Group #21434806 — subgroups

Subgroups — #21434806

Order 7552.

366 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 125 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	#16837812	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837797	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837772	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837761	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837641	C₂	1	2	yes	maximal, complemented
7	#16837629	C₂	1	2	yes	maximal
8	#16837507	C₂	1	2	yes	maximal, complemented
9	#16837502	C₂	1	2	yes	maximal, complemented
10	C₂×#14273638	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#529	C₂	1	1	yes	maximal, characteristic
12	C₂×#11745672	C₂²	1	2	yes	—
13	C₂×#11745670	C₂²	1	2	yes	—
14	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
15	#14273727	C₂²	1	1	yes	characteristic
16	#14273727	C₂²	1	1	yes	characteristic
17	#14273719	—	2	1	no	—
18	#14273706	—	2	1	no	—
19	#14273706	C₂²	1	2	yes	—
20	C₄×Dic₁₁₈	—	2	1	no	—
21	C₄×Dic₁₁₈	C₂²	1	2	yes	—
22	#14273686	—	2	1	no	—
23	#14273660	C₂²	1	2	yes	—
24	#14273658	C₂²	1	2	yes	—
25	#14273651	C₂²	1	2	yes	—
26	#14273650	C₂²	1	2	yes	—
27	#14273650	C₂²	1	2	yes	—
28	#14273648	C₂²	1	2	yes	—
29	#14273638	C₂²	1	2	yes	—
30	#14273638	C₂²	1	1	yes	characteristic
31	#14273638	C₂²	1	1	yes	characteristic
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	C₂³	1	2	yes	—
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	#11745672	—	2	4	no	—
70	#11745670	—	2	4	no	—
71	C₄⋊Dic₅₉	—	2	1	no	—
72	C₄⋊Dic₅₉	—	2	1	no	—
73	C₄⋊Dic₅₉	—	2	1	no	—
74	C₄⋊Dic₅₉	C₂³	1	2	yes	—
75	Dic₅₉⋊C₄	—	2	2	no	—
76	Dic₅₉⋊C₄	—	2	2	no	—
77	C₄×Dic₅₉	—	2	2	no	—
78	C₂×C₅₉⋊C₈	—	2	4	no	—
79	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
80	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
81	C₂³×C₅₉	—	2	1	no	—
82	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₅₉	—	2	2	no	—
84	D₄×C₅₉	—	2	2	no	—
85	D₄×C₅₉	—	4	2	no	—
86	C₂×C₄×C₅₉	—	2	2	no	—
87	C₂×C₄×C₅₉	—	2	2	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	—	2	2	no	—
102	Dic₁₁₈	—	2	2	no	—
103	Dic₁₁₈	—	4	2	no	—
104	C₅₉⋊C₈	—	2	2	no	—
105	C₅₉⋊C₈	#41	1	4	yes	—
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	#137	1	2	yes	—
112	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
113	C₄×C₅₉	—	2	1	no	—
114	C₄×C₅₉	—	2	1	no	—
115	C₄×C₅₉	—	2	1	no	—
116	C₄×C₅₉	—	2	1	no	—
117	C₄×C₅₉	—	2	1	no	—
118	C₄×C₅₉	—	4	1	no	—
119	C₄×C₅₉	—	4	1	no	—
120	C₄×C₅₉	—	4	1	no	—
121	C₄×C₅₉	C₂×#41	1	2	yes	—
122	Dic₅₉	—	4	2	no	—
123	Dic₅₉	—	4	2	no	—
124	#3181	—	59	1	no	maximal, Sylow
125	C₂×C₅₉	—	2	2	no	—
126	C₂×C₅₉	—	8	1	no	—
127	C₂×C₅₉	#532	1	1	yes	characteristic
128	C₂×C₅₉	C₂×#137	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	#501	—	59	1	no	—
133	#497	—	59	1	no	—
134	#491	—	59	1	no	—
135	#489	—	59	1	no	—
136	#467	—	59	2	no	—
137	#465	—	59	2	no	—
138	#441	—	59	2	no	—
139	#440	—	59	2	no	—
140	C₂×#97	—	59	1	no	—
141	C₅₉	#3181	1	1	yes	characteristic, complemented, Sylow
142	C₂×Q₁₆	—	59	2	no	—
143	C₂×SD₁₆	—	59	2	no	—
144	C₂²×C₈	—	59	2	no	—
145	C₄⋊Q₈	—	59	1	no	—
146	C₄⋊Q₈	—	59	1	no	—
147	#126	—	2	1	no	—
148	#125	—	118	1	no	—
149	#125	C₂×D₅₉	1	1	yes	characteristic
150	#124	C₂×D₅₉	1	1	yes	characteristic
151	#123	—	2	1	no	—
152	C₂²⋊Q₈	—	59	2	no	—
153	C₂²⋊Q₈	—	118	1	no	—
154	C₂²⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
155	#121	C₂×D₅₉	1	1	yes	characteristic
156	C₄×Q₈	—	59	2	no	—
157	C₄×Q₈	—	118	1	no	—
158	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
159	C₄×D₄	—	2	1	no	—
160	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	#117	—	118	1	no	—
163	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
164	#107	—	59	2	no	—
165	#106	—	59	2	no	—
166	#103	—	59	2	no	—
167	#103	—	59	2	no	—
168	#103	—	59	2	no	—
169	#102	—	59	2	no	—
170	#97	—	59	2	no	—
171	#97	—	59	1	no	—
172	#97	—	59	1	no	—
173	C₂×Q₈	—	59	2	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	Q₁₆	—	118	4	no	—
183	SD₁₆	—	118	4	no	—
184	C₂×C₈	—	59	2	no	—
185	C₂×C₈	—	59	2	no	—
186	C₂×C₈	—	118	4	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	59	2	no	—
192	C₄⋊C₄	—	118	1	no	—
193	C₄⋊C₄	—	118	1	no	—
194	C₄⋊C₄	—	118	2	no	—
195	C₄⋊C₄	—	118	2	no	—
196	C₄⋊C₄	—	118	1	no	—
197	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
198	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	2	1	no	—
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	118	2	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	118	2	no	—
207	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
208	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
209	C₄²	C₂²×D₅₉	1	1	yes	characteristic
210	C₄²	C₂²×D₅₉	1	1	yes	characteristic
211	C₂³	—	2	1	no	—
212	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
213	Q₈	—	2	2	no	—
214	Q₈	—	118	2	no	—
215	Q₈	—	118	2	no	—
216	Q₈	—	236	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	118	2	no	—
227	C₂×C₄	—	118	2	no	—
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	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
234	C₈	—	59	4	no	—
235	C₈	—	118	2	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	#14273757	1	2	yes	—
242	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	4	1	no	—
249	C₄	—	4	1	no	—
250	C₄	—	4	1	no	—
251	C₄	—	236	2	no	—
252	C₄	—	236	2	no	—
253	C₄	#41×D₅₉	1	2	yes	—
254	C₂	—	2	2	no	—
255	C₂	—	8	1	no	—
256	C₂	#16837948	1	1	yes	characteristic
257	C₂	C₂×#14273757	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

#16837812

C₂

yes

maximal, characteristic, complemented

#16837797

C₂

yes

maximal, characteristic, complemented

#16837772

C₂

yes

maximal, characteristic, complemented

#16837761

C₂

yes

maximal, characteristic, complemented

#16837641

C₂

yes

maximal, complemented

#16837629

C₂

yes

maximal

#16837507

C₂

yes

maximal, complemented

#16837502

C₂

yes

maximal, complemented

C₂×#14273638

C₂

yes

maximal, characteristic, complemented

C₅₉×#529

C₂

yes

maximal, characteristic

C₂×#11745672

C₂²

yes

—

C₂×#11745670

C₂²

yes

—

C₂²×C₅₉⋊C₈

C₂²

yes

—

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

—

—

C₂²

yes

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

C₂²

yes

—

#14273686

—

#14273660

C₂²

yes

—

#14273658

C₂²

yes

—

#14273651

C₂²

yes

—

#14273650

C₂²

yes

—

#14273650

C₂²

yes

—

#14273648

C₂²

yes

—

#14273638

C₂²

yes

—

#14273638

C₂²

yes

characteristic

#14273638

C₂²

yes

characteristic

#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

C₂³

yes

—

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

—

#11745672

—

#11745670

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

Q₈×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×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

Dic₁₁₈

—

104

C₅₉⋊C₈

—

105

C₅₉⋊C₈

#41

yes

—

106

C₂²×C₅₉

—

107

C₂²×C₅₉

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

—

111

C₂²×C₅₉

#137

yes

—

112

C₂²×C₅₉

C₂²×D₄

yes

characteristic

113

C₄×C₅₉

—

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

—

117

C₄×C₅₉

—

118

C₄×C₅₉

—

119

C₄×C₅₉

—

120

C₄×C₅₉

—

121

C₄×C₅₉

C₂×#41

yes

—

122

Dic₅₉

—

123

Dic₅₉

—

124

#3181

—

maximal, Sylow

125

C₂×C₅₉

—

126

C₂×C₅₉

—

127

C₂×C₅₉

#532

yes

characteristic

128

C₂×C₅₉

C₂×#137

yes

characteristic

129

C₂×C₅₉

#575

yes

characteristic

130

#533

—

131

#529

D₅₉

yes

characteristic

132

#501

—

133

#497

—

134

#491

—

135

#489

—

136

#467

—

137

#465

—

138

#441

—

139

#440

—

140

C₂×#97

—

141

C₅₉

#3181

yes

characteristic, complemented, Sylow

142

C₂×Q₁₆

—

143

C₂×SD₁₆

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

#126

—

148

#125

—

118

—

149

#125

C₂×D₅₉

yes

characteristic

150

#124

C₂×D₅₉

yes

characteristic

151

#123

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

118

—

154

C₂²⋊Q₈

C₂×D₅₉

yes

characteristic

155

#121

C₂×D₅₉

yes

characteristic

156

C₄×Q₈

—

157

C₄×Q₈

—

118

—

158

C₄×Q₈

C₂×D₅₉

yes

characteristic

159

C₄×D₄

—

160

C₄×D₄

C₂×D₅₉

yes

characteristic

161

#117

—

162

#117

—

118

—

163

C₂×C₄²

C₂×D₅₉

yes

characteristic

164

#107

—

165

#106

—

166

#103

—

167

#103

—

168

#103

—

169

#102

—

170

#97

—

171

#97

—

172

#97

—

173

C₂×Q₈

—

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

Q₁₆

—

118

—

183

SD₁₆

—

118

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

118

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

118

—

193

C₄⋊C₄

—

118

—

194

C₄⋊C₄

—

118

—

195

C₄⋊C₄

—

118

—

196

C₄⋊C₄

—

118

—

197

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

198

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

118

—

205

C₄²

—

206

C₄²

—

118

—

207

C₄²

C₂²⋊D₅₉

yes

characteristic

208

C₄²

C₂²⋊D₅₉

yes

characteristic

209

C₄²

C₂²×D₅₉

yes

characteristic

210

C₄²

C₂²×D₅₉

yes

characteristic

211

C₂³

—

212

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

213

Q₈

—

214

Q₈

—

118

—

215

Q₈

—

118

—

216

Q₈

—

236

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

118

—

227

C₂×C₄

—

118

—

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

C₂×C₂²⋊D₅₉

yes

characteristic

233

C₂×C₄

C₂³×D₅₉

yes

characteristic

234

C₈

—

235

C₈

—

118

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#14273757

yes

—

242

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

236

—

252

C₄

—

236

—

253

C₄

#41×D₅₉

yes

—

254

C₂

—

255

C₂

—

256

C₂

#16837948

yes

characteristic

257

C₂

C₂×#14273757

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	#3181
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. #16837812	C₂	semidirect
3. #16837797	C₂	semidirect
4. #16837772	C₂	semidirect
5. #16837761	C₂	semidirect
6. #16837641	C₂	semidirect
8. #16837507	C₂	semidirect
9. #16837502	C₂	semidirect
10. C₂×#14273638	C₂	semidirect
141. C₅₉	#3181	semidirect

H ≅ G/N

type

1. #16837959

C₂

semidirect

2. #16837812

C₂

semidirect

3. #16837797

C₂

semidirect

4. #16837772

C₂

semidirect

5. #16837761

C₂

semidirect

6. #16837641

C₂

semidirect

8. #16837507

C₂

semidirect

9. #16837502

C₂

semidirect

10. C₂×#14273638

C₂

semidirect

141. C₅₉

#3181

semidirect

Subgroups — #21434806

Conjugacy classes of subgroups

Complements