Subgroups — #72262676

Order 2048.

At least 6666 conjugacy classes of subgroups; only the 1660 normal subgroups are shown.

The subgroup lattice has 456 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262671	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262662	C₂	1	4	yes	maximal, complemented
3	#72262540	C₂	1	1	yes	maximal, characteristic, complemented
4	#72256331	C₂	1	2	yes	maximal, complemented
5	#72256222	C₂	1	2	yes	maximal, complemented
6	#72255822	C₂	1	2	yes	maximal, complemented
7	#72237618	C₂	1	1	yes	maximal, characteristic, complemented
8	#72237372	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#115204	C₂	1	4	yes	maximal, complemented
10	#72236431	C₂	1	4	yes	maximal, complemented
11	#72235924	C₂	1	4	yes	maximal, complemented
12	#72234675	C₂	1	1	yes	maximal, characteristic, complemented
13	#72232592	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#188035	C₂	1	1	yes	maximal, characteristic, complemented
15	#72225610	C₂	1	2	yes	maximal, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic
17	C₂³×D₄²	C₂²	1	1	yes	characteristic
18	#7643002	C₂²	1	2	yes	—
19	#7642350	C₂²	1	4	yes	—
20	#7642244	C₂²	1	2	yes	—
21	#7641845	C₂²	1	2	yes	complemented
22	C₂×#34981	C₂²	1	1	yes	characteristic
23	C₂×#34980	C₂²	1	4	yes	—
24	C₂×#34980	C₂²	1	2	yes	complemented
25	#7626202	C₂²	1	1	yes	characteristic
26	#6453039	C₂²	1	2	yes	complemented
27	#6451874	C₂²	1	2	yes	complemented
28	#6440460	C₂²	1	2	yes	complemented
29	#6437621	C₂²	1	2	yes	complemented
30	C₂×#21746	C₂²	1	1	yes	characteristic
31	C₂×#21746	C₂²	1	1	yes	characteristic
32	C₂×#21746	C₂²	1	4	yes	complemented
33	C₂×#21746	C₂²	1	2	yes	complemented
34	C₂²×#1898	C₂²	1	2	yes	complemented
35	C₂²×#1781	C₂²	1	4	yes	complemented
36	#618455	C₂²	1	2	yes	complemented
37	#618316	C₂²	1	2	yes	complemented
38	#617875	C₂²	1	1	yes	characteristic, complemented
39	#617710	C₂²	1	1	yes	characteristic, complemented
40	#617161	C₂²	1	1	yes	characteristic, complemented
41	#616960	C₂²	1	1	yes	characteristic, complemented
42	#556752	C₂²	1	1	yes	characteristic
43	C₂×#13867	C₂²	1	2	yes	complemented
44	#359921	C₂²	1	2	yes	complemented
45	#359811	C₂²	1	2	yes	complemented
46	#359705	C₂²	1	2	yes	complemented
47	#359442	C₂²	1	2	yes	complemented
48	C₂×#10735	C₂²	1	2	yes	complemented
49	#233542	C₂²	1	8	yes	complemented
50	#233542	C₂²	1	8	yes	complemented
51	#233541	C₂²	1	8	yes	complemented
52	#233541	C₂²	1	8	yes	complemented
53	C₂×#8546	C₂²	1	2	yes	complemented
54	C₂×#8542	C₂²	1	4	yes	complemented
55	C₂×#8541	C₂²	1	2	yes	complemented
56	#187945	C₂²	1	4	yes	complemented
57	#187944	C₂²	1	2	yes	complemented
58	#187944	C₂²	1	2	yes	complemented
59	C₂×#8101	C₂²	1	4	yes	complemented
60	#115204	C₂²	1	8	yes	complemented
61	#115204	C₂²	1	8	yes	complemented
62	#115204	C₂²	1	8	yes	complemented
63	#115204	C₂²	1	8	yes	complemented
64	#107115	C₂²	1	4	yes	complemented
65	#107114	C₂²	1	2	yes	complemented
66	#107114	C₂²	1	2	yes	complemented
67	C₂⁵×D₄	D₄	1	2	yes	complemented
68	C₂⁵×D₄	C₂³	1	2	yes	—
69	C₂×#3490	D₄	1	4	yes	complemented
70	C₂×#3490	C₂³	1	2	yes	—
71	C₂×#3484	D₄	1	4	yes	complemented
72	C₂×#3484	C₂³	1	2	yes	—
73	C₂²×#534	C₂³	1	1	yes	characteristic
74	C₂³×#127	C₂³	1	1	yes	characteristic
75	C₂³×#121	D₄	1	2	yes	complemented
76	C₂³×#121	C₂³	1	2	yes	—
77	C₂³×#120	D₄	1	2	yes	complemented
78	C₂³×#120	C₂³	1	2	yes	—
79	C₂³×#120	C₂³	1	1	yes	characteristic
80	C₂³×#120	C₂³	1	1	yes	characteristic
81	C₂³×#120	C₂³	1	1	yes	characteristic
82	C₂³×C₄×D₄	D₄	1	2	yes	complemented
83	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
84	#34992	C₂³	1	4	yes	—
85	#34980	D₄	1	16	yes	complemented
86	#34980	C₂³	1	4	yes	—
87	#34980	C₂³	1	8	yes	—
88	#34980	C₂³	1	8	yes	—
89	C₂×#2412	D₄	1	4	yes	complemented
90	C₂×#2405	D₄	1	8	yes	complemented
91	C₂×#2405	C₂³	1	2	yes	—
92	C₂×#2405	C₂³	1	2	yes	—
93	C₂×#2410	D₄	1	4	yes	complemented
94	C₂×#2403	D₄	1	8	yes	complemented
95	C₂×#2403	C₂³	1	2	yes	—
96	C₂×#2403	C₂³	1	2	yes	—
97	#34198	D₄	1	8	yes	complemented
98	#34176	C₂³	1	2	yes	—
99	#34171	C₂³	1	2	yes	—
100	C₂×#2315	C₂³	1	1	yes	characteristic
101	C₂×#2308	C₂³	1	1	yes	characteristic
102	C₂×#2308	C₂³	1	1	yes	characteristic
103	C₂²×#379	C₂³	1	2	yes	—
104	C₂²×#379	C₂³	1	2	yes	—
105	C₂²×#379	C₂³	1	2	yes	—
106	C₂²×#379	C₂³	1	2	yes	—
107	#21746	D₄	1	8	yes	complemented
108	#21746	C₂³	1	8	yes	—
109	#21746	C₂³	1	8	yes	—
110	C₂×#1898	C₂³	1	4	yes	—
111	C₂×#1898	C₂³	1	4	yes	—
112	C₂×#1819	C₂³	1	2	yes	—
113	C₂×#1819	C₂³	1	4	yes	—
114	C₂×#1819	C₂³	1	2	yes	—
115	C₂×#1781	C₂³	1	4	yes	—
116	C₂×#1781	C₂³	1	2	yes	—
117	C₂×#1781	C₂³	1	2	yes	—
118	C₂×#1781	C₂³	1	8	yes	—
119	C₂×#1781	C₂³	1	8	yes	—
120	#14657	D₄	1	4	yes	complemented
121	#14341	C₂³	1	2	yes	—
122	#14335	C₂³	1	1	yes	characteristic
123	#14335	C₂³	1	1	yes	characteristic
124	#14134	D₄	1	4	yes	complemented
125	#13867	C₂³	1	2	yes	—
126	#13867	C₂³	1	2	yes	—
127	#13867	C₂³	1	2	yes	—
128	#13867	C₂³	1	2	yes	—
129	#10735	C₂³	1	4	yes	—
130	#10735	C₂³	1	4	yes	—
131	#8101	C₂³	1	8	yes	—
132	#8101	C₂³	1	8	yes	—
133	C₂⁷	C₂×D₄	1	2	yes	—
134	C₂⁷	C₂×D₄	1	1	yes	characteristic
135	C₂⁷	C₂⁴	1	1	yes	characteristic
136	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
137	C₂⁴×D₄	C₂×D₄	1	8	yes	—
138	C₂⁴×D₄	C₂×D₄	1	8	yes	—
139	C₂⁴×D₄	C₂×D₄	1	4	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
146	C₂⁴×D₄	C₂×D₄	1	2	yes	—
147	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
148	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
149	C₂⁴×D₄	C₂⁴	1	2	yes	—
150	C₂⁴×D₄	C₂⁴	1	2	yes	—
151	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
152	C₂⁵×C₄	C₂×D₄	1	2	yes	—
153	C₂⁵×C₄	C₂×D₄	1	2	yes	—
154	C₂×#543	C₂×D₄	1	2	yes	—
155	C₂×#534	C₂×D₄	1	2	yes	—
156	C₂×#534	C₂×D₄	1	4	yes	—
157	C₂²×#123	C₂×D₄	1	2	yes	complemented
158	C₂²×#120	C₂×D₄	1	4	yes	—
159	C₂²×#120	C₂×D₄	1	4	yes	—
160	C₂²×#120	C₂×D₄	1	2	yes	—
161	C₂²×#120	C₂×D₄	1	2	yes	—
162	C₂²×#120	C₂×D₄	1	4	yes	—
163	C₂²×#120	C₂×D₄	1	4	yes	—
164	C₂²×#120	C₂×D₄	1	8	yes	—
165	C₂²×#120	C₂×D₄	1	4	yes	—
166	C₂²×#120	C₂×D₄	1	2	yes	complemented
167	C₂²×#120	#41	1	4	yes	—
168	C₂²×#120	C₂⁴	1	4	yes	—
169	C₂×#518	C₂×D₄	1	2	yes	—
170	C₂×#518	C₂×D₄	1	4	yes	—
171	C₂×#518	C₂×D₄	1	4	yes	—
172	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
173	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
174	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
175	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
176	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
178	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
179	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
180	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
181	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
182	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
183	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
185	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
186	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
187	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
188	#2405	C₂×D₄	1	16	yes	—
189	#2405	C₂×D₄	1	16	yes	—
190	#2403	C₂×D₄	1	16	yes	—
191	#2403	C₂×D₄	1	16	yes	—
192	#2315	C₂×D₄	1	4	yes	—
193	#2308	C₂×D₄	1	4	yes	—
194	C₂×#386	C₂×D₄	1	4	yes	complemented
195	C₂×#385	C₂×D₄	1	4	yes	complemented
196	C₂×#381	C₂×D₄	1	2	yes	complemented
197	C₂×#379	C₂×D₄	1	8	yes	—
198	C₂×#379	C₂×D₄	1	8	yes	—
199	C₂×#379	C₂×D₄	1	4	yes	—
200	C₂×#379	C₂×D₄	1	8	yes	complemented
201	C₂×#379	C₂×D₄	1	4	yes	complemented
202	C₂×#379	C₂×D₄	1	2	yes	complemented
203	C₂×#379	C₂⁴	1	4	yes	—
204	C₂×#379	C₂⁴	1	4	yes	—
205	C₂×#379	C₂⁴	1	2	yes	—
206	C₂×#379	C₂⁴	1	2	yes	—
207	C₂×#379	C₂⁴	1	4	yes	—
208	#2273	C₂×D₄	1	4	yes	—
209	#1819	C₂×D₄	1	8	yes	complemented
210	#1781	C₂×D₄	1	8	yes	complemented
211	#1440	C₂×D₄	1	8	yes	complemented
212	#1438	C₂×D₄	1	4	yes	complemented
213	#1438	C₂×D₄	1	4	yes	complemented
214	C₂⁶	#120	1	4	yes	—
215	C₂⁶	#120	1	4	yes	—
216	C₂⁶	#120	1	2	yes	complemented
217	C₂⁶	C₂²×D₄	1	1	yes	characteristic
218	C₂⁶	C₂²×D₄	1	2	yes	—
219	C₂⁶	C₂²×D₄	1	2	yes	—
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂⁶	C₂²×D₄	1	2	yes	—
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	2	yes	—
224	C₂⁶	C₂²×D₄	1	2	yes	—
225	C₂⁶	C₂²×D₄	1	4	yes	—
226	C₂⁶	C₂²×D₄	1	2	yes	—
227	C₂⁶	C₂²×D₄	1	4	yes	—
228	C₂⁶	C₂²×D₄	1	1	yes	characteristic
229	C₂⁶	C₂²×D₄	1	2	yes	—
230	C₂⁶	C₂×#41	1	2	yes	—
231	C₂⁶	H(5,𝔽₂)	1	4	yes	—
232	C₂⁶	H(5,𝔽₂)	1	4	yes	—
233	C₂⁶	C₂⁵	1	1	yes	characteristic
234	C₂³×D₄	#120	1	8	yes	—
235	C₂³×D₄	#120	1	8	yes	—
236	C₂³×D₄	#120	1	4	yes	—
237	C₂³×D₄	#120	1	8	yes	—
238	C₂³×D₄	#120	1	4	yes	—
239	C₂³×D₄	#120	1	4	yes	complemented
240	C₂³×D₄	#120	1	8	yes	complemented
241	C₂³×D₄	#121	1	8	yes	—
242	C₂³×D₄	C₂²×D₄	1	4	yes	—
243	C₂³×D₄	C₂²×D₄	1	8	yes	—
244	C₂³×D₄	C₂²×D₄	1	8	yes	—
245	C₂³×D₄	C₂²×D₄	1	8	yes	—
246	C₂³×D₄	C₂²×D₄	1	2	yes	—
247	C₂³×D₄	C₂²×D₄	1	2	yes	—
248	C₂³×D₄	C₂²×D₄	1	2	yes	—
249	C₂³×D₄	C₂²×D₄	1	2	yes	—
250	C₂³×D₄	C₂²×D₄	1	2	yes	—
251	C₂³×D₄	C₂×#41	1	2	yes	—
252	C₂⁴×C₄	#120	1	4	yes	—
253	C₂⁴×C₄	#120	1	4	yes	—
254	C₂⁴×C₄	#120	1	4	yes	complemented
255	C₂⁴×C₄	#120	1	2	yes	complemented
256	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
257	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
258	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
259	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
260	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
261	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
262	C₂×#120	#120	1	16	yes	—
263	C₂×#120	#121	1	8	yes	—
264	C₂×#120	#121	1	8	yes	—
265	C₂×#120	#121	1	16	yes	—
266	C₂×#120	#127	1	8	yes	—
267	C₂×#120	#127	1	8	yes	—
268	C₂²×C₂²⋊C₄	#120	1	8	yes	—
269	C₂²×C₂²⋊C₄	#120	1	4	yes	—
270	C₂²×C₂²⋊C₄	#120	1	4	yes	—
271	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
272	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
273	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
274	C₂²×C₂²⋊C₄	#121	1	8	yes	—
275	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
276	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
277	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
279	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
280	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
281	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
284	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
285	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
287	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
288	#379	#120	1	8	yes	complemented
289	#379	#120	1	8	yes	complemented
290	#379	C₂²×D₄	1	8	yes	—
291	#379	C₂²×D₄	1	16	yes	—
292	C₂⁵	C₂×#120	1	2	yes	—
293	C₂⁵	C₂×#120	1	2	yes	—
294	C₂⁵	C₂×#120	1	4	yes	—
295	C₂⁵	C₂×#120	1	2	yes	—
296	C₂⁵	C₂×#120	1	4	yes	—
297	C₂⁵	C₂×#120	1	4	yes	—
298	C₂⁵	C₂×#120	1	4	yes	—
299	C₂⁵	C₂×#120	1	2	yes	—
300	C₂⁵	C₂×#120	1	4	yes	—
301	C₂⁵	C₂×#120	1	2	yes	—
302	C₂⁵	C₂×#120	1	2	yes	—
303	C₂⁵	C₂×#120	1	2	yes	—
304	C₂⁵	C₂×#120	1	4	yes	—
305	C₂⁵	C₂×#120	1	2	yes	—
306	C₂⁵	C₂×#120	1	4	yes	—
307	C₂⁵	C₂×#120	1	4	yes	—
308	C₂⁵	C₂×#120	1	2	yes	—
309	C₂⁵	C₂×#120	1	2	yes	—
310	C₂⁵	C₂×#121	1	2	yes	—
311	C₂⁵	C₂×#121	1	2	yes	—
312	C₂⁵	C₂×#121	1	4	yes	—
313	C₂⁵	C₂×#121	1	4	yes	—
314	C₂⁵	C₂×#121	1	2	yes	—
315	C₂⁵	C₂×#127	1	2	yes	—
316	C₂⁵	C₂×#127	1	2	yes	—
317	C₂⁵	#534	1	2	yes	—
318	C₂⁵	#534	1	4	yes	—
319	C₂⁵	#534	1	2	yes	—
320	C₂⁵	#534	1	4	yes	—
321	C₂⁵	#534	1	2	yes	—
322	C₂⁵	#534	1	2	yes	—
323	C₂⁵	#535	1	2	yes	—
324	C₂⁵	#535	1	4	yes	—
325	C₂⁵	#535	1	2	yes	—
326	C₂⁵	D₄²	1	4	yes	—
327	C₂⁵	D₄²	1	4	yes	—
328	C₂⁵	D₄²	1	4	yes	—
329	C₂⁵	D₄²	1	4	yes	—
330	C₂⁵	D₄²	1	4	yes	—
331	C₂⁵	D₄²	1	4	yes	—
332	C₂⁵	D₄²	1	4	yes	—
333	C₂⁵	D₄²	1	4	yes	—
334	C₂⁵	D₄²	1	4	yes	—
335	C₂⁵	D₄²	1	4	yes	—
336	C₂⁵	D₄²	1	4	yes	—
337	C₂⁵	D₄²	1	4	yes	—
338	C₂⁵	#546	1	4	yes	—
339	C₂⁵	#546	1	4	yes	—
340	C₂⁵	#546	1	4	yes	—
341	C₂⁵	#546	1	4	yes	—
342	C₂⁵	C₂³×D₄	1	1	yes	characteristic
343	C₂⁵	C₂³×D₄	1	1	yes	characteristic
344	C₂⁵	C₂³×D₄	1	1	yes	characteristic
345	C₂⁵	C₂³×D₄	1	1	yes	characteristic
346	C₂⁵	C₂³×D₄	1	1	yes	characteristic
347	C₂⁵	C₂³×D₄	1	4	yes	—
348	C₂⁵	C₂³×D₄	1	1	yes	characteristic
349	C₂⁵	C₂²×#41	1	1	yes	characteristic
350	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
351	C₂²×D₄	#392	1	16	yes	—
352	C₂²×D₄	#392	1	16	yes	—
353	C₂²×D₄	C₂×#120	1	4	yes	—
354	C₂²×D₄	C₂×#121	1	4	yes	—
355	C₂²×D₄	C₂×#121	1	4	yes	—
356	C₂²×D₄	C₂×#127	1	4	yes	—
357	C₂³×C₄	C₂×#120	1	2	yes	—
358	C₂³×C₄	C₂×#120	1	4	yes	—
359	C₂³×C₄	C₂×#120	1	4	yes	—
360	C₂³×C₄	C₂×#120	1	4	yes	—
361	C₂³×C₄	C₂×#120	1	8	yes	—
362	C₂³×C₄	C₂×#120	1	2	yes	—
363	C₂³×C₄	C₂×#120	1	4	yes	—
364	C₂³×C₄	C₂×#120	1	4	yes	—
365	C₂³×C₄	C₂×#121	1	2	yes	—
366	C₂³×C₄	C₂×#121	1	4	yes	—
367	C₂×C₂²⋊C₄	#392	1	16	yes	—
368	C₂×C₂²⋊C₄	#392	1	16	yes	—
369	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
371	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂×#127	1	4	yes	—
374	C₂⁴	C₂×#392	1	4	yes	—
375	C₂⁴	C₂×#392	1	4	yes	—
376	C₂⁴	C₂×#392	1	4	yes	—
377	C₂⁴	#2403	1	4	yes	—
378	C₂⁴	#2403	1	2	yes	—
379	C₂⁴	#2403	1	4	yes	—
380	C₂⁴	#2403	1	2	yes	—
381	C₂⁴	#2403	1	2	yes	—
382	C₂⁴	#2403	1	4	yes	—
383	C₂⁴	#2403	1	4	yes	—
384	C₂⁴	#2403	1	4	yes	—
385	C₂⁴	#2403	1	4	yes	—
386	C₂⁴	#2403	1	2	yes	—
387	C₂⁴	#2408	1	4	yes	—
388	C₂⁴	#2408	1	4	yes	—
389	C₂⁴	#2408	1	4	yes	—
390	C₂⁴	#2408	1	4	yes	—
391	C₂⁴	#2410	1	2	yes	—
392	C₂⁴	#2410	1	4	yes	—
393	C₂⁴	#2410	1	4	yes	—
394	C₂⁴	#2410	1	4	yes	—
395	C₂⁴	#2410	1	4	yes	—
396	C₂⁴	#2410	1	4	yes	—
397	C₂⁴	#2410	1	2	yes	—
398	C₂⁴	#2410	1	2	yes	—
399	C₂⁴	#2410	1	4	yes	—
400	C₂⁴	#2410	1	2	yes	—
401	C₂⁴	#2433	1	2	yes	—
402	C₂⁴	#2433	1	4	yes	—
403	C₂⁴	#2433	1	2	yes	—
404	C₂⁴	#2433	1	4	yes	—
405	C₂⁴	#2433	1	2	yes	—
406	C₂⁴	#2433	1	2	yes	—
407	C₂⁴	#2613	1	4	yes	—
408	C₂⁴	#2613	1	4	yes	—
409	C₂⁴	#2846	1	4	yes	—
410	C₂⁴	#2846	1	4	yes	—
411	C₂⁴	C₂²×#120	1	1	yes	characteristic
412	C₂⁴	C₂²×#120	1	2	yes	—
413	C₂⁴	C₂²×#120	1	2	yes	—
414	C₂⁴	C₂²×#120	1	2	yes	—
415	C₂⁴	C₂²×#120	1	1	yes	characteristic
416	C₂⁴	C₂²×#120	1	1	yes	characteristic
417	C₂⁴	C₂²×#121	1	1	yes	characteristic
418	C₂⁴	C₂²×#121	1	1	yes	characteristic
419	C₂⁴	C₂²×#121	1	1	yes	characteristic
420	C₂⁴	C₂²×#127	1	1	yes	characteristic
421	C₂⁴	C₂×#534	1	2	yes	—
422	C₂⁴	C₂×#534	1	2	yes	—
423	C₂⁴	C₂×#535	1	2	yes	—
424	C₂⁴	C₂×D₄²	1	4	yes	—
425	C₂⁴	C₂×D₄²	1	4	yes	—
426	C₂⁴	C₂×D₄²	1	4	yes	—
427	C₂⁴	C₂×#546	1	4	yes	—
428	C₂²×C₄	C₂×#392	1	4	yes	—
429	C₂²×C₄	C₂×#392	1	8	yes	—
430	C₂³	#14715	1	4	yes	—
431	C₂³	#14715	1	4	yes	—
432	C₂³	#14715	1	4	yes	—
433	C₂³	#14715	1	4	yes	—
434	C₂³	#23895	1	8	yes	—
435	C₂³	C₂²×#392	1	1	yes	characteristic
436	C₂³	C₂×#2613	1	1	yes	characteristic
437	C₂³	C₂×#2403	1	2	yes	—
438	C₂³	C₂×#2403	1	2	yes	—
439	C₂³	C₂×#2410	1	2	yes	—
440	C₂³	C₂×#2410	1	2	yes	—
441	C₂³	C₂×#2408	1	2	yes	—
442	C₂³	C₂×#2433	1	2	yes	—
443	C₂³	C₂×#2846	1	1	yes	characteristic
444	C₂³	#60399	1	2	yes	—
445	C₂³	#60401	1	2	yes	—
446	C₂²	#394064	1	8	yes	—
447	C₂²	C₂×#14715	1	1	yes	characteristic
448	C₂²	#6431795	1	1	yes	characteristic
449	C₂²	#6431796	1	1	yes	characteristic
450	C₂²	#6432957	1	2	yes	—
451	C₂²	C₂×#23895	1	4	yes	—
452	C₂²	#6628900	1	2	yes	—
453	C₂	C₂×#394064	1	2	yes	—
454	C₂	#72251632	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. #72262671	C₂	semidirect
2. #72262662	C₂	semidirect
3. #72262540	C₂	semidirect
4. #72256331	C₂	semidirect
5. #72256222	C₂	semidirect
6. #72255822	C₂	semidirect
7. #72237618	C₂	semidirect
8. #72237372	C₂	semidirect
9. C₂×#115204	C₂	semidirect
10. #72236431	C₂	semidirect
11. #72235924	C₂	semidirect
12. #72234675	C₂	semidirect
13. #72232592	C₂	semidirect
14. C₂×#188035	C₂	semidirect
15. #72225610	C₂	semidirect
21. #7641845	C₂²	semidirect
24. C₂×#34980	C₂²	semidirect
26. #6453039	C₂²	semidirect
27. #6451874	C₂²	semidirect
28. #6440460	C₂²	semidirect
29. #6437621	C₂²	semidirect
32. C₂×#21746	C₂²	semidirect
33. C₂×#21746	C₂²	semidirect
34. C₂²×#1898	C₂²	semidirect
35. C₂²×#1781	C₂²	semidirect
36. #618455	C₂²	semidirect
37. #618316	C₂²	semidirect
38. #617875	C₂²	semidirect
39. #617710	C₂²	semidirect
40. #617161	C₂²	semidirect
41. #616960	C₂²	semidirect
43. C₂×#13867	C₂²	semidirect
44. #359921	C₂²	semidirect
45. #359811	C₂²	semidirect
46. #359705	C₂²	semidirect
47. #359442	C₂²	semidirect
48. C₂×#10735	C₂²	semidirect
49. #233542	C₂²	semidirect
50. #233542	C₂²	semidirect
51. #233541	C₂²	semidirect
52. #233541	C₂²	semidirect
53. C₂×#8546	C₂²	semidirect
54. C₂×#8542	C₂²	semidirect
55. C₂×#8541	C₂²	semidirect
56. #187945	C₂²	semidirect
57. #187944	C₂²	semidirect
58. #187944	C₂²	semidirect
59. C₂×#8101	C₂²	semidirect
60. #115204	C₂²	semidirect
61. #115204	C₂²	semidirect
62. #115204	C₂²	semidirect
63. #115204	C₂²	semidirect
64. #107115	C₂²	semidirect
65. #107114	C₂²	semidirect
66. #107114	C₂²	semidirect
67. C₂⁵×D₄	D₄	semidirect
69. C₂×#3490	D₄	semidirect
71. C₂×#3484	D₄	semidirect
75. C₂³×#121	D₄	semidirect
77. C₂³×#120	D₄	semidirect
82. C₂³×C₄×D₄	D₄	semidirect
85. #34980	D₄	semidirect
89. C₂×#2412	D₄	semidirect
90. C₂×#2405	D₄	semidirect
93. C₂×#2410	D₄	semidirect
94. C₂×#2403	D₄	semidirect
97. #34198	D₄	semidirect
107. #21746	D₄	semidirect
120. #14657	D₄	semidirect
124. #14134	D₄	semidirect
147. C₂⁴×D₄	C₂×D₄	semidirect
157. C₂²×#123	C₂×D₄	semidirect
166. C₂²×#120	C₂×D₄	semidirect
180. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
181. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
182. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
194. C₂×#386	C₂×D₄	semidirect
195. C₂×#385	C₂×D₄	semidirect
196. C₂×#381	C₂×D₄	semidirect
200. C₂×#379	C₂×D₄	semidirect
201. C₂×#379	C₂×D₄	semidirect
202. C₂×#379	C₂×D₄	semidirect
209. #1819	C₂×D₄	semidirect
210. #1781	C₂×D₄	semidirect
211. #1440	C₂×D₄	semidirect
212. #1438	C₂×D₄	semidirect
213. #1438	C₂×D₄	semidirect
216. C₂⁶	#120	semidirect
239. C₂³×D₄	#120	semidirect
240. C₂³×D₄	#120	semidirect
254. C₂⁴×C₄	#120	semidirect
255. C₂⁴×C₄	#120	semidirect
271. C₂²×C₂²⋊C₄	#120	semidirect
272. C₂²×C₂²⋊C₄	#120	semidirect
273. C₂²×C₂²⋊C₄	#120	semidirect
288. #379	#120	semidirect
289. #379	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262671	2
#72262662	2
#72262540	2
#72256331	2
#72256222	2
#72255822	2
#72237618	2
#72237372	2
C₂×#115204	2
#72236431	2
#72235924	2
#72234675	2
#72232592	2
C₂×#188035	2
#72225610	2