Subgroups — C₂²×#14583541 #26003516

Order 11008.

14462 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583541	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#13063311	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13063310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13063303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13063300	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13063298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13063297	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13063295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#13063295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13063287	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×(C₂²⋊D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#123×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₄₃	C₂²	1	1	yes	characteristic
18	C₂⁵×D₄₃	C₂²	1	1	yes	characteristic
19	C₂²×#10621898	—	2	16	no	—
20	C₂²×#10621898	C₂²	1	24	yes	complemented
21	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
23	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
24	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
26	C₂³×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
27	C₂³×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
28	C₂³×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₄×D₄₃	—	2	16	no	—
31	C₂²×D₄×D₄₃	C₂²	1	24	yes	complemented
32	C₂⁴×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
33	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic
34	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
36	C₂³×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
37	#14583541	C₂²	1	256	yes	direct product factor
38	C₂×#13063311	C₂²	1	24	yes	complemented
39	C₂×#13063310	C₂²	1	24	yes	complemented
40	C₂×#13063303	C₂²	1	24	yes	complemented
41	C₂×#13063300	C₂²	1	24	yes	complemented
42	C₂×#13063298	C₂²	1	24	yes	complemented
43	C₂×#13063297	C₂²	1	24	yes	complemented
44	C₂×#13063295	C₂²	1	24	yes	complemented
45	C₂×#13063295	C₂²	1	24	yes	complemented
46	C₂×#13063287	C₂²	1	24	yes	complemented
47	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	24	yes	complemented
48	C₂²×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂²×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	24	yes	complemented
60	C₂×C₂²⋊C₄×D₄₃	C₂²	1	24	yes	complemented
61	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
62	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
63	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#123×C₄₃	C₂²	1	24	yes	complemented
65	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
70	C₂⁴×D₄₃	—	2	8	no	—
71	C₂⁴×D₄₃	—	2	8	no	—
72	C₂⁴×D₄₃	—	2	8	no	—
73	C₂⁴×D₄₃	—	2	8	no	—
74	C₂⁴×D₄₃	—	4	4	no	—
75	C₂⁴×D₄₃	—	4	4	no	—
76	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
77	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
78	C₂⁴×D₄₃	C₂³	1	12	yes	—
79	C₂⁴×D₄₃	C₂³	1	12	yes	—
80	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
81	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
82	C₂×#10621898	—	2	192	no	—
83	C₂×#10621898	C₂³	1	64	yes	complemented
84	C₂²×Dic₈₆	—	2	8	no	—
85	C₂²×Dic₈₆	C₂³	1	12	yes	complemented
86	C₂²×D₁₇₂	—	2	8	no	—
87	C₂²×D₁₇₂	—	2	8	no	—
88	C₂²×D₁₇₂	—	2	8	no	—
89	C₂²×D₁₇₂	—	4	4	no	—
90	C₂²×D₁₇₂	C₂³	1	12	yes	—
91	C₂²×D₁₇₂	C₂³	1	12	yes	—
92	C₂²×D₁₇₂	C₂³	1	12	yes	complemented
93	C₂²×D₁₇₂	C₂³	1	12	yes	complemented
94	C₂²×C₂²⋊D₄₃	—	2	8	no	—
95	C₂²×C₂²⋊D₄₃	—	2	8	no	—
96	C₂²×C₂²⋊D₄₃	—	4	4	no	—
97	C₂²×C₂²⋊D₄₃	D₄	1	16	yes	complemented
98	C₂²×C₂²⋊D₄₃	C₂³	1	12	yes	—
99	C₂²×C₂²⋊D₄₃	C₂³	1	12	yes	—
100	C₂²×C₂²⋊D₄₃	C₂³	1	12	yes	complemented
101	C₂²×C₂²⋊D₄₃	C₂³	1	12	yes	complemented
102	C₂×D₄×D₄₃	—	2	192	no	—
103	C₂×D₄×D₄₃	C₂³	1	64	yes	complemented
104	C₂³×Dic₄₃	—	4	4	no	—
105	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
106	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
107	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
108	C₂³×Dic₄₃	C₂³	1	1	yes	characteristic
109	C₂³×Dic₄₃	C₂³	1	12	yes	complemented
110	C₂²×C₄×D₄₃	—	2	8	no	—
111	C₂²×C₄×D₄₃	—	2	8	no	—
112	C₂²×C₄×D₄₃	—	2	8	no	—
113	C₂²×C₄×D₄₃	—	4	4	no	—
114	C₂²×C₄×D₄₃	C₂³	1	12	yes	—
115	C₂²×C₄×D₄₃	C₂³	1	12	yes	complemented
116	C₂²×C₄×D₄₃	C₂³	1	12	yes	complemented
117	C₂²×C₄×D₄₃	C₂³	1	12	yes	complemented
118	#13063311	C₂³	1	64	yes	complemented
119	#13063310	C₂³	1	64	yes	complemented
120	#13063303	C₂³	1	64	yes	complemented
121	#13063300	C₂³	1	64	yes	complemented
122	#13063298	C₂³	1	64	yes	complemented
123	#13063297	C₂³	1	64	yes	complemented
124	#13063295	C₂³	1	64	yes	complemented
125	#13063295	C₂³	1	64	yes	complemented
126	#13063287	C₂³	1	64	yes	complemented
127	(C₂²⋊D₄₃)⋊C₄	C₂³	1	64	yes	complemented
128	C₂×Dic₄₃⋊C₄	C₂³	1	12	yes	complemented
129	C₂×Dic₄₃⋊C₄	C₂³	1	12	yes	complemented
130	C₂×C₂²⋊Dic₄₃	C₂³	1	12	yes	complemented
131	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	—
132	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	—
133	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	—
134	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	64	yes	complemented
135	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	complemented
136	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	complemented
137	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	complemented
138	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	complemented
139	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	complemented
140	C₂²⋊C₄×D₄₃	C₂³	1	64	yes	complemented
141	C₂×C₄×Dic₄₃	C₂³	1	12	yes	complemented
142	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
143	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₄₃	—	2	8	no	—
145	C₂²×D₄×C₄₃	C₂³	1	12	yes	—
146	C₂³×C₄×C₄₃	—	2	8	no	—
147	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₄₃	C₂³	1	12	yes	complemented
153	#123×C₄₃	C₂³	1	64	yes	complemented
154	C₂×C₄⋊C₄×C₄₃	C₂³	1	12	yes	complemented
155	C₂×C₄⋊C₄×C₄₃	C₂³	1	12	yes	complemented
156	C₂×C₂²⋊C₄×C₄₃	C₂³	1	12	yes	complemented
157	C₂×C₂²⋊C₄×C₄₃	C₂³	1	12	yes	complemented
158	C₂×C₂²⋊C₄×C₄₃	C₂³	1	12	yes	complemented
159	C₂⁴×C₄₃	—	2	4	no	—
160	C₂⁴×C₄₃	—	2	4	no	—
161	C₂⁴×C₄₃	—	2	4	no	—
162	C₂⁴×C₄₃	—	2	4	no	—
163	C₂⁴×C₄₃	—	2	4	no	—
164	C₂⁴×C₄₃	C₂×D₄	1	8	yes	—
165	C₂⁴×C₄₃	C₂⁴	1	6	yes	—
166	C₂⁴×C₄₃	C₂⁴	1	6	yes	—
167	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂³×D₄₃	—	2	4	no	—
169	C₂³×D₄₃	—	2	4	no	—
170	C₂³×D₄₃	—	2	4	no	—
171	C₂³×D₄₃	—	2	4	no	—
172	C₂³×D₄₃	—	2	4	no	—
173	C₂³×D₄₃	—	2	48	no	—
174	C₂³×D₄₃	—	2	4	no	—
175	C₂³×D₄₃	—	2	4	no	—
176	C₂³×D₄₃	—	2	4	no	—
177	C₂³×D₄₃	—	2	4	no	—
178	C₂³×D₄₃	—	2	4	no	—
179	C₂³×D₄₃	—	2	48	no	—
180	C₂³×D₄₃	—	2	48	no	—
181	C₂³×D₄₃	—	2	48	no	—
182	C₂³×D₄₃	—	4	24	no	—
183	C₂³×D₄₃	—	4	24	no	—
184	C₂³×D₄₃	—	4	64	no	—
185	C₂³×D₄₃	—	4	64	no	—
186	C₂³×D₄₃	C₂×D₄	1	8	yes	—
187	C₂³×D₄₃	#41	1	8	yes	complemented
188	C₂³×D₄₃	C₂⁴	1	6	yes	—
189	C₂³×D₄₃	C₂⁴	1	6	yes	—
190	C₂³×D₄₃	C₂⁴	1	16	yes	—
191	C₂³×D₄₃	C₂⁴	1	16	yes	—
192	C₂³×D₄₃	C₂⁴	1	6	yes	—
193	C₂³×D₄₃	C₂⁴	1	6	yes	—
194	C₂×D₄×C₄₃	—	2	48	no	—
195	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
196	C₂²×C₄×C₄₃	—	2	4	no	—
197	C₂²×C₄×C₄₃	—	2	4	no	—
198	C₂²×C₄×C₄₃	—	2	48	no	—
199	C₂²×C₄×C₄₃	—	2	4	no	—
200	C₂²×C₄×C₄₃	—	2	4	no	—
201	C₂²×C₄×C₄₃	—	2	4	no	—
202	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
203	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
204	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
205	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
206	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
207	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	complemented
208	C₂×C₂²⋊D₄₃	—	2	48	no	—
209	C₂×C₂²⋊D₄₃	—	2	48	no	—
210	C₂×C₂²⋊D₄₃	—	4	24	no	—
211	C₂×C₂²⋊D₄₃	C₂×D₄	1	96	yes	complemented
212	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
213	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
214	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	complemented
215	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	complemented
216	C₂²×Dic₄₃	—	2	4	no	—
217	C₂²×Dic₄₃	—	2	4	no	—
218	C₂²×Dic₄₃	—	2	4	no	—
219	C₂²×Dic₄₃	—	4	24	no	—
220	C₂²×Dic₄₃	C₂×D₄	1	8	yes	—
221	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
222	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
223	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
224	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
225	C₂²×Dic₄₃	C₂⁴	1	16	yes	complemented
226	D₄×D₄₃	—	2	256	no	—
227	#10621898	—	2	256	no	—
228	C₂×D₁₇₂	—	2	48	no	—
229	C₂×D₁₇₂	—	2	48	no	—
230	C₂×D₁₇₂	—	2	48	no	—
231	C₂×D₁₇₂	—	4	24	no	—
232	C₂×D₁₇₂	C₂⁴	1	16	yes	—
233	C₂×D₁₇₂	C₂⁴	1	16	yes	—
234	C₂×D₁₇₂	C₂⁴	1	16	yes	complemented
235	C₂×D₁₇₂	C₂⁴	1	16	yes	complemented
236	C₂×C₄×D₄₃	—	2	48	no	—
237	C₂×C₄×D₄₃	—	2	48	no	—
238	C₂×C₄×D₄₃	—	2	48	no	—
239	C₂×C₄×D₄₃	—	4	24	no	—
240	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
241	C₂×C₄×D₄₃	C₂⁴	1	16	yes	complemented
242	C₂×C₄×D₄₃	C₂⁴	1	16	yes	complemented
243	C₂×C₄×D₄₃	C₂⁴	1	16	yes	complemented
244	C₂×Dic₈₆	—	2	48	no	—
245	C₂×Dic₈₆	C₂⁴	1	16	yes	complemented
246	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	complemented
247	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	complemented
248	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	complemented
249	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	complemented
250	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	complemented
251	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	complemented
252	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
253	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
254	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
255	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	complemented
256	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	complemented
257	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	complemented
258	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	complemented
259	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	complemented
260	Dic₄₃⋊C₄	C₂⁴	1	16	yes	complemented
261	Dic₄₃⋊C₄	C₂⁴	1	16	yes	complemented
262	C₄×Dic₄₃	C₂⁴	1	16	yes	complemented
263	C₂³×C₄₃	—	2	32	no	—
264	C₂³×C₄₃	—	2	12	no	—
265	C₂³×C₄₃	—	2	12	no	—
266	C₂³×C₄₃	—	2	12	no	—
267	C₂³×C₄₃	—	2	12	no	—
268	C₂³×C₄₃	—	2	12	no	—
269	C₂³×C₄₃	—	4	16	no	—
270	C₂³×C₄₃	C₂²×D₄	1	24	yes	—
271	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
272	C₂³×C₄₃	C₂×#41	1	4	yes	—
273	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
274	C₂³×C₄₃	C₂⁵	1	4	yes	—
275	C₂³×C₄₃	C₂⁵	1	4	yes	—
276	C₂³×C₄₃	C₂⁵	1	3	yes	—
277	C₂²×D₄₃	—	2	32	no	—
278	C₂²×D₄₃	—	2	32	no	—
279	C₂²×D₄₃	—	2	12	no	—
280	C₂²×D₄₃	—	2	12	no	—
281	C₂²×D₄₃	—	2	12	no	—
282	C₂²×D₄₃	—	2	12	no	—
283	C₂²×D₄₃	—	2	12	no	—
284	C₂²×D₄₃	—	2	12	no	—
285	C₂²×D₄₃	—	2	32	no	—
286	C₂²×D₄₃	—	2	12	no	—
287	C₂²×D₄₃	—	2	12	no	—
288	C₂²×D₄₃	—	2	12	no	—
289	C₂²×D₄₃	—	2	12	no	—
290	C₂²×D₄₃	—	2	32	no	—
291	C₂²×D₄₃	—	2	32	no	—
292	C₂²×D₄₃	—	2	32	no	—
293	C₂²×D₄₃	—	4	16	no	—
294	C₂²×D₄₃	—	4	16	no	—
295	C₂²×D₄₃	—	4	192	no	—
296	C₂²×D₄₃	—	4	192	no	—
297	C₂²×D₄₃	—	4	16	no	—
298	C₂²×D₄₃	—	4	16	no	—
299	C₂²×D₄₃	C₂²×D₄	1	24	yes	—
300	C₂²×D₄₃	C₂×#41	1	24	yes	complemented
301	C₂²×D₄₃	C₂⁵	1	4	yes	—
302	C₂²×D₄₃	C₂⁵	1	4	yes	—
303	C₂²×D₄₃	C₂⁵	1	4	yes	—
304	C₂²×D₄₃	C₂⁵	1	4	yes	—
305	D₄×C₄₃	—	2	32	no	—
306	C₂×C₄×C₄₃	—	2	12	no	—
307	C₂×C₄×C₄₃	—	2	12	no	—
308	C₂×C₄×C₄₃	—	2	12	no	—
309	C₂×C₄×C₄₃	—	2	32	no	—
310	C₂×C₄×C₄₃	—	2	12	no	—
311	C₂×C₄×C₄₃	—	2	12	no	—
312	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
313	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
314	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
315	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
316	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
317	C₂²⋊D₄₃	—	2	32	no	—
318	C₂²⋊D₄₃	—	2	32	no	—
319	C₂²⋊D₄₃	—	4	16	no	—
320	C₂²⋊D₄₃	C₂²×D₄	1	64	yes	complemented
321	C₂×Dic₄₃	—	2	12	no	—
322	C₂×Dic₄₃	—	2	12	no	—
323	C₂×Dic₄₃	—	2	12	no	—
324	C₂×Dic₄₃	—	4	16	no	—
325	C₂×Dic₄₃	C₂²×D₄	1	24	yes	—
326	C₂×Dic₄₃	C₂⁵	1	4	yes	—
327	C₂×Dic₄₃	C₂⁵	1	4	yes	—
328	C₂×Dic₄₃	C₂⁵	1	4	yes	—
329	C₂×Dic₄₃	C₂⁵	1	4	yes	—
330	D₁₇₂	—	2	32	no	—
331	D₁₇₂	—	2	32	no	—
332	D₁₇₂	—	2	32	no	—
333	D₁₇₂	—	4	16	no	—
334	C₄×D₄₃	—	2	32	no	—
335	C₄×D₄₃	—	2	32	no	—
336	C₄×D₄₃	—	2	32	no	—
337	C₄×D₄₃	—	4	16	no	—
338	Dic₈₆	—	2	32	no	—
339	C₂²×#546	—	43	1	no	maximal, Sylow
340	C₂²×C₄₃	—	2	4	no	—
341	C₂²×C₄₃	—	2	4	no	—
342	C₂²×C₄₃	—	2	48	no	—
343	C₂²×C₄₃	—	2	4	no	—
344	C₂²×C₄₃	—	2	4	no	—
345	C₂²×C₄₃	—	2	4	no	—
346	C₂²×C₄₃	—	4	24	no	—
347	C₂²×C₄₃	#546	1	16	yes	complemented
348	C₂²×C₄₃	C₂³×D₄	1	8	yes	—
349	C₂²×C₄₃	C₂³×D₄	1	6	yes	—
350	C₂²×C₄₃	C₂²×#41	1	6	yes	—
351	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	6	yes	—
352	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
353	C₂×D₄₃	—	2	4	no	—
354	C₂×D₄₃	—	2	4	no	—
355	C₂×D₄₃	—	2	4	no	—
356	C₂×D₄₃	—	2	4	no	—
357	C₂×D₄₃	—	2	48	no	—
358	C₂×D₄₃	—	2	48	no	—
359	C₂×D₄₃	—	2	4	no	—
360	C₂×D₄₃	—	2	4	no	—
361	C₂×D₄₃	—	2	4	no	—
362	C₂×D₄₃	—	2	4	no	—
363	C₂×D₄₃	—	2	4	no	—
364	C₂×D₄₃	—	2	4	no	—
365	C₂×D₄₃	—	4	64	no	—
366	C₂×D₄₃	—	4	64	no	—
367	C₂×D₄₃	—	4	24	no	—
368	C₂×D₄₃	—	4	24	no	—
369	C₂×D₄₃	C₂³×D₄	1	8	yes	—
370	C₂×D₄₃	C₂²×#41	1	8	yes	complemented
371	C₄×C₄₃	—	2	4	no	—
372	C₄×C₄₃	—	2	4	no	—
373	C₄×C₄₃	—	2	4	no	—
374	C₄×C₄₃	—	2	4	no	—
375	C₄×C₄₃	—	2	4	no	—
376	Dic₄₃	—	2	4	no	—
377	Dic₄₃	—	2	4	no	—
378	Dic₄₃	—	2	4	no	—
379	Dic₄₃	C₂³×D₄	1	8	yes	—
380	C₂³×#41	—	43	1	no	—
381	C₂⁴×D₄	—	43	1	no	—
382	C₂×#546	—	43	48	no	—
383	C₂²×#124	—	43	1	no	—
384	C₂²×#123	—	43	1	no	—
385	C₂²×#123	D₄₃	1	1	yes	characteristic, complemented
386	C₂²×C₂²⋊Q₈	—	43	1	no	—
387	C₂²×#121	—	43	1	no	—
388	C₂²×#121	—	43	1	no	—
389	C₂²×#121	—	43	1	no	—
390	C₂²×#120	—	43	1	no	—
391	C₂²×#120	—	43	1	no	—
392	C₂²×C₄×D₄	—	43	1	no	—
393	C₂²×C₄×D₄	—	43	1	no	—
394	C₂³×C₂²⋊C₄	—	43	1	no	—
395	C₂³×C₂²⋊C₄	—	43	1	no	—
396	C₂×C₄₃	—	2	8	no	—
397	C₂×C₄₃	—	4	4	no	—
398	C₂×C₄₃	C₂×#546	1	12	yes	complemented
399	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
400	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
401	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
402	D₄₃	—	2	8	no	—
403	D₄₃	—	2	8	no	—
404	D₄₃	—	4	4	no	—
405	D₄₃	—	4	4	no	—
406	C₂⁶	—	43	1	no	—
407	C₂⁶	—	43	1	no	—
408	C₂²×#41	—	43	24	no	—
409	C₂²×#41	—	86	16	no	—
410	C₂³×Q₈	—	43	1	no	—
411	C₂³×D₄	—	43	1	no	—
412	C₂³×D₄	—	43	1	no	—
413	C₂³×D₄	—	43	1	no	—
414	C₂³×D₄	—	43	1	no	—
415	C₂³×D₄	—	43	24	no	—
416	C₂³×D₄	—	43	1	no	—
417	C₂³×D₄	—	43	1	no	—
418	C₂³×D₄	—	43	1	no	—
419	C₂³×D₄	—	43	1	no	—
420	C₂³×D₄	—	86	16	no	—
421	C₂³×D₄	C₂×D₄₃	1	1	yes	characteristic
422	C₂⁴×C₄	—	43	1	no	—
423	C₂⁴×C₄	—	43	1	no	—
424	C₂⁴×C₄	—	43	1	no	—
425	C₂⁴×C₄	—	43	1	no	—
426	C₂⁴×C₄	—	43	1	no	—
427	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
428	#546	—	43	256	no	—
429	C₂×#124	—	43	24	no	—
430	C₂×#123	—	43	24	no	—
431	C₂×#123	C₂×D₄₃	1	24	yes	complemented
432	C₂×C₂²⋊Q₈	—	43	24	no	—
433	C₂×#121	—	43	24	no	—
434	C₂×#121	—	43	24	no	—
435	C₂×#121	—	43	24	no	—
436	C₂×#120	—	43	24	no	—
437	C₂×#120	—	43	24	no	—
438	C₂×C₄×D₄	—	43	24	no	—
439	C₂×C₄×D₄	—	43	24	no	—
440	C₂²×C₄⋊C₄	—	43	1	no	—
441	C₂²×C₄⋊C₄	—	43	1	no	—
442	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
443	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
444	C₂²×C₂²⋊C₄	—	43	1	no	—
445	C₂²×C₂²⋊C₄	—	43	1	no	—
446	C₂²×C₂²⋊C₄	—	43	1	no	—
447	C₂²×C₂²⋊C₄	—	43	1	no	—
448	C₂²×C₂²⋊C₄	—	43	1	no	—
449	C₂²×C₂²⋊C₄	—	43	1	no	—
450	C₂²×C₂²⋊C₄	—	43	1	no	—
451	C₂²×C₂²⋊C₄	—	43	1	no	—
452	C₂²×C₂²⋊C₄	—	43	1	no	—
453	C₂²×C₂²⋊C₄	—	43	24	no	—
454	C₂²×C₂²⋊C₄	—	43	24	no	—
455	C₂²×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
456	C₂²×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
458	C₂²×C₄²	—	43	1	no	—
459	C₄₃	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
460	C₂⁵	—	43	1	no	—
461	C₂⁵	—	43	1	no	—
462	C₂⁵	—	43	1	no	—
463	C₂⁵	—	43	1	no	—
464	C₂⁵	—	43	12	no	—
465	C₂⁵	—	43	12	no	—
466	C₂⁵	—	86	8	no	—
467	C₂⁵	—	86	8	no	—
468	C₂⁵	—	86	8	no	—
469	C₂⁵	—	86	8	no	—
470	C₂⁵	—	172	4	no	—
471	C₂⁵	—	172	4	no	—
472	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
473	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
474	C₂×#41	—	43	64	no	—
475	C₂×#41	—	86	192	no	—
476	C₂²×Q₈	—	43	12	no	—
477	C₂²×Q₈	—	86	8	no	—
478	C₂²×D₄	—	2	8	no	—
479	C₂²×D₄	—	43	16	no	—
480	C₂²×D₄	—	43	12	no	—
481	C₂²×D₄	—	43	12	no	—
482	C₂²×D₄	—	43	12	no	—
483	C₂²×D₄	—	43	12	no	—
484	C₂²×D₄	—	43	64	no	—
485	C₂²×D₄	—	43	12	no	—
486	C₂²×D₄	—	43	12	no	—
487	C₂²×D₄	—	43	12	no	—
488	C₂²×D₄	—	43	12	no	—
489	C₂²×D₄	—	86	8	no	—
490	C₂²×D₄	—	86	8	no	—
491	C₂²×D₄	—	86	8	no	—
492	C₂²×D₄	—	86	8	no	—
493	C₂²×D₄	—	86	192	no	—
494	C₂²×D₄	—	86	8	no	—
495	C₂²×D₄	—	172	4	no	—
496	C₂²×D₄	—	172	4	no	—
497	C₂²×D₄	C₂²×D₄₃	1	12	yes	—
498	C₂³×C₄	—	2	8	no	—
499	C₂³×C₄	—	43	1	no	—
500	C₂³×C₄	—	43	1	no	—
501	C₂³×C₄	—	43	1	no	—
502	C₂³×C₄	—	43	1	no	—
503	C₂³×C₄	—	43	12	no	—
504	C₂³×C₄	—	43	12	no	—
505	C₂³×C₄	—	43	12	no	—
506	C₂³×C₄	—	43	12	no	—
507	C₂³×C₄	—	43	12	no	—
508	C₂³×C₄	—	86	8	no	—
509	C₂³×C₄	—	86	8	no	—
510	C₂³×C₄	—	86	8	no	—
511	C₂³×C₄	—	172	4	no	—
512	C₂³×C₄	—	172	4	no	—
513	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
514	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
515	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
516	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
517	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
518	C₂³×C₄	C₂²×D₄₃	1	12	yes	complemented
519	#124	—	43	64	no	—
520	#123	—	43	64	no	—
521	#123	C₂²×D₄₃	1	64	yes	complemented
522	C₂²⋊Q₈	—	43	64	no	—
523	#121	—	43	64	no	—
524	#121	—	43	64	no	—
525	#121	—	43	64	no	—
526	#120	—	43	64	no	—
527	#120	—	43	64	no	—
528	C₄×D₄	—	43	64	no	—
529	C₄×D₄	—	43	64	no	—
530	C₂×C₄⋊C₄	—	43	12	no	—
531	C₂×C₄⋊C₄	—	43	12	no	—
532	C₂×C₄⋊C₄	C₂²×D₄₃	1	12	yes	complemented
533	C₂×C₄⋊C₄	C₂²×D₄₃	1	12	yes	complemented
534	C₂×C₂²⋊C₄	—	43	12	no	—
535	C₂×C₂²⋊C₄	—	43	12	no	—
536	C₂×C₂²⋊C₄	—	43	12	no	—
537	C₂×C₂²⋊C₄	—	43	12	no	—
538	C₂×C₂²⋊C₄	—	43	12	no	—
539	C₂×C₂²⋊C₄	—	43	12	no	—
540	C₂×C₂²⋊C₄	—	43	12	no	—
541	C₂×C₂²⋊C₄	—	43	12	no	—
542	C₂×C₂²⋊C₄	—	43	12	no	—
543	C₂×C₂²⋊C₄	—	43	64	no	—
544	C₂×C₂²⋊C₄	—	43	64	no	—
545	C₂×C₂²⋊C₄	C₂²×D₄₃	1	12	yes	complemented
546	C₂×C₂²⋊C₄	C₂²×D₄₃	1	12	yes	complemented
547	C₂×C₂²⋊C₄	C₂²×D₄₃	1	12	yes	complemented
548	C₂×C₄²	—	43	12	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	43	8	no	—
555	C₂⁴	—	43	8	no	—
556	C₂⁴	—	43	6	no	—
557	C₂⁴	—	43	6	no	—
558	C₂⁴	—	43	6	no	—
559	C₂⁴	—	43	6	no	—
560	C₂⁴	—	43	16	no	—
561	C₂⁴	—	43	16	no	—
562	C₂⁴	—	86	48	no	—
563	C₂⁴	—	86	48	no	—
564	C₂⁴	—	86	48	no	—
565	C₂⁴	—	86	4	no	—
566	C₂⁴	—	86	4	no	—
567	C₂⁴	—	86	4	no	—
568	C₂⁴	—	86	4	no	—
569	C₂⁴	—	86	4	no	—
570	C₂⁴	—	86	48	no	—
571	C₂⁴	—	86	4	no	—
572	C₂⁴	—	86	4	no	—
573	C₂⁴	—	86	4	no	—
574	C₂⁴	—	86	4	no	—
575	C₂⁴	—	86	4	no	—
576	C₂⁴	—	172	24	no	—
577	C₂⁴	—	172	24	no	—
578	C₂⁴	—	172	64	no	—
579	C₂⁴	—	172	64	no	—
580	C₂⁴	D₄×D₄₃	1	8	yes	—
581	C₂⁴	C₂³×D₄₃	1	6	yes	—
582	C₂⁴	C₂³×D₄₃	1	6	yes	—
583	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
584	#41	—	86	256	no	—
585	C₂×Q₈	—	43	16	no	—
586	C₂×Q₈	—	86	48	no	—
587	C₂×D₄	—	2	48	no	—
588	C₂×D₄	—	43	96	no	—
589	C₂×D₄	—	43	16	no	—
590	C₂×D₄	—	43	16	no	—
591	C₂×D₄	—	43	16	no	—
592	C₂×D₄	—	43	16	no	—
593	C₂×D₄	—	43	16	no	—
594	C₂×D₄	—	43	16	no	—
595	C₂×D₄	—	43	16	no	—
596	C₂×D₄	—	43	16	no	—
597	C₂×D₄	—	86	48	no	—
598	C₂×D₄	—	86	48	no	—
599	C₂×D₄	—	86	48	no	—
600	C₂×D₄	—	86	48	no	—
601	C₂×D₄	—	86	256	no	—
602	C₂×D₄	—	86	48	no	—
603	C₂×D₄	—	172	24	no	—
604	C₂×D₄	—	172	24	no	—
605	C₂×D₄	C₂³×D₄₃	1	16	yes	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	48	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	43	8	no	—
613	C₂²×C₄	—	43	6	no	—
614	C₂²×C₄	—	43	6	no	—
615	C₂²×C₄	—	43	6	no	—
616	C₂²×C₄	—	43	6	no	—
617	C₂²×C₄	—	43	16	no	—
618	C₂²×C₄	—	43	16	no	—
619	C₂²×C₄	—	43	16	no	—
620	C₂²×C₄	—	43	16	no	—
621	C₂²×C₄	—	43	16	no	—
622	C₂²×C₄	—	86	48	no	—
623	C₂²×C₄	—	86	48	no	—
624	C₂²×C₄	—	86	48	no	—
625	C₂²×C₄	—	86	4	no	—
626	C₂²×C₄	—	86	4	no	—
627	C₂²×C₄	—	86	4	no	—
628	C₂²×C₄	—	172	24	no	—
629	C₂²×C₄	—	172	24	no	—
630	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
631	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
632	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
633	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
634	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
635	C₂²×C₄	C₂³×D₄₃	1	16	yes	complemented
636	C₄⋊C₄	—	43	16	no	—
637	C₄⋊C₄	—	43	16	no	—
638	C₄⋊C₄	C₂³×D₄₃	1	16	yes	complemented
639	C₄⋊C₄	C₂³×D₄₃	1	16	yes	complemented
640	C₂²⋊C₄	—	43	16	no	—
641	C₂²⋊C₄	—	43	16	no	—
642	C₂²⋊C₄	—	43	16	no	—
643	C₂²⋊C₄	—	43	16	no	—
644	C₂²⋊C₄	—	43	16	no	—
645	C₂²⋊C₄	—	43	16	no	—
646	C₂²⋊C₄	—	43	16	no	—
647	C₂²⋊C₄	—	43	16	no	—
648	C₂²⋊C₄	—	43	16	no	—
649	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	complemented
650	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	complemented
651	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	complemented
652	C₄²	—	43	16	no	—
653	C₂³	—	2	12	no	—
654	C₂³	—	2	12	no	—
655	C₂³	—	2	32	no	—
656	C₂³	—	2	12	no	—
657	C₂³	—	2	12	no	—
658	C₂³	—	2	12	no	—
659	C₂³	—	4	16	no	—
660	C₂³	—	43	24	no	—
661	C₂³	—	43	24	no	—
662	C₂³	—	43	4	no	—
663	C₂³	—	43	4	no	—
664	C₂³	—	43	4	no	—
665	C₂³	—	43	4	no	—
666	C₂³	—	86	32	no	—
667	C₂³	—	86	32	no	—
668	C₂³	—	86	32	no	—
669	C₂³	—	86	12	no	—
670	C₂³	—	86	12	no	—
671	C₂³	—	86	12	no	—
672	C₂³	—	86	12	no	—
673	C₂³	—	86	32	no	—
674	C₂³	—	86	32	no	—
675	C₂³	—	86	12	no	—
676	C₂³	—	86	32	no	—
677	C₂³	—	86	12	no	—
678	C₂³	—	86	12	no	—
679	C₂³	—	86	12	no	—
680	C₂³	—	86	12	no	—
681	C₂³	—	86	12	no	—
682	C₂³	—	172	16	no	—
683	C₂³	—	172	16	no	—
684	C₂³	—	172	192	no	—
685	C₂³	—	172	192	no	—
686	C₂³	—	172	16	no	—
687	C₂³	—	172	16	no	—
688	C₂³	C₂×D₄×D₄₃	1	24	yes	—
689	C₂³	C₂×D₄×D₄₃	1	4	yes	—
690	C₂³	#41×D₄₃	1	4	yes	—
691	C₂³	#13063371	1	4	yes	—
692	C₂³	C₂⁴×D₄₃	1	4	yes	—
693	C₂³	C₂⁴×D₄₃	1	4	yes	—
694	C₂³	C₂⁴×D₄₃	1	3	yes	—
695	Q₈	—	86	32	no	—
696	D₄	—	2	32	no	—
697	D₄	—	43	64	no	—
698	D₄	—	86	32	no	—
699	D₄	—	86	32	no	—
700	D₄	—	86	32	no	—
701	D₄	—	86	32	no	—
702	D₄	—	86	32	no	—
703	D₄	—	172	16	no	—
704	D₄	—	172	16	no	—
705	C₂×C₄	—	2	12	no	—
706	C₂×C₄	—	2	12	no	—
707	C₂×C₄	—	2	32	no	—
708	C₂×C₄	—	2	12	no	—
709	C₂×C₄	—	2	12	no	—
710	C₂×C₄	—	2	12	no	—
711	C₂×C₄	—	43	24	no	—
712	C₂×C₄	—	43	4	no	—
713	C₂×C₄	—	43	4	no	—
714	C₂×C₄	—	43	4	no	—
715	C₂×C₄	—	43	4	no	—
716	C₂×C₄	—	86	32	no	—
717	C₂×C₄	—	86	32	no	—
718	C₂×C₄	—	86	32	no	—
719	C₂×C₄	—	86	12	no	—
720	C₂×C₄	—	86	12	no	—
721	C₂×C₄	—	86	12	no	—
722	C₂×C₄	—	172	16	no	—
723	C₂×C₄	—	172	16	no	—
724	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
725	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
726	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
727	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
728	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
729	C₂²	—	2	48	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	24	no	—
736	C₂²	—	43	8	no	—
737	C₂²	—	43	8	no	—
738	C₂²	—	86	48	no	—
739	C₂²	—	86	48	no	—
740	C₂²	—	86	4	no	—
741	C₂²	—	86	4	no	—
742	C₂²	—	86	4	no	—
743	C₂²	—	86	4	no	—
744	C₂²	—	86	4	no	—
745	C₂²	—	86	4	no	—
746	C₂²	—	86	4	no	—
747	C₂²	—	86	4	no	—
748	C₂²	—	86	4	no	—
749	C₂²	—	86	4	no	—
750	C₂²	—	172	64	no	—
751	C₂²	—	172	64	no	—
752	C₂²	—	172	24	no	—
753	C₂²	—	172	24	no	—
754	C₂²	#14583541	1	16	yes	direct product factor
755	C₂²	C₂²×D₄×D₄₃	1	8	yes	—
756	C₂²	C₂²×D₄×D₄₃	1	6	yes	—
757	C₂²	C₂×#41×D₄₃	1	6	yes	—
758	C₂²	C₂×#13063371	1	6	yes	—
759	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	2	4	no	—
765	C₄	—	43	8	no	—
766	C₄	—	86	4	no	—
767	C₄	—	86	4	no	—
768	C₄	—	86	4	no	—
769	C₂	—	2	8	no	—
770	C₂	—	4	4	no	—
771	C₂	—	86	8	no	—
772	C₂	—	86	8	no	—
773	C₂	—	172	4	no	—
774	C₂	—	172	4	no	—
775	C₂	C₂×#14583541	1	12	yes	direct product factor
776	C₂	C₂³×D₄×D₄₃	1	1	yes	characteristic
777	C₂	C₂²×#41×D₄₃	1	1	yes	characteristic
778	C₂	C₂²×#13063371	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂²×#123×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂²×#123	D₄₃
hypocenter	C₄₃	C₂²×#546
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂³×#10621898	C₂	semidirect
2. C₂³×D₄×D₄₃	C₂	semidirect
3. C₂×#14583541	C₂	direct (N × H)
4. C₂²×#13063311	C₂	semidirect
5. C₂²×#13063310	C₂	semidirect
6. C₂²×#13063303	C₂	semidirect
7. C₂²×#13063300	C₂	semidirect
8. C₂²×#13063298	C₂	semidirect
9. C₂²×#13063297	C₂	semidirect
10. C₂²×#13063295	C₂	semidirect
11. C₂²×#13063295	C₂	semidirect
12. C₂²×#13063287	C₂	semidirect
13. C₂²×(C₂²⋊D₄₃)⋊C₄	C₂	semidirect
14. C₂³×(C₂×D₄₃)⋊C₄	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₄₃	C₂	semidirect
16. C₂²×#123×C₄₃	C₂	semidirect
20. C₂²×#10621898	C₂²	semidirect
21. C₂³×Dic₈₆	C₂²	semidirect
24. C₂³×D₁₇₂	C₂²	semidirect
25. C₂³×D₁₇₂	C₂²	semidirect
28. C₂³×C₂²⋊D₄₃	C₂²	semidirect
29. C₂³×C₂²⋊D₄₃	C₂²	semidirect
31. C₂²×D₄×D₄₃	C₂²	semidirect
32. C₂⁴×Dic₄₃	C₂²	semidirect
34. C₂³×C₄×D₄₃	C₂²	semidirect
35. C₂³×C₄×D₄₃	C₂²	semidirect
36. C₂³×C₄×D₄₃	C₂²	semidirect
37. #14583541	C₂²	direct (N × H)
38. C₂×#13063311	C₂²	semidirect
39. C₂×#13063310	C₂²	semidirect
40. C₂×#13063303	C₂²	semidirect
41. C₂×#13063300	C₂²	semidirect
42. C₂×#13063298	C₂²	semidirect
43. C₂×#13063297	C₂²	semidirect
44. C₂×#13063295	C₂²	semidirect
45. C₂×#13063295	C₂²	semidirect
46. C₂×#13063287	C₂²	semidirect
47. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
48. C₂²×Dic₄₃⋊C₄	C₂²	semidirect
49. C₂²×Dic₄₃⋊C₄	C₂²	semidirect
50. C₂²×C₂²⋊Dic₄₃	C₂²	semidirect
54. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
55. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
56. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
57. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
58. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
59. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
60. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
61. C₂²×C₄×Dic₄₃	C₂²	semidirect
63. C₂⁴×C₄×C₄₃	C₂²	semidirect
64. C₂×#123×C₄₃	C₂²	semidirect
65. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
66. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
67. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
68. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
69. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
83. C₂×#10621898	C₂³	semidirect
85. C₂²×Dic₈₆	C₂³	semidirect
92. C₂²×D₁₇₂	C₂³	semidirect
93. C₂²×D₁₇₂	C₂³	semidirect
97. C₂²×C₂²⋊D₄₃	D₄	semidirect
100. C₂²×C₂²⋊D₄₃	C₂³	semidirect
101. C₂²×C₂²⋊D₄₃	C₂³	semidirect
103. C₂×D₄×D₄₃	C₂³	semidirect
109. C₂³×Dic₄₃	C₂³	semidirect
115. C₂²×C₄×D₄₃	C₂³	semidirect
116. C₂²×C₄×D₄₃	C₂³	semidirect
117. C₂²×C₄×D₄₃	C₂³	semidirect
118. #13063311	C₂³	semidirect
119. #13063310	C₂³	semidirect
120. #13063303	C₂³	semidirect
121. #13063300	C₂³	semidirect
122. #13063298	C₂³	semidirect
123. #13063297	C₂³	semidirect
124. #13063295	C₂³	semidirect
125. #13063295	C₂³	semidirect
126. #13063287	C₂³	semidirect
127. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
128. C₂×Dic₄₃⋊C₄	C₂³	semidirect
129. C₂×Dic₄₃⋊C₄	C₂³	semidirect
130. C₂×C₂²⋊Dic₄₃	C₂³	semidirect
134. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
135. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
136. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
137. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
138. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
139. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
140. C₂²⋊C₄×D₄₃	C₂³	semidirect
141. C₂×C₄×Dic₄₃	C₂³	semidirect
152. C₂³×C₄×C₄₃	C₂³	semidirect
153. #123×C₄₃	C₂³	semidirect
154. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
155. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
156. C₂×C₂²⋊C₄×C₄₃	C₂³	semidirect
157. C₂×C₂²⋊C₄×C₄₃	C₂³	semidirect
158. C₂×C₂²⋊C₄×C₄₃	C₂³	semidirect
187. C₂³×D₄₃	#41	semidirect
207. C₂²×C₄×C₄₃	C₂⁴	semidirect
211. C₂×C₂²⋊D₄₃	C₂×D₄	semidirect
214. C₂×C₂²⋊D₄₃	C₂⁴	semidirect
215. C₂×C₂²⋊D₄₃	C₂⁴	semidirect
225. C₂²×Dic₄₃	C₂⁴	semidirect
234. C₂×D₁₇₂	C₂⁴	semidirect
235. C₂×D₁₇₂	C₂⁴	semidirect
241. C₂×C₄×D₄₃	C₂⁴	semidirect
242. C₂×C₄×D₄₃	C₂⁴	semidirect
243. C₂×C₄×D₄₃	C₂⁴	semidirect
245. C₂×Dic₈₆	C₂⁴	semidirect
246. C₄⋊C₄×C₄₃	C₂⁴	semidirect
247. C₄⋊C₄×C₄₃	C₂⁴	semidirect
248. C₂²⋊C₄×C₄₃	C₂⁴	semidirect
249. C₂²⋊C₄×C₄₃	C₂⁴	semidirect
250. C₂²⋊C₄×C₄₃	C₂⁴	semidirect
251. C₂²⋊Dic₄₃	C₂⁴	semidirect
255. (C₂×D₄₃)⋊C₄	C₂⁴	semidirect
256. (C₂×D₄₃)⋊C₄	C₂⁴	semidirect
257. (C₂×D₄₃)⋊C₄	C₂⁴	semidirect
258. (C₂×D₄₃)⋊C₄	C₂⁴	semidirect
259. (C₂×D₄₃)⋊C₄	C₂⁴	semidirect
260. Dic₄₃⋊C₄	C₂⁴	semidirect
261. Dic₄₃⋊C₄	C₂⁴	semidirect
262. C₄×Dic₄₃	C₂⁴	semidirect
300. C₂²×D₄₃	C₂×#41	semidirect
320. C₂²⋊D₄₃	C₂²×D₄	semidirect
347. C₂²×C₄₃	#546	semidirect
370. C₂×D₄₃	C₂²×#41	semidirect
385. C₂²×#123	D₄₃	semidirect
398. C₂×C₄₃	C₂×#546	semidirect
427. C₂⁴×C₄	C₂×D₄₃	semidirect
431. C₂×#123	C₂×D₄₃	semidirect
442. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
443. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
455. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
456. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
457. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
459. C₄₃	C₂²×#546	semidirect
518. C₂³×C₄	C₂²×D₄₃	semidirect
521. #123	C₂²×D₄₃	semidirect
532. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
533. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
545. C₂×C₂²⋊C₄	C₂²×D₄₃	semidirect
546. C₂×C₂²⋊C₄	C₂²×D₄₃	semidirect
547. C₂×C₂²⋊C₄	C₂²×D₄₃	semidirect
635. C₂²×C₄	C₂³×D₄₃	semidirect
638. C₄⋊C₄	C₂³×D₄₃	semidirect
639. C₄⋊C₄	C₂³×D₄₃	semidirect
649. C₂²⋊C₄	C₂³×D₄₃	semidirect
650. C₂²⋊C₄	C₂³×D₄₃	semidirect
651. C₂²⋊C₄	C₂³×D₄₃	semidirect
754. C₂²	#14583541	direct (N × H)
775. C₂	C₂×#14583541	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10621898	2
C₂³×D₄×D₄₃	2
C₂×#14583541	2
C₂²×#13063311	2
C₂²×#13063310	2
C₂²×#13063303	2
C₂²×#13063300	2
C₂²×#13063298	2
C₂²×#13063297	2
C₂²×#13063295	2
C₂²×#13063287	2
C₂²×(C₂²⋊D₄₃)⋊C₄	2
C₂³×(C₂×D₄₃)⋊C₄	2
C₂²×C₂²⋊C₄×D₄₃	2
C₂²×#123×C₄₃	2
C₂²×#546	43

Subgroups — C22×#14583541 #26003516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583541 #26003516