Group #25011873 — subgroups

Subgroups — #25011873

Order 11008.

422 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14583005	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582714	C₂	1	1	yes	maximal, characteristic
3	#19136316	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582676	C₂	1	1	yes	maximal, characteristic
5	#19134482	C₂	1	1	yes	maximal, characteristic
6	#19132702	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1383	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063290	—	2	1	no	—
10	C₂×#13063265	C₂²	1	1	yes	characteristic
11	#14583005	—	2	2	no	—
12	#14583005	C₄	1	4	yes	complemented
13	#14582937	C₂²	1	1	yes	characteristic
14	C₂×#13063248	—	2	1	no	—
15	#14582857	—	2	1	no	—
16	C₂×#13063235	C₂²	1	1	yes	characteristic
17	#14582714	C₄	1	4	yes	complemented
18	#14582704	C₄	1	4	yes	complemented
19	#14582676	—	2	2	no	—
20	#14582660	—	2	1	no	—
21	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×Dic₈₆	—	2	1	no	—
25	C₂×Dic₁₇₂	—	2	1	no	—
26	C₂×Dic₁₇₂	—	2	1	no	—
27	C₂×Dic₁₇₂	—	2	1	no	—
28	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
30	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
31	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
32	#13063290	—	2	4	no	—
33	#13063290	—	4	2	no	—
34	#13063284	—	2	1	no	—
35	C₂×Dic₄₃⋊C₄	—	4	1	no	—
36	C₂×C₄×Dic₄₃	—	4	1	no	—
37	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
38	#13063265	—	2	1	no	—
39	#13063265	C₂×C₄	1	2	yes	—
40	C₂×C₄₃⋊C₁₆	—	2	1	no	—
41	#13063259	C₂×C₄	1	2	yes	—
42	#13063257	—	2	1	no	—
43	#13063248	—	2	4	no	—
44	#13063235	—	4	1	no	—
45	#13063235	C₂×C₄	1	2	yes	—
46	#13063235	D₄	1	2	yes	—
47	C₈×Dic₄₃	—	4	1	no	—
48	C₂×M₁₆×C₄₃	—	2	1	no	—
49	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
51	M₃₂×C₄₃	—	2	1	no	—
52	M₃₂×C₄₃	—	2	1	no	—
53	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
54	#108×C₄₃	—	2	1	no	—
55	#108×C₄₃	C₂×C₄	1	2	yes	—
56	#106×C₄₃	—	2	1	no	—
57	#106×C₄₃	C₂×C₄	1	2	yes	—
58	C₂²×C₄×C₄₃	—	4	1	no	—
59	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₄₃	—	2	1	no	—
61	C₂²×Dic₄₃	—	4	1	no	—
62	C₂×Dic₈₆	—	2	2	no	—
63	C₂×Dic₈₆	—	2	2	no	—
64	C₂×Dic₈₆	—	2	2	no	—
65	C₂×Dic₈₆	—	4	1	no	—
66	C₂×Dic₈₆	—	4	1	no	—
67	C₂×Dic₈₆	—	4	1	no	—
68	M₁₆×C₄₃	—	2	2	no	—
69	M₁₆×C₄₃	—	4	1	no	—
70	C₂×C₈×C₄₃	—	4	1	no	—
71	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
76	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
77	C₄⋊C₄×C₄₃	—	2	2	no	—
78	C₄⋊C₄×C₄₃	—	4	1	no	—
79	C₂²⋊Dic₄₃	—	4	1	no	—
80	C₄⋊Dic₄₃	—	2	2	no	—
81	Dic₄₃⋊C₄	—	4	4	no	—
82	C₄×Dic₄₃	—	2	1	no	—
83	C₄×Dic₄₃	—	4	4	no	—
84	C₄×Dic₄₃	—	4	1	no	—
85	C₄×Dic₄₃	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄₃⋊C₈	—	2	1	no	—
87	C₂×C₄₃⋊C₈	—	2	1	no	—
88	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
89	Dic₁₇₂	—	2	2	no	—
90	Dic₁₇₂	—	2	2	no	—
91	Dic₁₇₂	—	2	2	no	—
92	Dic₁₇₂	C₄²	1	4	yes	—
93	C₁₆×C₄₃	—	2	2	no	—
94	C₄₃⋊C₁₆	—	2	2	no	—
95	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₄₃	—	4	2	no	—
97	C₂×C₄×C₄₃	—	8	2	no	—
98	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
104	C₂×Dic₄₃	—	2	2	no	—
105	C₂×Dic₄₃	—	4	2	no	—
106	C₂×Dic₄₃	—	4	2	no	—
107	C₂×Dic₄₃	—	4	2	no	—
108	C₂×Dic₄₃	—	4	2	no	—
109	C₂×Dic₄₃	—	4	2	no	—
110	Dic₈₆	—	2	4	no	—
111	Dic₈₆	—	4	2	no	—
112	Dic₈₆	—	4	2	no	—
113	Dic₈₆	—	4	2	no	—
114	C₈×C₄₃	—	4	2	no	—
115	C₈×C₄₃	C₂×C₄²	1	1	yes	characteristic
116	C₈×C₄₃	#117	1	1	yes	characteristic
117	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
118	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
119	C₄₃⋊C₈	—	2	2	no	—
120	#12648	—	43	1	no	maximal, Sylow
121	C₂²×C₄₃	—	2	2	no	—
122	C₂²×C₄₃	#418	1	1	yes	characteristic
123	C₂²×C₄₃	#440	1	1	yes	characteristic
124	C₂²×C₄₃	#442	1	1	yes	characteristic
125	C₄×C₄₃	—	8	2	no	—
126	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
127	C₄×C₄₃	#417	1	1	yes	characteristic
128	C₄×C₄₃	#440	1	1	yes	characteristic
129	C₄×C₄₃	#442	1	1	yes	characteristic
130	Dic₄₃	—	4	2	no	—
131	Dic₄₃	—	4	4	no	—
132	Dic₄₃	—	8	2	no	—
133	C₂×#441	—	43	1	no	—
134	C₂×#362	—	43	1	no	—
135	#2141	—	43	1	no	—
136	C₂×#347	—	43	1	no	—
137	#1773	—	43	1	no	—
138	#1386	—	43	1	no	—
139	#1383	D₄₃	1	1	yes	characteristic
140	C₂×C₄₃	—	2	1	no	—
141	C₂×C₄₃	—	2	1	no	—
142	C₂×C₄₃	#1762	1	1	yes	characteristic
143	C₂×C₄₃	#2180	1	2	yes	—
144	C₂²×Q₁₆	—	43	1	no	—
145	C₂×C₄×Q₈	—	86	1	no	—
146	C₂×M₃₂	—	43	1	no	—
147	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
148	#441	—	43	4	no	—
149	#441	—	86	2	no	—
150	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
151	#427	—	43	1	no	—
152	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
153	C₂×#103	—	86	1	no	—
154	#405	—	86	1	no	—
155	C₂×#97	—	43	1	no	—
156	#362	—	43	4	no	—
157	#358	—	43	4	no	—
158	#347	—	86	2	no	—
159	#339	—	86	1	no	—
160	C₄₃	#12648	1	1	yes	characteristic, complemented, Sylow
161	C₂²×Q₈	—	86	1	no	—
162	C₂×Q₁₆	—	43	2	no	—
163	C₂×Q₁₆	—	43	2	no	—
164	C₂×Q₁₆	—	43	2	no	—
165	C₂×Q₁₆	—	86	1	no	—
166	C₂×Q₁₆	—	86	1	no	—
167	C₂×Q₁₆	—	86	1	no	—
168	C₂×M₁₆	—	2	1	no	—
169	C₂²×C₈	—	43	1	no	—
170	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
171	C₄×Q₈	—	86	4	no	—
172	C₄×Q₈	—	172	2	no	—
173	#117	—	86	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	172	1	no	—
176	C₂×C₄²	—	43	1	no	—
177	C₂×C₄²	—	172	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	2	1	no	—
180	M₃₂	—	43	2	no	—
181	M₃₂	—	86	1	no	—
182	C₂×C₁₆	—	86	1	no	—
183	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
184	#108	—	2	1	no	—
185	#108	C₄×D₄₃	1	2	yes	—
186	#107	—	43	2	no	—
187	#106	—	2	1	no	—
188	#106	—	86	1	no	—
189	#106	C₄×D₄₃	1	2	yes	—
190	#103	—	86	4	no	—
191	#97	—	43	2	no	—
192	#97	—	43	2	no	—
193	#97	—	172	1	no	—
194	C₄×C₈	—	172	1	no	—
195	C₂×Q₈	—	86	2	no	—
196	C₂×Q₈	—	86	2	no	—
197	C₂×Q₈	—	86	2	no	—
198	C₂×Q₈	—	172	1	no	—
199	C₂×Q₈	—	172	1	no	—
200	C₂×Q₈	—	172	1	no	—
201	C₂²×C₄	—	4	1	no	—
202	C₂²×C₄	—	86	1	no	—
203	C₂²×C₄	—	172	1	no	—
204	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
205	Q₁₆	—	43	4	no	—
206	Q₁₆	—	86	2	no	—
207	Q₁₆	—	86	2	no	—
208	Q₁₆	—	86	2	no	—
209	M₁₆	—	2	2	no	—
210	M₁₆	—	4	1	no	—
211	C₂×C₈	—	4	1	no	—
212	C₂×C₈	—	43	2	no	—
213	C₂×C₈	—	86	1	no	—
214	C₂×C₈	—	86	1	no	—
215	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
216	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
217	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
218	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
219	C₂×C₈	#10621900	1	1	yes	characteristic
220	C₂×C₈	#10621902	1	1	yes	characteristic
221	C₄⋊C₄	—	2	2	no	—
222	C₄⋊C₄	—	4	1	no	—
223	C₄⋊C₄	—	86	2	no	—
224	C₄⋊C₄	—	172	4	no	—
225	C₂²⋊C₄	—	172	1	no	—
226	C₄²	—	43	2	no	—
227	C₄²	—	86	1	no	—
228	C₄²	—	172	4	no	—
229	C₄²	—	172	1	no	—
230	C₁₆	—	2	2	no	—
231	C₁₆	—	86	2	no	—
232	C₂³	#13063352	1	1	yes	characteristic
233	Q₈	—	86	4	no	—
234	Q₈	—	172	2	no	—
235	Q₈	—	172	2	no	—
236	Q₈	—	172	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	8	2	no	—
239	C₂×C₄	—	86	2	no	—
240	C₂×C₄	—	172	2	no	—
241	C₂×C₄	—	172	2	no	—
242	C₂×C₄	—	172	2	no	—
243	C₂×C₄	—	172	2	no	—
244	C₂×C₄	—	172	2	no	—
245	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
246	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
247	C₂×C₄	#13063287	1	1	yes	characteristic
248	C₂×C₄	#13063349	1	1	yes	characteristic
249	C₂×C₄	#13063352	1	1	yes	characteristic
250	C₂×C₄	#13063357	1	1	yes	characteristic
251	C₈	—	4	2	no	—
252	C₈	—	86	2	no	—
253	C₈	C₄²×D₄₃	1	1	yes	characteristic
254	C₈	#13063283	1	1	yes	characteristic
255	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
256	C₈	#13063287	1	1	yes	characteristic
257	C₂²	—	2	2	no	—
258	C₂²	#14582902	1	1	yes	characteristic
259	C₂²	#14583002	1	1	yes	characteristic
260	C₂²	#14583010	1	1	yes	characteristic
261	C₄	—	8	2	no	—
262	C₄	—	344	2	no	—
263	C₄	—	172	2	no	—
264	C₄	—	172	4	no	—
265	C₄	#14582746	1	1	yes	characteristic
266	C₄	#14582899	1	1	yes	characteristic
267	C₄	#14582998	1	1	yes	characteristic
268	C₄	#14583008	1	1	yes	characteristic
269	C₂	—	2	1	no	—
270	C₂	—	2	1	no	—
271	C₂	#19134419	1	1	yes	characteristic
272	C₂	#19136485	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583005

C₂

yes

maximal, characteristic

C₂×#14582714

C₂

yes

maximal, characteristic

#19136316

C₂

yes

maximal, characteristic

C₂×#14582676

C₂

yes

maximal, characteristic

#19134482

C₂

yes

maximal, characteristic

#19132702

C₂

yes

maximal, characteristic

C₄₃×#1383

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₂²

yes

characteristic

C₂×#13063290

—

C₂×#13063265

C₂²

yes

characteristic

#14583005

—

#14583005

C₄

yes

complemented

#14582937

C₂²

yes

—

—

C₂²

yes

characteristic

#14582714

C₄

yes

complemented

#14582704

C₄

yes

complemented

#14582676

—

#14582660

—

C₂×M₃₂×C₄₃

C₂²

yes

characteristic

C₂×#108×C₄₃

C₂²

yes

characteristic

C₂×#106×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

D₄

yes

—

—

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

D₄

yes

characteristic

#13063265

—

#13063265

C₂×C₄

yes

—

C₂×C₄₃⋊C₁₆

—

#13063259

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

#13063235

D₄

yes

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

#108×C₄₃

—

#108×C₄₃

C₂×C₄

yes

—

#106×C₄₃

—

#106×C₄₃

C₂×C₄

yes

—

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

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

C₄²

yes

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

100

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

101

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

102

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₄₃

#137

yes

characteristic

104

C₂×Dic₄₃

—

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

C₂×Dic₄₃

—

108

C₂×Dic₄₃

—

109

C₂×Dic₄₃

—

110

Dic₈₆

—

111

Dic₈₆

—

112

Dic₈₆

—

113

Dic₈₆

—

114

C₈×C₄₃

—

115

C₈×C₄₃

C₂×C₄²

yes

characteristic

116

C₈×C₄₃

#117

yes

characteristic

117

C₈×C₄₃

C₄×D₄

yes

characteristic

118

C₈×C₄₃

C₄×D₄

yes

characteristic

119

C₄₃⋊C₈

—

120

#12648

—

maximal, Sylow

121

C₂²×C₄₃

—

122

C₂²×C₄₃

#418

yes

characteristic

123

C₂²×C₄₃

#440

yes

characteristic

124

C₂²×C₄₃

#442

yes

characteristic

125

C₄×C₄₃

—

126

C₄×C₄₃

C₄×C₂²⋊C₄

yes

characteristic

127

C₄×C₄₃

#417

yes

characteristic

128

C₄×C₄₃

#440

yes

characteristic

129

C₄×C₄₃

#442

yes

characteristic

130

Dic₄₃

—

131

Dic₄₃

—

132

Dic₄₃

—

133

C₂×#441

—

134

C₂×#362

—

135

#2141

—

136

C₂×#347

—

137

#1773

—

138

#1386

—

139

#1383

D₄₃

yes

characteristic

140

C₂×C₄₃

—

141

C₂×C₄₃

—

142

C₂×C₄₃

#1762

yes

characteristic

143

C₂×C₄₃

#2180

yes

—

144

C₂²×Q₁₆

—

145

C₂×C₄×Q₈

—

146

C₂×M₃₂

—

147

C₂×M₃₂

C₂×D₄₃

yes

characteristic

148

#441

—

149

#441

—

150

C₂×#108

C₂×D₄₃

yes

characteristic

151

#427

—

152

C₂×#106

C₂×D₄₃

yes

characteristic

153

C₂×#103

—

154

#405

—

155

C₂×#97

—

156

#362

—

157

#358

—

158

#347

—

159

#339

—

160

C₄₃

#12648

yes

characteristic, complemented, Sylow

161

C₂²×Q₈

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

—

167

C₂×Q₁₆

—

168

C₂×M₁₆

—

169

C₂²×C₈

—

170

C₂²×C₈

C₂²×D₄₃

yes

characteristic

171

C₄×Q₈

—

172

C₄×Q₈

—

172

—

173

#117

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

172

—

176

C₂×C₄²

—

177

C₂×C₄²

—

172

—

178

M₃₂

—

179

M₃₂

—

180

M₃₂

—

181

M₃₂

—

182

C₂×C₁₆

—

183

C₂×C₁₆

C₄×D₄₃

yes

—

184

#108

—

185

#108

C₄×D₄₃

yes

—

186

#107

—

187

#106

—

188

#106

—

189

#106

C₄×D₄₃

yes

—

190

#103

—

191

#97

—

192

#97

—

193

#97

—

172

—

194

C₄×C₈

—

172

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

172

—

199

C₂×Q₈

—

172

—

200

C₂×Q₈

—

172

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

172

—

204

C₂²×C₄

D₄×D₄₃

yes

characteristic

205

Q₁₆

—

206

Q₁₆

—

207

Q₁₆

—

208

Q₁₆

—

209

M₁₆

—

210

M₁₆

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

216

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

217

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

218

C₂×C₈

D₄×D₄₃

yes

characteristic

219

C₂×C₈

#10621900

yes

characteristic

220

C₂×C₈

#10621902

yes

characteristic

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

172

—

225

C₂²⋊C₄

—

172

—

226

C₄²

—

227

C₄²

—

228

C₄²

—

172

—

229

C₄²

—

172

—

230

C₁₆

—

231

C₁₆

—

232

C₂³

#13063352

yes

characteristic

233

Q₈

—

234

Q₈

—

172

—

235

Q₈

—

172

—

236

Q₈

—

172

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

172

—

241

C₂×C₄

—

172

—

242

C₂×C₄

—

172

—

243

C₂×C₄

—

172

—

244

C₂×C₄

—

172

—

245

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

246

C₂×C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

247

C₂×C₄

#13063287

yes

characteristic

248

C₂×C₄

#13063349

yes

characteristic

249

C₂×C₄

#13063352

yes

characteristic

250

C₂×C₄

#13063357

yes

characteristic

251

C₈

—

252

C₈

—

253

C₈

C₄²×D₄₃

yes

characteristic

254

C₈

#13063283

yes

characteristic

255

C₈

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

256

C₈

#13063287

yes

characteristic

257

C₂²

—

258

C₂²

#14582902

yes

characteristic

259

C₂²

#14583002

yes

characteristic

260

C₂²

#14583010

yes

characteristic

261

C₄

—

262

C₄

—

344

—

263

C₄

—

172

—

264

C₄

—

172

—

265

C₄

#14582746

yes

characteristic

266

C₄

#14582899

yes

characteristic

267

C₄

#14582998

yes

characteristic

268

C₄

#14583008

yes

characteristic

269

C₂

—

270

C₂

—

271

C₂

#19134419

yes

characteristic

272

C₂

#19136485

yes

—

	subgroup	G/H
center	C₂²	#14583010
commutator	C₈×C₄₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1383	C₂
socle	C₂²×C₄₃	#442
prime radical	C₂³×C₄₃	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1383	D₄₃
hypocenter	C₄₃	#12648
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1383

subgroup

G/H

center

C₂²

#14583010

commutator

C₈×C₄₃

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1383

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1383

N	H ≅ G/N	type
12. #14583005	C₄	semidirect
17. #14582714	C₄	semidirect
18. #14582704	C₄	semidirect
160. C₄₃	#12648	semidirect

H ≅ G/N

type

12. #14583005

C₄

semidirect

17. #14582714

C₄

semidirect

18. #14582704

C₄

semidirect

160. C₄₃

#12648

semidirect

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

subgroup	index
C₂×#14583005	2
C₂×#14582714	2
#19136316	2
C₂×#14582676	2
#19134482	2
#19132702	2
C₄₃×#1383	2
#12648	43

subgroup

index

C₄₃×#1383

Subgroups — #25011873

Conjugacy classes of subgroups

Complements

Maximal subgroups