Subgroups — #72233840

Order 2048.

At least 8992 conjugacy classes of subgroups; only the 664 normal subgroups are shown.

The subgroup lattice has 431 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72233836	C₂	1	2	yes	maximal, complemented
2	#72233835	C₂	1	2	yes	maximal, complemented
3	#72233834	C₂	1	2	yes	maximal, complemented
4	#72233833	C₂	1	2	yes	maximal, complemented
5	#72233832	C₂	1	2	yes	maximal, complemented
6	#72233831	C₂	1	2	yes	maximal, complemented
7	#72233830	C₂	1	2	yes	maximal, complemented
8	#72233829	C₂	1	2	yes	maximal, complemented
9	#72233828	C₂	1	2	yes	maximal, complemented
10	#72233827	C₂	1	2	yes	maximal, complemented
11	#72233826	C₂	1	2	yes	maximal, complemented
12	#72233825	C₂	1	2	yes	maximal, complemented
13	#72233824	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233278	C₂	1	1	yes	maximal, characteristic, complemented
15	#72233221	C₂	1	1	yes	maximal, characteristic, complemented
16	#72233104	C₂	1	1	yes	maximal, characteristic, complemented
17	#72233035	C₂	1	1	yes	maximal, characteristic, complemented
18	#72232937	C₂	1	1	yes	maximal, characteristic, complemented
19	#72232716	C₂	1	1	yes	maximal, characteristic, complemented
20	#10586472	C₂²	1	1	yes	characteristic
21	#6385983	C₂²	1	1	yes	characteristic
22	#6347256	C₂²	1	2	yes	—
23	#6346599	C₂²	1	2	yes	—
24	#5522295	C₂²	1	1	yes	characteristic, complemented
25	#5519537	C₂²	1	1	yes	characteristic, complemented
26	#5482155	C₂²	1	1	yes	characteristic, complemented
27	#5119558	C₂²	1	1	yes	characteristic, complemented
28	#5118168	C₂²	1	1	yes	characteristic, complemented
29	#4861302	C₂²	1	1	yes	characteristic, complemented
30	#4417886	C₂²	1	1	yes	characteristic
31	#4123398	C₂²	1	1	yes	characteristic, complemented
32	#2535814	C₂²	1	1	yes	characteristic, complemented
33	#2177498	C₂²	1	1	yes	characteristic, complemented
34	#878571	C₂²	1	1	yes	characteristic, complemented
35	#649038	C₂²	1	1	yes	characteristic
36	#587425	C₂²	1	1	yes	characteristic, complemented
37	#556476	C₂²	1	1	yes	characteristic, complemented
38	#553180	C₂²	1	1	yes	characteristic
39	#482377	C₂²	1	2	yes	complemented
40	#481985	C₂²	1	2	yes	complemented
41	#346471	C₂²	1	2	yes	complemented
42	#346471	C₂²	1	2	yes	complemented
43	#346449	C₂²	1	2	yes	—
44	#346449	C₂²	1	2	yes	—
45	#346449	C₂²	1	2	yes	—
46	#346449	C₂²	1	2	yes	—
47	#346449	C₂²	1	2	yes	complemented
48	#346449	C₂²	1	2	yes	complemented
49	#188087	C₂²	1	1	yes	characteristic
50	#188087	C₂²	1	1	yes	characteristic
51	#186842	C₂²	1	2	yes	complemented
52	#186837	C₂²	1	2	yes	—
53	#186828	C₂²	1	2	yes	complemented
54	#186824	C₂²	1	2	yes	complemented
55	#186818	C₂²	1	2	yes	complemented
56	#186816	C₂²	1	2	yes	—
57	#185264	C₂²	1	2	yes	—
58	#185246	C₂²	1	2	yes	—
59	#144626	C₂²	1	4	yes	complemented
60	#144624	C₂²	1	4	yes	complemented
61	#144608	C₂²	1	4	yes	complemented
62	#144607	C₂²	1	4	yes	complemented
63	#142980	C₂²	1	4	yes	complemented
64	#142980	C₂²	1	4	yes	complemented
65	#142966	C₂²	1	4	yes	complemented
66	#142966	C₂²	1	4	yes	complemented
67	#140045	C₂²	1	4	yes	complemented
68	#140043	C₂²	1	4	yes	complemented
69	#140040	C₂²	1	4	yes	complemented
70	#140038	C₂²	1	4	yes	complemented
71	#140020	C₂²	1	4	yes	complemented
72	#140020	C₂²	1	4	yes	complemented
73	#140018	C₂²	1	4	yes	complemented
74	#140018	C₂²	1	4	yes	complemented
75	#139511	C₂²	1	2	yes	complemented
76	#139511	C₂²	1	2	yes	complemented
77	#139511	C₂²	1	2	yes	complemented
78	#139511	C₂²	1	2	yes	complemented
79	#139511	C₂²	1	2	yes	complemented
80	#139511	C₂²	1	2	yes	complemented
81	#139480	C₂²	1	2	yes	complemented
82	#139480	C₂²	1	2	yes	complemented
83	#135569	C₂²	1	2	yes	complemented
84	#135567	C₂²	1	2	yes	complemented
85	#135565	C₂²	1	2	yes	complemented
86	#135563	C₂²	1	2	yes	complemented
87	#128200	C₂²	1	2	yes	complemented
88	#128179	C₂²	1	2	yes	complemented
89	#127242	C₂²	1	2	yes	complemented
90	#127207	C₂²	1	2	yes	complemented
91	#62818	C₂³	1	2	yes	—
92	#62818	C₂³	1	2	yes	—
93	#62773	C₂³	1	2	yes	—
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂³×#127	D₄	1	1	yes	characteristic
96	C₂×#2815	D₄	1	1	yes	characteristic
97	C₂×#2433	D₄	1	1	yes	characteristic
98	C₂×#2433	D₄	1	1	yes	characteristic
99	C₂×#2408	C₂³	1	1	yes	characteristic
100	C₂×#2635	C₂³	1	1	yes	characteristic
101	C₂×#2353	D₄	1	1	yes	characteristic
102	C₂×#2318	D₄	1	1	yes	characteristic
103	#21752	C₂³	1	2	yes	—
104	#21752	C₂³	1	2	yes	—
105	#20726	C₂³	1	2	yes	—
106	#18172	C₂³	1	4	yes	—
107	#18164	C₂³	1	4	yes	—
108	#18164	C₂³	1	4	yes	—
109	#18164	C₂³	1	4	yes	—
110	#17362	C₂³	1	2	yes	—
111	#17362	C₂³	1	2	yes	—
112	#17141	C₂³	1	1	yes	characteristic, complemented
113	#17141	C₂³	1	1	yes	characteristic, complemented
114	#17082	C₂³	1	1	yes	characteristic, complemented
115	#17082	C₂³	1	1	yes	characteristic, complemented
116	#16242	C₂³	1	1	yes	characteristic, complemented
117	#16186	C₂³	1	1	yes	characteristic, complemented
118	#16171	C₂³	1	1	yes	characteristic, complemented
119	#15964	C₂³	1	1	yes	characteristic, complemented
120	#15674	C₂³	1	1	yes	characteristic
121	#15674	C₂³	1	1	yes	characteristic
122	#15310	C₂³	1	1	yes	characteristic
123	#15310	C₂³	1	1	yes	characteristic
124	#15310	C₂³	1	1	yes	characteristic
125	#15310	C₂³	1	1	yes	characteristic
126	#15310	C₂³	1	1	yes	characteristic
127	#15310	C₂³	1	1	yes	characteristic
128	#15283	D₄	1	1	yes	characteristic
129	#15283	D₄	1	1	yes	characteristic
130	#15258	D₄	1	1	yes	characteristic
131	#15258	D₄	1	1	yes	characteristic
132	#15258	D₄	1	1	yes	characteristic
133	#15258	D₄	1	1	yes	characteristic
134	#15258	D₄	1	1	yes	characteristic
135	#15258	D₄	1	1	yes	characteristic
136	#14698	D₄	1	1	yes	characteristic
137	#14661	D₄	1	1	yes	characteristic
138	#14659	C₂³	1	1	yes	characteristic
139	#14654	C₂³	1	1	yes	characteristic, complemented
140	#14641	C₂³	1	1	yes	characteristic, complemented
141	#14641	C₂³	1	1	yes	characteristic, complemented
142	#14617	C₂³	1	1	yes	characteristic, complemented
143	#14571	C₂³	1	1	yes	characteristic, complemented
144	#14345	C₂³	1	1	yes	characteristic
145	#14335	D₄	1	1	yes	characteristic
146	#14335	D₄	1	1	yes	characteristic
147	#14290	D₄	1	1	yes	characteristic
148	#14290	C₂³	1	1	yes	characteristic
149	#14272	D₄	1	1	yes	characteristic
150	#14271	C₂³	1	1	yes	characteristic
151	#14252	C₂³	1	1	yes	characteristic, complemented
152	#14181	C₂³	1	1	yes	characteristic, complemented
153	#14181	C₂³	1	1	yes	characteristic, complemented
154	#14152	C₂³	1	1	yes	characteristic
155	#13959	C₂³	1	1	yes	characteristic
156	#13940	C₂³	1	1	yes	characteristic
157	#13902	D₄	1	1	yes	characteristic
158	#13902	D₄	1	1	yes	characteristic
159	#13902	D₄	1	1	yes	characteristic
160	C₂×#1438	D₄	1	1	yes	characteristic
161	C₄×#386	C₂³	1	1	yes	characteristic
162	#11814	C₂³	1	4	yes	complemented
163	#11802	C₂³	1	4	yes	complemented
164	#11802	C₂³	1	4	yes	complemented
165	#11802	C₂³	1	4	yes	complemented
166	#8549	C₂³	1	2	yes	—
167	#8549	C₂³	1	2	yes	—
168	#8549	C₂³	1	2	yes	—
169	#8549	C₂³	1	2	yes	—
170	#8454	C₂³	1	4	yes	—
171	#8454	C₂³	1	4	yes	—
172	#8454	C₂³	1	4	yes	—
173	#8454	C₂³	1	4	yes	—
174	#8347	C₂³	1	4	yes	—
175	#8347	C₂³	1	4	yes	—
176	#8347	C₂³	1	4	yes	—
177	#8347	C₂³	1	4	yes	—
178	#7326	C₂³	1	4	yes	complemented
179	#7326	C₂³	1	4	yes	complemented
180	#7326	C₂³	1	4	yes	complemented
181	#7326	C₂³	1	4	yes	complemented
182	#7215	C₂³	1	4	yes	complemented
183	#7215	C₂³	1	4	yes	complemented
184	#7215	C₂³	1	4	yes	complemented
185	#7215	C₂³	1	4	yes	complemented
186	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	#3501	#41	1	2	yes	complemented
192	#3496	#41	1	2	yes	complemented
193	#3492	C₂⁴	1	4	yes	—
194	#3460	#41	1	4	yes	complemented
195	C₂²×#127	C₂×D₄	1	1	yes	characteristic
196	C₂²×#127	C₂×D₄	1	1	yes	characteristic
197	C₂²×#127	C₂×D₄	1	1	yes	characteristic
198	C₂²×#127	C₂×D₄	1	1	yes	characteristic
199	C₂²×#127	C₂×D₄	1	1	yes	characteristic
200	C₂²×#127	C₂×D₄	1	1	yes	characteristic
201	C₂²×#127	C₂×D₄	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×#121	C₂⁴	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×C₄×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
213	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
214	C₂×#400	C₂⁴	1	1	yes	characteristic
215	C₂×#399	C₂×D₄	1	1	yes	characteristic
216	C₂×#397	C₂×D₄	1	1	yes	characteristic
217	C₂×#397	C₂×D₄	1	1	yes	characteristic
218	C₂×#394	C₂⁴	1	1	yes	characteristic
219	C₂×#394	C₂⁴	1	1	yes	characteristic
220	C₂×#394	C₂⁴	1	1	yes	characteristic
221	C₂×#392	C₂×D₄	1	1	yes	characteristic
222	C₂×#392	C₂×D₄	1	1	yes	characteristic
223	C₂×#392	C₂×D₄	1	1	yes	characteristic
224	C₂×#392	C₂×D₄	1	1	yes	characteristic
225	C₂×#392	C₂×D₄	1	1	yes	characteristic
226	C₂×#392	C₂×D₄	1	1	yes	characteristic
227	C₂×#392	C₂×D₄	1	1	yes	characteristic
228	C₂×#392	C₂×D₄	1	1	yes	characteristic
229	C₂×#392	C₂×D₄	1	1	yes	characteristic
230	C₂×#390	C₂×D₄	1	1	yes	characteristic
231	C₂×#390	C₂×D₄	1	1	yes	characteristic
232	C₂×#383	C₂×D₄	1	1	yes	characteristic
233	C₂×#383	C₂×D₄	1	1	yes	characteristic
234	C₂×#382	C₂×D₄	1	1	yes	characteristic
235	C₂×#381	C₂×D₄	1	1	yes	characteristic
236	C₂×#381	C₂×D₄	1	1	yes	characteristic
237	C₂×#381	C₂×D₄	1	1	yes	characteristic
238	C₂×#381	C₂×D₄	1	1	yes	characteristic
239	C₂×#380	C₂×D₄	1	1	yes	characteristic
240	C₂×#380	C₂×D₄	1	1	yes	characteristic
241	C₂×#380	C₂×D₄	1	1	yes	characteristic
242	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
246	C₂×#376	C₂×D₄	1	1	yes	characteristic
247	C₂²×#95	C₂×D₄	1	1	yes	characteristic
248	C₂²×#95	C₂×D₄	1	1	yes	characteristic
249	#1821	C₂⁴	1	4	yes	—
250	#1463	C₂⁴	1	4	yes	—
251	#1463	C₂⁴	1	4	yes	—
252	#1445	C₂⁴	1	1	yes	characteristic
253	#1445	C₂⁴	1	1	yes	characteristic
254	#1445	C₂⁴	1	1	yes	characteristic
255	#1445	C₂⁴	1	1	yes	characteristic
256	#1438	C₂×D₄	1	1	yes	characteristic
257	#1438	C₂×D₄	1	1	yes	characteristic
258	#1438	C₂×D₄	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
272	#1438	C₂×D₄	1	1	yes	characteristic
273	#1438	C₂×D₄	1	1	yes	characteristic
274	#1438	C₂×D₄	1	1	yes	characteristic
275	#1438	C₂×D₄	1	1	yes	characteristic
276	#1437	C₂×D₄	1	1	yes	characteristic
277	#1437	C₂×D₄	1	1	yes	characteristic
278	#1437	C₂×D₄	1	1	yes	characteristic
279	#1437	C₂×D₄	1	1	yes	characteristic
280	#1437	C₂×D₄	1	1	yes	characteristic
281	#1437	C₂×D₄	1	1	yes	characteristic
282	#1437	C₂×D₄	1	1	yes	characteristic
283	#1437	C₂×D₄	1	1	yes	characteristic
284	#1437	C₂×D₄	1	1	yes	characteristic
285	#1437	C₂×D₄	1	1	yes	characteristic
286	#1437	C₂×D₄	1	1	yes	characteristic
287	#1437	C₂×D₄	1	1	yes	characteristic
288	#1436	C₂⁴	1	1	yes	characteristic
289	#1436	C₂⁴	1	1	yes	characteristic
290	#1436	C₂⁴	1	1	yes	characteristic
291	#1436	C₂⁴	1	1	yes	characteristic
292	C₂⁶	#120	1	1	yes	characteristic
293	C₂⁶	#120	1	1	yes	characteristic
294	C₂⁶	#120	1	1	yes	characteristic
295	C₂⁶	#120	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	#120	1	1	yes	characteristic
302	C₂³×D₄	#120	1	1	yes	characteristic
303	C₂³×D₄	#120	1	1	yes	characteristic
304	C₂³×D₄	#120	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	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
316	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
318	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
319	#544	C₂×#41	1	4	yes	—
320	#537	C₂×#41	1	4	yes	—
321	C₂×C₄×D₄	C₂×#41	1	2	yes	—
322	C₂×C₄×D₄	C₂×#41	1	2	yes	—
323	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
324	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
325	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	C₂⁵	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	#120	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×C₄²	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×D₄	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	C₂×#95	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	C₂×#95	C₂²×D₄	1	1	yes	characteristic
351	C₂×#95	C₂²×D₄	1	1	yes	characteristic
352	C₂×#95	C₂²×D₄	1	1	yes	characteristic
353	C₂×#95	C₂²×D₄	1	1	yes	characteristic
354	C₂×#95	C₂²×D₄	1	1	yes	characteristic
355	C₂×#95	C₂²×D₄	1	1	yes	characteristic
356	C₂×#95	C₂²×D₄	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	C₂×#120	1	1	yes	characteristic
361	C₂⁵	C₂×#120	1	1	yes	characteristic
362	C₂⁵	C₂×#120	1	1	yes	characteristic
363	C₂⁵	C₂×#120	1	1	yes	characteristic
364	C₂⁵	C₂×#120	1	1	yes	characteristic
365	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
366	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
367	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
368	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
369	C₂²×D₄	#525	1	1	yes	characteristic
370	C₂²×D₄	#525	1	1	yes	characteristic
371	C₂²×D₄	#535	1	1	yes	characteristic
372	C₂²×D₄	#535	1	1	yes	characteristic
373	C₂³×C₄	C₂×#120	1	1	yes	characteristic
374	C₂³×C₄	C₂×#120	1	1	yes	characteristic
375	C₂³×C₄	C₂×#120	1	1	yes	characteristic
376	C₂³×C₄	C₂×#120	1	1	yes	characteristic
377	C₂³×C₄	#546	1	2	yes	—
378	C₂³×C₄	#546	1	2	yes	—
379	C₂³×C₄	#546	1	2	yes	—
380	C₂³×C₄	#546	1	2	yes	—
381	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
382	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
383	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
384	C₂×C₄⋊C₄	B(4,𝔽₂)	1	4	yes	—
385	C₂×C₄⋊C₄	C₂²×#41	1	2	yes	—
386	C₂×C₄⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
387	C₂×C₂²⋊C₄	#546	1	2	yes	—
388	C₂×C₂²⋊C₄	#546	1	2	yes	—
389	C₂×C₂²⋊C₄	#546	1	2	yes	—
390	C₂×C₂²⋊C₄	#546	1	2	yes	—
391	C₂×C₄²	#525	1	2	yes	—
392	C₂×C₄²	#535	1	2	yes	—
393	C₂⁴	#2404	1	1	yes	characteristic
394	C₂⁴	#2404	1	1	yes	characteristic
395	C₂⁴	#2404	1	1	yes	characteristic
396	C₂⁴	#2404	1	1	yes	characteristic
397	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
398	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
399	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
400	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
401	C₂⁴	C₂²×#120	1	1	yes	characteristic
402	C₂²×C₄	#2404	1	2	yes	—
403	C₂²×C₄	#2404	1	2	yes	—
404	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
405	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
406	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
407	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
408	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
409	C₂²×C₄	C₂×#525	1	1	yes	characteristic
410	C₂²×C₄	C₂×#535	1	1	yes	characteristic
411	C₂²×C₄	C₂×#546	1	2	yes	—
412	C₂²×C₄	C₂×#546	1	2	yes	—
413	C₂³	#23998	1	2	yes	—
414	C₂³	#33551	1	2	yes	—
415	C₂³	C₂×#2404	1	1	yes	characteristic
416	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
417	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
418	C₂×C₄	#23984	1	2	yes	—
419	C₂×C₄	#23984	1	2	yes	—
420	C₂²	C₂×#23998	1	1	yes	characteristic
421	C₂²	#6451734	1	1	yes	characteristic
422	C₂²	C₂×#23984	1	1	yes	characteristic
423	C₂²	C₂×#33551	1	1	yes	characteristic
424	C₂²	#7622875	1	1	yes	characteristic
425	C₂²	#7622910	1	1	yes	characteristic
426	C₂²	#7622914	1	1	yes	characteristic
427	C₂	#72233180	1	1	yes	characteristic
428	C₂	#72233837	1	1	yes	characteristic
429	C₂	#72233839	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23984
commutator, Frattini, cosocle	C₂²×C₄⋊C₄	C₂⁵
LCS	G ▷ C₂²×C₄⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂²×C₄⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72233836	C₂	semidirect
2. #72233835	C₂	semidirect
3. #72233834	C₂	semidirect
4. #72233833	C₂	semidirect
5. #72233832	C₂	semidirect
6. #72233831	C₂	semidirect
7. #72233830	C₂	semidirect
8. #72233829	C₂	semidirect
9. #72233828	C₂	semidirect
10. #72233827	C₂	semidirect
11. #72233826	C₂	semidirect
12. #72233825	C₂	semidirect
13. #72233824	C₂	semidirect
14. #72233278	C₂	semidirect
15. #72233221	C₂	semidirect
16. #72233104	C₂	semidirect
17. #72233035	C₂	semidirect
18. #72232937	C₂	semidirect
19. #72232716	C₂	semidirect
24. #5522295	C₂²	semidirect
25. #5519537	C₂²	semidirect
26. #5482155	C₂²	semidirect
27. #5119558	C₂²	semidirect
28. #5118168	C₂²	semidirect
29. #4861302	C₂²	semidirect
31. #4123398	C₂²	semidirect
32. #2535814	C₂²	semidirect
33. #2177498	C₂²	semidirect
34. #878571	C₂²	semidirect
36. #587425	C₂²	semidirect
37. #556476	C₂²	semidirect
39. #482377	C₂²	semidirect
40. #481985	C₂²	semidirect
41. #346471	C₂²	semidirect
42. #346471	C₂²	semidirect
47. #346449	C₂²	semidirect
48. #346449	C₂²	semidirect
51. #186842	C₂²	semidirect
53. #186828	C₂²	semidirect
54. #186824	C₂²	semidirect
55. #186818	C₂²	semidirect
59. #144626	C₂²	semidirect
60. #144624	C₂²	semidirect
61. #144608	C₂²	semidirect
62. #144607	C₂²	semidirect
63. #142980	C₂²	semidirect
64. #142980	C₂²	semidirect
65. #142966	C₂²	semidirect
66. #142966	C₂²	semidirect
67. #140045	C₂²	semidirect
68. #140043	C₂²	semidirect
69. #140040	C₂²	semidirect
70. #140038	C₂²	semidirect
71. #140020	C₂²	semidirect
72. #140020	C₂²	semidirect
73. #140018	C₂²	semidirect
74. #140018	C₂²	semidirect
75. #139511	C₂²	semidirect
76. #139511	C₂²	semidirect
77. #139511	C₂²	semidirect
78. #139511	C₂²	semidirect
79. #139511	C₂²	semidirect
80. #139511	C₂²	semidirect
81. #139480	C₂²	semidirect
82. #139480	C₂²	semidirect
83. #135569	C₂²	semidirect
84. #135567	C₂²	semidirect
85. #135565	C₂²	semidirect
86. #135563	C₂²	semidirect
87. #128200	C₂²	semidirect
88. #128179	C₂²	semidirect
89. #127242	C₂²	semidirect
90. #127207	C₂²	semidirect
112. #17141	C₂³	semidirect
113. #17141	C₂³	semidirect
114. #17082	C₂³	semidirect
115. #17082	C₂³	semidirect
116. #16242	C₂³	semidirect
117. #16186	C₂³	semidirect
118. #16171	C₂³	semidirect
119. #15964	C₂³	semidirect
139. #14654	C₂³	semidirect
140. #14641	C₂³	semidirect
141. #14641	C₂³	semidirect
142. #14617	C₂³	semidirect
143. #14571	C₂³	semidirect
151. #14252	C₂³	semidirect
152. #14181	C₂³	semidirect
153. #14181	C₂³	semidirect
162. #11814	C₂³	semidirect
163. #11802	C₂³	semidirect
164. #11802	C₂³	semidirect
165. #11802	C₂³	semidirect
178. #7326	C₂³	semidirect
179. #7326	C₂³	semidirect
180. #7326	C₂³	semidirect
181. #7326	C₂³	semidirect
182. #7215	C₂³	semidirect
183. #7215	C₂³	semidirect
184. #7215	C₂³	semidirect
185. #7215	C₂³	semidirect
191. #3501	#41	semidirect
192. #3496	#41	semidirect
194. #3460	#41	semidirect

Maximal subgroups

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

subgroup	index
#72233836	2
#72233835	2
#72233834	2
#72233833	2
#72233832	2
#72233831	2
#72233830	2
#72233829	2
#72233828	2
#72233827	2
#72233826	2
#72233825	2
#72233824	2
#72233278	2
#72233221	2
#72233104	2
#72233035	2
#72232937	2
#72232716	2