Subgroups — #72337600

Order 4096.

At least 18040 conjugacy classes of subgroups; only the 401 normal subgroups are shown.

The subgroup lattice has 351 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337599	C₂	1	2	yes	maximal, complemented
2	#72337598	C₂	1	2	yes	maximal, complemented
3	#72337597	C₂	1	2	yes	maximal, complemented
4	#72337596	C₂	1	2	yes	maximal, complemented
5	#72327288	C₂	1	1	yes	maximal, characteristic
6	#72327248	C₂²	1	1	yes	characteristic
7	#72327244	C₄	1	1	yes	characteristic, complemented
8	#72327231	C₂²	1	1	yes	characteristic
9	#72326786	C₄	1	1	yes	characteristic, complemented
10	#72318215	C₂²	1	1	yes	characteristic
11	#72310535	C₂	1	1	yes	maximal, characteristic, complemented
12	#72310527	C₂²	1	2	yes	complemented
13	#72310524	C₂²	1	2	yes	complemented
14	#72309335	C₄	1	1	yes	characteristic, complemented
15	#72302078	C₂	1	1	yes	maximal, characteristic, complemented
16	#72283093	C₄	1	1	yes	characteristic, complemented
17	#72265926	C₂²	1	2	yes	complemented
18	#72265926	C₂²	1	2	yes	complemented
19	#72237771	C₂	1	1	yes	maximal, characteristic, complemented
20	#72237770	C₂	1	1	yes	maximal, characteristic, complemented
21	#72237756	C₂²	1	2	yes	complemented
22	#72237751	C₂²	1	2	yes	complemented
23	#72237733	C₂²	1	2	yes	complemented
24	#72237726	C₂²	1	2	yes	complemented
25	#72226357	C₂	1	1	yes	maximal, characteristic, complemented
26	#72226356	C₂²	1	2	yes	complemented
27	#72226356	C₂²	1	2	yes	complemented
28	#72226352	C₂	1	1	yes	maximal, characteristic, complemented
29	#72225873	C₂²	1	1	yes	characteristic, complemented
30	#72225873	C₂²	1	1	yes	characteristic, complemented
31	#72225777	C₂²	1	1	yes	characteristic, complemented
32	#72225776	C₂²	1	1	yes	characteristic, complemented
33	#72225733	C₂²	1	1	yes	characteristic
34	#72225660	C₂²	1	1	yes	characteristic
35	#72225655	C₂²	1	1	yes	characteristic
36	#72218920	C₄	1	1	yes	characteristic, complemented
37	#72217730	C₄	1	1	yes	characteristic, complemented
38	C₂×#449475	C₂²	1	1	yes	characteristic
39	#72216681	C₂²	1	2	yes	complemented
40	#72216681	C₂²	1	2	yes	complemented
41	#72216646	C₄	1	1	yes	characteristic, complemented
42	#72210024	C₄	1	1	yes	characteristic, complemented
43	#10586066	D₄	1	1	yes	characteristic
44	#8093108	C₂×C₄	1	1	yes	characteristic, complemented
45	#8093107	C₂×C₄	1	1	yes	characteristic, complemented
46	#7670230	C₂×C₄	1	1	yes	characteristic, complemented
47	#7670203	C₂×C₄	1	1	yes	characteristic, complemented
48	#7642273	C₂×C₄	1	1	yes	characteristic
49	#7642244	C₂×C₄	1	1	yes	characteristic
50	#7642244	C₂×C₄	1	1	yes	characteristic
51	C₂²×#2846	C₂×C₄	1	1	yes	characteristic
52	C₂²×#2846	D₄	1	1	yes	characteristic
53	C₂²×#2846	D₄	1	1	yes	characteristic
54	C₂×#35346	C₂³	1	1	yes	characteristic
55	#6629262	C₂×C₄	1	1	yes	characteristic
56	#6629262	D₄	1	1	yes	characteristic
57	#6628896	C₂×C₄	1	1	yes	characteristic
58	#6628896	D₄	1	1	yes	characteristic
59	#6451874	D₄	1	1	yes	characteristic
60	#6451874	D₄	1	1	yes	characteristic
61	#6432953	D₄	1	1	yes	characteristic
62	#6432953	D₄	1	1	yes	characteristic
63	#6432953	C₂³	1	1	yes	characteristic
64	#6432953	C₂³	1	1	yes	characteristic
65	#6374210	D₄	1	1	yes	characteristic
66	#6374210	D₄	1	1	yes	characteristic
67	#6370693	D₄	1	1	yes	characteristic
68	#449521	C₂×C₄	1	1	yes	characteristic, complemented
69	#449521	C₂×C₄	1	1	yes	characteristic, complemented
70	#449475	C₂×C₄	1	1	yes	characteristic
71	#449475	C₂×C₄	1	1	yes	characteristic
72	#449475	C₂×C₄	1	1	yes	characteristic, complemented
73	#449475	C₂×C₄	1	1	yes	characteristic, complemented
74	#449475	D₄	1	1	yes	characteristic
75	#449475	D₄	1	1	yes	characteristic
76	#449475	D₄	1	1	yes	characteristic
77	#449475	D₄	1	1	yes	characteristic
78	#449475	C₂³	1	1	yes	characteristic
79	#449475	C₂³	1	1	yes	characteristic
80	#418213	C₂×C₄	1	1	yes	characteristic, complemented
81	#418132	C₂×C₄	1	1	yes	characteristic, complemented
82	#417896	C₂×C₄	1	1	yes	characteristic
83	#417896	C₂×C₄	1	1	yes	characteristic, complemented
84	#417896	D₄	1	1	yes	characteristic
85	#417896	D₄	1	1	yes	characteristic
86	#417896	C₂³	1	1	yes	characteristic
87	#417824	C₂×C₄	1	1	yes	characteristic
88	#417824	C₂×C₄	1	1	yes	characteristic, complemented
89	#417824	D₄	1	1	yes	characteristic
90	#417824	D₄	1	1	yes	characteristic
91	#417824	C₂³	1	1	yes	characteristic
92	#391735	C₂×C₄	1	1	yes	characteristic, complemented
93	#391709	C₂×C₄	1	1	yes	characteristic, complemented
94	#382422	C₂×C₄	1	1	yes	characteristic
95	#375666	C₂×C₄	1	1	yes	characteristic, complemented
96	#374004	C₂×C₄	1	1	yes	characteristic, complemented
97	#359705	D₄	1	1	yes	characteristic
98	#359705	D₄	1	1	yes	characteristic
99	C₂×#10965	C₂×C₄	1	1	yes	characteristic
100	C₂×#10965	D₄	1	1	yes	characteristic
101	C₂×#10965	D₄	1	1	yes	characteristic
102	#213890	C₂³	1	2	yes	—
103	#213828	C₂³	1	2	yes	—
104	#134045	C₂³	1	2	yes	—
105	#134045	C₂³	1	2	yes	—
106	C₂⁸	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
109	#62842	C₂×D₄	1	1	yes	characteristic
110	#62842	C₂×D₄	1	1	yes	characteristic
111	C₂×#3490	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#3484	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#3484	C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
115	C₂³×#120	C₂×D₄	1	1	yes	characteristic
116	C₂³×#120	C₂×D₄	1	1	yes	characteristic
117	#62652	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
125	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
126	C₂×#2846	C₂×D₄	1	1	yes	characteristic
127	C₂×#2846	C₂×D₄	1	1	yes	characteristic
128	C₂×#2846	C₂×D₄	1	1	yes	characteristic
129	C₂×#2846	C₂×D₄	1	1	yes	characteristic
130	#35390	C₂²⋊C₄	1	1	yes	characteristic
131	#35390	C₂²×C₄	1	1	yes	characteristic
132	#35367	C₂²⋊C₄	1	1	yes	characteristic
133	#35367	C₂²×C₄	1	1	yes	characteristic
134	#35350	C₂²⋊C₄	1	1	yes	characteristic
135	#35350	C₂²⋊C₄	1	1	yes	characteristic
136	#35350	C₂²×C₄	1	1	yes	characteristic
137	#35350	C₂²×C₄	1	1	yes	characteristic
138	#35346	C₂²⋊C₄	1	1	yes	characteristic
139	#35346	C₂²⋊C₄	1	1	yes	characteristic
140	#35346	C₂²×C₄	1	1	yes	characteristic
141	#35346	C₂²×C₄	1	1	yes	characteristic
142	#35346	C₂²×C₄	1	1	yes	characteristic
143	#35346	C₂×D₄	1	1	yes	characteristic
144	#35346	C₂×D₄	1	1	yes	characteristic
145	#35346	C₂×D₄	1	1	yes	characteristic
146	#35346	C₂×D₄	1	1	yes	characteristic
147	#35346	C₂×D₄	1	1	yes	characteristic
148	#35346	C₂×D₄	1	1	yes	characteristic
149	#35346	C₂⁴	1	1	yes	characteristic
150	#34176	C₂²⋊C₄	1	1	yes	characteristic
151	#34171	C₂²⋊C₄	1	1	yes	characteristic
152	#34171	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#2308	C₂×D₄	1	1	yes	characteristic
154	C₂×#2308	C₂×D₄	1	1	yes	characteristic
155	C₂×#2308	C₂×D₄	1	1	yes	characteristic
156	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
159	#23468	C₂²⋊C₄	1	1	yes	characteristic
160	#23468	C₂²⋊C₄	1	1	yes	characteristic
161	#23468	C₂×D₄	1	1	yes	characteristic
162	#23468	C₂×D₄	1	1	yes	characteristic
163	#23444	C₂²⋊C₄	1	1	yes	characteristic
164	#23444	C₂²⋊C₄	1	1	yes	characteristic
165	#23444	C₂×D₄	1	1	yes	characteristic
166	#23444	C₂×D₄	1	1	yes	characteristic
167	#20689	C₂²⋊C₄	1	1	yes	characteristic
168	#20689	C₂²⋊C₄	1	1	yes	characteristic
169	#20689	C₂×D₄	1	1	yes	characteristic
170	#20689	C₂×D₄	1	1	yes	characteristic
171	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
173	#20585	C₂²⋊C₄	1	1	yes	characteristic
174	#20585	C₂²⋊C₄	1	1	yes	characteristic
175	#20585	C₂²⋊C₄	1	1	yes	characteristic
176	#20585	C₂²⋊C₄	1	1	yes	characteristic
177	#20585	C₂×D₄	1	1	yes	characteristic
178	#20585	C₂×D₄	1	1	yes	characteristic
179	#20585	C₂×D₄	1	1	yes	characteristic
180	#20585	C₂×D₄	1	1	yes	characteristic
181	#10965	C₂²⋊C₄	1	1	yes	characteristic
182	#10965	C₂²⋊C₄	1	1	yes	characteristic
183	#10965	C₂²⋊C₄	1	1	yes	characteristic
184	#10965	C₂²⋊C₄	1	1	yes	characteristic
185	#10965	C₂²⋊C₄	1	1	yes	characteristic
186	#10965	C₂²⋊C₄	1	1	yes	characteristic
187	#10965	C₂²⋊C₄	1	1	yes	characteristic
188	#10965	C₂²⋊C₄	1	1	yes	characteristic
189	#10965	C₂²×C₄	1	1	yes	characteristic
190	#10965	C₂²×C₄	1	1	yes	characteristic
191	#10965	C₂²×C₄	1	1	yes	characteristic
192	#10965	C₂²×C₄	1	1	yes	characteristic
193	#10965	C₂×D₄	1	1	yes	characteristic
194	#10965	C₂×D₄	1	1	yes	characteristic
195	#10965	C₂×D₄	1	1	yes	characteristic
196	#10965	C₂×D₄	1	1	yes	characteristic
197	#10938	C₂²⋊C₄	1	1	yes	characteristic
198	#10938	C₂²⋊C₄	1	1	yes	characteristic
199	#10938	C₂²⋊C₄	1	1	yes	characteristic
200	#10938	C₂²⋊C₄	1	1	yes	characteristic
201	#10938	C₂×D₄	1	1	yes	characteristic
202	#10938	C₂×D₄	1	1	yes	characteristic
203	#10938	C₂×D₄	1	1	yes	characteristic
204	#10938	C₂×D₄	1	1	yes	characteristic
205	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
212	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
213	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
214	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂⁴×D₄	#120	1	1	yes	characteristic
216	C₂⁴×D₄	#120	1	1	yes	characteristic
217	C₂×#543	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×#534	#99	1	2	yes	—
219	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×#120	#99	1	2	yes	—
221	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂²×#120	#120	1	1	yes	characteristic
227	C₂²×#120	#120	1	1	yes	characteristic
228	C₂²×#120	#120	1	1	yes	characteristic
229	C₂²×#120	#120	1	1	yes	characteristic
230	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
231	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
232	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
233	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
237	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
238	#2308	#99	1	2	yes	—
239	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	#2308	#120	1	1	yes	characteristic
247	#2308	#120	1	1	yes	characteristic
248	#2308	#120	1	1	yes	characteristic
249	#2308	#120	1	1	yes	characteristic
250	#2308	#120	1	1	yes	characteristic
251	#2308	#120	1	1	yes	characteristic
252	#2308	C₂²×D₄	1	1	yes	characteristic
253	#2308	C₂²×D₄	1	1	yes	characteristic
254	#2308	C₂²×D₄	1	1	yes	characteristic
255	#2280	#99	1	2	yes	—
256	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁶	#379	1	1	yes	characteristic
269	C₂⁶	#379	1	1	yes	characteristic
270	C₂⁶	C₂×#99	1	1	yes	characteristic
271	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
272	C₂⁶	#458	1	1	yes	characteristic
273	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
274	C₂³×D₄	#379	1	1	yes	characteristic
275	C₂³×D₄	#379	1	1	yes	characteristic
276	C₂³×D₄	#379	1	1	yes	characteristic
277	C₂³×D₄	C₂×#99	1	1	yes	characteristic
278	C₂³×D₄	C₂×#99	1	2	yes	—
279	C₂³×D₄	C₂×#99	1	1	yes	characteristic
280	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
281	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
282	C₂³×D₄	#458	1	1	yes	characteristic
283	C₂³×D₄	#458	1	1	yes	characteristic
284	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂³×D₄	C₂×#120	1	1	yes	characteristic
286	C₂³×D₄	C₂×#120	1	1	yes	characteristic
287	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
288	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
289	C₂⁴×C₄	#458	1	1	yes	characteristic
290	C₂×#123	AΣL(1,𝔽₁₆)	1	4	yes	complemented
291	C₂×#120	AΣL(1,𝔽₁₆)	1	4	yes	complemented
292	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
294	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
295	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
298	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
299	#381	C₂×#99	1	2	yes	—
300	#381	C₂×#99	1	2	yes	—
301	C₂⁵	#1781	1	1	yes	characteristic
302	C₂⁵	#1781	1	1	yes	characteristic
303	C₂⁵	#1781	1	1	yes	characteristic
304	C₂⁵	#1790	1	1	yes	characteristic
305	C₂⁵	#1790	1	1	yes	characteristic
306	C₂⁵	#1790	1	1	yes	characteristic
307	C₂⁵	#1790	1	1	yes	characteristic
308	C₂⁵	#1790	1	1	yes	characteristic
309	C₂⁵	#1790	1	1	yes	characteristic
310	C₂⁵	C₂×AΣL(1,𝔽₁₆)	1	2	yes	complemented
311	C₂⁵	C₂×#379	1	1	yes	characteristic
312	C₂⁵	C₂²×#99	1	1	yes	characteristic
313	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
314	C₂⁵	C₂×#458	1	1	yes	characteristic
315	C₂²×D₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
316	C₂³×C₄	#1781	1	1	yes	characteristic
317	C₂³×C₄	#1790	1	1	yes	characteristic
318	C₂³×C₄	#1790	1	1	yes	characteristic
319	C₂³×C₄	C₂×AΣL(1,𝔽₁₆)	1	2	yes	complemented
320	C₂³×C₄	C₂²×#99	1	1	yes	characteristic
321	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
322	C₂³×C₄	C₂×#458	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	complemented
324	C₂⁴	#8534	1	1	yes	characteristic
325	C₂⁴	#8534	1	1	yes	characteristic
326	C₂⁴	#8534	1	1	yes	characteristic
327	C₂⁴	#8534	1	1	yes	characteristic
328	C₂⁴	#12687	1	2	yes	—
329	C₂⁴	#12705	1	2	yes	—
330	C₂⁴	#12753	1	2	yes	—
331	C₂⁴	C₂×#1781	1	1	yes	characteristic
332	C₂⁴	C₂×#1790	1	1	yes	characteristic
333	C₂⁴	C₂×#1790	1	1	yes	characteristic
334	C₂⁴	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
335	C₂²×C₄	#12687	1	2	yes	—
336	C₂²×C₄	#12753	1	2	yes	—
337	C₂³	#133278	1	2	yes	—
338	C₂³	#133278	1	2	yes	—
339	C₂³	C₂×#8534	1	1	yes	characteristic
340	C₂³	C₂×#12687	1	1	yes	characteristic
341	C₂³	C₂×#12705	1	1	yes	characteristic
342	C₂³	C₂×#12753	1	1	yes	characteristic
343	C₂³	C₂×#12753	1	1	yes	characteristic
344	C₂³	#493594	1	1	yes	characteristic
345	C₂³	#493594	1	1	yes	characteristic
346	C₂²	C₂×#133278	1	1	yes	characteristic
347	C₂²	#72258234	1	1	yes	characteristic
348	C₂²	#72258234	1	1	yes	characteristic
349	C₂	#72259010	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72259010
commutator	C₂²×#120	C₂³×C₄
Frattini, cosocle	#35346	C₂⁴
prime radical	#72327288	C₂
LCS	G ▷ C₂²×#120 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#35346 ◁ G
LECS	G ▷ #35346 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337599	C₂	semidirect
2. #72337598	C₂	semidirect
3. #72337597	C₂	semidirect
4. #72337596	C₂	semidirect
7. #72327244	C₄	semidirect
9. #72326786	C₄	semidirect
11. #72310535	C₂	semidirect
12. #72310527	C₂²	semidirect
13. #72310524	C₂²	semidirect
14. #72309335	C₄	semidirect
15. #72302078	C₂	semidirect
16. #72283093	C₄	semidirect
17. #72265926	C₂²	semidirect
18. #72265926	C₂²	semidirect
19. #72237771	C₂	semidirect
20. #72237770	C₂	semidirect
21. #72237756	C₂²	semidirect
22. #72237751	C₂²	semidirect
23. #72237733	C₂²	semidirect
24. #72237726	C₂²	semidirect
25. #72226357	C₂	semidirect
26. #72226356	C₂²	semidirect
27. #72226356	C₂²	semidirect
28. #72226352	C₂	semidirect
29. #72225873	C₂²	semidirect
30. #72225873	C₂²	semidirect
31. #72225777	C₂²	semidirect
32. #72225776	C₂²	semidirect
36. #72218920	C₄	semidirect
37. #72217730	C₄	semidirect
39. #72216681	C₂²	semidirect
40. #72216681	C₂²	semidirect
41. #72216646	C₄	semidirect
42. #72210024	C₄	semidirect
44. #8093108	C₂×C₄	semidirect
45. #8093107	C₂×C₄	semidirect
46. #7670230	C₂×C₄	semidirect
47. #7670203	C₂×C₄	semidirect
68. #449521	C₂×C₄	semidirect
69. #449521	C₂×C₄	semidirect
72. #449475	C₂×C₄	semidirect
73. #449475	C₂×C₄	semidirect
80. #418213	C₂×C₄	semidirect
81. #418132	C₂×C₄	semidirect
83. #417896	C₂×C₄	semidirect
88. #417824	C₂×C₄	semidirect
92. #391735	C₂×C₄	semidirect
93. #391709	C₂×C₄	semidirect
95. #375666	C₂×C₄	semidirect
96. #374004	C₂×C₄	semidirect
290. C₂×#123	AΣL(1,𝔽₁₆)	semidirect
291. C₂×#120	AΣL(1,𝔽₁₆)	semidirect
310. C₂⁵	C₂×AΣL(1,𝔽₁₆)	semidirect
319. C₂³×C₄	C₂×AΣL(1,𝔽₁₆)	semidirect
323. C₂×C₂²⋊C₄	C₂×AΣL(1,𝔽₁₆)	semidirect

Maximal subgroups

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

subgroup	index
#72337599	2
#72337598	2
#72337597	2
#72337596	2
#72327288	2
#72310535	2
#72302078	2
#72237771	2
#72237770	2
#72226357	2
#72226352	2