Group #19145815 — subgroups

Subgroups — #19145815

Order 5504.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583431	C₂	1	1	yes	maximal, characteristic
3	#14583306	C₂	1	2	yes	maximal, complemented
4	#14583257	C₂	1	2	yes	maximal, complemented
5	#14583231	C₂	1	2	yes	maximal, complemented
6	#14583211	C₂	1	2	yes	maximal
7	#14583195	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583191	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583189	C₂	1	1	yes	maximal, characteristic, complemented
10	#14582955	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₄₃	—	2	1	no	—
13	#13063325	C₂²	1	1	yes	characteristic
14	#13063324	—	2	1	no	—
15	#13063324	C₂²	1	2	yes	—
16	#13063323	—	2	1	no	—
17	#13063318	—	2	1	no	—
18	#13063316	C₂²	1	1	yes	characteristic
19	#13063312	C₂²	1	1	yes	characteristic
20	#13063307	—	2	1	no	—
21	#13063305	C₂²	1	1	yes	characteristic
22	#13063296	C₂²	1	1	yes	characteristic
23	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₄₃	—	2	1	no	—
25	#13063284	—	2	1	no	—
26	C₄⋊C₄×D₄₃	—	2	1	no	—
27	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
28	C₄²×D₄₃	C₂²	1	1	yes	characteristic
29	#13063259	C₂²	1	2	yes	—
30	#13063258	C₂²	1	2	yes	—
31	#13063256	C₂²	1	2	yes	—
32	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
33	#13063250	C₂²	1	2	yes	—
34	#13063248	C₂²	1	2	yes	—
35	#13063246	C₂²	1	2	yes	—
36	(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
37	#13063235	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
40	#106×C₄₃	C₂²	1	2	yes	—
41	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
42	#102×C₄₃	C₂²	1	2	yes	—
43	C₂×Q₈×C₄₃	—	2	1	no	—
44	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	—	2	1	no	—
46	C₂×C₂²⋊D₄₃	—	2	1	no	—
47	Q₈×D₄₃	—	4	4	no	—
48	C₂×C₄×D₄₃	—	2	2	no	—
49	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
52	C₂×Dic₈₆	—	2	1	no	—
53	C₂×Dic₈₆	—	2	2	no	—
54	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
55	C₂×C₈×C₄₃	C₂³	1	2	yes	—
56	C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
58	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂²⋊C₄×C₄₃	—	2	1	no	—
60	C₄²×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²⋊Dic₄₃	—	2	1	no	—
62	C₂²⋊Dic₄₃	—	2	1	no	—
63	C₂²⋊Dic₄₃	—	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	Dic₄₃⋊C₄	—	2	1	no	—
71	Dic₄₃⋊C₄	—	2	2	no	—
72	Dic₄₃⋊C₄	—	2	2	no	—
73	Dic₄₃⋊C₄	—	2	1	no	—
74	C₄×Dic₄₃	—	2	1	no	—
75	C₄×Dic₄₃	D₄	1	1	yes	characteristic
76	C₄×Dic₄₃	D₄	1	1	yes	characteristic
77	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
79	C₂³×C₄₃	—	2	1	no	—
80	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₄₃	—	4	2	no	—
82	D₄×C₄₃	—	2	1	no	—
83	D₄×C₄₃	—	2	1	no	—
84	C₂×C₄×C₄₃	—	2	2	no	—
85	C₂×C₄×C₄₃	—	2	1	no	—
86	C₂×C₄×C₄₃	—	4	2	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	C₂⁴	1	1	yes	characteristic
90	C₂²⋊D₄₃	—	4	2	no	—
91	C₂×Dic₄₃	—	2	1	no	—
92	C₂×Dic₄₃	—	2	1	no	—
93	C₂×Dic₄₃	—	2	2	no	—
94	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
97	C₄×D₄₃	—	2	2	no	—
98	C₄×D₄₃	—	2	2	no	—
99	C₄×D₄₃	—	2	1	no	—
100	C₄×D₄₃	—	2	1	no	—
101	C₄×D₄₃	—	4	4	no	—
102	Dic₈₆	—	2	1	no	—
103	Dic₈₆	—	2	1	no	—
104	Dic₈₆	—	4	4	no	—
105	Dic₈₆	—	4	2	no	—
106	C₈×C₄₃	—	2	2	no	—
107	C₄₃⋊C₈	—	2	2	no	—
108	C₂²×C₄₃	—	4	1	no	—
109	C₂²×C₄₃	—	4	1	no	—
110	C₂²×C₄₃	—	4	1	no	—
111	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
112	C₂×D₄₃	—	2	1	no	—
113	C₂×D₄₃	—	2	1	no	—
114	C₂×D₄₃	AGL(1,ℤ/8)	1	2	yes	—
115	C₄×C₄₃	—	2	1	no	—
116	C₄×C₄₃	—	4	2	no	—
117	C₄×C₄₃	—	4	1	no	—
118	C₄×C₄₃	#137	1	2	yes	—
119	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
120	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
121	Dic₄₃	—	2	1	no	—
122	Dic₄₃	—	2	1	no	—
123	Dic₄₃	—	2	1	no	—
124	Dic₄₃	—	4	1	no	—
125	Dic₄₃	—	4	2	no	—
126	Dic₄₃	—	4	1	no	—
127	#3238	—	43	1	no	maximal, Sylow
128	C₂×C₄₃	—	8	1	no	—
129	C₂×C₄₃	#536	1	1	yes	characteristic
130	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
131	C₂×C₄₃	C₂×#137	1	1	yes	characteristic
132	D₄₃	—	2	2	no	—
133	C₂×C₄⋊Q₈	—	43	1	no	—
134	#529	—	43	1	no	—
135	#501	—	43	2	no	—
136	#489	—	43	2	no	—
137	#483	—	43	2	no	—
138	#480	—	43	2	no	—
139	#477	—	43	1	no	—
140	#477	—	43	1	no	—
141	#476	—	43	1	no	—
142	#476	D₄₃	1	1	yes	characteristic, complemented
143	#432	—	43	1	no	—
144	C₄₃	#3238	1	1	yes	characteristic, complemented, Sylow
145	C₂²×Q₈	—	86	1	no	—
146	C₄⋊Q₈	—	43	2	no	—
147	C₄⋊Q₈	—	43	1	no	—
148	C₄⋊Q₈	—	86	1	no	—
149	C₄⋊Q₈	—	86	1	no	—
150	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
151	#126	—	86	1	no	—
152	#125	—	43	1	no	—
153	#124	—	43	1	no	—
154	#123	—	86	1	no	—
155	C₂²⋊Q₈	—	43	1	no	—
156	#121	—	43	1	no	—
157	C₄×Q₈	—	43	1	no	—
158	C₄×D₄	—	86	1	no	—
159	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
160	#117	—	86	1	no	—
161	C₂×C₄⋊C₄	—	43	2	no	—
162	C₂×C₄⋊C₄	—	86	1	no	—
163	C₂×C₄²	—	43	1	no	—
164	#107	—	43	2	no	—
165	#107	—	43	2	no	—
166	#106	—	43	2	no	—
167	#106	C₂×D₄₃	1	2	yes	—
168	C₄⋊C₈	—	43	1	no	—
169	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
170	#103	—	43	2	no	—
171	#103	—	43	2	no	—
172	#102	—	43	2	no	—
173	#102	C₂×D₄₃	1	2	yes	—
174	C₂²⋊C₈	—	43	2	no	—
175	#97	—	43	2	no	—
176	C₂×Q₈	—	2	1	no	—
177	C₂×Q₈	—	43	1	no	—
178	C₂×Q₈	—	86	2	no	—
179	C₂×Q₈	—	86	1	no	—
180	C₂×Q₈	—	172	4	no	—
181	C₂×D₄	—	86	1	no	—
182	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	43	1	no	—
185	C₂²×C₄	—	43	1	no	—
186	C₂²×C₄	—	43	1	no	—
187	C₂²×C₄	—	86	2	no	—
188	C₂×C₈	—	43	2	no	—
189	C₂×C₈	C₂²×D₄₃	1	2	yes	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	43	2	no	—
192	C₄⋊C₄	—	43	1	no	—
193	C₄⋊C₄	—	86	2	no	—
194	C₄⋊C₄	—	86	2	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	1	no	—
200	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
201	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	86	1	no	—
204	C₂²⋊C₄	—	86	1	no	—
205	C₂²⋊C₄	—	86	1	no	—
206	C₂²⋊C₄	—	86	1	no	—
207	C₄²	—	43	1	no	—
208	C₄²	—	43	1	no	—
209	C₄²	—	43	1	no	—
210	C₄²	—	86	1	no	—
211	C₄²	C₂²×D₄₃	1	1	yes	characteristic
212	C₂³	—	2	1	no	—
213	C₂³	—	43	1	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	86	1	no	—
216	Q₈	—	86	1	no	—
217	Q₈	—	172	2	no	—
218	Q₈	—	172	4	no	—
219	D₄	—	2	1	no	—
220	D₄	—	2	1	no	—
221	D₄	—	172	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	43	1	no	—
226	C₂×C₄	—	43	1	no	—
227	C₂×C₄	—	43	1	no	—
228	C₂×C₄	—	86	2	no	—
229	C₂×C₄	—	86	2	no	—
230	C₂×C₄	—	86	1	no	—
231	C₂×C₄	—	86	1	no	—
232	C₂×C₄	—	86	1	no	—
233	C₂×C₄	—	86	1	no	—
234	C₂×C₄	—	86	2	no	—
235	C₂×C₄	—	172	4	no	—
236	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
237	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
238	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	—	86	2	no	—
241	C₂²	—	4	1	no	—
242	C₂²	—	4	1	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	43	2	no	—
245	C₂²	—	86	1	no	—
246	C₂²	—	86	1	no	—
247	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	—	4	1	no	—
251	C₄	—	86	1	no	—
252	C₄	—	86	1	no	—
253	C₄	—	86	1	no	—
254	C₄	—	172	2	no	—
255	C₄	—	172	1	no	—
256	C₄	—	172	1	no	—
257	C₄	#13063354	1	2	yes	—
258	C₄	#13063372	1	1	yes	characteristic
259	C₄	#13063373	1	1	yes	characteristic
260	C₂	—	8	1	no	—
261	C₂	—	86	2	no	—
262	C₂	#14583472	1	1	yes	characteristic
263	C₂	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
264	C₂	C₂×#13063354	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₄₃

C₂

yes

maximal, characteristic, complemented

#14583431

C₂

yes

maximal, characteristic

#14583306

C₂

yes

maximal, complemented

#14583257

C₂

yes

maximal, complemented

#14583231

C₂

yes

maximal, complemented

#14583211

C₂

yes

maximal

#14583195

C₂

yes

maximal, characteristic, complemented

#14583191

C₂

yes

maximal, characteristic, complemented

#14583189

C₂

yes

maximal, characteristic, complemented

#14582955

C₂

yes

maximal, characteristic, complemented

C₄₃×#476

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₃

—

#13063325

C₂²

yes

characteristic

#13063324

—

#13063324

C₂²

yes

—

#13063323

—

#13063318

—

#13063316

C₂²

yes

characteristic

#13063312

C₂²

yes

characteristic

#13063307

—

#13063305

C₂²

yes

characteristic

#13063296

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

characteristic

C₄×C₂²⋊D₄₃

—

#13063284

—

C₄⋊C₄×D₄₃

—

C₄⋊C₄×D₄₃

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063258

C₂²

yes

—

#13063256

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063250

C₂²

yes

—

#13063248

C₂²

yes

—

#13063246

C₂²

yes

—

(C₂×D₄₃)⋊C₈

C₂²

yes

—

#13063235

C₂²

yes

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄×D₄×C₄₃

C₂²

yes

characteristic

#106×C₄₃

C₂²

yes

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

#102×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂×C₂²⋊D₄₃

—

Q₈×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂³

yes

characteristic

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

characteristic

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

—

C₂²×D₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×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

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

100

C₄×D₄₃

—

101

C₄×D₄₃

—

102

Dic₈₆

—

103

Dic₈₆

—

104

Dic₈₆

—

105

Dic₈₆

—

106

C₈×C₄₃

—

107

C₄₃⋊C₈

—

108

C₂²×C₄₃

—

109

C₂²×C₄₃

—

110

C₂²×C₄₃

—

111

C₂²×C₄₃

C₂²×D₄

yes

characteristic

112

C₂×D₄₃

—

113

C₂×D₄₃

—

114

C₂×D₄₃

AGL(1,ℤ/8)

yes

—

115

C₄×C₄₃

—

116

C₄×C₄₃

—

117

C₄×C₄₃

—

118

C₄×C₄₃

#137

yes

—

119

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

120

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

121

Dic₄₃

—

122

Dic₄₃

—

123

Dic₄₃

—

124

Dic₄₃

—

125

Dic₄₃

—

126

Dic₄₃

—

127

#3238

—

maximal, Sylow

128

C₂×C₄₃

—

129

C₂×C₄₃

#536

yes

characteristic

130

C₂×C₄₃

C₂×AGL(1,ℤ/8)

yes

characteristic

131

C₂×C₄₃

C₂×#137

yes

characteristic

132

D₄₃

—

133

C₂×C₄⋊Q₈

—

134

#529

—

135

#501

—

136

#489

—

137

#483

—

138

#480

—

139

#477

—

140

#477

—

141

#476

—

142

#476

D₄₃

yes

characteristic, complemented

143

#432

—

144

C₄₃

#3238

yes

characteristic, complemented, Sylow

145

C₂²×Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

151

#126

—

152

#125

—

153

#124

—

154

#123

—

155

C₂²⋊Q₈

—

156

#121

—

157

C₄×Q₈

—

158

C₄×D₄

—

159

C₄×D₄

C₂×D₄₃

yes

characteristic

160

#117

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

—

164

#107

—

165

#107

—

166

#106

—

167

#106

C₂×D₄₃

yes

—

168

C₄⋊C₈

—

169

C₄⋊C₈

C₂×D₄₃

yes

characteristic

170

#103

—

171

#103

—

172

#102

—

173

#102

C₂×D₄₃

yes

—

174

C₂²⋊C₈

—

175

#97

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

172

—

181

C₂×D₄

—

182

C₂×D₄

C₂²×D₄₃

yes

characteristic

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂×C₈

—

189

C₂×C₈

C₂²×D₄₃

yes

—

190

C₄⋊C₄

—

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

C₂²×D₄₃

yes

—

201

C₄⋊C₄

C₂²×D₄₃

yes

characteristic

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

C₂²×D₄₃

yes

characteristic

212

C₂³

—

213

C₂³

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

172

—

218

Q₈

—

172

—

219

D₄

—

220

D₄

—

221

D₄

—

172

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

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

—

235

C₂×C₄

—

172

—

236

C₂×C₄

D₄×D₄₃

yes

characteristic

237

C₂×C₄

D₄×D₄₃

yes

characteristic

238

C₂×C₄

C₂³×D₄₃

yes

characteristic

239

C₈

—

240

C₈

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

C₂×D₄×D₄₃

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

172

—

255

C₄

—

172

—

256

C₄

—

172

—

257

C₄

#13063354

yes

—

258

C₄

#13063372

yes

characteristic

259

C₄

#13063373

yes

characteristic

260

C₂

—

261

C₂

—

262

C₂

#14583472

yes

characteristic

263

C₂

AGL(1,ℤ/8)×D₄₃

yes

characteristic

264

C₂

C₂×#13063354

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#476	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#476	D₄₃
hypocenter	C₄₃	#3238
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #476

subgroup

G/H

center

C₂²

C₂×D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#476

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #476

N	H ≅ G/N	type
1. C₄⋊Q₈×D₄₃	C₂	semidirect
3. #14583306	C₂	semidirect
4. #14583257	C₂	semidirect
5. #14583231	C₂	semidirect
7. #14583195	C₂	semidirect
8. #14583191	C₂	semidirect
9. #14583189	C₂	semidirect
10. #14582955	C₂	semidirect
11. C₄₃×#476	C₂	semidirect
142. #476	D₄₃	semidirect
144. C₄₃	#3238	semidirect

H ≅ G/N

type

1. C₄⋊Q₈×D₄₃

C₂

semidirect

3. #14583306

C₂

semidirect

4. #14583257

C₂

semidirect

5. #14583231

C₂

semidirect

7. #14583195

C₂

semidirect

8. #14583191

C₂

semidirect

9. #14583189

C₂

semidirect

10. #14582955

C₂

semidirect

11. C₄₃×#476

C₂

semidirect

142. #476

D₄₃

semidirect

144. C₄₃

#3238

semidirect

Subgroups — #19145815

Conjugacy classes of subgroups

Complements