Subgroups — #86158

Order 384.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5709	C₂	1	2	yes	maximal, complemented
3	#5705	C₂	1	2	yes	maximal, complemented
4	#5695	C₂	1	1	yes	maximal, characteristic, complemented
5	#5694	C₂	1	1	yes	maximal, characteristic, complemented
6	#5677	C₂	1	1	yes	maximal, characteristic, complemented
7	#5676	C₂	1	1	yes	maximal, characteristic, complemented
8	#5665	C₂	1	2	yes	maximal, complemented
9	#5653	C₂	1	2	yes	maximal, complemented
10	#5627	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#5606	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	#5581	C₂	1	1	yes	maximal, characteristic, complemented
15	#5576	C₂	1	1	yes	maximal, characteristic, complemented
16	#5560	C₂	1	2	yes	maximal, complemented
17	#5558	C₂	1	1	yes	maximal, characteristic, complemented
18	#5554	C₂	1	1	yes	maximal, characteristic, complemented
19	#5545	C₂	1	2	yes	maximal, complemented
20	#5530	C₂	1	2	yes	maximal, complemented
21	#5527	C₂	1	2	yes	maximal, complemented
22	#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
24	#3505	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×#237	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₃×D₄	C₂²	1	2	yes	—
29	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₁₂	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
33	C₃×#126	C₂²	1	2	yes	complemented
34	C₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃×#123	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#121	C₂²	1	1	yes	characteristic
39	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×D₄	C₂²	1	2	yes	complemented
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×#117	C₂²	1	2	yes	complemented
43	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
44	#946	C₂²	1	1	yes	characteristic, complemented
45	#946	C₂²	1	1	yes	characteristic, complemented
46	#939	C₂²	1	2	yes	—
47	#938	C₂²	1	1	yes	characteristic, complemented
48	#938	C₂²	1	1	yes	characteristic, complemented
49	#937	C₂²	1	2	yes	complemented
50	D₄×Dic₃	C₂²	1	2	yes	complemented
51	#930	C₂²	1	1	yes	characteristic
52	#930	C₂²	1	2	yes	complemented
53	#929	C₂²	1	2	yes	complemented
54	#929	C₂²	1	2	yes	complemented
55	C₄×#67	C₂²	1	2	yes	complemented
56	C₄×#67	C₂²	1	2	yes	complemented
57	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
60	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
61	#924	C₂²	1	1	yes	characteristic, complemented
62	#898	C₂²	1	2	yes	complemented
63	#898	C₂²	1	2	yes	complemented
64	#897	C₂²	1	2	yes	complemented
65	#897	C₂²	1	1	yes	characteristic, complemented
66	#897	C₂²	1	1	yes	characteristic, complemented
67	#896	C₂²	1	2	yes	complemented
68	#895	C₂²	1	2	yes	complemented
69	#895	C₂²	1	2	yes	complemented
70	#895	C₂²	1	1	yes	characteristic, complemented
71	#895	C₂²	1	1	yes	characteristic, complemented
72	#894	C₂²	1	2	yes	—
73	#894	C₂²	1	2	yes	—
74	#894	C₂²	1	2	yes	complemented
75	#894	C₂²	1	2	yes	complemented
76	#893	C₂²	1	2	yes	complemented
77	#893	C₂²	1	2	yes	complemented
78	#892	C₂²	1	2	yes	complemented
79	#892	C₂²	1	1	yes	characteristic, complemented
80	#892	C₂²	1	1	yes	characteristic, complemented
81	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
84	#890	C₂²	1	2	yes	complemented
85	#889	C₂²	1	2	yes	complemented
86	#886	C₂²	1	2	yes	complemented
87	#885	C₂²	1	2	yes	complemented
88	#884	C₂²	1	2	yes	complemented
89	#884	C₂²	1	2	yes	complemented
90	#884	C₂²	1	2	yes	complemented
91	#884	C₂²	1	2	yes	complemented
92	#883	C₂²	1	2	yes	complemented
93	#883	C₂²	1	2	yes	complemented
94	#882	C₂²	1	2	yes	—
95	#882	C₂²	1	2	yes	—
96	#882	C₂²	1	2	yes	complemented
97	#67⋊C₄	C₂²	1	2	yes	complemented
98	#67⋊C₄	C₂²	1	2	yes	complemented
99	#67⋊C₄	C₂²	1	2	yes	complemented
100	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	#879	C₂²	1	2	yes	complemented
104	#878	C₂²	1	2	yes	complemented
105	#878	C₂²	1	2	yes	complemented
106	#876	C₂²	1	2	yes	complemented
107	#876	C₂²	1	2	yes	complemented
108	#875	C₂²	1	1	yes	characteristic, complemented
109	#875	C₂²	1	2	yes	complemented
110	C₄×D₁₂	C₂²	1	1	yes	characteristic
111	C₄×D₁₂	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, complemented
115	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₁₂	C₂²	1	2	yes	complemented
120	#872	C₂²	1	2	yes	complemented
121	#872	C₂²	1	2	yes	complemented
122	#870	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#553	—	3	2	no	—
125	#553	—	3	1	no	—
126	#553	—	3	1	no	—
127	#553	—	3	2	no	—
128	#552	—	3	1	no	—
129	#552	—	3	1	no	—
130	#551	—	3	2	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	#539	—	3	2	no	—
137	#538	—	3	2	no	—
138	#534	—	3	2	no	—
139	#529	—	3	1	no	—
140	#529	D₃	1	1	yes	characteristic, complemented
141	#525	—	3	1	no	—
142	#525	—	3	1	no	—
143	C₂×C₂²⋊Q₈	—	3	1	no	—
144	C₂×#121	—	3	1	no	—
145	#518	—	3	2	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	1	yes	characteristic
149	C₂³×D₃	C₂³	1	1	yes	characteristic
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	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	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	2	yes	—
161	C₂×#67	C₂³	1	2	yes	—
162	C₂²×Dic₃	C₂³	1	1	yes	characteristic
163	C₂²×Dic₃	C₂³	1	2	yes	—
164	C₂²×Dic₃	C₂³	1	1	yes	characteristic
165	#239	—	4	2	no	—
166	D₃×Q₈	—	4	2	no	—
167	#237	—	4	2	no	—
168	D₃×D₄	—	2	8	no	—
169	D₃×D₄	—	4	2	no	—
170	C₂×D₁₂	—	2	4	no	—
171	C₂×D₁₂	C₂³	1	1	yes	characteristic
172	C₂×D₁₂	C₂³	1	1	yes	characteristic
173	C₂×D₁₂	C₂³	1	1	yes	characteristic
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	2	yes	—
178	C₂×D₁₂	C₂³	1	2	yes	—
179	C₂×C₄×D₃	—	4	2	no	—
180	C₂×C₄×D₃	—	4	2	no	—
181	C₂×C₄×D₃	C₂³	1	2	yes	—
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	1	yes	characteristic
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
191	C₂×C₄×D₃	C₂³	1	2	yes	—
192	C₂×C₄×D₃	C₂³	1	2	yes	—
193	C₂×C₄×D₃	C₂³	1	2	yes	—
194	C₂×Dic₆	C₂³	1	1	yes	characteristic
195	C₂×Dic₆	C₂³	1	2	yes	—
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×C₄⋊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	2	yes	—
205	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₃×C₄²	C₂³	1	2	yes	—
211	C₃×C₄²	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
222	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
233	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
235	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	2	yes	—
246	Dic₃⋊C₄	C₂³	1	2	yes	—
247	Dic₃⋊C₄	C₂³	1	2	yes	—
248	Dic₃⋊C₄	C₂³	1	2	yes	—
249	Dic₃⋊C₄	C₂³	1	2	yes	—
250	Dic₃⋊C₄	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₄×Dic₃	C₂³	1	2	yes	—
253	C₄×Dic₃	C₂³	1	2	yes	—
254	C₂×#41	—	3	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂²×Q₈	—	3	1	no	—
257	C₂²×D₄	—	3	2	no	—
258	C₂²×D₄	—	3	1	no	—
259	C₂²×D₄	—	3	1	no	—
260	C₂³×C₄	—	3	1	no	—
261	C₂³×C₄	—	3	1	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	2	no	—
269	#125	—	3	2	no	—
270	#125	—	3	1	no	—
271	#125	C₂×D₃	1	1	yes	characteristic, complemented
272	#124	—	3	2	no	—
273	#124	—	3	1	no	—
274	#124	—	3	2	no	—
275	#124	C₂×D₃	1	1	yes	characteristic, 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	#123	C₂×D₃	1	2	yes	complemented
286	C₂²⋊Q₈	—	3	1	no	—
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
296	#121	—	3	2	no	—
297	#121	—	3	1	no	—
298	#121	—	3	1	no	—
299	#121	—	3	1	no	—
300	#121	—	3	2	no	—
301	#121	—	3	1	no	—
302	#121	—	3	1	no	—
303	#121	—	3	2	no	—
304	#121	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic, complemented
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	—	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	—	3	1	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	—	3	1	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	C₂×D₃	1	2	yes	complemented
335	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	1	no	—
339	#117	—	3	2	no	—
340	#117	—	3	2	no	—
341	#117	C₂×D₃	1	2	yes	complemented
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	1	no	—
345	C₂×C₄⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	1	no	—
347	C₂×C₂²⋊C₄	—	3	1	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	4	1	no	—
358	C₂²×D₃	—	4	1	no	—
359	C₂²×D₃	—	4	1	no	—
360	C₂²×D₃	—	4	1	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	—	4	2	no	—
363	C₂²×D₃	#41	1	4	yes	complemented
364	C₂²×D₃	C₂⁴	1	1	yes	characteristic
365	C₂²×D₃	C₂⁴	1	1	yes	characteristic
366	C₂²×D₃	C₂⁴	1	2	yes	—
367	C₂²×D₃	C₂⁴	1	1	yes	characteristic
368	C₂²×D₃	C₂⁴	1	1	yes	characteristic
369	C₃×Q₈	—	2	2	no	—
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	4	1	no	—
375	C₂×C₃×C₄	—	4	2	no	—
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	C₂×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	#67	—	2	4	no	—
386	#67	—	2	4	no	—
387	#67	—	4	2	no	—
388	#67	—	4	2	no	—
389	#67	—	4	2	no	—
390	C₂×Dic₃	—	4	1	no	—
391	C₂×Dic₃	—	4	1	no	—
392	C₂×Dic₃	—	4	2	no	—
393	C₂×Dic₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
400	D₁₂	—	2	2	no	—
401	D₁₂	—	2	2	no	—
402	D₁₂	—	2	2	no	—
403	D₁₂	—	2	2	no	—
404	D₁₂	—	2	4	no	—
405	D₁₂	—	2	2	no	—
406	D₁₂	—	4	2	no	—
407	D₁₂	—	4	2	no	—
408	C₄×D₃	—	2	4	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	4	1	no	—
414	C₄×D₃	—	4	1	no	—
415	C₄×D₃	—	4	1	no	—
416	C₄×D₃	—	4	1	no	—
417	C₄×D₃	—	4	2	no	—
418	C₄×D₃	—	4	2	no	—
419	C₄×D₃	—	4	2	no	—
420	C₄×D₃	—	4	2	no	—
421	Dic₆	—	2	2	no	—
422	Dic₆	—	4	2	no	—
423	C₂⁴	—	3	1	no	—
424	C₂⁴	—	3	2	no	—
425	C₂⁴	—	3	1	no	—
426	#41	—	12	2	no	—
427	#41	—	12	2	no	—
428	C₂×Q₈	—	3	1	no	—
429	C₂×Q₈	—	3	2	no	—
430	C₂×Q₈	—	12	2	no	—
431	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	3	1	no	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	3	1	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	3	1	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	6	4	no	—
446	C₂×D₄	—	6	8	no	—
447	C₂×D₄	—	12	2	no	—
448	C₂×D₄	C₂²×D₃	1	2	yes	—
449	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	—	3	2	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	2	no	—
462	C₂²×C₄	—	3	2	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	12	2	no	—
467	C₂²×C₄	—	12	2	no	—
468	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
470	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
471	C₂²×C₄	C₂²×D₃	1	2	yes	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	1	no	—
475	C₄⋊C₄	—	3	1	no	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	1	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	2	no	—
480	C₄⋊C₄	—	3	2	no	—
481	C₄⋊C₄	—	3	2	no	—
482	C₄⋊C₄	—	3	2	no	—
483	C₄⋊C₄	—	3	2	no	—
484	C₄⋊C₄	—	3	2	no	—
485	C₄⋊C₄	—	3	2	no	—
486	C₄⋊C₄	—	3	2	no	—
487	C₄⋊C₄	—	3	2	no	—
488	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₃	1	2	yes	—
491	C₄⋊C₄	C₂²×D₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₃	1	2	yes	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	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	1	no	—
503	C₂²⋊C₄	—	3	1	no	—
504	C₂²⋊C₄	—	3	1	no	—
505	C₂²⋊C₄	—	3	1	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	1	no	—
509	C₂²⋊C₄	—	3	1	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	3	2	no	—
512	C₂²⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	2	no	—
514	C₂²⋊C₄	—	3	2	no	—
515	C₂²⋊C₄	—	3	2	no	—
516	C₂²⋊C₄	—	3	2	no	—
517	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
519	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
522	C₄²	—	3	2	no	—
523	C₄²	—	3	2	no	—
524	C₄²	—	3	2	no	—
525	C₄²	C₂²×D₃	1	1	yes	characteristic
526	C₄²	C₂²×D₃	1	1	yes	characteristic
527	C₄²	C₂²×D₃	1	1	yes	characteristic
528	C₄²	C₂²×D₃	1	1	yes	characteristic
529	C₄²	C₂²×D₃	1	2	yes	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	2	2	no	—
533	C₂²×C₃	—	2	2	no	—
534	C₂²×C₃	—	2	2	no	—
535	C₂²×C₃	C₂×#41	1	2	yes	—
536	C₂²×C₃	C₂⁵	1	1	yes	characteristic
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	1	no	—
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	2	2	no	—
544	C₂×D₃	—	2	1	no	—
545	C₂×D₃	—	2	1	no	—
546	C₂×D₃	—	2	2	no	—
547	C₂×D₃	—	2	2	no	—
548	C₂×D₃	—	2	1	no	—
549	C₂×D₃	—	2	1	no	—
550	C₂×D₃	—	4	4	no	—
551	C₂×D₃	—	4	4	no	—
552	C₂×D₃	—	8	4	no	—
553	C₂×D₃	C₂×#41	1	2	yes	—
554	C₂×D₃	C₂×#41	1	2	yes	—
555	C₃×C₄	—	2	2	no	—
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	2	2	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	2	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
564	Dic₃	—	2	2	no	—
565	Dic₃	—	2	2	no	—
566	Dic₃	—	2	1	no	—
567	Dic₃	—	2	1	no	—
568	Dic₃	—	2	1	no	—
569	Dic₃	—	2	1	no	—
570	Dic₃	—	2	2	no	—
571	C₂³	—	3	1	no	—
572	C₂³	—	3	1	no	—
573	C₂³	—	3	4	no	—
574	C₂³	—	3	1	no	—
575	C₂³	—	3	1	no	—
576	C₂³	—	3	2	no	—
577	C₂³	—	6	4	no	—
578	C₂³	—	6	2	no	—
579	C₂³	—	12	1	no	—
580	C₂³	—	12	1	no	—
581	C₂³	—	12	1	no	—
582	C₂³	—	12	1	no	—
583	C₂³	—	12	2	no	—
584	C₂³	—	12	2	no	—
585	C₂³	C₂³×D₃	1	2	yes	—
586	C₂³	C₂³×D₃	1	1	yes	characteristic
587	Q₈	—	2	2	no	—
588	Q₈	—	6	2	no	—
589	Q₈	—	12	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	6	2	no	—
593	D₄	—	6	2	no	—
594	D₄	—	6	2	no	—
595	D₄	—	6	2	no	—
596	D₄	—	6	4	no	—
597	D₄	—	6	4	no	—
598	D₄	—	6	4	no	—
599	D₄	—	6	2	no	—
600	D₄	—	12	2	no	—
601	D₄	—	12	2	no	—
602	D₄	—	12	2	no	—
603	D₄	—	12	2	no	—
604	D₄	—	12	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	3	2	no	—
608	C₂×C₄	—	3	1	no	—
609	C₂×C₄	—	3	1	no	—
610	C₂×C₄	—	3	2	no	—
611	C₂×C₄	—	3	2	no	—
612	C₂×C₄	—	3	1	no	—
613	C₂×C₄	—	3	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	6	4	no	—
617	C₂×C₄	—	6	2	no	—
618	C₂×C₄	—	6	2	no	—
619	C₂×C₄	—	6	2	no	—
620	C₂×C₄	—	6	2	no	—
621	C₂×C₄	—	12	1	no	—
622	C₂×C₄	—	12	1	no	—
623	C₂×C₄	—	12	1	no	—
624	C₂×C₄	—	12	1	no	—
625	C₂×C₄	—	12	2	no	—
626	C₂×C₄	—	12	2	no	—
627	C₂×C₄	—	12	2	no	—
628	C₂×C₄	—	12	2	no	—
629	C₂×C₄	—	12	1	no	—
630	C₂×C₄	—	12	1	no	—
631	C₂×C₄	—	12	2	no	—
632	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₃	1	2	yes	—
634	C₂×C₄	C₂³×D₃	1	2	yes	—
635	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₃	1	2	yes	—
640	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
641	C₂×C₃	—	2	2	no	—
642	C₂×C₃	—	4	2	no	—
643	C₂×C₃	C₂²×#41	1	1	yes	characteristic
644	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂×C₃	#585	1	1	yes	characteristic
646	D₃	—	2	2	no	—
647	D₃	—	2	2	no	—
648	D₃	—	4	1	no	—
649	D₃	—	4	1	no	—
650	D₃	—	4	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	3	2	no	—
657	C₂²	—	3	2	no	—
658	C₂²	—	6	1	no	—
659	C₂²	—	6	1	no	—
660	C₂²	—	6	1	no	—
661	C₂²	—	6	1	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	—	6	2	no	—
665	C₂²	—	6	1	no	—
666	C₂²	—	6	1	no	—
667	C₂²	—	6	2	no	—
668	C₂²	—	6	2	no	—
669	C₂²	—	6	1	no	—
670	C₂²	—	6	1	no	—
671	C₂²	—	12	4	no	—
672	C₂²	—	12	4	no	—
673	C₂²	—	24	4	no	—
674	C₂²	D₃×#41	1	2	yes	—
675	C₂²	C₂⁴×D₃	1	1	yes	characteristic
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	6	2	no	—
685	C₄	—	6	1	no	—
686	C₄	—	6	1	no	—
687	C₄	—	6	1	no	—
688	C₄	—	6	1	no	—
689	C₄	—	6	2	no	—
690	C₄	—	6	2	no	—
691	C₄	#1009	1	2	yes	—
692	C₃	#3505	1	1	yes	characteristic, complemented, Sylow
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	6	2	no	—
696	C₂	—	6	2	no	—
697	C₂	—	12	1	no	—
698	C₂	—	12	1	no	—
699	C₂	—	12	2	no	—
700	C₂	C₂×D₃×#41	1	1	yes	characteristic
701	C₂	C₂×#1009	1	1	yes	characteristic
702	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3505
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5709	C₂	semidirect
3. #5705	C₂	semidirect
4. #5695	C₂	semidirect
5. #5694	C₂	semidirect
6. #5677	C₂	semidirect
7. #5676	C₂	semidirect
8. #5665	C₂	semidirect
9. #5653	C₂	semidirect
10. #5627	C₂	semidirect
11. D₃×C₂²⋊Q₈	C₂	semidirect
12. #5606	C₂	semidirect
13. D₃×#121	C₂	semidirect
14. #5581	C₂	semidirect
15. #5576	C₂	semidirect
16. #5560	C₂	semidirect
17. #5558	C₂	semidirect
18. #5554	C₂	semidirect
19. #5545	C₂	semidirect
20. #5530	C₂	semidirect
21. #5527	C₂	semidirect
22. #5479	C₂	semidirect
23. C₂×C₄×D₁₂	C₂	semidirect
25. C₂×#239	C₂²	semidirect
26. C₂×D₃×Q₈	C₂²	semidirect
27. C₂×#237	C₂²	semidirect
29. C₂×D₃×D₄	C₂²	semidirect
32. C₂²×C₄×D₃	C₂²	semidirect
33. C₃×#126	C₂²	semidirect
34. C₃×#125	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
42. C₃×#117	C₂²	semidirect
43. C₂×C₃×C₄²	C₂²	semidirect
44. #946	C₂²	semidirect
45. #946	C₂²	semidirect
47. #938	C₂²	semidirect
48. #938	C₂²	semidirect
49. #937	C₂²	semidirect
50. D₄×Dic₃	C₂²	semidirect
52. #930	C₂²	semidirect
53. #929	C₂²	semidirect
54. #929	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
58. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
59. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
60. C₂×C₄⋊Dic₃	C₂²	semidirect
61. #924	C₂²	semidirect
62. #898	C₂²	semidirect
63. #898	C₂²	semidirect
64. #897	C₂²	semidirect
65. #897	C₂²	semidirect
66. #897	C₂²	semidirect
67. #896	C₂²	semidirect
68. #895	C₂²	semidirect
69. #895	C₂²	semidirect
70. #895	C₂²	semidirect
71. #895	C₂²	semidirect
74. #894	C₂²	semidirect
75. #894	C₂²	semidirect
76. #893	C₂²	semidirect
77. #893	C₂²	semidirect
78. #892	C₂²	semidirect
79. #892	C₂²	semidirect
80. #892	C₂²	semidirect
81. D₃×C₄⋊C₄	C₂²	semidirect
82. D₃×C₄⋊C₄	C₂²	semidirect
83. D₃×C₄⋊C₄	C₂²	semidirect
84. #890	C₂²	semidirect
85. #889	C₂²	semidirect
86. #886	C₂²	semidirect
87. #885	C₂²	semidirect
88. #884	C₂²	semidirect
89. #884	C₂²	semidirect
90. #884	C₂²	semidirect
91. #884	C₂²	semidirect
92. #883	C₂²	semidirect
93. #883	C₂²	semidirect
96. #882	C₂²	semidirect
97. #67⋊C₄	C₂²	semidirect
98. #67⋊C₄	C₂²	semidirect
99. #67⋊C₄	C₂²	semidirect
101. D₃×C₂²⋊C₄	C₂²	semidirect
102. D₃×C₂²⋊C₄	C₂²	semidirect
103. #879	C₂²	semidirect
104. #878	C₂²	semidirect
105. #878	C₂²	semidirect
106. #876	C₂²	semidirect
107. #876	C₂²	semidirect
108. #875	C₂²	semidirect
109. #875	C₂²	semidirect
114. C₄×D₁₂	C₂²	semidirect
115. C₄×D₁₂	C₂²	semidirect
116. C₄×D₁₂	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
118. C₄×D₁₂	C₂²	semidirect
119. C₄×D₁₂	C₂²	semidirect
120. #872	C₂²	semidirect
121. #872	C₂²	semidirect
122. #870	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
140. #529	D₃	semidirect
267. #126	C₂×D₃	semidirect
271. #125	C₂×D₃	semidirect
275. #124	C₂×D₃	semidirect
285. #123	C₂×D₃	semidirect
295. C₂²⋊Q₈	C₂×D₃	semidirect
315. C₄×Q₈	C₂×D₃	semidirect
334. C₄×D₄	C₂×D₃	semidirect
335. C₄×D₄	C₂×D₃	semidirect
341. #117	C₂×D₃	semidirect
352. C₂×C₄²	C₂×D₃	semidirect
363. C₂²×D₃	#41	semidirect
692. C₃	#3505	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5709	2
#5705	2
#5695	2
#5694	2
#5677	2
#5676	2
#5665	2
#5653	2
#5627	2
D₃×C₂²⋊Q₈	2
#5606	2
D₃×#121	2
#5581	2
#5576	2
#5560	2
#5558	2
#5554	2
#5545	2
#5530	2
#5527	2
#5479	2
C₂×C₄×D₁₂	2
#3505	3