Subgroups — #72324276

Order 2048.

At least 9172 conjugacy classes of subgroups; only the 612 normal subgroups are shown.

The subgroup lattice has 400 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72324275	C₂	1	2	yes	maximal, complemented
2	#72324274	C₂	1	2	yes	maximal, complemented
3	#72324273	C₂	1	2	yes	maximal, complemented
4	#72324272	C₂	1	2	yes	maximal, complemented
5	#72324271	C₂	1	2	yes	maximal, complemented
6	#72266553	C₂	1	1	yes	maximal, characteristic, complemented
7	#72266277	C₂	1	2	yes	maximal, complemented
8	#72259136	C₂	1	1	yes	maximal, characteristic, complemented
9	#72238480	C₂	1	2	yes	maximal, complemented
10	#72237583	C₂	1	1	yes	maximal, characteristic, complemented
11	#72235685	C₂	1	2	yes	maximal, complemented
12	#72235671	C₂	1	2	yes	maximal, complemented
13	#72233493	C₂	1	2	yes	maximal, complemented
14	#72232980	C₂	1	1	yes	maximal, characteristic, complemented
15	#72227564	C₂	1	2	yes	maximal, complemented
16	#72226008	C₂	1	1	yes	maximal, characteristic, complemented
17	#72225985	C₂	1	1	yes	maximal, characteristic, complemented
18	#72225712	C₂	1	1	yes	maximal, characteristic, complemented
19	#72213827	C₂	1	2	yes	maximal, complemented
20	#10586404	C₂²	1	1	yes	characteristic, complemented
21	#6499867	C₂²	1	2	yes	—
22	#6346727	C₂²	1	2	yes	complemented
23	#6346698	C₂²	1	2	yes	complemented
24	#5474299	C₂²	1	1	yes	characteristic, complemented
25	#5119613	C₂²	1	1	yes	characteristic, complemented
26	#5037287	C₂²	1	1	yes	characteristic, complemented
27	#5035967	C₂²	1	1	yes	characteristic, complemented
28	#5020751	C₂²	1	1	yes	characteristic, complemented
29	#4975876	C₂²	1	1	yes	characteristic, complemented
30	#4423579	C₂²	1	1	yes	characteristic, complemented
31	#4380237	C₂²	1	1	yes	characteristic
32	#4122215	C₂²	1	1	yes	characteristic, complemented
33	#2435299	C₂²	1	1	yes	characteristic, complemented
34	#2109240	C₂²	1	1	yes	characteristic, complemented
35	#1442757	C₂²	1	1	yes	characteristic, complemented
36	#763333	C₂²	1	1	yes	characteristic
37	#648360	C₂²	1	1	yes	characteristic, complemented
38	#616960	C₂²	1	1	yes	characteristic
39	#485081	C₂²	1	4	yes	complemented
40	#485039	C₂²	1	4	yes	complemented
41	#347044	C₂²	1	2	yes	—
42	#347044	C₂²	1	2	yes	complemented
43	#347043	C₂²	1	2	yes	—
44	#347043	C₂²	1	2	yes	complemented
45	#346462	C₂²	1	2	yes	complemented
46	#346459	C₂²	1	2	yes	complemented
47	#346456	C₂²	1	2	yes	complemented
48	#346456	C₂²	1	2	yes	complemented
49	#346452	C₂²	1	2	yes	complemented
50	#346449	C₂²	1	2	yes	complemented
51	#346446	C₂²	1	2	yes	—
52	#346446	C₂²	1	2	yes	—
53	#188122	C₂²	1	1	yes	characteristic, complemented
54	#188109	C₂²	1	1	yes	characteristic, complemented
55	#188049	C₂²	1	1	yes	characteristic, complemented
56	#187934	C₂²	1	2	yes	complemented
57	#185288	C₂²	1	2	yes	complemented
58	#185267	C₂²	1	2	yes	complemented
59	#144622	C₂²	1	4	yes	complemented
60	#144619	C₂²	1	4	yes	complemented
61	#142982	C₂²	1	4	yes	complemented
62	#142982	C₂²	1	4	yes	complemented
63	#142568	C₂²	1	4	yes	complemented
64	#142568	C₂²	1	4	yes	complemented
65	#142536	C₂²	1	4	yes	complemented
66	#142536	C₂²	1	4	yes	complemented
67	#140058	C₂²	1	4	yes	complemented
68	#140051	C₂²	1	4	yes	complemented
69	#140032	C₂²	1	4	yes	complemented
70	#140024	C₂²	1	4	yes	complemented
71	#139912	C₂²	1	2	yes	complemented
72	#139912	C₂²	1	2	yes	complemented
73	#139908	C₂²	1	2	yes	complemented
74	#139908	C₂²	1	2	yes	complemented
75	#139624	C₂²	1	4	yes	complemented
76	#139622	C₂²	1	4	yes	complemented
77	#139504	C₂²	1	2	yes	complemented
78	#139504	C₂²	1	2	yes	complemented
79	#139486	C₂²	1	2	yes	complemented
80	#139486	C₂²	1	2	yes	complemented
81	#139472	C₂²	1	2	yes	complemented
82	#139456	C₂²	1	2	yes	complemented
83	#139450	C₂²	1	2	yes	complemented
84	#139434	C₂²	1	2	yes	complemented
85	#135561	C₂²	1	2	yes	complemented
86	#135493	C₂²	1	2	yes	complemented
87	#135487	C₂²	1	2	yes	complemented
88	#134033	C₂²	1	2	yes	complemented
89	#133133	C₂²	1	2	yes	complemented
90	#133121	C₂²	1	2	yes	complemented
91	#62820	C₂³	1	2	yes	—
92	#62818	C₂³	1	2	yes	—
93	#62817	C₂³	1	2	yes	—
94	C₂²×#535	D₄	1	1	yes	characteristic, complemented
95	C₂²×#534	C₂³	1	1	yes	characteristic
96	C₂³×#120	D₄	1	1	yes	characteristic
97	C₂×#2840	C₂³	1	1	yes	characteristic, complemented
98	C₂×#2846	D₄	1	1	yes	characteristic
99	C₂×#2846	C₂³	1	1	yes	characteristic
100	C₂×#2430	D₄	1	1	yes	characteristic, complemented
101	C₂×#2430	C₂³	1	1	yes	characteristic
102	C₂×#2404	D₄	1	1	yes	characteristic, complemented
103	C₂×#2431	D₄	1	1	yes	characteristic, complemented
104	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
105	C₂×#2615	C₂³	1	1	yes	characteristic
106	#23984	C₂³	1	4	yes	—
107	#23984	C₂³	1	4	yes	—
108	#21746	C₂³	1	2	yes	—
109	#18163	C₂³	1	4	yes	—
110	#18163	C₂³	1	4	yes	—
111	#18162	C₂³	1	4	yes	—
112	#18162	C₂³	1	4	yes	—
113	#17396	C₂³	1	2	yes	—
114	#17392	C₂³	1	2	yes	—
115	#17105	C₂³	1	1	yes	characteristic, complemented
116	#17105	C₂³	1	1	yes	characteristic, complemented
117	#16247	C₂³	1	1	yes	characteristic, complemented
118	#16211	C₂³	1	1	yes	characteristic, complemented
119	#15948	C₂³	1	1	yes	characteristic
120	#15948	C₂³	1	1	yes	characteristic
121	#15947	D₄	1	1	yes	characteristic
122	#15947	D₄	1	1	yes	characteristic
123	#15673	D₄	1	1	yes	characteristic, complemented
124	#15673	C₂³	1	1	yes	characteristic
125	#15668	D₄	1	1	yes	characteristic, complemented
126	#15668	C₂³	1	1	yes	characteristic
127	#15467	C₂³	1	1	yes	characteristic, complemented
128	#15467	C₂³	1	1	yes	characteristic, complemented
129	#15412	D₄	1	1	yes	characteristic, complemented
130	#15412	C₂³	1	1	yes	characteristic
131	#15310	D₄	1	1	yes	characteristic, complemented
132	#15310	C₂³	1	1	yes	characteristic
133	#15267	C₂³	1	1	yes	characteristic, complemented
134	#15267	C₂³	1	1	yes	characteristic, complemented
135	#15262	D₄	1	1	yes	characteristic, complemented
136	#15261	D₄	1	1	yes	characteristic, complemented
137	#15259	D₄	1	1	yes	characteristic, complemented
138	#15259	C₂³	1	1	yes	characteristic
139	#15259	C₂³	1	1	yes	characteristic
140	#15258	D₄	1	1	yes	characteristic, complemented
141	#15258	C₂³	1	1	yes	characteristic
142	#15258	C₂³	1	1	yes	characteristic
143	#15257	D₄	1	1	yes	characteristic
144	#15257	D₄	1	1	yes	characteristic
145	#15257	C₂³	1	1	yes	characteristic
146	#15257	C₂³	1	1	yes	characteristic
147	#14659	D₄	1	1	yes	characteristic, complemented
148	#14649	C₂³	1	1	yes	characteristic, complemented
149	#14609	C₂³	1	1	yes	characteristic, complemented
150	#14533	C₂³	1	1	yes	characteristic, complemented
151	#14335	D₄	1	1	yes	characteristic
152	#14290	C₂³	1	1	yes	characteristic
153	#14255	D₄	1	1	yes	characteristic
154	#14255	C₂³	1	1	yes	characteristic
155	#14207	C₂³	1	1	yes	characteristic, complemented
156	#14135	D₄	1	1	yes	characteristic, complemented
157	#14135	C₂³	1	1	yes	characteristic
158	#13903	D₄	1	1	yes	characteristic, complemented
159	C₂×#1438	D₄	1	1	yes	characteristic, complemented
160	#13827	C₂³	1	1	yes	characteristic, complemented
161	C₂²⋊C₄²	C₂³	1	1	yes	characteristic, complemented
162	#11808	C₂³	1	4	yes	complemented
163	#11808	C₂³	1	4	yes	complemented
164	#11796	C₂³	1	4	yes	complemented
165	#11796	C₂³	1	4	yes	complemented
166	#11499	C₂³	1	4	yes	complemented
167	#11499	C₂³	1	4	yes	complemented
168	#8553	C₂³	1	2	yes	—
169	#8549	C₂³	1	2	yes	—
170	#8547	C₂³	1	2	yes	—
171	#8547	C₂³	1	2	yes	—
172	#8543	C₂³	1	2	yes	—
173	#8542	C₂³	1	2	yes	—
174	#8535	C₂³	1	4	yes	—
175	#8535	C₂³	1	4	yes	—
176	#8346	C₂³	1	4	yes	—
177	#8346	C₂³	1	4	yes	—
178	#8346	C₂³	1	4	yes	—
179	#8346	C₂³	1	4	yes	—
180	#7324	C₂³	1	4	yes	complemented
181	#7324	C₂³	1	4	yes	complemented
182	#7213	C₂³	1	4	yes	complemented
183	#7213	C₂³	1	4	yes	complemented
184	#7213	C₂³	1	4	yes	complemented
185	#7213	C₂³	1	4	yes	complemented
186	C₂⁷	C₂×D₄	1	1	yes	characteristic
187	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	#3490	C₂⁴	1	4	yes	—
192	C₂²×#127	C₂×D₄	1	1	yes	characteristic
193	C₂²×#127	C₂×D₄	1	1	yes	characteristic
194	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂²×#124	C₂×D₄	1	1	yes	characteristic
196	C₂²×#124	C₂×D₄	1	1	yes	characteristic
197	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂²×#123	C₂×D₄	1	1	yes	characteristic
199	C₂²×#123	C₂×D₄	1	1	yes	characteristic
200	C₂²×#123	C₂×D₄	1	1	yes	characteristic
201	C₂²×#123	C₂⁴	1	1	yes	characteristic
202	C₂²×#121	C₂×D₄	1	1	yes	characteristic
203	C₂²×#121	C₂×D₄	1	1	yes	characteristic
204	C₂²×#121	C₂×D₄	1	1	yes	characteristic
205	C₂²×#121	C₂⁴	1	1	yes	characteristic
206	C₂²×#120	C₂×D₄	1	1	yes	characteristic
207	C₂²×#120	C₂×D₄	1	1	yes	characteristic
208	C₂²×#120	C₂×D₄	1	1	yes	characteristic
209	C₂²×#120	C₂×D₄	1	1	yes	characteristic
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂×D₄	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	1	yes	characteristic
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic
215	C₂²×#120	C₂×D₄	1	1	yes	characteristic
216	C₂²×#120	C₂×D₄	1	1	yes	characteristic
217	C₂²×#120	C₂⁴	1	1	yes	characteristic
218	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₂×#395	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂×#395	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂×#393	C₂×D₄	1	1	yes	characteristic
226	C₂×#393	C₂×D₄	1	1	yes	characteristic
227	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
228	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
229	C₂×#393	C₂⁴	1	1	yes	characteristic
230	C₂×#393	C₂⁴	1	1	yes	characteristic
231	C₂×#392	C₂×D₄	1	1	yes	characteristic
232	C₂×#392	C₂×D₄	1	1	yes	characteristic
233	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂×#392	C₂⁴	1	1	yes	characteristic
236	C₂×#392	C₂⁴	1	1	yes	characteristic
237	C₂×#391	C₂×D₄	1	1	yes	characteristic, complemented
238	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
241	C₂×#379	C₂×D₄	1	1	yes	characteristic
242	C₂×#379	C₂×D₄	1	1	yes	characteristic
243	C₂×#379	C₂×D₄	1	1	yes	characteristic
244	C₂×#379	C₂×D₄	1	1	yes	characteristic
245	C₂×#379	C₂⁴	1	1	yes	characteristic
246	C₂×#379	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂²×#95	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂²×#95	C₂×D₄	1	1	yes	characteristic, complemented
250	#1819	C₂⁴	1	4	yes	—
251	#1462	C₂⁴	1	4	yes	—
252	#1462	C₂⁴	1	4	yes	—
253	#1445	C₂×D₄	1	1	yes	characteristic, complemented
254	#1445	C₂×D₄	1	1	yes	characteristic, complemented
255	#1440	C₂×D₄	1	1	yes	characteristic
256	#1440	C₂×D₄	1	1	yes	characteristic
257	#1440	C₂⁴	1	1	yes	characteristic
258	#1440	C₂⁴	1	1	yes	characteristic
259	#1438	C₂×D₄	1	1	yes	characteristic
260	#1438	C₂×D₄	1	1	yes	characteristic
261	#1438	C₂×D₄	1	1	yes	characteristic
262	#1438	C₂×D₄	1	1	yes	characteristic
263	#1438	C₂×D₄	1	1	yes	characteristic
264	#1438	C₂×D₄	1	1	yes	characteristic
265	#1438	C₂×D₄	1	1	yes	characteristic
266	#1438	C₂×D₄	1	1	yes	characteristic
267	#1438	C₂×D₄	1	1	yes	characteristic
268	#1438	C₂×D₄	1	1	yes	characteristic
269	#1438	C₂×D₄	1	1	yes	characteristic
270	#1438	C₂×D₄	1	1	yes	characteristic
271	#1438	C₂×D₄	1	1	yes	characteristic, complemented
272	#1438	C₂×D₄	1	1	yes	characteristic, complemented
273	#1437	C₂×D₄	1	1	yes	characteristic
274	#1437	C₂×D₄	1	1	yes	characteristic
275	#1437	C₂×D₄	1	1	yes	characteristic
276	#1437	C₂×D₄	1	1	yes	characteristic
277	#1437	C₂×D₄	1	1	yes	characteristic, complemented
278	#1437	C₂×D₄	1	1	yes	characteristic, complemented
279	#1437	C₂×D₄	1	1	yes	characteristic, complemented
280	#1437	C₂×D₄	1	1	yes	characteristic, complemented
281	#1437	C₂⁴	1	1	yes	characteristic
282	#1437	C₂⁴	1	1	yes	characteristic
283	#1437	C₂⁴	1	1	yes	characteristic
284	#1437	C₂⁴	1	1	yes	characteristic
285	#1436	C₂×D₄	1	1	yes	characteristic, complemented
286	#1436	C₂×D₄	1	1	yes	characteristic, complemented
287	#1436	C₂×D₄	1	1	yes	characteristic, complemented
288	#1436	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂⁶	#120	1	1	yes	characteristic
290	C₂⁶	#120	1	1	yes	characteristic
291	C₂⁶	C₂²×D₄	1	1	yes	characteristic
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂⁶	C₂²×D₄	1	1	yes	characteristic
294	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
295	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
296	C₂³×D₄	#120	1	1	yes	characteristic
297	C₂³×D₄	#120	1	1	yes	characteristic
298	C₂³×D₄	#120	1	1	yes	characteristic
299	C₂³×D₄	#120	1	1	yes	characteristic
300	C₂³×D₄	#120	1	1	yes	characteristic
301	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
302	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
304	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
307	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
308	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
309	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
310	C₂⁴×C₄	#120	1	1	yes	characteristic
311	C₂⁴×C₄	#120	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
314	#543	H(5,𝔽₂)	1	4	yes	—
315	#534	H(5,𝔽₂)	1	4	yes	—
316	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
325	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
338	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
342	C₂×#95	C₂²×D₄	1	1	yes	characteristic
343	C₂×#95	C₂²×D₄	1	1	yes	characteristic
344	C₂×#95	C₂²×D₄	1	1	yes	characteristic
345	C₂×#95	C₂²×D₄	1	1	yes	characteristic
346	C₂×#95	C₂²×D₄	1	1	yes	characteristic
347	C₂×#95	C₂²×D₄	1	1	yes	characteristic
348	C₂×#95	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂²×D₄	1	1	yes	characteristic
350	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
351	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
352	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
353	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#120	1	1	yes	characteristic
356	C₂⁵	C₂×#120	1	1	yes	characteristic
357	C₂⁵	C₂×#120	1	1	yes	characteristic
358	C₂⁵	C₂×#120	1	1	yes	characteristic
359	C₂⁵	C₂×#120	1	1	yes	characteristic
360	C₂⁵	C₂³×D₄	1	1	yes	characteristic
361	C₂³×C₄	C₂×#120	1	1	yes	characteristic
362	C₂³×C₄	C₂×#120	1	1	yes	characteristic
363	C₂³×C₄	C₂×#120	1	1	yes	characteristic
364	C₂³×C₄	C₂×#120	1	1	yes	characteristic
365	C₂³×C₄	C₂×#120	1	1	yes	characteristic
366	C₂³×C₄	C₂×#120	1	1	yes	characteristic
367	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
368	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	4	yes	—
371	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
372	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
373	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
374	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
375	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
376	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
377	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁴	C₂²×#120	1	1	yes	characteristic
379	C₂⁴	#3484	1	2	yes	—
380	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
381	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
382	C₂²×C₄	#3484	1	2	yes	—
383	C₂²×C₄	#3484	1	2	yes	—
384	C₂³	#33551	1	2	yes	—
385	C₂³	#33551	1	2	yes	—
386	C₂³	#35346	1	1	yes	characteristic
387	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
388	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
389	C₂²	#6499855	1	1	yes	characteristic
390	C₂²	#6499856	1	1	yes	characteristic
391	C₂²	#6499867	1	1	yes	characteristic
392	C₂²	C₂×#33551	1	1	yes	characteristic
393	C₂²	C₂×#33551	1	1	yes	characteristic
394	C₂²	#7622880	1	1	yes	characteristic
395	C₂²	#7622886	1	1	yes	characteristic
396	C₂	#72233499	1	1	yes	characteristic
397	C₂	#72256267	1	1	yes	characteristic
398	C₂	#72324264	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6499867
commutator, Frattini, cosocle	C₂²×C₂²⋊C₄	C₂⁵
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#534 ◁ G
LECS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72324275	C₂	semidirect
2. #72324274	C₂	semidirect
3. #72324273	C₂	semidirect
4. #72324272	C₂	semidirect
5. #72324271	C₂	semidirect
6. #72266553	C₂	semidirect
7. #72266277	C₂	semidirect
8. #72259136	C₂	semidirect
9. #72238480	C₂	semidirect
10. #72237583	C₂	semidirect
11. #72235685	C₂	semidirect
12. #72235671	C₂	semidirect
13. #72233493	C₂	semidirect
14. #72232980	C₂	semidirect
15. #72227564	C₂	semidirect
16. #72226008	C₂	semidirect
17. #72225985	C₂	semidirect
18. #72225712	C₂	semidirect
19. #72213827	C₂	semidirect
20. #10586404	C₂²	semidirect
22. #6346727	C₂²	semidirect
23. #6346698	C₂²	semidirect
24. #5474299	C₂²	semidirect
25. #5119613	C₂²	semidirect
26. #5037287	C₂²	semidirect
27. #5035967	C₂²	semidirect
28. #5020751	C₂²	semidirect
29. #4975876	C₂²	semidirect
30. #4423579	C₂²	semidirect
32. #4122215	C₂²	semidirect
33. #2435299	C₂²	semidirect
34. #2109240	C₂²	semidirect
35. #1442757	C₂²	semidirect
37. #648360	C₂²	semidirect
39. #485081	C₂²	semidirect
40. #485039	C₂²	semidirect
42. #347044	C₂²	semidirect
44. #347043	C₂²	semidirect
45. #346462	C₂²	semidirect
46. #346459	C₂²	semidirect
47. #346456	C₂²	semidirect
48. #346456	C₂²	semidirect
49. #346452	C₂²	semidirect
50. #346449	C₂²	semidirect
53. #188122	C₂²	semidirect
54. #188109	C₂²	semidirect
55. #188049	C₂²	semidirect
56. #187934	C₂²	semidirect
57. #185288	C₂²	semidirect
58. #185267	C₂²	semidirect
59. #144622	C₂²	semidirect
60. #144619	C₂²	semidirect
61. #142982	C₂²	semidirect
62. #142982	C₂²	semidirect
63. #142568	C₂²	semidirect
64. #142568	C₂²	semidirect
65. #142536	C₂²	semidirect
66. #142536	C₂²	semidirect
67. #140058	C₂²	semidirect
68. #140051	C₂²	semidirect
69. #140032	C₂²	semidirect
70. #140024	C₂²	semidirect
71. #139912	C₂²	semidirect
72. #139912	C₂²	semidirect
73. #139908	C₂²	semidirect
74. #139908	C₂²	semidirect
75. #139624	C₂²	semidirect
76. #139622	C₂²	semidirect
77. #139504	C₂²	semidirect
78. #139504	C₂²	semidirect
79. #139486	C₂²	semidirect
80. #139486	C₂²	semidirect
81. #139472	C₂²	semidirect
82. #139456	C₂²	semidirect
83. #139450	C₂²	semidirect
84. #139434	C₂²	semidirect
85. #135561	C₂²	semidirect
86. #135493	C₂²	semidirect
87. #135487	C₂²	semidirect
88. #134033	C₂²	semidirect
89. #133133	C₂²	semidirect
90. #133121	C₂²	semidirect
94. C₂²×#535	D₄	semidirect
97. C₂×#2840	C₂³	semidirect
100. C₂×#2430	D₄	semidirect
102. C₂×#2404	D₄	semidirect
103. C₂×#2431	D₄	semidirect
104. C₂×#2403	C₂³	semidirect
115. #17105	C₂³	semidirect
116. #17105	C₂³	semidirect
117. #16247	C₂³	semidirect
118. #16211	C₂³	semidirect
123. #15673	D₄	semidirect
125. #15668	D₄	semidirect
127. #15467	C₂³	semidirect
128. #15467	C₂³	semidirect
129. #15412	D₄	semidirect
131. #15310	D₄	semidirect
133. #15267	C₂³	semidirect
134. #15267	C₂³	semidirect
135. #15262	D₄	semidirect
136. #15261	D₄	semidirect
137. #15259	D₄	semidirect
140. #15258	D₄	semidirect
147. #14659	D₄	semidirect
148. #14649	C₂³	semidirect
149. #14609	C₂³	semidirect
150. #14533	C₂³	semidirect
155. #14207	C₂³	semidirect
156. #14135	D₄	semidirect
158. #13903	D₄	semidirect
159. C₂×#1438	D₄	semidirect
160. #13827	C₂³	semidirect
161. C₂²⋊C₄²	C₂³	semidirect
162. #11808	C₂³	semidirect
163. #11808	C₂³	semidirect
164. #11796	C₂³	semidirect
165. #11796	C₂³	semidirect
166. #11499	C₂³	semidirect
167. #11499	C₂³	semidirect
180. #7324	C₂³	semidirect
181. #7324	C₂³	semidirect
182. #7213	C₂³	semidirect
183. #7213	C₂³	semidirect
184. #7213	C₂³	semidirect
185. #7213	C₂³	semidirect
187. C₂³×#41	C₂×D₄	semidirect
188. C₂³×#41	C₂×D₄	semidirect
194. C₂²×#127	C₂×D₄	semidirect
197. C₂²×#124	C₂×D₄	semidirect
218. C₂²×#117	C₂×D₄	semidirect
221. C₂×#395	C₂×D₄	semidirect
222. C₂×#395	C₂×D₄	semidirect
223. C₂×#394	C₂×D₄	semidirect
224. C₂×#394	C₂×D₄	semidirect
227. C₂×#393	C₂×D₄	semidirect
228. C₂×#393	C₂×D₄	semidirect
233. C₂×#392	C₂×D₄	semidirect
234. C₂×#392	C₂×D₄	semidirect
237. C₂×#391	C₂×D₄	semidirect
238. C₂×#390	C₂×D₄	semidirect
239. C₂×#381	C₂×D₄	semidirect
240. C₂×#380	C₂×D₄	semidirect
247. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
248. C₂²×#95	C₂×D₄	semidirect
249. C₂²×#95	C₂×D₄	semidirect
253. #1445	C₂×D₄	semidirect
254. #1445	C₂×D₄	semidirect
271. #1438	C₂×D₄	semidirect
272. #1438	C₂×D₄	semidirect
277. #1437	C₂×D₄	semidirect
278. #1437	C₂×D₄	semidirect
279. #1437	C₂×D₄	semidirect
280. #1437	C₂×D₄	semidirect
285. #1436	C₂×D₄	semidirect
286. #1436	C₂×D₄	semidirect
287. #1436	C₂×D₄	semidirect
288. #1436	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72324275	2
#72324274	2
#72324273	2
#72324272	2
#72324271	2
#72266553	2
#72266277	2
#72259136	2
#72238480	2
#72237583	2
#72235685	2
#72235671	2
#72233493	2
#72232980	2
#72227564	2
#72226008	2
#72225985	2
#72225712	2
#72213827	2