Group #19145969 — subgroups

Subgroups — #19145969

Order 5504.

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

normal subgroups only

This group has 348 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	#14583456	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583433	C₂	1	1	yes	maximal, characteristic
3	#14583207	C₂	1	2	yes	maximal, complemented
4	#14583195	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583190	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583157	C₂	1	2	yes	maximal, complemented
7	#14583145	C₂	1	2	yes	maximal
8	#14583122	C₂	1	2	yes	maximal, complemented
9	#14583110	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583105	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₁₇₂	C₂²	1	2	yes	—
13	C₂×#10621873	C₂²	1	2	yes	—
14	#13063325	C₂²	1	1	yes	characteristic
15	#13063325	C₂²	1	1	yes	characteristic
16	#13063319	—	2	1	no	—
17	#13063317	—	2	1	no	—
18	#13063317	C₂²	1	1	yes	characteristic
19	#13063313	C₂²	1	1	yes	characteristic
20	#13063308	—	2	1	no	—
21	#13063304	—	2	1	no	—
22	#13063304	C₂²	1	2	yes	—
23	#13063304	C₂²	1	1	yes	characteristic
24	#13063299	C₂²	1	1	yes	characteristic
25	C₄×Dic₈₆	—	2	1	no	—
26	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
27	C₄×Dic₈₆	C₂²	1	2	yes	—
28	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊D₄₃	—	2	1	no	—
30	#13063284	—	2	1	no	—
31	#13063282	—	2	1	no	—
32	#13063259	C₂²	1	2	yes	—
33	#13063257	C₂²	1	2	yes	—
34	#13063250	C₂²	1	2	yes	—
35	#13063250	C₂²	1	2	yes	—
36	#13063250	C₂²	1	2	yes	—
37	#13063247	C₂²	1	2	yes	—
38	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
39	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
43	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊D₄₃	—	2	1	no	—
47	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₄₃	—	2	1	no	—
49	C₂×Dic₈₆	—	2	1	no	—
50	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
51	C₂×Dic₈₆	C₂³	1	2	yes	—
52	M₁₆×C₄₃	—	4	2	no	—
53	C₂×C₈×C₄₃	C₂³	1	2	yes	—
54	C₂×C₈×C₄₃	C₂³	1	2	yes	—
55	C₄²×C₄₃	D₄	1	1	yes	characteristic
56	C₄²×C₄₃	D₄	1	1	yes	characteristic
57	C₄²×C₄₃	C₂³	1	1	yes	characteristic
58	C₄²×C₄₃	C₂³	1	1	yes	characteristic
59	C₂²⋊Dic₄₃	—	2	2	no	—
60	C₂²⋊Dic₄₃	—	2	1	no	—
61	(C₂×D₄₃)⋊C₄	—	2	1	no	—
62	(C₂×D₄₃)⋊C₄	—	2	1	no	—
63	(C₂×D₄₃)⋊C₄	—	2	1	no	—
64	(C₂×D₄₃)⋊C₄	—	2	1	no	—
65	C₄⋊Dic₄₃	—	2	1	no	—
66	C₄⋊Dic₄₃	—	2	1	no	—
67	C₄⋊Dic₄₃	—	2	1	no	—
68	C₄⋊Dic₄₃	C₂³	1	2	yes	—
69	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
71	Dic₄₃⋊C₄	—	2	1	no	—
72	Dic₄₃⋊C₄	—	2	1	no	—
73	Dic₄₃⋊C₄	—	2	1	no	—
74	Dic₄₃⋊C₄	—	2	2	no	—
75	Dic₄₃⋊C₄	—	2	2	no	—
76	Dic₄₃⋊C₄	—	2	1	no	—
77	C₄×Dic₄₃	—	2	1	no	—
78	C₄×Dic₄₃	—	2	2	no	—
79	Dic₁₇₂	—	4	2	no	—
80	#10621873	—	4	2	no	—
81	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×D₄₃	—	2	1	no	—
83	C₂×C₄×C₄₃	—	2	2	no	—
84	C₂×C₄×C₄₃	—	2	1	no	—
85	C₂×C₄×C₄₃	—	2	1	no	—
86	C₂×C₄×C₄₃	—	4	1	no	—
87	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
93	C₂²⋊D₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	2	1	no	—
95	C₂×Dic₄₃	—	2	2	no	—
96	C₂×Dic₄₃	—	2	2	no	—
97	C₂×Dic₄₃	—	2	1	no	—
98	C₂×Dic₄₃	—	2	1	no	—
99	D₁₇₂	—	2	1	no	—
100	D₁₇₂	—	2	1	no	—
101	C₄×D₄₃	—	4	2	no	—
102	Dic₈₆	—	2	2	no	—
103	Dic₈₆	—	2	1	no	—
104	Dic₈₆	—	2	1	no	—
105	Dic₈₆	—	2	2	no	—
106	Dic₈₆	—	4	2	no	—
107	C₈×C₄₃	—	2	2	no	—
108	C₈×C₄₃	—	2	2	no	—
109	C₂²×C₄₃	—	2	1	no	—
110	C₂²×C₄₃	—	2	1	no	—
111	C₂²×C₄₃	—	2	1	no	—
112	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
113	C₂×D₄₃	—	4	1	no	—
114	C₂×D₄₃	—	4	1	no	—
115	C₂×D₄₃	—	4	1	no	—
116	C₄×C₄₃	—	2	1	no	—
117	C₄×C₄₃	—	2	1	no	—
118	C₄×C₄₃	—	2	1	no	—
119	C₄×C₄₃	—	2	1	no	—
120	C₄×C₄₃	#137	1	2	yes	—
121	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
122	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
123	Dic₄₃	—	4	2	no	—
124	Dic₄₃	—	4	1	no	—
125	Dic₄₃	—	4	1	no	—
126	Dic₄₃	—	4	2	no	—
127	Dic₄₃	—	4	1	no	—
128	#3252	—	43	1	no	maximal, Sylow
129	C₂×C₄₃	—	4	1	no	—
130	C₂×C₄₃	#537	1	1	yes	characteristic
131	C₂×C₄₃	C₂×#137	1	1	yes	characteristic
132	C₂×C₄₃	#575	1	1	yes	characteristic
133	D₄₃	—	8	1	no	—
134	#533	—	43	1	no	—
135	#529	—	43	1	no	—
136	#479	—	43	2	no	—
137	#477	—	43	1	no	—
138	#476	—	43	1	no	—
139	#470	—	43	2	no	—
140	#468	—	43	2	no	—
141	#464	—	43	2	no	—
142	#462	—	43	1	no	—
143	#461	—	43	1	no	—
144	#423	D₄₃	1	1	yes	characteristic, complemented
145	C₄₃	#3252	1	1	yes	characteristic, complemented, Sylow
146	C₂×Q₁₆	—	43	2	no	—
147	C₂×SD₁₆	—	43	2	no	—
148	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
149	C₄⋊Q₈	—	43	1	no	—
150	C₄⋊Q₈	—	43	1	no	—
151	#126	—	86	1	no	—
152	#125	—	43	1	no	—
153	#125	—	86	1	no	—
154	#124	—	43	1	no	—
155	#123	—	86	1	no	—
156	C₂²⋊Q₈	—	43	1	no	—
157	C₂²⋊Q₈	—	43	2	no	—
158	C₂²⋊Q₈	—	86	1	no	—
159	#121	—	43	1	no	—
160	C₄×Q₈	—	43	1	no	—
161	C₄×Q₈	—	43	2	no	—
162	C₄×Q₈	—	86	1	no	—
163	C₄×D₄	—	43	1	no	—
164	C₄×D₄	—	86	1	no	—
165	#117	—	86	1	no	—
166	#117	—	86	1	no	—
167	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
168	#107	—	43	2	no	—
169	#106	—	43	2	no	—
170	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
171	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
172	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
173	#103	—	43	2	no	—
174	#103	—	43	2	no	—
175	#103	—	43	2	no	—
176	#102	—	43	2	no	—
177	C₂×Q₈	—	43	1	no	—
178	C₂×Q₈	—	43	2	no	—
179	C₂×Q₈	—	86	1	no	—
180	C₂×D₄	—	43	1	no	—
181	C₂×D₄	—	86	1	no	—
182	C₂²×C₄	—	86	1	no	—
183	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
184	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
185	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
186	Q₁₆	—	172	2	no	—
187	SD₁₆	—	172	2	no	—
188	M₁₆	—	4	2	no	—
189	C₂×C₈	C₂²×D₄₃	1	2	yes	—
190	C₂×C₈	C₂²×D₄₃	1	2	yes	—
191	C₄⋊C₄	—	43	2	no	—
192	C₄⋊C₄	—	43	1	no	—
193	C₄⋊C₄	—	43	1	no	—
194	C₄⋊C₄	—	86	1	no	—
195	C₄⋊C₄	—	86	1	no	—
196	C₄⋊C₄	—	86	1	no	—
197	C₄⋊C₄	—	86	1	no	—
198	C₄⋊C₄	—	86	1	no	—
199	C₄⋊C₄	—	86	2	no	—
200	C₄⋊C₄	—	86	1	no	—
201	C₄⋊C₄	—	86	2	no	—
202	C₄⋊C₄	—	86	1	no	—
203	C₂²⋊C₄	—	86	2	no	—
204	C₂²⋊C₄	—	86	1	no	—
205	C₂²⋊C₄	—	86	1	no	—
206	C₂²⋊C₄	—	86	1	no	—
207	C₂²⋊C₄	—	86	1	no	—
208	C₂²⋊C₄	—	86	1	no	—
209	C₄²	—	86	1	no	—
210	C₄²	—	86	2	no	—
211	C₄²	D₁₇₂	1	1	yes	characteristic
212	C₄²	D₁₇₂	1	1	yes	characteristic
213	C₄²	C₂²×D₄₃	1	1	yes	characteristic
214	C₄²	C₂²×D₄₃	1	1	yes	characteristic
215	C₂³	—	86	1	no	—
216	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
217	Q₈	—	86	2	no	—
218	Q₈	—	86	1	no	—
219	Q₈	—	86	1	no	—
220	Q₈	—	86	2	no	—
221	Q₈	—	172	2	no	—
222	D₄	—	86	1	no	—
223	D₄	—	86	1	no	—
224	D₄	—	172	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	86	1	no	—
230	C₂×C₄	—	86	1	no	—
231	C₂×C₄	—	86	2	no	—
232	C₂×C₄	—	86	2	no	—
233	C₂×C₄	—	86	1	no	—
234	C₂×C₄	—	172	2	no	—
235	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
236	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
237	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
238	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
239	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
240	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
241	C₈	—	2	2	no	—
242	C₈	—	2	2	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	172	1	no	—
247	C₂²	—	172	1	no	—
248	C₂²	—	172	1	no	—
249	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	1	no	—
254	C₄	—	172	1	no	—
255	C₄	—	172	1	no	—
256	C₄	—	172	2	no	—
257	C₄	—	172	1	no	—
258	C₄	—	172	2	no	—
259	C₄	#13063358	1	2	yes	—
260	C₄	#13063370	1	1	yes	characteristic
261	C₄	#13063373	1	1	yes	characteristic
262	C₂	—	4	1	no	—
263	C₂	—	344	1	no	—
264	C₂	#14583480	1	1	yes	characteristic
265	C₂	C₂×#13063358	1	1	yes	characteristic
266	C₂	#14583699	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583456

C₂

yes

maximal, characteristic, complemented

#14583433

C₂

yes

maximal, characteristic

#14583207

C₂

yes

maximal, complemented

#14583195

C₂

yes

maximal, characteristic, complemented

#14583190

C₂

yes

maximal, characteristic, complemented

#14583157

C₂

yes

maximal, complemented

#14583145

C₂

yes

maximal

#14583122

C₂

yes

maximal, complemented

#14583110

C₂

yes

maximal, characteristic, complemented

#14583105

C₂

yes

maximal, characteristic, complemented

C₄₃×#423

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

—

C₂×#10621873

C₂²

yes

—

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

—

—

C₂²

yes

characteristic

#13063313

C₂²

yes

—

—

C₂²

yes

—

#13063304

C₂²

yes

characteristic

#13063299

C₂²

yes

characteristic

C₄×Dic₈₆

—

C₄×Dic₈₆

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

C₄×D₁₇₂

C₂²

yes

characteristic

C₄×C₂²⋊D₄₃

—

#13063284

—

#13063282

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

#13063250

C₂²

yes

—

#13063250

C₂²

yes

—

#13063247

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

C₂³

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

characteristic

C₂×Dic₈₆

C₂³

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

C₂³

yes

characteristic

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

Dic₁₇₂

—

#10621873

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

100

D₁₇₂

—

101

C₄×D₄₃

—

102

Dic₈₆

—

103

Dic₈₆

—

104

Dic₈₆

—

105

Dic₈₆

—

106

Dic₈₆

—

107

C₈×C₄₃

—

108

C₈×C₄₃

—

109

C₂²×C₄₃

—

110

C₂²×C₄₃

—

111

C₂²×C₄₃

—

112

C₂²×C₄₃

C₂²×D₄

yes

characteristic

113

C₂×D₄₃

—

114

C₂×D₄₃

—

115

C₂×D₄₃

—

116

C₄×C₄₃

—

117

C₄×C₄₃

—

118

C₄×C₄₃

—

119

C₄×C₄₃

—

120

C₄×C₄₃

#137

yes

—

121

C₄×C₄₃

H(5,𝔽₂)

yes

characteristic

122

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

123

Dic₄₃

—

124

Dic₄₃

—

125

Dic₄₃

—

126

Dic₄₃

—

127

Dic₄₃

—

128

#3252

—

maximal, Sylow

129

C₂×C₄₃

—

130

C₂×C₄₃

#537

yes

characteristic

131

C₂×C₄₃

C₂×#137

yes

characteristic

132

C₂×C₄₃

#575

yes

characteristic

133

D₄₃

—

134

#533

—

135

#529

—

136

#479

—

137

#477

—

138

#476

—

139

#470

—

140

#468

—

141

#464

—

142

#462

—

143

#461

—

144

#423

D₄₃

yes

characteristic, complemented

145

C₄₃

#3252

yes

characteristic, complemented, Sylow

146

C₂×Q₁₆

—

147

C₂×SD₁₆

—

148

C₂×M₁₆

C₂×D₄₃

yes

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

#126

—

152

#125

—

153

#125

—

154

#124

—

155

#123

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

C₂²⋊Q₈

—

159

#121

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

C₄×D₄

—

164

C₄×D₄

—

165

#117

—

166

#117

—

167

C₂×C₄²

C₂×D₄₃

yes

characteristic

168

#107

—

169

#106

—

170

C₄⋊C₈

C₂×D₄₃

yes

characteristic

171

C₄⋊C₈

C₂×D₄₃

yes

characteristic

172

C₄⋊C₈

C₂×D₄₃

yes

—

173

#103

—

174

#103

—

175

#103

—

176

#102

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

D₁₇₂

yes

characteristic

184

C₂²×C₄

D₁₇₂

yes

characteristic

185

C₂²×C₄

C₂²×D₄₃

yes

characteristic

186

Q₁₆

—

172

—

187

SD₁₆

—

172

—

188

M₁₆

—

189

C₂×C₈

C₂²×D₄₃

yes

—

190

C₂×C₈

C₂²×D₄₃

yes

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

D₁₇₂

yes

characteristic

212

C₄²

D₁₇₂

yes

characteristic

213

C₄²

C₂²×D₄₃

yes

characteristic

214

C₄²

C₂²×D₄₃

yes

characteristic

215

C₂³

—

216

C₂³

C₂×D₁₇₂

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

Q₈

—

172

—

222

D₄

—

223

D₄

—

224

D₄

—

172

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

172

—

235

C₂×C₄

C₂×D₁₇₂

yes

characteristic

236

C₂×C₄

C₂×D₁₇₂

yes

characteristic

237

C₂×C₄

C₂×D₁₇₂

yes

characteristic

238

C₂×C₄

C₂×D₁₇₂

yes

characteristic

239

C₂×C₄

C₂×D₁₇₂

yes

characteristic

240

C₂×C₄

C₂³×D₄₃

yes

characteristic

241

C₈

—

242

C₈

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

172

—

247

C₂²

—

172

—

248

C₂²

—

172

—

249

C₂²

C₂²×D₁₇₂

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

172

—

255

C₄

—

172

—

256

C₄

—

172

—

257

C₄

—

172

—

258

C₄

—

172

—

259

C₄

#13063358

yes

—

260

C₄

#13063370

yes

characteristic

261

C₄

#13063373

yes

characteristic

262

C₂

—

263

C₂

—

344

—

264

C₂

#14583480

yes

characteristic

265

C₂

C₂×#13063358

yes

characteristic

266

C₂

#14583699

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#423	D₄₃
hypocenter	C₄₃	#3252
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#423

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
1. #14583456	C₂	semidirect
3. #14583207	C₂	semidirect
4. #14583195	C₂	semidirect
5. #14583190	C₂	semidirect
6. #14583157	C₂	semidirect
8. #14583122	C₂	semidirect
9. #14583110	C₂	semidirect
10. #14583105	C₂	semidirect
11. C₄₃×#423	C₂	semidirect
144. #423	D₄₃	semidirect
145. C₄₃	#3252	semidirect

H ≅ G/N

type

1. #14583456

C₂

semidirect

3. #14583207

C₂

semidirect

4. #14583195

C₂

semidirect

5. #14583190

C₂

semidirect

6. #14583157

C₂

semidirect

8. #14583122

C₂

semidirect

9. #14583110

C₂

semidirect

10. #14583105

C₂

semidirect

11. C₄₃×#423

C₂

semidirect

144. #423

D₄₃

semidirect

145. C₄₃

#3252

semidirect

Subgroups — #19145969

Conjugacy classes of subgroups

Complements