Subgroups — #72266446

Order 2048.

At least 6827 conjugacy classes of subgroups; only the 480 normal subgroups are shown.

The subgroup lattice has 309 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266378	C₂	1	2	yes	maximal, complemented
2	#72266368	C₂	1	2	yes	maximal, complemented
3	#72265766	C₂	1	1	yes	maximal, characteristic, complemented
4	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
5	#72235186	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234668	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#139716	C₂	1	1	yes	maximal, characteristic, complemented
8	#72219264	C₂	1	1	yes	maximal, characteristic
9	#72219241	C₂	1	1	yes	maximal, characteristic, complemented
10	#72218980	C₂	1	2	yes	maximal, complemented
11	#72218840	C₂	1	2	yes	maximal, complemented
12	C₂²×#3532	C₂²	1	1	yes	characteristic
13	C₂×#34980	C₂²	1	1	yes	characteristic
14	#7626202	C₂²	1	1	yes	characteristic, complemented
15	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
16	#5025789	C₄	1	1	yes	characteristic, complemented
17	#5025782	C₄	1	1	yes	characteristic, complemented
18	#5021140	C₄	1	1	yes	characteristic, complemented
19	#5021138	C₄	1	1	yes	characteristic, complemented
20	#4422949	C₄	1	1	yes	characteristic, complemented
21	#4420586	C₄	1	1	yes	characteristic, complemented
22	#763333	C₂²	1	1	yes	characteristic
23	#686187	C₄	1	1	yes	characteristic, complemented
24	#647656	C₄	1	1	yes	characteristic, complemented
25	#616961	C₂²	1	1	yes	characteristic
26	#616960	C₂²	1	1	yes	characteristic
27	C₂×#15947	C₂²	1	1	yes	characteristic
28	#552670	C₂²	1	1	yes	characteristic
29	#493370	C₂²	1	2	yes	complemented
30	#493357	C₂²	1	2	yes	—
31	#493357	C₂²	1	2	yes	complemented
32	C₂×#12687	C₂²	1	2	yes	complemented
33	#359509	C₂²	1	2	yes	complemented
34	#359501	C₂²	1	2	yes	complemented
35	#359442	C₂²	1	2	yes	—
36	#359442	C₂²	1	2	yes	complemented
37	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
38	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
39	C₂×#7304	C₂²	1	2	yes	complemented
40	#128009	C₂²	1	2	yes	complemented
41	#108238	C₂²	1	2	yes	complemented
42	#108222	C₂²	1	2	yes	complemented
43	C₂⁵×D₄	D₄	1	1	yes	characteristic
44	C₂²×#551	C₂×C₄	1	1	yes	characteristic, complemented
45	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂²×H(3,𝔽₄)	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂²×#560	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂²×#535	C₂³	1	1	yes	characteristic
49	C₂²×#534	C₂³	1	1	yes	characteristic
50	C₂²×#534	C₂³	1	1	yes	characteristic
51	C₂³×#120	D₄	1	2	yes	—
52	C₂³×#120	C₂³	1	1	yes	characteristic
53	C₂³×#120	C₂³	1	1	yes	characteristic
54	C₂×#2849	C₂×C₄	1	1	yes	characteristic
55	C₂×#2849	D₄	1	1	yes	characteristic
56	C₂×#2846	C₂×C₄	1	1	yes	characteristic
57	C₂×#2846	D₄	1	1	yes	characteristic
58	C₂×#2404	D₄	1	2	yes	—
59	C₂×#2613	C₂×C₄	1	1	yes	characteristic
60	C₂×#2613	C₂×C₄	1	1	yes	characteristic
61	C₂×#2613	D₄	1	1	yes	characteristic
62	C₂×#2613	D₄	1	1	yes	characteristic
63	#34171	C₂³	1	2	yes	—
64	C₂×#2308	D₄	1	1	yes	characteristic
65	C₂×#2308	D₄	1	1	yes	characteristic
66	C₂²×#379	D₄	1	1	yes	characteristic
67	C₂×#1913	D₄	1	8	yes	complemented
68	C₂×#1783	C₂³	1	2	yes	—
69	C₂×#1781	C₂³	1	2	yes	—
70	C₂×#1781	C₂³	1	2	yes	—
71	#15948	C₂×C₄	1	1	yes	characteristic, complemented
72	#15948	C₂×C₄	1	1	yes	characteristic, complemented
73	#15947	C₂×C₄	1	1	yes	characteristic
74	#15947	C₂×C₄	1	1	yes	characteristic
75	#15947	C₂×C₄	1	1	yes	characteristic
76	#15947	C₂×C₄	1	1	yes	characteristic
77	#15947	C₂×C₄	1	1	yes	characteristic, complemented
78	#15947	C₂×C₄	1	1	yes	characteristic, complemented
79	#15947	D₄	1	2	yes	—
80	#15947	D₄	1	2	yes	—
81	#15262	C₂×C₄	1	1	yes	characteristic, complemented
82	#15261	C₂×C₄	1	1	yes	characteristic, complemented
83	#15259	C₂×C₄	1	1	yes	characteristic
84	#15259	C₂×C₄	1	1	yes	characteristic
85	#15259	C₂×C₄	1	1	yes	characteristic, complemented
86	#15259	D₄	1	2	yes	—
87	#15258	C₂×C₄	1	1	yes	characteristic
88	#15258	C₂×C₄	1	1	yes	characteristic
89	#15258	C₂×C₄	1	1	yes	characteristic, complemented
90	#15258	D₄	1	2	yes	—
91	#14658	C₂×C₄	1	1	yes	characteristic, complemented
92	#14657	C₂×C₄	1	1	yes	characteristic, complemented
93	#14335	C₂³	1	1	yes	characteristic
94	#14167	C₂×C₄	1	1	yes	characteristic, complemented
95	#14134	C₂×C₄	1	1	yes	characteristic, complemented
96	#13868	D₄	1	2	yes	—
97	C₂×#1438	D₄	1	2	yes	—
98	C₂×#1438	C₂³	1	1	yes	characteristic
99	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
100	C₂⁷	C₂×D₄	1	1	yes	characteristic
101	C₂⁷	C₂×D₄	1	1	yes	characteristic
102	C₂³×#41	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
105	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	2	yes	—
108	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
109	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
110	C₂×#534	C₂×D₄	1	4	yes	—
111	C₂×#534	#41	1	4	yes	—
112	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
113	C₂²×#127	C₂×D₄	1	1	yes	characteristic
114	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
115	C₂²×#124	C₂×D₄	1	1	yes	characteristic
116	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
117	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
118	C₂²×#123	C₂×D₄	1	1	yes	characteristic
119	C₂²×#123	C₂×D₄	1	1	yes	characteristic
120	C₂²×#120	C₂²⋊C₄	1	2	yes	—
121	C₂²×#120	C₂²⋊C₄	1	2	yes	—
122	C₂²×#120	C₂²⋊C₄	1	2	yes	—
123	C₂²×#120	C₂²⋊C₄	1	2	yes	—
124	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
126	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
127	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
128	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
129	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
130	C₂²×#120	C₂×D₄	1	1	yes	characteristic
131	C₂²×#120	C₂×D₄	1	1	yes	characteristic
132	C₂²×#120	C₂×D₄	1	1	yes	characteristic
133	C₂²×#120	C₂×D₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	2	yes	—
138	C₂×#518	C₂×D₄	1	4	yes	complemented
139	C₂²×#117	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
141	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
142	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
146	C₂²×#99	C₂×D₄	1	4	yes	complemented
147	C₂×#393	C₂²⋊C₄	1	2	yes	complemented
148	C₂×#393	C₂²⋊C₄	1	2	yes	complemented
149	C₂×#392	C₂²⋊C₄	1	2	yes	complemented
150	C₂×#392	C₂²⋊C₄	1	2	yes	complemented
151	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
152	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
153	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
154	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₂×#381	C₂×D₄	1	2	yes	—
156	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
158	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
159	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
161	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	#1438	C₂²⋊C₄	1	2	yes	—
165	#1438	C₂²⋊C₄	1	2	yes	—
166	#1438	C₂²⋊C₄	1	2	yes	—
167	#1438	C₂²⋊C₄	1	2	yes	—
168	#1438	C₂²×C₄	1	1	yes	characteristic
169	#1438	C₂²×C₄	1	1	yes	characteristic
170	#1438	C₂²×C₄	1	1	yes	characteristic
171	#1438	C₂²×C₄	1	1	yes	characteristic
172	#1438	C₂×D₄	1	2	yes	—
173	#1438	C₂×D₄	1	2	yes	—
174	#1437	C₂²⋊C₄	1	2	yes	complemented
175	#1437	C₂²⋊C₄	1	2	yes	complemented
176	#1437	C₂²⋊C₄	1	2	yes	complemented
177	#1437	C₂²⋊C₄	1	2	yes	complemented
178	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂⁶	#120	1	2	yes	—
185	C₂⁶	#120	1	2	yes	—
186	C₂⁶	C₂²×D₄	1	1	yes	characteristic
187	C₂⁶	C₂²×D₄	1	1	yes	characteristic
188	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂³×D₄	#120	1	2	yes	—
193	C₂³×D₄	#120	1	2	yes	—
194	C₂³×D₄	#120	1	2	yes	—
195	C₂³×D₄	#123	1	2	yes	—
196	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
197	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
198	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
199	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
200	C₂³×D₄	C₂²×D₄	1	2	yes	—
201	C₂³×D₄	C₂×#41	1	2	yes	—
202	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
203	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
204	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁴×C₄	#120	1	2	yes	—
207	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
208	C₂×#123	C₄×D₄	1	4	yes	—
209	C₂×#123	#121	1	4	yes	—
210	C₂×#120	C₄×D₄	1	4	yes	—
211	C₂×#120	#121	1	4	yes	—
212	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂²×C₂²⋊C₄	#120	1	2	yes	—
225	C₂²×C₂²⋊C₄	#120	1	2	yes	—
226	C₂²×C₂²⋊C₄	#120	1	2	yes	—
227	C₂²×C₂²⋊C₄	#120	1	2	yes	—
228	C₂²×C₂²⋊C₄	#123	1	2	yes	—
229	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂⁵	#379	1	2	yes	—
234	C₂⁵	#379	1	2	yes	—
235	C₂⁵	#386	1	2	yes	—
236	C₂⁵	B(4,𝔽₂)	1	2	yes	—
237	C₂⁵	B(4,𝔽₂)	1	2	yes	—
238	C₂⁵	#458	1	2	yes	—
239	C₂⁵	#458	1	2	yes	—
240	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
241	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁵	C₂×#120	1	1	yes	characteristic
243	C₂⁵	C₂×#120	1	1	yes	characteristic
244	C₂⁵	C₂×#120	1	1	yes	characteristic
245	C₂⁵	C₂×#120	1	1	yes	characteristic
246	C₂⁵	C₂×#123	1	1	yes	characteristic
247	C₂⁵	#534	1	1	yes	characteristic
248	C₂⁵	#534	1	1	yes	characteristic
249	C₂⁵	D₄²	1	2	yes	—
250	C₂⁵	#546	1	2	yes	—
251	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
252	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
253	C₂²×D₄	#518	1	2	yes	—
254	C₂²×D₄	C₂×#121	1	2	yes	—
255	C₂²×D₄	#534	1	2	yes	—
256	C₂²×D₄	D₄²	1	2	yes	—
257	C₂²×D₄	D₄²	1	2	yes	—
258	C₂²×D₄	#546	1	2	yes	—
259	C₂²×D₄	#546	1	2	yes	—
260	C₂³×C₄	#379	1	2	yes	—
261	C₂³×C₄	#379	1	2	yes	—
262	C₂³×C₄	#386	1	2	yes	—
263	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
264	C₂³×C₄	C₂×#120	1	1	yes	characteristic
265	C₂³×C₄	D₄²	1	2	yes	—
266	C₂³×C₄	#546	1	2	yes	—
267	C₂×C₂²⋊C₄	#386	1	2	yes	—
268	C₂×C₂²⋊C₄	#386	1	2	yes	—
269	C₂⁴	#1790	1	2	yes	—
270	C₂⁴	#1790	1	2	yes	—
271	C₂⁴	#1790	1	2	yes	—
272	C₂⁴	#1790	1	2	yes	—
273	C₂⁴	#1889	1	4	yes	complemented
274	C₂⁴	C₂×#379	1	1	yes	characteristic
275	C₂⁴	C₂×#386	1	1	yes	characteristic
276	C₂⁴	#2308	1	1	yes	characteristic
277	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
278	C₂⁴	#2403	1	1	yes	characteristic
279	C₂⁴	#2403	1	1	yes	characteristic
280	C₂⁴	#2405	1	1	yes	characteristic
281	C₂⁴	#2405	1	1	yes	characteristic
282	C₂⁴	#2410	1	2	yes	—
283	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
284	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
285	C₂⁴	C₂×#458	1	2	yes	—
286	C₂²×C₄	#1889	1	4	yes	complemented
287	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
288	C₂²×C₄	#2410	1	2	yes	—
289	C₂³	#12753	1	4	yes	complemented
290	C₂³	#13867	1	1	yes	characteristic
291	C₂³	C₂×#1790	1	2	yes	—
292	C₂³	C₂×#1889	1	2	yes	—
293	C₂³	#23895	1	2	yes	—
294	C₂³	#23900	1	1	yes	characteristic
295	C₂³	#23900	1	2	yes	—
296	C₂³	#23900	1	2	yes	—
297	C₂³	#23901	1	1	yes	characteristic
298	C₂³	#24056	1	2	yes	—
299	C₂²	#245225	1	2	yes	—
300	C₂²	#245226	1	2	yes	—
301	C₂²	#359501	1	1	yes	characteristic
302	C₂²	#359549	1	1	yes	characteristic
303	C₂²	#359552	1	1	yes	characteristic
304	C₂²	C₂×#12753	1	2	yes	—
305	C₂²	#493562	1	2	yes	—
306	C₂	#72235131	1	2	yes	—
307	C₂	#72236754	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359552
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72219264	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266378	C₂	semidirect
2. #72266368	C₂	semidirect
3. #72265766	C₂	semidirect
4. #72240132	C₂	semidirect
5. #72235186	C₂	semidirect
6. #72234668	C₂	semidirect
7. C₂×#139716	C₂	semidirect
9. #72219241	C₂	semidirect
10. #72218980	C₂	semidirect
11. #72218840	C₂	semidirect
14. #7626202	C₂²	semidirect
15. C₂×#21746	C₂²	semidirect
16. #5025789	C₄	semidirect
17. #5025782	C₄	semidirect
18. #5021140	C₄	semidirect
19. #5021138	C₄	semidirect
20. #4422949	C₄	semidirect
21. #4420586	C₄	semidirect
23. #686187	C₄	semidirect
24. #647656	C₄	semidirect
29. #493370	C₂²	semidirect
31. #493357	C₂²	semidirect
32. C₂×#12687	C₂²	semidirect
33. #359509	C₂²	semidirect
34. #359501	C₂²	semidirect
36. #359442	C₂²	semidirect
37. C₂×#8547	C₂²	semidirect
38. C₂×#8541	C₂²	semidirect
39. C₂×#7304	C₂²	semidirect
40. #128009	C₂²	semidirect
41. #108238	C₂²	semidirect
42. #108222	C₂²	semidirect
44. C₂²×#551	C₂×C₄	semidirect
45. C₂²×D₄²	C₂×C₄	semidirect
46. C₂²×H(3,𝔽₄)	C₂×C₄	semidirect
47. C₂²×#560	C₂×C₄	semidirect
67. C₂×#1913	D₄	semidirect
71. #15948	C₂×C₄	semidirect
72. #15948	C₂×C₄	semidirect
77. #15947	C₂×C₄	semidirect
78. #15947	C₂×C₄	semidirect
81. #15262	C₂×C₄	semidirect
82. #15261	C₂×C₄	semidirect
85. #15259	C₂×C₄	semidirect
89. #15258	C₂×C₄	semidirect
91. #14658	C₂×C₄	semidirect
92. #14657	C₂×C₄	semidirect
94. #14167	C₂×C₄	semidirect
95. #14134	C₂×C₄	semidirect
99. C₂⁷	C₂²⋊C₄	semidirect
103. C₂⁴×D₄	C₂²⋊C₄	semidirect
104. C₂⁴×D₄	C₂²⋊C₄	semidirect
109. C₂⁵×C₄	C₂²⋊C₄	semidirect
138. C₂×#518	C₂×D₄	semidirect
146. C₂²×#99	C₂×D₄	semidirect
147. C₂×#393	C₂²⋊C₄	semidirect
148. C₂×#393	C₂²⋊C₄	semidirect
149. C₂×#392	C₂²⋊C₄	semidirect
150. C₂×#392	C₂²⋊C₄	semidirect
151. C₂×#381	C₂²⋊C₄	semidirect
152. C₂×#381	C₂²⋊C₄	semidirect
153. C₂×#381	C₂²⋊C₄	semidirect
154. C₂×#381	C₂²⋊C₄	semidirect
156. C₂×#379	C₂²⋊C₄	semidirect
157. C₂×#379	C₂²⋊C₄	semidirect
158. C₂×#379	C₂²⋊C₄	semidirect
159. C₂×#379	C₂²⋊C₄	semidirect
160. C₂×#379	C₂²⋊C₄	semidirect
161. C₂×#379	C₂²⋊C₄	semidirect
162. C₂×#379	C₂²⋊C₄	semidirect
163. C₂×#379	C₂²⋊C₄	semidirect
174. #1437	C₂²⋊C₄	semidirect
175. #1437	C₂²⋊C₄	semidirect
176. #1437	C₂²⋊C₄	semidirect
177. #1437	C₂²⋊C₄	semidirect
273. C₂⁴	#1889	semidirect
286. C₂²×C₄	#1889	semidirect
289. C₂³	#12753	semidirect

Maximal subgroups

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

subgroup	index
#72266378	2
#72266368	2
#72265766	2
#72240132	2
#72235186	2
#72234668	2
C₂×#139716	2
#72219264	2
#72219241	2
#72218980	2
#72218840	2