Group #21435271 — subgroups

Subgroups — #21435271

Order 7552.

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

normal subgroups only

This group has 332 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	#16837959	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837801	C₂	1	2	yes	maximal, complemented
3	#16837756	C₂	1	2	yes	maximal, complemented
4	#16837740	C₂	1	2	yes	maximal, complemented
5	#16837723	C₂	1	2	yes	maximal
6	#16837697	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837692	C₂	1	1	yes	maximal, characteristic, complemented
8	#16837687	C₂	1	1	yes	maximal, characteristic, complemented
9	#16837682	C₂	1	1	yes	maximal, characteristic, complemented
10	#16837455	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#529	C₂	1	1	yes	maximal, characteristic
12	#14273727	C₂²	1	1	yes	characteristic
13	#14273727	C₂²	1	1	yes	characteristic
14	#14273719	C₂²	1	2	yes	—
15	#14273706	—	2	1	no	—
16	#14273706	—	2	1	no	—
17	C₄×Dic₁₁₈	—	2	1	no	—
18	C₄×Dic₁₁₈	—	2	1	no	—
19	#14273686	C₂²	1	2	yes	—
20	#14273660	C₂²	1	2	yes	—
21	#14273660	C₂²	1	2	yes	—
22	#14273658	C₂²	1	2	yes	—
23	#14273658	C₂²	1	2	yes	—
24	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	#14273651	C₂²	1	2	yes	—
27	#14273651	C₂²	1	2	yes	—
28	#14273648	C₂²	1	2	yes	—
29	#14273648	C₂²	1	2	yes	—
30	C₂²⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
31	C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
32	#126×C₅₉	—	2	1	no	—
33	#125×C₅₉	C₂²	1	1	yes	characteristic
34	#124×C₅₉	C₂²	1	1	yes	characteristic
35	#123×C₅₉	—	2	1	no	—
36	C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	#121×C₅₉	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₅₉	—	2	1	no	—
40	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
41	#117×C₅₉	—	2	1	no	—
42	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₅₉	—	2	1	no	—
45	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₅₉	—	2	1	no	—
47	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
49	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×Dic₁₁₈	—	2	1	no	—
51	C₂×Dic₁₁₈	—	2	1	no	—
52	C₄⋊C₄×C₅₉	—	2	1	no	—
53	C₄⋊C₄×C₅₉	—	2	1	no	—
54	C₄⋊C₄×C₅₉	—	2	1	no	—
55	C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
57	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
58	C₂²⋊C₄×C₅₉	—	2	1	no	—
59	C₂²⋊C₄×C₅₉	—	2	1	no	—
60	C₂²⋊C₄×C₅₉	—	2	1	no	—
61	C₂²⋊C₄×C₅₉	—	2	1	no	—
62	C₂²⋊C₄×C₅₉	—	2	1	no	—
63	C₄²×C₅₉	—	2	1	no	—
64	C₄²×C₅₉	D₄	1	1	yes	characteristic
65	C₄²×C₅₉	D₄	1	1	yes	characteristic
66	C₄²×C₅₉	C₂³	1	1	yes	characteristic
67	C₄²×C₅₉	C₂³	1	1	yes	characteristic
68	C₂²⋊Dic₅₉	—	2	2	no	—
69	C₄⋊Dic₅₉	—	2	1	no	—
70	C₄⋊Dic₅₉	—	2	1	no	—
71	C₄⋊Dic₅₉	C₂³	1	2	yes	—
72	C₄⋊Dic₅₉	C₂³	1	2	yes	—
73	Dic₅₉⋊C₄	—	2	2	no	—
74	Dic₅₉⋊C₄	—	2	2	no	—
75	C₄×Dic₅₉	—	2	2	no	—
76	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
77	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
78	C₂³×C₅₉	—	2	1	no	—
79	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
80	Q₈×C₅₉	—	2	1	no	—
81	Q₈×C₅₉	—	2	1	no	—
82	D₄×C₅₉	—	2	1	no	—
83	D₄×C₅₉	—	2	1	no	—
84	D₄×C₅₉	—	4	2	no	—
85	C₂×C₄×C₅₉	—	2	2	no	—
86	C₂×C₄×C₅₉	—	2	1	no	—
87	C₂×C₄×C₅₉	—	2	1	no	—
88	C₂×C₄×C₅₉	—	2	1	no	—
89	C₂×C₄×C₅₉	—	2	1	no	—
90	C₂×C₄×C₅₉	—	2	1	no	—
91	C₂×C₄×C₅₉	—	4	1	no	—
92	C₂×C₄×C₅₉	—	4	2	no	—
93	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₅₉	—	2	2	no	—
100	C₂×Dic₅₉	—	2	2	no	—
101	Dic₁₁₈	—	4	2	no	—
102	Dic₁₁₈	—	4	2	no	—
103	C₅₉⋊C₈	—	2	2	no	—
104	C₅₉⋊C₈	—	2	2	no	—
105	C₂²×C₅₉	—	2	1	no	—
106	C₂²×C₅₉	—	2	1	no	—
107	C₂²×C₅₉	—	2	1	no	—
108	C₂²×C₅₉	—	4	1	no	—
109	C₂²×C₅₉	—	4	1	no	—
110	C₂²×C₅₉	—	4	1	no	—
111	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
112	C₄×C₅₉	—	2	1	no	—
113	C₄×C₅₉	—	2	1	no	—
114	C₄×C₅₉	—	2	1	no	—
115	C₄×C₅₉	—	2	1	no	—
116	C₄×C₅₉	—	4	1	no	—
117	C₄×C₅₉	—	4	1	no	—
118	C₄×C₅₉	—	4	1	no	—
119	C₄×C₅₉	#135	1	2	yes	—
120	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
121	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
122	Dic₅₉	—	4	2	no	—
123	Dic₅₉	—	4	2	no	—
124	#3233	—	59	1	no	maximal, Sylow
125	C₂×C₅₉	—	4	1	no	—
126	C₂×C₅₉	—	8	1	no	—
127	C₂×C₅₉	#536	1	1	yes	characteristic
128	C₂×C₅₉	C₂×#135	1	1	yes	characteristic
129	C₂×C₅₉	#575	1	1	yes	characteristic
130	#533	—	59	1	no	—
131	#529	D₅₉	1	1	yes	characteristic
132	#499	—	59	2	no	—
133	#488	—	59	2	no	—
134	#485	—	59	2	no	—
135	#482	—	59	2	no	—
136	#477	—	59	1	no	—
137	#476	—	59	1	no	—
138	#475	—	59	1	no	—
139	#474	—	59	1	no	—
140	#431	—	59	1	no	—
141	C₅₉	#3233	1	1	yes	characteristic, complemented, Sylow
142	C₄⋊Q₈	—	59	1	no	—
143	C₄⋊Q₈	—	59	1	no	—
144	#126	—	2	1	no	—
145	#125	—	59	2	no	—
146	#125	C₂×D₅₉	1	1	yes	characteristic
147	#124	C₂×D₅₉	1	1	yes	characteristic
148	#123	—	2	1	no	—
149	C₂²⋊Q₈	—	118	1	no	—
150	C₂²⋊Q₈	—	118	1	no	—
151	C₂²⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
152	#121	C₂×D₅₉	1	1	yes	characteristic
153	C₄×Q₈	—	118	1	no	—
154	C₄×Q₈	—	118	1	no	—
155	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
156	C₄×D₄	—	2	1	no	—
157	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
158	#117	—	2	1	no	—
159	#117	—	59	2	no	—
160	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
161	#107	—	59	2	no	—
162	#107	—	59	2	no	—
163	#106	—	59	2	no	—
164	#106	—	59	2	no	—
165	C₄⋊C₈	—	59	1	no	—
166	C₄⋊C₈	—	59	1	no	—
167	#103	—	59	2	no	—
168	#103	—	59	2	no	—
169	#102	—	59	2	no	—
170	#102	—	59	2	no	—
171	C₂²⋊C₈	—	59	2	no	—
172	C₄×C₈	—	59	2	no	—
173	C₂×Q₈	—	118	1	no	—
174	C₂×Q₈	—	118	1	no	—
175	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
182	C₂×C₈	—	59	2	no	—
183	C₂×C₈	—	59	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	59	2	no	—
189	C₄⋊C₄	—	59	2	no	—
190	C₄⋊C₄	—	118	2	no	—
191	C₄⋊C₄	—	118	2	no	—
192	C₄⋊C₄	—	118	1	no	—
193	C₄⋊C₄	—	118	1	no	—
194	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
195	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
196	C₂²⋊C₄	—	2	1	no	—
197	C₂²⋊C₄	—	2	1	no	—
198	C₂²⋊C₄	—	2	1	no	—
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	118	2	no	—
202	C₄²	—	2	1	no	—
203	C₄²	—	118	2	no	—
204	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
205	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
206	C₄²	C₂²×D₅₉	1	1	yes	characteristic
207	C₄²	C₂²×D₅₉	1	1	yes	characteristic
208	C₂³	—	2	1	no	—
209	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
210	Q₈	—	2	1	no	—
211	Q₈	—	2	1	no	—
212	Q₈	—	236	2	no	—
213	Q₈	—	236	2	no	—
214	D₄	—	2	1	no	—
215	D₄	—	2	1	no	—
216	D₄	—	4	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	118	2	no	—
226	C₂×C₄	—	118	2	no	—
227	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
228	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
230	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
232	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
233	C₈	—	118	2	no	—
234	C₈	—	118	2	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	4	1	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	1	no	—
241	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	4	1	no	—
247	C₄	—	4	1	no	—
248	C₄	—	4	1	no	—
249	C₄	—	236	2	no	—
250	C₄	—	236	2	no	—
251	C₄	#14273747	1	2	yes	—
252	C₄	#14273774	1	1	yes	characteristic
253	C₄	#14273774	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	8	1	no	—
256	C₂	#16837973	1	1	yes	characteristic
257	C₂	C₂×#14273747	1	1	yes	characteristic
258	C₂	#16838200	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837959

C₂

yes

maximal, characteristic, complemented

#16837801

C₂

yes

maximal, complemented

#16837756

C₂

yes

maximal, complemented

#16837740

C₂

yes

maximal, complemented

#16837723

C₂

yes

maximal

#16837697

C₂

yes

maximal, characteristic, complemented

#16837692

C₂

yes

maximal, characteristic, complemented

#16837687

C₂

yes

maximal, characteristic, complemented

#16837682

C₂

yes

maximal, characteristic, complemented

#16837455

C₂

yes

maximal, characteristic, complemented

C₅₉×#529

C₂

yes

maximal, characteristic

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273719

C₂²

yes

—

#14273706

—

#14273706

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

#14273686

C₂²

yes

—

#14273660

C₂²

yes

—

#14273660

C₂²

yes

—

#14273658

C₂²

yes

—

#14273658

C₂²

yes

—

C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

#14273651

C₂²

yes

—

#14273651

C₂²

yes

—

#14273648

C₂²

yes

—

#14273648

C₂²

yes

—

C₂²⋊(C₅₉⋊C₈)

C₂²

yes

—

C₄×C₅₉⋊C₈

C₂²

yes

—

#126×C₅₉

—

#125×C₅₉

C₂²

yes

characteristic

#124×C₅₉

C₂²

yes

characteristic

#123×C₅₉

—

C₂²⋊Q₈×C₅₉

C₂²

yes

characteristic

#121×C₅₉

C₂²

yes

characteristic

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄×D₄×C₅₉

—

C₄×D₄×C₅₉

C₂²

yes

characteristic

#117×C₅₉

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

C₂³

yes

characteristic

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

C₂³

yes

characteristic

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

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

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

C₄⋊Dic₅₉

C₂³

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×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

C₂×Dic₅₉

—

100

C₂×Dic₅₉

—

101

Dic₁₁₈

—

102

Dic₁₁₈

—

103

C₅₉⋊C₈

—

104

C₅₉⋊C₈

—

105

C₂²×C₅₉

—

106

C₂²×C₅₉

—

107

C₂²×C₅₉

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

—

111

C₂²×C₅₉

C₂²×D₄

yes

characteristic

112

C₄×C₅₉

—

113

C₄×C₅₉

—

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

—

117

C₄×C₅₉

—

118

C₄×C₅₉

—

119

C₄×C₅₉

#135

yes

—

120

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

121

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

122

Dic₅₉

—

123

Dic₅₉

—

124

#3233

—

maximal, Sylow

125

C₂×C₅₉

—

126

C₂×C₅₉

—

127

C₂×C₅₉

#536

yes

characteristic

128

C₂×C₅₉

C₂×#135

yes

characteristic

129

C₂×C₅₉

#575

yes

characteristic

130

#533

—

131

#529

D₅₉

yes

characteristic

132

#499

—

133

#488

—

134

#485

—

135

#482

—

136

#477

—

137

#476

—

138

#475

—

139

#474

—

140

#431

—

141

C₅₉

#3233

yes

characteristic, complemented, Sylow

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#126

—

145

#125

—

146

#125

C₂×D₅₉

yes

characteristic

147

#124

C₂×D₅₉

yes

characteristic

148

#123

—

149

C₂²⋊Q₈

—

118

—

150

C₂²⋊Q₈

—

118

—

151

C₂²⋊Q₈

C₂×D₅₉

yes

characteristic

152

#121

C₂×D₅₉

yes

characteristic

153

C₄×Q₈

—

118

—

154

C₄×Q₈

—

118

—

155

C₄×Q₈

C₂×D₅₉

yes

characteristic

156

C₄×D₄

—

157

C₄×D₄

C₂×D₅₉

yes

characteristic

158

#117

—

159

#117

—

160

C₂×C₄²

C₂×D₅₉

yes

characteristic

161

#107

—

162

#107

—

163

#106

—

164

#106

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#103

—

168

#103

—

169

#102

—

170

#102

—

171

C₂²⋊C₈

—

172

C₄×C₈

—

173

C₂×Q₈

—

118

—

174

C₂×Q₈

—

118

—

175

C₂×Q₈

C₂²×D₅₉

yes

characteristic

176

C₂×D₄

—

177

C₂×D₄

C₂²×D₅₉

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

180

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

181

C₂²×C₄

C₂²×D₅₉

yes

characteristic

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

118

—

191

C₄⋊C₄

—

118

—

192

C₄⋊C₄

—

118

—

193

C₄⋊C₄

—

118

—

194

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

195

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

196

C₂²⋊C₄

—

197

C₂²⋊C₄

—

198

C₂²⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

118

—

202

C₄²

—

203

C₄²

—

118

—

204

C₄²

C₂²⋊D₅₉

yes

characteristic

205

C₄²

C₂²⋊D₅₉

yes

characteristic

206

C₄²

C₂²×D₅₉

yes

characteristic

207

C₄²

C₂²×D₅₉

yes

characteristic

208

C₂³

—

209

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

210

Q₈

—

211

Q₈

—

212

Q₈

—

236

—

213

Q₈

—

236

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

118

—

226

C₂×C₄

—

118

—

227

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

228

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

229

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

230

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

232

C₂×C₄

C₂³×D₅₉

yes

characteristic

233

C₈

—

118

—

234

C₈

—

118

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

236

—

250

C₄

—

236

—

251

C₄

#14273747

yes

—

252

C₄

#14273774

yes

characteristic

253

C₄

#14273774

yes

characteristic

254

C₂

—

255

C₂

—

256

C₂

#16837973

yes

characteristic

257

C₂

C₂×#14273747

yes

characteristic

258

C₂

#16838200

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#529	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#529	D₅₉
hypocenter	C₅₉	#3233
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #529

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#529

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #529

N	H ≅ G/N	type
1. #16837959	C₂	semidirect
2. #16837801	C₂	semidirect
3. #16837756	C₂	semidirect
4. #16837740	C₂	semidirect
6. #16837697	C₂	semidirect
7. #16837692	C₂	semidirect
8. #16837687	C₂	semidirect
9. #16837682	C₂	semidirect
10. #16837455	C₂	semidirect
141. C₅₉	#3233	semidirect

H ≅ G/N

type

1. #16837959

C₂

semidirect

2. #16837801

C₂

semidirect

3. #16837756

C₂

semidirect

4. #16837740

C₂

semidirect

6. #16837697

C₂

semidirect

7. #16837692

C₂

semidirect

8. #16837687

C₂

semidirect

9. #16837682

C₂

semidirect

10. #16837455

C₂

semidirect

141. C₅₉

#3233

semidirect

Subgroups — #21435271

Conjugacy classes of subgroups

Complements