Subgroups — C₁₁₃×#16608 #43284628

Order 28928.

1490 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#395×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×#391×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1444	C₂	1	2	yes	maximal
5	C₁₁₃×#1442	C₂	1	2	yes	maximal
6	C₁₁₃×#1441	C₂	1	4	yes	maximal
7	C₁₁₃×#1441	C₂	1	2	yes	maximal
8	C₁₁₃×#1434	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂×#125×C₁₁₃	—	2	8	no	—
11	C₂×#125×C₁₁₃	—	2	4	no	—
12	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
19	#395×C₁₁₃	—	2	8	no	—
20	#391×C₁₁₃	—	2	4	no	—
21	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
22	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
23	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
24	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
25	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
26	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
27	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
29	C₂²×Q₈×C₁₁₃	—	2	2	no	—
30	C₂²×Q₈×C₁₁₃	—	2	4	no	—
31	C₂²×Q₈×C₁₁₃	—	2	4	no	—
32	C₂²×Q₈×C₁₁₃	—	4	2	no	—
33	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
41	#125×C₁₁₃	—	2	32	no	—
42	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
53	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
54	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
55	C₂×C₄⋊C₄×C₁₁₃	—	4	2	no	—
56	C₂×C₄⋊C₄×C₁₁₃	D₄	1	8	yes	—
57	C₂×C₄²×C₁₁₃	—	2	4	no	—
58	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
59	#95×C₁₁₃	—	2	4	no	—
60	#95×C₁₁₃	—	2	4	no	—
61	#95×C₁₁₃	—	2	4	no	—
62	#95×C₁₁₃	—	2	8	no	—
63	#95×C₁₁₃	—	4	2	no	—
64	#95×C₁₁₃	—	4	4	no	—
65	#95×C₁₁₃	—	4	4	no	—
66	#95×C₁₁₃	Q₈	1	8	yes	complemented
67	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
68	C₂×Q₈×C₁₁₃	—	2	8	no	—
69	C₂×Q₈×C₁₁₃	—	4	16	no	—
70	C₂×Q₈×C₁₁₃	—	4	4	no	—
71	C₂×Q₈×C₁₁₃	—	4	4	no	—
72	C₂²×C₄×C₁₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂×Q₈	1	8	yes	—
112	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
114	C₄⋊C₄×C₁₁₃	—	2	8	no	—
115	C₄⋊C₄×C₁₁₃	—	2	8	no	—
116	C₄⋊C₄×C₁₁₃	—	2	16	no	—
117	C₄⋊C₄×C₁₁₃	—	2	16	no	—
118	C₄⋊C₄×C₁₁₃	—	4	16	no	—
119	C₄⋊C₄×C₁₁₃	—	4	4	no	—
120	C₄²×C₁₁₃	—	2	8	no	—
121	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
122	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
123	C₂³×C₁₁₃	C₂²×Q₈	1	2	yes	—
124	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
125	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
126	C₂³×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
127	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
128	C₂³×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
129	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
130	Q₈×C₁₁₃	—	4	16	no	—
131	C₂×C₄×C₁₁₃	—	2	2	no	—
132	C₂×C₄×C₁₁₃	—	2	2	no	—
133	C₂×C₄×C₁₁₃	—	2	2	no	—
134	C₂×C₄×C₁₁₃	—	2	2	no	—
135	C₂×C₄×C₁₁₃	—	2	8	no	—
136	C₂×C₄×C₁₁₃	—	2	8	no	—
137	C₂×C₄×C₁₁₃	—	2	2	no	—
138	C₂×C₄×C₁₁₃	—	2	4	no	—
139	C₂×C₄×C₁₁₃	—	2	4	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	2	no	—
144	C₂×C₄×C₁₁₃	—	2	4	no	—
145	C₂×C₄×C₁₁₃	—	2	8	no	—
146	C₂×C₄×C₁₁₃	—	2	8	no	—
147	C₂×C₄×C₁₁₃	—	2	8	no	—
148	C₂×C₄×C₁₁₃	—	2	8	no	—
149	C₂×C₄×C₁₁₃	—	2	8	no	—
150	C₂×C₄×C₁₁₃	—	4	2	no	—
151	C₂×C₄×C₁₁₃	—	4	2	no	—
152	C₂×C₄×C₁₁₃	—	4	2	no	—
153	C₂×C₄×C₁₁₃	—	4	2	no	—
154	C₂×C₄×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	4	2	no	—
158	C₂×C₄×C₁₁₃	—	4	2	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	—	4	4	no	—
161	C₂×C₄×C₁₁₃	—	4	4	no	—
162	C₂×C₄×C₁₁₃	—	4	4	no	—
163	C₂×C₄×C₁₁₃	—	4	4	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	4	no	—
166	C₂×C₄×C₁₁₃	—	4	2	no	—
167	C₂×C₄×C₁₁₃	—	4	2	no	—
168	C₂×C₄×C₁₁₃	—	4	2	no	—
169	C₂×C₄×C₁₁₃	—	4	4	no	—
170	C₂×C₄×C₁₁₃	—	4	4	no	—
171	C₂×C₄×C₁₁₃	#120	1	4	yes	—
172	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	4	yes	—
173	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
174	C₂²×C₁₁₃	#525	1	1	yes	characteristic
175	C₂²×C₁₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
176	C₂²×C₁₁₃	#535	1	1	yes	characteristic
177	C₂²×C₁₁₃	#536	1	1	yes	characteristic
178	C₂²×C₁₁₃	#536	1	1	yes	characteristic
179	C₂²×C₁₁₃	#536	1	2	yes	—
180	C₂²×C₁₁₃	#537	1	1	yes	characteristic
181	C₂²×C₁₁₃	#537	1	2	yes	—
182	C₂²×C₁₁₃	#541	1	4	yes	—
183	C₂²×C₁₁₃	#544	1	4	yes	—
184	C₂²×C₁₁₃	#546	1	4	yes	—
185	C₂²×C₁₁₃	D₄×Q₈	1	4	yes	—
186	C₂²×C₁₁₃	#554	1	2	yes	—
187	C₂²×C₁₁₃	#557	1	2	yes	—
188	C₂²×C₁₁₃	#562	1	2	yes	—
189	C₂²×C₁₁₃	#563	1	2	yes	—
190	C₄×C₁₁₃	—	2	4	no	—
191	C₄×C₁₁₃	—	2	4	no	—
192	C₄×C₁₁₃	—	4	2	no	—
193	C₄×C₁₁₃	—	4	4	no	—
194	C₄×C₁₁₃	—	4	4	no	—
195	C₄×C₁₁₃	—	4	4	no	—
196	C₄×C₁₁₃	—	4	8	no	—
197	C₄×C₁₁₃	—	8	2	no	—
198	#16608	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₁₁₃	#2404	1	1	yes	characteristic
200	C₂×C₁₁₃	#2434	1	1	yes	characteristic
201	C₂×C₁₁₃	#2584	1	1	yes	characteristic
202	C₂×C₁₁₃	#2616	1	1	yes	characteristic
203	C₂×C₁₁₃	#2634	1	1	yes	characteristic
204	C₂×C₁₁₃	#2660	1	1	yes	characteristic
205	C₂×C₁₁₃	#2704	1	4	yes	—
206	C₂×C₁₁₃	#2713	1	4	yes	—
207	C₂×C₁₁₃	#2820	1	1	yes	characteristic
208	C₂²×#125	C₂×C₁₁₃	1	1	yes	characteristic
209	C₂×#395	C₂×C₁₁₃	1	2	yes	—
210	C₂×#391	C₂×C₁₁₃	1	1	yes	characteristic
211	#1444	C₂×C₁₁₃	1	2	yes	—
212	#1442	C₂×C₁₁₃	1	2	yes	—
213	#1441	C₂×C₁₁₃	1	4	yes	—
214	#1441	C₂×C₁₁₃	1	2	yes	—
215	#1434	C₂×C₁₁₃	1	1	yes	characteristic
216	C₁₁₃	#16608	1	1	yes	characteristic, direct product factor, Sylow
217	C₂³×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
218	C₂×#125	—	2	8	no	—
219	C₂×#125	—	2	4	no	—
220	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
226	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
227	#395	—	2	8	no	—
228	#391	—	2	4	no	—
229	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
230	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
231	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
232	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
233	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
234	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
235	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
236	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	—	2	4	no	—
239	C₂²×Q₈	—	2	4	no	—
240	C₂²×Q₈	—	4	2	no	—
241	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
243	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
246	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
247	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
249	#125	—	2	32	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	8	no	—
261	C₂×C₄⋊C₄	—	2	8	no	—
262	C₂×C₄⋊C₄	—	4	4	no	—
263	C₂×C₄⋊C₄	—	4	2	no	—
264	C₂×C₄⋊C₄	D₄×C₁₁₃	1	8	yes	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
267	#95	—	2	4	no	—
268	#95	—	2	4	no	—
269	#95	—	2	4	no	—
270	#95	—	2	8	no	—
271	#95	—	4	2	no	—
272	#95	—	4	4	no	—
273	#95	—	4	4	no	—
274	#95	Q₈×C₁₁₃	1	8	yes	complemented
275	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	4	16	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
315	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
316	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
317	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
319	C₂²×C₄	C₂×Q₈×C₁₁₃	1	8	yes	—
320	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
321	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	16	no	—
325	C₄⋊C₄	—	2	16	no	—
326	C₄⋊C₄	—	4	16	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄²	—	2	8	no	—
329	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
330	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
331	C₂³	C₂²×Q₈×C₁₁₃	1	2	yes	—
332	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
333	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
334	C₂³	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
335	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
336	C₂³	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
337	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
338	Q₈	—	4	16	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	#120×C₁₁₃	1	4	yes	—
380	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	4	yes	—
381	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
382	C₂²	#525×C₁₁₃	1	1	yes	characteristic
383	C₂²	C₂×C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
384	C₂²	#535×C₁₁₃	1	1	yes	characteristic
385	C₂²	#536×C₁₁₃	1	1	yes	characteristic
386	C₂²	#536×C₁₁₃	1	1	yes	characteristic
387	C₂²	#536×C₁₁₃	1	2	yes	—
388	C₂²	#537×C₁₁₃	1	1	yes	characteristic
389	C₂²	#537×C₁₁₃	1	2	yes	—
390	C₂²	#541×C₁₁₃	1	4	yes	—
391	C₂²	#544×C₁₁₃	1	4	yes	—
392	C₂²	#546×C₁₁₃	1	4	yes	—
393	C₂²	D₄×Q₈×C₁₁₃	1	4	yes	—
394	C₂²	#554×C₁₁₃	1	2	yes	—
395	C₂²	#557×C₁₁₃	1	2	yes	—
396	C₂²	#562×C₁₁₃	1	2	yes	—
397	C₂²	#563×C₁₁₃	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	8	no	—
405	C₄	—	8	2	no	—
406	C₂	C₁₁₃×#2404	1	1	yes	characteristic
407	C₂	C₁₁₃×#2434	1	1	yes	characteristic
408	C₂	C₁₁₃×#2584	1	1	yes	characteristic
409	C₂	C₁₁₃×#2616	1	1	yes	characteristic
410	C₂	C₁₁₃×#2634	1	1	yes	characteristic
411	C₂	C₁₁₃×#2660	1	1	yes	characteristic
412	C₂	C₁₁₃×#2704	1	4	yes	—
413	C₂	C₁₁₃×#2713	1	4	yes	—
414	C₂	C₁₁₃×#2820	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
66. #95×C₁₁₃	Q₈	semidirect
198. #16608	C₁₁₃	direct (N × H)
216. C₁₁₃	#16608	direct (N × H)
274. #95	Q₈×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₁₁₃	2
C₂×#395×C₁₁₃	2
C₂×#391×C₁₁₃	2
C₁₁₃×#1444	2
C₁₁₃×#1442	2
C₁₁₃×#1441	2
C₁₁₃×#1434	2
#16608	113

Subgroups — C113×#16608 #43284628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#16608 #43284628