Subgroups — #86687

Order 384.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	#5829	C₂	1	1	yes	maximal, characteristic, complemented
4	#5827	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
6	#5732	C₂	1	1	yes	maximal, characteristic, complemented
7	#5731	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	2	yes	maximal, complemented
9	#5658	C₂	1	2	yes	maximal, complemented
10	#5658	C₂	1	2	yes	maximal, complemented
11	#5649	C₂	1	2	yes	maximal, complemented
12	#5643	C₂	1	1	yes	maximal, characteristic, complemented
13	#5642	C₂	1	1	yes	maximal, characteristic, complemented
14	#5641	C₂	1	1	yes	maximal, characteristic, complemented
15	#5624	C₂	1	1	yes	maximal, characteristic, complemented
16	#5617	C₂	1	2	yes	maximal, complemented
17	#5601	C₂	1	2	yes	maximal, complemented
18	#5565	C₂	1	1	yes	maximal, characteristic, complemented
19	#5545	C₂	1	1	yes	maximal, characteristic, complemented
20	#5539	C₂	1	1	yes	maximal, characteristic, complemented
21	#5538	C₂	1	1	yes	maximal, characteristic, complemented
22	#5513	C₂	1	2	yes	maximal, complemented
23	C₂×#898	C₂	1	2	yes	maximal, complemented
24	#3521	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×#41	C₂²	1	1	yes	characteristic
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#123	C₂²	1	2	yes	complemented
30	C₃×#123	C₂²	1	2	yes	complemented
31	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×#121	C₂²	1	2	yes	complemented
34	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
37	#947	C₂²	1	1	yes	characteristic
38	#947	C₂²	1	1	yes	characteristic
39	#946	C₂²	1	1	yes	characteristic
40	#946	C₂²	1	1	yes	characteristic
41	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	#939	C₂²	1	2	yes	—
46	#939	C₂²	1	2	yes	—
47	#939	C₂²	1	1	yes	characteristic
48	#939	C₂²	1	2	yes	complemented
49	#937	C₂²	1	2	yes	—
50	#937	C₂²	1	2	yes	—
51	#935	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₃	C₂²	1	1	yes	characteristic
53	D₄×Dic₃	C₂²	1	1	yes	characteristic
54	D₄×Dic₃	C₂²	1	1	yes	characteristic
55	D₄×Dic₃	C₂²	1	2	yes	complemented
56	D₄×Dic₃	C₂²	1	2	yes	complemented
57	D₄×Dic₃	C₂²	1	2	yes	complemented
58	D₄×Dic₃	C₂²	1	2	yes	complemented
59	#930	C₂²	1	1	yes	characteristic
60	#930	C₂²	1	1	yes	characteristic
61	#929	C₂²	1	2	yes	—
62	#929	C₂²	1	2	yes	—
63	C₄×#67	C₂²	1	1	yes	characteristic
64	C₄×#67	C₂²	1	1	yes	characteristic
65	C₄×#67	C₂²	1	2	yes	—
66	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
67	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
68	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
69	#926	C₂²	1	1	yes	characteristic, complemented
70	#926	C₂²	1	1	yes	characteristic, complemented
71	#926	C₂²	1	2	yes	complemented
72	#926	C₂²	1	2	yes	complemented
73	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊Dic₃	C₂²	1	2	yes	complemented
75	#924	C₂²	1	2	yes	complemented
76	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
77	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
78	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
79	#898	C₂²	1	2	yes	—
80	#898	C₂²	1	2	yes	—
81	#898	C₂²	1	2	yes	—
82	#898	C₂²	1	2	yes	—
83	#898	C₂²	1	1	yes	characteristic
84	#898	C₂²	1	2	yes	complemented
85	#898	C₂²	1	2	yes	complemented
86	#898	C₂²	1	2	yes	complemented
87	#898	C₂²	1	2	yes	complemented
88	#898	C₂²	1	2	yes	complemented
89	#897	C₂²	1	2	yes	complemented
90	#897	C₂²	1	2	yes	complemented
91	#893	C₂²	1	1	yes	characteristic
92	#892	C₂²	1	1	yes	characteristic
93	#892	C₂²	1	2	yes	complemented
94	#892	C₂²	1	2	yes	complemented
95	#890	C₂²	1	2	yes	complemented
96	#890	C₂²	1	1	yes	characteristic, complemented
97	#889	C₂²	1	2	yes	complemented
98	#889	C₂²	1	2	yes	complemented
99	#889	C₂²	1	1	yes	characteristic, complemented
100	#888	C₂²	1	1	yes	characteristic, complemented
101	#887	C₂²	1	2	yes	complemented
102	#886	C₂²	1	2	yes	—
103	#886	C₂²	1	1	yes	characteristic
104	#886	C₂²	1	2	yes	complemented
105	#885	C₂²	1	2	yes	—
106	#885	C₂²	1	1	yes	characteristic
107	#885	C₂²	1	2	yes	complemented
108	#883	C₂²	1	2	yes	complemented
109	#883	C₂²	1	2	yes	complemented
110	#67⋊C₄	C₂²	1	2	yes	—
111	#67⋊C₄	C₂²	1	2	yes	complemented
112	#67⋊C₄	C₂²	1	2	yes	complemented
113	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
114	#879	C₂²	1	2	yes	complemented
115	#879	C₂²	1	1	yes	characteristic, complemented
116	#878	C₂²	1	2	yes	complemented
117	#878	C₂²	1	2	yes	complemented
118	#878	C₂²	1	1	yes	characteristic, complemented
119	#877	C₂²	1	2	yes	complemented
120	C₄×D₁₂	C₂²	1	1	yes	characteristic
121	#872	C₂²	1	1	yes	characteristic
122	#870	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#556	—	3	1	no	—
125	#556	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	2	no	—
128	#553	—	3	1	no	—
129	#552	—	3	1	no	—
130	#552	—	3	2	no	—
131	#551	—	3	2	no	—
132	#551	—	3	2	no	—
133	#547	D₃	1	1	yes	characteristic, complemented
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#542	—	3	1	no	—
137	#541	—	3	1	no	—
138	#539	—	3	2	no	—
139	#538	—	3	2	no	—
140	#529	—	3	2	no	—
141	#529	—	3	1	no	—
142	#529	—	3	1	no	—
143	C₂×#126	—	3	2	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₄×#41	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₃×#41	—	2	4	no	—
149	C₃×#41	—	2	4	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂×C₃×D₄	C₂³	1	2	yes	—
154	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³	1	2	yes	—
157	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³	1	2	yes	—
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	1	yes	characteristic
165	C₂×#67	C₂³	1	1	yes	characteristic
166	C₂²×Dic₃	C₂³	1	2	yes	—
167	C₂²×Dic₃	C₂³	1	1	yes	characteristic
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	C₂²×Dic₃	C₂³	1	2	yes	—
170	C₂²×Dic₃	C₂³	1	2	yes	—
171	C₂²×Dic₃	C₂³	1	1	yes	characteristic
172	D₃×D₄	—	2	4	no	—
173	C₂×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₃	C₂³	1	2	yes	—
176	C₂×C₄×D₃	C₂³	1	2	yes	—
177	C₂×Dic₆	C₂³	1	1	yes	characteristic
178	C₂×Dic₆	C₂³	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄²	C₂³	1	1	yes	characteristic
191	#217	C₂³	1	1	yes	characteristic
192	#217	C₂³	1	1	yes	characteristic
193	#217	C₂³	1	2	yes	—
194	#217	C₂³	1	2	yes	—
195	#217	C₂³	1	2	yes	—
196	#217	C₂³	1	1	yes	characteristic
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	1	yes	characteristic
199	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
201	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₃	C₂³	1	2	yes	—
221	C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	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	2	yes	—
238	C₄×Dic₃	C₂³	1	1	yes	characteristic
239	C₄×Dic₃	C₂³	1	1	yes	characteristic
240	C₄×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×Dic₃	C₂³	1	2	yes	—
242	C₄×Dic₃	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₃	C₂³	1	2	yes	—
245	C₄×Dic₃	C₂³	1	2	yes	—
246	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₂×#41	C₂×D₃	1	1	yes	characteristic
250	C₂×#41	C₂×D₃	1	1	yes	characteristic
251	C₂²×D₄	—	3	1	no	—
252	C₄⋊Q₈	—	3	1	no	—
253	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
254	#126	—	3	1	no	—
255	#126	—	3	2	no	—
256	#126	—	3	2	no	—
257	#126	—	3	2	no	—
258	#126	—	3	2	no	—
259	#126	—	3	2	no	—
260	#126	—	3	2	no	—
261	#126	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	1	no	—
265	#126	—	3	2	no	—
266	#125	—	3	2	no	—
267	#125	—	3	1	no	—
268	#125	—	3	1	no	—
269	#125	—	3	2	no	—
270	#125	—	3	2	no	—
271	#125	—	3	1	no	—
272	#124	—	3	1	no	—
273	#124	—	3	1	no	—
274	#124	—	3	2	no	—
275	#124	—	3	1	no	—
276	#124	—	3	2	no	—
277	#123	—	3	1	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	1	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	C₂×D₃	1	2	yes	complemented
286	#123	C₂×D₃	1	2	yes	complemented
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
296	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	#121	—	3	1	no	—
298	#121	—	3	2	no	—
299	#121	—	3	2	no	—
300	#121	—	3	2	no	—
301	#121	—	3	1	no	—
302	#121	—	3	1	no	—
303	#121	C₂×D₃	1	2	yes	complemented
304	#120	—	3	2	no	—
305	#120	—	3	2	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×Q₈	—	3	1	no	—
309	C₄×Q₈	—	3	1	no	—
310	C₄×Q₈	—	3	2	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	2	no	—
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	2	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	C₂×D₃	1	1	yes	characteristic
328	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
329	#117	—	3	2	no	—
330	#117	—	3	1	no	—
331	#117	—	3	1	no	—
332	#117	—	3	2	no	—
333	#117	—	3	1	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	C₂×C₄⋊C₄	—	3	2	no	—
339	C₂×C₄⋊C₄	—	3	1	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂³×C₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₃	C₂⁴	1	2	yes	—
351	C₂²×D₃	—	2	4	no	—
352	C₂²×D₃	—	4	2	no	—
353	C₂²×D₃	—	4	2	no	—
354	C₂²×D₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₃	C₂⁴	1	2	yes	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	2	2	no	—
358	C₃×D₄	—	2	4	no	—
359	C₃×D₄	—	2	4	no	—
360	C₃×D₄	—	4	1	no	—
361	C₃×D₄	#41	1	4	yes	—
362	C₂×C₃×C₄	—	2	4	no	—
363	C₂×C₃×C₄	—	2	4	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
375	#67	—	2	4	no	—
376	#67	—	4	1	no	—
377	#67	—	4	2	no	—
378	#67	—	4	1	no	—
379	#67	—	4	2	no	—
380	C₂×Dic₃	—	4	2	no	—
381	C₂×Dic₃	—	4	2	no	—
382	C₂×Dic₃	—	4	1	no	—
383	C₂×Dic₃	—	4	1	no	—
384	C₂×Dic₃	—	4	2	no	—
385	C₂×Dic₃	—	4	2	no	—
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	1	yes	characteristic
392	C₂×Dic₃	C₂⁴	1	2	yes	—
393	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₃	C₂⁴	1	2	yes	—
395	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
396	D₁₂	—	2	2	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	—	4	2	no	—
399	C₄×D₃	—	4	2	no	—
400	Dic₆	—	4	2	no	—
401	Dic₆	—	4	1	no	—
402	C₂⁴	—	3	2	no	—
403	#41	—	2	4	no	—
404	#41	—	2	4	no	—
405	C₂×Q₈	—	3	1	no	—
406	C₂×Q₈	—	3	2	no	—
407	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
408	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
409	C₂×D₄	—	3	2	no	—
410	C₂×D₄	—	3	1	no	—
411	C₂×D₄	—	3	1	no	—
412	C₂×D₄	—	3	2	no	—
413	C₂×D₄	—	3	2	no	—
414	C₂×D₄	—	3	1	no	—
415	C₂×D₄	—	6	4	no	—
416	C₂×D₄	C₂²×D₃	1	2	yes	—
417	C₂×D₄	C₂²×D₃	1	2	yes	—
418	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
419	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
420	C₂²×C₄	—	3	2	no	—
421	C₂²×C₄	—	3	2	no	—
422	C₂²×C₄	—	3	1	no	—
423	C₂²×C₄	—	3	1	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	3	2	no	—
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	3	2	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	C₂²×D₃	1	2	yes	—
430	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₃	1	2	yes	—
432	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
433	C₂²×C₄	C₂²×D₃	1	2	yes	—
434	C₄⋊C₄	—	3	1	no	—
435	C₄⋊C₄	—	3	2	no	—
436	C₄⋊C₄	—	3	1	no	—
437	C₄⋊C₄	—	3	1	no	—
438	C₄⋊C₄	—	3	2	no	—
439	C₄⋊C₄	—	3	1	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	2	no	—
442	C₄⋊C₄	—	3	2	no	—
443	C₄⋊C₄	—	3	2	no	—
444	C₄⋊C₄	—	3	1	no	—
445	C₄⋊C₄	—	3	1	no	—
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×D₃	1	2	yes	—
460	C₄⋊C₄	C₂²×D₃	1	2	yes	—
461	C₄⋊C₄	C₂²×D₃	1	2	yes	—
462	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×D₃	1	2	yes	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	1	no	—
466	C₂²⋊C₄	—	3	2	no	—
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	—	3	1	no	—
470	C₂²⋊C₄	—	3	1	no	—
471	C₂²⋊C₄	—	3	1	no	—
472	C₂²⋊C₄	—	3	1	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	1	no	—
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
490	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
492	C₄²	—	3	1	no	—
493	C₄²	—	3	1	no	—
494	C₄²	—	3	1	no	—
495	C₄²	—	3	2	no	—
496	C₄²	—	3	2	no	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	2	no	—
499	C₄²	—	3	2	no	—
500	C₄²	—	3	2	no	—
501	C₄²	—	3	2	no	—
502	C₄²	—	3	1	no	—
503	C₄²	C₂²×D₃	1	1	yes	characteristic
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	1	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	C₂×#41	1	4	yes	—
513	C₂²×C₃	C₂⁵	1	1	yes	characteristic
514	C₂×D₃	—	2	1	no	—
515	C₂×D₃	—	2	2	no	—
516	C₂×D₃	—	2	2	no	—
517	C₂×D₃	—	2	2	no	—
518	C₂×D₃	—	2	1	no	—
519	C₂×D₃	—	2	1	no	—
520	C₂×D₃	—	8	4	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	2	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	C₂×#41	1	2	yes	—
529	Dic₃	—	2	1	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	1	no	—
532	Dic₃	—	2	2	no	—
533	Dic₃	—	2	1	no	—
534	Dic₃	—	2	1	no	—
535	Dic₃	—	2	2	no	—
536	Dic₃	—	2	1	no	—
537	Dic₃	—	2	1	no	—
538	Dic₃	—	2	2	no	—
539	C₂³	—	3	1	no	—
540	C₂³	—	3	2	no	—
541	C₂³	—	6	4	no	—
542	C₂³	—	12	2	no	—
543	C₂³	—	12	2	no	—
544	C₂³	C₂³×D₃	1	1	yes	characteristic
545	C₂³	C₂³×D₃	1	1	yes	characteristic
546	C₂³	C₂³×D₃	1	2	yes	—
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	12	2	no	—
550	Q₈	—	12	1	no	—
551	D₄	—	2	4	no	—
552	D₄	—	2	4	no	—
553	D₄	—	4	1	no	—
554	D₄	—	6	4	no	—
555	D₄	—	6	2	no	—
556	D₄	—	12	2	no	—
557	D₄	—	12	1	no	—
558	D₄	—	12	2	no	—
559	D₄	—	12	1	no	—
560	D₄	#237	1	4	yes	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	3	1	no	—
568	C₂×C₄	—	3	2	no	—
569	C₂×C₄	—	3	1	no	—
570	C₂×C₄	—	3	2	no	—
571	C₂×C₄	—	3	1	no	—
572	C₂×C₄	—	3	1	no	—
573	C₂×C₄	—	3	1	no	—
574	C₂×C₄	—	3	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	6	2	no	—
577	C₂×C₄	—	12	2	no	—
578	C₂×C₄	—	12	2	no	—
579	C₂×C₄	—	12	1	no	—
580	C₂×C₄	—	12	2	no	—
581	C₂×C₄	—	12	2	no	—
582	C₂×C₄	—	12	2	no	—
583	C₂×C₄	—	12	1	no	—
584	C₂×C₄	—	12	2	no	—
585	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₃	1	2	yes	—
587	C₂×C₄	C₂³×D₃	1	2	yes	—
588	C₂×C₄	C₂³×D₃	1	2	yes	—
589	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
593	C₂×C₃	—	2	4	no	—
594	C₂×C₃	—	4	1	no	—
595	C₂×C₃	—	4	1	no	—
596	C₂×C₃	C₂²×#41	1	1	yes	characteristic
597	C₂×C₃	#585	1	1	yes	characteristic
598	C₂×C₃	#585	1	1	yes	characteristic
599	D₃	—	4	2	no	—
600	D₃	—	4	1	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	6	1	no	—
610	C₂²	—	6	2	no	—
611	C₂²	—	6	2	no	—
612	C₂²	—	6	1	no	—
613	C₂²	—	6	2	no	—
614	C₂²	—	6	1	no	—
615	C₂²	—	24	4	no	—
616	C₂²	C₂×#237	1	4	yes	—
617	C₂²	C₂⁴×D₃	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	6	1	no	—
626	C₄	—	6	1	no	—
627	C₄	—	6	1	no	—
628	C₄	—	6	2	no	—
629	C₄	—	6	1	no	—
630	C₄	—	6	2	no	—
631	C₄	—	6	1	no	—
632	C₄	—	6	2	no	—
633	C₄	—	6	1	no	—
634	C₄	—	6	1	no	—
635	C₄	C₂×#237	1	2	yes	—
636	C₃	#3521	1	1	yes	characteristic, complemented, Sylow
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	1	no	—
640	C₂	—	12	1	no	—
641	C₂	—	12	2	no	—
642	C₂	C₂²×#237	1	1	yes	characteristic
643	C₂	#5964	1	1	yes	characteristic
644	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#547	C₂
hypercenter	#547	D₃
hypocenter	C₃	#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₃×#547	C₂	semidirect
2. #5829	C₂	semidirect
3. #5829	C₂	semidirect
4. #5827	C₂	semidirect
5. Dic₃×#41	C₂	semidirect
6. #5732	C₂	semidirect
7. #5731	C₂	semidirect
8. #5665	C₂	semidirect
9. #5658	C₂	semidirect
10. #5658	C₂	semidirect
11. #5649	C₂	semidirect
12. #5643	C₂	semidirect
13. #5642	C₂	semidirect
14. #5641	C₂	semidirect
15. #5624	C₂	semidirect
16. #5617	C₂	semidirect
17. #5601	C₂	semidirect
18. #5565	C₂	semidirect
19. #5545	C₂	semidirect
20. #5539	C₂	semidirect
21. #5538	C₂	semidirect
22. #5513	C₂	semidirect
23. C₂×#898	C₂	semidirect
28. C₃×C₄⋊Q₈	C₂²	semidirect
29. C₃×#123	C₂²	semidirect
30. C₃×#123	C₂²	semidirect
31. C₃×C₂²⋊Q₈	C₂²	semidirect
32. C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₃×#121	C₂²	semidirect
35. C₃×C₄×D₄	C₂²	semidirect
36. C₂×C₃×C₄⋊C₄	C₂²	semidirect
41. Q₈×Dic₃	C₂²	semidirect
42. Q₈×Dic₃	C₂²	semidirect
43. Q₈×Dic₃	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
48. #939	C₂²	semidirect
51. #935	C₂²	semidirect
55. D₄×Dic₃	C₂²	semidirect
56. D₄×Dic₃	C₂²	semidirect
57. D₄×Dic₃	C₂²	semidirect
58. D₄×Dic₃	C₂²	semidirect
69. #926	C₂²	semidirect
70. #926	C₂²	semidirect
71. #926	C₂²	semidirect
72. #926	C₂²	semidirect
73. C₂×C₄⋊Dic₃	C₂²	semidirect
74. C₂×C₄⋊Dic₃	C₂²	semidirect
75. #924	C₂²	semidirect
76. C₂×Dic₃⋊C₄	C₂²	semidirect
77. C₂×C₄×Dic₃	C₂²	semidirect
78. C₂×C₄×Dic₃	C₂²	semidirect
84. #898	C₂²	semidirect
85. #898	C₂²	semidirect
86. #898	C₂²	semidirect
87. #898	C₂²	semidirect
88. #898	C₂²	semidirect
89. #897	C₂²	semidirect
90. #897	C₂²	semidirect
93. #892	C₂²	semidirect
94. #892	C₂²	semidirect
95. #890	C₂²	semidirect
96. #890	C₂²	semidirect
97. #889	C₂²	semidirect
98. #889	C₂²	semidirect
99. #889	C₂²	semidirect
100. #888	C₂²	semidirect
101. #887	C₂²	semidirect
104. #886	C₂²	semidirect
107. #885	C₂²	semidirect
108. #883	C₂²	semidirect
109. #883	C₂²	semidirect
111. #67⋊C₄	C₂²	semidirect
112. #67⋊C₄	C₂²	semidirect
114. #879	C₂²	semidirect
115. #879	C₂²	semidirect
116. #878	C₂²	semidirect
117. #878	C₂²	semidirect
118. #878	C₂²	semidirect
119. #877	C₂²	semidirect
122. #870	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
133. #547	D₃	semidirect
253. C₄⋊Q₈	C₂×D₃	semidirect
285. #123	C₂×D₃	semidirect
286. #123	C₂×D₃	semidirect
295. C₂²⋊Q₈	C₂×D₃	semidirect
296. C₂²⋊Q₈	C₂×D₃	semidirect
303. #121	C₂×D₃	semidirect
328. C₄×D₄	C₂×D₃	semidirect
341. C₂×C₄⋊C₄	C₂×D₃	semidirect
636. C₃	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₃×#547	2
#5829	2
#5827	2
Dic₃×#41	2
#5732	2
#5731	2
#5665	2
#5658	2
#5649	2
#5643	2
#5642	2
#5641	2
#5624	2
#5617	2
#5601	2
#5565	2
#5545	2
#5539	2
#5538	2
#5513	2
C₂×#898	2
#3521	3