Subgroups — #28404239

Order 14464.

1658 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813667	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299266	C₂	1	2	yes	maximal, complemented
4	#20299254	C₂	1	2	yes	maximal, complemented
5	#20299245	C₂	1	2	yes	maximal, complemented
6	#20299238	C₂	1	4	yes	maximal, complemented
7	#20299232	C₂	1	2	yes	maximal, complemented
8	D₄×C₂²⋊D₁₁₃	C₂	1	4	yes	maximal, complemented
9	#20299179	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299177	C₂	1	2	yes	maximal, complemented
11	#20299165	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299164	C₂	1	2	yes	maximal, complemented
13	#20299109	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299108	C₂	1	2	yes	maximal, complemented
15	#121×D₁₁₃	C₂	1	2	yes	maximal, complemented
16	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#16813667	—	2	8	no	—
19	C₂×#14268647	—	2	8	no	—
20	C₂×#14268647	C₂²	1	1	yes	characteristic
21	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
23	C₂×#14268647	C₂²	1	2	yes	complemented
24	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14268647	C₂²	1	2	yes	complemented
26	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14268646	C₂²	1	2	yes	complemented
28	C₂×#14268646	C₂²	1	2	yes	complemented
29	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
32	C₂²×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
33	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
34	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
35	C₂×D₄×D₁₁₃	C₂²	1	4	yes	complemented
36	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
37	#16813618	C₂²	1	4	yes	complemented
38	#16813618	C₂²	1	2	yes	complemented
39	#16813609	C₂²	1	2	yes	complemented
40	#16813608	C₂²	1	4	yes	complemented
41	#16813605	C₂²	1	2	yes	complemented
42	#16813604	C₂²	1	4	yes	complemented
43	#16813602	C₂²	1	2	yes	complemented
44	#16813602	C₂²	1	2	yes	complemented
45	#16813601	C₂²	1	1	yes	characteristic, complemented
46	#16813601	C₂²	1	1	yes	characteristic, complemented
47	#16813599	C₂²	1	4	yes	complemented
48	#16813597	C₂²	1	2	yes	complemented
49	#16813597	C₂²	1	2	yes	complemented
50	#16813596	C₂²	1	1	yes	characteristic, complemented
51	#16813596	C₂²	1	1	yes	characteristic, complemented
52	#16813596	C₂²	1	4	yes	complemented
53	#16813595	C₂²	1	4	yes	complemented
54	#16813595	C₂²	1	4	yes	complemented
55	#16813594	C₂²	1	4	yes	complemented
56	#16813594	C₂²	1	4	yes	complemented
57	#16813593	C₂²	1	2	yes	complemented
58	#16813593	C₂²	1	2	yes	complemented
59	#16813593	C₂²	1	4	yes	complemented
60	#16813592	C₂²	1	4	yes	complemented
61	#16813591	C₂²	1	2	yes	complemented
62	#16813591	C₂²	1	4	yes	complemented
63	#16813590	C₂²	1	4	yes	complemented
64	#16813590	C₂²	1	4	yes	complemented
65	#16813587	C₂²	1	2	yes	complemented
66	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
67	#16813584	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
70	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
71	#16813582	C₂²	1	4	yes	complemented
72	#16813581	C₂²	1	1	yes	characteristic, complemented
73	#16813580	C₂²	1	2	yes	complemented
74	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
75	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
76	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
77	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	complemented
78	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
79	#121×C₁₁₃	C₂²	1	2	yes	complemented
80	#121×C₁₁₃	C₂²	1	2	yes	complemented
81	#121×C₁₁₃	C₂²	1	2	yes	complemented
82	#121×C₁₁₃	C₂²	1	2	yes	complemented
83	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
85	C₂³×D₁₁₃	C₂³	1	2	yes	—
86	C₂³×D₁₁₃	C₂³	1	4	yes	—
87	#14268647	—	2	4	no	—
88	#14268647	—	2	4	no	—
89	#14268647	—	2	8	no	—
90	#14268647	—	2	4	no	—
91	#14268647	—	2	8	no	—
92	#14268647	—	2	4	no	—
93	#14268647	D₄	1	8	yes	complemented
94	#14268646	—	2	8	no	—
95	#14268646	—	2	8	no	—
96	C₂×Dic₂₂₆	—	2	4	no	—
97	C₂×Dic₂₂₆	C₂³	1	2	yes	—
98	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
99	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
100	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
101	C₂×D₄₅₂	—	2	4	no	—
102	C₂×D₄₅₂	C₂³	1	2	yes	—
103	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
104	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
105	C₂×D₄₅₂	C₂³	1	4	yes	—
106	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
108	C₂×C₂²⋊D₁₁₃	—	2	16	no	—
109	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
110	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
111	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
112	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
113	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
114	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
120	D₄×D₁₁₃	—	2	8	no	—
121	D₄×D₁₁₃	—	2	8	no	—
122	D₄×D₁₁₃	—	4	8	no	—
123	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
124	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
125	C₂×C₄×D₁₁₃	—	2	8	no	—
126	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
127	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
128	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
129	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
130	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
131	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
132	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
135	#14268626	C₂³	1	4	yes	—
136	#14268626	C₂³	1	2	yes	—
137	#14268626	C₂³	1	2	yes	—
138	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
139	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
140	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
141	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
142	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
143	#14268624	C₂³	1	2	yes	—
144	#14268624	C₂³	1	4	yes	—
145	#14268624	C₂³	1	4	yes	—
146	#14268624	C₂³	1	4	yes	—
147	#14268624	C₂³	1	2	yes	—
148	C₄×Dic₁₁₃	C₂³	1	4	yes	—
149	C₄×Dic₁₁₃	C₂³	1	2	yes	—
150	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
151	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
152	C₂×D₄×C₁₁₃	—	2	4	no	—
153	C₂×D₄×C₁₁₃	—	4	4	no	—
154	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
155	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
156	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
157	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
158	C₂²×C₄×C₁₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
160	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
161	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
162	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
163	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
164	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
165	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
169	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
170	C₂³×C₁₁₃	—	2	2	no	—
171	C₂³×C₁₁₃	—	2	2	no	—
172	C₂³×C₁₁₃	—	2	4	no	—
173	C₂³×C₁₁₃	—	4	1	no	—
174	C₂³×C₁₁₃	—	4	2	no	—
175	C₂³×C₁₁₃	—	4	2	no	—
176	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
177	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
178	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
179	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×D₁₁₃	—	2	4	no	—
181	C₂²×D₁₁₃	—	2	4	no	—
182	C₂²×D₁₁₃	—	2	8	no	—
183	C₂²×D₁₁₃	—	4	2	no	—
184	C₂²×D₁₁₃	—	4	4	no	—
185	C₂²×D₁₁₃	—	4	4	no	—
186	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
187	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
188	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
189	D₄×C₁₁₃	—	2	8	no	—
190	D₄×C₁₁₃	—	2	4	no	—
191	D₄×C₁₁₃	—	2	4	no	—
192	D₄×C₁₁₃	—	4	4	no	—
193	C₂×C₄×C₁₁₃	—	2	2	no	—
194	C₂×C₄×C₁₁₃	—	2	2	no	—
195	C₂×C₄×C₁₁₃	—	2	2	no	—
196	C₂×C₄×C₁₁₃	—	2	2	no	—
197	C₂×C₄×C₁₁₃	—	2	2	no	—
198	C₂×C₄×C₁₁₃	—	4	2	no	—
199	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	complemented
200	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
201	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
202	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
203	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
204	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²⋊D₁₁₃	—	2	4	no	—
206	C₂²⋊D₁₁₃	—	2	4	no	—
207	C₂²⋊D₁₁₃	—	2	4	no	—
208	C₂²⋊D₁₁₃	—	2	8	no	—
209	C₂²⋊D₁₁₃	—	2	4	no	—
210	C₂²⋊D₁₁₃	—	2	8	no	—
211	C₂²⋊D₁₁₃	—	2	4	no	—
212	C₂²⋊D₁₁₃	—	4	4	no	—
213	C₂²⋊D₁₁₃	—	4	4	no	—
214	C₂²⋊D₁₁₃	—	4	2	no	—
215	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
216	C₂×Dic₁₁₃	—	2	4	no	—
217	C₂×Dic₁₁₃	—	2	8	no	—
218	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
219	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
220	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
221	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
222	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
223	D₄₅₂	—	2	4	no	—
224	D₄₅₂	—	2	2	no	—
225	D₄₅₂	—	2	2	no	—
226	D₄₅₂	—	4	4	no	—
227	D₄₅₂	C₂×D₄	1	4	yes	complemented
228	C₄×D₁₁₃	—	2	4	no	—
229	C₄×D₁₁₃	—	2	4	no	—
230	C₄×D₁₁₃	—	2	4	no	—
231	C₄×D₁₁₃	—	2	4	no	—
232	C₄×D₁₁₃	—	4	4	no	—
233	C₄×D₁₁₃	C₂×D₄	1	8	yes	complemented
234	Dic₂₂₆	—	2	2	no	—
235	Dic₂₂₆	—	2	2	no	—
236	Dic₂₂₆	—	2	4	no	—
237	Dic₂₂₆	C₂×D₄	1	4	yes	complemented
238	C₂²×C₁₁₃	—	2	1	no	—
239	C₂²×C₁₁₃	—	2	1	no	—
240	C₂²×C₁₁₃	—	2	1	no	—
241	C₂²×C₁₁₃	—	2	1	no	—
242	C₂²×C₁₁₃	—	2	4	no	—
243	C₂²×C₁₁₃	—	2	1	no	—
244	C₂²×C₁₁₃	—	2	4	no	—
245	C₂²×C₁₁₃	—	2	1	no	—
246	C₂²×C₁₁₃	—	2	1	no	—
247	C₂²×C₁₁₃	—	2	4	no	—
248	C₂²×C₁₁₃	—	4	4	no	—
249	C₂²×C₁₁₃	—	8	4	no	—
250	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
251	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	complemented
252	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
253	C₂×D₁₁₃	—	2	2	no	—
254	C₂×D₁₁₃	—	2	2	no	—
255	C₂×D₁₁₃	—	2	2	no	—
256	C₂×D₁₁₃	—	2	2	no	—
257	C₂×D₁₁₃	—	2	2	no	—
258	C₂×D₁₁₃	—	2	2	no	—
259	C₂×D₁₁₃	—	2	2	no	—
260	C₂×D₁₁₃	—	2	2	no	—
261	C₂×D₁₁₃	—	4	8	no	—
262	C₂×D₁₁₃	—	8	8	no	—
263	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
264	C₄×C₁₁₃	—	2	1	no	—
265	C₄×C₁₁₃	—	2	1	no	—
266	C₄×C₁₁₃	—	2	4	no	—
267	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
268	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
269	Dic₁₁₃	—	2	2	no	—
270	Dic₁₁₃	—	2	2	no	—
271	Dic₁₁₃	—	2	2	no	—
272	Dic₁₁₃	—	2	2	no	—
273	Dic₁₁₃	C₂²×D₄	1	4	yes	—
274	C₂×C₁₁₃	—	2	2	no	—
275	C₂×C₁₁₃	—	2	2	no	—
276	C₂×C₁₁₃	—	4	4	no	—
277	C₂×C₁₁₃	—	4	1	no	—
278	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
279	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₁₁₃	#585	1	1	yes	characteristic
281	D₁₁₃	—	2	4	no	—
282	D₁₁₃	—	4	2	no	—
283	D₁₁₃	—	4	2	no	—
284	#3488	—	113	1	no	maximal, Sylow
285	C₁₁₃	#3488	1	1	yes	characteristic, complemented, Sylow
286	C₂×H(5,𝔽₂)	—	113	1	no	—
287	C₂²×#41	—	113	1	no	—
288	#550	—	113	2	no	—
289	#548	—	113	2	no	—
290	#546	—	113	2	no	—
291	#546	—	113	4	no	—
292	D₄²	—	113	4	no	—
293	D₄²	—	113	2	no	—
294	#537	—	113	2	no	—
295	#537	—	113	1	no	—
296	#535	—	113	1	no	—
297	#535	—	113	2	no	—
298	#525	—	113	1	no	—
299	#525	—	113	2	no	—
300	C₂×#121	—	113	2	no	—
301	C₂×#121	D₁₁₃	1	1	yes	characteristic, complemented
302	#520	—	113	1	no	—
303	H(5,𝔽₂)	—	226	8	no	—
304	C₂×#41	—	113	2	no	—
305	C₂×#41	—	113	2	no	—
306	C₂×#41	—	113	1	no	—
307	C₂×#41	—	113	1	no	—
308	C₂×#41	—	113	2	no	—
309	C₂×#41	—	113	1	no	—
310	C₂×#41	—	113	1	no	—
311	C₂×#41	—	113	2	no	—
312	C₂×#41	—	113	1	no	—
313	C₂×#41	—	226	8	no	—
314	C₂²×Q₈	—	113	1	no	—
315	C₂²×D₄	—	113	2	no	—
316	C₂²×D₄	—	113	4	no	—
317	C₂²×D₄	—	113	4	no	—
318	C₂²×D₄	—	113	2	no	—
319	C₂²×D₄	—	113	2	no	—
320	C₂²×D₄	—	113	1	no	—
321	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
322	C₂²×D₄	C₂×D₁₁₃	1	2	yes	complemented
323	C₂³×C₄	—	113	2	no	—
324	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
325	#127	—	113	2	no	—
326	#127	—	113	4	no	—
327	#124	—	113	2	no	—
328	#124	—	113	4	no	—
329	#123	—	113	2	no	—
330	#123	—	113	4	no	—
331	C₂²⋊Q₈	—	113	1	no	—
332	C₂²⋊Q₈	—	113	1	no	—
333	C₂²⋊Q₈	—	113	2	no	—
334	C₂²⋊Q₈	—	113	2	no	—
335	C₂²⋊Q₈	—	113	4	no	—
336	#121	—	113	2	no	—
337	#121	—	113	4	no	—
338	#121	—	113	2	no	—
339	#121	—	113	4	no	—
340	#121	—	113	4	no	—
341	#121	—	113	1	no	—
342	#121	—	113	1	no	—
343	#121	—	113	4	no	—
344	#121	—	113	2	no	—
345	#121	—	113	2	no	—
346	#121	—	113	4	no	—
347	#121	—	113	4	no	—
348	#121	C₂×D₁₁₃	1	2	yes	complemented
349	#121	C₂×D₁₁₃	1	2	yes	complemented
350	#121	C₂×D₁₁₃	1	2	yes	complemented
351	#121	C₂×D₁₁₃	1	2	yes	complemented
352	#120	—	113	2	no	—
353	#120	—	113	4	no	—
354	#120	—	113	4	no	—
355	#120	—	113	4	no	—
356	#120	—	113	4	no	—
357	C₄×Q₈	—	113	2	no	—
358	C₄×D₄	—	113	4	no	—
359	C₄×D₄	—	113	4	no	—
360	C₄×D₄	—	113	2	no	—
361	C₄×D₄	—	113	2	no	—
362	C₄×D₄	—	113	2	no	—
363	C₄×D₄	—	113	4	no	—
364	#117	—	113	1	no	—
365	#117	—	113	2	no	—
366	C₂×C₄⋊C₄	—	113	2	no	—
367	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
368	C₂×C₂²⋊C₄	—	113	4	no	—
369	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
370	C₂⁴	—	113	4	no	—
371	C₂⁴	—	113	2	no	—
372	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
373	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
374	#41	—	113	8	no	—
375	#41	—	226	8	no	—
376	#41	—	226	8	no	—
377	#41	—	226	4	no	—
378	#41	—	226	4	no	—
379	#41	—	226	8	no	—
380	#41	—	226	8	no	—
381	#41	—	226	4	no	—
382	#41	—	226	4	no	—
383	C₂×Q₈	—	113	1	no	—
384	C₂×Q₈	—	113	1	no	—
385	C₂×Q₈	—	113	2	no	—
386	C₂×Q₈	—	113	1	no	—
387	C₂×Q₈	—	226	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	113	2	no	—
391	C₂×D₄	—	113	2	no	—
392	C₂×D₄	—	113	4	no	—
393	C₂×D₄	—	113	4	no	—
394	C₂×D₄	—	113	2	no	—
395	C₂×D₄	—	113	2	no	—
396	C₂×D₄	—	113	2	no	—
397	C₂×D₄	—	113	4	no	—
398	C₂×D₄	—	113	2	no	—
399	C₂×D₄	—	113	4	no	—
400	C₂×D₄	—	113	2	no	—
401	C₂×D₄	—	113	1	no	—
402	C₂×D₄	—	113	4	no	—
403	C₂×D₄	—	113	2	no	—
404	C₂×D₄	—	113	1	no	—
405	C₂×D₄	—	113	1	no	—
406	C₂×D₄	—	452	8	no	—
407	C₂×D₄	—	226	4	no	—
408	C₂×D₄	—	226	8	no	—
409	C₂×D₄	—	226	8	no	—
410	C₂×D₄	—	226	8	no	—
411	C₂×D₄	—	226	16	no	—
412	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
413	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
414	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
415	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	113	2	no	—
418	C₂²×C₄	—	113	2	no	—
419	C₂²×C₄	—	113	4	no	—
420	C₂²×C₄	—	113	4	no	—
421	C₂²×C₄	—	113	2	no	—
422	C₂²×C₄	—	113	2	no	—
423	C₂²×C₄	—	113	2	no	—
424	C₂²×C₄	—	113	2	no	—
425	C₂²×C₄	—	226	8	no	—
426	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
432	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
433	C₄⋊C₄	—	113	1	no	—
434	C₄⋊C₄	—	113	4	no	—
435	C₄⋊C₄	—	113	1	no	—
436	C₄⋊C₄	—	113	2	no	—
437	C₄⋊C₄	—	113	2	no	—
438	C₄⋊C₄	—	113	4	no	—
439	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
440	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
441	C₂²⋊C₄	—	113	4	no	—
442	C₂²⋊C₄	—	113	2	no	—
443	C₂²⋊C₄	—	113	2	no	—
444	C₂²⋊C₄	—	113	4	no	—
445	C₂²⋊C₄	—	113	2	no	—
446	C₂²⋊C₄	—	113	2	no	—
447	C₂²⋊C₄	—	113	4	no	—
448	C₂²⋊C₄	—	113	4	no	—
449	C₂²⋊C₄	—	113	2	no	—
450	C₂²⋊C₄	—	113	4	no	—
451	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
452	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
453	C₄²	—	113	4	no	—
454	C₄²	—	113	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	113	2	no	—
462	C₂³	—	113	2	no	—
463	C₂³	—	113	2	no	—
464	C₂³	—	452	4	no	—
465	C₂³	—	452	4	no	—
466	C₂³	—	452	2	no	—
467	C₂³	—	226	8	no	—
468	C₂³	—	226	4	no	—
469	C₂³	—	226	4	no	—
470	C₂³	C₂³×D₁₁₃	1	4	yes	—
471	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
472	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
473	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
474	Q₈	—	113	4	no	—
475	Q₈	—	226	4	no	—
476	Q₈	—	226	2	no	—
477	Q₈	—	226	2	no	—
478	D₄	—	2	8	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	113	8	no	—
483	D₄	—	113	4	no	—
484	D₄	—	452	4	no	—
485	D₄	—	452	4	no	—
486	D₄	—	452	2	no	—
487	D₄	—	452	4	no	—
488	D₄	—	226	4	no	—
489	D₄	—	226	8	no	—
490	D₄	—	226	4	no	—
491	D₄	—	226	8	no	—
492	D₄	—	226	4	no	—
493	D₄	—	226	4	no	—
494	D₄	—	226	4	no	—
495	D₄	—	226	4	no	—
496	D₄	—	226	2	no	—
497	D₄	—	226	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	113	2	no	—
505	C₂×C₄	—	113	8	no	—
506	C₂×C₄	—	113	2	no	—
507	C₂×C₄	—	113	2	no	—
508	C₂×C₄	—	113	2	no	—
509	C₂×C₄	—	113	2	no	—
510	C₂×C₄	—	452	4	no	—
511	C₂×C₄	—	226	4	no	—
512	C₂×C₄	—	226	4	no	—
513	C₂×C₄	—	226	4	no	—
514	C₂×C₄	—	226	8	no	—
515	C₂×C₄	—	226	4	no	—
516	C₂×C₄	—	226	4	no	—
517	C₂×C₄	D₄×D₁₁₃	1	4	yes	complemented
518	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
519	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	113	4	no	—
536	C₂²	—	904	8	no	—
537	C₂²	—	452	8	no	—
538	C₂²	—	226	2	no	—
539	C₂²	—	226	2	no	—
540	C₂²	—	226	2	no	—
541	C₂²	—	226	2	no	—
542	C₂²	—	226	2	no	—
543	C₂²	—	226	2	no	—
544	C₂²	—	226	2	no	—
545	C₂²	—	226	2	no	—
546	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
547	C₂²	#16813667	1	2	yes	complemented
548	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	4	no	—
552	C₄	—	113	4	no	—
553	C₄	—	226	2	no	—
554	C₄	—	226	2	no	—
555	C₄	—	226	2	no	—
556	C₄	—	226	2	no	—
557	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
558	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
559	C₂	—	2	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	1	no	—
562	C₂	—	4	4	no	—
563	C₂	—	452	2	no	—
564	C₂	—	452	2	no	—
565	C₂	—	226	4	no	—
566	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
567	C₂	C₂×#16813667	1	1	yes	characteristic
568	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#121×C₁₁₃	C₂
hypercenter	C₂×#121	D₁₁₃
hypocenter	C₁₁₃	#3488
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#16813667	C₂	semidirect
2. C₂²×#14268647	C₂	semidirect
3. #20299266	C₂	semidirect
4. #20299254	C₂	semidirect
5. #20299245	C₂	semidirect
6. #20299238	C₂	semidirect
7. #20299232	C₂	semidirect
8. D₄×C₂²⋊D₁₁₃	C₂	semidirect
9. #20299179	C₂	semidirect
10. #20299177	C₂	semidirect
11. #20299165	C₂	semidirect
12. #20299164	C₂	semidirect
13. #20299109	C₂	semidirect
14. #20299108	C₂	semidirect
15. #121×D₁₁₃	C₂	semidirect
16. #20299079	C₂	semidirect
17. C₂×#121×C₁₁₃	C₂	semidirect
21. C₂×#14268647	C₂²	semidirect
22. C₂×#14268647	C₂²	semidirect
23. C₂×#14268647	C₂²	semidirect
24. C₂×#14268647	C₂²	semidirect
25. C₂×#14268647	C₂²	semidirect
26. C₂×#14268647	C₂²	semidirect
27. C₂×#14268646	C₂²	semidirect
28. C₂×#14268646	C₂²	semidirect
29. C₂²×Dic₂₂₆	C₂²	semidirect
30. C₂²×D₄₅₂	C₂²	semidirect
31. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
32. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
33. C₂×D₄×D₁₁₃	C₂²	semidirect
34. C₂×D₄×D₁₁₃	C₂²	semidirect
35. C₂×D₄×D₁₁₃	C₂²	semidirect
36. C₂²×C₄×D₁₁₃	C₂²	semidirect
37. #16813618	C₂²	semidirect
38. #16813618	C₂²	semidirect
39. #16813609	C₂²	semidirect
40. #16813608	C₂²	semidirect
41. #16813605	C₂²	semidirect
42. #16813604	C₂²	semidirect
43. #16813602	C₂²	semidirect
44. #16813602	C₂²	semidirect
45. #16813601	C₂²	semidirect
46. #16813601	C₂²	semidirect
47. #16813599	C₂²	semidirect
48. #16813597	C₂²	semidirect
49. #16813597	C₂²	semidirect
50. #16813596	C₂²	semidirect
51. #16813596	C₂²	semidirect
52. #16813596	C₂²	semidirect
53. #16813595	C₂²	semidirect
54. #16813595	C₂²	semidirect
55. #16813594	C₂²	semidirect
56. #16813594	C₂²	semidirect
57. #16813593	C₂²	semidirect
58. #16813593	C₂²	semidirect
59. #16813593	C₂²	semidirect
60. #16813592	C₂²	semidirect
61. #16813591	C₂²	semidirect
62. #16813591	C₂²	semidirect
63. #16813590	C₂²	semidirect
64. #16813590	C₂²	semidirect
65. #16813587	C₂²	semidirect
66. D₄×Dic₁₁₃	C₂²	semidirect
67. #16813584	C₂²	semidirect
68. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
69. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
70. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
71. #16813582	C₂²	semidirect
72. #16813581	C₂²	semidirect
73. #16813580	C₂²	semidirect
74. C₄⋊C₄×D₁₁₃	C₂²	semidirect
75. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
76. C₂²×D₄×C₁₁₃	C₂²	semidirect
77. C₂²×D₄×C₁₁₃	C₂²	semidirect
78. C₂³×C₄×C₁₁₃	C₂²	semidirect
79. #121×C₁₁₃	C₂²	semidirect
80. #121×C₁₁₃	C₂²	semidirect
81. #121×C₁₁₃	C₂²	semidirect
82. #121×C₁₁₃	C₂²	semidirect
83. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
84. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
93. #14268647	D₄	semidirect
199. C₂×C₄×C₁₁₃	C₂×D₄	semidirect
215. C₂²⋊D₁₁₃	C₂×D₄	semidirect
227. D₄₅₂	C₂×D₄	semidirect
233. C₄×D₁₁₃	C₂×D₄	semidirect
237. Dic₂₂₆	C₂×D₄	semidirect
251. C₂²×C₁₁₃	H(5,𝔽₂)	semidirect
285. C₁₁₃	#3488	semidirect
301. C₂×#121	D₁₁₃	semidirect
321. C₂²×D₄	C₂×D₁₁₃	semidirect
322. C₂²×D₄	C₂×D₁₁₃	semidirect
324. C₂³×C₄	C₂×D₁₁₃	semidirect
348. #121	C₂×D₁₁₃	semidirect
349. #121	C₂×D₁₁₃	semidirect
350. #121	C₂×D₁₁₃	semidirect
351. #121	C₂×D₁₁₃	semidirect
367. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
369. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
517. C₂×C₄	D₄×D₁₁₃	semidirect
547. C₂²	#16813667	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813667	2
C₂²×#14268647	2
#20299266	2
#20299254	2
#20299245	2
#20299238	2
#20299232	2
D₄×C₂²⋊D₁₁₃	2
#20299179	2
#20299177	2
#20299165	2
#20299164	2
#20299109	2
#20299108	2
#121×D₁₁₃	2
#20299079	2
C₂×#121×C₁₁₃	2
#3488	113