Subgroups — #72312279

Order 4096.

At least 17433 conjugacy classes of subgroups; only the 489 normal subgroups are shown.

The subgroup lattice has 376 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312258	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312241	C₂	1	1	yes	maximal, characteristic, complemented
3	#72312226	C₂	1	1	yes	maximal, characteristic, complemented
4	#72312205	C₂	1	1	yes	maximal, characteristic, complemented
5	#72312179	C₂	1	1	yes	maximal, characteristic, complemented
6	#72310395	C₂	1	1	yes	maximal, characteristic, complemented
7	#72310339	C₂	1	1	yes	maximal, characteristic, complemented
8	#72310295	C₂	1	1	yes	maximal, characteristic, complemented
9	#72309519	C₂	1	1	yes	maximal, characteristic, complemented
10	#72309310	C₂	1	1	yes	maximal, characteristic, complemented
11	#72266831	C₂	1	1	yes	maximal, characteristic
12	#72266830	C₄	1	4	yes	complemented
13	#72266073	C₂²	1	1	yes	characteristic, complemented
14	#72264793	C₂	1	1	yes	maximal, characteristic, complemented
15	#72262328	C₂	1	1	yes	maximal, characteristic, complemented
16	#72251547	C₂	1	1	yes	maximal, characteristic, complemented
17	#72238718	C₄	1	4	yes	complemented
18	#72238614	C₂	1	1	yes	maximal, characteristic, complemented
19	#72237400	C₂²	1	1	yes	characteristic, complemented
20	#72234668	C₂²	1	1	yes	characteristic
21	#72234661	C₂²	1	1	yes	characteristic
22	#72225713	C₂²	1	1	yes	characteristic
23	#72225617	C₂²	1	1	yes	characteristic
24	#72225617	C₂²	1	1	yes	characteristic
25	#72225617	C₂²	1	1	yes	characteristic
26	#72225617	C₂²	1	1	yes	characteristic
27	C₂×#115348	C₂²	1	1	yes	characteristic
28	#72224136	C₂²	1	1	yes	characteristic
29	#72219418	C₂²	1	1	yes	characteristic, complemented
30	#72219415	C₂²	1	1	yes	characteristic, complemented
31	#72219414	C₂²	1	1	yes	characteristic, complemented
32	#72219414	C₂²	1	1	yes	characteristic, complemented
33	#72219300	C₂²	1	1	yes	characteristic
34	#72219300	C₂²	1	1	yes	characteristic
35	#72219251	C₂²	1	1	yes	characteristic, complemented
36	#72219248	C₂²	1	1	yes	characteristic, complemented
37	#72219243	C₂²	1	1	yes	characteristic
38	#72219237	C₂²	1	1	yes	characteristic
39	#72219229	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#8534	C₂²	1	1	yes	characteristic, complemented
41	#72218381	C₂²	1	1	yes	characteristic, complemented
42	#72218381	C₂²	1	1	yes	characteristic, complemented
43	#72218313	C₂²	1	1	yes	characteristic, complemented
44	#72218313	C₂²	1	1	yes	characteristic, complemented
45	#72218306	C₂²	1	1	yes	characteristic, complemented
46	#72218069	C₂²	1	1	yes	characteristic
47	#72218069	C₂²	1	1	yes	characteristic
48	#72218057	C₂²	1	1	yes	characteristic
49	#72218057	C₂²	1	1	yes	characteristic
50	#72213862	C₂²	1	1	yes	characteristic
51	#72210555	C₂²	1	1	yes	characteristic, complemented
52	#72210511	C₂²	1	1	yes	characteristic
53	#10586404	D₄	1	1	yes	characteristic
54	C₂²×#3484	C₂³	1	1	yes	characteristic
55	#7630939	C₂³	1	1	yes	characteristic
56	#7630939	C₂³	1	1	yes	characteristic
57	C₂×#34980	C₂³	1	1	yes	characteristic
58	#7626202	D₄	1	1	yes	characteristic, complemented
59	#6629258	C₂×C₄	1	2	yes	complemented
60	#6628892	C₂×C₄	1	2	yes	complemented
61	#6628892	C₂×C₄	1	2	yes	complemented
62	#6628867	C₂×C₄	1	2	yes	complemented
63	#6499892	C₂×C₄	1	4	yes	—
64	#6499892	D₄	1	4	yes	—
65	#6374251	D₄	1	1	yes	characteristic, complemented
66	#6374210	D₄	1	1	yes	characteristic
67	#6374210	D₄	1	1	yes	characteristic
68	C₂×#21776	D₄	1	1	yes	characteristic, complemented
69	C₂×#21776	D₄	1	1	yes	characteristic, complemented
70	C₂×#21776	D₄	1	1	yes	characteristic, complemented
71	C₂×#21776	D₄	1	1	yes	characteristic, complemented
72	#6374128	D₄	1	1	yes	characteristic
73	#6374128	D₄	1	1	yes	characteristic, complemented
74	C₂×#21746	D₄	1	1	yes	characteristic, complemented
75	C₂²×#1781	C₂³	1	1	yes	characteristic
76	C₂²×#1781	C₂³	1	1	yes	characteristic
77	C₂²×#1781	C₂³	1	1	yes	characteristic
78	C₂²×#1781	C₂³	1	1	yes	characteristic
79	C₂²×#1438	C₂³	1	1	yes	characteristic
80	#392699	C₂×C₄	1	2	yes	complemented
81	#392696	C₂×C₄	1	2	yes	complemented
82	#392113	C₂³	1	1	yes	characteristic
83	#392113	C₂³	1	1	yes	characteristic
84	#392109	C₂³	1	1	yes	characteristic
85	#392109	C₂³	1	1	yes	characteristic
86	#392109	C₂³	1	1	yes	characteristic
87	#392109	C₂³	1	1	yes	characteristic
88	#382707	D₄	1	1	yes	characteristic, complemented
89	#382707	D₄	1	1	yes	characteristic, complemented
90	#382544	D₄	1	1	yes	characteristic, complemented
91	#382544	D₄	1	1	yes	characteristic, complemented
92	#382544	D₄	1	1	yes	characteristic, complemented
93	#382544	D₄	1	1	yes	characteristic, complemented
94	#382434	D₄	1	1	yes	characteristic, complemented
95	#382434	D₄	1	1	yes	characteristic, complemented
96	#382434	D₄	1	1	yes	characteristic, complemented
97	#382434	D₄	1	1	yes	characteristic, complemented
98	#355913	D₄	1	1	yes	characteristic, complemented
99	#355913	D₄	1	1	yes	characteristic, complemented
100	#355096	D₄	1	1	yes	characteristic, complemented
101	#355096	D₄	1	1	yes	characteristic, complemented
102	#355096	D₄	1	1	yes	characteristic, complemented
103	#355096	D₄	1	1	yes	characteristic, complemented
104	#147569	C₂×C₄	1	4	yes	complemented
105	#147567	C₂×C₄	1	4	yes	complemented
106	#147567	C₂×C₄	1	4	yes	complemented
107	C₂³×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic, complemented
108	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
109	#62862	C₂²⋊C₄	1	4	yes	—
110	C₂×#3484	C₂×D₄	1	1	yes	characteristic
111	C₂×#3484	C₂×D₄	1	1	yes	characteristic
112	C₂×#3484	C₂×D₄	1	1	yes	characteristic
113	C₂×#3484	C₂×D₄	1	1	yes	characteristic
114	C₂×#3484	C₂×D₄	1	1	yes	characteristic
115	C₂×#3484	C₂×D₄	1	1	yes	characteristic
116	C₂²×#534	C₂×D₄	1	1	yes	characteristic
117	C₂²×#534	C₂×D₄	1	1	yes	characteristic
118	C₂³×#120	C₂×D₄	1	1	yes	characteristic
119	C₂²×#518	C₂²×C₄	1	1	yes	characteristic, complemented
120	#36614	#41	1	2	yes	—
121	C₂×#2846	#41	1	2	yes	—
122	#35222	C₂²×C₄	1	2	yes	—
123	#35222	C₂×D₄	1	2	yes	—
124	#35222	#41	1	2	yes	—
125	#34980	C₂²×C₄	1	2	yes	—
126	#34980	C₂²×C₄	1	2	yes	—
127	#34980	C₂×D₄	1	2	yes	—
128	#34980	C₂×D₄	1	2	yes	—
129	#34980	#41	1	2	yes	—
130	#34980	#41	1	2	yes	—
131	#34980	#41	1	2	yes	—
132	#34171	C₂×D₄	1	1	yes	characteristic
133	#34171	C₂×D₄	1	1	yes	characteristic
134	#34171	C₂×D₄	1	1	yes	characteristic
135	#34171	C₂×D₄	1	1	yes	characteristic
136	#34171	C₂×D₄	1	1	yes	characteristic
137	#34171	C₂×D₄	1	1	yes	characteristic
138	C₂×#2308	C₂×D₄	1	1	yes	characteristic
139	C₂×#2308	C₂×D₄	1	1	yes	characteristic
140	C₂²×#379	C₂×D₄	1	1	yes	characteristic
141	C₂²×#379	C₂×D₄	1	1	yes	characteristic
142	C₂²×#379	C₂×D₄	1	1	yes	characteristic
143	C₂²×#379	C₂×D₄	1	1	yes	characteristic
144	C₂²×#379	C₂×D₄	1	1	yes	characteristic
145	#21750	C₂²⋊C₄	1	4	yes	—
146	#21749	C₂²⋊C₄	1	4	yes	—
147	#21749	C₂²⋊C₄	1	4	yes	—
148	C₂×#1783	C₂²×C₄	1	2	yes	complemented
149	C₂×#1781	C₂²×C₄	1	2	yes	complemented
150	C₂×#1781	C₂²×C₄	1	2	yes	complemented
151	C₂×#1781	C₂×D₄	1	1	yes	characteristic
152	C₂×#1781	C₂×D₄	1	1	yes	characteristic
153	C₂×#1781	C₂×D₄	1	1	yes	characteristic
154	C₂×#1781	C₂×D₄	1	1	yes	characteristic
155	C₂×#1781	C₂×D₄	1	1	yes	characteristic
156	C₂×#1781	C₂×D₄	1	1	yes	characteristic
157	C₂×#1781	C₂×D₄	1	1	yes	characteristic
158	C₂×#1781	C₂×D₄	1	1	yes	characteristic
159	C₂×#1781	C₂×D₄	1	1	yes	characteristic
160	C₂×#1781	C₂×D₄	1	1	yes	characteristic
161	C₂×#1781	C₂×D₄	1	1	yes	characteristic
162	C₂×#1781	C₂×D₄	1	1	yes	characteristic
163	C₂×#1781	C₂×D₄	1	1	yes	characteristic
164	C₂×#1781	C₂×D₄	1	1	yes	characteristic
165	C₂×#1781	C₂×D₄	1	1	yes	characteristic
166	C₂×#1781	C₂×D₄	1	1	yes	characteristic
167	C₂×#1781	C₂×D₄	1	1	yes	characteristic
168	C₂×#1781	C₂×D₄	1	1	yes	characteristic
169	C₂×#1781	C₂×D₄	1	1	yes	characteristic
170	C₂×#1781	C₂×D₄	1	1	yes	characteristic
171	C₂⁷	C₂²×D₄	1	1	yes	characteristic
172	C₂⁷	C₂×#41	1	1	yes	characteristic
173	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
174	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
175	C₂⁴×D₄	#120	1	1	yes	characteristic
176	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
177	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
178	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
179	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
181	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
182	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
183	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
184	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
185	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
188	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
189	C₂×#535	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×#535	C₄×D₄	1	2	yes	—
191	C₂×#535	#121	1	2	yes	—
192	C₂×#534	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×#534	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×#534	C₄×D₄	1	2	yes	—
195	C₂×#534	C₄×D₄	1	2	yes	—
196	C₂×#534	#121	1	2	yes	—
197	C₂×#534	#121	1	2	yes	—
198	C₂×#534	#123	1	2	yes	—
199	C₂×#525	C₄×D₄	1	2	yes	—
200	C₂×#525	#121	1	2	yes	—
201	C₂×#525	#123	1	2	yes	—
202	C₂²×#120	C₄×D₄	1	2	yes	—
203	C₂²×#120	C₄×D₄	1	2	yes	—
204	C₂²×#120	#121	1	2	yes	—
205	C₂²×#120	#121	1	2	yes	—
206	C₂²×#120	#123	1	2	yes	—
207	C₂×#518	#120	1	1	yes	characteristic
208	C₂×#518	#120	1	1	yes	characteristic
209	C₂×#518	#120	1	1	yes	characteristic
210	C₂×#518	#120	1	1	yes	characteristic
211	C₂×#518	#120	1	1	yes	characteristic
212	C₂×#518	#120	1	1	yes	characteristic
213	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
214	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
215	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
216	C₂²×#99	#120	1	1	yes	characteristic
217	C₂²×#99	#120	1	1	yes	characteristic
218	C₂²×#99	#120	1	1	yes	characteristic
219	C₂²×#99	#120	1	1	yes	characteristic
220	C₂²×#99	#120	1	1	yes	characteristic
221	C₂²×#99	#120	1	1	yes	characteristic
222	C₂²×#99	#120	1	1	yes	characteristic
223	C₂²×#99	#120	1	1	yes	characteristic
224	#2309	C₂×C₂²⋊C₄	1	2	yes	—
225	#2309	C₄×D₄	1	2	yes	—
226	#2309	#121	1	2	yes	—
227	#2308	C₂×C₂²⋊C₄	1	2	yes	—
228	#2308	C₂×C₂²⋊C₄	1	2	yes	—
229	#2308	C₄×D₄	1	2	yes	—
230	#2308	C₄×D₄	1	2	yes	—
231	#2308	#121	1	2	yes	—
232	#2308	#121	1	2	yes	—
233	#2308	#123	1	2	yes	—
234	#2280	C₄×D₄	1	2	yes	—
235	#2280	#121	1	2	yes	—
236	#2280	#123	1	2	yes	—
237	C₂×#379	C₄×D₄	1	2	yes	—
238	C₂×#379	C₄×D₄	1	2	yes	—
239	C₂×#379	#120	1	1	yes	characteristic
240	C₂×#379	#120	1	1	yes	characteristic
241	C₂×#379	#120	1	1	yes	characteristic
242	C₂×#379	#120	1	1	yes	characteristic
243	C₂×#379	#120	1	1	yes	characteristic
244	C₂×#379	#120	1	1	yes	characteristic
245	C₂×#379	#120	1	1	yes	characteristic
246	C₂×#379	#120	1	1	yes	characteristic
247	C₂×#379	#121	1	2	yes	—
248	C₂×#379	#121	1	2	yes	—
249	C₂×#379	#123	1	2	yes	—
250	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
251	C₂⁶	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂⁶	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂⁶	C₂×#120	1	1	yes	characteristic
254	C₂⁶	C₂×#120	1	1	yes	characteristic
255	C₂⁶	C₂×#120	1	1	yes	characteristic
256	C₂⁶	C₂×#121	1	1	yes	characteristic
257	C₂⁶	C₂×#121	1	1	yes	characteristic
258	C₂⁶	C₂×#123	1	1	yes	characteristic
259	C₂⁶	#525	1	1	yes	characteristic
260	C₂⁶	#525	1	1	yes	characteristic
261	C₂⁶	#525	1	1	yes	characteristic
262	C₂⁶	#525	1	1	yes	characteristic
263	C₂⁶	#525	1	1	yes	characteristic
264	C₂²×#41	#386	1	2	yes	—
265	C₂³×D₄	#386	1	2	yes	—
266	C₂³×D₄	#386	1	2	yes	—
267	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
268	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₂×#120	1	1	yes	characteristic
273	C₂³×D₄	C₂×#120	1	1	yes	characteristic
274	C₂³×D₄	C₂×#120	1	1	yes	characteristic
275	C₂³×D₄	C₂×#120	1	1	yes	characteristic
276	C₂³×D₄	C₂×#121	1	1	yes	characteristic
277	C₂³×D₄	C₂×#121	1	1	yes	characteristic
278	C₂³×D₄	C₂×#121	1	1	yes	characteristic
279	C₂³×D₄	C₂×#123	1	1	yes	characteristic
280	C₂³×D₄	#525	1	1	yes	characteristic
281	C₂³×D₄	#525	1	1	yes	characteristic
282	C₂³×D₄	#525	1	1	yes	characteristic
283	C₂³×D₄	#525	1	1	yes	characteristic
284	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
285	C₂⁴×C₄	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
287	C₂⁴×C₄	C₂×#123	1	1	yes	characteristic
288	C₂⁴×C₄	#525	1	1	yes	characteristic
289	C₂⁴×C₄	#525	1	1	yes	characteristic
290	C₂⁴×C₄	#525	1	1	yes	characteristic
291	C₂×#117	#386	1	2	yes	—
292	C₂×#117	#386	1	2	yes	—
293	C₂×#117	#386	1	2	yes	—
294	C₂²×C₂²⋊C₄	#386	1	2	yes	—
295	C₂²×C₂²⋊C₄	#386	1	2	yes	—
296	C₂²×C₂²⋊C₄	#386	1	2	yes	—
297	C₂²×C₂²⋊C₄	#386	1	2	yes	—
298	C₂²×C₂²⋊C₄	#386	1	2	yes	—
299	C₂²×C₂²⋊C₄	#386	1	2	yes	—
300	#379	B(4,𝔽₂)	1	2	yes	—
301	#379	B(4,𝔽₂)	1	2	yes	—
302	C₂⁵	#1889	1	2	yes	—
303	C₂⁵	#1913	1	2	yes	complemented
304	C₂⁵	C₂×#386	1	1	yes	characteristic
305	C₂⁵	C₂×#386	1	1	yes	characteristic
306	C₂⁵	C₄×#120	1	1	yes	characteristic
307	C₂⁵	C₄×#120	1	1	yes	characteristic
308	C₂⁵	C₄×#120	1	1	yes	characteristic
309	C₂⁵	#2846	1	1	yes	characteristic
310	C₂⁵	#2847	1	1	yes	characteristic
311	C₂⁵	#2847	1	1	yes	characteristic
312	C₂⁵	#2847	1	1	yes	characteristic
313	C₂⁵	#2849	1	1	yes	characteristic
314	C₂⁵	#2849	1	1	yes	characteristic
315	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
316	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
317	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
318	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
319	C₂⁵	#3025	1	1	yes	characteristic
320	C₂⁵	#3025	1	1	yes	characteristic
321	C₂⁵	#3026	1	1	yes	characteristic
322	C₂⁵	#3026	1	1	yes	characteristic
323	C₂⁵	#3026	1	1	yes	characteristic
324	C₂⁵	#3026	1	1	yes	characteristic
325	C₂⁵	#3027	1	1	yes	characteristic
326	C₂⁵	#3027	1	1	yes	characteristic
327	C₂²×Q₈	#1913	1	2	yes	complemented
328	C₂²×D₄	#1913	1	2	yes	complemented
329	C₂³×C₄	#1889	1	2	yes	—
330	C₂³×C₄	#1913	1	2	yes	complemented
331	C₂³×C₄	C₂×#386	1	1	yes	characteristic
332	C₂³×C₄	C₄×#120	1	1	yes	characteristic
333	C₂³×C₄	#2847	1	1	yes	characteristic
334	C₂³×C₄	#2849	1	1	yes	characteristic
335	C₂⁴	#14694	1	1	yes	characteristic
336	C₂⁴	C₂×#1889	1	1	yes	characteristic
337	C₂⁴	#20960	1	1	yes	characteristic
338	C₂⁴	C₂×#1913	1	2	yes	—
339	C₂⁴	C₄×B(4,𝔽₂)	1	1	yes	characteristic
340	C₂⁴	C₄×B(4,𝔽₂)	1	1	yes	characteristic
341	C₂⁴	#21482	1	1	yes	characteristic
342	C₂⁴	#21482	1	1	yes	characteristic
343	C₂⁴	#32898	1	1	yes	characteristic
344	C₂⁴	#32898	1	1	yes	characteristic
345	C₂⁴	#32898	1	1	yes	characteristic
346	C₂⁴	#32898	1	1	yes	characteristic
347	C₂⁴	#32899	1	1	yes	characteristic
348	C₂⁴	#32899	1	1	yes	characteristic
349	C₂⁴	#32926	1	1	yes	characteristic
350	C₂⁴	#32926	1	1	yes	characteristic
351	C₂⁴	#32928	1	1	yes	characteristic
352	C₂⁴	#32928	1	1	yes	characteristic
353	C₂⁴	#33020	1	1	yes	characteristic
354	C₂⁴	#33020	1	1	yes	characteristic
355	C₂²×C₄	C₂×#1913	1	2	yes	—
356	C₂³	#347042	1	1	yes	characteristic
357	C₂³	#347043	1	1	yes	characteristic
358	C₂³	#347043	1	1	yes	characteristic
359	C₂³	#347044	1	1	yes	characteristic
360	C₂³	#392658	1	1	yes	characteristic
361	C₂³	#392663	1	1	yes	characteristic
362	C₂³	#392663	1	1	yes	characteristic
363	C₂³	#392699	1	1	yes	characteristic
364	C₂³	#392699	1	1	yes	characteristic
365	C₂³	#392719	1	1	yes	characteristic
366	C₂³	#392719	1	1	yes	characteristic
367	C₂²	#72219234	1	1	yes	characteristic
368	C₂²	#72234596	1	1	yes	characteristic
369	C₂²	#72258512	1	1	yes	characteristic
370	C₂²	#72261568	1	1	yes	characteristic
371	C₂²	#72261568	1	1	yes	characteristic
372	C₂²	#72261568	1	1	yes	characteristic
373	C₂²	#72261568	1	1	yes	characteristic
374	C₂	#72266138	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266138
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72266831	C₂
LCS	G ▷ C₂⁴×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312258	C₂	semidirect
2. #72312241	C₂	semidirect
3. #72312226	C₂	semidirect
4. #72312205	C₂	semidirect
5. #72312179	C₂	semidirect
6. #72310395	C₂	semidirect
7. #72310339	C₂	semidirect
8. #72310295	C₂	semidirect
9. #72309519	C₂	semidirect
10. #72309310	C₂	semidirect
12. #72266830	C₄	semidirect
13. #72266073	C₂²	semidirect
14. #72264793	C₂	semidirect
15. #72262328	C₂	semidirect
16. #72251547	C₂	semidirect
17. #72238718	C₄	semidirect
18. #72238614	C₂	semidirect
19. #72237400	C₂²	semidirect
29. #72219418	C₂²	semidirect
30. #72219415	C₂²	semidirect
31. #72219414	C₂²	semidirect
32. #72219414	C₂²	semidirect
35. #72219251	C₂²	semidirect
36. #72219248	C₂²	semidirect
39. #72219229	C₂²	semidirect
40. C₂²×#8534	C₂²	semidirect
41. #72218381	C₂²	semidirect
42. #72218381	C₂²	semidirect
43. #72218313	C₂²	semidirect
44. #72218313	C₂²	semidirect
45. #72218306	C₂²	semidirect
51. #72210555	C₂²	semidirect
58. #7626202	D₄	semidirect
59. #6629258	C₂×C₄	semidirect
60. #6628892	C₂×C₄	semidirect
61. #6628892	C₂×C₄	semidirect
62. #6628867	C₂×C₄	semidirect
65. #6374251	D₄	semidirect
68. C₂×#21776	D₄	semidirect
69. C₂×#21776	D₄	semidirect
70. C₂×#21776	D₄	semidirect
71. C₂×#21776	D₄	semidirect
73. #6374128	D₄	semidirect
74. C₂×#21746	D₄	semidirect
80. #392699	C₂×C₄	semidirect
81. #392696	C₂×C₄	semidirect
88. #382707	D₄	semidirect
89. #382707	D₄	semidirect
90. #382544	D₄	semidirect
91. #382544	D₄	semidirect
92. #382544	D₄	semidirect
93. #382544	D₄	semidirect
94. #382434	D₄	semidirect
95. #382434	D₄	semidirect
96. #382434	D₄	semidirect
97. #382434	D₄	semidirect
98. #355913	D₄	semidirect
99. #355913	D₄	semidirect
100. #355096	D₄	semidirect
101. #355096	D₄	semidirect
102. #355096	D₄	semidirect
103. #355096	D₄	semidirect
104. #147569	C₂×C₄	semidirect
105. #147567	C₂×C₄	semidirect
106. #147567	C₂×C₄	semidirect
107. C₂³×H(5,𝔽₂)	C₂²×C₄	semidirect
119. C₂²×#518	C₂²×C₄	semidirect
148. C₂×#1783	C₂²×C₄	semidirect
149. C₂×#1781	C₂²×C₄	semidirect
150. C₂×#1781	C₂²×C₄	semidirect
303. C₂⁵	#1913	semidirect
327. C₂²×Q₈	#1913	semidirect
328. C₂²×D₄	#1913	semidirect
330. C₂³×C₄	#1913	semidirect

Maximal subgroups

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

subgroup	index
#72312258	2
#72312241	2
#72312226	2
#72312205	2
#72312179	2
#72310395	2
#72310339	2
#72310295	2
#72309519	2
#72309310	2
#72266831	2
#72264793	2
#72262328	2
#72251547	2
#72238614	2