Group #19135909 — subgroups

Subgroups — #19135909

Order 5504.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×#10621884	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063247	C₂	1	1	yes	maximal, characteristic
4	#14582806	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582800	C₂	1	1	yes	maximal, characteristic
6	#14582661	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#103×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#10621884	—	2	2	no	—
10	C₂×#10621884	—	2	2	no	—
11	C₂×#10621884	—	2	2	no	—
12	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
15	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
16	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
17	Dic₄₃⋊C₈	—	2	2	no	—
18	#13063247	—	2	2	no	—
19	C₄₃⋊#95	—	2	1	no	—
20	C₄₃⋊#95	—	2	1	no	—
21	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	#103×C₄₃	—	2	2	no	—
25	C₂³×D₄₃	—	2	1	no	—
26	C₂×Q₈×C₄₃	—	2	1	no	—
27	C₂×Q₈×C₄₃	—	2	1	no	—
28	C₂×Q₈×C₄₃	—	2	1	no	—
29	C₂×Q₈×C₄₃	—	2	1	no	—
30	C₂×Q₈×C₄₃	—	2	1	no	—
31	C₂×Q₈×C₄₃	D₄	1	2	yes	—
32	C₂²×C₄×C₄₃	—	2	1	no	—
33	C₂²×C₄×C₄₃	—	2	1	no	—
34	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂²×Dic₄₃	—	2	1	no	—
36	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
37	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
38	C₂×D₁₇₂	—	2	1	no	—
39	C₂×D₁₇₂	—	2	1	no	—
40	C₂×D₁₇₂	—	2	1	no	—
41	C₂×D₁₇₂	—	2	1	no	—
42	C₂×D₁₇₂	—	2	1	no	—
43	C₂×D₁₇₂	D₄	1	2	yes	—
44	C₂×C₈×C₄₃	—	2	1	no	—
45	C₂×C₈×C₄₃	—	2	1	no	—
46	C₂×C₈×C₄₃	—	2	1	no	—
47	C₄⋊C₄×C₄₃	—	2	1	no	—
48	C₄⋊C₄×C₄₃	—	2	1	no	—
49	#10621884	—	2	8	no	—
50	(C₂×D₄₃)⋊C₄	—	4	2	no	—
51	(C₂×D₄₃)⋊C₄	—	4	2	no	—
52	C₄⋊Dic₄₃	—	2	1	no	—
53	C₄⋊Dic₄₃	—	2	1	no	—
54	C₄×Dic₄₃	—	2	1	no	—
55	C₄×Dic₄₃	—	2	1	no	—
56	C₂×C₄₃⋊C₈	—	2	1	no	—
57	C₂×C₄₃⋊C₈	—	2	1	no	—
58	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
59	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×D₄₃	—	2	2	no	—
61	C₂²×D₄₃	—	4	1	no	—
62	C₂²×D₄₃	—	4	1	no	—
63	C₂²×D₄₃	—	4	1	no	—
64	C₂²×D₄₃	—	4	1	no	—
65	C₂²×D₄₃	—	4	1	no	—
66	C₂²×D₄₃	—	4	1	no	—
67	Q₈×C₄₃	—	2	2	no	—
68	Q₈×C₄₃	—	2	2	no	—
69	Q₈×C₄₃	—	4	1	no	—
70	Q₈×C₄₃	—	4	1	no	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	4	1	no	—
73	C₂×C₄×C₄₃	—	4	1	no	—
74	C₂×C₄×C₄₃	—	4	1	no	—
75	C₂×C₄×C₄₃	—	4	1	no	—
76	C₂×C₄×C₄₃	—	4	1	no	—
77	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
81	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
83	C₂×Dic₄₃	—	2	1	no	—
84	C₂×Dic₄₃	—	2	1	no	—
85	C₂×Dic₄₃	—	2	1	no	—
86	C₂×Dic₄₃	—	2	1	no	—
87	C₂×Dic₄₃	—	2	1	no	—
88	C₂×Dic₄₃	—	4	1	no	—
89	C₂×Dic₄₃	—	4	1	no	—
90	C₂×Dic₄₃	—	4	1	no	—
91	C₂×Dic₄₃	SD₁₆	1	2	yes	complemented
92	D₁₇₂	—	2	2	no	—
93	D₁₇₂	—	2	2	no	—
94	D₁₇₂	—	4	1	no	—
95	D₁₇₂	—	4	1	no	—
96	C₈×C₄₃	—	4	1	no	—
97	C₄₃⋊C₈	—	2	2	no	—
98	C₂²×C₄₃	#121	1	1	yes	characteristic
99	C₂²×C₄₃	#121	1	1	yes	characteristic
100	C₂²×C₄₃	#121	1	1	yes	characteristic
101	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
102	C₂²×C₄₃	#135	1	1	yes	characteristic
103	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂²×C₄₃	#137	1	1	yes	characteristic
105	C₂×D₄₃	—	4	2	no	—
106	C₂×D₄₃	—	4	2	no	—
107	C₂×D₄₃	—	4	2	no	—
108	C₂×D₄₃	—	8	1	no	—
109	C₂×D₄₃	—	8	1	no	—
110	C₂×D₄₃	—	8	1	no	—
111	C₂×D₄₃	—	8	1	no	—
112	C₄×C₄₃	—	4	2	no	—
113	C₄×C₄₃	—	8	1	no	—
114	C₄×C₄₃	#120	1	1	yes	characteristic
115	C₄×C₄₃	#123	1	1	yes	characteristic
116	C₄×C₄₃	#123	1	1	yes	characteristic
117	C₄×C₄₃	#124	1	1	yes	characteristic
118	Dic₄₃	—	2	2	no	—
119	Dic₄₃	—	4	1	no	—
120	Dic₄₃	—	8	1	no	—
121	#2055	—	43	1	no	maximal, Sylow
122	C₂×C₄₃	#394	1	1	yes	characteristic
123	C₂×C₄₃	#460	1	1	yes	characteristic
124	C₂×C₄₃	#461	1	1	yes	characteristic
125	C₂×C₄₃	#463	1	1	yes	characteristic
126	C₂×C₄₃	#464	1	1	yes	characteristic
127	C₂×C₄₃	#465	1	1	yes	characteristic
128	C₂×C₄₃	#468	1	1	yes	characteristic
129	D₄₃	—	8	2	no	—
130	C₂²×SD₁₆	—	43	1	no	—
131	C₂×C₄⋊C₈	—	43	1	no	—
132	C₂×#103	D₄₃	1	1	yes	characteristic, complemented
133	C₂×#102	—	43	1	no	—
134	#391	—	43	1	no	—
135	#390	—	43	1	no	—
136	#340	—	43	1	no	—
137	C₄₃	#2055	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
139	C₂²×D₄	—	43	1	no	—
140	C₂×SD₁₆	—	86	2	no	—
141	C₂×SD₁₆	—	86	2	no	—
142	C₂×SD₁₆	—	86	2	no	—
143	C₂²×C₈	—	43	1	no	—
144	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
145	C₂×C₄⋊C₄	—	43	1	no	—
146	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
147	C₂×C₂²⋊C₄	—	86	1	no	—
148	C₂×C₂²⋊C₄	—	86	1	no	—
149	C₂×C₄²	—	43	1	no	—
150	C₄⋊C₈	—	86	2	no	—
151	#103	—	2	2	no	—
152	#102	—	86	2	no	—
153	#95	—	86	1	no	—
154	#95	—	86	1	no	—
155	C₂⁴	—	86	1	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	2	1	no	—
161	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
162	C₂×D₄	—	43	2	no	—
163	C₂×D₄	—	86	1	no	—
164	C₂×D₄	—	86	1	no	—
165	C₂×D₄	—	86	1	no	—
166	C₂×D₄	—	86	1	no	—
167	C₂×D₄	—	86	1	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	43	1	no	—
171	C₂²×C₄	—	43	1	no	—
172	C₂²×C₄	—	86	1	no	—
173	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
174	SD₁₆	—	86	8	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	43	2	no	—
179	C₂×C₈	—	86	1	no	—
180	C₂×C₈	—	86	1	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	86	1	no	—
184	C₄⋊C₄	—	86	1	no	—
185	C₂²⋊C₄	—	172	2	no	—
186	C₂²⋊C₄	—	172	2	no	—
187	C₄²	—	86	1	no	—
188	C₄²	—	86	1	no	—
189	C₂³	—	86	2	no	—
190	C₂³	—	172	1	no	—
191	C₂³	—	172	1	no	—
192	C₂³	—	172	1	no	—
193	C₂³	—	172	1	no	—
194	C₂³	—	172	1	no	—
195	C₂³	—	172	1	no	—
196	C₂³	D₄×D₄₃	1	1	yes	characteristic
197	Q₈	—	2	2	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	4	1	no	—
200	Q₈	—	4	1	no	—
201	D₄	—	86	2	no	—
202	D₄	—	86	2	no	—
203	D₄	—	172	1	no	—
204	D₄	—	172	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	43	2	no	—
212	C₂×C₄	—	86	1	no	—
213	C₂×C₄	—	86	1	no	—
214	C₂×C₄	—	86	1	no	—
215	C₂×C₄	—	86	1	no	—
216	C₂×C₄	—	86	1	no	—
217	C₂×C₄	—	172	1	no	—
218	C₂×C₄	—	172	1	no	—
219	C₂×C₄	—	172	1	no	—
220	C₂×C₄	#10621898	1	1	yes	characteristic
221	C₂×C₄	#10621898	1	1	yes	characteristic
222	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
223	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
224	C₂×C₄	#10621900	1	1	yes	characteristic
225	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
226	C₈	—	4	1	no	—
227	C₈	—	86	2	no	—
228	C₂²	—	344	1	no	—
229	C₂²	—	344	1	no	—
230	C₂²	—	344	1	no	—
231	C₂²	—	344	1	no	—
232	C₂²	—	172	2	no	—
233	C₂²	—	172	2	no	—
234	C₂²	—	172	2	no	—
235	C₂²	#13063297	1	1	yes	characteristic
236	C₂²	#13063298	1	1	yes	characteristic
237	C₂²	#13063298	1	1	yes	characteristic
238	C₂²	SD₁₆×D₄₃	1	1	yes	characteristic
239	C₂²	#13063348	1	1	yes	characteristic
240	C₂²	#13063352	1	1	yes	characteristic
241	C₂²	#13063357	1	1	yes	characteristic
242	C₄	—	4	2	no	—
243	C₄	—	8	1	no	—
244	C₄	—	86	2	no	—
245	C₄	—	344	1	no	—
246	C₄	—	172	1	no	—
247	C₄	#13063293	1	1	yes	characteristic
248	C₄	#13063307	1	1	yes	characteristic
249	C₄	#13063308	1	1	yes	characteristic
250	C₄	#13063311	1	1	yes	characteristic
251	C₂	—	344	2	no	—
252	C₂	#14582814	1	1	yes	characteristic
253	C₂	#14583097	1	1	yes	characteristic
254	C₂	#14583103	1	1	yes	characteristic
255	C₂	#14583117	1	1	yes	characteristic
256	C₂	#14583123	1	1	yes	characteristic
257	C₂	#14583131	1	1	yes	characteristic
258	C₂	#14583148	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10621884

C₂

yes

maximal, characteristic

C₂×Dic₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#13063247

C₂

yes

maximal, characteristic

#14582806

C₂

yes

maximal, characteristic, complemented

#14582800

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal, characteristic, complemented

C₂×#103×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

—

—

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063247

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

C₂³×D₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

#10621884

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

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

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

SD₁₆

yes

complemented

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

100

C₂²×C₄₃

#121

yes

characteristic

101

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

102

C₂²×C₄₃

#135

yes

characteristic

103

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

104

C₂²×C₄₃

#137

yes

characteristic

105

C₂×D₄₃

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₂×D₄₃

—

109

C₂×D₄₃

—

110

C₂×D₄₃

—

111

C₂×D₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

#120

yes

characteristic

115

C₄×C₄₃

#123

yes

characteristic

116

C₄×C₄₃

#123

yes

characteristic

117

C₄×C₄₃

#124

yes

characteristic

118

Dic₄₃

—

119

Dic₄₃

—

120

Dic₄₃

—

121

#2055

—

maximal, Sylow

122

C₂×C₄₃

#394

yes

characteristic

123

C₂×C₄₃

#460

yes

characteristic

124

C₂×C₄₃

#461

yes

characteristic

125

C₂×C₄₃

#463

yes

characteristic

126

C₂×C₄₃

#464

yes

characteristic

127

C₂×C₄₃

#465

yes

characteristic

128

C₂×C₄₃

#468

yes

characteristic

129

D₄₃

—

130

C₂²×SD₁₆

—

131

C₂×C₄⋊C₈

—

132

C₂×#103

D₄₃

yes

characteristic, complemented

133

C₂×#102

—

134

#391

—

135

#390

—

136

#340

—

137

C₄₃

#2055

yes

characteristic, complemented, Sylow

138

C₂²×Q₈

C₂×D₄₃

yes

characteristic

139

C₂²×D₄

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂×SD₁₆

—

143

C₂²×C₈

—

144

C₂²×C₈

C₂×D₄₃

yes

characteristic

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₄²

—

150

C₄⋊C₈

—

151

#103

—

152

#102

—

153

#95

—

154

#95

—

155

C₂⁴

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₂²⋊D₄₃

yes

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂²×D₄₃

yes

characteristic

174

SD₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

172

—

186

C₂²⋊C₄

—

172

—

187

C₄²

—

188

C₄²

—

189

C₂³

—

190

C₂³

—

172

—

191

C₂³

—

172

—

192

C₂³

—

172

—

193

C₂³

—

172

—

194

C₂³

—

172

—

195

C₂³

—

172

—

196

C₂³

D₄×D₄₃

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

D₄

—

202

D₄

—

203

D₄

—

172

—

204

D₄

—

172

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

172

—

218

C₂×C₄

—

172

—

219

C₂×C₄

—

172

—

220

C₂×C₄

#10621898

yes

characteristic

221

C₂×C₄

#10621898

yes

characteristic

222

C₂×C₄

D₄×D₄₃

yes

characteristic

223

C₂×C₄

D₄×D₄₃

yes

characteristic

224

C₂×C₄

#10621900

yes

characteristic

225

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

226

C₈

—

227

C₈

—

228

C₂²

—

344

—

229

C₂²

—

344

—

230

C₂²

—

344

—

231

C₂²

—

344

—

232

C₂²

—

172

—

233

C₂²

—

172

—

234

C₂²

—

172

—

235

C₂²

#13063297

yes

characteristic

236

C₂²

#13063298

yes

characteristic

237

C₂²

#13063298

yes

characteristic

238

C₂²

SD₁₆×D₄₃

yes

characteristic

239

C₂²

#13063348

yes

characteristic

240

C₂²

#13063352

yes

characteristic

241

C₂²

#13063357

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

344

—

246

C₄

—

172

—

247

C₄

#13063293

yes

characteristic

248

C₄

#13063307

yes

characteristic

249

C₄

#13063308

yes

characteristic

250

C₄

#13063311

yes

characteristic

251

C₂

—

344

—

252

C₂

#14582814

yes

characteristic

253

C₂

#14583097

yes

characteristic

254

C₂

#14583103

yes

characteristic

255

C₂

#14583117

yes

characteristic

256

C₂

#14583123

yes

characteristic

257

C₂

#14583131

yes

characteristic

258

C₂

#14583148

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#103×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#103	D₄₃
hypocenter	C₄₃	#2055
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#103×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
2. C₂×Dic₄₃⋊C₈	C₂	semidirect
4. #14582806	C₂	semidirect
6. #14582661	C₂	semidirect
7. C₂×#103×C₄₃	C₂	semidirect
91. C₂×Dic₄₃	SD₁₆	semidirect
132. C₂×#103	D₄₃	semidirect
137. C₄₃	#2055	semidirect

H ≅ G/N

type

2. C₂×Dic₄₃⋊C₈

C₂

semidirect

4. #14582806

C₂

semidirect

6. #14582661

C₂

semidirect

7. C₂×#103×C₄₃

C₂

semidirect

91. C₂×Dic₄₃

SD₁₆

semidirect

132. C₂×#103

D₄₃

semidirect

137. C₄₃

#2055

semidirect

Subgroups — #19135909

Conjugacy classes of subgroups

Complements