Group #24999218 — subgroups

Subgroups — #24999218

Order 11008.

562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14583304	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583190	C₂	1	2	yes	maximal
3	#19135389	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582647	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063325	C₂²	1	2	yes	—
7	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
8	#14583304	—	2	4	no	—
9	#14583190	—	2	4	no	—
10	#14583190	—	2	4	no	—
11	C₂×#13063259	—	2	2	no	—
12	C₂×#13063257	—	2	2	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063247	—	2	2	no	—
15	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
16	#14582647	—	2	4	no	—
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×Dic₈₆	—	2	2	no	—
20	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
21	C₂²×C₄×D₄₃	—	2	1	no	—
22	C₂²×C₄₃⋊C₈	—	2	1	no	—
23	#13063325	—	2	2	no	—
24	#13063325	—	2	2	no	—
25	#13063325	—	2	2	no	—
26	#13063325	D₄	1	4	yes	—
27	C₄×D₁₇₂	—	2	2	no	—
28	C₄×D₁₇₂	—	2	2	no	—
29	C₂×C₄⋊Dic₄₃	—	2	2	no	—
30	C₂×C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
32	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
33	#13063259	—	2	8	no	—
34	#13063257	—	2	8	no	—
35	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
36	#13063247	—	2	8	no	—
37	(C₂×D₄₃)⋊C₈	—	4	4	no	—
38	C₂²×C₈×C₄₃	—	2	2	no	—
39	C₂²×C₈×C₄₃	D₄	1	2	yes	—
40	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₄₃	—	2	2	no	—
42	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
43	C₄×C₈×C₄₃	—	2	2	no	—
44	C₂³×D₄₃	—	2	1	no	—
45	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
48	C₂²×Dic₄₃	—	2	1	no	—
49	C₂²×Dic₄₃	—	4	2	no	—
50	C₂×D₁₇₂	—	2	1	no	—
51	C₂×D₁₇₂	—	2	2	no	—
52	C₂×D₁₇₂	—	2	2	no	—
53	C₂×D₁₇₂	Q₁₆	1	2	yes	—
54	C₂×C₄×D₄₃	—	4	1	no	—
55	C₂×C₄×D₄₃	—	4	1	no	—
56	C₂×C₄×D₄₃	—	4	2	no	—
57	C₂×C₄×D₄₃	—	4	2	no	—
58	C₂×Dic₈₆	—	2	4	no	—
59	C₂×Dic₈₆	—	4	2	no	—
60	C₂×Dic₈₆	—	8	4	no	—
61	C₂×C₈×C₄₃	—	2	2	no	—
62	C₂×C₈×C₄₃	—	2	2	no	—
63	C₂×C₈×C₄₃	—	2	4	no	—
64	C₂×C₈×C₄₃	—	4	2	no	—
65	C₂×C₈×C₄₃	—	4	2	no	—
66	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
67	C₄²×C₄₃	C₂×D₄	1	2	yes	—
68	C₄²×C₄₃	C₂×D₄	1	2	yes	—
69	(C₂×D₄₃)⋊C₄	—	4	2	no	—
70	C₄⋊Dic₄₃	—	2	4	no	—
71	C₄⋊Dic₄₃	—	2	2	no	—
72	C₄⋊Dic₄₃	—	2	4	no	—
73	C₄⋊Dic₄₃	—	4	2	no	—
74	C₄⋊Dic₄₃	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	4	1	no	—
76	C₂×C₄₃⋊C₈	—	4	2	no	—
77	C₂³×C₄₃	#121	1	1	yes	characteristic
78	C₂²×D₄₃	—	2	2	no	—
79	C₂²×D₄₃	—	4	1	no	—
80	C₂²×D₄₃	—	4	2	no	—
81	C₂²×D₄₃	—	4	1	no	—
82	C₂²×D₄₃	—	4	2	no	—
83	C₂×C₄×C₄₃	—	2	2	no	—
84	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#120	1	2	yes	—
86	C₂×C₄×C₄₃	#121	1	2	yes	—
87	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
88	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
89	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
91	C₂×C₄×C₄₃	#137	1	2	yes	—
92	C₂×C₄×C₄₃	#137	1	2	yes	—
93	C₂×Dic₄₃	—	4	4	no	—
94	C₂×Dic₄₃	—	4	1	no	—
95	C₂×Dic₄₃	—	4	2	no	—
96	C₂×Dic₄₃	—	8	4	no	—
97	D₁₇₂	—	2	4	no	—
98	D₁₇₂	—	4	2	no	—
99	C₄×D₄₃	—	8	2	no	—
100	C₄×D₄₃	—	8	1	no	—
101	C₄×D₄₃	—	8	1	no	—
102	Dic₈₆	—	8	4	no	—
103	Dic₈₆	—	8	4	no	—
104	C₈×C₄₃	—	2	4	no	—
105	C₈×C₄₃	—	4	4	no	—
106	C₄₃⋊C₈	—	8	1	no	—
107	#10278	—	43	1	no	maximal, Sylow
108	C₂²×C₄₃	#392	1	1	yes	characteristic
109	C₂²×C₄₃	#461	1	2	yes	—
110	C₂²×C₄₃	#467	1	1	yes	characteristic
111	C₂²×C₄₃	#470	1	1	yes	characteristic
112	C₂²×C₄₃	#472	1	2	yes	—
113	C₂×D₄₃	—	4	4	no	—
114	C₂×D₄₃	—	4	2	no	—
115	C₂×D₄₃	—	8	2	no	—
116	C₂×D₄₃	—	8	1	no	—
117	C₂×D₄₃	—	8	1	no	—
118	C₄×C₄₃	—	2	2	no	—
119	C₄×C₄₃	#448	1	2	yes	—
120	C₄×C₄₃	#451	1	2	yes	—
121	C₄×C₄₃	#452	1	2	yes	—
122	C₄×C₄₃	#492	1	1	yes	characteristic
123	C₄×C₄₃	#497	1	1	yes	characteristic
124	Dic₄₃	—	8	1	no	—
125	Dic₄₃	—	8	4	no	—
126	C₂×#500	—	43	1	no	—
127	C₂×#476	—	43	2	no	—
128	#1954	—	43	1	no	—
129	C₂×#333	—	43	2	no	—
130	#1277	D₄₃	1	1	yes	characteristic, complemented
131	C₂×C₄₃	#1675	1	2	yes	—
132	C₂×C₄₃	#1695	1	2	yes	—
133	C₂×C₄₃	#2001	1	1	yes	characteristic
134	C₂×C₄₃	#2013	1	1	yes	characteristic
135	C₂×C₄₃	#2018	1	1	yes	characteristic
136	D₄₃	—	8	2	no	—
137	C₂×C₄⋊Q₈	—	43	2	no	—
138	C₂×C₄×D₄	—	43	1	no	—
139	#500	—	86	4	no	—
140	#476	—	86	4	no	—
141	#476	—	86	4	no	—
142	C₂×#107	—	86	2	no	—
143	C₂×#106	—	86	2	no	—
144	C₂×C₄⋊C₈	—	43	1	no	—
145	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
146	C₂×#102	—	86	2	no	—
147	C₂×C₂²⋊C₈	—	86	2	no	—
148	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
149	#333	—	86	4	no	—
150	C₄₃	#10278	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₈	—	86	2	no	—
152	C₂²×D₄	—	43	1	no	—
153	C₂³×C₄	—	86	1	no	—
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	—	86	1	no	—
156	C₂²×C₈	D₁₇₂	1	2	yes	—
157	C₄⋊Q₈	—	43	4	no	—
158	C₄⋊Q₈	—	86	2	no	—
159	C₄⋊Q₈	—	86	2	no	—
160	C₄⋊Q₈	—	86	2	no	—
161	C₄×D₄	—	86	2	no	—
162	C₄×D₄	—	86	2	no	—
163	C₂×C₄⋊C₄	—	43	1	no	—
164	C₂×C₄⋊C₄	—	86	2	no	—
165	C₂×C₄⋊C₄	—	86	2	no	—
166	C₂×C₂²⋊C₄	—	86	1	no	—
167	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
168	#107	—	86	8	no	—
169	#106	—	86	8	no	—
170	C₄⋊C₈	—	2	2	no	—
171	C₄⋊C₈	—	86	2	no	—
172	C₄⋊C₈	D₁₇₂	1	4	yes	—
173	#102	—	86	8	no	—
174	C₂²⋊C₈	—	172	4	no	—
175	C₄×C₈	—	2	2	no	—
176	C₂⁴	—	86	1	no	—
177	C₂×Q₈	—	86	4	no	—
178	C₂×Q₈	—	344	4	no	—
179	C₂×Q₈	—	172	2	no	—
180	C₂×D₄	—	43	2	no	—
181	C₂×D₄	—	86	2	no	—
182	C₂×D₄	—	86	1	no	—
183	C₂×D₄	—	86	2	no	—
184	C₂²×C₄	—	86	1	no	—
185	C₂²×C₄	—	172	2	no	—
186	C₂²×C₄	—	172	1	no	—
187	C₂²×C₄	—	172	1	no	—
188	C₂²×C₄	—	172	2	no	—
189	C₂²×C₄	—	172	2	no	—
190	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
191	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
192	C₂²×C₄	#10621902	1	1	yes	characteristic
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	4	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	4	2	no	—
198	C₂×C₈	—	172	1	no	—
199	C₂×C₈	—	172	2	no	—
200	C₂×C₈	#10621873	1	4	yes	—
201	C₄⋊C₄	—	86	4	no	—
202	C₄⋊C₄	—	86	2	no	—
203	C₄⋊C₄	—	86	4	no	—
204	C₄⋊C₄	—	172	2	no	—
205	C₄⋊C₄	—	172	2	no	—
206	C₂²⋊C₄	—	172	2	no	—
207	C₄²	C₂×D₁₇₂	1	2	yes	—
208	C₄²	D₄×D₄₃	1	2	yes	—
209	C₂³	—	86	2	no	—
210	C₂³	—	172	1	no	—
211	C₂³	—	172	2	no	—
212	C₂³	—	172	1	no	—
213	C₂³	—	172	2	no	—
214	C₂³	#13063300	1	1	yes	characteristic
215	Q₈	—	344	4	no	—
216	Q₈	—	344	4	no	—
217	D₄	—	86	4	no	—
218	D₄	—	172	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	344	4	no	—
221	C₂×C₄	—	344	2	no	—
222	C₂×C₄	—	344	1	no	—
223	C₂×C₄	—	344	1	no	—
224	C₂×C₄	—	172	1	no	—
225	C₂×C₄	—	172	4	no	—
226	C₂×C₄	—	172	2	no	—
227	C₂×C₄	#13063295	1	1	yes	characteristic
228	C₂×C₄	#13063295	1	2	yes	—
229	C₂×C₄	#13063300	1	2	yes	—
230	C₂×C₄	#13063322	1	1	yes	characteristic
231	C₂×C₄	C₂×#10621873	1	2	yes	—
232	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
233	C₂×C₄	#13063344	1	1	yes	characteristic
234	C₂×C₄	#13063354	1	2	yes	—
235	C₂×C₄	#13063358	1	2	yes	—
236	C₈	—	2	4	no	—
237	C₈	—	4	4	no	—
238	C₈	—	344	1	no	—
239	C₂²	—	344	2	no	—
240	C₂²	—	344	1	no	—
241	C₂²	—	344	1	no	—
242	C₂²	—	172	4	no	—
243	C₂²	—	172	2	no	—
244	C₂²	#14582809	1	1	yes	characteristic
245	C₂²	#14583105	1	2	yes	—
246	C₂²	#14583141	1	1	yes	characteristic
247	C₂²	#14583158	1	1	yes	characteristic
248	C₂²	#14583170	1	2	yes	—
249	C₄	—	2	2	no	—
250	C₄	—	344	1	no	—
251	C₄	—	344	4	no	—
252	C₄	#14583040	1	2	yes	—
253	C₄	#14583056	1	2	yes	—
254	C₄	#14583062	1	2	yes	—
255	C₄	#14583272	1	1	yes	characteristic
256	C₄	#14583293	1	1	yes	characteristic
257	C₂	—	344	2	no	—
258	C₂	#19133995	1	2	yes	—
259	C₂	#19134119	1	2	yes	—
260	C₂	#19135606	1	1	yes	characteristic
261	C₂	#19135680	1	1	yes	characteristic
262	C₂	#19135705	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583304

C₂

yes

maximal, characteristic, complemented

C₂×#14583190

C₂

yes

maximal

#19135389

C₂

yes

maximal, characteristic

C₂×#14582647

C₂

yes

maximal, complemented

C₄₃×#1277

C₂

yes

maximal, characteristic, complemented

C₂×#13063325

C₂²

yes

—

C₂×C₄×D₁₇₂

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063247

—

C₂×(C₂×D₄₃)⋊C₈

—

#14582647

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂²×D₁₇₂

D₄

yes

characteristic

C₂²×C₄×D₄₃

—

C₂²×C₄₃⋊C₈

—

—

—

—

D₄

yes

—

C₄×D₁₇₂

—

C₄×D₁₇₂

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

#13063259

—

#13063257

—

C₄⋊(C₄₃⋊C₈)

—

#13063247

—

(C₂×D₄₃)⋊C₈

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

Q₁₆

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#121

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

100

C₄×D₄₃

—

101

C₄×D₄₃

—

102

Dic₈₆

—

103

Dic₈₆

—

104

C₈×C₄₃

—

105

C₈×C₄₃

—

106

C₄₃⋊C₈

—

107

#10278

—

maximal, Sylow

108

C₂²×C₄₃

#392

yes

characteristic

109

C₂²×C₄₃

#461

yes

—

110

C₂²×C₄₃

#467

yes

characteristic

111

C₂²×C₄₃

#470

yes

characteristic

112

C₂²×C₄₃

#472

yes

—

113

C₂×D₄₃

—

114

C₂×D₄₃

—

115

C₂×D₄₃

—

116

C₂×D₄₃

—

117

C₂×D₄₃

—

118

C₄×C₄₃

—

119

C₄×C₄₃

#448

yes

—

120

C₄×C₄₃

#451

yes

—

121

C₄×C₄₃

#452

yes

—

122

C₄×C₄₃

#492

yes

characteristic

123

C₄×C₄₃

#497

yes

characteristic

124

Dic₄₃

—

125

Dic₄₃

—

126

C₂×#500

—

127

C₂×#476

—

128

#1954

—

129

C₂×#333

—

130

#1277

D₄₃

yes

characteristic, complemented

131

C₂×C₄₃

#1675

yes

—

132

C₂×C₄₃

#1695

yes

—

133

C₂×C₄₃

#2001

yes

characteristic

134

C₂×C₄₃

#2013

yes

characteristic

135

C₂×C₄₃

#2018

yes

characteristic

136

D₄₃

—

137

C₂×C₄⋊Q₈

—

138

C₂×C₄×D₄

—

139

#500

—

140

#476

—

141

#476

—

142

C₂×#107

—

143

C₂×#106

—

144

C₂×C₄⋊C₈

—

145

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

146

C₂×#102

—

147

C₂×C₂²⋊C₈

—

148

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

149

#333

—

150

C₄₃

#10278

yes

characteristic, complemented, Sylow

151

C₂²×Q₈

—

152

C₂²×D₄

—

153

C₂³×C₄

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

D₁₇₂

yes

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄×D₄

—

162

C₄×D₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₄²

C₂²×D₄₃

yes

characteristic

168

#107

—

169

#106

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

D₁₇₂

yes

—

173

#102

—

174

C₂²⋊C₈

—

172

—

175

C₄×C₈

—

176

C₂⁴

—

177

C₂×Q₈

—

178

C₂×Q₈

—

344

—

179

C₂×Q₈

—

172

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

172

—

186

C₂²×C₄

—

172

—

187

C₂²×C₄

—

172

—

188

C₂²×C₄

—

172

—

189

C₂²×C₄

—

172

—

190

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

191

C₂²×C₄

D₄×D₄₃

yes

characteristic

192

C₂²×C₄

#10621902

yes

characteristic

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

172

—

199

C₂×C₈

—

172

—

200

C₂×C₈

#10621873

yes

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

172

—

205

C₄⋊C₄

—

172

—

206

C₂²⋊C₄

—

172

—

207

C₄²

C₂×D₁₇₂

yes

—

208

C₄²

D₄×D₄₃

yes

—

209

C₂³

—

210

C₂³

—

172

—

211

C₂³

—

172

—

212

C₂³

—

172

—

213

C₂³

—

172

—

214

C₂³

#13063300

yes

characteristic

215

Q₈

—

344

—

216

Q₈

—

344

—

217

D₄

—

218

D₄

—

172

—

219

C₂×C₄

—

220

C₂×C₄

—

344

—

221

C₂×C₄

—

344

—

222

C₂×C₄

—

344

—

223

C₂×C₄

—

344

—

224

C₂×C₄

—

172

—

225

C₂×C₄

—

172

—

226

C₂×C₄

—

172

—

227

C₂×C₄

#13063295

yes

characteristic

228

C₂×C₄

#13063295

yes

—

229

C₂×C₄

#13063300

yes

—

230

C₂×C₄

#13063322

yes

characteristic

231

C₂×C₄

C₂×#10621873

yes

—

232

C₂×C₄

Q₁₆×D₄₃

yes

characteristic

233

C₂×C₄

#13063344

yes

characteristic

234

C₂×C₄

#13063354

yes

—

235

C₂×C₄

#13063358

yes

—

236

C₈

—

237

C₈

—

238

C₈

—

344

—

239

C₂²

—

344

—

240

C₂²

—

344

—

241

C₂²

—

344

—

242

C₂²

—

172

—

243

C₂²

—

172

—

244

C₂²

#14582809

yes

characteristic

245

C₂²

#14583105

yes

—

246

C₂²

#14583141

yes

characteristic

247

C₂²

#14583158

yes

characteristic

248

C₂²

#14583170

yes

—

249

C₄

—

250

C₄

—

344

—

251

C₄

—

344

—

252

C₄

#14583040

yes

—

253

C₄

#14583056

yes

—

254

C₄

#14583062

yes

—

255

C₄

#14583272

yes

characteristic

256

C₄

#14583293

yes

characteristic

257

C₂

—

344

—

258

C₂

#19133995

yes

—

259

C₂

#19134119

yes

—

260

C₂

#19135606

yes

characteristic

261

C₂

#19135680

yes

characteristic

262

C₂

#19135705

yes

characteristic

	subgroup	G/H
center	C₂³	#13063300
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1277	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂²×D₁₇₂	D₄
hypercenter	#1277	D₄₃
hypocenter	C₄₃	#10278
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂³

#13063300

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1277

C₂

socle

C₂³×C₄₃

#121

prime radical

C₂²×D₁₇₂

D₄

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
1. C₂×#14583304	C₂	semidirect
4. C₂×#14582647	C₂	semidirect
5. C₄₃×#1277	C₂	semidirect
130. #1277	D₄₃	semidirect
150. C₄₃	#10278	semidirect

H ≅ G/N

type

1. C₂×#14583304

C₂

semidirect

4. C₂×#14582647

C₂

semidirect

5. C₄₃×#1277

C₂

semidirect

130. #1277

D₄₃

semidirect

150. C₄₃

#10278

semidirect

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

subgroup	index
C₂×#14583304	2
C₂×#14583190	2
#19135389	2
C₂×#14582647	2
C₄₃×#1277	2
#10278	43

subgroup

index

C₄₃×#1277

Subgroups — #24999218

Conjugacy classes of subgroups

Complements

Maximal subgroups