Subgroups — #72324296

Order 4096.

At least 19202 conjugacy classes of subgroups; only the 727 normal subgroups are shown.

The subgroup lattice has 466 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72324295	C₂	1	2	yes	maximal, complemented
2	#72324291	C₂	1	2	yes	maximal, complemented
3	#72324287	C₂	1	2	yes	maximal, complemented
4	#72324269	C₂	1	2	yes	maximal, complemented
5	#72310205	C₂	1	1	yes	maximal, characteristic, complemented
6	#72309800	C₂²	1	1	yes	characteristic, complemented
7	#72309483	C₂	1	1	yes	maximal, characteristic, complemented
8	#72305966	C₂	1	1	yes	maximal, characteristic
9	#72305962	C₄	1	2	yes	complemented
10	#72305961	C₂²	1	2	yes	—
11	#72305944	C₄	1	1	yes	characteristic, complemented
12	#72305934	C₄	1	1	yes	characteristic, complemented
13	#72303517	C₄	1	2	yes	complemented
14	#72303442	C₄	1	1	yes	characteristic, complemented
15	#72266553	C₂²	1	2	yes	—
16	#72260562	C₂²	1	1	yes	characteristic, complemented
17	#72260562	C₂²	1	2	yes	complemented
18	#72259117	C₂²	1	2	yes	complemented
19	#72256119	C₂²	1	1	yes	characteristic, complemented
20	#72237886	C₂	1	1	yes	maximal, characteristic, complemented
21	#72237884	C₂²	1	2	yes	complemented
22	#72237603	C₂	1	1	yes	maximal, characteristic, complemented
23	#72237600	C₂²	1	2	yes	complemented
24	#72237583	C₂²	1	2	yes	complemented
25	#72235242	C₂²	1	1	yes	characteristic, complemented
26	#72234724	C₂²	1	2	yes	complemented
27	#72234640	C₄	1	1	yes	characteristic, complemented
28	#72234636	C₂²	1	1	yes	characteristic
29	#72226102	C₂	1	1	yes	maximal, characteristic, complemented
30	#72226018	C₂	1	1	yes	maximal, characteristic, complemented
31	#72226008	C₂²	1	2	yes	complemented
32	#72226008	C₂²	1	2	yes	complemented
33	#72226006	C₂²	1	2	yes	complemented
34	#72225987	C₂²	1	2	yes	complemented
35	#72225870	C₂²	1	1	yes	characteristic, complemented
36	#72225713	C₂²	1	1	yes	characteristic, complemented
37	#72219314	C₂²	1	1	yes	characteristic, complemented
38	#72219311	C₂²	1	1	yes	characteristic, complemented
39	#72219264	C₂²	1	1	yes	characteristic
40	#72219257	C₂²	1	1	yes	characteristic
41	C₂²×#3532	D₄	1	1	yes	characteristic
42	C₂²×#3484	D₄	1	1	yes	characteristic
43	C₂×#46996	D₄	1	1	yes	characteristic
44	C₂×#34980	C₂³	1	1	yes	characteristic
45	#6374251	C₂³	1	1	yes	characteristic, complemented
46	#6374128	C₂³	1	1	yes	characteristic, complemented
47	#5474299	C₂×C₄	1	2	yes	—
48	#5227995	D₄	1	2	yes	—
49	#5227995	D₄	1	2	yes	—
50	#5119613	D₄	1	2	yes	—
51	#5037287	D₄	1	2	yes	—
52	#5035967	D₄	1	2	yes	—
53	#5025789	D₄	1	1	yes	characteristic
54	#5025782	C₂×C₄	1	1	yes	characteristic
55	#5024691	C₂×C₄	1	1	yes	characteristic
56	#5021140	C₂×C₄	1	1	yes	characteristic
57	#5021138	D₄	1	1	yes	characteristic
58	#5020751	D₄	1	2	yes	—
59	#5020751	D₄	1	1	yes	characteristic
60	#4975876	C₂×C₄	1	2	yes	—
61	#4957774	C₂×C₄	1	2	yes	—
62	#4957774	D₄	1	2	yes	—
63	#4932466	D₄	1	2	yes	—
64	#4930495	C₂×C₄	1	1	yes	characteristic
65	#4930495	D₄	1	1	yes	characteristic
66	#4930494	C₂×C₄	1	1	yes	characteristic
67	#4930494	D₄	1	1	yes	characteristic
68	#4466055	D₄	1	2	yes	—
69	#4430405	C₂×C₄	1	1	yes	characteristic
70	#4423579	D₄	1	2	yes	—
71	#4422949	D₄	1	1	yes	characteristic
72	#4420586	C₂×C₄	1	1	yes	characteristic
73	#4380237	C₂³	1	2	yes	—
74	#4122215	C₂×C₄	1	2	yes	—
75	#4044431	C₂×C₄	1	2	yes	—
76	#4044431	D₄	1	2	yes	—
77	#4033842	C₂×C₄	1	2	yes	—
78	#4033842	D₄	1	2	yes	—
79	#2435299	D₄	1	2	yes	—
80	#2109240	D₄	1	2	yes	—
81	#2039918	C₂×C₄	1	2	yes	—
82	#1499560	C₂×C₄	1	2	yes	—
83	#1499560	D₄	1	2	yes	—
84	#1495667	D₄	1	2	yes	—
85	#1442757	C₂×C₄	1	2	yes	—
86	#845298	D₄	1	2	yes	—
87	#763514	D₄	1	2	yes	—
88	#763333	C₂³	1	2	yes	—
89	#763333	C₂³	1	1	yes	characteristic
90	#686187	C₂×C₄	1	1	yes	characteristic
91	#648360	D₄	1	2	yes	—
92	#648360	D₄	1	1	yes	characteristic
93	#647656	D₄	1	1	yes	characteristic
94	#616961	D₄	1	1	yes	characteristic
95	#616960	C₂³	1	1	yes	characteristic
96	#612460	C₂×C₄	1	2	yes	—
97	#612460	D₄	1	2	yes	—
98	C₂×#15947	D₄	1	1	yes	characteristic
99	#576160	D₄	1	1	yes	characteristic
100	#552670	D₄	1	1	yes	characteristic
101	C₂²×#1438	D₄	1	1	yes	characteristic
102	#188122	C₂³	1	2	yes	complemented
103	#188109	C₂³	1	1	yes	characteristic, complemented
104	#188049	C₂³	1	2	yes	complemented
105	#188049	C₂³	1	1	yes	characteristic, complemented
106	C₂³×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
107	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂²×#551	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×H(3,𝔽₄)	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×#560	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×#535	C₂×D₄	1	2	yes	—
113	C₂²×#535	C₂×D₄	1	1	yes	characteristic
114	C₂²×#534	C₂×D₄	1	1	yes	characteristic
115	C₂²×#534	C₂⁴	1	1	yes	characteristic
116	C₂²×#525	C₂²⋊C₄	1	2	yes	complemented
117	C₂³×#120	C₂×D₄	1	1	yes	characteristic
118	C₂³×#120	C₂×D₄	1	1	yes	characteristic
119	C₂²×#518	C₂²⋊C₄	1	1	yes	characteristic, complemented
120	C₂×#2811	C₂²⋊C₄	1	2	yes	complemented
121	C₂×#2760	C₂²⋊C₄	1	2	yes	complemented
122	C₂×#2679	C₂²⋊C₄	1	2	yes	complemented
123	C₂×#2840	C₂²⋊C₄	1	1	yes	characteristic, complemented
124	C₂×#2840	C₂²⋊C₄	1	2	yes	complemented
125	C₂×#2849	C₂²×C₄	1	1	yes	characteristic
126	C₂×#2849	C₂×D₄	1	1	yes	characteristic
127	C₂×#2846	C₂×D₄	1	1	yes	characteristic
128	C₂×#2846	C₂×D₄	1	1	yes	characteristic
129	C₂×#2846	C₂×D₄	1	2	yes	—
130	C₂×#2430	C₂²×C₄	1	2	yes	—
131	C₂×#2430	C₂×D₄	1	2	yes	—
132	C₂×#2430	C₂×D₄	1	2	yes	—
133	C₂×#2404	C₂×D₄	1	2	yes	—
134	C₂×#2431	C₂×D₄	1	2	yes	—
135	C₂×#2403	C₂²⋊C₄	1	1	yes	characteristic, complemented
136	C₂×#2403	C₂²⋊C₄	1	2	yes	complemented
137	C₂×#2615	C₂×D₄	1	2	yes	—
138	C₂×#2613	C₂²×C₄	1	1	yes	characteristic
139	C₂×#2613	C₂×D₄	1	1	yes	characteristic
140	C₂×#2613	C₂×D₄	1	1	yes	characteristic
141	C₂×#2613	C₂×D₄	1	1	yes	characteristic
142	C₂×#2308	C₂×D₄	1	1	yes	characteristic
143	C₂×#2308	C₂×D₄	1	1	yes	characteristic
144	C₂²×#379	C₂×D₄	1	1	yes	characteristic
145	C₂³×#95	C₂²⋊C₄	1	2	yes	complemented
146	#17105	C₂²⋊C₄	1	2	yes	complemented
147	#17105	C₂²⋊C₄	1	2	yes	complemented
148	#17084	C₂²⋊C₄	1	2	yes	complemented
149	#17084	C₂²⋊C₄	1	2	yes	complemented
150	#16247	C₂²⋊C₄	1	2	yes	complemented
151	#16211	C₂²⋊C₄	1	2	yes	complemented
152	#16167	C₂²⋊C₄	1	2	yes	complemented
153	#16167	C₂²⋊C₄	1	2	yes	complemented
154	#15948	C₂²×C₄	1	1	yes	characteristic
155	#15948	C₂²×C₄	1	1	yes	characteristic
156	#15947	C₂²⋊C₄	1	1	yes	characteristic
157	#15947	C₂²⋊C₄	1	1	yes	characteristic
158	#15947	C₂²⋊C₄	1	1	yes	characteristic
159	#15947	C₂²⋊C₄	1	1	yes	characteristic
160	#15947	C₂×D₄	1	1	yes	characteristic
161	#15947	C₂×D₄	1	1	yes	characteristic
162	#15833	C₂²⋊C₄	1	2	yes	complemented
163	#15833	C₂²⋊C₄	1	2	yes	complemented
164	#15673	C₂×D₄	1	2	yes	—
165	#15673	C₂×D₄	1	2	yes	—
166	#15673	C₂×D₄	1	2	yes	—
167	#15668	C₂²×C₄	1	2	yes	—
168	#15668	C₂×D₄	1	2	yes	—
169	#15662	C₂²⋊C₄	1	2	yes	complemented
170	#15662	C₂²⋊C₄	1	2	yes	complemented
171	#15467	C₂²⋊C₄	1	2	yes	complemented
172	#15467	C₂²⋊C₄	1	2	yes	complemented
173	#15467	C₂²⋊C₄	1	2	yes	complemented
174	#15467	C₂²⋊C₄	1	2	yes	complemented
175	#15412	C₂²×C₄	1	2	yes	—
176	#15412	C₂×D₄	1	2	yes	—
177	#15310	C₂×D₄	1	2	yes	—
178	#15310	C₂×D₄	1	2	yes	—
179	#15310	C₂×D₄	1	2	yes	—
180	#15267	C₂²⋊C₄	1	2	yes	complemented
181	#15267	C₂²⋊C₄	1	2	yes	complemented
182	#15267	C₂²⋊C₄	1	2	yes	complemented
183	#15267	C₂²⋊C₄	1	2	yes	complemented
184	#15262	C₂²×C₄	1	1	yes	characteristic
185	#15262	C₂×D₄	1	2	yes	—
186	#15261	C₂²×C₄	1	1	yes	characteristic
187	#15261	C₂×D₄	1	2	yes	—
188	#15259	C₂²⋊C₄	1	1	yes	characteristic
189	#15259	C₂²⋊C₄	1	1	yes	characteristic
190	#15259	C₂×D₄	1	2	yes	—
191	#15259	C₂×D₄	1	2	yes	—
192	#15259	C₂×D₄	1	2	yes	—
193	#15259	C₂×D₄	1	1	yes	characteristic
194	#15258	C₂²⋊C₄	1	1	yes	characteristic
195	#15258	C₂²⋊C₄	1	1	yes	characteristic
196	#15258	C₂×D₄	1	2	yes	—
197	#15258	C₂×D₄	1	2	yes	—
198	#15258	C₂×D₄	1	2	yes	—
199	#15258	C₂×D₄	1	1	yes	characteristic
200	#15257	C₂×D₄	1	2	yes	—
201	#15257	C₂×D₄	1	2	yes	—
202	#14659	C₂×D₄	1	2	yes	—
203	#14658	C₂²⋊C₄	1	1	yes	characteristic
204	#14657	C₂²⋊C₄	1	1	yes	characteristic
205	#14649	C₂²⋊C₄	1	2	yes	complemented
206	#14609	C₂²⋊C₄	1	2	yes	complemented
207	#14599	C₂²⋊C₄	1	2	yes	complemented
208	#14599	C₂²⋊C₄	1	2	yes	complemented
209	#14571	C₂²⋊C₄	1	2	yes	complemented
210	#14571	C₂²⋊C₄	1	2	yes	complemented
211	#14533	C₂²⋊C₄	1	2	yes	complemented
212	#14507	C₂²⋊C₄	1	2	yes	complemented
213	#14335	C₂×D₄	1	1	yes	characteristic
214	#14290	C₂×D₄	1	2	yes	—
215	#14255	C₂×D₄	1	2	yes	—
216	#14207	C₂²⋊C₄	1	2	yes	complemented
217	#14167	C₂²⋊C₄	1	1	yes	characteristic
218	#14135	C₂²×C₄	1	2	yes	—
219	#14135	C₂×D₄	1	2	yes	—
220	#14135	C₂×D₄	1	2	yes	—
221	#14134	C₂²⋊C₄	1	1	yes	characteristic
222	#13956	C₂²⋊C₄	1	2	yes	complemented
223	#13956	C₂²⋊C₄	1	2	yes	complemented
224	#13903	C₂×D₄	1	2	yes	—
225	#13878	C₂²⋊C₄	1	2	yes	complemented
226	#13878	C₂²⋊C₄	1	2	yes	complemented
227	C₂×#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
228	C₂×#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
229	C₂×#1438	C₂×D₄	1	1	yes	characteristic
230	C₂×#1438	C₂×D₄	1	2	yes	—
231	#13832	C₂²⋊C₄	1	2	yes	complemented
232	#13827	C₂²⋊C₄	1	2	yes	complemented
233	#13827	C₂²⋊C₄	1	1	yes	characteristic, complemented
234	#13826	C₂²⋊C₄	1	2	yes	complemented
235	C₂²⋊C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
236	C₂²⋊C₄²	C₂²⋊C₄	1	2	yes	complemented
237	C₂⁷	#120	1	1	yes	characteristic
238	C₂⁷	#120	1	1	yes	characteristic
239	C₂⁷	#120	1	1	yes	characteristic
240	C₂³×#41	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂³×#41	#120	1	1	yes	characteristic
242	C₂³×#41	#120	1	2	yes	—
243	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂⁴×D₄	#120	1	1	yes	characteristic
245	C₂⁴×D₄	#120	1	1	yes	characteristic
246	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
247	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
248	C₂⁵×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×#127	#120	1	2	yes	—
251	C₂²×#127	#120	1	1	yes	characteristic
252	C₂²×#127	#120	1	2	yes	—
253	C₂²×#127	#120	1	2	yes	—
254	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×#124	#120	1	2	yes	—
256	C₂²×#124	#120	1	2	yes	—
257	C₂²×#124	#120	1	1	yes	characteristic
258	C₂²×#124	#120	1	2	yes	—
259	C₂²×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×#123	#120	1	1	yes	characteristic
261	C₂²×#123	C₂³×C₄	1	1	yes	characteristic
262	C₂²×#123	C₂²×D₄	1	2	yes	—
263	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
264	C₂²×#121	C₂²×D₄	1	2	yes	—
265	C₂²×#121	C₂²×D₄	1	2	yes	—
266	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×#120	#120	1	1	yes	characteristic
272	C₂²×#120	#120	1	1	yes	characteristic
273	C₂²×#120	#120	1	1	yes	characteristic
274	C₂²×#120	#120	1	1	yes	characteristic
275	C₂²×#120	#120	1	1	yes	characteristic
276	C₂²×#120	#120	1	2	yes	—
277	C₂²×#120	#120	1	2	yes	—
278	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
279	C₂²×#120	C₂²×D₄	1	2	yes	—
280	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
281	C₂²×#117	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂²×#117	#120	1	1	yes	characteristic
283	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
284	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
285	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
286	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂×#395	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂×#395	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×#395	#120	1	2	yes	—
290	C₂×#394	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×#394	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×#394	#120	1	2	yes	—
293	C₂×#393	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×#393	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂×#393	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×#393	#120	1	2	yes	—
297	C₂×#393	#120	1	2	yes	—
298	C₂×#393	#120	1	2	yes	—
299	C₂×#393	#120	1	2	yes	—
300	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂×#392	#120	1	2	yes	—
304	C₂×#392	#120	1	2	yes	—
305	C₂×#392	#120	1	2	yes	—
306	C₂×#392	#120	1	2	yes	—
307	C₂×#391	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂×#390	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×#381	#120	1	2	yes	—
313	C₂×#381	#120	1	1	yes	characteristic
314	C₂×#380	#120	1	2	yes	—
315	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
320	C₂×#379	#120	1	1	yes	characteristic
321	C₂×#379	#120	1	1	yes	characteristic
322	C₂×#379	#120	1	1	yes	characteristic
323	C₂×#379	#120	1	1	yes	characteristic
324	C₂×#379	#120	1	1	yes	characteristic
325	C₂×#379	#120	1	2	yes	—
326	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	—
327	C₂²×#95	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂²×#95	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂²×#95	#120	1	2	yes	—
330	#1445	C₂×C₂²⋊C₄	1	2	yes	—
331	#1445	C₂×C₂²⋊C₄	1	2	yes	—
332	#1440	C₂×C₂²⋊C₄	1	2	yes	—
333	#1440	C₂×C₂²⋊C₄	1	2	yes	—
334	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	#1438	#120	1	2	yes	—
339	#1438	#120	1	2	yes	—
340	#1438	#120	1	2	yes	—
341	#1438	#120	1	2	yes	—
342	#1438	#120	1	2	yes	—
343	#1438	#120	1	2	yes	—
344	#1438	#120	1	2	yes	—
345	#1438	#120	1	2	yes	—
346	#1438	#120	1	2	yes	—
347	#1438	#120	1	2	yes	—
348	#1437	C₂×C₂²⋊C₄	1	2	yes	—
349	#1437	C₂×C₂²⋊C₄	1	2	yes	—
350	#1437	C₂×C₂²⋊C₄	1	2	yes	—
351	#1437	C₂×C₂²⋊C₄	1	2	yes	—
352	#1437	C₂×C₂²⋊C₄	1	2	yes	—
353	#1437	C₂×C₂²⋊C₄	1	2	yes	—
354	#1437	#120	1	2	yes	—
355	#1437	#120	1	2	yes	—
356	#1437	#120	1	2	yes	—
357	#1437	#120	1	2	yes	—
358	#1437	#120	1	2	yes	—
359	#1437	#120	1	2	yes	—
360	#1437	#120	1	2	yes	—
361	#1437	#120	1	2	yes	—
362	#1436	C₂×C₂²⋊C₄	1	2	yes	—
363	#1436	C₂×C₂²⋊C₄	1	2	yes	—
364	#1436	C₂×C₂²⋊C₄	1	2	yes	—
365	#1436	C₂×C₂²⋊C₄	1	2	yes	—
366	#1436	#120	1	2	yes	—
367	#1436	#120	1	2	yes	—
368	C₂⁶	#379	1	1	yes	characteristic
369	C₂⁶	#379	1	1	yes	characteristic
370	C₂⁶	#379	1	1	yes	characteristic
371	C₂⁶	#379	1	1	yes	characteristic
372	C₂⁶	#379	1	1	yes	characteristic
373	C₂⁶	C₂×#120	1	1	yes	characteristic
374	C₂⁶	C₂×#120	1	1	yes	characteristic
375	C₂⁶	C₂×#120	1	1	yes	characteristic
376	C₂³×Q₈	#379	1	2	yes	—
377	C₂³×Q₈	#379	1	2	yes	—
378	C₂³×Q₈	#379	1	1	yes	characteristic
379	C₂³×D₄	#379	1	2	yes	—
380	C₂³×D₄	#379	1	2	yes	—
381	C₂³×D₄	#379	1	1	yes	characteristic
382	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
383	C₂³×D₄	#458	1	2	yes	—
384	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
385	C₂³×D₄	C₂×#120	1	1	yes	characteristic
386	C₂³×D₄	C₂×#120	1	1	yes	characteristic
387	C₂³×D₄	C₂×#120	1	2	yes	—
388	C₂³×D₄	C₂×#120	1	2	yes	—
389	C₂³×D₄	C₂×#120	1	2	yes	—
390	C₂³×D₄	C₂×#120	1	1	yes	characteristic
391	C₂³×D₄	C₂×#120	1	2	yes	—
392	C₂⁴×C₄	#379	1	1	yes	characteristic
393	C₂⁴×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
394	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
395	C₂⁴×C₄	C₂×#120	1	2	yes	—
396	C₂²×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
397	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
398	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	#379	1	2	yes	—
404	C₂²×C₂²⋊C₄	#379	1	2	yes	—
405	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
408	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
410	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
411	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
412	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
413	C₂²×C₄²	#379	1	2	yes	—
414	C₂²×C₄²	#379	1	1	yes	characteristic
415	C₂²×C₄²	#379	1	1	yes	characteristic
416	C₂²×C₄²	#379	1	2	yes	—
417	C₂²×C₄²	#379	1	2	yes	—
418	C₂²×C₄²	#379	1	2	yes	—
419	C₂×#95	#379	1	2	yes	—
420	C₂×#95	#379	1	2	yes	—
421	C₂×#95	#379	1	2	yes	—
422	C₂×#95	#379	1	2	yes	—
423	C₂×#95	#379	1	2	yes	—
424	C₂×#95	#379	1	2	yes	—
425	C₂×#95	#379	1	2	yes	—
426	C₂×#95	#379	1	2	yes	—
427	C₂×#95	#379	1	2	yes	—
428	C₂×#95	#379	1	2	yes	—
429	C₂⁵	#1790	1	2	yes	—
430	C₂⁵	C₂×#379	1	1	yes	characteristic
431	C₂⁵	C₂×#379	1	1	yes	characteristic
432	C₂⁵	#2846	1	1	yes	characteristic
433	C₂⁵	#2846	1	1	yes	characteristic
434	C₂⁵	#2846	1	2	yes	—
435	C₂⁵	#2846	1	1	yes	characteristic
436	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
437	C₂⁵	C₂×#458	1	1	yes	characteristic
438	C₂⁵	#3026	1	1	yes	characteristic
439	C₂⁵	#3026	1	1	yes	characteristic
440	C₂³×C₄	#1790	1	2	yes	—
441	C₂³×C₄	C₂×#379	1	2	yes	—
442	C₂³×C₄	C₂×#379	1	1	yes	characteristic
443	C₂³×C₄	C₂×#379	1	2	yes	—
444	C₂³×C₄	#2846	1	2	yes	—
445	C₂³×C₄	#2846	1	1	yes	characteristic
446	C₂⁴	#12753	1	4	yes	—
447	C₂⁴	#14679	1	1	yes	characteristic
448	C₂⁴	C₂×#1790	1	1	yes	characteristic
449	C₂⁴	#20609	1	1	yes	characteristic
450	C₂⁴	#32898	1	1	yes	characteristic
451	C₂⁴	#32898	1	1	yes	characteristic
452	C₂⁴	#32900	1	1	yes	characteristic
453	C₂⁴	#32900	1	1	yes	characteristic
454	C₂³	#392125	1	1	yes	characteristic
455	C₂³	#392135	1	2	yes	—
456	C₂³	C₂×#12753	1	2	yes	—
457	C₂³	#511790	1	2	yes	—
458	C₂²	#72218475	1	1	yes	characteristic
459	C₂²	#72218980	1	1	yes	characteristic
460	C₂²	#72251779	1	1	yes	characteristic
461	C₂²	#72258948	1	2	yes	—
462	C₂²	#72303641	1	2	yes	—
463	C₂	#72266333	1	1	yes	characteristic
464	C₂	#72324282	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72251779
commutator	C₂²×#123	C₂³×C₄
Frattini, cosocle	C₂²×#534	C₂⁴
prime radical	#72305966	C₂
LCS	G ▷ C₂²×#123 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#534 ◁ G
LECS	G ▷ C₂²×#534 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72324295	C₂	semidirect
2. #72324291	C₂	semidirect
3. #72324287	C₂	semidirect
4. #72324269	C₂	semidirect
5. #72310205	C₂	semidirect
6. #72309800	C₂²	semidirect
7. #72309483	C₂	semidirect
9. #72305962	C₄	semidirect
11. #72305944	C₄	semidirect
12. #72305934	C₄	semidirect
13. #72303517	C₄	semidirect
14. #72303442	C₄	semidirect
16. #72260562	C₂²	semidirect
17. #72260562	C₂²	semidirect
18. #72259117	C₂²	semidirect
19. #72256119	C₂²	semidirect
20. #72237886	C₂	semidirect
21. #72237884	C₂²	semidirect
22. #72237603	C₂	semidirect
23. #72237600	C₂²	semidirect
24. #72237583	C₂²	semidirect
25. #72235242	C₂²	semidirect
26. #72234724	C₂²	semidirect
27. #72234640	C₄	semidirect
29. #72226102	C₂	semidirect
30. #72226018	C₂	semidirect
31. #72226008	C₂²	semidirect
32. #72226008	C₂²	semidirect
33. #72226006	C₂²	semidirect
34. #72225987	C₂²	semidirect
35. #72225870	C₂²	semidirect
36. #72225713	C₂²	semidirect
37. #72219314	C₂²	semidirect
38. #72219311	C₂²	semidirect
45. #6374251	C₂³	semidirect
46. #6374128	C₂³	semidirect
102. #188122	C₂³	semidirect
103. #188109	C₂³	semidirect
104. #188049	C₂³	semidirect
105. #188049	C₂³	semidirect
106. C₂³×H(5,𝔽₂)	C₂²⋊C₄	semidirect
116. C₂²×#525	C₂²⋊C₄	semidirect
119. C₂²×#518	C₂²⋊C₄	semidirect
120. C₂×#2811	C₂²⋊C₄	semidirect
121. C₂×#2760	C₂²⋊C₄	semidirect
122. C₂×#2679	C₂²⋊C₄	semidirect
123. C₂×#2840	C₂²⋊C₄	semidirect
124. C₂×#2840	C₂²⋊C₄	semidirect
135. C₂×#2403	C₂²⋊C₄	semidirect
136. C₂×#2403	C₂²⋊C₄	semidirect
145. C₂³×#95	C₂²⋊C₄	semidirect
146. #17105	C₂²⋊C₄	semidirect
147. #17105	C₂²⋊C₄	semidirect
148. #17084	C₂²⋊C₄	semidirect
149. #17084	C₂²⋊C₄	semidirect
150. #16247	C₂²⋊C₄	semidirect
151. #16211	C₂²⋊C₄	semidirect
152. #16167	C₂²⋊C₄	semidirect
153. #16167	C₂²⋊C₄	semidirect
162. #15833	C₂²⋊C₄	semidirect
163. #15833	C₂²⋊C₄	semidirect
169. #15662	C₂²⋊C₄	semidirect
170. #15662	C₂²⋊C₄	semidirect
171. #15467	C₂²⋊C₄	semidirect
172. #15467	C₂²⋊C₄	semidirect
173. #15467	C₂²⋊C₄	semidirect
174. #15467	C₂²⋊C₄	semidirect
180. #15267	C₂²⋊C₄	semidirect
181. #15267	C₂²⋊C₄	semidirect
182. #15267	C₂²⋊C₄	semidirect
183. #15267	C₂²⋊C₄	semidirect
205. #14649	C₂²⋊C₄	semidirect
206. #14609	C₂²⋊C₄	semidirect
207. #14599	C₂²⋊C₄	semidirect
208. #14599	C₂²⋊C₄	semidirect
209. #14571	C₂²⋊C₄	semidirect
210. #14571	C₂²⋊C₄	semidirect
211. #14533	C₂²⋊C₄	semidirect
212. #14507	C₂²⋊C₄	semidirect
216. #14207	C₂²⋊C₄	semidirect
222. #13956	C₂²⋊C₄	semidirect
223. #13956	C₂²⋊C₄	semidirect
225. #13878	C₂²⋊C₄	semidirect
226. #13878	C₂²⋊C₄	semidirect
227. C₂×#1438	C₂²⋊C₄	semidirect
228. C₂×#1438	C₂²⋊C₄	semidirect
231. #13832	C₂²⋊C₄	semidirect
232. #13827	C₂²⋊C₄	semidirect
233. #13827	C₂²⋊C₄	semidirect
234. #13826	C₂²⋊C₄	semidirect
235. C₂²⋊C₄²	C₂²⋊C₄	semidirect
236. C₂²⋊C₄²	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72324295	2
#72324291	2
#72324287	2
#72324269	2
#72310205	2
#72309483	2
#72305966	2
#72237886	2
#72237603	2
#72226102	2
#72226018	2