Subgroups — #86237

Order 384.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#5832	C₂	1	2	yes	maximal, complemented
3	#5828	C₂	1	2	yes	maximal, complemented
4	#5733	C₂	1	1	yes	maximal, characteristic, complemented
5	#5729	C₂	1	1	yes	maximal, characteristic, complemented
6	#5719	C₂	1	1	yes	maximal, characteristic, complemented
7	#5715	C₂	1	1	yes	maximal, characteristic, complemented
8	#5678	C₂	1	2	yes	maximal, complemented
9	#5669	C₂	1	2	yes	maximal, complemented
10	#5619	C₂	1	1	yes	maximal, characteristic, complemented
11	#5615	C₂	1	2	yes	maximal, complemented
12	#5613	C₂	1	2	yes	maximal, complemented
13	#5608	C₂	1	1	yes	maximal, characteristic, complemented
14	#5607	C₂	1	1	yes	maximal, characteristic, complemented
15	#5603	C₂	1	1	yes	maximal, characteristic, complemented
16	#5557	C₂	1	1	yes	maximal, characteristic, complemented
17	#5548	C₂	1	1	yes	maximal, characteristic, complemented
18	#5547	C₂	1	2	yes	maximal, complemented
19	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
20	#5538	C₂	1	2	yes	maximal, complemented
21	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
22	#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
24	#3460	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	2	yes	complemented
26	C₂×#237	C₂²	1	1	yes	characteristic
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂×#235	C₂²	1	2	yes	complemented
30	C₂²×C₄×D₃	C₂²	1	2	yes	—
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#127	C₂²	1	1	yes	characteristic
33	C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#121	C₂²	1	1	yes	characteristic
35	C₃×#121	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
41	#947	C₂²	1	2	yes	complemented
42	#946	C₂²	1	2	yes	—
43	#946	C₂²	1	2	yes	complemented
44	#944	C₂²	1	2	yes	complemented
45	#940	C₂²	1	1	yes	characteristic
46	#940	C₂²	1	2	yes	—
47	#939	C₂²	1	2	yes	—
48	#939	C₂²	1	2	yes	—
49	#939	C₂²	1	2	yes	complemented
50	#939	C₂²	1	2	yes	complemented
51	#939	C₂²	1	2	yes	complemented
52	#939	C₂²	1	2	yes	complemented
53	#938	C₂²	1	1	yes	characteristic
54	#938	C₂²	1	2	yes	—
55	#938	C₂²	1	1	yes	characteristic, complemented
56	#938	C₂²	1	2	yes	complemented
57	#937	C₂²	1	2	yes	—
58	#937	C₂²	1	2	yes	—
59	#937	C₂²	1	2	yes	—
60	#936	C₂²	1	1	yes	characteristic
61	#936	C₂²	1	2	yes	complemented
62	#935	C₂²	1	2	yes	complemented
63	#935	C₂²	1	2	yes	complemented
64	#935	C₂²	1	2	yes	complemented
65	D₄×Dic₃	C₂²	1	1	yes	characteristic
66	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
67	#930	C₂²	1	1	yes	characteristic
68	#929	C₂²	1	2	yes	complemented
69	C₄×#67	C₂²	1	1	yes	characteristic
70	C₄×#67	C₂²	1	1	yes	characteristic
71	C₄×#67	C₂²	1	2	yes	—
72	C₄×#67	C₂²	1	2	yes	—
73	C₄×#67	C₂²	1	1	yes	characteristic, complemented
74	C₄×#67	C₂²	1	1	yes	characteristic, complemented
75	C₄×#67	C₂²	1	2	yes	complemented
76	C₄×#67	C₂²	1	2	yes	complemented
77	C₄×#67	C₂²	1	2	yes	complemented
78	#926	C₂²	1	1	yes	characteristic, complemented
79	#926	C₂²	1	2	yes	complemented
80	#924	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
82	#898	C₂²	1	2	yes	complemented
83	#897	C₂²	1	1	yes	characteristic, complemented
84	#896	C₂²	1	2	yes	—
85	#895	C₂²	1	1	yes	characteristic
86	#894	C₂²	1	2	yes	complemented
87	#893	C₂²	1	1	yes	characteristic
88	#892	C₂²	1	1	yes	characteristic
89	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	complemented
95	#885	C₂²	1	2	yes	—
96	#885	C₂²	1	2	yes	complemented
97	#884	C₂²	1	2	yes	—
98	#884	C₂²	1	2	yes	complemented
99	#883	C₂²	1	2	yes	complemented
100	#883	C₂²	1	2	yes	complemented
101	#882	C₂²	1	2	yes	—
102	#67⋊C₄	C₂²	1	2	yes	—
103	#67⋊C₄	C₂²	1	2	yes	—
104	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	#879	C₂²	1	2	yes	complemented
106	#879	C₂²	1	2	yes	complemented
107	#878	C₂²	1	2	yes	complemented
108	#878	C₂²	1	2	yes	complemented
109	#877	C₂²	1	2	yes	complemented
110	#876	C₂²	1	2	yes	complemented
111	#875	C₂²	1	1	yes	characteristic
112	C₄×D₁₂	C₂²	1	1	yes	characteristic
113	C₄×D₁₂	C₂²	1	1	yes	characteristic
114	C₄×D₁₂	C₂²	1	1	yes	characteristic
115	#872	C₂²	1	1	yes	characteristic
116	#872	C₂²	1	1	yes	characteristic, complemented
117	#872	C₂²	1	2	yes	complemented
118	C₄²×D₃	C₂²	1	1	yes	characteristic
119	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
120	#870	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#544	—	3	1	no	—
125	#542	—	3	1	no	—
126	#542	—	3	2	no	—
127	#542	—	3	1	no	—
128	#540	—	3	1	no	—
129	#540	—	3	2	no	—
130	#540	—	3	1	no	—
131	#538	—	3	2	no	—
132	#538	—	3	2	no	—
133	#537	—	3	1	no	—
134	#535	—	3	1	no	—
135	#535	—	3	1	no	—
136	#532	—	3	2	no	—
137	#532	—	3	1	no	—
138	#532	D₃	1	1	yes	characteristic, complemented
139	#529	—	3	1	no	—
140	#529	—	3	2	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	#525	—	3	2	no	—
144	C₄×#41	—	3	1	no	—
145	C₄×#41	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₃×#41	—	4	4	no	—
149	C₂×C₃×Q₈	C₂³	1	2	yes	—
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	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	2	yes	—
155	C₂×C₃×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
161	C₂×#67	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
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	2	yes	—
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	2	yes	—
169	C₂×#67	C₂³	1	2	yes	—
170	C₂²×Dic₃	C₂³	1	2	yes	—
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	#237	—	2	4	no	—
174	D₃×D₄	—	2	4	no	—
175	#235	—	2	4	no	—
176	#235	—	4	4	no	—
177	C₂×D₁₂	C₂³	1	1	yes	characteristic
178	C₂×D₁₂	C₂³	1	1	yes	characteristic
179	C₂×D₁₂	C₂³	1	2	yes	—
180	C₂×C₄×D₃	—	4	4	no	—
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×C₄×D₃	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₃	C₂³	1	2	yes	—
188	C₂×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₄×D₃	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	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₃)⋊C₄	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	2	yes	—
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	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	2	yes	—
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	2	no	—
255	C₂×#41	C₂×D₃	1	2	yes	complemented
256	C₂²×D₄	—	3	1	no	—
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	2	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
261	#127	—	3	2	no	—
262	#127	—	3	1	no	—
263	#127	C₂×D₃	1	1	yes	characteristic
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#125	—	3	1	no	—
271	#124	—	3	2	no	—
272	#124	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	2	no	—
275	#124	—	3	2	no	—
276	#124	—	3	1	no	—
277	#124	C₂×D₃	1	2	yes	complemented
278	#123	—	3	2	no	—
279	#123	—	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	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	1	no	—
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	#121	—	3	2	no	—
294	#121	—	3	2	no	—
295	#121	—	3	2	no	—
296	#121	—	3	1	no	—
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	—	3	1	no	—
300	#121	—	3	2	no	—
301	#121	—	3	2	no	—
302	#121	—	3	2	no	—
303	#121	—	3	1	no	—
304	#121	—	3	1	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	C₂×D₃	1	1	yes	characteristic
308	#121	C₂×D₃	1	1	yes	characteristic, complemented
309	#121	C₂×D₃	1	2	yes	complemented
310	#120	—	3	2	no	—
311	#120	—	3	2	no	—
312	#120	—	3	2	no	—
313	#120	—	3	2	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×Q₈	—	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	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	—	3	1	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	C₂×D₃	1	1	yes	characteristic
336	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
337	C₄×D₄	C₂×D₃	1	2	yes	complemented
338	#117	—	3	1	no	—
339	#117	—	3	2	no	—
340	#117	—	3	1	no	—
341	#117	—	3	2	no	—
342	#117	—	3	1	no	—
343	#117	—	3	1	no	—
344	#117	—	3	2	no	—
345	C₂×C₄⋊C₄	—	3	1	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₄²	—	3	2	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂²×D₃	—	2	4	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	—	4	2	no	—
357	C₂²×D₃	C₂⁴	1	2	yes	—
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₃	C₂⁴	1	1	yes	characteristic
360	C₃×Q₈	—	4	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	4	2	no	—
364	C₃×D₄	—	4	2	no	—
365	C₃×D₄	—	4	2	no	—
366	C₃×D₄	—	4	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	4	no	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	1	no	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	2	no	—
381	#67	—	2	4	no	—
382	#67	—	2	2	no	—
383	#67	—	2	4	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	#67	—	4	2	no	—
387	#67	—	4	2	no	—
388	#67	—	4	2	no	—
389	C₂×Dic₃	—	2	4	no	—
390	C₂×Dic₃	—	4	2	no	—
391	C₂×Dic₃	—	4	2	no	—
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃	C₂⁴	1	2	yes	—
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	2	yes	—
400	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
401	D₁₂	—	2	2	no	—
402	D₁₂	—	2	2	no	—
403	D₁₂	—	4	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	2	4	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	—	4	2	no	—
410	C₄×D₃	—	4	1	no	—
411	C₄×D₃	—	4	1	no	—
412	C₄×D₃	#41	1	4	yes	complemented
413	Dic₆	—	2	2	no	—
414	Dic₆	—	2	2	no	—
415	Dic₆	—	4	2	no	—
416	C₂⁴	—	3	2	no	—
417	#41	—	4	4	no	—
418	#41	—	6	4	no	—
419	#41	—	6	4	no	—
420	#41	—	12	4	no	—
421	C₂×Q₈	—	3	1	no	—
422	C₂×Q₈	—	3	1	no	—
423	C₂×Q₈	—	3	2	no	—
424	C₂×Q₈	C₂²×D₃	1	2	yes	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	2	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	6	4	no	—
438	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
439	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
440	C₂×D₄	C₂²×D₃	1	2	yes	—
441	C₂×D₄	C₂²×D₃	1	2	yes	—
442	C₂×D₄	C₂²×D₃	1	2	yes	—
443	C₂×D₄	C₂²×D₃	1	2	yes	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	2	no	—
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	12	4	no	—
457	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₃	1	2	yes	—
459	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×D₃	1	2	yes	—
461	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	1	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	2	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	2	no	—
479	C₄⋊C₄	—	3	2	no	—
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	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	1	no	—
487	C₂²⋊C₄	—	3	2	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	1	no	—
497	C₂²⋊C₄	—	3	1	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	2	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
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	C₄²	—	3	1	no	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	2	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	1	no	—
515	C₄²	—	3	2	no	—
516	C₄²	—	3	1	no	—
517	C₄²	C₂²×D₃	1	1	yes	characteristic
518	C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₄²	C₂²×D₃	1	1	yes	characteristic
520	C₄²	C₂²×D₃	1	1	yes	characteristic
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	C₂⁵	1	1	yes	characteristic
531	C₂×D₃	—	2	1	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	2	no	—
539	C₂×D₃	—	4	8	no	—
540	C₂×D₃	C₂×#41	1	2	yes	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	C₂×#41	1	2	yes	—
548	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	2	no	—
553	Dic₃	—	2	1	no	—
554	Dic₃	—	2	1	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	2	no	—
557	Dic₃	C₂×#41	1	2	yes	—
558	C₂³	—	3	1	no	—
559	C₂³	—	3	2	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	6	4	no	—
562	C₂³	—	12	2	no	—
563	C₂³	—	12	2	no	—
564	C₂³	C₂³×D₃	1	2	yes	—
565	C₂³	C₂³×D₃	1	1	yes	characteristic
566	C₂³	C₂³×D₃	1	2	yes	—
567	Q₈	—	4	2	no	—
568	Q₈	—	6	2	no	—
569	Q₈	—	6	2	no	—
570	Q₈	—	12	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	6	2	no	—
578	D₄	—	6	4	no	—
579	D₄	—	6	2	no	—
580	D₄	—	6	2	no	—
581	D₄	—	6	4	no	—
582	D₄	—	6	2	no	—
583	D₄	—	12	2	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	2	no	—
586	D₄	—	12	2	no	—
587	D₄	—	12	2	no	—
588	D₄	—	12	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	4	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	3	2	no	—
598	C₂×C₄	—	3	1	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	6	4	no	—
605	C₂×C₄	—	6	2	no	—
606	C₂×C₄	—	6	4	no	—
607	C₂×C₄	—	6	2	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	12	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	—	12	1	no	—
612	C₂×C₄	—	12	1	no	—
613	C₂×C₄	—	12	2	no	—
614	C₂×C₄	—	12	2	no	—
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₃	1	2	yes	—
617	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
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×C₃	—	4	2	no	—
624	C₂×C₃	—	4	2	no	—
625	C₂×C₃	—	4	1	no	—
626	C₂×C₃	C₂²×#41	1	1	yes	characteristic
627	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₃	#585	1	1	yes	characteristic
629	D₃	—	2	2	no	—
630	D₃	—	4	1	no	—
631	D₃	—	4	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	3	2	no	—
642	C₂²	—	6	1	no	—
643	C₂²	—	6	1	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	6	1	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	6	2	no	—
648	C₂²	—	6	1	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	12	8	no	—
651	C₂²	C₂⁴×D₃	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	3	2	no	—
659	C₄	—	6	1	no	—
660	C₄	—	6	2	no	—
661	C₄	—	6	1	no	—
662	C₄	—	6	2	no	—
663	C₄	—	6	1	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	—	6	2	no	—
667	C₄	#1004	1	2	yes	—
668	C₄	D₃×#41	1	2	yes	—
669	C₃	#3460	1	1	yes	characteristic, complemented, Sylow
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	6	2	no	—
674	C₂	—	12	2	no	—
675	C₂	—	12	1	no	—
676	C₂	C₂×#1004	1	1	yes	characteristic
677	C₂	C₂×D₃×#41	1	1	yes	characteristic
678	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×#532	C₂
hypercenter	#532	D₃
hypocenter	C₃	#3460
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₃×#532	C₂	semidirect
2. #5832	C₂	semidirect
3. #5828	C₂	semidirect
4. #5733	C₂	semidirect
5. #5729	C₂	semidirect
6. #5719	C₂	semidirect
7. #5715	C₂	semidirect
8. #5678	C₂	semidirect
9. #5669	C₂	semidirect
10. #5619	C₂	semidirect
11. #5615	C₂	semidirect
12. #5613	C₂	semidirect
13. #5608	C₂	semidirect
14. #5607	C₂	semidirect
15. #5603	C₂	semidirect
16. #5557	C₂	semidirect
17. #5548	C₂	semidirect
18. #5547	C₂	semidirect
19. C₄×D₃×D₄	C₂	semidirect
20. #5538	C₂	semidirect
21. C₄×#237	C₂	semidirect
22. #5479	C₂	semidirect
23. C₄×#235	C₂	semidirect
25. C₂×C₃×#41	C₂²	semidirect
29. C₂×#235	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
35. C₃×#121	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
38. C₃×C₄×D₄	C₂²	semidirect
39. C₃×C₄×D₄	C₂²	semidirect
40. C₂×C₃×C₄²	C₂²	semidirect
41. #947	C₂²	semidirect
43. #946	C₂²	semidirect
44. #944	C₂²	semidirect
49. #939	C₂²	semidirect
50. #939	C₂²	semidirect
51. #939	C₂²	semidirect
52. #939	C₂²	semidirect
55. #938	C₂²	semidirect
56. #938	C₂²	semidirect
61. #936	C₂²	semidirect
62. #935	C₂²	semidirect
63. #935	C₂²	semidirect
64. #935	C₂²	semidirect
66. D₄×Dic₃	C₂²	semidirect
68. #929	C₂²	semidirect
73. C₄×#67	C₂²	semidirect
74. C₄×#67	C₂²	semidirect
75. C₄×#67	C₂²	semidirect
76. C₄×#67	C₂²	semidirect
77. C₄×#67	C₂²	semidirect
78. #926	C₂²	semidirect
79. #926	C₂²	semidirect
80. #924	C₂²	semidirect
81. C₂×C₄×Dic₃	C₂²	semidirect
82. #898	C₂²	semidirect
83. #897	C₂²	semidirect
86. #894	C₂²	semidirect
90. #890	C₂²	semidirect
91. #889	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
94. #886	C₂²	semidirect
96. #885	C₂²	semidirect
98. #884	C₂²	semidirect
99. #883	C₂²	semidirect
100. #883	C₂²	semidirect
105. #879	C₂²	semidirect
106. #879	C₂²	semidirect
107. #878	C₂²	semidirect
108. #878	C₂²	semidirect
109. #877	C₂²	semidirect
110. #876	C₂²	semidirect
116. #872	C₂²	semidirect
117. #872	C₂²	semidirect
119. C₄²×D₃	C₂²	semidirect
120. #870	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
138. #532	D₃	semidirect
255. C₂×#41	C₂×D₃	semidirect
260. C₄⋊Q₈	C₂×D₃	semidirect
277. #124	C₂×D₃	semidirect
308. #121	C₂×D₃	semidirect
309. #121	C₂×D₃	semidirect
336. C₄×D₄	C₂×D₃	semidirect
337. C₄×D₄	C₂×D₃	semidirect
350. C₂×C₄²	C₂×D₃	semidirect
412. C₄×D₃	#41	semidirect
669. C₃	#3460	semidirect

Maximal subgroups

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

subgroup	index
C₃×#532	2
#5832	2
#5828	2
#5733	2
#5729	2
#5719	2
#5715	2
#5678	2
#5669	2
#5619	2
#5615	2
#5613	2
#5608	2
#5607	2
#5603	2
#5557	2
#5548	2
#5547	2
C₄×D₃×D₄	2
#5538	2
C₄×#237	2
#5479	2
C₄×#235	2
#3460	3