Group #31897132 — subgroups

Subgroups — #31897132

Order 18176.

418 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17986349	C₂	1	1	yes	maximal, characteristic
2	#22589184	C₂	1	1	yes	maximal, characteristic
3	#22587098	C₂	1	1	yes	maximal, characteristic
4	#22587021	C₂	1	1	yes	maximal, characteristic
5	#22587013	C₂	1	1	yes	maximal, characteristic
6	#22586627	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1997	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556128	C₂²	1	1	yes	characteristic
9	#17986349	—	2	2	no	—
10	#17986349	—	2	2	no	—
11	#17986052	C₂²	1	1	yes	characteristic
12	#17986023	C₂²	1	1	yes	characteristic
13	C₂×#14556052	C₄	1	4	yes	—
14	C₂×#14556046	—	2	2	no	—
15	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
16	#17985751	—	2	2	no	—
17	#17985748	—	2	2	no	—
18	#17985746	—	2	2	no	—
19	#17985721	—	2	2	no	—
20	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
21	#423×C₇₁	C₂²	1	1	yes	characteristic
22	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
23	#343×C₇₁	—	2	2	no	—
24	C₂²×Dic₁₄₂	—	2	1	no	—
25	C₂×#11765849	—	2	1	no	—
26	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
27	#14556128	—	2	1	no	—
28	#14556128	—	2	1	no	—
29	#14556128	—	2	1	no	—
30	#14556128	—	2	1	no	—
31	C₂×C₄⋊Dic₇₁	—	2	1	no	—
32	C₂×C₄⋊Dic₇₁	C₂×C₄	1	2	yes	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
35	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
36	#14556052	—	2	8	no	—
37	#14556046	—	4	4	no	—
38	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
39	C₄×C₇₁⋊C₈	—	2	1	no	—
40	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
41	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
42	C₂²×Q₈×C₇₁	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₇₁	—	2	1	no	—
44	C₂×M₁₆×C₇₁	D₄	1	2	yes	—
45	C₄⋊Q₈×C₇₁	—	2	1	no	—
46	C₄⋊Q₈×C₇₁	—	2	1	no	—
47	C₄⋊Q₈×C₇₁	—	2	1	no	—
48	C₄⋊Q₈×C₇₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
51	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₇₁	—	2	1	no	—
53	C₄⋊C₈×C₇₁	—	2	1	no	—
54	#97×C₇₁	—	2	1	no	—
55	C₄×C₈×C₇₁	—	2	1	no	—
56	C₂×Dic₁₄₂	—	4	1	no	—
57	C₂×Dic₁₄₂	—	4	1	no	—
58	C₂×Dic₁₄₂	—	4	2	no	—
59	C₂×Dic₁₄₂	—	4	2	no	—
60	C₂²×Dic₇₁	—	2	2	no	—
61	#11765849	—	4	2	no	—
62	C₂×C₇₁⋊C₈	—	2	2	no	—
63	C₂×C₇₁⋊C₈	—	4	2	no	—
64	C₂×C₇₁⋊C₈	—	4	1	no	—
65	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	4	yes	—
66	C₄⋊Dic₇₁	—	2	2	no	—
67	C₄⋊Dic₇₁	—	2	2	no	—
68	C₄⋊Dic₇₁	—	4	1	no	—
69	C₄⋊Dic₇₁	—	4	1	no	—
70	C₂×Q₈×C₇₁	—	2	2	no	—
71	C₂×Q₈×C₇₁	—	2	2	no	—
72	C₂×Q₈×C₇₁	—	4	4	no	—
73	C₂²×C₄×C₇₁	—	2	2	no	—
74	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
77	M₁₆×C₇₁	—	2	2	no	—
78	M₁₆×C₇₁	—	2	2	no	—
79	M₁₆×C₇₁	—	4	2	no	—
80	C₂×C₈×C₇₁	—	2	2	no	—
81	C₂×C₈×C₇₁	—	4	1	no	—
82	C₄⋊C₄×C₇₁	—	4	1	no	—
83	C₄⋊C₄×C₇₁	—	4	1	no	—
84	C₄⋊C₄×C₇₁	—	4	1	no	—
85	C₄⋊C₄×C₇₁	—	4	1	no	—
86	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
88	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
89	C₄²×C₇₁	#41	1	1	yes	characteristic
90	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
91	Q₈×C₇₁	—	4	4	no	—
92	Q₈×C₇₁	—	8	2	no	—
93	C₂×C₄×C₇₁	—	2	2	no	—
94	C₂×C₄×C₇₁	—	2	2	no	—
95	C₂×C₄×C₇₁	—	4	2	no	—
96	C₂×C₄×C₇₁	—	8	2	no	—
97	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
100	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
101	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
102	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
103	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
104	C₂×C₄×C₇₁	#137	1	2	yes	—
105	C₂×Dic₇₁	—	4	2	no	—
106	C₂×Dic₇₁	—	4	4	no	—
107	Dic₁₄₂	—	8	2	no	—
108	Dic₁₄₂	—	8	1	no	—
109	Dic₁₄₂	—	8	1	no	—
110	C₈×C₇₁	—	4	2	no	—
111	C₈×C₇₁	—	8	1	no	—
112	C₇₁⋊C₈	—	2	4	no	—
113	C₇₁⋊C₈	—	4	2	no	—
114	C₇₁⋊C₈	—	8	1	no	—
115	C₂²×C₇₁	—	2	1	no	—
116	C₂²×C₇₁	—	2	1	no	—
117	C₂²×C₇₁	#390	1	1	yes	characteristic
118	C₂²×C₇₁	#440	1	2	yes	—
119	C₄×C₇₁	—	2	1	no	—
120	C₄×C₇₁	—	2	1	no	—
121	C₄×C₇₁	—	8	2	no	—
122	C₄×C₇₁	#413	1	2	yes	—
123	C₄×C₇₁	#468	1	2	yes	—
124	C₄×C₇₁	#473	1	2	yes	—
125	C₄×C₇₁	#496	1	1	yes	characteristic
126	C₄×C₇₁	#497	1	1	yes	characteristic
127	Dic₇₁	—	8	2	no	—
128	#9809	—	71	1	no	maximal, Sylow
129	C₂×C₇₁	—	2	2	no	—
130	C₂×C₇₁	#1967	1	1	yes	characteristic
131	C₂×C₇₁	#1973	1	1	yes	characteristic
132	C₂×C₇₁	#1979	1	1	yes	characteristic
133	C₂×#487	—	71	1	no	—
134	#1997	D₇₁	1	1	yes	characteristic
135	#1966	—	71	1	no	—
136	#1567	—	71	1	no	—
137	#1548	—	71	1	no	—
138	#1546	—	71	1	no	—
139	#1451	—	71	1	no	—
140	C₇₁	#9809	1	1	yes	characteristic, complemented, Sylow
141	C₂×C₄⋊Q₈	—	71	1	no	—
142	C₂×C₄⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
143	#487	—	142	2	no	—
144	#487	—	142	2	no	—
145	#431	—	71	1	no	—
146	#423	—	71	1	no	—
147	#423	C₂×D₇₁	1	1	yes	characteristic
148	C₂×#103	—	71	4	no	—
149	C₂×#101	—	142	2	no	—
150	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
151	C₂×C₄×C₈	—	71	1	no	—
152	#343	—	2	2	no	—
153	#335	—	142	2	no	—
154	#333	—	142	2	no	—
155	#332	—	142	2	no	—
156	#322	—	142	2	no	—
157	C₂²×Q₈	—	142	1	no	—
158	C₂²×Q₈	C₄×D₇₁	1	2	yes	—
159	C₂×M₁₆	—	2	1	no	—
160	C₂×M₁₆	—	142	1	no	—
161	C₂×M₁₆	C₂²⋊D₇₁	1	2	yes	—
162	C₂²×C₈	—	71	2	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	142	1	no	—
168	C₄⋊Q₈	—	142	1	no	—
169	C₄⋊Q₈	—	142	1	no	—
170	C₄⋊Q₈	—	142	1	no	—
171	C₂×C₄⋊C₄	—	2	1	no	—
172	C₂×C₄⋊C₄	—	2	1	no	—
173	C₂×C₄⋊C₄	—	71	2	no	—
174	C₂×C₄⋊C₄	—	142	1	no	—
175	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	71	2	no	—
179	C₄⋊C₈	—	142	1	no	—
180	C₄⋊C₈	—	142	1	no	—
181	#103	—	142	8	no	—
182	#101	—	284	4	no	—
183	C₂²⋊C₈	—	142	1	no	—
184	#97	—	2	1	no	—
185	C₄×C₈	—	2	1	no	—
186	C₄×C₈	—	71	2	no	—
187	C₄×C₈	—	71	2	no	—
188	C₄×C₈	—	142	1	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	—	4	4	no	—
192	C₂×Q₈	—	284	1	no	—
193	C₂×Q₈	—	284	1	no	—
194	C₂×Q₈	—	284	2	no	—
195	C₂×Q₈	—	284	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	142	2	no	—
198	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
200	C₂²×C₄	#11765865	1	1	yes	characteristic
201	M₁₆	—	2	2	no	—
202	M₁₆	—	2	2	no	—
203	M₁₆	—	4	2	no	—
204	M₁₆	—	284	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	284	1	no	—
208	C₂×C₈	—	284	2	no	—
209	C₂×C₈	—	71	4	no	—
210	C₂×C₈	—	142	2	no	—
211	C₄⋊C₄	—	4	1	no	—
212	C₄⋊C₄	—	4	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	1	no	—
215	C₄⋊C₄	—	284	1	no	—
216	C₄⋊C₄	—	284	1	no	—
217	C₄⋊C₄	—	142	2	no	—
218	C₄⋊C₄	—	142	2	no	—
219	C₄²	D₄×D₇₁	1	1	yes	characteristic
220	C₄²	D₄×D₇₁	1	1	yes	characteristic
221	C₄²	D₄×D₇₁	1	1	yes	characteristic
222	C₄²	#11765864	1	1	yes	characteristic
223	C₂³	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
224	Q₈	—	4	4	no	—
225	Q₈	—	8	2	no	—
226	Q₈	—	568	1	no	—
227	Q₈	—	568	1	no	—
228	Q₈	—	568	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	8	2	no	—
233	C₂×C₄	—	284	4	no	—
234	C₂×C₄	—	284	2	no	—
235	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
236	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	#14556100	1	1	yes	characteristic
238	C₂×C₄	#14556101	1	1	yes	characteristic
239	C₂×C₄	#14556114	1	1	yes	characteristic
240	C₂×C₄	#14556124	1	1	yes	characteristic
241	C₂×C₄	#14556153	1	2	yes	—
242	C₂×C₄	#14556159	1	2	yes	—
243	C₈	—	4	2	no	—
244	C₈	—	8	1	no	—
245	C₈	—	284	2	no	—
246	C₈	—	568	1	no	—
247	C₈	—	142	4	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	#17985899	1	1	yes	characteristic
251	C₂²	#17986097	1	2	yes	—
252	C₄	—	2	1	no	—
253	C₄	—	2	1	no	—
254	C₄	—	8	2	no	—
255	C₄	—	568	2	no	—
256	C₄	#17985980	1	2	yes	—
257	C₄	#17986247	1	2	yes	—
258	C₄	#17986273	1	2	yes	—
259	C₄	#17986389	1	1	yes	characteristic
260	C₄	#17986391	1	1	yes	characteristic
261	C₂	—	2	2	no	—
262	C₂	#22589186	1	1	yes	characteristic
263	C₂	#22589224	1	1	yes	characteristic
264	C₂	#22589252	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986349

C₂

yes

maximal, characteristic

#22589184

C₂

yes

maximal, characteristic

#22587098

C₂

yes

maximal, characteristic

#22587021

C₂

yes

maximal, characteristic

#22587013

C₂

yes

maximal, characteristic

#22586627

C₂

yes

maximal, characteristic

C₇₁×#1997

C₂

yes

maximal, characteristic

C₂×#14556128

C₂²

yes

—

—

C₂²

yes

characteristic

#17986023

C₂²

yes

characteristic

C₂×#14556052

C₄

yes

—

C₂×#14556046

—

C₂×C₄×C₇₁⋊C₈

C₂²

yes

—

—

—

—

C₂×C₄⋊Q₈×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

C₄×M₁₆×C₇₁

C₂²

yes

characteristic

#343×C₇₁

—

C₂²×Dic₁₄₂

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

C₂×C₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

#14556052

—

#14556046

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₁

C₂×C₄

yes

—

C₂×M₁₆×C₇₁

—

C₂×M₁₆×C₇₁

D₄

yes

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

#97×C₇₁

—

C₄×C₈×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

#41

yes

characteristic

C₂³×C₇₁

C₄×D₄

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

#121

yes

characteristic

100

C₂×C₄×C₇₁

#121

yes

characteristic

101

C₂×C₄×C₇₁

#124

yes

characteristic

102

C₂×C₄×C₇₁

#127

yes

characteristic

103

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

—

104

C₂×C₄×C₇₁

#137

yes

—

105

C₂×Dic₇₁

—

106

C₂×Dic₇₁

—

107

Dic₁₄₂

—

108

Dic₁₄₂

—

109

Dic₁₄₂

—

110

C₈×C₇₁

—

111

C₈×C₇₁

—

112

C₇₁⋊C₈

—

113

C₇₁⋊C₈

—

114

C₇₁⋊C₈

—

115

C₂²×C₇₁

—

116

C₂²×C₇₁

—

117

C₂²×C₇₁

#390

yes

characteristic

118

C₂²×C₇₁

#440

yes

—

119

C₄×C₇₁

—

120

C₄×C₇₁

—

121

C₄×C₇₁

—

122

C₄×C₇₁

#413

yes

—

123

C₄×C₇₁

#468

yes

—

124

C₄×C₇₁

#473

yes

—

125

C₄×C₇₁

#496

yes

characteristic

126

C₄×C₇₁

#497

yes

characteristic

127

Dic₇₁

—

128

#9809

—

maximal, Sylow

129

C₂×C₇₁

—

130

C₂×C₇₁

#1967

yes

characteristic

131

C₂×C₇₁

#1973

yes

characteristic

132

C₂×C₇₁

#1979

yes

characteristic

133

C₂×#487

—

134

#1997

D₇₁

yes

characteristic

135

#1966

—

136

#1567

—

137

#1548

—

138

#1546

—

139

#1451

—

140

C₇₁

#9809

yes

characteristic, complemented, Sylow

141

C₂×C₄⋊Q₈

—

142

C₂×C₄⋊Q₈

C₂×D₇₁

yes

characteristic

143

#487

—

142

—

144

#487

—

142

—

145

#431

—

146

#423

—

147

#423

C₂×D₇₁

yes

characteristic

148

C₂×#103

—

149

C₂×#101

—

142

—

150

C₄×M₁₆

C₂×D₇₁

yes

characteristic

151

C₂×C₄×C₈

—

152

#343

—

153

#335

—

142

—

154

#333

—

142

—

155

#332

—

142

—

156

#322

—

142

—

157

C₂²×Q₈

—

142

—

158

C₂²×Q₈

C₄×D₇₁

yes

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

142

—

161

C₂×M₁₆

C₂²⋊D₇₁

yes

—

162

C₂²×C₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

142

—

168

C₄⋊Q₈

—

142

—

169

C₄⋊Q₈

—

142

—

170

C₄⋊Q₈

—

142

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

142

—

175

C₂×C₄²

C₂²×D₇₁

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

142

—

180

C₄⋊C₈

—

142

—

181

#103

—

142

—

182

#101

—

284

—

183

C₂²⋊C₈

—

142

—

184

#97

—

185

C₄×C₈

—

186

C₄×C₈

—

187

C₄×C₈

—

188

C₄×C₈

—

142

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

284

—

193

C₂×Q₈

—

284

—

194

C₂×Q₈

—

284

—

195

C₂×Q₈

—

284

—

196

C₂²×C₄

—

197

C₂²×C₄

—

142

—

198

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

200

C₂²×C₄

#11765865

yes

characteristic

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

M₁₆

—

284

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

284

—

208

C₂×C₈

—

284

—

209

C₂×C₈

—

210

C₂×C₈

—

142

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

284

—

216

C₄⋊C₄

—

284

—

217

C₄⋊C₄

—

142

—

218

C₄⋊C₄

—

142

—

219

C₄²

D₄×D₇₁

yes

characteristic

220

C₄²

D₄×D₇₁

yes

characteristic

221

C₄²

D₄×D₇₁

yes

characteristic

222

C₄²

#11765864

yes

characteristic

223

C₂³

C₄×C₂²⋊D₇₁

yes

characteristic

224

Q₈

—

225

Q₈

—

226

Q₈

—

568

—

227

Q₈

—

568

—

228

Q₈

—

568

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

284

—

234

C₂×C₄

—

284

—

235

C₂×C₄

C₂²⋊C₄×D₇₁

yes

characteristic

236

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

characteristic

237

C₂×C₄

#14556100

yes

characteristic

238

C₂×C₄

#14556101

yes

characteristic

239

C₂×C₄

#14556114

yes

characteristic

240

C₂×C₄

#14556124

yes

characteristic

241

C₂×C₄

#14556153

yes

—

242

C₂×C₄

#14556159

yes

—

243

C₈

—

244

C₈

—

245

C₈

—

284

—

246

C₈

—

568

—

247

C₈

—

142

—

248

C₂²

—

249

C₂²

—

250

C₂²

#17985899

yes

characteristic

251

C₂²

#17986097

yes

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

568

—

256

C₄

#17985980

yes

—

257

C₄

#17986247

yes

—

258

C₄

#17986273

yes

—

259

C₄

#17986389

yes

characteristic

260

C₄

#17986391

yes

characteristic

261

C₂

—

262

C₂

#22589186

yes

characteristic

263

C₂

#22589224

yes

characteristic

264

C₂

#22589252

yes

characteristic

	subgroup	G/H
center	C₂²	#17985899
commutator	C₂²×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1997	C₂
socle	C₂²×C₇₁	#390
prime radical	C₂³×C₇₁	C₄×D₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1997	D₇₁
hypocenter	C₇₁	#9809
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

subgroup

G/H

center

C₂²

#17985899

commutator

C₂²×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1997

C₂

socle

C₂²×C₇₁

#390

prime radical

C₂³×C₇₁

C₄×D₄

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

N	H ≅ G/N	type
140. C₇₁	#9809	semidirect

H ≅ G/N

type

140. C₇₁

#9809

semidirect

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

subgroup	index
C₂×#17986349	2
#22589184	2
#22587098	2
#22587021	2
#22587013	2
#22586627	2
C₇₁×#1997	2
#9809	71

subgroup

index

C₇₁×#1997

Subgroups — #31897132

Conjugacy classes of subgroups

Complements

Maximal subgroups