Group #24996407 — subgroups

Subgroups — #24996407

Order 11008.

694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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×#14583276	C₂	1	1	yes	maximal, characteristic
2	#19135400	C₂	1	2	yes	maximal, complemented
3	#19135400	C₂	1	2	yes	maximal, complemented
4	C₂×#14582621	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₄₄	—	2	2	no	—
7	C₂×#13063322	C₂²	1	2	yes	—
8	#14583276	—	2	2	no	—
9	#14583276	C₄	1	4	yes	complemented
10	C₂×#13063245	—	2	4	no	—
11	C₂×#13063245	—	2	4	no	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582621	—	2	2	no	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#384	C₂²	1	2	yes	—
17	C₄₃×#340	—	2	2	no	—
18	C₂²×D₁₇₂	—	2	2	no	—
19	C₂²×D₁₇₂	—	2	2	no	—
20	C₂²×D₁₇₂	—	2	2	no	—
21	C₂×D₃₄₄	—	2	8	no	—
22	C₂×D₃₄₄	—	4	8	no	—
23	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
24	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
25	#13063322	—	2	2	no	—
26	#13063322	—	2	2	no	—
27	#13063322	—	2	2	no	—
28	#13063322	C₂×C₄	1	4	yes	—
29	#13063245	—	4	8	no	—
30	#13063245	—	4	8	no	—
31	C₄×C₄₃⋊C₈	—	2	1	no	—
32	C₄×C₄₃⋊C₈	—	2	1	no	—
33	C₄×C₄₃⋊C₈	—	2	1	no	—
34	C₄×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₈×C₄₃	D₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
39	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
40	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₄₃	D₄	1	2	yes	—
42	C₂³×D₄₃	—	4	2	no	—
43	C₂²×C₄×C₄₃	—	4	2	no	—
44	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×D₁₇₂	—	2	4	no	—
48	C₂×D₁₇₂	—	2	4	no	—
49	C₂×D₁₇₂	—	2	4	no	—
50	C₂×D₁₇₂	—	4	2	no	—
51	C₂×D₁₇₂	—	4	2	no	—
52	C₂×D₁₇₂	—	4	2	no	—
53	C₂×D₁₇₂	—	4	4	no	—
54	C₂×D₁₇₂	—	4	4	no	—
55	C₂×D₁₇₂	—	4	4	no	—
56	C₂×D₁₇₂	—	4	4	no	—
57	C₂×D₁₇₂	—	4	4	no	—
58	C₂×D₁₇₂	—	4	4	no	—
59	C₂×C₈×C₄₃	—	2	4	no	—
60	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
61	C₄⋊C₄×C₄₃	—	4	4	no	—
62	C₄⋊C₄×C₄₃	—	4	4	no	—
63	C₄⋊C₄×C₄₃	—	4	4	no	—
64	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₄₃	#41	1	1	yes	characteristic
67	C₄²×C₄₃	#41	1	1	yes	characteristic
68	C₂×C₄₃⋊C₈	—	2	2	no	—
69	C₂×C₄₃⋊C₈	—	2	2	no	—
70	C₂×C₄₃⋊C₈	—	2	2	no	—
71	C₂×C₄₃⋊C₈	—	2	4	no	—
72	C₂×C₄₃⋊C₈	D₈	1	4	yes	complemented
73	D₃₄₄	—	4	16	no	—
74	C₂³×C₄₃	#127	1	1	yes	characteristic
75	C₂²×D₄₃	—	4	4	no	—
76	C₂²×D₄₃	—	8	2	no	—
77	C₂²×D₄₃	—	8	2	no	—
78	C₂²×D₄₃	—	8	2	no	—
79	C₂²×D₄₃	—	8	2	no	—
80	C₂²×D₄₃	—	8	2	no	—
81	C₂²×D₄₃	—	8	2	no	—
82	C₂×C₄×C₄₃	—	8	2	no	—
83	C₂×C₄×C₄₃	—	8	2	no	—
84	C₂×C₄×C₄₃	—	8	2	no	—
85	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
91	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
92	C₂×C₄×C₄₃	#135	1	2	yes	—
93	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
94	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
95	D₁₇₂	—	4	8	no	—
96	D₁₇₂	—	4	8	no	—
97	D₁₇₂	—	4	8	no	—
98	D₁₇₂	—	8	4	no	—
99	D₁₇₂	—	8	4	no	—
100	D₁₇₂	—	8	4	no	—
101	C₈×C₄₃	—	2	4	no	—
102	C₄₃⋊C₈	—	2	4	no	—
103	C₄₃⋊C₈	—	4	2	no	—
104	#9832	—	43	1	no	maximal, Sylow
105	C₂²×C₄₃	#390	1	1	yes	characteristic
106	C₂²×C₄₃	#493	1	1	yes	characteristic
107	C₂²×C₄₃	#495	1	1	yes	characteristic
108	C₂²×C₄₃	#496	1	2	yes	—
109	C₂²×C₄₃	#496	1	2	yes	—
110	C₂×D₄₃	—	8	4	no	—
111	C₂×D₄₃	—	8	4	no	—
112	C₂×D₄₃	—	8	4	no	—
113	C₂×D₄₃	—	16	2	no	—
114	C₂×D₄₃	—	16	2	no	—
115	C₂×D₄₃	—	16	2	no	—
116	C₂×D₄₃	—	16	2	no	—
117	C₄×C₄₃	—	16	2	no	—
118	C₄×C₄₃	#418	1	2	yes	—
119	C₄×C₄₃	C₄×D₈	1	2	yes	—
120	C₄×C₄₃	#442	1	2	yes	—
121	C₄×C₄₃	#466	1	2	yes	—
122	C₄×C₄₃	#469	1	2	yes	—
123	C₄×C₄₃	#490	1	2	yes	—
124	C₂×#493	—	43	1	no	—
125	#1957	—	43	2	no	—
126	#1957	—	43	2	no	—
127	#1834	D₄₃	1	1	yes	characteristic, complemented
128	C₂×#322	—	43	1	no	—
129	C₂×C₄₃	#1717	1	2	yes	—
130	C₂×C₄₃	#1721	1	2	yes	—
131	C₂×C₄₃	#1961	1	1	yes	characteristic
132	C₂×C₄₃	#1970	1	1	yes	characteristic
133	C₂×C₄₃	#1972	1	1	yes	characteristic
134	D₄₃	—	16	4	no	—
135	C₂²×D₈	—	86	2	no	—
136	C₂×#127	—	43	2	no	—
137	#493	—	43	4	no	—
138	#493	—	86	2	no	—
139	C₂×#102	—	86	4	no	—
140	C₂×#102	—	86	4	no	—
141	C₂×C₄×C₈	—	43	1	no	—
142	C₂×C₄×C₈	—	43	1	no	—
143	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
144	#384	C₂×D₄₃	1	2	yes	—
145	#340	—	2	2	no	—
146	#322	—	86	2	no	—
147	C₄₃	#9832	1	1	yes	characteristic, complemented, Sylow
148	C₂²×D₄	—	86	2	no	—
149	C₂²×D₄	—	86	2	no	—
150	C₂²×D₄	—	86	2	no	—
151	C₂×D₈	—	86	8	no	—
152	C₂×D₈	—	172	8	no	—
153	C₂²×C₈	—	43	2	no	—
154	C₂²×C₈	—	43	2	no	—
155	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
156	#127	—	43	4	no	—
157	#127	—	86	2	no	—
158	#127	—	86	2	no	—
159	#127	—	86	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
164	#102	—	172	8	no	—
165	#102	—	172	8	no	—
166	C₄×C₈	—	86	1	no	—
167	C₄×C₈	—	86	1	no	—
168	C₄×C₈	—	86	1	no	—
169	C₄×C₈	—	86	1	no	—
170	C₄×C₈	C₄×D₄₃	1	2	yes	—
171	C₄×C₈	D₁₇₂	1	2	yes	—
172	C₂⁴	—	172	2	no	—
173	C₂×D₄	—	86	4	no	—
174	C₂×D₄	—	86	4	no	—
175	C₂×D₄	—	86	4	no	—
176	C₂×D₄	—	172	2	no	—
177	C₂×D₄	—	172	2	no	—
178	C₂×D₄	—	172	2	no	—
179	C₂×D₄	—	172	4	no	—
180	C₂×D₄	—	172	4	no	—
181	C₂×D₄	—	172	4	no	—
182	C₂×D₄	—	172	4	no	—
183	C₂×D₄	—	172	4	no	—
184	C₂×D₄	—	172	4	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
187	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
189	D₈	—	172	16	no	—
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	43	4	no	—
192	C₂×C₈	—	86	2	no	—
193	C₂×C₈	—	86	2	no	—
194	C₂×C₈	—	86	2	no	—
195	C₂×C₈	—	86	4	no	—
196	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
197	C₄⋊C₄	—	4	4	no	—
198	C₄⋊C₄	—	4	4	no	—
199	C₄⋊C₄	—	4	4	no	—
200	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
201	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
202	C₄²	#10621902	1	1	yes	characteristic
203	C₄²	#10621902	1	1	yes	characteristic
204	C₂³	—	344	2	no	—
205	C₂³	—	344	2	no	—
206	C₂³	—	344	2	no	—
207	C₂³	—	344	2	no	—
208	C₂³	—	344	2	no	—
209	C₂³	—	344	2	no	—
210	C₂³	—	172	4	no	—
211	C₂³	#13063321	1	1	yes	characteristic
212	D₄	—	344	4	no	—
213	D₄	—	344	4	no	—
214	D₄	—	344	4	no	—
215	D₄	—	172	8	no	—
216	D₄	—	172	8	no	—
217	D₄	—	172	8	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
222	C₂×C₄	#13063287	1	1	yes	characteristic
223	C₂×C₄	#13063287	1	1	yes	characteristic
224	C₂×C₄	#13063300	1	1	yes	characteristic
225	C₂×C₄	#13063300	1	1	yes	characteristic
226	C₂×C₄	#13063314	1	1	yes	characteristic
227	C₂×C₄	D₈×D₄₃	1	2	yes	—
228	C₂×C₄	#13063348	1	2	yes	—
229	C₂×C₄	#13063350	1	4	yes	—
230	C₂×C₄	#13063352	1	4	yes	—
231	C₈	—	2	4	no	—
232	C₈	—	86	4	no	—
233	C₈	—	172	2	no	—
234	C₂²	—	344	4	no	—
235	C₂²	—	344	4	no	—
236	C₂²	—	344	4	no	—
237	C₂²	—	688	2	no	—
238	C₂²	—	688	2	no	—
239	C₂²	—	688	2	no	—
240	C₂²	—	688	2	no	—
241	C₂²	#14582800	1	1	yes	characteristic
242	C₂²	#14583274	1	1	yes	characteristic
243	C₂²	#14583284	1	1	yes	characteristic
244	C₂²	#14583285	1	2	yes	—
245	C₂²	#14583289	1	2	yes	—
246	C₄	—	16	2	no	—
247	C₄	#14582903	1	2	yes	—
248	C₄	#14582981	1	2	yes	—
249	C₄	#14583010	1	2	yes	—
250	C₄	#14583136	1	2	yes	—
251	C₄	#14583153	1	2	yes	—
252	C₄	#14583265	1	2	yes	—
253	C₂	—	688	4	no	—
254	C₂	#19134237	1	2	yes	—
255	C₂	#19134263	1	2	yes	—
256	C₂	#19135418	1	1	yes	characteristic
257	C₂	#19135459	1	1	yes	characteristic
258	C₂	#19135469	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583276

C₂

yes

maximal, characteristic

#19135400

C₂

yes

maximal, complemented

#19135400

C₂

yes

maximal, complemented

C₂×#14582621

C₂

yes

maximal, characteristic, complemented

C₄₃×#1834

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

—

C₂×#13063322

C₂²

yes

—

#14583276

—

#14583276

C₄

yes

complemented

C₂×#13063245

—

C₂×#13063245

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582621

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#384

C₂²

yes

—

C₄₃×#340

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂²×C₄₃⋊C₈

D₄

yes

—

C₂²×C₄₃⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

#13063245

—

#13063245

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

C₄²×C₄₃

yes

C₄²×C₄₃

yes

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₈

yes

complemented

D₃₄₄

—

C₂³×C₄₃

#127

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

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

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×D₈

yes

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

100

D₁₇₂

—

101

C₈×C₄₃

—

102

C₄₃⋊C₈

—

103

C₄₃⋊C₈

—

104

#9832

—

maximal, Sylow

105

C₂²×C₄₃

#390

yes

characteristic

106

C₂²×C₄₃

#493

yes

characteristic

107

C₂²×C₄₃

#495

yes

characteristic

108

C₂²×C₄₃

#496

yes

—

109

C₂²×C₄₃

#496

yes

—

110

C₂×D₄₃

—

111

C₂×D₄₃

—

112

C₂×D₄₃

—

113

C₂×D₄₃

—

114

C₂×D₄₃

—

115

C₂×D₄₃

—

116

C₂×D₄₃

—

117

C₄×C₄₃

—

118

C₄×C₄₃

#418

yes

—

119

C₄×C₄₃

C₄×D₈

yes

—

120

C₄×C₄₃

#442

yes

—

121

C₄×C₄₃

#466

yes

—

122

C₄×C₄₃

#469

yes

—

123

C₄×C₄₃

#490

yes

—

124

C₂×#493

—

125

#1957

—

126

#1957

—

127

#1834

D₄₃

yes

characteristic, complemented

128

C₂×#322

—

129

C₂×C₄₃

#1717

yes

—

130

C₂×C₄₃

#1721

yes

—

131

C₂×C₄₃

#1961

yes

characteristic

132

C₂×C₄₃

#1970

yes

characteristic

133

C₂×C₄₃

#1972

yes

characteristic

134

D₄₃

—

135

C₂²×D₈

—

136

C₂×#127

—

137

#493

—

138

#493

—

139

C₂×#102

—

140

C₂×#102

—

141

C₂×C₄×C₈

—

142

C₂×C₄×C₈

—

143

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

144

#384

C₂×D₄₃

yes

—

145

#340

—

146

#322

—

147

C₄₃

#9832

yes

characteristic, complemented, Sylow

148

C₂²×D₄

—

149

C₂²×D₄

—

150

C₂²×D₄

—

151

C₂×D₈

—

152

C₂×D₈

—

172

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

C₂²⋊D₄₃

yes

—

156

#127

—

157

#127

—

158

#127

—

159

#127

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

C₂²×D₄₃

yes

characteristic

164

#102

—

172

—

165

#102

—

172

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

—

170

C₄×C₈

C₄×D₄₃

yes

—

171

C₄×C₈

D₁₇₂

yes

—

172

C₂⁴

—

172

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

172

—

177

C₂×D₄

—

172

—

178

C₂×D₄

—

172

—

179

C₂×D₄

—

172

—

180

C₂×D₄

—

172

—

181

C₂×D₄

—

172

—

182

C₂×D₄

—

172

—

183

C₂×D₄

—

172

—

184

C₂×D₄

—

172

—

185

C₂²×C₄

—

186

C₂²×C₄

D₄×D₄₃

yes

characteristic

187

C₂²×C₄

D₄×D₄₃

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

189

D₈

—

172

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄²

C₂×C₄×D₄₃

yes

characteristic

201

C₄²

C₂×D₁₇₂

yes

characteristic

202

C₄²

#10621902

yes

characteristic

203

C₄²

#10621902

yes

characteristic

204

C₂³

—

344

—

205

C₂³

—

344

—

206

C₂³

—

344

—

207

C₂³

—

344

—

208

C₂³

—

344

—

209

C₂³

—

344

—

210

C₂³

—

172

—

211

C₂³

#13063321

yes

characteristic

212

D₄

—

344

—

213

D₄

—

344

—

214

D₄

—

344

—

215

D₄

—

172

—

216

D₄

—

172

—

217

D₄

—

172

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

222

C₂×C₄

#13063287

yes

characteristic

223

C₂×C₄

#13063287

yes

characteristic

224

C₂×C₄

#13063300

yes

characteristic

225

C₂×C₄

#13063300

yes

characteristic

226

C₂×C₄

#13063314

yes

characteristic

227

C₂×C₄

D₈×D₄₃

yes

—

228

C₂×C₄

#13063348

yes

—

229

C₂×C₄

#13063350

yes

—

230

C₂×C₄

#13063352

yes

—

231

C₈

—

232

C₈

—

233

C₈

—

172

—

234

C₂²

—

344

—

235

C₂²

—

344

—

236

C₂²

—

344

—

237

C₂²

—

688

—

238

C₂²

—

688

—

239

C₂²

—

688

—

240

C₂²

—

688

—

241

C₂²

#14582800

yes

characteristic

242

C₂²

#14583274

yes

characteristic

243

C₂²

#14583284

yes

characteristic

244

C₂²

#14583285

yes

—

245

C₂²

#14583289

yes

—

246

C₄

—

247

C₄

#14582903

yes

—

248

C₄

#14582981

yes

—

249

C₄

#14583010

yes

—

250

C₄

#14583136

yes

—

251

C₄

#14583153

yes

—

252

C₄

#14583265

yes

—

253

C₂

—

688

—

254

C₂

#19134237

yes

—

255

C₂

#19134263

yes

—

256

C₂

#19135418

yes

characteristic

257

C₂

#19135459

yes

characteristic

258

C₂

#19135469

yes

characteristic

	subgroup	G/H
center	C₂³	#13063321
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1834	C₂
socle	C₂³×C₄₃	#127
prime radical	C₂×#14583276	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1834	D₄₃
hypocenter	C₄₃	#9832
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#13063321

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1834

C₂

C₂³×C₄₃

C₂

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
2. #19135400	C₂	semidirect
3. #19135400	C₂	semidirect
4. C₂×#14582621	C₂	semidirect
5. C₄₃×#1834	C₂	semidirect
9. #14583276	C₄	semidirect
72. C₂×C₄₃⋊C₈	D₈	semidirect
127. #1834	D₄₃	semidirect
147. C₄₃	#9832	semidirect

H ≅ G/N

type

2. #19135400

C₂

semidirect

3. #19135400

C₂

semidirect

4. C₂×#14582621

C₂

semidirect

5. C₄₃×#1834

C₂

semidirect

9. #14583276

C₄

semidirect

72. C₂×C₄₃⋊C₈

D₈

semidirect

127. #1834

D₄₃

semidirect

147. C₄₃

#9832

semidirect

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

subgroup	index
C₂×#14583276	2
#19135400	2
C₂×#14582621	2
C₄₃×#1834	2
#9832	43

subgroup

index

C₄₃×#1834

Subgroups — #24996407

Conjugacy classes of subgroups

Complements

Maximal subgroups