Group #32995290 — subgroups

Subgroups — #32995290

Order 18688.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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	#22611552	C₂	1	2	yes	maximal, complemented
2	#22607884	C₂	1	2	yes	maximal, complemented
3	#22607867	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2930	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556531	—	2	2	no	—
6	#17988369	—	2	2	no	—
7	#17988369	C₂²	1	4	yes	—
8	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₇₃	C₄	1	1	yes	characteristic
10	#525×C₇₃	C₄	1	1	yes	characteristic
11	#436×C₇₃	—	2	2	no	—
12	#435×C₇₃	—	2	2	no	—
13	#424×C₇₃	C₂²	1	1	yes	characteristic
14	#408×C₇₃	C₄	1	1	yes	characteristic
15	#407×C₇₃	C₂²	1	1	yes	characteristic
16	#405×C₇₃	C₄	1	1	yes	characteristic
17	#14556531	—	2	4	no	—
18	#14556531	—	4	2	no	—
19	C₂×#11924003	—	4	2	no	—
20	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
22	#131×C₇₃	—	4	2	no	—
23	C₂×M₁₆×C₇₃	—	2	1	no	—
24	C₂×M₁₆×C₇₃	—	2	1	no	—
25	C₂×M₁₆×C₇₃	—	4	2	no	—
26	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
28	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₇₃	D₄	1	2	yes	—
32	#123×C₇₃	C₈	1	2	yes	—
33	C₂²⋊Q₈×C₇₃	—	2	1	no	—
34	#121×C₇₃	—	2	1	no	—
35	#120×C₇₃	C₈	1	2	yes	—
36	C₄×D₄×C₇₃	—	2	2	no	—
37	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₄⋊C₈×C₇₃	—	2	2	no	—
39	C₂²⋊C₈×C₇₃	—	2	2	no	—
40	C₂²⋊C₈×C₇₃	—	2	2	no	—
41	#97×C₇₃	—	2	1	no	—
42	C₄×C₈×C₇₃	—	2	1	no	—
43	#11924003	—	4	4	no	—
44	C₂⁴×C₇₃	C₂×C₈	1	1	yes	characteristic
45	#41×C₇₃	—	4	1	no	—
46	#41×C₇₃	—	4	1	no	—
47	C₂×Q₈×C₇₃	M₁₆	1	1	yes	characteristic
48	C₂×D₄×C₇₃	—	2	2	no	—
49	C₂×D₄×C₇₃	C₂×C₈	1	2	yes	—
50	C₂×D₄×C₇₃	M₁₆	1	1	yes	characteristic
51	C₂²×C₄×C₇₃	—	2	1	no	—
52	C₂²×C₄×C₇₃	—	2	1	no	—
53	C₂²×C₄×C₇₃	—	4	1	no	—
54	C₂²×C₄×C₇₃	—	4	1	no	—
55	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
57	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
58	M₁₆×C₇₃	—	4	2	no	—
59	M₁₆×C₇₃	—	4	1	no	—
60	M₁₆×C₇₃	—	4	2	no	—
61	M₁₆×C₇₃	—	4	2	no	—
62	M₁₆×C₇₃	—	4	1	no	—
63	C₂×C₈×C₇₃	—	2	2	no	—
64	C₂×C₈×C₇₃	—	2	2	no	—
65	C₂×C₈×C₇₃	—	2	2	no	—
66	C₂×C₈×C₇₃	—	2	1	no	—
67	C₂×C₈×C₇₃	—	2	1	no	—
68	C₂×C₈×C₇₃	—	4	1	no	—
69	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
72	C₄⋊C₄×C₇₃	—	2	2	no	—
73	C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂²⋊C₄×C₇₃	C₂×C₈	1	2	yes	—
77	C₄²×C₇₃	—	2	1	no	—
78	C₂³×C₇₃	—	2	1	no	—
79	C₂³×C₇₃	—	4	1	no	—
80	C₂³×C₇₃	—	8	1	no	—
81	C₂³×C₇₃	C₂²⋊C₈	1	2	yes	—
82	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
83	Q₈×C₇₃	—	4	1	no	—
84	D₄×C₇₃	—	4	2	no	—
85	D₄×C₇₃	—	4	1	no	—
86	D₄×C₇₃	—	8	2	no	—
87	C₂×C₄×C₇₃	—	2	1	no	—
88	C₂×C₄×C₇₃	—	2	2	no	—
89	C₂×C₄×C₇₃	—	2	1	no	—
90	C₂×C₄×C₇₃	—	2	2	no	—
91	C₂×C₄×C₇₃	—	2	2	no	—
92	C₂×C₄×C₇₃	—	2	1	no	—
93	C₂×C₄×C₇₃	—	4	2	no	—
94	C₂×C₄×C₇₃	—	4	1	no	—
95	C₂×C₄×C₇₃	—	4	1	no	—
96	C₂×C₄×C₇₃	—	4	1	no	—
97	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
98	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
100	C₈×C₇₃	—	2	1	no	—
101	C₈×C₇₃	—	2	2	no	—
102	C₈×C₇₃	—	4	1	no	—
103	C₈×C₇₃	—	4	1	no	—
104	C₈×C₇₃	#99	1	2	yes	—
105	C₂²×C₇₃	—	2	1	no	—
106	C₂²×C₇₃	—	2	2	no	—
107	C₂²×C₇₃	—	4	2	no	—
108	C₂²×C₇₃	—	4	1	no	—
109	C₂²×C₇₃	—	4	1	no	—
110	C₂²×C₇₃	—	4	1	no	—
111	C₂²×C₇₃	—	4	1	no	—
112	C₂²×C₇₃	—	8	2	no	—
113	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
114	C₄×C₇₃	—	2	1	no	—
115	C₄×C₇₃	—	2	2	no	—
116	C₄×C₇₃	—	4	2	no	—
117	C₄×C₇₃	—	4	1	no	—
118	C₄×C₇₃	C₂×#99	1	1	yes	characteristic
119	C₄×C₇₃	#413	1	1	yes	characteristic
120	#11484	—	73	1	no	maximal, Sylow
121	C₂×C₇₃	—	2	1	no	—
122	C₂×C₇₃	—	4	2	no	—
123	C₂×C₇₃	—	4	1	no	—
124	C₂×C₇₃	—	8	1	no	—
125	C₂×C₇₃	#1459	1	1	yes	characteristic
126	#2930	D₇₃	1	1	yes	characteristic
127	#2115	—	73	2	no	—
128	#1328	—	73	2	no	—
129	#1320	—	73	2	no	—
130	C₇₃	#11484	1	1	yes	characteristic, complemented, Sylow
131	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
132	C₂²×M₁₆	Dic₇₃	1	1	yes	characteristic
133	#525	Dic₇₃	1	1	yes	characteristic
134	C₂×M₃₂	—	146	2	no	—
135	#436	—	2	2	no	—
136	#435	—	2	2	no	—
137	#424	C₂×D₇₃	1	1	yes	characteristic
138	#408	Dic₇₃	1	1	yes	characteristic
139	#407	C₂×D₇₃	1	1	yes	characteristic
140	#405	Dic₇₃	1	1	yes	characteristic
141	#349	—	73	4	no	—
142	#349	—	146	2	no	—
143	C₂×#41	C₂×Dic₇₃	1	1	yes	characteristic
144	C₂³×C₄	C₂×Dic₇₃	1	1	yes	characteristic
145	#131	—	4	2	no	—
146	C₂×M₁₆	—	2	1	no	—
147	C₂×M₁₆	—	2	1	no	—
148	C₂×M₁₆	—	4	2	no	—
149	C₂×M₁₆	C₂×Dic₇₃	1	1	yes	characteristic
150	C₂×M₁₆	C₂²⋊D₇₃	1	2	yes	—
151	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
152	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
153	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
154	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
155	#123	#10596831	1	2	yes	—
156	C₂²⋊Q₈	—	2	1	no	—
157	#121	—	2	1	no	—
158	#120	#10596831	1	2	yes	—
159	C₄×D₄	—	2	2	no	—
160	#117	C₂×Dic₇₃	1	1	yes	characteristic
161	M₃₂	—	292	2	no	—
162	M₃₂	—	146	4	no	—
163	C₂×C₁₆	—	292	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₂²⋊C₈	—	2	2	no	—
166	C₂²⋊C₈	—	2	2	no	—
167	#97	—	2	1	no	—
168	C₄×C₈	—	2	1	no	—
169	C₂⁴	C₂×#10596831	1	1	yes	characteristic
170	#41	—	4	1	no	—
171	#41	—	4	1	no	—
172	C₂×Q₈	#11924012	1	1	yes	characteristic
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	C₂×#10596831	1	2	yes	—
175	C₂×D₄	#11924012	1	1	yes	characteristic
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	4	1	no	—
179	C₂²×C₄	—	4	1	no	—
180	C₂²×C₄	C₂²⋊Dic₇₃	1	2	yes	—
181	C₂²×C₄	C₂×#10596831	1	1	yes	characteristic
182	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
183	M₁₆	—	4	2	no	—
184	M₁₆	—	4	1	no	—
185	M₁₆	—	4	2	no	—
186	M₁₆	—	4	2	no	—
187	M₁₆	—	4	1	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
195	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
196	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	1	no	—
199	C₂²⋊C₄	—	2	2	no	—
200	C₂²⋊C₄	—	2	2	no	—
201	C₂²⋊C₄	C₂×#10596831	1	2	yes	—
202	C₄²	—	2	1	no	—
203	C₁₆	—	292	4	no	—
204	C₂³	—	2	1	no	—
205	C₂³	—	4	1	no	—
206	C₂³	—	8	1	no	—
207	C₂³	C₂²⋊#10596831	1	2	yes	—
208	C₂³	C₂²×#10596831	1	1	yes	characteristic
209	Q₈	—	4	1	no	—
210	D₄	—	4	2	no	—
211	D₄	—	4	1	no	—
212	D₄	—	8	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	C₂²⋊#10596831	1	2	yes	—
224	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
225	C₂×C₄	C₂×#11924012	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	2	1	no	—
228	C₈	—	4	1	no	—
229	C₈	—	4	1	no	—
230	C₈	#14556506	1	2	yes	—
231	C₂²	—	2	1	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	4	2	no	—
234	C₂²	—	4	1	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	1	no	—
238	C₂²	—	8	2	no	—
239	C₂²	C₂×C₂²⋊#10596831	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	2	no	—
242	C₄	—	4	2	no	—
243	C₄	—	4	1	no	—
244	C₄	C₂×#14556506	1	1	yes	characteristic
245	C₄	#17988571	1	1	yes	characteristic
246	C₂	—	2	1	no	—
247	C₂	—	4	1	no	—
248	C₂	—	4	2	no	—
249	C₂	—	8	1	no	—
250	C₂	#22608249	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611552

C₂

yes

maximal, complemented

#22607884

C₂

yes

maximal, complemented

#22607867

C₂

yes

maximal, complemented

C₇₃×#2930

C₂

yes

maximal, characteristic

C₂×#14556531

—

#17988369

—

#17988369

C₂²

yes

—

C₂×#131×C₇₃

C₂²

yes

characteristic

C₂²×M₁₆×C₇₃

C₄

yes

characteristic

#525×C₇₃

C₄

yes

characteristic

#436×C₇₃

—

#435×C₇₃

—

#424×C₇₃

C₂²

yes

characteristic

#408×C₇₃

C₄

yes

characteristic

#407×C₇₃

C₂²

yes

characteristic

#405×C₇₃

C₄

yes

—

—

—

C₂×#41×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₇₃

C₂×C₄

yes

characteristic

#131×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₃

D₄

yes

—

C₂×M₁₆×C₇₃

C₂³

yes

characteristic

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

—

#123×C₇₃

C₈

yes

—

C₂²⋊Q₈×C₇₃

—

#121×C₇₃

—

#120×C₇₃

C₈

yes

—

C₄×D₄×C₇₃

—

#117×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

—

#11924003

—

C₂⁴×C₇₃

C₂×C₈

yes

characteristic

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

M₁₆

yes

characteristic

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

C₂×C₈

yes

—

C₂×D₄×C₇₃

M₁₆

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

C₂×C₈

yes

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₈

yes

—

C₂³×C₇₃

C₂²×C₈

yes

characteristic

Q₈×C₇₃

—

D₄×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×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

100

C₈×C₇₃

—

101

C₈×C₇₃

—

102

C₈×C₇₃

—

103

C₈×C₇₃

—

104

C₈×C₇₃

#99

yes

—

105

C₂²×C₇₃

—

106

C₂²×C₇₃

—

107

C₂²×C₇₃

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

—

111

C₂²×C₇₃

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

114

C₄×C₇₃

—

115

C₄×C₇₃

—

116

C₄×C₇₃

—

117

C₄×C₇₃

—

118

C₄×C₇₃

C₂×#99

yes

characteristic

119

C₄×C₇₃

yes

120

—

121

C₂×C₇₃

—

122

C₂×C₇₃

—

123

C₂×C₇₃

—

124

C₂×C₇₃

—

125

C₂×C₇₃

#1459

yes

characteristic

126

#2930

D₇₃

yes

characteristic

127

#2115

—

128

#1328

—

129

#1320

—

130

C₇₃

#11484

yes

characteristic, complemented, Sylow

131

C₂×#131

C₂×D₇₃

yes

characteristic

132

C₂²×M₁₆

Dic₇₃

yes

characteristic

133

#525

Dic₇₃

yes

characteristic

134

C₂×M₃₂

—

146

—

135

#436

—

136

#435

—

137

#424

C₂×D₇₃

yes

characteristic

138

#408

Dic₇₃

yes

characteristic

139

#407

C₂×D₇₃

yes

characteristic

140

#405

Dic₇₃

yes

characteristic

141

#349

—

142

#349

—

146

—

143

C₂×#41

C₂×Dic₇₃

yes

characteristic

144

C₂³×C₄

C₂×Dic₇₃

yes

characteristic

145

#131

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂×M₁₆

—

149

C₂×M₁₆

C₂×Dic₇₃

yes

characteristic

150

C₂×M₁₆

C₂²⋊D₇₃

yes

—

151

C₂×M₁₆

C₂²×D₇₃

yes

characteristic

152

C₂²×C₈

C₂×Dic₇₃

yes

characteristic

153

C₂²×C₈

C₂×Dic₇₃

yes

characteristic

154

C₂²×C₈

C₂²⋊D₇₃

yes

—

155

#123

#10596831

yes

—

156

C₂²⋊Q₈

—

157

#121

—

158

#120

#10596831

yes

—

159

C₄×D₄

—

160

#117

C₂×Dic₇₃

yes

characteristic

161

M₃₂

—

292

—

162

M₃₂

—

146

—

163

C₂×C₁₆

—

292

—

164

C₄⋊C₈

—

165

C₂²⋊C₈

—

166

C₂²⋊C₈

—

167

#97

—

168

C₄×C₈

—

169

C₂⁴

C₂×#10596831

yes

characteristic

170

#41

—

171

#41

—

172

C₂×Q₈

#11924012

yes

characteristic

173

C₂×D₄

—

174

C₂×D₄

C₂×#10596831

yes

—

175

C₂×D₄

#11924012

yes

characteristic

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

C₂²⋊Dic₇₃

yes

—

181

C₂²×C₄

C₂×#10596831

yes

characteristic

182

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

183

M₁₆

—

184

M₁₆

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

195

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

196

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

C₂×#10596831

yes

—

202

C₄²

—

203

C₁₆

—

292

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

C₂²⋊#10596831

yes

—

208

C₂³

C₂²×#10596831

yes

characteristic

209

Q₈

—

210

D₄

—

211

D₄

—

212

D₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

C₂²⋊#10596831

yes

—

224

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

225

C₂×C₄

C₂×#11924012

yes

characteristic

226

C₈

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

#14556506

yes

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

C₂×C₂²⋊#10596831

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

C₂×#14556506

yes

characteristic

245

C₄

#17988571

yes

characteristic

246

C₂

—

247

C₂

—

248

C₂

—

249

C₂

—

250

C₂

#22608249

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#14556506
commutator	C₂³×C₇₃	C₂²×C₈
Frattini	C₂×M₁₆	C₂²×D₇₃
Fitting	C₇₃×#2930	C₂
socle	C₂×C₇₃	#1459
prime radical	#525×C₇₃	C₄
cosocle	C₂×M₁₆×C₇₃	C₂³
hypercenter	#2930	D₇₃
hypocenter	C₇₃	#11484
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×#131 ◁ #2930

subgroup

G/H

center

C₄

C₂×#14556506

commutator

C₂³×C₇₃

C₂²×C₈

Frattini

C₂×M₁₆

C₂²×D₇₃

Fitting

C₇₃×#2930

C₂

socle

C₂×C₇₃

#1459

prime radical

#525×C₇₃

C₄

cosocle

C₂×M₁₆×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×#131 ◁ #2930

N	H ≅ G/N	type
1. #22611552	C₂	semidirect
2. #22607884	C₂	semidirect
3. #22607867	C₂	semidirect
130. C₇₃	#11484	semidirect

H ≅ G/N

type

1. #22611552

C₂

semidirect

2. #22607884

C₂

semidirect

3. #22607867

C₂

semidirect

130. C₇₃

#11484

semidirect

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

subgroup	index
#22611552	2
#22607884	2
#22607867	2
C₇₃×#2930	2
#11484	73

subgroup

index

C₇₃×#2930

Subgroups — #32995290

Conjugacy classes of subgroups

Complements

Maximal subgroups