Group #25013643 — subgroups

Subgroups — #25013643

Order 11008.

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

normal subgroups only

This group has 548 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	C₂×#14582948	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582712	C₂	1	2	yes	maximal, complemented
3	C₂×#14582681	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132693	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#469	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10621877	—	2	1	no	—
7	C₂×#13063265	C₂²	1	2	yes	—
8	#14582948	—	2	4	no	—
9	C₂×#13063261	—	2	1	no	—
10	C₂×#13063261	C₂²	1	2	yes	—
11	#14582712	—	2	4	no	—
12	#14582681	—	2	2	no	—
13	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₃	—	2	1	no	—
16	C₄₃×#469	—	2	2	no	—
17	C₄₃×#469	C₄	1	4	yes	—
18	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#102×C₄₃	—	2	1	no	—
20	C₂×#10621877	—	2	4	no	—
21	C₂×#10621877	—	2	2	no	—
22	C₂×#10621877	—	4	1	no	—
23	C₂×#10621877	—	4	2	no	—
24	C₂²×C₄₃⋊C₈	—	4	1	no	—
25	#13063265	—	2	2	no	—
26	#13063265	—	2	2	no	—
27	C₂×C₄₃⋊C₁₆	—	2	2	no	—
28	#13063261	—	2	4	no	—
29	#13063261	—	2	2	no	—
30	#13063261	D₄	1	4	yes	complemented
31	C₂²×D₄×C₄₃	—	2	1	no	—
32	C₂²×D₄×C₄₃	—	4	1	no	—
33	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
34	C₂×D₈×C₄₃	—	2	2	no	—
35	C₂×D₈×C₄₃	—	2	1	no	—
36	C₂×D₈×C₄₃	—	2	2	no	—
37	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₄₃	—	2	2	no	—
39	C₂×M₁₆×C₄₃	—	2	2	no	—
40	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
42	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
44	#121×C₄₃	—	2	4	no	—
45	#121×C₄₃	—	4	2	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₄₃	—	4	1	no	—
48	#106×C₄₃	—	2	1	no	—
49	#106×C₄₃	C₂×C₄	1	2	yes	—
50	#102×C₄₃	—	2	4	no	—
51	C₂⁴×C₄₃	—	4	1	no	—
52	C₂⁴×C₄₃	SD₁₆	1	1	yes	characteristic
53	C₂×D₄×C₄₃	—	2	2	no	—
54	C₂×D₄×C₄₃	—	4	1	no	—
55	C₂×D₄×C₄₃	—	4	4	no	—
56	C₂×D₄×C₄₃	—	4	1	no	—
57	C₂×D₄×C₄₃	—	4	1	no	—
58	C₂×D₄×C₄₃	—	4	1	no	—
59	C₂×D₄×C₄₃	—	4	1	no	—
60	C₂×D₄×C₄₃	—	8	4	no	—
61	C₂²×C₄×C₄₃	—	2	1	no	—
62	C₂²×C₄×C₄₃	—	2	1	no	—
63	C₂²×C₄×C₄₃	—	2	1	no	—
64	C₂²×C₄×C₄₃	—	2	1	no	—
65	C₂²×C₄×C₄₃	—	4	1	no	—
66	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₄₃	D₈	1	2	yes	—
68	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	D₈×C₄₃	—	2	4	no	—
71	D₈×C₄₃	—	4	2	no	—
72	M₁₆×C₄₃	—	2	4	no	—
73	M₁₆×C₄₃	—	2	4	no	—
74	C₂×C₈×C₄₃	—	2	1	no	—
75	C₂×C₈×C₄₃	—	2	1	no	—
76	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
77	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₄₃	#41	1	2	yes	—
81	C₄⋊C₄×C₄₃	—	2	2	no	—
82	C₄⋊C₄×C₄₃	—	4	1	no	—
83	C₂²⋊C₄×C₄₃	—	4	4	no	—
84	#10621877	—	2	4	no	—
85	#10621877	—	4	4	no	—
86	#10621877	—	4	2	no	—
87	C₂×C₄₃⋊C₈	—	4	4	no	—
88	C₂×C₄₃⋊C₈	—	4	2	no	—
89	C₄₃⋊C₁₆	—	4	2	no	—
90	C₂³×C₄₃	—	2	1	no	—
91	C₂³×C₄₃	—	2	1	no	—
92	C₂³×C₄₃	—	4	2	no	—
93	C₂³×C₄₃	—	4	2	no	—
94	C₂³×C₄₃	—	8	2	no	—
95	C₂³×C₄₃	—	8	2	no	—
96	C₂³×C₄₃	—	8	1	no	—
97	C₂³×C₄₃	—	8	1	no	—
98	C₂³×C₄₃	#102	1	2	yes	—
99	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
100	D₄×C₄₃	—	4	2	no	—
101	D₄×C₄₃	—	4	2	no	—
102	D₄×C₄₃	—	8	8	no	—
103	D₄×C₄₃	—	8	1	no	—
104	D₄×C₄₃	—	8	1	no	—
105	C₂×C₄×C₄₃	—	2	1	no	—
106	C₂×C₄×C₄₃	—	2	1	no	—
107	C₂×C₄×C₄₃	—	2	2	no	—
108	C₂×C₄×C₄₃	—	2	2	no	—
109	C₂×C₄×C₄₃	—	2	2	no	—
110	C₂×C₄×C₄₃	—	2	2	no	—
111	C₂×C₄×C₄₃	—	4	2	no	—
112	C₂×C₄×C₄₃	—	8	2	no	—
113	C₂×C₄×C₄₃	#102	1	2	yes	—
114	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
116	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
117	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
118	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
119	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
120	C₈×C₄₃	—	2	2	no	—
121	C₈×C₄₃	C₄×D₄	1	2	yes	—
122	C₈×C₄₃	#121	1	2	yes	—
123	C₄₃⋊C₈	—	4	4	no	—
124	#13010	—	43	1	no	maximal, Sylow
125	C₂²×C₄₃	—	2	2	no	—
126	C₂²×C₄₃	—	2	2	no	—
127	C₂²×C₄₃	—	4	2	no	—
128	C₂²×C₄₃	—	4	2	no	—
129	C₂²×C₄₃	—	8	1	no	—
130	C₂²×C₄₃	—	8	2	no	—
131	C₂²×C₄₃	—	8	2	no	—
132	C₂²×C₄₃	—	8	2	no	—
133	C₂²×C₄₃	—	16	2	no	—
134	C₂²×C₄₃	—	16	2	no	—
135	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
136	C₂²×C₄₃	#448	1	1	yes	characteristic
137	C₂²×C₄₃	#481	1	1	yes	characteristic
138	C₄×C₄₃	—	2	2	no	—
139	C₄×C₄₃	—	8	2	no	—
140	C₄×C₄₃	#386	1	1	yes	characteristic
141	C₄×C₄₃	#417	1	1	yes	characteristic
142	C₄×C₄₃	#447	1	1	yes	characteristic
143	C₄×C₄₃	#480	1	1	yes	characteristic
144	C₂×#469	D₄₃	1	1	yes	characteristic
145	C₂×#430	—	43	1	no	—
146	C₂×#361	—	43	2	no	—
147	C₂×#349	—	43	1	no	—
148	#1383	—	43	2	no	—
149	C₂×C₄₃	—	2	1	no	—
150	C₂×C₄₃	—	2	1	no	—
151	C₂×C₄₃	—	4	2	no	—
152	C₂×C₄₃	—	16	2	no	—
153	C₂×C₄₃	#1874	1	1	yes	characteristic
154	C₂×C₄₃	#2238	1	2	yes	—
155	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
156	C₂²×M₁₆	—	86	1	no	—
157	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
158	C₂×#121	—	2	1	no	—
159	C₂×M₃₂	—	43	2	no	—
160	#469	—	2	2	no	—
161	#469	Dic₄₃	1	4	yes	—
162	#430	—	86	4	no	—
163	C₂×#108	—	43	2	no	—
164	C₂×#108	—	86	1	no	—
165	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
166	C₂×#102	—	2	1	no	—
167	#361	—	86	4	no	—
168	#349	—	86	2	no	—
169	C₄₃	#13010	1	1	yes	characteristic, complemented, Sylow
170	C₂²×D₄	—	2	1	no	—
171	C₂²×D₄	—	4	1	no	—
172	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
173	C₂×D₈	—	2	2	no	—
174	C₂×D₈	—	2	2	no	—
175	C₂×D₈	—	2	1	no	—
176	C₂×D₈	C₂×Dic₄₃	1	2	yes	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂×M₁₆	—	2	2	no	—
179	C₂×M₁₆	—	86	4	no	—
180	C₂×M₁₆	—	86	2	no	—
181	C₂×M₁₆	—	172	1	no	—
182	C₂×M₁₆	—	172	2	no	—
183	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
184	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
185	C₂²×C₈	—	172	1	no	—
186	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
187	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
188	#121	—	2	4	no	—
189	#121	—	4	2	no	—
190	C₂×C₄⋊C₄	—	2	1	no	—
191	C₂×C₂²⋊C₄	—	4	1	no	—
192	M₃₂	—	86	2	no	—
193	M₃₂	—	86	2	no	—
194	C₂×C₁₆	—	86	2	no	—
195	#108	—	43	4	no	—
196	#108	—	86	4	no	—
197	#108	—	86	2	no	—
198	#106	—	2	1	no	—
199	#106	C₂×Dic₄₃	1	2	yes	—
200	#102	—	2	4	no	—
201	C₂⁴	—	4	1	no	—
202	C₂⁴	#10621883	1	1	yes	characteristic
203	C₂×D₄	—	2	2	no	—
204	C₂×D₄	—	4	4	no	—
205	C₂×D₄	—	4	1	no	—
206	C₂×D₄	—	4	1	no	—
207	C₂×D₄	—	4	1	no	—
208	C₂×D₄	—	4	1	no	—
209	C₂×D₄	—	4	1	no	—
210	C₂×D₄	—	8	4	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	2	1	no	—
214	C₂²×C₄	—	2	1	no	—
215	C₂²×C₄	—	4	1	no	—
216	C₂²×C₄	#10621882	1	2	yes	—
217	C₂²×C₄	#10621883	1	1	yes	characteristic
218	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
219	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
220	D₈	—	2	4	no	—
221	D₈	—	4	2	no	—
222	M₁₆	—	2	4	no	—
223	M₁₆	—	2	4	no	—
224	M₁₆	—	86	4	no	—
225	M₁₆	—	172	4	no	—
226	M₁₆	—	172	2	no	—
227	C₂×C₈	—	2	1	no	—
228	C₂×C₈	—	2	1	no	—
229	C₂×C₈	—	172	4	no	—
230	C₂×C₈	—	172	2	no	—
231	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
232	C₂×C₈	D₄×D₄₃	1	2	yes	—
233	C₂×C₈	#10621900	1	2	yes	—
234	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
235	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	4	1	no	—
238	C₂²⋊C₄	—	4	4	no	—
239	C₁₆	—	172	2	no	—
240	C₂³	—	2	1	no	—
241	C₂³	—	2	1	no	—
242	C₂³	—	4	2	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	8	2	no	—
245	C₂³	—	8	2	no	—
246	C₂³	—	8	1	no	—
247	C₂³	—	8	1	no	—
248	C₂³	#13063246	1	2	yes	—
249	C₂³	C₂×#10621883	1	1	yes	characteristic
250	D₄	—	4	2	no	—
251	D₄	—	4	2	no	—
252	D₄	—	8	8	no	—
253	D₄	—	8	1	no	—
254	D₄	—	8	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	8	2	no	—
263	C₂×C₄	#13063246	1	2	yes	—
264	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
265	C₂×C₄	#13063293	1	1	yes	characteristic
266	C₂×C₄	#13063306	1	1	yes	characteristic
267	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
268	C₂×C₄	#13063350	1	1	yes	characteristic
269	C₂×C₄	#13063355	1	1	yes	characteristic
270	C₈	—	2	2	no	—
271	C₈	—	172	4	no	—
272	C₈	D₄×Dic₄₃	1	2	yes	—
273	C₈	#13063297	1	2	yes	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	4	2	no	—
277	C₂²	—	4	2	no	—
278	C₂²	—	8	1	no	—
279	C₂²	—	8	2	no	—
280	C₂²	—	8	2	no	—
281	C₂²	—	8	2	no	—
282	C₂²	—	16	2	no	—
283	C₂²	—	16	2	no	—
284	C₂²	C₂×#13063246	1	1	yes	characteristic
285	C₂²	#14583037	1	1	yes	characteristic
286	C₂²	#14583215	1	1	yes	characteristic
287	C₄	—	2	2	no	—
288	C₄	—	8	2	no	—
289	C₄	#14582779	1	1	yes	characteristic
290	C₄	#14582900	1	1	yes	characteristic
291	C₄	#14583032	1	1	yes	characteristic
292	C₄	#14583210	1	1	yes	characteristic
293	C₂	—	2	1	no	—
294	C₂	—	2	1	no	—
295	C₂	—	4	2	no	—
296	C₂	—	16	2	no	—
297	C₂	#19134913	1	1	yes	characteristic
298	C₂	#19136807	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582948

C₂

yes

maximal, characteristic, complemented

C₂×#14582712

C₂

yes

maximal, complemented

C₂×#14582681

C₂

yes

maximal, characteristic, complemented

#19132693

C₂

yes

maximal, complemented

C₂×C₄₃×#469

C₂

yes

maximal, characteristic

C₂²×#10621877

—

C₂×#13063265

C₂²

yes

—

#14582948

—

C₂×#13063261

—

C₂×#13063261

C₂²

yes

—

#14582712

—

#14582681

—

C₂²×D₈×C₄₃

C₂²

yes

characteristic

C₂²×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×#121×C₄₃

—

C₄₃×#469

—

C₄₃×#469

C₄

yes

—

C₂×#106×C₄₃

C₂²

yes

characteristic

C₂×#102×C₄₃

—

—

—

—

—

C₂²×C₄₃⋊C₈

—

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

#13063261

—

#13063261

—

#13063261

D₄

yes

complemented

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂³×C₄×C₄₃

D₄

yes

characteristic

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

C₂×C₄

yes

—

C₂×M₁₆×C₄₃

—

C₂×M₁₆×C₄₃

—

C₂×M₁₆×C₄₃

C₂×C₄

yes

—

C₂×M₁₆×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

#121×C₄₃

—

#121×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

#106×C₄₃

—

#106×C₄₃

C₂×C₄

yes

—

#102×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

SD₁₆

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

D₈

yes

—

C₂²×C₄×C₄₃

SD₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

D₈×C₄₃

—

D₈×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

#10621877

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#102

yes

—

C₂³×C₄₃

C₂×SD₁₆

yes

characteristic

100

D₄×C₄₃

—

101

D₄×C₄₃

—

102

D₄×C₄₃

—

103

D₄×C₄₃

—

104

D₄×C₄₃

—

105

C₂×C₄×C₄₃

—

106

C₂×C₄×C₄₃

—

107

C₂×C₄×C₄₃

—

108

C₂×C₄×C₄₃

—

109

C₂×C₄×C₄₃

—

110

C₂×C₄×C₄₃

—

111

C₂×C₄×C₄₃

—

112

C₂×C₄×C₄₃

—

113

C₂×C₄×C₄₃

#102

yes

—

114

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

115

C₂×C₄×C₄₃

#120

yes

characteristic

116

C₂×C₄×C₄₃

#123

yes

characteristic

117

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

118

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

119

C₂×C₄×C₄₃

#137

yes

characteristic

120

C₈×C₄₃

—

121

C₈×C₄₃

C₄×D₄

yes

—

122

C₈×C₄₃

#121

yes

—

123

C₄₃⋊C₈

—

124

#13010

—

maximal, Sylow

125

C₂²×C₄₃

—

126

C₂²×C₄₃

—

127

C₂²×C₄₃

—

128

C₂²×C₄₃

—

129

C₂²×C₄₃

—

130

C₂²×C₄₃

—

131

C₂²×C₄₃

—

132

C₂²×C₄₃

—

133

C₂²×C₄₃

—

134

C₂²×C₄₃

—

135

C₂²×C₄₃

C₂×#102

yes

characteristic

136

C₂²×C₄₃

#448

yes

characteristic

137

C₂²×C₄₃

#481

yes

characteristic

138

C₄×C₄₃

—

139

C₄×C₄₃

—

140

C₄×C₄₃

#386

yes

characteristic

141

C₄×C₄₃

#417

yes

characteristic

142

C₄×C₄₃

#447

yes

characteristic

143

C₄×C₄₃

#480

yes

characteristic

144

C₂×#469

D₄₃

yes

characteristic

145

C₂×#430

—

146

C₂×#361

—

147

C₂×#349

—

148

#1383

—

149

C₂×C₄₃

—

150

C₂×C₄₃

—

151

C₂×C₄₃

—

152

C₂×C₄₃

—

153

C₂×C₄₃

#1874

yes

characteristic

154

C₂×C₄₃

#2238

yes

—

155

C₂²×D₈

C₂×D₄₃

yes

characteristic

156

C₂²×M₁₆

—

157

C₂²×M₁₆

C₂×D₄₃

yes

characteristic

158

C₂×#121

—

159

C₂×M₃₂

—

160

#469

—

161

#469

Dic₄₃

yes

—

162

#430

—

163

C₂×#108

—

164

C₂×#108

—

165

C₂×#106

C₂×D₄₃

yes

characteristic

166

C₂×#102

—

167

#361

—

168

#349

—

169

C₄₃

#13010

yes

characteristic, complemented, Sylow

170

C₂²×D₄

—

171

C₂²×D₄

—

172

C₂³×C₄

C₂²⋊D₄₃

yes

characteristic

173

C₂×D₈

—

174

C₂×D₈

—

175

C₂×D₈

—

176

C₂×D₈

C₂×Dic₄₃

yes

—

177

C₂×M₁₆

—

178

C₂×M₁₆

—

179

C₂×M₁₆

—

180

C₂×M₁₆

—

181

C₂×M₁₆

—

172

—

182

C₂×M₁₆

—

172

—

183

C₂×M₁₆

C₂×Dic₄₃

yes

—

184

C₂×M₁₆

C₂²⋊D₄₃

yes

—

185

C₂²×C₈

—

172

—

186

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

187

C₂²×C₈

C₂²×D₄₃

yes

characteristic

188

#121

—

189

#121

—

190

C₂×C₄⋊C₄

—

191

C₂×C₂²⋊C₄

—

192

M₃₂

—

193

M₃₂

—

194

C₂×C₁₆

—

195

#108

—

196

#108

—

197

#108

—

198

#106

—

199

#106

C₂×Dic₄₃

yes

—

200

#102

—

201

C₂⁴

—

202

C₂⁴

#10621883

yes

characteristic

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

#10621882

yes

—

217

C₂²×C₄

#10621883

yes

characteristic

218

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

219

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

220

D₈

—

221

D₈

—

222

M₁₆

—

223

M₁₆

—

224

M₁₆

—

225

M₁₆

—

172

—

226

M₁₆

—

172

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

172

—

230

C₂×C₈

—

172

—

231

C₂×C₈

C₂²⋊Dic₄₃

yes

—

232

C₂×C₈

D₄×D₄₃

yes

—

233

C₂×C₈

#10621900

yes

—

234

C₂×C₈

C₂²×Dic₄₃

yes

characteristic

235

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₂²⋊C₄

—

239

C₁₆

—

172

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

#13063246

yes

—

249

C₂³

C₂×#10621883

yes

characteristic

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

254

D₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

#13063246

yes

—

264

C₂×C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

265

C₂×C₄

#13063293

yes

characteristic

266

C₂×C₄

#13063306

yes

characteristic

267

C₂×C₄

C₂×#10621882

yes

characteristic

268

C₂×C₄

#13063350

yes

characteristic

269

C₂×C₄

#13063355

yes

characteristic

270

C₈

—

271

C₈

—

172

—

272

C₈

D₄×Dic₄₃

yes

—

273

C₈

#13063297

yes

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

C₂×#13063246

yes

characteristic

285

C₂²

#14583037

yes

characteristic

286

C₂²

#14583215

yes

characteristic

287

C₄

—

288

C₄

—

289

C₄

#14582779

yes

characteristic

290

C₄

#14582900

yes

characteristic

291

C₄

#14583032

yes

characteristic

292

C₄

#14583210

yes

characteristic

293

C₂

—

294

C₂

—

295

C₂

—

296

C₂

—

297

C₂

#19134913

yes

characteristic

298

C₂

#19136807

yes

—

	subgroup	G/H
center	C₂²	#14583215
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting, prime radical	C₂×C₄₃×#469	C₂
socle	C₂²×C₄₃	#481
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#469	D₄₃
hypocenter	C₄₃	#13010
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#469

subgroup

G/H

center

C₂²

#14583215

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting, prime radical

C₂×C₄₃×#469

C₂

socle

C₂²×C₄₃

#481

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#469

N	H ≅ G/N	type
1. C₂×#14582948	C₂	semidirect
2. C₂×#14582712	C₂	semidirect
3. C₂×#14582681	C₂	semidirect
4. #19132693	C₂	semidirect
30. #13063261	D₄	semidirect
169. C₄₃	#13010	semidirect

H ≅ G/N

type

1. C₂×#14582948

C₂

semidirect

2. C₂×#14582712

C₂

semidirect

3. C₂×#14582681

C₂

semidirect

4. #19132693

C₂

semidirect

30. #13063261

D₄

semidirect

169. C₄₃

#13010

semidirect

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

subgroup	index
C₂×#14582948	2
C₂×#14582712	2
C₂×#14582681	2
#19132693	2
C₂×C₄₃×#469	2
#13010	43

subgroup

index

C₂×C₄₃×#469

Subgroups — #25013643

Conjugacy classes of subgroups

Complements

Maximal subgroups