Group #33004492 — subgroups

Subgroups — #33004492

Order 18688.

566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 127 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×#17988964	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988401	C₂	1	2	yes	maximal, complemented
3	#22611648	C₂	1	2	yes	maximal, complemented
4	#22609810	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#364×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₈₄	—	2	1	no	—
7	C₂²×D₅₈₄	C₂²	1	2	yes	—
8	C₂×#14556588	—	2	1	no	—
9	#17988964	—	2	2	no	—
10	#17988964	C₄	1	4	yes	complemented
11	C₂×#14556527	C₂²	1	1	yes	characteristic
12	#17988625	C₂²	1	1	yes	characteristic
13	#17988542	—	2	1	no	—
14	#17988401	—	2	4	no	—
15	#17988389	—	2	4	no	—
16	#17988347	—	2	1	no	—
17	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	#364×C₇₃	—	2	2	no	—
20	C₂²×D₂₉₂	—	2	2	no	—
21	C₂²×D₂₉₂	—	4	2	no	—
22	C₂×D₅₈₄	—	2	4	no	—
23	C₂×D₅₈₄	—	2	2	no	—
24	C₂×D₅₈₄	—	2	2	no	—
25	C₂×D₅₈₄	—	2	2	no	—
26	C₂×D₅₈₄	—	2	2	no	—
27	C₂×D₅₈₄	—	2	2	no	—
28	C₂×D₅₈₄	—	4	1	no	—
29	C₂×D₅₈₄	—	4	1	no	—
30	C₂×D₅₈₄	—	4	2	no	—
31	C₂×D₅₈₄	C₂×C₄	1	4	yes	—
32	C₂×#11924012	—	2	1	no	—
33	#14556588	—	2	4	no	—
34	#14556588	—	4	2	no	—
35	#14556550	—	2	1	no	—
36	#14556527	—	2	1	no	—
37	#14556527	D₄	1	2	yes	complemented
38	#14556525	D₄	1	2	yes	complemented
39	#14556523	—	2	1	no	—
40	#14556501	—	4	1	no	—
41	C₈×Dic₇₃	—	4	1	no	—
42	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
45	M₃₂×C₇₃	—	2	2	no	—
46	M₃₂×C₇₃	—	2	2	no	—
47	C₂×C₁₆×C₇₃	—	2	2	no	—
48	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₇₃	D₄	1	2	yes	—
50	C₂³×D₇₃	—	4	2	no	—
51	C₂×D₂₉₂	—	2	4	no	—
52	C₂×D₂₉₂	—	4	2	no	—
53	C₂×D₂₉₂	—	4	2	no	—
54	C₂×D₂₉₂	—	4	2	no	—
55	C₂×D₂₉₂	—	4	2	no	—
56	C₂×D₂₉₂	—	4	8	no	—
57	C₂×D₂₉₂	—	4	2	no	—
58	C₂×D₂₉₂	—	8	8	no	—
59	D₅₈₄	—	2	4	no	—
60	D₅₈₄	—	2	4	no	—
61	D₅₈₄	—	4	4	no	—
62	D₅₈₄	—	4	4	no	—
63	D₅₈₄	—	4	2	no	—
64	D₅₈₄	—	4	2	no	—
65	#11924012	—	2	2	no	—
66	#11924012	—	4	1	no	—
67	C₂×#10596831	—	4	1	no	—
68	C₄⋊Dic₇₃	—	2	2	no	—
69	C₂²⋊Dic₇₃	—	4	1	no	—
70	C₄×Dic₇₃	—	4	1	no	—
71	C₂²×C₄×C₇₃	—	2	1	no	—
72	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
75	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
76	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
77	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
82	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
83	C₄²×C₇₃	—	2	1	no	—
84	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
85	C₁₆×C₇₃	—	4	2	no	—
86	C₂³×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₂²×D₇₃	—	4	4	no	—
88	C₂²×D₇₃	—	8	8	no	—
89	C₂²×D₇₃	—	8	2	no	—
90	C₂²×D₇₃	—	8	2	no	—
91	C₂×C₄×C₇₃	—	2	4	no	—
92	C₂×C₄×C₇₃	—	2	2	no	—
93	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
95	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×Dic₇₃	—	4	2	no	—
100	D₂₉₂	—	4	4	no	—
101	D₂₉₂	—	4	4	no	—
102	D₂₉₂	—	8	16	no	—
103	D₂₉₂	—	8	2	no	—
104	D₂₉₂	—	8	2	no	—
105	C₈×C₇₃	#102	1	2	yes	—
106	C₈×C₇₃	#102	1	2	yes	—
107	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
108	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
109	C₈×C₇₃	#124	1	1	yes	characteristic
110	C₈×C₇₃	#127	1	1	yes	characteristic
111	#10596831	—	4	2	no	—
112	C₂²×C₇₃	—	2	2	no	—
113	C₂²×C₇₃	#418	1	1	yes	characteristic
114	C₂²×C₇₃	#459	1	1	yes	characteristic
115	C₂²×C₇₃	#460	1	1	yes	characteristic
116	C₂×D₇₃	—	8	8	no	—
117	C₂×D₇₃	—	8	4	no	—
118	C₂×D₇₃	—	16	4	no	—
119	C₂×D₇₃	—	16	4	no	—
120	C₄×C₇₃	—	2	4	no	—
121	C₄×C₇₃	#390	1	1	yes	characteristic
122	C₄×C₇₃	C₂×#102	1	1	yes	characteristic
123	C₄×C₇₃	#459	1	1	yes	characteristic
124	C₄×C₇₃	#460	1	1	yes	characteristic
125	Dic₇₃	—	8	2	no	—
126	#13261	—	73	1	no	maximal, Sylow
127	C₂×C₇₃	—	2	1	no	—
128	C₂×C₇₃	—	2	1	no	—
129	C₂×C₇₃	#1982	1	1	yes	characteristic
130	C₂×C₇₃	#2213	1	2	yes	—
131	D₇₃	—	16	4	no	—
132	C₂×#493	—	73	1	no	—
133	C₂×#364	D₇₃	1	1	yes	characteristic, complemented
134	C₂×#361	—	73	2	no	—
135	#2140	—	73	2	no	—
136	#1772	—	73	1	no	—
137	C₇₃	#13261	1	1	yes	characteristic, complemented, Sylow
138	C₂²×D₈	—	73	2	no	—
139	C₂²×D₈	—	146	1	no	—
140	C₂×#127	—	146	1	no	—
141	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
142	#493	—	73	4	no	—
143	#493	—	146	2	no	—
144	C₂×#108	—	73	1	no	—
145	#427	—	73	1	no	—
146	#405	—	146	1	no	—
147	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
148	#364	—	2	2	no	—
149	#361	—	146	4	no	—
150	#357	—	146	4	no	—
151	#339	—	146	1	no	—
152	C₂²×D₄	—	292	2	no	—
153	C₂²×D₄	—	146	2	no	—
154	C₂×D₈	—	292	1	no	—
155	C₂×D₈	—	292	1	no	—
156	C₂×D₈	—	292	2	no	—
157	C₂×D₈	—	73	4	no	—
158	C₂×D₈	—	146	4	no	—
159	C₂×D₈	—	146	2	no	—
160	C₂×D₈	—	146	2	no	—
161	C₂×D₈	—	146	2	no	—
162	C₂×D₈	—	146	2	no	—
163	C₂×D₈	—	146	2	no	—
164	C₂×M₁₆	—	146	1	no	—
165	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
166	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
167	#127	—	292	2	no	—
168	#127	—	146	4	no	—
169	#117	—	146	1	no	—
170	C₂×C₄²	D₂₉₂	1	1	yes	characteristic
171	M₃₂	—	2	2	no	—
172	M₃₂	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#108	—	73	2	no	—
175	#108	—	146	1	no	—
176	#107	—	73	2	no	—
177	#106	—	146	1	no	—
178	#97	—	292	1	no	—
179	C₄×C₈	—	292	1	no	—
180	C₄×C₈	C₄×D₇₃	1	2	yes	—
181	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
182	C₂⁴	—	292	2	no	—
183	C₂×D₄	—	292	8	no	—
184	C₂×D₄	—	292	2	no	—
185	C₂×D₄	—	292	2	no	—
186	C₂×D₄	—	292	2	no	—
187	C₂×D₄	—	292	2	no	—
188	C₂×D₄	—	292	2	no	—
189	C₂×D₄	—	584	8	no	—
190	C₂×D₄	—	146	4	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
193	D₈	—	292	4	no	—
194	D₈	—	292	4	no	—
195	D₈	—	292	2	no	—
196	D₈	—	292	2	no	—
197	D₈	—	146	4	no	—
198	D₈	—	146	4	no	—
199	M₁₆	—	292	1	no	—
200	M₁₆	—	146	2	no	—
201	C₂×C₈	—	292	1	no	—
202	C₂×C₈	#11924005	1	2	yes	—
203	C₂×C₈	D₅₈₄	1	1	yes	characteristic
204	C₂×C₈	D₅₈₄	1	1	yes	characteristic
205	C₂×C₈	#11924017	1	2	yes	—
206	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
207	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
208	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
209	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
210	C₂×C₈	#11924029	1	1	yes	characteristic
211	C₂×C₈	#11924029	1	1	yes	characteristic
212	C₄⋊C₄	—	146	2	no	—
213	C₂²⋊C₄	—	292	1	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	292	1	no	—
216	C₄²	#11924005	1	2	yes	—
217	C₁₆	—	4	2	no	—
218	C₂³	—	292	4	no	—
219	C₂³	—	584	8	no	—
220	C₂³	—	584	2	no	—
221	C₂³	—	584	2	no	—
222	C₂³	#14556619	1	1	yes	characteristic
223	D₄	—	292	4	no	—
224	D₄	—	292	4	no	—
225	D₄	—	584	16	no	—
226	D₄	—	584	2	no	—
227	D₄	—	584	2	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	292	2	no	—
231	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
232	C₂×C₄	#14556566	1	1	yes	characteristic
233	C₂×C₄	#14556566	1	1	yes	characteristic
234	C₂×C₄	C₂×D₅₈₄	1	1	yes	characteristic
235	C₂×C₄	C₂×#11924017	1	1	yes	characteristic
236	C₂×C₄	#14556619	1	1	yes	characteristic
237	C₈	—	292	2	no	—
238	C₈	#14556513	1	2	yes	—
239	C₈	#14556513	1	2	yes	—
240	C₈	#14556553	1	1	yes	characteristic
241	C₈	#14556553	1	1	yes	characteristic
242	C₈	#14556580	1	1	yes	characteristic
243	C₈	#14556587	1	1	yes	characteristic
244	C₂²	—	2	2	no	—
245	C₂²	—	584	8	no	—
246	C₂²	—	584	4	no	—
247	C₂²	—	1168	4	no	—
248	C₂²	—	1168	4	no	—
249	C₂²	#17988593	1	1	yes	characteristic
250	C₂²	#17988783	1	1	yes	characteristic
251	C₂²	#17988788	1	1	yes	characteristic
252	C₄	—	2	4	no	—
253	C₄	—	584	2	no	—
254	C₄	#17988488	1	1	yes	characteristic
255	C₄	C₂×#14556513	1	1	yes	characteristic
256	C₄	#17988783	1	1	yes	characteristic
257	C₄	#17988788	1	1	yes	characteristic
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	—	1168	4	no	—
261	C₂	#22610857	1	1	yes	characteristic
262	C₂	#22612008	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988964

C₂

yes

maximal, characteristic

C₂×#17988401

C₂

yes

maximal, complemented

#22611648

C₂

yes

maximal, complemented

#22609810

C₂

yes

maximal, characteristic, complemented

C₂×#364×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₅₈₄

—

C₂²×D₅₈₄

C₂²

yes

—

C₂×#14556588

—

#17988964

—

#17988964

C₄

yes

complemented

C₂×#14556527

C₂²

yes

characteristic

#17988625

C₂²

yes

—

—

—

—

C₂×M₃₂×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#364×C₇₃

—

C₂²×D₂₉₂

—

C₂²×D₂₉₂

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

complemented

#14556525

D₄

yes

complemented

#14556523

—

#14556501

—

C₈×Dic₇₃

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

D₄

yes

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

D₈

yes

characteristic

C₂×C₈×C₇₃

D₈

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

C₄²×C₇₃

—

C₄²×C₇₃

C₂²⋊C₄

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₇₃

—

100

D₂₉₂

—

101

D₂₉₂

—

102

D₂₉₂

—

103

D₂₉₂

—

104

D₂₉₂

—

105

C₈×C₇₃

#102

yes

—

106

C₈×C₇₃

#102

yes

—

107

C₈×C₇₃

C₄×D₄

yes

characteristic

108

C₈×C₇₃

C₄×D₄

yes

characteristic

109

C₈×C₇₃

#124

yes

characteristic

110

C₈×C₇₃

#127

yes

characteristic

111

#10596831

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

#418

yes

characteristic

114

C₂²×C₇₃

#459

yes

characteristic

115

C₂²×C₇₃

#460

yes

characteristic

116

C₂×D₇₃

—

117

C₂×D₇₃

—

118

C₂×D₇₃

—

119

C₂×D₇₃

—

120

C₄×C₇₃

—

121

C₄×C₇₃

#390

yes

characteristic

122

C₄×C₇₃

C₂×#102

yes

characteristic

123

C₄×C₇₃

#459

yes

characteristic

124

C₄×C₇₃

#460

yes

characteristic

125

Dic₇₃

—

126

#13261

—

maximal, Sylow

127

C₂×C₇₃

—

128

C₂×C₇₃

—

129

C₂×C₇₃

#1982

yes

characteristic

130

C₂×C₇₃

#2213

yes

—

131

D₇₃

—

132

C₂×#493

—

133

C₂×#364

D₇₃

yes

characteristic, complemented

134

C₂×#361

—

135

#2140

—

136

#1772

—

137

C₇₃

#13261

yes

characteristic, complemented, Sylow

138

C₂²×D₈

—

139

C₂²×D₈

—

146

—

140

C₂×#127

—

146

—

141

C₂×M₃₂

C₂×D₇₃

yes

—

142

#493

—

143

#493

—

146

—

144

C₂×#108

—

145

#427

—

146

#405

—

146

—

147

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

148

#364

—

149

#361

—

146

—

150

#357

—

146

—

151

#339

—

146

—

152

C₂²×D₄

—

292

—

153

C₂²×D₄

—

146

—

154

C₂×D₈

—

292

—

155

C₂×D₈

—

292

—

156

C₂×D₈

—

292

—

157

C₂×D₈

—

158

C₂×D₈

—

146

—

159

C₂×D₈

—

146

—

160

C₂×D₈

—

146

—

161

C₂×D₈

—

146

—

162

C₂×D₈

—

146

—

163

C₂×D₈

—

146

—

164

C₂×M₁₆

—

146

—

165

C₂²×C₈

D₂₉₂

yes

characteristic

166

C₂²×C₈

C₂²×D₇₃

yes

characteristic

167

#127

—

292

—

168

#127

—

146

—

169

#117

—

146

—

170

C₂×C₄²

D₂₉₂

yes

characteristic

171

M₃₂

—

172

M₃₂

—

173

C₂×C₁₆

—

174

#108

—

175

#108

—

146

—

176

#107

—

177

#106

—

146

—

178

#97

—

292

—

179

C₄×C₈

—

292

—

180

C₄×C₈

C₄×D₇₃

yes

—

181

C₄×C₈

C₂²⋊D₇₃

yes

—

182

C₂⁴

—

292

—

183

C₂×D₄

—

292

—

184

C₂×D₄

—

292

—

185

C₂×D₄

—

292

—

186

C₂×D₄

—

292

—

187

C₂×D₄

—

292

—

188

C₂×D₄

—

292

—

189

C₂×D₄

—

584

—

190

C₂×D₄

—

146

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

193

D₈

—

292

—

194

D₈

—

292

—

195

D₈

—

292

—

196

D₈

—

292

—

197

D₈

—

146

—

198

D₈

—

146

—

199

M₁₆

—

292

—

200

M₁₆

—

146

—

201

C₂×C₈

—

292

—

202

C₂×C₈

#11924005

yes

—

203

C₂×C₈

D₅₈₄

yes

characteristic

204

C₂×C₈

D₅₈₄

yes

characteristic

205

C₂×C₈

#11924017

yes

—

206

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

207

C₂×C₈

D₄×D₇₃

yes

characteristic

208

C₂×C₈

D₄×D₇₃

yes

characteristic

209

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

210

C₂×C₈

#11924029

yes

characteristic

211

C₂×C₈

#11924029

yes

characteristic

212

C₄⋊C₄

—

146

—

213

C₂²⋊C₄

—

292

—

214

C₄²

—

215

C₄²

—

292

—

216

C₄²

#11924005

yes

—

217

C₁₆

—

218

C₂³

—

292

—

219

C₂³

—

584

—

220

C₂³

—

584

—

221

C₂³

—

584

—

222

C₂³

#14556619

yes

characteristic

223

D₄

—

292

—

224

D₄

—

292

—

225

D₄

—

584

—

226

D₄

—

584

—

227

D₄

—

584

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

292

—

231

C₂×C₄

C₂×#11924005

yes

characteristic

232

C₂×C₄

#14556566

yes

characteristic

233

C₂×C₄

#14556566

yes

characteristic

234

C₂×C₄

C₂×D₅₈₄

yes

characteristic

235

C₂×C₄

C₂×#11924017

yes

characteristic

236

C₂×C₄

#14556619

yes

characteristic

237

C₈

—

292

—

238

C₈

#14556513

yes

—

239

C₈

#14556513

yes

—

240

C₈

#14556553

yes

characteristic

241

C₈

#14556553

yes

characteristic

242

C₈

#14556580

yes

characteristic

243

C₈

#14556587

yes

characteristic

244

C₂²

—

245

C₂²

—

584

—

246

C₂²

—

584

—

247

C₂²

—

1168

—

248

C₂²

—

1168

—

249

C₂²

#17988593

yes

characteristic

250

C₂²

#17988783

yes

characteristic

251

C₂²

#17988788

yes

characteristic

252

C₄

—

253

C₄

—

584

—

254

C₄

#17988488

yes

characteristic

255

C₄

C₂×#14556513

yes

characteristic

256

C₄

#17988783

yes

characteristic

257

C₄

#17988788

yes

characteristic

258

C₂

—

259

C₂

—

260

C₂

—

1168

—

261

C₂

#22610857

yes

characteristic

262

C₂

#22612008

yes

—

	subgroup	G/H
center	C₂²	#17988783
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×#364×C₇₃	C₂
socle	C₂²×C₇₃	#459
prime radical	C₂×#17988964	C₂
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×#364	D₇₃
hypocenter	C₇₃	#13261
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

subgroup

G/H

center

C₂²

#17988783

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×#364×C₇₃

C₂

C₂²×C₇₃

C₂

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

N	H ≅ G/N	type
2. C₂×#17988401	C₂	semidirect
3. #22611648	C₂	semidirect
4. #22609810	C₂	semidirect
5. C₂×#364×C₇₃	C₂	semidirect
10. #17988964	C₄	semidirect
37. #14556527	D₄	semidirect
38. #14556525	D₄	semidirect
133. C₂×#364	D₇₃	semidirect
137. C₇₃	#13261	semidirect

H ≅ G/N

type

2. C₂×#17988401

C₂

semidirect

3. #22611648

C₂

semidirect

4. #22609810

C₂

semidirect

5. C₂×#364×C₇₃

C₂

semidirect

10. #17988964

C₄

semidirect

37. #14556527

D₄

semidirect

38. #14556525

D₄

semidirect

133. C₂×#364

D₇₃

semidirect

137. C₇₃

#13261

semidirect

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

subgroup	index
C₂×#17988964	2
C₂×#17988401	2
#22611648	2
#22609810	2
C₂×#364×C₇₃	2
#13261	73

subgroup

index

C₂×#364×C₇₃

Subgroups — #33004492

Conjugacy classes of subgroups

Complements

Maximal subgroups