Subgroups — #72280157

Order 2048.

At least 6471 conjugacy classes of subgroups; only the 1820 normal subgroups are shown.

The subgroup lattice has 621 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72280115	C₂	1	1	yes	maximal, characteristic, complemented
2	#72280000	C₂	1	1	yes	maximal, characteristic, complemented
3	#72279912	C₂	1	2	yes	maximal, complemented
4	#72279889	C₂	1	2	yes	maximal, complemented
5	#72279862	C₂	1	1	yes	maximal, characteristic, complemented
6	#72279851	C₂	1	1	yes	maximal, characteristic, complemented
7	#72279835	C₂	1	1	yes	maximal, characteristic, complemented
8	#72279812	C₂	1	2	yes	maximal, complemented
9	#72279795	C₂	1	2	yes	maximal, complemented
10	C₂×#10574963	C₂	1	1	yes	maximal, characteristic, complemented
11	#72279735	C₂	1	8	yes	maximal, complemented
12	#72279713	C₂	1	8	yes	maximal, complemented
13	#72279460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#3498	C₂²	1	1	yes	characteristic
15	C₂×C₄×#585	C₂²	1	1	yes	characteristic
16	C₂×#60803	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3151	C₂²	1	1	yes	characteristic, complemented
18	#10574963	C₂²	1	8	yes	—
19	C₂×#60415	C₂²	1	2	yes	—
20	C₂²×#3038	C₂²	1	2	yes	—
21	C₂×#60099	C₂²	1	1	yes	characteristic
22	#7628578	C₂²	1	1	yes	characteristic
23	#7628578	C₂²	1	2	yes	complemented
24	#6629121	C₂²	1	4	yes	complemented
25	#6628984	C₂²	1	4	yes	complemented
26	#6516758	C₂²	1	4	yes	complemented
27	#6516757	C₂²	1	4	yes	complemented
28	#6374304	C₂²	1	1	yes	characteristic, complemented
29	#6374304	C₂²	1	2	yes	complemented
30	#6372442	C₂²	1	1	yes	characteristic, complemented
31	#6372358	C₂²	1	1	yes	characteristic
32	#6370937	C₂²	1	1	yes	characteristic
33	#6370937	C₂²	1	2	yes	complemented
34	C₂×#17750	C₂²	1	2	yes	complemented
35	#6343377	C₂²	1	2	yes	complemented
36	#6342924	C₂²	1	2	yes	complemented
37	C₂×#17447	C₂²	1	2	yes	complemented
38	#6342561	C₂²	1	1	yes	characteristic
39	#237583	C₂²	1	8	yes	complemented
40	#237575	C₂²	1	8	yes	complemented
41	#235725	C₂²	1	8	yes	complemented
42	#235723	C₂²	1	8	yes	complemented
43	#197434	C₂²	1	4	yes	complemented
44	#197430	C₂²	1	4	yes	complemented
45	#185628	C₂²	1	8	yes	complemented
46	#184929	C₂²	1	8	yes	complemented
47	#181799	C₂²	1	2	yes	complemented
48	#181467	C₂²	1	2	yes	complemented
49	#181175	C₂²	1	2	yes	complemented
50	#115542	C₂²	1	16	yes	complemented
51	#111855	C₂²	1	16	yes	complemented
52	#106620	C₂²	1	8	yes	complemented
53	C₂²×#585	D₄	1	1	yes	characteristic
54	C₂×#3498	D₄	1	4	yes	complemented
55	C₂×#3498	C₂³	1	4	yes	—
56	C₂²×#532	D₄	1	2	yes	complemented
57	C₂²×#532	C₂³	1	1	yes	characteristic
58	C₂²×#532	C₂³	1	1	yes	characteristic
59	C₂³×#127	D₄	1	2	yes	complemented
60	C₂³×#127	C₂³	1	1	yes	characteristic
61	C₄×#585	D₄	1	4	yes	—
62	C₄×#585	C₂³	1	4	yes	—
63	C₂×#3428	D₄	1	1	yes	characteristic
64	C₂×#3428	D₄	1	2	yes	—
65	C₂²×C₄×#41	C₂³	1	2	yes	—
66	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
67	C₂×#3206	C₂³	1	2	yes	complemented
68	C₂×#3205	C₂³	1	2	yes	complemented
69	C₂²×#493	C₂³	1	2	yes	complemented
70	C₂²×#492	C₂³	1	2	yes	complemented
71	#60415	D₄	1	8	yes	complemented
72	#60415	C₂³	1	8	yes	—
73	C₂×#3038	D₄	1	8	yes	complemented
74	C₂×#3038	C₂³	1	8	yes	—
75	C₂×#3037	D₄	1	4	yes	complemented
76	C₂×#3036	D₄	1	4	yes	complemented
77	C₂²×#460	D₄	1	4	yes	complemented
78	C₂²×#459	D₄	1	4	yes	complemented
79	C₂×#2920	C₂³	1	2	yes	—
80	C₂×#2920	C₂³	1	1	yes	characteristic
81	#60099	D₄	1	4	yes	complemented
82	#60099	C₂³	1	4	yes	—
83	C₂×#2905	D₄	1	4	yes	complemented
84	C₂²×#423	C₂³	1	2	yes	—
85	C₂²×C₄×M₁₆	C₂³	1	1	yes	characteristic
86	#35279	C₂³	1	2	yes	—
87	#35279	C₂³	1	4	yes	complemented
88	#35272	C₂³	1	2	yes	—
89	#35272	C₂³	1	4	yes	complemented
90	#35129	D₄	1	4	yes	—
91	#34736	D₄	1	4	yes	—
92	#34012	C₂³	1	1	yes	characteristic
93	#34012	C₂³	1	2	yes	—
94	#21803	C₂³	1	4	yes	complemented
95	#21803	C₂³	1	8	yes	complemented
96	#21401	C₂³	1	4	yes	complemented
97	#21380	D₄	1	4	yes	complemented
98	#21373	C₂³	1	4	yes	—
99	#21303	D₄	1	2	yes	complemented
100	#21190	D₄	1	2	yes	complemented
101	#20723	D₄	1	4	yes	—
102	#20722	D₄	1	4	yes	—
103	#20632	C₂³	1	4	yes	—
104	#20632	C₂³	1	8	yes	complemented
105	C₂×#1548	C₂³	1	4	yes	complemented
106	C₂×#1545	C₂³	1	4	yes	complemented
107	#17574	C₂³	1	8	yes	complemented
108	#17437	C₂³	1	8	yes	complemented
109	C₂×#1476	C₂³	1	8	yes	complemented
110	#17349	C₂³	1	4	yes	—
111	#8095	C₂³	1	8	yes	complemented
112	#7957	C₂³	1	8	yes	complemented
113	#7897	C₂³	1	8	yes	complemented
114	C₂×#585	C₂×D₄	1	4	yes	—
115	C₂³×#41	C₂×D₄	1	2	yes	—
116	C₂³×#41	C₂×D₄	1	2	yes	—
117	C₂³×#41	C₂×D₄	1	1	yes	characteristic
118	C₂×#532	C₂×D₄	1	4	yes	—
119	C₂×#532	C₂×D₄	1	4	yes	—
120	C₂×#532	C₂×D₄	1	2	yes	—
121	C₂×#532	C₂×D₄	1	8	yes	—
122	C₂×#532	C₂⁴	1	2	yes	—
123	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄⋊Q₈	C₂⁴	1	1	yes	characteristic
125	C₂²×#127	C₂×D₄	1	4	yes	—
126	C₂²×#127	C₂×D₄	1	2	yes	—
127	C₂²×#127	C₂×D₄	1	4	yes	—
128	C₂²×#127	C₂×D₄	1	1	yes	characteristic
129	C₂²×#127	C₂×D₄	1	2	yes	—
130	C₂²×#127	C₂×D₄	1	8	yes	—
131	C₂²×#127	C₂⁴	1	1	yes	characteristic
132	C₂²×#127	C₂⁴	1	2	yes	—
133	C₂²×#124	C₂×D₄	1	2	yes	—
134	#3428	C₂×D₄	1	4	yes	—
135	#3428	C₂×D₄	1	8	yes	—
136	C₂×C₄×#41	C₂×D₄	1	4	yes	—
137	C₂×C₄×#41	C₂×D₄	1	4	yes	—
138	C₂×C₄×#41	C₂×D₄	1	4	yes	—
139	C₂×C₄×#41	C₂×D₄	1	2	yes	—
140	C₂×C₄×#41	C₂×D₄	1	2	yes	—
141	C₂×C₄×#41	C₂×D₄	1	2	yes	—
142	C₂×C₄×#41	C₂×D₄	1	2	yes	—
143	C₂×C₄×#41	C₂×D₄	1	2	yes	—
144	C₂×C₄×#41	C₂×D₄	1	2	yes	—
145	C₂×C₄×#41	#41	1	2	yes	—
146	C₂×C₄×#41	C₂⁴	1	4	yes	—
147	C₂×C₄×#41	C₂⁴	1	2	yes	—
148	C₂²×C₄×Q₈	C₂×D₄	1	2	yes	—
149	C₂²×C₄×Q₈	C₂×D₄	1	2	yes	—
150	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
152	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
153	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
154	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
155	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
156	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×D₄	#41	1	1	yes	characteristic
158	C₂²×#117	C₂×D₄	1	2	yes	—
159	C₂²×#117	C₂×D₄	1	1	yes	characteristic
160	C₂²×#117	C₂×D₄	1	2	yes	—
161	C₂³×C₄²	C₂×D₄	1	2	yes	—
162	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
163	#3037	C₂×D₄	1	16	yes	—
164	#3036	C₂×D₄	1	16	yes	—
165	C₂×#460	C₂×D₄	1	16	yes	—
166	C₂×#459	C₂×D₄	1	16	yes	—
167	C₂×#432	C₂×D₄	1	2	yes	—
168	C₂×#431	C₂⁴	1	4	yes	—
169	C₂×#431	C₂⁴	1	2	yes	—
170	#2905	C₂×D₄	1	16	yes	—
171	C₂×#423	C₂×D₄	1	4	yes	—
172	C₂×#423	C₂×D₄	1	4	yes	—
173	C₂×#423	C₂×D₄	1	4	yes	—
174	C₂×#423	C₂×D₄	1	4	yes	—
175	C₂×#423	C₂×D₄	1	2	yes	—
176	C₂×#423	C₂×D₄	1	4	yes	—
177	C₂×#423	C₂⁴	1	4	yes	—
178	C₂²×C₄⋊C₈	C₂×D₄	1	4	yes	—
179	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
180	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₈	C₂⁴	1	2	yes	—
182	#2409	C₂×D₄	1	8	yes	—
183	#2408	C₂×D₄	1	8	yes	—
184	#2285	C₂⁴	1	2	yes	—
185	#2285	C₂⁴	1	4	yes	—
186	#2283	C₂×D₄	1	2	yes	—
187	#2283	C₂×D₄	1	4	yes	—
188	#2280	C₂×D₄	1	4	yes	—
189	#2280	C₂×D₄	1	2	yes	—
190	#1984	C₂×D₄	1	8	yes	—
191	#1954	C₂×D₄	1	8	yes	—
192	#1799	C₂×D₄	1	16	yes	—
193	#585	AGL(1,ℤ/8)	1	16	yes	complemented
194	C₂²×#41	#120	1	4	yes	—
195	C₂²×#41	#120	1	2	yes	—
196	C₂²×#41	#120	1	2	yes	—
197	C₂²×#41	#121	1	2	yes	—
198	C₂²×#41	C₂²×D₄	1	4	yes	—
199	C₂²×#41	C₂²×D₄	1	2	yes	—
200	C₂³×Q₈	#120	1	2	yes	—
201	C₂³×Q₈	#121	1	1	yes	characteristic
202	C₂³×Q₈	C₂²×D₄	1	2	yes	—
203	C₂³×D₄	#120	1	2	yes	—
204	C₂³×D₄	#120	1	2	yes	—
205	C₂³×D₄	#121	1	1	yes	characteristic
206	C₂³×D₄	C₂²×D₄	1	2	yes	—
207	C₂⁴×C₄	#120	1	2	yes	—
208	C₂⁴×C₄	#120	1	2	yes	—
209	C₂⁴×C₄	#121	1	2	yes	—
210	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
212	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
213	#532	#120	1	8	yes	—
214	#532	C₂²×D₄	1	8	yes	—
215	C₂×C₄⋊Q₈	#120	1	2	yes	—
216	C₂×C₄⋊Q₈	#120	1	2	yes	—
217	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
218	C₂×#127	#120	1	2	yes	—
219	C₂×#127	#120	1	2	yes	—
220	C₂×#127	#120	1	4	yes	—
221	C₂×#127	#120	1	4	yes	—
222	C₂×#127	#120	1	8	yes	—
223	C₂×#127	C₂²×D₄	1	2	yes	—
224	C₂×#127	C₂²×D₄	1	4	yes	—
225	C₂×#127	C₂²×D₄	1	8	yes	—
226	C₂×C₄×Q₈	#120	1	4	yes	—
227	C₂×C₄×Q₈	#120	1	4	yes	—
228	C₂×C₄×Q₈	#120	1	2	yes	—
229	C₂×C₄×Q₈	#121	1	2	yes	—
230	C₂×C₄×Q₈	#121	1	2	yes	—
231	C₂×C₄×Q₈	#121	1	2	yes	—
232	C₂×C₄×Q₈	#121	1	2	yes	—
233	C₂×C₄×Q₈	#127	1	2	yes	—
234	C₂×C₄×Q₈	C₂²×D₄	1	4	yes	—
235	C₂×C₄×Q₈	C₂²×D₄	1	4	yes	—
236	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
237	C₂×C₄×Q₈	C₂×#41	1	2	yes	—
238	C₂×C₄×D₄	#120	1	4	yes	—
239	C₂×C₄×D₄	#120	1	4	yes	—
240	C₂×C₄×D₄	#120	1	4	yes	—
241	C₂×C₄×D₄	#120	1	2	yes	—
242	C₂×C₄×D₄	#120	1	4	yes	—
243	C₂×C₄×D₄	#120	1	4	yes	—
244	C₂×C₄×D₄	#121	1	2	yes	—
245	C₂×C₄×D₄	#121	1	2	yes	—
246	C₂×C₄×D₄	#121	1	2	yes	—
247	C₂×C₄×D₄	#121	1	4	yes	—
248	C₂×C₄×D₄	#121	1	2	yes	—
249	C₂×C₄×D₄	#121	1	4	yes	—
250	C₂×C₄×D₄	#127	1	2	yes	—
251	C₂×C₄×D₄	#127	1	4	yes	—
252	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
253	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
254	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
255	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
256	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
257	C₂×C₄×D₄	C₂×#41	1	2	yes	—
258	C₂×#117	#120	1	4	yes	—
259	C₂×#117	#120	1	4	yes	—
260	C₂×#117	#120	1	2	yes	—
261	C₂×#117	#120	1	2	yes	—
262	C₂×#117	#121	1	4	yes	—
263	C₂×#117	#121	1	2	yes	—
264	C₂×#117	#127	1	4	yes	—
265	C₂×#117	C₂²×D₄	1	4	yes	—
266	C₂×#117	C₂²×D₄	1	2	yes	—
267	C₂×#117	C₂²×D₄	1	4	yes	—
268	C₂²×C₄⋊C₄	#120	1	2	yes	—
269	C₂²×C₄⋊C₄	#120	1	2	yes	—
270	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	#121	1	2	yes	—
272	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	#127	1	2	yes	—
274	C₂²×C₂²⋊C₄	#120	1	2	yes	—
275	C₂²×C₂²⋊C₄	#121	1	2	yes	—
276	C₂²×C₂²⋊C₄	#127	1	2	yes	—
277	C₂²×C₄²	#120	1	4	yes	—
278	C₂²×C₄²	#120	1	2	yes	—
279	C₂²×C₄²	#120	1	4	yes	—
280	C₂²×C₄²	#120	1	2	yes	—
281	C₂²×C₄²	#121	1	2	yes	—
282	C₂²×C₄²	#121	1	4	yes	—
283	C₂²×C₄²	C₂²×D₄	1	4	yes	—
284	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
285	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
286	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
287	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×D₄	1	2	yes	—
290	C₂²×C₄²	C₂²×D₄	1	2	yes	—
291	C₂²×C₄²	C₂²×D₄	1	2	yes	—
292	C₂²×C₄²	C₂²×D₄	1	2	yes	—
293	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
294	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
295	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
296	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
297	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
298	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
299	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
300	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
301	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
302	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
303	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
304	#423	#120	1	8	yes	—
305	#423	#120	1	8	yes	—
306	#423	C₂²×D₄	1	8	yes	—
307	#423	C₂²×D₄	1	8	yes	—
308	C₂×C₄⋊C₈	#120	1	8	yes	—
309	C₂×C₄⋊C₈	#120	1	8	yes	—
310	C₂×C₄⋊C₈	C₂²×D₄	1	4	yes	—
311	C₂×C₄⋊C₈	C₂²×D₄	1	8	yes	—
312	C₂×C₄×C₈	C₂²×D₄	1	4	yes	—
313	#380	C₂²×D₄	1	4	yes	—
314	#380	C₂²×D₄	1	8	yes	—
315	C₂⁵	#392	1	2	yes	—
316	C₂⁵	C₂×#120	1	1	yes	characteristic
317	C₂×#41	C₂×AGL(1,ℤ/8)	1	16	yes	—
318	C₂×#41	C₂×AGL(1,ℤ/8)	1	8	yes	—
319	C₂×#41	#575	1	8	yes	—
320	C₂²×Q₈	#392	1	2	yes	—
321	C₂²×Q₈	C₂×#120	1	4	yes	—
322	C₂²×Q₈	C₂×#121	1	2	yes	—
323	C₂²×D₄	#392	1	4	yes	—
324	C₂²×D₄	#392	1	2	yes	—
325	C₂²×D₄	C₂×#120	1	4	yes	—
326	C₂²×D₄	C₂×#120	1	4	yes	—
327	C₂²×D₄	C₂×#121	1	2	yes	—
328	C₂³×C₄	#392	1	2	yes	—
329	C₂³×C₄	#392	1	4	yes	—
330	C₂³×C₄	#392	1	2	yes	—
331	C₂³×C₄	#392	1	4	yes	—
332	C₂³×C₄	#392	1	2	yes	—
333	C₂³×C₄	#392	1	4	yes	—
334	C₂³×C₄	C₂×#120	1	1	yes	characteristic
335	C₂³×C₄	C₂×#120	1	1	yes	characteristic
336	C₂³×C₄	C₂×#120	1	2	yes	—
337	C₂³×C₄	C₂×#120	1	2	yes	—
338	C₂³×C₄	C₂×#120	1	1	yes	characteristic
339	C₂³×C₄	C₂×#120	1	1	yes	characteristic
340	C₂³×C₄	C₂×#120	1	4	yes	—
341	C₂³×C₄	C₂×#120	1	4	yes	—
342	C₂³×C₄	C₂×#120	1	1	yes	characteristic
343	C₂³×C₄	C₂×#120	1	1	yes	characteristic
344	C₂³×C₄	C₂×#120	1	1	yes	characteristic
345	C₂³×C₄	C₂×#121	1	1	yes	characteristic
346	C₂³×C₄	C₂×#121	1	1	yes	characteristic
347	C₂³×C₄	C₂×#121	1	4	yes	—
348	C₂³×C₄	C₂×#121	1	1	yes	characteristic
349	C₂³×C₄	C₂×#121	1	1	yes	characteristic
350	C₂³×C₄	C₂×#121	1	1	yes	characteristic
351	C₂³×C₄	C₂×#121	1	1	yes	characteristic
352	C₂³×C₄	C₂×#127	1	1	yes	characteristic
353	C₂³×C₄	C₂×#127	1	1	yes	characteristic
354	C₂³×C₄	#534	1	2	yes	—
355	C₂³×C₄	#534	1	2	yes	—
356	C₂³×C₄	D₄²	1	2	yes	—
357	C₂³×C₄	D₄²	1	2	yes	—
358	C₂³×C₄	D₄²	1	2	yes	—
359	C₂³×C₄	D₄²	1	2	yes	—
360	C₂³×C₄	D₄²	1	2	yes	—
361	C₂³×C₄	D₄²	1	2	yes	—
362	C₂³×C₄	D₄²	1	2	yes	—
363	C₂³×C₄	D₄²	1	2	yes	—
364	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
365	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
366	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
367	C₄⋊Q₈	C₂×#120	1	4	yes	—
368	#127	C₂×#120	1	4	yes	—
369	#127	C₂×#120	1	8	yes	—
370	C₂×C₄⋊C₄	#392	1	2	yes	—
371	C₂×C₄⋊C₄	#392	1	2	yes	—
372	C₂×C₄⋊C₄	#392	1	4	yes	—
373	C₂×C₄⋊C₄	#392	1	4	yes	—
374	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
375	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
376	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
377	C₂×C₄⋊C₄	C₂×#121	1	4	yes	—
378	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
379	C₂×C₄⋊C₄	C₂×#127	1	4	yes	—
380	C₂×C₂²⋊C₄	#392	1	4	yes	—
381	C₂×C₂²⋊C₄	#392	1	4	yes	—
382	C₂×C₂²⋊C₄	#392	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂×#127	1	4	yes	—
386	C₂×C₄²	#392	1	4	yes	—
387	C₂×C₄²	#392	1	4	yes	—
388	C₂×C₄²	#392	1	4	yes	—
389	C₂×C₄²	C₂×#120	1	4	yes	—
390	C₂×C₄²	C₂×#120	1	4	yes	—
391	C₂×C₄²	C₂×#120	1	1	yes	characteristic
392	C₂×C₄²	C₂×#120	1	1	yes	characteristic
393	C₂×C₄²	C₂×#120	1	2	yes	—
394	C₂×C₄²	C₂×#120	1	2	yes	—
395	C₂×C₄²	C₂×#120	1	1	yes	characteristic
396	C₂×C₄²	C₂×#120	1	1	yes	characteristic
397	C₂×C₄²	C₂×#120	1	2	yes	—
398	C₂×C₄²	C₂×#120	1	2	yes	—
399	C₂×C₄²	C₂×#120	1	1	yes	characteristic
400	C₂×C₄²	C₂×#120	1	1	yes	characteristic
401	C₂×C₄²	C₂×#120	1	2	yes	—
402	C₂×C₄²	C₂×#120	1	2	yes	—
403	C₂×C₄²	C₂×#120	1	2	yes	—
404	C₂×C₄²	C₂×#120	1	2	yes	—
405	C₂×C₄²	C₂×#120	1	1	yes	characteristic
406	C₂×C₄²	C₂×#120	1	1	yes	characteristic
407	C₂×C₄²	C₂×#121	1	4	yes	—
408	C₂×C₄²	C₂×#121	1	1	yes	characteristic
409	C₂×C₄²	C₂×#121	1	1	yes	characteristic
410	C₂×C₄²	C₂×#121	1	1	yes	characteristic
411	C₂×C₄²	C₂×#121	1	1	yes	characteristic
412	C₂×C₄²	C₂×#121	1	1	yes	characteristic
413	C₂×C₄²	C₂×#121	1	1	yes	characteristic
414	C₂×C₄²	C₂×#127	1	1	yes	characteristic
415	C₂×C₄²	C₂×#127	1	1	yes	characteristic
416	C₂×C₄²	#534	1	2	yes	—
417	C₂×C₄²	#534	1	2	yes	—
418	C₂×C₄²	#534	1	1	yes	characteristic
419	C₂×C₄²	#534	1	2	yes	—
420	C₂×C₄²	#534	1	2	yes	—
421	C₂×C₄²	#534	1	1	yes	characteristic
422	C₂×C₄²	#534	1	1	yes	characteristic
423	C₂×C₄²	#534	1	1	yes	characteristic
424	C₂×C₄²	#535	1	2	yes	—
425	C₂×C₄²	#535	1	2	yes	—
426	C₂×C₄²	#535	1	2	yes	—
427	C₂×C₄²	#535	1	2	yes	—
428	C₂×C₄²	D₄²	1	2	yes	—
429	C₂×C₄²	D₄²	1	2	yes	—
430	C₂×C₄²	D₄²	1	2	yes	—
431	C₂×C₄²	D₄²	1	2	yes	—
432	C₂×C₄²	D₄²	1	2	yes	—
433	C₂×C₄²	D₄²	1	2	yes	—
434	C₂×C₄²	D₄²	1	2	yes	—
435	C₂×C₄²	D₄²	1	2	yes	—
436	C₂×C₄²	D₄²	1	2	yes	—
437	C₂×C₄²	D₄²	1	2	yes	—
438	C₂×C₄²	D₄²	1	2	yes	—
439	C₂×C₄²	D₄²	1	2	yes	—
440	C₂×C₄²	D₄²	1	2	yes	—
441	C₂×C₄²	D₄²	1	2	yes	—
442	C₂×C₄²	D₄²	1	2	yes	—
443	C₂×C₄²	D₄²	1	2	yes	—
444	C₂×C₄²	#546	1	2	yes	—
445	C₂×C₄²	#546	1	2	yes	—
446	C₂×C₄²	#546	1	2	yes	—
447	C₂×C₄²	#546	1	2	yes	—
448	C₂×C₄²	#546	1	2	yes	—
449	C₂×C₄²	#546	1	2	yes	—
450	C₂×C₄²	#546	1	2	yes	—
451	C₂×C₄²	#546	1	2	yes	—
452	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
453	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
454	C₂×C₄²	C₂³×D₄	1	2	yes	—
455	C₂×C₄²	C₂³×D₄	1	2	yes	—
456	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
457	C₂×C₄²	C₂²×#41	1	1	yes	characteristic
458	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
459	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
460	C₄⋊C₈	C₂×#120	1	16	yes	—
461	C₂⁴	C₂×#392	1	1	yes	characteristic
462	C₂⁴	C₂×#392	1	4	yes	—
463	C₂⁴	C₂×#392	1	1	yes	characteristic
464	C₂⁴	#2403	1	2	yes	—
465	C₂⁴	#2403	1	2	yes	—
466	C₂⁴	C₂²×#120	1	1	yes	characteristic
467	C₂×Q₈	#3003	1	8	yes	complemented
468	C₂×Q₈	#3055	1	8	yes	—
469	C₂×D₄	#3003	1	8	yes	complemented
470	C₂×D₄	#3006	1	16	yes	—
471	C₂×D₄	#3055	1	8	yes	—
472	C₂²×C₄	C₂×#392	1	4	yes	—
473	C₂²×C₄	C₂×#392	1	1	yes	characteristic
474	C₂²×C₄	C₂×#392	1	1	yes	characteristic
475	C₂²×C₄	C₂×#392	1	1	yes	characteristic
476	C₂²×C₄	C₂×#392	1	4	yes	—
477	C₂²×C₄	C₂×#392	1	4	yes	—
478	C₂²×C₄	C₂×#392	1	1	yes	characteristic
479	C₂²×C₄	C₂×#392	1	1	yes	characteristic
480	C₂²×C₄	C₂×#392	1	1	yes	characteristic
481	C₂²×C₄	#2403	1	2	yes	—
482	C₂²×C₄	#2403	1	1	yes	characteristic
483	C₂²×C₄	#2403	1	1	yes	characteristic
484	C₂²×C₄	#2403	1	1	yes	characteristic
485	C₂²×C₄	#2403	1	2	yes	—
486	C₂²×C₄	#2403	1	2	yes	—
487	C₂²×C₄	#2403	1	2	yes	—
488	C₂²×C₄	#2403	1	2	yes	—
489	C₂²×C₄	#2403	1	2	yes	—
490	C₂²×C₄	#2403	1	2	yes	—
491	C₂²×C₄	#2403	1	2	yes	—
492	C₂²×C₄	#2403	1	1	yes	characteristic
493	C₂²×C₄	#2408	1	2	yes	—
494	C₂²×C₄	#2408	1	2	yes	—
495	C₂²×C₄	#2408	1	2	yes	—
496	C₂²×C₄	#2408	1	2	yes	—
497	C₂²×C₄	#2410	1	1	yes	characteristic
498	C₂²×C₄	#2410	1	1	yes	characteristic
499	C₂²×C₄	#2410	1	2	yes	—
500	C₂²×C₄	#2410	1	2	yes	—
501	C₂²×C₄	#2410	1	2	yes	—
502	C₂²×C₄	#2410	1	2	yes	—
503	C₂²×C₄	#2410	1	2	yes	—
504	C₂²×C₄	#2410	1	1	yes	characteristic
505	C₂²×C₄	#2410	1	1	yes	characteristic
506	C₂²×C₄	#2410	1	2	yes	—
507	C₂²×C₄	#2433	1	2	yes	—
508	C₂²×C₄	#2433	1	2	yes	—
509	C₂²×C₄	#2433	1	2	yes	—
510	C₂²×C₄	#2433	1	2	yes	—
511	C₂²×C₄	#2613	1	1	yes	characteristic
512	C₂²×C₄	#2613	1	1	yes	characteristic
513	C₂²×C₄	#2613	1	2	yes	—
514	C₂²×C₄	#2846	1	1	yes	characteristic
515	C₂²×C₄	#2846	1	1	yes	characteristic
516	C₂²×C₄	#2846	1	2	yes	—
517	C₂²×C₄	#3003	1	8	yes	—
518	C₂²×C₄	#3005	1	8	yes	—
519	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
520	C₂²×C₄	C₂²×#120	1	2	yes	—
521	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
522	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
523	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
524	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
525	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
526	C₂²×C₄	C₂×#534	1	2	yes	—
527	C₂²×C₄	C₂×D₄²	1	2	yes	—
528	C₂²×C₄	C₂×D₄²	1	2	yes	—
529	C₂²×C₄	C₂×D₄²	1	2	yes	—
530	C₂²×C₄	C₂×D₄²	1	2	yes	—
531	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
532	C₂²×C₄	C₂×#575	1	4	yes	—
533	C₄²	#2403	1	1	yes	characteristic
534	C₄²	#2403	1	1	yes	characteristic
535	C₄²	#2403	1	1	yes	characteristic
536	C₄²	#2403	1	1	yes	characteristic
537	C₄²	#2403	1	2	yes	—
538	C₄²	#2403	1	2	yes	—
539	C₄²	#2408	1	2	yes	—
540	C₄²	#2408	1	2	yes	—
541	C₄²	#2408	1	2	yes	—
542	C₄²	#2408	1	2	yes	—
543	C₄²	#2410	1	1	yes	characteristic
544	C₄²	#2410	1	1	yes	characteristic
545	C₄²	#2410	1	1	yes	characteristic
546	C₄²	#2410	1	1	yes	characteristic
547	C₄²	#2410	1	2	yes	—
548	C₄²	#2410	1	2	yes	—
549	C₄²	#2410	1	2	yes	—
550	C₄²	#2410	1	2	yes	—
551	C₄²	#2410	1	2	yes	—
552	C₄²	#2410	1	2	yes	—
553	C₄²	#2433	1	2	yes	—
554	C₄²	#2433	1	2	yes	—
555	C₄²	#2433	1	2	yes	—
556	C₄²	#2433	1	2	yes	—
557	C₄²	#2613	1	1	yes	characteristic
558	C₄²	#2613	1	1	yes	characteristic
559	C₄²	#2613	1	2	yes	—
560	C₄²	#2846	1	1	yes	characteristic
561	C₄²	#2846	1	1	yes	characteristic
562	C₄²	#2846	1	2	yes	—
563	C₄²	C₂²×#120	1	1	yes	characteristic
564	C₄²	C₂²×#120	1	1	yes	characteristic
565	C₄²	C₂²×#120	1	2	yes	—
566	C₄²	C₂×#534	1	1	yes	characteristic
567	C₄²	C₂×#534	1	1	yes	characteristic
568	C₄²	C₂×#535	1	2	yes	—
569	C₄²	C₂×D₄²	1	2	yes	—
570	C₄²	C₂×D₄²	1	2	yes	—
571	C₄²	C₂×#546	1	2	yes	—
572	C₄²	C₂×#546	1	2	yes	—
573	C₂³	#14715	1	2	yes	—
574	C₂³	#14715	1	1	yes	characteristic
575	C₂³	#14715	1	1	yes	characteristic
576	C₂³	#23391	1	8	yes	—
577	C₂³	C₂²×#392	1	1	yes	characteristic
578	C₂³	C₂×#2403	1	2	yes	—
579	C₂³	C₂×#3006	1	4	yes	—
580	C₂×C₄	#14715	1	1	yes	characteristic
581	C₂×C₄	#14715	1	1	yes	characteristic
582	C₂×C₄	#14715	1	1	yes	characteristic
583	C₂×C₄	#14715	1	1	yes	characteristic
584	C₂×C₄	#14715	1	1	yes	characteristic
585	C₂×C₄	#14715	1	2	yes	—
586	C₂×C₄	#14715	1	2	yes	—
587	C₂×C₄	#14715	1	2	yes	—
588	C₂×C₄	#14715	1	1	yes	characteristic
589	C₂×C₄	#23391	1	8	yes	—
590	C₂×C₄	#23872	1	4	yes	—
591	C₂×C₄	C₂×#2613	1	1	yes	characteristic
592	C₂×C₄	C₂×#2403	1	1	yes	characteristic
593	C₂×C₄	C₂×#2403	1	1	yes	characteristic
594	C₂×C₄	C₂×#2410	1	1	yes	characteristic
595	C₂×C₄	C₂×#2410	1	2	yes	—
596	C₂×C₄	C₂×#2410	1	1	yes	characteristic
597	C₂×C₄	C₂×#2408	1	2	yes	—
598	C₂×C₄	C₂×#2433	1	2	yes	—
599	C₂×C₄	C₂×#2846	1	1	yes	characteristic
600	C₂×C₄	C₂×#3003	1	2	yes	—
601	C₂×C₄	C₂×#3003	1	4	yes	—
602	C₂×C₄	C₂×#3005	1	2	yes	—
603	C₂×C₄	#60359	1	4	yes	—
604	C₂×C₄	C₂×#3055	1	4	yes	—
605	C₂×C₄	#60750	1	8	yes	—
606	C₂²	#394076	1	2	yes	—
607	C₂²	C₂×#14715	1	1	yes	characteristic
608	C₂²	C₂×#23391	1	2	yes	—
609	C₂²	#6437412	1	4	yes	—
610	C₄	#394076	1	2	yes	—
611	C₄	#6432833	1	2	yes	—
612	C₄	C₂×#23872	1	2	yes	—
613	C₄	#6437748	1	4	yes	—
614	C₄	#6438013	1	2	yes	—
615	C₄	#6628842	1	1	yes	characteristic
616	C₄	#6628844	1	1	yes	characteristic
617	C₂	#72234257	1	1	yes	characteristic
618	C₂	C₂×#394076	1	1	yes	characteristic
619	C₂	#72279287	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14715
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72280115	C₂	semidirect
2. #72280000	C₂	semidirect
3. #72279912	C₂	semidirect
4. #72279889	C₂	semidirect
5. #72279862	C₂	semidirect
6. #72279851	C₂	semidirect
7. #72279835	C₂	semidirect
8. #72279812	C₂	semidirect
9. #72279795	C₂	semidirect
10. C₂×#10574963	C₂	semidirect
11. #72279735	C₂	semidirect
12. #72279713	C₂	semidirect
13. #72279460	C₂	semidirect
16. C₂×#60803	C₂²	semidirect
17. C₂²×#3151	C₂²	semidirect
23. #7628578	C₂²	semidirect
24. #6629121	C₂²	semidirect
25. #6628984	C₂²	semidirect
26. #6516758	C₂²	semidirect
27. #6516757	C₂²	semidirect
28. #6374304	C₂²	semidirect
29. #6374304	C₂²	semidirect
30. #6372442	C₂²	semidirect
33. #6370937	C₂²	semidirect
34. C₂×#17750	C₂²	semidirect
35. #6343377	C₂²	semidirect
36. #6342924	C₂²	semidirect
37. C₂×#17447	C₂²	semidirect
39. #237583	C₂²	semidirect
40. #237575	C₂²	semidirect
41. #235725	C₂²	semidirect
42. #235723	C₂²	semidirect
43. #197434	C₂²	semidirect
44. #197430	C₂²	semidirect
45. #185628	C₂²	semidirect
46. #184929	C₂²	semidirect
47. #181799	C₂²	semidirect
48. #181467	C₂²	semidirect
49. #181175	C₂²	semidirect
50. #115542	C₂²	semidirect
51. #111855	C₂²	semidirect
52. #106620	C₂²	semidirect
54. C₂×#3498	D₄	semidirect
56. C₂²×#532	D₄	semidirect
59. C₂³×#127	D₄	semidirect
67. C₂×#3206	C₂³	semidirect
68. C₂×#3205	C₂³	semidirect
69. C₂²×#493	C₂³	semidirect
70. C₂²×#492	C₂³	semidirect
71. #60415	D₄	semidirect
73. C₂×#3038	D₄	semidirect
75. C₂×#3037	D₄	semidirect
76. C₂×#3036	D₄	semidirect
77. C₂²×#460	D₄	semidirect
78. C₂²×#459	D₄	semidirect
81. #60099	D₄	semidirect
83. C₂×#2905	D₄	semidirect
87. #35279	C₂³	semidirect
89. #35272	C₂³	semidirect
94. #21803	C₂³	semidirect
95. #21803	C₂³	semidirect
96. #21401	C₂³	semidirect
97. #21380	D₄	semidirect
99. #21303	D₄	semidirect
100. #21190	D₄	semidirect
104. #20632	C₂³	semidirect
105. C₂×#1548	C₂³	semidirect
106. C₂×#1545	C₂³	semidirect
107. #17574	C₂³	semidirect
108. #17437	C₂³	semidirect
109. C₂×#1476	C₂³	semidirect
111. #8095	C₂³	semidirect
112. #7957	C₂³	semidirect
113. #7897	C₂³	semidirect
193. #585	AGL(1,ℤ/8)	semidirect
467. C₂×Q₈	#3003	semidirect
469. C₂×D₄	#3003	semidirect

Maximal subgroups

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

subgroup	index
#72280115	2
#72280000	2
#72279912	2
#72279889	2
#72279862	2
#72279851	2
#72279835	2
#72279812	2
#72279795	2
C₂×#10574963	2
#72279735	2
#72279713	2
#72279460	2