Group #34013020 — subgroups

Subgroups — #34013020

Order 18688.

478 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 148 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×#17989508	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊#11924031	C₂	1	2	yes	maximal
3	#22624970	C₂	1	2	yes	maximal, complemented
4	C₂×#17988545	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11924031	C₂²	1	4	yes	—
6	#17989508	—	2	4	no	—
7	C₂²⋊#11924031	—	2	4	no	—
8	C₂³×#10596831	C₂²	1	1	yes	characteristic
9	C₂×#14556550	C₄	1	1	yes	characteristic
10	#17988545	—	2	4	no	—
11	C₂×#14556501	C₄	1	1	yes	characteristic
12	C₂×#14556501	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₇₃	C₄	1	1	yes	characteristic
16	C₂×#11924031	—	2	4	no	—
17	C₂×#11924031	—	2	4	no	—
18	C₂×#11924031	—	2	4	no	—
19	C₂²×#10596831	—	2	2	no	—
20	C₂²×#10596831	—	2	2	no	—
21	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂²×#10596831	D₄	1	2	yes	—
23	C₂²×#10596831	Q₈	1	2	yes	—
24	C₂²×#10596831	C₂³	1	1	yes	characteristic
25	#14556550	—	2	2	no	—
26	#14556550	—	2	2	no	—
27	C₂×C₄⋊Dic₇₃	C₈	1	2	yes	—
28	C₂×C₂²⋊Dic₇₃	C₈	1	2	yes	—
29	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	#14556501	—	2	2	no	—
32	#14556501	—	2	2	no	—
33	C₈×Dic₇₃	—	2	2	no	—
34	C₈×Dic₇₃	D₄	1	4	yes	—
35	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂×M₁₆×C₇₃	—	2	2	no	—
37	C₂×M₁₆×C₇₃	—	2	2	no	—
38	C₂×M₁₆×C₇₃	—	2	2	no	—
39	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
41	#11924031	—	4	4	no	—
42	C₂²×Dic₇₃	C₂×C₈	1	2	yes	—
43	C₂²×Dic₇₃	C₂×C₈	1	2	yes	—
44	C₂×#10596831	—	2	1	no	—
45	C₂×#10596831	—	2	1	no	—
46	C₂×#10596831	—	2	4	no	—
47	C₂×#10596831	—	2	4	no	—
48	C₂×#10596831	C₄⋊C₄	1	2	yes	—
49	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
50	C₂×#10596831	C₂×D₄	1	2	yes	—
51	C₂×#10596831	C₂×Q₈	1	1	yes	characteristic
52	C₂×#10596831	#41	1	2	yes	—
53	C₄⋊Dic₇₃	—	2	4	no	—
54	C₂²⋊Dic₇₃	—	2	4	no	—
55	C₄×Dic₇₃	—	2	1	no	—
56	C₄×Dic₇₃	—	2	1	no	—
57	C₄×Dic₇₃	C₂²⋊C₄	1	2	yes	—
58	C₄×Dic₇₃	M₁₆	1	2	yes	—
59	C₂⁴×C₇₃	C₂×C₈	1	1	yes	characteristic
60	C₂²×C₄×C₇₃	—	2	1	no	—
61	C₂²×C₄×C₇₃	—	2	1	no	—
62	C₂²×C₄×C₇₃	—	2	1	no	—
63	C₂²×C₄×C₇₃	—	2	1	no	—
64	C₂²×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
66	C₂²×C₄×C₇₃	M₁₆	1	2	yes	—
67	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
68	M₁₆×C₇₃	—	2	8	no	—
69	C₂×C₈×C₇₃	—	2	1	no	—
70	C₂×C₈×C₇₃	—	2	1	no	—
71	C₂×C₈×C₇₃	—	2	1	no	—
72	C₂×C₈×C₇₃	—	2	1	no	—
73	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
75	C₂³×C₇₃	—	2	1	no	—
76	C₂³×C₇₃	—	2	1	no	—
77	C₂³×C₇₃	—	2	4	no	—
78	C₂³×C₇₃	C₄⋊C₈	1	2	yes	—
79	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₇₃	—	2	1	no	—
81	C₂×C₄×C₇₃	—	2	1	no	—
82	C₂×C₄×C₇₃	—	2	2	no	—
83	C₂×C₄×C₇₃	—	2	2	no	—
84	C₂×C₄×C₇₃	—	2	2	no	—
85	C₂×C₄×C₇₃	—	2	2	no	—
86	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
87	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×Dic₇₃	—	2	4	no	—
94	C₂×Dic₇₃	—	2	2	no	—
95	C₂×Dic₇₃	—	2	4	no	—
96	C₂×Dic₇₃	C₂²⋊C₈	1	4	yes	—
97	C₈×C₇₃	—	2	2	no	—
98	C₈×C₇₃	—	2	2	no	—
99	#10596831	—	2	2	no	—
100	#10596831	#121	1	2	yes	—
101	#10596831	C₂²⋊Q₈	1	2	yes	—
102	C₂²×C₇₃	—	2	2	no	—
103	C₂²×C₇₃	—	2	4	no	—
104	C₂²×C₇₃	—	4	2	no	—
105	C₂²×C₇₃	—	4	2	no	—
106	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
107	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
108	C₂²×C₇₃	#431	1	1	yes	characteristic
109	C₂²×C₇₃	#504	1	4	yes	—
110	C₄×C₇₃	—	2	2	no	—
111	C₄×C₇₃	#380	1	1	yes	characteristic
112	C₄×C₇₃	#407	1	1	yes	characteristic
113	C₄×C₇₃	#423	1	1	yes	characteristic
114	C₄×C₇₃	#432	1	1	yes	characteristic
115	Dic₇₃	—	2	4	no	—
116	Dic₇₃	—	4	2	no	—
117	#12784	—	73	1	no	maximal, Sylow
118	C₂×C₇₃	—	4	2	no	—
119	C₂×C₇₃	#1797	1	1	yes	characteristic
120	C₂×C₇₃	#2113	1	2	yes	—
121	C₂×C₇₃	#2151	1	2	yes	—
122	C₂×C₇₃	#2164	1	2	yes	—
123	C₂×#405	—	73	1	no	—
124	C₂×C₄⋊C₁₆	—	73	2	no	—
125	C₂×C₂²⋊C₁₆	—	73	2	no	—
126	#1374	—	73	2	no	—
127	C₇₃	#12784	1	1	yes	characteristic, complemented, Sylow
128	C₂²×M₁₆	#64408	1	1	yes	characteristic
129	C₂³×C₈	—	73	1	no	—
130	C₂×#117	—	73	1	no	—
131	C₂²×C₁₆	—	73	4	no	—
132	#405	—	146	4	no	—
133	C₂×#97	—	73	1	no	—
134	C₂×#97	—	73	1	no	—
135	C₂×C₄×C₈	—	73	1	no	—
136	C₂×C₄×C₈	—	73	1	no	—
137	C₄⋊C₁₆	—	146	4	no	—
138	C₂²⋊C₁₆	—	146	4	no	—
139	C₂³×C₄	C₂×#64408	1	1	yes	characteristic
140	C₂×M₁₆	—	2	2	no	—
141	C₂×M₁₆	—	2	2	no	—
142	C₂×M₁₆	—	2	2	no	—
143	C₂²×C₈	—	73	1	no	—
144	C₂²×C₈	—	73	2	no	—
145	C₂²×C₈	—	73	2	no	—
146	C₂²×C₈	—	73	1	no	—
147	C₂²×C₈	—	146	2	no	—
148	C₂²×C₈	—	146	2	no	—
149	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
150	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
151	#117	—	146	2	no	—
152	#117	—	146	2	no	—
153	C₂×C₄⋊C₄	—	73	2	no	—
154	C₂×C₂²⋊C₄	—	73	2	no	—
155	C₂×C₄²	—	73	1	no	—
156	C₂×C₄²	—	73	1	no	—
157	C₂×C₁₆	—	146	4	no	—
158	C₂×C₁₆	—	146	4	no	—
159	C₂×C₁₆	—	146	4	no	—
160	#97	—	146	2	no	—
161	#97	—	146	2	no	—
162	C₄×C₈	—	73	4	no	—
163	C₄×C₈	—	146	2	no	—
164	C₂⁴	#11924036	1	1	yes	characteristic
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	2	1	no	—
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	73	2	no	—
170	C₂²×C₄	—	73	2	no	—
171	C₂²×C₄	C₄⋊#64408	1	2	yes	—
172	C₂²×C₄	#11924036	1	1	yes	characteristic
173	C₂²×C₄	#11924037	1	2	yes	—
174	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
175	M₁₆	—	2	8	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	2	1	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	73	2	no	—
181	C₂×C₈	—	73	1	no	—
182	C₂×C₈	—	73	1	no	—
183	C₂×C₈	—	73	2	no	—
184	C₂×C₈	—	73	2	no	—
185	C₂×C₈	—	146	4	no	—
186	C₂×C₈	—	146	4	no	—
187	C₂×C₈	—	146	1	no	—
188	C₂×C₈	—	146	1	no	—
189	C₂×C₈	C₂²⋊#64408	1	2	yes	—
190	C₂×C₈	#11924037	1	2	yes	—
191	C₄⋊C₄	—	146	4	no	—
192	C₂²⋊C₄	—	146	4	no	—
193	C₄²	—	73	2	no	—
194	C₄²	—	73	2	no	—
195	C₄²	—	146	1	no	—
196	C₄²	—	146	1	no	—
197	C₁₆	—	292	4	no	—
198	C₂³	—	2	4	no	—
199	C₂³	—	2	1	no	—
200	C₂³	—	2	1	no	—
201	C₂³	#14556658	1	2	yes	—
202	C₂³	C₂×#11924036	1	1	yes	characteristic
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	73	4	no	—
210	C₂×C₄	—	146	4	no	—
211	C₂×C₄	—	146	2	no	—
212	C₂×C₄	—	146	4	no	—
213	C₂×C₄	#14556658	1	2	yes	—
214	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
215	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
216	C₂×C₄	#14556670	1	1	yes	characteristic
217	C₂×C₄	C₂×#11924037	1	1	yes	characteristic
218	C₂×C₄	C₂×#11924037	1	1	yes	characteristic
219	C₂×C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	73	2	no	—
223	C₈	—	73	2	no	—
224	C₈	—	146	2	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	4	2	no	—
228	C₂²	—	4	2	no	—
229	C₂²	#17989555	1	1	yes	characteristic
230	C₂²	C₂×#14556658	1	1	yes	characteristic
231	C₂²	#17989604	1	1	yes	characteristic
232	C₂²	#17989646	1	4	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	292	2	no	—
235	C₄	—	146	4	no	—
236	C₄	#17989529	1	1	yes	characteristic
237	C₄	#17989557	1	1	yes	characteristic
238	C₄	#17989590	1	1	yes	characteristic
239	C₄	#17989607	1	1	yes	characteristic
240	C₂	—	4	2	no	—
241	C₂	#22625787	1	1	yes	characteristic
242	C₂	#22626162	1	2	yes	—
243	C₂	#22626268	1	2	yes	—
244	C₂	#22626297	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17989508

C₂

yes

maximal, complemented

C₂×C₂²⋊#11924031

C₂

yes

maximal

#22624970

C₂

yes

maximal, complemented

C₂×#17988545

C₂

yes

maximal, characteristic

C₂²×#11924031

C₂²

yes

—

#17989508

—

C₂²⋊#11924031

—

C₂³×#10596831

C₂²

yes

characteristic

C₂×#14556550

C₄

yes

characteristic

#17988545

—

C₂×#14556501

C₄

yes

characteristic

C₂×#14556501

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₂²

yes

characteristic

C₂×C₈×Dic₇₃

C₂²

yes

characteristic

C₂²×M₁₆×C₇₃

C₄

yes

—

—

—

—

—

C₂×C₄

yes

characteristic

C₂²×#10596831

D₄

yes

—

C₂²×#10596831

Q₈

yes

—

C₂²×#10596831

C₂³

yes

characteristic

#14556550

—

#14556550

—

C₂×C₄⋊Dic₇₃

C₈

yes

—

C₂×C₂²⋊Dic₇₃

C₈

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

#14556501

—

#14556501

—

C₈×Dic₇₃

—

C₈×Dic₇₃

D₄

yes

—

C₂³×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

#11924031

—

C₂²×Dic₇₃

C₂×C₈

yes

—

C₂²×Dic₇₃

C₂×C₈

yes

—

—

—

—

—

C₄⋊C₄

yes

—

C₂×#10596831

C₂×D₄

yes

characteristic

C₂×#10596831

C₂×D₄

yes

—

C₂×#10596831

C₂×Q₈

yes

characteristic

C₂×#10596831

#41

yes

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂²⋊C₄

yes

—

C₄×Dic₇₃

M₁₆

yes

—

C₂⁴×C₇₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₄⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₃

M₁₆

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

M₁₆

yes

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₄⋊C₈

yes

—

C₂³×C₇₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₈

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#117

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₈

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

100

#10596831

#121

yes

—

101

#10596831

C₂²⋊Q₈

yes

—

102

C₂²×C₇₃

—

103

C₂²×C₇₃

—

104

C₂²×C₇₃

—

105

C₂²×C₇₃

—

106

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

107

C₂²×C₇₃

C₂×C₄⋊C₈

yes

characteristic

108

C₂²×C₇₃

#431

yes

characteristic

109

C₂²×C₇₃

#504

yes

—

110

C₄×C₇₃

—

111

C₄×C₇₃

#380

yes

characteristic

112

C₄×C₇₃

#407

yes

characteristic

113

C₄×C₇₃

#423

yes

characteristic

114

C₄×C₇₃

#432

yes

characteristic

115

Dic₇₃

—

116

Dic₇₃

—

117

#12784

—

maximal, Sylow

118

C₂×C₇₃

—

119

C₂×C₇₃

#1797

yes

characteristic

120

C₂×C₇₃

#2113

yes

—

121

C₂×C₇₃

#2151

yes

—

122

C₂×C₇₃

#2164

yes

—

123

C₂×#405

—

124

C₂×C₄⋊C₁₆

—

125

C₂×C₂²⋊C₁₆

—

126

#1374

—

127

C₇₃

#12784

yes

characteristic, complemented, Sylow

128

C₂²×M₁₆

#64408

yes

characteristic

129

C₂³×C₈

—

130

C₂×#117

—

131

C₂²×C₁₆

—

132

#405

—

146

—

133

C₂×#97

—

134

C₂×#97

—

135

C₂×C₄×C₈

—

136

C₂×C₄×C₈

—

137

C₄⋊C₁₆

—

146

—

138

C₂²⋊C₁₆

—

146

—

139

C₂³×C₄

C₂×#64408

yes

characteristic

140

C₂×M₁₆

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

—

146

—

148

C₂²×C₈

—

146

—

149

C₂²×C₈

C₂×#64408

yes

characteristic

150

C₂²×C₈

C₂×#64408

yes

characteristic

151

#117

—

146

—

152

#117

—

146

—

153

C₂×C₄⋊C₄

—

154

C₂×C₂²⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₁₆

—

146

—

158

C₂×C₁₆

—

146

—

159

C₂×C₁₆

—

146

—

160

#97

—

146

—

161

#97

—

146

—

162

C₄×C₈

—

163

C₄×C₈

—

146

—

164

C₂⁴

#11924036

yes

characteristic

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₄⋊#64408

yes

—

172

C₂²×C₄

#11924036

yes

characteristic

173

C₂²×C₄

#11924037

yes

—

174

C₂²×C₄

C₂²×#64408

yes

characteristic

175

M₁₆

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

146

—

186

C₂×C₈

—

146

—

187

C₂×C₈

—

146

—

188

C₂×C₈

—

146

—

189

C₂×C₈

C₂²⋊#64408

yes

—

190

C₂×C₈

#11924037

yes

—

191

C₄⋊C₄

—

146

—

192

C₂²⋊C₄

—

146

—

193

C₄²

—

194

C₄²

—

195

C₄²

—

146

—

196

C₄²

—

146

—

197

C₁₆

—

292

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

#14556658

yes

—

202

C₂³

C₂×#11924036

yes

characteristic

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

146

—

211

C₂×C₄

—

146

—

212

C₂×C₄

—

146

—

213

C₂×C₄

#14556658

yes

—

214

C₂×C₄

C₂×C₂²⋊#64408

yes

characteristic

215

C₂×C₄

C₂×C₄⋊#64408

yes

characteristic

216

C₂×C₄

#14556670

yes

characteristic

217

C₂×C₄

C₂×#11924037

yes

characteristic

218

C₂×C₄

C₂×#11924037

yes

characteristic

219

C₂×C₄

D₇₃⋊M₁₆

yes

characteristic

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

146

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

#17989555

yes

characteristic

230

C₂²

C₂×#14556658

yes

characteristic

231

C₂²

#17989604

yes

characteristic

232

C₂²

#17989646

yes

—

233

C₄

—

234

C₄

—

292

—

235

C₄

—

146

—

236

C₄

#17989529

yes

characteristic

237

C₄

#17989557

yes

characteristic

238

C₄

#17989590

yes

characteristic

239

C₄

#17989607

yes

characteristic

240

C₂

—

241

C₂

#22625787

yes

characteristic

242

C₂

#22626162

yes

—

243

C₂

#22626268

yes

—

244

C₂

#22626297

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#64408
commutator, socle	C₂³×C₇₃	C₂²×C₈
Fitting	C₂²×M₁₆×C₇₃	C₄
prime radical	C₂⁴×C₇₃	C₂×C₈
cosocle	C₂²×#10596831	C₂³
hypercenter	C₂²×M₁₆	#64408
hypocenter	C₇₃	#12784
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#64408

commutator, socle

C₂³×C₇₃

C₂²×C₈

Fitting

C₂²×M₁₆×C₇₃

C₄

prime radical

C₂⁴×C₇₃

C₂×C₈

C₂³

C₂²×M₁₆

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

N	H ≅ G/N	type
1. C₂×#17989508	C₂	semidirect
3. #22624970	C₂	semidirect
127. C₇₃	#12784	semidirect

H ≅ G/N

type

1. C₂×#17989508

C₂

semidirect

3. #22624970

C₂

semidirect

127. C₇₃

#12784

semidirect

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

subgroup	index
C₂×#17989508	2
C₂×C₂²⋊#11924031	2
#22624970	2
C₂×#17988545	2
#12784	73

subgroup

index

C₂×C₂²⋊#11924031

Subgroups — #34013020

Conjugacy classes of subgroups

Complements

Maximal subgroups