Group #25015303 — subgroups

Subgroups — #25015303

Order 11008.

566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14583137	C₂	1	2	yes	maximal
2	C₂×#14582703	C₂	1	2	yes	maximal, complemented
3	C₂×(C₂×D₄₃)⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#19132687	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
7	C₂×#13063301	—	2	2	no	—
8	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
9	#14583137	—	2	4	no	—
10	#14583137	—	2	4	no	—
11	C₂×#13063259	C₂²	1	2	yes	—
12	C₂×#13063249	—	2	2	no	—
13	#14582703	—	2	4	no	—
14	(C₂×D₄₃)⋊C₁₆	—	2	2	no	—
15	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂×Q₃₂×C₄₃	—	2	4	no	—
17	C₂×Q₃₂×C₄₃	—	2	2	no	—
18	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
20	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
21	C₂×C₈×D₄₃	—	2	2	no	—
22	C₂×C₈×D₄₃	—	2	2	no	—
23	C₂×C₈×D₄₃	—	2	1	no	—
24	C₂×C₈×D₄₃	—	2	1	no	—
25	#13063301	—	2	8	no	—
26	#13063301	—	4	4	no	—
27	C₂×C₄⋊Dic₄₃	—	2	2	no	—
28	C₂×Dic₄₃⋊C₄	—	4	2	no	—
29	C₂×(C₂×D₄₃)⋊C₄	—	4	2	no	—
30	C₂×C₄₃⋊C₁₆	—	2	1	no	—
31	C₂×C₄₃⋊C₁₆	—	2	2	no	—
32	#13063259	—	2	2	no	—
33	#13063259	D₄	1	4	yes	—
34	#13063249	—	2	8	no	—
35	C₂²×Q₈×C₄₃	—	2	2	no	—
36	C₂×Q₁₆×C₄₃	—	2	2	no	—
37	C₂×Q₁₆×C₄₃	—	2	2	no	—
38	C₂×Q₁₆×C₄₃	—	2	2	no	—
39	C₂×Q₁₆×C₄₃	—	2	2	no	—
40	C₂×Q₁₆×C₄₃	—	2	2	no	—
41	C₂×Q₁₆×C₄₃	D₄	1	4	yes	—
42	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
43	Q₃₂×C₄₃	—	2	8	no	—
44	C₂×C₁₆×C₄₃	—	2	2	no	—
45	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
46	C₂³×D₄₃	D₈	1	1	yes	characteristic
47	C₂×Q₈×C₄₃	—	2	4	no	—
48	C₂×Q₈×C₄₃	—	4	2	no	—
49	C₂×Q₈×C₄₃	—	4	2	no	—
50	C₂×Q₈×C₄₃	—	4	2	no	—
51	C₂×Q₈×C₄₃	—	4	2	no	—
52	C₂×Q₈×C₄₃	—	4	2	no	—
53	C₂²×C₄×C₄₃	—	4	2	no	—
54	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₄₃	—	4	2	no	—
56	C₂²×Dic₄₃	D₈	1	1	yes	characteristic
57	C₂×C₄×D₄₃	—	2	2	no	—
58	C₂×C₄×D₄₃	—	2	1	no	—
59	C₂×C₄×D₄₃	—	2	1	no	—
60	C₂×C₄×D₄₃	—	2	2	no	—
61	Q₁₆×C₄₃	—	2	4	no	—
62	Q₁₆×C₄₃	—	2	4	no	—
63	Q₁₆×C₄₃	—	4	2	no	—
64	Q₁₆×C₄₃	—	4	2	no	—
65	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
66	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
69	(C₂×D₄₃)⋊C₄	—	4	8	no	—
70	C₄⋊Dic₄₃	—	2	4	no	—
71	C₄⋊Dic₄₃	—	4	2	no	—
72	Dic₄₃⋊C₄	—	4	8	no	—
73	C₂×C₄₃⋊C₈	—	2	2	no	—
74	C₂×C₄₃⋊C₈	—	2	1	no	—
75	C₈×D₄₃	—	4	1	no	—
76	C₈×D₄₃	—	4	2	no	—
77	C₈×D₄₃	—	4	1	no	—
78	C₁₆×C₄₃	—	2	2	no	—
79	C₄₃⋊C₁₆	—	4	1	no	—
80	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
81	C₂²×D₄₃	—	2	2	no	—
82	C₂²×D₄₃	—	2	1	no	—
83	C₂²×D₄₃	—	2	1	no	—
84	C₂²×D₄₃	—	2	2	no	—
85	C₂²×D₄₃	Q₃₂	1	2	yes	complemented
86	Q₈×C₄₃	—	4	4	no	—
87	Q₈×C₄₃	—	4	4	no	—
88	Q₈×C₄₃	—	8	2	no	—
89	Q₈×C₄₃	—	8	2	no	—
90	C₂×C₄×C₄₃	—	4	4	no	—
91	C₂×C₄×C₄₃	—	8	2	no	—
92	C₂×C₄×C₄₃	—	8	2	no	—
93	C₂×C₄×C₄₃	#120	1	2	yes	—
94	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
96	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×Dic₄₃	—	2	2	no	—
98	C₂×Dic₄₃	—	2	1	no	—
99	C₂×Dic₄₃	—	4	4	no	—
100	C₂×Dic₄₃	—	8	2	no	—
101	C₂×Dic₄₃	—	8	2	no	—
102	C₄×D₄₃	—	4	1	no	—
103	C₄×D₄₃	—	4	2	no	—
104	C₄×D₄₃	—	4	1	no	—
105	C₈×C₄₃	#120	1	1	yes	characteristic
106	C₈×C₄₃	#121	1	2	yes	—
107	C₈×C₄₃	#127	1	1	yes	characteristic
108	C₄₃⋊C₈	—	4	1	no	—
109	#13306	—	43	1	no	maximal, Sylow
110	C₂²×C₄₃	#447	1	2	yes	—
111	C₂²×C₄₃	#466	1	1	yes	characteristic
112	C₂²×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
113	C₂²×C₄₃	#508	1	1	yes	characteristic
114	C₂²×C₄₃	#510	1	2	yes	—
115	C₂×D₄₃	—	2	4	no	—
116	C₂×D₄₃	—	2	2	no	—
117	C₂×D₄₃	—	4	2	no	—
118	C₂×D₄₃	—	4	1	no	—
119	C₂×D₄₃	—	4	1	no	—
120	C₄×C₄₃	—	8	4	no	—
121	C₄×C₄₃	#392	1	1	yes	characteristic
122	C₄×C₄₃	#449	1	2	yes	—
123	C₄×C₄₃	#469	1	1	yes	characteristic
124	Dic₄₃	—	4	1	no	—
125	Dic₄₃	—	8	4	no	—
126	C₂²×Q₃₂	D₄₃	1	1	yes	characteristic, complemented
127	C₂×#467	—	43	2	no	—
128	C₂×#358	—	43	2	no	—
129	C₂×C₂²⋊C₁₆	—	43	1	no	—
130	#1380	—	43	1	no	—
131	C₂×C₄₃	#1999	1	1	yes	characteristic
132	C₂×C₄₃	#2188	1	2	yes	—
133	C₂×C₄₃	#2189	1	2	yes	—
134	C₂×C₄₃	#2216	1	1	yes	characteristic
135	C₂×C₄₃	#2219	1	1	yes	characteristic
136	D₄₃	—	4	2	no	—
137	C₂²×Q₁₆	C₂×D₄₃	1	2	yes	—
138	C₂³×C₈	—	43	1	no	—
139	C₂×C₂²⋊Q₈	—	86	2	no	—
140	C₂×Q₃₂	—	2	4	no	—
141	C₂×Q₃₂	—	2	2	no	—
142	C₂²×C₁₆	—	43	1	no	—
143	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
144	#467	—	86	4	no	—
145	#467	—	86	4	no	—
146	C₂×#107	—	43	2	no	—
147	C₂×#103	—	86	2	no	—
148	#358	—	86	4	no	—
149	C₂²⋊C₁₆	—	86	2	no	—
150	C₄₃	#13306	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₈	—	2	2	no	—
152	C₂³×C₄	—	43	1	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×Q₁₆	—	2	2	no	—
155	C₂×Q₁₆	—	2	2	no	—
156	C₂×Q₁₆	—	2	2	no	—
157	C₂×Q₁₆	—	2	2	no	—
158	C₂×Q₁₆	C₂²⋊D₄₃	1	4	yes	—
159	C₂²×C₈	—	43	1	no	—
160	C₂²×C₈	—	86	2	no	—
161	C₂²×C₈	—	86	1	no	—
162	C₂²×C₈	—	86	1	no	—
163	C₂²×C₈	—	86	2	no	—
164	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
165	C₂²⋊Q₈	—	86	8	no	—
166	C₂²⋊Q₈	—	172	4	no	—
167	C₂×C₄⋊C₄	—	86	2	no	—
168	C₂×C₄⋊C₄	—	172	2	no	—
169	C₂×C₂²⋊C₄	—	172	2	no	—
170	Q₃₂	—	2	8	no	—
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	86	2	no	—
173	C₂×C₁₆	—	86	1	no	—
174	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
175	#107	—	43	4	no	—
176	#107	—	86	2	no	—
177	#103	—	86	8	no	—
178	C₂⁴	—	43	1	no	—
179	C₂×Q₈	—	2	4	no	—
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	—	43	1	no	—
187	C₂²×C₄	—	86	2	no	—
188	C₂²×C₄	—	86	1	no	—
189	C₂²×C₄	—	86	1	no	—
190	C₂²×C₄	—	86	2	no	—
191	C₂²×C₄	—	172	2	no	—
192	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
193	Q₁₆	—	2	4	no	—
194	Q₁₆	—	2	4	no	—
195	Q₁₆	—	4	2	no	—
196	Q₁₆	—	4	2	no	—
197	C₂×C₈	—	86	2	no	—
198	C₂×C₈	—	86	1	no	—
199	C₂×C₈	—	172	1	no	—
200	C₂×C₈	—	172	2	no	—
201	C₂×C₈	—	172	1	no	—
202	C₂×C₈	D₄×D₄₃	1	2	yes	—
203	C₂×C₈	#10621900	1	1	yes	characteristic
204	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
205	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
206	C₄⋊C₄	—	86	4	no	—
207	C₄⋊C₄	—	172	8	no	—
208	C₄⋊C₄	—	172	2	no	—
209	C₂²⋊C₄	—	172	8	no	—
210	C₁₆	—	2	2	no	—
211	C₁₆	—	172	1	no	—
212	C₂³	—	43	2	no	—
213	C₂³	—	86	1	no	—
214	C₂³	—	86	2	no	—
215	C₂³	—	86	1	no	—
216	C₂³	—	86	2	no	—
217	C₂³	D₈×D₄₃	1	1	yes	characteristic
218	Q₈	—	4	4	no	—
219	Q₈	—	4	4	no	—
220	Q₈	—	8	2	no	—
221	Q₈	—	8	2	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	8	2	no	—
224	C₂×C₄	—	8	2	no	—
225	C₂×C₄	—	86	1	no	—
226	C₂×C₄	—	86	2	no	—
227	C₂×C₄	—	344	2	no	—
228	C₂×C₄	—	344	2	no	—
229	C₂×C₄	—	172	4	no	—
230	C₂×C₄	—	172	2	no	—
231	C₂×C₄	—	172	1	no	—
232	C₂×C₄	—	172	1	no	—
233	C₂×C₄	#13063293	1	2	yes	—
234	C₂×C₄	#13063296	1	1	yes	characteristic
235	C₂×C₄	#13063344	1	1	yes	characteristic
236	C₂×C₄	#13063349	1	2	yes	—
237	C₈	—	172	1	no	—
238	C₈	#13063294	1	1	yes	characteristic
239	C₈	#13063297	1	2	yes	—
240	C₈	#13063321	1	1	yes	characteristic
241	C₂²	—	86	4	no	—
242	C₂²	—	86	2	no	—
243	C₂²	—	172	2	no	—
244	C₂²	—	172	1	no	—
245	C₂²	—	172	1	no	—
246	C₂²	#14583031	1	2	yes	—
247	C₂²	#14583132	1	1	yes	characteristic
248	C₂²	Q₃₂×D₄₃	1	1	yes	characteristic
249	C₂²	#14583332	1	1	yes	characteristic
250	C₂²	#14583341	1	2	yes	—
251	C₄	—	8	4	no	—
252	C₄	—	344	4	no	—
253	C₄	—	172	1	no	—
254	C₄	#14582807	1	1	yes	characteristic
255	C₄	#14583041	1	2	yes	—
256	C₄	#14583149	1	1	yes	characteristic
257	C₂	—	172	2	no	—
258	C₂	#19135590	1	1	yes	characteristic
259	C₂	#19136527	1	2	yes	—
260	C₂	#19136534	1	2	yes	—
261	C₂	#19136683	1	1	yes	characteristic
262	C₂	#19136700	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583137

C₂

yes

maximal

C₂×#14582703

C₂

yes

maximal, complemented

C₂×(C₂×D₄₃)⋊C₁₆

C₂

yes

maximal, characteristic

#19132687

C₂

yes

maximal, characteristic, complemented

C₂²×Q₃₂×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₃

C₂²

yes

characteristic

C₂×#13063301

—

C₂²×C₄₃⋊C₁₆

C₂²

yes

—

—

C₂²

yes

—

C₂×#13063249

—

#14582703

—

(C₂×D₄₃)⋊C₁₆

—

C₂²×Q₁₆×C₄₃

C₂²

yes

—

C₂×Q₃₂×C₄₃

—

C₂×Q₃₂×C₄₃

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₄×D₄₃

D₄

yes

characteristic

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

#13063301

—

#13063301

—

C₂×C₄⋊Dic₄₃

—

C₂×Dic₄₃⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

—

#13063259

—

#13063259

D₄

yes

—

#13063249

—

C₂²×Q₈×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

Q₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₂³×D₄₃

D₈

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₈

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

Q₃₂

yes

complemented

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

100

C₂×Dic₄₃

—

101

C₂×Dic₄₃

—

102

C₄×D₄₃

—

103

C₄×D₄₃

—

104

C₄×D₄₃

—

105

C₈×C₄₃

#120

yes

characteristic

106

C₈×C₄₃

#121

yes

—

107

C₈×C₄₃

#127

yes

characteristic

108

C₄₃⋊C₈

—

109

#13306

—

maximal, Sylow

110

C₂²×C₄₃

#447

yes

—

111

C₂²×C₄₃

#466

yes

characteristic

112

C₂²×C₄₃

C₂×Q₃₂

yes

characteristic

113

C₂²×C₄₃

#508

yes

characteristic

114

C₂²×C₄₃

#510

yes

—

115

C₂×D₄₃

—

116

C₂×D₄₃

—

117

C₂×D₄₃

—

118

C₂×D₄₃

—

119

C₂×D₄₃

—

120

C₄×C₄₃

—

121

C₄×C₄₃

#392

yes

characteristic

122

C₄×C₄₃

#449

yes

—

123

C₄×C₄₃

#469

yes

characteristic

124

Dic₄₃

—

125

Dic₄₃

—

126

C₂²×Q₃₂

D₄₃

yes

characteristic, complemented

127

C₂×#467

—

128

C₂×#358

—

129

C₂×C₂²⋊C₁₆

—

130

#1380

—

131

C₂×C₄₃

#1999

yes

characteristic

132

C₂×C₄₃

#2188

yes

—

133

C₂×C₄₃

#2189

yes

—

134

C₂×C₄₃

#2216

yes

characteristic

135

C₂×C₄₃

#2219

yes

characteristic

136

D₄₃

—

137

C₂²×Q₁₆

C₂×D₄₃

yes

—

138

C₂³×C₈

—

139

C₂×C₂²⋊Q₈

—

140

C₂×Q₃₂

—

141

C₂×Q₃₂

—

142

C₂²×C₁₆

—

143

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

144

#467

—

145

#467

—

146

C₂×#107

—

147

C₂×#103

—

148

#358

—

149

C₂²⋊C₁₆

—

150

C₄₃

#13306

yes

characteristic, complemented, Sylow

151

C₂²×Q₈

—

152

C₂³×C₄

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

C₂²⋊D₄₃

yes

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

C₂²×C₈

C₂²×D₄₃

yes

characteristic

165

C₂²⋊Q₈

—

166

C₂²⋊Q₈

—

172

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

172

—

169

C₂×C₂²⋊C₄

—

172

—

170

Q₃₂

—

171

C₂×C₁₆

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

C₂×C₁₆

C₂²⋊D₄₃

yes

—

175

#107

—

176

#107

—

177

#103

—

178

C₂⁴

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

172

—

192

C₂²×C₄

D₄×D₄₃

yes

characteristic

193

Q₁₆

—

194

Q₁₆

—

195

Q₁₆

—

196

Q₁₆

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

172

—

200

C₂×C₈

—

172

—

201

C₂×C₈

—

172

—

202

C₂×C₈

D₄×D₄₃

yes

—

203

C₂×C₈

#10621900

yes

characteristic

204

C₂×C₈

C₂×C₂²⋊D₄₃

yes

—

205

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

206

C₄⋊C₄

—

207

C₄⋊C₄

—

172

—

208

C₄⋊C₄

—

172

—

209

C₂²⋊C₄

—

172

—

210

C₁₆

—

211

C₁₆

—

172

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

D₈×D₄₃

yes

characteristic

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

344

—

228

C₂×C₄

—

344

—

229

C₂×C₄

—

172

—

230

C₂×C₄

—

172

—

231

C₂×C₄

—

172

—

232

C₂×C₄

—

172

—

233

C₂×C₄

#13063293

yes

—

234

C₂×C₄

#13063296

yes

characteristic

235

C₂×C₄

#13063344

yes

characteristic

236

C₂×C₄

#13063349

yes

—

237

C₈

—

172

—

238

C₈

#13063294

yes

characteristic

239

C₈

#13063297

yes

—

240

C₈

#13063321

yes

characteristic

241

C₂²

—

242

C₂²

—

243

C₂²

—

172

—

244

C₂²

—

172

—

245

C₂²

—

172

—

246

C₂²

#14583031

yes

—

247

C₂²

#14583132

yes

characteristic

248

C₂²

Q₃₂×D₄₃

yes

characteristic

249

C₂²

#14583332

yes

characteristic

250

C₂²

#14583341

yes

—

251

C₄

—

252

C₄

—

344

—

253

C₄

—

172

—

254

C₄

#14582807

yes

characteristic

255

C₄

#14583041

yes

—

256

C₄

#14583149

yes

characteristic

257

C₂

—

172

—

258

C₂

#19135590

yes

characteristic

259

C₂

#19136527

yes

—

260

C₂

#19136534

yes

—

261

C₂

#19136683

yes

characteristic

262

C₂

#19136700

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₄₃
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂²×Q₃₂×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂³×D₄₃	D₈
hypercenter	C₂²×Q₃₂	D₄₃
hypocenter	C₄₃	#13306
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₄₃

commutator, cosocle

C₂²×C₈×C₄₃

C₂³

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂²×Q₃₂×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₈

prime radical

C₂³×D₄₃

D₈

hypercenter

C₂²×Q₃₂

D₄₃

hypocenter

C₄₃

#13306

LCS

G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
2. C₂×#14582703	C₂	semidirect
4. #19132687	C₂	semidirect
5. C₂²×Q₃₂×C₄₃	C₂	semidirect
85. C₂²×D₄₃	Q₃₂	semidirect
126. C₂²×Q₃₂	D₄₃	semidirect
150. C₄₃	#13306	semidirect

H ≅ G/N

type

2. C₂×#14582703

C₂

semidirect

4. #19132687

C₂

semidirect

5. C₂²×Q₃₂×C₄₃

C₂

semidirect

85. C₂²×D₄₃

Q₃₂

semidirect

126. C₂²×Q₃₂

D₄₃

semidirect

150. C₄₃

#13306

semidirect

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

subgroup	index
C₂×#14583137	2
C₂×#14582703	2
C₂×(C₂×D₄₃)⋊C₁₆	2
#19132687	2
C₂²×Q₃₂×C₄₃	2
#13306	43

subgroup

index

C₂×(C₂×D₄₃)⋊C₁₆

C₂²×Q₃₂×C₄₃

Subgroups — #25015303

Conjugacy classes of subgroups

Complements

Maximal subgroups