Subgroups — C₁₁₃×#20632 #43288652

Order 28928.

1522 conjugacy classes of subgroups.

The subgroup lattice has 404 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×#410×C₁₁₃	C₂	1	2	yes	maximal
3	C₁₁₃×#2285	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#1799	C₂	1	8	yes	maximal, complemented
5	C₁₁₃×#1740	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₄×#41×C₁₁₃	—	2	4	no	—
8	C₄×#41×C₁₁₃	—	2	2	no	—
9	C₄×#41×C₁₁₃	—	2	2	no	—
10	C₂×C₄×Q₈×C₁₁₃	C₄	1	2	yes	complemented
11	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	complemented
12	C₂×C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
13	C₂×#117×C₁₁₃	C₄	1	2	yes	complemented
14	C₂×#117×C₁₁₃	C₂²	1	4	yes	—
15	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₁₃	C₄	1	2	yes	complemented
17	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
18	#410×C₁₁₃	—	2	8	no	—
19	C₂×#99×C₁₁₃	C₂²	1	8	yes	—
20	#384×C₁₁₃	—	2	2	no	—
21	#382×C₁₁₃	—	2	2	no	—
22	#380×C₁₁₃	C₂²	1	8	yes	—
23	C₄×C₄⋊C₄×C₁₁₃	—	2	4	no	—
24	#342×C₁₁₃	C₂²	1	8	yes	—
25	C₂×#41×C₁₁₃	—	2	2	no	—
26	C₂×#41×C₁₁₃	—	2	2	no	—
27	C₂×#41×C₁₁₃	—	2	4	no	—
28	C₂×#41×C₁₁₃	D₄	1	4	yes	—
29	C₂×#41×C₁₁₃	Q₈	1	4	yes	—
30	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₁₃	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
37	C₄×Q₈×C₁₁₃	—	2	4	no	—
38	C₄×Q₈×C₁₁₃	—	2	4	no	—
39	C₄×D₄×C₁₁₃	—	2	8	no	—
40	C₄×D₄×C₁₁₃	—	2	8	no	—
41	C₄×D₄×C₁₁₃	—	2	4	no	—
42	C₄×D₄×C₁₁₃	—	2	4	no	—
43	#117×C₁₁₃	—	2	2	no	—
44	#117×C₁₁₃	—	2	2	no	—
45	#117×C₁₁₃	—	2	4	no	—
46	#117×C₁₁₃	—	2	4	no	—
47	#117×C₁₁₃	—	2	8	no	—
48	#117×C₁₁₃	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
55	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₁₃	—	2	4	no	—
59	C₂×C₄²×C₁₁₃	—	2	4	no	—
60	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₁₁₃	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
66	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
67	C₂×C₄²×C₁₁₃	D₄	1	2	yes	—
68	#99×C₁₁₃	—	2	16	no	—
69	#95×C₁₁₃	—	2	8	no	—
70	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
72	#41×C₁₁₃	—	2	8	no	—
73	#41×C₁₁₃	—	2	8	no	—
74	#41×C₁₁₃	—	2	8	no	—
75	#41×C₁₁₃	—	2	8	no	—
76	C₂×Q₈×C₁₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₁₃	C₄⋊C₄	1	4	yes	complemented
79	C₂×D₄×C₁₁₃	—	2	4	no	—
80	C₂×D₄×C₁₁₃	—	2	4	no	—
81	C₂×D₄×C₁₁₃	—	2	2	no	—
82	C₂×D₄×C₁₁₃	—	2	2	no	—
83	C₂×D₄×C₁₁₃	C₄⋊C₄	1	4	yes	complemented
84	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
85	C₂×D₄×C₁₁₃	C₂×Q₈	1	4	yes	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₁₃	—	4	4	no	—
93	C₂²×C₄×C₁₁₃	—	4	8	no	—
94	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	8	yes	complemented
95	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
108	C₄⋊C₄×C₁₁₃	—	2	8	no	—
109	C₄⋊C₄×C₁₁₃	—	2	4	no	—
110	C₄⋊C₄×C₁₁₃	—	4	16	no	—
111	C₄⋊C₄×C₁₁₃	—	4	8	no	—
112	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
113	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
114	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
115	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
116	C₄²×C₁₁₃	—	2	2	no	—
117	C₄²×C₁₁₃	—	2	4	no	—
118	C₄²×C₁₁₃	—	2	4	no	—
119	C₄²×C₁₁₃	—	2	2	no	—
120	C₄²×C₁₁₃	—	4	8	no	—
121	C₄²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₄²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
126	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
128	C₂³×C₁₁₃	—	2	2	no	—
129	C₂³×C₁₁₃	—	2	2	no	—
130	C₂³×C₁₁₃	—	4	2	no	—
131	C₂³×C₁₁₃	—	4	4	no	—
132	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
133	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
134	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
135	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
136	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
137	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
138	Q₈×C₁₁₃	—	2	8	no	—
139	D₄×C₁₁₃	—	2	8	no	—
140	D₄×C₁₁₃	—	2	8	no	—
141	D₄×C₁₁₃	—	2	8	no	—
142	C₂×C₄×C₁₁₃	—	2	2	no	—
143	C₂×C₄×C₁₁₃	—	2	2	no	—
144	C₂×C₄×C₁₁₃	—	2	8	no	—
145	C₂×C₄×C₁₁₃	—	2	8	no	—
146	C₂×C₄×C₁₁₃	—	2	8	no	—
147	C₂×C₄×C₁₁₃	—	2	4	no	—
148	C₂×C₄×C₁₁₃	—	2	4	no	—
149	C₂×C₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	4	4	no	—
151	C₂×C₄×C₁₁₃	—	4	8	no	—
152	C₂×C₄×C₁₁₃	—	4	8	no	—
153	C₂×C₄×C₁₁₃	—	4	4	no	—
154	C₂×C₄×C₁₁₃	—	4	16	no	—
155	C₂×C₄×C₁₁₃	—	4	8	no	—
156	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
158	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	4	yes	—
163	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₁₃	#117	1	2	yes	—
166	C₂×C₄×C₁₁₃	#117	1	2	yes	—
167	C₂×C₄×C₁₁₃	#121	1	4	yes	—
168	C₂×C₄×C₁₁₃	#121	1	4	yes	—
169	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
171	C₂²×C₁₁₃	—	2	4	no	—
172	C₂²×C₁₁₃	—	2	2	no	—
173	C₂²×C₁₁₃	—	2	4	no	—
174	C₂²×C₁₁₃	—	4	1	no	—
175	C₂²×C₁₁₃	—	4	1	no	—
176	C₂²×C₁₁₃	—	4	2	no	—
177	C₂²×C₁₁₃	—	4	4	no	—
178	C₂²×C₁₁₃	—	4	4	no	—
179	C₂²×C₁₁₃	—	4	4	no	—
180	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₁₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×C₁₁₃	C₂×#117	1	1	yes	characteristic
183	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
184	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
185	C₄×C₁₁₃	—	2	2	no	—
186	C₄×C₁₁₃	—	2	4	no	—
187	C₄×C₁₁₃	—	2	4	no	—
188	C₄×C₁₁₃	—	4	4	no	—
189	C₄×C₁₁₃	—	8	8	no	—
190	C₄×C₁₁₃	#380	1	2	yes	—
191	C₄×C₁₁₃	#380	1	2	yes	—
192	C₄×C₁₁₃	#380	1	4	yes	—
193	C₄×C₁₁₃	#410	1	4	yes	complemented
194	#20632	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₁₁₃	—	2	2	no	—
196	C₂×C₁₁₃	—	2	1	no	—
197	C₂×C₁₁₃	—	2	1	no	—
198	C₂×C₁₁₃	—	2	2	no	—
199	C₂×C₁₁₃	—	4	4	no	—
200	C₂×C₁₁₃	C₂×#380	1	1	yes	characteristic
201	C₂×C₁₁₃	C₂×#410	1	2	yes	—
202	C₂×C₄×#41	C₂×C₁₁₃	1	1	yes	characteristic
203	C₂×#410	C₂×C₁₁₃	1	2	yes	—
204	#2285	C₂×C₁₁₃	1	2	yes	complemented
205	#1799	C₂×C₁₁₃	1	8	yes	complemented
206	#1740	C₂×C₁₁₃	1	2	yes	complemented
207	C₁₁₃	#20632	1	1	yes	characteristic, direct product factor, Sylow
208	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
209	C₄×#41	—	2	4	no	—
210	C₄×#41	—	2	2	no	—
211	C₄×#41	—	2	2	no	—
212	C₂×C₄×Q₈	C₄×C₁₁₃	1	2	yes	complemented
213	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	complemented
214	C₂×C₄×D₄	C₂²×C₁₁₃	1	4	yes	—
215	C₂×#117	C₄×C₁₁₃	1	2	yes	complemented
216	C₂×#117	C₂²×C₁₁₃	1	4	yes	—
217	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
218	C₂²×C₄²	C₄×C₁₁₃	1	2	yes	complemented
219	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
220	#410	—	2	8	no	—
221	C₂×#99	C₂²×C₁₁₃	1	8	yes	—
222	#384	—	2	2	no	—
223	#382	—	2	2	no	—
224	#380	C₂²×C₁₁₃	1	8	yes	—
225	C₄×C₄⋊C₄	—	2	4	no	—
226	#342	C₂²×C₁₁₃	1	8	yes	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	4	no	—
230	C₂×#41	D₄×C₁₁₃	1	4	yes	—
231	C₂×#41	Q₈×C₁₁₃	1	4	yes	—
232	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
233	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
234	C₂²×D₄	C₂³×C₁₁₃	1	2	yes	—
235	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₁₁₃	1	4	yes	—
237	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×D₄	—	2	8	no	—
242	C₄×D₄	—	2	8	no	—
243	C₄×D₄	—	2	4	no	—
244	C₄×D₄	—	2	4	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	—	2	4	no	—
248	#117	—	2	4	no	—
249	#117	—	2	8	no	—
250	#117	—	2	8	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	4	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	8	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	—	2	4	no	—
261	C₂×C₄²	—	2	4	no	—
262	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
263	C₂×C₄²	C₂×C₄×C₁₁₃	1	4	yes	—
264	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
266	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
268	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
269	C₂×C₄²	D₄×C₁₁₃	1	2	yes	—
270	#99	—	2	16	no	—
271	#95	—	2	8	no	—
272	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
273	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
274	#41	—	2	8	no	—
275	#41	—	2	8	no	—
276	#41	—	2	8	no	—
277	#41	—	2	8	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	C₄⋊C₄×C₁₁₃	1	4	yes	complemented
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	C₄⋊C₄×C₁₁₃	1	4	yes	complemented
286	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
287	C₂×D₄	C₂×Q₈×C₁₁₃	1	4	yes	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	8	no	—
296	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	8	yes	complemented
297	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₁₃	1	4	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
304	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
308	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
309	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	16	no	—
313	C₄⋊C₄	—	4	8	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	8	no	—
317	C₂²⋊C₄	—	2	8	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	4	8	no	—
323	C₄²	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
324	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
325	C₄²	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
326	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
327	C₄²	C₂²⋊C₄×C₁₁₃	1	2	yes	—
328	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
329	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	4	no	—
334	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
335	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
336	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
337	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
338	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
339	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
340	Q₈	—	2	8	no	—
341	D₄	—	2	8	no	—
342	D₄	—	2	8	no	—
343	D₄	—	2	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
364	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	4	yes	—
365	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
366	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
367	C₂×C₄	#117×C₁₁₃	1	2	yes	—
368	C₂×C₄	#117×C₁₁₃	1	2	yes	—
369	C₂×C₄	#121×C₁₁₃	1	4	yes	—
370	C₂×C₄	#121×C₁₁₃	1	4	yes	—
371	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
372	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
383	C₂²	C₂²×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
384	C₂²	C₂×#117×C₁₁₃	1	1	yes	characteristic
385	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
386	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	4	4	no	—
391	C₄	—	8	8	no	—
392	C₄	#380×C₁₁₃	1	2	yes	—
393	C₄	#380×C₁₁₃	1	2	yes	—
394	C₄	#380×C₁₁₃	1	4	yes	—
395	C₄	#410×C₁₁₃	1	4	yes	complemented
396	C₂	—	2	2	no	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	2	no	—
400	C₂	—	4	4	no	—
401	C₂	C₂×#380×C₁₁₃	1	1	yes	characteristic
402	C₂	C₂×#410×C₁₁₃	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₁₃×#2285	C₂	semidirect
4. C₁₁₃×#1799	C₂	semidirect
5. C₁₁₃×#1740	C₂	semidirect
10. C₂×C₄×Q₈×C₁₁₃	C₄	semidirect
11. C₂×C₄×D₄×C₁₁₃	C₄	semidirect
13. C₂×#117×C₁₁₃	C₄	semidirect
16. C₂²×C₄²×C₁₁₃	C₄	semidirect
78. C₂×Q₈×C₁₁₃	C₄⋊C₄	semidirect
83. C₂×D₄×C₁₁₃	C₄⋊C₄	semidirect
94. C₂²×C₄×C₁₁₃	C₄⋊C₄	semidirect
193. C₄×C₁₁₃	#410	semidirect
194. #20632	C₁₁₃	direct (N × H)
204. #2285	C₂×C₁₁₃	semidirect
205. #1799	C₂×C₁₁₃	semidirect
206. #1740	C₂×C₁₁₃	semidirect
207. C₁₁₃	#20632	direct (N × H)
212. C₂×C₄×Q₈	C₄×C₁₁₃	semidirect
213. C₂×C₄×D₄	C₄×C₁₁₃	semidirect
215. C₂×#117	C₄×C₁₁₃	semidirect
218. C₂²×C₄²	C₄×C₁₁₃	semidirect
280. C₂×Q₈	C₄⋊C₄×C₁₁₃	semidirect
285. C₂×D₄	C₄⋊C₄×C₁₁₃	semidirect
296. C₂²×C₄	C₄⋊C₄×C₁₁₃	semidirect
395. C₄	#410×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×#410×C₁₁₃	2
C₁₁₃×#2285	2
C₁₁₃×#1799	2
C₁₁₃×#1740	2
#20632	113

Subgroups — C113×#20632 #43288652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20632 #43288652