Subgroups — #72262702

Order 2048.

At least 6252 conjugacy classes of subgroups; only the 1660 normal subgroups are shown.

The subgroup lattice has 419 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262701	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262637	C₂	1	1	yes	maximal, characteristic, complemented
3	#72256222	C₂	1	4	yes	maximal, complemented
4	C₂×#233541	C₂	1	4	yes	maximal, complemented
5	#72235924	C₂	1	8	yes	maximal, complemented
6	#72234675	C₂	1	1	yes	maximal, characteristic, complemented
7	#72234668	C₂	1	1	yes	maximal, characteristic, complemented
8	#72234625	C₂	1	1	yes	maximal, characteristic, complemented
9	#72225801	C₂	1	4	yes	maximal, complemented
10	C₂×#188035	C₂	1	1	yes	maximal, characteristic, complemented
11	#72225665	C₂	1	1	yes	maximal, characteristic, complemented
12	#72225610	C₂	1	4	yes	maximal, complemented
13	C₂×#62817	C₂²	1	1	yes	characteristic
14	C₂³×D₄²	C₂²	1	1	yes	characteristic
15	#7643002	C₂²	1	2	yes	complemented
16	#7642350	C₂²	1	4	yes	complemented
17	#7642244	C₂²	1	2	yes	complemented
18	C₂×#34980	C₂²	1	4	yes	—
19	C₂×#34980	C₂²	1	1	yes	characteristic
20	C₂×#34980	C₂²	1	2	yes	complemented
21	C₂²×#2403	C₂²	1	2	yes	complemented
22	#7626202	C₂²	1	1	yes	characteristic
23	#6451874	C₂²	1	4	yes	complemented
24	#6437621	C₂²	1	4	yes	complemented
25	C₂×#21746	C₂²	1	1	yes	characteristic
26	C₂×#21746	C₂²	1	1	yes	characteristic
27	C₂×#21746	C₂²	1	2	yes	complemented
28	C₂×#21746	C₂²	1	4	yes	complemented
29	C₂²×#1781	C₂²	1	2	yes	complemented
30	C₂²×#1781	C₂²	1	4	yes	complemented
31	#618316	C₂²	1	4	yes	complemented
32	#617710	C₂²	1	2	yes	complemented
33	#616960	C₂²	1	2	yes	complemented
34	#556752	C₂²	1	1	yes	characteristic
35	#517411	C₂²	1	2	yes	complemented
36	#359705	C₂²	1	4	yes	complemented
37	#359442	C₂²	1	4	yes	complemented
38	#355913	C₂²	1	2	yes	complemented
39	#233541	C₂²	1	16	yes	complemented
40	#233541	C₂²	1	16	yes	complemented
41	C₂×#8546	C₂²	1	2	yes	complemented
42	C₂×#8542	C₂²	1	4	yes	complemented
43	C₂×#8541	C₂²	1	2	yes	complemented
44	#187945	C₂²	1	4	yes	complemented
45	#187944	C₂²	1	4	yes	complemented
46	C₂×#8101	C₂²	1	4	yes	complemented
47	#115204	C₂²	1	16	yes	complemented
48	#115204	C₂²	1	16	yes	complemented
49	#107115	C₂²	1	4	yes	complemented
50	#107114	C₂²	1	4	yes	complemented
51	C₂⁵×D₄	D₄	1	2	yes	complemented
52	C₂⁵×D₄	C₂³	1	2	yes	—
53	C₂⁵×D₄	C₂³	1	1	yes	characteristic
54	C₂×#3490	D₄	1	4	yes	complemented
55	C₂×#3490	C₂³	1	2	yes	—
56	C₂×#3484	D₄	1	4	yes	complemented
57	C₂×#3484	C₂³	1	2	yes	—
58	C₂²×#534	C₂³	1	2	yes	—
59	C₂³×#127	C₂³	1	1	yes	characteristic
60	C₂³×#121	D₄	1	2	yes	complemented
61	C₂³×#121	C₂³	1	2	yes	—
62	C₂³×#120	D₄	1	2	yes	complemented
63	C₂³×#120	C₂³	1	2	yes	—
64	C₂³×#120	C₂³	1	1	yes	characteristic
65	C₂³×#120	C₂³	1	1	yes	characteristic
66	C₂³×C₄×D₄	D₄	1	2	yes	complemented
67	C₂×#2849	D₄	1	2	yes	complemented
68	C₂×#2846	D₄	1	2	yes	complemented
69	#34980	D₄	1	16	yes	complemented
70	#34980	C₂³	1	8	yes	—
71	#34980	C₂³	1	8	yes	—
72	#34980	C₂³	1	8	yes	—
73	C₂×#2405	D₄	1	8	yes	complemented
74	C₂×#2403	D₄	1	8	yes	complemented
75	C₂×#2403	C₂³	1	4	yes	—
76	C₂×#2403	C₂³	1	4	yes	—
77	C₂×#2613	D₄	1	4	yes	complemented
78	#34198	D₄	1	8	yes	complemented
79	#34176	C₂³	1	2	yes	—
80	#34171	C₂³	1	2	yes	—
81	C₂×#2308	C₂³	1	2	yes	—
82	C₂²×#379	C₂³	1	2	yes	—
83	C₂²×#379	C₂³	1	2	yes	—
84	C₂²×#379	C₂³	1	2	yes	—
85	C₂²×#379	C₂³	1	2	yes	—
86	C₂²×#379	C₂³	1	1	yes	characteristic
87	#21746	D₄	1	8	yes	complemented
88	#21746	C₂³	1	16	yes	—
89	C₂×#1898	C₂³	1	8	yes	—
90	C₂×#1819	C₂³	1	2	yes	—
91	C₂×#1819	C₂³	1	2	yes	—
92	C₂×#1781	C₂³	1	2	yes	—
93	C₂×#1781	C₂³	1	8	yes	—
94	C₂×#1781	C₂³	1	2	yes	—
95	C₂×#1781	C₂³	1	8	yes	—
96	C₂×#1781	C₂³	1	8	yes	—
97	#14341	C₂³	1	2	yes	—
98	#14335	C₂³	1	2	yes	—
99	#14255	D₄	1	8	yes	complemented
100	#13867	C₂³	1	4	yes	—
101	#13867	C₂³	1	4	yes	—
102	#10735	C₂³	1	8	yes	—
103	#8101	C₂³	1	16	yes	—
104	C₂⁷	C₂×D₄	1	2	yes	—
105	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
106	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
107	C₂⁷	C₂⁴	1	1	yes	characteristic
108	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
109	C₂⁴×D₄	C₂×D₄	1	8	yes	—
110	C₂⁴×D₄	C₂×D₄	1	8	yes	—
111	C₂⁴×D₄	C₂×D₄	1	4	yes	—
112	C₂⁴×D₄	C₂×D₄	1	2	yes	—
113	C₂⁴×D₄	C₂×D₄	1	2	yes	—
114	C₂⁴×D₄	C₂×D₄	1	2	yes	—
115	C₂⁴×D₄	C₂×D₄	1	2	yes	—
116	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
117	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
118	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
120	C₂⁴×D₄	C₂⁴	1	2	yes	—
121	C₂⁴×D₄	C₂⁴	1	2	yes	—
122	C₂⁴×D₄	C₂⁴	1	2	yes	—
123	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
124	C₂⁵×C₄	C₂×D₄	1	2	yes	—
125	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
126	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
127	C₂×#543	C₂×D₄	1	2	yes	complemented
128	C₂×#534	C₂×D₄	1	2	yes	complemented
129	C₂×#534	C₂×D₄	1	4	yes	complemented
130	C₂²×#123	C₂×D₄	1	4	yes	complemented
131	C₂²×#120	C₂×D₄	1	2	yes	—
132	C₂²×#120	C₂×D₄	1	4	yes	—
133	C₂²×#120	C₂×D₄	1	2	yes	—
134	C₂²×#120	C₂×D₄	1	4	yes	—
135	C₂²×#120	C₂×D₄	1	4	yes	—
136	C₂²×#120	C₂×D₄	1	4	yes	—
137	C₂²×#120	C₂×D₄	1	8	yes	—
138	C₂²×#120	C₂×D₄	1	4	yes	—
139	C₂²×#120	C₂×D₄	1	4	yes	complemented
140	C₂²×#120	#41	1	4	yes	—
141	C₂²×#120	C₂⁴	1	4	yes	—
142	C₂×#518	C₂×D₄	1	2	yes	complemented
143	C₂×#518	C₂×D₄	1	4	yes	complemented
144	C₂×#518	C₂×D₄	1	4	yes	complemented
145	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
146	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
147	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
148	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
149	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
150	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
151	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
152	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
153	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
154	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
155	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
156	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
157	#2405	C₂×D₄	1	16	yes	complemented
158	#2405	C₂×D₄	1	16	yes	complemented
159	#2403	C₂×D₄	1	16	yes	complemented
160	#2403	C₂×D₄	1	16	yes	complemented
161	#2315	C₂×D₄	1	4	yes	complemented
162	#2308	C₂×D₄	1	4	yes	complemented
163	C₂×#381	C₂×D₄	1	4	yes	complemented
164	C₂×#379	C₂×D₄	1	8	yes	—
165	C₂×#379	C₂×D₄	1	8	yes	—
166	C₂×#379	C₂×D₄	1	4	yes	—
167	C₂×#379	C₂×D₄	1	4	yes	complemented
168	C₂×#379	C₂×D₄	1	4	yes	complemented
169	C₂×#379	C₂×D₄	1	2	yes	complemented
170	C₂×#379	C₂×D₄	1	4	yes	complemented
171	C₂×#379	C₂×D₄	1	4	yes	complemented
172	C₂×#379	C₂×D₄	1	2	yes	complemented
173	C₂×#379	C₂⁴	1	4	yes	—
174	C₂×#379	C₂⁴	1	4	yes	—
175	C₂×#379	C₂⁴	1	4	yes	—
176	C₂×#379	C₂⁴	1	4	yes	—
177	#2273	C₂×D₄	1	4	yes	complemented
178	#1819	C₂×D₄	1	8	yes	complemented
179	#1781	C₂×D₄	1	8	yes	complemented
180	#1440	C₂×D₄	1	8	yes	complemented
181	#1438	C₂×D₄	1	8	yes	complemented
182	C₂⁶	#120	1	4	yes	—
183	C₂⁶	#120	1	4	yes	—
184	C₂⁶	#120	1	2	yes	complemented
185	C₂⁶	C₂²×D₄	1	2	yes	—
186	C₂⁶	C₂²×D₄	1	2	yes	—
187	C₂⁶	C₂²×D₄	1	2	yes	—
188	C₂⁶	C₂²×D₄	1	1	yes	characteristic
189	C₂⁶	C₂²×D₄	1	2	yes	—
190	C₂⁶	C₂²×D₄	1	1	yes	characteristic
191	C₂⁶	C₂²×D₄	1	2	yes	—
192	C₂⁶	C₂²×D₄	1	2	yes	—
193	C₂⁶	C₂²×D₄	1	4	yes	—
194	C₂⁶	C₂²×D₄	1	2	yes	—
195	C₂⁶	C₂²×D₄	1	4	yes	—
196	C₂⁶	C₂²×D₄	1	1	yes	characteristic
197	C₂⁶	C₂²×D₄	1	2	yes	—
198	C₂⁶	C₂×#41	1	2	yes	—
199	C₂⁶	H(5,𝔽₂)	1	4	yes	—
200	C₂⁶	H(5,𝔽₂)	1	4	yes	—
201	C₂⁶	C₂⁵	1	1	yes	characteristic
202	C₂³×D₄	#120	1	8	yes	—
203	C₂³×D₄	#120	1	8	yes	—
204	C₂³×D₄	#120	1	4	yes	—
205	C₂³×D₄	#120	1	8	yes	—
206	C₂³×D₄	#120	1	4	yes	—
207	C₂³×D₄	#120	1	4	yes	complemented
208	C₂³×D₄	#120	1	8	yes	complemented
209	C₂³×D₄	#121	1	8	yes	—
210	C₂³×D₄	C₂²×D₄	1	4	yes	—
211	C₂³×D₄	C₂²×D₄	1	8	yes	—
212	C₂³×D₄	C₂²×D₄	1	8	yes	—
213	C₂³×D₄	C₂²×D₄	1	8	yes	—
214	C₂³×D₄	C₂²×D₄	1	2	yes	—
215	C₂³×D₄	C₂²×D₄	1	2	yes	—
216	C₂³×D₄	C₂²×D₄	1	2	yes	—
217	C₂³×D₄	C₂²×D₄	1	2	yes	—
218	C₂³×D₄	C₂²×D₄	1	2	yes	—
219	C₂³×D₄	C₂×#41	1	2	yes	—
220	C₂⁴×C₄	#120	1	4	yes	—
221	C₂⁴×C₄	#120	1	4	yes	—
222	C₂⁴×C₄	#120	1	4	yes	complemented
223	C₂⁴×C₄	#120	1	2	yes	complemented
224	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
225	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
226	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
227	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
229	C₂×#120	#120	1	8	yes	—
230	C₂×#120	#120	1	8	yes	—
231	C₂×#120	#121	1	8	yes	—
232	C₂×#120	#121	1	8	yes	—
233	C₂×#120	#121	1	16	yes	—
234	C₂×#120	#127	1	16	yes	—
235	C₂²×C₂²⋊C₄	#120	1	8	yes	—
236	C₂²×C₂²⋊C₄	#120	1	4	yes	—
237	C₂²×C₂²⋊C₄	#120	1	4	yes	—
238	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
239	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
240	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
241	C₂²×C₂²⋊C₄	#121	1	8	yes	—
242	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
243	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
244	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
246	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
247	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
249	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
250	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
251	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
252	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
253	#379	#120	1	8	yes	complemented
254	#379	#120	1	8	yes	complemented
255	#379	C₂²×D₄	1	8	yes	—
256	#379	C₂²×D₄	1	16	yes	—
257	C₂⁵	C₂×#120	1	2	yes	—
258	C₂⁵	C₂×#120	1	2	yes	—
259	C₂⁵	C₂×#120	1	4	yes	—
260	C₂⁵	C₂×#120	1	2	yes	—
261	C₂⁵	C₂×#120	1	4	yes	—
262	C₂⁵	C₂×#120	1	4	yes	—
263	C₂⁵	C₂×#120	1	4	yes	—
264	C₂⁵	C₂×#120	1	2	yes	—
265	C₂⁵	C₂×#120	1	2	yes	—
266	C₂⁵	C₂×#120	1	4	yes	—
267	C₂⁵	C₂×#120	1	2	yes	—
268	C₂⁵	C₂×#120	1	2	yes	—
269	C₂⁵	C₂×#120	1	2	yes	—
270	C₂⁵	C₂×#120	1	4	yes	—
271	C₂⁵	C₂×#120	1	2	yes	—
272	C₂⁵	C₂×#120	1	4	yes	—
273	C₂⁵	C₂×#120	1	2	yes	—
274	C₂⁵	C₂×#120	1	2	yes	—
275	C₂⁵	C₂×#120	1	2	yes	—
276	C₂⁵	C₂×#121	1	2	yes	—
277	C₂⁵	C₂×#121	1	2	yes	—
278	C₂⁵	C₂×#121	1	4	yes	—
279	C₂⁵	C₂×#121	1	4	yes	—
280	C₂⁵	C₂×#121	1	2	yes	—
281	C₂⁵	C₂×#127	1	4	yes	—
282	C₂⁵	#534	1	2	yes	—
283	C₂⁵	#534	1	2	yes	—
284	C₂⁵	#534	1	4	yes	—
285	C₂⁵	#534	1	4	yes	—
286	C₂⁵	#534	1	2	yes	—
287	C₂⁵	#534	1	2	yes	—
288	C₂⁵	#535	1	2	yes	—
289	C₂⁵	#535	1	4	yes	—
290	C₂⁵	#535	1	2	yes	—
291	C₂⁵	D₄²	1	4	yes	—
292	C₂⁵	D₄²	1	4	yes	—
293	C₂⁵	D₄²	1	4	yes	—
294	C₂⁵	D₄²	1	4	yes	—
295	C₂⁵	D₄²	1	4	yes	—
296	C₂⁵	D₄²	1	4	yes	—
297	C₂⁵	D₄²	1	4	yes	—
298	C₂⁵	D₄²	1	4	yes	—
299	C₂⁵	D₄²	1	4	yes	—
300	C₂⁵	D₄²	1	4	yes	—
301	C₂⁵	D₄²	1	4	yes	—
302	C₂⁵	D₄²	1	4	yes	—
303	C₂⁵	#546	1	4	yes	—
304	C₂⁵	#546	1	4	yes	—
305	C₂⁵	#546	1	4	yes	—
306	C₂⁵	#546	1	4	yes	—
307	C₂⁵	C₂³×D₄	1	1	yes	characteristic
308	C₂⁵	C₂³×D₄	1	1	yes	characteristic
309	C₂⁵	C₂³×D₄	1	1	yes	characteristic
310	C₂⁵	C₂³×D₄	1	1	yes	characteristic
311	C₂⁵	C₂³×D₄	1	1	yes	characteristic
312	C₂⁵	C₂³×D₄	1	4	yes	—
313	C₂⁵	C₂³×D₄	1	1	yes	characteristic
314	C₂⁵	C₂²×#41	1	1	yes	characteristic
315	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
316	C₂²×D₄	#392	1	16	yes	—
317	C₂²×D₄	#392	1	16	yes	—
318	C₂²×D₄	C₂×#120	1	4	yes	—
319	C₂²×D₄	C₂×#121	1	4	yes	—
320	C₂²×D₄	C₂×#121	1	4	yes	—
321	C₂²×D₄	C₂×#127	1	4	yes	—
322	C₂³×C₄	C₂×#120	1	2	yes	—
323	C₂³×C₄	C₂×#120	1	4	yes	—
324	C₂³×C₄	C₂×#120	1	4	yes	—
325	C₂³×C₄	C₂×#120	1	4	yes	—
326	C₂³×C₄	C₂×#120	1	8	yes	—
327	C₂³×C₄	C₂×#120	1	2	yes	—
328	C₂³×C₄	C₂×#120	1	4	yes	—
329	C₂³×C₄	C₂×#120	1	4	yes	—
330	C₂³×C₄	C₂×#121	1	2	yes	—
331	C₂³×C₄	C₂×#121	1	4	yes	—
332	C₂×C₂²⋊C₄	#392	1	16	yes	—
333	C₂×C₂²⋊C₄	#392	1	16	yes	—
334	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
335	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
336	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂×#127	1	4	yes	—
339	C₂⁴	C₂×#392	1	4	yes	—
340	C₂⁴	C₂×#392	1	4	yes	—
341	C₂⁴	C₂×#392	1	4	yes	—
342	C₂⁴	#2403	1	4	yes	—
343	C₂⁴	#2403	1	2	yes	—
344	C₂⁴	#2403	1	2	yes	—
345	C₂⁴	#2403	1	4	yes	—
346	C₂⁴	#2403	1	4	yes	—
347	C₂⁴	#2403	1	2	yes	—
348	C₂⁴	#2403	1	2	yes	—
349	C₂⁴	#2403	1	4	yes	—
350	C₂⁴	#2403	1	2	yes	—
351	C₂⁴	#2403	1	2	yes	—
352	C₂⁴	#2403	1	2	yes	—
353	C₂⁴	#2403	1	2	yes	—
354	C₂⁴	#2408	1	2	yes	—
355	C₂⁴	#2408	1	4	yes	—
356	C₂⁴	#2408	1	2	yes	—
357	C₂⁴	#2408	1	4	yes	—
358	C₂⁴	#2408	1	2	yes	—
359	C₂⁴	#2408	1	2	yes	—
360	C₂⁴	#2410	1	4	yes	—
361	C₂⁴	#2410	1	4	yes	—
362	C₂⁴	#2410	1	4	yes	—
363	C₂⁴	#2410	1	4	yes	—
364	C₂⁴	#2410	1	4	yes	—
365	C₂⁴	#2410	1	4	yes	—
366	C₂⁴	#2410	1	4	yes	—
367	C₂⁴	#2410	1	4	yes	—
368	C₂⁴	#2433	1	4	yes	—
369	C₂⁴	#2433	1	4	yes	—
370	C₂⁴	#2433	1	4	yes	—
371	C₂⁴	#2433	1	4	yes	—
372	C₂⁴	#2613	1	4	yes	—
373	C₂⁴	#2613	1	4	yes	—
374	C₂⁴	#2846	1	4	yes	—
375	C₂⁴	#2846	1	4	yes	—
376	C₂⁴	C₂²×#120	1	1	yes	characteristic
377	C₂⁴	C₂²×#120	1	2	yes	—
378	C₂⁴	C₂²×#120	1	2	yes	—
379	C₂⁴	C₂²×#120	1	2	yes	—
380	C₂⁴	C₂²×#120	1	1	yes	characteristic
381	C₂⁴	C₂²×#120	1	1	yes	characteristic
382	C₂⁴	C₂²×#121	1	1	yes	characteristic
383	C₂⁴	C₂²×#121	1	1	yes	characteristic
384	C₂⁴	C₂²×#121	1	1	yes	characteristic
385	C₂⁴	C₂²×#127	1	1	yes	characteristic
386	C₂⁴	C₂×#534	1	2	yes	—
387	C₂⁴	C₂×#534	1	2	yes	—
388	C₂⁴	C₂×#535	1	2	yes	—
389	C₂⁴	C₂×D₄²	1	4	yes	—
390	C₂⁴	C₂×D₄²	1	4	yes	—
391	C₂⁴	C₂×D₄²	1	4	yes	—
392	C₂⁴	C₂×#546	1	4	yes	—
393	C₂²×C₄	C₂×#392	1	4	yes	—
394	C₂²×C₄	C₂×#392	1	8	yes	—
395	C₂³	#14715	1	4	yes	—
396	C₂³	#14715	1	4	yes	—
397	C₂³	#14715	1	4	yes	—
398	C₂³	#14715	1	4	yes	—
399	C₂³	#23895	1	8	yes	—
400	C₂³	C₂²×#392	1	1	yes	characteristic
401	C₂³	C₂×#2613	1	1	yes	characteristic
402	C₂³	C₂×#2403	1	2	yes	—
403	C₂³	C₂×#2403	1	2	yes	—
404	C₂³	C₂×#2410	1	2	yes	—
405	C₂³	C₂×#2410	1	2	yes	—
406	C₂³	C₂×#2408	1	2	yes	—
407	C₂³	C₂×#2433	1	2	yes	—
408	C₂³	C₂×#2846	1	1	yes	characteristic
409	C₂³	#60399	1	4	yes	—
410	C₂²	#394064	1	8	yes	—
411	C₂²	C₂×#14715	1	1	yes	characteristic
412	C₂²	#6431795	1	2	yes	—
413	C₂²	#6432953	1	2	yes	—
414	C₂²	C₂×#23895	1	4	yes	—
415	C₂²	#6628896	1	2	yes	—
416	C₂	C₂×#394064	1	2	yes	—
417	C₂	#72251605	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. #72262701	C₂	semidirect
2. #72262637	C₂	semidirect
3. #72256222	C₂	semidirect
4. C₂×#233541	C₂	semidirect
5. #72235924	C₂	semidirect
6. #72234675	C₂	semidirect
7. #72234668	C₂	semidirect
8. #72234625	C₂	semidirect
9. #72225801	C₂	semidirect
10. C₂×#188035	C₂	semidirect
11. #72225665	C₂	semidirect
12. #72225610	C₂	semidirect
15. #7643002	C₂²	semidirect
16. #7642350	C₂²	semidirect
17. #7642244	C₂²	semidirect
20. C₂×#34980	C₂²	semidirect
21. C₂²×#2403	C₂²	semidirect
23. #6451874	C₂²	semidirect
24. #6437621	C₂²	semidirect
27. C₂×#21746	C₂²	semidirect
28. C₂×#21746	C₂²	semidirect
29. C₂²×#1781	C₂²	semidirect
30. C₂²×#1781	C₂²	semidirect
31. #618316	C₂²	semidirect
32. #617710	C₂²	semidirect
33. #616960	C₂²	semidirect
35. #517411	C₂²	semidirect
36. #359705	C₂²	semidirect
37. #359442	C₂²	semidirect
38. #355913	C₂²	semidirect
39. #233541	C₂²	semidirect
40. #233541	C₂²	semidirect
41. C₂×#8546	C₂²	semidirect
42. C₂×#8542	C₂²	semidirect
43. C₂×#8541	C₂²	semidirect
44. #187945	C₂²	semidirect
45. #187944	C₂²	semidirect
46. C₂×#8101	C₂²	semidirect
47. #115204	C₂²	semidirect
48. #115204	C₂²	semidirect
49. #107115	C₂²	semidirect
50. #107114	C₂²	semidirect
51. C₂⁵×D₄	D₄	semidirect
54. C₂×#3490	D₄	semidirect
56. C₂×#3484	D₄	semidirect
60. C₂³×#121	D₄	semidirect
62. C₂³×#120	D₄	semidirect
66. C₂³×C₄×D₄	D₄	semidirect
67. C₂×#2849	D₄	semidirect
68. C₂×#2846	D₄	semidirect
69. #34980	D₄	semidirect
73. C₂×#2405	D₄	semidirect
74. C₂×#2403	D₄	semidirect
77. C₂×#2613	D₄	semidirect
78. #34198	D₄	semidirect
87. #21746	D₄	semidirect
99. #14255	D₄	semidirect
105. C₂⁷	C₂×D₄	semidirect
106. C₂⁷	C₂×D₄	semidirect
108. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
116. C₂⁴×D₄	C₂×D₄	semidirect
117. C₂⁴×D₄	C₂×D₄	semidirect
118. C₂⁴×D₄	C₂×D₄	semidirect
119. C₂⁴×D₄	C₂×D₄	semidirect
125. C₂⁵×C₄	C₂×D₄	semidirect
126. C₂⁵×C₄	C₂×D₄	semidirect
127. C₂×#543	C₂×D₄	semidirect
128. C₂×#534	C₂×D₄	semidirect
129. C₂×#534	C₂×D₄	semidirect
130. C₂²×#123	C₂×D₄	semidirect
139. C₂²×#120	C₂×D₄	semidirect
142. C₂×#518	C₂×D₄	semidirect
143. C₂×#518	C₂×D₄	semidirect
144. C₂×#518	C₂×D₄	semidirect
145. C₂³×C₄⋊C₄	C₂×D₄	semidirect
150. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
151. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
152. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
153. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
156. C₂³×C₄²	C₂×D₄	semidirect
157. #2405	C₂×D₄	semidirect
158. #2405	C₂×D₄	semidirect
159. #2403	C₂×D₄	semidirect
160. #2403	C₂×D₄	semidirect
161. #2315	C₂×D₄	semidirect
162. #2308	C₂×D₄	semidirect
163. C₂×#381	C₂×D₄	semidirect
167. C₂×#379	C₂×D₄	semidirect
168. C₂×#379	C₂×D₄	semidirect
169. C₂×#379	C₂×D₄	semidirect
170. C₂×#379	C₂×D₄	semidirect
171. C₂×#379	C₂×D₄	semidirect
172. C₂×#379	C₂×D₄	semidirect
177. #2273	C₂×D₄	semidirect
178. #1819	C₂×D₄	semidirect
179. #1781	C₂×D₄	semidirect
180. #1440	C₂×D₄	semidirect
181. #1438	C₂×D₄	semidirect
184. C₂⁶	#120	semidirect
207. C₂³×D₄	#120	semidirect
208. C₂³×D₄	#120	semidirect
222. C₂⁴×C₄	#120	semidirect
223. C₂⁴×C₄	#120	semidirect
238. C₂²×C₂²⋊C₄	#120	semidirect
239. C₂²×C₂²⋊C₄	#120	semidirect
240. C₂²×C₂²⋊C₄	#120	semidirect
253. #379	#120	semidirect
254. #379	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262701	2
#72262637	2
#72256222	2
C₂×#233541	2
#72235924	2
#72234675	2
#72234668	2
#72234625	2
#72225801	2
C₂×#188035	2
#72225665	2
#72225610	2