Subgroups — #72313573

Order 2048.

At least 7299 conjugacy classes of subgroups; only the 898 normal subgroups are shown.

The subgroup lattice has 424 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313565	C₂	1	2	yes	maximal, complemented
2	#72313557	C₂	1	2	yes	maximal, complemented
3	#72313554	C₂	1	1	yes	maximal, characteristic, complemented
4	#72313549	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#500769	C₂	1	1	yes	maximal, characteristic, complemented
6	#72313544	C₂	1	1	yes	maximal, characteristic, complemented
7	#72313436	C₂	1	4	yes	maximal, complemented
8	#72313426	C₂	1	4	yes	maximal, complemented
9	#72313382	C₂	1	4	yes	maximal, complemented
10	#72313373	C₂	1	4	yes	maximal, complemented
11	#72312281	C₂	1	1	yes	maximal, characteristic, complemented
12	#72306044	C₂	1	2	yes	maximal, complemented
13	C₂×#486263	C₂	1	1	yes	maximal, characteristic, complemented
14	#72282436	C₂	1	2	yes	maximal, complemented
15	#72281282	C₂	1	1	yes	maximal, characteristic, complemented
16	#10586067	C₂²	1	1	yes	characteristic, complemented
17	#7671575	C₂²	1	1	yes	characteristic
18	C₂×#59816	C₂²	1	1	yes	characteristic, complemented
19	#7563047	C₂²	1	2	yes	complemented
20	#7534963	C₂²	1	2	yes	complemented
21	#7487728	C₂²	1	2	yes	complemented
22	#7487728	C₂²	1	2	yes	complemented
23	#6632008	C₂²	1	2	yes	complemented
24	C₂×#32926	C₂²	1	2	yes	complemented
25	#6628968	C₂²	1	1	yes	characteristic, complemented
26	#6573692	C₂²	1	2	yes	complemented
27	#6573687	C₂²	1	2	yes	complemented
28	#6573664	C₂²	1	2	yes	complemented
29	D₄×#453	C₂²	1	2	yes	complemented
30	#6499761	C₂²	1	2	yes	—
31	#6443328	C₂²	1	1	yes	characteristic, complemented
32	C₂×#24222	C₂²	1	1	yes	characteristic
33	#6408546	C₂²	1	1	yes	characteristic, complemented
34	#6379031	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×#453	C₂²	1	1	yes	characteristic
36	C₂×#18194	C₂²	1	2	yes	complemented
37	#500769	C₂²	1	4	yes	complemented
38	#500769	C₂²	1	4	yes	complemented
39	C₂×#13218	C₂²	1	2	yes	complemented
40	C₂×#12797	C₂²	1	1	yes	characteristic, complemented
41	#486263	C₂²	1	4	yes	complemented
42	#486263	C₂²	1	4	yes	complemented
43	C₂×#11880	C₂²	1	2	yes	complemented
44	#482050	C₂²	1	2	yes	complemented
45	C₂×#11475	C₂²	1	1	yes	characteristic, complemented
46	#346522	C₂²	1	8	yes	complemented
47	#346518	C₂²	1	8	yes	complemented
48	#185627	C₂²	1	2	yes	complemented
49	#185331	C₂²	1	2	yes	complemented
50	#184905	C₂²	1	2	yes	complemented
51	#144230	C₂²	1	8	yes	complemented
52	#144228	C₂²	1	8	yes	complemented
53	#142605	C₂²	1	8	yes	complemented
54	#142604	C₂²	1	8	yes	complemented
55	#139550	C₂²	1	4	yes	complemented
56	#139548	C₂²	1	4	yes	complemented
57	#138967	C₂²	1	8	yes	complemented
58	#138966	C₂²	1	8	yes	complemented
59	#136823	C₂²	1	4	yes	complemented
60	#136821	C₂²	1	4	yes	complemented
61	#130774	C₂²	1	2	yes	complemented
62	#130772	C₂²	1	2	yes	complemented
63	#130770	C₂²	1	2	yes	complemented
64	#130768	C₂²	1	2	yes	complemented
65	#127353	C₂²	1	2	yes	complemented
66	#127067	C₂²	1	2	yes	complemented
67	#62988	C₂³	1	2	yes	complemented
68	D₄×H(5,𝔽₂)	C₂³	1	2	yes	complemented
69	C₂×#3496	D₄	1	1	yes	characteristic, complemented
70	C₂×#3496	C₂³	1	1	yes	characteristic
71	C₂×#3496	C₂³	1	1	yes	characteristic
72	C₂×C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
73	C₂²×#453	D₄	1	1	yes	characteristic
74	C₂²×#447	D₄	1	2	yes	complemented
75	C₂²×#447	D₄	1	2	yes	complemented
76	#59816	C₂³	1	2	yes	complemented
77	#59816	C₂³	1	2	yes	complemented
78	#39362	D₄	1	1	yes	characteristic, complemented
79	#39362	D₄	1	1	yes	characteristic, complemented
80	#39362	C₂³	1	1	yes	characteristic
81	#39362	C₂³	1	1	yes	characteristic
82	#36644	D₄	1	1	yes	characteristic, complemented
83	#36127	D₄	1	1	yes	characteristic, complemented
84	#36127	C₂³	1	1	yes	characteristic
85	D₄×#127	D₄	1	1	yes	characteristic, complemented
86	D₄×#127	C₂³	1	1	yes	characteristic
87	#35165	D₄	1	1	yes	characteristic, complemented
88	#35165	C₂³	1	1	yes	characteristic
89	C₂×#2408	C₂³	1	2	yes	—
90	C₄×#532	D₄	1	1	yes	characteristic, complemented
91	C₂×C₄×#127	C₂³	1	1	yes	characteristic
92	#32926	C₂³	1	8	yes	—
93	#32922	C₂³	1	2	yes	complemented
94	#32920	C₂³	1	2	yes	complemented
95	#31260	C₂³	1	4	yes	complemented
96	#30499	C₂³	1	4	yes	complemented
97	#25739	C₂³	1	2	yes	complemented
98	#25738	C₂³	1	2	yes	complemented
99	#24222	D₄	1	2	yes	complemented
100	#24222	D₄	1	2	yes	complemented
101	#24222	C₂³	1	2	yes	—
102	#24222	C₂³	1	2	yes	—
103	#23960	D₄	1	4	yes	complemented
104	#23960	C₂³	1	4	yes	—
105	#23848	D₄	1	4	yes	complemented
106	#23848	C₂³	1	4	yes	—
107	C₂×#2039	D₄	1	2	yes	complemented
108	C₂×#2006	D₄	1	2	yes	complemented
109	#23355	C₂³	1	2	yes	complemented
110	#23173	C₂³	1	2	yes	complemented
111	#22411	C₂³	1	2	yes	complemented
112	D₄×#100	C₂³	1	2	yes	complemented
113	#21758	D₄	1	2	yes	complemented
114	#21758	D₄	1	2	yes	complemented
115	#21738	C₂³	1	2	yes	—
116	C₄×#453	D₄	1	2	yes	—
117	C₄×#453	D₄	1	2	yes	—
118	C₄×#453	C₂³	1	2	yes	—
119	C₄×#453	C₂³	1	2	yes	—
120	C₂×#1887	D₄	1	1	yes	characteristic
121	C₂×#1856	D₄	1	1	yes	characteristic
122	C₂×#1800	C₂³	1	1	yes	characteristic
123	C₂×#1799	C₂³	1	2	yes	—
124	C₂×#1792	D₄	1	1	yes	characteristic
125	C₂×C₄×#100	C₂³	1	1	yes	characteristic
126	#18194	C₂³	1	8	yes	—
127	C₂×#1459	C₂³	1	2	yes	—
128	#13218	C₂³	1	8	yes	complemented
129	#12797	C₂³	1	2	yes	complemented
130	#12797	C₂³	1	2	yes	complemented
131	#11880	C₂³	1	8	yes	complemented
132	#11878	C₂³	1	4	yes	complemented
133	#11877	C₂³	1	4	yes	complemented
134	#11475	C₂³	1	2	yes	complemented
135	#11475	C₂³	1	2	yes	complemented
136	#8376	C₂³	1	4	yes	complemented
137	#8375	C₂³	1	4	yes	complemented
138	#8350	C₂³	1	8	yes	complemented
139	#8316	C₂³	1	8	yes	complemented
140	#7236	C₂³	1	8	yes	complemented
141	#7203	C₂³	1	8	yes	complemented
142	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂×D₄	1	2	yes	—
144	C₂³×D₈	C₂×D₄	1	4	yes	complemented
145	#3496	C₂×D₄	1	2	yes	—
146	#3496	C₂⁴	1	2	yes	—
147	C₂×#547	C₂×D₄	1	1	yes	characteristic
148	C₂×#547	C₂×D₄	1	2	yes	—
149	C₂×#547	C₂×D₄	1	1	yes	characteristic, complemented
150	C₂×#547	C₂×D₄	1	1	yes	characteristic, complemented
151	C₂×#547	C₂⁴	1	1	yes	characteristic
152	C₂×D₄²	C₂×D₄	1	2	yes	—
153	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
155	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
156	C₂×D₄²	C₂⁴	1	1	yes	characteristic
157	C₂×#537	C₂×D₄	1	2	yes	—
158	C₂×#532	C₂×D₄	1	1	yes	characteristic
159	C₂×#532	C₂×D₄	1	1	yes	characteristic
160	C₂×#532	C₂×D₄	1	1	yes	characteristic
161	C₂²×#127	C₂×D₄	1	1	yes	characteristic
162	C₂²×#121	C₂×D₄	1	2	yes	—
163	C₂²×#121	C₂×D₄	1	2	yes	—
164	C₄×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
165	C₄×H(5,𝔽₂)	C₂⁴	1	2	yes	—
166	C₂×#518	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
169	C₂×#453	D₈	1	8	yes	complemented
170	C₂×#453	C₂×D₄	1	2	yes	—
171	C₂×#453	C₂×D₄	1	2	yes	—
172	C₂×#447	C₂×D₄	1	4	yes	complemented
173	C₂×#447	C₂×D₄	1	4	yes	complemented
174	C₂²×#102	C₂×D₄	1	4	yes	complemented
175	C₂²×#100	C₂×D₄	1	1	yes	characteristic
176	C₂²×#100	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₂²⋊C₈	C₂×D₄	1	2	yes	—
178	C₂²×C₂²⋊C₈	C₂×D₄	1	2	yes	—
179	#2868	C₂×D₄	1	1	yes	characteristic, complemented
180	#2867	C₂×D₄	1	1	yes	characteristic, complemented
181	#2858	C₂×D₄	1	1	yes	characteristic, complemented
182	#2858	C₂×D₄	1	1	yes	characteristic, complemented
183	#2547	C₂×D₄	1	1	yes	characteristic
184	#2547	C₂×D₄	1	1	yes	characteristic, complemented
185	#2547	C₂×D₄	1	1	yes	characteristic, complemented
186	#2547	C₂⁴	1	1	yes	characteristic
187	#2541	C₂×D₄	1	1	yes	characteristic
188	#2541	C₂×D₄	1	1	yes	characteristic, complemented
189	#2541	C₂×D₄	1	1	yes	characteristic, complemented
190	#2541	C₂⁴	1	1	yes	characteristic
191	#2408	C₂×D₄	1	4	yes	—
192	#2408	C₂⁴	1	4	yes	—
193	C₄×#127	C₂×D₄	1	1	yes	characteristic
194	C₄×#127	C₂×D₄	1	1	yes	characteristic
195	C₄×#127	C₂×D₄	1	1	yes	characteristic
196	C₄×#127	C₂×D₄	1	1	yes	characteristic
197	C₄×#127	C₂×D₄	1	1	yes	characteristic
198	C₄×#127	C₂×D₄	1	1	yes	characteristic
199	C₄×#127	C₂⁴	1	1	yes	characteristic
200	C₄×#127	C₂⁴	1	1	yes	characteristic
201	#2293	C₂×D₄	1	1	yes	characteristic, complemented
202	#2293	C₂×D₄	1	1	yes	characteristic, complemented
203	C₂×#390	C₂×D₄	1	1	yes	characteristic
204	C₂×#390	C₂×D₄	1	1	yes	characteristic
205	#2285	C₂×D₄	1	1	yes	characteristic
206	C₂×#384	C₂×D₄	1	1	yes	characteristic
207	C₂×#380	C₂×D₄	1	2	yes	—
208	C₄²×D₄	C₂×D₄	1	1	yes	characteristic, complemented
209	C₄²×D₄	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂×C₄³	C₂×D₄	1	1	yes	characteristic
211	#2039	C₂×D₄	1	4	yes	complemented
212	#2039	C₂×D₄	1	4	yes	complemented
213	#2006	C₂×D₄	1	4	yes	complemented
214	#2006	C₂×D₄	1	4	yes	complemented
215	#1893	C₂×D₄	1	4	yes	complemented
216	#1893	C₂×D₄	1	4	yes	complemented
217	#1887	C₂×D₄	1	2	yes	—
218	#1887	C₂×D₄	1	2	yes	—
219	#1869	C₂×D₄	1	4	yes	—
220	#1869	C₂⁴	1	4	yes	—
221	#1856	C₂×D₄	1	2	yes	—
222	#1856	C₂×D₄	1	2	yes	—
223	#1823	C₂×D₄	1	4	yes	complemented
224	#1800	C₂×D₄	1	2	yes	—
225	#1800	C₂⁴	1	2	yes	—
226	#1799	C₂⁴	1	4	yes	—
227	#1792	C₂×D₄	1	2	yes	—
228	#1792	C₂×D₄	1	2	yes	—
229	#1786	C₂×D₄	1	4	yes	complemented
230	C₄×#100	C₂×D₄	1	2	yes	—
231	C₄×#100	C₂⁴	1	2	yes	—
232	C₂×#343	C₂×D₄	1	2	yes	—
233	#1459	C₂⁴	1	4	yes	—
234	C₂×H(5,𝔽₂)	C₂×D₈	1	4	yes	complemented
235	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
236	C₂³×D₄	#120	1	1	yes	characteristic
237	C₂³×D₄	#120	1	2	yes	—
238	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
239	C₂³×D₄	C₂²×D₄	1	2	yes	—
240	C₂³×D₄	C₂²×D₄	1	4	yes	—
241	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
242	C₂³×C₈	C₂²×D₄	1	4	yes	—
243	#537	C₂²×D₄	1	4	yes	—
244	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
247	C₂×#127	#120	1	1	yes	characteristic
248	C₂×#127	#120	1	1	yes	characteristic
249	C₂×#127	#120	1	1	yes	characteristic
250	C₂×#127	C₂×D₈	1	4	yes	—
251	C₂×#127	AGL(1,ℤ/8)	1	4	yes	—
252	C₂×#127	C₂²×D₄	1	1	yes	characteristic
253	C₂×#127	C₂²×D₄	1	1	yes	characteristic
254	C₂×#127	C₂²×D₄	1	1	yes	characteristic
255	C₂×#127	C₂²×D₄	1	1	yes	characteristic
256	C₂×#121	#120	1	2	yes	—
257	C₂×#121	#120	1	2	yes	—
258	C₂×#121	#120	1	2	yes	—
259	C₂×#121	#120	1	1	yes	characteristic
260	C₂×#121	#120	1	1	yes	characteristic
261	C₂×#121	C₂²×D₄	1	2	yes	—
262	C₂×#121	C₂²×D₄	1	2	yes	—
263	#518	C₂²×D₄	1	2	yes	—
264	C₂×C₄×D₄	#120	1	2	yes	—
265	C₂×C₄×D₄	#120	1	1	yes	characteristic
266	C₂×C₄×D₄	#120	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
269	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
276	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	#120	1	2	yes	—
278	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
282	C₂²×C₄²	#120	1	1	yes	characteristic
283	C₂²×C₄²	#120	1	1	yes	characteristic
284	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
285	#453	C₂×D₈	1	8	yes	complemented
286	#453	C₂×D₈	1	8	yes	complemented
287	C₂×#100	C₂×D₈	1	4	yes	complemented
288	C₂×#100	C₂²×D₄	1	2	yes	—
289	C₂×#100	C₂²×D₄	1	2	yes	—
290	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
291	#390	#120	1	1	yes	characteristic
292	#390	#120	1	1	yes	characteristic
293	#390	#120	1	1	yes	characteristic
294	#390	#120	1	1	yes	characteristic
295	#390	C₂²×D₄	1	1	yes	characteristic
296	#390	C₂²×D₄	1	1	yes	characteristic
297	#390	C₂²×D₄	1	1	yes	characteristic
298	#390	C₂²×D₄	1	1	yes	characteristic
299	#384	#120	1	1	yes	characteristic
300	#384	#120	1	1	yes	characteristic
301	#384	C₂²×D₄	1	1	yes	characteristic
302	#384	C₂²×D₄	1	1	yes	characteristic
303	#380	C₂²×D₄	1	4	yes	—
304	C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
306	C₄³	#120	1	1	yes	characteristic
307	C₄³	#120	1	1	yes	characteristic
308	C₄³	C₂²×D₄	1	1	yes	characteristic
309	C₄³	C₂²×D₄	1	1	yes	characteristic
310	#343	C₂²×D₄	1	4	yes	—
311	C₂⁵	D₄²	1	2	yes	—
312	H(5,𝔽₂)	C₂²×D₈	1	4	yes	—
313	C₂²×D₄	#447	1	4	yes	complemented
314	C₂²×D₄	C₂×#120	1	2	yes	—
315	C₂²×D₄	C₂×#120	1	1	yes	characteristic
316	C₂²×D₄	C₂×#120	1	1	yes	characteristic
317	C₂²×D₄	C₂×#120	1	1	yes	characteristic
318	C₂²×D₄	C₂×#120	1	1	yes	characteristic
319	C₂²×D₄	C₂×#120	1	1	yes	characteristic
320	C₂²×D₄	D₄²	1	2	yes	—
321	C₂²×D₄	C₂²×D₈	1	2	yes	—
322	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
323	C₂²×D₄	#576	1	4	yes	—
324	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
325	C₂³×C₄	C₂×#120	1	1	yes	characteristic
326	C₂³×C₄	C₂×#120	1	2	yes	—
327	C₂³×C₄	C₂×#120	1	1	yes	characteristic
328	C₂³×C₄	#534	1	1	yes	characteristic
329	C₂³×C₄	D₄²	1	2	yes	—
330	C₂³×C₄	D₄²	1	2	yes	—
331	C₂³×C₄	D₄²	1	2	yes	—
332	C₂³×C₄	C₂³×D₄	1	2	yes	—
333	#127	#447	1	4	yes	complemented
334	#127	#447	1	4	yes	complemented
335	#127	C₂²×D₈	1	2	yes	—
336	#127	C₂²×D₈	1	2	yes	—
337	#127	C₂×AGL(1,ℤ/8)	1	2	yes	—
338	#127	C₂×AGL(1,ℤ/8)	1	2	yes	—
339	#121	B(4,𝔽₂)	1	2	yes	—
340	#121	B(4,𝔽₂)	1	2	yes	—
341	#121	B(4,𝔽₂)	1	2	yes	—
342	#121	B(4,𝔽₂)	1	2	yes	—
343	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
344	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
349	C₂×C₄⋊C₄	D₄²	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	#534	1	2	yes	—
352	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
353	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
355	C₂×C₄²	#447	1	4	yes	complemented
356	C₂×C₄²	C₂×#120	1	1	yes	characteristic
357	C₂×C₄²	C₂×#120	1	1	yes	characteristic
358	C₂×C₄²	C₂×#120	1	1	yes	characteristic
359	C₂×C₄²	C₂×#120	1	1	yes	characteristic
360	C₂×C₄²	C₂×#120	1	1	yes	characteristic
361	C₂×C₄²	C₂×#120	1	1	yes	characteristic
362	C₂×C₄²	#534	1	1	yes	characteristic
363	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
364	#100	C₂²×D₈	1	4	yes	—
365	C₂⁴	#2403	1	2	yes	—
366	C₂⁴	#2403	1	1	yes	characteristic
367	C₂⁴	#3264	1	4	yes	—
368	C₂⁴	D₄×D₈	1	4	yes	—
369	C₂⁴	C₂×D₄²	1	2	yes	—
370	C₂×D₄	C₂×#447	1	2	yes	—
371	C₂×D₄	C₂×#447	1	2	yes	—
372	C₂×D₄	C₂×#447	1	2	yes	—
373	C₂×D₄	#3008	1	2	yes	—
374	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
375	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
376	C₂×D₄	#3264	1	4	yes	—
377	C₂×D₄	D₄×D₈	1	4	yes	—
378	C₂×D₄	C₂³×D₈	1	1	yes	characteristic
379	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₂×D₄	C₂×#576	1	2	yes	—
381	C₂²×C₄	#2403	1	1	yes	characteristic
382	C₂²×C₄	#2403	1	2	yes	—
383	C₂²×C₄	#2403	1	1	yes	characteristic
384	C₂²×C₄	#2403	1	1	yes	characteristic
385	C₂²×C₄	C₂×#447	1	2	yes	—
386	C₂²×C₄	#3008	1	2	yes	—
387	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
390	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
391	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
392	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
393	C₂²×C₄	C₂×#534	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄²	1	2	yes	—
395	C₄⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
396	C₄⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
397	C₄²	C₂×#447	1	2	yes	—
398	C₄²	C₂×#447	1	2	yes	—
399	C₂³	#23848	1	4	yes	—
400	C₂³	#23848	1	2	yes	—
401	C₂³	#23882	1	2	yes	—
402	C₂³	#23900	1	1	yes	characteristic
403	C₂³	#23900	1	1	yes	characteristic
404	C₂³	C₂×#2403	1	1	yes	characteristic
405	C₂³	C₂×#3264	1	2	yes	—
406	C₂³	C₂×D₄×D₈	1	2	yes	—
407	C₂×C₄	#23848	1	2	yes	—
408	C₂×C₄	#23900	1	1	yes	characteristic
409	C₂×C₄	#23900	1	1	yes	characteristic
410	C₂×C₄	C₂²×#447	1	1	yes	characteristic
411	C₂×C₄	C₂×#3008	1	1	yes	characteristic
412	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
414	C₂²	#248455	1	2	yes	—
415	C₂²	#248455	1	2	yes	—
416	C₂²	C₂×#23848	1	1	yes	characteristic
417	C₂²	C₂×#23882	1	1	yes	characteristic
418	C₂²	C₂×#23900	1	1	yes	characteristic
419	C₄	#7622880	1	2	yes	—
420	C₂	#72234146	1	1	yes	characteristic
421	C₂	C₂×#248455	1	1	yes	characteristic
422	C₂	#72236949	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 ◁ C₂³×C₄ ◁ C₂×#3496 ◁ 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. #72313565	C₂	semidirect
2. #72313557	C₂	semidirect
3. #72313554	C₂	semidirect
4. #72313549	C₂	semidirect
5. C₂×#500769	C₂	semidirect
6. #72313544	C₂	semidirect
7. #72313436	C₂	semidirect
8. #72313426	C₂	semidirect
9. #72313382	C₂	semidirect
10. #72313373	C₂	semidirect
11. #72312281	C₂	semidirect
12. #72306044	C₂	semidirect
13. C₂×#486263	C₂	semidirect
14. #72282436	C₂	semidirect
15. #72281282	C₂	semidirect
16. #10586067	C₂²	semidirect
18. C₂×#59816	C₂²	semidirect
19. #7563047	C₂²	semidirect
20. #7534963	C₂²	semidirect
21. #7487728	C₂²	semidirect
22. #7487728	C₂²	semidirect
23. #6632008	C₂²	semidirect
24. C₂×#32926	C₂²	semidirect
25. #6628968	C₂²	semidirect
26. #6573692	C₂²	semidirect
27. #6573687	C₂²	semidirect
28. #6573664	C₂²	semidirect
29. D₄×#453	C₂²	semidirect
31. #6443328	C₂²	semidirect
33. #6408546	C₂²	semidirect
34. #6379031	C₂²	semidirect
36. C₂×#18194	C₂²	semidirect
37. #500769	C₂²	semidirect
38. #500769	C₂²	semidirect
39. C₂×#13218	C₂²	semidirect
40. C₂×#12797	C₂²	semidirect
41. #486263	C₂²	semidirect
42. #486263	C₂²	semidirect
43. C₂×#11880	C₂²	semidirect
44. #482050	C₂²	semidirect
45. C₂×#11475	C₂²	semidirect
46. #346522	C₂²	semidirect
47. #346518	C₂²	semidirect
48. #185627	C₂²	semidirect
49. #185331	C₂²	semidirect
50. #184905	C₂²	semidirect
51. #144230	C₂²	semidirect
52. #144228	C₂²	semidirect
53. #142605	C₂²	semidirect
54. #142604	C₂²	semidirect
55. #139550	C₂²	semidirect
56. #139548	C₂²	semidirect
57. #138967	C₂²	semidirect
58. #138966	C₂²	semidirect
59. #136823	C₂²	semidirect
60. #136821	C₂²	semidirect
61. #130774	C₂²	semidirect
62. #130772	C₂²	semidirect
63. #130770	C₂²	semidirect
64. #130768	C₂²	semidirect
65. #127353	C₂²	semidirect
66. #127067	C₂²	semidirect
67. #62988	C₂³	semidirect
68. D₄×H(5,𝔽₂)	C₂³	semidirect
69. C₂×#3496	D₄	semidirect
74. C₂²×#447	D₄	semidirect
75. C₂²×#447	D₄	semidirect
76. #59816	C₂³	semidirect
77. #59816	C₂³	semidirect
78. #39362	D₄	semidirect
79. #39362	D₄	semidirect
82. #36644	D₄	semidirect
83. #36127	D₄	semidirect
85. D₄×#127	D₄	semidirect
87. #35165	D₄	semidirect
90. C₄×#532	D₄	semidirect
93. #32922	C₂³	semidirect
94. #32920	C₂³	semidirect
95. #31260	C₂³	semidirect
96. #30499	C₂³	semidirect
97. #25739	C₂³	semidirect
98. #25738	C₂³	semidirect
99. #24222	D₄	semidirect
100. #24222	D₄	semidirect
103. #23960	D₄	semidirect
105. #23848	D₄	semidirect
107. C₂×#2039	D₄	semidirect
108. C₂×#2006	D₄	semidirect
109. #23355	C₂³	semidirect
110. #23173	C₂³	semidirect
111. #22411	C₂³	semidirect
112. D₄×#100	C₂³	semidirect
113. #21758	D₄	semidirect
114. #21758	D₄	semidirect
128. #13218	C₂³	semidirect
129. #12797	C₂³	semidirect
130. #12797	C₂³	semidirect
131. #11880	C₂³	semidirect
132. #11878	C₂³	semidirect
133. #11877	C₂³	semidirect
134. #11475	C₂³	semidirect
135. #11475	C₂³	semidirect
136. #8376	C₂³	semidirect
137. #8375	C₂³	semidirect
138. #8350	C₂³	semidirect
139. #8316	C₂³	semidirect
140. #7236	C₂³	semidirect
141. #7203	C₂³	semidirect
144. C₂³×D₈	C₂×D₄	semidirect
149. C₂×#547	C₂×D₄	semidirect
150. C₂×#547	C₂×D₄	semidirect
154. C₂×D₄²	C₂×D₄	semidirect
155. C₂×D₄²	C₂×D₄	semidirect
169. C₂×#453	D₈	semidirect
172. C₂×#447	C₂×D₄	semidirect
173. C₂×#447	C₂×D₄	semidirect
174. C₂²×#102	C₂×D₄	semidirect
179. #2868	C₂×D₄	semidirect
180. #2867	C₂×D₄	semidirect
181. #2858	C₂×D₄	semidirect
182. #2858	C₂×D₄	semidirect
184. #2547	C₂×D₄	semidirect
185. #2547	C₂×D₄	semidirect
188. #2541	C₂×D₄	semidirect
189. #2541	C₂×D₄	semidirect
201. #2293	C₂×D₄	semidirect
202. #2293	C₂×D₄	semidirect
208. C₄²×D₄	C₂×D₄	semidirect
209. C₄²×D₄	C₂×D₄	semidirect
211. #2039	C₂×D₄	semidirect
212. #2039	C₂×D₄	semidirect
213. #2006	C₂×D₄	semidirect
214. #2006	C₂×D₄	semidirect
215. #1893	C₂×D₄	semidirect
216. #1893	C₂×D₄	semidirect
223. #1823	C₂×D₄	semidirect
229. #1786	C₂×D₄	semidirect
234. C₂×H(5,𝔽₂)	C₂×D₈	semidirect
285. #453	C₂×D₈	semidirect
286. #453	C₂×D₈	semidirect
287. C₂×#100	C₂×D₈	semidirect
313. C₂²×D₄	#447	semidirect
333. #127	#447	semidirect
334. #127	#447	semidirect
355. C₂×C₄²	#447	semidirect

Maximal subgroups

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

subgroup	index
#72313565	2
#72313557	2
#72313554	2
#72313549	2
C₂×#500769	2
#72313544	2
#72313436	2
#72313426	2
#72313382	2
#72313373	2
#72312281	2
#72306044	2
C₂×#486263	2
#72282436	2
#72281282	2