Group #19135679 — subgroups

Subgroups — #19135679

Order 5504.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10621873	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10621884	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063323	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13063248	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582800	C₂	1	1	yes	maximal, characteristic
6	#14582653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#103×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#10621873	—	2	2	no	—
11	C₂×#10621873	—	2	2	no	—
12	C₂×#10621873	—	2	2	no	—
13	C₂×#10621884	—	2	2	no	—
14	C₂×#10621884	—	2	2	no	—
15	C₂×#10621884	—	2	2	no	—
16	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	#13063323	—	2	2	no	—
18	#13063323	—	2	2	no	—
19	C₂×Dic₄₃⋊C₄	—	2	2	no	—
20	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
21	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
22	#13063248	—	2	2	no	—
23	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	#103×C₄₃	—	2	2	no	—
27	C₂³×D₄₃	—	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	—	2	1	no	—
32	C₂×Q₈×C₄₃	—	2	1	no	—
33	C₂×Q₈×C₄₃	D₄	1	2	yes	—
34	C₂²×C₄×C₄₃	—	2	1	no	—
35	C₂²×C₄×C₄₃	—	2	1	no	—
36	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×Dic₄₃	—	2	1	no	—
38	C₂²×Dic₄₃	D₄	1	2	yes	—
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	—	2	1	no	—
44	C₂×D₁₇₂	D₄	1	2	yes	—
45	C₂×Dic₈₆	—	2	1	no	—
46	C₂×Dic₈₆	—	2	1	no	—
47	C₂×Dic₈₆	—	2	1	no	—
48	C₂×Dic₈₆	—	2	1	no	—
49	C₂×Dic₈₆	—	2	1	no	—
50	C₂×Dic₈₆	D₄	1	2	yes	—
51	C₂×C₈×C₄₃	—	2	1	no	—
52	C₂×C₈×C₄₃	—	2	1	no	—
53	C₂×C₈×C₄₃	D₄	1	2	yes	—
54	C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₄⋊C₄×C₄₃	—	2	1	no	—
56	#10621884	—	2	8	no	—
57	(C₂×D₄₃)⋊C₄	—	4	4	no	—
58	Dic₄₃⋊C₄	—	2	8	no	—
59	C₄×Dic₄₃	—	2	1	no	—
60	C₄×Dic₄₃	—	2	1	no	—
61	C₂×C₄₃⋊C₈	—	2	1	no	—
62	C₂×C₄₃⋊C₈	—	2	1	no	—
63	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
64	#10621873	—	2	8	no	—
65	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×D₄₃	—	2	2	no	—
67	C₂²×D₄₃	—	4	1	no	—
68	C₂²×D₄₃	—	4	1	no	—
69	C₂²×D₄₃	—	4	2	no	—
70	C₂²×D₄₃	—	4	2	no	—
71	Q₈×C₄₃	—	2	2	no	—
72	Q₈×C₄₃	—	2	2	no	—
73	Q₈×C₄₃	—	4	1	no	—
74	Q₈×C₄₃	—	4	1	no	—
75	C₂×C₄×C₄₃	—	2	2	no	—
76	C₂×C₄×C₄₃	—	4	1	no	—
77	C₂×C₄×C₄₃	—	4	1	no	—
78	C₂×C₄×C₄₃	—	4	1	no	—
79	C₂×C₄×C₄₃	—	4	2	no	—
80	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
86	C₂×Dic₄₃	—	2	2	no	—
87	C₂×Dic₄₃	—	2	2	no	—
88	C₂×Dic₄₃	—	2	2	no	—
89	C₂×Dic₄₃	—	4	1	no	—
90	C₂×Dic₄₃	—	4	1	no	—
91	C₂×Dic₄₃	SD₁₆	1	4	yes	complemented
92	D₁₇₂	—	2	2	no	—
93	D₁₇₂	—	2	2	no	—
94	D₁₇₂	—	4	1	no	—
95	D₁₇₂	—	4	1	no	—
96	Dic₈₆	—	2	2	no	—
97	Dic₈₆	—	2	2	no	—
98	Dic₈₆	—	4	1	no	—
99	Dic₈₆	—	4	1	no	—
100	C₈×C₄₃	—	2	2	no	—
101	C₄₃⋊C₈	—	2	2	no	—
102	C₂²×C₄₃	#120	1	1	yes	characteristic
103	C₂²×C₄₃	#121	1	1	yes	characteristic
104	C₂²×C₄₃	#127	1	1	yes	characteristic
105	C₂²×C₄₃	C₂×SD₁₆	1	2	yes	—
106	C₂²×C₄₃	#137	1	2	yes	—
107	C₂×D₄₃	—	4	2	no	—
108	C₂×D₄₃	—	4	4	no	—
109	C₂×D₄₃	—	8	2	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	#120	1	1	yes	characteristic
116	C₄×C₄₃	#121	1	1	yes	characteristic
117	C₄×C₄₃	#121	1	1	yes	characteristic
118	Dic₄₃	—	2	4	no	—
119	Dic₄₃	—	4	2	no	—
120	#2013	—	43	1	no	maximal, Sylow
121	C₂×C₄₃	#392	1	1	yes	characteristic
122	C₂×C₄₃	#448	1	2	yes	—
123	C₂×C₄₃	#461	1	2	yes	—
124	C₂×C₄₃	#492	1	1	yes	characteristic
125	C₂×C₄₃	#497	1	1	yes	characteristic
126	D₄₃	—	8	2	no	—
127	C₂²×SD₁₆	—	43	1	no	—
128	C₂²×SD₁₆	—	43	1	no	—
129	C₂×C₄⋊Q₈	—	43	1	no	—
130	C₂×#103	—	43	1	no	—
131	C₂×#103	D₄₃	1	1	yes	characteristic, complemented
132	#390	—	43	1	no	—
133	#336	—	43	1	no	—
134	C₄₃	#2013	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₈	—	43	1	no	—
136	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
137	C₂²×D₄	—	43	1	no	—
138	C₂×SD₁₆	—	86	2	no	—
139	C₂×SD₁₆	—	86	2	no	—
140	C₂×SD₁₆	—	86	2	no	—
141	C₂×SD₁₆	—	86	2	no	—
142	C₂×SD₁₆	—	86	2	no	—
143	C₂×SD₁₆	—	86	2	no	—
144	C₂²×C₈	—	43	1	no	—
145	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
146	C₄⋊Q₈	—	86	2	no	—
147	C₄⋊Q₈	—	86	2	no	—
148	C₂×C₄⋊C₄	—	86	2	no	—
149	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
150	C₂×C₂²⋊C₄	—	86	2	no	—
151	C₂×C₄²	—	43	1	no	—
152	#103	—	2	2	no	—
153	#103	—	86	2	no	—
154	C₂⁴	—	86	1	no	—
155	C₂×Q₈	—	2	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	—	43	2	no	—
161	C₂×Q₈	—	86	1	no	—
162	C₂×Q₈	—	86	1	no	—
163	C₂×Q₈	—	86	1	no	—
164	C₂×Q₈	—	86	1	no	—
165	C₂×Q₈	—	86	1	no	—
166	C₂×Q₈	D₁₇₂	1	2	yes	—
167	C₂×D₄	—	43	2	no	—
168	C₂×D₄	—	86	1	no	—
169	C₂×D₄	—	86	1	no	—
170	C₂×D₄	—	86	1	no	—
171	C₂×D₄	—	86	1	no	—
172	C₂×D₄	—	86	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	43	2	no	—
176	C₂²×C₄	—	86	1	no	—
177	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
178	SD₁₆	—	86	8	no	—
179	SD₁₆	—	86	8	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	43	2	no	—
183	C₂×C₈	—	86	1	no	—
184	C₂×C₈	—	86	1	no	—
185	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	86	8	no	—
189	C₂²⋊C₄	—	172	4	no	—
190	C₄²	—	86	1	no	—
191	C₄²	—	86	1	no	—
192	C₂³	—	86	2	no	—
193	C₂³	—	172	1	no	—
194	C₂³	—	172	1	no	—
195	C₂³	—	172	2	no	—
196	C₂³	—	172	2	no	—
197	C₂³	D₄×D₄₃	1	1	yes	characteristic
198	Q₈	—	2	2	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	4	1	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	86	2	no	—
203	Q₈	—	86	2	no	—
204	Q₈	—	172	1	no	—
205	Q₈	—	172	1	no	—
206	D₄	—	86	2	no	—
207	D₄	—	86	2	no	—
208	D₄	—	172	1	no	—
209	D₄	—	172	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	43	4	no	—
216	C₂×C₄	—	86	2	no	—
217	C₂×C₄	—	86	2	no	—
218	C₂×C₄	—	86	2	no	—
219	C₂×C₄	—	172	1	no	—
220	C₂×C₄	—	172	1	no	—
221	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
222	C₂×C₄	#10621898	1	1	yes	characteristic
223	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
224	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
225	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
226	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
227	C₈	—	2	2	no	—
228	C₈	—	86	2	no	—
229	C₂²	—	344	1	no	—
230	C₂²	—	344	1	no	—
231	C₂²	—	344	2	no	—
232	C₂²	—	172	2	no	—
233	C₂²	—	172	4	no	—
234	C₂²	#13063295	1	1	yes	characteristic
235	C₂²	#13063298	1	1	yes	characteristic
236	C₂²	#13063321	1	1	yes	characteristic
237	C₂²	SD₁₆×D₄₃	1	2	yes	—
238	C₂²	#13063357	1	2	yes	—
239	C₄	—	4	2	no	—
240	C₄	—	8	1	no	—
241	C₄	—	86	4	no	—
242	C₄	—	172	2	no	—
243	C₄	#13063293	1	1	yes	characteristic
244	C₄	#13063295	1	1	yes	characteristic
245	C₄	#13063298	1	1	yes	characteristic
246	C₄	#13063299	1	1	yes	characteristic
247	C₂	—	344	2	no	—
248	C₂	#14582808	1	1	yes	characteristic
249	C₂	#14583039	1	2	yes	—
250	C₂	#14583103	1	2	yes	—
251	C₂	#14583270	1	1	yes	characteristic
252	C₂	#14583292	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10621873

C₂

yes

maximal, characteristic

C₂²×#10621884

C₂

yes

maximal, characteristic

C₂×#13063323

C₂

yes

maximal, characteristic, complemented

C₂×#13063248

C₂

yes

maximal, characteristic, complemented

#14582800

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal, characteristic, complemented

C₂×#103×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×D₁₇₂

C₂²

yes

—

—

—

—

—

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063323

—

#13063323

—

C₂×Dic₄₃⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063248

—

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

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

D₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

#10621884

—

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

—

#10621873

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

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×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

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

SD₁₆

yes

complemented

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

100

C₈×C₄₃

—

101

C₄₃⋊C₈

—

102

C₂²×C₄₃

#120

yes

characteristic

103

C₂²×C₄₃

#121

yes

characteristic

104

C₂²×C₄₃

#127

yes

characteristic

105

C₂²×C₄₃

C₂×SD₁₆

yes

—

106

C₂²×C₄₃

#137

yes

—

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

#120

yes

characteristic

116

C₄×C₄₃

#121

yes

characteristic

117

C₄×C₄₃

#121

yes

characteristic

118

Dic₄₃

—

119

Dic₄₃

—

120

#2013

—

maximal, Sylow

121

C₂×C₄₃

#392

yes

characteristic

122

C₂×C₄₃

#448

yes

—

123

C₂×C₄₃

#461

yes

—

124

C₂×C₄₃

#492

yes

characteristic

125

C₂×C₄₃

#497

yes

characteristic

126

D₄₃

—

127

C₂²×SD₁₆

—

128

C₂²×SD₁₆

—

129

C₂×C₄⋊Q₈

—

130

C₂×#103

—

131

C₂×#103

D₄₃

yes

characteristic, complemented

132

#390

—

133

#336

—

134

C₄₃

#2013

yes

characteristic, complemented, Sylow

135

C₂²×Q₈

—

136

C₂²×Q₈

C₂×D₄₃

yes

characteristic

137

C₂²×D₄

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂×SD₁₆

—

143

C₂×SD₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

C₂×D₄₃

yes

characteristic

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

150

C₂×C₂²⋊C₄

—

151

C₂×C₄²

—

152

#103

—

153

#103

—

154

C₂⁴

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

D₁₇₂

yes

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂²×D₄₃

yes

characteristic

178

SD₁₆

—

179

SD₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

C₂²⋊D₄₃

yes

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

172

—

190

C₄²

—

191

C₄²

—

192

C₂³

—

193

C₂³

—

172

—

194

C₂³

—

172

—

195

C₂³

—

172

—

196

C₂³

—

172

—

197

C₂³

D₄×D₄₃

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

172

—

205

Q₈

—

172

—

206

D₄

—

207

D₄

—

208

D₄

—

172

—

209

D₄

—

172

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

172

—

220

C₂×C₄

—

172

—

221

C₂×C₄

C₂×D₁₇₂

yes

characteristic

222

C₂×C₄

#10621898

yes

characteristic

223

C₂×C₄

D₄×D₄₃

yes

characteristic

224

C₂×C₄

D₄×D₄₃

yes

characteristic

225

C₂×C₄

D₄×D₄₃

yes

characteristic

226

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

227

C₈

—

228

C₈

—

229

C₂²

—

344

—

230

C₂²

—

344

—

231

C₂²

—

344

—

232

C₂²

—

172

—

233

C₂²

—

172

—

234

C₂²

#13063295

yes

characteristic

235

C₂²

#13063298

yes

characteristic

236

C₂²

#13063321

yes

characteristic

237

C₂²

SD₁₆×D₄₃

yes

—

238

C₂²

#13063357

yes

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

172

—

243

C₄

#13063293

yes

characteristic

244

C₄

#13063295

yes

characteristic

245

C₄

#13063298

yes

characteristic

246

C₄

#13063299

yes

characteristic

247

C₂

—

344

—

248

C₂

#14582808

yes

characteristic

249

C₂

#14583039

yes

—

250

C₂

#14583103

yes

—

251

C₂

#14583270

yes

characteristic

252

C₂

#14583292

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	#2013
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
3. C₂×#13063323	C₂	semidirect
4. C₂×#13063248	C₂	semidirect
6. #14582653	C₂	semidirect
7. C₂×#103×C₄₃	C₂	semidirect
91. C₂×Dic₄₃	SD₁₆	semidirect
131. C₂×#103	D₄₃	semidirect
134. C₄₃	#2013	semidirect

H ≅ G/N

type

3. C₂×#13063323

C₂

semidirect

4. C₂×#13063248

C₂

semidirect

6. #14582653

C₂

semidirect

7. C₂×#103×C₄₃

C₂

semidirect

91. C₂×Dic₄₃

SD₁₆

semidirect

131. C₂×#103

D₄₃

semidirect

134. C₄₃

#2013

semidirect

Subgroups — #19135679

Conjugacy classes of subgroups

Complements