Subgroups — #86553

Order 384.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#5730	C₂	1	1	yes	maximal, characteristic, complemented
3	#5726	C₂	1	1	yes	maximal, characteristic, complemented
4	#5709	C₂	1	2	yes	maximal, complemented
5	#5705	C₂	1	2	yes	maximal, complemented
6	#5681	C₂	1	1	yes	maximal, characteristic, complemented
7	#5679	C₂	1	2	yes	maximal, complemented
8	#5676	C₂	1	1	yes	maximal, characteristic, complemented
9	#5676	C₂	1	2	yes	maximal, complemented
10	#5657	C₂	1	2	yes	maximal, complemented
11	D₃×#123	C₂	1	2	yes	maximal, complemented
12	#5639	C₂	1	1	yes	maximal, characteristic, complemented
13	#5638	C₂	1	2	yes	maximal, complemented
14	#5630	C₂	1	1	yes	maximal, characteristic, complemented
15	#5627	C₂	1	2	yes	maximal, complemented
16	#5614	C₂	1	1	yes	maximal, characteristic, complemented
17	#5609	C₂	1	1	yes	maximal, characteristic, complemented
18	#5580	C₂	1	1	yes	maximal, characteristic, complemented
19	#5574	C₂	1	1	yes	maximal, characteristic, complemented
20	#5562	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
22	#5528	C₂	1	1	yes	maximal, characteristic, complemented
23	#5521	C₂	1	1	yes	maximal, characteristic, complemented
24	#3513	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×#239	C₂²	1	2	yes	complemented
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×D₃×D₄	C₂²	1	2	yes	—
29	C₂²×D₁₂	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃	C₂²	1	2	yes	complemented
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×#123	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#121	C₂²	1	1	yes	characteristic
39	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#947	C₂²	1	1	yes	characteristic, complemented
43	#946	C₂²	1	2	yes	complemented
44	#946	C₂²	1	2	yes	complemented
45	#946	C₂²	1	1	yes	characteristic, complemented
46	#946	C₂²	1	2	yes	complemented
47	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
48	#940	C₂²	1	1	yes	characteristic
49	#938	C₂²	1	2	yes	complemented
50	#938	C₂²	1	1	yes	characteristic, complemented
51	#937	C₂²	1	2	yes	—
52	#935	C₂²	1	2	yes	complemented
53	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	#930	C₂²	1	2	yes	complemented
55	#929	C₂²	1	2	yes	complemented
56	C₄×#67	C₂²	1	1	yes	characteristic
57	C₄×#67	C₂²	1	2	yes	complemented
58	C₄×#67	C₂²	1	1	yes	characteristic, complemented
59	#926	C₂²	1	1	yes	characteristic, complemented
60	#898	C₂²	1	2	yes	complemented
61	#898	C₂²	1	1	yes	characteristic, complemented
62	#897	C₂²	1	2	yes	complemented
63	#896	C₂²	1	1	yes	characteristic, complemented
64	#895	C₂²	1	1	yes	characteristic
65	#895	C₂²	1	2	yes	complemented
66	#895	C₂²	1	1	yes	characteristic, complemented
67	#894	C₂²	1	2	yes	complemented
68	#894	C₂²	1	2	yes	complemented
69	#894	C₂²	1	2	yes	complemented
70	#894	C₂²	1	2	yes	complemented
71	#894	C₂²	1	1	yes	characteristic, complemented
72	#893	C₂²	1	1	yes	characteristic
73	#893	C₂²	1	1	yes	characteristic
74	#893	C₂²	1	2	yes	complemented
75	#893	C₂²	1	2	yes	complemented
76	#893	C₂²	1	2	yes	complemented
77	#892	C₂²	1	2	yes	complemented
78	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	#890	C₂²	1	1	yes	characteristic, complemented
83	#890	C₂²	1	1	yes	characteristic, complemented
84	#889	C₂²	1	1	yes	characteristic, complemented
85	#889	C₂²	1	2	yes	complemented
86	#886	C₂²	1	2	yes	complemented
87	#885	C₂²	1	1	yes	characteristic, complemented
88	#885	C₂²	1	2	yes	complemented
89	#884	C₂²	1	2	yes	—
90	#884	C₂²	1	1	yes	characteristic
91	#884	C₂²	1	2	yes	complemented
92	#884	C₂²	1	2	yes	complemented
93	#883	C₂²	1	2	yes	—
94	#883	C₂²	1	1	yes	characteristic
95	#883	C₂²	1	2	yes	complemented
96	#883	C₂²	1	2	yes	complemented
97	#883	C₂²	1	2	yes	complemented
98	#882	C₂²	1	2	yes	—
99	#882	C₂²	1	2	yes	complemented
100	#882	C₂²	1	2	yes	complemented
101	#67⋊C₄	C₂²	1	2	yes	complemented
102	#67⋊C₄	C₂²	1	2	yes	complemented
103	#67⋊C₄	C₂²	1	2	yes	complemented
104	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
109	#879	C₂²	1	2	yes	complemented
110	#879	C₂²	1	2	yes	complemented
111	#879	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₁₂	C₂²	1	1	yes	characteristic
113	C₄×D₁₂	C₂²	1	1	yes	characteristic
114	C₄×D₁₂	C₂²	1	2	yes	complemented
115	C₄×D₁₂	C₂²	1	2	yes	complemented
116	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
119	#872	C₂²	1	2	yes	complemented
120	#872	C₂²	1	2	yes	complemented
121	#872	C₂²	1	1	yes	characteristic, complemented
122	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#559	—	3	1	no	—
125	#554	—	3	1	no	—
126	#553	—	3	2	no	—
127	#553	—	3	1	no	—
128	#552	—	3	1	no	—
129	#551	—	3	2	no	—
130	#551	—	3	2	no	—
131	#547	—	3	1	no	—
132	#546	—	3	2	no	—
133	#546	—	3	1	no	—
134	#546	—	3	1	no	—
135	D₄²	—	3	1	no	—
136	#542	D₃	1	1	yes	characteristic, complemented
137	#540	—	3	1	no	—
138	#539	—	3	2	no	—
139	#538	—	3	2	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×#123	—	3	2	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	1	yes	characteristic
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	1	yes	characteristic
160	C₂×#67	C₂³	1	2	yes	—
161	C₂²×Dic₃	C₂³	1	2	yes	—
162	#239	—	2	4	no	—
163	#239	—	4	4	no	—
164	D₃×D₄	—	2	4	no	—
165	D₃×D₄	—	4	4	no	—
166	C₂×D₁₂	—	2	4	no	—
167	C₂×D₁₂	C₂³	1	1	yes	characteristic
168	C₂×D₁₂	C₂³	1	2	yes	—
169	C₂×D₁₂	C₂³	1	1	yes	characteristic
170	C₂×D₁₂	C₂³	1	2	yes	—
171	C₂×D₁₂	C₂³	1	2	yes	—
172	C₂×D₁₂	C₂³	1	2	yes	—
173	C₂×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	—	4	4	no	—
175	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₄×D₃	C₂³	1	2	yes	—
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	2	yes	—
182	C₂×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₄×D₃	C₂³	1	2	yes	—
184	C₂×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	2	yes	—
188	C₂×Dic₆	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₃×C₄²	C₂³	1	2	yes	—
206	#217	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	1	yes	characteristic
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
227	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂³	1	2	yes	—
233	C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₄⋊Dic₃	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	2	no	—
254	C₂²×D₄	—	3	1	no	—
255	C₂²×D₄	—	3	2	no	—
256	C₂²×D₄	—	3	1	no	—
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
259	#127	—	3	1	no	—
260	#126	—	3	2	no	—
261	#126	—	3	1	no	—
262	#126	—	3	1	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	C₂×D₃	1	2	yes	complemented
266	#125	—	3	1	no	—
267	#125	—	3	1	no	—
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#124	—	3	1	no	—
271	#124	—	3	1	no	—
272	#124	—	3	2	no	—
273	#124	C₂×D₃	1	2	yes	complemented
274	#124	C₂×D₃	1	1	yes	characteristic, complemented
275	#123	—	3	2	no	—
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	1	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	1	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	C₂×D₃	1	2	yes	complemented
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	1	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
296	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	#121	—	3	2	no	—
298	#121	—	3	1	no	—
299	#121	—	3	2	no	—
300	#121	—	3	2	no	—
301	#121	—	3	1	no	—
302	#121	—	3	1	no	—
303	#121	—	3	1	no	—
304	#121	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	C₂×D₃	1	1	yes	characteristic
308	#120	—	3	2	no	—
309	#120	—	3	2	no	—
310	#120	—	3	2	no	—
311	#120	—	3	2	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	2	no	—
322	C₄×D₄	—	3	2	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
335	#117	—	3	1	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	2	no	—
339	#117	—	3	2	no	—
340	#117	C₂×D₃	1	1	yes	characteristic, complemented
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	2	yes	—
353	C₂²×D₃	—	2	4	no	—
354	C₂²×D₃	—	2	4	no	—
355	C₂²×D₃	—	2	4	no	—
356	C₂²×D₃	—	4	2	no	—
357	C₂²×D₃	—	4	2	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	C₂⁴	1	2	yes	—
360	C₂²×D₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₃	C₂⁴	1	2	yes	—
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	4	2	no	—
365	C₃×D₄	—	2	2	no	—
366	C₃×D₄	—	4	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	2	yes	—
371	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	#67	—	2	4	no	—
379	#67	—	2	2	no	—
380	#67	—	4	2	no	—
381	#67	—	4	1	no	—
382	#67	—	4	2	no	—
383	#67	—	4	2	no	—
384	C₂×Dic₃	—	4	2	no	—
385	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	2	yes	—
390	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₃	C₂⁴	1	2	yes	—
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	D₁₂	—	2	4	no	—
394	D₁₂	—	2	4	no	—
395	D₁₂	—	2	4	no	—
396	D₁₂	—	2	2	no	—
397	D₁₂	—	2	2	no	—
398	D₁₂	—	4	2	no	—
399	D₁₂	#41	1	4	yes	complemented
400	C₄×D₃	—	2	4	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	4	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	4	2	no	—
406	C₄×D₃	—	4	2	no	—
407	C₄×D₃	—	4	1	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	—	4	2	no	—
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	C₄×D₃	—	4	2	no	—
413	Dic₆	—	4	1	no	—
414	C₂⁴	—	3	2	no	—
415	C₂⁴	—	3	2	no	—
416	#41	—	6	4	no	—
417	#41	—	12	4	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
420	C₂×Q₈	C₂²×D₃	1	2	yes	—
421	C₂×D₄	—	3	2	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	1	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	1	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	1	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	6	4	no	—
435	C₂×D₄	—	6	4	no	—
436	C₂×D₄	—	12	4	no	—
437	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
438	C₂×D₄	C₂²×D₃	1	2	yes	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	—	12	4	no	—
454	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₃	1	2	yes	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₃	1	2	yes	—
477	C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	1	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	1	no	—
498	C₂²⋊C₄	—	3	1	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	1	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	1	no	—
503	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
504	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
505	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
506	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	1	no	—
513	C₄²	—	3	2	no	—
514	C₄²	—	3	2	no	—
515	C₄²	—	3	1	no	—
516	C₄²	C₂²×D₃	1	1	yes	characteristic
517	C₄²	C₂²×D₃	1	2	yes	—
518	C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	C₂⁵	1	1	yes	characteristic
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	2	no	—
528	C₂×D₃	—	2	1	no	—
529	C₂×D₃	—	2	2	no	—
530	C₂×D₃	—	2	1	no	—
531	C₂×D₃	—	2	2	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	1	no	—
536	C₂×D₃	—	4	8	no	—
537	C₂×D₃	—	8	4	no	—
538	C₂×D₃	C₂×#41	1	4	yes	—
539	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	C₂×#41	1	2	yes	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	1	no	—
551	Dic₃	—	2	2	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	1	no	—
554	Dic₃	—	2	1	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	2	no	—
557	C₂³	—	3	2	no	—
558	C₂³	—	3	1	no	—
559	C₂³	—	3	2	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	6	4	no	—
562	C₂³	—	6	4	no	—
563	C₂³	—	6	4	no	—
564	C₂³	—	12	2	no	—
565	C₂³	—	12	2	no	—
566	C₂³	—	12	2	no	—
567	C₂³	C₂³×D₃	1	1	yes	characteristic
568	C₂³	C₂³×D₃	1	2	yes	—
569	Q₈	—	2	2	no	—
570	Q₈	—	4	2	no	—
571	Q₈	—	12	1	no	—
572	D₄	—	2	2	no	—
573	D₄	—	3	4	no	—
574	D₄	—	4	2	no	—
575	D₄	—	6	4	no	—
576	D₄	—	6	4	no	—
577	D₄	—	6	4	no	—
578	D₄	—	6	2	no	—
579	D₄	—	6	4	no	—
580	D₄	—	6	2	no	—
581	D₄	—	6	2	no	—
582	D₄	—	12	2	no	—
583	D₄	—	12	2	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	1	no	—
586	D₄	—	12	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	1	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	3	2	no	—
594	C₂×C₄	—	3	1	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	6	2	no	—
598	C₂×C₄	—	6	4	no	—
599	C₂×C₄	—	6	4	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	—	6	2	no	—
602	C₂×C₄	—	12	2	no	—
603	C₂×C₄	—	12	2	no	—
604	C₂×C₄	—	12	2	no	—
605	C₂×C₄	—	12	2	no	—
606	C₂×C₄	—	12	2	no	—
607	C₂×C₄	—	12	2	no	—
608	C₂×C₄	—	12	1	no	—
609	C₂×C₄	—	12	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₃	1	2	yes	—
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₃	1	2	yes	—
618	C₂×C₄	C₂³×D₃	1	2	yes	—
619	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₃	—	4	2	no	—
621	C₂×C₃	—	4	1	no	—
622	C₂×C₃	C₂²×#41	1	1	yes	characteristic
623	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂×C₃	#585	1	1	yes	characteristic
625	D₃	—	2	2	no	—
626	D₃	—	2	4	no	—
627	D₃	—	4	1	no	—
628	D₃	—	4	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	3	4	no	—
636	C₂²	—	3	2	no	—
637	C₂²	—	6	1	no	—
638	C₂²	—	6	2	no	—
639	C₂²	—	6	1	no	—
640	C₂²	—	6	2	no	—
641	C₂²	—	6	1	no	—
642	C₂²	—	6	2	no	—
643	C₂²	—	6	1	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	6	2	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	12	8	no	—
648	C₂²	—	24	4	no	—
649	C₂²	C₂⁴×D₃	1	1	yes	characteristic
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	6	1	no	—
659	C₄	—	6	1	no	—
660	C₄	—	6	1	no	—
661	C₄	—	6	2	no	—
662	C₄	—	6	1	no	—
663	C₄	—	6	2	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	D₃×#41	1	2	yes	—
667	C₃	#3513	1	1	yes	characteristic, complemented, Sylow
668	C₂	—	4	2	no	—
669	C₂	—	4	1	no	—
670	C₂	—	6	2	no	—
671	C₂	—	6	4	no	—
672	C₂	—	12	2	no	—
673	C₂	—	12	1	no	—
674	C₂	C₂×D₃×#41	1	1	yes	characteristic
675	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#542	C₂
hypercenter	#542	D₃
hypocenter	C₃	#3513
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₃×#542	C₂	semidirect
2. #5730	C₂	semidirect
3. #5726	C₂	semidirect
4. #5709	C₂	semidirect
5. #5705	C₂	semidirect
6. #5681	C₂	semidirect
7. #5679	C₂	semidirect
8. #5676	C₂	semidirect
9. #5676	C₂	semidirect
10. #5657	C₂	semidirect
11. D₃×#123	C₂	semidirect
12. #5639	C₂	semidirect
13. #5638	C₂	semidirect
14. #5630	C₂	semidirect
15. #5627	C₂	semidirect
16. #5614	C₂	semidirect
17. #5609	C₂	semidirect
18. #5580	C₂	semidirect
19. #5574	C₂	semidirect
20. #5562	C₂	semidirect
21. C₄×D₃×D₄	C₂	semidirect
22. #5528	C₂	semidirect
23. #5521	C₂	semidirect
26. C₂×#239	C₂²	semidirect
30. C₂²×C₄×D₃	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#126	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
42. #947	C₂²	semidirect
43. #946	C₂²	semidirect
44. #946	C₂²	semidirect
45. #946	C₂²	semidirect
46. #946	C₂²	semidirect
47. Q₈×Dic₃	C₂²	semidirect
49. #938	C₂²	semidirect
50. #938	C₂²	semidirect
52. #935	C₂²	semidirect
53. D₄×Dic₃	C₂²	semidirect
54. #930	C₂²	semidirect
55. #929	C₂²	semidirect
57. C₄×#67	C₂²	semidirect
58. C₄×#67	C₂²	semidirect
59. #926	C₂²	semidirect
60. #898	C₂²	semidirect
61. #898	C₂²	semidirect
62. #897	C₂²	semidirect
63. #896	C₂²	semidirect
65. #895	C₂²	semidirect
66. #895	C₂²	semidirect
67. #894	C₂²	semidirect
68. #894	C₂²	semidirect
69. #894	C₂²	semidirect
70. #894	C₂²	semidirect
71. #894	C₂²	semidirect
74. #893	C₂²	semidirect
75. #893	C₂²	semidirect
76. #893	C₂²	semidirect
77. #892	C₂²	semidirect
78. D₃×C₄⋊C₄	C₂²	semidirect
79. D₃×C₄⋊C₄	C₂²	semidirect
80. D₃×C₄⋊C₄	C₂²	semidirect
81. D₃×C₄⋊C₄	C₂²	semidirect
82. #890	C₂²	semidirect
83. #890	C₂²	semidirect
84. #889	C₂²	semidirect
85. #889	C₂²	semidirect
86. #886	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
91. #884	C₂²	semidirect
92. #884	C₂²	semidirect
95. #883	C₂²	semidirect
96. #883	C₂²	semidirect
97. #883	C₂²	semidirect
99. #882	C₂²	semidirect
100. #882	C₂²	semidirect
101. #67⋊C₄	C₂²	semidirect
102. #67⋊C₄	C₂²	semidirect
103. #67⋊C₄	C₂²	semidirect
104. D₃×C₂²⋊C₄	C₂²	semidirect
105. D₃×C₂²⋊C₄	C₂²	semidirect
106. D₃×C₂²⋊C₄	C₂²	semidirect
107. D₃×C₂²⋊C₄	C₂²	semidirect
108. D₃×C₂²⋊C₄	C₂²	semidirect
109. #879	C₂²	semidirect
110. #879	C₂²	semidirect
111. #879	C₂²	semidirect
114. C₄×D₁₂	C₂²	semidirect
115. C₄×D₁₂	C₂²	semidirect
116. C₄×D₁₂	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
118. C₄×D₁₂	C₂²	semidirect
119. #872	C₂²	semidirect
120. #872	C₂²	semidirect
121. #872	C₂²	semidirect
122. C₄²×D₃	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
136. #542	D₃	semidirect
258. C₄⋊Q₈	C₂×D₃	semidirect
265. #126	C₂×D₃	semidirect
273. #124	C₂×D₃	semidirect
274. #124	C₂×D₃	semidirect
288. #123	C₂×D₃	semidirect
295. C₂²⋊Q₈	C₂×D₃	semidirect
296. C₂²⋊Q₈	C₂×D₃	semidirect
314. C₄×Q₈	C₂×D₃	semidirect
334. C₄×D₄	C₂×D₃	semidirect
340. #117	C₂×D₃	semidirect
399. D₁₂	#41	semidirect
667. C₃	#3513	semidirect

Maximal subgroups

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

subgroup	index
C₃×#542	2
#5730	2
#5726	2
#5709	2
#5705	2
#5681	2
#5679	2
#5676	2
#5657	2
D₃×#123	2
#5639	2
#5638	2
#5630	2
#5627	2
#5614	2
#5609	2
#5580	2
#5574	2
#5562	2
C₄×D₃×D₄	2
#5528	2
#5521	2
#3513	3