Group #33005579 — subgroups

Subgroups — #33005579

Order 18688.

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

normal subgroups only

This group has 482 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	C₂²×D₁₁₆₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988389	C₂	1	2	yes	maximal, complemented
3	#22610797	C₂	1	2	yes	maximal, complemented
4	#22608023	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₈₄	C₂²	1	2	yes	—
7	C₂×D₁₁₆₈	—	2	4	no	—
8	C₂×D₁₁₆₈	—	2	2	no	—
9	C₂×#14556525	C₂²	1	2	yes	—
10	C₂×#14556513	—	2	2	no	—
11	#17988489	—	2	2	no	—
12	#17988389	—	2	4	no	—
13	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₁₆×C₇₃	—	2	2	no	—
17	C₂²×D₂₉₂	—	2	2	no	—
18	C₂×D₅₈₄	—	2	2	no	—
19	C₂×D₅₈₄	—	2	2	no	—
20	C₂×D₅₈₄	—	2	2	no	—
21	C₂×D₅₈₄	—	2	2	no	—
22	C₂×D₅₈₄	—	2	2	no	—
23	C₂×D₅₈₄	D₄	1	4	yes	—
24	C₂×C₄⋊Dic₇₃	—	2	2	no	—
25	C₂×#11924005	—	4	2	no	—
26	C₂×#11924005	—	4	2	no	—
27	D₁₁₆₈	—	2	8	no	—
28	#14556525	—	2	2	no	—
29	#14556525	—	2	2	no	—
30	#14556513	—	4	4	no	—
31	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
34	C₂×C₁₆×C₇₃	—	2	2	no	—
35	C₂×C₁₆×C₇₃	—	2	2	no	—
36	C₂×C₁₆×C₇₃	—	2	1	no	—
37	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
38	C₄×C₈×C₇₃	—	2	1	no	—
39	C₄×C₈×C₇₃	—	2	1	no	—
40	C₂³×D₇₃	—	4	2	no	—
41	C₂×D₂₉₂	—	2	4	no	—
42	C₂×D₂₉₂	—	4	2	no	—
43	C₂×D₂₉₂	—	4	2	no	—
44	C₂×D₂₉₂	—	4	2	no	—
45	C₂×D₂₉₂	—	4	2	no	—
46	C₂×D₂₉₂	—	4	2	no	—
47	C₂²×Dic₇₃	—	4	2	no	—
48	D₅₈₄	—	2	4	no	—
49	D₅₈₄	—	2	4	no	—
50	D₅₈₄	—	4	2	no	—
51	D₅₈₄	—	4	2	no	—
52	C₄⋊Dic₇₃	—	4	2	no	—
53	C₄⋊Dic₇₃	—	4	2	no	—
54	#11924005	—	8	4	no	—
55	#11924005	—	8	4	no	—
56	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₇₃	—	2	1	no	—
60	C₂×C₈×C₇₃	—	2	2	no	—
61	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
64	C₂×C₈×C₇₃	#41	1	2	yes	—
65	C₄²×C₇₃	—	2	1	no	—
66	C₄²×C₇₃	—	2	1	no	—
67	C₁₆×C₇₃	—	2	2	no	—
68	C₁₆×C₇₃	—	4	1	no	—
69	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
70	C₂²×D₇₃	—	4	4	no	—
71	C₂²×D₇₃	—	8	2	no	—
72	C₂²×D₇₃	—	8	2	no	—
73	C₂²×D₇₃	—	8	2	no	—
74	C₂²×D₇₃	—	8	2	no	—
75	C₂²×D₇₃	—	8	2	no	—
76	C₂²×D₇₃	—	8	2	no	—
77	C₂×C₄×C₇₃	—	2	1	no	—
78	C₂×C₄×C₇₃	—	2	1	no	—
79	C₂×C₄×C₇₃	—	2	1	no	—
80	C₂×C₄×C₇₃	—	2	2	no	—
81	C₂×C₄×C₇₃	D₁₆	1	2	yes	complemented
82	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₇₃	#121	1	2	yes	—
84	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
85	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
86	C₂×Dic₇₃	—	8	2	no	—
87	C₂×Dic₇₃	—	8	2	no	—
88	C₂×Dic₇₃	—	8	2	no	—
89	D₂₉₂	—	4	4	no	—
90	D₂₉₂	—	4	4	no	—
91	D₂₉₂	—	8	2	no	—
92	D₂₉₂	—	8	2	no	—
93	C₈×C₇₃	—	4	1	no	—
94	C₈×C₇₃	#120	1	1	yes	characteristic
95	C₈×C₇₃	#123	1	2	yes	—
96	C₈×C₇₃	#124	1	1	yes	characteristic
97	C₂²×C₇₃	#459	1	2	yes	—
98	C₂²×C₇₃	#466	1	1	yes	characteristic
99	C₂²×C₇₃	C₂×D₁₆	1	1	yes	characteristic
100	C₂²×C₇₃	#508	1	1	yes	characteristic
101	C₂²×C₇₃	#509	1	2	yes	—
102	C₂×D₇₃	—	8	4	no	—
103	C₂×D₇₃	—	8	4	no	—
104	C₂×D₇₃	—	8	4	no	—
105	C₂×D₇₃	—	16	2	no	—
106	C₂×D₇₃	—	16	2	no	—
107	C₂×D₇₃	—	16	2	no	—
108	C₂×D₇₃	—	16	2	no	—
109	C₄×C₇₃	—	2	2	no	—
110	C₄×C₇₃	—	4	1	no	—
111	C₄×C₇₃	#394	1	1	yes	characteristic
112	C₄×C₇₃	#463	1	2	yes	—
113	C₄×C₇₃	#469	1	1	yes	characteristic
114	Dic₇₃	—	16	2	no	—
115	#13448	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	#2054	1	1	yes	characteristic
117	C₂×C₇₃	#2206	1	2	yes	—
118	C₂×C₇₃	#2210	1	2	yes	—
119	C₂×C₇₃	#2215	1	1	yes	characteristic
120	C₂×C₇₃	#2218	1	1	yes	characteristic
121	D₇₃	—	16	4	no	—
122	C₂²×D₁₆	—	73	1	no	—
123	C₂×C₄⋊C₁₆	D₇₃	1	1	yes	characteristic, complemented
124	C₂×#357	—	73	2	no	—
125	#1970	—	73	2	no	—
126	#1380	—	73	1	no	—
127	C₇₃	#13448	1	1	yes	characteristic, complemented, Sylow
128	C₂²×D₈	—	73	2	no	—
129	C₂×D₁₆	—	146	4	no	—
130	C₂×D₁₆	—	146	2	no	—
131	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
132	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
133	C₂×#107	—	73	2	no	—
134	C₂×#102	—	146	2	no	—
135	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
136	#390	—	146	2	no	—
137	C₄⋊C₁₆	—	2	2	no	—
138	#357	—	146	4	no	—
139	C₂²×D₄	—	146	2	no	—
140	C₂×D₈	—	73	4	no	—
141	C₂×D₈	—	146	2	no	—
142	C₂×D₈	—	146	2	no	—
143	C₂×D₈	—	146	2	no	—
144	C₂×D₈	—	146	2	no	—
145	C₂×D₈	—	146	2	no	—
146	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
147	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
148	C₂×C₄⋊C₄	—	146	2	no	—
149	C₂×C₂²⋊C₄	—	292	2	no	—
150	C₂×C₂²⋊C₄	—	292	2	no	—
151	C₂×C₄²	D₂₉₂	1	1	yes	characteristic
152	D₁₆	—	146	8	no	—
153	C₂×C₁₆	—	2	2	no	—
154	C₂×C₁₆	—	2	2	no	—
155	C₂×C₁₆	—	2	1	no	—
156	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
157	#107	—	146	2	no	—
158	#107	—	146	2	no	—
159	#102	—	292	4	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	—	2	1	no	—
162	C₂⁴	—	292	2	no	—
163	C₂×D₄	—	292	2	no	—
164	C₂×D₄	—	292	2	no	—
165	C₂×D₄	—	292	2	no	—
166	C₂×D₄	—	292	2	no	—
167	C₂×D₄	—	292	2	no	—
168	C₂×D₄	—	146	4	no	—
169	C₂²×C₄	—	292	2	no	—
170	C₂²×C₄	D₅₈₄	1	1	yes	characteristic
171	C₂²×C₄	D₅₈₄	1	1	yes	characteristic
172	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
173	D₈	—	292	2	no	—
174	D₈	—	292	2	no	—
175	D₈	—	146	4	no	—
176	D₈	—	146	4	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	D₄×D₇₃	1	2	yes	—
180	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
181	C₂×C₈	#11924028	1	1	yes	characteristic
182	C₂×C₈	#11924029	1	2	yes	—
183	C₄⋊C₄	—	292	2	no	—
184	C₄⋊C₄	—	292	2	no	—
185	C₂²⋊C₄	—	584	4	no	—
186	C₂²⋊C₄	—	584	4	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₁₆	—	2	2	no	—
190	C₁₆	—	4	1	no	—
191	C₂³	—	292	4	no	—
192	C₂³	—	584	2	no	—
193	C₂³	—	584	2	no	—
194	C₂³	—	584	2	no	—
195	C₂³	—	584	2	no	—
196	C₂³	—	584	2	no	—
197	C₂³	—	584	2	no	—
198	C₂³	C₂×D₅₈₄	1	1	yes	characteristic
199	D₄	—	292	4	no	—
200	D₄	—	292	4	no	—
201	D₄	—	584	2	no	—
202	D₄	—	584	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	584	2	no	—
208	C₂×C₄	—	584	2	no	—
209	C₂×C₄	—	584	2	no	—
210	C₂×C₄	D₁₁₆₈	1	2	yes	complemented
211	C₂×C₄	#14556565	1	1	yes	characteristic
212	C₂×C₄	#14556566	1	2	yes	—
213	C₂×C₄	#14556613	1	1	yes	characteristic
214	C₂×C₄	#14556619	1	2	yes	—
215	C₈	—	4	1	no	—
216	C₈	#14556559	1	1	yes	characteristic
217	C₈	#14556576	1	2	yes	—
218	C₈	#14556580	1	1	yes	characteristic
219	C₂²	—	584	4	no	—
220	C₂²	—	584	4	no	—
221	C₂²	—	584	4	no	—
222	C₂²	—	1168	2	no	—
223	C₂²	—	1168	2	no	—
224	C₂²	—	1168	2	no	—
225	C₂²	—	1168	2	no	—
226	C₂²	#17988783	1	2	yes	—
227	C₂²	#17988823	1	1	yes	characteristic
228	C₂²	C₂×D₁₁₆₈	1	1	yes	characteristic
229	C₂²	#17989019	1	1	yes	characteristic
230	C₂²	#17989025	1	2	yes	—
231	C₄	—	2	2	no	—
232	C₄	—	4	1	no	—
233	C₄	—	1168	2	no	—
234	C₄	#17988504	1	1	yes	characteristic
235	C₄	#17988803	1	2	yes	—
236	C₄	#17988840	1	1	yes	characteristic
237	C₂	—	1168	4	no	—
238	C₂	#22611242	1	1	yes	characteristic
239	C₂	#22611967	1	2	yes	—
240	C₂	#22611987	1	2	yes	—
241	C₂	#22612017	1	1	yes	characteristic
242	C₂	#22612034	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₁₆₈

C₂

yes

maximal, characteristic

C₂×#17988389

C₂

yes

maximal, complemented

#22610797

C₂

yes

maximal, complemented

#22608023

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊C₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₅₈₄

C₂²

yes

—

C₂×D₁₁₆₈

—

C₂×D₁₁₆₈

—

C₂×#14556525

C₂²

yes

—

C₂×#14556513

—

#17988489

—

#17988389

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₃

—

C₂²×D₂₉₂

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

D₄

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×#11924005

—

C₂×#11924005

—

D₁₁₆₈

—

#14556525

—

#14556525

—

#14556513

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂²×Dic₇₃

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

#11924005

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

D₁₆

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#135

yes

characteristic

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

#120

yes

characteristic

C₈×C₇₃

#123

yes

—

C₈×C₇₃

#124

yes

characteristic

C₂²×C₇₃

#459

yes

—

C₂²×C₇₃

#466

yes

characteristic

C₂²×C₇₃

C₂×D₁₆

yes

characteristic

100

C₂²×C₇₃

#508

yes

characteristic

101

C₂²×C₇₃

#509

yes

—

102

C₂×D₇₃

—

103

C₂×D₇₃

—

104

C₂×D₇₃

—

105

C₂×D₇₃

—

106

C₂×D₇₃

—

107

C₂×D₇₃

—

108

C₂×D₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

—

111

C₄×C₇₃

#394

yes

characteristic

112

C₄×C₇₃

#463

yes

—

113

C₄×C₇₃

#469

yes

characteristic

114

Dic₇₃

—

115

#13448

—

maximal, Sylow

116

C₂×C₇₃

#2054

yes

characteristic

117

C₂×C₇₃

#2206

yes

—

118

C₂×C₇₃

#2210

yes

—

119

C₂×C₇₃

#2215

yes

characteristic

120

C₂×C₇₃

#2218

yes

characteristic

121

D₇₃

—

122

C₂²×D₁₆

—

123

C₂×C₄⋊C₁₆

D₇₃

yes

characteristic, complemented

124

C₂×#357

—

125

#1970

—

126

#1380

—

127

C₇₃

#13448

yes

characteristic, complemented, Sylow

128

C₂²×D₈

—

129

C₂×D₁₆

—

146

—

130

C₂×D₁₆

—

146

—

131

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

132

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

133

C₂×#107

—

134

C₂×#102

—

146

—

135

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

136

#390

—

146

—

137

C₄⋊C₁₆

—

138

#357

—

146

—

139

C₂²×D₄

—

146

—

140

C₂×D₈

—

141

C₂×D₈

—

146

—

142

C₂×D₈

—

146

—

143

C₂×D₈

—

146

—

144

C₂×D₈

—

146

—

145

C₂×D₈

—

146

—

146

C₂²×C₈

D₂₉₂

yes

characteristic

147

C₂²×C₈

C₂²×D₇₃

yes

characteristic

148

C₂×C₄⋊C₄

—

146

—

149

C₂×C₂²⋊C₄

—

292

—

150

C₂×C₂²⋊C₄

—

292

—

151

C₂×C₄²

D₂₉₂

yes

characteristic

152

D₁₆

—

146

—

153

C₂×C₁₆

—

154

C₂×C₁₆

—

155

C₂×C₁₆

—

156

C₂×C₁₆

C₂²⋊D₇₃

yes

—

157

#107

—

146

—

158

#107

—

146

—

159

#102

—

292

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂⁴

—

292

—

163

C₂×D₄

—

292

—

164

C₂×D₄

—

292

—

165

C₂×D₄

—

292

—

166

C₂×D₄

—

292

—

167

C₂×D₄

—

292

—

168

C₂×D₄

—

146

—

169

C₂²×C₄

—

292

—

170

C₂²×C₄

D₅₈₄

yes

characteristic

171

C₂²×C₄

D₅₈₄

yes

characteristic

172

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

173

D₈

—

292

—

174

D₈

—

292

—

175

D₈

—

146

—

176

D₈

—

146

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

D₄×D₇₃

yes

—

180

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

181

C₂×C₈

#11924028

yes

characteristic

182

C₂×C₈

#11924029

yes

—

183

C₄⋊C₄

—

292

—

184

C₄⋊C₄

—

292

—

185

C₂²⋊C₄

—

584

—

186

C₂²⋊C₄

—

584

—

187

C₄²

—

188

C₄²

—

189

C₁₆

—

190

C₁₆

—

191

C₂³

—

292

—

192

C₂³

—

584

—

193

C₂³

—

584

—

194

C₂³

—

584

—

195

C₂³

—

584

—

196

C₂³

—

584

—

197

C₂³

—

584

—

198

C₂³

C₂×D₅₈₄

yes

characteristic

199

D₄

—

292

—

200

D₄

—

292

—

201

D₄

—

584

—

202

D₄

—

584

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

584

—

208

C₂×C₄

—

584

—

209

C₂×C₄

—

584

—

210

C₂×C₄

D₁₁₆₈

yes

complemented

211

C₂×C₄

#14556565

yes

characteristic

212

C₂×C₄

#14556566

yes

—

213

C₂×C₄

#14556613

yes

characteristic

214

C₂×C₄

#14556619

yes

—

215

C₈

—

216

C₈

#14556559

yes

characteristic

217

C₈

#14556576

yes

—

218

C₈

#14556580

yes

characteristic

219

C₂²

—

584

—

220

C₂²

—

584

—

221

C₂²

—

584

—

222

C₂²

—

1168

—

223

C₂²

—

1168

—

224

C₂²

—

1168

—

225

C₂²

—

1168

—

226

C₂²

#17988783

yes

—

227

C₂²

#17988823

yes

characteristic

228

C₂²

C₂×D₁₁₆₈

yes

characteristic

229

C₂²

#17989019

yes

characteristic

230

C₂²

#17989025

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

1168

—

234

C₄

#17988504

yes

characteristic

235

C₄

#17988803

yes

—

236

C₄

#17988840

yes

characteristic

237

C₂

—

1168

—

238

C₂

#22611242

yes

characteristic

239

C₂

#22611967

yes

—

240

C₂

#22611987

yes

—

241

C₂

#22612017

yes

characteristic

242

C₂

#22612034

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₅₈₄
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×C₄⋊C₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂²×D₁₁₆₈	C₂
hypercenter	C₂×C₄⋊C₁₆	D₇₃
hypocenter	C₇₃	#13448
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₅₈₄

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×C₄⋊C₁₆×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂²×D₁₁₆₈

C₂

hypercenter

C₂×C₄⋊C₁₆

D₇₃

hypocenter

C₇₃

#13448

LCS

G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
2. C₂×#17988389	C₂	semidirect
3. #22610797	C₂	semidirect
4. #22608023	C₂	semidirect
5. C₂×C₄⋊C₁₆×C₇₃	C₂	semidirect
81. C₂×C₄×C₇₃	D₁₆	semidirect
123. C₂×C₄⋊C₁₆	D₇₃	semidirect
127. C₇₃	#13448	semidirect
210. C₂×C₄	D₁₁₆₈	semidirect

H ≅ G/N

type

2. C₂×#17988389

C₂

semidirect

3. #22610797

C₂

semidirect

4. #22608023

C₂

semidirect

5. C₂×C₄⋊C₁₆×C₇₃

C₂

semidirect

81. C₂×C₄×C₇₃

D₁₆

semidirect

123. C₂×C₄⋊C₁₆

D₇₃

semidirect

127. C₇₃

#13448

semidirect

210. C₂×C₄

D₁₁₆₈

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×D₁₁₆₈	2
C₂×#17988389	2
#22610797	2
#22608023	2
C₂×C₄⋊C₁₆×C₇₃	2
#13448	73

subgroup

index

C₂²×D₁₁₆₈

C₂×C₄⋊C₁₆×C₇₃

Subgroups — #33005579

Conjugacy classes of subgroups

Complements

Maximal subgroups