₁₁₃	—	2	4	no	—
48	C₄×Q₈×C₁₁₃	—	2	2	no	—
49	C₄×Q₈×C₁₁₃	—	2	2	no	—
50	C₄×D₄×C₁₁₃	—	2	8	no	—
51	C₄×D₄×C₁₁₃	—	2	4	no	—
52	C₄×D₄×C₁₁₃	—	2	4	no	—
53	C₄×D₄×C₁₁₃	—	2	4	no	—
54	C₄×D₄×C₁₁₃	—	2	2	no	—
55	C₄×D₄×C₁₁₃	—	2	2	no	—
56	#117×C₁₁₃	—	2	4	no	—
57	#117×C₁₁₃	—	2	8	no	—
58	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₁₃	—	2	4	no	—
66	C₂×C₄²×C₁₁₃	—	2	4	no	—
67	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
72	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
73	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₁₁₃	—	2	4	no	—
77	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
78	C₂²⋊C₈×C₁₁₃	—	2	16	no	—
79	C₄×C₈×C₁₁₃	—	2	4	no	—
80	C₄×C₈×C₁₁₃	—	2	4	no	—
81	C₄×C₈×C₁₁₃	—	2	4	no	—
82	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
83	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
84	#41×C₁₁₃	—	2	32	no	—
85	C₂×Q₈×C₁₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₁₃	C₂×C₈	1	4	yes	complemented
88	C₂×D₄×C₁₁₃	—	2	4	no	—
89	C₂×D₄×C₁₁₃	—	2	4	no	—
90	C₂×D₄×C₁₁₃	—	2	2	no	—
91	C₂×D₄×C₁₁₃	—	2	2	no	—
92	C₂×D₄×C₁₁₃	C₂×C₈	1	8	yes	—
93	C₂×D₄×C₁₁₃	C₂×C₈	1	4	yes	complemented
94	C₂²×C₄×C₁₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₁₃	—	2	8	no	—
103	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₁₃	C₂×C₈	1	4	yes	—
106	C₂²×C₄×C₁₁₃	C₂×C₈	1	8	yes	complemented
107	C₂²×C₄×C₁₁₃	M₁₆	1	4	yes	—
108	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₁₃	—	2	16	no	—
120	C₂×C₈×C₁₁₃	—	2	4	no	—
121	C₂×C₈×C₁₁₃	—	2	4	no	—
122	C₂×C₈×C₁₁₃	—	2	4	no	—
123	C₂×C₈×C₁₁₃	—	2	8	no	—
124	C₂×C₈×C₁₁₃	#41	1	8	yes	complemented
125	C₄⋊C₄×C₁₁₃	—	2	4	no	—
126	C₄⋊C₄×C₁₁₃	—	2	4	no	—
127	C₄⋊C₄×C₁₁₃	—	2	2	no	—
128	C₄⋊C₄×C₁₁₃	—	2	2	no	—
129	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
130	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
131	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
132	C₄²×C₁₁₃	—	2	4	no	—
133	C₄²×C₁₁₃	—	2	4	no	—
134	C₄²×C₁₁₃	—	2	2	no	—
135	C₄²×C₁₁₃	—	2	2	no	—
136	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
137	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
138	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
139	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
140	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
142	C₂³×C₁₁₃	—	2	2	no	—
143	C₂³×C₁₁₃	—	2	2	no	—
144	C₂³×C₁₁₃	—	2	2	no	—
145	C₂³×C₁₁₃	—	2	4	no	—
146	C₂³×C₁₁₃	—	2	2	no	—
147	C₂³×C₁₁₃	—	2	4	no	—
148	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂³×C₁₁₃	C₂²×C₈	1	4	yes	—
150	C₂³×C₁₁₃	C₂²×C₈	1	2	yes	—
151	C₂³×C₁₁₃	C₂×M₁₆	1	2	yes	—
152	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
153	Q₈×C₁₁₃	—	2	8	no	—
154	D₄×C₁₁₃	—	2	16	no	—
155	D₄×C₁₁₃	—	2	8	no	—
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	2	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	2	4	no	—
162	C₂×C₄×C₁₁₃	—	2	16	no	—
163	C₂×C₄×C₁₁₃	—	2	8	no	—
164	C₂×C₄×C₁₁₃	—	2	2	no	—
165	C₂×C₄×C₁₁₃	—	2	2	no	—
166	C₂×C₄×C₁₁₃	—	2	4	no	—
167	C₂×C₄×C₁₁₃	—	2	4	no	—
168	C₂×C₄×C₁₁₃	—	4	4	no	—
169	C₂×C₄×C₁₁₃	—	4	4	no	—
170	C₂×C₄×C₁₁₃	—	4	8	no	—
171	C₂×C₄×C₁₁₃	C₂²⋊C₈	1	16	yes	complemented
172	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₁₃	C₂²×C₈	1	4	yes	—
178	C₂×C₄×C₁₁₃	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₁₁₃	C₂²×C₈	1	2	yes	—
180	C₂×C₄×C₁₁₃	C₂×M₁₆	1	2	yes	—
181	C₂×C₄×C₁₁₃	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₁₁₃	#131	1	4	yes	—
183	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁₃	C₂×#41	1	4	yes	—
186	C₈×C₁₁₃	—	2	8	no	—
187	C₈×C₁₁₃	—	4	4	no	—
188	C₂²×C₁₁₃	—	2	2	no	—
189	C₂²×C₁₁₃	—	2	4	no	—
190	C₂²×C₁₁₃	—	2	4	no	—
191	C₂²×C₁₁₃	—	2	2	no	—
192	C₂²×C₁₁₃	—	2	4	no	—
193	C₂²×C₁₁₃	—	2	8	no	—
194	C₂²×C₁₁₃	—	4	2	no	—
195	C₂²×C₁₁₃	—	4	4	no	—
196	C₂²×C₁₁₃	—	4	2	no	—
197	C₂²×C₁₁₃	C₂×C₂²⋊C₈	1	4	yes	—
198	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₁₃	C₄×#41	1	2	yes	—
200	C₂²×C₁₁₃	C₂³×C₈	1	1	yes	characteristic
201	C₂²×C₁₁₃	C₂²×M₁₆	1	1	yes	characteristic
202	C₂²×C₁₁₃	C₂×#131	1	2	yes	—
203	C₄×C₁₁₃	—	2	4	no	—
204	C₄×C₁₁₃	—	2	2	no	—
205	C₄×C₁₁₃	—	2	2	no	—
206	C₄×C₁₁₃	—	4	2	no	—
207	C₄×C₁₁₃	—	4	2	no	—
208	C₄×C₁₁₃	C₂×C₂²⋊C₈	1	4	yes	—
209	C₄×C₁₁₃	C₂×C₂²⋊C₈	1	4	yes	—
210	C₄×C₁₁₃	#408	1	4	yes	—
211	C₄×C₁₁₃	#525	1	2	yes	—
212	C₄×C₁₁₃	#532	1	2	yes	—
213	#21373	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₁₁₃	—	2	4	no	—
215	C₂×C₁₁₃	—	4	4	no	—
216	C₂×C₁₁₃	#2297	1	1	yes	characteristic
217	C₂×C₁₁₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
218	C₂×C₁₁₃	C₂×#408	1	1	yes	characteristic
219	C₂×C₁₁₃	C₈×#41	1	2	yes	—
220	C₂×C₁₁₃	#2965	1	2	yes	—
221	C₂×C₄×#41	C₂×C₁₁₃	1	1	yes	characteristic
222	C₂×#431	C₂×C₁₁₃	1	1	yes	characteristic, complemented
223	C₂²×C₄×C₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
224	#1984	C₂×C₁₁₃	1	2	yes	complemented
225	#1954	C₂×C₁₁₃	1	2	yes	complemented
226	#1869	C₂×C₁₁₃	1	4	yes	complemented
227	C₄×C₂²⋊C₈	C₂×C₁₁₃	1	4	yes	complemented
228	C₁₁₃	#21373	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×#41	C₄×C₁₁₃	1	1	yes	characteristic
230	C₂³×C₈	C₂²×C₁₁₃	1	2	yes	—
231	C₄×#41	—	2	4	no	—
232	C₄×#41	—	2	4	no	—
233	C₂×C₄×Q₈	C₄×C₁₁₃	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
235	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	—
236	C₂×C₄×D₄	C₄×C₁₁₃	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂²×C₁₁₃	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
239	C₂×#117	C₄×C₁₁₃	1	1	yes	characteristic
240	C₂×#117	C₄×C₁₁₃	1	2	yes	—
241	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
242	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
243	#431	—	2	4	no	—
244	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
245	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	8	yes	—
247	C₂×C₄×C₈	—	2	4	no	—
248	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
249	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
250	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
251	#336	C₂²×C₁₁₃	1	8	yes	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	C₈×C₁₁₃	1	8	yes	complemented
255	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
256	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
257	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
259	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
260	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
261	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	—	2	8	no	—
266	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
267	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×D₄	—	2	8	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	#117	—	2	4	no	—
278	#117	—	2	8	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
286	C₂×C₄²	—	2	4	no	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
289	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
290	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
293	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
294	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	4	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	C₂²⋊C₈	—	2	16	no	—
300	C₄×C₈	—	2	4	no	—
301	C₄×C₈	—	2	4	no	—
302	C₄×C₈	—	2	4	no	—
303	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
304	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
305	#41	—	2	32	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	C₂×C₈×C₁₁₃	1	4	yes	complemented
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	C₂×C₈×C₁₁₃	1	8	yes	—
314	C₂×D₄	C₂×C₈×C₁₁₃	1	4	yes	complemented
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
325	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
326	C₂²×C₄	C₂×C₈×C₁₁₃	1	4	yes	—
327	C₂²×C₄	C₂×C₈×C₁₁₃	1	8	yes	complemented
328	C₂²×C₄	M₁₆×C₁₁₃	1	4	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
331	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
339	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
340	C₂×C₈	—	2	16	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	8	no	—
345	C₂×C₈	#41×C₁₁₃	1	8	yes	complemented
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
358	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
359	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
360	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
361	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
362	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	4	no	—
369	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
370	C₂³	C₂²×C₈×C₁₁₃	1	4	yes	—
371	C₂³	C₂²×C₈×C₁₁₃	1	2	yes	—
372	C₂³	C₂×M₁₆×C₁₁₃	1	2	yes	—
373	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
374	Q₈	—	2	8	no	—
375	D₄	—	2	16	no	—
376	D₄	—	2	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	16	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	C₂²⋊C₈×C₁₁₃	1	16	yes	complemented
393	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
396	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
398	C₂×C₄	C₂²×C₈×C₁₁₃	1	4	yes	—
399	C₂×C₄	C₂²×C₈×C₁₁₃	1	2	yes	—
400	C₂×C₄	C₂²×C₈×C₁₁₃	1	2	yes	—
401	C₂×C₄	C₂×M₁₆×C₁₁₃	1	2	yes	—
402	C₂×C₄	C₂×M₁₆×C₁₁₃	1	2	yes	—
403	C₂×C₄	#131×C₁₁₃	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₁₁₃	1	4	yes	—
407	C₈	—	2	8	no	—
408	C₈	—	4	4	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	4	no	—
418	C₂²	C₂×C₂²⋊C₈×C₁₁₃	1	4	yes	—
419	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
420	C₂²	C₄×#41×C₁₁₃	1	2	yes	—
421	C₂²	C₂³×C₈×C₁₁₃	1	1	yes	characteristic
422	C₂²	C₂²×M₁₆×C₁₁₃	1	1	yes	characteristic
423	C₂²	C₂×#131×C₁₁₃	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	2	4	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	C₂×C₂²⋊C₈×C₁₁₃	1	4	yes	—
430	C₄	C₂×C₂²⋊C₈×C₁₁₃	1	4	yes	—
431	C₄	#408×C₁₁₃	1	4	yes	—
432	C₄	#525×C₁₁₃	1	2	yes	—
433	C₄	#532×C₁₁₃	1	2	yes	—
434	C₂	—	2	4	no	—
435	C₂	—	4	4	no	—
436	C₂	C₁₁₃×#2297	1	1	yes	characteristic
437	C₂	C₂²×C₂²⋊C₈×C₁₁₃	1	1	yes	characteristic
438	C₂	C₂×#408×C₁₁₃	1	1	yes	characteristic
439	C₂	C₈×#41×C₁₁₃	1	2	yes	—
440	C₂	C₁₁₃×#2965	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₁₃	C₂³
commutator	C₂²	C₂³×C₈×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂³×C₄
prime radical	C₂²×#41×C₁₁₃	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₁₃	C₂	semidirect
3. C₂²×C₄×C₈×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1984	C₂	semidirect
5. C₁₁₃×#1954	C₂	semidirect
6. C₁₁₃×#1869	C₂	semidirect
7. C₄×C₂²⋊C₈×C₁₁₃	C₂	semidirect
33. C₂×#41×C₁₁₃	C₈	semidirect
87. C₂×Q₈×C₁₁₃	C₂×C₈	semidirect
93. C₂×D₄×C₁₁₃	C₂×C₈	semidirect
106. C₂²×C₄×C₁₁₃	C₂×C₈	semidirect
124. C₂×C₈×C₁₁₃	#41	semidirect
171. C₂×C₄×C₁₁₃	C₂²⋊C₈	semidirect
213. #21373	C₁₁₃	direct (N × H)
222. C₂×#431	C₂×C₁₁₃	semidirect
223. C₂²×C₄×C₈	C₂×C₁₁₃	semidirect
224. #1984	C₂×C₁₁₃	semidirect
225. #1954	C₂×C₁₁₃	semidirect
226. #1869	C₂×C₁₁₃	semidirect
227. C₄×C₂²⋊C₈	C₂×C₁₁₃	semidirect
228. C₁₁₃	#21373	direct (N × H)
254. C₂×#41	C₈×C₁₁₃	semidirect
308. C₂×Q₈	C₂×C₈×C₁₁₃	semidirect
314. C₂×D₄	C₂×C₈×C₁₁₃	semidirect
327. C₂²×C₄	C₂×C₈×C₁₁₃	semidirect
345. C₂×C₈	#41×C₁₁₃	semidirect
392. C₂×C₄	C₂²⋊C₈×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×#431×C₁₁₃	2
C₂²×C₄×C₈×C₁₁₃	2
C₁₁₃×#1984	2
C₁₁₃×#1954	2
C₁₁₃×#1869	2
C₄×C₂²⋊C₈×C₁₁₃	2
#21373	113

Subgroups — C113×#21373 #43289393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21373 #43289393