Subgroups — #28403867

Order 14464.

1212 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299152	C₂	1	2	yes	maximal, complemented
2	#20299151	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299145	C₂	1	2	yes	maximal, complemented
4	#20299144	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299135	C₂	1	2	yes	maximal, complemented
6	#20299130	C₂	1	2	yes	maximal, complemented
7	#20299128	C₂	1	4	yes	maximal, complemented
8	#20299126	C₂	1	4	yes	maximal, complemented
9	#20299110	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299107	C₂	1	4	yes	maximal, complemented
11	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#14268647	C₂	1	4	yes	maximal, complemented
13	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄²×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268647	C₂²	1	4	yes	—
17	C₂×#14268647	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
20	#16813621	C₂²	1	2	yes	complemented
21	#16813620	C₂²	1	1	yes	characteristic, complemented
22	#16813618	C₂²	1	1	yes	characteristic, complemented
23	#16813617	C₂²	1	4	yes	complemented
24	#16813615	C₂²	1	4	yes	complemented
25	#16813613	C₂²	1	2	yes	complemented
26	#16813612	C₂²	1	4	yes	complemented
27	#16813611	C₂²	1	1	yes	characteristic, complemented
28	#16813609	C₂²	1	1	yes	characteristic, complemented
29	#16813608	C₂²	1	4	yes	complemented
30	#16813607	C₂²	1	4	yes	—
31	#16813606	C₂²	1	2	yes	—
32	#16813604	C₂²	1	4	yes	—
33	#16813603	C₂²	1	2	yes	—
34	#16813602	C₂²	1	2	yes	—
35	#16813600	C₂²	1	4	yes	—
36	#16813599	C₂²	1	4	yes	—
37	#16813598	C₂²	1	2	yes	—
38	#16813597	C₂²	1	2	yes	—
39	#16813595	C₂²	1	4	yes	—
40	#16813594	C₂²	1	4	yes	—
41	#16813593	C₂²	1	2	yes	—
42	#16813592	C₂²	1	2	yes	—
43	#16813590	C₂²	1	2	yes	—
44	C₄×Dic₂₂₆	C₂²	1	4	yes	complemented
45	C₄×Dic₂₂₆	C₂²	1	4	yes	complemented
46	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
47	C₄×D₄₅₂	C₂²	1	4	yes	—
48	C₄×D₄₅₂	C₂²	1	4	yes	—
49	C₄×D₄₅₂	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
51	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
52	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
53	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
54	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
55	#16813581	C₂²	1	1	yes	characteristic
56	#16813581	C₂²	1	4	yes	complemented
57	#16813579	C₂²	1	4	yes	—
58	#16813579	C₂²	1	2	yes	complemented
59	#16813579	C₂²	1	4	yes	complemented
60	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
61	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
62	C₄²×D₁₁₃	C₂²	1	2	yes	—
63	C₄²×D₁₁₃	C₂²	1	2	yes	—
64	C₄²×D₁₁₃	C₂²	1	2	yes	—
65	C₄²×D₁₁₃	C₂²	1	2	yes	—
66	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
67	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
68	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	complemented
69	C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
70	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
71	#117×C₁₁₃	C₂²	1	1	yes	characteristic
72	#117×C₁₁₃	C₂²	1	2	yes	complemented
73	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
74	C₂×C₄²×C₁₁₃	C₂²	1	2	yes	complemented
75	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
76	#14268647	—	2	4	no	—
77	#14268647	—	2	16	no	—
78	C₂×Dic₂₂₆	C₂³	1	4	yes	—
79	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
80	C₂×D₄₅₂	C₂³	1	4	yes	—
81	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
85	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
86	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₁₁₃	—	2	4	no	—
88	C₂×C₄×D₁₁₃	—	2	8	no	—
89	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
90	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
91	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
97	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
100	#14268626	C₂³	1	4	yes	—
101	#14268626	C₂³	1	4	yes	—
102	#14268626	C₂³	1	4	yes	—
103	#14268626	C₂³	1	4	yes	—
104	#14268626	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
106	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
107	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
108	#14268624	C₂³	1	4	yes	—
109	#14268624	C₂³	1	4	yes	—
110	#14268624	C₂³	1	4	yes	—
111	#14268624	C₂³	1	4	yes	—
112	#14268624	C₂³	1	4	yes	—
113	C₄×Dic₁₁₃	C₂³	1	2	yes	—
114	C₄×Dic₁₁₃	C₂³	1	2	yes	—
115	C₄×Dic₁₁₃	C₂³	1	2	yes	—
116	C₄×Dic₁₁₃	C₂³	1	2	yes	—
117	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
118	C₄×Dic₁₁₃	C₂³	1	2	yes	—
119	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
120	C₄×Dic₁₁₃	C₂³	1	4	yes	—
121	C₄×Dic₁₁₃	C₂³	1	2	yes	—
122	#41×C₁₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
128	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
131	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
132	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
133	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
134	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₄²×C₁₁₃	C₂³	1	2	yes	—
136	C₄²×C₁₁₃	C₂³	1	4	yes	—
137	C₄²×C₁₁₃	C₂³	1	2	yes	—
138	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
140	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
141	C₂²×D₁₁₃	—	2	2	no	—
142	C₂²×D₁₁₃	—	2	4	no	—
143	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
144	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
145	Q₈×C₁₁₃	—	2	2	no	—
146	D₄×C₁₁₃	—	2	4	no	—
147	D₄×C₁₁₃	—	2	2	no	—
148	C₂×C₄×C₁₁₃	—	2	4	no	—
149	C₂×C₄×C₁₁₃	—	2	4	no	—
150	C₂×C₄×C₁₁₃	—	2	8	no	—
151	C₂×C₄×C₁₁₃	#41	1	4	yes	complemented
152	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
153	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
154	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²⋊D₁₁₃	—	2	4	no	—
159	C₂²⋊D₁₁₃	—	2	8	no	—
160	C₂²⋊D₁₁₃	—	2	8	no	—
161	C₂×Dic₁₁₃	—	2	2	no	—
162	C₂×Dic₁₁₃	—	2	4	no	—
163	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
164	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
165	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
166	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
167	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
168	D₄₅₂	—	2	8	no	—
169	D₄₅₂	—	2	2	no	—
170	C₄×D₁₁₃	—	2	4	no	—
171	C₄×D₁₁₃	—	2	4	no	—
172	C₄×D₁₁₃	—	2	4	no	—
173	C₄×D₁₁₃	—	2	4	no	—
174	C₄×D₁₁₃	—	2	8	no	—
175	C₄×D₁₁₃	—	2	4	no	—
176	C₄×D₁₁₃	—	2	4	no	—
177	C₄×D₁₁₃	#41	1	8	yes	complemented
178	Dic₂₂₆	—	2	2	no	—
179	Dic₂₂₆	—	2	8	no	—
180	C₂²×C₁₁₃	—	2	2	no	—
181	C₂²×C₁₁₃	—	2	4	no	—
182	C₂²×C₁₁₃	—	2	2	no	—
183	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
184	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
185	C₂×D₁₁₃	—	2	8	no	—
186	C₂×D₁₁₃	—	2	2	no	—
187	C₂×D₁₁₃	—	2	2	no	—
188	C₂×D₁₁₃	—	2	4	no	—
189	C₂×D₁₁₃	—	2	2	no	—
190	C₂×D₁₁₃	C₂×#41	1	4	yes	—
191	C₄×C₁₁₃	—	2	4	no	—
192	C₄×C₁₁₃	—	2	2	no	—
193	C₄×C₁₁₃	—	2	2	no	—
194	C₄×C₁₁₃	C₂×#41	1	4	yes	—
195	C₄×C₁₁₃	C₂×#41	1	2	yes	—
196	C₄×C₁₁₃	C₂×#41	1	2	yes	—
197	Dic₁₁₃	—	2	4	no	—
198	Dic₁₁₃	—	2	2	no	—
199	Dic₁₁₃	—	2	2	no	—
200	Dic₁₁₃	—	2	2	no	—
201	Dic₁₁₃	C₂×#41	1	4	yes	—
202	C₂×C₁₁₃	—	2	2	no	—
203	C₂×C₁₁₃	—	4	2	no	—
204	C₂×C₁₁₃	C₂²×#41	1	2	yes	—
205	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
206	D₁₁₃	—	2	4	no	—
207	D₁₁₃	—	4	2	no	—
208	#3444	—	113	1	no	maximal, Sylow
209	C₁₁₃	#3444	1	1	yes	characteristic, complemented, Sylow
210	#533	—	113	2	no	—
211	#533	—	113	1	no	—
212	#532	—	113	1	no	—
213	#532	—	113	2	no	—
214	#529	—	113	2	no	—
215	#529	—	113	4	no	—
216	#529	—	113	2	no	—
217	#529	—	113	4	no	—
218	#525	—	113	1	no	—
219	#525	—	113	4	no	—
220	#525	—	113	1	no	—
221	C₄×#41	—	113	1	no	—
222	C₄×#41	—	113	4	no	—
223	C₄×#41	D₁₁₃	1	1	yes	characteristic, complemented
224	C₂²×C₄²	—	113	1	no	—
225	C₂×#41	—	113	4	no	—
226	C₂×#41	—	113	1	no	—
227	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
228	C₂³×C₄	—	113	2	no	—
229	C₂³×C₄	—	113	1	no	—
230	C₄⋊Q₈	—	113	1	no	—
231	C₄⋊Q₈	—	113	2	no	—
232	#127	—	113	1	no	—
233	#126	—	113	4	no	—
234	#126	—	113	4	no	—
235	#125	—	113	4	no	—
236	#125	—	113	2	no	—
237	#124	—	113	1	no	—
238	#124	—	113	1	no	—
239	#124	—	113	4	no	—
240	#123	—	113	2	no	—
241	#123	—	113	4	no	—
242	#123	—	113	4	no	—
243	#123	—	113	2	no	—
244	C₂²⋊Q₈	—	113	2	no	—
245	C₂²⋊Q₈	—	113	4	no	—
246	C₂²⋊Q₈	—	113	2	no	—
247	C₂²⋊Q₈	—	113	4	no	—
248	#121	—	113	2	no	—
249	#121	—	113	4	no	—
250	#121	—	113	2	no	—
251	#121	—	113	4	no	—
252	#120	—	113	2	no	—
253	#120	—	113	2	no	—
254	C₄×Q₈	—	113	4	no	—
255	C₄×Q₈	—	113	4	no	—
256	C₄×Q₈	—	113	2	no	—
257	C₄×Q₈	C₂×D₁₁₃	1	2	yes	complemented
258	C₄×D₄	—	113	4	no	—
259	C₄×D₄	—	113	4	no	—
260	C₄×D₄	—	113	4	no	—
261	C₄×D₄	—	113	4	no	—
262	C₄×D₄	—	113	4	no	—
263	C₄×D₄	—	113	4	no	—
264	C₄×D₄	—	113	4	no	—
265	C₄×D₄	—	113	2	no	—
266	C₄×D₄	C₂×D₁₁₃	1	4	yes	—
267	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
268	#117	—	113	1	no	—
269	#117	—	113	4	no	—
270	#117	—	113	4	no	—
271	#117	—	113	4	no	—
272	#117	—	113	2	no	—
273	#117	C₂×D₁₁₃	1	1	yes	characteristic
274	#117	C₂×D₁₁₃	1	2	yes	complemented
275	C₂×C₄²	—	113	2	no	—
276	C₂×C₄²	—	113	1	no	—
277	C₂×C₄²	—	113	2	no	—
278	C₂×C₄²	—	113	2	no	—
279	C₂×C₄²	—	113	2	no	—
280	C₂×C₄²	—	113	2	no	—
281	C₂×C₄²	—	113	2	no	—
282	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂×D₁₁₃	1	2	yes	complemented
284	C₂⁴	—	113	1	no	—
285	#41	—	2	4	no	—
286	#41	—	226	16	no	—
287	#41	—	226	4	no	—
288	C₂×Q₈	—	113	4	no	—
289	C₂×Q₈	—	113	1	no	—
290	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
291	C₂×D₄	—	113	4	no	—
292	C₂×D₄	—	113	2	no	—
293	C₂×D₄	—	113	4	no	—
294	C₂×D₄	—	113	4	no	—
295	C₂×D₄	—	113	1	no	—
296	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
297	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
298	C₂²×C₄	—	113	2	no	—
299	C₂²×C₄	—	113	2	no	—
300	C₂²×C₄	—	113	1	no	—
301	C₂²×C₄	—	113	2	no	—
302	C₂²×C₄	—	113	2	no	—
303	C₂²×C₄	—	113	2	no	—
304	C₂²×C₄	—	113	2	no	—
305	C₂²×C₄	—	113	2	no	—
306	C₂²×C₄	—	113	4	no	—
307	C₂²×C₄	—	113	2	no	—
308	C₂²×C₄	—	226	8	no	—
309	C₂²×C₄	—	226	4	no	—
310	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
311	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
312	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
313	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
314	C₄⋊C₄	—	113	4	no	—
315	C₄⋊C₄	—	113	4	no	—
316	C₄⋊C₄	—	113	2	no	—
317	C₄⋊C₄	—	113	4	no	—
318	C₄⋊C₄	—	113	4	no	—
319	C₄⋊C₄	—	113	4	no	—
320	C₄⋊C₄	—	113	4	no	—
321	C₄⋊C₄	—	113	4	no	—
322	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
323	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
324	C₂²⋊C₄	—	113	2	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	—	113	4	no	—
327	C₂²⋊C₄	—	113	4	no	—
328	C₂²⋊C₄	—	113	4	no	—
329	C₂²⋊C₄	—	113	4	no	—
330	C₂²⋊C₄	—	113	4	no	—
331	C₂²⋊C₄	—	113	4	no	—
332	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
333	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
334	C₄²	—	113	2	no	—
335	C₄²	—	113	2	no	—
336	C₄²	—	113	2	no	—
337	C₄²	—	113	2	no	—
338	C₄²	—	113	1	no	—
339	C₄²	—	113	2	no	—
340	C₄²	—	113	1	no	—
341	C₄²	—	113	4	no	—
342	C₄²	—	113	2	no	—
343	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
344	C₄²	C₂²×D₁₁₃	1	2	yes	—
345	C₄²	C₂²×D₁₁₃	1	4	yes	—
346	C₄²	C₂²×D₁₁₃	1	2	yes	—
347	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
348	C₂³	—	113	2	no	—
349	C₂³	—	113	2	no	—
350	C₂³	—	226	4	no	—
351	C₂³	—	226	2	no	—
352	C₂³	C₂³×D₁₁₃	1	2	yes	—
353	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	226	8	no	—
356	Q₈	—	226	2	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	—	226	8	no	—
360	D₄	—	226	8	no	—
361	D₄	—	226	8	no	—
362	D₄	—	226	4	no	—
363	D₄	—	226	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	113	2	no	—
368	C₂×C₄	—	113	8	no	—
369	C₂×C₄	—	113	2	no	—
370	C₂×C₄	—	113	2	no	—
371	C₂×C₄	—	113	4	no	—
372	C₂×C₄	—	113	2	no	—
373	C₂×C₄	—	226	4	no	—
374	C₂×C₄	—	226	4	no	—
375	C₂×C₄	—	226	4	no	—
376	C₂×C₄	—	226	2	no	—
377	C₂×C₄	—	226	4	no	—
378	C₂×C₄	—	226	8	no	—
379	C₂×C₄	—	226	4	no	—
380	C₂×C₄	—	226	4	no	—
381	C₂×C₄	—	226	4	no	—
382	C₂×C₄	#14268647	1	4	yes	complemented
383	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
384	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
385	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
386	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
387	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	113	4	no	—
393	C₂²	—	226	8	no	—
394	C₂²	—	226	4	no	—
395	C₂²	—	226	2	no	—
396	C₂²	—	226	2	no	—
397	C₂²	—	226	2	no	—
398	C₂²	C₂×#14268647	1	2	yes	—
399	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	2	no	—
403	C₄	—	113	4	no	—
404	C₄	—	226	2	no	—
405	C₄	—	226	4	no	—
406	C₄	—	226	2	no	—
407	C₄	—	226	2	no	—
408	C₄	#41×D₁₁₃	1	4	yes	—
409	C₄	C₂×#14268647	1	2	yes	—
410	C₄	C₂×#14268647	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	4	2	no	—
413	C₂	—	452	2	no	—
414	C₂	—	226	4	no	—
415	C₂	C₂×#41×D₁₁₃	1	2	yes	—
416	C₂	C₂²×#14268647	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₄×#41×C₁₁₃	C₂
hypercenter	C₄×#41	D₁₁₃
hypocenter	C₁₁₃	#3444
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20299152	C₂	semidirect
2. #20299151	C₂	semidirect
3. #20299145	C₂	semidirect
4. #20299144	C₂	semidirect
5. #20299135	C₂	semidirect
6. #20299130	C₂	semidirect
7. #20299128	C₂	semidirect
8. #20299126	C₂	semidirect
9. #20299110	C₂	semidirect
10. #20299107	C₂	semidirect
11. #20299105	C₂	semidirect
12. C₄×#14268647	C₂	semidirect
13. C₄×#14268647	C₂	semidirect
14. C₂×C₄²×D₁₁₃	C₂	semidirect
15. C₄×#41×C₁₁₃	C₂	semidirect
20. #16813621	C₂²	semidirect
21. #16813620	C₂²	semidirect
22. #16813618	C₂²	semidirect
23. #16813617	C₂²	semidirect
24. #16813615	C₂²	semidirect
25. #16813613	C₂²	semidirect
26. #16813612	C₂²	semidirect
27. #16813611	C₂²	semidirect
28. #16813609	C₂²	semidirect
29. #16813608	C₂²	semidirect
44. C₄×Dic₂₂₆	C₂²	semidirect
45. C₄×Dic₂₂₆	C₂²	semidirect
46. C₄×Dic₂₂₆	C₂²	semidirect
49. C₄×D₄₅₂	C₂²	semidirect
53. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
54. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
56. #16813581	C₂²	semidirect
58. #16813579	C₂²	semidirect
59. #16813579	C₂²	semidirect
66. C₄²×D₁₁₃	C₂²	semidirect
68. C₄×Q₈×C₁₁₃	C₂²	semidirect
70. C₄×D₄×C₁₁₃	C₂²	semidirect
72. #117×C₁₁₃	C₂²	semidirect
74. C₂×C₄²×C₁₁₃	C₂²	semidirect
151. C₂×C₄×C₁₁₃	#41	semidirect
177. C₄×D₁₁₃	#41	semidirect
209. C₁₁₃	#3444	semidirect
223. C₄×#41	D₁₁₃	semidirect
257. C₄×Q₈	C₂×D₁₁₃	semidirect
267. C₄×D₄	C₂×D₁₁₃	semidirect
274. #117	C₂×D₁₁₃	semidirect
283. C₂×C₄²	C₂×D₁₁₃	semidirect
382. 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
#20299152	2
#20299151	2
#20299145	2
#20299144	2
#20299135	2
#20299130	2
#20299128	2
#20299126	2
#20299110	2
#20299107	2
#20299105	2
C₄×#14268647	2
C₂×C₄²×D₁₁₃	2
C₄×#41×C₁₁₃	2
#3444	113