Subgroups — #28407111

Order 14464.

496 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299549	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299548	C₂	1	1	yes	maximal, characteristic
3	#20299548	C₂	1	1	yes	maximal, characteristic
4	#20299548	C₂	1	1	yes	maximal, characteristic
5	#20299547	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299547	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299547	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299545	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₄×#90673	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₄×#90673	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊#90673	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×#90673	C₂	1	1	yes	maximal, characteristic
13	C₂²⋊C₄×#90673	C₂	1	1	yes	maximal, characteristic
14	#20299534	C₂	1	1	yes	maximal, characteristic, complemented
15	#126×D₁₁₃	C₂	1	1	yes	maximal, characteristic
16	C₂³×#90673	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#90673	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#90673	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#90673	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#90673	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#90673	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊#90673	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊#90673	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#90673	C₂²	1	1	yes	characteristic
25	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
26	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
27	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
28	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
29	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
30	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
31	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
32	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
33	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
34	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
35	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
36	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
42	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×#90673)⋊C₄	C₂²	1	1	yes	characteristic
44	#16813617	C₄	1	1	yes	characteristic, complemented
45	#16813617	C₄	1	1	yes	characteristic, complemented
46	#16813617	C₄	1	1	yes	characteristic, complemented
47	#16813616	C₄	1	1	yes	characteristic, complemented
48	#16813615	C₄	1	1	yes	characteristic, complemented
49	#16813615	C₄	1	1	yes	characteristic, complemented
50	#16813615	C₄	1	1	yes	characteristic, complemented
51	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
52	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
53	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
54	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
55	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
56	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
57	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
58	#126×C₁₁₃	C₄	1	1	yes	characteristic, complemented
59	C₂²×#90673	—	2	2	no	—
60	C₂²×#90673	—	2	2	no	—
61	C₂²×#90673	—	4	1	no	—
62	C₂²×#90673	C₂³	1	1	yes	characteristic
63	C₂²×#90673	C₂³	1	1	yes	characteristic
64	C₂²×#90673	C₂³	1	1	yes	characteristic
65	C₂²×#90673	C₂³	1	1	yes	characteristic
66	C₂²×#90673	C₂³	1	1	yes	characteristic
67	C₂²×#90673	C₂³	1	1	yes	characteristic
68	C₂²×#90673	C₂³	1	1	yes	characteristic
69	C₂²×#90673	C₂³	1	1	yes	characteristic
70	C₄⋊#90673	—	2	2	no	—
71	C₄⋊#90673	—	2	2	no	—
72	C₄⋊#90673	—	2	2	no	—
73	C₄⋊#90673	—	2	2	no	—
74	C₄⋊#90673	—	4	1	no	—
75	C₂²⋊#90673	—	2	2	no	—
76	C₂²⋊#90673	—	2	2	no	—
77	C₂²⋊#90673	—	4	1	no	—
78	C₄×#90673	—	2	2	no	—
79	C₄×#90673	—	2	2	no	—
80	C₄×#90673	—	2	2	no	—
81	C₄×#90673	—	2	2	no	—
82	C₄×#90673	—	4	1	no	—
83	C₄×#90673	—	4	1	no	—
84	C₄×#90673	—	4	1	no	—
85	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
92	C₄⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
93	C₄⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
94	C₄⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
95	#14268626	C₂×C₄	1	1	yes	characteristic, complemented
96	#14268626	C₂×C₄	1	1	yes	characteristic, complemented
97	#14268626	C₂×C₄	1	1	yes	characteristic, complemented
98	#14268626	C₂×C₄	1	1	yes	characteristic, complemented
99	#14268626	C₂×C₄	1	1	yes	characteristic, complemented
100	#14268626	C₂×C₄	1	1	yes	characteristic, complemented
101	C₂²⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
104	#14268624	C₂×C₄	1	1	yes	characteristic
105	#14268624	C₂×C₄	1	1	yes	characteristic
106	#14268624	C₂×C₄	1	1	yes	characteristic
107	#14268624	C₂×C₄	1	1	yes	characteristic
108	#14268624	C₂×C₄	1	1	yes	characteristic
109	#14268624	C₂×C₄	1	1	yes	characteristic
110	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
111	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
112	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
113	C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
114	C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
115	C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂³×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×D₁₁₃	—	2	1	no	—
122	C₂²×D₁₁₃	—	2	1	no	—
123	C₂²×D₁₁₃	—	2	1	no	—
124	C₂²×D₁₁₃	—	2	1	no	—
125	C₂²×D₁₁₃	—	2	1	no	—
126	C₂²×D₁₁₃	—	2	1	no	—
127	C₂²×D₁₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×#90673	—	2	1	no	—
130	C₂×#90673	—	2	1	no	—
131	C₂×#90673	—	2	1	no	—
132	C₂×#90673	—	2	1	no	—
133	C₂×#90673	—	2	1	no	—
134	C₂×#90673	—	2	1	no	—
135	C₂×#90673	—	2	1	no	—
136	C₂×#90673	—	2	1	no	—
137	C₂×#90673	—	2	1	no	—
138	C₂×#90673	—	2	1	no	—
139	C₂×#90673	—	2	1	no	—
140	C₂×#90673	—	2	1	no	—
141	C₂×#90673	—	2	1	no	—
142	C₂×#90673	—	2	1	no	—
143	C₂×#90673	—	2	1	no	—
144	C₂×#90673	—	2	1	no	—
145	C₂×#90673	—	2	1	no	—
146	C₂×#90673	—	2	1	no	—
147	C₂×#90673	—	2	1	no	—
148	C₂×#90673	—	2	1	no	—
149	C₂×#90673	—	4	4	no	—
150	C₂×#90673	#41	1	2	yes	—
151	C₂×#90673	#41	1	2	yes	—
152	C₂×#90673	#41	1	2	yes	—
153	C₂×#90673	#41	1	2	yes	—
154	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₄×D₁₁₃	—	2	1	no	—
167	C₄×D₁₁₃	—	2	1	no	—
168	C₄×D₁₁₃	—	2	1	no	—
169	C₄×D₁₁₃	—	2	1	no	—
170	C₄×D₁₁₃	—	2	1	no	—
171	C₄×D₁₁₃	—	2	1	no	—
172	C₄×D₁₁₃	—	2	1	no	—
173	C₄×D₁₁₃	—	2	1	no	—
174	C₄×D₁₁₃	—	2	1	no	—
175	C₄×D₁₁₃	—	2	1	no	—
176	C₄×D₁₁₃	—	2	1	no	—
177	C₄×D₁₁₃	—	2	1	no	—
178	C₂²×C₁₁₃	—	2	1	no	—
179	C₂²×C₁₁₃	—	2	1	no	—
180	C₂²×C₁₁₃	—	2	1	no	—
181	C₂²×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×D₁₁₃	—	2	1	no	—
183	C₂×D₁₁₃	—	2	1	no	—
184	C₂×D₁₁₃	—	2	1	no	—
185	C₂×D₁₁₃	—	4	1	no	—
186	C₂×D₁₁₃	—	4	1	no	—
187	C₂×D₁₁₃	—	4	1	no	—
188	C₂×D₁₁₃	—	4	1	no	—
189	C₂×D₁₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×D₁₁₃	C₂×#41	1	1	yes	characteristic
191	C₂×D₁₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×D₁₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×D₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×D₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
195	#90673	—	2	2	no	—
196	#90673	—	2	2	no	—
197	#90673	—	2	2	no	—
198	#90673	—	2	2	no	—
199	#90673	—	4	1	no	—
200	#90673	—	4	1	no	—
201	#90673	—	4	1	no	—
202	#90673	—	4	1	no	—
203	C₄×C₁₁₃	—	2	1	no	—
204	C₄×C₁₁₃	—	2	1	no	—
205	C₄×C₁₁₃	—	2	1	no	—
206	C₄×C₁₁₃	—	2	1	no	—
207	C₄×C₁₁₃	—	2	1	no	—
208	C₄×C₁₁₃	—	2	1	no	—
209	Dic₁₁₃	—	2	1	no	—
210	Dic₁₁₃	—	2	1	no	—
211	Dic₁₁₃	—	2	1	no	—
212	Dic₁₁₃	—	2	1	no	—
213	Dic₁₁₃	—	2	1	no	—
214	Dic₁₁₃	—	2	1	no	—
215	C₂×C₁₁₃	—	4	1	no	—
216	C₂×C₁₁₃	C₄×#41	1	1	yes	characteristic
217	C₂×C₁₁₃	C₄×#41	1	1	yes	characteristic
218	C₂×C₁₁₃	#520	1	1	yes	characteristic
219	D₁₁₃	—	4	1	no	—
220	D₁₁₃	#551	1	1	yes	characteristic
221	D₁₁₃	#552	1	1	yes	characteristic
222	D₁₁₃	#553	1	1	yes	characteristic
223	D₁₁₃	#556	1	1	yes	characteristic
224	#2373	—	113	1	no	maximal, Sylow
225	C₁₁₃	#2373	1	1	yes	characteristic, complemented, Sylow
226	C₂×#126	—	113	1	no	—
227	#389	—	113	1	no	—
228	#388	—	113	1	no	—
229	#388	—	113	1	no	—
230	#388	—	113	1	no	—
231	#387	—	113	1	no	—
232	#387	—	113	1	no	—
233	#387	—	113	1	no	—
234	#385	—	113	1	no	—
235	C₄×C₄⋊C₄	—	113	1	no	—
236	C₄×C₄⋊C₄	—	113	1	no	—
237	C₄×C₄⋊C₄	—	113	1	no	—
238	C₄×C₂²⋊C₄	—	113	1	no	—
239	C₄×C₂²⋊C₄	—	113	1	no	—
240	#376	—	113	1	no	—
241	C₂³×C₄	—	113	1	no	—
242	#126	—	113	1	no	—
243	#126	—	113	1	no	—
244	#126	—	113	1	no	—
245	#126	—	113	1	no	—
246	#126	—	113	1	no	—
247	#126	—	113	1	no	—
248	#126	—	113	1	no	—
249	#126	#90673	1	1	yes	characteristic, complemented
250	C₂×C₄⋊C₄	—	113	1	no	—
251	C₂×C₄⋊C₄	—	113	1	no	—
252	C₂×C₄⋊C₄	—	113	1	no	—
253	C₂×C₄⋊C₄	—	113	1	no	—
254	C₂×C₄⋊C₄	—	113	1	no	—
255	C₂×C₄⋊C₄	—	113	1	no	—
256	C₂×C₄⋊C₄	—	113	1	no	—
257	C₂×C₄⋊C₄	—	113	1	no	—
258	C₂×C₂²⋊C₄	—	113	1	no	—
259	C₂×C₂²⋊C₄	—	113	1	no	—
260	C₂×C₂²⋊C₄	—	113	1	no	—
261	C₂×C₂²⋊C₄	—	113	1	no	—
262	C₂×C₂²⋊C₄	—	113	1	no	—
263	C₂×C₂²⋊C₄	—	113	1	no	—
264	C₂×C₄²	—	113	1	no	—
265	C₂×C₄²	—	113	1	no	—
266	C₂×C₄²	—	113	1	no	—
267	C₂×C₄²	—	113	1	no	—
268	C₂×C₄²	—	113	1	no	—
269	C₂×C₄²	—	113	1	no	—
270	C₂×C₄²	—	113	1	no	—
271	C₂×C₄²	—	113	1	no	—
272	#95	—	113	1	no	—
273	#95	—	113	1	no	—
274	#95	—	113	1	no	—
275	#95	—	113	1	no	—
276	#95	—	113	1	no	—
277	#95	—	113	1	no	—
278	#95	—	113	1	no	—
279	#95	—	113	1	no	—
280	#95	—	113	1	no	—
281	#95	—	113	1	no	—
282	#95	—	113	1	no	—
283	#95	—	113	1	no	—
284	C₂⁴	—	113	1	no	—
285	C₂²×C₄	—	113	1	no	—
286	C₂²×C₄	—	113	1	no	—
287	C₂²×C₄	—	113	1	no	—
288	C₂²×C₄	—	113	1	no	—
289	C₂²×C₄	—	113	1	no	—
290	C₂²×C₄	—	113	1	no	—
291	C₂²×C₄	—	113	1	no	—
292	C₂²×C₄	—	113	1	no	—
293	C₂²×C₄	—	113	1	no	—
294	C₂²×C₄	—	113	1	no	—
295	C₂²×C₄	—	113	1	no	—
296	C₂²×C₄	—	113	1	no	—
297	C₂²×C₄	—	113	1	no	—
298	C₂²×C₄	—	113	1	no	—
299	C₂²×C₄	—	452	1	no	—
300	C₂²×C₄	—	226	2	no	—
301	C₂²×C₄	—	226	2	no	—
302	C₄⋊C₄	—	113	1	no	—
303	C₄⋊C₄	—	113	1	no	—
304	C₄⋊C₄	—	113	1	no	—
305	C₄⋊C₄	—	113	1	no	—
306	C₄⋊C₄	—	113	1	no	—
307	C₄⋊C₄	—	113	1	no	—
308	C₄⋊C₄	—	113	1	no	—
309	C₄⋊C₄	—	113	1	no	—
310	C₄⋊C₄	—	113	1	no	—
311	C₄⋊C₄	—	452	1	no	—
312	C₄⋊C₄	—	226	2	no	—
313	C₄⋊C₄	—	226	2	no	—
314	C₄⋊C₄	—	226	2	no	—
315	C₄⋊C₄	—	226	2	no	—
316	C₄⋊C₄	C₂×#90673	1	1	yes	characteristic, complemented
317	C₄⋊C₄	C₂×#90673	1	1	yes	characteristic, complemented
318	C₄⋊C₄	C₂×#90673	1	1	yes	characteristic, complemented
319	C₂²⋊C₄	—	113	1	no	—
320	C₂²⋊C₄	—	113	1	no	—
321	C₂²⋊C₄	—	113	1	no	—
322	C₂²⋊C₄	—	113	1	no	—
323	C₂²⋊C₄	—	113	1	no	—
324	C₂²⋊C₄	—	113	1	no	—
325	C₂²⋊C₄	—	113	1	no	—
326	C₂²⋊C₄	—	113	1	no	—
327	C₂²⋊C₄	—	113	1	no	—
328	C₂²⋊C₄	—	452	1	no	—
329	C₂²⋊C₄	—	226	2	no	—
330	C₂²⋊C₄	—	226	2	no	—
331	C₂²⋊C₄	C₂×#90673	1	1	yes	characteristic
332	C₂²⋊C₄	C₂×#90673	1	1	yes	characteristic
333	C₂²⋊C₄	C₂×#90673	1	1	yes	characteristic
334	C₄²	—	113	1	no	—
335	C₄²	—	113	1	no	—
336	C₄²	—	113	1	no	—
337	C₄²	—	452	1	no	—
338	C₄²	—	452	1	no	—
339	C₄²	—	452	1	no	—
340	C₄²	—	226	2	no	—
341	C₄²	—	226	2	no	—
342	C₄²	—	226	2	no	—
343	C₄²	—	226	2	no	—
344	C₄²	C₂×#90673	1	1	yes	characteristic, complemented
345	C₂³	—	113	1	no	—
346	C₂³	—	113	1	no	—
347	C₂³	—	226	1	no	—
348	C₂³	—	226	1	no	—
349	C₂³	—	226	1	no	—
350	C₂³	—	226	1	no	—
351	C₂³	—	226	1	no	—
352	C₂³	—	226	1	no	—
353	C₂³	C₂²×#90673	1	1	yes	characteristic
354	C₂×C₄	—	113	2	no	—
355	C₂×C₄	—	113	2	no	—
356	C₂×C₄	—	113	2	no	—
357	C₂×C₄	—	113	2	no	—
358	C₂×C₄	—	113	1	no	—
359	C₂×C₄	—	113	1	no	—
360	C₂×C₄	—	113	1	no	—
361	C₂×C₄	—	113	1	no	—
362	C₂×C₄	—	113	1	no	—
363	C₂×C₄	—	113	1	no	—
364	C₂×C₄	—	452	4	no	—
365	C₂×C₄	—	226	1	no	—
366	C₂×C₄	—	226	1	no	—
367	C₂×C₄	—	226	1	no	—
368	C₂×C₄	—	226	1	no	—
369	C₂×C₄	—	226	1	no	—
370	C₂×C₄	—	226	1	no	—
371	C₂×C₄	—	226	1	no	—
372	C₂×C₄	—	226	1	no	—
373	C₂×C₄	—	226	1	no	—
374	C₂×C₄	—	226	1	no	—
375	C₂×C₄	—	226	1	no	—
376	C₂×C₄	—	226	1	no	—
377	C₂×C₄	—	226	1	no	—
378	C₂×C₄	—	226	1	no	—
379	C₂×C₄	—	226	1	no	—
380	C₂×C₄	—	226	1	no	—
381	C₂×C₄	—	226	1	no	—
382	C₂×C₄	—	226	1	no	—
383	C₂×C₄	—	226	1	no	—
384	C₂×C₄	—	226	1	no	—
385	C₂×C₄	—	226	1	no	—
386	C₂×C₄	—	226	1	no	—
387	C₂×C₄	—	226	1	no	—
388	C₂×C₄	—	226	1	no	—
389	C₂×C₄	—	226	1	no	—
390	C₂×C₄	—	226	1	no	—
391	C₂×C₄	—	226	1	no	—
392	C₂×C₄	—	226	1	no	—
393	C₂×C₄	—	226	1	no	—
394	C₂×C₄	—	226	1	no	—
395	C₂×C₄	—	226	1	no	—
396	C₂×C₄	—	226	1	no	—
397	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
398	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
399	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
400	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
401	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
402	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	113	1	no	—
407	C₂²	—	113	1	no	—
408	C₂²	—	113	1	no	—
409	C₂²	—	113	1	no	—
410	C₂²	—	113	1	no	—
411	C₂²	—	113	1	no	—
412	C₂²	—	452	1	no	—
413	C₂²	—	452	1	no	—
414	C₂²	—	452	1	no	—
415	C₂²	—	452	1	no	—
416	C₂²	—	226	1	no	—
417	C₂²	—	226	1	no	—
418	C₂²	—	226	1	no	—
419	C₂²	C₂³×#90673	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	452	1	no	—
427	C₄	—	452	1	no	—
428	C₄	—	452	1	no	—
429	C₄	—	452	1	no	—
430	C₄	—	226	2	no	—
431	C₄	—	226	2	no	—
432	C₄	—	226	2	no	—
433	C₄	—	226	2	no	—
434	C₄	—	226	1	no	—
435	C₄	—	226	1	no	—
436	C₄	—	226	1	no	—
437	C₄	—	226	1	no	—
438	C₄	—	226	1	no	—
439	C₄	—	226	1	no	—
440	C₂	—	4	1	no	—
441	C₂	—	113	1	no	—
442	C₂	—	113	1	no	—
443	C₂	—	113	1	no	—
444	C₂	—	113	1	no	—
445	C₂	—	452	1	no	—
446	C₂	#41×#90673	1	1	yes	characteristic
447	C₂	#41×#90673	1	1	yes	characteristic
448	C₂	#20299667	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#90673
commutator, socle	C₂²×C₁₁₃	C₂³×C₄
Fitting	#126×C₁₁₃	C₄
prime radical	C₂³×D₁₁₃	C₂³
cosocle	C₂²×D₁₁₃	C₂⁴
hypercenter	#126	#90673
hypocenter	C₁₁₃	#2373
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #126

Complements

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

N	H ≅ G/N	type
1. #20299549	C₂	semidirect
5. #20299547	C₂	semidirect
6. #20299547	C₂	semidirect
7. #20299547	C₂	semidirect
9. C₄⋊C₄×#90673	C₂	semidirect
10. C₄⋊C₄×#90673	C₂	semidirect
11. C₄×C₄⋊#90673	C₂	semidirect
14. #20299534	C₂	semidirect
44. #16813617	C₄	semidirect
45. #16813617	C₄	semidirect
46. #16813617	C₄	semidirect
47. #16813616	C₄	semidirect
48. #16813615	C₄	semidirect
49. #16813615	C₄	semidirect
50. #16813615	C₄	semidirect
58. #126×C₁₁₃	C₄	semidirect
92. C₄⋊Dic₁₁₃	C₂×C₄	semidirect
93. C₄⋊Dic₁₁₃	C₂×C₄	semidirect
94. C₄⋊Dic₁₁₃	C₂×C₄	semidirect
95. #14268626	C₂×C₄	semidirect
96. #14268626	C₂×C₄	semidirect
97. #14268626	C₂×C₄	semidirect
98. #14268626	C₂×C₄	semidirect
99. #14268626	C₂×C₄	semidirect
100. #14268626	C₂×C₄	semidirect
110. C₄×Dic₁₁₃	C₂×C₄	semidirect
111. C₄×Dic₁₁₃	C₂×C₄	semidirect
112. C₄×Dic₁₁₃	C₂×C₄	semidirect
113. C₄⋊C₄×C₁₁₃	C₂×C₄	semidirect
114. C₄⋊C₄×C₁₁₃	C₂×C₄	semidirect
115. C₄⋊C₄×C₁₁₃	C₂×C₄	semidirect
119. C₄²×C₁₁₃	C₂×C₄	semidirect
225. C₁₁₃	#2373	semidirect
249. #126	#90673	semidirect
316. C₄⋊C₄	C₂×#90673	semidirect
317. C₄⋊C₄	C₂×#90673	semidirect
318. C₄⋊C₄	C₂×#90673	semidirect
344. C₄²	C₂×#90673	semidirect

Maximal subgroups

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

subgroup	index
#20299549	2
#20299548	2
#20299547	2
#20299545	2
C₄⋊C₄×#90673	2
C₄×C₄⋊#90673	2
C₂²⋊C₄×#90673	2
#20299534	2
#126×D₁₁₃	2
#2373	113