Subgroups — #72266017

Order 2048.

At least 6690 conjugacy classes of subgroups; only the 1432 normal subgroups are shown.

The subgroup lattice has 391 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266011	C₂	1	2	yes	maximal, complemented
2	#72261893	C₂	1	1	yes	maximal, characteristic, complemented
3	#72258613	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#10336	C₂	1	2	yes	maximal, complemented
5	#72241200	C₂	1	8	yes	maximal, complemented
6	#72241125	C₂	1	1	yes	maximal, characteristic, complemented
7	#72238531	C₂	1	1	yes	maximal, characteristic, complemented
8	#72237501	C₂	1	8	yes	maximal, complemented
9	C₂×#233541	C₂	1	2	yes	maximal, complemented
10	#72234629	C₂	1	2	yes	maximal, complemented
11	C₂×#6628892	C₂	1	1	yes	maximal, characteristic, complemented
12	#72233780	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#32898	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂×#34980	C₂²	1	2	yes	—
16	C₂×#34980	C₂²	1	1	yes	characteristic
17	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
18	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#2403	C₂²	1	1	yes	characteristic
20	C₂²×#2403	C₂²	1	2	yes	—
21	C₂²×#2403	C₂²	1	2	yes	—
22	C₂²×#2403	C₂²	1	1	yes	characteristic
23	C₂²×#2403	C₂²	1	1	yes	characteristic, complemented
24	C₂×#32900	C₂²	1	4	yes	complemented
25	C₂×#32898	C₂²	1	8	yes	complemented
26	C₂×#32898	C₂²	1	4	yes	complemented
27	C₂×#21746	C₂²	1	2	yes	complemented
28	C₂²×#1781	C₂²	1	1	yes	characteristic
29	C₂²×#1781	C₂²	1	1	yes	characteristic
30	C₂²×#1781	C₂²	1	2	yes	—
31	C₂²×#1781	C₂²	1	2	yes	—
32	C₂²×#1781	C₂²	1	2	yes	complemented
33	C₂²×#1781	C₂²	1	2	yes	complemented
34	#4928938	C₂²	1	8	yes	complemented
35	#765934	C₂²	1	4	yes	complemented
36	#763814	C₂²	1	4	yes	complemented
37	#517411	C₂²	1	1	yes	characteristic
38	#517411	C₂²	1	2	yes	—
39	#513778	C₂²	1	1	yes	characteristic, complemented
40	#405104	C₂²	1	8	yes	complemented
41	#393929	C₂²	1	8	yes	complemented
42	#355913	C₂²	1	2	yes	complemented
43	C₂×#10337	C₂²	1	8	yes	complemented
44	C₂×#10336	C₂²	1	16	yes	complemented
45	C₂×#10336	C₂²	1	8	yes	complemented
46	C₂×#8101	C₂²	1	2	yes	complemented
47	C₂²×#1304	C₂²	1	2	yes	complemented
48	#115135	C₂²	1	4	yes	complemented
49	#115133	C₂²	1	4	yes	complemented
50	#115133	C₂²	1	8	yes	complemented
51	#111516	C₂²	1	8	yes	complemented
52	#110401	C₂²	1	16	yes	complemented
53	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
54	C₂⁵×D₄	C₂³	1	1	yes	characteristic
55	C₂⁵×D₄	C₂³	1	1	yes	characteristic
56	C₂⁵×D₄	C₂³	1	1	yes	characteristic
57	C₂⁵×D₄	C₂³	1	2	yes	—
58	C₂²×#534	D₄	1	2	yes	complemented
59	C₂²×#534	C₂³	1	2	yes	complemented
60	C₂³×#120	D₄	1	2	yes	complemented
61	C₂³×#120	D₄	1	2	yes	complemented
62	C₂³×#120	D₄	1	2	yes	complemented
63	C₂³×#120	C₂³	1	1	yes	characteristic
64	C₂×#2405	D₄	1	2	yes	complemented
65	C₂×#2405	C₂³	1	2	yes	—
66	C₂×#2405	C₂³	1	4	yes	—
67	C₂×#2405	C₂³	1	2	yes	complemented
68	C₂×#2403	D₄	1	4	yes	complemented
69	C₂×#2403	D₄	1	2	yes	complemented
70	C₂×#2403	C₂³	1	8	yes	—
71	C₂×#2403	C₂³	1	4	yes	—
72	C₂×#2403	C₂³	1	2	yes	—
73	C₂×#2403	C₂³	1	8	yes	—
74	C₂×#2403	C₂³	1	4	yes	—
75	C₂×#2403	C₂³	1	4	yes	complemented
76	C₂×#2403	C₂³	1	2	yes	complemented
77	C₂²×#392	C₂³	1	4	yes	—
78	C₂×#2308	D₄	1	2	yes	complemented
79	C₂×#2308	C₂³	1	2	yes	complemented
80	C₂²×#386	D₄	1	2	yes	complemented
81	C₂²×#386	D₄	1	2	yes	complemented
82	C₂²×#386	D₄	1	2	yes	complemented
83	C₂²×#379	C₂³	1	2	yes	—
84	C₂²×#379	C₂³	1	2	yes	—
85	C₂²×#379	C₂³	1	2	yes	—
86	C₂²×#379	C₂³	1	1	yes	characteristic
87	C₂²×#379	C₂³	1	1	yes	characteristic
88	C₂²×#379	C₂³	1	1	yes	characteristic
89	C₂×#1819	C₂³	1	4	yes	complemented
90	C₂×#1781	D₄	1	16	yes	complemented
91	C₂×#1781	D₄	1	16	yes	complemented
92	C₂×#1781	C₂³	1	4	yes	—
93	C₂×#1781	C₂³	1	4	yes	—
94	C₂×#1781	C₂³	1	8	yes	—
95	C₂×#1781	C₂³	1	8	yes	—
96	C₂×#1781	C₂³	1	8	yes	complemented
97	C₂×#1781	C₂³	1	4	yes	complemented
98	C₂×#1781	C₂³	1	8	yes	complemented
99	#14681	D₄	1	4	yes	complemented
100	#14679	D₄	1	4	yes	complemented
101	#14335	C₂³	1	4	yes	—
102	#13867	D₄	1	8	yes	complemented
103	#13867	C₂³	1	8	yes	—
104	#13775	C₂³	1	4	yes	complemented
105	#10725	C₂³	1	8	yes	complemented
106	C₂×#1304	C₂³	1	8	yes	complemented
107	C₂×#1304	C₂³	1	8	yes	complemented
108	C₂⁷	C₂×D₄	1	1	yes	characteristic
109	C₂⁷	C₂×D₄	1	1	yes	characteristic
110	C₂⁷	C₂×D₄	1	1	yes	characteristic
111	C₂⁷	C₂×D₄	1	2	yes	—
112	C₂⁷	C₂⁴	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	2	yes	—
114	C₂⁴×D₄	C₂×D₄	1	2	yes	—
115	C₂⁴×D₄	C₂×D₄	1	2	yes	—
116	C₂⁴×D₄	C₂×D₄	1	2	yes	—
117	C₂⁴×D₄	C₂×D₄	1	8	yes	—
118	C₂⁴×D₄	C₂×D₄	1	8	yes	—
119	C₂⁴×D₄	C₂×D₄	1	2	yes	—
120	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×D₄	C₂×D₄	1	2	yes	—
122	C₂⁴×D₄	C₂×D₄	1	2	yes	—
123	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂⁴×D₄	C₂×D₄	1	4	yes	—
125	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
126	C₂⁴×D₄	C₂⁴	1	2	yes	—
127	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
128	C₂⁴×D₄	C₂⁴	1	2	yes	—
129	C₂⁴×D₄	C₂⁴	1	4	yes	—
130	C₂⁴×D₄	C₂⁴	1	2	yes	—
131	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
133	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
134	C₂⁵×C₄	C₂×D₄	1	2	yes	—
135	C₂²×#123	C₂×D₄	1	4	yes	complemented
136	C₂²×#120	C₂×D₄	1	4	yes	complemented
137	C₂²×#120	C₂×D₄	1	8	yes	complemented
138	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
141	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
142	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
143	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
144	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
145	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
146	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
147	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
149	C₂×#386	C₂×D₄	1	4	yes	complemented
150	C₂×#386	C₂×D₄	1	4	yes	complemented
151	C₂×#386	C₂×D₄	1	8	yes	complemented
152	C₂×#379	C₂×D₄	1	8	yes	—
153	C₂×#379	C₂×D₄	1	8	yes	—
154	C₂×#379	C₂×D₄	1	8	yes	—
155	C₂×#379	C₂×D₄	1	8	yes	—
156	C₂×#379	C₂×D₄	1	4	yes	—
157	C₂×#379	C₂×D₄	1	2	yes	—
158	C₂×#379	C₂×D₄	1	2	yes	—
159	C₂×#379	C₂×D₄	1	4	yes	—
160	C₂×#379	C₂×D₄	1	4	yes	—
161	C₂×#379	C₂×D₄	1	16	yes	complemented
162	C₂×#379	C₂⁴	1	4	yes	—
163	C₂×#379	C₂⁴	1	4	yes	—
164	C₂×#379	C₂⁴	1	4	yes	—
165	C₂×#379	C₂⁴	1	2	yes	—
166	C₂×#379	C₂⁴	1	2	yes	—
167	C₂²×#95	C₂×D₄	1	4	yes	complemented
168	#1781	C₂×D₄	1	32	yes	complemented
169	#1781	C₂×D₄	1	32	yes	complemented
170	C₂²⋊#95	C₂×D₄	1	16	yes	complemented
171	C₂⁶	#120	1	2	yes	—
172	C₂⁶	#120	1	2	yes	—
173	C₂⁶	#127	1	8	yes	complemented
174	C₂⁶	C₂²×D₄	1	2	yes	—
175	C₂⁶	C₂²×D₄	1	1	yes	characteristic
176	C₂⁶	C₂²×D₄	1	1	yes	characteristic
177	C₂⁶	C₂²×D₄	1	1	yes	characteristic
178	C₂⁶	C₂²×D₄	1	2	yes	—
179	C₂⁶	C₂²×D₄	1	2	yes	—
180	C₂⁶	C₂²×D₄	1	1	yes	characteristic
181	C₂⁶	C₂²×D₄	1	4	yes	—
182	C₂⁶	C₂²×D₄	1	1	yes	characteristic
183	C₂⁶	C₂²×D₄	1	2	yes	—
184	C₂⁶	C₂²×D₄	1	1	yes	characteristic
185	C₂⁶	C₂²×D₄	1	2	yes	—
186	C₂⁶	C₂²×D₄	1	1	yes	characteristic
187	C₂⁶	C₂²×D₄	1	4	yes	—
188	C₂⁶	C₂²×D₄	1	4	yes	—
189	C₂⁶	H(5,𝔽₂)	1	2	yes	—
190	C₂⁶	H(5,𝔽₂)	1	2	yes	—
191	C₂⁶	H(5,𝔽₂)	1	4	yes	—
192	C₂⁶	H(5,𝔽₂)	1	4	yes	—
193	C₂⁶	C₂⁵	1	1	yes	characteristic
194	C₂³×D₄	#120	1	4	yes	—
195	C₂³×D₄	#120	1	4	yes	—
196	C₂³×D₄	#127	1	16	yes	complemented
197	C₂³×D₄	C₂²×D₄	1	4	yes	—
198	C₂³×D₄	C₂²×D₄	1	4	yes	—
199	C₂³×D₄	C₂²×D₄	1	8	yes	—
200	C₂³×D₄	C₂²×D₄	1	8	yes	—
201	C₂⁴×C₄	#120	1	2	yes	—
202	C₂⁴×C₄	#120	1	2	yes	—
203	C₂⁴×C₄	#127	1	8	yes	complemented
204	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
205	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
206	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
207	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
208	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
209	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
210	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
211	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
212	C₂²×C₂²⋊C₄	#120	1	4	yes	—
213	C₂²×C₂²⋊C₄	#120	1	8	yes	—
214	C₂²×C₂²⋊C₄	#120	1	4	yes	—
215	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
216	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
217	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
218	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
219	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
220	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
221	#379	#120	1	8	yes	complemented
222	#379	#120	1	8	yes	complemented
223	#379	C₂²×D₄	1	8	yes	—
224	#379	C₂²×D₄	1	8	yes	—
225	#379	C₂²×D₄	1	8	yes	—
226	#379	C₂²×D₄	1	8	yes	—
227	C₂⁵	C₂×#120	1	1	yes	characteristic
228	C₂⁵	C₂×#120	1	1	yes	characteristic
229	C₂⁵	C₂×#120	1	2	yes	—
230	C₂⁵	C₂×#120	1	4	yes	—
231	C₂⁵	C₂×#120	1	1	yes	characteristic
232	C₂⁵	C₂×#120	1	1	yes	characteristic
233	C₂⁵	C₂×#120	1	1	yes	characteristic
234	C₂⁵	C₂×#120	1	2	yes	—
235	C₂⁵	C₂×#120	1	2	yes	—
236	C₂⁵	C₂×#120	1	2	yes	—
237	C₂⁵	C₂×#120	1	1	yes	characteristic
238	C₂⁵	C₂×#120	1	2	yes	—
239	C₂⁵	C₂×#127	1	8	yes	—
240	C₂⁵	C₂×#127	1	4	yes	—
241	C₂⁵	C₂×#127	1	4	yes	—
242	C₂⁵	#534	1	1	yes	characteristic
243	C₂⁵	#534	1	2	yes	—
244	C₂⁵	#534	1	2	yes	—
245	C₂⁵	#534	1	2	yes	—
246	C₂⁵	#534	1	1	yes	characteristic
247	C₂⁵	#534	1	2	yes	—
248	C₂⁵	#534	1	2	yes	—
249	C₂⁵	#535	1	4	yes	—
250	C₂⁵	#535	1	4	yes	—
251	C₂⁵	#535	1	4	yes	—
252	C₂⁵	#535	1	4	yes	—
253	C₂⁵	#535	1	4	yes	—
254	C₂⁵	#535	1	4	yes	—
255	C₂⁵	D₄²	1	2	yes	—
256	C₂⁵	D₄²	1	2	yes	—
257	C₂⁵	D₄²	1	2	yes	—
258	C₂⁵	D₄²	1	2	yes	—
259	C₂⁵	D₄²	1	2	yes	—
260	C₂⁵	D₄²	1	4	yes	—
261	C₂⁵	D₄²	1	4	yes	—
262	C₂⁵	D₄²	1	4	yes	—
263	C₂⁵	D₄²	1	4	yes	—
264	C₂⁵	D₄²	1	4	yes	—
265	C₂⁵	D₄²	1	2	yes	—
266	C₂⁵	D₄²	1	2	yes	—
267	C₂⁵	D₄²	1	2	yes	—
268	C₂⁵	D₄²	1	4	yes	—
269	C₂⁵	D₄²	1	4	yes	—
270	C₂⁵	D₄²	1	4	yes	—
271	C₂⁵	D₄²	1	4	yes	—
272	C₂⁵	D₄²	1	4	yes	—
273	C₂⁵	D₄²	1	4	yes	—
274	C₂⁵	D₄²	1	4	yes	—
275	C₂⁵	D₄²	1	4	yes	—
276	C₂⁵	D₄²	1	4	yes	—
277	C₂⁵	#560	1	4	yes	—
278	C₂⁵	#560	1	4	yes	—
279	C₂⁵	C₂³×D₄	1	1	yes	characteristic
280	C₂⁵	C₂³×D₄	1	1	yes	characteristic
281	C₂⁵	C₂³×D₄	1	1	yes	characteristic
282	C₂⁵	C₂³×D₄	1	2	yes	—
283	C₂⁵	C₂³×D₄	1	2	yes	—
284	C₂⁵	C₂³×D₄	1	2	yes	—
285	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
286	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
287	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
288	C₂²×D₄	B(4,𝔽₂)	1	16	yes	—
289	C₂³×C₄	C₂×#120	1	4	yes	—
290	C₂³×C₄	C₂×#120	1	8	yes	—
291	C₂³×C₄	C₂×#127	1	8	yes	—
292	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
293	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
294	C₂⁴	#2403	1	1	yes	characteristic
295	C₂⁴	#2403	1	1	yes	characteristic
296	C₂⁴	#2403	1	1	yes	characteristic
297	C₂⁴	#2403	1	2	yes	—
298	C₂⁴	#2403	1	2	yes	—
299	C₂⁴	#2403	1	2	yes	—
300	C₂⁴	#2403	1	1	yes	characteristic
301	C₂⁴	#2403	1	2	yes	—
302	C₂⁴	#2403	1	2	yes	—
303	C₂⁴	#2403	1	2	yes	—
304	C₂⁴	#2403	1	2	yes	—
305	C₂⁴	#2403	1	2	yes	—
306	C₂⁴	#2403	1	2	yes	—
307	C₂⁴	#2403	1	2	yes	—
308	C₂⁴	#2433	1	4	yes	—
309	C₂⁴	#2433	1	4	yes	—
310	C₂⁴	#2433	1	4	yes	—
311	C₂⁴	#2433	1	4	yes	—
312	C₂⁴	#2433	1	4	yes	—
313	C₂⁴	#2433	1	4	yes	—
314	C₂⁴	#2433	1	4	yes	—
315	C₂⁴	#2433	1	4	yes	—
316	C₂⁴	#2433	1	4	yes	—
317	C₂⁴	#2433	1	4	yes	—
318	C₂⁴	#2433	1	4	yes	—
319	C₂⁴	#2433	1	4	yes	—
320	C₂⁴	#2669	1	4	yes	—
321	C₂⁴	#2669	1	4	yes	—
322	C₂⁴	#2669	1	4	yes	—
323	C₂⁴	#2669	1	4	yes	—
324	C₂⁴	#2669	1	4	yes	—
325	C₂⁴	#2669	1	4	yes	—
326	C₂⁴	#2669	1	4	yes	—
327	C₂⁴	#2669	1	4	yes	—
328	C₂⁴	#2669	1	4	yes	—
329	C₂⁴	#2669	1	4	yes	—
330	C₂⁴	#2669	1	4	yes	—
331	C₂⁴	#2669	1	4	yes	—
332	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
333	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
334	C₂⁴	C₂²×#120	1	1	yes	characteristic
335	C₂⁴	C₂²×#120	1	1	yes	characteristic
336	C₂⁴	C₂²×#120	1	1	yes	characteristic
337	C₂⁴	C₂²×#120	1	1	yes	characteristic
338	C₂⁴	C₂²×#127	1	2	yes	—
339	C₂⁴	C₂×#534	1	1	yes	characteristic
340	C₂⁴	C₂×#534	1	1	yes	characteristic
341	C₂⁴	C₂×#534	1	1	yes	characteristic
342	C₂⁴	C₂×#535	1	2	yes	—
343	C₂⁴	C₂×#535	1	2	yes	—
344	C₂⁴	C₂×#535	1	2	yes	—
345	C₂⁴	C₂×D₄²	1	2	yes	—
346	C₂⁴	C₂×D₄²	1	2	yes	—
347	C₂⁴	C₂×D₄²	1	2	yes	—
348	C₂⁴	C₂×D₄²	1	2	yes	—
349	C₂⁴	C₂×D₄²	1	2	yes	—
350	C₂⁴	C₂×D₄²	1	2	yes	—
351	C₂⁴	C₂×D₄²	1	2	yes	—
352	C₂⁴	C₂×D₄²	1	2	yes	—
353	C₂⁴	C₂×D₄²	1	2	yes	—
354	C₂⁴	C₂×#560	1	2	yes	—
355	C₂²×C₄	C₂×B(4,𝔽₂)	1	8	yes	—
356	C₂³	#15258	1	2	yes	—
357	C₂³	#15258	1	4	yes	—
358	C₂³	#15258	1	2	yes	—
359	C₂³	#15258	1	2	yes	—
360	C₂³	#15258	1	2	yes	—
361	C₂³	#15258	1	4	yes	—
362	C₂³	#23895	1	4	yes	—
363	C₂³	#23900	1	8	yes	—
364	C₂³	#23900	1	8	yes	—
365	C₂³	#23900	1	8	yes	—
366	C₂³	C₂×#2403	1	1	yes	characteristic
367	C₂³	C₂×#2403	1	1	yes	characteristic
368	C₂³	C₂×#2403	1	1	yes	characteristic
369	C₂³	C₂×#2433	1	2	yes	—
370	C₂³	C₂×#2433	1	2	yes	—
371	C₂³	C₂×#2433	1	2	yes	—
372	C₂³	C₂×#2669	1	2	yes	—
373	C₂³	C₂×#2669	1	2	yes	—
374	C₂³	C₂×#2669	1	2	yes	—
375	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
376	C₂³	#60399	1	4	yes	—
377	C₂²	#417744	1	8	yes	—
378	C₂²	#417824	1	4	yes	—
379	C₂²	C₂×#15258	1	1	yes	characteristic
380	C₂²	C₂×#23900	1	2	yes	—
381	C₂²	C₂×#23900	1	2	yes	—
382	C₂²	C₂×#23900	1	2	yes	—
383	C₂²	C₂×#23895	1	2	yes	—
384	C₂²	#6437632	1	2	yes	—
385	C₂²	#6443353	1	4	yes	—
386	C₂	C₂×#417744	1	1	yes	characteristic
387	C₂	#72233042	1	4	yes	—
388	C₂	C₂×#417824	1	1	yes	characteristic
389	C₂	#72241086	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266011	C₂	semidirect
2. #72261893	C₂	semidirect
3. #72258613	C₂	semidirect
4. C₂²×#10336	C₂	semidirect
5. #72241200	C₂	semidirect
6. #72241125	C₂	semidirect
7. #72238531	C₂	semidirect
8. #72237501	C₂	semidirect
9. C₂×#233541	C₂	semidirect
10. #72234629	C₂	semidirect
11. C₂×#6628892	C₂	semidirect
12. #72233780	C₂	semidirect
13. C₂²×#32898	C₂	semidirect
17. C₂×#34980	C₂²	semidirect
18. C₂×#34980	C₂²	semidirect
23. C₂²×#2403	C₂²	semidirect
24. C₂×#32900	C₂²	semidirect
25. C₂×#32898	C₂²	semidirect
26. C₂×#32898	C₂²	semidirect
27. C₂×#21746	C₂²	semidirect
32. C₂²×#1781	C₂²	semidirect
33. C₂²×#1781	C₂²	semidirect
34. #4928938	C₂²	semidirect
35. #765934	C₂²	semidirect
36. #763814	C₂²	semidirect
39. #513778	C₂²	semidirect
40. #405104	C₂²	semidirect
41. #393929	C₂²	semidirect
42. #355913	C₂²	semidirect
43. C₂×#10337	C₂²	semidirect
44. C₂×#10336	C₂²	semidirect
45. C₂×#10336	C₂²	semidirect
46. C₂×#8101	C₂²	semidirect
47. C₂²×#1304	C₂²	semidirect
48. #115135	C₂²	semidirect
49. #115133	C₂²	semidirect
50. #115133	C₂²	semidirect
51. #111516	C₂²	semidirect
52. #110401	C₂²	semidirect
58. C₂²×#534	D₄	semidirect
59. C₂²×#534	C₂³	semidirect
60. C₂³×#120	D₄	semidirect
61. C₂³×#120	D₄	semidirect
62. C₂³×#120	D₄	semidirect
64. C₂×#2405	D₄	semidirect
67. C₂×#2405	C₂³	semidirect
68. C₂×#2403	D₄	semidirect
69. C₂×#2403	D₄	semidirect
75. C₂×#2403	C₂³	semidirect
76. C₂×#2403	C₂³	semidirect
78. C₂×#2308	D₄	semidirect
79. C₂×#2308	C₂³	semidirect
80. C₂²×#386	D₄	semidirect
81. C₂²×#386	D₄	semidirect
82. C₂²×#386	D₄	semidirect
89. C₂×#1819	C₂³	semidirect
90. C₂×#1781	D₄	semidirect
91. C₂×#1781	D₄	semidirect
96. C₂×#1781	C₂³	semidirect
97. C₂×#1781	C₂³	semidirect
98. C₂×#1781	C₂³	semidirect
99. #14681	D₄	semidirect
100. #14679	D₄	semidirect
102. #13867	D₄	semidirect
104. #13775	C₂³	semidirect
105. #10725	C₂³	semidirect
106. C₂×#1304	C₂³	semidirect
107. C₂×#1304	C₂³	semidirect
125. C₂⁴×D₄	C₂×D₄	semidirect
135. C₂²×#123	C₂×D₄	semidirect
136. C₂²×#120	C₂×D₄	semidirect
137. C₂²×#120	C₂×D₄	semidirect
145. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
146. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
149. C₂×#386	C₂×D₄	semidirect
150. C₂×#386	C₂×D₄	semidirect
151. C₂×#386	C₂×D₄	semidirect
161. C₂×#379	C₂×D₄	semidirect
167. C₂²×#95	C₂×D₄	semidirect
168. #1781	C₂×D₄	semidirect
169. #1781	C₂×D₄	semidirect
170. C₂²⋊#95	C₂×D₄	semidirect
173. C₂⁶	#127	semidirect
196. C₂³×D₄	#127	semidirect
203. C₂⁴×C₄	#127	semidirect
215. C₂²×C₂²⋊C₄	#120	semidirect
216. C₂²×C₂²⋊C₄	#120	semidirect
221. #379	#120	semidirect
222. #379	#120	semidirect

Maximal subgroups

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

subgroup	index
#72266011	2
#72261893	2
#72258613	2
C₂²×#10336	2
#72241200	2
#72241125	2
#72238531	2
#72237501	2
C₂×#233541	2
#72234629	2
C₂×#6628892	2
#72233780	2
C₂²×#32898	2