Group #35303610 — subgroups

Subgroups — #35303610

Order 21248.

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

normal subgroups only

This group has 392 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	C₄×#14581728	C₂	1	1	yes	maximal, characteristic
2	#24906058	C₂	1	2	yes	maximal
3	#24905884	C₂	1	2	yes	maximal
4	#24905752	C₂	1	1	yes	maximal, characteristic
5	C₈₃×#3170	C₂	1	1	yes	maximal, characteristic
6	#19127754	C₂²	1	1	yes	characteristic
7	C₂×#14581728	—	2	1	no	—
8	C₄×#13050574	C₂²	1	2	yes	—
9	C₄×#13050574	C₂²	1	1	yes	characteristic
10	#19127466	—	2	1	no	—
11	#19127443	—	2	4	no	—
12	Q₈⋊(C₈₃⋊C₈)	—	2	4	no	—
13	#19127423	—	2	1	no	—
14	#19127422	—	2	1	no	—
15	#533×C₈₃	C₂²	1	2	yes	—
16	#500×C₈₃	C₄	1	1	yes	characteristic
17	#494×C₈₃	C₄	1	1	yes	characteristic
18	#487×C₈₃	C₄	1	2	yes	—
19	#467×C₈₃	—	2	1	no	—
20	#467×C₈₃	—	2	1	no	—
21	C₄×Q₁₆×C₈₃	—	2	1	no	—
22	C₄×Q₁₆×C₈₃	—	2	1	no	—
23	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
24	C₂×#13050574	—	2	2	no	—
25	C₂×#13050574	—	2	1	no	—
26	#14581728	—	2	4	no	—
27	C₄⋊(C₈₃⋊C₈)	D₄	1	2	yes	—
28	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
29	#14581703	—	2	2	no	—
30	#14581703	D₄	1	2	yes	—
31	C₄×C₈₃⋊C₈	—	2	1	no	—
32	C₄×C₈₃⋊C₈	—	2	1	no	—
33	C₄×C₈₃⋊C₈	—	2	2	no	—
34	C₂×Q₁₆×C₈₃	—	2	1	no	—
35	C₂×Q₁₆×C₈₃	—	2	1	no	—
36	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
38	C₄⋊Q₈×C₈₃	C₂×C₄	1	2	yes	—
39	C₄⋊Q₈×C₈₃	C₂×C₄	1	2	yes	—
40	#125×C₈₃	—	2	2	no	—
41	C₂²⋊Q₈×C₈₃	—	2	2	no	—
42	C₂²⋊Q₈×C₈₃	—	2	2	no	—
43	C₄×Q₈×C₈₃	—	2	2	no	—
44	C₄×Q₈×C₈₃	—	2	2	no	—
45	#117×C₈₃	—	2	2	no	—
46	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
47	#107×C₈₃	—	2	1	no	—
48	#107×C₈₃	—	2	1	no	—
49	#103×C₈₃	—	2	2	no	—
50	#103×C₈₃	—	2	2	no	—
51	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
54	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
55	#13050574	—	2	4	no	—
56	#13050574	—	4	2	no	—
57	#13050574	—	4	2	no	—
58	C₂×C₈₃⋊C₈	—	2	2	no	—
59	C₂×C₈₃⋊C₈	—	2	2	no	—
60	C₂×C₈₃⋊C₈	—	4	2	no	—
61	C₂×Q₈×C₈₃	—	2	2	no	—
62	C₂×Q₈×C₈₃	—	2	2	no	—
63	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
65	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
66	Q₁₆×C₈₃	—	4	2	no	—
67	Q₁₆×C₈₃	—	4	2	no	—
68	C₂×C₈×C₈₃	—	2	2	no	—
69	C₂×C₈×C₈₃	—	4	1	no	—
70	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₄⋊C₄×C₈₃	—	2	2	no	—
75	C₄⋊C₄×C₈₃	—	2	2	no	—
76	C₄⋊C₄×C₈₃	—	2	2	no	—
77	C₄⋊C₄×C₈₃	—	2	2	no	—
78	C₄⋊C₄×C₈₃	—	4	2	no	—
79	C₄⋊C₄×C₈₃	—	4	2	no	—
80	C₂²⋊C₄×C₈₃	—	4	2	no	—
81	C₄²×C₈₃	—	4	2	no	—
82	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
86	C₂³×C₈₃	#124	1	1	yes	characteristic
87	Q₈×C₈₃	—	4	2	no	—
88	Q₈×C₈₃	—	4	2	no	—
89	Q₈×C₈₃	—	4	4	no	—
90	C₂×C₄×C₈₃	—	2	1	no	—
91	C₂×C₄×C₈₃	—	2	1	no	—
92	C₂×C₄×C₈₃	—	2	2	no	—
93	C₂×C₄×C₈₃	—	2	2	no	—
94	C₂×C₄×C₈₃	—	4	2	no	—
95	C₂×C₄×C₈₃	—	4	2	no	—
96	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
100	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
101	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
102	C₈×C₈₃	—	2	1	no	—
103	C₈×C₈₃	—	2	1	no	—
104	C₈×C₈₃	—	2	1	no	—
105	C₈×C₈₃	#104	1	2	yes	—
106	C₈₃⋊C₈	—	4	2	no	—
107	C₈₃⋊C₈	—	4	4	no	—
108	C₈₃⋊C₈	—	4	2	no	—
109	C₂²×C₈₃	—	2	1	no	—
110	C₂²×C₈₃	—	2	1	no	—
111	C₂²×C₈₃	—	2	1	no	—
112	C₂²×C₈₃	#390	1	1	yes	characteristic
113	C₄×C₈₃	—	2	1	no	—
114	C₄×C₈₃	—	2	1	no	—
115	C₄×C₈₃	—	2	1	no	—
116	C₄×C₈₃	—	8	2	no	—
117	C₄×C₈₃	—	8	2	no	—
118	C₄×C₈₃	C₂×#104	1	1	yes	characteristic
119	C₄×C₈₃	#421	1	1	yes	characteristic
120	C₄×C₈₃	#444	1	2	yes	—
121	C₄×C₈₃	#473	1	2	yes	—
122	#9727	—	83	1	no	maximal, Sylow
123	C₂×C₈₃	—	4	1	no	—
124	C₂×C₈₃	#1975	1	1	yes	characteristic
125	C₂×C₈₃	#1979	1	1	yes	characteristic
126	C₂×C₈₃	#1980	1	1	yes	characteristic
127	#3170	D₈₃	1	1	yes	characteristic
128	C₄×#108	—	83	1	no	—
129	#1526	—	83	2	no	—
130	#1485	—	83	2	no	—
131	#1451	—	83	1	no	—
132	C₈₃	#9727	1	1	yes	characteristic, complemented, Sylow
133	#533	C₂×D₈₃	1	2	yes	—
134	#500	Dic₈₃	1	1	yes	characteristic
135	#494	Dic₈₃	1	1	yes	characteristic
136	#487	Dic₈₃	1	2	yes	—
137	#467	—	2	1	no	—
138	#467	—	2	1	no	—
139	C₄×Q₁₆	—	2	1	no	—
140	C₄×Q₁₆	—	2	1	no	—
141	#431	—	83	1	no	—
142	C₂×#108	—	166	1	no	—
143	C₄×M₁₆	—	83	1	no	—
144	C₄×M₁₆	—	83	2	no	—
145	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
146	#341	—	166	1	no	—
147	#330	—	166	4	no	—
148	Q₈⋊C₈	—	166	4	no	—
149	#322	—	166	1	no	—
150	#322	—	166	1	no	—
151	C₂×Q₁₆	—	2	1	no	—
152	C₂×Q₁₆	—	2	1	no	—
153	C₂×M₁₆	—	166	2	no	—
154	C₂×M₁₆	—	166	1	no	—
155	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
156	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
157	C₄⋊Q₈	C₂×Dic₈₃	1	2	yes	—
158	C₄⋊Q₈	C₂×Dic₈₃	1	2	yes	—
159	#125	—	2	2	no	—
160	C₂²⋊Q₈	—	2	2	no	—
161	C₂²⋊Q₈	—	2	2	no	—
162	C₄×Q₈	—	2	2	no	—
163	C₄×Q₈	—	2	2	no	—
164	#117	—	2	2	no	—
165	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
166	#108	—	166	4	no	—
167	#107	—	2	1	no	—
168	#107	—	2	1	no	—
169	C₄⋊C₈	—	83	2	no	—
170	#103	—	2	2	no	—
171	#103	—	2	2	no	—
172	C₂²⋊C₈	—	166	1	no	—
173	#97	—	83	2	no	—
174	#97	—	166	2	no	—
175	C₄×C₈	—	166	2	no	—
176	C₄×C₈	—	166	1	no	—
177	C₄×C₈	—	166	1	no	—
178	C₄×C₈	C₂×Dic₈₃	1	1	yes	characteristic
179	C₄×C₈	C₂×Dic₈₃	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
181	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	2	no	—
184	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
185	C₂²×C₄	#13050589	1	1	yes	characteristic
186	C₂²×C₄	#13050589	1	1	yes	characteristic
187	Q₁₆	—	4	2	no	—
188	Q₁₆	—	4	2	no	—
189	M₁₆	—	332	2	no	—
190	M₁₆	—	332	2	no	—
191	M₁₆	—	166	4	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	332	2	no	—
195	C₂×C₈	—	166	2	no	—
196	C₂×C₈	—	166	2	no	—
197	C₂×C₈	C₂²⋊Dic₈₃	1	1	yes	characteristic
198	C₂×C₈	C₂²⋊Dic₈₃	1	1	yes	characteristic
199	C₂×C₈	C₂²⋊Dic₈₃	1	1	yes	characteristic
200	C₂×C₈	C₂²⋊Dic₈₃	1	1	yes	characteristic
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₄²	—	4	2	no	—
209	C₄²	C₂²×Dic₈₃	1	1	yes	characteristic
210	C₄²	D₄×D₈₃	1	1	yes	characteristic
211	C₄²	D₄×D₈₃	1	1	yes	characteristic
212	C₄²	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
213	C₂³	#14581779	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	2	no	—
216	Q₈	—	4	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
224	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
225	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
226	C₂×C₄	#14581763	1	1	yes	characteristic
227	C₂×C₄	#14581763	1	1	yes	characteristic
228	C₂×C₄	#14581788	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	332	4	no	—
233	C₈	—	332	2	no	—
234	C₈	—	332	2	no	—
235	C₈	#14581719	1	2	yes	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#19127604	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	8	2	no	—
244	C₄	—	8	2	no	—
245	C₄	C₂×#14581719	1	1	yes	characteristic
246	C₄	#19127718	1	1	yes	characteristic
247	C₄	#19127823	1	2	yes	—
248	C₄	#19127973	1	2	yes	—
249	C₂	—	4	1	no	—
250	C₂	#24908357	1	1	yes	characteristic
251	C₂	#24908379	1	1	yes	characteristic
252	C₂	#24908383	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#14581728

C₂

yes

maximal, characteristic

#24906058

C₂

yes

maximal

#24905884

C₂

yes

maximal

#24905752

C₂

yes

maximal, characteristic

C₈₃×#3170

C₂

yes

maximal, characteristic

#19127754

C₂²

yes

characteristic

C₂×#14581728

—

C₄×#13050574

C₂²

yes

—

C₄×#13050574

C₂²

yes

characteristic

#19127466

—

#19127443

—

Q₈⋊(C₈₃⋊C₈)

—

#19127423

—

#19127422

—

#533×C₈₃

C₂²

yes

—

#500×C₈₃

C₄

yes

characteristic

#494×C₈₃

C₄

yes

characteristic

#487×C₈₃

C₄

yes

—

#467×C₈₃

—

#467×C₈₃

—

C₄×Q₁₆×C₈₃

—

C₄×Q₁₆×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

—

—

—

C₄⋊(C₈₃⋊C₈)

D₄

yes

—

C₂²⋊(C₈₃⋊C₈)

—

#14581703

—

#14581703

D₄

yes

—

C₄×C₈₃⋊C₈

—

C₄×C₈₃⋊C₈

—

C₄×C₈₃⋊C₈

—

C₂×Q₁₆×C₈₃

—

C₂×Q₁₆×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₄⋊Q₈×C₈₃

C₂×C₄

yes

—

C₄⋊Q₈×C₈₃

C₂×C₄

yes

—

#125×C₈₃

—

C₂²⋊Q₈×C₈₃

—

C₂²⋊Q₈×C₈₃

—

C₄×Q₈×C₈₃

—

C₄×Q₈×C₈₃

—

#117×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

#107×C₈₃

—

#107×C₈₃

—

#103×C₈₃

—

#103×C₈₃

—

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

characteristic

C₄×C₈×C₈₃

D₄

yes

—

—

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

C₂²×C₄×C₈₃

yes

C₂²×C₄×C₈₃

yes

Q₁₆×C₈₃

—

Q₁₆×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₄²×C₈₃

C₂×D₄

yes

characteristic

C₂³×C₈₃

#124

yes

characteristic

Q₈×C₈₃

—

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

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

characteristic

C₂×C₄×C₈₃

C₄×D₄

yes

characteristic

C₂×C₄×C₈₃

#121

yes

characteristic

100

C₂×C₄×C₈₃

#121

yes

characteristic

101

C₂×C₄×C₈₃

#127

yes

characteristic

102

C₈×C₈₃

—

103

C₈×C₈₃

—

104

C₈×C₈₃

—

105

C₈×C₈₃

#104

yes

—

106

C₈₃⋊C₈

—

107

C₈₃⋊C₈

—

108

C₈₃⋊C₈

—

109

C₂²×C₈₃

—

110

C₂²×C₈₃

—

111

C₂²×C₈₃

—

112

C₂²×C₈₃

#390

yes

characteristic

113

C₄×C₈₃

—

114

C₄×C₈₃

—

115

C₄×C₈₃

—

116

C₄×C₈₃

—

117

C₄×C₈₃

—

118

C₄×C₈₃

C₂×#104

yes

characteristic

119

C₄×C₈₃

#421

yes

characteristic

120

C₄×C₈₃

#444

yes

—

121

C₄×C₈₃

#473

yes

—

122

#9727

—

maximal, Sylow

123

C₂×C₈₃

—

124

C₂×C₈₃

#1975

yes

characteristic

125

C₂×C₈₃

#1979

yes

characteristic

126

C₂×C₈₃

#1980

yes

characteristic

127

#3170

D₈₃

yes

characteristic

128

C₄×#108

—

129

#1526

—

130

#1485

—

131

#1451

—

132

C₈₃

#9727

yes

characteristic, complemented, Sylow

133

#533

C₂×D₈₃

yes

—

134

#500

Dic₈₃

yes

characteristic

135

#494

Dic₈₃

yes

characteristic

136

#487

Dic₈₃

yes

—

137

#467

—

138

#467

—

139

C₄×Q₁₆

—

140

C₄×Q₁₆

—

141

#431

—

142

C₂×#108

—

166

—

143

C₄×M₁₆

—

144

C₄×M₁₆

—

145

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

146

#341

—

166

—

147

#330

—

166

—

148

Q₈⋊C₈

—

166

—

149

#322

—

166

—

150

#322

—

166

—

151

C₂×Q₁₆

—

152

C₂×Q₁₆

—

153

C₂×M₁₆

—

166

—

154

C₂×M₁₆

—

166

—

155

C₂²×C₈

C₂²⋊D₈₃

yes

characteristic

156

C₂²×C₈

C₂²⋊D₈₃

yes

characteristic

157

C₄⋊Q₈

C₂×Dic₈₃

yes

—

158

C₄⋊Q₈

C₂×Dic₈₃

yes

—

159

#125

—

160

C₂²⋊Q₈

—

161

C₂²⋊Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

#117

—

165

C₂×C₄²

C₂²×D₈₃

yes

characteristic

166

#108

—

166

—

167

#107

—

168

#107

—

169

C₄⋊C₈

—

170

#103

—

171

#103

—

172

C₂²⋊C₈

—

166

—

173

#97

—

174

#97

—

166

—

175

C₄×C₈

—

166

—

176

C₄×C₈

—

166

—

177

C₄×C₈

—

166

—

178

C₄×C₈

C₂×Dic₈₃

yes

characteristic

179

C₄×C₈

C₂×Dic₈₃

yes

characteristic

180

C₄×C₈

C₂²⋊D₈₃

yes

characteristic

181

C₄×C₈

C₂²⋊D₈₃

yes

characteristic

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

185

C₂²×C₄

#13050589

yes

characteristic

186

C₂²×C₄

#13050589

yes

characteristic

187

Q₁₆

—

188

Q₁₆

—

189

M₁₆

—

332

—

190

M₁₆

—

332

—

191

M₁₆

—

166

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

332

—

195

C₂×C₈

—

166

—

196

C₂×C₈

—

166

—

197

C₂×C₈

C₂²⋊Dic₈₃

yes

characteristic

198

C₂×C₈

C₂²⋊Dic₈₃

yes

characteristic

199

C₂×C₈

C₂²⋊Dic₈₃

yes

characteristic

200

C₂×C₈

C₂²⋊Dic₈₃

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₄²

C₂²×Dic₈₃

yes

characteristic

210

C₄²

D₄×D₈₃

yes

characteristic

211

C₄²

D₄×D₈₃

yes

characteristic

212

C₄²

C₂×C₂²⋊D₈₃

yes

characteristic

213

C₂³

#14581779

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

C₂×C₂²⋊Dic₈₃

yes

characteristic

224

C₂×C₄

D₄×Dic₈₃

yes

characteristic

225

C₂×C₄

D₄×Dic₈₃

yes

characteristic

226

C₂×C₄

#14581763

yes

characteristic

227

C₂×C₄

#14581763

yes

characteristic

228

C₂×C₄

#14581788

yes

characteristic

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

332

—

233

C₈

—

332

—

234

C₈

—

332

—

235

C₈

#14581719

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#19127604

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

C₂×#14581719

yes

characteristic

246

C₄

#19127718

yes

characteristic

247

C₄

#19127823

yes

—

248

C₄

#19127973

yes

—

249

C₂

—

250

C₂

#24908357

yes

characteristic

251

C₂

#24908379

yes

characteristic

252

C₂

#24908383

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14581763
commutator	C₄²×C₈₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#3170	C₂
socle	C₂²×C₈₃	#390
prime radical	C₂³×C₈₃	#124
cosocle	C₂×C₄²×C₈₃	C₂³
hypercenter	#3170	D₈₃
hypocenter	C₈₃	#9727
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#14581763

commutator

C₄²×C₈₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#3170

C₂

C₂²×C₈₃

C₂³×C₈₃

C₂×C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
132. C₈₃	#9727	semidirect

H ≅ G/N

type

132. C₈₃

#9727

semidirect

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

subgroup	index
C₄×#14581728	2
#24906058	2
#24905884	2
#24905752	2
C₈₃×#3170	2
#9727	83

subgroup

index

C₈₃×#3170

Subgroups — #35303610

Conjugacy classes of subgroups

Complements

Maximal subgroups