Subgroups — C₁₁₃×#10871 #43278891

Order 28928.

746 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×#427×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#405×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1740	C₂	1	2	yes	maximal
5	C₁₁₃×#1733	C₂	1	2	yes	maximal
6	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
9	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
10	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
11	#427×C₁₁₃	—	2	2	no	—
12	#427×C₁₁₃	—	2	1	no	—
13	#427×C₁₁₃	—	2	1	no	—
14	#427×C₁₁₃	—	2	1	no	—
15	#427×C₁₁₃	—	2	1	no	—
16	#427×C₁₁₃	C₄	1	4	yes	complemented
17	C₂×#107×C₁₁₃	—	2	1	no	—
18	C₂×#107×C₁₁₃	C₄	1	2	yes	complemented
19	C₂×#106×C₁₁₃	—	2	1	no	—
20	C₂×#106×C₁₁₃	C₄	1	2	yes	complemented
21	#405×C₁₁₃	—	2	2	no	—
22	#405×C₁₁₃	C₄	1	4	yes	complemented
23	C₂×#97×C₁₁₃	—	2	1	no	—
24	C₂×C₄×C₈×C₁₁₃	—	2	1	no	—
25	#342×C₁₁₃	—	2	4	no	—
26	#339×C₁₁₃	—	2	4	no	—
27	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₁₁₃	—	2	1	no	—
29	C₂×M₁₆×C₁₁₃	—	2	1	no	—
30	C₂×M₁₆×C₁₁₃	—	2	1	no	—
31	C₂×M₁₆×C₁₁₃	C₂×C₄	1	2	yes	—
32	C₂×M₁₆×C₁₁₃	D₄	1	2	yes	—
33	C₂×M₁₆×C₁₁₃	Q₈	1	2	yes	—
34	C₂²×C₈×C₁₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₁₃	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁₃	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₁₃	D₄	1	2	yes	—
42	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₁₃	Q₈	1	2	yes	—
45	#117×C₁₁₃	—	2	1	no	—
46	#117×C₁₁₃	—	2	1	no	—
47	#117×C₁₁₃	—	2	2	no	—
48	#117×C₁₁₃	—	2	2	no	—
49	#117×C₁₁₃	—	2	2	no	—
50	#117×C₁₁₃	—	2	2	no	—
51	#117×C₁₁₃	—	2	2	no	—
52	#117×C₁₁₃	—	2	2	no	—
53	#117×C₁₁₃	—	2	2	no	—
54	#117×C₁₁₃	C₂×C₄	1	4	yes	—
55	#117×C₁₁₃	C₂×C₄	1	2	yes	—
56	#117×C₁₁₃	Q₈	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
63	C₂×C₄²×C₁₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₁₃	—	2	2	no	—
66	#107×C₁₁₃	—	2	4	no	—
67	#107×C₁₁₃	—	2	2	no	—
68	#107×C₁₁₃	—	2	2	no	—
69	#106×C₁₁₃	—	2	4	no	—
70	#106×C₁₁₃	—	2	2	no	—
71	#106×C₁₁₃	—	2	2	no	—
72	#97×C₁₁₃	—	2	4	no	—
73	C₄×C₈×C₁₁₃	—	2	4	no	—
74	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₁₃	—	4	2	no	—
78	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
92	M₁₆×C₁₁₃	—	2	2	no	—
93	M₁₆×C₁₁₃	—	2	2	no	—
94	M₁₆×C₁₁₃	—	2	2	no	—
95	M₁₆×C₁₁₃	C₄⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₁₃	—	2	2	no	—
97	C₂×C₈×C₁₁₃	—	2	2	no	—
98	C₂×C₈×C₁₁₃	—	2	2	no	—
99	C₂×C₈×C₁₁₃	C₄²	1	2	yes	—
100	C₂×C₈×C₁₁₃	C₄²	1	2	yes	—
101	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
104	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
107	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁₃	C₄⋊C₄	1	2	yes	—
110	C₂×C₈×C₁₁₃	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₁₁₃	C₄⋊C₄	1	2	yes	—
112	C₂×C₈×C₁₁₃	C₄⋊C₄	1	2	yes	—
113	C₂×C₈×C₁₁₃	C₄⋊C₄	1	2	yes	—
114	C₂×C₈×C₁₁₃	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₁₁₃	—	2	2	no	—
116	C₄⋊C₄×C₁₁₃	—	2	2	no	—
117	C₄⋊C₄×C₁₁₃	—	2	4	no	—
118	C₄⋊C₄×C₁₁₃	—	2	4	no	—
119	C₄⋊C₄×C₁₁₃	—	2	4	no	—
120	C₄⋊C₄×C₁₁₃	—	4	2	no	—
121	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
122	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
123	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
124	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
125	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
126	C₂²⋊C₄×C₁₁₃	C₄⋊C₄	1	4	yes	—
127	C₄²×C₁₁₃	—	2	2	no	—
128	C₄²×C₁₁₃	—	2	2	no	—
129	C₄²×C₁₁₃	—	2	4	no	—
130	C₄²×C₁₁₃	—	4	2	no	—
131	C₄²×C₁₁₃	—	4	2	no	—
132	C₄²×C₁₁₃	—	4	2	no	—
133	C₂³×C₁₁₃	—	4	2	no	—
134	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₁₁₃	C₄×D₄	1	1	yes	characteristic
136	C₂³×C₁₁₃	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₁₁₃	#121	1	1	yes	characteristic
138	C₂³×C₁₁₃	#121	1	1	yes	characteristic
139	C₂³×C₁₁₃	#127	1	1	yes	characteristic
140	C₂³×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₁₁₃	—	2	4	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	—	8	4	no	—
146	C₂×C₄×C₁₁₃	—	8	4	no	—
147	C₂×C₄×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁₃	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₁₃	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	#125	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	#125	1	1	yes	characteristic
173	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
175	C₈×C₁₁₃	—	2	4	no	—
176	C₈×C₁₁₃	#95	1	2	yes	—
177	C₈×C₁₁₃	#95	1	2	yes	—
178	C₈×C₁₁₃	#95	1	2	yes	—
179	C₈×C₁₁₃	#95	1	2	yes	—
180	C₂²×C₁₁₃	—	2	2	no	—
181	C₂²×C₁₁₃	—	2	2	no	—
182	C₂²×C₁₁₃	—	2	2	no	—
183	C₂²×C₁₁₃	—	4	1	no	—
184	C₂²×C₁₁₃	—	4	1	no	—
185	C₂²×C₁₁₃	—	4	1	no	—
186	C₂²×C₁₁₃	—	4	1	no	—
187	C₂²×C₁₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₁₁₃	#380	1	1	yes	characteristic
189	C₂²×C₁₁₃	#384	1	1	yes	characteristic
190	C₂²×C₁₁₃	#389	1	1	yes	characteristic
191	C₂²×C₁₁₃	#389	1	1	yes	characteristic
192	C₂²×C₁₁₃	#390	1	1	yes	characteristic
193	C₂²×C₁₁₃	#390	1	1	yes	characteristic
194	C₄×C₁₁₃	—	4	4	no	—
195	C₄×C₁₁₃	—	8	4	no	—
196	C₄×C₁₁₃	—	8	4	no	—
197	C₄×C₁₁₃	C₂×#95	1	1	yes	characteristic
198	C₄×C₁₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₁₁₃	#380	1	1	yes	characteristic
200	C₄×C₁₁₃	#382	1	1	yes	characteristic
201	C₄×C₁₁₃	#389	1	1	yes	characteristic
202	C₄×C₁₁₃	#389	1	1	yes	characteristic
203	C₄×C₁₁₃	#391	1	1	yes	characteristic
204	C₄×C₁₁₃	#391	1	1	yes	characteristic
205	#10871	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₁₁₃	—	2	1	no	—
207	C₂×C₁₁₃	—	2	1	no	—
208	C₂×C₁₁₃	—	2	1	no	—
209	C₂×C₁₁₃	—	2	1	no	—
210	C₂×C₁₁₃	—	2	1	no	—
211	C₂×C₁₁₃	—	2	1	no	—
212	C₂×C₁₁₃	C₄⋊#95	1	1	yes	characteristic
213	C₂×C₁₁₃	#1976	1	2	yes	—
214	C₂×#427	C₂×C₁₁₃	1	1	yes	characteristic
215	C₂×#427	C₂×C₁₁₃	1	1	yes	characteristic
216	C₂×#405	C₂×C₁₁₃	1	1	yes	characteristic
217	#1740	C₂×C₁₁₃	1	2	yes	—
218	#1733	C₂×C₁₁₃	1	2	yes	—
219	C₁₁₃	#10871	1	1	yes	characteristic, direct product factor, Sylow
220	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
221	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
222	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
223	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
224	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
225	#427	—	2	2	no	—
226	#427	—	2	1	no	—
227	#427	—	2	1	no	—
228	#427	—	2	1	no	—
229	#427	—	2	1	no	—
230	#427	C₄×C₁₁₃	1	4	yes	complemented
231	C₂×#107	—	2	1	no	—
232	C₂×#107	C₄×C₁₁₃	1	2	yes	complemented
233	C₂×#106	—	2	1	no	—
234	C₂×#106	C₄×C₁₁₃	1	2	yes	complemented
235	#405	—	2	2	no	—
236	#405	C₄×C₁₁₃	1	4	yes	complemented
237	C₂×#97	—	2	1	no	—
238	C₂×C₄×C₈	—	2	1	no	—
239	#342	—	2	4	no	—
240	#339	—	2	4	no	—
241	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	C₂×C₄×C₁₁₃	1	2	yes	—
246	C₂×M₁₆	D₄×C₁₁₃	1	2	yes	—
247	C₂×M₁₆	Q₈×C₁₁₃	1	2	yes	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	C₂×C₄×C₁₁₃	1	2	yes	—
250	C₂²×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂×C₄×C₁₁₃	1	2	yes	—
253	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
254	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
255	C₂²×C₈	D₄×C₁₁₃	1	2	yes	—
256	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
257	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
258	C₂²×C₈	Q₈×C₁₁₃	1	2	yes	—
259	#117	—	2	1	no	—
260	#117	—	2	1	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	C₂×C₄×C₁₁₃	1	4	yes	—
269	#117	C₂×C₄×C₁₁₃	1	2	yes	—
270	#117	Q₈×C₁₁₃	1	2	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	#107	—	2	4	no	—
281	#107	—	2	2	no	—
282	#107	—	2	2	no	—
283	#106	—	2	4	no	—
284	#106	—	2	2	no	—
285	#106	—	2	2	no	—
286	#97	—	2	4	no	—
287	C₄×C₈	—	2	4	no	—
288	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×Q₈×C₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
303	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
304	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
305	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	C₄⋊C₄×C₁₁₃	1	4	yes	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	C₄²×C₁₁₃	1	2	yes	—
314	C₂×C₈	C₄²×C₁₁₃	1	2	yes	—
315	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
316	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
317	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
318	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
321	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
323	C₂×C₈	C₄⋊C₄×C₁₁₃	1	2	yes	—
324	C₂×C₈	C₄⋊C₄×C₁₁₃	1	2	yes	—
325	C₂×C₈	C₄⋊C₄×C₁₁₃	1	2	yes	—
326	C₂×C₈	C₄⋊C₄×C₁₁₃	1	2	yes	—
327	C₂×C₈	C₄⋊C₄×C₁₁₃	1	2	yes	—
328	C₂×C₈	C₄⋊C₄×C₁₁₃	1	2	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	C₄⋊C₄×C₁₁₃	1	4	yes	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	4	2	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
349	C₂³	C₄×D₄×C₁₁₃	1	1	yes	characteristic
350	C₂³	C₄×D₄×C₁₁₃	1	1	yes	characteristic
351	C₂³	#121×C₁₁₃	1	1	yes	characteristic
352	C₂³	#121×C₁₁₃	1	1	yes	characteristic
353	C₂³	#127×C₁₁₃	1	1	yes	characteristic
354	C₂³	C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	—	8	4	no	—
361	C₂×C₄	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
369	C₂×C₄	#117×C₁₁₃	1	1	yes	characteristic
370	C₂×C₄	#117×C₁₁₃	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
372	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
373	C₂×C₄	C₄×Q₈×C₁₁₃	1	1	yes	characteristic
374	C₂×C₄	C₄×Q₈×C₁₁₃	1	1	yes	characteristic
375	C₂×C₄	C₄×Q₈×C₁₁₃	1	1	yes	characteristic
376	C₂×C₄	C₄×Q₈×C₁₁₃	1	1	yes	characteristic
377	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
378	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
383	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
384	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
385	C₂×C₄	#125×C₁₁₃	1	1	yes	characteristic
386	C₂×C₄	#125×C₁₁₃	1	1	yes	characteristic
387	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
388	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	#95×C₁₁₃	1	2	yes	—
391	C₈	#95×C₁₁₃	1	2	yes	—
392	C₈	#95×C₁₁₃	1	2	yes	—
393	C₈	#95×C₁₁₃	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₄×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
402	C₂²	#380×C₁₁₃	1	1	yes	characteristic
403	C₂²	#384×C₁₁₃	1	1	yes	characteristic
404	C₂²	#389×C₁₁₃	1	1	yes	characteristic
405	C₂²	#389×C₁₁₃	1	1	yes	characteristic
406	C₂²	#390×C₁₁₃	1	1	yes	characteristic
407	C₂²	#390×C₁₁₃	1	1	yes	characteristic
408	C₄	—	4	4	no	—
409	C₄	—	8	4	no	—
410	C₄	—	8	4	no	—
411	C₄	C₂×#95×C₁₁₃	1	1	yes	characteristic
412	C₄	C₄×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
413	C₄	#380×C₁₁₃	1	1	yes	characteristic
414	C₄	#382×C₁₁₃	1	1	yes	characteristic
415	C₄	#389×C₁₁₃	1	1	yes	characteristic
416	C₄	#389×C₁₁₃	1	1	yes	characteristic
417	C₄	#391×C₁₁₃	1	1	yes	characteristic
418	C₄	#391×C₁₁₃	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	C₁₁₃×C₄⋊#95	1	1	yes	characteristic
426	C₂	C₁₁₃×#1976	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁₃	#121
commutator	C₂×C₄	C₂×C₄²×C₁₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁₃
socle	C₂²×C₁₁₃	#390
prime radical	C₂⁴×C₁₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
16. #427×C₁₁₃	C₄	semidirect
18. C₂×#107×C₁₁₃	C₄	semidirect
20. C₂×#106×C₁₁₃	C₄	semidirect
22. #405×C₁₁₃	C₄	semidirect
205. #10871	C₁₁₃	direct (N × H)
219. C₁₁₃	#10871	direct (N × H)
230. #427	C₄×C₁₁₃	semidirect
232. C₂×#107	C₄×C₁₁₃	semidirect
234. C₂×#106	C₄×C₁₁₃	semidirect
236. #405	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×#427×C₁₁₃	2
C₂×#405×C₁₁₃	2
C₁₁₃×#1740	2
C₁₁₃×#1733	2
#10871	113

Subgroups — C113×#10871 #43278891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#10871 #43278891