Group #32990959 — subgroups

Subgroups — #32990959

Order 18688.

372 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 93 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	#22610728	C₂	1	1	yes	maximal, characteristic
2	#22610105	C₂	1	1	yes	maximal, characteristic, complemented
3	#22608705	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608357	C₂	1	1	yes	maximal, characteristic
5	#22608355	C₂	1	1	yes	maximal, characteristic
6	#22607761	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
9	#17988640	C₂²	1	1	yes	characteristic
10	C₂×#14556526	—	2	2	no	—
11	#17988611	C₂²	1	1	yes	characteristic
12	C₂×#14556503	—	2	2	no	—
13	C₂×#14556502	C₂²	1	1	yes	characteristic
14	#17988339	—	2	2	no	—
15	#17988316	—	2	2	no	—
16	#17988314	—	2	2	no	—
17	#431×C₇₃	C₂²	1	1	yes	characteristic
18	#423×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
20	#335×C₇₃	—	2	2	no	—
21	C₂²×D₂₉₂	Q₈	1	1	yes	characteristic
22	C₂²×C₄×D₇₃	—	2	1	no	—
23	C₂×#11924012	—	2	1	no	—
24	C₂²×#10596831	D₄	1	2	yes	—
25	C₄×D₂₉₂	—	2	1	no	—
26	C₄×D₂₉₂	—	2	1	no	—
27	C₄×D₂₉₂	—	2	1	no	—
28	C₄×D₂₉₂	—	2	1	no	—
29	C₂×C₄⋊Dic₇₃	Q₈	1	1	yes	characteristic
30	C₂×#11924005	—	2	1	no	—
31	#14556526	—	4	4	no	—
32	C₄⋊#10596831	—	2	1	no	—
33	C₄⋊#10596831	—	2	1	no	—
34	C₄⋊#10596831	—	2	1	no	—
35	C₂²⋊#10596831	—	2	1	no	—
36	#14556503	—	4	4	no	—
37	#14556502	—	2	1	no	—
38	#14556502	—	2	1	no	—
39	C₄×#10596831	D₄	1	2	yes	—
40	C₂×M₁₆×C₇₃	—	2	1	no	—
41	C₂²×C₈×C₇₃	—	2	1	no	—
42	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₃	—	2	1	no	—
44	C₄⋊C₈×C₇₃	—	2	1	no	—
45	C₄⋊C₈×C₇₃	—	2	1	no	—
46	C₄⋊C₈×C₇₃	—	2	1	no	—
47	C₄⋊C₈×C₇₃	—	2	1	no	—
48	C₂²⋊C₈×C₇₃	—	2	1	no	—
49	C₄×C₈×C₇₃	D₄	1	2	yes	—
50	C₂³×D₇₃	—	2	1	no	—
51	C₂×D₂₉₂	—	2	1	no	—
52	C₂×D₂₉₂	—	2	1	no	—
53	C₂×D₂₉₂	—	4	2	no	—
54	C₂²×Dic₇₃	—	2	1	no	—
55	C₂×C₄×D₇₃	—	4	1	no	—
56	C₂×C₄×D₇₃	—	4	1	no	—
57	C₂×C₄×D₇₃	—	4	2	no	—
58	C₂×C₄×D₇₃	—	4	2	no	—
59	#11924012	—	4	2	no	—
60	C₂×#10596831	—	2	2	no	—
61	C₂×#10596831	—	2	2	no	—
62	C₂×#10596831	—	2	2	no	—
63	C₂×#10596831	—	4	1	no	—
64	C₂×#10596831	D₈	1	4	yes	—
65	C₄⋊Dic₇₃	—	2	1	no	—
66	C₄⋊Dic₇₃	—	2	1	no	—
67	#11924005	—	4	1	no	—
68	#11924005	—	4	1	no	—
69	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
72	M₁₆×C₇₃	—	4	2	no	—
73	C₂×C₈×C₇₃	—	2	2	no	—
74	C₂×C₈×C₇₃	—	4	1	no	—
75	C₂×C₈×C₇₃	—	4	1	no	—
76	C₂×C₈×C₇₃	—	4	2	no	—
77	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₃	#41	1	1	yes	characteristic
80	C₄²×C₇₃	#41	1	1	yes	characteristic
81	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂²×D₇₃	—	2	2	no	—
83	C₂²×D₇₃	—	4	1	no	—
84	C₂²×D₇₃	—	4	2	no	—
85	C₂²×D₇₃	—	4	1	no	—
86	C₂²×D₇₃	—	4	2	no	—
87	C₂×C₄×C₇₃	—	4	1	no	—
88	C₂×C₄×C₇₃	—	4	1	no	—
89	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
92	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
93	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
94	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
95	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
96	C₂×C₄×C₇₃	#137	1	2	yes	—
97	C₂×Dic₇₃	—	4	1	no	—
98	C₂×Dic₇₃	—	4	2	no	—
99	D₂₉₂	—	2	2	no	—
100	D₂₉₂	—	2	2	no	—
101	D₂₉₂	—	4	1	no	—
102	D₂₉₂	—	4	1	no	—
103	C₄×D₇₃	—	8	2	no	—
104	C₄×D₇₃	—	8	1	no	—
105	C₄×D₇₃	—	8	1	no	—
106	C₈×C₇₃	—	4	2	no	—
107	C₈×C₇₃	—	8	1	no	—
108	C₈×C₇₃	—	8	1	no	—
109	#10596831	—	2	4	no	—
110	#10596831	—	4	2	no	—
111	#10596831	—	8	1	no	—
112	C₂²×C₇₃	—	2	1	no	—
113	C₂²×C₇₃	—	2	1	no	—
114	C₂²×C₇₃	#399	1	1	yes	characteristic
115	C₂²×C₇₃	#474	1	2	yes	—
116	C₂×D₇₃	—	4	4	no	—
117	C₂×D₇₃	—	4	2	no	—
118	C₂×D₇₃	—	8	2	no	—
119	C₂×D₇₃	—	8	1	no	—
120	C₂×D₇₃	—	8	1	no	—
121	C₄×C₇₃	—	2	1	no	—
122	C₄×C₇₃	—	2	1	no	—
123	C₄×C₇₃	—	2	1	no	—
124	C₄×C₇₃	—	2	1	no	—
125	C₄×C₇₃	#480	1	2	yes	—
126	C₄×C₇₃	#493	1	1	yes	characteristic
127	C₄×C₇₃	#497	1	1	yes	characteristic
128	Dic₇₃	—	8	1	no	—
129	#10660	—	73	1	no	maximal, Sylow
130	C₂×C₇₃	—	2	2	no	—
131	C₂×C₇₃	#2091	1	1	yes	characteristic
132	C₂×C₇₃	#2093	1	1	yes	characteristic
133	C₂×C₇₃	#2098	1	1	yes	characteristic
134	D₇₃	—	8	2	no	—
135	#1955	—	73	1	no	—
136	#1849	—	73	1	no	—
137	#1571	—	73	1	no	—
138	#1571	D₇₃	1	1	yes	characteristic, complemented
139	#1486	—	73	1	no	—
140	#1486	—	73	1	no	—
141	#1275	—	73	1	no	—
142	C₇₃	#10660	1	1	yes	characteristic, complemented, Sylow
143	C₂×C₄×D₄	—	73	1	no	—
144	#431	—	73	1	no	—
145	#431	C₂×D₇₃	1	1	yes	characteristic
146	C₂×#108	—	146	2	no	—
147	#423	—	73	1	no	—
148	#423	C₂×D₇₃	1	1	yes	characteristic
149	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
150	C₂×C₂²⋊C₈	—	146	2	no	—
151	C₂×#97	—	73	1	no	—
152	#335	—	2	2	no	—
153	#335	—	146	2	no	—
154	D₄⋊C₈	—	146	2	no	—
155	D₄⋊C₈	—	146	2	no	—
156	C₂²×D₄	—	73	1	no	—
157	C₂³×C₄	—	146	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	146	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	73	2	no	—
162	C₄×D₄	—	146	1	no	—
163	C₄×D₄	—	146	1	no	—
164	C₄×D₄	—	146	1	no	—
165	C₄×D₄	—	146	1	no	—
166	C₂×C₄⋊C₄	—	73	1	no	—
167	C₂×C₂²⋊C₄	—	146	1	no	—
168	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
169	#108	—	292	4	no	—
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	146	1	no	—
176	C₄⋊C₈	—	146	1	no	—
177	C₄⋊C₈	—	146	1	no	—
178	C₂²⋊C₈	—	2	1	no	—
179	C₂²⋊C₈	—	292	4	no	—
180	C₂²⋊C₈	—	146	1	no	—
181	#97	—	146	1	no	—
182	#97	—	146	1	no	—
183	C₄×C₈	—	73	2	no	—
184	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
185	C₂⁴	—	146	1	no	—
186	C₂×D₄	—	292	2	no	—
187	C₂×D₄	—	146	1	no	—
188	C₂×D₄	—	146	1	no	—
189	C₂²×C₄	—	292	1	no	—
190	C₂²×C₄	—	292	1	no	—
191	C₂²×C₄	—	292	2	no	—
192	C₂²×C₄	—	292	2	no	—
193	C₂²×C₄	—	146	1	no	—
194	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
195	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
196	C₂²×C₄	#11924028	1	1	yes	characteristic
197	M₁₆	—	4	2	no	—
198	M₁₆	—	292	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	292	1	no	—
204	C₂×C₈	—	73	4	no	—
205	C₂×C₈	—	146	2	no	—
206	C₂×C₈	—	146	2	no	—
207	C₂×C₈	—	146	2	no	—
208	C₄⋊C₄	—	146	1	no	—
209	C₄⋊C₄	—	146	1	no	—
210	C₂²⋊C₄	—	292	1	no	—
211	C₂²⋊C₄	—	292	1	no	—
212	C₄²	D₄×D₇₃	1	1	yes	characteristic
213	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
214	C₄²	#11924028	1	1	yes	characteristic
215	C₄²	#11924029	1	1	yes	characteristic
216	C₂³	—	292	1	no	—
217	C₂³	—	292	2	no	—
218	C₂³	—	292	2	no	—
219	C₂³	—	292	1	no	—
220	C₂³	—	146	2	no	—
221	C₂³	#14556569	1	1	yes	characteristic
222	D₄	—	292	1	no	—
223	D₄	—	292	1	no	—
224	D₄	—	146	2	no	—
225	D₄	—	146	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	292	2	no	—
229	C₂×C₄	—	292	1	no	—
230	C₂×C₄	—	584	2	no	—
231	C₂×C₄	—	584	1	no	—
232	C₂×C₄	—	584	1	no	—
233	C₂×C₄	#14556567	1	1	yes	characteristic
234	C₂×C₄	#14556569	1	1	yes	characteristic
235	C₂×C₄	#14556574	1	1	yes	characteristic
236	C₂×C₄	#14556576	1	1	yes	characteristic
237	C₂×C₄	#14556576	1	1	yes	characteristic
238	C₂×C₄	#14556587	1	1	yes	characteristic
239	C₂×C₄	D₈×D₇₃	1	2	yes	—
240	C₂×C₄	#14556623	1	2	yes	—
241	C₈	—	4	2	no	—
242	C₈	—	8	1	no	—
243	C₈	—	8	1	no	—
244	C₈	—	292	2	no	—
245	C₈	—	584	1	no	—
246	C₈	—	146	4	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	292	4	no	—
250	C₂²	—	292	2	no	—
251	C₂²	—	584	2	no	—
252	C₂²	—	584	1	no	—
253	C₂²	—	584	1	no	—
254	C₂²	#17988522	1	1	yes	characteristic
255	C₂²	#17988866	1	2	yes	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	584	1	no	—
261	C₄	#17988902	1	2	yes	—
262	C₄	#17988962	1	1	yes	characteristic
263	C₄	#17988980	1	1	yes	characteristic
264	C₂	—	2	2	no	—
265	C₂	—	584	2	no	—
266	C₂	#22611446	1	1	yes	characteristic
267	C₂	#22611456	1	1	yes	characteristic
268	C₂	#22611487	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22610728

C₂

yes

maximal, characteristic

#22610105

C₂

yes

maximal, characteristic, complemented

#22608705

C₂

yes

maximal, characteristic, complemented

#22608357

C₂

yes

maximal, characteristic

#22608355

C₂

yes

maximal, characteristic

#22607761

C₂

yes

maximal, characteristic, complemented

C₇₃×#1571

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₂₉₂

C₂²

yes

characteristic

#17988640

C₂²

yes

characteristic

C₂×#14556526

—

#17988611

C₂²

yes

characteristic

C₂×#14556503

—

C₂×#14556502

C₂²

yes

—

—

—

#431×C₇₃

C₂²

yes

characteristic

#423×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#335×C₇₃

—

C₂²×D₂₉₂

Q₈

yes

characteristic

C₂²×C₄×D₇₃

—

C₂×#11924012

—

C₂²×#10596831

D₄

yes

—

C₄×D₂₉₂

—

C₄×D₂₉₂

—

C₄×D₂₉₂

—

C₄×D₂₉₂

—

C₂×C₄⋊Dic₇₃

Q₈

yes

—

—

—

—

—

—

—

—

—

D₄

yes

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

D₄

yes

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

—

—

—

—

—

D₈

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

#11924005

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

C₄²×C₇₃

yes

C₄²×C₇₃

yes

C₂³×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

#137

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

100

D₂₉₂

—

101

D₂₉₂

—

102

D₂₉₂

—

103

C₄×D₇₃

—

104

C₄×D₇₃

—

105

C₄×D₇₃

—

106

C₈×C₇₃

—

107

C₈×C₇₃

—

108

C₈×C₇₃

—

109

#10596831

—

110

#10596831

—

111

#10596831

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

#399

yes

characteristic

115

C₂²×C₇₃

#474

yes

—

116

C₂×D₇₃

—

117

C₂×D₇₃

—

118

C₂×D₇₃

—

119

C₂×D₇₃

—

120

C₂×D₇₃

—

121

C₄×C₇₃

—

122

C₄×C₇₃

—

123

C₄×C₇₃

—

124

C₄×C₇₃

—

125

C₄×C₇₃

#480

yes

—

126

C₄×C₇₃

#493

yes

characteristic

127

C₄×C₇₃

#497

yes

characteristic

128

Dic₇₃

—

129

#10660

—

maximal, Sylow

130

C₂×C₇₃

—

131

C₂×C₇₃

#2091

yes

characteristic

132

C₂×C₇₃

#2093

yes

characteristic

133

C₂×C₇₃

#2098

yes

characteristic

134

D₇₃

—

135

#1955

—

136

#1849

—

137

#1571

—

138

#1571

D₇₃

yes

characteristic, complemented

139

#1486

—

140

#1486

—

141

#1275

—

142

C₇₃

#10660

yes

characteristic, complemented, Sylow

143

C₂×C₄×D₄

—

144

#431

—

145

#431

C₂×D₇₃

yes

characteristic

146

C₂×#108

—

146

—

147

#423

—

148

#423

C₂×D₇₃

yes

characteristic

149

C₂×C₄⋊C₈

C₂×D₇₃

yes

characteristic

150

C₂×C₂²⋊C₈

—

146

—

151

C₂×#97

—

152

#335

—

153

#335

—

146

—

154

D₄⋊C₈

—

146

—

155

D₄⋊C₈

—

146

—

156

C₂²×D₄

—

157

C₂³×C₄

—

146

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

146

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₄×D₄

—

146

—

163

C₄×D₄

—

146

—

164

C₄×D₄

—

146

—

165

C₄×D₄

—

146

—

166

C₂×C₄⋊C₄

—

167

C₂×C₂²⋊C₄

—

146

—

168

C₂×C₄²

C₂²×D₇₃

yes

characteristic

169

#108

—

292

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

146

—

176

C₄⋊C₈

—

146

—

177

C₄⋊C₈

—

146

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

292

—

180

C₂²⋊C₈

—

146

—

181

#97

—

146

—

182

#97

—

146

—

183

C₄×C₈

—

184

C₄×C₈

C₂²⋊D₇₃

yes

—

185

C₂⁴

—

146

—

186

C₂×D₄

—

292

—

187

C₂×D₄

—

146

—

188

C₂×D₄

—

146

—

189

C₂²×C₄

—

292

—

190

C₂²×C₄

—

292

—

191

C₂²×C₄

—

292

—

192

C₂²×C₄

—

292

—

193

C₂²×C₄

—

146

—

194

C₂²×C₄

D₄×D₇₃

yes

characteristic

195

C₂²×C₄

Q₈×D₇₃

yes

characteristic

196

C₂²×C₄

#11924028

yes

characteristic

197

M₁₆

—

198

M₁₆

—

292

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

292

—

204

C₂×C₈

—

205

C₂×C₈

—

146

—

206

C₂×C₈

—

146

—

207

C₂×C₈

—

146

—

208

C₄⋊C₄

—

146

—

209

C₄⋊C₄

—

146

—

210

C₂²⋊C₄

—

292

—

211

C₂²⋊C₄

—

292

—

212

C₄²

D₄×D₇₃

yes

characteristic

213

C₄²

C₂×C₂²⋊D₇₃

yes

characteristic

214

C₄²

#11924028

yes

characteristic

215

C₄²

#11924029

yes

characteristic

216

C₂³

—

292

—

217

C₂³

—

292

—

218

C₂³

—

292

—

219

C₂³

—

292

—

220

C₂³

—

146

—

221

C₂³

#14556569

yes

characteristic

222

D₄

—

292

—

223

D₄

—

292

—

224

D₄

—

146

—

225

D₄

—

146

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

292

—

229

C₂×C₄

—

292

—

230

C₂×C₄

—

584

—

231

C₂×C₄

—

584

—

232

C₂×C₄

—

584

—

233

C₂×C₄

#14556567

yes

characteristic

234

C₂×C₄

#14556569

yes

characteristic

235

C₂×C₄

#14556574

yes

characteristic

236

C₂×C₄

#14556576

yes

characteristic

237

C₂×C₄

#14556576

yes

characteristic

238

C₂×C₄

#14556587

yes

characteristic

239

C₂×C₄

D₈×D₇₃

yes

—

240

C₂×C₄

#14556623

yes

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

292

—

245

C₈

—

584

—

246

C₈

—

146

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

292

—

250

C₂²

—

292

—

251

C₂²

—

584

—

252

C₂²

—

584

—

253

C₂²

—

584

—

254

C₂²

#17988522

yes

characteristic

255

C₂²

#17988866

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

584

—

261

C₄

#17988902

yes

—

262

C₄

#17988962

yes

characteristic

263

C₄

#17988980

yes

characteristic

264

C₂

—

265

C₂

—

584

—

266

C₂

#22611446

yes

characteristic

267

C₂

#22611456

yes

characteristic

268

C₂

#22611487

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556587
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1571	C₂
socle	C₂²×C₇₃	#399
prime radical	C₂²×D₂₉₂	Q₈
hypercenter	#1571	D₇₃
hypocenter	C₇₃	#10660
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

subgroup

G/H

center

C₂×C₄

#14556587

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1571

C₂

socle

C₂²×C₇₃

#399

prime radical

C₂²×D₂₉₂

Q₈

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

N	H ≅ G/N	type
2. #22610105	C₂	semidirect
3. #22608705	C₂	semidirect
6. #22607761	C₂	semidirect
7. C₇₃×#1571	C₂	semidirect
138. #1571	D₇₃	semidirect
142. C₇₃	#10660	semidirect

H ≅ G/N

type

2. #22610105

C₂

semidirect

3. #22608705

C₂

semidirect

6. #22607761

C₂

semidirect

7. C₇₃×#1571

C₂

semidirect

138. #1571

D₇₃

semidirect

142. C₇₃

#10660

semidirect

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

subgroup	index
#22610728	2
#22610105	2
#22608705	2
#22608357	2
#22608355	2
#22607761	2
C₇₃×#1571	2
#10660	73

subgroup

index

C₇₃×#1571

Subgroups — #32990959

Conjugacy classes of subgroups

Complements

Maximal subgroups