Subgroups — #72312744

Order 2048.

At least 12615 conjugacy classes of subgroups; only the 758 normal subgroups are shown.

The subgroup lattice has 647 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312738	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312734	C₂	1	1	yes	maximal, characteristic, complemented
3	#72312732	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#494752	C₂	1	1	yes	maximal, characteristic, complemented
5	#72312725	C₂	1	1	yes	maximal, characteristic, complemented
6	#72312291	C₂	1	1	yes	maximal, characteristic, complemented
7	#72303721	C₂	1	1	yes	maximal, characteristic, complemented
8	#72303713	C₂	1	1	yes	maximal, characteristic, complemented
9	#72303711	C₂	1	1	yes	maximal, characteristic, complemented
10	#72303705	C₂	1	1	yes	maximal, characteristic, complemented
11	#72303318	C₂	1	1	yes	maximal, characteristic, complemented
12	#72302938	C₂	1	1	yes	maximal, characteristic, complemented
13	#72280895	C₂	1	1	yes	maximal, characteristic, complemented
14	#72267963	C₂	1	1	yes	maximal, characteristic, complemented
15	#72256637	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#63090	C₂²	1	1	yes	characteristic
17	C₂²×#3027	C₂²	1	1	yes	characteristic
18	#10574839	C₂²	1	1	yes	characteristic
19	C₂×#60369	C₂²	1	1	yes	characteristic
20	C₂×#60387	C₂²	1	1	yes	characteristic
21	C₂×#60076	C₂²	1	1	yes	characteristic
22	#7642121	C₂²	1	1	yes	characteristic
23	C₂²×#2134	C₂²	1	1	yes	characteristic
24	C₂×#33358	C₂²	1	1	yes	characteristic
25	C₂×#33347	C₂²	1	1	yes	characteristic
26	C₂²×#2122	C₂²	1	1	yes	characteristic
27	#6374181	C₂²	1	1	yes	characteristic
28	#6374164	C₂²	1	1	yes	characteristic
29	C₂×#21017	C₂²	1	1	yes	characteristic
30	C₂²×#1910	C₂²	1	1	yes	characteristic
31	C₂×#20860	C₂²	1	1	yes	characteristic
32	C₂×#20623	C₂²	1	1	yes	characteristic
33	C₂×#20620	C₂²	1	1	yes	characteristic
34	#6370746	C₂²	1	1	yes	characteristic
35	C₂×#20612	C₂²	1	1	yes	characteristic
36	#6370734	C₂²	1	1	yes	characteristic
37	#6370692	C₂²	1	1	yes	characteristic
38	#6370692	C₂²	1	1	yes	characteristic
39	C₂×#12589	C₂²	1	1	yes	characteristic
40	C₂×#12589	C₂²	1	1	yes	characteristic
41	C₂×#12579	C₂²	1	1	yes	characteristic
42	C₂×#12577	C₂²	1	1	yes	characteristic
43	#492886	C₂²	1	1	yes	characteristic
44	#492886	C₂²	1	1	yes	characteristic
45	#492886	C₂²	1	1	yes	characteristic
46	#492886	C₂²	1	1	yes	characteristic
47	#355933	C₂²	1	1	yes	characteristic
48	#353434	C₂²	1	1	yes	characteristic
49	#353430	C₂²	1	1	yes	characteristic
50	#353422	C₂²	1	1	yes	characteristic
51	C₂²×#585	C₂³	1	1	yes	characteristic
52	C₂²×#585	C₂³	1	1	yes	characteristic
53	C₂×#3586	D₄	1	2	yes	complemented
54	C₂×#3585	D₄	1	2	yes	complemented
55	C₂²×#575	D₄	1	1	yes	characteristic, complemented
56	C₂²×#575	D₄	1	1	yes	characteristic, complemented
57	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
58	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
59	C₂²×#568	C₂³	1	1	yes	characteristic
60	C₂×#3449	C₂³	1	1	yes	characteristic
61	C₂²×#535	C₂³	1	1	yes	characteristic
62	C₂×#3022	D₄	1	2	yes	—
63	C₂×#3021	D₄	1	2	yes	—
64	C₂×#2896	D₄	1	1	yes	characteristic
65	C₂×#2896	D₄	1	1	yes	characteristic
66	C₂×#2896	D₄	1	1	yes	characteristic, complemented
67	C₂×#2896	D₄	1	1	yes	characteristic, complemented
68	C₂×#2889	D₄	1	2	yes	complemented
69	C₂×#2888	D₄	1	2	yes	complemented
70	C₂²×#413	C₂³	1	1	yes	characteristic
71	C₂²×#413	C₂³	1	1	yes	characteristic
72	C₂²×#413	C₂³	1	1	yes	characteristic
73	C₂²×#410	D₄	1	1	yes	characteristic, complemented
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	C₂³	1	1	yes	characteristic
78	C₂²×#410	C₂³	1	1	yes	characteristic
79	C₂²×#410	C₂³	1	1	yes	characteristic
80	C₂×#2879	C₂³	1	1	yes	characteristic
81	C₂×#2879	C₂³	1	1	yes	characteristic
82	#34044	C₂³	1	1	yes	characteristic
83	#34044	C₂³	1	1	yes	characteristic
84	C₂×#2122	D₄	1	4	yes	—
85	C₂×#1915	D₄	1	2	yes	complemented
86	C₂×#1914	D₄	1	2	yes	complemented
87	C₂×#1858	D₄	1	4	yes	complemented
88	C₂×#1791	D₄	1	4	yes	complemented
89	#20587	D₄	1	2	yes	complemented
90	#20586	D₄	1	2	yes	complemented
91	#12579	D₄	1	4	yes	complemented
92	#12574	D₄	1	4	yes	—
93	C₂×#585	C₂×D₄	1	2	yes	—
94	C₂×#585	C₂×D₄	1	2	yes	—
95	C₂×#585	C₂×D₄	1	2	yes	—
96	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
97	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
98	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
99	C₂²×2₋¹⁺⁴	#41	1	1	yes	characteristic
100	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
101	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
102	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
103	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
104	C₂³×#41	C₂×D₄	1	1	yes	characteristic
105	C₂³×#41	C₂×D₄	1	1	yes	characteristic
106	C₂³×#41	C₂×D₄	1	1	yes	characteristic
107	C₂³×#41	C₂×D₄	1	1	yes	characteristic
108	C₂³×#41	C₂×D₄	1	1	yes	characteristic
109	C₂³×#41	C₂×D₄	1	1	yes	characteristic
110	C₂³×#41	C₂×D₄	1	1	yes	characteristic
111	C₂³×#41	C₂⁴	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂×#568	C₂×D₄	1	2	yes	—
114	C₂×#568	C₂×D₄	1	2	yes	—
115	C₂×#568	C₂×D₄	1	2	yes	—
116	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
117	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
118	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
119	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
120	C₂×#536	C₂×D₄	1	1	yes	characteristic
121	C₂×#536	C₂×D₄	1	1	yes	characteristic
122	C₂×#535	C₂×D₄	1	1	yes	characteristic
123	C₂×#535	C₂×D₄	1	1	yes	characteristic
124	C₂×#535	C₂×D₄	1	2	yes	—
125	C₂×#535	#41	1	2	yes	—
126	C₂²×#117	C₂×D₄	1	1	yes	characteristic
127	C₂²×#117	C₂×D₄	1	1	yes	characteristic
128	C₂²×#117	C₂×D₄	1	1	yes	characteristic
129	C₂²×#117	C₂×D₄	1	1	yes	characteristic
130	C₂²×#117	C₂×D₄	1	1	yes	characteristic
131	C₂²×#117	C₂×D₄	1	1	yes	characteristic
132	C₂×#413	C₂×D₄	1	2	yes	—
133	C₂×#413	C₂×D₄	1	2	yes	—
134	C₂×#413	C₂×D₄	1	2	yes	—
135	C₂×#413	C₂×D₄	1	2	yes	—
136	C₂×#413	C₂×D₄	1	2	yes	—
137	C₂×#413	C₂×D₄	1	2	yes	—
138	C₂×#413	C₂×D₄	1	2	yes	—
139	C₂×#413	C₂×D₄	1	2	yes	—
140	C₂×#413	C₂×D₄	1	2	yes	—
141	C₂×#413	#41	1	2	yes	—
142	C₂²×#100	C₂×D₄	1	2	yes	—
143	C₂×#410	C₂×D₄	1	2	yes	—
144	C₂×#410	C₂×D₄	1	2	yes	—
145	C₂×#410	C₂×D₄	1	2	yes	—
146	C₂×#410	#41	1	2	yes	—
147	C₂²×#99	C₂×D₄	1	2	yes	—
148	#2879	C₂×D₄	1	2	yes	—
149	#2879	#41	1	2	yes	—
150	C₂×#408	C₂×D₄	1	2	yes	—
151	C₂×#408	C₂×D₄	1	2	yes	—
152	#2308	C₂×D₄	1	2	yes	—
153	#2308	#41	1	2	yes	—
154	#585	#120	1	4	yes	—
155	C₂²×#41	#120	1	1	yes	characteristic
156	C₂²×#41	#120	1	1	yes	characteristic
157	C₂²×#41	#120	1	1	yes	characteristic
158	C₂²×#41	#120	1	1	yes	characteristic
159	C₂²×#41	#120	1	1	yes	characteristic
160	C₂²×#41	#120	1	1	yes	characteristic
161	C₂²×#41	#120	1	1	yes	characteristic
162	C₂²×#41	#120	1	1	yes	characteristic
163	C₂²×#41	#121	1	1	yes	characteristic
164	C₂²×#41	#121	1	1	yes	characteristic
165	C₂²×#41	#121	1	1	yes	characteristic
166	C₂²×#41	#121	1	1	yes	characteristic
167	C₂²×#41	#121	1	1	yes	characteristic
168	C₂²×#41	#121	1	1	yes	characteristic
169	C₂²×#41	#127	1	1	yes	characteristic
170	C₂²×#41	#127	1	1	yes	characteristic
171	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
172	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
173	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
174	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
175	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
176	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
177	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
178	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
179	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
180	C₂²×#41	C₂×#41	1	1	yes	characteristic
181	C₂²×#41	C₂×#41	1	1	yes	characteristic
182	C₂²×#41	C₂×#41	1	1	yes	characteristic
183	C₂²×#41	C₂×#41	1	1	yes	characteristic
184	C₂²×#41	C₂×#41	1	1	yes	characteristic
185	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂²×#41	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂³×Q₈	#120	1	1	yes	characteristic
196	C₂³×Q₈	#120	1	1	yes	characteristic
197	C₂³×Q₈	#120	1	1	yes	characteristic
198	C₂³×Q₈	#121	1	1	yes	characteristic
199	C₂³×Q₈	#121	1	1	yes	characteristic
200	C₂³×Q₈	#121	1	1	yes	characteristic
201	C₂³×Q₈	#127	1	1	yes	characteristic
202	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂³×D₄	#120	1	1	yes	characteristic
204	C₂³×D₄	#120	1	1	yes	characteristic
205	C₂³×D₄	#120	1	1	yes	characteristic
206	C₂³×D₄	#121	1	1	yes	characteristic
207	C₂³×D₄	#121	1	1	yes	characteristic
208	C₂³×D₄	#121	1	1	yes	characteristic
209	C₂³×D₄	#121	1	2	yes	—
210	C₂³×D₄	#127	1	1	yes	characteristic
211	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
212	C₂³×D₄	C₂×#41	1	1	yes	characteristic
213	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
215	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
216	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
217	#568	#120	1	4	yes	—
218	C₂²×M₁₆	#120	1	2	yes	—
219	C₂²×M₁₆	#121	1	2	yes	—
220	C₂²×M₁₆	#121	1	2	yes	—
221	C₂³×C₈	#120	1	2	yes	—
222	C₂×#117	#120	1	1	yes	characteristic
223	C₂×#117	#120	1	1	yes	characteristic
224	C₂×#117	#121	1	2	yes	—
225	C₂²×C₂²⋊C₄	#121	1	2	yes	—
226	C₂²×C₂²⋊C₄	#121	1	2	yes	—
227	#413	#120	1	4	yes	—
228	#413	#120	1	4	yes	—
229	#413	#120	1	4	yes	—
230	#413	#121	1	4	yes	—
231	#413	#121	1	4	yes	—
232	C₂×#100	#120	1	4	yes	—
233	C₂×#100	#121	1	4	yes	—
234	C₂×#100	#127	1	4	yes	—
235	C₂×#99	#121	1	4	yes	—
236	C₂⁵	C₂×#121	1	1	yes	characteristic
237	C₂⁵	D₄²	1	1	yes	characteristic
238	C₂⁵	#546	1	1	yes	characteristic
239	C₂×#41	B(4,𝔽₂)	1	2	yes	—
240	C₂×#41	B(4,𝔽₂)	1	2	yes	—
241	C₂×#41	B(4,𝔽₂)	1	2	yes	—
242	C₂×#41	B(4,𝔽₂)	1	2	yes	—
243	C₂×#41	C₂×#120	1	1	yes	characteristic
244	C₂×#41	C₂×#120	1	1	yes	characteristic
245	C₂×#41	C₂×#120	1	1	yes	characteristic
246	C₂×#41	C₂×#120	1	1	yes	characteristic
247	C₂×#41	C₂×#120	1	1	yes	characteristic
248	C₂×#41	C₂×#121	1	1	yes	characteristic
249	C₂×#41	C₂×#121	1	1	yes	characteristic
250	C₂×#41	#525	1	1	yes	characteristic
251	C₂×#41	#525	1	1	yes	characteristic
252	C₂×#41	#525	1	1	yes	characteristic
253	C₂×#41	#525	1	1	yes	characteristic
254	C₂×#41	#532	1	1	yes	characteristic
255	C₂×#41	#534	1	1	yes	characteristic
256	C₂×#41	#534	1	1	yes	characteristic
257	C₂×#41	#534	1	1	yes	characteristic
258	C₂×#41	#534	1	1	yes	characteristic
259	C₂×#41	#535	1	1	yes	characteristic
260	C₂×#41	#535	1	1	yes	characteristic
261	C₂×#41	#535	1	1	yes	characteristic
262	C₂×#41	#535	1	1	yes	characteristic
263	C₂×#41	#537	1	1	yes	characteristic
264	C₂×#41	#537	1	1	yes	characteristic
265	C₂×#41	#537	1	1	yes	characteristic
266	C₂×#41	#537	1	1	yes	characteristic
267	C₂×#41	#538	1	1	yes	characteristic
268	C₂×#41	#538	1	1	yes	characteristic
269	C₂×#41	#538	1	1	yes	characteristic
270	C₂×#41	#538	1	1	yes	characteristic
271	C₂×#41	#540	1	1	yes	characteristic
272	C₂×#41	#540	1	1	yes	characteristic
273	C₂×#41	#540	1	1	yes	characteristic
274	C₂×#41	#540	1	1	yes	characteristic
275	C₂×#41	D₄²	1	1	yes	characteristic
276	C₂×#41	D₄²	1	1	yes	characteristic
277	C₂×#41	D₄²	1	1	yes	characteristic
278	C₂×#41	D₄²	1	1	yes	characteristic
279	C₂×#41	D₄²	1	1	yes	characteristic
280	C₂×#41	D₄²	1	1	yes	characteristic
281	C₂×#41	D₄²	1	1	yes	characteristic
282	C₂×#41	D₄²	1	1	yes	characteristic
283	C₂×#41	D₄²	1	1	yes	characteristic
284	C₂×#41	D₄²	1	1	yes	characteristic
285	C₂×#41	#546	1	1	yes	characteristic
286	C₂×#41	#546	1	1	yes	characteristic
287	C₂×#41	#546	1	1	yes	characteristic
288	C₂×#41	#546	1	1	yes	characteristic
289	C₂×#41	#546	1	1	yes	characteristic
290	C₂×#41	#546	1	1	yes	characteristic
291	C₂×#41	#546	1	1	yes	characteristic
292	C₂×#41	#546	1	1	yes	characteristic
293	C₂×#41	#546	1	1	yes	characteristic
294	C₂×#41	#546	1	1	yes	characteristic
295	C₂×#41	#546	1	1	yes	characteristic
296	C₂×#41	#546	1	1	yes	characteristic
297	C₂×#41	#547	1	1	yes	characteristic
298	C₂×#41	#548	1	1	yes	characteristic
299	C₂×#41	#550	1	1	yes	characteristic
300	C₂×#41	#550	1	1	yes	characteristic
301	C₂×#41	#553	1	1	yes	characteristic
302	C₂×#41	#555	1	1	yes	characteristic
303	C₂×#41	#560	1	1	yes	characteristic
304	C₂×#41	#560	1	1	yes	characteristic
305	C₂×#41	#562	1	1	yes	characteristic
306	C₂×#41	#562	1	1	yes	characteristic
307	C₂²×Q₈	#392	1	1	yes	characteristic
308	C₂²×Q₈	#392	1	1	yes	characteristic
309	C₂²×Q₈	#392	1	1	yes	characteristic
310	C₂²×Q₈	#392	1	1	yes	characteristic
311	C₂²×Q₈	#534	1	1	yes	characteristic
312	C₂²×Q₈	#534	1	1	yes	characteristic
313	C₂²×Q₈	#535	1	1	yes	characteristic
314	C₂²×Q₈	#537	1	1	yes	characteristic
315	C₂²×Q₈	#538	1	1	yes	characteristic
316	C₂²×Q₈	#540	1	1	yes	characteristic
317	C₂²×Q₈	D₄²	1	1	yes	characteristic
318	C₂²×Q₈	D₄²	1	1	yes	characteristic
319	C₂²×Q₈	#546	1	1	yes	characteristic
320	C₂²×Q₈	#553	1	1	yes	characteristic
321	C₂²×Q₈	#560	1	1	yes	characteristic
322	C₂²×Q₈	#560	1	1	yes	characteristic
323	C₂²×D₄	#392	1	1	yes	characteristic
324	C₂²×D₄	#392	1	1	yes	characteristic
325	C₂²×D₄	#392	1	1	yes	characteristic
326	C₂²×D₄	#392	1	1	yes	characteristic
327	C₂²×D₄	C₂×#120	1	1	yes	characteristic
328	C₂²×D₄	C₂×#121	1	1	yes	characteristic
329	C₂²×D₄	C₂×#121	1	1	yes	characteristic
330	C₂²×D₄	#525	1	1	yes	characteristic
331	C₂²×D₄	C₂×#127	1	1	yes	characteristic
332	C₂²×D₄	#532	1	1	yes	characteristic
333	C₂²×D₄	#532	1	1	yes	characteristic
334	C₂²×D₄	#532	1	1	yes	characteristic
335	C₂²×D₄	#534	1	1	yes	characteristic
336	C₂²×D₄	#535	1	1	yes	characteristic
337	C₂²×D₄	#535	1	1	yes	characteristic
338	C₂²×D₄	#535	1	1	yes	characteristic
339	C₂²×D₄	#535	1	1	yes	characteristic
340	C₂²×D₄	#535	1	1	yes	characteristic
341	C₂²×D₄	#535	1	1	yes	characteristic
342	C₂²×D₄	#537	1	1	yes	characteristic
343	C₂²×D₄	#538	1	1	yes	characteristic
344	C₂²×D₄	#540	1	1	yes	characteristic
345	C₂²×D₄	D₄²	1	1	yes	characteristic
346	C₂²×D₄	D₄²	1	1	yes	characteristic
347	C₂²×D₄	D₄²	1	1	yes	characteristic
348	C₂²×D₄	#546	1	1	yes	characteristic
349	C₂²×D₄	#546	1	1	yes	characteristic
350	C₂²×D₄	#546	1	1	yes	characteristic
351	C₂²×D₄	#546	1	1	yes	characteristic
352	C₂²×D₄	#546	1	1	yes	characteristic
353	C₂²×D₄	#547	1	1	yes	characteristic
354	C₂²×D₄	#548	1	1	yes	characteristic
355	C₂²×D₄	#550	1	1	yes	characteristic
356	C₂²×D₄	#550	1	1	yes	characteristic
357	C₂²×D₄	#550	1	1	yes	characteristic
358	C₂²×D₄	#550	1	1	yes	characteristic
359	C₂²×D₄	#553	1	1	yes	characteristic
360	C₂²×D₄	#553	1	1	yes	characteristic
361	C₂²×D₄	#560	1	1	yes	characteristic
362	C₂²×D₄	#560	1	1	yes	characteristic
363	C₂³×C₄	C₂×#120	1	1	yes	characteristic
364	C₂³×C₄	C₂×#120	1	1	yes	characteristic
365	C₂³×C₄	C₂×#120	1	1	yes	characteristic
366	C₂³×C₄	C₂×#120	1	1	yes	characteristic
367	C₂³×C₄	C₂×#120	1	1	yes	characteristic
368	C₂³×C₄	C₂×#121	1	1	yes	characteristic
369	C₂³×C₄	C₂×#121	1	1	yes	characteristic
370	C₂³×C₄	C₂×#121	1	1	yes	characteristic
371	C₂³×C₄	C₂×#121	1	1	yes	characteristic
372	C₂³×C₄	C₂×#121	1	1	yes	characteristic
373	C₂³×C₄	C₂×#127	1	1	yes	characteristic
374	C₂³×C₄	#532	1	1	yes	characteristic
375	C₂³×C₄	#534	1	1	yes	characteristic
376	C₂³×C₄	#534	1	1	yes	characteristic
377	C₂³×C₄	#534	1	1	yes	characteristic
378	C₂³×C₄	#534	1	1	yes	characteristic
379	C₂³×C₄	#534	1	1	yes	characteristic
380	C₂³×C₄	#537	1	1	yes	characteristic
381	C₂³×C₄	D₄²	1	1	yes	characteristic
382	C₂³×C₄	D₄²	1	1	yes	characteristic
383	C₂³×C₄	D₄²	1	1	yes	characteristic
384	C₂³×C₄	D₄²	1	1	yes	characteristic
385	C₂³×C₄	D₄²	1	1	yes	characteristic
386	C₂³×C₄	D₄²	1	1	yes	characteristic
387	C₂³×C₄	D₄²	1	1	yes	characteristic
388	C₂³×C₄	D₄²	1	1	yes	characteristic
389	C₂³×C₄	D₄²	1	1	yes	characteristic
390	C₂³×C₄	D₄²	1	1	yes	characteristic
391	C₂³×C₄	D₄²	1	1	yes	characteristic
392	C₂³×C₄	D₄²	1	1	yes	characteristic
393	C₂³×C₄	D₄²	1	1	yes	characteristic
394	C₂³×C₄	#546	1	1	yes	characteristic
395	C₂³×C₄	#546	1	1	yes	characteristic
396	C₂³×C₄	#546	1	1	yes	characteristic
397	C₂³×C₄	#546	1	1	yes	characteristic
398	C₂³×C₄	#546	1	1	yes	characteristic
399	C₂³×C₄	#546	1	1	yes	characteristic
400	C₂³×C₄	#546	1	1	yes	characteristic
401	C₂³×C₄	#547	1	1	yes	characteristic
402	C₂³×C₄	#547	1	1	yes	characteristic
403	#100	#392	1	8	yes	—
404	C₂⁴	#2404	1	1	yes	characteristic
405	C₂⁴	#2408	1	1	yes	characteristic
406	C₂⁴	#2408	1	1	yes	characteristic
407	C₂⁴	#2410	1	1	yes	characteristic
408	C₂⁴	#2410	1	1	yes	characteristic
409	C₂⁴	#2416	1	1	yes	characteristic
410	C₂⁴	#2416	1	1	yes	characteristic
411	C₂⁴	#2424	1	1	yes	characteristic
412	C₂⁴	#2428	1	1	yes	characteristic
413	C₂⁴	#2430	1	1	yes	characteristic
414	C₂⁴	#2431	1	1	yes	characteristic
415	C₂⁴	#2541	1	1	yes	characteristic
416	C₂⁴	#2541	1	1	yes	characteristic
417	C₂⁴	#2543	1	1	yes	characteristic
418	C₂⁴	#2669	1	1	yes	characteristic
419	C₂⁴	#2669	1	1	yes	characteristic
420	C₂⁴	#2673	1	1	yes	characteristic
421	C₂⁴	#2678	1	1	yes	characteristic
422	C₂⁴	#2856	1	1	yes	characteristic
423	C₂×Q₈	#2021	1	2	yes	—
424	C₂×Q₈	#2021	1	2	yes	—
425	C₂×Q₈	#2403	1	1	yes	characteristic
426	C₂×Q₈	#2408	1	1	yes	characteristic
427	C₂×Q₈	#2410	1	1	yes	characteristic
428	C₂×Q₈	#2456	1	1	yes	characteristic
429	C₂×Q₈	#2464	1	1	yes	characteristic
430	C₂×Q₈	#2613	1	1	yes	characteristic
431	C₂×Q₈	#2635	1	1	yes	characteristic
432	C₂×Q₈	#2671	1	1	yes	characteristic
433	C₂×Q₈	#2675	1	1	yes	characteristic
434	C₂×Q₈	#2675	1	1	yes	characteristic
435	C₂×Q₈	#2676	1	1	yes	characteristic
436	C₂×Q₈	#2688	1	1	yes	characteristic
437	C₂×Q₈	#2688	1	1	yes	characteristic
438	C₂×Q₈	#2699	1	1	yes	characteristic
439	C₂×Q₈	#2714	1	1	yes	characteristic
440	C₂×Q₈	#2815	1	1	yes	characteristic
441	C₂×D₄	#2021	1	2	yes	—
442	C₂×D₄	#2021	1	2	yes	—
443	C₂×D₄	C₂×#392	1	1	yes	characteristic
444	C₂×D₄	#2388	1	1	yes	characteristic
445	C₂×D₄	#2403	1	1	yes	characteristic
446	C₂×D₄	#2404	1	1	yes	characteristic
447	C₂×D₄	#2407	1	1	yes	characteristic
448	C₂×D₄	#2407	1	1	yes	characteristic
449	C₂×D₄	#2407	1	1	yes	characteristic
450	C₂×D₄	#2408	1	1	yes	characteristic
451	C₂×D₄	#2410	1	1	yes	characteristic
452	C₂×D₄	#2414	1	1	yes	characteristic
453	C₂×D₄	#2414	1	1	yes	characteristic
454	C₂×D₄	#2424	1	1	yes	characteristic
455	C₂×D₄	#2428	1	1	yes	characteristic
456	C₂×D₄	#2428	1	1	yes	characteristic
457	C₂×D₄	#2428	1	1	yes	characteristic
458	C₂×D₄	#2430	1	1	yes	characteristic
459	C₂×D₄	#2431	1	1	yes	characteristic
460	C₂×D₄	#2431	1	1	yes	characteristic
461	C₂×D₄	#2431	1	1	yes	characteristic
462	C₂×D₄	#2433	1	1	yes	characteristic
463	C₂×D₄	#2456	1	1	yes	characteristic
464	C₂×D₄	#2464	1	1	yes	characteristic
465	C₂×D₄	#2464	1	1	yes	characteristic
466	C₂×D₄	#2535	1	1	yes	characteristic
467	C₂×D₄	#2540	1	1	yes	characteristic
468	C₂×D₄	#2541	1	1	yes	characteristic
469	C₂×D₄	#2555	1	1	yes	characteristic
470	C₂×D₄	#2615	1	1	yes	characteristic
471	C₂×D₄	#2615	1	1	yes	characteristic
472	C₂×D₄	#2619	1	1	yes	characteristic
473	C₂×D₄	#2661	1	1	yes	characteristic
474	C₂×D₄	#2668	1	1	yes	characteristic
475	C₂×D₄	#2669	1	1	yes	characteristic
476	C₂×D₄	#2669	1	1	yes	characteristic
477	C₂×D₄	#2671	1	1	yes	characteristic
478	C₂×D₄	#2673	1	1	yes	characteristic
479	C₂×D₄	#2673	1	1	yes	characteristic
480	C₂×D₄	#2673	1	1	yes	characteristic
481	C₂×D₄	#2676	1	1	yes	characteristic
482	C₂×D₄	#2676	1	1	yes	characteristic
483	C₂×D₄	#2678	1	1	yes	characteristic
484	C₂×D₄	#2678	1	1	yes	characteristic
485	C₂×D₄	#2682	1	1	yes	characteristic
486	C₂×D₄	#2688	1	1	yes	characteristic
487	C₂×D₄	#2703	1	1	yes	characteristic
488	C₂×D₄	#2703	1	1	yes	characteristic
489	C₂×D₄	#2714	1	1	yes	characteristic
490	C₂×D₄	#2813	1	1	yes	characteristic
491	C₂²×C₄	C₂×#392	1	1	yes	characteristic
492	C₂²×C₄	#2403	1	1	yes	characteristic
493	C₂²×C₄	#2403	1	1	yes	characteristic
494	C₂²×C₄	#2403	1	1	yes	characteristic
495	C₂²×C₄	#2403	1	1	yes	characteristic
496	C₂²×C₄	#2403	1	1	yes	characteristic
497	C₂²×C₄	#2403	1	1	yes	characteristic
498	C₂²×C₄	#2404	1	1	yes	characteristic
499	C₂²×C₄	#2407	1	1	yes	characteristic
500	C₂²×C₄	#2408	1	1	yes	characteristic
501	C₂²×C₄	#2408	1	1	yes	characteristic
502	C₂²×C₄	#2408	1	1	yes	characteristic
503	C₂²×C₄	#2410	1	1	yes	characteristic
504	C₂²×C₄	#2410	1	1	yes	characteristic
505	C₂²×C₄	#2410	1	1	yes	characteristic
506	C₂²×C₄	#2410	1	1	yes	characteristic
507	C₂²×C₄	#2410	1	1	yes	characteristic
508	C₂²×C₄	#2410	1	1	yes	characteristic
509	C₂²×C₄	#2410	1	1	yes	characteristic
510	C₂²×C₄	#2410	1	1	yes	characteristic
511	C₂²×C₄	#2410	1	1	yes	characteristic
512	C₂²×C₄	#2410	1	1	yes	characteristic
513	C₂²×C₄	#2416	1	1	yes	characteristic
514	C₂²×C₄	#2416	1	1	yes	characteristic
515	C₂²×C₄	#2424	1	1	yes	characteristic
516	C₂²×C₄	#2424	1	1	yes	characteristic
517	C₂²×C₄	#2424	1	1	yes	characteristic
518	C₂²×C₄	#2424	1	1	yes	characteristic
519	C₂²×C₄	#2424	1	1	yes	characteristic
520	C₂²×C₄	#2424	1	1	yes	characteristic
521	C₂²×C₄	#2428	1	1	yes	characteristic
522	C₂²×C₄	#2428	1	1	yes	characteristic
523	C₂²×C₄	#2428	1	1	yes	characteristic
524	C₂²×C₄	#2428	1	1	yes	characteristic
525	C₂²×C₄	#2430	1	1	yes	characteristic
526	C₂²×C₄	#2430	1	1	yes	characteristic
527	C₂²×C₄	#2430	1	1	yes	characteristic
528	C₂²×C₄	#2433	1	1	yes	characteristic
529	C₂²×C₄	#2433	1	1	yes	characteristic
530	C₂²×C₄	#2433	1	1	yes	characteristic
531	C₂²×C₄	#2433	1	1	yes	characteristic
532	C₂²×C₄	#2464	1	1	yes	characteristic
533	C₂²×C₄	#2537	1	1	yes	characteristic
534	C₂²×C₄	#2539	1	1	yes	characteristic
535	C₂²×C₄	#2543	1	1	yes	characteristic
536	C₂²×C₄	#2543	1	1	yes	characteristic
537	C₂²×C₄	#2555	1	1	yes	characteristic
538	C₂²×C₄	#2613	1	1	yes	characteristic
539	C₂²×C₄	#2617	1	1	yes	characteristic
540	C₂²×C₄	#2656	1	1	yes	characteristic
541	C₂²×C₄	#2668	1	1	yes	characteristic
542	C₂²×C₄	#2668	1	1	yes	characteristic
543	C₂²×C₄	#2668	1	1	yes	characteristic
544	C₂²×C₄	#2669	1	1	yes	characteristic
545	C₂²×C₄	#2669	1	1	yes	characteristic
546	C₂²×C₄	#2671	1	1	yes	characteristic
547	C₂²×C₄	#2671	1	1	yes	characteristic
548	C₂²×C₄	#2671	1	1	yes	characteristic
549	C₂²×C₄	#2671	1	1	yes	characteristic
550	C₂²×C₄	#2673	1	1	yes	characteristic
551	C₂²×C₄	#2673	1	1	yes	characteristic
552	C₂²×C₄	#2673	1	1	yes	characteristic
553	C₂²×C₄	#2673	1	1	yes	characteristic
554	C₂²×C₄	#2675	1	1	yes	characteristic
555	C₂²×C₄	#2675	1	1	yes	characteristic
556	C₂²×C₄	#2676	1	1	yes	characteristic
557	C₂²×C₄	#2678	1	1	yes	characteristic
558	C₂²×C₄	#2682	1	1	yes	characteristic
559	C₂²×C₄	#2688	1	1	yes	characteristic
560	C₂²×C₄	#2699	1	1	yes	characteristic
561	C₂²×C₄	#2846	1	1	yes	characteristic
562	C₂²×C₄	#2847	1	1	yes	characteristic
563	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
564	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
565	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
566	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
567	C₂²×C₄	#3026	1	1	yes	characteristic
568	C₂²×C₄	#3026	1	1	yes	characteristic
569	C₂²×C₄	#3026	1	1	yes	characteristic
570	C₂²×C₄	#3026	1	1	yes	characteristic
571	C₂³	#14757	1	1	yes	characteristic
572	C₂³	#14762	1	1	yes	characteristic
573	C₂³	#14885	1	1	yes	characteristic
574	C₂³	#15123	1	1	yes	characteristic
575	C₂³	#15124	1	1	yes	characteristic
576	C₂³	#15257	1	1	yes	characteristic
577	C₂³	#15257	1	1	yes	characteristic
578	C₂³	#15263	1	1	yes	characteristic
579	C₂³	#15273	1	1	yes	characteristic
580	C₂³	#15310	1	1	yes	characteristic
581	C₂³	#15310	1	1	yes	characteristic
582	C₂³	#15315	1	1	yes	characteristic
583	C₂³	#15320	1	1	yes	characteristic
584	C₂³	#16250	1	1	yes	characteristic
585	C₂³	#16260	1	1	yes	characteristic
586	C₂³	#24404	1	1	yes	characteristic
587	C₂³	#24404	1	1	yes	characteristic
588	C₂³	#24404	1	1	yes	characteristic
589	C₂³	#24404	1	1	yes	characteristic
590	C₂×C₄	#14715	1	1	yes	characteristic
591	C₂×C₄	#14715	1	1	yes	characteristic
592	C₂×C₄	#14716	1	1	yes	characteristic
593	C₂×C₄	#14722	1	1	yes	characteristic
594	C₂×C₄	#15263	1	1	yes	characteristic
595	C₂×C₄	#15263	1	1	yes	characteristic
596	C₂×C₄	#15263	1	1	yes	characteristic
597	C₂×C₄	#15273	1	1	yes	characteristic
598	C₂×C₄	#15278	1	1	yes	characteristic
599	C₂×C₄	#15278	1	1	yes	characteristic
600	C₂×C₄	#15315	1	1	yes	characteristic
601	C₂×C₄	#15320	1	1	yes	characteristic
602	C₂×C₄	#16252	1	1	yes	characteristic
603	C₂×C₄	#16258	1	1	yes	characteristic
604	C₂×C₄	#16500	1	1	yes	characteristic
605	C₂×C₄	#16508	1	1	yes	characteristic
606	C₂×C₄	C₂×#2021	1	1	yes	characteristic
607	C₂×C₄	C₂×#2021	1	1	yes	characteristic
608	C₂×C₄	#23444	1	1	yes	characteristic
609	C₂×C₄	#23444	1	1	yes	characteristic
610	C₂×C₄	#23900	1	1	yes	characteristic
611	C₂×C₄	#23900	1	1	yes	characteristic
612	C₂×C₄	#23900	1	1	yes	characteristic
613	C₂×C₄	#23900	1	1	yes	characteristic
614	C₂×C₄	#23903	1	1	yes	characteristic
615	C₂×C₄	#23903	1	1	yes	characteristic
616	C₂×C₄	#23903	1	1	yes	characteristic
617	C₂×C₄	#23903	1	1	yes	characteristic
618	C₂×C₄	#24404	1	1	yes	characteristic
619	C₂×C₄	#24404	1	1	yes	characteristic
620	C₂×C₄	#24404	1	1	yes	characteristic
621	C₂×C₄	#24404	1	1	yes	characteristic
622	C₂×C₄	#24404	1	1	yes	characteristic
623	C₂×C₄	#24404	1	1	yes	characteristic
624	C₂×C₄	#24404	1	1	yes	characteristic
625	C₂×C₄	#24404	1	1	yes	characteristic
626	C₂×C₄	#25563	1	1	yes	characteristic
627	C₂×C₄	#25563	1	1	yes	characteristic
628	C₂×C₄	#25563	1	1	yes	characteristic
629	C₂×C₄	#25563	1	1	yes	characteristic
630	C₂²	#156706	1	1	yes	characteristic
631	C₂²	#397910	1	1	yes	characteristic
632	C₂²	#397910	1	1	yes	characteristic
633	C₂²	#417508	1	1	yes	characteristic
634	C₂²	#417508	1	1	yes	characteristic
635	C₂²	#422797	1	1	yes	characteristic
636	C₂²	#422797	1	1	yes	characteristic
637	C₄	#394058	1	1	yes	characteristic
638	C₄	#394061	1	1	yes	characteristic
639	C₄	#394267	1	1	yes	characteristic
640	C₄	#394267	1	1	yes	characteristic
641	C₄	#418298	1	1	yes	characteristic
642	C₄	#418298	1	1	yes	characteristic
643	C₄	#420489	1	1	yes	characteristic
644	C₄	#420489	1	1	yes	characteristic
645	C₂	#72260761	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72260761
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. #72312738	C₂	semidirect
2. #72312734	C₂	semidirect
3. #72312732	C₂	semidirect
4. C₂×#494752	C₂	semidirect
5. #72312725	C₂	semidirect
6. #72312291	C₂	semidirect
7. #72303721	C₂	semidirect
8. #72303713	C₂	semidirect
9. #72303711	C₂	semidirect
10. #72303705	C₂	semidirect
11. #72303318	C₂	semidirect
12. #72302938	C₂	semidirect
13. #72280895	C₂	semidirect
14. #72267963	C₂	semidirect
15. #72256637	C₂	semidirect
53. C₂×#3586	D₄	semidirect
54. C₂×#3585	D₄	semidirect
55. C₂²×#575	D₄	semidirect
56. C₂²×#575	D₄	semidirect
66. C₂×#2896	D₄	semidirect
67. C₂×#2896	D₄	semidirect
68. C₂×#2889	D₄	semidirect
69. C₂×#2888	D₄	semidirect
73. C₂²×#410	D₄	semidirect
74. C₂²×#410	D₄	semidirect
75. C₂²×#410	D₄	semidirect
76. C₂²×#410	D₄	semidirect
85. C₂×#1915	D₄	semidirect
86. C₂×#1914	D₄	semidirect
87. C₂×#1858	D₄	semidirect
88. C₂×#1791	D₄	semidirect
89. #20587	D₄	semidirect
90. #20586	D₄	semidirect
91. #12579	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72312738	2
#72312734	2
#72312732	2
C₂×#494752	2
#72312725	2
#72312291	2
#72303721	2
#72303713	2
#72303711	2
#72303705	2
#72303318	2
#72302938	2
#72280895	2
#72267963	2
#72256637	2