Subgroups — #19146095

Order 5504.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063353	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583558	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583288	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583145	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583135	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583115	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583100	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583052	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583046	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583040	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583035	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583001	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
19	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₄₃	—	2	1	no	—
21	#13063353	—	2	4	no	—
22	C₂×#10621873	—	2	4	no	—
23	C₂×#10621873	C₂²	1	1	yes	characteristic
24	C₂×#10621873	C₂²	1	1	yes	characteristic
25	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
26	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
27	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
28	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
30	C₂×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
32	#13063322	C₂²	1	1	yes	characteristic
33	#13063313	C₂²	1	1	yes	characteristic, complemented
34	#13063311	—	2	1	no	—
35	#13063304	C₂²	1	1	yes	characteristic, complemented
36	#13063303	—	2	1	no	—
37	#13063300	—	2	1	no	—
38	#13063299	C₂²	1	1	yes	characteristic
39	#13063299	C₂²	1	1	yes	characteristic
40	#13063299	C₂²	1	1	yes	characteristic, complemented
41	#13063297	—	2	1	no	—
42	#13063295	—	2	1	no	—
43	#13063295	—	2	1	no	—
44	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
45	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
46	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
47	#13063259	C₂²	1	1	yes	characteristic, complemented
48	#13063250	C₂²	1	1	yes	characteristic, complemented
49	#13063250	C₂²	1	1	yes	characteristic, complemented
50	#13063247	C₂²	1	1	yes	characteristic
51	#13063247	C₂²	1	1	yes	characteristic, complemented
52	#13063247	C₂²	1	1	yes	characteristic, complemented
53	#13063247	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
60	#97×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₄₃	—	2	1	no	—
62	C₂³×D₄₃	—	2	1	no	—
63	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₄₃	—	2	1	no	—
67	C₂×C₂²⋊D₄₃	—	2	1	no	—
68	C₂×C₂²⋊D₄₃	—	2	1	no	—
69	C₂×C₂²⋊D₄₃	—	2	1	no	—
70	C₂²×Dic₄₃	—	2	1	no	—
71	D₄×D₄₃	—	4	4	no	—
72	#10621898	—	2	2	no	—
73	#10621898	—	4	1	no	—
74	C₂×D₁₇₂	—	2	1	no	—
75	C₂×D₁₇₂	—	2	1	no	—
76	C₂×D₁₇₂	—	2	1	no	—
77	C₂×D₁₇₂	—	2	1	no	—
78	C₂×D₁₇₂	—	2	2	no	—
79	C₂×D₁₇₂	—	2	2	no	—
80	C₂×D₁₇₂	—	4	1	no	—
81	C₂×D₁₇₂	—	4	1	no	—
82	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
83	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
84	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
85	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₄₃	—	2	1	no	—
87	C₂×C₄×D₄₃	—	2	1	no	—
88	C₂×Dic₈₆	—	2	2	no	—
89	C₂×Dic₈₆	—	2	1	no	—
90	C₂×Dic₈₆	—	4	1	no	—
91	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
92	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
93	M₁₆×C₄₃	—	2	2	no	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
100	C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
101	C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₂²⋊Dic₄₃	—	2	1	no	—
104	(C₂×D₄₃)⋊C₄	—	2	1	no	—
105	(C₂×D₄₃)⋊C₄	—	2	1	no	—
106	(C₂×D₄₃)⋊C₄	—	2	1	no	—
107	(C₂×D₄₃)⋊C₄	—	2	1	no	—
108	(C₂×D₄₃)⋊C₄	—	2	1	no	—
109	(C₂×D₄₃)⋊C₄	—	2	1	no	—
110	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
112	Dic₄₃⋊C₄	—	2	1	no	—
113	Dic₄₃⋊C₄	—	2	1	no	—
114	C₄×Dic₄₃	—	2	1	no	—
115	D₃₄₄	—	2	2	no	—
116	D₃₄₄	—	2	2	no	—
117	D₃₄₄	—	4	1	no	—
118	#10621873	—	2	2	no	—
119	#10621873	—	2	2	no	—
120	#10621873	—	2	2	no	—
121	#10621873	—	2	2	no	—
122	#10621873	—	4	1	no	—
123	#10621873	D₄	1	4	yes	complemented
124	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₄₃	—	2	1	no	—
127	C₂²×D₄₃	—	2	1	no	—
128	C₂²×D₄₃	—	2	1	no	—
129	C₂²×D₄₃	—	2	1	no	—
130	C₂²×D₄₃	—	4	2	no	—
131	C₂²×D₄₃	—	4	2	no	—
132	C₂²×D₄₃	—	4	2	no	—
133	C₂²×D₄₃	—	4	2	no	—
134	C₂²×D₄₃	—	8	1	no	—
135	C₂²×D₄₃	—	8	1	no	—
136	D₄×C₄₃	—	2	2	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
146	C₂²⋊D₄₃	—	4	2	no	—
147	C₂²⋊D₄₃	—	4	2	no	—
148	C₂²⋊D₄₃	—	4	2	no	—
149	C₂²⋊D₄₃	—	4	2	no	—
150	C₂×Dic₄₃	—	2	1	no	—
151	C₂×Dic₄₃	—	2	1	no	—
152	C₂×Dic₄₃	—	2	1	no	—
153	C₂×Dic₄₃	—	2	1	no	—
154	C₂×Dic₄₃	—	4	2	no	—
155	D₁₇₂	—	2	1	no	—
156	D₁₇₂	—	2	1	no	—
157	D₁₇₂	—	2	1	no	—
158	D₁₇₂	—	2	1	no	—
159	D₁₇₂	—	2	1	no	—
160	D₁₇₂	—	2	1	no	—
161	D₁₇₂	—	2	1	no	—
162	D₁₇₂	—	4	2	no	—
163	D₁₇₂	—	4	2	no	—
164	D₁₇₂	—	4	2	no	—
165	D₁₇₂	—	8	1	no	—
166	D₁₇₂	C₂×D₄	1	2	yes	—
167	C₄×D₄₃	—	4	2	no	—
168	C₄×D₄₃	—	4	2	no	—
169	Dic₈₆	—	2	1	no	—
170	Dic₈₆	—	2	1	no	—
171	Dic₈₆	—	2	1	no	—
172	Dic₈₆	—	4	2	no	—
173	Dic₈₆	C₂×D₄	1	2	yes	complemented
174	C₈×C₄₃	—	2	1	no	—
175	C₈×C₄₃	—	2	1	no	—
176	C₈×C₄₃	—	2	1	no	—
177	C₈×C₄₃	C₂×D₄	1	2	yes	complemented
178	C₂²×C₄₃	—	2	1	no	—
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	1	no	—
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	complemented
184	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×D₄₃	—	2	2	no	—
186	C₂×D₄₃	—	4	1	no	—
187	C₂×D₄₃	—	4	1	no	—
188	C₂×D₄₃	—	4	1	no	—
189	C₂×D₄₃	—	4	1	no	—
190	C₂×D₄₃	—	4	1	no	—
191	C₂×D₄₃	—	4	1	no	—
192	C₂×D₄₃	—	4	1	no	—
193	C₂×D₄₃	—	4	1	no	—
194	C₂×D₄₃	—	4	1	no	—
195	C₂×D₄₃	—	4	1	no	—
196	C₂×D₄₃	—	4	1	no	—
197	C₂×D₄₃	—	8	4	no	—
198	C₂×D₄₃	—	8	4	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
205	Dic₄₃	—	2	2	no	—
206	Dic₄₃	—	4	1	no	—
207	Dic₄₃	—	4	1	no	—
208	Dic₄₃	—	4	1	no	—
209	#3265	—	43	1	no	maximal, Sylow
210	C₂×C₄₃	—	2	2	no	—
211	C₂×C₄₃	—	4	1	no	—
212	C₂×C₄₃	D₄²	1	1	yes	characteristic
213	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₄₃	#577	1	1	yes	characteristic
215	D₄₃	—	4	2	no	—
216	D₄₃	—	8	1	no	—
217	D₄₃	—	8	1	no	—
218	D₄₃	—	8	1	no	—
219	C₂×AGL(1,ℤ/8)	—	43	1	no	—
220	C₂²×SD₁₆	—	43	1	no	—
221	#548	—	43	1	no	—
222	D₄²	—	43	1	no	—
223	#496	—	43	1	no	—
224	#468	—	43	1	no	—
225	#466	—	43	1	no	—
226	#463	—	43	1	no	—
227	#460	—	43	1	no	—
228	#450	—	43	1	no	—
229	#449	—	43	1	no	—
230	#448	—	43	1	no	—
231	#447	—	43	1	no	—
232	#440	—	43	1	no	—
233	#435	D₄₃	1	1	yes	characteristic, complemented
234	C₄₃	#3265	1	1	yes	characteristic, complemented, Sylow
235	C₂×#41	—	43	1	no	—
236	C₂²×Q₈	—	43	1	no	—
237	C₂²×D₄	—	43	1	no	—
238	C₂²×D₄	—	43	1	no	—
239	C₂²×D₄	—	86	1	no	—
240	AGL(1,ℤ/8)	—	86	4	no	—
241	C₂×SD₁₆	—	43	1	no	—
242	C₂×SD₁₆	—	43	1	no	—
243	C₂×SD₁₆	—	43	1	no	—
244	C₂×SD₁₆	—	43	1	no	—
245	C₂×SD₁₆	—	43	1	no	—
246	C₂×SD₁₆	—	43	1	no	—
247	C₂×SD₁₆	—	86	4	no	—
248	C₂×D₈	—	43	1	no	—
249	C₂×D₈	—	43	1	no	—
250	C₂×D₈	—	43	1	no	—
251	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
252	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
253	#127	—	43	1	no	—
254	#124	—	43	1	no	—
255	#124	—	86	1	no	—
256	C₂²⋊Q₈	—	43	1	no	—
257	C₂²⋊Q₈	—	86	1	no	—
258	#121	—	43	1	no	—
259	#121	—	43	1	no	—
260	#121	—	43	1	no	—
261	#121	—	86	1	no	—
262	#121	—	86	1	no	—
263	#120	—	86	1	no	—
264	#120	—	86	1	no	—
265	C₄×Q₈	—	43	1	no	—
266	C₄×D₄	—	43	1	no	—
267	C₄×D₄	—	86	1	no	—
268	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
269	#107	—	43	1	no	—
270	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
271	#103	—	43	1	no	—
272	#103	—	43	1	no	—
273	#102	—	43	1	no	—
274	#102	—	43	1	no	—
275	#102	—	43	1	no	—
276	#102	—	43	1	no	—
277	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
278	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
279	#97	C₂×D₄₃	1	1	yes	characteristic, complemented
280	C₂⁴	—	86	1	no	—
281	C₂⁴	—	86	1	no	—
282	#41	—	86	2	no	—
283	#41	—	172	1	no	—
284	C₂×Q₈	—	43	1	no	—
285	C₂×Q₈	—	43	1	no	—
286	C₂×Q₈	—	86	2	no	—
287	C₂×Q₈	—	86	1	no	—
288	C₂×Q₈	—	172	1	no	—
289	C₂×D₄	—	43	1	no	—
290	C₂×D₄	—	43	1	no	—
291	C₂×D₄	—	43	1	no	—
292	C₂×D₄	—	43	1	no	—
293	C₂×D₄	—	86	2	no	—
294	C₂×D₄	—	86	2	no	—
295	C₂×D₄	—	86	1	no	—
296	C₂×D₄	—	86	1	no	—
297	C₂×D₄	—	86	1	no	—
298	C₂×D₄	—	86	1	no	—
299	C₂×D₄	—	86	1	no	—
300	C₂×D₄	—	86	1	no	—
301	C₂×D₄	—	86	1	no	—
302	C₂×D₄	—	86	1	no	—
303	C₂×D₄	—	172	1	no	—
304	C₂×D₄	—	172	1	no	—
305	C₂×D₄	—	172	4	no	—
306	C₂×D₄	D₁₇₂	1	1	yes	characteristic
307	C₂²×C₄	—	86	1	no	—
308	C₂²×C₄	—	86	1	no	—
309	C₂²×C₄	—	86	1	no	—
310	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
312	SD₁₆	—	43	4	no	—
313	SD₁₆	—	86	2	no	—
314	SD₁₆	—	86	2	no	—
315	SD₁₆	—	86	2	no	—
316	SD₁₆	—	86	2	no	—
317	SD₁₆	—	172	1	no	—
318	D₈	—	86	2	no	—
319	D₈	—	86	2	no	—
320	D₈	—	172	1	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
324	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
325	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
327	C₄⋊C₄	—	43	1	no	—
328	C₄⋊C₄	—	43	1	no	—
329	C₄⋊C₄	—	86	1	no	—
330	C₄⋊C₄	—	86	1	no	—
331	C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
332	C₂²⋊C₄	—	86	1	no	—
333	C₂²⋊C₄	—	86	1	no	—
334	C₂²⋊C₄	—	86	1	no	—
335	C₂²⋊C₄	—	86	1	no	—
336	C₂²⋊C₄	—	86	1	no	—
337	C₂²⋊C₄	—	86	1	no	—
338	C₂²⋊C₄	—	86	1	no	—
339	C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
340	C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
341	C₄²	—	86	1	no	—
342	C₄²	C₂²×D₄₃	1	1	yes	characteristic
343	C₂³	—	86	1	no	—
344	C₂³	—	86	1	no	—
345	C₂³	—	86	1	no	—
346	C₂³	—	86	1	no	—
347	C₂³	—	344	1	no	—
348	C₂³	—	344	1	no	—
349	C₂³	—	172	2	no	—
350	C₂³	—	172	2	no	—
351	C₂³	—	172	2	no	—
352	C₂³	—	172	2	no	—
353	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
354	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
355	Q₈	—	43	2	no	—
356	Q₈	—	86	1	no	—
357	Q₈	—	86	1	no	—
358	Q₈	—	86	1	no	—
359	Q₈	—	172	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	43	2	no	—
362	D₄	—	86	1	no	—
363	D₄	—	86	1	no	—
364	D₄	—	86	1	no	—
365	D₄	—	86	1	no	—
366	D₄	—	86	1	no	—
367	D₄	—	86	1	no	—
368	D₄	—	86	1	no	—
369	D₄	—	344	1	no	—
370	D₄	—	172	2	no	—
371	D₄	—	172	2	no	—
372	D₄	—	172	2	no	—
373	D₄	—	172	2	no	—
374	D₄	—	172	2	no	—
375	D₄	—	172	2	no	—
376	D₄	—	172	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	86	1	no	—
382	C₂×C₄	—	86	1	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
389	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
390	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
391	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	D₄×D₄₃	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	86	2	no	—
403	C₂²	—	344	4	no	—
404	C₂²	—	344	4	no	—
405	C₂²	—	172	1	no	—
406	C₂²	—	172	1	no	—
407	C₂²	—	172	1	no	—
408	C₂²	—	172	1	no	—
409	C₂²	—	172	1	no	—
410	C₂²	—	172	1	no	—
411	C₂²	—	172	1	no	—
412	C₂²	—	172	1	no	—
413	C₂²	—	172	1	no	—
414	C₂²	—	172	1	no	—
415	C₂²	—	172	1	no	—
416	C₂²	#13063353	1	2	yes	complemented
417	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	86	2	no	—
423	C₄	—	172	1	no	—
424	C₄	—	172	1	no	—
425	C₄	—	172	1	no	—
426	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
427	C₄	#13063371	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	1	no	—
430	C₂	—	344	1	no	—
431	C₂	—	344	1	no	—
432	C₂	—	344	1	no	—
433	C₂	—	172	2	no	—
434	C₂	D₄×D₁₇₂	1	1	yes	characteristic
435	C₂	C₂×#13063353	1	1	yes	characteristic
436	C₂	#14583711	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#435	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#435	D₄₃
hypocenter	C₄₃	#3265
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#13063353	C₂	semidirect
2. C₂²×#10621873	C₂	semidirect
3. #14583558	C₂	semidirect
4. D₄×D₁₇₂	C₂	semidirect
5. #14583288	C₂	semidirect
6. #14583145	C₂	semidirect
7. #14583135	C₂	semidirect
8. #14583115	C₂	semidirect
9. #14583100	C₂	semidirect
10. #14583052	C₂	semidirect
11. #14583046	C₂	semidirect
12. #14583040	C₂	semidirect
13. #14583035	C₂	semidirect
14. #14583001	C₂	semidirect
15. C₄₃×#435	C₂	semidirect
16. C₂×#10621898	C₂²	semidirect
17. C₂²×Dic₈₆	C₂²	semidirect
25. C₂×#10621873	C₂²	semidirect
26. C₂×#10621873	C₂²	semidirect
27. C₂×#10621873	C₂²	semidirect
28. C₂×#10621873	C₂²	semidirect
30. C₂×D₃₄₄	C₂²	semidirect
31. C₂×D₃₄₄	C₂²	semidirect
33. #13063313	C₂²	semidirect
35. #13063304	C₂²	semidirect
40. #13063299	C₂²	semidirect
44. C₄×Dic₈₆	C₂²	semidirect
47. #13063259	C₂²	semidirect
48. #13063250	C₂²	semidirect
49. #13063250	C₂²	semidirect
51. #13063247	C₂²	semidirect
52. #13063247	C₂²	semidirect
53. #13063247	C₂²	semidirect
54. C₂×M₁₆×C₄₃	C₂²	semidirect
55. C₂²×C₈×C₄₃	C₂²	semidirect
57. C₄⋊C₈×C₄₃	C₂²	semidirect
58. C₂²⋊C₈×C₄₃	C₂²	semidirect
59. C₂²⋊C₈×C₄₃	C₂²	semidirect
60. #97×C₄₃	C₂²	semidirect
123. #10621873	D₄	semidirect
173. Dic₈₆	C₂×D₄	semidirect
177. C₈×C₄₃	C₂×D₄	semidirect
183. C₂²×C₄₃	AGL(1,ℤ/8)	semidirect
233. #435	D₄₃	semidirect
234. C₄₃	#3265	semidirect
251. C₂×M₁₆	C₂×D₄₃	semidirect
252. C₂²×C₈	C₂×D₄₃	semidirect
270. C₄⋊C₈	C₂×D₄₃	semidirect
277. C₂²⋊C₈	C₂×D₄₃	semidirect
278. C₂²⋊C₈	C₂×D₄₃	semidirect
279. #97	C₂×D₄₃	semidirect
396. C₈	D₄×D₄₃	semidirect
416. C₂²	#13063353	semidirect