Subgroups — C₂×#19148929 #26004191

Order 11008.

8814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148929	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583639	C₂	1	4	yes	maximal, complemented
3	C₂×#14583571	C₂	1	2	yes	maximal, complemented
4	C₂×#14583542	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×D₁₇₂	C₂	1	4	yes	maximal, complemented
6	C₂×#14583534	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14583500	C₂	1	4	yes	maximal, complemented
8	C₂×#14583467	C₂	1	4	yes	maximal, complemented
9	C₂×#14583460	C₂	1	4	yes	maximal, complemented
10	C₂×#127×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14583436	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10621902	C₂²	1	4	yes	complemented
14	C₂³×D₁₇₂	C₂²	1	4	yes	complemented
15	C₂²×D₄×D₄₃	C₂²	1	4	yes	complemented
16	C₂²×D₄×D₄₃	C₂²	1	4	yes	complemented
17	C₂²×D₄×D₄₃	C₂²	1	2	yes	complemented
18	#14583639	C₂²	1	64	yes	complemented
19	#14583571	C₂²	1	32	yes	complemented
20	#14583542	C₂²	1	64	yes	complemented
21	D₄×D₁₇₂	C₂²	1	64	yes	complemented
22	#14583534	C₂²	1	16	yes	complemented
23	#14583500	C₂²	1	64	yes	complemented
24	#14583467	C₂²	1	64	yes	complemented
25	#14583460	C₂²	1	64	yes	complemented
26	C₂×#13063322	C₂²	1	4	yes	complemented
27	C₂×#13063322	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13063321	C₂²	1	4	yes	complemented
29	C₂×#13063321	C₂²	1	2	yes	complemented
30	#127×D₄₃	C₂²	1	16	yes	complemented
31	#14583436	C₂²	1	32	yes	complemented
32	C₂×#13063320	C₂²	1	4	yes	complemented
33	C₂×#13063316	C₂²	1	2	yes	complemented
34	C₂×#13063314	C₂²	1	2	yes	complemented
35	C₂×#13063310	C₂²	1	4	yes	complemented
36	C₂×#13063308	C₂²	1	4	yes	complemented
37	C₂×#13063307	C₂²	1	8	yes	complemented
38	C₂×#13063301	C₂²	1	2	yes	complemented
39	C₂×#13063300	C₂²	1	2	yes	—
40	C₂×#13063300	C₂²	1	4	yes	complemented
41	C₂×#13063300	C₂²	1	8	yes	complemented
42	C₂×#13063299	C₂²	1	8	yes	complemented
43	C₂×#13063298	C₂²	1	8	yes	complemented
44	C₂×#13063298	C₂²	1	8	yes	complemented
45	C₂×#13063296	C₂²	1	4	yes	complemented
46	C₂×#13063295	C₂²	1	8	yes	complemented
47	C₂×#13063295	C₂²	1	8	yes	complemented
48	C₂×#13063295	C₂²	1	4	yes	complemented
49	C₂×#13063293	C₂²	1	4	yes	complemented
50	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
51	C₂×C₄×D₁₇₂	C₂²	1	4	yes	complemented
52	C₂×C₄×D₁₇₂	C₂²	1	4	yes	complemented
53	C₂×#13063282	C₂²	1	4	yes	complemented
54	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
55	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
56	C₄₃×#559	C₂²	1	16	yes	complemented
57	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
58	C₂×#124×C₄₃	C₂²	1	4	yes	complemented
59	C₂×#123×C₄₃	C₂²	1	4	yes	complemented
60	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
61	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	complemented
62	C₂⁴×D₄₃	C₂³	1	4	yes	—
63	C₂⁴×D₄₃	C₂³	1	4	yes	—
64	C₂×#10621902	—	4	16	no	—
65	C₂×#10621902	C₂³	1	32	yes	complemented
66	C₂²×D₁₇₂	—	4	16	no	—
67	C₂²×D₁₇₂	C₂³	1	4	yes	—
68	C₂²×D₁₇₂	C₂³	1	2	yes	—
69	C₂²×D₁₇₂	C₂³	1	4	yes	—
70	C₂²×D₁₇₂	C₂³	1	8	yes	—
71	C₂²×D₁₇₂	C₂³	1	8	yes	—
72	C₂²×D₁₇₂	C₂³	1	2	yes	—
73	C₂²×D₁₇₂	C₂³	1	32	yes	complemented
74	C₂²×C₂²⋊D₄₃	C₂³	1	8	yes	—
75	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
76	C₂²×C₂²⋊D₄₃	C₂³	1	8	yes	—
77	C₂×D₄×D₄₃	—	4	16	no	—
78	C₂×D₄×D₄₃	—	4	16	no	—
79	C₂×D₄×D₄₃	—	4	8	no	—
80	C₂×D₄×D₄₃	C₂³	1	16	yes	complemented
81	C₂×D₄×D₄₃	C₂³	1	32	yes	complemented
82	C₂×D₄×D₄₃	C₂³	1	32	yes	complemented
83	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
84	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
86	C₂²×C₄×D₄₃	C₂³	1	8	yes	—
87	#13063322	C₂³	1	8	yes	complemented
88	#13063322	C₂³	1	32	yes	complemented
89	#13063321	C₂³	1	16	yes	complemented
90	#13063321	C₂³	1	32	yes	complemented
91	#13063320	C₂³	1	32	yes	complemented
92	#13063316	C₂³	1	16	yes	complemented
93	#13063314	C₂³	1	16	yes	complemented
94	#13063310	C₂³	1	32	yes	complemented
95	#13063308	C₂³	1	32	yes	complemented
96	#13063307	C₂³	1	64	yes	complemented
97	#13063301	C₂³	1	16	yes	complemented
98	#13063300	C₂³	1	16	yes	—
99	#13063300	C₂³	1	64	yes	complemented
100	#13063300	C₂³	1	32	yes	complemented
101	#13063299	C₂³	1	64	yes	complemented
102	#13063298	C₂³	1	64	yes	complemented
103	#13063298	C₂³	1	64	yes	complemented
104	#13063296	C₂³	1	32	yes	complemented
105	#13063295	C₂³	1	64	yes	complemented
106	#13063295	C₂³	1	32	yes	complemented
107	#13063295	C₂³	1	64	yes	complemented
108	#13063293	C₂³	1	32	yes	complemented
109	C₄×D₁₇₂	C₂³	1	16	yes	complemented
110	C₄×D₁₇₂	C₂³	1	32	yes	complemented
111	C₄×D₁₇₂	C₂³	1	32	yes	complemented
112	#13063282	C₂³	1	32	yes	complemented
113	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
114	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
115	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
116	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
117	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
118	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
119	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
120	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
121	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
122	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
123	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
124	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	complemented
125	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
126	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
127	C₄²×D₄₃	C₂³	1	8	yes	complemented
128	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
130	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
132	#127×C₄₃	C₂³	1	8	yes	—
133	#124×C₄₃	C₂³	1	32	yes	complemented
134	#123×C₄₃	C₂³	1	32	yes	complemented
135	C₄×Q₈×C₄₃	C₂³	1	16	yes	complemented
136	C₄×D₄×C₄₃	C₂³	1	32	yes	complemented
137	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
140	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
143	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
144	C₂³×D₄₃	—	2	16	no	—
145	C₂³×D₄₃	—	4	16	no	—
146	C₂³×D₄₃	—	4	16	no	—
147	C₂³×D₄₃	—	4	8	no	—
148	C₂³×D₄₃	C₂⁴	1	4	yes	—
149	C₂³×D₄₃	C₂⁴	1	4	yes	—
150	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
151	C₂³×D₄₃	C₂⁴	1	16	yes	—
152	C₂³×D₄₃	C₂⁴	1	16	yes	—
153	C₂×Q₈×C₄₃	—	2	8	no	—
154	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
155	C₂×D₄×C₄₃	—	2	16	no	—
156	C₂×D₄×C₄₃	—	4	4	no	—
157	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
158	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
159	C₂²×C₄×C₄₃	—	4	8	no	—
160	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	—
164	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
165	C₂×C₂²⋊D₄₃	—	4	16	no	—
166	C₂×C₂²⋊D₄₃	—	4	16	no	—
167	C₂×C₂²⋊D₄₃	—	4	8	no	—
168	C₂×C₂²⋊D₄₃	C₂⁴	1	32	yes	—
169	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
170	C₂×C₂²⋊D₄₃	C₂⁴	1	32	yes	—
171	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
172	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
173	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
174	#10621902	—	4	64	no	—
175	D₄×D₄₃	—	4	32	no	—
176	D₄×D₄₃	—	4	64	no	—
177	D₄×D₄₃	—	4	64	no	—
178	C₂×D₁₇₂	—	2	8	no	—
179	C₂×D₁₇₂	—	2	16	no	—
180	C₂×D₁₇₂	—	2	16	no	—
181	C₂×D₁₇₂	—	4	4	no	—
182	C₂×D₁₇₂	—	4	16	no	—
183	C₂×D₁₇₂	—	4	16	no	—
184	C₂×D₁₇₂	—	4	64	no	—
185	C₂×D₁₇₂	C₂⁴	1	16	yes	—
186	C₂×D₁₇₂	C₂⁴	1	8	yes	—
187	C₂×D₁₇₂	C₂⁴	1	16	yes	—
188	C₂×D₁₇₂	C₂⁴	1	32	yes	—
189	C₂×D₁₇₂	C₂⁴	1	32	yes	—
190	C₂×D₁₇₂	C₂⁴	1	8	yes	—
191	C₂×C₄×D₄₃	—	2	8	no	—
192	C₂×C₄×D₄₃	—	2	16	no	—
193	C₂×C₄×D₄₃	—	2	4	no	—
194	C₂×C₄×D₄₃	—	4	16	no	—
195	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
196	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
197	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
198	C₂×C₄×D₄₃	C₂⁴	1	32	yes	—
199	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
200	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
201	C₂²⋊C₄×C₄₃	C₂⁴	1	32	yes	—
202	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
203	C₄²×C₄₃	C₂⁴	1	16	yes	—
204	C₄²×C₄₃	C₂⁴	1	4	yes	—
205	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
206	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
207	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
208	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
209	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
210	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
211	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
212	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
213	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
214	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
215	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
216	C₄×Dic₄₃	C₂⁴	1	8	yes	—
217	C₄×Dic₄₃	C₂⁴	1	4	yes	—
218	C₂³×C₄₃	—	2	16	no	—
219	C₂³×C₄₃	—	2	8	no	—
220	C₂³×C₄₃	C₂⁵	1	8	yes	—
221	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
222	C₂²×D₄₃	—	2	4	no	—
223	C₂²×D₄₃	—	2	8	no	—
224	C₂²×D₄₃	—	2	16	no	—
225	C₂²×D₄₃	—	2	8	no	—
226	C₂²×D₄₃	—	2	8	no	—
227	C₂²×D₄₃	—	2	8	no	—
228	C₂²×D₄₃	—	2	32	no	—
229	C₂²×D₄₃	—	4	16	no	—
230	C₂²×D₄₃	—	4	32	no	—
231	C₂²×D₄₃	—	4	32	no	—
232	C₂²×D₄₃	—	8	32	no	—
233	C₂²×D₄₃	—	8	32	no	—
234	C₂²×D₄₃	H(5,𝔽₂)	1	4	yes	—
235	C₂²×D₄₃	C₂⁵	1	8	yes	—
236	C₂²×D₄₃	C₂⁵	1	8	yes	—
237	C₂²×D₄₃	C₂⁵	1	2	yes	—
238	Q₈×C₄₃	—	2	16	no	—
239	D₄×C₄₃	—	2	32	no	—
240	D₄×C₄₃	—	4	8	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	8	no	—
243	C₂×C₄×C₄₃	—	2	8	no	—
244	C₂×C₄×C₄₃	—	4	16	no	—
245	C₂×C₄×C₄₃	H(5,𝔽₂)	1	8	yes	—
246	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
247	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
248	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
249	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
250	C₂²⋊D₄₃	—	4	32	no	—
251	C₂²⋊D₄₃	—	4	16	no	—
252	C₂²⋊D₄₃	—	4	32	no	—
253	C₂×Dic₄₃	—	2	8	no	—
254	C₂×Dic₄₃	—	2	2	no	—
255	C₂×Dic₄₃	—	2	4	no	—
256	C₂×Dic₄₃	C₂⁵	1	2	yes	—
257	C₂×Dic₄₃	C₂⁵	1	4	yes	—
258	C₂×Dic₄₃	C₂⁵	1	8	yes	—
259	D₁₇₂	—	2	32	no	—
260	D₁₇₂	—	2	16	no	—
261	D₁₇₂	—	2	32	no	—
262	D₁₇₂	—	4	32	no	—
263	D₁₇₂	—	4	8	no	—
264	D₁₇₂	—	4	32	no	—
265	C₄×D₄₃	—	2	8	no	—
266	C₄×D₄₃	—	2	16	no	—
267	C₄×D₄₃	—	2	32	no	—
268	C₄×D₄₃	—	4	32	no	—
269	C₂×#3543	—	43	1	no	maximal, Sylow
270	C₂²×C₄₃	—	2	8	no	—
271	C₂²×C₄₃	—	2	16	no	—
272	C₂²×C₄₃	—	4	16	no	—
273	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
274	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
275	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
276	C₂×D₄₃	—	2	4	no	—
277	C₂×D₄₃	—	2	8	no	—
278	C₂×D₄₃	—	2	8	no	—
279	C₂×D₄₃	—	2	8	no	—
280	C₂×D₄₃	—	2	8	no	—
281	C₂×D₄₃	—	2	8	no	—
282	C₂×D₄₃	—	2	16	no	—
283	C₂×D₄₃	—	4	16	no	—
284	C₂×D₄₃	—	4	16	no	—
285	C₂×D₄₃	—	8	32	no	—
286	C₂×D₄₃	—	8	32	no	—
287	C₂×D₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
288	C₄×C₄₃	—	2	2	no	—
289	C₄×C₄₃	—	2	8	no	—
290	C₄×C₄₃	—	2	8	no	—
291	C₄×C₄₃	C₂×H(5,𝔽₂)	1	8	yes	—
292	Dic₄₃	—	2	8	no	—
293	Dic₄₃	—	2	2	no	—
294	Dic₄₃	—	2	4	no	—
295	#3543	—	43	32	no	—
296	C₂×#560	—	43	4	no	—
297	C₂×#559	D₄₃	1	1	yes	characteristic, complemented
298	C₂×#550	—	43	2	no	—
299	C₂×#546	—	43	4	no	—
300	C₂×D₄²	—	43	1	no	—
301	C₂×D₄²	—	43	4	no	—
302	C₂×#540	—	43	4	no	—
303	C₂×#535	—	43	4	no	—
304	C₂×#534	—	43	4	no	—
305	C₂²×#127	—	43	1	no	—
306	C₂×#529	—	43	2	no	—
307	C₂×C₄₃	—	4	8	no	—
308	C₂×C₄₃	#3543	1	4	yes	complemented
309	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	2	yes	—
311	D₄₃	—	2	4	no	—
312	D₄₃	—	4	8	no	—
313	D₄₃	—	4	8	no	—
314	C₂²×#41	—	43	4	no	—
315	C₂³×D₄	—	43	2	no	—
316	C₂³×D₄	—	43	4	no	—
317	C₂³×D₄	—	43	4	no	—
318	C₂³×D₄	—	43	4	no	—
319	#560	—	43	64	no	—
320	#559	C₂×D₄₃	1	16	yes	complemented
321	#550	—	43	32	no	—
322	#546	—	43	64	no	—
323	D₄²	—	43	16	no	—
324	D₄²	—	43	64	no	—
325	#540	—	43	64	no	—
326	#535	—	43	64	no	—
327	#534	—	43	64	no	—
328	C₂×#127	—	43	4	no	—
329	C₂×#127	—	43	2	no	—
330	C₂×#127	—	43	16	no	—
331	C₂×#127	—	43	1	no	—
332	C₂×#127	—	43	4	no	—
333	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
334	#529	—	43	32	no	—
335	C₂×#126	—	43	4	no	—
336	C₂×#125	—	43	2	no	—
337	C₂×#124	—	43	2	no	—
338	C₂×#124	C₂×D₄₃	1	4	yes	complemented
339	C₂×#123	—	43	4	no	—
340	C₂×#123	—	43	4	no	—
341	C₂×#123	—	43	8	no	—
342	C₂×#123	C₂×D₄₃	1	4	yes	complemented
343	C₂×C₂²⋊Q₈	—	43	2	no	—
344	C₂×#121	—	43	4	no	—
345	C₂×#121	—	43	8	no	—
346	C₂×#121	—	43	2	no	—
347	C₂×#121	—	43	8	no	—
348	C₂×#121	—	43	4	no	—
349	C₂×#121	—	43	8	no	—
350	C₂×#121	—	43	8	no	—
351	C₂×#120	—	43	4	no	—
352	C₂×#120	—	43	4	no	—
353	C₂×#120	—	43	8	no	—
354	C₂×#120	—	43	8	no	—
355	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
356	C₂×C₄×D₄	—	43	4	no	—
357	C₂×C₄×D₄	—	43	2	no	—
358	C₂×C₄×D₄	—	43	4	no	—
359	C₂×C₄×D₄	C₂×D₄₃	1	4	yes	complemented
360	C₂×#117	—	43	4	no	—
361	C₂²×C₂²⋊C₄	—	43	4	no	—
362	C₂²×C₄²	—	43	1	no	—
363	C₄₃	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
364	C₂⁵	—	43	4	no	—
365	C₂⁵	—	43	4	no	—
366	C₂×#41	—	43	32	no	—
367	C₂×#41	—	172	16	no	—
368	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
369	C₂²×D₄	—	43	8	no	—
370	C₂²×D₄	—	43	4	no	—
371	C₂²×D₄	—	43	8	no	—
372	C₂²×D₄	—	43	16	no	—
373	C₂²×D₄	—	43	32	no	—
374	C₂²×D₄	—	43	32	no	—
375	C₂²×D₄	—	43	4	no	—
376	C₂²×D₄	—	43	2	no	—
377	C₂²×D₄	—	43	4	no	—
378	C₂²×D₄	—	43	8	no	—
379	C₂²×D₄	—	43	8	no	—
380	C₂²×D₄	—	43	2	no	—
381	C₂²×D₄	—	43	32	no	—
382	C₂²×D₄	—	172	16	no	—
383	C₂²×D₄	—	172	16	no	—
384	C₂²×D₄	—	172	16	no	—
385	C₂²×D₄	—	172	8	no	—
386	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
387	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
388	C₂³×C₄	—	43	4	no	—
389	C₂³×C₄	—	43	2	no	—
390	C₂³×C₄	—	43	1	no	—
391	C₂³×C₄	—	43	8	no	—
392	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
393	#127	—	43	32	no	—
394	#127	—	43	16	no	—
395	#127	—	43	8	no	—
396	#127	—	43	32	no	—
397	#127	C₂²×D₄₃	1	8	yes	—
398	#126	—	43	32	no	—
399	#125	—	43	16	no	—
400	#124	—	43	16	no	—
401	#124	C₂²×D₄₃	1	32	yes	complemented
402	#123	—	43	32	no	—
403	#123	—	43	32	no	—
404	#123	—	43	64	no	—
405	#123	C₂²×D₄₃	1	32	yes	complemented
406	C₂²⋊Q₈	—	43	16	no	—
407	#121	—	43	32	no	—
408	#121	—	43	64	no	—
409	#121	—	43	16	no	—
410	#121	—	43	64	no	—
411	#121	—	43	32	no	—
412	#121	—	43	64	no	—
413	#121	—	43	64	no	—
414	#120	—	43	32	no	—
415	#120	—	43	32	no	—
416	#120	—	43	64	no	—
417	#120	—	43	64	no	—
418	C₄×Q₈	C₂²×D₄₃	1	16	yes	complemented
419	C₄×D₄	—	43	32	no	—
420	C₄×D₄	—	43	16	no	—
421	C₄×D₄	—	43	32	no	—
422	C₄×D₄	C₂²×D₄₃	1	32	yes	complemented
423	#117	—	43	32	no	—
424	C₂×C₄⋊C₄	—	43	4	no	—
425	C₂×C₄⋊C₄	—	43	4	no	—
426	C₂×C₄⋊C₄	—	43	2	no	—
427	C₂×C₄⋊C₄	—	43	4	no	—
428	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
430	C₂×C₂²⋊C₄	—	43	4	no	—
431	C₂×C₂²⋊C₄	—	43	4	no	—
432	C₂×C₂²⋊C₄	—	43	4	no	—
433	C₂×C₂²⋊C₄	—	43	4	no	—
434	C₂×C₂²⋊C₄	—	43	4	no	—
435	C₂×C₂²⋊C₄	—	43	4	no	—
436	C₂×C₂²⋊C₄	—	43	8	no	—
437	C₂×C₂²⋊C₄	—	43	32	no	—
438	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
440	C₂×C₄²	—	43	2	no	—
441	C₂×C₄²	—	43	1	no	—
442	C₂×C₄²	—	43	8	no	—
443	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
444	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
445	C₂⁴	—	43	1	no	—
446	C₂⁴	—	43	4	no	—
447	C₂⁴	—	43	4	no	—
448	C₂⁴	—	43	16	no	—
449	C₂⁴	—	43	16	no	—
450	C₂⁴	—	86	16	no	—
451	C₂⁴	—	172	8	no	—
452	C₂⁴	—	172	16	no	—
453	C₂⁴	—	172	16	no	—
454	C₂⁴	C₂³×D₄₃	1	4	yes	—
455	#41	—	172	64	no	—
456	C₂×Q₈	—	2	8	no	—
457	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	43	32	no	—
461	C₂×D₄	—	43	16	no	—
462	C₂×D₄	—	43	32	no	—
463	C₂×D₄	—	43	16	no	—
464	C₂×D₄	—	43	8	no	—
465	C₂×D₄	—	43	16	no	—
466	C₂×D₄	—	43	32	no	—
467	C₂×D₄	—	43	32	no	—
468	C₂×D₄	—	43	8	no	—
469	C₂×D₄	—	86	16	no	—
470	C₂×D₄	—	86	8	no	—
471	C₂×D₄	—	86	16	no	—
472	C₂×D₄	—	172	16	no	—
473	C₂×D₄	—	172	4	no	—
474	C₂×D₄	—	172	16	no	—
475	C₂×D₄	—	172	64	no	—
476	C₂×D₄	—	172	64	no	—
477	C₂×D₄	—	172	64	no	—
478	C₂×D₄	—	172	32	no	—
479	C₂×D₄	—	172	8	no	—
480	C₂×D₄	—	172	16	no	—
481	C₂×D₄	—	172	16	no	—
482	C₂×D₄	C₂³×D₄₃	1	16	yes	—
483	C₂×D₄	C₂³×D₄₃	1	8	yes	—
484	C₂²×C₄	—	4	8	no	—
485	C₂²×C₄	—	43	1	no	—
486	C₂²×C₄	—	43	2	no	—
487	C₂²×C₄	—	43	4	no	—
488	C₂²×C₄	—	43	8	no	—
489	C₂²×C₄	—	43	4	no	—
490	C₂²×C₄	—	43	16	no	—
491	C₂²×C₄	—	43	32	no	—
492	C₂²×C₄	—	86	4	no	—
493	C₂²×C₄	—	86	8	no	—
494	C₂²×C₄	—	86	16	no	—
495	C₂²×C₄	—	172	16	no	—
496	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
497	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
498	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
499	C₂²×C₄	C₂³×D₄₃	1	16	yes	—
500	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
501	C₄⋊C₄	—	43	16	no	—
502	C₄⋊C₄	—	43	16	no	—
503	C₄⋊C₄	—	43	8	no	—
504	C₄⋊C₄	—	43	16	no	—
505	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
506	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
507	C₂²⋊C₄	—	43	16	no	—
508	C₂²⋊C₄	—	43	16	no	—
509	C₂²⋊C₄	—	43	16	no	—
510	C₂²⋊C₄	—	43	16	no	—
511	C₂²⋊C₄	—	43	16	no	—
512	C₂²⋊C₄	—	43	16	no	—
513	C₂²⋊C₄	—	43	32	no	—
514	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
515	C₂²⋊C₄	C₂³×D₄₃	1	32	yes	—
516	C₄²	—	43	8	no	—
517	C₄²	—	43	4	no	—
518	C₄²	C₂³×D₄₃	1	4	yes	—
519	C₄²	C₂³×D₄₃	1	16	yes	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	43	4	no	—
523	C₂³	—	43	2	no	—
524	C₂³	—	43	8	no	—
525	C₂³	—	43	8	no	—
526	C₂³	—	86	32	no	—
527	C₂³	—	86	4	no	—
528	C₂³	—	86	8	no	—
529	C₂³	—	86	8	no	—
530	C₂³	—	86	8	no	—
531	C₂³	—	86	16	no	—
532	C₂³	—	86	8	no	—
533	C₂³	—	344	32	no	—
534	C₂³	—	344	32	no	—
535	C₂³	—	172	16	no	—
536	C₂³	—	172	32	no	—
537	C₂³	—	172	32	no	—
538	C₂³	C₂⁴×D₄₃	1	8	yes	—
539	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
540	Q₈	—	2	16	no	—
541	D₄	—	2	32	no	—
542	D₄	—	4	8	no	—
543	D₄	—	86	32	no	—
544	D₄	—	86	16	no	—
545	D₄	—	86	32	no	—
546	D₄	—	172	32	no	—
547	D₄	—	172	8	no	—
548	D₄	—	172	32	no	—
549	D₄	—	172	16	no	—
550	D₄	—	172	32	no	—
551	D₄	—	172	32	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	4	16	no	—
556	C₂×C₄	—	43	2	no	—
557	C₂×C₄	—	43	4	no	—
558	C₂×C₄	—	43	8	no	—
559	C₂×C₄	—	86	8	no	—
560	C₂×C₄	—	86	2	no	—
561	C₂×C₄	—	86	8	no	—
562	C₂×C₄	—	86	4	no	—
563	C₂×C₄	—	86	16	no	—
564	C₂×C₄	—	86	32	no	—
565	C₂×C₄	—	172	32	no	—
566	C₂×C₄	#13063371	1	8	yes	—
567	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
568	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
569	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
570	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	16	no	—
573	C₂²	—	4	16	no	—
574	C₂²	—	43	4	no	—
575	C₂²	—	86	4	no	—
576	C₂²	—	86	8	no	—
577	C₂²	—	86	8	no	—
578	C₂²	—	86	8	no	—
579	C₂²	—	86	8	no	—
580	C₂²	—	86	16	no	—
581	C₂²	—	86	8	no	—
582	C₂²	—	344	32	no	—
583	C₂²	—	344	32	no	—
584	C₂²	—	172	16	no	—
585	C₂²	—	172	16	no	—
586	C₂²	H(5,𝔽₂)×D₄₃	1	2	yes	—
587	C₂²	C₂×#13063371	1	4	yes	—
588	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
589	C₄	—	2	8	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	8	no	—
592	C₄	—	86	2	no	—
593	C₄	—	86	8	no	—
594	C₄	—	86	4	no	—
595	C₄	C₂×#13063371	1	8	yes	—
596	C₂	—	4	8	no	—
597	C₂	—	86	4	no	—
598	C₂	—	172	8	no	—
599	C₂	—	172	8	no	—
600	C₂	#19148929	1	4	yes	direct product factor
601	C₂	C₂×H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
602	C₂	C₂²×#13063371	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#559	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#559	D₄₃
hypocenter	C₄₃	C₂×#3543
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#559

Complements

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

N	H ≅ G/N	type
1. #19148929	C₂	direct (N × H)
2. C₂×#14583639	C₂	semidirect
3. C₂×#14583571	C₂	semidirect
4. C₂×#14583542	C₂	semidirect
5. C₂×D₄×D₁₇₂	C₂	semidirect
6. C₂×#14583534	C₂	semidirect
7. C₂×#14583500	C₂	semidirect
8. C₂×#14583467	C₂	semidirect
9. C₂×#14583460	C₂	semidirect
10. C₂×#127×D₄₃	C₂	semidirect
11. C₂×#14583436	C₂	semidirect
12. C₂×C₄₃×#559	C₂	semidirect
13. C₂²×#10621902	C₂²	semidirect
14. C₂³×D₁₇₂	C₂²	semidirect
15. C₂²×D₄×D₄₃	C₂²	semidirect
16. C₂²×D₄×D₄₃	C₂²	semidirect
17. C₂²×D₄×D₄₃	C₂²	semidirect
18. #14583639	C₂²	semidirect
19. #14583571	C₂²	semidirect
20. #14583542	C₂²	semidirect
21. D₄×D₁₇₂	C₂²	semidirect
22. #14583534	C₂²	semidirect
23. #14583500	C₂²	semidirect
24. #14583467	C₂²	semidirect
25. #14583460	C₂²	semidirect
26. C₂×#13063322	C₂²	semidirect
27. C₂×#13063322	C₂²	semidirect
28. C₂×#13063321	C₂²	semidirect
29. C₂×#13063321	C₂²	semidirect
30. #127×D₄₃	C₂²	semidirect
31. #14583436	C₂²	semidirect
32. C₂×#13063320	C₂²	semidirect
33. C₂×#13063316	C₂²	semidirect
34. C₂×#13063314	C₂²	semidirect
35. C₂×#13063310	C₂²	semidirect
36. C₂×#13063308	C₂²	semidirect
37. C₂×#13063307	C₂²	semidirect
38. C₂×#13063301	C₂²	semidirect
40. C₂×#13063300	C₂²	semidirect
41. C₂×#13063300	C₂²	semidirect
42. C₂×#13063299	C₂²	semidirect
43. C₂×#13063298	C₂²	semidirect
44. C₂×#13063298	C₂²	semidirect
45. C₂×#13063296	C₂²	semidirect
46. C₂×#13063295	C₂²	semidirect
47. C₂×#13063295	C₂²	semidirect
48. C₂×#13063295	C₂²	semidirect
49. C₂×#13063293	C₂²	semidirect
50. C₂×C₄×D₁₇₂	C₂²	semidirect
51. C₂×C₄×D₁₇₂	C₂²	semidirect
52. C₂×C₄×D₁₇₂	C₂²	semidirect
53. C₂×#13063282	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
55. C₂×C₄²×D₄₃	C₂²	semidirect
56. C₄₃×#559	C₂²	semidirect
58. C₂×#124×C₄₃	C₂²	semidirect
59. C₂×#123×C₄₃	C₂²	semidirect
60. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
61. C₂×C₄×D₄×C₄₃	C₂²	semidirect
65. C₂×#10621902	C₂³	semidirect
73. C₂²×D₁₇₂	C₂³	semidirect
80. C₂×D₄×D₄₃	C₂³	semidirect
81. C₂×D₄×D₄₃	C₂³	semidirect
82. C₂×D₄×D₄₃	C₂³	semidirect
87. #13063322	C₂³	semidirect
88. #13063322	C₂³	semidirect
89. #13063321	C₂³	semidirect
90. #13063321	C₂³	semidirect
91. #13063320	C₂³	semidirect
92. #13063316	C₂³	semidirect
93. #13063314	C₂³	semidirect
94. #13063310	C₂³	semidirect
95. #13063308	C₂³	semidirect
96. #13063307	C₂³	semidirect
97. #13063301	C₂³	semidirect
99. #13063300	C₂³	semidirect
100. #13063300	C₂³	semidirect
101. #13063299	C₂³	semidirect
102. #13063298	C₂³	semidirect
103. #13063298	C₂³	semidirect
104. #13063296	C₂³	semidirect
105. #13063295	C₂³	semidirect
106. #13063295	C₂³	semidirect
107. #13063295	C₂³	semidirect
108. #13063293	C₂³	semidirect
109. C₄×D₁₇₂	C₂³	semidirect
110. C₄×D₁₇₂	C₂³	semidirect
111. C₄×D₁₇₂	C₂³	semidirect
112. #13063282	C₂³	semidirect
124. C₂²⋊C₄×D₄₃	C₂³	semidirect
127. C₄²×D₄₃	C₂³	semidirect
133. #124×C₄₃	C₂³	semidirect
134. #123×C₄₃	C₂³	semidirect
135. C₄×Q₈×C₄₃	C₂³	semidirect
136. C₄×D₄×C₄₃	C₂³	semidirect
297. C₂×#559	D₄₃	semidirect
308. C₂×C₄₃	#3543	semidirect
320. #559	C₂×D₄₃	semidirect
338. C₂×#124	C₂×D₄₃	semidirect
342. C₂×#123	C₂×D₄₃	semidirect
355. C₂×C₄×Q₈	C₂×D₄₃	semidirect
359. C₂×C₄×D₄	C₂×D₄₃	semidirect
363. C₄₃	C₂×#3543	semidirect
401. #124	C₂²×D₄₃	semidirect
405. #123	C₂²×D₄₃	semidirect
418. C₄×Q₈	C₂²×D₄₃	semidirect
422. C₄×D₄	C₂²×D₄₃	semidirect
600. C₂	#19148929	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148929	2
C₂×#14583639	2
C₂×#14583571	2
C₂×#14583542	2
C₂×D₄×D₁₇₂	2
C₂×#14583534	2
C₂×#14583500	2
C₂×#14583467	2
C₂×#14583460	2
C₂×#127×D₄₃	2
C₂×#14583436	2
C₂×C₄₃×#559	2
C₂×#3543	43

Subgroups — C2×#19148929 #26004191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148929 #26004191