Subgroups — C₁₁₃×#2407 #28387203

Order 14464.

908 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#394×C₁₁₃	C₂	1	2	yes	maximal, complemented
6	#392×C₁₁₃	C₂	1	2	yes	maximal, complemented
7	#391×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#390×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#386×C₁₁₃	C₂	1	2	yes	maximal, complemented
10	#385×C₁₁₃	C₂	1	2	yes	maximal, complemented
11	#380×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×C₁₁₃	—	2	4	no	—
13	C₂×#41×C₁₁₃	—	2	4	no	—
14	C₂×#41×C₁₁₃	—	2	4	no	—
15	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	—
18	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	—
19	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₁₁₃	C₂²	1	2	yes	—
22	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
24	#121×C₁₁₃	—	2	4	no	—
25	C₄×D₄×C₁₁₃	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
37	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
38	#95×C₁₁₃	C₂²	1	2	yes	—
39	#95×C₁₁₃	C₂²	1	2	yes	—
40	#95×C₁₁₃	C₂²	1	2	yes	—
41	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
42	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
43	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
44	#41×C₁₁₃	—	2	32	no	—
45	C₂×Q₈×C₁₁₃	—	2	2	no	—
46	C₂×Q₈×C₁₁₃	—	2	2	no	—
47	C₂×Q₈×C₁₁₃	D₄	1	4	yes	complemented
48	C₂×D₄×C₁₁₃	—	2	2	no	—
49	C₂×D₄×C₁₁₃	—	2	4	no	—
50	C₂×D₄×C₁₁₃	—	2	4	no	—
51	C₂×D₄×C₁₁₃	—	2	2	no	—
52	C₂×D₄×C₁₁₃	—	2	4	no	—
53	C₂×D₄×C₁₁₃	—	2	4	no	—
54	C₂×D₄×C₁₁₃	—	2	4	no	—
55	C₂×D₄×C₁₁₃	—	2	2	no	—
56	C₂×D₄×C₁₁₃	—	2	2	no	—
57	C₂×D₄×C₁₁₃	—	2	2	no	—
58	C₂×D₄×C₁₁₃	—	4	2	no	—
59	C₂×D₄×C₁₁₃	D₄	1	4	yes	complemented
60	C₂²×C₄×C₁₁₃	—	2	4	no	—
61	C₂²×C₄×C₁₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₁₃	—	2	4	no	—
63	C₂²×C₄×C₁₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₁₃	—	2	2	no	—
65	C₂²×C₄×C₁₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₁₃	D₄	1	4	yes	complemented
69	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
72	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
75	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
77	C₄⋊C₄×C₁₁₃	—	2	2	no	—
78	C₄⋊C₄×C₁₁₃	—	2	2	no	—
79	C₄⋊C₄×C₁₁₃	—	2	2	no	—
80	C₄⋊C₄×C₁₁₃	—	2	4	no	—
81	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
82	C₂²⋊C₄×C₁₁₃	—	2	4	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	—	4	2	no	—
87	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
88	C₄²×C₁₁₃	—	2	2	no	—
89	C₂³×C₁₁₃	—	2	1	no	—
90	C₂³×C₁₁₃	—	2	1	no	—
91	C₂³×C₁₁₃	—	2	2	no	—
92	C₂³×C₁₁₃	—	2	1	no	—
93	C₂³×C₁₁₃	—	2	2	no	—
94	C₂³×C₁₁₃	—	2	1	no	—
95	C₂³×C₁₁₃	—	2	1	no	—
96	C₂³×C₁₁₃	—	2	2	no	—
97	C₂³×C₁₁₃	—	2	1	no	—
98	C₂³×C₁₁₃	—	2	1	no	—
99	C₂³×C₁₁₃	—	2	1	no	—
100	C₂³×C₁₁₃	—	2	2	no	—
101	C₂³×C₁₁₃	—	2	1	no	—
102	C₂³×C₁₁₃	—	2	2	no	—
103	C₂³×C₁₁₃	—	2	1	no	—
104	C₂³×C₁₁₃	—	2	1	no	—
105	C₂³×C₁₁₃	—	2	2	no	—
106	C₂³×C₁₁₃	—	2	1	no	—
107	C₂³×C₁₁₃	C₂×D₄	1	4	yes	—
108	C₂³×C₁₁₃	C₂×D₄	1	2	yes	—
109	C₂³×C₁₁₃	#41	1	2	yes	complemented
110	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
111	Q₈×C₁₁₃	—	2	8	no	—
112	D₄×C₁₁₃	—	2	8	no	—
113	D₄×C₁₁₃	—	2	16	no	—
114	D₄×C₁₁₃	—	2	8	no	—
115	D₄×C₁₁₃	—	4	8	no	—
116	C₂×C₄×C₁₁₃	—	2	16	no	—
117	C₂×C₄×C₁₁₃	—	2	1	no	—
118	C₂×C₄×C₁₁₃	—	2	1	no	—
119	C₂×C₄×C₁₁₃	—	2	1	no	—
120	C₂×C₄×C₁₁₃	—	2	2	no	—
121	C₂×C₄×C₁₁₃	—	2	2	no	—
122	C₂×C₄×C₁₁₃	—	2	1	no	—
123	C₂×C₄×C₁₁₃	—	2	8	no	—
124	C₂×C₄×C₁₁₃	—	2	1	no	—
125	C₂×C₄×C₁₁₃	—	2	1	no	—
126	C₂×C₄×C₁₁₃	—	2	2	no	—
127	C₂×C₄×C₁₁₃	—	2	1	no	—
128	C₂×C₄×C₁₁₃	—	2	2	no	—
129	C₂×C₄×C₁₁₃	—	2	1	no	—
130	C₂×C₄×C₁₁₃	—	2	2	no	—
131	C₂×C₄×C₁₁₃	—	2	2	no	—
132	C₂×C₄×C₁₁₃	—	2	1	no	—
133	C₂×C₄×C₁₁₃	—	2	2	no	—
134	C₂×C₄×C₁₁₃	—	2	2	no	—
135	C₂×C₄×C₁₁₃	—	2	1	no	—
136	C₂×C₄×C₁₁₃	—	4	4	no	—
137	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
139	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
141	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
142	C₂×C₄×C₁₁₃	#41	1	2	yes	complemented
143	C₂²×C₁₁₃	—	2	4	no	—
144	C₂²×C₁₁₃	—	2	2	no	—
145	C₂²×C₁₁₃	—	2	2	no	—
146	C₂²×C₁₁₃	—	2	2	no	—
147	C₂²×C₁₁₃	—	2	2	no	—
148	C₂²×C₁₁₃	—	2	2	no	—
149	C₂²×C₁₁₃	—	2	4	no	—
150	C₂²×C₁₁₃	—	2	4	no	—
151	C₂²×C₁₁₃	—	2	2	no	—
152	C₂²×C₁₁₃	—	4	1	no	—
153	C₂²×C₁₁₃	—	4	2	no	—
154	C₂²×C₁₁₃	—	4	1	no	—
155	C₂²×C₁₁₃	—	4	2	no	—
156	C₂²×C₁₁₃	—	4	1	no	—
157	C₂²×C₁₁₃	—	4	1	no	—
158	C₂²×C₁₁₃	—	4	1	no	—
159	C₂²×C₁₁₃	—	4	1	no	—
160	C₂²×C₁₁₃	—	4	2	no	—
161	C₂²×C₁₁₃	—	4	1	no	—
162	C₂²×C₁₁₃	—	4	2	no	—
163	C₂²×C₁₁₃	—	4	1	no	—
164	C₂²×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₂²×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂²×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₂²×C₁₁₃	C₂×#41	1	1	yes	characteristic
168	C₂²×C₁₁₃	C₂×#41	1	1	yes	characteristic
169	C₂²×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
171	C₄×C₁₁₃	—	2	2	no	—
172	C₄×C₁₁₃	—	2	4	no	—
173	C₄×C₁₁₃	—	2	2	no	—
174	C₄×C₁₁₃	—	4	1	no	—
175	C₄×C₁₁₃	—	4	1	no	—
176	C₄×C₁₁₃	—	4	2	no	—
177	C₄×C₁₁₃	—	4	2	no	—
178	C₄×C₁₁₃	#120	1	4	yes	—
179	C₂×C₁₁₃	—	4	2	no	—
180	C₂×C₁₁₃	—	4	4	no	—
181	C₂×C₁₁₃	—	4	2	no	—
182	C₂×C₁₁₃	C₂×#120	1	1	yes	characteristic
183	C₂×C₁₁₃	#525	1	1	yes	characteristic
184	C₂×C₁₁₃	#537	1	1	yes	characteristic
185	C₂×C₁₁₃	#546	1	1	yes	characteristic
186	C₂×C₁₁₃	#547	1	1	yes	characteristic
187	C₂×C₁₁₃	#548	1	1	yes	characteristic
188	C₂×C₁₁₃	#550	1	1	yes	characteristic
189	#2407	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₁₃	#2407	1	1	yes	characteristic, direct product factor, Sylow
191	C₂²×#41	C₂×C₁₁₃	1	1	yes	characteristic, complemented
192	C₂×C₂²⋊Q₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
193	C₂×#121	C₂×C₁₁₃	1	1	yes	characteristic, complemented
194	C₂×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic, complemented
195	#394	C₂×C₁₁₃	1	2	yes	complemented
196	#392	C₂×C₁₁₃	1	2	yes	complemented
197	#391	C₂×C₁₁₃	1	1	yes	characteristic, complemented
198	#390	C₂×C₁₁₃	1	1	yes	characteristic, complemented
199	#386	C₂×C₁₁₃	1	2	yes	complemented
200	#385	C₂×C₁₁₃	1	2	yes	complemented
201	#380	C₂×C₁₁₃	1	1	yes	characteristic, complemented
202	C₂×#41	—	2	4	no	—
203	C₂×#41	—	2	4	no	—
204	C₂×#41	—	2	4	no	—
205	C₂²×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
206	C₂²×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
207	C₂²×D₄	C₂²×C₁₁₃	1	2	yes	—
208	C₂²×D₄	C₂²×C₁₁₃	1	2	yes	—
209	C₂²×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
210	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
211	C₂³×C₄	C₂²×C₁₁₃	1	2	yes	—
212	C₂³×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
213	C₂²⋊Q₈	—	2	4	no	—
214	#121	—	2	4	no	—
215	C₄×D₄	—	2	4	no	—
216	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
227	C₂×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
228	#95	C₂²×C₁₁₃	1	2	yes	—
229	#95	C₂²×C₁₁₃	1	2	yes	—
230	#95	C₂²×C₁₁₃	1	2	yes	—
231	C₂⁴	C₂³×C₁₁₃	1	2	yes	—
232	C₂⁴	C₂³×C₁₁₃	1	1	yes	characteristic
233	C₂⁴	C₂³×C₁₁₃	1	1	yes	characteristic
234	#41	—	2	32	no	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	D₄×C₁₁₃	1	4	yes	complemented
238	C₂×D₄	—	2	2	no	—
239	C₂×D₄	—	2	4	no	—
240	C₂×D₄	—	2	4	no	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	4	2	no	—
249	C₂×D₄	D₄×C₁₁₃	1	4	yes	complemented
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	D₄×C₁₁₃	1	4	yes	complemented
259	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
260	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
262	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
265	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₂²⋊C₄	—	2	2	no	—
272	C₂²⋊C₄	—	2	4	no	—
273	C₂²⋊C₄	—	2	2	no	—
274	C₂²⋊C₄	—	2	4	no	—
275	C₂²⋊C₄	—	2	4	no	—
276	C₂²⋊C₄	—	4	2	no	—
277	C₂²⋊C₄	—	4	2	no	—
278	C₄²	—	2	2	no	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	1	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	1	no	—
297	C₂³	C₂×D₄×C₁₁₃	1	4	yes	—
298	C₂³	C₂×D₄×C₁₁₃	1	2	yes	—
299	C₂³	#41×C₁₁₃	1	2	yes	complemented
300	C₂³	C₂⁴×C₁₁₃	1	1	yes	characteristic
301	Q₈	—	2	8	no	—
302	D₄	—	2	16	no	—
303	D₄	—	2	8	no	—
304	D₄	—	2	8	no	—
305	D₄	—	4	8	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
328	C₂×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
329	C₂×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
330	C₂×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
331	C₂×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
332	C₂×C₄	#41×C₁₁₃	1	2	yes	complemented
333	C₂²	—	2	4	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	1	no	—
354	C₂²	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
355	C₂²	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
356	C₂²	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
357	C₂²	C₂×#41×C₁₁₃	1	1	yes	characteristic
358	C₂²	C₂×#41×C₁₁₃	1	1	yes	characteristic
359	C₂²	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
360	C₂²	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	2	2	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	#120×C₁₁₃	1	4	yes	—
369	C₂	—	4	2	no	—
370	C₂	—	4	4	no	—
371	C₂	—	4	2	no	—
372	C₂	C₂×#120×C₁₁₃	1	1	yes	characteristic
373	C₂	#525×C₁₁₃	1	1	yes	characteristic
374	C₂	#537×C₁₁₃	1	1	yes	characteristic
375	C₂	#546×C₁₁₃	1	1	yes	characteristic
376	C₂	#547×C₁₁₃	1	1	yes	characteristic
377	C₂	#548×C₁₁₃	1	1	yes	characteristic
378	C₂	#550×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×C₁₁₃	C₂	semidirect
2. C₂×C₂²⋊Q₈×C₁₁₃	C₂	semidirect
3. C₂×#121×C₁₁₃	C₂	semidirect
4. C₂×C₄×D₄×C₁₁₃	C₂	semidirect
5. #394×C₁₁₃	C₂	semidirect
6. #392×C₁₁₃	C₂	semidirect
7. #391×C₁₁₃	C₂	semidirect
8. #390×C₁₁₃	C₂	semidirect
9. #386×C₁₁₃	C₂	semidirect
10. #385×C₁₁₃	C₂	semidirect
11. #380×C₁₁₃	C₂	semidirect
47. C₂×Q₈×C₁₁₃	D₄	semidirect
59. C₂×D₄×C₁₁₃	D₄	semidirect
68. C₂²×C₄×C₁₁₃	D₄	semidirect
109. C₂³×C₁₁₃	#41	semidirect
142. C₂×C₄×C₁₁₃	#41	semidirect
189. #2407	C₁₁₃	direct (N × H)
190. C₁₁₃	#2407	direct (N × H)
191. C₂²×#41	C₂×C₁₁₃	semidirect
192. C₂×C₂²⋊Q₈	C₂×C₁₁₃	semidirect
193. C₂×#121	C₂×C₁₁₃	semidirect
194. C₂×C₄×D₄	C₂×C₁₁₃	semidirect
195. #394	C₂×C₁₁₃	semidirect
196. #392	C₂×C₁₁₃	semidirect
197. #391	C₂×C₁₁₃	semidirect
198. #390	C₂×C₁₁₃	semidirect
199. #386	C₂×C₁₁₃	semidirect
200. #385	C₂×C₁₁₃	semidirect
201. #380	C₂×C₁₁₃	semidirect
237. C₂×Q₈	D₄×C₁₁₃	semidirect
249. C₂×D₄	D₄×C₁₁₃	semidirect
258. C₂²×C₄	D₄×C₁₁₃	semidirect
299. C₂³	#41×C₁₁₃	semidirect
332. C₂×C₄	#41×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#41×C₁₁₃	2
C₂×C₂²⋊Q₈×C₁₁₃	2
C₂×#121×C₁₁₃	2
C₂×C₄×D₄×C₁₁₃	2
#394×C₁₁₃	2
#392×C₁₁₃	2
#391×C₁₁₃	2
#390×C₁₁₃	2
#386×C₁₁₃	2
#385×C₁₁₃	2
#380×C₁₁₃	2
#2407	113

Subgroups — C113×#2407 #28387203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#2407 #28387203