Subgroups — #72262736

Order 2048.

At least 8188 conjugacy classes of subgroups; only the 2528 normal subgroups are shown.

The subgroup lattice has 688 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262513	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262381	C₂	1	1	yes	maximal, characteristic, complemented
3	#72262354	C₂	1	1	yes	maximal, characteristic, complemented
4	#72256546	C₂	1	1	yes	maximal, characteristic, complemented
5	#72255705	C₂	1	4	yes	maximal, complemented
6	#72251303	C₂	1	1	yes	maximal, characteristic, complemented
7	#72251204	C₂	1	1	yes	maximal, characteristic, complemented
8	#72251201	C₂	1	4	yes	maximal, complemented
9	#72249533	C₂	1	1	yes	maximal, characteristic, complemented
10	#72237236	C₂	1	1	yes	maximal, characteristic, complemented
11	#72236790	C₂	1	1	yes	maximal, characteristic, complemented
12	#72236780	C₂	1	1	yes	maximal, characteristic, complemented
13	#72235935	C₂	1	4	yes	maximal, complemented
14	C₂×#374114	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#394249	C₂	1	4	yes	maximal, complemented
16	#72235090	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#359472	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×#3003	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#6628842	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁶×D₄	C₂²	1	1	yes	characteristic
21	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂³×#525	C₂²	1	1	yes	characteristic
24	C₂×#60423	C₂²	1	2	yes	complemented
25	C₂²×#3003	C₂²	1	4	yes	—
26	C₂²×#3003	C₂²	1	4	yes	—
27	C₂²×#3003	C₂²	1	1	yes	characteristic
28	C₂²×#3003	C₂²	1	1	yes	characteristic
29	C₂²×#3003	C₂²	1	2	yes	complemented
30	C₂²×#3003	C₂²	1	2	yes	complemented
31	C₂³×#407	C₂²	1	1	yes	characteristic
32	C₂³×#418	C₂²	1	1	yes	characteristic
33	C₂³×#418	C₂²	1	1	yes	characteristic
34	C₂×#36614	C₂²	1	1	yes	characteristic
35	#7628649	C₂²	1	1	yes	characteristic, complemented
36	C₂×#34171	C₂²	1	1	yes	characteristic
37	C₂×#34171	C₂²	1	1	yes	characteristic
38	C₂×#34171	C₂²	1	4	yes	complemented
39	#6431965	C₂²	1	2	yes	complemented
40	C₂×#23443	C₂²	1	4	yes	complemented
41	#6431766	C₂²	1	2	yes	complemented
42	C₂×#23407	C₂²	1	4	yes	complemented
43	C₂²×#1904	C₂²	1	2	yes	complemented
44	C₂²×#1904	C₂²	1	4	yes	complemented
45	C₂×#20983	C₂²	1	1	yes	characteristic, complemented
46	#6371477	C₂²	1	1	yes	characteristic, complemented
47	#6371420	C₂²	1	2	yes	complemented
48	C₂×#20902	C₂²	1	1	yes	characteristic, complemented
49	#6371257	C₂²	1	1	yes	characteristic, complemented
50	C₂×#20605	C₂²	1	1	yes	characteristic, complemented
51	#6370715	C₂²	1	1	yes	characteristic, complemented
52	C₂×#20598	C₂²	1	1	yes	characteristic
53	C₂×#20598	C₂²	1	1	yes	characteristic
54	C₂×#20598	C₂²	1	2	yes	complemented
55	C₂×#20598	C₂²	1	2	yes	complemented
56	C₂×#20584	C₂²	1	1	yes	characteristic, complemented
57	C₂×#20579	C₂²	1	1	yes	characteristic
58	#607558	C₂²	1	1	yes	characteristic
59	#607558	C₂²	1	1	yes	characteristic
60	#517415	C₂²	1	1	yes	characteristic
61	#517415	C₂²	1	1	yes	characteristic
62	#517415	C₂²	1	4	yes	complemented
63	C₂×#11183	C₂²	1	2	yes	complemented
64	C₂×#11073	C₂²	1	4	yes	complemented
65	C₂×#11071	C₂²	1	4	yes	complemented
66	C₂×#11030	C₂²	1	4	yes	complemented
67	C₂×#11030	C₂²	1	4	yes	complemented
68	C₂×#11030	C₂²	1	4	yes	complemented
69	#357571	C₂²	1	4	yes	complemented
70	C₂×#11012	C₂²	1	2	yes	complemented
71	C₂×#11012	C₂²	1	4	yes	complemented
72	C₂×#10994	C₂²	1	4	yes	complemented
73	C₂×#10994	C₂²	1	4	yes	complemented
74	C₂×#10994	C₂²	1	4	yes	complemented
75	#357529	C₂²	1	4	yes	complemented
76	C₂×#10785	C₂²	1	2	yes	complemented
77	#353416	C₂²	1	1	yes	characteristic, complemented
78	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
79	#353407	C₂²	1	1	yes	characteristic, complemented
80	#353397	C₂²	1	1	yes	characteristic, complemented
81	#353386	C₂²	1	1	yes	characteristic, complemented
82	C₂×#10776	C₂²	1	4	yes	complemented
83	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
84	C₂×#10717	C₂²	1	1	yes	characteristic, complemented
85	C₂×#10716	C₂²	1	1	yes	characteristic, complemented
86	#123605	C₂²	1	4	yes	complemented
87	#123560	C₂²	1	4	yes	complemented
88	#123547	C₂²	1	4	yes	complemented
89	#123535	C₂²	1	4	yes	complemented
90	#123531	C₂²	1	4	yes	complemented
91	C₂⁴×#41	C₂³	1	1	yes	characteristic
92	C₂⁵×D₄	D₄	1	8	yes	complemented
93	C₂⁵×D₄	C₂³	1	2	yes	—
94	C₂⁵×D₄	C₂³	1	2	yes	—
95	C₂⁵×D₄	C₂³	1	1	yes	characteristic
96	C₂⁵×D₄	C₂³	1	1	yes	characteristic
97	C₂⁶×C₄	C₂³	1	1	yes	characteristic
98	C₂³×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
99	C₂³×AGL(1,ℤ/8)	C₂³	1	4	yes	—
100	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
101	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
102	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
103	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
104	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
105	C₂⁴×SD₁₆	D₄	1	2	yes	complemented
106	C₂⁴×D₈	D₄	1	2	yes	complemented
107	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
108	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×#3449	C₂³	1	2	yes	complemented
110	C₂²×#525	C₂³	1	4	yes	—
111	C₂²×#525	C₂³	1	2	yes	—
112	C₂²×#525	C₂³	1	1	yes	characteristic
113	C₂²×#518	C₂³	1	2	yes	—
114	C₂²×#518	C₂³	1	2	yes	—
115	C₂³×#117	C₂³	1	1	yes	characteristic
116	C₂×#3003	D₄	1	32	yes	complemented
117	C₂²×#450	D₄	1	4	yes	complemented
118	C₂²×#447	D₄	1	4	yes	complemented
119	C₂×#2905	C₂³	1	2	yes	complemented
120	C₂²×#421	C₂³	1	2	yes	complemented
121	C₂²×#421	C₂³	1	4	yes	complemented
122	C₂×#2896	C₂³	1	2	yes	complemented
123	C₂×#2896	C₂³	1	2	yes	complemented
124	C₂×#2896	C₂³	1	2	yes	complemented
125	C₂²×#418	D₄	1	8	yes	complemented
126	C₂²×#418	C₂³	1	4	yes	—
127	C₂²×#418	C₂³	1	2	yes	—
128	C₂²×#418	C₂³	1	2	yes	—
129	C₂²×#418	C₂³	1	2	yes	—
130	C₂²×#418	C₂³	1	2	yes	—
131	C₂²×#418	C₂³	1	2	yes	—
132	C₂²×#418	C₂³	1	2	yes	—
133	C₂²×#418	C₂³	1	2	yes	—
134	C₂²×#418	C₂³	1	1	yes	characteristic
135	C₂²×#418	C₂³	1	1	yes	characteristic
136	C₂²×#410	C₂³	1	2	yes	complemented
137	C₂²×#410	C₂³	1	4	yes	complemented
138	C₂²×#407	C₂³	1	4	yes	—
139	C₂²×#407	C₂³	1	2	yes	—
140	C₂²×#407	C₂³	1	2	yes	—
141	C₂²×#407	C₂³	1	1	yes	characteristic
142	C₂²×#407	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₂²⋊C₄	D₄	1	8	yes	complemented
144	#34044	C₂³	1	2	yes	complemented
145	C₂×#2309	C₂³	1	4	yes	—
146	C₂×#2309	C₂³	1	2	yes	—
147	C₂×#2309	C₂³	1	4	yes	—
148	C₂×#2309	C₂³	1	2	yes	—
149	C₂×#2280	C₂³	1	4	yes	—
150	C₂×#2280	C₂³	1	4	yes	—
151	C₂×#2280	C₂³	1	2	yes	—
152	C₂×#2280	C₂³	1	1	yes	characteristic
153	C₂×#2280	C₂³	1	1	yes	characteristic
154	C₂×#2280	C₂³	1	1	yes	characteristic
155	C₂×#2280	C₂³	1	1	yes	characteristic
156	C₂×#2280	C₂³	1	1	yes	characteristic
157	#20598	D₄	1	8	yes	complemented
158	C₂²×#344	C₂³	1	2	yes	complemented
159	C₂²×#344	C₂³	1	4	yes	complemented
160	C₂²×#344	C₂³	1	2	yes	complemented
161	C₂×#1742	C₂³	1	4	yes	complemented
162	C₂×#1740	C₂³	1	4	yes	complemented
163	C₂×#1740	C₂³	1	2	yes	complemented
164	#20347	C₂³	1	2	yes	complemented
165	C₂×#1733	C₂³	1	2	yes	complemented
166	C₂×#1733	C₂³	1	4	yes	complemented
167	C₂×#1733	C₂³	1	4	yes	complemented
168	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
169	C₂²×H(3,ℤ/4)	C₂³	1	4	yes	complemented
170	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
171	#20335	C₂³	1	2	yes	complemented
172	#14681	D₄	1	2	yes	—
173	#14681	D₄	1	4	yes	—
174	#14679	D₄	1	2	yes	—
175	#13902	D₄	1	8	yes	complemented
176	C₂⁷	C₂×D₄	1	1	yes	characteristic
177	C₂³×#41	C₂×D₄	1	2	yes	—
178	C₂³×#41	C₂⁴	1	1	yes	characteristic
179	C₂³×#41	C₂⁴	1	2	yes	—
180	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×D₄	C₂×D₄	1	8	yes	—
182	C₂⁴×D₄	C₂×D₄	1	16	yes	—
183	C₂⁴×D₄	C₂×D₄	1	4	yes	—
184	C₂⁴×D₄	C₂×D₄	1	4	yes	—
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	8	yes	—
187	C₂⁴×D₄	C₂×D₄	1	2	yes	—
188	C₂⁴×D₄	C₂×D₄	1	4	yes	—
189	C₂⁴×D₄	C₂×D₄	1	4	yes	—
190	C₂⁴×D₄	C₂×D₄	1	2	yes	—
191	C₂⁴×D₄	C₂×D₄	1	4	yes	—
192	C₂⁴×D₄	C₂×D₄	1	4	yes	—
193	C₂⁴×D₄	C₂×D₄	1	4	yes	—
194	C₂⁴×D₄	#41	1	4	yes	—
195	C₂⁴×D₄	#41	1	4	yes	—
196	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
197	C₂⁴×D₄	C₂⁴	1	2	yes	—
198	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
199	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
200	C₂⁵×C₄	C₂×D₄	1	2	yes	—
201	C₂⁵×C₄	C₂×D₄	1	4	yes	—
202	C₂⁵×C₄	#41	1	4	yes	—
203	C₂⁵×C₄	C₂⁴	1	2	yes	—
204	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
205	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
206	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
207	C₂³×SD₁₆	C₂×D₄	1	4	yes	—
208	C₂³×SD₁₆	C₂×D₄	1	4	yes	—
209	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
210	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
211	C₂³×D₈	C₂×D₄	1	4	yes	—
212	C₂³×D₈	C₂×D₄	1	4	yes	—
213	C₂³×D₈	C₂×D₄	1	2	yes	complemented
214	C₂³×D₈	C₂×D₄	1	2	yes	complemented
215	C₂³×M₁₆	C₂×D₄	1	4	yes	—
216	C₂³×M₁₆	C₂×D₄	1	2	yes	—
217	C₂³×M₁₆	C₂⁴	1	2	yes	—
218	C₂³×M₁₆	C₂⁴	1	2	yes	—
219	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
220	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
221	C₂³×M₁₆	C₂⁴	1	2	yes	—
222	C₂⁴×C₈	C₂×D₄	1	2	yes	—
223	C₂×#525	C₂×D₄	1	16	yes	—
224	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
225	C₂²×#121	C₂×D₄	1	2	yes	—
226	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
227	C₂²×#117	C₂×D₄	1	4	yes	—
228	C₂²×#117	C₂⁴	1	2	yes	—
229	C₂²×#117	C₂⁴	1	2	yes	—
230	C₂²×#117	C₂⁴	1	2	yes	—
231	C₂²×#117	C₂⁴	1	2	yes	—
232	C₂²×#117	C₂⁴	1	1	yes	characteristic
233	C₂²×#117	C₂⁴	1	2	yes	—
234	C₂²×#117	C₂⁴	1	2	yes	—
235	C₂×#418	C₂×D₄	1	8	yes	—
236	C₂×#418	C₂×D₄	1	16	yes	—
237	C₂×#418	C₂×D₄	1	16	yes	—
238	C₂×#418	C₂×D₄	1	8	yes	—
239	C₂×#418	C₂×D₄	1	8	yes	complemented
240	C₂×#418	C₂×D₄	1	8	yes	complemented
241	C₂²×#102	C₂×D₄	1	4	yes	complemented
242	C₂²×#102	C₂×D₄	1	4	yes	complemented
243	C₂×#407	C₂×D₄	1	16	yes	—
244	C₂×#407	C₂×D₄	1	4	yes	—
245	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
246	C₂×#390	C₂×D₄	1	16	yes	complemented
247	C₂×#390	C₂×D₄	1	8	yes	complemented
248	#2280	C₂×D₄	1	4	yes	—
249	C₂×#381	C₂×D₄	1	2	yes	—
250	C₂×#381	C₂×D₄	1	8	yes	—
251	C₂×#381	C₂×D₄	1	2	yes	—
252	C₂×#380	C₂×D₄	1	4	yes	—
253	C₂×#380	C₂×D₄	1	4	yes	—
254	C₂×#379	C₂×D₄	1	2	yes	—
255	C₂×#379	C₂×D₄	1	8	yes	—
256	C₂×#379	C₂×D₄	1	2	yes	—
257	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
258	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
259	C₂⁶	#121	1	4	yes	—
260	C₂⁶	C₂²×D₄	1	2	yes	—
261	C₂⁶	C₂²×D₄	1	1	yes	characteristic
262	C₂²×#41	C₂²×D₄	1	8	yes	—
263	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
264	C₂³×Q₈	C₂²×D₄	1	2	yes	—
265	C₂³×D₄	#120	1	8	yes	—
266	C₂³×D₄	#120	1	8	yes	—
267	C₂³×D₄	#120	1	16	yes	—
268	C₂³×D₄	#120	1	8	yes	—
269	C₂³×D₄	#120	1	8	yes	—
270	C₂³×D₄	#120	1	32	yes	complemented
271	C₂³×D₄	#121	1	16	yes	—
272	C₂³×D₄	#121	1	16	yes	—
273	C₂³×D₄	#121	1	16	yes	—
274	C₂³×D₄	#121	1	8	yes	—
275	C₂³×D₄	#121	1	8	yes	—
276	C₂³×D₄	#127	1	16	yes	—
277	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
278	C₂³×D₄	C₂²×D₄	1	2	yes	—
279	C₂³×D₄	C₂²×D₄	1	2	yes	—
280	C₂³×D₄	C₂²×D₄	1	2	yes	—
281	C₂³×D₄	C₂²×D₄	1	2	yes	—
282	C₂³×D₄	C₂²×D₄	1	2	yes	—
283	C₂³×D₄	C₂²×D₄	1	2	yes	—
284	C₂³×D₄	C₂²×D₄	1	2	yes	—
285	C₂³×D₄	C₂²×D₄	1	4	yes	—
286	C₂³×D₄	C₂²×D₄	1	8	yes	—
287	C₂³×D₄	C₂²×D₄	1	4	yes	—
288	C₂³×D₄	C₂²×D₄	1	2	yes	—
289	C₂³×D₄	C₂²×D₄	1	2	yes	—
290	C₂³×D₄	C₂²×D₄	1	2	yes	—
291	C₂³×D₄	C₂²×D₄	1	8	yes	—
292	C₂³×D₄	C₂²×D₄	1	2	yes	—
293	C₂³×D₄	C₂²×D₄	1	2	yes	—
294	C₂³×D₄	C₂²×D₄	1	2	yes	—
295	C₂³×D₄	C₂×#41	1	2	yes	—
296	C₂³×D₄	C₂×#41	1	4	yes	—
297	C₂³×D₄	C₂×#41	1	2	yes	—
298	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
299	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
300	C₂⁴×C₄	#121	1	4	yes	—
301	C₂⁴×C₄	#121	1	8	yes	—
302	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
303	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
304	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
305	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
306	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
307	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
308	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
309	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
312	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
313	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
314	C₂⁴×C₄	C₂×#41	1	4	yes	—
315	C₂⁴×C₄	C₂×#41	1	2	yes	—
316	C₂⁴×C₄	C₂×#41	1	2	yes	—
317	C₂⁴×C₄	C₂×#41	1	2	yes	—
318	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
319	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
322	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
323	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
324	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
325	C₂²×SD₁₆	#120	1	16	yes	complemented
326	C₂²×D₈	#120	1	16	yes	complemented
327	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
328	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
329	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
330	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
331	C₂³×C₈	C₂²×D₄	1	2	yes	—
332	C₂³×C₈	C₂²×D₄	1	2	yes	—
333	C₂³×C₈	C₂²×D₄	1	4	yes	—
334	C₂×#117	C₂²×D₄	1	4	yes	—
335	C₂×#117	C₂²×D₄	1	8	yes	—
336	C₂×#117	C₂²×D₄	1	4	yes	—
337	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
338	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
339	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
340	C₂²×C₂²⋊C₄	#120	1	8	yes	—
341	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
342	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
343	C₂²×C₄²	C₂²×D₄	1	4	yes	—
344	C₂²×C₄²	C₂²×D₄	1	4	yes	—
345	#418	#120	1	32	yes	complemented
346	C₂×#95	#120	1	8	yes	—
347	C₂⁵	C₂×#120	1	2	yes	—
348	C₂⁵	C₂×#121	1	4	yes	—
349	C₂⁵	C₂×#121	1	2	yes	—
350	C₂⁵	#525	1	2	yes	—
351	C₂⁵	D₄²	1	1	yes	characteristic
352	C₂⁵	D₄²	1	2	yes	—
353	C₂⁵	D₄²	1	8	yes	—
354	C₂⁵	D₄²	1	1	yes	characteristic
355	C₂⁵	D₄²	1	2	yes	—
356	C₂⁵	D₄²	1	2	yes	—
357	C₂⁵	C₂³×D₄	1	1	yes	characteristic
358	C₂²×Q₈	C₂×#120	1	4	yes	—
359	C₂²×D₄	#392	1	32	yes	—
360	C₂²×D₄	#392	1	32	yes	—
361	C₂²×D₄	C₂×#120	1	4	yes	—
362	C₂²×D₄	C₂×#120	1	4	yes	—
363	C₂²×D₄	C₂×#120	1	4	yes	—
364	C₂²×D₄	C₂×#120	1	4	yes	—
365	C₂²×D₄	C₂×#120	1	8	yes	—
366	C₂²×D₄	C₂×#120	1	4	yes	—
367	C₂²×D₄	C₂×#120	1	8	yes	—
368	C₂²×D₄	C₂×#120	1	8	yes	—
369	C₂²×D₄	C₂×#120	1	8	yes	—
370	C₂²×D₄	C₂×#120	1	4	yes	—
371	C₂²×D₄	C₂×#120	1	4	yes	—
372	C₂²×D₄	C₂×#121	1	4	yes	—
373	C₂²×D₄	C₂×#121	1	4	yes	—
374	C₂²×D₄	C₂×#121	1	4	yes	—
375	C₂²×D₄	C₂×#121	1	8	yes	—
376	C₂²×D₄	C₂×#121	1	4	yes	—
377	C₂²×D₄	C₂×#121	1	4	yes	—
378	C₂²×D₄	C₂×#121	1	4	yes	—
379	C₂²×D₄	C₂×#127	1	4	yes	—
380	C₂²×D₄	C₂×#127	1	4	yes	—
381	C₂²×D₄	#534	1	8	yes	—
382	C₂²×D₄	#534	1	8	yes	—
383	C₂²×D₄	#534	1	8	yes	—
384	C₂²×D₄	#535	1	8	yes	—
385	C₂²×D₄	D₄²	1	16	yes	—
386	C₂²×D₄	D₄²	1	16	yes	—
387	C₂²×D₄	D₄²	1	16	yes	—
388	C₂²×D₄	D₄²	1	16	yes	—
389	C₂²×D₄	#546	1	16	yes	—
390	C₂²×D₄	#546	1	16	yes	—
391	C₂³×C₄	C₂×#120	1	8	yes	—
392	C₂³×C₄	C₂×#120	1	2	yes	—
393	C₂³×C₄	C₂×#120	1	2	yes	—
394	C₂³×C₄	C₂×#120	1	2	yes	—
395	C₂³×C₄	C₂×#120	1	2	yes	—
396	C₂³×C₄	C₂×#120	1	2	yes	—
397	C₂³×C₄	C₂×#120	1	4	yes	—
398	C₂³×C₄	C₂×#120	1	8	yes	—
399	C₂³×C₄	C₂×#121	1	4	yes	—
400	C₂³×C₄	C₂×#121	1	2	yes	—
401	C₂³×C₄	C₂×#121	1	4	yes	—
402	C₂³×C₄	C₂×#121	1	4	yes	—
403	C₂³×C₄	C₂×#121	1	4	yes	—
404	C₂³×C₄	C₂×#121	1	2	yes	—
405	C₂³×C₄	C₂×#121	1	2	yes	—
406	C₂³×C₄	#525	1	2	yes	—
407	C₂³×C₄	#525	1	4	yes	—
408	C₂³×C₄	#525	1	4	yes	—
409	C₂³×C₄	C₂×#127	1	4	yes	—
410	C₂³×C₄	#534	1	8	yes	—
411	C₂³×C₄	#534	1	2	yes	—
412	C₂³×C₄	#534	1	2	yes	—
413	C₂³×C₄	#534	1	2	yes	—
414	C₂³×C₄	#534	1	4	yes	—
415	C₂³×C₄	#534	1	2	yes	—
416	C₂³×C₄	#535	1	4	yes	—
417	C₂³×C₄	#538	1	4	yes	—
418	C₂³×C₄	#538	1	2	yes	—
419	C₂³×C₄	#538	1	2	yes	—
420	C₂³×C₄	D₄²	1	8	yes	—
421	C₂³×C₄	D₄²	1	2	yes	—
422	C₂³×C₄	D₄²	1	1	yes	characteristic
423	C₂³×C₄	D₄²	1	1	yes	characteristic
424	C₂³×C₄	D₄²	1	2	yes	—
425	C₂³×C₄	D₄²	1	2	yes	—
426	C₂³×C₄	D₄²	1	2	yes	—
427	C₂³×C₄	D₄²	1	2	yes	—
428	C₂³×C₄	D₄²	1	2	yes	—
429	C₂³×C₄	D₄²	1	2	yes	—
430	C₂³×C₄	D₄²	1	4	yes	—
431	C₂³×C₄	D₄²	1	4	yes	—
432	C₂³×C₄	#546	1	16	yes	—
433	C₂³×C₄	#546	1	4	yes	—
434	C₂³×C₄	#546	1	2	yes	—
435	C₂³×C₄	#546	1	2	yes	—
436	C₂³×C₄	#546	1	2	yes	—
437	C₂³×C₄	#546	1	2	yes	—
438	C₂³×C₄	#546	1	4	yes	—
439	C₂³×C₄	#546	1	4	yes	—
440	C₂³×C₄	#546	1	2	yes	—
441	C₂³×C₄	#546	1	2	yes	—
442	C₂³×C₄	#546	1	2	yes	—
443	C₂³×C₄	#546	1	4	yes	—
444	C₂³×C₄	#546	1	2	yes	—
445	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
446	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
447	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
448	C₂³×C₄	C₂³×D₄	1	4	yes	—
449	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
450	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
451	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
452	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
453	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
454	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
455	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
456	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
457	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
462	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
463	C₂×M₁₆	C₂×#120	1	8	yes	—
464	C₂²×C₈	C₂×#120	1	8	yes	—
465	#117	C₂×#120	1	8	yes	—
466	C₂⁴	#2403	1	2	yes	—
467	C₂⁴	#2403	1	2	yes	—
468	C₂⁴	#2410	1	2	yes	—
469	C₂⁴	#2410	1	4	yes	—
470	C₂⁴	#2410	1	8	yes	—
471	C₂⁴	#2410	1	2	yes	—
472	C₂⁴	#2424	1	2	yes	—
473	C₂⁴	#2424	1	4	yes	—
474	C₂⁴	#2424	1	2	yes	—
475	C₂⁴	#2433	1	4	yes	—
476	C₂⁴	#2847	1	4	yes	—
477	C₂⁴	C₂²×#120	1	1	yes	characteristic
478	C₂⁴	C₂²×#121	1	1	yes	characteristic
479	C₂⁴	C₂×#525	1	1	yes	characteristic
480	C₂⁴	C₂×D₄²	1	1	yes	characteristic
481	C₂⁴	C₂×D₄²	1	1	yes	characteristic
482	C₂⁴	C₂×D₄²	1	4	yes	—
483	C₂⁴	C₂×D₄²	1	1	yes	characteristic
484	C₂⁴	C₂×D₄²	1	1	yes	characteristic
485	C₂⁴	#3484	1	4	yes	—
486	C₂×D₄	C₂×#392	1	8	yes	—
487	C₂×D₄	C₂×#392	1	8	yes	—
488	C₂×D₄	#2403	1	16	yes	—
489	C₂×D₄	#2403	1	16	yes	—
490	C₂×D₄	#2408	1	16	yes	—
491	C₂×D₄	#2410	1	16	yes	—
492	C₂×D₄	#2410	1	16	yes	—
493	C₂×D₄	#2410	1	16	yes	—
494	C₂×D₄	#2433	1	16	yes	—
495	C₂×D₄	#2613	1	8	yes	—
496	C₂×D₄	#2846	1	8	yes	—
497	C₂²×C₄	C₂×#392	1	4	yes	—
498	C₂²×C₄	C₂×#392	1	4	yes	—
499	C₂²×C₄	#2403	1	2	yes	—
500	C₂²×C₄	#2403	1	2	yes	—
501	C₂²×C₄	#2404	1	4	yes	—
502	C₂²×C₄	#2404	1	4	yes	—
503	C₂²×C₄	#2410	1	8	yes	—
504	C₂²×C₄	#2410	1	4	yes	—
505	C₂²×C₄	#2410	1	4	yes	—
506	C₂²×C₄	#2410	1	4	yes	—
507	C₂²×C₄	#2410	1	4	yes	—
508	C₂²×C₄	#2410	1	4	yes	—
509	C₂²×C₄	#2410	1	2	yes	—
510	C₂²×C₄	#2410	1	2	yes	—
511	C₂²×C₄	#2424	1	4	yes	—
512	C₂²×C₄	#2424	1	4	yes	—
513	C₂²×C₄	#2424	1	4	yes	—
514	C₂²×C₄	#2424	1	4	yes	—
515	C₂²×C₄	#2424	1	4	yes	—
516	C₂²×C₄	#2424	1	2	yes	—
517	C₂²×C₄	#2424	1	2	yes	—
518	C₂²×C₄	#2433	1	4	yes	—
519	C₂²×C₄	#2539	1	4	yes	—
520	C₂²×C₄	#2539	1	4	yes	—
521	C₂²×C₄	#2617	1	4	yes	—
522	C₂²×C₄	#2617	1	4	yes	—
523	C₂²×C₄	#2847	1	4	yes	—
524	C₂²×C₄	C₂²×#120	1	2	yes	—
525	C₂²×C₄	C₂²×#120	1	2	yes	—
526	C₂²×C₄	C₂²×#120	1	2	yes	—
527	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
528	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
529	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
530	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
531	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
532	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
533	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
534	C₂²×C₄	C₂×#525	1	1	yes	characteristic
535	C₂²×C₄	C₂×#525	1	1	yes	characteristic
536	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
537	C₂²×C₄	C₂×#534	1	1	yes	characteristic
538	C₂²×C₄	C₂×#534	1	2	yes	—
539	C₂²×C₄	C₂×#534	1	2	yes	—
540	C₂²×C₄	C₂×#534	1	1	yes	characteristic
541	C₂²×C₄	C₂×#534	1	1	yes	characteristic
542	C₂²×C₄	C₂×#534	1	2	yes	—
543	C₂²×C₄	C₂×#534	1	2	yes	—
544	C₂²×C₄	C₂×#535	1	1	yes	characteristic
545	C₂²×C₄	C₂×#535	1	2	yes	—
546	C₂²×C₄	C₂×#538	1	1	yes	characteristic
547	C₂²×C₄	C₂×#538	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄²	1	4	yes	—
549	C₂²×C₄	C₂×D₄²	1	4	yes	—
550	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄²	1	4	yes	—
553	C₂²×C₄	C₂×D₄²	1	4	yes	—
554	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
556	C₂²×C₄	C₂×#546	1	4	yes	—
557	C₂²×C₄	C₂×#546	1	4	yes	—
558	C₂²×C₄	C₂×#546	1	4	yes	—
559	C₂²×C₄	C₂×#546	1	1	yes	characteristic
560	C₂²×C₄	C₂×#546	1	1	yes	characteristic
561	C₂²×C₄	C₂×#546	1	1	yes	characteristic
562	C₂²×C₄	C₂×#546	1	1	yes	characteristic
563	C₂²×C₄	C₂×#546	1	1	yes	characteristic
564	C₂²×C₄	C₂×#546	1	1	yes	characteristic
565	C₂²×C₄	C₂×#546	1	1	yes	characteristic
566	C₂²×C₄	C₂×#546	1	1	yes	characteristic
567	C₂²×C₄	#3484	1	4	yes	—
568	C₂²×C₄	#3484	1	4	yes	—
569	C₂²×C₄	#3484	1	2	yes	—
570	C₂²×C₄	#3484	1	4	yes	—
571	C₂²×C₄	#3484	1	4	yes	—
572	C₂²×C₄	#3484	1	2	yes	—
573	C₂²×C₄	#3484	1	4	yes	—
574	C₂²×C₄	#3484	1	4	yes	—
575	C₂²×C₄	#3484	1	2	yes	—
576	C₂²×C₄	#3484	1	4	yes	—
577	C₂²×C₄	#3484	1	2	yes	—
578	C₂²×C₄	#3484	1	4	yes	—
579	C₂²×C₄	#3490	1	4	yes	—
580	C₂²×C₄	#3490	1	4	yes	—
581	C₂²×C₄	#3490	1	4	yes	—
582	C₂²×C₄	#3532	1	4	yes	—
583	C₂²×C₄	#3532	1	4	yes	—
584	C₂²×C₄	#3532	1	4	yes	—
585	C₂²×C₄	#3532	1	4	yes	—
586	C₂³	#14716	1	4	yes	—
587	C₂³	#14716	1	4	yes	—
588	C₂³	#23882	1	8	yes	—
589	C₂³	C₂×#2403	1	1	yes	characteristic
590	C₂³	C₂×#2410	1	1	yes	characteristic
591	C₂³	C₂×#2410	1	1	yes	characteristic
592	C₂³	C₂×#2410	1	2	yes	—
593	C₂³	C₂×#2424	1	1	yes	characteristic
594	C₂³	C₂×#2424	1	1	yes	characteristic
595	C₂³	C₂×#2433	1	1	yes	characteristic
596	C₂³	#34981	1	2	yes	—
597	C₂³	D₄×#120	1	2	yes	—
598	C₂³	D₄×#120	1	4	yes	—
599	C₂³	D₄×#120	1	2	yes	—
600	C₂³	#36098	1	4	yes	—
601	C₂³	C₂×#2847	1	1	yes	characteristic
602	C₂³	#37644	1	2	yes	—
603	C₂³	#37645	1	2	yes	—
604	C₂³	#58990	1	4	yes	—
605	C₂³	#58990	1	4	yes	—
606	D₄	#14715	1	16	yes	—
607	C₂×C₄	#14716	1	4	yes	—
608	C₂×C₄	#14716	1	4	yes	—
609	C₂×C₄	C₂²×#392	1	1	yes	characteristic
610	C₂×C₄	C₂×#2613	1	1	yes	characteristic
611	C₂×C₄	C₂×#2617	1	1	yes	characteristic
612	C₂×C₄	C₂×#2403	1	2	yes	—
613	C₂×C₄	C₂×#2403	1	2	yes	—
614	C₂×C₄	C₂×#2410	1	1	yes	characteristic
615	C₂×C₄	C₂×#2410	1	2	yes	—
616	C₂×C₄	C₂×#2410	1	2	yes	—
617	C₂×C₄	C₂×#2410	1	2	yes	—
618	C₂×C₄	C₂×#2410	1	1	yes	characteristic
619	C₂×C₄	C₂×#2424	1	1	yes	characteristic
620	C₂×C₄	C₂×#2424	1	1	yes	characteristic
621	C₂×C₄	C₂×#2408	1	2	yes	—
622	C₂×C₄	C₂×#2433	1	2	yes	—
623	C₂×C₄	C₂×#2404	1	1	yes	characteristic
624	C₂×C₄	C₂×#2539	1	1	yes	characteristic
625	C₂×C₄	#34980	1	2	yes	—
626	C₂×C₄	#34980	1	1	yes	characteristic
627	C₂×C₄	#34980	1	1	yes	characteristic
628	C₂×C₄	#34980	1	2	yes	—
629	C₂×C₄	#34980	1	2	yes	—
630	C₂×C₄	#34981	1	2	yes	—
631	C₂×C₄	#34981	1	2	yes	—
632	C₂×C₄	#35346	1	2	yes	—
633	C₂×C₄	#35348	1	2	yes	—
634	C₂×C₄	#35348	1	2	yes	—
635	C₂×C₄	#35390	1	2	yes	—
636	C₂×C₄	D₄×#120	1	2	yes	—
637	C₂×C₄	D₄×#120	1	2	yes	—
638	C₂×C₄	#36098	1	4	yes	—
639	C₂×C₄	#36098	1	4	yes	—
640	C₂×C₄	#36152	1	2	yes	—
641	C₂×C₄	#36152	1	2	yes	—
642	C₂×C₄	#36152	1	2	yes	—
643	C₂×C₄	#36152	1	2	yes	—
644	C₂×C₄	C₂×#2846	1	1	yes	characteristic
645	C₂×C₄	#37436	1	2	yes	—
646	C₂×C₄	#37436	1	2	yes	—
647	C₂×C₄	#37644	1	2	yes	—
648	C₂×C₄	#37644	1	4	yes	—
649	C₂×C₄	#37645	1	2	yes	—
650	C₂×C₄	#37645	1	4	yes	—
651	C₂×C₄	#37660	1	4	yes	—
652	C₂×C₄	#37660	1	4	yes	—
653	C₂×C₄	#37832	1	2	yes	—
654	C₂×C₄	#37832	1	2	yes	—
655	C₂×C₄	#37833	1	2	yes	—
656	C₂×C₄	#37833	1	2	yes	—
657	C₂×C₄	#58990	1	4	yes	—
658	C₂×C₄	#58990	1	4	yes	—
659	C₂×C₄	#58991	1	4	yes	—
660	C₂×C₄	#58991	1	4	yes	—
661	C₂×C₄	#58991	1	4	yes	—
662	C₂×C₄	#58991	1	4	yes	—
663	C₂²	#394249	1	8	yes	complemented
664	C₂²	C₂×#14716	1	1	yes	characteristic
665	C₂²	#612433	1	1	yes	characteristic
666	C₂²	#612459	1	2	yes	—
667	C₂²	#635993	1	1	yes	characteristic
668	C₂²	#647656	1	2	yes	—
669	C₂²	#647698	1	2	yes	—
670	C₂²	#648042	1	2	yes	—
671	C₂²	#648360	1	2	yes	—
672	C₂²	#759288	1	2	yes	—
673	C₂²	C₂×#23882	1	4	yes	—
674	C₄	C₂×#14715	1	1	yes	characteristic
675	C₄	#612433	1	1	yes	characteristic
676	C₄	#635993	1	1	yes	characteristic
677	C₄	#636019	1	2	yes	—
678	C₄	#647657	1	2	yes	—
679	C₄	#647698	1	2	yes	—
680	C₄	#648042	1	2	yes	—
681	C₄	#648361	1	2	yes	—
682	C₄	#759288	1	2	yes	—
683	C₄	#5955303	1	1	yes	characteristic
684	C₂	#72214076	1	4	yes	—
685	C₂	C₂×#394249	1	2	yes	—
686	C₂	#72250275	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262513	C₂	semidirect
2. #72262381	C₂	semidirect
3. #72262354	C₂	semidirect
4. #72256546	C₂	semidirect
5. #72255705	C₂	semidirect
6. #72251303	C₂	semidirect
7. #72251204	C₂	semidirect
8. #72251201	C₂	semidirect
9. #72249533	C₂	semidirect
10. #72237236	C₂	semidirect
11. #72236790	C₂	semidirect
12. #72236780	C₂	semidirect
13. #72235935	C₂	semidirect
14. C₂×#374114	C₂	semidirect
15. C₂×#394249	C₂	semidirect
16. #72235090	C₂	semidirect
17. C₂×#359472	C₂	semidirect
18. C₂³×#3003	C₂	semidirect
19. C₂×#6628842	C₂	semidirect
24. C₂×#60423	C₂²	semidirect
29. C₂²×#3003	C₂²	semidirect
30. C₂²×#3003	C₂²	semidirect
35. #7628649	C₂²	semidirect
38. C₂×#34171	C₂²	semidirect
39. #6431965	C₂²	semidirect
40. C₂×#23443	C₂²	semidirect
41. #6431766	C₂²	semidirect
42. C₂×#23407	C₂²	semidirect
43. C₂²×#1904	C₂²	semidirect
44. C₂²×#1904	C₂²	semidirect
45. C₂×#20983	C₂²	semidirect
46. #6371477	C₂²	semidirect
47. #6371420	C₂²	semidirect
48. C₂×#20902	C₂²	semidirect
49. #6371257	C₂²	semidirect
50. C₂×#20605	C₂²	semidirect
51. #6370715	C₂²	semidirect
54. C₂×#20598	C₂²	semidirect
55. C₂×#20598	C₂²	semidirect
56. C₂×#20584	C₂²	semidirect
62. #517415	C₂²	semidirect
63. C₂×#11183	C₂²	semidirect
64. C₂×#11073	C₂²	semidirect
65. C₂×#11071	C₂²	semidirect
66. C₂×#11030	C₂²	semidirect
67. C₂×#11030	C₂²	semidirect
68. C₂×#11030	C₂²	semidirect
69. #357571	C₂²	semidirect
70. C₂×#11012	C₂²	semidirect
71. C₂×#11012	C₂²	semidirect
72. C₂×#10994	C₂²	semidirect
73. C₂×#10994	C₂²	semidirect
74. C₂×#10994	C₂²	semidirect
75. #357529	C₂²	semidirect
76. C₂×#10785	C₂²	semidirect
77. #353416	C₂²	semidirect
78. C₂×#10737	C₂²	semidirect
79. #353407	C₂²	semidirect
80. #353397	C₂²	semidirect
81. #353386	C₂²	semidirect
82. C₂×#10776	C₂²	semidirect
83. C₂×#10729	C₂²	semidirect
84. C₂×#10717	C₂²	semidirect
85. C₂×#10716	C₂²	semidirect
86. #123605	C₂²	semidirect
87. #123560	C₂²	semidirect
88. #123547	C₂²	semidirect
89. #123535	C₂²	semidirect
90. #123531	C₂²	semidirect
92. C₂⁵×D₄	D₄	semidirect
98. C₂³×AGL(1,ℤ/8)	D₄	semidirect
105. C₂⁴×SD₁₆	D₄	semidirect
106. C₂⁴×D₈	D₄	semidirect
109. C₂×#3449	C₂³	semidirect
116. C₂×#3003	D₄	semidirect
117. C₂²×#450	D₄	semidirect
118. C₂²×#447	D₄	semidirect
119. C₂×#2905	C₂³	semidirect
120. C₂²×#421	C₂³	semidirect
121. C₂²×#421	C₂³	semidirect
122. C₂×#2896	C₂³	semidirect
123. C₂×#2896	C₂³	semidirect
124. C₂×#2896	C₂³	semidirect
125. C₂²×#418	D₄	semidirect
136. C₂²×#410	C₂³	semidirect
137. C₂²×#410	C₂³	semidirect
143. C₂×D₄×C₂²⋊C₄	D₄	semidirect
144. #34044	C₂³	semidirect
157. #20598	D₄	semidirect
158. C₂²×#344	C₂³	semidirect
159. C₂²×#344	C₂³	semidirect
160. C₂²×#344	C₂³	semidirect
161. C₂×#1742	C₂³	semidirect
162. C₂×#1740	C₂³	semidirect
163. C₂×#1740	C₂³	semidirect
164. #20347	C₂³	semidirect
165. C₂×#1733	C₂³	semidirect
166. C₂×#1733	C₂³	semidirect
167. C₂×#1733	C₂³	semidirect
168. C₂²×H(3,ℤ/4)	C₂³	semidirect
169. C₂²×H(3,ℤ/4)	C₂³	semidirect
170. C₂²×H(3,ℤ/4)	C₂³	semidirect
171. #20335	C₂³	semidirect
175. #13902	D₄	semidirect
209. C₂³×SD₁₆	C₂×D₄	semidirect
210. C₂³×SD₁₆	C₂×D₄	semidirect
213. C₂³×D₈	C₂×D₄	semidirect
214. C₂³×D₈	C₂×D₄	semidirect
226. C₂²×C₄×D₄	C₂×D₄	semidirect
239. C₂×#418	C₂×D₄	semidirect
240. C₂×#418	C₂×D₄	semidirect
241. C₂²×#102	C₂×D₄	semidirect
242. C₂²×#102	C₂×D₄	semidirect
246. C₂×#390	C₂×D₄	semidirect
247. C₂×#390	C₂×D₄	semidirect
270. C₂³×D₄	#120	semidirect
325. C₂²×SD₁₆	#120	semidirect
326. C₂²×D₈	#120	semidirect
345. #418	#120	semidirect
663. C₂²	#394249	semidirect

Maximal subgroups

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

subgroup	index
#72262513	2
#72262381	2
#72262354	2
#72256546	2
#72255705	2
#72251303	2
#72251204	2
#72251201	2
#72249533	2
#72237236	2
#72236790	2
#72236780	2
#72235935	2
C₂×#374114	2
C₂×#394249	2
#72235090	2
C₂×#359472	2
C₂³×#3003	2
C₂×#6628842	2