Group #25253037 — subgroups

Subgroups — #25253037

Order 11008.

488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 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	#19145235	C₂	1	2	yes	maximal, complemented
2	#19136745	C₂	1	2	yes	maximal, complemented
3	#19136731	C₂	1	2	yes	maximal, complemented
4	#19136710	C₂	1	2	yes	maximal, complemented
5	#19136681	C₂	1	1	yes	maximal, characteristic
6	#19136659	C₂	1	2	yes	maximal, complemented
7	#19136653	C₂	1	2	yes	maximal, complemented
8	#19136353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2216	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583522	—	2	2	no	—
11	C₂×#13063268	C₂²	1	2	yes	—
12	C₂×D₆₈₈	C₂²	1	1	yes	characteristic
13	C₂×#13063265	C₂²	1	1	yes	characteristic
14	#14583303	C₂²	1	2	yes	—
15	#14583284	C₂²	1	2	yes	—
16	#14583260	—	2	2	no	—
17	#14583147	—	2	2	no	—
18	#14583135	C₂²	1	2	yes	—
19	#14583002	—	2	2	no	—
20	Q₁₆×Dic₄₃	C₂²	1	2	yes	—
21	#14582981	C₂²	1	2	yes	—
22	#14582854	C₂²	1	1	yes	characteristic
23	#14582725	C₂²	1	1	yes	characteristic
24	#14582724	C₂²	1	2	yes	—
25	Dic₄₃⋊C₁₆	C₂²	1	2	yes	—
26	Dic₄₃⋊C₁₆	C₂²	1	2	yes	—
27	#14582703	C₂²	1	2	yes	—
28	#14582701	C₂²	1	2	yes	—
29	#14582699	C₂²	1	2	yes	—
30	C₂×Q₃₂×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#467	C₂²	1	2	yes	—
33	C₄₃×#366	C₂²	1	1	yes	characteristic
34	C₄₃×#358	C₂²	1	2	yes	—
35	C₂×#10621884	—	2	2	no	—
36	C₂×D₃₄₄	C₂³	1	2	yes	—
37	C₂×#10621877	D₄	1	1	yes	characteristic
38	#13063324	—	2	2	no	—
39	#13063320	—	4	2	no	—
40	#13063314	—	2	2	no	—
41	#13063311	—	4	2	no	—
42	#13063307	—	4	2	no	—
43	#13063305	—	4	2	no	—
44	#13063299	—	2	2	no	—
45	Q₈×Dic₄₃	—	2	2	no	—
46	#13063287	—	2	2	no	—
47	#13063284	D₄	1	1	yes	characteristic
48	#13063268	—	4	2	no	—
49	D₆₈₈	—	4	1	no	—
50	#13063265	—	4	1	no	—
51	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
52	#13063259	C₂³	1	2	yes	—
53	#13063258	—	2	2	no	—
54	#13063249	—	2	2	no	—
55	#13063247	—	2	2	no	—
56	#13063245	—	2	2	no	—
57	#13063235	D₄	1	2	yes	—
58	C₈×Dic₄₃	C₂³	1	2	yes	—
59	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₄₃	—	2	2	no	—
62	Q₃₂×C₄₃	—	4	1	no	—
63	C₂×C₁₆×C₄₃	—	4	1	no	—
64	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
66	#107×C₄₃	C₂³	1	2	yes	—
67	#103×C₄₃	—	2	2	no	—
68	C₂×Q₈×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₄₃	—	4	2	no	—
71	C₂×D₁₇₂	—	2	2	no	—
72	C₂×C₄×D₄₃	—	4	2	no	—
73	C₂×Dic₈₆	—	4	2	no	—
74	Q₁₆×C₄₃	—	2	2	no	—
75	Q₁₆×C₄₃	—	2	2	no	—
76	C₂×C₈×C₄₃	—	2	1	no	—
77	C₂×C₈×C₄₃	—	2	1	no	—
78	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
80	C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₄⋊C₄×C₄₃	—	4	2	no	—
82	C₂²⋊C₄×C₄₃	—	4	2	no	—
83	C₂²⋊Dic₄₃	D₈	1	2	yes	—
84	#10621884	—	4	4	no	—
85	(C₂×D₄₃)⋊C₄	—	4	2	no	—
86	(C₂×D₄₃)⋊C₄	—	4	2	no	—
87	(C₂×D₄₃)⋊C₄	—	4	2	no	—
88	(C₂×D₄₃)⋊C₄	—	4	2	no	—
89	C₄⋊Dic₄₃	—	2	2	no	—
90	C₄⋊Dic₄₃	—	4	2	no	—
91	C₄⋊Dic₄₃	D₈	1	1	yes	characteristic
92	C₄⋊Dic₄₃	D₈	1	1	yes	characteristic
93	Dic₄₃⋊C₄	—	4	2	no	—
94	C₄×Dic₄₃	—	4	2	no	—
95	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
96	#10621877	—	4	1	no	—
97	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
98	D₃₄₄	—	2	2	no	—
99	D₃₄₄	—	2	2	no	—
100	C₁₆×C₄₃	—	2	1	no	—
101	C₁₆×C₄₃	—	2	1	no	—
102	C₄₃⋊C₁₆	—	2	2	no	—
103	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
104	C₂²×D₄₃	—	4	2	no	—
105	Q₈×C₄₃	—	4	2	no	—
106	Q₈×C₄₃	—	4	2	no	—
107	C₂×C₄×C₄₃	—	2	1	no	—
108	C₂×C₄×C₄₃	—	2	1	no	—
109	C₂×C₄×C₄₃	—	4	2	no	—
110	C₂×C₄×C₄₃	—	4	2	no	—
111	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
113	C₂²⋊D₄₃	—	16	2	no	—
114	C₂×Dic₄₃	—	4	2	no	—
115	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
116	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
117	D₁₇₂	—	4	2	no	—
118	D₁₇₂	—	4	2	no	—
119	C₄×D₄₃	—	16	2	no	—
120	Dic₈₆	—	16	2	no	—
121	C₈×C₄₃	—	2	1	no	—
122	C₈×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
123	C₈×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
124	C₄₃⋊C₈	—	2	2	no	—
125	#33828	—	43	1	no	maximal, Sylow
126	C₂²×C₄₃	—	2	1	no	—
127	C₂²×C₄₃	—	2	1	no	—
128	C₂²×C₄₃	—	2	1	no	—
129	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
130	C₂×D₄₃	—	8	2	no	—
131	C₂×D₄₃	—	8	2	no	—
132	C₂×D₄₃	—	8	2	no	—
133	C₄×C₄₃	—	2	1	no	—
134	C₄×C₄₃	—	8	2	no	—
135	C₄×C₄₃	—	8	2	no	—
136	C₄×C₄₃	#537	1	1	yes	characteristic
137	C₄×C₄₃	#575	1	1	yes	characteristic
138	Dic₄₃	—	2	2	no	—
139	Dic₄₃	—	2	2	no	—
140	Dic₄₃	—	8	2	no	—
141	#3175	—	43	2	no	—
142	#2227	—	43	2	no	—
143	#2224	—	43	2	no	—
144	#2220	—	43	2	no	—
145	#2216	D₄₃	1	1	yes	characteristic, complemented
146	#2215	—	43	1	no	—
147	#2211	—	43	2	no	—
148	#2210	—	43	2	no	—
149	#2151	—	43	1	no	—
150	C₂×C₄₃	—	4	1	no	—
151	C₂×C₄₃	#3245	1	1	yes	characteristic
152	C₂×C₄₃	#3415	1	1	yes	characteristic
153	C₂×C₄₃	#3417	1	1	yes	characteristic
154	D₄₃	—	16	2	no	—
155	#542	—	86	2	no	—
156	C₂×Q₃₂	C₂×D₄₃	1	1	yes	characteristic
157	C₂×SD₃₂	—	43	2	no	—
158	C₂×D₁₆	—	43	1	no	—
159	C₂×M₃₂	—	43	1	no	—
160	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
161	#500	—	43	2	no	—
162	#495	—	43	2	no	—
163	#489	—	86	2	no	—
164	#468	—	86	2	no	—
165	#467	C₂×D₄₃	1	2	yes	—
166	#466	—	43	2	no	—
167	#440	—	86	2	no	—
168	C₄×Q₁₆	—	43	2	no	—
169	C₄×D₈	—	43	2	no	—
170	#405	—	43	1	no	—
171	#366	—	43	1	no	—
172	#366	—	43	2	no	—
173	#366	C₂×D₄₃	1	1	yes	characteristic
174	C₄⋊C₁₆	—	43	2	no	—
175	C₄⋊C₁₆	—	43	2	no	—
176	#358	—	43	2	no	—
177	#358	C₂×D₄₃	1	2	yes	—
178	#357	—	43	2	no	—
179	#357	—	43	2	no	—
180	C₄₃	#33828	1	1	yes	characteristic, complemented, Sylow
181	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
182	C₂×SD₁₆	—	86	2	no	—
183	C₂×D₈	—	43	2	no	—
184	C₂×M₁₆	—	43	1	no	—
185	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
186	C₄⋊Q₈	—	86	2	no	—
187	#126	—	172	2	no	—
188	#124	—	86	2	no	—
189	#124	—	172	2	no	—
190	#123	—	172	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	172	2	no	—
193	#121	—	86	2	no	—
194	C₄×Q₈	—	86	2	no	—
195	C₄×D₄	—	86	2	no	—
196	#117	—	43	1	no	—
197	Q₃₂	—	4	1	no	—
198	SD₃₂	—	172	2	no	—
199	D₁₆	—	172	1	no	—
200	M₃₂	—	172	1	no	—
201	C₂×C₁₆	—	4	1	no	—
202	C₂×C₁₆	—	43	2	no	—
203	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
204	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
205	#107	—	43	2	no	—
206	#107	—	86	2	no	—
207	#107	C₂²×D₄₃	1	2	yes	—
208	#103	—	2	2	no	—
209	#103	—	86	2	no	—
210	#102	—	86	2	no	—
211	#102	—	86	2	no	—
212	#97	—	43	2	no	—
213	C₄×C₈	—	43	2	no	—
214	C₂×Q₈	—	2	2	no	—
215	C₂×Q₈	—	172	2	no	—
216	C₂×D₄	—	86	2	no	—
217	C₂×D₄	—	172	2	no	—
218	C₂²×C₄	—	172	2	no	—
219	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
220	Q₁₆	—	2	2	no	—
221	Q₁₆	—	2	2	no	—
222	SD₁₆	—	172	4	no	—
223	D₈	—	86	2	no	—
224	D₈	—	86	2	no	—
225	M₁₆	—	172	1	no	—
226	C₂×C₈	—	2	1	no	—
227	C₂×C₈	—	2	1	no	—
228	C₂×C₈	—	43	2	no	—
229	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
230	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	4	2	no	—
233	C₄⋊C₄	—	43	1	no	—
234	C₄⋊C₄	—	43	1	no	—
235	C₄⋊C₄	—	86	2	no	—
236	C₄⋊C₄	—	172	2	no	—
237	C₄⋊C₄	—	172	2	no	—
238	C₂²⋊C₄	—	4	2	no	—
239	C₂²⋊C₄	—	43	2	no	—
240	C₂²⋊C₄	—	172	2	no	—
241	C₂²⋊C₄	—	172	2	no	—
242	C₂²⋊C₄	—	172	2	no	—
243	C₂²⋊C₄	—	172	2	no	—
244	C₄²	—	43	2	no	—
245	C₄²	—	172	2	no	—
246	C₁₆	—	2	1	no	—
247	C₁₆	—	2	1	no	—
248	C₁₆	—	86	2	no	—
249	C₂³	—	172	2	no	—
250	C₂³	D₈×D₄₃	1	1	yes	characteristic
251	Q₈	—	4	2	no	—
252	Q₈	—	4	2	no	—
253	Q₈	—	688	2	no	—
254	D₄	—	172	2	no	—
255	D₄	—	172	2	no	—
256	D₄	—	688	2	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	43	2	no	—
262	C₂×C₄	—	43	2	no	—
263	C₂×C₄	—	172	2	no	—
264	C₂×C₄	—	688	2	no	—
265	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
266	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
267	C₈	—	2	1	no	—
268	C₈	—	86	2	no	—
269	C₈	#13063370	1	1	yes	characteristic
270	C₈	#13063372	1	1	yes	characteristic
271	C₂²	—	2	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	344	2	no	—
275	C₂²	—	344	2	no	—
276	C₂²	—	344	2	no	—
277	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
278	C₄	—	2	1	no	—
279	C₄	—	8	2	no	—
280	C₄	—	8	2	no	—
281	C₄	—	86	2	no	—
282	C₄	—	86	2	no	—
283	C₄	—	344	2	no	—
284	C₄	#14583476	1	1	yes	characteristic
285	C₄	#14583696	1	1	yes	characteristic
286	C₂	—	4	1	no	—
287	C₂	—	688	2	no	—
288	C₂	#19145901	1	1	yes	characteristic
289	C₂	#19147733	1	1	yes	characteristic
290	C₂	#19147744	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145235

C₂

yes

maximal, complemented

#19136745

C₂

yes

maximal, complemented

#19136731

C₂

yes

maximal, complemented

#19136710

C₂

yes

maximal, complemented

#19136681

C₂

yes

maximal, characteristic

#19136659

C₂

yes

maximal, complemented

#19136653

C₂

yes

maximal, complemented

#19136353

C₂

yes

maximal, characteristic, complemented

C₄₃×#2216

C₂

yes

maximal, characteristic, complemented

#14583522

—

C₂×#13063268

C₂²

yes

—

C₂×D₆₈₈

C₂²

yes

characteristic

C₂×#13063265

C₂²

yes

characteristic

#14583303

C₂²

yes

—

#14583284

C₂²

yes

—

#14583260

—

#14583147

—

#14583135

C₂²

yes

—

#14583002

—

Q₁₆×Dic₄₃

C₂²

yes

—

#14582981

C₂²

yes

—

#14582854

C₂²

yes

characteristic

#14582725

C₂²

yes

characteristic

#14582724

C₂²

yes

—

Dic₄₃⋊C₁₆

C₂²

yes

—

Dic₄₃⋊C₁₆

C₂²

yes

—

#14582703

C₂²

yes

—

#14582701

C₂²

yes

—

#14582699

C₂²

yes

—

C₂×Q₃₂×C₄₃

C₂²

yes

characteristic

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₄₃×#467

C₂²

yes

—

C₄₃×#366

C₂²

yes

characteristic

C₄₃×#358

C₂²

yes

—

C₂×#10621884

—

C₂×D₃₄₄

C₂³

yes

—

C₂×#10621877

D₄

yes

—

—

—

—

—

—

—

Q₈×Dic₄₃

—

#13063287

—

#13063284

D₄

yes

characteristic

#13063268

—

D₆₈₈

—

#13063265

—

C₂×C₄₃⋊C₁₆

C₂³

yes

—

#13063259

C₂³

yes

—

—

—

—

—

D₄

yes

—

C₈×Dic₄₃

C₂³

yes

—

C₂×Q₁₆×C₄₃

C₂³

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Q₈×C₄₃

—

Q₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂³

yes

characteristic

C₂×C₁₆×C₄₃

C₂³

yes

characteristic

#107×C₄₃

C₂³

yes

—

#103×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

D₈

yes

—

#10621884

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₈

yes

characteristic

C₄⋊Dic₄₃

D₈

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×D₄

yes

—

#10621877

—

C₂×C₄₃⋊C₈

C₂×D₄

yes

—

D₃₄₄

—

D₃₄₄

—

100

C₁₆×C₄₃

—

101

C₁₆×C₄₃

—

102

C₄₃⋊C₁₆

—

103

C₂³×C₄₃

C₂×D₈

yes

characteristic

104

C₂²×D₄₃

—

105

Q₈×C₄₃

—

106

Q₈×C₄₃

—

107

C₂×C₄×C₄₃

—

108

C₂×C₄×C₄₃

—

109

C₂×C₄×C₄₃

—

110

C₂×C₄×C₄₃

—

111

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

112

C₂×C₄×C₄₃

C₂²×D₄

yes

characteristic

113

C₂²⋊D₄₃

—

114

C₂×Dic₄₃

—

115

C₂×Dic₄₃

C₂×D₈

yes

—

116

C₂×Dic₄₃

C₂×D₈

yes

—

117

D₁₇₂

—

118

D₁₇₂

—

119

C₄×D₄₃

—

120

Dic₈₆

—

121

C₈×C₄₃

—

122

C₈×C₄₃

H(5,𝔽₂)

yes

characteristic

123

C₈×C₄₃

2₋¹⁺⁴

yes

characteristic

124

C₄₃⋊C₈

—

125

#33828

—

maximal, Sylow

126

C₂²×C₄₃

—

127

C₂²×C₄₃

—

128

C₂²×C₄₃

—

129

C₂²×C₄₃

C₂²×D₈

yes

characteristic

130

C₂×D₄₃

—

131

C₂×D₄₃

—

132

C₂×D₄₃

—

133

C₄×C₄₃

—

134

C₄×C₄₃

—

135

C₄×C₄₃

—

136

C₄×C₄₃

#537

yes

characteristic

137

C₄×C₄₃

#575

yes

characteristic

138

Dic₄₃

—

139

Dic₄₃

—

140

Dic₄₃

—

141

#3175

—

142

#2227

—

143

#2224

—

144

#2220

—

145

#2216

D₄₃

yes

characteristic, complemented

146

#2215

—

147

#2211

—

148

#2210

—

149

#2151

—

150

C₂×C₄₃

—

151

C₂×C₄₃

#3245

yes

characteristic

152

C₂×C₄₃

#3415

yes

characteristic

153

C₂×C₄₃

#3417

yes

characteristic

154

D₄₃

—

155

#542

—

156

C₂×Q₃₂

C₂×D₄₃

yes

characteristic

157

C₂×SD₃₂

—

158

C₂×D₁₆

—

159

C₂×M₃₂

—

160

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

161

#500

—

162

#495

—

163

#489

—

164

#468

—

165

#467

C₂×D₄₃

yes

—

166

#466

—

167

#440

—

168

C₄×Q₁₆

—

169

C₄×D₈

—

170

#405

—

171

#366

—

172

#366

—

173

#366

C₂×D₄₃

yes

characteristic

174

C₄⋊C₁₆

—

175

C₄⋊C₁₆

—

176

#358

—

177

#358

C₂×D₄₃

yes

—

178

#357

—

179

#357

—

180

C₄₃

#33828

yes

characteristic, complemented, Sylow

181

C₂×Q₁₆

C₂²×D₄₃

yes

—

182

C₂×SD₁₆

—

183

C₂×D₈

—

184

C₂×M₁₆

—

185

C₂²×C₈

C₂²×D₄₃

yes

characteristic

186

C₄⋊Q₈

—

187

#126

—

172

—

188

#124

—

189

#124

—

172

—

190

#123

—

172

—

191

C₂²⋊Q₈

—

192

C₂²⋊Q₈

—

172

—

193

#121

—

194

C₄×Q₈

—

195

C₄×D₄

—

196

#117

—

197

Q₃₂

—

198

SD₃₂

—

172

—

199

D₁₆

—

172

—

200

M₃₂

—

172

—

201

C₂×C₁₆

—

202

C₂×C₁₆

—

203

C₂×C₁₆

C₂²×D₄₃

yes

characteristic

204

C₂×C₁₆

C₂²×D₄₃

yes

characteristic

205

#107

—

206

#107

—

207

#107

C₂²×D₄₃

yes

—

208

#103

—

209

#103

—

210

#102

—

211

#102

—

212

#97

—

213

C₄×C₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

172

—

216

C₂×D₄

—

217

C₂×D₄

—

172

—

218

C₂²×C₄

—

172

—

219

C₂²×C₄

D₄×D₄₃

yes

characteristic

220

Q₁₆

—

221

Q₁₆

—

222

SD₁₆

—

172

—

223

D₈

—

224

D₈

—

225

M₁₆

—

172

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

D₄×D₄₃

yes

characteristic

230

C₂×C₈

C₂³×D₄₃

yes

characteristic

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

172

—

237

C₄⋊C₄

—

172

—

238

C₂²⋊C₄

—

239

C₂²⋊C₄

—

240

C₂²⋊C₄

—

172

—

241

C₂²⋊C₄

—

172

—

242

C₂²⋊C₄

—

172

—

243

C₂²⋊C₄

—

172

—

244

C₄²

—

245

C₄²

—

172

—

246

C₁₆

—

247

C₁₆

—

248

C₁₆

—

249

C₂³

—

172

—

250

C₂³

D₈×D₄₃

yes

characteristic

251

Q₈

—

252

Q₈

—

253

Q₈

—

688

—

254

D₄

—

172

—

255

D₄

—

172

—

256

D₄

—

688

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

172

—

264

C₂×C₄

—

688

—

265

C₂×C₄

D₈×D₄₃

yes

characteristic

266

C₂×C₄

C₂×D₄×D₄₃

yes

characteristic

267

C₈

—

268

C₈

—

269

C₈

#13063370

yes

characteristic

270

C₈

#13063372

yes

characteristic

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

344

—

275

C₂²

—

344

—

276

C₂²

—

344

—

277

C₂²

C₂×D₈×D₄₃

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

344

—

284

C₄

#14583476

yes

characteristic

285

C₄

#14583696

yes

characteristic

286

C₂

—

287

C₂

—

688

—

288

C₂

#19145901

yes

characteristic

289

C₂

#19147733

yes

characteristic

290

C₂

#19147744

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₃
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2216	C₂
socle	C₂²×C₄₃	C₂²×D₈
prime radical	#19136681	C₂
hypercenter	#2216	D₄₃
hypocenter	C₄₃	#33828
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2216

subgroup

G/H

center

C₂²

C₂×D₈×D₄₃

commutator, cosocle

C₂×C₈×C₄₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₄₃

Fitting

C₄₃×#2216

C₂

socle

C₂²×C₄₃

C₂²×D₈

C₂

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2216

N	H ≅ G/N	type
1. #19145235	C₂	semidirect
2. #19136745	C₂	semidirect
3. #19136731	C₂	semidirect
4. #19136710	C₂	semidirect
6. #19136659	C₂	semidirect
7. #19136653	C₂	semidirect
8. #19136353	C₂	semidirect
9. C₄₃×#2216	C₂	semidirect
145. #2216	D₄₃	semidirect
180. C₄₃	#33828	semidirect

H ≅ G/N

type

1. #19145235

C₂

semidirect

2. #19136745

C₂

semidirect

3. #19136731

C₂

semidirect

4. #19136710

C₂

semidirect

6. #19136659

C₂

semidirect

7. #19136653

C₂

semidirect

8. #19136353

C₂

semidirect

9. C₄₃×#2216

C₂

semidirect

145. #2216

D₄₃

semidirect

180. C₄₃

#33828

semidirect

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

subgroup	index
#19145235	2
#19136745	2
#19136731	2
#19136710	2
#19136681	2
#19136659	2
#19136653	2
#19136353	2
C₄₃×#2216	2
#33828	43

subgroup

index

C₄₃×#2216

Subgroups — #25253037

Conjugacy classes of subgroups

Complements

Maximal subgroups