Group #33240484 — subgroups

Subgroups — #33240484

Order 18688.

650 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 171 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×#17989003	C₂	1	1	yes	maximal, characteristic
2	#22619582	C₂	1	2	yes	maximal
3	#22612036	C₂	1	4	yes	maximal, complemented
4	#22612019	C₂	1	4	yes	maximal, complemented
5	#22611715	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611651	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14556597	C₂²	1	1	yes	characteristic
9	#17989161	—	2	2	no	—
10	#17989003	—	2	4	no	—
11	C₂×#14556531	C₂²	1	1	yes	characteristic
12	C₂×#14556530	C₂²	1	2	yes	—
13	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
14	#17988842	—	2	4	no	—
15	#17988825	C₂²	1	8	yes	—
16	#17988625	C₂²	1	2	yes	—
17	#17988596	—	2	2	no	—
18	#17988415	C₂²	1	2	yes	—
19	#17988413	C₂²	1	2	yes	—
20	#17988391	C₂²	1	8	yes	—
21	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
22	C₂×Q₃₂×C₇₃	—	2	4	no	—
23	C₂×Q₃₂×C₇₃	C₂²	1	2	yes	—
24	C₂×Q₃₂×C₇₃	C₂²	1	2	yes	—
25	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#11924028	D₄	1	1	yes	characteristic
27	#14556597	—	2	2	no	—
28	#14556597	—	2	2	no	—
29	C₂×#11924012	D₄	1	1	yes	characteristic
30	C₂×#11924011	D₄	1	2	yes	—
31	C₂×C₈×D₇₃	C₂³	1	2	yes	—
32	#14556589	—	4	2	no	—
33	#14556580	—	4	2	no	—
34	#14556574	—	4	4	no	—
35	#14556567	—	2	8	no	—
36	#14556550	—	2	2	no	—
37	#14556531	—	2	2	no	—
38	#14556530	—	2	4	no	—
39	C₂×#11924003	C₂³	1	2	yes	—
40	C₁₆×D₇₃	—	2	4	no	—
41	#14556525	C₂³	1	4	yes	—
42	#14556523	—	2	2	no	—
43	#14556515	—	2	8	no	—
44	C₂²×Q₈×C₇₃	—	2	2	no	—
45	C₂×Q₁₆×C₇₃	—	2	4	no	—
46	C₂×Q₁₆×C₇₃	—	2	2	no	—
47	C₂×Q₁₆×C₇₃	—	2	4	no	—
48	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
49	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
50	Q₃₂×C₇₃	—	2	4	no	—
51	Q₃₂×C₇₃	—	2	4	no	—
52	C₂×C₁₆×C₇₃	D₄	1	4	yes	—
53	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
55	#11924028	—	2	2	no	—
56	#11924028	—	2	2	no	—
57	C₂×Dic₁₄₆	D₈	1	1	yes	characteristic
58	C₂×D₂₉₂	D₈	1	1	yes	characteristic
59	C₂×C₂²⋊D₇₃	D₈	1	2	yes	—
60	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
61	#11924012	—	2	2	no	—
62	#11924011	—	2	4	no	—
63	C₂×#10596831	C₂×D₄	1	2	yes	—
64	C₈×D₇₃	—	2	2	no	—
65	C₈×D₇₃	—	2	2	no	—
66	C₄⋊Dic₇₃	—	2	4	no	—
67	#11924007	—	4	8	no	—
68	C₂²⋊Dic₇₃	—	4	2	no	—
69	#11924005	—	4	8	no	—
70	C₄×Dic₇₃	—	4	2	no	—
71	#11924003	—	2	2	no	—
72	C₂×Q₈×C₇₃	—	2	4	no	—
73	C₂×Q₈×C₇₃	—	4	2	no	—
74	C₂×Q₈×C₇₃	—	4	4	no	—
75	C₂×Q₈×C₇₃	—	4	4	no	—
76	C₂²×C₄×C₇₃	—	4	2	no	—
77	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
78	Q₁₆×C₇₃	—	2	4	no	—
79	Q₁₆×C₇₃	—	2	4	no	—
80	Q₁₆×C₇₃	—	4	4	no	—
81	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₇₃	#41	1	2	yes	—
84	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
85	C₁₆×C₇₃	C₂×D₄	1	2	yes	—
86	C₁₆×C₇₃	C₂×D₄	1	2	yes	—
87	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
88	C₂²×D₇₃	C₂×D₈	1	2	yes	—
89	Q₈×C₇₃	—	4	4	no	—
90	Q₈×C₇₃	—	4	4	no	—
91	Q₈×C₇₃	—	8	4	no	—
92	C₂×C₄×C₇₃	—	4	4	no	—
93	C₂×C₄×C₇₃	—	8	4	no	—
94	C₂×C₄×C₇₃	#121	1	2	yes	—
95	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
96	C₂×C₄×C₇₃	#135	1	2	yes	—
97	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
98	C₂²⋊D₇₃	—	2	4	no	—
99	C₂×Dic₇₃	—	4	4	no	—
100	C₂×Dic₇₃	C₂×D₈	1	2	yes	—
101	D₂₉₂	—	2	2	no	—
102	C₄×D₇₃	—	2	2	no	—
103	C₄×D₇₃	—	2	2	no	—
104	Dic₁₄₆	—	2	2	no	—
105	C₈×C₇₃	#121	1	2	yes	—
106	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
107	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
108	#10596831	—	2	2	no	—
109	C₂²×C₇₃	—	2	2	no	—
110	C₂²×C₇₃	#466	1	2	yes	—
111	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
112	C₂×D₇₃	—	2	4	no	—
113	C₂×D₇₃	—	2	2	no	—
114	C₄×C₇₃	—	8	4	no	—
115	C₄×C₇₃	#466	1	2	yes	—
116	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
117	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
118	Dic₇₃	—	2	2	no	—
119	Dic₇₃	—	8	4	no	—
120	#33608	—	73	1	no	maximal, Sylow
121	C₂×C₇₃	—	2	2	no	—
122	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
123	C₂×C₇₃	#3417	1	2	yes	—
124	D₇₃	—	4	2	no	—
125	C₂²×Q₃₂	D₇₃	1	1	yes	characteristic, complemented
126	C₂×#504	—	73	1	no	—
127	#3059	—	73	2	no	—
128	#2219	—	73	4	no	—
129	#2216	—	73	4	no	—
130	#2158	—	73	1	no	—
131	#2141	—	73	2	no	—
132	C₇₃	#33608	1	1	yes	characteristic, complemented, Sylow
133	C₂²×Q₁₆	C₂×D₇₃	1	2	yes	—
134	C₂×#131	—	73	1	no	—
135	#536	—	146	2	no	—
136	C₂×Q₃₂	—	2	4	no	—
137	C₂×Q₃₂	C₂×D₇₃	1	2	yes	—
138	C₂×Q₃₂	C₂×D₇₃	1	2	yes	—
139	#504	—	146	4	no	—
140	C₂×M₃₂	—	73	1	no	—
141	C₂×M₃₂	—	73	2	no	—
142	C₂²×C₁₆	—	73	2	no	—
143	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
144	#470	—	146	4	no	—
145	#467	—	73	8	no	—
146	#427	—	73	2	no	—
147	#419	—	146	2	no	—
148	#367	—	73	2	no	—
149	#366	—	73	2	no	—
150	#358	—	73	8	no	—
151	C₂×#41	—	73	1	no	—
152	C₂²×Q₈	—	2	2	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×Q₁₆	—	2	4	no	—
155	C₂×Q₁₆	—	2	4	no	—
156	C₂×Q₁₆	C₂²×D₇₃	1	4	yes	—
157	#131	—	146	2	no	—
158	#131	—	146	2	no	—
159	C₂×M₁₆	—	73	1	no	—
160	C₂×M₁₆	—	73	2	no	—
161	C₂²×C₈	—	73	2	no	—
162	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
163	C₄⋊Q₈	—	292	2	no	—
164	#124	—	292	2	no	—
165	#123	—	292	4	no	—
166	C₂²⋊Q₈	—	146	8	no	—
167	#117	—	146	2	no	—
168	Q₃₂	—	2	4	no	—
169	Q₃₂	—	2	4	no	—
170	M₃₂	—	146	2	no	—
171	M₃₂	—	146	4	no	—
172	C₂×C₁₆	—	73	2	no	—
173	C₂×C₁₆	—	146	4	no	—
174	C₂×C₁₆	C₂²⋊D₇₃	1	4	yes	—
175	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
176	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
177	#107	—	73	4	no	—
178	#106	—	146	2	no	—
179	#103	—	146	8	no	—
180	#41	—	146	2	no	—
181	#41	—	146	2	no	—
182	C₂×Q₈	—	2	4	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	4	no	—
185	C₂×Q₈	—	4	4	no	—
186	C₂×Q₈	—	73	1	no	—
187	C₂×D₄	—	73	2	no	—
188	C₂×D₄	—	73	1	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	73	2	no	—
191	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	2	4	no	—
194	Q₁₆	—	4	4	no	—
195	M₁₆	—	146	2	no	—
196	M₁₆	—	146	4	no	—
197	C₂×C₈	—	73	2	no	—
198	C₂×C₈	—	146	2	no	—
199	C₂×C₈	—	146	2	no	—
200	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
201	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
202	C₂×C₈	#11924027	1	2	yes	—
203	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
204	C₄⋊C₄	—	292	8	no	—
205	C₄⋊C₄	—	146	4	no	—
206	C₂²⋊C₄	—	292	8	no	—
207	C₂²⋊C₄	—	292	2	no	—
208	C₄²	—	292	2	no	—
209	C₁₆	—	146	2	no	—
210	C₁₆	C₂×C₂²⋊D₇₃	1	2	yes	—
211	C₁₆	C₂×C₂²⋊D₇₃	1	2	yes	—
212	C₂³	—	73	2	no	—
213	C₂³	D₈×D₇₃	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	4	no	—
216	Q₈	—	8	4	no	—
217	Q₈	—	146	2	no	—
218	D₄	—	146	4	no	—
219	D₄	—	146	2	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	8	4	no	—
222	C₂×C₄	—	292	4	no	—
223	C₂×C₄	—	73	2	no	—
224	C₂×C₄	—	146	2	no	—
225	C₂×C₄	—	146	2	no	—
226	C₂×C₄	#14556562	1	2	yes	—
227	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
228	C₂×C₄	#14556610	1	2	yes	—
229	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
230	C₈	—	146	2	no	—
231	C₈	#14556562	1	2	yes	—
232	C₈	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
233	C₈	C₂×#11924027	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	146	2	no	—
236	C₂²	—	146	4	no	—
237	C₂²	#17988820	1	2	yes	—
238	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
239	C₄	—	8	4	no	—
240	C₄	—	584	4	no	—
241	C₄	—	146	2	no	—
242	C₄	#17988820	1	2	yes	—
243	C₄	C₂×#14556562	1	1	yes	characteristic
244	C₄	C₂×#14556610	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	292	2	no	—
247	C₂	C₂×#17988820	1	1	yes	characteristic
248	C₂	#22623080	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17989003

C₂

yes

maximal, characteristic

#22619582

C₂

yes

maximal

#22612036

C₂

yes

maximal, complemented

#22612019

C₂

yes

maximal, complemented

#22611715

C₂

yes

maximal, characteristic, complemented

#22611651

C₂

yes

maximal, complemented

C₂²×Q₃₂×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#14556597

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14556530

C₂²

yes

—

C₂×C₁₆×D₇₃

C₂²

yes

—

#17988842

—

#17988825

C₂²

yes

—

#17988625

C₂²

yes

—

#17988596

—

#17988415

C₂²

yes

—

#17988413

C₂²

yes

—

#17988391

C₂²

yes

—

C₂²×Q₁₆×C₇₃

C₂²

yes

—

C₂×Q₃₂×C₇₃

—

C₂×Q₃₂×C₇₃

C₂²

yes

—

C₂×Q₃₂×C₇₃

C₂²

yes

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#11924028

D₄

yes

—

—

D₄

yes

characteristic

C₂×#11924011

D₄

yes

—

C₂×C₈×D₇₃

C₂³

yes

—

—

—

—

—

—

—

—

C₂³

yes

—

C₁₆×D₇₃

—

#14556525

C₂³

yes

—

#14556523

—

#14556515

—

C₂²×Q₈×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂³

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

Q₃₂×C₇₃

—

Q₃₂×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

#11924028

—

#11924028

—

C₂×Dic₁₄₆

D₈

yes

characteristic

C₂×D₂₉₂

D₈

yes

characteristic

C₂×C₂²⋊D₇₃

D₈

yes

—

C₂×C₄×D₇₃

C₂×D₄

yes

—

#11924012

—

#11924011

—

C₂×#10596831

C₂×D₄

yes

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

#11924005

—

C₄×Dic₇₃

—

#11924003

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

C₂⁴

yes

characteristic

C₁₆×C₇₃

C₂×D₄

yes

—

C₁₆×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂²×D₇₃

C₂×D₈

yes

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

100

C₂×Dic₇₃

C₂×D₈

yes

—

101

D₂₉₂

—

102

C₄×D₇₃

—

103

C₄×D₇₃

—

104

Dic₁₄₆

—

105

C₈×C₇₃

#121

yes

—

106

C₈×C₇₃

C₂²×D₄

yes

characteristic

107

C₈×C₇₃

C₂×#41

yes

characteristic

108

#10596831

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

#466

yes

—

111

C₂²×C₇₃

C₂²×D₈

yes

characteristic

112

C₂×D₇₃

—

113

C₂×D₇₃

—

114

C₄×C₇₃

—

115

C₄×C₇₃

#466

yes

—

116

C₄×C₇₃

C₂×#121

yes

characteristic

117

C₄×C₇₃

C₂×#135

yes

characteristic

118

Dic₇₃

—

119

Dic₇₃

—

120

#33608

—

maximal, Sylow

121

C₂×C₇₃

—

122

C₂×C₇₃

C₂×#466

yes

characteristic

123

C₂×C₇₃

#3417

yes

—

124

D₇₃

—

125

C₂²×Q₃₂

D₇₃

yes

characteristic, complemented

126

C₂×#504

—

127

#3059

—

128

#2219

—

129

#2216

—

130

#2158

—

131

#2141

—

132

C₇₃

#33608

yes

characteristic, complemented, Sylow

133

C₂²×Q₁₆

C₂×D₇₃

yes

—

134

C₂×#131

—

135

#536

—

146

—

136

C₂×Q₃₂

—

137

C₂×Q₃₂

C₂×D₇₃

yes

—

138

C₂×Q₃₂

C₂×D₇₃

yes

—

139

#504

—

146

—

140

C₂×M₃₂

—

141

C₂×M₃₂

—

142

C₂²×C₁₆

—

143

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

144

#470

—

146

—

145

#467

—

146

#427

—

147

#419

—

146

—

148

#367

—

149

#366

—

150

#358

—

151

C₂×#41

—

152

C₂²×Q₈

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

C₂²×D₇₃

yes

—

157

#131

—

146

—

158

#131

—

146

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

C₂²×D₇₃

yes

characteristic

163

C₄⋊Q₈

—

292

—

164

#124

—

292

—

165

#123

—

292

—

166

C₂²⋊Q₈

—

146

—

167

#117

—

146

—

168

Q₃₂

—

169

Q₃₂

—

170

M₃₂

—

146

—

171

M₃₂

—

146

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

146

—

174

C₂×C₁₆

C₂²⋊D₇₃

yes

—

175

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

176

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

177

#107

—

178

#106

—

146

—

179

#103

—

146

—

180

#41

—

146

—

181

#41

—

146

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

D₄×D₇₃

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

M₁₆

—

146

—

196

M₁₆

—

146

—

197

C₂×C₈

—

198

C₂×C₈

—

146

—

199

C₂×C₈

—

146

—

200

C₂×C₈

D₄×D₇₃

yes

characteristic

201

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

202

C₂×C₈

#11924027

yes

—

203

C₂×C₈

C₂³×D₇₃

yes

characteristic

204

C₄⋊C₄

—

292

—

205

C₄⋊C₄

—

146

—

206

C₂²⋊C₄

—

292

—

207

C₂²⋊C₄

—

292

—

208

C₄²

—

292

—

209

C₁₆

—

146

—

210

C₁₆

C₂×C₂²⋊D₇₃

yes

—

211

C₁₆

C₂×C₂²⋊D₇₃

yes

—

212

C₂³

—

213

C₂³

D₈×D₇₃

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

146

—

218

D₄

—

146

—

219

D₄

—

146

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

292

—

223

C₂×C₄

—

224

C₂×C₄

—

146

—

225

C₂×C₄

—

146

—

226

C₂×C₄

#14556562

yes

—

227

C₂×C₄

D₈×D₇₃

yes

characteristic

228

C₂×C₄

#14556610

yes

—

229

C₂×C₄

C₂×D₄×D₇₃

yes

characteristic

230

C₈

—

146

—

231

C₈

#14556562

yes

—

232

C₈

C₂²×C₂²⋊D₇₃

yes

characteristic

233

C₈

C₂×#11924027

yes

characteristic

234

C₂²

—

235

C₂²

—

146

—

236

C₂²

—

146

—

237

C₂²

#17988820

yes

—

238

C₂²

C₂×D₈×D₇₃

yes

characteristic

239

C₄

—

240

C₄

—

584

—

241

C₄

—

146

—

242

C₄

#17988820

yes

—

243

C₄

C₂×#14556562

yes

characteristic

244

C₄

C₂×#14556610

yes

characteristic

245

C₂

—

246

C₂

—

292

—

247

C₂

C₂×#17988820

yes

characteristic

248

C₂

#22623080

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₂²×Q₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₈
prime radical	C₂×#11924028	D₄
hypercenter	C₂²×Q₃₂	D₇₃
hypocenter	C₇₃	#33608
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

C₂×D₈×D₇₃

commutator, cosocle

C₂×C₈×C₇₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₇₃

Fitting

C₂²×Q₃₂×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₈

prime radical

C₂×#11924028

D₄

hypercenter

C₂²×Q₃₂

D₇₃

hypocenter

C₇₃

#33608

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
3. #22612036	C₂	semidirect
4. #22612019	C₂	semidirect
5. #22611715	C₂	semidirect
6. #22611651	C₂	semidirect
7. C₂²×Q₃₂×C₇₃	C₂	semidirect
125. C₂²×Q₃₂	D₇₃	semidirect
132. C₇₃	#33608	semidirect

H ≅ G/N

type

3. #22612036

C₂

semidirect

4. #22612019

C₂

semidirect

5. #22611715

C₂

semidirect

6. #22611651

C₂

semidirect

7. C₂²×Q₃₂×C₇₃

C₂

semidirect

125. C₂²×Q₃₂

D₇₃

semidirect

132. C₇₃

#33608

semidirect

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

subgroup	index
C₂×#17989003	2
#22619582	2
#22612036	2
#22612019	2
#22611715	2
#22611651	2
C₂²×Q₃₂×C₇₃	2
#33608	73

subgroup

index

C₂²×Q₃₂×C₇₃

Subgroups — #33240484

Conjugacy classes of subgroups

Complements

Maximal subgroups