Subgroups — #72248142

Order 3072.

At least 7858 conjugacy classes of subgroups; only the 453 normal subgroups are shown.

The subgroup lattice has 383 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72248136	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10949270	C₂	1	1	yes	maximal, characteristic, complemented
3	#72248128	C₂	1	1	yes	maximal, characteristic, complemented
4	#72248126	C₂	1	1	yes	maximal, characteristic, complemented
5	#72248117	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10710962	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#147573	C₂	1	1	yes	maximal, characteristic, complemented
8	#72248110	C₂	1	1	yes	maximal, characteristic, complemented
9	#72248107	C₂	1	1	yes	maximal, characteristic, complemented
10	#72248105	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10826600	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10710732	C₂	1	1	yes	maximal, characteristic, complemented
13	#72248044	C₂	1	1	yes	maximal, characteristic, complemented
14	#72248004	C₂	1	1	yes	maximal, characteristic, complemented
15	#72247985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#87277	C₂²	1	1	yes	characteristic, complemented
17	C₂×#87284	C₂²	1	1	yes	characteristic
18	C₂×#86052	C₂²	1	1	yes	characteristic
19	C₂×#78691	C₂²	1	1	yes	characteristic, complemented
20	C₂×#78690	C₂²	1	1	yes	characteristic, complemented
21	C₂×#82936	C₂²	1	1	yes	characteristic, complemented
22	C₂×#78717	C₂²	1	1	yes	characteristic
23	#11430883	C₂²	1	1	yes	characteristic
24	#11016711	C₂²	1	1	yes	characteristic
25	#10978442	C₂²	1	1	yes	characteristic
26	#10958702	C₂²	1	1	yes	characteristic
27	C₂×#70149	C₂²	1	1	yes	characteristic
28	C₂×#70061	C₂²	1	1	yes	characteristic
29	C₂×#70146	C₂²	1	1	yes	characteristic, complemented
30	C₂×#70057	C₂²	1	1	yes	characteristic, complemented
31	C₂×#70145	C₂²	1	1	yes	characteristic, complemented
32	C₂×#70056	C₂²	1	1	yes	characteristic, complemented
33	C₂×#70137	C₂²	1	1	yes	characteristic, complemented
34	C₂×#70047	C₂²	1	1	yes	characteristic
35	C₂×#71714	C₂²	1	1	yes	characteristic, complemented
36	C₂×#70136	C₂²	1	1	yes	characteristic, complemented
37	C₂×#72141	C₂²	1	1	yes	characteristic, complemented
38	#10794502	C₂²	1	1	yes	characteristic, complemented
39	#10794486	C₂²	1	1	yes	characteristic, complemented
40	#10710168	C₂²	1	1	yes	characteristic, complemented
41	#10710156	C₂²	1	1	yes	characteristic, complemented
42	#10700562	C₂²	1	1	yes	characteristic, complemented
43	#10700514	C₂²	1	1	yes	characteristic, complemented
44	C₃×#35512	C₂²	1	1	yes	characteristic
45	C₂×C₃×#2120	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#2120	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#1795	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#1795	C₂²	1	1	yes	characteristic, complemented
49	C₃×#12587	C₂²	1	1	yes	characteristic, complemented
50	C₃×#12583	C₂²	1	1	yes	characteristic, complemented
51	#147573	D₃	1	1	yes	characteristic, complemented
52	C₂²×C₃×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
53	C₂×#5964	C₂³	1	1	yes	characteristic
54	C₂³×D₃×D₄	D₄	1	1	yes	characteristic, complemented
55	C₂×C₃×#525	D₄	1	1	yes	characteristic, complemented
56	C₂×C₃×#525	C₂³	1	1	yes	characteristic
57	C₂²×C₃×#121	D₄	1	1	yes	characteristic, complemented
58	C₂×#5830	D₄	1	1	yes	characteristic, complemented
59	C₂×#5830	D₄	1	1	yes	characteristic, complemented
60	C₂×#5830	C₂³	1	1	yes	characteristic
61	C₂×#5830	C₂³	1	1	yes	characteristic
62	C₂×#5828	D₄	1	1	yes	characteristic, complemented
63	C₂×#5828	C₂³	1	1	yes	characteristic
64	C₂×#5819	C₂³	1	1	yes	characteristic
65	C₂²×#940	D₄	1	1	yes	characteristic, complemented
66	C₂×#5798	D₄	1	1	yes	characteristic, complemented
67	C₂×#5666	D₄	1	2	yes	complemented
68	C₂×#5590	D₄	1	2	yes	complemented
69	C₂×C₃×#413	C₂³	1	1	yes	characteristic
70	C₂×C₃×#413	C₂³	1	1	yes	characteristic
71	C₂×C₃×#410	C₂³	1	1	yes	characteristic
72	C₂×C₃×#410	C₂³	1	1	yes	characteristic
73	C₃×#2311	D₄	1	1	yes	characteristic, complemented
74	C₃×#2311	C₂³	1	1	yes	characteristic
75	C₃×#2309	D₄	1	1	yes	characteristic, complemented
76	#84086	D₄	1	1	yes	characteristic, complemented
77	#84086	C₂³	1	1	yes	characteristic
78	C₂×#5240	C₂³	1	1	yes	characteristic
79	C₂×#5237	C₂³	1	1	yes	characteristic
80	#84044	D₄	1	1	yes	characteristic, complemented
81	#82908	D₄	1	1	yes	characteristic, complemented
82	#82888	D₄	1	1	yes	characteristic, complemented
83	#82600	D₄	1	1	yes	characteristic, complemented
84	#82597	D₄	1	1	yes	characteristic, complemented
85	#78717	D₄	1	4	yes	complemented
86	#76496	D₄	1	2	yes	complemented
87	#76495	D₄	1	2	yes	complemented
88	#76469	D₄	1	2	yes	complemented
89	#76464	D₄	1	2	yes	complemented
90	#70061	D₄	1	4	yes	complemented
91	#70047	D₄	1	4	yes	complemented
92	#35512	C₂×D₃	1	1	yes	characteristic
93	C₂×#2120	C₂×D₃	1	1	yes	characteristic, complemented
94	C₂×#2120	C₂×D₃	1	1	yes	characteristic, complemented
95	C₂×#1795	C₂×D₃	1	1	yes	characteristic, complemented
96	C₂×#1795	C₂×D₃	1	1	yes	characteristic, complemented
97	#12587	C₂×D₃	1	1	yes	characteristic, complemented
98	#12583	C₂×D₃	1	1	yes	characteristic, complemented
99	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
103	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
104	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
105	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₃×C₄	C₂×D₄	1	1	yes	characteristic
107	#5964	C₂×D₄	1	2	yes	complemented
108	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
109	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
110	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
118	#5830	C₂×D₄	1	2	yes	—
119	#5830	C₂×D₄	1	2	yes	—
120	#5830	C₂×D₄	1	2	yes	—
121	#5830	#41	1	2	yes	—
122	#5819	C₂×D₄	1	2	yes	complemented
123	C₂×#947	C₂×D₄	1	2	yes	—
124	C₂×#940	C₂×D₄	1	2	yes	—
125	C₂×#937	C₂×D₄	1	1	yes	characteristic
126	C₂×#937	C₂×D₄	1	2	yes	—
127	C₂×#937	C₂×D₄	1	2	yes	—
128	C₂×#937	C₂×D₄	1	1	yes	characteristic
129	C₂×#935	C₂×D₄	1	1	yes	characteristic
130	C₂×#935	C₂×D₄	1	1	yes	characteristic
131	C₂×#926	C₂×D₄	1	1	yes	characteristic
132	C₂×#926	C₂×D₄	1	1	yes	characteristic
133	C₂×#926	C₂×D₄	1	1	yes	characteristic
134	C₂×#926	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×Dic₃	C₂×D₄	1	1	yes	characteristic
136	C₃×#413	C₂×D₄	1	2	yes	complemented
137	C₃×#410	C₂×D₄	1	2	yes	complemented
138	C₃×#410	C₂×D₄	1	2	yes	complemented
139	C₃×#391	C₂×D₄	1	2	yes	—
140	C₃×#390	C₂×D₄	1	2	yes	—
141	#5240	C₂×D₄	1	2	yes	complemented
142	#5229	C₂×D₄	1	1	yes	characteristic
143	#5229	C₂×D₄	1	1	yes	characteristic
144	#5221	C₂×D₄	1	1	yes	characteristic
145	#5221	C₂×D₄	1	1	yes	characteristic
146	C₂²×H(5,𝔽₂)	C₂²×D₃	1	1	yes	characteristic
147	C₂×#525	D₁₂	1	1	yes	characteristic, complemented
148	C₂×#525	C₂²×D₃	1	1	yes	characteristic
149	C₂²×#121	D₁₂	1	1	yes	characteristic, complemented
150	C₂×#413	C₂²×D₃	1	1	yes	characteristic
151	C₂×#413	C₂²×D₃	1	1	yes	characteristic
152	C₂×#410	C₂²×D₃	1	1	yes	characteristic
153	C₂×#410	C₂²×D₃	1	1	yes	characteristic
154	#2311	D₁₂	1	1	yes	characteristic, complemented
155	#2311	C₂²×D₃	1	1	yes	characteristic
156	#2309	D₁₂	1	1	yes	characteristic, complemented
157	C₂⁵×C₃	#120	1	1	yes	characteristic
158	C₂⁴×D₃	#120	1	1	yes	characteristic
159	C₂⁴×D₃	#120	1	2	yes	—
160	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃×#41	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₃×#41	C₂×#41	1	1	yes	characteristic
164	C₂×C₃×#41	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₃×#41	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₃×#41	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₃×#41	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂²×C₃×Q₈	#120	1	1	yes	characteristic
169	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic
170	C₂²×C₃×D₄	#120	1	1	yes	characteristic
171	C₂²×C₃×D₄	#120	1	1	yes	characteristic
172	C₂²×C₃×D₄	#120	1	1	yes	characteristic
173	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
174	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
175	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
176	C₂³×C₃×C₄	#120	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
178	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
179	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
180	C₂³×Dic₃	#120	1	1	yes	characteristic
181	C₂²×D₁₂	#120	1	2	yes	—
182	C₂²×D₁₂	#120	1	2	yes	—
183	C₂²×D₁₂	#121	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	#120	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
186	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
187	C₂×C₃×C₄²	#120	1	2	yes	—
188	C₂×#217	#120	1	1	yes	characteristic
189	C₂×#217	#120	1	1	yes	characteristic
190	C₂×#217	#120	1	2	yes	—
191	#947	#121	1	4	yes	—
192	#947	#127	1	4	yes	—
193	#940	#120	1	4	yes	—
194	#940	#121	1	4	yes	—
195	#926	#120	1	2	yes	—
196	#926	#121	1	2	yes	—
197	C₂×C₄⋊Dic₃	#120	1	1	yes	characteristic
198	C₂×C₄⋊Dic₃	#120	1	1	yes	characteristic
199	C₂×C₄×Dic₃	#120	1	2	yes	—
200	C₂×C₄×Dic₃	#120	1	1	yes	characteristic
201	C₂×C₄×Dic₃	#120	1	1	yes	characteristic
202	C₂²×#41	C₂×D₁₂	1	1	yes	characteristic
203	C₂²×#41	D₃×D₄	1	1	yes	characteristic
204	C₂²×#41	D₃×D₄	1	1	yes	characteristic
205	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
206	C₂³×D₄	C₂×D₁₂	1	1	yes	characteristic
207	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
208	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
209	C₂⁴×C₄	C₂×D₁₂	1	1	yes	characteristic
210	C₂×#123	D₃×D₄	1	1	yes	characteristic
211	C₂×#123	D₃×D₄	1	1	yes	characteristic
212	C₂×#120	D₃×D₄	1	1	yes	characteristic
213	C₂×#120	D₃×D₄	1	1	yes	characteristic
214	C₂×#117	C₂×D₁₂	1	1	yes	characteristic
215	C₂×#117	C₂×D₁₂	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	C₂×D₁₂	1	1	yes	characteristic
217	#413	D₃×D₄	1	2	yes	complemented
218	#410	D₃×D₄	1	2	yes	complemented
219	#410	D₃×D₄	1	2	yes	complemented
220	#391	D₃×D₄	1	2	yes	—
221	#390	D₃×D₄	1	2	yes	—
222	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
223	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
224	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
225	C₂×C₃×Q₈	C₂×#121	1	1	yes	characteristic
226	C₂×C₃×Q₈	C₂×#127	1	1	yes	characteristic
227	C₂×C₃×Q₈	#535	1	1	yes	characteristic
228	C₂×C₃×Q₈	#535	1	1	yes	characteristic
229	C₂×C₃×D₄	B(4,𝔽₂)	1	2	yes	—
230	C₂×C₃×D₄	B(4,𝔽₂)	1	2	yes	—
231	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂×#121	1	1	yes	characteristic
233	C₂×C₃×D₄	#534	1	1	yes	characteristic
234	C₂×C₃×D₄	#534	1	1	yes	characteristic
235	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
236	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
237	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
238	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
239	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
240	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
241	C₂×C₃×D₄	#546	1	1	yes	characteristic
242	C₂×C₃×D₄	#546	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂×#121	1	1	yes	characteristic
249	C₂²×C₃×C₄	#534	1	1	yes	characteristic
250	C₂²×C₃×C₄	#534	1	1	yes	characteristic
251	C₂²×C₃×C₄	D₄²	1	1	yes	characteristic
252	C₂²×C₃×C₄	D₄²	1	1	yes	characteristic
253	C₂²×C₃×C₄	D₄²	1	1	yes	characteristic
254	C₂²×C₃×C₄	D₄²	1	1	yes	characteristic
255	C₂²×C₃×C₄	D₄²	1	1	yes	characteristic
256	C₂²×C₃×C₄	D₄²	1	1	yes	characteristic
257	C₂²×C₃×C₄	#546	1	1	yes	characteristic
258	C₂²×C₃×C₄	#546	1	1	yes	characteristic
259	C₂×D₁₂	#392	1	4	yes	—
260	C₄×Dic₃	#392	1	4	yes	—
261	C₂⁵	#882	1	1	yes	characteristic
262	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
263	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
264	C₂×#41	C₂×D₃×D₄	1	1	yes	characteristic
265	C₂×#41	#1004	1	1	yes	characteristic
266	C₂×#41	D₃×#41	1	1	yes	characteristic
267	C₂×#41	#1009	1	1	yes	characteristic
268	C₂×#41	#1009	1	1	yes	characteristic
269	C₂×#41	#1009	1	1	yes	characteristic
270	C₂²×Q₈	#882	1	1	yes	characteristic
271	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic
272	C₂²×D₄	#882	1	1	yes	characteristic
273	C₂²×D₄	#882	1	1	yes	characteristic
274	C₂²×D₄	#882	1	1	yes	characteristic
275	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
276	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
277	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
278	C₂³×C₄	#882	1	1	yes	characteristic
279	C₂³×C₄	C₂²×D₁₂	1	1	yes	characteristic
280	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
281	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
282	C₂×C₄⋊C₄	#882	1	2	yes	—
283	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
285	C₂×C₄²	#882	1	2	yes	—
286	C₂³×C₃	#2403	1	1	yes	characteristic
287	C₂³×C₃	#2403	1	1	yes	characteristic
288	C₂³×C₃	#2403	1	1	yes	characteristic
289	C₂³×C₃	#2410	1	1	yes	characteristic
290	C₂³×C₃	#2410	1	1	yes	characteristic
291	C₂³×C₃	#2410	1	1	yes	characteristic
292	C₂³×C₃	#2846	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×#392	1	1	yes	characteristic
294	C₂×C₃×C₄	#2403	1	1	yes	characteristic
295	C₂×C₃×C₄	#2408	1	1	yes	characteristic
296	C₂×C₃×C₄	#2408	1	1	yes	characteristic
297	C₂×C₃×C₄	#2410	1	1	yes	characteristic
298	C₂×C₃×C₄	#2433	1	1	yes	characteristic
299	C₂×C₃×C₄	#2433	1	1	yes	characteristic
300	C₂×C₃×C₄	#2613	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
303	C₂×C₃×C₄	#3026	1	1	yes	characteristic
304	C₂×C₃×C₄	#3026	1	1	yes	characteristic
305	C₂⁴	C₂×#882	1	1	yes	characteristic
306	C₂⁴	D₃×#120	1	1	yes	characteristic
307	C₂⁴	D₃×#120	1	1	yes	characteristic
308	C₂×Q₈	D₃×#121	1	1	yes	characteristic
309	C₂×Q₈	#5607	1	1	yes	characteristic
310	C₂×Q₈	#5674	1	1	yes	characteristic
311	C₂×Q₈	D₃×#127	1	1	yes	characteristic
312	C₂×D₄	#4741	1	2	yes	—
313	C₂×D₄	#4741	1	2	yes	—
314	C₂×D₄	D₃×#120	1	1	yes	characteristic
315	C₂×D₄	#5590	1	1	yes	characteristic
316	C₂×D₄	D₃×#121	1	1	yes	characteristic
317	C₂×D₄	#5605	1	1	yes	characteristic
318	C₂×D₄	#5609	1	1	yes	characteristic
319	C₂×D₄	#5609	1	1	yes	characteristic
320	C₂×D₄	#5609	1	1	yes	characteristic
321	C₂×D₄	#5609	1	1	yes	characteristic
322	C₂×D₄	#5653	1	1	yes	characteristic
323	C₂×D₄	#5654	1	1	yes	characteristic
324	C₂×D₄	#5676	1	1	yes	characteristic
325	C₂×D₄	#5717	1	1	yes	characteristic
326	C₂²×C₄	C₂×#882	1	1	yes	characteristic
327	C₂²×C₄	C₂×#882	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₁₂	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₁₂	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₁₂	1	1	yes	characteristic
331	C₂²×C₄	#5554	1	1	yes	characteristic
332	C₂²×C₄	D₃×#120	1	1	yes	characteristic
333	C₂²×C₄	D₃×#120	1	1	yes	characteristic
334	C₂²×C₄	D₃×#120	1	1	yes	characteristic
335	C₂²×C₄	#5590	1	1	yes	characteristic
336	C₂²×C₄	D₃×#121	1	1	yes	characteristic
337	C₂²×C₄	#5605	1	1	yes	characteristic
338	C₂²×C₄	#5609	1	1	yes	characteristic
339	C₂²×C₄	#5609	1	1	yes	characteristic
340	C₂²×C₄	#5653	1	1	yes	characteristic
341	C₂²×C₄	#5654	1	1	yes	characteristic
342	C₂²×C₃	#14715	1	1	yes	characteristic
343	C₂²×C₃	#32898	1	1	yes	characteristic
344	C₂²×C₃	#32898	1	1	yes	characteristic
345	C₃×C₄	#23900	1	1	yes	characteristic
346	C₃×C₄	#23903	1	1	yes	characteristic
347	C₃×C₄	#24404	1	1	yes	characteristic
348	C₃×C₄	#24404	1	1	yes	characteristic
349	C₂³	#73861	1	1	yes	characteristic
350	C₂³	#74884	1	1	yes	characteristic
351	C₂³	#74888	1	1	yes	characteristic
352	C₂³	#76753	1	1	yes	characteristic
353	C₂³	#76753	1	1	yes	characteristic
354	C₂³	#77108	1	1	yes	characteristic
355	C₂³	#77108	1	1	yes	characteristic
356	C₂×C₄	#74884	1	1	yes	characteristic
357	C₂×C₄	#74888	1	1	yes	characteristic
358	C₂×C₄	#76314	1	1	yes	characteristic
359	C₂×C₄	#76436	1	1	yes	characteristic
360	C₂×C₄	#76673	1	1	yes	characteristic
361	C₂×C₄	D₃×#392	1	1	yes	characteristic
362	C₂×C₄	#76895	1	1	yes	characteristic
363	C₂×C₄	#77122	1	1	yes	characteristic
364	C₂×C₄	C₂×#4741	1	1	yes	characteristic
365	C₂×C₄	C₂×#4741	1	1	yes	characteristic
366	C₂×C₄	#78686	1	1	yes	characteristic
367	C₂×C₄	#78686	1	1	yes	characteristic
368	C₂×C₃	#394066	1	1	yes	characteristic
369	C₂×C₃	#511819	1	1	yes	characteristic
370	C₂×C₃	#511827	1	1	yes	characteristic
371	C₂²	#10726564	1	1	yes	characteristic
372	C₂²	#10943960	1	1	yes	characteristic
373	C₂²	#10943960	1	1	yes	characteristic
374	C₄	#10826770	1	1	yes	characteristic
375	C₄	#10826799	1	1	yes	characteristic
376	C₄	#10832527	1	1	yes	characteristic
377	C₄	#10832527	1	1	yes	characteristic
378	C₃	#72215601	1	1	yes	characteristic, complemented, Sylow
379	C₂	#72245915	1	1	yes	characteristic
380	C₂	#72247717	1	1	yes	characteristic
381	C₂	#72247806	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10943960
commutator, cosocle	C₂²×C₃×#41	C₂⁴
Frattini	C₂²×#41	C₂³×D₃
Fitting	C₃×#147573	C₂
socle	C₂²×C₃	#32898
hypercenter	#147573	D₃
hypocenter	C₃	#72215601
LCS	G ▷ C₂²×C₃×#41 ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×H(5,𝔽₂) ◁ #147573

Complements

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

N	H ≅ G/N	type
1. #72248136	C₂	semidirect
2. C₂×#10949270	C₂	semidirect
3. #72248128	C₂	semidirect
4. #72248126	C₂	semidirect
5. #72248117	C₂	semidirect
6. C₂×#10710962	C₂	semidirect
7. C₃×#147573	C₂	semidirect
8. #72248110	C₂	semidirect
9. #72248107	C₂	semidirect
10. #72248105	C₂	semidirect
11. C₂×#10826600	C₂	semidirect
12. C₂×#10710732	C₂	semidirect
13. #72248044	C₂	semidirect
14. #72248004	C₂	semidirect
15. #72247985	C₂	semidirect
16. C₂×#87277	C₂²	semidirect
19. C₂×#78691	C₂²	semidirect
20. C₂×#78690	C₂²	semidirect
21. C₂×#82936	C₂²	semidirect
29. C₂×#70146	C₂²	semidirect
30. C₂×#70057	C₂²	semidirect
31. C₂×#70145	C₂²	semidirect
32. C₂×#70056	C₂²	semidirect
33. C₂×#70137	C₂²	semidirect
35. C₂×#71714	C₂²	semidirect
36. C₂×#70136	C₂²	semidirect
37. C₂×#72141	C₂²	semidirect
38. #10794502	C₂²	semidirect
39. #10794486	C₂²	semidirect
40. #10710168	C₂²	semidirect
41. #10710156	C₂²	semidirect
42. #10700562	C₂²	semidirect
43. #10700514	C₂²	semidirect
45. C₂×C₃×#2120	C₂²	semidirect
46. C₂×C₃×#2120	C₂²	semidirect
47. C₂×C₃×#1795	C₂²	semidirect
48. C₂×C₃×#1795	C₂²	semidirect
49. C₃×#12587	C₂²	semidirect
50. C₃×#12583	C₂²	semidirect
51. #147573	D₃	semidirect
54. C₂³×D₃×D₄	D₄	semidirect
55. C₂×C₃×#525	D₄	semidirect
57. C₂²×C₃×#121	D₄	semidirect
58. C₂×#5830	D₄	semidirect
59. C₂×#5830	D₄	semidirect
62. C₂×#5828	D₄	semidirect
65. C₂²×#940	D₄	semidirect
66. C₂×#5798	D₄	semidirect
67. C₂×#5666	D₄	semidirect
68. C₂×#5590	D₄	semidirect
73. C₃×#2311	D₄	semidirect
75. C₃×#2309	D₄	semidirect
76. #84086	D₄	semidirect
80. #84044	D₄	semidirect
81. #82908	D₄	semidirect
82. #82888	D₄	semidirect
83. #82600	D₄	semidirect
84. #82597	D₄	semidirect
85. #78717	D₄	semidirect
86. #76496	D₄	semidirect
87. #76495	D₄	semidirect
88. #76469	D₄	semidirect
89. #76464	D₄	semidirect
90. #70061	D₄	semidirect
91. #70047	D₄	semidirect
93. C₂×#2120	C₂×D₃	semidirect
94. C₂×#2120	C₂×D₃	semidirect
95. C₂×#1795	C₂×D₃	semidirect
96. C₂×#1795	C₂×D₃	semidirect
97. #12587	C₂×D₃	semidirect
98. #12583	C₂×D₃	semidirect
107. #5964	C₂×D₄	semidirect
122. #5819	C₂×D₄	semidirect
136. C₃×#413	C₂×D₄	semidirect
137. C₃×#410	C₂×D₄	semidirect
138. C₃×#410	C₂×D₄	semidirect
141. #5240	C₂×D₄	semidirect
147. C₂×#525	D₁₂	semidirect
149. C₂²×#121	D₁₂	semidirect
154. #2311	D₁₂	semidirect
156. #2309	D₁₂	semidirect
217. #413	D₃×D₄	semidirect
218. #410	D₃×D₄	semidirect
219. #410	D₃×D₄	semidirect
378. C₃	#72215601	semidirect

Maximal subgroups

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

subgroup	index
#72248136	2
C₂×#10949270	2
#72248128	2
#72248126	2
#72248117	2
C₂×#10710962	2
C₃×#147573	2
#72248110	2
#72248107	2
#72248105	2
C₂×#10826600	2
C₂×#10710732	2
#72248044	2
#72248004	2
#72247985	2
#72215601	3