Subgroups — #72339052

Order 4096.

At least 11732 conjugacy classes of subgroups; only the 605 normal subgroups are shown.

The subgroup lattice has 332 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72339050	C₂	1	1	yes	maximal, characteristic, complemented
2	#72339048	C₂	1	1	yes	maximal, characteristic, complemented
3	#72339038	C₂	1	2	yes	maximal, complemented
4	#72339036	C₂	1	2	yes	maximal, complemented
5	#72339035	C₂²	1	2	yes	complemented
6	#72339033	C₂²	1	2	yes	complemented
7	#72338797	C₂	1	2	yes	maximal, complemented
8	#72338795	C₂	1	2	yes	maximal, complemented
9	#72338794	C₂²	1	2	yes	complemented
10	#72338734	C₂	1	2	yes	maximal, complemented
11	#72338730	C₂	1	2	yes	maximal, complemented
12	#72338726	C₂²	1	2	yes	complemented
13	#72338723	C₂	1	2	yes	maximal, complemented
14	#72338721	C₂²	1	2	yes	complemented
15	#72338718	C₂	1	2	yes	maximal, complemented
16	#72338715	C₂²	1	2	yes	complemented
17	#72338712	C₂²	1	2	yes	complemented
18	#72337672	C₂	1	2	yes	maximal, complemented
19	#72337671	C₂	1	2	yes	maximal, complemented
20	#72337664	C₂²	1	2	yes	complemented
21	#72337656	C₂²	1	2	yes	complemented
22	#72337653	C₂²	1	2	yes	complemented
23	#72337650	C₂²	1	2	yes	complemented
24	#72337645	C₂²	1	2	yes	complemented
25	#72337637	C₂²	1	2	yes	complemented
26	#72337637	C₂²	1	2	yes	complemented
27	#72337636	C₂²	1	2	yes	complemented
28	#72337636	C₂²	1	2	yes	complemented
29	#72337635	C₂²	1	2	yes	complemented
30	#72337635	C₂²	1	2	yes	complemented
31	#72337629	C₂²	1	2	yes	complemented
32	#72337629	C₂²	1	2	yes	complemented
33	#72337627	C₂²	1	2	yes	complemented
34	#72337627	C₂²	1	2	yes	complemented
35	#72337625	C₂²	1	2	yes	complemented
36	#72337625	C₂²	1	2	yes	complemented
37	#72319290	C₂	1	1	yes	maximal, characteristic, complemented
38	#72319272	C₂²	1	1	yes	characteristic
39	#72319272	C₂²	1	1	yes	characteristic, complemented
40	#72319266	C₂²	1	1	yes	characteristic, complemented
41	#72319263	C₂²	1	2	yes	complemented
42	#72319263	C₂²	1	2	yes	complemented
43	#72318569	C₂²	1	2	yes	complemented
44	#72318569	C₂²	1	2	yes	complemented
45	#72262289	C₂²	1	2	yes	complemented
46	#72262288	C₂²	1	2	yes	complemented
47	#72252381	C₂	1	2	yes	maximal, complemented
48	#72252380	C₂	1	2	yes	maximal, complemented
49	#72252379	C₂²	1	2	yes	complemented
50	#72252379	C₂²	1	2	yes	complemented
51	#72252379	C₂²	1	2	yes	complemented
52	#72252378	C₂²	1	2	yes	complemented
53	#72241387	C₂²	1	2	yes	complemented
54	#72241350	C₂	1	1	yes	maximal, characteristic, complemented
55	#72241350	C₂	1	1	yes	maximal, characteristic, complemented
56	#72241343	C₂²	1	2	yes	complemented
57	#72241343	C₂²	1	2	yes	complemented
58	#72241322	C₂²	1	2	yes	complemented
59	#72241322	C₂²	1	2	yes	complemented
60	#72241322	C₂²	1	2	yes	complemented
61	#72241322	C₂²	1	2	yes	complemented
62	#72241322	C₂²	1	2	yes	complemented
63	#72241322	C₂²	1	2	yes	complemented
64	#72240077	C₂²	1	2	yes	complemented
65	#72236986	C₂	1	1	yes	maximal, characteristic, complemented
66	#72236986	C₂	1	1	yes	maximal, characteristic, complemented
67	#72236979	C₂²	1	1	yes	characteristic, complemented
68	#72236979	C₂²	1	1	yes	characteristic, complemented
69	#72236979	C₂²	1	1	yes	characteristic, complemented
70	#72236975	C₂²	1	1	yes	characteristic
71	#72236975	C₂²	1	1	yes	characteristic
72	#72236975	C₂²	1	1	yes	characteristic
73	#72236975	C₂²	1	1	yes	characteristic, complemented
74	#72236975	C₂²	1	1	yes	characteristic, complemented
75	#72236975	C₂²	1	1	yes	characteristic, complemented
76	#72236189	C₂²	1	1	yes	characteristic
77	#72227941	C₂²	1	2	yes	complemented
78	#72227940	C₂²	1	2	yes	complemented
79	#72227940	C₂²	1	2	yes	complemented
80	#72213269	C₂²	1	2	yes	complemented
81	#72213260	C₂²	1	2	yes	complemented
82	#72210572	C₂²	1	2	yes	complemented
83	#72210572	C₂²	1	2	yes	complemented
84	#72210569	C₂²	1	2	yes	complemented
85	#72210563	C₂²	1	2	yes	complemented
86	#72210563	C₂²	1	2	yes	complemented
87	#72210563	C₂²	1	2	yes	complemented
88	#72210563	C₂²	1	2	yes	complemented
89	#72210559	C₂²	1	2	yes	—
90	#72210559	C₂²	1	2	yes	—
91	#72210559	C₂²	1	2	yes	complemented
92	#72210559	C₂²	1	2	yes	complemented
93	#72210549	C₂²	1	2	yes	complemented
94	#72210539	C₂²	1	2	yes	complemented
95	#72210529	C₂²	1	2	yes	complemented
96	#72210529	C₂²	1	2	yes	complemented
97	#72210524	C₂²	1	1	yes	characteristic, complemented
98	#72210524	C₂²	1	1	yes	characteristic, complemented
99	#72210498	C₂²	1	2	yes	—
100	#72210498	C₂²	1	2	yes	—
101	#72210498	C₂²	1	2	yes	complemented
102	#72210498	C₂²	1	2	yes	complemented
103	#72210439	C₂²	1	1	yes	characteristic
104	#72210439	C₂²	1	1	yes	characteristic
105	#72210439	C₂²	1	1	yes	characteristic, complemented
106	#72210439	C₂²	1	1	yes	characteristic, complemented
107	#8934366	C₂³	1	1	yes	characteristic
108	#8934366	C₂³	1	1	yes	characteristic
109	#8934366	C₂³	1	1	yes	characteristic
110	#8934366	C₂³	1	1	yes	characteristic
111	#8933771	C₂³	1	2	yes	complemented
112	#7672751	C₂³	1	1	yes	characteristic
113	#7672751	C₂³	1	1	yes	characteristic
114	#7672751	C₂³	1	1	yes	characteristic
115	#6629267	C₂³	1	1	yes	characteristic
116	#6629262	D₄	1	2	yes	complemented
117	#6628901	C₂³	1	1	yes	characteristic
118	#6628901	C₂³	1	1	yes	characteristic
119	#6628896	D₄	1	2	yes	complemented
120	#6628896	D₄	1	2	yes	complemented
121	#449527	C₂³	1	2	yes	—
122	#449492	C₂³	1	2	yes	—
123	#449492	C₂³	1	2	yes	—
124	#418114	C₂³	1	2	yes	—
125	#417807	C₂³	1	2	yes	—
126	#417807	C₂³	1	2	yes	—
127	#374009	C₂³	1	1	yes	characteristic
128	#374009	C₂³	1	1	yes	characteristic
129	#374009	C₂³	1	1	yes	characteristic
130	#346283	C₂³	1	2	yes	complemented
131	#251830	D₄	1	4	yes	complemented
132	#251828	D₄	1	4	yes	complemented
133	#251828	D₄	1	4	yes	complemented
134	#245234	C₂³	1	2	yes	—
135	#245234	C₂³	1	2	yes	—
136	#245234	C₂³	1	2	yes	—
137	#245234	C₂³	1	2	yes	—
138	#245234	C₂³	1	2	yes	complemented
139	#245234	C₂³	1	2	yes	complemented
140	#245233	C₂³	1	2	yes	—
141	#245233	C₂³	1	2	yes	—
142	#245233	C₂³	1	2	yes	—
143	#245233	C₂³	1	2	yes	—
144	#245233	C₂³	1	2	yes	—
145	#245233	C₂³	1	2	yes	—
146	#245233	C₂³	1	2	yes	—
147	#245233	C₂³	1	2	yes	—
148	#245233	C₂³	1	2	yes	complemented
149	#213865	C₂³	1	2	yes	complemented
150	#213861	C₂³	1	2	yes	complemented
151	#213860	C₂³	1	1	yes	characteristic
152	#213860	C₂³	1	1	yes	characteristic
153	#213860	C₂³	1	1	yes	characteristic
154	#213860	C₂³	1	1	yes	characteristic
155	#213860	C₂³	1	1	yes	characteristic
156	#213860	C₂³	1	1	yes	characteristic
157	#213860	C₂³	1	2	yes	complemented
158	#213854	D₄	1	2	yes	complemented
159	#213854	D₄	1	2	yes	complemented
160	#213854	D₄	1	2	yes	complemented
161	#134009	C₂³	1	2	yes	—
162	#134009	C₂³	1	2	yes	—
163	#134009	C₂³	1	2	yes	—
164	#133936	C₂³	1	2	yes	complemented
165	#133835	C₂³	1	2	yes	—
166	#133835	C₂³	1	2	yes	—
167	#133835	C₂³	1	2	yes	—
168	#133835	C₂³	1	2	yes	complemented
169	#133835	C₂³	1	2	yes	complemented
170	#133309	C₂³	1	2	yes	complemented
171	#133309	C₂³	1	2	yes	complemented
172	#133308	C₂³	1	2	yes	—
173	#133308	C₂³	1	2	yes	—
174	#133308	C₂³	1	2	yes	—
175	#133308	C₂³	1	2	yes	—
176	#133308	C₂³	1	2	yes	—
177	#133308	C₂³	1	2	yes	—
178	#133308	C₂³	1	2	yes	—
179	#133308	C₂³	1	2	yes	—
180	#133308	C₂³	1	2	yes	—
181	#133308	C₂³	1	2	yes	—
182	#133308	C₂³	1	2	yes	—
183	#133308	C₂³	1	2	yes	—
184	#133308	C₂³	1	2	yes	complemented
185	#133308	C₂³	1	2	yes	complemented
186	#133308	C₂³	1	2	yes	complemented
187	#133308	C₂³	1	2	yes	complemented
188	#97466	C₂³	1	2	yes	complemented
189	#97460	C₂³	1	2	yes	complemented
190	#97460	C₂³	1	2	yes	complemented
191	#93146	C₂³	1	2	yes	complemented
192	#93146	C₂³	1	2	yes	complemented
193	#93146	C₂³	1	2	yes	complemented
194	#93139	C₂³	1	2	yes	complemented
195	#93139	C₂³	1	2	yes	complemented
196	#93139	C₂³	1	2	yes	complemented
197	#93113	C₂³	1	2	yes	complemented
198	#93113	C₂³	1	2	yes	complemented
199	#93113	C₂³	1	2	yes	complemented
200	#93113	C₂³	1	2	yes	complemented
201	#93113	C₂³	1	2	yes	complemented
202	#93113	C₂³	1	2	yes	complemented
203	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
205	#62652	C₂×D₄	1	1	yes	characteristic, complemented
206	#46384	C₂×D₄	1	2	yes	—
207	#46384	C₂×D₄	1	2	yes	—
208	#46384	C₂×D₄	1	2	yes	—
209	C₂×#2867	C₂⁴	1	1	yes	characteristic
210	#35554	C₂⁴	1	2	yes	—
211	#35527	C₂⁴	1	2	yes	—
212	#35527	C₂⁴	1	2	yes	—
213	#35527	C₂⁴	1	1	yes	characteristic
214	#35527	C₂⁴	1	1	yes	characteristic
215	#35527	C₂⁴	1	1	yes	characteristic
216	#35527	C₂⁴	1	1	yes	characteristic
217	#35527	C₂⁴	1	1	yes	characteristic
218	#35527	C₂⁴	1	1	yes	characteristic
219	#35346	C₂×D₄	1	2	yes	—
220	#35346	C₂×D₄	1	2	yes	—
221	#35346	C₂×D₄	1	2	yes	—
222	#33020	C₂×D₄	1	4	yes	complemented
223	#33020	C₂×D₄	1	4	yes	complemented
224	#32898	C₂×D₄	1	4	yes	—
225	#32898	C₂×D₄	1	4	yes	—
226	#32898	C₂×D₄	1	4	yes	complemented
227	#32898	C₂×D₄	1	4	yes	complemented
228	#20690	C₂×D₄	1	2	yes	complemented
229	#20586	C₂×D₄	1	2	yes	complemented
230	#20586	C₂×D₄	1	2	yes	complemented
231	#20586	C₂×D₄	1	1	yes	characteristic, complemented
232	#20586	C₂×D₄	1	1	yes	characteristic, complemented
233	#20586	C₂×D₄	1	1	yes	characteristic, complemented
234	#20585	C₂×D₄	1	2	yes	complemented
235	#20585	C₂×D₄	1	2	yes	complemented
236	#20585	C₂×D₄	1	2	yes	complemented
237	#10981	C₂⁴	1	2	yes	—
238	#10981	C₂⁴	1	2	yes	—
239	#10981	C₂⁴	1	2	yes	—
240	#9497	C₂×D₄	1	4	yes	—
241	#9497	C₂×D₄	1	4	yes	—
242	#9497	C₂×D₄	1	4	yes	complemented
243	#9497	C₂×D₄	1	4	yes	complemented
244	#9497	C₂×D₄	1	4	yes	complemented
245	#9497	C₂×D₄	1	4	yes	complemented
246	#8748	C₂×D₄	1	2	yes	complemented
247	#8748	C₂×D₄	1	2	yes	complemented
248	#8748	C₂×D₄	1	2	yes	complemented
249	#8546	C₂⁴	1	2	yes	—
250	#8546	C₂⁴	1	2	yes	—
251	#8546	C₂⁴	1	2	yes	—
252	#8546	C₂⁴	1	2	yes	—
253	#8546	C₂⁴	1	2	yes	—
254	#8546	C₂⁴	1	2	yes	—
255	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
256	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
257	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
258	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
259	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
260	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂²×#127	C₂⁵	1	1	yes	characteristic
265	C₂²×#120	#120	1	2	yes	—
266	C₂×#518	C₂²×D₄	1	2	yes	—
267	#2842	#120	1	2	yes	—
268	#2403	#120	1	2	yes	—
269	#2403	#120	1	2	yes	—
270	#2403	#120	1	2	yes	—
271	#2403	C₂²×D₄	1	2	yes	—
272	#2403	C₂²×D₄	1	2	yes	—
273	#2403	C₂²×D₄	1	2	yes	—
274	#2403	C₂²×D₄	1	2	yes	—
275	#2403	C₂²×D₄	1	2	yes	—
276	#2403	C₂²×D₄	1	2	yes	—
277	#2309	C₂²×D₄	1	2	yes	—
278	#2309	C₂²×D₄	1	2	yes	—
279	#2309	C₂²×D₄	1	2	yes	—
280	#2309	C₂²×D₄	1	1	yes	characteristic
281	#2309	C₂²×D₄	1	1	yes	characteristic
282	#2309	C₂²×D₄	1	1	yes	characteristic
283	#2309	H(5,𝔽₂)	1	1	yes	characteristic
284	#2309	H(5,𝔽₂)	1	1	yes	characteristic
285	#2309	H(5,𝔽₂)	1	1	yes	characteristic
286	#2308	#120	1	2	yes	—
287	#2308	#120	1	2	yes	—
288	#2308	#120	1	2	yes	—
289	C₂×C₄³	H(5,𝔽₂)	1	1	yes	characteristic
290	#1781	C₂²×D₄	1	4	yes	—
291	#1781	C₂²×D₄	1	4	yes	—
292	#1781	C₂²×D₄	1	4	yes	—
293	C₂⁶	B(4,𝔽₂)	1	2	yes	—
294	C₂³×D₄	C₂×#120	1	2	yes	—
295	C₂³×D₄	C₂×#120	1	2	yes	—
296	C₂³×D₄	C₂×#120	1	2	yes	—
297	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
298	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
299	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
300	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
304	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
305	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
306	C₂²×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	#379	C₂×#120	1	2	yes	—
308	#379	C₂×#120	1	2	yes	—
309	#379	C₂×#120	1	2	yes	—
310	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
311	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
312	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
313	C₂⁵	C₂²×#120	1	1	yes	characteristic
314	C₂⁵	#3484	1	1	yes	characteristic
315	C₂⁵	#3484	1	1	yes	characteristic
316	C₂⁵	#3484	1	1	yes	characteristic
317	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
318	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
319	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
320	C₂³×C₄	#3484	1	1	yes	characteristic
321	C₂³×C₄	#3484	1	1	yes	characteristic
322	C₂³×C₄	#3484	1	1	yes	characteristic
323	C₂⁴	#35346	1	1	yes	characteristic
324	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
325	C₂³	#6499867	1	1	yes	characteristic
326	C₂³	#6499874	1	2	yes	—
327	C₂²	#72216396	1	1	yes	characteristic
328	C₂	#72216398	1	1	yes	characteristic
329	C₂	#72216398	1	1	yes	characteristic
330	C₂	#72262507	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72216396
commutator, Frattini, cosocle	C₂²×#127	C₂⁵
LCS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#127 ◁ G
LECS	G ▷ C₂²×#127 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72339050	C₂	semidirect
2. #72339048	C₂	semidirect
3. #72339038	C₂	semidirect
4. #72339036	C₂	semidirect
5. #72339035	C₂²	semidirect
6. #72339033	C₂²	semidirect
7. #72338797	C₂	semidirect
8. #72338795	C₂	semidirect
9. #72338794	C₂²	semidirect
10. #72338734	C₂	semidirect
11. #72338730	C₂	semidirect
12. #72338726	C₂²	semidirect
13. #72338723	C₂	semidirect
14. #72338721	C₂²	semidirect
15. #72338718	C₂	semidirect
16. #72338715	C₂²	semidirect
17. #72338712	C₂²	semidirect
18. #72337672	C₂	semidirect
19. #72337671	C₂	semidirect
20. #72337664	C₂²	semidirect
21. #72337656	C₂²	semidirect
22. #72337653	C₂²	semidirect
23. #72337650	C₂²	semidirect
24. #72337645	C₂²	semidirect
25. #72337637	C₂²	semidirect
26. #72337637	C₂²	semidirect
27. #72337636	C₂²	semidirect
28. #72337636	C₂²	semidirect
29. #72337635	C₂²	semidirect
30. #72337635	C₂²	semidirect
31. #72337629	C₂²	semidirect
32. #72337629	C₂²	semidirect
33. #72337627	C₂²	semidirect
34. #72337627	C₂²	semidirect
35. #72337625	C₂²	semidirect
36. #72337625	C₂²	semidirect
37. #72319290	C₂	semidirect
39. #72319272	C₂²	semidirect
40. #72319266	C₂²	semidirect
41. #72319263	C₂²	semidirect
42. #72319263	C₂²	semidirect
43. #72318569	C₂²	semidirect
44. #72318569	C₂²	semidirect
45. #72262289	C₂²	semidirect
46. #72262288	C₂²	semidirect
47. #72252381	C₂	semidirect
48. #72252380	C₂	semidirect
49. #72252379	C₂²	semidirect
50. #72252379	C₂²	semidirect
51. #72252379	C₂²	semidirect
52. #72252378	C₂²	semidirect
53. #72241387	C₂²	semidirect
54. #72241350	C₂	semidirect
55. #72241350	C₂	semidirect
56. #72241343	C₂²	semidirect
57. #72241343	C₂²	semidirect
58. #72241322	C₂²	semidirect
59. #72241322	C₂²	semidirect
60. #72241322	C₂²	semidirect
61. #72241322	C₂²	semidirect
62. #72241322	C₂²	semidirect
63. #72241322	C₂²	semidirect
64. #72240077	C₂²	semidirect
65. #72236986	C₂	semidirect
66. #72236986	C₂	semidirect
67. #72236979	C₂²	semidirect
68. #72236979	C₂²	semidirect
69. #72236979	C₂²	semidirect
73. #72236975	C₂²	semidirect
74. #72236975	C₂²	semidirect
75. #72236975	C₂²	semidirect
77. #72227941	C₂²	semidirect
78. #72227940	C₂²	semidirect
79. #72227940	C₂²	semidirect
80. #72213269	C₂²	semidirect
81. #72213260	C₂²	semidirect
82. #72210572	C₂²	semidirect
83. #72210572	C₂²	semidirect
84. #72210569	C₂²	semidirect
85. #72210563	C₂²	semidirect
86. #72210563	C₂²	semidirect
87. #72210563	C₂²	semidirect
88. #72210563	C₂²	semidirect
91. #72210559	C₂²	semidirect
92. #72210559	C₂²	semidirect
93. #72210549	C₂²	semidirect
94. #72210539	C₂²	semidirect
95. #72210529	C₂²	semidirect
96. #72210529	C₂²	semidirect
97. #72210524	C₂²	semidirect
98. #72210524	C₂²	semidirect
101. #72210498	C₂²	semidirect
102. #72210498	C₂²	semidirect
105. #72210439	C₂²	semidirect
106. #72210439	C₂²	semidirect
111. #8933771	C₂³	semidirect
116. #6629262	D₄	semidirect
119. #6628896	D₄	semidirect
120. #6628896	D₄	semidirect
130. #346283	C₂³	semidirect
131. #251830	D₄	semidirect
132. #251828	D₄	semidirect
133. #251828	D₄	semidirect
138. #245234	C₂³	semidirect
139. #245234	C₂³	semidirect
148. #245233	C₂³	semidirect
149. #213865	C₂³	semidirect
150. #213861	C₂³	semidirect
157. #213860	C₂³	semidirect
158. #213854	D₄	semidirect
159. #213854	D₄	semidirect
160. #213854	D₄	semidirect
164. #133936	C₂³	semidirect
168. #133835	C₂³	semidirect
169. #133835	C₂³	semidirect
170. #133309	C₂³	semidirect
171. #133309	C₂³	semidirect
184. #133308	C₂³	semidirect
185. #133308	C₂³	semidirect
186. #133308	C₂³	semidirect
187. #133308	C₂³	semidirect
188. #97466	C₂³	semidirect
189. #97460	C₂³	semidirect
190. #97460	C₂³	semidirect
191. #93146	C₂³	semidirect
192. #93146	C₂³	semidirect
193. #93146	C₂³	semidirect
194. #93139	C₂³	semidirect
195. #93139	C₂³	semidirect
196. #93139	C₂³	semidirect
197. #93113	C₂³	semidirect
198. #93113	C₂³	semidirect
199. #93113	C₂³	semidirect
200. #93113	C₂³	semidirect
201. #93113	C₂³	semidirect
202. #93113	C₂³	semidirect
203. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
204. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
205. #62652	C₂×D₄	semidirect
222. #33020	C₂×D₄	semidirect
223. #33020	C₂×D₄	semidirect
226. #32898	C₂×D₄	semidirect
227. #32898	C₂×D₄	semidirect
228. #20690	C₂×D₄	semidirect
229. #20586	C₂×D₄	semidirect
230. #20586	C₂×D₄	semidirect
231. #20586	C₂×D₄	semidirect
232. #20586	C₂×D₄	semidirect
233. #20586	C₂×D₄	semidirect
234. #20585	C₂×D₄	semidirect
235. #20585	C₂×D₄	semidirect
236. #20585	C₂×D₄	semidirect
242. #9497	C₂×D₄	semidirect
243. #9497	C₂×D₄	semidirect
244. #9497	C₂×D₄	semidirect
245. #9497	C₂×D₄	semidirect
246. #8748	C₂×D₄	semidirect
247. #8748	C₂×D₄	semidirect
248. #8748	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72339050	2
#72339048	2
#72339038	2
#72339036	2
#72338797	2
#72338795	2
#72338734	2
#72338730	2
#72338723	2
#72338718	2
#72337672	2
#72337671	2
#72319290	2
#72252381	2
#72252380	2
#72241350	2
#72236986	2