Subgroups — #72317694

Order 2048.

At least 6486 conjugacy classes of subgroups; only the 766 normal subgroups are shown.

The subgroup lattice has 338 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317674	C₂	1	1	yes	maximal, characteristic, complemented
2	#72317659	C₂	1	2	yes	maximal, complemented
3	#72317645	C₂	1	1	yes	maximal, characteristic, complemented
4	#72306954	C₂	1	1	yes	maximal, characteristic, complemented
5	#72306730	C₂	1	2	yes	maximal, complemented
6	#72306621	C₂	1	4	yes	maximal, complemented
7	#72306557	C₂	1	1	yes	maximal, characteristic, complemented
8	#72306534	C₂	1	4	yes	maximal, complemented
9	#72281670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#512862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#152602	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#153189	C₂	1	2	yes	maximal, complemented
13	#72233522	C₂	1	2	yes	maximal, complemented
14	#72231244	C₂	1	4	yes	maximal, complemented
15	#72216600	C₂	1	4	yes	maximal, complemented
16	C₂×#63011	C₂²	1	1	yes	characteristic, complemented
17	C₂×#61110	C₂²	1	1	yes	characteristic, complemented
18	#10575552	C₂²	1	1	yes	characteristic
19	C₂×#33557	C₂²	1	2	yes	—
20	C₂²×#2196	C₂²	1	2	yes	—
21	C₂×#31282	C₂²	1	2	yes	complemented
22	#7487867	C₂²	1	4	yes	complemented
23	#7487865	C₂²	1	4	yes	complemented
24	#6437456	C₂²	1	2	yes	—
25	C₂×#23361	C₂²	1	1	yes	characteristic, complemented
26	#6349101	C₂²	1	2	yes	complemented
27	#6349099	C₂²	1	2	yes	complemented
28	#6348970	C₂²	1	2	yes	complemented
29	#6348967	C₂²	1	2	yes	complemented
30	#6348455	C₂²	1	1	yes	characteristic, complemented
31	#6348447	C₂²	1	1	yes	characteristic
32	C₂×#18529	C₂²	1	1	yes	characteristic, complemented
33	C₂×#18524	C₂²	1	1	yes	characteristic
34	#6344254	C₂²	1	1	yes	characteristic, complemented
35	#512863	C₂²	1	4	yes	complemented
36	#512862	C₂²	1	4	yes	complemented
37	#512862	C₂²	1	4	yes	complemented
38	#512862	C₂²	1	4	yes	complemented
39	C₂×#13595	C₂²	1	2	yes	complemented
40	C₂×#13584	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13584	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13561	C₂²	1	2	yes	complemented
43	C₂×#13561	C₂²	1	2	yes	complemented
44	#511787	C₂²	1	4	yes	complemented
45	#511785	C₂²	1	4	yes	complemented
46	#511774	C₂²	1	4	yes	complemented
47	#511771	C₂²	1	4	yes	complemented
48	#493629	C₂²	1	2	yes	complemented
49	C₂×#12759	C₂²	1	2	yes	complemented
50	#493430	C₂²	1	2	yes	complemented
51	#153190	C₂²	1	8	yes	complemented
52	#153189	C₂²	1	8	yes	complemented
53	#153189	C₂²	1	8	yes	complemented
54	#153189	C₂²	1	8	yes	complemented
55	#152679	C₂²	1	8	yes	complemented
56	#152678	C₂²	1	8	yes	complemented
57	#152603	C₂²	1	4	yes	complemented
58	#152602	C₂²	1	4	yes	complemented
59	#152602	C₂²	1	4	yes	complemented
60	#152602	C₂²	1	4	yes	complemented
61	#152104	C₂²	1	4	yes	complemented
62	#152103	C₂²	1	4	yes	complemented
63	C₂×#7493	C₂²	1	2	yes	complemented
64	C₂×#7493	C₂²	1	2	yes	complemented
65	#62842	D₄	1	2	yes	complemented
66	#62815	D₄	1	1	yes	characteristic, complemented
67	C₂×#3498	C₂³	1	1	yes	characteristic
68	C₂×#3549	C₂³	1	1	yes	characteristic, complemented
69	C₂×#3543	C₂³	1	1	yes	characteristic
70	C₂×#3543	C₂³	1	1	yes	characteristic, complemented
71	C₂×#3481	C₂³	1	1	yes	characteristic, complemented
72	C₂²×D₄²	C₂³	1	1	yes	characteristic
73	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
74	#61110	C₂³	1	4	yes	—
75	#60801	D₄	1	2	yes	complemented
76	#60801	C₂³	1	2	yes	—
77	#60798	D₄	1	2	yes	complemented
78	#60798	C₂³	1	2	yes	—
79	#60639	D₄	1	1	yes	characteristic, complemented
80	C₂×#3151	C₂³	1	1	yes	characteristic
81	#60618	D₄	1	1	yes	characteristic, complemented
82	C₂×#3138	C₂³	1	1	yes	characteristic
83	C₂×#3019	D₄	1	2	yes	complemented
84	C₂²×#453	C₂³	1	2	yes	—
85	#60123	D₄	1	1	yes	characteristic, complemented
86	C₂×#2198	C₂³	1	4	yes	—
87	C₂×#2196	C₂³	1	4	yes	—
88	C₂×#2196	C₂³	1	4	yes	—
89	C₂×#2196	C₂³	1	4	yes	—
90	C₂²×#353	C₂³	1	2	yes	—
91	C₂²×#353	C₂³	1	2	yes	—
92	#31282	C₂³	1	8	yes	—
93	#23913	D₄	1	4	yes	complemented
94	#23912	D₄	1	4	yes	complemented
95	#23908	C₂³	1	4	yes	—
96	#23906	C₂³	1	4	yes	—
97	#23361	C₂³	1	4	yes	—
98	#20953	D₄	1	2	yes	complemented
99	C₂×#1887	C₂³	1	2	yes	—
100	#20592	D₄	1	2	yes	complemented
101	#18712	D₄	1	4	yes	complemented
102	#18683	D₄	1	2	yes	complemented
103	#18682	D₄	1	2	yes	complemented
104	#18531	C₂³	1	2	yes	complemented
105	#18529	C₂³	1	2	yes	complemented
106	#18529	C₂³	1	2	yes	complemented
107	#18529	C₂³	1	2	yes	complemented
108	#18526	C₂³	1	2	yes	—
109	#18524	D₄	1	4	yes	complemented
110	#18524	C₂³	1	2	yes	—
111	#18524	C₂³	1	2	yes	—
112	#18524	C₂³	1	2	yes	—
113	C₂×#1629	D₄	1	2	yes	complemented
114	C₂×#1619	D₄	1	2	yes	complemented
115	#17754	C₂³	1	2	yes	complemented
116	#17741	C₂³	1	2	yes	complemented
117	C₂×#1555	C₂³	1	1	yes	characteristic
118	C₂×#1555	C₂³	1	1	yes	characteristic
119	#13595	C₂³	1	8	yes	complemented
120	#13584	C₂³	1	4	yes	—
121	#13584	C₂³	1	4	yes	—
122	#13561	C₂³	1	8	yes	—
123	#13561	C₂³	1	8	yes	—
124	#12760	C₂³	1	4	yes	complemented
125	#12759	C₂³	1	4	yes	complemented
126	#12759	C₂³	1	4	yes	complemented
127	#12759	C₂³	1	4	yes	complemented
128	#12695	C₂³	1	4	yes	complemented
129	#12693	C₂³	1	4	yes	complemented
130	#7493	C₂³	1	8	yes	complemented
131	#7493	C₂³	1	8	yes	complemented
132	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
133	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
134	#3543	C₂×D₄	1	2	yes	—
135	#3543	C₂×D₄	1	2	yes	—
136	#3485	C₂×D₄	1	4	yes	complemented
137	#3484	C₂×D₄	1	4	yes	complemented
138	C₂×#559	C₂⁴	1	1	yes	characteristic
139	C₂×D₄²	C₂×D₄	1	2	yes	—
140	C₂×D₄²	C₂×D₄	1	2	yes	—
141	C₂×D₄²	C₂⁴	1	1	yes	characteristic
142	C₂×D₄²	C₂⁴	1	1	yes	characteristic
143	C₂×D₄²	C₂⁴	1	1	yes	characteristic
144	C₂×#535	C₂×D₄	1	2	yes	—
145	C₂×#535	C₂×D₄	1	2	yes	—
146	C₂×#535	C₂×D₄	1	2	yes	—
147	#3444	C₂×D₄	1	2	yes	complemented
148	#3444	C₂×D₄	1	2	yes	complemented
149	C₂×#533	C₂×D₄	1	1	yes	characteristic
150	C₂×#532	C₂×D₄	1	1	yes	characteristic
151	C₂×#532	C₂×D₄	1	1	yes	characteristic
152	C₂×#532	C₂×D₄	1	1	yes	characteristic
153	C₂×#532	C₂⁴	1	1	yes	characteristic
154	C₂²×#127	C₂×D₄	1	1	yes	characteristic
155	C₂²×#127	C₂⁴	1	1	yes	characteristic
156	C₂²×#127	C₂⁴	1	1	yes	characteristic
157	C₂×#518	C₂×D₄	1	2	yes	—
158	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
159	#3152	C₂×D₄	1	2	yes	complemented
160	#3151	C₂×D₄	1	2	yes	—
161	#3151	C₂×D₄	1	2	yes	—
162	#3151	C₂×D₄	1	2	yes	—
163	#3151	C₂×D₄	1	2	yes	complemented
164	#3151	C₂⁴	1	2	yes	—
165	C₂×#493	C₂×D₄	1	1	yes	characteristic
166	C₂×#493	C₂×D₄	1	1	yes	characteristic
167	C₂×#492	C₂×D₄	1	1	yes	characteristic
168	C₂×#492	C₂×D₄	1	1	yes	characteristic
169	#3139	C₂×D₄	1	2	yes	complemented
170	#3138	C₂×D₄	1	2	yes	—
171	#3138	C₂×D₄	1	2	yes	complemented
172	#3138	C₂⁴	1	2	yes	—
173	C₂×#455	C₂×D₄	1	4	yes	complemented
174	C₂×#453	C₂×D₄	1	4	yes	—
175	C₂×#453	C₂×D₄	1	4	yes	complemented
176	C₂×#453	C₂⁴	1	4	yes	—
177	#2920	C₂×D₄	1	2	yes	complemented
178	#2920	C₂×D₄	1	2	yes	complemented
179	C₂²×#100	C₂×D₄	1	2	yes	—
180	C₂²×#100	C₂×D₄	1	2	yes	—
181	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
183	C₂×#353	C₂⁴	1	4	yes	—
184	C₂×#353	C₂⁴	1	4	yes	—
185	#1887	C₂×D₄	1	4	yes	—
186	#1887	C₂×D₄	1	4	yes	complemented
187	#1887	C₂⁴	1	4	yes	—
188	#1885	C₂×D₄	1	4	yes	complemented
189	#1785	C₂×D₄	1	4	yes	complemented
190	#1783	C₂×D₄	1	4	yes	complemented
191	#1630	C₂×D₄	1	4	yes	complemented
192	#1629	C₂×D₄	1	4	yes	complemented
193	#1629	C₂×D₄	1	4	yes	complemented
194	#1629	C₂×D₄	1	4	yes	complemented
195	#1620	C₂×D₄	1	4	yes	complemented
196	#1619	C₂×D₄	1	4	yes	complemented
197	#1619	C₂×D₄	1	4	yes	complemented
198	#1619	C₂×D₄	1	4	yes	complemented
199	#1555	C₂×D₄	1	2	yes	—
200	#1555	C₂×D₄	1	2	yes	—
201	#1555	C₂⁴	1	2	yes	—
202	#1555	C₂⁴	1	2	yes	—
203	C₂×#331	C₂×D₄	1	2	yes	—
204	C₂×#331	C₂×D₄	1	2	yes	—
205	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
206	C₂²×#41	#120	1	2	yes	—
207	C₂²×#41	#120	1	2	yes	—
208	C₂²×#41	#120	1	1	yes	characteristic
209	C₂²×#41	C₂²×D₄	1	2	yes	—
210	C₂³×D₄	#120	1	2	yes	—
211	C₂³×D₄	C₂²×D₄	1	2	yes	—
212	C₂³×D₄	C₂²×D₄	1	2	yes	—
213	#559	C₂²×D₄	1	2	yes	—
214	D₄²	C₂²×D₄	1	2	yes	—
215	D₄²	C₂²×D₄	1	2	yes	—
216	D₄²	C₂²×D₄	1	2	yes	—
217	#533	C₂²×D₄	1	2	yes	—
218	#532	#120	1	2	yes	complemented
219	#532	C₂²×D₄	1	2	yes	—
220	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic, complemented
221	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
222	C₂×#127	#120	1	2	yes	—
223	C₂×#127	#120	1	1	yes	characteristic, complemented
224	C₂×#127	C₂²×D₄	1	2	yes	—
225	C₂×#127	C₂²×D₄	1	1	yes	characteristic
226	C₂×#127	C₂²×D₄	1	1	yes	characteristic
227	C₂×#127	C₂²×D₄	1	1	yes	characteristic
228	C₂×#127	C₂²×D₄	1	1	yes	characteristic
229	C₂×#127	C₂²×D₄	1	2	yes	—
230	C₂×#127	C₂²×D₄	1	1	yes	characteristic
231	C₂×#127	C₂²×D₄	1	1	yes	characteristic
232	C₂×#127	H(5,𝔽₂)	1	2	yes	—
233	C₂×#127	H(5,𝔽₂)	1	2	yes	—
234	C₂×#127	C₂⁵	1	1	yes	characteristic
235	C₂×#124	#120	1	2	yes	—
236	C₂×#124	#120	1	2	yes	—
237	C₂×#124	C₂²×D₄	1	2	yes	—
238	#518	C₂²×D₄	1	4	yes	—
239	C₂×#117	#120	1	1	yes	characteristic
240	C₂×#117	#120	1	1	yes	characteristic
241	C₂×#117	#120	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
243	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
245	#493	#120	1	2	yes	complemented
246	#493	#120	1	2	yes	complemented
247	#493	C₂²×D₄	1	2	yes	—
248	#493	C₂²×D₄	1	2	yes	—
249	#492	#120	1	2	yes	complemented
250	#492	#120	1	2	yes	complemented
251	#492	C₂²×D₄	1	2	yes	—
252	#492	C₂²×D₄	1	2	yes	—
253	C₂×#100	C₂²×D₄	1	4	yes	—
254	C₂×#100	C₂²×D₄	1	4	yes	—
255	C₄×M₁₆	#120	1	2	yes	complemented
256	C₄×M₁₆	C₂²×D₄	1	2	yes	—
257	C₄×M₁₆	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₈	#120	1	1	yes	characteristic, complemented
259	C₂×C₄×C₈	#120	1	1	yes	characteristic, complemented
260	#331	C₂²×D₄	1	4	yes	—
261	#331	C₂²×D₄	1	4	yes	—
262	C₂²×Q₈	B(4,𝔽₂)	1	1	yes	characteristic
263	C₂²×Q₈	C₂×#120	1	2	yes	—
264	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
265	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
266	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
267	C₂²×D₄	C₂×#120	1	2	yes	—
268	C₂²×D₄	C₂×#120	1	2	yes	—
269	C₂²×D₄	D₄²	1	2	yes	—
270	C₂²×D₄	D₄²	1	2	yes	—
271	C₂²×D₄	D₄²	1	2	yes	—
272	C₂²×D₄	D₄²	1	2	yes	—
273	C₂²×D₄	C₂³×D₄	1	2	yes	—
274	C₂³×C₄	C₂×#120	1	1	yes	characteristic
275	C₂³×C₄	C₂×#120	1	1	yes	characteristic
276	C₂³×C₄	C₂×#120	1	1	yes	characteristic
277	C₄⋊Q₈	C₂×#120	1	2	yes	—
278	#127	C₂×#120	1	2	yes	—
279	#127	C₂×#120	1	1	yes	characteristic
280	#127	C₂×#120	1	1	yes	characteristic
281	#127	#534	1	2	yes	—
282	#127	D₄²	1	2	yes	—
283	#127	D₄²	1	2	yes	—
284	#127	D₄²	1	2	yes	—
285	#127	D₄²	1	2	yes	—
286	#127	C₂³×D₄	1	1	yes	characteristic
287	#127	C₂³×D₄	1	1	yes	characteristic
288	#127	C₂×H(5,𝔽₂)	1	2	yes	—
289	#117	B(4,𝔽₂)	1	2	yes	—
290	#117	B(4,𝔽₂)	1	2	yes	—
291	C₂×C₄²	C₂×#120	1	1	yes	characteristic
292	C₂×C₄²	C₂×#120	1	1	yes	characteristic
293	C₂×C₄²	C₂×#120	1	1	yes	characteristic
294	C₂×C₄²	C₂×#120	1	1	yes	characteristic
295	C₂×C₄²	C₂×#120	1	1	yes	characteristic
296	C₂×C₄²	#534	1	1	yes	characteristic
297	C₂×C₄²	#534	1	1	yes	characteristic
298	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
299	C₄×C₈	C₂×#120	1	2	yes	—
300	C₄×C₈	C₂×#120	1	2	yes	—
301	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
302	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
303	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
304	C₂×D₄	#2403	1	2	yes	—
305	C₂×D₄	#2403	1	2	yes	—
306	C₂×D₄	C₂×D₄²	1	2	yes	—
307	C₂×D₄	C₂×D₄²	1	2	yes	—
308	C₂²×C₄	#2403	1	1	yes	characteristic
309	C₂²×C₄	#2403	1	1	yes	characteristic
310	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
311	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
312	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
313	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
316	C₄²	#2403	1	1	yes	characteristic
317	C₄²	#2403	1	1	yes	characteristic
318	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
319	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
320	C₄²	C₂²×#120	1	1	yes	characteristic
321	C₄²	C₂×#534	1	1	yes	characteristic
322	C₂³	#23900	1	1	yes	characteristic
323	C₂³	#23900	1	1	yes	characteristic
324	C₂³	#33551	1	2	yes	—
325	C₂³	#33551	1	2	yes	—
326	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
327	C₂×C₄	#23900	1	1	yes	characteristic
328	C₂×C₄	#23900	1	1	yes	characteristic
329	C₂×C₄	C₂×#2403	1	1	yes	characteristic
330	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
331	C₂²	#499832	1	1	yes	characteristic
332	C₂²	#499832	1	1	yes	characteristic
333	C₂²	#499832	1	2	yes	—
334	C₂²	C₂×#23900	1	1	yes	characteristic
335	C₂²	C₂×#33551	1	2	yes	—
336	C₂	C₂×#499832	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#499832
commutator, Frattini, cosocle	C₂×#127	C₂⁵
LCS	G ▷ C₂×#127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂²×#41 ◁ C₂×#3498 ◁ G
LECS	G ▷ C₂×#127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72317674	C₂	semidirect
2. #72317659	C₂	semidirect
3. #72317645	C₂	semidirect
4. #72306954	C₂	semidirect
5. #72306730	C₂	semidirect
6. #72306621	C₂	semidirect
7. #72306557	C₂	semidirect
8. #72306534	C₂	semidirect
9. #72281670	C₂	semidirect
10. C₂×#512862	C₂	semidirect
11. C₂×#152602	C₂	semidirect
12. C₂×#153189	C₂	semidirect
13. #72233522	C₂	semidirect
14. #72231244	C₂	semidirect
15. #72216600	C₂	semidirect
16. C₂×#63011	C₂²	semidirect
17. C₂×#61110	C₂²	semidirect
21. C₂×#31282	C₂²	semidirect
22. #7487867	C₂²	semidirect
23. #7487865	C₂²	semidirect
25. C₂×#23361	C₂²	semidirect
26. #6349101	C₂²	semidirect
27. #6349099	C₂²	semidirect
28. #6348970	C₂²	semidirect
29. #6348967	C₂²	semidirect
30. #6348455	C₂²	semidirect
32. C₂×#18529	C₂²	semidirect
34. #6344254	C₂²	semidirect
35. #512863	C₂²	semidirect
36. #512862	C₂²	semidirect
37. #512862	C₂²	semidirect
38. #512862	C₂²	semidirect
39. C₂×#13595	C₂²	semidirect
40. C₂×#13584	C₂²	semidirect
41. C₂×#13584	C₂²	semidirect
42. C₂×#13561	C₂²	semidirect
43. C₂×#13561	C₂²	semidirect
44. #511787	C₂²	semidirect
45. #511785	C₂²	semidirect
46. #511774	C₂²	semidirect
47. #511771	C₂²	semidirect
48. #493629	C₂²	semidirect
49. C₂×#12759	C₂²	semidirect
50. #493430	C₂²	semidirect
51. #153190	C₂²	semidirect
52. #153189	C₂²	semidirect
53. #153189	C₂²	semidirect
54. #153189	C₂²	semidirect
55. #152679	C₂²	semidirect
56. #152678	C₂²	semidirect
57. #152603	C₂²	semidirect
58. #152602	C₂²	semidirect
59. #152602	C₂²	semidirect
60. #152602	C₂²	semidirect
61. #152104	C₂²	semidirect
62. #152103	C₂²	semidirect
63. C₂×#7493	C₂²	semidirect
64. C₂×#7493	C₂²	semidirect
65. #62842	D₄	semidirect
66. #62815	D₄	semidirect
68. C₂×#3549	C₂³	semidirect
70. C₂×#3543	C₂³	semidirect
71. C₂×#3481	C₂³	semidirect
73. C₂²×D₄²	C₂³	semidirect
75. #60801	D₄	semidirect
77. #60798	D₄	semidirect
79. #60639	D₄	semidirect
81. #60618	D₄	semidirect
83. C₂×#3019	D₄	semidirect
85. #60123	D₄	semidirect
93. #23913	D₄	semidirect
94. #23912	D₄	semidirect
98. #20953	D₄	semidirect
100. #20592	D₄	semidirect
101. #18712	D₄	semidirect
102. #18683	D₄	semidirect
103. #18682	D₄	semidirect
104. #18531	C₂³	semidirect
105. #18529	C₂³	semidirect
106. #18529	C₂³	semidirect
107. #18529	C₂³	semidirect
109. #18524	D₄	semidirect
113. C₂×#1629	D₄	semidirect
114. C₂×#1619	D₄	semidirect
115. #17754	C₂³	semidirect
116. #17741	C₂³	semidirect
119. #13595	C₂³	semidirect
124. #12760	C₂³	semidirect
125. #12759	C₂³	semidirect
126. #12759	C₂³	semidirect
127. #12759	C₂³	semidirect
128. #12695	C₂³	semidirect
129. #12693	C₂³	semidirect
130. #7493	C₂³	semidirect
131. #7493	C₂³	semidirect
136. #3485	C₂×D₄	semidirect
137. #3484	C₂×D₄	semidirect
147. #3444	C₂×D₄	semidirect
148. #3444	C₂×D₄	semidirect
159. #3152	C₂×D₄	semidirect
163. #3151	C₂×D₄	semidirect
169. #3139	C₂×D₄	semidirect
171. #3138	C₂×D₄	semidirect
173. C₂×#455	C₂×D₄	semidirect
175. C₂×#453	C₂×D₄	semidirect
177. #2920	C₂×D₄	semidirect
178. #2920	C₂×D₄	semidirect
186. #1887	C₂×D₄	semidirect
188. #1885	C₂×D₄	semidirect
189. #1785	C₂×D₄	semidirect
190. #1783	C₂×D₄	semidirect
191. #1630	C₂×D₄	semidirect
192. #1629	C₂×D₄	semidirect
193. #1629	C₂×D₄	semidirect
194. #1629	C₂×D₄	semidirect
195. #1620	C₂×D₄	semidirect
196. #1619	C₂×D₄	semidirect
197. #1619	C₂×D₄	semidirect
198. #1619	C₂×D₄	semidirect
218. #532	#120	semidirect
220. C₂×C₄⋊Q₈	#120	semidirect
223. C₂×#127	#120	semidirect
245. #493	#120	semidirect
246. #493	#120	semidirect
249. #492	#120	semidirect
250. #492	#120	semidirect
255. C₄×M₁₆	#120	semidirect
258. C₂×C₄×C₈	#120	semidirect
259. C₂×C₄×C₈	#120	semidirect

Maximal subgroups

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

subgroup	index
#72317674	2
#72317659	2
#72317645	2
#72306954	2
#72306730	2
#72306621	2
#72306557	2
#72306534	2
#72281670	2
C₂×#512862	2
C₂×#152602	2
C₂×#153189	2
#72233522	2
#72231244	2
#72216600	2