Subgroups — #25013603

Order 11008.

560 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583132	C₂	1	1	yes	maximal, characteristic
2	C₂×#108×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582712	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136205	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132705	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₃	—	2	1	no	—
9	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	C₂×#13063296	—	2	1	no	—
11	C₂×#13063265	C₂²	1	1	yes	characteristic
12	#14583132	—	2	1	no	—
13	#14583132	—	2	1	no	—
14	#14583132	C₄	1	2	yes	—
15	#14583132	C₄	1	2	yes	—
16	C₂×#13063261	C₂²	1	1	yes	characteristic
17	C₂×#13063260	—	2	1	no	—
18	#108×D₄₃	—	2	2	no	—
19	#108×D₄₃	—	2	2	no	—
20	C₂×#13063259	C₂²	1	1	yes	characteristic
21	C₂×#13063246	—	2	1	no	—
22	#14582712	—	2	2	no	—
23	(C₂×D₄₃)⋊C₁₆	—	2	1	no	—
24	(C₂×D₄₃)⋊C₁₆	—	2	1	no	—
25	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#361	—	2	2	no	—
29	C₂²×C₂²⋊D₄₃	—	4	1	no	—
30	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
31	C₂×#10621877	—	2	1	no	—
32	C₂×#10621872	—	4	1	no	—
33	M₁₆×D₄₃	—	2	4	no	—
34	M₁₆×D₄₃	—	4	2	no	—
35	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
36	C₂×C₈×D₄₃	—	2	1	no	—
37	C₂×C₈×D₄₃	—	2	1	no	—
38	C₂×C₈×D₄₃	—	2	1	no	—
39	C₂×C₈×D₄₃	—	2	1	no	—
40	C₂×C₈×D₄₃	—	4	1	no	—
41	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
44	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
45	#13063296	—	2	2	no	—
46	#13063296	—	2	2	no	—
47	#13063296	—	4	1	no	—
48	#13063296	—	4	1	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₂²⋊Dic₄₃	—	4	1	no	—
51	#13063265	—	2	1	no	—
52	#13063265	—	2	1	no	—
53	C₂×C₄₃⋊C₁₆	—	2	1	no	—
54	#13063261	—	2	1	no	—
55	#13063261	D₄	1	2	yes	complemented
56	#13063260	—	2	4	no	—
57	#13063259	—	2	1	no	—
58	#13063259	C₂×C₄	1	2	yes	—
59	#13063246	—	2	2	no	—
60	#13063246	—	2	2	no	—
61	C₂²×D₄×C₄₃	—	2	1	no	—
62	C₂×D₈×C₄₃	—	2	1	no	—
63	C₂×D₈×C₄₃	—	2	1	no	—
64	C₂×D₈×C₄₃	—	2	1	no	—
65	C₂×D₈×C₄₃	—	2	1	no	—
66	C₂×D₈×C₄₃	—	2	1	no	—
67	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
68	C₂×M₁₆×C₄₃	—	2	1	no	—
69	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	M₃₂×C₄₃	—	2	1	no	—
71	M₃₂×C₄₃	—	2	1	no	—
72	C₂×C₁₆×C₄₃	—	2	1	no	—
73	#108×C₄₃	—	2	1	no	—
74	#108×C₄₃	D₄	1	2	yes	complemented
75	C₂⁴×C₄₃	—	4	1	no	—
76	C₂³×D₄₃	SD₁₆	1	1	yes	characteristic
77	C₂×D₄×C₄₃	—	2	2	no	—
78	C₂×D₄×C₄₃	—	4	1	no	—
79	C₂×D₄×C₄₃	—	4	1	no	—
80	C₂×D₄×C₄₃	—	4	1	no	—
81	C₂×D₄×C₄₃	—	4	1	no	—
82	C₂×D₄×C₄₃	—	4	1	no	—
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₂²⋊D₄₃	—	4	2	no	—
85	C₂×C₂²⋊D₄₃	—	4	2	no	—
86	C₂×C₂²⋊D₄₃	—	8	4	no	—
87	C₂²×Dic₄₃	—	4	1	no	—
88	C₂²×Dic₄₃	SD₁₆	1	1	yes	characteristic
89	C₂×C₄×D₄₃	—	2	1	no	—
90	C₂×C₄×D₄₃	—	2	1	no	—
91	C₂×C₄×D₄₃	—	2	1	no	—
92	C₂×C₄×D₄₃	—	2	1	no	—
93	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₄₃	D₈	1	1	yes	characteristic
96	C₂×C₄×D₄₃	D₈	1	1	yes	characteristic
97	D₈×C₄₃	—	2	2	no	—
98	D₈×C₄₃	—	2	2	no	—
99	D₈×C₄₃	—	4	1	no	—
100	D₈×C₄₃	—	4	1	no	—
101	M₁₆×C₄₃	—	2	2	no	—
102	M₁₆×C₄₃	—	4	1	no	—
103	C₂×C₈×C₄₃	—	4	1	no	—
104	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
109	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
110	C₂²⋊Dic₄₃	—	4	2	no	—
111	C₂²⋊Dic₄₃	—	4	2	no	—
112	C₄⋊Dic₄₃	—	2	2	no	—
113	C₄⋊Dic₄₃	—	4	1	no	—
114	#10621877	—	2	2	no	—
115	#10621877	—	4	1	no	—
116	C₂×C₄₃⋊C₈	—	2	1	no	—
117	C₂×C₄₃⋊C₈	—	2	1	no	—
118	C₂×C₄₃⋊C₈	—	4	1	no	—
119	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
121	#10621872	—	4	4	no	—
122	C₈×D₄₃	—	2	1	no	—
123	C₈×D₄₃	—	2	1	no	—
124	C₈×D₄₃	—	2	1	no	—
125	C₈×D₄₃	—	2	1	no	—
126	C₈×D₄₃	—	2	1	no	—
127	C₈×D₄₃	—	2	1	no	—
128	C₈×D₄₃	—	2	1	no	—
129	C₈×D₄₃	—	2	1	no	—
130	C₈×D₄₃	—	4	4	no	—
131	C₁₆×C₄₃	—	4	1	no	—
132	C₄₃⋊C₁₆	—	4	1	no	—
133	C₂³×C₄₃	—	4	2	no	—
134	C₂³×C₄₃	—	8	2	no	—
135	C₂³×C₄₃	—	8	2	no	—
136	C₂³×C₄₃	—	8	1	no	—
137	C₂³×C₄₃	—	8	1	no	—
138	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
139	C₂²×D₄₃	—	2	1	no	—
140	C₂²×D₄₃	—	2	1	no	—
141	C₂²×D₄₃	—	2	2	no	—
142	C₂²×D₄₃	—	4	1	no	—
143	C₂²×D₄₃	#102	1	1	yes	characteristic
144	C₂²×D₄₃	#102	1	1	yes	characteristic
145	D₄×C₄₃	—	4	2	no	—
146	D₄×C₄₃	—	4	2	no	—
147	D₄×C₄₃	—	8	1	no	—
148	D₄×C₄₃	—	8	1	no	—
149	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
155	C₂²⋊D₄₃	—	8	4	no	—
156	C₂²⋊D₄₃	—	8	4	no	—
157	C₂×Dic₄₃	—	2	1	no	—
158	C₂×Dic₄₃	—	2	1	no	—
159	C₂×Dic₄₃	—	4	2	no	—
160	C₂×Dic₄₃	—	8	2	no	—
161	C₂×Dic₄₃	#102	1	1	yes	characteristic
162	C₂×Dic₄₃	#102	1	1	yes	characteristic
163	C₄×D₄₃	—	2	1	no	—
164	C₄×D₄₃	—	2	1	no	—
165	C₄×D₄₃	—	2	1	no	—
166	C₄×D₄₃	—	2	1	no	—
167	C₄×D₄₃	—	2	1	no	—
168	C₄×D₄₃	—	2	1	no	—
169	C₄×D₄₃	—	2	1	no	—
170	C₄×D₄₃	—	2	1	no	—
171	C₈×C₄₃	—	4	2	no	—
172	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
173	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
174	C₈×C₄₃	#121	1	1	yes	characteristic
175	C₈×C₄₃	#121	1	1	yes	characteristic
176	C₄₃⋊C₈	—	2	1	no	—
177	C₄₃⋊C₈	—	2	1	no	—
178	C₄₃⋊C₈	—	4	2	no	—
179	#13004	—	43	1	no	maximal, Sylow
180	C₂²×C₄₃	—	2	1	no	—
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	8	2	no	—
183	C₂²×C₄₃	—	8	2	no	—
184	C₂²×C₄₃	—	8	2	no	—
185	C₂²×C₄₃	—	16	2	no	—
186	C₂²×C₄₃	—	16	2	no	—
187	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
188	C₂²×C₄₃	#448	1	1	yes	characteristic
189	C₂²×C₄₃	#481	1	1	yes	characteristic
190	C₂×D₄₃	—	2	1	no	—
191	C₂×D₄₃	—	2	1	no	—
192	C₂×D₄₃	—	2	1	no	—
193	C₂×D₄₃	—	2	1	no	—
194	C₂×D₄₃	—	2	1	no	—
195	C₂×D₄₃	—	4	2	no	—
196	C₂×D₄₃	—	4	2	no	—
197	C₂×D₄₃	#361	1	2	yes	complemented
198	C₄×C₄₃	#386	1	1	yes	characteristic
199	C₄×C₄₃	#417	1	1	yes	characteristic
200	C₄×C₄₃	#447	1	1	yes	characteristic
201	C₄×C₄₃	#480	1	1	yes	characteristic
202	Dic₄₃	—	2	1	no	—
203	Dic₄₃	—	2	1	no	—
204	Dic₄₃	—	8	2	no	—
205	C₂×#466	—	43	1	no	—
206	C₂²×#108	—	43	1	no	—
207	C₂×#361	—	43	1	no	—
208	C₂×#361	D₄₃	1	1	yes	characteristic, complemented
209	#2112	—	43	1	no	—
210	#1387	—	43	1	no	—
211	#1387	—	43	1	no	—
212	C₂×C₄₃	—	2	1	no	—
213	C₂×C₄₃	—	2	1	no	—
214	C₂×C₄₃	—	16	2	no	—
215	C₂×C₄₃	#1874	1	1	yes	characteristic
216	C₂×C₄₃	C₂×#361	1	1	yes	characteristic
217	C₂×C₄₃	#2148	1	1	yes	characteristic
218	D₄₃	—	2	2	no	—
219	D₄₃	—	4	1	no	—
220	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
221	C₂²×M₁₆	—	86	1	no	—
222	C₂³×C₈	—	43	1	no	—
223	C₂×#121	—	86	1	no	—
224	C₂×M₃₂	—	43	1	no	—
225	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
226	#466	—	43	2	no	—
227	#466	—	43	2	no	—
228	#466	—	86	1	no	—
229	#466	—	86	1	no	—
230	C₂×#108	—	43	1	no	—
231	C₂×#108	—	86	2	no	—
232	C₂×#108	—	86	1	no	—
233	C₂×#108	—	86	2	no	—
234	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
235	C₂×#107	—	43	1	no	—
236	C₂×#102	—	86	1	no	—
237	#361	—	2	2	no	—
238	#361	—	86	2	no	—
239	C₂²⋊C₁₆	—	86	1	no	—
240	C₂²⋊C₁₆	—	86	1	no	—
241	C₄₃	#13004	1	1	yes	characteristic, complemented, Sylow
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	172	1	no	—
244	C₂³×C₄	—	43	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	C₄×D₄₃	1	2	yes	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	86	4	no	—
253	C₂×M₁₆	—	86	1	no	—
254	C₂×M₁₆	—	172	1	no	—
255	C₂×M₁₆	—	172	2	no	—
256	C₂²×C₈	—	43	1	no	—
257	C₂²×C₈	—	43	1	no	—
258	C₂²×C₈	—	43	1	no	—
259	C₂²×C₈	—	43	1	no	—
260	C₂²×C₈	—	43	1	no	—
261	C₂²×C₈	—	86	1	no	—
262	C₂²×C₈	—	86	1	no	—
263	C₂²×C₈	—	86	1	no	—
264	C₂²×C₈	—	86	1	no	—
265	C₂²×C₈	—	172	1	no	—
266	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
267	#121	—	86	2	no	—
268	#121	—	86	2	no	—
269	#121	—	172	1	no	—
270	#121	—	172	1	no	—
271	C₂×C₄⋊C₄	—	86	1	no	—
272	C₂×C₂²⋊C₄	—	172	1	no	—
273	M₃₂	—	2	1	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	—	86	1	no	—
276	M₃₂	—	86	1	no	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	86	1	no	—
279	#108	—	2	1	no	—
280	#108	—	43	2	no	—
281	#108	—	86	4	no	—
282	#108	—	86	1	no	—
283	#108	C₂²⋊D₄₃	1	2	yes	complemented
284	#107	—	43	2	no	—
285	#107	—	86	1	no	—
286	#102	—	86	2	no	—
287	#102	—	86	2	no	—
288	C₂⁴	—	4	1	no	—
289	C₂⁴	—	43	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	344	4	no	—
297	C₂×D₄	—	172	2	no	—
298	C₂×D₄	—	172	2	no	—
299	C₂²×C₄	—	43	1	no	—
300	C₂²×C₄	—	43	1	no	—
301	C₂²×C₄	—	43	1	no	—
302	C₂²×C₄	—	43	1	no	—
303	C₂²×C₄	—	43	1	no	—
304	C₂²×C₄	—	86	1	no	—
305	C₂²×C₄	—	86	1	no	—
306	C₂²×C₄	—	86	1	no	—
307	C₂²×C₄	—	86	1	no	—
308	C₂²×C₄	—	172	1	no	—
309	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	1	no	—
313	D₈	—	4	1	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	86	2	no	—
317	M₁₆	—	172	4	no	—
318	M₁₆	—	172	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	43	1	no	—
321	C₂×C₈	—	43	1	no	—
322	C₂×C₈	—	86	1	no	—
323	C₂×C₈	—	86	1	no	—
324	C₂×C₈	—	86	1	no	—
325	C₂×C₈	—	86	1	no	—
326	C₂×C₈	—	86	1	no	—
327	C₂×C₈	—	86	1	no	—
328	C₂×C₈	—	86	1	no	—
329	C₂×C₈	—	86	1	no	—
330	C₂×C₈	—	86	1	no	—
331	C₂×C₈	—	86	1	no	—
332	C₂×C₈	—	172	4	no	—
333	C₂×C₈	—	172	1	no	—
334	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
335	C₂×C₈	#10621898	1	1	yes	characteristic
336	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
337	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
338	C₂×C₈	#10621900	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	C₄⋊C₄	—	86	2	no	—
341	C₄⋊C₄	—	172	1	no	—
342	C₂²⋊C₄	—	172	2	no	—
343	C₂²⋊C₄	—	172	2	no	—
344	C₁₆	—	4	1	no	—
345	C₁₆	—	172	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	43	1	no	—
352	C₂³	—	43	1	no	—
353	C₂³	—	86	2	no	—
354	C₂³	—	86	1	no	—
355	C₂³	—	86	1	no	—
356	C₂³	—	172	1	no	—
357	C₂³	SD₁₆×D₄₃	1	1	yes	characteristic
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	1	no	—
361	D₄	—	8	1	no	—
362	D₄	—	344	4	no	—
363	D₄	—	344	4	no	—
364	C₂×C₄	—	43	1	no	—
365	C₂×C₄	—	43	1	no	—
366	C₂×C₄	—	86	1	no	—
367	C₂×C₄	—	86	1	no	—
368	C₂×C₄	—	86	1	no	—
369	C₂×C₄	—	86	1	no	—
370	C₂×C₄	—	86	1	no	—
371	C₂×C₄	—	86	1	no	—
372	C₂×C₄	—	86	1	no	—
373	C₂×C₄	—	86	1	no	—
374	C₂×C₄	—	86	1	no	—
375	C₂×C₄	—	86	1	no	—
376	C₂×C₄	—	344	2	no	—
377	C₂×C₄	—	172	2	no	—
378	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
379	C₂×C₄	#13063293	1	1	yes	characteristic
380	C₂×C₄	#13063307	1	1	yes	characteristic
381	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
382	C₂×C₄	#13063349	1	1	yes	characteristic
383	C₂×C₄	#13063354	1	1	yes	characteristic
384	C₈	—	4	2	no	—
385	C₈	—	86	1	no	—
386	C₈	—	86	1	no	—
387	C₈	—	172	2	no	—
388	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
389	C₈	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
390	C₈	#13063296	1	1	yes	characteristic
391	C₈	#13063298	1	1	yes	characteristic
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	16	2	no	—
398	C₂²	—	16	2	no	—
399	C₂²	—	43	2	no	—
400	C₂²	—	86	1	no	—
401	C₂²	—	86	1	no	—
402	C₂²	—	86	1	no	—
403	C₂²	—	86	1	no	—
404	C₂²	—	86	1	no	—
405	C₂²	—	172	2	no	—
406	C₂²	—	172	2	no	—
407	C₂²	#102×D₄₃	1	1	yes	characteristic
408	C₂²	#14583036	1	1	yes	characteristic
409	C₂²	#14583216	1	1	yes	characteristic
410	C₄	—	86	1	no	—
411	C₄	—	86	1	no	—
412	C₄	—	344	2	no	—
413	C₄	#14582775	1	1	yes	characteristic
414	C₄	#14582897	1	1	yes	characteristic
415	C₄	#14583031	1	1	yes	characteristic
416	C₄	#14583211	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	16	2	no	—
420	C₂	—	86	2	no	—
421	C₂	—	172	1	no	—
422	C₂	#19134909	1	1	yes	characteristic
423	C₂	#361×D₄₃	1	1	yes	characteristic
424	C₂	#19136341	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#102×D₄₃
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#361	C₂
socle	C₂²×C₄₃	C₂×#102
prime radical	C₂×#14583132	C₂
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#361	D₄₃
hypocenter	C₄₃	#13004
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#361

Complements

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

N	H ≅ G/N	type
2. C₂×#108×D₄₃	C₂	semidirect
3. C₂×#14582712	C₂	semidirect
4. #19136205	C₂	semidirect
5. #19132705	C₂	semidirect
6. #19132704	C₂	semidirect
7. C₂×C₄₃×#361	C₂	semidirect
55. #13063261	D₄	semidirect
74. #108×C₄₃	D₄	semidirect
197. C₂×D₄₃	#361	semidirect
208. C₂×#361	D₄₃	semidirect
241. C₄₃	#13004	semidirect
283. #108	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583132	2
C₂×#108×D₄₃	2
C₂×#14582712	2
#19136205	2
#19132705	2
#19132704	2
C₂×C₄₃×#361	2
#13004	43