Subgroups — C₁₁₃×#21219 #43289239

Order 28928.

1646 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#413×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁₃×#1967	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1965	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
12	#535×C₁₁₃	—	2	4	no	—
13	#535×C₁₁₃	—	2	4	no	—
14	C₂×#127×C₁₁₃	C₂²	1	2	yes	—
15	C₂×#124×C₁₁₃	C₂²	1	2	yes	—
16	C₂×#121×C₁₁₃	C₄	1	4	yes	—
17	C₂×#120×C₁₁₃	C₄	1	4	yes	—
18	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
19	#424×C₁₁₃	—	2	4	no	—
20	#423×C₁₁₃	C₂²	1	4	yes	complemented
21	#413×C₁₁₃	—	2	8	no	—
22	C₂×#101×C₁₁₃	C₂²	1	4	yes	complemented
23	C₂×#100×C₁₁₃	—	2	8	no	—
24	C₂×#100×C₁₁₃	C₂²	1	8	yes	—
25	C₂×#100×C₁₁₃	C₂²	1	4	yes	complemented
26	#405×C₁₁₃	—	2	4	no	—
27	C₄×M₁₆×C₁₁₃	C₂²	1	4	yes	complemented
28	C₂⁵×C₁₁₃	C₂×C₄	1	2	yes	—
29	C₂×#41×C₁₁₃	—	2	2	no	—
30	C₂×#41×C₁₁₃	—	2	2	no	—
31	C₂×#41×C₁₁₃	—	2	4	no	—
32	C₂×#41×C₁₁₃	—	2	4	no	—
33	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
34	C₂²×D₄×C₁₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₁₃	—	2	4	no	—
38	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
40	C₂²×D₄×C₁₁₃	C₂×C₄	1	8	yes	—
41	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₁₃	—	2	2	no	—
46	C₂×M₁₆×C₁₁₃	—	2	4	no	—
47	C₂×M₁₆×C₁₁₃	—	2	2	no	—
48	C₂×M₁₆×C₁₁₃	—	2	4	no	—
49	C₂×M₁₆×C₁₁₃	—	2	4	no	—
50	C₂×M₁₆×C₁₁₃	D₄	1	8	yes	complemented
51	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
52	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
53	C₂²×C₈×C₁₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₁₃	—	2	2	no	—
55	#127×C₁₁₃	—	2	4	no	—
56	#127×C₁₁₃	—	2	4	no	—
57	#124×C₁₁₃	—	2	4	no	—
58	#124×C₁₁₃	—	2	4	no	—
59	#121×C₁₁₃	—	2	16	no	—
60	#120×C₁₁₃	—	2	16	no	—
61	#117×C₁₁₃	D₄	1	4	yes	—
62	#117×C₁₁₃	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	8	yes	—
65	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₁₃	—	2	8	no	—
68	#101×C₁₁₃	—	2	8	no	—
69	#100×C₁₁₃	—	2	16	no	—
70	#100×C₁₁₃	—	2	8	no	—
71	#97×C₁₁₃	—	2	4	no	—
72	C₄×C₈×C₁₁₃	—	2	4	no	—
73	C₂⁴×C₁₁₃	—	2	4	no	—
74	C₂⁴×C₁₁₃	—	2	8	no	—
75	C₂⁴×C₁₁₃	—	8	4	no	—
76	C₂⁴×C₁₁₃	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
78	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
79	#41×C₁₁₃	—	4	4	no	—
80	#41×C₁₁₃	—	4	4	no	—
81	#41×C₁₁₃	—	4	4	no	—
82	#41×C₁₁₃	—	4	4	no	—
83	C₂×Q₈×C₁₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₁₃	—	2	2	no	—
87	C₂×D₄×C₁₁₃	—	2	4	no	—
88	C₂×D₄×C₁₁₃	—	2	8	no	—
89	C₂×D₄×C₁₁₃	—	2	4	no	—
90	C₂×D₄×C₁₁₃	—	2	16	no	—
91	C₂×D₄×C₁₁₃	—	2	8	no	—
92	C₂×D₄×C₁₁₃	—	2	4	no	—
93	C₂×D₄×C₁₁₃	—	2	2	no	—
94	C₂×D₄×C₁₁₃	—	2	2	no	—
95	C₂×D₄×C₁₁₃	—	2	2	no	—
96	C₂×D₄×C₁₁₃	—	2	1	no	—
97	C₂×D₄×C₁₁₃	—	2	1	no	—
98	C₂×D₄×C₁₁₃	—	2	4	no	—
99	C₂×D₄×C₁₁₃	—	2	2	no	—
100	C₂×D₄×C₁₁₃	—	4	4	no	—
101	C₂×D₄×C₁₁₃	—	4	4	no	—
102	C₂×D₄×C₁₁₃	—	4	4	no	—
103	C₂×D₄×C₁₁₃	—	4	4	no	—
104	C₂×D₄×C₁₁₃	—	8	8	no	—
105	C₂²×C₄×C₁₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₁₃	—	2	8	no	—
107	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
114	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₁₁₃	—	2	8	no	—
116	M₁₆×C₁₁₃	—	2	4	no	—
117	M₁₆×C₁₁₃	—	2	4	no	—
118	M₁₆×C₁₁₃	—	2	4	no	—
119	M₁₆×C₁₁₃	—	4	4	no	—
120	M₁₆×C₁₁₃	C₂×D₄	1	8	yes	—
121	C₂×C₈×C₁₁₃	—	2	8	no	—
122	C₂×C₈×C₁₁₃	—	2	4	no	—
123	C₂×C₈×C₁₁₃	—	2	4	no	—
124	C₂×C₈×C₁₁₃	—	4	4	no	—
125	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
126	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
127	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
128	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
129	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
130	C₂³×C₁₁₃	—	2	4	no	—
131	C₂³×C₁₁₃	—	2	2	no	—
132	C₂³×C₁₁₃	—	2	4	no	—
133	C₂³×C₁₁₃	—	2	8	no	—
134	C₂³×C₁₁₃	—	4	2	no	—
135	C₂³×C₁₁₃	—	4	4	no	—
136	C₂³×C₁₁₃	—	4	8	no	—
137	C₂³×C₁₁₃	—	4	8	no	—
138	C₂³×C₁₁₃	—	8	8	no	—
139	C₂³×C₁₁₃	—	8	16	no	—
140	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₁₁₃	C₄×D₄	1	4	yes	—
142	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
143	Q₈×C₁₁₃	—	4	2	no	—
144	Q₈×C₁₁₃	—	4	1	no	—
145	Q₈×C₁₁₃	—	4	1	no	—
146	D₄×C₁₁₃	—	4	8	no	—
147	D₄×C₁₁₃	—	4	4	no	—
148	D₄×C₁₁₃	—	4	2	no	—
149	D₄×C₁₁₃	—	4	2	no	—
150	D₄×C₁₁₃	—	4	1	no	—
151	D₄×C₁₁₃	—	4	2	no	—
152	D₄×C₁₁₃	—	4	1	no	—
153	D₄×C₁₁₃	—	4	8	no	—
154	D₄×C₁₁₃	—	8	16	no	—
155	C₂×C₄×C₁₁₃	—	2	2	no	—
156	C₂×C₄×C₁₁₃	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	4	4	no	—
158	C₂×C₄×C₁₁₃	—	4	8	no	—
159	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	8	yes	—
160	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
162	C₂×C₄×C₁₁₃	#121	1	4	yes	—
163	C₂×C₄×C₁₁₃	#121	1	4	yes	—
164	C₂×C₄×C₁₁₃	#124	1	4	yes	—
165	C₂×C₄×C₁₁₃	#127	1	4	yes	—
166	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
170	C₈×C₁₁₃	—	2	8	no	—
171	C₈×C₁₁₃	—	4	4	no	—
172	C₂²×C₁₁₃	—	2	2	no	—
173	C₂²×C₁₁₃	—	2	4	no	—
174	C₂²×C₁₁₃	—	4	4	no	—
175	C₂²×C₁₁₃	—	4	4	no	—
176	C₂²×C₁₁₃	—	4	8	no	—
177	C₂²×C₁₁₃	—	4	2	no	—
178	C₂²×C₁₁₃	—	4	4	no	—
179	C₂²×C₁₁₃	—	8	4	no	—
180	C₂²×C₁₁₃	—	8	8	no	—
181	C₂²×C₁₁₃	—	8	16	no	—
182	C₂²×C₁₁₃	#390	1	4	yes	—
183	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
185	C₄×C₁₁₃	—	2	8	no	—
186	C₄×C₁₁₃	—	4	2	no	—
187	C₄×C₁₁₃	#390	1	4	yes	—
188	C₄×C₁₁₃	C₂×#121	1	2	yes	—
189	C₄×C₁₁₃	C₂×#124	1	1	yes	characteristic
190	C₄×C₁₁₃	C₂×#127	1	1	yes	characteristic
191	#21219	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₁₁₃	—	2	2	no	—
193	C₂×C₁₁₃	—	2	4	no	—
194	C₂×C₁₁₃	—	8	2	no	—
195	C₂×C₁₁₃	—	8	4	no	—
196	C₂×C₁₁₃	C₂×#390	1	1	yes	characteristic
197	C₂×C₁₁₃	#2888	1	2	yes	—
198	C₂×#535	C₂×C₁₁₃	1	1	yes	characteristic
199	#2905	C₂×C₁₁₃	1	1	yes	characteristic, complemented
200	C₂×#413	C₂×C₁₁₃	1	2	yes	complemented
201	C₂²×#100	C₂×C₁₁₃	1	2	yes	complemented
202	#2873	C₂×C₁₁₃	1	1	yes	characteristic, complemented
203	#1967	C₂×C₁₁₃	1	4	yes	complemented
204	#1965	C₂×C₁₁₃	1	4	yes	complemented
205	C₁₁₃	#21219	1	1	yes	characteristic, direct product factor, Sylow
206	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
207	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
209	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
210	#535	—	2	4	no	—
211	#535	—	2	4	no	—
212	C₂×#127	C₂²×C₁₁₃	1	2	yes	—
213	C₂×#124	C₂²×C₁₁₃	1	2	yes	—
214	C₂×#121	C₄×C₁₁₃	1	4	yes	—
215	C₂×#120	C₄×C₁₁₃	1	4	yes	—
216	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
217	#424	—	2	4	no	—
218	#423	C₂²×C₁₁₃	1	4	yes	complemented
219	#413	—	2	8	no	—
220	C₂×#101	C₂²×C₁₁₃	1	4	yes	complemented
221	C₂×#100	—	2	8	no	—
222	C₂×#100	C₂²×C₁₁₃	1	8	yes	—
223	C₂×#100	C₂²×C₁₁₃	1	4	yes	complemented
224	#405	—	2	4	no	—
225	C₄×M₁₆	C₂²×C₁₁₃	1	4	yes	complemented
226	C₂⁵	C₂×C₄×C₁₁₃	1	2	yes	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	4	no	—
230	C₂×#41	—	2	4	no	—
231	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
237	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
238	C₂²×D₄	C₂×C₄×C₁₁₃	1	8	yes	—
239	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
240	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
241	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	D₄×C₁₁₃	1	8	yes	complemented
249	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
250	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	#127	—	2	4	no	—
254	#127	—	2	4	no	—
255	#124	—	2	4	no	—
256	#124	—	2	4	no	—
257	#121	—	2	16	no	—
258	#120	—	2	16	no	—
259	#117	D₄×C₁₁₃	1	4	yes	—
260	#117	D₄×C₁₁₃	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	8	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
265	C₄⋊C₈	—	2	8	no	—
266	#101	—	2	8	no	—
267	#100	—	2	16	no	—
268	#100	—	2	8	no	—
269	#97	—	2	4	no	—
270	C₄×C₈	—	2	4	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	—	8	4	no	—
274	C₂⁴	C₂²×C₄×C₁₁₃	1	4	yes	—
275	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
276	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
277	#41	—	4	4	no	—
278	#41	—	4	4	no	—
279	#41	—	4	4	no	—
280	#41	—	4	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	8	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
311	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
313	M₁₆	—	2	8	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	2	4	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	4	4	no	—
318	M₁₆	C₂×D₄×C₁₁₃	1	8	yes	—
319	C₂×C₈	—	2	8	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	4	4	no	—
323	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
324	C₂²⋊C₄	—	2	16	no	—
325	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
326	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
327	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	8	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	8	8	no	—
337	C₂³	—	8	16	no	—
338	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
339	C₂³	C₄×D₄×C₁₁₃	1	4	yes	—
340	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
341	Q₈	—	4	2	no	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	1	no	—
344	D₄	—	4	8	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	8	no	—
352	D₄	—	8	16	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	8	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
359	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
360	C₂×C₄	#121×C₁₁₃	1	4	yes	—
361	C₂×C₄	#121×C₁₁₃	1	4	yes	—
362	C₂×C₄	#124×C₁₁₃	1	4	yes	—
363	C₂×C₄	#127×C₁₁₃	1	4	yes	—
364	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
368	C₈	—	2	8	no	—
369	C₈	—	4	4	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	8	8	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	8	16	no	—
380	C₂²	#390×C₁₁₃	1	4	yes	—
381	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
382	C₂²	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
383	C₄	—	2	8	no	—
384	C₄	—	4	2	no	—
385	C₄	#390×C₁₁₃	1	4	yes	—
386	C₄	C₂×#121×C₁₁₃	1	2	yes	—
387	C₄	C₂×#124×C₁₁₃	1	1	yes	characteristic
388	C₄	C₂×#127×C₁₁₃	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	4	no	—
391	C₂	—	8	4	no	—
392	C₂	—	8	2	no	—
393	C₂	C₂×#390×C₁₁₃	1	1	yes	characteristic
394	C₂	C₁₁₃×#2888	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂×#535×C₁₁₃	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂×#117×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₃×#2905	C₂	semidirect
3. C₂×#413×C₁₁₃	C₂	semidirect
4. C₂²×#100×C₁₁₃	C₂	semidirect
5. C₁₁₃×#2873	C₂	semidirect
6. C₁₁₃×#1967	C₂	semidirect
7. C₁₁₃×#1965	C₂	semidirect
20. #423×C₁₁₃	C₂²	semidirect
22. C₂×#101×C₁₁₃	C₂²	semidirect
25. C₂×#100×C₁₁₃	C₂²	semidirect
27. C₄×M₁₆×C₁₁₃	C₂²	semidirect
50. C₂×M₁₆×C₁₁₃	D₄	semidirect
191. #21219	C₁₁₃	direct (N × H)
199. #2905	C₂×C₁₁₃	semidirect
200. C₂×#413	C₂×C₁₁₃	semidirect
201. C₂²×#100	C₂×C₁₁₃	semidirect
202. #2873	C₂×C₁₁₃	semidirect
203. #1967	C₂×C₁₁₃	semidirect
204. #1965	C₂×C₁₁₃	semidirect
205. C₁₁₃	#21219	direct (N × H)
218. #423	C₂²×C₁₁₃	semidirect
220. C₂×#101	C₂²×C₁₁₃	semidirect
223. C₂×#100	C₂²×C₁₁₃	semidirect
225. C₄×M₁₆	C₂²×C₁₁₃	semidirect
248. C₂×M₁₆	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₁₁₃	2
C₁₁₃×#2905	2
C₂×#413×C₁₁₃	2
C₂²×#100×C₁₁₃	2
C₁₁₃×#2873	2
C₁₁₃×#1967	2
C₁₁₃×#1965	2
#21219	113

Subgroups — C113×#21219 #43289239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#21219 #43289239