Group #31915421 — subgroups

Subgroups — #31915421

Order 18176.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#22590056	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985776	C₂	1	1	yes	maximal, characteristic, complemented
3	#22589217	C₂	1	1	yes	maximal, characteristic
4	#22589091	C₂	1	1	yes	maximal, characteristic, complemented
5	#22586446	C₂	1	1	yes	maximal, characteristic, complemented
6	#22586440	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#361×C₇₁	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556068	C₂²	1	1	yes	characteristic
9	#17986037	C₂²	1	1	yes	characteristic
10	C₂×#14556060	C₂²	1	1	yes	characteristic
11	#17986027	—	2	1	no	—
12	C₂×#14556049	—	2	1	no	—
13	C₂×#14556038	C₂²	1	1	yes	characteristic
14	#17985902	—	2	1	no	—
15	#17985800	C₄	1	4	yes	complemented
16	#17985776	—	2	2	no	—
17	#17985760	—	2	1	no	—
18	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
21	#361×C₇₁	—	2	2	no	—
22	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
23	#14556087	—	2	1	no	—
24	C₂×C₄⋊Dic₇₁	—	2	1	no	—
25	C₂×C₂²⋊Dic₇₁	—	4	2	no	—
26	C₂×C₄×Dic₇₁	D₄	1	1	yes	characteristic
27	#14556068	—	2	1	no	—
28	#14556068	—	2	1	no	—
29	C₂×C₇₁⋊C₁₆	C₂×C₄	1	2	yes	—
30	#14556062	C₂×C₄	1	2	yes	—
31	#14556060	—	2	1	no	—
32	#14556060	—	2	1	no	—
33	#14556060	—	2	1	no	—
34	Dic₇₁⋊C₈	—	4	2	no	—
35	#14556049	—	4	2	no	—
36	#14556038	—	2	1	no	—
37	#14556038	—	2	1	no	—
38	C₂²×D₄×C₇₁	—	2	1	no	—
39	C₂×D₈×C₇₁	—	2	1	no	—
40	C₂×D₈×C₇₁	—	2	1	no	—
41	C₂×D₈×C₇₁	—	2	1	no	—
42	C₂×D₈×C₇₁	—	2	1	no	—
43	C₂×D₈×C₇₁	—	2	1	no	—
44	C₂×D₈×C₇₁	C₂×C₄	1	2	yes	—
45	C₂×M₁₆×C₇₁	—	2	1	no	—
46	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
47	M₃₂×C₇₁	—	2	1	no	—
48	M₃₂×C₇₁	D₄	1	2	yes	—
49	C₂×C₁₆×C₇₁	—	2	1	no	—
50	#108×C₇₁	—	2	1	no	—
51	#108×C₇₁	—	2	1	no	—
52	C₂²×Dic₇₁	—	2	1	no	—
53	C₂²×Dic₇₁	—	4	1	no	—
54	C₂×C₇₁⋊C₈	—	2	1	no	—
55	C₂×C₇₁⋊C₈	—	2	1	no	—
56	C₂×C₇₁⋊C₈	—	2	1	no	—
57	C₄⋊Dic₇₁	—	2	2	no	—
58	C₄⋊Dic₇₁	—	4	1	no	—
59	C₄⋊Dic₇₁	—	4	1	no	—
60	C₂²⋊Dic₇₁	—	4	1	no	—
61	C₂²⋊Dic₇₁	—	8	4	no	—
62	C₄×Dic₇₁	—	2	1	no	—
63	C₄×Dic₇₁	—	2	1	no	—
64	C₄×Dic₇₁	—	4	1	no	—
65	C₇₁⋊C₁₆	—	2	2	no	—
66	C₂⁴×C₇₁	—	4	1	no	—
67	C₂×D₄×C₇₁	—	2	2	no	—
68	C₂×D₄×C₇₁	—	4	1	no	—
69	C₂×D₄×C₇₁	—	4	1	no	—
70	C₂×D₄×C₇₁	—	4	1	no	—
71	C₂×D₄×C₇₁	—	4	1	no	—
72	C₂×D₄×C₇₁	—	4	1	no	—
73	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
74	D₈×C₇₁	—	2	2	no	—
75	D₈×C₇₁	—	2	2	no	—
76	D₈×C₇₁	—	4	1	no	—
77	D₈×C₇₁	—	4	1	no	—
78	M₁₆×C₇₁	—	4	1	no	—
79	M₁₆×C₇₁	—	4	1	no	—
80	C₂×C₈×C₇₁	—	4	1	no	—
81	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
84	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
85	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
86	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
87	C₁₆×C₇₁	—	2	2	no	—
88	C₂³×C₇₁	—	4	2	no	—
89	C₂³×C₇₁	—	8	2	no	—
90	C₂³×C₇₁	—	8	2	no	—
91	C₂³×C₇₁	—	8	1	no	—
92	C₂³×C₇₁	—	8	1	no	—
93	C₂³×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
94	D₄×C₇₁	—	4	2	no	—
95	D₄×C₇₁	—	4	2	no	—
96	D₄×C₇₁	—	8	1	no	—
97	D₄×C₇₁	—	8	1	no	—
98	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
100	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
101	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
104	C₂×Dic₇₁	—	4	2	no	—
105	C₂×Dic₇₁	—	4	2	no	—
106	C₂×Dic₇₁	—	4	1	no	—
107	C₂×Dic₇₁	—	8	2	no	—
108	C₂×Dic₇₁	—	8	1	no	—
109	C₈×C₇₁	—	8	1	no	—
110	C₈×C₇₁	#117	1	1	yes	characteristic
111	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
112	C₈×C₇₁	#123	1	1	yes	characteristic
113	C₈×C₇₁	#126	1	1	yes	characteristic
114	C₇₁⋊C₈	—	4	1	no	—
115	C₂²×C₇₁	—	2	2	no	—
116	C₂²×C₇₁	—	8	4	no	—
117	C₂²×C₇₁	—	8	2	no	—
118	C₂²×C₇₁	—	16	2	no	—
119	C₂²×C₇₁	—	16	1	no	—
120	C₂²×C₇₁	—	16	1	no	—
121	C₂²×C₇₁	#442	1	1	yes	characteristic
122	C₂²×C₇₁	#468	1	1	yes	characteristic
123	C₂²×C₇₁	#490	1	1	yes	characteristic
124	C₄×C₇₁	#388	1	1	yes	characteristic
125	C₄×C₇₁	#440	1	1	yes	characteristic
126	C₄×C₇₁	#469	1	1	yes	characteristic
127	C₄×C₇₁	#489	1	1	yes	characteristic
128	Dic₇₁	—	8	1	no	—
129	Dic₇₁	—	8	2	no	—
130	Dic₇₁	—	16	1	no	—
131	#13155	—	71	1	no	maximal, Sylow
132	C₂×C₇₁	—	2	1	no	—
133	C₂×C₇₁	—	2	1	no	—
134	C₂×C₇₁	—	16	2	no	—
135	C₂×C₇₁	#1936	1	1	yes	characteristic
136	C₂×C₇₁	AGL(1,ℤ/16)	1	2	yes	—
137	C₂×#361	D₇₁	1	1	yes	characteristic
138	#2140	—	71	1	no	—
139	C₂×#347	—	71	1	no	—
140	#1972	—	71	1	no	—
141	#1946	—	71	1	no	—
142	#1386	—	71	1	no	—
143	#1383	—	71	1	no	—
144	C₇₁	#13155	1	1	yes	characteristic, complemented, Sylow
145	C₂²×D₈	C₂×D₇₁	1	1	yes	characteristic
146	C₂×M₃₂	—	71	1	no	—
147	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic
148	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
149	#427	—	71	1	no	—
150	C₂×#106	—	71	1	no	—
151	#424	—	142	1	no	—
152	C₂×#102	—	142	1	no	—
153	C₂×#97	—	71	1	no	—
154	#390	—	142	1	no	—
155	#361	—	2	2	no	—
156	#357	—	71	4	no	—
157	#347	—	142	2	no	—
158	#339	—	142	1	no	—
159	C₂²×D₄	—	2	1	no	—
160	C₂×D₈	—	2	1	no	—
161	C₂×D₈	—	2	1	no	—
162	C₂×D₈	—	2	1	no	—
163	C₂×D₈	—	2	1	no	—
164	C₂×D₈	—	2	1	no	—
165	C₂×D₈	C₄×D₇₁	1	2	yes	—
166	C₂×M₁₆	—	2	1	no	—
167	C₂²×C₈	—	71	1	no	—
168	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
169	#117	—	142	1	no	—
170	C₂×C₄⋊C₄	—	142	1	no	—
171	C₂×C₂²⋊C₄	—	284	2	no	—
172	C₂×C₄²	—	71	1	no	—
173	M₃₂	—	2	1	no	—
174	M₃₂	—	142	1	no	—
175	M₃₂	—	142	1	no	—
176	M₃₂	C₂²⋊D₇₁	1	2	yes	—
177	C₂×C₁₆	—	2	1	no	—
178	C₂×C₁₆	—	71	2	no	—
179	#108	—	2	1	no	—
180	#108	—	2	1	no	—
181	#107	—	71	2	no	—
182	#106	—	142	1	no	—
183	#106	—	142	1	no	—
184	#106	—	142	1	no	—
185	C₄⋊C₈	—	284	2	no	—
186	#102	—	284	2	no	—
187	#97	—	142	1	no	—
188	#97	—	142	1	no	—
189	C₂⁴	—	4	1	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂×D₄	—	4	1	no	—
195	C₂×D₄	—	4	1	no	—
196	C₂²×C₄	—	284	1	no	—
197	C₂²×C₄	—	142	1	no	—
198	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
199	D₈	—	2	2	no	—
200	D₈	—	2	2	no	—
201	D₈	—	4	1	no	—
202	D₈	—	4	1	no	—
203	M₁₆	—	4	1	no	—
204	M₁₆	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	142	1	no	—
207	C₂×C₈	—	142	1	no	—
208	C₂×C₈	—	142	1	no	—
209	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
210	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
211	C₂×C₈	#11765864	1	1	yes	characteristic
212	C₂×C₈	#11765864	1	1	yes	characteristic
213	C₂×C₈	#11765864	1	1	yes	characteristic
214	C₂×C₈	#11765865	1	1	yes	characteristic
215	C₄⋊C₄	—	284	1	no	—
216	C₄⋊C₄	—	284	1	no	—
217	C₄⋊C₄	—	142	2	no	—
218	C₂²⋊C₄	—	284	1	no	—
219	C₂²⋊C₄	—	568	4	no	—
220	C₄²	—	284	1	no	—
221	C₄²	—	142	1	no	—
222	C₄²	—	142	1	no	—
223	C₁₆	—	2	2	no	—
224	C₁₆	—	142	2	no	—
225	C₂³	—	4	2	no	—
226	C₂³	—	8	2	no	—
227	C₂³	—	8	2	no	—
228	C₂³	—	8	1	no	—
229	C₂³	—	8	1	no	—
230	C₂³	#14556155	1	1	yes	characteristic
231	D₄	—	4	2	no	—
232	D₄	—	4	2	no	—
233	D₄	—	8	1	no	—
234	D₄	—	8	1	no	—
235	C₂×C₄	—	284	2	no	—
236	C₂×C₄	—	284	2	no	—
237	C₂×C₄	—	284	1	no	—
238	C₂×C₄	—	568	2	no	—
239	C₂×C₄	—	568	1	no	—
240	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
241	C₂×C₄	#14556099	1	1	yes	characteristic
242	C₂×C₄	#14556114	1	1	yes	characteristic
243	C₂×C₄	#14556152	1	1	yes	characteristic
244	C₂×C₄	#14556152	1	1	yes	characteristic
245	C₂×C₄	#14556157	1	1	yes	characteristic
246	C₈	—	8	1	no	—
247	C₈	—	284	1	no	—
248	C₈	#14556084	1	1	yes	characteristic
249	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
250	C₈	#14556109	1	1	yes	characteristic
251	C₈	#14556121	1	1	yes	characteristic
252	C₂²	—	2	2	no	—
253	C₂²	—	8	4	no	—
254	C₂²	—	8	2	no	—
255	C₂²	—	16	2	no	—
256	C₂²	—	16	1	no	—
257	C₂²	—	16	1	no	—
258	C₂²	#17986108	1	1	yes	characteristic
259	C₂²	#17986242	1	1	yes	characteristic
260	C₂²	#17986362	1	1	yes	characteristic
261	C₄	—	568	1	no	—
262	C₄	—	568	2	no	—
263	C₄	—	1136	1	no	—
264	C₄	#17985887	1	1	yes	characteristic
265	C₄	#17986096	1	1	yes	characteristic
266	C₄	#17986249	1	1	yes	characteristic
267	C₄	#17986357	1	1	yes	characteristic
268	C₂	—	2	1	no	—
269	C₂	—	2	1	no	—
270	C₂	—	16	2	no	—
271	C₂	#22589034	1	1	yes	characteristic
272	C₂	#22590241	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22590056

C₂

yes

maximal, characteristic

C₂×#17985776

C₂

yes

maximal, characteristic, complemented

#22589217

C₂

yes

maximal, characteristic

#22589091

C₂

yes

maximal, characteristic, complemented

#22586446

C₂

yes

maximal, characteristic, complemented

#22586440

C₂

yes

maximal, characteristic, complemented

C₂×#361×C₇₁

C₂

yes

maximal, characteristic

C₂×#14556068

C₂²

yes

characteristic

#17986037

C₂²

yes

characteristic

C₂×#14556060

C₂²

yes

—

—

C₂²

yes

characteristic

#17985902

—

#17985800

C₄

yes

complemented

#17985776

—

#17985760

—

C₂²×D₈×C₇₁

C₂²

yes

characteristic

C₂×M₃₂×C₇₁

C₂²

yes

characteristic

C₂×#108×C₇₁

C₂²

yes

characteristic

#361×C₇₁

—

C₂²×C₇₁⋊C₈

D₄

yes

characteristic

#14556087

—

C₂×C₄⋊Dic₇₁

—

C₂×C₂²⋊Dic₇₁

—

C₂×C₄×Dic₇₁

D₄

yes

characteristic

#14556068

—

#14556068

—

C₂×C₇₁⋊C₁₆

C₂×C₄

yes

—

#14556062

C₂×C₄

yes

—

#14556060

—

#14556060

—

#14556060

—

Dic₇₁⋊C₈

—

#14556049

—

#14556038

—

#14556038

—

C₂²×D₄×C₇₁

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

—

C₂×D₈×C₇₁

C₂×C₄

yes

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

C₂³

yes

characteristic

M₃₂×C₇₁

—

M₃₂×C₇₁

D₄

yes

—

C₂×C₁₆×C₇₁

—

#108×C₇₁

—

#108×C₇₁

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂⁴×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

D₈×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₁₆×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

—

C₂³×C₇₁

AGL(1,ℤ/8)

yes

characteristic

D₄×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

#121

yes

characteristic

100

C₂×C₄×C₇₁

#124

yes

characteristic

101

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

characteristic

102

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₇₁

#137

yes

characteristic

104

C₂×Dic₇₁

—

105

C₂×Dic₇₁

—

106

C₂×Dic₇₁

—

107

C₂×Dic₇₁

—

108

C₂×Dic₇₁

—

109

C₈×C₇₁

—

110

C₈×C₇₁

#117

yes

characteristic

111

C₈×C₇₁

C₄×D₄

yes

characteristic

112

C₈×C₇₁

#123

yes

characteristic

113

C₈×C₇₁

#126

yes

characteristic

114

C₇₁⋊C₈

—

115

C₂²×C₇₁

—

116

C₂²×C₇₁

—

117

C₂²×C₇₁

—

118

C₂²×C₇₁

—

119

C₂²×C₇₁

—

120

C₂²×C₇₁

—

121

C₂²×C₇₁

#442

yes

characteristic

122

C₂²×C₇₁

#468

yes

characteristic

123

C₂²×C₇₁

#490

yes

characteristic

124

C₄×C₇₁

#388

yes

characteristic

125

C₄×C₇₁

#440

yes

characteristic

126

C₄×C₇₁

#469

yes

characteristic

127

C₄×C₇₁

#489

yes

characteristic

128

Dic₇₁

—

129

Dic₇₁

—

130

Dic₇₁

—

131

#13155

—

maximal, Sylow

132

C₂×C₇₁

—

133

C₂×C₇₁

—

134

C₂×C₇₁

—

135

C₂×C₇₁

#1936

yes

characteristic

136

C₂×C₇₁

AGL(1,ℤ/16)

yes

—

137

C₂×#361

D₇₁

yes

characteristic

138

#2140

—

139

C₂×#347

—

140

#1972

—

141

#1946

—

142

#1386

—

143

#1383

—

144

C₇₁

#13155

yes

characteristic, complemented, Sylow

145

C₂²×D₈

C₂×D₇₁

yes

characteristic

146

C₂×M₃₂

—

147

C₂×M₃₂

C₂×D₇₁

yes

characteristic

148

C₂×#108

C₂×D₇₁

yes

characteristic

149

#427

—

150

C₂×#106

—

151

#424

—

142

—

152

C₂×#102

—

142

—

153

C₂×#97

—

154

#390

—

142

—

155

#361

—

156

#357

—

157

#347

—

142

—

158

#339

—

142

—

159

C₂²×D₄

—

160

C₂×D₈

—

161

C₂×D₈

—

162

C₂×D₈

—

163

C₂×D₈

—

164

C₂×D₈

—

165

C₂×D₈

C₄×D₇₁

yes

—

166

C₂×M₁₆

—

167

C₂²×C₈

—

168

C₂²×C₈

C₂²×D₇₁

yes

characteristic

169

#117

—

142

—

170

C₂×C₄⋊C₄

—

142

—

171

C₂×C₂²⋊C₄

—

284

—

172

C₂×C₄²

—

173

M₃₂

—

174

M₃₂

—

142

—

175

M₃₂

—

142

—

176

M₃₂

C₂²⋊D₇₁

yes

—

177

C₂×C₁₆

—

178

C₂×C₁₆

—

179

#108

—

180

#108

—

181

#107

—

182

#106

—

142

—

183

#106

—

142

—

184

#106

—

142

—

185

C₄⋊C₈

—

284

—

186

#102

—

284

—

187

#97

—

142

—

188

#97

—

142

—

189

C₂⁴

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

284

—

197

C₂²×C₄

—

142

—

198

C₂²×C₄

D₄×D₇₁

yes

characteristic

199

D₈

—

200

D₈

—

201

D₈

—

202

D₈

—

203

M₁₆

—

204

M₁₆

—

205

C₂×C₈

—

206

C₂×C₈

—

142

—

207

C₂×C₈

—

142

—

208

C₂×C₈

—

142

—

209

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

210

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

211

C₂×C₈

#11765864

yes

characteristic

212

C₂×C₈

#11765864

yes

characteristic

213

C₂×C₈

#11765864

yes

characteristic

214

C₂×C₈

#11765865

yes

characteristic

215

C₄⋊C₄

—

284

—

216

C₄⋊C₄

—

284

—

217

C₄⋊C₄

—

142

—

218

C₂²⋊C₄

—

284

—

219

C₂²⋊C₄

—

568

—

220

C₄²

—

284

—

221

C₄²

—

142

—

222

C₄²

—

142

—

223

C₁₆

—

224

C₁₆

—

142

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

#14556155

yes

characteristic

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

C₂×C₄

—

284

—

236

C₂×C₄

—

284

—

237

C₂×C₄

—

284

—

238

C₂×C₄

—

568

—

239

C₂×C₄

—

568

—

240

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

characteristic

241

C₂×C₄

#14556099

yes

characteristic

242

C₂×C₄

#14556114

yes

characteristic

243

C₂×C₄

#14556152

yes

characteristic

244

C₂×C₄

#14556152

yes

characteristic

245

C₂×C₄

#14556157

yes

characteristic

246

C₈

—

247

C₈

—

284

—

248

C₈

#14556084

yes

characteristic

249

C₈

C₄×C₂²⋊D₇₁

yes

characteristic

250

C₈

#14556109

yes

characteristic

251

C₈

#14556121

yes

characteristic

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

#17986108

yes

characteristic

259

C₂²

#17986242

yes

characteristic

260

C₂²

#17986362

yes

characteristic

261

C₄

—

568

—

262

C₄

—

568

—

263

C₄

—

1136

—

264

C₄

#17985887

yes

characteristic

265

C₄

#17986096

yes

characteristic

266

C₄

#17986249

yes

characteristic

267

C₄

#17986357

yes

characteristic

268

C₂

—

269

C₂

—

270

C₂

—

271

C₂

#22589034

yes

characteristic

272

C₂

#22590241

yes

—

	subgroup	G/H
center	C₂²	#17986108
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂×#361×C₇₁	C₂
socle	C₂²×C₇₁	#442
prime radical	C₂²×D₈×C₇₁	C₂²
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂×#361	D₇₁
hypocenter	C₇₁	#13155
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#361

subgroup

G/H

center

C₂²

#17986108

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₂×#361×C₇₁

C₂

socle

C₂²×C₇₁

#442

prime radical

C₂²×D₈×C₇₁

C₂²

cosocle

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#361

N	H ≅ G/N	type
2. C₂×#17985776	C₂	semidirect
4. #22589091	C₂	semidirect
5. #22586446	C₂	semidirect
6. #22586440	C₂	semidirect
15. #17985800	C₄	semidirect
144. C₇₁	#13155	semidirect

H ≅ G/N

type

2. C₂×#17985776

C₂

semidirect

4. #22589091

C₂

semidirect

5. #22586446

C₂

semidirect

6. #22586440

C₂

semidirect

15. #17985800

C₄

semidirect

144. C₇₁

#13155

semidirect

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

subgroup	index
#22590056	2
C₂×#17985776	2
#22589217	2
#22589091	2
#22586446	2
#22586440	2
C₂×#361×C₇₁	2
#13155	71

subgroup

index

C₂×#361×C₇₁

Subgroups — #31915421

Conjugacy classes of subgroups

Complements

Maximal subgroups