Group #24995417 — subgroups

Subgroups — #24995417

Order 11008.

726 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₄×#13063322	C₂	1	1	yes	maximal, characteristic
2	#19134712	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582628	C₂	1	4	yes	maximal, complemented
4	C₄×#97×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13063322	C₄	1	1	yes	characteristic
6	C₂×C₄×D₁₇₂	—	2	2	no	—
7	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
9	#14582801	—	2	2	no	—
10	#14582801	C₄	1	2	yes	—
11	#14582769	C₄	1	1	yes	characteristic
12	#14582654	—	2	2	no	—
13	#14582628	—	2	8	no	—
14	C₂×#97×C₄₃	—	2	2	no	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
16	C₄³×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×D₁₇₂	—	2	2	no	—
18	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
19	C₂²×C₄×D₄₃	—	2	2	no	—
20	C₂²×C₄₃⋊C₈	—	2	2	no	—
21	#13063322	—	2	4	no	—
22	C₄×D₁₇₂	—	2	4	no	—
23	C₄×D₁₇₂	—	2	4	no	—
24	C₄×D₁₇₂	—	4	8	no	—
25	C₂×C₄⋊Dic₄₃	—	2	2	no	—
26	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
27	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
28	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
30	C₂²×C₈×C₄₃	—	2	2	no	—
31	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₄₃	D₄	1	2	yes	—
34	C₂×C₄²×C₄₃	D₄	1	2	yes	—
35	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	#97×C₄₃	—	2	8	no	—
37	C₄×C₈×C₄₃	—	2	2	no	—
38	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
39	C₂³×D₄₃	—	2	2	no	—
40	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
41	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₄₃	—	2	2	no	—
46	C₂×D₁₇₂	—	2	8	no	—
47	C₂×D₁₇₂	—	2	2	no	—
48	C₂×D₁₇₂	—	2	4	no	—
49	C₂×D₁₇₂	—	2	4	no	—
50	C₂×D₁₇₂	—	4	4	no	—
51	C₂×D₁₇₂	—	4	4	no	—
52	C₂×D₁₇₂	M₁₆	1	4	yes	—
53	C₂×C₄×D₄₃	—	4	2	no	—
54	C₂×C₄×D₄₃	—	4	2	no	—
55	C₂×C₄×D₄₃	—	4	8	no	—
56	C₂×C₈×C₄₃	—	2	8	no	—
57	C₂×C₈×C₄₃	—	2	4	no	—
58	C₄²×C₄₃	—	2	4	no	—
59	C₄²×C₄₃	—	2	2	no	—
60	C₄²×C₄₃	—	2	2	no	—
61	C₄²×C₄₃	—	2	4	no	—
62	C₄²×C₄₃	C₂×D₄	1	2	yes	—
63	C₄²×C₄₃	#41	1	2	yes	—
64	(C₂×D₄₃)⋊C₄	—	4	8	no	—
65	(C₂×D₄₃)⋊C₄	—	4	4	no	—
66	C₄⋊Dic₄₃	—	2	4	no	—
67	C₄⋊Dic₄₃	—	4	4	no	—
68	C₂×C₄₃⋊C₈	—	4	2	no	—
69	C₂×C₄₃⋊C₈	—	4	4	no	—
70	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×D₄₃	—	2	4	no	—
72	C₂²×D₄₃	—	4	2	no	—
73	C₂²×D₄₃	—	4	2	no	—
74	C₂²×D₄₃	—	4	4	no	—
75	C₂²×D₄₃	—	4	4	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	#104	1	4	yes	—
83	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₄₃	#121	1	2	yes	—
85	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
88	C₂×C₄×C₄₃	#131	1	2	yes	—
89	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
90	C₂×Dic₄₃	—	4	2	no	—
91	C₂×Dic₄₃	—	4	4	no	—
92	D₁₇₂	—	2	8	no	—
93	D₁₇₂	—	4	16	no	—
94	D₁₇₂	—	4	4	no	—
95	C₄×D₄₃	—	8	4	no	—
96	C₄×D₄₃	—	8	4	no	—
97	C₈×C₄₃	—	2	8	no	—
98	C₄₃⋊C₈	—	8	2	no	—
99	#9648	—	43	1	no	maximal, Sylow
100	C₂²×C₄₃	#390	1	1	yes	characteristic
101	C₂²×C₄₃	#407	1	1	yes	characteristic
102	C₂²×C₄₃	#408	1	1	yes	characteristic
103	C₂²×C₄₃	#418	1	2	yes	—
104	C₂²×C₄₃	C₂×#104	1	2	yes	—
105	C₂×D₄₃	—	4	4	no	—
106	C₂×D₄₃	—	4	8	no	—
107	C₂×D₄₃	—	8	2	no	—
108	C₂×D₄₃	—	8	2	no	—
109	C₂×D₄₃	—	8	4	no	—
110	C₄×C₄₃	—	2	2	no	—
111	C₄×C₄₃	—	2	4	no	—
112	C₄×C₄₃	—	4	2	no	—
113	C₄×C₄₃	#435	1	4	yes	—
114	C₄×C₄₃	#490	1	2	yes	—
115	C₄×C₄₃	#496	1	2	yes	—
116	Dic₄₃	—	8	2	no	—
117	C₄×#127	—	43	1	no	—
118	#1831	—	43	1	no	—
119	C₄×#97	D₄₃	1	1	yes	characteristic, complemented
120	C₂×D₄⋊C₈	—	43	4	no	—
121	C₂×C₄₃	#1484	1	2	yes	—
122	C₂×C₄₃	#1490	1	2	yes	—
123	C₂×C₄₃	#1955	1	1	yes	characteristic
124	C₂×C₄₃	#1961	1	1	yes	characteristic
125	C₂×C₄₃	#1962	1	1	yes	characteristic
126	D₄₃	—	8	4	no	—
127	C₂×#127	—	43	1	no	—
128	C₂×C₄×D₄	—	43	2	no	—
129	C₂×C₄×D₄	—	86	2	no	—
130	C₂×C₄⋊C₈	—	43	2	no	—
131	C₂×#97	—	2	2	no	—
132	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
133	#390	—	43	2	no	—
134	#390	—	86	2	no	—
135	#384	—	43	1	no	—
136	C₄³	C₂×D₄₃	1	1	yes	characteristic
137	#336	—	86	2	no	—
138	D₄⋊C₈	—	86	8	no	—
139	C₄₃	#9648	1	1	yes	characteristic, complemented, Sylow
140	C₂²×D₄	—	43	2	no	—
141	C₂²×D₄	—	86	2	no	—
142	C₂³×C₄	—	86	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	86	2	no	—
145	#127	—	86	4	no	—
146	C₄×D₄	—	86	4	no	—
147	C₄×D₄	—	86	4	no	—
148	C₄×D₄	—	172	8	no	—
149	C₂×C₄⋊C₄	—	43	2	no	—
150	C₂×C₄⋊C₄	—	86	2	no	—
151	C₂×C₂²⋊C₄	—	86	4	no	—
152	C₂×C₂²⋊C₄	—	86	2	no	—
153	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
154	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
155	C₂×C₄²	D₁₇₂	1	2	yes	—
156	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
157	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
158	C₄⋊C₈	—	86	4	no	—
159	#97	—	2	8	no	—
160	C₄×C₈	—	2	2	no	—
161	C₄×C₈	D₁₇₂	1	4	yes	complemented
162	C₂⁴	—	86	2	no	—
163	C₂×D₄	—	43	4	no	—
164	C₂×D₄	—	86	8	no	—
165	C₂×D₄	—	86	4	no	—
166	C₂×D₄	—	86	2	no	—
167	C₂×D₄	—	86	4	no	—
168	C₂×D₄	—	172	4	no	—
169	C₂×D₄	—	172	4	no	—
170	C₂²×C₄	—	86	2	no	—
171	C₂²×C₄	—	172	2	no	—
172	C₂²×C₄	—	172	2	no	—
173	C₂²×C₄	—	172	8	no	—
174	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
175	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
176	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
179	C₂×C₈	—	2	8	no	—
180	C₂×C₈	—	2	4	no	—
181	C₂×C₈	—	172	2	no	—
182	C₂×C₈	—	172	4	no	—
183	C₄⋊C₄	—	86	4	no	—
184	C₄⋊C₄	—	172	4	no	—
185	C₂²⋊C₄	—	172	8	no	—
186	C₂²⋊C₄	—	172	4	no	—
187	C₄²	—	2	4	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	4	no	—
191	C₄²	C₂×D₁₇₂	1	2	yes	—
192	C₄²	#10621898	1	2	yes	—
193	C₂³	—	86	4	no	—
194	C₂³	—	172	2	no	—
195	C₂³	—	172	2	no	—
196	C₂³	—	172	4	no	—
197	C₂³	—	172	4	no	—
198	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
199	D₄	—	86	8	no	—
200	D₄	—	172	16	no	—
201	D₄	—	172	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	344	4	no	—
209	C₂×C₄	—	344	4	no	—
210	C₂×C₄	—	172	2	no	—
211	C₂×C₄	—	172	4	no	—
212	C₂×C₄	#13063253	1	4	yes	—
213	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
214	C₂×C₄	#13063299	1	2	yes	—
215	C₂×C₄	#13063313	1	1	yes	characteristic
216	C₂×C₄	#13063322	1	1	yes	characteristic
217	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
218	C₂×C₄	#13063333	1	2	yes	—
219	C₂×C₄	#13063353	1	4	yes	—
220	C₈	—	2	8	no	—
221	C₈	—	344	2	no	—
222	C₂²	—	344	4	no	—
223	C₂²	—	344	2	no	—
224	C₂²	—	344	2	no	—
225	C₂²	—	172	8	no	—
226	C₂²	—	172	4	no	—
227	C₂²	#14582801	1	1	yes	characteristic
228	C₂²	#14582862	1	1	yes	characteristic
229	C₂²	#14582867	1	1	yes	characteristic
230	C₂²	#14582905	1	2	yes	—
231	C₂²	C₂×#13063253	1	2	yes	—
232	C₄	—	2	4	no	—
233	C₄	—	2	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	344	2	no	—
236	C₄	#14582972	1	4	yes	—
237	C₄	#14583264	1	2	yes	—
238	C₄	#14583288	1	2	yes	—
239	C₂	—	344	4	no	—
240	C₂	#19133013	1	2	yes	—
241	C₂	#19133039	1	2	yes	—
242	C₂	#19135393	1	1	yes	characteristic
243	C₂	#19135419	1	1	yes	characteristic
244	C₂	#19135423	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063322

C₂

yes

maximal, characteristic

#19134712

C₂

yes

maximal, characteristic, complemented

C₂×#14582628

C₂

yes

maximal, complemented

C₄×#97×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#13063322

C₄

yes

characteristic

C₂×C₄×D₁₇₂

—

C₂×C₄×D₁₇₂

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#14582801

—

#14582801

C₄

yes

—

#14582769

C₄

yes

characteristic

#14582654

—

#14582628

—

C₂×#97×C₄₃

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×D₁₇₂

—

C₂²×D₁₇₂

C₂×C₄

yes

—

C₂²×C₄×D₄₃

—

C₂²×C₄₃⋊C₈

—

#13063322

—

C₄×D₁₇₂

—

C₄×D₁₇₂

—

C₄×D₁₇₂

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₄⋊(C₄₃⋊C₈)

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

complemented

C₂³×D₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

M₁₆

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#104

yes

—

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#9648

—

maximal, Sylow

100

C₂²×C₄₃

#390

yes

characteristic

101

C₂²×C₄₃

#407

yes

characteristic

102

C₂²×C₄₃

#408

yes

characteristic

103

C₂²×C₄₃

#418

yes

—

104

C₂²×C₄₃

C₂×#104

yes

—

105

C₂×D₄₃

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₂×D₄₃

—

109

C₂×D₄₃

—

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

#435

yes

—

114

C₄×C₄₃

#490

yes

—

115

C₄×C₄₃

#496

yes

—

116

Dic₄₃

—

117

C₄×#127

—

118

#1831

—

119

C₄×#97

D₄₃

yes

characteristic, complemented

120

C₂×D₄⋊C₈

—

121

C₂×C₄₃

#1484

yes

—

122

C₂×C₄₃

#1490

yes

—

123

C₂×C₄₃

#1955

yes

characteristic

124

C₂×C₄₃

#1961

yes

characteristic

125

C₂×C₄₃

#1962

yes

characteristic

126

D₄₃

—

127

C₂×#127

—

128

C₂×C₄×D₄

—

129

C₂×C₄×D₄

—

130

C₂×C₄⋊C₈

—

131

C₂×#97

—

132

C₂×C₄×C₈

C₂×D₄₃

yes

—

133

#390

—

134

#390

—

135

#384

—

136

C₄³

C₂×D₄₃

yes

characteristic

137

#336

—

138

D₄⋊C₈

—

139

C₄₃

#9648

yes

characteristic, complemented, Sylow

140

C₂²×D₄

—

141

C₂²×D₄

—

142

C₂³×C₄

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

#127

—

146

C₄×D₄

—

147

C₄×D₄

—

148

C₄×D₄

—

172

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₂²⋊C₄

—

152

C₂×C₂²⋊C₄

—

153

C₂×C₄²

C₄×D₄₃

yes

characteristic

154

C₂×C₄²

C₄×D₄₃

yes

characteristic

155

C₂×C₄²

D₁₇₂

yes

—

156

C₂×C₄²

C₂²⋊D₄₃

yes

—

157

C₂×C₄²

C₂²×D₄₃

yes

characteristic

158

C₄⋊C₈

—

159

#97

—

160

C₄×C₈

—

161

C₄×C₈

D₁₇₂

yes

complemented

162

C₂⁴

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

172

—

169

C₂×D₄

—

172

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

—

172

C₂²×C₄

—

172

—

173

C₂²×C₄

—

172

—

174

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

175

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

176

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

177

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

172

—

182

C₂×C₈

—

172

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

172

—

185

C₂²⋊C₄

—

172

—

186

C₂²⋊C₄

—

172

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

C₂×D₁₇₂

yes

—

192

C₄²

#10621898

yes

—

193

C₂³

—

194

C₂³

—

172

—

195

C₂³

—

172

—

196

C₂³

—

172

—

197

C₂³

—

172

—

198

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

199

D₄

—

200

D₄

—

172

—

201

D₄

—

172

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

344

—

209

C₂×C₄

—

344

—

210

C₂×C₄

—

172

—

211

C₂×C₄

—

172

—

212

C₂×C₄

#13063253

yes

—

213

C₂×C₄

C₄×D₁₇₂

yes

—

214

C₂×C₄

#13063299

yes

—

215

C₂×C₄

#13063313

yes

characteristic

216

C₂×C₄

#13063322

yes

characteristic

217

C₂×C₄

M₁₆×D₄₃

yes

—

218

C₂×C₄

#13063333

yes

—

219

C₂×C₄

#13063353

yes

—

220

C₈

—

221

C₈

—

344

—

222

C₂²

—

344

—

223

C₂²

—

344

—

224

C₂²

—

344

—

225

C₂²

—

172

—

226

C₂²

—

172

—

227

C₂²

#14582801

yes

characteristic

228

C₂²

#14582862

yes

characteristic

229

C₂²

#14582867

yes

characteristic

230

C₂²

#14582905

yes

—

231

C₂²

C₂×#13063253

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

344

—

236

C₄

#14582972

yes

—

237

C₄

#14583264

yes

—

238

C₄

#14583288

yes

—

239

C₂

—

344

—

240

C₂

#19133013

yes

—

241

C₂

#19133039

yes

—

242

C₂

#19135393

yes

characteristic

243

C₂

#19135419

yes

characteristic

244

C₂

#19135423

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄×#97×C₄₃	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×#13063322	C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₄×#97	D₄₃
hypocenter	C₄₃	#9648
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

subgroup

G/H

center

C₂²×C₄

C₂×D₁₇₂

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄×#97×C₄₃

C₂

socle

C₂³×C₄₃

C₂×C₂²⋊C₄

prime radical

C₂×#13063322

C₄

cosocle

C₂×C₄²×C₄₃

C₂³

hypercenter

C₄×#97

D₄₃

hypocenter

C₄₃

#9648

LCS

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
2. #19134712	C₂	semidirect
3. C₂×#14582628	C₂	semidirect
4. C₄×#97×C₄₃	C₂	semidirect
38. C₄×C₈×C₄₃	D₄	semidirect
119. C₄×#97	D₄₃	semidirect
139. C₄₃	#9648	semidirect
161. C₄×C₈	D₁₇₂	semidirect

H ≅ G/N

type

2. #19134712

C₂

semidirect

3. C₂×#14582628

C₂

semidirect

4. C₄×#97×C₄₃

C₂

semidirect

38. C₄×C₈×C₄₃

D₄

semidirect

119. C₄×#97

D₄₃

semidirect

139. C₄₃

#9648

semidirect

161. C₄×C₈

D₁₇₂

semidirect

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

subgroup	index
C₄×#13063322	2
#19134712	2
C₂×#14582628	2
C₄×#97×C₄₃	2
#9648	43

subgroup

index

C₄×#97×C₄₃

Subgroups — #24995417

Conjugacy classes of subgroups

Complements

Maximal subgroups