Subgroups — #86240

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 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	#5829	C₂	1	2	yes	maximal, complemented
3	#5824	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	#5679	C₂	1	2	yes	maximal, complemented
9	#5670	C₂	1	2	yes	maximal, complemented
10	#5610	C₂	1	2	yes	maximal, complemented
11	#5606	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	#5601	C₂	1	2	yes	maximal, complemented
14	#5600	C₂	1	1	yes	maximal, characteristic, complemented
15	#5596	C₂	1	1	yes	maximal, characteristic, complemented
16	#5562	C₂	1	1	yes	maximal, characteristic, complemented
17	#5561	C₂	1	1	yes	maximal, characteristic, complemented
18	#5556	C₂	1	2	yes	maximal, complemented
19	#5546	C₂	1	1	yes	maximal, characteristic, complemented
20	#5545	C₂	1	1	yes	maximal, characteristic, complemented
21	#5540	C₂	1	2	yes	maximal, complemented
22	#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#872	C₂	1	1	yes	maximal, characteristic, complemented
24	#3494	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	2	yes	complemented
26	C₂×#237	C₂²	1	1	yes	characteristic
27	C₂×#237	C₂²	1	2	yes	complemented
28	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₂×D₃×D₄	C₂²	1	2	yes	—
30	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#127	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, 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, complemented
46	#939	C₂²	1	2	yes	—
47	#939	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	complemented
49	#939	C₂²	1	2	yes	complemented
50	#939	C₂²	1	2	yes	complemented
51	#939	C₂²	1	2	yes	complemented
52	#938	C₂²	1	1	yes	characteristic
53	#938	C₂²	1	1	yes	characteristic, complemented
54	#937	C₂²	1	2	yes	—
55	#937	C₂²	1	2	yes	—
56	#937	C₂²	1	2	yes	—
57	#936	C₂²	1	1	yes	characteristic, complemented
58	#935	C₂²	1	2	yes	complemented
59	#935	C₂²	1	2	yes	complemented
60	#935	C₂²	1	2	yes	complemented
61	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₃	C₂²	1	2	yes	complemented
64	D₄×Dic₃	C₂²	1	2	yes	complemented
65	#930	C₂²	1	1	yes	characteristic
66	#930	C₂²	1	2	yes	complemented
67	#929	C₂²	1	2	yes	complemented
68	#929	C₂²	1	2	yes	complemented
69	#929	C₂²	1	2	yes	complemented
70	C₄×#67	C₂²	1	2	yes	—
71	C₄×#67	C₂²	1	2	yes	complemented
72	C₄×#67	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
74	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
75	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
76	#924	C₂²	1	1	yes	characteristic, complemented
77	#924	C₂²	1	2	yes	complemented
78	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, 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, complemented
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	#885	C₂²	1	2	yes	complemented
95	#885	C₂²	1	2	yes	complemented
96	#884	C₂²	1	2	yes	—
97	#884	C₂²	1	2	yes	complemented
98	#883	C₂²	1	2	yes	—
99	#883	C₂²	1	2	yes	complemented
100	#67⋊C₄	C₂²	1	2	yes	—
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	—
105	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	#879	C₂²	1	2	yes	complemented
107	#879	C₂²	1	2	yes	complemented
108	#877	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, complemented
112	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
113	#872	C₂²	1	1	yes	characteristic
114	#872	C₂²	1	1	yes	characteristic
115	#872	C₂²	1	1	yes	characteristic
116	#872	C₂²	1	1	yes	characteristic
117	#872	C₂²	1	1	yes	characteristic, complemented
118	#872	C₂²	1	2	yes	complemented
119	#872	C₂²	1	1	yes	characteristic, complemented
120	#872	C₂²	1	1	yes	characteristic, complemented
121	#872	C₂²	1	1	yes	characteristic, complemented
122	#870	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#555	—	3	2	no	—
125	#553	—	3	2	no	—
126	#553	—	3	2	no	—
127	#551	—	3	2	no	—
128	#551	—	3	2	no	—
129	#547	—	3	2	no	—
130	#546	—	3	2	no	—
131	#546	—	3	2	no	—
132	#544	—	3	1	no	—
133	#542	—	3	1	no	—
134	#542	—	3	1	no	—
135	#540	—	3	1	no	—
136	#540	—	3	1	no	—
137	#535	—	3	1	no	—
138	#532	—	3	1	no	—
139	#532	D₃	1	1	yes	characteristic, complemented
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	1	no	—
143	C₂×#121	—	3	1	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₃×#41	—	4	4	no	—
150	C₂×C₃×Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂×C₃×D₄	C₂³	1	2	yes	—
157	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
161	C₂²×C₃×C₄	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	2	yes	—
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	C₂²×Dic₃	C₂³	1	2	yes	—
170	C₂²×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×Dic₃	C₂³	1	1	yes	characteristic
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	2	yes	—
174	C₂²×Dic₃	C₂³	1	1	yes	characteristic
175	#237	—	2	4	no	—
176	#237	—	4	4	no	—
177	D₃×D₄	—	2	4	no	—
178	D₃×D₄	—	4	4	no	—
179	C₂×D₁₂	C₂³	1	1	yes	characteristic
180	C₂×D₁₂	C₂³	1	2	yes	—
181	C₂×C₄×D₃	—	2	4	no	—
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×C₄×D₃	C₂³	1	1	yes	characteristic
189	C₂×Dic₆	C₂³	1	1	yes	characteristic
190	C₂×Dic₆	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄²	C₂³	1	1	yes	characteristic
199	C₃×C₄²	C₂³	1	1	yes	characteristic
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	1	yes	characteristic
202	#217	C₂³	1	2	yes	—
203	#217	C₂³	1	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
212	(C₂×D₃)⋊C₄	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	2	yes	—
228	C₄⋊Dic₃	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	1	yes	characteristic
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₃	C₂³	1	2	yes	—
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	C₂×#41	C₂×D₃	1	2	yes	complemented
255	C₂²×D₄	—	3	1	no	—
256	C₂²×D₄	—	3	2	no	—
257	C₂³×C₄	—	3	1	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	1	no	—
262	#127	C₂×D₃	1	1	yes	characteristic, complemented
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#125	—	3	1	no	—
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#124	—	3	2	no	—
271	#124	—	3	1	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	C₂×D₃	1	2	yes	complemented
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
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	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	#121	—	3	1	no	—
292	#121	—	3	2	no	—
293	#121	—	3	1	no	—
294	#121	—	3	2	no	—
295	#121	—	3	2	no	—
296	#121	—	3	2	no	—
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	—	3	1	no	—
300	#121	—	3	2	no	—
301	#121	—	3	1	no	—
302	#121	—	3	2	no	—
303	#121	—	3	2	no	—
304	#121	C₂×D₃	1	1	yes	characteristic
305	#121	C₂×D₃	1	1	yes	characteristic, complemented
306	#121	C₂×D₃	1	2	yes	complemented
307	#120	—	3	2	no	—
308	#120	—	3	2	no	—
309	#120	—	3	2	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	2	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	2	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
326	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
327	C₄×D₄	C₂×D₃	1	2	yes	complemented
328	#117	—	3	1	no	—
329	#117	—	3	2	no	—
330	#117	—	3	2	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	1	no	—
334	#117	—	3	1	no	—
335	#117	—	3	1	no	—
336	#117	—	3	1	no	—
337	#117	—	3	1	no	—
338	#117	—	3	1	no	—
339	#117	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₂²⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	1	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	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	2	yes	—
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	4	1	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
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	—	4	2	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	4	2	no	—
369	C₃×D₄	—	4	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	4	1	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	—	4	2	no	—
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	2	yes	—
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	#67	—	2	4	no	—
384	#67	—	2	4	no	—
385	#67	—	2	4	no	—
386	#67	—	4	2	no	—
387	#67	—	4	2	no	—
388	#67	—	4	2	no	—
389	#67	—	4	2	no	—
390	C₂×Dic₃	—	2	2	no	—
391	C₂×Dic₃	—	2	2	no	—
392	C₂×Dic₃	—	2	4	no	—
393	C₂×Dic₃	—	4	2	no	—
394	C₂×Dic₃	—	4	2	no	—
395	C₂×Dic₃	—	4	1	no	—
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	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	2	yes	—
401	C₂×Dic₃	C₂⁴	1	2	yes	—
402	C₂×Dic₃	C₂⁴	1	2	yes	—
403	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
405	D₁₂	—	2	2	no	—
406	D₁₂	—	4	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	2	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	C₄×D₃	—	4	2	no	—
413	C₄×D₃	#41	1	4	yes	complemented
414	Dic₆	—	2	2	no	—
415	Dic₆	—	4	2	no	—
416	C₂⁴	—	3	1	no	—
417	C₂⁴	—	3	2	no	—
418	#41	—	4	4	no	—
419	#41	—	6	4	no	—
420	#41	—	12	4	no	—
421	C₂×Q₈	—	3	1	no	—
422	C₂×Q₈	—	3	2	no	—
423	C₂×Q₈	C₂²×D₃	1	2	yes	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	6	4	no	—
434	C₂×D₄	—	12	4	no	—
435	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
436	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
437	C₂×D₄	C₂²×D₃	1	2	yes	—
438	C₂×D₄	C₂²×D₃	1	2	yes	—
439	C₂×D₄	C₂²×D₃	1	2	yes	—
440	C₂×D₄	C₂²×D₃	1	2	yes	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	1	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	2	no	—
453	C₂²×C₄	—	3	2	no	—
454	C₂²×C₄	—	6	4	no	—
455	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₃	1	2	yes	—
459	C₂²×C₄	C₂²×D₃	1	2	yes	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	1	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	1	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	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	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	2	no	—
485	C₂²⋊C₄	—	3	2	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	1	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	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	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
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	1	no	—
514	C₄²	—	3	2	no	—
515	C₄²	—	3	2	no	—
516	C₄²	—	3	2	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	1	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	2	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
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	2	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	4	4	no	—
540	C₂×D₃	—	8	4	no	—
541	C₂×D₃	C₂×#41	1	2	yes	—
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	—	2	1	no	—
549	C₃×C₄	C₂×#41	1	2	yes	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	2	no	—
554	Dic₃	—	2	1	no	—
555	Dic₃	—	2	2	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	1	no	—
558	Dic₃	C₂×#41	1	2	yes	—
559	C₂³	—	3	1	no	—
560	C₂³	—	3	2	no	—
561	C₂³	—	3	1	no	—
562	C₂³	—	6	2	no	—
563	C₂³	—	6	4	no	—
564	C₂³	—	6	2	no	—
565	C₂³	—	12	1	no	—
566	C₂³	—	12	2	no	—
567	C₂³	—	12	2	no	—
568	C₂³	C₂³×D₃	1	2	yes	—
569	C₂³	C₂³×D₃	1	2	yes	—
570	C₂³	C₂³×D₃	1	1	yes	characteristic
571	Q₈	—	4	2	no	—
572	Q₈	—	6	2	no	—
573	Q₈	—	12	2	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	4	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	6	4	no	—
581	D₄	—	6	4	no	—
582	D₄	—	6	4	no	—
583	D₄	—	6	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	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	4	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	3	1	no	—
598	C₂×C₄	—	3	2	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	6	2	no	—
605	C₂×C₄	—	6	2	no	—
606	C₂×C₄	—	6	2	no	—
607	C₂×C₄	—	6	4	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	6	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	—	12	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	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₃	1	2	yes	—
619	C₂×C₄	C₂³×D₃	1	2	yes	—
620	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
624	C₂×C₃	—	2	2	no	—
625	C₂×C₃	—	4	2	no	—
626	C₂×C₃	—	4	2	no	—
627	C₂×C₃	C₂²×#41	1	1	yes	characteristic
628	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂×C₃	#585	1	1	yes	characteristic
630	D₃	—	2	2	no	—
631	D₃	—	4	1	no	—
632	D₃	—	4	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	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	2	no	—
649	C₂²	—	6	1	no	—
650	C₂²	—	12	4	no	—
651	C₂²	—	24	4	no	—
652	C₂²	#1004	1	2	yes	—
653	C₂²	C₂⁴×D₃	1	1	yes	characteristic
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	3	2	no	—
662	C₄	—	6	1	no	—
663	C₄	—	6	1	no	—
664	C₄	—	6	2	no	—
665	C₄	—	6	1	no	—
666	C₄	—	6	2	no	—
667	C₄	—	6	1	no	—
668	C₄	—	6	2	no	—
669	C₄	—	6	1	no	—
670	C₄	D₃×#41	1	2	yes	—
671	C₃	#3494	1	1	yes	characteristic, complemented, Sylow
672	C₂	—	2	2	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	6	2	no	—
676	C₂	—	12	1	no	—
677	C₂	—	12	2	no	—
678	C₂	C₂×#1004	1	1	yes	characteristic
679	C₂	C₂×D₃×#41	1	1	yes	characteristic
680	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#532	C₂
hypercenter	#532	D₃
hypocenter	C₃	#3494
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₃×#532	C₂	semidirect
2. #5829	C₂	semidirect
3. #5824	C₂	semidirect
4. #5733	C₂	semidirect
5. #5729	C₂	semidirect
6. #5719	C₂	semidirect
7. #5715	C₂	semidirect
8. #5679	C₂	semidirect
9. #5670	C₂	semidirect
10. #5610	C₂	semidirect
11. #5606	C₂	semidirect
12. D₃×#121	C₂	semidirect
13. #5601	C₂	semidirect
14. #5600	C₂	semidirect
15. #5596	C₂	semidirect
16. #5562	C₂	semidirect
17. #5561	C₂	semidirect
18. #5556	C₂	semidirect
19. #5546	C₂	semidirect
20. #5545	C₂	semidirect
21. #5540	C₂	semidirect
22. #5479	C₂	semidirect
23. C₂×#872	C₂	semidirect
25. C₂×C₃×#41	C₂²	semidirect
27. C₂×#237	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#127	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
35. C₃×#121	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
37. C₃×C₄×D₄	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
45. #940	C₂²	semidirect
47. #939	C₂²	semidirect
48. #939	C₂²	semidirect
49. #939	C₂²	semidirect
50. #939	C₂²	semidirect
51. #939	C₂²	semidirect
53. #938	C₂²	semidirect
57. #936	C₂²	semidirect
58. #935	C₂²	semidirect
59. #935	C₂²	semidirect
60. #935	C₂²	semidirect
61. D₄×Dic₃	C₂²	semidirect
62. D₄×Dic₃	C₂²	semidirect
63. D₄×Dic₃	C₂²	semidirect
64. D₄×Dic₃	C₂²	semidirect
66. #930	C₂²	semidirect
67. #929	C₂²	semidirect
68. #929	C₂²	semidirect
69. #929	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
72. C₄×#67	C₂²	semidirect
76. #924	C₂²	semidirect
77. #924	C₂²	semidirect
78. C₂×Dic₃⋊C₄	C₂²	semidirect
79. C₂×Dic₃⋊C₄	C₂²	semidirect
80. C₂×Dic₃⋊C₄	C₂²	semidirect
81. C₂×C₄×Dic₃	C₂²	semidirect
82. #898	C₂²	semidirect
83. #897	C₂²	semidirect
86. #894	C₂²	semidirect
87. #893	C₂²	semidirect
90. #890	C₂²	semidirect
91. #889	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
94. #885	C₂²	semidirect
95. #885	C₂²	semidirect
97. #884	C₂²	semidirect
99. #883	C₂²	semidirect
101. #67⋊C₄	C₂²	semidirect
102. #67⋊C₄	C₂²	semidirect
103. #67⋊C₄	C₂²	semidirect
106. #879	C₂²	semidirect
107. #879	C₂²	semidirect
108. #877	C₂²	semidirect
109. #877	C₂²	semidirect
110. #876	C₂²	semidirect
111. #875	C₂²	semidirect
112. C₄×D₁₂	C₂²	semidirect
117. #872	C₂²	semidirect
118. #872	C₂²	semidirect
119. #872	C₂²	semidirect
120. #872	C₂²	semidirect
121. #872	C₂²	semidirect
122. #870	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
139. #532	D₃	semidirect
254. C₂×#41	C₂×D₃	semidirect
260. C₄⋊Q₈	C₂×D₃	semidirect
262. #127	C₂×D₃	semidirect
275. #124	C₂×D₃	semidirect
305. #121	C₂×D₃	semidirect
306. #121	C₂×D₃	semidirect
325. C₄×D₄	C₂×D₃	semidirect
326. C₄×D₄	C₂×D₃	semidirect
327. C₄×D₄	C₂×D₃	semidirect
350. C₂×C₄²	C₂×D₃	semidirect
413. C₄×D₃	#41	semidirect
671. C₃	#3494	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
#5829	2
#5824	2
#5733	2
#5729	2
#5719	2
#5715	2
#5679	2
#5670	2
#5610	2
#5606	2
D₃×#121	2
#5601	2
#5600	2
#5596	2
#5562	2
#5561	2
#5556	2
#5546	2
#5545	2
#5540	2
#5479	2
C₂×#872	2
#3494	3