Group #24989523 — subgroups

Subgroups — #24989523

Order 11008.

486 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 137 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×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#19134587	C₂	1	1	yes	maximal, characteristic
3	#19133353	C₂	1	2	yes	maximal, complemented
4	#19132469	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1800	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₃⋊C₈	C₄	1	2	yes	—
7	D₄×C₄₃⋊C₈	—	2	2	no	—
8	D₄×C₄₃⋊C₈	—	2	2	no	—
9	#14582923	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#13063242	—	2	1	no	—
12	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582668	—	2	1	no	—
15	#14582651	—	2	2	no	—
16	#14582651	—	2	2	no	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#423	C₂²	1	2	yes	—
19	C₂×#100×C₄₃	—	2	1	no	—
20	C₄₃×#343	—	2	1	no	—
21	C₂×#10621877	—	2	2	no	—
22	C₂²×C₄₃⋊C₈	—	2	2	no	—
23	C₂²×C₄₃⋊C₈	—	2	2	no	—
24	C₂²×C₄₃⋊C₈	—	4	4	no	—
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
27	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
29	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
31	#13063242	—	4	2	no	—
32	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
33	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
34	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
35	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₄₃	—	2	2	no	—
38	C₄×D₄×C₄₃	—	2	2	no	—
39	C₄×D₄×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₄₃	Q₈	1	2	yes	—
42	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₃	—	2	2	no	—
44	C₄⋊C₈×C₄₃	—	2	2	no	—
45	#100×C₄₃	—	4	2	no	—
46	C₂⁴×C₄₃	C₄⋊C₄	1	2	yes	—
47	C₂×D₄×C₄₃	—	2	2	no	—
48	C₂×D₄×C₄₃	—	2	2	no	—
49	C₂×D₄×C₄₃	D₈	1	2	yes	—
50	C₂×D₄×C₄₃	Q₁₆	1	2	yes	—
51	C₂²×C₄×C₄₃	—	2	2	no	—
52	C₂²×C₄×C₄₃	—	2	2	no	—
53	C₂²×C₄×C₄₃	—	4	2	no	—
54	C₂²×C₄×C₄₃	—	4	2	no	—
55	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
59	M₁₆×C₄₃	—	4	2	no	—
60	M₁₆×C₄₃	—	4	2	no	—
61	C₂×C₈×C₄₃	—	4	2	no	—
62	C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂²⋊C₄×C₄₃	—	2	4	no	—
64	C₄²×C₄₃	C₂×D₄	1	2	yes	—
65	C₄²×C₄₃	#41	1	2	yes	—
66	#10621877	—	4	2	no	—
67	#10621877	—	4	2	no	—
68	C₂×C₄₃⋊C₈	—	2	2	no	—
69	C₂×C₄₃⋊C₈	—	2	2	no	—
70	C₂×C₄₃⋊C₈	—	4	1	no	—
71	C₂×C₄₃⋊C₈	—	4	4	no	—
72	C₂×C₄₃⋊C₈	—	4	4	no	—
73	C₂×C₄₃⋊C₈	—	4	2	no	—
74	C₂×C₄₃⋊C₈	—	4	2	no	—
75	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
76	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
78	C₂³×C₄₃	—	2	2	no	—
79	C₂³×C₄₃	—	2	2	no	—
80	C₂³×C₄₃	—	4	2	no	—
81	C₂³×C₄₃	—	4	2	no	—
82	C₂³×C₄₃	#107	1	4	yes	—
83	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	D₄×C₄₃	—	2	4	no	—
85	D₄×C₄₃	—	2	4	no	—
86	C₂×C₄×C₄₃	—	2	1	no	—
87	C₂×C₄×C₄₃	—	2	1	no	—
88	C₂×C₄×C₄₃	—	2	2	no	—
89	C₂×C₄×C₄₃	—	4	1	no	—
90	C₂×C₄×C₄₃	—	4	4	no	—
91	C₂×C₄×C₄₃	—	4	2	no	—
92	C₂×C₄×C₄₃	—	4	2	no	—
93	C₂×C₄×C₄₃	—	4	2	no	—
94	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
96	C₂×C₄×C₄₃	#121	1	2	yes	—
97	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
100	C₂×C₄×C₄₃	#135	1	2	yes	—
101	C₈×C₄₃	—	8	2	no	—
102	C₄₃⋊C₈	—	2	1	no	—
103	C₄₃⋊C₈	—	2	2	no	—
104	C₄₃⋊C₈	—	4	2	no	—
105	C₄₃⋊C₈	—	8	2	no	—
106	C₄₃⋊C₈	#100	1	2	yes	complemented
107	#8616	—	43	1	no	maximal, Sylow
108	C₂²×C₄₃	—	2	1	no	—
109	C₂²×C₄₃	—	2	1	no	—
110	C₂²×C₄₃	—	2	4	no	—
111	C₂²×C₄₃	—	4	4	no	—
112	C₂²×C₄₃	—	4	4	no	—
113	C₂²×C₄₃	—	4	2	no	—
114	C₂²×C₄₃	—	4	2	no	—
115	C₂²×C₄₃	#380	1	1	yes	characteristic
116	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
117	C₂²×C₄₃	#427	1	1	yes	characteristic
118	C₄×C₄₃	—	2	1	no	—
119	C₄×C₄₃	—	2	2	no	—
120	C₄×C₄₃	—	4	2	no	—
121	C₄×C₄₃	C₂×#100	1	1	yes	characteristic
122	C₄×C₄₃	#413	1	1	yes	characteristic
123	C₄×C₄₃	#466	1	2	yes	—
124	C₄×C₄₃	#467	1	2	yes	—
125	C₂×C₈×D₄	—	43	1	no	—
126	#1800	—	43	1	no	—
127	#1800	D₄₃	1	1	yes	characteristic
128	#1567	—	43	2	no	—
129	#1292	—	43	2	no	—
130	C₂×C₄₃	—	2	1	no	—
131	C₂×C₄₃	—	2	1	no	—
132	C₂×C₄₃	—	4	4	no	—
133	C₂×C₄₃	#1800	1	1	yes	characteristic
134	C₂×C₄₃	#1808	1	1	yes	characteristic
135	C₂×C₄₃	#1813	1	1	yes	characteristic
136	C₂³×C₈	—	43	2	no	—
137	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
138	C₈×D₄	—	86	2	no	—
139	C₈×D₄	—	86	2	no	—
140	#423	—	43	2	no	—
141	#423	C₂×D₄₃	1	2	yes	—
142	C₂×C₄⋊C₈	—	43	1	no	—
143	C₂×#100	—	2	1	no	—
144	C₂×#100	—	86	1	no	—
145	C₂×C₂²⋊C₈	—	43	2	no	—
146	C₂×C₄×C₈	—	43	1	no	—
147	#343	—	2	1	no	—
148	#343	—	86	1	no	—
149	#335	—	86	2	no	—
150	#335	—	86	2	no	—
151	C₄₃	#8616	1	1	yes	characteristic, complemented, Sylow
152	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
153	C₂³×C₄	C₄×D₄₃	1	2	yes	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	86	2	no	—
156	C₂²×C₈	—	43	1	no	—
157	C₂²×C₈	—	43	1	no	—
158	C₂²×C₈	—	43	2	no	—
159	C₂²×C₈	—	86	2	no	—
160	C₂²×C₈	—	86	2	no	—
161	C₂²×C₈	—	172	4	no	—
162	C₄×D₄	—	2	2	no	—
163	C₄×D₄	—	2	2	no	—
164	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	Dic₈₆	1	2	yes	—
166	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	86	2	no	—
170	C₄⋊C₈	—	86	2	no	—
171	C₄⋊C₈	—	86	2	no	—
172	#100	—	4	2	no	—
173	#100	—	172	2	no	—
174	C₂²⋊C₈	—	86	4	no	—
175	C₄×C₈	—	43	2	no	—
176	C₄×C₈	—	43	2	no	—
177	C₂⁴	Dic₄₃⋊C₄	1	2	yes	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	#10621882	1	2	yes	—
181	C₂×D₄	#10621885	1	2	yes	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
187	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
190	M₁₆	—	4	2	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	172	2	no	—
193	M₁₆	—	172	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	43	1	no	—
196	C₂×C₈	—	43	2	no	—
197	C₂×C₈	—	43	1	no	—
198	C₂×C₈	—	86	2	no	—
199	C₂×C₈	—	86	2	no	—
200	C₂×C₈	—	172	4	no	—
201	C₂×C₈	—	172	1	no	—
202	C₂×C₈	—	172	4	no	—
203	C₂×C₈	—	172	2	no	—
204	C₂×C₈	—	172	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₂²⋊C₄	—	2	4	no	—
207	C₄²	D₄×D₄₃	1	2	yes	—
208	C₄²	#10621900	1	2	yes	—
209	C₂³	—	2	2	no	—
210	C₂³	—	2	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	—	4	2	no	—
213	C₂³	#13063258	1	4	yes	—
214	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
226	C₂×C₄	#13063281	1	1	yes	characteristic
227	C₂×C₄	#13063297	1	2	yes	—
228	C₂×C₄	#13063302	1	2	yes	—
229	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
230	C₂×C₄	C₂×#10621885	1	1	yes	characteristic
231	C₂×C₄	#13063345	1	2	yes	—
232	C₈	—	8	2	no	—
233	C₈	—	43	2	no	—
234	C₈	—	86	1	no	—
235	C₈	—	86	2	no	—
236	C₈	—	344	2	no	—
237	C₈	—	172	2	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	4	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	4	4	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	#14582757	1	1	yes	characteristic
246	C₂²	C₂×#13063258	1	1	yes	characteristic
247	C₂²	#14582935	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	2	2	no	—
250	C₄	—	4	2	no	—
251	C₄	#100×D₄₃	1	1	yes	characteristic
252	C₄	#14582880	1	1	yes	characteristic
253	C₄	#14583133	1	2	yes	—
254	C₄	#14583138	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	#19134585	1	1	yes	characteristic
259	C₂	#19134622	1	1	yes	characteristic
260	C₂	#19134643	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

#19134587

C₂

yes

maximal, characteristic

#19133353

C₂

yes

maximal, complemented

#19132469

C₂

yes

maximal, complemented

C₄₃×#1800

C₂

yes

maximal, characteristic

C₂³×C₄₃⋊C₈

C₄

yes

—

D₄×C₄₃⋊C₈

—

D₄×C₄₃⋊C₈

—

#14582923

C₂²

yes

—

C₂×C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂×#13063242

—

C₂×C₂²⋊(C₄₃⋊C₈)

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

—

—

C₂×C₄×D₄×C₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#100×C₄₃

—

C₄₃×#343

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

—

#13063242

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂²×D₄×C₄₃

D₄

yes

characteristic

C₂³×C₄×C₄₃

C₂×C₄

yes

—

C₂×M₁₆×C₄₃

—

C₄×D₄×C₄₃

—

C₄×D₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

Q₈

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

—

#100×C₄₃

—

C₂⁴×C₄₃

C₄⋊C₄

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₈

yes

—

C₂×D₄×C₄₃

Q₁₆

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#107

yes

—

C₂³×C₄₃

C₂×C₄⋊C₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

100

C₂×C₄×C₄₃

#135

yes

—

101

C₈×C₄₃

—

102

C₄₃⋊C₈

—

103

C₄₃⋊C₈

—

104

C₄₃⋊C₈

—

105

C₄₃⋊C₈

—

106

C₄₃⋊C₈

yes

107

—

108

C₂²×C₄₃

—

109

C₂²×C₄₃

—

110

C₂²×C₄₃

—

111

C₂²×C₄₃

—

112

C₂²×C₄₃

—

113

C₂²×C₄₃

—

114

C₂²×C₄₃

—

115

C₂²×C₄₃

#380

yes

characteristic

116

C₂²×C₄₃

C₂×#107

yes

characteristic

117

C₂²×C₄₃

#427

yes

characteristic

118

C₄×C₄₃

—

119

C₄×C₄₃

—

120

C₄×C₄₃

—

121

C₄×C₄₃

C₂×#100

yes

characteristic

122

C₄×C₄₃

#413

yes

characteristic

123

C₄×C₄₃

#466

yes

—

124

C₄×C₄₃

#467

yes

—

125

C₂×C₈×D₄

—

126

#1800

—

127

#1800

D₄₃

yes

characteristic

128

#1567

—

129

#1292

—

130

C₂×C₄₃

—

131

C₂×C₄₃

—

132

C₂×C₄₃

—

133

C₂×C₄₃

#1800

yes

characteristic

134

C₂×C₄₃

#1808

yes

characteristic

135

C₂×C₄₃

#1813

yes

characteristic

136

C₂³×C₈

—

137

C₂×C₄×D₄

C₂×D₄₃

yes

characteristic

138

C₈×D₄

—

139

C₈×D₄

—

140

#423

—

141

#423

C₂×D₄₃

yes

—

142

C₂×C₄⋊C₈

—

143

C₂×#100

—

144

C₂×#100

—

145

C₂×C₂²⋊C₈

—

146

C₂×C₄×C₈

—

147

#343

—

148

#343

—

149

#335

—

150

#335

—

151

C₄₃

#8616

yes

characteristic, complemented, Sylow

152

C₂²×D₄

C₂²⋊D₄₃

yes

characteristic

153

C₂³×C₄

C₄×D₄₃

yes

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

—

172

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

characteristic

165

C₂×C₂²⋊C₄

Dic₈₆

yes

—

166

C₂×C₄²

C₂²×D₄₃

yes

characteristic

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

#100

—

173

#100

—

172

—

174

C₂²⋊C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₂⁴

Dic₄₃⋊C₄

yes

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

#10621882

yes

—

181

C₂×D₄

#10621885

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

Dic₄₃⋊C₄

yes

—

187

C₂²×C₄

C₂×Dic₈₆

yes

characteristic

188

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

189

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

172

—

193

M₁₆

—

172

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

172

—

201

C₂×C₈

—

172

—

202

C₂×C₈

—

172

—

203

C₂×C₈

—

172

—

204

C₂×C₈

—

172

—

205

C₄⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

D₄×D₄₃

yes

—

208

C₄²

#10621900

yes

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

#13063258

yes

—

214

C₂³

C₂×Dic₄₃⋊C₄

yes

characteristic

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

C₂²⋊C₄×D₄₃

yes

characteristic

226

C₂×C₄

#13063281

yes

characteristic

227

C₂×C₄

#13063297

yes

—

228

C₂×C₄

#13063302

yes

—

229

C₂×C₄

C₂×#10621882

yes

characteristic

230

C₂×C₄

C₂×#10621885

yes

characteristic

231

C₂×C₄

#13063345

yes

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

344

—

237

C₈

—

172

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#14582757

yes

characteristic

246

C₂²

C₂×#13063258

yes

characteristic

247

C₂²

#14582935

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

#100×D₄₃

yes

characteristic

252

C₄

#14582880

yes

characteristic

253

C₄

#14583133

yes

—

254

C₄

#14583138

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

#19134585

yes

characteristic

259

C₂

#19134622

yes

characteristic

260

C₂

#19134643

yes

characteristic

	subgroup	G/H
center	C₂²	#14582757
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1800	C₂
socle	C₂²×C₄₃	#380
prime radical	C₂²×D₄×C₄₃	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1800	D₄₃
hypocenter	C₄₃	#8616
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#14582757

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1800

C₂

socle

C₂²×C₄₃

#380

prime radical

C₂²×D₄×C₄₃

D₄

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

N	H ≅ G/N	type
3. #19133353	C₂	semidirect
4. #19132469	C₂	semidirect
106. C₄₃⋊C₈	#100	semidirect
151. C₄₃	#8616	semidirect

H ≅ G/N

type

3. #19133353

C₂

semidirect

4. #19132469

C₂

semidirect

106. C₄₃⋊C₈

#100

semidirect

151. C₄₃

#8616

semidirect

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

subgroup	index
C₂×D₄×C₄₃⋊C₈	2
#19134587	2
#19133353	2
#19132469	2
C₄₃×#1800	2
#8616	43

subgroup

index

C₂×D₄×C₄₃⋊C₈

C₄₃×#1800

Subgroups — #24989523

Conjugacy classes of subgroups

Complements

Maximal subgroups