Group #24996055 — subgroups

Subgroups — #24996055

Order 11008.

414 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14583302	C₂	1	1	yes	maximal, characteristic
2	#19134766	C₂	1	1	yes	maximal, characteristic
3	#19133279	C₂	1	1	yes	maximal, characteristic
4	#19133277	C₂	1	1	yes	maximal, characteristic
5	#19133276	C₂	1	1	yes	maximal, characteristic
6	#19132879	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1549	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063325	C₂²	1	1	yes	characteristic
9	#14583302	—	2	1	no	—
10	#14583302	—	2	1	no	—
11	#14583302	C₄	1	4	yes	—
12	#14582952	C₂²	1	1	yes	characteristic
13	C₂×#13063260	—	2	2	no	—
14	C₂×#13063258	—	2	2	no	—
15	#14582923	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	#14582648	—	2	2	no	—
18	#14582647	—	2	2	no	—
19	#14582646	—	2	2	no	—
20	#14582621	—	2	1	no	—
21	C₈×C₄₃⋊C₈	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#431	C₂²	1	1	yes	characteristic
24	C₄₃×#423	C₂²	1	1	yes	characteristic
25	C₄₃×#332	—	2	2	no	—
26	C₂²×Dic₈₆	—	2	1	no	—
27	C₂×#10621877	—	2	1	no	—
28	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
29	#13063325	—	2	1	no	—
30	#13063325	—	2	1	no	—
31	#13063325	—	2	1	no	—
32	#13063325	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₄₃	—	2	1	no	—
34	C₂×C₄⋊Dic₄₃	—	2	1	no	—
35	#13063260	—	4	4	no	—
36	#13063258	—	2	4	no	—
37	#13063258	—	2	4	no	—
38	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
39	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
40	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
41	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
42	C₄×C₄₃⋊C₈	—	2	1	no	—
43	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
44	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
45	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₃	—	2	1	no	—
47	C₂×M₁₆×C₄₃	—	2	1	no	—
48	C₄⋊Q₈×C₄₃	—	2	1	no	—
49	C₄⋊Q₈×C₄₃	—	2	1	no	—
50	C₄⋊Q₈×C₄₃	—	2	1	no	—
51	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₄₃	—	2	1	no	—
56	C₄⋊C₈×C₄₃	—	2	1	no	—
57	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
58	C₂²⋊C₈×C₄₃	—	2	1	no	—
59	C₄×C₈×C₄₃	—	2	1	no	—
60	C₂×Q₈×C₄₃	—	2	2	no	—
61	C₂×Q₈×C₄₃	—	4	1	no	—
62	C₂×Q₈×C₄₃	—	8	2	no	—
63	C₂²×C₄×C₄₃	—	4	1	no	—
64	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
66	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
67	C₂²×Dic₄₃	—	4	1	no	—
68	C₂×Dic₈₆	—	2	2	no	—
69	C₂×Dic₈₆	—	4	1	no	—
70	C₂×Dic₈₆	—	8	2	no	—
71	M₁₆×C₄₃	—	4	2	no	—
72	C₂×C₈×C₄₃	—	2	2	no	—
73	C₂×C₈×C₄₃	—	4	1	no	—
74	C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₄⋊C₄×C₄₃	—	2	2	no	—
76	C₄⋊C₄×C₄₃	—	4	1	no	—
77	C₄⋊C₄×C₄₃	—	4	1	no	—
78	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₄⋊Dic₄₃	—	2	2	no	—
83	C₄⋊Dic₄₃	—	2	2	no	—
84	C₄⋊Dic₄₃	—	4	1	no	—
85	C₄⋊Dic₄₃	—	4	1	no	—
86	#10621877	—	4	2	no	—
87	C₂×C₄₃⋊C₈	—	2	2	no	—
88	C₂×C₄₃⋊C₈	—	4	1	no	—
89	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
90	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
91	C₂×C₄₃⋊C₈	SD₁₆	1	4	yes	—
92	C₂×C₄₃⋊C₈	Q₁₆	1	4	yes	—
93	C₂³×C₄₃	#124	1	1	yes	characteristic
94	Q₈×C₄₃	—	8	2	no	—
95	Q₈×C₄₃	—	8	2	no	—
96	C₂×C₄×C₄₃	—	2	2	no	—
97	C₂×C₄×C₄₃	—	2	2	no	—
98	C₂×C₄×C₄₃	—	4	2	no	—
99	C₂×C₄×C₄₃	—	8	2	no	—
100	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
104	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
105	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
106	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
107	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
108	C₂×Dic₄₃	—	4	2	no	—
109	C₂×Dic₄₃	—	8	2	no	—
110	Dic₈₆	—	8	2	no	—
111	Dic₈₆	—	8	2	no	—
112	C₈×C₄₃	—	4	2	no	—
113	C₈×C₄₃	—	8	1	no	—
114	C₄₃⋊C₈	—	4	2	no	—
115	C₄₃⋊C₈	—	8	1	no	—
116	C₄₃⋊C₈	#103	1	4	yes	—
117	C₄₃⋊C₈	#103	1	4	yes	—
118	#9771	—	43	1	no	maximal, Sylow
119	C₂²×C₄₃	—	2	1	no	—
120	C₂²×C₄₃	—	2	1	no	—
121	C₂²×C₄₃	#390	1	1	yes	characteristic
122	C₂²×C₄₃	#487	1	2	yes	—
123	C₄×C₄₃	—	2	1	no	—
124	C₄×C₄₃	—	2	1	no	—
125	C₄×C₄₃	—	8	2	no	—
126	C₄×C₄₃	C₂×#103	1	2	yes	—
127	C₄×C₄₃	#472	1	2	yes	—
128	C₄×C₄₃	#473	1	2	yes	—
129	C₄×C₄₃	#492	1	1	yes	characteristic
130	C₄×C₄₃	#494	1	1	yes	characteristic
131	Dic₄₃	—	8	2	no	—
132	C₂×#500	—	43	1	no	—
133	#1848	—	43	1	no	—
134	#1549	—	43	1	no	—
135	#1549	D₄₃	1	1	yes	characteristic
136	#1548	—	43	1	no	—
137	#1548	—	43	1	no	—
138	#1450	—	43	1	no	—
139	C₂×C₄₃	—	2	2	no	—
140	C₂×C₄₃	#1956	1	1	yes	characteristic
141	C₂×C₄₃	#1978	1	1	yes	characteristic
142	C₂×C₄₃	#1979	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	—	43	1	no	—
144	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
145	#500	—	43	4	no	—
146	#500	—	86	1	no	—
147	#500	—	86	1	no	—
148	#431	—	43	1	no	—
149	#431	C₂×D₄₃	1	1	yes	characteristic
150	C₂×#108	—	86	2	no	—
151	C₂×#107	—	86	2	no	—
152	#423	—	43	1	no	—
153	#423	C₂×D₄₃	1	1	yes	characteristic
154	C₂×C₄×C₈	—	43	1	no	—
155	#333	—	86	2	no	—
156	#333	—	86	2	no	—
157	#332	—	2	2	no	—
158	#332	—	86	2	no	—
159	#322	—	86	1	no	—
160	C₈²	—	86	1	no	—
161	C₄₃	#9771	1	1	yes	characteristic, complemented, Sylow
162	C₂²×Q₈	—	2	1	no	—
163	C₂²×Q₈	—	86	1	no	—
164	C₂×M₁₆	—	2	1	no	—
165	C₂×M₁₆	—	86	1	no	—
166	C₂²×C₈	—	43	2	no	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	—	43	2	no	—
171	C₄⋊Q₈	—	86	1	no	—
172	C₄⋊Q₈	—	86	1	no	—
173	C₄⋊Q₈	—	86	1	no	—
174	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	2	1	no	—
177	C₂×C₄⋊C₄	—	86	1	no	—
178	C₂×C₄⋊C₄	—	86	1	no	—
179	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
180	#108	—	172	4	no	—
181	#107	—	86	4	no	—
182	#107	—	86	4	no	—
183	C₄⋊C₈	—	2	1	no	—
184	C₄⋊C₈	—	2	1	no	—
185	C₄⋊C₈	—	43	2	no	—
186	C₄⋊C₈	—	86	1	no	—
187	C₄⋊C₈	—	86	1	no	—
188	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
189	C₂²⋊C₈	—	2	1	no	—
190	C₂²⋊C₈	—	86	1	no	—
191	C₄×C₈	—	2	1	no	—
192	C₄×C₈	—	43	2	no	—
193	C₄×C₈	—	43	1	no	—
194	C₄×C₈	—	43	1	no	—
195	C₄×C₈	—	86	1	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂×Q₈	—	8	2	no	—
199	C₂×Q₈	—	86	2	no	—
200	C₂×Q₈	—	344	2	no	—
201	C₂×Q₈	—	172	1	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	—	172	1	no	—
204	C₂²×C₄	#10621898	1	1	yes	characteristic
205	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
206	C₂²×C₄	#10621900	1	1	yes	characteristic
207	M₁₆	—	4	2	no	—
208	M₁₆	—	172	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	4	1	no	—
211	C₂×C₈	—	43	2	no	—
212	C₂×C₈	—	43	2	no	—
213	C₂×C₈	—	43	4	no	—
214	C₂×C₈	—	43	4	no	—
215	C₂×C₈	—	86	2	no	—
216	C₂×C₈	—	172	1	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	2	no	—
219	C₄⋊C₄	—	4	1	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	86	2	no	—
222	C₄⋊C₄	—	86	2	no	—
223	C₄⋊C₄	—	172	1	no	—
224	C₄⋊C₄	—	172	1	no	—
225	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
226	C₄²	D₄×D₄₃	1	1	yes	characteristic
227	C₄²	D₄×D₄₃	1	1	yes	characteristic
228	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
229	C₂³	#13063311	1	1	yes	characteristic
230	Q₈	—	8	2	no	—
231	Q₈	—	8	2	no	—
232	Q₈	—	344	2	no	—
233	Q₈	—	344	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	8	2	no	—
238	C₂×C₄	—	344	2	no	—
239	C₂×C₄	—	172	2	no	—
240	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
241	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
243	C₂×C₄	#13063297	1	1	yes	characteristic
244	C₂×C₄	#13063298	1	1	yes	characteristic
245	C₂×C₄	#13063321	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
247	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
248	C₈	—	4	2	no	—
249	C₈	—	8	1	no	—
250	C₈	—	43	4	no	—
251	C₈	—	43	4	no	—
252	C₈	—	344	1	no	—
253	C₈	—	172	2	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	#14582799	1	1	yes	characteristic
257	C₂²	#14583248	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	8	2	no	—
261	C₄	—	344	2	no	—
262	C₄	#103×D₄₃	1	2	yes	—
263	C₄	#14583167	1	2	yes	—
264	C₄	#14583173	1	2	yes	—
265	C₄	#14583270	1	1	yes	characteristic
266	C₄	#14583277	1	1	yes	characteristic
267	C₂	—	2	2	no	—
268	C₂	#19135395	1	1	yes	characteristic
269	C₂	#19135504	1	1	yes	characteristic
270	C₂	#19135507	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583302

C₂

yes

maximal, characteristic

#19134766

C₂

yes

maximal, characteristic

#19133279

C₂

yes

maximal, characteristic

#19133277

C₂

yes

maximal, characteristic

#19133276

C₂

yes

maximal, characteristic

#19132879

C₂

yes

maximal, characteristic

C₄₃×#1549

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

—

—

C₄

yes

—

#14582952

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

—

—

C₈×C₄₃⋊C₈

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄₃×#431

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

characteristic

C₄₃×#332

—

C₂²×Dic₈₆

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063260

—

#13063258

—

#13063258

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

characteristic

C₄×C₄₃⋊C₈

D₄

yes

characteristic

C₂²×Q₈×C₄₃

—

C₂×M₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

D₄

yes

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

C₂²×C₄×C₄₃

yes

C₂²×C₄×C₄₃

yes

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

SD₁₆

yes

—

C₂×C₄₃⋊C₈

Q₁₆

yes

—

C₂³×C₄₃

#124

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

100

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

101

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

102

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

103

C₂×C₄×C₄₃

#121

yes

characteristic

104

C₂×C₄×C₄₃

#121

yes

characteristic

105

C₂×C₄×C₄₃

#127

yes

characteristic

106

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

107

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

108

C₂×Dic₄₃

—

109

C₂×Dic₄₃

—

110

Dic₈₆

—

111

Dic₈₆

—

112

C₈×C₄₃

—

113

C₈×C₄₃

—

114

C₄₃⋊C₈

—

115

C₄₃⋊C₈

—

116

C₄₃⋊C₈

#103

yes

—

117

C₄₃⋊C₈

#103

yes

—

118

#9771

—

maximal, Sylow

119

C₂²×C₄₃

—

120

C₂²×C₄₃

—

121

C₂²×C₄₃

#390

yes

characteristic

122

C₂²×C₄₃

#487

yes

—

123

C₄×C₄₃

—

124

C₄×C₄₃

—

125

C₄×C₄₃

—

126

C₄×C₄₃

C₂×#103

yes

—

127

C₄×C₄₃

#472

yes

—

128

C₄×C₄₃

#473

yes

—

129

C₄×C₄₃

#492

yes

characteristic

130

C₄×C₄₃

#494

yes

characteristic

131

Dic₄₃

—

132

C₂×#500

—

133

#1848

—

134

#1549

—

135

#1549

D₄₃

yes

characteristic

136

#1548

—

137

#1548

—

138

#1450

—

139

C₂×C₄₃

—

140

C₂×C₄₃

#1956

yes

characteristic

141

C₂×C₄₃

#1978

yes

characteristic

142

C₂×C₄₃

#1979

yes

characteristic

143

C₂×C₄⋊Q₈

—

144

C₂×C₄⋊Q₈

C₂×D₄₃

yes

characteristic

145

#500

—

146

#500

—

147

#500

—

148

#431

—

149

#431

C₂×D₄₃

yes

characteristic

150

C₂×#108

—

151

C₂×#107

—

152

#423

—

153

#423

C₂×D₄₃

yes

characteristic

154

C₂×C₄×C₈

—

155

#333

—

156

#333

—

157

#332

—

158

#332

—

159

#322

—

160

C₈²

—

161

C₄₃

#9771

yes

characteristic, complemented, Sylow

162

C₂²×Q₈

—

163

C₂²×Q₈

—

164

C₂×M₁₆

—

165

C₂×M₁₆

—

166

C₂²×C₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

C₄×D₄₃

yes

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄²

C₂²×D₄₃

yes

characteristic

180

#108

—

172

—

181

#107

—

182

#107

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

C₂²⋊D₄₃

yes

—

189

C₂²⋊C₈

—

190

C₂²⋊C₈

—

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

344

—

201

C₂×Q₈

—

172

—

202

C₂²×C₄

—

203

C₂²×C₄

—

172

—

204

C₂²×C₄

#10621898

yes

characteristic

205

C₂²×C₄

D₄×D₄₃

yes

characteristic

206

C₂²×C₄

#10621900

yes

characteristic

207

M₁₆

—

208

M₁₆

—

172

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

172

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

172

—

224

C₄⋊C₄

—

172

—

225

C₄²

C₂×C₄×D₄₃

yes

characteristic

226

C₄²

D₄×D₄₃

yes

characteristic

227

C₄²

D₄×D₄₃

yes

characteristic

228

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

229

C₂³

#13063311

yes

characteristic

230

Q₈

—

231

Q₈

—

232

Q₈

—

344

—

233

Q₈

—

344

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

344

—

239

C₂×C₄

—

172

—

240

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

241

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

242

C₂×C₄

C₄×C₂²⋊D₄₃

yes

characteristic

243

C₂×C₄

#13063297

yes

characteristic

244

C₂×C₄

#13063298

yes

characteristic

245

C₂×C₄

#13063321

yes

characteristic

246

C₂×C₄

SD₁₆×D₄₃

yes

—

247

C₂×C₄

Q₁₆×D₄₃

yes

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

344

—

253

C₈

—

172

—

254

C₂²

—

255

C₂²

—

256

C₂²

#14582799

yes

characteristic

257

C₂²

#14583248

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

344

—

262

C₄

#103×D₄₃

yes

—

263

C₄

#14583167

yes

—

264

C₄

#14583173

yes

—

265

C₄

#14583270

yes

characteristic

266

C₄

#14583277

yes

characteristic

267

C₂

—

268

C₂

#19135395

yes

characteristic

269

C₂

#19135504

yes

characteristic

270

C₂

#19135507

yes

characteristic

	subgroup	G/H
center	C₂²	#14582799
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1549	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	#124
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1549	D₄₃
hypocenter	C₄₃	#9771
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1549

subgroup

G/H

center

C₂²

#14582799

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1549

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1549

N	H ≅ G/N	type
161. C₄₃	#9771	semidirect

H ≅ G/N

type

161. C₄₃

#9771

semidirect

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

subgroup	index
C₂×#14583302	2
#19134766	2
#19133279	2
#19133277	2
#19133276	2
#19132879	2
C₄₃×#1549	2
#9771	43

subgroup

index

C₄₃×#1549

Subgroups — #24996055

Conjugacy classes of subgroups

Complements

Maximal subgroups