Group #28498024 — subgroups

Subgroups — #28498024

Order 15104.

342 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16837526	C₂	1	1	yes	maximal, characteristic
2	#21425892	C₂	1	2	yes	maximal
3	#21422036	C₂	1	1	yes	maximal, characteristic
4	#21422035	C₂	1	2	yes	maximal
5	C₅₉×#1322	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	C₄	1	1	yes	characteristic
7	#16837526	—	2	2	no	—
8	#16837526	—	2	2	no	—
9	C₂×Dic₅₉⋊C₈	C₄	1	1	yes	characteristic
10	C₂×Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₅₉	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
14	Dic₅₉⋊C₁₆	—	2	2	no	—
15	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	—
16	C₁₆×Dic₅₉	—	2	2	no	—
17	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
19	C₂²×Dic₁₁₈	C₈	1	1	yes	characteristic
20	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₁₈	—	2	2	no	—
23	C₄×Dic₁₁₈	—	2	2	no	—
24	C₂×C₄⋊Dic₅₉	C₈	1	1	yes	characteristic
25	C₂×Dic₅₉⋊C₄	C₈	1	1	yes	characteristic
26	C₂×Dic₅₉⋊C₄	C₈	1	1	yes	characteristic
27	C₂×C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₅₉⋊C₁₆	—	2	2	no	—
30	Dic₅₉⋊C₈	—	2	2	no	—
31	Dic₅₉⋊C₈	—	2	2	no	—
32	C₄×C₅₉⋊C₈	—	2	1	no	—
33	C₄×C₅₉⋊C₈	—	2	1	no	—
34	C₈×Dic₅₉	—	2	1	no	—
35	C₈×Dic₅₉	—	2	1	no	—
36	C₈×Dic₅₉	D₄	1	2	yes	—
37	C₈×Dic₅₉	D₄	1	2	yes	—
38	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₆×C₅₉	—	2	2	no	—
42	C₄⋊C₈×C₅₉	—	2	2	no	—
43	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
44	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
45	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×Dic₅₉	C₂×C₈	1	1	yes	characteristic
47	C₂²×Dic₅₉	C₂×C₈	1	1	yes	characteristic
48	C₂²×Dic₅₉	C₂×C₈	1	1	yes	characteristic
49	C₂²×Dic₅₉	C₂×C₈	1	1	yes	characteristic
50	C₂×Dic₁₁₈	—	2	2	no	—
51	C₂×Dic₁₁₈	—	2	2	no	—
52	C₂×Dic₁₁₈	C₁₆	1	4	yes	complemented
53	C₂×C₈×C₅₉	—	2	1	no	—
54	C₂×C₈×C₅₉	—	4	1	no	—
55	C₂×C₈×C₅₉	—	4	1	no	—
56	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
57	C₄²×C₅₉	—	2	1	no	—
58	C₄²×C₅₉	—	2	1	no	—
59	C₄⋊Dic₅₉	—	2	2	no	—
60	Dic₅₉⋊C₄	—	2	2	no	—
61	Dic₅₉⋊C₄	—	2	2	no	—
62	C₄×Dic₅₉	—	2	1	no	—
63	C₄×Dic₅₉	—	2	1	no	—
64	C₄×Dic₅₉	C₂²⋊C₄	1	2	yes	—
65	C₄×Dic₅₉	M₁₆	1	2	yes	—
66	C₂×C₅₉⋊C₈	—	2	2	no	—
67	C₂×C₅₉⋊C₈	—	2	1	no	—
68	C₂×C₅₉⋊C₈	—	4	1	no	—
69	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
71	C₁₆×C₅₉	—	4	2	no	—
72	C₅₉⋊C₁₆	—	4	2	no	—
73	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₅₉	—	2	1	no	—
75	C₂×C₄×C₅₉	—	2	1	no	—
76	C₂×C₄×C₅₉	—	2	1	no	—
77	C₂×C₄×C₅₉	—	2	1	no	—
78	C₂×C₄×C₅₉	—	2	1	no	—
79	C₂×C₄×C₅₉	—	4	1	no	—
80	C₂×C₄×C₅₉	C₂×C₁₆	1	2	yes	—
81	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₅₉	—	2	1	no	—
84	C₂×Dic₅₉	—	2	1	no	—
85	C₂×Dic₅₉	—	2	1	no	—
86	C₂×Dic₅₉	—	4	1	no	—
87	C₂×Dic₅₉	—	4	1	no	—
88	C₂×Dic₅₉	C₂²⋊C₈	1	2	yes	—
89	C₂×Dic₅₉	C₂²⋊C₈	1	2	yes	—
90	C₂×Dic₅₉	C₂×C₁₆	1	2	yes	—
91	C₂×Dic₅₉	C₂×C₁₆	1	2	yes	—
92	C₂×Dic₅₉	M₃₂	1	2	yes	—
93	Dic₁₁₈	—	2	8	no	—
94	C₈×C₅₉	—	2	2	no	—
95	C₈×C₅₉	—	4	1	no	—
96	C₅₉⋊C₈	—	2	1	no	—
97	C₅₉⋊C₈	—	4	1	no	—
98	C₅₉⋊C₈	#101	1	2	yes	—
99	#11493	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	—	2	1	no	—
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
103	C₂²×C₅₉	C₂²×C₁₆	1	1	yes	characteristic
104	C₂²×C₅₉	C₂×M₃₂	1	1	yes	characteristic
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	—	2	1	no	—
107	C₄×C₅₉	—	4	1	no	—
108	C₄×C₅₉	#410	1	1	yes	characteristic
109	C₄×C₅₉	C₂×#101	1	1	yes	characteristic
110	Dic₅₉	—	2	2	no	—
111	Dic₅₉	—	2	2	no	—
112	Dic₅₉	—	4	1	no	—
113	Dic₅₉	C₂²⋊C₁₆	1	4	yes	—
114	C₂×C₈×Q₈	—	59	1	no	—
115	#2162	—	59	2	no	—
116	#1322	—	59	1	no	—
117	#1322	—	59	2	no	—
118	#1322	D₅₉	1	1	yes	characteristic
119	C₂×C₅₉	—	2	1	no	—
120	C₂×C₅₉	—	2	1	no	—
121	C₂×C₅₉	#1461	1	1	yes	characteristic
122	C₂×C₅₉	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
123	C₂×C₅₉	#2115	1	1	yes	characteristic
124	C₂×C₄×Q₈	—	59	1	no	—
125	C₈×Q₈	—	118	2	no	—
126	C₈×Q₈	—	118	2	no	—
127	C₂×C₄⋊C₈	—	59	1	no	—
128	C₂×C₄⋊C₈	—	59	1	no	—
129	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
130	C₂×C₄×C₈	—	59	1	no	—
131	C₂×C₄×C₈	—	59	1	no	—
132	C₂×C₄×C₈	—	59	1	no	—
133	C₄⋊C₁₆	—	118	2	no	—
134	C₂²⋊C₁₆	—	59	2	no	—
135	C₂²⋊C₁₆	C₂×D₅₉	1	2	yes	—
136	C₄×C₁₆	—	118	2	no	—
137	C₅₉	#11493	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₈	—	59	1	no	—
139	C₂²×C₈	—	59	1	no	—
140	C₂²×C₈	—	59	1	no	—
141	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
143	C₄×Q₈	—	118	2	no	—
144	C₄×Q₈	—	118	2	no	—
145	C₂×C₄⋊C₄	—	59	1	no	—
146	C₂×C₄⋊C₄	—	59	1	no	—
147	C₂×C₄⋊C₄	—	59	1	no	—
148	C₂×C₄²	—	59	1	no	—
149	C₂×C₄²	—	59	1	no	—
150	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
151	C₂×C₁₆	—	2	2	no	—
152	C₂×C₁₆	—	118	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	118	2	no	—
155	C₄⋊C₈	—	118	2	no	—
156	C₄×C₈	—	59	2	no	—
157	C₄×C₈	—	59	2	no	—
158	C₄×C₈	—	118	1	no	—
159	C₄×C₈	—	118	1	no	—
160	C₄×C₈	—	118	1	no	—
161	C₄×C₈	—	118	1	no	—
162	C₂×Q₈	—	59	4	no	—
163	C₂×Q₈	—	118	2	no	—
164	C₂×Q₈	—	118	2	no	—
165	C₂²×C₄	—	59	1	no	—
166	C₂²×C₄	—	59	1	no	—
167	C₂²×C₄	—	59	1	no	—
168	C₂²×C₄	—	59	1	no	—
169	C₂²×C₄	C₈×D₅₉	1	1	yes	characteristic
170	C₂²×C₄	C₈×D₅₉	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	59	1	no	—
176	C₂×C₈	—	59	1	no	—
177	C₂×C₈	—	118	2	no	—
178	C₂×C₈	—	118	1	no	—
179	C₂×C₈	—	236	1	no	—
180	C₂×C₈	D₄×D₅₉	1	2	yes	—
181	C₄⋊C₄	—	118	2	no	—
182	C₄⋊C₄	—	118	2	no	—
183	C₄⋊C₄	—	118	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	59	2	no	—
187	C₄²	—	59	2	no	—
188	C₄²	—	118	1	no	—
189	C₄²	—	118	1	no	—
190	C₁₆	—	4	2	no	—
191	C₁₆	—	236	2	no	—
192	C₂³	C₂×C₈×D₅₉	1	1	yes	characteristic
193	Q₈	—	118	8	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	59	2	no	—
201	C₂×C₄	—	59	2	no	—
202	C₂×C₄	—	59	2	no	—
203	C₂×C₄	—	59	2	no	—
204	C₂×C₄	—	59	2	no	—
205	C₂×C₄	—	118	1	no	—
206	C₂×C₄	—	118	1	no	—
207	C₂×C₄	—	118	1	no	—
208	C₂×C₄	—	236	1	no	—
209	C₂×C₄	—	236	1	no	—
210	C₂×C₄	C₁₆×D₅₉	1	2	yes	—
211	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
212	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	4	1	no	—
215	C₈	—	59	2	no	—
216	C₈	—	118	1	no	—
217	C₈	—	236	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	C₂²⋊C₈×D₅₉	1	1	yes	characteristic
221	C₂²	C₂×C₁₆×D₅₉	1	1	yes	characteristic
222	C₂²	M₃₂×D₅₉	1	1	yes	characteristic
223	C₄	—	2	2	no	—
224	C₄	—	2	1	no	—
225	C₄	—	4	1	no	—
226	C₄	—	59	4	no	—
227	C₄	—	118	2	no	—
228	C₄	—	118	2	no	—
229	C₄	—	236	1	no	—
230	C₄	#16837374	1	1	yes	characteristic
231	C₄	#101×D₅₉	1	1	yes	characteristic
232	C₂	—	2	1	no	—
233	C₂	—	2	1	no	—
234	C₂	#21422418	1	1	yes	characteristic
235	C₂	C₂²⋊C₁₆×D₅₉	1	1	yes	characteristic
236	C₂	#21425715	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837526

C₂

yes

maximal, characteristic

#21425892

C₂

yes

maximal

#21422036

C₂

yes

maximal, characteristic

#21422035

C₂

yes

maximal

C₅₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₁₈

C₄

yes

characteristic

#16837526

—

#16837526

—

C₂×Dic₅₉⋊C₈

C₄

yes

characteristic

C₂×Dic₅₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₅₉⋊C₈

C₄

yes

characteristic

C₂×C₈×Dic₅₉

C₄

yes

characteristic

C₂×C₈×Dic₅₉

C₂²

yes

characteristic

Dic₅₉⋊C₁₆

—

C₂²⋊(C₅₉⋊C₁₆)

C₂²

yes

—

C₁₆×Dic₅₉

—

C₂×C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₅₉×C₂²⋊C₁₆

C₂²

yes

—

C₂²×Dic₁₁₈

C₈

yes

characteristic

C₂²×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₂×C₄⋊Dic₅₉

C₈

yes

characteristic

C₂×Dic₅₉⋊C₄

C₈

yes

characteristic

C₂×Dic₅₉⋊C₄

C₈

yes

characteristic

C₂×C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₁₆

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₈×Dic₅₉

—

C₈×Dic₅₉

—

C₈×Dic₅₉

D₄

yes

—

C₈×Dic₅₉

D₄

yes

—

C₂²×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₄²×C₅₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₅₉

—

C₄⋊C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂²×Dic₅₉

C₂×C₈

yes

characteristic

C₂²×Dic₅₉

C₂×C₈

yes

characteristic

C₂²×Dic₅₉

C₂×C₈

yes

characteristic

C₂²×Dic₅₉

C₂×C₈

yes

characteristic

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₁₆

yes

complemented

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂²⋊C₄

yes

—

C₄×Dic₅₉

M₁₆

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₁₆

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×M₁₆

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₂²⋊C₈

yes

—

C₂×Dic₅₉

C₂²⋊C₈

yes

—

C₂×Dic₅₉

C₂×C₁₆

yes

—

C₂×Dic₅₉

C₂×C₁₆

yes

—

C₂×Dic₅₉

M₃₂

yes

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

#101

yes

—

#11493

—

maximal, Sylow

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

C₂×C₂²⋊C₈

yes

characteristic

103

C₂²×C₅₉

C₂²×C₁₆

yes

characteristic

104

C₂²×C₅₉

C₂×M₃₂

yes

characteristic

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

#410

yes

characteristic

109

C₄×C₅₉

C₂×#101

yes

characteristic

110

Dic₅₉

—

111

Dic₅₉

—

112

Dic₅₉

—

113

Dic₅₉

C₂²⋊C₁₆

yes

—

114

C₂×C₈×Q₈

—

115

#2162

—

116

#1322

—

117

#1322

—

118

#1322

D₅₉

yes

characteristic

119

C₂×C₅₉

—

120

C₂×C₅₉

—

121

C₂×C₅₉

#1461

yes

characteristic

122

C₂×C₅₉

C₂×C₂²⋊C₁₆

yes

characteristic

123

C₂×C₅₉

#2115

yes

characteristic

124

C₂×C₄×Q₈

—

125

C₈×Q₈

—

118

—

126

C₈×Q₈

—

118

—

127

C₂×C₄⋊C₈

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

C₂×D₅₉

yes

characteristic

130

C₂×C₄×C₈

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

C₄⋊C₁₆

—

118

—

134

C₂²⋊C₁₆

—

135

C₂²⋊C₁₆

C₂×D₅₉

yes

—

136

C₄×C₁₆

—

118

—

137

C₅₉

#11493

yes

characteristic, complemented, Sylow

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

C₄×D₅₉

yes

characteristic

142

C₂²×C₈

C₂²×D₅₉

yes

characteristic

143

C₄×Q₈

—

118

—

144

C₄×Q₈

—

118

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₄×D₅₉

yes

characteristic

151

C₂×C₁₆

—

152

C₂×C₁₆

—

118

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

118

—

155

C₄⋊C₈

—

118

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

118

—

159

C₄×C₈

—

118

—

160

C₄×C₈

—

118

—

161

C₄×C₈

—

118

—

162

C₂×Q₈

—

163

C₂×Q₈

—

118

—

164

C₂×Q₈

—

118

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₈×D₅₉

yes

characteristic

170

C₂²×C₄

C₈×D₅₉

yes

characteristic

171

C₂²×C₄

C₂×C₄×D₅₉

yes

characteristic

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

118

—

178

C₂×C₈

—

118

—

179

C₂×C₈

—

236

—

180

C₂×C₈

D₄×D₅₉

yes

—

181

C₄⋊C₄

—

118

—

182

C₄⋊C₄

—

118

—

183

C₄⋊C₄

—

118

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

118

—

189

C₄²

—

118

—

190

C₁₆

—

191

C₁₆

—

236

—

192

C₂³

C₂×C₈×D₅₉

yes

characteristic

193

Q₈

—

118

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

118

—

206

C₂×C₄

—

118

—

207

C₂×C₄

—

118

—

208

C₂×C₄

—

236

—

209

C₂×C₄

—

236

—

210

C₂×C₄

C₁₆×D₅₉

yes

—

211

C₂×C₄

C₂²⋊C₄×D₅₉

yes

characteristic

212

C₂×C₄

M₁₆×D₅₉

yes

characteristic

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

118

—

217

C₈

—

236

—

218

C₂²

—

219

C₂²

—

220

C₂²

C₂²⋊C₈×D₅₉

yes

characteristic

221

C₂²

C₂×C₁₆×D₅₉

yes

characteristic

222

C₂²

M₃₂×D₅₉

yes

characteristic

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

118

—

228

C₄

—

118

—

229

C₄

—

236

—

230

C₄

#16837374

yes

characteristic

231

C₄

#101×D₅₉

yes

characteristic

232

C₂

—

233

C₂

—

234

C₂

#21422418

yes

characteristic

235

C₂

C₂²⋊C₁₆×D₅₉

yes

characteristic

236

C₂

#21425715

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₅₉
commutator	C₂²×C₅₉	C₂²×C₁₆
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#1322	C₂
socle	C₂²×C₅₉	C₂×C₂²⋊C₈
prime radical	C₂³×C₅₉	C₂²×C₈
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1322	D₅₉
hypocenter	C₅₉	#11493
LCS	G ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₅₉

commutator

C₂²×C₅₉

C₂²×C₁₆

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#1322

C₂

socle

C₂²×C₅₉

C₂×C₂²⋊C₈

prime radical

C₂³×C₅₉

C₂²×C₈

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1322

N	H ≅ G/N	type
52. C₂×Dic₁₁₈	C₁₆	semidirect
137. C₅₉	#11493	semidirect

H ≅ G/N

type

52. C₂×Dic₁₁₈

C₁₆

semidirect

137. C₅₉

#11493

semidirect

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

subgroup	index
C₂×#16837526	2
#21425892	2
#21422036	2
#21422035	2
C₅₉×#1322	2
#11493	59

subgroup

index

C₅₉×#1322

Subgroups — #28498024

Conjugacy classes of subgroups

Complements

Maximal subgroups