Subgroups — #72310458

Order 4096.

At least 19668 conjugacy classes of subgroups; only the 551 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	#72310377	C₂	1	2	yes	maximal, complemented
2	#72310295	C₂	1	2	yes	maximal, complemented
3	#72309519	C₂	1	2	yes	maximal, complemented
4	#72264784	C₂	1	2	yes	maximal, complemented
5	#72225738	C₂	1	1	yes	maximal, characteristic
6	#72225736	C₄	1	1	yes	characteristic, complemented
7	#72225735	C₄	1	1	yes	characteristic, complemented
8	#72225734	C₄	1	2	yes	complemented
9	#72225713	C₄	1	1	yes	characteristic, complemented
10	#72225713	C₂²	1	1	yes	characteristic
11	#72225654	C₄	1	2	yes	complemented
12	#72225629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#115348	C₂²	1	2	yes	—
14	#72224136	C₄	1	1	yes	characteristic, complemented
15	#72224136	C₂²	1	1	yes	characteristic
16	#72219309	C₂	1	1	yes	maximal, characteristic, complemented
17	#72219301	C₂²	1	1	yes	characteristic, complemented
18	#72219300	C₂²	1	2	yes	—
19	#72219299	C₂²	1	1	yes	characteristic, complemented
20	#72219256	C₂	1	2	yes	maximal, complemented
21	#72219251	C₂²	1	2	yes	complemented
22	#72219248	C₂²	1	2	yes	complemented
23	#72219243	C₂²	1	2	yes	complemented
24	#72219237	C₂²	1	2	yes	complemented
25	#72219227	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#8534	C₂²	1	2	yes	complemented
27	C₂×#7670203	C₂²	1	1	yes	characteristic
28	#72218393	C₂	1	2	yes	maximal, complemented
29	#72218381	C₂²	1	2	yes	complemented
30	#72218375	C₂²	1	1	yes	characteristic, complemented
31	#72218313	C₂²	1	2	yes	complemented
32	#72218069	C₂²	1	2	yes	complemented
33	#72218057	C₂²	1	2	yes	complemented
34	#72215858	C₂²	1	2	yes	—
35	#72215179	C₂²	1	2	yes	complemented
36	#72213862	C₂²	1	2	yes	—
37	#10586404	C₂×C₄	1	1	yes	characteristic, complemented
38	C₂²×#3484	D₄	1	1	yes	characteristic
39	C₂²×#3484	C₂³	1	1	yes	characteristic
40	C₂⁴×#120	D₄	1	1	yes	characteristic
41	C₂⁴×#120	C₂³	1	1	yes	characteristic
42	C₂²×#2846	D₄	1	1	yes	characteristic
43	#7630939	C₂³	1	2	yes	—
44	C₂×#35390	C₂×C₄	1	1	yes	characteristic
45	C₂×#35348	C₂×C₄	1	1	yes	characteristic
46	C₂×#35348	D₄	1	1	yes	characteristic
47	C₂×#35346	D₄	1	1	yes	characteristic
48	C₂×#34981	C₂×C₄	1	1	yes	characteristic
49	C₂×#34981	D₄	1	1	yes	characteristic
50	C₂×#34980	C₂×C₄	1	1	yes	characteristic
51	C₂×#34980	C₂³	1	1	yes	characteristic
52	C₂×#34198	D₄	1	1	yes	characteristic
53	C₂×#34198	D₄	1	1	yes	characteristic
54	C₂×#23895	D₄	1	2	yes	—
55	C₂×#23895	D₄	1	2	yes	—
56	C₂×#23895	D₄	1	2	yes	—
57	C₂×#23895	D₄	1	2	yes	—
58	#6437621	C₂×C₄	1	2	yes	—
59	#6437621	C₂×C₄	1	2	yes	—
60	C₂×#23900	C₂×C₄	1	2	yes	complemented
61	C₂×#23900	C₂×C₄	1	2	yes	complemented
62	#6374251	C₂×C₄	1	1	yes	characteristic, complemented
63	#6374210	C₂×C₄	1	2	yes	complemented
64	#6374128	C₂×C₄	1	1	yes	characteristic, complemented
65	#6374128	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂²×#1781	C₂³	1	2	yes	—
67	C₂²×#1438	C₂³	1	2	yes	—
68	#392113	C₂³	1	2	yes	—
69	#392109	C₂³	1	2	yes	—
70	#392109	C₂³	1	2	yes	—
71	#382707	C₂×C₄	1	2	yes	complemented
72	#359549	D₄	1	2	yes	—
73	#359549	D₄	1	2	yes	—
74	#359549	D₄	1	2	yes	—
75	#359549	D₄	1	2	yes	—
76	#359501	C₂×C₄	1	2	yes	complemented
77	#359501	C₂×C₄	1	2	yes	complemented
78	#359442	C₂×C₄	1	2	yes	—
79	#359442	C₂×C₄	1	2	yes	—
80	#147567	D₄	1	8	yes	complemented
81	C₂⁸	C₂×D₄	1	1	yes	characteristic
82	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
83	C₂⁵×D₄	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
85	C₂×#3484	C₂²×C₄	1	2	yes	—
86	C₂×#3484	C₂×D₄	1	2	yes	—
87	C₂×#3484	C₂×D₄	1	2	yes	—
88	C₂×#3484	C₂×D₄	1	2	yes	—
89	C₂×#3484	C₂×D₄	1	2	yes	—
90	C₂×#3484	C₂×D₄	1	2	yes	—
91	C₂×#3484	C₂×D₄	1	2	yes	—
92	C₂²×#534	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×#534	C₂²×C₄	1	1	yes	characteristic
94	C₂²×#534	C₂²×C₄	1	1	yes	characteristic
95	C₂²×#534	C₂²×C₄	1	1	yes	characteristic
96	C₂²×#534	C₂×D₄	1	1	yes	characteristic
97	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
98	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
99	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
100	C₂³×#120	C₂²⋊C₄	1	1	yes	characteristic
101	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
102	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
103	C₂³×#120	C₂×D₄	1	1	yes	characteristic
104	C₂³×#120	C₂×D₄	1	1	yes	characteristic
105	C₂³×#120	C₂×D₄	1	1	yes	characteristic
106	C₂³×#120	C₂×D₄	1	1	yes	characteristic
107	C₂³×#120	C₂×D₄	1	1	yes	characteristic
108	C₂²×#518	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×#518	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×#3026	C₂²⋊C₄	1	2	yes	complemented
113	C₂×#3026	C₂²⋊C₄	1	2	yes	complemented
114	C₂×#3026	C₂²⋊C₄	1	2	yes	complemented
115	C₂×#3026	C₂²⋊C₄	1	2	yes	complemented
116	#34980	C₂×D₄	1	4	yes	—
117	#34980	#41	1	4	yes	—
118	#34171	C₂²×C₄	1	2	yes	—
119	#34171	C₂×D₄	1	2	yes	—
120	#34171	C₂×D₄	1	2	yes	—
121	C₂×#2315	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×#2315	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×#2308	C₂²×C₄	1	1	yes	characteristic
127	C₂×#2308	C₂×D₄	1	1	yes	characteristic
128	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#379	C₂×D₄	1	1	yes	characteristic
131	C₂×#2273	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
133	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
134	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
135	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
136	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
137	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
138	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
139	C₂×#1913	C₂²⋊C₄	1	2	yes	complemented
140	#20960	C₂²⋊C₄	1	2	yes	complemented
141	#20960	C₂²⋊C₄	1	2	yes	complemented
142	#20960	C₂²⋊C₄	1	2	yes	complemented
143	#20960	C₂²⋊C₄	1	2	yes	complemented
144	C₂×#1783	C₂×D₄	1	4	yes	complemented
145	C₂×#1781	C₂²×C₄	1	2	yes	—
146	C₂×#1781	C₂²×C₄	1	2	yes	—
147	C₂×#1781	C₂×D₄	1	2	yes	—
148	C₂×#1781	C₂×D₄	1	2	yes	—
149	C₂×#1781	C₂×D₄	1	2	yes	—
150	C₂×#1781	C₂×D₄	1	2	yes	—
151	C₂×#1781	C₂×D₄	1	4	yes	complemented
152	C₂⁷	#99	1	1	yes	characteristic, complemented
153	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂⁷	C₂²×D₄	1	1	yes	characteristic
156	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
159	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
160	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
161	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
162	C₂⁴×D₄	#99	1	1	yes	characteristic, complemented
163	C₂⁴×D₄	#99	1	1	yes	characteristic, complemented
164	C₂⁴×D₄	#99	1	2	yes	complemented
165	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
171	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
172	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
173	C₂⁴×D₄	C₂×#41	1	2	yes	—
174	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂⁵×C₄	#99	1	1	yes	characteristic, complemented
177	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×#534	#99	1	2	yes	complemented
179	C₂×#534	#99	1	2	yes	complemented
180	C₂×#534	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×#534	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×#534	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×#534	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×#534	C₄×D₄	1	4	yes	—
185	C₂×#534	#120	1	2	yes	—
186	C₂×#534	#123	1	2	yes	—
187	C₂²×#120	#120	1	2	yes	—
188	C₂²×#120	#120	1	2	yes	—
189	C₂²×#120	#120	1	2	yes	—
190	C₂²×#120	#120	1	2	yes	—
191	C₂²×#120	#121	1	4	yes	—
192	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×#518	#120	1	2	yes	—
196	C₂×#518	#120	1	2	yes	—
197	C₂³×C₂²⋊C₄	#99	1	2	yes	complemented
198	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
209	#2308	#99	1	2	yes	complemented
210	#2308	#99	1	2	yes	complemented
211	#2308	C₄×D₄	1	4	yes	—
212	#2308	#120	1	2	yes	—
213	#2308	#123	1	2	yes	—
214	C₂×#379	#121	1	4	yes	—
215	C₂⁶	C₂×#99	1	1	yes	characteristic
216	C₂⁶	C₂×#99	1	1	yes	characteristic
217	C₂⁶	C₂×#99	1	1	yes	characteristic
218	C₂⁶	C₂×#99	1	2	yes	—
219	C₂⁶	C₂×#99	1	1	yes	characteristic
220	C₂⁶	C₂×#99	1	1	yes	characteristic
221	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
222	C₂⁶	#518	1	1	yes	characteristic
223	C₂⁶	C₂×#120	1	2	yes	—
224	C₂⁶	C₂×#121	1	2	yes	—
225	C₂⁶	#534	1	1	yes	characteristic
226	C₂⁶	#534	1	1	yes	characteristic
227	C₂⁶	#534	1	1	yes	characteristic
228	C₂⁶	D₄²	1	2	yes	—
229	C₂⁶	#546	1	2	yes	—
230	C₂³×D₄	#379	1	1	yes	characteristic
231	C₂³×D₄	#379	1	1	yes	characteristic
232	C₂³×D₄	#379	1	1	yes	characteristic
233	C₂³×D₄	#379	1	1	yes	characteristic
234	C₂³×D₄	#386	1	2	yes	—
235	C₂³×D₄	C₂×#99	1	2	yes	—
236	C₂³×D₄	C₂×#99	1	1	yes	characteristic
237	C₂³×D₄	C₂×#99	1	1	yes	characteristic
238	C₂³×D₄	C₂×#99	1	1	yes	characteristic
239	C₂³×D₄	C₂×#99	1	1	yes	characteristic
240	C₂³×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
241	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
242	C₂³×D₄	C₂×#120	1	1	yes	characteristic
243	C₂³×D₄	C₂×#120	1	1	yes	characteristic
244	C₂³×D₄	C₂×#120	1	1	yes	characteristic
245	C₂³×D₄	C₂×#123	1	1	yes	characteristic
246	C₂³×D₄	D₄²	1	2	yes	—
247	C₂³×D₄	D₄²	1	2	yes	—
248	C₂³×D₄	#546	1	2	yes	—
249	C₂³×D₄	#546	1	2	yes	—
250	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
251	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
252	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
253	C₂⁴×C₄	C₂×#99	1	2	yes	—
254	C₂⁴×C₄	#518	1	1	yes	characteristic
255	C₂⁴×C₄	#534	1	1	yes	characteristic
256	C₂⁴×C₄	D₄²	1	2	yes	—
257	C₂⁴×C₄	#546	1	2	yes	—
258	C₂×#120	B(4,𝔽₂)	1	4	yes	—
259	C₂×#120	#458	1	4	yes	—
260	C₂²×C₂²⋊C₄	#379	1	2	yes	—
261	C₂²×C₂²⋊C₄	#379	1	2	yes	—
262	C₂²×C₂²⋊C₄	#386	1	2	yes	—
263	C₂²×C₂²⋊C₄	#386	1	2	yes	—
264	C₂²×C₂²⋊C₄	#386	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
268	C₂⁵	#1781	1	1	yes	characteristic
269	C₂⁵	#1781	1	1	yes	characteristic
270	C₂⁵	#1781	1	1	yes	characteristic
271	C₂⁵	#1781	1	1	yes	characteristic
272	C₂⁵	#1898	1	2	yes	—
273	C₂⁵	C₂×#379	1	1	yes	characteristic
274	C₂⁵	C₂×#386	1	1	yes	characteristic
275	C₂⁵	#2308	1	1	yes	characteristic
276	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
277	C₂⁵	#2403	1	1	yes	characteristic
278	C₂⁵	#2405	1	1	yes	characteristic
279	C₂⁵	#2410	1	2	yes	—
280	C₂⁵	#2410	1	2	yes	—
281	C₂⁵	C₂²×#99	1	1	yes	characteristic
282	C₂⁵	C₂²×#99	1	1	yes	characteristic
283	C₂⁵	C₂²×#99	1	1	yes	characteristic
284	C₂⁵	C₂²×#99	1	1	yes	characteristic
285	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
286	C₂⁵	C₂×#458	1	2	yes	—
287	C₂⁵	#3026	1	2	yes	—
288	C₂⁵	#3026	1	2	yes	—
289	C₂²×D₄	#1790	1	4	yes	—
290	C₂³×C₄	#1781	1	1	yes	characteristic
291	C₂³×C₄	#1781	1	1	yes	characteristic
292	C₂³×C₄	#1781	1	1	yes	characteristic
293	C₂³×C₄	#1781	1	1	yes	characteristic
294	C₂³×C₄	#1898	1	2	yes	—
295	C₂³×C₄	#1898	1	4	yes	—
296	C₂³×C₄	D₄×C₂²⋊C₄	1	2	yes	—
297	C₂³×C₄	#2403	1	1	yes	characteristic
298	C₂³×C₄	#2405	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	#1790	1	4	yes	—
300	C₂⁴	#8534	1	2	yes	—
301	C₂⁴	#13867	1	1	yes	characteristic
302	C₂⁴	C₂×#1781	1	1	yes	characteristic
303	C₂⁴	C₂×#1781	1	1	yes	characteristic
304	C₂⁴	C₂×#1790	1	2	yes	—
305	C₂⁴	#20609	1	2	yes	—
306	C₂⁴	C₂×#1898	1	1	yes	characteristic
307	C₂⁴	C₂×#1898	1	1	yes	characteristic
308	C₂⁴	#21746	1	1	yes	characteristic
309	C₂⁴	#21746	1	1	yes	characteristic
310	C₂⁴	#21776	1	4	yes	—
311	C₂⁴	#23895	1	2	yes	—
312	C₂⁴	#24404	1	2	yes	—
313	C₂⁴	#24404	1	2	yes	—
314	C₂⁴	#24405	1	2	yes	—
315	C₂⁴	#24405	1	2	yes	—
316	C₂²×C₄	#8534	1	2	yes	—
317	C₂²×C₄	#23895	1	2	yes	—
318	C₂³	C₂×#8534	1	1	yes	characteristic
319	C₂³	#187928	1	2	yes	—
320	C₂³	#187944	1	1	yes	characteristic
321	C₂³	#213828	1	2	yes	—
322	C₂³	#213854	1	2	yes	—
323	C₂³	#359428	1	1	yes	characteristic
324	C₂³	#359531	1	2	yes	—
325	C₂³	#359549	1	1	yes	characteristic
326	C₂³	#359549	1	1	yes	characteristic
327	C₂³	#359591	1	2	yes	—
328	C₂²	#72216376	1	2	yes	—
329	C₂²	#72218180	1	1	yes	characteristic
330	C₂²	#72219460	1	1	yes	characteristic
331	C₂²	#72225673	1	1	yes	characteristic
332	C₂²	#72232821	1	2	yes	—
333	C₂²	#72232821	1	2	yes	—
334	C₂²	#72258229	1	2	yes	—
335	C₂	#72258350	1	2	yes	—
336	C₂	#72258946	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72219460
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72225738	C₂
LCS	G ▷ C₂⁴×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72310377	C₂	semidirect
2. #72310295	C₂	semidirect
3. #72309519	C₂	semidirect
4. #72264784	C₂	semidirect
6. #72225736	C₄	semidirect
7. #72225735	C₄	semidirect
8. #72225734	C₄	semidirect
9. #72225713	C₄	semidirect
11. #72225654	C₄	semidirect
12. #72225629	C₂	semidirect
14. #72224136	C₄	semidirect
16. #72219309	C₂	semidirect
17. #72219301	C₂²	semidirect
19. #72219299	C₂²	semidirect
20. #72219256	C₂	semidirect
21. #72219251	C₂²	semidirect
22. #72219248	C₂²	semidirect
23. #72219243	C₂²	semidirect
24. #72219237	C₂²	semidirect
25. #72219227	C₂²	semidirect
26. C₂²×#8534	C₂²	semidirect
28. #72218393	C₂	semidirect
29. #72218381	C₂²	semidirect
30. #72218375	C₂²	semidirect
31. #72218313	C₂²	semidirect
32. #72218069	C₂²	semidirect
33. #72218057	C₂²	semidirect
35. #72215179	C₂²	semidirect
37. #10586404	C₂×C₄	semidirect
60. C₂×#23900	C₂×C₄	semidirect
61. C₂×#23900	C₂×C₄	semidirect
62. #6374251	C₂×C₄	semidirect
63. #6374210	C₂×C₄	semidirect
64. #6374128	C₂×C₄	semidirect
65. #6374128	C₂×C₄	semidirect
71. #382707	C₂×C₄	semidirect
76. #359501	C₂×C₄	semidirect
77. #359501	C₂×C₄	semidirect
80. #147567	D₄	semidirect
112. C₂×#3026	C₂²⋊C₄	semidirect
113. C₂×#3026	C₂²⋊C₄	semidirect
114. C₂×#3026	C₂²⋊C₄	semidirect
115. C₂×#3026	C₂²⋊C₄	semidirect
132. C₂×#1913	C₂²⋊C₄	semidirect
133. C₂×#1913	C₂²⋊C₄	semidirect
134. C₂×#1913	C₂²⋊C₄	semidirect
135. C₂×#1913	C₂²⋊C₄	semidirect
136. C₂×#1913	C₂²⋊C₄	semidirect
137. C₂×#1913	C₂²⋊C₄	semidirect
138. C₂×#1913	C₂²⋊C₄	semidirect
139. C₂×#1913	C₂²⋊C₄	semidirect
140. #20960	C₂²⋊C₄	semidirect
141. #20960	C₂²⋊C₄	semidirect
142. #20960	C₂²⋊C₄	semidirect
143. #20960	C₂²⋊C₄	semidirect
144. C₂×#1783	C₂×D₄	semidirect
151. C₂×#1781	C₂×D₄	semidirect
152. C₂⁷	#99	semidirect
162. C₂⁴×D₄	#99	semidirect
163. C₂⁴×D₄	#99	semidirect
164. C₂⁴×D₄	#99	semidirect
176. C₂⁵×C₄	#99	semidirect
178. C₂×#534	#99	semidirect
179. C₂×#534	#99	semidirect
197. C₂³×C₂²⋊C₄	#99	semidirect
209. #2308	#99	semidirect
210. #2308	#99	semidirect

Maximal subgroups

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

subgroup	index
#72310377	2
#72310295	2
#72309519	2
#72264784	2
#72225738	2
#72225629	2
#72219309	2
#72219256	2
#72218393	2