Group #31914195 — subgroups

Subgroups — #31914195

Order 18176.

396 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 107 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×#17986105	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985814	C₂	1	1	yes	maximal, characteristic
3	#22590061	C₂	1	1	yes	maximal, characteristic
4	#22589091	C₂	1	1	yes	maximal, characteristic
5	#22586447	C₂	1	1	yes	maximal, characteristic
6	#22586419	C₂	1	1	yes	maximal, characteristic
7	C₂×#365×C₇₁	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₈₄	C₂²	1	1	yes	characteristic
9	C₂×#14556093	—	2	1	no	—
10	C₂×#14556068	C₂²	1	1	yes	characteristic
11	#17986105	—	2	2	no	—
12	#17986105	—	2	2	no	—
13	#17986037	C₂²	1	1	yes	characteristic
14	#17986027	—	2	1	no	—
15	C₂×#14556051	—	2	1	no	—
16	C₂×#14556038	C₂²	1	1	yes	characteristic
17	#17985814	—	2	2	no	—
18	#17985804	C₄	1	4	yes	complemented
19	#17985760	—	2	1	no	—
20	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
23	#365×C₇₁	—	2	2	no	—
24	C₂²×Dic₁₄₂	—	2	1	no	—
25	C₂×Dic₂₈₄	—	2	1	no	—
26	C₂×Dic₂₈₄	—	2	1	no	—
27	C₂×Dic₂₈₄	—	2	1	no	—
28	C₂×Dic₂₈₄	C₂×C₄	1	2	yes	—
29	C₂×Dic₂₈₄	D₄	1	2	yes	—
30	C₂×Dic₂₈₄	Q₈	1	2	yes	—
31	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
32	#14556093	—	2	4	no	—
33	#14556093	—	4	2	no	—
34	#14556087	—	2	1	no	—
35	C₂×Dic₇₁⋊C₄	—	4	1	no	—
36	C₂×C₄×Dic₇₁	—	4	1	no	—
37	C₂×C₄×Dic₇₁	D₄	1	1	yes	characteristic
38	#14556068	—	2	1	no	—
39	#14556068	—	2	1	no	—
40	C₂×C₇₁⋊C₁₆	—	2	1	no	—
41	#14556062	C₂×C₄	1	2	yes	—
42	#14556060	—	2	1	no	—
43	Dic₇₁⋊C₈	—	4	2	no	—
44	#14556051	—	2	4	no	—
45	#14556038	—	2	1	no	—
46	#14556038	—	2	1	no	—
47	C₂×M₁₆×C₇₁	—	2	1	no	—
48	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
50	M₃₂×C₇₁	—	2	1	no	—
51	M₃₂×C₇₁	—	2	1	no	—
52	C₂×C₁₆×C₇₁	C₂×C₄	1	2	yes	—
53	#108×C₇₁	—	2	1	no	—
54	#108×C₇₁	—	2	1	no	—
55	#106×C₇₁	—	2	1	no	—
56	#106×C₇₁	D₄	1	2	yes	—
57	C₂×Dic₁₄₂	—	2	2	no	—
58	C₂×Dic₁₄₂	—	2	2	no	—
59	C₂×Dic₁₄₂	—	2	2	no	—
60	C₂×Dic₁₄₂	—	4	1	no	—
61	C₂×Dic₁₄₂	—	4	1	no	—
62	C₂×Dic₁₄₂	—	4	1	no	—
63	C₂²×Dic₇₁	—	2	1	no	—
64	C₂²×Dic₇₁	—	4	1	no	—
65	Dic₂₈₄	—	2	2	no	—
66	Dic₂₈₄	—	2	2	no	—
67	Dic₂₈₄	—	2	2	no	—
68	Dic₂₈₄	C₄⋊C₄	1	4	yes	—
69	C₂×C₇₁⋊C₈	—	2	1	no	—
70	C₂×C₇₁⋊C₈	—	2	1	no	—
71	C₂×C₇₁⋊C₈	—	2	1	no	—
72	C₄⋊Dic₇₁	—	2	2	no	—
73	Dic₇₁⋊C₄	—	4	4	no	—
74	C₂²⋊Dic₇₁	—	4	1	no	—
75	C₄×Dic₇₁	—	2	1	no	—
76	C₄×Dic₇₁	—	4	4	no	—
77	C₄×Dic₇₁	—	4	1	no	—
78	C₄×Dic₇₁	SD₁₆	1	2	yes	—
79	C₇₁⋊C₁₆	—	4	1	no	—
80	C₂²×C₄×C₇₁	—	4	1	no	—
81	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
82	M₁₆×C₇₁	—	4	1	no	—
83	M₁₆×C₇₁	—	4	1	no	—
84	C₂×C₈×C₇₁	—	4	1	no	—
85	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
87	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
90	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
91	C₄⋊C₄×C₇₁	—	2	2	no	—
92	C₄⋊C₄×C₇₁	—	4	1	no	—
93	C₁₆×C₇₁	—	2	2	no	—
94	C₂³×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₇₁	—	4	2	no	—
96	C₂×C₄×C₇₁	—	8	2	no	—
97	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
99	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
102	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×Dic₇₁	—	2	2	no	—
104	C₂×Dic₇₁	—	4	2	no	—
105	C₂×Dic₇₁	—	4	2	no	—
106	C₂×Dic₇₁	—	4	2	no	—
107	C₂×Dic₇₁	—	4	2	no	—
108	C₂×Dic₇₁	—	4	2	no	—
109	Dic₁₄₂	—	2	4	no	—
110	Dic₁₄₂	—	4	2	no	—
111	Dic₁₄₂	—	4	2	no	—
112	Dic₁₄₂	—	4	2	no	—
113	C₈×C₇₁	—	8	1	no	—
114	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
116	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
117	C₈×C₇₁	#123	1	1	yes	characteristic
118	C₇₁⋊C₈	—	4	1	no	—
119	C₂²×C₇₁	—	2	2	no	—
120	C₂²×C₇₁	#442	1	1	yes	characteristic
121	C₂²×C₇₁	#450	1	1	yes	characteristic
122	C₂²×C₇₁	#478	1	1	yes	characteristic
123	C₄×C₇₁	—	8	2	no	—
124	C₄×C₇₁	#385	1	1	yes	characteristic
125	C₄×C₇₁	C₄×SD₁₆	1	1	yes	characteristic
126	C₄×C₇₁	#449	1	1	yes	characteristic
127	C₄×C₇₁	#476	1	1	yes	characteristic
128	Dic₇₁	—	4	2	no	—
129	Dic₇₁	—	4	4	no	—
130	Dic₇₁	—	8	2	no	—
131	#12957	—	71	1	no	maximal, Sylow
132	C₂×C₇₁	—	2	1	no	—
133	C₂×C₇₁	—	2	1	no	—
134	C₂×C₇₁	#1864	1	1	yes	characteristic
135	C₂×C₇₁	#2180	1	2	yes	—
136	C₂×#441	—	71	1	no	—
137	C₂×#365	D₇₁	1	1	yes	characteristic
138	C₂×#362	—	71	1	no	—
139	#2141	—	71	1	no	—
140	#1946	—	71	1	no	—
141	#1386	—	71	1	no	—
142	#1375	—	71	1	no	—
143	C₇₁	#12957	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₁₆	—	71	1	no	—
145	C₂×C₄×Q₈	—	142	1	no	—
146	C₂×M₃₂	—	71	1	no	—
147	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic
148	#441	—	142	2	no	—
149	#441	—	142	2	no	—
150	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
151	#427	—	71	1	no	—
152	C₂×#106	C₂×D₇₁	1	1	yes	characteristic
153	#424	—	142	1	no	—
154	C₂×#103	—	142	1	no	—
155	C₂×#97	—	71	1	no	—
156	#365	—	2	2	no	—
157	#362	—	142	2	no	—
158	#358	—	71	4	no	—
159	#339	—	142	1	no	—
160	C₂²×Q₈	—	142	1	no	—
161	C₂×Q₁₆	—	71	2	no	—
162	C₂×Q₁₆	—	71	2	no	—
163	C₂×Q₁₆	—	71	2	no	—
164	C₂×Q₁₆	—	142	1	no	—
165	C₂×Q₁₆	—	142	1	no	—
166	C₂×Q₁₆	—	142	1	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂²×C₈	—	71	1	no	—
169	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
170	C₄×Q₈	—	284	2	no	—
171	C₄×Q₈	—	142	4	no	—
172	#117	—	142	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	284	1	no	—
175	C₂×C₄²	—	284	1	no	—
176	C₂×C₄²	—	71	1	no	—
177	M₃₂	—	2	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	142	1	no	—
180	M₃₂	—	142	1	no	—
181	C₂×C₁₆	—	142	1	no	—
182	C₂×C₁₆	C₄×D₇₁	1	2	yes	—
183	#108	—	2	1	no	—
184	#108	—	2	1	no	—
185	#107	—	71	2	no	—
186	#106	—	2	1	no	—
187	#106	—	142	1	no	—
188	#106	C₂²⋊D₇₁	1	2	yes	—
189	C₄⋊C₈	—	284	2	no	—
190	#103	—	142	4	no	—
191	#97	—	142	1	no	—
192	#97	—	142	1	no	—
193	C₂×Q₈	—	284	1	no	—
194	C₂×Q₈	—	284	1	no	—
195	C₂×Q₈	—	284	1	no	—
196	C₂×Q₈	—	142	2	no	—
197	C₂×Q₈	—	142	2	no	—
198	C₂×Q₈	—	142	2	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	284	1	no	—
201	C₂²×C₄	—	142	1	no	—
202	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
203	Q₁₆	—	71	4	no	—
204	Q₁₆	—	142	2	no	—
205	Q₁₆	—	142	2	no	—
206	Q₁₆	—	142	2	no	—
207	M₁₆	—	4	1	no	—
208	M₁₆	—	4	1	no	—
209	C₂×C₈	—	4	1	no	—
210	C₂×C₈	—	142	1	no	—
211	C₂×C₈	—	142	1	no	—
212	C₂×C₈	—	142	1	no	—
213	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
214	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
215	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
216	C₂×C₈	Q₈×D₇₁	1	1	yes	characteristic
217	C₂×C₈	#11765865	1	1	yes	characteristic
218	C₂×C₈	#11765866	1	1	yes	characteristic
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	284	4	no	—
222	C₄⋊C₄	—	142	2	no	—
223	C₂²⋊C₄	—	284	1	no	—
224	C₄²	—	284	4	no	—
225	C₄²	—	284	1	no	—
226	C₄²	—	71	2	no	—
227	C₄²	—	142	1	no	—
228	C₁₆	—	2	2	no	—
229	C₁₆	—	284	1	no	—
230	C₂³	#14556155	1	1	yes	characteristic
231	Q₈	—	284	2	no	—
232	Q₈	—	284	2	no	—
233	Q₈	—	284	2	no	—
234	Q₈	—	142	4	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	8	2	no	—
237	C₂×C₄	—	284	2	no	—
238	C₂×C₄	—	284	2	no	—
239	C₂×C₄	—	284	2	no	—
240	C₂×C₄	—	284	2	no	—
241	C₂×C₄	—	284	2	no	—
242	C₂×C₄	—	142	2	no	—
243	C₂×C₄	#14556090	1	1	yes	characteristic
244	C₂×C₄	#14556096	1	1	yes	characteristic
245	C₂×C₄	#14556106	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₇₁	1	1	yes	characteristic
247	C₂×C₄	#14556149	1	1	yes	characteristic
248	C₂×C₄	#14556155	1	1	yes	characteristic
249	C₈	—	8	1	no	—
250	C₈	—	284	1	no	—
251	C₈	C₄⋊C₄×D₇₁	1	1	yes	characteristic
252	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
253	C₈	#14556104	1	1	yes	characteristic
254	C₈	#14556113	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	#17986110	1	1	yes	characteristic
257	C₂²	#17986148	1	1	yes	characteristic
258	C₂²	#17986298	1	1	yes	characteristic
259	C₄	—	8	2	no	—
260	C₄	—	284	2	no	—
261	C₄	—	284	4	no	—
262	C₄	—	568	2	no	—
263	C₄	#17985870	1	1	yes	characteristic
264	C₄	#17986086	1	1	yes	characteristic
265	C₄	#17986143	1	1	yes	characteristic
266	C₄	#17986288	1	1	yes	characteristic
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	#22588598	1	1	yes	characteristic
270	C₂	#22590230	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986105

C₂

yes

maximal, characteristic

C₂×#17985814

C₂

yes

maximal, characteristic

#22590061

C₂

yes

maximal, characteristic

#22589091

C₂

yes

maximal, characteristic

#22586447

C₂

yes

maximal, characteristic

#22586419

C₂

yes

maximal, characteristic

C₂×#365×C₇₁

C₂

yes

maximal, characteristic

C₂²×Dic₂₈₄

C₂²

yes

characteristic

C₂×#14556093

—

C₂×#14556068

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

characteristic

#17985814

—

#17985804

C₄

yes

complemented

#17985760

—

C₂×M₃₂×C₇₁

C₂²

yes

characteristic

C₂×#108×C₇₁

C₂²

yes

characteristic

C₂×#106×C₇₁

C₂²

yes

characteristic

#365×C₇₁

—

C₂²×Dic₁₄₂

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂×C₄

yes

—

C₂×Dic₂₈₄

D₄

yes

—

C₂×Dic₂₈₄

Q₈

yes

—

C₂²×C₇₁⋊C₈

D₄

yes

—

—

—

C₂×Dic₇₁⋊C₄

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

D₄

yes

characteristic

#14556068

—

#14556068

—

C₂×C₇₁⋊C₁₆

—

#14556062

C₂×C₄

yes

—

#14556060

—

Dic₇₁⋊C₈

—

#14556051

—

#14556038

—

#14556038

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₁

—

M₃₂×C₇₁

—

M₃₂×C₇₁

—

C₂×C₁₆×C₇₁

C₂×C₄

yes

—

#108×C₇₁

—

#108×C₇₁

—

#106×C₇₁

—

#106×C₇₁

D₄

yes

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

C₄⋊C₄

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

SD₁₆

yes

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×Q₈

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₁₆×C₇₁

—

C₂³×C₇₁

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

#120

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

100

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₇₁

#135

yes

characteristic

102

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

characteristic

103

C₂×Dic₇₁

—

104

C₂×Dic₇₁

—

105

C₂×Dic₇₁

—

106

C₂×Dic₇₁

—

107

C₂×Dic₇₁

—

108

C₂×Dic₇₁

—

109

Dic₁₄₂

—

110

Dic₁₄₂

—

111

Dic₁₄₂

—

112

Dic₁₄₂

—

113

C₈×C₇₁

—

114

C₈×C₇₁

C₂×C₄⋊C₄

yes

characteristic

115

C₈×C₇₁

C₄×D₄

yes

characteristic

116

C₈×C₇₁

C₂²⋊Q₈

yes

characteristic

117

C₈×C₇₁

#123

yes

characteristic

118

C₇₁⋊C₈

—

119

C₂²×C₇₁

—

120

C₂²×C₇₁

#442

yes

characteristic

121

C₂²×C₇₁

#450

yes

characteristic

122

C₂²×C₇₁

#478

yes

characteristic

123

C₄×C₇₁

—

124

C₄×C₇₁

#385

yes

characteristic

125

C₄×C₇₁

C₄×SD₁₆

yes

characteristic

126

C₄×C₇₁

#449

yes

characteristic

127

C₄×C₇₁

#476

yes

characteristic

128

Dic₇₁

—

129

Dic₇₁

—

130

Dic₇₁

—

131

#12957

—

maximal, Sylow

132

C₂×C₇₁

—

133

C₂×C₇₁

—

134

C₂×C₇₁

#1864

yes

characteristic

135

C₂×C₇₁

#2180

yes

—

136

C₂×#441

—

137

C₂×#365

D₇₁

yes

characteristic

138

C₂×#362

—

139

#2141

—

140

#1946

—

141

#1386

—

142

#1375

—

143

C₇₁

#12957

yes

characteristic, complemented, Sylow

144

C₂²×Q₁₆

—

145

C₂×C₄×Q₈

—

142

—

146

C₂×M₃₂

—

147

C₂×M₃₂

C₂×D₇₁

yes

characteristic

148

#441

—

142

—

149

#441

—

142

—

150

C₂×#108

C₂×D₇₁

yes

characteristic

151

#427

—

152

C₂×#106

C₂×D₇₁

yes

characteristic

153

#424

—

142

—

154

C₂×#103

—

142

—

155

C₂×#97

—

156

#365

—

157

#362

—

142

—

158

#358

—

159

#339

—

142

—

160

C₂²×Q₈

—

142

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

142

—

165

C₂×Q₁₆

—

142

—

166

C₂×Q₁₆

—

142

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₂²×C₈

C₂²×D₇₁

yes

characteristic

170

C₄×Q₈

—

284

—

171

C₄×Q₈

—

142

—

172

#117

—

142

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

284

—

175

C₂×C₄²

—

284

—

176

C₂×C₄²

—

177

M₃₂

—

178

M₃₂

—

179

M₃₂

—

142

—

180

M₃₂

—

142

—

181

C₂×C₁₆

—

142

—

182

C₂×C₁₆

C₄×D₇₁

yes

—

183

#108

—

184

#108

—

185

#107

—

186

#106

—

187

#106

—

142

—

188

#106

C₂²⋊D₇₁

yes

—

189

C₄⋊C₈

—

284

—

190

#103

—

142

—

191

#97

—

142

—

192

#97

—

142

—

193

C₂×Q₈

—

284

—

194

C₂×Q₈

—

284

—

195

C₂×Q₈

—

284

—

196

C₂×Q₈

—

142

—

197

C₂×Q₈

—

142

—

198

C₂×Q₈

—

142

—

199

C₂²×C₄

—

200

C₂²×C₄

—

284

—

201

C₂²×C₄

—

142

—

202

C₂²×C₄

D₄×D₇₁

yes

characteristic

203

Q₁₆

—

204

Q₁₆

—

142

—

205

Q₁₆

—

142

—

206

Q₁₆

—

142

—

207

M₁₆

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

142

—

211

C₂×C₈

—

142

—

212

C₂×C₈

—

142

—

213

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

214

C₂×C₈

D₄×D₇₁

yes

characteristic

215

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

216

C₂×C₈

Q₈×D₇₁

yes

characteristic

217

C₂×C₈

#11765865

yes

characteristic

218

C₂×C₈

#11765866

yes

characteristic

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

284

—

222

C₄⋊C₄

—

142

—

223

C₂²⋊C₄

—

284

—

224

C₄²

—

284

—

225

C₄²

—

284

—

226

C₄²

—

227

C₄²

—

142

—

228

C₁₆

—

229

C₁₆

—

284

—

230

C₂³

#14556155

yes

characteristic

231

Q₈

—

284

—

232

Q₈

—

284

—

233

Q₈

—

284

—

234

Q₈

—

142

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

284

—

238

C₂×C₄

—

284

—

239

C₂×C₄

—

284

—

240

C₂×C₄

—

284

—

241

C₂×C₄

—

284

—

242

C₂×C₄

—

142

—

243

C₂×C₄

#14556090

yes

characteristic

244

C₂×C₄

#14556096

yes

characteristic

245

C₂×C₄

#14556106

yes

characteristic

246

C₂×C₄

SD₁₆×D₇₁

yes

characteristic

247

C₂×C₄

#14556149

yes

characteristic

248

C₂×C₄

#14556155

yes

characteristic

249

C₈

—

250

C₈

—

284

—

251

C₈

C₄⋊C₄×D₇₁

yes

characteristic

252

C₈

C₄×C₂²⋊D₇₁

yes

characteristic

253

C₈

#14556104

yes

characteristic

254

C₈

#14556113

yes

characteristic

255

C₂²

—

256

C₂²

#17986110

yes

characteristic

257

C₂²

#17986148

yes

characteristic

258

C₂²

#17986298

yes

characteristic

259

C₄

—

260

C₄

—

284

—

261

C₄

—

284

—

262

C₄

—

568

—

263

C₄

#17985870

yes

characteristic

264

C₄

#17986086

yes

characteristic

265

C₄

#17986143

yes

characteristic

266

C₄

#17986288

yes

characteristic

267

C₂

—

268

C₂

—

269

C₂

#22588598

yes

characteristic

270

C₂

#22590230

yes

—

	subgroup	G/H
center	C₂²	#17986110
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₂×#365×C₇₁	C₂
socle	C₂²×C₇₁	#442
prime radical	C₂³×C₇₁	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	C₂×#365	D₇₁
hypocenter	C₇₁	#12957
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

subgroup

G/H

center

C₂²

#17986110

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₂×#365×C₇₁

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

N	H ≅ G/N	type
18. #17985804	C₄	semidirect
143. C₇₁	#12957	semidirect

H ≅ G/N

type

18. #17985804

C₄

semidirect

143. C₇₁

#12957

semidirect

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

subgroup	index
C₂×#17986105	2
C₂×#17985814	2
#22590061	2
#22589091	2
#22586447	2
#22586419	2
C₂×#365×C₇₁	2
#12957	71

subgroup

index

C₂×#365×C₇₁

Subgroups — #31914195

Conjugacy classes of subgroups

Complements

Maximal subgroups