Group #21467071 — subgroups

Subgroups — C₃₁×#10312 #21467071

Order 7936.

638 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 170 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×C₃₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#486	C₂	1	2	yes	maximal
3	C₃₁×#1957	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1956	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
8	C₃₁×#498	—	2	4	no	—
9	C₃₁×#486	—	2	4	no	—
10	C₃₁×#486	—	2	4	no	—
11	C₂×C₃₁×#106	—	2	2	no	—
12	C₂×C₃₁×#103	—	2	4	no	—
13	C₂×C₃₁×#102	—	2	4	no	—
14	C₂×C₃₁×#102	—	2	2	no	—
15	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#384	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₃₁	—	2	2	no	—
19	C₂²×D₄×C₃₁	—	2	1	no	—
20	C₂²×D₄×C₃₁	—	2	2	no	—
21	C₂²×C₈×C₃₁	D₄	1	4	yes	—
22	C₂²×C₈×C₃₁	D₄	1	2	yes	—
23	C₃₁×C₄⋊Q₈	—	2	2	no	—
24	C₃₁×C₄⋊Q₈	—	2	2	no	—
25	C₃₁×C₄⋊Q₈	—	2	2	no	—
26	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
27	C₃₁×#127	—	2	2	no	—
28	C₃₁×#127	—	2	1	no	—
29	C₃₁×#127	D₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
31	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
32	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
33	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
34	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
35	C₃₁×#106	—	2	8	no	—
36	C₃₁×#103	—	4	8	no	—
37	C₃₁×#102	—	2	16	no	—
38	C₃₁×#102	—	4	4	no	—
39	C₄×C₈×C₃₁	—	2	2	no	—
40	C₄×C₈×C₃₁	—	2	2	no	—
41	C₄×C₈×C₃₁	—	2	2	no	—
42	C₂⁴×C₃₁	—	4	1	no	—
43	C₂×Q₈×C₃₁	—	2	4	no	—
44	C₂×Q₈×C₃₁	—	4	2	no	—
45	C₂×Q₈×C₃₁	—	4	4	no	—
46	C₂×Q₈×C₃₁	—	4	4	no	—
47	C₂×D₄×C₃₁	—	2	4	no	—
48	C₂×D₄×C₃₁	—	2	2	no	—
49	C₂×D₄×C₃₁	—	4	1	no	—
50	C₂×D₄×C₃₁	—	4	2	no	—
51	C₂×D₄×C₃₁	—	4	2	no	—
52	C₂×D₄×C₃₁	—	4	4	no	—
53	C₂×D₄×C₃₁	—	4	4	no	—
54	C₂×D₄×C₃₁	—	4	2	no	—
55	C₂²×C₄×C₃₁	—	4	2	no	—
56	C₂²×C₄×C₃₁	—	4	1	no	—
57	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₃₁	—	2	2	no	—
60	C₂×C₈×C₃₁	—	2	2	no	—
61	C₂×C₈×C₃₁	—	2	4	no	—
62	C₂×C₈×C₃₁	—	2	4	no	—
63	C₂×C₈×C₃₁	—	2	4	no	—
64	C₂×C₈×C₃₁	SD₁₆	1	4	yes	—
65	C₄⋊C₄×C₃₁	—	2	4	no	—
66	C₄⋊C₄×C₃₁	—	2	4	no	—
67	C₄⋊C₄×C₃₁	—	4	2	no	—
68	C₄⋊C₄×C₃₁	—	4	2	no	—
69	C₄⋊C₄×C₃₁	—	4	2	no	—
70	C₄⋊C₄×C₃₁	—	4	4	no	—
71	C₄²×C₃₁	C₂×D₄	1	2	yes	—
72	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₃₁	#41	1	1	yes	characteristic
74	#10312	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₃₁	—	4	2	no	—
76	C₂³×C₃₁	—	8	1	no	—
77	C₂³×C₃₁	—	8	2	no	—
78	C₂³×C₃₁	—	8	2	no	—
79	C₂³×C₃₁	—	8	1	no	—
80	C₂³×C₃₁	#127	1	1	yes	characteristic
81	Q₈×C₃₁	—	4	8	no	—
82	Q₈×C₃₁	—	8	4	no	—
83	D₄×C₃₁	—	4	8	no	—
84	D₄×C₃₁	—	4	4	no	—
85	D₄×C₃₁	—	8	2	no	—
86	D₄×C₃₁	—	8	4	no	—
87	C₂×C₄×C₃₁	—	4	4	no	—
88	C₂×C₄×C₃₁	—	8	2	no	—
89	C₂×C₄×C₃₁	—	8	2	no	—
90	C₂×C₄×C₃₁	—	8	1	no	—
91	C₂×C₄×C₃₁	—	8	2	no	—
92	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
93	C₂×C₄×C₃₁	#120	1	2	yes	—
94	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
95	C₂×C₄×C₃₁	#121	1	2	yes	—
96	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
97	C₂×C₄×C₃₁	#135	1	4	yes	—
98	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
99	C₂×C₄×C₃₁	#137	1	2	yes	—
100	C₈×C₃₁	—	2	4	no	—
101	C₈×C₃₁	—	4	4	no	—
102	C₂×#498	C₂×C₃₁	1	1	yes	characteristic, complemented
103	C₂×#486	C₂×C₃₁	1	2	yes	—
104	#1957	C₂×C₃₁	1	1	yes	characteristic
105	#1956	C₂×C₃₁	1	2	yes	complemented
106	#1273	C₂×C₃₁	1	1	yes	characteristic, complemented
107	C₂²×C₃₁	—	8	4	no	—
108	C₂²×C₃₁	—	8	2	no	—
109	C₂²×C₃₁	—	16	1	no	—
110	C₂²×C₃₁	—	16	1	no	—
111	C₂²×C₃₁	—	16	2	no	—
112	C₂²×C₃₁	#392	1	1	yes	characteristic
113	C₂²×C₃₁	#492	1	1	yes	characteristic
114	C₂²×C₃₁	#495	1	2	yes	—
115	C₂²×C₃₁	#496	1	2	yes	—
116	C₂²×C₃₁	#497	1	1	yes	characteristic
117	C₄×C₃₁	—	8	4	no	—
118	C₄×C₃₁	—	16	1	no	—
119	C₄×C₃₁	#448	1	2	yes	—
120	C₄×C₃₁	#449	1	4	yes	—
121	C₄×C₃₁	#461	1	2	yes	—
122	C₄×C₃₁	#463	1	4	yes	—
123	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
124	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
125	#498	—	2	4	no	—
126	#486	—	2	4	no	—
127	#486	—	2	4	no	—
128	C₂×#106	—	2	2	no	—
129	C₂×#103	—	2	4	no	—
130	C₂×#102	—	2	4	no	—
131	C₂×#102	—	2	2	no	—
132	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
133	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
134	#384	C₂²×C₃₁	1	1	yes	characteristic
135	C₂×C₃₁	—	16	2	no	—
136	C₂×C₃₁	#1708	1	1	yes	characteristic
137	C₂×C₃₁	#1715	1	1	yes	characteristic
138	C₂×C₃₁	#1720	1	2	yes	—
139	C₂×C₃₁	#2012	1	2	yes	—
140	C₂×C₃₁	#2013	1	1	yes	characteristic
141	C₂²×Q₈	—	2	2	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	—	2	2	no	—
144	C₂²×C₈	D₄×C₃₁	1	4	yes	—
145	C₂²×C₈	D₄×C₃₁	1	2	yes	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
150	#127	—	2	2	no	—
151	#127	—	2	1	no	—
152	#127	D₄×C₃₁	1	2	yes	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
158	#106	—	2	8	no	—
159	#103	—	4	8	no	—
160	#102	—	2	16	no	—
161	#102	—	4	4	no	—
162	C₄×C₈	—	2	2	no	—
163	C₄×C₈	—	2	2	no	—
164	C₄×C₈	—	2	2	no	—
165	C₃₁	#10312	1	1	yes	characteristic, direct product factor, Sylow
166	C₂⁴	—	4	1	no	—
167	C₂×Q₈	—	2	4	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	4	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×D₄	—	2	4	no	—
172	C₂×D₄	—	2	2	no	—
173	C₂×D₄	—	4	1	no	—
174	C₂×D₄	—	4	2	no	—
175	C₂×D₄	—	4	2	no	—
176	C₂×D₄	—	4	4	no	—
177	C₂×D₄	—	4	4	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	—	4	1	no	—
181	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	2	4	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	SD₁₆×C₃₁	1	4	yes	—
189	C₄⋊C₄	—	2	4	no	—
190	C₄⋊C₄	—	2	4	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄⋊C₄	—	4	4	no	—
195	C₄²	C₂×D₄×C₃₁	1	2	yes	—
196	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
197	C₄²	#41×C₃₁	1	1	yes	characteristic
198	C₂³	—	4	2	no	—
199	C₂³	—	8	1	no	—
200	C₂³	—	8	2	no	—
201	C₂³	—	8	2	no	—
202	C₂³	—	8	1	no	—
203	C₂³	C₃₁×#127	1	1	yes	characteristic
204	Q₈	—	4	8	no	—
205	Q₈	—	8	4	no	—
206	D₄	—	4	8	no	—
207	D₄	—	4	4	no	—
208	D₄	—	8	2	no	—
209	D₄	—	8	4	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	8	2	no	—
212	C₂×C₄	—	8	2	no	—
213	C₂×C₄	—	8	1	no	—
214	C₂×C₄	—	8	2	no	—
215	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
216	C₂×C₄	C₃₁×#120	1	2	yes	—
217	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
218	C₂×C₄	C₃₁×#121	1	2	yes	—
219	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
220	C₂×C₄	C₃₁×#135	1	4	yes	—
221	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
222	C₂×C₄	C₃₁×#137	1	2	yes	—
223	C₈	—	2	4	no	—
224	C₈	—	4	4	no	—
225	C₂²	—	8	4	no	—
226	C₂²	—	8	2	no	—
227	C₂²	—	16	1	no	—
228	C₂²	—	16	1	no	—
229	C₂²	—	16	2	no	—
230	C₂²	C₃₁×#392	1	1	yes	characteristic
231	C₂²	C₃₁×#492	1	1	yes	characteristic
232	C₂²	C₃₁×#495	1	2	yes	—
233	C₂²	C₃₁×#496	1	2	yes	—
234	C₂²	C₃₁×#497	1	1	yes	characteristic
235	C₄	—	8	4	no	—
236	C₄	—	16	1	no	—
237	C₄	C₃₁×#448	1	2	yes	—
238	C₄	C₃₁×#449	1	4	yes	—
239	C₄	C₃₁×#461	1	2	yes	—
240	C₄	C₃₁×#463	1	4	yes	—
241	C₂	—	16	2	no	—
242	C₂	C₃₁×#1708	1	1	yes	characteristic
243	C₂	C₃₁×#1715	1	1	yes	characteristic
244	C₂	C₃₁×#1720	1	2	yes	—
245	C₂	C₃₁×#2012	1	2	yes	—
246	C₂	C₃₁×#2013	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃₁×#498

C₂

yes

maximal, characteristic, complemented

C₂×C₃₁×#486

C₂

yes

maximal

C₃₁×#1957

C₂

yes

maximal, characteristic

C₃₁×#1956

C₂

yes

maximal, complemented

C₃₁×#1273

C₂

yes

maximal, characteristic, complemented

C₂×C₃₁×C₄⋊Q₈

C₂²

yes

—

C₂×C₃₁×#127

C₂²

yes

characteristic

C₃₁×#498

—

C₃₁×#486

—

C₃₁×#486

—

C₂×C₃₁×#106

—

C₂×C₃₁×#103

—

C₂×C₃₁×#102

—

C₂×C₃₁×#102

—

C₂×C₄×C₈×C₃₁

C₂²

yes

—

C₂×C₄×C₈×C₃₁

C₂²

yes

characteristic

C₃₁×#384

C₂²

yes

characteristic

C₂²×Q₈×C₃₁

—

C₂²×D₄×C₃₁

—

C₂²×D₄×C₃₁

—

C₂²×C₈×C₃₁

D₄

yes

—

C₂²×C₈×C₃₁

D₄

yes

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

D₄

yes

—

C₃₁×#127

—

C₃₁×#127

—

C₃₁×#127

D₄

yes

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄²×C₃₁

C₂³

yes

characteristic

C₃₁×#106

—

C₃₁×#103

—

C₃₁×#102

—

C₃₁×#102

—

C₄×C₈×C₃₁

—

C₄×C₈×C₃₁

—

C₄×C₈×C₃₁

—

C₂⁴×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₃₁

C₂×D₄

yes

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

SD₁₆

yes

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂×D₄

yes

—

C₄²×C₃₁

C₂×D₄

yes

C₄²×C₃₁

yes

C₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

#127

yes

characteristic

Q₈×C₃₁

—

Q₈×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

#120

yes

characteristic

C₂×C₄×C₃₁

#120

yes

—

C₂×C₄×C₃₁

#121

yes

characteristic

C₂×C₄×C₃₁

#121

yes

—

C₂×C₄×C₃₁

C₂×SD₁₆

yes

—

C₂×C₄×C₃₁

#135

yes

—

C₂×C₄×C₃₁

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₃₁

#137

yes

—

100

C₈×C₃₁

—

101

C₈×C₃₁

—

102

C₂×#498

C₂×C₃₁

yes

characteristic, complemented

103

C₂×#486

C₂×C₃₁

yes

—

104

#1957

C₂×C₃₁

yes

characteristic

105

#1956

C₂×C₃₁

yes

complemented

106

#1273

C₂×C₃₁

yes

characteristic, complemented

107

C₂²×C₃₁

—

108

C₂²×C₃₁

—

109

C₂²×C₃₁

—

110

C₂²×C₃₁

—

111

C₂²×C₃₁

—

112

C₂²×C₃₁

#392

yes

characteristic

113

C₂²×C₃₁

#492

yes

characteristic

114

C₂²×C₃₁

#495

yes

—

115

C₂²×C₃₁

#496

yes

—

116

C₂²×C₃₁

#497

yes

characteristic

117

C₄×C₃₁

—

118

C₄×C₃₁

—

119

C₄×C₃₁

#448

yes

—

120

C₄×C₃₁

#449

yes

—

121

C₄×C₃₁

#461

yes

—

122

C₄×C₃₁

#463

yes

—

123

C₂×C₄⋊Q₈

C₂²×C₃₁

yes

—

124

C₂×#127

C₂²×C₃₁

yes

characteristic

125

#498

—

126

#486

—

127

#486

—

128

C₂×#106

—

129

C₂×#103

—

130

C₂×#102

—

131

C₂×#102

—

132

C₂×C₄×C₈

C₂²×C₃₁

yes

—

133

C₂×C₄×C₈

C₂²×C₃₁

yes

characteristic

134

#384

C₂²×C₃₁

yes

characteristic

135

C₂×C₃₁

—

136

C₂×C₃₁

#1708

yes

characteristic

137

C₂×C₃₁

#1715

yes

characteristic

138

C₂×C₃₁

#1720

yes

—

139

C₂×C₃₁

#2012

yes

—

140

C₂×C₃₁

#2013

yes

characteristic

141

C₂²×Q₈

—

142

C₂²×D₄

—

143

C₂²×D₄

—

144

C₂²×C₈

D₄×C₃₁

yes

—

145

C₂²×C₈

D₄×C₃₁

yes

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

D₄×C₃₁

yes

—

150

#127

—

151

#127

—

152

#127

D₄×C₃₁

yes

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄²

C₂³×C₃₁

yes

characteristic

158

#106

—

159

#103

—

160

#102

—

161

#102

—

162

C₄×C₈

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₃₁

#10312

yes

characteristic, direct product factor, Sylow

166

C₂⁴

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

C₂×D₄×C₃₁

yes

characteristic

182

C₂²×C₄

C₂×D₄×C₃₁

yes

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

SD₁₆×C₃₁

yes

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄²

C₂×D₄×C₃₁

yes

—

196

C₄²

C₂×D₄×C₃₁

yes

characteristic

197

C₄²

#41×C₃₁

yes

characteristic

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

C₃₁×#127

yes

characteristic

204

Q₈

—

205

Q₈

—

206

D₄

—

207

D₄

—

208

D₄

—

209

D₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

C₃₁×#120

yes

characteristic

216

C₂×C₄

C₃₁×#120

yes

—

217

C₂×C₄

C₃₁×#121

yes

characteristic

218

C₂×C₄

C₃₁×#121

yes

—

219

C₂×C₄

C₂×SD₁₆×C₃₁

yes

—

220

C₂×C₄

C₃₁×#135

yes

—

221

C₂×C₄

C₃₁×AGL(1,ℤ/8)

yes

—

222

C₂×C₄

C₃₁×#137

yes

—

223

C₈

—

224

C₈

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₃₁×#392

yes

characteristic

231

C₂²

C₃₁×#492

yes

characteristic

232

C₂²

C₃₁×#495

yes

—

233

C₂²

C₃₁×#496

yes

—

234

C₂²

C₃₁×#497

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

C₃₁×#448

yes

—

238

C₄

C₃₁×#449

yes

—

239

C₄

C₃₁×#461

yes

—

240

C₄

C₃₁×#463

yes

—

241

C₂

—

242

C₂

C₃₁×#1708

yes

characteristic

243

C₂

C₃₁×#1715

yes

characteristic

244

C₂

C₃₁×#1720

yes

—

245

C₂

C₃₁×#2012

yes

—

246

C₂

C₃₁×#2013

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₃₁

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₃₁

prime radical

C₂×C₃₁×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

N	H ≅ G/N	type
1. C₂×C₃₁×#498	C₂	semidirect
4. C₃₁×#1956	C₂	semidirect
5. C₃₁×#1273	C₂	semidirect
74. #10312	C₃₁	direct (N × H)
102. C₂×#498	C₂×C₃₁	semidirect
105. #1956	C₂×C₃₁	semidirect
106. #1273	C₂×C₃₁	semidirect
165. C₃₁	#10312	direct (N × H)

H ≅ G/N

type

1. C₂×C₃₁×#498

C₂

semidirect

4. C₃₁×#1956

C₂

semidirect

5. C₃₁×#1273

C₂

semidirect

74. #10312

C₃₁

direct (N × H)

102. C₂×#498

C₂×C₃₁

semidirect

105. #1956

C₂×C₃₁

semidirect

106. #1273

C₂×C₃₁

semidirect

165. C₃₁

#10312

direct (N × H)

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

subgroup	index
C₂×C₃₁×#498	2
C₂×C₃₁×#486	2
C₃₁×#1957	2
C₃₁×#1956	2
C₃₁×#1273	2
#10312	31

subgroup

index

C₂×C₃₁×#498

C₂×C₃₁×#486

C₃₁×#1957

C₃₁×#1956

C₃₁×#1273

#10312

Subgroups — C₃₁×#10312 #21467071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C31×#10312 #21467071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10312 #21467071