Subgroups — #72226710

Order 4096.

At least 12483 conjugacy classes of subgroups; only the 1177 normal subgroups are shown.

The subgroup lattice has 333 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72226663	C₂	1	1	yes	maximal, characteristic, complemented
2	#72226648	C₂	1	2	yes	maximal, complemented
3	#72224610	C₂	1	2	yes	maximal, complemented
4	#72224571	C₂	1	2	yes	maximal, complemented
5	#72219639	C₂	1	1	yes	maximal, characteristic, complemented
6	#72219626	C₂	1	8	yes	maximal, complemented
7	#72219621	C₂²	1	8	yes	complemented
8	#72219620	C₂²	1	8	yes	complemented
9	#72219617	C₂	1	2	yes	maximal, complemented
10	#72219615	C₂²	1	2	yes	complemented
11	#72219613	C₂²	1	4	yes	complemented
12	#72219609	C₂	1	2	yes	maximal, complemented
13	#72219608	C₂²	1	2	yes	complemented
14	#72219607	C₂²	1	4	yes	complemented
15	#72219602	C₂	1	2	yes	maximal, complemented
16	#72219594	C₂²	1	4	yes	complemented
17	#72219593	C₂²	1	4	yes	complemented
18	#72219591	C₂²	1	4	yes	complemented
19	#72219590	C₂²	1	4	yes	complemented
20	#72219586	C₂²	1	2	yes	complemented
21	#72219585	C₂	1	8	yes	maximal, complemented
22	#72219582	C₂²	1	8	yes	complemented
23	#72219581	C₂²	1	8	yes	complemented
24	#72219580	C₂²	1	8	yes	complemented
25	#72219579	C₂²	1	8	yes	complemented
26	#72219578	C₂²	1	8	yes	complemented
27	#72219577	C₂²	1	16	yes	complemented
28	#72219576	C₂²	1	16	yes	complemented
29	#72219575	C₂²	1	4	yes	complemented
30	#72219574	C₂²	1	4	yes	complemented
31	#72219573	C₂	1	1	yes	maximal, characteristic, complemented
32	#72219569	C₂²	1	8	yes	—
33	#72219559	C₂²	1	2	yes	—
34	#72214656	C₂²	1	1	yes	characteristic, complemented
35	#72214607	C₂²	1	1	yes	characteristic, complemented
36	#72214576	C₂²	1	1	yes	characteristic, complemented
37	#72214488	C₂²	1	4	yes	complemented
38	#72214439	C₂²	1	1	yes	characteristic, complemented
39	#72214391	C₂²	1	1	yes	characteristic, complemented
40	#72214347	C₂²	1	1	yes	characteristic, complemented
41	#72214129	C₂²	1	4	yes	complemented
42	#72213663	C₂²	1	2	yes	—
43	#72213590	C₂²	1	2	yes	—
44	C₂×#6443095	C₂²	1	1	yes	characteristic
45	C₂⁴×#127	D₄	1	1	yes	characteristic
46	C₂×#61110	D₄	1	2	yes	complemented
47	#10575416	D₄	1	2	yes	—
48	#10575323	C₂³	1	1	yes	characteristic, complemented
49	C₂²×#3151	D₄	1	1	yes	characteristic
50	C₂²×#3151	C₂³	1	1	yes	characteristic
51	C₂×#36624	D₄	1	1	yes	characteristic
52	#7613479	C₂³	1	8	yes	—
53	#7613467	D₄	1	8	yes	complemented
54	#7563344	C₂³	1	4	yes	—
55	#7563342	C₂³	1	4	yes	—
56	#7563325	D₄	1	4	yes	complemented
57	#7563319	D₄	1	4	yes	complemented
58	#7503924	D₄	1	2	yes	complemented
59	#7503841	D₄	1	4	yes	complemented
60	#7503372	D₄	1	2	yes	complemented
61	#6465682	D₄	1	4	yes	complemented
62	#6443095	D₄	1	4	yes	—
63	#6443095	C₂³	1	4	yes	—
64	#6396163	D₄	1	8	yes	—
65	#6396163	C₂³	1	8	yes	—
66	#6382816	D₄	1	2	yes	complemented
67	#6376214	D₄	1	4	yes	—
68	#6374880	D₄	1	2	yes	—
69	#6372902	C₂³	1	4	yes	—
70	C₂×#21203	D₄	1	1	yes	characteristic
71	C₂×#21203	C₂³	1	1	yes	characteristic
72	C₂×C₄×#407	C₂³	1	1	yes	characteristic
73	#6357179	C₂³	1	2	yes	complemented
74	#6357172	C₂³	1	2	yes	complemented
75	#6342514	C₂³	1	1	yes	characteristic, complemented
76	#500893	C₂³	1	8	yes	complemented
77	#500684	C₂³	1	8	yes	complemented
78	#493945	C₂³	1	4	yes	complemented
79	#414764	C₂³	1	2	yes	complemented
80	#411779	C₂³	1	2	yes	complemented
81	#353776	C₂³	1	1	yes	characteristic, complemented
82	#233894	C₂³	1	2	yes	complemented
83	#233889	C₂³	1	2	yes	complemented
84	#181055	C₂³	1	1	yes	characteristic, complemented
85	#137630	C₂³	1	8	yes	complemented
86	#137629	C₂³	1	8	yes	complemented
87	#134520	C₂³	1	16	yes	complemented
88	#134296	C₂³	1	8	yes	complemented
89	#129996	C₂³	1	4	yes	complemented
90	#129996	C₂³	1	4	yes	complemented
91	#124937	C₂³	1	8	yes	complemented
92	#124440	C₂³	1	16	yes	complemented
93	#114129	C₂³	1	4	yes	complemented
94	#110216	C₂³	1	4	yes	complemented
95	#110048	C₂³	1	4	yes	complemented
96	C₂²×#532	C₂×D₄	1	1	yes	characteristic
97	C₂³×#127	C₂×D₄	1	1	yes	characteristic
98	C₂³×#127	C₂×D₄	1	1	yes	characteristic
99	C₂³×#127	C₂×D₄	1	4	yes	—
100	C₂⁴×C₄²	C₂×D₄	1	1	yes	characteristic
101	C₂×#3292	C₂×D₄	1	4	yes	—
102	C₂×#3291	C₂×D₄	1	4	yes	—
103	#60741	C₂×D₄	1	8	yes	—
104	#60663	C₂⁴	1	1	yes	characteristic, complemented
105	#60639	C₂⁴	1	1	yes	characteristic, complemented
106	C₂×#3151	C₂×D₄	1	4	yes	—
107	C₂×#3151	C₂×D₄	1	2	yes	—
108	C₂×#3151	C₂×D₄	1	2	yes	—
109	C₂×#3151	C₂×D₄	1	2	yes	—
110	C₂×#3151	C₂⁴	1	2	yes	—
111	C₂²×#493	C₂×D₄	1	2	yes	—
112	C₂²×#492	C₂×D₄	1	2	yes	—
113	#60444	C₂×D₄	1	4	yes	—
114	C₂×#2956	C₂×D₄	1	4	yes	—
115	C₂²×#407	C₂×D₄	1	2	yes	—
116	C₂²×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×M₁₆	C₂⁴	1	1	yes	characteristic
118	#36624	C₂×D₄	1	4	yes	—
119	C₂×#2285	C₂×D₄	1	1	yes	characteristic
120	#31258	C₂×D₄	1	8	yes	—
121	#31231	C₂×D₄	1	16	yes	—
122	#31074	C₂×D₄	1	8	yes	—
123	#28504	C₂×D₄	1	8	yes	—
124	#28502	C₂×D₄	1	8	yes	—
125	#23201	C₂×D₄	1	4	yes	—
126	#23198	C₂×D₄	1	4	yes	—
127	#22207	C₂×D₄	1	16	yes	—
128	#21949	C₂×D₄	1	8	yes	—
129	#21551	C₂×D₄	1	8	yes	—
130	#21549	C₂⁴	1	8	yes	—
131	#21546	C₂×D₄	1	8	yes	—
132	#21544	C₂×D₄	1	8	yes	—
133	#21241	C₂×D₄	1	4	yes	—
134	#21203	C₂×D₄	1	2	yes	—
135	#21203	C₂×D₄	1	2	yes	—
136	#21203	C₂×D₄	1	4	yes	—
137	#21203	C₂×D₄	1	2	yes	—
138	#21203	C₂⁴	1	2	yes	—
139	C₂×#1961	C₂×D₄	1	4	yes	—
140	#21165	C₂×D₄	1	4	yes	—
141	#20667	C₂×D₄	1	4	yes	—
142	#20445	C₂×D₄	1	4	yes	—
143	C₄×#407	C₂×D₄	1	4	yes	—
144	C₄×#407	C₂×D₄	1	2	yes	—
145	C₄×#407	C₂⁴	1	2	yes	—
146	C₂×#1728	C₂×D₄	1	2	yes	—
147	#17314	C₂⁴	1	2	yes	complemented
148	#12791	C₂⁴	1	8	yes	complemented
149	#10837	C₂⁴	1	2	yes	complemented
150	#7918	C₂⁴	1	2	yes	complemented
151	C₂⁵×C₄	#120	1	1	yes	characteristic
152	C₂×#575	#120	1	4	yes	—
153	C₂³×M₁₆	#120	1	2	yes	—
154	C₂³×M₁₆	C₂²×D₄	1	2	yes	—
155	C₂×#532	#120	1	2	yes	—
156	C₂×#532	C₂²×D₄	1	2	yes	—
157	C₂²×C₄⋊Q₈	#120	1	1	yes	characteristic
158	C₂²×#127	#120	1	1	yes	characteristic
159	C₂²×#127	#120	1	1	yes	characteristic
160	C₂²×#127	#120	1	2	yes	—
161	C₂²×#127	#120	1	2	yes	—
162	C₂²×#127	#120	1	1	yes	characteristic
163	C₂²×#127	#120	1	1	yes	characteristic
164	C₂²×#127	#120	1	1	yes	characteristic
165	C₂²×#127	C₂²×D₄	1	2	yes	—
166	C₂²×#127	C₂²×D₄	1	2	yes	—
167	C₂³×C₄²	#120	1	1	yes	characteristic
168	C₂³×C₄²	#120	1	2	yes	—
169	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
170	C₂³×C₄²	C₂²×D₄	1	2	yes	—
171	#3197	AGL(1,ℤ/8)	1	16	yes	complemented
172	#3195	AGL(1,ℤ/8)	1	8	yes	complemented
173	#3192	AGL(1,ℤ/8)	1	8	yes	complemented
174	C₂×#493	#120	1	2	yes	—
175	C₂×#493	#120	1	2	yes	—
176	C₂×#493	C₂²×D₄	1	2	yes	—
177	C₂×#493	C₂²×D₄	1	2	yes	—
178	C₂×#492	#120	1	2	yes	—
179	C₂×#492	#120	1	2	yes	—
180	C₂×#492	C₂²×D₄	1	2	yes	—
181	C₂×#492	C₂²×D₄	1	2	yes	—
182	#3054	C₂²×D₄	1	8	yes	—
183	#3050	#120	1	8	yes	—
184	C₂×#444	#120	1	8	yes	—
185	C₂×#443	C₂²×D₄	1	8	yes	—
186	C₂×#430	#120	1	4	yes	—
187	C₂×#430	#120	1	4	yes	—
188	#2911	#120	1	4	yes	—
189	C₂×#407	#120	1	4	yes	—
190	C₂×#407	C₂²×D₄	1	4	yes	—
191	C₂×C₄×M₁₆	#120	1	2	yes	—
192	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
193	C₂×C₄×M₁₆	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
195	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
196	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
197	C₂×C₄×M₁₆	C₂⁵	1	1	yes	characteristic
198	C₂²×#97	C₂²×D₄	1	2	yes	—
199	C₂²×C₄×C₈	C₂²×D₄	1	2	yes	—
200	#2285	#120	1	2	yes	—
201	#2285	C₂²×D₄	1	2	yes	—
202	C₂×#382	#120	1	2	yes	—
203	#1975	C₂²×D₄	1	8	yes	—
204	#1974	#120	1	8	yes	—
205	#1961	#120	1	4	yes	—
206	#1961	#120	1	4	yes	—
207	#1961	C₂²×D₄	1	4	yes	—
208	#1961	C₂²×D₄	1	4	yes	—
209	#1946	C₂²×D₄	1	8	yes	—
210	#1945	#120	1	8	yes	—
211	#1811	C₂²×D₄	1	8	yes	—
212	#1810	#120	1	8	yes	—
213	#1773	#120	1	8	yes	—
214	#1772	C₂²×D₄	1	8	yes	—
215	#1728	#120	1	4	yes	—
216	#1728	C₂²×D₄	1	4	yes	—
217	C₂⁶	#453	1	1	yes	characteristic
218	C₂⁴×C₄	#453	1	1	yes	characteristic
219	C₂⁴×C₄	#453	1	2	yes	—
220	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
221	C₂⁴×C₄	C₂×#120	1	2	yes	—
222	C₂×#135	C₂×#120	1	8	yes	—
223	C₂²×M₁₆	C₂×#120	1	4	yes	—
224	C₂²×M₁₆	C₂×#120	1	2	yes	—
225	C₂²×M₁₆	C₂×#120	1	4	yes	—
226	C₂²×M₁₆	C₂³×D₄	1	2	yes	—
227	C₂³×C₈	C₂×#120	1	4	yes	—
228	C₂×C₄⋊Q₈	C₂×#120	1	2	yes	—
229	C₂×#127	#453	1	2	yes	—
230	C₂×#127	#453	1	2	yes	—
231	C₂×#127	B(4,𝔽₂)	1	2	yes	—
232	C₂×#127	B(4,𝔽₂)	1	2	yes	—
233	C₂×#127	C₂×#120	1	2	yes	—
234	C₂×#127	C₂×#120	1	2	yes	—
235	C₂×#127	C₂×#120	1	2	yes	—
236	C₂×#127	C₂×#120	1	2	yes	—
237	C₂×#127	C₂×#120	1	2	yes	—
238	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
239	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
240	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
241	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
242	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
243	C₂²×C₄²	C₂×#120	1	2	yes	—
244	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
245	#470	C₂×AGL(1,ℤ/8)	1	16	yes	—
246	#469	C₂×AGL(1,ℤ/8)	1	16	yes	—
247	C₂×#108	C₂×#120	1	8	yes	—
248	C₂×#108	C₂×#120	1	8	yes	—
249	#427	C₂×#120	1	8	yes	—
250	#407	C₂×AGL(1,ℤ/8)	1	8	yes	—
251	#407	C₂×AGL(1,ℤ/8)	1	8	yes	—
252	C₂×#97	C₂×#120	1	4	yes	—
253	C₂×#97	C₂×#120	1	2	yes	—
254	C₂×#97	C₂³×D₄	1	2	yes	—
255	C₂×C₄×C₈	C₂×#120	1	2	yes	—
256	C₂×C₄×C₈	C₂×#120	1	4	yes	—
257	C₂×C₄×C₈	C₂³×D₄	1	2	yes	—
258	#382	C₂×#120	1	4	yes	—
259	C₂⁵	C₂×#453	1	1	yes	characteristic
260	C₂⁵	C₂×#453	1	2	yes	—
261	C₂³×C₄	#2846	1	1	yes	characteristic
262	C₂³×C₄	#2846	1	1	yes	characteristic
263	C₂³×C₄	#3003	1	4	yes	—
264	C₂³×C₄	#3003	1	4	yes	—
265	C₂³×C₄	C₂×#453	1	1	yes	characteristic
266	C₂³×C₄	C₂×#453	1	2	yes	—
267	C₂³×C₄	#3019	1	1	yes	characteristic
268	C₂³×C₄	#3019	1	1	yes	characteristic
269	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
270	C₂×Q₁₆	#3003	1	8	yes	complemented
271	C₂×D₈	#3003	1	8	yes	complemented
272	C₂×M₁₆	#3003	1	8	yes	—
273	C₂×M₁₆	C₂²×AGL(1,ℤ/8)	1	8	yes	—
274	C₂²×C₈	#2846	1	4	yes	—
275	C₂²×C₈	C₂²×#120	1	4	yes	—
276	#127	C₂×#453	1	4	yes	—
277	#127	C₂×B(4,𝔽₂)	1	4	yes	—
278	C₂×C₄²	#2846	1	1	yes	characteristic
279	C₂×C₄²	#2846	1	1	yes	characteristic
280	C₂×C₄²	C₂×#453	1	1	yes	characteristic
281	C₂×C₄²	C₂×#453	1	1	yes	characteristic
282	C₂×C₄²	#3019	1	1	yes	characteristic
283	C₂×C₄²	#3019	1	1	yes	characteristic
284	C₂×C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
285	C₂×C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
286	C₂×C₄²	#3026	1	1	yes	characteristic
287	C₂×C₄²	#3026	1	1	yes	characteristic
288	C₂×C₄²	C₂²×#120	1	1	yes	characteristic
289	C₂×C₄²	C₂²×#120	1	1	yes	characteristic
290	#106	#3003	1	16	yes	complemented
291	C₂⁴	#18524	1	2	yes	—
292	C₂⁴	#18524	1	2	yes	—
293	C₂⁴	#32888	1	1	yes	characteristic
294	C₂⁴	#32888	1	1	yes	characteristic
295	C₂⁴	C₂²×#453	1	1	yes	characteristic
296	C₂²×C₄	#18524	1	4	yes	—
297	C₂²×C₄	#32888	1	1	yes	characteristic
298	C₂²×C₄	#32888	1	1	yes	characteristic
299	C₂²×C₄	#32888	1	1	yes	characteristic
300	C₂²×C₄	#32888	1	1	yes	characteristic
301	C₂²×C₄	#32898	1	1	yes	characteristic
302	C₂²×C₄	#32898	1	1	yes	characteristic
303	C₂²×C₄	C₂×#2846	1	1	yes	characteristic
304	C₂²×C₄	C₂×#3003	1	4	yes	—
305	C₂²×C₄	C₂×#3019	1	1	yes	characteristic
306	C₂×C₈	C₂×#3003	1	8	yes	—
307	C₄²	#32888	1	1	yes	characteristic
308	C₄²	#32888	1	1	yes	characteristic
309	C₄²	#32898	1	1	yes	characteristic
310	C₄²	#32898	1	1	yes	characteristic
311	C₄²	C₂²×#453	1	1	yes	characteristic
312	C₄²	C₂×#3019	1	1	yes	characteristic
313	C₄²	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
314	C₄²	C₂×#3026	1	1	yes	characteristic
315	C₂³	#346446	1	1	yes	characteristic
316	C₂³	#346446	1	1	yes	characteristic
317	C₂³	C₂×#18524	1	2	yes	—
318	C₂³	C₂×#32888	1	1	yes	characteristic
319	C₂×C₄	#346446	1	1	yes	characteristic
320	C₂×C₄	#346446	1	1	yes	characteristic
321	C₂×C₄	#6348967	1	2	yes	—
322	C₂×C₄	#6628842	1	2	yes	—
323	C₂×C₄	C₂×#32888	1	1	yes	characteristic
324	C₂×C₄	#6628883	1	2	yes	—
325	C₂×C₄	C₂×#32898	1	1	yes	characteristic
326	C₂²	C₂×#346446	1	1	yes	characteristic
327	C₂²	#72226686	1	1	yes	characteristic
328	C₂²	#72226694	1	1	yes	characteristic
329	C₄	#72226680	1	2	yes	—
330	C₄	#72226690	1	2	yes	—
331	C₂	#72226708	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72226708
commutator, Frattini, cosocle	C₂×C₄×M₁₆	C₂⁵
LCS	G ▷ C₂×C₄×M₁₆ ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂²×C₄×M₁₆ ◁ G
LECS	G ▷ C₂×C₄×M₁₆ ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72226663	C₂	semidirect
2. #72226648	C₂	semidirect
3. #72224610	C₂	semidirect
4. #72224571	C₂	semidirect
5. #72219639	C₂	semidirect
6. #72219626	C₂	semidirect
7. #72219621	C₂²	semidirect
8. #72219620	C₂²	semidirect
9. #72219617	C₂	semidirect
10. #72219615	C₂²	semidirect
11. #72219613	C₂²	semidirect
12. #72219609	C₂	semidirect
13. #72219608	C₂²	semidirect
14. #72219607	C₂²	semidirect
15. #72219602	C₂	semidirect
16. #72219594	C₂²	semidirect
17. #72219593	C₂²	semidirect
18. #72219591	C₂²	semidirect
19. #72219590	C₂²	semidirect
20. #72219586	C₂²	semidirect
21. #72219585	C₂	semidirect
22. #72219582	C₂²	semidirect
23. #72219581	C₂²	semidirect
24. #72219580	C₂²	semidirect
25. #72219579	C₂²	semidirect
26. #72219578	C₂²	semidirect
27. #72219577	C₂²	semidirect
28. #72219576	C₂²	semidirect
29. #72219575	C₂²	semidirect
30. #72219574	C₂²	semidirect
31. #72219573	C₂	semidirect
34. #72214656	C₂²	semidirect
35. #72214607	C₂²	semidirect
36. #72214576	C₂²	semidirect
37. #72214488	C₂²	semidirect
38. #72214439	C₂²	semidirect
39. #72214391	C₂²	semidirect
40. #72214347	C₂²	semidirect
41. #72214129	C₂²	semidirect
46. C₂×#61110	D₄	semidirect
48. #10575323	C₂³	semidirect
53. #7613467	D₄	semidirect
56. #7563325	D₄	semidirect
57. #7563319	D₄	semidirect
58. #7503924	D₄	semidirect
59. #7503841	D₄	semidirect
60. #7503372	D₄	semidirect
61. #6465682	D₄	semidirect
66. #6382816	D₄	semidirect
73. #6357179	C₂³	semidirect
74. #6357172	C₂³	semidirect
75. #6342514	C₂³	semidirect
76. #500893	C₂³	semidirect
77. #500684	C₂³	semidirect
78. #493945	C₂³	semidirect
79. #414764	C₂³	semidirect
80. #411779	C₂³	semidirect
81. #353776	C₂³	semidirect
82. #233894	C₂³	semidirect
83. #233889	C₂³	semidirect
84. #181055	C₂³	semidirect
85. #137630	C₂³	semidirect
86. #137629	C₂³	semidirect
87. #134520	C₂³	semidirect
88. #134296	C₂³	semidirect
89. #129996	C₂³	semidirect
90. #129996	C₂³	semidirect
91. #124937	C₂³	semidirect
92. #124440	C₂³	semidirect
93. #114129	C₂³	semidirect
94. #110216	C₂³	semidirect
95. #110048	C₂³	semidirect
104. #60663	C₂⁴	semidirect
105. #60639	C₂⁴	semidirect
147. #17314	C₂⁴	semidirect
148. #12791	C₂⁴	semidirect
149. #10837	C₂⁴	semidirect
150. #7918	C₂⁴	semidirect
171. #3197	AGL(1,ℤ/8)	semidirect
172. #3195	AGL(1,ℤ/8)	semidirect
173. #3192	AGL(1,ℤ/8)	semidirect
270. C₂×Q₁₆	#3003	semidirect
271. C₂×D₈	#3003	semidirect
290. #106	#3003	semidirect

Maximal subgroups

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

subgroup	index
#72226663	2
#72226648	2
#72224610	2
#72224571	2
#72219639	2
#72219626	2
#72219617	2
#72219609	2
#72219602	2
#72219585	2
#72219573	2