Subgroups — #26005148

Order 11008.

11346 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583735	C₂	1	2	yes	maximal, complemented
2	#19148388	C₂	1	8	yes	maximal, complemented
3	#19148380	C₂	1	4	yes	maximal, complemented
4	#19148373	C₂	1	4	yes	maximal, complemented
5	#19148366	C₂	1	4	yes	maximal, complemented
6	#19148359	C₂	1	12	yes	maximal, complemented
7	#41×D₁₇₂	C₂	1	16	yes	maximal, complemented
8	#19147928	C₂	1	6	yes	maximal, complemented
9	C₂×#14583449	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583735	—	2	32	no	—
12	C₂×#13063373	C₂²	1	4	yes	complemented
13	C₂×#13063372	C₂²	1	8	yes	complemented
14	C₂×#13063371	C₂²	1	8	yes	complemented
15	C₂×#13063370	C₂²	1	12	yes	complemented
16	C₂²×#10621898	C₂²	1	12	yes	complemented
17	C₂×#41×D₄₃	C₂²	1	16	yes	complemented
18	#14583571	C₂²	1	16	yes	complemented
19	Q₈×D₁₇₂	C₂²	1	16	yes	complemented
20	#14583561	C₂²	1	32	yes	complemented
21	#14583553	C₂²	1	48	yes	complemented
22	#14583544	C₂²	1	96	yes	complemented
23	D₄×D₁₇₂	C₂²	1	48	yes	complemented
24	#14583480	C₂²	1	24	yes	complemented
25	#14583475	C₂²	1	24	yes	complemented
26	#14583468	C₂²	1	24	yes	complemented
27	#14583461	C₂²	1	24	yes	complemented
28	#14583449	C₂²	1	24	yes	complemented
29	#14583449	C₂²	1	24	yes	complemented
30	#14583449	C₂²	1	12	yes	complemented
31	#14583449	C₂²	1	12	yes	complemented
32	#14583449	C₂²	1	4	yes	complemented
33	#14583449	C₂²	1	12	yes	complemented
34	C₂×#13063325	C₂²	1	6	yes	complemented
35	C₂×#13063322	C₂²	1	6	yes	complemented
36	C₂×#13063313	C₂²	1	12	yes	complemented
37	#14583411	C₂²	1	48	yes	complemented
38	C₂×#13063299	C₂²	1	24	yes	complemented
39	C₂×C₄×D₁₇₂	C₂²	1	24	yes	complemented
40	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×#41×C₄₃	C₂²	1	8	yes	complemented
42	C₄×#41×C₄₃	C₂²	1	4	yes	complemented
43	C₄×#41×C₄₃	C₂²	1	4	yes	complemented
44	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₄₃	C₂²	1	6	yes	complemented
46	C₂×#117×C₄₃	C₂²	1	3	yes	complemented
47	C₂²×C₄²×C₄₃	C₂²	1	3	yes	complemented
48	#13063373	—	2	32	no	—
49	#13063372	—	2	64	no	—
50	#13063371	—	2	64	no	—
51	#13063370	—	2	96	no	—
52	C₂×#10621902	C₂³	1	16	yes	—
53	C₂×#10621898	—	2	96	no	—
54	C₂×#10621898	C₂³	1	24	yes	—
55	C₂×#10621898	C₂³	1	8	yes	—
56	C₂×#10621898	C₂³	1	24	yes	—
57	C₂×#10621898	C₂³	1	24	yes	—
58	C₂×#10621900	C₂³	1	48	yes	—
59	#41×D₄₃	—	2	128	no	—
60	C₂²×Dic₈₆	C₂³	1	12	yes	—
61	C₂×Q₈×D₄₃	C₂³	1	16	yes	—
62	C₂²×D₁₇₂	C₂³	1	12	yes	—
63	C₂²×D₁₇₂	C₂³	1	24	yes	—
64	C₂²×C₂²⋊D₄₃	C₂³	1	24	yes	—
65	C₂×D₄×D₄₃	C₂³	1	48	yes	—
66	C₂²×C₄×D₄₃	C₂³	1	24	yes	—
67	#13063325	C₂³	1	24	yes	—
68	#13063325	C₂³	1	4	yes	—
69	#13063325	C₂³	1	12	yes	—
70	#13063322	C₂³	1	24	yes	—
71	#13063322	C₂³	1	4	yes	—
72	#13063322	C₂³	1	12	yes	—
73	#13063313	C₂³	1	48	yes	—
74	#13063313	C₂³	1	8	yes	—
75	#13063313	C₂³	1	24	yes	—
76	#13063309	C₂³	1	96	yes	—
77	#13063305	C₂³	1	96	yes	—
78	#13063300	C₂³	1	96	yes	—
79	#13063299	C₂³	1	48	yes	—
80	#13063299	C₂³	1	16	yes	—
81	#13063299	C₂³	1	48	yes	—
82	#13063299	C₂³	1	48	yes	—
83	#13063295	C₂³	1	96	yes	—
84	C₄×D₁₇₂	C₂³	1	48	yes	—
85	C₄×D₁₇₂	C₂³	1	48	yes	—
86	C₄×D₁₇₂	C₂³	1	16	yes	—
87	C₄×D₁₇₂	C₂³	1	48	yes	—
88	C₂×C₄⋊Dic₄₃	C₂³	1	24	yes	—
89	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	48	yes	—
90	C₂×#41×C₄₃	D₄	1	16	yes	complemented
91	C₂×#41×C₄₃	C₂³	1	4	yes	—
92	C₂×#41×C₄₃	C₂³	1	4	yes	—
93	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₄₃	C₂³	1	3	yes	—
95	C₂³×C₄×C₄₃	C₂³	1	6	yes	—
96	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
97	C₄×Q₈×C₄₃	C₂³	1	8	yes	—
98	C₄×Q₈×C₄₃	C₂³	1	8	yes	—
99	C₄×D₄×C₄₃	C₂³	1	24	yes	—
100	C₄×D₄×C₄₃	C₂³	1	24	yes	—
101	#117×C₄₃	C₂³	1	12	yes	—
102	#117×C₄₃	C₂³	1	12	yes	—
103	C₂×C₄⋊C₄×C₄₃	C₂³	1	6	yes	—
104	C₂×C₂²⋊C₄×C₄₃	C₂³	1	6	yes	—
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
107	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
108	C₂×C₄²×C₄₃	C₂³	1	12	yes	—
109	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
110	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
111	C₂⁴×C₄₃	C₂⁴	1	3	yes	—
112	C₂³×D₄₃	C₂⁴	1	24	yes	—
113	#41×C₄₃	C₂×D₄	1	32	yes	complemented
114	#41×C₄₃	C₂×D₄	1	32	yes	complemented
115	C₂×Q₈×C₄₃	C₂×D₄	1	8	yes	complemented
116	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
117	C₂×D₄×C₄₃	C₂×D₄	1	24	yes	complemented
118	C₂×D₄×C₄₃	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₄₃	—	4	12	no	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	24	yes	complemented
121	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
123	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
125	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
129	C₂×C₂²⋊D₄₃	—	2	96	no	—
130	C₂×C₂²⋊D₄₃	C₂⁴	1	48	yes	—
131	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
132	C₂²×Dic₄₃	C₂⁴	1	24	yes	—
133	#10621902	—	2	64	no	—
134	Q₈×D₄₃	—	2	64	no	—
135	#10621900	—	2	192	no	—
136	D₄×D₄₃	—	2	192	no	—
137	#10621898	—	2	96	no	—
138	#10621898	—	2	32	no	—
139	#10621898	—	2	96	no	—
140	#10621898	—	2	96	no	—
141	C₂×D₁₇₂	—	2	48	no	—
142	C₂×D₁₇₂	—	4	48	no	—
143	C₂×D₁₇₂	C₂⁴	1	16	yes	—
144	C₂×D₁₇₂	C₂⁴	1	24	yes	—
145	C₂×D₁₇₂	C₂⁴	1	8	yes	—
146	C₂×D₁₇₂	C₂⁴	1	48	yes	—
147	C₂×C₄×D₄₃	—	2	96	no	—
148	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
149	C₂×C₄×D₄₃	C₂⁴	1	48	yes	—
150	C₂×Dic₈₆	—	2	48	no	—
151	C₂×Dic₈₆	C₂⁴	1	24	yes	—
152	C₂×Dic₈₆	C₂⁴	1	8	yes	—
153	C₄⋊C₄×C₄₃	C₂⁴	1	24	yes	—
154	C₂²⋊C₄×C₄₃	C₂⁴	1	24	yes	—
155	C₄²×C₄₃	C₂⁴	1	2	yes	—
156	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₄²×C₄₃	C₂⁴	1	6	yes	—
159	C₄²×C₄₃	C₂⁴	1	6	yes	—
160	C₄²×C₄₃	C₂⁴	1	12	yes	—
161	C₄²×C₄₃	C₂⁴	1	12	yes	—
162	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
163	(C₂×D₄₃)⋊C₄	C₂⁴	1	96	yes	—
164	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
165	C₄⋊Dic₄₃	C₂⁴	1	48	yes	—
166	C₂³×C₄₃	—	4	6	no	—
167	C₂³×C₄₃	C₂²×D₄	1	12	yes	—
168	C₂³×C₄₃	C₂⁵	1	6	yes	—
169	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
170	C₂²×D₄₃	—	2	48	no	—
171	C₂²×D₄₃	—	4	48	no	—
172	C₂²×D₄₃	C₂⁵	1	16	yes	—
173	Q₈×C₄₃	C₂²×D₄	1	16	yes	—
174	D₄×C₄₃	C₂²×D₄	1	48	yes	—
175	C₂×C₄×C₄₃	—	2	24	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	4	6	no	—
178	C₂×C₄×C₄₃	—	4	12	no	—
179	C₂×C₄×C₄₃	C₂²×D₄	1	24	yes	—
180	C₂×C₄×C₄₃	C₂²×D₄	1	24	yes	—
181	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₄₃	C₂²×D₄	1	12	yes	—
183	C₂×C₄×C₄₃	C₂⁵	1	12	yes	—
184	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
185	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
187	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
188	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
189	C₂²⋊D₄₃	—	2	32	no	—
190	C₂²⋊D₄₃	—	2	96	no	—
191	C₂×Dic₄₃	—	2	48	no	—
192	C₂×Dic₄₃	C₂⁵	1	16	yes	—
193	D₁₇₂	—	2	16	no	—
194	D₁₇₂	—	2	48	no	—
195	D₁₇₂	—	2	32	no	—
196	D₁₇₂	—	4	48	no	—
197	C₄×D₄₃	—	2	32	no	—
198	C₄×D₄₃	—	2	96	no	—
199	Dic₈₆	—	2	16	no	—
200	Dic₈₆	—	2	48	no	—
201	#62812	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	12	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	4	12	no	—
205	C₂²×C₄₃	C₂³×D₄	1	12	yes	—
206	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
207	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
208	C₂×D₄₃	—	2	16	no	—
209	C₂×D₄₃	—	2	32	no	—
210	C₂×D₄₃	—	8	48	no	—
211	C₄×C₄₃	—	2	12	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	C₂³×D₄	1	2	yes	—
214	C₄×C₄₃	C₂³×D₄	1	12	yes	—
215	C₄×C₄₃	C₂³×D₄	1	2	yes	—
216	C₄×C₄₃	#585	1	4	yes	complemented
217	Dic₄₃	—	2	16	no	—
218	C₂×#585	—	43	2	no	—
219	#3500	—	43	8	no	—
220	#3499	—	43	4	no	—
221	#3498	—	43	4	no	—
222	#3497	—	43	4	no	—
223	#3496	—	43	12	no	—
224	D₄×#41	—	43	16	no	—
225	#3449	—	43	6	no	—
226	C₂×#532	—	43	6	no	—
227	C₂×C₄×#41	D₄₃	1	1	yes	characteristic, complemented
228	C₂×C₄₃	—	2	12	no	—
229	C₂×C₄₃	—	2	2	no	—
230	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
231	C₂×C₄₃	C₂×#585	1	2	yes	—
232	D₄₃	—	4	16	no	—
233	#585	—	86	32	no	—
234	C₂×2₋¹⁺⁴	—	43	8	no	—
235	C₂×2₋¹⁺⁴	—	43	4	no	—
236	C₂×H(5,𝔽₂)	—	43	8	no	—
237	C₂×H(5,𝔽₂)	—	43	12	no	—
238	C₂²×#41	—	43	16	no	—
239	C₂²×#41	—	43	12	no	—
240	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
241	#550	—	43	16	no	—
242	D₄×Q₈	—	43	16	no	—
243	#548	—	43	32	no	—
244	#547	—	43	48	no	—
245	#546	—	43	96	no	—
246	D₄²	—	43	48	no	—
247	#537	—	43	24	no	—
248	#536	—	43	24	no	—
249	#535	—	43	24	no	—
250	#534	—	43	24	no	—
251	#532	—	43	4	no	—
252	#532	—	43	12	no	—
253	#532	—	43	24	no	—
254	#532	—	43	24	no	—
255	#532	—	43	12	no	—
256	#532	—	43	12	no	—
257	C₂×C₄⋊Q₈	—	43	6	no	—
258	C₂×#127	—	43	6	no	—
259	C₂×#124	—	43	12	no	—
260	#525	—	43	48	no	—
261	C₂×#121	—	43	24	no	—
262	C₄×#41	C₂×D₄₃	1	8	yes	complemented
263	C₄×#41	C₂×D₄₃	1	4	yes	complemented
264	C₄×#41	C₂×D₄₃	1	4	yes	complemented
265	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
266	C₂×C₄×D₄	—	43	24	no	—
267	C₂×C₄×D₄	C₂×D₄₃	1	6	yes	complemented
268	C₂×#117	C₂×D₄₃	1	3	yes	complemented
269	C₂²×C₄²	C₂×D₄₃	1	3	yes	complemented
270	C₄₃	#62812	1	1	yes	characteristic, complemented, Sylow
271	2₋¹⁺⁴	—	86	64	no	—
272	2₋¹⁺⁴	—	86	32	no	—
273	H(5,𝔽₂)	—	86	64	no	—
274	H(5,𝔽₂)	—	86	96	no	—
275	C₂×#41	—	43	16	no	—
276	C₂×#41	—	43	48	no	—
277	C₂×#41	—	43	24	no	—
278	C₂×#41	—	43	8	no	—
279	C₂×#41	—	43	24	no	—
280	C₂×#41	—	43	24	no	—
281	C₂×#41	—	86	128	no	—
282	C₂×#41	—	86	96	no	—
283	C₂×#41	D₁₇₂	1	16	yes	complemented
284	C₂×#41	C₂²×D₄₃	1	4	yes	—
285	C₂×#41	C₂²×D₄₃	1	4	yes	—
286	C₂²×Q₈	—	43	16	no	—
287	C₂²×Q₈	—	43	12	no	—
288	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
289	C₂²×D₄	—	43	24	no	—
290	C₂²×D₄	—	43	48	no	—
291	C₂²×D₄	—	43	12	no	—
292	C₂²×D₄	—	43	24	no	—
293	C₂²×D₄	C₂²×D₄₃	1	3	yes	—
294	C₂³×C₄	—	43	24	no	—
295	C₂³×C₄	C₂²×D₄₃	1	6	yes	—
296	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
297	C₄⋊Q₈	—	43	4	no	—
298	C₄⋊Q₈	—	43	12	no	—
299	C₄⋊Q₈	—	43	24	no	—
300	#127	—	43	4	no	—
301	#127	—	43	12	no	—
302	#127	—	43	24	no	—
303	#124	—	43	8	no	—
304	#124	—	43	24	no	—
305	#124	—	43	48	no	—
306	#123	—	43	96	no	—
307	C₂²⋊Q₈	—	43	96	no	—
308	#121	—	43	16	no	—
309	#121	—	43	48	no	—
310	#121	—	43	48	no	—
311	#121	—	43	48	no	—
312	#121	—	43	96	no	—
313	#120	—	43	96	no	—
314	C₄×Q₈	C₂²×D₄₃	1	8	yes	—
315	C₄×Q₈	C₂²×D₄₃	1	8	yes	—
316	C₄×D₄	—	43	16	no	—
317	C₄×D₄	—	43	48	no	—
318	C₄×D₄	—	43	48	no	—
319	C₄×D₄	—	43	48	no	—
320	C₄×D₄	C₂²×D₄₃	1	24	yes	—
321	C₄×D₄	C₂²×D₄₃	1	24	yes	—
322	#117	C₂²×D₄₃	1	12	yes	—
323	#117	C₂²×D₄₃	1	12	yes	—
324	C₂×C₄⋊C₄	—	43	24	no	—
325	C₂×C₄⋊C₄	C₂²×D₄₃	1	6	yes	—
326	C₂×C₂²⋊C₄	—	43	48	no	—
327	C₂×C₂²⋊C₄	C₂²×D₄₃	1	6	yes	—
328	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
329	C₂×C₄²	C₂²×D₄₃	1	12	yes	—
330	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
331	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
332	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
333	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
334	C₂⁴	—	43	24	no	—
335	C₂⁴	C₂³×D₄₃	1	3	yes	—
336	#41	—	86	64	no	—
337	#41	—	86	192	no	—
338	#41	—	86	96	no	—
339	#41	—	86	32	no	—
340	#41	—	86	96	no	—
341	#41	—	86	96	no	—
342	#41	C₂×D₁₇₂	1	32	yes	complemented
343	#41	C₂×D₁₇₂	1	32	yes	complemented
344	C₂×Q₈	—	43	24	no	—
345	C₂×Q₈	—	43	8	no	—
346	C₂×Q₈	—	86	64	no	—
347	C₂×Q₈	—	86	48	no	—
348	C₂×Q₈	C₂×D₁₇₂	1	8	yes	complemented
349	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
350	C₂×D₄	—	43	48	no	—
351	C₂×D₄	—	43	16	no	—
352	C₂×D₄	—	43	16	no	—
353	C₂×D₄	—	43	24	no	—
354	C₂×D₄	—	43	8	no	—
355	C₂×D₄	—	43	48	no	—
356	C₂×D₄	—	86	96	no	—
357	C₂×D₄	—	86	192	no	—
358	C₂×D₄	—	86	48	no	—
359	C₂×D₄	—	172	48	no	—
360	C₂×D₄	C₂×D₁₇₂	1	24	yes	complemented
361	C₂×D₄	C₂³×D₄₃	1	12	yes	—
362	C₂²×C₄	—	4	12	no	—
363	C₂²×C₄	—	43	24	no	—
364	C₂²×C₄	—	43	48	no	—
365	C₂²×C₄	—	43	16	no	—
366	C₂²×C₄	—	86	96	no	—
367	C₂²×C₄	C₂×D₁₇₂	1	24	yes	complemented
368	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
369	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
370	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
371	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
372	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
373	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
374	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
376	C₄⋊C₄	—	43	16	no	—
377	C₄⋊C₄	—	43	48	no	—
378	C₄⋊C₄	C₂³×D₄₃	1	24	yes	—
379	C₂²⋊C₄	—	43	32	no	—
380	C₂²⋊C₄	—	43	96	no	—
381	C₂²⋊C₄	C₂³×D₄₃	1	24	yes	—
382	C₄²	C₂³×D₄₃	1	1	yes	characteristic
383	C₄²	C₂³×D₄₃	1	1	yes	characteristic
384	C₄²	C₂³×D₄₃	1	6	yes	—
385	C₄²	C₂³×D₄₃	1	12	yes	—
386	C₄²	C₂³×D₄₃	1	12	yes	—
387	C₄²	C₂³×D₄₃	1	2	yes	—
388	C₄²	C₂³×D₄₃	1	6	yes	—
389	C₂³	—	4	6	no	—
390	C₂³	—	43	16	no	—
391	C₂³	—	86	48	no	—
392	C₂³	—	172	48	no	—
393	C₂³	C₂²×D₁₇₂	1	12	yes	—
394	C₂³	C₂⁴×D₄₃	1	6	yes	—
395	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
396	Q₈	—	86	48	no	—
397	Q₈	—	86	16	no	—
398	Q₈	C₂²×D₁₇₂	1	16	yes	—
399	D₄	—	86	96	no	—
400	D₄	—	86	32	no	—
401	D₄	—	86	48	no	—
402	D₄	—	86	16	no	—
403	D₄	—	86	32	no	—
404	D₄	—	172	48	no	—
405	D₄	C₂²×D₁₇₂	1	48	yes	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	24	no	—
408	C₂×C₄	—	4	12	no	—
409	C₂×C₄	—	4	6	no	—
410	C₂×C₄	—	43	16	no	—
411	C₂×C₄	—	86	48	no	—
412	C₂×C₄	—	86	32	no	—
413	C₂×C₄	—	86	96	no	—
414	C₂×C₄	C₂²×D₁₇₂	1	24	yes	—
415	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
416	C₂×C₄	C₂²×D₁₇₂	1	24	yes	—
417	C₂×C₄	C₂²×D₁₇₂	1	12	yes	—
418	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
419	C₂×C₄	C₂⁴×D₄₃	1	12	yes	—
420	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
421	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
422	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
423	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
424	C₂²	—	2	2	no	—
425	C₂²	—	2	12	no	—
426	C₂²	—	4	12	no	—
427	C₂²	—	86	16	no	—
428	C₂²	—	86	32	no	—
429	C₂²	—	344	48	no	—
430	C₂²	C₂³×D₁₇₂	1	12	yes	—
431	C₂²	C₂³×D₁₇₂	1	2	yes	—
432	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	12	no	—
435	C₄	—	86	16	no	—
436	C₄	C₂³×D₁₇₂	1	2	yes	—
437	C₄	C₂³×D₁₇₂	1	12	yes	—
438	C₄	C₂³×D₁₇₂	1	2	yes	—
439	C₄	#14583735	1	4	yes	complemented
440	C₂	—	2	2	no	—
441	C₂	—	2	12	no	—
442	C₂	—	172	16	no	—
443	C₂	C₂⁴×D₁₇₂	1	1	yes	characteristic
444	C₂	C₂×#14583735	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄×#41×C₄₃	C₂
hypercenter	C₂×C₄×#41	D₄₃
hypocenter	C₄₃	#62812
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#14583735	C₂	semidirect
2. #19148388	C₂	semidirect
3. #19148380	C₂	semidirect
4. #19148373	C₂	semidirect
5. #19148366	C₂	semidirect
6. #19148359	C₂	semidirect
7. #41×D₁₇₂	C₂	semidirect
8. #19147928	C₂	semidirect
9. C₂×#14583449	C₂	semidirect
10. C₂×C₄×#41×C₄₃	C₂	semidirect
12. C₂×#13063373	C₂²	semidirect
13. C₂×#13063372	C₂²	semidirect
14. C₂×#13063371	C₂²	semidirect
15. C₂×#13063370	C₂²	semidirect
16. C₂²×#10621898	C₂²	semidirect
17. C₂×#41×D₄₃	C₂²	semidirect
18. #14583571	C₂²	semidirect
19. Q₈×D₁₇₂	C₂²	semidirect
20. #14583561	C₂²	semidirect
21. #14583553	C₂²	semidirect
22. #14583544	C₂²	semidirect
23. D₄×D₁₇₂	C₂²	semidirect
24. #14583480	C₂²	semidirect
25. #14583475	C₂²	semidirect
26. #14583468	C₂²	semidirect
27. #14583461	C₂²	semidirect
28. #14583449	C₂²	semidirect
29. #14583449	C₂²	semidirect
30. #14583449	C₂²	semidirect
31. #14583449	C₂²	semidirect
32. #14583449	C₂²	semidirect
33. #14583449	C₂²	semidirect
34. C₂×#13063325	C₂²	semidirect
35. C₂×#13063322	C₂²	semidirect
36. C₂×#13063313	C₂²	semidirect
37. #14583411	C₂²	semidirect
38. C₂×#13063299	C₂²	semidirect
39. C₂×C₄×D₁₇₂	C₂²	semidirect
41. C₄×#41×C₄₃	C₂²	semidirect
42. C₄×#41×C₄₃	C₂²	semidirect
43. C₄×#41×C₄₃	C₂²	semidirect
44. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
45. C₂×C₄×D₄×C₄₃	C₂²	semidirect
46. C₂×#117×C₄₃	C₂²	semidirect
47. C₂²×C₄²×C₄₃	C₂²	semidirect
90. C₂×#41×C₄₃	D₄	semidirect
113. #41×C₄₃	C₂×D₄	semidirect
114. #41×C₄₃	C₂×D₄	semidirect
115. C₂×Q₈×C₄₃	C₂×D₄	semidirect
117. C₂×D₄×C₄₃	C₂×D₄	semidirect
120. C₂²×C₄×C₄₃	C₂×D₄	semidirect
216. C₄×C₄₃	#585	semidirect
227. C₂×C₄×#41	D₄₃	semidirect
262. C₄×#41	C₂×D₄₃	semidirect
263. C₄×#41	C₂×D₄₃	semidirect
264. C₄×#41	C₂×D₄₃	semidirect
265. C₂×C₄×Q₈	C₂×D₄₃	semidirect
267. C₂×C₄×D₄	C₂×D₄₃	semidirect
268. C₂×#117	C₂×D₄₃	semidirect
269. C₂²×C₄²	C₂×D₄₃	semidirect
270. C₄₃	#62812	semidirect
283. C₂×#41	D₁₇₂	semidirect
342. #41	C₂×D₁₇₂	semidirect
343. #41	C₂×D₁₇₂	semidirect
348. C₂×Q₈	C₂×D₁₇₂	semidirect
360. C₂×D₄	C₂×D₁₇₂	semidirect
367. C₂²×C₄	C₂×D₁₇₂	semidirect
439. C₄	#14583735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583735	2
#19148388	2
#19148380	2
#19148373	2
#19148366	2
#19148359	2
#41×D₁₇₂	2
#19147928	2
C₂×#14583449	2
C₂×C₄×#41×C₄₃	2
#62812	43