Subgroups — #72311077

Order 2048.

At least 7250 conjugacy classes of subgroups; only the 2936 normal subgroups are shown.

The subgroup lattice has 709 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72311061	C₂	1	1	yes	maximal, characteristic, complemented
2	#72311051	C₂	1	1	yes	maximal, characteristic, complemented
3	#72311040	C₂	1	1	yes	maximal, characteristic, complemented
4	#72311032	C₂	1	1	yes	maximal, characteristic, complemented
5	#72311020	C₂	1	8	yes	maximal, complemented
6	#72311018	C₂	1	4	yes	maximal, complemented
7	C₂×D₄×#379	C₂	1	1	yes	maximal, characteristic, complemented
8	#72264272	C₂	1	4	yes	maximal, complemented
9	#72240593	C₂	1	4	yes	maximal, complemented
10	C₂³×#3003	C₂	1	1	yes	maximal, characteristic
11	C₂×#198404	C₂	1	4	yes	maximal, complemented
12	#72231771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×D₄	C₂²	1	1	yes	characteristic
14	C₂⁴×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
15	C₂³×#525	C₂²	1	1	yes	characteristic
16	C₂³×#450	C₄	1	2	yes	complemented
17	C₂³×#450	C₂²	1	2	yes	—
18	C₂²×#3003	C₄	1	4	yes	complemented
19	C₂²×#3003	C₄	1	4	yes	complemented
20	C₂²×#3003	C₂²	1	2	yes	—
21	C₂²×#3003	C₂²	1	2	yes	—
22	C₂²×#3003	C₂²	1	4	yes	—
23	C₂³×#447	C₄	1	2	yes	complemented
24	C₂³×#447	C₂²	1	2	yes	—
25	C₂³×#407	C₂²	1	1	yes	characteristic
26	C₂³×#418	C₄	1	2	yes	complemented
27	C₂²×D₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₂×#21420	C₂²	1	4	yes	complemented
29	C₂×#20598	C₂²	1	2	yes	complemented
30	C₂×#20598	C₂²	1	2	yes	complemented
31	C₂×#20579	C₂²	1	1	yes	characteristic
32	C₂×#17592	C₂²	1	4	yes	complemented
33	#607558	C₂²	1	1	yes	characteristic
34	C₂×#14680	C₂²	1	1	yes	characteristic
35	D₄×#379	C₂²	1	4	yes	—
36	D₄×#379	C₂²	1	4	yes	complemented
37	C₂×#13902	C₂²	1	2	yes	complemented
38	C₂×C₄×#379	C₂²	1	1	yes	characteristic
39	#392118	C₂²	1	4	yes	—
40	#392118	C₂²	1	4	yes	complemented
41	#363168	C₂²	1	4	yes	complemented
42	#362712	C₂²	1	2	yes	complemented
43	#361599	C₂²	1	2	yes	complemented
44	C₂×#9259	C₂²	1	16	yes	complemented
45	C₂×#9255	C₂²	1	16	yes	complemented
46	#185050	C₂²	1	4	yes	complemented
47	#185047	C₂²	1	2	yes	complemented
48	#185046	C₂²	1	2	yes	complemented
49	C₂×#7983	C₂²	1	4	yes	complemented
50	C₂×#7929	C₂²	1	4	yes	complemented
51	#114509	C₂²	1	16	yes	complemented
52	#114505	C₂²	1	16	yes	complemented
53	#105544	C₂²	1	4	yes	complemented
54	#105542	C₂²	1	4	yes	complemented
55	#105522	C₂²	1	4	yes	complemented
56	#105520	C₂²	1	4	yes	complemented
57	C₂⁴×#41	C₂×C₄	1	1	yes	characteristic, complemented
58	C₂⁵×D₄	C₂×C₄	1	2	yes	—
59	C₂⁵×D₄	C₂×C₄	1	2	yes	—
60	C₂⁵×D₄	C₂×C₄	1	2	yes	—
61	C₂⁵×D₄	C₂×C₄	1	2	yes	—
62	C₂⁵×D₄	D₄	1	2	yes	—
63	C₂⁵×D₄	D₄	1	4	yes	—
64	C₂⁵×D₄	D₄	1	4	yes	—
65	C₂⁵×D₄	D₄	1	2	yes	—
66	C₂⁵×D₄	D₄	1	4	yes	—
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic
68	C₂⁵×D₄	C₂³	1	2	yes	—
69	C₂⁵×D₄	C₂³	1	2	yes	—
70	C₂⁵×D₄	C₂³	1	1	yes	characteristic
71	C₂⁶×C₄	C₂³	1	1	yes	characteristic
72	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
73	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	complemented
74	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
75	C₂⁴×SD₁₆	C₂×C₄	1	4	yes	complemented
76	C₂⁴×D₈	C₂×C₄	1	4	yes	complemented
77	C₂⁴×M₁₆	C₂×C₄	1	2	yes	complemented
78	C₂²×#525	C₂×C₄	1	2	yes	complemented
79	C₂²×#525	C₂×C₄	1	2	yes	complemented
80	C₂²×#525	C₂³	1	2	yes	—
81	C₂²×#525	C₂³	1	2	yes	—
82	C₂³×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
83	C₂³×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂³×#121	C₂×C₄	1	1	yes	characteristic, complemented
85	C₂³×#121	C₂³	1	1	yes	characteristic
86	C₂³×#117	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×#3003	D₄	1	32	yes	—
88	C₂²×#450	C₂×C₄	1	4	yes	—
89	C₂²×#450	C₂×C₄	1	4	yes	complemented
90	C₂²×#450	C₂×C₄	1	8	yes	complemented
91	C₂²×#450	C₂×C₄	1	8	yes	complemented
92	C₂²×#450	C₂³	1	4	yes	—
93	C₂²×#450	C₂³	1	4	yes	—
94	C₂²×#447	C₂×C₄	1	4	yes	—
95	C₂²×#447	C₂×C₄	1	4	yes	complemented
96	C₂²×#447	C₂×C₄	1	8	yes	complemented
97	C₂²×#447	C₂×C₄	1	8	yes	complemented
98	C₂²×#447	C₂³	1	4	yes	—
99	C₂²×#447	C₂³	1	4	yes	—
100	C₂²×#418	C₂×C₄	1	4	yes	—
101	C₂²×#418	C₂×C₄	1	8	yes	complemented
102	C₂²×#418	C₂×C₄	1	4	yes	complemented
103	C₂³×#102	C₂×C₄	1	4	yes	complemented
104	C₂³×#102	C₂×C₄	1	4	yes	complemented
105	C₂²×#407	C₂×C₄	1	2	yes	complemented
106	C₂²×#407	C₂×C₄	1	2	yes	complemented
107	C₂²×#407	C₂³	1	2	yes	—
108	C₂²×#407	C₂³	1	2	yes	—
109	C₂²×#407	C₂³	1	2	yes	—
110	C₂³×C₂²⋊C₈	C₂×C₄	1	2	yes	complemented
111	C₂³×C₂²⋊C₈	C₂³	1	2	yes	—
112	C₂×D₄×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×#2280	C₂³	1	2	yes	—
114	C₂²×#380	C₂³	1	2	yes	—
115	C₂²×#379	D₄	1	1	yes	characteristic
116	C₂²×#379	D₄	1	1	yes	characteristic
117	C₂²×C₄×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×#1996	C₂³	1	8	yes	complemented
119	C₂×#1964	C₂³	1	8	yes	complemented
120	C₂×#1786	C₂³	1	8	yes	—
121	C₂×#1786	C₂³	1	8	yes	—
122	C₂×#1779	C₂³	1	2	yes	—
123	C₂×#1779	C₂³	1	2	yes	—
124	C₂×#1520	C₂³	1	8	yes	complemented
125	C₂×#1519	C₂³	1	8	yes	complemented
126	#14680	D₄	1	4	yes	—
127	#14680	C₂³	1	2	yes	—
128	#14680	C₂³	1	2	yes	—
129	#14680	C₂³	1	2	yes	—
130	#14680	C₂³	1	2	yes	—
131	#13902	C₂³	1	8	yes	—
132	C₄×#379	D₄	1	2	yes	—
133	C₄×#379	D₄	1	2	yes	—
134	C₄×#379	C₂³	1	2	yes	—
135	C₄×#379	C₂³	1	2	yes	—
136	C₂×C₂²⋊#95	D₄	1	4	yes	—
137	C₂×C₂²⋊#95	D₄	1	2	yes	—
138	C₂×#1289	C₂³	1	16	yes	complemented
139	C₂×#1282	C₂³	1	16	yes	complemented
140	C₂⁷	C₂×D₄	1	1	yes	characteristic
141	C₂³×#41	C₂²×C₄	1	2	yes	—
142	C₂³×#41	C₂²×C₄	1	2	yes	complemented
143	C₂⁴×Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
144	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
145	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
146	C₂⁴×D₄	C₂²⋊C₄	1	8	yes	—
147	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
148	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
149	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
150	C₂⁴×D₄	C₂²⋊C₄	1	8	yes	—
151	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
152	C₂⁴×D₄	C₂²⋊C₄	1	8	yes	—
153	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
154	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
155	C₂⁴×D₄	C₂²⋊C₄	1	8	yes	—
156	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
157	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
158	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
159	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
160	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
161	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
162	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
163	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
164	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
165	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂×D₄	1	2	yes	—
167	C₂⁴×D₄	C₂×D₄	1	2	yes	—
168	C₂⁴×D₄	C₂×D₄	1	4	yes	—
169	C₂⁴×D₄	C₂×D₄	1	4	yes	—
170	C₂⁴×D₄	C₂×D₄	1	2	yes	—
171	C₂⁴×D₄	C₂×D₄	1	2	yes	—
172	C₂⁴×D₄	C₂×D₄	1	8	yes	—
173	C₂⁴×D₄	C₂×D₄	1	8	yes	—
174	C₂⁴×D₄	C₂×D₄	1	2	yes	—
175	C₂⁴×D₄	C₂×D₄	1	4	yes	—
176	C₂⁴×D₄	C₂×D₄	1	4	yes	—
177	C₂⁴×D₄	C₂×D₄	1	2	yes	—
178	C₂⁴×D₄	C₂×D₄	1	16	yes	—
179	C₂⁴×D₄	C₂×D₄	1	2	yes	—
180	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×D₄	C₂⁴	1	2	yes	—
182	C₂⁴×D₄	C₂⁴	1	2	yes	—
183	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
184	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
185	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
186	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
187	C₂⁵×C₄	C₂×D₄	1	2	yes	—
188	C₂⁵×C₄	C₂×D₄	1	2	yes	—
189	C₂⁵×C₄	C₂×D₄	1	2	yes	—
190	C₂⁵×C₄	C₂×D₄	1	2	yes	—
191	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁵×C₄	C₂×D₄	1	2	yes	—
195	C₂⁵×C₄	C₂×D₄	1	2	yes	—
196	C₂⁵×C₄	#41	1	2	yes	—
197	C₂⁵×C₄	#41	1	2	yes	—
198	C₂⁵×C₄	#41	1	1	yes	characteristic
199	C₂⁵×C₄	#41	1	1	yes	characteristic
200	C₂⁵×C₄	#41	1	1	yes	characteristic
201	C₂⁵×C₄	#41	1	1	yes	characteristic
202	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
203	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
204	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
205	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	32	yes	complemented
206	C₂³×SD₁₆	C₂²×C₄	1	8	yes	—
207	C₂³×SD₁₆	C₂²×C₄	1	8	yes	complemented
208	C₂³×D₈	C₂²×C₄	1	8	yes	—
209	C₂³×D₈	C₂²×C₄	1	8	yes	complemented
210	C₂³×M₁₆	C₂²×C₄	1	4	yes	—
211	C₂³×M₁₆	C₂²×C₄	1	4	yes	complemented
212	C₂⁴×C₈	C₂²×C₄	1	4	yes	complemented
213	C₂×#525	C₂×D₄	1	16	yes	—
214	C₂²×C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
215	C₂²×C₂²⋊Q₈	C₂²×C₄	1	2	yes	complemented
216	C₂²×C₂²⋊Q₈	C₂²×C₄	1	2	yes	complemented
217	C₂²×C₂²⋊Q₈	C₂⁴	1	2	yes	—
218	C₂²×#121	C₂²×C₄	1	2	yes	—
219	C₂²×#121	C₂²×C₄	1	2	yes	complemented
220	C₂²×#121	C₂²×C₄	1	2	yes	complemented
221	C₂²×#121	C₂⁴	1	2	yes	—
222	C₂²×#117	C₂²×C₄	1	2	yes	—
223	C₂²×#117	C₂²×C₄	1	2	yes	complemented
224	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
225	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
226	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
227	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
228	C₂×#450	C₂²⋊C₄	1	32	yes	complemented
229	C₂×#450	C₂×D₄	1	32	yes	—
230	C₂×#447	C₂²⋊C₄	1	32	yes	complemented
231	C₂×#447	C₂×D₄	1	32	yes	—
232	C₂×#418	C₂²⋊C₄	1	32	yes	complemented
233	C₂²×#102	C₂²×C₄	1	8	yes	—
234	C₂²×#102	C₂²×C₄	1	8	yes	—
235	C₂²×#102	C₂²×C₄	1	8	yes	complemented
236	C₂²×#102	C₂²×C₄	1	8	yes	complemented
237	C₂×#407	C₂×D₄	1	16	yes	—
238	C₂²×C₂²⋊C₈	C₂²×C₄	1	4	yes	—
239	C₂²×C₂²⋊C₈	C₂²×C₄	1	4	yes	complemented
240	C₂²×C₂²⋊C₈	C₂²×C₄	1	4	yes	complemented
241	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
242	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
243	C₂×#380	C₂×D₄	1	4	yes	—
244	C₂×#380	C₂⁴	1	4	yes	—
245	C₂×#380	C₂⁴	1	4	yes	—
246	C₂×#379	C₂×D₄	1	2	yes	—
247	C₂×#379	C₂×D₄	1	2	yes	—
248	C₂×#379	C₂×D₄	1	2	yes	—
249	C₂×#379	C₂×D₄	1	2	yes	—
250	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
251	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	—
252	C₂²×#95	C₂×D₄	1	4	yes	—
253	C₂²⋊#95	C₂×D₄	1	8	yes	—
254	C₂²⋊#95	C₂×D₄	1	8	yes	—
255	C₂²⋊#95	C₂×D₄	1	4	yes	—
256	C₂²⋊#95	C₂×D₄	1	4	yes	—
257	C₂⁶	C₄×D₄	1	1	yes	characteristic
258	C₂⁶	C₄×D₄	1	1	yes	characteristic
259	C₂⁶	C₄×D₄	1	1	yes	characteristic
260	C₂⁶	C₄×D₄	1	1	yes	characteristic
261	C₂⁶	#120	1	2	yes	—
262	C₂⁶	#120	1	2	yes	—
263	C₂⁶	#121	1	2	yes	—
264	C₂⁶	#121	1	2	yes	—
265	C₂⁶	C₂²×D₄	1	1	yes	characteristic
266	C₂⁶	C₂²×D₄	1	1	yes	characteristic
267	C₂⁶	C₂²×D₄	1	1	yes	characteristic
268	C₂²×#41	C₂×C₂²⋊C₄	1	8	yes	complemented
269	C₂³×Q₈	C₂³×C₄	1	2	yes	—
270	C₂³×D₄	#99	1	32	yes	complemented
271	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
274	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
275	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
276	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
277	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
278	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
279	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
280	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
281	C₂³×D₄	C₂×C₂²⋊C₄	1	16	yes	—
282	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
283	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
284	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
285	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
286	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
288	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
289	C₂³×D₄	C₂×C₂²⋊C₄	1	16	yes	—
290	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂³×D₄	#120	1	8	yes	—
292	C₂³×D₄	#120	1	16	yes	—
293	C₂³×D₄	#120	1	16	yes	—
294	C₂³×D₄	#120	1	8	yes	—
295	C₂³×D₄	#120	1	16	yes	—
296	C₂³×D₄	C₂³×C₄	1	4	yes	—
297	C₂³×D₄	C₂³×C₄	1	4	yes	—
298	C₂³×D₄	C₂³×C₄	1	2	yes	—
299	C₂³×D₄	C₂²×D₄	1	2	yes	—
300	C₂³×D₄	C₂²×D₄	1	4	yes	—
301	C₂³×D₄	C₂²×D₄	1	4	yes	—
302	C₂³×D₄	C₂²×D₄	1	4	yes	—
303	C₂³×D₄	C₂²×D₄	1	16	yes	—
304	C₂³×D₄	C₂²×D₄	1	2	yes	—
305	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
311	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
312	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂⁴×C₄	C₄×D₄	1	2	yes	—
314	C₂⁴×C₄	C₄×D₄	1	2	yes	—
315	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
316	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
318	C₂⁴×C₄	C₄×D₄	1	2	yes	—
319	C₂⁴×C₄	C₄×D₄	1	2	yes	—
320	C₂⁴×C₄	C₄×D₄	1	2	yes	—
321	C₂⁴×C₄	C₄×D₄	1	2	yes	—
322	C₂⁴×C₄	C₄×D₄	1	2	yes	—
323	C₂⁴×C₄	C₄×D₄	1	2	yes	—
324	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
325	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
329	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
330	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
331	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
332	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
333	C₂⁴×C₄	#120	1	2	yes	—
334	C₂⁴×C₄	#120	1	2	yes	—
335	C₂⁴×C₄	#120	1	2	yes	—
336	C₂⁴×C₄	#120	1	2	yes	—
337	C₂⁴×C₄	#120	1	2	yes	—
338	C₂⁴×C₄	#120	1	2	yes	—
339	C₂⁴×C₄	#121	1	2	yes	—
340	C₂⁴×C₄	#121	1	2	yes	—
341	C₂⁴×C₄	#121	1	2	yes	—
342	C₂⁴×C₄	#121	1	2	yes	—
343	C₂⁴×C₄	#121	1	2	yes	—
344	C₂⁴×C₄	#121	1	2	yes	—
345	C₂⁴×C₄	#121	1	2	yes	—
346	C₂⁴×C₄	#121	1	2	yes	—
347	C₂⁴×C₄	#121	1	2	yes	—
348	C₂⁴×C₄	#121	1	2	yes	—
349	C₂⁴×C₄	#121	1	2	yes	—
350	C₂⁴×C₄	#121	1	2	yes	—
351	C₂⁴×C₄	#121	1	2	yes	—
352	C₂⁴×C₄	#121	1	2	yes	—
353	C₂⁴×C₄	#123	1	2	yes	—
354	C₂⁴×C₄	#123	1	2	yes	—
355	C₂⁴×C₄	#123	1	2	yes	—
356	C₂⁴×C₄	#123	1	2	yes	—
357	C₂⁴×C₄	#123	1	2	yes	—
358	C₂⁴×C₄	#123	1	2	yes	—
359	C₂⁴×C₄	#123	1	2	yes	—
360	C₂⁴×C₄	#123	1	2	yes	—
361	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
362	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
363	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
364	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
365	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
366	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
367	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
368	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
369	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
370	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
371	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
372	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
373	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
374	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
375	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
376	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
377	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
378	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
380	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
382	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
383	C₂⁴×C₄	C₂×#41	1	2	yes	—
384	C₂⁴×C₄	C₂×#41	1	2	yes	—
385	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
386	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
387	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
388	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
389	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
390	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
391	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
392	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
393	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
394	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
395	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	32	yes	complemented
396	C₂²×D₈	C₂×C₂²⋊C₄	1	32	yes	complemented
397	C₂²×M₁₆	C₂×C₂²⋊C₄	1	16	yes	complemented
398	C₂³×C₈	C₂³×C₄	1	8	yes	—
399	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
400	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
401	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
402	C₂×#121	C₂²×D₄	1	8	yes	—
403	C₂×#117	C₂×C₂²⋊C₄	1	8	yes	complemented
404	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
405	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
406	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
407	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
408	C₂×#102	C₂×C₂²⋊C₄	1	32	yes	complemented
409	C₂×#102	C₂×C₂²⋊C₄	1	32	yes	complemented
410	C₂×C₂²⋊C₈	C₂×C₂²⋊C₄	1	16	yes	complemented
411	C₂×C₂²⋊C₈	C₂²×D₄	1	16	yes	—
412	#379	AGL(1,ℤ/8)	1	8	yes	complemented
413	C₂×#95	C₂²×D₄	1	8	yes	—
414	C₂⁵	#386	1	2	yes	—
415	C₂⁵	#386	1	2	yes	—
416	C₂⁵	#386	1	2	yes	—
417	C₂⁵	#386	1	2	yes	—
418	C₂⁵	#386	1	2	yes	—
419	C₂⁵	#386	1	2	yes	—
420	C₂⁵	#386	1	2	yes	—
421	C₂⁵	#386	1	2	yes	—
422	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
423	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
424	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
426	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
427	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
428	C₂⁵	C₂×#120	1	1	yes	characteristic
429	C₂⁵	C₂×#120	1	2	yes	—
430	C₂⁵	C₂×#120	1	2	yes	—
431	C₂⁵	C₂×#120	1	1	yes	characteristic
432	C₂⁵	C₂×#121	1	2	yes	—
433	C₂⁵	C₂×#121	1	1	yes	characteristic
434	C₂⁵	C₂×#121	1	1	yes	characteristic
435	C₂⁵	C₂×#121	1	2	yes	—
436	C₂⁵	D₄²	1	8	yes	—
437	C₂⁵	C₂×AGL(1,ℤ/8)	1	4	yes	—
438	C₂⁵	#575	1	4	yes	—
439	C₂⁵	C₂³×D₄	1	1	yes	characteristic
440	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	complemented
441	C₂²×D₄	#379	1	8	yes	—
442	C₂²×D₄	#379	1	8	yes	—
443	C₂²×D₄	#379	1	16	yes	—
444	C₂²×D₄	#379	1	16	yes	—
445	C₂²×D₄	#379	1	8	yes	—
446	C₂²×D₄	#379	1	8	yes	—
447	C₂²×D₄	C₂×#99	1	16	yes	—
448	C₂²×D₄	C₂×#99	1	32	yes	—
449	C₂²×D₄	C₂×#99	1	32	yes	—
450	C₂²×D₄	C₂×#99	1	16	yes	—
451	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
452	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
453	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
454	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
455	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
456	C₂²×D₄	C₂×#120	1	8	yes	—
457	C₂²×D₄	C₂×#120	1	16	yes	—
458	C₂²×D₄	C₂×#120	1	8	yes	—
459	C₂³×C₄	#386	1	2	yes	—
460	C₂³×C₄	#386	1	2	yes	—
461	C₂³×C₄	#386	1	2	yes	—
462	C₂³×C₄	#386	1	2	yes	—
463	C₂³×C₄	#386	1	2	yes	—
464	C₂³×C₄	#386	1	2	yes	—
465	C₂³×C₄	#386	1	2	yes	—
466	C₂³×C₄	#386	1	2	yes	—
467	C₂³×C₄	#386	1	2	yes	—
468	C₂³×C₄	#386	1	2	yes	—
469	C₂³×C₄	#386	1	2	yes	—
470	C₂³×C₄	#386	1	2	yes	—
471	C₂³×C₄	#386	1	2	yes	—
472	C₂³×C₄	#386	1	2	yes	—
473	C₂³×C₄	#386	1	2	yes	—
474	C₂³×C₄	#386	1	2	yes	—
475	C₂³×C₄	#386	1	2	yes	—
476	C₂³×C₄	#386	1	2	yes	—
477	C₂³×C₄	#386	1	2	yes	—
478	C₂³×C₄	#386	1	2	yes	—
479	C₂³×C₄	#386	1	2	yes	—
480	C₂³×C₄	#386	1	2	yes	—
481	C₂³×C₄	#386	1	2	yes	—
482	C₂³×C₄	#386	1	2	yes	—
483	C₂³×C₄	C₂×#99	1	16	yes	—
484	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
485	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
486	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
487	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
488	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
489	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
490	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
491	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
492	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
493	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
494	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
495	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
496	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
497	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
498	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
500	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
501	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
502	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
503	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
506	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
508	C₂³×C₄	#518	1	4	yes	—
509	C₂³×C₄	#518	1	4	yes	—
510	C₂³×C₄	C₂×#120	1	2	yes	—
511	C₂³×C₄	C₂×#120	1	2	yes	—
512	C₂³×C₄	C₂×#120	1	1	yes	characteristic
513	C₂³×C₄	C₂×#120	1	4	yes	—
514	C₂³×C₄	C₂×#120	1	4	yes	—
515	C₂³×C₄	C₂×#120	1	1	yes	characteristic
516	C₂³×C₄	C₂×#120	1	4	yes	—
517	C₂³×C₄	C₂×#120	1	4	yes	—
518	C₂³×C₄	C₂×#121	1	2	yes	—
519	C₂³×C₄	C₂×#121	1	2	yes	—
520	C₂³×C₄	C₂×#121	1	2	yes	—
521	C₂³×C₄	C₂×#121	1	2	yes	—
522	C₂³×C₄	C₂×#121	1	2	yes	—
523	C₂³×C₄	C₂×#121	1	2	yes	—
524	C₂³×C₄	C₂×#121	1	1	yes	characteristic
525	C₂³×C₄	C₂×#121	1	1	yes	characteristic
526	C₂³×C₄	C₂×#121	1	1	yes	characteristic
527	C₂³×C₄	C₂×#121	1	1	yes	characteristic
528	C₂³×C₄	C₂×#121	1	1	yes	characteristic
529	C₂³×C₄	C₂×#121	1	1	yes	characteristic
530	C₂³×C₄	C₂×#123	1	2	yes	—
531	C₂³×C₄	C₂×#123	1	2	yes	—
532	C₂³×C₄	C₂×#123	1	2	yes	—
533	C₂³×C₄	C₂×#123	1	2	yes	—
534	C₂³×C₄	C₂×#123	1	1	yes	characteristic
535	C₂³×C₄	C₂×#123	1	1	yes	characteristic
536	C₂³×C₄	C₂×#123	1	1	yes	characteristic
537	C₂³×C₄	C₂×#123	1	1	yes	characteristic
538	C₂³×C₄	#534	1	4	yes	—
539	C₂³×C₄	#534	1	4	yes	—
540	C₂³×C₄	#534	1	4	yes	—
541	C₂³×C₄	#534	1	4	yes	—
542	C₂³×C₄	D₄²	1	8	yes	—
543	C₂³×C₄	D₄²	1	8	yes	—
544	C₂³×C₄	D₄²	1	8	yes	—
545	C₂³×C₄	#546	1	8	yes	—
546	C₂³×C₄	#546	1	8	yes	—
547	C₂³×C₄	#546	1	8	yes	—
548	C₂³×C₄	#546	1	8	yes	—
549	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
550	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
551	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
552	C₂³×C₄	C₂³×D₄	1	4	yes	—
553	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
554	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
555	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
556	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
557	C₂²×C₈	C₂²×C₂²⋊C₄	1	16	yes	complemented
558	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
559	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
560	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	8	yes	complemented
561	C₂⁴	#1898	1	8	yes	—
562	C₂⁴	#1904	1	8	yes	—
563	C₂⁴	C₂×#386	1	2	yes	—
564	C₂⁴	C₂×#386	1	1	yes	characteristic
565	C₂⁴	C₂×#386	1	1	yes	characteristic
566	C₂⁴	C₂×#386	1	2	yes	—
567	C₂⁴	C₂×#386	1	2	yes	—
568	C₂⁴	C₂×#386	1	1	yes	characteristic
569	C₂⁴	C₂×#386	1	2	yes	—
570	C₂⁴	C₂×#386	1	1	yes	characteristic
571	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
572	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
573	C₂⁴	#2403	1	4	yes	—
574	C₂⁴	#2403	1	4	yes	—
575	C₂⁴	#2410	1	4	yes	—
576	C₂⁴	#2410	1	4	yes	—
577	C₂⁴	C₄×AGL(1,ℤ/8)	1	4	yes	—
578	C₂⁴	C₄×AGL(1,ℤ/8)	1	4	yes	—
579	C₂⁴	#3003	1	4	yes	—
580	C₂⁴	#3005	1	4	yes	—
581	C₂⁴	#3036	1	8	yes	—
582	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
583	C₂⁴	C₂²×#120	1	1	yes	characteristic
584	C₂⁴	C₂²×#121	1	1	yes	characteristic
585	C₂⁴	C₂×D₄²	1	4	yes	—
586	C₂⁴	C₂²×AGL(1,ℤ/8)	1	2	yes	—
587	C₂⁴	C₂×#575	1	2	yes	—
588	C₂⁴	#3585	1	4	yes	—
589	C₂×D₄	#1781	1	32	yes	complemented
590	C₂×D₄	C₂×#379	1	8	yes	—
591	C₂×D₄	C₂×#379	1	8	yes	—
592	C₂×D₄	C₂²×#99	1	16	yes	—
593	C₂×D₄	C₂²×#99	1	16	yes	—
594	C₂²×C₄	#1898	1	8	yes	—
595	C₂²×C₄	#1898	1	8	yes	—
596	C₂²×C₄	#1898	1	8	yes	—
597	C₂²×C₄	C₂×#379	1	2	yes	—
598	C₂²×C₄	C₂×#379	1	2	yes	—
599	C₂²×C₄	C₂×#379	1	2	yes	—
600	C₂²×C₄	C₂×#379	1	2	yes	—
601	C₂²×C₄	C₂×#386	1	2	yes	—
602	C₂²×C₄	C₂×#386	1	2	yes	—
603	C₂²×C₄	C₂×#386	1	1	yes	characteristic
604	C₂²×C₄	C₂×#386	1	1	yes	characteristic
605	C₂²×C₄	C₂×#386	1	1	yes	characteristic
606	C₂²×C₄	C₂×#386	1	2	yes	—
607	C₂²×C₄	C₂×#386	1	2	yes	—
608	C₂²×C₄	C₂×#386	1	1	yes	characteristic
609	C₂²×C₄	#2308	1	2	yes	—
610	C₂²×C₄	#2308	1	2	yes	—
611	C₂²×C₄	#2308	1	2	yes	—
612	C₂²×C₄	#2308	1	2	yes	—
613	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
614	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
615	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
616	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
617	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
618	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
619	C₂²×C₄	#2403	1	4	yes	—
620	C₂²×C₄	#2403	1	4	yes	—
621	C₂²×C₄	#2405	1	4	yes	—
622	C₂²×C₄	#2405	1	4	yes	—
623	C₂²×C₄	#2405	1	4	yes	—
624	C₂²×C₄	#2405	1	4	yes	—
625	C₂²×C₄	#2410	1	4	yes	—
626	C₂²×C₄	#2410	1	4	yes	—
627	C₂²×C₄	#2410	1	4	yes	—
628	C₂²×C₄	#2410	1	4	yes	—
629	C₂²×C₄	#2410	1	4	yes	—
630	C₂²×C₄	#2410	1	4	yes	—
631	C₂²×C₄	C₂²×#99	1	8	yes	—
632	C₂²×C₄	C₂²×#99	1	8	yes	—
633	C₂²×C₄	C₂²×#99	1	8	yes	—
634	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
635	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
636	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
637	C₂²×C₄	C₂×#518	1	2	yes	—
638	C₂²×C₄	C₂²×#120	1	2	yes	—
639	C₂²×C₄	C₂²×#120	1	2	yes	—
640	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
641	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
642	C₂²×C₄	C₂×#534	1	2	yes	—
643	C₂²×C₄	C₂×#534	1	2	yes	—
644	C₂²×C₄	C₂×D₄²	1	4	yes	—
645	C₂²×C₄	C₂×#546	1	4	yes	—
646	C₂²×C₄	C₂×#546	1	4	yes	—
647	C₂³	#13867	1	2	yes	—
648	C₂³	#13867	1	2	yes	—
649	C₂³	#13867	1	2	yes	—
650	C₂³	#13867	1	2	yes	—
651	C₂³	#20925	1	4	yes	—
652	C₂³	#20925	1	4	yes	—
653	C₂³	C₂×#1898	1	4	yes	—
654	C₂³	C₂×#1898	1	4	yes	—
655	C₂³	C₂×#1898	1	4	yes	—
656	C₂³	C₂×#1904	1	4	yes	—
657	C₂³	C₂×#1904	1	4	yes	—
658	C₂³	C₂×#1904	1	4	yes	—
659	C₂³	C₂²×#386	1	1	yes	characteristic
660	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
661	C₂³	C₂×#2403	1	2	yes	—
662	C₂³	C₂×#2410	1	2	yes	—
663	C₂³	C₂×C₄×AGL(1,ℤ/8)	1	2	yes	—
664	C₂³	#60168	1	2	yes	—
665	C₂³	C₂×#3003	1	1	yes	characteristic
666	C₂³	C₂×#3005	1	1	yes	characteristic
667	C₂³	#60367	1	2	yes	—
668	C₂³	C₂×#3036	1	2	yes	—
669	C₂³	#60423	1	2	yes	—
670	C₂³	D₄×AGL(1,ℤ/8)	1	8	yes	—
671	C₂³	#61066	1	8	yes	—
672	D₄	C₂×#1781	1	16	yes	—
673	C₂×C₄	#13867	1	2	yes	—
674	C₂×C₄	#13867	1	2	yes	—
675	C₂×C₄	#13867	1	2	yes	—
676	C₂×C₄	#13867	1	2	yes	—
677	C₂×C₄	C₂×#1781	1	8	yes	—
678	C₂×C₄	C₂×#1898	1	4	yes	—
679	C₂×C₄	C₂×#1898	1	4	yes	—
680	C₂×C₄	C₂×#1898	1	4	yes	—
681	C₂×C₄	#21746	1	8	yes	—
682	C₂×C₄	C₂²×#379	1	1	yes	characteristic
683	C₂×C₄	C₂×#2308	1	1	yes	characteristic
684	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
685	C₂×C₄	C₂×#2410	1	2	yes	—
686	C₂×C₄	C₂×#2405	1	2	yes	—
687	C₂×C₄	C₂³×#99	1	4	yes	—
688	C₂²	#198404	1	8	yes	complemented
689	C₂²	#359428	1	4	yes	—
690	C₂²	#359472	1	4	yes	—
691	C₂²	C₂×#13867	1	1	yes	characteristic
692	C₂²	C₂×#20925	1	1	yes	characteristic
693	C₂²	#6371420	1	1	yes	characteristic
694	C₂²	C₂²×#1898	1	2	yes	—
695	C₂²	C₂²×#1904	1	2	yes	—
696	C₂²	C₂²⋊C₄×AGL(1,ℤ/8)	1	4	yes	—
697	C₂²	#6437510	1	2	yes	—
698	C₂²	#6437511	1	2	yes	—
699	C₂²	#6437680	1	4	yes	—
700	C₄	#359428	1	4	yes	—
701	C₄	C₂²×#1781	1	2	yes	—
702	C₄	C₂×#21746	1	2	yes	—
703	C₂	C₂×#359428	1	1	yes	characteristic
704	C₂	C₂×#198404	1	2	yes	—
705	C₂	C₂×#359472	1	1	yes	characteristic
706	C₂	#72235984	1	2	yes	—
707	C₂	#72310936	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×#386
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂³×#3003	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72311061	C₂	semidirect
2. #72311051	C₂	semidirect
3. #72311040	C₂	semidirect
4. #72311032	C₂	semidirect
5. #72311020	C₂	semidirect
6. #72311018	C₂	semidirect
7. C₂×D₄×#379	C₂	semidirect
8. #72264272	C₂	semidirect
9. #72240593	C₂	semidirect
11. C₂×#198404	C₂	semidirect
12. #72231771	C₂	semidirect
14. C₂⁴×AGL(1,ℤ/8)	C₄	semidirect
16. C₂³×#450	C₄	semidirect
18. C₂²×#3003	C₄	semidirect
19. C₂²×#3003	C₄	semidirect
23. C₂³×#447	C₄	semidirect
26. C₂³×#418	C₄	semidirect
27. C₂²×D₄×C₂²⋊C₄	C₂²	semidirect
28. C₂×#21420	C₂²	semidirect
29. C₂×#20598	C₂²	semidirect
30. C₂×#20598	C₂²	semidirect
32. C₂×#17592	C₂²	semidirect
36. D₄×#379	C₂²	semidirect
37. C₂×#13902	C₂²	semidirect
40. #392118	C₂²	semidirect
41. #363168	C₂²	semidirect
42. #362712	C₂²	semidirect
43. #361599	C₂²	semidirect
44. C₂×#9259	C₂²	semidirect
45. C₂×#9255	C₂²	semidirect
46. #185050	C₂²	semidirect
47. #185047	C₂²	semidirect
48. #185046	C₂²	semidirect
49. C₂×#7983	C₂²	semidirect
50. C₂×#7929	C₂²	semidirect
51. #114509	C₂²	semidirect
52. #114505	C₂²	semidirect
53. #105544	C₂²	semidirect
54. #105542	C₂²	semidirect
55. #105522	C₂²	semidirect
56. #105520	C₂²	semidirect
57. C₂⁴×#41	C₂×C₄	semidirect
73. C₂³×AGL(1,ℤ/8)	C₂×C₄	semidirect
74. C₂³×AGL(1,ℤ/8)	C₂×C₄	semidirect
75. C₂⁴×SD₁₆	C₂×C₄	semidirect
76. C₂⁴×D₈	C₂×C₄	semidirect
77. C₂⁴×M₁₆	C₂×C₄	semidirect
78. C₂²×#525	C₂×C₄	semidirect
79. C₂²×#525	C₂×C₄	semidirect
82. C₂³×C₂²⋊Q₈	C₂×C₄	semidirect
84. C₂³×#121	C₂×C₄	semidirect
86. C₂³×#117	C₂×C₄	semidirect
89. C₂²×#450	C₂×C₄	semidirect
90. C₂²×#450	C₂×C₄	semidirect
91. C₂²×#450	C₂×C₄	semidirect
95. C₂²×#447	C₂×C₄	semidirect
96. C₂²×#447	C₂×C₄	semidirect
97. C₂²×#447	C₂×C₄	semidirect
101. C₂²×#418	C₂×C₄	semidirect
102. C₂²×#418	C₂×C₄	semidirect
103. C₂³×#102	C₂×C₄	semidirect
104. C₂³×#102	C₂×C₄	semidirect
105. C₂²×#407	C₂×C₄	semidirect
106. C₂²×#407	C₂×C₄	semidirect
110. C₂³×C₂²⋊C₈	C₂×C₄	semidirect
118. C₂×#1996	C₂³	semidirect
119. C₂×#1964	C₂³	semidirect
124. C₂×#1520	C₂³	semidirect
125. C₂×#1519	C₂³	semidirect
138. C₂×#1289	C₂³	semidirect
139. C₂×#1282	C₂³	semidirect
142. C₂³×#41	C₂²×C₄	semidirect
143. C₂⁴×Q₈	C₂²×C₄	semidirect
164. C₂⁴×D₄	C₂²×C₄	semidirect
205. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
207. C₂³×SD₁₆	C₂²×C₄	semidirect
209. C₂³×D₈	C₂²×C₄	semidirect
211. C₂³×M₁₆	C₂²×C₄	semidirect
212. C₂⁴×C₈	C₂²×C₄	semidirect
215. C₂²×C₂²⋊Q₈	C₂²×C₄	semidirect
216. C₂²×C₂²⋊Q₈	C₂²×C₄	semidirect
219. C₂²×#121	C₂²×C₄	semidirect
220. C₂²×#121	C₂²×C₄	semidirect
223. C₂²×#117	C₂²×C₄	semidirect
224. C₂³×C₄⋊C₄	C₂²×C₄	semidirect
225. C₂³×C₄⋊C₄	C₂²×C₄	semidirect
228. C₂×#450	C₂²⋊C₄	semidirect
230. C₂×#447	C₂²⋊C₄	semidirect
232. C₂×#418	C₂²⋊C₄	semidirect
235. C₂²×#102	C₂²×C₄	semidirect
236. C₂²×#102	C₂²×C₄	semidirect
239. C₂²×C₂²⋊C₈	C₂²×C₄	semidirect
240. C₂²×C₂²⋊C₈	C₂²×C₄	semidirect
268. C₂²×#41	C₂×C₂²⋊C₄	semidirect
270. C₂³×D₄	#99	semidirect
395. C₂²×SD₁₆	C₂×C₂²⋊C₄	semidirect
396. C₂²×D₈	C₂×C₂²⋊C₄	semidirect
397. C₂²×M₁₆	C₂×C₂²⋊C₄	semidirect
399. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
401. C₂×#121	C₂×C₂²⋊C₄	semidirect
403. C₂×#117	C₂×C₂²⋊C₄	semidirect
408. C₂×#102	C₂×C₂²⋊C₄	semidirect
409. C₂×#102	C₂×C₂²⋊C₄	semidirect
410. C₂×C₂²⋊C₈	C₂×C₂²⋊C₄	semidirect
412. #379	AGL(1,ℤ/8)	semidirect
440. C₂²×Q₈	C₂²×C₂²⋊C₄	semidirect
455. C₂²×D₄	C₂²×C₂²⋊C₄	semidirect
557. C₂²×C₈	C₂²×C₂²⋊C₄	semidirect
558. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
559. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
560. C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	semidirect
589. C₂×D₄	#1781	semidirect
688. C₂²	#198404	semidirect

Maximal subgroups

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

subgroup	index
#72311061	2
#72311051	2
#72311040	2
#72311032	2
#72311020	2
#72311018	2
C₂×D₄×#379	2
#72264272	2
#72240593	2
C₂³×#3003	2
C₂×#198404	2
#72231771	2