Subgroups — C₂×#72216741 #72337614

Order 8192.

At least 53390 conjugacy classes of subgroups; only the 846 normal subgroups are shown.

The subgroup lattice has 307 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#72216719	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72216682	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#72216698	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72216504	C₂	1	2	yes	maximal, complemented
5	C₂×#72216490	C₂	1	2	yes	maximal, complemented
6	C₂×#72216484	C₂²	1	2	yes	complemented
7	C₂×#72216398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#72216329	C₂²	1	1	yes	characteristic, complemented
9	C₂×#72216433	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#72216466	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#72216449	C₂²	1	1	yes	characteristic, complemented
12	C₂×#72216427	C₂²	1	2	yes	complemented
13	C₂×#72216427	C₂²	1	1	yes	characteristic, complemented
14	C₂×#72216662	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#72216481	C₂²	1	1	yes	characteristic, complemented
16	C₂×#72210578	C₂²	1	1	yes	characteristic
17	C₂×#72210578	C₂²	1	1	yes	characteristic, complemented
18	C₂×#72216323	C₂²	1	1	yes	characteristic
19	C₂×#187940	D₄	1	1	yes	characteristic, complemented
20	C₂×#187940	D₄	1	1	yes	characteristic, complemented
21	C₂×#72215688	C₂	1	2	yes	maximal, complemented
22	C₂×#72215653	C₂²	1	2	yes	complemented
23	C₂×#72213827	C₂²	1	2	yes	complemented
24	C₂×#72215671	C₂²	1	2	yes	complemented
25	C₂×#120²	C₂²	1	1	yes	characteristic, complemented
26	C₂×#72216292	C₂²	1	1	yes	characteristic, complemented
27	C₂×#110086	D₄	1	2	yes	complemented
28	C₂×#648360	C₂³	1	1	yes	characteristic
29	C₂×#72210587	C₂²	1	2	yes	—
30	C₂×#139718	D₄	1	2	yes	complemented
31	C₂×#233541	D₄	1	2	yes	complemented
32	C₂×#10586472	D₄	1	1	yes	characteristic, complemented
33	C₂×#346446	D₄	1	2	yes	complemented
34	C₂×#188035	D₄	1	1	yes	characteristic, complemented
35	C₂×#139716	D₄	1	2	yes	complemented
36	C₂×#647656	C₂³	1	1	yes	characteristic
37	C₂×#72210568	C₂	1	2	yes	maximal, complemented
38	C₂×#72210489	C₂²	1	2	yes	complemented
39	C₂×#72210547	C₂²	1	2	yes	complemented
40	C₂×#72210482	C₂²	1	2	yes	complemented
41	C₂×#72210482	C₂²	1	2	yes	complemented
42	C₂×#134033	C₂³	1	2	yes	—
43	C₂×#72209844	C₂²	1	2	yes	complemented
44	C₂×#133822	C₂³	1	2	yes	—
45	C₂×#72209716	C₂²	1	1	yes	characteristic
46	C₂×#72209716	C₂²	1	1	yes	characteristic, complemented
47	C₂×#72209716	C₂²	1	2	yes	complemented
48	C₂×#115690	D₄	1	2	yes	complemented
49	C₂×#115690	C₂³	1	2	yes	—
50	C₂×#115690	C₂³	1	1	yes	characteristic
51	C₂×#115690	C₂³	1	1	yes	characteristic
52	C₂×#6499867	C₂³	1	2	yes	—
53	C₂×#6499867	C₂³	1	1	yes	characteristic
54	C₂×#6499867	C₂³	1	1	yes	characteristic
55	#72216741	C₂	1	16	yes	maximal, direct product factor
56	#72216719	C₂²	1	8	yes	complemented
57	#72216698	C₂²	1	8	yes	complemented
58	#72216682	C₂²	1	8	yes	complemented
59	#72216662	C₂²	1	8	yes	complemented
60	#72216504	C₂²	1	16	yes	complemented
61	#72216490	C₂²	1	16	yes	complemented
62	#72216484	C₂³	1	8	yes	complemented
63	#72216481	C₂³	1	4	yes	complemented
64	#72216466	C₂²	1	8	yes	complemented
65	#72216449	C₂³	1	4	yes	complemented
66	#72216433	C₂²	1	8	yes	complemented
67	#72216427	C₂³	1	4	yes	complemented
68	#72216427	C₂³	1	8	yes	complemented
69	#72216398	C₂²	1	8	yes	complemented
70	#72216329	C₂³	1	4	yes	complemented
71	#72216323	D₄	1	4	yes	complemented
72	#72216323	C₂³	1	4	yes	—
73	#72216292	C₂³	1	4	yes	complemented
74	#72215688	C₂²	1	16	yes	complemented
75	#72215671	C₂³	1	8	yes	complemented
76	#72215653	C₂³	1	8	yes	complemented
77	#120²	C₂³	1	4	yes	complemented
78	C₂×#347042	D₄	1	2	yes	complemented
79	#72213827	C₂³	1	8	yes	complemented
80	#72210587	D₄	1	8	yes	complemented
81	#72210587	C₂³	1	8	yes	—
82	#72210578	D₄	1	4	yes	complemented
83	#72210578	C₂³	1	4	yes	—
84	#72210578	C₂³	1	4	yes	complemented
85	#72210568	C₂²	1	16	yes	complemented
86	#72210547	C₂³	1	8	yes	complemented
87	#72210489	C₂³	1	8	yes	complemented
88	#72210482	C₂³	1	8	yes	complemented
89	#72210482	C₂³	1	8	yes	complemented
90	C₂×#6342371	D₄	1	2	yes	complemented
91	C₂×#6342371	C₂³	1	1	yes	characteristic
92	#72209844	C₂³	1	8	yes	complemented
93	#72209716	D₄	1	4	yes	complemented
94	#72209716	C₂³	1	4	yes	—
95	#72209716	C₂³	1	4	yes	complemented
96	#72209716	C₂³	1	8	yes	complemented
97	C₂⁹	C₂×D₄	1	1	yes	characteristic, complemented
98	#10586472	C₂×D₄	1	4	yes	complemented
99	C₂×#62817	C₂×D₄	1	1	yes	characteristic
100	C₂×#62817	C₂×D₄	1	1	yes	characteristic
101	C₂×#62817	C₂×D₄	1	2	yes	complemented
102	C₂³×D₄²	C₂×D₄	1	1	yes	characteristic
103	C₂²×#2846	C₂×D₄	1	2	yes	—
104	C₂²×#2846	C₂⁴	1	1	yes	characteristic
105	C₂²×#2403	C₂×D₄	1	1	yes	characteristic, complemented
106	#6499867	C₂×D₄	1	2	yes	—
107	#6499867	C₂×D₄	1	2	yes	—
108	#6499867	C₂×D₄	1	2	yes	—
109	#6499867	C₂×D₄	1	2	yes	—
110	#6499867	C₂×D₄	1	4	yes	complemented
111	#6499867	C₂⁴	1	4	yes	—
112	#6499867	C₂⁴	1	2	yes	—
113	#6499867	C₂⁴	1	2	yes	—
114	C₂×#21746	C₂×D₄	1	2	yes	—
115	C₂×#21746	C₂×D₄	1	1	yes	characteristic
116	C₂×#21746	C₂×D₄	1	1	yes	characteristic
117	C₂×#21746	C₂×D₄	1	2	yes	complemented
118	#6342371	C₂×D₄	1	2	yes	complemented
119	#6342371	C₂×D₄	1	8	yes	complemented
120	#6342371	C₂⁴	1	2	yes	—
121	#648360	C₂×D₄	1	2	yes	complemented
122	#648360	C₂⁴	1	2	yes	—
123	#647656	C₂×D₄	1	4	yes	—
124	#647656	C₂×D₄	1	2	yes	—
125	#647656	C₂⁴	1	2	yes	—
126	C₂×#15947	C₂×D₄	1	2	yes	—
127	C₂×#15258	C₂×D₄	1	2	yes	—
128	C₂×#14679	C₂×D₄	1	1	yes	characteristic, complemented
129	C₂×#14679	C₂×D₄	1	2	yes	complemented
130	C₂×#14134	C₂×D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄²	C₂×D₄	1	1	yes	characteristic, complemented
132	#347042	C₂×D₄	1	8	yes	complemented
133	#346446	C₂×D₄	1	8	yes	complemented
134	#233541	C₂×D₄	1	8	yes	complemented
135	C₂×#8547	C₂×D₄	1	2	yes	complemented
136	#188035	C₂×D₄	1	4	yes	complemented
137	C₂×#8541	C₂×D₄	1	2	yes	complemented
138	#187940	C₂×D₄	1	4	yes	complemented
139	#187940	C₂×D₄	1	4	yes	complemented
140	C₂×#8101	C₂×D₄	1	2	yes	complemented
141	#139718	C₂×D₄	1	8	yes	complemented
142	#139716	C₂×D₄	1	8	yes	complemented
143	#134033	C₂⁴	1	4	yes	—
144	#133822	C₂×D₄	1	4	yes	complemented
145	#133822	C₂⁴	1	4	yes	—
146	#115690	C₂×D₄	1	2	yes	complemented
147	#115690	C₂×D₄	1	8	yes	complemented
148	#115690	C₂×D₄	1	2	yes	complemented
149	#115690	C₂⁴	1	4	yes	—
150	#115690	C₂⁴	1	2	yes	—
151	#115690	C₂⁴	1	2	yes	—
152	#110086	C₂×D₄	1	8	yes	complemented
153	C₂⁸	C₂²×D₄	1	1	yes	characteristic
154	C₂⁸	C₂²×D₄	1	2	yes	complemented
155	#62817	#120	1	2	yes	—
156	#62817	C₂²×D₄	1	2	yes	—
157	#62817	C₂²×D₄	1	2	yes	—
158	#62817	C₂²×D₄	1	4	yes	complemented
159	C₂²×D₄²	#120	1	2	yes	—
160	C₂²×D₄²	C₂²×D₄	1	2	yes	—
161	C₂³×#127	#120	1	1	yes	characteristic
162	C₂³×#120	#120	1	1	yes	characteristic
163	C₂³×#120	#120	1	2	yes	—
164	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
165	C₂³×#120	C₂²×D₄	1	2	yes	—
166	C₂×#2846	#120	1	4	yes	—
167	C₂×#2846	C₂²×D₄	1	1	yes	characteristic
168	C₂×#2846	C₂²×D₄	1	1	yes	characteristic
169	C₂×#2846	C₂²×D₄	1	2	yes	—
170	C₂×#2846	C₂²×D₄	1	4	yes	—
171	C₂×#2846	C₂²×D₄	1	1	yes	characteristic
172	C₂×#2846	H(5,𝔽₂)	1	2	yes	—
173	C₂×#2846	C₂⁵	1	1	yes	characteristic
174	C₂×#2403	C₂²×D₄	1	2	yes	complemented
175	C₂²×#379	#120	1	2	yes	—
176	C₂²×#379	C₂²×D₄	1	1	yes	characteristic
177	C₂²×#379	H(5,𝔽₂)	1	2	yes	—
178	#21746	#120	1	4	yes	—
179	#21746	#120	1	2	yes	—
180	#21746	C₂²×D₄	1	4	yes	—
181	#21746	C₂²×D₄	1	2	yes	—
182	#21746	C₂²×D₄	1	2	yes	—
183	#21746	C₂²×D₄	1	4	yes	complemented
184	#15947	#120	1	4	yes	—
185	#15947	C₂²×D₄	1	4	yes	—
186	#15258	#120	1	4	yes	—
187	#15258	C₂²×D₄	1	4	yes	—
188	#14679	C₂²×D₄	1	2	yes	complemented
189	#14679	C₂²×D₄	1	4	yes	complemented
190	#14134	#120	1	2	yes	—
191	#14134	C₂²×D₄	1	2	yes	—
192	C₂×#1438	#120	1	2	yes	—
193	C₂²⋊C₄²	C₂²×D₄	1	2	yes	complemented
194	#8547	C₂²×D₄	1	4	yes	complemented
195	#8541	C₂²×D₄	1	4	yes	complemented
196	#8101	C₂²×D₄	1	4	yes	complemented
197	C₂⁷	B(4,𝔽₂)	1	1	yes	characteristic, complemented
198	C₂⁷	C₂×#120	1	1	yes	characteristic
199	C₂⁷	C₂×#120	1	1	yes	characteristic
200	C₂⁷	D₄²	1	2	yes	—
201	C₂⁷	D₄²	1	2	yes	—
202	C₂⁷	C₂³×D₄	1	1	yes	characteristic
203	C₂⁴×D₄	B(4,𝔽₂)	1	2	yes	—
204	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic, complemented
205	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
206	C₂²×#127	B(4,𝔽₂)	1	2	yes	complemented
207	C₂²×#127	C₂×#120	1	2	yes	—
208	C₂²×#120	B(4,𝔽₂)	1	4	yes	—
209	C₂²×#120	B(4,𝔽₂)	1	2	yes	complemented
210	C₂²×#120	C₂×#120	1	1	yes	characteristic
211	C₂²×#120	C₂×#120	1	1	yes	characteristic
212	C₂²×#120	C₂×#120	1	2	yes	—
213	C₂²×#120	C₂×#120	1	4	yes	—
214	C₂²×#120	C₂×#120	1	2	yes	—
215	C₂²×#120	#534	1	1	yes	characteristic
216	C₂²×#120	D₄²	1	2	yes	—
217	C₂²×#120	D₄²	1	2	yes	—
218	C₂²×#120	C₂³×D₄	1	1	yes	characteristic
219	C₂²×#120	C₂³×D₄	1	2	yes	—
220	C₂³×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
221	C₂³×C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic, complemented
222	C₂³×C₂²⋊C₄	#534	1	1	yes	characteristic
223	C₂³×C₂²⋊C₄	D₄²	1	2	yes	—
224	C₂³×C₄²	B(4,𝔽₂)	1	1	yes	characteristic, complemented
225	C₂×#379	C₂×#120	1	4	yes	—
226	C₂×#379	C₂×#120	1	1	yes	characteristic
227	C₂×#379	#534	1	2	yes	—
228	C₂×#379	D₄²	1	2	yes	—
229	C₂×#379	D₄²	1	2	yes	—
230	C₂×#379	D₄²	1	2	yes	—
231	C₂×#379	C₂³×D₄	1	1	yes	characteristic
232	C₂×#379	C₂×H(5,𝔽₂)	1	2	yes	—
233	#1438	C₂×#120	1	4	yes	—
234	C₂⁶	#2196	1	2	yes	complemented
235	C₂⁶	#2403	1	1	yes	characteristic
236	C₂⁶	#2403	1	2	yes	—
237	C₂⁶	#2403	1	1	yes	characteristic
238	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
239	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
240	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
241	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	complemented
242	C₂⁶	C₂²×#120	1	1	yes	characteristic
243	C₂⁶	C₂×D₄²	1	2	yes	—
244	C₂³×D₄	#2196	1	4	yes	complemented
245	C₂³×D₄	#2403	1	1	yes	characteristic
246	C₂³×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
247	C₂³×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
248	C₂³×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
249	C₂³×D₄	C₂×B(4,𝔽₂)	1	2	yes	complemented
250	C₂³×D₄	C₂²×#120	1	1	yes	characteristic
251	C₂⁴×C₄	#2196	1	2	yes	complemented
252	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	#2403	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	#2403	1	2	yes	—
255	C₂²×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
256	C₂²×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	complemented
257	C₂²×C₂²⋊C₄	C₂×#534	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₂×D₄²	1	2	yes	—
259	C₂²×C₄²	C₂×B(4,𝔽₂)	1	2	yes	complemented
260	C₂⁵	#23895	1	1	yes	characteristic
261	C₂⁵	#23895	1	1	yes	characteristic
262	C₂⁵	#23900	1	1	yes	characteristic
263	C₂⁵	#23900	1	1	yes	characteristic
264	C₂⁵	#23900	1	2	yes	—
265	C₂⁵	#23900	1	1	yes	characteristic
266	C₂⁵	#23900	1	1	yes	characteristic
267	C₂⁵	#23900	1	1	yes	characteristic
268	C₂⁵	C₂×#2196	1	2	yes	—
269	C₂⁵	C₂×#2196	1	2	yes	—
270	C₂⁵	C₂×#2196	1	4	yes	complemented
271	C₂⁵	#33551	1	2	yes	—
272	C₂⁵	#33551	1	2	yes	—
273	C₂⁵	C₂×#2403	1	1	yes	characteristic
274	C₂⁵	C₂²×B(4,𝔽₂)	1	2	yes	—
275	C₂⁵	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
276	C₂³×C₄	#23900	1	1	yes	characteristic
277	C₂³×C₄	C₂×#2196	1	4	yes	complemented
278	C₂³×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
279	C₂⁴	#245225	1	1	yes	characteristic
280	C₂⁴	#245225	1	1	yes	characteristic
281	C₂⁴	#245225	1	1	yes	characteristic
282	C₂⁴	#245225	1	1	yes	characteristic
283	C₂⁴	#499787	1	2	yes	—
284	C₂⁴	#499787	1	2	yes	—
285	C₂⁴	#499787	1	2	yes	—
286	C₂⁴	#499787	1	2	yes	—
287	C₂⁴	C₂×#23900	1	1	yes	characteristic
288	C₂⁴	C₂×#23900	1	1	yes	characteristic
289	C₂⁴	C₂×#23895	1	1	yes	characteristic
290	C₂⁴	C₂²×#2196	1	2	yes	—
291	C₂⁴	C₂×#33551	1	2	yes	—
292	C₂³	B(5,𝔽₂)	1	2	yes	—
293	C₂³	B(5,𝔽₂)	1	2	yes	—
294	C₂³	#72210587	1	1	yes	characteristic
295	C₂³	#72210587	1	2	yes	—
296	C₂³	#72210587	1	1	yes	characteristic
297	C₂³	C₂×#245225	1	1	yes	characteristic
298	C₂³	C₂×#499787	1	2	yes	—
299	C₂²	#72216737	1	1	yes	characteristic
300	C₂²	#72216737	1	2	yes	—
301	C₂²	#72216737	1	1	yes	characteristic
302	C₂²	C₂×B(5,𝔽₂)	1	2	yes	—
303	C₂²	C₂×#72210587	1	1	yes	characteristic
304	C₂	#72216741	1	2	yes	direct product factor
305	C₂	C₂×#72216737	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72216737
commutator, Frattini, cosocle	C₂×#2846	C₂⁵
LCS	G ▷ C₂×#2846 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁶ ◁ C₂²×#2846 ◁ G
LECS	G ▷ C₂×#2846 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#72216719	C₂	semidirect
2. C₂×#72216682	C₂	semidirect
3. C₂×#72216698	C₂	semidirect
4. C₂×#72216504	C₂	semidirect
5. C₂×#72216490	C₂	semidirect
6. C₂×#72216484	C₂²	semidirect
7. C₂×#72216398	C₂	semidirect
8. C₂×#72216329	C₂²	semidirect
9. C₂×#72216433	C₂	semidirect
10. C₂×#72216466	C₂	semidirect
11. C₂×#72216449	C₂²	semidirect
12. C₂×#72216427	C₂²	semidirect
13. C₂×#72216427	C₂²	semidirect
14. C₂×#72216662	C₂	semidirect
15. C₂×#72216481	C₂²	semidirect
17. C₂×#72210578	C₂²	semidirect
19. C₂×#187940	D₄	semidirect
20. C₂×#187940	D₄	semidirect
21. C₂×#72215688	C₂	semidirect
22. C₂×#72215653	C₂²	semidirect
23. C₂×#72213827	C₂²	semidirect
24. C₂×#72215671	C₂²	semidirect
25. C₂×#120²	C₂²	semidirect
26. C₂×#72216292	C₂²	semidirect
27. C₂×#110086	D₄	semidirect
30. C₂×#139718	D₄	semidirect
31. C₂×#233541	D₄	semidirect
32. C₂×#10586472	D₄	semidirect
33. C₂×#346446	D₄	semidirect
34. C₂×#188035	D₄	semidirect
35. C₂×#139716	D₄	semidirect
37. C₂×#72210568	C₂	semidirect
38. C₂×#72210489	C₂²	semidirect
39. C₂×#72210547	C₂²	semidirect
40. C₂×#72210482	C₂²	semidirect
41. C₂×#72210482	C₂²	semidirect
43. C₂×#72209844	C₂²	semidirect
46. C₂×#72209716	C₂²	semidirect
47. C₂×#72209716	C₂²	semidirect
48. C₂×#115690	D₄	semidirect
55. #72216741	C₂	direct (N × H)
56. #72216719	C₂²	semidirect
57. #72216698	C₂²	semidirect
58. #72216682	C₂²	semidirect
59. #72216662	C₂²	semidirect
60. #72216504	C₂²	semidirect
61. #72216490	C₂²	semidirect
62. #72216484	C₂³	semidirect
63. #72216481	C₂³	semidirect
64. #72216466	C₂²	semidirect
65. #72216449	C₂³	semidirect
66. #72216433	C₂²	semidirect
67. #72216427	C₂³	semidirect
68. #72216427	C₂³	semidirect
69. #72216398	C₂²	semidirect
70. #72216329	C₂³	semidirect
71. #72216323	D₄	semidirect
73. #72216292	C₂³	semidirect
74. #72215688	C₂²	semidirect
75. #72215671	C₂³	semidirect
76. #72215653	C₂³	semidirect
77. #120²	C₂³	semidirect
78. C₂×#347042	D₄	semidirect
79. #72213827	C₂³	semidirect
80. #72210587	D₄	semidirect
82. #72210578	D₄	semidirect
84. #72210578	C₂³	semidirect
85. #72210568	C₂²	semidirect
86. #72210547	C₂³	semidirect
87. #72210489	C₂³	semidirect
88. #72210482	C₂³	semidirect
89. #72210482	C₂³	semidirect
90. C₂×#6342371	D₄	semidirect
92. #72209844	C₂³	semidirect
93. #72209716	D₄	semidirect
95. #72209716	C₂³	semidirect
96. #72209716	C₂³	semidirect
97. C₂⁹	C₂×D₄	semidirect
98. #10586472	C₂×D₄	semidirect
101. C₂×#62817	C₂×D₄	semidirect
105. C₂²×#2403	C₂×D₄	semidirect
110. #6499867	C₂×D₄	semidirect
117. C₂×#21746	C₂×D₄	semidirect
118. #6342371	C₂×D₄	semidirect
119. #6342371	C₂×D₄	semidirect
121. #648360	C₂×D₄	semidirect
128. C₂×#14679	C₂×D₄	semidirect
129. C₂×#14679	C₂×D₄	semidirect
131. C₂×C₂²⋊C₄²	C₂×D₄	semidirect
132. #347042	C₂×D₄	semidirect
133. #346446	C₂×D₄	semidirect
134. #233541	C₂×D₄	semidirect
135. C₂×#8547	C₂×D₄	semidirect
136. #188035	C₂×D₄	semidirect
137. C₂×#8541	C₂×D₄	semidirect
138. #187940	C₂×D₄	semidirect
139. #187940	C₂×D₄	semidirect
140. C₂×#8101	C₂×D₄	semidirect
141. #139718	C₂×D₄	semidirect
142. #139716	C₂×D₄	semidirect
144. #133822	C₂×D₄	semidirect
146. #115690	C₂×D₄	semidirect
147. #115690	C₂×D₄	semidirect
148. #115690	C₂×D₄	semidirect
152. #110086	C₂×D₄	semidirect
154. C₂⁸	C₂²×D₄	semidirect
158. #62817	C₂²×D₄	semidirect
174. C₂×#2403	C₂²×D₄	semidirect
183. #21746	C₂²×D₄	semidirect
188. #14679	C₂²×D₄	semidirect
189. #14679	C₂²×D₄	semidirect
193. C₂²⋊C₄²	C₂²×D₄	semidirect
194. #8547	C₂²×D₄	semidirect
195. #8541	C₂²×D₄	semidirect
196. #8101	C₂²×D₄	semidirect
197. C₂⁷	B(4,𝔽₂)	semidirect
204. C₂⁴×D₄	B(4,𝔽₂)	semidirect
206. C₂²×#127	B(4,𝔽₂)	semidirect
209. C₂²×#120	B(4,𝔽₂)	semidirect
221. C₂³×C₂²⋊C₄	B(4,𝔽₂)	semidirect
224. C₂³×C₄²	B(4,𝔽₂)	semidirect
234. C₂⁶	#2196	semidirect
241. C₂⁶	C₂×B(4,𝔽₂)	semidirect
244. C₂³×D₄	#2196	semidirect
249. C₂³×D₄	C₂×B(4,𝔽₂)	semidirect
251. C₂⁴×C₄	#2196	semidirect
256. C₂²×C₂²⋊C₄	C₂×B(4,𝔽₂)	semidirect
259. C₂²×C₄²	C₂×B(4,𝔽₂)	semidirect
270. C₂⁵	C₂×#2196	semidirect
277. C₂³×C₄	C₂×#2196	semidirect
304. C₂	#72216741	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#72216719	2
C₂×#72216682	2
C₂×#72216698	2
C₂×#72216504	2
C₂×#72216490	2
C₂×#72216398	2
C₂×#72216433	2
C₂×#72216466	2
C₂×#72216662	2
C₂×#72215688	2
C₂×#72210568	2
#72216741	2

Subgroups — C2×#72216741 #72337614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72216741 #72337614