Subgroups — #72312852

Order 2048.

At least 19885 conjugacy classes of subgroups; only the 834 normal subgroups are shown.

The subgroup lattice has 672 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312834	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312832	C₂	1	1	yes	maximal, characteristic, complemented
3	#72312725	C₂	1	1	yes	maximal, characteristic, complemented
4	#72312697	C₂	1	1	yes	maximal, characteristic, complemented
5	#72303706	C₂	1	1	yes	maximal, characteristic, complemented
6	#72303321	C₂	1	1	yes	maximal, characteristic, complemented
7	#72303318	C₂	1	1	yes	maximal, characteristic, complemented
8	#72303203	C₂	1	1	yes	maximal, characteristic, complemented
9	#72280881	C₂	1	1	yes	maximal, characteristic, complemented
10	#72280748	C₂	1	1	yes	maximal, characteristic, complemented
11	#72280532	C₂	1	1	yes	maximal, characteristic, complemented
12	#72267963	C₂	1	1	yes	maximal, characteristic, complemented
13	#72262985	C₂	1	1	yes	maximal, characteristic, complemented
14	#72256637	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#6628885	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#63103	C₂²	1	1	yes	characteristic
17	C₂×#60398	C₂²	1	1	yes	characteristic
18	C₂²×#3027	C₂²	1	1	yes	characteristic
19	#10574839	C₂²	1	1	yes	characteristic
20	C₂×#60369	C₂²	1	1	yes	characteristic
21	C₂×#60387	C₂²	1	1	yes	characteristic
22	C₂²×#3021	C₂²	1	1	yes	characteristic
23	#7642121	C₂²	1	1	yes	characteristic, complemented
24	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#2128	C₂²	1	1	yes	characteristic, complemented
26	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
28	#6374181	C₂²	1	1	yes	characteristic, complemented
29	#6374164	C₂²	1	1	yes	characteristic, complemented
30	C₂×#20623	C₂²	1	1	yes	characteristic
31	C₂×#20623	C₂²	1	1	yes	characteristic
32	C₂×#20620	C₂²	1	1	yes	characteristic
33	C₂×#20620	C₂²	1	1	yes	characteristic
34	C₂×#20612	C₂²	1	1	yes	characteristic
35	C₂×#20612	C₂²	1	1	yes	characteristic
36	#6370734	C₂²	1	1	yes	characteristic
37	#6370734	C₂²	1	1	yes	characteristic
38	#6370734	C₂²	1	1	yes	characteristic
39	#6370734	C₂²	1	1	yes	characteristic
40	#6370692	C₂²	1	1	yes	characteristic
41	#6370692	C₂²	1	1	yes	characteristic
42	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
43	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
44	#492906	C₂²	1	1	yes	characteristic, complemented
45	#492899	C₂²	1	1	yes	characteristic, complemented
46	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
47	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
48	#492886	C₂²	1	1	yes	characteristic, complemented
49	#492886	C₂²	1	1	yes	characteristic, complemented
50	#355933	C₂²	1	1	yes	characteristic, complemented
51	C₂×2₋¹⁺⁶	D₄	1	2	yes	complemented
52	C₂×H(7,𝔽₂)	D₄	1	2	yes	complemented
53	C₂²×#585	C₂³	1	1	yes	characteristic
54	C₂²×#585	C₂³	1	1	yes	characteristic
55	C₂²×#585	C₂³	1	1	yes	characteristic
56	C₂²×#575	D₄	1	1	yes	characteristic, complemented
57	C₂²×#575	D₄	1	1	yes	characteristic, complemented
58	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
59	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
60	C₂×#3449	C₂³	1	1	yes	characteristic
61	C₂²×#535	C₂³	1	1	yes	characteristic
62	C₂×#3028	D₄	1	2	yes	complemented
63	C₂×#3027	D₄	1	4	yes	complemented
64	C₂×#3027	D₄	1	2	yes	complemented
65	C₂×#3022	D₄	1	2	yes	—
66	C₂×#3021	D₄	1	4	yes	—
67	C₂×#3021	D₄	1	2	yes	—
68	C₂×#2896	D₄	1	1	yes	characteristic, complemented
69	C₂×#2896	D₄	1	1	yes	characteristic, complemented
70	C₂×#2896	D₄	1	1	yes	characteristic, complemented
71	C₂×#2896	D₄	1	1	yes	characteristic, complemented
72	C₂²×#413	C₂³	1	1	yes	characteristic
73	C₂²×#413	C₂³	1	1	yes	characteristic
74	C₂²×#410	D₄	1	1	yes	characteristic, complemented
75	C₂²×#410	D₄	1	1	yes	characteristic, complemented
76	C₂²×#410	D₄	1	1	yes	characteristic, complemented
77	C₂²×#410	D₄	1	1	yes	characteristic, complemented
78	C₂²×#410	C₂³	1	1	yes	characteristic
79	C₂²×#410	C₂³	1	1	yes	characteristic
80	C₂²×#410	C₂³	1	1	yes	characteristic
81	C₂²×#410	C₂³	1	1	yes	characteristic
82	C₂×#2879	C₂³	1	1	yes	characteristic
83	C₂×#2879	C₂³	1	1	yes	characteristic
84	#34044	C₂³	1	1	yes	characteristic
85	#34044	C₂³	1	1	yes	characteristic
86	C₂×#1796	D₄	1	2	yes	complemented
87	C₂×#1796	D₄	1	2	yes	complemented
88	C₂×#1795	D₄	1	2	yes	complemented
89	C₂×#1795	D₄	1	2	yes	complemented
90	#20620	D₄	1	4	yes	complemented
91	C₂×#1794	D₄	1	4	yes	complemented
92	#20612	D₄	1	4	yes	complemented
93	C₂×#1791	D₄	1	4	yes	complemented
94	#20609	D₄	1	4	yes	complemented
95	#20609	D₄	1	4	yes	complemented
96	C₂×#585	C₂×D₄	1	2	yes	—
97	C₂×#585	C₂×D₄	1	2	yes	—
98	C₂×#585	C₂×D₄	1	2	yes	—
99	C₂×#585	C₂×D₄	1	2	yes	—
100	C₂×#585	C₂×D₄	1	2	yes	—
101	C₂×#585	C₂×D₄	1	2	yes	—
102	C₂×#585	C₂×D₄	1	2	yes	—
103	C₂×#585	C₂×D₄	1	2	yes	—
104	C₂×#585	C₂×D₄	1	2	yes	—
105	C₂×#585	C₂×D₄	1	2	yes	—
106	C₂×#585	#41	1	2	yes	—
107	C₂×#585	#41	1	2	yes	—
108	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
109	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
110	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
111	C₂²×2₋¹⁺⁴	#41	1	1	yes	characteristic
112	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
113	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
114	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
115	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
116	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
117	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
118	C₂³×#41	C₂×D₄	1	1	yes	characteristic
119	C₂³×#41	C₂×D₄	1	1	yes	characteristic
120	C₂³×#41	C₂×D₄	1	1	yes	characteristic
121	C₂³×#41	C₂×D₄	1	1	yes	characteristic
122	C₂³×#41	C₂×D₄	1	1	yes	characteristic
123	C₂³×#41	C₂×D₄	1	1	yes	characteristic
124	C₂³×#41	C₂×D₄	1	1	yes	characteristic
125	C₂³×#41	C₂⁴	1	1	yes	characteristic
126	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
127	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
128	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
129	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
130	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
131	C₂×#536	C₂×D₄	1	1	yes	characteristic
132	C₂×#536	C₂×D₄	1	1	yes	characteristic
133	C₂×#535	C₂×D₄	1	2	yes	—
134	C₂×#535	C₂×D₄	1	1	yes	characteristic
135	C₂×#535	C₂×D₄	1	2	yes	—
136	C₂×#535	C₂×D₄	1	1	yes	characteristic
137	C₂²×#117	C₂×D₄	1	1	yes	characteristic
138	C₂²×#117	C₂×D₄	1	1	yes	characteristic
139	C₂²×#117	C₂×D₄	1	1	yes	characteristic
140	C₂²×#117	C₂×D₄	1	1	yes	characteristic
141	C₂²×#117	C₂×D₄	1	1	yes	characteristic
142	C₂²×#117	C₂×D₄	1	1	yes	characteristic
143	C₂×#413	C₂×D₄	1	2	yes	—
144	C₂×#413	C₂×D₄	1	2	yes	—
145	C₂×#413	C₂×D₄	1	2	yes	—
146	C₂×#413	C₂×D₄	1	2	yes	—
147	C₂×#413	C₂×D₄	1	2	yes	—
148	C₂×#413	C₂×D₄	1	2	yes	—
149	C₂×#410	C₂×D₄	1	2	yes	—
150	C₂×#410	C₂×D₄	1	2	yes	—
151	C₂×#410	C₂×D₄	1	2	yes	—
152	C₂×#410	C₂×D₄	1	2	yes	—
153	C₂×#410	C₂×D₄	1	2	yes	—
154	C₂×#410	C₂×D₄	1	2	yes	—
155	C₂²×#99	C₂×D₄	1	2	yes	—
156	C₂²×#99	C₂×D₄	1	2	yes	—
157	#2879	C₂×D₄	1	2	yes	—
158	#2879	C₂×D₄	1	2	yes	—
159	C₂×#408	C₂×D₄	1	2	yes	—
160	C₂×#408	C₂×D₄	1	2	yes	—
161	#2308	C₂×D₄	1	2	yes	—
162	#2308	C₂×D₄	1	2	yes	—
163	#585	#120	1	4	yes	—
164	#585	#120	1	4	yes	—
165	#585	#120	1	4	yes	—
166	#585	#120	1	4	yes	—
167	#585	#121	1	4	yes	—
168	#585	#121	1	4	yes	—
169	#585	#121	1	4	yes	—
170	#585	#121	1	4	yes	—
171	C₂×H(5,𝔽₂)	#120	1	4	yes	—
172	C₂×H(5,𝔽₂)	#120	1	4	yes	—
173	C₂×H(5,𝔽₂)	#121	1	4	yes	—
174	C₂×H(5,𝔽₂)	#121	1	4	yes	—
175	C₂×H(5,𝔽₂)	#127	1	4	yes	—
176	C₂×H(5,𝔽₂)	#127	1	4	yes	—
177	C₂²×#41	#120	1	1	yes	characteristic
178	C₂²×#41	#120	1	1	yes	characteristic
179	C₂²×#41	#120	1	1	yes	characteristic
180	C₂²×#41	#120	1	1	yes	characteristic
181	C₂²×#41	#120	1	1	yes	characteristic
182	C₂²×#41	#120	1	1	yes	characteristic
183	C₂²×#41	#120	1	1	yes	characteristic
184	C₂²×#41	#120	1	1	yes	characteristic
185	C₂²×#41	#121	1	1	yes	characteristic
186	C₂²×#41	#121	1	1	yes	characteristic
187	C₂²×#41	#121	1	1	yes	characteristic
188	C₂²×#41	#121	1	1	yes	characteristic
189	C₂²×#41	#121	1	1	yes	characteristic
190	C₂²×#41	#121	1	1	yes	characteristic
191	C₂²×#41	#127	1	1	yes	characteristic
192	C₂²×#41	#127	1	1	yes	characteristic
193	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
194	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
195	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
196	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
197	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
198	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
199	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
200	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
201	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
202	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
203	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
204	C₂²×#41	C₂×#41	1	1	yes	characteristic
205	C₂²×#41	C₂×#41	1	1	yes	characteristic
206	C₂²×#41	C₂×#41	1	1	yes	characteristic
207	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂³×Q₈	#120	1	1	yes	characteristic
218	C₂³×Q₈	#120	1	1	yes	characteristic
219	C₂³×Q₈	#120	1	1	yes	characteristic
220	C₂³×Q₈	#121	1	1	yes	characteristic
221	C₂³×Q₈	#121	1	1	yes	characteristic
222	C₂³×Q₈	#121	1	1	yes	characteristic
223	C₂³×Q₈	#127	1	1	yes	characteristic
224	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂³×D₄	#120	1	1	yes	characteristic
226	C₂³×D₄	#120	1	1	yes	characteristic
227	C₂³×D₄	#120	1	2	yes	—
228	C₂³×D₄	#120	1	1	yes	characteristic
229	C₂³×D₄	#121	1	1	yes	characteristic
230	C₂³×D₄	#121	1	1	yes	characteristic
231	C₂³×D₄	#121	1	1	yes	characteristic
232	C₂³×D₄	#127	1	1	yes	characteristic
233	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
234	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
235	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
237	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
239	C₂²×M₁₆	#120	1	2	yes	—
240	C₂²×M₁₆	#120	1	2	yes	—
241	C₂²×M₁₆	#120	1	2	yes	—
242	C₂³×C₈	#120	1	2	yes	—
243	C₂×#117	#120	1	2	yes	—
244	C₂×#117	#120	1	1	yes	characteristic
245	C₂×#117	#120	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	#120	1	2	yes	—
247	C₂²×C₂²⋊C₄	#120	1	2	yes	—
248	#413	#120	1	4	yes	—
249	#413	#120	1	4	yes	—
250	#410	#120	1	4	yes	—
251	#410	#120	1	4	yes	—
252	C₂⁵	C₂×#120	1	1	yes	characteristic
253	C₂⁵	D₄²	1	1	yes	characteristic
254	C₂⁵	D₄²	1	1	yes	characteristic
255	H(5,𝔽₂)	#392	1	8	yes	—
256	H(5,𝔽₂)	#392	1	8	yes	—
257	C₂×#41	B(4,𝔽₂)	1	2	yes	—
258	C₂×#41	B(4,𝔽₂)	1	2	yes	—
259	C₂×#41	B(4,𝔽₂)	1	2	yes	—
260	C₂×#41	B(4,𝔽₂)	1	2	yes	—
261	C₂×#41	B(4,𝔽₂)	1	2	yes	—
262	C₂×#41	B(4,𝔽₂)	1	2	yes	—
263	C₂×#41	B(4,𝔽₂)	1	2	yes	—
264	C₂×#41	B(4,𝔽₂)	1	2	yes	—
265	C₂×#41	C₂×#120	1	1	yes	characteristic
266	C₂×#41	C₂×#120	1	1	yes	characteristic
267	C₂×#41	C₂×#120	1	1	yes	characteristic
268	C₂×#41	C₂×#120	1	1	yes	characteristic
269	C₂×#41	C₂×#120	1	1	yes	characteristic
270	C₂×#41	C₂×#120	1	1	yes	characteristic
271	C₂×#41	C₂×#120	1	1	yes	characteristic
272	C₂×#41	C₂×#120	1	1	yes	characteristic
273	C₂×#41	C₂×#121	1	1	yes	characteristic
274	C₂×#41	C₂×#121	1	1	yes	characteristic
275	C₂×#41	C₂×#121	1	1	yes	characteristic
276	C₂×#41	C₂×#121	1	1	yes	characteristic
277	C₂×#41	#534	1	1	yes	characteristic
278	C₂×#41	#534	1	1	yes	characteristic
279	C₂×#41	#534	1	1	yes	characteristic
280	C₂×#41	#534	1	1	yes	characteristic
281	C₂×#41	#534	1	1	yes	characteristic
282	C₂×#41	#534	1	1	yes	characteristic
283	C₂×#41	#534	1	1	yes	characteristic
284	C₂×#41	#534	1	1	yes	characteristic
285	C₂×#41	#535	1	1	yes	characteristic
286	C₂×#41	#535	1	1	yes	characteristic
287	C₂×#41	#535	1	1	yes	characteristic
288	C₂×#41	#535	1	1	yes	characteristic
289	C₂×#41	#535	1	1	yes	characteristic
290	C₂×#41	#535	1	1	yes	characteristic
291	C₂×#41	#535	1	1	yes	characteristic
292	C₂×#41	#535	1	1	yes	characteristic
293	C₂×#41	#538	1	1	yes	characteristic
294	C₂×#41	#538	1	1	yes	characteristic
295	C₂×#41	#538	1	1	yes	characteristic
296	C₂×#41	#538	1	1	yes	characteristic
297	C₂×#41	D₄²	1	1	yes	characteristic
298	C₂×#41	D₄²	1	1	yes	characteristic
299	C₂×#41	D₄²	1	1	yes	characteristic
300	C₂×#41	D₄²	1	1	yes	characteristic
301	C₂×#41	D₄²	1	1	yes	characteristic
302	C₂×#41	D₄²	1	1	yes	characteristic
303	C₂×#41	D₄²	1	1	yes	characteristic
304	C₂×#41	D₄²	1	1	yes	characteristic
305	C₂×#41	D₄²	1	1	yes	characteristic
306	C₂×#41	D₄²	1	1	yes	characteristic
307	C₂×#41	D₄²	1	1	yes	characteristic
308	C₂×#41	D₄²	1	1	yes	characteristic
309	C₂×#41	#546	1	1	yes	characteristic
310	C₂×#41	#546	1	1	yes	characteristic
311	C₂×#41	#546	1	1	yes	characteristic
312	C₂×#41	#546	1	1	yes	characteristic
313	C₂×#41	#546	1	1	yes	characteristic
314	C₂×#41	#546	1	1	yes	characteristic
315	C₂×#41	#546	1	1	yes	characteristic
316	C₂×#41	#546	1	1	yes	characteristic
317	C₂×#41	#546	1	1	yes	characteristic
318	C₂×#41	#546	1	1	yes	characteristic
319	C₂×#41	#546	1	1	yes	characteristic
320	C₂×#41	#546	1	1	yes	characteristic
321	C₂×#41	#546	1	1	yes	characteristic
322	C₂×#41	#546	1	1	yes	characteristic
323	C₂×#41	#546	1	1	yes	characteristic
324	C₂×#41	#546	1	1	yes	characteristic
325	C₂×#41	#560	1	1	yes	characteristic
326	C₂×#41	#560	1	1	yes	characteristic
327	C₂×#41	#560	1	1	yes	characteristic
328	C₂×#41	#560	1	1	yes	characteristic
329	C₂²×Q₈	#392	1	1	yes	characteristic
330	C₂²×Q₈	#392	1	1	yes	characteristic
331	C₂²×Q₈	#392	1	1	yes	characteristic
332	C₂²×Q₈	#392	1	1	yes	characteristic
333	C₂²×Q₈	#534	1	1	yes	characteristic
334	C₂²×Q₈	#534	1	1	yes	characteristic
335	C₂²×Q₈	#534	1	1	yes	characteristic
336	C₂²×Q₈	#535	1	1	yes	characteristic
337	C₂²×Q₈	#535	1	1	yes	characteristic
338	C₂²×Q₈	#538	1	1	yes	characteristic
339	C₂²×Q₈	D₄²	1	1	yes	characteristic
340	C₂²×Q₈	D₄²	1	1	yes	characteristic
341	C₂²×Q₈	#546	1	1	yes	characteristic
342	C₂²×Q₈	#546	1	1	yes	characteristic
343	C₂²×Q₈	#560	1	1	yes	characteristic
344	C₂²×Q₈	H(3,𝔽₄)	1	1	yes	characteristic
345	C₂²×D₄	#392	1	1	yes	characteristic
346	C₂²×D₄	#392	1	1	yes	characteristic
347	C₂²×D₄	#392	1	1	yes	characteristic
348	C₂²×D₄	#392	1	1	yes	characteristic
349	C₂²×D₄	C₂×#120	1	1	yes	characteristic
350	C₂²×D₄	C₂×#120	1	1	yes	characteristic
351	C₂²×D₄	C₂×#121	1	1	yes	characteristic
352	C₂²×D₄	C₂×#121	1	1	yes	characteristic
353	C₂²×D₄	#525	1	1	yes	characteristic
354	C₂²×D₄	#525	1	1	yes	characteristic
355	C₂²×D₄	C₂×#127	1	1	yes	characteristic
356	C₂²×D₄	C₂×#127	1	1	yes	characteristic
357	C₂²×D₄	#534	1	1	yes	characteristic
358	C₂²×D₄	#534	1	1	yes	characteristic
359	C₂²×D₄	#534	1	1	yes	characteristic
360	C₂²×D₄	#534	1	1	yes	characteristic
361	C₂²×D₄	#534	1	1	yes	characteristic
362	C₂²×D₄	#535	1	1	yes	characteristic
363	C₂²×D₄	#535	1	1	yes	characteristic
364	C₂²×D₄	#535	1	1	yes	characteristic
365	C₂²×D₄	#535	1	1	yes	characteristic
366	C₂²×D₄	#538	1	1	yes	characteristic
367	C₂²×D₄	D₄²	1	1	yes	characteristic
368	C₂²×D₄	D₄²	1	1	yes	characteristic
369	C₂²×D₄	D₄²	1	1	yes	characteristic
370	C₂²×D₄	D₄²	1	1	yes	characteristic
371	C₂²×D₄	D₄²	1	1	yes	characteristic
372	C₂²×D₄	D₄²	1	1	yes	characteristic
373	C₂²×D₄	D₄²	1	1	yes	characteristic
374	C₂²×D₄	D₄²	1	1	yes	characteristic
375	C₂²×D₄	D₄²	1	1	yes	characteristic
376	C₂²×D₄	D₄²	1	1	yes	characteristic
377	C₂²×D₄	D₄²	1	1	yes	characteristic
378	C₂²×D₄	D₄²	1	1	yes	characteristic
379	C₂²×D₄	D₄²	1	1	yes	characteristic
380	C₂²×D₄	D₄²	1	1	yes	characteristic
381	C₂²×D₄	#546	1	1	yes	characteristic
382	C₂²×D₄	#546	1	1	yes	characteristic
383	C₂²×D₄	#560	1	1	yes	characteristic
384	C₂²×D₄	H(3,𝔽₄)	1	1	yes	characteristic
385	C₂³×C₄	C₂×#120	1	1	yes	characteristic
386	C₂³×C₄	C₂×#120	1	1	yes	characteristic
387	C₂³×C₄	C₂×#120	1	1	yes	characteristic
388	C₂³×C₄	C₂×#120	1	1	yes	characteristic
389	C₂³×C₄	C₂×#120	1	1	yes	characteristic
390	C₂³×C₄	C₂×#120	1	1	yes	characteristic
391	C₂³×C₄	C₂×#120	1	1	yes	characteristic
392	C₂³×C₄	C₂×#121	1	1	yes	characteristic
393	C₂³×C₄	C₂×#121	1	1	yes	characteristic
394	C₂³×C₄	C₂×#121	1	1	yes	characteristic
395	C₂³×C₄	#525	1	1	yes	characteristic
396	C₂³×C₄	C₂×#127	1	1	yes	characteristic
397	C₂³×C₄	#534	1	1	yes	characteristic
398	C₂³×C₄	#534	1	1	yes	characteristic
399	C₂³×C₄	#534	1	1	yes	characteristic
400	C₂³×C₄	#534	1	1	yes	characteristic
401	C₂³×C₄	#534	1	1	yes	characteristic
402	C₂³×C₄	#535	1	1	yes	characteristic
403	C₂³×C₄	D₄²	1	1	yes	characteristic
404	C₂³×C₄	D₄²	1	1	yes	characteristic
405	C₂³×C₄	D₄²	1	1	yes	characteristic
406	C₂³×C₄	D₄²	1	1	yes	characteristic
407	C₂³×C₄	D₄²	1	1	yes	characteristic
408	C₂³×C₄	D₄²	1	1	yes	characteristic
409	C₂³×C₄	D₄²	1	1	yes	characteristic
410	C₂³×C₄	D₄²	1	1	yes	characteristic
411	C₂³×C₄	D₄²	1	1	yes	characteristic
412	C₂³×C₄	D₄²	1	1	yes	characteristic
413	C₂³×C₄	D₄²	1	1	yes	characteristic
414	C₂³×C₄	D₄²	1	1	yes	characteristic
415	C₂³×C₄	D₄²	1	1	yes	characteristic
416	C₂³×C₄	D₄²	1	1	yes	characteristic
417	C₂³×C₄	D₄²	1	1	yes	characteristic
418	C₂³×C₄	D₄²	1	1	yes	characteristic
419	C₂³×C₄	D₄²	1	1	yes	characteristic
420	C₂³×C₄	D₄²	1	1	yes	characteristic
421	C₂³×C₄	#546	1	1	yes	characteristic
422	C₂³×C₄	#546	1	1	yes	characteristic
423	C₂³×C₄	#546	1	1	yes	characteristic
424	C₂³×C₄	#546	1	1	yes	characteristic
425	C₂⁴	#2403	1	1	yes	characteristic
426	C₂⁴	#2403	1	1	yes	characteristic
427	C₂⁴	#2403	1	1	yes	characteristic
428	C₂⁴	#2403	1	1	yes	characteristic
429	C₂⁴	#2403	1	1	yes	characteristic
430	C₂⁴	#2410	1	1	yes	characteristic
431	C₂⁴	#2410	1	1	yes	characteristic
432	C₂⁴	#2424	1	1	yes	characteristic
433	C₂⁴	#2424	1	1	yes	characteristic
434	C₂⁴	#2433	1	1	yes	characteristic
435	C₂⁴	#2433	1	1	yes	characteristic
436	C₂⁴	#2433	1	1	yes	characteristic
437	C₂⁴	#2433	1	1	yes	characteristic
438	C₂⁴	#2433	1	1	yes	characteristic
439	C₂⁴	#2669	1	1	yes	characteristic
440	C₂⁴	#2669	1	1	yes	characteristic
441	C₂⁴	#2679	1	1	yes	characteristic
442	C₂⁴	#2679	1	1	yes	characteristic
443	C₂⁴	#2847	1	1	yes	characteristic
444	C₂×Q₈	#2021	1	2	yes	—
445	C₂×Q₈	#2021	1	2	yes	—
446	C₂×Q₈	#2021	1	2	yes	—
447	C₂×Q₈	#2021	1	2	yes	—
448	C₂×Q₈	#2403	1	1	yes	characteristic
449	C₂×Q₈	#2408	1	1	yes	characteristic
450	C₂×Q₈	#2408	1	1	yes	characteristic
451	C₂×Q₈	#2410	1	1	yes	characteristic
452	C₂×Q₈	#2410	1	1	yes	characteristic
453	C₂×Q₈	#2613	1	1	yes	characteristic
454	C₂×Q₈	#2613	1	1	yes	characteristic
455	C₂×Q₈	#2668	1	1	yes	characteristic
456	C₂×Q₈	#2670	1	1	yes	characteristic
457	C₂×Q₈	#2670	1	1	yes	characteristic
458	C₂×Q₈	#2670	1	1	yes	characteristic
459	C₂×Q₈	#2678	1	1	yes	characteristic
460	C₂×Q₈	#2678	1	1	yes	characteristic
461	C₂×Q₈	#2678	1	1	yes	characteristic
462	C₂×Q₈	#2678	1	1	yes	characteristic
463	C₂×Q₈	#2812	1	1	yes	characteristic
464	C₂×D₄	#2021	1	2	yes	—
465	C₂×D₄	#2021	1	2	yes	—
466	C₂×D₄	#2021	1	2	yes	—
467	C₂×D₄	#2021	1	2	yes	—
468	C₂×D₄	C₂×#392	1	1	yes	characteristic
469	C₂×D₄	C₂×#392	1	1	yes	characteristic
470	C₂×D₄	#2403	1	1	yes	characteristic
471	C₂×D₄	#2403	1	1	yes	characteristic
472	C₂×D₄	#2403	1	1	yes	characteristic
473	C₂×D₄	#2403	1	1	yes	characteristic
474	C₂×D₄	#2403	1	1	yes	characteristic
475	C₂×D₄	#2404	1	1	yes	characteristic
476	C₂×D₄	#2404	1	1	yes	characteristic
477	C₂×D₄	#2408	1	1	yes	characteristic
478	C₂×D₄	#2408	1	1	yes	characteristic
479	C₂×D₄	#2410	1	1	yes	characteristic
480	C₂×D₄	#2410	1	1	yes	characteristic
481	C₂×D₄	#2410	1	1	yes	characteristic
482	C₂×D₄	#2410	1	1	yes	characteristic
483	C₂×D₄	#2410	1	1	yes	characteristic
484	C₂×D₄	#2410	1	1	yes	characteristic
485	C₂×D₄	#2424	1	1	yes	characteristic
486	C₂×D₄	#2424	1	1	yes	characteristic
487	C₂×D₄	#2424	1	1	yes	characteristic
488	C₂×D₄	#2424	1	1	yes	characteristic
489	C₂×D₄	#2433	1	1	yes	characteristic
490	C₂×D₄	#2433	1	1	yes	characteristic
491	C₂×D₄	#2433	1	1	yes	characteristic
492	C₂×D₄	#2433	1	1	yes	characteristic
493	C₂×D₄	#2539	1	1	yes	characteristic
494	C₂×D₄	#2539	1	1	yes	characteristic
495	C₂×D₄	#2613	1	1	yes	characteristic
496	C₂×D₄	#2613	1	1	yes	characteristic
497	C₂×D₄	#2617	1	1	yes	characteristic
498	C₂×D₄	#2617	1	1	yes	characteristic
499	C₂×D₄	#2668	1	1	yes	characteristic
500	C₂×D₄	#2669	1	1	yes	characteristic
501	C₂×D₄	#2669	1	1	yes	characteristic
502	C₂×D₄	#2669	1	1	yes	characteristic
503	C₂×D₄	#2669	1	1	yes	characteristic
504	C₂×D₄	#2669	1	1	yes	characteristic
505	C₂×D₄	#2669	1	1	yes	characteristic
506	C₂×D₄	#2669	1	1	yes	characteristic
507	C₂×D₄	#2669	1	1	yes	characteristic
508	C₂×D₄	#2670	1	1	yes	characteristic
509	C₂×D₄	#2670	1	1	yes	characteristic
510	C₂×D₄	#2670	1	1	yes	characteristic
511	C₂×D₄	#2678	1	1	yes	characteristic
512	C₂×D₄	#2678	1	1	yes	characteristic
513	C₂×D₄	#2678	1	1	yes	characteristic
514	C₂×D₄	#2678	1	1	yes	characteristic
515	C₂×D₄	#2812	1	1	yes	characteristic
516	C₂²×C₄	C₂×#392	1	1	yes	characteristic
517	C₂²×C₄	#2403	1	1	yes	characteristic
518	C₂²×C₄	#2403	1	1	yes	characteristic
519	C₂²×C₄	#2403	1	1	yes	characteristic
520	C₂²×C₄	#2403	1	1	yes	characteristic
521	C₂²×C₄	#2403	1	1	yes	characteristic
522	C₂²×C₄	#2403	1	1	yes	characteristic
523	C₂²×C₄	#2403	1	1	yes	characteristic
524	C₂²×C₄	#2403	1	1	yes	characteristic
525	C₂²×C₄	#2403	1	1	yes	characteristic
526	C₂²×C₄	#2403	1	1	yes	characteristic
527	C₂²×C₄	#2404	1	1	yes	characteristic
528	C₂²×C₄	#2408	1	1	yes	characteristic
529	C₂²×C₄	#2408	1	1	yes	characteristic
530	C₂²×C₄	#2408	1	1	yes	characteristic
531	C₂²×C₄	#2408	1	1	yes	characteristic
532	C₂²×C₄	#2408	1	1	yes	characteristic
533	C₂²×C₄	#2408	1	1	yes	characteristic
534	C₂²×C₄	#2408	1	1	yes	characteristic
535	C₂²×C₄	#2408	1	1	yes	characteristic
536	C₂²×C₄	#2410	1	1	yes	characteristic
537	C₂²×C₄	#2410	1	1	yes	characteristic
538	C₂²×C₄	#2410	1	1	yes	characteristic
539	C₂²×C₄	#2410	1	1	yes	characteristic
540	C₂²×C₄	#2410	1	1	yes	characteristic
541	C₂²×C₄	#2410	1	1	yes	characteristic
542	C₂²×C₄	#2410	1	1	yes	characteristic
543	C₂²×C₄	#2410	1	1	yes	characteristic
544	C₂²×C₄	#2410	1	1	yes	characteristic
545	C₂²×C₄	#2410	1	1	yes	characteristic
546	C₂²×C₄	#2410	1	1	yes	characteristic
547	C₂²×C₄	#2410	1	1	yes	characteristic
548	C₂²×C₄	#2410	1	1	yes	characteristic
549	C₂²×C₄	#2410	1	1	yes	characteristic
550	C₂²×C₄	#2424	1	1	yes	characteristic
551	C₂²×C₄	#2424	1	1	yes	characteristic
552	C₂²×C₄	#2424	1	1	yes	characteristic
553	C₂²×C₄	#2424	1	1	yes	characteristic
554	C₂²×C₄	#2424	1	1	yes	characteristic
555	C₂²×C₄	#2424	1	1	yes	characteristic
556	C₂²×C₄	#2433	1	1	yes	characteristic
557	C₂²×C₄	#2433	1	1	yes	characteristic
558	C₂²×C₄	#2433	1	1	yes	characteristic
559	C₂²×C₄	#2433	1	1	yes	characteristic
560	C₂²×C₄	#2433	1	1	yes	characteristic
561	C₂²×C₄	#2433	1	1	yes	characteristic
562	C₂²×C₄	#2539	1	1	yes	characteristic
563	C₂²×C₄	#2613	1	1	yes	characteristic
564	C₂²×C₄	#2613	1	1	yes	characteristic
565	C₂²×C₄	#2617	1	1	yes	characteristic
566	C₂²×C₄	#2668	1	1	yes	characteristic
567	C₂²×C₄	#2668	1	1	yes	characteristic
568	C₂²×C₄	#2668	1	1	yes	characteristic
569	C₂²×C₄	#2668	1	1	yes	characteristic
570	C₂²×C₄	#2669	1	1	yes	characteristic
571	C₂²×C₄	#2669	1	1	yes	characteristic
572	C₂²×C₄	#2669	1	1	yes	characteristic
573	C₂²×C₄	#2669	1	1	yes	characteristic
574	C₂²×C₄	#2669	1	1	yes	characteristic
575	C₂²×C₄	#2669	1	1	yes	characteristic
576	C₂²×C₄	#2669	1	1	yes	characteristic
577	C₂²×C₄	#2669	1	1	yes	characteristic
578	C₂²×C₄	#2678	1	1	yes	characteristic
579	C₂²×C₄	#2678	1	1	yes	characteristic
580	C₂²×C₄	#2678	1	1	yes	characteristic
581	C₂²×C₄	#2678	1	1	yes	characteristic
582	C₂²×C₄	#2679	1	1	yes	characteristic
583	C₂²×C₄	#2679	1	1	yes	characteristic
584	C₂²×C₄	#2679	1	1	yes	characteristic
585	C₂²×C₄	#2679	1	1	yes	characteristic
586	C₂²×C₄	#2846	1	1	yes	characteristic
587	C₂²×C₄	#2846	1	1	yes	characteristic
588	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
589	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
590	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
591	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
592	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
593	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
594	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
595	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
596	C₂³	#14715	1	1	yes	characteristic
597	C₂³	#14715	1	1	yes	characteristic
598	C₂³	#14716	1	1	yes	characteristic
599	C₂³	#14716	1	1	yes	characteristic
600	C₂³	#14716	1	1	yes	characteristic
601	C₂³	#15257	1	1	yes	characteristic
602	C₂³	#15257	1	1	yes	characteristic
603	C₂³	#15258	1	1	yes	characteristic
604	C₂³	#15258	1	1	yes	characteristic
605	C₂³	#15258	1	1	yes	characteristic
606	C₂³	#15267	1	1	yes	characteristic
607	C₂³	#15267	1	1	yes	characteristic
608	C₂³	#15947	1	1	yes	characteristic
609	C₂³	#16249	1	1	yes	characteristic
610	C₂³	#16249	1	1	yes	characteristic
611	C₂³	#23900	1	1	yes	characteristic
612	C₂³	#23900	1	1	yes	characteristic
613	C₂³	#23900	1	1	yes	characteristic
614	C₂³	#23900	1	1	yes	characteristic
615	C₂×C₄	#14715	1	1	yes	characteristic
616	C₂×C₄	#14715	1	1	yes	characteristic
617	C₂×C₄	#14715	1	1	yes	characteristic
618	C₂×C₄	#14715	1	1	yes	characteristic
619	C₂×C₄	#15257	1	1	yes	characteristic
620	C₂×C₄	#15257	1	1	yes	characteristic
621	C₂×C₄	#15257	1	1	yes	characteristic
622	C₂×C₄	#15257	1	1	yes	characteristic
623	C₂×C₄	#15267	1	1	yes	characteristic
624	C₂×C₄	#15267	1	1	yes	characteristic
625	C₂×C₄	#15267	1	1	yes	characteristic
626	C₂×C₄	#15267	1	1	yes	characteristic
627	C₂×C₄	#16249	1	1	yes	characteristic
628	C₂×C₄	#16249	1	1	yes	characteristic
629	C₂×C₄	#16249	1	1	yes	characteristic
630	C₂×C₄	#16249	1	1	yes	characteristic
631	C₂×C₄	C₂×#2021	1	1	yes	characteristic
632	C₂×C₄	C₂×#2021	1	1	yes	characteristic
633	C₂×C₄	C₂×#2021	1	1	yes	characteristic
634	C₂×C₄	C₂×#2021	1	1	yes	characteristic
635	C₂×C₄	#23900	1	1	yes	characteristic
636	C₂×C₄	#23900	1	1	yes	characteristic
637	C₂×C₄	#23900	1	1	yes	characteristic
638	C₂×C₄	#23900	1	1	yes	characteristic
639	C₂×C₄	#23900	1	1	yes	characteristic
640	C₂×C₄	#23900	1	1	yes	characteristic
641	C₂×C₄	#23900	1	1	yes	characteristic
642	C₂×C₄	#23900	1	1	yes	characteristic
643	C₂×C₄	#23900	1	1	yes	characteristic
644	C₂×C₄	#23900	1	1	yes	characteristic
645	C₂×C₄	#23900	1	1	yes	characteristic
646	C₂×C₄	#23900	1	1	yes	characteristic
647	C₂×C₄	#23900	1	1	yes	characteristic
648	C₂×C₄	#23900	1	1	yes	characteristic
649	C₂×C₄	#23900	1	1	yes	characteristic
650	C₂×C₄	#23900	1	1	yes	characteristic
651	C₂×C₄	#23984	1	1	yes	characteristic
652	C₂×C₄	#23984	1	1	yes	characteristic
653	C₂×C₄	#23984	1	1	yes	characteristic
654	C₂×C₄	#23984	1	1	yes	characteristic
655	C₂²	#156684	1	1	yes	characteristic
656	C₂²	#394167	1	1	yes	characteristic
657	C₂²	#394167	1	1	yes	characteristic
658	C₂²	#417744	1	1	yes	characteristic
659	C₂²	#417744	1	1	yes	characteristic
660	C₂²	#449475	1	1	yes	characteristic
661	C₂²	#449475	1	1	yes	characteristic
662	C₄	#394058	1	1	yes	characteristic
663	C₄	#394058	1	1	yes	characteristic
664	C₄	#394058	1	1	yes	characteristic
665	C₄	#394058	1	1	yes	characteristic
666	C₄	#417493	1	1	yes	characteristic
667	C₄	#417493	1	1	yes	characteristic
668	C₄	#417493	1	1	yes	characteristic
669	C₄	#417493	1	1	yes	characteristic
670	C₂	#72218776	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72218776
commutator, Frattini, cosocle	C₂³×#41	C₂⁴
LCS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312834	C₂	semidirect
2. #72312832	C₂	semidirect
3. #72312725	C₂	semidirect
4. #72312697	C₂	semidirect
5. #72303706	C₂	semidirect
6. #72303321	C₂	semidirect
7. #72303318	C₂	semidirect
8. #72303203	C₂	semidirect
9. #72280881	C₂	semidirect
10. #72280748	C₂	semidirect
11. #72280532	C₂	semidirect
12. #72267963	C₂	semidirect
13. #72262985	C₂	semidirect
14. #72256637	C₂	semidirect
15. C₂×#6628885	C₂	semidirect
23. #7642121	C₂²	semidirect
24. C₂×#33358	C₂²	semidirect
25. C₂²×#2128	C₂²	semidirect
26. C₂×#33347	C₂²	semidirect
27. C₂²×#2122	C₂²	semidirect
28. #6374181	C₂²	semidirect
29. #6374164	C₂²	semidirect
42. C₂×#12589	C₂²	semidirect
43. C₂×#12589	C₂²	semidirect
44. #492906	C₂²	semidirect
45. #492899	C₂²	semidirect
46. C₂×#12577	C₂²	semidirect
47. C₂×#12577	C₂²	semidirect
48. #492886	C₂²	semidirect
49. #492886	C₂²	semidirect
50. #355933	C₂²	semidirect
51. C₂×2₋¹⁺⁶	D₄	semidirect
52. C₂×H(7,𝔽₂)	D₄	semidirect
56. C₂²×#575	D₄	semidirect
57. C₂²×#575	D₄	semidirect
58. C₂³×AGL(1,ℤ/8)	D₄	semidirect
59. C₂³×AGL(1,ℤ/8)	D₄	semidirect
62. C₂×#3028	D₄	semidirect
63. C₂×#3027	D₄	semidirect
64. C₂×#3027	D₄	semidirect
68. C₂×#2896	D₄	semidirect
69. C₂×#2896	D₄	semidirect
70. C₂×#2896	D₄	semidirect
71. C₂×#2896	D₄	semidirect
74. C₂²×#410	D₄	semidirect
75. C₂²×#410	D₄	semidirect
76. C₂²×#410	D₄	semidirect
77. C₂²×#410	D₄	semidirect
86. C₂×#1796	D₄	semidirect
87. C₂×#1796	D₄	semidirect
88. C₂×#1795	D₄	semidirect
89. C₂×#1795	D₄	semidirect
90. #20620	D₄	semidirect
91. C₂×#1794	D₄	semidirect
92. #20612	D₄	semidirect
93. C₂×#1791	D₄	semidirect
94. #20609	D₄	semidirect
95. #20609	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72312834	2
#72312832	2
#72312725	2
#72312697	2
#72303706	2
#72303321	2
#72303318	2
#72303203	2
#72280881	2
#72280748	2
#72280532	2
#72267963	2
#72262985	2
#72256637	2
C₂×#6628885	2