Subgroups — #72266831

Order 2048.

At least 9505 conjugacy classes of subgroups; only the 850 normal subgroups are shown.

The subgroup lattice has 375 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266830	C₂	1	4	yes	maximal, complemented
2	#72256113	C₂	1	2	yes	maximal, complemented
3	#72256025	C₂	1	2	yes	maximal, complemented
4	#72255863	C₂	1	2	yes	maximal, complemented
5	#72238718	C₂	1	4	yes	maximal, complemented
6	#72238717	C₂	1	8	yes	maximal, complemented
7	#72235130	C₂	1	2	yes	maximal, complemented
8	#72234661	C₂	1	1	yes	maximal, characteristic, complemented
9	#72224136	C₂	1	1	yes	maximal, characteristic, complemented
10	#72219300	C₂	1	1	yes	maximal, characteristic, complemented
11	#72218069	C₂	1	1	yes	maximal, characteristic, complemented
12	#72218057	C₂	1	1	yes	maximal, characteristic, complemented
13	#72213862	C₂	1	1	yes	maximal, characteristic, complemented
14	#72210511	C₂	1	1	yes	maximal, characteristic, complemented
15	#10586404	C₂²	1	1	yes	characteristic, complemented
16	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
17	#7630939	C₂²	1	1	yes	characteristic
18	#7630939	C₂²	1	1	yes	characteristic
19	C₂×#34980	C₂²	1	1	yes	characteristic
20	#7622875	C₂²	1	8	yes	complemented
21	#6629258	C₂²	1	2	yes	complemented
22	#6628892	C₂²	1	2	yes	complemented
23	#6628892	C₂²	1	2	yes	complemented
24	#6628867	C₂²	1	2	yes	complemented
25	#6499892	C₂²	1	4	yes	—
26	#6499892	C₂²	1	4	yes	complemented
27	#6440460	C₂²	1	2	yes	complemented
28	#6437995	C₂²	1	4	yes	complemented
29	C₂×#23895	C₂²	1	2	yes	—
30	#6437621	C₂²	1	2	yes	—
31	C₂×#23897	C₂²	1	2	yes	—
32	#6374210	C₂²	1	1	yes	characteristic, complemented
33	#6374210	C₂²	1	1	yes	characteristic, complemented
34	#6374128	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
36	#494713	C₂²	1	4	yes	complemented
37	#494695	C₂²	1	4	yes	complemented
38	#493879	C₂²	1	2	yes	complemented
39	#493562	C₂²	1	8	yes	complemented
40	C₂×#12707	C₂²	1	2	yes	complemented
41	C₂×#12705	C₂²	1	2	yes	complemented
42	#493357	C₂²	1	2	yes	complemented
43	#394064	C₂²	1	4	yes	complemented
44	#393975	C₂²	1	4	yes	complemented
45	#392699	C₂²	1	2	yes	complemented
46	#392696	C₂²	1	2	yes	complemented
47	#392113	C₂²	1	1	yes	characteristic, complemented
48	#392109	C₂²	1	1	yes	characteristic, complemented
49	#359558	C₂²	1	2	yes	complemented
50	#359549	C₂²	1	2	yes	complemented
51	#148467	C₂²	1	8	yes	complemented
52	#148249	C₂²	1	8	yes	complemented
53	#148246	C₂²	1	8	yes	complemented
54	#147767	C₂²	1	8	yes	complemented
55	#147752	C₂²	1	8	yes	complemented
56	#147752	C₂²	1	8	yes	complemented
57	#147569	C₂²	1	4	yes	complemented
58	#147567	C₂²	1	4	yes	complemented
59	#147567	C₂²	1	4	yes	complemented
60	#147567	C₂²	1	4	yes	complemented
61	#146479	C₂²	1	2	yes	complemented
62	#146475	C₂²	1	2	yes	complemented
63	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
64	C₂⁵×D₄	C₂³	1	1	yes	characteristic
65	#62862	C₂³	1	4	yes	—
66	C₂×#3484	D₄	1	1	yes	characteristic, complemented
67	C₂×#3484	D₄	1	1	yes	characteristic, complemented
68	C₂×#3484	D₄	1	1	yes	characteristic, complemented
69	C₂×#3484	D₄	1	1	yes	characteristic, complemented
70	C₂×#3484	C₂³	1	1	yes	characteristic
71	C₂×#3484	C₂³	1	1	yes	characteristic
72	C₂×#3484	C₂³	1	2	yes	—
73	C₂×#3484	C₂³	1	2	yes	complemented
74	C₂²×#534	D₄	1	1	yes	characteristic, complemented
75	C₂²×#534	C₂³	1	1	yes	characteristic
76	C₂³×#120	D₄	1	1	yes	characteristic, complemented
77	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
78	C₂×#3026	C₂³	1	4	yes	—
79	C₂×#3026	C₂³	1	4	yes	—
80	C₂×#3019	C₂³	1	4	yes	—
81	C₂³×#99	C₂³	1	2	yes	complemented
82	#36614	D₄	1	2	yes	complemented
83	C₂×#2846	D₄	1	2	yes	complemented
84	#35222	D₄	1	2	yes	complemented
85	#35222	C₂³	1	2	yes	—
86	#35222	C₂³	1	2	yes	—
87	#34980	D₄	1	2	yes	complemented
88	#34980	D₄	1	2	yes	complemented
89	#34980	D₄	1	2	yes	complemented
90	#34980	C₂³	1	2	yes	—
91	#34980	C₂³	1	2	yes	—
92	#34980	C₂³	1	2	yes	—
93	#34980	C₂³	1	2	yes	—
94	#34171	D₄	1	1	yes	characteristic, complemented
95	#34171	D₄	1	1	yes	characteristic, complemented
96	#34171	D₄	1	1	yes	characteristic, complemented
97	#34171	D₄	1	1	yes	characteristic, complemented
98	#34171	C₂³	1	1	yes	characteristic
99	#34171	C₂³	1	1	yes	characteristic
100	C₂×#2308	D₄	1	1	yes	characteristic, complemented
101	C₂×#2308	C₂³	1	1	yes	characteristic
102	C₂²×#379	D₄	1	1	yes	characteristic, complemented
103	C₂×#2127	C₂³	1	8	yes	—
104	C₂×#2121	C₂³	1	8	yes	—
105	C₂×#2121	C₂³	1	8	yes	—
106	#23903	D₄	1	8	yes	complemented
107	#23901	D₄	1	4	yes	complemented
108	#23900	D₄	1	4	yes	complemented
109	#21750	C₂³	1	4	yes	—
110	#21749	C₂³	1	4	yes	—
111	#21749	C₂³	1	4	yes	—
112	C₂×#1913	C₂³	1	4	yes	—
113	C₂×#1911	C₂³	1	4	yes	—
114	#20960	C₂³	1	4	yes	—
115	#20889	C₂³	1	4	yes	complemented
116	#20616	C₂³	1	4	yes	complemented
117	#20609	C₂³	1	4	yes	complemented
118	#20609	C₂³	1	4	yes	complemented
119	C₂×#1783	C₂³	1	2	yes	—
120	C₂×#1783	C₂³	1	2	yes	complemented
121	C₂×#1783	C₂³	1	2	yes	complemented
122	C₂×#1781	C₂³	1	2	yes	—
123	C₂×#1781	C₂³	1	2	yes	—
124	C₂×#1781	C₂³	1	2	yes	complemented
125	C₂×#1781	C₂³	1	2	yes	complemented
126	C₂×#1781	C₂³	1	2	yes	complemented
127	#12582	C₂³	1	8	yes	complemented
128	#12574	C₂³	1	8	yes	complemented
129	#12574	C₂³	1	8	yes	complemented
130	#10754	C₂³	1	4	yes	complemented
131	#10740	C₂³	1	4	yes	complemented
132	C₂⁷	C₂×D₄	1	1	yes	characteristic
133	C₂⁷	C₂×D₄	1	1	yes	characteristic
134	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
135	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
136	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
137	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
138	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
148	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
149	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
150	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
151	#3484	C₂×D₄	1	4	yes	—
152	#3484	C₂×D₄	1	4	yes	—
153	C₂×#535	C₂×D₄	1	2	yes	—
154	C₂×#535	C₂×D₄	1	2	yes	—
155	C₂×#535	C₂⁴	1	2	yes	—
156	C₂×#534	C₂×D₄	1	4	yes	—
157	C₂×#534	C₂×D₄	1	2	yes	—
158	C₂×#534	C₂×D₄	1	2	yes	—
159	C₂×#534	C₂×D₄	1	2	yes	—
160	C₂×#534	C₂×D₄	1	2	yes	—
161	C₂×#534	C₂×D₄	1	2	yes	—
162	C₂×#534	C₂⁴	1	2	yes	—
163	C₂×#534	C₂⁴	1	2	yes	—
164	C₂×#525	C₂×D₄	1	2	yes	—
165	C₂×#525	C₂×D₄	1	2	yes	—
166	C₂×#525	C₂×D₄	1	2	yes	—
167	C₂²×#123	C₂×D₄	1	2	yes	—
168	C₂²×#120	C₂×D₄	1	2	yes	—
169	C₂²×#120	C₂×D₄	1	2	yes	—
170	C₂²×#120	C₂×D₄	1	2	yes	—
171	C₂²×#120	C₂×D₄	1	2	yes	—
172	C₂²×#120	C₂×D₄	1	2	yes	—
173	C₂²×#120	C₂×D₄	1	2	yes	—
174	C₂×#518	C₂×D₄	1	1	yes	characteristic
175	C₂×#518	C₂×D₄	1	1	yes	characteristic
176	C₂×#518	C₂×D₄	1	1	yes	characteristic
177	C₂×#518	C₂×D₄	1	1	yes	characteristic
178	C₂×#518	C₂×D₄	1	1	yes	characteristic
179	C₂×#518	C₂×D₄	1	1	yes	characteristic
180	C₂×#518	C₂⁴	1	2	yes	—
181	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
182	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₂×#458	C₂×D₄	1	8	yes	complemented
185	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
186	C₂²×#100	C₂⁴	1	4	yes	—
187	C₂²×#99	C₂⁴	1	4	yes	—
188	C₂²×#99	C₂⁴	1	4	yes	—
189	#2309	C₂×D₄	1	2	yes	—
190	#2309	C₂×D₄	1	2	yes	—
191	#2309	C₂⁴	1	2	yes	—
192	#2308	C₂×D₄	1	2	yes	—
193	#2308	C₂×D₄	1	2	yes	—
194	#2308	C₂×D₄	1	2	yes	—
195	#2308	C₂×D₄	1	2	yes	—
196	#2308	C₂×D₄	1	2	yes	—
197	#2308	C₂⁴	1	2	yes	—
198	#2308	C₂⁴	1	2	yes	—
199	#2280	C₂×D₄	1	2	yes	—
200	#2280	C₂×D₄	1	2	yes	—
201	#2280	C₂×D₄	1	2	yes	—
202	C₂×#379	C₂×D₄	1	2	yes	—
203	C₂×#379	C₂×D₄	1	2	yes	—
204	C₂×#379	C₂×D₄	1	2	yes	—
205	C₂×#379	C₂×D₄	1	2	yes	—
206	C₂×#379	C₂×D₄	1	2	yes	—
207	#1890	C₂×D₄	1	8	yes	complemented
208	#1889	C₂×D₄	1	8	yes	complemented
209	#1781	C₂×D₄	1	4	yes	—
210	#1781	C₂×D₄	1	4	yes	—
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂⁶	#120	1	1	yes	characteristic
213	C₂⁶	#120	1	1	yes	characteristic
214	C₂⁶	#120	1	1	yes	characteristic
215	C₂⁶	#120	1	1	yes	characteristic
216	C₂⁶	#120	1	1	yes	characteristic
217	C₂⁶	#120	1	1	yes	characteristic
218	C₂⁶	#120	1	1	yes	characteristic, complemented
219	C₂⁶	C₂²×D₄	1	1	yes	characteristic
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
225	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
226	C₂²×#41	C₂²×D₄	1	2	yes	—
227	C₂³×D₄	#120	1	1	yes	characteristic
228	C₂³×D₄	#120	1	1	yes	characteristic
229	C₂³×D₄	#120	1	1	yes	characteristic
230	C₂³×D₄	#120	1	1	yes	characteristic
231	C₂³×D₄	#120	1	1	yes	characteristic
232	C₂³×D₄	#120	1	1	yes	characteristic
233	C₂³×D₄	#120	1	2	yes	complemented
234	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
235	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
237	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
238	C₂³×D₄	C₂²×D₄	1	2	yes	—
239	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
240	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
241	C₂³×D₄	C₂²×D₄	1	2	yes	—
242	C₂³×D₄	C₂²×D₄	1	2	yes	—
243	C₂³×D₄	C₂²×D₄	1	2	yes	—
244	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
245	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
246	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
247	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
248	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
249	C₂³×D₄	C₂⁵	1	1	yes	characteristic
250	C₂⁴×C₄	#120	1	1	yes	characteristic
251	C₂⁴×C₄	#120	1	1	yes	characteristic
252	C₂⁴×C₄	#120	1	1	yes	characteristic
253	C₂⁴×C₄	#120	1	1	yes	characteristic, complemented
254	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
257	C₂×#127	H(5,𝔽₂)	1	4	yes	—
258	C₂×#124	H(5,𝔽₂)	1	4	yes	—
259	C₂×#123	#120	1	4	yes	complemented
260	C₂×#123	C₂²×D₄	1	4	yes	—
261	C₂×#123	H(5,𝔽₂)	1	4	yes	—
262	C₂×#120	#120	1	4	yes	complemented
263	C₂×#120	C₂²×D₄	1	4	yes	—
264	C₂×#120	H(5,𝔽₂)	1	4	yes	—
265	#518	C₂²×D₄	1	4	yes	—
266	C₂×#117	C₂²×D₄	1	2	yes	—
267	C₂×#117	C₂²×D₄	1	2	yes	—
268	C₂×#117	C₂²×D₄	1	2	yes	—
269	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
270	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
271	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
277	C₂×#99	C₂²×D₄	1	8	yes	—
278	C₂⁵	B(4,𝔽₂)	1	2	yes	—
279	C₂⁵	B(4,𝔽₂)	1	2	yes	—
280	C₂⁵	B(4,𝔽₂)	1	2	yes	—
281	C₂⁵	B(4,𝔽₂)	1	2	yes	—
282	C₂⁵	C₂×#120	1	1	yes	characteristic
283	C₂⁵	C₂×#120	1	1	yes	characteristic
284	C₂⁵	C₂×#120	1	1	yes	characteristic
285	C₂⁵	C₂×#120	1	1	yes	characteristic
286	C₂⁵	C₂×#120	1	1	yes	characteristic
287	C₂⁵	C₂×#120	1	1	yes	characteristic
288	C₂⁵	C₂×#120	1	1	yes	characteristic
289	C₂⁵	C₂×#120	1	1	yes	characteristic
290	C₂⁵	C₂×#120	1	1	yes	characteristic
291	C₂⁵	C₂×#120	1	1	yes	characteristic
292	C₂⁵	C₂×#120	1	1	yes	characteristic
293	C₂⁵	C₂×#120	1	2	yes	—
294	C₂⁵	#534	1	1	yes	characteristic
295	C₂⁵	#534	1	1	yes	characteristic
296	C₂⁵	#534	1	2	yes	complemented
297	C₂⁵	D₄²	1	2	yes	—
298	C₂⁵	D₄²	1	2	yes	—
299	C₂⁵	C₂³×D₄	1	1	yes	characteristic
300	C₂⁵	C₂³×D₄	1	1	yes	characteristic
301	C₂²×Q₈	#534	1	2	yes	complemented
302	C₂²×D₄	C₂×#120	1	2	yes	—
303	C₂²×D₄	#534	1	2	yes	—
304	C₂²×D₄	#534	1	2	yes	complemented
305	C₂²×D₄	D₄²	1	2	yes	—
306	C₂²×D₄	D₄²	1	2	yes	—
307	C₂²×D₄	D₄²	1	2	yes	—
308	C₂²×D₄	D₄²	1	2	yes	—
309	C₂²×D₄	C₂³×D₄	1	2	yes	—
310	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
311	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
312	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
313	C₂³×C₄	C₂×#120	1	1	yes	characteristic
314	C₂³×C₄	C₂×#120	1	1	yes	characteristic
315	C₂³×C₄	C₂×#120	1	1	yes	characteristic
316	C₂³×C₄	C₂×#120	1	2	yes	—
317	C₂³×C₄	#534	1	2	yes	complemented
318	C₂³×C₄	D₄²	1	2	yes	—
319	C₂³×C₄	D₄²	1	2	yes	—
320	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
322	C₂×C₂²⋊C₄	#534	1	4	yes	complemented
323	C₂×C₄²	#534	1	4	yes	complemented
324	C₂⁴	#2403	1	1	yes	characteristic
325	C₂⁴	#2403	1	2	yes	—
326	C₂⁴	#2403	1	1	yes	characteristic
327	C₂⁴	#2403	1	1	yes	characteristic
328	C₂⁴	#2403	1	1	yes	characteristic
329	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
330	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
331	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
332	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
333	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
334	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
335	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
336	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
337	C₂⁴	#3026	1	2	yes	—
338	C₂⁴	C₂²×#120	1	1	yes	characteristic
339	C₂⁴	C₂²×#120	1	1	yes	characteristic
340	C₂⁴	C₂×#534	1	2	yes	—
341	C₂⁴	C₂×#534	1	1	yes	characteristic
342	C₂⁴	C₂×D₄²	1	2	yes	—
343	C₂⁴	#3484	1	2	yes	—
344	C₂⁴	#3484	1	2	yes	—
345	C₂⁴	#3484	1	2	yes	—
346	C₂×D₄	#3484	1	8	yes	—
347	C₂×D₄	#3532	1	8	yes	—
348	C₂²×C₄	#2403	1	2	yes	—
349	C₂²×C₄	#3026	1	2	yes	—
350	C₂²×C₄	C₂×#534	1	2	yes	—
351	C₂²×C₄	C₂×D₄²	1	2	yes	—
352	C₂²×C₄	#3484	1	2	yes	—
353	C₂³	#23900	1	2	yes	—
354	C₂³	#23900	1	2	yes	—
355	C₂³	C₂×#2403	1	1	yes	characteristic
356	C₂³	#34980	1	1	yes	characteristic
357	C₂³	#34980	1	1	yes	characteristic
358	C₂³	#35346	1	2	yes	—
359	C₂³	#36714	1	2	yes	—
360	C₂³	#37644	1	4	yes	—
361	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
362	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
363	C₂³	C₂×#3026	1	1	yes	characteristic
364	C₂³	C₂×#3026	1	1	yes	characteristic
365	C₂×C₄	#37644	1	4	yes	—
366	C₂²	#616960	1	1	yes	characteristic
367	C₂²	C₂×#23900	1	1	yes	characteristic
368	C₂²	#6437621	1	1	yes	characteristic
369	C₂²	#6470225	1	1	yes	characteristic
370	C₂²	#6470225	1	1	yes	characteristic
371	C₂²	#6470225	1	1	yes	characteristic
372	C₂²	#6470225	1	1	yes	characteristic
373	C₂	#72238594	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72238594
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266830	C₂	semidirect
2. #72256113	C₂	semidirect
3. #72256025	C₂	semidirect
4. #72255863	C₂	semidirect
5. #72238718	C₂	semidirect
6. #72238717	C₂	semidirect
7. #72235130	C₂	semidirect
8. #72234661	C₂	semidirect
9. #72224136	C₂	semidirect
10. #72219300	C₂	semidirect
11. #72218069	C₂	semidirect
12. #72218057	C₂	semidirect
13. #72213862	C₂	semidirect
14. #72210511	C₂	semidirect
15. #10586404	C₂²	semidirect
16. C₂²×#3484	C₂²	semidirect
20. #7622875	C₂²	semidirect
21. #6629258	C₂²	semidirect
22. #6628892	C₂²	semidirect
23. #6628892	C₂²	semidirect
24. #6628867	C₂²	semidirect
26. #6499892	C₂²	semidirect
27. #6440460	C₂²	semidirect
28. #6437995	C₂²	semidirect
32. #6374210	C₂²	semidirect
33. #6374210	C₂²	semidirect
34. #6374128	C₂²	semidirect
35. C₂²×#1781	C₂²	semidirect
36. #494713	C₂²	semidirect
37. #494695	C₂²	semidirect
38. #493879	C₂²	semidirect
39. #493562	C₂²	semidirect
40. C₂×#12707	C₂²	semidirect
41. C₂×#12705	C₂²	semidirect
42. #493357	C₂²	semidirect
43. #394064	C₂²	semidirect
44. #393975	C₂²	semidirect
45. #392699	C₂²	semidirect
46. #392696	C₂²	semidirect
47. #392113	C₂²	semidirect
48. #392109	C₂²	semidirect
49. #359558	C₂²	semidirect
50. #359549	C₂²	semidirect
51. #148467	C₂²	semidirect
52. #148249	C₂²	semidirect
53. #148246	C₂²	semidirect
54. #147767	C₂²	semidirect
55. #147752	C₂²	semidirect
56. #147752	C₂²	semidirect
57. #147569	C₂²	semidirect
58. #147567	C₂²	semidirect
59. #147567	C₂²	semidirect
60. #147567	C₂²	semidirect
61. #146479	C₂²	semidirect
62. #146475	C₂²	semidirect
63. C₂³×H(5,𝔽₂)	C₂³	semidirect
66. C₂×#3484	D₄	semidirect
67. C₂×#3484	D₄	semidirect
68. C₂×#3484	D₄	semidirect
69. C₂×#3484	D₄	semidirect
73. C₂×#3484	C₂³	semidirect
74. C₂²×#534	D₄	semidirect
76. C₂³×#120	D₄	semidirect
77. C₂²×#518	C₂³	semidirect
81. C₂³×#99	C₂³	semidirect
82. #36614	D₄	semidirect
83. C₂×#2846	D₄	semidirect
84. #35222	D₄	semidirect
87. #34980	D₄	semidirect
88. #34980	D₄	semidirect
89. #34980	D₄	semidirect
94. #34171	D₄	semidirect
95. #34171	D₄	semidirect
96. #34171	D₄	semidirect
97. #34171	D₄	semidirect
100. C₂×#2308	D₄	semidirect
102. C₂²×#379	D₄	semidirect
106. #23903	D₄	semidirect
107. #23901	D₄	semidirect
108. #23900	D₄	semidirect
115. #20889	C₂³	semidirect
116. #20616	C₂³	semidirect
117. #20609	C₂³	semidirect
118. #20609	C₂³	semidirect
120. C₂×#1783	C₂³	semidirect
121. C₂×#1783	C₂³	semidirect
124. C₂×#1781	C₂³	semidirect
125. C₂×#1781	C₂³	semidirect
126. C₂×#1781	C₂³	semidirect
127. #12582	C₂³	semidirect
128. #12574	C₂³	semidirect
129. #12574	C₂³	semidirect
130. #10754	C₂³	semidirect
131. #10740	C₂³	semidirect
184. C₂×#458	C₂×D₄	semidirect
185. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
207. #1890	C₂×D₄	semidirect
208. #1889	C₂×D₄	semidirect
218. C₂⁶	#120	semidirect
233. C₂³×D₄	#120	semidirect
253. C₂⁴×C₄	#120	semidirect
259. C₂×#123	#120	semidirect
262. C₂×#120	#120	semidirect
269. C₂²×C₂²⋊C₄	#120	semidirect
270. C₂²×C₂²⋊C₄	#120	semidirect
296. C₂⁵	#534	semidirect
301. C₂²×Q₈	#534	semidirect
304. C₂²×D₄	#534	semidirect
317. C₂³×C₄	#534	semidirect
322. C₂×C₂²⋊C₄	#534	semidirect
323. C₂×C₄²	#534	semidirect

Maximal subgroups

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

subgroup	index
#72266830	2
#72256113	2
#72256025	2
#72255863	2
#72238718	2
#72238717	2
#72235130	2
#72234661	2
#72224136	2
#72219300	2
#72218069	2
#72218057	2
#72213862	2
#72210511	2