Group #33240437 — subgroups

Subgroups — C₂×#22612040 #33240437

Order 18688.

682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 187 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×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14556530	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988829	C₂	1	2	yes	maximal
4	#22612040	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17988390	C₂	1	2	yes	maximal, complemented
6	C₂×#367×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
8	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
9	C₂×#14556571	—	2	2	no	—
10	C₂×Dic₅₈₄	—	2	4	no	—
11	C₂×Dic₅₈₄	C₂²	1	4	yes	complemented
12	C₂×#14556530	—	2	4	no	—
13	C₂×#14556530	C₂²	1	4	yes	—
14	C₂²×#11924003	C₂²	1	1	yes	characteristic
15	#17988829	—	2	4	no	—
16	#17988829	C₂²	1	8	yes	—
17	C₂×#14556514	—	2	2	no	—
18	#17988390	C₂²	1	8	yes	complemented
19	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#107×C₇₃	C₂²	1	2	yes	—
21	#367×C₇₃	C₂²	1	4	yes	complemented
22	C₂²×Dic₁₄₆	—	2	2	no	—
23	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
24	C₂×Dic₂₉₂	—	2	4	no	—
25	C₂×Dic₂₉₂	—	2	2	no	—
26	C₂×Dic₂₉₂	—	2	4	no	—
27	C₂×Dic₂₉₂	C₂³	1	4	yes	—
28	C₂²×#10596831	D₄	1	1	yes	characteristic
29	C₂×C₈×D₇₃	—	2	2	no	—
30	C₂×C₈×D₇₃	—	2	2	no	—
31	C₂×C₈×D₇₃	D₄	1	2	yes	—
32	C₂×C₈×D₇₃	C₂³	1	2	yes	—
33	#14556571	—	2	8	no	—
34	#14556571	—	4	4	no	—
35	C₂×C₄⋊Dic₇₃	—	4	2	no	—
36	C₂×#11924005	—	4	2	no	—
37	Dic₅₈₄	—	2	8	no	—
38	#14556530	—	2	8	no	—
39	C₂×#11924003	—	2	2	no	—
40	C₂×#11924003	C₂³	1	2	yes	—
41	#14556514	—	2	8	no	—
42	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
44	C₂×C₁₆×C₇₃	D₄	1	4	yes	—
45	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
46	#107×C₇₃	—	2	2	no	—
47	#107×C₇₃	C₂³	1	4	yes	—
48	C₂³×D₇₃	D₈	1	1	yes	characteristic
49	C₂×Dic₁₄₆	—	2	4	no	—
50	C₂×Dic₁₄₆	—	4	4	no	—
51	C₂×Dic₁₄₆	—	4	4	no	—
52	C₂×Dic₁₄₆	—	4	2	no	—
53	C₂²×Dic₇₃	—	4	2	no	—
54	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
55	C₂×C₄×D₇₃	—	2	2	no	—
56	C₂×C₄×D₇₃	—	2	2	no	—
57	C₂×C₄×D₇₃	D₈	1	2	yes	—
58	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
59	Dic₂₉₂	—	2	4	no	—
60	Dic₂₉₂	—	2	4	no	—
61	Dic₂₉₂	—	4	4	no	—
62	C₂×#10596831	—	2	2	no	—
63	C₂×#10596831	C₂×D₄	1	2	yes	—
64	C₈×D₇₃	—	2	4	no	—
65	C₈×D₇₃	—	2	2	no	—
66	C₈×D₇₃	—	2	2	no	—
67	C₄⋊Dic₇₃	—	4	8	no	—
68	#11924005	—	4	8	no	—
69	#11924003	—	2	2	no	—
70	C₂²×C₄×C₇₃	—	4	2	no	—
71	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₇₃	#41	1	2	yes	—
75	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
76	C₄⋊C₄×C₇₃	—	2	4	no	—
77	C₄⋊C₄×C₇₃	—	4	2	no	—
78	C₁₆×C₇₃	C₂×D₄	1	4	yes	—
79	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
80	C₂²×D₇₃	—	2	2	no	—
81	C₂²×D₇₃	—	2	4	no	—
82	C₂²×D₇₃	C₂×D₈	1	2	yes	—
83	C₂×C₄×C₇₃	—	4	4	no	—
84	C₂×C₄×C₇₃	—	8	4	no	—
85	C₂×C₄×C₇₃	#121	1	2	yes	—
86	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₇₃	#135	1	2	yes	—
88	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
89	C₂×Dic₇₃	—	2	2	no	—
90	C₂×Dic₇₃	—	4	4	no	—
91	C₂×Dic₇₃	—	8	4	no	—
92	C₂×Dic₇₃	C₂×D₈	1	2	yes	—
93	C₄×D₇₃	—	2	2	no	—
94	C₄×D₇₃	—	2	2	no	—
95	C₄×D₇₃	—	2	4	no	—
96	Dic₁₄₆	—	4	4	no	—
97	Dic₁₄₆	—	4	4	no	—
98	Dic₁₄₆	—	8	4	no	—
99	C₈×C₇₃	#121	1	2	yes	—
100	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
101	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
102	#10596831	—	2	2	no	—
103	C₂²×C₇₃	#466	1	2	yes	—
104	C₂²×C₇₃	#510	1	4	yes	—
105	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
106	C₂×D₇₃	—	2	4	no	—
107	C₂×D₇₃	—	2	2	no	—
108	C₂×D₇₃	—	4	4	no	—
109	C₄×C₇₃	—	8	4	no	—
110	C₄×C₇₃	#466	1	2	yes	—
111	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
112	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
113	Dic₇₃	—	2	2	no	—
114	Dic₇₃	—	8	4	no	—
115	C₂×#2219	—	73	1	no	maximal, Sylow
116	C₂×C₇₃	#2219	1	4	yes	complemented
117	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
118	C₂×C₇₃	C₂×#510	1	2	yes	—
119	D₇₃	—	4	2	no	—
120	C₂²×Q₃₂	—	73	1	no	—
121	C₂²×M₃₂	—	73	1	no	—
122	C₂×#467	—	73	2	no	—
123	#2219	—	73	8	no	—
124	C₂×#367	D₇₃	1	1	yes	characteristic, complemented
125	C₂×#358	—	73	2	no	—
126	C₇₃	C₂×#2219	1	1	yes	characteristic, complemented, Sylow
127	C₂²×Q₁₆	—	73	2	no	—
128	C₂³×C₈	—	73	1	no	—
129	C₂×C₂²⋊Q₈	—	146	2	no	—
130	C₂×Q₃₂	—	73	4	no	—
131	C₂×Q₃₂	—	146	4	no	—
132	C₂×M₃₂	—	73	4	no	—
133	C₂×M₃₂	—	146	4	no	—
134	C₂²×C₁₆	—	73	1	no	—
135	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
136	#467	—	73	8	no	—
137	#467	—	146	4	no	—
138	C₂×#107	C₂×D₇₃	1	2	yes	—
139	C₂×#103	—	146	2	no	—
140	#367	C₂×D₇₃	1	4	yes	complemented
141	#358	—	73	8	no	—
142	C₂²×Q₈	—	146	2	no	—
143	C₂³×C₄	—	73	1	no	—
144	C₂×Q₁₆	—	73	4	no	—
145	C₂×Q₁₆	—	146	2	no	—
146	C₂×Q₁₆	—	146	4	no	—
147	C₂×Q₁₆	—	146	4	no	—
148	C₂²×C₈	—	73	1	no	—
149	C₂²×C₈	—	73	2	no	—
150	C₂²×C₈	—	73	2	no	—
151	C₂²×C₈	—	146	2	no	—
152	C₂²×C₈	—	146	2	no	—
153	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
154	C₂²⋊Q₈	—	292	4	no	—
155	C₂²⋊Q₈	—	146	8	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄⋊C₄	—	292	2	no	—
158	C₂×C₂²⋊C₄	—	292	2	no	—
159	Q₃₂	—	146	8	no	—
160	M₃₂	—	146	8	no	—
161	C₂×C₁₆	—	73	2	no	—
162	C₂×C₁₆	—	146	2	no	—
163	C₂×C₁₆	D₂₉₂	1	4	yes	—
164	C₂×C₁₆	C₂²×D₇₃	1	2	yes	—
165	#107	—	2	2	no	—
166	#107	C₂²×D₇₃	1	4	yes	—
167	#103	—	146	8	no	—
168	C₂⁴	—	73	1	no	—
169	C₂×Q₈	—	292	2	no	—
170	C₂×Q₈	—	292	4	no	—
171	C₂×Q₈	—	292	4	no	—
172	C₂×Q₈	—	146	4	no	—
173	C₂²×C₄	—	4	2	no	—
174	C₂²×C₄	—	292	2	no	—
175	C₂²×C₄	—	73	1	no	—
176	C₂²×C₄	—	73	2	no	—
177	C₂²×C₄	—	73	2	no	—
178	C₂²×C₄	—	146	2	no	—
179	C₂²×C₄	—	146	2	no	—
180	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
181	Q₁₆	—	292	4	no	—
182	Q₁₆	—	146	4	no	—
183	Q₁₆	—	146	4	no	—
184	C₂×C₈	—	73	2	no	—
185	C₂×C₈	—	146	2	no	—
186	C₂×C₈	—	146	4	no	—
187	C₂×C₈	—	146	2	no	—
188	C₂×C₈	—	146	2	no	—
189	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
190	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
191	C₂×C₈	#11924029	1	2	yes	—
192	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	292	8	no	—
196	C₂²⋊C₄	—	292	8	no	—
197	C₁₆	—	146	2	no	—
198	C₁₆	C₂×D₂₉₂	1	4	yes	—
199	C₂³	—	73	2	no	—
200	C₂³	—	146	4	no	—
201	C₂³	—	146	2	no	—
202	C₂³	D₈×D₇₃	1	1	yes	characteristic
203	Q₈	—	292	4	no	—
204	Q₈	—	292	4	no	—
205	Q₈	—	584	4	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	8	4	no	—
208	C₂×C₄	—	292	4	no	—
209	C₂×C₄	—	584	4	no	—
210	C₂×C₄	—	73	2	no	—
211	C₂×C₄	—	146	2	no	—
212	C₂×C₄	—	146	4	no	—
213	C₂×C₄	—	146	2	no	—
214	C₂×C₄	—	146	2	no	—
215	C₂×C₄	#14556566	1	2	yes	—
216	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
217	C₂×C₄	#14556614	1	2	yes	—
218	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
219	C₈	—	146	2	no	—
220	C₈	#14556566	1	2	yes	—
221	C₈	C₂²×D₂₉₂	1	1	yes	characteristic
222	C₈	C₂×#11924029	1	1	yes	characteristic
223	C₂²	—	292	4	no	—
224	C₂²	—	146	4	no	—
225	C₂²	—	146	2	no	—
226	C₂²	#17988824	1	2	yes	—
227	C₂²	#17989026	1	4	yes	—
228	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
229	C₄	—	8	4	no	—
230	C₄	—	584	4	no	—
231	C₄	—	146	2	no	—
232	C₄	#17988824	1	2	yes	—
233	C₄	C₂×#14556566	1	1	yes	characteristic
234	C₄	C₂×#14556614	1	1	yes	characteristic
235	C₂	—	292	2	no	—
236	C₂	#22612040	1	4	yes	direct product factor
237	C₂	C₂×#17988824	1	1	yes	characteristic
238	C₂	C₂×#17989026	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₈₄

C₂

yes

maximal, characteristic, complemented

C₂²×#14556530

C₂

yes

maximal, characteristic

C₂×#17988829

C₂

yes

maximal

#22612040

C₂

yes

maximal, direct product factor

C₂×#17988390

C₂

yes

maximal, complemented

C₂×#367×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₂₉₂

C₂²

yes

—

C₂²×C₈×D₇₃

C₂²

yes

characteristic

C₂×#14556571

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

C₂²

yes

complemented

C₂×#14556530

—

C₂×#14556530

C₂²

yes

—

C₂²×#11924003

C₂²

yes

characteristic

#17988829

—

#17988829

C₂²

yes

—

C₂×#14556514

—

#17988390

C₂²

yes

complemented

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

—

#367×C₇₃

C₂²

yes

complemented

C₂²×Dic₁₄₆

—

C₂²×C₄×D₇₃

D₄

yes

characteristic

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂³

yes

—

C₂²×#10596831

D₄

yes

characteristic

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

D₄

yes

—

C₂×C₈×D₇₃

C₂³

yes

—

#14556571

—

#14556571

—

C₂×C₄⋊Dic₇₃

—

C₂×#11924005

—

Dic₅₈₄

—

#14556530

—

C₂×#11924003

—

C₂×#11924003

C₂³

yes

—

#14556514

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

C₂³

yes

—

#107×C₇₃

—

#107×C₇₃

C₂³

yes

—

C₂³×D₇₃

D₈

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₈

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

D₈

yes

—

C₂×C₄×D₇₃

C₂×D₄

yes

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₂×#10596831

—

C₂×#10596831

C₂×D₄

yes

—

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

#121

yes

—

100

C₈×C₇₃

C₂²×D₄

yes

characteristic

101

C₈×C₇₃

C₂×#41

yes

characteristic

102

#10596831

—

103

C₂²×C₇₃

#466

yes

—

104

C₂²×C₇₃

#510

yes

—

105

C₂²×C₇₃

C₂²×D₈

yes

characteristic

106

C₂×D₇₃

—

107

C₂×D₇₃

—

108

C₂×D₇₃

—

109

C₄×C₇₃

—

110

C₄×C₇₃

#466

yes

—

111

C₄×C₇₃

C₂×#121

yes

characteristic

112

C₄×C₇₃

C₂×#135

yes

characteristic

113

Dic₇₃

—

114

Dic₇₃

—

115

C₂×#2219

—

maximal, Sylow

116

C₂×C₇₃

#2219

yes

complemented

117

C₂×C₇₃

C₂×#466

yes

characteristic

118

C₂×C₇₃

C₂×#510

yes

—

119

D₇₃

—

120

C₂²×Q₃₂

—

121

C₂²×M₃₂

—

122

C₂×#467

—

123

#2219

—

124

C₂×#367

D₇₃

yes

characteristic, complemented

125

C₂×#358

—

126

C₇₃

C₂×#2219

yes

characteristic, complemented, Sylow

127

C₂²×Q₁₆

—

128

C₂³×C₈

—

129

C₂×C₂²⋊Q₈

—

146

—

130

C₂×Q₃₂

—

131

C₂×Q₃₂

—

146

—

132

C₂×M₃₂

—

133

C₂×M₃₂

—

146

—

134

C₂²×C₁₆

—

135

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

136

#467

—

137

#467

—

146

—

138

C₂×#107

C₂×D₇₃

yes

—

139

C₂×#103

—

146

—

140

#367

C₂×D₇₃

yes

complemented

141

#358

—

142

C₂²×Q₈

—

146

—

143

C₂³×C₄

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

—

146

C₂×Q₁₆

—

146

—

147

C₂×Q₁₆

—

146

—

148

C₂²×C₈

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₂²×C₈

—

146

—

152

C₂²×C₈

—

146

—

153

C₂²×C₈

C₂²×D₇₃

yes

characteristic

154

C₂²⋊Q₈

—

292

—

155

C₂²⋊Q₈

—

146

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

292

—

158

C₂×C₂²⋊C₄

—

292

—

159

Q₃₂

—

146

—

160

M₃₂

—

146

—

161

C₂×C₁₆

—

162

C₂×C₁₆

—

146

—

163

C₂×C₁₆

D₂₉₂

yes

—

164

C₂×C₁₆

C₂²×D₇₃

yes

—

165

#107

—

166

#107

C₂²×D₇₃

yes

—

167

#103

—

146

—

168

C₂⁴

—

169

C₂×Q₈

—

292

—

170

C₂×Q₈

—

292

—

171

C₂×Q₈

—

292

—

172

C₂×Q₈

—

146

—

173

C₂²×C₄

—

174

C₂²×C₄

—

292

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

146

—

179

C₂²×C₄

—

146

—

180

C₂²×C₄

D₄×D₇₃

yes

characteristic

181

Q₁₆

—

292

—

182

Q₁₆

—

146

—

183

Q₁₆

—

146

—

184

C₂×C₈

—

185

C₂×C₈

—

146

—

186

C₂×C₈

—

146

—

187

C₂×C₈

—

146

—

188

C₂×C₈

—

146

—

189

C₂×C₈

D₄×D₇₃

yes

characteristic

190

C₂×C₈

C₂×D₂₉₂

yes

—

191

C₂×C₈

#11924029

yes

—

192

C₂×C₈

C₂³×D₇₃

yes

characteristic

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

292

—

196

C₂²⋊C₄

—

292

—

197

C₁₆

—

146

—

198

C₁₆

C₂×D₂₉₂

yes

—

199

C₂³

—

200

C₂³

—

146

—

201

C₂³

—

146

—

202

C₂³

D₈×D₇₃

yes

characteristic

203

Q₈

—

292

—

204

Q₈

—

292

—

205

Q₈

—

584

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

292

—

209

C₂×C₄

—

584

—

210

C₂×C₄

—

211

C₂×C₄

—

146

—

212

C₂×C₄

—

146

—

213

C₂×C₄

—

146

—

214

C₂×C₄

—

146

—

215

C₂×C₄

#14556566

yes

—

216

C₂×C₄

D₈×D₇₃

yes

characteristic

217

C₂×C₄

#14556614

yes

—

218

C₂×C₄

C₂×D₄×D₇₃

yes

characteristic

219

C₈

—

146

—

220

C₈

#14556566

yes

—

221

C₈

C₂²×D₂₉₂

yes

characteristic

222

C₈

C₂×#11924029

yes

characteristic

223

C₂²

—

292

—

224

C₂²

—

146

—

225

C₂²

—

146

—

226

C₂²

#17988824

yes

—

227

C₂²

#17989026

yes

—

228

C₂²

C₂×D₈×D₇₃

yes

characteristic

229

C₄

—

230

C₄

—

584

—

231

C₄

—

146

—

232

C₄

#17988824

yes

—

233

C₄

C₂×#14556566

yes

characteristic

234

C₄

C₂×#14556614

yes

characteristic

235

C₂

—

292

—

236

C₂

#22612040

yes

direct product factor

237

C₂

C₂×#17988824

yes

characteristic

238

C₂

C₂×#17989026

yes

—

	subgroup	G/H
center	C₂³	D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₂×#367×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂³×D₇₃	D₈
hypercenter	C₂×#367	D₇₃
hypocenter	C₇₃	C₂×#2219
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

subgroup

G/H

center

C₂³

D₈×D₇₃

commutator, cosocle

C₂×C₈×C₇₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₇₃

Fitting

C₂×#367×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂³×D₇₃

D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

N	H ≅ G/N	type
1. C₂²×Dic₅₈₄	C₂	semidirect
4. #22612040	C₂	direct (N × H)
5. C₂×#17988390	C₂	semidirect
6. C₂×#367×C₇₃	C₂	semidirect
11. C₂×Dic₅₈₄	C₂²	semidirect
18. #17988390	C₂²	semidirect
21. #367×C₇₃	C₂²	semidirect
116. C₂×C₇₃	#2219	semidirect
124. C₂×#367	D₇₃	semidirect
126. C₇₃	C₂×#2219	semidirect
140. #367	C₂×D₇₃	semidirect
236. C₂	#22612040	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₅₈₄

C₂

semidirect

4. #22612040

C₂

direct (N × H)

5. C₂×#17988390

C₂

semidirect

6. C₂×#367×C₇₃

C₂

semidirect

11. C₂×Dic₅₈₄

C₂²

semidirect

18. #17988390

C₂²

semidirect

21. #367×C₇₃

C₂²

semidirect

116. C₂×C₇₃

#2219

semidirect

124. C₂×#367

D₇₃

semidirect

126. C₇₃

C₂×#2219

semidirect

140. #367

C₂×D₇₃

semidirect

236. C₂

#22612040

direct (N × H)

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

subgroup	index
C₂²×Dic₅₈₄	2
C₂²×#14556530	2
C₂×#17988829	2
#22612040	2
C₂×#17988390	2
C₂×#367×C₇₃	2
C₂×#2219	73

subgroup

index

C₂²×Dic₅₈₄

C₂×#367×C₇₃

Subgroups — C₂×#22612040 #33240437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#22612040 #33240437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22612040 #33240437