Group #24989444 — subgroups

Subgroups — #24989444

Order 11008.

478 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14582950	C₂	1	1	yes	maximal, characteristic
2	#19134572	C₂	1	2	yes	maximal
3	C₂×#14582649	C₂	1	2	yes	maximal, complemented
4	#19132430	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
7	#14582950	—	2	4	no	—
8	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
9	C₂×Dic₄₃⋊C₈	C₄	1	2	yes	—
10	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
11	C₂×(C₂×D₄₃)⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	#14582653	—	2	2	no	—
14	#14582649	—	2	4	no	—
15	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
20	C₂²×C₄₃⋊C₈	—	2	2	no	—
21	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
24	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
25	C₄²×D₄₃	—	2	2	no	—
26	C₄²×D₄₃	—	2	2	no	—
27	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
29	Dic₄₃⋊C₈	—	2	4	no	—
30	(C₂×D₄₃)⋊C₈	—	2	4	no	—
31	(C₂×D₄₃)⋊C₈	—	4	4	no	—
32	C₄×C₄₃⋊C₈	D₄	1	4	yes	—
33	C₂²×C₈×C₄₃	—	2	2	no	—
34	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₄₃	—	2	2	no	—
37	C₄⋊C₈×C₄₃	—	2	2	no	—
38	C₄×C₈×C₄₃	—	2	2	no	—
39	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
43	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₄₃	—	2	2	no	—
47	C₂×C₄×D₄₃	—	2	1	no	—
48	C₂×C₄×D₄₃	—	2	1	no	—
49	C₂×C₄×D₄₃	—	2	1	no	—
50	C₂×C₄×D₄₃	—	2	1	no	—
51	C₂×C₄×D₄₃	—	2	2	no	—
52	C₂×C₄×D₄₃	—	2	2	no	—
53	C₂×C₄×D₄₃	—	2	2	no	—
54	C₂×C₄×D₄₃	—	4	2	no	—
55	C₂×C₄×D₄₃	SD₁₆	1	4	yes	—
56	C₂×C₈×C₄₃	—	2	2	no	—
57	C₂×C₈×C₄₃	—	2	2	no	—
58	C₂×C₈×C₄₃	—	2	2	no	—
59	C₂×C₈×C₄₃	—	4	2	no	—
60	C₂×C₈×C₄₃	—	4	2	no	—
61	C₂×C₈×C₄₃	—	4	2	no	—
62	C₄²×C₄₃	C₂×D₄	1	2	yes	—
63	C₄²×C₄₃	#41	1	2	yes	—
64	C₄×Dic₄₃	—	2	1	no	—
65	C₄×Dic₄₃	—	2	1	no	—
66	C₄×Dic₄₃	—	2	2	no	—
67	C₄×Dic₄₃	—	2	2	no	—
68	C₂×C₄₃⋊C₈	—	2	2	no	—
69	C₂×C₄₃⋊C₈	—	2	2	no	—
70	C₂×C₄₃⋊C₈	—	4	2	no	—
71	C₂×C₄₃⋊C₈	—	4	2	no	—
72	C₂×C₄₃⋊C₈	—	4	2	no	—
73	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
74	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂²×D₄₃	—	2	1	no	—
76	C₂²×D₄₃	—	2	2	no	—
77	C₂²×D₄₃	—	2	1	no	—
78	C₂²×D₄₃	—	2	2	no	—
79	C₂²×D₄₃	#106	1	2	yes	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#121	1	2	yes	—
84	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₄₃	#131	1	2	yes	—
86	C₂×C₄×C₄₃	#131	1	2	yes	—
87	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
90	C₂×Dic₄₃	—	2	1	no	—
91	C₂×Dic₄₃	—	2	1	no	—
92	C₂×Dic₄₃	—	2	1	no	—
93	C₂×Dic₄₃	—	2	1	no	—
94	C₂×Dic₄₃	—	2	2	no	—
95	C₂×Dic₄₃	—	2	2	no	—
96	C₂×Dic₄₃	#106	1	2	yes	—
97	C₄×D₄₃	—	2	4	no	—
98	C₄×D₄₃	—	2	4	no	—
99	C₄×D₄₃	—	4	4	no	—
100	C₄×D₄₃	—	4	2	no	—
101	C₄×D₄₃	—	4	1	no	—
102	C₄×D₄₃	—	4	1	no	—
103	C₈×C₄₃	—	4	2	no	—
104	C₈×C₄₃	—	8	2	no	—
105	C₄₃⋊C₈	—	2	4	no	—
106	C₄₃⋊C₈	—	8	2	no	—
107	#8598	—	43	1	no	maximal, Sylow
108	C₂²×C₄₃	#380	1	1	yes	characteristic
109	C₂²×C₄₃	#424	1	2	yes	—
110	C₂²×C₄₃	C₂×#106	1	1	yes	characteristic
111	C₂²×C₄₃	#427	1	1	yes	characteristic
112	C₂²×C₄₃	#430	1	2	yes	—
113	C₂×D₄₃	—	2	2	no	—
114	C₂×D₄₃	—	2	4	no	—
115	C₂×D₄₃	—	4	1	no	—
116	C₂×D₄₃	—	4	1	no	—
117	C₂×D₄₃	—	4	2	no	—
118	C₄×C₄₃	—	2	2	no	—
119	C₄×C₄₃	#408	1	2	yes	—
120	C₄×C₄₃	#433	1	1	yes	characteristic
121	C₄×C₄₃	#433	1	1	yes	characteristic
122	C₄×C₄₃	#465	1	2	yes	—
123	C₄×C₄₃	#465	1	2	yes	—
124	Dic₄₃	—	2	2	no	—
125	Dic₄₃	—	4	1	no	—
126	Dic₄₃	—	4	1	no	—
127	C₂×#431	—	43	1	no	—
128	#1797	—	43	2	no	—
129	C₂×#334	—	43	2	no	—
130	#1277	—	43	1	no	—
131	#1277	D₄₃	1	1	yes	characteristic, complemented
132	C₂×C₄₃	#1570	1	2	yes	—
133	C₂×C₄₃	#1572	1	2	yes	—
134	C₂×C₄₃	#1798	1	1	yes	characteristic
135	C₂×C₄₃	#1807	1	1	yes	characteristic
136	C₂×C₄₃	#1811	1	1	yes	characteristic
137	D₄₃	—	4	2	no	—
138	C₂²×C₄²	—	43	1	no	—
139	#431	—	86	4	no	—
140	C₂×C₄⋊C₈	—	43	2	no	—
141	C₂×C₄⋊C₈	—	43	2	no	—
142	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
143	C₂×C₂²⋊C₈	—	43	2	no	—
144	C₂×C₂²⋊C₈	—	86	2	no	—
145	C₂×C₄×C₈	—	43	1	no	—
146	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
147	#336	—	86	2	no	—
148	#334	—	86	4	no	—
149	C₄₃	#8598	1	1	yes	characteristic, complemented, Sylow
150	C₂³×C₄	—	43	1	no	—
151	C₂³×C₄	—	43	1	no	—
152	C₂³×C₄	—	43	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	—	43	2	no	—
155	C₂²×C₈	—	86	2	no	—
156	C₂²×C₈	C₄×D₄₃	1	2	yes	—
157	C₂×C₄²	—	43	1	no	—
158	C₂×C₄²	—	43	1	no	—
159	C₂×C₄²	—	43	1	no	—
160	C₂×C₄²	—	86	2	no	—
161	C₂×C₄²	—	86	2	no	—
162	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	86	4	no	—
166	C₄⋊C₈	—	86	2	no	—
167	C₄⋊C₈	—	86	2	no	—
168	C₂²⋊C₈	—	86	4	no	—
169	C₂²⋊C₈	—	172	4	no	—
170	C₄×C₈	—	2	2	no	—
171	C₄×C₈	—	43	4	no	—
172	C₂⁴	—	43	1	no	—
173	C₂²×C₄	—	43	1	no	—
174	C₂²×C₄	—	43	4	no	—
175	C₂²×C₄	—	43	1	no	—
176	C₂²×C₄	—	43	1	no	—
177	C₂²×C₄	—	86	2	no	—
178	C₂²×C₄	—	86	1	no	—
179	C₂²×C₄	—	86	1	no	—
180	C₂²×C₄	—	86	1	no	—
181	C₂²×C₄	—	86	1	no	—
182	C₂²×C₄	—	86	2	no	—
183	C₂²×C₄	—	86	2	no	—
184	C₂²×C₄	—	86	2	no	—
185	C₂²×C₄	—	172	2	no	—
186	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
187	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
188	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	43	4	no	—
196	C₂×C₈	—	86	2	no	—
197	C₂×C₈	—	86	2	no	—
198	C₂×C₈	—	172	2	no	—
199	C₂×C₈	—	172	2	no	—
200	C₂×C₈	—	172	2	no	—
201	C₄²	—	86	1	no	—
202	C₄²	—	86	1	no	—
203	C₄²	—	86	2	no	—
204	C₄²	—	86	2	no	—
205	C₄²	#10621898	1	2	yes	—
206	C₄²	D₄×D₄₃	1	2	yes	—
207	C₂³	—	43	2	no	—
208	C₂³	—	86	2	no	—
209	C₂³	—	86	1	no	—
210	C₂³	—	86	2	no	—
211	C₂³	—	86	1	no	—
212	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	43	2	no	—
215	C₂×C₄	—	86	1	no	—
216	C₂×C₄	—	86	1	no	—
217	C₂×C₄	—	86	4	no	—
218	C₂×C₄	—	86	4	no	—
219	C₂×C₄	—	86	2	no	—
220	C₂×C₄	—	86	2	no	—
221	C₂×C₄	—	86	1	no	—
222	C₂×C₄	—	86	1	no	—
223	C₂×C₄	—	172	4	no	—
224	C₂×C₄	—	172	2	no	—
225	C₂×C₄	—	172	1	no	—
226	C₂×C₄	—	172	1	no	—
227	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
228	C₂×C₄	#13063282	1	1	yes	characteristic
229	C₂×C₄	#13063298	1	2	yes	—
230	C₂×C₄	#13063303	1	2	yes	—
231	C₂×C₄	#13063331	1	2	yes	—
232	C₂×C₄	#13063333	1	2	yes	—
233	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
234	C₂×C₄	#13063344	1	1	yes	characteristic
235	C₂×C₄	#13063348	1	1	yes	characteristic
236	C₈	—	4	2	no	—
237	C₈	—	8	2	no	—
238	C₈	—	86	4	no	—
239	C₈	—	344	2	no	—
240	C₂²	—	86	2	no	—
241	C₂²	—	86	4	no	—
242	C₂²	—	172	1	no	—
243	C₂²	—	172	1	no	—
244	C₂²	—	172	2	no	—
245	C₂²	#14582758	1	1	yes	characteristic
246	C₂²	#14582924	1	2	yes	—
247	C₂²	#106×D₄₃	1	1	yes	characteristic
248	C₂²	#14582936	1	1	yes	characteristic
249	C₂²	#14582946	1	2	yes	—
250	C₄	—	2	2	no	—
251	C₄	—	86	2	no	—
252	C₄	—	172	1	no	—
253	C₄	—	172	1	no	—
254	C₄	#14582864	1	2	yes	—
255	C₄	#14582958	1	1	yes	characteristic
256	C₄	#14582961	1	1	yes	characteristic
257	C₄	#14583127	1	2	yes	—
258	C₄	#14583131	1	2	yes	—
259	C₂	—	172	2	no	—
260	C₂	#19133364	1	2	yes	—
261	C₂	#19133374	1	2	yes	—
262	C₂	#19134578	1	1	yes	characteristic
263	C₂	#19134619	1	1	yes	characteristic
264	C₂	#19134636	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582950

C₂

yes

maximal, characteristic

#19134572

C₂

yes

maximal

C₂×#14582649

C₂

yes

maximal, complemented

#19132430

C₂

yes

maximal, characteristic, complemented

C₄₃×#1277

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₄₃

C₂²

yes

characteristic

#14582950

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂×Dic₄₃⋊C₈

C₄

yes

—

C₂×(C₂×D₄₃)⋊C₈

—

C₂×(C₂×D₄₃)⋊C₈

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582653

—

#14582649

—

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×D₄₃

D₄

yes

characteristic

C₂²×C₄×D₄₃

Q₈

yes

characteristic

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄×Dic₄₃

Q₈

yes

characteristic

C₄²×D₄₃

—

C₄²×D₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

Dic₄₃⋊C₈

—

(C₂×D₄₃)⋊C₈

—

(C₂×D₄₃)⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂³×D₄₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂²×Dic₄₃

C₄⋊C₄

yes

characteristic

C₂²×Dic₄₃

C₄⋊C₄

yes

characteristic

C₂²×Dic₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

#106

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#106

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

100

C₄×D₄₃

—

101

C₄×D₄₃

—

102

C₄×D₄₃

—

103

C₈×C₄₃

—

104

C₈×C₄₃

—

105

C₄₃⋊C₈

—

106

C₄₃⋊C₈

—

107

#8598

—

maximal, Sylow

108

C₂²×C₄₃

#380

yes

characteristic

109

C₂²×C₄₃

#424

yes

—

110

C₂²×C₄₃

C₂×#106

yes

characteristic

111

C₂²×C₄₃

#427

yes

characteristic

112

C₂²×C₄₃

#430

yes

—

113

C₂×D₄₃

—

114

C₂×D₄₃

—

115

C₂×D₄₃

—

116

C₂×D₄₃

—

117

C₂×D₄₃

—

118

C₄×C₄₃

—

119

C₄×C₄₃

#408

yes

—

120

C₄×C₄₃

#433

yes

characteristic

121

C₄×C₄₃

#433

yes

characteristic

122

C₄×C₄₃

#465

yes

—

123

C₄×C₄₃

#465

yes

—

124

Dic₄₃

—

125

Dic₄₃

—

126

Dic₄₃

—

127

C₂×#431

—

128

#1797

—

129

C₂×#334

—

130

#1277

—

131

#1277

D₄₃

yes

characteristic, complemented

132

C₂×C₄₃

#1570

yes

—

133

C₂×C₄₃

#1572

yes

—

134

C₂×C₄₃

#1798

yes

characteristic

135

C₂×C₄₃

#1807

yes

characteristic

136

C₂×C₄₃

#1811

yes

characteristic

137

D₄₃

—

138

C₂²×C₄²

—

139

#431

—

140

C₂×C₄⋊C₈

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

143

C₂×C₂²⋊C₈

—

144

C₂×C₂²⋊C₈

—

145

C₂×C₄×C₈

—

146

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

147

#336

—

148

#334

—

149

C₄₃

#8598

yes

characteristic, complemented, Sylow

150

C₂³×C₄

—

151

C₂³×C₄

—

152

C₂³×C₄

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

C₄×D₄₃

yes

—

157

C₂×C₄²

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

C₂×C₄²

—

161

C₂×C₄²

—

162

C₂×C₄²

C₂²×D₄₃

yes

characteristic

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₂²⋊C₈

—

169

C₂²⋊C₈

—

172

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₂⁴

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

172

—

186

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

187

C₂²×C₄

D₄×D₄₃

yes

characteristic

188

C₂²×C₄

Q₈×D₄₃

yes

characteristic

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

172

—

199

C₂×C₈

—

172

—

200

C₂×C₈

—

172

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

#10621898

yes

—

206

C₄²

D₄×D₄₃

yes

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₄⋊C₄×D₄₃

yes

characteristic

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

—

172

—

224

C₂×C₄

—

172

—

225

C₂×C₄

—

172

—

226

C₂×C₄

—

172

—

227

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

228

C₂×C₄

#13063282

yes

characteristic

229

C₂×C₄

#13063298

yes

—

230

C₂×C₄

#13063303

yes

—

231

C₂×C₄

#13063331

yes

—

232

C₂×C₄

#13063333

yes

—

233

C₂×C₄

SD₁₆×D₄₃

yes

—

234

C₂×C₄

#13063344

yes

characteristic

235

C₂×C₄

#13063348

yes

characteristic

236

C₈

—

237

C₈

—

238

C₈

—

239

C₈

—

344

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

172

—

243

C₂²

—

172

—

244

C₂²

—

172

—

245

C₂²

#14582758

yes

characteristic

246

C₂²

#14582924

yes

—

247

C₂²

#106×D₄₃

yes

characteristic

248

C₂²

#14582936

yes

characteristic

249

C₂²

#14582946

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

172

—

253

C₄

—

172

—

254

C₄

#14582864

yes

—

255

C₄

#14582958

yes

characteristic

256

C₄

#14582961

yes

characteristic

257

C₄

#14583127

yes

—

258

C₄

#14583131

yes

—

259

C₂

—

172

—

260

C₂

#19133364

yes

—

261

C₂

#19133374

yes

—

262

C₂

#19134578

yes

characteristic

263

C₂

#19134619

yes

characteristic

264

C₂

#19134636

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1277	C₂
socle	C₂³×C₄₃	C₂×C₄⋊C₄
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1277	D₄₃
hypocenter	C₄₃	#8598
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂²×C₄

D₄×D₄₃

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1277

C₂

socle

C₂³×C₄₃

C₂×C₄⋊C₄

prime radical

C₂³×D₄₃

C₄⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
3. C₂×#14582649	C₂	semidirect
4. #19132430	C₂	semidirect
5. C₄₃×#1277	C₂	semidirect
131. #1277	D₄₃	semidirect
149. C₄₃	#8598	semidirect

H ≅ G/N

type

3. C₂×#14582649

C₂

semidirect

4. #19132430

C₂

semidirect

5. C₄₃×#1277

C₂

semidirect

131. #1277

D₄₃

semidirect

149. C₄₃

#8598

semidirect

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

subgroup	index
C₂×#14582950	2
#19134572	2
C₂×#14582649	2
#19132430	2
C₄₃×#1277	2
#8598	43

subgroup

index

C₄₃×#1277

Subgroups — #24989444

Conjugacy classes of subgroups

Complements

Maximal subgroups