Subgroups — C₁₁₃×#15180 #43283200

Order 28928.

1750 conjugacy classes of subgroups.

The subgroup lattice has 374 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	C₂×#391×C₁₁₃	C₂	1	2	yes	maximal
3	C₂×#391×C₁₁₃	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₁₃×#1442	C₂	1	4	yes	maximal
6	C₁₁₃×#1441	C₂	1	4	yes	maximal
7	C₁₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₁₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₁₁₃	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₁₁₃	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
17	#391×C₁₁₃	—	2	8	no	—
18	#391×C₁₁₃	—	2	8	no	—
19	C₄×C₄⋊C₄×C₁₁₃	—	2	4	no	—
20	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
21	C₂×#95×C₁₁₃	C₂²	1	8	yes	—
22	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
23	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
24	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
25	C₂²×Q₈×C₁₁₃	—	2	4	no	—
26	C₂²×Q₈×C₁₁₃	—	2	4	no	—
27	C₂²×Q₈×C₁₁₃	—	2	4	no	—
28	C₂²×Q₈×C₁₁₃	—	2	4	no	—
29	C₂²×Q₈×C₁₁₃	—	2	4	no	—
30	C₂²×Q₈×C₁₁₃	—	2	4	no	—
31	C₂²×Q₈×C₁₁₃	D₄	1	8	yes	—
32	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₄⋊Q₈×C₁₁₃	—	2	32	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	16	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	8	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	Q₈	1	8	yes	complemented
48	C₂×C₄²×C₁₁₃	—	2	4	no	—
49	C₂×C₄²×C₁₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₁₃	—	2	4	no	—
53	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
54	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
55	#95×C₁₁₃	—	2	4	no	—
56	#95×C₁₁₃	—	2	16	no	—
57	#95×C₁₁₃	—	2	8	no	—
58	#95×C₁₁₃	—	2	8	no	—
59	#95×C₁₁₃	—	2	8	no	—
60	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
61	C₂×Q₈×C₁₁₃	—	2	16	no	—
62	C₂×Q₈×C₁₁₃	—	2	16	no	—
63	C₂×Q₈×C₁₁₃	—	2	16	no	—
64	C₂×Q₈×C₁₁₃	—	4	8	no	—
65	C₂×Q₈×C₁₁₃	—	4	8	no	—
66	C₂×Q₈×C₁₁₃	—	4	8	no	—
67	C₂×Q₈×C₁₁₃	—	4	8	no	—
68	C₂²×C₄×C₁₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₁₃	—	2	1	no	—
71	C₂²×C₄×C₁₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₁₃	—	2	1	no	—
74	C₂²×C₄×C₁₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₁₃	—	2	4	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	8	no	—
91	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
93	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
100	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
102	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
103	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
104	C₄⋊C₄×C₁₁₃	—	2	32	no	—
105	C₄⋊C₄×C₁₁₃	—	2	16	no	—
106	C₄⋊C₄×C₁₁₃	—	4	8	no	—
107	C₄²×C₁₁₃	—	2	8	no	—
108	C₄²×C₁₁₃	—	2	8	no	—
109	C₄²×C₁₁₃	—	4	4	no	—
110	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
111	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
112	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
113	C₂³×C₁₁₃	C₂²×Q₈	1	2	yes	—
114	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
115	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
116	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
117	C₂³×C₁₁₃	2₋¹⁺⁴	1	4	yes	—
118	Q₈×C₁₁₃	—	4	32	no	—
119	C₂×C₄×C₁₁₃	—	2	4	no	—
120	C₂×C₄×C₁₁₃	—	2	2	no	—
121	C₂×C₄×C₁₁₃	—	2	4	no	—
122	C₂×C₄×C₁₁₃	—	2	2	no	—
123	C₂×C₄×C₁₁₃	—	2	4	no	—
124	C₂×C₄×C₁₁₃	—	2	4	no	—
125	C₂×C₄×C₁₁₃	—	2	8	no	—
126	C₂×C₄×C₁₁₃	—	2	8	no	—
127	C₂×C₄×C₁₁₃	—	2	8	no	—
128	C₂×C₄×C₁₁₃	—	2	2	no	—
129	C₂×C₄×C₁₁₃	—	2	8	no	—
130	C₂×C₄×C₁₁₃	—	2	4	no	—
131	C₂×C₄×C₁₁₃	—	2	8	no	—
132	C₂×C₄×C₁₁₃	—	2	4	no	—
133	C₂×C₄×C₁₁₃	—	2	8	no	—
134	C₂×C₄×C₁₁₃	—	4	2	no	—
135	C₂×C₄×C₁₁₃	—	4	4	no	—
136	C₂×C₄×C₁₁₃	—	4	4	no	—
137	C₂×C₄×C₁₁₃	—	4	4	no	—
138	C₂×C₄×C₁₁₃	—	4	4	no	—
139	C₂×C₄×C₁₁₃	—	4	2	no	—
140	C₂×C₄×C₁₁₃	—	4	2	no	—
141	C₂×C₄×C₁₁₃	—	4	2	no	—
142	C₂×C₄×C₁₁₃	—	4	4	no	—
143	C₂×C₄×C₁₁₃	—	4	4	no	—
144	C₂×C₄×C₁₁₃	—	4	4	no	—
145	C₂×C₄×C₁₁₃	—	4	4	no	—
146	C₂×C₄×C₁₁₃	—	4	8	no	—
147	C₂×C₄×C₁₁₃	—	4	8	no	—
148	C₂×C₄×C₁₁₃	#120	1	4	yes	—
149	C₂×C₄×C₁₁₃	#121	1	4	yes	—
150	C₂×C₄×C₁₁₃	#121	1	8	yes	—
151	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	8	yes	—
152	C₂×C₄×C₁₁₃	#123	1	8	yes	—
153	C₂×C₄×C₁₁₃	#124	1	4	yes	—
154	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	4	yes	complemented
155	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
156	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
157	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
158	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
159	C₂²×C₁₁₃	C₂×#123	1	2	yes	—
160	C₂²×C₁₁₃	C₂×#124	1	1	yes	characteristic
161	C₂²×C₁₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
162	C₂²×C₁₁₃	#532	1	1	yes	characteristic
163	C₂²×C₁₁₃	#533	1	2	yes	—
164	C₂²×C₁₁₃	#536	1	2	yes	—
165	C₂²×C₁₁₃	#536	1	2	yes	—
166	C₂²×C₁₁₃	#541	1	2	yes	—
167	C₂²×C₁₁₃	#548	1	4	yes	—
168	C₂²×C₁₁₃	D₄×Q₈	1	4	yes	—
169	C₂²×C₁₁₃	#556	1	4	yes	—
170	C₂²×C₁₁₃	#557	1	4	yes	—
171	C₄×C₁₁₃	—	2	4	no	—
172	C₄×C₁₁₃	—	2	8	no	—
173	C₄×C₁₁₃	—	4	2	no	—
174	C₄×C₁₁₃	—	4	8	no	—
175	C₄×C₁₁₃	—	4	4	no	—
176	C₄×C₁₁₃	—	8	4	no	—
177	C₄×C₁₁₃	#394	1	8	yes	—
178	#15180	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₁₁₃	C₂×#394	1	1	yes	characteristic
180	C₂×C₁₁₃	#2409	1	2	yes	—
181	C₂×C₁₁₃	#2446	1	4	yes	—
182	C₂×C₁₁₃	#2545	1	2	yes	—
183	C₂×C₁₁₃	#2546	1	2	yes	—
184	C₂×C₁₁₃	#2568	1	2	yes	—
185	C₂×C₁₁₃	#2621	1	1	yes	characteristic
186	C₂×C₁₁₃	#2857	1	1	yes	characteristic
187	C₂²×C₄⋊Q₈	C₂×C₁₁₃	1	1	yes	characteristic
188	C₂×#391	C₂×C₁₁₃	1	2	yes	—
189	C₂×#391	C₂×C₁₁₃	1	2	yes	—
190	C₂×C₄×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
191	#1442	C₂×C₁₁₃	1	4	yes	—
192	#1441	C₂×C₁₁₃	1	4	yes	—
193	C₄⋊#95	C₂×C₁₁₃	1	1	yes	characteristic
194	C₁₁₃	#15180	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³×Q₈	C₂²×C₁₁₃	1	2	yes	—
196	C₂×C₄⋊Q₈	—	2	8	no	—
197	C₂×C₄⋊Q₈	—	2	4	no	—
198	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
200	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
201	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
203	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
204	#391	—	2	8	no	—
205	#391	—	2	8	no	—
206	C₄×C₄⋊C₄	—	2	4	no	—
207	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
208	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
209	C₂×#95	C₂²×C₁₁₃	1	8	yes	—
210	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
211	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
212	C₂²×Q₈	—	2	4	no	—
213	C₂²×Q₈	—	2	4	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	—	2	4	no	—
218	C₂²×Q₈	D₄×C₁₁₃	1	8	yes	—
219	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
221	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
223	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
225	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
226	C₄⋊Q₈	—	2	32	no	—
227	C₂×C₄⋊C₄	—	2	16	no	—
228	C₂×C₄⋊C₄	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	Q₈×C₁₁₃	1	8	yes	complemented
235	C₂×C₄²	—	2	4	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	4	no	—
240	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
241	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
242	#95	—	2	4	no	—
243	#95	—	2	16	no	—
244	#95	—	2	8	no	—
245	#95	—	2	8	no	—
246	#95	—	2	8	no	—
247	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
248	C₂×Q₈	—	2	16	no	—
249	C₂×Q₈	—	2	16	no	—
250	C₂×Q₈	—	2	16	no	—
251	C₂×Q₈	—	4	8	no	—
252	C₂×Q₈	—	4	8	no	—
253	C₂×Q₈	—	4	8	no	—
254	C₂×Q₈	—	4	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
280	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
281	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
283	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
285	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
286	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
287	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
288	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
289	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
290	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
291	C₄⋊C₄	—	2	32	no	—
292	C₄⋊C₄	—	2	16	no	—
293	C₄⋊C₄	—	4	8	no	—
294	C₄²	—	2	8	no	—
295	C₄²	—	2	8	no	—
296	C₄²	—	4	4	no	—
297	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
298	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
299	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
300	C₂³	C₂²×Q₈×C₁₁₃	1	2	yes	—
301	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
302	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
303	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
304	C₂³	2₋¹⁺⁴×C₁₁₃	1	4	yes	—
305	Q₈	—	4	32	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	#120×C₁₁₃	1	4	yes	—
336	C₂×C₄	#121×C₁₁₃	1	4	yes	—
337	C₂×C₄	#121×C₁₁₃	1	8	yes	—
338	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	8	yes	—
339	C₂×C₄	#123×C₁₁₃	1	8	yes	—
340	C₂×C₄	#124×C₁₁₃	1	4	yes	—
341	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	4	yes	complemented
342	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
343	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
344	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
345	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
346	C₂²	C₂×#123×C₁₁₃	1	2	yes	—
347	C₂²	C₂×#124×C₁₁₃	1	1	yes	characteristic
348	C₂²	C₂×C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
349	C₂²	#532×C₁₁₃	1	1	yes	characteristic
350	C₂²	#533×C₁₁₃	1	2	yes	—
351	C₂²	#536×C₁₁₃	1	2	yes	—
352	C₂²	#536×C₁₁₃	1	2	yes	—
353	C₂²	#541×C₁₁₃	1	2	yes	—
354	C₂²	#548×C₁₁₃	1	4	yes	—
355	C₂²	D₄×Q₈×C₁₁₃	1	4	yes	—
356	C₂²	#556×C₁₁₃	1	4	yes	—
357	C₂²	#557×C₁₁₃	1	4	yes	—
358	C₄	—	2	4	no	—
359	C₄	—	2	8	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	4	no	—
363	C₄	—	8	4	no	—
364	C₄	#394×C₁₁₃	1	8	yes	—
365	C₂	C₂×#394×C₁₁₃	1	1	yes	characteristic
366	C₂	C₁₁₃×#2409	1	2	yes	—
367	C₂	C₁₁₃×#2446	1	4	yes	—
368	C₂	C₁₁₃×#2545	1	2	yes	—
369	C₂	C₁₁₃×#2546	1	2	yes	—
370	C₂	C₁₁₃×#2568	1	2	yes	—
371	C₂	C₁₁₃×#2621	1	1	yes	characteristic
372	C₂	C₁₁₃×#2857	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
47. C₂×C₄⋊C₄×C₁₁₃	Q₈	semidirect
154. C₂×C₄×C₁₁₃	C₄⋊Q₈	semidirect
178. #15180	C₁₁₃	direct (N × H)
194. C₁₁₃	#15180	direct (N × H)
234. C₂×C₄⋊C₄	Q₈×C₁₁₃	semidirect
341. C₂×C₄	C₄⋊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×C₄⋊Q₈×C₁₁₃	2
C₂×#391×C₁₁₃	2
C₂×C₄×C₄⋊C₄×C₁₁₃	2
C₁₁₃×#1442	2
C₁₁₃×#1441	2
C₁₁₃×C₄⋊#95	2
#15180	113

Subgroups — C113×#15180 #43283200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#15180 #43283200