Group #21465101 — subgroups

Subgroups — C₃₁×#8342 #21465101

Order 7936.

1030 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 238 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	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1797	C₂	1	2	yes	maximal
3	C₂×C₃₁×#333	C₂	1	4	yes	maximal, complemented
4	C₂³×Q₈×C₃₁	C₄	1	2	yes	—
5	C₂×C₃₁×C₄⋊Q₈	—	2	8	no	—
6	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
7	C₂×C₃₁×C₄⋊Q₈	C₄	1	2	yes	—
8	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
10	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
12	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
13	C₃₁×#336	—	2	2	no	—
14	C₃₁×#333	—	2	8	no	—
15	C₂²×Q₈×C₃₁	—	2	8	no	—
16	C₂²×Q₈×C₃₁	—	2	2	no	—
17	C₂²×Q₈×C₃₁	—	4	4	no	—
18	C₂²×Q₈×C₃₁	—	4	4	no	—
19	C₂²×Q₈×C₃₁	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₃₁	—	2	2	no	—
21	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₃₁	D₄	1	2	yes	—
23	C₂²×C₈×C₃₁	—	2	4	no	—
24	C₃₁×C₄⋊Q₈	—	2	16	no	—
25	C₃₁×C₄⋊Q₈	—	2	8	no	—
26	C₃₁×C₄⋊Q₈	—	2	4	no	—
27	C₃₁×C₄⋊Q₈	D₄	1	8	yes	—
28	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
29	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
30	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
31	C₂×C₄²×C₃₁	—	2	4	no	—
32	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₃₁	D₄	1	2	yes	—
34	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
35	C₃₁×C₄⋊C₈	—	2	8	no	—
36	C₃₁×C₂²⋊C₈	—	4	4	no	—
37	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Q₈×C₃₁	—	2	8	no	—
39	C₂×Q₈×C₃₁	—	2	4	no	—
40	C₂×Q₈×C₃₁	—	4	32	no	—
41	C₂×Q₈×C₃₁	—	4	4	no	—
42	C₂×Q₈×C₃₁	—	4	4	no	—
43	C₂×Q₈×C₃₁	—	4	4	no	—
44	C₂×Q₈×C₃₁	—	4	4	no	—
45	C₂×Q₈×C₃₁	C₂²⋊C₄	1	8	yes	—
46	C₂²×C₄×C₃₁	—	2	2	no	—
47	C₂²×C₄×C₃₁	—	2	2	no	—
48	C₂²×C₄×C₃₁	—	2	2	no	—
49	C₂²×C₄×C₃₁	—	2	4	no	—
50	C₂²×C₄×C₃₁	—	2	4	no	—
51	C₂²×C₄×C₃₁	—	2	8	no	—
52	C₂²×C₄×C₃₁	—	2	4	no	—
53	C₂²×C₄×C₃₁	—	4	4	no	—
54	C₂²×C₄×C₃₁	—	4	4	no	—
55	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
58	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
59	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₃₁	—	4	4	no	—
62	C₂×C₈×C₃₁	—	4	4	no	—
63	C₂×C₈×C₃₁	—	4	4	no	—
64	C₄⋊C₄×C₃₁	—	2	16	no	—
65	C₄⋊C₄×C₃₁	—	2	16	no	—
66	C₄²×C₃₁	—	2	2	no	—
67	C₄²×C₃₁	—	2	4	no	—
68	C₄²×C₃₁	C₂×D₄	1	4	yes	—
69	#8342	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂³×C₃₁	—	2	1	no	—
71	C₂³×C₃₁	—	2	1	no	—
72	C₂³×C₃₁	—	2	2	no	—
73	C₂³×C₃₁	#100	1	2	yes	—
74	C₂³×C₃₁	#103	1	4	yes	—
75	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₃₁	—	4	8	no	—
77	Q₈×C₃₁	—	4	16	no	—
78	Q₈×C₃₁	—	4	8	no	—
79	C₂×C₄×C₃₁	—	2	8	no	—
80	C₂×C₄×C₃₁	—	2	2	no	—
81	C₂×C₄×C₃₁	—	2	1	no	—
82	C₂×C₄×C₃₁	—	2	1	no	—
83	C₂×C₄×C₃₁	—	2	1	no	—
84	C₂×C₄×C₃₁	—	2	1	no	—
85	C₂×C₄×C₃₁	—	2	2	no	—
86	C₂×C₄×C₃₁	—	2	8	no	—
87	C₂×C₄×C₃₁	—	2	8	no	—
88	C₂×C₄×C₃₁	—	2	8	no	—
89	C₂×C₄×C₃₁	—	4	16	no	—
90	C₂×C₄×C₃₁	—	4	4	no	—
91	C₂×C₄×C₃₁	—	4	4	no	—
92	C₂×C₄×C₃₁	#100	1	2	yes	—
93	C₂×C₄×C₃₁	#103	1	4	yes	—
94	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
95	C₂×C₄×C₃₁	#120	1	4	yes	—
96	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
97	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
98	C₂×C₄×C₃₁	#137	1	4	yes	—
99	C₈×C₃₁	—	8	4	no	—
100	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
101	#1797	C₂×C₃₁	1	2	yes	—
102	C₂×#333	C₂×C₃₁	1	4	yes	complemented
103	C₂²×C₃₁	—	2	4	no	—
104	C₂²×C₃₁	—	2	2	no	—
105	C₂²×C₃₁	—	2	2	no	—
106	C₂²×C₃₁	—	2	4	no	—
107	C₂²×C₃₁	#333	1	4	yes	complemented
108	C₂²×C₃₁	#379	1	1	yes	characteristic
109	C₂²×C₃₁	C₂×#100	1	1	yes	characteristic
110	C₂²×C₃₁	C₂×#100	1	1	yes	characteristic
111	C₂²×C₃₁	C₂×#103	1	2	yes	—
112	C₂²×C₃₁	#419	1	2	yes	—
113	C₄×C₃₁	—	2	2	no	—
114	C₄×C₃₁	—	2	2	no	—
115	C₄×C₃₁	—	2	4	no	—
116	C₄×C₃₁	—	4	8	no	—
117	C₄×C₃₁	#448	1	4	yes	—
118	C₄×C₃₁	#451	1	4	yes	—
119	C₂³×Q₈	C₄×C₃₁	1	2	yes	—
120	C₂×C₄⋊Q₈	—	2	8	no	—
121	C₂×C₄⋊Q₈	—	2	2	no	—
122	C₂×C₄⋊Q₈	C₄×C₃₁	1	2	yes	—
123	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
124	C₂²×C₄⋊C₄	—	2	2	no	—
125	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
126	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
127	C₂×C₂²⋊C₈	—	2	2	no	—
128	#336	—	2	2	no	—
129	#333	—	2	8	no	—
130	C₂×C₃₁	—	2	4	no	—
131	C₂×C₃₁	C₂×#333	1	1	yes	characteristic
132	C₂×C₃₁	#1548	1	2	yes	—
133	C₂×C₃₁	#1558	1	1	yes	characteristic
134	C₂×C₃₁	#1783	1	1	yes	characteristic
135	C₂×C₃₁	#1787	1	2	yes	—
136	C₂²×Q₈	—	2	8	no	—
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	4	4	no	—
139	C₂²×Q₈	—	4	4	no	—
140	C₂²×Q₈	C₂×C₄×C₃₁	1	4	yes	—
141	C₂³×C₄	—	2	2	no	—
142	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
143	C₂³×C₄	D₄×C₃₁	1	2	yes	—
144	C₂²×C₈	—	2	4	no	—
145	C₄⋊Q₈	—	2	16	no	—
146	C₄⋊Q₈	—	2	8	no	—
147	C₄⋊Q₈	—	2	4	no	—
148	C₄⋊Q₈	D₄×C₃₁	1	8	yes	—
149	C₂×C₄⋊C₄	—	2	16	no	—
150	C₂×C₄⋊C₄	—	2	4	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄²	—	2	4	no	—
153	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
154	C₂×C₄²	D₄×C₃₁	1	2	yes	—
155	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
156	C₄⋊C₈	—	2	8	no	—
157	C₂²⋊C₈	—	4	4	no	—
158	C₃₁	#8342	1	1	yes	characteristic, direct product factor, Sylow
159	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
160	C₂×Q₈	—	2	8	no	—
161	C₂×Q₈	—	2	4	no	—
162	C₂×Q₈	—	4	32	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂×Q₈	—	4	4	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂×Q₈	C₂²⋊C₄×C₃₁	1	8	yes	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	4	no	—
173	C₂²×C₄	—	2	8	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	—	4	4	no	—
176	C₂²×C₄	—	4	4	no	—
177	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
178	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
179	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
180	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
181	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
183	C₂×C₈	—	4	4	no	—
184	C₂×C₈	—	4	4	no	—
185	C₂×C₈	—	4	4	no	—
186	C₄⋊C₄	—	2	16	no	—
187	C₄⋊C₄	—	2	16	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	4	no	—
190	C₄²	C₂×D₄×C₃₁	1	4	yes	—
191	C₂³	—	2	1	no	—
192	C₂³	—	2	2	no	—
193	C₂³	—	2	1	no	—
194	C₂³	C₃₁×#100	1	2	yes	—
195	C₂³	C₃₁×#103	1	4	yes	—
196	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
197	Q₈	—	4	8	no	—
198	Q₈	—	4	16	no	—
199	Q₈	—	4	8	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	2	8	no	—
210	C₂×C₄	—	4	16	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	C₃₁×#100	1	2	yes	—
214	C₂×C₄	C₃₁×#103	1	4	yes	—
215	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
216	C₂×C₄	C₃₁×#120	1	4	yes	—
217	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
218	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
219	C₂×C₄	C₃₁×#137	1	4	yes	—
220	C₈	—	8	4	no	—
221	C₂²	—	2	4	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	2	no	—
224	C₂²	—	2	4	no	—
225	C₂²	C₃₁×#333	1	4	yes	complemented
226	C₂²	C₃₁×#379	1	1	yes	characteristic
227	C₂²	C₂×C₃₁×#100	1	1	yes	characteristic
228	C₂²	C₂×C₃₁×#100	1	1	yes	characteristic
229	C₂²	C₂×C₃₁×#103	1	2	yes	—
230	C₂²	C₃₁×#419	1	2	yes	—
231	C₄	—	2	2	no	—
232	C₄	—	2	2	no	—
233	C₄	—	2	4	no	—
234	C₄	—	4	8	no	—
235	C₄	C₃₁×#448	1	4	yes	—
236	C₄	C₃₁×#451	1	4	yes	—
237	C₂	—	2	4	no	—
238	C₂	C₂×C₃₁×#333	1	1	yes	characteristic
239	C₂	C₃₁×#1548	1	2	yes	—
240	C₂	C₃₁×#1558	1	1	yes	characteristic
241	C₂	C₃₁×#1783	1	1	yes	characteristic
242	C₂	C₃₁×#1787	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₃₁×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₃₁×#1797

C₂

yes

maximal

C₂×C₃₁×#333

C₂

yes

maximal, complemented

C₂³×Q₈×C₃₁

C₄

yes

—

C₂×C₃₁×C₄⋊Q₈

—

C₂×C₃₁×C₄⋊Q₈

—

C₂×C₃₁×C₄⋊Q₈

C₄

yes

—

C₂×C₃₁×C₄⋊Q₈

C₂²

yes

—

C₂²×C₄⋊C₄×C₃₁

—

C₂²×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₃₁×C₄⋊C₈

C₂²

yes

—

C₂×C₃₁×C₂²⋊C₈

—

C₃₁×#336

—

C₃₁×#333

—

C₂²×Q₈×C₃₁

—

C₂²×Q₈×C₃₁

—

C₂²×Q₈×C₃₁

—

C₂²×Q₈×C₃₁

—

C₂²×Q₈×C₃₁

C₂×C₄

yes

—

C₂³×C₄×C₃₁

—

C₂³×C₄×C₃₁

C₂×C₄

yes

characteristic

C₂³×C₄×C₃₁

D₄

yes

—

C₂²×C₈×C₃₁

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄²×C₃₁

—

C₂×C₄²×C₃₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₃₁

D₄

yes

—

C₂×C₄²×C₃₁

C₂³

yes

characteristic

C₃₁×C₄⋊C₈

—

C₃₁×C₂²⋊C₈

—

C₂⁴×C₃₁

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₃₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₃₁

SD₁₆

yes

—

C₂²×C₄×C₃₁

Q₁₆

yes

—

C₂²×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₃₁

C₂×D₄

yes

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

—

C₄²×C₃₁

—

C₄²×C₃₁

C₂×D₄

yes

—

#8342

C₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

#100

yes

—

C₂³×C₃₁

#103

yes

—

C₂³×C₃₁

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₃₁

—

Q₈×C₃₁

—

Q₈×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

#100

yes

—

C₂×C₄×C₃₁

#103

yes

—

C₂×C₄×C₃₁

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₃₁

#120

yes

—

C₂×C₄×C₃₁

C₂×SD₁₆

yes

—

C₂×C₄×C₃₁

C₂×Q₁₆

yes

—

C₂×C₄×C₃₁

#137

yes

—

C₈×C₃₁

—

100

C₂²×C₄⋊Q₈

C₂×C₃₁

yes

characteristic

101

#1797

C₂×C₃₁

yes

—

102

C₂×#333

C₂×C₃₁

yes

complemented

103

C₂²×C₃₁

—

104

C₂²×C₃₁

—

105

C₂²×C₃₁

—

106

C₂²×C₃₁

—

107

C₂²×C₃₁

#333

yes

complemented

108

C₂²×C₃₁

#379

yes

characteristic

109

C₂²×C₃₁

C₂×#100

yes

characteristic

110

C₂²×C₃₁

C₂×#100

yes

characteristic

111

C₂²×C₃₁

C₂×#103

yes

—

112

C₂²×C₃₁

#419

yes

—

113

C₄×C₃₁

—

114

C₄×C₃₁

—

115

C₄×C₃₁

—

116

C₄×C₃₁

—

117

C₄×C₃₁

#448

yes

—

118

C₄×C₃₁

#451

yes

—

119

C₂³×Q₈

C₄×C₃₁

yes

—

120

C₂×C₄⋊Q₈

—

121

C₂×C₄⋊Q₈

—

122

C₂×C₄⋊Q₈

C₄×C₃₁

yes

—

123

C₂×C₄⋊Q₈

C₂²×C₃₁

yes

—

124

C₂²×C₄⋊C₄

—

125

C₂²×C₄²

C₂²×C₃₁

yes

characteristic

126

C₂×C₄⋊C₈

C₂²×C₃₁

yes

—

127

C₂×C₂²⋊C₈

—

128

#336

—

129

#333

—

130

C₂×C₃₁

—

131

C₂×C₃₁

C₂×#333

yes

characteristic

132

C₂×C₃₁

#1548

yes

—

133

C₂×C₃₁

#1558

yes

characteristic

134

C₂×C₃₁

#1783

yes

characteristic

135

C₂×C₃₁

#1787

yes

—

136

C₂²×Q₈

—

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×Q₈

C₂×C₄×C₃₁

yes

—

141

C₂³×C₄

—

142

C₂³×C₄

C₂×C₄×C₃₁

yes

characteristic

143

C₂³×C₄

D₄×C₃₁

yes

—

144

C₂²×C₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

D₄×C₃₁

yes

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂×C₄×C₃₁

yes

characteristic

154

C₂×C₄²

D₄×C₃₁

yes

—

155

C₂×C₄²

C₂³×C₃₁

yes

characteristic

156

C₄⋊C₈

—

157

C₂²⋊C₈

—

158

C₃₁

#8342

yes

characteristic, direct product factor, Sylow

159

C₂⁴

C₂²⋊C₄×C₃₁

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

C₂²⋊C₄×C₃₁

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂²⋊C₄×C₃₁

yes

characteristic

178

C₂²×C₄

C₂²⋊C₄×C₃₁

yes

—

179

C₂²×C₄

SD₁₆×C₃₁

yes

—

180

C₂²×C₄

Q₁₆×C₃₁

yes

—

181

C₂²×C₄

C₂²×C₄×C₃₁

yes

characteristic

182

C₂²×C₄

C₂×D₄×C₃₁

yes

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×D₄×C₃₁

yes

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

C₃₁×#100

yes

—

195

C₂³

C₃₁×#103

yes

—

196

C₂³

C₂×C₂²⋊C₄×C₃₁

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

C₃₁×#100

yes

—

214

C₂×C₄

C₃₁×#103

yes

—

215

C₂×C₄

C₂×C₂²⋊C₄×C₃₁

yes

—

216

C₂×C₄

C₃₁×#120

yes

—

217

C₂×C₄

C₂×SD₁₆×C₃₁

yes

—

218

C₂×C₄

C₂×Q₁₆×C₃₁

yes

—

219

C₂×C₄

C₃₁×#137

yes

—

220

C₈

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₃₁×#333

yes

complemented

226

C₂²

C₃₁×#379

yes

characteristic

227

C₂²

C₂×C₃₁×#100

yes

characteristic

228

C₂²

C₂×C₃₁×#100

yes

characteristic

229

C₂²

C₂×C₃₁×#103

yes

—

230

C₂²

C₃₁×#419

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

C₃₁×#448

yes

—

236

C₄

C₃₁×#451

yes

—

237

C₂

—

238

C₂

C₂×C₃₁×#333

yes

characteristic

239

C₂

C₃₁×#1548

yes

—

240

C₂

C₃₁×#1558

yes

characteristic

241

C₂

C₃₁×#1783

yes

characteristic

242

C₂

C₃₁×#1787

yes

—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂⁴×C₃₁	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₃₁

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₃₁

Frattini, cosocle

C₂×C₄²

C₂³×C₃₁

prime radical

C₂⁴×C₃₁

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

N	H ≅ G/N	type
3. C₂×C₃₁×#333	C₂	semidirect
69. #8342	C₃₁	direct (N × H)
102. C₂×#333	C₂×C₃₁	semidirect
107. C₂²×C₃₁	#333	semidirect
158. C₃₁	#8342	direct (N × H)
225. C₂²	C₃₁×#333	semidirect

H ≅ G/N

type

3. C₂×C₃₁×#333

C₂

semidirect

69. #8342

C₃₁

direct (N × H)

102. C₂×#333

C₂×C₃₁

semidirect

107. C₂²×C₃₁

#333

semidirect

158. C₃₁

#8342

direct (N × H)

225. C₂²

C₃₁×#333

semidirect

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

subgroup	index
C₂²×C₃₁×C₄⋊Q₈	2
C₃₁×#1797	2
C₂×C₃₁×#333	2
#8342	31

subgroup

index

C₂²×C₃₁×C₄⋊Q₈

C₃₁×#1797

C₂×C₃₁×#333

#8342

Subgroups — C₃₁×#8342 #21465101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C31×#8342 #21465101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#8342 #21465101