Subgroups — #72263833

Order 2048.

At least 9999 conjugacy classes of subgroups; only the 1056 normal subgroups are shown.

The subgroup lattice has 550 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263832	C₂	1	1	yes	maximal, characteristic, complemented
2	#72263831	C₂	1	2	yes	maximal, complemented
3	#72263830	C₂	1	2	yes	maximal, complemented
4	#72263823	C₂	1	2	yes	maximal, complemented
5	#72263822	C₂	1	2	yes	maximal, complemented
6	#72263731	C₂	1	1	yes	maximal, characteristic, complemented
7	#72263635	C₂	1	1	yes	maximal, characteristic, complemented
8	#72263425	C₂	1	2	yes	maximal, complemented
9	#72260584	C₂	1	2	yes	maximal, complemented
10	#72256817	C₂	1	2	yes	maximal, complemented
11	#72251183	C₂	1	1	yes	maximal, characteristic, complemented
12	#72240278	C₂	1	1	yes	maximal, characteristic, complemented
13	#72236734	C₂	1	1	yes	maximal, characteristic, complemented
14	#72236694	C₂	1	2	yes	maximal, complemented
15	C₂×#144415	C₂	1	2	yes	maximal, complemented
16	#72236685	C₂	1	2	yes	maximal, complemented
17	#72236679	C₂	1	2	yes	maximal, complemented
18	#72233659	C₂	1	1	yes	maximal, characteristic, complemented
19	#72213293	C₂	1	2	yes	maximal, complemented
20	#10586472	C₂²	1	1	yes	characteristic
21	C₂×#38020	C₂²	1	1	yes	characteristic
22	C₂×#37677	C₂²	1	1	yes	characteristic
23	#6496266	C₂²	1	2	yes	—
24	#6490937	C₂²	1	2	yes	—
25	#6470225	C₂²	1	2	yes	—
26	#6470225	C₂²	1	2	yes	—
27	#6470020	C₂²	1	2	yes	—
28	#6470019	C₂²	1	2	yes	—
29	#6454047	C₂²	1	2	yes	—
30	#6453842	C₂²	1	2	yes	—
31	#6440460	C₂²	1	2	yes	—
32	C₂×#24056	C₂²	1	2	yes	—
33	#6437445	C₂²	1	2	yes	—
34	C₂×#23907	C₂²	1	2	yes	—
35	#6385983	C₂²	1	1	yes	characteristic
36	#6385971	C₂²	1	1	yes	characteristic
37	#6385971	C₂²	1	1	yes	characteristic
38	#4375545	C₂²	1	1	yes	characteristic, complemented
39	#4375184	C₂²	1	1	yes	characteristic, complemented
40	#4328628	C₂²	1	1	yes	characteristic, complemented
41	#4312024	C₂²	1	1	yes	characteristic, complemented
42	#948453	C₂²	1	1	yes	characteristic, complemented
43	#947141	C₂²	1	1	yes	characteristic, complemented
44	#945697	C₂²	1	1	yes	characteristic, complemented
45	#848801	C₂²	1	1	yes	characteristic, complemented
46	#848397	C₂²	1	1	yes	characteristic, complemented
47	#771668	C₂²	1	1	yes	characteristic, complemented
48	#763514	C₂²	1	1	yes	characteristic, complemented
49	C₂×#15784	C₂²	1	1	yes	characteristic, complemented
50	#518019	C₂²	1	1	yes	characteristic
51	#496416	C₂²	1	2	yes	complemented
52	#496307	C₂²	1	2	yes	complemented
53	#496225	C₂²	1	2	yes	complemented
54	#496225	C₂²	1	2	yes	complemented
55	#496191	C₂²	1	2	yes	complemented
56	#496189	C₂²	1	2	yes	complemented
57	#493998	C₂²	1	2	yes	complemented
58	#493963	C₂²	1	2	yes	complemented
59	#493879	C₂²	1	2	yes	complemented
60	C₂×#12852	C₂²	1	2	yes	complemented
61	#493370	C₂²	1	2	yes	complemented
62	C₂×#12694	C₂²	1	2	yes	complemented
63	#187930	C₂²	1	2	yes	—
64	#187928	C₂²	1	2	yes	—
65	#187928	C₂²	1	2	yes	—
66	#187925	C₂²	1	2	yes	—
67	C₂×#8534	C₂²	1	2	yes	—
68	C₂×#8534	C₂²	1	2	yes	—
69	#144429	C₂²	1	4	yes	complemented
70	#144429	C₂²	1	4	yes	complemented
71	#144428	C₂²	1	4	yes	complemented
72	#144415	C₂²	1	4	yes	complemented
73	#144415	C₂²	1	4	yes	complemented
74	#144415	C₂²	1	4	yes	complemented
75	#144415	C₂²	1	4	yes	complemented
76	#144415	C₂²	1	4	yes	complemented
77	#144415	C₂²	1	4	yes	complemented
78	#144414	C₂²	1	4	yes	complemented
79	#144414	C₂²	1	4	yes	complemented
80	#144414	C₂²	1	4	yes	complemented
81	#144404	C₂²	1	4	yes	complemented
82	#144388	C₂²	1	4	yes	complemented
83	#144388	C₂²	1	4	yes	complemented
84	#144386	C₂²	1	4	yes	complemented
85	#128081	C₂²	1	2	yes	complemented
86	#128073	C₂²	1	2	yes	complemented
87	#128073	C₂²	1	2	yes	complemented
88	#128043	C₂²	1	2	yes	complemented
89	C₂×#7304	C₂²	1	2	yes	complemented
90	C₂×#7304	C₂²	1	2	yes	complemented
91	#62983	D₄	1	4	yes	complemented
92	D₄×H(5,𝔽₂)	D₄	1	4	yes	complemented
93	#62773	C₂³	1	2	yes	—
94	C₂×#3484	C₂³	1	2	yes	—
95	C₂×#3484	C₂³	1	2	yes	—
96	C₂²×#548	D₄	1	1	yes	characteristic, complemented
97	C₂²×D₄²	C₂³	1	1	yes	characteristic
98	C₂²×#535	C₂³	1	1	yes	characteristic
99	C₂³×#124	C₂³	1	1	yes	characteristic
100	C₂³×#121	D₄	1	1	yes	characteristic
101	C₂²×#518	D₄	1	1	yes	characteristic, complemented
102	C₂×#2856	D₄	1	1	yes	characteristic, complemented
103	C₂×#2849	D₄	1	1	yes	characteristic
104	C₂×#2548	D₄	1	1	yes	characteristic, complemented
105	C₂×#2544	C₂³	1	1	yes	characteristic
106	C₂×#2591	D₄	1	1	yes	characteristic
107	C₂×#2579	C₂³	1	1	yes	characteristic
108	C₂×#2431	D₄	1	1	yes	characteristic, complemented
109	C₂×#2436	D₄	1	1	yes	characteristic, complemented
110	C₂×#2435	C₂³	1	1	yes	characteristic
111	C₂×#2433	C₂³	1	1	yes	characteristic
112	C₂×#2410	D₄	1	1	yes	characteristic
113	C₂×#2410	D₄	1	1	yes	characteristic
114	C₂×#2403	C₂³	1	1	yes	characteristic
115	C₂×#2403	C₂³	1	1	yes	characteristic
116	C₂×#2657	D₄	1	1	yes	characteristic, complemented
117	C₂×#2620	D₄	1	1	yes	characteristic, complemented
118	C₂×#2622	D₄	1	1	yes	characteristic
119	C₂×#2617	D₄	1	1	yes	characteristic
120	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
122	C₂×#2326	C₂³	1	1	yes	characteristic
123	C₂×#2321	C₂³	1	1	yes	characteristic
124	C₂×#2308	C₂³	1	1	yes	characteristic
125	C₂×#2290	D₄	1	1	yes	characteristic, complemented
126	C₂²×#386	C₂³	1	1	yes	characteristic
127	#24056	C₂³	1	4	yes	—
128	#24056	C₂³	1	4	yes	—
129	#24056	C₂³	1	4	yes	—
130	#24018	C₂³	1	4	yes	—
131	#23907	C₂³	1	4	yes	—
132	#23907	C₂³	1	4	yes	—
133	#23906	C₂³	1	4	yes	—
134	#23900	C₂³	1	4	yes	—
135	D₄×#100	D₄	1	8	yes	complemented
136	D₄×#99	D₄	1	8	yes	complemented
137	#20726	C₂³	1	2	yes	—
138	#20722	C₂³	1	2	yes	—
139	#20722	C₂³	1	2	yes	—
140	C₂×#1783	C₂³	1	2	yes	—
141	C₂×#1783	C₂³	1	2	yes	—
142	C₂×#1781	C₂³	1	2	yes	—
143	C₂×#1781	C₂³	1	2	yes	—
144	C₂×#1781	C₂³	1	2	yes	—
145	C₂×#1781	C₂³	1	2	yes	—
146	#16074	C₂³	1	1	yes	characteristic
147	#16074	C₂³	1	1	yes	characteristic
148	#15784	C₂³	1	1	yes	characteristic
149	#15784	C₂³	1	1	yes	characteristic
150	#15784	C₂³	1	1	yes	characteristic
151	#15784	C₂³	1	1	yes	characteristic
152	#15784	C₂³	1	1	yes	characteristic
153	#15784	C₂³	1	1	yes	characteristic
154	#15342	C₂³	1	1	yes	characteristic
155	#15313	C₂³	1	1	yes	characteristic
156	#15313	C₂³	1	1	yes	characteristic
157	#15313	C₂³	1	1	yes	characteristic
158	#15281	C₂³	1	1	yes	characteristic
159	#15259	C₂³	1	1	yes	characteristic
160	#15259	C₂³	1	1	yes	characteristic
161	#15258	C₂³	1	1	yes	characteristic
162	#14257	D₄	1	1	yes	characteristic, complemented
163	#14255	D₄	1	1	yes	characteristic, complemented
164	#14255	D₄	1	1	yes	characteristic, complemented
165	#14136	D₄	1	1	yes	characteristic, complemented
166	#14134	D₄	1	1	yes	characteristic, complemented
167	#14134	D₄	1	1	yes	characteristic, complemented
168	#13871	C₂³	1	1	yes	characteristic
169	#13867	C₂³	1	1	yes	characteristic
170	#13867	C₂³	1	1	yes	characteristic
171	#13839	C₂³	1	1	yes	characteristic
172	C₂×#1438	C₂³	1	1	yes	characteristic
173	C₂×#1438	C₂³	1	1	yes	characteristic
174	#12856	C₂³	1	4	yes	—
175	#12852	C₂³	1	4	yes	—
176	#12852	C₂³	1	4	yes	—
177	#12852	C₂³	1	4	yes	—
178	#12694	C₂³	1	4	yes	—
179	#12694	C₂³	1	4	yes	—
180	#12693	C₂³	1	4	yes	—
181	#12687	C₂³	1	4	yes	—
182	#8534	C₂³	1	4	yes	—
183	#8534	C₂³	1	4	yes	—
184	#8534	C₂³	1	4	yes	—
185	#8534	C₂³	1	4	yes	—
186	#7304	C₂³	1	4	yes	—
187	#7304	C₂³	1	4	yes	—
188	#7304	C₂³	1	4	yes	—
189	#7304	C₂³	1	4	yes	—
190	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
191	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
192	C₂³×#41	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
199	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
200	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
201	#3501	C₂×D₄	1	2	yes	—
202	#3496	C₂×D₄	1	2	yes	—
203	#3484	C₂×D₄	1	4	yes	—
204	#3484	C₂×D₄	1	4	yes	—
205	#3484	C₂⁴	1	4	yes	—
206	C₂×D₄²	C₂×D₄	1	4	yes	—
207	C₂×D₄²	C₂×D₄	1	4	yes	—
208	C₂×D₄²	C₂×D₄	1	4	yes	—
209	C₂×D₄²	#41	1	4	yes	—
210	C₂²×#127	C₂×D₄	1	1	yes	characteristic
211	C₂²×#127	C₂×D₄	1	1	yes	characteristic
212	C₂²×#127	C₂×D₄	1	1	yes	characteristic
213	C₂²×#127	C₂⁴	1	1	yes	characteristic
214	C₂²×#124	C₂×D₄	1	1	yes	characteristic
215	C₂²×#124	C₂×D₄	1	1	yes	characteristic
216	C₂²×#124	C₂×D₄	1	1	yes	characteristic
217	C₂²×#124	C₂×D₄	1	1	yes	characteristic
218	C₂²×#124	C₂×D₄	1	1	yes	characteristic
219	C₂²×#124	C₂⁴	1	1	yes	characteristic
220	C₂²×#124	C₂⁴	1	1	yes	characteristic
221	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
222	C₂²×#121	C₂×D₄	1	1	yes	characteristic
223	C₂²×#121	C₂×D₄	1	1	yes	characteristic
224	C₂²×#121	C₂×D₄	1	1	yes	characteristic
225	C₂²×#121	C₂×D₄	1	1	yes	characteristic
226	C₂²×#121	C₂×D₄	1	1	yes	characteristic
227	C₂²×#120	C₂×D₄	1	1	yes	characteristic
228	C₂²×#120	C₂×D₄	1	1	yes	characteristic
229	C₂²×#120	C₂×D₄	1	1	yes	characteristic
230	C₂²×#120	C₂×D₄	1	1	yes	characteristic
231	C₂²×#120	C₂×D₄	1	1	yes	characteristic
232	C₂²×#120	C₂×D₄	1	1	yes	characteristic
233	C₂²×#120	C₂⁴	1	1	yes	characteristic
234	C₄×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
235	C₂×#518	C₂×D₄	1	2	yes	—
236	C₂×#518	C₂×D₄	1	2	yes	—
237	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
240	C₂²×#117	C₂×D₄	1	1	yes	characteristic
241	C₂²×#117	C₂×D₄	1	1	yes	characteristic
242	C₂²×#117	C₂×D₄	1	1	yes	characteristic
243	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
246	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
247	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
251	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
254	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
255	C₂²×#100	C₂×D₄	1	4	yes	—
256	C₂²×#100	C₂×D₄	1	4	yes	—
257	C₂²×#99	C₂×D₄	1	4	yes	—
258	C₂²×#99	C₂×D₄	1	4	yes	—
259	C₂×#391	C₂×D₄	1	1	yes	characteristic
260	C₂×#391	C₂×D₄	1	1	yes	characteristic
261	C₂×#390	C₂×D₄	1	1	yes	characteristic
262	C₂×#390	C₂×D₄	1	1	yes	characteristic
263	C₂×#390	C₂×D₄	1	1	yes	characteristic
264	C₂×#390	C₂⁴	1	1	yes	characteristic
265	C₂×#386	C₂×D₄	1	1	yes	characteristic
266	C₂×#386	C₂×D₄	1	1	yes	characteristic
267	C₂×#386	C₂×D₄	1	1	yes	characteristic
268	C₂×#386	C₂×D₄	1	1	yes	characteristic
269	C₂×#386	C₂×D₄	1	1	yes	characteristic
270	C₂×#386	C₂×D₄	1	1	yes	characteristic
271	C₂×#386	C₂⁴	1	1	yes	characteristic
272	C₂×#386	C₂⁴	1	1	yes	characteristic
273	C₂×#386	C₂⁴	1	1	yes	characteristic
274	C₂×#385	C₂×D₄	1	1	yes	characteristic
275	C₂×#385	C₂×D₄	1	1	yes	characteristic
276	C₂×#385	C₂×D₄	1	1	yes	characteristic
277	C₂×#384	C₂×D₄	1	1	yes	characteristic
278	C₂×#380	C₂×D₄	1	1	yes	characteristic
279	C₂×#380	C₂×D₄	1	1	yes	characteristic
280	C₂×#379	C₂×D₄	1	1	yes	characteristic
281	C₂×#379	C₂×D₄	1	1	yes	characteristic
282	C₂×#379	C₂×D₄	1	1	yes	characteristic
283	C₂×#379	C₂×D₄	1	1	yes	characteristic
284	C₂×#379	C₂×D₄	1	1	yes	characteristic
285	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
288	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
289	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
290	C₂×#376	C₂×D₄	1	1	yes	characteristic
291	#1800	C₂×D₄	1	4	yes	—
292	#1799	C₂×D₄	1	4	yes	—
293	#1783	C₂×D₄	1	4	yes	—
294	#1783	C₂×D₄	1	4	yes	—
295	#1783	C₂⁴	1	4	yes	—
296	#1781	C₂×D₄	1	4	yes	—
297	#1781	C₂×D₄	1	4	yes	—
298	#1781	C₂⁴	1	4	yes	—
299	#1781	C₂⁴	1	4	yes	—
300	C₄×#100	C₂×D₄	1	4	yes	—
301	C₄×#99	C₂×D₄	1	4	yes	—
302	#1440	C₂×D₄	1	1	yes	characteristic
303	#1440	C₂×D₄	1	1	yes	characteristic
304	#1440	C₂×D₄	1	1	yes	characteristic
305	#1440	C₂×D₄	1	1	yes	characteristic
306	#1438	C₂×D₄	1	1	yes	characteristic
307	#1438	C₂×D₄	1	1	yes	characteristic
308	#1438	C₂×D₄	1	1	yes	characteristic
309	#1438	C₂×D₄	1	1	yes	characteristic
310	#1438	C₂×D₄	1	1	yes	characteristic
311	#1438	C₂×D₄	1	1	yes	characteristic
312	#1438	C₂×D₄	1	1	yes	characteristic
313	#1438	C₂×D₄	1	1	yes	characteristic
314	#1438	C₂⁴	1	1	yes	characteristic
315	#1438	C₂⁴	1	1	yes	characteristic
316	#1438	C₂⁴	1	1	yes	characteristic
317	#1438	C₂⁴	1	1	yes	characteristic
318	C₂⁶	C₂²×D₄	1	1	yes	characteristic
319	C₂⁶	C₂²×D₄	1	1	yes	characteristic
320	C₂⁶	C₂²×D₄	1	1	yes	characteristic
321	C₂⁶	C₂²×D₄	1	1	yes	characteristic
322	C₂⁶	C₂²×D₄	1	1	yes	characteristic
323	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
324	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
325	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
326	C₂³×D₄	#120	1	1	yes	characteristic
327	C₂³×D₄	#120	1	1	yes	characteristic
328	C₂³×D₄	#120	1	4	yes	—
329	C₂³×D₄	#120	1	1	yes	characteristic
330	C₂³×D₄	#120	1	1	yes	characteristic
331	C₂³×D₄	#120	1	1	yes	characteristic
332	C₂³×D₄	#120	1	1	yes	characteristic
333	C₂³×D₄	#120	1	1	yes	characteristic
334	C₂³×D₄	#120	1	1	yes	characteristic
335	C₂³×D₄	#120	1	1	yes	characteristic
336	C₂³×D₄	#121	1	4	yes	—
337	C₂³×D₄	#121	1	4	yes	—
338	C₂³×D₄	#127	1	4	yes	—
339	C₂³×D₄	C₂²×D₄	1	2	yes	—
340	C₂³×D₄	C₂²×D₄	1	2	yes	—
341	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂³×D₄	C₂²×D₄	1	2	yes	—
344	C₂³×D₄	C₂²×D₄	1	2	yes	—
345	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
347	C₂³×D₄	C₂²×D₄	1	2	yes	—
348	C₂³×D₄	C₂²×D₄	1	2	yes	—
349	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
350	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
351	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
352	C₂³×D₄	C₂×#41	1	2	yes	—
353	C₂³×D₄	C₂×#41	1	2	yes	—
354	C₂³×D₄	C₂⁵	1	1	yes	characteristic
355	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
359	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
360	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
361	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
362	C₂×#127	#120	1	4	yes	—
363	C₂×#127	#121	1	4	yes	—
364	C₂×#121	#120	1	4	yes	—
365	C₂×#121	#120	1	4	yes	—
366	C₂×#121	#120	1	4	yes	—
367	C₂×#121	#121	1	4	yes	—
368	C₂×#121	#121	1	4	yes	—
369	C₂×#121	#121	1	4	yes	—
370	C₂×#121	#121	1	4	yes	—
371	C₂×#121	#127	1	4	yes	—
372	C₂×#120	#120	1	4	yes	—
373	C₂×#120	#120	1	4	yes	—
374	C₂×#120	#121	1	4	yes	—
375	C₂×#120	#121	1	4	yes	—
376	C₂×#120	#121	1	4	yes	—
377	C₂×#120	#121	1	4	yes	—
378	C₂×#120	#127	1	4	yes	—
379	C₂×#120	#127	1	4	yes	—
380	#518	C₂²×D₄	1	4	yes	—
381	C₂×C₄×D₄	#120	1	4	yes	—
382	C₂×C₄×D₄	#121	1	4	yes	—
383	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
384	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
385	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
386	C₂×C₄×D₄	C₂×#41	1	2	yes	—
387	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
398	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
412	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
413	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
414	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
415	C₂×#100	C₂²×D₄	1	8	yes	—
416	C₂×#99	C₂²×D₄	1	8	yes	—
417	C₂⁵	C₂×#120	1	1	yes	characteristic
418	C₂⁵	C₂×#120	1	2	yes	—
419	C₂⁵	C₂×#120	1	2	yes	—
420	C₂⁵	C₂×#120	1	1	yes	characteristic
421	C₂⁵	C₂×#120	1	1	yes	characteristic
422	C₂⁵	C₂×#120	1	1	yes	characteristic
423	C₂⁵	C₂×#120	1	1	yes	characteristic
424	C₂⁵	C₂×#120	1	1	yes	characteristic
425	C₂⁵	C₂×#121	1	2	yes	—
426	C₂⁵	C₂×#121	1	2	yes	—
427	C₂⁵	C₂×#121	1	2	yes	—
428	C₂⁵	C₂×#121	1	2	yes	—
429	C₂⁵	C₂×#127	1	2	yes	—
430	C₂⁵	C₂×#127	1	2	yes	—
431	C₂⁵	C₂³×D₄	1	1	yes	characteristic
432	C₂⁵	C₂³×D₄	1	1	yes	characteristic
433	C₂²×D₄	#392	1	4	yes	—
434	C₂²×D₄	#392	1	4	yes	—
435	C₂²×D₄	#392	1	4	yes	—
436	C₂²×D₄	#392	1	4	yes	—
437	C₂²×D₄	#392	1	4	yes	—
438	C₂²×D₄	#392	1	4	yes	—
439	C₂²×D₄	#392	1	4	yes	—
440	C₂²×D₄	#392	1	4	yes	—
441	C₂²×D₄	#392	1	4	yes	—
442	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
443	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
444	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
445	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
446	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
447	C₂²×D₄	C₂×#120	1	2	yes	—
448	C₂²×D₄	C₂×#120	1	2	yes	—
449	C₂²×D₄	C₂×#120	1	2	yes	—
450	C₂²×D₄	C₂×#120	1	2	yes	—
451	C₂²×D₄	C₂×#121	1	2	yes	—
452	C₂²×D₄	C₂×#121	1	2	yes	—
453	C₂²×D₄	C₂×#121	1	2	yes	—
454	C₂²×D₄	C₂×#121	1	2	yes	—
455	C₂²×D₄	C₂×#121	1	2	yes	—
456	C₂²×D₄	C₂×#121	1	2	yes	—
457	C₂²×D₄	C₂×#127	1	2	yes	—
458	C₂²×D₄	C₂×#127	1	2	yes	—
459	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
460	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
461	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
462	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
463	C₂³×C₄	C₂×#120	1	2	yes	—
464	C₂³×C₄	C₂×#120	1	2	yes	—
465	C₂³×C₄	C₂×#120	1	1	yes	characteristic
466	C₂³×C₄	C₂×#120	1	1	yes	characteristic
467	C₂³×C₄	C₂×#120	1	1	yes	characteristic
468	C₂³×C₄	C₂×#120	1	1	yes	characteristic
469	C₂³×C₄	C₂×#120	1	1	yes	characteristic
470	C₂³×C₄	C₂×#120	1	2	yes	—
471	C₂³×C₄	C₂×#120	1	1	yes	characteristic
472	C₂³×C₄	C₂×#121	1	2	yes	—
473	C₂³×C₄	C₂×#121	1	2	yes	—
474	C₂³×C₄	C₂×#121	1	2	yes	—
475	C₂³×C₄	C₂×#121	1	2	yes	—
476	C₂³×C₄	C₂×#127	1	2	yes	—
477	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
478	C₂×C₄⋊C₄	#392	1	4	yes	—
479	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
480	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
481	C₂×C₂²⋊C₄	#392	1	4	yes	—
482	C₂×C₂²⋊C₄	#392	1	4	yes	—
483	C₂×C₂²⋊C₄	#392	1	4	yes	—
484	C₂×C₂²⋊C₄	#392	1	4	yes	—
485	C₂×C₂²⋊C₄	#392	1	4	yes	—
486	C₂×C₂²⋊C₄	#392	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂×#127	1	2	yes	—
491	C₂×C₄²	C₂×#120	1	2	yes	—
492	C₂×C₄²	C₂×#121	1	2	yes	—
493	C₂⁴	C₂×#392	1	2	yes	—
494	C₂⁴	C₂×#392	1	2	yes	—
495	C₂⁴	C₂×#392	1	2	yes	—
496	C₂⁴	C₂×#392	1	2	yes	—
497	C₂⁴	C₂×#392	1	2	yes	—
498	C₂⁴	C₂×#392	1	2	yes	—
499	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
500	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
501	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
502	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
503	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
504	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
505	C₂⁴	C₂²×#120	1	1	yes	characteristic
506	C₂⁴	C₂²×#120	1	1	yes	characteristic
507	C₂⁴	C₂²×#121	1	1	yes	characteristic
508	C₂⁴	C₂²×#121	1	1	yes	characteristic
509	C₂⁴	C₂²×#127	1	1	yes	characteristic
510	C₂×D₄	#2021	1	4	yes	—
511	C₂×D₄	#2021	1	4	yes	—
512	C₂×D₄	#2021	1	4	yes	—
513	C₂×D₄	#2021	1	4	yes	—
514	C₂²×C₄	C₂×#392	1	2	yes	—
515	C₂²×C₄	C₂×#392	1	2	yes	—
516	C₂²×C₄	C₂×#392	1	2	yes	—
517	C₂²×C₄	C₂×#392	1	2	yes	—
518	C₂²×C₄	C₂×#392	1	2	yes	—
519	C₂²×C₄	C₂×#392	1	2	yes	—
520	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
521	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
523	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
524	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
525	C₂³	C₂×#2021	1	2	yes	—
526	C₂³	C₂×#2021	1	2	yes	—
527	C₂³	C₂×#2021	1	2	yes	—
528	C₂³	C₂×#2021	1	2	yes	—
529	C₂³	#33551	1	2	yes	—
530	C₂³	#33552	1	2	yes	—
531	C₂³	C₂²×#392	1	1	yes	characteristic
532	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
533	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
534	C₂³	#60399	1	2	yes	—
535	C₂×C₄	C₂×#2021	1	2	yes	—
536	C₂×C₄	C₂×#2021	1	2	yes	—
537	C₂×C₄	#60401	1	2	yes	—
538	C₂²	#498931	1	4	yes	—
539	C₂²	C₂²×#2021	1	1	yes	characteristic
540	C₂²	#6431795	1	1	yes	characteristic
541	C₂²	#6431796	1	1	yes	characteristic
542	C₂²	C₂×#33551	1	1	yes	characteristic
543	C₂²	C₂×#33552	1	1	yes	characteristic
544	C₂²	#7622881	1	1	yes	characteristic
545	C₂²	#7622886	1	1	yes	characteristic
546	C₂	C₂×#498931	1	1	yes	characteristic
547	C₂	#72251254	1	1	yes	characteristic
548	C₂	#72256635	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2021
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×D₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72263832	C₂	semidirect
2. #72263831	C₂	semidirect
3. #72263830	C₂	semidirect
4. #72263823	C₂	semidirect
5. #72263822	C₂	semidirect
6. #72263731	C₂	semidirect
7. #72263635	C₂	semidirect
8. #72263425	C₂	semidirect
9. #72260584	C₂	semidirect
10. #72256817	C₂	semidirect
11. #72251183	C₂	semidirect
12. #72240278	C₂	semidirect
13. #72236734	C₂	semidirect
14. #72236694	C₂	semidirect
15. C₂×#144415	C₂	semidirect
16. #72236685	C₂	semidirect
17. #72236679	C₂	semidirect
18. #72233659	C₂	semidirect
19. #72213293	C₂	semidirect
38. #4375545	C₂²	semidirect
39. #4375184	C₂²	semidirect
40. #4328628	C₂²	semidirect
41. #4312024	C₂²	semidirect
42. #948453	C₂²	semidirect
43. #947141	C₂²	semidirect
44. #945697	C₂²	semidirect
45. #848801	C₂²	semidirect
46. #848397	C₂²	semidirect
47. #771668	C₂²	semidirect
48. #763514	C₂²	semidirect
49. C₂×#15784	C₂²	semidirect
51. #496416	C₂²	semidirect
52. #496307	C₂²	semidirect
53. #496225	C₂²	semidirect
54. #496225	C₂²	semidirect
55. #496191	C₂²	semidirect
56. #496189	C₂²	semidirect
57. #493998	C₂²	semidirect
58. #493963	C₂²	semidirect
59. #493879	C₂²	semidirect
60. C₂×#12852	C₂²	semidirect
61. #493370	C₂²	semidirect
62. C₂×#12694	C₂²	semidirect
69. #144429	C₂²	semidirect
70. #144429	C₂²	semidirect
71. #144428	C₂²	semidirect
72. #144415	C₂²	semidirect
73. #144415	C₂²	semidirect
74. #144415	C₂²	semidirect
75. #144415	C₂²	semidirect
76. #144415	C₂²	semidirect
77. #144415	C₂²	semidirect
78. #144414	C₂²	semidirect
79. #144414	C₂²	semidirect
80. #144414	C₂²	semidirect
81. #144404	C₂²	semidirect
82. #144388	C₂²	semidirect
83. #144388	C₂²	semidirect
84. #144386	C₂²	semidirect
85. #128081	C₂²	semidirect
86. #128073	C₂²	semidirect
87. #128073	C₂²	semidirect
88. #128043	C₂²	semidirect
89. C₂×#7304	C₂²	semidirect
90. C₂×#7304	C₂²	semidirect
91. #62983	D₄	semidirect
92. D₄×H(5,𝔽₂)	D₄	semidirect
96. C₂²×#548	D₄	semidirect
101. C₂²×#518	D₄	semidirect
102. C₂×#2856	D₄	semidirect
104. C₂×#2548	D₄	semidirect
108. C₂×#2431	D₄	semidirect
109. C₂×#2436	D₄	semidirect
116. C₂×#2657	D₄	semidirect
117. C₂×#2620	D₄	semidirect
121. C₂×D₄×C₂²⋊C₄	D₄	semidirect
125. C₂×#2290	D₄	semidirect
135. D₄×#100	D₄	semidirect
136. D₄×#99	D₄	semidirect
162. #14257	D₄	semidirect
163. #14255	D₄	semidirect
164. #14255	D₄	semidirect
165. #14136	D₄	semidirect
166. #14134	D₄	semidirect
167. #14134	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72263832	2
#72263831	2
#72263830	2
#72263823	2
#72263822	2
#72263731	2
#72263635	2
#72263425	2
#72260584	2
#72256817	2
#72251183	2
#72240278	2
#72236734	2
#72236694	2
C₂×#144415	2
#72236685	2
#72236679	2
#72233659	2
#72213293	2