Subgroups — C₁₁₃×#15177 #43283197

Order 28928.

2770 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₁₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#391×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#380×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1444	C₂	1	2	yes	maximal, complemented
6	C₁₁₃×#1439	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1438	C₂	1	2	yes	maximal
8	C₁₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₁₃	C₂²	1	2	yes	—
12	C₂×C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
13	C₂×C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
14	C₂×C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
15	C₂×C₄×D₄×C₁₁₃	—	2	8	no	—
16	C₂×C₄×D₄×C₁₁₃	—	2	4	no	—
17	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
23	C₂²×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	—
24	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
25	#391×C₁₁₃	—	2	4	no	—
26	#380×C₁₁₃	—	2	8	no	—
27	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
28	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
29	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
30	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
31	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
32	C₂⁵×C₁₁₃	C₂³	1	2	yes	—
33	C₂²×Q₈×C₁₁₃	—	2	4	no	—
34	C₂²×Q₈×C₁₁₃	—	2	4	no	—
35	C₂²×Q₈×C₁₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₁₃	D₄	1	4	yes	complemented
38	C₂²×D₄×C₁₁₃	—	2	4	no	—
39	C₂²×D₄×C₁₁₃	—	2	4	no	—
40	C₂²×D₄×C₁₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₁₃	Q₈	1	4	yes	complemented
43	C₂³×C₄×C₁₁₃	—	2	4	no	—
44	C₂³×C₄×C₁₁₃	—	2	4	no	—
45	C₂³×C₄×C₁₁₃	—	2	4	no	—
46	C₂³×C₄×C₁₁₃	—	2	4	no	—
47	C₂³×C₄×C₁₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₁₃	—	2	4	no	—
49	C₂³×C₄×C₁₁₃	D₄	1	8	yes	—
50	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
57	C₂²⋊Q₈×C₁₁₃	—	2	64	no	—
58	C₄×D₄×C₁₁₃	—	2	32	no	—
59	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
62	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
63	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
64	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₁₃	D₄	1	8	yes	complemented
69	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₁₃	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₁₁₃	—	4	4	no	—
78	C₂×C₄²×C₁₁₃	—	2	4	no	—
79	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
80	#95×C₁₁₃	—	2	8	no	—
81	#95×C₁₁₃	—	2	4	no	—
82	#95×C₁₁₃	—	2	4	no	—
83	#95×C₁₁₃	—	2	4	no	—
84	#95×C₁₁₃	—	4	2	no	—
85	C₂⁴×C₁₁₃	—	2	2	no	—
86	C₂⁴×C₁₁₃	—	2	2	no	—
87	C₂⁴×C₁₁₃	—	2	2	no	—
88	C₂⁴×C₁₁₃	—	2	2	no	—
89	C₂⁴×C₁₁₃	—	2	2	no	—
90	C₂⁴×C₁₁₃	—	2	2	no	—
91	C₂⁴×C₁₁₃	—	2	2	no	—
92	C₂⁴×C₁₁₃	—	2	2	no	—
93	C₂⁴×C₁₁₃	—	2	2	no	—
94	C₂⁴×C₁₁₃	—	2	2	no	—
95	C₂⁴×C₁₁₃	—	2	2	no	—
96	C₂⁴×C₁₁₃	—	2	2	no	—
97	C₂⁴×C₁₁₃	C₂×D₄	1	4	yes	—
98	C₂⁴×C₁₁₃	C₂×Q₈	1	4	yes	—
99	C₂⁴×C₁₁₃	#41	1	4	yes	—
100	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×Q₈×C₁₁₃	—	2	16	no	—
102	C₂×Q₈×C₁₁₃	—	2	8	no	—
103	C₂×Q₈×C₁₁₃	—	4	4	no	—
104	C₂×Q₈×C₁₁₃	—	4	8	no	—
105	C₂×Q₈×C₁₁₃	—	4	4	no	—
106	C₂×D₄×C₁₁₃	—	2	8	no	—
107	C₂×D₄×C₁₁₃	—	2	8	no	—
108	C₂×D₄×C₁₁₃	—	2	16	no	—
109	C₂×D₄×C₁₁₃	—	2	16	no	—
110	C₂×D₄×C₁₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₁₃	—	2	16	no	—
134	C₂²×C₄×C₁₁₃	—	2	16	no	—
135	C₂²×C₄×C₁₁₃	—	2	16	no	—
136	C₂²×C₄×C₁₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₁₃	—	4	8	no	—
142	C₂²×C₄×C₁₁₃	—	4	8	no	—
143	C₂²×C₄×C₁₁₃	—	4	8	no	—
144	C₂²×C₄×C₁₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
147	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
155	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
156	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
157	C₄⋊C₄×C₁₁₃	—	2	8	no	—
158	C₄⋊C₄×C₁₁₃	—	2	32	no	—
159	C₄⋊C₄×C₁₁₃	—	2	16	no	—
160	C₄⋊C₄×C₁₁₃	—	4	4	no	—
161	C₂²⋊C₄×C₁₁₃	—	2	16	no	—
162	C₂²⋊C₄×C₁₁₃	—	2	32	no	—
163	C₂²⋊C₄×C₁₁₃	—	4	16	no	—
164	C₄²×C₁₁₃	—	2	8	no	—
165	C₂³×C₁₁₃	—	2	4	no	—
166	C₂³×C₁₁₃	—	2	4	no	—
167	C₂³×C₁₁₃	—	2	4	no	—
168	C₂³×C₁₁₃	—	2	4	no	—
169	C₂³×C₁₁₃	—	2	4	no	—
170	C₂³×C₁₁₃	—	2	4	no	—
171	C₂³×C₁₁₃	—	2	4	no	—
172	C₂³×C₁₁₃	—	2	4	no	—
173	C₂³×C₁₁₃	—	2	4	no	—
174	C₂³×C₁₁₃	—	2	4	no	—
175	C₂³×C₁₁₃	—	2	4	no	—
176	C₂³×C₁₁₃	—	2	4	no	—
177	C₂³×C₁₁₃	—	2	4	no	—
178	C₂³×C₁₁₃	—	2	4	no	—
179	C₂³×C₁₁₃	—	2	4	no	—
180	C₂³×C₁₁₃	—	2	4	no	—
181	C₂³×C₁₁₃	—	2	4	no	—
182	C₂³×C₁₁₃	—	2	4	no	—
183	C₂³×C₁₁₃	—	4	2	no	—
184	C₂³×C₁₁₃	—	4	2	no	—
185	C₂³×C₁₁₃	—	4	2	no	—
186	C₂³×C₁₁₃	—	4	2	no	—
187	C₂³×C₁₁₃	—	4	2	no	—
188	C₂³×C₁₁₃	—	4	2	no	—
189	C₂³×C₁₁₃	—	4	2	no	—
190	C₂³×C₁₁₃	—	4	2	no	—
191	C₂³×C₁₁₃	—	4	2	no	—
192	C₂³×C₁₁₃	—	4	2	no	—
193	C₂³×C₁₁₃	—	4	2	no	—
194	C₂³×C₁₁₃	—	4	2	no	—
195	C₂³×C₁₁₃	—	4	2	no	—
196	C₂³×C₁₁₃	—	4	2	no	—
197	C₂³×C₁₁₃	—	4	2	no	—
198	C₂³×C₁₁₃	—	4	2	no	—
199	C₂³×C₁₁₃	C₂²⋊Q₈	1	8	yes	complemented
200	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
201	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂³×C₁₁₃	C₂²×D₄	1	2	yes	—
204	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
205	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
206	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
207	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
208	C₂³×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂³×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
210	C₂³×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
211	Q₈×C₁₁₃	—	4	16	no	—
212	D₄×C₁₁₃	—	2	32	no	—
213	C₂×C₄×C₁₁₃	—	2	2	no	—
214	C₂×C₄×C₁₁₃	—	2	4	no	—
215	C₂×C₄×C₁₁₃	—	2	2	no	—
216	C₂×C₄×C₁₁₃	—	2	4	no	—
217	C₂×C₄×C₁₁₃	—	2	2	no	—
218	C₂×C₄×C₁₁₃	—	2	8	no	—
219	C₂×C₄×C₁₁₃	—	2	4	no	—
220	C₂×C₄×C₁₁₃	—	2	8	no	—
221	C₂×C₄×C₁₁₃	—	2	4	no	—
222	C₂×C₄×C₁₁₃	—	2	4	no	—
223	C₂×C₄×C₁₁₃	—	2	4	no	—
224	C₂×C₄×C₁₁₃	—	2	2	no	—
225	C₂×C₄×C₁₁₃	—	2	2	no	—
226	C₂×C₄×C₁₁₃	—	2	8	no	—
227	C₂×C₄×C₁₁₃	—	2	8	no	—
228	C₂×C₄×C₁₁₃	—	4	2	no	—
229	C₂×C₄×C₁₁₃	—	4	2	no	—
230	C₂×C₄×C₁₁₃	—	4	2	no	—
231	C₂×C₄×C₁₁₃	—	4	2	no	—
232	C₂×C₄×C₁₁₃	—	4	4	no	—
233	C₂×C₄×C₁₁₃	—	4	4	no	—
234	C₂×C₄×C₁₁₃	—	4	2	no	—
235	C₂×C₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	—	4	2	no	—
237	C₂×C₄×C₁₁₃	—	4	2	no	—
238	C₂×C₄×C₁₁₃	—	4	4	no	—
239	C₂×C₄×C₁₁₃	—	4	4	no	—
240	C₂×C₄×C₁₁₃	—	4	4	no	—
241	C₂×C₄×C₁₁₃	—	4	32	no	—
242	C₂×C₄×C₁₁₃	—	4	2	no	—
243	C₂×C₄×C₁₁₃	—	4	2	no	—
244	C₂×C₄×C₁₁₃	—	4	2	no	—
245	C₂×C₄×C₁₁₃	—	4	4	no	—
246	C₂×C₄×C₁₁₃	—	4	4	no	—
247	C₂×C₄×C₁₁₃	#120	1	4	yes	—
248	C₂×C₄×C₁₁₃	#120	1	8	yes	—
249	C₂×C₄×C₁₁₃	#121	1	8	yes	—
250	C₂×C₄×C₁₁₃	#121	1	4	yes	—
251	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	complemented
252	C₂×C₄×C₁₁₃	#127	1	4	yes	—
253	C₂²×C₁₁₃	—	2	8	no	—
254	C₂²×C₁₁₃	—	2	8	no	—
255	C₂²×C₁₁₃	—	2	8	no	—
256	C₂²×C₁₁₃	—	4	4	no	—
257	C₂²×C₁₁₃	—	4	4	no	—
258	C₂²×C₁₁₃	—	4	4	no	—
259	C₂²×C₁₁₃	—	4	4	no	—
260	C₂²×C₁₁₃	—	4	4	no	—
261	C₂²×C₁₁₃	—	4	4	no	—
262	C₂²×C₁₁₃	—	4	4	no	—
263	C₂²×C₁₁₃	—	4	4	no	—
264	C₂²×C₁₁₃	—	4	4	no	—
265	C₂²×C₁₁₃	—	4	4	no	—
266	C₂²×C₁₁₃	—	4	4	no	—
267	C₂²×C₁₁₃	—	4	4	no	—
268	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
269	C₂²×C₁₁₃	C₂×#120	1	2	yes	—
270	C₂²×C₁₁₃	C₂×#121	1	2	yes	—
271	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
272	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
273	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
274	C₂²×C₁₁₃	#525	1	2	yes	—
275	C₂²×C₁₁₃	#525	1	1	yes	characteristic
276	C₂²×C₁₁₃	C₂×#127	1	1	yes	characteristic
277	C₂²×C₁₁₃	#536	1	2	yes	—
278	C₂²×C₁₁₃	#536	1	1	yes	characteristic
279	C₂²×C₁₁₃	#537	1	2	yes	—
280	C₂²×C₁₁₃	#537	1	1	yes	characteristic
281	C₂²×C₁₁₃	#546	1	2	yes	—
282	C₂²×C₁₁₃	#547	1	2	yes	—
283	C₂²×C₁₁₃	#548	1	2	yes	—
284	C₂²×C₁₁₃	#548	1	2	yes	—
285	C₂²×C₁₁₃	D₄×Q₈	1	1	yes	characteristic
286	C₂²×C₁₁₃	D₄×Q₈	1	2	yes	—
287	C₂²×C₁₁₃	#550	1	1	yes	characteristic
288	C₂²×C₁₁₃	#552	1	2	yes	—
289	C₂²×C₁₁₃	#554	1	1	yes	characteristic
290	C₂²×C₁₁₃	#556	1	1	yes	characteristic
291	C₄×C₁₁₃	—	2	4	no	—
292	C₄×C₁₁₃	—	4	2	no	—
293	C₄×C₁₁₃	—	4	4	no	—
294	C₄×C₁₁₃	—	4	4	no	—
295	C₄×C₁₁₃	—	4	8	no	—
296	C₄×C₁₁₃	—	8	2	no	—
297	C₄×C₁₁₃	#392	1	8	yes	—
298	#15177	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂×C₁₁₃	—	4	8	no	—
300	C₂×C₁₁₃	C₂×#392	1	1	yes	characteristic
301	C₂×C₁₁₃	#2407	1	2	yes	—
302	C₂×C₁₁₃	#2409	1	2	yes	—
303	C₂×C₁₁₃	#2415	1	2	yes	—
304	C₂×C₁₁₃	#2417	1	2	yes	—
305	C₂×C₁₁₃	#2536	1	1	yes	characteristic
306	C₂×C₁₁₃	#2538	1	1	yes	characteristic
307	C₂×C₁₁₃	#2540	1	1	yes	characteristic
308	C₂×C₁₁₃	#2542	1	1	yes	characteristic
309	C₂×C₁₁₃	#2616	1	1	yes	characteristic
310	C₂×C₁₁₃	#2848	1	1	yes	characteristic
311	C₂²×C₂²⋊Q₈	C₂×C₁₁₃	1	2	yes	complemented
312	C₂²×C₄×D₄	C₂×C₁₁₃	1	1	yes	characteristic
313	C₂×#391	C₂×C₁₁₃	1	1	yes	characteristic, complemented
314	C₂×#380	C₂×C₁₁₃	1	2	yes	complemented
315	#1444	C₂×C₁₁₃	1	2	yes	complemented
316	#1439	C₂×C₁₁₃	1	4	yes	complemented
317	#1438	C₂×C₁₁₃	1	2	yes	—
318	C₄⋊#95	C₂×C₁₁₃	1	1	yes	characteristic, complemented
319	C₁₁₃	#15177	1	1	yes	characteristic, direct product factor, Sylow
320	C₂³×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
321	C₂³×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
322	C₂⁴×C₄	C₂²×C₁₁₃	1	2	yes	—
323	C₂×C₂²⋊Q₈	—	2	8	no	—
324	C₂×C₂²⋊Q₈	—	2	8	no	—
325	C₂×C₂²⋊Q₈	—	2	8	no	—
326	C₂×C₄×D₄	—	2	8	no	—
327	C₂×C₄×D₄	—	2	4	no	—
328	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
330	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
331	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	—
333	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
334	C₂²×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	—
335	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
336	#391	—	2	4	no	—
337	#380	—	2	8	no	—
338	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
339	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
340	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
341	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
342	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
343	C₂⁵	C₂³×C₁₁₃	1	2	yes	—
344	C₂²×Q₈	—	2	4	no	—
345	C₂²×Q₈	—	2	4	no	—
346	C₂²×Q₈	—	2	2	no	—
347	C₂²×Q₈	—	2	2	no	—
348	C₂²×Q₈	D₄×C₁₁₃	1	4	yes	complemented
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	Q₈×C₁₁₃	1	4	yes	complemented
354	C₂³×C₄	—	2	4	no	—
355	C₂³×C₄	—	2	4	no	—
356	C₂³×C₄	—	2	4	no	—
357	C₂³×C₄	—	2	4	no	—
358	C₂³×C₄	—	2	4	no	—
359	C₂³×C₄	—	2	4	no	—
360	C₂³×C₄	D₄×C₁₁₃	1	8	yes	—
361	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
368	C₂²⋊Q₈	—	2	64	no	—
369	C₄×D₄	—	2	32	no	—
370	C₂×C₄⋊C₄	—	2	4	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	8	no	—
373	C₂×C₄⋊C₄	—	2	8	no	—
374	C₂×C₄⋊C₄	—	2	8	no	—
375	C₂×C₄⋊C₄	—	2	4	no	—
376	C₂×C₄⋊C₄	—	2	4	no	—
377	C₂×C₄⋊C₄	—	2	4	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	D₄×C₁₁₃	1	8	yes	complemented
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₂²⋊C₄	—	2	4	no	—
384	C₂×C₂²⋊C₄	—	2	8	no	—
385	C₂×C₂²⋊C₄	—	2	8	no	—
386	C₂×C₂²⋊C₄	—	2	8	no	—
387	C₂×C₂²⋊C₄	—	2	8	no	—
388	C₂×C₂²⋊C₄	—	4	4	no	—
389	C₂×C₄²	—	2	4	no	—
390	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
391	#95	—	2	8	no	—
392	#95	—	2	4	no	—
393	#95	—	2	4	no	—
394	#95	—	2	4	no	—
395	#95	—	4	2	no	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	C₂×D₄×C₁₁₃	1	4	yes	—
409	C₂⁴	C₂×Q₈×C₁₁₃	1	4	yes	—
410	C₂⁴	#41×C₁₁₃	1	4	yes	—
411	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
412	C₂×Q₈	—	2	16	no	—
413	C₂×Q₈	—	2	8	no	—
414	C₂×Q₈	—	4	4	no	—
415	C₂×Q₈	—	4	8	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	16	no	—
420	C₂×D₄	—	2	16	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	16	no	—
445	C₂²×C₄	—	2	16	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	4	8	no	—
453	C₂²×C₄	—	4	8	no	—
454	C₂²×C₄	—	4	8	no	—
455	C₂²×C₄	—	4	8	no	—
456	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
458	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
462	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
465	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
466	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
467	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	32	no	—
470	C₄⋊C₄	—	2	16	no	—
471	C₄⋊C₄	—	4	4	no	—
472	C₂²⋊C₄	—	2	16	no	—
473	C₂²⋊C₄	—	2	32	no	—
474	C₂²⋊C₄	—	4	16	no	—
475	C₄²	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	C₂²⋊Q₈×C₁₁₃	1	8	yes	complemented
511	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
512	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
513	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
514	C₂³	C₂²×D₄×C₁₁₃	1	2	yes	—
515	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
516	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
517	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
518	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
519	C₂³	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
520	C₂³	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
521	C₂³	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
522	Q₈	—	4	16	no	—
523	D₄	—	2	32	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	32	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	#120×C₁₁₃	1	4	yes	—
559	C₂×C₄	#120×C₁₁₃	1	8	yes	—
560	C₂×C₄	#121×C₁₁₃	1	8	yes	—
561	C₂×C₄	#121×C₁₁₃	1	4	yes	—
562	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	complemented
563	C₂×C₄	#127×C₁₁₃	1	4	yes	—
564	C₂²	—	2	8	no	—
565	C₂²	—	2	8	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
580	C₂²	C₂×#120×C₁₁₃	1	2	yes	—
581	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
582	C₂²	C₂×#121×C₁₁₃	1	2	yes	—
583	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
584	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
585	C₂²	#525×C₁₁₃	1	1	yes	characteristic
586	C₂²	#525×C₁₁₃	1	2	yes	—
587	C₂²	C₂×#127×C₁₁₃	1	1	yes	characteristic
588	C₂²	#536×C₁₁₃	1	1	yes	characteristic
589	C₂²	#536×C₁₁₃	1	2	yes	—
590	C₂²	#537×C₁₁₃	1	1	yes	characteristic
591	C₂²	#537×C₁₁₃	1	2	yes	—
592	C₂²	#546×C₁₁₃	1	2	yes	—
593	C₂²	#547×C₁₁₃	1	2	yes	—
594	C₂²	#548×C₁₁₃	1	2	yes	—
595	C₂²	#548×C₁₁₃	1	2	yes	—
596	C₂²	D₄×Q₈×C₁₁₃	1	1	yes	characteristic
597	C₂²	D₄×Q₈×C₁₁₃	1	2	yes	—
598	C₂²	#550×C₁₁₃	1	1	yes	characteristic
599	C₂²	#552×C₁₁₃	1	2	yes	—
600	C₂²	#554×C₁₁₃	1	1	yes	characteristic
601	C₂²	#556×C₁₁₃	1	1	yes	characteristic
602	C₄	—	2	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	8	no	—
607	C₄	—	8	2	no	—
608	C₄	#392×C₁₁₃	1	8	yes	—
609	C₂	—	4	8	no	—
610	C₂	C₂×#392×C₁₁₃	1	1	yes	characteristic
611	C₂	C₁₁₃×#2407	1	2	yes	—
612	C₂	C₁₁₃×#2409	1	2	yes	—
613	C₂	C₁₁₃×#2415	1	2	yes	—
614	C₂	C₁₁₃×#2417	1	2	yes	—
615	C₂	C₁₁₃×#2536	1	1	yes	characteristic
616	C₂	C₁₁₃×#2538	1	1	yes	characteristic
617	C₂	C₁₁₃×#2540	1	1	yes	characteristic
618	C₂	C₁₁₃×#2542	1	1	yes	characteristic
619	C₂	C₁₁₃×#2616	1	1	yes	characteristic
620	C₂	C₁₁₃×#2848	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
prime radical	C₂³×D₄×C₁₁₃	C₂²
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
1. C₂²×C₂²⋊Q₈×C₁₁₃	C₂	semidirect
3. C₂×#391×C₁₁₃	C₂	semidirect
4. C₂×#380×C₁₁₃	C₂	semidirect
5. C₁₁₃×#1444	C₂	semidirect
6. C₁₁₃×#1439	C₂	semidirect
8. C₁₁₃×C₄⋊#95	C₂	semidirect
37. C₂²×Q₈×C₁₁₃	D₄	semidirect
42. C₂²×D₄×C₁₁₃	Q₈	semidirect
68. C₂×C₄⋊C₄×C₁₁₃	D₄	semidirect
199. C₂³×C₁₁₃	C₂²⋊Q₈	semidirect
251. C₂×C₄×C₁₁₃	C₂²⋊Q₈	semidirect
298. #15177	C₁₁₃	direct (N × H)
311. C₂²×C₂²⋊Q₈	C₂×C₁₁₃	semidirect
313. C₂×#391	C₂×C₁₁₃	semidirect
314. C₂×#380	C₂×C₁₁₃	semidirect
315. #1444	C₂×C₁₁₃	semidirect
316. #1439	C₂×C₁₁₃	semidirect
318. C₄⋊#95	C₂×C₁₁₃	semidirect
319. C₁₁₃	#15177	direct (N × H)
348. C₂²×Q₈	D₄×C₁₁₃	semidirect
353. C₂²×D₄	Q₈×C₁₁₃	semidirect
379. C₂×C₄⋊C₄	D₄×C₁₁₃	semidirect
510. C₂³	C₂²⋊Q₈×C₁₁₃	semidirect
562. C₂×C₄	C₂²⋊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×C₂²⋊Q₈×C₁₁₃	2
C₂²×C₄×D₄×C₁₁₃	2
C₂×#391×C₁₁₃	2
C₂×#380×C₁₁₃	2
C₁₁₃×#1444	2
C₁₁₃×#1439	2
C₁₁₃×#1438	2
C₁₁₃×C₄⋊#95	2
#15177	113

Subgroups — C113×#15177 #43283197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#15177 #43283197