Group #24984870 — subgroups

Subgroups — #24984870

Order 11008.

468 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄×#13063325	C₂	1	1	yes	maximal, characteristic
2	#19134344	C₂	1	1	yes	maximal, characteristic
3	#19132420	C₂	1	4	yes	maximal
4	C₄₃×#1745	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063325	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₈₆	C₄	1	2	yes	—
7	C₂×#13063236	—	2	1	no	—
8	#14582805	C₂²	1	2	yes	—
9	#14582797	—	2	1	no	—
10	#14582797	—	2	1	no	—
11	#14582769	C₄	1	1	yes	characteristic
12	C₄×C₄⋊Dic₄₃	—	2	1	no	—
13	C₄×C₄⋊Dic₄₃	—	2	1	no	—
14	#14582654	—	2	1	no	—
15	#14582654	C₂²	1	2	yes	—
16	C₂×#97×C₄₃	—	2	1	no	—
17	C₄³×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#336	—	2	1	no	—
19	C₄₃×#336	C₂²	1	2	yes	—
20	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
21	C₂²×C₄₃⋊C₈	—	2	2	no	—
22	#13063325	—	2	4	no	—
23	C₄×Dic₈₆	—	4	4	no	—
24	C₂×C₄⋊Dic₄₃	—	2	1	no	—
25	C₂×C₄⋊Dic₄₃	—	2	1	no	—
26	C₂×C₄⋊Dic₄₃	—	2	1	no	—
27	C₂×C₄⋊Dic₄₃	—	2	1	no	—
28	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
29	C₂×Dic₄₃⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₄₃	—	2	2	no	—
31	#13063236	—	2	4	no	—
32	C₄₃⋊#95	—	2	2	no	—
33	C₄₃⋊#95	—	2	2	no	—
34	C₂²×C₈×C₄₃	—	2	2	no	—
35	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
42	#97×C₄₃	—	2	4	no	—
43	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₄₃	—	2	2	no	—
51	C₂²×Dic₄₃	—	2	2	no	—
52	C₂×Dic₈₆	—	2	2	no	—
53	C₂×Dic₈₆	—	4	2	no	—
54	C₂×Dic₈₆	—	4	2	no	—
55	C₂×Dic₈₆	M₁₆	1	4	yes	—
56	C₂×C₈×C₄₃	—	2	4	no	—
57	C₂×C₈×C₄₃	—	4	2	no	—
58	C₂×C₈×C₄₃	—	4	2	no	—
59	C₄²×C₄₃	—	2	2	no	—
60	C₄²×C₄₃	—	2	2	no	—
61	C₄²×C₄₃	—	2	2	no	—
62	C₄²×C₄₃	—	2	2	no	—
63	C₄²×C₄₃	—	2	2	no	—
64	C₄²×C₄₃	—	2	2	no	—
65	C₄²×C₄₃	—	4	1	no	—
66	C₄⋊Dic₄₃	—	2	4	no	—
67	C₄⋊Dic₄₃	—	2	4	no	—
68	C₄⋊Dic₄₃	—	4	2	no	—
69	C₄⋊Dic₄₃	—	4	2	no	—
70	C₄⋊Dic₄₃	—	4	2	no	—
71	Dic₄₃⋊C₄	—	4	4	no	—
72	C₄×Dic₄₃	—	4	4	no	—
73	C₂×C₄₃⋊C₈	—	2	4	no	—
74	C₂×C₄₃⋊C₈	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	4	2	no	—
76	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	—	2	1	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	—	2	1	no	—
81	C₂×C₄×C₄₃	—	2	1	no	—
82	C₂×C₄×C₄₃	—	2	1	no	—
83	C₂×C₄×C₄₃	—	2	1	no	—
84	C₂×C₄×C₄₃	—	2	1	no	—
85	C₂×C₄×C₄₃	—	2	1	no	—
86	C₂×C₄×C₄₃	—	2	1	no	—
87	C₂×C₄×C₄₃	—	2	1	no	—
88	C₂×C₄×C₄₃	—	2	1	no	—
89	C₂×C₄×C₄₃	—	2	1	no	—
90	C₂×C₄×C₄₃	—	2	1	no	—
91	C₂×C₄×C₄₃	—	2	1	no	—
92	C₂×C₄×C₄₃	#100	1	2	yes	—
93	C₂×C₄×C₄₃	#104	1	2	yes	—
94	C₂×C₄×C₄₃	#104	1	2	yes	—
95	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
96	C₂×C₄×C₄₃	#137	1	2	yes	—
97	C₂×C₄×C₄₃	#137	1	2	yes	—
98	C₂×Dic₄₃	—	2	4	no	—
99	C₂×Dic₄₃	—	4	2	no	—
100	C₂×Dic₄₃	—	4	2	no	—
101	C₂×Dic₄₃	—	4	2	no	—
102	C₂×Dic₄₃	—	4	2	no	—
103	C₂×Dic₄₃	—	4	2	no	—
104	Dic₈₆	—	4	4	no	—
105	Dic₈₆	—	4	4	no	—
106	C₈×C₄₃	—	4	4	no	—
107	C₄₃⋊C₈	—	4	4	no	—
108	#7639	—	43	1	no	maximal, Sylow
109	C₂²×C₄₃	#407	1	1	yes	characteristic
110	C₂²×C₄₃	#410	1	1	yes	characteristic
111	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
112	C₂²×C₄₃	#419	1	1	yes	characteristic
113	C₂²×C₄₃	#419	1	1	yes	characteristic
114	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
115	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
116	C₄×C₄₃	—	2	2	no	—
117	C₄×C₄₃	—	2	2	no	—
118	C₄×C₄₃	—	2	2	no	—
119	C₄×C₄₃	—	2	2	no	—
120	C₄×C₄₃	—	2	2	no	—
121	C₄×C₄₃	—	2	2	no	—
122	C₄×C₄₃	—	4	1	no	—
123	Dic₄₃	—	4	4	no	—
124	Dic₄₃	—	8	2	no	—
125	C₄×C₄⋊Q₈	—	43	1	no	—
126	#1745	—	43	1	no	—
127	#1745	D₄₃	1	1	yes	characteristic
128	#1272	—	43	4	no	—
129	C₂×C₄₃	#1466	1	1	yes	characteristic
130	C₂×C₄₃	#1491	1	1	yes	characteristic
131	C₂×C₄₃	#1491	1	1	yes	characteristic
132	C₂×C₄₃	#1506	1	1	yes	characteristic
133	C₂×C₄₃	#1506	1	1	yes	characteristic
134	C₂×C₄₃	#1525	1	1	yes	characteristic
135	C₂×C₄₃	#1558	1	1	yes	characteristic
136	C₂×C₄⋊Q₈	—	43	1	no	—
137	C₂×C₄×Q₈	—	43	2	no	—
138	C₂×#97	—	2	1	no	—
139	C₂×#97	—	86	1	no	—
140	#391	—	43	2	no	—
141	#389	—	86	1	no	—
142	#389	—	86	1	no	—
143	#384	—	43	1	no	—
144	C₄×C₄⋊C₄	—	86	1	no	—
145	C₄×C₄⋊C₄	—	86	1	no	—
146	C₄³	C₂×D₄₃	1	1	yes	characteristic
147	#336	—	2	1	no	—
148	#336	—	43	2	no	—
149	#336	—	86	1	no	—
150	#336	C₂×D₄₃	1	2	yes	—
151	C₄₃	#7639	1	1	yes	characteristic, complemented, Sylow
152	C₂²×Q₈	—	43	2	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	—	86	2	no	—
155	C₄⋊Q₈	—	86	4	no	—
156	C₄×Q₈	—	172	4	no	—
157	C₂×C₄⋊C₄	—	43	2	no	—
158	C₂×C₄⋊C₄	—	86	1	no	—
159	C₂×C₄⋊C₄	—	86	1	no	—
160	C₂×C₄⋊C₄	—	86	2	no	—
161	C₂×C₄⋊C₄	—	86	1	no	—
162	C₂×C₄⋊C₄	—	86	1	no	—
163	C₂×C₄²	—	86	2	no	—
164	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
165	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
166	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
167	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
168	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
169	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
170	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
171	#97	—	2	4	no	—
172	#97	—	86	4	no	—
173	#95	—	86	2	no	—
174	#95	—	86	2	no	—
175	C₂×Q₈	—	43	4	no	—
176	C₂×Q₈	—	86	2	no	—
177	C₂×Q₈	—	172	2	no	—
178	C₂×Q₈	—	172	2	no	—
179	C₂²×C₄	—	86	2	no	—
180	C₂²×C₄	—	86	2	no	—
181	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
182	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
183	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
186	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	86	4	no	—
192	C₂×C₈	—	172	2	no	—
193	C₂×C₈	—	172	2	no	—
194	C₄⋊C₄	—	86	4	no	—
195	C₄⋊C₄	—	86	4	no	—
196	C₄⋊C₄	—	172	2	no	—
197	C₄⋊C₄	—	172	4	no	—
198	C₄⋊C₄	—	172	2	no	—
199	C₄⋊C₄	—	172	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	—	172	4	no	—
208	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
209	Q₈	—	172	4	no	—
210	Q₈	—	172	4	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	86	4	no	—
227	C₂×C₄	—	172	2	no	—
228	C₂×C₄	—	172	2	no	—
229	C₂×C₄	—	172	2	no	—
230	C₂×C₄	—	172	2	no	—
231	C₂×C₄	—	172	2	no	—
232	C₂×C₄	#13063241	1	2	yes	—
233	C₂×C₄	#13063251	1	2	yes	—
234	C₂×C₄	#13063253	1	2	yes	—
235	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
236	C₂×C₄	#13063355	1	2	yes	—
237	C₂×C₄	#13063358	1	2	yes	—
238	C₈	—	4	4	no	—
239	C₈	—	172	4	no	—
240	C₂²	#14582862	1	1	yes	characteristic
241	C₂²	#14582872	1	1	yes	characteristic
242	C₂²	C₂×#13063241	1	1	yes	characteristic
243	C₂²	#14582907	1	1	yes	characteristic
244	C₂²	#14582909	1	1	yes	characteristic
245	C₂²	C₂×#13063251	1	1	yes	characteristic
246	C₂²	C₂×#13063253	1	1	yes	characteristic
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	2	2	no	—
252	C₄	—	2	2	no	—
253	C₄	—	4	1	no	—
254	C₄	—	344	2	no	—
255	C₄	—	172	4	no	—
256	C₂	#19132935	1	1	yes	characteristic
257	C₂	#19133041	1	1	yes	characteristic
258	C₂	#19133043	1	1	yes	characteristic
259	C₂	#19133106	1	1	yes	characteristic
260	C₂	#19133108	1	1	yes	characteristic
261	C₂	#19133186	1	1	yes	characteristic
262	C₂	#19133320	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063325

C₂

yes

maximal, characteristic

#19134344

C₂

yes

maximal, characteristic

#19132420

C₂

yes

maximal

C₄₃×#1745

C₂

yes

maximal, characteristic

C₂×#13063325

C₄

yes

characteristic

C₂×C₄×Dic₈₆

C₄

yes

—

C₂×#13063236

—

#14582805

C₂²

yes

—

#14582797

—

#14582797

—

#14582769

C₄

yes

characteristic

C₄×C₄⋊Dic₄₃

—

C₄×C₄⋊Dic₄₃

—

#14582654

—

#14582654

C₂²

yes

—

C₂×#97×C₄₃

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

—

C₄₃×#336

C₂²

yes

—

C₂²×Dic₈₆

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

—

#13063325

—

C₄×Dic₈₆

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

#13063236

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

M₁₆

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#100

yes

—

C₂×C₄×C₄₃

#104

yes

—

C₂×C₄×C₄₃

#104

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

100

C₂×Dic₄₃

—

101

C₂×Dic₄₃

—

102

C₂×Dic₄₃

—

103

C₂×Dic₄₃

—

104

Dic₈₆

—

105

Dic₈₆

—

106

C₈×C₄₃

—

107

C₄₃⋊C₈

—

108

#7639

—

maximal, Sylow

109

C₂²×C₄₃

#407

yes

characteristic

110

C₂²×C₄₃

#410

yes

characteristic

111

C₂²×C₄₃

C₂×#100

yes

characteristic

112

C₂²×C₄₃

#419

yes

characteristic

113

C₂²×C₄₃

#419

yes

characteristic

114

C₂²×C₄₃

C₂×#104

yes

characteristic

115

C₂²×C₄₃

C₂×#104

yes

characteristic

116

C₄×C₄₃

—

117

C₄×C₄₃

—

118

C₄×C₄₃

—

119

C₄×C₄₃

—

120

C₄×C₄₃

—

121

C₄×C₄₃

—

122

C₄×C₄₃

—

123

Dic₄₃

—

124

Dic₄₃

—

125

C₄×C₄⋊Q₈

—

126

#1745

—

127

#1745

D₄₃

yes

characteristic

128

#1272

—

129

C₂×C₄₃

#1466

yes

characteristic

130

C₂×C₄₃

#1491

yes

characteristic

131

C₂×C₄₃

#1491

yes

characteristic

132

C₂×C₄₃

#1506

yes

characteristic

133

C₂×C₄₃

#1506

yes

characteristic

134

C₂×C₄₃

#1525

yes

characteristic

135

C₂×C₄₃

#1558

yes

characteristic

136

C₂×C₄⋊Q₈

—

137

C₂×C₄×Q₈

—

138

C₂×#97

—

139

C₂×#97

—

140

#391

—

141

#389

—

142

#389

—

143

#384

—

144

C₄×C₄⋊C₄

—

145

C₄×C₄⋊C₄

—

146

C₄³

C₂×D₄₃

yes

characteristic

147

#336

—

148

#336

—

149

#336

—

150

#336

C₂×D₄₃

yes

—

151

C₄₃

#7639

yes

characteristic, complemented, Sylow

152

C₂²×Q₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₄⋊Q₈

—

156

C₄×Q₈

—

172

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

—

164

C₂×C₄²

C₄×D₄₃

yes

characteristic

165

C₂×C₄²

C₄×D₄₃

yes

characteristic

166

C₂×C₄²

D₁₇₂

yes

characteristic

167

C₂×C₄²

D₁₇₂

yes

characteristic

168

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

169

C₂×C₄²

C₂²⋊D₄₃

yes

characteristic

170

C₂×C₄²

C₂²×D₄₃

yes

characteristic

171

#97

—

172

#97

—

173

#95

—

174

#95

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

172

—

178

C₂×Q₈

—

172

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

182

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

183

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

184

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

185

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

186

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

172

—

193

C₂×C₈

—

172

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

172

—

197

C₄⋊C₄

—

172

—

198

C₄⋊C₄

—

172

—

199

C₄⋊C₄

—

172

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

172

—

208

C₂³

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

209

Q₈

—

172

—

210

Q₈

—

172

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

172

—

228

C₂×C₄

—

172

—

229

C₂×C₄

—

172

—

230

C₂×C₄

—

172

—

231

C₂×C₄

—

172

—

232

C₂×C₄

#13063241

yes

—

233

C₂×C₄

#13063251

yes

—

234

C₂×C₄

#13063253

yes

—

235

C₂×C₄

M₁₆×D₄₃

yes

—

236

C₂×C₄

#13063355

yes

—

237

C₂×C₄

#13063358

yes

—

238

C₈

—

239

C₈

—

172

—

240

C₂²

#14582862

yes

characteristic

241

C₂²

#14582872

yes

characteristic

242

C₂²

C₂×#13063241

yes

characteristic

243

C₂²

#14582907

yes

characteristic

244

C₂²

#14582909

yes

characteristic

245

C₂²

C₂×#13063251

yes

characteristic

246

C₂²

C₂×#13063253

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

344

—

255

C₄

—

172

—

256

C₂

#19132935

yes

characteristic

257

C₂

#19133041

yes

characteristic

258

C₂

#19133043

yes

characteristic

259

C₂

#19133106

yes

characteristic

260

C₂

#19133108

yes

characteristic

261

C₂

#19133186

yes

characteristic

262

C₂

#19133320

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1745	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1745	D₄₃
hypocenter	C₄₃	#7639
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

subgroup

G/H

center

C₂³

C₂×(C₂×D₄₃)⋊C₄

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1745

C₂

socle, prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

N	H ≅ G/N	type
151. C₄₃	#7639	semidirect

H ≅ G/N

type

151. C₄₃

#7639

semidirect

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

subgroup	index
C₄×#13063325	2
#19134344	2
#19132420	2
C₄₃×#1745	2
#7639	43

subgroup

index

C₄₃×#1745

Subgroups — #24984870

Conjugacy classes of subgroups

Complements

Maximal subgroups