Subgroups — #72257856

Order 2048.

At least 6542 conjugacy classes of subgroups; only the 422 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	#72257855	C₂	1	1	yes	maximal, characteristic, complemented
2	#72257853	C₂	1	1	yes	maximal, characteristic, complemented
3	#72257851	C₂	1	1	yes	maximal, characteristic, complemented
4	#72257847	C₂	1	1	yes	maximal, characteristic
5	#72257846	C₂	1	1	yes	maximal, characteristic, complemented
6	#72257816	C₂	1	1	yes	maximal, characteristic, complemented
7	#72257813	C₂	1	1	yes	maximal, characteristic, complemented
8	#72257810	C₂	1	1	yes	maximal, characteristic, complemented
9	#72257809	C₂	1	1	yes	maximal, characteristic, complemented
10	#72257805	C₂	1	1	yes	maximal, characteristic, complemented
11	#72257793	C₂	1	1	yes	maximal, characteristic, complemented
12	#72257788	C₂	1	1	yes	maximal, characteristic, complemented
13	#72240707	C₂	1	1	yes	maximal, characteristic, complemented
14	#72239975	C₂	1	1	yes	maximal, characteristic, complemented
15	#72239859	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#59814	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	#6458932	C₂²	1	1	yes	characteristic, complemented
19	C₂×#27585	C₂²	1	1	yes	characteristic
20	#6458238	C₂²	1	1	yes	characteristic, complemented
21	C₂×#20732	C₂²	1	1	yes	characteristic, complemented
22	#615223	C₂²	1	1	yes	characteristic
23	#614082	C₂²	1	1	yes	characteristic, complemented
24	#612797	C₂²	1	1	yes	characteristic
25	#607767	C₂²	1	1	yes	characteristic
26	#530711	C₂²	1	1	yes	characteristic
27	#517108	C₂²	1	1	yes	characteristic
28	#392266	C₂²	1	1	yes	characteristic, complemented
29	#362839	C₂²	1	1	yes	characteristic, complemented
30	#359772	C₂²	1	1	yes	characteristic
31	#359689	C₂²	1	1	yes	characteristic, complemented
32	#195868	C₂²	1	1	yes	characteristic, complemented
33	#195812	C₂²	1	1	yes	characteristic, complemented
34	#191064	C₂²	1	1	yes	characteristic, complemented
35	#190447	C₂²	1	1	yes	characteristic, complemented
36	#189852	C₂²	1	1	yes	characteristic, complemented
37	#188470	C₂²	1	1	yes	characteristic, complemented
38	#188292	C₂²	1	1	yes	characteristic, complemented
39	#184859	C₂²	1	1	yes	characteristic, complemented
40	#184859	C₂²	1	1	yes	characteristic, complemented
41	#161044	C₂²	1	1	yes	characteristic, complemented
42	#160976	C₂²	1	1	yes	characteristic
43	#160976	C₂²	1	1	yes	characteristic
44	#160613	C₂²	1	1	yes	characteristic, complemented
45	#108811	C₂²	1	1	yes	characteristic, complemented
46	#105536	C₂²	1	1	yes	characteristic, complemented
47	#105492	C₂²	1	1	yes	characteristic, complemented
48	#95838	C₂²	1	1	yes	characteristic, complemented
49	#95213	C₂²	1	1	yes	characteristic, complemented
50	#94960	C₂²	1	1	yes	characteristic, complemented
51	C₂⁵×D₄	D₄	1	1	yes	characteristic
52	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
53	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
54	C₂²×#431	C₂³	1	1	yes	characteristic
55	C₂×#2683	D₄	1	1	yes	characteristic
56	C₂×#2682	D₄	1	1	yes	characteristic
57	C₂×#2682	D₄	1	1	yes	characteristic
58	C₂×#2679	D₄	1	1	yes	characteristic
59	C₂×#2535	D₄	1	2	yes	—
60	C₂×#2539	D₄	1	1	yes	characteristic
61	C₂×#2397	D₄	1	2	yes	—
62	C₂×C₄×#121	C₂³	1	1	yes	characteristic
63	C₂×C₄×#121	C₂³	1	1	yes	characteristic
64	C₂²×#390	D₄	1	1	yes	characteristic
65	C₂²×#390	C₂³	1	1	yes	characteristic
66	C₂×#2285	C₂³	1	1	yes	characteristic
67	C₂²×#380	D₄	1	1	yes	characteristic
68	C₂²×C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×#2094	D₄	1	2	yes	complemented
70	C₂×#2071	D₄	1	2	yes	complemented
71	#20714	C₂³	1	1	yes	characteristic
72	#20714	C₂³	1	1	yes	characteristic
73	C₂×#1817	C₂³	1	1	yes	characteristic
74	#20626	C₂³	1	1	yes	characteristic
75	#20626	C₂³	1	1	yes	characteristic
76	#15019	D₄	1	1	yes	characteristic
77	#14926	D₄	1	1	yes	characteristic
78	#14820	D₄	1	1	yes	characteristic
79	#14716	D₄	1	1	yes	characteristic
80	#14685	C₂³	1	1	yes	characteristic
81	#14682	C₂³	1	1	yes	characteristic
82	#14278	D₄	1	2	yes	—
83	#14152	D₄	1	1	yes	characteristic
84	#13966	D₄	1	1	yes	characteristic
85	#13905	D₄	1	2	yes	—
86	#13903	D₄	1	1	yes	characteristic
87	#13847	D₄	1	2	yes	—
88	#13791	D₄	1	2	yes	—
89	#13753	C₂³	1	1	yes	characteristic
90	#10925	D₄	1	4	yes	complemented
91	#7572	D₄	1	4	yes	complemented
92	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
94	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
95	C₂²×#121	C₂×D₄	1	1	yes	characteristic
96	C₂²×#121	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
98	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
99	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
101	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
102	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
103	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
104	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
105	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
106	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
107	C₂²×C₄×C₈	C₂×D₄	1	2	yes	complemented
108	#2539	SD₁₆	1	4	yes	—
109	C₂×#390	C₂×D₄	1	1	yes	characteristic
110	C₂×#390	C₂×D₄	1	1	yes	characteristic
111	C₂×#390	C₂×D₄	1	2	yes	—
112	C₂×#390	C₂×D₄	1	1	yes	characteristic
113	C₂×#390	C₂×D₄	1	1	yes	characteristic
114	C₂×#390	C₂×D₄	1	1	yes	characteristic
115	C₂×#390	C₂×D₄	1	2	yes	—
116	C₂×#390	C₂×D₄	1	1	yes	characteristic
117	C₂×#390	C₂×D₄	1	2	yes	—
118	C₂×#390	#41	1	2	yes	—
119	C₂×#389	C₂×D₄	1	1	yes	characteristic
120	C₂×#389	C₂×D₄	1	1	yes	characteristic
121	C₂×#384	C₂×D₄	1	1	yes	characteristic, complemented
122	C₂×#384	C₂×D₄	1	1	yes	characteristic, complemented
123	C₂×#382	C₂×D₄	1	2	yes	—
124	C₂×#380	C₂×D₄	1	1	yes	characteristic
125	C₂×#380	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×#376	C₂×D₄	1	2	yes	—
131	C₂²×#95	C₂×D₄	1	1	yes	characteristic
132	C₂²×#95	C₂×D₄	1	1	yes	characteristic
133	#1797	C₂×D₄	1	2	yes	complemented
134	C₄×C₂²⋊C₈	C₂×D₄	1	2	yes	complemented
135	C₂×#336	C₂×D₄	1	2	yes	complemented
136	C₄⋊#95	C₂×D₄	1	2	yes	complemented
137	#1434	C₂×D₄	1	2	yes	—
138	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
139	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
140	C₄×#95	C₂×D₄	1	2	yes	—
141	C₂⁶	#120	1	1	yes	characteristic
142	C₂³×D₄	#120	1	1	yes	characteristic
143	C₂³×D₄	#120	1	2	yes	—
144	C₂³×D₄	#120	1	1	yes	characteristic
145	C₂³×D₄	#120	1	2	yes	—
146	C₂³×D₄	#120	1	1	yes	characteristic
147	C₂³×D₄	#120	1	1	yes	characteristic
148	C₂³×D₄	#121	1	2	yes	—
149	C₂⁴×C₄	#120	1	1	yes	characteristic
150	C₂⁴×C₄	#120	1	1	yes	characteristic
151	C₂⁴×C₄	#120	1	1	yes	characteristic
152	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
153	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
154	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
155	C₂×#121	C₂×SD₁₆	1	2	yes	—
156	C₂×#121	AGL(1,ℤ/8)	1	2	yes	—
157	C₂²×C₄⋊C₄	#120	1	2	yes	—
158	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
159	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
160	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
161	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
162	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
163	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	#120	1	2	yes	—
165	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
166	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
167	C₂²×C₄⋊C₄	#121	1	2	yes	—
168	C₂²×C₂²⋊C₄	C₂×SD₁₆	1	2	yes	—
169	C₂²×C₂²⋊C₄	AGL(1,ℤ/8)	1	2	yes	—
170	C₂²×C₄²	#120	1	2	yes	—
171	C₂²×C₄²	#120	1	2	yes	—
172	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
173	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
175	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
176	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
178	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
180	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
184	#390	#120	1	2	yes	—
185	#390	#120	1	2	yes	—
186	#390	#121	1	2	yes	—
187	#390	#121	1	2	yes	—
188	#390	#121	1	2	yes	—
189	#390	#121	1	2	yes	—
190	#390	#127	1	2	yes	—
191	#390	#127	1	2	yes	—
192	C₄×C₂²⋊C₄	C₂×SD₁₆	1	2	yes	—
193	C₄×C₂²⋊C₄	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×#95	#120	1	2	yes	—
195	C₂×#95	#120	1	2	yes	—
196	C₂⁵	#450	1	2	yes	—
197	C₂⁵	C₂×#120	1	1	yes	characteristic
198	C₂²×D₄	#392	1	2	yes	—
199	C₂²×D₄	#392	1	2	yes	—
200	C₂²×D₄	#450	1	2	yes	—
201	C₂²×D₄	#458	1	4	yes	—
202	C₂³×C₄	#450	1	2	yes	—
203	C₂³×C₄	C₂×#120	1	1	yes	characteristic
204	C₂³×C₄	C₂×#120	1	1	yes	characteristic
205	C₂³×C₄	C₂×#120	1	1	yes	characteristic
206	C₂³×C₄	C₂×#120	1	1	yes	characteristic
207	C₂³×C₄	C₂×#120	1	1	yes	characteristic
208	C₂³×C₄	C₂×#120	1	1	yes	characteristic
209	C₂³×C₄	C₂×#120	1	1	yes	characteristic
210	C₂³×C₄	C₂×#121	1	1	yes	characteristic
211	C₂³×C₄	#534	1	1	yes	characteristic
212	C₂³×C₄	#534	1	1	yes	characteristic
213	C₂³×C₄	D₄²	1	1	yes	characteristic
214	C₂³×C₄	D₄²	1	1	yes	characteristic
215	C₂³×C₄	D₄²	1	1	yes	characteristic
216	C₂³×C₄	D₄²	1	1	yes	characteristic
217	C₂³×C₄	D₄²	1	1	yes	characteristic
218	C₂³×C₄	D₄²	1	1	yes	characteristic
219	C₂³×C₄	#546	1	1	yes	characteristic
220	C₂³×C₄	#546	1	1	yes	characteristic
221	C₂³×C₄	C₂²×SD₁₆	1	1	yes	characteristic
222	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₂³×C₄	#576	1	1	yes	characteristic
226	C₂³×C₄	#577	1	1	yes	characteristic
227	C₂³×C₄	#577	1	1	yes	characteristic
228	C₂³×C₄	#577	1	1	yes	characteristic
229	C₂×C₄⋊C₄	#392	1	2	yes	—
230	C₂×C₄⋊C₄	#392	1	2	yes	—
231	C₂×C₄⋊C₄	#450	1	2	yes	—
232	C₂×C₄²	#450	1	4	yes	—
233	C₂×C₄²	C₂×#120	1	1	yes	characteristic
234	C₂×C₄²	C₂×#121	1	1	yes	characteristic
235	C₂×C₄²	C₂×#121	1	1	yes	characteristic
236	C₂×C₄²	C₂×#127	1	1	yes	characteristic
237	C₂×C₄²	#534	1	1	yes	characteristic
238	C₂×C₄²	#534	1	1	yes	characteristic
239	C₂×C₄²	#535	1	1	yes	characteristic
240	C₂×C₄²	#535	1	1	yes	characteristic
241	C₂×C₄²	D₄²	1	1	yes	characteristic
242	C₂×C₄²	D₄²	1	1	yes	characteristic
243	C₂×C₄²	D₄²	1	1	yes	characteristic
244	C₂×C₄²	D₄²	1	1	yes	characteristic
245	C₂×C₄²	D₄²	1	1	yes	characteristic
246	C₂×C₄²	D₄²	1	1	yes	characteristic
247	C₂×C₄²	#546	1	1	yes	characteristic
248	C₂×C₄²	#546	1	1	yes	characteristic
249	C₂⁴	#2403	1	1	yes	characteristic
250	C₂⁴	#2410	1	1	yes	characteristic
251	C₂⁴	#2846	1	1	yes	characteristic
252	C₂⁴	C₂×#450	1	1	yes	characteristic
253	C₂⁴	#3003	1	1	yes	characteristic
254	C₂⁴	#3009	1	1	yes	characteristic
255	C₂⁴	#3012	1	1	yes	characteristic
256	C₂×D₄	#2010	1	4	yes	—
257	C₂²×C₄	C₂×#392	1	1	yes	characteristic
258	C₂²×C₄	#2403	1	1	yes	characteristic
259	C₂²×C₄	#2403	1	1	yes	characteristic
260	C₂²×C₄	#2403	1	1	yes	characteristic
261	C₂²×C₄	#2408	1	1	yes	characteristic
262	C₂²×C₄	#2408	1	1	yes	characteristic
263	C₂²×C₄	#2410	1	1	yes	characteristic
264	C₂²×C₄	#2410	1	1	yes	characteristic
265	C₂²×C₄	#2410	1	1	yes	characteristic
266	C₂²×C₄	#2433	1	1	yes	characteristic
267	C₂²×C₄	#2433	1	1	yes	characteristic
268	C₂²×C₄	#2613	1	1	yes	characteristic
269	C₂²×C₄	C₂×#450	1	1	yes	characteristic
270	C₂²×C₄	C₂×#450	1	1	yes	characteristic
271	C₂²×C₄	#3003	1	1	yes	characteristic
272	C₂²×C₄	#3003	1	1	yes	characteristic
273	C₂²×C₄	#3009	1	1	yes	characteristic
274	C₂²×C₄	#3009	1	1	yes	characteristic
275	C₂²×C₄	#3012	1	1	yes	characteristic
276	C₂²×C₄	#3012	1	1	yes	characteristic
277	C₂²×C₄	C₂×#458	1	2	yes	—
278	C₂²×C₄	#3026	1	2	yes	—
279	C₂²×C₄	#3264	1	1	yes	characteristic
280	C₂²×C₄	#3264	1	1	yes	characteristic
281	C₂²×C₄	#3265	1	1	yes	characteristic
282	C₂²×C₄	#3265	1	1	yes	characteristic
283	C₂²×C₄	#3265	1	1	yes	characteristic
284	C₂²×C₄	#3265	1	1	yes	characteristic
285	C₂²×C₄	#3272	1	1	yes	characteristic
286	C₂²×C₄	#3272	1	1	yes	characteristic
287	C₂²×C₄	#3274	1	1	yes	characteristic
288	C₂²×C₄	D₄×SD₁₆	1	1	yes	characteristic
289	C₂²×C₄	D₄×SD₁₆	1	1	yes	characteristic
290	C₂²×C₄	D₄×SD₁₆	1	1	yes	characteristic
291	C₂²×C₄	#3295	1	1	yes	characteristic
292	C₂²×C₄	#3310	1	1	yes	characteristic
293	C₂²×C₄	#3310	1	1	yes	characteristic
294	C₂²×C₄	#3324	1	1	yes	characteristic
295	C₂³	#14715	1	1	yes	characteristic
296	C₂³	#23849	1	1	yes	characteristic
297	C₂³	#23860	1	1	yes	characteristic
298	C₂³	#23882	1	2	yes	—
299	C₂³	#23897	1	2	yes	—
300	C₂³	#24432	1	1	yes	characteristic
301	C₂³	#24448	1	1	yes	characteristic
302	C₂³	#32881	1	1	yes	characteristic
303	C₂³	#32886	1	1	yes	characteristic
304	C₂³	#32894	1	2	yes	—
305	C₂³	#32900	1	2	yes	—
306	C₂×C₄	C₂×#2010	1	2	yes	—
307	C₂×C₄	#23849	1	1	yes	characteristic
308	C₂×C₄	#23860	1	1	yes	characteristic
309	C₂×C₄	#23901	1	1	yes	characteristic
310	C₂×C₄	#23903	1	1	yes	characteristic
311	C₂×C₄	#24240	1	1	yes	characteristic
312	C₂×C₄	#24252	1	1	yes	characteristic
313	C₂×C₄	#24405	1	2	yes	—
314	C₂×C₄	#24432	1	1	yes	characteristic
315	C₂×C₄	#24448	1	1	yes	characteristic
316	C₂×C₄	#25753	1	1	yes	characteristic
317	C₂×C₄	#25763	1	1	yes	characteristic
318	C₂²	#245712	1	2	yes	—
319	C₂²	#245807	1	2	yes	—
320	C₂²	#346542	1	2	yes	—
321	C₂²	#346574	1	2	yes	—
322	C₂²	#393915	1	1	yes	characteristic
323	C₂²	#393975	1	1	yes	characteristic
324	C₂²	#393988	1	1	yes	characteristic
325	C₂²	#394068	1	1	yes	characteristic
326	C₂²	#394102	1	1	yes	characteristic
327	C₂²	#394108	1	1	yes	characteristic
328	C₂²	#394109	1	1	yes	characteristic
329	C₂	#72240389	1	1	yes	characteristic
330	C₂	#72240785	1	1	yes	characteristic
331	C₂	#72249943	1	1	yes	characteristic
332	C₂	#72250419	1	1	yes	characteristic
333	C₂	#72257700	1	1	yes	characteristic
334	C₂	#72257770	1	1	yes	characteristic
335	C₂	#72257777	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#14715
commutator, Frattini, cosocle	C₂³×C₄²	C₂⁴
prime radical	#72257847	C₂
LCS	G ▷ C₂³×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂³×C₄² ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72257855	C₂	semidirect
2. #72257853	C₂	semidirect
3. #72257851	C₂	semidirect
5. #72257846	C₂	semidirect
6. #72257816	C₂	semidirect
7. #72257813	C₂	semidirect
8. #72257810	C₂	semidirect
9. #72257809	C₂	semidirect
10. #72257805	C₂	semidirect
11. #72257793	C₂	semidirect
12. #72257788	C₂	semidirect
13. #72240707	C₂	semidirect
14. #72239975	C₂	semidirect
15. #72239859	C₂	semidirect
18. #6458932	C₂²	semidirect
20. #6458238	C₂²	semidirect
21. C₂×#20732	C₂²	semidirect
23. #614082	C₂²	semidirect
28. #392266	C₂²	semidirect
29. #362839	C₂²	semidirect
31. #359689	C₂²	semidirect
32. #195868	C₂²	semidirect
33. #195812	C₂²	semidirect
34. #191064	C₂²	semidirect
35. #190447	C₂²	semidirect
36. #189852	C₂²	semidirect
37. #188470	C₂²	semidirect
38. #188292	C₂²	semidirect
39. #184859	C₂²	semidirect
40. #184859	C₂²	semidirect
41. #161044	C₂²	semidirect
44. #160613	C₂²	semidirect
45. #108811	C₂²	semidirect
46. #105536	C₂²	semidirect
47. #105492	C₂²	semidirect
48. #95838	C₂²	semidirect
49. #95213	C₂²	semidirect
50. #94960	C₂²	semidirect
69. C₂×#2094	D₄	semidirect
70. C₂×#2071	D₄	semidirect
90. #10925	D₄	semidirect
91. #7572	D₄	semidirect
107. C₂²×C₄×C₈	C₂×D₄	semidirect
121. C₂×#384	C₂×D₄	semidirect
122. C₂×#384	C₂×D₄	semidirect
133. #1797	C₂×D₄	semidirect
134. C₄×C₂²⋊C₈	C₂×D₄	semidirect
135. C₂×#336	C₂×D₄	semidirect
136. C₄⋊#95	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72257855	2
#72257853	2
#72257851	2
#72257847	2
#72257846	2
#72257816	2
#72257813	2
#72257810	2
#72257809	2
#72257805	2
#72257793	2
#72257788	2
#72240707	2
#72239975	2
#72239859	2