Subgroups — #86897

Order 384.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#5712	C₂	1	2	yes	maximal, complemented
3	#5704	C₂	1	2	yes	maximal, complemented
4	#5694	C₂	1	1	yes	maximal, characteristic, complemented
5	#5691	C₂	1	1	yes	maximal, characteristic, complemented
6	#5663	C₂	1	2	yes	maximal, complemented
7	#5658	C₂	1	2	yes	maximal, complemented
8	#5620	C₂	1	2	yes	maximal, complemented
9	#5619	C₂	1	2	yes	maximal, complemented
10	#5612	C₂	1	1	yes	maximal, characteristic, complemented
11	#5608	C₂	1	1	yes	maximal, characteristic, complemented
12	#5607	C₂	1	1	yes	maximal, characteristic, complemented
13	#5598	C₂	1	1	yes	maximal, characteristic, complemented
14	#5563	C₂	1	2	yes	maximal, complemented
15	#5560	C₂	1	2	yes	maximal, complemented
16	#5557	C₂	1	1	yes	maximal, characteristic, complemented
17	#5554	C₂	1	1	yes	maximal, characteristic, complemented
18	#5552	C₂	1	1	yes	maximal, characteristic, complemented
19	#5548	C₂	1	1	yes	maximal, characteristic, complemented
20	#5530	C₂	1	1	yes	maximal, characteristic, complemented
21	#5526	C₂	1	1	yes	maximal, characteristic, complemented
22	#5513	C₂	1	1	yes	maximal, characteristic, complemented
23	#5510	C₂	1	1	yes	maximal, characteristic, complemented
24	#3551	—	3	1	no	maximal, Sylow
25	C₂×#237	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂×#235	C₂²	1	1	yes	characteristic, complemented
30	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#126	C₂²	1	2	yes	complemented
32	C₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₃×#123	C₂²	1	2	yes	complemented
34	C₃×#121	C₂²	1	1	yes	characteristic
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#121	C₂²	1	2	yes	complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×D₄	C₂²	1	2	yes	complemented
40	C₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	#940	C₂²	1	2	yes	—
43	#940	C₂²	1	1	yes	characteristic
44	#939	C₂²	1	2	yes	complemented
45	#939	C₂²	1	2	yes	complemented
46	#939	C₂²	1	2	yes	complemented
47	#938	C₂²	1	1	yes	characteristic
48	#938	C₂²	1	2	yes	—
49	#938	C₂²	1	1	yes	characteristic, complemented
50	#938	C₂²	1	2	yes	complemented
51	#937	C₂²	1	2	yes	—
52	#937	C₂²	1	2	yes	—
53	#936	C₂²	1	1	yes	characteristic
54	D₄×Dic₃	C₂²	1	2	yes	complemented
55	#930	C₂²	1	2	yes	—
56	#930	C₂²	1	1	yes	characteristic
57	#930	C₂²	1	2	yes	complemented
58	#930	C₂²	1	2	yes	complemented
59	#929	C₂²	1	2	yes	—
60	C₄×#67	C₂²	1	1	yes	characteristic
61	C₄×#67	C₂²	1	2	yes	complemented
62	C₄×#67	C₂²	1	1	yes	characteristic, complemented
63	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
64	#926	C₂²	1	2	yes	complemented
65	#926	C₂²	1	2	yes	complemented
66	#924	C₂²	1	1	yes	characteristic, complemented
67	#898	C₂²	1	2	yes	—
68	#898	C₂²	1	2	yes	—
69	#898	C₂²	1	2	yes	complemented
70	#897	C₂²	1	1	yes	characteristic
71	#897	C₂²	1	1	yes	characteristic
72	#897	C₂²	1	2	yes	complemented
73	#897	C₂²	1	1	yes	characteristic, complemented
74	#897	C₂²	1	1	yes	characteristic, complemented
75	#897	C₂²	1	1	yes	characteristic, complemented
76	#896	C₂²	1	2	yes	complemented
77	#895	C₂²	1	1	yes	characteristic
78	#895	C₂²	1	1	yes	characteristic
79	#895	C₂²	1	1	yes	characteristic
80	#895	C₂²	1	2	yes	complemented
81	#894	C₂²	1	2	yes	—
82	#894	C₂²	1	2	yes	complemented
83	#893	C₂²	1	1	yes	characteristic
84	#893	C₂²	1	2	yes	complemented
85	#892	C₂²	1	1	yes	characteristic
86	#892	C₂²	1	2	yes	complemented
87	#892	C₂²	1	2	yes	complemented
88	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	#890	C₂²	1	2	yes	complemented
90	#890	C₂²	1	1	yes	characteristic, complemented
91	#889	C₂²	1	2	yes	complemented
92	#888	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	—
95	#886	C₂²	1	2	yes	—
96	#886	C₂²	1	2	yes	complemented
97	#885	C₂²	1	1	yes	characteristic
98	#885	C₂²	1	2	yes	—
99	#885	C₂²	1	2	yes	complemented
100	#885	C₂²	1	1	yes	characteristic, complemented
101	#885	C₂²	1	2	yes	complemented
102	#884	C₂²	1	1	yes	characteristic
103	#884	C₂²	1	1	yes	characteristic, complemented
104	#884	C₂²	1	2	yes	complemented
105	#884	C₂²	1	2	yes	complemented
106	#883	C₂²	1	2	yes	—
107	#883	C₂²	1	2	yes	complemented
108	#883	C₂²	1	2	yes	complemented
109	#882	C₂²	1	2	yes	—
110	#882	C₂²	1	2	yes	—
111	#67⋊C₄	C₂²	1	2	yes	complemented
112	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
113	#879	C₂²	1	2	yes	complemented
114	#878	C₂²	1	2	yes	complemented
115	#878	C₂²	1	2	yes	complemented
116	#876	C₂²	1	2	yes	complemented
117	#875	C₂²	1	1	yes	characteristic
118	#875	C₂²	1	2	yes	—
119	C₄×D₁₂	C₂²	1	1	yes	characteristic
120	C₄×D₁₂	C₂²	1	2	yes	complemented
121	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
122	#869	C₂²	1	2	yes	complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#563	—	3	2	no	—
125	#560	—	3	2	no	—
126	#555	—	3	2	no	—
127	#553	—	3	1	no	—
128	#553	D₃	1	1	yes	characteristic, complemented
129	#552	—	3	1	no	—
130	#552	—	3	1	no	—
131	#551	—	3	2	no	—
132	#548	—	3	1	no	—
133	#548	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#540	—	3	2	no	—
137	#540	—	3	2	no	—
138	#538	—	3	2	no	—
139	#538	—	3	2	no	—
140	#537	—	3	1	no	—
141	#537	—	3	1	no	—
142	#536	—	3	1	no	—
143	#535	—	3	1	no	—
144	#532	—	3	1	no	—
145	#529	—	3	1	no	—
146	#529	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×D₄	C₂³	1	2	yes	—
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	2	yes	—
155	C₂²×C₃×C₄	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	1	yes	characteristic
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂×#67	C₂³	1	1	yes	characteristic
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	1	yes	characteristic
165	C₂×#67	C₂³	1	2	yes	—
166	C₂×#67	C₂³	1	1	yes	characteristic
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	#237	—	4	2	no	—
170	D₃×D₄	—	4	2	no	—
171	#235	—	4	2	no	—
172	#235	—	4	2	no	—
173	#235	—	4	2	no	—
174	C₂×D₁₂	C₂³	1	1	yes	characteristic
175	C₂×D₁₂	C₂³	1	1	yes	characteristic
176	C₂×D₁₂	C₂³	1	2	yes	—
177	C₂×D₁₂	C₂³	1	1	yes	characteristic
178	C₂×D₁₂	C₂³	1	2	yes	—
179	C₂×D₁₂	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
189	C₂×Dic₆	C₂³	1	1	yes	characteristic
190	C₂×Dic₆	C₂³	1	1	yes	characteristic
191	C₂×Dic₆	C₂³	1	1	yes	characteristic
192	C₂×Dic₆	C₂³	1	2	yes	—
193	C₂×Dic₆	C₂³	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₃×C₄²	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	2	yes	—
212	#217	C₂³	1	1	yes	characteristic
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₃	C₂³	1	2	yes	—
236	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₃	C₂³	1	2	yes	—
238	C₄⋊Dic₃	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	no	—
254	C₂×#41	—	3	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂²×Q₈	—	3	1	no	—
257	C₂²×D₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	2	no	—
260	#127	—	3	1	no	—
261	#127	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	C₂×D₃	1	2	yes	complemented
268	#125	—	3	1	no	—
269	#125	—	3	2	no	—
270	#125	—	3	2	no	—
271	#125	C₂×D₃	1	1	yes	characteristic, complemented
272	#124	—	3	1	no	—
273	#124	—	3	1	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	1	no	—
279	#124	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	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	—	3	2	no	—
289	#123	C₂×D₃	1	2	yes	complemented
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	1	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	#121	—	3	1	no	—
301	#121	—	3	1	no	—
302	#121	—	3	2	no	—
303	#121	—	3	2	no	—
304	#121	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	1	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	2	no	—
311	#121	—	3	1	no	—
312	#121	—	3	1	no	—
313	#121	—	3	2	no	—
314	#121	—	3	1	no	—
315	#121	—	3	1	no	—
316	#121	—	3	1	no	—
317	#121	—	3	2	no	—
318	#121	—	3	2	no	—
319	#121	C₂×D₃	1	1	yes	characteristic
320	#121	C₂×D₃	1	1	yes	characteristic
321	#121	C₂×D₃	1	2	yes	complemented
322	#120	—	3	2	no	—
323	#120	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	C₄×Q₈	—	3	1	no	—
327	C₄×Q₈	—	3	1	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	1	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	1	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	C₂×D₃	1	1	yes	characteristic
338	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
339	C₄×D₄	C₂×D₃	1	2	yes	complemented
340	#117	—	3	2	no	—
341	#117	—	3	2	no	—
342	#117	—	3	2	no	—
343	#117	—	3	1	no	—
344	#117	—	3	2	no	—
345	#117	C₂×D₃	1	1	yes	characteristic, complemented
346	C₂×C₄⋊C₄	—	3	1	no	—
347	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	2	yes	—
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	—	4	2	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	—	4	2	no	—
357	C₂²×D₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃	C₂⁴	1	2	yes	—
359	C₂²×D₃	C₂⁴	1	1	yes	characteristic
360	C₂²×D₃	C₂⁴	1	1	yes	characteristic
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	4	2	no	—
363	C₃×D₄	—	4	1	no	—
364	C₃×D₄	—	4	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	4	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	2	yes	—
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	#67	—	4	2	no	—
378	#67	—	4	1	no	—
379	#67	—	4	1	no	—
380	#67	—	4	1	no	—
381	#67	—	4	1	no	—
382	#67	—	4	2	no	—
383	#67	—	4	2	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	#67	—	4	1	no	—
387	#67	—	4	1	no	—
388	C₂×Dic₃	—	4	2	no	—
389	C₂×Dic₃	—	4	2	no	—
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	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	D₁₂	—	2	2	no	—
399	D₁₂	—	4	1	no	—
400	D₁₂	—	4	2	no	—
401	D₁₂	—	4	2	no	—
402	D₁₂	—	4	1	no	—
403	D₁₂	—	4	1	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	4	2	no	—
408	C₄×D₃	—	4	1	no	—
409	C₄×D₃	—	4	2	no	—
410	C₄×D₃	—	4	1	no	—
411	C₄×D₃	—	4	2	no	—
412	Dic₆	—	2	2	no	—
413	Dic₆	—	2	2	no	—
414	Dic₆	—	4	2	no	—
415	Dic₆	—	4	1	no	—
416	Dic₆	—	4	1	no	—
417	C₂⁴	—	3	2	no	—
418	#41	—	12	2	no	—
419	#41	—	12	2	no	—
420	#41	—	12	2	no	—
421	#41	—	12	2	no	—
422	C₂×Q₈	—	3	1	no	—
423	C₂×Q₈	—	3	1	no	—
424	C₂×Q₈	—	3	1	no	—
425	C₂×Q₈	—	3	2	no	—
426	C₂×Q₈	—	3	1	no	—
427	C₂×Q₈	—	12	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	1	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	3	1	no	—
440	C₂×D₄	—	3	1	no	—
441	C₂×D₄	—	3	2	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	1	no	—
444	C₂×D₄	—	3	1	no	—
445	C₂×D₄	—	12	2	no	—
446	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
447	C₂×D₄	C₂²×D₃	1	2	yes	—
448	C₂×D₄	C₂²×D₃	1	2	yes	—
449	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	2	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₃	1	2	yes	—
463	C₂²×C₄	C₂²×D₃	1	2	yes	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	—	3	1	no	—
475	C₄⋊C₄	—	3	1	no	—
476	C₄⋊C₄	—	3	2	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	2	no	—
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₃	1	2	yes	—
483	C₄⋊C₄	C₂²×D₃	1	2	yes	—
484	C₄⋊C₄	C₂²×D₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	1	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	1	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	1	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
513	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
514	C₄²	—	3	1	no	—
515	C₄²	—	3	1	no	—
516	C₄²	—	3	1	no	—
517	C₄²	—	3	2	no	—
518	C₄²	—	3	2	no	—
519	C₄²	—	3	2	no	—
520	C₄²	C₂²×D₃	1	1	yes	characteristic
521	C₄²	C₂²×D₃	1	2	yes	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	C₂⁵	1	1	yes	characteristic
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	2	no	—
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	2	1	no	—
544	C₂×D₃	—	8	4	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	—	2	2	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
553	Dic₃	—	2	2	no	—
554	Dic₃	—	2	2	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	2	no	—
560	Dic₃	—	2	1	no	—
561	C₂³	—	3	1	no	—
562	C₂³	—	3	2	no	—
563	C₂³	—	3	1	no	—
564	C₂³	—	3	1	no	—
565	C₂³	—	12	2	no	—
566	C₂³	—	12	2	no	—
567	C₂³	—	12	2	no	—
568	C₂³	C₂³×D₃	1	2	yes	—
569	C₂³	C₂³×D₃	1	1	yes	characteristic
570	C₂³	C₂³×D₃	1	1	yes	characteristic
571	Q₈	—	6	2	no	—
572	Q₈	—	6	2	no	—
573	Q₈	—	12	2	no	—
574	Q₈	—	12	1	no	—
575	Q₈	—	12	1	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	2	no	—
580	D₄	—	6	2	no	—
581	D₄	—	12	1	no	—
582	D₄	—	12	1	no	—
583	D₄	—	12	1	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	2	no	—
586	D₄	—	12	2	no	—
587	D₄	—	12	1	no	—
588	D₄	—	12	1	no	—
589	D₄	—	12	1	no	—
590	D₄	—	12	1	no	—
591	D₄	—	12	2	no	—
592	D₄	—	12	2	no	—
593	D₄	—	12	2	no	—
594	D₄	—	12	2	no	—
595	D₄	—	12	1	no	—
596	D₄	—	12	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	3	1	no	—
600	C₂×C₄	—	3	2	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	1	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	3	2	no	—
605	C₂×C₄	—	3	2	no	—
606	C₂×C₄	—	3	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	6	2	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	—	12	2	no	—
613	C₂×C₄	—	12	2	no	—
614	C₂×C₄	—	12	2	no	—
615	C₂×C₄	—	12	1	no	—
616	C₂×C₄	—	12	1	no	—
617	C₂×C₄	—	12	2	no	—
618	C₂×C₄	—	12	2	no	—
619	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₃	1	2	yes	—
621	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	2	yes	—
624	C₂×C₄	C₂³×D₃	1	2	yes	—
625	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
627	C₂×C₃	—	4	2	no	—
628	C₂×C₃	—	4	1	no	—
629	C₂×C₃	—	4	1	no	—
630	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂×C₃	#585	1	1	yes	characteristic
632	C₂×C₃	#585	1	1	yes	characteristic
633	D₃	—	4	1	no	—
634	D₃	—	4	1	no	—
635	D₃	—	4	2	no	—
636	D₃	—	4	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	6	1	no	—
648	C₂²	—	6	1	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	6	1	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	2	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	6	1	no	—
655	C₂²	—	6	1	no	—
656	C₂²	—	6	2	no	—
657	C₂²	—	6	1	no	—
658	C₂²	—	24	4	no	—
659	C₂²	C₂⁴×D₃	1	1	yes	characteristic
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	6	1	no	—
668	C₄	—	6	1	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	2	no	—
671	C₄	—	6	2	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	2	no	—
674	C₄	—	6	1	no	—
675	C₄	#1009	1	2	yes	—
676	C₃	#3551	1	1	yes	characteristic, complemented, Sylow
677	C₂	—	4	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	4	1	no	—
680	C₂	—	12	1	no	—
681	C₂	—	12	2	no	—
682	C₂	—	12	1	no	—
683	C₂	—	12	1	no	—
684	C₂	C₂×#1009	1	1	yes	characteristic
685	C₂	#5964	1	1	yes	characteristic
686	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#553	C₂
hypercenter	#553	D₃
hypocenter	C₃	#3551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₃×#553	C₂	semidirect
2. #5712	C₂	semidirect
3. #5704	C₂	semidirect
4. #5694	C₂	semidirect
5. #5691	C₂	semidirect
6. #5663	C₂	semidirect
7. #5658	C₂	semidirect
8. #5620	C₂	semidirect
9. #5619	C₂	semidirect
10. #5612	C₂	semidirect
11. #5608	C₂	semidirect
12. #5607	C₂	semidirect
13. #5598	C₂	semidirect
14. #5563	C₂	semidirect
15. #5560	C₂	semidirect
16. #5557	C₂	semidirect
17. #5554	C₂	semidirect
18. #5552	C₂	semidirect
19. #5548	C₂	semidirect
20. #5530	C₂	semidirect
21. #5526	C₂	semidirect
22. #5513	C₂	semidirect
23. #5510	C₂	semidirect
29. C₂×#235	C₂²	semidirect
30. C₂²×Dic₆	C₂²	semidirect
31. C₃×#126	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
38. C₃×C₄×D₄	C₂²	semidirect
39. C₃×C₄×D₄	C₂²	semidirect
40. C₃×#117	C₂²	semidirect
41. C₂×C₃×C₄⋊C₄	C₂²	semidirect
44. #939	C₂²	semidirect
45. #939	C₂²	semidirect
46. #939	C₂²	semidirect
49. #938	C₂²	semidirect
50. #938	C₂²	semidirect
54. D₄×Dic₃	C₂²	semidirect
57. #930	C₂²	semidirect
58. #930	C₂²	semidirect
61. C₄×#67	C₂²	semidirect
62. C₄×#67	C₂²	semidirect
64. #926	C₂²	semidirect
65. #926	C₂²	semidirect
66. #924	C₂²	semidirect
69. #898	C₂²	semidirect
72. #897	C₂²	semidirect
73. #897	C₂²	semidirect
74. #897	C₂²	semidirect
75. #897	C₂²	semidirect
76. #896	C₂²	semidirect
80. #895	C₂²	semidirect
82. #894	C₂²	semidirect
84. #893	C₂²	semidirect
86. #892	C₂²	semidirect
87. #892	C₂²	semidirect
88. D₃×C₄⋊C₄	C₂²	semidirect
89. #890	C₂²	semidirect
90. #890	C₂²	semidirect
91. #889	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
96. #886	C₂²	semidirect
99. #885	C₂²	semidirect
100. #885	C₂²	semidirect
101. #885	C₂²	semidirect
103. #884	C₂²	semidirect
104. #884	C₂²	semidirect
105. #884	C₂²	semidirect
107. #883	C₂²	semidirect
108. #883	C₂²	semidirect
111. #67⋊C₄	C₂²	semidirect
113. #879	C₂²	semidirect
114. #878	C₂²	semidirect
115. #878	C₂²	semidirect
116. #876	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. #869	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
128. #553	D₃	semidirect
267. #126	C₂×D₃	semidirect
271. #125	C₂×D₃	semidirect
289. #123	C₂×D₃	semidirect
321. #121	C₂×D₃	semidirect
338. C₄×D₄	C₂×D₃	semidirect
339. C₄×D₄	C₂×D₃	semidirect
345. #117	C₂×D₃	semidirect
347. C₂×C₄⋊C₄	C₂×D₃	semidirect
676. C₃	#3551	semidirect

Maximal subgroups

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

subgroup	index
C₃×#553	2
#5712	2
#5704	2
#5694	2
#5691	2
#5663	2
#5658	2
#5620	2
#5619	2
#5612	2
#5608	2
#5607	2
#5598	2
#5563	2
#5560	2
#5557	2
#5554	2
#5552	2
#5548	2
#5530	2
#5526	2
#5513	2
#5510	2
#3551	3