Group #32985621 — subgroups

Subgroups — #32985621

Order 18688.

402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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×#17988938	C₂	1	1	yes	maximal, characteristic
2	#22610919	C₂	1	1	yes	maximal, characteristic
3	#22610919	C₂	1	1	yes	maximal, characteristic
4	#22608617	C₂	1	1	yes	maximal, characteristic
5	#22608613	C₂	1	1	yes	maximal, characteristic
6	#22608220	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1566	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556591	C₂²	1	1	yes	characteristic
9	C₂×#14556591	C₂²	1	1	yes	characteristic
10	#17988938	—	2	1	no	—
11	#17988938	—	2	1	no	—
12	#17988938	—	2	2	no	—
13	#17988640	C₂²	1	1	yes	characteristic
14	C₂×#14556516	C₄	1	4	yes	—
15	C₄×#11924012	C₂²	1	1	yes	characteristic
16	#17988355	—	2	2	no	—
17	#17988355	—	2	2	no	—
18	#17988335	—	2	2	no	—
19	#17988332	—	2	2	no	—
20	#17988309	—	2	1	no	—
21	#17988308	—	2	1	no	—
22	#423×C₇₃	C₂²	1	1	yes	characteristic
23	#423×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
25	#334×C₇₃	—	2	2	no	—
26	C₂²×Dic₁₄₆	—	2	1	no	—
27	C₂²×Dic₁₄₆	C₂×C₄	1	2	yes	—
28	C₂×#11924012	D₄	1	2	yes	—
29	#14556591	—	2	1	no	—
30	#14556591	—	2	1	no	—
31	#14556591	—	2	1	no	—
32	#14556591	—	2	1	no	—
33	#14556591	—	2	1	no	—
34	#14556591	—	2	1	no	—
35	#14556591	—	2	1	no	—
36	#14556591	—	2	1	no	—
37	C₂×C₄⋊Dic₇₃	—	2	1	no	—
38	C₂×C₄⋊Dic₇₃	—	2	1	no	—
39	C₂×C₄⋊Dic₇₃	—	2	1	no	—
40	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
41	C₄⋊#10596831	D₄	1	2	yes	—
42	#14556516	—	2	4	no	—
43	#14556516	—	2	4	no	—
44	C₂²⋊#10596831	—	2	1	no	—
45	#14556502	—	2	1	no	—
46	C₄×#10596831	—	2	1	no	—
47	C₄×#10596831	—	2	1	no	—
48	C₂×M₁₆×C₇₃	—	2	1	no	—
49	C₂×M₁₆×C₇₃	—	2	1	no	—
50	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₇₃	—	2	1	no	—
53	C₄⋊C₈×C₇₃	—	2	1	no	—
54	C₄⋊C₈×C₇₃	—	2	1	no	—
55	C₄⋊C₈×C₇₃	—	2	1	no	—
56	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
57	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
58	C₄×C₈×C₇₃	D₄	1	2	yes	—
59	C₂×Dic₁₄₆	—	2	2	no	—
60	C₂×Dic₁₄₆	—	2	2	no	—
61	C₂×Dic₁₄₆	—	4	4	no	—
62	C₂×Dic₁₄₆	—	4	1	no	—
63	C₂×Dic₁₄₆	—	4	1	no	—
64	C₂×Dic₁₄₆	—	8	2	no	—
65	C₂²×Dic₇₃	—	2	2	no	—
66	C₂²×Dic₇₃	—	2	2	no	—
67	#11924012	—	2	2	no	—
68	#11924012	—	2	2	no	—
69	C₂×#10596831	—	2	2	no	—
70	C₂×#10596831	—	2	2	no	—
71	C₄⋊Dic₇₃	—	2	2	no	—
72	C₄⋊Dic₇₃	—	2	2	no	—
73	C₄⋊Dic₇₃	—	4	1	no	—
74	C₄⋊Dic₇₃	—	4	1	no	—
75	C₄⋊Dic₇₃	—	4	1	no	—
76	C₄⋊Dic₇₃	—	4	1	no	—
77	C₄⋊Dic₇₃	—	4	1	no	—
78	C₄⋊Dic₇₃	—	4	1	no	—
79	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
82	M₁₆×C₇₃	—	4	2	no	—
83	M₁₆×C₇₃	—	4	2	no	—
84	C₂×C₈×C₇₃	—	4	2	no	—
85	C₂×C₈×C₇₃	—	4	1	no	—
86	C₂×C₈×C₇₃	—	4	1	no	—
87	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
88	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
89	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
90	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
92	C₄²×C₇₃	#41	1	1	yes	characteristic
93	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₇₃	—	2	2	no	—
95	C₂×C₄×C₇₃	—	2	2	no	—
96	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
99	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
100	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
101	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
102	C₂×C₄×C₇₃	#137	1	2	yes	—
103	C₂×C₄×C₇₃	#137	1	2	yes	—
104	C₂×Dic₇₃	—	4	2	no	—
105	C₂×Dic₇₃	—	4	2	no	—
106	C₂×Dic₇₃	—	8	2	no	—
107	C₂×Dic₇₃	—	8	2	no	—
108	Dic₁₄₆	—	4	4	no	—
109	Dic₁₄₆	—	8	2	no	—
110	Dic₁₄₆	—	8	2	no	—
111	Dic₁₄₆	—	8	2	no	—
112	C₈×C₇₃	—	2	2	no	—
113	C₈×C₇₃	—	2	2	no	—
114	C₈×C₇₃	—	8	1	no	—
115	C₈×C₇₃	—	8	1	no	—
116	#10596831	—	4	2	no	—
117	#10596831	—	4	2	no	—
118	C₂²×C₇₃	—	2	1	no	—
119	C₂²×C₇₃	—	2	1	no	—
120	C₂²×C₇₃	#390	1	1	yes	characteristic
121	C₂²×C₇₃	#441	1	2	yes	—
122	C₄×C₇₃	—	2	1	no	—
123	C₄×C₇₃	—	2	1	no	—
124	C₄×C₇₃	#413	1	2	yes	—
125	C₄×C₇₃	#470	1	2	yes	—
126	C₄×C₇₃	#471	1	2	yes	—
127	C₄×C₇₃	#497	1	1	yes	characteristic
128	C₄×C₇₃	#497	1	1	yes	characteristic
129	Dic₇₃	—	8	2	no	—
130	Dic₇₃	—	8	2	no	—
131	#9803	—	73	1	no	maximal, Sylow
132	C₂×C₇₃	—	2	2	no	—
133	C₂×C₇₃	#1967	1	1	yes	characteristic
134	C₂×C₇₃	#1971	1	1	yes	characteristic
135	C₂×C₇₃	#1977	1	1	yes	characteristic
136	C₂×#487	—	73	1	no	—
137	#1997	—	73	1	no	—
138	#1997	—	73	1	no	—
139	#1566	D₇₃	1	1	yes	characteristic
140	#1549	—	73	1	no	—
141	#1548	—	73	1	no	—
142	#1451	—	73	1	no	—
143	C₇₃	#9803	1	1	yes	characteristic, complemented, Sylow
144	C₂×C₄⋊Q₈	—	73	1	no	—
145	C₂×C₄⋊Q₈	—	73	1	no	—
146	#487	—	146	1	no	—
147	#487	—	146	1	no	—
148	#487	—	146	2	no	—
149	#431	—	73	1	no	—
150	#423	C₂×D₇₃	1	1	yes	characteristic
151	#423	C₂×D₇₃	1	1	yes	characteristic
152	C₂×#103	—	73	4	no	—
153	C₄×M₁₆	—	73	1	no	—
154	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
155	#343	—	146	2	no	—
156	#343	—	146	2	no	—
157	#334	—	2	2	no	—
158	#333	—	146	2	no	—
159	#332	—	146	2	no	—
160	#322	—	146	1	no	—
161	#322	—	146	1	no	—
162	C₂²×Q₈	—	73	2	no	—
163	C₂²×Q₈	—	146	1	no	—
164	C₂×M₁₆	—	2	1	no	—
165	C₂×M₁₆	—	2	1	no	—
166	C₂×M₁₆	—	73	2	no	—
167	C₂²×C₈	C₄×D₇₃	1	2	yes	—
168	C₄⋊Q₈	—	146	1	no	—
169	C₄⋊Q₈	—	146	1	no	—
170	C₄⋊Q₈	—	146	1	no	—
171	C₄⋊Q₈	—	146	1	no	—
172	C₄⋊Q₈	—	146	1	no	—
173	C₄⋊Q₈	—	146	1	no	—
174	C₄⋊Q₈	—	146	1	no	—
175	C₄⋊Q₈	—	146	1	no	—
176	C₂×C₄⋊C₄	—	73	2	no	—
177	C₂×C₄⋊C₄	—	146	1	no	—
178	C₂×C₄⋊C₄	—	146	1	no	—
179	C₂×C₄⋊C₄	—	146	1	no	—
180	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	2	1	no	—
183	C₄⋊C₈	—	2	1	no	—
184	C₄⋊C₈	—	2	1	no	—
185	C₄⋊C₈	—	73	2	no	—
186	#103	—	146	4	no	—
187	#103	—	146	4	no	—
188	C₂²⋊C₈	—	146	1	no	—
189	#97	—	146	1	no	—
190	C₄×C₈	—	146	1	no	—
191	C₄×C₈	—	146	1	no	—
192	C₄×C₈	D₂₉₂	1	1	yes	characteristic
193	C₄×C₈	D₂₉₂	1	1	yes	characteristic
194	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
195	C₂×Q₈	—	292	4	no	—
196	C₂×Q₈	—	292	1	no	—
197	C₂×Q₈	—	292	1	no	—
198	C₂×Q₈	—	584	2	no	—
199	C₂×Q₈	—	146	2	no	—
200	C₂×Q₈	—	146	2	no	—
201	C₂²×C₄	—	146	2	no	—
202	C₂²×C₄	—	146	2	no	—
203	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
204	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
205	C₂²×C₄	#11924029	1	1	yes	characteristic
206	M₁₆	—	4	2	no	—
207	M₁₆	—	4	2	no	—
208	M₁₆	—	146	2	no	—
209	M₁₆	—	146	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₂×C₈	—	4	1	no	—
212	C₂×C₈	—	4	1	no	—
213	C₂×C₈	—	146	2	no	—
214	C₂×C₈	—	146	2	no	—
215	C₂×C₈	#11924005	1	2	yes	—
216	C₂×C₈	#11924005	1	2	yes	—
217	C₄⋊C₄	—	292	1	no	—
218	C₄⋊C₄	—	292	1	no	—
219	C₄⋊C₄	—	292	1	no	—
220	C₄⋊C₄	—	292	1	no	—
221	C₄⋊C₄	—	292	1	no	—
222	C₄⋊C₄	—	292	1	no	—
223	C₄⋊C₄	—	146	2	no	—
224	C₄⋊C₄	—	146	2	no	—
225	C₄²	D₄×D₇₃	1	1	yes	characteristic
226	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
227	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
228	C₄²	#11924029	1	1	yes	characteristic
229	C₂³	#14556553	1	1	yes	characteristic
230	Q₈	—	292	4	no	—
231	Q₈	—	584	2	no	—
232	Q₈	—	584	2	no	—
233	Q₈	—	584	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	292	2	no	—
237	C₂×C₄	—	292	2	no	—
238	C₂×C₄	—	584	2	no	—
239	C₂×C₄	—	584	2	no	—
240	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
241	C₂×C₄	#14556553	1	1	yes	characteristic
242	C₂×C₄	#14556566	1	1	yes	characteristic
243	C₂×C₄	#14556566	1	1	yes	characteristic
244	C₂×C₄	#14556580	1	1	yes	characteristic
245	C₂×C₄	#14556587	1	1	yes	characteristic
246	C₂×C₄	#14556620	1	2	yes	—
247	C₂×C₄	#14556620	1	2	yes	—
248	C₈	—	2	2	no	—
249	C₈	—	2	2	no	—
250	C₈	—	8	1	no	—
251	C₈	—	8	1	no	—
252	C₈	—	292	2	no	—
253	C₈	—	292	2	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	#17988488	1	1	yes	characteristic
257	C₂²	#17988693	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	584	2	no	—
261	C₄	—	584	2	no	—
262	C₄	#17988569	1	2	yes	—
263	C₄	#17988846	1	2	yes	—
264	C₄	#17988851	1	2	yes	—
265	C₄	#17988978	1	1	yes	characteristic
266	C₄	#17988978	1	1	yes	characteristic
267	C₂	—	2	2	no	—
268	C₂	#22610778	1	1	yes	characteristic
269	C₂	#22610800	1	1	yes	characteristic
270	C₂	#22610832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988938

C₂

yes

maximal, characteristic

#22610919

C₂

yes

maximal, characteristic

#22610919

C₂

yes

maximal, characteristic

#22608617

C₂

yes

maximal, characteristic

#22608613

C₂

yes

maximal, characteristic

#22608220

C₂

yes

maximal, characteristic

C₇₃×#1566

C₂

yes

maximal, characteristic

C₂×#14556591

C₂²

yes

characteristic

C₂×#14556591

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×#14556516

C₄

yes

—

C₄×#11924012

C₂²

yes

—

—

—

—

—

—

#423×C₇₃

C₂²

yes

characteristic

#423×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#334×C₇₃

—

C₂²×Dic₁₄₆

—

C₂²×Dic₁₄₆

C₂×C₄

yes

—

C₂×#11924012

D₄

yes

—

—

—

—

—

—

—

—

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

C₄⋊#10596831

D₄

yes

—

—

—

—

—

—

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

—

—

—

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

#41

yes

characteristic

C₂³×C₇₃

C₄×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

100

C₂×C₄×C₇₃

#124

yes

characteristic

101

C₂×C₄×C₇₃

#127

yes

characteristic

102

C₂×C₄×C₇₃

#137

yes

—

103

C₂×C₄×C₇₃

#137

yes

—

104

C₂×Dic₇₃

—

105

C₂×Dic₇₃

—

106

C₂×Dic₇₃

—

107

C₂×Dic₇₃

—

108

Dic₁₄₆

—

109

Dic₁₄₆

—

110

Dic₁₄₆

—

111

Dic₁₄₆

—

112

C₈×C₇₃

—

113

C₈×C₇₃

—

114

C₈×C₇₃

—

115

C₈×C₇₃

—

116

#10596831

—

117

#10596831

—

118

C₂²×C₇₃

—

119

C₂²×C₇₃

—

120

C₂²×C₇₃

#390

yes

characteristic

121

C₂²×C₇₃

#441

yes

—

122

C₄×C₇₃

—

123

C₄×C₇₃

—

124

C₄×C₇₃

#413

yes

—

125

C₄×C₇₃

#470

yes

—

126

C₄×C₇₃

#471

yes

—

127

C₄×C₇₃

#497

yes

characteristic

128

C₄×C₇₃

#497

yes

characteristic

129

Dic₇₃

—

130

Dic₇₃

—

131

#9803

—

maximal, Sylow

132

C₂×C₇₃

—

133

C₂×C₇₃

#1967

yes

characteristic

134

C₂×C₇₃

#1971

yes

characteristic

135

C₂×C₇₃

#1977

yes

characteristic

136

C₂×#487

—

137

#1997

—

138

#1997

—

139

#1566

D₇₃

yes

characteristic

140

#1549

—

141

#1548

—

142

#1451

—

143

C₇₃

#9803

yes

characteristic, complemented, Sylow

144

C₂×C₄⋊Q₈

—

145

C₂×C₄⋊Q₈

—

146

#487

—

146

—

147

#487

—

146

—

148

#487

—

146

—

149

#431

—

150

#423

C₂×D₇₃

yes

characteristic

151

#423

C₂×D₇₃

yes

characteristic

152

C₂×#103

—

153

C₄×M₁₆

—

154

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

155

#343

—

146

—

156

#343

—

146

—

157

#334

—

158

#333

—

146

—

159

#332

—

146

—

160

#322

—

146

—

161

#322

—

146

—

162

C₂²×Q₈

—

163

C₂²×Q₈

—

146

—

164

C₂×M₁₆

—

165

C₂×M₁₆

—

166

C₂×M₁₆

—

167

C₂²×C₈

C₄×D₇₃

yes

—

168

C₄⋊Q₈

—

146

—

169

C₄⋊Q₈

—

146

—

170

C₄⋊Q₈

—

146

—

171

C₄⋊Q₈

—

146

—

172

C₄⋊Q₈

—

146

—

173

C₄⋊Q₈

—

146

—

174

C₄⋊Q₈

—

146

—

175

C₄⋊Q₈

—

146

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

146

—

178

C₂×C₄⋊C₄

—

146

—

179

C₂×C₄⋊C₄

—

146

—

180

C₂×C₄²

C₂²×D₇₃

yes

characteristic

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

#103

—

146

—

187

#103

—

146

—

188

C₂²⋊C₈

—

146

—

189

#97

—

146

—

190

C₄×C₈

—

146

—

191

C₄×C₈

—

146

—

192

C₄×C₈

D₂₉₂

yes

characteristic

193

C₄×C₈

D₂₉₂

yes

characteristic

194

C₄×C₈

C₂²⋊D₇₃

yes

—

195

C₂×Q₈

—

292

—

196

C₂×Q₈

—

292

—

197

C₂×Q₈

—

292

—

198

C₂×Q₈

—

584

—

199

C₂×Q₈

—

146

—

200

C₂×Q₈

—

146

—

201

C₂²×C₄

—

146

—

202

C₂²×C₄

—

146

—

203

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

204

C₂²×C₄

D₄×D₇₃

yes

characteristic

205

C₂²×C₄

#11924029

yes

characteristic

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

146

—

209

M₁₆

—

146

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

146

—

214

C₂×C₈

—

146

—

215

C₂×C₈

#11924005

yes

—

216

C₂×C₈

#11924005

yes

—

217

C₄⋊C₄

—

292

—

218

C₄⋊C₄

—

292

—

219

C₄⋊C₄

—

292

—

220

C₄⋊C₄

—

292

—

221

C₄⋊C₄

—

292

—

222

C₄⋊C₄

—

292

—

223

C₄⋊C₄

—

146

—

224

C₄⋊C₄

—

146

—

225

C₄²

D₄×D₇₃

yes

characteristic

226

C₄²

C₂×C₂²⋊D₇₃

yes

characteristic

227

C₄²

C₂×D₂₉₂

yes

characteristic

228

C₄²

#11924029

yes

characteristic

229

C₂³

#14556553

yes

characteristic

230

Q₈

—

292

—

231

Q₈

—

584

—

232

Q₈

—

584

—

233

Q₈

—

584

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

292

—

237

C₂×C₄

—

292

—

238

C₂×C₄

—

584

—

239

C₂×C₄

—

584

—

240

C₂×C₄

C₂×#11924005

yes

characteristic

241

C₂×C₄

#14556553

yes

characteristic

242

C₂×C₄

#14556566

yes

characteristic

243

C₂×C₄

#14556566

yes

characteristic

244

C₂×C₄

#14556580

yes

characteristic

245

C₂×C₄

#14556587

yes

characteristic

246

C₂×C₄

#14556620

yes

—

247

C₂×C₄

#14556620

yes

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

292

—

253

C₈

—

292

—

254

C₂²

—

255

C₂²

—

256

C₂²

#17988488

yes

characteristic

257

C₂²

#17988693

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

584

—

261

C₄

—

584

—

262

C₄

#17988569

yes

—

263

C₄

#17988846

yes

—

264

C₄

#17988851

yes

—

265

C₄

#17988978

yes

characteristic

266

C₄

#17988978

yes

characteristic

267

C₂

—

268

C₂

#22610778

yes

characteristic

269

C₂

#22610800

yes

characteristic

270

C₂

#22610832

yes

characteristic

	subgroup	G/H
center	C₂²	#17988488
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1566	C₂
socle	C₂²×C₇₃	#390
prime radical	C₂³×C₇₃	C₄×D₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1566	D₇₃
hypocenter	C₇₃	#9803
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂²

#17988488

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1566

C₂

socle

C₂²×C₇₃

#390

prime radical

C₂³×C₇₃

C₄×D₄

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
143. C₇₃	#9803	semidirect

H ≅ G/N

type

143. C₇₃

#9803

semidirect

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

subgroup	index
C₂×#17988938	2
#22610919	2
#22608617	2
#22608613	2
#22608220	2
C₇₃×#1566	2
#9803	73

subgroup

index

C₇₃×#1566

Subgroups — #32985621

Conjugacy classes of subgroups

Complements

Maximal subgroups