Group #19138912 — subgroups

Subgroups — #19138912

Order 5504.

584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582838	C₂	1	2	yes	maximal, complemented
3	#14582835	C₂	1	2	yes	maximal, complemented
4	#14582797	C₂	1	2	yes	maximal, complemented
5	#14582779	C₂	1	2	yes	maximal
6	#14582771	C₂	1	2	yes	maximal, complemented
7	#14582759	C₂	1	2	yes	maximal, complemented
8	#14582759	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₄₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₄₃	—	2	4	no	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
15	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
16	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
18	C₄₃⋊#95	C₂²	1	4	yes	—
19	C₄₃⋊#95	C₂²	1	2	yes	—
20	C₄₃⋊#95	C₂²	1	4	yes	—
21	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄×D₄×C₄₃	—	2	4	no	—
25	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
29	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
30	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
31	C₂×D₄×C₄₃	—	2	2	no	—
32	C₂×D₄×C₄₃	—	2	2	no	—
33	C₂×D₄×C₄₃	Q₈	1	4	yes	—
34	C₂²×C₄×C₄₃	—	2	4	no	—
35	C₂²×C₄×C₄₃	—	2	2	no	—
36	C₂²×C₄×C₄₃	—	2	4	no	—
37	C₂²×C₄×C₄₃	D₄	1	4	yes	—
38	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×Dic₄₃	—	2	4	no	—
44	C₂²×Dic₄₃	—	4	4	no	—
45	C₂²×Dic₄₃	C₂³	1	4	yes	—
46	C₂²×Dic₄₃	C₂³	1	4	yes	—
47	C₄⋊C₄×C₄₃	—	2	2	no	—
48	C₂²⋊C₄×C₄₃	—	2	2	no	—
49	C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₄²×C₄₃	—	2	2	no	—
51	C₂²⋊Dic₄₃	—	2	4	no	—
52	C₂²⋊Dic₄₃	—	4	4	no	—
53	C₄⋊Dic₄₃	—	2	4	no	—
54	C₄⋊Dic₄₃	—	2	4	no	—
55	C₄⋊Dic₄₃	—	2	4	no	—
56	Dic₄₃⋊C₄	—	4	4	no	—
57	C₂³×C₄₃	—	2	2	no	—
58	C₂³×C₄₃	—	2	2	no	—
59	C₂³×C₄₃	—	2	1	no	—
60	C₂³×C₄₃	—	2	2	no	—
61	C₂³×C₄₃	—	2	1	no	—
62	C₂³×C₄₃	—	2	2	no	—
63	C₂³×C₄₃	C₂×D₄	1	2	yes	—
64	C₂³×C₄₃	C₂×Q₈	1	2	yes	—
65	C₂³×C₄₃	C₂×Q₈	1	2	yes	—
66	C₂³×C₄₃	#41	1	2	yes	—
67	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
68	D₄×C₄₃	—	2	8	no	—
69	C₂×C₄×C₄₃	—	2	1	no	—
70	C₂×C₄×C₄₃	—	2	2	no	—
71	C₂×C₄×C₄₃	—	2	1	no	—
72	C₂×C₄×C₄₃	—	2	8	no	—
73	C₂×C₄×C₄₃	—	2	1	no	—
74	C₂×C₄×C₄₃	—	2	1	no	—
75	C₂×C₄×C₄₃	—	2	2	no	—
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	—	4	4	no	—
78	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
81	C₂×C₄×C₄₃	#41	1	4	yes	—
82	C₂×Dic₄₃	—	2	4	no	—
83	C₂×Dic₄₃	—	2	4	no	—
84	C₂×Dic₄₃	—	2	4	no	—
85	C₂×Dic₄₃	—	2	4	no	—
86	C₂×Dic₄₃	—	2	4	no	—
87	C₂×Dic₄₃	—	2	4	no	—
88	C₂×Dic₄₃	—	4	8	no	—
89	C₂²×C₄₃	—	2	2	no	—
90	C₂²×C₄₃	—	2	2	no	—
91	C₂²×C₄₃	—	2	4	no	—
92	C₂²×C₄₃	—	2	4	no	—
93	C₂²×C₄₃	—	2	2	no	—
94	C₂²×C₄₃	—	2	4	no	—
95	C₂²×C₄₃	—	4	1	no	—
96	C₂²×C₄₃	—	4	1	no	—
97	C₂²×C₄₃	—	4	2	no	—
98	C₂²×C₄₃	C₂²⋊Q₈	1	4	yes	—
99	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
100	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
101	C₂²×C₄₃	C₂×#41	1	2	yes	—
102	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
103	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
104	C₄×C₄₃	—	2	2	no	—
105	C₄×C₄₃	—	2	2	no	—
106	C₄×C₄₃	—	4	1	no	—
107	C₄×C₄₃	—	4	1	no	—
108	C₄×C₄₃	#123	1	4	yes	—
109	Dic₄₃	—	4	4	no	—
110	Dic₄₃	—	4	4	no	—
111	#2487	—	43	1	no	maximal, Sylow
112	C₂×C₄₃	—	2	4	no	—
113	C₂×C₄₃	—	4	2	no	—
114	C₂×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
115	C₂×C₄₃	C₂×#123	1	1	yes	characteristic
116	C₂×C₄₃	#535	1	1	yes	characteristic
117	C₂×C₄₃	#553	1	2	yes	—
118	C₂×C₄₃	#554	1	2	yes	—
119	C₂×C₄×D₄	D₄₃	1	1	yes	characteristic
120	C₂²×C₄⋊C₄	—	43	1	no	—
121	#400	—	43	2	no	—
122	#399	—	43	2	no	—
123	#389	—	43	2	no	—
124	#386	—	43	2	no	—
125	#385	—	43	2	no	—
126	#380	—	43	2	no	—
127	#380	—	43	1	no	—
128	C₄₃	#2487	1	1	yes	characteristic, complemented, Sylow
129	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
130	C₂³×C₄	—	43	2	no	—
131	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
132	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
133	C₄×D₄	—	2	4	no	—
134	C₂×C₄⋊C₄	—	43	2	no	—
135	C₂×C₄⋊C₄	—	43	2	no	—
136	C₂×C₄⋊C₄	—	43	2	no	—
137	C₂×C₄⋊C₄	—	43	4	no	—
138	C₂×C₄⋊C₄	—	86	4	no	—
139	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
140	C₂×C₂²⋊C₄	—	43	2	no	—
141	C₂×C₂²⋊C₄	—	43	4	no	—
142	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
143	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
144	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
145	#95	—	43	4	no	—
146	#95	—	43	2	no	—
147	#95	—	43	4	no	—
148	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
149	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
150	C₂×D₄	—	2	2	no	—
151	C₂×D₄	—	2	2	no	—
152	C₂×D₄	Dic₈₆	1	4	yes	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	43	4	no	—
157	C₂²×C₄	—	43	4	no	—
158	C₂²×C₄	—	86	4	no	—
159	C₂²×C₄	—	172	4	no	—
160	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
161	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
162	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
163	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
165	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	86	4	no	—
168	C₄⋊C₄	—	86	4	no	—
169	C₄⋊C₄	—	86	4	no	—
170	C₄⋊C₄	—	172	4	no	—
171	C₂²⋊C₄	—	2	2	no	—
172	C₂²⋊C₄	—	2	2	no	—
173	C₂²⋊C₄	—	86	4	no	—
174	C₂²⋊C₄	—	172	4	no	—
175	C₄²	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	2	no	—
178	C₂³	—	2	1	no	—
179	C₂³	—	2	2	no	—
180	C₂³	—	2	1	no	—
181	C₂³	—	2	2	no	—
182	C₂³	C₂×Dic₈₆	1	2	yes	—
183	C₂³	C₂×Dic₈₆	1	2	yes	—
184	C₂³	#10621898	1	2	yes	—
185	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
186	C₂³	C₂³×D₄₃	1	1	yes	characteristic
187	D₄	—	2	8	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	8	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	86	4	no	—
198	C₂×C₄	—	86	4	no	—
199	C₂×C₄	—	86	4	no	—
200	C₂×C₄	—	86	4	no	—
201	C₂×C₄	—	86	4	no	—
202	C₂×C₄	—	86	4	no	—
203	C₂×C₄	—	172	8	no	—
204	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
205	C₂×C₄	#10621900	1	4	yes	—
206	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
207	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
208	C₂²	—	2	4	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	4	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	4	1	no	—
217	C₂²	#13063304	1	4	yes	—
218	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
219	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
220	C₂²	C₂×#10621900	1	2	yes	—
221	C₂²	C₂×#10621898	1	1	yes	characteristic
222	C₂²	#13063371	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	2	2	no	—
225	C₄	—	4	1	no	—
226	C₄	—	4	1	no	—
227	C₄	—	172	4	no	—
228	C₄	—	172	4	no	—
229	C₄	#13063306	1	4	yes	—
230	C₂	—	2	4	no	—
231	C₂	—	4	2	no	—
232	C₂	C₂×#13063304	1	1	yes	characteristic
233	C₂	C₂×#13063306	1	1	yes	characteristic
234	C₂	#14583463	1	1	yes	characteristic
235	C₂	#14583595	1	2	yes	—
236	C₂	#14583606	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic, complemented

#14582838

C₂

yes

maximal, complemented

#14582835

C₂

yes

maximal, complemented

#14582797

C₂

yes

maximal, complemented

#14582779

C₂

yes

maximal

#14582771

C₂

yes

maximal, complemented

#14582759

C₂

yes

maximal, complemented

#14582759

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₄×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₄×D₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×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

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

100

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

101

C₂²×C₄₃

C₂×#41

yes

—

102

C₂²×C₄₃

C₂×#41

yes

characteristic

103

C₂²×C₄₃

H(5,𝔽₂)

yes

—

104

C₄×C₄₃

—

105

C₄×C₄₃

—

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

#123

yes

—

109

Dic₄₃

—

110

Dic₄₃

—

111

#2487

—

maximal, Sylow

112

C₂×C₄₃

—

113

C₂×C₄₃

—

114

C₂×C₄₃

C₂×C₂²⋊Q₈

yes

characteristic

115

C₂×C₄₃

C₂×#123

yes

characteristic

116

C₂×C₄₃

#535

yes

characteristic

117

C₂×C₄₃

#553

yes

—

118

C₂×C₄₃

#554

yes

—

119

C₂×C₄×D₄

D₄₃

yes

characteristic

120

C₂²×C₄⋊C₄

—

121

#400

—

122

#399

—

123

#389

—

124

#386

—

125

#385

—

126

#380

—

127

#380

—

128

C₄₃

#2487

yes

characteristic, complemented, Sylow

129

C₂²×D₄

C₂×D₄₃

yes

characteristic

130

C₂³×C₄

—

131

C₂³×C₄

C₂×D₄₃

yes

characteristic

132

C₂³×C₄

C₂×D₄₃

yes

characteristic

133

C₄×D₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

140

C₂×C₂²⋊C₄

—

141

C₂×C₂²⋊C₄

—

142

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

143

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

144

C₂×C₄²

C₂×D₄₃

yes

characteristic

145

#95

—

146

#95

—

147

#95

—

148

C₂⁴

C₂²×D₄₃

yes

characteristic

149

C₂⁴

C₂²×D₄₃

yes

characteristic

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

Dic₈₆

yes

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

172

—

160

C₂²×C₄

C₂²⋊D₄₃

yes

—

161

C₂²×C₄

C₂²×D₄₃

yes

characteristic

162

C₂²×C₄

C₂²×D₄₃

yes

characteristic

163

C₂²×C₄

C₂²×D₄₃

yes

characteristic

164

C₂²×C₄

C₂²×D₄₃

yes

characteristic

165

C₂²×C₄

C₂²×D₄₃

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

172

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

172

—

175

C₄²

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

C₂×Dic₈₆

yes

—

183

C₂³

C₂×Dic₈₆

yes

—

184

C₂³

#10621898

yes

—

185

C₂³

C₂×C₂²⋊D₄₃

yes

—

186

C₂³

C₂³×D₄₃

yes

characteristic

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

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

—

172

—

204

C₂×C₄

C₂×Dic₈₆

yes

—

205

C₂×C₄

#10621900

yes

—

206

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

207

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

#13063304

yes

—

218

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

219

C₂²

C₂²×Dic₈₆

yes

characteristic

220

C₂²

C₂×#10621900

yes

—

221

C₂²

C₂×#10621898

yes

characteristic

222

C₂²

#13063371

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

172

—

228

C₄

—

172

—

229

C₄

#13063306

yes

—

230

C₂

—

231

C₂

—

232

C₂

C₂×#13063304

yes

characteristic

233

C₂

C₂×#13063306

yes

characteristic

234

C₂

#14583463

yes

characteristic

235

C₂

#14583595

yes

—

236

C₂

#14583606

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×C₄×D₄×C₄₃	C₂
hypercenter	C₂×C₄×D₄	D₄₃
hypocenter	C₄₃	#2487
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×C₄×D₄×C₄₃

C₂

hypercenter

C₂×C₄×D₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×C₄×D₄

N	H ≅ G/N	type
1. C₂²×C₄⋊Dic₄₃	C₂	semidirect
2. #14582838	C₂	semidirect
3. #14582835	C₂	semidirect
4. #14582797	C₂	semidirect
6. #14582771	C₂	semidirect
7. #14582759	C₂	semidirect
8. #14582759	C₂	semidirect
128. C₄₃	#2487	semidirect

H ≅ G/N

type

1. C₂²×C₄⋊Dic₄₃

C₂

semidirect

2. #14582838

C₂

semidirect

3. #14582835

C₂

semidirect

4. #14582797

C₂

semidirect

6. #14582771

C₂

semidirect

7. #14582759

C₂

semidirect

8. #14582759

C₂

semidirect

128. C₄₃

#2487

semidirect

Subgroups — #19138912

Conjugacy classes of subgroups

Complements