Group #28488171 — subgroups

Subgroups — #28488171

Order 15104.

406 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837752	C₂	1	1	yes	maximal, characteristic
2	#21424267	C₂	1	1	yes	maximal, characteristic
3	#21422782	C₂	1	1	yes	maximal, characteristic
4	#21422776	C₂	1	1	yes	maximal, characteristic
5	#21422768	C₂	1	1	yes	maximal, characteristic
6	#21422389	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1546	C₂	1	1	yes	maximal, characteristic
8	C₂×#14273727	C₂²	1	1	yes	characteristic
9	#16837752	—	2	1	no	—
10	#16837752	—	2	1	no	—
11	#16837752	C₄	1	4	yes	—
12	#16837455	C₂²	1	1	yes	characteristic
13	C₂×#14273662	—	2	2	no	—
14	#16837426	C₂²	1	1	yes	characteristic
15	C₂×#14273651	—	2	2	no	—
16	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
17	#16837150	—	2	2	no	—
18	#16837148	—	2	2	no	—
19	#16837147	—	2	2	no	—
20	#16837124	—	2	1	no	—
21	#16837123	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#431	C₂²	1	1	yes	characteristic
24	C₅₉×#423	C₂²	1	1	yes	characteristic
25	C₅₉×#332	—	2	2	no	—
26	C₂²×Dic₁₁₈	—	2	1	no	—
27	C₂×#11745664	—	2	1	no	—
28	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
29	#14273727	—	2	1	no	—
30	#14273727	—	2	1	no	—
31	#14273727	—	2	1	no	—
32	#14273727	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₅₉	—	2	1	no	—
34	C₂×C₄⋊Dic₅₉	—	2	1	no	—
35	#14273662	—	4	4	no	—
36	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
37	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
39	#14273651	—	2	4	no	—
40	#14273651	—	2	4	no	—
41	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
42	C₄×C₅₉⋊C₈	—	2	1	no	—
43	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
44	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
45	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₅₉	—	2	1	no	—
47	C₂×M₁₆×C₅₉	—	2	1	no	—
48	C₄⋊Q₈×C₅₉	—	2	1	no	—
49	C₄⋊Q₈×C₅₉	—	2	1	no	—
50	C₄⋊Q₈×C₅₉	—	2	1	no	—
51	C₄⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
54	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₅₉	—	2	1	no	—
56	C₄⋊C₈×C₅₉	—	2	1	no	—
57	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
58	C₂²⋊C₈×C₅₉	—	2	1	no	—
59	C₄×C₈×C₅₉	—	2	1	no	—
60	C₂×Q₈×C₅₉	—	2	2	no	—
61	C₂×Q₈×C₅₉	—	4	1	no	—
62	C₂×Q₈×C₅₉	—	4	2	no	—
63	C₂×Q₈×C₅₉	—	4	2	no	—
64	C₂²×C₄×C₅₉	—	4	1	no	—
65	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
67	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
68	C₂²×Dic₅₉	—	4	1	no	—
69	C₂×Dic₁₁₈	—	2	2	no	—
70	C₂×Dic₁₁₈	—	4	1	no	—
71	C₂×Dic₁₁₈	—	8	2	no	—
72	M₁₆×C₅₉	—	4	2	no	—
73	C₂×C₈×C₅₉	—	2	2	no	—
74	C₂×C₈×C₅₉	—	4	1	no	—
75	C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₄⋊C₄×C₅₉	—	2	2	no	—
77	C₄⋊C₄×C₅₉	—	4	1	no	—
78	C₄⋊C₄×C₅₉	—	4	1	no	—
79	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
83	C₄⋊Dic₅₉	—	2	2	no	—
84	C₄⋊Dic₅₉	—	2	2	no	—
85	C₄⋊Dic₅₉	—	4	1	no	—
86	C₄⋊Dic₅₉	—	4	1	no	—
87	#11745664	—	4	2	no	—
88	C₂×C₅₉⋊C₈	—	2	2	no	—
89	C₂×C₅₉⋊C₈	—	2	2	no	—
90	C₂×C₅₉⋊C₈	—	2	2	no	—
91	C₂×C₅₉⋊C₈	—	4	1	no	—
92	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
93	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
94	C₂³×C₅₉	#124	1	1	yes	characteristic
95	Q₈×C₅₉	—	4	4	no	—
96	Q₈×C₅₉	—	8	1	no	—
97	Q₈×C₅₉	—	8	1	no	—
98	C₂×C₄×C₅₉	—	2	2	no	—
99	C₂×C₄×C₅₉	—	2	2	no	—
100	C₂×C₄×C₅₉	—	4	2	no	—
101	C₂×C₄×C₅₉	—	8	2	no	—
102	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
107	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
108	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
109	C₂×C₄×C₅₉	#137	1	2	yes	—
110	C₂×Dic₅₉	—	4	2	no	—
111	C₂×Dic₅₉	—	8	2	no	—
112	Dic₁₁₈	—	8	2	no	—
113	Dic₁₁₈	—	8	2	no	—
114	C₈×C₅₉	—	4	2	no	—
115	C₈×C₅₉	—	8	1	no	—
116	C₅₉⋊C₈	—	2	2	no	—
117	C₅₉⋊C₈	—	2	2	no	—
118	C₅₉⋊C₈	—	4	2	no	—
119	C₅₉⋊C₈	—	8	1	no	—
120	#9775	—	59	1	no	maximal, Sylow
121	C₂²×C₅₉	—	2	1	no	—
122	C₂²×C₅₉	—	2	1	no	—
123	C₂²×C₅₉	#390	1	1	yes	characteristic
124	C₂²×C₅₉	#489	1	2	yes	—
125	C₄×C₅₉	—	2	1	no	—
126	C₄×C₅₉	—	2	1	no	—
127	C₄×C₅₉	—	8	2	no	—
128	C₄×C₅₉	#417	1	2	yes	—
129	C₄×C₅₉	#471	1	2	yes	—
130	C₄×C₅₉	#473	1	2	yes	—
131	C₄×C₅₉	#496	1	1	yes	characteristic
132	C₄×C₅₉	#497	1	1	yes	characteristic
133	Dic₅₉	—	8	2	no	—
134	C₂×#487	—	59	1	no	—
135	#1848	—	59	1	no	—
136	#1549	—	59	1	no	—
137	#1548	—	59	1	no	—
138	#1546	—	59	1	no	—
139	#1546	D₅₉	1	1	yes	characteristic
140	#1452	—	59	1	no	—
141	C₂×C₅₉	—	2	2	no	—
142	C₂×C₅₉	#1959	1	1	yes	characteristic
143	C₂×C₅₉	#1977	1	1	yes	characteristic
144	C₂×C₅₉	#1979	1	1	yes	characteristic
145	C₂×C₄⋊Q₈	—	59	1	no	—
146	C₂×C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
147	#487	—	59	4	no	—
148	#487	—	118	1	no	—
149	#487	—	118	1	no	—
150	#431	—	59	1	no	—
151	#431	C₂×D₅₉	1	1	yes	characteristic
152	C₂×#108	—	118	2	no	—
153	#423	—	59	1	no	—
154	#423	C₂×D₅₉	1	1	yes	characteristic
155	C₂×#103	—	118	2	no	—
156	C₂×C₄×C₈	—	59	1	no	—
157	#333	—	118	2	no	—
158	#332	—	2	2	no	—
159	#332	—	118	2	no	—
160	#332	—	118	2	no	—
161	#322	—	118	1	no	—
162	#322	—	118	1	no	—
163	C₅₉	#9775	1	1	yes	characteristic, complemented, Sylow
164	C₂²×Q₈	—	2	1	no	—
165	C₂²×Q₈	—	118	1	no	—
166	C₂×M₁₆	—	2	1	no	—
167	C₂×M₁₆	—	118	1	no	—
168	C₂²×C₈	—	59	2	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	—	2	1	no	—
171	C₄⋊Q₈	—	2	1	no	—
172	C₄⋊Q₈	—	59	2	no	—
173	C₄⋊Q₈	—	118	1	no	—
174	C₄⋊Q₈	—	118	1	no	—
175	C₄⋊Q₈	—	118	1	no	—
176	C₄⋊Q₈	C₄×D₅₉	1	2	yes	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₄⋊C₄	—	2	1	no	—
179	C₂×C₄⋊C₄	—	118	1	no	—
180	C₂×C₄⋊C₄	—	118	1	no	—
181	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
182	#108	—	236	4	no	—
183	C₄⋊C₈	—	2	1	no	—
184	C₄⋊C₈	—	2	1	no	—
185	C₄⋊C₈	—	59	2	no	—
186	C₄⋊C₈	—	118	1	no	—
187	C₄⋊C₈	—	118	1	no	—
188	C₄⋊C₈	C₂²⋊D₅₉	1	2	yes	—
189	#103	—	118	4	no	—
190	#103	—	118	4	no	—
191	C₂²⋊C₈	—	2	1	no	—
192	C₂²⋊C₈	—	118	1	no	—
193	C₄×C₈	—	2	1	no	—
194	C₄×C₈	—	59	2	no	—
195	C₄×C₈	—	59	1	no	—
196	C₄×C₈	—	59	1	no	—
197	C₄×C₈	—	118	1	no	—
198	C₂×Q₈	—	2	2	no	—
199	C₂×Q₈	—	4	1	no	—
200	C₂×Q₈	—	4	2	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	118	2	no	—
203	C₂×Q₈	—	472	2	no	—
204	C₂×Q₈	—	236	1	no	—
205	C₂²×C₄	—	4	1	no	—
206	C₂²×C₄	—	236	1	no	—
207	C₂²×C₄	#11745685	1	1	yes	characteristic
208	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
209	C₂²×C₄	#11745687	1	1	yes	characteristic
210	M₁₆	—	4	2	no	—
211	M₁₆	—	236	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	4	1	no	—
214	C₂×C₈	—	59	2	no	—
215	C₂×C₈	—	59	2	no	—
216	C₂×C₈	—	118	2	no	—
217	C₂×C₈	—	118	2	no	—
218	C₂×C₈	—	118	2	no	—
219	C₂×C₈	—	236	1	no	—
220	C₄⋊C₄	—	2	2	no	—
221	C₄⋊C₄	—	2	2	no	—
222	C₄⋊C₄	—	4	1	no	—
223	C₄⋊C₄	—	4	1	no	—
224	C₄⋊C₄	—	118	2	no	—
225	C₄⋊C₄	—	118	2	no	—
226	C₄⋊C₄	—	236	1	no	—
227	C₄⋊C₄	—	236	1	no	—
228	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
229	C₄²	D₄×D₅₉	1	1	yes	characteristic
230	C₄²	D₄×D₅₉	1	1	yes	characteristic
231	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
232	C₂³	#14273713	1	1	yes	characteristic
233	Q₈	—	4	4	no	—
234	Q₈	—	8	1	no	—
235	Q₈	—	8	1	no	—
236	Q₈	—	472	2	no	—
237	Q₈	—	472	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	8	2	no	—
242	C₂×C₄	—	472	2	no	—
243	C₂×C₄	—	236	2	no	—
244	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
245	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
246	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
247	C₂×C₄	#14273699	1	1	yes	characteristic
248	C₂×C₄	#14273700	1	1	yes	characteristic
249	C₂×C₄	#14273723	1	1	yes	characteristic
250	C₂×C₄	#14273751	1	2	yes	—
251	C₂×C₄	#14273756	1	2	yes	—
252	C₈	—	4	2	no	—
253	C₈	—	8	1	no	—
254	C₈	—	118	2	no	—
255	C₈	—	118	2	no	—
256	C₈	—	472	1	no	—
257	C₈	—	236	2	no	—
258	C₂²	—	2	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	#16837302	1	1	yes	characteristic
261	C₂²	#16837760	1	2	yes	—
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	—	8	2	no	—
265	C₄	—	472	2	no	—
266	C₄	#16837400	1	2	yes	—
267	C₄	#16837668	1	2	yes	—
268	C₄	#16837675	1	2	yes	—
269	C₄	#16837790	1	1	yes	characteristic
270	C₄	#16837793	1	1	yes	characteristic
271	C₂	—	2	2	no	—
272	C₂	#21424911	1	1	yes	characteristic
273	C₂	#21425000	1	1	yes	characteristic
274	C₂	#21425010	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837752

C₂

yes

maximal, characteristic

#21424267

C₂

yes

maximal, characteristic

#21422782

C₂

yes

maximal, characteristic

#21422776

C₂

yes

maximal, characteristic

#21422768

C₂

yes

maximal, characteristic

#21422389

C₂

yes

maximal, characteristic

C₅₉×#1546

C₂

yes

maximal, characteristic

C₂×#14273727

C₂²

yes

—

—

C₄

yes

—

#16837455

C₂²

yes

characteristic

C₂×#14273662

—

#16837426

C₂²

yes

characteristic

C₂×#14273651

—

C₂×C₄×C₅₉⋊C₈

C₂²

yes

—

—

—

—

—

C₂×C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

C₅₉×#431

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₅₉×#332

—

C₂²×Dic₁₁₈

—

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

#14273662

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

#14273651

—

#14273651

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

C₂×C₄

yes

—

C₄×C₅₉⋊C₈

D₄

yes

characteristic

C₄×C₅₉⋊C₈

D₄

yes

characteristic

C₂²×Q₈×C₅₉

—

C₂×M₁₆×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

D₄

yes

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₅₉

#124

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

100

C₂×C₄×C₅₉

—

101

C₂×C₄×C₅₉

—

102

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

104

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

105

C₂×C₄×C₅₉

#121

yes

characteristic

106

C₂×C₄×C₅₉

#121

yes

characteristic

107

C₂×C₄×C₅₉

#127

yes

characteristic

108

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

109

C₂×C₄×C₅₉

#137

yes

—

110

C₂×Dic₅₉

—

111

C₂×Dic₅₉

—

112

Dic₁₁₈

—

113

Dic₁₁₈

—

114

C₈×C₅₉

—

115

C₈×C₅₉

—

116

C₅₉⋊C₈

—

117

C₅₉⋊C₈

—

118

C₅₉⋊C₈

—

119

C₅₉⋊C₈

—

120

#9775

—

maximal, Sylow

121

C₂²×C₅₉

—

122

C₂²×C₅₉

—

123

C₂²×C₅₉

#390

yes

characteristic

124

C₂²×C₅₉

#489

yes

—

125

C₄×C₅₉

—

126

C₄×C₅₉

—

127

C₄×C₅₉

—

128

C₄×C₅₉

#417

yes

—

129

C₄×C₅₉

#471

yes

—

130

C₄×C₅₉

#473

yes

—

131

C₄×C₅₉

#496

yes

characteristic

132

C₄×C₅₉

#497

yes

characteristic

133

Dic₅₉

—

134

C₂×#487

—

135

#1848

—

136

#1549

—

137

#1548

—

138

#1546

—

139

#1546

D₅₉

yes

characteristic

140

#1452

—

141

C₂×C₅₉

—

142

C₂×C₅₉

#1959

yes

characteristic

143

C₂×C₅₉

#1977

yes

characteristic

144

C₂×C₅₉

#1979

yes

characteristic

145

C₂×C₄⋊Q₈

—

146

C₂×C₄⋊Q₈

C₂×D₅₉

yes

characteristic

147

#487

—

148

#487

—

118

—

149

#487

—

118

—

150

#431

—

151

#431

C₂×D₅₉

yes

characteristic

152

C₂×#108

—

118

—

153

#423

—

154

#423

C₂×D₅₉

yes

characteristic

155

C₂×#103

—

118

—

156

C₂×C₄×C₈

—

157

#333

—

118

—

158

#332

—

159

#332

—

118

—

160

#332

—

118

—

161

#322

—

118

—

162

#322

—

118

—

163

C₅₉

#9775

yes

characteristic, complemented, Sylow

164

C₂²×Q₈

—

165

C₂²×Q₈

—

118

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

118

—

168

C₂²×C₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

118

—

174

C₄⋊Q₈

—

118

—

175

C₄⋊Q₈

—

118

—

176

C₄⋊Q₈

C₄×D₅₉

yes

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄⋊C₄

—

118

—

180

C₂×C₄⋊C₄

—

118

—

181

C₂×C₄²

C₂²×D₅₉

yes

characteristic

182

#108

—

236

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

118

—

187

C₄⋊C₈

—

118

—

188

C₄⋊C₈

C₂²⋊D₅₉

yes

—

189

#103

—

118

—

190

#103

—

118

—

191

C₂²⋊C₈

—

192

C₂²⋊C₈

—

118

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

197

C₄×C₈

—

118

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

118

—

203

C₂×Q₈

—

472

—

204

C₂×Q₈

—

236

—

205

C₂²×C₄

—

206

C₂²×C₄

—

236

—

207

C₂²×C₄

#11745685

yes

characteristic

208

C₂²×C₄

D₄×D₅₉

yes

characteristic

209

C₂²×C₄

#11745687

yes

characteristic

210

M₁₆

—

211

M₁₆

—

236

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

118

—

217

C₂×C₈

—

118

—

218

C₂×C₈

—

118

—

219

C₂×C₈

—

236

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

118

—

225

C₄⋊C₄

—

118

—

226

C₄⋊C₄

—

236

—

227

C₄⋊C₄

—

236

—

228

C₄²

C₂×C₄×D₅₉

yes

characteristic

229

C₄²

D₄×D₅₉

yes

characteristic

230

C₄²

D₄×D₅₉

yes

characteristic

231

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

232

C₂³

#14273713

yes

characteristic

233

Q₈

—

234

Q₈

—

235

Q₈

—

236

Q₈

—

472

—

237

Q₈

—

472

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

472

—

243

C₂×C₄

—

236

—

244

C₂×C₄

C₂²⋊C₄×D₅₉

yes

characteristic

245

C₂×C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

246

C₂×C₄

C₄×C₂²⋊D₅₉

yes

characteristic

247

C₂×C₄

#14273699

yes

characteristic

248

C₂×C₄

#14273700

yes

characteristic

249

C₂×C₄

#14273723

yes

characteristic

250

C₂×C₄

#14273751

yes

—

251

C₂×C₄

#14273756

yes

—

252

C₈

—

253

C₈

—

254

C₈

—

118

—

255

C₈

—

118

—

256

C₈

—

472

—

257

C₈

—

236

—

258

C₂²

—

259

C₂²

—

260

C₂²

#16837302

yes

characteristic

261

C₂²

#16837760

yes

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

472

—

266

C₄

#16837400

yes

—

267

C₄

#16837668

yes

—

268

C₄

#16837675

yes

—

269

C₄

#16837790

yes

characteristic

270

C₄

#16837793

yes

characteristic

271

C₂

—

272

C₂

#21424911

yes

characteristic

273

C₂

#21425000

yes

characteristic

274

C₂

#21425010

yes

characteristic

	subgroup	G/H
center	C₂²	#16837302
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1546	C₂
socle	C₂²×C₅₉	#390
prime radical	C₂³×C₅₉	#124
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1546	D₅₉
hypocenter	C₅₉	#9775
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

subgroup

G/H

center

C₂²

#16837302

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1546

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

N	H ≅ G/N	type
163. C₅₉	#9775	semidirect

H ≅ G/N

type

163. C₅₉

#9775

semidirect

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

subgroup	index
C₂×#16837752	2
#21424267	2
#21422782	2
#21422776	2
#21422768	2
#21422389	2
C₅₉×#1546	2
#9775	59

subgroup

index

C₅₉×#1546

Subgroups — #28488171

Conjugacy classes of subgroups

Complements

Maximal subgroups