Subgroups — C₄×#14583283 #25105043

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583283	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#10621873	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic
5	C₄×#13063313	C₂	1	2	yes	maximal, complemented
6	#19135461	C₂	1	1	yes	maximal, characteristic
7	#19135456	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135449	C₂	1	2	yes	maximal, complemented
9	#19135406	C₂	1	2	yes	maximal, complemented
10	#19134759	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
13	C₂²×#10621873	C₂²	1	2	yes	—
14	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
15	C₂×#13063313	C₂²	1	2	yes	—
16	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
17	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
18	#14583283	C₄	1	8	yes	direct product factor
19	C₄×Dic₁₇₂	—	2	4	no	—
20	C₄×#10621873	—	2	8	no	—
21	C₄×D₃₄₄	—	2	4	no	—
22	C₂×#13063259	C₂²	1	1	yes	characteristic
23	C₂×#13063259	C₂²	1	1	yes	characteristic
24	C₂×#13063257	C₂²	1	2	yes	—
25	C₂×#13063250	C₂²	1	2	yes	—
26	C₂×#13063250	C₂²	1	2	yes	—
27	C₂×#13063247	C₂²	1	2	yes	—
28	C₂×#13063247	C₂²	1	2	yes	—
29	#14582805	C₂²	1	2	yes	—
30	#14582801	C₂²	1	2	yes	—
31	#14582790	—	2	4	no	—
32	#14582765	C₂²	1	2	yes	—
33	C₄×(C₂×D₄₃)⋊C₄	—	2	4	no	—
34	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄³×C₄₃	C₂²	1	1	yes	characteristic
41	C₂²×Dic₈₆	C₂³	1	2	yes	—
42	C₂²×D₁₇₂	C₂³	1	2	yes	—
43	C₂²×C₄×D₄₃	—	2	2	no	—
44	C₂×Dic₁₇₂	—	2	2	no	—
45	C₂×Dic₁₇₂	—	2	2	no	—
46	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	complemented
47	C₂×#10621873	—	2	4	no	—
48	C₂×#10621873	—	2	4	no	—
49	C₂×#10621873	C₂×C₄	1	8	yes	complemented
50	C₂×D₃₄₄	—	2	2	no	—
51	C₂×D₃₄₄	—	2	2	no	—
52	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
53	#13063313	—	2	4	no	—
54	#13063313	C₂×C₄	1	8	yes	complemented
55	C₄×Dic₈₆	—	2	4	no	—
56	C₄×Dic₈₆	—	2	4	no	—
57	C₄×D₁₇₂	—	2	4	no	—
58	C₄×D₁₇₂	—	2	4	no	—
59	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
61	C₂×Dic₄₃⋊C₄	—	2	2	no	—
62	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
63	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
65	C₂×C₄×Dic₄₃	—	2	2	no	—
66	#13063259	—	2	2	no	—
67	#13063259	—	2	2	no	—
68	#13063257	—	2	4	no	—
69	#13063250	—	2	4	no	—
70	#13063250	—	2	4	no	—
71	#13063247	—	2	4	no	—
72	#13063247	—	2	4	no	—
73	C₄₃⋊#95	—	2	4	no	—
74	C₄₃⋊#95	—	2	4	no	—
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	D₄	1	2	yes	—
80	C₂×C₄²×C₄₃	D₄	1	2	yes	—
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₄₃	—	2	2	no	—
85	C₄×C₈×C₄₃	—	2	2	no	—
86	C₄×C₈×C₄₃	—	2	2	no	—
87	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
88	C₄×C₈×C₄₃	D₄	1	4	yes	—
89	C₄×C₈×C₄₃	D₄	1	4	yes	—
90	C₂³×D₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₃	—	2	2	no	—
97	C₂²×Dic₄₃	—	2	2	no	—
98	C₂²×Dic₄₃	—	2	2	no	—
99	C₂×D₁₇₂	—	2	2	no	—
100	C₂×D₁₇₂	—	2	2	no	—
101	C₂×D₁₇₂	—	2	2	no	—
102	C₂×D₁₇₂	—	2	2	no	—
103	C₂×D₁₇₂	—	2	2	no	—
104	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
105	C₂×C₄×D₄₃	—	4	4	no	—
106	C₂×C₄×D₄₃	—	4	8	no	—
107	C₂×Dic₈₆	—	2	2	no	—
108	C₂×Dic₈₆	—	2	2	no	—
109	C₂×Dic₈₆	—	2	2	no	—
110	C₂×Dic₈₆	—	2	2	no	—
111	C₂×Dic₈₆	—	2	2	no	—
112	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	—	2	1	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₃	#41	1	2	yes	—
124	C₂×C₈×C₄₃	#41	1	2	yes	—
125	C₄²×C₄₃	—	2	4	no	—
126	C₄²×C₄₃	—	2	4	no	—
127	C₄²×C₄₃	—	2	1	no	—
128	C₄²×C₄₃	—	2	1	no	—
129	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₃	C₂×D₄	1	2	yes	—
131	C₄²×C₄₃	C₂×D₄	1	2	yes	—
132	C₄²×C₄₃	#41	1	2	yes	—
133	(C₂×D₄₃)⋊C₄	—	2	16	no	—
134	(C₂×D₄₃)⋊C₄	—	4	4	no	—
135	(C₂×D₄₃)⋊C₄	—	4	8	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	Dic₄₃⋊C₄	—	4	4	no	—
141	C₄×Dic₄₃	—	4	4	no	—
142	Dic₁₇₂	—	2	8	no	—
143	D₃₄₄	—	2	8	no	—
144	#10621873	—	2	16	no	—
145	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
146	C₂²×D₄₃	—	2	4	no	—
147	C₂²×D₄₃	—	4	2	no	—
148	C₂²×D₄₃	—	4	2	no	—
149	C₂²×D₄₃	—	4	4	no	—
150	C₂²×D₄₃	—	4	4	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
157	C₂×C₄×C₄₃	#127	1	2	yes	—
158	C₂×C₄×C₄₃	#127	1	2	yes	—
159	C₂×C₄×C₄₃	#135	1	4	yes	—
160	C₂×C₄×C₄₃	#135	1	4	yes	—
161	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₃	—	2	4	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	4	4	no	—
173	C₂×Dic₄₃	—	4	4	no	—
174	D₁₇₂	—	2	4	no	—
175	D₁₇₂	—	2	4	no	—
176	D₁₇₂	—	4	2	no	—
177	D₁₇₂	—	4	2	no	—
178	C₄×D₄₃	—	8	8	no	—
179	Dic₈₆	—	2	4	no	—
180	Dic₈₆	—	2	4	no	—
181	Dic₈₆	—	4	2	no	—
182	Dic₈₆	—	4	2	no	—
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	—	2	2	no	—
185	C₈×C₄₃	C₄×D₄	1	4	yes	—
186	C₈×C₄₃	C₄×D₄	1	4	yes	—
187	C₄×#495	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
190	C₂²×C₄₃	#532	1	1	yes	characteristic
191	C₂²×C₄₃	C₂×#135	1	2	yes	—
192	C₂²×C₄₃	C₂×#135	1	2	yes	—
193	C₂×D₄₃	—	4	4	no	—
194	C₂×D₄₃	—	4	8	no	—
195	C₂×D₄₃	—	8	2	no	—
196	C₂×D₄₃	—	8	2	no	—
197	C₂×D₄₃	—	8	4	no	—
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	2	4	no	—
200	C₄×C₄₃	—	2	4	no	—
201	C₄×C₄₃	#495	1	4	yes	complemented
202	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₃	#532	1	1	yes	characteristic
205	C₄×C₄₃	#532	1	1	yes	characteristic
206	Dic₄₃	—	4	4	no	—
207	Dic₄₃	—	8	2	no	—
208	Dic₄₃	—	8	2	no	—
209	C₂×#495	—	43	1	no	—
210	C₂×C₄×Q₁₆	—	43	1	no	—
211	C₂×C₄×SD₁₆	—	43	2	no	—
212	C₂×C₄×D₈	—	43	1	no	—
213	C₄×#124	—	43	2	no	—
214	#1970	—	43	1	no	—
215	#1969	—	43	1	no	—
216	#1968	—	43	2	no	—
217	#1958	—	43	2	no	—
218	#1846	—	43	1	no	—
219	C₄²×C₈	D₄₃	1	1	yes	characteristic, complemented
220	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
221	C₂×C₄₃	C₄×#135	1	2	yes	—
222	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
223	C₂×C₄₃	#3147	1	1	yes	characteristic
224	C₂×C₄₃	#3168	1	2	yes	—
225	D₄₃	—	8	4	no	—
226	C₂²×Q₁₆	—	43	1	no	—
227	C₂²×SD₁₆	—	43	2	no	—
228	C₂²×D₈	—	43	1	no	—
229	C₂×#124	—	43	2	no	—
230	C₂×C₄×Q₈	—	43	2	no	—
231	C₂×C₄×D₄	—	43	2	no	—
232	#495	—	43	8	no	—
233	C₄×Q₁₆	—	86	4	no	—
234	C₄×SD₁₆	—	86	8	no	—
235	C₄×D₈	—	86	4	no	—
236	C₂×#107	—	43	1	no	—
237	C₂×#107	—	43	1	no	—
238	C₂×#106	—	43	2	no	—
239	C₂×#103	—	43	2	no	—
240	C₂×#103	—	43	2	no	—
241	C₂×#102	—	43	2	no	—
242	C₂×#102	—	43	2	no	—
243	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
249	#391	—	43	2	no	—
250	#390	—	43	2	no	—
251	#388	—	86	4	no	—
252	#382	—	43	2	no	—
253	C₄×C₂²⋊C₄	—	86	4	no	—
254	C₄³	C₂×D₄₃	1	1	yes	characteristic
255	C₄₃	C₄×#495	1	1	yes	characteristic, complemented, Sylow
256	C₂²×Q₈	—	43	2	no	—
257	C₂²×D₄	—	43	2	no	—
258	C₂³×C₄	—	86	2	no	—
259	C₂×Q₁₆	—	43	4	no	—
260	C₂×Q₁₆	—	86	2	no	—
261	C₂×Q₁₆	—	86	2	no	—
262	C₂×SD₁₆	—	43	8	no	—
263	C₂×SD₁₆	—	86	4	no	—
264	C₂×SD₁₆	—	86	4	no	—
265	C₂×D₈	—	43	4	no	—
266	C₂×D₈	—	86	2	no	—
267	C₂×D₈	—	86	2	no	—
268	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
272	#124	—	43	8	no	—
273	#124	—	86	4	no	—
274	C₄×Q₈	—	86	4	no	—
275	C₄×Q₈	—	86	4	no	—
276	C₄×D₄	—	86	4	no	—
277	C₄×D₄	—	86	4	no	—
278	C₂×C₄⋊C₄	—	43	2	no	—
279	C₂×C₄⋊C₄	—	43	2	no	—
280	C₂×C₄⋊C₄	—	86	2	no	—
281	C₂×C₂²⋊C₄	—	86	4	no	—
282	C₂×C₂²⋊C₄	—	86	2	no	—
283	C₂×C₂²⋊C₄	—	86	4	no	—
284	C₂×C₄²	—	86	2	no	—
285	C₂×C₄²	D₁₇₂	1	2	yes	—
286	C₂×C₄²	D₁₇₂	1	2	yes	—
287	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
288	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
289	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
290	#107	—	86	2	no	—
291	#107	—	86	2	no	—
292	#106	—	86	4	no	—
293	#103	—	86	4	no	—
294	#103	—	86	4	no	—
295	#102	—	86	4	no	—
296	#102	—	86	4	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	C₄×D₄₃	1	4	yes	complemented
301	C₄×C₈	D₁₇₂	1	4	yes	—
302	C₄×C₈	D₁₇₂	1	4	yes	—
303	#95	—	86	4	no	—
304	#95	—	86	4	no	—
305	C₂⁴	—	86	2	no	—
306	C₂×Q₈	—	43	4	no	—
307	C₂×Q₈	—	86	2	no	—
308	C₂×Q₈	—	86	2	no	—
309	C₂×Q₈	—	86	2	no	—
310	C₂×Q₈	—	86	2	no	—
311	C₂×Q₈	—	86	2	no	—
312	C₂×D₄	—	43	4	no	—
313	C₂×D₄	—	86	2	no	—
314	C₂×D₄	—	86	2	no	—
315	C₂×D₄	—	86	2	no	—
316	C₂×D₄	—	86	2	no	—
317	C₂×D₄	—	86	2	no	—
318	C₂²×C₄	—	86	2	no	—
319	C₂²×C₄	—	86	2	no	—
320	C₂²×C₄	—	86	2	no	—
321	C₂²×C₄	—	172	4	no	—
322	C₂²×C₄	—	172	8	no	—
323	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
324	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
326	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
328	Q₁₆	—	86	8	no	—
329	SD₁₆	—	86	16	no	—
330	D₈	—	86	8	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
337	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
338	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
339	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
340	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
341	C₂×C₈	#10621898	1	2	yes	—
342	C₂×C₈	#10621898	1	2	yes	—
343	C₄⋊C₄	—	86	2	no	—
344	C₄⋊C₄	—	86	2	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	172	4	no	—
348	C₂²⋊C₄	—	86	16	no	—
349	C₂²⋊C₄	—	172	4	no	—
350	C₂²⋊C₄	—	172	8	no	—
351	C₄²	—	2	4	no	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	172	4	no	—
356	C₄²	C₂×C₄×D₄₃	1	2	yes	—
357	C₄²	C₂×D₁₇₂	1	2	yes	—
358	C₄²	C₂×D₁₇₂	1	2	yes	—
359	C₄²	#10621898	1	2	yes	—
360	C₂³	—	86	4	no	—
361	C₂³	—	172	4	no	—
362	C₂³	—	172	4	no	—
363	C₂³	—	172	2	no	—
364	C₂³	—	172	2	no	—
365	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
366	Q₈	—	86	4	no	—
367	Q₈	—	86	4	no	—
368	Q₈	—	172	2	no	—
369	Q₈	—	172	2	no	—
370	D₄	—	86	4	no	—
371	D₄	—	86	4	no	—
372	D₄	—	172	2	no	—
373	D₄	—	172	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	86	4	no	—
380	C₂×C₄	—	344	8	no	—
381	C₂×C₄	—	172	4	no	—
382	C₂×C₄	—	172	4	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	—	172	2	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
388	C₂×C₄	#13063322	1	2	yes	—
389	C₂×C₄	#13063322	1	2	yes	—
390	C₂×C₄	#13063347	1	4	yes	—
391	C₂×C₄	#13063347	1	4	yes	—
392	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
395	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
396	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	C₄×D₁₇₂	1	4	yes	—
401	C₈	C₄×D₁₇₂	1	4	yes	—
402	C₂²	—	344	2	no	—
403	C₂²	—	344	2	no	—
404	C₂²	—	344	4	no	—
405	C₂²	—	172	4	no	—
406	C₂²	—	172	8	no	—
407	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
408	C₂²	C₂×#13063322	1	1	yes	characteristic
409	C₂²	#14583449	1	1	yes	characteristic
410	C₂²	C₂×#13063347	1	2	yes	—
411	C₂²	C₂×#13063347	1	2	yes	—
412	C₄	—	2	2	no	—
413	C₄	—	2	4	no	—
414	C₄	—	2	4	no	—
415	C₄	—	344	2	no	—
416	C₄	—	344	2	no	—
417	C₄	—	172	4	no	—
418	C₄	#14583283	1	4	yes	direct product factor
419	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
420	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
421	C₄	#14583449	1	1	yes	characteristic
422	C₄	#14583449	1	1	yes	characteristic
423	C₂	—	344	4	no	—
424	C₂	C₄×#13063322	1	1	yes	characteristic
425	C₂	C₄×#13063347	1	2	yes	—
426	C₂	C₂×#14583283	1	1	yes	characteristic
427	C₂	#19145023	1	1	yes	characteristic
428	C₂	#19145165	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄²×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₃₄₄	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄²×C₈	D₄₃
hypocenter	C₄₃	C₄×#495
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₁₇₂	C₂	semidirect
3. C₂×C₄×#10621873	C₂	semidirect
5. C₄×#13063313	C₂	semidirect
7. #19135456	C₂	semidirect
8. #19135449	C₂	semidirect
9. #19135406	C₂	semidirect
10. #19134759	C₂	semidirect
11. C₄²×C₈×C₄₃	C₂	semidirect
18. #14583283	C₄	direct (N × H)
46. C₂×Dic₁₇₂	C₂×C₄	semidirect
49. C₂×#10621873	C₂×C₄	semidirect
54. #13063313	C₂×C₄	semidirect
87. C₄×C₈×C₄₃	C₂×C₄	semidirect
201. C₄×C₄₃	#495	semidirect
219. C₄²×C₈	D₄₃	semidirect
255. C₄₃	C₄×#495	semidirect
300. C₄×C₈	C₄×D₄₃	semidirect
418. C₄	#14583283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14583283	2
C₂×C₄×Dic₁₇₂	2
C₂×C₄×#10621873	2
C₂×C₄×D₃₄₄	2
C₄×#13063313	2
#19135461	2
#19135456	2
#19135449	2
#19135406	2
#19134759	2
C₄²×C₈×C₄₃	2
C₄×#495	43

Subgroups — C4×#14583283 #25105043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14583283 #25105043