Subgroups — #28607696

Order 15104.

622 conjugacy classes of subgroups.

The subgroup lattice has 394 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
2	C₂×#16837533	C₂	1	1	yes	maximal, characteristic
3	#21424871	C₂	1	2	yes	maximal
4	#21424871	C₂	1	1	yes	maximal, characteristic
5	#21424869	C₂	1	2	yes	maximal
6	#21424869	C₂	1	1	yes	maximal, characteristic
7	#21424236	C₂	1	2	yes	maximal
8	#21424233	C₂	1	1	yes	maximal, characteristic
9	#21424003	C₂	1	2	yes	maximal
10	C₄×#14273662	C₂	1	1	yes	maximal, characteristic
11	Q₈×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
12	#16837533	—	2	1	no	—
13	#16837533	—	2	2	no	—
14	#16837533	C₄	1	2	yes	—
15	#16837533	C₄	1	2	yes	—
16	#16837533	C₄	1	4	yes	—
17	Q₈×C₅₉⋊C₈	—	2	1	no	—
18	C₂×#14273662	C₂²	1	1	yes	characteristic
19	C₂×#14273662	C₂²	1	1	yes	characteristic
20	C₂×#14273662	C₂²	1	2	yes	—
21	C₂×#14273662	C₂²	1	2	yes	—
22	#16837426	C₂²	1	1	yes	characteristic
23	#16837426	C₂²	1	2	yes	—
24	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
26	C₄×#11745664	C₂²	1	1	yes	characteristic
27	C₄×#11745664	C₂²	1	2	yes	—
28	C₂×#14273638	C₂²	1	2	yes	—
29	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
30	#16837166	C₂²	1	2	yes	—
31	#16837166	C₂²	1	2	yes	—
32	#16837166	C₂²	1	1	yes	characteristic
33	#16837166	C₂²	1	2	yes	—
34	#16837166	C₂²	1	2	yes	—
35	#16837166	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#446	—	2	1	no	—
38	C₅₉×#446	—	2	2	no	—
39	C₈×Q₈×C₅₉	—	2	1	no	—
40	C₅₉×#423	C₂²	1	1	yes	characteristic
41	C₅₉×#423	C₂²	1	2	yes	—
42	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
44	C₂×#11745664	C₂³	1	2	yes	—
45	C₂×#11745664	C₂³	1	1	yes	characteristic
46	C₂×#11745664	C₂³	1	1	yes	characteristic
47	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
50	#14273662	—	2	2	no	—
51	#14273662	—	2	4	no	—
52	#14273662	—	2	2	no	—
53	#14273662	—	2	4	no	—
54	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
59	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
60	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
61	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
62	#14273638	—	2	2	no	—
63	#14273638	—	2	1	no	—
64	#14273638	C₂×C₄	1	4	yes	—
65	#14273638	C₂×C₄	1	4	yes	—
66	C₄×C₅₉⋊C₈	—	2	1	no	—
67	C₄×C₅₉⋊C₈	—	2	2	no	—
68	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
69	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
70	C₂²×Q₈×C₅₉	Q₈	1	1	yes	characteristic
71	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
72	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
74	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
76	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
77	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₅₉	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₅₉	Q₈	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₅₉	Q₈	1	2	yes	—
82	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
84	C₄⋊C₈×C₅₉	—	2	1	no	—
85	C₄⋊C₈×C₅₉	—	2	2	no	—
86	C₄⋊C₈×C₅₉	—	2	2	no	—
87	C₄⋊C₈×C₅₉	—	2	1	no	—
88	#97×C₅₉	—	2	2	no	—
89	#97×C₅₉	—	2	1	no	—
90	C₄×C₈×C₅₉	—	2	1	no	—
91	C₄×C₈×C₅₉	—	2	2	no	—
92	C₂×Q₈×C₅₉	—	4	2	no	—
93	C₂×Q₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂×Q₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
95	C₂×Q₈×C₅₉	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
101	M₁₆×C₅₉	—	2	1	no	—
102	M₁₆×C₅₉	—	2	2	no	—
103	M₁₆×C₅₉	—	2	1	no	—
104	M₁₆×C₅₉	—	2	2	no	—
105	M₁₆×C₅₉	—	2	1	no	—
106	M₁₆×C₅₉	#41	1	2	yes	—
107	C₂×C₈×C₅₉	—	2	1	no	—
108	C₂×C₈×C₅₉	—	2	1	no	—
109	C₂×C₈×C₅₉	—	2	2	no	—
110	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
111	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
112	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
113	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
120	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
121	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅₉	C₂×D₄	1	2	yes	—
123	C₄²×C₅₉	C₂×D₄	1	2	yes	—
124	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
125	#11745664	—	2	1	no	—
126	#11745664	—	2	1	no	—
127	#11745664	—	2	2	no	—
128	#11745664	—	2	2	no	—
129	#11745664	—	2	1	no	—
130	#11745664	#41	1	2	yes	—
131	C₂×C₅₉⋊C₈	—	2	1	no	—
132	C₂×C₅₉⋊C₈	—	2	1	no	—
133	C₂×C₅₉⋊C₈	—	2	2	no	—
134	C₂×C₅₉⋊C₈	—	2	1	no	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	1	no	—
137	C₂×C₅₉⋊C₈	—	2	1	no	—
138	C₂×C₅₉⋊C₈	—	2	1	no	—
139	C₂×C₅₉⋊C₈	—	2	2	no	—
140	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
143	C₂³×C₅₉	C₂²×Q₈	1	1	yes	characteristic
144	Q₈×C₅₉	—	2	2	no	—
145	Q₈×C₅₉	—	2	2	no	—
146	Q₈×C₅₉	—	4	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	4	1	no	—
149	C₂×C₄×C₅₉	—	4	2	no	—
150	C₂×C₄×C₅₉	—	4	2	no	—
151	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
165	C₈×C₅₉	—	2	2	no	—
166	C₈×C₅₉	—	4	1	no	—
167	C₈×C₅₉	—	4	2	no	—
168	C₅₉⋊C₈	—	2	2	no	—
169	C₅₉⋊C₈	—	2	4	no	—
170	C₅₉⋊C₈	—	2	2	no	—
171	C₅₉⋊C₈	—	2	2	no	—
172	C₅₉⋊C₈	—	4	1	no	—
173	C₅₉⋊C₈	—	4	2	no	—
174	#22747	—	59	1	no	maximal, Sylow
175	C₂²×C₅₉	—	2	1	no	—
176	C₂²×C₅₉	—	2	1	no	—
177	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₅₉	#557	1	1	yes	characteristic
179	C₂²×C₅₉	#557	1	1	yes	characteristic
180	C₄×C₅₉	—	2	1	no	—
181	C₄×C₅₉	—	2	2	no	—
182	C₄×C₅₉	—	2	2	no	—
183	C₄×C₅₉	—	2	1	no	—
184	C₄×C₅₉	—	2	1	no	—
185	C₄×C₅₉	—	2	2	no	—
186	C₄×C₅₉	—	2	2	no	—
187	C₄×C₅₉	#430	1	2	yes	—
188	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
189	C₄×C₅₉	#519	1	1	yes	characteristic
190	C₄×C₅₉	#548	1	1	yes	characteristic
191	C₄×C₅₉	#548	1	1	yes	characteristic
192	Q₈×M₁₆	—	59	1	no	—
193	Q₈×M₁₆	D₅₉	1	1	yes	characteristic
194	C₂×#446	—	59	1	no	—
195	#1950	—	59	2	no	—
196	#1950	—	59	1	no	—
197	#1950	—	59	2	no	—
198	#1950	—	59	1	no	—
199	#1838	—	59	2	no	—
200	#1837	—	59	1	no	—
201	#1778	—	59	2	no	—
202	C₄×#108	—	59	1	no	—
203	C₂×C₅₉	—	2	1	no	—
204	C₂×C₅₉	—	2	1	no	—
205	C₂×C₅₉	#2351	1	1	yes	characteristic
206	C₂×C₅₉	C₂×#430	1	1	yes	characteristic
207	C₂×C₅₉	#2916	1	1	yes	characteristic
208	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
209	#446	—	2	1	no	—
210	#446	—	2	2	no	—
211	#446	—	59	2	no	—
212	#446	—	59	2	no	—
213	#446	—	59	4	no	—
214	#446	—	118	1	no	—
215	#446	—	118	2	no	—
216	C₈×Q₈	—	2	1	no	—
217	C₈×Q₈	—	118	1	no	—
218	C₂×#108	—	59	1	no	—
219	C₂×#108	—	59	1	no	—
220	C₂×#108	—	59	2	no	—
221	C₂×#108	—	59	2	no	—
222	#423	—	59	1	no	—
223	#423	—	59	2	no	—
224	#423	C₂×D₅₉	1	1	yes	characteristic
225	#423	C₂×D₅₉	1	2	yes	—
226	C₂×C₄⋊C₈	—	59	1	no	—
227	C₂×C₄⋊C₈	—	59	2	no	—
228	C₄×M₁₆	—	59	1	no	—
229	C₄×M₁₆	—	59	2	no	—
230	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
231	C₄×M₁₆	C₂×D₅₉	1	2	yes	—
232	C₂×#97	—	59	2	no	—
233	C₂×C₄×C₈	—	59	1	no	—
234	#341	—	59	2	no	—
235	#341	—	59	2	no	—
236	#341	—	59	1	no	—
237	#341	—	59	2	no	—
238	#341	—	59	2	no	—
239	#341	—	59	1	no	—
240	C₅₉	#22747	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	Dic₁₁₈	1	1	yes	characteristic
242	C₂×M₁₆	—	59	1	no	—
243	C₂×M₁₆	—	59	2	no	—
244	C₂×M₁₆	—	59	1	no	—
245	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
246	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
247	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
248	C₂²×C₈	—	59	1	no	—
249	C₂²×C₈	—	59	1	no	—
250	C₂²×C₈	—	59	2	no	—
251	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
252	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
253	C₄×Q₈	C₄×D₅₉	1	2	yes	—
254	C₄×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
255	C₄×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
256	C₄×Q₈	C₂²⋊D₅₉	1	2	yes	—
257	C₂×C₄⋊C₄	Dic₁₁₈	1	1	yes	characteristic
258	C₂×C₄⋊C₄	Dic₁₁₈	1	2	yes	—
259	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₅₉	1	2	yes	—
261	#108	—	118	2	no	—
262	#108	—	118	4	no	—
263	#108	—	118	2	no	—
264	#108	—	118	4	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	59	2	no	—
270	C₄⋊C₈	—	59	2	no	—
271	C₄⋊C₈	—	59	4	no	—
272	C₄⋊C₈	—	59	4	no	—
273	C₄⋊C₈	—	118	1	no	—
274	C₄⋊C₈	—	118	2	no	—
275	C₄⋊C₈	—	118	2	no	—
276	C₄⋊C₈	—	118	1	no	—
277	#97	—	2	2	no	—
278	#97	—	2	1	no	—
279	#97	—	59	4	no	—
280	#97	—	59	4	no	—
281	#97	—	118	2	no	—
282	#97	—	118	1	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	59	2	no	—
286	C₄×C₈	—	59	2	no	—
287	C₄×C₈	—	118	1	no	—
288	C₄×C₈	—	118	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	Dic₅₉⋊C₄	1	1	yes	characteristic
291	C₂×Q₈	Dic₅₉⋊C₄	1	1	yes	characteristic
292	C₂×Q₈	Dic₅₉⋊C₄	1	2	yes	—
293	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
294	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
295	C₂²×C₄	C₂×Dic₁₁₈	1	2	yes	—
296	C₂²×C₄	C₂×Dic₁₁₈	1	2	yes	—
297	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
298	M₁₆	—	2	1	no	—
299	M₁₆	—	2	1	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	1	no	—
303	M₁₆	—	59	2	no	—
304	M₁₆	—	118	1	no	—
305	M₁₆	—	118	1	no	—
306	M₁₆	—	118	2	no	—
307	M₁₆	—	118	2	no	—
308	M₁₆	—	118	1	no	—
309	M₁₆	#11745689	1	2	yes	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	59	2	no	—
314	C₂×C₈	—	59	2	no	—
315	C₂×C₈	—	59	4	no	—
316	C₂×C₈	—	118	1	no	—
317	C₂×C₈	—	118	1	no	—
318	C₂×C₈	—	118	2	no	—
319	C₂×C₈	—	118	1	no	—
320	C₂×C₈	—	118	2	no	—
321	C₂×C₈	—	118	1	no	—
322	C₂×C₈	—	118	1	no	—
323	C₂×C₈	—	118	1	no	—
324	C₂×C₈	—	118	2	no	—
325	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
326	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
327	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
328	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
329	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
330	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
331	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
332	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
333	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₅₉	1	2	yes	—
335	C₄²	C₂×C₄×D₅₉	1	2	yes	—
336	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
337	C₄²	C₂×C₂²⋊D₅₉	1	2	yes	—
338	C₄²	C₂×C₂²⋊D₅₉	1	2	yes	—
339	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
340	C₂³	C₂²×Dic₁₁₈	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
351	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
352	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
354	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
355	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
358	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
359	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
360	C₂×C₄	#14273774	1	1	yes	characteristic
361	C₂×C₄	#14273775	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	4	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	118	2	no	—
366	C₈	—	118	2	no	—
367	C₈	—	118	4	no	—
368	C₈	—	118	2	no	—
369	C₈	—	236	1	no	—
370	C₈	—	236	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic
374	C₂²	#16838128	1	1	yes	characteristic
375	C₂²	#16838131	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	#16837450	1	2	yes	—
384	C₄	C₄×#11745689	1	1	yes	characteristic
385	C₄	#16837878	1	1	yes	characteristic
386	C₄	#16838059	1	1	yes	characteristic
387	C₄	#16838063	1	1	yes	characteristic
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	#21427014	1	1	yes	characteristic
391	C₂	C₂×#16837450	1	1	yes	characteristic
392	C₂	#21432705	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	Q₈×M₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂³×C₅₉	C₂²×Q₈
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	Q₈×M₁₆	D₅₉
hypocenter	C₅₉	#22747
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈ ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
240. C₅₉	#22747	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
C₂×#16837533	2
#21424871	2
#21424869	2
#21424236	2
#21424233	2
#21424003	2
C₄×#14273662	2
Q₈×M₁₆×C₅₉	2
#22747	59