Group #28487421 — subgroups

Subgroups — #28487421

Order 15104.

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

normal subgroups only

This group has 306 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	#21424233	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#21422871	C₂	1	1	yes	maximal, characteristic
4	#21422868	C₂	1	1	yes	maximal, characteristic
5	#21422842	C₂	1	1	yes	maximal, characteristic
6	#21421999	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1303	C₂	1	1	yes	maximal, characteristic
8	#16837455	C₂²	1	1	yes	characteristic
9	#16837426	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
12	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
13	#16837166	—	2	1	no	—
14	#16837166	—	2	1	no	—
15	#16837157	—	2	1	no	—
16	#16837155	—	2	2	no	—
17	#16837154	C₄	1	2	yes	complemented
18	#16837152	—	2	2	no	—
19	#16837152	C₄	1	2	yes	complemented
20	C₅₉×#431	C₂²	1	1	yes	characteristic
21	C₅₉×#423	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#11745664	—	2	1	no	—
24	C₂²×C₅₉⋊C₈	—	2	1	no	—
25	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
26	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
27	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
28	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
29	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
30	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
31	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
32	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
33	C₄×C₅₉⋊C₈	—	2	1	no	—
34	C₄×C₅₉⋊C₈	—	4	2	no	—
35	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅₉⋊C₈	Q₈	1	1	yes	characteristic
38	C₄×C₅₉⋊C₈	Q₈	1	1	yes	characteristic
39	C₂×M₁₆×C₅₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
41	C₂×C₄²×C₅₉	—	2	1	no	—
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₅₉	—	2	1	no	—
44	C₄⋊C₈×C₅₉	—	2	1	no	—
45	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
46	C₂²⋊C₈×C₅₉	—	2	1	no	—
47	C₄×C₈×C₅₉	—	2	1	no	—
48	#95×C₅₉	Q₈	1	2	yes	—
49	C₂²×C₄×C₅₉	—	2	2	no	—
50	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
53	M₁₆×C₅₉	—	4	1	no	—
54	M₁₆×C₅₉	—	4	1	no	—
55	C₂×C₈×C₅₉	—	2	2	no	—
56	C₂×C₈×C₅₉	—	4	1	no	—
57	C₄⋊C₄×C₅₉	—	2	4	no	—
58	C₄²×C₅₉	—	4	1	no	—
59	C₄²×C₅₉	—	4	1	no	—
60	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₅₉	#41	1	1	yes	characteristic
64	#11745664	—	4	1	no	—
65	#11745664	—	4	1	no	—
66	C₂×C₅₉⋊C₈	—	2	1	no	—
67	C₂×C₅₉⋊C₈	—	2	1	no	—
68	C₂×C₅₉⋊C₈	—	2	1	no	—
69	C₂×C₅₉⋊C₈	—	2	1	no	—
70	C₂×C₅₉⋊C₈	—	2	2	no	—
71	C₂×C₅₉⋊C₈	—	2	2	no	—
72	C₂×C₅₉⋊C₈	—	4	1	no	—
73	C₂×C₅₉⋊C₈	—	4	1	no	—
74	C₂×C₅₉⋊C₈	—	4	1	no	—
75	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
79	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₅₉	—	2	2	no	—
81	C₂×C₄×C₅₉	—	2	4	no	—
82	C₂×C₄×C₅₉	—	4	1	no	—
83	C₂×C₄×C₅₉	—	4	2	no	—
84	C₂×C₄×C₅₉	—	4	2	no	—
85	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₅₉	#125	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
92	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
93	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
95	C₈×C₅₉	—	4	2	no	—
96	C₈×C₅₉	—	8	1	no	—
97	C₅₉⋊C₈	—	2	1	no	—
98	C₅₉⋊C₈	—	2	1	no	—
99	C₅₉⋊C₈	—	2	1	no	—
100	C₅₉⋊C₈	—	2	1	no	—
101	C₅₉⋊C₈	—	4	2	no	—
102	C₅₉⋊C₈	—	4	2	no	—
103	C₅₉⋊C₈	—	8	1	no	—
104	#9629	—	59	1	no	maximal, Sylow
105	C₂²×C₅₉	—	2	1	no	—
106	C₂²×C₅₉	—	2	1	no	—
107	C₂²×C₅₉	#389	1	1	yes	characteristic
108	C₂²×C₅₉	#478	1	1	yes	characteristic
109	C₂²×C₅₉	#479	1	1	yes	characteristic
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	—	2	1	no	—
112	C₄×C₅₉	—	2	1	no	—
113	C₄×C₅₉	—	4	4	no	—
114	C₄×C₅₉	#427	1	1	yes	characteristic
115	C₄×C₅₉	#428	1	1	yes	characteristic
116	C₄×C₅₉	#443	1	2	yes	—
117	C₄×C₅₉	#463	1	1	yes	characteristic
118	C₄×C₅₉	#464	1	1	yes	characteristic
119	#1837	—	59	1	no	—
120	C₈×C₄⋊C₄	—	59	1	no	—
121	#1571	—	59	1	no	—
122	#1570	—	59	1	no	—
123	#1564	—	59	1	no	—
124	#1303	—	59	1	no	—
125	#1303	D₅₉	1	1	yes	characteristic
126	C₂×C₅₉	—	2	1	no	—
127	C₂×C₅₉	—	2	1	no	—
128	C₂×C₅₉	#1945	1	1	yes	characteristic
129	C₂×C₅₉	#1949	1	1	yes	characteristic
130	C₂×C₅₉	#1953	1	1	yes	characteristic
131	#431	—	59	1	no	—
132	#431	C₂×D₅₉	1	1	yes	characteristic
133	#423	—	59	1	no	—
134	#423	C₂×D₅₉	1	1	yes	characteristic
135	C₂×C₄⋊C₈	—	59	1	no	—
136	C₂×C₄×C₈	—	59	1	no	—
137	C₂×C₄×C₈	—	118	1	no	—
138	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
139	#341	—	118	1	no	—
140	#341	—	118	1	no	—
141	#336	—	118	1	no	—
142	#335	—	59	2	no	—
143	#335	—	118	2	no	—
144	#334	—	59	2	no	—
145	#334	—	118	2	no	—
146	C₅₉	#9629	1	1	yes	characteristic, complemented, Sylow
147	C₂×M₁₆	—	2	1	no	—
148	C₂×M₁₆	—	118	1	no	—
149	C₂²×C₈	—	59	1	no	—
150	C₂²×C₈	—	59	1	no	—
151	C₂²×C₈	—	118	1	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	59	2	no	—
158	C₄⋊C₈	—	59	2	no	—
159	C₄⋊C₈	—	118	1	no	—
160	C₄⋊C₈	—	118	1	no	—
161	C₄⋊C₈	—	118	1	no	—
162	C₄⋊C₈	C₄×D₅₉	1	2	yes	—
163	C₂²⋊C₈	—	2	1	no	—
164	C₂²⋊C₈	—	118	1	no	—
165	C₄×C₈	—	2	1	no	—
166	C₄×C₈	—	59	1	no	—
167	C₄×C₈	—	59	1	no	—
168	C₄×C₈	—	59	1	no	—
169	C₄×C₈	—	59	1	no	—
170	C₄×C₈	—	118	1	no	—
171	C₄×C₈	—	236	2	no	—
172	#95	Dic₁₁₈	1	2	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
175	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
176	C₂²×C₄	#11745687	1	1	yes	characteristic
177	M₁₆	—	4	1	no	—
178	M₁₆	—	4	1	no	—
179	M₁₆	—	236	1	no	—
180	M₁₆	—	236	1	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	59	1	no	—
184	C₂×C₈	—	59	1	no	—
185	C₂×C₈	—	59	1	no	—
186	C₂×C₈	—	59	1	no	—
187	C₂×C₈	—	118	1	no	—
188	C₂×C₈	—	118	1	no	—
189	C₂×C₈	—	118	1	no	—
190	C₂×C₈	—	118	1	no	—
191	C₂×C₈	—	118	2	no	—
192	C₂×C₈	—	118	2	no	—
193	C₂×C₈	—	236	1	no	—
194	C₂×C₈	—	236	1	no	—
195	C₂×C₈	—	236	1	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄²	—	4	1	no	—
198	C₄²	—	4	1	no	—
199	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
200	C₄²	#11745685	1	1	yes	characteristic
201	C₄²	D₄×D₅₉	1	1	yes	characteristic
202	C₄²	Q₈×D₅₉	1	1	yes	characteristic
203	C₂³	#14273704	1	1	yes	characteristic
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
210	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
211	C₂×C₄	C₄×Dic₁₁₈	1	1	yes	characteristic
212	C₂×C₄	#14273700	1	1	yes	characteristic
213	C₂×C₄	#14273717	1	1	yes	characteristic
214	C₂×C₄	#14273726	1	1	yes	characteristic
215	C₂×C₄	#14273746	1	1	yes	characteristic
216	C₂×C₄	#14273750	1	1	yes	characteristic
217	C₂×C₄	#14273754	1	1	yes	characteristic
218	C₂×C₄	#14273756	1	1	yes	characteristic
219	C₈	—	4	2	no	—
220	C₈	—	8	1	no	—
221	C₈	—	118	1	no	—
222	C₈	—	118	1	no	—
223	C₈	—	118	1	no	—
224	C₈	—	118	1	no	—
225	C₈	—	472	1	no	—
226	C₈	—	236	2	no	—
227	C₈	—	236	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#16837299	1	1	yes	characteristic
231	C₂²	#16837700	1	1	yes	characteristic
232	C₂²	#16837711	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	4	4	no	—
237	C₄	#16837439	1	1	yes	characteristic
238	C₄	#16837441	1	1	yes	characteristic
239	C₄	#16837516	1	2	yes	—
240	C₄	#16837620	1	1	yes	characteristic
241	C₄	#16837623	1	1	yes	characteristic
242	C₂	—	2	1	no	—
243	C₂	—	2	1	no	—
244	C₂	#21424843	1	1	yes	characteristic
245	C₂	#21424867	1	1	yes	characteristic
246	C₂	#21424885	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21424233

C₂

yes

maximal, characteristic

C₄⋊C₄×C₅₉⋊C₈

C₂

yes

maximal, characteristic

#21422871

C₂

yes

maximal, characteristic

#21422868

C₂

yes

maximal, characteristic

#21422842

C₂

yes

maximal, characteristic

#21421999

C₂

yes

maximal, characteristic

C₅₉×#1303

C₂

yes

maximal, characteristic

#16837455

C₂²

yes

characteristic

#16837426

C₂²

yes

characteristic

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₅₉⋊C₈

—

C₂×C₄×C₅₉⋊C₈

C₂²

yes

—

—

—

—

C₄

yes

complemented

#16837152

—

#16837152

C₄

yes

complemented

C₅₉×#431

C₂²

yes

characteristic

C₅₉×#423

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₅₉

C₂²

yes

characteristic

C₂×#11745664

—

C₂²×C₅₉⋊C₈

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₅₉⋊C₈

Q₈

yes

characteristic

C₄×C₅₉⋊C₈

Q₈

yes

characteristic

C₂×M₁₆×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

C₂×C₄

yes

—

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

—

#95×C₅₉

Q₈

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×Q₈

yes

C₄²×C₅₉

yes

—

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂³×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

C₂×C₄×C₅₉

C₄×Q₈

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₄⋊Q₈

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

100

C₅₉⋊C₈

—

101

C₅₉⋊C₈

—

102

C₅₉⋊C₈

—

103

C₅₉⋊C₈

—

104

#9629

—

maximal, Sylow

105

C₂²×C₅₉

—

106

C₂²×C₅₉

—

107

C₂²×C₅₉

#389

yes

characteristic

108

C₂²×C₅₉

#478

yes

characteristic

109

C₂²×C₅₉

#479

yes

characteristic

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

—

114

C₄×C₅₉

#427

yes

characteristic

115

C₄×C₅₉

#428

yes

characteristic

116

C₄×C₅₉

#443

yes

—

117

C₄×C₅₉

#463

yes

characteristic

118

C₄×C₅₉

#464

yes

characteristic

119

#1837

—

120

C₈×C₄⋊C₄

—

121

#1571

—

122

#1570

—

123

#1564

—

124

#1303

—

125

#1303

D₅₉

yes

characteristic

126

C₂×C₅₉

—

127

C₂×C₅₉

—

128

C₂×C₅₉

#1945

yes

characteristic

129

C₂×C₅₉

#1949

yes

characteristic

130

C₂×C₅₉

#1953

yes

characteristic

131

#431

—

132

#431

C₂×D₅₉

yes

characteristic

133

#423

—

134

#423

C₂×D₅₉

yes

characteristic

135

C₂×C₄⋊C₈

—

136

C₂×C₄×C₈

—

137

C₂×C₄×C₈

—

118

—

138

C₄×C₄⋊C₄

C₂×D₅₉

yes

characteristic

139

#341

—

118

—

140

#341

—

118

—

141

#336

—

118

—

142

#335

—

143

#335

—

118

—

144

#334

—

145

#334

—

118

—

146

C₅₉

#9629

yes

characteristic, complemented, Sylow

147

C₂×M₁₆

—

148

C₂×M₁₆

—

118

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₂²×C₈

—

118

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₅₉

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

118

—

160

C₄⋊C₈

—

118

—

161

C₄⋊C₈

—

118

—

162

C₄⋊C₈

C₄×D₅₉

yes

—

163

C₂²⋊C₈

—

164

C₂²⋊C₈

—

118

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

118

—

171

C₄×C₈

—

236

—

172

#95

Dic₁₁₈

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×Dic₁₁₈

yes

characteristic

175

C₂²×C₄

D₄×D₅₉

yes

characteristic

176

C₂²×C₄

#11745687

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

236

—

180

M₁₆

—

236

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

118

—

188

C₂×C₈

—

118

—

189

C₂×C₈

—

118

—

190

C₂×C₈

—

118

—

191

C₂×C₈

—

118

—

192

C₂×C₈

—

118

—

193

C₂×C₈

—

236

—

194

C₂×C₈

—

236

—

195

C₂×C₈

—

236

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

C₂×C₄×D₅₉

yes

characteristic

200

C₄²

#11745685

yes

characteristic

201

C₄²

D₄×D₅₉

yes

characteristic

202

C₄²

Q₈×D₅₉

yes

characteristic

203

C₂³

#14273704

yes

characteristic

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

210

C₂×C₄

(C₂²⋊D₅₉)⋊C₄

yes

characteristic

211

C₂×C₄

C₄×Dic₁₁₈

yes

characteristic

212

C₂×C₄

#14273700

yes

characteristic

213

C₂×C₄

#14273717

yes

characteristic

214

C₂×C₄

#14273726

yes

characteristic

215

C₂×C₄

#14273746

yes

characteristic

216

C₂×C₄

#14273750

yes

characteristic

217

C₂×C₄

#14273754

yes

characteristic

218

C₂×C₄

#14273756

yes

characteristic

219

C₈

—

220

C₈

—

221

C₈

—

118

—

222

C₈

—

118

—

223

C₈

—

118

—

224

C₈

—

118

—

225

C₈

—

472

—

226

C₈

—

236

—

227

C₈

—

236

—

228

C₂²

—

229

C₂²

—

230

C₂²

#16837299

yes

characteristic

231

C₂²

#16837700

yes

characteristic

232

C₂²

#16837711

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#16837439

yes

characteristic

238

C₄

#16837441

yes

characteristic

239

C₄

#16837516

yes

—

240

C₄

#16837620

yes

characteristic

241

C₄

#16837623

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

#21424843

yes

characteristic

245

C₂

#21424867

yes

characteristic

246

C₂

#21424885

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273700
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1303	C₂
socle	C₂²×C₅₉	#389
prime radical	C₂³×C₅₉	C₂²⋊Q₈
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1303	D₅₉
hypocenter	C₅₉	#9629
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂×C₄

#14273700

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1303

C₂

socle

C₂²×C₅₉

#389

prime radical

C₂³×C₅₉

C₂²⋊Q₈

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
17. #16837154	C₄	semidirect
19. #16837152	C₄	semidirect
146. C₅₉	#9629	semidirect

H ≅ G/N

type

17. #16837154

C₄

semidirect

19. #16837152

C₄

semidirect

146. C₅₉

#9629

semidirect

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

subgroup	index
#21424233	2
C₄⋊C₄×C₅₉⋊C₈	2
#21422871	2
#21422868	2
#21422842	2
#21421999	2
C₅₉×#1303	2
#9629	59

subgroup

index

C₄⋊C₄×C₅₉⋊C₈

C₅₉×#1303

Subgroups — #28487421

Conjugacy classes of subgroups

Complements

Maximal subgroups