Subgroups — #72238032

Order 2048.

At least 12381 conjugacy classes of subgroups; only the 1788 normal subgroups are shown.

The subgroup lattice has 632 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72238031	C₂	1	1	yes	maximal, characteristic, complemented
2	#72238030	C₂	1	1	yes	maximal, characteristic, complemented
3	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
4	#72236431	C₂	1	2	yes	maximal, complemented
5	C₂×#392109	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234661	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233891	C₂	1	8	yes	maximal, complemented
8	#72233691	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#7630939	C₂	1	1	yes	maximal, characteristic, complemented
10	#72225801	C₂	1	2	yes	maximal, complemented
11	#72217699	C₂	1	2	yes	maximal, complemented
12	C₂×#115690	C₂	1	2	yes	maximal, complemented
13	#72210600	C₂	1	8	yes	maximal, complemented
14	C₂⁶×D₄	C₂²	1	1	yes	characteristic
15	C₂²×#3484	C₂²	1	1	yes	characteristic
16	#7641845	C₂²	1	2	yes	complemented
17	C₂²×#2846	C₂²	1	2	yes	—
18	C₂²×#2846	C₂²	1	1	yes	characteristic, complemented
19	#7630939	C₂²	1	8	yes	—
20	C₂×#34980	C₂²	1	2	yes	—
21	C₂×#34980	C₂²	1	1	yes	characteristic
22	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
23	C₂×#34171	C₂²	1	1	yes	characteristic
24	#6470226	C₂²	1	4	yes	complemented
25	#6470225	C₂²	1	4	yes	complemented
26	C₂×#21746	C₂²	1	2	yes	complemented
27	C₂×#21746	C₂²	1	2	yes	complemented
28	C₂×#21746	C₂²	1	2	yes	complemented
29	C₂×#21746	C₂²	1	2	yes	complemented
30	C₂²×#1781	C₂²	1	1	yes	characteristic
31	C₂²×#1781	C₂²	1	1	yes	characteristic
32	C₂²×#1781	C₂²	1	2	yes	complemented
33	#612617	C₂²	1	4	yes	complemented
34	#612424	C₂²	1	4	yes	complemented
35	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
36	C₂×#14679	C₂²	1	2	yes	complemented
37	#517411	C₂²	1	1	yes	characteristic
38	#517411	C₂²	1	1	yes	characteristic, complemented
39	#405156	C₂²	1	8	yes	complemented
40	#394058	C₂²	1	8	yes	complemented
41	#392109	C₂²	1	8	yes	complemented
42	#355913	C₂²	1	2	yes	complemented
43	#233542	C₂²	1	8	yes	complemented
44	#233541	C₂²	1	8	yes	complemented
45	#201668	C₂²	1	4	yes	complemented
46	#201664	C₂²	1	4	yes	complemented
47	#187928	C₂²	1	8	yes	complemented
48	C₂×#8101	C₂²	1	2	yes	complemented
49	C₂×#8101	C₂²	1	2	yes	complemented
50	#115690	C₂²	1	16	yes	complemented
51	#115204	C₂²	1	16	yes	complemented
52	#106766	C₂²	1	8	yes	complemented
53	C₂⁸	D₄	1	1	yes	characteristic, complemented
54	C₂⁸	C₂³	1	1	yes	characteristic
55	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
56	C₂⁵×D₄	D₄	1	4	yes	complemented
57	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
58	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
59	C₂⁵×D₄	C₂³	1	1	yes	characteristic
60	C₂⁵×D₄	C₂³	1	4	yes	—
61	C₂⁵×D₄	C₂³	1	1	yes	characteristic
62	C₂⁶×C₄	D₄	1	1	yes	characteristic, complemented
63	C₂×#3484	D₄	1	4	yes	complemented
64	C₂×#3484	C₂³	1	4	yes	—
65	C₂²×#534	D₄	1	2	yes	complemented
66	C₂²×#534	D₄	1	2	yes	complemented
67	C₂³×#120	D₄	1	4	yes	complemented
68	C₂³×#120	C₂³	1	2	yes	—
69	C₂³×#120	C₂³	1	1	yes	characteristic
70	C₂³×#120	C₂³	1	2	yes	complemented
71	C₂²×#518	D₄	1	1	yes	characteristic, complemented
72	C₂³×#99	D₄	1	4	yes	complemented
73	C₂×#2846	D₄	1	8	yes	complemented
74	C₂×#2846	C₂³	1	8	yes	—
75	#34992	C₂³	1	4	yes	complemented
76	#34980	D₄	1	8	yes	complemented
77	#34980	C₂³	1	8	yes	—
78	#34980	C₂³	1	4	yes	complemented
79	C₂×#2405	D₄	1	4	yes	complemented
80	C₂×#2405	D₄	1	2	yes	complemented
81	C₂×#2405	C₂³	1	2	yes	—
82	C₂×#2405	C₂³	1	2	yes	complemented
83	C₂×#2403	D₄	1	4	yes	complemented
84	C₂×#2403	D₄	1	2	yes	complemented
85	C₂×#2403	C₂³	1	2	yes	—
86	C₂×#2403	C₂³	1	2	yes	complemented
87	#34171	D₄	1	4	yes	complemented
88	#34171	C₂³	1	4	yes	—
89	C₂×#2309	D₄	1	2	yes	complemented
90	C₂×#2308	D₄	1	2	yes	complemented
91	C₂×#2308	D₄	1	2	yes	complemented
92	C₂²×#379	D₄	1	4	yes	complemented
93	C₂²×#379	C₂³	1	2	yes	—
94	C₂²×#379	C₂³	1	2	yes	—
95	C₂²×#379	C₂³	1	1	yes	characteristic
96	C₂²×#379	C₂³	1	1	yes	characteristic
97	C₂²×#379	C₂³	1	2	yes	—
98	C₂²×#379	C₂³	1	1	yes	characteristic
99	C₂²×#379	C₂³	1	2	yes	complemented
100	#21746	C₂³	1	8	yes	complemented
101	#21746	C₂³	1	8	yes	complemented
102	C₂×#1898	C₂³	1	8	yes	complemented
103	C₂×#1819	C₂³	1	4	yes	complemented
104	C₂×#1781	D₄	1	4	yes	complemented
105	C₂×#1781	C₂³	1	4	yes	—
106	C₂×#1781	C₂³	1	4	yes	—
107	C₂×#1781	C₂³	1	4	yes	complemented
108	C₂×#1781	C₂³	1	8	yes	complemented
109	#14679	C₂³	1	4	yes	complemented
110	#14679	C₂³	1	8	yes	complemented
111	#14335	D₄	1	4	yes	complemented
112	#13867	D₄	1	4	yes	complemented
113	#13867	C₂³	1	4	yes	—
114	#13867	C₂³	1	4	yes	complemented
115	#10735	C₂³	1	8	yes	complemented
116	#8101	C₂³	1	8	yes	complemented
117	#8101	C₂³	1	8	yes	complemented
118	C₂⁷	C₂×D₄	1	1	yes	characteristic
119	C₂⁷	C₂×D₄	1	2	yes	—
120	C₂⁷	C₂×D₄	1	4	yes	—
121	C₂⁷	C₂×D₄	1	4	yes	—
122	C₂⁷	C₂×D₄	1	1	yes	characteristic
123	C₂⁷	C₂×D₄	1	1	yes	characteristic
124	C₂⁷	C₂×D₄	1	4	yes	—
125	C₂⁷	C₂×D₄	1	1	yes	characteristic
126	C₂⁷	C₂⁴	1	2	yes	—
127	C₂⁷	C₂⁴	1	1	yes	characteristic
128	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
129	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×D₄	C₂×D₄	1	2	yes	—
131	C₂⁴×D₄	C₂×D₄	1	4	yes	—
132	C₂⁴×D₄	C₂×D₄	1	4	yes	—
133	C₂⁴×D₄	C₂×D₄	1	2	yes	—
134	C₂⁴×D₄	C₂×D₄	1	2	yes	—
135	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×D₄	C₂×D₄	1	2	yes	—
137	C₂⁴×D₄	C₂×D₄	1	2	yes	—
138	C₂⁴×D₄	C₂×D₄	1	2	yes	—
139	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×D₄	C₂×D₄	1	2	yes	—
142	C₂⁴×D₄	C₂×D₄	1	2	yes	—
143	C₂⁴×D₄	C₂×D₄	1	2	yes	—
144	C₂⁴×D₄	C₂×D₄	1	2	yes	—
145	C₂⁴×D₄	C₂×D₄	1	2	yes	—
146	C₂⁴×D₄	C₂×D₄	1	2	yes	—
147	C₂⁴×D₄	C₂×D₄	1	4	yes	—
148	C₂⁴×D₄	C₂×D₄	1	4	yes	—
149	C₂⁴×D₄	C₂×D₄	1	2	yes	—
150	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
152	C₂⁴×D₄	#41	1	2	yes	—
153	C₂⁴×D₄	#41	1	2	yes	—
154	C₂⁴×D₄	C₂⁴	1	2	yes	—
155	C₂⁴×D₄	C₂⁴	1	2	yes	—
156	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
157	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
158	C₂⁵×C₄	C₂×D₄	1	4	yes	—
159	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂×#534	C₂×D₄	1	8	yes	—
161	C₂²×#123	C₂×D₄	1	4	yes	complemented
162	C₂²×#120	C₂×D₄	1	16	yes	—
163	C₂²×#120	C₂×D₄	1	4	yes	—
164	C₂²×#120	C₂×D₄	1	4	yes	—
165	C₂²×#120	C₂×D₄	1	4	yes	—
166	C₂²×#120	C₂×D₄	1	4	yes	complemented
167	C₂²×#120	C₂⁴	1	4	yes	—
168	C₂×#518	C₂×D₄	1	4	yes	—
169	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
170	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
171	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
172	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
173	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
174	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
175	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
176	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
177	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
178	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
179	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
180	C₂²×#99	C₂×D₄	1	16	yes	complemented
181	#2405	C₂×D₄	1	16	yes	—
182	#2403	C₂×D₄	1	16	yes	—
183	#2309	C₂×D₄	1	8	yes	—
184	#2308	C₂×D₄	1	8	yes	—
185	C₂×#386	C₂×D₄	1	4	yes	complemented
186	C₂×#386	C₂×D₄	1	4	yes	complemented
187	C₂×#379	C₂×D₄	1	4	yes	—
188	C₂×#379	C₂×D₄	1	4	yes	—
189	C₂×#379	C₂×D₄	1	4	yes	—
190	C₂×#379	C₂×D₄	1	4	yes	—
191	C₂×#379	C₂×D₄	1	16	yes	—
192	C₂×#379	C₂×D₄	1	4	yes	—
193	C₂×#379	C₂×D₄	1	2	yes	complemented
194	C₂×#379	C₂×D₄	1	2	yes	complemented
195	C₂×#379	C₂×D₄	1	2	yes	complemented
196	C₂×#379	C₂×D₄	1	4	yes	complemented
197	C₂×#379	C₂×D₄	1	2	yes	complemented
198	C₂×#379	C₂⁴	1	4	yes	—
199	C₂×#379	C₂⁴	1	4	yes	—
200	C₂×#379	C₂⁴	1	2	yes	—
201	C₂×#379	C₂⁴	1	2	yes	—
202	C₂×#379	C₂⁴	1	4	yes	—
203	#1438	C₂×D₄	1	16	yes	complemented
204	C₂⁶	#120	1	1	yes	characteristic
205	C₂⁶	#120	1	2	yes	—
206	C₂⁶	#120	1	2	yes	—
207	C₂⁶	#120	1	8	yes	—
208	C₂⁶	#120	1	2	yes	—
209	C₂⁶	#120	1	2	yes	—
210	C₂⁶	#120	1	2	yes	—
211	C₂⁶	#120	1	2	yes	—
212	C₂⁶	#120	1	2	yes	—
213	C₂⁶	#120	1	2	yes	—
214	C₂⁶	#120	1	1	yes	characteristic
215	C₂⁶	#120	1	2	yes	—
216	C₂⁶	#120	1	2	yes	complemented
217	C₂⁶	#121	1	2	yes	—
218	C₂⁶	#121	1	2	yes	—
219	C₂⁶	C₂²×D₄	1	2	yes	—
220	C₂⁶	C₂²×D₄	1	8	yes	—
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	1	yes	characteristic
224	C₂⁶	C₂²×D₄	1	2	yes	—
225	C₂⁶	C₂²×D₄	1	2	yes	—
226	C₂⁶	C₂²×D₄	1	2	yes	—
227	C₂⁶	C₂²×D₄	1	1	yes	characteristic
228	C₂⁶	C₂²×D₄	1	1	yes	characteristic
229	C₂⁶	C₂²×D₄	1	2	yes	—
230	C₂⁶	C₂²×D₄	1	2	yes	—
231	C₂⁶	C₂²×D₄	1	2	yes	—
232	C₂⁶	C₂²×D₄	1	1	yes	characteristic
233	C₂⁶	C₂²×D₄	1	1	yes	characteristic
234	C₂⁶	C₂²×D₄	1	1	yes	characteristic
235	C₂⁶	C₂²×D₄	1	1	yes	characteristic
236	C₂⁶	C₂²×D₄	1	1	yes	characteristic
237	C₂⁶	C₂²×D₄	1	2	yes	—
238	C₂⁶	C₂²×D₄	1	1	yes	characteristic
239	C₂⁶	C₂²×D₄	1	1	yes	characteristic
240	C₂⁶	C₂²×D₄	1	1	yes	characteristic, complemented
241	C₂⁶	C₂×#41	1	1	yes	characteristic
242	C₂⁶	C₂×#41	1	1	yes	characteristic
243	C₂⁶	H(5,𝔽₂)	1	2	yes	—
244	C₂⁶	H(5,𝔽₂)	1	2	yes	—
245	C₂⁶	H(5,𝔽₂)	1	2	yes	—
246	C₂⁶	H(5,𝔽₂)	1	2	yes	—
247	C₂⁶	C₂⁵	1	1	yes	characteristic
248	C₂³×D₄	#120	1	2	yes	—
249	C₂³×D₄	#120	1	4	yes	—
250	C₂³×D₄	#120	1	8	yes	—
251	C₂³×D₄	#120	1	2	yes	—
252	C₂³×D₄	#120	1	2	yes	—
253	C₂³×D₄	#120	1	2	yes	—
254	C₂³×D₄	#120	1	4	yes	—
255	C₂³×D₄	#120	1	2	yes	—
256	C₂³×D₄	#120	1	2	yes	—
257	C₂³×D₄	#120	1	4	yes	—
258	C₂³×D₄	#120	1	4	yes	—
259	C₂³×D₄	#120	1	2	yes	—
260	C₂³×D₄	#120	1	2	yes	—
261	C₂³×D₄	#120	1	4	yes	complemented
262	C₂³×D₄	#120	1	4	yes	complemented
263	C₂³×D₄	#120	1	4	yes	complemented
264	C₂³×D₄	#121	1	4	yes	—
265	C₂³×D₄	#121	1	4	yes	—
266	C₂³×D₄	#121	1	2	yes	—
267	C₂³×D₄	#121	1	2	yes	—
268	C₂³×D₄	#121	1	2	yes	—
269	C₂³×D₄	#121	1	2	yes	—
270	C₂³×D₄	#121	1	4	yes	—
271	C₂³×D₄	#121	1	2	yes	—
272	C₂³×D₄	#121	1	4	yes	—
273	C₂³×D₄	#121	1	2	yes	—
274	C₂³×D₄	#121	1	2	yes	—
275	C₂³×D₄	#121	1	4	yes	—
276	C₂³×D₄	#121	1	2	yes	—
277	C₂³×D₄	#121	1	4	yes	—
278	C₂³×D₄	#127	1	2	yes	—
279	C₂³×D₄	#127	1	2	yes	—
280	C₂³×D₄	#127	1	4	yes	—
281	C₂³×D₄	#127	1	4	yes	—
282	C₂³×D₄	#127	1	2	yes	—
283	C₂³×D₄	#127	1	2	yes	—
284	C₂³×D₄	C₂²×D₄	1	2	yes	—
285	C₂³×D₄	C₂²×D₄	1	4	yes	—
286	C₂³×D₄	C₂²×D₄	1	4	yes	—
287	C₂³×D₄	C₂²×D₄	1	8	yes	—
288	C₂³×D₄	C₂²×D₄	1	4	yes	—
289	C₂³×D₄	C₂²×D₄	1	4	yes	—
290	C₂³×D₄	C₂²×D₄	1	2	yes	—
291	C₂³×D₄	C₂²×D₄	1	2	yes	—
292	C₂³×D₄	C₂²×D₄	1	2	yes	—
293	C₂³×D₄	C₂²×D₄	1	4	yes	—
294	C₂³×D₄	C₂²×D₄	1	4	yes	—
295	C₂³×D₄	C₂×#41	1	4	yes	—
296	C₂⁴×C₄	#120	1	1	yes	characteristic
297	C₂⁴×C₄	#120	1	2	yes	—
298	C₂⁴×C₄	#120	1	2	yes	—
299	C₂⁴×C₄	#120	1	2	yes	—
300	C₂⁴×C₄	#120	1	1	yes	characteristic
301	C₂⁴×C₄	#120	1	2	yes	—
302	C₂⁴×C₄	#120	1	2	yes	—
303	C₂⁴×C₄	#120	1	2	yes	complemented
304	C₂⁴×C₄	#120	1	2	yes	complemented
305	C₂⁴×C₄	#120	1	2	yes	complemented
306	C₂⁴×C₄	#121	1	2	yes	—
307	C₂⁴×C₄	#121	1	2	yes	—
308	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
309	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
311	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
313	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
314	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
315	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
316	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
317	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
318	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
319	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
320	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
321	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
322	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
323	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
324	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
325	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
326	#379	#120	1	8	yes	complemented
327	#379	#120	1	8	yes	complemented
328	#379	C₂²×D₄	1	8	yes	—
329	#379	C₂²×D₄	1	8	yes	—
330	C₂⁵	#392	1	2	yes	—
331	C₂⁵	#392	1	2	yes	—
332	C₂⁵	#392	1	4	yes	—
333	C₂⁵	#392	1	4	yes	—
334	C₂⁵	#392	1	2	yes	—
335	C₂⁵	#392	1	2	yes	—
336	C₂⁵	C₂×#120	1	4	yes	—
337	C₂⁵	C₂×#120	1	4	yes	—
338	C₂⁵	C₂×#120	1	2	yes	—
339	C₂⁵	C₂×#120	1	4	yes	—
340	C₂⁵	C₂×#120	1	1	yes	characteristic
341	C₂⁵	C₂×#120	1	1	yes	characteristic
342	C₂⁵	C₂×#120	1	1	yes	characteristic
343	C₂⁵	C₂×#120	1	2	yes	—
344	C₂⁵	C₂×#120	1	1	yes	characteristic
345	C₂⁵	C₂×#120	1	1	yes	characteristic
346	C₂⁵	C₂×#120	1	1	yes	characteristic
347	C₂⁵	C₂×#120	1	1	yes	characteristic
348	C₂⁵	C₂×#120	1	1	yes	characteristic
349	C₂⁵	C₂×#120	1	2	yes	—
350	C₂⁵	C₂×#120	1	2	yes	—
351	C₂⁵	C₂×#120	1	1	yes	characteristic
352	C₂⁵	C₂×#120	1	1	yes	characteristic
353	C₂⁵	C₂×#120	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	4	yes	—
355	C₂⁵	C₂×#120	1	4	yes	—
356	C₂⁵	C₂×#120	1	2	yes	—
357	C₂⁵	C₂×#120	1	1	yes	characteristic
358	C₂⁵	C₂×#120	1	2	yes	—
359	C₂⁵	C₂×#120	1	2	yes	—
360	C₂⁵	C₂×#120	1	1	yes	characteristic
361	C₂⁵	C₂×#120	1	2	yes	—
362	C₂⁵	C₂×#120	1	2	yes	—
363	C₂⁵	C₂×#120	1	1	yes	characteristic
364	C₂⁵	C₂×#120	1	1	yes	characteristic
365	C₂⁵	C₂×#120	1	2	yes	—
366	C₂⁵	C₂×#120	1	2	yes	—
367	C₂⁵	C₂×#120	1	2	yes	—
368	C₂⁵	C₂×#120	1	1	yes	characteristic
369	C₂⁵	C₂×#121	1	1	yes	characteristic
370	C₂⁵	C₂×#121	1	4	yes	—
371	C₂⁵	C₂×#121	1	1	yes	characteristic
372	C₂⁵	C₂×#121	1	1	yes	characteristic
373	C₂⁵	C₂×#121	1	1	yes	characteristic
374	C₂⁵	C₂×#121	1	1	yes	characteristic
375	C₂⁵	C₂×#121	1	1	yes	characteristic
376	C₂⁵	C₂×#121	1	1	yes	characteristic
377	C₂⁵	C₂×#121	1	1	yes	characteristic
378	C₂⁵	C₂×#121	1	1	yes	characteristic
379	C₂⁵	C₂×#121	1	1	yes	characteristic
380	C₂⁵	C₂×#121	1	1	yes	characteristic
381	C₂⁵	C₂×#121	1	1	yes	characteristic
382	C₂⁵	C₂×#127	1	1	yes	characteristic
383	C₂⁵	C₂×#127	1	1	yes	characteristic
384	C₂⁵	C₂×#127	1	1	yes	characteristic
385	C₂⁵	C₂×#127	1	1	yes	characteristic
386	C₂⁵	#534	1	1	yes	characteristic
387	C₂⁵	#534	1	2	yes	—
388	C₂⁵	#534	1	2	yes	—
389	C₂⁵	#534	1	2	yes	—
390	C₂⁵	#534	1	1	yes	characteristic
391	C₂⁵	#534	1	1	yes	characteristic
392	C₂⁵	#534	1	1	yes	characteristic
393	C₂⁵	#534	1	2	yes	—
394	C₂⁵	#534	1	2	yes	—
395	C₂⁵	#534	1	2	yes	—
396	C₂⁵	#535	1	2	yes	—
397	C₂⁵	#535	1	2	yes	—
398	C₂⁵	#535	1	2	yes	—
399	C₂⁵	#535	1	2	yes	—
400	C₂⁵	D₄²	1	2	yes	—
401	C₂⁵	D₄²	1	2	yes	—
402	C₂⁵	D₄²	1	2	yes	—
403	C₂⁵	D₄²	1	2	yes	—
404	C₂⁵	D₄²	1	2	yes	—
405	C₂⁵	D₄²	1	2	yes	—
406	C₂⁵	D₄²	1	2	yes	—
407	C₂⁵	D₄²	1	2	yes	—
408	C₂⁵	D₄²	1	2	yes	—
409	C₂⁵	D₄²	1	2	yes	—
410	C₂⁵	D₄²	1	2	yes	—
411	C₂⁵	D₄²	1	2	yes	—
412	C₂⁵	D₄²	1	2	yes	—
413	C₂⁵	D₄²	1	2	yes	—
414	C₂⁵	D₄²	1	2	yes	—
415	C₂⁵	D₄²	1	2	yes	—
416	C₂⁵	D₄²	1	2	yes	—
417	C₂⁵	D₄²	1	2	yes	—
418	C₂⁵	D₄²	1	2	yes	—
419	C₂⁵	D₄²	1	2	yes	—
420	C₂⁵	D₄²	1	2	yes	—
421	C₂⁵	D₄²	1	2	yes	—
422	C₂⁵	D₄²	1	2	yes	—
423	C₂⁵	D₄²	1	2	yes	—
424	C₂⁵	#546	1	2	yes	—
425	C₂⁵	#546	1	2	yes	—
426	C₂⁵	#546	1	2	yes	—
427	C₂⁵	#546	1	2	yes	—
428	C₂⁵	#546	1	2	yes	—
429	C₂⁵	#546	1	2	yes	—
430	C₂⁵	#546	1	2	yes	—
431	C₂⁵	#546	1	2	yes	—
432	C₂⁵	C₂³×D₄	1	1	yes	characteristic
433	C₂⁵	C₂³×D₄	1	1	yes	characteristic
434	C₂⁵	C₂³×D₄	1	1	yes	characteristic
435	C₂⁵	C₂³×D₄	1	2	yes	—
436	C₂⁵	C₂³×D₄	1	1	yes	characteristic
437	C₂⁵	C₂³×D₄	1	2	yes	—
438	C₂⁵	C₂³×D₄	1	1	yes	characteristic
439	C₂⁵	C₂³×D₄	1	1	yes	characteristic
440	C₂⁵	C₂²×#41	1	1	yes	characteristic
441	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
442	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂²×D₄	#392	1	4	yes	—
444	C₂²×D₄	#392	1	4	yes	—
445	C₂²×D₄	#392	1	4	yes	—
446	C₂²×D₄	#392	1	4	yes	—
447	C₂²×D₄	#392	1	4	yes	—
448	C₂²×D₄	#392	1	4	yes	—
449	C₂²×D₄	#392	1	4	yes	—
450	C₂²×D₄	#392	1	4	yes	—
451	C₂²×D₄	B(4,𝔽₂)	1	16	yes	—
452	C₂²×D₄	C₂×#120	1	4	yes	—
453	C₂²×D₄	C₂×#120	1	4	yes	—
454	C₂²×D₄	C₂×#121	1	4	yes	—
455	C₂²×D₄	C₂×#121	1	4	yes	—
456	C₂²×D₄	C₂×#121	1	4	yes	—
457	C₂²×D₄	C₂×#121	1	4	yes	—
458	C₂²×D₄	C₂×#127	1	4	yes	—
459	C₂²×D₄	C₂×#127	1	4	yes	—
460	C₂³×C₄	#392	1	2	yes	—
461	C₂³×C₄	#392	1	2	yes	—
462	C₂³×C₄	#392	1	4	yes	—
463	C₂³×C₄	#392	1	4	yes	—
464	C₂³×C₄	#392	1	2	yes	—
465	C₂³×C₄	#392	1	2	yes	—
466	C₂³×C₄	C₂×#120	1	2	yes	—
467	C₂³×C₄	C₂×#120	1	4	yes	—
468	C₂³×C₄	C₂×#120	1	4	yes	—
469	C₂³×C₄	C₂×#120	1	4	yes	—
470	C₂³×C₄	C₂×#120	1	4	yes	—
471	C₂³×C₄	C₂×#120	1	4	yes	—
472	C₂³×C₄	C₂×#120	1	2	yes	—
473	C₂³×C₄	C₂×#121	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
475	C₂⁴	#2021	1	8	yes	complemented
476	C₂⁴	C₂×#392	1	1	yes	characteristic
477	C₂⁴	C₂×#392	1	1	yes	characteristic
478	C₂⁴	C₂×#392	1	4	yes	—
479	C₂⁴	C₂×#392	1	1	yes	characteristic
480	C₂⁴	C₂×#392	1	1	yes	characteristic
481	C₂⁴	C₂×#392	1	1	yes	characteristic
482	C₂⁴	C₂×#392	1	1	yes	characteristic
483	C₂⁴	C₂×#392	1	4	yes	—
484	C₂⁴	C₂×#392	1	1	yes	characteristic
485	C₂⁴	C₂×#392	1	1	yes	characteristic
486	C₂⁴	#2403	1	2	yes	—
487	C₂⁴	#2403	1	1	yes	characteristic
488	C₂⁴	#2403	1	1	yes	characteristic
489	C₂⁴	#2403	1	1	yes	characteristic
490	C₂⁴	#2403	1	2	yes	—
491	C₂⁴	#2403	1	2	yes	—
492	C₂⁴	#2403	1	1	yes	characteristic
493	C₂⁴	#2403	1	1	yes	characteristic
494	C₂⁴	#2403	1	1	yes	characteristic
495	C₂⁴	#2403	1	2	yes	—
496	C₂⁴	#2403	1	2	yes	—
497	C₂⁴	#2403	1	2	yes	—
498	C₂⁴	#2403	1	2	yes	—
499	C₂⁴	#2403	1	2	yes	—
500	C₂⁴	#2403	1	2	yes	—
501	C₂⁴	#2403	1	2	yes	—
502	C₂⁴	#2403	1	1	yes	characteristic
503	C₂⁴	#2403	1	1	yes	characteristic
504	C₂⁴	#2403	1	2	yes	—
505	C₂⁴	#2403	1	2	yes	—
506	C₂⁴	#2408	1	2	yes	—
507	C₂⁴	#2408	1	2	yes	—
508	C₂⁴	#2408	1	2	yes	—
509	C₂⁴	#2408	1	2	yes	—
510	C₂⁴	#2408	1	2	yes	—
511	C₂⁴	#2408	1	2	yes	—
512	C₂⁴	#2408	1	2	yes	—
513	C₂⁴	#2408	1	2	yes	—
514	C₂⁴	#2410	1	1	yes	characteristic
515	C₂⁴	#2410	1	1	yes	characteristic
516	C₂⁴	#2410	1	1	yes	characteristic
517	C₂⁴	#2410	1	1	yes	characteristic
518	C₂⁴	#2410	1	2	yes	—
519	C₂⁴	#2410	1	2	yes	—
520	C₂⁴	#2410	1	2	yes	—
521	C₂⁴	#2410	1	2	yes	—
522	C₂⁴	#2410	1	2	yes	—
523	C₂⁴	#2410	1	1	yes	characteristic
524	C₂⁴	#2410	1	2	yes	—
525	C₂⁴	#2410	1	2	yes	—
526	C₂⁴	#2410	1	2	yes	—
527	C₂⁴	#2410	1	1	yes	characteristic
528	C₂⁴	#2410	1	1	yes	characteristic
529	C₂⁴	#2410	1	2	yes	—
530	C₂⁴	#2410	1	2	yes	—
531	C₂⁴	#2410	1	2	yes	—
532	C₂⁴	#2410	1	2	yes	—
533	C₂⁴	#2410	1	1	yes	characteristic
534	C₂⁴	#2433	1	2	yes	—
535	C₂⁴	#2433	1	2	yes	—
536	C₂⁴	#2433	1	2	yes	—
537	C₂⁴	#2433	1	2	yes	—
538	C₂⁴	#2433	1	2	yes	—
539	C₂⁴	#2433	1	2	yes	—
540	C₂⁴	#2433	1	2	yes	—
541	C₂⁴	#2433	1	2	yes	—
542	C₂⁴	#2613	1	1	yes	characteristic
543	C₂⁴	#2613	1	1	yes	characteristic
544	C₂⁴	#2613	1	2	yes	—
545	C₂⁴	#2613	1	1	yes	characteristic
546	C₂⁴	#2613	1	1	yes	characteristic
547	C₂⁴	#2613	1	2	yes	—
548	C₂⁴	#2846	1	1	yes	characteristic
549	C₂⁴	#2846	1	1	yes	characteristic
550	C₂⁴	#2846	1	1	yes	characteristic
551	C₂⁴	#2846	1	2	yes	—
552	C₂⁴	#2846	1	1	yes	characteristic
553	C₂⁴	#2846	1	2	yes	—
554	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
555	C₂⁴	#3026	1	8	yes	complemented
556	C₂⁴	C₂²×#120	1	1	yes	characteristic
557	C₂⁴	C₂²×#120	1	1	yes	characteristic
558	C₂⁴	C₂²×#120	1	2	yes	—
559	C₂⁴	C₂²×#120	1	1	yes	characteristic
560	C₂⁴	C₂²×#120	1	2	yes	—
561	C₂⁴	C₂²×#120	1	1	yes	characteristic
562	C₂⁴	C₂²×#120	1	1	yes	characteristic
563	C₂⁴	C₂²×#121	1	1	yes	characteristic
564	C₂⁴	C₂²×#121	1	1	yes	characteristic
565	C₂⁴	C₂²×#121	1	1	yes	characteristic
566	C₂⁴	C₂²×#127	1	1	yes	characteristic
567	C₂⁴	C₂×#534	1	1	yes	characteristic
568	C₂⁴	C₂×#534	1	2	yes	—
569	C₂⁴	C₂×#534	1	1	yes	characteristic
570	C₂⁴	C₂×#535	1	2	yes	—
571	C₂⁴	C₂×D₄²	1	2	yes	—
572	C₂⁴	C₂×D₄²	1	2	yes	—
573	C₂⁴	C₂×D₄²	1	2	yes	—
574	C₂⁴	C₂×D₄²	1	2	yes	—
575	C₂⁴	C₂×D₄²	1	2	yes	—
576	C₂⁴	C₂×D₄²	1	2	yes	—
577	C₂⁴	C₂×#546	1	2	yes	—
578	C₂⁴	C₂×#546	1	2	yes	—
579	C₂×D₄	#2021	1	16	yes	complemented
580	C₂×D₄	C₂×B(4,𝔽₂)	1	16	yes	—
581	C₂²×C₄	#2021	1	8	yes	complemented
582	C₂²×C₄	C₂×#392	1	4	yes	—
583	C₂²×C₄	C₂×#392	1	4	yes	—
584	C₂³	#14715	1	1	yes	characteristic
585	C₂³	#14715	1	1	yes	characteristic
586	C₂³	#14715	1	1	yes	characteristic
587	C₂³	#14715	1	1	yes	characteristic
588	C₂³	#14715	1	2	yes	—
589	C₂³	#14715	1	2	yes	—
590	C₂³	#14715	1	2	yes	—
591	C₂³	#14715	1	1	yes	characteristic
592	C₂³	#14715	1	2	yes	—
593	C₂³	#14715	1	1	yes	characteristic
594	C₂³	#14715	1	1	yes	characteristic
595	C₂³	#14715	1	1	yes	characteristic
596	C₂³	C₂×#2021	1	8	yes	—
597	C₂³	C₂×#2021	1	4	yes	—
598	C₂³	C₂×#2021	1	4	yes	—
599	C₂³	#23895	1	4	yes	—
600	C₂³	#23900	1	8	yes	—
601	C₂³	#23900	1	8	yes	—
602	C₂³	C₂²×#392	1	1	yes	characteristic
603	C₂³	C₂×#2613	1	1	yes	characteristic
604	C₂³	C₂×#2403	1	2	yes	—
605	C₂³	C₂×#2403	1	1	yes	characteristic
606	C₂³	C₂×#2403	1	1	yes	characteristic
607	C₂³	C₂×#2410	1	1	yes	characteristic
608	C₂³	C₂×#2410	1	2	yes	—
609	C₂³	C₂×#2410	1	1	yes	characteristic
610	C₂³	C₂×#2408	1	2	yes	—
611	C₂³	C₂×#2433	1	2	yes	—
612	C₂³	C₂×#2846	1	1	yes	characteristic
613	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
614	C₂³	C₂×#3026	1	4	yes	—
615	C₂×C₄	C₂×#2021	1	8	yes	—
616	C₂²	#394058	1	2	yes	—
617	C₂²	#394058	1	2	yes	—
618	C₂²	#394058	1	4	yes	—
619	C₂²	#394064	1	2	yes	—
620	C₂²	#394064	1	2	yes	—
621	C₂²	C₂×#14715	1	1	yes	characteristic
622	C₂²	C₂²×#2021	1	2	yes	—
623	C₂²	C₂×#23900	1	4	yes	—
624	C₂²	#6437621	1	2	yes	—
625	C₂²	C₂×#23895	1	2	yes	—
626	C₂²	#6437995	1	2	yes	—
627	C₂²	#6628892	1	2	yes	—
628	C₂	C₂×#394058	1	1	yes	characteristic
629	C₂	C₂×#394064	1	1	yes	characteristic
630	C₂	#72238029	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14715
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72238031	C₂	semidirect
2. #72238030	C₂	semidirect
3. #72237398	C₂	semidirect
4. #72236431	C₂	semidirect
5. C₂×#392109	C₂	semidirect
6. #72234661	C₂	semidirect
7. #72233891	C₂	semidirect
8. #72233691	C₂	semidirect
9. C₂×#7630939	C₂	semidirect
10. #72225801	C₂	semidirect
11. #72217699	C₂	semidirect
12. C₂×#115690	C₂	semidirect
13. #72210600	C₂	semidirect
16. #7641845	C₂²	semidirect
18. C₂²×#2846	C₂²	semidirect
22. C₂×#34980	C₂²	semidirect
24. #6470226	C₂²	semidirect
25. #6470225	C₂²	semidirect
26. C₂×#21746	C₂²	semidirect
27. C₂×#21746	C₂²	semidirect
28. C₂×#21746	C₂²	semidirect
29. C₂×#21746	C₂²	semidirect
32. C₂²×#1781	C₂²	semidirect
33. #612617	C₂²	semidirect
34. #612424	C₂²	semidirect
35. C₂×#14679	C₂²	semidirect
36. C₂×#14679	C₂²	semidirect
38. #517411	C₂²	semidirect
39. #405156	C₂²	semidirect
40. #394058	C₂²	semidirect
41. #392109	C₂²	semidirect
42. #355913	C₂²	semidirect
43. #233542	C₂²	semidirect
44. #233541	C₂²	semidirect
45. #201668	C₂²	semidirect
46. #201664	C₂²	semidirect
47. #187928	C₂²	semidirect
48. C₂×#8101	C₂²	semidirect
49. C₂×#8101	C₂²	semidirect
50. #115690	C₂²	semidirect
51. #115204	C₂²	semidirect
52. #106766	C₂²	semidirect
53. C₂⁸	D₄	semidirect
55. C₂³×H(5,𝔽₂)	D₄	semidirect
56. C₂⁵×D₄	D₄	semidirect
57. C₂⁵×D₄	D₄	semidirect
58. C₂⁵×D₄	D₄	semidirect
62. C₂⁶×C₄	D₄	semidirect
63. C₂×#3484	D₄	semidirect
65. C₂²×#534	D₄	semidirect
66. C₂²×#534	D₄	semidirect
67. C₂³×#120	D₄	semidirect
70. C₂³×#120	C₂³	semidirect
71. C₂²×#518	D₄	semidirect
72. C₂³×#99	D₄	semidirect
73. C₂×#2846	D₄	semidirect
75. #34992	C₂³	semidirect
76. #34980	D₄	semidirect
78. #34980	C₂³	semidirect
79. C₂×#2405	D₄	semidirect
80. C₂×#2405	D₄	semidirect
82. C₂×#2405	C₂³	semidirect
83. C₂×#2403	D₄	semidirect
84. C₂×#2403	D₄	semidirect
86. C₂×#2403	C₂³	semidirect
87. #34171	D₄	semidirect
89. C₂×#2309	D₄	semidirect
90. C₂×#2308	D₄	semidirect
91. C₂×#2308	D₄	semidirect
92. C₂²×#379	D₄	semidirect
99. C₂²×#379	C₂³	semidirect
100. #21746	C₂³	semidirect
101. #21746	C₂³	semidirect
102. C₂×#1898	C₂³	semidirect
103. C₂×#1819	C₂³	semidirect
104. C₂×#1781	D₄	semidirect
107. C₂×#1781	C₂³	semidirect
108. C₂×#1781	C₂³	semidirect
109. #14679	C₂³	semidirect
110. #14679	C₂³	semidirect
111. #14335	D₄	semidirect
112. #13867	D₄	semidirect
114. #13867	C₂³	semidirect
115. #10735	C₂³	semidirect
116. #8101	C₂³	semidirect
117. #8101	C₂³	semidirect
150. C₂⁴×D₄	C₂×D₄	semidirect
151. C₂⁴×D₄	C₂×D₄	semidirect
161. C₂²×#123	C₂×D₄	semidirect
166. C₂²×#120	C₂×D₄	semidirect
173. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
174. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
175. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
176. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
177. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
180. C₂²×#99	C₂×D₄	semidirect
185. C₂×#386	C₂×D₄	semidirect
186. C₂×#386	C₂×D₄	semidirect
193. C₂×#379	C₂×D₄	semidirect
194. C₂×#379	C₂×D₄	semidirect
195. C₂×#379	C₂×D₄	semidirect
196. C₂×#379	C₂×D₄	semidirect
197. C₂×#379	C₂×D₄	semidirect
203. #1438	C₂×D₄	semidirect
216. C₂⁶	#120	semidirect
240. C₂⁶	C₂²×D₄	semidirect
261. C₂³×D₄	#120	semidirect
262. C₂³×D₄	#120	semidirect
263. C₂³×D₄	#120	semidirect
303. C₂⁴×C₄	#120	semidirect
304. C₂⁴×C₄	#120	semidirect
305. C₂⁴×C₄	#120	semidirect
310. C₂⁴×C₄	C₂²×D₄	semidirect
311. C₂⁴×C₄	C₂²×D₄	semidirect
312. C₂⁴×C₄	C₂²×D₄	semidirect
313. C₂²×C₂²⋊C₄	#120	semidirect
314. C₂²×C₂²⋊C₄	#120	semidirect
315. C₂²×C₂²⋊C₄	#120	semidirect
316. C₂²×C₂²⋊C₄	#120	semidirect
317. C₂²×C₂²⋊C₄	#120	semidirect
322. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
323. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
324. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
325. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
326. #379	#120	semidirect
327. #379	#120	semidirect
475. C₂⁴	#2021	semidirect
555. C₂⁴	#3026	semidirect
579. C₂×D₄	#2021	semidirect
581. C₂²×C₄	#2021	semidirect

Maximal subgroups

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

subgroup	index
#72238031	2
#72238030	2
#72237398	2
#72236431	2
C₂×#392109	2
#72234661	2
#72233891	2
#72233691	2
C₂×#7630939	2
#72225801	2
#72217699	2
C₂×#115690	2
#72210600	2