Group #31890407 — subgroups

Subgroups — #31890407

Order 18176.

362 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 111 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×C₈×Dic₁₄₂	C₂	1	1	yes	maximal, characteristic
2	#22587103	C₂	1	1	yes	maximal, characteristic
3	#22586683	C₂	1	2	yes	maximal
4	#22586209	C₂	1	2	yes	maximal
5	C₇₁×#1568	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₄₂	C₂²	1	1	yes	characteristic
7	C₈×Dic₁₄₂	—	2	1	no	—
8	C₈×Dic₁₄₂	—	2	1	no	—
9	C₈×Dic₁₄₂	—	2	1	no	—
10	C₈×Dic₁₄₂	—	2	1	no	—
11	#17986056	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₇₁⋊C₈	C₄	1	2	yes	—
14	C₂×C₈×Dic₇₁	C₄	1	2	yes	—
15	#17985752	—	2	1	no	—
16	#17985750	—	2	1	no	—
17	#17985724	—	2	4	no	—
18	#432×C₇₁	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	#335×C₇₁	—	2	1	no	—
21	#334×C₇₁	—	2	1	no	—
22	C₂²×Dic₁₄₂	Q₈	1	1	yes	characteristic
23	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₄₂	—	2	1	no	—
25	C₄×Dic₁₄₂	—	2	1	no	—
26	C₄×Dic₁₄₂	—	2	1	no	—
27	C₄×Dic₁₄₂	—	2	1	no	—
28	C₂×C₄⋊Dic₇₁	Q₈	1	1	yes	characteristic
29	C₂×Dic₇₁⋊C₄	D₄	1	2	yes	—
30	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
31	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
32	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
34	Dic₇₁⋊C₈	—	2	2	no	—
35	Dic₇₁⋊C₈	—	2	2	no	—
36	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
37	#14556039	—	2	2	no	—
38	C₈×Dic₇₁	—	2	2	no	—
39	C₈×Dic₇₁	—	2	2	no	—
40	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₁	—	2	2	no	—
44	C₂²⋊C₈×C₇₁	—	2	2	no	—
45	#97×C₇₁	—	2	2	no	—
46	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
48	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
49	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
50	C₂×Dic₁₄₂	—	2	1	no	—
51	C₂×Dic₁₄₂	—	2	1	no	—
52	C₂×Dic₁₄₂	—	2	4	no	—
53	C₂²×Dic₇₁	C₄⋊C₄	1	2	yes	—
54	C₂²×Dic₇₁	C₄⋊C₄	1	2	yes	—
55	C₂×C₇₁⋊C₈	—	2	2	no	—
56	C₂×C₇₁⋊C₈	—	4	2	no	—
57	C₂×C₇₁⋊C₈	—	4	2	no	—
58	C₄⋊Dic₇₁	—	2	1	no	—
59	C₄⋊Dic₇₁	—	2	1	no	—
60	Dic₇₁⋊C₄	—	2	2	no	—
61	Dic₇₁⋊C₄	—	2	2	no	—
62	C₄×Dic₇₁	—	2	2	no	—
63	C₄×Dic₇₁	—	2	2	no	—
64	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₈×C₇₁	—	2	2	no	—
68	C₂×C₈×C₇₁	—	4	1	no	—
69	C₂×C₈×C₇₁	—	4	2	no	—
70	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₁	#41	1	1	yes	characteristic
77	C₄²×C₇₁	#41	1	1	yes	characteristic
78	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₇₁	—	2	2	no	—
80	C₂×C₄×C₇₁	—	2	1	no	—
81	C₂×C₄×C₇₁	—	2	1	no	—
82	C₂×C₄×C₇₁	—	4	1	no	—
83	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
87	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×Dic₇₁	—	2	2	no	—
90	C₂×Dic₇₁	—	2	2	no	—
91	C₂×Dic₇₁	—	2	2	no	—
92	C₂×Dic₇₁	—	4	2	no	—
93	C₂×Dic₇₁	#108	1	4	yes	—
94	Dic₁₄₂	—	2	4	no	—
95	Dic₁₄₂	—	2	4	no	—
96	C₈×C₇₁	—	2	1	no	—
97	C₈×C₇₁	—	2	1	no	—
98	C₈×C₇₁	—	2	1	no	—
99	C₈×C₇₁	—	8	2	no	—
100	C₈×C₇₁	#101	1	2	yes	—
101	C₇₁⋊C₈	—	4	2	no	—
102	C₇₁⋊C₈	—	8	2	no	—
103	C₂²×C₇₁	—	2	1	no	—
104	C₂²×C₇₁	—	2	1	no	—
105	C₂²×C₇₁	#380	1	1	yes	characteristic
106	C₂²×C₇₁	C₂×#108	1	2	yes	—
107	C₄×C₇₁	—	2	1	no	—
108	C₄×C₇₁	—	2	1	no	—
109	C₄×C₇₁	—	2	1	no	—
110	C₄×C₇₁	—	2	1	no	—
111	C₄×C₇₁	—	2	1	no	—
112	C₄×C₇₁	C₂×#101	1	1	yes	characteristic
113	C₄×C₇₁	#413	1	1	yes	characteristic
114	Dic₇₁	—	2	4	no	—
115	Dic₇₁	—	4	2	no	—
116	#8623	—	71	1	no	maximal, Sylow
117	C₂×C₇₁	—	2	2	no	—
118	C₂×C₇₁	#1801	1	1	yes	characteristic
119	C₂×C₇₁	#1810	1	1	yes	characteristic
120	C₂×C₇₁	#1812	1	1	yes	characteristic
121	C₂×C₈×Q₈	—	71	1	no	—
122	#1568	—	71	1	no	—
123	#1568	D₇₁	1	1	yes	characteristic
124	#1467	—	71	2	no	—
125	#1290	—	71	2	no	—
126	C₇₁	#8623	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄×Q₈	—	71	1	no	—
128	C₈×Q₈	—	142	1	no	—
129	C₈×Q₈	—	142	1	no	—
130	C₈×Q₈	—	142	1	no	—
131	C₈×Q₈	—	142	1	no	—
132	#432	—	71	2	no	—
133	#432	C₂×D₇₁	1	2	yes	—
134	C₂×C₄⋊C₈	—	71	2	no	—
135	C₂×C₄⋊C₈	—	71	1	no	—
136	C₂×C₄×C₈	—	71	2	no	—
137	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
138	#335	—	2	1	no	—
139	#335	—	142	1	no	—
140	#334	—	2	1	no	—
141	#334	—	142	1	no	—
142	#324	—	142	4	no	—
143	C₂²×Q₈	—	71	1	no	—
144	C₂²×C₈	—	71	2	no	—
145	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
146	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
147	C₄×Q₈	—	142	1	no	—
148	C₄×Q₈	—	142	1	no	—
149	C₄×Q₈	—	142	1	no	—
150	C₄×Q₈	—	142	1	no	—
151	C₂×C₄⋊C₄	—	71	2	no	—
152	C₂×C₄⋊C₄	—	71	1	no	—
153	C₂×C₄²	—	71	2	no	—
154	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	142	2	no	—
157	C₄⋊C₈	—	142	2	no	—
158	C₄⋊C₈	—	142	1	no	—
159	C₄⋊C₈	—	142	2	no	—
160	C₄⋊C₈	—	142	1	no	—
161	C₂²⋊C₈	—	2	2	no	—
162	C₂²⋊C₈	—	142	2	no	—
163	#97	—	2	2	no	—
164	#97	—	142	2	no	—
165	C₄×C₈	—	142	2	no	—
166	C₄×C₈	—	142	2	no	—
167	C₄×C₈	D₂₈₄	1	1	yes	characteristic
168	C₄×C₈	D₂₈₄	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
170	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
171	C₂×Q₈	—	142	4	no	—
172	C₂×Q₈	—	142	1	no	—
173	C₂×Q₈	—	142	1	no	—
174	C₂²×C₄	—	71	2	no	—
175	C₂²×C₄	—	71	2	no	—
176	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
177	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
178	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	284	2	no	—
183	C₂×C₈	—	284	2	no	—
184	C₂×C₈	—	142	2	no	—
185	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
186	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
187	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
188	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄	—	142	2	no	—
190	C₄⋊C₄	—	142	2	no	—
191	C₄⋊C₄	—	142	1	no	—
192	C₄⋊C₄	—	142	1	no	—
193	C₄²	—	142	2	no	—
194	C₄²	—	142	2	no	—
195	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
196	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
197	C₄²	#11765864	1	1	yes	characteristic
198	C₄²	#11765866	1	1	yes	characteristic
199	C₂³	C₄⋊C₄×D₇₁	1	1	yes	characteristic
200	Q₈	—	142	4	no	—
201	Q₈	—	142	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	284	2	no	—
207	C₂×C₄	—	71	4	no	—
208	C₂×C₄	—	142	2	no	—
209	C₂×C₄	—	142	2	no	—
210	C₂×C₄	—	142	2	no	—
211	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
212	C₂×C₄	#14556086	1	1	yes	characteristic
213	C₂×C₄	#14556099	1	1	yes	characteristic
214	C₂×C₄	#14556103	1	1	yes	characteristic
215	C₂×C₄	#14556104	1	1	yes	characteristic
216	C₂×C₄	#14556108	1	1	yes	characteristic
217	C₈	—	2	1	no	—
218	C₈	—	2	1	no	—
219	C₈	—	2	1	no	—
220	C₈	—	8	2	no	—
221	C₈	—	284	2	no	—
222	C₈	—	568	2	no	—
223	C₈	#14556046	1	2	yes	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#17985856	1	1	yes	characteristic
227	C₂²	#108×D₇₁	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	284	2	no	—
234	C₄	—	142	4	no	—
235	C₄	C₂×#14556046	1	1	yes	characteristic
236	C₄	#17985981	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#22588333	1	1	yes	characteristic
239	C₂	#22588375	1	1	yes	characteristic
240	C₂	#22588383	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₄₂

C₂

yes

maximal, characteristic

#22587103

C₂

yes

maximal, characteristic

#22586683

C₂

yes

maximal

#22586209

C₂

yes

maximal

C₇₁×#1568

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₂

C₂²

yes

characteristic

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

—

#17986056

C₂²

yes

—

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×Dic₇₁⋊C₈

C₄

yes

—

C₂×C₈×Dic₇₁

C₄

yes

—

#17985752

—

#17985750

—

#17985724

—

#432×C₇₁

C₂²

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#335×C₇₁

—

#334×C₇₁

—

C₂²×Dic₁₄₂

Q₈

yes

characteristic

C₂²×C₇₁⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₂×C₄⋊Dic₇₁

Q₈

yes

characteristic

C₂×Dic₇₁⋊C₄

D₄

yes

—

C₂×C₄×Dic₇₁

C₂×C₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

C₂²⋊(C₇₁⋊C₈)

—

#14556039

—

C₈×Dic₇₁

—

C₈×Dic₇₁

—

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

#97×C₇₁

—

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

C₄⋊C₄

yes

—

C₂²×Dic₇₁

C₄⋊C₄

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₂³×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

#108

yes

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

100

C₈×C₇₁

#101

yes

—

101

C₇₁⋊C₈

—

102

C₇₁⋊C₈

—

103

C₂²×C₇₁

—

104

C₂²×C₇₁

—

105

C₂²×C₇₁

#380

yes

characteristic

106

C₂²×C₇₁

C₂×#108

yes

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

—

111

C₄×C₇₁

—

112

C₄×C₇₁

C₂×#101

yes

characteristic

113

C₄×C₇₁

#413

yes

characteristic

114

Dic₇₁

—

115

Dic₇₁

—

116

#8623

—

maximal, Sylow

117

C₂×C₇₁

—

118

C₂×C₇₁

#1801

yes

characteristic

119

C₂×C₇₁

#1810

yes

characteristic

120

C₂×C₇₁

#1812

yes

characteristic

121

C₂×C₈×Q₈

—

122

#1568

—

123

#1568

D₇₁

yes

characteristic

124

#1467

—

125

#1290

—

126

C₇₁

#8623

yes

characteristic, complemented, Sylow

127

C₂×C₄×Q₈

—

128

C₈×Q₈

—

142

—

129

C₈×Q₈

—

142

—

130

C₈×Q₈

—

142

—

131

C₈×Q₈

—

142

—

132

#432

—

133

#432

C₂×D₇₁

yes

—

134

C₂×C₄⋊C₈

—

135

C₂×C₄⋊C₈

—

136

C₂×C₄×C₈

—

137

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

138

#335

—

139

#335

—

142

—

140

#334

—

141

#334

—

142

—

142

#324

—

142

—

143

C₂²×Q₈

—

144

C₂²×C₈

—

145

C₂²×C₈

C₄×D₇₁

yes

characteristic

146

C₂²×C₈

C₄×D₇₁

yes

characteristic

147

C₄×Q₈

—

142

—

148

C₄×Q₈

—

142

—

149

C₄×Q₈

—

142

—

150

C₄×Q₈

—

142

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₇₁

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

142

—

157

C₄⋊C₈

—

142

—

158

C₄⋊C₈

—

142

—

159

C₄⋊C₈

—

142

—

160

C₄⋊C₈

—

142

—

161

C₂²⋊C₈

—

162

C₂²⋊C₈

—

142

—

163

#97

—

164

#97

—

142

—

165

C₄×C₈

—

142

—

166

C₄×C₈

—

142

—

167

C₄×C₈

D₂₈₄

yes

characteristic

168

C₄×C₈

D₂₈₄

yes

characteristic

169

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

170

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

171

C₂×Q₈

—

142

—

172

C₂×Q₈

—

142

—

173

C₂×Q₈

—

142

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

177

C₂²×C₄

D₄×D₇₁

yes

characteristic

178

C₂²×C₄

Q₈×D₇₁

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

284

—

183

C₂×C₈

—

284

—

184

C₂×C₈

—

142

—

185

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

186

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

187

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

188

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

189

C₄⋊C₄

—

142

—

190

C₄⋊C₄

—

142

—

191

C₄⋊C₄

—

142

—

192

C₄⋊C₄

—

142

—

193

C₄²

—

142

—

194

C₄²

—

142

—

195

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

196

C₄²

C₂×D₂₈₄

yes

characteristic

197

C₄²

#11765864

yes

characteristic

198

C₄²

#11765866

yes

characteristic

199

C₂³

C₄⋊C₄×D₇₁

yes

characteristic

200

Q₈

—

142

—

201

Q₈

—

142

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

284

—

207

C₂×C₄

—

208

C₂×C₄

—

142

—

209

C₂×C₄

—

142

—

210

C₂×C₄

—

142

—

211

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

212

C₂×C₄

#14556086

yes

characteristic

213

C₂×C₄

#14556099

yes

characteristic

214

C₂×C₄

#14556103

yes

characteristic

215

C₂×C₄

#14556104

yes

characteristic

216

C₂×C₄

#14556108

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

221

C₈

—

284

—

222

C₈

—

568

—

223

C₈

#14556046

yes

—

224

C₂²

—

225

C₂²

—

226

C₂²

#17985856

yes

characteristic

227

C₂²

#108×D₇₁

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

284

—

234

C₄

—

142

—

235

C₄

C₂×#14556046

yes

characteristic

236

C₄

#17985981

yes

characteristic

237

C₂

—

238

C₂

#22588333

yes

characteristic

239

C₂

#22588375

yes

characteristic

240

C₂

#22588383

yes

characteristic

	subgroup	G/H
center	C₂²	#17985856
commutator	C₂²×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1568	C₂
socle	C₂²×C₇₁	#380
prime radical	C₂³×C₇₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1568	D₇₁
hypocenter	C₇₁	#8623
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#17985856

commutator

C₂²×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1568

C₂

socle

C₂²×C₇₁

#380

prime radical

C₂³×C₇₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
126. C₇₁	#8623	semidirect

H ≅ G/N

type

126. C₇₁

#8623

semidirect

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

subgroup	index
C₂×C₈×Dic₁₄₂	2
#22587103	2
#22586683	2
#22586209	2
C₇₁×#1568	2
#8623	71

subgroup

index

C₂×C₈×Dic₁₄₂

C₇₁×#1568

Subgroups — #31890407

Conjugacy classes of subgroups

Complements

Maximal subgroups