Subgroups — #72262432

Order 2048.

At least 6223 conjugacy classes of subgroups; only the 1256 normal subgroups are shown.

The subgroup lattice has 337 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262429	C₂	1	4	yes	maximal, complemented
2	#72256426	C₂	1	2	yes	maximal, complemented
3	#72255822	C₂	1	2	yes	maximal, complemented
4	#72241256	C₂	1	1	yes	maximal, characteristic, complemented
5	#72237453	C₂	1	1	yes	maximal, characteristic, complemented
6	#72236085	C₂	1	4	yes	maximal, complemented
7	#72234609	C₂	1	1	yes	maximal, characteristic, complemented
8	#72234596	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233891	C₂	1	4	yes	maximal, complemented
10	#72233581	C₂	1	1	yes	maximal, characteristic, complemented
11	#72225650	C₂	1	2	yes	maximal, complemented
12	#72225610	C₂	1	2	yes	maximal, complemented
13	#72218518	C₂	1	1	yes	maximal, characteristic, complemented
14	#72217511	C₂	1	1	yes	maximal, characteristic, complemented
15	#72210600	C₂	1	4	yes	maximal, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic
17	C₂⁴×#120	C₂²	1	1	yes	characteristic
18	#7642244	C₂²	1	2	yes	—
19	#7642244	C₂²	1	4	yes	—
20	C₂×#36714	C₂²	1	2	yes	complemented
21	#7630939	C₂²	1	4	yes	—
22	#7630939	C₂²	1	2	yes	—
23	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
24	#7626202	C₂²	1	1	yes	characteristic
25	#6470226	C₂²	1	4	yes	complemented
26	#6470225	C₂²	1	4	yes	complemented
27	#6440460	C₂²	1	2	yes	complemented
28	#6437621	C₂²	1	2	yes	complemented
29	#6432949	C₂²	1	4	yes	complemented
30	#617161	C₂²	1	1	yes	characteristic
31	#617161	C₂²	1	1	yes	characteristic, complemented
32	#616960	C₂²	1	1	yes	characteristic
33	#616960	C₂²	1	1	yes	characteristic, complemented
34	#612617	C₂²	1	2	yes	complemented
35	#612424	C₂²	1	2	yes	complemented
36	#555894	C₂²	1	2	yes	complemented
37	#517415	C₂²	1	1	yes	characteristic, complemented
38	#405156	C₂²	1	4	yes	complemented
39	#394058	C₂²	1	4	yes	complemented
40	#392109	C₂²	1	2	yes	complemented
41	#392109	C₂²	1	4	yes	complemented
42	#379733	C₂²	1	4	yes	complemented
43	#359811	C₂²	1	2	yes	complemented
44	#359442	C₂²	1	2	yes	complemented
45	#233542	C₂²	1	8	yes	complemented
46	#233541	C₂²	1	8	yes	complemented
47	#201690	C₂²	1	8	yes	complemented
48	#201668	C₂²	1	4	yes	complemented
49	#201664	C₂²	1	4	yes	complemented
50	C₂×#8541	C₂²	1	1	yes	characteristic
51	C₂×#8541	C₂²	1	1	yes	characteristic
52	C₂×#8541	C₂²	1	4	yes	complemented
53	C₂×#8541	C₂²	1	2	yes	complemented
54	#187944	C₂²	1	2	yes	complemented
55	#187944	C₂²	1	2	yes	complemented
56	#187928	C₂²	1	4	yes	complemented
57	#187928	C₂²	1	4	yes	complemented
58	#115690	C₂²	1	8	yes	complemented
59	#115204	C₂²	1	8	yes	complemented
60	#115204	C₂²	1	8	yes	complemented
61	#107114	C₂²	1	2	yes	complemented
62	#107114	C₂²	1	2	yes	complemented
63	#106766	C₂²	1	4	yes	complemented
64	#106766	C₂²	1	4	yes	complemented
65	C₂⁸	D₄	1	1	yes	characteristic, complemented
66	C₂⁵×D₄	C₂³	1	2	yes	—
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic
68	C₂×#3484	D₄	1	4	yes	complemented
69	C₂×#3484	C₂³	1	2	yes	—
70	C₂×#3484	C₂³	1	4	yes	—
71	C₂²×#534	C₂³	1	1	yes	characteristic
72	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
73	C₂³×#120	D₄	1	2	yes	complemented
74	C₂³×#120	D₄	1	1	yes	characteristic, complemented
75	C₂³×#120	D₄	1	1	yes	characteristic, complemented
76	C₂³×#120	C₂³	1	1	yes	characteristic
77	C₂³×#120	C₂³	1	1	yes	characteristic
78	C₂³×#120	C₂³	1	2	yes	—
79	C₂³×#120	C₂³	1	1	yes	characteristic, complemented
80	C₂⁴×C₂²⋊C₄	D₄	1	2	yes	complemented
81	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
82	#36714	D₄	1	16	yes	complemented
83	C₂×#2846	C₂³	1	4	yes	—
84	#35350	D₄	1	8	yes	complemented
85	#35346	D₄	1	8	yes	complemented
86	#34992	C₂³	1	4	yes	complemented
87	#34980	D₄	1	8	yes	complemented
88	#34980	C₂³	1	8	yes	—
89	#34980	C₂³	1	4	yes	—
90	#34980	C₂³	1	4	yes	complemented
91	C₂×#2405	C₂³	1	2	yes	—
92	C₂×#2405	C₂³	1	2	yes	complemented
93	C₂×#2403	C₂³	1	2	yes	—
94	C₂×#2403	C₂³	1	2	yes	complemented
95	#34171	D₄	1	4	yes	complemented
96	#34171	C₂³	1	2	yes	—
97	#34171	C₂³	1	4	yes	—
98	C₂×#2309	C₂³	1	2	yes	complemented
99	C₂×#2308	C₂³	1	1	yes	characteristic
100	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
101	C₂²×#379	C₂³	1	1	yes	characteristic, complemented
102	#21746	C₂³	1	8	yes	complemented
103	#21746	C₂³	1	8	yes	complemented
104	C₂×#1898	C₂³	1	4	yes	complemented
105	C₂×#1898	C₂³	1	4	yes	complemented
106	C₂×#1819	C₂³	1	4	yes	complemented
107	C₂×#1781	C₂³	1	2	yes	—
108	C₂×#1781	C₂³	1	4	yes	—
109	C₂×#1781	C₂³	1	4	yes	—
110	C₂×#1781	C₂³	1	2	yes	—
111	C₂×#1781	C₂³	1	4	yes	complemented
112	C₂×#1781	C₂³	1	4	yes	complemented
113	C₂×#1781	C₂³	1	8	yes	complemented
114	#15948	D₄	1	4	yes	complemented
115	#15948	D₄	1	8	yes	complemented
116	#15947	D₄	1	4	yes	complemented
117	#14679	C₂³	1	2	yes	complemented
118	#14679	C₂³	1	4	yes	complemented
119	#14335	C₂³	1	1	yes	characteristic
120	#14335	C₂³	1	1	yes	characteristic
121	#13867	C₂³	1	2	yes	—
122	#13867	C₂³	1	2	yes	—
123	#13867	C₂³	1	2	yes	complemented
124	#13867	C₂³	1	2	yes	complemented
125	#10735	C₂³	1	4	yes	complemented
126	#10735	C₂³	1	4	yes	complemented
127	#8101	C₂³	1	8	yes	complemented
128	#8101	C₂³	1	8	yes	complemented
129	C₂⁷	C₂×D₄	1	1	yes	characteristic
130	C₂⁷	C₂×D₄	1	2	yes	—
131	C₂⁷	C₂×D₄	1	1	yes	characteristic
132	C₂⁷	C₂×D₄	1	1	yes	characteristic
133	C₂⁷	C₂×D₄	1	2	yes	—
134	C₂⁷	C₂⁴	1	1	yes	characteristic
135	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
136	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
137	C₂⁴×D₄	C₂×D₄	1	4	yes	—
138	C₂⁴×D₄	C₂×D₄	1	4	yes	—
139	C₂⁴×D₄	C₂×D₄	1	2	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂⁴	1	2	yes	—
144	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
145	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
146	C₂⁴×D₄	C₂⁴	1	2	yes	—
147	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
148	C₂⁵×C₄	C₂×D₄	1	2	yes	—
149	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂×#534	C₂×D₄	1	4	yes	—
151	C₂×#534	C₂×D₄	1	8	yes	—
152	C₂×#534	C₂×D₄	1	8	yes	—
153	C₂²×#123	C₂×D₄	1	2	yes	complemented
154	C₂²×#123	C₂×D₄	1	4	yes	complemented
155	C₂²×#120	C₂×D₄	1	8	yes	—
156	C₂²×#120	C₂×D₄	1	4	yes	—
157	C₂²×#120	C₂×D₄	1	4	yes	—
158	C₂²×#120	C₂×D₄	1	8	yes	—
159	C₂²×#120	C₂×D₄	1	8	yes	—
160	C₂²×#120	C₂×D₄	1	2	yes	complemented
161	C₂²×#120	C₂×D₄	1	4	yes	complemented
162	C₂²×#120	C₂⁴	1	4	yes	—
163	C₂×#518	C₂×D₄	1	2	yes	—
164	C₂×#518	C₂×D₄	1	4	yes	—
165	C₂×#518	C₂×D₄	1	4	yes	—
166	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
167	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
169	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
171	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
172	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
173	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
174	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
175	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
176	#2405	C₂×D₄	1	16	yes	—
177	#2405	C₂×D₄	1	16	yes	—
178	#2403	C₂×D₄	1	16	yes	—
179	#2403	C₂×D₄	1	16	yes	—
180	#2309	C₂×D₄	1	8	yes	—
181	#2308	C₂×D₄	1	8	yes	—
182	#2308	C₂×D₄	1	4	yes	—
183	#2308	C₂×D₄	1	8	yes	—
184	C₂×#386	C₂×D₄	1	4	yes	complemented
185	C₂×#386	C₂×D₄	1	4	yes	complemented
186	C₂×#386	C₂×D₄	1	4	yes	complemented
187	C₂×#379	C₂×D₄	1	8	yes	—
188	C₂×#379	C₂⁴	1	4	yes	—
189	C₂×#379	C₂⁴	1	4	yes	—
190	C₂×#379	C₂⁴	1	4	yes	—
191	C₂×#379	C₂⁴	1	2	yes	—
192	C₂×#379	C₂⁴	1	2	yes	—
193	#1438	C₂×D₄	1	8	yes	complemented
194	#1438	C₂×D₄	1	8	yes	complemented
195	#1438	C₂×D₄	1	4	yes	complemented
196	#1438	C₂×D₄	1	4	yes	complemented
197	C₂⁶	#120	1	2	yes	—
198	C₂⁶	#120	1	4	yes	—
199	C₂⁶	#120	1	2	yes	—
200	C₂⁶	#120	1	4	yes	—
201	C₂⁶	#120	1	4	yes	—
202	C₂⁶	C₂²×D₄	1	1	yes	characteristic
203	C₂⁶	C₂²×D₄	1	4	yes	—
204	C₂⁶	C₂²×D₄	1	1	yes	characteristic
205	C₂⁶	C₂²×D₄	1	2	yes	—
206	C₂⁶	C₂²×D₄	1	1	yes	characteristic
207	C₂⁶	C₂²×D₄	1	2	yes	—
208	C₂⁶	C₂²×D₄	1	1	yes	characteristic
209	C₂⁶	C₂²×D₄	1	1	yes	characteristic, complemented
210	C₂⁶	C₂⁵	1	1	yes	characteristic
211	C₂³×D₄	#120	1	2	yes	—
212	C₂³×D₄	#120	1	4	yes	—
213	C₂³×D₄	#120	1	2	yes	—
214	C₂³×D₄	C₂²×D₄	1	2	yes	—
215	C₂³×D₄	C₂²×D₄	1	4	yes	—
216	C₂³×D₄	C₂²×D₄	1	8	yes	—
217	C₂³×D₄	C₂²×D₄	1	8	yes	—
218	C₂³×D₄	C₂²×D₄	1	4	yes	—
219	C₂³×D₄	C₂²×D₄	1	2	yes	—
220	C₂³×D₄	C₂²×D₄	1	4	yes	—
221	C₂³×D₄	C₂²×D₄	1	4	yes	—
222	C₂³×D₄	C₂²×D₄	1	4	yes	—
223	C₂³×D₄	C₂²×D₄	1	2	yes	—
224	C₂³×D₄	C₂²×D₄	1	2	yes	—
225	C₂³×D₄	C₂²×D₄	1	8	yes	—
226	C₂³×D₄	C₂²×D₄	1	4	yes	—
227	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
228	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
229	C₂⁴×C₄	#120	1	4	yes	—
230	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
231	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
232	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
234	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
235	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
236	C₂×#123	#120	1	16	yes	complemented
237	C₂×#120	#120	1	16	yes	complemented
238	C₂²×C₂²⋊C₄	#120	1	4	yes	—
239	C₂²×C₂²⋊C₄	#120	1	8	yes	—
240	C₂²×C₂²⋊C₄	#120	1	4	yes	—
241	C₂²×C₂²⋊C₄	#120	1	4	yes	—
242	C₂²×C₂²⋊C₄	#120	1	8	yes	—
243	C₂²×C₂²⋊C₄	#120	1	8	yes	—
244	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
245	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
246	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
247	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
248	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
249	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	complemented
250	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	complemented
251	#386	#120	1	32	yes	complemented
252	#379	C₂²×D₄	1	16	yes	—
253	C₂⁵	C₂×#120	1	2	yes	—
254	C₂⁵	C₂×#120	1	2	yes	—
255	C₂⁵	C₂×#120	1	2	yes	—
256	C₂⁵	C₂×#120	1	2	yes	—
257	C₂⁵	C₂×#120	1	1	yes	characteristic
258	C₂⁵	C₂×#120	1	4	yes	—
259	C₂⁵	C₂×#120	1	2	yes	—
260	C₂⁵	C₂×#120	1	1	yes	characteristic
261	C₂⁵	C₂×#120	1	4	yes	—
262	C₂⁵	C₂×#120	1	4	yes	—
263	C₂⁵	C₂×#120	1	4	yes	—
264	C₂⁵	C₂×#120	1	2	yes	—
265	C₂⁵	#534	1	4	yes	—
266	C₂⁵	#534	1	2	yes	—
267	C₂⁵	C₂³×D₄	1	1	yes	characteristic
268	C₂⁵	C₂³×D₄	1	2	yes	—
269	C₂⁵	C₂³×D₄	1	1	yes	characteristic
270	C₂⁵	C₂³×D₄	1	1	yes	characteristic
271	C₂⁵	C₂³×D₄	1	4	yes	—
272	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
273	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
274	C₂²×D₄	C₂×#120	1	16	yes	—
275	C₂²×D₄	D₄²	1	8	yes	—
276	C₂²×D₄	D₄²	1	8	yes	—
277	C₂²×D₄	D₄²	1	4	yes	—
278	C₂²×D₄	D₄²	1	4	yes	—
279	C₂²×D₄	D₄²	1	8	yes	—
280	C₂²×D₄	D₄²	1	8	yes	—
281	C₂²×D₄	D₄²	1	4	yes	—
282	C₂²×D₄	D₄²	1	4	yes	—
283	C₂³×C₄	C₂×#120	1	2	yes	—
284	C₂³×C₄	C₂×#120	1	2	yes	—
285	C₂³×C₄	C₂×#120	1	4	yes	—
286	C₂³×C₄	C₂×#120	1	4	yes	—
287	C₂³×C₄	C₂×#120	1	8	yes	—
288	C₂³×C₄	C₂×#120	1	4	yes	—
289	C₂³×C₄	C₂×#120	1	2	yes	—
290	C₂³×C₄	C₂×#120	1	4	yes	—
291	C₂³×C₄	C₂×#120	1	4	yes	—
292	C₂³×C₄	#534	1	2	yes	—
293	C₂³×C₄	#534	1	4	yes	—
294	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
295	C₂⁴	#2403	1	4	yes	—
296	C₂⁴	#2403	1	2	yes	—
297	C₂⁴	#2403	1	4	yes	—
298	C₂⁴	#2403	1	2	yes	—
299	C₂⁴	#2846	1	4	yes	—
300	C₂⁴	#3026	1	4	yes	—
301	C₂⁴	#3026	1	4	yes	—
302	C₂⁴	C₂²×#120	1	1	yes	characteristic
303	C₂⁴	C₂²×#120	1	2	yes	—
304	C₂⁴	C₂²×#120	1	4	yes	—
305	C₂⁴	C₂²×#120	1	1	yes	characteristic
306	C₂⁴	C₂×#534	1	2	yes	—
307	C₂⁴	C₂×#534	1	1	yes	characteristic
308	C₂⁴	C₂×D₄²	1	4	yes	—
309	C₂⁴	C₂×D₄²	1	4	yes	—
310	C₂⁴	C₂×D₄²	1	2	yes	—
311	C₂⁴	C₂×D₄²	1	2	yes	—
312	C₂⁴	#3484	1	4	yes	—
313	C₂⁴	#3484	1	8	yes	—
314	C₂²×C₄	#2403	1	8	yes	—
315	C₂²×C₄	#2403	1	4	yes	—
316	C₂²×C₄	#2846	1	4	yes	—
317	C₂³	#23895	1	8	yes	—
318	C₂³	#23903	1	4	yes	—
319	C₂³	C₂×#2403	1	1	yes	characteristic
320	C₂³	C₂×#2403	1	2	yes	—
321	C₂³	#34980	1	2	yes	—
322	C₂³	#34980	1	1	yes	characteristic
323	C₂³	D₄×#120	1	4	yes	—
324	C₂³	D₄×#120	1	4	yes	—
325	C₂³	C₂×#2846	1	1	yes	characteristic
326	C₂³	C₂×#3026	1	2	yes	—
327	C₂³	C₂×#3026	1	2	yes	—
328	C₂²	#612424	1	1	yes	characteristic
329	C₂²	C₂×#23903	1	1	yes	characteristic
330	C₂²	#6437621	1	1	yes	characteristic
331	C₂²	C₂×#23895	1	4	yes	—
332	C₂²	#6470237	1	2	yes	—
333	C₂²	#6628892	1	2	yes	—
334	C₂	#72213862	1	2	yes	—
335	C₂	#72240108	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262429	C₂	semidirect
2. #72256426	C₂	semidirect
3. #72255822	C₂	semidirect
4. #72241256	C₂	semidirect
5. #72237453	C₂	semidirect
6. #72236085	C₂	semidirect
7. #72234609	C₂	semidirect
8. #72234596	C₂	semidirect
9. #72233891	C₂	semidirect
10. #72233581	C₂	semidirect
11. #72225650	C₂	semidirect
12. #72225610	C₂	semidirect
13. #72218518	C₂	semidirect
14. #72217511	C₂	semidirect
15. #72210600	C₂	semidirect
20. C₂×#36714	C₂²	semidirect
23. C₂×#34980	C₂²	semidirect
25. #6470226	C₂²	semidirect
26. #6470225	C₂²	semidirect
27. #6440460	C₂²	semidirect
28. #6437621	C₂²	semidirect
29. #6432949	C₂²	semidirect
31. #617161	C₂²	semidirect
33. #616960	C₂²	semidirect
34. #612617	C₂²	semidirect
35. #612424	C₂²	semidirect
36. #555894	C₂²	semidirect
37. #517415	C₂²	semidirect
38. #405156	C₂²	semidirect
39. #394058	C₂²	semidirect
40. #392109	C₂²	semidirect
41. #392109	C₂²	semidirect
42. #379733	C₂²	semidirect
43. #359811	C₂²	semidirect
44. #359442	C₂²	semidirect
45. #233542	C₂²	semidirect
46. #233541	C₂²	semidirect
47. #201690	C₂²	semidirect
48. #201668	C₂²	semidirect
49. #201664	C₂²	semidirect
52. C₂×#8541	C₂²	semidirect
53. C₂×#8541	C₂²	semidirect
54. #187944	C₂²	semidirect
55. #187944	C₂²	semidirect
56. #187928	C₂²	semidirect
57. #187928	C₂²	semidirect
58. #115690	C₂²	semidirect
59. #115204	C₂²	semidirect
60. #115204	C₂²	semidirect
61. #107114	C₂²	semidirect
62. #107114	C₂²	semidirect
63. #106766	C₂²	semidirect
64. #106766	C₂²	semidirect
65. C₂⁸	D₄	semidirect
68. C₂×#3484	D₄	semidirect
72. C₂²×#534	C₂³	semidirect
73. C₂³×#120	D₄	semidirect
74. C₂³×#120	D₄	semidirect
75. C₂³×#120	D₄	semidirect
79. C₂³×#120	C₂³	semidirect
80. C₂⁴×C₂²⋊C₄	D₄	semidirect
81. C₂⁴×C₂²⋊C₄	D₄	semidirect
82. #36714	D₄	semidirect
84. #35350	D₄	semidirect
85. #35346	D₄	semidirect
86. #34992	C₂³	semidirect
87. #34980	D₄	semidirect
90. #34980	C₂³	semidirect
92. C₂×#2405	C₂³	semidirect
94. C₂×#2403	C₂³	semidirect
95. #34171	D₄	semidirect
98. C₂×#2309	C₂³	semidirect
100. C₂×#2308	C₂³	semidirect
101. C₂²×#379	C₂³	semidirect
102. #21746	C₂³	semidirect
103. #21746	C₂³	semidirect
104. C₂×#1898	C₂³	semidirect
105. C₂×#1898	C₂³	semidirect
106. C₂×#1819	C₂³	semidirect
111. C₂×#1781	C₂³	semidirect
112. C₂×#1781	C₂³	semidirect
113. C₂×#1781	C₂³	semidirect
114. #15948	D₄	semidirect
115. #15948	D₄	semidirect
116. #15947	D₄	semidirect
117. #14679	C₂³	semidirect
118. #14679	C₂³	semidirect
123. #13867	C₂³	semidirect
124. #13867	C₂³	semidirect
125. #10735	C₂³	semidirect
126. #10735	C₂³	semidirect
127. #8101	C₂³	semidirect
128. #8101	C₂³	semidirect
153. C₂²×#123	C₂×D₄	semidirect
154. C₂²×#123	C₂×D₄	semidirect
160. C₂²×#120	C₂×D₄	semidirect
161. C₂²×#120	C₂×D₄	semidirect
184. C₂×#386	C₂×D₄	semidirect
185. C₂×#386	C₂×D₄	semidirect
186. C₂×#386	C₂×D₄	semidirect
193. #1438	C₂×D₄	semidirect
194. #1438	C₂×D₄	semidirect
195. #1438	C₂×D₄	semidirect
196. #1438	C₂×D₄	semidirect
209. C₂⁶	C₂²×D₄	semidirect
234. C₂⁴×C₄	C₂²×D₄	semidirect
235. C₂⁴×C₄	C₂²×D₄	semidirect
236. C₂×#123	#120	semidirect
237. C₂×#120	#120	semidirect
247. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
248. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
249. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
250. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
251. #386	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262429	2
#72256426	2
#72255822	2
#72241256	2
#72237453	2
#72236085	2
#72234609	2
#72234596	2
#72233891	2
#72233581	2
#72225650	2
#72225610	2
#72218518	2
#72217511	2
#72210600	2