Group #28481644 — subgroups

Subgroups — #28481644

Order 15104.

362 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 111 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×C₈×Dic₁₁₈	C₂	1	1	yes	maximal, characteristic
2	#21422859	C₂	1	1	yes	maximal, characteristic
3	#21422439	C₂	1	2	yes	maximal
4	#21421965	C₂	1	2	yes	maximal
5	C₅₉×#1568	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
7	C₈×Dic₁₁₈	—	2	1	no	—
8	C₈×Dic₁₁₈	—	2	1	no	—
9	C₈×Dic₁₁₈	—	2	1	no	—
10	C₈×Dic₁₁₈	—	2	1	no	—
11	#16837459	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₅₉⋊C₈	C₄	1	2	yes	—
14	C₂×C₈×Dic₅₉	C₄	1	2	yes	—
15	#16837155	—	2	1	no	—
16	#16837153	—	2	1	no	—
17	#16837127	—	2	4	no	—
18	C₅₉×#432	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#335	—	2	1	no	—
21	C₅₉×#334	—	2	1	no	—
22	C₂²×Dic₁₁₈	Q₈	1	1	yes	characteristic
23	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₁₈	—	2	1	no	—
25	C₄×Dic₁₁₈	—	2	1	no	—
26	C₄×Dic₁₁₈	—	2	1	no	—
27	C₄×Dic₁₁₈	—	2	1	no	—
28	C₂×C₄⋊Dic₅₉	Q₈	1	1	yes	characteristic
29	C₂×Dic₅₉⋊C₄	D₄	1	2	yes	—
30	C₂×C₄×Dic₅₉	C₂×C₄	1	2	yes	—
31	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
33	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
34	Dic₅₉⋊C₈	—	2	2	no	—
35	Dic₅₉⋊C₈	—	2	2	no	—
36	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
37	#14273638	—	2	2	no	—
38	C₈×Dic₅₉	—	2	2	no	—
39	C₈×Dic₅₉	—	2	2	no	—
40	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₅₉	—	2	2	no	—
44	C₂²⋊C₈×C₅₉	—	2	2	no	—
45	#97×C₅₉	—	2	2	no	—
46	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
53	C₂²×Dic₅₉	C₄⋊C₄	1	2	yes	—
54	C₂²×Dic₅₉	C₄⋊C₄	1	2	yes	—
55	C₂×Dic₁₁₈	—	2	1	no	—
56	C₂×Dic₁₁₈	—	2	1	no	—
57	C₂×Dic₁₁₈	—	2	4	no	—
58	C₂×C₈×C₅₉	—	2	2	no	—
59	C₂×C₈×C₅₉	—	4	1	no	—
60	C₂×C₈×C₅₉	—	4	2	no	—
61	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₅₉	#41	1	1	yes	characteristic
68	C₄²×C₅₉	#41	1	1	yes	characteristic
69	C₄⋊Dic₅₉	—	2	1	no	—
70	C₄⋊Dic₅₉	—	2	1	no	—
71	Dic₅₉⋊C₄	—	2	2	no	—
72	Dic₅₉⋊C₄	—	2	2	no	—
73	C₄×Dic₅₉	—	2	2	no	—
74	C₄×Dic₅₉	—	2	2	no	—
75	C₂×C₅₉⋊C₈	—	2	2	no	—
76	C₂×C₅₉⋊C₈	—	4	2	no	—
77	C₂×C₅₉⋊C₈	—	4	2	no	—
78	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	—	2	1	no	—
81	C₂×C₄×C₅₉	—	2	1	no	—
82	C₂×C₄×C₅₉	—	4	1	no	—
83	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×Dic₅₉	—	2	2	no	—
90	C₂×Dic₅₉	—	2	2	no	—
91	C₂×Dic₅₉	—	2	2	no	—
92	C₂×Dic₅₉	—	4	2	no	—
93	C₂×Dic₅₉	#108	1	4	yes	—
94	Dic₁₁₈	—	2	4	no	—
95	Dic₁₁₈	—	2	4	no	—
96	C₈×C₅₉	—	2	1	no	—
97	C₈×C₅₉	—	2	1	no	—
98	C₈×C₅₉	—	2	1	no	—
99	C₈×C₅₉	—	8	2	no	—
100	C₈×C₅₉	#101	1	2	yes	—
101	C₅₉⋊C₈	—	4	2	no	—
102	C₅₉⋊C₈	—	8	2	no	—
103	#8623	—	59	1	no	maximal, Sylow
104	C₂²×C₅₉	—	2	1	no	—
105	C₂²×C₅₉	—	2	1	no	—
106	C₂²×C₅₉	#380	1	1	yes	characteristic
107	C₂²×C₅₉	C₂×#108	1	2	yes	—
108	C₄×C₅₉	—	2	1	no	—
109	C₄×C₅₉	—	2	1	no	—
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	—	2	1	no	—
112	C₄×C₅₉	—	2	1	no	—
113	C₄×C₅₉	C₂×#101	1	1	yes	characteristic
114	C₄×C₅₉	#413	1	1	yes	characteristic
115	Dic₅₉	—	2	4	no	—
116	Dic₅₉	—	4	2	no	—
117	C₂×C₈×Q₈	—	59	1	no	—
118	#1568	—	59	1	no	—
119	#1568	D₅₉	1	1	yes	characteristic
120	#1467	—	59	2	no	—
121	#1290	—	59	2	no	—
122	C₂×C₅₉	—	2	2	no	—
123	C₂×C₅₉	#1801	1	1	yes	characteristic
124	C₂×C₅₉	#1810	1	1	yes	characteristic
125	C₂×C₅₉	#1812	1	1	yes	characteristic
126	C₂×C₄×Q₈	—	59	1	no	—
127	C₈×Q₈	—	118	1	no	—
128	C₈×Q₈	—	118	1	no	—
129	C₈×Q₈	—	118	1	no	—
130	C₈×Q₈	—	118	1	no	—
131	#432	—	59	2	no	—
132	#432	C₂×D₅₉	1	2	yes	—
133	C₂×C₄⋊C₈	—	59	2	no	—
134	C₂×C₄⋊C₈	—	59	1	no	—
135	C₂×C₄×C₈	—	59	2	no	—
136	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
137	#335	—	2	1	no	—
138	#335	—	118	1	no	—
139	#334	—	2	1	no	—
140	#334	—	118	1	no	—
141	#324	—	118	4	no	—
142	C₅₉	#8623	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	—	59	1	no	—
144	C₂²×C₈	—	59	2	no	—
145	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
146	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
147	C₄×Q₈	—	118	1	no	—
148	C₄×Q₈	—	118	1	no	—
149	C₄×Q₈	—	118	1	no	—
150	C₄×Q₈	—	118	1	no	—
151	C₂×C₄⋊C₄	—	59	2	no	—
152	C₂×C₄⋊C₄	—	59	1	no	—
153	C₂×C₄²	—	59	2	no	—
154	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	118	2	no	—
157	C₄⋊C₈	—	118	2	no	—
158	C₄⋊C₈	—	118	1	no	—
159	C₄⋊C₈	—	118	2	no	—
160	C₄⋊C₈	—	118	1	no	—
161	C₂²⋊C₈	—	2	2	no	—
162	C₂²⋊C₈	—	118	2	no	—
163	#97	—	2	2	no	—
164	#97	—	118	2	no	—
165	C₄×C₈	—	118	2	no	—
166	C₄×C₈	—	118	2	no	—
167	C₄×C₈	D₂₃₆	1	1	yes	characteristic
168	C₄×C₈	D₂₃₆	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
170	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
171	C₂×Q₈	—	118	4	no	—
172	C₂×Q₈	—	118	1	no	—
173	C₂×Q₈	—	118	1	no	—
174	C₂²×C₄	—	59	2	no	—
175	C₂²×C₄	—	59	2	no	—
176	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
177	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
178	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	118	2	no	—
183	C₂×C₈	—	236	2	no	—
184	C₂×C₈	—	236	2	no	—
185	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
187	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
188	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄	—	118	2	no	—
190	C₄⋊C₄	—	118	2	no	—
191	C₄⋊C₄	—	118	1	no	—
192	C₄⋊C₄	—	118	1	no	—
193	C₄²	—	118	2	no	—
194	C₄²	—	118	2	no	—
195	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
196	C₄²	#11745687	1	1	yes	characteristic
197	C₄²	#11745689	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
199	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
200	Q₈	—	118	4	no	—
201	Q₈	—	118	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	59	4	no	—
207	C₂×C₄	—	118	2	no	—
208	C₂×C₄	—	118	2	no	—
209	C₂×C₄	—	118	2	no	—
210	C₂×C₄	—	236	2	no	—
211	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	#14273685	1	1	yes	characteristic
213	C₂×C₄	#14273698	1	1	yes	characteristic
214	C₂×C₄	#14273702	1	1	yes	characteristic
215	C₂×C₄	#14273703	1	1	yes	characteristic
216	C₂×C₄	#14273707	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	8	2	no	—
221	C₈	—	472	2	no	—
222	C₈	—	236	2	no	—
223	C₈	#14273645	1	2	yes	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#16837259	1	1	yes	characteristic
227	C₂²	#108×D₅₉	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	118	4	no	—
234	C₄	—	236	2	no	—
235	C₄	C₂×#14273645	1	1	yes	characteristic
236	C₄	#16837384	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#21424089	1	1	yes	characteristic
239	C₂	#21424131	1	1	yes	characteristic
240	C₂	#21424139	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₁₈

C₂

yes

maximal, characteristic

#21422859

C₂

yes

maximal, characteristic

#21422439

C₂

yes

maximal

#21421965

C₂

yes

maximal

C₅₉×#1568

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₁₈

C₂²

yes

characteristic

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

—

C₈×Dic₁₁₈

—

#16837459

C₂²

yes

—

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₈

C₄

yes

—

C₂×C₈×Dic₅₉

C₄

yes

—

#16837155

—

#16837153

—

#16837127

—

C₅₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#335

—

C₅₉×#334

—

C₂²×Dic₁₁₈

Q₈

yes

characteristic

C₂²×C₅₉⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

C₂×C₄⋊Dic₅₉

Q₈

yes

characteristic

C₂×Dic₅₉⋊C₄

D₄

yes

—

C₂×C₄×Dic₅₉

C₂×C₄

yes

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

#14273638

—

C₈×Dic₅₉

—

C₈×Dic₅₉

—

C₂²×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²⋊C₈×C₅₉

—

#97×C₅₉

—

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂²×Dic₅₉

C₄⋊C₄

yes

—

C₂²×Dic₅₉

C₄⋊C₄

yes

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

#108

yes

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

100

C₈×C₅₉

#101

yes

—

101

C₅₉⋊C₈

—

102

C₅₉⋊C₈

—

103

#8623

—

maximal, Sylow

104

C₂²×C₅₉

—

105

C₂²×C₅₉

—

106

C₂²×C₅₉

#380

yes

characteristic

107

C₂²×C₅₉

C₂×#108

yes

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

C₂×#101

yes

characteristic

114

C₄×C₅₉

#413

yes

characteristic

115

Dic₅₉

—

116

Dic₅₉

—

117

C₂×C₈×Q₈

—

118

#1568

—

119

#1568

D₅₉

yes

characteristic

120

#1467

—

121

#1290

—

122

C₂×C₅₉

—

123

C₂×C₅₉

#1801

yes

characteristic

124

C₂×C₅₉

#1810

yes

characteristic

125

C₂×C₅₉

#1812

yes

characteristic

126

C₂×C₄×Q₈

—

127

C₈×Q₈

—

118

—

128

C₈×Q₈

—

118

—

129

C₈×Q₈

—

118

—

130

C₈×Q₈

—

118

—

131

#432

—

132

#432

C₂×D₅₉

yes

—

133

C₂×C₄⋊C₈

—

134

C₂×C₄⋊C₈

—

135

C₂×C₄×C₈

—

136

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

137

#335

—

138

#335

—

118

—

139

#334

—

140

#334

—

118

—

141

#324

—

118

—

142

C₅₉

#8623

yes

characteristic, complemented, Sylow

143

C₂²×Q₈

—

144

C₂²×C₈

—

145

C₂²×C₈

C₄×D₅₉

yes

characteristic

146

C₂²×C₈

C₄×D₅₉

yes

characteristic

147

C₄×Q₈

—

118

—

148

C₄×Q₈

—

118

—

149

C₄×Q₈

—

118

—

150

C₄×Q₈

—

118

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₅₉

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

118

—

157

C₄⋊C₈

—

118

—

158

C₄⋊C₈

—

118

—

159

C₄⋊C₈

—

118

—

160

C₄⋊C₈

—

118

—

161

C₂²⋊C₈

—

162

C₂²⋊C₈

—

118

—

163

#97

—

164

#97

—

118

—

165

C₄×C₈

—

118

—

166

C₄×C₈

—

118

—

167

C₄×C₈

D₂₃₆

yes

characteristic

168

C₄×C₈

D₂₃₆

yes

characteristic

169

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

170

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

171

C₂×Q₈

—

118

—

172

C₂×Q₈

—

118

—

173

C₂×Q₈

—

118

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

C₂×C₄×D₅₉

yes

characteristic

177

C₂²×C₄

D₄×D₅₉

yes

characteristic

178

C₂²×C₄

Q₈×D₅₉

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

118

—

183

C₂×C₈

—

236

—

184

C₂×C₈

—

236

—

185

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

187

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

188

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

189

C₄⋊C₄

—

118

—

190

C₄⋊C₄

—

118

—

191

C₄⋊C₄

—

118

—

192

C₄⋊C₄

—

118

—

193

C₄²

—

118

—

194

C₄²

—

118

—

195

C₄²

C₂×D₂₃₆

yes

characteristic

196

C₄²

#11745687

yes

characteristic

197

C₄²

#11745689

yes

characteristic

198

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

199

C₂³

C₄⋊C₄×D₅₉

yes

characteristic

200

Q₈

—

118

—

201

Q₈

—

118

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

118

—

208

C₂×C₄

—

118

—

209

C₂×C₄

—

118

—

210

C₂×C₄

—

236

—

211

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

212

C₂×C₄

#14273685

yes

characteristic

213

C₂×C₄

#14273698

yes

characteristic

214

C₂×C₄

#14273702

yes

characteristic

215

C₂×C₄

#14273703

yes

characteristic

216

C₂×C₄

#14273707

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

472

—

222

C₈

—

236

—

223

C₈

#14273645

yes

—

224

C₂²

—

225

C₂²

—

226

C₂²

#16837259

yes

characteristic

227

C₂²

#108×D₅₉

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

118

—

234

C₄

—

236

—

235

C₄

C₂×#14273645

yes

characteristic

236

C₄

#16837384

yes

characteristic

237

C₂

—

238

C₂

#21424089

yes

characteristic

239

C₂

#21424131

yes

characteristic

240

C₂

#21424139

yes

characteristic

	subgroup	G/H
center	C₂²	#16837259
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1568	C₂
socle	C₂²×C₅₉	#380
prime radical	C₂³×C₅₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1568	D₅₉
hypocenter	C₅₉	#8623
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#16837259

commutator

C₂²×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1568

C₂

socle

C₂²×C₅₉

#380

prime radical

C₂³×C₅₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
142. C₅₉	#8623	semidirect

H ≅ G/N

type

142. C₅₉

#8623

semidirect

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

subgroup	index
C₂×C₈×Dic₁₁₈	2
#21422859	2
#21422439	2
#21421965	2
C₅₉×#1568	2
#8623	59

subgroup

index

C₂×C₈×Dic₁₁₈

C₅₉×#1568

Subgroups — #28481644

Conjugacy classes of subgroups

Complements

Maximal subgroups