Group #22620538 — subgroups

Subgroups — #22620538

Order 9344.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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	#17989144	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988997	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988982	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988957	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988946	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988843	C₂	1	2	yes	maximal, complemented
7	#17988831	C₂	1	2	yes	maximal
8	C₄×#11924018	C₂	1	2	yes	maximal, complemented
9	C₄×#11924016	C₂	1	2	yes	maximal, complemented
10	C₄×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	#529×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#11924018	C₂²	1	2	yes	—
13	C₂×#11924016	C₂²	1	2	yes	—
14	C₂×#11924012	C₂²	1	2	yes	—
15	#14556591	C₂²	1	1	yes	characteristic
16	#14556591	C₂²	1	1	yes	characteristic
17	#14556583	—	2	1	no	—
18	#14556570	—	2	1	no	—
19	#14556570	C₂²	1	2	yes	—
20	C₄×Dic₁₄₆	—	2	1	no	—
21	C₄×Dic₁₄₆	C₂²	1	2	yes	—
22	#14556550	—	2	1	no	—
23	#14556524	C₂²	1	2	yes	—
24	#14556522	C₂²	1	2	yes	—
25	#14556515	C₂²	1	2	yes	—
26	#14556514	C₂²	1	2	yes	—
27	#14556514	C₂²	1	2	yes	—
28	#14556512	C₂²	1	2	yes	—
29	#14556502	C₂²	1	1	yes	characteristic
30	#14556502	C₂²	1	1	yes	characteristic
31	C₄×#10596831	C₂²	1	2	yes	—
32	#126×C₇₃	—	2	1	no	—
33	#125×C₇₃	C₂²	1	1	yes	characteristic
34	#124×C₇₃	C₂²	1	1	yes	characteristic
35	#123×C₇₃	—	2	1	no	—
36	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
37	#121×C₇₃	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₇₃	—	2	1	no	—
40	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
41	#117×C₇₃	—	2	1	no	—
42	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₄₆	—	2	1	no	—
44	C₂×Dic₁₄₆	C₂³	1	2	yes	—
45	#11924018	—	2	4	no	—
46	#11924016	—	2	4	no	—
47	#11924012	—	2	4	no	—
48	C₂×#10596831	C₂³	1	2	yes	—
49	C₂×#10596831	C₂³	1	2	yes	—
50	C₄⋊Dic₇₃	—	2	1	no	—
51	C₄⋊Dic₇₃	—	2	1	no	—
52	C₄⋊Dic₇₃	—	2	1	no	—
53	C₄⋊Dic₇₃	C₂³	1	2	yes	—
54	#11924007	—	2	2	no	—
55	#11924007	—	2	2	no	—
56	C₂²⋊Dic₇₃	—	2	2	no	—
57	C₄×Dic₇₃	—	2	2	no	—
58	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
59	C₂×D₄×C₇₃	—	2	1	no	—
60	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₇₃	—	2	1	no	—
62	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
65	C₄⋊C₄×C₇₃	—	2	1	no	—
66	C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₄⋊C₄×C₇₃	—	2	1	no	—
69	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
71	C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₂²⋊C₄×C₇₃	—	2	1	no	—
74	C₂²⋊C₄×C₇₃	—	2	1	no	—
75	C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₄²×C₇₃	—	2	1	no	—
77	C₄²×C₇₃	D₄	1	1	yes	characteristic
78	C₄²×C₇₃	D₄	1	1	yes	characteristic
79	C₄²×C₇₃	C₂³	1	1	yes	characteristic
80	C₄²×C₇₃	C₂³	1	1	yes	characteristic
81	C₂³×C₇₃	—	2	1	no	—
82	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₇₃	—	2	2	no	—
84	D₄×C₇₃	—	2	2	no	—
85	D₄×C₇₃	—	4	2	no	—
86	C₂×C₄×C₇₃	—	2	2	no	—
87	C₂×C₄×C₇₃	—	2	2	no	—
88	C₂×C₄×C₇₃	—	2	1	no	—
89	C₂×C₄×C₇₃	—	2	1	no	—
90	C₂×C₄×C₇₃	—	2	1	no	—
91	C₂×C₄×C₇₃	—	4	1	no	—
92	C₂×C₄×C₇₃	—	4	2	no	—
93	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₇₃	—	2	2	no	—
100	C₂×Dic₇₃	—	2	2	no	—
101	Dic₁₄₆	—	2	2	no	—
102	Dic₁₄₆	—	2	2	no	—
103	Dic₁₄₆	—	4	2	no	—
104	#10596831	—	2	2	no	—
105	#10596831	#41	1	4	yes	—
106	C₂²×C₇₃	—	2	1	no	—
107	C₂²×C₇₃	—	2	1	no	—
108	C₂²×C₇₃	—	2	1	no	—
109	C₂²×C₇₃	—	4	1	no	—
110	C₂²×C₇₃	—	4	1	no	—
111	C₂²×C₇₃	—	4	1	no	—
112	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
113	C₄×C₇₃	—	2	1	no	—
114	C₄×C₇₃	—	2	1	no	—
115	C₄×C₇₃	—	2	1	no	—
116	C₄×C₇₃	—	2	1	no	—
117	C₄×C₇₃	—	4	1	no	—
118	C₄×C₇₃	—	4	1	no	—
119	C₄×C₇₃	—	4	1	no	—
120	C₄×C₇₃	#137	1	2	yes	—
121	C₄×C₇₃	C₂×#41	1	2	yes	—
122	Dic₇₃	—	4	2	no	—
123	Dic₇₃	—	4	2	no	—
124	C₂×C₇₃	—	4	1	no	—
125	C₂×C₇₃	—	8	1	no	—
126	C₂×C₇₃	#532	1	1	yes	characteristic
127	C₂×C₇₃	C₂×#137	1	1	yes	characteristic
128	C₂×C₇₃	#575	1	1	yes	characteristic
129	#3172	—	73	1	no	maximal, Sylow
130	C₇₃	#3172	1	1	yes	characteristic, complemented, Sylow
131	#533	—	73	1	no	—
132	#529	D₇₃	1	1	yes	characteristic
133	#501	—	73	1	no	—
134	#497	—	73	1	no	—
135	#491	—	73	1	no	—
136	#489	—	73	1	no	—
137	#470	—	73	2	no	—
138	#468	—	73	2	no	—
139	C₄×Q₁₆	—	73	2	no	—
140	C₄×SD₁₆	—	73	2	no	—
141	C₄×M₁₆	—	73	1	no	—
142	C₂×Q₁₆	—	73	2	no	—
143	C₂×SD₁₆	—	73	2	no	—
144	C₂×M₁₆	—	73	2	no	—
145	C₄⋊Q₈	—	73	1	no	—
146	C₄⋊Q₈	—	73	1	no	—
147	#126	—	2	1	no	—
148	#125	—	146	1	no	—
149	#125	C₂×D₇₃	1	1	yes	characteristic
150	#124	C₂×D₇₃	1	1	yes	characteristic
151	#123	—	2	1	no	—
152	C₂²⋊Q₈	—	73	2	no	—
153	C₂²⋊Q₈	—	146	1	no	—
154	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
155	#121	C₂×D₇₃	1	1	yes	characteristic
156	C₄×Q₈	—	73	2	no	—
157	C₄×Q₈	—	146	1	no	—
158	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
159	C₄×D₄	—	2	1	no	—
160	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	#117	—	146	1	no	—
163	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
164	#107	—	73	2	no	—
165	#106	—	73	2	no	—
166	#103	—	73	2	no	—
167	#103	—	73	2	no	—
168	#103	—	73	2	no	—
169	#102	—	73	2	no	—
170	#97	—	73	1	no	—
171	#97	—	73	1	no	—
172	C₄×C₈	—	73	2	no	—
173	C₂×Q₈	—	73	2	no	—
174	C₂×Q₈	—	146	1	no	—
175	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
182	Q₁₆	—	146	4	no	—
183	SD₁₆	—	146	4	no	—
184	M₁₆	—	146	4	no	—
185	C₂×C₈	—	73	2	no	—
186	C₂×C₈	—	73	2	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	73	2	no	—
192	C₄⋊C₄	—	146	2	no	—
193	C₄⋊C₄	—	146	2	no	—
194	C₄⋊C₄	—	146	1	no	—
195	C₄⋊C₄	—	146	1	no	—
196	C₄⋊C₄	—	146	1	no	—
197	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
198	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	2	1	no	—
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	146	2	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	146	2	no	—
207	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
208	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
209	C₄²	C₂²×D₇₃	1	1	yes	characteristic
210	C₄²	C₂²×D₇₃	1	1	yes	characteristic
211	C₂³	—	2	1	no	—
212	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
213	Q₈	—	2	2	no	—
214	Q₈	—	292	2	no	—
215	Q₈	—	146	2	no	—
216	Q₈	—	146	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	146	2	no	—
227	C₂×C₄	—	146	2	no	—
228	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
230	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
232	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
234	C₈	—	73	4	no	—
235	C₈	—	146	2	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	1	no	—
241	C₂²	—	4	1	no	—
242	C₂²	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	4	1	no	—
248	C₄	—	4	1	no	—
249	C₄	—	4	1	no	—
250	C₄	—	292	2	no	—
251	C₄	—	292	2	no	—
252	C₄	#14556621	1	2	yes	—
253	C₄	#41×D₇₃	1	2	yes	—
254	C₂	—	4	1	no	—
255	C₂	—	8	1	no	—
256	C₂	#17989133	1	1	yes	characteristic
257	C₂	C₂×#14556621	1	1	yes	characteristic
258	C₂	#17989385	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989144

C₂

yes

maximal, characteristic, complemented

#17988997

C₂

yes

maximal, characteristic, complemented

#17988982

C₂

yes

maximal, characteristic, complemented

#17988957

C₂

yes

maximal, characteristic, complemented

#17988946

C₂

yes

maximal, characteristic, complemented

#17988843

C₂

yes

maximal, complemented

#17988831

C₂

yes

maximal

C₄×#11924018

C₂

yes

maximal, complemented

C₄×#11924016

C₂

yes

maximal, complemented

C₄×#11924012

C₂

yes

maximal, characteristic, complemented

#529×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924018

C₂²

yes

—

C₂×#11924016

C₂²

yes

—

C₂×#11924012

C₂²

yes

—

#14556591

C₂²

yes

characteristic

#14556591

C₂²

yes

—

—

C₂²

yes

—

C₄×Dic₁₄₆

—

C₄×Dic₁₄₆

C₂²

yes

—

#14556550

—

#14556524

C₂²

yes

—

#14556522

C₂²

yes

—

#14556515

C₂²

yes

—

#14556514

C₂²

yes

—

#14556514

C₂²

yes

—

#14556512

C₂²

yes

—

#14556502

C₂²

yes

characteristic

#14556502

C₂²

yes

characteristic

C₄×#10596831

C₂²

yes

—

#126×C₇₃

—

#125×C₇₃

C₂²

yes

characteristic

#124×C₇₃

C₂²

yes

characteristic

#123×C₇₃

—

C₂²⋊Q₈×C₇₃

C₂²

yes

characteristic

#121×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

C₂²

yes

characteristic

C₄×D₄×C₇₃

—

C₄×D₄×C₇₃

C₂²

yes

characteristic

#117×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂³

yes

—

—

—

—

C₂³

yes

—

C₂×#10596831

C₂³

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂³

yes

—

#11924007

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

C₂³

yes

characteristic

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

C₂³

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×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

C₂⁴

yes

characteristic

C₂×Dic₇₃

—

100

C₂×Dic₇₃

—

101

Dic₁₄₆

—

102

Dic₁₄₆

—

103

Dic₁₄₆

—

104

#10596831

—

105

#10596831

#41

yes

—

106

C₂²×C₇₃

—

107

C₂²×C₇₃

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

—

111

C₂²×C₇₃

—

112

C₂²×C₇₃

C₂²×D₄

yes

characteristic

113

C₄×C₇₃

—

114

C₄×C₇₃

—

115

C₄×C₇₃

—

116

C₄×C₇₃

—

117

C₄×C₇₃

—

118

C₄×C₇₃

—

119

C₄×C₇₃

—

120

C₄×C₇₃

#137

yes

—

121

C₄×C₇₃

C₂×#41

yes

—

122

Dic₇₃

—

123

Dic₇₃

—

124

C₂×C₇₃

—

125

C₂×C₇₃

—

126

C₂×C₇₃

#532

yes

characteristic

127

C₂×C₇₃

C₂×#137

yes

characteristic

128

C₂×C₇₃

yes

129

—

130

C₇₃

#3172

yes

characteristic, complemented, Sylow

131

#533

—

132

#529

D₇₃

yes

characteristic

133

#501

—

134

#497

—

135

#491

—

136

#489

—

137

#470

—

138

#468

—

139

C₄×Q₁₆

—

140

C₄×SD₁₆

—

141

C₄×M₁₆

—

142

C₂×Q₁₆

—

143

C₂×SD₁₆

—

144

C₂×M₁₆

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

#126

—

148

#125

—

146

—

149

#125

C₂×D₇₃

yes

characteristic

150

#124

C₂×D₇₃

yes

characteristic

151

#123

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

146

—

154

C₂²⋊Q₈

C₂×D₇₃

yes

characteristic

155

#121

C₂×D₇₃

yes

characteristic

156

C₄×Q₈

—

157

C₄×Q₈

—

146

—

158

C₄×Q₈

C₂×D₇₃

yes

characteristic

159

C₄×D₄

—

160

C₄×D₄

C₂×D₇₃

yes

characteristic

161

#117

—

162

#117

—

146

—

163

C₂×C₄²

C₂×D₇₃

yes

characteristic

164

#107

—

165

#106

—

166

#103

—

167

#103

—

168

#103

—

169

#102

—

170

#97

—

171

#97

—

172

C₄×C₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

146

—

175

C₂×Q₈

C₂²×D₇₃

yes

characteristic

176

C₂×D₄

—

177

C₂×D₄

C₂²×D₇₃

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

180

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

181

C₂²×C₄

C₂²×D₇₃

yes

characteristic

182

Q₁₆

—

146

—

183

SD₁₆

—

146

—

184

M₁₆

—

146

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

146

—

193

C₄⋊C₄

—

146

—

194

C₄⋊C₄

—

146

—

195

C₄⋊C₄

—

146

—

196

C₄⋊C₄

—

146

—

197

C₄⋊C₄

C₂²×D₇₃

yes

characteristic

198

C₄⋊C₄

C₂²×D₇₃

yes

characteristic

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

146

—

205

C₄²

—

206

C₄²

—

146

—

207

C₄²

C₂²⋊D₇₃

yes

characteristic

208

C₄²

C₂²⋊D₇₃

yes

characteristic

209

C₄²

C₂²×D₇₃

yes

characteristic

210

C₄²

C₂²×D₇₃

yes

characteristic

211

C₂³

—

212

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

213

Q₈

—

214

Q₈

—

292

—

215

Q₈

—

146

—

216

Q₈

—

146

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

146

—

227

C₂×C₄

—

146

—

228

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

229

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

230

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

232

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

233

C₂×C₄

C₂³×D₇₃

yes

characteristic

234

C₈

—

235

C₈

—

146

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

C₂²×C₂²⋊D₇₃

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

292

—

251

C₄

—

292

—

252

C₄

#14556621

yes

—

253

C₄

#41×D₇₃

yes

—

254

C₂

—

255

C₂

—

256

C₂

#17989133

yes

characteristic

257

C₂

C₂×#14556621

yes

characteristic

258

C₂

#17989385

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	#529×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₄
hypercenter	#529	D₇₃
hypocenter	C₇₃	#3172
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

#529×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

N	H ≅ G/N	type
1. #17989144	C₂	semidirect
2. #17988997	C₂	semidirect
3. #17988982	C₂	semidirect
4. #17988957	C₂	semidirect
5. #17988946	C₂	semidirect
6. #17988843	C₂	semidirect
8. C₄×#11924018	C₂	semidirect
9. C₄×#11924016	C₂	semidirect
10. C₄×#11924012	C₂	semidirect
130. C₇₃	#3172	semidirect

H ≅ G/N

type

1. #17989144

C₂

semidirect

2. #17988997

C₂

semidirect

3. #17988982

C₂

semidirect

4. #17988957

C₂

semidirect

5. #17988946

C₂

semidirect

6. #17988843

C₂

semidirect

8. C₄×#11924018

C₂

semidirect

9. C₄×#11924016

C₂

semidirect

10. C₄×#11924012

C₂

semidirect

130. C₇₃

#3172

semidirect

Subgroups — #22620538

Conjugacy classes of subgroups

Complements