Group #21435336 — subgroups

Subgroups — #21435336

Order 7552.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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	#16837936	C₂	1	1	yes	maximal, characteristic
2	#16837808	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837808	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837764	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837764	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837743	C₂	1	2	yes	maximal, complemented
7	#16837726	C₂	1	2	yes	maximal
8	#16837706	C₂	1	2	yes	maximal, complemented
9	#16837699	C₂	1	2	yes	maximal, complemented
10	#16837459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	#14273721	—	2	1	no	—
13	#14273719	C₂²	1	1	yes	characteristic
14	#14273715	C₂²	1	1	yes	characteristic
15	#14273710	—	2	1	no	—
16	#14273706	C₂²	1	1	yes	characteristic
17	#14273701	C₂²	1	1	yes	characteristic
18	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
19	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊D₅₉	—	2	1	no	—
21	#14273684	—	2	1	no	—
22	#14273660	C₂²	1	2	yes	—
23	#14273660	C₂²	1	2	yes	—
24	#14273658	C₂²	1	2	yes	—
25	#14273658	C₂²	1	2	yes	—
26	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
27	#14273650	C₂²	1	2	yes	—
28	#14273650	C₂²	1	2	yes	—
29	#14273647	C₂²	1	2	yes	—
30	#14273647	C₂²	1	2	yes	—
31	C₂²⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
32	#14273638	C₂²	1	1	yes	characteristic
33	#14273638	C₂²	1	1	yes	characteristic
34	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
35	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
36	#125×C₅₉	C₂²	1	2	yes	—
37	C₂²⋊Q₈×C₅₉	—	2	1	no	—
38	C₂²⋊Q₈×C₅₉	—	2	1	no	—
39	C₄×Q₈×C₅₉	—	2	1	no	—
40	C₄×Q₈×C₅₉	—	2	1	no	—
41	#117×C₅₉	C₂²	1	2	yes	—
42	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₅₉	—	2	1	no	—
44	C₂×Q₈×C₅₉	—	2	1	no	—
45	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
48	C₂×C₂²⋊D₅₉	—	2	1	no	—
49	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
50	C₂×C₄×D₅₉	—	2	1	no	—
51	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
52	C₄⋊C₄×C₅₉	—	2	2	no	—
53	C₄⋊C₄×C₅₉	—	2	2	no	—
54	C₄⋊C₄×C₅₉	—	2	1	no	—
55	C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
57	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
58	C₂²⋊C₄×C₅₉	—	2	2	no	—
59	C₄²×C₅₉	—	2	2	no	—
60	C₄²×C₅₉	D₄	1	1	yes	characteristic
61	C₄²×C₅₉	D₄	1	1	yes	characteristic
62	C₄²×C₅₉	C₂³	1	1	yes	characteristic
63	C₄²×C₅₉	C₂³	1	1	yes	characteristic
64	C₂²⋊Dic₅₉	—	2	1	no	—
65	(C₂×D₅₉)⋊C₄	—	2	1	no	—
66	(C₂×D₅₉)⋊C₄	—	2	1	no	—
67	(C₂×D₅₉)⋊C₄	—	2	1	no	—
68	(C₂×D₅₉)⋊C₄	—	2	1	no	—
69	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
71	Dic₅₉⋊C₄	—	2	1	no	—
72	Dic₅₉⋊C₄	—	2	1	no	—
73	Dic₅₉⋊C₄	—	2	1	no	—
74	Dic₅₉⋊C₄	—	2	1	no	—
75	C₄×Dic₅₉	—	2	1	no	—
76	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
77	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
78	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×D₅₉	—	2	1	no	—
80	Q₈×C₅₉	—	4	2	no	—
81	Q₈×C₅₉	—	4	2	no	—
82	C₂×C₄×C₅₉	—	2	2	no	—
83	C₂×C₄×C₅₉	—	2	2	no	—
84	C₂×C₄×C₅₉	—	2	2	no	—
85	C₂×C₄×C₅₉	—	4	1	no	—
86	C₂×C₄×C₅₉	—	4	1	no	—
87	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
93	C₂²⋊D₅₉	—	4	2	no	—
94	C₂×Dic₅₉	—	2	1	no	—
95	C₂×Dic₅₉	—	2	1	no	—
96	C₂×Dic₅₉	—	2	1	no	—
97	D₂₃₆	—	2	2	no	—
98	C₄×D₅₉	—	4	2	no	—
99	Dic₁₁₈	—	2	2	no	—
100	C₅₉⋊C₈	—	2	2	no	—
101	C₅₉⋊C₈	—	2	2	no	—
102	C₂²×C₅₉	—	2	1	no	—
103	C₂²×C₅₉	—	2	1	no	—
104	C₂²×C₅₉	—	2	1	no	—
105	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
106	C₂×D₅₉	—	4	1	no	—
107	C₂×D₅₉	—	4	1	no	—
108	C₂×D₅₉	—	4	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	—	2	1	no	—
114	C₄×C₅₉	—	4	2	no	—
115	C₄×C₅₉	—	4	2	no	—
116	C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
117	Dic₅₉	—	4	1	no	—
118	Dic₅₉	—	4	1	no	—
119	Dic₅₉	—	4	1	no	—
120	#3240	—	59	1	no	maximal, Sylow
121	C₂×C₅₉	—	4	1	no	—
122	C₂×C₅₉	#536	1	1	yes	characteristic
123	C₂×C₅₉	#575	1	1	yes	characteristic
124	C₂×C₅₉	#575	1	1	yes	characteristic
125	D₅₉	—	8	1	no	—
126	#533	D₅₉	1	1	yes	characteristic, complemented
127	#529	—	59	1	no	—
128	#501	—	59	1	no	—
129	#501	—	59	1	no	—
130	#489	—	59	1	no	—
131	#489	—	59	1	no	—
132	#485	—	59	2	no	—
133	#482	—	59	2	no	—
134	#479	—	59	2	no	—
135	#478	—	59	2	no	—
136	#432	—	59	1	no	—
137	C₅₉	#3240	1	1	yes	characteristic, complemented, Sylow
138	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
139	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
140	#126	—	118	1	no	—
141	#125	—	59	1	no	—
142	#125	C₂×D₅₉	1	2	yes	—
143	#124	—	59	1	no	—
144	#123	—	118	1	no	—
145	C₂²⋊Q₈	—	2	1	no	—
146	C₂²⋊Q₈	—	2	1	no	—
147	C₂²⋊Q₈	—	59	1	no	—
148	#121	—	59	1	no	—
149	C₄×Q₈	—	2	1	no	—
150	C₄×Q₈	—	2	1	no	—
151	C₄×Q₈	—	59	1	no	—
152	C₄×D₄	—	59	1	no	—
153	C₄×D₄	—	118	1	no	—
154	#117	—	118	1	no	—
155	#117	C₂×D₅₉	1	2	yes	—
156	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
157	#107	—	59	2	no	—
158	#107	—	59	2	no	—
159	#106	—	59	2	no	—
160	#106	—	59	2	no	—
161	C₄⋊C₈	—	59	2	no	—
162	#103	—	59	2	no	—
163	#103	—	59	2	no	—
164	#102	—	59	2	no	—
165	#102	—	59	2	no	—
166	C₂²⋊C₈	—	59	2	no	—
167	#97	—	59	1	no	—
168	#97	—	59	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	1	no	—
171	C₂×Q₈	—	59	1	no	—
172	C₂×D₄	—	59	1	no	—
173	C₂×D₄	—	118	1	no	—
174	C₂²×C₄	—	118	1	no	—
175	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
176	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
177	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
178	C₂×C₈	—	59	2	no	—
179	C₂×C₈	—	59	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	59	1	no	—
185	C₄⋊C₄	—	59	1	no	—
186	C₄⋊C₄	—	118	1	no	—
187	C₄⋊C₄	—	118	1	no	—
188	C₄⋊C₄	—	118	1	no	—
189	C₄⋊C₄	—	118	1	no	—
190	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
191	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	118	1	no	—
194	C₂²⋊C₄	—	118	1	no	—
195	C₂²⋊C₄	—	118	1	no	—
196	C₂²⋊C₄	—	118	1	no	—
197	C₂²⋊C₄	—	118	1	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	118	1	no	—
200	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
201	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
202	C₄²	C₂²×D₅₉	1	1	yes	characteristic
203	C₄²	C₂²×D₅₉	1	1	yes	characteristic
204	C₂³	—	118	1	no	—
205	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
206	Q₈	—	4	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	118	2	no	—
209	D₄	—	118	2	no	—
210	D₄	—	236	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	118	1	no	—
217	C₂×C₄	—	118	1	no	—
218	C₂×C₄	—	118	1	no	—
219	C₂×C₄	—	236	2	no	—
220	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
221	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
222	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
223	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
224	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
225	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
226	C₈	—	118	2	no	—
227	C₈	—	118	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	236	1	no	—
232	C₂²	—	236	1	no	—
233	C₂²	—	236	1	no	—
234	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	4	2	no	—
241	C₄	—	4	2	no	—
242	C₄	—	236	1	no	—
243	C₄	—	236	1	no	—
244	C₄	—	236	1	no	—
245	C₄	#14273775	1	2	yes	—
246	C₂	—	4	1	no	—
247	C₂	—	472	1	no	—
248	C₂	#16837976	1	1	yes	characteristic
249	C₂	#16838200	1	1	yes	characteristic
250	C₂	#16838200	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837936

C₂

yes

maximal, characteristic

#16837808

C₂

yes

maximal, characteristic, complemented

#16837808

C₂

yes

maximal, characteristic, complemented

#16837764

C₂

yes

maximal, characteristic, complemented

#16837764

C₂

yes

maximal, characteristic, complemented

#16837743

C₂

yes

maximal, complemented

#16837726

C₂

yes

maximal

#16837706

C₂

yes

maximal, complemented

#16837699

C₂

yes

maximal, complemented

#16837459

C₂

yes

maximal, characteristic, complemented

C₅₉×#533

C₂

yes

maximal, characteristic, complemented

#14273721

—

#14273719

C₂²

yes

characteristic

#14273715

C₂²

yes

characteristic

#14273710

—

#14273706

C₂²

yes

characteristic

#14273701

C₂²

yes

characteristic

C₄×Dic₁₁₈

C₂²

yes

characteristic

C₄×D₂₃₆

C₂²

yes

characteristic

C₄×C₂²⋊D₅₉

—

#14273684

—

#14273660

C₂²

yes

—

#14273660

C₂²

yes

—

#14273658

C₂²

yes

—

#14273658

C₂²

yes

—

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273650

C₂²

yes

—

#14273650

C₂²

yes

—

#14273647

C₂²

yes

—

#14273647

C₂²

yes

—

C₂²⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273638

C₂²

yes

characteristic

#14273638

C₂²

yes

characteristic

C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

#125×C₅₉

C₂²

yes

—

C₂²⋊Q₈×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

#117×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂×C₂²⋊D₅₉

—

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

C₂³

yes

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

D₄

yes

characteristic

C₄²×C₅₉

D₄

yes

characteristic

C₄²×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂³

yes

characteristic

C₂²⋊Dic₅₉

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

C₂³

yes

characteristic

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

C₂²×D₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

C₄×D₅₉

—

Dic₁₁₈

—

100

C₅₉⋊C₈

—

101

C₅₉⋊C₈

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

—

104

C₂²×C₅₉

—

105

C₂²×C₅₉

C₂²×D₄

yes

characteristic

106

C₂×D₅₉

—

107

C₂×D₅₉

—

108

C₂×D₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

—

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

2₋¹⁺⁴

yes

—

117

Dic₅₉

—

118

Dic₅₉

—

119

Dic₅₉

—

120

#3240

—

maximal, Sylow

121

C₂×C₅₉

—

122

C₂×C₅₉

#536

yes

characteristic

123

C₂×C₅₉

#575

yes

characteristic

124

C₂×C₅₉

#575

yes

characteristic

125

D₅₉

—

126

#533

D₅₉

yes

characteristic, complemented

127

#529

—

128

#501

—

129

#501

—

130

#489

—

131

#489

—

132

#485

—

133

#482

—

134

#479

—

135

#478

—

136

#432

—

137

C₅₉

#3240

yes

characteristic, complemented, Sylow

138

C₄⋊Q₈

C₂×D₅₉

yes

characteristic

139

C₄⋊Q₈

C₂×D₅₉

yes

characteristic

140

#126

—

118

—

141

#125

—

142

#125

C₂×D₅₉

yes

—

143

#124

—

144

#123

—

118

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

147

C₂²⋊Q₈

—

148

#121

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×D₄

—

153

C₄×D₄

—

118

—

154

#117

—

118

—

155

#117

C₂×D₅₉

yes

—

156

C₂×C₄²

C₂×D₅₉

yes

characteristic

157

#107

—

158

#107

—

159

#106

—

160

#106

—

161

C₄⋊C₈

—

162

#103

—

163

#103

—

164

#102

—

165

#102

—

166

C₂²⋊C₈

—

167

#97

—

168

#97

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×D₄

—

173

C₂×D₄

—

118

—

174

C₂²×C₄

—

118

—

175

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

176

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

177

C₂²×C₄

C₂²×D₅₉

yes

characteristic

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

118

—

187

C₄⋊C₄

—

118

—

188

C₄⋊C₄

—

118

—

189

C₄⋊C₄

—

118

—

190

C₄⋊C₄

C₂²×D₅₉

yes

—

191

C₄⋊C₄

C₂²×D₅₉

yes

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

118

—

194

C₂²⋊C₄

—

118

—

195

C₂²⋊C₄

—

118

—

196

C₂²⋊C₄

—

118

—

197

C₂²⋊C₄

—

118

—

198

C₄²

—

199

C₄²

—

118

—

200

C₄²

C₂²⋊D₅₉

yes

characteristic

201

C₄²

C₂²⋊D₅₉

yes

characteristic

202

C₄²

C₂²×D₅₉

yes

characteristic

203

C₄²

C₂²×D₅₉

yes

characteristic

204

C₂³

—

118

—

205

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

118

—

209

D₄

—

118

—

210

D₄

—

236

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

118

—

217

C₂×C₄

—

118

—

218

C₂×C₄

—

118

—

219

C₂×C₄

—

236

—

220

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

221

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

222

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

223

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

224

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

225

C₂×C₄

C₂³×D₅₉

yes

characteristic

226

C₈

—

118

—

227

C₈

—

118

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

236

—

232

C₂²

—

236

—

233

C₂²

—

236

—

234

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

236

—

243

C₄

—

236

—

244

C₄

—

236

—

245

C₄

#14273775

yes

—

246

C₂

—

247

C₂

—

472

—

248

C₂

#16837976

yes

characteristic

249

C₂

#16838200

yes

characteristic

250

C₂

#16838200

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#533	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#533	D₅₉
hypocenter	C₅₉	#3240
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#533

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #16837808	C₂	semidirect
3. #16837808	C₂	semidirect
4. #16837764	C₂	semidirect
5. #16837764	C₂	semidirect
6. #16837743	C₂	semidirect
8. #16837706	C₂	semidirect
9. #16837699	C₂	semidirect
10. #16837459	C₂	semidirect
11. C₅₉×#533	C₂	semidirect
126. #533	D₅₉	semidirect
137. C₅₉	#3240	semidirect

H ≅ G/N

type

2. #16837808

C₂

semidirect

3. #16837808

C₂

semidirect

4. #16837764

C₂

semidirect

5. #16837764

C₂

semidirect

6. #16837743

C₂

semidirect

8. #16837706

C₂

semidirect

9. #16837699

C₂

semidirect

10. #16837459

C₂

semidirect

11. C₅₉×#533

C₂

semidirect

126. #533

D₅₉

semidirect

137. C₅₉

#3240

semidirect

Subgroups — #21435336

Conjugacy classes of subgroups

Complements