Subgroups — #72316802

Order 2048.

At least 7767 conjugacy classes of subgroups; only the 780 normal subgroups are shown.

The subgroup lattice has 442 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72316792	C₂	1	1	yes	maximal, characteristic, complemented
2	#72316772	C₂	1	1	yes	maximal, characteristic, complemented
3	#72316758	C₂	1	1	yes	maximal, characteristic, complemented
4	#72316752	C₂	1	1	yes	maximal, characteristic, complemented
5	#72316751	C₂	1	1	yes	maximal, characteristic, complemented
6	#72316749	C₂	1	1	yes	maximal, characteristic, complemented
7	#72316740	C₂	1	1	yes	maximal, characteristic, complemented
8	#72316730	C₂	1	1	yes	maximal, characteristic, complemented
9	#72316726	C₂	1	1	yes	maximal, characteristic, complemented
10	#72316725	C₂	1	1	yes	maximal, characteristic, complemented
11	#72316709	C₂	1	4	yes	maximal, complemented
12	#72316692	C₂	1	4	yes	maximal, complemented
13	#72313433	C₂	1	1	yes	maximal, characteristic, complemented
14	#72306039	C₂	1	1	yes	maximal, characteristic, complemented
15	#72285018	C₂	1	1	yes	maximal, characteristic, complemented
16	#72282557	C₂	1	4	yes	maximal, complemented
17	#72282272	C₂	1	4	yes	maximal, complemented
18	#72236702	C₂	1	1	yes	maximal, characteristic, complemented
19	#72236596	C₂	1	1	yes	maximal, characteristic, complemented
20	#10586097	C₂²	1	1	yes	characteristic, complemented
21	#8195808	C₂²	1	1	yes	characteristic, complemented
22	#7737411	C₂²	1	1	yes	characteristic
23	#7513980	C₂²	1	2	yes	complemented
24	#7511801	C₂²	1	1	yes	characteristic, complemented
25	#7308986	C₂²	1	2	yes	complemented
26	#7301422	C₂²	1	2	yes	complemented
27	#7200002	C₂²	1	2	yes	complemented
28	#6653018	C₂²	1	1	yes	characteristic, complemented
29	#6629390	C₂²	1	1	yes	characteristic
30	#6629390	C₂²	1	1	yes	characteristic, complemented
31	#6629390	C₂²	1	1	yes	characteristic, complemented
32	#6628970	C₂²	1	1	yes	characteristic, complemented
33	#6591514	C₂²	1	4	yes	complemented
34	D₄×B(4,𝔽₂)	C₂²	1	4	yes	complemented
35	#6516757	C₂²	1	1	yes	characteristic
36	#6512761	C₂²	1	1	yes	characteristic
37	#6487648	C₂²	1	1	yes	characteristic
38	#6487648	C₂²	1	1	yes	characteristic, complemented
39	#6412324	C₂²	1	1	yes	characteristic, complemented
40	#6385980	C₂²	1	1	yes	characteristic, complemented
41	#6347443	C₂²	1	1	yes	characteristic, complemented
42	#6346637	C₂²	1	1	yes	characteristic, complemented
43	#500757	C₂²	1	4	yes	complemented
44	#500507	C₂²	1	4	yes	complemented
45	#496508	C₂²	1	1	yes	characteristic, complemented
46	#496508	C₂²	1	1	yes	characteristic, complemented
47	#496311	C₂²	1	1	yes	characteristic, complemented
48	#486513	C₂²	1	4	yes	complemented
49	#486243	C₂²	1	4	yes	complemented
50	#482657	C₂²	1	1	yes	characteristic, complemented
51	#482363	C₂²	1	1	yes	characteristic, complemented
52	#482234	C₂²	1	1	yes	characteristic, complemented
53	#482234	C₂²	1	1	yes	characteristic, complemented
54	#480580	C₂²	1	1	yes	characteristic, complemented
55	#347226	C₂²	1	4	yes	complemented
56	#347226	C₂²	1	4	yes	complemented
57	#346542	C₂²	1	4	yes	complemented
58	#346518	C₂²	1	4	yes	complemented
59	#185733	C₂²	1	1	yes	characteristic, complemented
60	#185660	C₂²	1	1	yes	characteristic, complemented
61	#185373	C₂²	1	1	yes	characteristic, complemented
62	#185348	C₂²	1	1	yes	characteristic, complemented
63	#184929	C₂²	1	1	yes	characteristic, complemented
64	#184914	C₂²	1	1	yes	characteristic, complemented
65	#144282	C₂²	1	2	yes	complemented
66	#144270	C₂²	1	4	yes	complemented
67	#144266	C₂²	1	2	yes	complemented
68	#144266	C₂²	1	2	yes	complemented
69	#144228	C₂²	1	4	yes	complemented
70	#144204	C₂²	1	2	yes	complemented
71	#142747	C₂²	1	2	yes	complemented
72	#142730	C₂²	1	2	yes	complemented
73	#142656	C₂²	1	4	yes	complemented
74	#142649	C₂²	1	2	yes	complemented
75	#142608	C₂²	1	4	yes	complemented
76	#142600	C₂²	1	2	yes	complemented
77	#139612	C₂²	1	4	yes	complemented
78	#139544	C₂²	1	4	yes	complemented
79	#138960	C₂²	1	4	yes	complemented
80	#138952	C₂²	1	4	yes	complemented
81	#138952	C₂²	1	4	yes	complemented
82	#138884	C₂²	1	4	yes	complemented
83	#136847	C₂²	1	4	yes	complemented
84	#136817	C₂²	1	4	yes	complemented
85	#130982	C₂²	1	4	yes	complemented
86	#130740	C₂²	1	4	yes	complemented
87	#127399	C₂²	1	1	yes	characteristic, complemented
88	#127377	C₂²	1	1	yes	characteristic, complemented
89	#127126	C₂²	1	1	yes	characteristic, complemented
90	#127106	C₂²	1	1	yes	characteristic, complemented
91	D₄×H(5,𝔽₂)	C₂³	1	4	yes	—
92	#62812	C₂³	1	1	yes	characteristic
93	C₂×#3498	C₂³	1	1	yes	characteristic
94	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
95	C₄×#585	C₂³	1	1	yes	characteristic
96	C₂×#3205	D₄	1	1	yes	characteristic, complemented
97	C₂²×#493	D₄	1	1	yes	characteristic, complemented
98	C₂×#3109	D₄	1	1	yes	characteristic, complemented
99	C₂²×#459	D₄	1	1	yes	characteristic, complemented
100	#58997	C₂³	1	2	yes	complemented
101	#45599	C₂³	1	2	yes	complemented
102	#38904	D₄	1	2	yes	complemented
103	#38904	C₂³	1	2	yes	—
104	D₄×#120	D₄	1	2	yes	complemented
105	D₄×#120	C₂³	1	2	yes	—
106	#35272	C₂³	1	1	yes	characteristic
107	#35237	D₄	1	1	yes	characteristic, complemented
108	#35237	D₄	1	1	yes	characteristic, complemented
109	#34963	C₂³	1	1	yes	characteristic
110	#34963	C₂³	1	1	yes	characteristic
111	#34963	C₂³	1	1	yes	characteristic
112	#34364	D₄	1	1	yes	characteristic, complemented
113	#33021	D₄	1	2	yes	—
114	#32976	D₄	1	2	yes	—
115	#32976	C₂³	1	2	yes	—
116	#32976	C₂³	1	2	yes	—
117	#32926	D₄	1	2	yes	—
118	#32926	C₂³	1	2	yes	—
119	#32926	C₂³	1	2	yes	—
120	#32920	C₂³	1	4	yes	—
121	#32899	D₄	1	2	yes	—
122	#32460	C₂³	1	1	yes	characteristic, complemented
123	#32028	C₂³	1	2	yes	complemented
124	#31667	C₂³	1	1	yes	characteristic, complemented
125	#31667	C₂³	1	1	yes	characteristic, complemented
126	#31056	C₂³	1	1	yes	characteristic, complemented
127	#30499	C₂³	1	2	yes	complemented
128	#29636	D₄	1	4	yes	complemented
129	#25900	D₄	1	2	yes	complemented
130	#25900	C₂³	1	2	yes	—
131	#25771	D₄	1	2	yes	complemented
132	#25771	C₂³	1	2	yes	—
133	#25757	C₂³	1	2	yes	—
134	#25757	C₂³	1	2	yes	—
135	#25631	D₄	1	2	yes	complemented
136	#25631	D₄	1	2	yes	complemented
137	#24260	C₂³	1	4	yes	—
138	#24033	D₄	1	2	yes	complemented
139	#24033	C₂³	1	2	yes	—
140	#23848	D₄	1	2	yes	complemented
141	#23848	C₂³	1	2	yes	—
142	#23307	C₂³	1	2	yes	complemented
143	#22842	C₂³	1	2	yes	complemented
144	D₄×#99	C₂³	1	4	yes	—
145	#21888	D₄	1	1	yes	characteristic, complemented
146	#21851	C₂³	1	1	yes	characteristic
147	#21810	D₄	1	1	yes	characteristic, complemented
148	#21803	D₄	1	1	yes	characteristic, complemented
149	C₄×B(4,𝔽₂)	C₂³	1	4	yes	—
150	#21401	D₄	1	1	yes	characteristic, complemented
151	#21373	C₂³	1	1	yes	characteristic
152	#20723	C₂³	1	1	yes	characteristic
153	#20723	C₂³	1	1	yes	characteristic
154	#20723	C₂³	1	1	yes	characteristic
155	#20637	C₂³	1	1	yes	characteristic
156	#18387	C₂³	1	4	yes	—
157	#18203	C₂³	1	2	yes	—
158	#18194	C₂³	1	2	yes	—
159	#17363	C₂³	1	1	yes	characteristic
160	#17349	C₂³	1	1	yes	characteristic
161	#13295	C₂³	1	2	yes	complemented
162	#13223	C₂³	1	4	yes	complemented
163	#13221	C₂³	1	2	yes	complemented
164	#12793	C₂³	1	4	yes	complemented
165	#11903	C₂³	1	2	yes	complemented
166	#11899	C₂³	1	2	yes	complemented
167	#11899	C₂³	1	2	yes	complemented
168	#11880	C₂³	1	2	yes	complemented
169	#11877	C₂³	1	4	yes	complemented
170	#11873	C₂³	1	2	yes	complemented
171	#11873	C₂³	1	2	yes	complemented
172	#11471	C₂³	1	4	yes	complemented
173	#8383	C₂³	1	4	yes	—
174	#8375	C₂³	1	4	yes	—
175	#8353	C₂³	1	2	yes	—
176	#8353	C₂³	1	2	yes	—
177	#8350	C₂³	1	4	yes	—
178	#8318	C₂³	1	2	yes	—
179	#8318	C₂³	1	2	yes	—
180	#8316	C₂³	1	4	yes	—
181	#7237	C₂³	1	2	yes	complemented
182	#7237	C₂³	1	2	yes	complemented
183	#7236	C₂³	1	4	yes	complemented
184	#7205	C₂³	1	2	yes	complemented
185	#7205	C₂³	1	2	yes	complemented
186	#7204	C₂³	1	4	yes	complemented
187	C₂×#585	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	2	yes	—
189	C₂³×D₈	C₂×D₄	1	2	yes	complemented
190	#3496	C₂×D₄	1	2	yes	—
191	#3496	C₂⁴	1	2	yes	—
192	C₂×#550	C₂×D₄	1	2	yes	—
193	C₂×D₄²	C₂×D₄	1	2	yes	—
194	C₂×D₄²	C₂×D₄	1	2	yes	—
195	C₂×D₄²	C₂⁴	1	2	yes	—
196	#3449	C₂×D₄	1	2	yes	—
197	C₂×#532	C₂×D₄	1	1	yes	characteristic
198	C₂×#532	C₂×D₄	1	1	yes	characteristic
199	C₂×#532	C₂×D₄	1	1	yes	characteristic
200	C₂²×#127	C₂×D₄	1	1	yes	characteristic
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic
202	C₂²×#127	C₂×D₄	1	1	yes	characteristic
203	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂²×#121	C₂×D₄	1	2	yes	—
205	C₄×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
206	C₄×H(5,𝔽₂)	C₂⁴	1	2	yes	—
207	#3428	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
212	C₂×#493	C₂×D₄	1	2	yes	complemented
213	C₂×#493	C₂×D₄	1	2	yes	complemented
214	C₂×#481	C₂×D₄	1	2	yes	complemented
215	C₂×#459	C₂×D₄	1	2	yes	complemented
216	C₂×#459	C₂×D₄	1	2	yes	complemented
217	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	—
218	C₂×#447	C₂×D₄	1	2	yes	complemented
219	C₂×#432	C₂×D₄	1	1	yes	characteristic, complemented
220	C₂×#431	C₂×D₄	1	1	yes	characteristic, complemented
221	C₂²×C₄⋊C₈	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂²×#102	C₂×D₄	1	2	yes	complemented
223	C₂²×C₄×C₈	C₂×D₄	1	1	yes	characteristic, complemented
224	#2847	C₂×D₄	1	2	yes	—
225	#2847	C₂×D₄	1	2	yes	—
226	#2548	C₂×D₄	1	2	yes	complemented
227	#2541	C₂⁴	1	2	yes	—
228	#2504	C₂×D₄	1	2	yes	—
229	#2487	C₂×D₄	1	1	yes	characteristic
230	#2487	C₂×D₄	1	1	yes	characteristic
231	#2487	C₂×D₄	1	1	yes	characteristic
232	#2487	C₂×D₄	1	1	yes	characteristic, complemented
233	#2487	C₂⁴	1	1	yes	characteristic
234	#2487	C₂⁴	1	1	yes	characteristic
235	#2482	C₂×D₄	1	2	yes	—
236	#2433	C₂×D₄	1	2	yes	—
237	#2408	C₂×D₄	1	1	yes	characteristic
238	#2408	C₂×D₄	1	1	yes	characteristic
239	#2408	C₂×D₄	1	1	yes	characteristic
240	#2408	C₂×D₄	1	1	yes	characteristic, complemented
241	#2408	C₂⁴	1	1	yes	characteristic
242	#2408	C₂⁴	1	1	yes	characteristic
243	#2404	C₂×D₄	1	2	yes	—
244	D₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
245	D₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
246	C₄×#120	C₂×D₄	1	2	yes	—
247	C₄×#120	C₂⁴	1	2	yes	—
248	#2285	C₂×D₄	1	1	yes	characteristic, complemented
249	#2283	C₂×D₄	1	1	yes	characteristic
250	#2283	C₂×D₄	1	1	yes	characteristic
251	#2283	C₂×D₄	1	1	yes	characteristic, complemented
252	#2044	C₂×D₄	1	8	yes	—
253	#2021	C₂×D₄	1	8	yes	—
254	#1984	C₂×D₄	1	1	yes	characteristic, complemented
255	#1984	C₂×D₄	1	1	yes	characteristic, complemented
256	#1982	C₂×D₄	1	2	yes	complemented
257	#1982	C₂×D₄	1	2	yes	complemented
258	#1954	C₂⁴	1	1	yes	characteristic
259	#1954	C₂⁴	1	1	yes	characteristic
260	#1893	C₂×D₄	1	2	yes	complemented
261	#1893	C₂×D₄	1	2	yes	complemented
262	#1889	C₂×D₄	1	4	yes	—
263	#1869	C₂×D₄	1	2	yes	complemented
264	#1869	C₂⁴	1	2	yes	—
265	#1867	C₂×D₄	1	4	yes	—
266	#1820	C₂×D₄	1	2	yes	—
267	#1800	C₂⁴	1	2	yes	—
268	#1799	C₂×D₄	1	2	yes	—
269	#1799	C₂⁴	1	2	yes	—
270	#1799	C₂⁴	1	2	yes	—
271	#1790	C₂×D₄	1	4	yes	—
272	#1786	C₂×D₄	1	2	yes	complemented
273	#1786	C₂×D₄	1	2	yes	complemented
274	#1782	C₂×D₄	1	2	yes	—
275	C₄×#102	C₂×D₄	1	2	yes	complemented
276	C₄×#102	C₂×D₄	1	2	yes	complemented
277	C₄×#99	C₂×D₄	1	2	yes	—
278	C₄×#99	C₂⁴	1	2	yes	—
279	#1460	C₂⁴	1	2	yes	—
280	#1459	C₂⁴	1	2	yes	—
281	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
282	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
283	C₂³×D₄	#120	1	2	yes	—
284	C₂³×D₄	#120	1	1	yes	characteristic
285	C₂³×D₄	C₂²×D₄	1	2	yes	—
286	C₂³×D₄	C₂²×D₄	1	2	yes	—
287	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
288	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
289	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
290	C₂³×C₈	C₂²×D₄	1	2	yes	—
291	#534	C₂²×D₄	1	4	yes	—
292	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
293	C₂×#127	#120	1	2	yes	—
294	C₂×#127	#120	1	2	yes	—
295	C₂×#127	#120	1	1	yes	characteristic
296	C₂×#127	#120	1	1	yes	characteristic
297	C₂×#127	#120	1	1	yes	characteristic
298	C₂×#127	C₂²×D₄	1	2	yes	—
299	C₂×#127	C₂²×D₄	1	2	yes	—
300	C₂×#121	#120	1	2	yes	—
301	C₂×#121	C₂²×D₄	1	2	yes	—
302	C₂×#121	C₂²×D₄	1	2	yes	—
303	C₂×#120	#120	1	2	yes	—
304	C₂×#120	C₂²×D₄	1	2	yes	—
305	#518	C₂²×D₄	1	2	yes	—
306	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×D₄	#120	1	2	yes	—
309	C₂×C₄×D₄	#120	1	2	yes	—
310	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
315	C₂×C₄×D₄	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
317	C₂×#117	C₂²×D₄	1	1	yes	characteristic
318	C₂×#117	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×#117	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	#120	1	2	yes	—
324	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
325	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
326	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄⋊C₈	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄⋊C₈	C₂²×D₄	1	1	yes	characteristic
329	C₂×#99	C₂²×D₄	1	4	yes	—
330	C₂×C₂²⋊C₈	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
333	#386	#120	1	2	yes	—
334	#386	C₂²×D₄	1	2	yes	—
335	#385	#120	1	2	yes	—
336	#385	C₂²×D₄	1	2	yes	—
337	#381	#120	1	2	yes	—
338	#380	#120	1	1	yes	characteristic
339	#380	#120	1	1	yes	characteristic
340	#380	C₂²×D₄	1	1	yes	characteristic
341	#380	C₂²×D₄	1	1	yes	characteristic
342	#380	C₂²×D₄	1	1	yes	characteristic
343	#380	C₂²×D₄	1	1	yes	characteristic
344	#379	#120	1	2	yes	—
345	#379	C₂²×D₄	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
347	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
348	#342	C₂²×D₄	1	4	yes	—
349	C₂⁵	C₂×#120	1	2	yes	—
350	H(5,𝔽₂)	#576	1	4	yes	—
351	C₂²×Q₈	D₄²	1	1	yes	characteristic
352	C₂²×D₄	C₂×#120	1	1	yes	characteristic
353	C₂²×D₄	C₂×#120	1	2	yes	—
354	C₂²×D₄	C₂×#120	1	2	yes	—
355	C₂²×D₄	C₂×#120	1	2	yes	—
356	C₂²×D₄	D₄²	1	1	yes	characteristic
357	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
358	C₂³×C₄	C₂×#120	1	1	yes	characteristic
359	C₂³×C₄	C₂×#120	1	1	yes	characteristic
360	C₂³×C₄	C₂×#120	1	1	yes	characteristic
361	C₂³×C₄	C₂×#120	1	2	yes	—
362	C₂³×C₄	D₄²	1	1	yes	characteristic
363	C₂³×C₄	D₄²	1	1	yes	characteristic
364	C₂³×C₄	D₄²	1	1	yes	characteristic
365	C₂³×C₄	D₄²	1	1	yes	characteristic
366	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
367	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
368	#127	B(4,𝔽₂)	1	2	yes	—
369	#127	B(4,𝔽₂)	1	2	yes	—
370	#127	B(4,𝔽₂)	1	2	yes	—
371	#127	B(4,𝔽₂)	1	2	yes	—
372	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
373	C₂×C₄⋊C₄	#534	1	1	yes	characteristic
374	C₂×C₄⋊C₄	D₄²	1	1	yes	characteristic
375	C₂×C₄⋊C₄	D₄²	1	1	yes	characteristic
376	C₂×C₄⋊C₄	D₄²	1	1	yes	characteristic
377	C₂×C₄⋊C₄	D₄²	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	#534	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	D₄²	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	D₄²	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄²	C₂×#120	1	1	yes	characteristic
388	C₂×C₄²	C₂×#120	1	1	yes	characteristic
389	C₂×C₄²	C₂×#120	1	1	yes	characteristic
390	C₂×C₄²	#534	1	1	yes	characteristic
391	C₂×C₄²	#534	1	1	yes	characteristic
392	C₂×C₄²	D₄²	1	1	yes	characteristic
393	C₂×C₄²	D₄²	1	1	yes	characteristic
394	C₂×C₄²	D₄²	1	1	yes	characteristic
395	C₂×C₄²	D₄²	1	1	yes	characteristic
396	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
397	C₂⁴	#2403	1	1	yes	characteristic
398	C₂⁴	C₂²×#120	1	1	yes	characteristic
399	C₂⁴	C₂×D₄²	1	1	yes	characteristic
400	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
401	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
402	C₂×D₄	C₂×#576	1	2	yes	—
403	C₂×D₄	#3585	1	2	yes	—
404	C₂²×C₄	#2403	1	1	yes	characteristic
405	C₂²×C₄	#2403	1	1	yes	characteristic
406	C₂²×C₄	#2403	1	1	yes	characteristic
407	C₂²×C₄	#2403	1	1	yes	characteristic
408	C₂²×C₄	#2403	1	1	yes	characteristic
409	C₂²×C₄	#2403	1	1	yes	characteristic
410	C₂²×C₄	#2403	1	1	yes	characteristic
411	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
412	C₂²×C₄	C₂×#534	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
416	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
417	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
418	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
419	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
420	C₂³	#23882	1	2	yes	—
421	C₂³	C₂×#2403	1	1	yes	characteristic
422	C₂³	#60372	1	2	yes	—
423	C₂³	#61072	1	2	yes	—
424	C₂×C₄	#23900	1	1	yes	characteristic
425	C₂×C₄	#23900	1	1	yes	characteristic
426	C₂×C₄	#23900	1	1	yes	characteristic
427	C₂×C₄	#23900	1	1	yes	characteristic
428	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
429	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄	#61049	1	1	yes	characteristic
431	C₂×C₄	#61058	1	1	yes	characteristic
432	C₂²	#6437563	1	1	yes	characteristic
433	C₂²	C₂×#23882	1	1	yes	characteristic
434	C₂²	C₂×#23900	1	1	yes	characteristic
435	C₄	#499819	1	2	yes	—
436	C₄	#7622880	1	1	yes	characteristic
437	C₄	#7622887	1	1	yes	characteristic
438	C₂	#72233302	1	1	yes	characteristic
439	C₂	C₂×#499819	1	1	yes	characteristic
440	C₂	#72316674	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂×C₄×D₄	C₂⁵
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#3498 ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72316792	C₂	semidirect
2. #72316772	C₂	semidirect
3. #72316758	C₂	semidirect
4. #72316752	C₂	semidirect
5. #72316751	C₂	semidirect
6. #72316749	C₂	semidirect
7. #72316740	C₂	semidirect
8. #72316730	C₂	semidirect
9. #72316726	C₂	semidirect
10. #72316725	C₂	semidirect
11. #72316709	C₂	semidirect
12. #72316692	C₂	semidirect
13. #72313433	C₂	semidirect
14. #72306039	C₂	semidirect
15. #72285018	C₂	semidirect
16. #72282557	C₂	semidirect
17. #72282272	C₂	semidirect
18. #72236702	C₂	semidirect
19. #72236596	C₂	semidirect
20. #10586097	C₂²	semidirect
21. #8195808	C₂²	semidirect
23. #7513980	C₂²	semidirect
24. #7511801	C₂²	semidirect
25. #7308986	C₂²	semidirect
26. #7301422	C₂²	semidirect
27. #7200002	C₂²	semidirect
28. #6653018	C₂²	semidirect
30. #6629390	C₂²	semidirect
31. #6629390	C₂²	semidirect
32. #6628970	C₂²	semidirect
33. #6591514	C₂²	semidirect
34. D₄×B(4,𝔽₂)	C₂²	semidirect
38. #6487648	C₂²	semidirect
39. #6412324	C₂²	semidirect
40. #6385980	C₂²	semidirect
41. #6347443	C₂²	semidirect
42. #6346637	C₂²	semidirect
43. #500757	C₂²	semidirect
44. #500507	C₂²	semidirect
45. #496508	C₂²	semidirect
46. #496508	C₂²	semidirect
47. #496311	C₂²	semidirect
48. #486513	C₂²	semidirect
49. #486243	C₂²	semidirect
50. #482657	C₂²	semidirect
51. #482363	C₂²	semidirect
52. #482234	C₂²	semidirect
53. #482234	C₂²	semidirect
54. #480580	C₂²	semidirect
55. #347226	C₂²	semidirect
56. #347226	C₂²	semidirect
57. #346542	C₂²	semidirect
58. #346518	C₂²	semidirect
59. #185733	C₂²	semidirect
60. #185660	C₂²	semidirect
61. #185373	C₂²	semidirect
62. #185348	C₂²	semidirect
63. #184929	C₂²	semidirect
64. #184914	C₂²	semidirect
65. #144282	C₂²	semidirect
66. #144270	C₂²	semidirect
67. #144266	C₂²	semidirect
68. #144266	C₂²	semidirect
69. #144228	C₂²	semidirect
70. #144204	C₂²	semidirect
71. #142747	C₂²	semidirect
72. #142730	C₂²	semidirect
73. #142656	C₂²	semidirect
74. #142649	C₂²	semidirect
75. #142608	C₂²	semidirect
76. #142600	C₂²	semidirect
77. #139612	C₂²	semidirect
78. #139544	C₂²	semidirect
79. #138960	C₂²	semidirect
80. #138952	C₂²	semidirect
81. #138952	C₂²	semidirect
82. #138884	C₂²	semidirect
83. #136847	C₂²	semidirect
84. #136817	C₂²	semidirect
85. #130982	C₂²	semidirect
86. #130740	C₂²	semidirect
87. #127399	C₂²	semidirect
88. #127377	C₂²	semidirect
89. #127126	C₂²	semidirect
90. #127106	C₂²	semidirect
94. C₂²×D₄²	D₄	semidirect
96. C₂×#3205	D₄	semidirect
97. C₂²×#493	D₄	semidirect
98. C₂×#3109	D₄	semidirect
99. C₂²×#459	D₄	semidirect
100. #58997	C₂³	semidirect
101. #45599	C₂³	semidirect
102. #38904	D₄	semidirect
104. D₄×#120	D₄	semidirect
107. #35237	D₄	semidirect
108. #35237	D₄	semidirect
112. #34364	D₄	semidirect
122. #32460	C₂³	semidirect
123. #32028	C₂³	semidirect
124. #31667	C₂³	semidirect
125. #31667	C₂³	semidirect
126. #31056	C₂³	semidirect
127. #30499	C₂³	semidirect
128. #29636	D₄	semidirect
129. #25900	D₄	semidirect
131. #25771	D₄	semidirect
135. #25631	D₄	semidirect
136. #25631	D₄	semidirect
138. #24033	D₄	semidirect
140. #23848	D₄	semidirect
142. #23307	C₂³	semidirect
143. #22842	C₂³	semidirect
145. #21888	D₄	semidirect
147. #21810	D₄	semidirect
148. #21803	D₄	semidirect
150. #21401	D₄	semidirect
161. #13295	C₂³	semidirect
162. #13223	C₂³	semidirect
163. #13221	C₂³	semidirect
164. #12793	C₂³	semidirect
165. #11903	C₂³	semidirect
166. #11899	C₂³	semidirect
167. #11899	C₂³	semidirect
168. #11880	C₂³	semidirect
169. #11877	C₂³	semidirect
170. #11873	C₂³	semidirect
171. #11873	C₂³	semidirect
172. #11471	C₂³	semidirect
181. #7237	C₂³	semidirect
182. #7237	C₂³	semidirect
183. #7236	C₂³	semidirect
184. #7205	C₂³	semidirect
185. #7205	C₂³	semidirect
186. #7204	C₂³	semidirect
189. C₂³×D₈	C₂×D₄	semidirect
203. C₂²×#127	C₂×D₄	semidirect
211. C₂²×C₄×D₄	C₂×D₄	semidirect
212. C₂×#493	C₂×D₄	semidirect
213. C₂×#493	C₂×D₄	semidirect
214. C₂×#481	C₂×D₄	semidirect
215. C₂×#459	C₂×D₄	semidirect
216. C₂×#459	C₂×D₄	semidirect
218. C₂×#447	C₂×D₄	semidirect
219. C₂×#432	C₂×D₄	semidirect
220. C₂×#431	C₂×D₄	semidirect
221. C₂²×C₄⋊C₈	C₂×D₄	semidirect
222. C₂²×#102	C₂×D₄	semidirect
223. C₂²×C₄×C₈	C₂×D₄	semidirect
226. #2548	C₂×D₄	semidirect
232. #2487	C₂×D₄	semidirect
240. #2408	C₂×D₄	semidirect
248. #2285	C₂×D₄	semidirect
251. #2283	C₂×D₄	semidirect
254. #1984	C₂×D₄	semidirect
255. #1984	C₂×D₄	semidirect
256. #1982	C₂×D₄	semidirect
257. #1982	C₂×D₄	semidirect
260. #1893	C₂×D₄	semidirect
261. #1893	C₂×D₄	semidirect
263. #1869	C₂×D₄	semidirect
272. #1786	C₂×D₄	semidirect
273. #1786	C₂×D₄	semidirect
275. C₄×#102	C₂×D₄	semidirect
276. C₄×#102	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72316792	2
#72316772	2
#72316758	2
#72316752	2
#72316751	2
#72316749	2
#72316740	2
#72316730	2
#72316726	2
#72316725	2
#72316709	2
#72316692	2
#72313433	2
#72306039	2
#72285018	2
#72282557	2
#72282272	2
#72236702	2
#72236596	2