Group #25014802 — subgroups

Subgroups — #25014802

Order 11008.

438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19143291	C₂	1	1	yes	maximal, characteristic
2	#19136361	C₂	1	1	yes	maximal, characteristic, complemented
3	#19136222	C₂	1	2	yes	maximal, complemented
4	#19136205	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2110	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063331	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	#14583411	C₄	1	1	yes	characteristic
9	C₂×#13063265	C₂²	1	2	yes	—
10	#14582972	—	2	2	no	—
11	C₈×D₁₇₂	—	2	2	no	—
12	#14582926	C₄	1	1	yes	characteristic
13	#14582867	C₄	1	1	yes	characteristic
14	#14582862	C₄	1	1	yes	characteristic
15	#14582720	—	2	2	no	—
16	#14582682	—	2	4	no	—
17	(C₂×D₄₃)⋊C₁₆	—	2	4	no	—
18	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#405	C₂²	1	1	yes	characteristic
20	C₄₃×#347	—	2	2	no	—
21	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
23	#13063331	—	2	2	no	—
24	#13063331	—	2	2	no	—
25	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
26	C₂×#10621872	—	2	1	no	—
27	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×D₄₃	—	2	2	no	—
29	C₂×C₈×D₄₃	—	2	1	no	—
30	C₂×C₈×D₄₃	—	2	1	no	—
31	C₂×C₈×D₄₃	—	2	1	no	—
32	C₂×C₈×D₄₃	—	2	2	no	—
33	#13063309	—	2	1	no	—
34	#13063305	—	2	1	no	—
35	#13063300	—	2	1	no	—
36	#13063295	—	2	1	no	—
37	C₄×D₁₇₂	—	2	2	no	—
38	#13063265	—	2	2	no	—
39	#13063265	—	2	2	no	—
40	C₂×C₄₃⋊C₁₆	—	2	2	no	—
41	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
42	(C₂×D₄₃)⋊C₈	—	2	2	no	—
43	(C₂×D₄₃)⋊C₈	—	2	2	no	—
44	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
46	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
47	M₃₂×C₄₃	—	2	2	no	—
48	M₃₂×C₄₃	—	2	2	no	—
49	C₂×C₁₆×C₄₃	D₄	1	4	yes	complemented
50	#97×C₄₃	D₄	1	2	yes	—
51	C₄×C₈×C₄₃	D₄	1	2	yes	—
52	C₂³×D₄₃	M₁₆	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊D₄₃	—	2	1	no	—
55	C₂²×Dic₄₃	M₁₆	1	1	yes	characteristic
56	#10621898	—	2	2	no	—
57	#10621898	—	2	2	no	—
58	C₂×D₁₇₂	—	2	2	no	—
59	C₂×D₁₇₂	M₁₆	1	1	yes	characteristic
60	C₂×C₄×D₄₃	—	2	1	no	—
61	C₂×C₄×D₄₃	—	2	1	no	—
62	C₂×C₄×D₄₃	—	2	2	no	—
63	C₂×C₄×D₄₃	—	2	1	no	—
64	C₂×C₄×D₄₃	—	2	2	no	—
65	C₂×Dic₈₆	M₁₆	1	1	yes	characteristic
66	M₁₆×C₄₃	—	2	2	no	—
67	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₄₃	#41	1	2	yes	—
72	C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
75	(C₂×D₄₃)⋊C₄	—	2	2	no	—
76	(C₂×D₄₃)⋊C₄	—	2	2	no	—
77	C₄⋊Dic₄₃	—	2	2	no	—
78	#10621877	—	2	2	no	—
79	C₂×C₄₃⋊C₈	—	2	1	no	—
80	C₂×C₄₃⋊C₈	—	2	1	no	—
81	C₂×C₄₃⋊C₈	—	2	2	no	—
82	#10621872	—	4	2	no	—
83	C₈×D₄₃	—	4	2	no	—
84	C₈×D₄₃	—	4	1	no	—
85	C₈×D₄₃	—	4	1	no	—
86	C₈×D₄₃	—	4	1	no	—
87	C₈×D₄₃	—	4	1	no	—
88	C₁₆×C₄₃	—	2	4	no	—
89	C₄₃⋊C₁₆	—	4	2	no	—
90	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
91	C₂²×D₄₃	—	2	1	no	—
92	C₂²×D₄₃	—	2	2	no	—
93	C₂²×D₄₃	—	2	1	no	—
94	C₂²×D₄₃	—	4	2	no	—
95	C₂×C₄×C₄₃	—	2	2	no	—
96	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#131	1	2	yes	—
100	C₂²⋊D₄₃	—	4	2	no	—
101	C₂×Dic₄₃	—	2	1	no	—
102	C₂×Dic₄₃	—	2	1	no	—
103	C₂×Dic₄₃	—	2	2	no	—
104	D₁₇₂	—	2	2	no	—
105	D₁₇₂	—	4	4	no	—
106	C₄×D₄₃	—	4	1	no	—
107	C₄×D₄₃	—	4	1	no	—
108	C₄×D₄₃	—	4	1	no	—
109	C₄×D₄₃	—	4	1	no	—
110	C₄×D₄₃	—	4	2	no	—
111	Dic₈₆	—	2	2	no	—
112	C₈×C₄₃	—	2	2	no	—
113	C₈×C₄₃	#121	1	2	yes	—
114	C₈×C₄₃	#124	1	1	yes	characteristic
115	C₈×C₄₃	#127	1	1	yes	characteristic
116	C₄₃⋊C₈	—	4	1	no	—
117	C₄₃⋊C₈	—	4	1	no	—
118	#13200	—	43	1	no	maximal, Sylow
119	C₂²×C₄₃	—	4	1	no	—
120	C₂²×C₄₃	#407	1	1	yes	characteristic
121	C₂²×C₄₃	#435	1	2	yes	—
122	C₂×D₄₃	—	2	4	no	—
123	C₂×D₄₃	—	2	2	no	—
124	C₂×D₄₃	—	4	1	no	—
125	C₂×D₄₃	—	4	2	no	—
126	C₂×D₄₃	—	4	1	no	—
127	C₂×D₄₃	—	4	2	no	—
128	C₂×D₄₃	—	4	1	no	—
129	C₄×C₄₃	—	4	2	no	—
130	C₄×C₄₃	#390	1	1	yes	characteristic
131	C₄×C₄₃	#408	1	1	yes	characteristic
132	C₄×C₄₃	#435	1	2	yes	—
133	Dic₄₃	—	4	1	no	—
134	Dic₄₃	—	4	1	no	—
135	#2929	—	43	1	no	—
136	#2153	—	43	1	no	—
137	#2117	—	43	2	no	—
138	#2112	—	43	2	no	—
139	#2110	D₄₃	1	1	yes	characteristic, complemented
140	C₂×C₄₃	—	2	1	no	—
141	C₂×C₄₃	—	2	2	no	—
142	C₂×C₄₃	#1955	1	1	yes	characteristic
143	D₄₃	—	4	2	no	—
144	D₄₃	—	8	1	no	—
145	C₂×#131	—	43	1	no	—
146	C₂³×C₈	—	43	1	no	—
147	#525	—	43	1	no	—
148	C₂×M₃₂	—	43	2	no	—
149	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
150	#435	—	86	2	no	—
151	C₈×D₄	—	86	2	no	—
152	#424	—	43	1	no	—
153	#408	—	43	1	no	—
154	#407	—	43	1	no	—
155	#405	C₂×D₄₃	1	1	yes	characteristic
156	#364	—	86	2	no	—
157	#350	—	86	4	no	—
158	C₂²⋊C₁₆	—	86	4	no	—
159	#347	—	2	2	no	—
160	C₄₃	#13200	1	1	yes	characteristic, complemented, Sylow
161	C₂×#41	—	43	1	no	—
162	C₂³×C₄	—	43	1	no	—
163	#131	—	86	2	no	—
164	#131	—	86	2	no	—
165	C₂×M₁₆	—	43	1	no	—
166	C₂×M₁₆	—	86	1	no	—
167	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
168	C₂²×C₈	—	43	1	no	—
169	C₂²×C₈	—	86	2	no	—
170	C₂²×C₈	—	86	1	no	—
171	C₂²×C₈	—	86	1	no	—
172	C₂²×C₈	—	86	2	no	—
173	C₂²×C₈	—	86	1	no	—
174	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
175	#123	—	86	1	no	—
176	C₂²⋊Q₈	—	86	1	no	—
177	#121	—	86	1	no	—
178	#120	—	86	1	no	—
179	C₄×D₄	—	86	2	no	—
180	#117	C₄×D₄₃	1	1	yes	characteristic
181	M₃₂	—	2	2	no	—
182	M₃₂	—	2	2	no	—
183	M₃₂	—	86	2	no	—
184	M₃₂	—	86	2	no	—
185	C₂×C₁₆	—	86	2	no	—
186	C₂×C₁₆	D₁₇₂	1	4	yes	complemented
187	C₄⋊C₈	—	86	2	no	—
188	C₂²⋊C₈	—	86	2	no	—
189	C₂²⋊C₈	—	86	2	no	—
190	#97	C₂²⋊D₄₃	1	2	yes	—
191	C₄×C₈	D₁₇₂	1	2	yes	—
192	C₂⁴	—	43	1	no	—
193	#41	—	86	2	no	—
194	#41	—	86	2	no	—
195	C₂×Q₈	—	43	1	no	—
196	C₂×D₄	—	43	1	no	—
197	C₂×D₄	—	86	2	no	—
198	C₂×D₄	—	86	1	no	—
199	C₂²×C₄	—	43	1	no	—
200	C₂²×C₄	—	86	1	no	—
201	C₂²×C₄	—	86	1	no	—
202	C₂²×C₄	—	86	2	no	—
203	C₂²×C₄	—	86	1	no	—
204	C₂²×C₄	—	86	2	no	—
205	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
206	M₁₆	—	2	2	no	—
207	M₁₆	—	86	2	no	—
208	M₁₆	—	172	2	no	—
209	C₂×C₈	—	86	1	no	—
210	C₂×C₈	—	86	1	no	—
211	C₂×C₈	—	86	2	no	—
212	C₂×C₈	—	172	2	no	—
213	C₂×C₈	—	172	1	no	—
214	C₂×C₈	—	172	1	no	—
215	C₂×C₈	—	172	1	no	—
216	C₂×C₈	—	172	1	no	—
217	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
218	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
219	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
220	C₂×C₈	#10621898	1	2	yes	—
221	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
222	C₄⋊C₄	—	2	1	no	—
223	C₄⋊C₄	—	86	2	no	—
224	C₂²⋊C₄	—	2	1	no	—
225	C₂²⋊C₄	—	86	2	no	—
226	C₂²⋊C₄	—	86	2	no	—
227	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
228	C₁₆	—	2	4	no	—
229	C₁₆	—	172	2	no	—
230	C₂³	—	86	1	no	—
231	C₂³	—	86	2	no	—
232	C₂³	—	86	1	no	—
233	C₂³	—	172	2	no	—
234	C₂³	M₁₆×D₄₃	1	1	yes	characteristic
235	Q₈	—	86	2	no	—
236	D₄	—	86	2	no	—
237	D₄	—	172	4	no	—
238	D₄	—	172	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	86	1	no	—
241	C₂×C₄	—	86	1	no	—
242	C₂×C₄	—	86	2	no	—
243	C₂×C₄	—	172	1	no	—
244	C₂×C₄	—	172	1	no	—
245	C₂×C₄	—	172	1	no	—
246	C₂×C₄	—	172	1	no	—
247	C₂×C₄	—	172	2	no	—
248	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
249	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
250	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
251	C₂×C₄	#13063333	1	2	yes	—
252	C₈	—	2	2	no	—
253	C₈	—	172	1	no	—
254	C₈	—	172	1	no	—
255	C₈	#13063299	1	2	yes	—
256	C₈	#13063313	1	1	yes	characteristic
257	C₈	#13063322	1	1	yes	characteristic
258	C₂²	—	4	1	no	—
259	C₂²	—	86	2	no	—
260	C₂²	—	86	4	no	—
261	C₂²	—	172	2	no	—
262	C₂²	—	172	1	no	—
263	C₂²	—	172	2	no	—
264	C₂²	—	172	1	no	—
265	C₂²	—	172	1	no	—
266	C₂²	#14582862	1	1	yes	characteristic
267	C₂²	#14582972	1	2	yes	—
268	C₄	—	4	2	no	—
269	C₄	—	172	1	no	—
270	C₄	—	172	1	no	—
271	C₄	#14582801	1	1	yes	characteristic
272	C₄	#14582867	1	1	yes	characteristic
273	C₄	#14582972	1	2	yes	—
274	C₂	—	2	1	no	—
275	C₂	—	2	2	no	—
276	C₂	—	344	1	no	—
277	C₂	—	172	2	no	—
278	C₂	#19135393	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19143291

C₂

yes

maximal, characteristic

#19136361

C₂

yes

maximal, characteristic, complemented

#19136222

C₂

yes

maximal, complemented

#19136205

C₂

yes

maximal, complemented

C₄₃×#2110

C₂

yes

maximal, characteristic, complemented

C₂×#13063331

C₂²

yes

characteristic

C₂²×C₈×D₄₃

C₂²

yes

characteristic

#14583411

C₄

yes

characteristic

C₂×#13063265

C₂²

yes

—

#14582972

—

C₈×D₁₇₂

—

#14582926

C₄

yes

characteristic

#14582867

C₄

yes

characteristic

#14582862

C₄

yes

characteristic

#14582720

—

#14582682

—

(C₂×D₄₃)⋊C₁₆

—

C₂×M₃₂×C₄₃

C₂²

yes

—

C₄₃×#405

C₂²

yes

characteristic

C₄₃×#347

—

C₂×#10621898

C₂×C₄

yes

characteristic

C₂²×C₄×D₄₃

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#10621872

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

—

—

—

—

C₄×D₁₇₂

—

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

C₄⋊(C₄₃⋊C₈)

—

(C₂×D₄₃)⋊C₈

—

(C₂×D₄₃)⋊C₈

—

C₂×M₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#117×C₄₃

C₂×C₄

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

complemented

#97×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂³×D₄₃

M₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

M₁₆

yes

characteristic

#10621898

—

#10621898

—

C₂×D₁₇₂

—

C₂×D₁₇₂

M₁₆

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

M₁₆

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²⋊C₄

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

#10621872

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×M₁₆

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₃

#131

yes

—

100

C₂²⋊D₄₃

—

101

C₂×Dic₄₃

—

102

C₂×Dic₄₃

—

103

C₂×Dic₄₃

—

104

D₁₇₂

—

105

D₁₇₂

—

106

C₄×D₄₃

—

107

C₄×D₄₃

—

108

C₄×D₄₃

—

109

C₄×D₄₃

—

110

C₄×D₄₃

—

111

Dic₈₆

—

112

C₈×C₄₃

—

113

C₈×C₄₃

#121

yes

—

114

C₈×C₄₃

#124

yes

characteristic

115

C₈×C₄₃

#127

yes

characteristic

116

C₄₃⋊C₈

—

117

C₄₃⋊C₈

—

118

#13200

—

maximal, Sylow

119

C₂²×C₄₃

—

120

C₂²×C₄₃

#407

yes

characteristic

121

C₂²×C₄₃

#435

yes

—

122

C₂×D₄₃

—

123

C₂×D₄₃

—

124

C₂×D₄₃

—

125

C₂×D₄₃

—

126

C₂×D₄₃

—

127

C₂×D₄₃

—

128

C₂×D₄₃

—

129

C₄×C₄₃

—

130

C₄×C₄₃

#390

yes

characteristic

131

C₄×C₄₃

#408

yes

characteristic

132

C₄×C₄₃

#435

yes

—

133

Dic₄₃

—

134

Dic₄₃

—

135

#2929

—

136

#2153

—

137

#2117

—

138

#2112

—

139

#2110

D₄₃

yes

characteristic, complemented

140

C₂×C₄₃

—

141

C₂×C₄₃

—

142

C₂×C₄₃

#1955

yes

characteristic

143

D₄₃

—

144

D₄₃

—

145

C₂×#131

—

146

C₂³×C₈

—

147

#525

—

148

C₂×M₃₂

—

149

C₂×M₃₂

C₂×D₄₃

yes

—

150

#435

—

151

C₈×D₄

—

152

#424

—

153

#408

—

154

#407

—

155

#405

C₂×D₄₃

yes

characteristic

156

#364

—

157

#350

—

158

C₂²⋊C₁₆

—

159

#347

—

160

C₄₃

#13200

yes

characteristic, complemented, Sylow

161

C₂×#41

—

162

C₂³×C₄

—

163

#131

—

164

#131

—

165

C₂×M₁₆

—

166

C₂×M₁₆

—

167

C₂×M₁₆

C₄×D₄₃

yes

characteristic

168

C₂²×C₈

—

169

C₂²×C₈

—

170

C₂²×C₈

—

171

C₂²×C₈

—

172

C₂²×C₈

—

173

C₂²×C₈

—

174

C₂²×C₈

C₂²×D₄₃

yes

characteristic

175

#123

—

176

C₂²⋊Q₈

—

177

#121

—

178

#120

—

179

C₄×D₄

—

180

#117

C₄×D₄₃

yes

characteristic

181

M₃₂

—

182

M₃₂

—

183

M₃₂

—

184

M₃₂

—

185

C₂×C₁₆

—

186

C₂×C₁₆

D₁₇₂

yes

complemented

187

C₄⋊C₈

—

188

C₂²⋊C₈

—

189

C₂²⋊C₈

—

190

#97

C₂²⋊D₄₃

yes

—

191

C₄×C₈

D₁₇₂

yes

—

192

C₂⁴

—

193

#41

—

194

#41

—

195

C₂×Q₈

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

172

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

172

—

213

C₂×C₈

—

172

—

214

C₂×C₈

—

172

—

215

C₂×C₈

—

172

—

216

C₂×C₈

—

172

—

217

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

218

C₂×C₈

C₂×D₁₇₂

yes

—

219

C₂×C₈

C₂×D₁₇₂

yes

characteristic

220

C₂×C₈

#10621898

yes

—

221

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₂²⋊C₄

—

225

C₂²⋊C₄

—

226

C₂²⋊C₄

—

227

C₄²

(C₂×D₄₃)⋊C₄

yes

—

228

C₁₆

—

229

C₁₆

—

172

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

172

—

234

C₂³

M₁₆×D₄₃

yes

characteristic

235

Q₈

—

236

D₄

—

237

D₄

—

172

—

238

D₄

—

172

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

172

—

244

C₂×C₄

—

172

—

245

C₂×C₄

—

172

—

246

C₂×C₄

—

172

—

247

C₂×C₄

—

172

—

248

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

249

C₂×C₄

C₄×D₁₇₂

yes

—

250

C₂×C₄

M₁₆×D₄₃

yes

characteristic

251

C₂×C₄

#13063333

yes

—

252

C₈

—

253

C₈

—

172

—

254

C₈

—

172

—

255

C₈

#13063299

yes

—

256

C₈

#13063313

yes

characteristic

257

C₈

#13063322

yes

characteristic

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

172

—

262

C₂²

—

172

—

263

C₂²

—

172

—

264

C₂²

—

172

—

265

C₂²

—

172

—

266

C₂²

#14582862

yes

characteristic

267

C₂²

#14582972

yes

—

268

C₄

—

269

C₄

—

172

—

270

C₄

—

172

—

271

C₄

#14582801

yes

characteristic

272

C₄

#14582867

yes

characteristic

273

C₄

#14582972

yes

—

274

C₂

—

275

C₂

—

276

C₂

—

344

—

277

C₂

—

172

—

278

C₂

#19135393

yes

characteristic

	subgroup	G/H
center	C₈	#13063322
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#2110	C₂
socle	C₂×C₄₃	#1955
prime radical	#14583411	C₄
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#2110	D₄₃
hypocenter	C₄₃	#13200
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2110

subgroup

G/H

center

C₈

#13063322

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#2110

C₂

C₂×C₄₃

C₄

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2110

N	H ≅ G/N	type
2. #19136361	C₂	semidirect
3. #19136222	C₂	semidirect
4. #19136205	C₂	semidirect
5. C₄₃×#2110	C₂	semidirect
49. C₂×C₁₆×C₄₃	D₄	semidirect
139. #2110	D₄₃	semidirect
160. C₄₃	#13200	semidirect
186. C₂×C₁₆	D₁₇₂	semidirect

H ≅ G/N

type

2. #19136361

C₂

semidirect

3. #19136222

C₂

semidirect

4. #19136205

C₂

semidirect

5. C₄₃×#2110

C₂

semidirect

49. C₂×C₁₆×C₄₃

D₄

semidirect

139. #2110

D₄₃

semidirect

160. C₄₃

#13200

semidirect

186. C₂×C₁₆

D₁₇₂

semidirect

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

subgroup	index
#19143291	2
#19136361	2
#19136222	2
#19136205	2
C₄₃×#2110	2
#13200	43

subgroup

index

C₄₃×#2110

Subgroups — #25014802

Conjugacy classes of subgroups

Complements

Maximal subgroups