Group #19134593 — subgroups

Subgroups — #19134593

Order 5504.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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×D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063246	C₂	1	1	yes	maximal, characteristic
4	#14582768	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582662	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582661	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#102×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₄₃	—	2	1	no	—
9	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	D₄×Dic₄₃	—	2	2	no	—
11	D₄×Dic₄₃	C₄	1	4	yes	complemented
12	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₃⋊C₄	—	2	1	no	—
15	C₂×Dic₄₃⋊C₄	—	2	1	no	—
16	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
17	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
18	Dic₄₃⋊C₈	—	2	2	no	—
19	#13063246	—	2	2	no	—
20	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	#102×C₄₃	—	2	2	no	—
24	C₂⁴×C₄₃	—	2	1	no	—
25	C₂×D₄×C₄₃	—	2	1	no	—
26	C₂×D₄×C₄₃	—	2	1	no	—
27	C₂×D₄×C₄₃	—	2	1	no	—
28	C₂×D₄×C₄₃	C₂×C₄	1	2	yes	—
29	C₂×D₄×C₄₃	D₄	1	2	yes	—
30	C₂×D₄×C₄₃	Q₈	1	2	yes	—
31	C₂²×C₄×C₄₃	—	2	1	no	—
32	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂²×Dic₄₃	—	2	4	no	—
34	C₂²×Dic₄₃	—	2	1	no	—
35	C₂²×Dic₄₃	—	2	1	no	—
36	C₂²×Dic₄₃	—	4	2	no	—
37	C₂²×Dic₄₃	—	4	2	no	—
38	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
39	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
40	C₂×C₈×C₄₃	—	2	1	no	—
41	C₂×C₈×C₄₃	—	2	1	no	—
42	C₂×C₈×C₄₃	—	2	1	no	—
43	C₄⋊C₄×C₄₃	—	2	1	no	—
44	C₄⋊C₄×C₄₃	—	2	1	no	—
45	C₂²⋊Dic₄₃	—	2	4	no	—
46	C₄⋊Dic₄₃	—	2	1	no	—
47	C₄⋊Dic₄₃	—	2	1	no	—
48	C₄⋊Dic₄₃	—	2	1	no	—
49	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
50	Dic₄₃⋊C₄	—	4	2	no	—
51	Dic₄₃⋊C₄	—	4	2	no	—
52	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
53	C₄×Dic₄₃	D₄	1	2	yes	—
54	C₂×C₄₃⋊C₈	—	2	1	no	—
55	C₂×C₄₃⋊C₈	—	2	1	no	—
56	C₂×C₄₃⋊C₈	—	2	1	no	—
57	C₂³×C₄₃	—	2	2	no	—
58	C₂³×C₄₃	—	2	2	no	—
59	C₂³×C₄₃	—	2	2	no	—
60	C₂³×C₄₃	—	4	1	no	—
61	C₂³×C₄₃	—	4	1	no	—
62	C₂³×C₄₃	—	4	1	no	—
63	C₂³×C₄₃	—	4	1	no	—
64	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
65	D₄×C₄₃	—	2	2	no	—
66	D₄×C₄₃	—	2	2	no	—
67	D₄×C₄₃	—	2	2	no	—
68	D₄×C₄₃	C₄⋊C₄	1	4	yes	complemented
69	C₂×C₄×C₄₃	—	4	1	no	—
70	C₂×C₄×C₄₃	—	4	1	no	—
71	C₂×C₄×C₄₃	—	4	1	no	—
72	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
77	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
78	C₂×Dic₄₃	—	2	1	no	—
79	C₂×Dic₄₃	—	2	1	no	—
80	C₂×Dic₄₃	—	2	2	no	—
81	C₂×Dic₄₃	—	4	1	no	—
82	C₂×Dic₄₃	—	4	1	no	—
83	C₂×Dic₄₃	—	4	8	no	—
84	C₂×Dic₄₃	—	4	1	no	—
85	C₂×Dic₄₃	—	4	1	no	—
86	C₂×Dic₄₃	—	4	1	no	—
87	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
88	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
89	C₂×Dic₄₃	D₈	1	2	yes	—
90	C₂×Dic₄₃	SD₁₆	1	2	yes	—
91	C₈×C₄₃	—	4	1	no	—
92	C₄₃⋊C₈	—	4	1	no	—
93	C₂²×C₄₃	—	2	4	no	—
94	C₂²×C₄₃	—	4	2	no	—
95	C₂²×C₄₃	—	4	2	no	—
96	C₂²×C₄₃	—	4	2	no	—
97	C₂²×C₄₃	—	4	2	no	—
98	C₂²×C₄₃	—	4	2	no	—
99	C₂²×C₄₃	—	4	2	no	—
100	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄₃	#121	1	1	yes	characteristic
102	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
103	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
104	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
105	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂²×C₄₃	#137	1	1	yes	characteristic
107	C₄×C₄₃	—	8	1	no	—
108	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₄×C₄₃	#117	1	1	yes	characteristic
110	C₄×C₄₃	#121	1	1	yes	characteristic
111	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
112	Dic₄₃	—	2	2	no	—
113	Dic₄₃	—	4	2	no	—
114	Dic₄₃	—	8	1	no	—
115	Dic₄₃	#102	1	4	yes	complemented
116	#1802	—	43	1	no	maximal, Sylow
117	C₂×C₄₃	—	4	4	no	—
118	C₂×C₄₃	#380	1	1	yes	characteristic
119	C₂×C₄₃	C₂×#102	1	1	yes	characteristic
120	C₂×C₄₃	#417	1	1	yes	characteristic
121	C₂×C₄₃	#459	1	1	yes	characteristic
122	C₂×C₄₃	#461	1	1	yes	characteristic
123	C₂×C₄₃	#474	1	1	yes	characteristic
124	C₂×C₄₃	#476	1	1	yes	characteristic
125	C₂×C₄×D₄	—	43	1	no	—
126	C₂×C₄⋊C₈	—	43	1	no	—
127	C₂×#102	—	43	1	no	—
128	C₂×#102	D₄₃	1	1	yes	characteristic
129	#384	—	43	1	no	—
130	#340	—	43	1	no	—
131	#340	—	43	1	no	—
132	C₄₃	#1802	1	1	yes	characteristic, complemented, Sylow
133	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
134	C₂³×C₄	—	86	1	no	—
135	C₂²×C₈	—	43	1	no	—
136	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
137	C₄×D₄	—	43	4	no	—
138	C₄×D₄	—	86	2	no	—
139	C₂×C₄⋊C₄	—	43	1	no	—
140	C₂×C₄⋊C₄	—	43	1	no	—
141	C₂×C₄⋊C₄	—	86	1	no	—
142	C₂×C₄⋊C₄	—	86	1	no	—
143	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	—	86	1	no	—
145	C₂×C₄²	—	43	1	no	—
146	C₄⋊C₈	—	86	2	no	—
147	#102	—	2	2	no	—
148	#102	—	86	2	no	—
149	C₂⁴	—	2	1	no	—
150	C₂×D₄	—	2	1	no	—
151	C₂×D₄	—	2	1	no	—
152	C₂×D₄	—	2	1	no	—
153	C₂×D₄	Dic₈₆	1	2	yes	—
154	C₂×D₄	C₄×D₄₃	1	2	yes	—
155	C₂×D₄	C₂²⋊D₄₃	1	2	yes	—
156	C₂²×C₄	—	2	1	no	—
157	C₂²×C₄	—	43	1	no	—
158	C₂²×C₄	—	43	1	no	—
159	C₂²×C₄	—	86	4	no	—
160	C₂²×C₄	—	86	1	no	—
161	C₂²×C₄	—	86	1	no	—
162	C₂²×C₄	—	172	2	no	—
163	C₂²×C₄	—	172	2	no	—
164	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	86	1	no	—
169	C₂×C₈	—	86	1	no	—
170	C₂×C₈	—	86	1	no	—
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	43	2	no	—
174	C₄⋊C₄	—	86	1	no	—
175	C₄⋊C₄	—	86	1	no	—
176	C₄⋊C₄	—	86	1	no	—
177	C₄⋊C₄	—	172	2	no	—
178	C₄⋊C₄	—	172	2	no	—
179	C₂²⋊C₄	—	86	4	no	—
180	C₄²	—	43	2	no	—
181	C₄²	—	43	2	no	—
182	C₂³	—	2	2	no	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	1	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	1	no	—
189	C₂³	D₄×D₄₃	1	1	yes	characteristic
190	D₄	—	2	2	no	—
191	D₄	—	2	2	no	—
192	D₄	—	2	2	no	—
193	D₄	Dic₄₃⋊C₄	1	4	yes	complemented
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	43	2	no	—
198	C₂×C₄	—	43	2	no	—
199	C₂×C₄	—	43	2	no	—
200	C₂×C₄	—	43	2	no	—
201	C₂×C₄	—	86	1	no	—
202	C₂×C₄	—	86	1	no	—
203	C₂×C₄	—	86	2	no	—
204	C₂×C₄	—	172	8	no	—
205	C₂×C₄	—	172	1	no	—
206	C₂×C₄	—	172	1	no	—
207	C₂×C₄	—	172	1	no	—
208	C₂×C₄	—	172	1	no	—
209	C₂×C₄	—	172	1	no	—
210	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
211	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
212	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
213	C₂×C₄	#10621900	1	1	yes	characteristic
214	C₂×C₄	#10621900	1	1	yes	characteristic
215	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
216	C₈	—	4	1	no	—
217	C₈	—	172	1	no	—
218	C₂²	—	2	4	no	—
219	C₂²	—	4	2	no	—
220	C₂²	—	4	2	no	—
221	C₂²	—	4	2	no	—
222	C₂²	—	4	2	no	—
223	C₂²	—	4	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
226	C₂²	#13063297	1	1	yes	characteristic
227	C₂²	#13063302	1	1	yes	characteristic
228	C₂²	D₈×D₄₃	1	1	yes	characteristic
229	C₂²	SD₁₆×D₄₃	1	1	yes	characteristic
230	C₂²	#13063349	1	1	yes	characteristic
231	C₂²	#13063354	1	1	yes	characteristic
232	C₄	—	8	1	no	—
233	C₄	—	43	4	no	—
234	C₄	—	86	2	no	—
235	C₄	—	344	1	no	—
236	C₄	—	172	2	no	—
237	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
238	C₄	#13063281	1	1	yes	characteristic
239	C₄	#13063297	1	1	yes	characteristic
240	C₄	#13063302	1	1	yes	characteristic
241	C₂	—	4	4	no	—
242	C₂	#14582757	1	1	yes	characteristic
243	C₂	#102×D₄₃	1	1	yes	characteristic
244	C₂	#14582897	1	1	yes	characteristic
245	C₂	#14583092	1	1	yes	characteristic
246	C₂	#14583102	1	1	yes	characteristic
247	C₂	#14583177	1	1	yes	characteristic
248	C₂	#14583187	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×Dic₄₃

C₂

yes

maximal, characteristic

C₂×Dic₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#13063246

C₂

yes

maximal, characteristic

#14582768

C₂

yes

maximal, characteristic, complemented

#14582662

C₂

yes

maximal, characteristic, complemented

#14582661

C₂

yes

maximal, characteristic, complemented

C₂×#102×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

D₄×Dic₄₃

—

D₄×Dic₄₃

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063246

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂×D₄×C₄₃

D₄

yes

—

C₂×D₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

C₄⋊C₄

yes

complemented

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

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

—

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

D₈

yes

—

C₂×Dic₄₃

SD₁₆

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

100

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

101

C₂²×C₄₃

#121

yes

characteristic

102

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

103

C₂²×C₄₃

C₂×D₈

yes

characteristic

104

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

105

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

106

C₂²×C₄₃

#137

yes

characteristic

107

C₄×C₄₃

—

108

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

109

C₄×C₄₃

#117

yes

characteristic

110

C₄×C₄₃

#121

yes

characteristic

111

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

112

Dic₄₃

—

113

Dic₄₃

—

114

Dic₄₃

—

115

Dic₄₃

yes

116

—

117

C₂×C₄₃

—

118

C₂×C₄₃

#380

yes

characteristic

119

C₂×C₄₃

C₂×#102

yes

characteristic

120

C₂×C₄₃

#417

yes

characteristic

121

C₂×C₄₃

#459

yes

characteristic

122

C₂×C₄₃

#461

yes

characteristic

123

C₂×C₄₃

#474

yes

characteristic

124

C₂×C₄₃

#476

yes

characteristic

125

C₂×C₄×D₄

—

126

C₂×C₄⋊C₈

—

127

C₂×#102

—

128

C₂×#102

D₄₃

yes

characteristic

129

#384

—

130

#340

—

131

#340

—

132

C₄₃

#1802

yes

characteristic, complemented, Sylow

133

C₂²×D₄

C₂×D₄₃

yes

characteristic

134

C₂³×C₄

—

135

C₂²×C₈

—

136

C₂²×C₈

C₂×D₄₃

yes

characteristic

137

C₄×D₄

—

138

C₄×D₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

144

C₂×C₂²⋊C₄

—

145

C₂×C₄²

—

146

C₄⋊C₈

—

147

#102

—

148

#102

—

149

C₂⁴

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

Dic₈₆

yes

—

154

C₂×D₄

C₄×D₄₃

yes

—

155

C₂×D₄

C₂²⋊D₄₃

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

172

—

163

C₂²×C₄

—

172

—

164

C₂²×C₄

C₂²×D₄₃

yes

characteristic

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

172

—

178

C₄⋊C₄

—

172

—

179

C₂²⋊C₄

—

180

C₄²

—

181

C₄²

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

D₄×D₄₃

yes

characteristic

190

D₄

—

191

D₄

—

192

D₄

—

193

D₄

Dic₄₃⋊C₄

yes

complemented

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

172

—

205

C₂×C₄

—

172

—

206

C₂×C₄

—

172

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

C₂×Dic₈₆

yes

characteristic

211

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

212

C₂×C₄

D₄×D₄₃

yes

characteristic

213

C₂×C₄

#10621900

yes

characteristic

214

C₂×C₄

#10621900

yes

characteristic

215

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

216

C₈

—

217

C₈

—

172

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

226

C₂²

#13063297

yes

characteristic

227

C₂²

#13063302

yes

characteristic

228

C₂²

D₈×D₄₃

yes

characteristic

229

C₂²

SD₁₆×D₄₃

yes

characteristic

230

C₂²

#13063349

yes

characteristic

231

C₂²

#13063354

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

344

—

236

C₄

—

172

—

237

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

238

C₄

#13063281

yes

characteristic

239

C₄

#13063297

yes

characteristic

240

C₄

#13063302

yes

characteristic

241

C₂

—

242

C₂

#14582757

yes

characteristic

243

C₂

#102×D₄₃

yes

characteristic

244

C₂

#14582897

yes

characteristic

245

C₂

#14583092

yes

characteristic

246

C₂

#14583102

yes

characteristic

247

C₂

#14583177

yes

characteristic

248

C₂

#14583187

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#102×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#102	D₄₃
hypocenter	C₄₃	#1802
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#102×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
2. C₂×Dic₄₃⋊C₈	C₂	semidirect
4. #14582768	C₂	semidirect
5. #14582662	C₂	semidirect
6. #14582661	C₂	semidirect
11. D₄×Dic₄₃	C₄	semidirect
68. D₄×C₄₃	C₄⋊C₄	semidirect
115. Dic₄₃	#102	semidirect
132. C₄₃	#1802	semidirect
193. D₄	Dic₄₃⋊C₄	semidirect

H ≅ G/N

type

2. C₂×Dic₄₃⋊C₈

C₂

semidirect

4. #14582768

C₂

semidirect

5. #14582662

C₂

semidirect

6. #14582661

C₂

semidirect

11. D₄×Dic₄₃

C₄

semidirect

68. D₄×C₄₃

C₄⋊C₄

semidirect

115. Dic₄₃

#102

semidirect

132. C₄₃

#1802

semidirect

193. D₄

Dic₄₃⋊C₄

semidirect

Subgroups — #19134593

Conjugacy classes of subgroups

Complements