Subgroups — #87069

Order 384.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	#5717	C₂	1	1	yes	maximal, characteristic, complemented
3	#5715	C₂	1	1	yes	maximal, characteristic, complemented
4	#5683	C₂	1	2	yes	maximal, complemented
5	#5678	C₂	1	2	yes	maximal, complemented
6	#5677	C₂	1	1	yes	maximal, characteristic, complemented
7	#5676	C₂	1	1	yes	maximal, characteristic, complemented
8	#5674	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	#5667	C₂	1	2	yes	maximal, complemented
11	#5657	C₂	1	2	yes	maximal, complemented
12	#5654	C₂	1	2	yes	maximal, complemented
13	#5653	C₂	1	2	yes	maximal, complemented
14	#5585	C₂	1	1	yes	maximal, characteristic, complemented
15	#5582	C₂	1	1	yes	maximal, characteristic, complemented
16	#5580	C₂	1	1	yes	maximal, characteristic, complemented
17	#5576	C₂	1	1	yes	maximal, characteristic, complemented
18	#5561	C₂	1	1	yes	maximal, characteristic, complemented
19	#5560	C₂	1	2	yes	maximal, complemented
20	#5554	C₂	1	1	yes	maximal, characteristic, complemented
21	#5550	C₂	1	2	yes	maximal, complemented
22	D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
23	#5548	C₂	1	1	yes	maximal, characteristic, complemented
24	#3558	—	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	1	yes	characteristic
29	C₂×D₃×D₄	C₂²	1	2	yes	complemented
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×#235	C₂²	1	2	yes	complemented
33	C₂²×D₁₂	C₂²	1	2	yes	complemented
34	C₃×#127	C₂²	1	1	yes	characteristic
35	C₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃×#124	C₂²	1	1	yes	characteristic, complemented
37	C₃×#124	C₂²	1	2	yes	complemented
38	C₃×#123	C₂²	1	2	yes	complemented
39	C₃×#123	C₂²	1	2	yes	complemented
40	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₄×D₄	C₂²	1	2	yes	complemented
45	#947	C₂²	1	1	yes	characteristic, complemented
46	#947	C₂²	1	2	yes	complemented
47	#947	C₂²	1	1	yes	characteristic, complemented
48	#946	C₂²	1	1	yes	characteristic, complemented
49	#946	C₂²	1	1	yes	characteristic, complemented
50	#940	C₂²	1	1	yes	characteristic, 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	complemented
55	#938	C₂²	1	1	yes	characteristic, complemented
56	#937	C₂²	1	2	yes	complemented
57	#937	C₂²	1	2	yes	complemented
58	#937	C₂²	1	2	yes	complemented
59	#937	C₂²	1	2	yes	complemented
60	#936	C₂²	1	1	yes	characteristic, complemented
61	#930	C₂²	1	2	yes	complemented
62	#930	C₂²	1	2	yes	complemented
63	#929	C₂²	1	2	yes	complemented
64	C₄×#67	C₂²	1	2	yes	complemented
65	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
66	#924	C₂²	1	2	yes	complemented
67	#898	C₂²	1	1	yes	characteristic, complemented
68	#898	C₂²	1	1	yes	characteristic, complemented
69	#897	C₂²	1	2	yes	complemented
70	#897	C₂²	1	1	yes	characteristic, complemented
71	#896	C₂²	1	2	yes	complemented
72	#895	C₂²	1	1	yes	characteristic
73	#895	C₂²	1	1	yes	characteristic
74	#895	C₂²	1	2	yes	complemented
75	#895	C₂²	1	1	yes	characteristic, complemented
76	#894	C₂²	1	2	yes	complemented
77	#894	C₂²	1	2	yes	complemented
78	#894	C₂²	1	1	yes	characteristic, complemented
79	#894	C₂²	1	1	yes	characteristic, complemented
80	#894	C₂²	1	2	yes	complemented
81	#893	C₂²	1	2	yes	complemented
82	#890	C₂²	1	1	yes	characteristic, complemented
83	#888	C₂²	1	1	yes	characteristic, complemented
84	#886	C₂²	1	2	yes	complemented
85	#885	C₂²	1	2	yes	complemented
86	#885	C₂²	1	2	yes	complemented
87	#885	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	complemented
89	#885	C₂²	1	2	yes	complemented
90	#884	C₂²	1	2	yes	complemented
91	#884	C₂²	1	2	yes	complemented
92	#884	C₂²	1	2	yes	complemented
93	#884	C₂²	1	2	yes	complemented
94	#884	C₂²	1	2	yes	complemented
95	#883	C₂²	1	2	yes	complemented
96	#882	C₂²	1	2	yes	complemented
97	#882	C₂²	1	2	yes	complemented
98	#882	C₂²	1	2	yes	complemented
99	#882	C₂²	1	2	yes	complemented
100	#882	C₂²	1	2	yes	complemented
101	#882	C₂²	1	2	yes	complemented
102	#67⋊C₄	C₂²	1	2	yes	complemented
103	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	#879	C₂²	1	2	yes	complemented
107	#878	C₂²	1	2	yes	complemented
108	#876	C₂²	1	2	yes	complemented
109	#875	C₂²	1	1	yes	characteristic, complemented
110	#875	C₂²	1	2	yes	complemented
111	#875	C₂²	1	2	yes	complemented
112	#875	C₂²	1	1	yes	characteristic, complemented
113	#874	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	2	yes	complemented
118	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
120	#872	C₂²	1	1	yes	characteristic, complemented
121	#872	C₂²	1	1	yes	characteristic, complemented
122	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#562	—	3	2	no	—
125	H(3,𝔽₄)	—	3	2	no	—
126	#559	—	3	1	no	—
127	#559	D₃	1	1	yes	characteristic, complemented
128	#548	—	3	1	no	—
129	#548	—	3	1	no	—
130	#546	—	3	1	no	—
131	#546	—	3	2	no	—
132	#546	—	3	2	no	—
133	#546	—	3	1	no	—
134	D₄²	—	3	1	no	—
135	D₄²	—	3	1	no	—
136	#542	—	3	1	no	—
137	#542	—	3	1	no	—
138	#538	—	3	2	no	—
139	#538	—	3	2	no	—
140	#538	—	3	2	no	—
141	#535	—	3	1	no	—
142	#535	—	3	1	no	—
143	#534	—	3	2	no	—
144	#532	—	3	1	no	—
145	#529	—	3	1	no	—
146	C₂×#124	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂³×D₃	C₂³	1	2	yes	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
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	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	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	C₂²×Dic₃	C₂³	1	2	yes	—
167	#239	—	4	2	no	—
168	D₃×Q₈	—	4	2	no	—
169	#237	—	4	2	no	—
170	D₃×D₄	—	4	2	no	—
171	D₃×D₄	—	4	2	no	—
172	D₃×D₄	—	4	2	no	—
173	D₃×D₄	—	4	4	no	—
174	#235	—	4	4	no	—
175	C₂×D₁₂	—	4	4	no	—
176	C₂×D₁₂	C₂³	1	1	yes	characteristic
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×D₁₂	C₂³	1	1	yes	characteristic
181	C₂×D₁₂	C₂³	1	1	yes	characteristic
182	C₂×D₁₂	C₂³	1	2	yes	—
183	C₂×D₁₂	C₂³	1	2	yes	—
184	C₂×D₁₂	C₂³	1	2	yes	—
185	C₂×D₁₂	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
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×C₄×D₃	C₂³	1	2	yes	—
195	C₂×Dic₆	C₂³	1	1	yes	characteristic
196	C₂×Dic₆	C₂³	1	2	yes	—
197	C₂×Dic₆	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	1	yes	characteristic
201	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₄⋊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×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₃×C₄²	C₂³	1	1	yes	characteristic
211	C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₃×C₄²	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	2	yes	—
215	#217	C₂³	1	2	yes	—
216	#217	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
227	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
236	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
237	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
243	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
253	C₄×Dic₃	C₂³	1	1	yes	characteristic
254	C₄×Dic₃	C₂³	1	1	yes	characteristic
255	C₂×#41	—	3	1	no	—
256	C₂×#41	—	3	1	no	—
257	C₂×#41	—	3	2	no	—
258	C₂²×Q₈	—	3	1	no	—
259	C₂²×D₄	—	3	1	no	—
260	C₂²×D₄	—	3	2	no	—
261	C₂²×D₄	—	3	1	no	—
262	C₂²×D₄	—	3	1	no	—
263	C₂²×D₄	—	3	2	no	—
264	C₄⋊Q₈	—	3	1	no	—
265	#127	—	3	1	no	—
266	#127	—	3	1	no	—
267	#127	C₂×D₃	1	1	yes	characteristic
268	#126	—	3	1	no	—
269	#126	—	3	1	no	—
270	#126	—	3	2	no	—
271	#126	—	3	2	no	—
272	#125	—	3	1	no	—
273	#124	—	3	1	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	—	3	1	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	—	3	2	no	—
282	#124	—	3	1	no	—
283	#124	—	3	1	no	—
284	#124	—	3	2	no	—
285	#124	—	3	2	no	—
286	#124	C₂×D₃	1	1	yes	characteristic, complemented
287	#124	C₂×D₃	1	1	yes	characteristic, complemented
288	#124	C₂×D₃	1	2	yes	complemented
289	#123	—	3	2	no	—
290	#123	—	3	1	no	—
291	#123	—	3	1	no	—
292	#123	—	3	2	no	—
293	#123	—	3	2	no	—
294	#123	—	3	2	no	—
295	#123	—	3	2	no	—
296	#123	—	3	2	no	—
297	#123	C₂×D₃	1	2	yes	complemented
298	#123	C₂×D₃	1	2	yes	complemented
299	C₂²⋊Q₈	—	3	1	no	—
300	C₂²⋊Q₈	—	3	1	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	—	3	1	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	#121	—	3	1	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	1	no	—
311	#121	—	3	2	no	—
312	#121	—	3	2	no	—
313	#121	—	3	1	no	—
314	#121	—	3	1	no	—
315	#121	—	3	2	no	—
316	#121	—	3	1	no	—
317	#121	—	3	2	no	—
318	#121	—	3	2	no	—
319	#121	—	3	2	no	—
320	#121	—	3	2	no	—
321	#121	—	3	2	no	—
322	#120	—	3	2	no	—
323	#120	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	#120	—	3	2	no	—
327	#120	—	3	2	no	—
328	#120	—	3	2	no	—
329	#120	—	3	2	no	—
330	#120	—	3	2	no	—
331	#120	—	3	2	no	—
332	C₄×Q₈	—	3	1	no	—
333	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
334	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
335	C₄×D₄	—	3	2	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	—	3	1	no	—
340	C₄×D₄	—	3	1	no	—
341	C₄×D₄	—	3	1	no	—
342	C₄×D₄	—	3	2	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
345	C₄×D₄	C₂×D₃	1	2	yes	complemented
346	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
347	#117	—	3	1	no	—
348	#117	—	3	1	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₄²	—	3	1	no	—
354	C₂³×C₃	C₂⁴	1	2	yes	—
355	C₂³×C₃	C₂⁴	1	2	yes	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	4	2	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	—	4	2	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	—	4	2	no	—
363	C₂²×D₃	—	4	2	no	—
364	C₂²×D₃	—	4	2	no	—
365	C₂²×D₃	C₂⁴	1	1	yes	characteristic
366	C₂²×D₃	C₂⁴	1	1	yes	characteristic
367	C₂²×D₃	C₂⁴	1	2	yes	—
368	C₂²×D₃	C₂⁴	1	2	yes	—
369	C₂²×D₃	C₂⁴	1	1	yes	characteristic
370	C₃×Q₈	—	2	2	no	—
371	C₃×Q₈	—	4	1	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	4	2	no	—
375	C₃×D₄	—	4	2	no	—
376	C₂×C₃×C₄	—	4	2	no	—
377	C₂×C₃×C₄	—	4	2	no	—
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	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	#67	—	2	4	no	—
388	#67	—	4	2	no	—
389	#67	—	4	2	no	—
390	#67	—	4	2	no	—
391	#67	—	4	2	no	—
392	#67	—	4	2	no	—
393	#67	—	4	2	no	—
394	#67	—	4	2	no	—
395	C₂×Dic₃	—	4	2	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	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	D₁₂	—	2	2	no	—
404	D₁₂	—	2	4	no	—
405	D₁₂	—	2	2	no	—
406	D₁₂	—	2	2	no	—
407	D₁₂	—	2	2	no	—
408	D₁₂	—	4	2	no	—
409	D₁₂	—	4	2	no	—
410	D₁₂	—	4	1	no	—
411	D₁₂	—	4	2	no	—
412	D₁₂	—	4	2	no	—
413	C₄×D₃	—	2	2	no	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	4	1	no	—
418	C₄×D₃	—	4	2	no	—
419	C₄×D₃	—	4	2	no	—
420	C₄×D₃	—	4	2	no	—
421	C₄×D₃	—	4	2	no	—
422	Dic₆	—	2	2	no	—
423	Dic₆	—	4	2	no	—
424	Dic₆	—	4	2	no	—
425	C₂⁴	—	3	2	no	—
426	C₂⁴	—	3	2	no	—
427	C₂⁴	—	3	2	no	—
428	#41	—	12	4	no	—
429	#41	—	12	2	no	—
430	#41	—	12	2	no	—
431	C₂×Q₈	—	3	1	no	—
432	C₂×Q₈	—	3	2	no	—
433	C₂×Q₈	—	3	2	no	—
434	C₂×Q₈	—	12	2	no	—
435	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
436	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	3	2	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	1	no	—
447	C₂×D₄	—	3	1	no	—
448	C₂×D₄	—	3	1	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	12	4	no	—
456	C₂×D₄	—	12	2	no	—
457	C₂×D₄	—	12	2	no	—
458	C₂×D₄	—	12	2	no	—
459	C₂×D₄	—	12	4	no	—
460	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
462	C₂×D₄	C₂²×D₃	1	2	yes	—
463	C₂×D₄	C₂²×D₃	1	2	yes	—
464	C₂²×C₄	—	3	2	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	3	1	no	—
467	C₂²×C₄	—	3	1	no	—
468	C₂²×C₄	—	3	1	no	—
469	C₂²×C₄	—	3	1	no	—
470	C₂²×C₄	—	3	2	no	—
471	C₂²×C₄	—	3	2	no	—
472	C₂²×C₄	—	3	2	no	—
473	C₂²×C₄	—	3	2	no	—
474	C₂²×C₄	C₂²×D₃	1	2	yes	—
475	C₂²×C₄	C₂²×D₃	1	2	yes	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	1	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	1	no	—
480	C₄⋊C₄	—	3	1	no	—
481	C₄⋊C₄	—	3	1	no	—
482	C₄⋊C₄	—	3	1	no	—
483	C₄⋊C₄	—	3	2	no	—
484	C₄⋊C₄	—	3	2	no	—
485	C₄⋊C₄	—	3	2	no	—
486	C₄⋊C₄	—	3	1	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	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
493	C₂²⋊C₄	—	3	2	no	—
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	2	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	1	no	—
507	C₂²⋊C₄	—	3	1	no	—
508	C₂²⋊C₄	—	3	1	no	—
509	C₂²⋊C₄	—	3	1	no	—
510	C₂²⋊C₄	—	3	1	no	—
511	C₂²⋊C₄	—	3	1	no	—
512	C₂²⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	1	no	—
514	C₂²⋊C₄	—	3	1	no	—
515	C₂²⋊C₄	—	3	2	no	—
516	C₂²⋊C₄	—	3	2	no	—
517	C₂²⋊C₄	—	3	2	no	—
518	C₂²⋊C₄	—	3	2	no	—
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	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
525	C₄²	—	3	1	no	—
526	C₄²	—	3	1	no	—
527	C₄²	—	3	1	no	—
528	C₄²	—	3	2	no	—
529	C₄²	C₂²×D₃	1	1	yes	characteristic
530	C₄²	C₂²×D₃	1	1	yes	characteristic
531	C₄²	C₂²×D₃	1	1	yes	characteristic
532	C₄²	C₂²×D₃	1	2	yes	—
533	C₂²×C₃	—	2	2	no	—
534	C₂²×C₃	—	2	2	no	—
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	C₂⁵	1	1	yes	characteristic
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	1	no	—
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	2	1	no	—
544	C₂×D₃	—	2	2	no	—
545	C₂×D₃	—	2	2	no	—
546	C₂×D₃	—	2	2	no	—
547	C₂×D₃	—	2	1	no	—
548	C₂×D₃	—	2	2	no	—
549	C₂×D₃	—	2	1	no	—
550	C₂×D₃	—	2	2	no	—
551	C₂×D₃	—	2	1	no	—
552	C₂×D₃	—	2	1	no	—
553	C₂×D₃	—	2	2	no	—
554	C₂×D₃	—	8	4	no	—
555	C₂×D₃	—	8	4	no	—
556	C₂×D₃	—	8	4	no	—
557	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
558	C₃×C₄	—	2	2	no	—
559	C₃×C₄	—	2	2	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
567	Dic₃	—	2	2	no	—
568	Dic₃	—	2	1	no	—
569	Dic₃	—	2	1	no	—
570	Dic₃	—	2	2	no	—
571	Dic₃	—	2	1	no	—
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	C₂³	—	3	1	no	—
575	C₂³	—	3	1	no	—
576	C₂³	—	3	1	no	—
577	C₂³	—	3	2	no	—
578	C₂³	—	3	2	no	—
579	C₂³	—	6	4	no	—
580	C₂³	—	12	2	no	—
581	C₂³	—	12	2	no	—
582	C₂³	—	12	2	no	—
583	C₂³	—	12	2	no	—
584	C₂³	—	12	2	no	—
585	C₂³	—	12	2	no	—
586	C₂³	—	12	2	no	—
587	C₂³	—	12	2	no	—
588	C₂³	C₂³×D₃	1	2	yes	—
589	C₂³	C₂³×D₃	1	2	yes	—
590	Q₈	—	2	2	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	6	2	no	—
593	Q₈	—	12	2	no	—
594	Q₈	—	12	2	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	6	2	no	—
600	D₄	—	6	2	no	—
601	D₄	—	6	4	no	—
602	D₄	—	6	4	no	—
603	D₄	—	6	2	no	—
604	D₄	—	6	2	no	—
605	D₄	—	12	2	no	—
606	D₄	—	12	2	no	—
607	D₄	—	12	2	no	—
608	D₄	—	12	1	no	—
609	D₄	—	12	2	no	—
610	D₄	—	12	2	no	—
611	D₄	—	12	2	no	—
612	D₄	—	12	2	no	—
613	D₄	—	12	2	no	—
614	D₄	—	12	2	no	—
615	D₄	—	12	2	no	—
616	D₄	—	12	2	no	—
617	C₂×C₄	—	3	1	no	—
618	C₂×C₄	—	3	1	no	—
619	C₂×C₄	—	3	1	no	—
620	C₂×C₄	—	3	2	no	—
621	C₂×C₄	—	3	2	no	—
622	C₂×C₄	—	3	1	no	—
623	C₂×C₄	—	3	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	6	2	no	—
627	C₂×C₄	—	6	2	no	—
628	C₂×C₄	—	6	2	no	—
629	C₂×C₄	—	6	2	no	—
630	C₂×C₄	—	12	2	no	—
631	C₂×C₄	—	12	2	no	—
632	C₂×C₄	—	12	2	no	—
633	C₂×C₄	—	12	2	no	—
634	C₂×C₄	—	12	1	no	—
635	C₂×C₄	—	12	2	no	—
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	1	yes	characteristic
640	C₂×C₄	C₂³×D₃	1	2	yes	—
641	C₂×C₄	C₂³×D₃	1	2	yes	—
642	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
643	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
644	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
645	C₂×C₃	—	4	2	no	—
646	C₂×C₃	—	4	2	no	—
647	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂×C₃	#585	1	1	yes	characteristic
650	D₃	—	2	2	no	—
651	D₃	—	4	2	no	—
652	D₃	—	4	1	no	—
653	D₃	—	4	1	no	—
654	D₃	—	4	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	3	2	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	—	6	1	no	—
665	C₂²	—	6	1	no	—
666	C₂²	—	6	2	no	—
667	C₂²	—	6	2	no	—
668	C₂²	—	6	2	no	—
669	C₂²	—	6	1	no	—
670	C₂²	—	6	1	no	—
671	C₂²	—	6	2	no	—
672	C₂²	—	6	2	no	—
673	C₂²	—	6	2	no	—
674	C₂²	—	6	1	no	—
675	C₂²	—	6	1	no	—
676	C₂²	—	24	4	no	—
677	C₂²	—	24	4	no	—
678	C₂²	—	24	4	no	—
679	C₂²	C₂⁴×D₃	1	1	yes	characteristic
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	6	1	no	—
689	C₄	—	6	1	no	—
690	C₄	—	6	1	no	—
691	C₄	—	6	2	no	—
692	C₄	—	6	1	no	—
693	C₄	—	6	1	no	—
694	C₄	—	6	2	no	—
695	C₄	#1009	1	2	yes	—
696	C₃	#3558	1	1	yes	characteristic, complemented, Sylow
697	C₂	—	4	2	no	—
698	C₂	—	4	2	no	—
699	C₂	—	6	2	no	—
700	C₂	—	12	1	no	—
701	C₂	—	12	1	no	—
702	C₂	—	12	2	no	—
703	C₂	—	12	2	no	—
704	C₂	C₂×#1009	1	1	yes	characteristic
705	C₂	#5964	1	1	yes	characteristic
706	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#559	C₂
hypercenter	#559	D₃
hypocenter	C₃	#3558
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. C₃×#559	C₂	semidirect
2. #5717	C₂	semidirect
3. #5715	C₂	semidirect
4. #5683	C₂	semidirect
5. #5678	C₂	semidirect
6. #5677	C₂	semidirect
7. #5676	C₂	semidirect
8. #5674	C₂	semidirect
9. D₃×#124	C₂	semidirect
10. #5667	C₂	semidirect
11. #5657	C₂	semidirect
12. #5654	C₂	semidirect
13. #5653	C₂	semidirect
14. #5585	C₂	semidirect
15. #5582	C₂	semidirect
16. #5580	C₂	semidirect
17. #5576	C₂	semidirect
18. #5561	C₂	semidirect
19. #5560	C₂	semidirect
20. #5554	C₂	semidirect
21. #5550	C₂	semidirect
22. D₄×D₁₂	C₂	semidirect
23. #5548	C₂	semidirect
25. C₂×#239	C₂²	semidirect
26. C₂×D₃×Q₈	C₂²	semidirect
27. C₂×#237	C₂²	semidirect
29. C₂×D₃×D₄	C₂²	semidirect
30. C₂×D₃×D₄	C₂²	semidirect
31. C₂×D₃×D₄	C₂²	semidirect
32. C₂×#235	C₂²	semidirect
33. C₂²×D₁₂	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
36. C₃×#124	C₂²	semidirect
37. C₃×#124	C₂²	semidirect
38. C₃×#123	C₂²	semidirect
39. C₃×#123	C₂²	semidirect
40. C₃×C₄×Q₈	C₂²	semidirect
41. C₃×C₄×Q₈	C₂²	semidirect
42. C₃×C₄×D₄	C₂²	semidirect
43. C₃×C₄×D₄	C₂²	semidirect
44. C₃×C₄×D₄	C₂²	semidirect
45. #947	C₂²	semidirect
46. #947	C₂²	semidirect
47. #947	C₂²	semidirect
48. #946	C₂²	semidirect
49. #946	C₂²	semidirect
50. #940	C₂²	semidirect
51. #939	C₂²	semidirect
52. #939	C₂²	semidirect
54. #938	C₂²	semidirect
55. #938	C₂²	semidirect
56. #937	C₂²	semidirect
57. #937	C₂²	semidirect
58. #937	C₂²	semidirect
59. #937	C₂²	semidirect
60. #936	C₂²	semidirect
61. #930	C₂²	semidirect
62. #930	C₂²	semidirect
63. #929	C₂²	semidirect
64. C₄×#67	C₂²	semidirect
65. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
66. #924	C₂²	semidirect
67. #898	C₂²	semidirect
68. #898	C₂²	semidirect
69. #897	C₂²	semidirect
70. #897	C₂²	semidirect
71. #896	C₂²	semidirect
74. #895	C₂²	semidirect
75. #895	C₂²	semidirect
76. #894	C₂²	semidirect
77. #894	C₂²	semidirect
78. #894	C₂²	semidirect
79. #894	C₂²	semidirect
80. #894	C₂²	semidirect
81. #893	C₂²	semidirect
82. #890	C₂²	semidirect
83. #888	C₂²	semidirect
84. #886	C₂²	semidirect
85. #885	C₂²	semidirect
86. #885	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
89. #885	C₂²	semidirect
90. #884	C₂²	semidirect
91. #884	C₂²	semidirect
92. #884	C₂²	semidirect
93. #884	C₂²	semidirect
94. #884	C₂²	semidirect
95. #883	C₂²	semidirect
96. #882	C₂²	semidirect
97. #882	C₂²	semidirect
98. #882	C₂²	semidirect
99. #882	C₂²	semidirect
100. #882	C₂²	semidirect
101. #882	C₂²	semidirect
102. #67⋊C₄	C₂²	semidirect
103. D₃×C₂²⋊C₄	C₂²	semidirect
104. D₃×C₂²⋊C₄	C₂²	semidirect
105. D₃×C₂²⋊C₄	C₂²	semidirect
106. #879	C₂²	semidirect
107. #878	C₂²	semidirect
108. #876	C₂²	semidirect
109. #875	C₂²	semidirect
110. #875	C₂²	semidirect
111. #875	C₂²	semidirect
112. #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. C₄²×D₃	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
127. #559	D₃	semidirect
286. #124	C₂×D₃	semidirect
287. #124	C₂×D₃	semidirect
288. #124	C₂×D₃	semidirect
297. #123	C₂×D₃	semidirect
298. #123	C₂×D₃	semidirect
333. C₄×Q₈	C₂×D₃	semidirect
334. C₄×Q₈	C₂×D₃	semidirect
344. C₄×D₄	C₂×D₃	semidirect
345. C₄×D₄	C₂×D₃	semidirect
346. C₄×D₄	C₂×D₃	semidirect
696. C₃	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₃×#559	2
#5717	2
#5715	2
#5683	2
#5678	2
#5677	2
#5676	2
#5674	2
D₃×#124	2
#5667	2
#5657	2
#5654	2
#5653	2
#5585	2
#5582	2
#5580	2
#5576	2
#5561	2
#5560	2
#5554	2
#5550	2
D₄×D₁₂	2
#5548	2
#3558	3