Group #25013481 — subgroups

Subgroups — #25013481

Order 11008.

488 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 135 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	#19143287	C₂	1	1	yes	maximal, characteristic
2	#19136216	C₂	1	1	yes	maximal, characteristic, complemented
3	#19136205	C₂	1	2	yes	maximal, complemented
4	#19132680	C₂	1	2	yes	maximal, complemented
5	C₄₃×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
7	#14583406	C₄	1	1	yes	characteristic
8	C₂×#13063265	C₂²	1	2	yes	—
9	#14582968	—	2	2	no	—
10	C₈×C₂²⋊D₄₃	—	2	2	no	—
11	#14582927	C₄	1	1	yes	characteristic
12	#14582866	C₄	1	1	yes	characteristic
13	#14582862	C₄	1	1	yes	characteristic
14	#14582854	C₂²	1	1	yes	characteristic
15	#14582681	—	2	2	no	—
16	(C₂×D₄₃)⋊C₁₆	—	2	4	no	—
17	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#504	—	2	4	no	—
19	C₂×M₃₂×C₄₃	—	2	2	no	—
20	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₄₃	—	2	2	no	—
25	C₂×C₈×D₄₃	—	2	1	no	—
26	C₂×C₈×D₄₃	—	2	1	no	—
27	C₂×C₈×D₄₃	—	2	2	no	—
28	#13063306	C₈	1	2	yes	—
29	#13063301	—	2	1	no	—
30	#13063296	—	2	1	no	—
31	#13063293	C₈	1	2	yes	—
32	C₄×C₂²⋊D₄₃	—	2	2	no	—
33	#13063284	C₂×C₄	1	1	yes	characteristic
34	#13063265	—	2	2	no	—
35	#13063265	—	2	2	no	—
36	C₂×C₄₃⋊C₁₆	—	2	2	no	—
37	Dic₄₃⋊C₈	—	2	2	no	—
38	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
39	(C₂×D₄₃)⋊C₈	—	2	2	no	—
40	#13063235	—	2	1	no	—
41	C₈×Dic₄₃	—	2	1	no	—
42	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
43	#131×C₄₃	—	2	2	no	—
44	#131×C₄₃	—	2	2	no	—
45	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
47	C₂²×C₈×C₄₃	D₄	1	2	yes	—
48	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
49	M₃₂×C₄₃	—	2	4	no	—
50	M₃₂×C₄₃	—	2	2	no	—
51	M₃₂×C₄₃	—	2	2	no	—
52	C₂×C₁₆×C₄₃	—	2	4	no	—
53	C₂×C₁₆×C₄₃	D₄	1	4	yes	complemented
54	C₂³×D₄₃	C₂×C₈	1	1	yes	characteristic
55	#41×C₄₃	—	2	2	no	—
56	#41×C₄₃	—	2	2	no	—
57	C₂×Q₈×C₄₃	M₁₆	1	1	yes	characteristic
58	C₂×D₄×C₄₃	C₂×C₈	1	2	yes	—
59	C₂×D₄×C₄₃	M₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₄₃	—	2	2	no	—
63	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
64	C₂×C₄×D₄₃	—	2	1	no	—
65	C₂×C₄×D₄₃	—	2	2	no	—
66	C₂×C₄×D₄₃	—	2	1	no	—
67	C₂×C₄×D₄₃	—	2	2	no	—
68	M₁₆×C₄₃	—	2	2	no	—
69	M₁₆×C₄₃	—	2	4	no	—
70	C₂×C₈×C₄₃	—	2	2	no	—
71	C₂×C₈×C₄₃	—	2	2	no	—
72	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₄₃	#41	1	2	yes	—
77	C₂²⋊Dic₄₃	—	2	2	no	—
78	C₂²⋊Dic₄₃	C₂×C₈	1	2	yes	—
79	(C₂×D₄₃)⋊C₄	—	2	2	no	—
80	C₄⋊Dic₄₃	—	2	1	no	—
81	Dic₄₃⋊C₄	—	2	2	no	—
82	C₄×Dic₄₃	—	2	1	no	—
83	#10621877	—	2	2	no	—
84	C₂×C₄₃⋊C₈	—	2	1	no	—
85	C₂×C₄₃⋊C₈	—	2	1	no	—
86	C₂×C₄₃⋊C₈	—	2	2	no	—
87	C₈×D₄₃	—	4	1	no	—
88	C₈×D₄₃	—	4	2	no	—
89	C₈×D₄₃	—	4	1	no	—
90	C₁₆×C₄₃	—	2	4	no	—
91	C₄₃⋊C₁₆	—	4	2	no	—
92	C₂³×C₄₃	C₂²⋊C₈	1	2	yes	—
93	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
94	C₂²×D₄₃	—	2	1	no	—
95	C₂²×D₄₃	—	2	2	no	—
96	C₂²×D₄₃	—	4	2	no	—
97	Q₈×C₄₃	—	2	2	no	—
98	D₄×C₄₃	—	2	4	no	—
99	D₄×C₄₃	—	2	2	no	—
100	C₂×C₄×C₄₃	—	2	2	no	—
101	C₂×C₄×C₄₃	—	2	2	no	—
102	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
103	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₄₃	#131	1	2	yes	—
107	C₂²⋊D₄₃	—	4	4	no	—
108	C₂×Dic₄₃	—	2	2	no	—
109	C₂×Dic₄₃	—	2	1	no	—
110	C₂×Dic₄₃	—	2	2	no	—
111	C₄×D₄₃	—	4	1	no	—
112	C₄×D₄₃	—	4	1	no	—
113	C₄×D₄₃	—	4	2	no	—
114	C₈×C₄₃	—	2	2	no	—
115	C₈×C₄₃	#120	1	1	yes	characteristic
116	C₈×C₄₃	#121	1	2	yes	—
117	C₈×C₄₃	#123	1	1	yes	characteristic
118	C₄₃⋊C₈	—	4	1	no	—
119	C₄₃⋊C₈	—	4	1	no	—
120	#12981	—	43	1	no	maximal, Sylow
121	C₂²×C₄₃	—	2	2	no	—
122	C₂²×C₄₃	—	4	1	no	—
123	C₂²×C₄₃	—	4	2	no	—
124	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₂²×C₄₃	C₈×D₄	1	2	yes	—
126	C₂×D₄₃	—	2	4	no	—
127	C₂×D₄₃	—	2	2	no	—
128	C₂×D₄₃	—	4	1	no	—
129	C₂×D₄₃	—	4	2	no	—
130	C₂×D₄₃	—	4	1	no	—
131	C₄×C₄₃	—	2	2	no	—
132	C₄×C₄₃	#386	1	1	yes	characteristic
133	C₄×C₄₃	#408	1	1	yes	characteristic
134	C₄×C₄₃	#435	1	2	yes	—
135	Dic₄₃	—	4	2	no	—
136	Dic₄₃	—	4	1	no	—
137	#3407	D₄₃	1	1	yes	characteristic, complemented
138	#2929	—	43	1	no	—
139	#2115	—	43	1	no	—
140	#2112	—	43	2	no	—
141	#1378	—	43	2	no	—
142	C₂×C₄₃	—	2	1	no	—
143	C₂×C₄₃	—	2	2	no	—
144	C₂×C₄₃	—	4	2	no	—
145	C₂×C₄₃	#1869	1	1	yes	characteristic
146	D₄₃	—	4	2	no	—
147	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
148	C₂³×C₈	—	43	1	no	—
149	#525	—	43	1	no	—
150	#504	—	2	4	no	—
151	C₂×M₃₂	—	2	2	no	—
152	C₂×M₃₂	—	43	2	no	—
153	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
154	#435	—	86	2	no	—
155	C₈×D₄	—	86	2	no	—
156	#424	—	43	1	no	—
157	#408	—	43	1	no	—
158	#407	—	43	1	no	—
159	#405	—	43	1	no	—
160	#349	—	86	2	no	—
161	C₂²⋊C₁₆	—	86	4	no	—
162	C₄₃	#12981	1	1	yes	characteristic, complemented, Sylow
163	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
164	C₂³×C₄	—	43	1	no	—
165	#131	—	2	2	no	—
166	#131	—	2	2	no	—
167	C₂×M₁₆	—	43	1	no	—
168	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
169	C₂×M₁₆	D₁₇₂	1	2	yes	—
170	C₂²×C₈	—	43	1	no	—
171	C₂²×C₈	—	86	1	no	—
172	C₂²×C₈	—	86	2	no	—
173	C₂²×C₈	—	86	2	no	—
174	C₂²×C₈	—	86	1	no	—
175	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
176	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
177	#123	—	43	2	no	—
178	C₂²⋊Q₈	—	86	1	no	—
179	#121	—	86	1	no	—
180	#120	—	43	2	no	—
181	C₄×D₄	—	86	2	no	—
182	#117	—	43	1	no	—
183	M₃₂	—	2	4	no	—
184	M₃₂	—	2	2	no	—
185	M₃₂	—	2	2	no	—
186	M₃₂	—	86	2	no	—
187	M₃₂	—	86	2	no	—
188	C₂×C₁₆	—	2	4	no	—
189	C₂×C₁₆	—	86	2	no	—
190	C₂×C₁₆	C₂²⋊D₄₃	1	4	yes	complemented
191	C₄⋊C₈	—	86	2	no	—
192	C₂²⋊C₈	—	86	2	no	—
193	C₂²⋊C₈	—	86	2	no	—
194	#97	—	86	1	no	—
195	C₄×C₈	—	86	1	no	—
196	C₂⁴	—	43	1	no	—
197	#41	—	2	2	no	—
198	#41	—	2	2	no	—
199	C₂×Q₈	#10621872	1	1	yes	characteristic
200	C₂×D₄	—	86	2	no	—
201	C₂×D₄	C₈×D₄₃	1	2	yes	—
202	C₂×D₄	#10621872	1	1	yes	characteristic
203	C₂²×C₄	—	43	1	no	—
204	C₂²×C₄	—	86	1	no	—
205	C₂²×C₄	—	86	2	no	—
206	C₂²×C₄	—	86	1	no	—
207	C₂²×C₄	—	86	2	no	—
208	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
209	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
210	M₁₆	—	2	2	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	86	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	86	1	no	—
216	C₂×C₈	—	86	1	no	—
217	C₂×C₈	—	86	2	no	—
218	C₂×C₈	—	172	1	no	—
219	C₂×C₈	—	172	2	no	—
220	C₂×C₈	—	172	1	no	—
221	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
222	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
223	C₂×C₈	#10621898	1	2	yes	—
224	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
225	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
226	C₄⋊C₄	—	86	2	no	—
227	C₄⋊C₄	—	86	1	no	—
228	C₂²⋊C₄	—	43	2	no	—
229	C₂²⋊C₄	—	86	2	no	—
230	C₂²⋊C₄	—	86	2	no	—
231	C₄²	—	86	1	no	—
232	C₁₆	—	2	4	no	—
233	C₁₆	—	172	2	no	—
234	C₂³	—	86	1	no	—
235	C₂³	—	86	2	no	—
236	C₂³	—	172	2	no	—
237	C₂³	(C₂×D₄₃)⋊C₈	1	2	yes	—
238	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
239	Q₈	—	2	2	no	—
240	D₄	—	2	4	no	—
241	D₄	—	2	2	no	—
242	D₄	—	172	4	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	86	2	no	—
246	C₂×C₄	—	86	1	no	—
247	C₂×C₄	—	86	2	no	—
248	C₂×C₄	—	172	1	no	—
249	C₂×C₄	—	172	2	no	—
250	C₂×C₄	—	172	1	no	—
251	C₂×C₄	(C₂×D₄₃)⋊C₈	1	2	yes	—
252	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
253	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
254	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
255	C₂×C₄	#13063331	1	2	yes	—
256	C₈	—	2	2	no	—
257	C₈	—	172	1	no	—
258	C₈	—	172	1	no	—
259	C₈	#13063294	1	1	yes	characteristic
260	C₈	#13063299	1	2	yes	—
261	C₈	#13063308	1	1	yes	characteristic
262	C₂²	—	2	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	86	2	no	—
266	C₂²	—	86	4	no	—
267	C₂²	—	172	1	no	—
268	C₂²	—	172	2	no	—
269	C₂²	—	172	1	no	—
270	C₂²	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
271	C₂²	C₈×C₂²⋊D₄₃	1	2	yes	—
272	C₄	—	2	2	no	—
273	C₄	—	172	2	no	—
274	C₄	—	172	1	no	—
275	C₄	#14582778	1	1	yes	characteristic
276	C₄	#14582865	1	1	yes	characteristic
277	C₄	#14582970	1	2	yes	—
278	C₂	—	2	1	no	—
279	C₂	—	2	2	no	—
280	C₂	—	4	2	no	—
281	C₂	—	172	2	no	—
282	C₂	#19134887	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19143287

C₂

yes

maximal, characteristic

#19136216

C₂

yes

maximal, characteristic, complemented

#19136205

C₂

yes

maximal, complemented

#19132680

C₂

yes

maximal, complemented

C₄₃×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₃

C₂²

yes

characteristic

#14583406

C₄

yes

characteristic

C₂×#13063265

C₂²

yes

—

#14582968

—

C₈×C₂²⋊D₄₃

—

#14582927

C₄

yes

characteristic

#14582866

C₄

yes

characteristic

#14582862

C₄

yes

characteristic

#14582854

C₂²

yes

characteristic

#14582681

—

(C₂×D₄₃)⋊C₁₆

—

C₂×#131×C₄₃

C₂²

yes

characteristic

C₄₃×#504

—

C₂×M₃₂×C₄₃

—

C₂×M₃₂×C₄₃

C₂²

yes

—

C₂²×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×#10621877

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

#13063306

C₈

yes

—

#13063301

—

#13063296

—

#13063293

C₈

yes

—

C₄×C₂²⋊D₄₃

—

#13063284

C₂×C₄

yes

characteristic

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

(C₂×D₄₃)⋊C₈

—

#13063235

—

C₈×Dic₄₃

—

C₂×#41×C₄₃

C₂×C₄

yes

characteristic

#131×C₄₃

—

#131×C₄₃

—

C₂×M₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

complemented

C₂³×D₄₃

C₂×C₈

yes

characteristic

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

M₁₆

yes

characteristic

C₂×D₄×C₄₃

C₂×C₈

yes

—

C₂×D₄×C₄₃

M₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

C₂×C₈

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

C₂×C₈

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂²⋊C₈

yes

—

C₂³×C₄₃

C₂²×C₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

100

C₂×C₄×C₄₃

—

101

C₂×C₄×C₄₃

—

102

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

103

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₄₃

C₄×D₄

yes

—

105

C₂×C₄×C₄₃

C₂×M₁₆

yes

characteristic

106

C₂×C₄×C₄₃

#131

yes

—

107

C₂²⋊D₄₃

—

108

C₂×Dic₄₃

—

109

C₂×Dic₄₃

—

110

C₂×Dic₄₃

—

111

C₄×D₄₃

—

112

C₄×D₄₃

—

113

C₄×D₄₃

—

114

C₈×C₄₃

—

115

C₈×C₄₃

#120

yes

characteristic

116

C₈×C₄₃

#121

yes

—

117

C₈×C₄₃

#123

yes

characteristic

118

C₄₃⋊C₈

—

119

C₄₃⋊C₈

—

120

#12981

—

maximal, Sylow

121

C₂²×C₄₃

—

122

C₂²×C₄₃

—

123

C₂²×C₄₃

—

124

C₂²×C₄₃

C₂×C₂²⋊C₈

yes

characteristic

125

C₂²×C₄₃

C₈×D₄

yes

—

126

C₂×D₄₃

—

127

C₂×D₄₃

—

128

C₂×D₄₃

—

129

C₂×D₄₃

—

130

C₂×D₄₃

—

131

C₄×C₄₃

—

132

C₄×C₄₃

#386

yes

characteristic

133

C₄×C₄₃

#408

yes

characteristic

134

C₄×C₄₃

#435

yes

—

135

Dic₄₃

—

136

Dic₄₃

—

137

#3407

D₄₃

yes

characteristic, complemented

138

#2929

—

139

#2115

—

140

#2112

—

141

#1378

—

142

C₂×C₄₃

—

143

C₂×C₄₃

—

144

C₂×C₄₃

—

145

C₂×C₄₃

#1869

yes

characteristic

146

D₄₃

—

147

C₂×#131

C₂×D₄₃

yes

characteristic

148

C₂³×C₈

—

149

#525

—

150

#504

—

151

C₂×M₃₂

—

152

C₂×M₃₂

—

153

C₂×M₃₂

C₂×D₄₃

yes

—

154

#435

—

155

C₈×D₄

—

156

#424

—

157

#408

—

158

#407

—

159

#405

—

160

#349

—

161

C₂²⋊C₁₆

—

162

C₄₃

#12981

yes

characteristic, complemented, Sylow

163

C₂×#41

C₄×D₄₃

yes

characteristic

164

C₂³×C₄

—

165

#131

—

166

#131

—

167

C₂×M₁₆

—

168

C₂×M₁₆

C₄×D₄₃

yes

characteristic

169

C₂×M₁₆

D₁₇₂

yes

—

170

C₂²×C₈

—

171

C₂²×C₈

—

172

C₂²×C₈

—

173

C₂²×C₈

—

174

C₂²×C₈

—

175

C₂²×C₈

C₂²⋊D₄₃

yes

—

176

C₂²×C₈

C₂²×D₄₃

yes

characteristic

177

#123

—

178

C₂²⋊Q₈

—

179

#121

—

180

#120

—

181

C₄×D₄

—

182

#117

—

183

M₃₂

—

184

M₃₂

—

185

M₃₂

—

186

M₃₂

—

187

M₃₂

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

190

C₂×C₁₆

C₂²⋊D₄₃

yes

complemented

191

C₄⋊C₈

—

192

C₂²⋊C₈

—

193

C₂²⋊C₈

—

194

#97

—

195

C₄×C₈

—

196

C₂⁴

—

197

#41

—

198

#41

—

199

C₂×Q₈

#10621872

yes

characteristic

200

C₂×D₄

—

201

C₂×D₄

C₈×D₄₃

yes

—

202

C₂×D₄

#10621872

yes

characteristic

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

209

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

210

M₁₆

—

211

M₁₆

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

172

—

219

C₂×C₈

—

172

—

220

C₂×C₈

—

172

—

221

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

222

C₂×C₈

C₂×D₁₇₂

yes

characteristic

223

C₂×C₈

#10621898

yes

—

224

C₂×C₈

C₂×C₂²⋊D₄₃

yes

—

225

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₂²⋊C₄

—

229

C₂²⋊C₄

—

230

C₂²⋊C₄

—

231

C₄²

—

232

C₁₆

—

233

C₁₆

—

172

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

172

—

237

C₂³

(C₂×D₄₃)⋊C₈

yes

—

238

C₂³

C₂×C₈×D₄₃

yes

characteristic

239

Q₈

—

240

D₄

—

241

D₄

—

242

D₄

—

172

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

172

—

249

C₂×C₄

—

172

—

250

C₂×C₄

—

172

—

251

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

—

252

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

253

C₂×C₄

C₄×C₂²⋊D₄₃

yes

—

254

C₂×C₄

C₂×#10621872

yes

characteristic

255

C₂×C₄

#13063331

yes

—

256

C₈

—

257

C₈

—

172

—

258

C₈

—

172

—

259

C₈

#13063294

yes

characteristic

260

C₈

#13063299

yes

—

261

C₈

#13063308

yes

characteristic

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

172

—

268

C₂²

—

172

—

269

C₂²

—

172

—

270

C₂²

C₂×(C₂×D₄₃)⋊C₈

yes

characteristic

271

C₂²

C₈×C₂²⋊D₄₃

yes

—

272

C₄

—

273

C₄

—

172

—

274

C₄

—

172

—

275

C₄

#14582778

yes

characteristic

276

C₄

#14582865

yes

characteristic

277

C₄

#14582970

yes

—

278

C₂

—

279

C₂

—

280

C₂

—

281

C₂

—

172

—

282

C₂

#19134887

yes

characteristic

	subgroup	G/H
center	C₈	#13063294
commutator	C₂³×C₄₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#3407	C₂
socle	C₂×C₄₃	#1869
prime radical	#14583406	C₄
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#3407	D₄₃
hypocenter	C₄₃	#12981
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3407

subgroup

G/H

center

C₈

#13063294

commutator

C₂³×C₄₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#3407

C₂

C₂×C₄₃

C₄

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3407

N	H ≅ G/N	type
2. #19136216	C₂	semidirect
3. #19136205	C₂	semidirect
4. #19132680	C₂	semidirect
5. C₄₃×#3407	C₂	semidirect
53. C₂×C₁₆×C₄₃	D₄	semidirect
137. #3407	D₄₃	semidirect
162. C₄₃	#12981	semidirect
190. C₂×C₁₆	C₂²⋊D₄₃	semidirect

H ≅ G/N

type

2. #19136216

C₂

semidirect

3. #19136205

C₂

semidirect

4. #19132680

C₂

semidirect

5. C₄₃×#3407

C₂

semidirect

53. C₂×C₁₆×C₄₃

D₄

semidirect

137. #3407

D₄₃

semidirect

162. C₄₃

#12981

semidirect

190. C₂×C₁₆

C₂²⋊D₄₃

semidirect

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

subgroup	index
#19143287	2
#19136216	2
#19136205	2
#19132680	2
C₄₃×#3407	2
#12981	43

subgroup

index

C₄₃×#3407

Subgroups — #25013481

Conjugacy classes of subgroups

Complements

Maximal subgroups