Subgroups — #72262717

Order 2048.

At least 9128 conjugacy classes of subgroups; only the 1516 normal subgroups are shown.

The subgroup lattice has 646 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262716	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256170	C₂	1	2	yes	maximal, complemented
3	#72256143	C₂	1	2	yes	maximal, complemented
4	#72256123	C₂	1	2	yes	maximal, complemented
5	#72256069	C₂	1	2	yes	maximal, complemented
6	#72256042	C₂	1	2	yes	maximal, complemented
7	#72255951	C₂	1	2	yes	maximal, complemented
8	#72255634	C₂	1	1	yes	maximal, characteristic, complemented
9	#72255628	C₂	1	1	yes	maximal, characteristic, complemented
10	#72252179	C₂	1	2	yes	maximal, complemented
11	#72252165	C₂	1	1	yes	maximal, characteristic, complemented
12	#72252114	C₂	1	2	yes	maximal, complemented
13	#72252110	C₂	1	2	yes	maximal, complemented
14	C₂×#427268	C₂	1	2	yes	maximal, complemented
15	C₂×#395193	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10575416	C₂	1	1	yes	maximal, characteristic, complemented
17	#72240119	C₂	1	2	yes	maximal, complemented
18	C₂×#364416	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#393988	C₂	1	2	yes	maximal, complemented
20	C₂³×#525	C₂²	1	2	yes	—
21	C₂×#60511	C₂²	1	2	yes	—
22	C₂×#60511	C₂²	1	2	yes	—
23	C₂×#60469	C₂²	1	1	yes	characteristic, complemented
24	C₂×#60444	C₂²	1	2	yes	—
25	C₂×#60444	C₂²	1	1	yes	characteristic
26	C₂×#60444	C₂²	1	1	yes	characteristic
27	C₂×#60359	C₂²	1	2	yes	—
28	C₂×#60359	C₂²	1	2	yes	—
29	C₂×#60359	C₂²	1	2	yes	complemented
30	C₂×#60141	C₂²	1	1	yes	characteristic, complemented
31	C₂³×#407	C₂²	1	1	yes	characteristic
32	C₂×#36614	C₂²	1	1	yes	characteristic
33	C₂×#23527	C₂²	1	1	yes	characteristic, complemented
34	#6431784	C₂²	1	2	yes	complemented
35	C₂×#23434	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#2010	C₂²	1	2	yes	—
37	C₂²×#2010	C₂²	1	2	yes	—
38	C₂²×#2010	C₂²	1	2	yes	complemented
39	C₂²×#2010	C₂²	1	2	yes	complemented
40	#6372017	C₂²	1	1	yes	characteristic, complemented
41	C₂×#20995	C₂²	1	2	yes	complemented
42	C₂×#20989	C₂²	1	1	yes	characteristic, complemented
43	C₂×#20979	C₂²	1	2	yes	complemented
44	C₂²×#1891	C₂²	1	2	yes	complemented
45	C₂×#20675	C₂²	1	1	yes	characteristic, complemented
46	C₂×#20667	C₂²	1	1	yes	characteristic, complemented
47	C₂×#20605	C₂²	1	2	yes	complemented
48	C₂×#20591	C₂²	1	2	yes	complemented
49	#6370684	C₂²	1	2	yes	complemented
50	C₂×#20579	C₂²	1	2	yes	—
51	C₂×#20579	C₂²	1	1	yes	characteristic
52	C₂×#11360	C₂²	1	2	yes	complemented
53	C₂×#11265	C₂²	1	2	yes	complemented
54	C₂×#11245	C₂²	1	1	yes	characteristic, complemented
55	#357917	C₂²	1	2	yes	complemented
56	C₂×#11153	C₂²	1	2	yes	complemented
57	C₂×#11141	C₂²	1	2	yes	complemented
58	#357823	C₂²	1	2	yes	complemented
59	C₂×#11131	C₂²	1	2	yes	complemented
60	#357758	C₂²	1	2	yes	complemented
61	C₂×#11109	C₂²	1	1	yes	characteristic, complemented
62	C₂×#11101	C₂²	1	2	yes	complemented
63	C₂×#11101	C₂²	1	2	yes	complemented
64	C₂×#11071	C₂²	1	2	yes	complemented
65	C₂×#11037	C₂²	1	2	yes	complemented
66	C₂×#11037	C₂²	1	2	yes	complemented
67	#357591	C₂²	1	2	yes	complemented
68	#357591	C₂²	1	2	yes	complemented
69	C₂×#11032	C₂²	1	2	yes	complemented
70	#357575	C₂²	1	2	yes	complemented
71	#357575	C₂²	1	2	yes	complemented
72	#357567	C₂²	1	2	yes	complemented
73	C₂×#10994	C₂²	1	2	yes	—
74	C₂×#10994	C₂²	1	2	yes	—
75	C₂×#10994	C₂²	1	2	yes	complemented
76	C₂×#10994	C₂²	1	2	yes	complemented
77	C₂×#10993	C₂²	1	2	yes	—
78	C₂×#10993	C₂²	1	2	yes	—
79	C₂×#10993	C₂²	1	2	yes	—
80	C₂×#10993	C₂²	1	2	yes	—
81	C₂×#10993	C₂²	1	2	yes	complemented
82	C₂×#10993	C₂²	1	2	yes	complemented
83	C₂×#10993	C₂²	1	2	yes	complemented
84	C₂×#10993	C₂²	1	2	yes	complemented
85	C₂×#10993	C₂²	1	2	yes	complemented
86	C₂×#10950	C₂²	1	2	yes	complemented
87	C₂×#10937	C₂²	1	2	yes	complemented
88	#353666	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10738	C₂²	1	2	yes	complemented
90	C₂×#10738	C₂²	1	2	yes	complemented
91	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
92	#353403	C₂²	1	2	yes	complemented
93	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₂²⋊#338	C₂²	1	1	yes	characteristic, complemented
95	C₂×#10716	C₂²	1	2	yes	complemented
96	#124000	C₂²	1	2	yes	complemented
97	#123976	C₂²	1	2	yes	complemented
98	#123941	C₂²	1	2	yes	complemented
99	#123638	C₂²	1	2	yes	complemented
100	#123636	C₂²	1	2	yes	complemented
101	#123602	C₂²	1	2	yes	complemented
102	#123569	C₂²	1	2	yes	complemented
103	#123556	C₂²	1	2	yes	complemented
104	#123549	C₂²	1	2	yes	complemented
105	#123532	C₂²	1	2	yes	complemented
106	#123532	C₂²	1	2	yes	complemented
107	C₂⁴×#41	C₂³	1	2	yes	—
108	C₂⁶×C₄	C₂³	1	1	yes	characteristic
109	C₂²×#575	C₂³	1	2	yes	—
110	C₂²×#575	C₂³	1	1	yes	characteristic
111	C₂²×#575	C₂³	1	2	yes	—
112	C₂²×#575	C₂³	1	2	yes	—
113	C₂²×#575	C₂³	1	1	yes	characteristic
114	C₂²×#568	C₂³	1	1	yes	characteristic
115	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
116	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
117	C₂²×#525	C₂³	1	1	yes	characteristic
118	C₂²×#525	C₂³	1	2	yes	—
119	C₂²×#525	C₂³	1	2	yes	—
120	C₂²×#525	C₂³	1	2	yes	—
121	C₂²×#525	C₂³	1	2	yes	—
122	C₂²×#525	C₂³	1	2	yes	—
123	C₂³×#117	C₂³	1	2	yes	—
124	#60511	D₄	1	16	yes	complemented
125	#60444	D₄	1	8	yes	complemented
126	C₂×#3054	D₄	1	4	yes	complemented
127	C₂×#3050	D₄	1	4	yes	complemented
128	C₂×#3005	D₄	1	4	yes	complemented
129	C₂×#3005	D₄	1	4	yes	complemented
130	C₂×#3004	D₄	1	4	yes	complemented
131	C₂×#3003	D₄	1	4	yes	complemented
132	C₂²×#430	C₂³	1	1	yes	characteristic
133	C₂²×#430	C₂³	1	1	yes	characteristic
134	C₂×#2911	C₂³	1	1	yes	characteristic
135	C₂×#2911	C₂³	1	2	yes	—
136	C₂×#2911	C₂³	1	1	yes	characteristic
137	C₂×#2905	C₂³	1	1	yes	characteristic
138	C₂²×#421	C₂³	1	2	yes	—
139	C₂²×#421	C₂³	1	2	yes	—
140	C₂²×#421	C₂³	1	2	yes	—
141	C₂²×#421	C₂³	1	2	yes	—
142	C₂²×#421	C₂³	1	2	yes	—
143	C₂²×#421	C₂³	1	2	yes	—
144	C₂×#2896	C₂³	1	2	yes	—
145	C₂×#2896	C₂³	1	2	yes	—
146	C₂×#2896	C₂³	1	2	yes	—
147	C₂×#2896	C₂³	1	2	yes	—
148	C₂×#2896	C₂³	1	2	yes	—
149	C₂×#2896	C₂³	1	2	yes	—
150	C₂²×#413	C₂³	1	2	yes	—
151	C₂²×#413	C₂³	1	2	yes	—
152	C₂²×#413	C₂³	1	2	yes	—
153	C₂²×#413	C₂³	1	2	yes	—
154	C₂²×#413	C₂³	1	2	yes	—
155	C₂×#2879	C₂³	1	1	yes	characteristic
156	C₂×#2879	C₂³	1	2	yes	—
157	C₂×#2879	C₂³	1	2	yes	—
158	C₂×#2879	C₂³	1	2	yes	—
159	C₂×#2879	C₂³	1	2	yes	—
160	C₂²×#407	D₄	1	8	yes	—
161	C₂²×#407	C₂³	1	2	yes	—
162	C₂²×#407	C₂³	1	2	yes	—
163	C₂²×#407	C₂³	1	1	yes	characteristic
164	C₂²×#407	C₂³	1	2	yes	—
165	C₂²×#407	C₂³	1	2	yes	—
166	C₂²×#407	C₂³	1	2	yes	—
167	C₂²×#407	C₂³	1	2	yes	—
168	C₂²×#407	C₂³	1	2	yes	—
169	C₂²×#407	C₂³	1	2	yes	—
170	C₂²×#407	C₂³	1	2	yes	—
171	C₂²×#407	C₂³	1	1	yes	characteristic
172	C₂²×#407	C₂³	1	2	yes	—
173	C₂×#2873	C₂³	1	1	yes	characteristic
174	#36614	D₄	1	8	yes	—
175	C₂×#2280	C₂³	1	2	yes	—
176	C₂×#2280	C₂³	1	1	yes	characteristic
177	C₂²×#344	C₂³	1	2	yes	—
178	C₂²×#344	C₂³	1	2	yes	—
179	C₂²×#344	C₂³	1	2	yes	—
180	C₂²×#344	C₂³	1	2	yes	—
181	C₂²×#344	C₂³	1	2	yes	—
182	C₂²×#344	C₂³	1	2	yes	—
183	C₂²×#344	C₂³	1	2	yes	—
184	C₂²×#344	C₂³	1	2	yes	—
185	C₂²×#344	C₂³	1	2	yes	—
186	C₂²×#344	C₂³	1	2	yes	—
187	C₂²×#344	C₂³	1	2	yes	—
188	C₂²×#344	C₂³	1	2	yes	—
189	C₂×#1742	C₂³	1	2	yes	—
190	C₂×#1738	C₂³	1	2	yes	—
191	C₂×#1738	C₂³	1	2	yes	—
192	C₂×#1738	C₂³	1	2	yes	—
193	C₂×#1738	C₂³	1	2	yes	—
194	C₂×#1738	C₂³	1	2	yes	—
195	C₂×#1733	C₂³	1	2	yes	—
196	C₂×#1733	C₂³	1	2	yes	—
197	C₂²×#338	C₂³	1	2	yes	—
198	C₂²×#338	C₂³	1	1	yes	characteristic
199	C₂²×#338	C₂³	1	1	yes	characteristic
200	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
201	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
202	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
203	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
204	C₂⁷	#41	1	1	yes	characteristic
205	C₂³×#41	C₂×D₄	1	2	yes	—
206	C₂³×#41	C₂×D₄	1	2	yes	—
207	C₂³×#41	C₂⁴	1	2	yes	—
208	C₂³×#41	C₂⁴	1	2	yes	—
209	C₂³×#41	C₂⁴	1	1	yes	characteristic
210	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
211	C₂⁴×D₄	C₂×D₄	1	2	yes	—
212	C₂⁵×C₄	C₂×D₄	1	4	yes	—
213	C₂⁵×C₄	C₂×D₄	1	4	yes	—
214	C₂⁵×C₄	#41	1	2	yes	—
215	C₂⁵×C₄	#41	1	1	yes	characteristic
216	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
217	C₂⁵×C₄	C₂⁴	1	2	yes	—
218	C₂×#575	C₂×D₄	1	4	yes	—
219	C₂²×#137	C₂×D₄	1	4	yes	—
220	C₂²×#137	C₂×D₄	1	4	yes	—
221	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
222	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
223	C₂²×#135	C₂×D₄	1	4	yes	—
224	C₂³×M₁₆	C₂×D₄	1	4	yes	—
225	C₂³×M₁₆	C₂×D₄	1	4	yes	—
226	C₂³×M₁₆	C₂×D₄	1	4	yes	—
227	C₂³×M₁₆	C₂×D₄	1	2	yes	—
228	C₂³×M₁₆	C₂⁴	1	2	yes	—
229	C₂³×M₁₆	C₂⁴	1	2	yes	—
230	C₂³×M₁₆	C₂⁴	1	2	yes	—
231	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
232	C₂³×M₁₆	C₂⁴	1	2	yes	—
233	C₂³×M₁₆	C₂⁴	1	2	yes	—
234	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
235	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
236	C₂³×M₁₆	C₂⁴	1	2	yes	—
237	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₈	C₂×D₄	1	2	yes	—
239	C₂×#525	C₂×D₄	1	4	yes	—
240	C₂×#525	C₂×D₄	1	4	yes	—
241	C₂×#525	C₂×D₄	1	4	yes	—
242	C₂×#525	C₂×D₄	1	8	yes	—
243	C₂×#525	C₂×D₄	1	4	yes	—
244	C₂×#525	C₂×D₄	1	4	yes	—
245	C₂×#525	C₂×D₄	1	8	yes	—
246	C₂×#525	C₂×D₄	1	8	yes	—
247	C₂²×#117	C₂×D₄	1	8	yes	—
248	C₂²×#117	C₂⁴	1	2	yes	—
249	C₂²×#117	C₂⁴	1	1	yes	characteristic
250	C₂²×#117	C₂⁴	1	2	yes	—
251	C₂²×#117	C₂⁴	1	2	yes	—
252	#2911	C₂×D₄	1	8	yes	—
253	#2911	C₂×D₄	1	4	yes	—
254	#2911	C₂×D₄	1	8	yes	—
255	C₂×#427	C₂×D₄	1	4	yes	—
256	#2896	C₂×D₄	1	8	yes	—
257	#2896	C₂×D₄	1	8	yes	—
258	#2896	C₂×D₄	1	8	yes	—
259	C₂×#419	C₂×D₄	1	4	yes	—
260	C₂×#419	C₂×D₄	1	4	yes	—
261	C₂×#418	C₂×D₄	1	4	yes	—
262	C₂×#418	C₂×D₄	1	4	yes	—
263	C₂×#416	C₂×D₄	1	8	yes	—
264	C₂×#407	C₂×D₄	1	8	yes	—
265	C₂×#407	C₂×D₄	1	4	yes	—
266	C₂×#407	C₂×D₄	1	4	yes	—
267	C₂×#407	C₂×D₄	1	8	yes	—
268	C₂×#407	C₂×D₄	1	8	yes	—
269	#2280	C₂×D₄	1	8	yes	—
270	#2280	C₂×D₄	1	4	yes	—
271	C₂⁶	#121	1	4	yes	—
272	C₂⁶	C₂×#41	1	2	yes	—
273	C₂⁶	C₂×#41	1	1	yes	characteristic
274	C₂²×#41	C₂²×D₄	1	4	yes	—
275	C₂²×#41	C₂²×D₄	1	4	yes	—
276	C₂²×#41	C₂²×D₄	1	4	yes	—
277	C₂²×#41	C₂²×D₄	1	4	yes	—
278	C₂²×#41	C₂²×D₄	1	2	yes	—
279	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
280	C₂³×Q₈	C₂²×D₄	1	2	yes	—
281	C₂³×Q₈	C₂²×D₄	1	2	yes	—
282	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂³×D₄	C₂²×D₄	1	2	yes	—
284	C₂³×D₄	C₂²×D₄	1	2	yes	—
285	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
286	C₂⁴×C₄	#121	1	8	yes	—
287	C₂⁴×C₄	#121	1	4	yes	—
288	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
289	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
290	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
291	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
292	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
293	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
294	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
295	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
296	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
297	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
298	C₂⁴×C₄	C₂×#41	1	2	yes	—
299	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
300	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
301	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
302	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
303	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
305	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
306	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
307	C₂²×Q₁₆	#120	1	4	yes	complemented
308	C₂²×SD₁₆	#120	1	8	yes	complemented
309	C₂²×D₈	#120	1	4	yes	complemented
310	C₂²×M₁₆	#120	1	8	yes	—
311	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
312	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
313	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
314	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
315	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
316	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
317	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
318	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
319	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
320	C₂²×M₁₆	H(5,𝔽₂)	1	2	yes	—
321	C₂²×M₁₆	H(5,𝔽₂)	1	4	yes	—
322	C₂³×C₈	#120	1	8	yes	—
323	C₂³×C₈	C₂²×D₄	1	2	yes	—
324	C₂³×C₈	C₂²×D₄	1	2	yes	—
325	C₂³×C₈	H(5,𝔽₂)	1	2	yes	—
326	C₂³×C₈	H(5,𝔽₂)	1	4	yes	—
327	C₂×#117	C₂²×D₄	1	4	yes	—
328	C₂×#117	C₂²×D₄	1	4	yes	—
329	C₂×#117	C₂²×D₄	1	4	yes	—
330	C₂×#117	C₂²×D₄	1	4	yes	—
331	C₂×#117	C₂²×D₄	1	4	yes	—
332	C₂×#117	C₂²×D₄	1	4	yes	—
333	C₂×#117	C₂²×D₄	1	4	yes	—
334	C₂×#117	C₂²×D₄	1	2	yes	—
335	C₂×#117	H(5,𝔽₂)	1	2	yes	—
336	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
337	#427	#120	1	16	yes	complemented
338	#419	#120	1	16	yes	complemented
339	#418	#120	1	16	yes	complemented
340	#407	#120	1	16	yes	—
341	#407	#120	1	16	yes	—
342	C₂⁵	C₂×#121	1	4	yes	—
343	C₂⁵	C₂×#121	1	2	yes	—
344	C₂⁵	#546	1	1	yes	characteristic
345	C₂⁵	#546	1	2	yes	—
346	C₂⁵	#546	1	4	yes	—
347	C₂⁵	#546	1	2	yes	—
348	C₂⁵	#546	1	1	yes	characteristic
349	C₂⁵	#546	1	2	yes	—
350	C₂⁵	C₂²×#41	1	1	yes	characteristic
351	C₂²×Q₈	C₂×#120	1	4	yes	—
352	C₂²×Q₈	C₂×#120	1	4	yes	—
353	C₂²×Q₈	#534	1	2	yes	—
354	C₂²×D₄	C₂×#120	1	4	yes	—
355	C₂²×D₄	C₂×#120	1	4	yes	—
356	C₂²×D₄	#534	1	2	yes	—
357	C₂³×C₄	C₂×#120	1	4	yes	—
358	C₂³×C₄	C₂×#120	1	4	yes	—
359	C₂³×C₄	C₂×#120	1	2	yes	—
360	C₂³×C₄	C₂×#120	1	2	yes	—
361	C₂³×C₄	C₂×#121	1	4	yes	—
362	C₂³×C₄	C₂×#121	1	2	yes	—
363	C₂³×C₄	#535	1	4	yes	—
364	C₂³×C₄	#535	1	2	yes	—
365	C₂³×C₄	#535	1	2	yes	—
366	C₂³×C₄	#535	1	4	yes	—
367	C₂³×C₄	D₄²	1	4	yes	—
368	C₂³×C₄	D₄²	1	4	yes	—
369	C₂³×C₄	D₄²	1	4	yes	—
370	C₂³×C₄	D₄²	1	2	yes	—
371	C₂³×C₄	D₄²	1	2	yes	—
372	C₂³×C₄	D₄²	1	2	yes	—
373	C₂³×C₄	D₄²	1	2	yes	—
374	C₂³×C₄	D₄²	1	4	yes	—
375	C₂³×C₄	#546	1	2	yes	—
376	C₂³×C₄	#546	1	4	yes	—
377	C₂³×C₄	#546	1	2	yes	—
378	C₂³×C₄	#546	1	1	yes	characteristic
379	C₂³×C₄	#546	1	1	yes	characteristic
380	C₂³×C₄	#546	1	2	yes	—
381	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
382	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
383	C₂³×C₄	C₂³×D₄	1	2	yes	—
384	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
385	C₂³×C₄	C₂³×D₄	1	2	yes	—
386	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
387	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
392	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
393	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
397	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
399	C₂³×C₄	#585	1	1	yes	characteristic
400	C₂³×C₄	#585	1	2	yes	—
401	C₂³×C₄	#585	1	2	yes	—
402	C₂³×C₄	#585	1	1	yes	characteristic
403	C₂×M₁₆	C₂×#120	1	8	yes	—
404	C₂×M₁₆	C₂×#120	1	8	yes	—
405	C₂×M₁₆	C₂×#120	1	8	yes	—
406	C₂²×C₈	C₂×#120	1	4	yes	—
407	C₂²×C₈	C₂×#120	1	4	yes	—
408	C₂²×C₈	C₂×#120	1	4	yes	—
409	C₂²×C₈	C₂×#120	1	4	yes	—
410	#117	C₂×#120	1	8	yes	—
411	#117	C₂×#120	1	8	yes	—
412	C₂×C₄²	#534	1	4	yes	—
413	C₂⁴	#2408	1	2	yes	—
414	C₂⁴	#2408	1	4	yes	—
415	C₂⁴	#2408	1	4	yes	—
416	C₂⁴	#2408	1	2	yes	—
417	C₂⁴	C₂²×#121	1	1	yes	characteristic
418	C₂⁴	#3459	1	1	yes	characteristic
419	C₂⁴	#3459	1	1	yes	characteristic
420	C₂⁴	C₂×#546	1	2	yes	—
421	C₂⁴	C₂×#546	1	1	yes	characteristic
422	C₂⁴	C₂×#546	1	2	yes	—
423	C₂⁴	C₂×#546	1	1	yes	characteristic
424	C₂⁴	#3490	1	1	yes	characteristic
425	C₂⁴	#3490	1	1	yes	characteristic
426	C₂⁴	#3505	1	2	yes	—
427	C₂⁴	#3505	1	2	yes	—
428	C₂²×C₄	#2408	1	4	yes	—
429	C₂²×C₄	#2408	1	4	yes	—
430	C₂²×C₄	#2408	1	2	yes	—
431	C₂²×C₄	#2408	1	2	yes	—
432	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
433	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
434	C₂²×C₄	C₂²×#120	1	2	yes	—
435	C₂²×C₄	C₂²×#120	1	2	yes	—
436	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
437	C₂²×C₄	C₂×#534	1	1	yes	characteristic
438	C₂²×C₄	C₂×#534	1	1	yes	characteristic
439	C₂²×C₄	C₂×#535	1	2	yes	—
440	C₂²×C₄	C₂×#535	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄²	1	2	yes	—
442	C₂²×C₄	C₂×D₄²	1	2	yes	—
443	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
445	C₂²×C₄	#3484	1	2	yes	—
446	C₂²×C₄	#3484	1	2	yes	—
447	C₂²×C₄	#3484	1	2	yes	—
448	C₂²×C₄	#3484	1	2	yes	—
449	C₂²×C₄	#3484	1	2	yes	—
450	C₂²×C₄	#3484	1	2	yes	—
451	C₂²×C₄	#3484	1	1	yes	characteristic
452	C₂²×C₄	#3484	1	1	yes	characteristic
453	C₂²×C₄	#3484	1	1	yes	characteristic
454	C₂²×C₄	#3484	1	1	yes	characteristic
455	C₂²×C₄	#3484	1	1	yes	characteristic
456	C₂²×C₄	#3484	1	1	yes	characteristic
457	C₂²×C₄	#3484	1	1	yes	characteristic
458	C₂²×C₄	#3484	1	1	yes	characteristic
459	C₂²×C₄	#3484	1	1	yes	characteristic
460	C₂²×C₄	#3484	1	2	yes	—
461	C₂²×C₄	#3484	1	2	yes	—
462	C₂²×C₄	#3484	1	2	yes	—
463	C₂²×C₄	#3484	1	1	yes	characteristic
464	C₂²×C₄	#3485	1	2	yes	—
465	C₂²×C₄	#3485	1	2	yes	—
466	C₂²×C₄	#3485	1	1	yes	characteristic
467	C₂²×C₄	#3485	1	1	yes	characteristic
468	C₂²×C₄	#3488	1	2	yes	—
469	C₂²×C₄	#3488	1	2	yes	—
470	C₂²×C₄	#3488	1	2	yes	—
471	C₂²×C₄	#3488	1	1	yes	characteristic
472	C₂²×C₄	#3488	1	1	yes	characteristic
473	C₂²×C₄	#3488	1	1	yes	characteristic
474	C₂²×C₄	#3488	1	1	yes	characteristic
475	C₂²×C₄	#3488	1	2	yes	—
476	C₂²×C₄	#3488	1	2	yes	—
477	C₂²×C₄	#3496	1	1	yes	characteristic
478	C₂²×C₄	#3496	1	2	yes	—
479	C₂²×C₄	#3496	1	2	yes	—
480	C₂²×C₄	#3496	1	2	yes	—
481	C₂²×C₄	#3496	1	2	yes	—
482	C₂²×C₄	#3496	1	2	yes	—
483	C₂²×C₄	#3496	1	2	yes	—
484	C₂²×C₄	#3496	1	2	yes	—
485	C₂²×C₄	#3496	1	1	yes	characteristic
486	C₂²×C₄	#3498	1	1	yes	characteristic
487	C₂²×C₄	#3498	1	2	yes	—
488	C₂²×C₄	#3498	1	2	yes	—
489	C₂²×C₄	#3498	1	2	yes	—
490	C₂²×C₄	#3500	1	1	yes	characteristic
491	C₂²×C₄	#3500	1	2	yes	—
492	C₂²×C₄	#3532	1	2	yes	—
493	C₂²×C₄	#3532	1	2	yes	—
494	C₂²×C₄	#3532	1	2	yes	—
495	C₂²×C₄	#3533	1	2	yes	—
496	C₂²×C₄	#3534	1	2	yes	—
497	C₂²×C₄	#3534	1	2	yes	—
498	C₂²×C₄	#3534	1	2	yes	—
499	C₂²×C₄	#3534	1	1	yes	characteristic
500	C₂²×C₄	#3534	1	2	yes	—
501	C₂²×C₄	#3534	1	2	yes	—
502	C₂²×C₄	#3534	1	1	yes	characteristic
503	C₂²×C₄	#3534	1	1	yes	characteristic
504	C₂²×C₄	#3534	1	1	yes	characteristic
505	C₂²×C₄	#3537	1	1	yes	characteristic
506	C₂²×C₄	#3537	1	2	yes	—
507	C₂²×C₄	#3537	1	1	yes	characteristic
508	C₂²×C₄	#3537	1	1	yes	characteristic
509	C₂²×C₄	#3537	1	1	yes	characteristic
510	C₂²×C₄	#3542	1	2	yes	—
511	C₂²×C₄	#3542	1	2	yes	—
512	C₂²×C₄	#3542	1	2	yes	—
513	C₂²×C₄	#3542	1	2	yes	—
514	C₂²×C₄	#3543	1	2	yes	—
515	C₂²×C₄	#3543	1	2	yes	—
516	C₂²×C₄	#3543	1	2	yes	—
517	C₂²×C₄	#3545	1	2	yes	—
518	C₂²×C₄	#3558	1	2	yes	—
519	C₂²×C₄	#3560	1	2	yes	—
520	C₂×C₈	#2846	1	8	yes	—
521	C₂³	C₂×#2408	1	2	yes	—
522	C₂³	C₂×#2408	1	1	yes	characteristic
523	C₂³	#34981	1	1	yes	characteristic
524	C₂³	#34984	1	1	yes	characteristic
525	C₂³	#35358	1	2	yes	—
526	C₂³	#36152	1	1	yes	characteristic
527	C₂³	#36152	1	2	yes	—
528	C₂³	#36152	1	1	yes	characteristic
529	C₂³	#37744	1	1	yes	characteristic
530	C₂³	#37744	1	1	yes	characteristic
531	C₂³	#37744	1	1	yes	characteristic
532	C₂³	#37744	1	1	yes	characteristic
533	C₂³	#37776	1	2	yes	—
534	C₂³	#37778	1	2	yes	—
535	C₂³	#39428	1	2	yes	—
536	C₂³	#39430	1	2	yes	—
537	C₂³	#42997	1	2	yes	—
538	C₂³	#42997	1	2	yes	—
539	C₂³	#43000	1	1	yes	characteristic
540	C₂³	#43022	1	2	yes	—
541	C₂³	#43491	1	1	yes	characteristic
542	C₂³	#43932	1	2	yes	—
543	C₂³	#43932	1	2	yes	—
544	C₂×C₄	#35222	1	1	yes	characteristic
545	C₂×C₄	#35222	1	2	yes	—
546	C₂×C₄	#35346	1	1	yes	characteristic
547	C₂×C₄	#35346	1	1	yes	characteristic
548	C₂×C₄	#35347	1	1	yes	characteristic
549	C₂×C₄	#35347	1	1	yes	characteristic
550	C₂×C₄	#35512	1	1	yes	characteristic
551	C₂×C₄	#35512	1	2	yes	—
552	C₂×C₄	#35512	1	1	yes	characteristic
553	C₂×C₄	#35513	1	2	yes	—
554	C₂×C₄	#35513	1	1	yes	characteristic
555	C₂×C₄	#35527	1	1	yes	characteristic
556	C₂×C₄	#35680	1	2	yes	—
557	C₂×C₄	#35680	1	1	yes	characteristic
558	C₂×C₄	#35680	1	2	yes	—
559	C₂×C₄	#35680	1	2	yes	—
560	C₂×C₄	#35680	1	2	yes	—
561	C₂×C₄	#35680	1	2	yes	—
562	C₂×C₄	#35750	1	1	yes	characteristic
563	C₂×C₄	#35750	1	2	yes	—
564	C₂×C₄	#36082	1	1	yes	characteristic
565	C₂×C₄	#36091	1	1	yes	characteristic
566	C₂×C₄	D₄×#120	1	2	yes	—
567	C₂×C₄	D₄×#120	1	1	yes	characteristic
568	C₂×C₄	D₄×#120	1	1	yes	characteristic
569	C₂×C₄	C₂×#2846	1	1	yes	characteristic
570	C₂×C₄	#36717	1	1	yes	characteristic
571	C₂×C₄	#36721	1	1	yes	characteristic
572	C₂×C₄	#36739	1	2	yes	—
573	C₂×C₄	#37644	1	2	yes	—
574	C₂×C₄	#37646	1	2	yes	—
575	C₂×C₄	#37672	1	1	yes	characteristic
576	C₂×C₄	#37672	1	1	yes	characteristic
577	C₂×C₄	#37672	1	1	yes	characteristic
578	C₂×C₄	#37672	1	1	yes	characteristic
579	C₂×C₄	#39336	1	2	yes	—
580	C₂×C₄	#39338	1	2	yes	—
581	C₂×C₄	#40485	1	2	yes	—
582	C₂×C₄	#40485	1	2	yes	—
583	C₂×C₄	#40485	1	2	yes	—
584	C₂×C₄	#40509	1	2	yes	—
585	C₂×C₄	#42996	1	2	yes	—
586	C₂×C₄	#43001	1	1	yes	characteristic
587	C₂×C₄	#43017	1	2	yes	—
588	C₂×C₄	#43023	1	2	yes	—
589	C₂×C₄	#43492	1	1	yes	characteristic
590	C₂×C₄	#43886	1	2	yes	—
591	C₂×C₄	#43904	1	2	yes	—
592	C₂×C₄	#46350	1	2	yes	—
593	C₂×C₄	#46350	1	2	yes	—
594	C₂×C₄	#46351	1	2	yes	—
595	C₂×C₄	#46354	1	1	yes	characteristic
596	C₂×C₄	#46354	1	1	yes	characteristic
597	C₂×C₄	#46355	1	1	yes	characteristic
598	C₂×C₄	#46355	1	1	yes	characteristic
599	C₂×C₄	#46362	1	2	yes	—
600	C₂×C₄	#46364	1	2	yes	—
601	C₂×C₄	#46372	1	2	yes	—
602	C₂×C₄	#46413	1	2	yes	—
603	C₂×C₄	#46419	1	2	yes	—
604	C₂×C₄	#46419	1	2	yes	—
605	C₂×C₄	#46830	1	2	yes	—
606	C₂×C₄	#47826	1	2	yes	—
607	C₂×C₄	#47827	1	2	yes	—
608	C₂×C₄	#47830	1	1	yes	characteristic
609	C₂×C₄	#47830	1	2	yes	—
610	C₂×C₄	#47831	1	2	yes	—
611	C₂×C₄	#47831	1	1	yes	characteristic
612	C₂×C₄	#47846	1	2	yes	—
613	C₂×C₄	#47847	1	2	yes	—
614	C₂×C₄	#48776	1	1	yes	characteristic
615	C₂×C₄	#48777	1	1	yes	characteristic
616	C₂×C₄	#50634	1	2	yes	—
617	C₂×C₄	#50646	1	2	yes	—
618	C₂×C₄	#50647	1	2	yes	—
619	C₂×C₄	#50856	1	2	yes	—
620	C₂²	#612792	1	1	yes	characteristic
621	C₂²	#625760	1	1	yes	characteristic
622	C₂²	#686894	1	2	yes	—
623	C₂²	#687270	1	2	yes	—
624	C₂²	#763807	1	1	yes	characteristic
625	C₂²	#1083750	1	1	yes	characteristic
626	C₂²	#1083751	1	2	yes	—
627	C₂²	#1083754	1	1	yes	characteristic
628	C₂²	#1085253	1	2	yes	—
629	C₂²	#1085256	1	1	yes	characteristic
630	C₂²	#1085258	1	1	yes	characteristic
631	C₄	#1082737	1	1	yes	characteristic
632	C₄	#1082739	1	2	yes	—
633	C₄	#1082741	1	1	yes	characteristic
634	C₄	#1084729	1	2	yes	—
635	C₄	#1084731	1	1	yes	characteristic
636	C₄	#1084733	1	1	yes	characteristic
637	C₄	#4312298	1	2	yes	—
638	C₄	#4312301	1	2	yes	—
639	C₄	#4380236	1	1	yes	characteristic
640	C₄	#4380237	1	1	yes	characteristic
641	C₄	#4928938	1	1	yes	characteristic
642	C₄	#4929082	1	1	yes	characteristic
643	C₂	#72216253	1	2	yes	—
644	C₂	#72251017	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#46355
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
socle	C₂²	#1085256
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262716	C₂	semidirect
2. #72256170	C₂	semidirect
3. #72256143	C₂	semidirect
4. #72256123	C₂	semidirect
5. #72256069	C₂	semidirect
6. #72256042	C₂	semidirect
7. #72255951	C₂	semidirect
8. #72255634	C₂	semidirect
9. #72255628	C₂	semidirect
10. #72252179	C₂	semidirect
11. #72252165	C₂	semidirect
12. #72252114	C₂	semidirect
13. #72252110	C₂	semidirect
14. C₂×#427268	C₂	semidirect
15. C₂×#395193	C₂	semidirect
16. C₂×#10575416	C₂	semidirect
17. #72240119	C₂	semidirect
18. C₂×#364416	C₂	semidirect
19. C₂×#393988	C₂	semidirect
23. C₂×#60469	C₂²	semidirect
29. C₂×#60359	C₂²	semidirect
30. C₂×#60141	C₂²	semidirect
33. C₂×#23527	C₂²	semidirect
34. #6431784	C₂²	semidirect
35. C₂×#23434	C₂²	semidirect
38. C₂²×#2010	C₂²	semidirect
39. C₂²×#2010	C₂²	semidirect
40. #6372017	C₂²	semidirect
41. C₂×#20995	C₂²	semidirect
42. C₂×#20989	C₂²	semidirect
43. C₂×#20979	C₂²	semidirect
44. C₂²×#1891	C₂²	semidirect
45. C₂×#20675	C₂²	semidirect
46. C₂×#20667	C₂²	semidirect
47. C₂×#20605	C₂²	semidirect
48. C₂×#20591	C₂²	semidirect
49. #6370684	C₂²	semidirect
52. C₂×#11360	C₂²	semidirect
53. C₂×#11265	C₂²	semidirect
54. C₂×#11245	C₂²	semidirect
55. #357917	C₂²	semidirect
56. C₂×#11153	C₂²	semidirect
57. C₂×#11141	C₂²	semidirect
58. #357823	C₂²	semidirect
59. C₂×#11131	C₂²	semidirect
60. #357758	C₂²	semidirect
61. C₂×#11109	C₂²	semidirect
62. C₂×#11101	C₂²	semidirect
63. C₂×#11101	C₂²	semidirect
64. C₂×#11071	C₂²	semidirect
65. C₂×#11037	C₂²	semidirect
66. C₂×#11037	C₂²	semidirect
67. #357591	C₂²	semidirect
68. #357591	C₂²	semidirect
69. C₂×#11032	C₂²	semidirect
70. #357575	C₂²	semidirect
71. #357575	C₂²	semidirect
72. #357567	C₂²	semidirect
75. C₂×#10994	C₂²	semidirect
76. C₂×#10994	C₂²	semidirect
81. C₂×#10993	C₂²	semidirect
82. C₂×#10993	C₂²	semidirect
83. C₂×#10993	C₂²	semidirect
84. C₂×#10993	C₂²	semidirect
85. C₂×#10993	C₂²	semidirect
86. C₂×#10950	C₂²	semidirect
87. C₂×#10937	C₂²	semidirect
88. #353666	C₂²	semidirect
89. C₂×#10738	C₂²	semidirect
90. C₂×#10738	C₂²	semidirect
91. C₂×#10737	C₂²	semidirect
92. #353403	C₂²	semidirect
93. C₂×#10729	C₂²	semidirect
94. C₂×C₂²⋊#338	C₂²	semidirect
95. C₂×#10716	C₂²	semidirect
96. #124000	C₂²	semidirect
97. #123976	C₂²	semidirect
98. #123941	C₂²	semidirect
99. #123638	C₂²	semidirect
100. #123636	C₂²	semidirect
101. #123602	C₂²	semidirect
102. #123569	C₂²	semidirect
103. #123556	C₂²	semidirect
104. #123549	C₂²	semidirect
105. #123532	C₂²	semidirect
106. #123532	C₂²	semidirect
124. #60511	D₄	semidirect
125. #60444	D₄	semidirect
126. C₂×#3054	D₄	semidirect
127. C₂×#3050	D₄	semidirect
128. C₂×#3005	D₄	semidirect
129. C₂×#3005	D₄	semidirect
130. C₂×#3004	D₄	semidirect
131. C₂×#3003	D₄	semidirect
307. C₂²×Q₁₆	#120	semidirect
308. C₂²×SD₁₆	#120	semidirect
309. C₂²×D₈	#120	semidirect
337. #427	#120	semidirect
338. #419	#120	semidirect
339. #418	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262716	2
#72256170	2
#72256143	2
#72256123	2
#72256069	2
#72256042	2
#72255951	2
#72255634	2
#72255628	2
#72252179	2
#72252165	2
#72252114	2
#72252110	2
C₂×#427268	2
C₂×#395193	2
C₂×#10575416	2
#72240119	2
C₂×#364416	2
C₂×#393988	2