Group #32985461 — subgroups

Subgroups — #32985461

Order 18688.

406 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 119 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×#17988938	C₂	1	1	yes	maximal, characteristic
2	#22608617	C₂	1	1	yes	maximal, characteristic
3	#22608613	C₂	1	1	yes	maximal, characteristic
4	#22608604	C₂	1	1	yes	maximal, characteristic
5	#22608604	C₂	1	1	yes	maximal, characteristic
6	#22608223	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1848	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556591	C₂²	1	1	yes	characteristic
9	C₂×#14556591	C₂²	1	1	yes	characteristic
10	#17988938	—	2	2	no	—
11	#17988938	C₄	1	4	yes	—
12	#17988640	C₂²	1	1	yes	characteristic
13	#17988640	C₂²	1	1	yes	characteristic
14	C₂×#14556516	—	2	2	no	—
15	#17988335	—	2	2	no	—
16	#17988334	—	2	2	no	—
17	#17988334	—	2	2	no	—
18	#17988332	—	2	2	no	—
19	#17988309	—	2	2	no	—
20	C₂×#108×C₇₃	—	2	2	no	—
21	#423×C₇₃	C₂²	1	1	yes	characteristic
22	#423×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×Dic₁₄₆	—	2	1	no	—
25	C₂²×Dic₁₄₆	—	2	1	no	—
26	#14556591	—	2	1	no	—
27	#14556591	—	2	1	no	—
28	#14556591	—	2	1	no	—
29	#14556591	—	2	1	no	—
30	#14556591	—	2	1	no	—
31	#14556591	—	2	1	no	—
32	#14556591	C₂×C₄	1	2	yes	—
33	#14556591	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊Dic₇₃	—	2	1	no	—
35	C₂×C₄⋊Dic₇₃	—	2	1	no	—
36	C₂×C₄⋊Dic₇₃	—	2	1	no	—
37	C₂×C₄⋊Dic₇₃	—	2	1	no	—
38	C₄⋊#10596831	D₄	1	2	yes	—
39	C₄⋊#10596831	D₄	1	2	yes	—
40	#14556516	—	2	8	no	—
41	C₂²⋊#10596831	—	2	1	no	—
42	C₂²⋊#10596831	—	2	1	no	—
43	C₄×#10596831	—	2	1	no	—
44	C₄×#10596831	—	2	1	no	—
45	C₂×M₁₆×C₇₃	—	2	1	no	—
46	C₂×M₁₆×C₇₃	—	2	1	no	—
47	C₂²×C₈×C₇₃	D₄	1	2	yes	—
48	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
49	#108×C₇₃	—	4	4	no	—
50	C₄⋊C₈×C₇₃	—	2	1	no	—
51	C₄⋊C₈×C₇₃	—	2	1	no	—
52	C₄⋊C₈×C₇₃	—	2	1	no	—
53	C₄⋊C₈×C₇₃	—	2	1	no	—
54	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
55	C₄×C₈×C₇₃	D₄	1	2	yes	—
56	C₂×Dic₁₄₆	—	2	2	no	—
57	C₂×Dic₁₄₆	—	2	2	no	—
58	C₂×Dic₁₄₆	—	4	2	no	—
59	C₂×Dic₁₄₆	—	4	2	no	—
60	C₂×Dic₁₄₆	—	4	1	no	—
61	C₂×Dic₁₄₆	—	4	1	no	—
62	C₂×Dic₁₄₆	—	8	2	no	—
63	C₂²×Dic₇₃	—	4	1	no	—
64	C₂²×Dic₇₃	—	4	1	no	—
65	C₂×#10596831	—	2	2	no	—
66	C₂×#10596831	—	2	2	no	—
67	C₄⋊Dic₇₃	—	2	2	no	—
68	C₄⋊Dic₇₃	—	2	2	no	—
69	C₄⋊Dic₇₃	—	2	2	no	—
70	C₄⋊Dic₇₃	—	2	2	no	—
71	C₄⋊Dic₇₃	—	4	1	no	—
72	C₄⋊Dic₇₃	—	4	1	no	—
73	C₄⋊Dic₇₃	—	4	1	no	—
74	C₄⋊Dic₇₃	—	4	1	no	—
75	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
77	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
78	M₁₆×C₇₃	—	4	2	no	—
79	M₁₆×C₇₃	—	4	2	no	—
80	C₂×C₈×C₇₃	—	2	2	no	—
81	C₂×C₈×C₇₃	—	2	2	no	—
82	C₂×C₈×C₇₃	—	4	1	no	—
83	C₂×C₈×C₇₃	—	4	1	no	—
84	C₂×C₈×C₇₃	C₂²⋊C₄	1	4	yes	—
85	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
86	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
88	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
89	C₂³×C₇₃	#124	1	1	yes	characteristic
90	C₂×C₄×C₇₃	—	2	2	no	—
91	C₂×C₄×C₇₃	—	2	2	no	—
92	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
97	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
98	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
99	C₂×C₄×C₇₃	#137	1	2	yes	—
100	C₂×Dic₇₃	—	4	2	no	—
101	C₂×Dic₇₃	—	4	2	no	—
102	C₂×Dic₇₃	—	8	2	no	—
103	C₂×Dic₇₃	—	8	2	no	—
104	Dic₁₄₆	—	4	4	no	—
105	Dic₁₄₆	—	8	2	no	—
106	Dic₁₄₆	—	8	1	no	—
107	Dic₁₄₆	—	8	1	no	—
108	Dic₁₄₆	—	8	2	no	—
109	C₈×C₇₃	—	2	4	no	—
110	C₈×C₇₃	—	8	1	no	—
111	C₈×C₇₃	—	8	1	no	—
112	#10596831	—	4	2	no	—
113	#10596831	—	4	2	no	—
114	C₂²×C₇₃	—	2	1	no	—
115	C₂²×C₇₃	—	2	1	no	—
116	C₂²×C₇₃	#390	1	1	yes	characteristic
117	C₂²×C₇₃	#489	1	2	yes	—
118	C₄×C₇₃	—	2	1	no	—
119	C₄×C₇₃	—	2	1	no	—
120	C₄×C₇₃	#417	1	2	yes	—
121	C₄×C₇₃	#471	1	2	yes	—
122	C₄×C₇₃	#473	1	2	yes	—
123	C₄×C₇₃	#496	1	1	yes	characteristic
124	C₄×C₇₃	#497	1	1	yes	characteristic
125	Dic₇₃	—	8	2	no	—
126	Dic₇₃	—	8	2	no	—
127	#9775	—	73	1	no	maximal, Sylow
128	C₂×C₇₃	—	2	2	no	—
129	C₂×C₇₃	#1959	1	1	yes	characteristic
130	C₂×C₇₃	#1977	1	1	yes	characteristic
131	C₂×C₇₃	#1979	1	1	yes	characteristic
132	C₂×#487	—	73	1	no	—
133	#1848	D₇₃	1	1	yes	characteristic
134	#1549	—	73	1	no	—
135	#1548	—	73	1	no	—
136	#1546	—	73	1	no	—
137	#1546	—	73	1	no	—
138	#1452	—	73	1	no	—
139	C₇₃	#9775	1	1	yes	characteristic, complemented, Sylow
140	C₂×C₄⋊Q₈	—	73	1	no	—
141	C₂×C₄⋊Q₈	—	73	1	no	—
142	#487	—	73	4	no	—
143	#487	—	146	2	no	—
144	#431	—	73	1	no	—
145	#431	—	73	1	no	—
146	C₂×#108	—	2	2	no	—
147	#423	C₂×D₇₃	1	1	yes	characteristic
148	#423	C₂×D₇₃	1	1	yes	characteristic
149	C₂×#103	—	146	2	no	—
150	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
151	#333	—	146	2	no	—
152	#332	—	146	2	no	—
153	#332	—	146	2	no	—
154	#332	—	146	2	no	—
155	#322	—	146	2	no	—
156	C₂²×Q₈	—	146	1	no	—
157	C₂²×Q₈	—	146	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	2	1	no	—
160	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
161	C₄⋊Q₈	—	73	2	no	—
162	C₄⋊Q₈	—	73	2	no	—
163	C₄⋊Q₈	—	146	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	C₄⋊Q₈	—	146	1	no	—
169	C₂×C₄⋊C₄	—	146	1	no	—
170	C₂×C₄⋊C₄	—	146	1	no	—
171	C₂×C₄⋊C₄	—	146	1	no	—
172	C₂×C₄⋊C₄	—	146	1	no	—
173	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
174	#108	—	4	4	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	73	2	no	—
180	C₄⋊C₈	—	73	2	no	—
181	#103	—	146	8	no	—
182	C₂²⋊C₈	—	146	1	no	—
183	C₂²⋊C₈	—	146	1	no	—
184	C₄×C₈	—	146	1	no	—
185	C₄×C₈	—	146	1	no	—
186	C₄×C₈	C₄×D₇₃	1	2	yes	—
187	C₄×C₈	D₂₉₂	1	2	yes	—
188	C₂×Q₈	—	292	1	no	—
189	C₂×Q₈	—	292	1	no	—
190	C₂×Q₈	—	292	2	no	—
191	C₂×Q₈	—	292	2	no	—
192	C₂×Q₈	—	584	2	no	—
193	C₂×Q₈	—	146	2	no	—
194	C₂×Q₈	—	146	2	no	—
195	C₂²×C₄	—	292	1	no	—
196	C₂²×C₄	—	292	1	no	—
197	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
198	C₂²×C₄	#11924029	1	1	yes	characteristic
199	C₂²×C₄	#11924029	1	1	yes	characteristic
200	M₁₆	—	4	2	no	—
201	M₁₆	—	4	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	146	2	no	—
207	C₂×C₈	—	146	2	no	—
208	C₂×C₈	#11924005	1	4	yes	—
209	C₄⋊C₄	—	292	1	no	—
210	C₄⋊C₄	—	292	1	no	—
211	C₄⋊C₄	—	292	1	no	—
212	C₄⋊C₄	—	292	1	no	—
213	C₄⋊C₄	—	146	2	no	—
214	C₄⋊C₄	—	146	2	no	—
215	C₄⋊C₄	—	146	2	no	—
216	C₄⋊C₄	—	146	2	no	—
217	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
218	C₄²	D₄×D₇₃	1	1	yes	characteristic
219	C₄²	D₄×D₇₃	1	1	yes	characteristic
220	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
221	C₂³	#14556580	1	1	yes	characteristic
222	Q₈	—	292	4	no	—
223	Q₈	—	584	2	no	—
224	Q₈	—	584	1	no	—
225	Q₈	—	584	1	no	—
226	Q₈	—	584	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	292	2	no	—
230	C₂×C₄	—	292	2	no	—
231	C₂×C₄	—	584	2	no	—
232	C₂×C₄	—	584	2	no	—
233	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
234	C₂×C₄	#14556553	1	1	yes	characteristic
235	C₂×C₄	#14556553	1	1	yes	characteristic
236	C₂×C₄	#14556566	1	1	yes	characteristic
237	C₂×C₄	#14556566	1	1	yes	characteristic
238	C₂×C₄	#14556587	1	1	yes	characteristic
239	C₂×C₄	#14556617	1	2	yes	—
240	C₂×C₄	#14556622	1	2	yes	—
241	C₈	—	2	4	no	—
242	C₈	—	8	1	no	—
243	C₈	—	8	1	no	—
244	C₈	—	292	2	no	—
245	C₈	—	292	2	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	#17988488	1	1	yes	characteristic
249	C₂²	#17988949	1	2	yes	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	584	2	no	—
253	C₄	—	584	2	no	—
254	C₄	#17988586	1	2	yes	—
255	C₄	#17988851	1	2	yes	—
256	C₄	#17988863	1	2	yes	—
257	C₄	#17988974	1	1	yes	characteristic
258	C₄	#17988979	1	1	yes	characteristic
259	C₂	—	2	2	no	—
260	C₂	#22610745	1	1	yes	characteristic
261	C₂	#22610832	1	1	yes	characteristic
262	C₂	#22610844	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988938

C₂

yes

maximal, characteristic

#22608617

C₂

yes

maximal, characteristic

#22608613

C₂

yes

maximal, characteristic

#22608604

C₂

yes

maximal, characteristic

#22608604

C₂

yes

maximal, characteristic

#22608223

C₂

yes

maximal, characteristic

C₇₃×#1848

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

characteristic

C₂×#14556591

C₂²

yes

characteristic

#17988938

—

#17988938

C₄

yes

—

#17988640

C₂²

yes

characteristic

#17988640

C₂²

yes

—

—

—

—

—

—

C₂×#108×C₇₃

—

#423×C₇₃

C₂²

yes

characteristic

#423×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂²×Dic₁₄₆

—

C₂²×Dic₁₄₆

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14556591

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₄⋊#10596831

D₄

yes

—

C₄⋊#10596831

D₄

yes

—

—

—

—

—

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#108×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

D₄

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

C₂²×C₄×C₇₃

yes

C₂²×C₄×C₇₃

yes

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₂³×C₇₃

#124

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#137

yes

—

100

C₂×Dic₇₃

—

101

C₂×Dic₇₃

—

102

C₂×Dic₇₃

—

103

C₂×Dic₇₃

—

104

Dic₁₄₆

—

105

Dic₁₄₆

—

106

Dic₁₄₆

—

107

Dic₁₄₆

—

108

Dic₁₄₆

—

109

C₈×C₇₃

—

110

C₈×C₇₃

—

111

C₈×C₇₃

—

112

#10596831

—

113

#10596831

—

114

C₂²×C₇₃

—

115

C₂²×C₇₃

—

116

C₂²×C₇₃

#390

yes

characteristic

117

C₂²×C₇₃

#489

yes

—

118

C₄×C₇₃

—

119

C₄×C₇₃

—

120

C₄×C₇₃

#417

yes

—

121

C₄×C₇₃

#471

yes

—

122

C₄×C₇₃

#473

yes

—

123

C₄×C₇₃

#496

yes

characteristic

124

C₄×C₇₃

#497

yes

characteristic

125

Dic₇₃

—

126

Dic₇₃

—

127

#9775

—

maximal, Sylow

128

C₂×C₇₃

—

129

C₂×C₇₃

#1959

yes

characteristic

130

C₂×C₇₃

#1977

yes

characteristic

131

C₂×C₇₃

#1979

yes

characteristic

132

C₂×#487

—

133

#1848

D₇₃

yes

characteristic

134

#1549

—

135

#1548

—

136

#1546

—

137

#1546

—

138

#1452

—

139

C₇₃

#9775

yes

characteristic, complemented, Sylow

140

C₂×C₄⋊Q₈

—

141

C₂×C₄⋊Q₈

—

142

#487

—

143

#487

—

146

—

144

#431

—

145

#431

—

146

C₂×#108

—

147

#423

C₂×D₇₃

yes

characteristic

148

#423

C₂×D₇₃

yes

characteristic

149

C₂×#103

—

146

—

150

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

151

#333

—

146

—

152

#332

—

146

—

153

#332

—

146

—

154

#332

—

146

—

155

#322

—

146

—

156

C₂²×Q₈

—

146

—

157

C₂²×Q₈

—

146

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

C₂²⋊D₇₃

yes

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

146

—

164

C₄⋊Q₈

—

146

—

165

C₄⋊Q₈

—

146

—

166

C₄⋊Q₈

—

146

—

167

C₄⋊Q₈

—

146

—

168

C₄⋊Q₈

—

146

—

169

C₂×C₄⋊C₄

—

146

—

170

C₂×C₄⋊C₄

—

146

—

171

C₂×C₄⋊C₄

—

146

—

172

C₂×C₄⋊C₄

—

146

—

173

C₂×C₄²

C₂²×D₇₃

yes

characteristic

174

#108

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

#103

—

146

—

182

C₂²⋊C₈

—

146

—

183

C₂²⋊C₈

—

146

—

184

C₄×C₈

—

146

—

185

C₄×C₈

—

146

—

186

C₄×C₈

C₄×D₇₃

yes

—

187

C₄×C₈

D₂₉₂

yes

—

188

C₂×Q₈

—

292

—

189

C₂×Q₈

—

292

—

190

C₂×Q₈

—

292

—

191

C₂×Q₈

—

292

—

192

C₂×Q₈

—

584

—

193

C₂×Q₈

—

146

—

194

C₂×Q₈

—

146

—

195

C₂²×C₄

—

292

—

196

C₂²×C₄

—

292

—

197

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

198

C₂²×C₄

#11924029

yes

characteristic

199

C₂²×C₄

#11924029

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

146

—

207

C₂×C₈

—

146

—

208

C₂×C₈

#11924005

yes

—

209

C₄⋊C₄

—

292

—

210

C₄⋊C₄

—

292

—

211

C₄⋊C₄

—

292

—

212

C₄⋊C₄

—

292

—

213

C₄⋊C₄

—

146

—

214

C₄⋊C₄

—

146

—

215

C₄⋊C₄

—

146

—

216

C₄⋊C₄

—

146

—

217

C₄²

C₂×C₄×D₇₃

yes

characteristic

218

C₄²

D₄×D₇₃

yes

characteristic

219

C₄²

D₄×D₇₃

yes

characteristic

220

C₄²

C₂×D₂₉₂

yes

characteristic

221

C₂³

#14556580

yes

characteristic

222

Q₈

—

292

—

223

Q₈

—

584

—

224

Q₈

—

584

—

225

Q₈

—

584

—

226

Q₈

—

584

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

292

—

230

C₂×C₄

—

292

—

231

C₂×C₄

—

584

—

232

C₂×C₄

—

584

—

233

C₂×C₄

C₂×#11924005

yes

characteristic

234

C₂×C₄

#14556553

yes

characteristic

235

C₂×C₄

#14556553

yes

characteristic

236

C₂×C₄

#14556566

yes

characteristic

237

C₂×C₄

#14556566

yes

characteristic

238

C₂×C₄

#14556587

yes

characteristic

239

C₂×C₄

#14556617

yes

—

240

C₂×C₄

#14556622

yes

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

292

—

245

C₈

—

292

—

246

C₂²

—

247

C₂²

—

248

C₂²

#17988488

yes

characteristic

249

C₂²

#17988949

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

584

—

253

C₄

—

584

—

254

C₄

#17988586

yes

—

255

C₄

#17988851

yes

—

256

C₄

#17988863

yes

—

257

C₄

#17988974

yes

characteristic

258

C₄

#17988979

yes

characteristic

259

C₂

—

260

C₂

#22610745

yes

characteristic

261

C₂

#22610832

yes

characteristic

262

C₂

#22610844

yes

characteristic

	subgroup	G/H
center	C₂²	#17988488
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1848	C₂
socle	C₂²×C₇₃	#390
prime radical	C₂³×C₇₃	#124
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1848	D₇₃
hypocenter	C₇₃	#9775
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂²

#17988488

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1848

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
139. C₇₃	#9775	semidirect

H ≅ G/N

type

139. C₇₃

#9775

semidirect

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

subgroup	index
C₂×#17988938	2
#22608617	2
#22608613	2
#22608604	2
#22608223	2
C₇₃×#1848	2
#9775	73

subgroup

index

C₇₃×#1848

Subgroups — #32985461

Conjugacy classes of subgroups

Complements

Maximal subgroups