Group #33002210 — subgroups

Subgroups — #33002210

Order 18688.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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×#17988539	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988368	C₂	1	2	yes	maximal
3	#22608012	C₂	1	2	yes	maximal, complemented
4	#22608011	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#11924011	C₄	1	1	yes	characteristic
7	C₂²×#11924011	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
9	C₂×#14556531	C₂²	1	2	yes	—
10	#17988539	—	2	4	no	—
11	C₂×#14556502	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	#17988368	—	2	4	no	—
15	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
16	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₇₃	—	2	1	no	—
18	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#11924011	—	2	2	no	—
20	C₂×#11924011	—	2	2	no	—
21	C₂×#11924011	—	2	2	no	—
22	C₂×#11924011	—	2	1	no	—
23	C₂×#11924011	—	2	2	no	—
24	C₂×#11924011	—	2	1	no	—
25	C₂×#11924011	D₄	1	4	yes	—
26	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
27	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₇₃	—	2	1	no	—
29	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
30	C₄²×D₇₃	—	2	2	no	—
31	C₄²×D₇₃	C₈	1	4	yes	—
32	#14556531	—	2	2	no	—
33	#14556531	—	2	2	no	—
34	C₂×#11924003	—	2	2	no	—
35	#14556502	—	2	2	no	—
36	C₈×Dic₇₃	—	2	2	no	—
37	C₈×Dic₇₃	—	2	2	no	—
38	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
41	M₃₂×C₇₃	—	2	2	no	—
42	M₃₂×C₇₃	—	2	2	no	—
43	C₂×C₁₆×C₇₃	—	2	2	no	—
44	#97×C₇₃	—	2	2	no	—
45	C₂³×D₇₃	M₁₆	1	1	yes	characteristic
46	C₂²×Dic₇₃	—	2	1	no	—
47	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
48	C₂×C₄×D₇₃	—	2	1	no	—
49	C₂×C₄×D₇₃	—	2	1	no	—
50	C₂×C₄×D₇₃	—	2	1	no	—
51	C₂×C₄×D₇₃	—	2	1	no	—
52	C₂×C₄×D₇₃	—	2	4	no	—
53	C₂×C₄×D₇₃	—	4	4	no	—
54	C₂×C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₄×D₇₃	C₂×C₈	1	2	yes	—
56	#11924011	—	2	8	no	—
57	#11924011	—	2	4	no	—
58	#11924011	—	2	4	no	—
59	C₂×#10596831	—	2	1	no	—
60	C₂×#10596831	—	2	1	no	—
61	C₂×#10596831	—	2	1	no	—
62	C₂×#10596831	—	2	1	no	—
63	C₂×#10596831	C₂²⋊C₄	1	2	yes	—
64	C₂×#10596831	M₁₆	1	2	yes	—
65	C₄×Dic₇₃	—	2	1	no	—
66	C₄×Dic₇₃	—	2	4	no	—
67	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
68	#11924003	—	4	2	no	—
69	C₂²×C₄×C₇₃	—	2	1	no	—
70	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₃	—	2	1	no	—
72	C₂×C₈×C₇₃	—	2	1	no	—
73	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
74	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
76	C₂×C₈×C₇₃	#41	1	2	yes	—
77	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
78	C₄²×C₇₃	—	2	1	no	—
79	C₄²×C₇₃	C₂×C₈	1	2	yes	—
80	C₁₆×C₇₃	—	4	2	no	—
81	C₂³×C₇₃	C₂×M₁₆	1	1	yes	characteristic
82	C₂²×D₇₃	—	2	1	no	—
83	C₂²×D₇₃	—	2	1	no	—
84	C₂²×D₇₃	—	4	2	no	—
85	C₂²×D₇₃	C₂²⋊C₈	1	2	yes	—
86	C₂×C₄×C₇₃	—	2	2	no	—
87	C₂×C₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
90	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
94	C₂×Dic₇₃	—	2	4	no	—
95	C₂×Dic₇₃	—	2	2	no	—
96	C₂×Dic₇₃	—	2	1	no	—
97	C₂×Dic₇₃	—	2	1	no	—
98	C₂×Dic₇₃	C₂²⋊C₈	1	2	yes	—
99	C₄×D₇₃	—	2	2	no	—
100	C₄×D₇₃	—	2	2	no	—
101	C₄×D₇₃	—	2	2	no	—
102	C₄×D₇₃	—	2	2	no	—
103	C₄×D₇₃	—	4	8	no	—
104	C₈×C₇₃	—	2	2	no	—
105	C₈×C₇₃	#123	1	2	yes	—
106	C₈×C₇₃	#123	1	2	yes	—
107	#10596831	—	2	2	no	—
108	#10596831	—	2	2	no	—
109	C₂²×C₇₃	—	2	2	no	—
110	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
111	C₂²×C₇₃	#432	1	1	yes	characteristic
112	C₂²×C₇₃	#432	1	1	yes	characteristic
113	C₂×D₇₃	—	2	2	no	—
114	C₂×D₇₃	—	4	2	no	—
115	C₂×D₇₃	—	4	2	no	—
116	C₂×D₇₃	—	4	2	no	—
117	C₄×C₇₃	—	4	2	no	—
118	C₄×C₇₃	#381	1	1	yes	characteristic
119	C₄×C₇₃	#407	1	1	yes	characteristic
120	C₄×C₇₃	#431	1	1	yes	characteristic
121	C₄×C₇₃	#431	1	1	yes	characteristic
122	Dic₇₃	—	2	4	no	—
123	Dic₇₃	—	2	2	no	—
124	#12849	—	73	1	no	maximal, Sylow
125	C₂×C₇₃	—	2	1	no	—
126	C₂×C₇₃	—	2	1	no	—
127	C₂×C₇₃	#1817	1	1	yes	characteristic
128	C₂×C₇₃	#2165	1	2	yes	—
129	D₇₃	—	4	2	no	—
130	C₂×C₄×M₁₆	—	73	1	no	—
131	C₂×#349	—	73	2	no	—
132	#1376	—	73	2	no	—
133	#1375	—	73	1	no	—
134	#1375	D₇₃	1	1	yes	characteristic, complemented
135	C₇₃	#12849	1	1	yes	characteristic, complemented, Sylow
136	C₂²×M₁₆	—	73	1	no	—
137	C₂²×M₁₆	—	73	1	no	—
138	C₂²×C₄²	—	73	1	no	—
139	C₂×M₃₂	—	73	2	no	—
140	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
141	C₄×M₁₆	—	146	4	no	—
142	C₂×#97	—	73	1	no	—
143	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
144	C₂×C₄×C₈	—	73	1	no	—
145	C₂×C₄×C₈	—	73	1	no	—
146	#349	—	146	4	no	—
147	C₂³×C₄	—	73	1	no	—
148	C₂³×C₄	—	146	1	no	—
149	C₂×M₁₆	—	73	4	no	—
150	C₂×M₁₆	—	146	2	no	—
151	C₂×M₁₆	—	146	2	no	—
152	C₂×M₁₆	—	146	2	no	—
153	C₂×M₁₆	—	146	1	no	—
154	C₂×M₁₆	—	146	2	no	—
155	C₂×M₁₆	—	146	1	no	—
156	C₂²×C₈	—	73	1	no	—
157	C₂²×C₈	—	73	1	no	—
158	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
159	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
160	C₂×C₄²	—	73	1	no	—
161	C₂×C₄²	—	73	4	no	—
162	C₂×C₄²	—	146	2	no	—
163	C₂×C₄²	—	146	1	no	—
164	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
165	M₃₂	—	2	2	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	146	2	no	—
168	M₃₂	—	146	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	146	2	no	—
171	#97	—	2	2	no	—
172	#97	—	146	2	no	—
173	C₄×C₈	—	146	2	no	—
174	C₄×C₈	—	146	2	no	—
175	C₂⁴	—	73	1	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	292	4	no	—
178	C₂²×C₄	—	73	1	no	—
179	C₂²×C₄	—	73	2	no	—
180	C₂²×C₄	—	73	2	no	—
181	C₂²×C₄	—	146	4	no	—
182	C₂²×C₄	—	146	1	no	—
183	C₂²×C₄	—	146	1	no	—
184	C₂²×C₄	—	146	1	no	—
185	C₂²×C₄	—	146	1	no	—
186	C₂²×C₄	—	146	1	no	—
187	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
188	M₁₆	—	146	8	no	—
189	M₁₆	—	146	4	no	—
190	M₁₆	—	146	4	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	73	2	no	—
194	C₂×C₈	—	73	2	no	—
195	C₂×C₈	—	146	1	no	—
196	C₂×C₈	—	146	1	no	—
197	C₂×C₈	—	146	1	no	—
198	C₂×C₈	—	146	1	no	—
199	C₂×C₈	#11924011	1	2	yes	—
200	C₂×C₈	D₄×D₇₃	1	2	yes	—
201	C₂×C₈	#11924027	1	1	yes	characteristic
202	C₂×C₈	#11924028	1	2	yes	—
203	C₂×C₈	#11924029	1	1	yes	characteristic
204	C₄²	—	2	1	no	—
205	C₄²	—	73	2	no	—
206	C₄²	—	146	4	no	—
207	C₄²	—	146	1	no	—
208	C₄²	C₈×D₇₃	1	2	yes	—
209	C₁₆	—	4	2	no	—
210	C₁₆	—	292	2	no	—
211	C₂³	—	292	2	no	—
212	C₂³	—	73	2	no	—
213	C₂³	—	146	1	no	—
214	C₂³	—	146	1	no	—
215	C₂³	M₁₆×D₇₃	1	1	yes	characteristic
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	292	8	no	—
219	C₂×C₄	—	73	2	no	—
220	C₂×C₄	—	146	4	no	—
221	C₂×C₄	—	146	1	no	—
222	C₂×C₄	—	146	1	no	—
223	C₂×C₄	—	146	2	no	—
224	C₂×C₄	—	146	2	no	—
225	C₂×C₄	—	146	2	no	—
226	C₂×C₄	—	146	2	no	—
227	C₂×C₄	—	146	2	no	—
228	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
229	C₂×C₄	#14556548	1	1	yes	characteristic
230	C₂×C₄	#14556549	1	1	yes	characteristic
231	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
232	C₂×C₄	M₁₆×D₇₃	1	1	yes	characteristic
233	C₂×C₄	C₂×#11924011	1	1	yes	characteristic
234	C₈	—	2	2	no	—
235	C₈	—	146	2	no	—
236	C₈	—	146	2	no	—
237	C₈	#14556573	1	2	yes	—
238	C₈	#14556576	1	2	yes	—
239	C₂²	—	2	2	no	—
240	C₂²	—	292	2	no	—
241	C₂²	—	292	2	no	—
242	C₂²	—	292	2	no	—
243	C₂²	—	146	2	no	—
244	C₂²	C₂²⋊C₈×D₇₃	1	1	yes	characteristic
245	C₂²	#17988642	1	1	yes	characteristic
246	C₂²	#17988643	1	1	yes	characteristic
247	C₄	—	4	2	no	—
248	C₄	—	146	4	no	—
249	C₄	—	146	2	no	—
250	C₄	#17988449	1	1	yes	characteristic
251	C₄	#17988549	1	1	yes	characteristic
252	C₄	#17988638	1	1	yes	characteristic
253	C₄	#17988639	1	1	yes	characteristic
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	—	292	2	no	—
257	C₂	#22609998	1	1	yes	characteristic
258	C₂	#22611741	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988539

C₂

yes

maximal, characteristic

C₂×#17988368

C₂

yes

maximal

#22608012

C₂

yes

maximal, complemented

#22608011

C₂

yes

maximal, characteristic, complemented

C₇₃×#1375

C₂

yes

maximal, characteristic, complemented

C₂²×#11924011

C₄

yes

characteristic

C₂²×#11924011

C₂²

yes

characteristic

C₂×C₄²×D₇₃

C₄

yes

characteristic

C₂×#14556531

C₂²

yes

—

#17988539

—

C₂×#14556502

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₂²

yes

characteristic

#17988368

—

C₂×M₃₂×C₇₃

C₂²

yes

—

C₂×#97×C₇₃

C₂²

yes

characteristic

C₂²×C₄×D₇₃

—

C₂²×C₄×D₇₃

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

—

C₂²×#10596831

C₂×C₄

yes

characteristic

C₂²×#10596831

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₃

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄²×D₇₃

—

C₄²×D₇₃

C₈

yes

—

—

—

—

—

C₈×Dic₇₃

—

C₈×Dic₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

#97×C₇₃

—

C₂³×D₇₃

M₁₆

yes

characteristic

C₂²×Dic₇₃

—

C₂²×Dic₇₃

M₁₆

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂²⋊C₄

yes

—

C₂×C₄×D₇₃

C₂×C₈

yes

—

—

—

—

—

—

—

—

C₂²⋊C₄

yes

—

C₂×#10596831

M₁₆

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₈

yes

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

M₁₆

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

#41

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

#41

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂×C₈

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

C₂×M₁₆

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

C₂²⋊C₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₈

yes

—

C₄×D₇₃

—

100

C₄×D₇₃

—

101

C₄×D₇₃

—

102

C₄×D₇₃

—

103

C₄×D₇₃

—

104

C₈×C₇₃

—

105

C₈×C₇₃

#123

yes

—

106

C₈×C₇₃

#123

yes

—

107

#10596831

—

108

#10596831

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

111

C₂²×C₇₃

#432

yes

characteristic

112

C₂²×C₇₃

#432

yes

characteristic

113

C₂×D₇₃

—

114

C₂×D₇₃

—

115

C₂×D₇₃

—

116

C₂×D₇₃

—

117

C₄×C₇₃

—

118

C₄×C₇₃

#381

yes

characteristic

119

C₄×C₇₃

#407

yes

characteristic

120

C₄×C₇₃

#431

yes

characteristic

121

C₄×C₇₃

#431

yes

characteristic

122

Dic₇₃

—

123

Dic₇₃

—

124

#12849

—

maximal, Sylow

125

C₂×C₇₃

—

126

C₂×C₇₃

—

127

C₂×C₇₃

#1817

yes

characteristic

128

C₂×C₇₃

#2165

yes

—

129

D₇₃

—

130

C₂×C₄×M₁₆

—

131

C₂×#349

—

132

#1376

—

133

#1375

—

134

#1375

D₇₃

yes

characteristic, complemented

135

C₇₃

#12849

yes

characteristic, complemented, Sylow

136

C₂²×M₁₆

—

137

C₂²×M₁₆

—

138

C₂²×C₄²

—

139

C₂×M₃₂

—

140

C₂×M₃₂

C₂×D₇₃

yes

—

141

C₄×M₁₆

—

146

—

142

C₂×#97

—

143

C₂×#97

C₂×D₇₃

yes

characteristic

144

C₂×C₄×C₈

—

145

C₂×C₄×C₈

—

146

#349

—

146

—

147

C₂³×C₄

—

148

C₂³×C₄

—

146

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

146

—

151

C₂×M₁₆

—

146

—

152

C₂×M₁₆

—

146

—

153

C₂×M₁₆

—

146

—

154

C₂×M₁₆

—

146

—

155

C₂×M₁₆

—

146

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

C₄×D₇₃

yes

characteristic

159

C₂²×C₈

C₂²×D₇₃

yes

characteristic

160

C₂×C₄²

—

161

C₂×C₄²

—

162

C₂×C₄²

—

146

—

163

C₂×C₄²

—

146

—

164

C₂×C₄²

C₄×D₇₃

yes

characteristic

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

146

—

168

M₃₂

—

146

—

169

C₂×C₁₆

—

170

C₂×C₁₆

—

146

—

171

#97

—

172

#97

—

146

—

173

C₄×C₈

—

146

—

174

C₄×C₈

—

146

—

175

C₂⁴

—

176

C₂²×C₄

—

177

C₂²×C₄

—

292

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

146

—

182

C₂²×C₄

—

146

—

183

C₂²×C₄

—

146

—

184

C₂²×C₄

—

146

—

185

C₂²×C₄

—

146

—

186

C₂²×C₄

—

146

—

187

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

188

M₁₆

—

146

—

189

M₁₆

—

146

—

190

M₁₆

—

146

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

146

—

196

C₂×C₈

—

146

—

197

C₂×C₈

—

146

—

198

C₂×C₈

—

146

—

199

C₂×C₈

#11924011

yes

—

200

C₂×C₈

D₄×D₇₃

yes

—

201

C₂×C₈

#11924027

yes

characteristic

202

C₂×C₈

#11924028

yes

—

203

C₂×C₈

#11924029

yes

characteristic

204

C₄²

—

205

C₄²

—

206

C₄²

—

146

—

207

C₄²

—

146

—

208

C₄²

C₈×D₇₃

yes

—

209

C₁₆

—

210

C₁₆

—

292

—

211

C₂³

—

292

—

212

C₂³

—

213

C₂³

—

146

—

214

C₂³

—

146

—

215

C₂³

M₁₆×D₇₃

yes

characteristic

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

292

—

219

C₂×C₄

—

220

C₂×C₄

—

146

—

221

C₂×C₄

—

146

—

222

C₂×C₄

—

146

—

223

C₂×C₄

—

146

—

224

C₂×C₄

—

146

—

225

C₂×C₄

—

146

—

226

C₂×C₄

—

146

—

227

C₂×C₄

—

146

—

228

C₂×C₄

C₂²⋊C₄×D₇₃

yes

characteristic

229

C₂×C₄

#14556548

yes

characteristic

230

C₂×C₄

#14556549

yes

characteristic

231

C₂×C₄

C₂×C₈×D₇₃

yes

characteristic

232

C₂×C₄

M₁₆×D₇₃

yes

characteristic

233

C₂×C₄

C₂×#11924011

yes

characteristic

234

C₈

—

235

C₈

—

146

—

236

C₈

—

146

—

237

C₈

#14556573

yes

—

238

C₈

#14556576

yes

—

239

C₂²

—

240

C₂²

—

292

—

241

C₂²

—

292

—

242

C₂²

—

292

—

243

C₂²

—

146

—

244

C₂²

C₂²⋊C₈×D₇₃

yes

characteristic

245

C₂²

#17988642

yes

characteristic

246

C₂²

#17988643

yes

characteristic

247

C₄

—

248

C₄

—

146

—

249

C₄

—

146

—

250

C₄

#17988449

yes

characteristic

251

C₄

#17988549

yes

characteristic

252

C₄

#17988638

yes

characteristic

253

C₄

#17988639

yes

characteristic

254

C₂

—

255

C₂

—

256

C₂

—

292

—

257

C₂

#22609998

yes

characteristic

258

C₂

#22611741

yes

—

	subgroup	G/H
center	C₂×C₄	#14556548
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#1375	C₂
socle	C₂²×C₇₃	#432
prime radical	C₂³×D₇₃	M₁₆
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#1375	D₇₃
hypocenter	C₇₃	#12849
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1375

subgroup

G/H

center

C₂×C₄

#14556548

commutator

C₂×C₄×C₇₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#1375

C₂

socle

C₂²×C₇₃

#432

prime radical

C₂³×D₇₃

M₁₆

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1375

N	H ≅ G/N	type
3. #22608012	C₂	semidirect
4. #22608011	C₂	semidirect
5. C₇₃×#1375	C₂	semidirect
134. #1375	D₇₃	semidirect
135. C₇₃	#12849	semidirect

H ≅ G/N

type

3. #22608012

C₂

semidirect

4. #22608011

C₂

semidirect

5. C₇₃×#1375

C₂

semidirect

134. #1375

D₇₃

semidirect

135. C₇₃

#12849

semidirect

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

subgroup	index
C₂×#17988539	2
C₂×#17988368	2
#22608012	2
#22608011	2
C₇₃×#1375	2
#12849	73

subgroup

index

C₇₃×#1375

Subgroups — #33002210

Conjugacy classes of subgroups

Complements

Maximal subgroups