Subgroups — #72339868

Order 4096.

At least 36237 conjugacy classes of subgroups; only the 737 normal subgroups are shown.

The subgroup lattice has 572 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72339867	C₂	1	1	yes	maximal, characteristic, complemented
2	#72339864	C₂	1	1	yes	maximal, characteristic, complemented
3	#72339863	C₂	1	1	yes	maximal, characteristic, complemented
4	#72339860	C₂	1	1	yes	maximal, characteristic, complemented
5	#72339857	C₂	1	1	yes	maximal, characteristic, complemented
6	#72339853	C₂	1	1	yes	maximal, characteristic, complemented
7	#72339852	C₂	1	1	yes	maximal, characteristic, complemented
8	#72339851	C₂	1	1	yes	maximal, characteristic, complemented
9	#72339850	C₂	1	1	yes	maximal, characteristic, complemented
10	#72339849	C₂²	1	1	yes	characteristic, complemented
11	#72339848	C₂²	1	1	yes	characteristic, complemented
12	#72339845	C₂	1	1	yes	maximal, characteristic, complemented
13	#72339844	C₂²	1	1	yes	characteristic, complemented
14	#72339842	C₂²	1	1	yes	characteristic, complemented
15	#72339838	C₂	1	1	yes	maximal, characteristic, complemented
16	#72339837	C₂²	1	1	yes	characteristic, complemented
17	#72339834	C₂	1	1	yes	maximal, characteristic, complemented
18	#72339829	C₂	1	1	yes	maximal, characteristic, complemented
19	#72339828	C₂²	1	1	yes	characteristic, complemented
20	#72339828	C₂²	1	1	yes	characteristic, complemented
21	#72339827	C₂²	1	1	yes	characteristic, complemented
22	#72339826	C₂²	1	1	yes	characteristic, complemented
23	#72339824	C₂	1	1	yes	maximal, characteristic, complemented
24	#72339823	C₂²	1	1	yes	characteristic, complemented
25	#72339821	C₂²	1	1	yes	characteristic, complemented
26	#72339820	C₂²	1	1	yes	characteristic, complemented
27	#72339819	C₂²	1	1	yes	characteristic, complemented
28	#72339817	C₂²	1	1	yes	characteristic, complemented
29	#72339815	C₂	1	1	yes	maximal, characteristic
30	#72339814	C₂²	1	1	yes	characteristic
31	#72339803	C₂²	1	1	yes	characteristic
32	#72339802	C₂²	1	1	yes	characteristic
33	#72339799	C₂²	1	1	yes	characteristic
34	#72339793	C₂²	1	1	yes	characteristic
35	#72339721	C₄	1	2	yes	complemented
36	#72339718	C₄	1	2	yes	complemented
37	#72339717	C₄	1	2	yes	complemented
38	#72339704	C₄	1	2	yes	complemented
39	#72338371	C₂²	1	1	yes	characteristic
40	#72306824	C₂²	1	1	yes	characteristic, complemented
41	#72306823	C₂²	1	1	yes	characteristic, complemented
42	#72306818	C₂²	1	1	yes	characteristic, complemented
43	#72306804	C₂²	1	1	yes	characteristic, complemented
44	#72306804	C₂²	1	1	yes	characteristic, complemented
45	#72306803	C₂²	1	1	yes	characteristic, complemented
46	#72306622	C₂²	1	1	yes	characteristic, complemented
47	#72306593	C₂²	1	1	yes	characteristic, complemented
48	#72306590	C₂²	1	1	yes	characteristic, complemented
49	#72306588	C₂²	1	1	yes	characteristic, complemented
50	#72306573	C₂²	1	1	yes	characteristic, complemented
51	#72306568	C₂²	1	1	yes	characteristic
52	#72279391	C₂²	1	1	yes	characteristic, complemented
53	#72214702	C₂²	1	1	yes	characteristic, complemented
54	#72214114	C₂²	1	1	yes	characteristic, complemented
55	#10586363	D₄	1	1	yes	characteristic
56	C₂×#63011	D₄	1	1	yes	characteristic
57	#10575937	D₄	1	1	yes	characteristic
58	#10575552	C₂³	1	1	yes	characteristic
59	#6407634	C₂³	1	1	yes	characteristic, complemented
60	#6382803	C₂³	1	1	yes	characteristic, complemented
61	#6369179	D₄	1	1	yes	characteristic
62	#6369151	D₄	1	1	yes	characteristic
63	#6369095	D₄	1	1	yes	characteristic
64	#6369084	D₄	1	1	yes	characteristic
65	#6368877	C₂×C₄	1	2	yes	—
66	#6368864	C₂×C₄	1	2	yes	—
67	#6367510	D₄	1	1	yes	characteristic
68	#6367504	D₄	1	1	yes	characteristic
69	#6367493	D₄	1	1	yes	characteristic
70	#6367483	D₄	1	1	yes	characteristic
71	#6367441	D₄	1	1	yes	characteristic
72	#6367441	D₄	1	1	yes	characteristic
73	#6367410	D₄	1	1	yes	characteristic
74	#6367410	D₄	1	1	yes	characteristic
75	#6365658	C₂×C₄	1	2	yes	—
76	#6365607	C₂×C₄	1	2	yes	—
77	#6363909	C₂×C₄	1	2	yes	—
78	#6363808	C₂×C₄	1	2	yes	—
79	#6363083	D₄	1	1	yes	characteristic
80	#6363083	D₄	1	2	yes	—
81	#6363080	C₂×C₄	1	1	yes	characteristic
82	#6363076	D₄	1	2	yes	—
83	#6363063	D₄	1	1	yes	characteristic
84	#6363053	C₂×C₄	1	1	yes	characteristic
85	#6363044	C₂×C₄	1	1	yes	characteristic
86	#6363023	C₂×C₄	1	1	yes	characteristic
87	#6363008	D₄	1	1	yes	characteristic
88	#6363004	D₄	1	2	yes	—
89	#6363004	D₄	1	2	yes	—
90	#6363004	D₄	1	2	yes	—
91	#6362952	D₄	1	1	yes	characteristic
92	#6362952	D₄	1	2	yes	—
93	#6361272	D₄	1	1	yes	characteristic
94	#6359505	D₄	1	1	yes	characteristic
95	#6359500	D₄	1	1	yes	characteristic
96	#6358422	D₄	1	1	yes	characteristic
97	#6358075	C₂×C₄	1	2	yes	—
98	#6358059	D₄	1	2	yes	—
99	#6358039	D₄	1	2	yes	—
100	#6358021	C₂×C₄	1	2	yes	—
101	#6357807	D₄	1	1	yes	characteristic
102	#6357800	C₂³	1	1	yes	characteristic
103	#6357770	C₂³	1	1	yes	characteristic
104	C₂×#19747	D₄	1	1	yes	characteristic
105	#6350247	C₂×C₄	1	2	yes	—
106	#6350247	D₄	1	2	yes	—
107	#6350245	C₂×C₄	1	2	yes	—
108	#6350245	D₄	1	2	yes	—
109	#6350080	C₂×C₄	1	2	yes	—
110	#6350080	C₂×C₄	1	2	yes	—
111	#6350079	D₄	1	2	yes	—
112	#6350079	D₄	1	2	yes	—
113	#6348457	D₄	1	1	yes	characteristic
114	#6348454	C₂³	1	1	yes	characteristic
115	#6348452	D₄	1	1	yes	characteristic
116	#6348449	C₂³	1	1	yes	characteristic
117	#6348098	C₂³	1	1	yes	characteristic
118	C₂×#18548	D₄	1	1	yes	characteristic
119	#6348078	D₄	1	1	yes	characteristic
120	#6348073	C₂³	1	1	yes	characteristic
121	#6344273	D₄	1	1	yes	characteristic
122	#6344269	D₄	1	1	yes	characteristic
123	#6342523	D₄	1	1	yes	characteristic
124	#512608	C₂³	1	1	yes	characteristic, complemented
125	#512601	C₂³	1	1	yes	characteristic, complemented
126	#512601	C₂³	1	1	yes	characteristic, complemented
127	#512601	C₂³	1	1	yes	characteristic, complemented
128	#483304	C₂³	1	1	yes	characteristic, complemented
129	#483304	C₂³	1	1	yes	characteristic, complemented
130	#63038	C₂²⋊C₄	1	2	yes	complemented
131	#63028	C₂²⋊C₄	1	2	yes	complemented
132	#63011	C₂²⋊C₄	1	2	yes	—
133	#63011	C₂²⋊C₄	1	2	yes	—
134	#62815	C₂×D₄	1	1	yes	characteristic
135	C₂×#3498	C₂×D₄	1	1	yes	characteristic
136	#62759	C₂×D₄	1	1	yes	characteristic
137	C₂×#3549	C₂×D₄	1	1	yes	characteristic
138	C₂×#3483	C₂×D₄	1	1	yes	characteristic
139	C₂×#3481	C₂×D₄	1	1	yes	characteristic
140	#61015	C₂²⋊C₄	1	2	yes	complemented
141	#61011	C₂²⋊C₄	1	2	yes	complemented
142	#60818	C₂²×C₄	1	2	yes	—
143	#60818	C₂×D₄	1	2	yes	—
144	#60817	C₂×D₄	1	2	yes	—
145	#60817	C₂×D₄	1	2	yes	—
146	#60693	C₂×D₄	1	1	yes	characteristic
147	C₂×#3184	C₂×D₄	1	1	yes	characteristic
148	#60639	C₂⁴	1	1	yes	characteristic
149	C₂×#3151	C₂×D₄	1	1	yes	characteristic
150	#60618	C₂×D₄	1	1	yes	characteristic
151	C₂×#3138	C₂×D₄	1	1	yes	characteristic
152	#60123	C₂×D₄	1	1	yes	characteristic
153	#20324	C₂²⋊C₄	1	2	yes	complemented
154	#20323	C₂²⋊C₄	1	2	yes	complemented
155	#20323	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	#20314	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	#20314	C₂²⋊C₄	1	2	yes	complemented
158	#20302	C₂²⋊C₄	1	2	yes	complemented
159	#20302	C₂²⋊C₄	1	2	yes	complemented
160	#20302	C₂²⋊C₄	1	2	yes	complemented
161	#20294	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	#20289	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	#20157	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	#20150	C₂²⋊C₄	1	2	yes	complemented
165	#20150	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	#20143	C₂²⋊C₄	1	2	yes	complemented
167	#20143	C₂²⋊C₄	1	2	yes	complemented
168	#20143	C₂²⋊C₄	1	2	yes	complemented
169	#20143	C₂²⋊C₄	1	2	yes	complemented
170	#20138	C₂²⋊C₄	1	2	yes	complemented
171	#20138	C₂²⋊C₄	1	1	yes	characteristic, complemented
172	#20131	C₂²⋊C₄	1	1	yes	characteristic, complemented
173	#20125	C₂²⋊C₄	1	2	yes	complemented
174	#20117	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	#20107	C₂²⋊C₄	1	2	yes	complemented
176	#20107	C₂²⋊C₄	1	2	yes	complemented
177	#20107	C₂²⋊C₄	1	2	yes	complemented
178	#20084	C₂²⋊C₄	1	2	yes	complemented
179	#20084	C₂²⋊C₄	1	1	yes	characteristic, complemented
180	#20053	C₂²⋊C₄	1	2	yes	complemented
181	#20053	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	#20040	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	#20019	C₂²⋊C₄	1	2	yes	complemented
184	#20017	C₂²⋊C₄	1	2	yes	complemented
185	#20017	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	#20013	C₂²⋊C₄	1	1	yes	characteristic, complemented
187	#20003	C₂²⋊C₄	1	2	yes	complemented
188	#20003	C₂²⋊C₄	1	2	yes	complemented
189	#20003	C₂²⋊C₄	1	2	yes	complemented
190	#19987	C₂²⋊C₄	1	1	yes	characteristic, complemented
191	SD₁₆²	C₂²⋊C₄	1	2	yes	complemented
192	SD₁₆²	C₂²⋊C₄	1	1	yes	characteristic, complemented
193	#19750	C₂²×C₄	1	1	yes	characteristic
194	#19750	C₂×D₄	1	1	yes	characteristic
195	#19750	C₂×D₄	1	2	yes	—
196	#19749	C₂×D₄	1	1	yes	characteristic
197	#19749	C₂×D₄	1	1	yes	characteristic
198	#19747	C₂²⋊C₄	1	2	yes	complemented
199	#19747	C₂²⋊C₄	1	2	yes	complemented
200	#19746	C₂²×C₄	1	1	yes	characteristic
201	#19746	C₂×D₄	1	1	yes	characteristic
202	#19745	C₂×D₄	1	1	yes	characteristic
203	#19745	C₂×D₄	1	1	yes	characteristic
204	#19745	C₂×D₄	1	2	yes	—
205	#19729	C₂²⋊C₄	1	2	yes	complemented
206	#19727	C₂×D₄	1	2	yes	—
207	#19721	C₂²×C₄	1	2	yes	—
208	#19717	C₂²⋊C₄	1	2	yes	complemented
209	#19661	C₂×D₄	1	1	yes	characteristic
210	#19661	C₂×D₄	1	1	yes	characteristic
211	#19654	C₂×D₄	1	1	yes	characteristic
212	#19654	C₂×D₄	1	1	yes	characteristic
213	#19616	C₂×D₄	1	1	yes	characteristic
214	#19608	C₂×D₄	1	1	yes	characteristic
215	#19603	C₂×D₄	1	1	yes	characteristic
216	#19596	C₂×D₄	1	1	yes	characteristic
217	#18715	C₂²×C₄	1	2	yes	—
218	#18714	C₂×D₄	1	2	yes	—
219	#18713	C₂²×C₄	1	2	yes	—
220	#18713	C₂×D₄	1	2	yes	—
221	#18691	C₂²⋊C₄	1	2	yes	—
222	#18691	C₂²⋊C₄	1	2	yes	—
223	#18688	C₂×D₄	1	1	yes	characteristic
224	#18688	C₂×D₄	1	1	yes	characteristic
225	#18686	C₂×D₄	1	1	yes	characteristic
226	#18686	C₂×D₄	1	1	yes	characteristic
227	#18686	C₂×D₄	1	1	yes	characteristic
228	#18686	C₂×D₄	1	1	yes	characteristic
229	#18686	C₂×D₄	1	1	yes	characteristic
230	#18686	C₂×D₄	1	1	yes	characteristic
231	#18684	C₂²⋊C₄	1	2	yes	complemented
232	#18684	C₂²⋊C₄	1	2	yes	complemented
233	#18549	C₂×D₄	1	2	yes	—
234	#18549	C₂×D₄	1	1	yes	characteristic
235	#18549	C₂×D₄	1	1	yes	characteristic
236	#18548	C₂×D₄	1	2	yes	—
237	#18548	C₂×D₄	1	1	yes	characteristic
238	#18548	C₂×D₄	1	1	yes	characteristic
239	#18547	C₂²×C₄	1	1	yes	characteristic
240	#18547	C₂×D₄	1	1	yes	characteristic
241	#18547	C₂×D₄	1	2	yes	—
242	#18547	C₂×D₄	1	2	yes	—
243	#18546	C₂²×C₄	1	1	yes	characteristic
244	#18546	C₂×D₄	1	1	yes	characteristic
245	#18528	C₂²×C₄	1	1	yes	characteristic
246	#18528	C₂²×C₄	1	1	yes	characteristic
247	#18527	C₂×D₄	1	1	yes	characteristic
248	#18527	C₂×D₄	1	1	yes	characteristic
249	#18526	C₂×D₄	1	1	yes	characteristic
250	#18526	C₂×D₄	1	1	yes	characteristic
251	#18524	C₂×D₄	1	1	yes	characteristic
252	#18524	C₂×D₄	1	1	yes	characteristic
253	#18510	C₂×D₄	1	1	yes	characteristic
254	#18510	C₂×D₄	1	1	yes	characteristic
255	#18510	C₂×D₄	1	1	yes	characteristic
256	#18510	C₂×D₄	1	1	yes	characteristic
257	C₂×#1624	C₂²⋊C₄	1	2	yes	complemented
258	C₂×#1623	C₂²⋊C₄	1	2	yes	complemented
259	#18485	C₂²⋊C₄	1	2	yes	—
260	#18485	C₂²⋊C₄	1	2	yes	—
261	#18480	C₂×D₄	1	1	yes	characteristic
262	#18480	C₂×D₄	1	1	yes	characteristic
263	#18480	C₂×D₄	1	1	yes	characteristic
264	#18480	C₂×D₄	1	1	yes	characteristic
265	#17782	C₂²⋊C₄	1	2	yes	—
266	#17782	C₂²⋊C₄	1	2	yes	—
267	#17780	C₂²⋊C₄	1	2	yes	complemented
268	#17780	C₂²⋊C₄	1	2	yes	complemented
269	#17738	C₂×D₄	1	1	yes	characteristic
270	#17738	C₂×D₄	1	1	yes	characteristic
271	#17738	C₂×D₄	1	1	yes	characteristic
272	C₂×#1560	C₂×D₄	1	1	yes	characteristic
273	#17342	C₂²⋊C₄	1	2	yes	complemented
274	#17341	C₂²⋊C₄	1	2	yes	complemented
275	#17334	C₂×D₄	1	1	yes	characteristic
276	C₂×#1455	C₂×D₄	1	1	yes	characteristic
277	#3550	#120	1	1	yes	characteristic
278	#3549	C₂×C₂²⋊C₄	1	2	yes	—
279	#3549	#120	1	1	yes	characteristic
280	#3549	#120	1	1	yes	characteristic
281	#3549	#120	1	1	yes	characteristic
282	#3544	C₂×C₂²⋊C₄	1	2	yes	—
283	#3509	C₂×C₂²⋊C₄	1	2	yes	—
284	#3508	#120	1	2	yes	—
285	#3498	C₂×C₂²⋊C₄	1	2	yes	—
286	#3498	#120	1	2	yes	—
287	#3483	#120	1	1	yes	characteristic
288	#3483	#120	1	2	yes	—
289	#3483	#120	1	1	yes	characteristic
290	#3483	#120	1	1	yes	characteristic
291	#3483	#120	1	1	yes	characteristic
292	#3481	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	#3481	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	#3481	#120	1	1	yes	characteristic
295	#3481	#120	1	1	yes	characteristic
296	C₂×#559	#120	1	1	yes	characteristic
297	C₂×Q₈²	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×#555	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×#555	#120	1	2	yes	—
300	C₂×D₄²	#120	1	1	yes	characteristic
301	C₂×#533	#120	1	1	yes	characteristic
302	C₂×#532	C₂²×D₄	1	1	yes	characteristic
303	C₂×#532	C₂²×D₄	1	1	yes	characteristic
304	C₂²×#127	#120	1	1	yes	characteristic
305	C₂×C₄×#41	#120	1	1	yes	characteristic
306	#3185	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	#3185	#120	1	1	yes	characteristic
308	#3184	C₂×C₂²⋊C₄	1	2	yes	—
309	#3184	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	#3184	#120	1	2	yes	—
311	#3184	#120	1	1	yes	characteristic
312	#3160	#120	1	1	yes	characteristic
313	C₂×#498	#120	1	1	yes	characteristic
314	#3152	C₂³×C₄	1	1	yes	characteristic
315	#3152	C₂²×D₄	1	1	yes	characteristic
316	#3152	C₂²×D₄	1	1	yes	characteristic
317	#3152	C₂²×D₄	1	1	yes	characteristic
318	#3151	C₂²×D₄	1	1	yes	characteristic
319	#3151	C₂²×D₄	1	1	yes	characteristic
320	#3151	C₂²×D₄	1	1	yes	characteristic
321	#3151	C₂²×D₄	1	1	yes	characteristic
322	#3147	#120	1	1	yes	characteristic
323	#3147	C₂²×D₄	1	1	yes	characteristic
324	#3147	C₂²×D₄	1	1	yes	characteristic
325	#3147	C₂²×D₄	1	1	yes	characteristic
326	#3147	C₂²×D₄	1	1	yes	characteristic
327	C₂×#493	#120	1	1	yes	characteristic
328	C₂×#493	#120	1	2	yes	—
329	C₂×#492	C₂×C₂²⋊C₄	1	2	yes	—
330	#3138	C₂×C₂²⋊C₄	1	2	yes	—
331	#3138	#120	1	2	yes	—
332	#3131	C₂×C₂²⋊C₄	1	2	yes	—
333	#3131	#120	1	2	yes	—
334	#2922	C₂×C₂²⋊C₄	1	2	yes	—
335	#2922	#120	1	2	yes	—
336	C₂×C₄×M₁₆	#120	1	1	yes	characteristic
337	C₂×C₄×M₁₆	C₂²×D₄	1	1	yes	characteristic
338	#1722	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	#1722	#120	1	1	yes	characteristic
340	#1721	C₂×C₂²⋊C₄	1	2	yes	—
341	#1721	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	#1721	#120	1	2	yes	—
343	#1721	#120	1	1	yes	characteristic
344	#1716	C₂×C₂²⋊C₄	1	2	yes	—
345	#1716	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	#1716	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	#1715	#120	1	2	yes	—
348	#1715	#120	1	1	yes	characteristic
349	#1715	#120	1	1	yes	characteristic
350	#1713	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	#1712	#120	1	2	yes	—
352	#1712	#120	1	1	yes	characteristic
353	#1709	C₂×C₂²⋊C₄	1	2	yes	—
354	#1709	C₂×C₂²⋊C₄	1	1	yes	characteristic
355	#1709	#120	1	1	yes	characteristic
356	#1708	C₂×C₂²⋊C₄	1	1	yes	characteristic
357	#1708	#120	1	2	yes	—
358	#1708	#120	1	1	yes	characteristic
359	#1705	C₂×C₂²⋊C₄	1	2	yes	—
360	#1705	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	#1705	#120	1	1	yes	characteristic
362	#1634	C₂×C₂²⋊C₄	1	2	yes	—
363	#1634	C₂×C₂²⋊C₄	1	2	yes	—
364	#1634	C₂×C₂²⋊C₄	1	2	yes	—
365	#1634	C₂×C₂²⋊C₄	1	2	yes	—
366	#1634	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	#1634	C₂×C₂²⋊C₄	1	2	yes	—
368	#1634	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	#1634	#120	1	1	yes	characteristic
370	#1634	#120	1	1	yes	characteristic
371	#1634	#120	1	2	yes	—
372	#1633	C₂×C₂²⋊C₄	1	2	yes	—
373	#1633	C₂×C₂²⋊C₄	1	1	yes	characteristic
374	#1633	C₂×C₂²⋊C₄	1	1	yes	characteristic
375	#1633	#120	1	2	yes	—
376	#1633	#120	1	1	yes	characteristic
377	#1633	#120	1	1	yes	characteristic
378	#1630	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	#1630	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	#1630	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	#1630	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	#1629	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	#1629	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	#1629	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	#1629	C₂×C₂²⋊C₄	1	1	yes	characteristic
386	#1624	C₂×C₂²⋊C₄	1	1	yes	characteristic
387	#1624	C₂×C₂²⋊C₄	1	2	yes	—
388	#1624	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	#1624	#120	1	1	yes	characteristic
390	#1624	#120	1	1	yes	characteristic
391	#1624	#120	1	2	yes	—
392	#1624	#120	1	2	yes	—
393	#1624	#120	1	2	yes	—
394	#1624	#120	1	2	yes	—
395	#1624	#120	1	2	yes	—
396	#1623	C₂×C₂²⋊C₄	1	2	yes	—
397	#1623	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	#1623	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	#1623	#120	1	2	yes	—
400	#1623	#120	1	1	yes	characteristic
401	#1623	#120	1	1	yes	characteristic
402	#1620	#120	1	1	yes	characteristic
403	#1620	#120	1	1	yes	characteristic
404	#1620	#120	1	1	yes	characteristic
405	#1620	#120	1	1	yes	characteristic
406	#1619	#120	1	1	yes	characteristic
407	#1619	#120	1	1	yes	characteristic
408	#1619	#120	1	1	yes	characteristic
409	#1619	#120	1	1	yes	characteristic
410	#1560	C₂×C₂²⋊C₄	1	1	yes	characteristic
411	#1560	C₂×C₂²⋊C₄	1	1	yes	characteristic
412	#1560	#120	1	1	yes	characteristic
413	#1560	#120	1	1	yes	characteristic
414	#1560	#120	1	1	yes	characteristic
415	#1560	#120	1	1	yes	characteristic
416	#1560	#120	1	2	yes	—
417	#1560	#120	1	1	yes	characteristic
418	#1560	#120	1	1	yes	characteristic
419	#1558	C₂×C₂²⋊C₄	1	1	yes	characteristic
420	#1558	C₂×C₂²⋊C₄	1	1	yes	characteristic
421	#1558	#120	1	2	yes	—
422	#1555	#120	1	1	yes	characteristic
423	#1555	#120	1	1	yes	characteristic
424	#1543	C₂×C₂²⋊C₄	1	2	yes	—
425	#1543	#120	1	1	yes	characteristic
426	#1543	#120	1	1	yes	characteristic
427	#1543	#120	1	1	yes	characteristic
428	#1543	#120	1	1	yes	characteristic
429	C₂×#333	C₂×C₂²⋊C₄	1	2	yes	—
430	#1455	C₂×C₂²⋊C₄	1	1	yes	characteristic
431	#1455	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	#1455	#120	1	1	yes	characteristic
433	#1455	#120	1	2	yes	—
434	#1455	#120	1	1	yes	characteristic
435	#1453	C₂×C₂²⋊C₄	1	2	yes	—
436	#1450	#120	1	1	yes	characteristic
437	#1450	#120	1	1	yes	characteristic
438	C₂×#322	#120	1	1	yes	characteristic
439	C₂×C₈²	#120	1	1	yes	characteristic
440	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
441	#559	#379	1	1	yes	characteristic
442	#559	#379	1	1	yes	characteristic
443	Q₈²	#379	1	1	yes	characteristic
444	Q₈²	#379	1	1	yes	characteristic
445	Q₈²	#379	1	2	yes	—
446	#555	#379	1	2	yes	—
447	#555	#379	1	1	yes	characteristic
448	#555	#379	1	2	yes	—
449	#555	#379	1	1	yes	characteristic
450	#555	#379	1	2	yes	—
451	D₄²	#379	1	1	yes	characteristic
452	D₄²	#379	1	1	yes	characteristic
453	#533	#379	1	2	yes	—
454	#532	C₂²×C₂²⋊C₄	1	1	yes	characteristic
455	#532	C₂×#120	1	1	yes	characteristic
456	#532	C₂×#120	1	1	yes	characteristic
457	#532	C₂×#120	1	1	yes	characteristic
458	#532	C₂×#120	1	1	yes	characteristic
459	#532	C₂×#120	1	1	yes	characteristic
460	#532	C₂×#120	1	1	yes	characteristic
461	#532	C₂×#120	1	1	yes	characteristic
462	C₂×C₄⋊Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄⋊Q₈	C₂×#120	1	1	yes	characteristic
464	C₂×#127	#379	1	2	yes	—
465	C₂×#127	C₂×#120	1	1	yes	characteristic
466	C₂×#127	C₂×#120	1	1	yes	characteristic
467	C₄×#41	#379	1	2	yes	—
468	C₄×#41	#458	1	2	yes	—
469	C₂×#117	B(4,𝔽₂)	1	1	yes	characteristic
470	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
471	#498	#379	1	2	yes	—
472	#498	#379	1	1	yes	characteristic
473	#498	#379	1	1	yes	characteristic
474	#494	#379	1	1	yes	characteristic
475	#494	C₂²×C₂²⋊C₄	1	1	yes	characteristic
476	#494	C₂²×C₂²⋊C₄	1	1	yes	characteristic
477	#494	C₂×#120	1	1	yes	characteristic
478	#494	C₂×#120	1	1	yes	characteristic
479	#493	#379	1	2	yes	—
480	#493	#379	1	1	yes	characteristic
481	#493	C₂×#120	1	1	yes	characteristic
482	#493	C₂×#120	1	1	yes	characteristic
483	#493	C₂×#120	1	1	yes	characteristic
484	#493	C₂×#120	1	1	yes	characteristic
485	#492	C₂²×C₂²⋊C₄	1	1	yes	characteristic
486	#492	C₂²×C₂²⋊C₄	1	1	yes	characteristic
487	#492	C₂×#120	1	1	yes	characteristic
488	#492	C₂×#120	1	1	yes	characteristic
489	#492	C₂×#120	1	1	yes	characteristic
490	#492	C₂×#120	1	1	yes	characteristic
491	#492	C₂×#120	1	1	yes	characteristic
492	#492	C₂×#120	1	1	yes	characteristic
493	C₄×M₁₆	C₂²×C₂²⋊C₄	1	1	yes	characteristic
494	C₄×M₁₆	C₂×#120	1	1	yes	characteristic
495	C₄×M₁₆	C₂×#120	1	1	yes	characteristic
496	C₄×M₁₆	C₂×#120	1	1	yes	characteristic
497	C₂×C₄×C₈	#379	1	2	yes	—
498	C₂×C₄×C₈	C₂×#120	1	1	yes	characteristic
499	C₂×C₄×C₈	C₂×#120	1	1	yes	characteristic
500	#333	#379	1	2	yes	—
501	#333	#379	1	2	yes	—
502	#333	#379	1	2	yes	—
503	#333	#379	1	2	yes	—
504	#333	#379	1	1	yes	characteristic
505	#333	#379	1	1	yes	characteristic
506	#333	#379	1	1	yes	characteristic
507	#333	#379	1	1	yes	characteristic
508	#331	#379	1	1	yes	characteristic
509	#331	#379	1	1	yes	characteristic
510	#331	#379	1	1	yes	characteristic
511	#331	#379	1	1	yes	characteristic
512	#322	#379	1	1	yes	characteristic
513	#322	#379	1	1	yes	characteristic
514	#322	#379	1	2	yes	—
515	C₈²	#379	1	1	yes	characteristic
516	C₈²	#379	1	1	yes	characteristic
517	C₈²	#379	1	2	yes	—
518	C₂×#41	#1790	1	2	yes	—
519	C₂×#41	#2196	1	2	yes	—
520	C₂²×Q₈	#2196	1	1	yes	characteristic
521	C₂²×D₄	#2196	1	1	yes	characteristic
522	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
523	C₄⋊Q₈	C₂×#379	1	1	yes	characteristic
524	C₄⋊Q₈	C₂×#379	1	1	yes	characteristic
525	C₄⋊Q₈	C₂×#379	1	1	yes	characteristic
526	C₄⋊Q₈	#2846	1	1	yes	characteristic
527	#127	C₂×#379	1	1	yes	characteristic
528	#127	#2846	1	1	yes	characteristic
529	#127	#2846	1	1	yes	characteristic
530	#127	#2846	1	1	yes	characteristic
531	#117	#1790	1	2	yes	—
532	#117	#2196	1	1	yes	characteristic
533	#117	#2196	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	#2196	1	2	yes	—
535	C₂×C₄²	C₂×#379	1	1	yes	characteristic
536	C₂×C₄²	#2846	1	1	yes	characteristic
537	C₂×C₄²	#2846	1	1	yes	characteristic
538	C₂×C₄²	C₂×#458	1	1	yes	characteristic
539	C₂×C₄²	#3026	1	1	yes	characteristic
540	C₂×C₄²	#3026	1	1	yes	characteristic
541	C₄×C₈	C₂×#379	1	1	yes	characteristic
542	C₄×C₈	C₂×#379	1	1	yes	characteristic
543	C₄×C₈	#2846	1	1	yes	characteristic
544	C₄×C₈	#2846	1	1	yes	characteristic
545	C₂⁴	C₂×#2196	1	1	yes	characteristic
546	C₂×Q₈	#12759	1	2	yes	—
547	C₂×D₄	#12759	1	2	yes	—
548	C₂²×C₄	C₂×#1790	1	1	yes	characteristic
549	C₂²×C₄	#32898	1	1	yes	characteristic
550	C₂²×C₄	#32898	1	1	yes	characteristic
551	C₂²×C₄	C₂×#2196	1	1	yes	characteristic
552	C₂²×C₄	C₂×#2196	1	1	yes	characteristic
553	C₂²×C₄	C₂×#2196	1	1	yes	characteristic
554	C₂²⋊C₄	#12759	1	2	yes	—
555	C₂²⋊C₄	#12759	1	2	yes	—
556	C₄²	#14679	1	1	yes	characteristic
557	C₄²	#20609	1	1	yes	characteristic
558	C₄²	#32900	1	1	yes	characteristic
559	C₄²	#32900	1	1	yes	characteristic
560	C₂³	C₂×#12759	1	1	yes	characteristic
561	C₂³	#511771	1	1	yes	characteristic
562	C₂³	#511771	1	1	yes	characteristic
563	C₂×C₄	#392125	1	1	yes	characteristic
564	C₂×C₄	C₂×#12759	1	1	yes	characteristic
565	C₂×C₄	#511771	1	1	yes	characteristic
566	C₂×C₄	#511771	1	1	yes	characteristic
567	C₂²	#72231692	1	1	yes	characteristic
568	C₄	#72213671	1	1	yes	characteristic
569	C₄	#72281791	1	1	yes	characteristic
570	C₂	#72282167	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72282167
commutator	#3152	C₂³×C₄
Frattini, cosocle	#60639	C₂⁴
prime radical	#72339815	C₂
LCS	G ▷ #3152 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×C₄×#41 ◁ #10575552 ◁ G
LECS	G ▷ #60639 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72339867	C₂	semidirect
2. #72339864	C₂	semidirect
3. #72339863	C₂	semidirect
4. #72339860	C₂	semidirect
5. #72339857	C₂	semidirect
6. #72339853	C₂	semidirect
7. #72339852	C₂	semidirect
8. #72339851	C₂	semidirect
9. #72339850	C₂	semidirect
10. #72339849	C₂²	semidirect
11. #72339848	C₂²	semidirect
12. #72339845	C₂	semidirect
13. #72339844	C₂²	semidirect
14. #72339842	C₂²	semidirect
15. #72339838	C₂	semidirect
16. #72339837	C₂²	semidirect
17. #72339834	C₂	semidirect
18. #72339829	C₂	semidirect
19. #72339828	C₂²	semidirect
20. #72339828	C₂²	semidirect
21. #72339827	C₂²	semidirect
22. #72339826	C₂²	semidirect
23. #72339824	C₂	semidirect
24. #72339823	C₂²	semidirect
25. #72339821	C₂²	semidirect
26. #72339820	C₂²	semidirect
27. #72339819	C₂²	semidirect
28. #72339817	C₂²	semidirect
35. #72339721	C₄	semidirect
36. #72339718	C₄	semidirect
37. #72339717	C₄	semidirect
38. #72339704	C₄	semidirect
40. #72306824	C₂²	semidirect
41. #72306823	C₂²	semidirect
42. #72306818	C₂²	semidirect
43. #72306804	C₂²	semidirect
44. #72306804	C₂²	semidirect
45. #72306803	C₂²	semidirect
46. #72306622	C₂²	semidirect
47. #72306593	C₂²	semidirect
48. #72306590	C₂²	semidirect
49. #72306588	C₂²	semidirect
50. #72306573	C₂²	semidirect
52. #72279391	C₂²	semidirect
53. #72214702	C₂²	semidirect
54. #72214114	C₂²	semidirect
59. #6407634	C₂³	semidirect
60. #6382803	C₂³	semidirect
124. #512608	C₂³	semidirect
125. #512601	C₂³	semidirect
126. #512601	C₂³	semidirect
127. #512601	C₂³	semidirect
128. #483304	C₂³	semidirect
129. #483304	C₂³	semidirect
130. #63038	C₂²⋊C₄	semidirect
131. #63028	C₂²⋊C₄	semidirect
140. #61015	C₂²⋊C₄	semidirect
141. #61011	C₂²⋊C₄	semidirect
153. #20324	C₂²⋊C₄	semidirect
154. #20323	C₂²⋊C₄	semidirect
155. #20323	C₂²⋊C₄	semidirect
156. #20314	C₂²⋊C₄	semidirect
157. #20314	C₂²⋊C₄	semidirect
158. #20302	C₂²⋊C₄	semidirect
159. #20302	C₂²⋊C₄	semidirect
160. #20302	C₂²⋊C₄	semidirect
161. #20294	C₂²⋊C₄	semidirect
162. #20289	C₂²⋊C₄	semidirect
163. #20157	C₂²⋊C₄	semidirect
164. #20150	C₂²⋊C₄	semidirect
165. #20150	C₂²⋊C₄	semidirect
166. #20143	C₂²⋊C₄	semidirect
167. #20143	C₂²⋊C₄	semidirect
168. #20143	C₂²⋊C₄	semidirect
169. #20143	C₂²⋊C₄	semidirect
170. #20138	C₂²⋊C₄	semidirect
171. #20138	C₂²⋊C₄	semidirect
172. #20131	C₂²⋊C₄	semidirect
173. #20125	C₂²⋊C₄	semidirect
174. #20117	C₂²⋊C₄	semidirect
175. #20107	C₂²⋊C₄	semidirect
176. #20107	C₂²⋊C₄	semidirect
177. #20107	C₂²⋊C₄	semidirect
178. #20084	C₂²⋊C₄	semidirect
179. #20084	C₂²⋊C₄	semidirect
180. #20053	C₂²⋊C₄	semidirect
181. #20053	C₂²⋊C₄	semidirect
182. #20040	C₂²⋊C₄	semidirect
183. #20019	C₂²⋊C₄	semidirect
184. #20017	C₂²⋊C₄	semidirect
185. #20017	C₂²⋊C₄	semidirect
186. #20013	C₂²⋊C₄	semidirect
187. #20003	C₂²⋊C₄	semidirect
188. #20003	C₂²⋊C₄	semidirect
189. #20003	C₂²⋊C₄	semidirect
190. #19987	C₂²⋊C₄	semidirect
191. SD₁₆²	C₂²⋊C₄	semidirect
192. SD₁₆²	C₂²⋊C₄	semidirect
198. #19747	C₂²⋊C₄	semidirect
199. #19747	C₂²⋊C₄	semidirect
205. #19729	C₂²⋊C₄	semidirect
208. #19717	C₂²⋊C₄	semidirect
231. #18684	C₂²⋊C₄	semidirect
232. #18684	C₂²⋊C₄	semidirect
257. C₂×#1624	C₂²⋊C₄	semidirect
258. C₂×#1623	C₂²⋊C₄	semidirect
267. #17780	C₂²⋊C₄	semidirect
268. #17780	C₂²⋊C₄	semidirect
273. #17342	C₂²⋊C₄	semidirect
274. #17341	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72339867	2
#72339864	2
#72339863	2
#72339860	2
#72339857	2
#72339853	2
#72339852	2
#72339851	2
#72339850	2
#72339845	2
#72339838	2
#72339834	2
#72339829	2
#72339824	2
#72339815	2