Group #25303009 — subgroups

Subgroups — C₂×#19142860 #25303009

Order 11008.

3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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	#19142860	C₂	1	16	yes	maximal, direct product factor
2	C₂×#14582835	C₂	1	3	yes	maximal, complemented
3	C₂×#14582823	C₂	1	2	yes	maximal, complemented
4	C₂×#14582821	C₂	1	6	yes	maximal, complemented
5	C₂×#14582754	C₂	1	3	yes	maximal
6	C₂×C₄₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵×D₄₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₃	C₂²	1	3	yes	complemented
9	C₂²×Dic₄₃⋊C₄	C₂²	1	6	yes	complemented
10	C₂²×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
11	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
12	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
13	#14582835	C₂²	1	24	yes	complemented
14	#14582823	C₂²	1	16	yes	complemented
15	#14582821	C₂²	1	48	yes	complemented
16	#14582754	C₂²	1	24	yes	—
17	C₂×C₄₃⋊#95	C₂²	1	3	yes	complemented
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	3	yes	complemented
19	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
20	C₄₃×#399	C₂²	1	8	yes	complemented
21	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×D₄₃	—	4	6	no	—
23	C₂⁴×D₄₃	—	4	6	no	—
24	C₂⁴×D₄₃	Q₈	1	8	yes	—
25	C₂⁴×D₄₃	C₂³	1	2	yes	—
26	C₂⁴×D₄₃	C₂³	1	4	yes	—
27	C₂³×Dic₄₃	C₂³	1	6	yes	—
28	C₂×C₄⋊Dic₄₃	—	4	6	no	—
29	C₂×C₄⋊Dic₄₃	C₂³	1	12	yes	complemented
30	C₂×Dic₄₃⋊C₄	—	4	12	no	—
31	C₂×Dic₄₃⋊C₄	C₂³	1	24	yes	complemented
32	C₂×C₂²⋊Dic₄₃	—	4	6	no	—
33	C₂×C₂²⋊Dic₄₃	C₂³	1	12	yes	—
34	C₂×(C₂×D₄₃)⋊C₄	—	4	12	no	—
35	C₂×(C₂×D₄₃)⋊C₄	—	4	12	no	—
36	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	24	yes	—
37	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	24	yes	—
38	C₄₃⋊#95	C₂³	1	12	yes	complemented
39	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
42	C₂×C₄⋊C₄×C₄₃	—	4	6	no	—
43	C₂×C₄⋊C₄×C₄₃	C₂³	1	12	yes	complemented
44	C₂×C₂²⋊C₄×C₄₃	—	4	6	no	—
45	C₂×C₂²⋊C₄×C₄₃	C₂³	1	12	yes	—
46	#95×C₄₃	C₂³	1	4	yes	complemented
47	C₂⁴×C₄₃	—	2	6	no	—
48	C₂⁴×C₄₃	—	2	6	no	—
49	C₂⁴×C₄₃	C₂×Q₈	1	4	yes	—
50	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
51	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
52	C₂³×D₄₃	—	2	12	no	—
53	C₂³×D₄₃	—	2	12	no	—
54	C₂³×D₄₃	—	4	48	no	—
55	C₂³×D₄₃	—	4	12	no	—
56	C₂³×D₄₃	—	4	12	no	—
57	C₂³×D₄₃	—	4	16	no	—
58	C₂³×D₄₃	—	4	48	no	—
59	C₂³×D₄₃	C₂×Q₈	1	8	yes	—
60	C₂³×D₄₃	C₂×Q₈	1	16	yes	—
61	C₂³×D₄₃	C₂⁴	1	4	yes	—
62	C₂²×C₄×C₄₃	—	2	6	no	—
63	C₂²×C₄×C₄₃	—	2	6	no	—
64	C₂²×C₄×C₄₃	—	2	12	no	—
65	C₂²×C₄×C₄₃	—	2	12	no	—
66	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
67	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
68	C₂²×Dic₄₃	—	2	12	no	—
69	C₂²×Dic₄₃	—	2	12	no	—
70	C₂²×Dic₄₃	—	2	12	no	—
71	C₂²×Dic₄₃	C₂⁴	1	12	yes	—
72	C₄⋊C₄×C₄₃	—	4	12	no	—
73	C₂²⋊C₄×C₄₃	—	4	12	no	—
74	C₂²⋊Dic₄₃	—	4	12	no	—
75	(C₂×D₄₃)⋊C₄	—	4	24	no	—
76	(C₂×D₄₃)⋊C₄	—	4	24	no	—
77	C₄⋊Dic₄₃	—	4	12	no	—
78	Dic₄₃⋊C₄	—	4	24	no	—
79	C₂³×C₄₃	—	2	24	no	—
80	C₂³×C₄₃	—	2	6	no	—
81	C₂³×C₄₃	—	2	6	no	—
82	C₂³×C₄₃	—	4	4	no	—
83	C₂³×C₄₃	—	4	12	no	—
84	C₂³×C₄₃	C₂²×Q₈	1	4	yes	—
85	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
86	C₂³×C₄₃	H(5,𝔽₂)	1	6	yes	—
87	C₂³×C₄₃	H(5,𝔽₂)	1	6	yes	—
88	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
89	C₂²×D₄₃	—	2	48	no	—
90	C₂²×D₄₃	—	2	12	no	—
91	C₂²×D₄₃	—	2	12	no	—
92	C₂²×D₄₃	—	4	48	no	—
93	C₂²×D₄₃	—	4	128	no	—
94	C₂²×D₄₃	—	4	16	no	—
95	C₂²×D₄₃	—	4	48	no	—
96	C₂²×D₄₃	—	4	8	no	—
97	C₂²×D₄₃	—	4	24	no	—
98	C₂²×D₄₃	C₂²×Q₈	1	8	yes	—
99	C₂×C₄×C₄₃	—	2	12	no	—
100	C₂×C₄×C₄₃	—	2	6	no	—
101	C₂×C₄×C₄₃	—	2	12	no	—
102	C₂×C₄×C₄₃	—	2	6	no	—
103	C₂×C₄×C₄₃	—	4	12	no	—
104	C₂×C₄×C₄₃	—	4	12	no	—
105	C₂×Dic₄₃	—	2	12	no	—
106	C₂×Dic₄₃	—	2	12	no	—
107	C₂×Dic₄₃	—	2	12	no	—
108	C₂×Dic₄₃	—	4	24	no	—
109	C₂×#2842	—	43	1	no	maximal, Sylow
110	C₂²×C₄₃	—	2	12	no	—
111	C₂²×C₄₃	—	4	16	no	—
112	C₂²×C₄₃	—	4	2	no	—
113	C₂²×C₄₃	—	4	6	no	—
114	C₂²×C₄₃	#543	1	12	yes	—
115	C₂²×C₄₃	#560	1	4	yes	—
116	C₂²×C₄₃	#560	1	12	yes	—
117	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
118	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	3	yes	—
119	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	3	yes	—
120	C₂×D₄₃	—	2	24	no	—
121	C₂×D₄₃	—	4	64	no	—
122	C₂×D₄₃	—	4	32	no	—
123	C₂×D₄₃	—	4	4	no	—
124	C₂×D₄₃	—	4	12	no	—
125	C₄×C₄₃	—	4	6	no	—
126	C₄×C₄₃	—	4	6	no	—
127	Dic₄₃	—	4	12	no	—
128	#2842	—	43	16	no	—
129	C₂×#399	—	43	3	no	—
130	C₂×#399	D₄₃	1	1	yes	characteristic, complemented
131	C₂×#396	—	43	2	no	—
132	C₂×#396	—	43	6	no	—
133	C₂×#379	—	43	3	no	—
134	C₂×C₄₃	—	4	4	no	—
135	C₂×C₄₃	#2842	1	8	yes	complemented
136	C₂×C₄₃	C₂×#543	1	3	yes	—
137	C₂×C₄₃	C₂×#560	1	1	yes	characteristic
138	C₂×C₄₃	C₂×#560	1	3	yes	—
139	D₄₃	—	4	8	no	—
140	C₂⁶	—	43	1	no	—
141	C₂²×C₄⋊C₄	—	43	6	no	—
142	C₂²×C₄⋊C₄	—	43	3	no	—
143	C₂²×C₄⋊C₄	C₂×D₄₃	1	3	yes	complemented
144	C₂²×C₂²⋊C₄	—	43	3	no	—
145	C₂²×C₂²⋊C₄	—	43	6	no	—
146	C₂²×C₂²⋊C₄	—	43	6	no	—
147	C₂²×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
148	#399	—	43	24	no	—
149	#399	C₂×D₄₃	1	8	yes	complemented
150	#396	—	43	48	no	—
151	#396	—	43	16	no	—
152	#379	—	43	24	no	—
153	C₂×#95	—	43	3	no	—
154	C₂×#95	C₂×D₄₃	1	1	yes	characteristic, complemented
155	C₄₃	C₂×#2842	1	1	yes	characteristic, complemented, Sylow
156	C₂⁵	—	43	2	no	—
157	C₂⁵	—	43	8	no	—
158	C₂⁵	—	43	4	no	—
159	C₂⁵	—	172	6	no	—
160	C₂⁵	—	172	6	no	—
161	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
162	C₂³×C₄	—	43	6	no	—
163	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
164	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
165	C₂×C₄⋊C₄	—	4	6	no	—
166	C₂×C₄⋊C₄	—	43	24	no	—
167	C₂×C₄⋊C₄	—	43	12	no	—
168	C₂×C₄⋊C₄	—	172	12	no	—
169	C₂×C₄⋊C₄	—	172	6	no	—
170	C₂×C₄⋊C₄	C₂²×D₄₃	1	12	yes	complemented
171	C₂×C₂²⋊C₄	—	4	6	no	—
172	C₂×C₂²⋊C₄	—	43	12	no	—
173	C₂×C₂²⋊C₄	—	43	24	no	—
174	C₂×C₂²⋊C₄	—	43	24	no	—
175	C₂×C₂²⋊C₄	—	172	12	no	—
176	C₂×C₂²⋊C₄	—	172	12	no	—
177	C₂×C₂²⋊C₄	—	172	6	no	—
178	C₂×C₂²⋊C₄	C₂²×D₄₃	1	12	yes	—
179	#95	—	43	12	no	—
180	#95	C₂²×D₄₃	1	4	yes	complemented
181	C₂⁴	—	2	6	no	—
182	C₂⁴	—	2	6	no	—
183	C₂⁴	—	43	8	no	—
184	C₂⁴	—	43	4	no	—
185	C₂⁴	—	43	16	no	—
186	C₂⁴	—	86	12	no	—
187	C₂⁴	—	86	12	no	—
188	C₂⁴	—	172	12	no	—
189	C₂⁴	—	172	12	no	—
190	C₂⁴	—	172	48	no	—
191	C₂⁴	—	172	16	no	—
192	C₂⁴	—	172	48	no	—
193	C₂⁴	Q₈×D₄₃	1	4	yes	—
194	C₂⁴	C₂³×D₄₃	1	2	yes	—
195	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
196	C₂²×C₄	—	2	6	no	—
197	C₂²×C₄	—	2	6	no	—
198	C₂²×C₄	—	2	12	no	—
199	C₂²×C₄	—	2	12	no	—
200	C₂²×C₄	—	43	12	no	—
201	C₂²×C₄	—	86	12	no	—
202	C₂²×C₄	—	86	12	no	—
203	C₂²×C₄	—	86	12	no	—
204	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
205	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
206	C₄⋊C₄	—	4	12	no	—
207	C₄⋊C₄	—	172	24	no	—
208	C₄⋊C₄	—	172	12	no	—
209	C₂²⋊C₄	—	4	12	no	—
210	C₂²⋊C₄	—	172	24	no	—
211	C₂²⋊C₄	—	172	24	no	—
212	C₂²⋊C₄	—	172	12	no	—
213	C₂³	—	2	6	no	—
214	C₂³	—	2	6	no	—
215	C₂³	—	2	24	no	—
216	C₂³	—	4	4	no	—
217	C₂³	—	4	12	no	—
218	C₂³	—	43	8	no	—
219	C₂³	—	86	12	no	—
220	C₂³	—	86	12	no	—
221	C₂³	—	86	48	no	—
222	C₂³	—	172	48	no	—
223	C₂³	—	172	16	no	—
224	C₂³	—	172	48	no	—
225	C₂³	—	172	128	no	—
226	C₂³	—	172	8	no	—
227	C₂³	—	172	24	no	—
228	C₂³	C₂×Q₈×D₄₃	1	4	yes	—
229	C₂³	C₂×Q₈×D₄₃	1	2	yes	—
230	C₂³	#13063370	1	6	yes	—
231	C₂³	#13063371	1	6	yes	—
232	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
233	C₂×C₄	—	2	6	no	—
234	C₂×C₄	—	2	6	no	—
235	C₂×C₄	—	2	12	no	—
236	C₂×C₄	—	2	12	no	—
237	C₂×C₄	—	4	12	no	—
238	C₂×C₄	—	4	12	no	—
239	C₂×C₄	—	86	12	no	—
240	C₂×C₄	—	86	12	no	—
241	C₂×C₄	—	86	12	no	—
242	C₂×C₄	—	172	24	no	—
243	C₂²	—	2	12	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	4	6	no	—
246	C₂²	—	4	16	no	—
247	C₂²	—	86	24	no	—
248	C₂²	—	172	64	no	—
249	C₂²	—	172	4	no	—
250	C₂²	—	172	12	no	—
251	C₂²	—	172	32	no	—
252	C₂²	#14583524	1	12	yes	—
253	C₂²	#14583636	1	4	yes	—
254	C₂²	#14583639	1	12	yes	—
255	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
256	C₂²	C₂×#13063370	1	3	yes	—
257	C₂²	C₂×#13063371	1	3	yes	—
258	C₄	—	4	6	no	—
259	C₄	—	4	6	no	—
260	C₄	—	172	12	no	—
261	C₂	—	4	4	no	—
262	C₂	—	172	8	no	—
263	C₂	#19142860	1	8	yes	direct product factor
264	C₂	C₂×#14583524	1	3	yes	—
265	C₂	C₂×#14583636	1	1	yes	characteristic
266	C₂	C₂×#14583639	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19142860

C₂

yes

maximal, direct product factor

C₂×#14582835

C₂

yes

maximal, complemented

C₂×#14582823

C₂

yes

maximal, complemented

C₂×#14582821

C₂

yes

maximal, complemented

C₂×#14582754

C₂

yes

maximal

C₂×C₄₃×#399

C₂

yes

maximal, characteristic, complemented

C₂⁵×D₄₃

C₂²

yes

characteristic

C₂²×C₄⋊Dic₄₃

C₂²

yes

complemented

C₂²×Dic₄₃⋊C₄

C₂²

yes

complemented

C₂²×C₂²⋊Dic₄₃

C₂²

yes

—

C₂²×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂²×(C₂×D₄₃)⋊C₄

C₂²

yes

—

#14582835

C₂²

yes

complemented

#14582823

C₂²

yes

complemented

#14582821

C₂²

yes

complemented

#14582754

C₂²

yes

—

C₂×C₄₃⋊#95

C₂²

yes

complemented

C₂²×C₄⋊C₄×C₄₃

C₂²

yes

complemented

C₂²×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₄₃×#399

C₂²

yes

complemented

C₂×#95×C₄₃

C₂²

yes

characteristic, complemented

C₂⁴×D₄₃

—

C₂⁴×D₄₃

—

C₂⁴×D₄₃

Q₈

yes

—

C₂⁴×D₄₃

C₂³

yes

—

C₂⁴×D₄₃

C₂³

yes

—

C₂³×Dic₄₃

C₂³

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂³

yes

complemented

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

C₂³

yes

complemented

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

C₂³

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

C₂³

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂³

yes

—

C₄₃⋊#95

C₂³

yes

complemented

C₂⁵×C₄₃

C₂³

yes

characteristic

C₂³×C₄×C₄₃

C₂³

yes

—

C₂³×C₄×C₄₃

C₂³

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂³

yes

complemented

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

C₂³

yes

—

#95×C₄₃

C₂³

yes

complemented

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

C₂×Q₈

yes

—

C₂⁴×C₄₃

C₂⁴

yes

—

C₂⁴×C₄₃

C₂⁴

yes

characteristic

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

C₂×Q₈

yes

—

C₂³×D₄₃

C₂×Q₈

yes

—

C₂³×D₄₃

C₂⁴

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂⁴

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂⁴

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×Q₈

yes

—

C₂³×C₄₃

C₂²×Q₈

yes

—

C₂³×C₄₃

H(5,𝔽₂)

yes

—

C₂³×C₄₃

H(5,𝔽₂)

yes

—

C₂³×C₄₃

C₂⁵

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

128

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂²×Q₈

yes

—

C₂×C₄×C₄₃

—

100

C₂×C₄×C₄₃

—

101

C₂×C₄×C₄₃

—

102

C₂×C₄×C₄₃

—

103

C₂×C₄×C₄₃

—

104

C₂×C₄×C₄₃

—

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

C₂×Dic₄₃

—

108

C₂×Dic₄₃

—

109

C₂×#2842

—

maximal, Sylow

110

C₂²×C₄₃

—

111

C₂²×C₄₃

—

112

C₂²×C₄₃

—

113

C₂²×C₄₃

—

114

C₂²×C₄₃

#543

yes

—

115

C₂²×C₄₃

#560

yes

—

116

C₂²×C₄₃

#560

yes

—

117

C₂²×C₄₃

C₂³×Q₈

yes

characteristic

118

C₂²×C₄₃

C₂×H(5,𝔽₂)

yes

—

119

C₂²×C₄₃

C₂×H(5,𝔽₂)

yes

—

120

C₂×D₄₃

—

121

C₂×D₄₃

—

122

C₂×D₄₃

—

123

C₂×D₄₃

—

124

C₂×D₄₃

—

125

C₄×C₄₃

—

126

C₄×C₄₃

—

127

Dic₄₃

—

128

#2842

—

129

C₂×#399

—

130

C₂×#399

D₄₃

yes

characteristic, complemented

131

C₂×#396

—

132

C₂×#396

—

133

C₂×#379

—

134

C₂×C₄₃

—

135

C₂×C₄₃

#2842

yes

complemented

136

C₂×C₄₃

C₂×#543

yes

—

137

C₂×C₄₃

C₂×#560

yes

characteristic

138

C₂×C₄₃

C₂×#560

yes

—

139

D₄₃

—

140

C₂⁶

—

141

C₂²×C₄⋊C₄

—

142

C₂²×C₄⋊C₄

—

143

C₂²×C₄⋊C₄

C₂×D₄₃

yes

complemented

144

C₂²×C₂²⋊C₄

—

145

C₂²×C₂²⋊C₄

—

146

C₂²×C₂²⋊C₄

—

147

C₂²×C₂²⋊C₄

C₂×D₄₃

yes

—

148

#399

—

149

#399

C₂×D₄₃

yes

complemented

150

#396

—

151

#396

—

152

#379

—

153

C₂×#95

—

154

C₂×#95

C₂×D₄₃

yes

characteristic, complemented

155

C₄₃

C₂×#2842

yes

characteristic, complemented, Sylow

156

C₂⁵

—

157

C₂⁵

—

158

C₂⁵

—

159

C₂⁵

—

172

—

160

C₂⁵

—

172

—

161

C₂⁵

C₂²×D₄₃

yes

characteristic

162

C₂³×C₄

—

163

C₂³×C₄

C₂²×D₄₃

yes

—

164

C₂³×C₄

C₂²×D₄₃

yes

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

172

—

169

C₂×C₄⋊C₄

—

172

—

170

C₂×C₄⋊C₄

C₂²×D₄₃

yes

complemented

171

C₂×C₂²⋊C₄

—

172

C₂×C₂²⋊C₄

—

173

C₂×C₂²⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

172

—

176

C₂×C₂²⋊C₄

—

172

—

177

C₂×C₂²⋊C₄

—

172

—

178

C₂×C₂²⋊C₄

C₂²×D₄₃

yes

—

179

#95

—

180

#95

C₂²×D₄₃

yes

complemented

181

C₂⁴

—

182

C₂⁴

—

183

C₂⁴

—

184

C₂⁴

—

185

C₂⁴

—

186

C₂⁴

—

187

C₂⁴

—

188

C₂⁴

—

172

—

189

C₂⁴

—

172

—

190

C₂⁴

—

172

—

191

C₂⁴

—

172

—

192

C₂⁴

—

172

—

193

C₂⁴

Q₈×D₄₃

yes

—

194

C₂⁴

C₂³×D₄₃

yes

—

195

C₂⁴

C₂³×D₄₃

yes

characteristic

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

C₂³×D₄₃

yes

—

205

C₂²×C₄

C₂³×D₄₃

yes

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

172

—

208

C₄⋊C₄

—

172

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

172

—

211

C₂²⋊C₄

—

172

—

212

C₂²⋊C₄

—

172

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

172

—

223

C₂³

—

172

—

224

C₂³

—

172

—

225

C₂³

—

172

128

—

226

C₂³

—

172

—

227

C₂³

—

172

—

228

C₂³

C₂×Q₈×D₄₃

yes

—

229

C₂³

C₂×Q₈×D₄₃

yes

—

230

C₂³

#13063370

yes

—

231

C₂³

#13063371

yes

—

232

C₂³

C₂⁴×D₄₃

yes

characteristic

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

172

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

172

—

249

C₂²

—

172

—

250

C₂²

—

172

—

251

C₂²

—

172

—

252

C₂²

#14583524

yes

—

253

C₂²

#14583636

yes

—

254

C₂²

#14583639

yes

—

255

C₂²

C₂²×Q₈×D₄₃

yes

characteristic

256

C₂²

C₂×#13063370

yes

—

257

C₂²

C₂×#13063371

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

172

—

261

C₂

—

262

C₂

—

172

—

263

C₂

#19142860

yes

direct product factor

264

C₂

C₂×#14583524

yes

—

265

C₂

C₂×#14583636

yes

characteristic

266

C₂

C₂×#14583639

yes

—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₃
commutator, cosocle	C₂³×C₄₃	C₂⁵
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#399	C₂
socle	C₂⁴×C₄₃	C₂⁴
prime radical	C₂⁵×D₄₃	C₂²
hypercenter	C₂×#399	D₄₃
hypocenter	C₄₃	C₂×#2842
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#399

subgroup

G/H

center

C₂⁴

C₂³×D₄₃

commutator, cosocle

C₂³×C₄₃

C₂⁵

Frattini

C₂³

C₂⁴×D₄₃

Fitting

C₂×C₄₃×#399

C₂

socle

C₂⁴×C₄₃

C₂⁴

prime radical

C₂⁵×D₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂⁴ ◁ C₂×#399

N	H ≅ G/N	type
1. #19142860	C₂	direct (N × H)
2. C₂×#14582835	C₂	semidirect
3. C₂×#14582823	C₂	semidirect
4. C₂×#14582821	C₂	semidirect
6. C₂×C₄₃×#399	C₂	semidirect
8. C₂²×C₄⋊Dic₄₃	C₂²	semidirect
9. C₂²×Dic₄₃⋊C₄	C₂²	semidirect
13. #14582835	C₂²	semidirect
14. #14582823	C₂²	semidirect
15. #14582821	C₂²	semidirect
17. C₂×C₄₃⋊#95	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
20. C₄₃×#399	C₂²	semidirect
21. C₂×#95×C₄₃	C₂²	semidirect
29. C₂×C₄⋊Dic₄₃	C₂³	semidirect
31. C₂×Dic₄₃⋊C₄	C₂³	semidirect
38. C₄₃⋊#95	C₂³	semidirect
43. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
46. #95×C₄₃	C₂³	semidirect
130. C₂×#399	D₄₃	semidirect
135. C₂×C₄₃	#2842	semidirect
143. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
149. #399	C₂×D₄₃	semidirect
154. C₂×#95	C₂×D₄₃	semidirect
155. C₄₃	C₂×#2842	semidirect
170. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
180. #95	C₂²×D₄₃	semidirect
263. C₂	#19142860	direct (N × H)

H ≅ G/N

type

1. #19142860

C₂

direct (N × H)

2. C₂×#14582835

C₂

semidirect

3. C₂×#14582823

C₂

semidirect

4. C₂×#14582821

C₂

semidirect

6. C₂×C₄₃×#399

C₂

semidirect

8. C₂²×C₄⋊Dic₄₃

C₂²

semidirect

9. C₂²×Dic₄₃⋊C₄

C₂²

semidirect

13. #14582835

C₂²

semidirect

14. #14582823

C₂²

semidirect

15. #14582821

C₂²

semidirect

17. C₂×C₄₃⋊#95

C₂²

semidirect

18. C₂²×C₄⋊C₄×C₄₃

C₂²

semidirect

20. C₄₃×#399

C₂²

semidirect

21. C₂×#95×C₄₃

C₂²

semidirect

29. C₂×C₄⋊Dic₄₃

C₂³

semidirect

31. C₂×Dic₄₃⋊C₄

C₂³

semidirect

38. C₄₃⋊#95

C₂³

semidirect

43. C₂×C₄⋊C₄×C₄₃

C₂³

semidirect

46. #95×C₄₃

C₂³

semidirect

130. C₂×#399

D₄₃

semidirect

135. C₂×C₄₃

#2842

semidirect

143. C₂²×C₄⋊C₄

C₂×D₄₃

semidirect

149. #399

C₂×D₄₃

semidirect

154. C₂×#95

C₂×D₄₃

semidirect

155. C₄₃

C₂×#2842

semidirect

170. C₂×C₄⋊C₄

C₂²×D₄₃

semidirect

180. #95

C₂²×D₄₃

semidirect

263. C₂

#19142860

direct (N × H)

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

subgroup	index
#19142860	2
C₂×#14582835	2
C₂×#14582823	2
C₂×#14582821	2
C₂×#14582754	2
C₂×C₄₃×#399	2
C₂×#2842	43

subgroup

index

C₂×C₄₃×#399

Subgroups — C₂×#19142860 #25303009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#19142860 #25303009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19142860 #25303009