Subgroups — #72317153

Order 4096.

At least 19860 conjugacy classes of subgroups; only the 487 normal subgroups are shown.

The subgroup lattice has 322 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312360	C₂	1	2	yes	maximal, complemented
2	#72310327	C₂	1	2	yes	maximal, complemented
3	#72309548	C₂	1	2	yes	maximal, complemented
4	#72264815	C₂	1	2	yes	maximal, complemented
5	#72225666	C₂	1	1	yes	maximal, characteristic
6	#72225658	C₄	1	1	yes	characteristic, complemented
7	#72225656	C₄	1	2	yes	complemented
8	#72225655	C₄	1	1	yes	characteristic, complemented
9	#72225653	C₄	1	2	yes	complemented
10	#72225650	C₂²	1	2	yes	—
11	#72225629	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#115348	C₂²	1	2	yes	complemented
13	#72219397	C₂	1	1	yes	maximal, characteristic, complemented
14	#72219311	C₂²	1	1	yes	characteristic, complemented
15	#72219310	C₂²	1	1	yes	characteristic, complemented
16	#72219301	C₄	1	1	yes	characteristic, complemented
17	#72219301	C₂²	1	1	yes	characteristic
18	#72219256	C₂	1	2	yes	maximal, complemented
19	#72219251	C₂²	1	2	yes	complemented
20	#72219248	C₂²	1	2	yes	complemented
21	#72219243	C₂²	1	2	yes	complemented
22	#72219237	C₂²	1	2	yes	complemented
23	#72219227	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#8534	C₂²	1	2	yes	—
25	C₂×#7670203	C₂²	1	1	yes	characteristic
26	#72218393	C₂	1	2	yes	maximal, complemented
27	#72218381	C₂²	1	2	yes	complemented
28	#72218375	C₂²	1	1	yes	characteristic, complemented
29	#72218313	C₂²	1	2	yes	complemented
30	#72218306	C₂²	1	2	yes	—
31	#72218069	C₂²	1	2	yes	complemented
32	#72218057	C₂²	1	2	yes	complemented
33	#72216064	C₄	1	1	yes	characteristic, complemented
34	#72216064	C₂²	1	1	yes	characteristic
35	#72215858	C₂²	1	2	yes	—
36	#72215179	C₂²	1	2	yes	complemented
37	#10586066	C₂×C₄	1	1	yes	characteristic
38	C₂²×#3484	C₂×C₄	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	C₂×#60399	D₄	1	2	yes	—
43	C₂²×#2846	D₄	1	1	yes	characteristic
44	#7630939	C₂³	1	2	yes	—
45	C₂×#35390	D₄	1	1	yes	characteristic
46	C₂×#35348	C₂×C₄	1	1	yes	characteristic
47	C₂×#35348	D₄	1	1	yes	characteristic
48	C₂×#35346	C₂×C₄	1	1	yes	characteristic
49	C₂×#34981	D₄	1	1	yes	characteristic
50	C₂×#34981	D₄	1	1	yes	characteristic
51	C₂×#34980	D₄	1	1	yes	characteristic
52	C₂×#34980	C₂³	1	1	yes	characteristic
53	C₂×#34198	C₂×C₄	1	1	yes	characteristic
54	C₂×#34198	D₄	1	1	yes	characteristic
55	#6440460	C₂×C₄	1	2	yes	—
56	#6437621	C₂×C₄	1	2	yes	—
57	C₂×#23900	C₂×C₄	1	2	yes	—
58	C₂×#23900	C₂×C₄	1	2	yes	—
59	#6431795	D₄	1	2	yes	—
60	#6431795	D₄	1	2	yes	—
61	C₂×#21776	D₄	1	2	yes	—
62	C₂×#21776	D₄	1	2	yes	—
63	#6371558	D₄	1	2	yes	—
64	#6371504	C₂×C₄	1	2	yes	—
65	#6370693	C₂×C₄	1	1	yes	characteristic
66	#6370693	C₂×C₄	1	1	yes	characteristic
67	#6370693	C₂×C₄	1	1	yes	characteristic
68	C₂²×#1781	C₂³	1	2	yes	—
69	C₂²×#1438	C₂³	1	2	yes	—
70	#392231	C₂×C₄	1	2	yes	—
71	#392113	C₂³	1	2	yes	—
72	#392109	C₂³	1	2	yes	—
73	#392109	C₂³	1	2	yes	—
74	#382434	D₄	1	2	yes	—
75	#382434	D₄	1	2	yes	—
76	#359811	C₂×C₄	1	2	yes	—
77	#359501	C₂×C₄	1	2	yes	—
78	#359501	C₂×C₄	1	2	yes	—
79	#359442	C₂×C₄	1	2	yes	—
80	C₂⁸	C₂×D₄	1	1	yes	characteristic
81	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
82	C₂³×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
83	C₂⁵×D₄	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
85	#62842	C₂²⋊C₄	1	2	yes	complemented
86	C₂×#3484	C₂²×C₄	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	C₂×#3484	C₂×D₄	1	2	yes	—
93	C₂²×#534	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×#534	C₂²×C₄	1	1	yes	characteristic
95	C₂²×#534	C₂×D₄	1	1	yes	characteristic
96	C₂²×#534	C₂×D₄	1	1	yes	characteristic
97	C₂²×#534	C₂×D₄	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	C₂²×C₄	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	C₂³×#120	C₂×D₄	1	1	yes	characteristic
109	#62652	C₂²⋊C₄	1	1	yes	characteristic, complemented
110	C₂²×#518	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×#518	C₂²×C₄	1	1	yes	characteristic
112	C₂⁴×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
113	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
114	C₂×#2883	C₂²⋊C₄	1	2	yes	complemented
115	C₂×#2883	C₂²⋊C₄	1	2	yes	complemented
116	C₂×#2883	C₂²⋊C₄	1	2	yes	complemented
117	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
118	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
119	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
120	C₂×#2883	C₂²⋊C₄	1	2	yes	complemented
121	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic, complemented
122	#34171	C₂²×C₄	1	2	yes	—
123	#34171	C₂×D₄	1	2	yes	—
124	#34171	C₂×D₄	1	2	yes	—
125	C₂×#2315	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×#2315	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×#2308	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×#2308	C₂²×C₄	1	1	yes	characteristic
131	C₂×#2308	C₂×D₄	1	1	yes	characteristic
132	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×#379	C₂×D₄	1	1	yes	characteristic
135	C₂×#2273	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×#1828	C₂²⋊C₄	1	2	yes	complemented
137	C₂×#1828	C₂²⋊C₄	1	2	yes	complemented
138	C₂×#1828	C₂²⋊C₄	1	2	yes	complemented
139	C₂×#1828	C₂²⋊C₄	1	2	yes	complemented
140	#20585	C₂²⋊C₄	1	2	yes	complemented
141	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
142	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
143	C₂×#1781	C₂²×C₄	1	2	yes	—
144	C₂×#1781	C₂²×C₄	1	2	yes	—
145	C₂×#1781	C₂×D₄	1	2	yes	—
146	C₂×#1781	C₂×D₄	1	2	yes	—
147	C₂×#1781	C₂×D₄	1	2	yes	—
148	C₂×#1781	C₂×D₄	1	2	yes	—
149	#20354	C₂²⋊C₄	1	2	yes	complemented
150	#20354	C₂²⋊C₄	1	2	yes	complemented
151	C₂⁷	#99	1	1	yes	characteristic, complemented
152	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂⁷	C₂²×D₄	1	1	yes	characteristic
155	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂⁴×D₄	#99	1	1	yes	characteristic, complemented
162	C₂⁴×D₄	#99	1	1	yes	characteristic, complemented
163	C₂⁴×D₄	#99	1	2	yes	complemented
164	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
169	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
171	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
174	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
175	C₂⁵×C₄	#99	1	1	yes	characteristic, complemented
176	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×#534	#120	1	2	yes	—
178	C₂×#534	#120	1	2	yes	—
179	C₂×#534	#120	1	2	yes	—
180	C₂×#534	#120	1	2	yes	—
181	C₂²×#120	#120	1	2	yes	—
182	C₂²×#120	#120	1	2	yes	—
183	C₂²×#120	#120	1	2	yes	—
184	C₂²×#120	#120	1	2	yes	—
185	C₂×#518	#99	1	2	yes	complemented
186	C₂×#518	#99	1	2	yes	complemented
187	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂³×C₂²⋊C₄	#99	1	2	yes	complemented
193	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂²×#99	C₂×C₂²⋊C₄	1	2	yes	—
204	#2308	#99	1	2	yes	complemented
205	#2308	#99	1	2	yes	complemented
206	C₂⁶	C₂×#99	1	1	yes	characteristic
207	C₂⁶	C₂×#99	1	1	yes	characteristic
208	C₂⁶	C₂×#99	1	1	yes	characteristic
209	C₂⁶	C₂×#99	1	2	yes	—
210	C₂⁶	C₂×#99	1	1	yes	characteristic
211	C₂⁶	C₂×#99	1	1	yes	characteristic
212	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁶	#518	1	1	yes	characteristic
214	C₂⁶	C₂×#120	1	2	yes	—
215	C₂⁶	#534	1	1	yes	characteristic
216	C₂⁶	#534	1	1	yes	characteristic
217	C₂⁶	#534	1	2	yes	—
218	C₂⁶	#534	1	1	yes	characteristic
219	C₂⁶	#534	1	2	yes	—
220	C₂⁶	#535	1	2	yes	—
221	C₂³×D₄	#379	1	1	yes	characteristic
222	C₂³×D₄	#379	1	1	yes	characteristic
223	C₂³×D₄	#379	1	1	yes	characteristic
224	C₂³×D₄	#379	1	1	yes	characteristic
225	C₂³×D₄	C₂×#99	1	1	yes	characteristic
226	C₂³×D₄	C₂×#99	1	1	yes	characteristic
227	C₂³×D₄	C₂×#99	1	1	yes	characteristic
228	C₂³×D₄	C₂×#99	1	1	yes	characteristic
229	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×D₄	#518	1	1	yes	characteristic
232	C₂³×D₄	#518	1	1	yes	characteristic
233	C₂³×D₄	C₂×#120	1	2	yes	—
234	C₂³×D₄	#534	1	2	yes	—
235	C₂³×D₄	#534	1	2	yes	—
236	C₂³×D₄	#534	1	2	yes	—
237	C₂³×D₄	#535	1	2	yes	—
238	C₂³×D₄	#535	1	2	yes	—
239	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
240	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
241	C₂⁴×C₄	C₂×#99	1	2	yes	—
242	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
243	C₂⁴×C₄	#518	1	1	yes	characteristic
244	C₂⁴×C₄	#534	1	1	yes	characteristic
245	C₂⁴×C₄	#534	1	2	yes	—
246	C₂⁴×C₄	#535	1	2	yes	—
247	C₂×#120	B(4,𝔽₂)	1	4	yes	—
248	C₂×#120	#458	1	4	yes	—
249	C₂²×C₂²⋊C₄	#379	1	2	yes	—
250	C₂²×C₂²⋊C₄	#379	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
254	C₂²×C₂²⋊C₄	C₂×#99	1	2	yes	—
255	C₂⁵	#1781	1	1	yes	characteristic
256	C₂⁵	#1781	1	1	yes	characteristic
257	C₂⁵	#1781	1	1	yes	characteristic
258	C₂⁵	#1781	1	1	yes	characteristic
259	C₂⁵	C₂×#379	1	1	yes	characteristic
260	C₂⁵	#2308	1	1	yes	characteristic
261	C₂⁵	#2308	1	1	yes	characteristic
262	C₂⁵	#2308	1	1	yes	characteristic
263	C₂⁵	#2309	1	1	yes	characteristic
264	C₂⁵	#2613	1	2	yes	—
265	C₂⁵	#2613	1	2	yes	—
266	C₂⁵	#2613	1	2	yes	—
267	C₂⁵	C₂²×#99	1	1	yes	characteristic
268	C₂⁵	C₂²×#99	1	1	yes	characteristic
269	C₂⁵	C₂²×#99	1	1	yes	characteristic
270	C₂⁵	C₂²×#99	1	1	yes	characteristic
271	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
272	C₂⁵	C₂×#458	1	2	yes	—
273	C₂⁵	#3026	1	2	yes	—
274	C₂⁵	#3026	1	2	yes	—
275	C₂²×D₄	#1790	1	4	yes	—
276	C₂³×C₄	#1781	1	1	yes	characteristic
277	C₂³×C₄	#1781	1	1	yes	characteristic
278	C₂³×C₄	#1781	1	1	yes	characteristic
279	C₂³×C₄	#1781	1	1	yes	characteristic
280	C₂³×C₄	#2308	1	1	yes	characteristic
281	C₂³×C₄	#2309	1	1	yes	characteristic
282	C₂³×C₄	#2613	1	2	yes	—
283	C₂×C₂²⋊C₄	#1790	1	4	yes	—
284	C₂⁴	#8534	1	2	yes	—
285	C₂⁴	#14335	1	1	yes	characteristic
286	C₂⁴	C₂×#1781	1	1	yes	characteristic
287	C₂⁴	C₂×#1781	1	1	yes	characteristic
288	C₂⁴	C₂×#1790	1	2	yes	—
289	C₂⁴	#20609	1	2	yes	—
290	C₂⁴	#21746	1	1	yes	characteristic
291	C₂⁴	#21746	1	1	yes	characteristic
292	C₂⁴	#21746	1	1	yes	characteristic
293	C₂⁴	#21746	1	1	yes	characteristic
294	C₂⁴	#21776	1	4	yes	—
295	C₂⁴	#21776	1	2	yes	—
296	C₂⁴	#29634	1	2	yes	—
297	C₂⁴	#29634	1	2	yes	—
298	C₂⁴	#29635	1	2	yes	—
299	C₂⁴	#29635	1	2	yes	—
300	C₂²×C₄	#8534	1	2	yes	—
301	C₂²×C₄	#21776	1	2	yes	—
302	C₂³	C₂×#8534	1	1	yes	characteristic
303	C₂³	#187928	1	2	yes	—
304	C₂³	#187944	1	1	yes	characteristic
305	C₂³	#213828	1	2	yes	—
306	C₂³	#213829	1	2	yes	—
307	C₂³	#382387	1	2	yes	—
308	C₂³	#382422	1	1	yes	characteristic
309	C₂³	#382434	1	2	yes	—
310	C₂³	#382434	1	1	yes	characteristic
311	C₂³	#382434	1	1	yes	characteristic
312	C₂²	#72216376	1	2	yes	—
313	C₂²	#72219311	1	1	yes	characteristic
314	C₂²	#72233032	1	2	yes	—
315	C₂²	#72233032	1	2	yes	—
316	C₂²	#72236929	1	1	yes	characteristic
317	C₂²	#72251607	1	1	yes	characteristic
318	C₂²	#72258229	1	2	yes	—
319	C₂	#72258387	1	2	yes	—
320	C₂	#72258939	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72251607
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂⁵×D₄	C₂⁴
prime radical	#72225666	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. #72312360	C₂	semidirect
2. #72310327	C₂	semidirect
3. #72309548	C₂	semidirect
4. #72264815	C₂	semidirect
6. #72225658	C₄	semidirect
7. #72225656	C₄	semidirect
8. #72225655	C₄	semidirect
9. #72225653	C₄	semidirect
11. #72225629	C₂	semidirect
12. C₂×#115348	C₂²	semidirect
13. #72219397	C₂	semidirect
14. #72219311	C₂²	semidirect
15. #72219310	C₂²	semidirect
16. #72219301	C₄	semidirect
18. #72219256	C₂	semidirect
19. #72219251	C₂²	semidirect
20. #72219248	C₂²	semidirect
21. #72219243	C₂²	semidirect
22. #72219237	C₂²	semidirect
23. #72219227	C₂²	semidirect
26. #72218393	C₂	semidirect
27. #72218381	C₂²	semidirect
28. #72218375	C₂²	semidirect
29. #72218313	C₂²	semidirect
31. #72218069	C₂²	semidirect
32. #72218057	C₂²	semidirect
33. #72216064	C₄	semidirect
36. #72215179	C₂²	semidirect
81. C₂×H(7,𝔽₂)	C₂²⋊C₄	semidirect
85. #62842	C₂²⋊C₄	semidirect
109. #62652	C₂²⋊C₄	semidirect
114. C₂×#2883	C₂²⋊C₄	semidirect
115. C₂×#2883	C₂²⋊C₄	semidirect
116. C₂×#2883	C₂²⋊C₄	semidirect
117. C₂×#2883	C₂²⋊C₄	semidirect
118. C₂×#2883	C₂²⋊C₄	semidirect
119. C₂×#2883	C₂²⋊C₄	semidirect
120. C₂×#2883	C₂²⋊C₄	semidirect
121. C₂×#2883	C₂²⋊C₄	semidirect
136. C₂×#1828	C₂²⋊C₄	semidirect
137. C₂×#1828	C₂²⋊C₄	semidirect
138. C₂×#1828	C₂²⋊C₄	semidirect
139. C₂×#1828	C₂²⋊C₄	semidirect
140. #20585	C₂²⋊C₄	semidirect
141. #20585	C₂²⋊C₄	semidirect
142. #20585	C₂²⋊C₄	semidirect
149. #20354	C₂²⋊C₄	semidirect
150. #20354	C₂²⋊C₄	semidirect
151. C₂⁷	#99	semidirect
161. C₂⁴×D₄	#99	semidirect
162. C₂⁴×D₄	#99	semidirect
163. C₂⁴×D₄	#99	semidirect
175. C₂⁵×C₄	#99	semidirect
185. C₂×#518	#99	semidirect
186. C₂×#518	#99	semidirect
192. C₂³×C₂²⋊C₄	#99	semidirect
204. #2308	#99	semidirect
205. #2308	#99	semidirect

Maximal subgroups

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

subgroup	index
#72312360	2
#72310327	2
#72309548	2
#72264815	2
#72225666	2
#72225629	2
#72219397	2
#72219256	2
#72218393	2