Subgroups — #72338830

Order 4096.

At least 15608 conjugacy classes of subgroups; only the 605 normal subgroups are shown.

The subgroup lattice has 520 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338825	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338815	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338811	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338809	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338806	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338801	C₂	1	1	yes	maximal, characteristic, complemented
7	#72338797	C₂	1	1	yes	maximal, characteristic, complemented
8	#72338795	C₂	1	1	yes	maximal, characteristic, complemented
9	#72338794	C₂²	1	1	yes	characteristic, complemented
10	#72338794	C₂²	1	1	yes	characteristic, complemented
11	#72338788	C₂	1	1	yes	maximal, characteristic, complemented
12	#72338787	C₂²	1	1	yes	characteristic, complemented
13	#72338787	C₂²	1	1	yes	characteristic, complemented
14	#72338787	C₂²	1	1	yes	characteristic, complemented
15	#72338771	C₂	1	1	yes	maximal, characteristic, complemented
16	#72338767	C₂	1	1	yes	maximal, characteristic, complemented
17	#72338766	C₂	1	1	yes	maximal, characteristic, complemented
18	#72338748	C₂	1	1	yes	maximal, characteristic, complemented
19	#72338738	C₂	1	1	yes	maximal, characteristic, complemented
20	#72338736	C₂²	1	1	yes	characteristic, complemented
21	#72338734	C₂	1	1	yes	maximal, characteristic, complemented
22	#72338730	C₂	1	1	yes	maximal, characteristic, complemented
23	#72338726	C₂²	1	1	yes	characteristic, complemented
24	#72338723	C₂	1	1	yes	maximal, characteristic, complemented
25	#72338721	C₂²	1	1	yes	characteristic, complemented
26	#72338718	C₂	1	1	yes	maximal, characteristic, complemented
27	#72338715	C₂²	1	1	yes	characteristic, complemented
28	#72338712	C₂²	1	1	yes	characteristic, complemented
29	#72337678	C₂	1	1	yes	maximal, characteristic, complemented
30	#72337670	C₂	1	1	yes	maximal, characteristic, complemented
31	#72337669	C₂	1	1	yes	maximal, characteristic, complemented
32	#72337667	C₂²	1	1	yes	characteristic, complemented
33	#72337665	C₂²	1	1	yes	characteristic, complemented
34	#72337664	C₂²	1	1	yes	characteristic, complemented
35	#72337663	C₂	1	1	yes	maximal, characteristic, complemented
36	#72337662	C₂²	1	1	yes	characteristic, complemented
37	#72337662	C₂²	1	1	yes	characteristic, complemented
38	#72337661	C₂²	1	1	yes	characteristic, complemented
39	#72337661	C₂²	1	1	yes	characteristic, complemented
40	#72337660	C₂	1	1	yes	maximal, characteristic, complemented
41	#72337659	C₂²	1	1	yes	characteristic
42	#72337659	C₂²	1	1	yes	characteristic, complemented
43	#72337659	C₂²	1	1	yes	characteristic, complemented
44	#72337656	C₂²	1	1	yes	characteristic, complemented
45	#72337654	C₂²	1	1	yes	characteristic, complemented
46	#72337652	C₂²	1	1	yes	characteristic, complemented
47	#72337650	C₂²	1	1	yes	characteristic, complemented
48	#72337648	C₂²	1	1	yes	characteristic, complemented
49	#72337648	C₂²	1	1	yes	characteristic, complemented
50	#72337648	C₂²	1	1	yes	characteristic, complemented
51	#72337648	C₂²	1	1	yes	characteristic, complemented
52	#72337647	C₂²	1	1	yes	characteristic, complemented
53	#72337645	C₂²	1	1	yes	characteristic, complemented
54	#72337644	C₂²	1	1	yes	characteristic, complemented
55	#72337637	C₂²	1	1	yes	characteristic, complemented
56	#72337637	C₂²	1	1	yes	characteristic, complemented
57	#72337636	C₂²	1	1	yes	characteristic, complemented
58	#72337636	C₂²	1	1	yes	characteristic, complemented
59	#72337635	C₂²	1	1	yes	characteristic, complemented
60	#72337635	C₂²	1	1	yes	characteristic, complemented
61	#72337629	C₂²	1	1	yes	characteristic, complemented
62	#72337629	C₂²	1	1	yes	characteristic, complemented
63	#72337627	C₂²	1	1	yes	characteristic, complemented
64	#72337627	C₂²	1	1	yes	characteristic, complemented
65	#72337625	C₂²	1	1	yes	characteristic, complemented
66	#72337625	C₂²	1	1	yes	characteristic, complemented
67	#72319263	C₂²	1	1	yes	characteristic, complemented
68	#72319263	C₂²	1	1	yes	characteristic, complemented
69	#72318569	C₂²	1	1	yes	characteristic, complemented
70	#72318569	C₂²	1	1	yes	characteristic, complemented
71	#72262289	C₂²	1	1	yes	characteristic, complemented
72	#72262288	C₂²	1	1	yes	characteristic, complemented
73	#72252381	C₂	1	1	yes	maximal, characteristic, complemented
74	#72252380	C₂	1	1	yes	maximal, characteristic, complemented
75	#72252379	C₂²	1	1	yes	characteristic, complemented
76	#72252379	C₂²	1	1	yes	characteristic, complemented
77	#72252379	C₂²	1	1	yes	characteristic, complemented
78	#72252378	C₂²	1	1	yes	characteristic, complemented
79	#72252378	C₂²	1	1	yes	characteristic, complemented
80	#72241387	C₂²	1	1	yes	characteristic, complemented
81	#72241387	C₂²	1	1	yes	characteristic, complemented
82	#72241343	C₂²	1	1	yes	characteristic, complemented
83	#72241343	C₂²	1	1	yes	characteristic, complemented
84	#72241323	C₂	1	1	yes	maximal, characteristic, complemented
85	#72241323	C₂	1	1	yes	maximal, characteristic, complemented
86	#72241322	C₂²	1	1	yes	characteristic, complemented
87	#72241322	C₂²	1	1	yes	characteristic, complemented
88	#72241322	C₂²	1	1	yes	characteristic, complemented
89	#72241322	C₂²	1	1	yes	characteristic, complemented
90	#72241322	C₂²	1	1	yes	characteristic, complemented
91	#72241322	C₂²	1	1	yes	characteristic, complemented
92	#72241322	C₂²	1	1	yes	characteristic, complemented
93	#72241322	C₂²	1	1	yes	characteristic, complemented
94	#72241322	C₂²	1	1	yes	characteristic, complemented
95	#72241322	C₂²	1	1	yes	characteristic, complemented
96	#72241322	C₂²	1	1	yes	characteristic, complemented
97	#72241322	C₂²	1	1	yes	characteristic, complemented
98	#72240077	C₂²	1	1	yes	characteristic, complemented
99	#72236986	C₂	1	1	yes	maximal, characteristic, complemented
100	#72236986	C₂	1	1	yes	maximal, characteristic, complemented
101	#72236979	C₂²	1	1	yes	characteristic, complemented
102	#72236979	C₂²	1	1	yes	characteristic, complemented
103	#72236975	C₂²	1	1	yes	characteristic, complemented
104	#72236975	C₂²	1	1	yes	characteristic, complemented
105	#72236975	C₂²	1	1	yes	characteristic, complemented
106	#72236975	C₂²	1	1	yes	characteristic, complemented
107	#72236189	C₂²	1	1	yes	characteristic, complemented
108	#72227941	C₂²	1	1	yes	characteristic, complemented
109	#72227941	C₂²	1	1	yes	characteristic, complemented
110	#72227941	C₂²	1	1	yes	characteristic, complemented
111	#72227941	C₂²	1	1	yes	characteristic, complemented
112	#72227940	C₂²	1	1	yes	characteristic, complemented
113	#72227940	C₂²	1	1	yes	characteristic, complemented
114	#72227940	C₂²	1	1	yes	characteristic, complemented
115	#72227940	C₂²	1	1	yes	characteristic, complemented
116	#72227940	C₂²	1	1	yes	characteristic, complemented
117	#72227940	C₂²	1	1	yes	characteristic, complemented
118	#72227940	C₂²	1	1	yes	characteristic, complemented
119	#72227940	C₂²	1	1	yes	characteristic, complemented
120	#72227556	C₂²	1	1	yes	characteristic, complemented
121	#72213269	C₂²	1	1	yes	characteristic, complemented
122	#72213269	C₂²	1	1	yes	characteristic, complemented
123	#72213260	C₂²	1	1	yes	characteristic, complemented
124	#72213260	C₂²	1	1	yes	characteristic, complemented
125	#72210591	C₂	1	1	yes	maximal, characteristic, complemented
126	#72210591	C₂	1	1	yes	maximal, characteristic, complemented
127	#72210572	C₂²	1	1	yes	characteristic, complemented
128	#72210572	C₂²	1	1	yes	characteristic, complemented
129	#72210572	C₂²	1	1	yes	characteristic, complemented
130	#72210572	C₂²	1	1	yes	characteristic, complemented
131	#72210572	C₂²	1	1	yes	characteristic, complemented
132	#72210572	C₂²	1	1	yes	characteristic, complemented
133	#72210572	C₂²	1	1	yes	characteristic, complemented
134	#72210572	C₂²	1	1	yes	characteristic, complemented
135	#72210569	C₂²	1	1	yes	characteristic, complemented
136	#72210569	C₂²	1	1	yes	characteristic, complemented
137	#72210569	C₂²	1	1	yes	characteristic, complemented
138	#72210569	C₂²	1	1	yes	characteristic, complemented
139	#72210563	C₂²	1	1	yes	characteristic, complemented
140	#72210563	C₂²	1	1	yes	characteristic, complemented
141	#72210563	C₂²	1	1	yes	characteristic, complemented
142	#72210563	C₂²	1	1	yes	characteristic, complemented
143	#72210563	C₂²	1	1	yes	characteristic, complemented
144	#72210563	C₂²	1	1	yes	characteristic, complemented
145	#72210559	C₂²	1	1	yes	characteristic
146	#72210559	C₂²	1	1	yes	characteristic
147	#72210559	C₂²	1	1	yes	characteristic, complemented
148	#72210559	C₂²	1	1	yes	characteristic, complemented
149	#72210559	C₂²	1	1	yes	characteristic, complemented
150	#72210559	C₂²	1	1	yes	characteristic, complemented
151	#72210559	C₂²	1	1	yes	characteristic, complemented
152	#72210559	C₂²	1	1	yes	characteristic, complemented
153	#72210559	C₂²	1	1	yes	characteristic, complemented
154	#72210559	C₂²	1	1	yes	characteristic, complemented
155	#72210549	C₂²	1	1	yes	characteristic, complemented
156	#72210549	C₂²	1	1	yes	characteristic, complemented
157	#72210549	C₂²	1	1	yes	characteristic, complemented
158	#72210539	C₂²	1	1	yes	characteristic, complemented
159	#72210539	C₂²	1	1	yes	characteristic, complemented
160	#72210539	C₂²	1	1	yes	characteristic, complemented
161	#72210529	C₂²	1	1	yes	characteristic, complemented
162	#72210529	C₂²	1	1	yes	characteristic, complemented
163	#72210529	C₂²	1	1	yes	characteristic, complemented
164	#72210529	C₂²	1	1	yes	characteristic, complemented
165	#72210524	C₂²	1	1	yes	characteristic, complemented
166	#72210524	C₂²	1	1	yes	characteristic, complemented
167	#72210498	C₂²	1	1	yes	characteristic
168	#72210498	C₂²	1	1	yes	characteristic
169	#72210498	C₂²	1	1	yes	characteristic, complemented
170	#72210498	C₂²	1	1	yes	characteristic, complemented
171	#72210498	C₂²	1	1	yes	characteristic, complemented
172	#72210498	C₂²	1	1	yes	characteristic, complemented
173	#72210498	C₂²	1	1	yes	characteristic, complemented
174	#72210498	C₂²	1	1	yes	characteristic, complemented
175	#72210498	C₂²	1	1	yes	characteristic, complemented
176	#72210498	C₂²	1	1	yes	characteristic, complemented
177	#72210498	C₂²	1	1	yes	characteristic, complemented
178	#72210498	C₂²	1	1	yes	characteristic, complemented
179	#72210498	C₂²	1	1	yes	characteristic, complemented
180	#72210483	C₂²	1	1	yes	characteristic, complemented
181	#72210439	C₂²	1	1	yes	characteristic
182	#72210439	C₂²	1	1	yes	characteristic
183	#72210439	C₂²	1	1	yes	characteristic, complemented
184	#72210439	C₂²	1	1	yes	characteristic, complemented
185	#72210439	C₂²	1	1	yes	characteristic, complemented
186	#72210439	C₂²	1	1	yes	characteristic, complemented
187	#8934366	C₂³	1	1	yes	characteristic
188	#8934366	C₂³	1	1	yes	characteristic
189	#8934366	C₂³	1	1	yes	characteristic
190	#8934366	C₂³	1	1	yes	characteristic
191	#8934366	C₂³	1	1	yes	characteristic, complemented
192	#8933771	C₂³	1	1	yes	characteristic, complemented
193	#7672751	C₂³	1	1	yes	characteristic
194	#7672751	C₂³	1	1	yes	characteristic
195	#7672751	C₂³	1	1	yes	characteristic
196	#6628901	C₂³	1	1	yes	characteristic
197	#6628901	C₂³	1	1	yes	characteristic
198	#6628896	D₄	1	2	yes	complemented
199	#6628896	D₄	1	2	yes	complemented
200	#6470231	D₄	1	2	yes	complemented
201	#6432958	C₂³	1	1	yes	characteristic
202	#449527	C₂³	1	1	yes	characteristic
203	#449492	C₂³	1	1	yes	characteristic
204	#449492	C₂³	1	1	yes	characteristic
205	#449492	C₂³	1	1	yes	characteristic
206	#449492	C₂³	1	1	yes	characteristic
207	#449492	C₂³	1	1	yes	characteristic
208	#418114	C₂³	1	1	yes	characteristic
209	#417807	C₂³	1	1	yes	characteristic
210	#417807	C₂³	1	1	yes	characteristic
211	#417807	C₂³	1	1	yes	characteristic
212	#417807	C₂³	1	1	yes	characteristic
213	#417807	C₂³	1	1	yes	characteristic
214	#391714	C₂³	1	1	yes	characteristic
215	#374009	C₂³	1	1	yes	characteristic
216	#374009	C₂³	1	1	yes	characteristic
217	#346283	C₂³	1	1	yes	characteristic, complemented
218	#346283	C₂³	1	1	yes	characteristic, complemented
219	#251830	D₄	1	2	yes	complemented
220	#251828	D₄	1	2	yes	complemented
221	#251828	D₄	1	2	yes	complemented
222	#251828	D₄	1	2	yes	complemented
223	#251828	D₄	1	2	yes	complemented
224	#251828	D₄	1	2	yes	complemented
225	#245234	C₂³	1	1	yes	characteristic
226	#245234	C₂³	1	1	yes	characteristic
227	#245234	C₂³	1	1	yes	characteristic
228	#245234	C₂³	1	1	yes	characteristic
229	#245234	C₂³	1	1	yes	characteristic, complemented
230	#245234	C₂³	1	1	yes	characteristic, complemented
231	#245233	C₂³	1	1	yes	characteristic
232	#245233	C₂³	1	1	yes	characteristic
233	#245233	C₂³	1	1	yes	characteristic
234	#245233	C₂³	1	1	yes	characteristic
235	#245233	C₂³	1	1	yes	characteristic
236	#245233	C₂³	1	1	yes	characteristic
237	#245233	C₂³	1	1	yes	characteristic
238	#245233	C₂³	1	1	yes	characteristic
239	#245233	C₂³	1	1	yes	characteristic
240	#245233	C₂³	1	1	yes	characteristic
241	#245233	C₂³	1	1	yes	characteristic
242	#245233	C₂³	1	1	yes	characteristic
243	#245233	C₂³	1	1	yes	characteristic
244	#245233	C₂³	1	1	yes	characteristic
245	#245233	C₂³	1	1	yes	characteristic
246	#245233	C₂³	1	1	yes	characteristic
247	#245233	C₂³	1	1	yes	characteristic
248	#245233	C₂³	1	1	yes	characteristic
249	#245233	C₂³	1	1	yes	characteristic
250	#245233	C₂³	1	1	yes	characteristic
251	#245233	C₂³	1	1	yes	characteristic, complemented
252	#245233	C₂³	1	1	yes	characteristic, complemented
253	#245233	C₂³	1	1	yes	characteristic, complemented
254	#245233	C₂³	1	1	yes	characteristic, complemented
255	#213865	C₂³	1	1	yes	characteristic, complemented
256	#213861	C₂³	1	1	yes	characteristic
257	#213861	C₂³	1	1	yes	characteristic
258	#213861	C₂³	1	1	yes	characteristic, complemented
259	#213861	C₂³	1	1	yes	characteristic, complemented
260	#213860	C₂³	1	1	yes	characteristic
261	#213860	C₂³	1	1	yes	characteristic
262	#213860	C₂³	1	1	yes	characteristic
263	#213860	C₂³	1	1	yes	characteristic
264	#213860	C₂³	1	1	yes	characteristic, complemented
265	#213860	C₂³	1	1	yes	characteristic, complemented
266	#213860	C₂³	1	1	yes	characteristic, complemented
267	#213854	D₄	1	2	yes	complemented
268	#213854	D₄	1	2	yes	complemented
269	#213829	D₄	1	2	yes	complemented
270	#134009	C₂³	1	1	yes	characteristic
271	#134009	C₂³	1	1	yes	characteristic
272	#134009	C₂³	1	1	yes	characteristic
273	#134009	C₂³	1	1	yes	characteristic
274	#134009	C₂³	1	1	yes	characteristic
275	#134009	C₂³	1	1	yes	characteristic
276	#133936	C₂³	1	1	yes	characteristic, complemented
277	#133835	C₂³	1	1	yes	characteristic
278	#133835	C₂³	1	1	yes	characteristic
279	#133835	C₂³	1	1	yes	characteristic
280	#133835	C₂³	1	1	yes	characteristic
281	#133835	C₂³	1	1	yes	characteristic
282	#133835	C₂³	1	1	yes	characteristic
283	#133835	C₂³	1	1	yes	characteristic, complemented
284	#133835	C₂³	1	1	yes	characteristic, complemented
285	#133835	C₂³	1	1	yes	characteristic, complemented
286	#133835	C₂³	1	1	yes	characteristic, complemented
287	#133835	C₂³	1	1	yes	characteristic, complemented
288	#133309	C₂³	1	1	yes	characteristic, complemented
289	#133309	C₂³	1	1	yes	characteristic, complemented
290	#133308	C₂³	1	1	yes	characteristic
291	#133308	C₂³	1	1	yes	characteristic
292	#133308	C₂³	1	1	yes	characteristic
293	#133308	C₂³	1	1	yes	characteristic
294	#133308	C₂³	1	1	yes	characteristic
295	#133308	C₂³	1	1	yes	characteristic
296	#133308	C₂³	1	1	yes	characteristic
297	#133308	C₂³	1	1	yes	characteristic
298	#133308	C₂³	1	1	yes	characteristic
299	#133308	C₂³	1	1	yes	characteristic
300	#133308	C₂³	1	1	yes	characteristic
301	#133308	C₂³	1	1	yes	characteristic
302	#133308	C₂³	1	1	yes	characteristic
303	#133308	C₂³	1	1	yes	characteristic
304	#133308	C₂³	1	1	yes	characteristic
305	#133308	C₂³	1	1	yes	characteristic
306	#133308	C₂³	1	1	yes	characteristic
307	#133308	C₂³	1	1	yes	characteristic
308	#133308	C₂³	1	1	yes	characteristic
309	#133308	C₂³	1	1	yes	characteristic
310	#133308	C₂³	1	1	yes	characteristic
311	#133308	C₂³	1	1	yes	characteristic
312	#133308	C₂³	1	1	yes	characteristic
313	#133308	C₂³	1	1	yes	characteristic
314	#133308	C₂³	1	1	yes	characteristic, complemented
315	#133308	C₂³	1	1	yes	characteristic, complemented
316	#133308	C₂³	1	1	yes	characteristic, complemented
317	#133308	C₂³	1	1	yes	characteristic, complemented
318	#133308	C₂³	1	1	yes	characteristic, complemented
319	#133308	C₂³	1	1	yes	characteristic, complemented
320	#133308	C₂³	1	1	yes	characteristic, complemented
321	#133308	C₂³	1	1	yes	characteristic, complemented
322	#133308	C₂³	1	1	yes	characteristic, complemented
323	#133308	C₂³	1	1	yes	characteristic, complemented
324	#97466	C₂³	1	1	yes	characteristic, complemented
325	#97460	C₂³	1	1	yes	characteristic, complemented
326	#97460	C₂³	1	1	yes	characteristic, complemented
327	#97460	C₂³	1	1	yes	characteristic, complemented
328	#97460	C₂³	1	1	yes	characteristic, complemented
329	#97460	C₂³	1	1	yes	characteristic, complemented
330	#93146	C₂³	1	1	yes	characteristic, complemented
331	#93146	C₂³	1	1	yes	characteristic, complemented
332	#93146	C₂³	1	1	yes	characteristic, complemented
333	#93146	C₂³	1	1	yes	characteristic, complemented
334	#93146	C₂³	1	1	yes	characteristic, complemented
335	#93146	C₂³	1	1	yes	characteristic, complemented
336	#93139	C₂³	1	1	yes	characteristic, complemented
337	#93139	C₂³	1	1	yes	characteristic, complemented
338	#93139	C₂³	1	1	yes	characteristic, complemented
339	#93139	C₂³	1	1	yes	characteristic, complemented
340	#93139	C₂³	1	1	yes	characteristic, complemented
341	#93139	C₂³	1	1	yes	characteristic, complemented
342	#93113	C₂³	1	1	yes	characteristic, complemented
343	#93113	C₂³	1	1	yes	characteristic, complemented
344	#93113	C₂³	1	1	yes	characteristic, complemented
345	#93113	C₂³	1	1	yes	characteristic, complemented
346	#93113	C₂³	1	1	yes	characteristic, complemented
347	#93113	C₂³	1	1	yes	characteristic, complemented
348	#93113	C₂³	1	1	yes	characteristic, complemented
349	#93113	C₂³	1	1	yes	characteristic, complemented
350	#93113	C₂³	1	1	yes	characteristic, complemented
351	#93113	C₂³	1	1	yes	characteristic, complemented
352	#93113	C₂³	1	1	yes	characteristic, complemented
353	#93113	C₂³	1	1	yes	characteristic, complemented
354	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
355	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
356	#62842	C₂×D₄	1	1	yes	characteristic, complemented
357	#46384	C₂×D₄	1	2	yes	—
358	#46384	C₂×D₄	1	2	yes	—
359	#46384	C₂×D₄	1	2	yes	—
360	C₂×#2867	C₂⁴	1	1	yes	characteristic
361	#35554	C₂⁴	1	1	yes	characteristic
362	#35527	C₂⁴	1	1	yes	characteristic
363	#35527	C₂⁴	1	1	yes	characteristic
364	#35527	C₂⁴	1	1	yes	characteristic
365	#35527	C₂⁴	1	1	yes	characteristic
366	#35527	C₂⁴	1	1	yes	characteristic
367	#35527	C₂⁴	1	1	yes	characteristic
368	#35527	C₂⁴	1	1	yes	characteristic
369	#35527	C₂⁴	1	1	yes	characteristic
370	#35527	C₂⁴	1	1	yes	characteristic
371	#35527	C₂⁴	1	1	yes	characteristic
372	#35527	C₂⁴	1	1	yes	characteristic
373	#35346	C₂×D₄	1	2	yes	—
374	#35346	C₂×D₄	1	2	yes	—
375	#35346	C₂×D₄	1	2	yes	—
376	#33020	C₂×D₄	1	2	yes	complemented
377	#33020	C₂×D₄	1	2	yes	complemented
378	#32898	C₂×D₄	1	2	yes	—
379	#32898	C₂×D₄	1	2	yes	—
380	#32898	C₂×D₄	1	2	yes	—
381	#32898	C₂×D₄	1	2	yes	—
382	#32898	C₂×D₄	1	2	yes	complemented
383	#32898	C₂×D₄	1	2	yes	complemented
384	#32898	C₂×D₄	1	2	yes	complemented
385	#32898	C₂×D₄	1	2	yes	complemented
386	#32898	C₂×D₄	1	2	yes	complemented
387	#32898	C₂×D₄	1	2	yes	complemented
388	#20690	C₂×D₄	1	1	yes	characteristic, complemented
389	#20586	C₂×D₄	1	2	yes	complemented
390	#20586	C₂×D₄	1	1	yes	characteristic, complemented
391	#20586	C₂×D₄	1	1	yes	characteristic, complemented
392	#20586	C₂×D₄	1	1	yes	characteristic, complemented
393	#20586	C₂×D₄	1	1	yes	characteristic, complemented
394	#20586	C₂×D₄	1	1	yes	characteristic, complemented
395	#20586	C₂×D₄	1	1	yes	characteristic, complemented
396	#20586	C₂×D₄	1	1	yes	characteristic, complemented
397	#20586	C₂×D₄	1	1	yes	characteristic, complemented
398	#20585	C₂×D₄	1	2	yes	complemented
399	#20585	C₂×D₄	1	2	yes	complemented
400	#10981	C₂⁴	1	1	yes	characteristic
401	#10981	C₂⁴	1	1	yes	characteristic
402	#10981	C₂⁴	1	1	yes	characteristic
403	#10981	C₂⁴	1	1	yes	characteristic
404	#10981	C₂⁴	1	1	yes	characteristic
405	#10981	C₂⁴	1	1	yes	characteristic
406	#9497	C₂×D₄	1	2	yes	—
407	#9497	C₂×D₄	1	2	yes	—
408	#9497	C₂×D₄	1	2	yes	—
409	#9497	C₂×D₄	1	2	yes	—
410	#9497	C₂×D₄	1	2	yes	complemented
411	#9497	C₂×D₄	1	2	yes	complemented
412	#9497	C₂×D₄	1	2	yes	complemented
413	#9497	C₂×D₄	1	2	yes	complemented
414	#9497	C₂×D₄	1	2	yes	complemented
415	#9497	C₂×D₄	1	2	yes	complemented
416	#9497	C₂×D₄	1	2	yes	complemented
417	#9497	C₂×D₄	1	2	yes	complemented
418	#8748	C₂×D₄	1	2	yes	complemented
419	#8748	C₂×D₄	1	2	yes	complemented
420	#8748	C₂×D₄	1	2	yes	complemented
421	#8546	C₂⁴	1	1	yes	characteristic
422	#8546	C₂⁴	1	1	yes	characteristic
423	#8546	C₂⁴	1	1	yes	characteristic
424	#8546	C₂⁴	1	1	yes	characteristic
425	#8546	C₂⁴	1	1	yes	characteristic
426	#8546	C₂⁴	1	1	yes	characteristic
427	#8546	C₂⁴	1	1	yes	characteristic
428	#8546	C₂⁴	1	1	yes	characteristic
429	#8546	C₂⁴	1	1	yes	characteristic
430	#8546	C₂⁴	1	1	yes	characteristic
431	#8546	C₂⁴	1	1	yes	characteristic
432	#8546	C₂⁴	1	1	yes	characteristic
433	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
434	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
435	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
436	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
437	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
438	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
439	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
440	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
441	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
442	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
445	C₂²×#127	C₂⁵	1	1	yes	characteristic
446	C₂²×#120	#120	1	2	yes	—
447	C₂×#518	C₂²×D₄	1	1	yes	characteristic
448	#2842	#120	1	2	yes	—
449	#2403	#120	1	2	yes	—
450	#2403	#120	1	2	yes	—
451	#2403	#120	1	2	yes	—
452	#2403	C₂²×D₄	1	2	yes	—
453	#2403	C₂²×D₄	1	2	yes	—
454	#2403	C₂²×D₄	1	2	yes	—
455	#2403	C₂²×D₄	1	2	yes	—
456	#2403	C₂²×D₄	1	2	yes	—
457	#2403	C₂²×D₄	1	2	yes	—
458	#2309	C₂²×D₄	1	1	yes	characteristic
459	#2309	C₂²×D₄	1	1	yes	characteristic
460	#2309	C₂²×D₄	1	1	yes	characteristic
461	#2309	C₂²×D₄	1	1	yes	characteristic
462	#2309	C₂²×D₄	1	1	yes	characteristic
463	#2309	C₂²×D₄	1	1	yes	characteristic
464	#2309	C₂²×D₄	1	1	yes	characteristic
465	#2309	C₂²×D₄	1	1	yes	characteristic
466	#2309	C₂²×D₄	1	1	yes	characteristic
467	#2309	H(5,𝔽₂)	1	1	yes	characteristic
468	#2309	H(5,𝔽₂)	1	1	yes	characteristic
469	#2309	H(5,𝔽₂)	1	1	yes	characteristic
470	#2308	#120	1	2	yes	—
471	#2308	#120	1	2	yes	—
472	#2308	#120	1	2	yes	—
473	C₂×C₄³	H(5,𝔽₂)	1	1	yes	characteristic
474	#1781	C₂²×D₄	1	2	yes	—
475	#1781	C₂²×D₄	1	2	yes	—
476	#1781	C₂²×D₄	1	2	yes	—
477	#1781	C₂²×D₄	1	2	yes	—
478	#1781	C₂²×D₄	1	2	yes	—
479	#1781	C₂²×D₄	1	2	yes	—
480	C₂⁶	B(4,𝔽₂)	1	2	yes	—
481	C₂³×D₄	C₂×#120	1	2	yes	—
482	C₂³×D₄	C₂×#120	1	2	yes	—
483	C₂³×D₄	C₂×#120	1	2	yes	—
484	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
485	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
486	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
487	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
491	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
492	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
493	C₂²×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	#379	C₂×#120	1	2	yes	—
495	#379	C₂×#120	1	2	yes	—
496	#379	C₂×#120	1	2	yes	—
497	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
498	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
499	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
500	C₂⁵	C₂²×#120	1	1	yes	characteristic
501	C₂⁵	#3484	1	1	yes	characteristic
502	C₂⁵	#3484	1	1	yes	characteristic
503	C₂⁵	#3484	1	1	yes	characteristic
504	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
505	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
506	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
507	C₂³×C₄	#3484	1	1	yes	characteristic
508	C₂³×C₄	#3484	1	1	yes	characteristic
509	C₂³×C₄	#3484	1	1	yes	characteristic
510	C₂⁴	#35346	1	1	yes	characteristic
511	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
512	C₂³	#6499867	1	1	yes	characteristic
513	C₂³	#6499874	1	1	yes	characteristic
514	C₂³	#6499874	1	1	yes	characteristic
515	C₂²	#72216396	1	1	yes	characteristic
516	C₂	#72216398	1	1	yes	characteristic
517	C₂	#72216398	1	1	yes	characteristic
518	C₂	#72262472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72216396
commutator, Frattini, cosocle	C₂²×#127	C₂⁵
LCS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#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. #72338825	C₂	semidirect
2. #72338815	C₂	semidirect
3. #72338811	C₂	semidirect
4. #72338809	C₂	semidirect
5. #72338806	C₂	semidirect
6. #72338801	C₂	semidirect
7. #72338797	C₂	semidirect
8. #72338795	C₂	semidirect
9. #72338794	C₂²	semidirect
10. #72338794	C₂²	semidirect
11. #72338788	C₂	semidirect
12. #72338787	C₂²	semidirect
13. #72338787	C₂²	semidirect
14. #72338787	C₂²	semidirect
15. #72338771	C₂	semidirect
16. #72338767	C₂	semidirect
17. #72338766	C₂	semidirect
18. #72338748	C₂	semidirect
19. #72338738	C₂	semidirect
20. #72338736	C₂²	semidirect
21. #72338734	C₂	semidirect
22. #72338730	C₂	semidirect
23. #72338726	C₂²	semidirect
24. #72338723	C₂	semidirect
25. #72338721	C₂²	semidirect
26. #72338718	C₂	semidirect
27. #72338715	C₂²	semidirect
28. #72338712	C₂²	semidirect
29. #72337678	C₂	semidirect
30. #72337670	C₂	semidirect
31. #72337669	C₂	semidirect
32. #72337667	C₂²	semidirect
33. #72337665	C₂²	semidirect
34. #72337664	C₂²	semidirect
35. #72337663	C₂	semidirect
36. #72337662	C₂²	semidirect
37. #72337662	C₂²	semidirect
38. #72337661	C₂²	semidirect
39. #72337661	C₂²	semidirect
40. #72337660	C₂	semidirect
42. #72337659	C₂²	semidirect
43. #72337659	C₂²	semidirect
44. #72337656	C₂²	semidirect
45. #72337654	C₂²	semidirect
46. #72337652	C₂²	semidirect
47. #72337650	C₂²	semidirect
48. #72337648	C₂²	semidirect
49. #72337648	C₂²	semidirect
50. #72337648	C₂²	semidirect
51. #72337648	C₂²	semidirect
52. #72337647	C₂²	semidirect
53. #72337645	C₂²	semidirect
54. #72337644	C₂²	semidirect
55. #72337637	C₂²	semidirect
56. #72337637	C₂²	semidirect
57. #72337636	C₂²	semidirect
58. #72337636	C₂²	semidirect
59. #72337635	C₂²	semidirect
60. #72337635	C₂²	semidirect
61. #72337629	C₂²	semidirect
62. #72337629	C₂²	semidirect
63. #72337627	C₂²	semidirect
64. #72337627	C₂²	semidirect
65. #72337625	C₂²	semidirect
66. #72337625	C₂²	semidirect
67. #72319263	C₂²	semidirect
68. #72319263	C₂²	semidirect
69. #72318569	C₂²	semidirect
70. #72318569	C₂²	semidirect
71. #72262289	C₂²	semidirect
72. #72262288	C₂²	semidirect
73. #72252381	C₂	semidirect
74. #72252380	C₂	semidirect
75. #72252379	C₂²	semidirect
76. #72252379	C₂²	semidirect
77. #72252379	C₂²	semidirect
78. #72252378	C₂²	semidirect
79. #72252378	C₂²	semidirect
80. #72241387	C₂²	semidirect
81. #72241387	C₂²	semidirect
82. #72241343	C₂²	semidirect
83. #72241343	C₂²	semidirect
84. #72241323	C₂	semidirect
85. #72241323	C₂	semidirect
86. #72241322	C₂²	semidirect
87. #72241322	C₂²	semidirect
88. #72241322	C₂²	semidirect
89. #72241322	C₂²	semidirect
90. #72241322	C₂²	semidirect
91. #72241322	C₂²	semidirect
92. #72241322	C₂²	semidirect
93. #72241322	C₂²	semidirect
94. #72241322	C₂²	semidirect
95. #72241322	C₂²	semidirect
96. #72241322	C₂²	semidirect
97. #72241322	C₂²	semidirect
98. #72240077	C₂²	semidirect
99. #72236986	C₂	semidirect
100. #72236986	C₂	semidirect
101. #72236979	C₂²	semidirect
102. #72236979	C₂²	semidirect
103. #72236975	C₂²	semidirect
104. #72236975	C₂²	semidirect
105. #72236975	C₂²	semidirect
106. #72236975	C₂²	semidirect
107. #72236189	C₂²	semidirect
108. #72227941	C₂²	semidirect
109. #72227941	C₂²	semidirect
110. #72227941	C₂²	semidirect
111. #72227941	C₂²	semidirect
112. #72227940	C₂²	semidirect
113. #72227940	C₂²	semidirect
114. #72227940	C₂²	semidirect
115. #72227940	C₂²	semidirect
116. #72227940	C₂²	semidirect
117. #72227940	C₂²	semidirect
118. #72227940	C₂²	semidirect
119. #72227940	C₂²	semidirect
120. #72227556	C₂²	semidirect
121. #72213269	C₂²	semidirect
122. #72213269	C₂²	semidirect
123. #72213260	C₂²	semidirect
124. #72213260	C₂²	semidirect
125. #72210591	C₂	semidirect
126. #72210591	C₂	semidirect
127. #72210572	C₂²	semidirect
128. #72210572	C₂²	semidirect
129. #72210572	C₂²	semidirect
130. #72210572	C₂²	semidirect
131. #72210572	C₂²	semidirect
132. #72210572	C₂²	semidirect
133. #72210572	C₂²	semidirect
134. #72210572	C₂²	semidirect
135. #72210569	C₂²	semidirect
136. #72210569	C₂²	semidirect
137. #72210569	C₂²	semidirect
138. #72210569	C₂²	semidirect
139. #72210563	C₂²	semidirect
140. #72210563	C₂²	semidirect
141. #72210563	C₂²	semidirect
142. #72210563	C₂²	semidirect
143. #72210563	C₂²	semidirect
144. #72210563	C₂²	semidirect
147. #72210559	C₂²	semidirect
148. #72210559	C₂²	semidirect
149. #72210559	C₂²	semidirect
150. #72210559	C₂²	semidirect
151. #72210559	C₂²	semidirect
152. #72210559	C₂²	semidirect
153. #72210559	C₂²	semidirect
154. #72210559	C₂²	semidirect
155. #72210549	C₂²	semidirect
156. #72210549	C₂²	semidirect
157. #72210549	C₂²	semidirect
158. #72210539	C₂²	semidirect
159. #72210539	C₂²	semidirect
160. #72210539	C₂²	semidirect
161. #72210529	C₂²	semidirect
162. #72210529	C₂²	semidirect
163. #72210529	C₂²	semidirect
164. #72210529	C₂²	semidirect
165. #72210524	C₂²	semidirect
166. #72210524	C₂²	semidirect
169. #72210498	C₂²	semidirect
170. #72210498	C₂²	semidirect
171. #72210498	C₂²	semidirect
172. #72210498	C₂²	semidirect
173. #72210498	C₂²	semidirect
174. #72210498	C₂²	semidirect
175. #72210498	C₂²	semidirect
176. #72210498	C₂²	semidirect
177. #72210498	C₂²	semidirect
178. #72210498	C₂²	semidirect
179. #72210498	C₂²	semidirect
180. #72210483	C₂²	semidirect
183. #72210439	C₂²	semidirect
184. #72210439	C₂²	semidirect
185. #72210439	C₂²	semidirect
186. #72210439	C₂²	semidirect
191. #8934366	C₂³	semidirect
192. #8933771	C₂³	semidirect
198. #6628896	D₄	semidirect
199. #6628896	D₄	semidirect
200. #6470231	D₄	semidirect
217. #346283	C₂³	semidirect
218. #346283	C₂³	semidirect
219. #251830	D₄	semidirect
220. #251828	D₄	semidirect
221. #251828	D₄	semidirect
222. #251828	D₄	semidirect
223. #251828	D₄	semidirect
224. #251828	D₄	semidirect
229. #245234	C₂³	semidirect
230. #245234	C₂³	semidirect
251. #245233	C₂³	semidirect
252. #245233	C₂³	semidirect
253. #245233	C₂³	semidirect
254. #245233	C₂³	semidirect
255. #213865	C₂³	semidirect
258. #213861	C₂³	semidirect
259. #213861	C₂³	semidirect
264. #213860	C₂³	semidirect
265. #213860	C₂³	semidirect
266. #213860	C₂³	semidirect
267. #213854	D₄	semidirect
268. #213854	D₄	semidirect
269. #213829	D₄	semidirect
276. #133936	C₂³	semidirect
283. #133835	C₂³	semidirect
284. #133835	C₂³	semidirect
285. #133835	C₂³	semidirect
286. #133835	C₂³	semidirect
287. #133835	C₂³	semidirect
288. #133309	C₂³	semidirect
289. #133309	C₂³	semidirect
314. #133308	C₂³	semidirect
315. #133308	C₂³	semidirect
316. #133308	C₂³	semidirect
317. #133308	C₂³	semidirect
318. #133308	C₂³	semidirect
319. #133308	C₂³	semidirect
320. #133308	C₂³	semidirect
321. #133308	C₂³	semidirect
322. #133308	C₂³	semidirect
323. #133308	C₂³	semidirect
324. #97466	C₂³	semidirect
325. #97460	C₂³	semidirect
326. #97460	C₂³	semidirect
327. #97460	C₂³	semidirect
328. #97460	C₂³	semidirect
329. #97460	C₂³	semidirect
330. #93146	C₂³	semidirect
331. #93146	C₂³	semidirect
332. #93146	C₂³	semidirect
333. #93146	C₂³	semidirect
334. #93146	C₂³	semidirect
335. #93146	C₂³	semidirect
336. #93139	C₂³	semidirect
337. #93139	C₂³	semidirect
338. #93139	C₂³	semidirect
339. #93139	C₂³	semidirect
340. #93139	C₂³	semidirect
341. #93139	C₂³	semidirect
342. #93113	C₂³	semidirect
343. #93113	C₂³	semidirect
344. #93113	C₂³	semidirect
345. #93113	C₂³	semidirect
346. #93113	C₂³	semidirect
347. #93113	C₂³	semidirect
348. #93113	C₂³	semidirect
349. #93113	C₂³	semidirect
350. #93113	C₂³	semidirect
351. #93113	C₂³	semidirect
352. #93113	C₂³	semidirect
353. #93113	C₂³	semidirect
354. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
355. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
356. #62842	C₂×D₄	semidirect
376. #33020	C₂×D₄	semidirect
377. #33020	C₂×D₄	semidirect
382. #32898	C₂×D₄	semidirect
383. #32898	C₂×D₄	semidirect
384. #32898	C₂×D₄	semidirect
385. #32898	C₂×D₄	semidirect
386. #32898	C₂×D₄	semidirect
387. #32898	C₂×D₄	semidirect
388. #20690	C₂×D₄	semidirect
389. #20586	C₂×D₄	semidirect
390. #20586	C₂×D₄	semidirect
391. #20586	C₂×D₄	semidirect
392. #20586	C₂×D₄	semidirect
393. #20586	C₂×D₄	semidirect
394. #20586	C₂×D₄	semidirect
395. #20586	C₂×D₄	semidirect
396. #20586	C₂×D₄	semidirect
397. #20586	C₂×D₄	semidirect
398. #20585	C₂×D₄	semidirect
399. #20585	C₂×D₄	semidirect
410. #9497	C₂×D₄	semidirect
411. #9497	C₂×D₄	semidirect
412. #9497	C₂×D₄	semidirect
413. #9497	C₂×D₄	semidirect
414. #9497	C₂×D₄	semidirect
415. #9497	C₂×D₄	semidirect
416. #9497	C₂×D₄	semidirect
417. #9497	C₂×D₄	semidirect
418. #8748	C₂×D₄	semidirect
419. #8748	C₂×D₄	semidirect
420. #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
#72338825	2
#72338815	2
#72338811	2
#72338809	2
#72338806	2
#72338801	2
#72338797	2
#72338795	2
#72338788	2
#72338771	2
#72338767	2
#72338766	2
#72338748	2
#72338738	2
#72338734	2
#72338730	2
#72338723	2
#72338718	2
#72337678	2
#72337670	2
#72337669	2
#72337663	2
#72337660	2
#72252381	2
#72252380	2
#72241323	2
#72236986	2
#72210591	2