Group #31895889 — subgroups

Subgroups — #31895889

Order 18176.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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	#22589316	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₇₁	C₂	1	1	yes	maximal, characteristic
3	#22587112	C₂	1	1	yes	maximal, characteristic
4	#22586998	C₂	1	1	yes	maximal, characteristic
5	#22586744	C₂	1	1	yes	maximal, characteristic
6	#22586172	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1301	C₂	1	1	yes	maximal, characteristic
8	#17986556	C₂²	1	1	yes	characteristic
9	#17986052	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₇₁	—	2	1	no	—
12	C₄²×Dic₇₁	C₂²	1	1	yes	characteristic
13	#17985760	—	2	1	no	—
14	#17985760	—	2	1	no	—
15	#17985753	—	2	1	no	—
16	#17985749	—	2	2	no	—
17	#17985747	C₄	1	2	yes	complemented
18	#17985744	C₄	1	2	yes	complemented
19	#17985731	—	2	2	no	—
20	#431×C₇₁	C₂²	1	1	yes	characteristic
21	#423×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
23	C₂²×C₇₁⋊C₈	—	2	1	no	—
24	#14556128	C₂×C₄	1	1	yes	characteristic
25	#14556128	C₂×C₄	1	1	yes	characteristic
26	#14556120	—	2	1	no	—
27	#14556107	—	2	1	no	—
28	#14556107	—	2	1	no	—
29	C₄×Dic₁₄₂	—	2	1	no	—
30	C₄×Dic₁₄₂	—	2	1	no	—
31	#14556087	—	2	1	no	—
32	C₂×C₄×Dic₇₁	—	2	1	no	—
33	C₂×C₄×Dic₇₁	—	2	1	no	—
34	C₂×C₄×Dic₇₁	D₄	1	1	yes	characteristic
35	C₂×C₄×Dic₇₁	D₄	1	1	yes	characteristic
36	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
37	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
38	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
39	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
40	C₄×C₇₁⋊C₈	—	2	1	no	—
41	C₈×Dic₇₁	—	4	2	no	—
42	C₂×M₁₆×C₇₁	—	2	1	no	—
43	C₂²×C₈×C₇₁	—	2	1	no	—
44	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₇₁	—	2	1	no	—
46	C₄⋊C₈×C₇₁	—	2	1	no	—
47	C₄⋊C₈×C₇₁	—	2	1	no	—
48	C₄⋊C₈×C₇₁	—	2	1	no	—
49	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
50	C₂²⋊C₈×C₇₁	—	2	1	no	—
51	C₄×C₈×C₇₁	—	2	1	no	—
52	C₂×Dic₁₄₂	—	2	1	no	—
53	C₂×Dic₁₄₂	—	2	1	no	—
54	C₂²×Dic₇₁	—	2	1	no	—
55	C₂²×Dic₇₁	—	2	1	no	—
56	C₂×C₇₁⋊C₈	—	2	2	no	—
57	C₂×C₇₁⋊C₈	—	2	2	no	—
58	C₂×C₇₁⋊C₈	—	4	1	no	—
59	C₂×C₇₁⋊C₈	—	4	1	no	—
60	C₄⋊Dic₇₁	—	2	1	no	—
61	C₄⋊Dic₇₁	—	2	1	no	—
62	C₄⋊Dic₇₁	—	2	1	no	—
63	C₄⋊Dic₇₁	—	2	1	no	—
64	Dic₇₁⋊C₄	—	4	1	no	—
65	Dic₇₁⋊C₄	—	4	1	no	—
66	C₂²⋊Dic₇₁	—	4	1	no	—
67	C₄×Dic₇₁	—	2	4	no	—
68	C₄×Dic₇₁	—	2	1	no	—
69	C₄×Dic₇₁	—	2	1	no	—
70	C₄×Dic₇₁	—	2	1	no	—
71	C₄×Dic₇₁	—	4	2	no	—
72	C₄×Dic₇₁	—	4	1	no	—
73	C₄×Dic₇₁	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
76	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
77	M₁₆×C₇₁	—	4	1	no	—
78	M₁₆×C₇₁	—	4	1	no	—
79	C₂×C₈×C₇₁	—	2	2	no	—
80	C₂×C₈×C₇₁	—	4	1	no	—
81	C₂×C₈×C₇₁	—	4	1	no	—
82	C₂×C₈×C₇₁	—	4	1	no	—
83	C₂×C₈×C₇₁	—	4	1	no	—
84	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
85	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₇₁	#41	1	1	yes	characteristic
87	C₄²×C₇₁	#41	1	1	yes	characteristic
88	C₂³×C₇₁	#123	1	1	yes	characteristic
89	C₂×C₄×C₇₁	—	2	2	no	—
90	C₂×C₄×C₇₁	—	4	1	no	—
91	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
92	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
95	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
96	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
97	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
99	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
100	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
101	C₂×Dic₇₁	—	2	2	no	—
102	C₂×Dic₇₁	—	2	2	no	—
103	C₂×Dic₇₁	—	2	2	no	—
104	C₂×Dic₇₁	—	2	2	no	—
105	C₂×Dic₇₁	—	4	1	no	—
106	C₂×Dic₇₁	—	4	1	no	—
107	C₂×Dic₇₁	—	4	1	no	—
108	C₂×Dic₇₁	—	4	1	no	—
109	Dic₁₄₂	—	4	2	no	—
110	Dic₁₄₂	—	8	1	no	—
111	C₈×C₇₁	—	4	2	no	—
112	C₈×C₇₁	—	8	1	no	—
113	C₈×C₇₁	—	8	1	no	—
114	C₇₁⋊C₈	—	4	2	no	—
115	C₇₁⋊C₈	—	4	2	no	—
116	C₂²×C₇₁	—	2	1	no	—
117	C₂²×C₇₁	—	2	1	no	—
118	C₂²×C₇₁	#388	1	1	yes	characteristic
119	C₂²×C₇₁	#483	1	1	yes	characteristic
120	C₂²×C₇₁	#485	1	1	yes	characteristic
121	C₄×C₇₁	—	2	1	no	—
122	C₄×C₇₁	—	2	1	no	—
123	C₄×C₇₁	—	2	1	no	—
124	C₄×C₇₁	C₄×SD₁₆	1	1	yes	characteristic
125	C₄×C₇₁	#441	1	1	yes	characteristic
126	C₄×C₇₁	#443	1	2	yes	—
127	C₄×C₇₁	#461	1	1	yes	characteristic
128	C₄×C₇₁	#464	1	1	yes	characteristic
129	Dic₇₁	—	2	4	no	—
130	Dic₇₁	—	4	2	no	—
131	Dic₇₁	—	8	1	no	—
132	Dic₇₁	—	8	1	no	—
133	#9579	—	71	1	no	maximal, Sylow
134	C₂×C₇₁	—	2	1	no	—
135	C₂×C₇₁	—	2	1	no	—
136	C₂×C₇₁	#1927	1	1	yes	characteristic
137	C₂×C₇₁	#1932	1	1	yes	characteristic
138	C₂×C₇₁	#1937	1	1	yes	characteristic
139	#1994	—	71	1	no	—
140	C₄×C₄⋊C₈	—	71	1	no	—
141	#1570	—	71	1	no	—
142	#1542	—	71	1	no	—
143	#1481	—	71	1	no	—
144	#1301	D₇₁	1	1	yes	characteristic
145	#1276	—	71	1	no	—
146	C₇₁	#9579	1	1	yes	characteristic, complemented, Sylow
147	#533	—	71	1	no	—
148	#431	—	71	1	no	—
149	#431	C₂×D₇₁	1	1	yes	characteristic
150	#423	C₂×D₇₁	1	1	yes	characteristic
151	C₂×C₄⋊C₈	—	71	1	no	—
152	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
153	C₂×C₄×C₈	—	142	1	no	—
154	C₄³	—	71	1	no	—
155	#339	—	142	1	no	—
156	#339	—	142	1	no	—
157	#336	—	142	1	no	—
158	#334	—	142	2	no	—
159	#333	—	71	2	no	—
160	#332	—	71	2	no	—
161	Q₈⋊C₈	—	142	2	no	—
162	C₂×M₁₆	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	142	1	no	—
165	C₄⋊Q₈	—	71	1	no	—
166	C₄⋊Q₈	—	71	1	no	—
167	#125	—	142	1	no	—
168	C₂²⋊Q₈	—	142	1	no	—
169	C₂²⋊Q₈	—	142	1	no	—
170	C₄×Q₈	—	142	1	no	—
171	C₄×Q₈	—	142	1	no	—
172	#117	—	142	1	no	—
173	C₂×C₄²	—	71	1	no	—
174	C₂×C₄²	—	71	1	no	—
175	C₂×C₄²	—	142	1	no	—
176	C₂×C₄²	—	142	1	no	—
177	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	2	1	no	—
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	71	2	no	—
183	C₄⋊C₈	—	71	2	no	—
184	C₄⋊C₈	—	142	1	no	—
185	C₄⋊C₈	C₄×D₇₁	1	2	yes	—
186	C₂²⋊C₈	—	2	1	no	—
187	C₂²⋊C₈	—	142	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	284	2	no	—
190	C₄×C₈	—	142	1	no	—
191	C₂×Q₈	—	142	1	no	—
192	C₂×Q₈	—	142	1	no	—
193	C₂²×C₄	—	142	1	no	—
194	C₂²×C₄	—	142	1	no	—
195	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
196	C₂²×C₄	#11765865	1	1	yes	characteristic
197	C₂²×C₄	#11765866	1	1	yes	characteristic
198	M₁₆	—	4	1	no	—
199	M₁₆	—	4	1	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	1	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	284	1	no	—
206	C₂×C₈	—	284	1	no	—
207	C₂×C₈	—	142	2	no	—
208	C₂×C₈	—	142	2	no	—
209	C₄⋊C₄	—	284	1	no	—
210	C₄⋊C₄	—	284	1	no	—
211	C₄⋊C₄	—	142	1	no	—
212	C₄⋊C₄	—	142	1	no	—
213	C₄⋊C₄	—	142	1	no	—
214	C₄⋊C₄	—	142	1	no	—
215	C₂²⋊C₄	—	284	1	no	—
216	C₄²	—	284	2	no	—
217	C₄²	—	284	1	no	—
218	C₄²	—	71	2	no	—
219	C₄²	—	142	4	no	—
220	C₄²	—	142	1	no	—
221	C₄²	—	142	1	no	—
222	C₄²	—	142	1	no	—
223	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
224	C₄²	D₄×D₇₁	1	1	yes	characteristic
225	C₄²	#11765864	1	1	yes	characteristic
226	C₄²	#11765865	1	1	yes	characteristic
227	C₂³	#14556113	1	1	yes	characteristic
228	Q₈	—	284	2	no	—
229	Q₈	—	568	1	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	284	1	no	—
233	C₂×C₄	—	284	1	no	—
234	C₂×C₄	—	284	1	no	—
235	C₂×C₄	—	284	1	no	—
236	C₂×C₄	—	142	2	no	—
237	C₂×C₄	—	142	2	no	—
238	C₂×C₄	—	142	2	no	—
239	C₂×C₄	—	142	2	no	—
240	C₂×C₄	#14556085	1	1	yes	characteristic
241	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	#14556090	1	1	yes	characteristic
243	C₂×C₄	#14556101	1	1	yes	characteristic
244	C₂×C₄	#14556114	1	1	yes	characteristic
245	C₂×C₄	#14556123	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₇₁	1	1	yes	characteristic
247	C₂×C₄	#14556147	1	1	yes	characteristic
248	C₂×C₄	#14556157	1	1	yes	characteristic
249	C₂×C₄	#14556160	1	1	yes	characteristic
250	C₈	—	4	2	no	—
251	C₈	—	8	1	no	—
252	C₈	—	8	1	no	—
253	C₈	—	284	2	no	—
254	C₈	—	284	2	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	#17985888	1	1	yes	characteristic
258	C₂²	#17986331	1	1	yes	characteristic
259	C₂²	#17986342	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	284	2	no	—
264	C₄	—	568	1	no	—
265	C₄	—	568	1	no	—
266	C₄	—	142	4	no	—
267	C₄	#17986090	1	1	yes	characteristic
268	C₄	#17986103	1	1	yes	characteristic
269	C₄	#17986115	1	2	yes	—
270	C₄	#17986203	1	1	yes	characteristic
271	C₄	#17986220	1	1	yes	characteristic
272	C₂	—	2	1	no	—
273	C₂	—	2	1	no	—
274	C₂	#22588972	1	1	yes	characteristic
275	C₂	#22589007	1	1	yes	characteristic
276	C₂	#22589042	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589316

C₂

yes

maximal, characteristic

C₄⋊C₈×Dic₇₁

C₂

yes

maximal, characteristic

#22587112

C₂

yes

maximal, characteristic

#22586998

C₂

yes

maximal, characteristic

#22586744

C₂

yes

maximal, characteristic

#22586172

C₂

yes

maximal, characteristic

C₇₁×#1301

C₂

yes

maximal, characteristic

#17986556

C₂²

yes

characteristic

#17986052

C₂²

yes

characteristic

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×C₈×Dic₇₁

—

C₄²×Dic₇₁

C₂²

yes

—

—

—

—

C₄

yes

complemented

#17985744

C₄

yes

complemented

#17985731

—

#431×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₁

C₂²

yes

characteristic

C₂²×C₇₁⋊C₈

—

#14556128

C₂×C₄

yes

characteristic

#14556128

C₂×C₄

yes

—

—

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

#14556087

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

D₄

yes

characteristic

C₂×C₄×Dic₇₁

D₄

yes

characteristic

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

—

C₈×Dic₇₁

—

C₂×M₁₆×C₇₁

—

C₂²×C₈×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

C₂×C₄

yes

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

SD₁₆

yes

—

C₂²×C₄×C₇₁

C₂×D₄

yes

C₂²×C₄×C₇₁

yes

C₂²×C₄×C₇₁

yes

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₂³×C₇₁

yes

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

#117

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×SD₁₆

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

100

C₂×C₄×C₇₁

#137

yes

characteristic

101

C₂×Dic₇₁

—

102

C₂×Dic₇₁

—

103

C₂×Dic₇₁

—

104

C₂×Dic₇₁

—

105

C₂×Dic₇₁

—

106

C₂×Dic₇₁

—

107

C₂×Dic₇₁

—

108

C₂×Dic₇₁

—

109

Dic₁₄₂

—

110

Dic₁₄₂

—

111

C₈×C₇₁

—

112

C₈×C₇₁

—

113

C₈×C₇₁

—

114

C₇₁⋊C₈

—

115

C₇₁⋊C₈

—

116

C₂²×C₇₁

—

117

C₂²×C₇₁

—

118

C₂²×C₇₁

#388

yes

characteristic

119

C₂²×C₇₁

#483

yes

characteristic

120

C₂²×C₇₁

#485

yes

characteristic

121

C₄×C₇₁

—

122

C₄×C₇₁

—

123

C₄×C₇₁

—

124

C₄×C₇₁

C₄×SD₁₆

yes

characteristic

125

C₄×C₇₁

#441

yes

characteristic

126

C₄×C₇₁

#443

yes

—

127

C₄×C₇₁

#461

yes

characteristic

128

C₄×C₇₁

#464

yes

characteristic

129

Dic₇₁

—

130

Dic₇₁

—

131

Dic₇₁

—

132

Dic₇₁

—

133

#9579

—

maximal, Sylow

134

C₂×C₇₁

—

135

C₂×C₇₁

—

136

C₂×C₇₁

#1927

yes

characteristic

137

C₂×C₇₁

#1932

yes

characteristic

138

C₂×C₇₁

#1937

yes

characteristic

139

#1994

—

140

C₄×C₄⋊C₈

—

141

#1570

—

142

#1542

—

143

#1481

—

144

#1301

D₇₁

yes

characteristic

145

#1276

—

146

C₇₁

#9579

yes

characteristic, complemented, Sylow

147

#533

—

148

#431

—

149

#431

C₂×D₇₁

yes

characteristic

150

#423

C₂×D₇₁

yes

characteristic

151

C₂×C₄⋊C₈

—

152

C₂×C₄⋊C₈

C₂×D₇₁

yes

characteristic

153

C₂×C₄×C₈

—

142

—

154

C₄³

—

155

#339

—

142

—

156

#339

—

142

—

157

#336

—

142

—

158

#334

—

142

—

159

#333

—

160

#332

—

161

Q₈⋊C₈

—

142

—

162

C₂×M₁₆

—

163

C₂²×C₈

—

164

C₂²×C₈

—

142

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

#125

—

142

—

168

C₂²⋊Q₈

—

142

—

169

C₂²⋊Q₈

—

142

—

170

C₄×Q₈

—

142

—

171

C₄×Q₈

—

142

—

172

#117

—

142

—

173

C₂×C₄²

—

174

C₂×C₄²

—

175

C₂×C₄²

—

142

—

176

C₂×C₄²

—

142

—

177

C₂×C₄²

C₂²×D₇₁

yes

characteristic

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

142

—

185

C₄⋊C₈

C₄×D₇₁

yes

—

186

C₂²⋊C₈

—

187

C₂²⋊C₈

—

142

—

188

C₄×C₈

—

189

C₄×C₈

—

284

—

190

C₄×C₈

—

142

—

191

C₂×Q₈

—

142

—

192

C₂×Q₈

—

142

—

193

C₂²×C₄

—

142

—

194

C₂²×C₄

—

142

—

195

C₂²×C₄

D₄×D₇₁

yes

characteristic

196

C₂²×C₄

#11765865

yes

characteristic

197

C₂²×C₄

#11765866

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

284

—

206

C₂×C₈

—

284

—

207

C₂×C₈

—

142

—

208

C₂×C₈

—

142

—

209

C₄⋊C₄

—

284

—

210

C₄⋊C₄

—

284

—

211

C₄⋊C₄

—

142

—

212

C₄⋊C₄

—

142

—

213

C₄⋊C₄

—

142

—

214

C₄⋊C₄

—

142

—

215

C₂²⋊C₄

—

284

—

216

C₄²

—

284

—

217

C₄²

—

284

—

218

C₄²

—

219

C₄²

—

142

—

220

C₄²

—

142

—

221

C₄²

—

142

—

222

C₄²

—

142

—

223

C₄²

C₂×C₄×D₇₁

yes

characteristic

224

C₄²

D₄×D₇₁

yes

characteristic

225

C₄²

#11765864

yes

characteristic

226

C₄²

#11765865

yes

characteristic

227

C₂³

#14556113

yes

characteristic

228

Q₈

—

284

—

229

Q₈

—

568

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

284

—

233

C₂×C₄

—

284

—

234

C₂×C₄

—

284

—

235

C₂×C₄

—

284

—

236

C₂×C₄

—

142

—

237

C₂×C₄

—

142

—

238

C₂×C₄

—

142

—

239

C₂×C₄

—

142

—

240

C₂×C₄

#14556085

yes

characteristic

241

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

characteristic

242

C₂×C₄

#14556090

yes

characteristic

243

C₂×C₄

#14556101

yes

characteristic

244

C₂×C₄

#14556114

yes

characteristic

245

C₂×C₄

#14556123

yes

characteristic

246

C₂×C₄

SD₁₆×D₇₁

yes

characteristic

247

C₂×C₄

#14556147

yes

characteristic

248

C₂×C₄

#14556157

yes

characteristic

249

C₂×C₄

#14556160

yes

characteristic

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

284

—

254

C₈

—

284

—

255

C₂²

—

256

C₂²

—

257

C₂²

#17985888

yes

characteristic

258

C₂²

#17986331

yes

characteristic

259

C₂²

#17986342

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

284

—

264

C₄

—

568

—

265

C₄

—

568

—

266

C₄

—

142

—

267

C₄

#17986090

yes

characteristic

268

C₄

#17986103

yes

characteristic

269

C₄

#17986115

yes

—

270

C₄

#17986203

yes

characteristic

271

C₄

#17986220

yes

characteristic

272

C₂

—

273

C₂

—

274

C₂

#22588972

yes

characteristic

275

C₂

#22589007

yes

characteristic

276

C₂

#22589042

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556101
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1301	C₂
socle	C₂²×C₇₁	#388
prime radical	C₂³×C₇₁	#123
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1301	D₇₁
hypocenter	C₇₁	#9579
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#14556101

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1301

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
17. #17985747	C₄	semidirect
18. #17985744	C₄	semidirect
146. C₇₁	#9579	semidirect

H ≅ G/N

type

17. #17985747

C₄

semidirect

18. #17985744

C₄

semidirect

146. C₇₁

#9579

semidirect

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

subgroup	index
#22589316	2
C₄⋊C₈×Dic₇₁	2
#22587112	2
#22586998	2
#22586744	2
#22586172	2
C₇₁×#1301	2
#9579	71

subgroup

index

C₄⋊C₈×Dic₇₁

C₇₁×#1301

Subgroups — #31895889

Conjugacy classes of subgroups

Complements

Maximal subgroups