Group #24995034 — subgroups

Subgroups — #24995034

Order 11008.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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	#19135571	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#19133367	C₂	1	1	yes	maximal, characteristic
4	#19133253	C₂	1	1	yes	maximal, characteristic
5	#19132999	C₂	1	1	yes	maximal, characteristic
6	#19132427	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1301	C₂	1	1	yes	maximal, characteristic
8	#14583456	C₂²	1	1	yes	characteristic
9	#14582952	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₄₃	—	2	1	no	—
12	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
13	#14582660	—	2	1	no	—
14	#14582660	—	2	1	no	—
15	#14582653	—	2	1	no	—
16	#14582649	—	2	2	no	—
17	#14582647	C₄	1	2	yes	complemented
18	#14582644	C₄	1	2	yes	complemented
19	#14582631	—	2	2	no	—
20	C₄₃×#431	C₂²	1	1	yes	characteristic
21	C₄₃×#423	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄₃⋊C₈	—	2	1	no	—
24	#13063325	C₂×C₄	1	1	yes	characteristic
25	#13063325	C₂×C₄	1	1	yes	characteristic
26	#13063317	—	2	1	no	—
27	#13063304	—	2	1	no	—
28	#13063304	—	2	1	no	—
29	C₄×Dic₈₆	—	2	1	no	—
30	C₄×Dic₈₆	—	2	1	no	—
31	#13063284	—	2	1	no	—
32	C₂×C₄×Dic₄₃	—	2	1	no	—
33	C₂×C₄×Dic₄₃	—	2	1	no	—
34	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
35	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
36	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
37	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
38	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
39	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
40	C₄×C₄₃⋊C₈	—	2	1	no	—
41	C₈×Dic₄₃	—	4	2	no	—
42	C₂×M₁₆×C₄₃	—	2	1	no	—
43	C₂²×C₈×C₄₃	—	2	1	no	—
44	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₄₃	—	2	1	no	—
46	C₄⋊C₈×C₄₃	—	2	1	no	—
47	C₄⋊C₈×C₄₃	—	2	1	no	—
48	C₄⋊C₈×C₄₃	—	2	1	no	—
49	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
50	C₂²⋊C₈×C₄₃	—	2	1	no	—
51	C₄×C₈×C₄₃	—	2	1	no	—
52	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
54	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
55	C₂²×Dic₄₃	—	2	1	no	—
56	C₂²×Dic₄₃	—	2	1	no	—
57	C₂×Dic₈₆	—	2	1	no	—
58	C₂×Dic₈₆	—	2	1	no	—
59	M₁₆×C₄₃	—	4	1	no	—
60	M₁₆×C₄₃	—	4	1	no	—
61	C₂×C₈×C₄₃	—	2	2	no	—
62	C₂×C₈×C₄₃	—	4	1	no	—
63	C₂×C₈×C₄₃	—	4	1	no	—
64	C₂×C₈×C₄₃	—	4	1	no	—
65	C₂×C₈×C₄₃	—	4	1	no	—
66	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₄₃	#41	1	1	yes	characteristic
69	C₄²×C₄₃	#41	1	1	yes	characteristic
70	C₂²⋊Dic₄₃	—	4	1	no	—
71	C₄⋊Dic₄₃	—	2	1	no	—
72	C₄⋊Dic₄₃	—	2	1	no	—
73	C₄⋊Dic₄₃	—	2	1	no	—
74	C₄⋊Dic₄₃	—	2	1	no	—
75	Dic₄₃⋊C₄	—	4	1	no	—
76	Dic₄₃⋊C₄	—	4	1	no	—
77	C₄×Dic₄₃	—	2	4	no	—
78	C₄×Dic₄₃	—	2	1	no	—
79	C₄×Dic₄₃	—	2	1	no	—
80	C₄×Dic₄₃	—	2	1	no	—
81	C₄×Dic₄₃	—	4	2	no	—
82	C₄×Dic₄₃	—	4	1	no	—
83	C₄×Dic₄₃	SD₁₆	1	2	yes	—
84	C₂×C₄₃⋊C₈	—	2	2	no	—
85	C₂×C₄₃⋊C₈	—	2	2	no	—
86	C₂×C₄₃⋊C₈	—	4	1	no	—
87	C₂×C₄₃⋊C₈	—	4	1	no	—
88	C₂³×C₄₃	#123	1	1	yes	characteristic
89	C₂×C₄×C₄₃	—	2	2	no	—
90	C₂×C₄×C₄₃	—	4	1	no	—
91	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
92	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
96	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
100	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
101	C₂×Dic₄₃	—	2	2	no	—
102	C₂×Dic₄₃	—	2	2	no	—
103	C₂×Dic₄₃	—	2	2	no	—
104	C₂×Dic₄₃	—	2	2	no	—
105	C₂×Dic₄₃	—	4	1	no	—
106	C₂×Dic₄₃	—	4	1	no	—
107	C₂×Dic₄₃	—	4	1	no	—
108	C₂×Dic₄₃	—	4	1	no	—
109	Dic₈₆	—	4	2	no	—
110	Dic₈₆	—	8	1	no	—
111	C₈×C₄₃	—	4	2	no	—
112	C₈×C₄₃	—	8	1	no	—
113	C₈×C₄₃	—	8	1	no	—
114	C₄₃⋊C₈	—	4	2	no	—
115	C₄₃⋊C₈	—	4	2	no	—
116	#9579	—	43	1	no	maximal, Sylow
117	C₂²×C₄₃	—	2	1	no	—
118	C₂²×C₄₃	—	2	1	no	—
119	C₂²×C₄₃	#388	1	1	yes	characteristic
120	C₂²×C₄₃	#483	1	1	yes	characteristic
121	C₂²×C₄₃	#485	1	1	yes	characteristic
122	C₄×C₄₃	—	2	1	no	—
123	C₄×C₄₃	—	2	1	no	—
124	C₄×C₄₃	—	2	1	no	—
125	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
126	C₄×C₄₃	#441	1	1	yes	characteristic
127	C₄×C₄₃	#443	1	2	yes	—
128	C₄×C₄₃	#461	1	1	yes	characteristic
129	C₄×C₄₃	#464	1	1	yes	characteristic
130	Dic₄₃	—	2	4	no	—
131	Dic₄₃	—	4	2	no	—
132	Dic₄₃	—	8	1	no	—
133	Dic₄₃	—	8	1	no	—
134	#1994	—	43	1	no	—
135	C₄×C₄⋊C₈	—	43	1	no	—
136	#1570	—	43	1	no	—
137	#1542	—	43	1	no	—
138	#1481	—	43	1	no	—
139	#1301	D₄₃	1	1	yes	characteristic
140	#1276	—	43	1	no	—
141	C₂×C₄₃	—	2	1	no	—
142	C₂×C₄₃	—	2	1	no	—
143	C₂×C₄₃	#1927	1	1	yes	characteristic
144	C₂×C₄₃	#1932	1	1	yes	characteristic
145	C₂×C₄₃	#1937	1	1	yes	characteristic
146	#533	—	43	1	no	—
147	#431	—	43	1	no	—
148	#431	C₂×D₄₃	1	1	yes	characteristic
149	#423	C₂×D₄₃	1	1	yes	characteristic
150	C₂×C₄⋊C₈	—	43	1	no	—
151	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
152	C₂×C₄×C₈	—	86	1	no	—
153	C₄³	—	43	1	no	—
154	#339	—	86	1	no	—
155	#339	—	86	1	no	—
156	#336	—	86	1	no	—
157	#334	—	86	2	no	—
158	#333	—	43	2	no	—
159	#332	—	43	2	no	—
160	Q₈⋊C₈	—	86	2	no	—
161	C₄₃	#9579	1	1	yes	characteristic, complemented, Sylow
162	C₂×M₁₆	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	86	1	no	—
165	C₄⋊Q₈	—	43	1	no	—
166	C₄⋊Q₈	—	43	1	no	—
167	#125	—	86	1	no	—
168	C₂²⋊Q₈	—	86	1	no	—
169	C₂²⋊Q₈	—	86	1	no	—
170	C₄×Q₈	—	86	1	no	—
171	C₄×Q₈	—	86	1	no	—
172	#117	—	86	1	no	—
173	C₂×C₄²	—	43	1	no	—
174	C₂×C₄²	—	43	1	no	—
175	C₂×C₄²	—	86	1	no	—
176	C₂×C₄²	—	86	1	no	—
177	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	2	1	no	—
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	43	2	no	—
183	C₄⋊C₈	—	43	2	no	—
184	C₄⋊C₈	—	86	1	no	—
185	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
186	C₂²⋊C₈	—	2	1	no	—
187	C₂²⋊C₈	—	86	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	86	1	no	—
190	C₄×C₈	—	172	2	no	—
191	C₂×Q₈	—	86	1	no	—
192	C₂×Q₈	—	86	1	no	—
193	C₂²×C₄	—	86	1	no	—
194	C₂²×C₄	—	86	1	no	—
195	C₂²×C₄	#10621898	1	1	yes	characteristic
196	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
197	C₂²×C₄	#10621902	1	1	yes	characteristic
198	M₁₆	—	4	1	no	—
199	M₁₆	—	4	1	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	1	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	86	2	no	—
206	C₂×C₈	—	86	2	no	—
207	C₂×C₈	—	172	1	no	—
208	C₂×C₈	—	172	1	no	—
209	C₄⋊C₄	—	86	1	no	—
210	C₄⋊C₄	—	86	1	no	—
211	C₄⋊C₄	—	86	1	no	—
212	C₄⋊C₄	—	86	1	no	—
213	C₄⋊C₄	—	172	1	no	—
214	C₄⋊C₄	—	172	1	no	—
215	C₂²⋊C₄	—	172	1	no	—
216	C₄²	—	43	2	no	—
217	C₄²	—	86	4	no	—
218	C₄²	—	86	1	no	—
219	C₄²	—	86	1	no	—
220	C₄²	—	86	1	no	—
221	C₄²	—	172	2	no	—
222	C₄²	—	172	1	no	—
223	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
224	C₄²	#10621898	1	1	yes	characteristic
225	C₄²	D₄×D₄₃	1	1	yes	characteristic
226	C₄²	#10621900	1	1	yes	characteristic
227	C₂³	#13063310	1	1	yes	characteristic
228	Q₈	—	344	1	no	—
229	Q₈	—	172	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	86	2	no	—
233	C₂×C₄	—	86	2	no	—
234	C₂×C₄	—	86	2	no	—
235	C₂×C₄	—	86	2	no	—
236	C₂×C₄	—	172	1	no	—
237	C₂×C₄	—	172	1	no	—
238	C₂×C₄	—	172	1	no	—
239	C₂×C₄	—	172	1	no	—
240	C₂×C₄	#13063282	1	1	yes	characteristic
241	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	#13063287	1	1	yes	characteristic
243	C₂×C₄	#13063298	1	1	yes	characteristic
244	C₂×C₄	#13063311	1	1	yes	characteristic
245	C₂×C₄	#13063320	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
247	C₂×C₄	#13063344	1	1	yes	characteristic
248	C₂×C₄	#13063354	1	1	yes	characteristic
249	C₂×C₄	#13063357	1	1	yes	characteristic
250	C₈	—	4	2	no	—
251	C₈	—	8	1	no	—
252	C₈	—	8	1	no	—
253	C₈	—	172	2	no	—
254	C₈	—	172	2	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	#14582788	1	1	yes	characteristic
258	C₂²	#14583231	1	1	yes	characteristic
259	C₂²	#14583242	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	2	1	no	—
263	C₄	—	86	4	no	—
264	C₄	—	344	1	no	—
265	C₄	—	344	1	no	—
266	C₄	—	172	2	no	—
267	C₄	#14582990	1	1	yes	characteristic
268	C₄	#14583003	1	1	yes	characteristic
269	C₄	#14583015	1	2	yes	—
270	C₄	#14583103	1	1	yes	characteristic
271	C₄	#14583120	1	1	yes	characteristic
272	C₂	—	2	1	no	—
273	C₂	—	2	1	no	—
274	C₂	#19135227	1	1	yes	characteristic
275	C₂	#19135262	1	1	yes	characteristic
276	C₂	#19135297	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135571

C₂

yes

maximal, characteristic

C₄⋊C₈×Dic₄₃

C₂

yes

maximal, characteristic

#19133367

C₂

yes

maximal, characteristic

#19133253

C₂

yes

maximal, characteristic

#19132999

C₂

yes

maximal, characteristic

#19132427

C₂

yes

maximal, characteristic

C₄₃×#1301

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

characteristic

#14582952

C₂²

yes

characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×C₈×Dic₄₃

—

C₄²×Dic₄₃

C₂²

yes

—

—

—

—

C₄

yes

complemented

#14582644

C₄

yes

complemented

#14582631

—

C₄₃×#431

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

—

#13063325

C₂×C₄

yes

characteristic

#13063325

C₂×C₄

yes

—

—

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄×Dic₄₃

D₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

D₄

yes

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂×C₄

yes

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

C₂²×C₄×C₄₃

yes

C₂²×C₄×C₄₃

yes

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

C₄²×C₄₃

yes

C₄²×C₄₃

yes

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

SD₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#123

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×SD₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

100

C₂×C₄×C₄₃

#137

yes

characteristic

101

C₂×Dic₄₃

—

102

C₂×Dic₄₃

—

103

C₂×Dic₄₃

—

104

C₂×Dic₄₃

—

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

C₂×Dic₄₃

—

108

C₂×Dic₄₃

—

109

Dic₈₆

—

110

Dic₈₆

—

111

C₈×C₄₃

—

112

C₈×C₄₃

—

113

C₈×C₄₃

—

114

C₄₃⋊C₈

—

115

C₄₃⋊C₈

—

116

#9579

—

maximal, Sylow

117

C₂²×C₄₃

—

118

C₂²×C₄₃

—

119

C₂²×C₄₃

#388

yes

characteristic

120

C₂²×C₄₃

#483

yes

characteristic

121

C₂²×C₄₃

#485

yes

characteristic

122

C₄×C₄₃

—

123

C₄×C₄₃

—

124

C₄×C₄₃

—

125

C₄×C₄₃

C₄×SD₁₆

yes

characteristic

126

C₄×C₄₃

#441

yes

characteristic

127

C₄×C₄₃

#443

yes

—

128

C₄×C₄₃

#461

yes

characteristic

129

C₄×C₄₃

#464

yes

characteristic

130

Dic₄₃

—

131

Dic₄₃

—

132

Dic₄₃

—

133

Dic₄₃

—

134

#1994

—

135

C₄×C₄⋊C₈

—

136

#1570

—

137

#1542

—

138

#1481

—

139

#1301

D₄₃

yes

characteristic

140

#1276

—

141

C₂×C₄₃

—

142

C₂×C₄₃

—

143

C₂×C₄₃

#1927

yes

characteristic

144

C₂×C₄₃

#1932

yes

characteristic

145

C₂×C₄₃

#1937

yes

characteristic

146

#533

—

147

#431

—

148

#431

C₂×D₄₃

yes

characteristic

149

#423

C₂×D₄₃

yes

characteristic

150

C₂×C₄⋊C₈

—

151

C₂×C₄⋊C₈

C₂×D₄₃

yes

characteristic

152

C₂×C₄×C₈

—

153

C₄³

—

154

#339

—

155

#339

—

156

#336

—

157

#334

—

158

#333

—

159

#332

—

160

Q₈⋊C₈

—

161

C₄₃

#9579

yes

characteristic, complemented, Sylow

162

C₂×M₁₆

—

163

C₂²×C₈

—

164

C₂²×C₈

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

#125

—

168

C₂²⋊Q₈

—

169

C₂²⋊Q₈

—

170

C₄×Q₈

—

171

C₄×Q₈

—

172

#117

—

173

C₂×C₄²

—

174

C₂×C₄²

—

175

C₂×C₄²

—

176

C₂×C₄²

—

177

C₂×C₄²

C₂²×D₄₃

yes

characteristic

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

C₄×D₄₃

yes

—

186

C₂²⋊C₈

—

187

C₂²⋊C₈

—

188

C₄×C₈

—

189

C₄×C₈

—

190

C₄×C₈

—

172

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

#10621898

yes

characteristic

196

C₂²×C₄

D₄×D₄₃

yes

characteristic

197

C₂²×C₄

#10621902

yes

characteristic

198

M₁₆

—

199

M₁₆

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

172

—

208

C₂×C₈

—

172

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

172

—

214

C₄⋊C₄

—

172

—

215

C₂²⋊C₄

—

172

—

216

C₄²

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

172

—

222

C₄²

—

172

—

223

C₄²

C₂×C₄×D₄₃

yes

characteristic

224

C₄²

#10621898

yes

characteristic

225

C₄²

D₄×D₄₃

yes

characteristic

226

C₄²

#10621900

yes

characteristic

227

C₂³

#13063310

yes

characteristic

228

Q₈

—

344

—

229

Q₈

—

172

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

172

—

237

C₂×C₄

—

172

—

238

C₂×C₄

—

172

—

239

C₂×C₄

—

172

—

240

C₂×C₄

#13063282

yes

characteristic

241

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

242

C₂×C₄

#13063287

yes

characteristic

243

C₂×C₄

#13063298

yes

characteristic

244

C₂×C₄

#13063311

yes

characteristic

245

C₂×C₄

#13063320

yes

characteristic

246

C₂×C₄

SD₁₆×D₄₃

yes

characteristic

247

C₂×C₄

#13063344

yes

characteristic

248

C₂×C₄

#13063354

yes

characteristic

249

C₂×C₄

#13063357

yes

characteristic

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

172

—

254

C₈

—

172

—

255

C₂²

—

256

C₂²

—

257

C₂²

#14582788

yes

characteristic

258

C₂²

#14583231

yes

characteristic

259

C₂²

#14583242

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

344

—

265

C₄

—

344

—

266

C₄

—

172

—

267

C₄

#14582990

yes

characteristic

268

C₄

#14583003

yes

characteristic

269

C₄

#14583015

yes

—

270

C₄

#14583103

yes

characteristic

271

C₄

#14583120

yes

characteristic

272

C₂

—

273

C₂

—

274

C₂

#19135227

yes

characteristic

275

C₂

#19135262

yes

characteristic

276

C₂

#19135297

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063298
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1301	C₂
socle	C₂²×C₄₃	#388
prime radical	C₂³×C₄₃	#123
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1301	D₄₃
hypocenter	C₄₃	#9579
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#13063298

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1301

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
17. #14582647	C₄	semidirect
18. #14582644	C₄	semidirect
161. C₄₃	#9579	semidirect

H ≅ G/N

type

17. #14582647

C₄

semidirect

18. #14582644

C₄

semidirect

161. C₄₃

#9579

semidirect

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

subgroup	index
#19135571	2
C₄⋊C₈×Dic₄₃	2
#19133367	2
#19133253	2
#19132999	2
#19132427	2
C₄₃×#1301	2
#9579	43

subgroup

index

C₄⋊C₈×Dic₄₃

C₄₃×#1301

Subgroups — #24995034

Conjugacy classes of subgroups

Complements

Maximal subgroups