Subgroups — C₃×#61869 #10680476

Order 768.

1644 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3503	C₂	1	1	yes	maximal, characteristic
3	C₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₃×#3383	C₂	1	2	yes	maximal, complemented
6	C₃×#3381	C₂	1	2	yes	maximal, complemented
7	C₃×#3374	C₂	1	2	yes	maximal, complemented
8	C₃×#3372	C₂	1	2	yes	maximal, complemented
9	C₃×#3363	C₂	1	2	yes	maximal, complemented
10	C₃×#3359	C₂	1	2	yes	maximal, complemented
11	C₃×#3242	C₂	1	4	yes	maximal, complemented
12	C₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3120	C₂	1	4	yes	maximal
15	C₃×#3107	C₂	1	1	yes	maximal, characteristic
16	C₃×#3107	C₂	1	1	yes	maximal, characteristic
17	C₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	#61869	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#564	—	2	2	no	—
20	C₃×Q₈²	C₂²	1	2	yes	—
21	C₃×#557	—	2	1	no	—
22	C₃×#557	—	2	1	no	—
23	C₃×#557	C₂²	1	2	yes	—
24	C₃×#557	C₂²	1	2	yes	—
25	C₃×#557	C₂²	1	2	yes	—
26	C₃×#557	C₂²	1	2	yes	—
27	C₃×#557	C₂²	1	2	yes	—
28	C₃×#554	—	2	2	no	—
29	C₃×#554	C₂²	1	2	yes	—
30	C₃×D₄×Q₈	—	2	2	no	—
31	C₃×D₄×Q₈	C₂²	1	2	yes	—
32	C₃×#544	—	2	2	no	—
33	C₃×#544	C₂²	1	2	yes	—
34	C₃×#541	—	2	2	no	—
35	C₃×#541	—	2	2	no	—
36	C₃×#541	C₂²	1	4	yes	—
37	C₃×#533	—	2	1	no	—
38	C₃×#533	C₂²	1	1	yes	characteristic
39	C₃×#533	C₂²	1	1	yes	characteristic
40	C₃×#533	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
42	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃×#520	C₂²	1	2	yes	—
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic
45	C₃×#501	C₂²	1	4	yes	—
46	C₃×#500	C₂²	1	2	yes	—
47	C₃×#499	C₂²	1	4	yes	—
48	C₃×#498	C₂²	1	2	yes	—
49	C₃×#491	C₂²	1	4	yes	—
50	C₃×#487	C₂²	1	2	yes	—
51	C₃×#487	C₂²	1	2	yes	—
52	C₃×#487	C₂²	1	4	yes	—
53	C₃×#485	C₂²	1	2	yes	—
54	C₃×#485	C₂²	1	2	yes	—
55	C₃×#484	C₂²	1	4	yes	—
56	C₃×#483	C₂²	1	4	yes	—
57	C₃×#479	C₂²	1	4	yes	—
58	C₃×#479	C₂²	1	4	yes	—
59	C₃×#479	C₂²	1	4	yes	—
60	C₃×#478	C₂²	1	4	yes	—
61	C₃×#477	C₂²	1	4	yes	—
62	C₃×#477	C₂²	1	2	yes	—
63	C₃×#477	C₂²	1	2	yes	—
64	C₃×#475	C₂²	1	2	yes	—
65	C₃×#475	C₂²	1	1	yes	characteristic
66	C₃×#475	C₂²	1	4	yes	—
67	C₃×#475	C₂²	1	2	yes	—
68	C₃×#475	C₂²	1	1	yes	characteristic
69	C₃×#474	C₂²	1	1	yes	characteristic
70	C₃×#474	C₂²	1	1	yes	characteristic
71	C₃×#462	C₂²	1	1	yes	characteristic
72	C₃×#462	C₂²	1	1	yes	characteristic
73	C₃×#462	C₂²	1	4	yes	—
74	C₃×#461	C₂²	1	1	yes	characteristic
75	C₃×#461	C₂²	1	4	yes	—
76	C₃×#461	C₂²	1	1	yes	characteristic
77	C₃×#452	C₂²	1	2	yes	—
78	C₃×#452	C₂²	1	2	yes	—
79	C₃×#446	C₂²	1	2	yes	—
80	C₃×#446	C₂²	1	2	yes	—
81	C₃×C₈×Q₈	C₂²	1	2	yes	—
82	C₃×C₈×Q₈	C₂²	1	2	yes	—
83	C₃×#441	C₂²	1	4	yes	—
84	C₃×#440	C₂²	1	4	yes	—
85	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
86	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
87	C₃×C₄×Q₁₆	C₂²	1	4	yes	—
88	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
89	C₃×C₄×SD₁₆	C₂²	1	4	yes	—
90	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
91	C₃×#433	C₂²	1	4	yes	—
92	C₃×#431	C₂²	1	1	yes	characteristic
93	C₃×#431	C₂²	1	1	yes	characteristic
94	#3556	C₂×C₃	1	1	yes	characteristic, complemented
95	#3503	C₂×C₃	1	1	yes	characteristic
96	#3387	C₂×C₃	1	2	yes	complemented
97	#3386	C₂×C₃	1	2	yes	complemented
98	#3383	C₂×C₃	1	2	yes	complemented
99	#3381	C₂×C₃	1	2	yes	complemented
100	#3374	C₂×C₃	1	2	yes	complemented
101	#3372	C₂×C₃	1	2	yes	complemented
102	#3363	C₂×C₃	1	2	yes	complemented
103	#3359	C₂×C₃	1	2	yes	complemented
104	#3242	C₂×C₃	1	4	yes	complemented
105	#3230	C₂×C₃	1	1	yes	characteristic, complemented
106	#3229	C₂×C₃	1	1	yes	characteristic, complemented
107	#3120	C₂×C₃	1	4	yes	—
108	#3107	C₂×C₃	1	1	yes	characteristic
109	#3107	C₂×C₃	1	1	yes	characteristic
110	#2986	C₂×C₃	1	1	yes	characteristic, complemented
111	C₂×C₃×#41	C₂³	1	1	yes	characteristic
112	C₂²×C₃×Q₈	—	2	2	no	—
113	C₂²×C₃×Q₈	—	2	1	no	—
114	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
115	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
118	C₃×C₄⋊Q₈	—	2	2	no	—
119	C₃×C₄⋊Q₈	—	2	2	no	—
120	C₃×C₄⋊Q₈	—	2	2	no	—
121	C₃×C₄⋊Q₈	—	2	2	no	—
122	C₃×C₄⋊Q₈	—	2	4	no	—
123	C₃×C₄⋊Q₈	—	2	2	no	—
124	C₃×C₄⋊Q₈	—	2	1	no	—
125	C₃×C₄⋊Q₈	—	2	1	no	—
126	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
127	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃×#126	—	2	4	no	—
137	C₃×#126	—	2	4	no	—
138	C₃×#125	—	2	4	no	—
139	C₃×#125	—	2	4	no	—
140	C₃×#125	—	2	4	no	—
141	C₃×#125	—	2	4	no	—
142	C₃×#125	—	2	4	no	—
143	C₃×#125	—	2	4	no	—
144	C₃×#125	—	2	2	no	—
145	C₃×#125	—	2	2	no	—
146	C₃×#125	—	2	2	no	—
147	C₃×#125	—	2	4	no	—
148	C₃×#125	—	2	1	no	—
149	C₃×#125	—	2	1	no	—
150	C₃×#125	D₄	1	2	yes	—
151	C₃×#125	C₂³	1	4	yes	—
152	C₃×#125	C₂³	1	4	yes	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	1	no	—
155	C₃×C₂²⋊Q₈	—	2	1	no	—
156	C₃×C₂²⋊Q₈	—	2	2	no	—
157	C₃×C₂²⋊Q₈	—	2	4	no	—
158	C₃×C₂²⋊Q₈	—	2	4	no	—
159	C₃×C₂²⋊Q₈	—	2	4	no	—
160	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
161	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
162	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
163	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
164	C₃×C₄×Q₈	—	2	2	no	—
165	C₃×C₄×Q₈	—	2	2	no	—
166	C₃×C₄×Q₈	—	2	2	no	—
167	C₃×C₄×Q₈	—	2	2	no	—
168	C₃×C₄×Q₈	—	2	2	no	—
169	C₃×C₄×Q₈	—	2	2	no	—
170	C₃×C₄×Q₈	—	2	1	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
173	C₃×C₄×Q₈	C₂³	1	4	yes	—
174	C₃×C₄×Q₈	C₂³	1	2	yes	—
175	C₃×C₄×Q₈	C₂³	1	2	yes	—
176	C₃×C₄×Q₈	C₂³	1	4	yes	—
177	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
178	C₃×C₄×Q₈	C₂³	1	4	yes	—
179	C₃×C₄×Q₈	C₂³	1	2	yes	—
180	C₃×C₄×Q₈	C₂³	1	2	yes	—
181	C₃×C₄×D₄	—	2	1	no	—
182	C₃×C₄×D₄	—	2	1	no	—
183	C₃×C₄×D₄	—	2	4	no	—
184	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
185	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
186	C₃×C₄×D₄	C₂³	1	4	yes	—
187	C₃×#117	—	2	1	no	—
188	C₃×#117	—	2	1	no	—
189	C₃×#117	—	2	2	no	—
190	C₃×#117	—	2	1	no	—
191	C₃×#117	C₂³	1	1	yes	characteristic
192	C₃×#117	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	—	2	1	no	—
198	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
199	C₃×#107	C₂³	1	2	yes	—
200	C₃×#107	C₂³	1	2	yes	—
201	C₃×#107	C₂³	1	4	yes	—
202	C₃×#107	C₂³	1	4	yes	—
203	C₃×#106	C₂³	1	2	yes	—
204	C₃×#106	C₂³	1	4	yes	—
205	C₃×#106	C₂³	1	2	yes	—
206	C₃×#106	C₂³	1	4	yes	—
207	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
208	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
209	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃×#103	C₂³	1	2	yes	—
214	C₃×#103	C₂³	1	4	yes	—
215	C₃×#103	C₂³	1	2	yes	—
216	C₃×#103	C₂³	1	2	yes	—
217	C₃×#103	C₂³	1	2	yes	—
218	C₃×#103	C₂³	1	2	yes	—
219	C₃×#103	C₂³	1	4	yes	—
220	C₃×#103	C₂³	1	2	yes	—
221	C₃×#103	C₂³	1	4	yes	—
222	C₃×#103	C₂³	1	4	yes	—
223	C₃×#102	C₂³	1	2	yes	—
224	C₃×#102	C₂³	1	2	yes	—
225	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃×#97	C₂³	1	4	yes	—
228	C₃×C₄×C₈	C₂³	1	2	yes	—
229	C₃×C₄×C₈	C₂³	1	2	yes	—
230	C₃×C₄×C₈	C₂³	1	4	yes	—
231	#564	—	2	2	no	—
232	Q₈²	C₂²×C₃	1	2	yes	—
233	#557	—	2	1	no	—
234	#557	—	2	1	no	—
235	#557	C₂²×C₃	1	2	yes	—
236	#557	C₂²×C₃	1	2	yes	—
237	#557	C₂²×C₃	1	2	yes	—
238	#557	C₂²×C₃	1	2	yes	—
239	#557	C₂²×C₃	1	2	yes	—
240	#554	—	2	2	no	—
241	#554	C₂²×C₃	1	2	yes	—
242	D₄×Q₈	—	2	2	no	—
243	D₄×Q₈	C₂²×C₃	1	2	yes	—
244	#544	—	2	2	no	—
245	#544	C₂²×C₃	1	2	yes	—
246	#541	—	2	2	no	—
247	#541	—	2	2	no	—
248	#541	C₂²×C₃	1	4	yes	—
249	#533	—	2	1	no	—
250	#533	C₂²×C₃	1	1	yes	characteristic
251	#533	C₂²×C₃	1	1	yes	characteristic
252	#533	C₂²×C₃	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	—	2	1	no	—
254	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
255	#520	C₂²×C₃	1	2	yes	—
256	C₄×#41	C₂²×C₃	1	1	yes	characteristic
257	#501	C₂²×C₃	1	4	yes	—
258	#500	C₂²×C₃	1	2	yes	—
259	#499	C₂²×C₃	1	4	yes	—
260	#498	C₂²×C₃	1	2	yes	—
261	#491	C₂²×C₃	1	4	yes	—
262	#487	C₂²×C₃	1	4	yes	—
263	#487	C₂²×C₃	1	2	yes	—
264	#487	C₂²×C₃	1	2	yes	—
265	#485	C₂²×C₃	1	2	yes	—
266	#485	C₂²×C₃	1	2	yes	—
267	#484	C₂²×C₃	1	4	yes	—
268	#483	C₂²×C₃	1	4	yes	—
269	#479	C₂²×C₃	1	4	yes	—
270	#479	C₂²×C₃	1	4	yes	—
271	#479	C₂²×C₃	1	4	yes	—
272	#478	C₂²×C₃	1	4	yes	—
273	#477	C₂²×C₃	1	2	yes	—
274	#477	C₂²×C₃	1	4	yes	—
275	#477	C₂²×C₃	1	2	yes	—
276	#475	C₂²×C₃	1	2	yes	—
277	#475	C₂²×C₃	1	4	yes	—
278	#475	C₂²×C₃	1	1	yes	characteristic
279	#475	C₂²×C₃	1	1	yes	characteristic
280	#475	C₂²×C₃	1	2	yes	—
281	#474	C₂²×C₃	1	1	yes	characteristic
282	#474	C₂²×C₃	1	1	yes	characteristic
283	#462	C₂²×C₃	1	1	yes	characteristic
284	#462	C₂²×C₃	1	1	yes	characteristic
285	#462	C₂²×C₃	1	4	yes	—
286	#461	C₂²×C₃	1	1	yes	characteristic
287	#461	C₂²×C₃	1	4	yes	—
288	#461	C₂²×C₃	1	1	yes	characteristic
289	#452	C₂²×C₃	1	2	yes	—
290	#452	C₂²×C₃	1	2	yes	—
291	#446	C₂²×C₃	1	2	yes	—
292	#446	C₂²×C₃	1	2	yes	—
293	C₈×Q₈	C₂²×C₃	1	2	yes	—
294	C₈×Q₈	C₂²×C₃	1	2	yes	—
295	#441	C₂²×C₃	1	4	yes	—
296	#440	C₂²×C₃	1	4	yes	—
297	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
298	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
299	C₄×Q₁₆	C₂²×C₃	1	4	yes	—
300	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
301	C₄×SD₁₆	C₂²×C₃	1	4	yes	—
302	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
303	#433	C₂²×C₃	1	4	yes	—
304	#431	C₂²×C₃	1	1	yes	characteristic
305	#431	C₂²×C₃	1	1	yes	characteristic
306	C₃×#41	—	2	2	no	—
307	C₃×#41	—	2	2	no	—
308	C₂×C₃×Q₈	—	2	1	no	—
309	C₂×C₃×Q₈	—	2	1	no	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	—	2	4	no	—
312	C₂×C₃×Q₈	—	2	2	no	—
313	C₂×C₃×Q₈	—	8	2	no	—
314	C₂×C₃×Q₈	—	8	4	no	—
315	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
316	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
317	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
318	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
319	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
320	C₂×C₃×D₄	—	2	1	no	—
321	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
322	C₂²×C₃×C₄	—	2	1	no	—
323	C₂²×C₃×C₄	—	2	2	no	—
324	C₂²×C₃×C₄	—	2	1	no	—
325	C₂²×C₃×C₄	—	2	1	no	—
326	C₂²×C₃×C₄	—	2	4	no	—
327	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
330	C₃×Q₁₆	—	2	4	no	—
331	C₃×Q₁₆	—	2	4	no	—
332	C₃×SD₁₆	—	2	4	no	—
333	C₃×SD₁₆	—	2	4	no	—
334	C₂×C₃×C₈	C₂⁴	1	2	yes	—
335	C₂×C₃×C₈	C₂⁴	1	2	yes	—
336	C₂×C₃×C₈	C₂⁴	1	2	yes	—
337	C₂×C₃×C₈	C₂⁴	1	2	yes	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	2	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	1	no	—
344	C₃×C₄⋊C₄	—	2	1	no	—
345	C₃×C₄⋊C₄	—	2	1	no	—
346	C₃×C₄⋊C₄	—	2	1	no	—
347	C₃×C₄⋊C₄	—	2	1	no	—
348	C₃×C₄⋊C₄	—	2	1	no	—
349	C₃×C₄⋊C₄	—	2	1	no	—
350	C₃×C₄⋊C₄	—	2	1	no	—
351	C₃×C₄⋊C₄	—	2	4	no	—
352	C₃×C₄⋊C₄	—	2	4	no	—
353	C₃×C₄⋊C₄	—	2	2	no	—
354	C₃×C₄⋊C₄	—	2	2	no	—
355	C₃×C₄⋊C₄	—	2	4	no	—
356	C₃×C₄⋊C₄	—	2	4	no	—
357	C₃×C₄⋊C₄	—	2	4	no	—
358	C₃×C₄⋊C₄	—	2	4	no	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	—	2	2	no	—
361	C₃×C₄⋊C₄	—	2	4	no	—
362	C₃×C₄⋊C₄	—	2	4	no	—
363	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
365	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
366	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
367	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
368	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
369	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
372	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
373	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
374	C₃×C₂²⋊C₄	—	2	2	no	—
375	C₃×C₂²⋊C₄	—	2	2	no	—
376	C₃×C₂²⋊C₄	—	2	1	no	—
377	C₃×C₂²⋊C₄	—	2	1	no	—
378	C₃×C₂²⋊C₄	—	2	1	no	—
379	C₃×C₂²⋊C₄	—	2	4	no	—
380	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
381	C₃×C₄²	—	2	1	no	—
382	C₃×C₄²	—	2	1	no	—
383	C₃×C₄²	—	2	1	no	—
384	C₃×C₄²	—	2	4	no	—
385	C₃×C₄²	—	2	2	no	—
386	C₃×C₄²	—	2	2	no	—
387	C₃×C₄²	—	2	4	no	—
388	C₃×C₄²	—	2	4	no	—
389	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
390	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
391	C₃×C₄²	C₂⁴	1	1	yes	characteristic
392	C₃×C₄²	C₂⁴	1	1	yes	characteristic
393	C₃×C₄²	C₂⁴	1	4	yes	—
394	C₂×#41	C₂³×C₃	1	1	yes	characteristic
395	C₂²×Q₈	—	2	2	no	—
396	C₂²×Q₈	—	2	1	no	—
397	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
398	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
399	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
400	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
401	C₄⋊Q₈	—	2	2	no	—
402	C₄⋊Q₈	—	2	2	no	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	2	no	—
405	C₄⋊Q₈	—	2	2	no	—
406	C₄⋊Q₈	—	2	4	no	—
407	C₄⋊Q₈	—	2	1	no	—
408	C₄⋊Q₈	—	2	1	no	—
409	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
410	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
411	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
412	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
413	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
414	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
415	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
416	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
417	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
418	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
419	#126	—	2	4	no	—
420	#126	—	2	4	no	—
421	#125	—	2	2	no	—
422	#125	—	2	2	no	—
423	#125	—	2	2	no	—
424	#125	—	2	4	no	—
425	#125	—	2	4	no	—
426	#125	—	2	4	no	—
427	#125	—	2	4	no	—
428	#125	—	2	4	no	—
429	#125	—	2	4	no	—
430	#125	—	2	4	no	—
431	#125	—	2	1	no	—
432	#125	—	2	1	no	—
433	#125	C₃×D₄	1	2	yes	—
434	#125	C₂³×C₃	1	4	yes	—
435	#125	C₂³×C₃	1	4	yes	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	4	no	—
441	C₂²⋊Q₈	—	2	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
444	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
445	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
446	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
447	C₄×Q₈	—	2	2	no	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	—	2	2	no	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
456	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
457	C₄×Q₈	C₂³×C₃	1	4	yes	—
458	C₄×Q₈	C₂³×C₃	1	2	yes	—
459	C₄×Q₈	C₂³×C₃	1	2	yes	—
460	C₄×Q₈	C₂³×C₃	1	4	yes	—
461	C₄×Q₈	C₂³×C₃	1	4	yes	—
462	C₄×Q₈	C₂³×C₃	1	2	yes	—
463	C₄×Q₈	C₂³×C₃	1	2	yes	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
468	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
469	C₄×D₄	C₂³×C₃	1	4	yes	—
470	#117	—	2	1	no	—
471	#117	—	2	1	no	—
472	#117	—	2	2	no	—
473	#117	—	2	1	no	—
474	#117	C₂³×C₃	1	1	yes	characteristic
475	#117	C₂³×C₃	1	2	yes	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	2	no	—
478	C₂×C₄⋊C₄	—	2	2	no	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₄²	—	2	1	no	—
481	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
482	#107	C₂³×C₃	1	2	yes	—
483	#107	C₂³×C₃	1	2	yes	—
484	#107	C₂³×C₃	1	4	yes	—
485	#107	C₂³×C₃	1	4	yes	—
486	#106	C₂³×C₃	1	2	yes	—
487	#106	C₂³×C₃	1	4	yes	—
488	#106	C₂³×C₃	1	2	yes	—
489	#106	C₂³×C₃	1	4	yes	—
490	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
491	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
492	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
493	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
494	C₄⋊C₈	C₂³×C₃	1	4	yes	—
495	C₄⋊C₈	C₂³×C₃	1	4	yes	—
496	#103	C₂³×C₃	1	2	yes	—
497	#103	C₂³×C₃	1	4	yes	—
498	#103	C₂³×C₃	1	2	yes	—
499	#103	C₂³×C₃	1	2	yes	—
500	#103	C₂³×C₃	1	2	yes	—
501	#103	C₂³×C₃	1	2	yes	—
502	#103	C₂³×C₃	1	4	yes	—
503	#103	C₂³×C₃	1	2	yes	—
504	#103	C₂³×C₃	1	4	yes	—
505	#103	C₂³×C₃	1	4	yes	—
506	#102	C₂³×C₃	1	2	yes	—
507	#102	C₂³×C₃	1	2	yes	—
508	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
509	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
510	#97	C₂³×C₃	1	4	yes	—
511	C₄×C₈	C₂³×C₃	1	2	yes	—
512	C₄×C₈	C₂³×C₃	1	2	yes	—
513	C₄×C₈	C₂³×C₃	1	4	yes	—
514	C₂³×C₃	—	2	1	no	—
515	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
516	C₃×Q₈	—	2	4	no	—
517	C₃×Q₈	—	2	4	no	—
518	C₃×Q₈	—	2	1	no	—
519	C₃×Q₈	—	2	2	no	—
520	C₃×Q₈	—	2	2	no	—
521	C₃×Q₈	—	2	2	no	—
522	C₃×Q₈	—	2	2	no	—
523	C₃×Q₈	—	4	2	no	—
524	C₃×Q₈	—	4	4	no	—
525	C₃×Q₈	—	4	2	no	—
526	C₃×Q₈	—	8	2	no	—
527	C₃×Q₈	—	8	4	no	—
528	C₃×Q₈	2₋¹⁺⁴	1	2	yes	—
529	C₃×D₄	—	2	4	no	—
530	C₃×D₄	—	2	1	no	—
531	C₃×D₄	2₋¹⁺⁴	1	2	yes	—
532	C₂×C₃×C₄	—	2	4	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	2	1	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	4	no	—
545	C₂×C₃×C₄	—	4	2	no	—
546	C₂×C₃×C₄	—	4	2	no	—
547	C₂×C₃×C₄	—	8	4	no	—
548	C₂×C₃×C₄	—	8	2	no	—
549	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
550	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
552	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
557	C₃×C₈	—	2	2	no	—
558	C₃×C₈	—	2	2	no	—
559	C₃×C₈	—	2	2	no	—
560	C₃×C₈	—	2	2	no	—
561	#41	—	2	2	no	—
562	#41	—	2	2	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	8	2	no	—
569	C₂×Q₈	—	8	4	no	—
570	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
571	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
572	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
573	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
574	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
583	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
585	Q₁₆	—	2	4	no	—
586	Q₁₆	—	2	4	no	—
587	SD₁₆	—	2	4	no	—
588	SD₁₆	—	2	4	no	—
589	C₂×C₈	C₂⁴×C₃	1	2	yes	—
590	C₂×C₈	C₂⁴×C₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₃	1	2	yes	—
592	C₂×C₈	C₂⁴×C₃	1	2	yes	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
619	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
620	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
621	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
622	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
623	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
624	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
627	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
628	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
645	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
646	C₄²	C₂⁴×C₃	1	1	yes	characteristic
647	C₄²	C₂⁴×C₃	1	1	yes	characteristic
648	C₄²	C₂⁴×C₃	1	4	yes	—
649	C₂²×C₃	—	2	1	no	—
650	C₂²×C₃	—	2	2	no	—
651	C₂²×C₃	—	2	1	no	—
652	C₂²×C₃	—	2	1	no	—
653	C₂²×C₃	—	4	1	no	—
654	C₂²×C₃	—	4	1	no	—
655	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	2	2	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	4	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	2	4	no	—
662	C₃×C₄	—	4	2	no	—
663	C₃×C₄	—	4	2	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	4	no	—
666	C₃×C₄	—	4	2	no	—
667	C₃×C₄	—	4	1	no	—
668	C₃×C₄	—	4	2	no	—
669	C₃×C₄	#577	1	2	yes	—
670	C₃×C₄	#578	1	2	yes	—
671	C₃×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
672	C₃×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂³	—	2	1	no	—
674	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
675	Q₈	—	2	4	no	—
676	Q₈	—	2	4	no	—
677	Q₈	—	2	1	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	4	2	no	—
684	Q₈	—	4	2	no	—
685	Q₈	—	8	2	no	—
686	Q₈	—	8	4	no	—
687	Q₈	C₃×2₋¹⁺⁴	1	2	yes	—
688	D₄	—	2	4	no	—
689	D₄	—	2	1	no	—
690	D₄	C₃×2₋¹⁺⁴	1	2	yes	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	8	4	no	—
707	C₂×C₄	—	8	2	no	—
708	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
709	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
711	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
712	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
713	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
714	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
715	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	2	no	—
718	C₈	—	2	2	no	—
719	C₈	—	2	2	no	—
720	C₂×C₃	—	4	1	no	—
721	C₂×C₃	—	4	2	no	—
722	C₂×C₃	#3486	1	1	yes	characteristic
723	C₂×C₃	C₂×#577	1	1	yes	characteristic
724	C₂×C₃	C₂×#578	1	1	yes	characteristic
725	C₂²	—	2	1	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	4	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	C₃×#577	1	2	yes	—
746	C₄	C₃×#578	1	2	yes	—
747	C₄	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
748	C₄	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
749	C₃	#61869	1	1	yes	characteristic, direct product factor, Sylow
750	C₂	—	4	1	no	—
751	C₂	—	4	2	no	—
752	C₂	C₃×#3486	1	1	yes	characteristic
753	C₂	C₂×C₃×#577	1	1	yes	characteristic
754	C₂	C₂×C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3556	C₂	semidirect
3. C₃×#3387	C₂	semidirect
4. C₃×#3386	C₂	semidirect
5. C₃×#3383	C₂	semidirect
6. C₃×#3381	C₂	semidirect
7. C₃×#3374	C₂	semidirect
8. C₃×#3372	C₂	semidirect
9. C₃×#3363	C₂	semidirect
10. C₃×#3359	C₂	semidirect
11. C₃×#3242	C₂	semidirect
12. C₃×#3230	C₂	semidirect
13. C₃×#3229	C₂	semidirect
17. C₃×#2986	C₂	semidirect
18. #61869	C₃	direct (N × H)
94. #3556	C₂×C₃	semidirect
96. #3387	C₂×C₃	semidirect
97. #3386	C₂×C₃	semidirect
98. #3383	C₂×C₃	semidirect
99. #3381	C₂×C₃	semidirect
100. #3374	C₂×C₃	semidirect
101. #3372	C₂×C₃	semidirect
102. #3363	C₂×C₃	semidirect
103. #3359	C₂×C₃	semidirect
104. #3242	C₂×C₃	semidirect
105. #3230	C₂×C₃	semidirect
106. #3229	C₂×C₃	semidirect
110. #2986	C₂×C₃	semidirect
749. C₃	#61869	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3556	2
C₃×#3503	2
C₃×#3387	2
C₃×#3386	2
C₃×#3383	2
C₃×#3381	2
C₃×#3374	2
C₃×#3372	2
C₃×#3363	2
C₃×#3359	2
C₃×#3242	2
C₃×#3230	2
C₃×#3229	2
C₃×#3120	2
C₃×#3107	2
C₃×#2986	2
#61869	3

Subgroups — C3×#61869 #10680476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61869 #10680476