Group #24990469 — subgroups

Subgroups — #24990469

Order 11008.

454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 123 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	#19135390	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063242	C₂	1	1	yes	maximal, characteristic
3	#19133348	C₂	1	2	yes	maximal, complemented
4	#19132431	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2975	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂×#13063242	C₄	1	2	yes	—
8	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
9	C₄×#10621877	C₂²	1	2	yes	—
10	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	#14582668	C₄	1	1	yes	characteristic
12	#14582668	C₄	1	1	yes	characteristic
13	#14582651	—	2	2	no	—
14	#14582649	—	2	2	no	—
15	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#436	—	2	2	no	—
17	C₄₃×#436	—	2	2	no	—
18	C₄₃×#431	C₂²	1	2	yes	—
19	C₄₃×#407	—	2	2	no	—
20	C₂×#10621877	C₂×C₄	1	2	yes	—
21	C₂×#10621877	C₂×C₄	1	2	yes	—
22	C₂²×C₄₃⋊C₈	—	2	1	no	—
23	C₂²×C₄₃⋊C₈	—	2	1	no	—
24	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
25	#13063242	—	2	4	no	—
26	C₂²⋊(C₄₃⋊C₈)	—	4	4	no	—
27	#13063236	—	2	2	no	—
28	C₄×C₄₃⋊C₈	—	2	2	no	—
29	C₄×C₄₃⋊C₈	—	2	2	no	—
30	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	D₄	1	2	yes	—
32	C₂×M₁₆×C₄₃	—	2	2	no	—
33	C₂×M₁₆×C₄₃	—	2	2	no	—
34	C₄×D₄×C₄₃	—	2	2	no	—
35	C₄×D₄×C₄₃	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₄₃	Q₈	1	2	yes	—
38	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
40	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
41	C₂²⋊C₈×C₄₃	—	2	4	no	—
42	C₂²⋊C₈×C₄₃	—	2	2	no	—
43	C₄×C₈×C₄₃	—	2	2	no	—
44	C₂⁴×C₄₃	C₄⋊C₄	1	2	yes	—
45	C₂×D₄×C₄₃	—	2	2	no	—
46	C₂×D₄×C₄₃	—	2	2	no	—
47	C₂×D₄×C₄₃	—	2	1	no	—
48	C₂×D₄×C₄₃	—	2	1	no	—
49	C₂²×C₄×C₄₃	—	2	2	no	—
50	C₂²×C₄×C₄₃	—	2	2	no	—
51	C₂²×C₄×C₄₃	—	4	2	no	—
52	C₂²×C₄×C₄₃	—	4	2	no	—
53	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
57	M₁₆×C₄₃	—	8	2	no	—
58	M₁₆×C₄₃	—	8	2	no	—
59	C₂×C₈×C₄₃	—	2	2	no	—
60	C₂×C₈×C₄₃	—	2	2	no	—
61	C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂²⋊C₄×C₄₃	—	2	4	no	—
63	C₄²×C₄₃	C₂×D₄	1	2	yes	—
64	C₄²×C₄₃	#41	1	2	yes	—
65	#10621877	—	2	2	no	—
66	#10621877	—	2	2	no	—
67	#10621877	—	2	2	no	—
68	#10621877	M₁₆	1	4	yes	complemented
69	C₂×C₄₃⋊C₈	—	2	2	no	—
70	C₂×C₄₃⋊C₈	—	2	2	no	—
71	C₂×C₄₃⋊C₈	—	2	2	no	—
72	C₂×C₄₃⋊C₈	—	4	1	no	—
73	C₂×C₄₃⋊C₈	—	4	1	no	—
74	C₂×C₄₃⋊C₈	—	4	2	no	—
75	C₂×C₄₃⋊C₈	—	4	1	no	—
76	C₂³×C₄₃	—	2	2	no	—
77	C₂³×C₄₃	—	2	2	no	—
78	C₂³×C₄₃	—	2	2	no	—
79	C₂³×C₄₃	—	4	2	no	—
80	C₂³×C₄₃	—	4	2	no	—
81	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	D₄×C₄₃	—	4	2	no	—
83	D₄×C₄₃	—	4	2	no	—
84	C₂×C₄×C₄₃	—	2	1	no	—
85	C₂×C₄×C₄₃	—	2	1	no	—
86	C₂×C₄×C₄₃	—	2	2	no	—
87	C₂×C₄×C₄₃	—	4	1	no	—
88	C₂×C₄×C₄₃	—	4	2	no	—
89	C₂×C₄×C₄₃	—	4	2	no	—
90	C₂×C₄×C₄₃	—	4	2	no	—
91	C₂×C₄×C₄₃	—	8	2	no	—
92	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
94	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
95	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
96	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
98	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
99	C₈×C₄₃	—	4	2	no	—
100	C₈×C₄₃	—	4	2	no	—
101	C₄₃⋊C₈	—	2	4	no	—
102	C₄₃⋊C₈	—	4	2	no	—
103	C₄₃⋊C₈	—	4	2	no	—
104	C₄₃⋊C₈	—	8	1	no	—
105	#8837	—	43	1	no	maximal, Sylow
106	C₂²×C₄₃	—	2	1	no	—
107	C₂²×C₄₃	—	2	1	no	—
108	C₂²×C₄₃	—	4	4	no	—
109	C₂²×C₄₃	—	4	2	no	—
110	C₂²×C₄₃	—	4	2	no	—
111	C₂²×C₄₃	—	4	2	no	—
112	C₂²×C₄₃	—	8	2	no	—
113	C₂²×C₄₃	#385	1	1	yes	characteristic
114	C₂²×C₄₃	#423	1	1	yes	characteristic
115	C₂²×C₄₃	#424	1	1	yes	characteristic
116	C₄×C₄₃	—	2	1	no	—
117	C₄×C₄₃	—	2	2	no	—
118	C₄×C₄₃	—	4	2	no	—
119	C₄×C₄₃	#435	1	2	yes	—
120	C₄×C₄₃	#436	1	2	yes	—
121	C₄×C₄₃	#453	1	1	yes	characteristic
122	C₄×C₄₃	#455	1	1	yes	characteristic
123	#2975	D₄₃	1	1	yes	characteristic
124	#1954	—	43	1	no	—
125	C₄×#100	—	43	1	no	—
126	#1565	—	43	2	no	—
127	#1278	—	43	2	no	—
128	C₂×C₄₃	—	2	1	no	—
129	C₂×C₄₃	—	2	1	no	—
130	C₂×C₄₃	—	8	2	no	—
131	C₂×C₄₃	#1851	1	1	yes	characteristic
132	C₂×C₄₃	#1856	1	1	yes	characteristic
133	C₂×C₄₃	#1858	1	1	yes	characteristic
134	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
135	#436	—	2	2	no	—
136	#436	—	2	2	no	—
137	#431	C₂×D₄₃	1	2	yes	—
138	C₂×C₄⋊C₈	—	43	1	no	—
139	C₂×#100	—	43	2	no	—
140	#407	—	2	2	no	—
141	C₂×C₂²⋊C₈	—	86	2	no	—
142	C₄×M₁₆	—	43	2	no	—
143	C₂×C₄×C₈	—	43	1	no	—
144	#343	—	43	1	no	—
145	#343	—	43	1	no	—
146	#335	—	86	2	no	—
147	#334	—	86	2	no	—
148	C₄₃	#8837	1	1	yes	characteristic, complemented, Sylow
149	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
150	C₂³×C₄	C₂²⋊D₄₃	1	2	yes	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	43	2	no	—
154	C₂×M₁₆	—	43	2	no	—
155	C₂²×C₈	—	86	1	no	—
156	C₂²×C₈	—	86	1	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	Dic₈₆	1	2	yes	—
161	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
162	C₄⋊C₈	—	86	2	no	—
163	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
164	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
165	#100	—	86	4	no	—
166	C₂²⋊C₈	—	2	4	no	—
167	C₂²⋊C₈	—	2	2	no	—
168	C₂²⋊C₈	—	172	4	no	—
169	#97	—	86	2	no	—
170	C₄×C₈	—	2	2	no	—
171	C₄×C₈	—	86	2	no	—
172	C₄×C₈	—	86	2	no	—
173	C₂⁴	Dic₄₃⋊C₄	1	2	yes	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	—	2	1	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
183	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
184	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
186	M₁₆	—	8	2	no	—
187	M₁₆	—	8	2	no	—
188	M₁₆	—	43	4	no	—
189	M₁₆	—	86	2	no	—
190	M₁₆	—	86	2	no	—
191	M₁₆	—	86	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	86	2	no	—
195	C₂×C₈	—	86	2	no	—
196	C₂×C₈	—	86	2	no	—
197	C₂×C₈	—	172	2	no	—
198	C₂×C₈	—	172	1	no	—
199	C₂×C₈	—	172	1	no	—
200	C₂×C₈	—	172	1	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	#10621898	1	2	yes	—
204	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
222	C₂×C₄	#13063294	1	1	yes	characteristic
223	C₂×C₄	#13063304	1	2	yes	—
224	C₂×C₄	#13063308	1	1	yes	characteristic
225	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
226	C₂×C₄	#13063333	1	1	yes	characteristic
227	C₂×C₄	#13063333	1	1	yes	characteristic
228	C₈	—	4	2	no	—
229	C₈	—	4	2	no	—
230	C₈	—	86	4	no	—
231	C₈	—	344	1	no	—
232	C₈	—	172	2	no	—
233	C₈	—	172	2	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	#14582772	1	1	yes	characteristic
242	C₂²	#14582922	1	1	yes	characteristic
243	C₂²	#14582927	1	1	yes	characteristic
244	C₄	—	2	1	no	—
245	C₄	—	2	2	no	—
246	C₄	—	4	2	no	—
247	C₄	#14582968	1	2	yes	—
248	C₄	#14582975	1	2	yes	—
249	C₄	#14583067	1	1	yes	characteristic
250	C₄	#14583077	1	1	yes	characteristic
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	—	8	2	no	—
254	C₂	#19134778	1	1	yes	characteristic
255	C₂	#19134805	1	1	yes	characteristic
256	C₂	#19134815	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135390

C₂

yes

maximal, characteristic

C₄×#13063242

C₂

yes

maximal, characteristic

#19133348

C₂

yes

maximal, complemented

#19132431

C₂

yes

maximal, complemented

C₄₃×#2975

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063242

C₄

yes

—

C₂×C₂²⋊(C₄₃⋊C₈)

—

C₄×#10621877

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582668

C₄

yes

characteristic

#14582668

C₄

yes

characteristic

#14582651

—

#14582649

—

C₂×C₄×D₄×C₄₃

C₂²

yes

characteristic

C₄₃×#436

—

C₄₃×#436

—

C₄₃×#431

C₂²

yes

—

C₄₃×#407

—

C₂×#10621877

C₂×C₄

yes

—

C₂×#10621877

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₄⋊(C₄₃⋊C₈)

—

#13063242

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂²×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

D₄

yes

—

C₂×M₁₆×C₄₃

—

C₂×M₁₆×C₄₃

—

C₄×D₄×C₄₃

—

C₄×D₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

Q₈

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

D₄

yes

—

C₄⋊C₈×C₄₃

D₄

yes

—

C₂²⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂⁴×C₄₃

C₄⋊C₄

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

—

—

—

M₁₆

yes

complemented

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×C₄⋊C₄

yes

characteristic

D₄×C₄₃

—

D₄×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

C₄×D₄

yes

—

C₂×C₄×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

100

C₈×C₄₃

—

101

C₄₃⋊C₈

—

102

C₄₃⋊C₈

—

103

C₄₃⋊C₈

—

104

C₄₃⋊C₈

—

105

#8837

—

maximal, Sylow

106

C₂²×C₄₃

—

107

C₂²×C₄₃

—

108

C₂²×C₄₃

—

109

C₂²×C₄₃

—

110

C₂²×C₄₃

—

111

C₂²×C₄₃

—

112

C₂²×C₄₃

—

113

C₂²×C₄₃

#385

yes

characteristic

114

C₂²×C₄₃

#423

yes

characteristic

115

C₂²×C₄₃

#424

yes

characteristic

116

C₄×C₄₃

—

117

C₄×C₄₃

—

118

C₄×C₄₃

—

119

C₄×C₄₃

#435

yes

—

120

C₄×C₄₃

#436

yes

—

121

C₄×C₄₃

#453

yes

characteristic

122

C₄×C₄₃

#455

yes

characteristic

123

#2975

D₄₃

yes

characteristic

124

#1954

—

125

C₄×#100

—

126

#1565

—

127

#1278

—

128

C₂×C₄₃

—

129

C₂×C₄₃

—

130

C₂×C₄₃

—

131

C₂×C₄₃

#1851

yes

characteristic

132

C₂×C₄₃

#1856

yes

characteristic

133

C₂×C₄₃

#1858

yes

characteristic

134

C₂×C₄×D₄

C₂×D₄₃

yes

characteristic

135

#436

—

136

#436

—

137

#431

C₂×D₄₃

yes

—

138

C₂×C₄⋊C₈

—

139

C₂×#100

—

140

#407

—

141

C₂×C₂²⋊C₈

—

142

C₄×M₁₆

—

143

C₂×C₄×C₈

—

144

#343

—

145

#343

—

146

#335

—

147

#334

—

148

C₄₃

#8837

yes

characteristic, complemented, Sylow

149

C₂²×D₄

C₄×D₄₃

yes

characteristic

150

C₂³×C₄

C₂²⋊D₄₃

yes

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

C₄×D₄₃

yes

characteristic

160

C₂×C₂²⋊C₄

Dic₈₆

yes

—

161

C₂×C₄²

C₂²×D₄₃

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

C₂²⋊D₄₃

yes

—

164

C₄⋊C₈

C₂²⋊D₄₃

yes

—

165

#100

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

172

—

169

#97

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₄×C₈

—

173

C₂⁴

Dic₄₃⋊C₄

yes

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

Dic₄₃⋊C₄

yes

—

183

C₂²×C₄

C₂×Dic₈₆

yes

characteristic

184

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

185

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

172

—

198

C₂×C₈

—

172

—

199

C₂×C₈

—

172

—

200

C₂×C₈

—

172

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

#10621898

yes

—

204

C₄²

C₂×C₂²⋊D₄₃

yes

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×Dic₄₃⋊C₄

yes

characteristic

211

D₄

—

212

D₄

—

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

C₄×C₂²⋊D₄₃

yes

—

222

C₂×C₄

#13063294

yes

characteristic

223

C₂×C₄

#13063304

yes

—

224

C₂×C₄

#13063308

yes

characteristic

225

C₂×C₄

M₁₆×D₄₃

yes

—

226

C₂×C₄

#13063333

yes

characteristic

227

C₂×C₄

#13063333

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

344

—

232

C₈

—

172

—

233

C₈

—

172

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#14582772

yes

characteristic

242

C₂²

#14582922

yes

characteristic

243

C₂²

#14582927

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#14582968

yes

—

248

C₄

#14582975

yes

—

249

C₄

#14583067

yes

characteristic

250

C₄

#14583077

yes

characteristic

251

C₂

—

252

C₂

—

253

C₂

—

254

C₂

#19134778

yes

characteristic

255

C₂

#19134805

yes

characteristic

256

C₂

#19134815

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063294
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2975	C₂
socle	C₂²×C₄₃	#385
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#2975	D₄₃
hypocenter	C₄₃	#8837
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2975

subgroup

G/H

center

C₂×C₄

#13063294

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2975

C₂

socle

C₂²×C₄₃

#385

prime radical

C₂²×D₄×C₄₃

C₂×C₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2975

N	H ≅ G/N	type
3. #19133348	C₂	semidirect
4. #19132431	C₂	semidirect
68. #10621877	M₁₆	semidirect
148. C₄₃	#8837	semidirect

H ≅ G/N

type

3. #19133348

C₂

semidirect

4. #19132431

C₂

semidirect

68. #10621877

M₁₆

semidirect

148. C₄₃

#8837

semidirect

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

subgroup	index
#19135390	2
C₄×#13063242	2
#19133348	2
#19132431	2
C₄₃×#2975	2
#8837	43

subgroup

index

C₄₃×#2975

Subgroups — #24990469

Conjugacy classes of subgroups

Complements

Maximal subgroups