Group #32985626 — subgroups

Subgroups — #32985626

Order 18688.

402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988937	C₂	1	1	yes	maximal, characteristic
2	#22610920	C₂	1	1	yes	maximal, characteristic
3	#22608686	C₂	1	1	yes	maximal, characteristic
4	#22608617	C₂	1	1	yes	maximal, characteristic
5	#22608612	C₂	1	1	yes	maximal, characteristic
6	#22608218	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1997	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556591	C₂²	1	1	yes	characteristic
9	#17988937	—	2	2	no	—
10	#17988937	—	2	2	no	—
11	#17988640	C₂²	1	1	yes	characteristic
12	#17988611	C₂²	1	1	yes	characteristic
13	C₂×#14556515	C₄	1	4	yes	—
14	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
15	#17988355	—	2	2	no	—
16	#17988337	—	2	2	no	—
17	#17988336	—	2	2	no	—
18	#17988332	—	2	2	no	—
19	#17988309	—	2	2	no	—
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	#423×C₇₃	C₂²	1	1	yes	characteristic
22	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
23	#343×C₇₃	—	2	2	no	—
24	C₂²×Dic₁₄₆	—	2	1	no	—
25	C₂×#11924012	—	2	1	no	—
26	C₂²×#10596831	C₂×C₄	1	2	yes	—
27	#14556591	—	2	1	no	—
28	#14556591	—	2	1	no	—
29	#14556591	—	2	1	no	—
30	#14556591	—	2	1	no	—
31	C₂×C₄⋊Dic₇₃	—	2	1	no	—
32	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
33	C₄⋊#10596831	—	2	1	no	—
34	C₄⋊#10596831	—	2	1	no	—
35	C₄⋊#10596831	D₄	1	2	yes	—
36	#14556515	—	2	8	no	—
37	C₂²⋊#10596831	—	2	1	no	—
38	C₄×#10596831	—	2	1	no	—
39	C₄×#10596831	D₄	1	2	yes	—
40	C₄×#10596831	D₄	1	2	yes	—
41	C₂²×Q₈×C₇₃	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₇₃	—	2	1	no	—
43	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
44	C₄⋊Q₈×C₇₃	—	2	1	no	—
45	C₄⋊Q₈×C₇₃	—	2	1	no	—
46	C₄⋊Q₈×C₇₃	—	2	1	no	—
47	C₄⋊Q₈×C₇₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
50	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
51	C₄⋊C₈×C₇₃	—	2	1	no	—
52	C₄⋊C₈×C₇₃	—	2	1	no	—
53	#97×C₇₃	—	2	1	no	—
54	C₄×C₈×C₇₃	—	2	1	no	—
55	C₂×Dic₁₄₆	—	4	1	no	—
56	C₂×Dic₁₄₆	—	4	1	no	—
57	C₂×Dic₁₄₆	—	8	2	no	—
58	C₂²×Dic₇₃	—	2	2	no	—
59	#11924012	—	4	2	no	—
60	C₂×#10596831	—	2	2	no	—
61	C₂×#10596831	—	4	2	no	—
62	C₂×#10596831	—	4	1	no	—
63	C₂×#10596831	C₂²⋊C₄	1	4	yes	—
64	C₄⋊Dic₇₃	—	2	2	no	—
65	C₄⋊Dic₇₃	—	2	2	no	—
66	C₄⋊Dic₇₃	—	4	1	no	—
67	C₄⋊Dic₇₃	—	4	1	no	—
68	C₂×Q₈×C₇₃	—	2	2	no	—
69	C₂×Q₈×C₇₃	—	2	2	no	—
70	C₂×Q₈×C₇₃	—	4	4	no	—
71	C₂²×C₄×C₇₃	—	2	2	no	—
72	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
75	M₁₆×C₇₃	—	2	2	no	—
76	M₁₆×C₇₃	—	2	2	no	—
77	M₁₆×C₇₃	—	4	2	no	—
78	C₂×C₈×C₇₃	—	2	2	no	—
79	C₂×C₈×C₇₃	—	4	1	no	—
80	C₄⋊C₄×C₇₃	—	4	1	no	—
81	C₄⋊C₄×C₇₃	—	4	1	no	—
82	C₄⋊C₄×C₇₃	—	4	1	no	—
83	C₄⋊C₄×C₇₃	—	4	1	no	—
84	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₇₃	#41	1	1	yes	characteristic
88	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
89	Q₈×C₇₃	—	4	4	no	—
90	Q₈×C₇₃	—	8	2	no	—
91	C₂×C₄×C₇₃	—	2	2	no	—
92	C₂×C₄×C₇₃	—	2	2	no	—
93	C₂×C₄×C₇₃	—	4	2	no	—
94	C₂×C₄×C₇₃	—	8	2	no	—
95	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
98	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
99	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
100	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
101	C₂×C₄×C₇₃	#137	1	2	yes	—
102	C₂×C₄×C₇₃	#137	1	2	yes	—
103	C₂×Dic₇₃	—	4	2	no	—
104	C₂×Dic₇₃	—	8	2	no	—
105	Dic₁₄₆	—	8	2	no	—
106	Dic₁₄₆	—	8	2	no	—
107	C₈×C₇₃	—	4	2	no	—
108	C₈×C₇₃	—	8	1	no	—
109	#10596831	—	2	4	no	—
110	#10596831	—	4	2	no	—
111	#10596831	—	8	1	no	—
112	C₂²×C₇₃	—	2	1	no	—
113	C₂²×C₇₃	—	2	1	no	—
114	C₂²×C₇₃	#390	1	1	yes	characteristic
115	C₂²×C₇₃	#441	1	2	yes	—
116	C₄×C₇₃	—	2	1	no	—
117	C₄×C₇₃	—	2	1	no	—
118	C₄×C₇₃	—	8	2	no	—
119	C₄×C₇₃	#413	1	2	yes	—
120	C₄×C₇₃	#470	1	2	yes	—
121	C₄×C₇₃	#471	1	2	yes	—
122	C₄×C₇₃	#497	1	1	yes	characteristic
123	C₄×C₇₃	#497	1	1	yes	characteristic
124	Dic₇₃	—	8	2	no	—
125	#9803	—	73	1	no	maximal, Sylow
126	C₂×C₇₃	—	2	2	no	—
127	C₂×C₇₃	#1967	1	1	yes	characteristic
128	C₂×C₇₃	#1971	1	1	yes	characteristic
129	C₂×C₇₃	#1977	1	1	yes	characteristic
130	C₂×#487	—	73	1	no	—
131	#1997	—	73	1	no	—
132	#1997	D₇₃	1	1	yes	characteristic
133	#1566	—	73	1	no	—
134	#1549	—	73	1	no	—
135	#1548	—	73	1	no	—
136	#1451	—	73	1	no	—
137	C₇₃	#9803	1	1	yes	characteristic, complemented, Sylow
138	C₂×C₄⋊Q₈	—	73	1	no	—
139	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
140	#487	—	146	2	no	—
141	#487	—	146	2	no	—
142	#431	—	73	1	no	—
143	#423	—	73	1	no	—
144	#423	C₂×D₇₃	1	1	yes	characteristic
145	C₂×#103	—	73	4	no	—
146	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
147	C₂×C₄×C₈	—	73	1	no	—
148	#343	—	2	2	no	—
149	#343	—	146	2	no	—
150	#334	—	146	2	no	—
151	#333	—	146	2	no	—
152	#332	—	146	2	no	—
153	#322	—	146	2	no	—
154	C₂²×Q₈	—	146	1	no	—
155	C₂²×Q₈	C₄×D₇₃	1	2	yes	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	146	1	no	—
158	C₂×M₁₆	C₂²⋊D₇₃	1	2	yes	—
159	C₂²×C₈	—	73	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	146	1	no	—
165	C₄⋊Q₈	—	146	1	no	—
166	C₄⋊Q₈	—	146	1	no	—
167	C₄⋊Q₈	—	146	1	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	2	1	no	—
170	C₂×C₄⋊C₄	—	73	2	no	—
171	C₂×C₄⋊C₄	—	146	1	no	—
172	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	73	2	no	—
176	C₄⋊C₈	—	146	1	no	—
177	C₄⋊C₈	—	146	1	no	—
178	#103	—	146	8	no	—
179	C₂²⋊C₈	—	146	1	no	—
180	#97	—	2	1	no	—
181	C₄×C₈	—	2	1	no	—
182	C₄×C₈	—	73	2	no	—
183	C₄×C₈	—	73	2	no	—
184	C₄×C₈	—	146	1	no	—
185	C₂×Q₈	—	2	2	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	4	4	no	—
188	C₂×Q₈	—	292	1	no	—
189	C₂×Q₈	—	292	1	no	—
190	C₂×Q₈	—	584	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	146	2	no	—
193	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
194	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
195	C₂²×C₄	#11924028	1	1	yes	characteristic
196	M₁₆	—	2	2	no	—
197	M₁₆	—	2	2	no	—
198	M₁₆	—	4	2	no	—
199	M₁₆	—	292	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	292	1	no	—
203	C₂×C₈	—	292	2	no	—
204	C₂×C₈	—	73	4	no	—
205	C₂×C₈	—	146	2	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₄⋊C₄	—	4	1	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₄⋊C₄	—	292	1	no	—
211	C₄⋊C₄	—	292	1	no	—
212	C₄⋊C₄	—	146	2	no	—
213	C₄⋊C₄	—	146	2	no	—
214	C₄²	D₄×D₇₃	1	1	yes	characteristic
215	C₄²	D₄×D₇₃	1	1	yes	characteristic
216	C₄²	D₄×D₇₃	1	1	yes	characteristic
217	C₄²	#11924027	1	1	yes	characteristic
218	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
219	Q₈	—	4	4	no	—
220	Q₈	—	8	2	no	—
221	Q₈	—	584	2	no	—
222	Q₈	—	584	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	8	2	no	—
227	C₂×C₄	—	292	2	no	—
228	C₂×C₄	—	584	2	no	—
229	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
230	C₂×C₄	#14556551	1	1	yes	characteristic
231	C₂×C₄	#14556563	1	1	yes	characteristic
232	C₂×C₄	#14556564	1	1	yes	characteristic
233	C₂×C₄	#14556577	1	1	yes	characteristic
234	C₂×C₄	#14556587	1	1	yes	characteristic
235	C₂×C₄	#14556621	1	2	yes	—
236	C₂×C₄	#14556622	1	2	yes	—
237	C₈	—	4	2	no	—
238	C₈	—	8	1	no	—
239	C₈	—	292	2	no	—
240	C₈	—	584	1	no	—
241	C₈	—	146	4	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	#17988487	1	1	yes	characteristic
245	C₂²	#17988692	1	2	yes	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	8	2	no	—
249	C₄	—	584	2	no	—
250	C₄	#17988568	1	2	yes	—
251	C₄	#17988843	1	2	yes	—
252	C₄	#17988853	1	2	yes	—
253	C₄	#17988979	1	1	yes	characteristic
254	C₄	#17988982	1	1	yes	characteristic
255	C₂	—	2	2	no	—
256	C₂	#22610777	1	1	yes	characteristic
257	C₂	#22610801	1	1	yes	characteristic
258	C₂	#22610835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988937

C₂

yes

maximal, characteristic

#22610920

C₂

yes

maximal, characteristic

#22608686

C₂

yes

maximal, characteristic

#22608617

C₂

yes

maximal, characteristic

#22608612

C₂

yes

maximal, characteristic

#22608218

C₂

yes

maximal, characteristic

C₇₃×#1997

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

—

—

C₂²

yes

characteristic

#17988611

C₂²

yes

characteristic

C₂×#14556515

C₄

yes

—

C₂×C₄×#10596831

C₂²

yes

—

—

—

—

—

C₂×C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

#423×C₇₃

C₂²

yes

characteristic

C₄×M₁₆×C₇₃

C₂²

yes

characteristic

#343×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×#11924012

—

C₂²×#10596831

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

C₄⋊#10596831

—

C₄⋊#10596831

—

C₄⋊#10596831

D₄

yes

—

—

—

—

D₄

yes

—

C₄×#10596831

D₄

yes

—

C₂²×Q₈×C₇₃

C₂×C₄

yes

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

—

—

—

—

C₂²⋊C₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

#41

yes

characteristic

C₂³×C₇₃

C₄×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

100

C₂×C₄×C₇₃

#127

yes

characteristic

101

C₂×C₄×C₇₃

#137

yes

—

102

C₂×C₄×C₇₃

#137

yes

—

103

C₂×Dic₇₃

—

104

C₂×Dic₇₃

—

105

Dic₁₄₆

—

106

Dic₁₄₆

—

107

C₈×C₇₃

—

108

C₈×C₇₃

—

109

#10596831

—

110

#10596831

—

111

#10596831

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

#390

yes

characteristic

115

C₂²×C₇₃

#441

yes

—

116

C₄×C₇₃

—

117

C₄×C₇₃

—

118

C₄×C₇₃

—

119

C₄×C₇₃

#413

yes

—

120

C₄×C₇₃

#470

yes

—

121

C₄×C₇₃

#471

yes

—

122

C₄×C₇₃

#497

yes

characteristic

123

C₄×C₇₃

#497

yes

characteristic

124

Dic₇₃

—

125

#9803

—

maximal, Sylow

126

C₂×C₇₃

—

127

C₂×C₇₃

#1967

yes

characteristic

128

C₂×C₇₃

#1971

yes

characteristic

129

C₂×C₇₃

#1977

yes

characteristic

130

C₂×#487

—

131

#1997

—

132

#1997

D₇₃

yes

characteristic

133

#1566

—

134

#1549

—

135

#1548

—

136

#1451

—

137

C₇₃

#9803

yes

characteristic, complemented, Sylow

138

C₂×C₄⋊Q₈

—

139

C₂×C₄⋊Q₈

C₂×D₇₃

yes

characteristic

140

#487

—

146

—

141

#487

—

146

—

142

#431

—

143

#423

—

144

#423

C₂×D₇₃

yes

characteristic

145

C₂×#103

—

146

C₄×M₁₆

C₂×D₇₃

yes

characteristic

147

C₂×C₄×C₈

—

148

#343

—

149

#343

—

146

—

150

#334

—

146

—

151

#333

—

146

—

152

#332

—

146

—

153

#322

—

146

—

154

C₂²×Q₈

—

146

—

155

C₂²×Q₈

C₄×D₇₃

yes

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

146

—

158

C₂×M₁₆

C₂²⋊D₇₃

yes

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

146

—

165

C₄⋊Q₈

—

146

—

166

C₄⋊Q₈

—

146

—

167

C₄⋊Q₈

—

146

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

146

—

172

C₂×C₄²

C₂²×D₇₃

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

146

—

177

C₄⋊C₈

—

146

—

178

#103

—

146

—

179

C₂²⋊C₈

—

146

—

180

#97

—

181

C₄×C₈

—

182

C₄×C₈

—

183

C₄×C₈

—

184

C₄×C₈

—

146

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

292

—

189

C₂×Q₈

—

292

—

190

C₂×Q₈

—

584

—

191

C₂²×C₄

—

192

C₂²×C₄

—

146

—

193

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

194

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

195

C₂²×C₄

#11924028

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

292

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

292

—

203

C₂×C₈

—

292

—

204

C₂×C₈

—

205

C₂×C₈

—

146

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

292

—

211

C₄⋊C₄

—

292

—

212

C₄⋊C₄

—

146

—

213

C₄⋊C₄

—

146

—

214

C₄²

D₄×D₇₃

yes

characteristic

215

C₄²

D₄×D₇₃

yes

characteristic

216

C₄²

D₄×D₇₃

yes

characteristic

217

C₄²

#11924027

yes

characteristic

218

C₂³

C₄×C₂²⋊D₇₃

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

584

—

222

Q₈

—

584

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

292

—

228

C₂×C₄

—

584

—

229

C₂×C₄

C₂²⋊C₄×D₇₃

yes

characteristic

230

C₂×C₄

#14556551

yes

characteristic

231

C₂×C₄

#14556563

yes

characteristic

232

C₂×C₄

#14556564

yes

characteristic

233

C₂×C₄

#14556577

yes

characteristic

234

C₂×C₄

#14556587

yes

characteristic

235

C₂×C₄

#14556621

yes

—

236

C₂×C₄

#14556622

yes

—

237

C₈

—

238

C₈

—

239

C₈

—

292

—

240

C₈

—

584

—

241

C₈

—

146

—

242

C₂²

—

243

C₂²

—

244

C₂²

#17988487

yes

characteristic

245

C₂²

#17988692

yes

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

584

—

250

C₄

#17988568

yes

—

251

C₄

#17988843

yes

—

252

C₄

#17988853

yes

—

253

C₄

#17988979

yes

characteristic

254

C₄

#17988982

yes

characteristic

255

C₂

—

256

C₂

#22610777

yes

characteristic

257

C₂

#22610801

yes

characteristic

258

C₂

#22610835

yes

characteristic

	subgroup	G/H
center	C₂²	#17988487
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1997	C₂
socle	C₂²×C₇₃	#390
prime radical	C₂³×C₇₃	C₄×D₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1997	D₇₃
hypocenter	C₇₃	#9803
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

subgroup

G/H

center

C₂²

#17988487

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1997

C₂

socle

C₂²×C₇₃

#390

prime radical

C₂³×C₇₃

C₄×D₄

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

N	H ≅ G/N	type
137. C₇₃	#9803	semidirect

H ≅ G/N

type

137. C₇₃

#9803

semidirect

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

subgroup	index
C₂×#17988937	2
#22610920	2
#22608686	2
#22608617	2
#22608612	2
#22608218	2
C₇₃×#1997	2
#9803	73

subgroup

index

C₇₃×#1997

Subgroups — #32985626

Conjugacy classes of subgroups

Complements

Maximal subgroups