Group #35306937 — subgroups

Subgroups — #35306937

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×#19127908	C₂	1	2	yes	maximal
2	#24908399	C₂	1	1	yes	maximal, characteristic
3	C₂×#19127447	C₂	1	2	yes	maximal
4	#24905298	C₂	1	1	yes	maximal, characteristic
5	C₂×#500×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13050580	—	2	2	no	—
7	C₂×C₄×Dic₁₆₆	C₂²	1	1	yes	characteristic
8	#19127908	—	2	4	no	—
9	#19127908	—	2	4	no	—
10	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
12	C₂×#14581716	—	2	2	no	—
13	#19127455	—	2	2	no	—
14	#19127447	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₈₃	C₂²	1	2	yes	—
16	#500×C₈₃	—	2	4	no	—
17	C₂×#107×C₈₃	—	2	2	no	—
18	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₆₆	D₄	1	1	yes	characteristic
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	C₂²×C₈₃⋊C₈	—	2	1	no	—
25	C₄×Dic₁₆₆	—	2	2	no	—
26	C₄×Dic₁₆₆	—	2	2	no	—
27	C₂×C₄⋊Dic₈₃	D₄	1	1	yes	characteristic
28	C₂×Dic₈₃⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₈₃	—	2	1	no	—
30	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
31	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
32	C₄⋊(C₈₃⋊C₈)	D₄	1	4	yes	—
33	#14581716	—	2	8	no	—
34	C₂²×Q₈×C₈₃	—	2	2	no	—
35	C₂²×C₈×C₈₃	D₄	1	2	yes	—
36	C₄⋊Q₈×C₈₃	—	2	2	no	—
37	C₄⋊Q₈×C₈₃	—	2	2	no	—
38	C₄⋊Q₈×C₈₃	—	2	2	no	—
39	C₄⋊Q₈×C₈₃	D₄	1	4	yes	—
40	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
42	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
43	#107×C₈₃	—	2	8	no	—
44	C₄×C₈×C₈₃	—	2	2	no	—
45	C₂×Dic₁₆₆	—	2	2	no	—
46	C₂×Dic₁₆₆	—	2	2	no	—
47	C₂×Dic₁₆₆	—	2	1	no	—
48	C₂×Dic₁₆₆	D₈	1	2	yes	—
49	C₂²×Dic₈₃	—	2	1	no	—
50	C₂²×Dic₈₃	—	2	1	no	—
51	#13050580	—	4	16	no	—
52	C₂×C₈₃⋊C₈	—	2	4	no	—
53	C₂×C₈₃⋊C₈	—	4	2	no	—
54	C₂×C₈₃⋊C₈	—	4	2	no	—
55	C₂×C₈₃⋊C₈	—	4	1	no	—
56	C₂×C₈₃⋊C₈	—	4	2	no	—
57	C₄⋊Dic₈₃	—	2	2	no	—
58	Dic₈₃⋊C₄	—	4	2	no	—
59	C₄×Dic₈₃	—	4	1	no	—
60	C₄×Dic₈₃	—	4	1	no	—
61	C₂×Q₈×C₈₃	—	2	4	no	—
62	C₂×Q₈×C₈₃	—	4	2	no	—
63	C₂×Q₈×C₈₃	—	4	2	no	—
64	C₂×Q₈×C₈₃	—	4	2	no	—
65	C₂×Q₈×C₈₃	—	4	2	no	—
66	C₂×Q₈×C₈₃	—	4	2	no	—
67	C₂²×C₄×C₈₃	—	4	2	no	—
68	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
71	C₂×C₈×C₈₃	—	2	2	no	—
72	C₂×C₈×C₈₃	—	2	2	no	—
73	C₂×C₈×C₈₃	Q₁₆	1	4	yes	complemented
74	C₄⋊C₄×C₈₃	—	2	4	no	—
75	C₄⋊C₄×C₈₃	—	2	4	no	—
76	C₄⋊C₄×C₈₃	—	4	2	no	—
77	C₄⋊C₄×C₈₃	—	4	2	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	—	4	4	no	—
82	Q₈×C₈₃	—	4	4	no	—
83	Q₈×C₈₃	—	8	2	no	—
84	Q₈×C₈₃	—	8	2	no	—
85	C₂×C₄×C₈₃	—	2	2	no	—
86	C₂×C₄×C₈₃	—	4	4	no	—
87	C₂×C₄×C₈₃	—	8	2	no	—
88	C₂×C₄×C₈₃	—	8	2	no	—
89	C₂×C₄×C₈₃	#120	1	2	yes	—
90	C₂×C₄×C₈₃	#120	1	1	yes	characteristic
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	—	2	2	no	—
99	C₂×Dic₈₃	—	4	1	no	—
100	C₂×Dic₈₃	—	4	1	no	—
101	C₂×Dic₈₃	—	4	1	no	—
102	C₂×Dic₈₃	—	4	2	no	—
103	Dic₁₆₆	—	2	4	no	—
104	Dic₁₆₆	—	4	2	no	—
105	C₈×C₈₃	—	2	4	no	—
106	C₈₃⋊C₈	—	4	4	no	—
107	C₈₃⋊C₈	—	8	1	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	—	8	4	no	—
115	C₄×C₈₃	#447	1	2	yes	—
116	C₄×C₈₃	#449	1	2	yes	—
117	C₄×C₈₃	#451	1	2	yes	—
118	C₄×C₈₃	#494	1	1	yes	characteristic
119	C₄×C₈₃	#497	1	1	yes	characteristic
120	Dic₈₃	—	4	2	no	—
121	Dic₈₃	—	8	1	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	D₈₃	1	1	yes	characteristic
129	C₂×#462	—	83	2	no	—
130	#1984	—	83	1	no	—
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	C₂×D₈₃	1	2	yes	—
136	C₂×C₄×Q₈	—	83	1	no	—
137	#500	—	2	4	no	—
138	#462	—	166	4	no	—
139	#462	—	166	4	no	—
140	C₂×#107	—	2	2	no	—
141	C₂×C₄⋊C₈	—	83	2	no	—
142	C₂×C₄⋊C₈	—	83	1	no	—
143	C₂×#103	—	166	2	no	—
144	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
145	#336	—	166	2	no	—
146	#332	—	166	4	no	—
147	C₂²×Q₈	—	2	2	no	—
148	C₂²×Q₈	—	83	1	no	—
149	C₂×Q₁₆	—	332	4	no	—
150	C₂×Q₁₆	—	332	4	no	—
151	C₂×Q₁₆	—	166	8	no	—
152	C₂²×C₈	—	166	1	no	—
153	C₂²×C₈	—	166	2	no	—
154	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
155	C₄⋊Q₈	—	2	2	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	C₂²⋊D₈₃	1	4	yes	—
159	C₄×Q₈	—	166	2	no	—
160	C₄×Q₈	—	166	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	83	1	no	—
164	C₂×C₄⋊C₄	—	166	1	no	—
165	C₂×C₄²	—	166	1	no	—
166	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
167	#107	—	2	8	no	—
168	C₄⋊C₈	—	83	4	no	—
169	C₄⋊C₈	—	166	2	no	—
170	C₄⋊C₈	—	166	2	no	—
171	#103	—	166	8	no	—
172	C₄×C₈	—	2	2	no	—
173	C₂×Q₈	—	2	4	no	—
174	C₂×Q₈	—	4	2	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	—	83	2	no	—
180	C₂×Q₈	—	166	2	no	—
181	C₂×Q₈	—	166	2	no	—
182	C₂×Q₈	—	166	1	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	—	166	1	no	—
185	C₂²×C₄	—	166	1	no	—
186	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
188	C₂²×C₄	#13050589	1	1	yes	characteristic
189	Q₁₆	—	332	16	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	332	2	no	—
193	C₂×C₈	—	332	2	no	—
194	C₂×C₈	—	332	1	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	4	no	—
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	332	2	no	—
203	C₄⋊C₄	—	166	2	no	—
204	C₄²	—	332	1	no	—
205	C₄²	—	332	1	no	—
206	C₄²	D₄×D₈₃	1	2	yes	—
207	C₄²	C₂×C₂²⋊D₈₃	1	2	yes	—
208	C₂³	#14581763	1	1	yes	characteristic
209	Q₈	—	4	4	no	—
210	Q₈	—	4	4	no	—
211	Q₈	—	8	2	no	—
212	Q₈	—	8	2	no	—
213	Q₈	—	332	2	no	—
214	Q₈	—	166	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	8	2	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	—	332	1	no	—
220	C₂×C₄	—	332	1	no	—
221	C₂×C₄	—	332	1	no	—
222	C₂×C₄	—	332	2	no	—
223	C₂×C₄	—	166	2	no	—
224	C₂×C₄	#14581760	1	2	yes	—
225	C₂×C₄	#14581761	1	1	yes	characteristic
226	C₂×C₄	#14581764	1	2	yes	—
227	C₂×C₄	#14581788	1	1	yes	characteristic
228	C₂×C₄	D₈×D₈₃	1	1	yes	characteristic
229	C₂×C₄	C₂×#13050580	1	2	yes	—
230	C₂×C₄	#14581811	1	1	yes	characteristic
231	C₂×C₄	#14581816	1	2	yes	—
232	C₂×C₄	#14581823	1	2	yes	—
233	C₈	—	2	4	no	—
234	C₈	—	332	4	no	—
235	C₈	—	664	1	no	—
236	C₂²	#19127609	1	1	yes	characteristic
237	C₂²	#19127908	1	2	yes	—
238	C₂²	#19127934	1	1	yes	characteristic
239	C₂²	#19127951	1	1	yes	characteristic
240	C₂²	#19127973	1	2	yes	—
241	C₄	—	2	2	no	—
242	C₄	—	8	4	no	—
243	C₄	—	332	2	no	—
244	C₄	—	664	1	no	—
245	C₄	#19127833	1	2	yes	—
246	C₄	#19127843	1	2	yes	—
247	C₄	#19127857	1	2	yes	—
248	C₄	#19128080	1	1	yes	characteristic
249	C₄	#19128093	1	1	yes	characteristic
250	C₂	#24906854	1	2	yes	—
251	C₂	#24906978	1	2	yes	—
252	C₂	#24908458	1	1	yes	characteristic
253	C₂	#24908563	1	1	yes	characteristic
254	C₂	#24908582	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19127908

C₂

yes

maximal

#24908399

C₂

yes

maximal, characteristic

C₂×#19127447

C₂

yes

maximal

#24905298

C₂

yes

maximal, characteristic

C₂×#500×C₈₃

C₂

yes

maximal, characteristic

C₂²×#13050580

—

C₂×C₄×Dic₁₆₆

C₂²

yes

characteristic

#19127908

—

#19127908

—

C₂×C₄⋊(C₈₃⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₈₃⋊C₈)

C₂²

yes

—

C₂×#14581716

—

#19127455

—

#19127447

—

C₂×C₄⋊Q₈×C₈₃

C₂²

yes

—

#500×C₈₃

—

C₂×#107×C₈₃

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂²×Dic₁₆₆

D₄

yes

—

—

—

C₂²×C₈₃⋊C₈

—

C₂²×C₈₃⋊C₈

—

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

—

C₂×C₄⋊Dic₈₃

D₄

yes

characteristic

C₂×Dic₈₃⋊C₄

—

C₂×C₄×Dic₈₃

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

D₄

yes

—

#14581716

—

C₂²×Q₈×C₈₃

—

C₂²×C₈×C₈₃

D₄

yes

—

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

—

C₄⋊Q₈×C₈₃

D₄

yes

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

#107×C₈₃

—

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

D₈

yes

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

#13050580

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×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

Q₁₆

yes

complemented

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

—

C₄²×C₈₃

C₂×D₄

yes

—

C₂³×C₈₃

#121

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#120

yes

—

C₂×C₄×C₈₃

#120

yes

characteristic

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

C₂×Dic₈₃

—

102

C₂×Dic₈₃

—

103

Dic₁₆₆

—

104

Dic₁₆₆

—

105

C₈×C₈₃

—

106

C₈₃⋊C₈

—

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

#447

yes

—

116

C₄×C₈₃

#449

yes

—

117

C₄×C₈₃

#451

yes

—

118

C₄×C₈₃

#494

yes

characteristic

119

C₄×C₈₃

#497

yes

characteristic

120

Dic₈₃

—

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

D₈₃

yes

characteristic

129

C₂×#462

—

130

#1984

—

131

C₂×#332

—

132

#1277

—

133

C₈₃

#10265

yes

characteristic, complemented, Sylow

134

C₂²×Q₁₆

—

166

—

135

C₂×C₄⋊Q₈

C₂×D₈₃

yes

—

136

C₂×C₄×Q₈

—

137

#500

—

138

#462

—

166

—

139

#462

—

166

—

140

C₂×#107

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

—

143

C₂×#103

—

166

—

144

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

145

#336

—

166

—

146

#332

—

166

—

147

C₂²×Q₈

—

148

C₂²×Q₈

—

149

C₂×Q₁₆

—

332

—

150

C₂×Q₁₆

—

332

—

151

C₂×Q₁₆

—

166

—

152

C₂²×C₈

—

166

—

153

C₂²×C₈

—

166

—

154

C₂²×C₈

C₂²⋊D₈₃

yes

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

C₂²⋊D₈₃

yes

—

159

C₄×Q₈

—

166

—

160

C₄×Q₈

—

166

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

166

—

165

C₂×C₄²

—

166

—

166

C₂×C₄²

C₂²×D₈₃

yes

characteristic

167

#107

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

166

—

170

C₄⋊C₈

—

166

—

171

#103

—

166

—

172

C₄×C₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

166

—

181

C₂×Q₈

—

166

—

182

C₂×Q₈

—

166

—

183

C₂²×C₄

—

184

C₂²×C₄

—

166

—

185

C₂²×C₄

—

166

—

186

C₂²×C₄

D₄×D₈₃

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

188

C₂²×C₄

#13050589

yes

characteristic

189

Q₁₆

—

332

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

332

—

193

C₂×C₈

—

332

—

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

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

332

—

203

C₄⋊C₄

—

166

—

204

C₄²

—

332

—

205

C₄²

—

332

—

206

C₄²

D₄×D₈₃

yes

—

207

C₄²

C₂×C₂²⋊D₈₃

yes

—

208

C₂³

#14581763

yes

characteristic

209

Q₈

—

210

Q₈

—

211

Q₈

—

212

Q₈

—

213

Q₈

—

332

—

214

Q₈

—

166

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

332

—

220

C₂×C₄

—

332

—

221

C₂×C₄

—

332

—

222

C₂×C₄

—

332

—

223

C₂×C₄

—

166

—

224

C₂×C₄

#14581760

yes

—

225

C₂×C₄

#14581761

yes

characteristic

226

C₂×C₄

#14581764

yes

—

227

C₂×C₄

#14581788

yes

characteristic

228

C₂×C₄

D₈×D₈₃

yes

characteristic

229

C₂×C₄

C₂×#13050580

yes

—

230

C₂×C₄

#14581811

yes

characteristic

231

C₂×C₄

#14581816

yes

—

232

C₂×C₄

#14581823

yes

—

233

C₈

—

234

C₈

—

332

—

235

C₈

—

664

—

236

C₂²

#19127609

yes

characteristic

237

C₂²

#19127908

yes

—

238

C₂²

#19127934

yes

characteristic

239

C₂²

#19127951

yes

characteristic

240

C₂²

#19127973

yes

—

241

C₄

—

242

C₄

—

243

C₄

—

332

—

244

C₄

—

664

—

245

C₄

#19127833

yes

—

246

C₄

#19127843

yes

—

247

C₄

#19127857

yes

—

248

C₄

#19128080

yes

characteristic

249

C₄

#19128093

yes

characteristic

250

C₂

#24906854

yes

—

251

C₂

#24906978

yes

—

252

C₂

#24908458

yes

characteristic

253

C₂

#24908563

yes

characteristic

254

C₂

#24908582

yes

characteristic

	subgroup	G/H
center	C₂³	#14581763
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₂×#500×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	#121
hypercenter	C₂×#500	D₈₃
hypocenter	C₈₃	#10265
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#14581763

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₂×#500×C₈₃

C₂

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

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×#19127908	2
#24908399	2
C₂×#19127447	2
#24905298	2
C₂×#500×C₈₃	2
#10265	83

subgroup

index

C₂×#500×C₈₃

Subgroups — #35306937

Conjugacy classes of subgroups

Complements

Maximal subgroups