Subgroups — #72236956

Order 2048.

At least 6298 conjugacy classes of subgroups; only the 398 normal subgroups are shown.

The subgroup lattice has 343 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72236953	C₂	1	1	yes	maximal, characteristic
2	#72236952	C₂	1	2	yes	maximal, complemented
3	#72236951	C₂	1	2	yes	maximal, complemented
4	#72236947	C₂	1	2	yes	maximal, complemented
5	#72233610	C₂	1	1	yes	maximal, characteristic, complemented
6	#72233479	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233318	C₂	1	2	yes	maximal, complemented
8	#72233291	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233041	C₂	1	1	yes	maximal, characteristic, complemented
10	#72232741	C₂	1	1	yes	maximal, characteristic
11	#72216481	C₂	1	1	yes	maximal, characteristic
12	#6385971	C₂²	1	1	yes	characteristic
13	#6385971	C₂²	1	1	yes	characteristic
14	#6385971	C₂²	1	1	yes	characteristic
15	#5486624	C₄	1	1	yes	characteristic, complemented
16	#5486602	C₄	1	1	yes	characteristic, complemented
17	#5486439	C₄	1	1	yes	characteristic, complemented
18	#5486276	C₄	1	1	yes	characteristic, complemented
19	#2600505	C₄	1	1	yes	characteristic, complemented
20	#2549486	C₄	1	1	yes	characteristic, complemented
21	#2306524	C₄	1	1	yes	characteristic, complemented
22	#2177857	C₄	1	1	yes	characteristic, complemented
23	#949904	C₂²	1	1	yes	characteristic
24	#845677	C₂²	1	1	yes	characteristic
25	#705152	C₂²	1	1	yes	characteristic
26	#647656	C₂²	1	1	yes	characteristic
27	#582871	C₂²	1	1	yes	characteristic
28	#553180	C₂²	1	1	yes	characteristic
29	C₂×#14134	C₂²	1	1	yes	characteristic
30	#496226	C₂²	1	2	yes	—
31	C₂×#12687	C₂²	1	2	yes	—
32	#359501	C₂²	1	2	yes	—
33	#201668	C₂²	1	2	yes	—
34	#188087	C₂²	1	1	yes	characteristic
35	#128073	C₂²	1	2	yes	—
36	#128058	C₂²	1	2	yes	—
37	C₂×#7304	C₂²	1	2	yes	—
38	C₂×#7307	C₂²	1	2	yes	—
39	#108222	C₂²	1	2	yes	—
40	#107130	C₂²	1	2	yes	—
41	#106766	C₂²	1	2	yes	—
42	#106744	C₂²	1	2	yes	—
43	C₂²×D₄²	C₂³	1	1	yes	characteristic
44	C₂³×#120	D₄	1	1	yes	characteristic
45	C₂³×#120	C₂³	1	1	yes	characteristic
46	C₂×#2846	D₄	1	1	yes	characteristic
47	C₂×#2412	D₄	1	1	yes	characteristic
48	C₂×#2405	C₂³	1	1	yes	characteristic
49	#34171	C₂³	1	2	yes	—
50	C₂×#2353	D₄	1	1	yes	characteristic
51	C₂×#2318	D₄	1	1	yes	characteristic
52	C₂×#2308	D₄	1	1	yes	characteristic
53	C₂×#1783	C₂³	1	2	yes	—
54	C₂×#1781	C₂³	1	2	yes	—
55	C₂×#1781	C₂³	1	2	yes	—
56	#17273	C₂×C₄	1	1	yes	characteristic, complemented
57	#17272	C₂×C₄	1	1	yes	characteristic, complemented
58	#17272	C₂×C₄	1	1	yes	characteristic, complemented
59	#17137	C₂×C₄	1	1	yes	characteristic, complemented
60	#15984	C₂×C₄	1	1	yes	characteristic
61	#15984	D₄	1	1	yes	characteristic
62	#15950	C₂×C₄	1	1	yes	characteristic
63	#15948	C₂×C₄	1	1	yes	characteristic, complemented
64	#15948	C₂×C₄	1	1	yes	characteristic, complemented
65	#15948	D₄	1	1	yes	characteristic
66	#15948	D₄	1	1	yes	characteristic
67	#15947	D₄	1	1	yes	characteristic
68	#15947	D₄	1	1	yes	characteristic
69	#15266	C₂×C₄	1	1	yes	characteristic, complemented
70	#15266	C₂×C₄	1	1	yes	characteristic, complemented
71	#15261	C₂×C₄	1	1	yes	characteristic
72	#15261	C₂×C₄	1	1	yes	characteristic
73	#15260	D₄	1	1	yes	characteristic
74	#15258	C₂×C₄	1	1	yes	characteristic
75	#15258	C₂×C₄	1	1	yes	characteristic
76	#15257	C₂×C₄	1	1	yes	characteristic
77	#15257	C₂×C₄	1	1	yes	characteristic
78	#15257	D₄	1	1	yes	characteristic
79	#15257	D₄	1	1	yes	characteristic
80	#14666	C₂×C₄	1	1	yes	characteristic, complemented
81	#14661	C₂×C₄	1	1	yes	characteristic
82	#14659	C₂×C₄	1	1	yes	characteristic
83	#14658	C₂×C₄	1	1	yes	characteristic, complemented
84	#14506	C₂×C₄	1	1	yes	characteristic, complemented
85	#14410	C₂×C₄	1	1	yes	characteristic, complemented
86	#14345	D₄	1	1	yes	characteristic
87	#14335	D₄	1	1	yes	characteristic
88	#14290	C₂×C₄	1	1	yes	characteristic
89	#14272	C₂×C₄	1	1	yes	characteristic
90	#14271	D₄	1	1	yes	characteristic
91	#14255	D₄	1	1	yes	characteristic
92	#14152	D₄	1	1	yes	characteristic
93	#14134	C₂×C₄	1	1	yes	characteristic, complemented
94	#14134	C₂×C₄	1	1	yes	characteristic, complemented
95	#14134	C₂×C₄	1	1	yes	characteristic, complemented
96	#14134	C₂×C₄	1	1	yes	characteristic, complemented
97	#14134	D₄	1	1	yes	characteristic
98	#13959	D₄	1	1	yes	characteristic
99	#13902	D₄	1	1	yes	characteristic
100	#13902	C₂³	1	1	yes	characteristic
101	#13867	D₄	1	1	yes	characteristic
102	#13867	D₄	1	1	yes	characteristic
103	#13867	C₂³	1	1	yes	characteristic
104	C₂×#1438	C₂³	1	1	yes	characteristic
105	C₂×#1438	C₂³	1	1	yes	characteristic
106	C₂⁷	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
111	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
112	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic, complemented
113	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
114	C₂²×#123	C₂×D₄	1	1	yes	characteristic
115	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
116	C₂²×#121	C₂×D₄	1	1	yes	characteristic
117	C₂²×#121	C₂×D₄	1	1	yes	characteristic
118	C₂²×#121	C₂×D₄	1	1	yes	characteristic
119	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
126	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
127	C₂²×#120	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂×D₄	1	1	yes	characteristic
129	C₂²×#120	C₂×D₄	1	1	yes	characteristic
130	C₂²×#120	C₂×D₄	1	1	yes	characteristic
131	C₂²×#120	C₂×D₄	1	1	yes	characteristic
132	C₂²×#120	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
136	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×#99	#41	1	4	yes	—
141	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
142	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
143	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
144	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
145	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂×#386	C₂²×C₄	1	1	yes	characteristic
147	C₂×#386	C₂×D₄	1	1	yes	characteristic
148	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic, complemented
149	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic, complemented
150	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic, complemented
151	C₂×#382	C₂²⋊C₄	1	1	yes	characteristic, complemented
152	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
153	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
154	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	C₂×#380	C₂×D₄	1	1	yes	characteristic
157	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#379	C₂×D₄	1	1	yes	characteristic
160	C₂×#379	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
163	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	C₂²×#95	C₂×D₄	1	1	yes	characteristic
165	C₂²×#95	C₂×D₄	1	1	yes	characteristic
166	#1781	#41	1	4	yes	—
167	#1445	C₂²⋊C₄	1	1	yes	characteristic, complemented
168	#1445	C₂²⋊C₄	1	1	yes	characteristic, complemented
169	#1445	C₂²⋊C₄	1	1	yes	characteristic, complemented
170	#1445	C₂²⋊C₄	1	1	yes	characteristic, complemented
171	#1440	C₂²⋊C₄	1	1	yes	characteristic
172	#1440	C₂²⋊C₄	1	1	yes	characteristic
173	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	#1438	C₂²⋊C₄	1	1	yes	characteristic
176	#1438	C₂²⋊C₄	1	1	yes	characteristic
177	#1438	C₂²⋊C₄	1	1	yes	characteristic
178	#1438	C₂²⋊C₄	1	1	yes	characteristic
179	#1438	C₂²⋊C₄	1	1	yes	characteristic
180	#1438	C₂²⋊C₄	1	1	yes	characteristic
181	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
185	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
187	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
188	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
189	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
190	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
191	#1438	C₂²×C₄	1	1	yes	characteristic
192	#1438	C₂²×C₄	1	1	yes	characteristic
193	#1438	C₂²×C₄	1	1	yes	characteristic
194	#1438	C₂²×C₄	1	1	yes	characteristic
195	#1438	C₂²×C₄	1	1	yes	characteristic
196	#1438	C₂²×C₄	1	1	yes	characteristic
197	#1438	C₂²×C₄	1	1	yes	characteristic
198	#1438	C₂²×C₄	1	1	yes	characteristic
199	#1438	C₂×D₄	1	1	yes	characteristic
200	#1438	C₂×D₄	1	1	yes	characteristic
201	#1438	C₂×D₄	1	1	yes	characteristic
202	#1438	C₂×D₄	1	1	yes	characteristic
203	#1438	C₂×D₄	1	1	yes	characteristic
204	#1438	C₂×D₄	1	1	yes	characteristic
205	#1438	C₂×D₄	1	1	yes	characteristic
206	#1438	C₂×D₄	1	1	yes	characteristic
207	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂⁶	#120	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂⁶	C₂²×D₄	1	1	yes	characteristic
212	C₂⁶	C₂²×D₄	1	1	yes	characteristic
213	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×D₄	#120	1	1	yes	characteristic
221	C₂³×D₄	#120	1	1	yes	characteristic
222	C₂³×D₄	#120	1	1	yes	characteristic
223	C₂³×D₄	#120	1	1	yes	characteristic
224	C₂³×D₄	#120	1	1	yes	characteristic
225	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
226	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
227	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₂×#41	1	2	yes	—
230	C₂³×D₄	C₂×#41	1	2	yes	—
231	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
232	C₂³×D₄	2₋¹⁺⁴	1	2	yes	—
233	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂⁴×C₄	#120	1	1	yes	characteristic
237	C₂⁴×C₄	#120	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
261	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂⁵	#379	1	1	yes	characteristic
271	C₂⁵	#379	1	1	yes	characteristic
272	C₂⁵	#379	1	1	yes	characteristic
273	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
274	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₂⁵	C₂×#120	1	1	yes	characteristic
276	C₂⁵	C₂×#120	1	1	yes	characteristic
277	C₂⁵	C₂×#120	1	1	yes	characteristic
278	C₂⁵	#546	1	2	yes	—
279	C₂⁵	#546	1	2	yes	—
280	C₂⁵	#547	1	2	yes	—
281	C₂⁵	#547	1	2	yes	—
282	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
283	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
284	C₂²×D₄	#458	1	1	yes	characteristic
285	C₂²×D₄	#458	1	1	yes	characteristic
286	C₂²×D₄	C₄×#41	1	2	yes	—
287	C₂²×D₄	#520	1	2	yes	—
288	C₂²×D₄	#525	1	1	yes	characteristic
289	C₂²×D₄	#525	1	1	yes	characteristic
290	C₂²×D₄	#535	1	1	yes	characteristic
291	C₂²×D₄	#536	1	1	yes	characteristic
292	C₂²×D₄	#546	1	2	yes	—
293	C₂²×D₄	#546	1	2	yes	—
294	C₂²×D₄	#547	1	2	yes	—
295	C₂²×D₄	#547	1	2	yes	—
296	C₂³×C₄	#379	1	1	yes	characteristic
297	C₂³×C₄	#379	1	1	yes	characteristic
298	C₂³×C₄	#379	1	1	yes	characteristic
299	C₂³×C₄	#379	1	1	yes	characteristic
300	C₂³×C₄	#379	1	1	yes	characteristic
301	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
302	C₂³×C₄	C₂×#120	1	1	yes	characteristic
303	C₂³×C₄	#532	1	2	yes	—
304	C₂³×C₄	#537	1	2	yes	—
305	C₂⁴	#1790	1	1	yes	characteristic
306	C₂⁴	#1790	1	1	yes	characteristic
307	C₂⁴	C₂×#379	1	1	yes	characteristic
308	C₂⁴	#2339	1	2	yes	—
309	C₂⁴	#2339	1	2	yes	—
310	C₂⁴	#2404	1	1	yes	characteristic
311	C₂⁴	#2404	1	1	yes	characteristic
312	C₂⁴	#2406	1	1	yes	characteristic
313	C₂⁴	#2406	1	1	yes	characteristic
314	C₂⁴	#2430	1	2	yes	—
315	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
316	C₂⁴	C₂×#458	1	1	yes	characteristic
317	C₂⁴	#3026	1	2	yes	—
318	C₂²×C₄	#1790	1	1	yes	characteristic
319	C₂²×C₄	#1790	1	1	yes	characteristic
320	C₂²×C₄	#2297	1	1	yes	characteristic
321	C₂²×C₄	#2311	1	1	yes	characteristic
322	C₂²×C₄	#2430	1	2	yes	—
323	C₂³	#13956	1	1	yes	characteristic
324	C₂³	C₂×#1790	1	1	yes	characteristic
325	C₂³	#20609	1	1	yes	characteristic
326	C₂³	#23996	1	2	yes	—
327	C₂³	#25563	1	2	yes	—
328	C₂³	#25565	1	2	yes	—
329	C₂³	#33551	1	2	yes	—
330	C₂³	#33552	1	2	yes	—
331	C₂²	#363895	1	1	yes	characteristic
332	C₂²	#363953	1	1	yes	characteristic
333	C₂²	#363969	1	1	yes	characteristic
334	C₂²	#493582	1	1	yes	characteristic
335	C₂²	#493583	1	1	yes	characteristic
336	C₂²	#493635	1	1	yes	characteristic
337	C₂²	#493636	1	1	yes	characteristic
338	C₂²	#502687	1	4	yes	—
339	C₂	#72233201	1	1	yes	characteristic
340	C₂	#72234957	1	1	yes	characteristic
341	C₂	#72234966	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#363895
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#647656	C₂²
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #72236952	C₂	semidirect
3. #72236951	C₂	semidirect
4. #72236947	C₂	semidirect
5. #72233610	C₂	semidirect
6. #72233479	C₂	semidirect
7. #72233318	C₂	semidirect
8. #72233291	C₂	semidirect
9. #72233041	C₂	semidirect
15. #5486624	C₄	semidirect
16. #5486602	C₄	semidirect
17. #5486439	C₄	semidirect
18. #5486276	C₄	semidirect
19. #2600505	C₄	semidirect
20. #2549486	C₄	semidirect
21. #2306524	C₄	semidirect
22. #2177857	C₄	semidirect
56. #17273	C₂×C₄	semidirect
57. #17272	C₂×C₄	semidirect
58. #17272	C₂×C₄	semidirect
59. #17137	C₂×C₄	semidirect
63. #15948	C₂×C₄	semidirect
64. #15948	C₂×C₄	semidirect
69. #15266	C₂×C₄	semidirect
70. #15266	C₂×C₄	semidirect
80. #14666	C₂×C₄	semidirect
83. #14658	C₂×C₄	semidirect
84. #14506	C₂×C₄	semidirect
85. #14410	C₂×C₄	semidirect
93. #14134	C₂×C₄	semidirect
94. #14134	C₂×C₄	semidirect
95. #14134	C₂×C₄	semidirect
96. #14134	C₂×C₄	semidirect
112. C₂²×#123	C₂²⋊C₄	semidirect
141. C₂×#386	C₂²⋊C₄	semidirect
142. C₂×#386	C₂²⋊C₄	semidirect
143. C₂×#386	C₂²⋊C₄	semidirect
144. C₂×#386	C₂²⋊C₄	semidirect
145. C₂×#386	C₂²⋊C₄	semidirect
148. C₂×#385	C₂²⋊C₄	semidirect
149. C₂×#383	C₂²⋊C₄	semidirect
150. C₂×#383	C₂²⋊C₄	semidirect
151. C₂×#382	C₂²⋊C₄	semidirect
152. C₂×#381	C₂²⋊C₄	semidirect
153. C₂×#381	C₂²⋊C₄	semidirect
154. C₂×#381	C₂²⋊C₄	semidirect
155. C₂×#380	C₂²⋊C₄	semidirect
161. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
163. C₂×#376	C₂²⋊C₄	semidirect
167. #1445	C₂²⋊C₄	semidirect
168. #1445	C₂²⋊C₄	semidirect
169. #1445	C₂²⋊C₄	semidirect
170. #1445	C₂²⋊C₄	semidirect
173. #1440	C₂²⋊C₄	semidirect
174. #1440	C₂²⋊C₄	semidirect
181. #1438	C₂²⋊C₄	semidirect
182. #1438	C₂²⋊C₄	semidirect
183. #1438	C₂²⋊C₄	semidirect
184. #1438	C₂²⋊C₄	semidirect
185. #1438	C₂²⋊C₄	semidirect
186. #1438	C₂²⋊C₄	semidirect
187. #1438	C₂²⋊C₄	semidirect
188. #1438	C₂²⋊C₄	semidirect
189. #1438	C₂²⋊C₄	semidirect
190. #1438	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72236953	2
#72236952	2
#72236951	2
#72236947	2
#72233610	2
#72233479	2
#72233318	2
#72233291	2
#72233041	2
#72232741	2
#72216481	2