Group #24928362 — subgroups

Subgroups — C₄₃×#8345 #24928362

Order 11008.

802 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 198 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×C₄₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1797	C₂	1	2	yes	maximal
3	C₂×C₄₃×#332	C₂	1	4	yes	maximal, complemented
4	C₄₃×#533	—	2	8	no	—
5	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
6	C₂×#125×C₄₃	C₄	1	2	yes	—
7	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
8	C₂×C₄×Q₈×C₄₃	—	2	2	no	—
9	C₂×#117×C₄₃	C₄	1	2	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
12	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
13	C₄₃×#336	—	2	2	no	—
14	C₄₃×#332	—	2	8	no	—
15	C₂²×Q₈×C₄₃	—	2	2	no	—
16	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₄₃	D₄	1	2	yes	—
18	C₂²×C₈×C₄₃	—	2	4	no	—
19	C₄⋊Q₈×C₄₃	—	2	4	no	—
20	C₄⋊Q₈×C₄₃	D₄	1	8	yes	—
21	#125×C₄₃	—	2	8	no	—
22	C₂²⋊Q₈×C₄₃	—	2	16	no	—
23	C₄×Q₈×C₄₃	—	2	16	no	—
24	#117×C₄₃	—	2	8	no	—
25	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
28	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
29	C₂×C₄²×C₄₃	—	2	2	no	—
30	C₂×C₄²×C₄₃	—	2	4	no	—
31	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₃	D₄	1	2	yes	—
33	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	C₄⋊C₈×C₄₃	—	2	8	no	—
35	C₂²⋊C₈×C₄₃	—	4	4	no	—
36	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Q₈×C₄₃	—	2	8	no	—
38	C₂×Q₈×C₄₃	—	4	4	no	—
39	C₂×Q₈×C₄₃	—	4	2	no	—
40	C₂×Q₈×C₄₃	—	4	2	no	—
41	C₂²×C₄×C₄₃	—	2	2	no	—
42	C₂²×C₄×C₄₃	—	2	2	no	—
43	C₂²×C₄×C₄₃	—	2	4	no	—
44	C₂²×C₄×C₄₃	—	2	4	no	—
45	C₂²×C₄×C₄₃	—	2	2	no	—
46	C₂²×C₄×C₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	—	2	2	no	—
48	C₂²×C₄×C₄₃	—	2	4	no	—
49	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₄₃	—	4	4	no	—
54	C₂×C₈×C₄₃	—	4	4	no	—
55	C₂×C₈×C₄₃	—	4	4	no	—
56	C₄⋊C₄×C₄₃	—	2	16	no	—
57	C₄⋊C₄×C₄₃	—	2	4	no	—
58	C₄⋊C₄×C₄₃	—	2	8	no	—
59	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
60	C₂²⋊C₄×C₄₃	—	2	8	no	—
61	C₄²×C₄₃	—	2	8	no	—
62	C₄²×C₄₃	—	2	2	no	—
63	C₄²×C₄₃	—	2	4	no	—
64	C₄²×C₄₃	C₂×D₄	1	4	yes	—
65	C₂³×C₄₃	—	2	1	no	—
66	C₂³×C₄₃	—	2	1	no	—
67	C₂³×C₄₃	—	2	2	no	—
68	C₂³×C₄₃	—	2	2	no	—
69	C₂³×C₄₃	#101	1	2	yes	—
70	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	Q₈×C₄₃	—	4	8	no	—
72	Q₈×C₄₃	—	4	8	no	—
73	C₂×C₄×C₄₃	—	2	8	no	—
74	C₂×C₄×C₄₃	—	2	1	no	—
75	C₂×C₄×C₄₃	—	2	1	no	—
76	C₂×C₄×C₄₃	—	2	1	no	—
77	C₂×C₄×C₄₃	—	2	1	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	8	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	—	4	4	no	—
83	C₂×C₄×C₄₃	—	4	4	no	—
84	C₂×C₄×C₄₃	—	4	4	no	—
85	C₂×C₄×C₄₃	—	4	4	no	—
86	C₂×C₄×C₄₃	#101	1	2	yes	—
87	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×C₄₃	#120	1	4	yes	—
89	C₂×C₄×C₄₃	#135	1	4	yes	—
90	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
91	C₂×C₄×C₄₃	#137	1	2	yes	—
92	C₈×C₄₃	—	8	4	no	—
93	#8345	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂²×C₄₃	—	2	4	no	—
95	C₂²×C₄₃	—	2	2	no	—
96	C₂²×C₄₃	—	4	1	no	—
97	C₂²×C₄₃	—	4	1	no	—
98	C₂²×C₄₃	—	4	2	no	—
99	C₂²×C₄₃	#379	1	1	yes	characteristic
100	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
101	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
102	C₂²×C₄₃	#416	1	2	yes	—
103	C₂²×C₄₃	#417	1	2	yes	—
104	C₄×C₄₃	—	2	2	no	—
105	C₄×C₄₃	—	2	2	no	—
106	C₄×C₄₃	—	4	2	no	—
107	C₄×C₄₃	—	4	8	no	—
108	C₄×C₄₃	#449	1	4	yes	—
109	C₄×C₄₃	#452	1	4	yes	—
110	C₂×#533	C₂×C₄₃	1	1	yes	characteristic
111	#1797	C₂×C₄₃	1	2	yes	—
112	C₂×#332	C₂×C₄₃	1	4	yes	complemented
113	C₂×C₄₃	—	4	2	no	—
114	C₂×C₄₃	#1544	1	1	yes	characteristic
115	C₂×C₄₃	#1552	1	2	yes	—
116	C₂×C₄₃	#1561	1	1	yes	characteristic
117	C₂×C₄₃	#1784	1	1	yes	characteristic
118	C₂×C₄₃	#1788	1	2	yes	—
119	#533	—	2	8	no	—
120	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
121	C₂×#125	C₄×C₄₃	1	2	yes	—
122	C₂×C₂²⋊Q₈	—	2	2	no	—
123	C₂×C₄×Q₈	—	2	2	no	—
124	C₂×#117	C₄×C₄₃	1	2	yes	—
125	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
126	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
127	C₂×C₂²⋊C₈	—	2	2	no	—
128	#336	—	2	2	no	—
129	#332	—	2	8	no	—
130	C₄₃	#8345	1	1	yes	characteristic, direct product factor, Sylow
131	C₂²×Q₈	—	2	2	no	—
132	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
133	C₂³×C₄	D₄×C₄₃	1	2	yes	—
134	C₂²×C₈	—	2	4	no	—
135	C₄⋊Q₈	—	2	4	no	—
136	C₄⋊Q₈	D₄×C₄₃	1	8	yes	—
137	#125	—	2	8	no	—
138	C₂²⋊Q₈	—	2	16	no	—
139	C₄×Q₈	—	2	16	no	—
140	#117	—	2	8	no	—
141	C₂×C₄⋊C₄	—	2	4	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
144	C₂×C₂²⋊C₄	—	2	2	no	—
145	C₂×C₄²	—	2	2	no	—
146	C₂×C₄²	—	2	4	no	—
147	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
148	C₂×C₄²	D₄×C₄₃	1	2	yes	—
149	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
150	C₄⋊C₈	—	2	8	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
153	C₂×Q₈	—	2	8	no	—
154	C₂×Q₈	—	4	4	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	4	no	—
162	C₂²×C₄	—	2	4	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
166	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
167	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
168	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
169	C₂×C₈	—	4	4	no	—
170	C₂×C₈	—	4	4	no	—
171	C₂×C₈	—	4	4	no	—
172	C₄⋊C₄	—	2	16	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	2	8	no	—
175	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
176	C₂²⋊C₄	—	2	8	no	—
177	C₄²	—	2	8	no	—
178	C₄²	—	2	2	no	—
179	C₄²	—	2	4	no	—
180	C₄²	C₂×D₄×C₄₃	1	4	yes	—
181	C₂³	—	2	1	no	—
182	C₂³	—	2	1	no	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	2	no	—
185	C₂³	#101×C₄₃	1	2	yes	—
186	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
187	Q₈	—	4	8	no	—
188	Q₈	—	4	8	no	—
189	C₂×C₄	—	2	8	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	#101×C₄₃	1	2	yes	—
203	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
204	C₂×C₄	#120×C₄₃	1	4	yes	—
205	C₂×C₄	#135×C₄₃	1	4	yes	—
206	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
207	C₂×C₄	#137×C₄₃	1	2	yes	—
208	C₈	—	8	4	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	4	1	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	C₄₃×#379	1	1	yes	characteristic
215	C₂²	C₂×#101×C₄₃	1	1	yes	characteristic
216	C₂²	C₂×#101×C₄₃	1	1	yes	characteristic
217	C₂²	C₄₃×#416	1	2	yes	—
218	C₂²	C₄₃×#417	1	2	yes	—
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	—	4	8	no	—
223	C₄	C₄₃×#449	1	4	yes	—
224	C₄	C₄₃×#452	1	4	yes	—
225	C₂	—	4	2	no	—
226	C₂	C₄₃×#1544	1	1	yes	characteristic
227	C₂	C₄₃×#1552	1	2	yes	—
228	C₂	C₄₃×#1561	1	1	yes	characteristic
229	C₂	C₄₃×#1784	1	1	yes	characteristic
230	C₂	C₄₃×#1788	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄₃×#533

C₂

yes

maximal, characteristic

C₄₃×#1797

C₂

yes

maximal

C₂×C₄₃×#332

C₂

yes

maximal, complemented

C₄₃×#533

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

—

C₂×#125×C₄₃

C₄

yes

—

C₂×C₂²⋊Q₈×C₄₃

—

C₂×C₄×Q₈×C₄₃

—

C₂×#117×C₄₃

C₄

yes

—

C₂²×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₈×C₄₃

—

C₄₃×#336

—

C₄₃×#332

—

C₂²×Q₈×C₄₃

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

D₄

yes

—

#125×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#101

yes

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

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×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#101

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₈×C₄₃

—

#8345

C₄₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#379

yes

characteristic

100

C₂²×C₄₃

C₂×#101

yes

characteristic

101

C₂²×C₄₃

C₂×#101

yes

characteristic

102

C₂²×C₄₃

#416

yes

—

103

C₂²×C₄₃

#417

yes

—

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

#449

yes

—

109

C₄×C₄₃

#452

yes

—

110

C₂×#533

C₂×C₄₃

yes

characteristic

111

#1797

C₂×C₄₃

yes

—

112

C₂×#332

C₂×C₄₃

yes

complemented

113

C₂×C₄₃

—

114

C₂×C₄₃

#1544

yes

characteristic

115

C₂×C₄₃

#1552

yes

—

116

C₂×C₄₃

#1561

yes

characteristic

117

C₂×C₄₃

#1784

yes

characteristic

118

C₂×C₄₃

#1788

yes

—

119

#533

—

120

C₂×C₄⋊Q₈

C₂²×C₄₃

yes

—

121

C₂×#125

C₄×C₄₃

yes

—

122

C₂×C₂²⋊Q₈

—

123

C₂×C₄×Q₈

—

124

C₂×#117

C₄×C₄₃

yes

—

125

C₂²×C₄²

C₂²×C₄₃

yes

characteristic

126

C₂×C₄⋊C₈

C₂²×C₄₃

yes

—

127

C₂×C₂²⋊C₈

—

128

#336

—

129

#332

—

130

C₄₃

#8345

yes

characteristic, direct product factor, Sylow

131

C₂²×Q₈

—

132

C₂³×C₄

C₂×C₄×C₄₃

yes

characteristic

133

C₂³×C₄

D₄×C₄₃

yes

—

134

C₂²×C₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

D₄×C₄₃

yes

—

137

#125

—

138

C₂²⋊Q₈

—

139

C₄×Q₈

—

140

#117

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

C₂×C₄×C₄₃

yes

—

144

C₂×C₂²⋊C₄

—

145

C₂×C₄²

—

146

C₂×C₄²

—

147

C₂×C₄²

C₂×C₄×C₄₃

yes

characteristic

148

C₂×C₄²

D₄×C₄₃

yes

—

149

C₂×C₄²

C₂³×C₄₃

yes

characteristic

150

C₄⋊C₈

—

151

C₂²⋊C₈

—

152

C₂⁴

C₂²⋊C₄×C₄₃

yes

characteristic

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

C₂²⋊C₄×C₄₃

yes

—

166

C₂²×C₄

C₂²⋊C₄×C₄₃

yes

characteristic

167

C₂²×C₄

C₂²×C₄×C₄₃

yes

characteristic

168

C₂²×C₄

C₂×D₄×C₄₃

yes

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

C₂²⋊C₄×C₄₃

yes

—

176

C₂²⋊C₄

—

177

C₄²

—

178

C₄²

—

179

C₄²

—

180

C₄²

C₂×D₄×C₄₃

yes

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

#101×C₄₃

yes

—

186

C₂³

C₂×C₂²⋊C₄×C₄₃

yes

characteristic

187

Q₈

—

188

Q₈

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

#101×C₄₃

yes

—

203

C₂×C₄

C₂×C₂²⋊C₄×C₄₃

yes

—

204

C₂×C₄

#120×C₄₃

yes

—

205

C₂×C₄

#135×C₄₃

yes

—

206

C₂×C₄

AGL(1,ℤ/8)×C₄₃

yes

—

207

C₂×C₄

#137×C₄₃

yes

—

208

C₈

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

C₄₃×#379

yes

characteristic

215

C₂²

C₂×#101×C₄₃

yes

characteristic

216

C₂²

C₂×#101×C₄₃

yes

characteristic

217

C₂²

C₄₃×#416

yes

—

218

C₂²

C₄₃×#417

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

C₄₃×#449

yes

—

224

C₄

C₄₃×#452

yes

—

225

C₂

—

226

C₂

C₄₃×#1544

yes

characteristic

227

C₂

C₄₃×#1552

yes

—

228

C₂

C₄₃×#1561

yes

characteristic

229

C₂

C₄₃×#1784

yes

characteristic

230

C₂

C₄₃×#1788

yes

—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
prime radical	C₂⁴×C₄₃	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₃

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₄₃

Frattini, cosocle

C₂×C₄²

C₂³×C₄₃

prime radical

C₂⁴×C₄₃

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

N	H ≅ G/N	type
3. C₂×C₄₃×#332	C₂	semidirect
93. #8345	C₄₃	direct (N × H)
112. C₂×#332	C₂×C₄₃	semidirect
130. C₄₃	#8345	direct (N × H)

H ≅ G/N

type

3. C₂×C₄₃×#332

C₂

semidirect

93. #8345

C₄₃

direct (N × H)

112. C₂×#332

C₂×C₄₃

semidirect

130. C₄₃

#8345

direct (N × H)

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

subgroup	index
C₂×C₄₃×#533	2
C₄₃×#1797	2
C₂×C₄₃×#332	2
#8345	43

subgroup

index

C₂×C₄₃×#533

C₄₃×#1797

C₂×C₄₃×#332

#8345

Subgroups — C₄₃×#8345 #24928362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43×#8345 #24928362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8345 #24928362