Subgroups — #72259009

Order 2048.

Only the 2208 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 382 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72259004	C₂	1	1	yes	maximal, characteristic, complemented
2	#72258984	C₂	1	4	yes	maximal, complemented
3	#72258980	C₂	1	2	yes	maximal, complemented
4	#72258957	C₂	1	4	yes	maximal, complemented
5	C₂×#6628900	C₂	1	2	yes	maximal, complemented
6	#72240552	C₂	1	4	yes	maximal, complemented
7	C₂×#449469	C₂	1	4	yes	maximal, complemented
8	C₂²×#23895	C₂	1	2	yes	maximal, complemented
9	C₂²×#60399	C₂	1	1	yes	maximal, characteristic, complemented
10	#72225808	C₂	1	1	yes	maximal, characteristic, complemented
11	#72225659	C₂	1	4	yes	maximal, complemented
12	#72225622	C₂	1	2	yes	maximal, complemented
13	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
14	C₂²×#3484	C₂²	1	2	yes	—
15	C₂²×#3484	C₂²	1	1	yes	characteristic
16	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3026	C₂²	1	4	yes	—
18	C₂²×#3026	C₂²	1	4	yes	—
19	C₂²×#3026	C₂²	1	4	yes	complemented
20	C₂²×#3026	C₂²	1	4	yes	complemented
21	C₂³×B(4,𝔽₂)	C₂²	1	4	yes	complemented
22	C₂²×#2883	C₂²	1	2	yes	complemented
23	C₂²×#2883	C₂²	1	1	yes	characteristic, complemented
24	C₂×#35347	C₂²	1	2	yes	—
25	C₂×#35347	C₂²	1	4	yes	complemented
26	C₂×#35347	C₂²	1	2	yes	complemented
27	C₂²×#2021	C₂²	1	8	yes	complemented
28	C₂²×#1913	C₂²	1	4	yes	complemented
29	C₂²×#1913	C₂²	1	4	yes	complemented
30	C₂²×#1790	C₂²	1	4	yes	complemented
31	C₂²×#1790	C₂²	1	4	yes	complemented
32	C₂×#20585	C₂²	1	2	yes	complemented
33	C₂×#20585	C₂²	1	4	yes	complemented
34	C₂²×#1781	C₂²	1	2	yes	complemented
35	#5955303	C₂²	1	2	yes	complemented
36	C₂×#14716	C₂²	1	2	yes	complemented
37	#515529	C₂²	1	2	yes	complemented
38	#515529	C₂²	1	2	yes	complemented
39	C₂×#13867	C₂²	1	1	yes	characteristic, complemented
40	C₂×#10991	C₂²	1	4	yes	complemented
41	C₂×#10995	C₂²	1	8	yes	complemented
42	C₂×#10995	C₂²	1	8	yes	complemented
43	C₂×#10980	C₂²	1	4	yes	complemented
44	C₂×#10972	C₂²	1	8	yes	complemented
45	C₂×#10972	C₂²	1	4	yes	complemented
46	C₂×#10972	C₂²	1	4	yes	complemented
47	C₂×#10965	C₂²	1	4	yes	complemented
48	C₂×#10745	C₂²	1	4	yes	complemented
49	C₂×#10768	C₂²	1	2	yes	complemented
50	#154195	C₂²	1	4	yes	complemented
51	#123590	C₂²	1	4	yes	complemented
52	#123574	C₂²	1	8	yes	complemented
53	#123527	C₂²	1	4	yes	complemented
54	#123520	C₂²	1	8	yes	complemented
55	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
56	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
57	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
58	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
59	C₂⁵×D₄	C₂³	1	1	yes	characteristic
60	C₂×#3484	D₄	1	16	yes	complemented
61	C₂²×#535	D₄	1	2	yes	complemented
62	C₂²×#534	D₄	1	2	yes	complemented
63	C₂²×#534	C₂³	1	2	yes	—
64	C₂²×#534	C₂³	1	2	yes	—
65	C₂²×#534	C₂³	1	2	yes	—
66	C₂²×#534	C₂³	1	4	yes	—
67	C₂²×#534	C₂³	1	8	yes	—
68	C₂²×#525	D₄	1	2	yes	complemented
69	C₂³×#121	C₂³	1	2	yes	—
70	C₂³×#120	D₄	1	2	yes	complemented
71	C₂³×#120	C₂³	1	4	yes	—
72	C₂³×#120	C₂³	1	2	yes	—
73	C₂³×#120	C₂³	1	2	yes	complemented
74	C₂²×#518	C₂³	1	1	yes	characteristic
75	C₂²×#518	C₂³	1	2	yes	—
76	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
77	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
78	C₂×#3026	D₄	1	32	yes	complemented
79	C₂×#3026	D₄	1	32	yes	complemented
80	C₂³×#99	C₂³	1	4	yes	—
81	C₂³×#99	C₂³	1	4	yes	—
82	C₂³×#99	C₂³	1	8	yes	—
83	C₂³×#99	C₂³	1	8	yes	—
84	C₂³×#99	C₂³	1	8	yes	—
85	C₂³×#99	C₂³	1	4	yes	—
86	C₂³×#99	C₂³	1	8	yes	complemented
87	C₂³×#99	C₂³	1	4	yes	complemented
88	C₂×#2406	D₄	1	4	yes	complemented
89	C₂×#2404	D₄	1	4	yes	complemented
90	C₂×#2405	D₄	1	4	yes	complemented
91	C₂×#2403	D₄	1	4	yes	complemented
92	C₂×#2308	C₂³	1	4	yes	—
93	C₂×#2308	C₂³	1	2	yes	—
94	C₂×#2308	C₂³	1	2	yes	complemented
95	C₂²×#386	C₂³	1	8	yes	—
96	C₂²×#386	C₂³	1	2	yes	—
97	C₂²×#386	C₂³	1	2	yes	—
98	C₂²×#386	C₂³	1	2	yes	complemented
99	C₂²×#386	C₂³	1	2	yes	complemented
100	C₂²×#379	C₂³	1	1	yes	characteristic, complemented
101	C₂²×#379	C₂³	1	4	yes	complemented
102	C₂²×#342	C₂³	1	8	yes	complemented
103	C₂²×#342	C₂³	1	8	yes	complemented
104	C₂²×#342	C₂³	1	8	yes	complemented
105	#13794	C₂³	1	2	yes	complemented
106	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
107	C₂×C₂²⋊#95	C₂³	1	2	yes	complemented
108	C₂⁷	C₂×D₄	1	1	yes	characteristic
109	C₂⁷	C₂⁴	1	1	yes	characteristic
110	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
111	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
112	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	complemented
113	C₂³×#41	C₂×D₄	1	4	yes	—
114	C₂³×#41	C₂×D₄	1	2	yes	—
115	C₂⁴×D₄	C₂×D₄	1	4	yes	—
116	C₂⁴×D₄	C₂×D₄	1	2	yes	—
117	C₂⁴×D₄	C₂×D₄	1	8	yes	—
118	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
121	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
122	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
123	C₂⁴×D₄	C₂⁴	1	2	yes	—
124	C₂⁴×D₄	C₂⁴	1	2	yes	—
125	C₂⁴×D₄	C₂⁴	1	4	yes	—
126	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
127	C₂⁵×C₄	C₂⁴	1	2	yes	—
128	C₂×#534	C₂×D₄	1	16	yes	—
129	C₂×#534	C₂×D₄	1	16	yes	—
130	C₂×#534	C₂×D₄	1	16	yes	—
131	C₂×#534	C₂×D₄	1	32	yes	—
132	C₂×#534	C₂×D₄	1	32	yes	complemented
133	C₂²×#123	C₂×D₄	1	4	yes	—
134	C₂²×#123	C₂×D₄	1	4	yes	—
135	C₂²×#123	C₂×D₄	1	4	yes	complemented
136	C₂²×#120	C₂×D₄	1	4	yes	—
137	C₂²×#120	C₂×D₄	1	4	yes	—
138	C₂²×#120	C₂×D₄	1	16	yes	—
139	C₂²×#120	C₂×D₄	1	4	yes	—
140	C₂²×#120	C₂×D₄	1	4	yes	—
141	C₂²×#120	C₂×D₄	1	4	yes	complemented
142	C₂×#518	C₂×D₄	1	8	yes	—
143	C₂²×#117	C₂×D₄	1	2	yes	—
144	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
145	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
146	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
147	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
148	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
149	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
150	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
151	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
152	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
153	C₂²×#99	C₂×D₄	1	16	yes	—
154	C₂²×#99	C₂×D₄	1	16	yes	complemented
155	C₂²×#99	C₂×D₄	1	32	yes	complemented
156	C₂²×#99	C₂×D₄	1	32	yes	complemented
157	C₂×#386	C₂×D₄	1	4	yes	—
158	C₂×#386	C₂×D₄	1	4	yes	—
159	C₂×#386	C₂×D₄	1	4	yes	complemented
160	C₂×#386	C₂×D₄	1	4	yes	complemented
161	C₂×#381	C₂×D₄	1	4	yes	complemented
162	C₂×#379	C₂×D₄	1	4	yes	complemented
163	C₂⁶	#120	1	2	yes	—
164	C₂⁶	#120	1	4	yes	complemented
165	C₂⁶	C₂²×D₄	1	1	yes	characteristic
166	C₂⁶	C₂²×D₄	1	1	yes	characteristic
167	C₂⁶	C₂²×D₄	1	2	yes	—
168	C₂⁶	C₂²×D₄	1	1	yes	characteristic
169	C₂⁶	C₂²×D₄	1	4	yes	—
170	C₂⁶	C₂²×D₄	1	1	yes	characteristic
171	C₂⁶	C₂²×D₄	1	2	yes	—
172	C₂⁶	H(5,𝔽₂)	1	4	yes	—
173	C₂⁶	C₂⁵	1	1	yes	characteristic
174	C₂×H(5,𝔽₂)	#120	1	32	yes	complemented
175	C₂³×Q₈	#120	1	2	yes	—
176	C₂³×D₄	#120	1	2	yes	—
177	C₂³×D₄	#120	1	4	yes	—
178	C₂³×D₄	#120	1	4	yes	complemented
179	C₂³×D₄	#120	1	4	yes	complemented
180	C₂³×D₄	C₂²×D₄	1	4	yes	—
181	C₂³×D₄	C₂²×D₄	1	8	yes	—
182	C₂³×D₄	C₂²×D₄	1	4	yes	—
183	C₂³×D₄	C₂²×D₄	1	4	yes	—
184	C₂³×D₄	C₂²×D₄	1	4	yes	—
185	C₂³×D₄	C₂²×D₄	1	4	yes	—
186	C₂³×D₄	C₂²×D₄	1	8	yes	—
187	C₂³×D₄	C₂²×D₄	1	8	yes	—
188	C₂³×D₄	C₂²×D₄	1	8	yes	—
189	C₂³×D₄	C₂²×D₄	1	16	yes	—
190	C₂³×D₄	C₂²×D₄	1	8	yes	—
191	C₂³×D₄	C₂²×D₄	1	16	yes	—
192	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
193	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
194	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
195	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
196	C₂⁴×C₄	#120	1	4	yes	—
197	C₂⁴×C₄	#120	1	2	yes	—
198	C₂⁴×C₄	#120	1	4	yes	complemented
199	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
201	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
202	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
203	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
204	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
205	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
206	#534	#120	1	64	yes	complemented
207	C₂×#123	#120	1	16	yes	complemented
208	C₂×#123	#120	1	16	yes	complemented
209	C₂×#120	#120	1	16	yes	complemented
210	C₂×#120	#120	1	16	yes	complemented
211	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
212	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
213	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
214	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
215	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
216	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
217	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
218	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
219	C₂⁵	C₂×#120	1	4	yes	—
220	C₂⁵	C₂×#120	1	2	yes	—
221	C₂⁵	C₂×#120	1	2	yes	—
222	C₂⁵	C₂×#120	1	2	yes	—
223	C₂⁵	C₂×#120	1	4	yes	—
224	C₂⁵	C₂×#120	1	4	yes	—
225	C₂⁵	C₂×#120	1	2	yes	—
226	C₂⁵	C₂×#120	1	2	yes	—
227	C₂⁵	#534	1	2	yes	—
228	C₂⁵	#534	1	8	yes	—
229	C₂⁵	D₄²	1	8	yes	—
230	C₂⁵	D₄²	1	8	yes	—
231	C₂⁵	D₄²	1	16	yes	—
232	C₂⁵	C₂³×D₄	1	1	yes	characteristic
233	C₂⁵	C₂³×D₄	1	2	yes	—
234	C₂⁵	C₂³×D₄	1	4	yes	—
235	C₂⁵	C₂³×D₄	1	4	yes	—
236	C₂⁵	C₂³×D₄	1	2	yes	—
237	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
239	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
240	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
241	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
242	C₂²×D₄	C₂×#120	1	16	yes	—
243	C₂²×D₄	C₂×#120	1	8	yes	—
244	C₂²×D₄	C₂×#120	1	8	yes	—
245	C₂²×D₄	C₂×#120	1	8	yes	—
246	C₂²×D₄	C₂×#120	1	16	yes	—
247	C₂²×D₄	C₂×#120	1	16	yes	—
248	C₂²×D₄	#534	1	8	yes	—
249	C₂²×D₄	#534	1	8	yes	—
250	C₂²×D₄	#534	1	8	yes	—
251	C₂²×D₄	#534	1	16	yes	—
252	C₂²×D₄	D₄²	1	16	yes	—
253	C₂²×D₄	D₄²	1	16	yes	—
254	C₂²×D₄	D₄²	1	16	yes	—
255	C₂²×D₄	D₄²	1	16	yes	—
256	C₂²×D₄	D₄²	1	32	yes	—
257	C₂²×D₄	D₄²	1	8	yes	—
258	C₂²×D₄	H(3,𝔽₄)	1	8	yes	—
259	C₂³×C₄	C₂×#120	1	4	yes	—
260	C₂³×C₄	C₂×#120	1	2	yes	—
261	C₂³×C₄	C₂×#120	1	2	yes	—
262	C₂³×C₄	C₂×#120	1	2	yes	—
263	C₂³×C₄	C₂×#120	1	4	yes	—
264	C₂³×C₄	C₂×#120	1	4	yes	—
265	C₂³×C₄	#534	1	2	yes	—
266	C₂³×C₄	#534	1	8	yes	—
267	C₂³×C₄	D₄²	1	8	yes	—
268	C₂³×C₄	D₄²	1	8	yes	—
269	C₂³×C₄	D₄²	1	16	yes	—
270	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
271	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
272	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
273	C₂⁴	#2403	1	8	yes	—
274	C₂⁴	#2403	1	8	yes	—
275	C₂⁴	#2403	1	4	yes	—
276	C₂⁴	#2403	1	8	yes	—
277	C₂⁴	#2403	1	16	yes	complemented
278	C₂⁴	#2679	1	8	yes	—
279	C₂⁴	#2846	1	4	yes	—
280	C₂⁴	C₂²×#120	1	1	yes	characteristic
281	C₂⁴	C₂²×#120	1	2	yes	—
282	C₂⁴	C₂²×#120	1	4	yes	—
283	C₂⁴	C₂²×#120	1	2	yes	—
284	C₂⁴	C₂²×#120	1	1	yes	characteristic
285	C₂⁴	C₂²×#120	1	2	yes	—
286	C₂⁴	C₂×#534	1	2	yes	—
287	C₂⁴	C₂×#534	1	4	yes	—
288	C₂⁴	C₂×#534	1	4	yes	—
289	C₂⁴	C₂×#534	1	2	yes	—
290	C₂⁴	C₂×#534	1	1	yes	characteristic
291	C₂⁴	C₂×#534	1	2	yes	—
292	C₂⁴	C₂×D₄²	1	4	yes	—
293	C₂⁴	C₂×D₄²	1	4	yes	—
294	C₂⁴	C₂×D₄²	1	4	yes	—
295	C₂⁴	C₂×D₄²	1	4	yes	—
296	C₂⁴	C₂×D₄²	1	8	yes	—
297	C₂⁴	C₂×D₄²	1	4	yes	—
298	C₂⁴	C₂×D₄²	1	8	yes	—
299	C₂⁴	C₂×D₄²	1	4	yes	—
300	C₂⁴	C₂×D₄²	1	2	yes	—
301	C₂⁴	#3484	1	8	yes	—
302	C₂⁴	#3484	1	8	yes	—
303	C₂⁴	#3484	1	4	yes	—
304	C₂⁴	#3484	1	4	yes	—
305	C₂⁴	#3484	1	2	yes	—
306	C₂⁴	#3484	1	4	yes	—
307	C₂⁴	#3484	1	4	yes	—
308	C₂⁴	#3484	1	2	yes	—
309	C₂⁴	#3484	1	8	yes	—
310	C₂⁴	#3484	1	8	yes	—
311	C₂⁴	#3484	1	8	yes	—
312	C₂⁴	C₂×H(3,𝔽₄)	1	2	yes	—
313	C₂⁴	#3532	1	8	yes	—
314	C₂⁴	#3532	1	8	yes	—
315	C₂⁴	#3532	1	8	yes	—
316	C₂×D₄	#2403	1	32	yes	—
317	C₂×D₄	#2679	1	32	yes	—
318	C₂²×C₄	#2403	1	4	yes	—
319	C₂²×C₄	#2403	1	8	yes	—
320	C₂²×C₄	#2403	1	8	yes	—
321	C₂²×C₄	#2403	1	8	yes	—
322	C₂²×C₄	#2403	1	16	yes	complemented
323	C₂²×C₄	#2679	1	8	yes	—
324	C₂²×C₄	#2846	1	4	yes	—
325	C₂³	#15947	1	8	yes	—
326	C₂³	C₂×#2403	1	1	yes	characteristic
327	C₂³	C₂×#2403	1	2	yes	—
328	C₂³	C₂×#2403	1	2	yes	—
329	C₂³	C₂×#2403	1	4	yes	—
330	C₂³	C₂×#2403	1	2	yes	—
331	C₂³	C₂×#2403	1	4	yes	—
332	C₂³	#34980	1	2	yes	—
333	C₂³	#34980	1	1	yes	characteristic
334	C₂³	#34980	1	2	yes	—
335	C₂³	#34980	1	4	yes	—
336	C₂³	#35346	1	1	yes	characteristic
337	C₂³	#35346	1	4	yes	—
338	C₂³	#35346	1	1	yes	characteristic
339	C₂³	D₄×#120	1	4	yes	—
340	C₂³	D₄×#120	1	4	yes	—
341	C₂³	D₄×#120	1	8	yes	—
342	C₂³	D₄×#120	1	8	yes	—
343	C₂³	D₄×#120	1	4	yes	—
344	C₂³	D₄×#120	1	4	yes	—
345	C₂³	C₂×#2846	1	1	yes	characteristic
346	C₂³	#36714	1	2	yes	—
347	C₂³	#36714	1	4	yes	—
348	C₂³	#37644	1	8	yes	—
349	C₂³	#37644	1	4	yes	—
350	C₂³	#37644	1	8	yes	—
351	C₂³	#37644	1	4	yes	—
352	C₂³	#37644	1	4	yes	—
353	C₂³	#37644	1	8	yes	—
354	C₂³	#37644	1	4	yes	—
355	C₂³	#37644	1	8	yes	—
356	C₂³	#45439	1	8	yes	—
357	C₂³	C₂×#2679	1	2	yes	—
358	C₂³	C₂×#2679	1	4	yes	—
359	C₂³	#58990	1	8	yes	—
360	C₂³	#58990	1	8	yes	—
361	C₂³	#58990	1	8	yes	—
362	C₂×C₄	#15947	1	8	yes	—
363	C₂²	C₂×#15947	1	1	yes	characteristic
364	C₂²	#612424	1	1	yes	characteristic
365	C₂²	#612424	1	2	yes	—
366	C₂²	#616960	1	1	yes	characteristic
367	C₂²	#616960	1	2	yes	—
368	C₂²	#647656	1	2	yes	—
369	C₂²	#647656	1	2	yes	—
370	C₂²	#647656	1	8	yes	—
371	C₂²	#845297	1	4	yes	—
372	C₂²	#845297	1	8	yes	—
373	C₂²	#6499874	1	1	yes	characteristic
374	C₂²	#6499875	1	1	yes	characteristic
375	C₂²	#6499876	1	2	yes	—
376	C₂	#72218795	1	1	yes	characteristic
377	C₂	#72233072	1	2	yes	—
378	C₂	#72234617	1	1	yes	characteristic
379	C₂	#72241081	1	2	yes	—
380	C₂	#72251380	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#35346
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72259004	C₂	semidirect
2. #72258984	C₂	semidirect
3. #72258980	C₂	semidirect
4. #72258957	C₂	semidirect
5. C₂×#6628900	C₂	semidirect
6. #72240552	C₂	semidirect
7. C₂×#449469	C₂	semidirect
8. C₂²×#23895	C₂	semidirect
9. C₂²×#60399	C₂	semidirect
10. #72225808	C₂	semidirect
11. #72225659	C₂	semidirect
12. #72225622	C₂	semidirect
13. C₂²×H(7,𝔽₂)	C₂²	semidirect
16. C₂²×#3484	C₂²	semidirect
19. C₂²×#3026	C₂²	semidirect
20. C₂²×#3026	C₂²	semidirect
21. C₂³×B(4,𝔽₂)	C₂²	semidirect
22. C₂²×#2883	C₂²	semidirect
23. C₂²×#2883	C₂²	semidirect
25. C₂×#35347	C₂²	semidirect
26. C₂×#35347	C₂²	semidirect
27. C₂²×#2021	C₂²	semidirect
28. C₂²×#1913	C₂²	semidirect
29. C₂²×#1913	C₂²	semidirect
30. C₂²×#1790	C₂²	semidirect
31. C₂²×#1790	C₂²	semidirect
32. C₂×#20585	C₂²	semidirect
33. C₂×#20585	C₂²	semidirect
34. C₂²×#1781	C₂²	semidirect
35. #5955303	C₂²	semidirect
36. C₂×#14716	C₂²	semidirect
37. #515529	C₂²	semidirect
38. #515529	C₂²	semidirect
39. C₂×#13867	C₂²	semidirect
40. C₂×#10991	C₂²	semidirect
41. C₂×#10995	C₂²	semidirect
42. C₂×#10995	C₂²	semidirect
43. C₂×#10980	C₂²	semidirect
44. C₂×#10972	C₂²	semidirect
45. C₂×#10972	C₂²	semidirect
46. C₂×#10972	C₂²	semidirect
47. C₂×#10965	C₂²	semidirect
48. C₂×#10745	C₂²	semidirect
49. C₂×#10768	C₂²	semidirect
50. #154195	C₂²	semidirect
51. #123590	C₂²	semidirect
52. #123574	C₂²	semidirect
53. #123527	C₂²	semidirect
54. #123520	C₂²	semidirect
58. C₂³×H(5,𝔽₂)	C₂³	semidirect
60. C₂×#3484	D₄	semidirect
61. C₂²×#535	D₄	semidirect
62. C₂²×#534	D₄	semidirect
68. C₂²×#525	D₄	semidirect
70. C₂³×#120	D₄	semidirect
73. C₂³×#120	C₂³	semidirect
76. C₂²×#518	C₂³	semidirect
77. C₂⁴×C₂²⋊C₄	C₂³	semidirect
78. C₂×#3026	D₄	semidirect
79. C₂×#3026	D₄	semidirect
86. C₂³×#99	C₂³	semidirect
87. C₂³×#99	C₂³	semidirect
88. C₂×#2406	D₄	semidirect
89. C₂×#2404	D₄	semidirect
90. C₂×#2405	D₄	semidirect
91. C₂×#2403	D₄	semidirect
94. C₂×#2308	C₂³	semidirect
98. C₂²×#386	C₂³	semidirect
99. C₂²×#386	C₂³	semidirect
100. C₂²×#379	C₂³	semidirect
101. C₂²×#379	C₂³	semidirect
102. C₂²×#342	C₂³	semidirect
103. C₂²×#342	C₂³	semidirect
104. C₂²×#342	C₂³	semidirect
105. #13794	C₂³	semidirect
106. C₂×C₂²⋊#95	C₂³	semidirect
107. C₂×C₂²⋊#95	C₂³	semidirect
112. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
120. C₂⁴×D₄	C₂×D₄	semidirect
132. C₂×#534	C₂×D₄	semidirect
135. C₂²×#123	C₂×D₄	semidirect
141. C₂²×#120	C₂×D₄	semidirect
144. C₂³×C₄⋊C₄	C₂×D₄	semidirect
146. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
147. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
154. C₂²×#99	C₂×D₄	semidirect
155. C₂²×#99	C₂×D₄	semidirect
156. C₂²×#99	C₂×D₄	semidirect
159. C₂×#386	C₂×D₄	semidirect
160. C₂×#386	C₂×D₄	semidirect
161. C₂×#381	C₂×D₄	semidirect
162. C₂×#379	C₂×D₄	semidirect
164. C₂⁶	#120	semidirect
174. C₂×H(5,𝔽₂)	#120	semidirect
178. C₂³×D₄	#120	semidirect
179. C₂³×D₄	#120	semidirect
198. C₂⁴×C₄	#120	semidirect
206. #534	#120	semidirect
207. C₂×#123	#120	semidirect
208. C₂×#123	#120	semidirect
209. C₂×#120	#120	semidirect
210. C₂×#120	#120	semidirect
277. C₂⁴	#2403	semidirect
322. C₂²×C₄	#2403	semidirect

Maximal subgroups

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

subgroup	index
#72259004	2
#72258984	2
#72258980	2
#72258957	2
C₂×#6628900	2
#72240552	2
C₂×#449469	2
C₂²×#23895	2
C₂²×#60399	2
#72225808	2
#72225659	2
#72225622	2