Group #24928359 — subgroups

Subgroups — C₄₃×#8342 #24928359

Order 11008.

1030 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 238 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	C₂²×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1797	C₂	1	2	yes	maximal
3	C₂×C₄₃×#333	C₂	1	4	yes	maximal, complemented
4	C₂³×Q₈×C₄₃	C₄	1	2	yes	—
5	C₂×C₄⋊Q₈×C₄₃	—	2	8	no	—
6	C₂×C₄⋊Q₈×C₄₃	—	2	2	no	—
7	C₂×C₄⋊Q₈×C₄₃	C₄	1	2	yes	—
8	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₃	—	2	2	no	—
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
12	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
13	C₄₃×#336	—	2	2	no	—
14	C₄₃×#333	—	2	8	no	—
15	C₂²×Q₈×C₄₃	—	2	8	no	—
16	C₂²×Q₈×C₄₃	—	2	2	no	—
17	C₂²×Q₈×C₄₃	—	4	4	no	—
18	C₂²×Q₈×C₄₃	—	4	4	no	—
19	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₄₃	—	2	2	no	—
21	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₄₃	D₄	1	2	yes	—
23	C₂²×C₈×C₄₃	—	2	4	no	—
24	C₄⋊Q₈×C₄₃	—	2	16	no	—
25	C₄⋊Q₈×C₄₃	—	2	8	no	—
26	C₄⋊Q₈×C₄₃	—	2	4	no	—
27	C₄⋊Q₈×C₄₃	D₄	1	8	yes	—
28	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
29	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
31	C₂×C₄²×C₄₃	—	2	4	no	—
32	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₄₃	D₄	1	2	yes	—
34	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
35	C₄⋊C₈×C₄₃	—	2	8	no	—
36	C₂²⋊C₈×C₄₃	—	4	4	no	—
37	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Q₈×C₄₃	—	2	8	no	—
39	C₂×Q₈×C₄₃	—	2	4	no	—
40	C₂×Q₈×C₄₃	—	4	32	no	—
41	C₂×Q₈×C₄₃	—	4	4	no	—
42	C₂×Q₈×C₄₃	—	4	4	no	—
43	C₂×Q₈×C₄₃	—	4	4	no	—
44	C₂×Q₈×C₄₃	—	4	4	no	—
45	C₂×Q₈×C₄₃	C₂²⋊C₄	1	8	yes	—
46	C₂²×C₄×C₄₃	—	2	2	no	—
47	C₂²×C₄×C₄₃	—	2	2	no	—
48	C₂²×C₄×C₄₃	—	2	4	no	—
49	C₂²×C₄×C₄₃	—	2	4	no	—
50	C₂²×C₄×C₄₃	—	2	8	no	—
51	C₂²×C₄×C₄₃	—	2	2	no	—
52	C₂²×C₄×C₄₃	—	2	4	no	—
53	C₂²×C₄×C₄₃	—	4	4	no	—
54	C₂²×C₄×C₄₃	—	4	4	no	—
55	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
58	C₂²×C₄×C₄₃	Q₁₆	1	4	yes	—
59	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₄₃	—	4	4	no	—
62	C₂×C₈×C₄₃	—	4	4	no	—
63	C₂×C₈×C₄₃	—	4	4	no	—
64	C₄⋊C₄×C₄₃	—	2	16	no	—
65	C₄⋊C₄×C₄₃	—	2	16	no	—
66	C₄²×C₄₃	—	2	2	no	—
67	C₄²×C₄₃	—	2	4	no	—
68	C₄²×C₄₃	C₂×D₄	1	4	yes	—
69	C₂³×C₄₃	—	2	1	no	—
70	C₂³×C₄₃	—	2	1	no	—
71	C₂³×C₄₃	—	2	2	no	—
72	C₂³×C₄₃	#100	1	2	yes	—
73	C₂³×C₄₃	#103	1	4	yes	—
74	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₄₃	—	4	8	no	—
76	Q₈×C₄₃	—	4	16	no	—
77	Q₈×C₄₃	—	4	8	no	—
78	C₂×C₄×C₄₃	—	2	8	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	1	no	—
81	C₂×C₄×C₄₃	—	2	1	no	—
82	C₂×C₄×C₄₃	—	2	1	no	—
83	C₂×C₄×C₄₃	—	2	1	no	—
84	C₂×C₄×C₄₃	—	2	2	no	—
85	C₂×C₄×C₄₃	—	2	8	no	—
86	C₂×C₄×C₄₃	—	2	8	no	—
87	C₂×C₄×C₄₃	—	2	8	no	—
88	C₂×C₄×C₄₃	—	4	16	no	—
89	C₂×C₄×C₄₃	—	4	4	no	—
90	C₂×C₄×C₄₃	—	4	4	no	—
91	C₂×C₄×C₄₃	#100	1	2	yes	—
92	C₂×C₄×C₄₃	#103	1	4	yes	—
93	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
94	C₂×C₄×C₄₃	#120	1	4	yes	—
95	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
96	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
97	C₂×C₄×C₄₃	#137	1	4	yes	—
98	C₈×C₄₃	—	8	4	no	—
99	#8342	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂²×C₄₃	—	2	4	no	—
101	C₂²×C₄₃	—	2	2	no	—
102	C₂²×C₄₃	—	2	2	no	—
103	C₂²×C₄₃	—	2	4	no	—
104	C₂²×C₄₃	#333	1	4	yes	complemented
105	C₂²×C₄₃	#379	1	1	yes	characteristic
106	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
107	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
108	C₂²×C₄₃	C₂×#103	1	2	yes	—
109	C₂²×C₄₃	#419	1	2	yes	—
110	C₄×C₄₃	—	2	2	no	—
111	C₄×C₄₃	—	2	2	no	—
112	C₄×C₄₃	—	2	4	no	—
113	C₄×C₄₃	—	4	8	no	—
114	C₄×C₄₃	#448	1	4	yes	—
115	C₄×C₄₃	#451	1	4	yes	—
116	C₂²×C₄⋊Q₈	C₂×C₄₃	1	1	yes	characteristic
117	#1797	C₂×C₄₃	1	2	yes	—
118	C₂×#333	C₂×C₄₃	1	4	yes	complemented
119	C₂×C₄₃	—	2	4	no	—
120	C₂×C₄₃	C₂×#333	1	1	yes	characteristic
121	C₂×C₄₃	#1548	1	2	yes	—
122	C₂×C₄₃	#1558	1	1	yes	characteristic
123	C₂×C₄₃	#1783	1	1	yes	characteristic
124	C₂×C₄₃	#1787	1	2	yes	—
125	C₂³×Q₈	C₄×C₄₃	1	2	yes	—
126	C₂×C₄⋊Q₈	—	2	8	no	—
127	C₂×C₄⋊Q₈	—	2	2	no	—
128	C₂×C₄⋊Q₈	C₄×C₄₃	1	2	yes	—
129	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
130	C₂²×C₄⋊C₄	—	2	2	no	—
131	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
132	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
133	C₂×C₂²⋊C₈	—	2	2	no	—
134	#336	—	2	2	no	—
135	#333	—	2	8	no	—
136	C₄₃	#8342	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²×Q₈	—	2	8	no	—
138	C₂²×Q₈	—	2	2	no	—
139	C₂²×Q₈	—	4	4	no	—
140	C₂²×Q₈	—	4	4	no	—
141	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
142	C₂³×C₄	—	2	2	no	—
143	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
144	C₂³×C₄	D₄×C₄₃	1	2	yes	—
145	C₂²×C₈	—	2	4	no	—
146	C₄⋊Q₈	—	2	16	no	—
147	C₄⋊Q₈	—	2	8	no	—
148	C₄⋊Q₈	—	2	4	no	—
149	C₄⋊Q₈	D₄×C₄₃	1	8	yes	—
150	C₂×C₄⋊C₄	—	2	16	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄⋊C₄	—	2	4	no	—
153	C₂×C₄²	—	2	4	no	—
154	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
155	C₂×C₄²	D₄×C₄₃	1	2	yes	—
156	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
157	C₄⋊C₈	—	2	8	no	—
158	C₂²⋊C₈	—	4	4	no	—
159	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
160	C₂×Q₈	—	2	8	no	—
161	C₂×Q₈	—	2	4	no	—
162	C₂×Q₈	—	4	32	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂×Q₈	—	4	4	no	—
166	C₂×Q₈	—	4	4	no	—
167	C₂×Q₈	C₂²⋊C₄×C₄₃	1	8	yes	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	4	no	—
173	C₂²×C₄	—	2	8	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	—	4	4	no	—
176	C₂²×C₄	—	4	4	no	—
177	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
178	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
179	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	—
180	C₂²×C₄	Q₁₆×C₄₃	1	4	yes	—
181	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
183	C₂×C₈	—	4	4	no	—
184	C₂×C₈	—	4	4	no	—
185	C₂×C₈	—	4	4	no	—
186	C₄⋊C₄	—	2	16	no	—
187	C₄⋊C₄	—	2	16	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	4	no	—
190	C₄²	C₂×D₄×C₄₃	1	4	yes	—
191	C₂³	—	2	1	no	—
192	C₂³	—	2	1	no	—
193	C₂³	—	2	2	no	—
194	C₂³	#100×C₄₃	1	2	yes	—
195	C₂³	#103×C₄₃	1	4	yes	—
196	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
197	Q₈	—	4	8	no	—
198	Q₈	—	4	16	no	—
199	Q₈	—	4	8	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	2	8	no	—
210	C₂×C₄	—	4	16	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	#100×C₄₃	1	2	yes	—
214	C₂×C₄	#103×C₄₃	1	4	yes	—
215	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
216	C₂×C₄	#120×C₄₃	1	4	yes	—
217	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
218	C₂×C₄	C₂×Q₁₆×C₄₃	1	2	yes	—
219	C₂×C₄	#137×C₄₃	1	4	yes	—
220	C₈	—	8	4	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	4	no	—
224	C₂²	—	2	4	no	—
225	C₂²	C₄₃×#333	1	4	yes	complemented
226	C₂²	C₄₃×#379	1	1	yes	characteristic
227	C₂²	C₂×#100×C₄₃	1	1	yes	characteristic
228	C₂²	C₂×#100×C₄₃	1	1	yes	characteristic
229	C₂²	C₂×#103×C₄₃	1	2	yes	—
230	C₂²	C₄₃×#419	1	2	yes	—
231	C₄	—	2	2	no	—
232	C₄	—	2	2	no	—
233	C₄	—	2	4	no	—
234	C₄	—	4	8	no	—
235	C₄	C₄₃×#448	1	4	yes	—
236	C₄	C₄₃×#451	1	4	yes	—
237	C₂	—	2	4	no	—
238	C₂	C₂×C₄₃×#333	1	1	yes	characteristic
239	C₂	C₄₃×#1548	1	2	yes	—
240	C₂	C₄₃×#1558	1	1	yes	characteristic
241	C₂	C₄₃×#1783	1	1	yes	characteristic
242	C₂	C₄₃×#1787	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Q₈×C₄₃

C₂

yes

maximal, characteristic

C₄₃×#1797

C₂

yes

maximal

C₂×C₄₃×#333

C₂

yes

maximal, complemented

C₂³×Q₈×C₄₃

C₄

yes

—

C₂×C₄⋊Q₈×C₄₃

—

C₂×C₄⋊Q₈×C₄₃

—

C₂×C₄⋊Q₈×C₄₃

C₄

yes

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

—

C₂²×C₄⋊C₄×C₄₃

—

C₂²×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₈×C₄₃

—

C₄₃×#336

—

C₄₃×#333

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

—

C₂²×Q₈×C₄₃

C₂×C₄

yes

—

C₂³×C₄×C₄₃

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

SD₁₆

yes

—

C₂²×C₄×C₄₃

Q₁₆

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#100

yes

—

C₂³×C₄₃

#103

yes

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×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×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#100

yes

—

C₂×C₄×C₄₃

#103

yes

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₈×C₄₃

—

#8342

C₄₃

yes

maximal, characteristic, direct product factor, Sylow

100

C₂²×C₄₃

—

101

C₂²×C₄₃

—

102

C₂²×C₄₃

—

103

C₂²×C₄₃

—

104

C₂²×C₄₃

#333

yes

complemented

105

C₂²×C₄₃

#379

yes

characteristic

106

C₂²×C₄₃

C₂×#100

yes

characteristic

107

C₂²×C₄₃

C₂×#100

yes

characteristic

108

C₂²×C₄₃

C₂×#103

yes

—

109

C₂²×C₄₃

#419

yes

—

110

C₄×C₄₃

—

111

C₄×C₄₃

—

112

C₄×C₄₃

—

113

C₄×C₄₃

—

114

C₄×C₄₃

#448

yes

—

115

C₄×C₄₃

#451

yes

—

116

C₂²×C₄⋊Q₈

C₂×C₄₃

yes

characteristic

117

#1797

C₂×C₄₃

yes

—

118

C₂×#333

C₂×C₄₃

yes

complemented

119

C₂×C₄₃

—

120

C₂×C₄₃

C₂×#333

yes

characteristic

121

C₂×C₄₃

#1548

yes

—

122

C₂×C₄₃

#1558

yes

characteristic

123

C₂×C₄₃

#1783

yes

characteristic

124

C₂×C₄₃

#1787

yes

—

125

C₂³×Q₈

C₄×C₄₃

yes

—

126

C₂×C₄⋊Q₈

—

127

C₂×C₄⋊Q₈

—

128

C₂×C₄⋊Q₈

C₄×C₄₃

yes

—

129

C₂×C₄⋊Q₈

C₂²×C₄₃

yes

—

130

C₂²×C₄⋊C₄

—

131

C₂²×C₄²

C₂²×C₄₃

yes

characteristic

132

C₂×C₄⋊C₈

C₂²×C₄₃

yes

—

133

C₂×C₂²⋊C₈

—

134

#336

—

135

#333

—

136

C₄₃

#8342

yes

characteristic, direct product factor, Sylow

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×Q₈

—

141

C₂²×Q₈

C₂×C₄×C₄₃

yes

—

142

C₂³×C₄

—

143

C₂³×C₄

C₂×C₄×C₄₃

yes

characteristic

144

C₂³×C₄

D₄×C₄₃

yes

—

145

C₂²×C₈

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

D₄×C₄₃

yes

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂×C₄×C₄₃

yes

characteristic

155

C₂×C₄²

D₄×C₄₃

yes

—

156

C₂×C₄²

C₂³×C₄₃

yes

characteristic

157

C₄⋊C₈

—

158

C₂²⋊C₈

—

159

C₂⁴

C₂²⋊C₄×C₄₃

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

C₂²⋊C₄×C₄₃

yes

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂²⋊C₄×C₄₃

yes

characteristic

178

C₂²×C₄

C₂²⋊C₄×C₄₃

yes

—

179

C₂²×C₄

SD₁₆×C₄₃

yes

—

180

C₂²×C₄

Q₁₆×C₄₃

yes

—

181

C₂²×C₄

C₂²×C₄×C₄₃

yes

characteristic

182

C₂²×C₄

C₂×D₄×C₄₃

yes

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×D₄×C₄₃

yes

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

#100×C₄₃

yes

—

195

C₂³

#103×C₄₃

yes

—

196

C₂³

C₂×C₂²⋊C₄×C₄₃

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#100×C₄₃

yes

—

214

C₂×C₄

#103×C₄₃

yes

—

215

C₂×C₄

C₂×C₂²⋊C₄×C₄₃

yes

—

216

C₂×C₄

#120×C₄₃

yes

—

217

C₂×C₄

C₂×SD₁₆×C₄₃

yes

—

218

C₂×C₄

C₂×Q₁₆×C₄₃

yes

—

219

C₂×C₄

#137×C₄₃

yes

—

220

C₈

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₄₃×#333

yes

complemented

226

C₂²

C₄₃×#379

yes

characteristic

227

C₂²

C₂×#100×C₄₃

yes

characteristic

228

C₂²

C₂×#100×C₄₃

yes

characteristic

229

C₂²

C₂×#103×C₄₃

yes

—

230

C₂²

C₄₃×#419

yes

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

C₄₃×#448

yes

—

236

C₄

C₄₃×#451

yes

—

237

C₂

—

238

C₂

C₂×C₄₃×#333

yes

characteristic

239

C₂

C₄₃×#1548

yes

—

240

C₂

C₄₃×#1558

yes

characteristic

241

C₂

C₄₃×#1783

yes

characteristic

242

C₂

C₄₃×#1787

yes

—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
prime radical	C₂⁴×C₄₃	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₃

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₄₃

Frattini, cosocle

C₂×C₄²

C₂³×C₄₃

prime radical

C₂⁴×C₄₃

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

N	H ≅ G/N	type
3. C₂×C₄₃×#333	C₂	semidirect
99. #8342	C₄₃	direct (N × H)
104. C₂²×C₄₃	#333	semidirect
118. C₂×#333	C₂×C₄₃	semidirect
136. C₄₃	#8342	direct (N × H)
225. C₂²	C₄₃×#333	semidirect

H ≅ G/N

type

3. C₂×C₄₃×#333

C₂

semidirect

99. #8342

C₄₃

direct (N × H)

104. C₂²×C₄₃

#333

semidirect

118. C₂×#333

C₂×C₄₃

semidirect

136. C₄₃

#8342

direct (N × H)

225. C₂²

C₄₃×#333

semidirect

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₃	2
C₄₃×#1797	2
C₂×C₄₃×#333	2
#8342	43

subgroup

index

C₂²×C₄⋊Q₈×C₄₃

C₄₃×#1797

C₂×C₄₃×#333

#8342

Subgroups — C₄₃×#8342 #24928359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43×#8342 #24928359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8342 #24928359