Subgroups — #548×D₁₁₃ #28404036

Order 14464.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299260	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299259	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299258	C₂	1	3	yes	maximal, complemented
6	#20299257	C₂	1	3	yes	maximal, complemented
7	#20299256	C₂	1	3	yes	maximal, complemented
8	#20299255	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299254	C₂	1	3	yes	maximal, complemented
10	#124×D₁₁₃	C₂	1	3	yes	maximal, complemented
11	C₂²⋊Q₈×D₁₁₃	C₂	1	3	yes	maximal, complemented
12	#121×D₁₁₃	C₂	1	3	yes	maximal, complemented
13	C₄×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₁₁₃	C₂	1	3	yes	maximal, complemented
15	#548×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
17	C₂×#14268647	C₂²	1	3	yes	complemented
18	C₂×#14268646	C₂²	1	3	yes	complemented
19	#41×D₁₁₃	—	2	8	no	—
20	C₂²×Dic₂₂₆	C₂²	1	3	yes	complemented
21	C₂×Q₈×D₁₁₃	—	2	8	no	—
22	C₂×Q₈×D₁₁₃	C₂²	1	3	yes	—
23	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₁₁₃	C₂²	1	3	yes	complemented
26	C₂×D₄×D₁₁₃	C₂²	1	3	yes	—
27	C₂×D₄×D₁₁₃	C₂²	1	3	yes	—
28	C₂²×C₄×D₁₁₃	C₂²	1	3	yes	—
29	C₂²×C₄×D₁₁₃	C₂²	1	3	yes	—
30	#16813611	C₂²	1	3	yes	complemented
31	#16813610	C₂²	1	3	yes	complemented
32	#16813609	C₂²	1	3	yes	complemented
33	#16813608	C₂²	1	6	yes	complemented
34	#16813608	C₂²	1	6	yes	complemented
35	#16813602	C₂²	1	3	yes	complemented
36	#16813601	C₂²	1	3	yes	complemented
37	#16813600	C₂²	1	6	yes	complemented
38	#16813599	C₂²	1	6	yes	complemented
39	#16813598	C₂²	1	3	yes	complemented
40	#16813597	C₂²	1	3	yes	complemented
41	#16813596	C₂²	1	3	yes	complemented
42	#16813595	C₂²	1	6	yes	complemented
43	#16813594	C₂²	1	6	yes	complemented
44	#16813593	C₂²	1	3	yes	complemented
45	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₂₂₆	C₂²	1	3	yes	complemented
47	#16813587	C₂²	1	3	yes	complemented
48	C₄×D₄₅₂	C₂²	1	3	yes	complemented
49	D₄×Dic₁₁₃	C₂²	1	3	yes	complemented
50	#16813584	C₂²	1	3	yes	complemented
51	C₄×C₂²⋊D₁₁₃	C₂²	1	3	yes	complemented
52	C₄×C₂²⋊D₁₁₃	C₂²	1	3	yes	complemented
53	#16813582	C₂²	1	3	yes	complemented
54	#16813582	C₂²	1	3	yes	complemented
55	C₄⋊C₄×D₁₁₃	C₂²	1	3	yes	—
56	C₄⋊C₄×D₁₁₃	C₂²	1	3	yes	—
57	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
58	C₂²⋊C₄×D₁₁₃	C₂²	1	3	yes	—
59	C₂²⋊C₄×D₁₁₃	C₂²	1	6	yes	—
60	C₄²×D₁₁₃	C₂²	1	3	yes	—
61	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
63	#124×C₁₁₃	C₂²	1	3	yes	complemented
64	C₂²⋊Q₈×C₁₁₃	C₂²	1	3	yes	complemented
65	#121×C₁₁₃	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₁₁₃	C₂²	1	3	yes	complemented
68	C₂³×D₁₁₃	C₂³	1	3	yes	—
69	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
70	#14268648	—	2	4	no	—
71	#14268647	—	2	12	no	—
72	#14268646	—	2	12	no	—
73	C₂×Dic₂₂₆	—	2	12	no	—
74	C₂×Dic₂₂₆	C₂³	1	6	yes	—
75	C₂×Dic₂₂₆	C₂³	1	3	yes	—
76	C₂×Dic₂₂₆	C₂³	1	3	yes	—
77	Q₈×D₁₁₃	—	2	4	no	—
78	Q₈×D₁₁₃	—	2	12	no	—
79	Q₈×D₁₁₃	—	2	12	no	—
80	Q₈×D₁₁₃	D₄	1	8	yes	complemented
81	C₂×D₄₅₂	C₂³	1	3	yes	—
82	C₂×D₄₅₂	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₁₁₃	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₁₁₃	C₂³	1	3	yes	—
85	C₂×C₂²⋊D₁₁₃	C₂³	1	6	yes	—
86	D₄×D₁₁₃	—	2	12	no	—
87	D₄×D₁₁₃	—	2	12	no	—
88	C₂²×Dic₁₁₃	C₂³	1	3	yes	—
89	C₂²×Dic₁₁₃	C₂³	1	3	yes	—
90	C₂×C₄×D₁₁₃	—	2	12	no	—
91	C₂×C₄×D₁₁₃	—	2	12	no	—
92	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
99	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	3	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	3	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	3	yes	—
103	#14268626	C₂³	1	3	yes	—
104	#14268626	C₂³	1	3	yes	—
105	#14268626	C₂³	1	6	yes	—
106	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
107	C₂²⋊Dic₁₁₃	C₂³	1	3	yes	—
108	C₂²⋊Dic₁₁₃	C₂³	1	6	yes	—
109	#14268624	C₂³	1	1	yes	characteristic
110	#14268624	C₂³	1	3	yes	—
111	#14268624	C₂³	1	1	yes	characteristic
112	#14268624	C₂³	1	3	yes	—
113	#14268624	C₂³	1	6	yes	—
114	#14268624	C₂³	1	6	yes	—
115	C₄×Dic₁₁₃	C₂³	1	3	yes	—
116	C₄×Dic₁₁₃	C₂³	1	3	yes	—
117	C₄×Dic₁₁₃	C₂³	1	3	yes	—
118	#41×C₁₁₃	—	2	4	no	—
119	C₂×Q₈×C₁₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₁₃	C₂³	1	3	yes	—
121	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₁₁₃	C₂³	1	3	yes	—
123	C₂×D₄×C₁₁₃	C₂³	1	3	yes	—
124	C₂²×C₄×C₁₁₃	C₂³	1	3	yes	—
125	C₂²×C₄×C₁₁₃	C₂³	1	3	yes	—
126	C₄⋊C₄×C₁₁₃	C₂³	1	3	yes	—
127	C₄⋊C₄×C₁₁₃	C₂³	1	3	yes	—
128	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₁₃	C₂³	1	3	yes	—
130	C₂²⋊C₄×C₁₁₃	C₂³	1	6	yes	—
131	C₄²×C₁₁₃	C₂³	1	3	yes	—
132	C₂³×C₁₁₃	C₂⁴	1	3	yes	—
133	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
134	C₂²×D₁₁₃	—	2	2	no	—
135	C₂²×D₁₁₃	—	2	2	no	—
136	C₂²×D₁₁₃	—	2	6	no	—
137	C₂²×D₁₁₃	—	2	6	no	—
138	C₂²×D₁₁₃	—	2	6	no	—
139	C₂²×D₁₁₃	#41	1	4	yes	complemented
140	C₂²×D₁₁₃	C₂⁴	1	3	yes	—
141	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
143	Q₈×C₁₁₃	—	2	6	no	—
144	Q₈×C₁₁₃	C₂×D₄	1	4	yes	complemented
145	D₄×C₁₁₃	—	2	6	no	—
146	D₄×C₁₁₃	—	2	6	no	—
147	C₂×C₄×C₁₁₃	—	2	6	no	—
148	C₂×C₄×C₁₁₃	—	2	6	no	—
149	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₁₁₃	C₂⁴	1	3	yes	—
151	C₂×C₄×C₁₁₃	C₂⁴	1	3	yes	—
152	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₁₁₃	C₂⁴	1	3	yes	—
154	C₂²⋊D₁₁₃	—	2	6	no	—
155	C₂²⋊D₁₁₃	—	2	6	no	—
156	C₂²⋊D₁₁₃	—	2	12	no	—
157	C₂×Dic₁₁₃	—	2	6	no	—
158	C₂×Dic₁₁₃	—	2	6	no	—
159	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₁₁₃	C₂⁴	1	3	yes	—
161	C₂×Dic₁₁₃	C₂⁴	1	3	yes	—
162	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₁₁₃	C₂⁴	1	3	yes	—
164	D₄₅₂	—	2	6	no	—
165	D₄₅₂	—	2	6	no	—
166	C₄×D₁₁₃	—	2	2	no	—
167	C₄×D₁₁₃	—	2	6	no	—
168	C₄×D₁₁₃	—	2	6	no	—
169	C₄×D₁₁₃	—	2	2	no	—
170	C₄×D₁₁₃	—	2	6	no	—
171	C₄×D₁₁₃	—	2	6	no	—
172	C₄×D₁₁₃	—	2	6	no	—
173	C₄×D₁₁₃	—	2	6	no	—
174	C₄×D₁₁₃	C₂×D₄	1	12	yes	—
175	Dic₂₂₆	—	2	6	no	—
176	Dic₂₂₆	—	2	12	no	—
177	Dic₂₂₆	C₂×D₄	1	12	yes	complemented
178	C₂²×C₁₁₃	—	2	1	no	—
179	C₂²×C₁₁₃	—	2	1	no	—
180	C₂²×C₁₁₃	—	2	3	no	—
181	C₂²×C₁₁₃	—	2	3	no	—
182	C₂²×C₁₁₃	—	2	3	no	—
183	C₂²×C₁₁₃	C₂×#41	1	2	yes	complemented
184	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
185	C₂×D₁₁₃	—	2	1	no	—
186	C₂×D₁₁₃	—	2	1	no	—
187	C₂×D₁₁₃	—	2	8	no	—
188	C₂×D₁₁₃	—	2	3	no	—
189	C₂×D₁₁₃	—	2	3	no	—
190	C₂×D₁₁₃	—	2	3	no	—
191	C₂×D₁₁₃	—	4	12	no	—
192	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
193	C₂×D₁₁₃	C₂×#41	1	2	yes	—
194	C₂×D₁₁₃	C₂×#41	1	2	yes	complemented
195	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
196	C₄×C₁₁₃	—	2	3	no	—
197	C₄×C₁₁₃	—	2	1	no	—
198	C₄×C₁₁₃	—	2	3	no	—
199	C₄×C₁₁₃	—	2	1	no	—
200	C₄×C₁₁₃	C₂²×D₄	1	6	yes	—
201	Dic₁₁₃	—	2	3	no	—
202	Dic₁₁₃	—	2	1	no	—
203	Dic₁₁₃	—	2	3	no	—
204	Dic₁₁₃	—	2	1	no	—
205	Dic₁₁₃	C₂²×D₄	1	6	yes	—
206	C₂×C₁₁₃	—	2	2	no	—
207	C₂×C₁₁₃	—	4	3	no	—
208	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
209	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
210	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
211	D₁₁₃	—	2	2	no	—
212	D₁₁₃	—	4	3	no	—
213	D₁₁₃	#548	1	4	yes	direct product factor
214	C₂×#548	—	113	1	no	maximal, Sylow
215	C₁₁₃	C₂×#548	1	1	yes	characteristic, complemented, Sylow
216	C₂²×#41	—	113	1	no	—
217	C₂³×Q₈	—	113	1	no	—
218	#548	—	113	1	no	—
219	#548	—	113	1	no	—
220	#548	—	113	3	no	—
221	#548	—	113	3	no	—
222	#548	—	113	3	no	—
223	#548	—	113	1	no	—
224	#548	—	113	3	no	—
225	#548	D₁₁₃	1	1	yes	characteristic, direct product factor
226	C₂×#124	—	113	3	no	—
227	C₂×C₂²⋊Q₈	—	113	3	no	—
228	C₂×#121	—	113	3	no	—
229	C₂×C₄×Q₈	—	113	1	no	—
230	C₂×C₄×D₄	—	113	3	no	—
231	C₂×#41	—	113	1	no	—
232	C₂×#41	—	113	3	no	—
233	C₂×#41	—	113	3	no	—
234	C₂×#41	—	226	8	no	—
235	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
236	C₂²×Q₈	—	113	1	no	—
237	C₂²×Q₈	—	113	3	no	—
238	C₂²×Q₈	—	113	3	no	—
239	C₂²×Q₈	—	113	1	no	—
240	C₂²×Q₈	—	113	3	no	—
241	C₂²×Q₈	—	226	8	no	—
242	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	113	3	no	—
244	C₂²×D₄	—	113	3	no	—
245	C₂³×C₄	—	113	3	no	—
246	C₂³×C₄	—	113	3	no	—
247	#124	—	113	3	no	—
248	#124	—	113	3	no	—
249	#124	—	113	6	no	—
250	#124	—	113	6	no	—
251	#124	—	113	3	no	—
252	#124	C₂×D₁₁₃	1	3	yes	complemented
253	C₂²⋊Q₈	—	113	3	no	—
254	C₂²⋊Q₈	—	113	3	no	—
255	C₂²⋊Q₈	—	113	6	no	—
256	C₂²⋊Q₈	—	113	3	no	—
257	C₂²⋊Q₈	—	113	6	no	—
258	C₂²⋊Q₈	C₂×D₁₁₃	1	3	yes	complemented
259	#121	—	113	3	no	—
260	#121	—	113	6	no	—
261	#121	—	113	3	no	—
262	#121	—	113	3	no	—
263	#121	—	113	6	no	—
264	#121	C₂×D₁₁₃	1	3	yes	complemented
265	C₄×Q₈	—	113	1	no	—
266	C₄×Q₈	—	113	3	no	—
267	C₄×Q₈	—	113	3	no	—
268	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
269	C₄×D₄	—	113	3	no	—
270	C₄×D₄	—	113	3	no	—
271	C₄×D₄	—	113	3	no	—
272	C₄×D₄	—	113	3	no	—
273	C₄×D₄	—	113	3	no	—
274	C₄×D₄	—	113	3	no	—
275	C₄×D₄	—	113	3	no	—
276	C₄×D₄	C₂×D₁₁₃	1	3	yes	complemented
277	C₂×C₄⋊C₄	—	113	3	no	—
278	C₂×C₄⋊C₄	—	113	3	no	—
279	C₂×C₂²⋊C₄	—	113	1	no	—
280	C₂×C₂²⋊C₄	—	113	3	no	—
281	C₂×C₂²⋊C₄	—	113	6	no	—
282	C₂×C₄²	—	113	3	no	—
283	C₂⁴	—	113	1	no	—
284	C₂⁴	—	113	3	no	—
285	#41	—	2	4	no	—
286	#41	—	226	12	no	—
287	#41	—	226	12	no	—
288	#41	—	226	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	113	8	no	—
291	C₂×Q₈	—	113	3	no	—
292	C₂×Q₈	—	113	6	no	—
293	C₂×Q₈	—	113	3	no	—
294	C₂×Q₈	—	226	12	no	—
295	C₂×Q₈	—	226	12	no	—
296	C₂×Q₈	—	226	12	no	—
297	C₂×Q₈	—	226	4	no	—
298	C₂×Q₈	C₂²×D₁₁₃	1	3	yes	—
299	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
300	C₂×D₄	—	113	3	no	—
301	C₂×D₄	—	113	3	no	—
302	C₂×D₄	—	113	6	no	—
303	C₂×D₄	—	113	3	no	—
304	C₂×D₄	—	113	3	no	—
305	C₂×D₄	—	226	12	no	—
306	C₂×D₄	—	226	12	no	—
307	C₂×D₄	C₂²×D₁₁₃	1	3	yes	—
308	C₂×D₄	C₂²×D₁₁₃	1	3	yes	—
309	C₂²×C₄	—	113	3	no	—
310	C₂²×C₄	—	113	3	no	—
311	C₂²×C₄	—	113	3	no	—
312	C₂²×C₄	—	113	1	no	—
313	C₂²×C₄	—	113	3	no	—
314	C₂²×C₄	—	113	3	no	—
315	C₂²×C₄	—	113	1	no	—
316	C₂²×C₄	—	113	3	no	—
317	C₂²×C₄	—	113	3	no	—
318	C₂²×C₄	—	113	3	no	—
319	C₂²×C₄	—	113	3	no	—
320	C₂²×C₄	—	226	12	no	—
321	C₂²×C₄	—	226	12	no	—
322	C₂²×C₄	C₂²×D₁₁₃	1	3	yes	—
323	C₂²×C₄	C₂²×D₁₁₃	1	3	yes	—
324	C₄⋊C₄	—	113	3	no	—
325	C₄⋊C₄	—	113	3	no	—
326	C₄⋊C₄	—	113	3	no	—
327	C₄⋊C₄	—	113	6	no	—
328	C₄⋊C₄	—	113	3	no	—
329	C₄⋊C₄	C₂²×D₁₁₃	1	3	yes	—
330	C₄⋊C₄	C₂²×D₁₁₃	1	3	yes	—
331	C₂²⋊C₄	—	113	1	no	—
332	C₂²⋊C₄	—	113	3	no	—
333	C₂²⋊C₄	—	113	6	no	—
334	C₂²⋊C₄	—	113	1	no	—
335	C₂²⋊C₄	—	113	1	no	—
336	C₂²⋊C₄	—	113	3	no	—
337	C₂²⋊C₄	—	113	3	no	—
338	C₂²⋊C₄	—	113	6	no	—
339	C₂²⋊C₄	—	113	6	no	—
340	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
341	C₂²⋊C₄	C₂²×D₁₁₃	1	3	yes	—
342	C₂²⋊C₄	C₂²×D₁₁₃	1	6	yes	—
343	C₄²	—	113	3	no	—
344	C₄²	—	113	3	no	—
345	C₄²	—	113	3	no	—
346	C₄²	C₂²×D₁₁₃	1	3	yes	—
347	C₂³	—	113	1	no	—
348	C₂³	—	113	4	no	—
349	C₂³	—	113	1	no	—
350	C₂³	—	113	3	no	—
351	C₂³	—	226	6	no	—
352	C₂³	—	226	6	no	—
353	C₂³	—	226	6	no	—
354	C₂³	—	226	2	no	—
355	C₂³	—	226	2	no	—
356	C₂³	C₂³×D₁₁₃	1	3	yes	—
357	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
358	Q₈	—	2	6	no	—
359	Q₈	—	113	12	no	—
360	Q₈	—	226	12	no	—
361	Q₈	—	226	6	no	—
362	Q₈	D₄×D₁₁₃	1	4	yes	complemented
363	D₄	—	2	6	no	—
364	D₄	—	2	6	no	—
365	D₄	—	226	6	no	—
366	D₄	—	226	12	no	—
367	D₄	—	226	6	no	—
368	D₄	—	226	6	no	—
369	D₄	—	226	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	113	3	no	—
373	C₂×C₄	—	113	12	no	—
374	C₂×C₄	—	113	1	no	—
375	C₂×C₄	—	113	3	no	—
376	C₂×C₄	—	113	3	no	—
377	C₂×C₄	—	113	1	no	—
378	C₂×C₄	—	226	6	no	—
379	C₂×C₄	—	226	6	no	—
380	C₂×C₄	—	226	2	no	—
381	C₂×C₄	—	226	6	no	—
382	C₂×C₄	—	226	6	no	—
383	C₂×C₄	—	226	2	no	—
384	C₂×C₄	—	226	6	no	—
385	C₂×C₄	—	226	6	no	—
386	C₂×C₄	—	226	6	no	—
387	C₂×C₄	—	226	6	no	—
388	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₁₁₃	1	3	yes	—
390	C₂×C₄	C₂³×D₁₁₃	1	3	yes	—
391	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₁₃	1	3	yes	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	113	2	no	—
399	C₂²	—	113	2	no	—
400	C₂²	—	113	2	no	—
401	C₂²	—	113	2	no	—
402	C₂²	—	452	12	no	—
403	C₂²	—	226	8	no	—
404	C₂²	—	226	3	no	—
405	C₂²	—	226	3	no	—
406	C₂²	—	226	3	no	—
407	C₂²	—	226	1	no	—
408	C₂²	—	226	1	no	—
409	C₂²	#41×D₁₁₃	1	2	yes	complemented
410	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	3	no	—
413	C₄	—	2	3	no	—
414	C₄	—	2	1	no	—
415	C₄	—	113	6	no	—
416	C₄	—	226	1	no	—
417	C₄	—	226	3	no	—
418	C₄	—	226	3	no	—
419	C₄	—	226	1	no	—
420	C₄	C₂×D₄×D₁₁₃	1	6	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	4	3	no	—
423	C₂	—	113	4	no	—
424	C₂	—	452	3	no	—
425	C₂	—	226	2	no	—
426	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
427	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
428	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#548×C₁₁₃	C₂
hypercenter	#548	D₁₁₃
hypocenter	C₁₁₃	C₂×#548
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₁₃	C₂	semidirect
2. C₂²×Q₈×D₁₁₃	C₂	semidirect
3. #20299260	C₂	semidirect
4. #20299259	C₂	semidirect
5. #20299258	C₂	semidirect
6. #20299257	C₂	semidirect
7. #20299256	C₂	semidirect
8. #20299255	C₂	semidirect
9. #20299254	C₂	semidirect
10. #124×D₁₁₃	C₂	semidirect
11. C₂²⋊Q₈×D₁₁₃	C₂	semidirect
12. #121×D₁₁₃	C₂	semidirect
13. C₄×Q₈×D₁₁₃	C₂	semidirect
14. C₄×D₄×D₁₁₃	C₂	semidirect
15. #548×C₁₁₃	C₂	semidirect
16. C₂×#14268648	C₂²	semidirect
17. C₂×#14268647	C₂²	semidirect
18. C₂×#14268646	C₂²	semidirect
20. C₂²×Dic₂₂₆	C₂²	semidirect
24. C₂×Q₈×D₁₁₃	C₂²	semidirect
25. C₂×Q₈×D₁₁₃	C₂²	semidirect
30. #16813611	C₂²	semidirect
31. #16813610	C₂²	semidirect
32. #16813609	C₂²	semidirect
33. #16813608	C₂²	semidirect
34. #16813608	C₂²	semidirect
35. #16813602	C₂²	semidirect
36. #16813601	C₂²	semidirect
37. #16813600	C₂²	semidirect
38. #16813599	C₂²	semidirect
39. #16813598	C₂²	semidirect
40. #16813597	C₂²	semidirect
41. #16813596	C₂²	semidirect
42. #16813595	C₂²	semidirect
43. #16813594	C₂²	semidirect
44. #16813593	C₂²	semidirect
45. Q₈×Dic₁₁₃	C₂²	semidirect
46. C₄×Dic₂₂₆	C₂²	semidirect
47. #16813587	C₂²	semidirect
48. C₄×D₄₅₂	C₂²	semidirect
49. D₄×Dic₁₁₃	C₂²	semidirect
50. #16813584	C₂²	semidirect
51. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
52. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
53. #16813582	C₂²	semidirect
54. #16813582	C₂²	semidirect
61. C₂×#41×C₁₁₃	C₂²	semidirect
62. C₂²×Q₈×C₁₁₃	C₂²	semidirect
63. #124×C₁₁₃	C₂²	semidirect
64. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
65. #121×C₁₁₃	C₂²	semidirect
66. C₄×Q₈×C₁₁₃	C₂²	semidirect
67. C₄×D₄×C₁₁₃	C₂²	semidirect
80. Q₈×D₁₁₃	D₄	semidirect
139. C₂²×D₁₁₃	#41	semidirect
144. Q₈×C₁₁₃	C₂×D₄	semidirect
177. Dic₂₂₆	C₂×D₄	semidirect
183. C₂²×C₁₁₃	C₂×#41	semidirect
194. C₂×D₁₁₃	C₂×#41	semidirect
213. D₁₁₃	#548	direct (N × H)
215. C₁₁₃	C₂×#548	semidirect
225. #548	D₁₁₃	direct (N × H)
235. C₂×#41	C₂×D₁₁₃	semidirect
242. C₂²×Q₈	C₂×D₁₁₃	semidirect
252. #124	C₂×D₁₁₃	semidirect
258. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
264. #121	C₂×D₁₁₃	semidirect
268. C₄×Q₈	C₂×D₁₁₃	semidirect
276. C₄×D₄	C₂×D₁₁₃	semidirect
362. Q₈	D₄×D₁₁₃	semidirect
409. C₂²	#41×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₁₃	2
C₂²×Q₈×D₁₁₃	2
#20299260	2
#20299259	2
#20299258	2
#20299257	2
#20299256	2
#20299255	2
#20299254	2
#124×D₁₁₃	2
C₂²⋊Q₈×D₁₁₃	2
#121×D₁₁₃	2
C₄×Q₈×D₁₁₃	2
C₄×D₄×D₁₁₃	2
#548×C₁₁₃	2
C₂×#548	113

Subgroups — #548×D113 #28404036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #548×D₁₁₃ #28404036