Subgroups — #72248482

Order 3072.

At least 10686 conjugacy classes of subgroups; only the 453 normal subgroups are shown.

The subgroup lattice has 411 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72248479	C₂	1	1	yes	maximal, characteristic, complemented
2	#72248478	C₂	1	1	yes	maximal, characteristic, complemented
3	#72248477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10949242	C₂	1	1	yes	maximal, characteristic, complemented
5	#72248461	C₂	1	1	yes	maximal, characteristic, complemented
6	#72248441	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#394064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10710947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10710720	C₂	1	1	yes	maximal, characteristic, complemented
10	#72248359	C₂	1	1	yes	maximal, characteristic, complemented
11	#72248315	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10826746	C₂	1	1	yes	maximal, characteristic, complemented
13	#72248192	C₂	1	1	yes	maximal, characteristic, complemented
14	#72248029	C₂	1	1	yes	maximal, characteristic, complemented
15	#72247726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#87239	C₂²	1	1	yes	characteristic
17	C₂×#86310	C₂²	1	1	yes	characteristic
18	C₂²×#5244	C₂²	1	1	yes	characteristic, complemented
19	C₂×#84104	C₂²	1	1	yes	characteristic
20	C₂×#84104	C₂²	1	1	yes	characteristic, complemented
21	#11002553	C₂²	1	1	yes	characteristic
22	#11001922	C₂²	1	1	yes	characteristic
23	C₂×#84052	C₂²	1	1	yes	characteristic
24	#10958535	C₂²	1	1	yes	characteristic
25	C₂×#70019	C₂²	1	1	yes	characteristic
26	C₂×#70019	C₂²	1	1	yes	characteristic
27	C₂×#70019	C₂²	1	1	yes	characteristic, complemented
28	C₂×#70019	C₂²	1	1	yes	characteristic, complemented
29	C₂×#71847	C₂²	1	1	yes	characteristic, complemented
30	C₂×#71847	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#4471	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#4471	C₂²	1	1	yes	characteristic, complemented
33	C₂×#71652	C₂²	1	1	yes	characteristic
34	C₂×#71652	C₂²	1	1	yes	characteristic, complemented
35	C₂×#71654	C₂²	1	1	yes	characteristic, complemented
36	C₂×#72142	C₂²	1	1	yes	characteristic, complemented
37	C₂×#72129	C₂²	1	1	yes	characteristic, complemented
38	C₂×#72130	C₂²	1	1	yes	characteristic, complemented
39	#10710134	C₂²	1	1	yes	characteristic, complemented
40	#10710134	C₂²	1	1	yes	characteristic, complemented
41	C₂×#67694	C₂²	1	1	yes	characteristic, complemented
42	C₂×#67694	C₂²	1	1	yes	characteristic, complemented
43	#10700530	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#3484	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#3026	C₂²	1	1	yes	characteristic, complemented
46	C₃×#34980	C₂²	1	1	yes	characteristic
47	C₂×C₃×#1913	C₂²	1	1	yes	characteristic, complemented
48	C₃×#20609	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#1781	C₂²	1	1	yes	characteristic, complemented
50	C₃×#10754	C₂²	1	1	yes	characteristic, complemented
51	#394064	D₃	1	1	yes	characteristic, complemented
52	C₂²×C₃×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
53	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
54	C₂⁴×#67	D₄	1	1	yes	characteristic, complemented
55	C₂²×#1004	D₄	1	1	yes	characteristic, complemented
56	C₂×C₃×#534	D₄	1	1	yes	characteristic, complemented
57	C₂×C₃×#534	C₂³	1	1	yes	characteristic
58	C₂²×C₃×#120	D₄	1	1	yes	characteristic, complemented
59	C₂×C₃×#518	C₂³	1	1	yes	characteristic
60	C₂×#5805	C₂³	1	1	yes	characteristic
61	C₂×#5805	C₂³	1	1	yes	characteristic
62	C₂²×#937	D₄	1	1	yes	characteristic, complemented
63	C₂²×#937	C₂³	1	1	yes	characteristic
64	C₂×#5798	D₄	1	1	yes	characteristic, complemented
65	C₂×#5791	D₄	1	1	yes	characteristic, complemented
66	C₂×#5791	D₄	1	1	yes	characteristic, complemented
67	C₂×#5666	D₄	1	1	yes	characteristic, complemented
68	C₂×#5659	D₄	1	1	yes	characteristic, complemented
69	C₂×#5590	D₄	1	1	yes	characteristic, complemented
70	C₂×#5594	D₄	1	1	yes	characteristic, complemented
71	C₂²×C₃×#99	C₂³	1	1	yes	characteristic
72	C₂²×C₃×#99	C₂³	1	1	yes	characteristic
73	C₃×#2308	D₄	1	1	yes	characteristic, complemented
74	C₃×#2308	C₂³	1	1	yes	characteristic
75	C₂×C₃×#379	D₄	1	1	yes	characteristic, complemented
76	C₂×#5247	D₄	1	1	yes	characteristic, complemented
77	#84104	D₄	1	4	yes	complemented
78	C₂×#5220	D₄	1	1	yes	characteristic, complemented
79	C₂×#5220	C₂³	1	1	yes	characteristic
80	C₂²×#834	C₂³	1	1	yes	characteristic
81	C₂²×#834	C₂³	1	1	yes	characteristic
82	C₂²×#833	C₂³	1	1	yes	characteristic
83	C₂²×#833	C₂³	1	1	yes	characteristic
84	#82886	D₄	1	1	yes	characteristic, complemented
85	#82884	D₄	1	1	yes	characteristic, complemented
86	#82598	D₄	1	1	yes	characteristic, complemented
87	#82594	D₄	1	1	yes	characteristic, complemented
88	#74918	D₄	1	1	yes	characteristic, complemented
89	#74918	D₄	1	1	yes	characteristic, complemented
90	#74912	D₄	1	1	yes	characteristic, complemented
91	#74912	D₄	1	1	yes	characteristic, complemented
92	#74685	D₄	1	1	yes	characteristic, complemented
93	#74684	D₄	1	1	yes	characteristic, complemented
94	#74680	D₄	1	1	yes	characteristic, complemented
95	#74679	D₄	1	1	yes	characteristic, complemented
96	#71652	D₄	1	4	yes	complemented
97	#70019	D₄	1	4	yes	complemented
98	C₂×#3484	C₂×D₃	1	1	yes	characteristic, complemented
99	C₂×#3026	C₂×D₃	1	1	yes	characteristic, complemented
100	#34980	C₂×D₃	1	1	yes	characteristic
101	C₂×#1913	C₂×D₃	1	1	yes	characteristic, complemented
102	#20609	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂×#1781	C₂×D₃	1	1	yes	characteristic, complemented
104	#10754	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂⁶×C₃	C₂×D₄	1	1	yes	characteristic
106	C₂⁶×C₃	C₂×D₄	1	1	yes	characteristic
107	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
109	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
114	C₂⁴×C₃×C₄	C₂×D₄	1	1	yes	characteristic
115	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×#235	C₂×D₄	1	1	yes	characteristic
117	C₂²×#235	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
122	C₃×#518	C₂×D₄	1	2	yes	complemented
123	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
126	C₂²×#217	C₂×D₄	1	1	yes	characteristic
127	C₂²×#217	C₂×D₄	1	1	yes	characteristic
128	#5805	C₂×D₄	1	2	yes	—
129	#5805	C₂×D₄	1	2	yes	—
130	#5805	C₂×D₄	1	2	yes	—
131	#5805	#41	1	2	yes	—
132	C₂×#940	C₂×D₄	1	1	yes	characteristic
133	C₂×#940	C₂×D₄	1	1	yes	characteristic
134	C₂×#940	C₂×D₄	1	1	yes	characteristic
135	C₂×#940	C₂×D₄	1	1	yes	characteristic
136	C₂×#937	C₂×D₄	1	1	yes	characteristic
137	C₂×#937	C₂×D₄	1	1	yes	characteristic
138	C₂×#937	C₂×D₄	1	1	yes	characteristic
139	C₂×#937	C₂×D₄	1	1	yes	characteristic
140	C₂×#936	C₂×D₄	1	1	yes	characteristic
141	C₂×#936	C₂×D₄	1	1	yes	characteristic
142	C₂×#936	C₂×D₄	1	1	yes	characteristic
143	C₂×#936	C₂×D₄	1	1	yes	characteristic
144	C₂×#926	C₂×D₄	1	1	yes	characteristic
145	C₂×#926	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×#99	C₂×D₄	1	2	yes	complemented
147	C₃×#386	C₂×D₄	1	1	yes	characteristic
148	C₃×#386	C₂×D₄	1	1	yes	characteristic
149	C₃×#386	C₂×D₄	1	1	yes	characteristic
150	C₃×#386	C₂×D₄	1	1	yes	characteristic
151	#5220	C₂×D₄	1	1	yes	characteristic
152	#5220	C₂×D₄	1	1	yes	characteristic
153	#5220	C₂×D₄	1	1	yes	characteristic
154	#5220	C₂×D₄	1	1	yes	characteristic
155	C₂×#834	C₂×D₄	1	2	yes	complemented
156	C₂×#833	C₂×D₄	1	2	yes	complemented
157	C₂×#833	C₂×D₄	1	2	yes	complemented
158	C₂²×H(5,𝔽₂)	C₂²×D₃	1	1	yes	characteristic
159	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
160	C₂×#534	#67	1	1	yes	characteristic, complemented
161	C₂×#534	C₂²×D₃	1	1	yes	characteristic
162	C₂²×#120	#67	1	1	yes	characteristic, complemented
163	C₂×#518	C₂²×D₃	1	1	yes	characteristic
164	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
165	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
166	#2308	#67	1	1	yes	characteristic, complemented
167	#2308	C₂²×D₃	1	1	yes	characteristic
168	C₂×#379	#67	1	1	yes	characteristic, complemented
169	C₂⁵×C₃	#120	1	1	yes	characteristic
170	C₂⁵×C₃	#120	1	1	yes	characteristic
171	C₂⁵×C₃	#120	1	1	yes	characteristic
172	C₂⁵×C₃	#120	1	1	yes	characteristic
173	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
174	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
175	C₂⁴×D₃	#120	1	1	yes	characteristic
176	C₂⁴×D₃	#120	1	1	yes	characteristic
177	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
178	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
180	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
181	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
183	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂×#41	1	1	yes	characteristic
185	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂³×C₃×C₄	#120	1	1	yes	characteristic
190	C₂³×C₃×C₄	#120	1	1	yes	characteristic
191	C₂³×C₃×C₄	#120	1	1	yes	characteristic
192	C₂³×C₃×C₄	#120	1	1	yes	characteristic
193	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
194	C₂³×Dic₃	#120	1	1	yes	characteristic
195	C₂³×Dic₃	#120	1	1	yes	characteristic
196	C₂×#235	#120	1	2	yes	—
197	C₂×#235	#121	1	2	yes	—
198	C₂²×D₁₂	#120	1	1	yes	characteristic
199	C₂²×D₁₂	#120	1	1	yes	characteristic
200	C₂²×Dic₆	#120	1	1	yes	characteristic
201	C₂²×Dic₆	#120	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
206	C₂×#217	#120	1	1	yes	characteristic
207	C₂×#217	#120	1	1	yes	characteristic
208	C₂×#217	#120	1	1	yes	characteristic
209	C₂×#217	#120	1	1	yes	characteristic
210	#940	#120	1	2	yes	—
211	#940	#121	1	2	yes	—
212	#940	#121	1	2	yes	—
213	#940	#127	1	2	yes	—
214	#936	#120	1	2	yes	—
215	#936	#121	1	2	yes	—
216	#936	#121	1	2	yes	—
217	#936	#127	1	2	yes	—
218	#926	#120	1	2	yes	—
219	#926	#121	1	2	yes	—
220	C₂×C₄×Dic₃	#120	1	1	yes	characteristic
221	C₂×C₄×Dic₃	#120	1	1	yes	characteristic
222	C₂×C₄×Dic₃	#120	1	1	yes	characteristic
223	C₂×C₄×Dic₃	#120	1	1	yes	characteristic
224	C₂⁶	D₃×D₄	1	1	yes	characteristic
225	C₂⁶	C₂×#67	1	1	yes	characteristic
226	C₂×H(5,𝔽₂)	D₃×D₄	1	2	yes	complemented
227	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
228	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₂×#67	1	1	yes	characteristic
230	C₂³×D₄	C₂×#67	1	1	yes	characteristic
231	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
232	C₂⁴×C₄	D₃×D₄	1	1	yes	characteristic
233	C₂×#123	D₃×D₄	1	1	yes	characteristic
234	C₂×#123	D₃×D₄	1	1	yes	characteristic
235	C₂×#120	D₃×D₄	1	1	yes	characteristic
236	C₂×#120	D₃×D₄	1	1	yes	characteristic
237	#518	D₃×D₄	1	2	yes	complemented
238	C₂²×C₂²⋊C₄	C₂×#67	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂×#67	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂×#67	1	1	yes	characteristic
241	C₂×#99	D₃×D₄	1	2	yes	complemented
242	#386	D₃×D₄	1	1	yes	characteristic
243	#386	D₃×D₄	1	1	yes	characteristic
244	#386	D₃×D₄	1	1	yes	characteristic
245	#386	D₃×D₄	1	1	yes	characteristic
246	C₂⁴×C₃	B(4,𝔽₂)	1	2	yes	—
247	C₂⁴×C₃	B(4,𝔽₂)	1	2	yes	—
248	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
249	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
250	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
251	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
252	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
253	C₂⁴×C₃	D₄²	1	1	yes	characteristic
254	C₂⁴×C₃	D₄²	1	1	yes	characteristic
255	C₂⁴×C₃	D₄²	1	1	yes	characteristic
256	C₂⁴×C₃	D₄²	1	1	yes	characteristic
257	C₂⁴×C₃	D₄²	1	1	yes	characteristic
258	C₂⁴×C₃	D₄²	1	1	yes	characteristic
259	C₂⁴×C₃	#546	1	1	yes	characteristic
260	C₂⁴×C₃	#546	1	1	yes	characteristic
261	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
262	C₂×C₃×D₄	C₂×#121	1	1	yes	characteristic
263	C₂×C₃×D₄	C₂×#121	1	1	yes	characteristic
264	C₂×C₃×D₄	C₂×#127	1	1	yes	characteristic
265	C₂×C₃×D₄	#534	1	1	yes	characteristic
266	C₂×C₃×D₄	#534	1	1	yes	characteristic
267	C₂×C₃×D₄	#535	1	1	yes	characteristic
268	C₂×C₃×D₄	#535	1	1	yes	characteristic
269	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
270	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
271	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
272	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
273	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
274	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
275	C₂×C₃×D₄	#546	1	1	yes	characteristic
276	C₂×C₃×D₄	#546	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂×#121	1	1	yes	characteristic
281	C₂²×C₃×C₄	#534	1	1	yes	characteristic
282	C₂²×C₃×C₄	#534	1	1	yes	characteristic
283	C₂×D₁₂	#392	1	2	yes	complemented
284	C₂×Dic₆	#392	1	2	yes	complemented
285	C₄×Dic₃	#392	1	2	yes	complemented
286	C₄×Dic₃	#392	1	2	yes	complemented
287	C₂⁵	#937	1	1	yes	characteristic
288	C₂⁵	#937	1	1	yes	characteristic
289	C₂⁵	#937	1	1	yes	characteristic
290	C₂⁵	#937	1	1	yes	characteristic
291	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
292	C₂⁵	C₂²×#67	1	1	yes	characteristic
293	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
294	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
295	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
296	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
297	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
298	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
299	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
300	C₂²×D₄	#1004	1	1	yes	characteristic
301	C₂²×D₄	#1004	1	1	yes	characteristic
302	C₂²×D₄	#1004	1	1	yes	characteristic
303	C₂²×D₄	D₃×#41	1	1	yes	characteristic
304	C₂²×D₄	#1009	1	1	yes	characteristic
305	C₂³×C₄	#937	1	1	yes	characteristic
306	C₂³×C₄	#937	1	1	yes	characteristic
307	C₂³×C₄	#937	1	1	yes	characteristic
308	C₂³×C₄	#937	1	1	yes	characteristic
309	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	#937	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	#937	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	#937	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	#937	1	1	yes	characteristic
314	C₂³×C₃	#2403	1	1	yes	characteristic
315	C₂³×C₃	#2403	1	1	yes	characteristic
316	C₂³×C₃	#2403	1	1	yes	characteristic
317	C₂³×C₃	#2408	1	1	yes	characteristic
318	C₂³×C₃	#2408	1	1	yes	characteristic
319	C₂³×C₃	#2410	1	1	yes	characteristic
320	C₂³×C₃	#2410	1	1	yes	characteristic
321	C₂³×C₃	#2410	1	1	yes	characteristic
322	C₂³×C₃	#2433	1	1	yes	characteristic
323	C₂³×C₃	#2433	1	1	yes	characteristic
324	C₂³×C₃	#2846	1	1	yes	characteristic
325	C₂³×C₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
326	C₂³×C₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
327	C₂³×C₃	#3026	1	1	yes	characteristic
328	C₂³×C₃	#3026	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×#392	1	1	yes	characteristic
330	C₂×C₃×C₄	#2403	1	1	yes	characteristic
331	C₂×C₃×C₄	#2410	1	1	yes	characteristic
332	C₂×C₃×C₄	#2613	1	1	yes	characteristic
333	C₂⁴	#5032	1	2	yes	—
334	C₂⁴	#5032	1	2	yes	—
335	C₂⁴	D₃×#120	1	1	yes	characteristic
336	C₂⁴	D₃×#120	1	1	yes	characteristic
337	C₂⁴	#5590	1	1	yes	characteristic
338	C₂⁴	#5590	1	1	yes	characteristic
339	C₂⁴	#5609	1	1	yes	characteristic
340	C₂⁴	#5610	1	1	yes	characteristic
341	C₂⁴	C₂×#937	1	1	yes	characteristic
342	C₂⁴	C₂×#937	1	1	yes	characteristic
343	C₂⁴	C₂×#937	1	1	yes	characteristic
344	C₂⁴	D₄×#67	1	1	yes	characteristic
345	C₂⁴	D₄×#67	1	1	yes	characteristic
346	C₂⁴	D₄×#67	1	1	yes	characteristic
347	C₂⁴	#5829	1	1	yes	characteristic
348	C₂×D₄	D₃×#120	1	1	yes	characteristic
349	C₂×D₄	#5589	1	1	yes	characteristic
350	C₂×D₄	#5590	1	1	yes	characteristic
351	C₂×D₄	#5590	1	1	yes	characteristic
352	C₂×D₄	D₃×#121	1	1	yes	characteristic
353	C₂×D₄	D₃×#121	1	1	yes	characteristic
354	C₂×D₄	#5605	1	1	yes	characteristic
355	C₂×D₄	#5607	1	1	yes	characteristic
356	C₂×D₄	#5609	1	1	yes	characteristic
357	C₂×D₄	#5609	1	1	yes	characteristic
358	C₂×D₄	#5610	1	1	yes	characteristic
359	C₂×D₄	#5612	1	1	yes	characteristic
360	C₂×D₄	D₃×#127	1	1	yes	characteristic
361	C₂×D₄	#5715	1	1	yes	characteristic
362	C₂×D₄	#5717	1	1	yes	characteristic
363	C₂×D₄	#5717	1	1	yes	characteristic
364	C₂²×C₄	D₃×#120	1	1	yes	characteristic
365	C₂²×C₄	D₃×#120	1	1	yes	characteristic
366	C₂²×C₄	D₃×#120	1	1	yes	characteristic
367	C₂²×C₄	#5589	1	1	yes	characteristic
368	C₂²×C₄	D₃×#121	1	1	yes	characteristic
369	C₂²×C₄	#5605	1	1	yes	characteristic
370	C₂²×C₃	#14715	1	1	yes	characteristic
371	C₂²×C₃	#23900	1	1	yes	characteristic
372	C₂²×C₃	#23903	1	1	yes	characteristic
373	C₂²×C₃	#24404	1	1	yes	characteristic
374	C₂²×C₃	#24404	1	1	yes	characteristic
375	C₂²×C₃	#32898	1	1	yes	characteristic
376	C₂²×C₃	#32898	1	1	yes	characteristic
377	C₂³	#76669	1	1	yes	characteristic
378	C₂³	#76673	1	1	yes	characteristic
379	C₂³	#76753	1	1	yes	characteristic
380	C₂³	#76755	1	1	yes	characteristic
381	C₂³	C₂×#5032	1	1	yes	characteristic
382	C₂³	C₂×#5032	1	1	yes	characteristic
383	C₂³	#82604	1	1	yes	characteristic
384	C₂³	#82604	1	1	yes	characteristic
385	C₂³	#82612	1	1	yes	characteristic
386	C₂³	#82640	1	1	yes	characteristic
387	C₂³	#82702	1	1	yes	characteristic
388	C₂³	#82702	1	1	yes	characteristic
389	C₂³	#83175	1	1	yes	characteristic
390	C₂³	#83375	1	1	yes	characteristic
391	C₂³	#83375	1	1	yes	characteristic
392	C₂×C₄	D₃×#392	1	1	yes	characteristic
393	C₂×C₄	#76753	1	1	yes	characteristic
394	C₂×C₄	#76755	1	1	yes	characteristic
395	C₂×C₄	#76760	1	1	yes	characteristic
396	C₂×C₃	#394066	1	1	yes	characteristic
397	C₂×C₃	#511790	1	1	yes	characteristic
398	C₂×C₃	#511793	1	1	yes	characteristic
399	C₂²	#10726560	1	1	yes	characteristic
400	C₂²	#10826766	1	1	yes	characteristic
401	C₂²	#10826793	1	1	yes	characteristic
402	C₂²	#10832525	1	1	yes	characteristic
403	C₂²	#10832525	1	1	yes	characteristic
404	C₂²	#10943957	1	1	yes	characteristic
405	C₂²	#10943957	1	1	yes	characteristic
406	C₃	#72213329	1	1	yes	characteristic, complemented, Sylow
407	C₂	#72231641	1	1	yes	characteristic
408	C₂	#72247727	1	1	yes	characteristic
409	C₂	#72248281	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10943957
commutator, cosocle	C₂³×C₃×D₄	C₂⁴
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₃×#394064	C₂
socle	C₂²×C₃	#32898
hypercenter	#394064	D₃
hypocenter	C₃	#72213329
LCS	G ▷ C₂³×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ #394064

Complements

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

N	H ≅ G/N	type
1. #72248479	C₂	semidirect
2. #72248478	C₂	semidirect
3. #72248477	C₂	semidirect
4. C₂×#10949242	C₂	semidirect
5. #72248461	C₂	semidirect
6. #72248441	C₂	semidirect
7. C₃×#394064	C₂	semidirect
8. C₂×#10710947	C₂	semidirect
9. C₂×#10710720	C₂	semidirect
10. #72248359	C₂	semidirect
11. #72248315	C₂	semidirect
12. C₂×#10826746	C₂	semidirect
13. #72248192	C₂	semidirect
14. #72248029	C₂	semidirect
15. #72247726	C₂	semidirect
18. C₂²×#5244	C₂²	semidirect
20. C₂×#84104	C₂²	semidirect
27. C₂×#70019	C₂²	semidirect
28. C₂×#70019	C₂²	semidirect
29. C₂×#71847	C₂²	semidirect
30. C₂×#71847	C₂²	semidirect
31. C₂²×#4471	C₂²	semidirect
32. C₂²×#4471	C₂²	semidirect
34. C₂×#71652	C₂²	semidirect
35. C₂×#71654	C₂²	semidirect
36. C₂×#72142	C₂²	semidirect
37. C₂×#72129	C₂²	semidirect
38. C₂×#72130	C₂²	semidirect
39. #10710134	C₂²	semidirect
40. #10710134	C₂²	semidirect
41. C₂×#67694	C₂²	semidirect
42. C₂×#67694	C₂²	semidirect
43. #10700530	C₂²	semidirect
44. C₂×C₃×#3484	C₂²	semidirect
45. C₂×C₃×#3026	C₂²	semidirect
47. C₂×C₃×#1913	C₂²	semidirect
48. C₃×#20609	C₂²	semidirect
49. C₂×C₃×#1781	C₂²	semidirect
50. C₃×#10754	C₂²	semidirect
51. #394064	D₃	semidirect
54. C₂⁴×#67	D₄	semidirect
55. C₂²×#1004	D₄	semidirect
56. C₂×C₃×#534	D₄	semidirect
58. C₂²×C₃×#120	D₄	semidirect
62. C₂²×#937	D₄	semidirect
64. C₂×#5798	D₄	semidirect
65. C₂×#5791	D₄	semidirect
66. C₂×#5791	D₄	semidirect
67. C₂×#5666	D₄	semidirect
68. C₂×#5659	D₄	semidirect
69. C₂×#5590	D₄	semidirect
70. C₂×#5594	D₄	semidirect
73. C₃×#2308	D₄	semidirect
75. C₂×C₃×#379	D₄	semidirect
76. C₂×#5247	D₄	semidirect
77. #84104	D₄	semidirect
78. C₂×#5220	D₄	semidirect
84. #82886	D₄	semidirect
85. #82884	D₄	semidirect
86. #82598	D₄	semidirect
87. #82594	D₄	semidirect
88. #74918	D₄	semidirect
89. #74918	D₄	semidirect
90. #74912	D₄	semidirect
91. #74912	D₄	semidirect
92. #74685	D₄	semidirect
93. #74684	D₄	semidirect
94. #74680	D₄	semidirect
95. #74679	D₄	semidirect
96. #71652	D₄	semidirect
97. #70019	D₄	semidirect
98. C₂×#3484	C₂×D₃	semidirect
99. C₂×#3026	C₂×D₃	semidirect
101. C₂×#1913	C₂×D₃	semidirect
102. #20609	C₂×D₃	semidirect
103. C₂×#1781	C₂×D₃	semidirect
104. #10754	C₂×D₃	semidirect
108. C₂×C₃×H(5,𝔽₂)	C₂×D₄	semidirect
122. C₃×#518	C₂×D₄	semidirect
146. C₂×C₃×#99	C₂×D₄	semidirect
155. C₂×#834	C₂×D₄	semidirect
156. C₂×#833	C₂×D₄	semidirect
157. C₂×#833	C₂×D₄	semidirect
160. C₂×#534	#67	semidirect
162. C₂²×#120	#67	semidirect
166. #2308	#67	semidirect
168. C₂×#379	#67	semidirect
226. C₂×H(5,𝔽₂)	D₃×D₄	semidirect
237. #518	D₃×D₄	semidirect
241. C₂×#99	D₃×D₄	semidirect
283. C₂×D₁₂	#392	semidirect
284. C₂×Dic₆	#392	semidirect
285. C₄×Dic₃	#392	semidirect
286. C₄×Dic₃	#392	semidirect
406. C₃	#72213329	semidirect

Maximal subgroups

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

subgroup	index
#72248479	2
#72248478	2
#72248477	2
C₂×#10949242	2
#72248461	2
#72248441	2
C₃×#394064	2
C₂×#10710947	2
C₂×#10710720	2
#72248359	2
#72248315	2
C₂×#10826746	2
#72248192	2
#72248029	2
#72247726	2
#72213329	3