Subgroups — #72248556

Order 3072.

At least 10686 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

The subgroup lattice has 409 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72248554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10949250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10710944	C₂	1	1	yes	maximal, characteristic, complemented
4	#72248525	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#147811	C₂	1	1	yes	maximal, characteristic, complemented
6	#72248456	C₂	1	1	yes	maximal, characteristic, complemented
7	#72248443	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10710719	C₂	1	1	yes	maximal, characteristic, complemented
9	#72248326	C₂	1	1	yes	maximal, characteristic, complemented
10	#72248315	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10826748	C₂	1	1	yes	maximal, characteristic, complemented
12	#72248171	C₂	1	1	yes	maximal, characteristic, complemented
13	#72248124	C₂	1	1	yes	maximal, characteristic, complemented
14	#72248033	C₂	1	1	yes	maximal, characteristic, complemented
15	#72247656	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#85867	C₂²	1	1	yes	characteristic, complemented
17	C₂×#86330	C₂²	1	1	yes	characteristic
18	C₂×#85921	C₂²	1	1	yes	characteristic
19	C₂×#78686	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#5032	C₂²	1	1	yes	characteristic, complemented
21	C₂×#78700	C₂²	1	1	yes	characteristic
22	C₂×#83394	C₂²	1	1	yes	characteristic, complemented
23	#11002541	C₂²	1	1	yes	characteristic
24	#10967725	C₂²	1	1	yes	characteristic
25	C₂×#82604	C₂²	1	1	yes	characteristic
26	#10958535	C₂²	1	1	yes	characteristic
27	C₂×#71860	C₂²	1	1	yes	characteristic, complemented
28	C₂×#70019	C₂²	1	1	yes	characteristic
29	C₂×#70019	C₂²	1	1	yes	characteristic
30	C₂×#70094	C₂²	1	1	yes	characteristic, complemented
31	C₂×#70015	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#4536	C₂²	1	1	yes	characteristic, complemented
33	C₂×#71656	C₂²	1	1	yes	characteristic, complemented
34	C₂×#71652	C₂²	1	1	yes	characteristic
35	#10794454	C₂²	1	1	yes	characteristic, complemented
36	C₂×#70033	C₂²	1	1	yes	characteristic, complemented
37	C₂×#70079	C₂²	1	1	yes	characteristic, complemented
38	C₂×#70035	C₂²	1	1	yes	characteristic, complemented
39	C₂×#70035	C₂²	1	1	yes	characteristic, complemented
40	#10710134	C₂²	1	1	yes	characteristic, complemented
41	C₂×#67698	C₂²	1	1	yes	characteristic, complemented
42	C₂×#67694	C₂²	1	1	yes	characteristic, complemented
43	#10700530	C₂²	1	1	yes	characteristic, complemented
44	C₃×#36702	C₂²	1	1	yes	characteristic
45	C₂×C₃×#2127	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₃×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#1911	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#1889	C₂²	1	1	yes	characteristic, complemented
49	C₃×#12574	C₂²	1	1	yes	characteristic, complemented
50	C₃×#10754	C₂²	1	1	yes	characteristic, complemented
51	#147811	D₃	1	1	yes	characteristic, complemented
52	C₂⁴×#67	D₄	1	1	yes	characteristic, complemented
53	C₂²×#1009	D₄	1	1	yes	characteristic, complemented
54	C₂²×#1004	C₂³	1	1	yes	characteristic
55	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×#535	C₂³	1	1	yes	characteristic
57	C₂²×C₃×#120	C₂³	1	1	yes	characteristic
58	C₂×C₃×#518	C₂³	1	1	yes	characteristic
59	C₂²×#953	D₄	1	1	yes	characteristic, complemented
60	C₂×#5828	D₄	1	1	yes	characteristic, complemented
61	C₂×#5805	C₂³	1	1	yes	characteristic
62	C₂×#5804	C₂³	1	1	yes	characteristic
63	C₂×#5595	D₄	1	1	yes	characteristic, complemented
64	C₂×#5590	D₄	1	1	yes	characteristic, complemented
65	C₂×#5594	D₄	1	1	yes	characteristic, complemented
66	C₂×#5587	D₄	1	1	yes	characteristic, complemented
67	C₂×#5524	D₄	1	1	yes	characteristic, complemented
68	C₂×#5521	D₄	1	1	yes	characteristic, complemented
69	C₂×#5493	D₄	1	1	yes	characteristic, complemented
70	C₂²×#882	D₄	1	1	yes	characteristic, complemented
71	C₂²×C₃×#100	C₂³	1	1	yes	characteristic
72	C₂²×C₃×#99	C₂³	1	1	yes	characteristic
73	C₂²×C₃×#99	C₂³	1	1	yes	characteristic
74	C₃×#2684	D₄	1	1	yes	characteristic, complemented
75	C₃×#2684	D₄	1	1	yes	characteristic, complemented
76	C₃×#2669	D₄	1	1	yes	characteristic, complemented
77	C₃×#2669	D₄	1	1	yes	characteristic, complemented
78	C₃×#2308	C₂³	1	1	yes	characteristic
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	#83190	D₄	1	1	yes	characteristic, complemented
84	#83183	D₄	1	1	yes	characteristic, complemented
85	#83005	D₄	1	1	yes	characteristic, complemented
86	#82989	D₄	1	1	yes	characteristic, complemented
87	#82121	D₄	1	1	yes	characteristic, complemented
88	C₂×#4955	D₄	1	1	yes	characteristic, complemented
89	C₂×#4955	D₄	1	1	yes	characteristic, complemented
90	C₂×#4958	D₄	1	1	yes	characteristic, complemented
91	#78700	D₄	1	4	yes	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	#36702	C₂×D₃	1	1	yes	characteristic
99	C₂×#2127	C₂×D₃	1	1	yes	characteristic, complemented
100	C₂²×AΣL(1,𝔽₁₆)	C₂×D₃	1	1	yes	characteristic, complemented
101	C₂×#1911	C₂×D₃	1	1	yes	characteristic, complemented
102	C₂×#1889	C₂×D₃	1	1	yes	characteristic, complemented
103	#12574	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	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
107	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic
109	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
110	C₂³×#67	C₂×D₄	1	1	yes	characteristic
111	C₂³×#67	C₂×D₄	1	1	yes	characteristic
112	C₂³×#67	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
114	C₂×#1004	C₂×D₄	1	2	yes	complemented
115	C₂²×#235	C₂×D₄	1	1	yes	characteristic
116	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
117	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
126	C₃×#518	C₂×D₄	1	2	yes	complemented
127	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
131	C₂²×#217	C₂×D₄	1	1	yes	characteristic
132	C₂²×#217	C₂×D₄	1	1	yes	characteristic
133	#5805	C₂×D₄	1	2	yes	—
134	#5805	C₂×D₄	1	2	yes	—
135	#5805	C₂×D₄	1	2	yes	—
136	#5805	#41	1	2	yes	—
137	C₂×#940	C₂×D₄	1	1	yes	characteristic
138	C₂×#940	C₂×D₄	1	1	yes	characteristic
139	C₂×#937	C₂×D₄	1	1	yes	characteristic
140	C₂×#937	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×#935	C₂×D₄	1	1	yes	characteristic
144	C₂×#935	C₂×D₄	1	1	yes	characteristic
145	C₂×#926	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×#100	C₂×D₄	1	2	yes	complemented
147	C₂×C₃×#99	C₂×D₄	1	2	yes	complemented
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	C₃×#386	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	#5220	C₂×D₄	1	1	yes	characteristic
156	C₂×#834	C₂×D₄	1	2	yes	complemented
157	C₂×#833	C₂×D₄	1	2	yes	complemented
158	C₂×#535	C₂²×D₃	1	1	yes	characteristic
159	C₂²×#120	C₂²×D₃	1	1	yes	characteristic
160	C₂×#518	C₂²×D₃	1	1	yes	characteristic
161	C₂²×#100	C₂²×D₃	1	1	yes	characteristic
162	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
163	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
164	#2684	D₁₂	1	1	yes	characteristic, complemented
165	#2684	D₁₂	1	1	yes	characteristic, complemented
166	#2669	D₁₂	1	1	yes	characteristic, complemented
167	#2669	D₁₂	1	1	yes	characteristic, complemented
168	#2308	C₂²×D₃	1	1	yes	characteristic
169	C₂⁵×C₃	#120	1	1	yes	characteristic
170	C₂⁵×C₃	#120	1	1	yes	characteristic
171	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
172	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
173	C₂⁴×D₃	#120	1	1	yes	characteristic
174	C₂⁴×D₃	#120	1	1	yes	characteristic
175	C₂⁴×D₃	#120	1	1	yes	characteristic
176	C₂⁴×D₃	#120	1	1	yes	characteristic
177	C₂²×C₃×Q₈	#120	1	1	yes	characteristic
178	C₂²×C₃×D₄	#120	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	C₂²×D₄	1	1	yes	characteristic
185	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
186	C₂²×C₃×D₄	C₂×#41	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	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂²×C₃×D₄	H(5,𝔽₂)	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	C₂³×Dic₃	#120	1	1	yes	characteristic
197	C₂³×Dic₃	#120	1	1	yes	characteristic
198	C₂×#235	#120	1	2	yes	—
199	C₂×#235	#121	1	2	yes	—
200	C₂²×D₁₂	#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×C₃×C₄²	#120	1	1	yes	characteristic
207	C₂×C₃×C₄²	#120	1	1	yes	characteristic
208	C₂×#217	#120	1	1	yes	characteristic
209	C₂×#217	#120	1	1	yes	characteristic
210	C₂×#217	#120	1	1	yes	characteristic
211	C₂×#217	#120	1	1	yes	characteristic
212	#940	#120	1	2	yes	—
213	#940	#121	1	2	yes	—
214	#940	#121	1	2	yes	—
215	#940	#127	1	2	yes	—
216	#936	#120	1	2	yes	—
217	#936	#121	1	2	yes	—
218	#936	#121	1	2	yes	—
219	#936	#127	1	2	yes	—
220	#926	#120	1	2	yes	—
221	#926	#121	1	2	yes	—
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	C₂²×#41	D₃×D₄	1	1	yes	characteristic
226	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
227	C₂×#127	C₂×D₁₂	1	1	yes	characteristic
228	C₂×#127	D₃×D₄	1	1	yes	characteristic
229	C₂×#124	C₂×D₁₂	1	1	yes	characteristic
230	C₂×#124	D₃×D₄	1	1	yes	characteristic
231	C₂×#120	C₂×D₁₂	1	1	yes	characteristic
232	C₂×#120	C₂×D₁₂	1	1	yes	characteristic
233	C₂×#120	D₃×D₄	1	1	yes	characteristic
234	C₂×#120	D₃×D₄	1	1	yes	characteristic
235	#518	D₃×D₄	1	2	yes	complemented
236	C₂×#117	D₃×D₄	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
240	C₂×#100	D₃×D₄	1	2	yes	complemented
241	C₂×#99	D₃×D₄	1	2	yes	complemented
242	#386	C₂×D₁₂	1	1	yes	characteristic
243	#386	C₂×D₁₂	1	1	yes	characteristic
244	#386	D₃×D₄	1	1	yes	characteristic
245	#386	D₃×D₄	1	1	yes	characteristic
246	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
247	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
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	D₄²	1	1	yes	characteristic
252	C₂⁴×C₃	D₄²	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	#546	1	1	yes	characteristic
258	C₂⁴×C₃	#546	1	1	yes	characteristic
259	C₂³×D₃	B(4,𝔽₂)	1	2	yes	—
260	C₂³×D₃	B(4,𝔽₂)	1	2	yes	—
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	#882	1	1	yes	characteristic
288	C₂⁵	#882	1	1	yes	characteristic
289	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
290	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
291	C₂²×Q₈	#882	1	1	yes	characteristic
292	C₂²×D₄	#882	1	1	yes	characteristic
293	C₂²×D₄	C₂²×D₁₂	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	D₃×#41	1	1	yes	characteristic
302	C₂²×D₄	#1009	1	1	yes	characteristic
303	C₂²×D₄	#1009	1	1	yes	characteristic
304	C₂²×D₄	#1009	1	1	yes	characteristic
305	C₂³×C₄	#882	1	1	yes	characteristic
306	C₂³×C₄	#882	1	1	yes	characteristic
307	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
312	C₂×C₄²	#882	1	1	yes	characteristic
313	C₂×C₄²	#882	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	C₂×#882	1	1	yes	characteristic
334	C₂⁴	C₂×#882	1	1	yes	characteristic
335	C₂⁴	D₃×#120	1	1	yes	characteristic
336	C₂⁴	D₃×#120	1	1	yes	characteristic
337	C₂⁴	D₃×#120	1	1	yes	characteristic
338	C₂⁴	#5590	1	1	yes	characteristic
339	C₂⁴	#5609	1	1	yes	characteristic
340	C₂⁴	#5609	1	1	yes	characteristic
341	C₂⁴	#5609	1	1	yes	characteristic
342	C₂⁴	#5609	1	1	yes	characteristic
343	C₂⁴	#5654	1	1	yes	characteristic
344	C₂⁴	#5676	1	1	yes	characteristic
345	C₂⁴	#5717	1	1	yes	characteristic
346	C₂×D₄	D₄×D₁₂	1	1	yes	characteristic
347	C₂×D₄	D₄×D₁₂	1	1	yes	characteristic
348	C₂×D₄	D₄×D₁₂	1	1	yes	characteristic
349	C₂×D₄	#5554	1	1	yes	characteristic
350	C₂×D₄	D₃×#120	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	#5653	1	1	yes	characteristic
359	C₂×D₄	#5654	1	1	yes	characteristic
360	C₂×D₄	#5674	1	1	yes	characteristic
361	C₂×D₄	D₃×#127	1	1	yes	characteristic
362	C₂²×C₄	C₂×#882	1	1	yes	characteristic
363	C₂²×C₄	D₃×#120	1	1	yes	characteristic
364	C₂²×C₄	D₃×#120	1	1	yes	characteristic
365	C₂²×C₄	D₃×#121	1	1	yes	characteristic
366	C₂²×C₄	#5605	1	1	yes	characteristic
367	C₂²×C₄	#5653	1	1	yes	characteristic
368	C₂²×C₃	#14715	1	1	yes	characteristic
369	C₂²×C₃	#23900	1	1	yes	characteristic
370	C₂²×C₃	#23903	1	1	yes	characteristic
371	C₂²×C₃	#24404	1	1	yes	characteristic
372	C₂²×C₃	#24404	1	1	yes	characteristic
373	C₂²×C₃	#32898	1	1	yes	characteristic
374	C₂²×C₃	#32898	1	1	yes	characteristic
375	C₂³	#73861	1	1	yes	characteristic
376	C₂³	#74884	1	1	yes	characteristic
377	C₂³	#74888	1	1	yes	characteristic
378	C₂³	#76314	1	1	yes	characteristic
379	C₂³	#76436	1	1	yes	characteristic
380	C₂³	#76673	1	1	yes	characteristic
381	C₂³	#76753	1	1	yes	characteristic
382	C₂³	#76753	1	1	yes	characteristic
383	C₂³	#76895	1	1	yes	characteristic
384	C₂³	#77108	1	1	yes	characteristic
385	C₂³	#77108	1	1	yes	characteristic
386	C₂³	D₃×B(4,𝔽₂)	1	1	yes	characteristic
387	C₂³	D₃×B(4,𝔽₂)	1	1	yes	characteristic
388	C₂³	#80311	1	1	yes	characteristic
389	C₂³	#80311	1	1	yes	characteristic
390	C₂×C₄	#74884	1	1	yes	characteristic
391	C₂×C₄	#74888	1	1	yes	characteristic
392	C₂×C₄	D₃×#392	1	1	yes	characteristic
393	C₂×C₄	#77122	1	1	yes	characteristic
394	C₂×C₃	#394066	1	1	yes	characteristic
395	C₂×C₃	#511790	1	1	yes	characteristic
396	C₂×C₃	#511793	1	1	yes	characteristic
397	C₂²	#10726564	1	1	yes	characteristic
398	C₂²	#10826763	1	1	yes	characteristic
399	C₂²	#10826796	1	1	yes	characteristic
400	C₂²	#10832523	1	1	yes	characteristic
401	C₂²	#10832523	1	1	yes	characteristic
402	C₂²	#10943959	1	1	yes	characteristic
403	C₂²	#10943959	1	1	yes	characteristic
404	C₃	#72213329	1	1	yes	characteristic, complemented, Sylow
405	C₂	#72219819	1	1	yes	characteristic
406	C₂	#72247597	1	1	yes	characteristic
407	C₂	#72248284	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10943959
commutator, cosocle	C₂³×C₃×D₄	C₂⁴
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₃×#147811	C₂
socle	C₂²×C₃	#32898
hypercenter	#147811	D₃
hypocenter	C₃	#72213329
LCS	G ▷ C₂³×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ #147811

Complements

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

N	H ≅ G/N	type
1. #72248554	C₂	semidirect
2. C₂×#10949250	C₂	semidirect
3. C₂×#10710944	C₂	semidirect
4. #72248525	C₂	semidirect
5. C₃×#147811	C₂	semidirect
6. #72248456	C₂	semidirect
7. #72248443	C₂	semidirect
8. C₂×#10710719	C₂	semidirect
9. #72248326	C₂	semidirect
10. #72248315	C₂	semidirect
11. C₂×#10826748	C₂	semidirect
12. #72248171	C₂	semidirect
13. #72248124	C₂	semidirect
14. #72248033	C₂	semidirect
15. #72247656	C₂	semidirect
16. C₂×#85867	C₂²	semidirect
19. C₂×#78686	C₂²	semidirect
20. C₂²×#5032	C₂²	semidirect
22. C₂×#83394	C₂²	semidirect
27. C₂×#71860	C₂²	semidirect
30. C₂×#70094	C₂²	semidirect
31. C₂×#70015	C₂²	semidirect
32. C₂²×#4536	C₂²	semidirect
33. C₂×#71656	C₂²	semidirect
35. #10794454	C₂²	semidirect
36. C₂×#70033	C₂²	semidirect
37. C₂×#70079	C₂²	semidirect
38. C₂×#70035	C₂²	semidirect
39. C₂×#70035	C₂²	semidirect
40. #10710134	C₂²	semidirect
41. C₂×#67698	C₂²	semidirect
42. C₂×#67694	C₂²	semidirect
43. #10700530	C₂²	semidirect
45. C₂×C₃×#2127	C₂²	semidirect
46. C₂²×C₃×AΣL(1,𝔽₁₆)	C₂²	semidirect
47. C₂×C₃×#1911	C₂²	semidirect
48. C₂×C₃×#1889	C₂²	semidirect
49. C₃×#12574	C₂²	semidirect
50. C₃×#10754	C₂²	semidirect
51. #147811	D₃	semidirect
52. C₂⁴×#67	D₄	semidirect
53. C₂²×#1009	D₄	semidirect
59. C₂²×#953	D₄	semidirect
60. C₂×#5828	D₄	semidirect
63. C₂×#5595	D₄	semidirect
64. C₂×#5590	D₄	semidirect
65. C₂×#5594	D₄	semidirect
66. C₂×#5587	D₄	semidirect
67. C₂×#5524	D₄	semidirect
68. C₂×#5521	D₄	semidirect
69. C₂×#5493	D₄	semidirect
70. C₂²×#882	D₄	semidirect
74. C₃×#2684	D₄	semidirect
75. C₃×#2684	D₄	semidirect
76. C₃×#2669	D₄	semidirect
77. C₃×#2669	D₄	semidirect
83. #83190	D₄	semidirect
84. #83183	D₄	semidirect
85. #83005	D₄	semidirect
86. #82989	D₄	semidirect
87. #82121	D₄	semidirect
88. C₂×#4955	D₄	semidirect
89. C₂×#4955	D₄	semidirect
90. C₂×#4958	D₄	semidirect
91. #78700	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
99. C₂×#2127	C₂×D₃	semidirect
100. C₂²×AΣL(1,𝔽₁₆)	C₂×D₃	semidirect
101. C₂×#1911	C₂×D₃	semidirect
102. C₂×#1889	C₂×D₃	semidirect
103. #12574	C₂×D₃	semidirect
104. #10754	C₂×D₃	semidirect
114. C₂×#1004	C₂×D₄	semidirect
126. C₃×#518	C₂×D₄	semidirect
146. C₂×C₃×#100	C₂×D₄	semidirect
147. C₂×C₃×#99	C₂×D₄	semidirect
156. C₂×#834	C₂×D₄	semidirect
157. C₂×#833	C₂×D₄	semidirect
164. #2684	D₁₂	semidirect
165. #2684	D₁₂	semidirect
166. #2669	D₁₂	semidirect
167. #2669	D₁₂	semidirect
235. #518	D₃×D₄	semidirect
240. C₂×#100	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
404. C₃	#72213329	semidirect

Maximal subgroups

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

subgroup	index
#72248554	2
C₂×#10949250	2
C₂×#10710944	2
#72248525	2
C₃×#147811	2
#72248456	2
#72248443	2
C₂×#10710719	2
#72248326	2
#72248315	2
C₂×#10826748	2
#72248171	2
#72248124	2
#72248033	2
#72247656	2
#72213329	3