Group #28487853 — subgroups

Subgroups — #28487853

Order 15104.

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

normal subgroups only

This group has 422 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	#21434682	C₂	1	1	yes	maximal, characteristic
2	#21425039	C₂	1	2	yes	maximal
3	#21422594	C₂	1	2	yes	maximal
4	#21422385	C₂	1	1	yes	maximal, characteristic
5	C₄×#106×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#16837959	C₂²	1	2	yes	—
7	#16837807	C₄	1	1	yes	characteristic, complemented
8	#16837782	C₄	1	1	yes	characteristic, complemented
9	#16837753	C₄	1	2	yes	complemented
10	#16837643	—	2	1	no	—
11	#16837643	—	2	1	no	—
12	C₄×Dic₂₃₆	—	2	1	no	—
13	C₄×Dic₂₃₆	—	2	1	no	—
14	#16837455	C₂²	1	1	yes	characteristic
15	C₄×#11745664	C₂²	1	1	yes	characteristic
16	#16837162	—	2	4	no	—
17	#16837138	—	2	4	no	—
18	#16837124	—	2	1	no	—
19	#16837123	—	2	1	no	—
20	C₂×#106×C₅₉	—	2	1	no	—
21	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
23	C₅₉×#340	—	2	1	no	—
24	C₂×Dic₂₃₆	—	2	1	no	—
25	C₂×Dic₂₃₆	—	2	1	no	—
26	C₂×#11745664	D₄	1	2	yes	—
27	#14273727	C₂×C₄	1	2	yes	—
28	#14273727	C₂×C₄	1	2	yes	—
29	#14273719	—	2	2	no	—
30	#14273706	—	2	2	no	—
31	#14273706	—	2	2	no	—
32	C₄×Dic₁₁₈	—	2	2	no	—
33	C₄×Dic₁₁₈	—	2	2	no	—
34	#14273686	—	2	2	no	—
35	#14273661	—	2	1	no	—
36	#14273661	—	2	1	no	—
37	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
38	#14273652	—	2	2	no	—
39	#14273652	—	2	2	no	—
40	C₂²⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
41	#14273638	—	2	1	no	—
42	C₄×C₅₉⋊C₈	—	2	1	no	—
43	C₄×C₅₉⋊C₈	—	2	1	no	—
44	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
47	C₂×C₄²×C₅₉	—	2	2	no	—
48	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
49	#106×C₅₉	—	2	4	no	—
50	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
53	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
54	#95×C₅₉	—	2	2	no	—
55	C₂²×C₄×C₅₉	—	4	2	no	—
56	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
59	C₂×Dic₁₁₈	—	2	2	no	—
60	C₂×Dic₁₁₈	—	2	2	no	—
61	C₂×C₈×C₅₉	—	2	2	no	—
62	C₂×C₈×C₅₉	—	4	1	no	—
63	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₄⋊C₄×C₅₉	—	2	4	no	—
68	C₄⋊C₄×C₅₉	—	4	2	no	—
69	C₄²×C₅₉	—	4	4	no	—
70	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₅₉	#41	1	1	yes	characteristic
73	C₄²×C₅₉	#41	1	1	yes	characteristic
74	C₂²⋊Dic₅₉	—	4	2	no	—
75	C₄⋊Dic₅₉	—	2	2	no	—
76	C₄⋊Dic₅₉	—	2	2	no	—
77	C₄⋊Dic₅₉	—	2	2	no	—
78	C₄⋊Dic₅₉	—	2	2	no	—
79	Dic₅₉⋊C₄	—	4	2	no	—
80	Dic₅₉⋊C₄	—	4	2	no	—
81	C₄×Dic₅₉	—	4	2	no	—
82	#11745664	—	2	4	no	—
83	C₂×C₅₉⋊C₈	—	2	2	no	—
84	C₂×C₅₉⋊C₈	—	2	2	no	—
85	Dic₂₃₆	—	4	2	no	—
86	Dic₂₃₆	—	4	2	no	—
87	C₂³×C₅₉	#127	1	1	yes	characteristic
88	C₂×C₄×C₅₉	—	2	1	no	—
89	C₂×C₄×C₅₉	—	2	1	no	—
90	C₂×C₄×C₅₉	—	4	1	no	—
91	C₂×C₄×C₅₉	—	4	4	no	—
92	C₂×C₄×C₅₉	—	8	2	no	—
93	C₂×C₄×C₅₉	—	8	2	no	—
94	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
99	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
100	C₂×C₄×C₅₉	#137	1	4	yes	—
101	C₂×Dic₅₉	—	4	2	no	—
102	C₂×Dic₅₉	—	4	2	no	—
103	Dic₁₁₈	—	4	2	no	—
104	Dic₁₁₈	—	4	2	no	—
105	Dic₁₁₈	—	8	2	no	—
106	C₈×C₅₉	—	2	1	no	—
107	C₈×C₅₉	—	2	1	no	—
108	C₈×C₅₉	—	2	1	no	—
109	C₈×C₅₉	#104	1	2	yes	—
110	C₅₉⋊C₈	—	4	2	no	—
111	C₅₉⋊C₈	—	4	2	no	—
112	#9720	—	59	1	no	maximal, Sylow
113	C₂²×C₅₉	—	2	1	no	—
114	C₂²×C₅₉	—	2	1	no	—
115	C₂²×C₅₉	#390	1	1	yes	characteristic
116	C₂²×C₅₉	#497	1	2	yes	—
117	C₄×C₅₉	—	2	1	no	—
118	C₄×C₅₉	—	2	1	no	—
119	C₄×C₅₉	—	2	1	no	—
120	C₄×C₅₉	—	8	4	no	—
121	C₄×C₅₉	C₂×#104	1	1	yes	characteristic
122	C₄×C₅₉	#421	1	1	yes	characteristic
123	C₄×C₅₉	#441	1	2	yes	—
124	C₄×C₅₉	#470	1	2	yes	—
125	Dic₅₉	—	8	2	no	—
126	Dic₅₉	—	8	2	no	—
127	#3170	—	59	1	no	—
128	#1986	—	59	2	no	—
129	C₄×#106	D₅₉	1	1	yes	characteristic
130	#1503	—	59	2	no	—
131	#1451	—	59	1	no	—
132	C₂×C₅₉	—	2	2	no	—
133	C₂×C₅₉	#1971	1	1	yes	characteristic
134	C₂×C₅₉	#1976	1	1	yes	characteristic
135	C₂×C₅₉	#1980	1	1	yes	characteristic
136	#533	—	59	2	no	—
137	#500	—	59	1	no	—
138	#494	—	59	1	no	—
139	#487	—	59	2	no	—
140	#467	—	118	1	no	—
141	#467	—	118	1	no	—
142	C₄×Q₁₆	—	118	1	no	—
143	C₄×Q₁₆	—	118	1	no	—
144	#431	—	59	1	no	—
145	C₂×#106	—	2	1	no	—
146	C₄×M₁₆	—	59	1	no	—
147	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
149	#340	—	2	1	no	—
150	#339	—	118	4	no	—
151	#328	—	118	4	no	—
152	#322	—	118	1	no	—
153	#322	—	118	1	no	—
154	C₅₉	#9720	1	1	yes	characteristic, complemented, Sylow
155	C₂×Q₁₆	—	118	1	no	—
156	C₂×Q₁₆	—	118	1	no	—
157	C₂×M₁₆	—	59	2	no	—
158	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
159	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
160	C₄⋊Q₈	—	59	2	no	—
161	C₄⋊Q₈	—	59	2	no	—
162	#125	—	118	2	no	—
163	C₂²⋊Q₈	—	118	2	no	—
164	C₂²⋊Q₈	—	118	2	no	—
165	C₄×Q₈	—	118	2	no	—
166	C₄×Q₈	—	118	2	no	—
167	#117	—	118	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄²	—	2	2	no	—
170	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
171	#107	—	118	1	no	—
172	#107	—	118	1	no	—
173	#106	—	2	4	no	—
174	C₄⋊C₈	—	118	1	no	—
175	#103	—	118	2	no	—
176	#103	—	118	2	no	—
177	C₂²⋊C₈	—	59	2	no	—
178	#97	—	118	1	no	—
179	C₄×C₈	—	118	1	no	—
180	C₄×C₈	—	118	1	no	—
181	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
182	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
183	C₄×C₈	D₂₃₆	1	1	yes	characteristic
184	C₄×C₈	D₂₃₆	1	1	yes	characteristic
185	#95	—	2	2	no	—
186	C₂×Q₈	—	118	2	no	—
187	C₂×Q₈	—	118	2	no	—
188	C₂²×C₄	—	4	2	no	—
189	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
190	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
192	Q₁₆	—	236	2	no	—
193	Q₁₆	—	236	2	no	—
194	M₁₆	—	118	4	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	118	2	no	—
198	C₂×C₈	—	118	2	no	—
199	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
201	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	118	2	no	—
206	C₄⋊C₄	—	118	2	no	—
207	C₄⋊C₄	—	118	2	no	—
208	C₄⋊C₄	—	118	2	no	—
209	C₄⋊C₄	—	236	2	no	—
210	C₄⋊C₄	—	236	2	no	—
211	C₂²⋊C₄	—	236	2	no	—
212	C₄²	—	4	4	no	—
213	C₄²	—	236	2	no	—
214	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
215	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
216	C₄²	#11745689	1	1	yes	characteristic
217	C₄²	#11745689	1	1	yes	characteristic
218	C₂³	#14273723	1	1	yes	characteristic
219	Q₈	—	472	2	no	—
220	Q₈	—	236	2	no	—
221	Q₈	—	236	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	—	8	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	—	236	2	no	—
229	C₂×C₄	—	236	2	no	—
230	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
231	C₂×C₄	#14273689	1	1	yes	characteristic
232	C₂×C₄	#14273689	1	1	yes	characteristic
233	C₂×C₄	#14273702	1	1	yes	characteristic
234	C₂×C₄	#14273702	1	1	yes	characteristic
235	C₂×C₄	#14273716	1	1	yes	characteristic
236	C₂×C₄	#14273756	1	4	yes	—
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	236	2	no	—
241	C₈	—	236	2	no	—
242	C₈	#14273655	1	2	yes	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	#16837303	1	1	yes	characteristic
246	C₂²	#16837793	1	2	yes	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	8	4	no	—
251	C₄	—	472	2	no	—
252	C₄	—	472	2	no	—
253	C₄	C₂×#14273655	1	1	yes	characteristic
254	C₄	#16837420	1	1	yes	characteristic
255	C₄	#16837508	1	2	yes	—
256	C₄	#16837661	1	2	yes	—
257	C₂	—	2	2	no	—
258	C₂	#21424965	1	1	yes	characteristic
259	C₂	#21424992	1	1	yes	characteristic
260	C₂	#21425014	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21434682

C₂

yes

maximal, characteristic

#21425039

C₂

yes

maximal

#21422594

C₂

yes

maximal

#21422385

C₂

yes

maximal, characteristic

C₄×#106×C₅₉

C₂

yes

maximal, characteristic

#16837959

C₂²

yes

—

#16837807

C₄

yes

characteristic, complemented

#16837782

C₄

yes

characteristic, complemented

#16837753

C₄

yes

complemented

#16837643

—

#16837643

—

C₄×Dic₂₃₆

—

C₄×Dic₂₃₆

—

#16837455

C₂²

yes

characteristic

C₄×#11745664

C₂²

yes

—

—

—

—

C₂×#106×C₅₉

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₅₉

C₂²

yes

—

C₅₉×#340

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×#11745664

D₄

yes

—

#14273727

C₂×C₄

yes

—

#14273727

C₂×C₄

yes

—

#14273719

—

#14273706

—

#14273706

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

#14273686

—

#14273661

—

#14273661

—

C₄⋊(C₅₉⋊C₈)

—

#14273652

—

#14273652

—

C₂²⋊(C₅₉⋊C₈)

D₄

yes

—

#14273638

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#106×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

#95×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

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

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

C₄²×C₅₉

yes

C₄²×C₅₉

yes

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

Dic₂₃₆

—

Dic₂₃₆

—

C₂³×C₅₉

#127

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

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

100

C₂×C₄×C₅₉

#137

yes

—

101

C₂×Dic₅₉

—

102

C₂×Dic₅₉

—

103

Dic₁₁₈

—

104

Dic₁₁₈

—

105

Dic₁₁₈

—

106

C₈×C₅₉

—

107

C₈×C₅₉

—

108

C₈×C₅₉

—

109

C₈×C₅₉

#104

yes

—

110

C₅₉⋊C₈

—

111

C₅₉⋊C₈

—

112

#9720

—

maximal, Sylow

113

C₂²×C₅₉

—

114

C₂²×C₅₉

—

115

C₂²×C₅₉

#390

yes

characteristic

116

C₂²×C₅₉

#497

yes

—

117

C₄×C₅₉

—

118

C₄×C₅₉

—

119

C₄×C₅₉

—

120

C₄×C₅₉

—

121

C₄×C₅₉

C₂×#104

yes

characteristic

122

C₄×C₅₉

#421

yes

characteristic

123

C₄×C₅₉

#441

yes

—

124

C₄×C₅₉

#470

yes

—

125

Dic₅₉

—

126

Dic₅₉

—

127

#3170

—

128

#1986

—

129

C₄×#106

D₅₉

yes

characteristic

130

#1503

—

131

#1451

—

132

C₂×C₅₉

—

133

C₂×C₅₉

#1971

yes

characteristic

134

C₂×C₅₉

#1976

yes

characteristic

135

C₂×C₅₉

#1980

yes

characteristic

136

#533

—

137

#500

—

138

#494

—

139

#487

—

140

#467

—

118

—

141

#467

—

118

—

142

C₄×Q₁₆

—

118

—

143

C₄×Q₁₆

—

118

—

144

#431

—

145

C₂×#106

—

146

C₄×M₁₆

—

147

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

148

C₄×C₄⋊C₄

C₂×D₅₉

yes

—

149

#340

—

150

#339

—

118

—

151

#328

—

118

—

152

#322

—

118

—

153

#322

—

118

—

154

C₅₉

#9720

yes

characteristic, complemented, Sylow

155

C₂×Q₁₆

—

118

—

156

C₂×Q₁₆

—

118

—

157

C₂×M₁₆

—

158

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

159

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

#125

—

118

—

163

C₂²⋊Q₈

—

118

—

164

C₂²⋊Q₈

—

118

—

165

C₄×Q₈

—

118

—

166

C₄×Q₈

—

118

—

167

#117

—

118

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄²

—

170

C₂×C₄²

C₂²×D₅₉

yes

characteristic

171

#107

—

118

—

172

#107

—

118

—

173

#106

—

174

C₄⋊C₈

—

118

—

175

#103

—

118

—

176

#103

—

118

—

177

C₂²⋊C₈

—

178

#97

—

118

—

179

C₄×C₈

—

118

—

180

C₄×C₈

—

118

—

181

C₄×C₈

C₄×D₅₉

yes

characteristic

182

C₄×C₈

C₄×D₅₉

yes

characteristic

183

C₄×C₈

D₂₃₆

yes

characteristic

184

C₄×C₈

D₂₃₆

yes

characteristic

185

#95

—

186

C₂×Q₈

—

118

—

187

C₂×Q₈

—

118

—

188

C₂²×C₄

—

189

C₂²×C₄

D₄×D₅₉

yes

characteristic

190

C₂²×C₄

D₄×D₅₉

yes

characteristic

191

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

192

Q₁₆

—

236

—

193

Q₁₆

—

236

—

194

M₁₆

—

118

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

118

—

198

C₂×C₈

—

118

—

199

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

200

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

201

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

202

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

118

—

206

C₄⋊C₄

—

118

—

207

C₄⋊C₄

—

118

—

208

C₄⋊C₄

—

118

—

209

C₄⋊C₄

—

236

—

210

C₄⋊C₄

—

236

—

211

C₂²⋊C₄

—

236

—

212

C₄²

—

213

C₄²

—

236

—

214

C₄²

C₂×C₄×D₅₉

yes

characteristic

215

C₄²

C₂×D₂₃₆

yes

characteristic

216

C₄²

#11745689

yes

characteristic

217

C₄²

#11745689

yes

characteristic

218

C₂³

#14273723

yes

characteristic

219

Q₈

—

472

—

220

Q₈

—

236

—

221

Q₈

—

236

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

236

—

229

C₂×C₄

—

236

—

230

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

231

C₂×C₄

#14273689

yes

characteristic

232

C₂×C₄

#14273689

yes

characteristic

233

C₂×C₄

#14273702

yes

characteristic

234

C₂×C₄

#14273702

yes

characteristic

235

C₂×C₄

#14273716

yes

characteristic

236

C₂×C₄

#14273756

yes

—

237

C₈

—

238

C₈

—

239

C₈

—

240

C₈

—

236

—

241

C₈

—

236

—

242

C₈

#14273655

yes

—

243

C₂²

—

244

C₂²

—

245

C₂²

#16837303

yes

characteristic

246

C₂²

#16837793

yes

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

472

—

252

C₄

—

472

—

253

C₄

C₂×#14273655

yes

characteristic

254

C₄

#16837420

yes

characteristic

255

C₄

#16837508

yes

—

256

C₄

#16837661

yes

—

257

C₂

—

258

C₂

#21424965

yes

characteristic

259

C₂

#21424992

yes

characteristic

260

C₂

#21425014

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273702
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₄×#106×C₅₉	C₂
socle	C₂²×C₅₉	#390
prime radical	C₂³×C₅₉	#127
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₄×#106	D₅₉
hypocenter	C₅₉	#9720
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

subgroup

G/H

center

C₂×C₄

#14273702

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₄×#106×C₅₉

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#106

N	H ≅ G/N	type
7. #16837807	C₄	semidirect
8. #16837782	C₄	semidirect
9. #16837753	C₄	semidirect
154. C₅₉	#9720	semidirect

H ≅ G/N

type

7. #16837807

C₄

semidirect

8. #16837782

C₄

semidirect

9. #16837753

C₄

semidirect

154. C₅₉

#9720

semidirect

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

subgroup	index
#21434682	2
#21425039	2
#21422594	2
#21422385	2
C₄×#106×C₅₉	2
#9720	59

subgroup

index

C₄×#106×C₅₉

Subgroups — #28487853

Conjugacy classes of subgroups

Complements

Maximal subgroups