Subgroups — #72266280

Order 4096.

At least 14868 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

The subgroup lattice has 358 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266279	C₂	1	2	yes	maximal, complemented
2	#72266278	C₂	1	2	yes	maximal, complemented
3	#72266275	C₂	1	8	yes	maximal, complemented
4	#72266274	C₂²	1	4	yes	complemented
5	#72266273	C₂²	1	4	yes	complemented
6	#72266267	C₂	1	1	yes	maximal, characteristic, complemented
7	#72266265	C₂²	1	2	yes	—
8	#72266264	C₂²	1	4	yes	complemented
9	#72266172	C₂	1	2	yes	maximal, complemented
10	#72266171	C₂²	1	4	yes	complemented
11	#72262702	C₂	1	1	yes	maximal, characteristic, complemented
12	#72262701	C₂²	1	1	yes	characteristic, complemented
13	#72262637	C₂²	1	1	yes	characteristic, complemented
14	#72238447	C₂	1	1	yes	maximal, characteristic, complemented
15	#72238446	C₂²	1	2	yes	complemented
16	#72235963	C₂	1	2	yes	maximal, complemented
17	#72235937	C₂²	1	2	yes	complemented
18	#72235930	C₂²	1	2	yes	—
19	#72235929	C₂	1	8	yes	maximal, complemented
20	#72235928	C₂²	1	4	yes	complemented
21	#72235926	C₂²	1	8	yes	complemented
22	#72235925	C₂²	1	4	yes	complemented
23	#72235924	C₂²	1	8	yes	complemented
24	#72235923	C₂²	1	8	yes	complemented
25	#72235922	C₂²	1	4	yes	complemented
26	#72235919	C₂²	1	8	yes	complemented
27	#72235868	C₂²	1	8	yes	complemented
28	#72235864	C₂²	1	4	yes	complemented
29	#72235820	C₂²	1	8	yes	complemented
30	#72235808	C₂²	1	4	yes	complemented
31	#72235740	C₂	1	2	yes	maximal, complemented
32	#72235732	C₂²	1	4	yes	complemented
33	#72235729	C₂²	1	8	yes	complemented
34	#72235725	C₂	1	2	yes	maximal, complemented
35	#72235718	C₂²	1	2	yes	complemented
36	#72235704	C₂²	1	4	yes	complemented
37	#72235690	C₂²	1	8	yes	complemented
38	#72235186	C₂²	1	4	yes	complemented
39	#72234675	C₂²	1	1	yes	characteristic, complemented
40	#72234668	C₂²	1	1	yes	characteristic, complemented
41	#72234636	C₂²	1	2	yes	—
42	#72234625	C₂²	1	1	yes	characteristic, complemented
43	#72232723	C₂²	1	4	yes	complemented
44	#72232723	C₂²	1	4	yes	complemented
45	#72232667	C₂²	1	4	yes	complemented
46	#72231950	C₂²	1	4	yes	complemented
47	#72231851	C₂²	1	4	yes	complemented
48	#72231809	C₂²	1	4	yes	complemented
49	C₂×#188035	C₂²	1	1	yes	characteristic, complemented
50	#72225665	C₂²	1	1	yes	characteristic
51	C₂×#62817	C₂³	1	1	yes	characteristic
52	C₂²×#3484	D₄	1	2	yes	complemented
53	C₂³×D₄²	C₂³	1	1	yes	characteristic
54	C₂×#46996	C₂³	1	2	yes	—
55	#7642350	C₂³	1	4	yes	—
56	C₂×#35347	C₂³	1	2	yes	—
57	C₂×#35346	D₄	1	2	yes	complemented
58	C₂×#34980	C₂³	1	1	yes	characteristic
59	C₂²×#2403	D₄	1	2	yes	—
60	#7626202	C₂³	1	1	yes	characteristic
61	#6451874	C₂³	1	4	yes	—
62	C₂×#21746	C₂³	1	1	yes	characteristic
63	C₂×#21746	C₂³	1	1	yes	characteristic
64	#6346594	C₂³	1	8	yes	—
65	#5123779	D₄	1	4	yes	complemented
66	#5119613	D₄	1	4	yes	complemented
67	#5024691	D₄	1	2	yes	complemented
68	#5020751	D₄	1	2	yes	complemented
69	#4893962	C₂³	1	2	yes	—
70	#4866548	C₂³	1	2	yes	—
71	#4466055	D₄	1	4	yes	complemented
72	#4430405	D₄	1	2	yes	complemented
73	#4335643	C₂³	1	4	yes	—
74	#2435299	D₄	1	4	yes	complemented
75	#2108865	D₄	1	4	yes	complemented
76	#2039146	D₄	1	4	yes	complemented
77	#648360	D₄	1	2	yes	complemented
78	#635987	C₂³	1	4	yes	—
79	#618316	C₂³	1	4	yes	—
80	#617710	D₄	1	2	yes	—
81	#617709	D₄	1	4	yes	complemented
82	#616961	C₂³	1	4	yes	—
83	#616960	D₄	1	2	yes	—
84	#612429	D₄	1	4	yes	complemented
85	#587363	C₂³	1	4	yes	—
86	#576160	C₂³	1	2	yes	—
87	#556752	C₂³	1	1	yes	characteristic
88	#517411	D₄	1	2	yes	—
89	#517411	D₄	1	2	yes	complemented
90	#515362	C₂³	1	2	yes	—
91	#515285	D₄	1	2	yes	complemented
92	#482549	C₂³	1	8	yes	—
93	#482549	C₂³	1	8	yes	—
94	#480250	C₂³	1	4	yes	—
95	#480250	C₂³	1	4	yes	—
96	#359705	C₂³	1	4	yes	—
97	#201462	C₂³	1	8	yes	—
98	C₂×#8549	C₂³	1	4	yes	—
99	C₂×#8547	C₂³	1	4	yes	—
100	C₂×#8542	C₂³	1	4	yes	—
101	#187945	C₂³	1	4	yes	—
102	#185255	C₂³	1	8	yes	—
103	#184796	C₂³	1	4	yes	—
104	#128157	C₂³	1	4	yes	—
105	#128157	C₂³	1	4	yes	—
106	#127215	C₂³	1	8	yes	—
107	#127215	C₂³	1	8	yes	—
108	#107115	C₂³	1	4	yes	—
109	#106326	C₂³	1	8	yes	—
110	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
111	C₂⁵×D₄	C₂×D₄	1	2	yes	—
112	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁵×D₄	C₂×D₄	1	2	yes	—
114	C₂×#3490	C₂⁴	1	2	yes	—
115	C₂²×#535	C₂×D₄	1	4	yes	—
116	C₂²×#534	C₂×D₄	1	2	yes	—
117	C₂³×#127	C₂×D₄	1	1	yes	characteristic
118	C₂²×#525	C₂×D₄	1	4	yes	complemented
119	C₂³×#121	C₂×D₄	1	2	yes	—
120	C₂³×#121	C₂⁴	1	2	yes	—
121	C₂³×#120	C₂×D₄	1	2	yes	—
122	C₂³×#120	C₂×D₄	1	1	yes	characteristic
123	C₂³×#120	C₂⁴	1	1	yes	characteristic
124	C₂²×#518	C₂×D₄	1	2	yes	complemented
125	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
126	C₂×#2760	C₂×D₄	1	4	yes	complemented
127	C₂×#2840	C₂×D₄	1	2	yes	complemented
128	C₂×#2849	C₂×D₄	1	2	yes	—
129	C₂×#2846	C₂×D₄	1	2	yes	—
130	C₂×#2406	C₂×D₄	1	4	yes	complemented
131	C₂×#2404	C₂×D₄	1	4	yes	—
132	C₂×#2404	C₂×D₄	1	4	yes	complemented
133	C₂×#2404	C₂⁴	1	4	yes	—
134	C₂×#2403	C₂×D₄	1	4	yes	—
135	C₂×#2403	C₂×D₄	1	4	yes	—
136	C₂×#2403	C₂×D₄	1	2	yes	complemented
137	C₂×#2613	C₂×D₄	1	2	yes	—
138	C₂×#2613	C₂×D₄	1	2	yes	—
139	#34176	C₂⁴	1	2	yes	—
140	C₂×#2308	C₂×D₄	1	2	yes	complemented
141	C₂×#2308	C₂×D₄	1	2	yes	complemented
142	C₂×#2308	C₂⁴	1	2	yes	—
143	C₂²×#379	C₂×D₄	1	2	yes	—
144	C₂²×#379	C₂×D₄	1	1	yes	characteristic
145	C₂×#1819	C₂⁴	1	2	yes	—
146	C₂×#1819	C₂⁴	1	2	yes	—
147	C₂×#1462	C₂⁴	1	8	yes	—
148	#17198	C₂×D₄	1	2	yes	complemented
149	#17105	C₂×D₄	1	4	yes	complemented
150	#17102	C₂×D₄	1	2	yes	complemented
151	#16247	C₂×D₄	1	2	yes	complemented
152	#16211	C₂×D₄	1	2	yes	complemented
153	#15930	C₂×D₄	1	4	yes	complemented
154	#15636	C₂×D₄	1	4	yes	complemented
155	#15561	C₂×D₄	1	4	yes	complemented
156	#15467	C₂×D₄	1	4	yes	complemented
157	#15267	C₂×D₄	1	4	yes	complemented
158	#15259	C₂×D₄	1	4	yes	—
159	#15259	C₂×D₄	1	4	yes	—
160	#15259	C₂×D₄	1	4	yes	—
161	#15259	C₂×D₄	1	4	yes	—
162	#15258	C₂×D₄	1	4	yes	—
163	#15258	C₂×D₄	1	4	yes	—
164	#15258	C₂×D₄	1	4	yes	—
165	#15258	C₂×D₄	1	4	yes	—
166	#14681	C₂×D₄	1	4	yes	complemented
167	#14649	C₂×D₄	1	4	yes	complemented
168	#14609	C₂×D₄	1	4	yes	complemented
169	#14533	C₂×D₄	1	4	yes	complemented
170	#14507	C₂×D₄	1	4	yes	complemented
171	#14341	C₂⁴	1	2	yes	—
172	#14335	C₂×D₄	1	4	yes	—
173	#14335	C₂×D₄	1	2	yes	—
174	#14255	C₂×D₄	1	4	yes	—
175	#14255	C₂×D₄	1	4	yes	—
176	#14207	C₂×D₄	1	4	yes	complemented
177	#13870	C₂×D₄	1	4	yes	complemented
178	#13868	C₂×D₄	1	4	yes	—
179	#13868	C₂×D₄	1	4	yes	complemented
180	#13868	C₂⁴	1	4	yes	—
181	#13867	C₂×D₄	1	4	yes	—
182	#13867	C₂×D₄	1	4	yes	—
183	#13827	C₂×D₄	1	2	yes	complemented
184	C₂²⋊C₄²	C₂×D₄	1	2	yes	complemented
185	C₂⁷	#120	1	1	yes	characteristic
186	C₂⁷	#120	1	2	yes	—
187	C₂⁷	#120	1	1	yes	characteristic
188	C₂⁷	C₂²×D₄	1	1	yes	characteristic
189	C₂³×#41	C₂²×D₄	1	4	yes	—
190	C₂⁴×D₄	#120	1	2	yes	—
191	C₂⁴×D₄	#120	1	2	yes	—
192	C₂⁴×D₄	#120	1	1	yes	characteristic
193	C₂⁴×D₄	#120	1	2	yes	—
194	C₂⁴×D₄	#120	1	2	yes	—
195	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
196	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
197	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
198	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
200	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
201	C₂⁵×C₄	#120	1	2	yes	—
202	C₂⁵×C₄	#120	1	1	yes	characteristic
203	C₂⁵×C₄	C₂²×D₄	1	2	yes	—
204	C₂×#543	H(5,𝔽₂)	1	2	yes	complemented
205	C₂×#534	H(5,𝔽₂)	1	2	yes	complemented
206	C₂²×#127	#120	1	4	yes	—
207	C₂²×#127	#120	1	4	yes	—
208	C₂²×#124	#120	1	4	yes	—
209	C₂²×#124	#120	1	4	yes	—
210	C₂²×#123	#120	1	2	yes	—
211	C₂²×#123	#120	1	2	yes	—
212	C₂²×#120	#120	1	2	yes	—
213	C₂²×#120	#120	1	2	yes	—
214	C₂²×#120	C₂²×D₄	1	2	yes	—
215	C₂²×#120	C₂²×D₄	1	2	yes	—
216	C₂²×#120	C₂²×D₄	1	4	yes	—
217	C₂²×#117	C₂²×D₄	1	4	yes	—
218	C₂³×C₄⋊C₄	C₂²×D₄	1	2	yes	—
219	C₂³×C₂²⋊C₄	#120	1	2	yes	—
220	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	#120	1	2	yes	—
222	C₂³×C₂²⋊C₄	#120	1	2	yes	—
223	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
224	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
225	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
226	C₂³×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
227	C₂³×C₄²	#120	1	1	yes	characteristic
228	C₂×#393	#120	1	4	yes	—
229	C₂×#393	#120	1	4	yes	—
230	C₂×#393	C₂²×D₄	1	4	yes	—
231	C₂×#393	C₂²×D₄	1	4	yes	—
232	C₂×#392	#120	1	4	yes	—
233	C₂×#392	#120	1	4	yes	—
234	C₂×#392	C₂²×D₄	1	4	yes	—
235	C₂×#392	C₂²×D₄	1	4	yes	—
236	C₂×#381	C₂²×D₄	1	4	yes	—
237	C₂×#381	C₂²×D₄	1	4	yes	—
238	C₂×#381	C₂²×D₄	1	2	yes	—
239	C₂×#381	C₂²×D₄	1	2	yes	—
240	C₂×#379	#120	1	2	yes	—
241	C₂×#379	#120	1	4	yes	—
242	C₂×#379	#120	1	1	yes	characteristic
243	C₂×#379	#120	1	1	yes	characteristic
244	C₂×#379	C₂²×D₄	1	4	yes	—
245	C₂×#379	C₂²×D₄	1	2	yes	—
246	C₂×#379	C₂²×D₄	1	2	yes	—
247	#2273	H(5,𝔽₂)	1	4	yes	complemented
248	#1819	H(5,𝔽₂)	1	4	yes	complemented
249	#1440	C₂²×D₄	1	4	yes	—
250	#1440	C₂²×D₄	1	2	yes	—
251	#1440	C₂²×D₄	1	2	yes	—
252	#1438	#120	1	4	yes	—
253	#1438	#120	1	4	yes	—
254	#1438	#120	1	4	yes	—
255	#1438	#120	1	4	yes	—
256	#1438	#120	1	4	yes	—
257	#1438	#120	1	2	yes	—
258	#1438	#120	1	2	yes	—
259	#1437	#120	1	4	yes	—
260	#1437	#120	1	4	yes	—
261	#1437	#120	1	4	yes	—
262	#1437	#120	1	4	yes	—
263	#1437	C₂²×D₄	1	4	yes	—
264	#1437	C₂²×D₄	1	4	yes	—
265	#1437	C₂²×D₄	1	4	yes	—
266	#1437	C₂²×D₄	1	4	yes	—
267	C₂⁶	B(4,𝔽₂)	1	4	yes	—
268	C₂⁶	B(4,𝔽₂)	1	4	yes	—
269	C₂⁶	C₂×#120	1	1	yes	characteristic
270	C₂⁶	C₂×#120	1	2	yes	—
271	C₂⁶	C₂×#120	1	2	yes	—
272	C₂⁶	C₂×#120	1	1	yes	characteristic
273	C₂⁶	C₂×#120	1	1	yes	characteristic
274	C₂⁶	C₂×#120	1	2	yes	—
275	C₂⁶	C₂×#120	1	2	yes	—
276	C₂⁶	C₂×#120	1	2	yes	—
277	C₂⁶	C₂³×D₄	1	1	yes	characteristic
278	C₂³×Q₈	C₂×#120	1	4	yes	—
279	C₂³×D₄	C₂×#120	1	2	yes	—
280	C₂³×D₄	C₂×#120	1	2	yes	—
281	C₂³×D₄	C₂×#120	1	4	yes	—
282	C₂³×D₄	C₂×#120	1	4	yes	—
283	C₂³×D₄	C₂×#120	1	4	yes	—
284	C₂⁴×C₄	C₂×#120	1	2	yes	—
285	C₂⁴×C₄	C₂×#120	1	2	yes	—
286	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
287	C₂⁴×C₄	C₂×#120	1	2	yes	—
288	C₂⁴×C₄	C₂³×D₄	1	2	yes	—
289	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
290	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
291	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
292	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
293	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
294	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
295	C₂²×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
297	C₂²×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
300	C₂²×C₂²⋊C₄	#585	1	2	yes	—
301	C₂²×C₄²	C₂×#120	1	4	yes	—
302	C₂²×C₄²	C₂×#120	1	4	yes	—
303	C₂×#95	C₂×#120	1	4	yes	—
304	C₂×#95	C₂×#120	1	4	yes	—
305	C₂×#95	C₂×#120	1	4	yes	—
306	C₂×#95	C₂×#120	1	4	yes	—
307	C₂⁵	#2846	1	2	yes	—
308	C₂⁵	#2846	1	2	yes	—
309	C₂⁵	#2846	1	2	yes	—
310	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
311	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
312	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
313	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
314	C₂⁵	#3026	1	2	yes	—
315	C₂⁵	#3026	1	2	yes	—
316	C₂⁵	C₂²×#120	1	1	yes	characteristic
317	C₂⁵	C₂²×#120	1	1	yes	characteristic
318	C₂⁵	C₂²×#120	1	1	yes	characteristic
319	C₂⁵	#3484	1	1	yes	characteristic
320	C₂⁵	#3484	1	1	yes	characteristic
321	C₂⁵	#3484	1	1	yes	characteristic
322	C₂⁵	#3485	1	1	yes	characteristic
323	C₂³×C₄	#2846	1	2	yes	—
324	C₂³×C₄	C₂²×#120	1	4	yes	—
325	C₂³×C₄	#3484	1	4	yes	—
326	C₂³×C₄	#3496	1	4	yes	—
327	C₂×C₂²⋊C₄	#3484	1	4	yes	—
328	C₂×C₂²⋊C₄	#3488	1	4	yes	—
329	C₂×C₂²⋊C₄	#3496	1	4	yes	—
330	C₂×C₂²⋊C₄	#3498	1	4	yes	—
331	C₂⁴	#32898	1	2	yes	—
332	C₂⁴	#32898	1	2	yes	—
333	C₂⁴	#32898	1	2	yes	—
334	C₂⁴	#32898	1	2	yes	—
335	C₂⁴	#35346	1	1	yes	characteristic
336	C₂⁴	#35346	1	1	yes	characteristic
337	C₂⁴	#35347	1	1	yes	characteristic
338	C₂⁴	#35347	1	1	yes	characteristic
339	C₂⁴	#35512	1	1	yes	characteristic
340	C₂⁴	#35527	1	1	yes	characteristic
341	C₂⁴	C₂×#2846	1	1	yes	characteristic
342	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
343	C₂⁴	C₂×#3026	1	2	yes	—
344	C₂²×C₄	#35680	1	8	yes	—
345	C₂³	#511790	1	4	yes	—
346	C₂³	#4928938	1	1	yes	characteristic
347	C₂³	#6499867	1	1	yes	characteristic
348	C₂³	#6499870	1	1	yes	characteristic
349	C₂³	#6500010	1	2	yes	—
350	C₂³	C₂×#32898	1	2	yes	—
351	C₂²	C₂×#511790	1	2	yes	—
352	C₂²	#72234100	1	2	yes	—
353	C₂²	#72235130	1	2	yes	—
354	C₂²	#72240103	1	1	yes	characteristic
355	C₂	#72240123	1	2	yes	—
356	C₂	#72256412	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72240103
commutator, Frattini, cosocle	C₂³×C₂²⋊C₄	C₂⁵
LCS	G ▷ C₂³×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×D₄² ◁ G
LECS	G ▷ C₂³×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266279	C₂	semidirect
2. #72266278	C₂	semidirect
3. #72266275	C₂	semidirect
4. #72266274	C₂²	semidirect
5. #72266273	C₂²	semidirect
6. #72266267	C₂	semidirect
8. #72266264	C₂²	semidirect
9. #72266172	C₂	semidirect
10. #72266171	C₂²	semidirect
11. #72262702	C₂	semidirect
12. #72262701	C₂²	semidirect
13. #72262637	C₂²	semidirect
14. #72238447	C₂	semidirect
15. #72238446	C₂²	semidirect
16. #72235963	C₂	semidirect
17. #72235937	C₂²	semidirect
19. #72235929	C₂	semidirect
20. #72235928	C₂²	semidirect
21. #72235926	C₂²	semidirect
22. #72235925	C₂²	semidirect
23. #72235924	C₂²	semidirect
24. #72235923	C₂²	semidirect
25. #72235922	C₂²	semidirect
26. #72235919	C₂²	semidirect
27. #72235868	C₂²	semidirect
28. #72235864	C₂²	semidirect
29. #72235820	C₂²	semidirect
30. #72235808	C₂²	semidirect
31. #72235740	C₂	semidirect
32. #72235732	C₂²	semidirect
33. #72235729	C₂²	semidirect
34. #72235725	C₂	semidirect
35. #72235718	C₂²	semidirect
36. #72235704	C₂²	semidirect
37. #72235690	C₂²	semidirect
38. #72235186	C₂²	semidirect
39. #72234675	C₂²	semidirect
40. #72234668	C₂²	semidirect
42. #72234625	C₂²	semidirect
43. #72232723	C₂²	semidirect
44. #72232723	C₂²	semidirect
45. #72232667	C₂²	semidirect
46. #72231950	C₂²	semidirect
47. #72231851	C₂²	semidirect
48. #72231809	C₂²	semidirect
49. C₂×#188035	C₂²	semidirect
52. C₂²×#3484	D₄	semidirect
57. C₂×#35346	D₄	semidirect
65. #5123779	D₄	semidirect
66. #5119613	D₄	semidirect
67. #5024691	D₄	semidirect
68. #5020751	D₄	semidirect
71. #4466055	D₄	semidirect
72. #4430405	D₄	semidirect
74. #2435299	D₄	semidirect
75. #2108865	D₄	semidirect
76. #2039146	D₄	semidirect
77. #648360	D₄	semidirect
81. #617709	D₄	semidirect
84. #612429	D₄	semidirect
89. #517411	D₄	semidirect
91. #515285	D₄	semidirect
110. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
118. C₂²×#525	C₂×D₄	semidirect
124. C₂²×#518	C₂×D₄	semidirect
126. C₂×#2760	C₂×D₄	semidirect
127. C₂×#2840	C₂×D₄	semidirect
130. C₂×#2406	C₂×D₄	semidirect
132. C₂×#2404	C₂×D₄	semidirect
136. C₂×#2403	C₂×D₄	semidirect
140. C₂×#2308	C₂×D₄	semidirect
141. C₂×#2308	C₂×D₄	semidirect
148. #17198	C₂×D₄	semidirect
149. #17105	C₂×D₄	semidirect
150. #17102	C₂×D₄	semidirect
151. #16247	C₂×D₄	semidirect
152. #16211	C₂×D₄	semidirect
153. #15930	C₂×D₄	semidirect
154. #15636	C₂×D₄	semidirect
155. #15561	C₂×D₄	semidirect
156. #15467	C₂×D₄	semidirect
157. #15267	C₂×D₄	semidirect
166. #14681	C₂×D₄	semidirect
167. #14649	C₂×D₄	semidirect
168. #14609	C₂×D₄	semidirect
169. #14533	C₂×D₄	semidirect
170. #14507	C₂×D₄	semidirect
176. #14207	C₂×D₄	semidirect
177. #13870	C₂×D₄	semidirect
179. #13868	C₂×D₄	semidirect
183. #13827	C₂×D₄	semidirect
184. C₂²⋊C₄²	C₂×D₄	semidirect
204. C₂×#543	H(5,𝔽₂)	semidirect
205. C₂×#534	H(5,𝔽₂)	semidirect
247. #2273	H(5,𝔽₂)	semidirect
248. #1819	H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72266279	2
#72266278	2
#72266275	2
#72266267	2
#72266172	2
#72262702	2
#72238447	2
#72235963	2
#72235929	2
#72235740	2
#72235725	2