Subgroups — #25960883

Order 11008.

2818 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583704	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063371	C₂	1	2	yes	maximal, complemented
3	#19143480	C₂	1	3	yes	maximal, complemented
4	#19143448	C₂	1	3	yes	maximal, complemented
5	#19143429	C₂	1	6	yes	maximal, complemented
6	C₄×#13063353	C₂	1	6	yes	maximal, complemented
7	#19143397	C₂	1	3	yes	maximal, complemented
8	C₂×#14583012	C₂	1	3	yes	maximal, complemented
9	#19143190	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143122	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063371	C₂²	1	2	yes	—
13	#14583704	C₄	1	16	yes	complemented
14	C₂×#13063353	C₂²	1	6	yes	—
15	C₂×#13063347	C₂²	1	3	yes	—
16	C₂²×D₃₄₄	C₂²	1	3	yes	—
17	#14583382	C₂²	1	2	yes	—
18	#14583381	—	2	2	no	—
19	#14583379	C₂²	1	6	yes	complemented
20	#14583373	C₂²	1	6	yes	complemented
21	#14583371	—	2	6	no	—
22	C₄×#10621902	—	2	2	no	—
23	C₄×#10621898	C₂²	1	6	yes	complemented
24	C₂×C₄×D₁₇₂	C₂²	1	6	yes	complemented
25	C₄×D₄×D₄₃	—	2	6	no	—
26	#14583012	C₂²	1	6	yes	complemented
27	#14583012	C₂²	1	3	yes	complemented
28	#14583012	C₂²	1	6	yes	complemented
29	#14583012	C₂²	1	3	yes	complemented
30	#14583012	C₂²	1	6	yes	complemented
31	#14583007	C₂²	1	3	yes	complemented
32	#14583007	C₂²	1	1	yes	characteristic, complemented
33	#14583001	C₂²	1	6	yes	complemented
34	#14583001	C₂²	1	6	yes	complemented
35	C₄×#10621873	C₂²	1	12	yes	complemented
36	C₄×D₃₄₄	C₂²	1	12	yes	complemented
37	#14582941	C₂²	1	6	yes	complemented
38	#14582937	C₂²	1	3	yes	complemented
39	C₂×#13063257	C₂²	1	3	yes	complemented
40	#14582905	C₂²	1	6	yes	complemented
41	#14582901	C₂²	1	6	yes	complemented
42	#14582896	C₂²	1	6	yes	complemented
43	C₂×#13063247	C₂²	1	6	yes	complemented
44	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#405	C₂²	1	3	yes	complemented
48	C₄₃×#405	C₂²	1	3	yes	complemented
49	C₄×M₁₆×C₄₃	C₂²	1	3	yes	complemented
50	C₂×#97×C₄₃	C₂²	1	3	yes	complemented
51	#13063371	—	2	8	no	—
52	#13063371	C₂×C₄	1	16	yes	complemented
53	C₂×#10621902	—	2	2	no	—
54	C₂×#10621898	C₂³	1	6	yes	—
55	C₂²×D₁₇₂	C₂³	1	6	yes	—
56	C₂×D₄×D₄₃	—	2	6	no	—
57	C₂²×C₄×D₄₃	—	2	6	no	—
58	#13063353	C₂×C₄	1	48	yes	complemented
59	#13063347	C₂×C₄	1	24	yes	complemented
60	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
61	C₂×#10621873	C₂³	1	6	yes	—
62	C₂×D₃₄₄	C₂×C₄	1	24	yes	complemented
63	C₂×D₃₄₄	C₂³	1	3	yes	—
64	C₂×D₃₄₄	C₂³	1	6	yes	—
65	Q₈×Dic₄₃	—	2	2	no	—
66	C₄×Dic₈₆	C₂³	1	2	yes	—
67	C₄×Dic₈₆	C₂³	1	6	yes	—
68	C₄×D₁₇₂	—	2	6	no	—
69	C₄×D₁₇₂	—	2	6	no	—
70	C₄×D₁₇₂	C₂³	1	6	yes	—
71	C₄×D₁₇₂	C₂³	1	12	yes	—
72	C₄×D₁₇₂	C₂³	1	6	yes	—
73	D₄×Dic₄₃	—	2	6	no	—
74	#13063287	—	2	6	no	—
75	#13063287	—	2	6	no	—
76	C₄×C₂²⋊D₄₃	—	2	6	no	—
77	C₄×C₂²⋊D₄₃	—	2	6	no	—
78	(C₂²⋊D₄₃)⋊C₄	—	2	12	no	—
79	#13063284	C₂³	1	6	yes	—
80	#13063283	—	2	6	no	—
81	#13063282	—	2	6	no	—
82	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
83	C₄⋊C₄×D₄₃	—	2	6	no	—
84	C₂×(C₂×D₄₃)⋊C₄	—	2	6	no	—
85	C₂²⋊C₄×D₄₃	—	2	12	no	—
86	C₄²×D₄₃	—	2	6	no	—
87	#13063259	C₂³	1	6	yes	—
88	#13063257	C₂³	1	3	yes	—
89	#13063257	C₂³	1	6	yes	—
90	#13063257	C₂³	1	1	yes	characteristic
91	#13063250	C₂³	1	2	yes	—
92	#13063250	C₂³	1	6	yes	—
93	#13063247	C₂³	1	6	yes	—
94	#13063247	C₂³	1	12	yes	—
95	#13063247	C₂³	1	6	yes	—
96	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
97	#131×C₄₃	—	2	4	no	—
98	#131×C₄₃	C₂×C₄	1	8	yes	complemented
99	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
100	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
101	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
102	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
103	C₄×Q₈×C₄₃	D₄	1	2	yes	—
104	C₄×D₄×C₄₃	D₄	1	6	yes	—
105	#117×C₄₃	C₂³	1	3	yes	—
106	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
107	#97×C₄₃	C₂³	1	1	yes	characteristic
108	#97×C₄₃	C₂³	1	3	yes	—
109	#97×C₄₃	C₂³	1	3	yes	—
110	#97×C₄₃	C₂³	1	3	yes	—
111	C₄×C₈×C₄₃	C₂³	1	6	yes	—
112	C₂³×D₄₃	—	2	6	no	—
113	#41×C₄₃	C₂²×C₄	1	4	yes	—
114	#41×C₄₃	#41	1	4	yes	—
115	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₄₃	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
118	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
119	C₂×C₂²⋊D₄₃	—	2	6	no	—
120	C₂²×Dic₄₃	—	2	6	no	—
121	#10621902	—	2	16	no	—
122	D₄×D₄₃	—	2	48	no	—
123	#10621898	—	2	12	no	—
124	#10621898	C₂²×C₄	1	24	yes	complemented
125	C₂×D₁₇₂	—	2	6	no	—
126	C₂×D₁₇₂	—	2	12	no	—
127	C₂×D₁₇₂	C₂²×C₄	1	24	yes	complemented
128	C₂×D₁₇₂	C₂⁴	1	6	yes	—
129	C₂×C₄×D₄₃	—	2	6	no	—
130	C₂×C₄×D₄₃	—	2	6	no	—
131	C₂×C₄×D₄₃	—	2	6	no	—
132	C₂×C₄×D₄₃	—	2	12	no	—
133	C₂×C₄×D₄₃	—	8	12	no	—
134	C₂×Dic₈₆	C₂⁴	1	2	yes	—
135	M₁₆×C₄₃	—	2	6	no	—
136	M₁₆×C₄₃	C₂²×C₄	1	12	yes	complemented
137	C₂×C₈×C₄₃	—	2	6	no	—
138	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	complemented
139	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
140	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
141	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
142	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₄⋊C₄×C₄₃	C₂×D₄	1	6	yes	—
144	C₂²⋊C₄×C₄₃	C₂×D₄	1	6	yes	—
145	C₄²×C₄₃	C₂×D₄	1	6	yes	—
146	C₄²×C₄₃	C₂⁴	1	3	yes	—
147	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
148	C₂²⋊Dic₄₃	—	2	6	no	—
149	(C₂×D₄₃)⋊C₄	—	2	6	no	—
150	(C₂×D₄₃)⋊C₄	—	2	12	no	—
151	(C₂×D₄₃)⋊C₄	—	2	6	no	—
152	C₄⋊Dic₄₃	—	2	6	no	—
153	C₄⋊Dic₄₃	C₂⁴	1	6	yes	—
154	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
155	Dic₄₃⋊C₄	—	2	6	no	—
156	Dic₄₃⋊C₄	—	2	2	no	—
157	C₄×Dic₄₃	—	2	2	no	—
158	C₄×Dic₄₃	—	2	6	no	—
159	C₄×Dic₄₃	—	2	6	no	—
160	Dic₁₇₂	C₂²×C₄	1	4	yes	complemented
161	D₃₄₄	C₂²×C₄	1	12	yes	complemented
162	D₃₄₄	C₂²×C₄	1	24	yes	complemented
163	#10621873	C₂²×C₄	1	24	yes	complemented
164	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
165	C₂²×D₄₃	—	2	6	no	—
166	C₂²×D₄₃	—	2	24	no	—
167	C₂²×D₄₃	—	8	6	no	—
168	C₂²×D₄₃	—	8	6	no	—
169	Q₈×C₄₃	C₄×D₄	1	4	yes	—
170	D₄×C₄₃	C₄×D₄	1	12	yes	—
171	C₂×C₄×C₄₃	—	4	6	no	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
173	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
175	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
177	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
178	C₂²⋊D₄₃	—	2	24	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	2	6	no	—
182	C₂×Dic₄₃	—	8	6	no	—
183	D₁₇₂	—	2	24	no	—
184	D₁₇₂	—	2	6	no	—
185	D₁₇₂	C₂³×C₄	1	12	yes	—
186	C₄×D₄₃	—	2	24	no	—
187	C₄×D₄₃	—	4	12	no	—
188	C₄×D₄₃	—	8	6	no	—
189	C₄×D₄₃	—	8	12	no	—
190	Dic₈₆	—	2	2	no	—
191	Dic₈₆	C₂³×C₄	1	4	yes	—
192	C₈×C₄₃	—	2	1	no	—
193	C₈×C₄₃	—	2	3	no	—
194	C₈×C₄₃	C₂³×C₄	1	6	yes	—
195	C₈×C₄₃	C₂³×C₄	1	2	yes	—
196	#60176	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	6	no	—
198	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
199	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
200	C₂×D₄₃	—	2	12	no	—
201	C₂×D₄₃	—	4	6	no	—
202	C₂×D₄₃	—	4	6	no	—
203	C₂×D₄₃	—	8	24	no	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	6	no	—
206	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
207	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
208	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
209	Dic₄₃	—	2	4	no	—
210	Dic₄₃	—	4	6	no	—
211	Dic₄₃	—	4	2	no	—
212	C₂×#576	—	43	1	no	—
213	C₄×H(5,𝔽₂)	—	43	2	no	—
214	#2952	—	43	3	no	—
215	#2948	—	43	3	no	—
216	#2946	—	43	6	no	—
217	C₄×AGL(1,ℤ/8)	—	43	6	no	—
218	#2943	—	43	3	no	—
219	C₂×#442	—	43	3	no	—
220	#2912	—	43	1	no	—
221	#2897	—	43	2	no	—
222	#2875	D₄₃	1	1	yes	characteristic, complemented
223	C₂×C₄₃	—	2	6	no	—
224	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
225	C₂×C₄₃	#3585	1	2	yes	—
226	D₄₃	—	4	12	no	—
227	C₂×H(5,𝔽₂)	—	43	2	no	—
228	#576	—	43	16	no	—
229	C₂×AGL(1,ℤ/8)	—	43	6	no	—
230	C₂×#135	—	43	3	no	—
231	C₂²×D₈	—	43	3	no	—
232	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
233	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
234	#520	—	43	2	no	—
235	#520	—	43	6	no	—
236	#520	—	86	2	no	—
237	#518	—	43	6	no	—
238	#518	—	86	6	no	—
239	C₄×#41	—	43	6	no	—
240	C₄×#41	—	86	2	no	—
241	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
242	C₂×C₄×D₄	—	43	6	no	—
243	C₂×C₄×D₄	—	86	6	no	—
244	#442	—	43	3	no	—
245	#442	—	43	6	no	—
246	#442	—	43	6	no	—
247	#442	—	43	6	no	—
248	#442	—	43	3	no	—
249	#441	—	43	1	no	—
250	#441	—	43	3	no	—
251	#440	—	43	6	no	—
252	#440	—	43	6	no	—
253	C₄×SD₁₆	—	43	12	no	—
254	C₄×D₈	—	43	12	no	—
255	#428	—	43	6	no	—
256	#427	—	43	3	no	—
257	C₂×#106	—	43	3	no	—
258	#418	—	43	6	no	—
259	#417	—	43	6	no	—
260	#416	—	43	6	no	—
261	C₂×#102	—	43	6	no	—
262	#405	C₂×D₄₃	1	3	yes	complemented
263	#405	C₂×D₄₃	1	3	yes	complemented
264	C₄×M₁₆	C₂×D₄₃	1	3	yes	complemented
265	C₂×#97	C₂×D₄₃	1	3	yes	complemented
266	C₄₃	#60176	1	1	yes	characteristic, complemented, Sylow
267	H(5,𝔽₂)	—	43	16	no	—
268	H(5,𝔽₂)	—	86	8	no	—
269	C₂×#41	—	43	6	no	—
270	C₂×#41	—	86	2	no	—
271	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
272	C₂²×D₄	—	43	6	no	—
273	C₂²×D₄	—	86	6	no	—
274	C₂³×C₄	—	86	6	no	—
275	AGL(1,ℤ/8)	—	43	48	no	—
276	#135	—	43	24	no	—
277	C₂×Q₁₆	—	43	1	no	—
278	C₂×SD₁₆	—	43	6	no	—
279	C₂×D₈	—	43	24	no	—
280	C₂×D₈	—	43	3	no	—
281	C₂×D₈	—	43	6	no	—
282	#131	—	2	4	no	—
283	#131	C₄×D₄₃	1	8	yes	complemented
284	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
285	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
286	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
287	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	—	43	6	no	—
290	C₄×Q₈	—	86	2	no	—
291	C₄×Q₈	D₁₇₂	1	2	yes	—
292	C₄×D₄	—	43	6	no	—
293	C₄×D₄	—	43	12	no	—
294	C₄×D₄	—	43	6	no	—
295	C₄×D₄	—	86	6	no	—
296	C₄×D₄	—	86	6	no	—
297	C₄×D₄	—	86	6	no	—
298	C₄×D₄	—	86	6	no	—
299	C₄×D₄	—	86	6	no	—
300	C₄×D₄	—	86	12	no	—
301	C₄×D₄	—	86	6	no	—
302	C₄×D₄	—	86	6	no	—
303	C₄×D₄	D₁₇₂	1	6	yes	—
304	#117	—	43	6	no	—
305	#117	—	86	6	no	—
306	#117	—	86	6	no	—
307	#117	C₂²×D₄₃	1	3	yes	—
308	C₂×C₄⋊C₄	—	43	6	no	—
309	C₂×C₄⋊C₄	—	86	6	no	—
310	C₂×C₂²⋊C₄	—	86	6	no	—
311	C₂×C₂²⋊C₄	—	86	12	no	—
312	C₂×C₄²	—	86	6	no	—
313	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
314	#107	—	43	6	no	—
315	#106	—	43	3	no	—
316	#106	—	43	6	no	—
317	#106	—	43	1	no	—
318	#103	—	43	2	no	—
319	#103	—	43	6	no	—
320	#102	—	43	6	no	—
321	#102	—	43	12	no	—
322	#102	—	43	6	no	—
323	#97	C₂²×D₄₃	1	1	yes	characteristic
324	#97	C₂²×D₄₃	1	3	yes	—
325	#97	C₂²×D₄₃	1	3	yes	—
326	#97	C₂²×D₄₃	1	3	yes	—
327	C₄×C₈	C₂²×D₄₃	1	6	yes	—
328	C₂⁴	—	86	6	no	—
329	#41	—	43	24	no	—
330	#41	—	86	16	no	—
331	#41	—	86	12	no	—
332	#41	C₂×C₄×D₄₃	1	4	yes	—
333	#41	#10621898	1	4	yes	—
334	C₂×Q₈	—	43	2	no	—
335	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
336	C₂×D₄	—	43	24	no	—
337	C₂×D₄	—	43	6	no	—
338	C₂×D₄	—	86	6	no	—
339	C₂×D₄	—	86	48	no	—
340	C₂×D₄	—	86	6	no	—
341	C₂×D₄	—	86	12	no	—
342	C₂×D₄	C₂×D₁₇₂	1	3	yes	—
343	C₂²×C₄	—	86	6	no	—
344	C₂²×C₄	—	86	6	no	—
345	C₂²×C₄	—	86	6	no	—
346	C₂²×C₄	—	86	12	no	—
347	C₂²×C₄	—	86	6	no	—
348	C₂²×C₄	—	344	12	no	—
349	C₂²×C₄	C₂×D₁₇₂	1	6	yes	—
350	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
351	Q₁₆	—	43	4	no	—
352	SD₁₆	—	43	24	no	—
353	D₈	—	43	12	no	—
354	D₈	—	43	24	no	—
355	M₁₆	—	2	6	no	—
356	M₁₆	C₂×C₄×D₄₃	1	12	yes	complemented
357	C₂×C₈	—	2	6	no	—
358	C₂×C₈	C₂×C₄×D₄₃	1	12	yes	complemented
359	C₂×C₈	C₂³×D₄₃	1	3	yes	—
360	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
361	C₂×C₈	C₂³×D₄₃	1	3	yes	—
362	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
363	C₄⋊C₄	—	43	6	no	—
364	C₄⋊C₄	—	43	2	no	—
365	C₄⋊C₄	—	86	6	no	—
366	C₄⋊C₄	—	86	6	no	—
367	C₄⋊C₄	—	86	2	no	—
368	C₄⋊C₄	C₂×D₁₇₂	1	6	yes	—
369	C₂²⋊C₄	—	86	6	no	—
370	C₂²⋊C₄	—	86	6	no	—
371	C₂²⋊C₄	—	86	6	no	—
372	C₂²⋊C₄	—	86	12	no	—
373	C₂²⋊C₄	C₂×D₁₇₂	1	6	yes	—
374	C₄²	—	86	2	no	—
375	C₄²	—	86	6	no	—
376	C₄²	—	86	6	no	—
377	C₄²	C₂×D₁₇₂	1	6	yes	—
378	C₄²	C₂³×D₄₃	1	3	yes	—
379	C₄²	C₂³×D₄₃	1	1	yes	characteristic
380	C₂³	—	86	24	no	—
381	C₂³	—	86	6	no	—
382	C₂³	—	344	6	no	—
383	C₂³	—	344	6	no	—
384	C₂³	C₂²×D₁₇₂	1	3	yes	—
385	Q₈	—	43	4	no	—
386	Q₈	—	86	2	no	—
387	Q₈	C₄×D₁₇₂	1	4	yes	—
388	D₄	—	43	12	no	—
389	D₄	—	86	24	no	—
390	D₄	—	86	24	no	—
391	D₄	—	86	6	no	—
392	D₄	C₄×D₁₇₂	1	12	yes	—
393	C₂×C₄	—	4	6	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	86	24	no	—
396	C₂×C₄	—	86	2	no	—
397	C₂×C₄	—	86	6	no	—
398	C₂×C₄	—	344	12	no	—
399	C₂×C₄	—	344	6	no	—
400	C₂×C₄	—	344	6	no	—
401	C₂×C₄	—	172	12	no	—
402	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
403	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
404	C₂×C₄	C₂²×D₁₇₂	1	6	yes	—
405	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
406	C₂×C₄	C₂×#10621898	1	6	yes	—
407	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	2	3	no	—
410	C₈	C₂²×C₄×D₄₃	1	2	yes	—
411	C₈	C₂²×C₄×D₄₃	1	6	yes	—
412	C₂²	—	2	6	no	—
413	C₂²	—	86	12	no	—
414	C₂²	—	344	24	no	—
415	C₂²	—	172	6	no	—
416	C₂²	—	172	6	no	—
417	C₂²	C₂×C₄×D₁₇₂	1	6	yes	—
418	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	6	no	—
421	C₄	—	86	4	no	—
422	C₄	—	172	6	no	—
423	C₄	—	172	2	no	—
424	C₄	C₂×C₄×D₁₇₂	1	6	yes	—
425	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
426	C₄	C₂²×#10621898	1	1	yes	characteristic
427	C₂	—	2	6	no	—
428	C₂	—	172	12	no	—
429	C₂	C₂²×C₄×D₁₇₂	1	1	yes	characteristic
430	C₂	#19149376	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂³×D₁₇₂
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#2875	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×#14583704	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2875	D₄₃
hypocenter	C₄₃	#60176
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2875

Complements

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

N	H ≅ G/N	type
2. C₄×#13063371	C₂	semidirect
3. #19143480	C₂	semidirect
4. #19143448	C₂	semidirect
5. #19143429	C₂	semidirect
6. C₄×#13063353	C₂	semidirect
7. #19143397	C₂	semidirect
8. C₂×#14583012	C₂	semidirect
9. #19143190	C₂	semidirect
10. #19143122	C₂	semidirect
11. C₄₃×#2875	C₂	semidirect
13. #14583704	C₄	semidirect
19. #14583379	C₂²	semidirect
20. #14583373	C₂²	semidirect
23. C₄×#10621898	C₂²	semidirect
24. C₂×C₄×D₁₇₂	C₂²	semidirect
26. #14583012	C₂²	semidirect
27. #14583012	C₂²	semidirect
28. #14583012	C₂²	semidirect
29. #14583012	C₂²	semidirect
30. #14583012	C₂²	semidirect
31. #14583007	C₂²	semidirect
32. #14583007	C₂²	semidirect
33. #14583001	C₂²	semidirect
34. #14583001	C₂²	semidirect
35. C₄×#10621873	C₂²	semidirect
36. C₄×D₃₄₄	C₂²	semidirect
37. #14582941	C₂²	semidirect
38. #14582937	C₂²	semidirect
39. C₂×#13063257	C₂²	semidirect
40. #14582905	C₂²	semidirect
41. #14582901	C₂²	semidirect
42. #14582896	C₂²	semidirect
43. C₂×#13063247	C₂²	semidirect
47. C₄₃×#405	C₂²	semidirect
48. C₄₃×#405	C₂²	semidirect
49. C₄×M₁₆×C₄₃	C₂²	semidirect
50. C₂×#97×C₄₃	C₂²	semidirect
52. #13063371	C₂×C₄	semidirect
58. #13063353	C₂×C₄	semidirect
59. #13063347	C₂×C₄	semidirect
62. C₂×D₃₄₄	C₂×C₄	semidirect
98. #131×C₄₃	C₂×C₄	semidirect
124. #10621898	C₂²×C₄	semidirect
127. C₂×D₁₇₂	C₂²×C₄	semidirect
136. M₁₆×C₄₃	C₂²×C₄	semidirect
138. C₂×C₈×C₄₃	C₂²×C₄	semidirect
160. Dic₁₇₂	C₂²×C₄	semidirect
161. D₃₄₄	C₂²×C₄	semidirect
162. D₃₄₄	C₂²×C₄	semidirect
163. #10621873	C₂²×C₄	semidirect
222. #2875	D₄₃	semidirect
262. #405	C₂×D₄₃	semidirect
263. #405	C₂×D₄₃	semidirect
264. C₄×M₁₆	C₂×D₄₃	semidirect
265. C₂×#97	C₂×D₄₃	semidirect
266. C₄₃	#60176	semidirect
283. #131	C₄×D₄₃	semidirect
356. M₁₆	C₂×C₄×D₄₃	semidirect
358. C₂×C₈	C₂×C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583704	2
C₄×#13063371	2
#19143480	2
#19143448	2
#19143429	2
C₄×#13063353	2
#19143397	2
C₂×#14583012	2
#19143190	2
#19143122	2
C₄₃×#2875	2
#60176	43