Group #22611012 — subgroups

Subgroups — #22611012

Order 9344.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11924016	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556589	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14556516	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14556515	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988490	C₂	1	1	yes	maximal, characteristic
6	#17988341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×SD₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
9	C₂×#11924016	—	2	2	no	—
10	C₂×#11924016	—	2	2	no	—
11	C₂×#11924016	—	2	2	no	—
12	C₂²×#10596831	C₂²	1	1	yes	characteristic
13	#14556589	—	2	2	no	—
14	#14556589	—	2	2	no	—
15	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×#11924007	—	2	2	no	—
17	C₂×C₂²⋊Dic₇₃	—	2	2	no	—
18	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
19	#14556516	—	2	2	no	—
20	#14556515	—	2	2	no	—
21	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×SD₁₆×C₇₃	—	2	2	no	—
24	C₂×SD₁₆×C₇₃	—	2	2	no	—
25	C₂×SD₁₆×C₇₃	—	2	2	no	—
26	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×Dic₁₄₆	—	2	1	no	—
28	C₂×Dic₁₄₆	—	2	1	no	—
29	C₂×Dic₁₄₆	—	2	1	no	—
30	C₂×Dic₁₄₆	—	2	1	no	—
31	C₂×Dic₁₄₆	—	2	1	no	—
32	C₂×Dic₁₄₆	D₄	1	2	yes	—
33	C₂²×Dic₇₃	—	2	1	no	—
34	C₂²×Dic₇₃	—	2	1	no	—
35	C₂²×Dic₇₃	D₄	1	2	yes	—
36	#11924016	—	2	8	no	—
37	C₂×#10596831	—	2	1	no	—
38	C₂×#10596831	—	2	1	no	—
39	C₂×#10596831	D₄	1	2	yes	—
40	C₄⋊Dic₇₃	—	2	1	no	—
41	C₄⋊Dic₇₃	—	2	1	no	—
42	#11924007	—	2	8	no	—
43	C₂²⋊Dic₇₃	—	4	4	no	—
44	C₄×Dic₇₃	—	2	1	no	—
45	C₄×Dic₇₃	—	2	1	no	—
46	C₂⁴×C₇₃	—	2	1	no	—
47	C₂×Q₈×C₇₃	—	2	1	no	—
48	C₂×Q₈×C₇₃	—	2	1	no	—
49	C₂×Q₈×C₇₃	—	2	1	no	—
50	C₂×Q₈×C₇₃	—	2	1	no	—
51	C₂×Q₈×C₇₃	—	2	1	no	—
52	C₂×Q₈×C₇₃	D₄	1	2	yes	—
53	C₂×D₄×C₇₃	—	2	1	no	—
54	C₂×D₄×C₇₃	—	2	1	no	—
55	C₂×D₄×C₇₃	—	2	1	no	—
56	C₂×D₄×C₇₃	—	2	1	no	—
57	C₂×D₄×C₇₃	—	2	1	no	—
58	C₂×D₄×C₇₃	D₄	1	2	yes	—
59	C₂²×C₄×C₇₃	—	2	1	no	—
60	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
61	SD₁₆×C₇₃	—	2	8	no	—
62	C₂×C₈×C₇₃	—	2	1	no	—
63	C₂×C₈×C₇₃	—	2	1	no	—
64	C₂×C₈×C₇₃	D₄	1	2	yes	—
65	C₂³×C₇₃	—	2	2	no	—
66	C₂³×C₇₃	—	4	1	no	—
67	C₂³×C₇₃	—	4	1	no	—
68	C₂³×C₇₃	—	4	2	no	—
69	C₂³×C₇₃	—	4	2	no	—
70	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
71	Q₈×C₇₃	—	2	2	no	—
72	Q₈×C₇₃	—	2	2	no	—
73	Q₈×C₇₃	—	4	1	no	—
74	Q₈×C₇₃	—	4	1	no	—
75	D₄×C₇₃	—	2	2	no	—
76	D₄×C₇₃	—	2	2	no	—
77	D₄×C₇₃	—	4	1	no	—
78	D₄×C₇₃	—	4	1	no	—
79	C₂×C₄×C₇₃	—	2	2	no	—
80	C₂×C₄×C₇₃	—	4	1	no	—
81	C₂×C₄×C₇₃	—	4	1	no	—
82	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
88	C₂×Dic₇₃	—	2	2	no	—
89	C₂×Dic₇₃	—	2	2	no	—
90	C₂×Dic₇₃	—	2	2	no	—
91	C₂×Dic₇₃	—	4	1	no	—
92	C₂×Dic₇₃	—	4	1	no	—
93	C₂×Dic₇₃	—	4	1	no	—
94	C₂×Dic₇₃	—	4	2	no	—
95	C₂×Dic₇₃	SD₁₆	1	4	yes	complemented
96	Dic₁₄₆	—	2	2	no	—
97	Dic₁₄₆	—	2	2	no	—
98	Dic₁₄₆	—	4	1	no	—
99	Dic₁₄₆	—	4	1	no	—
100	C₈×C₇₃	—	2	2	no	—
101	#10596831	—	2	2	no	—
102	C₂²×C₇₃	—	4	2	no	—
103	C₂²×C₇₃	—	4	4	no	—
104	C₂²×C₇₃	—	8	2	no	—
105	C₂²×C₇₃	—	8	1	no	—
106	C₂²×C₇₃	—	8	1	no	—
107	C₂²×C₇₃	#120	1	1	yes	characteristic
108	C₂²×C₇₃	#121	1	1	yes	characteristic
109	C₂²×C₇₃	#127	1	1	yes	characteristic
110	C₂²×C₇₃	C₂×SD₁₆	1	2	yes	—
111	C₂²×C₇₃	#137	1	2	yes	—
112	C₄×C₇₃	—	4	2	no	—
113	C₄×C₇₃	#120	1	1	yes	characteristic
114	C₄×C₇₃	#120	1	1	yes	characteristic
115	C₄×C₇₃	#121	1	1	yes	characteristic
116	C₄×C₇₃	#121	1	1	yes	characteristic
117	Dic₇₃	—	2	4	no	—
118	Dic₇₃	—	4	2	no	—
119	Dic₇₃	—	8	1	no	—
120	C₂×C₇₃	—	8	2	no	—
121	C₂×C₇₃	#392	1	1	yes	characteristic
122	C₂×C₇₃	#448	1	2	yes	—
123	C₂×C₇₃	#461	1	2	yes	—
124	C₂×C₇₃	#492	1	1	yes	characteristic
125	C₂×C₇₃	#497	1	1	yes	characteristic
126	#2013	—	73	1	no	maximal, Sylow
127	C₇₃	#2013	1	1	yes	characteristic, complemented, Sylow
128	C₂²×SD₁₆	—	73	1	no	—
129	C₂²×SD₁₆	D₇₃	1	1	yes	characteristic
130	C₂×C₄⋊Q₈	—	73	1	no	—
131	C₂×#103	—	73	1	no	—
132	C₂×#103	—	73	1	no	—
133	#390	—	73	1	no	—
134	#336	—	73	1	no	—
135	C₂²×Q₈	—	73	1	no	—
136	C₂²×Q₈	C₂×D₇₃	1	1	yes	characteristic
137	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
138	C₂×SD₁₆	—	2	2	no	—
139	C₂×SD₁₆	—	2	2	no	—
140	C₂×SD₁₆	—	2	2	no	—
141	C₂×SD₁₆	—	146	2	no	—
142	C₂×SD₁₆	—	146	2	no	—
143	C₂×SD₁₆	—	146	2	no	—
144	C₂²×C₈	—	73	1	no	—
145	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
146	C₄⋊Q₈	—	146	2	no	—
147	C₄⋊Q₈	—	146	2	no	—
148	C₂×C₄⋊C₄	—	73	1	no	—
149	C₂×C₄⋊C₄	—	146	2	no	—
150	C₂×C₂²⋊C₄	—	146	2	no	—
151	C₂×C₄²	—	73	1	no	—
152	#103	—	146	2	no	—
153	#103	—	146	2	no	—
154	C₂⁴	—	2	1	no	—
155	C₂×Q₈	—	2	1	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	73	2	no	—
161	C₂×Q₈	—	146	1	no	—
162	C₂×Q₈	—	146	1	no	—
163	C₂×Q₈	—	146	1	no	—
164	C₂×Q₈	—	146	1	no	—
165	C₂×Q₈	—	146	1	no	—
166	C₂×Q₈	C₂²⋊D₇₃	1	2	yes	—
167	C₂×D₄	—	2	1	no	—
168	C₂×D₄	—	2	1	no	—
169	C₂×D₄	—	2	1	no	—
170	C₂×D₄	—	2	1	no	—
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	C₂²⋊D₇₃	1	2	yes	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	73	2	no	—
175	C₂²×C₄	—	146	1	no	—
176	C₂²×C₄	—	146	1	no	—
177	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
178	SD₁₆	—	2	8	no	—
179	SD₁₆	—	146	8	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	73	2	no	—
183	C₂×C₈	—	146	1	no	—
184	C₂×C₈	—	146	1	no	—
185	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
186	C₄⋊C₄	—	146	8	no	—
187	C₄⋊C₄	—	146	1	no	—
188	C₄⋊C₄	—	146	1	no	—
189	C₂²⋊C₄	—	292	4	no	—
190	C₄²	—	146	1	no	—
191	C₄²	—	146	1	no	—
192	C₂³	—	2	2	no	—
193	C₂³	—	4	1	no	—
194	C₂³	—	4	1	no	—
195	C₂³	—	4	2	no	—
196	C₂³	—	4	2	no	—
197	C₂³	D₄×D₇₃	1	1	yes	characteristic
198	Q₈	—	2	2	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	4	1	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	292	1	no	—
203	Q₈	—	292	1	no	—
204	Q₈	—	146	2	no	—
205	Q₈	—	146	2	no	—
206	D₄	—	2	2	no	—
207	D₄	—	2	2	no	—
208	D₄	—	4	1	no	—
209	D₄	—	4	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	292	1	no	—
214	C₂×C₄	—	292	1	no	—
215	C₂×C₄	—	292	1	no	—
216	C₂×C₄	—	292	2	no	—
217	C₂×C₄	—	73	4	no	—
218	C₂×C₄	—	146	2	no	—
219	C₂×C₄	—	146	2	no	—
220	C₂×C₄	—	146	2	no	—
221	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
222	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
223	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
224	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
225	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
226	C₂×C₄	#11924027	1	1	yes	characteristic
227	C₈	—	2	2	no	—
228	C₈	—	146	2	no	—
229	C₂²	—	4	2	no	—
230	C₂²	—	4	4	no	—
231	C₂²	—	8	1	no	—
232	C₂²	—	8	1	no	—
233	C₂²	—	8	2	no	—
234	C₂²	#14556559	1	1	yes	characteristic
235	C₂²	#14556563	1	1	yes	characteristic
236	C₂²	#14556587	1	1	yes	characteristic
237	C₂²	SD₁₆×D₇₃	1	2	yes	—
238	C₂²	#14556620	1	2	yes	—
239	C₄	—	4	2	no	—
240	C₄	—	292	2	no	—
241	C₄	—	584	1	no	—
242	C₄	—	146	4	no	—
243	C₄	#14556559	1	1	yes	characteristic
244	C₄	#14556560	1	1	yes	characteristic
245	C₄	#14556562	1	1	yes	characteristic
246	C₄	#14556563	1	1	yes	characteristic
247	C₂	—	8	2	no	—
248	C₂	#17988495	1	1	yes	characteristic
249	C₂	#17988724	1	2	yes	—
250	C₂	#17988790	1	2	yes	—
251	C₂	#17988958	1	1	yes	characteristic
252	C₂	#17988978	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924016

C₂

yes

maximal, characteristic

C₂×#14556589

C₂

yes

maximal, characteristic, complemented

C₂×#14556516

C₂

yes

maximal, characteristic, complemented

C₂×#14556515

C₂

yes

maximal, characteristic, complemented

#17988490

C₂

yes

maximal, characteristic

#17988341

C₂

yes

maximal, characteristic, complemented

C₂²×SD₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14556589

—

#14556589

—

C₂×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂×#11924007

—

C₂×C₂²⋊Dic₇₃

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556516

—

#14556515

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₂²×D₄×C₇₃

C₂²

yes

characteristic

C₂×SD₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂×SD₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

—

—

—

D₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂⁴×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

SD₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

SD₁₆

yes

complemented

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

100

C₈×C₇₃

—

101

#10596831

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

—

105

C₂²×C₇₃

—

106

C₂²×C₇₃

—

107

C₂²×C₇₃

#120

yes

characteristic

108

C₂²×C₇₃

#121

yes

characteristic

109

C₂²×C₇₃

#127

yes

characteristic

110

C₂²×C₇₃

C₂×SD₁₆

yes

—

111

C₂²×C₇₃

#137

yes

—

112

C₄×C₇₃

—

113

C₄×C₇₃

#120

yes

characteristic

114

C₄×C₇₃

#120

yes

characteristic

115

C₄×C₇₃

#121

yes

characteristic

116

C₄×C₇₃

#121

yes

characteristic

117

Dic₇₃

—

118

Dic₇₃

—

119

Dic₇₃

—

120

C₂×C₇₃

—

121

C₂×C₇₃

#392

yes

characteristic

122

C₂×C₇₃

#448

yes

—

123

C₂×C₇₃

#461

yes

—

124

C₂×C₇₃

#492

yes

characteristic

125

C₂×C₇₃

yes

126

—

127

C₇₃

#2013

yes

characteristic, complemented, Sylow

128

C₂²×SD₁₆

—

129

C₂²×SD₁₆

D₇₃

yes

characteristic

130

C₂×C₄⋊Q₈

—

131

C₂×#103

—

132

C₂×#103

—

133

#390

—

134

#336

—

135

C₂²×Q₈

—

136

C₂²×Q₈

C₂×D₇₃

yes

characteristic

137

C₂²×D₄

C₂×D₇₃

yes

characteristic

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

146

—

142

C₂×SD₁₆

—

146

—

143

C₂×SD₁₆

—

146

—

144

C₂²×C₈

—

145

C₂²×C₈

C₂×D₇₃

yes

characteristic

146

C₄⋊Q₈

—

146

—

147

C₄⋊Q₈

—

146

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

146

—

150

C₂×C₂²⋊C₄

—

146

—

151

C₂×C₄²

—

152

#103

—

146

—

153

#103

—

146

—

154

C₂⁴

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

146

—

162

C₂×Q₈

—

146

—

163

C₂×Q₈

—

146

—

164

C₂×Q₈

—

146

—

165

C₂×Q₈

—

146

—

166

C₂×Q₈

C₂²⋊D₇₃

yes

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

C₂²⋊D₇₃

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

146

—

176

C₂²×C₄

—

146

—

177

C₂²×C₄

C₂²×D₇₃

yes

characteristic

178

SD₁₆

—

179

SD₁₆

—

146

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

146

—

184

C₂×C₈

—

146

—

185

C₂×C₈

C₂²⋊D₇₃

yes

—

186

C₄⋊C₄

—

146

—

187

C₄⋊C₄

—

146

—

188

C₄⋊C₄

—

146

—

189

C₂²⋊C₄

—

292

—

190

C₄²

—

146

—

191

C₄²

—

146

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

D₄×D₇₃

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

292

—

203

Q₈

—

292

—

204

Q₈

—

146

—

205

Q₈

—

146

—

206

D₄

—

207

D₄

—

208

D₄

—

209

D₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

292

—

214

C₂×C₄

—

292

—

215

C₂×C₄

—

292

—

216

C₂×C₄

—

292

—

217

C₂×C₄

—

218

C₂×C₄

—

146

—

219

C₂×C₄

—

146

—

220

C₂×C₄

—

146

—

221

C₂×C₄

D₄×D₇₃

yes

characteristic

222

C₂×C₄

D₄×D₇₃

yes

characteristic

223

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

224

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

225

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

226

C₂×C₄

#11924027

yes

characteristic

227

C₈

—

228

C₈

—

146

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

#14556559

yes

characteristic

235

C₂²

#14556563

yes

characteristic

236

C₂²

#14556587

yes

characteristic

237

C₂²

SD₁₆×D₇₃

yes

—

238

C₂²

#14556620

yes

—

239

C₄

—

240

C₄

—

292

—

241

C₄

—

584

—

242

C₄

—

146

—

243

C₄

#14556559

yes

characteristic

244

C₄

#14556560

yes

characteristic

245

C₄

#14556562

yes

characteristic

246

C₄

#14556563

yes

characteristic

247

C₂

—

248

C₂

#17988495

yes

characteristic

249

C₂

#17988724

yes

—

250

C₂

#17988790

yes

—

251

C₂

#17988958

yes

characteristic

252

C₂

#17988978

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂²×SD₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂²×SD₁₆	D₇₃
hypocenter	C₇₃	#2013
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×SD₁₆

subgroup

G/H

center

C₂³

D₄×D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂²×SD₁₆×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

hypercenter

C₂²×SD₁₆

D₇₃

hypocenter

C₇₃

#2013

LCS

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×SD₁₆

N	H ≅ G/N	type
2. C₂×#14556589	C₂	semidirect
3. C₂×#14556516	C₂	semidirect
4. C₂×#14556515	C₂	semidirect
6. #17988341	C₂	semidirect
95. C₂×Dic₇₃	SD₁₆	semidirect
127. C₇₃	#2013	semidirect

H ≅ G/N

type

2. C₂×#14556589

C₂

semidirect

3. C₂×#14556516

C₂

semidirect

4. C₂×#14556515

C₂

semidirect

6. #17988341

C₂

semidirect

95. C₂×Dic₇₃

SD₁₆

semidirect

127. C₇₃

#2013

semidirect

Subgroups — #22611012

Conjugacy classes of subgroups

Complements