Subgroups — #72248495

Order 3072.

At least 10686 conjugacy classes of subgroups; only the 495 normal subgroups are shown.

The subgroup lattice has 431 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72248492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10949251	C₂	1	1	yes	maximal, characteristic, complemented
3	#72248486	C₂	1	1	yes	maximal, characteristic, complemented
4	#72248470	C₂	1	1	yes	maximal, characteristic, complemented
5	#72248443	C₂	1	1	yes	maximal, characteristic, complemented
6	#72248413	C₂	1	1	yes	maximal, characteristic, complemented
7	#72248395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#12707	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10710945	C₂	1	1	yes	maximal, characteristic, complemented
10	#72248338	C₂	1	1	yes	maximal, characteristic, complemented
11	#72248311	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10826746	C₂	1	1	yes	maximal, characteristic, complemented
13	#72248197	C₂	1	1	yes	maximal, characteristic, complemented
14	#72248029	C₂	1	1	yes	maximal, characteristic, complemented
15	#72247737	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#87239	C₂²	1	1	yes	characteristic, complemented
17	C₂×#86333	C₂²	1	1	yes	characteristic
18	C₂×#78686	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#4741	C₂²	1	1	yes	characteristic, complemented
20	C₂×#83394	C₂²	1	1	yes	characteristic
21	C₂×#83394	C₂²	1	1	yes	characteristic, complemented
22	#11002541	C₂²	1	1	yes	characteristic
23	#11001916	C₂²	1	1	yes	characteristic
24	#10967723	C₂²	1	1	yes	characteristic
25	C₂×#84052	C₂²	1	1	yes	characteristic
26	#10958547	C₂²	1	1	yes	characteristic
27	C₂×#70015	C₂²	1	1	yes	characteristic, complemented
28	C₂×#70015	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#4471	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#4471	C₂²	1	1	yes	characteristic, complemented
31	C₂×#70024	C₂²	1	1	yes	characteristic, complemented
32	C₂×#71853	C₂²	1	1	yes	characteristic
33	C₂×#71853	C₂²	1	1	yes	characteristic, complemented
34	C₂×#70022	C₂²	1	1	yes	characteristic, complemented
35	#10794453	C₂²	1	1	yes	characteristic, complemented
36	C₂×#70033	C₂²	1	1	yes	characteristic, complemented
37	C₂×#72129	C₂²	1	1	yes	characteristic, complemented
38	#10710133	C₂²	1	1	yes	characteristic, complemented
39	#10710133	C₂²	1	1	yes	characteristic, complemented
40	C₂×#67694	C₂²	1	1	yes	characteristic, complemented
41	C₂×#67694	C₂²	1	1	yes	characteristic, complemented
42	#10700577	C₂²	1	1	yes	characteristic, complemented
43	#10700532	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#3484	C₂²	1	1	yes	characteristic
45	C₂×C₃×#2127	C₂²	1	1	yes	characteristic
46	C₂×C₃×#2127	C₂²	1	1	yes	characteristic
47	C₂×C₃×#2127	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#2127	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#1781	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×#1781	C₂²	1	1	yes	characteristic, complemented
51	C₂×#12707	D₃	1	1	yes	characteristic, complemented
52	C₂²×C₃×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
53	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
54	C₂⁴×#67	D₄	1	1	yes	characteristic, complemented
55	C₂²×#1004	C₂³	1	1	yes	characteristic
56	C₂×C₃×#535	C₂³	1	1	yes	characteristic
57	C₂×C₃×#535	C₂³	1	1	yes	characteristic
58	C₂×C₃×#525	D₄	1	1	yes	characteristic, complemented
59	C₂×C₃×#525	D₄	1	1	yes	characteristic, complemented
60	C₂×C₃×#518	D₄	1	1	yes	characteristic, complemented
61	C₂²×#953	D₄	1	1	yes	characteristic, complemented
62	C₂×#5804	D₄	1	1	yes	characteristic, complemented
63	C₂×#5804	C₂³	1	1	yes	characteristic
64	C₂²×#937	D₄	1	1	yes	characteristic, complemented
65	C₂²×#937	C₂³	1	1	yes	characteristic
66	C₂×#5798	C₂³	1	1	yes	characteristic
67	C₂×#5720	D₄	1	1	yes	characteristic, complemented
68	C₂×#5717	D₄	1	1	yes	characteristic, complemented
69	C₂×#5683	D₄	1	1	yes	characteristic, complemented
70	C₂×#5679	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	C₂²×C₃×#99	C₂³	1	1	yes	characteristic
74	C₂²×C₃×#99	C₂³	1	1	yes	characteristic
75	C₂×#5247	D₄	1	1	yes	characteristic, complemented
76	C₂×#5247	D₄	1	1	yes	characteristic, complemented
77	#84043	D₄	1	1	yes	characteristic, complemented
78	#84043	C₂³	1	1	yes	characteristic
79	C₂×#5220	D₄	1	1	yes	characteristic, complemented
80	C₂×#5220	C₂³	1	1	yes	characteristic
81	C₂²×#833	C₂³	1	1	yes	characteristic
82	C₂²×#833	C₂³	1	1	yes	characteristic
83	#83394	D₄	1	4	yes	complemented
84	#83190	D₄	1	1	yes	characteristic, complemented
85	#83190	D₄	1	1	yes	characteristic, complemented
86	#83190	D₄	1	1	yes	characteristic, complemented
87	#83183	D₄	1	1	yes	characteristic, complemented
88	#83174	D₄	1	1	yes	characteristic, complemented
89	#83173	D₄	1	1	yes	characteristic, complemented
90	#83005	D₄	1	1	yes	characteristic, complemented
91	#83005	D₄	1	1	yes	characteristic, complemented
92	#83005	D₄	1	1	yes	characteristic, complemented
93	#82989	D₄	1	1	yes	characteristic, complemented
94	#82957	D₄	1	1	yes	characteristic, complemented
95	#82956	D₄	1	1	yes	characteristic, complemented
96	C₃×#2127	D₄	1	4	yes	complemented
97	#71853	D₄	1	4	yes	complemented
98	C₂×#3484	C₂×D₃	1	1	yes	characteristic
99	C₂×#2127	C₂×D₃	1	1	yes	characteristic
100	C₂×#2127	C₂×D₃	1	1	yes	characteristic
101	C₂×#2127	C₂×D₃	1	1	yes	characteristic, complemented
102	C₂×#2127	C₂×D₃	1	1	yes	characteristic, complemented
103	C₂×#1781	C₂×D₃	1	1	yes	characteristic, complemented
104	C₂×#1781	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	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₃×#41	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	C₂³×#67	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
117	C₂×#1004	C₂×D₄	1	2	yes	complemented
118	C₃×#535	C₂×D₄	1	2	yes	—
119	C₃×#535	C₂×D₄	1	2	yes	—
120	C₃×#535	C₂×D₄	1	2	yes	—
121	C₃×#535	#41	1	2	yes	—
122	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
132	C₂²×#217	C₂×D₄	1	1	yes	characteristic
133	C₂²×#217	C₂×D₄	1	1	yes	characteristic
134	C₂²×#217	C₂×D₄	1	1	yes	characteristic
135	C₂²×#217	C₂×D₄	1	1	yes	characteristic
136	C₂²×#217	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×#937	C₂×D₄	1	1	yes	characteristic
141	C₂×#937	C₂×D₄	1	1	yes	characteristic
142	C₂×#937	C₂×D₄	1	1	yes	characteristic
143	#5798	C₂×D₄	1	2	yes	complemented
144	C₂×#935	C₂×D₄	1	1	yes	characteristic
145	C₂×#935	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×#99	C₂×D₄	1	2	yes	complemented
147	C₂×C₃×#99	C₂×D₄	1	2	yes	complemented
148	#5220	C₂×D₄	1	1	yes	characteristic
149	#5220	C₂×D₄	1	1	yes	characteristic
150	#5220	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	#5220	C₂×D₄	1	1	yes	characteristic
156	C₂×#833	C₂×D₄	1	2	yes	complemented
157	C₂×#833	C₂×D₄	1	2	yes	complemented
158	C₂²×H(5,𝔽₂)	D₁₂	1	1	yes	characteristic, complemented
159	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
160	C₂×#535	C₂²×D₃	1	1	yes	characteristic
161	C₂×#535	C₂²×D₃	1	1	yes	characteristic
162	C₂×#525	D₁₂	1	1	yes	characteristic, complemented
163	C₂×#525	D₁₂	1	1	yes	characteristic, complemented
164	C₂×#518	D₁₂	1	1	yes	characteristic, complemented
165	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
166	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
167	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
168	C₂²×#99	C₂²×D₃	1	1	yes	characteristic
169	#2127	#67	1	4	yes	complemented
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	C₂⁴×D₃	#120	1	1	yes	characteristic
178	C₂×C₃×#41	#120	1	2	yes	—
179	C₂×C₃×#41	#121	1	2	yes	—
180	C₂²×C₃×Q₈	#120	1	1	yes	characteristic
181	C₂²×C₃×Q₈	#120	1	1	yes	characteristic
182	C₂²×C₃×D₄	#120	1	1	yes	characteristic
183	C₂²×C₃×D₄	#120	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	C₂²×D₄	1	1	yes	characteristic
187	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
188	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
190	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
191	C₂²×C₃×D₄	C₂×#41	1	1	yes	characteristic
192	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂²×C₃×D₄	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂³×C₃×C₄	#120	1	1	yes	characteristic
197	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
198	C₂³×Dic₃	#120	1	1	yes	characteristic
199	C₂³×Dic₃	#120	1	1	yes	characteristic
200	C₂³×Dic₃	#120	1	1	yes	characteristic
201	C₂³×Dic₃	#120	1	1	yes	characteristic
202	C₂³×Dic₃	#120	1	1	yes	characteristic
203	C₃×#127	#120	1	2	yes	—
204	C₃×#127	#121	1	2	yes	—
205	C₃×#127	#121	1	2	yes	—
206	C₃×#127	#127	1	2	yes	—
207	C₃×#124	#120	1	2	yes	—
208	C₃×#124	#121	1	2	yes	—
209	C₃×#124	#121	1	2	yes	—
210	C₃×#124	#127	1	2	yes	—
211	C₃×#117	#120	1	2	yes	—
212	C₃×#117	#121	1	2	yes	—
213	C₂×C₃×C₄²	#120	1	1	yes	characteristic
214	C₂×C₃×C₄²	#120	1	1	yes	characteristic
215	C₂×C₃×C₄²	#120	1	1	yes	characteristic
216	C₂×C₃×C₄²	#120	1	1	yes	characteristic
217	C₂×#217	#120	1	1	yes	characteristic
218	C₂×#217	#120	1	1	yes	characteristic
219	C₂×#217	#120	1	1	yes	characteristic
220	C₂×#217	#120	1	1	yes	characteristic
221	C₂×#217	#120	1	1	yes	characteristic
222	C₂×#217	#120	1	1	yes	characteristic
223	C₂×#217	#120	1	1	yes	characteristic
224	C₂×#217	#120	1	1	yes	characteristic
225	C₂⁶	D₃×D₄	1	1	yes	characteristic
226	C₂⁶	D₃×D₄	1	1	yes	characteristic
227	C₂²×#41	C₂×D₁₂	1	1	yes	characteristic
228	C₂²×#41	C₂×D₁₂	1	1	yes	characteristic
229	C₂³×D₄	C₂×D₁₂	1	1	yes	characteristic
230	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
231	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
232	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
233	C₂⁴×C₄	C₂×D₁₂	1	1	yes	characteristic
234	#535	#235	1	2	yes	—
235	#535	D₃×D₄	1	2	yes	—
236	#535	D₃×D₄	1	2	yes	—
237	#535	C₂×#67	1	2	yes	—
238	C₂×#127	D₃×D₄	1	1	yes	characteristic
239	C₂×#127	D₃×D₄	1	1	yes	characteristic
240	C₂×#127	D₃×D₄	1	1	yes	characteristic
241	C₂×#127	D₃×D₄	1	1	yes	characteristic
242	C₂×#124	D₃×D₄	1	1	yes	characteristic
243	C₂×#124	D₃×D₄	1	1	yes	characteristic
244	C₂×#124	D₃×D₄	1	1	yes	characteristic
245	C₂×#124	D₃×D₄	1	1	yes	characteristic
246	C₂×#117	C₂×D₁₂	1	1	yes	characteristic
247	C₂×#117	C₂×D₁₂	1	1	yes	characteristic
248	C₂×#99	C₂×#67	1	2	yes	complemented
249	C₂×#99	C₂×#67	1	2	yes	complemented
250	C₂⁴×C₃	B(4,𝔽₂)	1	2	yes	—
251	C₂⁴×C₃	B(4,𝔽₂)	1	2	yes	—
252	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
253	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
254	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
255	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
256	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
257	C₂⁴×C₃	D₄²	1	1	yes	characteristic
258	C₂⁴×C₃	D₄²	1	1	yes	characteristic
259	C₂⁴×C₃	D₄²	1	1	yes	characteristic
260	C₂⁴×C₃	D₄²	1	1	yes	characteristic
261	C₂⁴×C₃	D₄²	1	1	yes	characteristic
262	C₂⁴×C₃	D₄²	1	1	yes	characteristic
263	C₂⁴×C₃	#546	1	1	yes	characteristic
264	C₂⁴×C₃	#546	1	1	yes	characteristic
265	C₂×C₃×Q₈	#392	1	2	yes	complemented
266	C₂×C₃×D₄	#392	1	2	yes	complemented
267	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
268	C₂×C₃×D₄	C₂×#121	1	1	yes	characteristic
269	C₂×C₃×D₄	C₂×#121	1	1	yes	characteristic
270	C₂×C₃×D₄	C₂×#127	1	1	yes	characteristic
271	C₂×C₃×D₄	#534	1	1	yes	characteristic
272	C₂×C₃×D₄	#534	1	1	yes	characteristic
273	C₂×C₃×D₄	#535	1	1	yes	characteristic
274	C₂×C₃×D₄	#535	1	1	yes	characteristic
275	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
276	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
277	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
278	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
279	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
280	C₂×C₃×D₄	D₄²	1	1	yes	characteristic
281	C₂×C₃×D₄	#546	1	1	yes	characteristic
282	C₂×C₃×D₄	#546	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂×#121	1	1	yes	characteristic
287	C₂²×C₃×C₄	#534	1	1	yes	characteristic
288	C₂²×C₃×C₄	#534	1	1	yes	characteristic
289	C₃×C₄²	#392	1	2	yes	complemented
290	C₃×C₄²	#392	1	2	yes	complemented
291	C₂⁵	#882	1	1	yes	characteristic
292	C₂⁵	#882	1	1	yes	characteristic
293	C₂⁵	#882	1	1	yes	characteristic
294	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
295	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
296	C₂×#41	#882	1	2	yes	—
297	C₂×#41	#930	1	2	yes	—
298	C₂²×Q₈	#882	1	1	yes	characteristic
299	C₂²×Q₈	#882	1	1	yes	characteristic
300	C₂²×D₄	#882	1	1	yes	characteristic
301	C₂²×D₄	#882	1	1	yes	characteristic
302	C₂²×D₄	C₂×#235	1	1	yes	characteristic
303	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
304	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
305	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
306	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
307	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
308	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
309	C₂²×D₄	#1004	1	1	yes	characteristic
310	C₂²×D₄	#1004	1	1	yes	characteristic
311	C₂²×D₄	#1004	1	1	yes	characteristic
312	C₂²×D₄	#1004	1	1	yes	characteristic
313	C₂²×D₄	C₂²×#67	1	1	yes	characteristic
314	C₂³×C₄	#882	1	1	yes	characteristic
315	C₂³×C₄	C₂²×D₁₂	1	1	yes	characteristic
316	#127	#884	1	2	yes	—
317	#127	#884	1	2	yes	—
318	#127	#937	1	2	yes	—
319	#127	#940	1	2	yes	—
320	#124	#884	1	2	yes	—
321	#124	#884	1	2	yes	—
322	#124	#937	1	2	yes	—
323	#124	#940	1	2	yes	—
324	#117	#882	1	2	yes	—
325	#117	#930	1	2	yes	—
326	C₂×C₄²	#882	1	1	yes	characteristic
327	C₂×C₄²	#882	1	1	yes	characteristic
328	C₂×C₄²	#882	1	1	yes	characteristic
329	C₂×C₄²	#882	1	1	yes	characteristic
330	C₂³×C₃	#2403	1	1	yes	characteristic
331	C₂³×C₃	#2403	1	1	yes	characteristic
332	C₂³×C₃	#2403	1	1	yes	characteristic
333	C₂³×C₃	#2408	1	1	yes	characteristic
334	C₂³×C₃	#2408	1	1	yes	characteristic
335	C₂³×C₃	#2410	1	1	yes	characteristic
336	C₂³×C₃	#2410	1	1	yes	characteristic
337	C₂³×C₃	#2410	1	1	yes	characteristic
338	C₂³×C₃	#2433	1	1	yes	characteristic
339	C₂³×C₃	#2433	1	1	yes	characteristic
340	C₂³×C₃	#2846	1	1	yes	characteristic
341	C₂³×C₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
342	C₂³×C₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
343	C₂³×C₃	#3026	1	1	yes	characteristic
344	C₂³×C₃	#3026	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×#392	1	1	yes	characteristic
346	C₂×C₃×C₄	#2403	1	1	yes	characteristic
347	C₂×C₃×C₄	#2410	1	1	yes	characteristic
348	C₂×C₃×C₄	#2613	1	1	yes	characteristic
349	C₂⁴	#4741	1	2	yes	—
350	C₂⁴	#4741	1	2	yes	—
351	C₂⁴	C₂×#882	1	1	yes	characteristic
352	C₂⁴	#5490	1	1	yes	characteristic
353	C₂⁴	#5490	1	1	yes	characteristic
354	C₂⁴	D₃×#120	1	1	yes	characteristic
355	C₂⁴	D₃×#120	1	1	yes	characteristic
356	C₂⁴	D₃×#120	1	1	yes	characteristic
357	C₂⁴	D₃×#120	1	1	yes	characteristic
358	C₂⁴	#5590	1	1	yes	characteristic
359	C₂⁴	#5590	1	1	yes	characteristic
360	C₂⁴	#5590	1	1	yes	characteristic
361	C₂⁴	#5590	1	1	yes	characteristic
362	C₂⁴	D₄×#67	1	1	yes	characteristic
363	C₂⁴	D₄×#67	1	1	yes	characteristic
364	C₂×Q₈	#4960	1	2	yes	complemented
365	C₂×D₄	#4960	1	2	yes	complemented
366	C₂×D₄	C₂×#884	1	1	yes	characteristic
367	C₂×D₄	C₂×#884	1	1	yes	characteristic
368	C₂×D₄	#5490	1	1	yes	characteristic
369	C₂×D₄	#5490	1	1	yes	characteristic
370	C₂×D₄	#5589	1	1	yes	characteristic
371	C₂×D₄	#5589	1	1	yes	characteristic
372	C₂×D₄	#5590	1	1	yes	characteristic
373	C₂×D₄	#5590	1	1	yes	characteristic
374	C₂×D₄	#5590	1	1	yes	characteristic
375	C₂×D₄	#5590	1	1	yes	characteristic
376	C₂×D₄	#5592	1	1	yes	characteristic
377	C₂×D₄	#5592	1	1	yes	characteristic
378	C₂×D₄	C₂×#937	1	1	yes	characteristic
379	C₂×D₄	D₄×#67	1	1	yes	characteristic
380	C₂×D₄	D₄×#67	1	1	yes	characteristic
381	C₂×D₄	C₂×#940	1	1	yes	characteristic
382	C₂²×C₄	C₂×#882	1	1	yes	characteristic
383	C₂²×C₄	C₂×#882	1	1	yes	characteristic
384	C₂²×C₄	C₂×#882	1	1	yes	characteristic
385	C₂²×C₄	#5493	1	1	yes	characteristic
386	C₂²×C₄	#5493	1	1	yes	characteristic
387	C₂²×C₄	C₂×#930	1	1	yes	characteristic
388	C₄²	#4960	1	2	yes	complemented
389	C₄²	#4960	1	2	yes	complemented
390	C₂²×C₃	#14715	1	1	yes	characteristic
391	C₂²×C₃	#23900	1	1	yes	characteristic
392	C₂²×C₃	#23903	1	1	yes	characteristic
393	C₂²×C₃	#24404	1	1	yes	characteristic
394	C₂²×C₃	#24404	1	1	yes	characteristic
395	C₂²×C₃	#32898	1	1	yes	characteristic
396	C₂²×C₃	#32898	1	1	yes	characteristic
397	C₂³	#73824	1	1	yes	characteristic
398	C₂³	#73824	1	1	yes	characteristic
399	C₂³	#73852	1	1	yes	characteristic
400	C₂³	#73854	1	1	yes	characteristic
401	C₂³	#73854	1	1	yes	characteristic
402	C₂³	#73861	1	1	yes	characteristic
403	C₂³	C₂×#4741	1	1	yes	characteristic
404	C₂³	C₂×#4741	1	1	yes	characteristic
405	C₂³	#78686	1	1	yes	characteristic
406	C₂³	#78686	1	1	yes	characteristic
407	C₂³	#82127	1	1	yes	characteristic
408	C₂³	#82588	1	1	yes	characteristic
409	C₂³	#82588	1	1	yes	characteristic
410	C₂³	#82604	1	1	yes	characteristic
411	C₂³	#82604	1	1	yes	characteristic
412	C₂×C₄	#73852	1	1	yes	characteristic
413	C₂×C₄	#73855	1	1	yes	characteristic
414	C₂×C₄	C₂×#4960	1	1	yes	characteristic
415	C₂×C₄	#82127	1	1	yes	characteristic
416	C₂×C₃	#394066	1	1	yes	characteristic
417	C₂×C₃	#511790	1	1	yes	characteristic
418	C₂×C₃	#511793	1	1	yes	characteristic
419	C₂²	#10726565	1	1	yes	characteristic
420	C₂²	#10826769	1	1	yes	characteristic
421	C₂²	#10826797	1	1	yes	characteristic
422	C₂²	#10832522	1	1	yes	characteristic
423	C₂²	#10832522	1	1	yes	characteristic
424	C₂²	#10943960	1	1	yes	characteristic
425	C₂²	#10943960	1	1	yes	characteristic
426	C₃	#72213329	1	1	yes	characteristic, complemented, Sylow
427	C₂	#72231723	1	1	yes	characteristic
428	C₂	#72247737	1	1	yes	characteristic
429	C₂	#72248282	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10943960
commutator, cosocle	C₂³×C₃×D₄	C₂⁴
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₂×C₃×#12707	C₂
socle	C₂²×C₃	#32898
hypercenter	C₂×#12707	D₃
hypocenter	C₃	#72213329
LCS	G ▷ C₂³×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ C₂×#12707

Complements

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

N	H ≅ G/N	type
1. #72248492	C₂	semidirect
2. C₂×#10949251	C₂	semidirect
3. #72248486	C₂	semidirect
4. #72248470	C₂	semidirect
5. #72248443	C₂	semidirect
6. #72248413	C₂	semidirect
7. #72248395	C₂	semidirect
8. C₂×C₃×#12707	C₂	semidirect
9. C₂×#10710945	C₂	semidirect
10. #72248338	C₂	semidirect
11. #72248311	C₂	semidirect
12. C₂×#10826746	C₂	semidirect
13. #72248197	C₂	semidirect
14. #72248029	C₂	semidirect
15. #72247737	C₂	semidirect
16. C₂×#87239	C₂²	semidirect
18. C₂×#78686	C₂²	semidirect
19. C₂²×#4741	C₂²	semidirect
21. C₂×#83394	C₂²	semidirect
27. C₂×#70015	C₂²	semidirect
28. C₂×#70015	C₂²	semidirect
29. C₂²×#4471	C₂²	semidirect
30. C₂²×#4471	C₂²	semidirect
31. C₂×#70024	C₂²	semidirect
33. C₂×#71853	C₂²	semidirect
34. C₂×#70022	C₂²	semidirect
35. #10794453	C₂²	semidirect
36. C₂×#70033	C₂²	semidirect
37. C₂×#72129	C₂²	semidirect
38. #10710133	C₂²	semidirect
39. #10710133	C₂²	semidirect
40. C₂×#67694	C₂²	semidirect
41. C₂×#67694	C₂²	semidirect
42. #10700577	C₂²	semidirect
43. #10700532	C₂²	semidirect
47. C₂×C₃×#2127	C₂²	semidirect
48. C₂×C₃×#2127	C₂²	semidirect
49. C₂×C₃×#1781	C₂²	semidirect
50. C₂×C₃×#1781	C₂²	semidirect
51. C₂×#12707	D₃	semidirect
52. C₂²×C₃×H(5,𝔽₂)	D₄	semidirect
54. C₂⁴×#67	D₄	semidirect
58. C₂×C₃×#525	D₄	semidirect
59. C₂×C₃×#525	D₄	semidirect
60. C₂×C₃×#518	D₄	semidirect
61. C₂²×#953	D₄	semidirect
62. C₂×#5804	D₄	semidirect
64. C₂²×#937	D₄	semidirect
67. C₂×#5720	D₄	semidirect
68. C₂×#5717	D₄	semidirect
69. C₂×#5683	D₄	semidirect
70. C₂×#5679	D₄	semidirect
75. C₂×#5247	D₄	semidirect
76. C₂×#5247	D₄	semidirect
77. #84043	D₄	semidirect
79. C₂×#5220	D₄	semidirect
83. #83394	D₄	semidirect
84. #83190	D₄	semidirect
85. #83190	D₄	semidirect
86. #83190	D₄	semidirect
87. #83183	D₄	semidirect
88. #83174	D₄	semidirect
89. #83173	D₄	semidirect
90. #83005	D₄	semidirect
91. #83005	D₄	semidirect
92. #83005	D₄	semidirect
93. #82989	D₄	semidirect
94. #82957	D₄	semidirect
95. #82956	D₄	semidirect
96. C₃×#2127	D₄	semidirect
97. #71853	D₄	semidirect
101. C₂×#2127	C₂×D₃	semidirect
102. C₂×#2127	C₂×D₃	semidirect
103. C₂×#1781	C₂×D₃	semidirect
104. C₂×#1781	C₂×D₃	semidirect
117. C₂×#1004	C₂×D₄	semidirect
143. #5798	C₂×D₄	semidirect
146. C₂×C₃×#99	C₂×D₄	semidirect
147. C₂×C₃×#99	C₂×D₄	semidirect
156. C₂×#833	C₂×D₄	semidirect
157. C₂×#833	C₂×D₄	semidirect
158. C₂²×H(5,𝔽₂)	D₁₂	semidirect
162. C₂×#525	D₁₂	semidirect
163. C₂×#525	D₁₂	semidirect
164. C₂×#518	D₁₂	semidirect
169. #2127	#67	semidirect
248. C₂×#99	C₂×#67	semidirect
249. C₂×#99	C₂×#67	semidirect
265. C₂×C₃×Q₈	#392	semidirect
266. C₂×C₃×D₄	#392	semidirect
289. C₃×C₄²	#392	semidirect
290. C₃×C₄²	#392	semidirect
364. C₂×Q₈	#4960	semidirect
365. C₂×D₄	#4960	semidirect
388. C₄²	#4960	semidirect
389. C₄²	#4960	semidirect
426. C₃	#72213329	semidirect

Maximal subgroups

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

subgroup	index
#72248492	2
C₂×#10949251	2
#72248486	2
#72248470	2
#72248443	2
#72248413	2
#72248395	2
C₂×C₃×#12707	2
C₂×#10710945	2
#72248338	2
#72248311	2
C₂×#10826746	2
#72248197	2
#72248029	2
#72247737	2
#72213329	3