Subgroups — #86827

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×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#5706	C₂	1	2	yes	maximal, complemented
3	#5705	C₂	1	2	yes	maximal, complemented
4	#5695	C₂	1	1	yes	maximal, characteristic, complemented
5	#5693	C₂	1	2	yes	maximal, complemented
6	#5691	C₂	1	2	yes	maximal, complemented
7	#5688	C₂	1	1	yes	maximal, characteristic, complemented
8	#5654	C₂	1	2	yes	maximal, complemented
9	#5649	C₂	1	2	yes	maximal, complemented
10	#5641	C₂	1	1	yes	maximal, characteristic, complemented
11	#5635	C₂	1	1	yes	maximal, characteristic, complemented
12	#5627	C₂	1	1	yes	maximal, characteristic, complemented
13	#5627	C₂	1	1	yes	maximal, characteristic, complemented
14	#5581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
16	#5565	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	#5532	C₂	1	1	yes	maximal, characteristic, complemented
19	#5527	C₂	1	2	yes	maximal, complemented
20	#5522	C₂	1	2	yes	maximal, complemented
21	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
22	#5507	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#892	C₂	1	1	yes	maximal, characteristic, complemented
24	#3475	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×#235	C₂²	1	2	yes	—
28	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
30	C₃×#126	C₂²	1	2	yes	complemented
31	C₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃×#125	C₂²	1	2	yes	complemented
33	C₃×#123	C₂²	1	2	yes	—
34	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×#117	C₂²	1	1	yes	characteristic, complemented
39	C₃×#117	C₂²	1	2	yes	complemented
40	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	#939	C₂²	1	2	yes	—
45	D₄×Dic₃	C₂²	1	1	yes	characteristic
46	#930	C₂²	1	1	yes	characteristic, complemented
47	#930	C₂²	1	1	yes	characteristic, complemented
48	#929	C₂²	1	2	yes	complemented
49	C₄×#67	C₂²	1	1	yes	characteristic
50	C₄×#67	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
52	#926	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
55	#898	C₂²	1	2	yes	complemented
56	#898	C₂²	1	2	yes	complemented
57	#898	C₂²	1	2	yes	complemented
58	#897	C₂²	1	2	yes	complemented
59	#896	C₂²	1	2	yes	—
60	#896	C₂²	1	2	yes	—
61	#896	C₂²	1	2	yes	complemented
62	#895	C₂²	1	2	yes	—
63	#895	C₂²	1	1	yes	characteristic, complemented
64	#895	C₂²	1	1	yes	characteristic, complemented
65	#894	C₂²	1	2	yes	—
66	#894	C₂²	1	2	yes	—
67	#894	C₂²	1	2	yes	—
68	#894	C₂²	1	2	yes	complemented
69	#894	C₂²	1	2	yes	complemented
70	#893	C₂²	1	2	yes	—
71	#893	C₂²	1	1	yes	characteristic
72	#893	C₂²	1	2	yes	complemented
73	#893	C₂²	1	2	yes	complemented
74	#893	C₂²	1	2	yes	complemented
75	#893	C₂²	1	1	yes	characteristic, complemented
76	#892	C₂²	1	1	yes	characteristic
77	#892	C₂²	1	1	yes	characteristic
78	#892	C₂²	1	2	yes	—
79	#892	C₂²	1	1	yes	characteristic
80	#892	C₂²	1	1	yes	characteristic, complemented
81	#892	C₂²	1	2	yes	complemented
82	#892	C₂²	1	2	yes	complemented
83	#892	C₂²	1	1	yes	characteristic, complemented
84	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
85	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	#889	C₂²	1	2	yes	complemented
88	#889	C₂²	1	2	yes	complemented
89	#888	C₂²	1	1	yes	characteristic, complemented
90	#888	C₂²	1	1	yes	characteristic, complemented
91	#887	C₂²	1	2	yes	complemented
92	#887	C₂²	1	2	yes	complemented
93	#887	C₂²	1	2	yes	complemented
94	#885	C₂²	1	2	yes	—
95	#885	C₂²	1	2	yes	complemented
96	#884	C₂²	1	2	yes	—
97	#883	C₂²	1	2	yes	complemented
98	#882	C₂²	1	2	yes	—
99	#882	C₂²	1	2	yes	—
100	#67⋊C₄	C₂²	1	2	yes	—
101	#67⋊C₄	C₂²	1	1	yes	characteristic
102	#67⋊C₄	C₂²	1	1	yes	characteristic
103	#67⋊C₄	C₂²	1	2	yes	complemented
104	#67⋊C₄	C₂²	1	2	yes	complemented
105	#67⋊C₄	C₂²	1	2	yes	complemented
106	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
108	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
109	#879	C₂²	1	2	yes	complemented
110	#878	C₂²	1	2	yes	complemented
111	#877	C₂²	1	2	yes	complemented
112	#876	C₂²	1	2	yes	complemented
113	#875	C₂²	1	2	yes	complemented
114	C₄×D₁₂	C₂²	1	1	yes	characteristic
115	C₄×D₁₂	C₂²	1	2	yes	—
116	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
117	#872	C₂²	1	2	yes	—
118	#872	C₂²	1	2	yes	complemented
119	#872	C₂²	1	2	yes	complemented
120	C₄²×D₃	C₂²	1	1	yes	characteristic
121	C₄²×D₃	C₂²	1	2	yes	complemented
122	C₄²×D₃	C₂²	1	2	yes	complemented
123	#870	C₂²	1	1	yes	characteristic, 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	D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
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	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂³	1	2	yes	—
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂×#67	C₂³	1	1	yes	characteristic
155	C₂×#67	C₂³	1	2	yes	—
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	1	yes	characteristic
158	C₂²×Dic₃	C₂³	1	1	yes	characteristic
159	C₂²×Dic₃	C₂³	1	1	yes	characteristic
160	C₂²×Dic₃	C₂³	1	2	yes	—
161	#239	—	2	4	no	—
162	D₃×D₄	—	2	4	no	—
163	#235	—	2	8	no	—
164	C₂×D₁₂	C₂³	1	2	yes	—
165	C₂×D₁₂	C₂³	1	1	yes	characteristic
166	C₂×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×D₁₂	C₂³	1	2	yes	—
168	C₂×D₁₂	C₂³	1	2	yes	—
169	C₂×C₄×D₃	—	2	4	no	—
170	C₂×C₄×D₃	—	2	4	no	—
171	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₃	C₂³	1	2	yes	—
174	C₂×C₄×D₃	C₂³	1	2	yes	—
175	C₂×C₄×D₃	C₂³	1	2	yes	—
176	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₄×D₃	C₂³	1	2	yes	—
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
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	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₃×C₄²	C₂³	1	2	yes	—
204	C₃×C₄²	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	1	yes	characteristic
208	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	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	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
241	C₄×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×Dic₃	C₂³	1	1	yes	characteristic
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	2	yes	—
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₂×#41	—	3	1	no	—
252	C₂×#41	—	3	2	no	—
253	C₂²×D₄	—	3	1	no	—
254	C₂³×C₄	—	3	1	no	—
255	C₂³×C₄	—	3	1	no	—
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	C₂×D₃	1	2	yes	complemented
264	#125	—	3	2	no	—
265	#125	—	3	2	no	—
266	#125	—	3	1	no	—
267	#125	C₂×D₃	1	2	yes	complemented
268	#125	C₂×D₃	1	1	yes	characteristic, complemented
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	2	no	—
290	#121	—	3	1	no	—
291	#121	—	3	1	no	—
292	#121	—	3	1	no	—
293	#121	—	3	1	no	—
294	#121	—	3	2	no	—
295	#121	—	3	2	no	—
296	#120	—	3	2	no	—
297	#120	—	3	2	no	—
298	C₄×Q₈	—	3	1	no	—
299	C₄×Q₈	—	3	2	no	—
300	C₄×Q₈	—	3	2	no	—
301	C₄×Q₈	—	3	2	no	—
302	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
303	C₄×D₄	—	3	1	no	—
304	C₄×D₄	—	3	1	no	—
305	C₄×D₄	—	3	1	no	—
306	C₄×D₄	—	3	1	no	—
307	C₄×D₄	—	3	2	no	—
308	C₄×D₄	—	3	2	no	—
309	C₄×D₄	—	3	1	no	—
310	C₄×D₄	—	3	2	no	—
311	C₄×D₄	—	3	2	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	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	C₂×D₃	1	1	yes	characteristic
322	#117	—	3	1	no	—
323	#117	—	3	1	no	—
324	#117	—	3	1	no	—
325	#117	—	3	1	no	—
326	#117	—	3	2	no	—
327	#117	—	3	2	no	—
328	#117	—	3	1	no	—
329	#117	—	3	1	no	—
330	#117	—	3	2	no	—
331	#117	—	3	2	no	—
332	#117	—	3	2	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	C₂×D₃	1	1	yes	characteristic, complemented
336	#117	C₂×D₃	1	2	yes	complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	1	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	—	3	2	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	2	no	—
350	C₂³×C₃	C₂⁴	1	1	yes	characteristic
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₃	—	2	2	no	—
353	C₂²×D₃	—	2	2	no	—
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	4	1	no	—
357	C₂²×D₃	—	4	1	no	—
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₃	C₂⁴	1	2	yes	—
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	2	no	—
364	C₂×C₃×C₄	—	2	4	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	C₂⁴	1	2	yes	—
368	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴	1	2	yes	—
371	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	4	no	—
377	#67	—	2	2	no	—
378	#67	—	4	2	no	—
379	#67	#41	1	4	yes	complemented
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	2	2	no	—
382	C₂×Dic₃	—	4	2	no	—
383	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₃	C₂⁴	1	2	yes	—
385	C₂×Dic₃	C₂⁴	1	2	yes	—
386	C₂×Dic₃	C₂⁴	1	2	yes	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
391	D₁₂	—	2	4	no	—
392	D₁₂	—	2	2	no	—
393	D₁₂	—	2	4	no	—
394	D₁₂	—	2	2	no	—
395	D₁₂	—	4	2	no	—
396	C₄×D₃	—	2	2	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	—	2	4	no	—
399	C₄×D₃	—	2	2	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	4	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	4	no	—
406	C₄×D₃	—	4	1	no	—
407	C₄×D₃	—	4	2	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	#41	1	4	yes	complemented
410	Dic₆	—	2	4	no	—
411	Dic₆	—	4	2	no	—
412	C₂⁴	—	3	1	no	—
413	C₂⁴	—	3	1	no	—
414	#41	—	6	8	no	—
415	#41	—	6	4	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	2	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	6	4	no	—
429	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	—	3	1	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	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	6	4	no	—
448	C₂²×C₄	—	6	4	no	—
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	2	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	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	C₂²×D₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₃	1	2	yes	—
473	C₄⋊C₄	C₂²×D₃	1	2	yes	—
474	C₄⋊C₄	C₂²×D₃	1	2	yes	—
475	C₄⋊C₄	C₂²×D₃	1	2	yes	—
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	1	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	1	no	—
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	1	no	—
488	C₂²⋊C₄	—	3	1	no	—
489	C₂²⋊C₄	—	3	1	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	2	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	1	yes	characteristic
500	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
501	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
503	C₄²	—	3	2	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	2	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	2	no	—
508	C₄²	—	3	2	no	—
509	C₄²	—	3	2	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	2	no	—
513	C₄²	C₂²×D₃	1	2	yes	—
514	C₄²	C₂²×D₃	1	2	yes	—
515	C₄²	C₂²×D₃	1	1	yes	characteristic
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	1	no	—
521	C₂²×C₃	C₂×#41	1	2	yes	—
522	C₂²×C₃	C₂⁵	1	1	yes	characteristic
523	C₂×D₃	—	2	1	no	—
524	C₂×D₃	—	2	1	no	—
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	2	no	—
529	C₂×D₃	—	2	2	no	—
530	C₂×D₃	—	2	1	no	—
531	C₂×D₃	—	2	2	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	4	4	no	—
534	C₂×D₃	—	4	4	no	—
535	C₂×D₃	C₂×#41	1	2	yes	—
536	C₂×D₃	C₂×#41	1	2	yes	—
537	C₃×C₄	—	2	2	no	—
538	C₃×C₄	—	2	2	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	1	no	—
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	C₂×#41	1	2	yes	—
546	Dic₃	—	2	2	no	—
547	Dic₃	—	2	1	no	—
548	Dic₃	—	2	1	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	2	no	—
552	Dic₃	C₂×#41	1	2	yes	—
553	Dic₃	C₂×#41	1	2	yes	—
554	C₂³	—	3	1	no	—
555	C₂³	—	3	1	no	—
556	C₂³	—	3	1	no	—
557	C₂³	—	3	2	no	—
558	C₂³	—	6	2	no	—
559	C₂³	—	6	2	no	—
560	C₂³	—	6	2	no	—
561	C₂³	—	6	2	no	—
562	C₂³	—	12	1	no	—
563	C₂³	—	12	1	no	—
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	2	no	—
570	D₄	—	3	4	no	—
571	D₄	—	6	2	no	—
572	D₄	—	6	4	no	—
573	D₄	—	6	4	no	—
574	D₄	—	6	2	no	—
575	D₄	—	6	4	no	—
576	D₄	—	6	2	no	—
577	D₄	—	12	2	no	—
578	D₄	—	12	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	4	no	—
585	C₂×C₄	—	3	1	no	—
586	C₂×C₄	—	3	2	no	—
587	C₂×C₄	—	3	1	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	6	2	no	—
593	C₂×C₄	—	6	2	no	—
594	C₂×C₄	—	6	4	no	—
595	C₂×C₄	—	6	4	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	2	no	—
598	C₂×C₄	—	6	4	no	—
599	C₂×C₄	—	6	2	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	—	6	2	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	12	2	no	—
604	C₂×C₄	—	12	1	no	—
605	C₂×C₄	—	12	2	no	—
606	C₂×C₄	—	12	2	no	—
607	C₂×C₄	C₂³×D₃	1	2	yes	—
608	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₃	1	2	yes	—
610	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
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	—	4	1	no	—
618	C₂×C₃	C₂²×#41	1	1	yes	characteristic
619	C₂×C₃	C₂²×#41	1	1	yes	characteristic
620	C₂×C₃	#585	1	1	yes	characteristic
621	D₃	—	2	2	no	—
622	D₃	—	2	2	no	—
623	D₃	—	4	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	—	3	2	no	—
631	C₂²	—	3	2	no	—
632	C₂²	—	6	1	no	—
633	C₂²	—	6	1	no	—
634	C₂²	—	6	1	no	—
635	C₂²	—	6	1	no	—
636	C₂²	—	6	1	no	—
637	C₂²	—	6	2	no	—
638	C₂²	—	6	2	no	—
639	C₂²	—	6	1	no	—
640	C₂²	—	6	2	no	—
641	C₂²	—	6	1	no	—
642	C₂²	—	12	4	no	—
643	C₂²	—	12	4	no	—
644	C₂²	D₃×#41	1	2	yes	—
645	C₂²	C₂⁴×D₃	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	3	2	no	—
655	C₄	—	3	2	no	—
656	C₄	—	6	1	no	—
657	C₄	—	6	1	no	—
658	C₄	—	6	2	no	—
659	C₄	—	6	2	no	—
660	C₄	—	6	2	no	—
661	C₄	—	6	1	no	—
662	C₄	D₃×#41	1	2	yes	—
663	C₃	#3475	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	6	2	no	—
667	C₂	—	6	2	no	—
668	C₂	—	12	1	no	—
669	C₂	—	12	2	no	—
670	C₂	C₂×D₃×#41	1	1	yes	characteristic
671	C₂	C₂×D₃×#41	1	1	yes	characteristic
672	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#552	C₂
hypercenter	#552	D₃
hypocenter	C₃	#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₃×#552	C₂	semidirect
2. #5706	C₂	semidirect
3. #5705	C₂	semidirect
4. #5695	C₂	semidirect
5. #5693	C₂	semidirect
6. #5691	C₂	semidirect
7. #5688	C₂	semidirect
8. #5654	C₂	semidirect
9. #5649	C₂	semidirect
10. #5641	C₂	semidirect
11. #5635	C₂	semidirect
12. #5627	C₂	semidirect
13. #5627	C₂	semidirect
14. #5581	C₂	semidirect
15. C₄×#239	C₂	semidirect
16. #5565	C₂	semidirect
17. C₄×D₃×D₄	C₂	semidirect
18. #5532	C₂	semidirect
19. #5527	C₂	semidirect
20. #5522	C₂	semidirect
21. D₃×#117	C₂	semidirect
22. #5507	C₂	semidirect
23. C₂×#892	C₂	semidirect
30. C₃×#126	C₂²	semidirect
31. C₃×#125	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
35. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×#117	C₂²	semidirect
39. C₃×#117	C₂²	semidirect
40. C₂×C₃×C₄⋊C₄	C₂²	semidirect
41. #946	C₂²	semidirect
42. #946	C₂²	semidirect
43. Q₈×Dic₃	C₂²	semidirect
46. #930	C₂²	semidirect
47. #930	C₂²	semidirect
48. #929	C₂²	semidirect
52. #926	C₂²	semidirect
53. C₂×C₄⋊Dic₃	C₂²	semidirect
54. C₂×C₄×Dic₃	C₂²	semidirect
55. #898	C₂²	semidirect
56. #898	C₂²	semidirect
57. #898	C₂²	semidirect
58. #897	C₂²	semidirect
61. #896	C₂²	semidirect
63. #895	C₂²	semidirect
64. #895	C₂²	semidirect
68. #894	C₂²	semidirect
69. #894	C₂²	semidirect
72. #893	C₂²	semidirect
73. #893	C₂²	semidirect
74. #893	C₂²	semidirect
75. #893	C₂²	semidirect
80. #892	C₂²	semidirect
81. #892	C₂²	semidirect
82. #892	C₂²	semidirect
83. #892	C₂²	semidirect
85. D₃×C₄⋊C₄	C₂²	semidirect
86. D₃×C₄⋊C₄	C₂²	semidirect
87. #889	C₂²	semidirect
88. #889	C₂²	semidirect
89. #888	C₂²	semidirect
90. #888	C₂²	semidirect
91. #887	C₂²	semidirect
92. #887	C₂²	semidirect
93. #887	C₂²	semidirect
95. #885	C₂²	semidirect
97. #883	C₂²	semidirect
103. #67⋊C₄	C₂²	semidirect
104. #67⋊C₄	C₂²	semidirect
105. #67⋊C₄	C₂²	semidirect
109. #879	C₂²	semidirect
110. #878	C₂²	semidirect
111. #877	C₂²	semidirect
112. #876	C₂²	semidirect
113. #875	C₂²	semidirect
116. C₄×D₁₂	C₂²	semidirect
118. #872	C₂²	semidirect
119. #872	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. C₄²×D₃	C₂²	semidirect
123. #870	C₂²	semidirect
131. #552	D₃	semidirect
263. #126	C₂×D₃	semidirect
267. #125	C₂×D₃	semidirect
268. #125	C₂×D₃	semidirect
287. C₂²⋊Q₈	C₂×D₃	semidirect
288. C₂²⋊Q₈	C₂×D₃	semidirect
302. C₄×Q₈	C₂×D₃	semidirect
335. #117	C₂×D₃	semidirect
336. #117	C₂×D₃	semidirect
341. C₂×C₄⋊C₄	C₂×D₃	semidirect
379. #67	#41	semidirect
409. C₄×D₃	#41	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×#552	2
#5706	2
#5705	2
#5695	2
#5693	2
#5691	2
#5688	2
#5654	2
#5649	2
#5641	2
#5635	2
#5627	2
#5581	2
C₄×#239	2
#5565	2
C₄×D₃×D₄	2
#5532	2
#5527	2
#5522	2
D₃×#117	2
#5507	2
C₂×#892	2
#3475	3