Subgroups — #72338994

Order 4096.

At least 14176 conjugacy classes of subgroups; only the 669 normal subgroups are shown.

The subgroup lattice has 449 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338992	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338991	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338988	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338986	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338985	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338984	C₂	1	1	yes	maximal, characteristic, complemented
7	#72338983	C₂	1	1	yes	maximal, characteristic, complemented
8	#72338981	C₂	1	1	yes	maximal, characteristic, complemented
9	#72338964	C₂	1	1	yes	maximal, characteristic, complemented
10	#72338962	C₂²	1	1	yes	characteristic, complemented
11	#72338962	C₂²	1	1	yes	characteristic, complemented
12	#72338961	C₂²	1	1	yes	characteristic, complemented
13	#72338957	C₂	1	1	yes	maximal, characteristic, complemented
14	#72338956	C₂²	1	1	yes	characteristic, complemented
15	#72338956	C₂²	1	1	yes	characteristic, complemented
16	#72338954	C₂²	1	1	yes	characteristic, complemented
17	C₂×#72236979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#133835	C₂²	1	1	yes	characteristic
19	C₂×#133835	C₂²	1	1	yes	characteristic
20	C₂×#213860	C₂²	1	1	yes	characteristic
21	C₂×#213860	C₂²	1	1	yes	characteristic
22	#72338888	C₂	1	1	yes	maximal, characteristic, complemented
23	#72338886	C₂²	1	1	yes	characteristic, complemented
24	#72338884	C₂²	1	1	yes	characteristic, complemented
25	#72338879	C₂	1	1	yes	maximal, characteristic, complemented
26	#72338878	C₂²	1	1	yes	characteristic, complemented
27	#72338878	C₂²	1	1	yes	characteristic, complemented
28	C₂×#72210559	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#133308	C₂²	1	1	yes	characteristic
30	C₂×#133308	C₂²	1	1	yes	characteristic
31	C₂×#417807	C₂²	1	1	yes	characteristic
32	#72338809	C₂	1	2	yes	maximal, complemented
33	#72338801	C₂	1	2	yes	maximal, complemented
34	#72338797	C₂	1	2	yes	maximal, complemented
35	#72338794	C₂²	1	1	yes	characteristic, complemented
36	#72338794	C₂²	1	1	yes	characteristic, complemented
37	#72338787	C₂²	1	2	yes	complemented
38	#72338476	C₂²	1	1	yes	characteristic, complemented
39	#72338460	C₂	1	1	yes	maximal, characteristic, complemented
40	#72338459	C₂²	1	1	yes	characteristic
41	#72337709	C₂	1	2	yes	maximal, complemented
42	#72337703	C₂²	1	1	yes	characteristic, complemented
43	#72337671	C₂	1	2	yes	maximal, complemented
44	#72337664	C₂²	1	2	yes	complemented
45	#72337662	C₂²	1	1	yes	characteristic, complemented
46	#72337656	C₂²	1	2	yes	complemented
47	#72337653	C₂²	1	1	yes	characteristic, complemented
48	#72337645	C₂²	1	2	yes	complemented
49	#72337645	C₂²	1	2	yes	complemented
50	#72337637	C₂²	1	2	yes	complemented
51	#72337637	C₂²	1	2	yes	complemented
52	#72337636	C₂²	1	2	yes	complemented
53	#72337636	C₂²	1	2	yes	complemented
54	#72337625	C₂²	1	2	yes	complemented
55	#72337625	C₂²	1	2	yes	complemented
56	#72319263	C₂²	1	2	yes	complemented
57	#72319263	C₂²	1	2	yes	complemented
58	C₂×#7672751	C₂²	1	1	yes	characteristic
59	#72266199	C₂²	1	1	yes	characteristic, complemented
60	#72266169	C₂²	1	1	yes	characteristic, complemented
61	#72252381	C₂	1	2	yes	maximal, complemented
62	#72252381	C₂	1	2	yes	maximal, complemented
63	#72252379	C₂²	1	2	yes	complemented
64	#72252379	C₂²	1	2	yes	complemented
65	#72252378	C₂²	1	2	yes	complemented
66	#72252378	C₂²	1	2	yes	complemented
67	#72241387	C₂²	1	1	yes	characteristic, complemented
68	#72241387	C₂²	1	1	yes	characteristic, complemented
69	#72241346	C₂	1	2	yes	maximal, complemented
70	#72241344	C₂²	1	2	yes	complemented
71	#72241343	C₂²	1	2	yes	complemented
72	#72241343	C₂²	1	2	yes	complemented
73	#72241342	C₂²	1	1	yes	characteristic, complemented
74	#72241322	C₂²	1	2	yes	complemented
75	#72241322	C₂²	1	2	yes	complemented
76	#72241322	C₂²	1	2	yes	complemented
77	#72241322	C₂²	1	2	yes	complemented
78	#72241322	C₂²	1	2	yes	complemented
79	#72241322	C₂²	1	2	yes	complemented
80	#72241322	C₂²	1	2	yes	complemented
81	#72241322	C₂²	1	2	yes	complemented
82	#72241322	C₂²	1	2	yes	complemented
83	C₂×#134009	C₂²	1	1	yes	characteristic
84	C₂×#134009	C₂²	1	1	yes	characteristic
85	C₂×#134009	C₂²	1	1	yes	characteristic
86	C₂×#134009	C₂²	1	1	yes	characteristic
87	#72240077	C₂²	1	2	yes	complemented
88	#72240077	C₂²	1	2	yes	complemented
89	#72236979	C₂²	1	2	yes	complemented
90	#72236979	C₂²	1	2	yes	complemented
91	#72236979	C₂²	1	2	yes	complemented
92	#72236979	C₂²	1	2	yes	complemented
93	#72236834	C₂²	1	1	yes	characteristic, complemented
94	#72236108	C₂²	1	1	yes	characteristic
95	#72236108	C₂²	1	1	yes	characteristic
96	#72236108	C₂²	1	1	yes	characteristic, complemented
97	C₂×#245233	C₂²	1	1	yes	characteristic
98	C₂×#245233	C₂²	1	1	yes	characteristic
99	#72227941	C₂²	1	2	yes	complemented
100	#72227941	C₂²	1	2	yes	complemented
101	#72227940	C₂²	1	2	yes	complemented
102	#72227940	C₂²	1	2	yes	complemented
103	#72227940	C₂²	1	2	yes	complemented
104	#72227556	C₂²	1	2	yes	complemented
105	#72226077	C₂²	1	1	yes	characteristic
106	#72226077	C₂²	1	1	yes	characteristic
107	#72226077	C₂²	1	1	yes	characteristic, complemented
108	#72213260	C₂²	1	2	yes	complemented
109	#72213260	C₂²	1	2	yes	complemented
110	#72213260	C₂²	1	2	yes	complemented
111	#72210569	C₂²	1	2	yes	complemented
112	#72210569	C₂²	1	2	yes	complemented
113	#72210559	C₂²	1	2	yes	—
114	#72210559	C₂²	1	2	yes	—
115	#72210559	C₂²	1	2	yes	—
116	#72210559	C₂²	1	2	yes	—
117	#72210559	C₂²	1	2	yes	complemented
118	#72210559	C₂²	1	2	yes	complemented
119	#72210539	C₂²	1	2	yes	complemented
120	#72210539	C₂²	1	2	yes	complemented
121	#72210539	C₂²	1	2	yes	complemented
122	#72210015	C₂²	1	2	yes	complemented
123	#7672751	C₂³	1	2	yes	—
124	#7672751	C₂³	1	2	yes	—
125	#7643002	C₂³	1	1	yes	characteristic
126	C₂²×#2867	C₂³	1	1	yes	characteristic
127	C₂×#35527	C₂³	1	1	yes	characteristic
128	C₂×#35527	C₂³	1	1	yes	characteristic
129	C₂×#35527	C₂³	1	1	yes	characteristic
130	C₂×#32898	D₄	1	2	yes	complemented
131	#6470225	D₄	1	2	yes	complemented
132	C₂×#20585	D₄	1	2	yes	complemented
133	#418114	C₂³	1	2	yes	—
134	#417807	C₂³	1	2	yes	—
135	#417807	C₂³	1	2	yes	—
136	#417807	C₂³	1	2	yes	—
137	#382394	C₂³	1	1	yes	characteristic
138	C₂×#10981	C₂³	1	1	yes	characteristic
139	#346283	C₂³	1	1	yes	characteristic, complemented
140	#346283	C₂³	1	1	yes	characteristic, complemented
141	#346283	C₂³	1	1	yes	characteristic, complemented
142	#346282	C₂³	1	1	yes	characteristic, complemented
143	#245234	D₄	1	2	yes	complemented
144	#245234	C₂³	1	2	yes	—
145	#245234	C₂³	1	1	yes	characteristic
146	#245234	C₂³	1	1	yes	characteristic
147	#245234	C₂³	1	1	yes	characteristic, complemented
148	#245234	C₂³	1	1	yes	characteristic, complemented
149	#245233	D₄	1	2	yes	complemented
150	#245233	D₄	1	2	yes	complemented
151	#245233	D₄	1	2	yes	complemented
152	#245233	C₂³	1	2	yes	—
153	#245233	C₂³	1	2	yes	—
154	#245233	C₂³	1	2	yes	—
155	#245233	C₂³	1	1	yes	characteristic
156	#245233	C₂³	1	1	yes	characteristic
157	#245233	C₂³	1	1	yes	characteristic
158	#245233	C₂³	1	1	yes	characteristic
159	#245233	C₂³	1	1	yes	characteristic
160	#245233	C₂³	1	1	yes	characteristic
161	#245233	C₂³	1	1	yes	characteristic, complemented
162	#245233	C₂³	1	1	yes	characteristic, complemented
163	#213865	C₂³	1	1	yes	characteristic, complemented
164	#213865	C₂³	1	1	yes	characteristic, complemented
165	#213861	C₂³	1	1	yes	characteristic, complemented
166	#213861	C₂³	1	1	yes	characteristic, complemented
167	#213861	C₂³	1	1	yes	characteristic, complemented
168	#213860	D₄	1	2	yes	complemented
169	#213860	D₄	1	2	yes	complemented
170	#213860	C₂³	1	1	yes	characteristic
171	#213860	C₂³	1	1	yes	characteristic
172	#213860	C₂³	1	1	yes	characteristic
173	#213860	C₂³	1	1	yes	characteristic
174	#213860	C₂³	1	2	yes	—
175	#213860	C₂³	1	2	yes	—
176	#213860	C₂³	1	1	yes	characteristic, complemented
177	#213860	C₂³	1	1	yes	characteristic, complemented
178	#213860	C₂³	1	1	yes	characteristic, complemented
179	#201664	D₄	1	2	yes	complemented
180	C₂×#9497	D₄	1	2	yes	complemented
181	C₂×#8748	D₄	1	2	yes	complemented
182	C₂×#8546	C₂³	1	1	yes	characteristic
183	C₂×#8546	C₂³	1	1	yes	characteristic
184	C₂×#8546	C₂³	1	1	yes	characteristic
185	C₂×#8546	C₂³	1	1	yes	characteristic
186	C₂×#8546	C₂³	1	1	yes	characteristic
187	C₂×#8546	C₂³	1	1	yes	characteristic
188	C₂×#8546	C₂³	1	1	yes	characteristic
189	C₂×#8546	C₂³	1	1	yes	characteristic
190	#134009	C₂³	1	2	yes	—
191	#134009	C₂³	1	2	yes	—
192	#134009	C₂³	1	2	yes	—
193	#134009	C₂³	1	2	yes	—
194	#134009	C₂³	1	2	yes	—
195	#134009	C₂³	1	2	yes	—
196	#134009	C₂³	1	2	yes	—
197	#134009	C₂³	1	2	yes	—
198	#133936	C₂³	1	2	yes	complemented
199	#133835	C₂³	1	2	yes	—
200	#133835	C₂³	1	2	yes	—
201	#133835	C₂³	1	2	yes	—
202	#133835	C₂³	1	2	yes	—
203	#133835	C₂³	1	2	yes	complemented
204	#133835	C₂³	1	2	yes	complemented
205	#133835	C₂³	1	2	yes	complemented
206	#133309	C₂³	1	2	yes	complemented
207	#133308	C₂³	1	2	yes	—
208	#133308	C₂³	1	2	yes	—
209	#133308	C₂³	1	2	yes	—
210	#133308	C₂³	1	2	yes	—
211	#133308	C₂³	1	2	yes	—
212	#133308	C₂³	1	2	yes	—
213	#133308	C₂³	1	2	yes	—
214	#133308	C₂³	1	2	yes	—
215	#133308	C₂³	1	2	yes	complemented
216	#133308	C₂³	1	2	yes	complemented
217	#133308	C₂³	1	2	yes	complemented
218	#93146	C₂³	1	2	yes	complemented
219	#93146	C₂³	1	2	yes	complemented
220	#93139	C₂³	1	2	yes	complemented
221	#93139	C₂³	1	2	yes	complemented
222	#93139	C₂³	1	2	yes	complemented
223	#93139	C₂³	1	2	yes	complemented
224	#93139	C₂³	1	2	yes	complemented
225	#93139	C₂³	1	2	yes	complemented
226	#93113	C₂³	1	2	yes	complemented
227	#93113	C₂³	1	2	yes	complemented
228	#93113	C₂³	1	2	yes	complemented
229	#93113	C₂³	1	2	yes	complemented
230	#93113	C₂³	1	2	yes	complemented
231	#93113	C₂³	1	2	yes	complemented
232	#93113	C₂³	1	2	yes	complemented
233	#93113	C₂³	1	2	yes	complemented
234	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
235	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
236	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
237	C₂×#3484	C₂×D₄	1	1	yes	characteristic
238	C₂³×#127	#41	1	1	yes	characteristic, complemented
239	C₂³×#127	C₂⁴	1	1	yes	characteristic
240	C₂×#2867	#41	1	2	yes	complemented
241	C₂×#2867	C₂⁴	1	2	yes	—
242	#35554	C₂×D₄	1	1	yes	characteristic
243	#35554	C₂⁴	1	1	yes	characteristic
244	#35527	C₂×D₄	1	2	yes	—
245	#35527	C₂×D₄	1	2	yes	—
246	#35527	C₂×D₄	1	1	yes	characteristic
247	#35527	C₂×D₄	1	1	yes	characteristic
248	#35527	C₂×D₄	1	1	yes	characteristic
249	#35527	C₂×D₄	1	1	yes	characteristic
250	#35527	C₂×D₄	1	1	yes	characteristic
251	#35527	#41	1	2	yes	complemented
252	#35527	C₂⁴	1	1	yes	characteristic
253	#35527	C₂⁴	1	1	yes	characteristic
254	#35527	C₂⁴	1	1	yes	characteristic
255	#35527	C₂⁴	1	1	yes	characteristic
256	#35527	C₂⁴	1	1	yes	characteristic
257	#35527	C₂⁴	1	2	yes	—
258	C₂×#2403	C₂×D₄	1	2	yes	—
259	C₂×#2403	C₂×D₄	1	2	yes	—
260	#34171	C₂×D₄	1	1	yes	characteristic
261	C₂×#2309	C₂×D₄	1	1	yes	characteristic
262	C₂×#2309	C₂×D₄	1	1	yes	characteristic
263	C₂×#2309	#41	1	1	yes	characteristic, complemented
264	C₂²×C₄³	#41	1	1	yes	characteristic, complemented
265	#33020	C₂×D₄	1	2	yes	complemented
266	#33020	C₂×D₄	1	2	yes	complemented
267	#32898	C₂×D₄	1	2	yes	—
268	#32898	C₂×D₄	1	2	yes	—
269	#32898	C₂×D₄	1	2	yes	—
270	#32898	C₂×D₄	1	2	yes	—
271	#32898	C₂×D₄	1	2	yes	complemented
272	#32898	C₂×D₄	1	2	yes	complemented
273	#20585	C₂×D₄	1	2	yes	complemented
274	#20585	C₂×D₄	1	2	yes	complemented
275	#20585	C₂×D₄	1	2	yes	complemented
276	#20585	C₂×D₄	1	2	yes	complemented
277	C₂×#1781	C₂×D₄	1	2	yes	—
278	C₂×#1781	C₂×D₄	1	2	yes	—
279	C₂×#1781	C₂×D₄	1	2	yes	—
280	C₂×#1781	C₂×D₄	1	2	yes	—
281	#10981	C₂⁴	1	2	yes	—
282	#10981	C₂⁴	1	2	yes	—
283	#9497	C₂×D₄	1	2	yes	—
284	#9497	C₂×D₄	1	2	yes	—
285	#9497	C₂×D₄	1	2	yes	—
286	#9497	C₂×D₄	1	2	yes	—
287	#9497	C₂×D₄	1	2	yes	complemented
288	#9497	C₂×D₄	1	2	yes	complemented
289	#9497	C₂×D₄	1	2	yes	complemented
290	#9497	C₂×D₄	1	2	yes	complemented
291	#8748	C₂×D₄	1	2	yes	complemented
292	#8748	C₂×D₄	1	2	yes	complemented
293	#8748	C₂×D₄	1	2	yes	complemented
294	#8748	C₂×D₄	1	2	yes	complemented
295	#8546	C₂×D₄	1	2	yes	—
296	#8546	C₂×D₄	1	2	yes	—
297	#8546	C₂×D₄	1	2	yes	—
298	#8546	C₂×D₄	1	2	yes	—
299	#8546	C₂⁴	1	2	yes	—
300	#8546	C₂⁴	1	2	yes	—
301	#8546	C₂⁴	1	2	yes	—
302	#8546	C₂⁴	1	2	yes	—
303	#8546	C₂⁴	1	1	yes	characteristic
304	#8546	C₂⁴	1	1	yes	characteristic
305	#8546	C₂⁴	1	1	yes	characteristic
306	#8546	C₂⁴	1	1	yes	characteristic
307	#8546	C₂⁴	1	1	yes	characteristic
308	#8546	C₂⁴	1	1	yes	characteristic
309	#8546	C₂⁴	1	1	yes	characteristic
310	#8546	C₂⁴	1	1	yes	characteristic
311	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
312	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
313	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
314	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
315	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
316	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
317	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
318	C₂⁴×D₄	#120	1	2	yes	—
319	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
322	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
323	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
326	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
327	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
328	C₂²×#127	C₂×#41	1	2	yes	—
329	C₂²×#127	C₂×#41	1	1	yes	characteristic
330	C₂²×#127	C₂×#41	1	1	yes	characteristic
331	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×#127	C₂⁵	1	1	yes	characteristic
334	C₂×#518	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₄²	C₂×#41	1	1	yes	characteristic
336	#2403	#120	1	2	yes	—
337	#2403	#120	1	2	yes	—
338	#2403	#120	1	2	yes	—
339	#2403	#120	1	2	yes	—
340	#2403	C₂²×D₄	1	2	yes	—
341	#2403	C₂²×D₄	1	2	yes	—
342	#2403	C₂²×D₄	1	2	yes	—
343	#2403	C₂²×D₄	1	2	yes	—
344	#2309	#120	1	2	yes	—
345	#2309	C₂²×D₄	1	1	yes	characteristic
346	#2309	C₂²×D₄	1	1	yes	characteristic
347	#2309	C₂²×D₄	1	1	yes	characteristic
348	#2309	C₂²×D₄	1	1	yes	characteristic
349	#2309	C₂²×D₄	1	1	yes	characteristic
350	#2309	C₂²×D₄	1	1	yes	characteristic
351	#2309	C₂×#41	1	2	yes	—
352	C₂×#379	#120	1	2	yes	—
353	C₂×C₄³	C₂×#41	1	2	yes	—
354	#1781	C₂²×D₄	1	2	yes	—
355	#1781	C₂²×D₄	1	2	yes	—
356	#1781	C₂²×D₄	1	2	yes	—
357	#1781	C₂²×D₄	1	2	yes	—
358	#1781	C₂²×D₄	1	2	yes	—
359	#1781	C₂²×D₄	1	2	yes	—
360	#1781	C₂²×D₄	1	2	yes	—
361	#1781	C₂²×D₄	1	2	yes	—
362	C₂⁶	B(4,𝔽₂)	1	2	yes	—
363	C₂⁶	C₂×#120	1	1	yes	characteristic
364	C₂⁶	#535	1	1	yes	characteristic
365	C₂⁶	#546	1	1	yes	characteristic
366	C₂⁶	#546	1	1	yes	characteristic
367	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
368	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
369	C₂³×D₄	C₂×#120	1	1	yes	characteristic
370	C₂³×D₄	C₂×#120	1	1	yes	characteristic
371	C₂³×D₄	C₂×#120	1	1	yes	characteristic
372	C₂³×D₄	C₂×#120	1	2	yes	—
373	C₂³×D₄	C₂×#120	1	2	yes	—
374	C₂³×D₄	#525	1	1	yes	characteristic
375	C₂³×D₄	#525	1	1	yes	characteristic
376	C₂³×D₄	#535	1	1	yes	characteristic
377	C₂³×D₄	#535	1	1	yes	characteristic
378	C₂³×D₄	#535	1	1	yes	characteristic
379	C₂³×D₄	#546	1	1	yes	characteristic
380	C₂³×D₄	#546	1	1	yes	characteristic
381	C₂³×D₄	#546	1	1	yes	characteristic
382	C₂³×D₄	#546	1	1	yes	characteristic
383	C₂³×D₄	#546	1	1	yes	characteristic
384	C₂³×D₄	#546	1	1	yes	characteristic
385	C₂³×D₄	#546	1	1	yes	characteristic
386	C₂³×D₄	#546	1	1	yes	characteristic
387	C₂³×D₄	#546	1	1	yes	characteristic
388	C₂³×D₄	#546	1	1	yes	characteristic
389	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
390	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
391	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
392	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
393	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
396	C₂⁴×C₄	#525	1	1	yes	characteristic
397	C₂⁴×C₄	#546	1	1	yes	characteristic
398	C₂⁴×C₄	#546	1	1	yes	characteristic
399	C₂²×C₄²	#525	1	1	yes	characteristic
400	C₂²×C₄²	#546	1	1	yes	characteristic
401	C₂²×C₄²	#546	1	1	yes	characteristic
402	C₂²×C₄²	C₂²×#41	1	1	yes	characteristic
403	#379	C₂×#120	1	2	yes	—
404	#379	C₂×#120	1	2	yes	—
405	C₂⁵	#2404	1	1	yes	characteristic
406	C₂⁵	#2404	1	1	yes	characteristic
407	C₂⁵	#2404	1	1	yes	characteristic
408	C₂⁵	#2404	1	1	yes	characteristic
409	C₂⁵	#2404	1	1	yes	characteristic
410	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
411	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
412	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
413	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
414	C₂⁵	C₂²×#120	1	1	yes	characteristic
415	C₂⁵	C₂×#535	1	1	yes	characteristic
416	C₂⁵	C₂×#546	1	1	yes	characteristic
417	C₂⁵	C₂×#546	1	1	yes	characteristic
418	C₂³×C₄	#2404	1	1	yes	characteristic
419	C₂³×C₄	#2404	1	1	yes	characteristic
420	C₂³×C₄	#2404	1	1	yes	characteristic
421	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
422	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
423	C₂³×C₄	C₂×#525	1	1	yes	characteristic
424	C₂³×C₄	C₂×#546	1	1	yes	characteristic
425	C₂³×C₄	C₂×#546	1	1	yes	characteristic
426	C₂⁴	#23984	1	1	yes	characteristic
427	C₂⁴	#23984	1	2	yes	—
428	C₂⁴	#23984	1	1	yes	characteristic
429	C₂⁴	#23996	1	1	yes	characteristic
430	C₂⁴	#23996	1	1	yes	characteristic
431	C₂⁴	#23996	1	1	yes	characteristic
432	C₂⁴	#23996	1	1	yes	characteristic
433	C₂⁴	C₂×#2404	1	1	yes	characteristic
434	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
435	C₂³	#251827	1	1	yes	characteristic
436	C₂³	#251827	1	1	yes	characteristic
437	C₂³	#251827	1	1	yes	characteristic
438	C₂³	#251827	1	1	yes	characteristic
439	C₂³	C₂×#23996	1	1	yes	characteristic
440	C₂³	C₂×#23996	1	1	yes	characteristic
441	C₂³	C₂×#23984	1	1	yes	characteristic
442	C₂²	#72216336	1	2	yes	—
443	C₂²	#72216370	1	2	yes	—
444	C₂²	C₂×#251827	1	1	yes	characteristic
445	C₂	#72256070	1	1	yes	characteristic
446	C₂	C₂×#72216370	1	1	yes	characteristic
447	C₂	C₂×#72216336	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#251827
commutator, Frattini, cosocle	C₂²×#127	C₂⁵
LCS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#127 ◁ G
LECS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72338992	C₂	semidirect
2. #72338991	C₂	semidirect
3. #72338988	C₂	semidirect
4. #72338986	C₂	semidirect
5. #72338985	C₂	semidirect
6. #72338984	C₂	semidirect
7. #72338983	C₂	semidirect
8. #72338981	C₂	semidirect
9. #72338964	C₂	semidirect
10. #72338962	C₂²	semidirect
11. #72338962	C₂²	semidirect
12. #72338961	C₂²	semidirect
13. #72338957	C₂	semidirect
14. #72338956	C₂²	semidirect
15. #72338956	C₂²	semidirect
16. #72338954	C₂²	semidirect
17. C₂×#72236979	C₂	semidirect
22. #72338888	C₂	semidirect
23. #72338886	C₂²	semidirect
24. #72338884	C₂²	semidirect
25. #72338879	C₂	semidirect
26. #72338878	C₂²	semidirect
27. #72338878	C₂²	semidirect
28. C₂×#72210559	C₂	semidirect
32. #72338809	C₂	semidirect
33. #72338801	C₂	semidirect
34. #72338797	C₂	semidirect
35. #72338794	C₂²	semidirect
36. #72338794	C₂²	semidirect
37. #72338787	C₂²	semidirect
38. #72338476	C₂²	semidirect
39. #72338460	C₂	semidirect
41. #72337709	C₂	semidirect
42. #72337703	C₂²	semidirect
43. #72337671	C₂	semidirect
44. #72337664	C₂²	semidirect
45. #72337662	C₂²	semidirect
46. #72337656	C₂²	semidirect
47. #72337653	C₂²	semidirect
48. #72337645	C₂²	semidirect
49. #72337645	C₂²	semidirect
50. #72337637	C₂²	semidirect
51. #72337637	C₂²	semidirect
52. #72337636	C₂²	semidirect
53. #72337636	C₂²	semidirect
54. #72337625	C₂²	semidirect
55. #72337625	C₂²	semidirect
56. #72319263	C₂²	semidirect
57. #72319263	C₂²	semidirect
59. #72266199	C₂²	semidirect
60. #72266169	C₂²	semidirect
61. #72252381	C₂	semidirect
62. #72252381	C₂	semidirect
63. #72252379	C₂²	semidirect
64. #72252379	C₂²	semidirect
65. #72252378	C₂²	semidirect
66. #72252378	C₂²	semidirect
67. #72241387	C₂²	semidirect
68. #72241387	C₂²	semidirect
69. #72241346	C₂	semidirect
70. #72241344	C₂²	semidirect
71. #72241343	C₂²	semidirect
72. #72241343	C₂²	semidirect
73. #72241342	C₂²	semidirect
74. #72241322	C₂²	semidirect
75. #72241322	C₂²	semidirect
76. #72241322	C₂²	semidirect
77. #72241322	C₂²	semidirect
78. #72241322	C₂²	semidirect
79. #72241322	C₂²	semidirect
80. #72241322	C₂²	semidirect
81. #72241322	C₂²	semidirect
82. #72241322	C₂²	semidirect
87. #72240077	C₂²	semidirect
88. #72240077	C₂²	semidirect
89. #72236979	C₂²	semidirect
90. #72236979	C₂²	semidirect
91. #72236979	C₂²	semidirect
92. #72236979	C₂²	semidirect
93. #72236834	C₂²	semidirect
96. #72236108	C₂²	semidirect
99. #72227941	C₂²	semidirect
100. #72227941	C₂²	semidirect
101. #72227940	C₂²	semidirect
102. #72227940	C₂²	semidirect
103. #72227940	C₂²	semidirect
104. #72227556	C₂²	semidirect
107. #72226077	C₂²	semidirect
108. #72213260	C₂²	semidirect
109. #72213260	C₂²	semidirect
110. #72213260	C₂²	semidirect
111. #72210569	C₂²	semidirect
112. #72210569	C₂²	semidirect
117. #72210559	C₂²	semidirect
118. #72210559	C₂²	semidirect
119. #72210539	C₂²	semidirect
120. #72210539	C₂²	semidirect
121. #72210539	C₂²	semidirect
122. #72210015	C₂²	semidirect
130. C₂×#32898	D₄	semidirect
131. #6470225	D₄	semidirect
132. C₂×#20585	D₄	semidirect
139. #346283	C₂³	semidirect
140. #346283	C₂³	semidirect
141. #346283	C₂³	semidirect
142. #346282	C₂³	semidirect
143. #245234	D₄	semidirect
147. #245234	C₂³	semidirect
148. #245234	C₂³	semidirect
149. #245233	D₄	semidirect
150. #245233	D₄	semidirect
151. #245233	D₄	semidirect
161. #245233	C₂³	semidirect
162. #245233	C₂³	semidirect
163. #213865	C₂³	semidirect
164. #213865	C₂³	semidirect
165. #213861	C₂³	semidirect
166. #213861	C₂³	semidirect
167. #213861	C₂³	semidirect
168. #213860	D₄	semidirect
169. #213860	D₄	semidirect
176. #213860	C₂³	semidirect
177. #213860	C₂³	semidirect
178. #213860	C₂³	semidirect
179. #201664	D₄	semidirect
180. C₂×#9497	D₄	semidirect
181. C₂×#8748	D₄	semidirect
198. #133936	C₂³	semidirect
203. #133835	C₂³	semidirect
204. #133835	C₂³	semidirect
205. #133835	C₂³	semidirect
206. #133309	C₂³	semidirect
215. #133308	C₂³	semidirect
216. #133308	C₂³	semidirect
217. #133308	C₂³	semidirect
218. #93146	C₂³	semidirect
219. #93146	C₂³	semidirect
220. #93139	C₂³	semidirect
221. #93139	C₂³	semidirect
222. #93139	C₂³	semidirect
223. #93139	C₂³	semidirect
224. #93139	C₂³	semidirect
225. #93139	C₂³	semidirect
226. #93113	C₂³	semidirect
227. #93113	C₂³	semidirect
228. #93113	C₂³	semidirect
229. #93113	C₂³	semidirect
230. #93113	C₂³	semidirect
231. #93113	C₂³	semidirect
232. #93113	C₂³	semidirect
233. #93113	C₂³	semidirect
236. C₂³×H(5,𝔽₂)	#41	semidirect
238. C₂³×#127	#41	semidirect
240. C₂×#2867	#41	semidirect
251. #35527	#41	semidirect
263. C₂×#2309	#41	semidirect
264. C₂²×C₄³	#41	semidirect
265. #33020	C₂×D₄	semidirect
266. #33020	C₂×D₄	semidirect
271. #32898	C₂×D₄	semidirect
272. #32898	C₂×D₄	semidirect
273. #20585	C₂×D₄	semidirect
274. #20585	C₂×D₄	semidirect
275. #20585	C₂×D₄	semidirect
276. #20585	C₂×D₄	semidirect
287. #9497	C₂×D₄	semidirect
288. #9497	C₂×D₄	semidirect
289. #9497	C₂×D₄	semidirect
290. #9497	C₂×D₄	semidirect
291. #8748	C₂×D₄	semidirect
292. #8748	C₂×D₄	semidirect
293. #8748	C₂×D₄	semidirect
294. #8748	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72338992	2
#72338991	2
#72338988	2
#72338986	2
#72338985	2
#72338984	2
#72338983	2
#72338981	2
#72338964	2
#72338957	2
C₂×#72236979	2
#72338888	2
#72338879	2
C₂×#72210559	2
#72338809	2
#72338801	2
#72338797	2
#72338460	2
#72337709	2
#72337671	2
#72252381	2
#72241346	2