Group #25013635 — subgroups

Subgroups — #25013635

Order 11008.

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

normal subgroups only

This group has 496 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×#14583157	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582948	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582716	C₂	1	2	yes	maximal, complemented
4	#19132694	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#349	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	C₂²×#10621877	—	2	1	no	—
8	C₂×#13063304	—	2	1	no	—
9	#14583157	—	2	2	no	—
10	#14583157	C₄	1	4	yes	—
11	#14582948	—	2	4	no	—
12	C₂×#13063261	—	2	1	no	—
13	C₂×#13063261	C₂²	1	2	yes	—
14	C₂×#13063257	C₂²	1	1	yes	characteristic
15	C₂×#13063250	—	2	1	no	—
16	#14582716	—	2	4	no	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#349	—	2	2	no	—
20	C₂²×Dic₈₆	—	2	1	no	—
21	C₂×Dic₁₇₂	—	2	2	no	—
22	C₂×Dic₁₇₂	—	2	2	no	—
23	C₂×Dic₁₇₂	—	2	1	no	—
24	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
25	C₂×#10621877	—	2	4	no	—
26	C₂×#10621877	—	2	2	no	—
27	C₂×#10621877	—	4	1	no	—
28	C₂×#10621877	—	4	2	no	—
29	C₂²×C₄₃⋊C₈	—	4	1	no	—
30	#13063304	—	2	4	no	—
31	#13063304	—	4	2	no	—
32	C₂×C₄⋊Dic₄₃	—	2	1	no	—
33	C₂×Dic₄₃⋊C₄	—	4	1	no	—
34	C₂×C₂²⋊Dic₄₃	—	4	1	no	—
35	#13063261	—	2	4	no	—
36	#13063261	—	2	2	no	—
37	#13063261	D₄	1	4	yes	—
38	#13063257	—	2	1	no	—
39	#13063257	C₂×C₄	1	2	yes	—
40	#13063250	—	2	4	no	—
41	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂×M₁₆×C₄₃	—	2	2	no	—
43	C₂×M₁₆×C₄₃	—	2	2	no	—
44	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
45	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
46	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
48	M₃₂×C₄₃	—	2	2	no	—
49	M₃₂×C₄₃	—	2	2	no	—
50	C₂×C₁₆×C₄₃	—	2	2	no	—
51	C₂⁴×C₄₃	SD₁₆	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	—	2	1	no	—
53	C₂²×C₄×C₄₃	—	2	1	no	—
54	C₂²×C₄×C₄₃	—	2	1	no	—
55	C₂²×C₄×C₄₃	—	2	1	no	—
56	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₄₃	D₈	1	2	yes	—
58	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₄₃	—	4	1	no	—
61	C₂²×Dic₄₃	—	4	1	no	—
62	C₂×Dic₈₆	—	2	2	no	—
63	C₂×Dic₈₆	—	4	1	no	—
64	C₂×Dic₈₆	—	4	1	no	—
65	C₂×Dic₈₆	—	4	1	no	—
66	C₂×Dic₈₆	—	4	1	no	—
67	C₂×Dic₈₆	—	4	1	no	—
68	M₁₆×C₄₃	—	2	4	no	—
69	M₁₆×C₄₃	—	2	4	no	—
70	C₂×C₈×C₄₃	—	2	1	no	—
71	C₂×C₈×C₄₃	—	2	1	no	—
72	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₄₃	#41	1	2	yes	—
77	C₂²⋊Dic₄₃	—	4	4	no	—
78	C₄⋊Dic₄₃	—	2	2	no	—
79	C₄⋊Dic₄₃	—	4	1	no	—
80	Dic₄₃⋊C₄	—	4	4	no	—
81	#10621877	—	2	4	no	—
82	#10621877	—	4	4	no	—
83	#10621877	—	4	2	no	—
84	C₂×C₄₃⋊C₈	—	4	4	no	—
85	C₂×C₄₃⋊C₈	—	4	2	no	—
86	Dic₁₇₂	—	2	4	no	—
87	Dic₁₇₂	—	4	2	no	—
88	C₁₆×C₄₃	—	4	2	no	—
89	C₂³×C₄₃	—	2	1	no	—
90	C₂³×C₄₃	—	2	1	no	—
91	C₂³×C₄₃	—	4	2	no	—
92	C₂³×C₄₃	#102	1	2	yes	—
93	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
94	C₂×C₄×C₄₃	—	2	1	no	—
95	C₂×C₄×C₄₃	—	2	1	no	—
96	C₂×C₄×C₄₃	—	2	2	no	—
97	C₂×C₄×C₄₃	—	2	2	no	—
98	C₂×C₄×C₄₃	—	2	2	no	—
99	C₂×C₄×C₄₃	—	2	2	no	—
100	C₂×C₄×C₄₃	#102	1	2	yes	—
101	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
103	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
104	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
106	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
107	C₂×Dic₄₃	—	4	2	no	—
108	C₂×Dic₄₃	—	4	2	no	—
109	C₂×Dic₄₃	—	8	2	no	—
110	C₂×Dic₄₃	—	8	1	no	—
111	C₂×Dic₄₃	—	8	1	no	—
112	Dic₈₆	—	4	2	no	—
113	Dic₈₆	—	4	2	no	—
114	Dic₈₆	—	8	1	no	—
115	Dic₈₆	—	8	1	no	—
116	C₈×C₄₃	—	2	2	no	—
117	C₈×C₄₃	C₄×D₄	1	2	yes	—
118	C₈×C₄₃	#121	1	2	yes	—
119	C₄₃⋊C₈	—	4	4	no	—
120	#13009	—	43	1	no	maximal, Sylow
121	C₂²×C₄₃	—	2	2	no	—
122	C₂²×C₄₃	—	2	2	no	—
123	C₂²×C₄₃	—	4	2	no	—
124	C₂²×C₄₃	—	4	2	no	—
125	C₂²×C₄₃	—	8	1	no	—
126	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
127	C₂²×C₄₃	#448	1	1	yes	characteristic
128	C₂²×C₄₃	#481	1	1	yes	characteristic
129	C₄×C₄₃	—	2	2	no	—
130	C₄×C₄₃	#386	1	1	yes	characteristic
131	C₄×C₄₃	#417	1	1	yes	characteristic
132	C₄×C₄₃	#447	1	1	yes	characteristic
133	C₄×C₄₃	#480	1	1	yes	characteristic
134	Dic₄₃	—	8	2	no	—
135	Dic₄₃	—	8	2	no	—
136	C₂×#470	—	43	1	no	—
137	C₂×#430	—	43	1	no	—
138	C₂×#362	—	43	2	no	—
139	C₂×#349	D₄₃	1	1	yes	characteristic
140	#1383	—	43	2	no	—
141	C₂×C₄₃	—	2	1	no	—
142	C₂×C₄₃	—	2	1	no	—
143	C₂×C₄₃	—	4	2	no	—
144	C₂×C₄₃	#1874	1	1	yes	characteristic
145	C₂×C₄₃	#2239	1	2	yes	—
146	C₂²×Q₁₆	—	43	1	no	—
147	C₂²×M₁₆	—	86	1	no	—
148	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
149	C₂×C₂²⋊Q₈	—	86	1	no	—
150	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
151	#470	—	43	4	no	—
152	#470	—	86	2	no	—
153	#430	—	86	4	no	—
154	C₂×#108	—	43	2	no	—
155	C₂×#108	—	86	1	no	—
156	C₂×#106	—	43	1	no	—
157	C₂×#103	—	86	1	no	—
158	#362	—	86	4	no	—
159	#349	—	2	2	no	—
160	C₄₃	#13009	1	1	yes	characteristic, complemented, Sylow
161	C₂²×Q₈	—	86	1	no	—
162	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
163	C₂×Q₁₆	—	43	2	no	—
164	C₂×Q₁₆	—	86	2	no	—
165	C₂×Q₁₆	—	86	2	no	—
166	C₂×Q₁₆	—	86	1	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	—	86	4	no	—
170	C₂×M₁₆	—	86	2	no	—
171	C₂×M₁₆	—	172	1	no	—
172	C₂×M₁₆	—	172	2	no	—
173	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
174	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
175	C₂²×C₈	—	172	1	no	—
176	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
177	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
178	C₂²⋊Q₈	—	86	4	no	—
179	C₂²⋊Q₈	—	172	2	no	—
180	C₂×C₄⋊C₄	—	86	1	no	—
181	C₂×C₄⋊C₄	—	172	1	no	—
182	C₂×C₂²⋊C₄	—	172	1	no	—
183	M₃₂	—	2	2	no	—
184	M₃₂	—	2	2	no	—
185	C₂×C₁₆	—	2	2	no	—
186	#108	—	43	4	no	—
187	#108	—	86	4	no	—
188	#108	—	86	2	no	—
189	#106	—	43	2	no	—
190	#106	—	86	1	no	—
191	#103	—	86	4	no	—
192	C₂⁴	#10621873	1	1	yes	characteristic
193	C₂×Q₈	—	86	2	no	—
194	C₂×Q₈	—	172	1	no	—
195	C₂×Q₈	—	172	1	no	—
196	C₂×Q₈	—	172	1	no	—
197	C₂×Q₈	—	172	1	no	—
198	C₂×Q₈	—	172	1	no	—
199	C₂²×C₄	—	2	1	no	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	172	1	no	—
204	C₂²×C₄	—	172	1	no	—
205	C₂²×C₄	#10621873	1	1	yes	characteristic
206	C₂²×C₄	D₃₄₄	1	2	yes	—
207	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
208	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
209	Q₁₆	—	86	4	no	—
210	Q₁₆	—	172	2	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	2	4	no	—
213	M₁₆	—	86	4	no	—
214	M₁₆	—	172	4	no	—
215	M₁₆	—	172	2	no	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	172	4	no	—
219	C₂×C₈	—	172	2	no	—
220	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
221	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
222	C₂×C₈	D₄×D₄₃	1	2	yes	—
223	C₂×C₈	#10621900	1	2	yes	—
224	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
225	C₄⋊C₄	—	86	2	no	—
226	C₄⋊C₄	—	172	4	no	—
227	C₄⋊C₄	—	172	1	no	—
228	C₂²⋊C₄	—	172	4	no	—
229	C₁₆	—	4	2	no	—
230	C₂³	—	2	1	no	—
231	C₂³	—	2	1	no	—
232	C₂³	—	4	2	no	—
233	C₂³	#13063247	1	2	yes	—
234	C₂³	C₂×#10621873	1	1	yes	characteristic
235	Q₈	—	344	1	no	—
236	Q₈	—	344	1	no	—
237	Q₈	—	172	2	no	—
238	Q₈	—	172	2	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	344	2	no	—
246	C₂×C₄	—	344	1	no	—
247	C₂×C₄	—	344	1	no	—
248	C₂×C₄	—	172	2	no	—
249	C₂×C₄	—	172	2	no	—
250	C₂×C₄	#13063247	1	2	yes	—
251	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
252	C₂×C₄	#13063295	1	1	yes	characteristic
253	C₂×C₄	#13063309	1	1	yes	characteristic
254	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
255	C₂×C₄	#13063353	1	1	yes	characteristic
256	C₂×C₄	#13063358	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	172	4	no	—
259	C₈	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
260	C₈	#13063297	1	2	yes	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	4	2	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	8	1	no	—
266	C₂²	C₂×#13063247	1	1	yes	characteristic
267	C₂²	#14583040	1	1	yes	characteristic
268	C₂²	#14583218	1	1	yes	characteristic
269	C₄	—	2	2	no	—
270	C₄	—	344	2	no	—
271	C₄	—	344	2	no	—
272	C₄	#14582776	1	1	yes	characteristic
273	C₄	#14582901	1	1	yes	characteristic
274	C₄	#14583035	1	1	yes	characteristic
275	C₄	#14583213	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	4	2	no	—
279	C₂	#19134910	1	1	yes	characteristic
280	C₂	#19136815	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583157

C₂

yes

maximal, characteristic

C₂×#14582948

C₂

yes

maximal, characteristic

C₂×#14582716

C₂

yes

maximal, complemented

#19132694

C₂

yes

maximal, complemented

C₂×C₄₃×#349

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₂²

yes

—

—

—

C₄

yes

—

#14582948

—

C₂×#13063261

—

C₂×#13063261

C₂²

yes

—

C₂×#13063257

C₂²

yes

characteristic

C₂×#13063250

—

#14582716

—

C₂²×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₃₂×C₄₃

C₂²

yes

—

C₄₃×#349

—

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

—

—

—

—

C₂²×C₄₃⋊C₈

—

#13063304

—

#13063304

—

C₂×C₄⋊Dic₄₃

—

C₂×Dic₄₃⋊C₄

—

C₂×C₂²⋊Dic₄₃

—

#13063261

—

#13063261

—

#13063261

D₄

yes

—

#13063257

—

#13063257

C₂×C₄

yes

—

#13063250

—

C₂³×C₄×C₄₃

D₄

yes

characteristic

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

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂⁴×C₄₃

SD₁₆

yes

characteristic

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

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

—

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

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

#10621877

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#102

yes

—

C₂³×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

100

C₂×C₄×C₄₃

#102

yes

—

101

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

102

C₂×C₄×C₄₃

#120

yes

characteristic

103

C₂×C₄×C₄₃

#123

yes

characteristic

104

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

105

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

106

C₂×C₄×C₄₃

#137

yes

characteristic

107

C₂×Dic₄₃

—

108

C₂×Dic₄₃

—

109

C₂×Dic₄₃

—

110

C₂×Dic₄₃

—

111

C₂×Dic₄₃

—

112

Dic₈₆

—

113

Dic₈₆

—

114

Dic₈₆

—

115

Dic₈₆

—

116

C₈×C₄₃

—

117

C₈×C₄₃

C₄×D₄

yes

—

118

C₈×C₄₃

#121

yes

—

119

C₄₃⋊C₈

—

120

#13009

—

maximal, Sylow

121

C₂²×C₄₃

—

122

C₂²×C₄₃

—

123

C₂²×C₄₃

—

124

C₂²×C₄₃

—

125

C₂²×C₄₃

—

126

C₂²×C₄₃

C₂×#102

yes

characteristic

127

C₂²×C₄₃

#448

yes

characteristic

128

C₂²×C₄₃

#481

yes

characteristic

129

C₄×C₄₃

—

130

C₄×C₄₃

#386

yes

characteristic

131

C₄×C₄₃

#417

yes

characteristic

132

C₄×C₄₃

#447

yes

characteristic

133

C₄×C₄₃

#480

yes

characteristic

134

Dic₄₃

—

135

Dic₄₃

—

136

C₂×#470

—

137

C₂×#430

—

138

C₂×#362

—

139

C₂×#349

D₄₃

yes

characteristic

140

#1383

—

141

C₂×C₄₃

—

142

C₂×C₄₃

—

143

C₂×C₄₃

—

144

C₂×C₄₃

#1874

yes

characteristic

145

C₂×C₄₃

#2239

yes

—

146

C₂²×Q₁₆

—

147

C₂²×M₁₆

—

148

C₂²×M₁₆

C₂×D₄₃

yes

characteristic

149

C₂×C₂²⋊Q₈

—

150

C₂×M₃₂

C₂×D₄₃

yes

—

151

#470

—

152

#470

—

153

#430

—

154

C₂×#108

—

155

C₂×#108

—

156

C₂×#106

—

157

C₂×#103

—

158

#362

—

159

#349

—

160

C₄₃

#13009

yes

characteristic, complemented, Sylow

161

C₂²×Q₈

—

162

C₂³×C₄

D₁₇₂

yes

characteristic

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₂×M₁₆

—

170

C₂×M₁₆

—

171

C₂×M₁₆

—

172

—

172

C₂×M₁₆

—

172

—

173

C₂×M₁₆

C₄×D₄₃

yes

—

174

C₂×M₁₆

C₂²⋊D₄₃

yes

—

175

C₂²×C₈

—

172

—

176

C₂²×C₈

D₁₇₂

yes

characteristic

177

C₂²×C₈

C₂²×D₄₃

yes

characteristic

178

C₂²⋊Q₈

—

179

C₂²⋊Q₈

—

172

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

—

172

—

182

C₂×C₂²⋊C₄

—

172

—

183

M₃₂

—

184

M₃₂

—

185

C₂×C₁₆

—

186

#108

—

187

#108

—

188

#108

—

189

#106

—

190

#106

—

191

#103

—

192

C₂⁴

#10621873

yes

characteristic

193

C₂×Q₈

—

194

C₂×Q₈

—

172

—

195

C₂×Q₈

—

172

—

196

C₂×Q₈

—

172

—

197

C₂×Q₈

—

172

—

198

C₂×Q₈

—

172

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

172

—

204

C₂²×C₄

—

172

—

205

C₂²×C₄

#10621873

yes

characteristic

206

C₂²×C₄

D₃₄₄

yes

—

207

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

—

208

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

209

Q₁₆

—

210

Q₁₆

—

172

—

211

M₁₆

—

212

M₁₆

—

213

M₁₆

—

214

M₁₆

—

172

—

215

M₁₆

—

172

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

172

—

219

C₂×C₈

—

172

—

220

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

221

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

222

C₂×C₈

D₄×D₄₃

yes

—

223

C₂×C₈

#10621900

yes

—

224

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

225

C₄⋊C₄

—

226

C₄⋊C₄

—

172

—

227

C₄⋊C₄

—

172

—

228

C₂²⋊C₄

—

172

—

229

C₁₆

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

#13063247

yes

—

234

C₂³

C₂×#10621873

yes

characteristic

235

Q₈

—

344

—

236

Q₈

—

344

—

237

Q₈

—

172

—

238

Q₈

—

172

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

344

—

246

C₂×C₄

—

344

—

247

C₂×C₄

—

344

—

248

C₂×C₄

—

172

—

249

C₂×C₄

—

172

—

250

C₂×C₄

#13063247

yes

—

251

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

252

C₂×C₄

#13063295

yes

characteristic

253

C₂×C₄

#13063309

yes

characteristic

254

C₂×C₄

C₂×D₃₄₄

yes

characteristic

255

C₂×C₄

#13063353

yes

characteristic

256

C₂×C₄

#13063358

yes

characteristic

257

C₈

—

258

C₈

—

172

—

259

C₈

(C₂²⋊D₄₃)⋊C₄

yes

—

260

C₈

#13063297

yes

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

C₂×#13063247

yes

characteristic

267

C₂²

#14583040

yes

characteristic

268

C₂²

#14583218

yes

characteristic

269

C₄

—

270

C₄

—

344

—

271

C₄

—

344

—

272

C₄

#14582776

yes

characteristic

273

C₄

#14582901

yes

characteristic

274

C₄

#14583035

yes

characteristic

275

C₄

#14583213

yes

characteristic

276

C₂

—

277

C₂

—

278

C₂

—

279

C₂

#19134910

yes

characteristic

280

C₂

#19136815

yes

—

	subgroup	G/H
center	C₂²	#14583218
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#349	C₂
socle	C₂²×C₄₃	#481
prime radical	C₂⁴×C₄₃	SD₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#349	D₄₃
hypocenter	C₄₃	#13009
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#349

subgroup

G/H

center

C₂²

#14583218

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#349

C₂

socle

C₂²×C₄₃

#481

prime radical

C₂⁴×C₄₃

SD₁₆

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#349

N	H ≅ G/N	type
3. C₂×#14582716	C₂	semidirect
4. #19132694	C₂	semidirect
160. C₄₃	#13009	semidirect

H ≅ G/N

type

3. C₂×#14582716

C₂

semidirect

4. #19132694

C₂

semidirect

160. C₄₃

#13009

semidirect

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

subgroup	index
C₂×#14583157	2
C₂×#14582948	2
C₂×#14582716	2
#19132694	2
C₂×C₄₃×#349	2
#13009	43

subgroup

index

C₂×C₄₃×#349

Subgroups — #25013635

Conjugacy classes of subgroups

Complements

Maximal subgroups