Subgroups — C₃²×#3519 #11770568

Order 1152.

3756 conjugacy classes of subgroups.

The subgroup lattice has 735 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#553	C₂	1	2	yes	maximal, complemented
4	C₃²×#553	C₂	1	2	yes	maximal, complemented
5	C₃²×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#546	C₂	1	2	yes	maximal, complemented
7	C₃²×#546	C₂	1	4	yes	maximal, complemented
8	C₃²×D₄²	C₂	1	2	yes	maximal, complemented
9	C₃²×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#540	C₂	1	2	yes	maximal, complemented
11	C₃²×#538	C₂	1	4	yes	maximal, complemented
12	C₃²×#532	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₃²×#121	C₂	1	2	yes	maximal, complemented
16	C₃²×#518	C₂	1	2	yes	maximal, complemented
17	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3519	C₃	1	4	yes	maximal, direct product factor
19	C₂×C₃²×#41	C₂²	1	2	yes	complemented
20	C₂×C₃²×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃²×D₄	C₂²	1	2	yes	—
23	C₂²×C₃²×D₄	C₂²	1	4	yes	complemented
24	C₂²×C₃²×D₄	C₂²	1	2	yes	complemented
25	C₂³×C₃²×C₄	C₂²	1	2	yes	complemented
26	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃²×#127	C₂²	1	1	yes	characteristic, complemented
28	C₃²×#127	C₂²	1	2	yes	complemented
29	C₃²×#126	C₂²	1	4	yes	complemented
30	C₃²×#126	C₂²	1	2	yes	complemented
31	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#125	C₂²	1	2	yes	complemented
33	C₃²×#124	C₂²	1	4	yes	complemented
34	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#124	C₂²	1	2	yes	complemented
36	C₃²×#123	C₂²	1	4	yes	complemented
37	C₃²×#123	C₂²	1	4	yes	complemented
38	C₃²×#123	C₂²	1	4	yes	complemented
39	C₃²×#123	C₂²	1	2	yes	complemented
40	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₃²×#121	C₂²	1	1	yes	characteristic
44	C₃²×#121	C₂²	1	4	yes	complemented
45	C₃²×#121	C₂²	1	2	yes	complemented
46	C₃²×#121	C₂²	1	2	yes	complemented
47	C₃²×#121	C₂²	1	2	yes	complemented
48	C₃²×#121	C₂²	1	4	yes	complemented
49	C₃²×#121	C₂²	1	2	yes	complemented
50	C₃²×#121	C₂²	1	2	yes	complemented
51	C₃²×#121	C₂²	1	2	yes	complemented
52	C₃²×#121	C₂²	1	2	yes	complemented
53	C₃²×#121	C₂²	1	4	yes	complemented
54	C₃²×#121	C₂²	1	4	yes	complemented
55	C₃²×#121	C₂²	1	4	yes	complemented
56	C₃²×#120	C₂²	1	4	yes	complemented
57	C₃²×#120	C₂²	1	4	yes	complemented
58	C₃²×#120	C₂²	1	4	yes	complemented
59	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
61	C₃²×C₄×D₄	C₂²	1	2	yes	—
62	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
63	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
64	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
65	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
66	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
67	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
68	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
69	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
70	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
71	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
72	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
73	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
74	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
75	C₃²×#117	C₂²	1	2	yes	complemented
76	C₃²×#117	C₂²	1	2	yes	complemented
77	C₃²×#117	C₂²	1	2	yes	complemented
78	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
82	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
84	C₃×#555	C₂×C₃	1	4	yes	complemented
85	C₃×#554	C₂×C₃	1	4	yes	complemented
86	C₃×#553	C₂×C₃	1	8	yes	complemented
87	C₃×#553	C₂×C₃	1	8	yes	complemented
88	C₃×#550	C₂×C₃	1	4	yes	complemented
89	C₃×#546	C₂×C₃	1	16	yes	complemented
90	C₃×#546	C₂×C₃	1	8	yes	complemented
91	C₃×D₄²	C₂×C₃	1	4	yes	complemented
92	C₃×D₄²	C₂×C₃	1	8	yes	complemented
93	C₃×#540	C₂×C₃	1	8	yes	complemented
94	C₃×#538	C₂×C₃	1	16	yes	complemented
95	C₃×#532	C₂×C₃	1	4	yes	complemented
96	C₃×#529	C₂×C₃	1	4	yes	complemented
97	C₃×#525	C₂×C₃	1	8	yes	complemented
98	C₂×C₃×#121	C₂×C₃	1	8	yes	complemented
99	C₃×#518	C₂×C₃	1	8	yes	complemented
100	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	complemented
101	C₂⁴×C₃²	C₂³	1	2	yes	—
102	C₂⁴×C₃²	C₂³	1	4	yes	—
103	C₃²×#41	—	4	4	no	—
104	C₃²×#41	—	4	4	no	—
105	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃²×Q₈	C₂³	1	2	yes	—
107	C₂×C₃²×D₄	—	2	4	no	—
108	C₂×C₃²×D₄	—	2	8	no	—
109	C₂×C₃²×D₄	—	4	4	no	—
110	C₂×C₃²×D₄	—	4	8	no	—
111	C₂×C₃²×D₄	C₂³	1	2	yes	—
112	C₂×C₃²×D₄	C₂³	1	4	yes	—
113	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃²×D₄	C₂³	1	2	yes	—
115	C₂×C₃²×D₄	C₂³	1	2	yes	—
116	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
117	C₂×C₃²×D₄	C₂³	1	4	yes	—
118	C₂×C₃²×D₄	C₂³	1	2	yes	—
119	C₂×C₃²×D₄	C₂³	1	4	yes	—
120	C₂×C₃²×D₄	C₂³	1	4	yes	—
121	C₂×C₃²×D₄	C₂³	1	4	yes	—
122	C₂×C₃²×D₄	C₂³	1	4	yes	—
123	C₂×C₃²×D₄	C₂³	1	2	yes	—
124	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃²×C₄	—	4	4	no	—
126	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
127	C₂²×C₃²×C₄	C₂³	1	2	yes	—
128	C₂²×C₃²×C₄	C₂³	1	2	yes	—
129	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
130	C₂²×C₃²×C₄	C₂³	1	2	yes	—
131	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
132	C₂²×C₃²×C₄	C₂³	1	2	yes	—
133	C₂²×C₃²×C₄	C₂³	1	2	yes	—
134	C₂²×C₃²×C₄	C₂³	1	2	yes	—
135	C₂²×C₃²×C₄	C₂³	1	4	yes	—
136	C₂²×C₃²×C₄	C₂³	1	4	yes	—
137	C₂²×C₃²×C₄	C₂³	1	4	yes	—
138	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
146	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₃²×C₄²	C₂³	1	1	yes	characteristic
168	C₃²×C₄²	C₂³	1	1	yes	characteristic
169	C₃²×C₄²	C₂³	1	1	yes	characteristic
170	C₃²×C₄²	C₂³	1	1	yes	characteristic
171	C₃²×C₄²	C₂³	1	4	yes	—
172	C₃²×C₄²	C₂³	1	2	yes	—
173	#3519	C₃²	1	1	yes	characteristic, direct product factor, Sylow
174	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
175	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
176	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
177	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
178	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	complemented
179	C₂²×C₃×D₄	C₂²×C₃	1	16	yes	complemented
180	C₂³×C₃×C₄	C₂²×C₃	1	8	yes	complemented
181	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
182	C₃×#127	C₂²×C₃	1	4	yes	complemented
183	C₃×#127	C₂²×C₃	1	8	yes	complemented
184	C₃×#126	C₂²×C₃	1	8	yes	complemented
185	C₃×#126	C₂²×C₃	1	16	yes	complemented
186	C₃×#125	C₂²×C₃	1	4	yes	complemented
187	C₃×#125	C₂²×C₃	1	8	yes	complemented
188	C₃×#124	C₂²×C₃	1	4	yes	complemented
189	C₃×#124	C₂²×C₃	1	8	yes	complemented
190	C₃×#124	C₂²×C₃	1	16	yes	complemented
191	C₃×#123	C₂²×C₃	1	16	yes	complemented
192	C₃×#123	C₂²×C₃	1	8	yes	complemented
193	C₃×#123	C₂²×C₃	1	16	yes	complemented
194	C₃×#123	C₂²×C₃	1	16	yes	complemented
195	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
196	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
197	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
198	C₃×#121	C₂²×C₃	1	4	yes	—
199	C₃×#121	C₂²×C₃	1	8	yes	complemented
200	C₃×#121	C₂²×C₃	1	16	yes	complemented
201	C₃×#121	C₂²×C₃	1	16	yes	complemented
202	C₃×#121	C₂²×C₃	1	8	yes	complemented
203	C₃×#121	C₂²×C₃	1	8	yes	complemented
204	C₃×#121	C₂²×C₃	1	8	yes	complemented
205	C₃×#121	C₂²×C₃	1	8	yes	complemented
206	C₃×#121	C₂²×C₃	1	16	yes	complemented
207	C₃×#121	C₂²×C₃	1	16	yes	complemented
208	C₃×#121	C₂²×C₃	1	8	yes	complemented
209	C₃×#121	C₂²×C₃	1	8	yes	complemented
210	C₃×#121	C₂²×C₃	1	16	yes	complemented
211	C₃×#120	C₂²×C₃	1	16	yes	complemented
212	C₃×#120	C₂²×C₃	1	16	yes	complemented
213	C₃×#120	C₂²×C₃	1	16	yes	complemented
214	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
215	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
216	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
217	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
218	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
219	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
220	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
221	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
222	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
223	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
224	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
225	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
226	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
227	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
228	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
229	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
230	C₃×#117	C₂²×C₃	1	8	yes	complemented
231	C₃×#117	C₂²×C₃	1	8	yes	complemented
232	C₃×#117	C₂²×C₃	1	8	yes	complemented
233	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
234	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
235	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
236	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
237	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
238	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	complemented
239	C₂³×C₃²	—	2	4	no	—
240	C₂³×C₃²	—	2	4	no	—
241	C₂³×C₃²	—	2	8	no	—
242	C₂³×C₃²	—	4	2	no	—
243	C₂³×C₃²	—	4	4	no	—
244	C₂³×C₃²	—	4	4	no	—
245	C₂³×C₃²	C₂⁴	1	2	yes	—
246	C₂³×C₃²	C₂⁴	1	2	yes	—
247	C₂³×C₃²	C₂⁴	1	4	yes	—
248	C₂³×C₃²	C₂⁴	1	2	yes	—
249	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
250	C₃²×Q₈	—	2	2	no	—
251	C₃²×Q₈	—	4	2	no	—
252	C₃²×D₄	—	2	4	no	—
253	C₃²×D₄	—	2	8	no	—
254	C₃²×D₄	—	2	4	no	—
255	C₃²×D₄	—	2	8	no	—
256	C₃²×D₄	—	2	2	no	—
257	C₃²×D₄	—	2	4	no	—
258	C₃²×D₄	—	2	2	no	—
259	C₃²×D₄	—	2	4	no	—
260	C₃²×D₄	—	4	4	no	—
261	C₃²×D₄	—	4	4	no	—
262	C₃²×D₄	—	4	4	no	—
263	C₃²×D₄	—	4	2	no	—
264	C₃²×D₄	—	4	4	no	—
265	C₃²×D₄	#41	1	4	yes	complemented
266	C₂×C₃²×C₄	—	2	2	no	—
267	C₂×C₃²×C₄	—	2	2	no	—
268	C₂×C₃²×C₄	—	2	4	no	—
269	C₂×C₃²×C₄	—	2	2	no	—
270	C₂×C₃²×C₄	—	2	4	no	—
271	C₂×C₃²×C₄	—	2	4	no	—
272	C₂×C₃²×C₄	—	4	2	no	—
273	C₂×C₃²×C₄	—	4	2	no	—
274	C₂×C₃²×C₄	—	4	2	no	—
275	C₂×C₃²×C₄	—	4	4	no	—
276	C₂×C₃²×C₄	—	4	4	no	—
277	C₂×C₃²×C₄	—	4	4	no	—
278	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
279	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
280	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
281	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
282	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
283	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
284	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
285	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
286	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
287	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
288	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
289	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
290	#555	C₂×C₃²	1	1	yes	characteristic, complemented
291	#554	C₂×C₃²	1	1	yes	characteristic, complemented
292	#553	C₂×C₃²	1	2	yes	complemented
293	#553	C₂×C₃²	1	2	yes	complemented
294	#550	C₂×C₃²	1	1	yes	characteristic, complemented
295	#546	C₂×C₃²	1	4	yes	complemented
296	#546	C₂×C₃²	1	2	yes	complemented
297	D₄²	C₂×C₃²	1	1	yes	characteristic, complemented
298	D₄²	C₂×C₃²	1	2	yes	complemented
299	#540	C₂×C₃²	1	2	yes	complemented
300	#538	C₂×C₃²	1	4	yes	complemented
301	#532	C₂×C₃²	1	1	yes	characteristic, complemented
302	#529	C₂×C₃²	1	1	yes	characteristic, complemented
303	#525	C₂×C₃²	1	2	yes	complemented
304	C₂×#121	C₂×C₃²	1	2	yes	complemented
305	#518	C₂×C₃²	1	2	yes	complemented
306	C₂×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
307	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
308	C₂⁴×C₃	C₂³×C₃	1	16	yes	—
309	C₃×#41	—	4	16	no	—
310	C₃×#41	—	4	16	no	—
311	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
312	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
313	C₂×C₃×D₄	—	2	16	no	—
314	C₂×C₃×D₄	—	2	32	no	—
315	C₂×C₃×D₄	—	4	16	no	—
316	C₂×C₃×D₄	—	4	32	no	—
317	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
318	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
319	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
320	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
321	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
322	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
323	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
324	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
325	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
326	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
327	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
328	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
329	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
330	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
331	C₂²×C₃×C₄	—	4	16	no	—
332	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
333	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
334	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
335	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
336	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
337	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
338	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
339	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
340	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
341	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
342	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
343	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
344	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
345	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
346	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
347	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
348	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
349	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
350	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
351	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
352	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
353	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
354	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
355	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
356	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
357	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
358	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
359	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
360	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
361	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
362	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
363	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
364	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
365	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
366	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
367	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
368	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
369	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
370	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
371	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
372	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
373	C₃×C₄²	C₂³×C₃	1	4	yes	—
374	C₃×C₄²	C₂³×C₃	1	4	yes	—
375	C₃×C₄²	C₂³×C₃	1	4	yes	—
376	C₃×C₄²	C₂³×C₃	1	4	yes	—
377	C₃×C₄²	C₂³×C₃	1	16	yes	—
378	C₃×C₄²	C₂³×C₃	1	8	yes	—
379	C₂²×C₃²	—	2	1	no	—
380	C₂²×C₃²	—	2	1	no	—
381	C₂²×C₃²	—	2	2	no	—
382	C₂²×C₃²	—	2	2	no	—
383	C₂²×C₃²	—	2	2	no	—
384	C₂²×C₃²	—	2	2	no	—
385	C₂²×C₃²	—	2	4	no	—
386	C₂²×C₃²	—	2	2	no	—
387	C₂²×C₃²	—	2	4	no	—
388	C₂²×C₃²	—	2	4	no	—
389	C₂²×C₃²	—	2	2	no	—
390	C₂²×C₃²	—	2	2	no	—
391	C₂²×C₃²	—	2	2	no	—
392	C₂²×C₃²	—	4	8	no	—
393	C₂²×C₃²	—	8	8	no	—
394	C₂²×C₃²	C₂×#41	1	4	yes	—
395	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
396	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
397	C₃²×C₄	—	2	1	no	—
398	C₃²×C₄	—	2	2	no	—
399	C₃²×C₄	—	2	1	no	—
400	C₃²×C₄	—	2	1	no	—
401	C₃²×C₄	—	2	2	no	—
402	C₃²×C₄	—	2	2	no	—
403	C₃²×C₄	—	2	1	no	—
404	C₃²×C₄	—	2	2	no	—
405	C₃²×C₄	—	2	4	no	—
406	C₃²×C₄	—	2	2	no	—
407	C₃²×C₄	C₂×#41	1	2	yes	—
408	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
409	C₂×#41	C₂²×C₃²	1	2	yes	complemented
410	C₂×#41	C₂²×C₃²	1	2	yes	complemented
411	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
412	C₂²×D₄	C₂²×C₃²	1	2	yes	—
413	C₂²×D₄	C₂²×C₃²	1	2	yes	complemented
414	C₂²×D₄	C₂²×C₃²	1	4	yes	complemented
415	C₂³×C₄	C₂²×C₃²	1	2	yes	complemented
416	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
417	#127	C₂²×C₃²	1	1	yes	characteristic, complemented
418	#127	C₂²×C₃²	1	2	yes	complemented
419	#126	C₂²×C₃²	1	2	yes	complemented
420	#126	C₂²×C₃²	1	4	yes	complemented
421	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
422	#125	C₂²×C₃²	1	2	yes	complemented
423	#124	C₂²×C₃²	1	1	yes	characteristic, complemented
424	#124	C₂²×C₃²	1	2	yes	complemented
425	#124	C₂²×C₃²	1	4	yes	complemented
426	#123	C₂²×C₃²	1	4	yes	complemented
427	#123	C₂²×C₃²	1	2	yes	complemented
428	#123	C₂²×C₃²	1	4	yes	complemented
429	#123	C₂²×C₃²	1	4	yes	complemented
430	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
431	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
432	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
433	#121	C₂²×C₃²	1	1	yes	characteristic
434	#121	C₂²×C₃²	1	2	yes	complemented
435	#121	C₂²×C₃²	1	4	yes	complemented
436	#121	C₂²×C₃²	1	4	yes	complemented
437	#121	C₂²×C₃²	1	2	yes	complemented
438	#121	C₂²×C₃²	1	2	yes	complemented
439	#121	C₂²×C₃²	1	2	yes	complemented
440	#121	C₂²×C₃²	1	2	yes	complemented
441	#121	C₂²×C₃²	1	4	yes	complemented
442	#121	C₂²×C₃²	1	4	yes	complemented
443	#121	C₂²×C₃²	1	2	yes	complemented
444	#121	C₂²×C₃²	1	2	yes	complemented
445	#121	C₂²×C₃²	1	4	yes	complemented
446	#120	C₂²×C₃²	1	4	yes	complemented
447	#120	C₂²×C₃²	1	4	yes	complemented
448	#120	C₂²×C₃²	1	4	yes	complemented
449	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
450	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
451	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
452	C₄×D₄	C₂²×C₃²	1	2	yes	—
453	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
454	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
455	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
456	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
457	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
458	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
459	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
460	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
461	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
462	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
463	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
464	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
465	#117	C₂²×C₃²	1	2	yes	complemented
466	#117	C₂²×C₃²	1	2	yes	complemented
467	#117	C₂²×C₃²	1	2	yes	complemented
468	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
469	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
470	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
471	C₂×C₂²⋊C₄	C₂²×C₃²	1	4	yes	complemented
472	C₂×C₂²⋊C₄	C₂²×C₃²	1	4	yes	complemented
473	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
474	C₂³×C₃	—	2	16	no	—
475	C₂³×C₃	—	2	16	no	—
476	C₂³×C₃	—	2	32	no	—
477	C₂³×C₃	—	4	8	no	—
478	C₂³×C₃	—	4	16	no	—
479	C₂³×C₃	—	4	16	no	—
480	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
481	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
482	C₂³×C₃	C₂⁴×C₃	1	16	yes	—
483	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
484	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
485	C₃×Q₈	—	2	8	no	—
486	C₃×Q₈	—	4	8	no	—
487	C₃×D₄	—	2	16	no	—
488	C₃×D₄	—	2	32	no	—
489	C₃×D₄	—	2	16	no	—
490	C₃×D₄	—	2	32	no	—
491	C₃×D₄	—	2	8	no	—
492	C₃×D₄	—	2	16	no	—
493	C₃×D₄	—	2	8	no	—
494	C₃×D₄	—	2	16	no	—
495	C₃×D₄	—	4	16	no	—
496	C₃×D₄	—	4	16	no	—
497	C₃×D₄	—	4	16	no	—
498	C₃×D₄	—	4	8	no	—
499	C₃×D₄	—	4	16	no	—
500	C₃×D₄	C₃×#41	1	16	yes	complemented
501	C₂×C₃×C₄	—	2	8	no	—
502	C₂×C₃×C₄	—	2	8	no	—
503	C₂×C₃×C₄	—	2	16	no	—
504	C₂×C₃×C₄	—	2	8	no	—
505	C₂×C₃×C₄	—	2	16	no	—
506	C₂×C₃×C₄	—	2	16	no	—
507	C₂×C₃×C₄	—	4	8	no	—
508	C₂×C₃×C₄	—	4	8	no	—
509	C₂×C₃×C₄	—	4	8	no	—
510	C₂×C₃×C₄	—	4	16	no	—
511	C₂×C₃×C₄	—	4	16	no	—
512	C₂×C₃×C₄	—	4	16	no	—
513	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
514	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
515	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
516	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
517	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
518	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
519	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
520	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
521	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
522	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
523	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
524	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
525	C₂×C₃²	—	2	2	no	—
526	C₂×C₃²	—	2	4	no	—
527	C₂×C₃²	—	4	2	no	—
528	C₂×C₃²	—	4	4	no	—
529	C₂×C₃²	—	4	2	no	—
530	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
531	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂⁴	C₂³×C₃²	1	2	yes	—
534	C₂⁴	C₂³×C₃²	1	4	yes	—
535	#41	—	4	4	no	—
536	#41	—	4	4	no	—
537	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
538	C₂×Q₈	C₂³×C₃²	1	2	yes	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	8	no	—
543	C₂×D₄	C₂³×C₃²	1	2	yes	—
544	C₂×D₄	C₂³×C₃²	1	4	yes	—
545	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
546	C₂×D₄	C₂³×C₃²	1	2	yes	—
547	C₂×D₄	C₂³×C₃²	1	4	yes	—
548	C₂×D₄	C₂³×C₃²	1	2	yes	—
549	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
550	C₂×D₄	C₂³×C₃²	1	2	yes	—
551	C₂×D₄	C₂³×C₃²	1	4	yes	—
552	C₂×D₄	C₂³×C₃²	1	2	yes	—
553	C₂×D₄	C₂³×C₃²	1	4	yes	—
554	C₂×D₄	C₂³×C₃²	1	4	yes	—
555	C₂×D₄	C₂³×C₃²	1	4	yes	—
556	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
559	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
560	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
561	C₂²×C₄	C₂³×C₃²	1	2	yes	—
562	C₂²×C₄	C₂³×C₃²	1	2	yes	—
563	C₂²×C₄	C₂³×C₃²	1	2	yes	—
564	C₂²×C₄	C₂³×C₃²	1	2	yes	—
565	C₂²×C₄	C₂³×C₃²	1	4	yes	—
566	C₂²×C₄	C₂³×C₃²	1	2	yes	—
567	C₂²×C₄	C₂³×C₃²	1	4	yes	—
568	C₂²×C₄	C₂³×C₃²	1	4	yes	—
569	C₂²×C₄	C₂³×C₃²	1	2	yes	—
570	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
571	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
572	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
573	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
574	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
575	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
576	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
577	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
578	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
579	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
580	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
581	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
582	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
583	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
584	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
585	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
586	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
587	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
588	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
589	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
590	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
591	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
592	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
593	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
594	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
595	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
596	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
597	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
598	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
599	C₄²	C₂³×C₃²	1	1	yes	characteristic
600	C₄²	C₂³×C₃²	1	1	yes	characteristic
601	C₄²	C₂³×C₃²	1	1	yes	characteristic
602	C₄²	C₂³×C₃²	1	1	yes	characteristic
603	C₄²	C₂³×C₃²	1	4	yes	—
604	C₄²	C₂³×C₃²	1	2	yes	—
605	C₂²×C₃	—	2	4	no	—
606	C₂²×C₃	—	2	4	no	—
607	C₂²×C₃	—	2	8	no	—
608	C₂²×C₃	—	2	8	no	—
609	C₂²×C₃	—	2	8	no	—
610	C₂²×C₃	—	2	8	no	—
611	C₂²×C₃	—	2	16	no	—
612	C₂²×C₃	—	2	8	no	—
613	C₂²×C₃	—	2	16	no	—
614	C₂²×C₃	—	2	16	no	—
615	C₂²×C₃	—	2	8	no	—
616	C₂²×C₃	—	2	8	no	—
617	C₂²×C₃	—	2	8	no	—
618	C₂²×C₃	—	4	32	no	—
619	C₂²×C₃	—	8	32	no	—
620	C₂²×C₃	C₂×C₃×#41	1	16	yes	—
621	C₂²×C₃	C₃×H(5,𝔽₂)	1	8	yes	—
622	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
623	C₃×C₄	—	2	4	no	—
624	C₃×C₄	—	2	8	no	—
625	C₃×C₄	—	2	4	no	—
626	C₃×C₄	—	2	4	no	—
627	C₃×C₄	—	2	8	no	—
628	C₃×C₄	—	2	8	no	—
629	C₃×C₄	—	2	4	no	—
630	C₃×C₄	—	2	8	no	—
631	C₃×C₄	—	2	16	no	—
632	C₃×C₄	—	2	8	no	—
633	C₃×C₄	C₂×C₃×#41	1	8	yes	—
634	C₃×C₄	C₃×H(5,𝔽₂)	1	8	yes	—
635	C₃²	#3519	1	1	yes	characteristic, direct product factor, Sylow
636	C₂³	—	2	4	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	8	no	—
639	C₂³	—	4	2	no	—
640	C₂³	—	4	4	no	—
641	C₂³	—	4	4	no	—
642	C₂³	C₂⁴×C₃²	1	2	yes	—
643	C₂³	C₂⁴×C₃²	1	2	yes	—
644	C₂³	C₂⁴×C₃²	1	4	yes	—
645	C₂³	C₂⁴×C₃²	1	2	yes	—
646	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
647	Q₈	—	2	2	no	—
648	Q₈	—	4	2	no	—
649	D₄	—	2	4	no	—
650	D₄	—	2	8	no	—
651	D₄	—	2	4	no	—
652	D₄	—	2	8	no	—
653	D₄	—	2	2	no	—
654	D₄	—	2	4	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	4	no	—
657	D₄	—	4	4	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	4	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	4	no	—
662	D₄	C₃²×#41	1	4	yes	complemented
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
676	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
677	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
678	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
679	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
680	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
681	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
682	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
683	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
684	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
685	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
686	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
687	C₂×C₃	—	2	8	no	—
688	C₂×C₃	—	2	16	no	—
689	C₂×C₃	—	4	8	no	—
690	C₂×C₃	—	4	8	no	—
691	C₂×C₃	—	4	16	no	—
692	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
693	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
694	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	4	8	no	—
709	C₂²	—	8	8	no	—
710	C₂²	C₂×C₃²×#41	1	4	yes	—
711	C₂²	C₃²×H(5,𝔽₂)	1	2	yes	—
712	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	4	no	—
722	C₄	—	2	2	no	—
723	C₄	C₂×C₃²×#41	1	2	yes	—
724	C₄	C₃²×H(5,𝔽₂)	1	2	yes	—
725	C₃	C₃×#3519	1	4	yes	direct product factor
726	C₂	—	2	2	no	—
727	C₂	—	2	4	no	—
728	C₂	—	4	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	4	4	no	—
731	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
732	C₂	C₂×C₃²×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂	C₂×C₃²×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#555	C₂	semidirect
2. C₃²×#554	C₂	semidirect
3. C₃²×#553	C₂	semidirect
4. C₃²×#553	C₂	semidirect
5. C₃²×#550	C₂	semidirect
6. C₃²×#546	C₂	semidirect
7. C₃²×#546	C₂	semidirect
8. C₃²×D₄²	C₂	semidirect
9. C₃²×D₄²	C₂	semidirect
10. C₃²×#540	C₂	semidirect
11. C₃²×#538	C₂	semidirect
12. C₃²×#532	C₂	semidirect
13. C₃²×#529	C₂	semidirect
14. C₃²×#525	C₂	semidirect
15. C₂×C₃²×#121	C₂	semidirect
16. C₃²×#518	C₂	semidirect
17. C₂×C₃²×C₄×D₄	C₂	semidirect
18. C₃×#3519	C₃	direct (N × H)
19. C₂×C₃²×#41	C₂²	semidirect
20. C₂×C₃²×#41	C₂²	semidirect
23. C₂²×C₃²×D₄	C₂²	semidirect
24. C₂²×C₃²×D₄	C₂²	semidirect
25. C₂³×C₃²×C₄	C₂²	semidirect
26. C₃²×C₄⋊Q₈	C₂²	semidirect
27. C₃²×#127	C₂²	semidirect
28. C₃²×#127	C₂²	semidirect
29. C₃²×#126	C₂²	semidirect
30. C₃²×#126	C₂²	semidirect
31. C₃²×#125	C₂²	semidirect
32. C₃²×#125	C₂²	semidirect
33. C₃²×#124	C₂²	semidirect
34. C₃²×#124	C₂²	semidirect
35. C₃²×#124	C₂²	semidirect
36. C₃²×#123	C₂²	semidirect
37. C₃²×#123	C₂²	semidirect
38. C₃²×#123	C₂²	semidirect
39. C₃²×#123	C₂²	semidirect
40. C₃²×C₂²⋊Q₈	C₂²	semidirect
41. C₃²×C₂²⋊Q₈	C₂²	semidirect
42. C₃²×C₂²⋊Q₈	C₂²	semidirect
44. C₃²×#121	C₂²	semidirect
45. C₃²×#121	C₂²	semidirect
46. C₃²×#121	C₂²	semidirect
47. C₃²×#121	C₂²	semidirect
48. C₃²×#121	C₂²	semidirect
49. C₃²×#121	C₂²	semidirect
50. C₃²×#121	C₂²	semidirect
51. C₃²×#121	C₂²	semidirect
52. C₃²×#121	C₂²	semidirect
53. C₃²×#121	C₂²	semidirect
54. C₃²×#121	C₂²	semidirect
55. C₃²×#121	C₂²	semidirect
56. C₃²×#120	C₂²	semidirect
57. C₃²×#120	C₂²	semidirect
58. C₃²×#120	C₂²	semidirect
59. C₃²×C₄×Q₈	C₂²	semidirect
63. C₃²×C₄×D₄	C₂²	semidirect
64. C₃²×C₄×D₄	C₂²	semidirect
65. C₃²×C₄×D₄	C₂²	semidirect
66. C₃²×C₄×D₄	C₂²	semidirect
67. C₃²×C₄×D₄	C₂²	semidirect
68. C₃²×C₄×D₄	C₂²	semidirect
69. C₃²×C₄×D₄	C₂²	semidirect
70. C₃²×C₄×D₄	C₂²	semidirect
71. C₃²×C₄×D₄	C₂²	semidirect
72. C₃²×C₄×D₄	C₂²	semidirect
73. C₃²×C₄×D₄	C₂²	semidirect
74. C₃²×C₄×D₄	C₂²	semidirect
75. C₃²×#117	C₂²	semidirect
76. C₃²×#117	C₂²	semidirect
77. C₃²×#117	C₂²	semidirect
78. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
79. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
80. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
81. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
82. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
83. C₂×C₃²×C₄²	C₂²	semidirect
84. C₃×#555	C₂×C₃	semidirect
85. C₃×#554	C₂×C₃	semidirect
86. C₃×#553	C₂×C₃	semidirect
87. C₃×#553	C₂×C₃	semidirect
88. C₃×#550	C₂×C₃	semidirect
89. C₃×#546	C₂×C₃	semidirect
90. C₃×#546	C₂×C₃	semidirect
91. C₃×D₄²	C₂×C₃	semidirect
92. C₃×D₄²	C₂×C₃	semidirect
93. C₃×#540	C₂×C₃	semidirect
94. C₃×#538	C₂×C₃	semidirect
95. C₃×#532	C₂×C₃	semidirect
96. C₃×#529	C₂×C₃	semidirect
97. C₃×#525	C₂×C₃	semidirect
98. C₂×C₃×#121	C₂×C₃	semidirect
99. C₃×#518	C₂×C₃	semidirect
100. C₂×C₃×C₄×D₄	C₂×C₃	semidirect
173. #3519	C₃²	direct (N × H)
174. C₂×C₃×#41	C₂²×C₃	semidirect
175. C₂×C₃×#41	C₂²×C₃	semidirect
178. C₂²×C₃×D₄	C₂²×C₃	semidirect
179. C₂²×C₃×D₄	C₂²×C₃	semidirect
180. C₂³×C₃×C₄	C₂²×C₃	semidirect
181. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
182. C₃×#127	C₂²×C₃	semidirect
183. C₃×#127	C₂²×C₃	semidirect
184. C₃×#126	C₂²×C₃	semidirect
185. C₃×#126	C₂²×C₃	semidirect
186. C₃×#125	C₂²×C₃	semidirect
187. C₃×#125	C₂²×C₃	semidirect
188. C₃×#124	C₂²×C₃	semidirect
189. C₃×#124	C₂²×C₃	semidirect
190. C₃×#124	C₂²×C₃	semidirect
191. C₃×#123	C₂²×C₃	semidirect
192. C₃×#123	C₂²×C₃	semidirect
193. C₃×#123	C₂²×C₃	semidirect
194. C₃×#123	C₂²×C₃	semidirect
195. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
196. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
197. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₃×#121	C₂²×C₃	semidirect
200. C₃×#121	C₂²×C₃	semidirect
201. C₃×#121	C₂²×C₃	semidirect
202. C₃×#121	C₂²×C₃	semidirect
203. C₃×#121	C₂²×C₃	semidirect
204. C₃×#121	C₂²×C₃	semidirect
205. C₃×#121	C₂²×C₃	semidirect
206. C₃×#121	C₂²×C₃	semidirect
207. C₃×#121	C₂²×C₃	semidirect
208. C₃×#121	C₂²×C₃	semidirect
209. C₃×#121	C₂²×C₃	semidirect
210. C₃×#121	C₂²×C₃	semidirect
211. C₃×#120	C₂²×C₃	semidirect
212. C₃×#120	C₂²×C₃	semidirect
213. C₃×#120	C₂²×C₃	semidirect
214. C₃×C₄×Q₈	C₂²×C₃	semidirect
218. C₃×C₄×D₄	C₂²×C₃	semidirect
219. C₃×C₄×D₄	C₂²×C₃	semidirect
220. C₃×C₄×D₄	C₂²×C₃	semidirect
221. C₃×C₄×D₄	C₂²×C₃	semidirect
222. C₃×C₄×D₄	C₂²×C₃	semidirect
223. C₃×C₄×D₄	C₂²×C₃	semidirect
224. C₃×C₄×D₄	C₂²×C₃	semidirect
225. C₃×C₄×D₄	C₂²×C₃	semidirect
226. C₃×C₄×D₄	C₂²×C₃	semidirect
227. C₃×C₄×D₄	C₂²×C₃	semidirect
228. C₃×C₄×D₄	C₂²×C₃	semidirect
229. C₃×C₄×D₄	C₂²×C₃	semidirect
230. C₃×#117	C₂²×C₃	semidirect
231. C₃×#117	C₂²×C₃	semidirect
232. C₃×#117	C₂²×C₃	semidirect
233. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
234. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
235. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
236. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
237. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
238. C₂×C₃×C₄²	C₂²×C₃	semidirect
265. C₃²×D₄	#41	semidirect
290. #555	C₂×C₃²	semidirect
291. #554	C₂×C₃²	semidirect
292. #553	C₂×C₃²	semidirect
293. #553	C₂×C₃²	semidirect
294. #550	C₂×C₃²	semidirect
295. #546	C₂×C₃²	semidirect
296. #546	C₂×C₃²	semidirect
297. D₄²	C₂×C₃²	semidirect
298. D₄²	C₂×C₃²	semidirect
299. #540	C₂×C₃²	semidirect
300. #538	C₂×C₃²	semidirect
301. #532	C₂×C₃²	semidirect
302. #529	C₂×C₃²	semidirect
303. #525	C₂×C₃²	semidirect
304. C₂×#121	C₂×C₃²	semidirect
305. #518	C₂×C₃²	semidirect
306. C₂×C₄×D₄	C₂×C₃²	semidirect
409. C₂×#41	C₂²×C₃²	semidirect
410. C₂×#41	C₂²×C₃²	semidirect
413. C₂²×D₄	C₂²×C₃²	semidirect
414. C₂²×D₄	C₂²×C₃²	semidirect
415. C₂³×C₄	C₂²×C₃²	semidirect
416. C₄⋊Q₈	C₂²×C₃²	semidirect
417. #127	C₂²×C₃²	semidirect
418. #127	C₂²×C₃²	semidirect
419. #126	C₂²×C₃²	semidirect
420. #126	C₂²×C₃²	semidirect
421. #125	C₂²×C₃²	semidirect
422. #125	C₂²×C₃²	semidirect
423. #124	C₂²×C₃²	semidirect
424. #124	C₂²×C₃²	semidirect
425. #124	C₂²×C₃²	semidirect
426. #123	C₂²×C₃²	semidirect
427. #123	C₂²×C₃²	semidirect
428. #123	C₂²×C₃²	semidirect
429. #123	C₂²×C₃²	semidirect
430. C₂²⋊Q₈	C₂²×C₃²	semidirect
431. C₂²⋊Q₈	C₂²×C₃²	semidirect
432. C₂²⋊Q₈	C₂²×C₃²	semidirect
434. #121	C₂²×C₃²	semidirect
435. #121	C₂²×C₃²	semidirect
436. #121	C₂²×C₃²	semidirect
437. #121	C₂²×C₃²	semidirect
438. #121	C₂²×C₃²	semidirect
439. #121	C₂²×C₃²	semidirect
440. #121	C₂²×C₃²	semidirect
441. #121	C₂²×C₃²	semidirect
442. #121	C₂²×C₃²	semidirect
443. #121	C₂²×C₃²	semidirect
444. #121	C₂²×C₃²	semidirect
445. #121	C₂²×C₃²	semidirect
446. #120	C₂²×C₃²	semidirect
447. #120	C₂²×C₃²	semidirect
448. #120	C₂²×C₃²	semidirect
449. C₄×Q₈	C₂²×C₃²	semidirect
453. C₄×D₄	C₂²×C₃²	semidirect
454. C₄×D₄	C₂²×C₃²	semidirect
455. C₄×D₄	C₂²×C₃²	semidirect
456. C₄×D₄	C₂²×C₃²	semidirect
457. C₄×D₄	C₂²×C₃²	semidirect
458. C₄×D₄	C₂²×C₃²	semidirect
459. C₄×D₄	C₂²×C₃²	semidirect
460. C₄×D₄	C₂²×C₃²	semidirect
461. C₄×D₄	C₂²×C₃²	semidirect
462. C₄×D₄	C₂²×C₃²	semidirect
463. C₄×D₄	C₂²×C₃²	semidirect
464. C₄×D₄	C₂²×C₃²	semidirect
465. #117	C₂²×C₃²	semidirect
466. #117	C₂²×C₃²	semidirect
467. #117	C₂²×C₃²	semidirect
468. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
469. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
470. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
471. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
472. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
473. C₂×C₄²	C₂²×C₃²	semidirect
500. C₃×D₄	C₃×#41	semidirect
635. C₃²	#3519	direct (N × H)
662. D₄	C₃²×#41	semidirect
725. C₃	C₃×#3519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#555	2
C₃²×#554	2
C₃²×#553	2
C₃²×#550	2
C₃²×#546	2
C₃²×D₄²	2
C₃²×#540	2
C₃²×#538	2
C₃²×#532	2
C₃²×#529	2
C₃²×#525	2
C₂×C₃²×#121	2
C₃²×#518	2
C₂×C₃²×C₄×D₄	2
C₃×#3519	3

Subgroups — C32×#3519 #11770568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3519 #11770568