Group #24995497 — subgroups

Subgroups — #24995497

Order 11008.

482 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 147 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×C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	#19135530	C₂	1	2	yes	maximal
3	C₂×#14582629	C₂	1	2	yes	maximal
4	C₂×#14582621	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₃×#334	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₇₂	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
8	C₄×Dic₁₇₂	—	2	2	no	—
9	C₄×Dic₁₇₂	—	2	2	no	—
10	C₂×#13063259	C₄	1	1	yes	characteristic
11	C₂×#13063250	C₄	1	2	yes	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582653	—	2	4	no	—
15	#14582629	—	2	4	no	—
16	#14582621	—	2	2	no	—
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#334	—	2	2	no	—
20	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
21	C₂×Dic₁₇₂	—	2	4	no	—
22	C₂×Dic₁₇₂	—	2	2	no	—
23	C₂²×C₄₃⋊C₈	—	2	1	no	—
24	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
25	C₄×Dic₈₆	—	2	2	no	—
26	C₄×Dic₈₆	—	2	2	no	—
27	C₄×Dic₈₆	—	2	2	no	—
28	C₄×Dic₈₆	—	2	2	no	—
29	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
30	C₂×Dic₄₃⋊C₄	—	2	2	no	—
31	C₂×C₄×Dic₄₃	—	2	2	no	—
32	#13063259	—	2	2	no	—
33	#13063250	—	2	4	no	—
34	C₄×C₄₃⋊C₈	—	2	1	no	—
35	C₄×C₄₃⋊C₈	—	2	1	no	—
36	C₄×C₄₃⋊C₈	—	2	1	no	—
37	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
38	C₂²×C₈×C₄₃	—	2	2	no	—
39	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₃	—	2	2	no	—
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₄×C₈×C₄₃	D₄	1	2	yes	—
45	C₄×C₈×C₄₃	D₄	1	2	yes	—
46	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
49	C₂²×Dic₄₃	—	2	2	no	—
50	C₂²×Dic₄₃	—	2	2	no	—
51	C₂×Dic₈₆	—	2	2	no	—
52	C₂×Dic₈₆	—	2	2	no	—
53	C₂×Dic₈₆	—	2	2	no	—
54	C₂×Dic₈₆	—	2	2	no	—
55	C₂×Dic₈₆	—	2	2	no	—
56	C₂×Dic₈₆	M₁₆	1	4	yes	—
57	C₂×C₈×C₄₃	—	2	2	no	—
58	C₂×C₈×C₄₃	—	2	2	no	—
59	C₂×C₈×C₄₃	—	4	2	no	—
60	C₂×C₈×C₄₃	—	4	4	no	—
61	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₄₃	#41	1	1	yes	characteristic
67	C₄⋊Dic₄₃	—	2	2	no	—
68	C₄⋊Dic₄₃	—	2	2	no	—
69	Dic₄₃⋊C₄	—	4	2	no	—
70	Dic₄₃⋊C₄	—	4	2	no	—
71	C₄×Dic₄₃	—	4	2	no	—
72	C₄×Dic₄₃	—	4	2	no	—
73	C₂×C₄₃⋊C₈	—	2	4	no	—
74	C₂×C₄₃⋊C₈	—	2	2	no	—
75	C₂×C₄₃⋊C₈	—	2	2	no	—
76	C₂×C₄₃⋊C₈	—	2	4	no	—
77	Dic₁₇₂	—	2	8	no	—
78	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₄₃	#131	1	2	yes	—
88	C₂×C₄×C₄₃	#137	1	4	yes	—
89	C₂×Dic₄₃	—	2	4	no	—
90	C₂×Dic₄₃	—	4	2	no	—
91	C₂×Dic₄₃	—	4	2	no	—
92	C₂×Dic₄₃	—	4	2	no	—
93	C₂×Dic₄₃	—	4	4	no	—
94	Dic₈₆	—	2	4	no	—
95	Dic₈₆	—	2	4	no	—
96	Dic₈₆	—	4	2	no	—
97	Dic₈₆	—	4	2	no	—
98	C₈×C₄₃	—	2	2	no	—
99	C₈×C₄₃	—	2	2	no	—
100	C₈×C₄₃	—	8	2	no	—
101	C₄₃⋊C₈	—	2	4	no	—
102	C₄₃⋊C₈	—	4	2	no	—
103	#9664	—	43	1	no	maximal, Sylow
104	C₂²×C₄₃	#390	1	1	yes	characteristic
105	C₂²×C₄₃	#435	1	2	yes	—
106	C₂²×C₄₃	#441	1	2	yes	—
107	C₂²×C₄₃	#443	1	2	yes	—
108	C₄×C₄₃	—	2	1	no	—
109	C₄×C₄₃	—	2	1	no	—
110	C₄×C₄₃	#407	1	1	yes	characteristic
111	C₄×C₄₃	#408	1	1	yes	characteristic
112	C₄×C₄₃	#435	1	2	yes	—
113	C₄×C₄₃	#470	1	2	yes	—
114	C₄×C₄₃	#497	1	2	yes	—
115	Dic₄₃	—	4	4	no	—
116	Dic₄₃	—	8	2	no	—
117	C₂×C₄×Q₁₆	—	43	1	no	—
118	#1984	—	43	2	no	—
119	C₂×#334	D₄₃	1	1	yes	characteristic
120	C₂×Q₈⋊C₈	—	43	2	no	—
121	C₂×#322	—	43	1	no	—
122	C₂×C₄₃	#1587	1	4	yes	—
123	C₂×C₄₃	#1955	1	1	yes	characteristic
124	C₂×C₄₃	#1971	1	1	yes	characteristic
125	C₂×C₄₃	#1974	1	1	yes	characteristic
126	C₂²×Q₁₆	—	43	1	no	—
127	C₂×C₄×Q₈	—	43	2	no	—
128	C₄×Q₁₆	—	86	2	no	—
129	C₄×Q₁₆	—	86	2	no	—
130	C₂×#107	—	43	1	no	—
131	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
132	C₂×#103	—	43	2	no	—
133	C₂×C₄×C₈	—	43	1	no	—
134	C₂×C₄×C₈	—	43	1	no	—
135	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
136	#336	—	86	4	no	—
137	#334	—	2	2	no	—
138	Q₈⋊C₈	—	86	4	no	—
139	#322	—	86	2	no	—
140	C₄₃	#9664	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	43	2	no	—
142	C₂×Q₁₆	—	86	4	no	—
143	C₂×Q₁₆	—	86	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	43	2	no	—
146	C₂²×C₈	—	86	1	no	—
147	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
148	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
149	C₄×Q₈	—	86	2	no	—
150	C₄×Q₈	—	86	2	no	—
151	C₄×Q₈	—	86	2	no	—
152	C₄×Q₈	—	86	2	no	—
153	C₂×C₄⋊C₄	—	43	2	no	—
154	C₂×C₄⋊C₄	—	86	2	no	—
155	C₂×C₄²	—	86	2	no	—
156	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
157	#107	—	86	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	#103	—	86	4	no	—
161	C₄×C₈	—	43	2	no	—
162	C₄×C₈	—	86	1	no	—
163	C₄×C₈	—	86	1	no	—
164	C₄×C₈	—	86	1	no	—
165	C₄×C₈	D₁₇₂	1	2	yes	—
166	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
167	C₂×Q₈	—	43	4	no	—
168	C₂×Q₈	—	86	2	no	—
169	C₂×Q₈	—	86	2	no	—
170	C₂×Q₈	—	86	2	no	—
171	C₂×Q₈	—	86	2	no	—
172	C₂×Q₈	—	86	2	no	—
173	C₂²×C₄	—	86	2	no	—
174	C₂²×C₄	—	86	2	no	—
175	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
177	C₂²×C₄	#10621902	1	1	yes	characteristic
178	Q₁₆	—	86	8	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	4	no	—
183	C₂×C₈	—	86	4	no	—
184	C₂×C₈	—	86	2	no	—
185	C₂×C₈	—	86	2	no	—
186	C₂×C₈	—	86	4	no	—
187	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
188	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
189	C₄⋊C₄	—	86	2	no	—
190	C₄⋊C₄	—	86	2	no	—
191	C₄⋊C₄	—	172	2	no	—
192	C₄⋊C₄	—	172	2	no	—
193	C₄²	—	172	2	no	—
194	C₄²	—	172	2	no	—
195	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
196	C₄²	D₄×D₄₃	1	1	yes	characteristic
197	C₄²	#10621902	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
199	C₂³	#13063287	1	1	yes	characteristic
200	Q₈	—	86	4	no	—
201	Q₈	—	86	4	no	—
202	Q₈	—	172	2	no	—
203	Q₈	—	172	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	86	4	no	—
206	C₂×C₄	—	172	2	no	—
207	C₂×C₄	—	172	4	no	—
208	C₂×C₄	—	172	2	no	—
209	C₂×C₄	—	172	2	no	—
210	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
211	C₂×C₄	#13063287	1	1	yes	characteristic
212	C₂×C₄	#13063300	1	1	yes	characteristic
213	C₂×C₄	#13063300	1	1	yes	characteristic
214	C₂×C₄	#13063314	1	1	yes	characteristic
215	C₂×C₄	#13063321	1	1	yes	characteristic
216	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
217	C₂×C₄	#13063331	1	2	yes	—
218	C₂×C₄	#13063354	1	4	yes	—
219	C₈	—	2	2	no	—
220	C₈	—	2	2	no	—
221	C₈	—	8	2	no	—
222	C₈	—	86	4	no	—
223	C₈	—	172	2	no	—
224	C₂²	#14582800	1	1	yes	characteristic
225	C₂²	#14582969	1	2	yes	—
226	C₂²	#14583005	1	2	yes	—
227	C₂²	#14583015	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	344	2	no	—
231	C₄	—	172	4	no	—
232	C₄	#14582862	1	1	yes	characteristic
233	C₄	#14582865	1	1	yes	characteristic
234	C₄	#14582969	1	2	yes	—
235	C₄	#14583158	1	2	yes	—
236	C₄	#14583290	1	2	yes	—
237	C₂	#19133465	1	4	yes	—
238	C₂	#19135392	1	1	yes	characteristic
239	C₂	#19135464	1	1	yes	characteristic
240	C₂	#19135481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₁₇₂

C₂

yes

maximal, characteristic

#19135530

C₂

yes

maximal

C₂×#14582629

C₂

yes

maximal

C₂×#14582621

C₂

yes

maximal, characteristic

C₂×C₄₃×#334

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₄

yes

characteristic

C₂×C₄×Dic₈₆

C₂²

yes

—

C₄×Dic₁₇₂

—

C₄×Dic₁₇₂

—

C₂×#13063259

C₄

yes

characteristic

C₂×#13063250

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#334

—

C₂²×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

D₄

yes

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

#13063259

—

#13063250

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄×C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

M₁₆

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂³×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

100

C₈×C₄₃

—

101

C₄₃⋊C₈

—

102

C₄₃⋊C₈

—

103

#9664

—

maximal, Sylow

104

C₂²×C₄₃

#390

yes

characteristic

105

C₂²×C₄₃

#435

yes

—

106

C₂²×C₄₃

#441

yes

—

107

C₂²×C₄₃

#443

yes

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

#407

yes

characteristic

111

C₄×C₄₃

#408

yes

characteristic

112

C₄×C₄₃

#435

yes

—

113

C₄×C₄₃

#470

yes

—

114

C₄×C₄₃

#497

yes

—

115

Dic₄₃

—

116

Dic₄₃

—

117

C₂×C₄×Q₁₆

—

118

#1984

—

119

C₂×#334

D₄₃

yes

characteristic

120

C₂×Q₈⋊C₈

—

121

C₂×#322

—

122

C₂×C₄₃

#1587

yes

—

123

C₂×C₄₃

#1955

yes

characteristic

124

C₂×C₄₃

#1971

yes

characteristic

125

C₂×C₄₃

#1974

yes

characteristic

126

C₂²×Q₁₆

—

127

C₂×C₄×Q₈

—

128

C₄×Q₁₆

—

129

C₄×Q₁₆

—

130

C₂×#107

—

131

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

132

C₂×#103

—

133

C₂×C₄×C₈

—

134

C₂×C₄×C₈

—

135

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

136

#336

—

137

#334

—

138

Q₈⋊C₈

—

139

#322

—

140

C₄₃

#9664

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

—

142

C₂×Q₁₆

—

143

C₂×Q₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

C₄×D₄₃

yes

characteristic

148

C₂²×C₈

C₄×D₄₃

yes

characteristic

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₄₃

yes

characteristic

157

#107

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

161

C₄×C₈

—

162

C₄×C₈

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

D₁₇₂

yes

—

166

C₄×C₈

C₂²⋊D₄₃

yes

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

176

C₂²×C₄

D₄×D₄₃

yes

characteristic

177

C₂²×C₄

#10621902

yes

characteristic

178

Q₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

188

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

172

—

192

C₄⋊C₄

—

172

—

193

C₄²

—

172

—

194

C₄²

—

172

—

195

C₄²

C₂×D₁₇₂

yes

characteristic

196

C₄²

D₄×D₄₃

yes

characteristic

197

C₄²

#10621902

yes

characteristic

198

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

199

C₂³

#13063287

yes

characteristic

200

Q₈

—

201

Q₈

—

202

Q₈

—

172

—

203

Q₈

—

172

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

172

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

211

C₂×C₄

#13063287

yes

characteristic

212

C₂×C₄

#13063300

yes

characteristic

213

C₂×C₄

#13063300

yes

characteristic

214

C₂×C₄

#13063314

yes

characteristic

215

C₂×C₄

#13063321

yes

characteristic

216

C₂×C₄

M₁₆×D₄₃

yes

—

217

C₂×C₄

#13063331

yes

—

218

C₂×C₄

#13063354

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

172

—

224

C₂²

#14582800

yes

characteristic

225

C₂²

#14582969

yes

—

226

C₂²

#14583005

yes

—

227

C₂²

#14583015

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

344

—

231

C₄

—

172

—

232

C₄

#14582862

yes

characteristic

233

C₄

#14582865

yes

characteristic

234

C₄

#14582969

yes

—

235

C₄

#14583158

yes

—

236

C₄

#14583290

yes

—

237

C₂

#19133465

yes

—

238

C₂

#19135392

yes

characteristic

239

C₂

#19135464

yes

characteristic

240

C₂

#19135481

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#334	C₂
socle, prime radical	C₂³×C₄₃	C₄×D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#334	D₄₃
hypocenter	C₄₃	#9664
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

subgroup

G/H

center

C₂²×C₄

D₄×D₄₃

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₂×C₄₃×#334

C₂

socle, prime radical

C₂³×C₄₃

C₄×D₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

N	H ≅ G/N	type
140. C₄₃	#9664	semidirect

H ≅ G/N

type

140. C₄₃

#9664

semidirect

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

subgroup	index
C₂×C₄×Dic₁₇₂	2
#19135530	2
C₂×#14582629	2
C₂×#14582621	2
C₂×C₄₃×#334	2
#9664	43

subgroup

index

C₂×C₄×Dic₁₇₂

C₂×C₄₃×#334

Subgroups — #24995497

Conjugacy classes of subgroups

Complements

Maximal subgroups