Group #35306939 — subgroups

Subgroups — #35306939

Order 21248.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19128106	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127911	C₂	1	2	yes	maximal
3	C₂×#19127446	C₂	1	2	yes	maximal
4	#24905298	C₂	1	1	yes	maximal, characteristic
5	C₈₃×#1984	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13050580	—	2	2	no	—
7	C₂×#14581792	C₂²	1	2	yes	—
8	#19128106	—	2	4	no	—
9	#19127911	—	2	4	no	—
10	#19127911	—	2	4	no	—
11	C₂×#14581726	—	2	2	no	—
12	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
13	C₂×#14581715	—	2	2	no	—
14	#19127446	—	2	4	no	—
15	C₂×C₄×Q₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₈₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
18	#336×C₈₃	—	2	2	no	—
19	C₂²×Dic₁₆₆	—	2	2	no	—
20	C₂×#13050580	—	2	8	no	—
21	C₂×#13050580	—	4	4	no	—
22	C₂×#13050580	—	4	4	no	—
23	C₂²×C₈₃⋊C₈	—	2	2	no	—
24	#14581792	—	2	2	no	—
25	#14581792	—	2	2	no	—
26	#14581792	—	2	2	no	—
27	#14581792	D₄	1	4	yes	—
28	C₂×C₄⋊Dic₈₃	—	2	2	no	—
29	C₂×C₄⋊Dic₈₃	—	2	2	no	—
30	#14581726	—	2	8	no	—
31	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₈₃⋊C₈)	D₄	1	4	yes	—
33	#14581715	—	2	8	no	—
34	C₂²×Q₈×C₈₃	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₈₃	—	2	1	no	—
36	C₂²×C₈×C₈₃	D₄	1	2	yes	—
37	C₄×Q₈×C₈₃	—	2	2	no	—
38	C₄×Q₈×C₈₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₈₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₈₃	—	2	1	no	—
42	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₈₃	—	2	2	no	—
44	C₄×C₈×C₈₃	—	2	2	no	—
45	C₂×Dic₁₆₆	—	2	4	no	—
46	C₂×Dic₁₆₆	—	4	2	no	—
47	C₂×Dic₁₆₆	—	4	2	no	—
48	C₂×Dic₁₆₆	—	4	2	no	—
49	C₂×Dic₁₆₆	—	4	2	no	—
50	C₂×Dic₁₆₆	—	4	2	no	—
51	C₂²×Dic₈₃	—	4	2	no	—
52	#13050580	—	4	16	no	—
53	C₂×C₈₃⋊C₈	—	2	4	no	—
54	C₂×C₈₃⋊C₈	—	4	2	no	—
55	C₂×C₈₃⋊C₈	—	4	2	no	—
56	C₄⋊Dic₈₃	—	2	4	no	—
57	C₄⋊Dic₈₃	—	2	4	no	—
58	C₄⋊Dic₈₃	—	4	2	no	—
59	C₄⋊Dic₈₃	—	4	2	no	—
60	C₂×Q₈×C₈₃	—	2	1	no	—
61	C₂×Q₈×C₈₃	—	2	2	no	—
62	C₂×Q₈×C₈₃	—	2	2	no	—
63	C₂×Q₈×C₈₃	D₈	1	2	yes	—
64	C₂²×C₄×C₈₃	—	2	1	no	—
65	C₂²×C₄×C₈₃	—	2	1	no	—
66	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
69	C₂×C₈×C₈₃	—	2	2	no	—
70	C₂×C₈×C₈₃	—	2	2	no	—
71	C₂×C₈×C₈₃	—	4	1	no	—
72	C₂×C₈×C₈₃	—	4	2	no	—
73	C₂×C₈×C₈₃	Q₁₆	1	4	yes	complemented
74	C₄⋊C₄×C₈₃	—	2	2	no	—
75	C₄⋊C₄×C₈₃	—	4	2	no	—
76	C₄²×C₈₃	—	4	1	no	—
77	C₄²×C₈₃	—	4	1	no	—
78	C₄²×C₈₃	C₂×D₄	1	2	yes	—
79	C₄²×C₈₃	C₂×D₄	1	2	yes	—
80	C₂³×C₈₃	#121	1	1	yes	characteristic
81	Q₈×C₈₃	—	2	4	no	—
82	Q₈×C₈₃	—	4	2	no	—
83	C₂×C₄×C₈₃	—	2	2	no	—
84	C₂×C₄×C₈₃	—	2	2	no	—
85	C₂×C₄×C₈₃	—	4	1	no	—
86	C₂×C₄×C₈₃	—	4	1	no	—
87	C₂×C₄×C₈₃	—	4	1	no	—
88	C₂×C₄×C₈₃	—	4	2	no	—
89	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
90	C₂×C₄×C₈₃	#120	1	2	yes	—
91	C₂×C₄×C₈₃	#121	1	2	yes	—
92	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
93	C₂×C₄×C₈₃	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₈₃	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₈₃	#135	1	1	yes	characteristic
96	C₂×C₄×C₈₃	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×C₄×C₈₃	#137	1	2	yes	—
98	C₂×Dic₈₃	—	4	4	no	—
99	C₂×Dic₈₃	—	8	2	no	—
100	C₂×Dic₈₃	—	8	2	no	—
101	Dic₁₆₆	—	4	4	no	—
102	Dic₁₆₆	—	4	4	no	—
103	Dic₁₆₆	—	8	2	no	—
104	Dic₁₆₆	—	8	2	no	—
105	C₈×C₈₃	—	2	4	no	—
106	C₈×C₈₃	—	8	1	no	—
107	C₈₃⋊C₈	—	4	4	no	—
108	C₂²×C₈₃	#392	1	1	yes	characteristic
109	C₂²×C₈₃	#462	1	2	yes	—
110	C₂²×C₈₃	#466	1	1	yes	characteristic
111	C₂²×C₈₃	#469	1	1	yes	characteristic
112	C₂²×C₈₃	#473	1	2	yes	—
113	C₄×C₈₃	—	2	2	no	—
114	C₄×C₈₃	—	4	2	no	—
115	C₄×C₈₃	—	8	1	no	—
116	C₄×C₈₃	#447	1	2	yes	—
117	C₄×C₈₃	#449	1	2	yes	—
118	C₄×C₈₃	#451	1	2	yes	—
119	C₄×C₈₃	#494	1	1	yes	characteristic
120	C₄×C₈₃	#497	1	1	yes	characteristic
121	Dic₈₃	—	8	4	no	—
122	#10265	—	83	1	no	maximal, Sylow
123	C₂×C₈₃	#1674	1	2	yes	—
124	C₂×C₈₃	#1694	1	2	yes	—
125	C₂×C₈₃	#1999	1	1	yes	characteristic
126	C₂×C₈₃	#2016	1	1	yes	characteristic
127	C₂×C₈₃	#2020	1	1	yes	characteristic
128	C₂×#500	—	83	1	no	—
129	C₂×#462	—	83	2	no	—
130	#1984	D₈₃	1	1	yes	characteristic
131	C₂×#332	—	83	2	no	—
132	#1277	—	83	1	no	—
133	C₈₃	#10265	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₁₆	—	166	2	no	—
135	C₂×C₄⋊Q₈	—	83	2	no	—
136	C₂×C₄×Q₈	C₂×D₈₃	1	1	yes	characteristic
137	#500	—	166	4	no	—
138	#462	—	166	4	no	—
139	#462	—	166	4	no	—
140	C₂×#107	—	166	2	no	—
141	C₂×C₄⋊C₈	—	83	2	no	—
142	C₂×C₄⋊C₈	C₂×D₈₃	1	1	yes	characteristic
143	C₂×#103	—	166	2	no	—
144	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
145	#336	—	2	2	no	—
146	#332	—	166	4	no	—
147	C₂²×Q₈	—	166	2	no	—
148	C₂²×Q₈	D₃₃₂	1	1	yes	characteristic
149	C₂×Q₁₆	—	332	4	no	—
150	C₂×Q₁₆	—	332	4	no	—
151	C₂×Q₁₆	—	166	8	no	—
152	C₂²×C₈	—	2	1	no	—
153	C₂²×C₈	—	166	2	no	—
154	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
155	C₄⋊Q₈	—	83	4	no	—
156	C₄⋊Q₈	—	166	2	no	—
157	C₄⋊Q₈	—	166	2	no	—
158	C₄⋊Q₈	—	166	2	no	—
159	C₄×Q₈	—	2	2	no	—
160	C₄×Q₈	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	—	166	2	no	—
163	C₂×C₄⋊C₄	—	166	2	no	—
164	C₂×C₄⋊C₄	D₃₃₂	1	1	yes	characteristic
165	C₂×C₄²	—	2	1	no	—
166	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
167	#107	—	166	8	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	83	4	no	—
170	C₄⋊C₈	—	166	2	no	—
171	#103	—	166	8	no	—
172	C₄×C₈	—	2	2	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	332	2	no	—
177	C₂×Q₈	—	332	2	no	—
178	C₂×Q₈	—	332	2	no	—
179	C₂×Q₈	—	332	2	no	—
180	C₂×Q₈	—	332	2	no	—
181	C₂×Q₈	—	166	4	no	—
182	C₂×Q₈	D₆₆₄	1	2	yes	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	332	2	no	—
186	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
187	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
188	C₂²×C₄	#13050590	1	1	yes	characteristic
189	Q₁₆	—	332	16	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	332	2	no	—
195	C₂×C₈	—	332	2	no	—
196	C₂×C₈	—	166	4	no	—
197	C₂×C₈	#13050580	1	4	yes	complemented
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	332	2	no	—
201	C₄⋊C₄	—	332	2	no	—
202	C₄⋊C₄	—	166	4	no	—
203	C₄⋊C₄	—	166	4	no	—
204	C₄²	—	4	1	no	—
205	C₄²	—	4	1	no	—
206	C₄²	D₄×D₈₃	1	2	yes	—
207	C₄²	D₄×D₈₃	1	2	yes	—
208	C₂³	#14581766	1	1	yes	characteristic
209	Q₈	—	2	4	no	—
210	Q₈	—	4	2	no	—
211	Q₈	—	332	4	no	—
212	Q₈	—	332	4	no	—
213	Q₈	—	664	2	no	—
214	Q₈	—	664	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	332	4	no	—
222	C₂×C₄	—	664	2	no	—
223	C₂×C₄	—	664	2	no	—
224	C₂×C₄	#14581760	1	1	yes	characteristic
225	C₂×C₄	#14581762	1	2	yes	—
226	C₂×C₄	#14581765	1	2	yes	—
227	C₂×C₄	#14581788	1	1	yes	characteristic
228	C₂×C₄	C₂×D₆₆₄	1	1	yes	characteristic
229	C₂×C₄	C₂×#13050580	1	2	yes	—
230	C₂×C₄	#14581814	1	1	yes	characteristic
231	C₂×C₄	#14581820	1	2	yes	—
232	C₂×C₄	#14581822	1	2	yes	—
233	C₈	—	2	4	no	—
234	C₈	—	8	1	no	—
235	C₈	—	332	4	no	—
236	C₂²	#19127610	1	1	yes	characteristic
237	C₂²	#19127911	1	2	yes	—
238	C₂²	#19127937	1	1	yes	characteristic
239	C₂²	#19127954	1	1	yes	characteristic
240	C₂²	#19127976	1	2	yes	—
241	C₄	—	2	2	no	—
242	C₄	—	4	2	no	—
243	C₄	—	8	1	no	—
244	C₄	—	664	4	no	—
245	C₄	#19127837	1	2	yes	—
246	C₄	#19127848	1	2	yes	—
247	C₄	#19127856	1	2	yes	—
248	C₄	#19128080	1	1	yes	characteristic
249	C₄	#19128096	1	1	yes	characteristic
250	C₂	#24906857	1	2	yes	—
251	C₂	#24906981	1	2	yes	—
252	C₂	#24908461	1	1	yes	characteristic
253	C₂	#24908562	1	1	yes	characteristic
254	C₂	#24908584	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128106

C₂

yes

maximal, characteristic

C₂×#19127911

C₂

yes

maximal

C₂×#19127446

C₂

yes

maximal

#24905298

C₂

yes

maximal, characteristic

C₈₃×#1984

C₂

yes

maximal, characteristic

C₂²×#13050580

—

C₂×#14581792

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₈₃⋊C₈)

C₂²

yes

—

C₂×#14581715

—

#19127446

—

C₂×C₄×Q₈×C₈₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

#336×C₈₃

—

C₂²×Dic₁₆₆

—

C₂×#13050580

—

C₂×#13050580

—

C₂×#13050580

—

C₂²×C₈₃⋊C₈

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

#14581726

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

D₄

yes

—

#14581715

—

C₂²×Q₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₄×Q₈×C₈₃

—

C₄×Q₈×C₈₃

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

D₄

yes

characteristic

C₂×C₄²×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

#13050580

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

D₈

yes

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

Q₁₆

yes

complemented

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

—

C₄²×C₈₃

C₂×D₄

yes

—

C₂³×C₈₃

#121

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#120

yes

characteristic

C₂×C₄×C₈₃

#120

yes

—

C₂×C₄×C₈₃

#121

yes

—

C₂×C₄×C₈₃

#127

yes

characteristic

C₂×C₄×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

C₂×Q₁₆

yes

—

C₂×C₄×C₈₃

#135

yes

characteristic

C₂×C₄×C₈₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₃

#137

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

100

C₂×Dic₈₃

—

101

Dic₁₆₆

—

102

Dic₁₆₆

—

103

Dic₁₆₆

—

104

Dic₁₆₆

—

105

C₈×C₈₃

—

106

C₈×C₈₃

—

107

C₈₃⋊C₈

—

108

C₂²×C₈₃

#392

yes

characteristic

109

C₂²×C₈₃

#462

yes

—

110

C₂²×C₈₃

#466

yes

characteristic

111

C₂²×C₈₃

#469

yes

characteristic

112

C₂²×C₈₃

#473

yes

—

113

C₄×C₈₃

—

114

C₄×C₈₃

—

115

C₄×C₈₃

—

116

C₄×C₈₃

#447

yes

—

117

C₄×C₈₃

#449

yes

—

118

C₄×C₈₃

#451

yes

—

119

C₄×C₈₃

#494

yes

characteristic

120

C₄×C₈₃

#497

yes

characteristic

121

Dic₈₃

—

122

#10265

—

maximal, Sylow

123

C₂×C₈₃

#1674

yes

—

124

C₂×C₈₃

#1694

yes

—

125

C₂×C₈₃

#1999

yes

characteristic

126

C₂×C₈₃

#2016

yes

characteristic

127

C₂×C₈₃

#2020

yes

characteristic

128

C₂×#500

—

129

C₂×#462

—

130

#1984

D₈₃

yes

characteristic

131

C₂×#332

—

132

#1277

—

133

C₈₃

#10265

yes

characteristic, complemented, Sylow

134

C₂²×Q₁₆

—

166

—

135

C₂×C₄⋊Q₈

—

136

C₂×C₄×Q₈

C₂×D₈₃

yes

characteristic

137

#500

—

166

—

138

#462

—

166

—

139

#462

—

166

—

140

C₂×#107

—

166

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

C₂×D₈₃

yes

characteristic

143

C₂×#103

—

166

—

144

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

145

#336

—

146

#332

—

166

—

147

C₂²×Q₈

—

166

—

148

C₂²×Q₈

D₃₃₂

yes

characteristic

149

C₂×Q₁₆

—

332

—

150

C₂×Q₁₆

—

332

—

151

C₂×Q₁₆

—

166

—

152

C₂²×C₈

—

153

C₂²×C₈

—

166

—

154

C₂²×C₈

C₂²⋊D₈₃

yes

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

166

—

157

C₄⋊Q₈

—

166

—

158

C₄⋊Q₈

—

166

—

159

C₄×Q₈

—

160

C₄×Q₈

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

166

—

163

C₂×C₄⋊C₄

—

166

—

164

C₂×C₄⋊C₄

D₃₃₂

yes

characteristic

165

C₂×C₄²

—

166

C₂×C₄²

C₂²×D₈₃

yes

characteristic

167

#107

—

166

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

166

—

171

#103

—

166

—

172

C₄×C₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

332

—

177

C₂×Q₈

—

332

—

178

C₂×Q₈

—

332

—

179

C₂×Q₈

—

332

—

180

C₂×Q₈

—

332

—

181

C₂×Q₈

—

166

—

182

C₂×Q₈

D₆₆₄

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

332

—

186

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

187

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

188

C₂²×C₄

#13050590

yes

characteristic

189

Q₁₆

—

332

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

332

—

195

C₂×C₈

—

332

—

196

C₂×C₈

—

166

—

197

C₂×C₈

#13050580

yes

complemented

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

332

—

201

C₄⋊C₄

—

332

—

202

C₄⋊C₄

—

166

—

203

C₄⋊C₄

—

166

—

204

C₄²

—

205

C₄²

—

206

C₄²

D₄×D₈₃

yes

—

207

C₄²

D₄×D₈₃

yes

—

208

C₂³

#14581766

yes

characteristic

209

Q₈

—

210

Q₈

—

211

Q₈

—

332

—

212

Q₈

—

332

—

213

Q₈

—

664

—

214

Q₈

—

664

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

332

—

222

C₂×C₄

—

664

—

223

C₂×C₄

—

664

—

224

C₂×C₄

#14581760

yes

characteristic

225

C₂×C₄

#14581762

yes

—

226

C₂×C₄

#14581765

yes

—

227

C₂×C₄

#14581788

yes

characteristic

228

C₂×C₄

C₂×D₆₆₄

yes

characteristic

229

C₂×C₄

C₂×#13050580

yes

—

230

C₂×C₄

#14581814

yes

characteristic

231

C₂×C₄

#14581820

yes

—

232

C₂×C₄

#14581822

yes

—

233

C₈

—

234

C₈

—

235

C₈

—

332

—

236

C₂²

#19127610

yes

characteristic

237

C₂²

#19127911

yes

—

238

C₂²

#19127937

yes

characteristic

239

C₂²

#19127954

yes

characteristic

240

C₂²

#19127976

yes

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

664

—

245

C₄

#19127837

yes

—

246

C₄

#19127848

yes

—

247

C₄

#19127856

yes

—

248

C₄

#19128080

yes

characteristic

249

C₄

#19128096

yes

characteristic

250

C₂

#24906857

yes

—

251

C₂

#24906981

yes

—

252

C₂

#24908461

yes

characteristic

253

C₂

#24908562

yes

characteristic

254

C₂

#24908584

yes

characteristic

	subgroup	G/H
center	C₂³	#14581766
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1984	C₂
socle, prime radical	C₂³×C₈₃	#121
hypercenter	#1984	D₈₃
hypocenter	C₈₃	#10265
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

subgroup

G/H

center

C₂³

#14581766

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1984

C₂

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1984

N	H ≅ G/N	type
73. C₂×C₈×C₈₃	Q₁₆	semidirect
133. C₈₃	#10265	semidirect
197. C₂×C₈	#13050580	semidirect

H ≅ G/N

type

73. C₂×C₈×C₈₃

Q₁₆

semidirect

133. C₈₃

#10265

semidirect

197. C₂×C₈

#13050580

semidirect

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

subgroup	index
C₂×#19128106	2
C₂×#19127911	2
C₂×#19127446	2
#24905298	2
C₈₃×#1984	2
#10265	83

subgroup

index

C₈₃×#1984

Subgroups — #35306939

Conjugacy classes of subgroups

Complements

Maximal subgroups