Subgroups — #72324277

Order 4096.

At least 23142 conjugacy classes of subgroups; only the 987 normal subgroups are shown.

The subgroup lattice has 551 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72324276	C₂	1	2	yes	maximal, complemented
2	#72324270	C₂	1	2	yes	maximal, complemented
3	#72324269	C₂	1	2	yes	maximal, complemented
4	#72324268	C₂	1	2	yes	maximal, complemented
5	#72324258	C₂	1	2	yes	maximal, complemented
6	#72324255	C₂	1	2	yes	maximal, complemented
7	#72310189	C₂	1	1	yes	maximal, characteristic, complemented
8	#72266709	C₂	1	4	yes	maximal, complemented
9	#72266708	C₂²	1	4	yes	complemented
10	#72266698	C₂²	1	4	yes	complemented
11	#72266581	C₂	1	1	yes	maximal, characteristic, complemented
12	#72266557	C₂²	1	2	yes	complemented
13	#72266555	C₂²	1	1	yes	characteristic, complemented
14	#72266553	C₂²	1	2	yes	—
15	#72266521	C₂²	1	1	yes	characteristic, complemented
16	#72266305	C₂²	1	4	yes	complemented
17	#72266277	C₂²	1	4	yes	complemented
18	#72263169	C₂	1	4	yes	maximal, complemented
19	#72263168	C₂²	1	2	yes	complemented
20	#72263146	C₂²	1	4	yes	complemented
21	#72263135	C₂²	1	4	yes	complemented
22	#72263134	C₂²	1	4	yes	complemented
23	#72259157	C₂²	1	2	yes	complemented
24	#72259147	C₂²	1	2	yes	complemented
25	#72259136	C₂²	1	1	yes	characteristic, complemented
26	#72259117	C₂²	1	1	yes	characteristic, complemented
27	#72258968	C₂	1	1	yes	maximal, characteristic, complemented
28	#72258884	C₂²	1	2	yes	—
29	#72256119	C₂²	1	2	yes	complemented
30	#72238595	C₂²	1	2	yes	complemented
31	#72238480	C₂²	1	4	yes	complemented
32	#72237603	C₂	1	1	yes	maximal, characteristic, complemented
33	#72237600	C₂²	1	2	yes	complemented
34	#72237598	C₂²	1	4	yes	complemented
35	#72237583	C₂²	1	2	yes	complemented
36	#72237033	C₂²	1	1	yes	characteristic, complemented
37	#72234789	C₂	1	1	yes	maximal, characteristic, complemented
38	#72234757	C₂²	1	4	yes	complemented
39	#72234724	C₂²	1	2	yes	complemented
40	#72234636	C₂²	1	1	yes	characteristic
41	#72233067	C₂²	1	4	yes	complemented
42	#72232980	C₂²	1	2	yes	complemented
43	#72227568	C₂	1	2	yes	maximal, complemented
44	#72227566	C₂²	1	4	yes	complemented
45	#72227566	C₂²	1	2	yes	complemented
46	#72227564	C₂²	1	4	yes	complemented
47	#72227564	C₂²	1	2	yes	complemented
48	#72226102	C₂	1	1	yes	maximal, characteristic, complemented
49	#72226097	C₂²	1	2	yes	complemented
50	#72226093	C₂²	1	2	yes	complemented
51	#72226093	C₂²	1	4	yes	complemented
52	#72226091	C₂²	1	2	yes	complemented
53	#72226008	C₂²	1	2	yes	complemented
54	#72225997	C₂	1	1	yes	maximal, characteristic, complemented
55	#72225991	C₂²	1	2	yes	complemented
56	#72225989	C₂²	1	4	yes	complemented
57	#72225987	C₂²	1	2	yes	complemented
58	#72225987	C₂²	1	2	yes	complemented
59	#72225985	C₂²	1	2	yes	complemented
60	#72225870	C₂²	1	1	yes	characteristic, complemented
61	#72225712	C₂²	1	1	yes	characteristic, complemented
62	#72225712	C₂²	1	2	yes	complemented
63	#72224136	C₂²	1	1	yes	characteristic, complemented
64	#72219314	C₂²	1	1	yes	characteristic, complemented
65	#72219311	C₂²	1	1	yes	characteristic, complemented
66	#72219264	C₂²	1	1	yes	characteristic
67	#72219254	C₂²	1	1	yes	characteristic
68	#72215688	C₂	1	2	yes	maximal, complemented
69	#72215671	C₂²	1	4	yes	complemented
70	#72215671	C₂²	1	2	yes	complemented
71	#72215653	C₂²	1	2	yes	complemented
72	#72215653	C₂²	1	4	yes	complemented
73	#120²	C₂²	1	1	yes	characteristic, complemented
74	#72213827	C₂²	1	2	yes	complemented
75	#72213827	C₂²	1	4	yes	complemented
76	#72210587	C₂²	1	2	yes	—
77	#72210587	C₂²	1	4	yes	complemented
78	#72210547	C₂²	1	2	yes	complemented
79	#72209835	C₂²	1	2	yes	complemented
80	#72209835	C₂²	1	4	yes	complemented
81	#72209716	C₂²	1	2	yes	complemented
82	#72209699	C₂²	1	1	yes	characteristic, complemented
83	#10586404	C₂³	1	1	yes	characteristic, complemented
84	C₂²×#3532	D₄	1	1	yes	characteristic, complemented
85	C₂⁴×#120	D₄	1	1	yes	characteristic, complemented
86	C₂×#46996	D₄	1	1	yes	characteristic, complemented
87	C₂×#34980	C₂³	1	1	yes	characteristic
88	#6499870	C₂³	1	2	yes	complemented
89	#6499867	C₂³	1	2	yes	—
90	#6499867	C₂³	1	4	yes	—
91	#6374128	C₂³	1	1	yes	characteristic, complemented
92	#6342371	D₄	1	1	yes	characteristic, complemented
93	#6342371	C₂³	1	1	yes	characteristic
94	#5486275	D₄	1	2	yes	complemented
95	#5486275	D₄	1	2	yes	complemented
96	#5474299	D₄	1	2	yes	complemented
97	#5119613	C₂³	1	2	yes	—
98	#5063443	D₄	1	2	yes	complemented
99	#5063443	C₂³	1	2	yes	—
100	#5037287	D₄	1	2	yes	complemented
101	#5035967	D₄	1	2	yes	complemented
102	#5025789	C₂³	1	1	yes	characteristic
103	#5025782	D₄	1	1	yes	characteristic, complemented
104	#5024691	D₄	1	1	yes	characteristic, complemented
105	#5021140	D₄	1	1	yes	characteristic, complemented
106	#5021138	D₄	1	2	yes	complemented
107	#5021138	C₂³	1	1	yes	characteristic
108	#5021138	C₂³	1	2	yes	—
109	#5020751	C₂³	1	2	yes	—
110	#5020751	C₂³	1	1	yes	characteristic
111	#4975876	D₄	1	2	yes	complemented
112	#4941678	D₄	1	2	yes	complemented
113	#4466055	C₂³	1	2	yes	—
114	#4430405	D₄	1	1	yes	characteristic, complemented
115	#4423579	D₄	1	2	yes	complemented
116	#4422949	C₂³	1	1	yes	characteristic
117	#4420586	D₄	1	1	yes	characteristic, complemented
118	#4380237	C₂³	1	2	yes	—
119	#4308128	D₄	1	1	yes	characteristic, complemented
120	#4308128	C₂³	1	1	yes	characteristic
121	#4122215	D₄	1	2	yes	complemented
122	#2435299	C₂³	1	2	yes	—
123	#2356274	D₄	1	2	yes	complemented
124	#2356274	C₂³	1	2	yes	—
125	#2109240	D₄	1	2	yes	complemented
126	#2039918	D₄	1	2	yes	complemented
127	#1442757	D₄	1	2	yes	complemented
128	#1419371	D₄	1	2	yes	complemented
129	#845298	D₄	1	2	yes	complemented
130	#763333	C₂³	1	1	yes	characteristic
131	#686187	D₄	1	1	yes	characteristic, complemented
132	#648360	C₂³	1	2	yes	—
133	#648360	C₂³	1	1	yes	characteristic
134	#647656	D₄	1	2	yes	complemented
135	#647656	C₂³	1	1	yes	characteristic
136	#647656	C₂³	1	2	yes	—
137	#617161	D₄	1	2	yes	complemented
138	#616969	D₄	1	2	yes	complemented
139	#616969	C₂³	1	2	yes	—
140	#616961	D₄	1	1	yes	characteristic, complemented
141	#616960	C₂³	1	1	yes	characteristic
142	#616960	C₂³	1	2	yes	—
143	C₂×#15947	D₄	1	1	yes	characteristic, complemented
144	#576160	D₄	1	1	yes	characteristic, complemented
145	#552670	D₄	1	1	yes	characteristic, complemented
146	#517411	D₄	1	1	yes	characteristic, complemented
147	#347042	C₂³	1	2	yes	—
148	#347042	C₂³	1	2	yes	complemented
149	#346456	C₂³	1	4	yes	complemented
150	#346456	C₂³	1	2	yes	complemented
151	#346446	C₂³	1	4	yes	—
152	#346446	C₂³	1	2	yes	—
153	#188122	C₂³	1	2	yes	complemented
154	#188109	C₂³	1	1	yes	characteristic, complemented
155	#188049	C₂³	1	2	yes	complemented
156	#188049	C₂³	1	1	yes	characteristic, complemented
157	#187934	C₂³	1	4	yes	complemented
158	#139720	C₂³	1	4	yes	complemented
159	#139720	C₂³	1	2	yes	complemented
160	#139718	C₂³	1	4	yes	—
161	#139718	C₂³	1	2	yes	—
162	#139716	C₂³	1	4	yes	—
163	#139716	C₂³	1	2	yes	—
164	#139716	C₂³	1	4	yes	complemented
165	#139716	C₂³	1	2	yes	complemented
166	#139504	C₂³	1	4	yes	—
167	#139504	C₂³	1	4	yes	—
168	#139504	C₂³	1	4	yes	—
169	#139486	C₂³	1	4	yes	complemented
170	#139486	C₂³	1	4	yes	complemented
171	#139486	C₂³	1	4	yes	complemented
172	#135561	C₂³	1	4	yes	complemented
173	#135507	C₂³	1	4	yes	complemented
174	#134036	C₂³	1	2	yes	complemented
175	#134033	C₂³	1	2	yes	—
176	#134033	C₂³	1	4	yes	—
177	#133825	C₂³	1	2	yes	complemented
178	#133822	C₂³	1	2	yes	—
179	#133822	C₂³	1	4	yes	—
180	#119550	C₂³	1	4	yes	complemented
181	#115690	C₂³	1	2	yes	—
182	#115690	C₂³	1	4	yes	—
183	#115631	C₂³	1	2	yes	complemented
184	C₂⁸	C₂×D₄	1	1	yes	characteristic, complemented
185	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
186	#62817	C₂⁴	1	2	yes	—
187	C₂²×#551	C₂×D₄	1	1	yes	characteristic
188	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
189	C₂²×D₄²	C₂×D₄	1	2	yes	complemented
190	C₂²×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
191	C₂²×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
192	C₂²×#560	C₂×D₄	1	1	yes	characteristic
193	C₂²×#535	C₂×D₄	1	1	yes	characteristic
194	C₂²×#534	C₂×D₄	1	1	yes	characteristic
195	C₂²×#534	C₂⁴	1	1	yes	characteristic
196	C₂³×#120	C₂×D₄	1	1	yes	characteristic
197	C₂³×#120	C₂×D₄	1	1	yes	characteristic
198	C₂³×#120	C₂×D₄	1	2	yes	—
199	C₂³×#120	C₂×D₄	1	2	yes	complemented
200	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
201	C₂×#2760	C₂×D₄	1	2	yes	complemented
202	C₂×#2840	C₂×D₄	1	1	yes	characteristic, complemented
203	C₂×#2840	C₂×D₄	1	2	yes	complemented
204	C₂×#2849	C₂×D₄	1	1	yes	characteristic
205	C₂×#2849	C₂×D₄	1	1	yes	characteristic
206	C₂×#2846	C₂×D₄	1	2	yes	—
207	C₂×#2846	C₂×D₄	1	1	yes	characteristic
208	C₂×#2846	C₂×D₄	1	2	yes	—
209	C₂×#2846	C₂⁴	1	1	yes	characteristic
210	C₂×#2846	C₂⁴	1	2	yes	—
211	C₂×#2430	C₂×D₄	1	2	yes	—
212	C₂×#2404	C₂×D₄	1	2	yes	—
213	C₂×#2431	C₂×D₄	1	2	yes	—
214	C₂×#2403	C₂×D₄	1	1	yes	characteristic, complemented
215	C₂×#2403	C₂×D₄	1	2	yes	complemented
216	C₂×#2615	C₂×D₄	1	2	yes	—
217	C₂×#2613	C₂×D₄	1	1	yes	characteristic
218	C₂×#2613	C₂×D₄	1	1	yes	characteristic
219	C₂×#2613	C₂×D₄	1	1	yes	characteristic
220	C₂×#2613	C₂⁴	1	1	yes	characteristic
221	C₂×#2308	C₂×D₄	1	1	yes	characteristic
222	C₂×#2308	C₂×D₄	1	1	yes	characteristic
223	C₂×#2308	C₂×D₄	1	2	yes	complemented
224	C₂²×#379	C₂×D₄	1	1	yes	characteristic
225	#21746	C₂⁴	1	2	yes	—
226	#21746	C₂⁴	1	4	yes	—
227	#17271	C₂×D₄	1	2	yes	complemented
228	#17271	C₂×D₄	1	2	yes	complemented
229	#17105	C₂×D₄	1	2	yes	complemented
230	#17105	C₂×D₄	1	2	yes	complemented
231	#16247	C₂×D₄	1	2	yes	complemented
232	#16211	C₂×D₄	1	2	yes	complemented
233	#15948	C₂×D₄	1	2	yes	—
234	#15948	C₂×D₄	1	2	yes	—
235	#15948	C₂×D₄	1	1	yes	characteristic
236	#15948	C₂×D₄	1	1	yes	characteristic
237	#15947	C₂×D₄	1	1	yes	characteristic
238	#15947	C₂×D₄	1	1	yes	characteristic
239	#15947	C₂×D₄	1	1	yes	characteristic
240	#15947	C₂×D₄	1	1	yes	characteristic
241	#15947	C₂×D₄	1	2	yes	—
242	#15947	C₂×D₄	1	2	yes	—
243	#15947	C₂×D₄	1	2	yes	complemented
244	#15947	C₂×D₄	1	2	yes	complemented
245	#15947	C₂⁴	1	1	yes	characteristic
246	#15947	C₂⁴	1	1	yes	characteristic
247	#15673	C₂×D₄	1	2	yes	—
248	#15668	C₂×D₄	1	2	yes	—
249	#15668	C₂×D₄	1	2	yes	—
250	#15467	C₂×D₄	1	2	yes	complemented
251	#15467	C₂×D₄	1	2	yes	complemented
252	#15467	C₂×D₄	1	2	yes	complemented
253	#15467	C₂×D₄	1	2	yes	complemented
254	#15412	C₂×D₄	1	2	yes	—
255	#15412	C₂×D₄	1	2	yes	—
256	#15310	C₂×D₄	1	2	yes	—
257	#15267	C₂×D₄	1	2	yes	complemented
258	#15267	C₂×D₄	1	2	yes	complemented
259	#15267	C₂×D₄	1	2	yes	complemented
260	#15267	C₂×D₄	1	2	yes	complemented
261	#15262	C₂×D₄	1	1	yes	characteristic
262	#15261	C₂×D₄	1	1	yes	characteristic
263	#15259	C₂×D₄	1	1	yes	characteristic
264	#15259	C₂×D₄	1	1	yes	characteristic
265	#15259	C₂×D₄	1	2	yes	—
266	#15259	C₂×D₄	1	2	yes	complemented
267	#15259	C₂×D₄	1	2	yes	complemented
268	#15259	C₂⁴	1	1	yes	characteristic
269	#15259	C₂⁴	1	2	yes	—
270	#15258	C₂×D₄	1	1	yes	characteristic
271	#15258	C₂×D₄	1	1	yes	characteristic
272	#15258	C₂×D₄	1	2	yes	—
273	#15258	C₂×D₄	1	2	yes	complemented
274	#15258	C₂×D₄	1	2	yes	complemented
275	#15258	C₂⁴	1	2	yes	—
276	#15258	C₂⁴	1	1	yes	characteristic
277	#15257	C₂×D₄	1	2	yes	—
278	#15257	C₂×D₄	1	2	yes	—
279	#15257	C₂×D₄	1	2	yes	—
280	#15257	C₂×D₄	1	2	yes	—
281	#15257	C₂×D₄	1	2	yes	—
282	#15257	C₂×D₄	1	2	yes	—
283	#14679	C₂×D₄	1	2	yes	complemented
284	#14679	C₂×D₄	1	1	yes	characteristic, complemented
285	#14679	C₂×D₄	1	2	yes	complemented
286	#14679	C₂×D₄	1	1	yes	characteristic, complemented
287	#14659	C₂×D₄	1	2	yes	—
288	#14658	C₂×D₄	1	1	yes	characteristic
289	#14657	C₂×D₄	1	1	yes	characteristic
290	#14657	C₂×D₄	1	2	yes	complemented
291	#14657	C₂×D₄	1	2	yes	complemented
292	#14649	C₂×D₄	1	2	yes	complemented
293	#14609	C₂×D₄	1	2	yes	complemented
294	#14533	C₂×D₄	1	2	yes	complemented
295	#14507	C₂×D₄	1	2	yes	complemented
296	#14492	C₂×D₄	1	2	yes	complemented
297	#14419	C₂×D₄	1	2	yes	complemented
298	#14335	C₂×D₄	1	2	yes	—
299	#14335	C₂×D₄	1	1	yes	characteristic
300	#14290	C₂×D₄	1	2	yes	—
301	#14262	C₂×D₄	1	2	yes	complemented
302	#14262	C₂×D₄	1	2	yes	complemented
303	#14255	C₂×D₄	1	2	yes	—
304	#14255	C₂×D₄	1	2	yes	—
305	#14255	C₂⁴	1	2	yes	—
306	#14207	C₂×D₄	1	2	yes	complemented
307	#14167	C₂×D₄	1	1	yes	characteristic
308	#14135	C₂×D₄	1	2	yes	—
309	#14134	C₂×D₄	1	1	yes	characteristic
310	#14134	C₂×D₄	1	2	yes	complemented
311	#14134	C₂×D₄	1	2	yes	complemented
312	#13903	C₂×D₄	1	2	yes	—
313	C₂×#1438	C₂×D₄	1	1	yes	characteristic
314	#13827	C₂×D₄	1	2	yes	complemented
315	#13827	C₂×D₄	1	1	yes	characteristic, complemented
316	C₂²⋊C₄²	C₂×D₄	1	2	yes	complemented
317	C₂²⋊C₄²	C₂×D₄	1	1	yes	characteristic, complemented
318	#8547	C₂⁴	1	4	yes	—
319	#8547	C₂⁴	1	2	yes	—
320	#8541	C₂⁴	1	2	yes	—
321	C₂⁷	#120	1	1	yes	characteristic
322	C₂⁷	#120	1	1	yes	characteristic, complemented
323	C₂⁷	C₂²×D₄	1	1	yes	characteristic
324	C₂⁷	C₂²×D₄	1	2	yes	—
325	C₂³×#41	#120	1	1	yes	characteristic, complemented
326	C₂³×#41	#120	1	2	yes	complemented
327	C₂⁴×D₄	#120	1	1	yes	characteristic
328	C₂⁴×D₄	#120	1	1	yes	characteristic
329	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
330	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
331	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂⁵×C₄	#120	1	1	yes	characteristic
333	C₂²×#127	#120	1	1	yes	characteristic, complemented
334	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
335	C₂²×#127	C₂²×D₄	1	2	yes	—
336	C₂²×#124	#120	1	1	yes	characteristic, complemented
337	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
338	C₂²×#124	C₂²×D₄	1	2	yes	—
339	C₂²×#123	#120	1	1	yes	characteristic
340	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
341	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
342	C₂²×#123	C₂²×D₄	1	2	yes	—
343	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
344	C₂²×#121	C₂²×D₄	1	2	yes	—
345	C₂²×#121	C₂²×D₄	1	2	yes	—
346	C₂²×#120	#120	1	1	yes	characteristic
347	C₂²×#120	#120	1	2	yes	—
348	C₂²×#120	#120	1	1	yes	characteristic
349	C₂²×#120	#120	1	2	yes	—
350	C₂²×#120	#120	1	1	yes	characteristic
351	C₂²×#120	#120	1	2	yes	—
352	C₂²×#120	#120	1	2	yes	—
353	C₂²×#120	#120	1	2	yes	—
354	C₂²×#120	#120	1	2	yes	—
355	C₂²×#120	#120	1	1	yes	characteristic, complemented
356	C₂²×#120	#120	1	1	yes	characteristic, complemented
357	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
358	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
359	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
360	C₂²×#120	C₂²×D₄	1	2	yes	—
361	C₂²×#120	C₂²×D₄	1	2	yes	—
362	C₂²×#120	C₂²×D₄	1	2	yes	—
363	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
364	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
365	C₂²×#120	C₂²×D₄	1	2	yes	—
366	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
367	C₂²×#120	C₂²×D₄	1	2	yes	—
368	C₂²×#120	C₂⁵	1	1	yes	characteristic
369	C₂²×#117	#120	1	1	yes	characteristic, complemented
370	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
371	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
372	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
373	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
374	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
375	C₂×#395	#120	1	2	yes	complemented
376	C₂×#394	#120	1	2	yes	complemented
377	C₂×#393	#120	1	2	yes	complemented
378	C₂×#393	#120	1	2	yes	complemented
379	C₂×#393	C₂²×D₄	1	2	yes	—
380	C₂×#393	C₂²×D₄	1	2	yes	—
381	C₂×#393	C₂²×D₄	1	2	yes	—
382	C₂×#392	#120	1	2	yes	complemented
383	C₂×#392	#120	1	2	yes	complemented
384	C₂×#392	C₂²×D₄	1	2	yes	—
385	C₂×#392	C₂²×D₄	1	2	yes	—
386	C₂×#392	C₂²×D₄	1	2	yes	—
387	C₂×#391	#120	1	2	yes	complemented
388	C₂×#390	#120	1	2	yes	complemented
389	C₂×#381	#120	1	1	yes	characteristic
390	C₂×#381	#120	1	1	yes	characteristic
391	C₂×#381	#120	1	1	yes	characteristic
392	C₂×#381	#120	1	2	yes	complemented
393	C₂×#381	C₂²×D₄	1	1	yes	characteristic
394	C₂×#380	#120	1	2	yes	complemented
395	C₂×#379	#120	1	1	yes	characteristic
396	C₂×#379	#120	1	1	yes	characteristic
397	C₂×#379	#120	1	1	yes	characteristic
398	C₂×#379	#120	1	2	yes	—
399	C₂×#379	#120	1	2	yes	—
400	C₂×#379	#120	1	2	yes	complemented
401	C₂×#379	#120	1	2	yes	complemented
402	C₂×#379	#120	1	2	yes	complemented
403	C₂×#379	C₂²×D₄	1	2	yes	—
404	C₂×#379	C₂²×D₄	1	1	yes	characteristic
405	C₂×#379	C₂²×D₄	1	2	yes	—
406	C₂×#379	C₂²×D₄	1	1	yes	characteristic
407	C₂×#379	C₂²×D₄	1	1	yes	characteristic
408	C₂×#379	C₂²×D₄	1	2	yes	—
409	C₂×#379	C₂²×D₄	1	1	yes	characteristic
410	C₂×#379	C₂²×D₄	1	2	yes	—
411	C₂×#379	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	complemented
413	C₂²×#95	#120	1	2	yes	complemented
414	#1445	#120	1	2	yes	complemented
415	#1445	#120	1	2	yes	complemented
416	#1440	#120	1	2	yes	—
417	#1440	#120	1	2	yes	—
418	#1440	#120	1	2	yes	complemented
419	#1440	#120	1	2	yes	complemented
420	#1440	C₂²×D₄	1	2	yes	—
421	#1440	C₂²×D₄	1	2	yes	—
422	#1438	#120	1	2	yes	—
423	#1438	#120	1	2	yes	—
424	#1438	#120	1	2	yes	—
425	#1438	#120	1	2	yes	—
426	#1438	#120	1	2	yes	—
427	#1438	#120	1	2	yes	—
428	#1438	#120	1	2	yes	complemented
429	#1438	#120	1	2	yes	complemented
430	#1438	C₂²×D₄	1	1	yes	characteristic
431	#1438	C₂²×D₄	1	1	yes	characteristic
432	#1438	C₂²×D₄	1	2	yes	—
433	#1438	C₂²×D₄	1	2	yes	—
434	#1438	C₂²×D₄	1	1	yes	characteristic
435	#1438	C₂²×D₄	1	2	yes	—
436	#1438	C₂²×D₄	1	2	yes	—
437	#1438	C₂²×D₄	1	2	yes	—
438	#1438	C₂²×D₄	1	2	yes	—
439	#1438	C₂²×D₄	1	1	yes	characteristic
440	#1437	#120	1	2	yes	complemented
441	#1437	#120	1	2	yes	complemented
442	#1437	#120	1	2	yes	complemented
443	#1437	#120	1	2	yes	complemented
444	#1437	C₂²×D₄	1	2	yes	—
445	#1437	C₂²×D₄	1	2	yes	—
446	#1437	C₂²×D₄	1	2	yes	—
447	#1437	C₂²×D₄	1	2	yes	—
448	#1437	C₂²×D₄	1	2	yes	—
449	#1437	C₂²×D₄	1	2	yes	—
450	#1436	#120	1	2	yes	complemented
451	#1436	#120	1	2	yes	complemented
452	C₂⁶	C₂×#120	1	1	yes	characteristic
453	C₂⁶	C₂×#120	1	1	yes	characteristic
454	C₂⁶	C₂×#120	1	2	yes	—
455	C₂⁶	C₂×#120	1	1	yes	characteristic
456	C₂⁶	C₂×#120	1	2	yes	—
457	C₂⁶	C₂×#120	1	1	yes	characteristic
458	C₂⁶	C₂×#120	1	1	yes	characteristic
459	C₂⁶	C₂×#120	1	1	yes	characteristic
460	C₂⁶	C₂×#120	1	1	yes	characteristic
461	C₂⁶	C₂³×D₄	1	1	yes	characteristic
462	C₂³×Q₈	C₂×#120	1	2	yes	—
463	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
464	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
465	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
466	C₂³×D₄	C₂×#120	1	2	yes	—
467	C₂³×D₄	C₂×#120	1	2	yes	—
468	C₂³×D₄	C₂×#120	1	1	yes	characteristic
469	C₂³×D₄	C₂×#120	1	1	yes	characteristic
470	C₂³×D₄	C₂×#120	1	2	yes	—
471	C₂³×D₄	C₂×#120	1	1	yes	characteristic
472	C₂³×D₄	C₂×#120	1	2	yes	—
473	C₂³×D₄	C₂×#120	1	1	yes	characteristic
474	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
475	C₂³×D₄	C₂³×D₄	1	2	yes	—
476	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
477	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
478	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
479	C₂⁴×C₄	C₂×#120	1	2	yes	—
480	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
481	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
482	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
483	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
484	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
486	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
487	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
488	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
489	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
490	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
492	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
493	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
494	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
495	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
496	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
497	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
498	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
499	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
501	C₂²×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
502	C₂²×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
503	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
504	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
505	C₂²×C₄²	C₂×#120	1	2	yes	—
506	C₂²×C₄²	C₂×#120	1	2	yes	—
507	C₂×#95	C₂×#120	1	2	yes	—
508	C₂×#95	C₂×#120	1	2	yes	—
509	C₂×#95	C₂×#120	1	2	yes	—
510	C₂×#95	C₂×#120	1	2	yes	—
511	C₂×#95	C₂×#120	1	2	yes	—
512	C₂×#95	C₂×#120	1	2	yes	—
513	C₂⁵	#2846	1	1	yes	characteristic
514	C₂⁵	#2846	1	1	yes	characteristic
515	C₂⁵	#2846	1	1	yes	characteristic
516	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
517	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
518	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
519	C₂⁵	#3026	1	1	yes	characteristic
520	C₂⁵	#3026	1	1	yes	characteristic
521	C₂⁵	C₂²×#120	1	1	yes	characteristic
522	C₂⁵	C₂²×#120	1	1	yes	characteristic
523	C₂⁵	C₂²×#120	1	2	yes	—
524	C₂³×C₄	#2846	1	2	yes	—
525	C₂³×C₄	#2846	1	1	yes	characteristic
526	C₂³×C₄	#2846	1	2	yes	—
527	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
528	C₂³×C₄	C₂²×#120	1	2	yes	—
529	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
530	C₂⁴	#32898	1	1	yes	characteristic
531	C₂⁴	#32898	1	1	yes	characteristic
532	C₂⁴	#32898	1	1	yes	characteristic
533	C₂⁴	#32898	1	1	yes	characteristic
534	C₂⁴	#33551	1	4	yes	—
535	C₂⁴	C₂×#2846	1	1	yes	characteristic
536	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
537	C₂⁴	C₂×#3026	1	1	yes	characteristic
538	C₂⁴	#60399	1	4	yes	—
539	C₂³	#511790	1	2	yes	—
540	C₂³	C₂×#32898	1	1	yes	characteristic
541	C₂³	#6628896	1	2	yes	—
542	C₂³	C₂×#33551	1	2	yes	—
543	C₂²	C₂×#511790	1	1	yes	characteristic
544	C₂²	#72216366	1	2	yes	—
545	C₂²	#72219040	1	1	yes	characteristic
546	C₂²	#72225712	1	1	yes	characteristic
547	C₂²	#72234419	1	2	yes	—
548	C₂	#72266330	1	1	yes	characteristic
549	C₂	#72324265	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72225712
commutator, Frattini, cosocle	C₂²×#120	C₂⁵
LCS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#534 ◁ G
LECS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72324276	C₂	semidirect
2. #72324270	C₂	semidirect
3. #72324269	C₂	semidirect
4. #72324268	C₂	semidirect
5. #72324258	C₂	semidirect
6. #72324255	C₂	semidirect
7. #72310189	C₂	semidirect
8. #72266709	C₂	semidirect
9. #72266708	C₂²	semidirect
10. #72266698	C₂²	semidirect
11. #72266581	C₂	semidirect
12. #72266557	C₂²	semidirect
13. #72266555	C₂²	semidirect
15. #72266521	C₂²	semidirect
16. #72266305	C₂²	semidirect
17. #72266277	C₂²	semidirect
18. #72263169	C₂	semidirect
19. #72263168	C₂²	semidirect
20. #72263146	C₂²	semidirect
21. #72263135	C₂²	semidirect
22. #72263134	C₂²	semidirect
23. #72259157	C₂²	semidirect
24. #72259147	C₂²	semidirect
25. #72259136	C₂²	semidirect
26. #72259117	C₂²	semidirect
27. #72258968	C₂	semidirect
29. #72256119	C₂²	semidirect
30. #72238595	C₂²	semidirect
31. #72238480	C₂²	semidirect
32. #72237603	C₂	semidirect
33. #72237600	C₂²	semidirect
34. #72237598	C₂²	semidirect
35. #72237583	C₂²	semidirect
36. #72237033	C₂²	semidirect
37. #72234789	C₂	semidirect
38. #72234757	C₂²	semidirect
39. #72234724	C₂²	semidirect
41. #72233067	C₂²	semidirect
42. #72232980	C₂²	semidirect
43. #72227568	C₂	semidirect
44. #72227566	C₂²	semidirect
45. #72227566	C₂²	semidirect
46. #72227564	C₂²	semidirect
47. #72227564	C₂²	semidirect
48. #72226102	C₂	semidirect
49. #72226097	C₂²	semidirect
50. #72226093	C₂²	semidirect
51. #72226093	C₂²	semidirect
52. #72226091	C₂²	semidirect
53. #72226008	C₂²	semidirect
54. #72225997	C₂	semidirect
55. #72225991	C₂²	semidirect
56. #72225989	C₂²	semidirect
57. #72225987	C₂²	semidirect
58. #72225987	C₂²	semidirect
59. #72225985	C₂²	semidirect
60. #72225870	C₂²	semidirect
61. #72225712	C₂²	semidirect
62. #72225712	C₂²	semidirect
63. #72224136	C₂²	semidirect
64. #72219314	C₂²	semidirect
65. #72219311	C₂²	semidirect
68. #72215688	C₂	semidirect
69. #72215671	C₂²	semidirect
70. #72215671	C₂²	semidirect
71. #72215653	C₂²	semidirect
72. #72215653	C₂²	semidirect
73. #120²	C₂²	semidirect
74. #72213827	C₂²	semidirect
75. #72213827	C₂²	semidirect
77. #72210587	C₂²	semidirect
78. #72210547	C₂²	semidirect
79. #72209835	C₂²	semidirect
80. #72209835	C₂²	semidirect
81. #72209716	C₂²	semidirect
82. #72209699	C₂²	semidirect
83. #10586404	C₂³	semidirect
84. C₂²×#3532	D₄	semidirect
85. C₂⁴×#120	D₄	semidirect
86. C₂×#46996	D₄	semidirect
88. #6499870	C₂³	semidirect
91. #6374128	C₂³	semidirect
92. #6342371	D₄	semidirect
94. #5486275	D₄	semidirect
95. #5486275	D₄	semidirect
96. #5474299	D₄	semidirect
98. #5063443	D₄	semidirect
100. #5037287	D₄	semidirect
101. #5035967	D₄	semidirect
103. #5025782	D₄	semidirect
104. #5024691	D₄	semidirect
105. #5021140	D₄	semidirect
106. #5021138	D₄	semidirect
111. #4975876	D₄	semidirect
112. #4941678	D₄	semidirect
114. #4430405	D₄	semidirect
115. #4423579	D₄	semidirect
117. #4420586	D₄	semidirect
119. #4308128	D₄	semidirect
121. #4122215	D₄	semidirect
123. #2356274	D₄	semidirect
125. #2109240	D₄	semidirect
126. #2039918	D₄	semidirect
127. #1442757	D₄	semidirect
128. #1419371	D₄	semidirect
129. #845298	D₄	semidirect
131. #686187	D₄	semidirect
134. #647656	D₄	semidirect
137. #617161	D₄	semidirect
138. #616969	D₄	semidirect
140. #616961	D₄	semidirect
143. C₂×#15947	D₄	semidirect
144. #576160	D₄	semidirect
145. #552670	D₄	semidirect
146. #517411	D₄	semidirect
148. #347042	C₂³	semidirect
149. #346456	C₂³	semidirect
150. #346456	C₂³	semidirect
153. #188122	C₂³	semidirect
154. #188109	C₂³	semidirect
155. #188049	C₂³	semidirect
156. #188049	C₂³	semidirect
157. #187934	C₂³	semidirect
158. #139720	C₂³	semidirect
159. #139720	C₂³	semidirect
164. #139716	C₂³	semidirect
165. #139716	C₂³	semidirect
169. #139486	C₂³	semidirect
170. #139486	C₂³	semidirect
171. #139486	C₂³	semidirect
172. #135561	C₂³	semidirect
173. #135507	C₂³	semidirect
174. #134036	C₂³	semidirect
177. #133825	C₂³	semidirect
180. #119550	C₂³	semidirect
183. #115631	C₂³	semidirect
184. C₂⁸	C₂×D₄	semidirect
189. C₂²×D₄²	C₂×D₄	semidirect
191. C₂²×H(3,𝔽₄)	C₂×D₄	semidirect
199. C₂³×#120	C₂×D₄	semidirect
200. C₂⁴×C₂²⋊C₄	C₂×D₄	semidirect
201. C₂×#2760	C₂×D₄	semidirect
202. C₂×#2840	C₂×D₄	semidirect
203. C₂×#2840	C₂×D₄	semidirect
214. C₂×#2403	C₂×D₄	semidirect
215. C₂×#2403	C₂×D₄	semidirect
223. C₂×#2308	C₂×D₄	semidirect
227. #17271	C₂×D₄	semidirect
228. #17271	C₂×D₄	semidirect
229. #17105	C₂×D₄	semidirect
230. #17105	C₂×D₄	semidirect
231. #16247	C₂×D₄	semidirect
232. #16211	C₂×D₄	semidirect
243. #15947	C₂×D₄	semidirect
244. #15947	C₂×D₄	semidirect
250. #15467	C₂×D₄	semidirect
251. #15467	C₂×D₄	semidirect
252. #15467	C₂×D₄	semidirect
253. #15467	C₂×D₄	semidirect
257. #15267	C₂×D₄	semidirect
258. #15267	C₂×D₄	semidirect
259. #15267	C₂×D₄	semidirect
260. #15267	C₂×D₄	semidirect
266. #15259	C₂×D₄	semidirect
267. #15259	C₂×D₄	semidirect
273. #15258	C₂×D₄	semidirect
274. #15258	C₂×D₄	semidirect
283. #14679	C₂×D₄	semidirect
284. #14679	C₂×D₄	semidirect
285. #14679	C₂×D₄	semidirect
286. #14679	C₂×D₄	semidirect
290. #14657	C₂×D₄	semidirect
291. #14657	C₂×D₄	semidirect
292. #14649	C₂×D₄	semidirect
293. #14609	C₂×D₄	semidirect
294. #14533	C₂×D₄	semidirect
295. #14507	C₂×D₄	semidirect
296. #14492	C₂×D₄	semidirect
297. #14419	C₂×D₄	semidirect
301. #14262	C₂×D₄	semidirect
302. #14262	C₂×D₄	semidirect
306. #14207	C₂×D₄	semidirect
310. #14134	C₂×D₄	semidirect
311. #14134	C₂×D₄	semidirect
314. #13827	C₂×D₄	semidirect
315. #13827	C₂×D₄	semidirect
316. C₂²⋊C₄²	C₂×D₄	semidirect
317. C₂²⋊C₄²	C₂×D₄	semidirect
322. C₂⁷	#120	semidirect
325. C₂³×#41	#120	semidirect
326. C₂³×#41	#120	semidirect
333. C₂²×#127	#120	semidirect
336. C₂²×#124	#120	semidirect
355. C₂²×#120	#120	semidirect
356. C₂²×#120	#120	semidirect
369. C₂²×#117	#120	semidirect
372. C₂³×C₂²⋊C₄	#120	semidirect
375. C₂×#395	#120	semidirect
376. C₂×#394	#120	semidirect
377. C₂×#393	#120	semidirect
378. C₂×#393	#120	semidirect
382. C₂×#392	#120	semidirect
383. C₂×#392	#120	semidirect
387. C₂×#391	#120	semidirect
388. C₂×#390	#120	semidirect
392. C₂×#381	#120	semidirect
394. C₂×#380	#120	semidirect
400. C₂×#379	#120	semidirect
401. C₂×#379	#120	semidirect
402. C₂×#379	#120	semidirect
412. C₂×C₄×C₂²⋊C₄	#120	semidirect
413. C₂²×#95	#120	semidirect
414. #1445	#120	semidirect
415. #1445	#120	semidirect
418. #1440	#120	semidirect
419. #1440	#120	semidirect
428. #1438	#120	semidirect
429. #1438	#120	semidirect
440. #1437	#120	semidirect
441. #1437	#120	semidirect
442. #1437	#120	semidirect
443. #1437	#120	semidirect
450. #1436	#120	semidirect
451. #1436	#120	semidirect

Maximal subgroups

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

subgroup	index
#72324276	2
#72324270	2
#72324269	2
#72324268	2
#72324258	2
#72324255	2
#72310189	2
#72266709	2
#72266581	2
#72263169	2
#72258968	2
#72237603	2
#72234789	2
#72227568	2
#72226102	2
#72225997	2
#72215688	2