Subgroups — #86021

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#5828	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#926	C₂	1	1	yes	maximal, characteristic, complemented
6	#5658	C₂	1	2	yes	maximal, complemented
7	#5650	C₂	1	2	yes	maximal, complemented
8	#5642	C₂	1	1	yes	maximal, characteristic, complemented
9	#5641	C₂	1	1	yes	maximal, characteristic, complemented
10	#5639	C₂	1	1	yes	maximal, characteristic, complemented
11	#5635	C₂	1	1	yes	maximal, characteristic, complemented
12	#5618	C₂	1	1	yes	maximal, characteristic, complemented
13	#5616	C₂	1	1	yes	maximal, characteristic, complemented
14	#5614	C₂	1	1	yes	maximal, characteristic, complemented
15	#5611	C₂	1	1	yes	maximal, characteristic, complemented
16	#5591	C₂	1	2	yes	maximal, complemented
17	#5587	C₂	1	2	yes	maximal, complemented
18	#5557	C₂	1	2	yes	maximal, complemented
19	#5538	C₂	1	2	yes	maximal, complemented
20	#5538	C₂	1	2	yes	maximal, complemented
21	C₄×#237	C₂	1	2	yes	maximal, complemented
22	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	#5517	C₂	1	1	yes	maximal, characteristic, complemented
24	#3475	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
27	C₂²×#67	C₂²	1	1	yes	characteristic
28	C₂×#237	C₂²	1	2	yes	—
29	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
30	C₃×#123	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
34	C₃×#121	C₂²	1	1	yes	characteristic, complemented
35	C₃×#120	C₂²	1	2	yes	—
36	C₃×C₄×D₄	C₂²	1	2	yes	complemented
37	C₃×C₄×D₄	C₂²	1	2	yes	complemented
38	C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×#217	C₂²	1	2	yes	—
40	C₂×#217	C₂²	1	1	yes	characteristic
41	#946	C₂²	1	1	yes	characteristic, complemented
42	#946	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	#938	C₂²	1	2	yes	—
48	#938	C₂²	1	1	yes	characteristic, complemented
49	#938	C₂²	1	1	yes	characteristic, complemented
50	#937	C₂²	1	2	yes	—
51	#936	C₂²	1	2	yes	complemented
52	#935	C₂²	1	2	yes	—
53	#935	C₂²	1	2	yes	complemented
54	#935	C₂²	1	2	yes	complemented
55	D₄×Dic₃	C₂²	1	2	yes	—
56	D₄×Dic₃	C₂²	1	2	yes	—
57	D₄×Dic₃	C₂²	1	2	yes	complemented
58	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	C₄×#67	C₂²	1	1	yes	characteristic
61	C₄×#67	C₂²	1	1	yes	characteristic
62	C₄×#67	C₂²	1	1	yes	characteristic
63	C₄×#67	C₂²	1	1	yes	characteristic
64	C₄×#67	C₂²	1	1	yes	characteristic
65	C₄×#67	C₂²	1	1	yes	characteristic
66	C₄×#67	C₂²	1	1	yes	characteristic
67	C₄×#67	C₂²	1	1	yes	characteristic
68	C₄×#67	C₂²	1	2	yes	complemented
69	C₄×#67	C₂²	1	2	yes	complemented
70	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
71	#926	C₂²	1	2	yes	—
72	#926	C₂²	1	1	yes	characteristic
73	#926	C₂²	1	1	yes	characteristic
74	#926	C₂²	1	1	yes	characteristic, complemented
75	#926	C₂²	1	1	yes	characteristic, complemented
76	#926	C₂²	1	2	yes	complemented
77	#926	C₂²	1	2	yes	complemented
78	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
81	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
82	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
83	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
84	#898	C₂²	1	2	yes	complemented
85	#898	C₂²	1	2	yes	complemented
86	#897	C₂²	1	2	yes	complemented
87	#892	C₂²	1	2	yes	complemented
88	#892	C₂²	1	1	yes	characteristic, complemented
89	#892	C₂²	1	1	yes	characteristic, complemented
90	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
92	#890	C₂²	1	1	yes	characteristic, complemented
93	#890	C₂²	1	2	yes	complemented
94	#890	C₂²	1	1	yes	characteristic, complemented
95	#889	C₂²	1	2	yes	complemented
96	#889	C₂²	1	2	yes	complemented
97	#888	C₂²	1	1	yes	characteristic, complemented
98	#888	C₂²	1	1	yes	characteristic, complemented
99	#887	C₂²	1	2	yes	complemented
100	#886	C₂²	1	2	yes	—
101	#886	C₂²	1	2	yes	complemented
102	#885	C₂²	1	2	yes	—
103	#885	C₂²	1	2	yes	complemented
104	#883	C₂²	1	2	yes	—
105	#883	C₂²	1	2	yes	complemented
106	#67⋊C₄	C₂²	1	2	yes	—
107	#67⋊C₄	C₂²	1	2	yes	complemented
108	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
109	#879	C₂²	1	2	yes	complemented
110	#879	C₂²	1	2	yes	complemented
111	#879	C₂²	1	2	yes	complemented
112	#879	C₂²	1	2	yes	complemented
113	#878	C₂²	1	2	yes	—
114	#878	C₂²	1	2	yes	—
115	#878	C₂²	1	2	yes	complemented
116	#878	C₂²	1	2	yes	complemented
117	#877	C₂²	1	2	yes	—
118	#877	C₂²	1	2	yes	complemented
119	#877	C₂²	1	2	yes	complemented
120	#872	C₂²	1	2	yes	complemented
121	C₄²×D₃	C₂²	1	2	yes	complemented
122	C₄×Dic₆	C₂²	1	2	yes	complemented
123	C₄×Dic₆	C₂²	1	2	yes	complemented
124	#556	—	3	1	no	—
125	#555	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	1	no	—
128	#553	—	3	1	no	—
129	#552	—	3	2	no	—
130	#552	—	3	1	no	—
131	#552	—	3	1	no	—
132	#551	—	3	2	no	—
133	#551	—	3	2	no	—
134	#547	—	3	1	no	—
135	#546	—	3	2	no	—
136	#533	—	3	1	no	—
137	#529	—	3	2	no	—
138	#529	—	3	2	no	—
139	#529	—	3	2	no	—
140	#525	—	3	1	no	—
141	#525	D₃	1	1	yes	characteristic, complemented
142	C₄×#41	—	3	1	no	—
143	C₄×#41	—	3	2	no	—
144	C₂×C₄×D₄	—	3	1	no	—
145	C₂×#117	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	1	yes	characteristic
149	C₃×#41	—	2	4	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂³	1	2	yes	—
154	C₂×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂×#67	—	2	4	no	—
164	C₂×#67	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	1	yes	characteristic
166	C₂×#67	C₂³	1	1	yes	characteristic
167	C₂×#67	C₂³	1	1	yes	characteristic
168	C₂×#67	C₂³	1	2	yes	—
169	C₂×#67	C₂³	1	1	yes	characteristic
170	C₂²×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	1	yes	characteristic
174	C₂²×Dic₃	C₂³	1	1	yes	characteristic
175	C₂²×Dic₃	C₂³	1	2	yes	—
176	C₂²×Dic₃	C₂³	1	2	yes	—
177	#237	—	2	8	no	—
178	C₂×C₄×D₃	—	2	4	no	—
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	2	yes	—
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	2	yes	—
185	C₂×Dic₆	C₂³	1	2	yes	—
186	C₂×Dic₆	C₂³	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄²	C₂³	1	2	yes	—
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	1	yes	characteristic
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	#217	C₂³	1	1	yes	characteristic
202	#217	C₂³	1	2	yes	—
203	#217	C₂³	1	2	yes	—
204	#217	C₂³	1	1	yes	characteristic
205	#217	C₂³	1	1	yes	characteristic
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	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	1	yes	characteristic
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	2	yes	—
218	C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₄⋊Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	2	yes	—
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₃⋊C₄	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	2	yes	—
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	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₂×#41	—	3	2	no	—
252	C₂×#41	C₂×D₃	1	1	yes	characteristic
253	C₂²×D₄	—	3	1	no	—
254	C₂³×C₄	—	3	1	no	—
255	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
256	C₄⋊Q₈	—	3	1	no	—
257	C₄⋊Q₈	—	3	1	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	#125	—	3	2	no	—
265	#125	—	3	2	no	—
266	#125	—	3	2	no	—
267	#125	—	3	1	no	—
268	#125	—	3	1	no	—
269	#124	—	3	2	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#123	—	3	2	no	—
273	#123	—	3	2	no	—
274	#123	—	3	2	no	—
275	#123	—	3	2	no	—
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	C₂×D₃	1	2	yes	—
280	C₂²⋊Q₈	—	3	1	no	—
281	C₂²⋊Q₈	—	3	1	no	—
282	C₂²⋊Q₈	—	3	2	no	—
283	C₂²⋊Q₈	—	3	2	no	—
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
288	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
289	#121	—	3	1	no	—
290	#121	—	3	1	no	—
291	#121	—	3	2	no	—
292	#121	—	3	2	no	—
293	#121	—	3	2	no	—
294	#121	C₂×D₃	1	1	yes	characteristic, complemented
295	#121	C₂×D₃	1	1	yes	characteristic, complemented
296	#120	—	3	2	no	—
297	#120	C₂×D₃	1	2	yes	—
298	C₄×Q₈	—	3	1	no	—
299	C₄×Q₈	—	3	1	no	—
300	C₄×Q₈	—	3	2	no	—
301	C₄×Q₈	—	3	2	no	—
302	C₄×Q₈	—	3	2	no	—
303	C₄×D₄	—	3	2	no	—
304	C₄×D₄	—	3	1	no	—
305	C₄×D₄	—	3	2	no	—
306	C₄×D₄	—	3	2	no	—
307	C₄×D₄	—	3	1	no	—
308	C₄×D₄	—	3	1	no	—
309	C₄×D₄	—	3	1	no	—
310	C₄×D₄	—	3	1	no	—
311	C₄×D₄	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	C₂×D₃	1	2	yes	complemented
321	C₄×D₄	C₂×D₃	1	2	yes	complemented
322	#117	—	3	1	no	—
323	#117	—	3	1	no	—
324	#117	—	3	2	no	—
325	#117	—	3	2	no	—
326	#117	—	3	1	no	—
327	#117	—	3	1	no	—
328	#117	—	3	2	no	—
329	#117	—	3	1	no	—
330	#117	—	3	1	no	—
331	#117	—	3	2	no	—
332	#117	—	3	2	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	C₂×D₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	—	3	1	no	—
338	C₂×C₄⋊C₄	—	3	1	no	—
339	C₂×C₄⋊C₄	—	3	1	no	—
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	1	no	—
344	C₂×C₂²⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	—	3	2	no	—
349	C₂×C₄²	—	3	2	no	—
350	C₂³×C₃	—	2	2	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	4	1	no	—
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂³×C₃	C₂⁴	1	2	yes	—
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	—	2	2	no	—
358	C₂²×D₃	—	2	2	no	—
359	C₂²×D₃	—	4	1	no	—
360	C₂²×D₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₃	C₂⁴	1	1	yes	characteristic
362	C₃×Q₈	—	2	2	no	—
363	C₃×D₄	—	2	4	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	2	no	—
366	C₃×D₄	—	4	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	#41	1	4	yes	complemented
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	#67	—	2	2	no	—
382	#67	—	2	4	no	—
383	#67	—	2	2	no	—
384	#67	—	2	2	no	—
385	#67	—	4	2	no	—
386	#67	#41	1	4	yes	complemented
387	C₂×Dic₃	—	2	2	no	—
388	C₂×Dic₃	—	2	4	no	—
389	C₂×Dic₃	—	2	4	no	—
390	C₂×Dic₃	—	2	2	no	—
391	C₂×Dic₃	—	4	1	no	—
392	C₂×Dic₃	—	4	2	no	—
393	C₂×Dic₃	—	4	2	no	—
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	2	yes	—
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	2	yes	—
400	C₂×Dic₃	C₂⁴	1	2	yes	—
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
404	C₄×D₃	—	2	4	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	2	no	—
409	C₄×D₃	—	4	2	no	—
410	Dic₆	—	2	4	no	—
411	Dic₆	—	4	2	no	—
412	C₂⁴	—	3	1	no	—
413	C₂⁴	C₂²×D₃	1	1	yes	characteristic
414	#41	—	2	4	no	—
415	#41	—	6	8	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	3	2	no	—
418	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
419	C₂×D₄	—	3	1	no	—
420	C₂×D₄	—	3	2	no	—
421	C₂×D₄	—	3	1	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	1	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	6	4	no	—
426	C₂×D₄	C₂²×D₃	1	2	yes	—
427	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
428	C₂×D₄	C₂²×D₃	1	2	yes	—
429	C₂×D₄	C₂²×D₃	1	2	yes	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	6	4	no	—
445	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
446	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₃	1	2	yes	—
450	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
452	C₄⋊C₄	—	3	1	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	2	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	1	no	—
464	C₄⋊C₄	—	3	2	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	2	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	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	1	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	2	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	2	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
503	C₄²	—	3	2	no	—
504	C₄²	—	3	2	no	—
505	C₄²	—	3	2	no	—
506	C₄²	—	3	2	no	—
507	C₄²	—	3	2	no	—
508	C₄²	—	3	1	no	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	2	no	—
512	C₄²	—	3	1	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	2	no	—
515	C₄²	C₂²×D₃	1	2	yes	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	4	4	no	—
527	C₂²×C₃	C₂×#41	1	2	yes	—
528	C₂²×C₃	C₂×#41	1	2	yes	—
529	C₂²×C₃	C₂⁵	1	1	yes	characteristic
530	C₂×D₃	—	2	1	no	—
531	C₂×D₃	—	2	1	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	4	4	no	—
536	C₂×D₃	C₂×#41	1	2	yes	—
537	C₃×C₄	—	2	2	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	C₂×#41	1	2	yes	—
543	C₃×C₄	C₂×#41	1	2	yes	—
544	Dic₃	—	2	2	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	1	no	—
547	Dic₃	—	2	2	no	—
548	Dic₃	—	2	1	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	2	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	C₂×#41	1	2	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	3	1	no	—
557	C₂³	—	3	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	6	2	no	—
560	C₂³	—	6	2	no	—
561	C₂³	—	12	1	no	—
562	C₂³	C₂³×D₃	1	1	yes	characteristic
563	C₂³	C₂³×D₃	1	2	yes	—
564	C₂³	C₂³×D₃	1	1	yes	characteristic
565	C₂³	C₂³×D₃	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	6	4	no	—
568	Q₈	—	12	2	no	—
569	D₄	—	2	4	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	2	no	—
572	D₄	—	3	4	no	—
573	D₄	—	4	2	no	—
574	D₄	—	6	2	no	—
575	D₄	—	6	2	no	—
576	D₄	—	6	4	no	—
577	D₄	—	6	2	no	—
578	D₄	—	12	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	3	1	no	—
586	C₂×C₄	—	3	1	no	—
587	C₂×C₄	—	3	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	2	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	1	no	—
595	C₂×C₄	—	6	4	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	4	no	—
598	C₂×C₄	—	6	2	no	—
599	C₂×C₄	—	6	4	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	—	6	2	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	6	2	no	—
604	C₂×C₄	—	12	2	no	—
605	C₂×C₄	—	12	2	no	—
606	C₂×C₄	—	12	2	no	—
607	C₂×C₄	—	12	1	no	—
608	C₂×C₄	#237	1	4	yes	complemented
609	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₃	1	2	yes	—
611	C₂×C₄	C₂³×D₃	1	2	yes	—
612	C₂×C₄	C₂³×D₃	1	2	yes	—
613	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₃	—	2	2	no	—
617	C₂×C₃	—	2	2	no	—
618	C₂×C₃	—	4	2	no	—
619	C₂×C₃	—	4	1	no	—
620	C₂×C₃	C₂²×#41	1	1	yes	characteristic
621	C₂×C₃	C₂²×#41	1	1	yes	characteristic
622	C₂×C₃	#585	1	1	yes	characteristic
623	D₃	—	2	2	no	—
624	D₃	—	4	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	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	2	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	6	1	no	—
638	C₂²	—	6	1	no	—
639	C₂²	—	6	1	no	—
640	C₂²	—	6	1	no	—
641	C₂²	—	6	1	no	—
642	C₂²	—	12	4	no	—
643	C₂²	C₂×#237	1	2	yes	—
644	C₂²	D₃×#41	1	2	yes	—
645	C₂²	C₂⁴×D₃	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	3	2	no	—
652	C₄	—	6	1	no	—
653	C₄	—	6	1	no	—
654	C₄	—	6	2	no	—
655	C₄	—	6	1	no	—
656	C₄	—	6	2	no	—
657	C₄	—	6	2	no	—
658	C₄	—	6	1	no	—
659	C₄	—	6	2	no	—
660	C₄	—	6	1	no	—
661	C₄	C₂×#237	1	2	yes	—
662	C₄	C₂×#237	1	2	yes	—
663	C₃	#3475	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	2	2	no	—
665	C₂	—	2	2	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	—	6	2	no	—
669	C₂	—	12	1	no	—
670	C₂	C₂²×#237	1	1	yes	characteristic
671	C₂	C₂×D₃×#41	1	1	yes	characteristic
672	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Frattini	C₂²	C₂⁴×D₃
Fitting	C₃×#525	C₂
hypercenter	#525	D₃
hypocenter	C₃	#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₃×#525	C₂	semidirect
2. #5828	C₂	semidirect
3. Dic₃×#41	C₂	semidirect
4. C₂×C₄×#67	C₂	semidirect
5. C₂×#926	C₂	semidirect
6. #5658	C₂	semidirect
7. #5650	C₂	semidirect
8. #5642	C₂	semidirect
9. #5641	C₂	semidirect
10. #5639	C₂	semidirect
11. #5635	C₂	semidirect
12. #5618	C₂	semidirect
13. #5616	C₂	semidirect
14. #5614	C₂	semidirect
15. #5611	C₂	semidirect
16. #5591	C₂	semidirect
17. #5587	C₂	semidirect
18. #5557	C₂	semidirect
19. #5538	C₂	semidirect
20. #5538	C₂	semidirect
21. C₄×#237	C₂	semidirect
22. D₃×#117	C₂	semidirect
23. #5517	C₂	semidirect
31. C₃×C₂²⋊Q₈	C₂²	semidirect
32. C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₃×#121	C₂²	semidirect
34. C₃×#121	C₂²	semidirect
36. C₃×C₄×D₄	C₂²	semidirect
37. C₃×C₄×D₄	C₂²	semidirect
41. #946	C₂²	semidirect
42. #946	C₂²	semidirect
43. Q₈×Dic₃	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
48. #938	C₂²	semidirect
49. #938	C₂²	semidirect
51. #936	C₂²	semidirect
53. #935	C₂²	semidirect
54. #935	C₂²	semidirect
57. D₄×Dic₃	C₂²	semidirect
58. D₄×Dic₃	C₂²	semidirect
59. D₄×Dic₃	C₂²	semidirect
68. C₄×#67	C₂²	semidirect
69. C₄×#67	C₂²	semidirect
74. #926	C₂²	semidirect
75. #926	C₂²	semidirect
76. #926	C₂²	semidirect
77. #926	C₂²	semidirect
78. C₂×C₄⋊Dic₃	C₂²	semidirect
79. C₂×C₄⋊Dic₃	C₂²	semidirect
82. C₂×C₄×Dic₃	C₂²	semidirect
83. C₂×C₄×Dic₃	C₂²	semidirect
84. #898	C₂²	semidirect
85. #898	C₂²	semidirect
86. #897	C₂²	semidirect
87. #892	C₂²	semidirect
88. #892	C₂²	semidirect
89. #892	C₂²	semidirect
90. D₃×C₄⋊C₄	C₂²	semidirect
91. D₃×C₄⋊C₄	C₂²	semidirect
92. #890	C₂²	semidirect
93. #890	C₂²	semidirect
94. #890	C₂²	semidirect
95. #889	C₂²	semidirect
96. #889	C₂²	semidirect
97. #888	C₂²	semidirect
98. #888	C₂²	semidirect
99. #887	C₂²	semidirect
101. #886	C₂²	semidirect
103. #885	C₂²	semidirect
105. #883	C₂²	semidirect
107. #67⋊C₄	C₂²	semidirect
109. #879	C₂²	semidirect
110. #879	C₂²	semidirect
111. #879	C₂²	semidirect
112. #879	C₂²	semidirect
115. #878	C₂²	semidirect
116. #878	C₂²	semidirect
118. #877	C₂²	semidirect
119. #877	C₂²	semidirect
120. #872	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
141. #525	D₃	semidirect
287. C₂²⋊Q₈	C₂×D₃	semidirect
288. C₂²⋊Q₈	C₂×D₃	semidirect
294. #121	C₂×D₃	semidirect
295. #121	C₂×D₃	semidirect
320. C₄×D₄	C₂×D₃	semidirect
321. C₄×D₄	C₂×D₃	semidirect
373. C₂×C₃×C₄	#41	semidirect
386. #67	#41	semidirect
608. C₂×C₄	#237	semidirect
663. C₃	#3475	semidirect

Maximal subgroups

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

subgroup	index
C₃×#525	2
#5828	2
Dic₃×#41	2
C₂×C₄×#67	2
C₂×#926	2
#5658	2
#5650	2
#5642	2
#5641	2
#5639	2
#5635	2
#5618	2
#5616	2
#5614	2
#5611	2
#5591	2
#5587	2
#5557	2
#5538	2
C₄×#237	2
D₃×#117	2
#5517	2
#3475	3