Group #25015109 — subgroups

Subgroups — #25015109

Order 11008.

462 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14583277	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582719	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582716	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582715	C₂	1	1	yes	maximal, characteristic
5	#19136314	C₂	1	1	yes	maximal, characteristic
6	#19134476	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2141	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂²×#10621885	—	2	1	no	—
10	C₂×#13063323	—	2	1	no	—
11	C₂×#13063265	C₂²	1	1	yes	characteristic
12	#14583277	—	2	2	no	—
13	#14583277	C₄	1	4	yes	complemented
14	C₂×#13063261	C₂²	1	1	yes	characteristic
15	#14582855	—	2	1	no	—
16	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
17	#14582719	—	2	2	no	—
18	#14582716	—	2	2	no	—
19	#14582715	—	2	2	no	—
20	#14582702	—	2	2	no	—
21	#14582658	—	2	1	no	—
22	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#427	C₂²	1	1	yes	characteristic
25	C₄₃×#358	—	2	2	no	—
26	C₂²×Dic₈₆	—	2	1	no	—
27	C₂×Dic₁₇₂	—	2	1	no	—
28	C₂×Dic₁₇₂	—	2	1	no	—
29	C₂×Dic₁₇₂	—	2	1	no	—
30	C₂×Dic₁₇₂	—	2	1	no	—
31	C₂×Dic₁₇₂	—	2	1	no	—
32	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
33	C₂×#10621885	—	2	4	no	—
34	C₂×#10621885	—	4	1	no	—
35	C₂×#10621885	—	4	1	no	—
36	C₂×#10621885	—	4	2	no	—
37	C₂×#10621877	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
39	#13063323	—	2	4	no	—
40	#13063323	—	4	2	no	—
41	C₂×Dic₄₃⋊C₄	—	4	2	no	—
42	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
43	#13063265	—	2	1	no	—
44	#13063265	—	2	1	no	—
45	C₂×C₄₃⋊C₁₆	—	2	1	no	—
46	#13063261	—	2	1	no	—
47	#13063261	D₄	1	2	yes	—
48	#13063236	—	4	1	no	—
49	C₄×C₄₃⋊C₈	—	4	1	no	—
50	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
51	C₈×Dic₄₃	D₄	1	2	yes	—
52	C₂²×Q₈×C₄₃	—	2	1	no	—
53	C₂×Q₁₆×C₄₃	—	2	1	no	—
54	C₂×Q₁₆×C₄₃	—	2	1	no	—
55	C₂×Q₁₆×C₄₃	—	2	1	no	—
56	C₂×Q₁₆×C₄₃	—	2	1	no	—
57	C₂×Q₁₆×C₄₃	—	2	1	no	—
58	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
60	#117×C₄₃	—	2	1	no	—
61	M₃₂×C₄₃	—	2	1	no	—
62	M₃₂×C₄₃	—	2	1	no	—
63	C₂×C₁₆×C₄₃	—	2	1	no	—
64	#107×C₄₃	D₄	1	2	yes	—
65	#106×C₄₃	—	2	1	no	—
66	C₂×Q₈×C₄₃	—	2	2	no	—
67	C₂×Q₈×C₄₃	—	4	1	no	—
68	C₂×Q₈×C₄₃	—	4	1	no	—
69	C₂×Q₈×C₄₃	—	4	1	no	—
70	C₂×Q₈×C₄₃	—	4	1	no	—
71	C₂×Q₈×C₄₃	—	4	1	no	—
72	C₂²×C₄×C₄₃	—	4	1	no	—
73	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₄₃	—	2	1	no	—
75	C₂²×Dic₄₃	—	4	1	no	—
76	C₂×Dic₈₆	—	2	2	no	—
77	C₂×Dic₈₆	—	4	1	no	—
78	C₂×Dic₈₆	—	4	1	no	—
79	C₂×Dic₈₆	—	4	1	no	—
80	C₂×Dic₈₆	—	4	1	no	—
81	C₂×Dic₈₆	—	4	1	no	—
82	Q₁₆×C₄₃	—	2	2	no	—
83	Q₁₆×C₄₃	—	2	2	no	—
84	Q₁₆×C₄₃	—	4	1	no	—
85	Q₁₆×C₄₃	—	4	1	no	—
86	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
91	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
92	C₄⋊C₄×C₄₃	—	2	2	no	—
93	C₂²⋊C₄×C₄₃	—	4	1	no	—
94	C₄²×C₄₃	—	4	1	no	—
95	#10621885	—	4	4	no	—
96	#10621885	—	4	4	no	—
97	Dic₄₃⋊C₄	—	4	8	no	—
98	C₄×Dic₄₃	—	2	1	no	—
99	C₄×Dic₄₃	C₂²⋊C₄	1	2	yes	—
100	#10621877	—	2	2	no	—
101	#10621877	—	4	1	no	—
102	C₂×C₄₃⋊C₈	—	4	1	no	—
103	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
104	C₂×C₄₃⋊C₈	D₈	1	1	yes	characteristic
105	C₂×C₄₃⋊C₈	D₈	1	1	yes	characteristic
106	C₂×C₄₃⋊C₈	SD₁₆	1	2	yes	—
107	Dic₁₇₂	—	2	2	no	—
108	Dic₁₇₂	—	2	2	no	—
109	Dic₁₇₂	—	4	1	no	—
110	Dic₁₇₂	—	4	1	no	—
111	C₁₆×C₄₃	—	4	1	no	—
112	C₄₃⋊C₁₆	—	4	1	no	—
113	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
114	Q₈×C₄₃	—	4	2	no	—
115	Q₈×C₄₃	—	4	2	no	—
116	Q₈×C₄₃	—	8	1	no	—
117	Q₈×C₄₃	—	8	1	no	—
118	C₂×C₄×C₄₃	—	4	2	no	—
119	C₂×C₄×C₄₃	—	4	2	no	—
120	C₂×C₄×C₄₃	—	8	1	no	—
121	C₂×C₄×C₄₃	—	8	1	no	—
122	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
124	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
125	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
126	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
127	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
128	C₂×Dic₄₃	—	2	4	no	—
129	C₂×Dic₄₃	—	2	2	no	—
130	C₂×Dic₄₃	—	4	2	no	—
131	C₂×Dic₄₃	—	8	1	no	—
132	C₂×Dic₄₃	—	8	1	no	—
133	Dic₈₆	—	4	2	no	—
134	Dic₈₆	—	4	2	no	—
135	Dic₈₆	—	8	1	no	—
136	Dic₈₆	—	8	1	no	—
137	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
138	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
139	C₈×C₄₃	#124	1	1	yes	characteristic
140	C₈×C₄₃	#127	1	1	yes	characteristic
141	C₄₃⋊C₈	—	4	2	no	—
142	C₄₃⋊C₈	#102	1	2	yes	—
143	C₄₃⋊C₈	#102	1	2	yes	—
144	#13262	—	43	1	no	maximal, Sylow
145	C₂²×C₄₃	—	2	2	no	—
146	C₂²×C₄₃	#418	1	1	yes	characteristic
147	C₂²×C₄₃	#459	1	1	yes	characteristic
148	C₂²×C₄₃	#460	1	1	yes	characteristic
149	C₄×C₄₃	—	8	2	no	—
150	C₄×C₄₃	—	8	2	no	—
151	C₄×C₄₃	#390	1	1	yes	characteristic
152	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
153	C₄×C₄₃	#459	1	1	yes	characteristic
154	C₄×C₄₃	#460	1	1	yes	characteristic
155	Dic₄₃	—	2	4	no	—
156	Dic₄₃	—	8	2	no	—
157	C₂×#494	—	43	1	no	—
158	C₂×#364	—	43	1	no	—
159	C₂×#362	—	43	1	no	—
160	C₂×#362	—	43	1	no	—
161	#2141	—	43	1	no	—
162	#2141	D₄₃	1	1	yes	characteristic
163	#1772	—	43	1	no	—
164	C₂×C₄₃	—	2	1	no	—
165	C₂×C₄₃	—	2	1	no	—
166	C₂×C₄₃	#1982	1	1	yes	characteristic
167	C₂×C₄₃	#2214	1	2	yes	—
168	C₂²×Q₁₆	—	43	1	no	—
169	C₂²×Q₁₆	—	86	1	no	—
170	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
171	C₂×C₄⋊Q₈	—	86	1	no	—
172	C₂×M₃₂	—	43	1	no	—
173	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
174	#494	—	43	4	no	—
175	#494	—	86	2	no	—
176	C₂×#108	—	43	1	no	—
177	#427	C₂×D₄₃	1	1	yes	characteristic
178	#405	—	86	1	no	—
179	C₂×C₄×C₈	—	43	1	no	—
180	#364	—	86	2	no	—
181	#362	—	86	2	no	—
182	#362	—	86	2	no	—
183	#358	—	2	2	no	—
184	#358	—	86	2	no	—
185	#339	—	86	1	no	—
186	C₄₃	#13262	1	1	yes	characteristic, complemented, Sylow
187	C₂²×Q₈	—	2	1	no	—
188	C₂²×Q₈	—	86	1	no	—
189	C₂×Q₁₆	—	2	1	no	—
190	C₂×Q₁₆	—	2	1	no	—
191	C₂×Q₁₆	—	2	1	no	—
192	C₂×Q₁₆	—	2	1	no	—
193	C₂×Q₁₆	—	2	1	no	—
194	C₂×Q₁₆	—	43	2	no	—
195	C₂×Q₁₆	—	86	4	no	—
196	C₂×Q₁₆	—	86	1	no	—
197	C₂×Q₁₆	—	86	1	no	—
198	C₂×Q₁₆	—	86	1	no	—
199	C₂×Q₁₆	—	86	1	no	—
200	C₂×Q₁₆	—	86	1	no	—
201	C₂×Q₁₆	—	172	1	no	—
202	C₂×Q₁₆	—	172	1	no	—
203	C₂×Q₁₆	—	172	2	no	—
204	C₂×Q₁₆	C₄×D₄₃	1	2	yes	—
205	C₂×M₁₆	—	86	1	no	—
206	C₂²×C₈	—	43	1	no	—
207	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
208	C₄⋊Q₈	—	86	4	no	—
209	C₄⋊Q₈	—	172	2	no	—
210	#117	—	2	1	no	—
211	C₂×C₄⋊C₄	—	172	2	no	—
212	C₂×C₄²	—	43	1	no	—
213	M₃₂	—	2	1	no	—
214	M₃₂	—	2	1	no	—
215	M₃₂	—	86	1	no	—
216	M₃₂	—	86	1	no	—
217	C₂×C₁₆	—	2	1	no	—
218	C₂×C₁₆	—	86	1	no	—
219	#108	—	43	2	no	—
220	#108	—	86	1	no	—
221	#107	C₂²⋊D₄₃	1	2	yes	—
222	#106	—	2	1	no	—
223	#97	—	172	1	no	—
224	C₄×C₈	—	43	2	no	—
225	C₄×C₈	—	43	2	no	—
226	C₄×C₈	—	172	1	no	—
227	C₂×Q₈	—	2	2	no	—
228	C₂×Q₈	—	4	1	no	—
229	C₂×Q₈	—	4	1	no	—
230	C₂×Q₈	—	4	1	no	—
231	C₂×Q₈	—	4	1	no	—
232	C₂×Q₈	—	4	1	no	—
233	C₂×Q₈	—	86	2	no	—
234	C₂×Q₈	—	172	1	no	—
235	C₂×Q₈	—	172	1	no	—
236	C₂×Q₈	—	172	1	no	—
237	C₂×Q₈	—	172	1	no	—
238	C₂×Q₈	—	172	1	no	—
239	C₂²×C₄	—	4	1	no	—
240	C₂²×C₄	—	86	1	no	—
241	C₂²×C₄	—	172	1	no	—
242	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
243	Q₁₆	—	2	2	no	—
244	Q₁₆	—	2	2	no	—
245	Q₁₆	—	4	1	no	—
246	Q₁₆	—	4	1	no	—
247	Q₁₆	—	86	2	no	—
248	Q₁₆	—	86	2	no	—
249	Q₁₆	—	172	4	no	—
250	Q₁₆	—	172	4	no	—
251	Q₁₆	—	172	1	no	—
252	Q₁₆	—	172	1	no	—
253	M₁₆	—	86	2	no	—
254	M₁₆	—	172	1	no	—
255	C₂×C₈	—	43	2	no	—
256	C₂×C₈	—	43	1	no	—
257	C₂×C₈	—	43	1	no	—
258	C₂×C₈	—	43	2	no	—
259	C₂×C₈	—	172	1	no	—
260	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
261	C₂×C₈	#10621898	1	1	yes	characteristic
262	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
263	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
264	C₂×C₈	#10621900	1	1	yes	characteristic
265	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	172	8	no	—
268	C₂²⋊C₄	—	4	1	no	—
269	C₄²	—	4	1	no	—
270	C₄²	—	43	2	no	—
271	C₄²	—	86	1	no	—
272	C₁₆	—	4	1	no	—
273	C₁₆	—	172	1	no	—
274	C₂³	#13063349	1	1	yes	characteristic
275	Q₈	—	4	2	no	—
276	Q₈	—	4	2	no	—
277	Q₈	—	8	1	no	—
278	Q₈	—	8	1	no	—
279	Q₈	—	344	1	no	—
280	Q₈	—	344	1	no	—
281	Q₈	—	172	2	no	—
282	Q₈	—	172	2	no	—
283	C₂×C₄	—	4	2	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	8	1	no	—
286	C₂×C₄	—	8	1	no	—
287	C₂×C₄	—	86	4	no	—
288	C₂×C₄	—	86	2	no	—
289	C₂×C₄	—	344	1	no	—
290	C₂×C₄	—	344	1	no	—
291	C₂×C₄	—	172	2	no	—
292	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
293	C₂×C₄	#13063297	1	1	yes	characteristic
294	C₂×C₄	#13063298	1	1	yes	characteristic
295	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
296	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
297	C₂×C₄	#13063352	1	1	yes	characteristic
298	C₈	—	43	2	no	—
299	C₈	—	43	2	no	—
300	C₈	—	172	2	no	—
301	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
302	C₈	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
303	C₈	#13063311	1	1	yes	characteristic
304	C₈	#13063321	1	1	yes	characteristic
305	C₂²	—	2	2	no	—
306	C₂²	#14582902	1	1	yes	characteristic
307	C₂²	#14583092	1	1	yes	characteristic
308	C₂²	#14583098	1	1	yes	characteristic
309	C₄	—	8	2	no	—
310	C₄	—	8	2	no	—
311	C₄	—	86	4	no	—
312	C₄	—	344	2	no	—
313	C₄	#14582799	1	1	yes	characteristic
314	C₄	#102×D₄₃	1	1	yes	characteristic
315	C₄	#14583093	1	1	yes	characteristic
316	C₄	#14583097	1	1	yes	characteristic
317	C₂	—	2	1	no	—
318	C₂	—	2	1	no	—
319	C₂	#19135520	1	1	yes	characteristic
320	C₂	#19136674	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583277

C₂

yes

maximal, characteristic

C₂×#14582719

C₂

yes

maximal, characteristic

C₂×#14582716

C₂

yes

maximal, characteristic

C₂×#14582715

C₂

yes

maximal, characteristic

#19136314

C₂

yes

maximal, characteristic

#19134476

C₂

yes

maximal, characteristic

C₄₃×#2141

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₂²

yes

—

—

C₂²

yes

characteristic

#14583277

—

#14583277

C₄

yes

complemented

C₂×#13063261

C₂²

yes

characteristic

#14582855

—

C₂×C₈×Dic₄₃

C₂²

yes

—

—

—

—

—

C₂²×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₃₂×C₄₃

C₂²

yes

characteristic

C₄₃×#427

C₂²

yes

characteristic

C₄₃×#358

—

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

—

—

—

—

—

C₂²×C₄₃⋊C₈

D₄

yes

characteristic

#13063323

—

#13063323

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

#13063261

—

#13063261

D₄

yes

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₈×Dic₄₃

C₂×C₄

yes

—

C₈×Dic₄₃

D₄

yes

—

C₂²×Q₈×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

—

C₂×Q₁₆×C₄₃

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#117×C₄₃

—

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

#107×C₄₃

D₄

yes

—

#106×C₄₃

—

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

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

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×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

#10621885

—

#10621885

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂²⋊C₄

yes

—

100

#10621877

—

101

#10621877

—

102

C₂×C₄₃⋊C₈

—

103

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

104

C₂×C₄₃⋊C₈

D₈

yes

characteristic

105

C₂×C₄₃⋊C₈

D₈

yes

characteristic

106

C₂×C₄₃⋊C₈

SD₁₆

yes

—

107

Dic₁₇₂

—

108

Dic₁₇₂

—

109

Dic₁₇₂

—

110

Dic₁₇₂

—

111

C₁₆×C₄₃

—

112

C₄₃⋊C₁₆

—

113

C₂³×C₄₃

AGL(1,ℤ/8)

yes

characteristic

114

Q₈×C₄₃

—

115

Q₈×C₄₃

—

116

Q₈×C₄₃

—

117

Q₈×C₄₃

—

118

C₂×C₄×C₄₃

—

119

C₂×C₄×C₄₃

—

120

C₂×C₄×C₄₃

—

121

C₂×C₄×C₄₃

—

122

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

123

C₂×C₄×C₄₃

#121

yes

characteristic

124

C₂×C₄×C₄₃

#121

yes

characteristic

125

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

126

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

127

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

128

C₂×Dic₄₃

—

129

C₂×Dic₄₃

—

130

C₂×Dic₄₃

—

131

C₂×Dic₄₃

—

132

C₂×Dic₄₃

—

133

Dic₈₆

—

134

Dic₈₆

—

135

Dic₈₆

—

136

Dic₈₆

—

137

C₈×C₄₃

C₄×D₄

yes

characteristic

138

C₈×C₄₃

C₄×D₄

yes

characteristic

139

C₈×C₄₃

#124

yes

characteristic

140

C₈×C₄₃

#127

yes

characteristic

141

C₄₃⋊C₈

—

142

C₄₃⋊C₈

#102

yes

—

143

C₄₃⋊C₈

#102

yes

—

144

#13262

—

maximal, Sylow

145

C₂²×C₄₃

—

146

C₂²×C₄₃

#418

yes

characteristic

147

C₂²×C₄₃

#459

yes

characteristic

148

C₂²×C₄₃

#460

yes

characteristic

149

C₄×C₄₃

—

150

C₄×C₄₃

—

151

C₄×C₄₃

#390

yes

characteristic

152

C₄×C₄₃

C₂×#102

yes

characteristic

153

C₄×C₄₃

#459

yes

characteristic

154

C₄×C₄₃

#460

yes

characteristic

155

Dic₄₃

—

156

Dic₄₃

—

157

C₂×#494

—

158

C₂×#364

—

159

C₂×#362

—

160

C₂×#362

—

161

#2141

—

162

#2141

D₄₃

yes

characteristic

163

#1772

—

164

C₂×C₄₃

—

165

C₂×C₄₃

—

166

C₂×C₄₃

#1982

yes

characteristic

167

C₂×C₄₃

#2214

yes

—

168

C₂²×Q₁₆

—

169

C₂²×Q₁₆

—

170

C₂²×Q₁₆

C₂×D₄₃

yes

characteristic

171

C₂×C₄⋊Q₈

—

172

C₂×M₃₂

—

173

C₂×M₃₂

C₂×D₄₃

yes

characteristic

174

#494

—

175

#494

—

176

C₂×#108

—

177

#427

C₂×D₄₃

yes

characteristic

178

#405

—

179

C₂×C₄×C₈

—

180

#364

—

181

#362

—

182

#362

—

183

#358

—

184

#358

—

185

#339

—

186

C₄₃

#13262

yes

characteristic, complemented, Sylow

187

C₂²×Q₈

—

188

C₂²×Q₈

—

189

C₂×Q₁₆

—

190

C₂×Q₁₆

—

191

C₂×Q₁₆

—

192

C₂×Q₁₆

—

193

C₂×Q₁₆

—

194

C₂×Q₁₆

—

195

C₂×Q₁₆

—

196

C₂×Q₁₆

—

197

C₂×Q₁₆

—

198

C₂×Q₁₆

—

199

C₂×Q₁₆

—

200

C₂×Q₁₆

—

201

C₂×Q₁₆

—

172

—

202

C₂×Q₁₆

—

172

—

203

C₂×Q₁₆

—

172

—

204

C₂×Q₁₆

C₄×D₄₃

yes

—

205

C₂×M₁₆

—

206

C₂²×C₈

—

207

C₂²×C₈

C₂²×D₄₃

yes

characteristic

208

C₄⋊Q₈

—

209

C₄⋊Q₈

—

172

—

210

#117

—

211

C₂×C₄⋊C₄

—

172

—

212

C₂×C₄²

—

213

M₃₂

—

214

M₃₂

—

215

M₃₂

—

216

M₃₂

—

217

C₂×C₁₆

—

218

C₂×C₁₆

—

219

#108

—

220

#108

—

221

#107

C₂²⋊D₄₃

yes

—

222

#106

—

223

#97

—

172

—

224

C₄×C₈

—

225

C₄×C₈

—

226

C₄×C₈

—

172

—

227

C₂×Q₈

—

228

C₂×Q₈

—

229

C₂×Q₈

—

230

C₂×Q₈

—

231

C₂×Q₈

—

232

C₂×Q₈

—

233

C₂×Q₈

—

234

C₂×Q₈

—

172

—

235

C₂×Q₈

—

172

—

236

C₂×Q₈

—

172

—

237

C₂×Q₈

—

172

—

238

C₂×Q₈

—

172

—

239

C₂²×C₄

—

240

C₂²×C₄

—

241

C₂²×C₄

—

172

—

242

C₂²×C₄

D₄×D₄₃

yes

characteristic

243

Q₁₆

—

244

Q₁₆

—

245

Q₁₆

—

246

Q₁₆

—

247

Q₁₆

—

248

Q₁₆

—

249

Q₁₆

—

172

—

250

Q₁₆

—

172

—

251

Q₁₆

—

172

—

252

Q₁₆

—

172

—

253

M₁₆

—

254

M₁₆

—

172

—

255

C₂×C₈

—

256

C₂×C₈

—

257

C₂×C₈

—

258

C₂×C₈

—

259

C₂×C₈

—

172

—

260

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

261

C₂×C₈

#10621898

yes

characteristic

262

C₂×C₈

D₄×D₄₃

yes

characteristic

263

C₂×C₈

D₄×D₄₃

yes

characteristic

264

C₂×C₈

#10621900

yes

characteristic

265

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

266

C₄⋊C₄

—

267

C₄⋊C₄

—

172

—

268

C₂²⋊C₄

—

269

C₄²

—

270

C₄²

—

271

C₄²

—

272

C₁₆

—

273

C₁₆

—

172

—

274

C₂³

#13063349

yes

characteristic

275

Q₈

—

276

Q₈

—

277

Q₈

—

278

Q₈

—

279

Q₈

—

344

—

280

Q₈

—

344

—

281

Q₈

—

172

—

282

Q₈

—

172

—

283

C₂×C₄

—

284

C₂×C₄

—

285

C₂×C₄

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

344

—

290

C₂×C₄

—

344

—

291

C₂×C₄

—

172

—

292

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

293

C₂×C₄

#13063297

yes

characteristic

294

C₂×C₄

#13063298

yes

characteristic

295

C₂×C₄

D₈×D₄₃

yes

characteristic

296

C₂×C₄

SD₁₆×D₄₃

yes

characteristic

297

C₂×C₄

#13063352

yes

characteristic

298

C₈

—

299

C₈

—

300

C₈

—

172

—

301

C₈

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

302

C₈

C₄×C₂²⋊D₄₃

yes

characteristic

303

C₈

#13063311

yes

characteristic

304

C₈

#13063321

yes

characteristic

305

C₂²

—

306

C₂²

#14582902

yes

characteristic

307

C₂²

#14583092

yes

characteristic

308

C₂²

#14583098

yes

characteristic

309

C₄

—

310

C₄

—

311

C₄

—

312

C₄

—

344

—

313

C₄

#14582799

yes

characteristic

314

C₄

#102×D₄₃

yes

characteristic

315

C₄

#14583093

yes

characteristic

316

C₄

#14583097

yes

characteristic

317

C₂

—

318

C₂

—

319

C₂

#19135520

yes

characteristic

320

C₂

#19136674

yes

—

	subgroup	G/H
center	C₂²	#14583092
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#2141	C₂
socle	C₂²×C₄₃	#459
prime radical	C₂³×C₄₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#2141	D₄₃
hypocenter	C₄₃	#13262
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2141

subgroup

G/H

center

C₂²

#14583092

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#2141

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 ◁ #2141

N	H ≅ G/N	type
13. #14583277	C₄	semidirect
186. C₄₃	#13262	semidirect

H ≅ G/N

type

13. #14583277

C₄

semidirect

186. C₄₃

#13262

semidirect

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

subgroup	index
C₂×#14583277	2
C₂×#14582719	2
C₂×#14582716	2
C₂×#14582715	2
#19136314	2
#19134476	2
C₄₃×#2141	2
#13262	43

subgroup

index

C₄₃×#2141

Subgroups — #25015109

Conjugacy classes of subgroups

Complements

Maximal subgroups