Group #24996185 — subgroups

Subgroups — #24996185

Order 11008.

410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14583249	C₂	1	1	yes	maximal, characteristic
2	#19135585	C₂	1	1	yes	maximal, characteristic
3	#19135583	C₂	1	1	yes	maximal, characteristic
4	#19133353	C₂	1	1	yes	maximal, characteristic
5	#19133279	C₂	1	1	yes	maximal, characteristic
6	#19132876	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1548	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063325	C₂²	1	1	yes	characteristic
9	#14583249	—	2	1	no	—
10	#14583249	—	2	1	no	—
11	#14583249	—	2	2	no	—
12	#14582923	C₂²	1	1	yes	characteristic
13	C₂×#13063249	C₄	1	4	yes	—
14	C₄×#10621877	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	#14582668	—	2	2	no	—
17	#14582667	—	2	2	no	—
18	#14582651	—	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×#333	—	2	2	no	—
26	C₂²×Dic₈₆	—	2	1	no	—
27	C₂×#10621877	—	2	1	no	—
28	C₂×#10621877	D₄	1	2	yes	—
29	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
30	#13063325	—	2	1	no	—
31	#13063325	—	2	1	no	—
32	#13063325	—	2	1	no	—
33	#13063325	—	2	1	no	—
34	C₂×C₄⋊Dic₄₃	—	2	1	no	—
35	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
36	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
37	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
38	#13063249	—	2	4	no	—
39	#13063249	—	2	4	no	—
40	#13063236	—	2	1	no	—
41	C₄×C₄₃⋊C₈	—	2	1	no	—
42	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
43	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
44	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₄₃	—	2	1	no	—
47	C₄⋊Q₈×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	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₃	—	2	1	no	—
55	C₄⋊C₈×C₄₃	—	2	1	no	—
56	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
57	C₂²⋊C₈×C₄₃	—	2	1	no	—
58	C₄×C₈×C₄₃	—	2	1	no	—
59	C₂×Q₈×C₄₃	—	2	2	no	—
60	C₂×Q₈×C₄₃	—	2	2	no	—
61	C₂×Q₈×C₄₃	—	4	4	no	—
62	C₂²×C₄×C₄₃	—	2	2	no	—
63	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
66	C₂²×Dic₄₃	—	2	2	no	—
67	C₂×Dic₈₆	—	4	1	no	—
68	C₂×Dic₈₆	—	4	1	no	—
69	C₂×Dic₈₆	—	8	2	no	—
70	M₁₆×C₄₃	—	4	2	no	—
71	C₂×C₈×C₄₃	—	2	2	no	—
72	C₂×C₈×C₄₃	—	4	1	no	—
73	C₄⋊C₄×C₄₃	—	4	1	no	—
74	C₄⋊C₄×C₄₃	—	4	1	no	—
75	C₄⋊C₄×C₄₃	—	4	1	no	—
76	C₄⋊C₄×C₄₃	—	4	1	no	—
77	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₄₃	#41	1	1	yes	characteristic
81	C₄⋊Dic₄₃	—	2	2	no	—
82	C₄⋊Dic₄₃	—	2	2	no	—
83	C₄⋊Dic₄₃	—	4	1	no	—
84	C₄⋊Dic₄₃	—	4	1	no	—
85	#10621877	—	2	2	no	—
86	#10621877	—	4	2	no	—
87	#10621877	Q₁₆	1	4	yes	—
88	C₂×C₄₃⋊C₈	—	2	2	no	—
89	C₂×C₄₃⋊C₈	—	4	2	no	—
90	C₂×C₄₃⋊C₈	—	4	1	no	—
91	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
92	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
93	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
94	Q₈×C₄₃	—	4	4	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	#121	1	1	yes	characteristic
103	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
104	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
105	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
106	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
107	C₂×C₄×C₄₃	#135	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	—	2	2	no	—
115	C₄₃⋊C₈	—	2	2	no	—
116	C₄₃⋊C₈	—	2	4	no	—
117	C₄₃⋊C₈	—	8	1	no	—
118	#9795	—	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	C₄×Q₁₆	1	2	yes	—
123	C₄×C₄₃	—	2	1	no	—
124	C₄×C₄₃	—	2	1	no	—
125	C₄×C₄₃	—	8	2	no	—
126	C₄×C₄₃	#413	1	2	yes	—
127	C₄×C₄₃	#467	1	2	yes	—
128	C₄×C₄₃	#471	1	2	yes	—
129	C₄×C₄₃	#494	1	1	yes	characteristic
130	C₄×C₄₃	#495	1	1	yes	characteristic
131	Dic₄₃	—	8	2	no	—
132	C₂×#487	—	43	1	no	—
133	#1997	—	43	1	no	—
134	#1997	—	43	1	no	—
135	#1567	—	43	1	no	—
136	#1549	—	43	1	no	—
137	#1548	D₄₃	1	1	yes	characteristic
138	C₈×M₁₆	—	43	1	no	—
139	C₂×C₄₃	—	2	2	no	—
140	C₂×C₄₃	#1967	1	1	yes	characteristic
141	C₂×C₄₃	#1969	1	1	yes	characteristic
142	C₂×C₄₃	#1977	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	—	43	1	no	—
144	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
145	#487	—	86	1	no	—
146	#487	—	86	1	no	—
147	#487	—	86	2	no	—
148	#431	C₂×D₄₃	1	1	yes	characteristic
149	#423	—	43	1	no	—
150	#423	C₂×D₄₃	1	1	yes	characteristic
151	C₂×#103	—	43	4	no	—
152	C₄×M₁₆	—	43	1	no	—
153	C₂×C₄×C₈	—	43	1	no	—
154	#343	—	86	2	no	—
155	#343	—	86	2	no	—
156	#335	—	86	2	no	—
157	#333	—	2	2	no	—
158	#332	—	86	2	no	—
159	#322	—	86	1	no	—
160	C₈²	—	86	1	no	—
161	C₄₃	#9795	1	1	yes	characteristic, complemented, Sylow
162	C₂²×Q₈	—	86	1	no	—
163	C₂²×Q₈	C₄×D₄₃	1	2	yes	—
164	C₂×M₁₆	—	2	1	no	—
165	C₂×M₁₆	—	43	2	no	—
166	C₂×M₁₆	—	86	1	no	—
167	C₂²×C₈	—	43	2	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	—	2	1	no	—
171	C₄⋊Q₈	—	2	1	no	—
172	C₄⋊Q₈	—	86	1	no	—
173	C₄⋊Q₈	—	86	1	no	—
174	C₄⋊Q₈	—	86	1	no	—
175	C₄⋊Q₈	—	86	1	no	—
176	C₂×C₄⋊C₄	—	2	1	no	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₄⋊C₄	—	43	2	no	—
179	C₂×C₄⋊C₄	—	86	1	no	—
180	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	2	1	no	—
183	C₄⋊C₈	—	86	1	no	—
184	C₄⋊C₈	—	86	1	no	—
185	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
186	#103	—	86	4	no	—
187	#103	—	86	4	no	—
188	C₂²⋊C₈	—	2	1	no	—
189	#97	—	86	1	no	—
190	C₄×C₈	—	2	1	no	—
191	C₄×C₈	—	43	1	no	—
192	C₄×C₈	—	43	1	no	—
193	C₄×C₈	—	43	2	no	—
194	C₄×C₈	—	86	1	no	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	4	4	no	—
198	C₂×Q₈	—	344	2	no	—
199	C₂×Q₈	—	172	1	no	—
200	C₂×Q₈	—	172	1	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	86	2	no	—
203	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
204	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
205	C₂²×C₄	#10621900	1	1	yes	characteristic
206	M₁₆	—	4	2	no	—
207	M₁₆	—	43	4	no	—
208	M₁₆	—	86	2	no	—
209	M₁₆	—	172	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	4	1	no	—
212	C₂×C₈	—	43	2	no	—
213	C₂×C₈	—	43	2	no	—
214	C₂×C₈	—	86	2	no	—
215	C₂×C₈	—	172	2	no	—
216	C₂×C₈	—	172	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	4	1	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	#10621898	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	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
230	Q₈	—	4	4	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	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
242	C₂×C₄	#13063297	1	1	yes	characteristic
243	C₂×C₄	#13063298	1	1	yes	characteristic
244	C₂×C₄	#13063311	1	1	yes	characteristic
245	C₂×C₄	#13063321	1	1	yes	characteristic
246	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
247	C₂×C₄	#13063346	1	2	yes	—
248	C₈	—	4	2	no	—
249	C₈	—	8	1	no	—
250	C₈	—	86	2	no	—
251	C₈	—	86	2	no	—
252	C₈	—	86	4	no	—
253	C₈	—	344	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	#14582799	1	1	yes	characteristic
257	C₂²	#14582991	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	#14582880	1	2	yes	—
263	C₄	#14583139	1	2	yes	—
264	C₄	#14583164	1	2	yes	—
265	C₄	#14583277	1	1	yes	characteristic
266	C₄	#14583280	1	1	yes	characteristic
267	C₂	—	2	2	no	—
268	C₂	#19135441	1	1	yes	characteristic
269	C₂	#19135453	1	1	yes	characteristic
270	C₂	#19135497	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583249

C₂

yes

maximal, characteristic

#19135585

C₂

yes

maximal, characteristic

#19135583

C₂

yes

maximal, characteristic

#19133353

C₂

yes

maximal, characteristic

#19133279

C₂

yes

maximal, characteristic

#19132876

C₂

yes

maximal, characteristic

C₄₃×#1548

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×#13063249

C₄

yes

—

C₄×#10621877

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×#333

—

C₂²×Dic₈₆

—

C₂×#10621877

—

C₂×#10621877

D₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063249

—

#13063249

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

characteristic

C₄×C₄₃⋊C₈

D₄

yes

characteristic

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×Q₈×C₄₃

C₂×C₄

yes

—

C₂×M₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

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

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

characteristic

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

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

#10621877

—

#10621877

Q₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₄×D₄

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

#121

yes

characteristic

103

C₂×C₄×C₄₃

#121

yes

characteristic

104

C₂×C₄×C₄₃

#124

yes

characteristic

105

C₂×C₄×C₄₃

#127

yes

characteristic

106

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

107

C₂×C₄×C₄₃

#135

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

—

117

C₄₃⋊C₈

—

118

#9795

—

maximal, Sylow

119

C₂²×C₄₃

—

120

C₂²×C₄₃

—

121

C₂²×C₄₃

#390

yes

characteristic

122

C₂²×C₄₃

C₄×Q₁₆

yes

—

123

C₄×C₄₃

—

124

C₄×C₄₃

—

125

C₄×C₄₃

—

126

C₄×C₄₃

#413

yes

—

127

C₄×C₄₃

#467

yes

—

128

C₄×C₄₃

#471

yes

—

129

C₄×C₄₃

#494

yes

characteristic

130

C₄×C₄₃

#495

yes

characteristic

131

Dic₄₃

—

132

C₂×#487

—

133

#1997

—

134

#1997

—

135

#1567

—

136

#1549

—

137

#1548

D₄₃

yes

characteristic

138

C₈×M₁₆

—

139

C₂×C₄₃

—

140

C₂×C₄₃

#1967

yes

characteristic

141

C₂×C₄₃

#1969

yes

characteristic

142

C₂×C₄₃

#1977

yes

characteristic

143

C₂×C₄⋊Q₈

—

144

C₂×C₄⋊Q₈

C₂×D₄₃

yes

characteristic

145

#487

—

146

#487

—

147

#487

—

148

#431

C₂×D₄₃

yes

characteristic

149

#423

—

150

#423

C₂×D₄₃

yes

characteristic

151

C₂×#103

—

152

C₄×M₁₆

—

153

C₂×C₄×C₈

—

154

#343

—

155

#343

—

156

#335

—

157

#333

—

158

#332

—

159

#322

—

160

C₈²

—

161

C₄₃

#9795

yes

characteristic, complemented, Sylow

162

C₂²×Q₈

—

163

C₂²×Q₈

C₄×D₄₃

yes

—

164

C₂×M₁₆

—

165

C₂×M₁₆

—

166

C₂×M₁₆

—

167

C₂²×C₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄²

C₂²×D₄₃

yes

characteristic

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

C₂²⋊D₄₃

yes

—

186

#103

—

187

#103

—

188

C₂²⋊C₈

—

189

#97

—

190

C₄×C₈

—

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

344

—

199

C₂×Q₈

—

172

—

200

C₂×Q₈

—

172

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

204

C₂²×C₄

D₄×D₄₃

yes

characteristic

205

C₂²×C₄

#10621900

yes

characteristic

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

209

M₁₆

—

172

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

172

—

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

#10621898

yes

characteristic

226

C₄²

D₄×D₄₃

yes

characteristic

227

C₄²

D₄×D₄₃

yes

characteristic

228

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

229

C₂³

(C₂²⋊D₄₃)⋊C₄

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

C₄×C₂²⋊D₄₃

yes

characteristic

242

C₂×C₄

#13063297

yes

characteristic

243

C₂×C₄

#13063298

yes

characteristic

244

C₂×C₄

#13063311

yes

characteristic

245

C₂×C₄

#13063321

yes

characteristic

246

C₂×C₄

Q₁₆×D₄₃

yes

—

247

C₂×C₄

#13063346

yes

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

253

C₈

—

344

—

254

C₂²

—

255

C₂²

—

256

C₂²

#14582799

yes

characteristic

257

C₂²

#14582991

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

344

—

262

C₄

#14582880

yes

—

263

C₄

#14583139

yes

—

264

C₄

#14583164

yes

—

265

C₄

#14583277

yes

characteristic

266

C₄

#14583280

yes

characteristic

267

C₂

—

268

C₂

#19135441

yes

characteristic

269

C₂

#19135453

yes

characteristic

270

C₂

#19135497

yes

characteristic

	subgroup	G/H
center	C₂²	#14582799
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1548	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	C₄×D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1548	D₄₃
hypocenter	C₄₃	#9795
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#14582799

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1548

C₂

socle

C₂²×C₄₃

#390

prime radical

C₂³×C₄₃

C₄×D₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

N	H ≅ G/N	type
161. C₄₃	#9795	semidirect

H ≅ G/N

type

161. C₄₃

#9795

semidirect

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

subgroup	index
C₂×#14583249	2
#19135585	2
#19135583	2
#19133353	2
#19133279	2
#19132876	2
C₄₃×#1548	2
#9795	43

subgroup

index

C₄₃×#1548

Subgroups — #24996185

Conjugacy classes of subgroups

Complements

Maximal subgroups