Subgroups — #28404388

Order 14464.

1060 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299328	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299325	C₂	1	2	yes	maximal, complemented
4	#20299306	C₂	1	2	yes	maximal, complemented
5	#20299305	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299303	C₂	1	2	yes	maximal, complemented
7	D₄×Dic₂₂₆	C₂	1	2	yes	maximal, complemented
8	#20299261	C₂	1	4	yes	maximal, complemented
9	#20299228	C₂	1	2	yes	maximal, complemented
10	#20299227	C₂	1	4	yes	maximal, complemented
11	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299150	C₂	1	2	yes	maximal, complemented
13	C₂×#16813621	C₂	1	2	yes	maximal, complemented
14	C₄⋊Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299077	C₂	1	2	yes	maximal
16	C₄×#14268646	C₂	1	1	yes	maximal, characteristic
17	#554×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268646	C₂²	1	1	yes	characteristic
19	C₂²×Dic₂₂₆	C₂²	1	4	yes	—
20	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
21	#16813622	C₂²	1	2	yes	—
22	#16813622	C₂²	1	1	yes	characteristic
23	#16813621	C₂²	1	2	yes	—
24	#16813621	C₂²	1	2	yes	—
25	#16813621	C₂²	1	2	yes	—
26	#16813621	C₂²	1	2	yes	—
27	#16813621	C₂²	1	4	yes	—
28	#16813621	C₂²	1	4	yes	—
29	#16813621	C₂²	1	2	yes	—
30	#16813621	C₂²	1	1	yes	characteristic
31	#16813621	C₂²	1	4	yes	—
32	#16813620	C₂²	1	4	yes	—
33	#16813620	C₂²	1	2	yes	—
34	#16813620	C₂²	1	1	yes	characteristic
35	#16813613	C₂²	1	2	yes	—
36	#16813612	C₂²	1	4	yes	—
37	#16813612	C₂²	1	4	yes	—
38	#16813612	C₂²	1	4	yes	—
39	#16813612	C₂²	1	2	yes	—
40	#16813602	C₂²	1	1	yes	characteristic
41	#16813602	C₂²	1	4	yes	—
42	#16813601	C₂²	1	4	yes	—
43	#16813601	C₂²	1	2	yes	—
44	#16813600	C₂²	1	4	yes	—
45	#16813600	C₂²	1	2	yes	—
46	#16813599	C₂²	1	4	yes	—
47	#16813599	C₂²	1	4	yes	—
48	#16813599	C₂²	1	4	yes	—
49	#16813598	C₂²	1	1	yes	characteristic
50	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
51	C₄×Dic₂₂₆	C₂²	1	2	yes	—
52	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
53	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
54	C₄×Dic₂₂₆	C₂²	1	2	yes	—
55	#16813587	C₂²	1	2	yes	—
56	#16813587	C₂²	1	1	yes	characteristic
57	#16813587	C₂²	1	2	yes	—
58	#16813587	C₂²	1	4	yes	—
59	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
60	D₄×Dic₁₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
63	#16813582	C₂²	1	4	yes	—
64	#16813582	C₂²	1	2	yes	—
65	#16813580	C₂²	1	1	yes	characteristic
66	#16813579	C₂²	1	2	yes	—
67	#16813578	C₂²	1	2	yes	—
68	#16813578	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
70	C₂×#14268626	C₂²	1	4	yes	—
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
73	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
76	#125×C₁₁₃	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	—
79	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
81	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
83	#14268646	Q₈	1	8	yes	complemented
84	C₂×Dic₂₂₆	—	4	8	no	—
85	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₂₆	C₂³	1	4	yes	—
87	C₂×Dic₂₂₆	C₂³	1	2	yes	—
88	C₂×Dic₂₂₆	C₂³	1	2	yes	—
89	C₂×Dic₂₂₆	C₂³	1	4	yes	—
90	C₂×Dic₂₂₆	C₂³	1	4	yes	—
91	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
92	Q₈×D₁₁₃	—	4	4	no	—
93	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
94	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
95	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
96	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
105	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
107	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
108	#14268626	C₂³	1	4	yes	—
109	#14268626	C₂³	1	4	yes	—
110	#14268626	C₂³	1	2	yes	—
111	#14268626	C₂³	1	4	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	2	yes	—
114	#14268626	C₂³	1	2	yes	—
115	#14268626	C₂³	1	2	yes	—
116	#14268626	C₂³	1	2	yes	—
117	#14268626	C₂³	1	4	yes	—
118	#14268626	C₂³	1	4	yes	—
119	#14268626	C₂³	1	2	yes	—
120	#14268626	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
123	#14268624	C₂³	1	2	yes	—
124	#14268624	C₂³	1	2	yes	—
125	#14268624	C₂³	1	2	yes	—
126	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
127	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
128	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
129	C₄×Dic₁₁₃	C₂³	1	2	yes	—
130	C₄×Dic₁₁₃	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	2	yes	—
132	C₄×Dic₁₁₃	C₂³	1	4	yes	—
133	C₄×Dic₁₁₃	C₂³	1	4	yes	—
134	C₄×Dic₁₁₃	C₂³	1	2	yes	—
135	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
137	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
148	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
149	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₁₃	C₂³	1	2	yes	—
151	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
152	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
153	Q₈×C₁₁₃	—	2	2	no	—
154	Q₈×C₁₁₃	—	4	2	no	—
155	D₄×C₁₁₃	C₂×Q₈	1	4	yes	complemented
156	C₂×C₄×C₁₁₃	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	4	4	no	—
158	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
163	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂²⋊D₁₁₃	C₂×Q₈	1	8	yes	complemented
166	C₂×Dic₁₁₃	—	2	4	no	—
167	C₂×Dic₁₁₃	—	4	4	no	—
168	C₂×Dic₁₁₃	C₂×Q₈	1	8	yes	complemented
169	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
170	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
171	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
177	C₄×D₁₁₃	—	2	2	no	—
178	C₄×D₁₁₃	—	2	2	no	—
179	C₄×D₁₁₃	—	4	4	no	—
180	C₄×D₁₁₃	C₂×Q₈	1	4	yes	complemented
181	Dic₂₂₆	—	2	2	no	—
182	Dic₂₂₆	—	2	8	no	—
183	Dic₂₂₆	—	2	4	no	—
184	Dic₂₂₆	—	4	2	no	—
185	Dic₂₂₆	—	4	4	no	—
186	Dic₂₂₆	—	4	4	no	—
187	Dic₂₂₆	C₂×Q₈	1	4	yes	complemented
188	C₂²×C₁₁₃	—	2	2	no	—
189	C₂²×C₁₁₃	—	2	2	no	—
190	C₂²×C₁₁₃	C₂²×Q₈	1	4	yes	—
191	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
192	C₂×D₁₁₃	—	2	1	no	—
193	C₂×D₁₁₃	—	2	1	no	—
194	C₂×D₁₁₃	C₂²×Q₈	1	2	yes	—
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	4	no	—
197	C₄×C₁₁₃	—	2	1	no	—
198	C₄×C₁₁₃	—	2	2	no	—
199	C₄×C₁₁₃	—	2	2	no	—
200	C₄×C₁₁₃	C₂²×Q₈	1	2	yes	—
201	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
202	Dic₁₁₃	—	2	4	no	—
203	Dic₁₁₃	—	2	2	no	—
204	Dic₁₁₃	—	2	2	no	—
205	Dic₁₁₃	—	2	2	no	—
206	Dic₁₁₃	—	2	1	no	—
207	Dic₁₁₃	C₂²×Q₈	1	4	yes	—
208	Dic₁₁₃	C₂²×Q₈	1	2	yes	—
209	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
210	C₂×C₁₁₃	—	2	4	no	—
211	C₂×C₁₁₃	C₂³×Q₈	1	1	yes	characteristic
212	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
214	D₁₁₃	—	2	2	no	—
215	#3503	—	113	1	no	maximal, Sylow
216	C₁₁₃	#3503	1	1	yes	characteristic, complemented, Sylow
217	Q₈²	—	113	1	no	—
218	Q₈²	—	113	1	no	—
219	#557	—	113	2	no	—
220	#554	—	113	2	no	—
221	#554	—	113	1	no	—
222	#554	—	113	2	no	—
223	#554	D₁₁₃	1	1	yes	characteristic, complemented
224	D₄×Q₈	—	113	4	no	—
225	D₄×Q₈	—	113	2	no	—
226	#544	—	113	2	no	—
227	#544	—	113	4	no	—
228	#533	—	113	2	no	—
229	#533	—	113	1	no	—
230	C₂×C₄⋊Q₈	—	113	1	no	—
231	C₂×C₄⋊Q₈	—	113	2	no	—
232	#520	—	113	2	no	—
233	C₄×#41	—	113	1	no	—
234	C₂×#41	—	113	1	no	—
235	C₂²×Q₈	—	113	2	no	—
236	C₂²×Q₈	—	113	4	no	—
237	C₄⋊Q₈	—	113	2	no	—
238	C₄⋊Q₈	—	113	1	no	—
239	C₄⋊Q₈	—	113	4	no	—
240	C₄⋊Q₈	—	113	2	no	—
241	C₄⋊Q₈	—	113	1	no	—
242	C₄⋊Q₈	—	113	4	no	—
243	C₄⋊Q₈	—	113	4	no	—
244	C₄⋊Q₈	—	113	2	no	—
245	C₄⋊Q₈	—	113	2	no	—
246	C₄⋊Q₈	—	113	2	no	—
247	C₄⋊Q₈	—	113	4	no	—
248	C₄⋊Q₈	—	113	2	no	—
249	C₄⋊Q₈	—	113	1	no	—
250	C₄⋊Q₈	—	113	2	no	—
251	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
252	#125	—	113	2	no	—
253	#125	—	113	4	no	—
254	#125	—	113	4	no	—
255	#125	—	113	4	no	—
256	#125	—	113	2	no	—
257	#125	C₂×D₁₁₃	1	2	yes	—
258	C₂²⋊Q₈	—	113	1	no	—
259	C₂²⋊Q₈	—	113	2	no	—
260	C₂²⋊Q₈	—	113	4	no	—
261	C₂²⋊Q₈	—	113	2	no	—
262	C₂²⋊Q₈	—	113	1	no	—
263	C₂²⋊Q₈	—	113	4	no	—
264	C₂²⋊Q₈	—	113	4	no	—
265	C₂²⋊Q₈	—	113	4	no	—
266	C₂²⋊Q₈	—	113	4	no	—
267	C₂²⋊Q₈	—	113	4	no	—
268	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
269	C₂²⋊Q₈	C₂×D₁₁₃	1	4	yes	—
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	1	no	—
272	C₄×Q₈	—	113	2	no	—
273	C₄×Q₈	—	113	4	no	—
274	C₄×Q₈	—	113	2	no	—
275	C₄×Q₈	—	113	1	no	—
276	C₄×Q₈	—	113	2	no	—
277	C₄×Q₈	—	113	2	no	—
278	C₄×Q₈	—	113	1	no	—
279	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
280	C₄×D₄	—	113	1	no	—
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	4	no	—
284	C₄×D₄	—	113	2	no	—
285	C₄×D₄	—	113	4	no	—
286	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
287	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
288	#117	—	113	1	no	—
289	#117	—	113	2	no	—
290	#117	—	113	4	no	—
291	#117	—	113	2	no	—
292	C₂×C₄⋊C₄	—	113	4	no	—
293	C₂×C₄⋊C₄	—	113	2	no	—
294	C₂×C₄⋊C₄	—	113	2	no	—
295	C₂×C₄⋊C₄	—	113	2	no	—
296	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	—
297	C₂×C₄²	—	113	2	no	—
298	C₂×C₄²	—	113	1	no	—
299	#41	—	113	8	no	—
300	C₂×Q₈	—	113	1	no	—
301	C₂×Q₈	—	113	4	no	—
302	C₂×Q₈	—	113	4	no	—
303	C₂×Q₈	—	113	2	no	—
304	C₂×Q₈	—	113	1	no	—
305	C₂×Q₈	—	113	4	no	—
306	C₂×Q₈	—	113	2	no	—
307	C₂×Q₈	—	452	8	no	—
308	C₂×Q₈	—	452	4	no	—
309	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
310	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
311	C₂×D₄	—	113	2	no	—
312	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
313	C₂²×C₄	—	113	2	no	—
314	C₂²×C₄	—	113	1	no	—
315	C₂²×C₄	—	113	4	no	—
316	C₂²×C₄	—	113	2	no	—
317	C₂²×C₄	—	113	4	no	—
318	C₂²×C₄	—	113	1	no	—
319	C₂²×C₄	—	113	1	no	—
320	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
321	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
322	C₄⋊C₄	—	113	4	no	—
323	C₄⋊C₄	—	113	2	no	—
324	C₄⋊C₄	—	113	1	no	—
325	C₄⋊C₄	—	113	2	no	—
326	C₄⋊C₄	—	113	4	no	—
327	C₄⋊C₄	—	113	4	no	—
328	C₄⋊C₄	—	113	2	no	—
329	C₄⋊C₄	—	113	4	no	—
330	C₄⋊C₄	—	113	4	no	—
331	C₄⋊C₄	—	113	2	no	—
332	C₄⋊C₄	—	113	2	no	—
333	C₄⋊C₄	—	113	2	no	—
334	C₄⋊C₄	—	113	1	no	—
335	C₄⋊C₄	—	113	2	no	—
336	C₄⋊C₄	—	113	4	no	—
337	C₄⋊C₄	—	113	2	no	—
338	C₄⋊C₄	—	113	2	no	—
339	C₄⋊C₄	—	113	4	no	—
340	C₄⋊C₄	—	113	2	no	—
341	C₄⋊C₄	—	113	4	no	—
342	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
343	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
345	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
346	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
348	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
349	C₂²⋊C₄	—	113	4	no	—
350	C₂²⋊C₄	—	113	2	no	—
351	C₂²⋊C₄	—	113	2	no	—
352	C₂²⋊C₄	—	113	2	no	—
353	C₂²⋊C₄	—	113	2	no	—
354	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
355	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
356	C₄²	—	113	1	no	—
357	C₄²	—	113	1	no	—
358	C₄²	—	113	2	no	—
359	C₄²	—	113	2	no	—
360	C₄²	—	113	2	no	—
361	C₄²	—	113	1	no	—
362	C₄²	—	113	4	no	—
363	C₄²	—	113	4	no	—
364	C₄²	—	113	2	no	—
365	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
366	C₄²	C₂²×D₁₁₃	1	2	yes	—
367	C₂³	—	113	1	no	—
368	C₂³	C₂³×D₁₁₃	1	2	yes	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	113	4	no	—
372	Q₈	—	452	4	no	—
373	Q₈	—	452	4	no	—
374	Q₈	—	452	2	no	—
375	Q₈	—	226	4	no	—
376	Q₈	—	226	8	no	—
377	Q₈	—	226	2	no	—
378	D₄	—	113	8	no	—
379	D₄	Q₈×D₁₁₃	1	4	yes	complemented
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	113	8	no	—
383	C₂×C₄	—	113	2	no	—
384	C₂×C₄	—	113	1	no	—
385	C₂×C₄	—	113	1	no	—
386	C₂×C₄	—	113	4	no	—
387	C₂×C₄	—	113	2	no	—
388	C₂×C₄	—	113	1	no	—
389	C₂×C₄	—	113	2	no	—
390	C₂×C₄	—	113	4	no	—
391	C₂×C₄	—	113	2	no	—
392	C₂×C₄	—	452	4	no	—
393	C₂×C₄	—	452	4	no	—
394	C₂×C₄	—	226	2	no	—
395	C₂×C₄	—	226	4	no	—
396	C₂×C₄	—	226	2	no	—
397	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
398	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
399	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
401	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
402	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	113	2	no	—
407	C₂²	—	226	1	no	—
408	C₂²	—	226	1	no	—
409	C₂²	C₂×Q₈×D₁₁₃	1	4	yes	—
410	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	113	2	no	—
417	C₄	—	113	4	no	—
418	C₄	—	113	2	no	—
419	C₄	—	226	4	no	—
420	C₄	—	226	2	no	—
421	C₄	—	226	2	no	—
422	C₄	—	226	1	no	—
423	C₄	—	226	2	no	—
424	C₄	C₂×Q₈×D₁₁₃	1	2	yes	—
425	C₄	#16813669	1	2	yes	—
426	C₂	—	2	4	no	—
427	C₂	—	226	2	no	—
428	C₂	C₂²×Q₈×D₁₁₃	1	1	yes	characteristic
429	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
430	C₂	C₂×#16813669	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#554×C₁₁₃	C₂
prime radical	C₂×#14268646	C₂²
hypercenter	#554	D₁₁₃
hypocenter	C₁₁₃	#3503
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. Q₈×Dic₂₂₆	C₂	semidirect
2. #20299328	C₂	semidirect
3. #20299325	C₂	semidirect
4. #20299306	C₂	semidirect
5. #20299305	C₂	semidirect
6. #20299303	C₂	semidirect
7. D₄×Dic₂₂₆	C₂	semidirect
8. #20299261	C₂	semidirect
9. #20299228	C₂	semidirect
10. #20299227	C₂	semidirect
11. #20299152	C₂	semidirect
12. #20299150	C₂	semidirect
13. C₂×#16813621	C₂	semidirect
14. C₄⋊Q₈×D₁₁₃	C₂	semidirect
17. #554×C₁₁₃	C₂	semidirect
83. #14268646	Q₈	semidirect
155. D₄×C₁₁₃	C₂×Q₈	semidirect
165. C₂²⋊D₁₁₃	C₂×Q₈	semidirect
168. C₂×Dic₁₁₃	C₂×Q₈	semidirect
180. C₄×D₁₁₃	C₂×Q₈	semidirect
187. Dic₂₂₆	C₂×Q₈	semidirect
216. C₁₁₃	#3503	semidirect
223. #554	D₁₁₃	semidirect
379. D₄	Q₈×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₂₂₆	2
#20299328	2
#20299325	2
#20299306	2
#20299305	2
#20299303	2
D₄×Dic₂₂₆	2
#20299261	2
#20299228	2
#20299227	2
#20299152	2
#20299150	2
C₂×#16813621	2
C₄⋊Q₈×D₁₁₃	2
#20299077	2
C₄×#14268646	2
#554×C₁₁₃	2
#3503	113