Group #24989524 — subgroups

Subgroups — #24989524

Order 11008.

486 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14582964	C₂	1	1	yes	maximal, characteristic
2	#19134584	C₂	1	2	yes	maximal
3	#19133353	C₂	1	2	yes	maximal, complemented
4	#19132470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1292	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₃	C₄	1	2	yes	—
7	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
8	#14582964	—	2	2	no	—
9	#14582964	—	2	2	no	—
10	#14582923	C₂²	1	2	yes	—
11	C₂×#13063241	—	2	2	no	—
12	C₂×(C₂×D₄₃)⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582667	—	2	2	no	—
15	#14582651	—	2	2	no	—
16	#14582651	—	2	2	no	—
17	C₄₃×#423	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₄₃	C₂×C₄	1	2	yes	—
21	C₂×#10621877	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₄₃	—	2	2	no	—
25	C₂×C₈×D₄₃	—	2	2	no	—
26	C₂×C₈×D₄₃	—	4	4	no	—
27	C₄×D₁₇₂	—	2	2	no	—
28	C₄×D₁₇₂	—	2	2	no	—
29	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
30	C₂×(C₂×D₄₃)⋊C₄	Q₈	1	2	yes	—
31	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
33	#13063241	—	4	4	no	—
34	(C₂×D₄₃)⋊C₈	—	2	4	no	—
35	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
36	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
37	C₂×M₁₆×C₄₃	—	2	2	no	—
38	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₃	—	2	2	no	—
41	C₄⋊C₈×C₄₃	—	2	2	no	—
42	C₄⋊C₈×C₄₃	—	2	2	no	—
43	C₂³×D₄₃	C₄⋊C₄	1	2	yes	—
44	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
47	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
48	C₂×D₁₇₂	—	2	2	no	—
49	C₂×D₁₇₂	—	2	2	no	—
50	C₂×D₁₇₂	D₈	1	2	yes	—
51	C₂×D₁₇₂	Q₁₆	1	2	yes	—
52	C₂×C₄×D₄₃	—	2	2	no	—
53	C₂×C₄×D₄₃	—	2	2	no	—
54	C₂×C₄×D₄₃	—	4	2	no	—
55	C₂×C₄×D₄₃	—	4	2	no	—
56	M₁₆×C₄₃	—	4	2	no	—
57	M₁₆×C₄₃	—	4	2	no	—
58	C₂×C₈×C₄₃	—	2	2	no	—
59	C₂×C₈×C₄₃	—	4	2	no	—
60	C₂×C₈×C₄₃	—	4	2	no	—
61	C₄²×C₄₃	C₂×D₄	1	2	yes	—
62	C₄²×C₄₃	#41	1	2	yes	—
63	(C₂×D₄₃)⋊C₄	—	2	4	no	—
64	C₄⋊Dic₄₃	—	2	2	no	—
65	#10621877	—	4	2	no	—
66	#10621877	—	4	2	no	—
67	C₂×C₄₃⋊C₈	—	2	2	no	—
68	C₂×C₄₃⋊C₈	—	4	1	no	—
69	C₂×C₄₃⋊C₈	—	4	2	no	—
70	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	C₈×D₄₃	—	4	4	no	—
74	C₈×D₄₃	—	4	4	no	—
75	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×D₄₃	—	2	2	no	—
77	C₂²×D₄₃	—	2	2	no	—
78	C₂²×D₄₃	—	4	2	no	—
79	C₂²×D₄₃	—	4	2	no	—
80	C₂²×D₄₃	#107	1	4	yes	—
81	C₂×C₄×C₄₃	—	2	1	no	—
82	C₂×C₄×C₄₃	—	2	1	no	—
83	C₂×C₄×C₄₃	—	4	1	no	—
84	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₃	#121	1	2	yes	—
87	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#135	1	2	yes	—
91	C₂×Dic₄₃	—	2	2	no	—
92	C₂×Dic₄₃	—	4	2	no	—
93	D₁₇₂	—	2	4	no	—
94	D₁₇₂	—	2	4	no	—
95	C₄×D₄₃	—	4	4	no	—
96	C₄×D₄₃	—	4	2	no	—
97	C₄×D₄₃	—	4	2	no	—
98	C₈×C₄₃	—	4	2	no	—
99	C₈×C₄₃	—	8	2	no	—
100	C₄₃⋊C₈	—	2	1	no	—
101	C₄₃⋊C₈	—	2	2	no	—
102	C₄₃⋊C₈	—	8	2	no	—
103	C₄₃⋊C₈	#100	1	2	yes	complemented
104	#8616	—	43	1	no	maximal, Sylow
105	C₂²×C₄₃	—	2	1	no	—
106	C₂²×C₄₃	—	2	1	no	—
107	C₂²×C₄₃	#380	1	1	yes	characteristic
108	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
109	C₂²×C₄₃	#427	1	1	yes	characteristic
110	C₂×D₄₃	—	2	4	no	—
111	C₂×D₄₃	—	4	4	no	—
112	C₂×D₄₃	—	4	2	no	—
113	C₂×D₄₃	—	4	2	no	—
114	C₂×D₄₃	—	4	4	no	—
115	C₄×C₄₃	—	2	1	no	—
116	C₄×C₄₃	—	2	2	no	—
117	C₄×C₄₃	C₂×#100	1	1	yes	characteristic
118	C₄×C₄₃	#413	1	1	yes	characteristic
119	C₄×C₄₃	#466	1	2	yes	—
120	C₄×C₄₃	#467	1	2	yes	—
121	Dic₄₃	—	4	2	no	—
122	C₂×C₈×D₄	—	43	1	no	—
123	#1800	—	43	2	no	—
124	#1567	—	43	2	no	—
125	#1292	—	43	1	no	—
126	#1292	D₄₃	1	1	yes	characteristic, complemented
127	C₂×C₄₃	—	2	1	no	—
128	C₂×C₄₃	—	2	1	no	—
129	C₂×C₄₃	#1800	1	1	yes	characteristic
130	C₂×C₄₃	#1808	1	1	yes	characteristic
131	C₂×C₄₃	#1813	1	1	yes	characteristic
132	D₄₃	—	4	4	no	—
133	C₂³×C₈	—	43	2	no	—
134	C₂×C₄×D₄	—	43	1	no	—
135	C₈×D₄	—	86	2	no	—
136	C₈×D₄	—	86	2	no	—
137	#423	—	43	2	no	—
138	#423	C₂×D₄₃	1	2	yes	—
139	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
140	C₂×#100	—	86	2	no	—
141	C₂×C₂²⋊C₈	—	43	2	no	—
142	C₂×C₄×C₈	—	43	1	no	—
143	#343	—	86	2	no	—
144	#335	—	86	2	no	—
145	#335	—	86	2	no	—
146	C₄₃	#8616	1	1	yes	characteristic, complemented, Sylow
147	C₂²×D₄	—	43	1	no	—
148	C₂³×C₄	—	43	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	—	86	2	no	—
151	C₂²×C₈	—	43	1	no	—
152	C₂²×C₈	—	43	1	no	—
153	C₂²×C₈	—	86	2	no	—
154	C₂²×C₈	—	86	2	no	—
155	C₂²×C₈	—	172	4	no	—
156	C₂²×C₈	C₄×D₄₃	1	2	yes	—
157	C₄×D₄	—	86	2	no	—
158	C₄×D₄	—	86	2	no	—
159	C₂×C₄⋊C₄	—	43	1	no	—
160	C₂×C₂²⋊C₄	—	43	2	no	—
161	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	86	2	no	—
166	C₄⋊C₈	—	86	2	no	—
167	#100	—	172	4	no	—
168	C₂²⋊C₈	—	86	4	no	—
169	C₄×C₈	—	43	2	no	—
170	C₄×C₈	—	43	2	no	—
171	C₂⁴	—	43	2	no	—
172	C₂×D₄	—	43	2	no	—
173	C₂×D₄	—	43	2	no	—
174	C₂×D₄	—	86	2	no	—
175	C₂×D₄	—	86	2	no	—
176	C₂²×C₄	—	43	2	no	—
177	C₂²×C₄	—	86	2	no	—
178	C₂²×C₄	—	86	2	no	—
179	C₂²×C₄	—	172	2	no	—
180	C₂²×C₄	—	172	2	no	—
181	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
182	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
183	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
184	M₁₆	—	4	2	no	—
185	M₁₆	—	4	2	no	—
186	M₁₆	—	172	2	no	—
187	M₁₆	—	172	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	43	1	no	—
192	C₂×C₈	—	43	2	no	—
193	C₂×C₈	—	43	1	no	—
194	C₂×C₈	—	86	2	no	—
195	C₂×C₈	—	172	4	no	—
196	C₂×C₈	—	172	4	no	—
197	C₂×C₈	—	172	1	no	—
198	C₂×C₈	—	172	2	no	—
199	C₄⋊C₄	—	86	2	no	—
200	C₂²⋊C₄	—	86	4	no	—
201	C₄²	#10621898	1	2	yes	—
202	C₄²	D₄×D₄₃	1	2	yes	—
203	C₂³	—	43	4	no	—
204	C₂³	—	86	2	no	—
205	C₂³	—	86	2	no	—
206	C₂³	—	172	2	no	—
207	C₂³	—	172	2	no	—
208	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
209	D₄	—	86	4	no	—
210	D₄	—	86	4	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	86	2	no	—
215	C₂×C₄	—	172	4	no	—
216	C₂×C₄	—	172	2	no	—
217	C₂×C₄	—	172	2	no	—
218	C₂×C₄	—	172	2	no	—
219	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
220	C₂×C₄	#13063282	1	1	yes	characteristic
221	C₂×C₄	#13063298	1	2	yes	—
222	C₂×C₄	#13063303	1	2	yes	—
223	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
224	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
225	C₂×C₄	#13063346	1	2	yes	—
226	C₈	—	4	2	no	—
227	C₈	—	8	2	no	—
228	C₈	—	43	2	no	—
229	C₈	—	86	1	no	—
230	C₈	—	86	2	no	—
231	C₈	—	344	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	86	4	no	—
235	C₂²	—	172	4	no	—
236	C₂²	—	172	4	no	—
237	C₂²	—	172	2	no	—
238	C₂²	—	172	2	no	—
239	C₂²	#14582758	1	1	yes	characteristic
240	C₂²	#107×D₄₃	1	1	yes	characteristic
241	C₂²	#14582934	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	2	no	—
244	C₄	—	172	2	no	—
245	C₄	#100×D₄₃	1	1	yes	characteristic
246	C₄	#14582882	1	1	yes	characteristic
247	C₄	#14583134	1	2	yes	—
248	C₄	#14583139	1	2	yes	—
249	C₂	—	2	1	no	—
250	C₂	—	2	1	no	—
251	C₂	—	172	4	no	—
252	C₂	#19134586	1	1	yes	characteristic
253	C₂	#19134623	1	1	yes	characteristic
254	C₂	#19134644	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582964

C₂

yes

maximal, characteristic

#19134584

C₂

yes

maximal

#19133353

C₂

yes

maximal, complemented

#19132470

C₂

yes

maximal, characteristic, complemented

C₄₃×#1292

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₃

C₄

yes

—

C₂×C₄×D₁₇₂

C₂²

yes

—

—

C₂²

yes

—

C₂×#13063241

—

C₂×(C₂×D₄₃)⋊C₈

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

—

C₄₃×#423

C₂²

yes

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂²×D₁₇₂

D₄

yes

characteristic

C₂²×C₄×D₄₃

C₂×C₄

yes

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₄×D₁₇₂

—

C₄×D₁₇₂

—

C₂×C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

Q₈

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063241

—

(C₂×D₄₃)⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂³×D₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂²×Dic₄₃

C₄⋊C₄

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

D₈

yes

—

C₂×D₁₇₂

Q₁₆

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₄₃

—

C₈×D₄₃

—

C₂³×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

#107

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

100

C₄₃⋊C₈

—

101

C₄₃⋊C₈

—

102

C₄₃⋊C₈

—

103

C₄₃⋊C₈

yes

104

—

105

C₂²×C₄₃

—

106

C₂²×C₄₃

—

107

C₂²×C₄₃

#380

yes

characteristic

108

C₂²×C₄₃

C₂×#107

yes

characteristic

109

C₂²×C₄₃

#427

yes

characteristic

110

C₂×D₄₃

—

111

C₂×D₄₃

—

112

C₂×D₄₃

—

113

C₂×D₄₃

—

114

C₂×D₄₃

—

115

C₄×C₄₃

—

116

C₄×C₄₃

—

117

C₄×C₄₃

C₂×#100

yes

characteristic

118

C₄×C₄₃

#413

yes

characteristic

119

C₄×C₄₃

#466

yes

—

120

C₄×C₄₃

#467

yes

—

121

Dic₄₃

—

122

C₂×C₈×D₄

—

123

#1800

—

124

#1567

—

125

#1292

—

126

#1292

D₄₃

yes

characteristic, complemented

127

C₂×C₄₃

—

128

C₂×C₄₃

—

129

C₂×C₄₃

#1800

yes

characteristic

130

C₂×C₄₃

#1808

yes

characteristic

131

C₂×C₄₃

#1813

yes

characteristic

132

D₄₃

—

133

C₂³×C₈

—

134

C₂×C₄×D₄

—

135

C₈×D₄

—

136

C₈×D₄

—

137

#423

—

138

#423

C₂×D₄₃

yes

—

139

C₂×C₄⋊C₈

C₂×D₄₃

yes

characteristic

140

C₂×#100

—

141

C₂×C₂²⋊C₈

—

142

C₂×C₄×C₈

—

143

#343

—

144

#335

—

145

#335

—

146

C₄₃

#8616

yes

characteristic, complemented, Sylow

147

C₂²×D₄

—

148

C₂³×C₄

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

172

—

156

C₂²×C₈

C₄×D₄₃

yes

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₂²⋊C₄

—

161

C₂×C₄²

C₂²×D₄₃

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#100

—

172

—

168

C₂²⋊C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₂⁴

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

172

—

180

C₂²×C₄

—

172

—

181

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

182

C₂²×C₄

D₄×D₄₃

yes

characteristic

183

C₂²×C₄

Q₈×D₄₃

yes

characteristic

184

M₁₆

—

185

M₁₆

—

186

M₁₆

—

172

—

187

M₁₆

—

172

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

172

—

196

C₂×C₈

—

172

—

197

C₂×C₈

—

172

—

198

C₂×C₈

—

172

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₄²

#10621898

yes

—

202

C₄²

D₄×D₄₃

yes

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

172

—

207

C₂³

—

172

—

208

C₂³

C₄⋊C₄×D₄₃

yes

characteristic

209

D₄

—

210

D₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

172

—

216

C₂×C₄

—

172

—

217

C₂×C₄

—

172

—

218

C₂×C₄

—

172

—

219

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

220

C₂×C₄

#13063282

yes

characteristic

221

C₂×C₄

#13063298

yes

—

222

C₂×C₄

#13063303

yes

—

223

C₂×C₄

D₈×D₄₃

yes

characteristic

224

C₂×C₄

Q₁₆×D₄₃

yes

characteristic

225

C₂×C₄

#13063346

yes

—

226

C₈

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

344

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

172

—

236

C₂²

—

172

—

237

C₂²

—

172

—

238

C₂²

—

172

—

239

C₂²

#14582758

yes

characteristic

240

C₂²

#107×D₄₃

yes

characteristic

241

C₂²

#14582934

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

172

—

245

C₄

#100×D₄₃

yes

characteristic

246

C₄

#14582882

yes

characteristic

247

C₄

#14583134

yes

—

248

C₄

#14583139

yes

—

249

C₂

—

250

C₂

—

251

C₂

—

172

—

252

C₂

#19134586

yes

characteristic

253

C₂

#19134623

yes

characteristic

254

C₂

#19134644

yes

characteristic

	subgroup	G/H
center	C₂²	#14582758
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1292	C₂
socle	C₂²×C₄₃	#380
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1292	D₄₃
hypocenter	C₄₃	#8616
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

subgroup

G/H

center

C₂²

#14582758

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1292

C₂

socle

C₂²×C₄₃

#380

prime radical

C₂²×D₁₇₂

D₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

N	H ≅ G/N	type
3. #19133353	C₂	semidirect
4. #19132470	C₂	semidirect
5. C₄₃×#1292	C₂	semidirect
103. C₄₃⋊C₈	#100	semidirect
126. #1292	D₄₃	semidirect
146. C₄₃	#8616	semidirect

H ≅ G/N

type

3. #19133353

C₂

semidirect

4. #19132470

C₂

semidirect

5. C₄₃×#1292

C₂

semidirect

103. C₄₃⋊C₈

#100

semidirect

126. #1292

D₄₃

semidirect

146. C₄₃

#8616

semidirect

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

subgroup	index
C₂×#14582964	2
#19134584	2
#19133353	2
#19132470	2
C₄₃×#1292	2
#8616	43

subgroup

index

C₄₃×#1292

Subgroups — #24989524

Conjugacy classes of subgroups

Complements

Maximal subgroups