Subgroups — #28559614

Order 15104.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#11745664	C₂	1	1	yes	maximal, characteristic, complemented
2	#21432840	C₂	1	1	yes	maximal, characteristic
3	#21422987	C₂	1	2	yes	maximal, complemented
4	#21422940	C₂	1	2	yes	maximal, complemented
5	#21422933	C₂	1	2	yes	maximal, complemented
6	SD₁₆×C₅₉⋊C₈	C₂	1	2	yes	maximal, complemented
7	#21422867	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422547	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422377	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3103	C₂	1	1	yes	maximal, characteristic
12	C₂×#14273734	—	2	1	no	—
13	#16837533	—	2	2	no	—
14	#16837533	C₂²	1	2	yes	—
15	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
16	#16837480	C₂²	1	2	yes	—
17	#16837474	—	2	2	no	—
18	D₄×C₅₉⋊C₈	C₂²	1	2	yes	—
19	#16837426	—	2	1	no	—
20	#16837426	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
22	#16837369	—	2	1	no	—
23	C₄×#11745664	—	2	1	no	—
24	C₄×#11745664	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
26	#16837153	C₂²	1	2	yes	—
27	#16837153	C₂²	1	2	yes	—
28	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
29	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
30	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
31	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
32	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
34	#16837124	C₂²	1	2	yes	—
35	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
36	C₅₉×#532	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#481	C₄	1	2	yes	—
39	C₅₉×#475	C₄	1	1	yes	characteristic
40	C₅₉×#475	C₄	1	1	yes	characteristic
41	C₅₉×#460	C₄	1	1	yes	characteristic
42	C₅₉×#460	C₄	1	1	yes	characteristic
43	C₅₉×#448	C₄	1	2	yes	—
44	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
46	C₅₉×#431	C₂²	1	1	yes	characteristic
47	#14273734	—	4	4	no	—
48	C₂×#11745664	—	2	1	no	—
49	C₂×#11745664	—	2	2	no	—
50	C₂×#11745664	D₄	1	1	yes	characteristic
51	C₂×#11745664	D₄	1	1	yes	characteristic
52	C₂²×C₅₉⋊C₈	—	2	1	no	—
53	C₂²×C₅₉⋊C₈	—	2	1	no	—
54	C₂²×C₅₉⋊C₈	—	2	2	no	—
55	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
61	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
62	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
64	#14273638	—	2	2	no	—
65	#14273638	D₄	1	2	yes	—
66	C₄×C₅₉⋊C₈	—	2	1	no	—
67	C₄×C₅₉⋊C₈	—	2	2	no	—
68	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
71	C₂×#41×C₅₉	—	2	1	no	—
72	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
74	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
75	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
76	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
77	#124×C₅₉	—	2	1	no	—
78	#121×C₅₉	—	2	1	no	—
79	#121×C₅₉	C₂×C₄	1	2	yes	—
80	C₄×Q₈×C₅₉	—	2	1	no	—
81	C₄×Q₈×C₅₉	—	2	1	no	—
82	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₅₉	—	2	1	no	—
87	C₄×D₄×C₅₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₅₉	—	2	1	no	—
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	#106×C₅₉	C₂×C₄	1	2	yes	—
93	#106×C₅₉	C₂×C₄	1	2	yes	—
94	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
95	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
96	#103×C₅₉	C₂×C₄	1	2	yes	—
97	#103×C₅₉	C₂×C₄	1	2	yes	—
98	#102×C₅₉	C₂×C₄	1	2	yes	—
99	#102×C₅₉	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₅₉	C₂³	1	2	yes	—
102	#41×C₅₉	—	4	2	no	—
103	#41×C₅₉	—	4	2	no	—
104	C₂×Q₈×C₅₉	—	2	1	no	—
105	C₂×Q₈×C₅₉	—	2	1	no	—
106	C₂×Q₈×C₅₉	—	2	2	no	—
107	C₂×Q₈×C₅₉	—	4	1	no	—
108	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₅₉	—	2	2	no	—
111	C₂×D₄×C₅₉	—	2	1	no	—
112	C₂×D₄×C₅₉	—	2	1	no	—
113	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	—	2	2	no	—
117	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
120	SD₁₆×C₅₉	—	2	4	no	—
121	SD₁₆×C₅₉	—	4	2	no	—
122	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	—	2	1	no	—
127	C₄⋊C₄×C₅₉	—	2	1	no	—
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
133	C₂²⋊C₄×C₅₉	—	2	2	no	—
134	C₂²⋊C₄×C₅₉	—	2	2	no	—
135	C₄²×C₅₉	—	2	1	no	—
136	C₄²×C₅₉	—	2	1	no	—
137	C₄²×C₅₉	—	2	1	no	—
138	C₄²×C₅₉	—	2	1	no	—
139	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₅₉	#41	1	1	yes	characteristic
142	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
143	#11745664	—	2	2	no	—
144	#11745664	—	4	2	no	—
145	#11745664	—	4	4	no	—
146	#11745664	SD₁₆	1	4	yes	complemented
147	C₂×C₅₉⋊C₈	—	2	1	no	—
148	C₂×C₅₉⋊C₈	—	2	2	no	—
149	C₂×C₅₉⋊C₈	—	2	1	no	—
150	C₂×C₅₉⋊C₈	—	2	1	no	—
151	C₂×C₅₉⋊C₈	—	2	1	no	—
152	C₂×C₅₉⋊C₈	—	4	2	no	—
153	C₂×C₅₉⋊C₈	—	4	2	no	—
154	C₂×C₅₉⋊C₈	—	4	4	no	—
155	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
156	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
157	C₂³×C₅₉	—	2	2	no	—
158	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
159	Q₈×C₅₉	—	2	1	no	—
160	Q₈×C₅₉	—	2	1	no	—
161	Q₈×C₅₉	—	2	1	no	—
162	Q₈×C₅₉	—	4	2	no	—
163	Q₈×C₅₉	—	4	2	no	—
164	Q₈×C₅₉	#131	1	2	yes	complemented
165	D₄×C₅₉	—	2	2	no	—
166	D₄×C₅₉	—	2	2	no	—
167	D₄×C₅₉	—	4	4	no	—
168	D₄×C₅₉	—	4	2	no	—
169	D₄×C₅₉	—	8	1	no	—
170	C₂×C₄×C₅₉	—	2	1	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	1	no	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	2	1	no	—
175	C₂×C₄×C₅₉	—	2	1	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	4	1	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	4	2	no	—
180	C₂×C₄×C₅₉	—	4	2	no	—
181	C₂×C₄×C₅₉	—	8	1	no	—
182	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
186	C₂×C₄×C₅₉	#135	1	2	yes	—
187	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₅₉	—	2	2	no	—
191	C₈×C₅₉	—	2	2	no	—
192	C₅₉⋊C₈	—	2	2	no	—
193	C₅₉⋊C₈	—	2	2	no	—
194	C₅₉⋊C₈	—	4	1	no	—
195	C₅₉⋊C₈	—	4	1	no	—
196	C₅₉⋊C₈	—	4	1	no	—
197	C₅₉⋊C₈	—	4	2	no	—
198	C₅₉⋊C₈	C₂×SD₁₆	1	4	yes	—
199	#17997	—	59	1	no	maximal, Sylow
200	C₂²×C₅₉	—	2	1	no	—
201	C₂²×C₅₉	—	2	1	no	—
202	C₂²×C₅₉	—	4	2	no	—
203	C₂²×C₅₉	—	4	2	no	—
204	C₂²×C₅₉	—	4	2	no	—
205	C₂²×C₅₉	C₄×SD₁₆	1	2	yes	—
206	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₅₉	—	2	1	no	—
208	C₄×C₅₉	—	2	2	no	—
209	C₄×C₅₉	—	2	1	no	—
210	C₄×C₅₉	—	2	1	no	—
211	C₄×C₅₉	—	4	1	no	—
212	C₄×C₅₉	—	4	2	no	—
213	C₄×C₅₉	—	4	1	no	—
214	C₄×C₅₉	—	4	1	no	—
215	C₄×C₅₉	C₄×SD₁₆	1	2	yes	—
216	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
217	C₄×C₅₉	#568	1	1	yes	characteristic
218	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
219	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
220	#3103	D₅₉	1	1	yes	characteristic
221	Q₈×M₁₆	—	59	1	no	—
222	#2935	—	59	1	no	—
223	#1590	—	59	2	no	—
224	#1583	—	59	2	no	—
225	#1582	—	59	2	no	—
226	C₈×SD₁₆	—	59	2	no	—
227	#1570	—	59	1	no	—
228	#1492	—	59	1	no	—
229	C₂×Q₈⋊C₈	—	59	1	no	—
230	C₈×M₁₆	—	59	1	no	—
231	C₂×C₅₉	—	2	2	no	—
232	C₂×C₅₉	—	8	2	no	—
233	C₂×C₅₉	#2933	1	1	yes	characteristic
234	C₂×C₅₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
235	C₂×C₅₉	#2956	1	1	yes	characteristic
236	C₂×#131	—	118	1	no	—
237	#532	C₂×D₅₉	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
239	#481	Dic₅₉	1	2	yes	—
240	#475	Dic₅₉	1	1	yes	characteristic
241	#475	Dic₅₉	1	1	yes	characteristic
242	#460	Dic₅₉	1	1	yes	characteristic
243	#460	Dic₅₉	1	1	yes	characteristic
244	#448	Dic₅₉	1	2	yes	—
245	#446	—	59	2	no	—
246	#446	—	118	2	no	—
247	C₈×Q₈	—	59	2	no	—
248	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
249	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
250	#436	—	59	2	no	—
251	#435	—	118	2	no	—
252	C₈×D₄	—	59	2	no	—
253	#431	C₂×D₅₉	1	1	yes	characteristic
254	#423	—	59	1	no	—
255	#423	—	118	1	no	—
256	C₂×C₄⋊C₈	—	59	1	no	—
257	#408	—	118	1	no	—
258	C₄×M₁₆	—	59	1	no	—
259	C₄×M₁₆	—	118	1	no	—
260	C₂×C₄×C₈	—	59	1	no	—
261	#334	—	59	2	no	—
262	#334	—	59	2	no	—
263	Q₈⋊C₈	—	59	1	no	—
264	Q₈⋊C₈	—	59	1	no	—
265	Q₈⋊C₈	—	59	1	no	—
266	Q₈⋊C₈	—	59	1	no	—
267	D₄⋊C₈	—	59	2	no	—
268	D₄⋊C₈	—	59	2	no	—
269	#322	—	59	2	no	—
270	C₈²	—	59	2	no	—
271	C₅₉	#17997	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
274	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
275	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
276	#131	—	236	4	no	—
277	C₂×M₁₆	—	59	1	no	—
278	C₂×M₁₆	—	59	1	no	—
279	C₂×M₁₆	—	118	2	no	—
280	C₂×M₁₆	—	118	1	no	—
281	C₂²×C₈	—	118	2	no	—
282	C₂²×C₈	—	118	1	no	—
283	C₂²×C₈	—	118	1	no	—
284	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
285	#127	C₂×Dic₅₉	1	1	yes	characteristic
286	#124	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	C₂×Dic₅₉	1	2	yes	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
292	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂²×D₅₉	1	2	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
301	#106	C₂×Dic₅₉	1	2	yes	—
302	#106	C₂×Dic₅₉	1	2	yes	—
303	C₄⋊C₈	—	59	2	no	—
304	C₄⋊C₈	—	59	1	no	—
305	C₄⋊C₈	—	59	1	no	—
306	C₄⋊C₈	—	118	2	no	—
307	C₄⋊C₈	—	118	2	no	—
308	C₄⋊C₈	—	118	1	no	—
309	C₄⋊C₈	—	118	1	no	—
310	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
311	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
312	#103	C₂×Dic₅₉	1	2	yes	—
313	#103	C₂×Dic₅₉	1	2	yes	—
314	#102	C₂×Dic₅₉	1	2	yes	—
315	#102	C₂×Dic₅₉	1	2	yes	—
316	C₂²⋊C₈	—	118	2	no	—
317	C₂²⋊C₈	—	118	2	no	—
318	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
319	#97	—	59	2	no	—
320	#97	—	118	2	no	—
321	C₄×C₈	—	59	2	no	—
322	C₄×C₈	—	59	1	no	—
323	C₄×C₈	—	59	1	no	—
324	C₄×C₈	—	118	2	no	—
325	C₄×C₈	—	118	1	no	—
326	C₄×C₈	C₂²×D₅₉	1	2	yes	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
334	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
343	C₂²×C₄	#11745687	1	1	yes	characteristic
344	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
345	SD₁₆	—	2	4	no	—
346	SD₁₆	—	4	2	no	—
347	M₁₆	—	59	4	no	—
348	M₁₆	—	118	2	no	—
349	M₁₆	—	236	4	no	—
350	M₁₆	—	236	2	no	—
351	C₂×C₈	—	59	2	no	—
352	C₂×C₈	—	59	2	no	—
353	C₂×C₈	—	118	1	no	—
354	C₂×C₈	—	118	2	no	—
355	C₂×C₈	—	118	1	no	—
356	C₂×C₈	—	118	1	no	—
357	C₂×C₈	—	118	1	no	—
358	C₂×C₈	—	236	4	no	—
359	C₂×C₈	—	236	2	no	—
360	C₂×C₈	—	236	2	no	—
361	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
362	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	D₄×D₅₉	1	1	yes	characteristic
379	C₄²	#11745687	1	1	yes	characteristic
380	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
381	C₄²	C₂³×D₅₉	1	1	yes	characteristic
382	C₂³	—	2	2	no	—
383	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	#14273734	1	2	yes	complemented
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
408	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
409	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₅₉	1	2	yes	—
411	C₂×C₄	#14273748	1	2	yes	—
412	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
414	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	59	4	no	—
418	C₈	—	118	2	no	—
419	C₈	—	118	2	no	—
420	C₈	—	236	1	no	—
421	C₈	—	236	1	no	—
422	C₈	—	236	1	no	—
423	C₈	—	236	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	SD₁₆×Dic₅₉	1	2	yes	—
430	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	SD₁₆×Dic₅₉	1	2	yes	—
440	C₄	C₂×#14273734	1	1	yes	characteristic
441	C₄	#16838169	1	1	yes	characteristic
442	C₄	C₂×SD₁₆×D₅₉	1	1	yes	characteristic
443	C₄	C₂×#14273748	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	8	2	no	—
446	C₂	#21432823	1	1	yes	characteristic
447	C₂	C₂×SD₁₆×Dic₅₉	1	1	yes	characteristic
448	C₂	#21433006	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#3103	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#532	C₂²
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3103	D₅₉
hypocenter	C₅₉	#17997
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3103

Complements

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

N	H ≅ G/N	type
1. Q₈×#11745664	C₂	semidirect
3. #21422987	C₂	semidirect
4. #21422940	C₂	semidirect
5. #21422933	C₂	semidirect
6. SD₁₆×C₅₉⋊C₈	C₂	semidirect
7. #21422867	C₂	semidirect
9. C₂×Q₈⋊(C₅₉⋊C₈)	C₂	semidirect
10. #21422377	C₂	semidirect
146. #11745664	SD₁₆	semidirect
164. Q₈×C₅₉	#131	semidirect
271. C₅₉	#17997	semidirect
389. Q₈	#14273734	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#11745664	2
#21432840	2
#21422987	2
#21422940	2
#21422933	2
SD₁₆×C₅₉⋊C₈	2
#21422867	2
#21422547	2
C₂×Q₈⋊(C₅₉⋊C₈)	2
#21422377	2
C₅₉×#3103	2
#17997	59