Subgroups — #72264413

Order 2048.

At least 6777 conjugacy classes of subgroups; only the 1258 normal subgroups are shown.

The subgroup lattice has 428 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72264408	C₂	1	1	yes	maximal, characteristic, complemented
2	#72264359	C₂	1	2	yes	maximal, complemented
3	#72264357	C₂	1	2	yes	maximal, complemented
4	#72264333	C₂	1	2	yes	maximal, complemented
5	#72264229	C₂	1	4	yes	maximal, complemented
6	#72264227	C₂	1	2	yes	maximal, complemented
7	#72264188	C₂	1	1	yes	maximal, characteristic, complemented
8	#72264132	C₂	1	4	yes	maximal, complemented
9	#72264097	C₂	1	1	yes	maximal, characteristic, complemented
10	#72264086	C₂	1	1	yes	maximal, characteristic, complemented
11	#72264043	C₂	1	4	yes	maximal, complemented
12	#72263995	C₂	1	4	yes	maximal, complemented
13	C₂×#6386001	C₂	1	1	yes	maximal, characteristic, complemented
14	#72237676	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#2403	C₂	1	1	yes	maximal, characteristic
16	C₂³×D₄²	C₂²	1	1	yes	characteristic
17	C₂³×D₄²	C₂²	1	1	yes	characteristic
18	C₂²×#2972	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×#120	C₂²	1	2	yes	—
20	C₂×#34181	C₂²	1	1	yes	characteristic, complemented
21	C₂×#24005	C₂²	1	2	yes	complemented
22	#6386001	C₂²	1	4	yes	—
23	#6386001	C₂²	1	4	yes	complemented
24	C₂×#21758	C₂²	1	2	yes	complemented
25	C₂²×#1786	C₂²	1	2	yes	—
26	#759292	C₂²	1	1	yes	characteristic
27	#649038	C₂²	1	2	yes	—
28	#647663	C₂²	1	2	yes	—
29	#612625	C₂²	1	2	yes	complemented
30	#612431	C₂²	1	1	yes	characteristic
31	#612431	C₂²	1	1	yes	characteristic
32	D₄×#379	C₂²	1	1	yes	characteristic
33	D₄×#386	C₂²	1	2	yes	—
34	C₄×#2403	C₂²	1	1	yes	characteristic
35	#395437	C₂²	1	4	yes	complemented
36	#395372	C₂²	1	4	yes	complemented
37	#392585	C₂²	1	4	yes	complemented
38	#392147	C₂²	1	1	yes	characteristic, complemented
39	#392118	C₂²	1	2	yes	—
40	#392118	C₂²	1	4	yes	complemented
41	#373842	C₂²	1	4	yes	complemented
42	#362849	C₂²	1	2	yes	complemented
43	#360155	C₂²	1	4	yes	complemented
44	#359519	C₂²	1	2	yes	complemented
45	#359422	C₂²	1	2	yes	complemented
46	C₂×#9468	C₂²	1	4	yes	complemented
47	#194755	C₂²	1	4	yes	complemented
48	C₂×#8965	C₂²	1	4	yes	complemented
49	#192094	C₂²	1	4	yes	complemented
50	#189842	C₂²	1	2	yes	complemented
51	C₂×#8375	C₂²	1	4	yes	—
52	C₂×#8375	C₂²	1	4	yes	complemented
53	#185046	C₂²	1	2	yes	complemented
54	#184743	C₂²	1	1	yes	characteristic, complemented
55	#119520	C₂²	1	8	yes	complemented
56	#118313	C₂²	1	8	yes	complemented
57	#116309	C₂²	1	8	yes	complemented
58	#113914	C₂²	1	8	yes	complemented
59	#111636	C₂²	1	8	yes	complemented
60	#108186	C₂²	1	4	yes	complemented
61	#106962	C₂²	1	8	yes	complemented
62	#106314	C₂²	1	4	yes	complemented
63	#105542	C₂²	1	2	yes	complemented
64	#105520	C₂²	1	2	yes	complemented
65	C₂⁵×D₄	D₄	1	1	yes	characteristic
66	C₂⁵×D₄	C₂³	1	1	yes	characteristic
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic
68	C₂²×D₄²	D₄	1	2	yes	—
69	C₂²×D₄²	D₄	1	2	yes	—
70	C₂²×D₄²	C₂³	1	2	yes	—
71	C₂²×D₄²	C₂³	1	2	yes	—
72	C₂³×#127	D₄	1	1	yes	characteristic
73	C₂³×#127	C₂³	1	1	yes	characteristic
74	C₂³×#121	D₄	1	1	yes	characteristic
75	C₂³×#121	C₂³	1	1	yes	characteristic
76	C₂³×#121	C₂³	1	1	yes	characteristic
77	C₂³×#121	C₂³	1	1	yes	characteristic
78	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
79	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
80	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
81	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
82	C₂×#2972	C₂³	1	4	yes	—
83	C₂³×#102	D₄	1	4	yes	complemented
84	C₂³×#102	D₄	1	4	yes	complemented
85	C₂³×C₂²⋊C₈	C₂³	1	2	yes	—
86	C₂×#2847	C₂³	1	2	yes	—
87	C₂×#2433	C₂³	1	2	yes	—
88	C₂×#2408	C₂³	1	2	yes	—
89	C₂×#2403	D₄	1	1	yes	characteristic
90	#34181	C₂³	1	4	yes	—
91	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	—
92	C₂×C₄×#120	C₂³	1	2	yes	—
93	C₂²×#380	C₂³	1	2	yes	—
94	#21758	C₂³	1	8	yes	—
95	C₂×#1853	C₂³	1	4	yes	complemented
96	C₂×#1799	C₂³	1	4	yes	—
97	C₂×#1786	D₄	1	8	yes	complemented
98	C₂×#1786	C₂³	1	4	yes	—
99	C₂×#1786	C₂³	1	4	yes	—
100	C₂×#1786	C₂³	1	4	yes	—
101	C₂×#1786	C₂³	1	4	yes	—
102	C₂×#1786	C₂³	1	4	yes	complemented
103	C₂×#1786	C₂³	1	4	yes	complemented
104	C₂×#1779	C₂³	1	2	yes	—
105	C₂×#1779	C₂³	1	4	yes	complemented
106	C₂×#1519	C₂³	1	8	yes	—
107	C₂×#1459	C₂³	1	4	yes	—
108	#14722	D₄	1	4	yes	—
109	#14719	D₄	1	2	yes	—
110	#14716	D₄	1	2	yes	—
111	#14698	C₂³	1	2	yes	—
112	#14697	C₂³	1	4	yes	complemented
113	#14680	C₂³	1	2	yes	—
114	#14680	C₂³	1	1	yes	characteristic
115	#14680	C₂³	1	4	yes	complemented
116	#14137	C₂³	1	2	yes	—
117	#14127	D₄	1	1	yes	characteristic
118	#14015	D₄	1	2	yes	—
119	#13967	D₄	1	2	yes	—
120	#13902	C₂³	1	2	yes	—
121	#13872	C₂³	1	2	yes	—
122	#13867	D₄	1	1	yes	characteristic
123	#13867	D₄	1	1	yes	characteristic
124	C₄×#379	C₂³	1	1	yes	characteristic
125	C₄×#386	C₂³	1	2	yes	—
126	#10854	C₂³	1	8	yes	complemented
127	#10730	C₂³	1	4	yes	complemented
128	#10712	C₂³	1	4	yes	complemented
129	#8023	C₂³	1	8	yes	complemented
130	C₂×#1289	C₂³	1	8	yes	complemented
131	C₂×#1282	C₂³	1	8	yes	complemented
132	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×D₄	C₂×D₄	1	4	yes	—
136	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
137	C₂⁴×D₄	C₂×D₄	1	2	yes	—
138	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂⁴×D₄	C₂×D₄	1	2	yes	—
140	C₂⁴×D₄	C₂×D₄	1	4	yes	—
141	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
144	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
145	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
146	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
148	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₈	C₂×D₄	1	4	yes	complemented
150	C₂×D₄²	#41	1	16	yes	—
151	C₂²×#127	C₂×D₄	1	2	yes	—
152	C₂²×#127	C₂×D₄	1	2	yes	—
153	C₂²×#121	C₂×D₄	1	2	yes	—
154	C₂²×#121	C₂×D₄	1	2	yes	—
155	C₂²×#121	C₂×D₄	1	2	yes	—
156	C₂²×#121	C₂×D₄	1	2	yes	—
157	C₂²×#121	C₂×D₄	1	2	yes	—
158	C₂²×#121	C₂⁴	1	2	yes	—
159	C₂²×#120	C₂×D₄	1	2	yes	—
160	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
161	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
162	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
163	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
164	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
165	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
166	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
170	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
171	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
172	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
177	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
178	C₂²×#102	C₂×D₄	1	8	yes	—
179	C₂²×#102	C₂×D₄	1	8	yes	—
180	C₂²×#102	C₂×D₄	1	8	yes	complemented
181	C₂²×#102	C₂×D₄	1	8	yes	complemented
182	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	complemented
183	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
184	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
185	#2403	SD₁₆	1	8	yes	—
186	C₂×#394	C₂×D₄	1	4	yes	—
187	C₂×#392	C₂×D₄	1	4	yes	—
188	C₂×#386	C₂×D₄	1	2	yes	—
189	C₂×#386	C₂×D₄	1	2	yes	—
190	C₂×#386	C₂×D₄	1	2	yes	—
191	C₂×#385	C₂×D₄	1	2	yes	—
192	C₂×#380	C₂×D₄	1	4	yes	complemented
193	C₂×#380	C₂⁴	1	4	yes	—
194	C₂×#380	C₂⁴	1	2	yes	—
195	C₂×#380	C₂⁴	1	4	yes	—
196	C₂×#379	C₂×D₄	1	2	yes	—
197	C₂×#379	C₂×D₄	1	1	yes	characteristic
198	C₂×#379	C₂×D₄	1	1	yes	characteristic
199	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
200	#1441	C₂×D₄	1	4	yes	—
201	#1439	C₂×D₄	1	4	yes	—
202	C₂²⋊#95	C₂×D₄	1	2	yes	—
203	C₂²⋊#95	C₂×D₄	1	2	yes	—
204	C₂²⋊#95	C₂×D₄	1	2	yes	—
205	C₂²⋊#95	C₂×D₄	1	2	yes	—
206	C₂²⋊#95	C₂×D₄	1	2	yes	—
207	C₂⁶	#120	1	1	yes	characteristic
208	C₂⁶	C₂²×D₄	1	1	yes	characteristic
209	C₂⁶	C₂²×D₄	1	1	yes	characteristic
210	C₂³×D₄	#120	1	2	yes	—
211	C₂³×D₄	#120	1	2	yes	—
212	C₂³×D₄	#120	1	2	yes	—
213	C₂³×D₄	#120	1	4	yes	—
214	C₂³×D₄	#120	1	2	yes	—
215	C₂³×D₄	#120	1	4	yes	—
216	C₂³×D₄	#120	1	2	yes	—
217	C₂³×D₄	#123	1	8	yes	—
218	C₂³×D₄	C₂×SD₁₆	1	4	yes	—
219	C₂³×D₄	C₂×SD₁₆	1	4	yes	—
220	C₂³×D₄	AGL(1,ℤ/8)	1	4	yes	—
221	C₂³×D₄	C₂²×D₄	1	2	yes	—
222	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
223	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
224	C₂³×D₄	C₂²×D₄	1	4	yes	—
225	C₂³×D₄	C₂²×D₄	1	4	yes	—
226	C₂³×D₄	C₂²×D₄	1	2	yes	—
227	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	2	yes	—
229	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₂×#41	1	8	yes	—
231	C₂⁴×C₄	#120	1	1	yes	characteristic
232	C₂⁴×C₄	#120	1	1	yes	characteristic
233	C₂⁴×C₄	#120	1	2	yes	—
234	C₂⁴×C₄	#120	1	1	yes	characteristic
235	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
236	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
237	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
241	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
242	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
243	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
244	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
246	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
247	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
248	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
249	C₂³×C₈	C₂²×D₄	1	8	yes	—
250	C₂×#127	#123	1	8	yes	—
251	C₂×#121	#123	1	8	yes	—
252	C₂×#121	C₂×#41	1	8	yes	—
253	C₂×#120	C₂×SD₁₆	1	8	yes	—
254	C₂×C₄×D₄	#123	1	8	yes	—
255	C₂×C₄×D₄	C₂×#41	1	8	yes	—
256	C₂×C₄×D₄	H(5,𝔽₂)	1	8	yes	—
257	C₂²×C₄⋊C₄	#120	1	2	yes	—
258	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
261	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
262	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
263	C₂²×C₂²⋊C₄	#120	1	2	yes	—
264	C₂²×C₂²⋊C₄	#120	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
268	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
269	C₂²×C₄²	#120	1	2	yes	—
270	C₂²×C₄²	C₂²×D₄	1	2	yes	—
271	#386	C₂×SD₁₆	1	8	yes	—
272	#379	C₂×SD₁₆	1	4	yes	—
273	C₂×#95	C₂²×D₄	1	4	yes	—
274	C₂⁵	#450	1	4	yes	—
275	C₂⁵	C₂×#120	1	1	yes	characteristic
276	C₂⁵	C₂×#120	1	1	yes	characteristic
277	C₂⁵	C₂×#120	1	2	yes	—
278	C₂⁵	D₄²	1	2	yes	—
279	C₂⁵	D₄²	1	2	yes	—
280	C₂⁵	C₂²×SD₁₆	1	2	yes	—
281	C₂⁵	C₂²×SD₁₆	1	2	yes	—
282	C₂⁵	C₂×AGL(1,ℤ/8)	1	2	yes	—
283	C₂⁵	#577	1	4	yes	—
284	C₂⁵	C₂³×D₄	1	1	yes	characteristic
285	C₂²×D₄	#450	1	8	yes	—
286	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
287	C₂²×D₄	C₂×#120	1	2	yes	—
288	C₂²×D₄	C₂×#120	1	2	yes	—
289	C₂²×D₄	C₂×#120	1	2	yes	—
290	C₂²×D₄	C₂×#120	1	2	yes	—
291	C₂²×D₄	C₂×#123	1	4	yes	—
292	C₂²×D₄	C₂×#123	1	4	yes	—
293	C₂²×D₄	C₂×#123	1	4	yes	—
294	C₂²×D₄	#525	1	16	yes	—
295	C₂²×D₄	#546	1	8	yes	—
296	C₂²×D₄	C₂²×SD₁₆	1	4	yes	—
297	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
298	C₂²×D₄	#576	1	8	yes	—
299	C₂³×C₄	#450	1	4	yes	—
300	C₂³×C₄	C₂×#120	1	2	yes	—
301	C₂³×C₄	C₂×#120	1	1	yes	characteristic
302	C₂³×C₄	C₂×#120	1	1	yes	characteristic
303	C₂³×C₄	C₂×#120	1	1	yes	characteristic
304	C₂³×C₄	C₂×#120	1	2	yes	—
305	C₂³×C₄	C₂×#120	1	1	yes	characteristic
306	C₂³×C₄	C₂×#120	1	2	yes	—
307	C₂³×C₄	C₂×#120	1	2	yes	—
308	C₂³×C₄	C₂×#123	1	4	yes	—
309	C₂³×C₄	#534	1	1	yes	characteristic
310	C₂³×C₄	#534	1	1	yes	characteristic
311	C₂³×C₄	#534	1	2	yes	—
312	C₂³×C₄	#534	1	4	yes	—
313	C₂³×C₄	D₄²	1	2	yes	—
314	C₂³×C₄	D₄²	1	2	yes	—
315	C₂³×C₄	D₄²	1	2	yes	—
316	C₂³×C₄	D₄²	1	2	yes	—
317	C₂³×C₄	D₄²	1	2	yes	—
318	C₂³×C₄	D₄²	1	2	yes	—
319	C₂³×C₄	C₂²×SD₁₆	1	2	yes	—
320	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
321	C₂³×C₄	C₂³×D₄	1	2	yes	—
322	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
323	C₂³×C₄	C₂²×#41	1	4	yes	—
324	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
325	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
326	C₂×C₄⋊C₄	C₂×#123	1	4	yes	—
327	C₂×C₄⋊C₄	#546	1	8	yes	—
328	C₂×C₂²⋊C₄	#546	1	8	yes	—
329	C₂×C₂²⋊C₄	#546	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂²×SD₁₆	1	4	yes	—
331	C₂×C₄²	C₂×#123	1	4	yes	—
332	C₂×C₄²	#534	1	4	yes	—
333	C₂⁴	#2403	1	2	yes	—
334	C₂⁴	#2403	1	1	yes	characteristic
335	C₂⁴	#2403	1	1	yes	characteristic
336	C₂⁴	#2405	1	4	yes	—
337	C₂⁴	C₂×#450	1	2	yes	—
338	C₂⁴	C₂×#450	1	2	yes	—
339	C₂⁴	C₂×#450	1	4	yes	—
340	C₂⁴	#3008	1	4	yes	—
341	C₂⁴	#3009	1	2	yes	—
342	C₂⁴	#3009	1	2	yes	—
343	C₂⁴	#3265	1	4	yes	—
344	C₂⁴	#3265	1	4	yes	—
345	C₂⁴	D₄×SD₁₆	1	4	yes	—
346	C₂⁴	D₄×SD₁₆	1	4	yes	—
347	C₂⁴	C₂²×#120	1	1	yes	characteristic
348	C₂⁴	C₂×D₄²	1	2	yes	—
349	C₂⁴	C₂×#546	1	4	yes	—
350	C₂⁴	C₂³×SD₁₆	1	1	yes	characteristic
351	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂⁴	C₂×#576	1	4	yes	—
353	C₂⁴	C₂×#577	1	2	yes	—
354	C₂×D₄	#2849	1	4	yes	—
355	C₂×D₄	#2849	1	4	yes	—
356	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
357	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
358	C₂×D₄	#3026	1	4	yes	—
359	C₂×D₄	#3295	1	16	yes	—
360	C₂×D₄	#3318	1	16	yes	—
361	C₂²×C₄	#2403	1	1	yes	characteristic
362	C₂²×C₄	#2403	1	2	yes	—
363	C₂²×C₄	#2403	1	1	yes	characteristic
364	C₂²×C₄	#2405	1	4	yes	—
365	C₂²×C₄	#2405	1	4	yes	—
366	C₂²×C₄	#2405	1	4	yes	—
367	C₂²×C₄	C₂×#450	1	4	yes	—
368	C₂²×C₄	#3008	1	4	yes	—
369	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
370	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
371	C₂²×C₄	C₂²×#123	1	2	yes	—
372	C₂²×C₄	C₂×#525	1	4	yes	—
373	C₂²×C₄	C₂×#534	1	2	yes	—
374	C₂²×C₄	C₂×#534	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄²	1	2	yes	—
376	C₂²×C₄	C₂×#546	1	4	yes	—
377	C₂²×C₄	#3484	1	4	yes	—
378	C₂²×C₄	#3490	1	8	yes	—
379	C₂³	#23849	1	2	yes	—
380	C₂³	#23849	1	4	yes	—
381	C₂³	#23849	1	2	yes	—
382	C₂³	#23882	1	2	yes	—
383	C₂³	#23900	1	2	yes	—
384	C₂³	#24033	1	8	yes	complemented
385	C₂³	C₂×#2403	1	1	yes	characteristic
386	C₂³	C₂×#2405	1	2	yes	—
387	C₂³	#36098	1	4	yes	—
388	C₂³	C₂²×#450	1	1	yes	characteristic
389	C₂³	C₂×#3008	1	2	yes	—
390	C₂³	C₂×#3009	1	1	yes	characteristic
391	C₂³	C₂×#3265	1	2	yes	—
392	C₂³	C₂×D₄×SD₁₆	1	2	yes	—
393	C₂³	#61049	1	4	yes	—
394	C₂³	C₂×#3295	1	4	yes	—
395	C₂³	C₂×#3318	1	4	yes	—
396	C₂³	#61167	1	8	yes	—
397	D₄	#33020	1	8	yes	—
398	C₂×C₄	#23900	1	2	yes	—
399	C₂×C₄	#24033	1	8	yes	complemented
400	C₂×C₄	#34980	1	1	yes	characteristic
401	C₂×C₄	#34992	1	2	yes	—
402	C₂×C₄	#36098	1	4	yes	—
403	C₂×C₄	C₂×#2849	1	1	yes	characteristic
404	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
405	C₂×C₄	C₂×#3026	1	2	yes	—
406	C₂²	#248456	1	4	yes	—
407	C₂²	#612426	1	1	yes	characteristic
408	C₂²	C₂×#23849	1	1	yes	characteristic
409	C₂²	#6437521	1	1	yes	characteristic
410	C₂²	C₂×#23882	1	1	yes	characteristic
411	C₂²	#6437576	1	1	yes	characteristic
412	C₂²	C₂×#23900	1	1	yes	characteristic
413	C₂²	#6437621	1	1	yes	characteristic
414	C₂²	C₂×#24033	1	2	yes	—
415	C₂²	#6440405	1	2	yes	—
416	C₂²	#6576546	1	4	yes	—
417	C₂²	#6576606	1	4	yes	—
418	C₄	#6470225	1	2	yes	—
419	C₄	C₂×#33020	1	2	yes	—
420	C₂	C₂×#248456	1	1	yes	characteristic
421	C₂	#72237125	1	1	yes	characteristic
422	C₂	#72257496	1	1	yes	characteristic
423	C₂	#72257682	1	1	yes	characteristic
424	C₂	#72257826	1	1	yes	characteristic
425	C₂	#72263884	1	1	yes	characteristic
426	C₂	#72263907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	D₄×#2403	C₂
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72264408	C₂	semidirect
2. #72264359	C₂	semidirect
3. #72264357	C₂	semidirect
4. #72264333	C₂	semidirect
5. #72264229	C₂	semidirect
6. #72264227	C₂	semidirect
7. #72264188	C₂	semidirect
8. #72264132	C₂	semidirect
9. #72264097	C₂	semidirect
10. #72264086	C₂	semidirect
11. #72264043	C₂	semidirect
12. #72263995	C₂	semidirect
13. C₂×#6386001	C₂	semidirect
14. #72237676	C₂	semidirect
18. C₂²×#2972	C₂²	semidirect
20. C₂×#34181	C₂²	semidirect
21. C₂×#24005	C₂²	semidirect
23. #6386001	C₂²	semidirect
24. C₂×#21758	C₂²	semidirect
29. #612625	C₂²	semidirect
35. #395437	C₂²	semidirect
36. #395372	C₂²	semidirect
37. #392585	C₂²	semidirect
38. #392147	C₂²	semidirect
40. #392118	C₂²	semidirect
41. #373842	C₂²	semidirect
42. #362849	C₂²	semidirect
43. #360155	C₂²	semidirect
44. #359519	C₂²	semidirect
45. #359422	C₂²	semidirect
46. C₂×#9468	C₂²	semidirect
47. #194755	C₂²	semidirect
48. C₂×#8965	C₂²	semidirect
49. #192094	C₂²	semidirect
50. #189842	C₂²	semidirect
52. C₂×#8375	C₂²	semidirect
53. #185046	C₂²	semidirect
54. #184743	C₂²	semidirect
55. #119520	C₂²	semidirect
56. #118313	C₂²	semidirect
57. #116309	C₂²	semidirect
58. #113914	C₂²	semidirect
59. #111636	C₂²	semidirect
60. #108186	C₂²	semidirect
61. #106962	C₂²	semidirect
62. #106314	C₂²	semidirect
63. #105542	C₂²	semidirect
64. #105520	C₂²	semidirect
83. C₂³×#102	D₄	semidirect
84. C₂³×#102	D₄	semidirect
95. C₂×#1853	C₂³	semidirect
97. C₂×#1786	D₄	semidirect
102. C₂×#1786	C₂³	semidirect
103. C₂×#1786	C₂³	semidirect
105. C₂×#1779	C₂³	semidirect
112. #14697	C₂³	semidirect
115. #14680	C₂³	semidirect
126. #10854	C₂³	semidirect
127. #10730	C₂³	semidirect
128. #10712	C₂³	semidirect
129. #8023	C₂³	semidirect
130. C₂×#1289	C₂³	semidirect
131. C₂×#1282	C₂³	semidirect
149. C₂⁴×C₈	C₂×D₄	semidirect
169. C₂³×C₄⋊C₄	C₂×D₄	semidirect
170. C₂³×C₄⋊C₄	C₂×D₄	semidirect
180. C₂²×#102	C₂×D₄	semidirect
181. C₂²×#102	C₂×D₄	semidirect
182. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
192. C₂×#380	C₂×D₄	semidirect
384. C₂³	#24033	semidirect
399. C₂×C₄	#24033	semidirect

Maximal subgroups

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

subgroup	index
#72264408	2
#72264359	2
#72264357	2
#72264333	2
#72264229	2
#72264227	2
#72264188	2
#72264132	2
#72264097	2
#72264086	2
#72264043	2
#72263995	2
C₂×#6386001	2
#72237676	2
D₄×#2403	2