Subgroups — #28404192

Order 14464.

1094 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299323	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299322	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299319	C₂	1	2	yes	maximal, complemented
4	#20299282	C₂	1	2	yes	maximal, complemented
5	#20299280	C₂	1	4	yes	maximal, complemented
6	#20299263	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299258	C₂	1	2	yes	maximal, complemented
8	#20299251	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299250	C₂	1	2	yes	maximal, complemented
10	#20299152	C₂	1	2	yes	maximal, complemented
11	#20299135	C₂	1	2	yes	maximal, complemented
12	#20299126	C₂	1	4	yes	maximal, complemented
13	C₄×#14268648	C₂	1	2	yes	maximal, complemented
14	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×Q₈×D₁₁₃	C₂	1	2	yes	maximal, complemented
17	#533×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	—
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	C₂×#14268647	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
22	#16813621	C₂²	1	2	yes	—
23	#16813620	C₂²	1	2	yes	—
24	#16813617	C₂²	1	4	yes	—
25	#16813617	C₂²	1	4	yes	—
26	#16813615	C₂²	1	4	yes	—
27	#16813613	C₂²	1	2	yes	—
28	#16813612	C₂²	1	4	yes	—
29	#16813612	C₂²	1	4	yes	—
30	#16813611	C₂²	1	2	yes	—
31	#16813608	C₂²	1	4	yes	—
32	#16813607	C₂²	1	4	yes	—
33	#16813607	C₂²	1	4	yes	—
34	#16813604	C₂²	1	4	yes	—
35	#16813602	C₂²	1	2	yes	—
36	#16813600	C₂²	1	4	yes	—
37	#16813600	C₂²	1	4	yes	—
38	#16813598	C₂²	1	2	yes	—
39	#16813598	C₂²	1	2	yes	—
40	#16813597	C₂²	1	2	yes	—
41	#16813595	C₂²	1	4	yes	—
42	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
43	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
44	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
45	C₄×Dic₂₂₆	C₂²	1	4	yes	—
46	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
47	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
48	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
49	#16813587	C₂²	1	4	yes	—
50	#16813587	C₂²	1	2	yes	—
51	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
52	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
53	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
54	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
55	C₄×D₄₅₂	C₂²	1	4	yes	—
56	#16813584	C₂²	1	4	yes	—
57	#16813584	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	#16813581	C₂²	1	1	yes	characteristic
63	#16813581	C₂²	1	1	yes	characteristic
64	#16813580	C₂²	1	4	yes	—
65	#16813580	C₂²	1	2	yes	—
66	#16813579	C₂²	1	2	yes	—
67	#16813579	C₂²	1	2	yes	—
68	#16813579	C₂²	1	4	yes	—
69	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
70	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
71	C₄²×D₁₁₃	C₂²	1	2	yes	—
72	C₄²×D₁₁₃	C₂²	1	4	yes	—
73	C₄²×D₁₁₃	C₂²	1	2	yes	—
74	C₄⋊Q₈×C₁₁₃	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	2	yes	—
79	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
80	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
81	#117×C₁₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
83	#14268648	—	2	8	no	—
84	#14268647	—	2	4	no	—
85	#14268647	—	2	4	no	—
86	C₂×Dic₂₂₆	C₂³	1	4	yes	—
87	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
88	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
89	Q₈×D₁₁₃	—	2	8	no	—
90	C₂×D₄₅₂	C₂³	1	4	yes	—
91	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
92	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
99	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
101	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
102	C₂×C₄×D₁₁₃	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	4	yes	—
107	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
109	#14268626	C₂³	1	2	yes	—
110	#14268626	C₂³	1	4	yes	—
111	#14268626	C₂³	1	4	yes	—
112	#14268626	C₂³	1	2	yes	—
113	#14268626	C₂³	1	2	yes	—
114	#14268626	C₂³	1	2	yes	—
115	#14268626	C₂³	1	4	yes	—
116	#14268626	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
119	#14268624	C₂³	1	2	yes	—
120	#14268624	C₂³	1	2	yes	—
121	#14268624	C₂³	1	2	yes	—
122	#14268624	C₂³	1	2	yes	—
123	#14268624	C₂³	1	4	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	4	yes	—
126	#14268624	C₂³	1	4	yes	—
127	C₄×Dic₁₁₃	C₂³	1	2	yes	—
128	C₄×Dic₁₁₃	C₂³	1	2	yes	—
129	C₄×Dic₁₁₃	C₂³	1	2	yes	—
130	C₄×Dic₁₁₃	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	4	yes	—
132	C₄×Dic₁₁₃	C₂³	1	2	yes	—
133	C₄×Dic₁₁₃	C₂³	1	2	yes	—
134	C₄×Dic₁₁₃	C₂³	1	4	yes	—
135	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
142	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
147	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁₃	C₂³	1	4	yes	—
150	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
152	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
154	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
155	Q₈×C₁₁₃	—	2	4	no	—
156	Q₈×C₁₁₃	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	2	2	no	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
164	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
165	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₁₁₃	—	2	4	no	—
169	C₂²⋊D₁₁₃	—	2	4	no	—
170	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
171	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
176	D₄₅₂	—	2	8	no	—
177	D₄₅₂	—	2	2	no	—
178	D₄₅₂	#41	1	4	yes	complemented
179	C₄×D₁₁₃	—	2	4	no	—
180	C₄×D₁₁₃	—	2	8	no	—
181	C₄×D₁₁₃	—	2	4	no	—
182	C₄×D₁₁₃	—	2	4	no	—
183	C₄×D₁₁₃	—	2	4	no	—
184	C₄×D₁₁₃	—	2	4	no	—
185	C₄×D₁₁₃	—	2	8	no	—
186	C₄×D₁₁₃	—	2	4	no	—
187	Dic₂₂₆	—	2	2	no	—
188	Dic₂₂₆	—	2	8	no	—
189	Dic₂₂₆	#41	1	4	yes	complemented
190	C₂²×C₁₁₃	—	2	1	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	—	2	1	no	—
193	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
194	C₂×D₁₁₃	—	2	2	no	—
195	C₂×D₁₁₃	—	2	2	no	—
196	C₂×D₁₁₃	—	2	2	no	—
197	C₂×D₁₁₃	—	2	2	no	—
198	C₂×D₁₁₃	—	2	2	no	—
199	C₂×D₁₁₃	C₂×#41	1	4	yes	—
200	C₄×C₁₁₃	—	2	4	no	—
201	C₄×C₁₁₃	—	2	1	no	—
202	C₄×C₁₁₃	—	2	1	no	—
203	C₄×C₁₁₃	—	2	4	no	—
204	C₄×C₁₁₃	—	2	1	no	—
205	C₄×C₁₁₃	C₂×#41	1	2	yes	—
206	C₄×C₁₁₃	C₂×#41	1	2	yes	—
207	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
208	Dic₁₁₃	—	2	2	no	—
209	Dic₁₁₃	—	2	2	no	—
210	Dic₁₁₃	—	2	2	no	—
211	Dic₁₁₃	—	2	2	no	—
212	Dic₁₁₃	—	2	2	no	—
213	Dic₁₁₃	C₂×#41	1	4	yes	—
214	C₂×C₁₁₃	—	4	1	no	—
215	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
216	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
217	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
218	D₁₁₃	—	2	4	no	—
219	D₁₁₃	—	4	2	no	—
220	#3482	—	113	1	no	maximal, Sylow
221	C₁₁₃	#3482	1	1	yes	characteristic, complemented, Sylow
222	#557	—	113	1	no	—
223	#556	—	113	1	no	—
224	#556	—	113	2	no	—
225	#552	—	113	4	no	—
226	#552	—	113	2	no	—
227	D₄×Q₈	—	113	1	no	—
228	#548	—	113	2	no	—
229	#547	—	113	1	no	—
230	#547	—	113	2	no	—
231	#533	—	113	2	no	—
232	#533	D₁₁₃	1	1	yes	characteristic, complemented
233	#529	—	113	2	no	—
234	#529	—	113	4	no	—
235	C₄×#41	—	113	2	no	—
236	C₄×#41	—	113	1	no	—
237	C₄×#41	—	113	1	no	—
238	C₂×C₄×Q₈	—	113	2	no	—
239	C₂×#41	—	113	2	no	—
240	C₂×#41	—	113	1	no	—
241	C₂×#41	—	113	1	no	—
242	C₂²×Q₈	—	113	2	no	—
243	C₄⋊Q₈	—	113	2	no	—
244	C₄⋊Q₈	—	113	2	no	—
245	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
246	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
247	#126	—	113	4	no	—
248	#126	—	113	4	no	—
249	#126	—	113	4	no	—
250	#125	—	113	4	no	—
251	#125	—	113	2	no	—
252	#125	—	113	4	no	—
253	#125	C₂×D₁₁₃	1	2	yes	—
254	#124	—	113	2	no	—
255	#124	—	113	4	no	—
256	#123	—	113	4	no	—
257	#123	—	113	4	no	—
258	#123	—	113	4	no	—
259	C₂²⋊Q₈	—	113	2	no	—
260	C₂²⋊Q₈	—	113	2	no	—
261	C₂²⋊Q₈	—	113	4	no	—
262	C₂²⋊Q₈	—	113	4	no	—
263	C₂²⋊Q₈	—	113	2	no	—
264	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
265	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
266	#121	—	113	2	no	—
267	#121	—	113	4	no	—
268	C₄×Q₈	—	113	2	no	—
269	C₄×Q₈	—	113	2	no	—
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	4	no	—
272	C₄×Q₈	—	113	1	no	—
273	C₄×Q₈	—	113	4	no	—
274	C₄×Q₈	—	113	1	no	—
275	C₄×Q₈	—	113	1	no	—
276	C₄×Q₈	—	113	1	no	—
277	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
278	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
279	C₄×D₄	—	113	2	no	—
280	C₄×D₄	—	113	2	no	—
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	2	no	—
284	C₄×D₄	—	113	4	no	—
285	C₄×D₄	—	113	1	no	—
286	C₄×D₄	—	113	1	no	—
287	C₄×D₄	—	113	4	no	—
288	C₄×D₄	—	113	1	no	—
289	C₄×D₄	—	113	1	no	—
290	#117	—	113	1	no	—
291	#117	—	113	1	no	—
292	#117	—	113	4	no	—
293	#117	—	113	2	no	—
294	#117	—	113	2	no	—
295	#117	—	113	2	no	—
296	#117	—	113	4	no	—
297	#117	C₂×D₁₁₃	1	2	yes	—
298	C₂×C₄⋊C₄	—	113	4	no	—
299	C₂×C₄⋊C₄	—	113	2	no	—
300	C₂×C₄²	—	113	4	no	—
301	C₂×C₄²	—	113	2	no	—
302	C₂×C₄²	—	113	2	no	—
303	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
304	#41	—	226	4	no	—
305	#41	—	226	4	no	—
306	#41	—	226	8	no	—
307	C₂×Q₈	—	113	1	no	—
308	C₂×Q₈	—	113	4	no	—
309	C₂×Q₈	—	113	1	no	—
310	C₂×Q₈	—	226	8	no	—
311	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
312	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
313	C₂×D₄	—	113	2	no	—
314	C₂×D₄	—	113	2	no	—
315	C₂×D₄	—	113	1	no	—
316	C₂×D₄	—	113	4	no	—
317	C₂×D₄	—	113	1	no	—
318	C₂²×C₄	—	113	4	no	—
319	C₂²×C₄	—	113	2	no	—
320	C₂²×C₄	—	113	4	no	—
321	C₂²×C₄	—	113	2	no	—
322	C₂²×C₄	—	113	2	no	—
323	C₂²×C₄	—	113	2	no	—
324	C₂²×C₄	—	113	2	no	—
325	C₂²×C₄	—	113	2	no	—
326	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
329	C₄⋊C₄	—	113	2	no	—
330	C₄⋊C₄	—	113	1	no	—
331	C₄⋊C₄	—	113	4	no	—
332	C₄⋊C₄	—	113	4	no	—
333	C₄⋊C₄	—	113	4	no	—
334	C₄⋊C₄	—	113	1	no	—
335	C₄⋊C₄	—	113	2	no	—
336	C₄⋊C₄	—	113	2	no	—
337	C₄⋊C₄	—	113	1	no	—
338	C₄⋊C₄	—	113	1	no	—
339	C₄⋊C₄	—	113	2	no	—
340	C₄⋊C₄	—	113	4	no	—
341	C₄⋊C₄	—	113	4	no	—
342	C₄⋊C₄	—	113	4	no	—
343	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
345	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
346	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
347	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
348	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
349	C₂²⋊C₄	—	113	2	no	—
350	C₂²⋊C₄	—	113	2	no	—
351	C₂²⋊C₄	—	113	2	no	—
352	C₂²⋊C₄	—	113	4	no	—
353	C₂²⋊C₄	—	113	2	no	—
354	C₂²⋊C₄	—	113	2	no	—
355	C₂²⋊C₄	—	113	2	no	—
356	C₂²⋊C₄	—	113	4	no	—
357	C₂²⋊C₄	—	113	4	no	—
358	C₂²⋊C₄	—	113	4	no	—
359	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
360	C₄²	—	113	2	no	—
361	C₄²	—	113	4	no	—
362	C₄²	—	113	2	no	—
363	C₄²	—	113	2	no	—
364	C₄²	—	113	4	no	—
365	C₄²	—	113	2	no	—
366	C₄²	—	113	2	no	—
367	C₄²	—	113	2	no	—
368	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
369	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
370	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
371	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
372	C₄²	C₂²×D₁₁₃	1	4	yes	—
373	C₂³	—	113	2	no	—
374	C₂³	—	113	2	no	—
375	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
376	Q₈	—	2	4	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	113	4	no	—
379	Q₈	—	226	8	no	—
380	Q₈	—	226	2	no	—
381	D₄	—	113	4	no	—
382	D₄	—	226	8	no	—
383	D₄	—	226	4	no	—
384	D₄	—	226	4	no	—
385	D₄	—	226	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	113	2	no	—
390	C₂×C₄	—	113	2	no	—
391	C₂×C₄	—	113	2	no	—
392	C₂×C₄	—	113	2	no	—
393	C₂×C₄	—	113	2	no	—
394	C₂×C₄	—	113	2	no	—
395	C₂×C₄	—	226	8	no	—
396	C₂×C₄	—	226	4	no	—
397	C₂×C₄	—	226	4	no	—
398	C₂×C₄	—	226	8	no	—
399	C₂×C₄	—	226	4	no	—
400	C₂×C₄	—	226	4	no	—
401	C₂×C₄	—	226	4	no	—
402	C₂×C₄	—	226	4	no	—
403	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
406	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
407	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	113	4	no	—
415	C₂²	—	226	2	no	—
416	C₂²	—	226	2	no	—
417	C₂²	—	226	2	no	—
418	C₂²	—	226	2	no	—
419	C₂²	—	226	2	no	—
420	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	1	no	—
426	C₄	—	113	4	no	—
427	C₄	—	226	2	no	—
428	C₄	—	226	2	no	—
429	C₄	—	226	2	no	—
430	C₄	—	226	2	no	—
431	C₄	—	226	2	no	—
432	C₄	#41×D₁₁₃	1	2	yes	—
433	C₄	#41×D₁₁₃	1	2	yes	—
434	C₄	#16813670	1	2	yes	—
435	C₂	—	4	1	no	—
436	C₂	—	452	2	no	—
437	C₂	—	226	4	no	—
438	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
439	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
440	C₂	C₂×#16813670	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	#533×C₁₁₃	C₂
hypercenter	#533	D₁₁₃
hypocenter	C₁₁₃	#3482
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #20299323	C₂	semidirect
2. #20299322	C₂	semidirect
3. #20299319	C₂	semidirect
4. #20299282	C₂	semidirect
5. #20299280	C₂	semidirect
6. #20299263	C₂	semidirect
7. #20299258	C₂	semidirect
8. #20299251	C₂	semidirect
9. #20299250	C₂	semidirect
10. #20299152	C₂	semidirect
11. #20299135	C₂	semidirect
12. #20299126	C₂	semidirect
13. C₄×#14268648	C₂	semidirect
14. C₄×#14268647	C₂	semidirect
15. C₄×#14268647	C₂	semidirect
16. C₄×Q₈×D₁₁₃	C₂	semidirect
17. #533×C₁₁₃	C₂	semidirect
178. D₄₅₂	#41	semidirect
189. Dic₂₂₆	#41	semidirect
221. C₁₁₃	#3482	semidirect
232. #533	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299323	2
#20299322	2
#20299319	2
#20299282	2
#20299280	2
#20299263	2
#20299258	2
#20299251	2
#20299250	2
#20299152	2
#20299135	2
#20299126	2
C₄×#14268648	2
C₄×#14268647	2
C₄×Q₈×D₁₁₃	2
#533×C₁₁₃	2
#3482	113