Subgroups — #28404167

Order 14464.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299333	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299331	C₂	1	2	yes	maximal, complemented
3	#20299326	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299320	C₂	1	2	yes	maximal, complemented
5	#20299318	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299297	C₂	1	4	yes	maximal, complemented
7	#20299294	C₂	1	2	yes	maximal, complemented
8	#20299269	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299257	C₂	1	2	yes	maximal, complemented
10	#20299148	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299144	C₂	1	2	yes	maximal, complemented
12	#20299132	C₂	1	2	yes	maximal, complemented
13	#20299126	C₂	1	4	yes	maximal, complemented
14	C₄×#14268647	C₂	1	2	yes	maximal, complemented
15	#20299066	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268647	C₂²	1	2	yes	—
19	C₂×#14268647	C₂²	1	2	yes	—
20	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
21	#16813622	C₂²	1	1	yes	characteristic
22	#16813620	C₂²	1	2	yes	—
23	#16813619	C₂²	1	1	yes	characteristic
24	#16813618	C₂²	1	2	yes	—
25	#16813617	C₂²	1	4	yes	—
26	#16813616	C₂²	1	4	yes	—
27	#16813615	C₂²	1	4	yes	—
28	#16813614	C₂²	1	2	yes	—
29	#16813612	C₂²	1	4	yes	—
30	#16813611	C₂²	1	2	yes	—
31	#16813610	C₂²	1	2	yes	—
32	#16813610	C₂²	1	2	yes	—
33	#16813609	C₂²	1	2	yes	—
34	#16813608	C₂²	1	4	yes	—
35	#16813607	C₂²	1	4	yes	—
36	#16813605	C₂²	1	4	yes	—
37	#16813604	C₂²	1	4	yes	—
38	#16813601	C₂²	1	2	yes	—
39	#16813600	C₂²	1	4	yes	—
40	#16813596	C₂²	1	2	yes	—
41	#16813596	C₂²	1	2	yes	—
42	#16813596	C₂²	1	2	yes	—
43	#16813595	C₂²	1	4	yes	—
44	#16813594	C₂²	1	4	yes	—
45	#16813594	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	2	yes	—
49	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
50	C₄×Dic₂₂₆	C₂²	1	2	yes	—
51	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
52	C₄×Dic₂₂₆	C₂²	1	2	yes	—
53	#16813587	C₂²	1	2	yes	—
54	#16813587	C₂²	1	2	yes	—
55	C₄×D₄₅₂	C₂²	1	2	yes	—
56	C₄×D₄₅₂	C₂²	1	2	yes	—
57	C₄×D₄₅₂	C₂²	1	2	yes	—
58	#16813584	C₂²	1	2	yes	—
59	#16813584	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
63	#16813582	C₂²	1	4	yes	—
64	#16813582	C₂²	1	4	yes	—
65	#16813581	C₂²	1	2	yes	—
66	#16813579	C₂²	1	4	yes	—
67	#16813579	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
69	C₂×#14268626	C₂²	1	2	yes	—
70	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
71	C₄²×D₁₁₃	C₂²	1	4	yes	—
72	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
74	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
77	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
78	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
79	#117×C₁₁₃	C₂²	1	1	yes	characteristic
80	#117×C₁₁₃	C₂²	1	2	yes	—
81	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄²×C₁₁₃	C₂²	1	2	yes	—
83	#14268647	—	2	8	no	—
84	#14268647	—	2	8	no	—
85	C₂×Dic₂₂₆	—	2	4	no	—
86	C₂×Dic₂₂₆	C₂³	1	2	yes	—
87	C₂×Dic₂₂₆	C₂³	1	2	yes	—
88	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
89	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
90	C₂×D₄₅₂	C₂³	1	2	yes	—
91	C₂×D₄₅₂	C₂³	1	2	yes	—
92	C₂×D₄₅₂	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
96	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
97	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
99	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
104	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
105	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
106	#14268626	C₂³	1	2	yes	—
107	#14268626	C₂³	1	2	yes	—
108	#14268626	C₂³	1	2	yes	—
109	#14268626	C₂³	1	2	yes	—
110	#14268626	C₂³	1	4	yes	—
111	#14268626	C₂³	1	4	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
116	#14268624	C₂³	1	4	yes	—
117	#14268624	C₂³	1	4	yes	—
118	#14268624	C₂³	1	4	yes	—
119	#14268624	C₂³	1	4	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	C₄×Dic₁₁₃	C₂³	1	2	yes	—
123	C₄×Dic₁₁₃	C₂³	1	4	yes	—
124	C₄×Dic₁₁₃	C₂³	1	4	yes	—
125	C₄×Dic₁₁₃	C₂³	1	2	yes	—
126	C₄×Dic₁₁₃	C₂³	1	2	yes	—
127	C₄×Dic₁₁₃	C₂³	1	2	yes	—
128	#41×C₁₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄²×C₁₁₃	C₂³	1	2	yes	—
146	C₄²×C₁₁₃	C₂³	1	2	yes	—
147	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁₃	C₂³	1	2	yes	—
150	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
152	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
153	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
155	Q₈×C₁₁₃	—	2	2	no	—
156	D₄×C₁₁₃	—	2	4	no	—
157	D₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	4	no	—
159	C₂×C₄×C₁₁₃	—	2	2	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	4	2	no	—
162	C₂×C₄×C₁₁₃	—	4	1	no	—
163	C₂×C₄×C₁₁₃	#41	1	4	yes	complemented
164	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₁₁₃	—	2	8	no	—
174	C₂²⋊D₁₁₃	—	2	8	no	—
175	C₂²⋊D₁₁₃	—	4	4	no	—
176	C₂×Dic₁₁₃	—	2	4	no	—
177	C₂×Dic₁₁₃	—	4	2	no	—
178	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
179	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
181	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	D₄₅₂	—	2	4	no	—
184	D₄₅₂	—	2	4	no	—
185	D₄₅₂	—	4	2	no	—
186	C₄×D₁₁₃	—	2	8	no	—
187	C₄×D₁₁₃	—	2	8	no	—
188	C₄×D₁₁₃	—	4	4	no	—
189	Dic₂₂₆	—	2	2	no	—
190	Dic₂₂₆	—	2	4	no	—
191	Dic₂₂₆	—	2	4	no	—
192	Dic₂₂₆	#41	1	4	yes	complemented
193	C₂²×C₁₁₃	—	2	1	no	—
194	C₂²×C₁₁₃	—	2	1	no	—
195	C₂²×C₁₁₃	—	2	2	no	—
196	C₂²×C₁₁₃	—	2	2	no	—
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
199	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
200	C₂×D₁₁₃	—	2	4	no	—
201	C₂×D₁₁₃	—	2	4	no	—
202	C₂×D₁₁₃	—	2	4	no	—
203	C₄×C₁₁₃	—	2	1	no	—
204	C₄×C₁₁₃	—	2	2	no	—
205	C₄×C₁₁₃	—	2	2	no	—
206	C₄×C₁₁₃	—	2	2	no	—
207	C₄×C₁₁₃	—	2	1	no	—
208	C₄×C₁₁₃	—	2	1	no	—
209	C₄×C₁₁₃	C₂×#41	1	2	yes	—
210	C₄×C₁₁₃	C₂×#41	1	2	yes	—
211	C₄×C₁₁₃	C₂×#41	1	2	yes	—
212	Dic₁₁₃	—	2	2	no	—
213	Dic₁₁₃	—	2	4	no	—
214	Dic₁₁₃	—	2	2	no	—
215	Dic₁₁₃	—	2	2	no	—
216	Dic₁₁₃	C₂×#41	1	4	yes	—
217	C₂×C₁₁₃	—	2	2	no	—
218	C₂×C₁₁₃	—	4	2	no	—
219	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
220	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
221	C₂×C₁₁₃	#585	1	1	yes	characteristic
222	D₁₁₃	—	4	4	no	—
223	#3480	—	113	1	no	maximal, Sylow
224	C₁₁₃	#3480	1	1	yes	characteristic, complemented, Sylow
225	#559	—	113	1	no	—
226	#559	—	113	2	no	—
227	#557	—	113	1	no	—
228	#556	—	113	2	no	—
229	#556	—	113	1	no	—
230	#553	—	113	2	no	—
231	#553	—	113	4	no	—
232	#550	—	113	1	no	—
233	#548	—	113	2	no	—
234	#532	—	113	2	no	—
235	#532	—	113	1	no	—
236	#529	—	113	4	no	—
237	#529	—	113	2	no	—
238	C₄×#41	—	113	2	no	—
239	C₄×#41	—	113	2	no	—
240	C₄×#41	D₁₁₃	1	1	yes	characteristic, complemented
241	C₂×C₄×Q₈	—	113	1	no	—
242	C₂×#41	—	113	2	no	—
243	C₂×#41	—	113	2	no	—
244	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
245	C₂²×Q₈	—	113	1	no	—
246	C₄⋊Q₈	—	113	2	no	—
247	C₄⋊Q₈	—	113	1	no	—
248	#127	—	113	2	no	—
249	#127	—	113	1	no	—
250	#126	—	113	4	no	—
251	#126	—	113	4	no	—
252	#126	—	113	4	no	—
253	#125	—	113	4	no	—
254	#125	—	113	2	no	—
255	#124	—	113	2	no	—
256	#124	—	113	2	no	—
257	#124	—	113	4	no	—
258	#124	—	113	2	no	—
259	#124	—	113	2	no	—
260	#123	—	113	4	no	—
261	#123	—	113	4	no	—
262	#123	—	113	4	no	—
263	C₂²⋊Q₈	—	113	2	no	—
264	C₂²⋊Q₈	—	113	4	no	—
265	#121	—	113	4	no	—
266	#121	—	113	4	no	—
267	#121	—	113	2	no	—
268	#121	—	113	2	no	—
269	#121	—	113	2	no	—
270	#121	—	113	4	no	—
271	C₄×Q₈	—	113	2	no	—
272	C₄×Q₈	—	113	2	no	—
273	C₄×Q₈	—	113	1	no	—
274	C₄×Q₈	—	113	2	no	—
275	C₄×Q₈	—	113	1	no	—
276	C₄×Q₈	—	113	1	no	—
277	C₄×Q₈	—	113	1	no	—
278	C₄×Q₈	—	113	2	no	—
279	C₄×Q₈	—	113	2	no	—
280	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
281	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
282	C₄×D₄	—	113	4	no	—
283	C₄×D₄	—	113	4	no	—
284	C₄×D₄	—	113	4	no	—
285	C₄×D₄	—	113	2	no	—
286	C₄×D₄	—	113	2	no	—
287	C₄×D₄	—	113	4	no	—
288	C₄×D₄	—	113	4	no	—
289	C₄×D₄	—	113	2	no	—
290	C₄×D₄	—	113	2	no	—
291	C₄×D₄	—	113	2	no	—
292	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
293	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
294	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
295	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
296	#117	—	113	2	no	—
297	#117	—	113	4	no	—
298	#117	—	113	4	no	—
299	#117	C₂×D₁₁₃	1	1	yes	characteristic
300	#117	C₂×D₁₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	—	113	2	no	—
302	C₂×C₄⋊C₄	—	113	1	no	—
303	C₂×C₄²	—	113	2	no	—
304	C₂×C₄²	—	113	4	no	—
305	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
306	C₂×C₄²	C₂×D₁₁₃	1	2	yes	—
307	#41	—	2	4	no	—
308	#41	—	226	8	no	—
309	#41	—	226	8	no	—
310	C₂×Q₈	—	113	1	no	—
311	C₂×Q₈	—	113	2	no	—
312	C₂×Q₈	—	113	1	no	—
313	C₂×Q₈	—	113	2	no	—
314	C₂×Q₈	—	226	4	no	—
315	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
316	C₂×D₄	—	113	4	no	—
317	C₂×D₄	—	113	4	no	—
318	C₂×D₄	—	113	4	no	—
319	C₂×D₄	—	113	2	no	—
320	C₂×D₄	—	113	2	no	—
321	C₂×D₄	—	113	2	no	—
322	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
323	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
324	C₂²×C₄	—	113	2	no	—
325	C₂²×C₄	—	113	2	no	—
326	C₂²×C₄	—	113	4	no	—
327	C₂²×C₄	—	113	4	no	—
328	C₂²×C₄	—	113	4	no	—
329	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
331	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
332	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
334	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
335	C₄⋊C₄	—	113	2	no	—
336	C₄⋊C₄	—	113	1	no	—
337	C₄⋊C₄	—	113	2	no	—
338	C₄⋊C₄	—	113	1	no	—
339	C₄⋊C₄	—	113	2	no	—
340	C₄⋊C₄	—	113	2	no	—
341	C₄⋊C₄	—	113	2	no	—
342	C₄⋊C₄	—	113	4	no	—
343	C₄⋊C₄	—	113	2	no	—
344	C₄⋊C₄	—	113	4	no	—
345	C₄⋊C₄	—	113	4	no	—
346	C₄⋊C₄	—	113	4	no	—
347	C₄⋊C₄	—	113	2	no	—
348	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
350	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
351	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
352	C₂²⋊C₄	—	113	4	no	—
353	C₂²⋊C₄	—	113	4	no	—
354	C₂²⋊C₄	—	113	4	no	—
355	C₂²⋊C₄	—	113	4	no	—
356	C₂²⋊C₄	—	113	4	no	—
357	C₂²⋊C₄	—	113	4	no	—
358	C₂²⋊C₄	—	113	4	no	—
359	C₂²⋊C₄	—	113	4	no	—
360	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
361	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
363	C₄²	—	113	4	no	—
364	C₄²	—	113	4	no	—
365	C₄²	—	113	2	no	—
366	C₄²	—	113	2	no	—
367	C₄²	—	113	2	no	—
368	C₄²	—	113	2	no	—
369	C₄²	C₂²×D₁₁₃	1	2	yes	—
370	C₄²	C₂²×D₁₁₃	1	2	yes	—
371	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
372	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
373	C₄²	C₂²×D₁₁₃	1	2	yes	—
374	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
375	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
376	C₂³	—	113	4	no	—
377	C₂³	C₂³×D₁₁₃	1	2	yes	—
378	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	113	4	no	—
381	Q₈	—	226	4	no	—
382	Q₈	—	226	2	no	—
383	Q₈	—	226	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	452	2	no	—
387	D₄	—	452	4	no	—
388	D₄	—	226	8	no	—
389	D₄	—	226	8	no	—
390	D₄	—	226	4	no	—
391	D₄	—	226	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	113	2	no	—
398	C₂×C₄	—	113	2	no	—
399	C₂×C₄	—	113	2	no	—
400	C₂×C₄	—	113	4	no	—
401	C₂×C₄	—	113	2	no	—
402	C₂×C₄	—	452	4	no	—
403	C₂×C₄	—	452	2	no	—
404	C₂×C₄	—	226	8	no	—
405	C₂×C₄	—	226	4	no	—
406	C₂×C₄	—	226	8	no	—
407	C₂×C₄	#14268647	1	4	yes	complemented
408	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
409	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
410	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
411	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
413	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	226	4	no	—
423	C₂²	—	226	4	no	—
424	C₂²	—	226	4	no	—
425	C₂²	C₂×#14268647	1	2	yes	—
426	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	1	no	—
433	C₄	—	113	4	no	—
434	C₄	—	226	2	no	—
435	C₄	—	226	4	no	—
436	C₄	—	226	2	no	—
437	C₄	—	226	2	no	—
438	C₄	#41×D₁₁₃	1	2	yes	—
439	C₄	C₂×#14268647	1	2	yes	—
440	C₄	C₂×#14268647	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	452	4	no	—
444	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
445	C₂	C₂²×#14268647	1	1	yes	characteristic
446	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₄×#41×C₁₁₃	C₂
hypercenter	C₄×#41	D₁₁₃
hypocenter	C₁₁₃	#3480
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20299333	C₂	semidirect
2. #20299331	C₂	semidirect
3. #20299326	C₂	semidirect
4. #20299320	C₂	semidirect
5. #20299318	C₂	semidirect
6. #20299297	C₂	semidirect
7. #20299294	C₂	semidirect
8. #20299269	C₂	semidirect
9. #20299257	C₂	semidirect
10. #20299148	C₂	semidirect
11. #20299144	C₂	semidirect
12. #20299132	C₂	semidirect
13. #20299126	C₂	semidirect
14. C₄×#14268647	C₂	semidirect
15. #20299066	C₂	semidirect
16. C₂×C₄×Dic₂₂₆	C₂	semidirect
17. C₄×#41×C₁₁₃	C₂	semidirect
163. C₂×C₄×C₁₁₃	#41	semidirect
192. Dic₂₂₆	#41	semidirect
224. C₁₁₃	#3480	semidirect
240. C₄×#41	D₁₁₃	semidirect
407. C₂×C₄	#14268647	semidirect

Maximal subgroups

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

subgroup	index
#20299333	2
#20299331	2
#20299326	2
#20299320	2
#20299318	2
#20299297	2
#20299294	2
#20299269	2
#20299257	2
#20299148	2
#20299144	2
#20299132	2
#20299126	2
C₄×#14268647	2
#20299066	2
C₂×C₄×Dic₂₂₆	2
C₄×#41×C₁₁₃	2
#3480	113