Subgroups — #72340735

Order 4096.

At least 20881 conjugacy classes of subgroups; only the 835 normal subgroups are shown.

The subgroup lattice has 389 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72340732	C₂	1	1	yes	maximal, characteristic, complemented
2	#72340729	C₂	1	1	yes	maximal, characteristic, complemented
3	#72340723	C₂	1	1	yes	maximal, characteristic, complemented
4	#72340722	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#72213400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#496222	C₂²	1	1	yes	characteristic, complemented
7	#72340701	C₂	1	1	yes	maximal, characteristic, complemented
8	#72340699	C₂²	1	1	yes	characteristic, complemented
9	#72340695	C₂	1	8	yes	maximal, complemented
10	#72340694	C₂²	1	4	yes	complemented
11	C₂×#134056	C₂²	1	1	yes	characteristic, complemented
12	#72340691	C₂²	1	4	yes	complemented
13	#72340688	C₂	1	2	yes	maximal, complemented
14	#72340685	C₂²	1	1	yes	characteristic, complemented
15	#72340677	C₂	1	2	yes	maximal, complemented
16	C₂×#72226293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#150570	C₂²	1	2	yes	complemented
18	#72340671	C₂²	1	2	yes	complemented
19	#72340669	C₂	1	2	yes	maximal, complemented
20	#72340668	C₂²	1	2	yes	complemented
21	#72340667	C₂²	1	2	yes	complemented
22	#72340664	C₂	1	2	yes	maximal, complemented
23	#72340662	C₂²	1	2	yes	complemented
24	#72340660	C₂²	1	2	yes	complemented
25	#72340658	C₂²	1	2	yes	—
26	#72340658	C₂²	1	2	yes	complemented
27	C₂×#94178	C₂²	1	2	yes	complemented
28	#72340652	C₂²	1	2	yes	complemented
29	C₂×#418906	C₂²	1	1	yes	characteristic, complemented
30	#72340602	C₂²	1	2	yes	complemented
31	C₂×#356069	C₂²	1	1	yes	characteristic, complemented
32	#72340590	C₂²	1	2	yes	complemented
33	C₂×#418909	C₂²	1	1	yes	characteristic, complemented
34	C₂×#417807	C₂²	1	1	yes	characteristic
35	#72337682	C₂	1	4	yes	maximal, complemented
36	#72337681	C₂²	1	2	yes	complemented
37	#72337680	C₂²	1	2	yes	complemented
38	#72337679	C₂²	1	2	yes	complemented
39	#72337677	C₂²	1	8	yes	complemented
40	#72337676	C₂²	1	8	yes	complemented
41	#72337675	C₂²	1	8	yes	complemented
42	#72337674	C₂²	1	8	yes	complemented
43	C₂×#6437610	C₂²	1	1	yes	characteristic, complemented
44	#72262727	C₂²	1	4	yes	complemented
45	C₂×#417798	C₂²	1	1	yes	characteristic
46	#72241405	C₂	1	4	yes	maximal, complemented
47	#72241404	C₂²	1	8	yes	complemented
48	#72241403	C₂²	1	8	yes	complemented
49	C₂×#6628872	C₂²	1	1	yes	characteristic
50	#72228070	C₂²	1	4	yes	complemented
51	#72228070	C₂²	1	4	yes	complemented
52	#72227583	C₂²	1	2	yes	complemented
53	#72226293	C₂²	1	4	yes	—
54	#72226293	C₂²	1	4	yes	complemented
55	#72213442	C₂²	1	8	yes	complemented
56	#72213434	C₂²	1	8	yes	complemented
57	#72213406	C₂²	1	4	yes	complemented
58	#72213406	C₂²	1	4	yes	complemented
59	#72213400	C₂²	1	4	yes	complemented
60	#72213400	C₂²	1	4	yes	complemented
61	#72213362	C₂²	1	2	yes	complemented
62	#72213214	C₂²	1	2	yes	complemented
63	C₂²×H(7,𝔽₂)	D₄	1	1	yes	characteristic
64	C₂×#60644	D₄	1	1	yes	characteristic
65	C₂²×#3021	D₄	1	1	yes	characteristic
66	C₂²×#3021	D₄	1	1	yes	characteristic
67	#8934620	C₂³	1	1	yes	characteristic, complemented
68	#8933848	C₂³	1	1	yes	characteristic, complemented
69	#8933774	C₂³	1	2	yes	complemented
70	#7711375	C₂³	1	2	yes	—
71	C₂²×#2867	D₄	1	1	yes	characteristic
72	C₂×#35527	C₂³	1	1	yes	characteristic
73	#6628872	D₄	1	2	yes	—
74	#6628872	D₄	1	2	yes	—
75	#6628872	C₂³	1	2	yes	—
76	#6628872	C₂³	1	2	yes	—
77	#6437610	C₂³	1	4	yes	—
78	C₂×#23445	D₄	1	1	yes	characteristic
79	C₂×#23430	D₄	1	1	yes	characteristic
80	C₂×#23430	C₂³	1	1	yes	characteristic
81	C₂×#23406	C₂³	1	1	yes	characteristic
82	C₂×#20615	C₂³	1	1	yes	characteristic
83	C₂×#20615	C₂³	1	1	yes	characteristic
84	C₂×#20592	D₄	1	1	yes	characteristic
85	#500030	C₂³	1	4	yes	—
86	#500030	C₂³	1	4	yes	complemented
87	#500028	C₂³	1	4	yes	—
88	#500028	C₂³	1	4	yes	complemented
89	#500024	D₄	1	4	yes	complemented
90	#500022	D₄	1	4	yes	complemented
91	#498990	D₄	1	4	yes	complemented
92	#498908	D₄	1	4	yes	complemented
93	#496222	C₂³	1	2	yes	complemented
94	#496222	C₂³	1	2	yes	complemented
95	C₂×#12861	C₂³	1	2	yes	—
96	#485668	C₂³	1	4	yes	complemented
97	#485667	C₂³	1	4	yes	complemented
98	C₂×#11507	C₂³	1	2	yes	—
99	#418909	C₂³	1	4	yes	—
100	#418906	C₂³	1	4	yes	—
101	#417807	D₄	1	2	yes	—
102	#417807	D₄	1	2	yes	—
103	#417807	C₂³	1	2	yes	—
104	#417807	C₂³	1	2	yes	—
105	#417798	D₄	1	2	yes	—
106	#417798	D₄	1	2	yes	—
107	#417798	C₂³	1	2	yes	—
108	#417798	C₂³	1	2	yes	—
109	C₂×#11006	D₄	1	1	yes	characteristic
110	C₂×#10981	D₄	1	1	yes	characteristic
111	#356069	C₂³	1	4	yes	—
112	C₂×#10939	D₄	1	1	yes	characteristic
113	C₂×#10923	D₄	1	1	yes	characteristic
114	C₂×#10923	C₂³	1	1	yes	characteristic
115	C₂×#10959	C₂³	1	1	yes	characteristic
116	#177884	C₂³	1	4	yes	complemented
117	#177875	C₂³	1	4	yes	complemented
118	#161199	C₂³	1	2	yes	—
119	#150581	C₂³	1	8	yes	complemented
120	#150570	C₂³	1	8	yes	complemented
121	#149750	C₂³	1	8	yes	—
122	#149748	C₂³	1	8	yes	complemented
123	#134056	C₂³	1	2	yes	complemented
124	#134056	C₂³	1	2	yes	complemented
125	#130079	C₂³	1	4	yes	complemented
126	#130078	C₂³	1	4	yes	complemented
127	#97517	C₂³	1	4	yes	complemented
128	#97515	C₂³	1	4	yes	complemented
129	#97460	C₂³	1	2	yes	complemented
130	#97460	C₂³	1	2	yes	complemented
131	#94191	C₂³	1	8	yes	complemented
132	#94178	C₂³	1	8	yes	complemented
133	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
134	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
135	C₂²×#585	C₂×D₄	1	1	yes	characteristic
136	C₂²×#585	C₂×D₄	1	1	yes	characteristic
137	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
138	C₂×#3449	C₂×D₄	1	1	yes	characteristic
139	C₂²×#535	C₂×D₄	1	1	yes	characteristic
140	C₂²×#535	C₂×D₄	1	1	yes	characteristic
141	C₂³×#127	C₂×D₄	1	1	yes	characteristic
142	C₂³×#127	C₂×D₄	1	1	yes	characteristic
143	#60644	C₂×D₄	1	2	yes	—
144	#60644	C₂×D₄	1	2	yes	—
145	C₂×#3021	C₂×D₄	1	2	yes	—
146	C₂×#3021	C₂×D₄	1	2	yes	—
147	C₂×#3021	C₂×D₄	1	2	yes	—
148	C₂×#3021	C₂×D₄	1	2	yes	—
149	C₂²×#413	C₂×D₄	1	1	yes	characteristic
150	C₂²×#413	C₂×D₄	1	1	yes	characteristic
151	C₂×#2873	C₂×D₄	1	1	yes	characteristic
152	#60048	C₂⁴	1	2	yes	—
153	#60047	C₂⁴	1	2	yes	—
154	#46318	C₂×D₄	1	2	yes	complemented
155	#46316	C₂×D₄	1	2	yes	complemented
156	#37194	C₂×D₄	1	2	yes	complemented
157	#37190	C₂×D₄	1	2	yes	complemented
158	C₂×#2867	C₂×D₄	1	2	yes	—
159	C₂×#2867	C₂×D₄	1	2	yes	—
160	#35527	C₂×D₄	1	1	yes	characteristic
161	#35527	C₂×D₄	1	1	yes	characteristic
162	#35527	C₂×D₄	1	1	yes	characteristic
163	#35527	C₂×D₄	1	1	yes	characteristic
164	#35527	C₂×D₄	1	1	yes	characteristic
165	#35527	C₂×D₄	1	1	yes	characteristic
166	#35527	C₂⁴	1	1	yes	characteristic
167	#35527	C₂⁴	1	1	yes	characteristic
168	C₂×#2309	C₂×D₄	1	1	yes	characteristic
169	C₂×#2297	C₂×D₄	1	1	yes	characteristic
170	C₂×#2297	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄³	C₂×D₄	1	1	yes	characteristic
172	#23445	C₂×D₄	1	2	yes	—
173	#23445	C₂×D₄	1	2	yes	—
174	#23430	C₂×D₄	1	2	yes	—
175	#23430	C₂×D₄	1	2	yes	—
176	#23430	C₂×D₄	1	2	yes	—
177	#23430	C₂⁴	1	2	yes	—
178	#23406	C₂×D₄	1	2	yes	—
179	#23406	C₂⁴	1	2	yes	—
180	#20615	C₂×D₄	1	2	yes	—
181	#20615	C₂×D₄	1	2	yes	—
182	#20615	C₂×D₄	1	4	yes	—
183	#20615	C₂⁴	1	2	yes	—
184	#20615	C₂⁴	1	2	yes	—
185	C₂×#1793	C₂×D₄	1	4	yes	—
186	#20592	C₂×D₄	1	2	yes	—
187	#20592	C₂×D₄	1	2	yes	—
188	C₂×#1742	C₂×D₄	1	1	yes	characteristic
189	C₂×#1740	C₂×D₄	1	1	yes	characteristic
190	C₂×#1728	C₂×D₄	1	1	yes	characteristic
191	C₂×#1728	C₂×D₄	1	1	yes	characteristic
192	#13379	C₂×D₄	1	8	yes	complemented
193	#13378	C₂×D₄	1	8	yes	complemented
194	#13359	C₂×D₄	1	8	yes	complemented
195	#13357	C₂×D₄	1	8	yes	complemented
196	#12861	C₂×D₄	1	4	yes	complemented
197	#12861	C₂⁴	1	4	yes	—
198	C₂×#1394	C₂×D₄	1	4	yes	complemented
199	#11507	C₂⁴	1	4	yes	—
200	#11006	C₂×D₄	1	2	yes	—
201	#11006	C₂×D₄	1	2	yes	—
202	#10981	C₂×D₄	1	2	yes	—
203	#10981	C₂×D₄	1	2	yes	—
204	#10959	C₂×D₄	1	2	yes	—
205	#10959	C₂⁴	1	2	yes	—
206	#10939	C₂×D₄	1	2	yes	—
207	#10939	C₂×D₄	1	2	yes	—
208	#10923	C₂×D₄	1	2	yes	—
209	#10923	C₂×D₄	1	2	yes	—
210	#10923	C₂×D₄	1	2	yes	—
211	#10923	C₂⁴	1	2	yes	—
212	#7631	C₂⁴	1	4	yes	—
213	C₂×#585	#120	1	2	yes	—
214	C₂×#585	C₂²×D₄	1	2	yes	—
215	C₂×#585	C₂²×D₄	1	2	yes	—
216	C₂²×2₋¹⁺⁴	#120	1	2	yes	—
217	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
218	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
219	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
220	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
221	C₂³×#41	#120	1	1	yes	characteristic
222	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
223	C₂⁴×D₄	#120	1	1	yes	characteristic
224	C₂⁴×D₄	#120	1	1	yes	characteristic
225	#3449	C₂²×D₄	1	2	yes	—
226	C₂×#535	#120	1	1	yes	characteristic
227	C₂×#535	#120	1	1	yes	characteristic
228	C₂×#535	#120	1	1	yes	characteristic
229	C₂×#535	#120	1	1	yes	characteristic
230	C₂×#535	C₂²×D₄	1	1	yes	characteristic
231	C₂×#535	C₂²×D₄	1	1	yes	characteristic
232	C₂×#535	C₂²×D₄	1	1	yes	characteristic
233	C₂×#535	C₂²×D₄	1	1	yes	characteristic
234	C₂²×#127	#120	1	1	yes	characteristic
235	C₂²×#127	#120	1	1	yes	characteristic
236	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
237	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
238	C₂²×#127	C₂²×D₄	1	2	yes	—
239	C₂²×#117	#120	1	1	yes	characteristic
240	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
241	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
242	C₂×#413	#120	1	2	yes	—
243	C₂×#413	C₂²×D₄	1	2	yes	—
244	C₂×#413	C₂²×D₄	1	2	yes	—
245	C₂²×#101	#120	1	2	yes	—
246	#2873	C₂²×D₄	1	2	yes	—
247	#2811	C₂²×D₄	1	2	yes	complemented
248	#2809	C₂²×D₄	1	2	yes	complemented
249	#2734	C₂²×D₄	1	2	yes	complemented
250	#2733	C₂²×D₄	1	2	yes	complemented
251	#2309	#120	1	1	yes	characteristic
252	#2309	#120	1	1	yes	characteristic
253	#2309	C₂²×D₄	1	1	yes	characteristic
254	#2309	C₂²×D₄	1	1	yes	characteristic
255	#2297	#120	1	1	yes	characteristic
256	#2297	#120	1	1	yes	characteristic
257	#2297	C₂²×D₄	1	1	yes	characteristic
258	#2297	C₂²×D₄	1	1	yes	characteristic
259	#2297	C₂²×D₄	1	1	yes	characteristic
260	#2297	C₂²×D₄	1	1	yes	characteristic
261	#2297	C₂²×D₄	1	2	yes	—
262	#2297	C₂²×D₄	1	1	yes	characteristic
263	#2297	H(5,𝔽₂)	1	2	yes	—
264	#2297	C₂⁵	1	1	yes	characteristic
265	C₂×#391	C₂²×D₄	1	2	yes	—
266	C₂×#390	H(5,𝔽₂)	1	2	yes	—
267	C₂×C₄³	C₂²×D₄	1	2	yes	—
268	#1793	#120	1	8	yes	—
269	#1793	C₂²×D₄	1	8	yes	—
270	#1742	C₂²×D₄	1	2	yes	—
271	#1740	C₂²×D₄	1	2	yes	—
272	#1728	C₂²×D₄	1	2	yes	—
273	#1728	C₂²×D₄	1	2	yes	—
274	#1394	C₂²×D₄	1	8	yes	complemented
275	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
276	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
277	C₂×2₋¹⁺⁴	#453	1	8	yes	complemented
278	C₂×2₋¹⁺⁴	C₂×#120	1	4	yes	—
279	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
280	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
281	C₂²×#41	C₂×#120	1	1	yes	characteristic
282	C₂²×#41	C₂×#120	1	1	yes	characteristic
283	C₂²×#41	C₂×#120	1	1	yes	characteristic
284	C₂²×#41	C₂×#120	1	1	yes	characteristic
285	C₂²×#41	#534	1	1	yes	characteristic
286	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
287	C₂³×Q₈	B(4,𝔽₂)	1	1	yes	characteristic
288	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
289	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
290	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
291	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
292	C₂³×D₄	C₂×#120	1	1	yes	characteristic
293	C₂³×D₄	C₂×#120	1	1	yes	characteristic
294	C₂³×D₄	C₂×#120	1	1	yes	characteristic
295	C₂³×D₄	C₂×#120	1	1	yes	characteristic
296	C₂³×D₄	#534	1	1	yes	characteristic
297	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
298	C₂×#117	C₂×#120	1	1	yes	characteristic
299	C₂×#117	C₂×#120	1	1	yes	characteristic
300	C₂×#117	C₂×#120	1	1	yes	characteristic
301	C₂×#117	D₄²	1	2	yes	—
302	C₂×#117	C₂³×D₄	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	D₄²	1	2	yes	—
304	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
305	C₂²×C₄²	D₄²	1	2	yes	—
306	C₂²×C₄²	D₄²	1	2	yes	—
307	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
308	C₂×#101	C₂×#120	1	4	yes	—
309	#391	C₂×#120	1	2	yes	—
310	#391	D₄²	1	2	yes	—
311	#391	D₄²	1	2	yes	—
312	#391	C₂³×D₄	1	2	yes	—
313	#390	#534	1	2	yes	—
314	#390	D₄²	1	2	yes	—
315	#390	D₄²	1	2	yes	—
316	#390	C₂×H(5,𝔽₂)	1	2	yes	—
317	C₂⁵	#2196	1	4	yes	—
318	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
319	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
320	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
321	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
322	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
323	2₋¹⁺⁴	C₂×#453	1	8	yes	—
324	C₂²×Q₈	#2196	1	2	yes	—
325	C₂²×Q₈	#2196	1	2	yes	—
326	C₂²×Q₈	#2403	1	1	yes	characteristic
327	C₂²×Q₈	C₂×#453	1	4	yes	—
328	C₂²×Q₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
329	C₂²×Q₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
330	C₂²×Q₈	C₂²×#120	1	1	yes	characteristic
331	C₂²×D₄	#2403	1	1	yes	characteristic
332	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
333	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
334	C₂²×D₄	C₂×#534	1	1	yes	characteristic
335	C₂³×C₄	#2403	1	1	yes	characteristic
336	C₂³×C₄	#2403	1	1	yes	characteristic
337	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
338	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
339	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
340	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
341	C₂×C₄⋊C₄	#2403	1	2	yes	—
342	C₂×C₄⋊C₄	C₂×D₄²	1	2	yes	—
343	C₂×C₄²	#2403	1	2	yes	—
344	C₂×C₄²	C₂×D₄²	1	2	yes	—
345	C₂⁴	#23900	1	1	yes	characteristic
346	C₂⁴	#23900	1	1	yes	characteristic
347	C₂⁴	C₂×#2196	1	2	yes	—
348	C₂⁴	C₂×#2196	1	2	yes	—
349	C₂⁴	C₂×#2196	1	2	yes	—
350	C₂⁴	#33551	1	2	yes	—
351	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
352	C₂×Q₈	#23906	1	2	yes	—
353	C₂×Q₈	C₂×#2196	1	2	yes	—
354	C₂×Q₈	C₂×#2196	1	2	yes	—
355	C₂×Q₈	C₂²×#453	1	2	yes	—
356	C₂²×C₄	#23897	1	2	yes	—
357	C₂²×C₄	#23900	1	1	yes	characteristic
358	C₂²×C₄	#23900	1	1	yes	characteristic
359	C₂²×C₄	#23906	1	2	yes	—
360	C₂²×C₄	C₂×#2196	1	1	yes	characteristic
361	C₂²×C₄	C₂×#2196	1	1	yes	characteristic
362	C₂²×C₄	#33551	1	1	yes	characteristic
363	C₂²×C₄	#33551	1	1	yes	characteristic
364	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
365	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
366	C₂³	#249319	1	2	yes	—
367	C₂³	#499787	1	1	yes	characteristic
368	C₂³	#499787	1	1	yes	characteristic
369	C₂³	#499787	1	2	yes	—
370	C₂³	#499787	1	2	yes	—
371	C₂³	C₂×#23900	1	1	yes	characteristic
372	C₂³	C₂²×#2196	1	1	yes	characteristic
373	C₂³	C₂×#33551	1	1	yes	characteristic
374	C₂×C₄	#249319	1	2	yes	—
375	C₂×C₄	#499787	1	1	yes	characteristic
376	C₂×C₄	#499787	1	1	yes	characteristic
377	C₂×C₄	C₂×#23906	1	1	yes	characteristic
378	C₂×C₄	C₂×#23897	1	1	yes	characteristic
379	C₂×C₄	C₂²×#2196	1	1	yes	characteristic
380	C₂×C₄	C₂×#33551	1	1	yes	characteristic
381	C₂²	#72213827	1	2	yes	—
382	C₂²	#72213827	1	2	yes	—
383	C₂²	C₂×#499787	1	1	yes	characteristic
384	C₂²	C₂×#499787	1	1	yes	characteristic
385	C₂²	C₂×#249319	1	1	yes	characteristic
386	C₂	C₂×#72213827	1	1	yes	characteristic
387	C₂	#72340650	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#499787
commutator, Frattini, cosocle	#2297	C₂⁵
LCS	G ▷ #2297 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×#41 ◁ C₂×#35527 ◁ G
LECS	G ▷ #2297 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72340732	C₂	semidirect
2. #72340729	C₂	semidirect
3. #72340723	C₂	semidirect
4. #72340722	C₂	semidirect
5. C₂×#72213400	C₂	semidirect
6. C₂×#496222	C₂²	semidirect
7. #72340701	C₂	semidirect
8. #72340699	C₂²	semidirect
9. #72340695	C₂	semidirect
10. #72340694	C₂²	semidirect
11. C₂×#134056	C₂²	semidirect
12. #72340691	C₂²	semidirect
13. #72340688	C₂	semidirect
14. #72340685	C₂²	semidirect
15. #72340677	C₂	semidirect
16. C₂×#72226293	C₂	semidirect
17. C₂×#150570	C₂²	semidirect
18. #72340671	C₂²	semidirect
19. #72340669	C₂	semidirect
20. #72340668	C₂²	semidirect
21. #72340667	C₂²	semidirect
22. #72340664	C₂	semidirect
23. #72340662	C₂²	semidirect
24. #72340660	C₂²	semidirect
26. #72340658	C₂²	semidirect
27. C₂×#94178	C₂²	semidirect
28. #72340652	C₂²	semidirect
29. C₂×#418906	C₂²	semidirect
30. #72340602	C₂²	semidirect
31. C₂×#356069	C₂²	semidirect
32. #72340590	C₂²	semidirect
33. C₂×#418909	C₂²	semidirect
35. #72337682	C₂	semidirect
36. #72337681	C₂²	semidirect
37. #72337680	C₂²	semidirect
38. #72337679	C₂²	semidirect
39. #72337677	C₂²	semidirect
40. #72337676	C₂²	semidirect
41. #72337675	C₂²	semidirect
42. #72337674	C₂²	semidirect
43. C₂×#6437610	C₂²	semidirect
44. #72262727	C₂²	semidirect
46. #72241405	C₂	semidirect
47. #72241404	C₂²	semidirect
48. #72241403	C₂²	semidirect
50. #72228070	C₂²	semidirect
51. #72228070	C₂²	semidirect
52. #72227583	C₂²	semidirect
54. #72226293	C₂²	semidirect
55. #72213442	C₂²	semidirect
56. #72213434	C₂²	semidirect
57. #72213406	C₂²	semidirect
58. #72213406	C₂²	semidirect
59. #72213400	C₂²	semidirect
60. #72213400	C₂²	semidirect
61. #72213362	C₂²	semidirect
62. #72213214	C₂²	semidirect
67. #8934620	C₂³	semidirect
68. #8933848	C₂³	semidirect
69. #8933774	C₂³	semidirect
86. #500030	C₂³	semidirect
88. #500028	C₂³	semidirect
89. #500024	D₄	semidirect
90. #500022	D₄	semidirect
91. #498990	D₄	semidirect
92. #498908	D₄	semidirect
93. #496222	C₂³	semidirect
94. #496222	C₂³	semidirect
96. #485668	C₂³	semidirect
97. #485667	C₂³	semidirect
116. #177884	C₂³	semidirect
117. #177875	C₂³	semidirect
119. #150581	C₂³	semidirect
120. #150570	C₂³	semidirect
122. #149748	C₂³	semidirect
123. #134056	C₂³	semidirect
124. #134056	C₂³	semidirect
125. #130079	C₂³	semidirect
126. #130078	C₂³	semidirect
127. #97517	C₂³	semidirect
128. #97515	C₂³	semidirect
129. #97460	C₂³	semidirect
130. #97460	C₂³	semidirect
131. #94191	C₂³	semidirect
132. #94178	C₂³	semidirect
154. #46318	C₂×D₄	semidirect
155. #46316	C₂×D₄	semidirect
156. #37194	C₂×D₄	semidirect
157. #37190	C₂×D₄	semidirect
192. #13379	C₂×D₄	semidirect
193. #13378	C₂×D₄	semidirect
194. #13359	C₂×D₄	semidirect
195. #13357	C₂×D₄	semidirect
196. #12861	C₂×D₄	semidirect
198. C₂×#1394	C₂×D₄	semidirect
247. #2811	C₂²×D₄	semidirect
248. #2809	C₂²×D₄	semidirect
249. #2734	C₂²×D₄	semidirect
250. #2733	C₂²×D₄	semidirect
274. #1394	C₂²×D₄	semidirect
277. C₂×2₋¹⁺⁴	#453	semidirect

Maximal subgroups

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

subgroup	index
#72340732	2
#72340729	2
#72340723	2
#72340722	2
C₂×#72213400	2
#72340701	2
#72340695	2
#72340688	2
#72340677	2
C₂×#72226293	2
#72340669	2
#72340664	2
#72337682	2
#72241405	2