Group #25013344 — subgroups

Subgroups — #25013344

Order 11008.

396 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14583005	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582721	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582716	C₂	1	1	yes	maximal, characteristic
4	#19136314	C₂	1	1	yes	maximal, characteristic
5	#19135349	C₂	1	1	yes	maximal, characteristic
6	#19132674	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1386	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063290	—	2	1	no	—
10	C₂×#13063265	C₂²	1	1	yes	characteristic
11	#14583005	—	2	2	no	—
12	#14583005	—	2	2	no	—
13	C₂×#13063261	C₂²	1	1	yes	characteristic
14	#14582926	—	2	1	no	—
15	C₂×#13063248	—	2	1	no	—
16	C₂×#13063235	C₂²	1	1	yes	characteristic
17	#14582721	—	2	2	no	—
18	#14582716	—	2	2	no	—
19	#14582702	C₄	1	4	yes	complemented
20	#14582658	—	2	1	no	—
21	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#427	C₂²	1	1	yes	characteristic
23	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×Dic₈₆	—	2	1	no	—
25	C₂×Dic₁₇₂	—	2	1	no	—
26	C₂×Dic₁₇₂	—	2	1	no	—
27	C₂×Dic₁₇₂	—	2	1	no	—
28	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₇₂	D₄	1	2	yes	—
30	C₂×Dic₁₇₂	Q₈	1	2	yes	—
31	C₂×#10621877	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
33	#13063290	—	2	4	no	—
34	#13063290	—	4	2	no	—
35	C₂×Dic₄₃⋊C₄	—	4	1	no	—
36	C₂×C₄×Dic₄₃	—	4	1	no	—
37	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
38	#13063265	—	2	1	no	—
39	#13063265	—	2	1	no	—
40	C₂×C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
41	#13063261	—	2	1	no	—
42	#13063261	—	2	1	no	—
43	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
44	#13063248	—	2	4	no	—
45	#13063235	—	2	1	no	—
46	#13063235	—	2	1	no	—
47	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
48	#117×C₄₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
50	M₃₂×C₄₃	—	2	1	no	—
51	M₃₂×C₄₃	—	2	1	no	—
52	C₂×C₁₆×C₄₃	—	2	1	no	—
53	#107×C₄₃	C₂×C₄	1	2	yes	—
54	#106×C₄₃	—	2	1	no	—
55	#106×C₄₃	—	2	1	no	—
56	#106×C₄₃	D₄	1	2	yes	—
57	C₂²×C₄×C₄₃	—	4	1	no	—
58	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×Dic₄₃	—	2	1	no	—
60	C₂²×Dic₄₃	—	4	1	no	—
61	C₂×Dic₈₆	—	2	2	no	—
62	C₂×Dic₈₆	—	2	2	no	—
63	C₂×Dic₈₆	—	2	2	no	—
64	C₂×Dic₈₆	—	4	1	no	—
65	C₂×Dic₈₆	—	4	1	no	—
66	C₂×Dic₈₆	—	4	1	no	—
67	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
71	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
72	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
73	C₄⋊C₄×C₄₃	—	2	2	no	—
74	C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₄⋊C₄×C₄₃	—	4	1	no	—
76	C₂²⋊C₄×C₄₃	—	4	1	no	—
77	C₄²×C₄₃	—	4	1	no	—
78	Dic₄₃⋊C₄	—	4	4	no	—
79	C₄×Dic₄₃	—	2	1	no	—
80	C₄×Dic₄₃	—	4	4	no	—
81	C₄×Dic₄₃	SD₁₆	1	2	yes	—
82	#10621877	—	4	1	no	—
83	#10621877	—	4	1	no	—
84	C₂×C₄₃⋊C₈	—	2	1	no	—
85	C₂×C₄₃⋊C₈	—	2	1	no	—
86	C₂×C₄₃⋊C₈	—	2	1	no	—
87	C₂×C₄₃⋊C₈	—	4	1	no	—
88	Dic₁₇₂	—	2	2	no	—
89	Dic₁₇₂	—	2	2	no	—
90	Dic₁₇₂	—	2	2	no	—
91	Dic₁₇₂	C₄⋊C₄	1	4	yes	—
92	C₁₆×C₄₃	—	4	1	no	—
93	C₄₃⋊C₁₆	—	2	2	no	—
94	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₄₃	—	4	2	no	—
96	C₂×C₄×C₄₃	—	4	2	no	—
97	C₂×C₄×C₄₃	—	8	2	no	—
98	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
100	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
101	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
103	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×Dic₄₃	—	2	2	no	—
105	C₂×Dic₄₃	—	4	2	no	—
106	C₂×Dic₄₃	—	4	2	no	—
107	C₂×Dic₄₃	—	4	2	no	—
108	C₂×Dic₄₃	—	4	2	no	—
109	Dic₈₆	—	2	4	no	—
110	Dic₈₆	—	4	2	no	—
111	Dic₈₆	—	4	2	no	—
112	Dic₈₆	—	4	2	no	—
113	C₈×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
115	C₈×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
116	C₈×C₄₃	#123	1	1	yes	characteristic
117	C₄₃⋊C₈	—	4	1	no	—
118	C₄₃⋊C₈	—	8	1	no	—
119	#12957	—	43	1	no	maximal, Sylow
120	C₂²×C₄₃	—	2	2	no	—
121	C₂²×C₄₃	#442	1	1	yes	characteristic
122	C₂²×C₄₃	#450	1	1	yes	characteristic
123	C₂²×C₄₃	#478	1	1	yes	characteristic
124	C₄×C₄₃	—	8	2	no	—
125	C₄×C₄₃	—	8	2	no	—
126	C₄×C₄₃	#385	1	1	yes	characteristic
127	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
128	C₄×C₄₃	#449	1	1	yes	characteristic
129	C₄×C₄₃	#476	1	1	yes	characteristic
130	Dic₄₃	—	4	2	no	—
131	Dic₄₃	—	4	4	no	—
132	C₂×#441	—	43	1	no	—
133	C₂×#365	—	43	1	no	—
134	C₂×#362	—	43	1	no	—
135	#2141	—	43	1	no	—
136	#1946	—	43	1	no	—
137	#1386	D₄₃	1	1	yes	characteristic
138	#1375	—	43	1	no	—
139	C₂×C₄₃	—	2	1	no	—
140	C₂×C₄₃	—	2	1	no	—
141	C₂×C₄₃	#1864	1	1	yes	characteristic
142	C₂×C₄₃	#2180	1	2	yes	—
143	C₂²×Q₁₆	—	43	1	no	—
144	C₂×C₄×Q₈	—	86	1	no	—
145	C₂×M₃₂	—	43	1	no	—
146	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
147	#441	—	86	2	no	—
148	#441	—	86	2	no	—
149	C₂×#108	—	43	1	no	—
150	#427	C₂×D₄₃	1	1	yes	characteristic
151	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
152	#424	—	86	1	no	—
153	C₂×#103	—	86	1	no	—
154	C₂×#97	—	43	1	no	—
155	#365	—	86	2	no	—
156	#362	—	86	2	no	—
157	#358	—	43	4	no	—
158	#339	—	86	1	no	—
159	C₄₃	#12957	1	1	yes	characteristic, complemented, Sylow
160	C₂²×Q₈	—	86	1	no	—
161	C₂×Q₁₆	—	43	2	no	—
162	C₂×Q₁₆	—	43	2	no	—
163	C₂×Q₁₆	—	43	2	no	—
164	C₂×Q₁₆	—	86	1	no	—
165	C₂×Q₁₆	—	86	1	no	—
166	C₂×Q₁₆	—	86	1	no	—
167	C₂×M₁₆	—	86	1	no	—
168	C₂²×C₈	—	43	1	no	—
169	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
170	C₄×Q₈	—	86	4	no	—
171	C₄×Q₈	—	172	2	no	—
172	#117	—	2	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	172	1	no	—
175	C₂×C₄²	—	43	1	no	—
176	C₂×C₄²	—	172	1	no	—
177	M₃₂	—	2	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	86	1	no	—
180	M₃₂	—	86	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	43	2	no	—
183	#108	—	86	1	no	—
184	#108	—	86	1	no	—
185	#107	C₄×D₄₃	1	2	yes	—
186	#106	—	2	1	no	—
187	#106	—	2	1	no	—
188	#106	D₁₇₂	1	2	yes	—
189	C₄⋊C₈	—	172	2	no	—
190	#103	—	86	4	no	—
191	#97	—	86	1	no	—
192	#97	—	86	1	no	—
193	C₂×Q₈	—	86	2	no	—
194	C₂×Q₈	—	86	2	no	—
195	C₂×Q₈	—	86	2	no	—
196	C₂×Q₈	—	172	1	no	—
197	C₂×Q₈	—	172	1	no	—
198	C₂×Q₈	—	172	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	86	1	no	—
201	C₂²×C₄	—	172	1	no	—
202	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
203	Q₁₆	—	43	4	no	—
204	Q₁₆	—	86	2	no	—
205	Q₁₆	—	86	2	no	—
206	Q₁₆	—	86	2	no	—
207	M₁₆	—	172	1	no	—
208	M₁₆	—	172	1	no	—
209	C₂×C₈	—	86	1	no	—
210	C₂×C₈	—	86	1	no	—
211	C₂×C₈	—	86	1	no	—
212	C₂×C₈	—	172	1	no	—
213	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
214	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
215	C₂×C₈	#10621898	1	1	yes	characteristic
216	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
217	C₂×C₈	#10621900	1	1	yes	characteristic
218	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	2	2	no	—
221	C₄⋊C₄	—	4	1	no	—
222	C₄⋊C₄	—	172	4	no	—
223	C₂²⋊C₄	—	4	1	no	—
224	C₄²	—	4	1	no	—
225	C₄²	—	43	2	no	—
226	C₄²	—	86	1	no	—
227	C₄²	—	172	4	no	—
228	C₁₆	—	4	1	no	—
229	C₁₆	—	86	2	no	—
230	C₂³	#13063349	1	1	yes	characteristic
231	Q₈	—	86	4	no	—
232	Q₈	—	172	2	no	—
233	Q₈	—	172	2	no	—
234	Q₈	—	172	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	8	2	no	—
238	C₂×C₄	—	86	2	no	—
239	C₂×C₄	—	172	2	no	—
240	C₂×C₄	—	172	2	no	—
241	C₂×C₄	—	172	2	no	—
242	C₂×C₄	—	172	2	no	—
243	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
244	C₂×C₄	#13063295	1	1	yes	characteristic
245	C₂×C₄	#13063303	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
247	C₂×C₄	#13063348	1	1	yes	characteristic
248	C₂×C₄	#13063352	1	1	yes	characteristic
249	C₈	—	344	1	no	—
250	C₈	—	172	1	no	—
251	C₈	C₄⋊C₄×D₄₃	1	1	yes	characteristic
252	C₈	C₄×D₁₇₂	1	1	yes	characteristic
253	C₈	#13063305	1	1	yes	characteristic
254	C₈	#13063307	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	#14583008	1	1	yes	characteristic
257	C₂²	#14583051	1	1	yes	characteristic
258	C₂²	#14583202	1	1	yes	characteristic
259	C₄	—	8	2	no	—
260	C₄	—	8	2	no	—
261	C₄	—	172	2	no	—
262	C₄	—	172	4	no	—
263	C₄	#14582773	1	1	yes	characteristic
264	C₄	#14582984	1	1	yes	characteristic
265	C₄	#14583047	1	1	yes	characteristic
266	C₄	#14583188	1	1	yes	characteristic
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	#19134857	1	1	yes	characteristic
270	C₂	#19136483	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583005

C₂

yes

maximal, characteristic

C₂×#14582721

C₂

yes

maximal, characteristic

C₂×#14582716

C₂

yes

maximal, characteristic

#19136314

C₂

yes

maximal, characteristic

#19135349

C₂

yes

maximal, characteristic

#19132674

C₂

yes

maximal, characteristic

C₄₃×#1386

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₂²

yes

characteristic

C₂×#13063290

—

C₂×#13063265

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#14582658

—

C₂×M₃₂×C₄₃

C₂²

yes

characteristic

C₄₃×#427

C₂²

yes

characteristic

C₂×#106×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

C₂×Dic₁₇₂

D₄

yes

—

C₂×Dic₁₇₂

Q₈

yes

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

#13063290

—

#13063290

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

#13063261

—

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

#13063248

—

#13063235

—

#13063235

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#117×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

#107×C₄₃

C₂×C₄

yes

—

#106×C₄₃

—

#106×C₄₃

—

#106×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

SD₁₆

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

C₄⋊C₄

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

#120

yes

characteristic

100

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

101

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₄₃

#135

yes

characteristic

103

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

104

C₂×Dic₄₃

—

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

C₂×Dic₄₃

—

108

C₂×Dic₄₃

—

109

Dic₈₆

—

110

Dic₈₆

—

111

Dic₈₆

—

112

Dic₈₆

—

113

C₈×C₄₃

C₂×C₄⋊C₄

yes

characteristic

114

C₈×C₄₃

C₄×D₄

yes

characteristic

115

C₈×C₄₃

C₂²⋊Q₈

yes

characteristic

116

C₈×C₄₃

#123

yes

characteristic

117

C₄₃⋊C₈

—

118

C₄₃⋊C₈

—

119

#12957

—

maximal, Sylow

120

C₂²×C₄₃

—

121

C₂²×C₄₃

#442

yes

characteristic

122

C₂²×C₄₃

#450

yes

characteristic

123

C₂²×C₄₃

#478

yes

characteristic

124

C₄×C₄₃

—

125

C₄×C₄₃

—

126

C₄×C₄₃

#385

yes

characteristic

127

C₄×C₄₃

C₄×SD₁₆

yes

characteristic

128

C₄×C₄₃

#449

yes

characteristic

129

C₄×C₄₃

#476

yes

characteristic

130

Dic₄₃

—

131

Dic₄₃

—

132

C₂×#441

—

133

C₂×#365

—

134

C₂×#362

—

135

#2141

—

136

#1946

—

137

#1386

D₄₃

yes

characteristic

138

#1375

—

139

C₂×C₄₃

—

140

C₂×C₄₃

—

141

C₂×C₄₃

#1864

yes

characteristic

142

C₂×C₄₃

#2180

yes

—

143

C₂²×Q₁₆

—

144

C₂×C₄×Q₈

—

145

C₂×M₃₂

—

146

C₂×M₃₂

C₂×D₄₃

yes

characteristic

147

#441

—

148

#441

—

149

C₂×#108

—

150

#427

C₂×D₄₃

yes

characteristic

151

C₂×#106

C₂×D₄₃

yes

characteristic

152

#424

—

153

C₂×#103

—

154

C₂×#97

—

155

#365

—

156

#362

—

157

#358

—

158

#339

—

159

C₄₃

#12957

yes

characteristic, complemented, Sylow

160

C₂²×Q₈

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₂²×C₈

C₂²×D₄₃

yes

characteristic

170

C₄×Q₈

—

171

C₄×Q₈

—

172

—

172

#117

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

172

—

175

C₂×C₄²

—

176

C₂×C₄²

—

172

—

177

M₃₂

—

178

M₃₂

—

179

M₃₂

—

180

M₃₂

—

181

C₂×C₁₆

—

182

C₂×C₁₆

—

183

#108

—

184

#108

—

185

#107

C₄×D₄₃

yes

—

186

#106

—

187

#106

—

188

#106

D₁₇₂

yes

—

189

C₄⋊C₈

—

172

—

190

#103

—

191

#97

—

192

#97

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

172

—

197

C₂×Q₈

—

172

—

198

C₂×Q₈

—

172

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

172

—

202

C₂²×C₄

D₄×D₄₃

yes

characteristic

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

—

207

M₁₆

—

172

—

208

M₁₆

—

172

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

172

—

213

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

214

C₂×C₈

C₂×D₁₇₂

yes

characteristic

215

C₂×C₈

#10621898

yes

characteristic

216

C₂×C₈

D₄×D₄₃

yes

characteristic

217

C₂×C₈

#10621900

yes

characteristic

218

C₂×C₈

Q₈×D₄₃

yes

characteristic

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

172

—

223

C₂²⋊C₄

—

224

C₄²

—

225

C₄²

—

226

C₄²

—

227

C₄²

—

172

—

228

C₁₆

—

229

C₁₆

—

230

C₂³

#13063349

yes

characteristic

231

Q₈

—

232

Q₈

—

172

—

233

Q₈

—

172

—

234

Q₈

—

172

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

172

—

240

C₂×C₄

—

172

—

241

C₂×C₄

—

172

—

242

C₂×C₄

—

172

—

243

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

244

C₂×C₄

#13063295

yes

characteristic

245

C₂×C₄

#13063303

yes

characteristic

246

C₂×C₄

SD₁₆×D₄₃

yes

characteristic

247

C₂×C₄

#13063348

yes

characteristic

248

C₂×C₄

#13063352

yes

characteristic

249

C₈

—

344

—

250

C₈

—

172

—

251

C₈

C₄⋊C₄×D₄₃

yes

characteristic

252

C₈

C₄×D₁₇₂

yes

characteristic

253

C₈

#13063305

yes

characteristic

254

C₈

#13063307

yes

characteristic

255

C₂²

—

256

C₂²

#14583008

yes

characteristic

257

C₂²

#14583051

yes

characteristic

258

C₂²

#14583202

yes

characteristic

259

C₄

—

260

C₄

—

261

C₄

—

172

—

262

C₄

—

172

—

263

C₄

#14582773

yes

characteristic

264

C₄

#14582984

yes

characteristic

265

C₄

#14583047

yes

characteristic

266

C₄

#14583188

yes

characteristic

267

C₂

—

268

C₂

—

269

C₂

#19134857

yes

characteristic

270

C₂

#19136483

yes

—

	subgroup	G/H
center	C₂²	#14583008
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1386	C₂
socle	C₂²×C₄₃	#442
prime radical	C₂³×C₄₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1386	D₄₃
hypocenter	C₄₃	#12957
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

subgroup

G/H

center

C₂²

#14583008

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1386

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

N	H ≅ G/N	type
19. #14582702	C₄	semidirect
159. C₄₃	#12957	semidirect

H ≅ G/N

type

19. #14582702

C₄

semidirect

159. C₄₃

#12957

semidirect

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

subgroup	index
C₂×#14583005	2
C₂×#14582721	2
C₂×#14582716	2
#19136314	2
#19135349	2
#19132674	2
C₄₃×#1386	2
#12957	43

subgroup

index

C₄₃×#1386

Subgroups — #25013344

Conjugacy classes of subgroups

Complements

Maximal subgroups