Group #28505437 — subgroups

Subgroups — #28505437

Order 15104.

396 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 121 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×#16837509	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837225	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837218	C₂	1	1	yes	maximal, characteristic
4	#21424850	C₂	1	1	yes	maximal, characteristic
5	#21422201	C₂	1	1	yes	maximal, characteristic
6	#21422175	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2141	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×Dic₅₉	—	2	1	no	—
9	C₂×#14273667	C₂²	1	1	yes	characteristic
10	#16837509	—	2	2	no	—
11	#16837509	—	2	2	no	—
12	C₂×#14273663	C₂²	1	1	yes	characteristic
13	C₂×#14273659	C₂²	1	1	yes	characteristic
14	#16837429	—	2	1	no	—
15	C₂×#14273651	—	2	1	no	—
16	C₂×#14273637	C₂²	1	1	yes	characteristic
17	#16837225	—	2	2	no	—
18	#16837218	—	2	2	no	—
19	#16837161	—	2	1	no	—
20	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#427	C₂²	1	1	yes	characteristic
23	C₅₉×#358	C₄	1	4	yes	complemented
24	C₂×#11745664	—	2	1	no	—
25	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
26	Q₈×Dic₅₉	—	2	4	no	—
27	Q₈×Dic₅₉	—	4	2	no	—
28	C₂×C₄⋊Dic₅₉	—	2	1	no	—
29	C₂×C₄⋊Dic₅₉	—	4	1	no	—
30	C₂×C₄×Dic₅₉	—	4	1	no	—
31	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
32	#14273667	—	2	1	no	—
33	#14273667	—	2	1	no	—
34	C₂×C₅₉⋊C₁₆	—	2	1	no	—
35	#14273663	—	2	1	no	—
36	#14273663	—	2	1	no	—
37	#14273659	—	2	1	no	—
38	#14273659	D₄	1	2	yes	—
39	C₄⋊(C₅₉⋊C₈)	—	4	2	no	—
40	#14273651	—	2	4	no	—
41	#14273637	—	2	1	no	—
42	#14273637	—	2	1	no	—
43	C₂²×Q₈×C₅₉	—	2	1	no	—
44	C₂×Q₁₆×C₅₉	—	2	1	no	—
45	C₂×Q₁₆×C₅₉	—	2	1	no	—
46	C₂×Q₁₆×C₅₉	—	2	1	no	—
47	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
48	C₂×Q₁₆×C₅₉	D₄	1	2	yes	—
49	C₂×Q₁₆×C₅₉	Q₈	1	2	yes	—
50	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
51	#117×C₅₉	—	2	1	no	—
52	M₃₂×C₅₉	—	2	1	no	—
53	M₃₂×C₅₉	—	2	1	no	—
54	C₂×C₁₆×C₅₉	C₂×C₄	1	2	yes	—
55	#107×C₅₉	C₂×C₄	1	2	yes	—
56	#106×C₅₉	—	2	1	no	—
57	C₂×Q₈×C₅₉	—	2	2	no	—
58	C₂×Q₈×C₅₉	—	2	2	no	—
59	C₂×Q₈×C₅₉	—	2	2	no	—
60	C₂×Q₈×C₅₉	—	4	1	no	—
61	C₂×Q₈×C₅₉	—	4	1	no	—
62	C₂×Q₈×C₅₉	—	4	1	no	—
63	C₂²×C₄×C₅₉	—	4	1	no	—
64	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×Dic₅₉	—	2	1	no	—
66	C₂²×Dic₅₉	—	4	1	no	—
67	Q₁₆×C₅₉	—	2	2	no	—
68	Q₁₆×C₅₉	—	2	2	no	—
69	Q₁₆×C₅₉	—	2	2	no	—
70	Q₁₆×C₅₉	C₄⋊C₄	1	4	yes	—
71	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
75	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
76	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
77	C₄⋊C₄×C₅₉	—	2	2	no	—
78	C₂²⋊C₄×C₅₉	—	4	1	no	—
79	C₄²×C₅₉	—	4	1	no	—
80	C₄⋊Dic₅₉	—	2	2	no	—
81	C₄⋊Dic₅₉	—	4	4	no	—
82	C₄⋊Dic₅₉	—	4	1	no	—
83	C₄×Dic₅₉	—	2	1	no	—
84	C₄×Dic₅₉	—	4	4	no	—
85	C₄×Dic₅₉	SD₁₆	1	2	yes	—
86	#11745664	—	4	1	no	—
87	#11745664	—	4	1	no	—
88	C₂×C₅₉⋊C₈	—	2	1	no	—
89	C₂×C₅₉⋊C₈	—	2	1	no	—
90	C₂×C₅₉⋊C₈	—	2	1	no	—
91	C₂×C₅₉⋊C₈	—	4	1	no	—
92	C₁₆×C₅₉	—	2	2	no	—
93	C₅₉⋊C₁₆	—	4	1	no	—
94	C₂³×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	Q₈×C₅₉	—	2	4	no	—
96	Q₈×C₅₉	—	4	2	no	—
97	Q₈×C₅₉	—	4	2	no	—
98	Q₈×C₅₉	—	4	2	no	—
99	C₂×C₄×C₅₉	—	4	2	no	—
100	C₂×C₄×C₅₉	—	4	2	no	—
101	C₂×C₄×C₅₉	—	4	2	no	—
102	C₂×C₄×C₅₉	—	4	2	no	—
103	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
105	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
106	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
107	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
108	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×Dic₅₉	—	2	2	no	—
110	C₂×Dic₅₉	—	4	2	no	—
111	C₂×Dic₅₉	—	4	2	no	—
112	C₂×Dic₅₉	—	8	2	no	—
113	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
115	C₈×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
116	C₈×C₅₉	#123	1	1	yes	characteristic
117	C₅₉⋊C₈	—	4	1	no	—
118	C₅₉⋊C₈	—	8	1	no	—
119	#12957	—	59	1	no	maximal, Sylow
120	C₂²×C₅₉	—	2	2	no	—
121	C₂²×C₅₉	#442	1	1	yes	characteristic
122	C₂²×C₅₉	#450	1	1	yes	characteristic
123	C₂²×C₅₉	#478	1	1	yes	characteristic
124	C₄×C₅₉	—	4	4	no	—
125	C₄×C₅₉	—	8	2	no	—
126	C₄×C₅₉	#385	1	1	yes	characteristic
127	C₄×C₅₉	C₄×SD₁₆	1	1	yes	characteristic
128	C₄×C₅₉	#449	1	1	yes	characteristic
129	C₄×C₅₉	#476	1	1	yes	characteristic
130	Dic₅₉	—	4	2	no	—
131	Dic₅₉	—	8	2	no	—
132	C₂×#441	—	59	1	no	—
133	C₂×#365	—	59	1	no	—
134	C₂×#362	—	59	1	no	—
135	#2141	D₅₉	1	1	yes	characteristic
136	#1946	—	59	1	no	—
137	#1386	—	59	1	no	—
138	#1375	—	59	1	no	—
139	C₂×C₅₉	—	2	1	no	—
140	C₂×C₅₉	—	2	1	no	—
141	C₂×C₅₉	#1864	1	1	yes	characteristic
142	C₂×C₅₉	#2180	1	2	yes	—
143	C₂²×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
144	C₂×C₄×Q₈	—	118	1	no	—
145	C₂×M₃₂	—	59	1	no	—
146	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
147	#441	—	118	2	no	—
148	#441	—	118	2	no	—
149	C₂×#108	—	59	1	no	—
150	#427	C₂×D₅₉	1	1	yes	characteristic
151	C₂×#106	—	59	1	no	—
152	#424	—	118	1	no	—
153	C₂×#103	—	118	1	no	—
154	C₂×#97	—	59	1	no	—
155	#365	—	118	2	no	—
156	#362	—	118	2	no	—
157	#358	Dic₅₉	1	4	yes	complemented
158	#339	—	118	1	no	—
159	C₅₉	#12957	1	1	yes	characteristic, complemented, Sylow
160	C₂²×Q₈	—	2	1	no	—
161	C₂×Q₁₆	—	2	1	no	—
162	C₂×Q₁₆	—	2	1	no	—
163	C₂×Q₁₆	—	2	1	no	—
164	C₂×Q₁₆	Dic₁₁₈	1	2	yes	—
165	C₂×Q₁₆	D₂₃₆	1	2	yes	—
166	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	—
167	C₂×M₁₆	—	118	1	no	—
168	C₂²×C₈	—	59	1	no	—
169	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
170	C₄×Q₈	—	118	4	no	—
171	C₄×Q₈	—	236	2	no	—
172	#117	—	2	1	no	—
173	C₂×C₄⋊C₄	—	118	1	no	—
174	C₂×C₄⋊C₄	—	236	1	no	—
175	C₂×C₄²	—	59	1	no	—
176	C₂×C₄²	—	236	1	no	—
177	M₃₂	—	2	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	118	1	no	—
180	M₃₂	—	118	1	no	—
181	C₂×C₁₆	—	118	1	no	—
182	C₂×C₁₆	C₂×Dic₅₉	1	2	yes	—
183	#108	—	118	1	no	—
184	#108	—	118	1	no	—
185	#107	C₂×Dic₅₉	1	2	yes	—
186	#106	—	2	1	no	—
187	#106	—	59	2	no	—
188	#106	—	118	1	no	—
189	C₄⋊C₈	—	236	2	no	—
190	#103	—	118	4	no	—
191	#97	—	118	1	no	—
192	#97	—	118	1	no	—
193	C₂×Q₈	—	2	2	no	—
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	4	1	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂×Q₈	—	4	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	118	1	no	—
201	C₂²×C₄	—	236	1	no	—
202	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
203	Q₁₆	—	2	2	no	—
204	Q₁₆	—	2	2	no	—
205	Q₁₆	—	2	2	no	—
206	Q₁₆	C₄⋊Dic₅₉	1	4	yes	—
207	M₁₆	—	236	1	no	—
208	M₁₆	—	236	1	no	—
209	C₂×C₈	—	118	1	no	—
210	C₂×C₈	—	118	1	no	—
211	C₂×C₈	—	118	1	no	—
212	C₂×C₈	—	236	1	no	—
213	C₂×C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
214	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
215	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
216	C₂×C₈	#11745687	1	1	yes	characteristic
217	C₂×C₈	#11745687	1	1	yes	characteristic
218	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	118	2	no	—
221	C₄⋊C₄	—	236	4	no	—
222	C₄⋊C₄	—	236	1	no	—
223	C₂²⋊C₄	—	4	1	no	—
224	C₄²	—	4	1	no	—
225	C₄²	—	59	2	no	—
226	C₄²	—	118	1	no	—
227	C₄²	—	236	4	no	—
228	C₁₆	—	2	2	no	—
229	C₁₆	—	236	1	no	—
230	C₂³	#14273751	1	1	yes	characteristic
231	Q₈	—	2	4	no	—
232	Q₈	—	4	2	no	—
233	Q₈	—	4	2	no	—
234	Q₈	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	118	2	no	—
240	C₂×C₄	—	472	2	no	—
241	C₂×C₄	—	236	2	no	—
242	C₂×C₄	—	236	2	no	—
243	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
244	C₂×C₄	#14273697	1	1	yes	characteristic
245	C₂×C₄	#14273704	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
247	C₂×C₄	#14273748	1	1	yes	characteristic
248	C₂×C₄	#14273751	1	1	yes	characteristic
249	C₈	—	472	1	no	—
250	C₈	—	236	1	no	—
251	C₈	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
252	C₈	D₄×Dic₅₉	1	1	yes	characteristic
253	C₈	#14273704	1	1	yes	characteristic
254	C₈	#14273711	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	#16837514	1	1	yes	characteristic
257	C₂²	#16837554	1	1	yes	characteristic
258	C₂²	#16837704	1	1	yes	characteristic
259	C₄	—	4	4	no	—
260	C₄	—	8	2	no	—
261	C₄	—	472	2	no	—
262	C₄	—	236	2	no	—
263	C₄	#16837277	1	1	yes	characteristic
264	C₄	SD₁₆×Dic₅₉	1	1	yes	characteristic
265	C₄	#16837548	1	1	yes	characteristic
266	C₄	#16837690	1	1	yes	characteristic
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	#21424359	1	1	yes	characteristic
270	C₂	#21425988	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837509

C₂

yes

maximal, characteristic

C₂×#16837225

C₂

yes

maximal, characteristic

C₂×#16837218

C₂

yes

maximal, characteristic

#21424850

C₂

yes

maximal, characteristic

#21422201

C₂

yes

maximal, characteristic

#21422175

C₂

yes

maximal, characteristic

C₅₉×#2141

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₅₉

—

C₂×#14273667

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14273659

C₂²

yes

—

—

C₂²

yes

—

—

—

C₂²×Q₁₆×C₅₉

C₂²

yes

characteristic

C₂×M₃₂×C₅₉

C₂²

yes

characteristic

C₅₉×#427

C₂²

yes

characteristic

C₅₉×#358

C₄

yes

complemented

C₂×#11745664

—

C₂²×C₅₉⋊C₈

D₄

yes

characteristic

Q₈×Dic₅₉

—

Q₈×Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

D₄

yes

characteristic

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

—

—

—

—

D₄

yes

—

C₄⋊(C₅₉⋊C₈)

—

#14273651

—

#14273637

—

#14273637

—

C₂²×Q₈×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

C₂×C₄

yes

—

C₂×Q₁₆×C₅₉

D₄

yes

—

C₂×Q₁₆×C₅₉

Q₈

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

#117×C₅₉

—

M₃₂×C₅₉

—

M₃₂×C₅₉

—

C₂×C₁₆×C₅₉

C₂×C₄

yes

—

#107×C₅₉

C₂×C₄

yes

—

#106×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

C₄⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×Q₈

yes

C₂×C₈×C₅₉

yes

C₂×C₈×C₅₉

yes

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

SD₁₆

yes

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

100

C₂×C₄×C₅₉

—

101

C₂×C₄×C₅₉

—

102

C₂×C₄×C₅₉

—

103

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

104

C₂×C₄×C₅₉

#120

yes

characteristic

105

C₂×C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

106

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

107

C₂×C₄×C₅₉

#135

yes

characteristic

108

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

characteristic

109

C₂×Dic₅₉

—

110

C₂×Dic₅₉

—

111

C₂×Dic₅₉

—

112

C₂×Dic₅₉

—

113

C₈×C₅₉

C₂×C₄⋊C₄

yes

characteristic

114

C₈×C₅₉

C₄×D₄

yes

characteristic

115

C₈×C₅₉

C₂²⋊Q₈

yes

characteristic

116

C₈×C₅₉

#123

yes

characteristic

117

C₅₉⋊C₈

—

118

C₅₉⋊C₈

—

119

#12957

—

maximal, Sylow

120

C₂²×C₅₉

—

121

C₂²×C₅₉

#442

yes

characteristic

122

C₂²×C₅₉

#450

yes

characteristic

123

C₂²×C₅₉

#478

yes

characteristic

124

C₄×C₅₉

—

125

C₄×C₅₉

—

126

C₄×C₅₉

#385

yes

characteristic

127

C₄×C₅₉

C₄×SD₁₆

yes

characteristic

128

C₄×C₅₉

#449

yes

characteristic

129

C₄×C₅₉

#476

yes

characteristic

130

Dic₅₉

—

131

Dic₅₉

—

132

C₂×#441

—

133

C₂×#365

—

134

C₂×#362

—

135

#2141

D₅₉

yes

characteristic

136

#1946

—

137

#1386

—

138

#1375

—

139

C₂×C₅₉

—

140

C₂×C₅₉

—

141

C₂×C₅₉

#1864

yes

characteristic

142

C₂×C₅₉

#2180

yes

—

143

C₂²×Q₁₆

C₂×D₅₉

yes

characteristic

144

C₂×C₄×Q₈

—

118

—

145

C₂×M₃₂

—

146

C₂×M₃₂

C₂×D₅₉

yes

characteristic

147

#441

—

118

—

148

#441

—

118

—

149

C₂×#108

—

150

#427

C₂×D₅₉

yes

characteristic

151

C₂×#106

—

152

#424

—

118

—

153

C₂×#103

—

118

—

154

C₂×#97

—

155

#365

—

118

—

156

#362

—

118

—

157

#358

Dic₅₉

yes

complemented

158

#339

—

118

—

159

C₅₉

#12957

yes

characteristic, complemented, Sylow

160

C₂²×Q₈

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

Dic₁₁₈

yes

—

165

C₂×Q₁₆

D₂₃₆

yes

—

166

C₂×Q₁₆

C₂×Dic₅₉

yes

—

167

C₂×M₁₆

—

118

—

168

C₂²×C₈

—

169

C₂²×C₈

C₂²×D₅₉

yes

characteristic

170

C₄×Q₈

—

118

—

171

C₄×Q₈

—

236

—

172

#117

—

173

C₂×C₄⋊C₄

—

118

—

174

C₂×C₄⋊C₄

—

236

—

175

C₂×C₄²

—

176

C₂×C₄²

—

236

—

177

M₃₂

—

178

M₃₂

—

179

M₃₂

—

118

—

180

M₃₂

—

118

—

181

C₂×C₁₆

—

118

—

182

C₂×C₁₆

C₂×Dic₅₉

yes

—

183

#108

—

118

—

184

#108

—

118

—

185

#107

C₂×Dic₅₉

yes

—

186

#106

—

187

#106

—

188

#106

—

118

—

189

C₄⋊C₈

—

236

—

190

#103

—

118

—

191

#97

—

118

—

192

#97

—

118

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂²×C₄

—

200

C₂²×C₄

—

118

—

201

C₂²×C₄

—

236

—

202

C₂²×C₄

D₄×D₅₉

yes

characteristic

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

C₄⋊Dic₅₉

yes

—

207

M₁₆

—

236

—

208

M₁₆

—

236

—

209

C₂×C₈

—

118

—

210

C₂×C₈

—

118

—

211

C₂×C₈

—

118

—

212

C₂×C₈

—

236

—

213

C₂×C₈

C₂×Dic₁₁₈

yes

characteristic

214

C₂×C₈

C₂×D₂₃₆

yes

characteristic

215

C₂×C₈

D₄×D₅₉

yes

characteristic

216

C₂×C₈

#11745687

yes

characteristic

217

C₂×C₈

#11745687

yes

characteristic

218

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

219

C₄⋊C₄

—

220

C₄⋊C₄

—

118

—

221

C₄⋊C₄

—

236

—

222

C₄⋊C₄

—

236

—

223

C₂²⋊C₄

—

224

C₄²

—

225

C₄²

—

226

C₄²

—

118

—

227

C₄²

—

236

—

228

C₁₆

—

229

C₁₆

—

236

—

230

C₂³

#14273751

yes

characteristic

231

Q₈

—

232

Q₈

—

233

Q₈

—

234

Q₈

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

118

—

240

C₂×C₄

—

472

—

241

C₂×C₄

—

236

—

242

C₂×C₄

—

236

—

243

C₂×C₄

D₄×Dic₅₉

yes

characteristic

244

C₂×C₄

#14273697

yes

characteristic

245

C₂×C₄

#14273704

yes

characteristic

246

C₂×C₄

SD₁₆×D₅₉

yes

characteristic

247

C₂×C₄

#14273748

yes

characteristic

248

C₂×C₄

#14273751

yes

characteristic

249

C₈

—

472

—

250

C₈

—

236

—

251

C₈

C₂×C₄⋊Dic₅₉

yes

characteristic

252

C₈

D₄×Dic₅₉

yes

characteristic

253

C₈

#14273704

yes

characteristic

254

C₈

#14273711

yes

characteristic

255

C₂²

—

256

C₂²

#16837514

yes

characteristic

257

C₂²

#16837554

yes

characteristic

258

C₂²

#16837704

yes

characteristic

259

C₄

—

260

C₄

—

261

C₄

—

472

—

262

C₄

—

236

—

263

C₄

#16837277

yes

characteristic

264

C₄

SD₁₆×Dic₅₉

yes

characteristic

265

C₄

#16837548

yes

characteristic

266

C₄

#16837690

yes

characteristic

267

C₂

—

268

C₂

—

269

C₂

#21424359

yes

characteristic

270

C₂

#21425988

yes

—

	subgroup	G/H
center	C₂²	#16837514
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#2141	C₂
socle	C₂²×C₅₉	#442
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#2141	D₅₉
hypocenter	C₅₉	#12957
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

subgroup

G/H

center

C₂²

#16837514

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#2141

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

N	H ≅ G/N	type
23. C₅₉×#358	C₄	semidirect
157. #358	Dic₅₉	semidirect
159. C₅₉	#12957	semidirect

H ≅ G/N

type

23. C₅₉×#358

C₄

semidirect

157. #358

Dic₅₉

semidirect

159. C₅₉

#12957

semidirect

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

subgroup	index
C₂×#16837509	2
C₂×#16837225	2
C₂×#16837218	2
#21424850	2
#21422201	2
#21422175	2
C₅₉×#2141	2
#12957	59

subgroup

index

C₅₉×#2141

Subgroups — #28505437

Conjugacy classes of subgroups

Complements

Maximal subgroups