Subgroups — #72240248

Order 2048.

At least 6632 conjugacy classes of subgroups; only the 1232 normal subgroups are shown.

The subgroup lattice has 341 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240243	C₂	1	1	yes	maximal, characteristic, complemented
2	#72240239	C₂	1	1	yes	maximal, characteristic, complemented
3	#72240221	C₂	1	4	yes	maximal, complemented
4	#72240220	C₂	1	4	yes	maximal, complemented
5	#72240219	C₂	1	2	yes	maximal, complemented
6	#72240217	C₂	1	2	yes	maximal, complemented
7	#72240216	C₂	1	4	yes	maximal, complemented
8	#72233920	C₂	1	1	yes	maximal, characteristic, complemented
9	#72215564	C₂	1	4	yes	maximal, complemented
10	#72213883	C₂	1	4	yes	maximal, complemented
11	#72213843	C₂	1	2	yes	maximal, complemented
12	#72213768	C₂	1	2	yes	maximal, complemented
13	#10586169	C₂²	1	1	yes	characteristic, complemented
14	C₂²×#3537	C₂²	1	1	yes	characteristic
15	#10577998	C₂²	1	4	yes	complemented
16	#10577301	C₂²	1	4	yes	—
17	#10575880	C₂²	1	2	yes	—
18	#10575880	C₂²	1	2	yes	complemented
19	#10574294	C₂²	1	1	yes	characteristic, complemented
20	C₂×#52008	C₂²	1	1	yes	characteristic, complemented
21	C₂×#45355	C₂²	1	2	yes	complemented
22	#6453841	C₂²	1	4	yes	complemented
23	#6348967	C₂²	1	4	yes	complemented
24	#6346631	C₂²	1	4	yes	complemented
25	#6346626	C₂²	1	4	yes	complemented
26	#4453254	C₂²	1	2	yes	complemented
27	#4422091	C₂²	1	2	yes	complemented
28	#754560	C₂²	1	2	yes	complemented
29	#619101	C₂²	1	2	yes	—
30	#581593	C₂²	1	1	yes	characteristic, complemented
31	#574938	C₂²	1	2	yes	complemented
32	#235446	C₂²	1	8	yes	complemented
33	#235245	C₂²	1	8	yes	complemented
34	#233610	C₂²	1	8	yes	complemented
35	#201616	C₂²	1	4	yes	complemented
36	#201549	C₂²	1	4	yes	complemented
37	#200876	C₂²	1	4	yes	complemented
38	#199076	C₂²	1	8	yes	complemented
39	#196279	C₂²	1	4	yes	complemented
40	#188081	C₂²	1	2	yes	complemented
41	#187814	C₂²	1	2	yes	complemented
42	#186837	C₂²	1	4	yes	complemented
43	#185755	C₂²	1	4	yes	complemented
44	#185561	C₂²	1	4	yes	complemented
45	#185259	C₂²	1	4	yes	complemented
46	#185257	C₂²	1	4	yes	complemented
47	#184986	C₂²	1	2	yes	complemented
48	#114859	C₂²	1	4	yes	complemented
49	#113024	C₂²	1	8	yes	complemented
50	#112929	C₂²	1	8	yes	complemented
51	#112157	C₂²	1	4	yes	complemented
52	#108241	C₂²	1	4	yes	complemented
53	#106329	C₂²	1	4	yes	complemented
54	#106328	C₂²	1	4	yes	complemented
55	#62814	C₂³	1	2	yes	—
56	#62773	C₂³	1	4	yes	—
57	C₂²×#553	D₄	1	2	yes	—
58	C₂²×#553	C₂³	1	2	yes	—
59	C₂²×D₄²	D₄	1	2	yes	—
60	C₂²×D₄²	C₂³	1	2	yes	—
61	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
62	C₂²×#540	C₂³	1	1	yes	characteristic
63	C₂²×#540	C₂³	1	1	yes	characteristic
64	C₂²×#535	D₄	1	2	yes	—
65	C₂²×#525	C₂³	1	1	yes	characteristic
66	C₂³×#121	D₄	1	2	yes	—
67	#61582	D₄	1	16	yes	complemented
68	#61560	D₄	1	8	yes	complemented
69	#61559	D₄	1	8	yes	complemented
70	#60868	D₄	1	4	yes	complemented
71	#60861	C₂³	1	4	yes	—
72	#60808	D₄	1	4	yes	complemented
73	#60798	C₂³	1	4	yes	—
74	#60704	D₄	1	8	yes	complemented
75	#60558	C₂³	1	8	yes	—
76	#60558	C₂³	1	8	yes	—
77	#60230	C₂³	1	4	yes	—
78	#60124	C₂³	1	2	yes	—
79	C₂×#2535	C₂³	1	2	yes	—
80	C₂×#2535	C₂³	1	2	yes	complemented
81	C₂×#2598	C₂³	1	2	yes	—
82	C₂×#2633	C₂³	1	2	yes	complemented
83	C₂×#2397	C₂³	1	2	yes	complemented
84	C₂×#2380	C₂³	1	1	yes	characteristic, complemented
85	C₂×#2328	C₂³	1	2	yes	—
86	C₂×#2328	C₂³	1	2	yes	complemented
87	#21417	C₂³	1	8	yes	—
88	#20726	C₂³	1	4	yes	—
89	#17741	C₂³	1	4	yes	complemented
90	#17667	C₂³	1	4	yes	complemented
91	#17593	C₂³	1	8	yes	—
92	#17588	C₂³	1	8	yes	—
93	#17448	C₂³	1	8	yes	complemented
94	#17448	C₂³	1	8	yes	complemented
95	#17364	C₂³	1	4	yes	—
96	#17357	C₂³	1	4	yes	—
97	#15674	D₄	1	2	yes	—
98	#15670	D₄	1	2	yes	—
99	#15669	D₄	1	2	yes	—
100	#15453	D₄	1	2	yes	—
101	#15412	D₄	1	2	yes	—
102	#15310	D₄	1	2	yes	—
103	#15283	D₄	1	2	yes	—
104	#15258	D₄	1	2	yes	—
105	#14664	C₂³	1	1	yes	characteristic, complemented
106	#14345	C₂³	1	2	yes	—
107	#14345	C₂³	1	2	yes	complemented
108	#14170	C₂³	1	1	yes	characteristic, complemented
109	#13959	C₂³	1	2	yes	—
110	#13959	C₂³	1	2	yes	complemented
111	#13957	C₂³	1	2	yes	—
112	#7975	C₂³	1	8	yes	complemented
113	#7959	C₂³	1	8	yes	complemented
114	#7855	C₂³	1	8	yes	complemented
115	C₂³×#41	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	2	yes	—
117	C₂⁴×D₄	C₂×D₄	1	2	yes	—
118	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
119	#3506	C₂×D₄	1	8	yes	complemented
120	#3501	C₂×D₄	1	4	yes	complemented
121	#3496	C₂×D₄	1	4	yes	complemented
122	C₂×D₄²	C₂×D₄	1	8	yes	—
123	C₂×D₄²	C₂×D₄	1	8	yes	—
124	#3458	C₂×D₄	1	2	yes	complemented
125	#3455	C₂×D₄	1	4	yes	complemented
126	C₂×#540	C₂×D₄	1	4	yes	—
127	C₂×#540	C₂×D₄	1	4	yes	—
128	#3449	C₂×D₄	1	2	yes	complemented
129	#3444	C₂⁴	1	4	yes	—
130	C₂²×#127	C₂×D₄	1	1	yes	characteristic
131	C₂²×#127	C₂×D₄	1	2	yes	—
132	C₂²×#127	C₂⁴	1	1	yes	characteristic
133	C₂²×#125	C₂×D₄	1	1	yes	characteristic
134	C₂²×#125	C₂⁴	1	1	yes	characteristic
135	C₂²×#123	C₂×D₄	1	2	yes	—
136	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
137	C₂²×#121	C₂×D₄	1	2	yes	—
138	C₂²×#121	C₂×D₄	1	2	yes	—
139	C₂²×#121	C₂×D₄	1	2	yes	—
140	C₂²×#121	C₂×D₄	1	2	yes	—
141	C₂²×#121	C₂×D₄	1	2	yes	—
142	C₂²×#121	C₂×D₄	1	2	yes	—
143	C₂²×#121	C₂×D₄	1	2	yes	—
144	C₂²×#120	C₂×D₄	1	2	yes	—
145	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
146	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
147	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
148	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
149	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
150	C₂²×#117	C₂×D₄	1	2	yes	—
151	C₂²×#117	C₂⁴	1	1	yes	characteristic
152	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	#3208	C₂×D₄	1	16	yes	—
154	#3205	C₂×D₄	1	16	yes	—
155	#3166	C₂×D₄	1	8	yes	complemented
156	#3151	C₂×D₄	1	8	yes	—
157	#3142	C₂×D₄	1	8	yes	complemented
158	#3138	C₂×D₄	1	8	yes	—
159	#3101	C₂×D₄	1	16	yes	complemented
160	#3100	C₂×D₄	1	16	yes	complemented
161	#2975	C₂×D₄	1	8	yes	complemented
162	#2972	C₂×D₄	1	8	yes	complemented
163	#2921	C₂×D₄	1	4	yes	complemented
164	#2920	C₂⁴	1	8	yes	—
165	#2920	C₂⁴	1	4	yes	—
166	#2873	C₂×D₄	1	4	yes	complemented
167	C₂×#400	C₂×D₄	1	2	yes	—
168	C₂×#399	C₂×D₄	1	2	yes	—
169	C₂×#397	C₂×D₄	1	2	yes	—
170	C₂×#397	C₂×D₄	1	2	yes	—
171	C₂×#394	C₂×D₄	1	2	yes	—
172	C₂×#392	C₂×D₄	1	2	yes	—
173	C₂×#392	C₂×D₄	1	2	yes	—
174	C₂×#392	C₂×D₄	1	2	yes	—
175	C₂×#390	C₂×D₄	1	2	yes	—
176	C₂×#390	C₂×D₄	1	2	yes	—
177	C₂×#383	C₂⁴	1	2	yes	—
178	C₂×#382	C₂×D₄	1	2	yes	—
179	C₂×#382	C₂⁴	1	2	yes	—
180	C₂×#376	C₂⁴	1	2	yes	—
181	#1445	C₂×D₄	1	2	yes	—
182	#1445	C₂×D₄	1	2	yes	—
183	#1438	C₂×D₄	1	2	yes	—
184	#1438	C₂×D₄	1	2	yes	—
185	#1437	C₂×D₄	1	2	yes	—
186	#1437	C₂×D₄	1	2	yes	—
187	#1437	C₂×D₄	1	2	yes	—
188	#1437	C₂×D₄	1	2	yes	—
189	#1437	C₂×D₄	1	2	yes	—
190	#1437	C₂×D₄	1	2	yes	—
191	#1436	C₂×D₄	1	2	yes	—
192	#1436	C₂×D₄	1	2	yes	—
193	C₂⁶	#120	1	1	yes	characteristic
194	C₂³×Q₈	#120	1	1	yes	characteristic
195	C₂³×D₄	#120	1	2	yes	—
196	C₂³×D₄	#120	1	1	yes	characteristic
197	C₂³×D₄	#120	1	2	yes	—
198	C₂³×D₄	#120	1	4	yes	—
199	C₂³×D₄	#120	1	4	yes	—
200	C₂³×D₄	#120	1	8	yes	—
201	C₂³×D₄	C₂²×D₄	1	2	yes	—
202	C₂³×D₄	C₂²×D₄	1	2	yes	—
203	C₂³×D₄	C₂²×D₄	1	2	yes	—
204	C₂³×D₄	C₂²×D₄	1	2	yes	—
205	C₂⁴×C₄	#120	1	2	yes	—
206	C₂⁴×C₄	#120	1	1	yes	characteristic
207	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
208	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
209	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
210	#533	C₂²×D₄	1	4	yes	—
211	#533	C₂²×D₄	1	8	yes	—
212	#532	C₂²×D₄	1	8	yes	—
213	#532	C₂²×D₄	1	4	yes	—
214	C₂×#127	C₂²×D₄	1	8	yes	—
215	C₂×#127	C₂²×D₄	1	4	yes	—
216	C₂×#125	C₂²×D₄	1	4	yes	—
217	C₂×#121	#120	1	4	yes	—
218	C₂×#121	#120	1	4	yes	—
219	C₂×#121	#120	1	4	yes	—
220	C₂×#121	#120	1	4	yes	—
221	C₂×#121	#120	1	8	yes	—
222	C₂×C₄×D₄	#120	1	8	yes	—
223	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
224	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
225	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
226	C₂×C₄×D₄	H(5,𝔽₂)	1	4	yes	—
227	C₂×C₄×D₄	H(5,𝔽₂)	1	4	yes	—
228	C₂×#117	C₂²×D₄	1	2	yes	—
229	C₂×#117	C₂²×D₄	1	2	yes	—
230	C₂×#117	H(5,𝔽₂)	1	2	yes	—
231	C₂×#117	H(5,𝔽₂)	1	2	yes	—
232	C₂²×C₄⋊C₄	#120	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
236	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
237	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
238	C₂²×C₂²⋊C₄	#120	1	2	yes	—
239	C₂²×C₂²⋊C₄	#120	1	2	yes	—
240	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
243	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×D₄	1	2	yes	—
245	C₂²×C₄²	C₂²×D₄	1	2	yes	—
246	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
247	#493	#120	1	16	yes	complemented
248	#492	#120	1	16	yes	complemented
249	#486	#120	1	32	yes	complemented
250	#431	C₂²×D₄	1	16	yes	—
251	C₄×M₁₆	C₂²×D₄	1	8	yes	—
252	C₂×#95	C₂²×D₄	1	2	yes	—
253	C₂×#95	C₂²×D₄	1	2	yes	—
254	C₂×#95	C₂²×D₄	1	2	yes	—
255	C₂×#95	C₂²×D₄	1	2	yes	—
256	C₂⁵	C₂×#120	1	2	yes	—
257	C₂⁵	C₂×#120	1	2	yes	—
258	C₂⁵	C₂×#120	1	1	yes	characteristic
259	C₂²×D₄	C₂×#120	1	4	yes	—
260	C₂²×D₄	C₂×#120	1	4	yes	—
261	C₂²×D₄	C₂×#120	1	4	yes	—
262	C₂²×D₄	C₂×#120	1	4	yes	—
263	C₂²×D₄	D₄²	1	4	yes	—
264	C₂²×D₄	D₄²	1	4	yes	—
265	C₂³×C₄	C₂×#120	1	1	yes	characteristic
266	C₂³×C₄	C₂×#120	1	2	yes	—
267	C₂³×C₄	C₂×#120	1	2	yes	—
268	C₂³×C₄	C₂×#120	1	2	yes	—
269	C₂³×C₄	C₂×#120	1	1	yes	characteristic
270	C₂³×C₄	C₂×#120	1	1	yes	characteristic
271	C₂³×C₄	C₂×#120	1	2	yes	—
272	C₂³×C₄	C₂×#120	1	2	yes	—
273	C₂³×C₄	C₂×#120	1	4	yes	—
274	C₂³×C₄	#534	1	1	yes	characteristic
275	C₂³×C₄	#534	1	1	yes	characteristic
276	C₂³×C₄	#534	1	2	yes	—
277	C₂³×C₄	#534	1	2	yes	—
278	C₂³×C₄	#534	1	4	yes	—
279	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
280	C₂³×C₄	C₂³×D₄	1	2	yes	—
281	C₄⋊Q₈	C₂×#120	1	4	yes	—
282	C₄⋊Q₈	C₂×#120	1	8	yes	—
283	#127	C₂×#120	1	4	yes	—
284	#127	C₂×#120	1	16	yes	—
285	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
286	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
287	C₂×C₄⋊C₄	D₄²	1	4	yes	—
288	C₂×C₄⋊C₄	D₄²	1	4	yes	—
289	C₂×C₄⋊C₄	D₄²	1	4	yes	—
290	C₂×C₄⋊C₄	D₄²	1	4	yes	—
291	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
292	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
293	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
294	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
295	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
296	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
297	C₂×C₄²	C₂×#120	1	2	yes	—
298	C₂×C₄²	#534	1	2	yes	—
299	C₂×C₄²	C₂³×D₄	1	4	yes	—
300	C₂×C₄²	C₂³×D₄	1	2	yes	—
301	C₂×C₄²	C₂×H(5,𝔽₂)	1	4	yes	—
302	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
303	C₄×C₈	C₂×#120	1	16	yes	—
304	C₂⁴	#2403	1	4	yes	—
305	C₂⁴	#2403	1	2	yes	—
306	C₂⁴	#2403	1	1	yes	characteristic
307	C₂⁴	#2403	1	1	yes	characteristic
308	C₂⁴	#2403	1	2	yes	—
309	C₂⁴	C₂²×#120	1	1	yes	characteristic
310	C₂×D₄	#2846	1	8	yes	—
311	C₂²×C₄	#2403	1	1	yes	characteristic
312	C₂²×C₄	#2403	1	1	yes	characteristic
313	C₂²×C₄	#2403	1	4	yes	—
314	C₂²×C₄	#2403	1	2	yes	—
315	C₂²×C₄	#2403	1	2	yes	—
316	C₂²×C₄	#2403	1	4	yes	—
317	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
318	C₂²×C₄	C₂²×#120	1	2	yes	—
319	C₂²×C₄	C₂×#534	1	1	yes	characteristic
320	C₂²×C₄	C₂×#534	1	2	yes	—
321	C₂²×C₄	C₂×D₄²	1	4	yes	—
322	C₂²×C₄	C₂×D₄²	1	4	yes	—
323	C₂²×C₄	C₂×D₄²	1	4	yes	—
324	C₄²	C₂²×#120	1	4	yes	—
325	C₄²	#3484	1	8	yes	—
326	C₄²	#3484	1	4	yes	—
327	C₂³	#23882	1	4	yes	—
328	C₂³	C₂×#2403	1	1	yes	characteristic
329	C₂³	C₂×#2403	1	2	yes	—
330	C₂×C₄	#34980	1	1	yes	characteristic
331	C₂×C₄	#34980	1	2	yes	—
332	C₂×C₄	D₄×#120	1	8	yes	—
333	C₂×C₄	C₂×#2846	1	1	yes	characteristic
334	C₂²	#612424	1	1	yes	characteristic
335	C₂²	#6437464	1	2	yes	—
336	C₂²	C₂×#23882	1	2	yes	—
337	C₂²	#6437576	1	2	yes	—
338	C₂	#72214896	1	2	yes	—
339	C₂	#72235458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72240243	C₂	semidirect
2. #72240239	C₂	semidirect
3. #72240221	C₂	semidirect
4. #72240220	C₂	semidirect
5. #72240219	C₂	semidirect
6. #72240217	C₂	semidirect
7. #72240216	C₂	semidirect
8. #72233920	C₂	semidirect
9. #72215564	C₂	semidirect
10. #72213883	C₂	semidirect
11. #72213843	C₂	semidirect
12. #72213768	C₂	semidirect
13. #10586169	C₂²	semidirect
15. #10577998	C₂²	semidirect
18. #10575880	C₂²	semidirect
19. #10574294	C₂²	semidirect
20. C₂×#52008	C₂²	semidirect
21. C₂×#45355	C₂²	semidirect
22. #6453841	C₂²	semidirect
23. #6348967	C₂²	semidirect
24. #6346631	C₂²	semidirect
25. #6346626	C₂²	semidirect
26. #4453254	C₂²	semidirect
27. #4422091	C₂²	semidirect
28. #754560	C₂²	semidirect
30. #581593	C₂²	semidirect
31. #574938	C₂²	semidirect
32. #235446	C₂²	semidirect
33. #235245	C₂²	semidirect
34. #233610	C₂²	semidirect
35. #201616	C₂²	semidirect
36. #201549	C₂²	semidirect
37. #200876	C₂²	semidirect
38. #199076	C₂²	semidirect
39. #196279	C₂²	semidirect
40. #188081	C₂²	semidirect
41. #187814	C₂²	semidirect
42. #186837	C₂²	semidirect
43. #185755	C₂²	semidirect
44. #185561	C₂²	semidirect
45. #185259	C₂²	semidirect
46. #185257	C₂²	semidirect
47. #184986	C₂²	semidirect
48. #114859	C₂²	semidirect
49. #113024	C₂²	semidirect
50. #112929	C₂²	semidirect
51. #112157	C₂²	semidirect
52. #108241	C₂²	semidirect
53. #106329	C₂²	semidirect
54. #106328	C₂²	semidirect
61. C₂²×D₄²	C₂³	semidirect
67. #61582	D₄	semidirect
68. #61560	D₄	semidirect
69. #61559	D₄	semidirect
70. #60868	D₄	semidirect
72. #60808	D₄	semidirect
74. #60704	D₄	semidirect
80. C₂×#2535	C₂³	semidirect
82. C₂×#2633	C₂³	semidirect
83. C₂×#2397	C₂³	semidirect
84. C₂×#2380	C₂³	semidirect
86. C₂×#2328	C₂³	semidirect
89. #17741	C₂³	semidirect
90. #17667	C₂³	semidirect
93. #17448	C₂³	semidirect
94. #17448	C₂³	semidirect
105. #14664	C₂³	semidirect
107. #14345	C₂³	semidirect
108. #14170	C₂³	semidirect
110. #13959	C₂³	semidirect
112. #7975	C₂³	semidirect
113. #7959	C₂³	semidirect
114. #7855	C₂³	semidirect
119. #3506	C₂×D₄	semidirect
120. #3501	C₂×D₄	semidirect
121. #3496	C₂×D₄	semidirect
124. #3458	C₂×D₄	semidirect
125. #3455	C₂×D₄	semidirect
128. #3449	C₂×D₄	semidirect
155. #3166	C₂×D₄	semidirect
157. #3142	C₂×D₄	semidirect
159. #3101	C₂×D₄	semidirect
160. #3100	C₂×D₄	semidirect
161. #2975	C₂×D₄	semidirect
162. #2972	C₂×D₄	semidirect
163. #2921	C₂×D₄	semidirect
166. #2873	C₂×D₄	semidirect
247. #493	#120	semidirect
248. #492	#120	semidirect
249. #486	#120	semidirect

Maximal subgroups

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

subgroup	index
#72240243	2
#72240239	2
#72240221	2
#72240220	2
#72240219	2
#72240217	2
#72240216	2
#72233920	2
#72215564	2
#72213883	2
#72213843	2
#72213768	2