Group #28488166 — subgroups

Subgroups — #28488166

Order 15104.

406 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16837753	C₂	1	1	yes	maximal, characteristic
2	#21422782	C₂	1	1	yes	maximal, characteristic
3	#21422778	C₂	1	1	yes	maximal, characteristic
4	#21422769	C₂	1	1	yes	maximal, characteristic
5	#21422769	C₂	1	1	yes	maximal, characteristic
6	#21422388	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1848	C₂	1	1	yes	maximal, characteristic
8	C₂×#14273727	C₂²	1	1	yes	characteristic
9	C₂×#14273727	C₂²	1	1	yes	characteristic
10	#16837753	—	2	2	no	—
11	#16837753	C₄	1	4	yes	—
12	#16837455	C₂²	1	1	yes	characteristic
13	#16837455	C₂²	1	1	yes	characteristic
14	C₂×#14273652	—	2	2	no	—
15	#16837150	—	2	2	no	—
16	#16837149	—	2	2	no	—
17	#16837149	—	2	2	no	—
18	#16837147	—	2	2	no	—
19	#16837124	—	2	2	no	—
20	C₂×#108×C₅₉	—	2	2	no	—
21	C₅₉×#423	C₂²	1	1	yes	characteristic
22	C₅₉×#423	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×Dic₁₁₈	—	2	1	no	—
25	C₂²×Dic₁₁₈	—	2	1	no	—
26	#14273727	—	2	1	no	—
27	#14273727	—	2	1	no	—
28	#14273727	—	2	1	no	—
29	#14273727	—	2	1	no	—
30	#14273727	—	2	1	no	—
31	#14273727	—	2	1	no	—
32	#14273727	C₂×C₄	1	2	yes	—
33	#14273727	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊Dic₅₉	—	2	1	no	—
35	C₂×C₄⋊Dic₅₉	—	2	1	no	—
36	C₂×C₄⋊Dic₅₉	—	2	1	no	—
37	C₂×C₄⋊Dic₅₉	—	2	1	no	—
38	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
39	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
40	#14273652	—	2	8	no	—
41	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
42	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
43	C₄×C₅₉⋊C₈	—	2	1	no	—
44	C₄×C₅₉⋊C₈	—	2	1	no	—
45	C₂×M₁₆×C₅₉	—	2	1	no	—
46	C₂×M₁₆×C₅₉	—	2	1	no	—
47	C₂²×C₈×C₅₉	D₄	1	2	yes	—
48	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
49	#108×C₅₉	—	4	4	no	—
50	C₄⋊C₈×C₅₉	—	2	1	no	—
51	C₄⋊C₈×C₅₉	—	2	1	no	—
52	C₄⋊C₈×C₅₉	—	2	1	no	—
53	C₄⋊C₈×C₅₉	—	2	1	no	—
54	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
55	C₄×C₈×C₅₉	D₄	1	2	yes	—
56	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
58	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
59	C₂²×Dic₅₉	—	4	1	no	—
60	C₂²×Dic₅₉	—	4	1	no	—
61	C₂×Dic₁₁₈	—	2	2	no	—
62	C₂×Dic₁₁₈	—	2	2	no	—
63	C₂×Dic₁₁₈	—	4	2	no	—
64	C₂×Dic₁₁₈	—	4	2	no	—
65	C₂×Dic₁₁₈	—	4	1	no	—
66	C₂×Dic₁₁₈	—	4	1	no	—
67	C₂×Dic₁₁₈	—	8	2	no	—
68	M₁₆×C₅₉	—	4	2	no	—
69	M₁₆×C₅₉	—	4	2	no	—
70	C₂×C₈×C₅₉	—	2	2	no	—
71	C₂×C₈×C₅₉	—	2	2	no	—
72	C₂×C₈×C₅₉	—	4	1	no	—
73	C₂×C₈×C₅₉	—	4	1	no	—
74	C₂×C₈×C₅₉	C₂²⋊C₄	1	4	yes	—
75	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
79	C₄⋊Dic₅₉	—	2	2	no	—
80	C₄⋊Dic₅₉	—	2	2	no	—
81	C₄⋊Dic₅₉	—	2	2	no	—
82	C₄⋊Dic₅₉	—	2	2	no	—
83	C₄⋊Dic₅₉	—	4	1	no	—
84	C₄⋊Dic₅₉	—	4	1	no	—
85	C₄⋊Dic₅₉	—	4	1	no	—
86	C₄⋊Dic₅₉	—	4	1	no	—
87	C₂×C₅₉⋊C₈	—	2	2	no	—
88	C₂×C₅₉⋊C₈	—	2	2	no	—
89	C₂³×C₅₉	#124	1	1	yes	characteristic
90	C₂×C₄×C₅₉	—	2	2	no	—
91	C₂×C₄×C₅₉	—	2	2	no	—
92	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
98	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
99	C₂×C₄×C₅₉	#137	1	2	yes	—
100	C₂×Dic₅₉	—	4	2	no	—
101	C₂×Dic₅₉	—	4	2	no	—
102	C₂×Dic₅₉	—	8	2	no	—
103	C₂×Dic₅₉	—	8	2	no	—
104	Dic₁₁₈	—	4	4	no	—
105	Dic₁₁₈	—	8	2	no	—
106	Dic₁₁₈	—	8	1	no	—
107	Dic₁₁₈	—	8	1	no	—
108	Dic₁₁₈	—	8	2	no	—
109	C₈×C₅₉	—	2	4	no	—
110	C₈×C₅₉	—	8	1	no	—
111	C₈×C₅₉	—	8	1	no	—
112	C₅₉⋊C₈	—	4	2	no	—
113	C₅₉⋊C₈	—	4	2	no	—
114	#9775	—	59	1	no	maximal, Sylow
115	C₂²×C₅₉	—	2	1	no	—
116	C₂²×C₅₉	—	2	1	no	—
117	C₂²×C₅₉	#390	1	1	yes	characteristic
118	C₂²×C₅₉	#489	1	2	yes	—
119	C₄×C₅₉	—	2	1	no	—
120	C₄×C₅₉	—	2	1	no	—
121	C₄×C₅₉	#417	1	2	yes	—
122	C₄×C₅₉	#471	1	2	yes	—
123	C₄×C₅₉	#473	1	2	yes	—
124	C₄×C₅₉	#496	1	1	yes	characteristic
125	C₄×C₅₉	#497	1	1	yes	characteristic
126	Dic₅₉	—	8	2	no	—
127	Dic₅₉	—	8	2	no	—
128	C₂×#487	—	59	1	no	—
129	#1848	D₅₉	1	1	yes	characteristic
130	#1549	—	59	1	no	—
131	#1548	—	59	1	no	—
132	#1546	—	59	1	no	—
133	#1546	—	59	1	no	—
134	#1452	—	59	1	no	—
135	C₂×C₅₉	—	2	2	no	—
136	C₂×C₅₉	#1959	1	1	yes	characteristic
137	C₂×C₅₉	#1977	1	1	yes	characteristic
138	C₂×C₅₉	#1979	1	1	yes	characteristic
139	C₂×C₄⋊Q₈	—	59	1	no	—
140	C₂×C₄⋊Q₈	—	59	1	no	—
141	#487	—	59	4	no	—
142	#487	—	118	2	no	—
143	#431	—	59	1	no	—
144	#431	—	59	1	no	—
145	C₂×#108	—	2	2	no	—
146	#423	C₂×D₅₉	1	1	yes	characteristic
147	#423	C₂×D₅₉	1	1	yes	characteristic
148	C₂×#103	—	118	2	no	—
149	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
150	#333	—	118	2	no	—
151	#332	—	118	2	no	—
152	#332	—	118	2	no	—
153	#332	—	118	2	no	—
154	#322	—	118	2	no	—
155	C₅₉	#9775	1	1	yes	characteristic, complemented, Sylow
156	C₂²×Q₈	—	118	1	no	—
157	C₂²×Q₈	—	118	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	2	1	no	—
160	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
161	C₄⋊Q₈	—	59	2	no	—
162	C₄⋊Q₈	—	59	2	no	—
163	C₄⋊Q₈	—	118	1	no	—
164	C₄⋊Q₈	—	118	1	no	—
165	C₄⋊Q₈	—	118	1	no	—
166	C₄⋊Q₈	—	118	1	no	—
167	C₄⋊Q₈	—	118	1	no	—
168	C₄⋊Q₈	—	118	1	no	—
169	C₂×C₄⋊C₄	—	118	1	no	—
170	C₂×C₄⋊C₄	—	118	1	no	—
171	C₂×C₄⋊C₄	—	118	1	no	—
172	C₂×C₄⋊C₄	—	118	1	no	—
173	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
174	#108	—	4	4	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	59	2	no	—
180	C₄⋊C₈	—	59	2	no	—
181	#103	—	118	8	no	—
182	C₂²⋊C₈	—	118	1	no	—
183	C₂²⋊C₈	—	118	1	no	—
184	C₄×C₈	—	118	1	no	—
185	C₄×C₈	—	118	1	no	—
186	C₄×C₈	C₄×D₅₉	1	2	yes	—
187	C₄×C₈	D₂₃₆	1	2	yes	—
188	C₂×Q₈	—	118	2	no	—
189	C₂×Q₈	—	118	2	no	—
190	C₂×Q₈	—	472	2	no	—
191	C₂×Q₈	—	236	2	no	—
192	C₂×Q₈	—	236	2	no	—
193	C₂×Q₈	—	236	1	no	—
194	C₂×Q₈	—	236	1	no	—
195	C₂²×C₄	—	236	1	no	—
196	C₂²×C₄	—	236	1	no	—
197	C₂²×C₄	#11745689	1	1	yes	characteristic
198	C₂²×C₄	#11745689	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
200	M₁₆	—	4	2	no	—
201	M₁₆	—	4	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	118	2	no	—
207	C₂×C₈	—	118	2	no	—
208	C₂×C₈	(C₂×D₅₉)⋊C₄	1	4	yes	—
209	C₄⋊C₄	—	118	2	no	—
210	C₄⋊C₄	—	118	2	no	—
211	C₄⋊C₄	—	118	2	no	—
212	C₄⋊C₄	—	118	2	no	—
213	C₄⋊C₄	—	236	1	no	—
214	C₄⋊C₄	—	236	1	no	—
215	C₄⋊C₄	—	236	1	no	—
216	C₄⋊C₄	—	236	1	no	—
217	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
218	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
219	C₄²	D₄×D₅₉	1	1	yes	characteristic
220	C₄²	D₄×D₅₉	1	1	yes	characteristic
221	C₂³	#14273716	1	1	yes	characteristic
222	Q₈	—	472	2	no	—
223	Q₈	—	472	2	no	—
224	Q₈	—	472	1	no	—
225	Q₈	—	472	1	no	—
226	Q₈	—	236	4	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	472	2	no	—
230	C₂×C₄	—	472	2	no	—
231	C₂×C₄	—	236	2	no	—
232	C₂×C₄	—	236	2	no	—
233	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
234	C₂×C₄	#14273689	1	1	yes	characteristic
235	C₂×C₄	#14273689	1	1	yes	characteristic
236	C₂×C₄	#14273702	1	1	yes	characteristic
237	C₂×C₄	#14273702	1	1	yes	characteristic
238	C₂×C₄	#14273723	1	1	yes	characteristic
239	C₂×C₄	#14273753	1	2	yes	—
240	C₂×C₄	#14273758	1	2	yes	—
241	C₈	—	2	4	no	—
242	C₈	—	8	1	no	—
243	C₈	—	8	1	no	—
244	C₈	—	236	2	no	—
245	C₈	—	236	2	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	#16837303	1	1	yes	characteristic
249	C₂²	#16837764	1	2	yes	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	472	2	no	—
253	C₄	—	472	2	no	—
254	C₄	#16837401	1	2	yes	—
255	C₄	#16837666	1	2	yes	—
256	C₄	#16837678	1	2	yes	—
257	C₄	#16837789	1	1	yes	characteristic
258	C₄	#16837794	1	1	yes	characteristic
259	C₂	—	2	2	no	—
260	C₂	#21424910	1	1	yes	characteristic
261	C₂	#21424997	1	1	yes	characteristic
262	C₂	#21425009	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837753

C₂

yes

maximal, characteristic

#21422782

C₂

yes

maximal, characteristic

#21422778

C₂

yes

maximal, characteristic

#21422769

C₂

yes

maximal, characteristic

#21422769

C₂

yes

maximal, characteristic

#21422388

C₂

yes

maximal, characteristic

C₅₉×#1848

C₂

yes

maximal, characteristic

C₂×#14273727

C₂²

yes

characteristic

C₂×#14273727

C₂²

yes

characteristic

#16837753

—

#16837753

C₄

yes

—

#16837455

C₂²

yes

characteristic

#16837455

C₂²

yes

—

—

—

—

—

—

C₂×#108×C₅₉

—

C₅₉×#423

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂²×Dic₁₁₈

—

C₂²×Dic₁₁₈

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14273727

C₂×C₄

yes

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

#14273652

—

C₂²⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₂×M₁₆×C₅₉

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#108×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

—

C₄×C₈×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

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

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#124

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

—

C₂×C₄×C₅₉

#137

yes

—

100

C₂×Dic₅₉

—

101

C₂×Dic₅₉

—

102

C₂×Dic₅₉

—

103

C₂×Dic₅₉

—

104

Dic₁₁₈

—

105

Dic₁₁₈

—

106

Dic₁₁₈

—

107

Dic₁₁₈

—

108

Dic₁₁₈

—

109

C₈×C₅₉

—

110

C₈×C₅₉

—

111

C₈×C₅₉

—

112

C₅₉⋊C₈

—

113

C₅₉⋊C₈

—

114

#9775

—

maximal, Sylow

115

C₂²×C₅₉

—

116

C₂²×C₅₉

—

117

C₂²×C₅₉

#390

yes

characteristic

118

C₂²×C₅₉

#489

yes

—

119

C₄×C₅₉

—

120

C₄×C₅₉

—

121

C₄×C₅₉

#417

yes

—

122

C₄×C₅₉

#471

yes

—

123

C₄×C₅₉

#473

yes

—

124

C₄×C₅₉

#496

yes

characteristic

125

C₄×C₅₉

#497

yes

characteristic

126

Dic₅₉

—

127

Dic₅₉

—

128

C₂×#487

—

129

#1848

D₅₉

yes

characteristic

130

#1549

—

131

#1548

—

132

#1546

—

133

#1546

—

134

#1452

—

135

C₂×C₅₉

—

136

C₂×C₅₉

#1959

yes

characteristic

137

C₂×C₅₉

#1977

yes

characteristic

138

C₂×C₅₉

#1979

yes

characteristic

139

C₂×C₄⋊Q₈

—

140

C₂×C₄⋊Q₈

—

141

#487

—

142

#487

—

118

—

143

#431

—

144

#431

—

145

C₂×#108

—

146

#423

C₂×D₅₉

yes

characteristic

147

#423

C₂×D₅₉

yes

characteristic

148

C₂×#103

—

118

—

149

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

150

#333

—

118

—

151

#332

—

118

—

152

#332

—

118

—

153

#332

—

118

—

154

#322

—

118

—

155

C₅₉

#9775

yes

characteristic, complemented, Sylow

156

C₂²×Q₈

—

118

—

157

C₂²×Q₈

—

118

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

C₂²⋊D₅₉

yes

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

118

—

164

C₄⋊Q₈

—

118

—

165

C₄⋊Q₈

—

118

—

166

C₄⋊Q₈

—

118

—

167

C₄⋊Q₈

—

118

—

168

C₄⋊Q₈

—

118

—

169

C₂×C₄⋊C₄

—

118

—

170

C₂×C₄⋊C₄

—

118

—

171

C₂×C₄⋊C₄

—

118

—

172

C₂×C₄⋊C₄

—

118

—

173

C₂×C₄²

C₂²×D₅₉

yes

characteristic

174

#108

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

#103

—

118

—

182

C₂²⋊C₈

—

118

—

183

C₂²⋊C₈

—

118

—

184

C₄×C₈

—

118

—

185

C₄×C₈

—

118

—

186

C₄×C₈

C₄×D₅₉

yes

—

187

C₄×C₈

D₂₃₆

yes

—

188

C₂×Q₈

—

118

—

189

C₂×Q₈

—

118

—

190

C₂×Q₈

—

472

—

191

C₂×Q₈

—

236

—

192

C₂×Q₈

—

236

—

193

C₂×Q₈

—

236

—

194

C₂×Q₈

—

236

—

195

C₂²×C₄

—

236

—

196

C₂²×C₄

—

236

—

197

C₂²×C₄

#11745689

yes

characteristic

198

C₂²×C₄

#11745689

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

118

—

207

C₂×C₈

—

118

—

208

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

209

C₄⋊C₄

—

118

—

210

C₄⋊C₄

—

118

—

211

C₄⋊C₄

—

118

—

212

C₄⋊C₄

—

118

—

213

C₄⋊C₄

—

236

—

214

C₄⋊C₄

—

236

—

215

C₄⋊C₄

—

236

—

216

C₄⋊C₄

—

236

—

217

C₄²

C₂×C₄×D₅₉

yes

characteristic

218

C₄²

C₂×D₂₃₆

yes

characteristic

219

C₄²

D₄×D₅₉

yes

characteristic

220

C₄²

D₄×D₅₉

yes

characteristic

221

C₂³

#14273716

yes

characteristic

222

Q₈

—

472

—

223

Q₈

—

472

—

224

Q₈

—

472

—

225

Q₈

—

472

—

226

Q₈

—

236

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

472

—

230

C₂×C₄

—

472

—

231

C₂×C₄

—

236

—

232

C₂×C₄

—

236

—

233

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

234

C₂×C₄

#14273689

yes

characteristic

235

C₂×C₄

#14273689

yes

characteristic

236

C₂×C₄

#14273702

yes

characteristic

237

C₂×C₄

#14273702

yes

characteristic

238

C₂×C₄

#14273723

yes

characteristic

239

C₂×C₄

#14273753

yes

—

240

C₂×C₄

#14273758

yes

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

236

—

245

C₈

—

236

—

246

C₂²

—

247

C₂²

—

248

C₂²

#16837303

yes

characteristic

249

C₂²

#16837764

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

472

—

253

C₄

—

472

—

254

C₄

#16837401

yes

—

255

C₄

#16837666

yes

—

256

C₄

#16837678

yes

—

257

C₄

#16837789

yes

characteristic

258

C₄

#16837794

yes

characteristic

259

C₂

—

260

C₂

#21424910

yes

characteristic

261

C₂

#21424997

yes

characteristic

262

C₂

#21425009

yes

characteristic

	subgroup	G/H
center	C₂²	#16837303
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1848	C₂
socle	C₂²×C₅₉	#390
prime radical	C₂³×C₅₉	#124
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1848	D₅₉
hypocenter	C₅₉	#9775
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂²

#16837303

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1848

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

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

H ≅ G/N

type

155. C₅₉

#9775

semidirect

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

subgroup	index
C₂×#16837753	2
#21422782	2
#21422778	2
#21422769	2
#21422388	2
C₅₉×#1848	2
#9775	59

subgroup

index

C₅₉×#1848

Subgroups — #28488166

Conjugacy classes of subgroups

Complements

Maximal subgroups