Group #24995803 — subgroups

Subgroups — #24995803

Order 11008.

392 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 115 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×#13063261	C₂	1	1	yes	maximal, characteristic
2	#19133190	C₂	1	2	yes	maximal
3	#19133016	C₂	1	2	yes	maximal
4	#19132884	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#3170	C₂	1	1	yes	maximal, characteristic
6	#14582952	C₂²	1	1	yes	characteristic
7	C₂×#13063261	—	2	1	no	—
8	C₄×#10621877	C₂²	1	2	yes	—
9	C₄×#10621877	C₂²	1	1	yes	characteristic
10	#14582664	—	2	1	no	—
11	#14582641	—	2	4	no	—
12	Q₈⋊(C₄₃⋊C₈)	—	2	4	no	—
13	#14582621	—	2	1	no	—
14	#14582620	—	2	1	no	—
15	C₄₃×#533	C₂²	1	2	yes	—
16	C₄₃×#500	C₄	1	1	yes	characteristic
17	C₄₃×#494	C₄	1	1	yes	characteristic
18	C₄₃×#487	C₄	1	2	yes	—
19	C₄₃×#467	—	2	1	no	—
20	C₄₃×#467	—	2	1	no	—
21	C₄×Q₁₆×C₄₃	—	2	1	no	—
22	C₄×Q₁₆×C₄₃	—	2	1	no	—
23	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#10621877	—	2	1	no	—
25	C₂×#10621877	—	2	2	no	—
26	#13063261	—	2	4	no	—
27	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
28	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
29	#13063236	—	2	2	no	—
30	#13063236	D₄	1	2	yes	—
31	C₄×C₄₃⋊C₈	—	2	1	no	—
32	C₄×C₄₃⋊C₈	—	2	1	no	—
33	C₄×C₄₃⋊C₈	—	2	2	no	—
34	C₂×Q₁₆×C₄₃	—	2	1	no	—
35	C₂×Q₁₆×C₄₃	—	2	1	no	—
36	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
38	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
39	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
40	#125×C₄₃	—	2	2	no	—
41	C₂²⋊Q₈×C₄₃	—	2	2	no	—
42	C₂²⋊Q₈×C₄₃	—	2	2	no	—
43	C₄×Q₈×C₄₃	—	2	2	no	—
44	C₄×Q₈×C₄₃	—	2	2	no	—
45	#117×C₄₃	—	2	2	no	—
46	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
47	#107×C₄₃	—	2	1	no	—
48	#107×C₄₃	—	2	1	no	—
49	#103×C₄₃	—	2	2	no	—
50	#103×C₄₃	—	2	2	no	—
51	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
54	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
55	C₂×Q₈×C₄₃	—	2	2	no	—
56	C₂×Q₈×C₄₃	—	2	2	no	—
57	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
59	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
60	Q₁₆×C₄₃	—	4	2	no	—
61	Q₁₆×C₄₃	—	4	2	no	—
62	C₂×C₈×C₄₃	—	2	2	no	—
63	C₂×C₈×C₄₃	—	4	1	no	—
64	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
68	C₄⋊C₄×C₄₃	—	2	2	no	—
69	C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₄⋊C₄×C₄₃	—	2	2	no	—
72	C₄⋊C₄×C₄₃	—	4	2	no	—
73	C₄⋊C₄×C₄₃	—	4	2	no	—
74	C₂²⋊C₄×C₄₃	—	4	2	no	—
75	C₄²×C₄₃	—	4	2	no	—
76	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
80	#10621877	—	2	4	no	—
81	#10621877	—	4	2	no	—
82	#10621877	—	4	2	no	—
83	C₂×C₄₃⋊C₈	—	2	2	no	—
84	C₂×C₄₃⋊C₈	—	2	2	no	—
85	C₂×C₄₃⋊C₈	—	4	2	no	—
86	C₂³×C₄₃	#124	1	1	yes	characteristic
87	Q₈×C₄₃	—	4	2	no	—
88	Q₈×C₄₃	—	4	2	no	—
89	Q₈×C₄₃	—	4	4	no	—
90	C₂×C₄×C₄₃	—	2	1	no	—
91	C₂×C₄×C₄₃	—	2	1	no	—
92	C₂×C₄×C₄₃	—	2	2	no	—
93	C₂×C₄×C₄₃	—	2	2	no	—
94	C₂×C₄×C₄₃	—	4	2	no	—
95	C₂×C₄×C₄₃	—	4	2	no	—
96	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
100	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
101	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
102	C₈×C₄₃	—	2	1	no	—
103	C₈×C₄₃	—	2	1	no	—
104	C₈×C₄₃	—	2	1	no	—
105	C₈×C₄₃	#104	1	2	yes	—
106	C₄₃⋊C₈	—	4	2	no	—
107	C₄₃⋊C₈	—	4	4	no	—
108	C₄₃⋊C₈	—	4	2	no	—
109	#9727	—	43	1	no	maximal, Sylow
110	C₂²×C₄₃	—	2	1	no	—
111	C₂²×C₄₃	—	2	1	no	—
112	C₂²×C₄₃	—	2	1	no	—
113	C₂²×C₄₃	#390	1	1	yes	characteristic
114	C₄×C₄₃	—	2	1	no	—
115	C₄×C₄₃	—	2	1	no	—
116	C₄×C₄₃	—	2	1	no	—
117	C₄×C₄₃	—	8	2	no	—
118	C₄×C₄₃	—	8	2	no	—
119	C₄×C₄₃	C₂×#104	1	1	yes	characteristic
120	C₄×C₄₃	#421	1	1	yes	characteristic
121	C₄×C₄₃	#444	1	2	yes	—
122	C₄×C₄₃	#473	1	2	yes	—
123	#3170	D₄₃	1	1	yes	characteristic
124	C₄×#108	—	43	1	no	—
125	#1526	—	43	2	no	—
126	#1485	—	43	2	no	—
127	#1451	—	43	1	no	—
128	C₂×C₄₃	—	4	1	no	—
129	C₂×C₄₃	#1975	1	1	yes	characteristic
130	C₂×C₄₃	#1979	1	1	yes	characteristic
131	C₂×C₄₃	#1980	1	1	yes	characteristic
132	#533	C₂×D₄₃	1	2	yes	—
133	#500	Dic₄₃	1	1	yes	characteristic
134	#494	Dic₄₃	1	1	yes	characteristic
135	#487	Dic₄₃	1	2	yes	—
136	#467	—	2	1	no	—
137	#467	—	2	1	no	—
138	C₄×Q₁₆	—	2	1	no	—
139	C₄×Q₁₆	—	2	1	no	—
140	#431	—	43	1	no	—
141	C₂×#108	—	86	1	no	—
142	C₄×M₁₆	—	43	1	no	—
143	C₄×M₁₆	—	43	2	no	—
144	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
145	#341	—	86	1	no	—
146	#330	—	86	4	no	—
147	Q₈⋊C₈	—	86	4	no	—
148	#322	—	86	1	no	—
149	#322	—	86	1	no	—
150	C₄₃	#9727	1	1	yes	characteristic, complemented, Sylow
151	C₂×Q₁₆	—	2	1	no	—
152	C₂×Q₁₆	—	2	1	no	—
153	C₂×M₁₆	—	86	1	no	—
154	C₂×M₁₆	—	86	2	no	—
155	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
156	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
157	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
158	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
159	#125	—	2	2	no	—
160	C₂²⋊Q₈	—	2	2	no	—
161	C₂²⋊Q₈	—	2	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	#117	—	2	2	no	—
165	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
166	#108	—	86	4	no	—
167	#107	—	2	1	no	—
168	#107	—	2	1	no	—
169	C₄⋊C₈	—	43	2	no	—
170	#103	—	2	2	no	—
171	#103	—	2	2	no	—
172	C₂²⋊C₈	—	86	1	no	—
173	#97	—	43	2	no	—
174	#97	—	86	2	no	—
175	C₄×C₈	—	86	2	no	—
176	C₄×C₈	—	86	1	no	—
177	C₄×C₈	—	86	1	no	—
178	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
179	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
181	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂²×C₄	#10621900	1	1	yes	characteristic
185	C₂²×C₄	#10621900	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
187	Q₁₆	—	4	2	no	—
188	Q₁₆	—	4	2	no	—
189	M₁₆	—	86	4	no	—
190	M₁₆	—	172	2	no	—
191	M₁₆	—	172	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	86	2	no	—
195	C₂×C₈	—	86	2	no	—
196	C₂×C₈	—	172	2	no	—
197	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
198	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
199	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
200	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₄²	—	4	2	no	—
209	C₄²	D₄×D₄₃	1	1	yes	characteristic
210	C₄²	D₄×D₄₃	1	1	yes	characteristic
211	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
212	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
213	C₂³	#13063312	1	1	yes	characteristic
214	Q₈	—	4	2	no	—
215	Q₈	—	4	2	no	—
216	Q₈	—	4	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
224	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
225	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
226	C₂×C₄	#13063296	1	1	yes	characteristic
227	C₂×C₄	#13063296	1	1	yes	characteristic
228	C₂×C₄	#13063321	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	172	2	no	—
233	C₈	—	172	4	no	—
234	C₈	—	172	2	no	—
235	C₈	#13063252	1	2	yes	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#14582802	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	8	2	no	—
244	C₄	—	8	2	no	—
245	C₄	C₂×#13063252	1	1	yes	characteristic
246	C₄	#14582916	1	1	yes	characteristic
247	C₄	#14583021	1	2	yes	—
248	C₄	#14583171	1	2	yes	—
249	C₂	—	4	1	no	—
250	C₂	#19135489	1	1	yes	characteristic
251	C₂	#19135511	1	1	yes	characteristic
252	C₂	#19135515	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063261

C₂

yes

maximal, characteristic

#19133190

C₂

yes

maximal

#19133016

C₂

yes

maximal

#19132884

C₂

yes

maximal, characteristic

C₄₃×#3170

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

characteristic

C₂×#13063261

—

C₄×#10621877

C₂²

yes

—

C₄×#10621877

C₂²

yes

characteristic

#14582664

—

#14582641

—

Q₈⋊(C₄₃⋊C₈)

—

#14582621

—

#14582620

—

C₄₃×#533

C₂²

yes

—

C₄₃×#500

C₄

yes

characteristic

C₄₃×#494

C₄

yes

characteristic

C₄₃×#487

C₄

yes

—

C₄₃×#467

—

C₄₃×#467

—

C₄×Q₁₆×C₄₃

—

C₄×Q₁₆×C₄₃

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

—

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

#13063236

D₄

yes

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

#125×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#107×C₄₃

—

#107×C₄₃

—

#103×C₄₃

—

#103×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

C₂²×C₄×C₄₃

yes

C₂²×C₄×C₄₃

yes

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#124

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

#121

yes

characteristic

100

C₂×C₄×C₄₃

#121

yes

characteristic

101

C₂×C₄×C₄₃

#127

yes

characteristic

102

C₈×C₄₃

—

103

C₈×C₄₃

—

104

C₈×C₄₃

—

105

C₈×C₄₃

#104

yes

—

106

C₄₃⋊C₈

—

107

C₄₃⋊C₈

—

108

C₄₃⋊C₈

—

109

#9727

—

maximal, Sylow

110

C₂²×C₄₃

—

111

C₂²×C₄₃

—

112

C₂²×C₄₃

—

113

C₂²×C₄₃

#390

yes

characteristic

114

C₄×C₄₃

—

115

C₄×C₄₃

—

116

C₄×C₄₃

—

117

C₄×C₄₃

—

118

C₄×C₄₃

—

119

C₄×C₄₃

C₂×#104

yes

characteristic

120

C₄×C₄₃

#421

yes

characteristic

121

C₄×C₄₃

#444

yes

—

122

C₄×C₄₃

#473

yes

—

123

#3170

D₄₃

yes

characteristic

124

C₄×#108

—

125

#1526

—

126

#1485

—

127

#1451

—

128

C₂×C₄₃

—

129

C₂×C₄₃

#1975

yes

characteristic

130

C₂×C₄₃

#1979

yes

characteristic

131

C₂×C₄₃

#1980

yes

characteristic

132

#533

C₂×D₄₃

yes

—

133

#500

Dic₄₃

yes

characteristic

134

#494

Dic₄₃

yes

characteristic

135

#487

Dic₄₃

yes

—

136

#467

—

137

#467

—

138

C₄×Q₁₆

—

139

C₄×Q₁₆

—

140

#431

—

141

C₂×#108

—

142

C₄×M₁₆

—

143

C₄×M₁₆

—

144

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

145

#341

—

146

#330

—

147

Q₈⋊C₈

—

148

#322

—

149

#322

—

150

C₄₃

#9727

yes

characteristic, complemented, Sylow

151

C₂×Q₁₆

—

152

C₂×Q₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

156

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

157

C₄⋊Q₈

C₂×Dic₄₃

yes

—

158

C₄⋊Q₈

C₂×Dic₄₃

yes

—

159

#125

—

160

C₂²⋊Q₈

—

161

C₂²⋊Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

#117

—

165

C₂×C₄²

C₂²×D₄₃

yes

characteristic

166

#108

—

167

#107

—

168

#107

—

169

C₄⋊C₈

—

170

#103

—

171

#103

—

172

C₂²⋊C₈

—

173

#97

—

174

#97

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₄×C₈

C₂×Dic₄₃

yes

characteristic

179

C₄×C₈

C₂×Dic₄₃

yes

characteristic

180

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

181

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂²×C₄

#10621900

yes

characteristic

185

C₂²×C₄

#10621900

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

187

Q₁₆

—

188

Q₁₆

—

189

M₁₆

—

190

M₁₆

—

172

—

191

M₁₆

—

172

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

172

—

197

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

198

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

199

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

200

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₄²

D₄×D₄₃

yes

characteristic

210

C₄²

D₄×D₄₃

yes

characteristic

211

C₄²

C₂²×Dic₄₃

yes

characteristic

212

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

213

C₂³

#13063312

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

224

C₂×C₄

D₄×Dic₄₃

yes

characteristic

225

C₂×C₄

D₄×Dic₄₃

yes

characteristic

226

C₂×C₄

#13063296

yes

characteristic

227

C₂×C₄

#13063296

yes

characteristic

228

C₂×C₄

#13063321

yes

characteristic

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

172

—

233

C₈

—

172

—

234

C₈

—

172

—

235

C₈

#13063252

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#14582802

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

C₂×#13063252

yes

characteristic

246

C₄

#14582916

yes

characteristic

247

C₄

#14583021

yes

—

248

C₄

#14583171

yes

—

249

C₂

—

250

C₂

#19135489

yes

characteristic

251

C₂

#19135511

yes

characteristic

252

C₂

#19135515

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063296
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#3170	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	#124
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#3170	D₄₃
hypocenter	C₄₃	#9727
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#13063296

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#3170

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
150. C₄₃	#9727	semidirect

H ≅ G/N

type

150. C₄₃

#9727

semidirect

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

subgroup	index
C₄×#13063261	2
#19133190	2
#19133016	2
#19132884	2
C₄₃×#3170	2
#9727	43

subgroup

index

C₄₃×#3170

Subgroups — #24995803

Conjugacy classes of subgroups

Complements

Maximal subgroups