Subgroups — #86551

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#5729	C₂	1	1	yes	maximal, characteristic, complemented
3	#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	#5708	C₂	1	2	yes	maximal, complemented
5	#5708	C₂	1	2	yes	maximal, complemented
6	#5680	C₂	1	1	yes	maximal, characteristic, complemented
7	#5679	C₂	1	2	yes	maximal, complemented
8	#5675	C₂	1	1	yes	maximal, characteristic, complemented
9	#5671	C₂	1	2	yes	maximal, complemented
10	#5659	C₂	1	2	yes	maximal, complemented
11	#5650	C₂	1	2	yes	maximal, complemented
12	#5639	C₂	1	2	yes	maximal, complemented
13	#5636	C₂	1	2	yes	maximal, complemented
14	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#5625	C₂	1	1	yes	maximal, characteristic, complemented
16	#5606	C₂	1	1	yes	maximal, characteristic
17	#5603	C₂	1	1	yes	maximal, characteristic, complemented
18	#5578	C₂	1	1	yes	maximal, characteristic, complemented
19	#5572	C₂	1	1	yes	maximal, characteristic, complemented
20	#5557	C₂	1	1	yes	maximal, characteristic, complemented
21	#5546	C₂	1	1	yes	maximal, characteristic, complemented
22	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	#5518	C₂	1	1	yes	maximal, characteristic, complemented
24	#3495	—	3	1	no	maximal, Sylow
25	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×#237	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#126	C₂²	1	2	yes	complemented
30	C₃×#124	C₂²	1	2	yes	—
31	C₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₃×#123	C₂²	1	2	yes	—
33	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×#117	C₂²	1	1	yes	characteristic
39	#946	C₂²	1	2	yes	—
40	#946	C₂²	1	2	yes	—
41	#946	C₂²	1	1	yes	characteristic
42	Q₈×Dic₃	C₂²	1	2	yes	complemented
43	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	#944	C₂²	1	2	yes	complemented
45	#944	C₂²	1	1	yes	characteristic, complemented
46	#938	C₂²	1	1	yes	characteristic
47	#937	C₂²	1	2	yes	—
48	#936	C₂²	1	2	yes	—
49	#936	C₂²	1	1	yes	characteristic, complemented
50	#935	C₂²	1	2	yes	—
51	D₄×Dic₃	C₂²	1	2	yes	—
52	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₄×#67	C₂²	1	2	yes	—
54	C₄×#67	C₂²	1	2	yes	—
55	#926	C₂²	1	1	yes	characteristic
56	#926	C₂²	1	2	yes	complemented
57	#924	C₂²	1	1	yes	characteristic
58	#924	C₂²	1	1	yes	characteristic
59	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
60	#897	C₂²	1	1	yes	characteristic
61	#897	C₂²	1	1	yes	characteristic
62	#896	C₂²	1	2	yes	—
63	#896	C₂²	1	2	yes	—
64	#896	C₂²	1	2	yes	—
65	#892	C₂²	1	1	yes	characteristic
66	#892	C₂²	1	2	yes	—
67	#892	C₂²	1	2	yes	—
68	#892	C₂²	1	1	yes	characteristic
69	#892	C₂²	1	1	yes	characteristic
70	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	D₃×C₄⋊C₄	C₂²	1	2	yes	—
72	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	#890	C₂²	1	2	yes	complemented
75	#890	C₂²	1	2	yes	complemented
76	#890	C₂²	1	1	yes	characteristic, complemented
77	#889	C₂²	1	2	yes	complemented
78	#889	C₂²	1	2	yes	complemented
79	#889	C₂²	1	2	yes	complemented
80	#889	C₂²	1	2	yes	complemented
81	#889	C₂²	1	2	yes	complemented
82	#888	C₂²	1	1	yes	characteristic, complemented
83	#887	C₂²	1	2	yes	complemented
84	#887	C₂²	1	1	yes	characteristic, complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#883	C₂²	1	2	yes	—
87	#883	C₂²	1	2	yes	—
88	#883	C₂²	1	2	yes	—
89	#883	C₂²	1	2	yes	—
90	#883	C₂²	1	2	yes	—
91	#67⋊C₄	C₂²	1	2	yes	—
92	#67⋊C₄	C₂²	1	2	yes	—
93	#67⋊C₄	C₂²	1	2	yes	—
94	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
95	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
97	#879	C₂²	1	2	yes	—
98	#879	C₂²	1	2	yes	—
99	#879	C₂²	1	2	yes	—
100	#879	C₂²	1	2	yes	—
101	#879	C₂²	1	2	yes	complemented
102	#879	C₂²	1	2	yes	complemented
103	#879	C₂²	1	2	yes	complemented
104	#878	C₂²	1	2	yes	—
105	#878	C₂²	1	2	yes	complemented
106	#878	C₂²	1	2	yes	complemented
107	#878	C₂²	1	2	yes	complemented
108	#877	C₂²	1	1	yes	characteristic
109	#877	C₂²	1	1	yes	characteristic
110	#877	C₂²	1	2	yes	complemented
111	#877	C₂²	1	2	yes	complemented
112	#872	C₂²	1	1	yes	characteristic
113	#872	C₂²	1	2	yes	—
114	#872	C₂²	1	2	yes	—
115	#872	C₂²	1	1	yes	characteristic
116	C₄²×D₃	C₂²	1	1	yes	characteristic
117	C₄²×D₃	C₂²	1	1	yes	characteristic
118	#870	C₂²	1	1	yes	characteristic, complemented
119	#869	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₆	C₂²	1	2	yes	complemented
121	C₄×Dic₆	C₂²	1	2	yes	complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#556	—	3	2	no	—
125	#554	—	3	2	no	—
126	#552	—	3	2	no	—
127	#552	—	3	2	no	—
128	#552	—	3	2	no	—
129	#552	—	3	2	no	—
130	#551	—	3	2	no	—
131	#551	—	3	2	no	—
132	#544	—	3	1	no	—
133	#542	—	3	1	no	—
134	#542	D₃	1	1	yes	characteristic, complemented
135	#541	—	3	1	no	—
136	#541	—	3	1	no	—
137	#536	—	3	1	no	—
138	#533	—	3	1	no	—
139	#533	—	3	1	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	1	no	—
143	C₂×C₂²⋊Q₈	—	3	1	no	—
144	#520	—	3	1	no	—
145	#519	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	2	yes	—
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	2	yes	—
154	C₂×#67	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	2	yes	—
156	C₂²×Dic₃	C₂³	1	1	yes	characteristic
157	C₂²×Dic₃	C₂³	1	2	yes	—
158	C₂²×Dic₃	C₂³	1	2	yes	—
159	D₃×Q₈	—	2	4	no	—
160	#237	—	2	4	no	—
161	C₂×C₄×D₃	—	2	4	no	—
162	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂³	1	2	yes	—
166	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
172	C₂×Dic₆	C₂³	1	1	yes	characteristic
173	C₂×Dic₆	C₂³	1	1	yes	characteristic
174	C₂×Dic₆	C₂³	1	2	yes	—
175	C₂×Dic₆	C₂³	1	2	yes	—
176	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₃×C₄²	C₂³	1	2	yes	—
192	C₃×C₄²	C₂³	1	1	yes	characteristic
193	#217	C₂³	1	1	yes	characteristic
194	#217	C₂³	1	1	yes	characteristic
195	#217	C₂³	1	2	yes	—
196	#217	C₂³	1	2	yes	—
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₃	C₂³	1	2	yes	—
212	C₄⋊Dic₃	C₂³	1	2	yes	—
213	C₄⋊Dic₃	C₂³	1	2	yes	—
214	C₄⋊Dic₃	C₂³	1	2	yes	—
215	C₄⋊Dic₃	C₂³	1	2	yes	—
216	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	2	yes	—
218	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
219	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₃⋊C₄	C₂³	1	2	yes	—
221	Dic₃⋊C₄	C₂³	1	2	yes	—
222	Dic₃⋊C₄	C₂³	1	2	yes	—
223	Dic₃⋊C₄	C₂³	1	2	yes	—
224	Dic₃⋊C₄	C₂³	1	2	yes	—
225	Dic₃⋊C₄	C₂³	1	2	yes	—
226	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₄×Dic₃	C₂³	1	1	yes	characteristic
238	C₄×Dic₃	C₂³	1	2	yes	—
239	C₄×Dic₃	C₂³	1	2	yes	—
240	C₄×Dic₃	C₂³	1	2	yes	—
241	C₄×Dic₃	C₂³	1	2	yes	—
242	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	2	yes	—
249	C₂×#41	—	3	1	no	—
250	C₂²×Q₈	—	3	1	no	—
251	C₂³×C₄	—	3	1	no	—
252	C₄⋊Q₈	—	3	1	no	—
253	C₄⋊Q₈	—	3	2	no	—
254	C₄⋊Q₈	—	3	1	no	—
255	C₄⋊Q₈	—	3	1	no	—
256	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
257	#126	—	3	2	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	—	3	2	no	—
264	#126	C₂×D₃	1	2	yes	complemented
265	#125	—	3	1	no	—
266	#125	—	3	2	no	—
267	#125	—	3	2	no	—
268	#125	—	3	2	no	—
269	#125	—	3	2	no	—
270	#125	—	3	2	no	—
271	#125	—	3	2	no	—
272	#125	—	3	2	no	—
273	#125	—	3	1	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	C₂×D₃	1	2	yes	—
277	#124	C₂×D₃	1	1	yes	characteristic, 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	C₂×D₃	1	2	yes	—
285	C₂²⋊Q₈	—	3	1	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
300	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
301	#121	—	3	1	no	—
302	#121	C₂×D₃	1	1	yes	characteristic
303	#120	—	3	2	no	—
304	C₄×Q₈	—	3	1	no	—
305	C₄×Q₈	—	3	2	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	2	no	—
308	C₄×Q₈	—	3	1	no	—
309	C₄×Q₈	—	3	1	no	—
310	C₄×Q₈	—	3	2	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
314	C₄×D₄	—	3	1	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	2	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
322	#117	—	3	1	no	—
323	#117	—	3	2	no	—
324	#117	—	3	1	no	—
325	#117	—	3	1	no	—
326	#117	—	3	1	no	—
327	#117	—	3	2	no	—
328	#117	—	3	2	no	—
329	#117	—	3	1	no	—
330	#117	—	3	1	no	—
331	#117	—	3	2	no	—
332	#117	—	3	2	no	—
333	#117	—	3	1	no	—
334	#117	—	3	1	no	—
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	C₂×D₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	—	3	2	no	—
339	C₂×C₄⋊C₄	—	3	1	no	—
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	1	no	—
344	C₂×C₂²⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂³×C₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₃	C₂⁴	1	2	yes	—
350	C₂²×D₃	—	2	2	no	—
351	C₂²×D₃	—	2	2	no	—
352	C₂²×D₃	—	4	1	no	—
353	C₂²×D₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	C₂⁴	1	1	yes	characteristic
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	4	2	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	4	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	4	2	no	—
361	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂⁴	1	2	yes	—
364	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴	1	2	yes	—
367	C₂×C₃×C₄	C₂⁴	1	2	yes	—
368	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	#67	—	2	4	no	—
371	#67	—	2	4	no	—
372	C₂×Dic₃	—	2	2	no	—
373	C₂×Dic₃	—	2	4	no	—
374	C₂×Dic₃	—	4	2	no	—
375	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₃	C₂⁴	1	2	yes	—
379	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₃	C₂⁴	1	2	yes	—
381	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₃	C₂⁴	1	2	yes	—
383	C₂×Dic₃	C₂⁴	1	2	yes	—
384	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
385	C₄×D₃	—	2	2	no	—
386	C₄×D₃	—	2	4	no	—
387	C₄×D₃	—	2	2	no	—
388	C₄×D₃	—	2	2	no	—
389	C₄×D₃	—	2	2	no	—
390	C₄×D₃	—	2	2	no	—
391	C₄×D₃	—	4	1	no	—
392	C₄×D₃	—	4	2	no	—
393	C₄×D₃	—	4	1	no	—
394	C₄×D₃	#41	1	4	yes	—
395	Dic₆	—	2	2	no	—
396	Dic₆	—	2	2	no	—
397	Dic₆	—	2	4	no	—
398	Dic₆	—	4	2	no	—
399	C₂⁴	—	3	1	no	—
400	#41	—	6	4	no	—
401	C₂×Q₈	—	3	2	no	—
402	C₂×Q₈	—	3	1	no	—
403	C₂×Q₈	—	3	1	no	—
404	C₂×Q₈	—	3	2	no	—
405	C₂×Q₈	—	6	4	no	—
406	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
407	C₂×Q₈	C₂²×D₃	1	2	yes	—
408	C₂×D₄	—	3	2	no	—
409	C₂×D₄	—	3	2	no	—
410	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
411	C₂×D₄	C₂²×D₃	1	2	yes	—
412	C₂²×C₄	—	3	1	no	—
413	C₂²×C₄	—	3	2	no	—
414	C₂²×C₄	—	3	1	no	—
415	C₂²×C₄	—	3	2	no	—
416	C₂²×C₄	—	3	1	no	—
417	C₂²×C₄	—	3	1	no	—
418	C₂²×C₄	—	3	1	no	—
419	C₂²×C₄	—	3	2	no	—
420	C₂²×C₄	—	3	1	no	—
421	C₂²×C₄	—	3	1	no	—
422	C₂²×C₄	—	3	1	no	—
423	C₂²×C₄	—	3	1	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	6	4	no	—
426	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×D₃	1	2	yes	—
428	C₄⋊C₄	—	3	1	no	—
429	C₄⋊C₄	—	3	2	no	—
430	C₄⋊C₄	—	3	1	no	—
431	C₄⋊C₄	—	3	1	no	—
432	C₄⋊C₄	—	3	1	no	—
433	C₄⋊C₄	—	3	1	no	—
434	C₄⋊C₄	—	3	1	no	—
435	C₄⋊C₄	—	3	2	no	—
436	C₄⋊C₄	—	3	2	no	—
437	C₄⋊C₄	—	3	1	no	—
438	C₄⋊C₄	—	3	2	no	—
439	C₄⋊C₄	—	3	2	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	1	no	—
442	C₄⋊C₄	—	3	2	no	—
443	C₄⋊C₄	—	3	2	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	3	2	no	—
446	C₄⋊C₄	—	3	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×D₃	1	2	yes	—
460	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×D₃	1	2	yes	—
462	C₄⋊C₄	C₂²×D₃	1	2	yes	—
463	C₂²⋊C₄	—	3	1	no	—
464	C₂²⋊C₄	—	3	1	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	2	no	—
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	1	no	—
472	C₂²⋊C₄	—	3	1	no	—
473	C₂²⋊C₄	—	3	1	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	2	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
486	C₄²	—	3	1	no	—
487	C₄²	—	3	1	no	—
488	C₄²	—	3	1	no	—
489	C₄²	—	3	1	no	—
490	C₄²	—	3	1	no	—
491	C₄²	—	3	1	no	—
492	C₄²	—	3	2	no	—
493	C₄²	—	3	2	no	—
494	C₄²	—	3	2	no	—
495	C₄²	—	3	2	no	—
496	C₄²	—	3	2	no	—
497	C₄²	—	3	2	no	—
498	C₄²	C₂²×D₃	1	1	yes	characteristic
499	C₄²	C₂²×D₃	1	1	yes	characteristic
500	C₄²	C₂²×D₃	1	2	yes	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	1	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	C₂⁵	1	1	yes	characteristic
508	C₂×D₃	—	2	1	no	—
509	C₂×D₃	—	2	1	no	—
510	C₂×D₃	—	2	1	no	—
511	C₂×D₃	—	2	1	no	—
512	C₂×D₃	—	4	4	no	—
513	C₂×D₃	C₂×#41	1	2	yes	—
514	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	C₂×#41	1	2	yes	—
524	Dic₃	—	2	2	no	—
525	Dic₃	—	2	2	no	—
526	Dic₃	—	2	1	no	—
527	Dic₃	—	2	1	no	—
528	Dic₃	—	2	1	no	—
529	Dic₃	—	2	2	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	2	no	—
532	Dic₃	—	2	1	no	—
533	Dic₃	C₂×#41	1	2	yes	—
534	C₂³	—	3	1	no	—
535	C₂³	—	3	1	no	—
536	C₂³	—	6	2	no	—
537	C₂³	—	6	2	no	—
538	C₂³	—	12	1	no	—
539	C₂³	C₂³×D₃	1	1	yes	characteristic
540	C₂³	C₂³×D₃	1	2	yes	—
541	Q₈	—	2	2	no	—
542	Q₈	—	4	2	no	—
543	Q₈	—	6	4	no	—
544	Q₈	—	6	2	no	—
545	Q₈	—	6	2	no	—
546	Q₈	—	12	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	6	4	no	—
550	D₄	—	6	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	3	1	no	—
553	C₂×C₄	—	3	4	no	—
554	C₂×C₄	—	3	1	no	—
555	C₂×C₄	—	3	1	no	—
556	C₂×C₄	—	3	1	no	—
557	C₂×C₄	—	3	2	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	3	2	no	—
560	C₂×C₄	—	3	1	no	—
561	C₂×C₄	—	3	2	no	—
562	C₂×C₄	—	3	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	6	2	no	—
565	C₂×C₄	—	6	2	no	—
566	C₂×C₄	—	6	4	no	—
567	C₂×C₄	—	6	2	no	—
568	C₂×C₄	—	6	2	no	—
569	C₂×C₄	—	6	2	no	—
570	C₂×C₄	—	6	4	no	—
571	C₂×C₄	—	6	2	no	—
572	C₂×C₄	—	12	1	no	—
573	C₂×C₄	—	12	2	no	—
574	C₂×C₄	—	12	1	no	—
575	C₂×C₄	—	12	2	no	—
576	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
577	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
578	C₂×C₄	C₂³×D₃	1	2	yes	—
579	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₃	1	2	yes	—
582	C₂×C₄	C₂³×D₃	1	2	yes	—
583	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
585	C₂×C₃	—	4	1	no	—
586	C₂×C₃	—	4	2	no	—
587	C₂×C₃	C₂²×#41	1	1	yes	characteristic
588	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
589	C₂×C₃	#585	1	1	yes	characteristic
590	D₃	—	2	2	no	—
591	D₃	—	2	2	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	3	2	no	—
599	C₂²	—	3	2	no	—
600	C₂²	—	6	1	no	—
601	C₂²	—	6	1	no	—
602	C₂²	—	6	1	no	—
603	C₂²	—	6	1	no	—
604	C₂²	—	12	4	no	—
605	C₂²	C₂⁴×D₃	1	1	yes	characteristic
606	C₄	—	2	1	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	3	2	no	—
615	C₄	—	6	1	no	—
616	C₄	—	6	2	no	—
617	C₄	—	6	2	no	—
618	C₄	—	6	1	no	—
619	C₄	—	6	2	no	—
620	C₄	—	6	1	no	—
621	C₄	—	6	1	no	—
622	C₄	—	6	1	no	—
623	C₄	—	6	2	no	—
624	C₄	D₃×#41	1	2	yes	—
625	C₃	#3495	1	1	yes	characteristic, complemented, Sylow
626	C₂	—	4	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	6	2	no	—
629	C₂	—	6	2	no	—
630	C₂	C₂×D₃×#41	1	1	yes	characteristic
631	C₂	#5966	1	1	yes	characteristic
632	C₂	D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#542	C₂
prime radical	#5606	C₂
hypercenter	#542	D₃
hypocenter	C₃	#3495
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₃×#542	C₂	semidirect
2. #5729	C₂	semidirect
3. #5728	C₂	semidirect
4. #5708	C₂	semidirect
5. #5708	C₂	semidirect
6. #5680	C₂	semidirect
7. #5679	C₂	semidirect
8. #5675	C₂	semidirect
9. #5671	C₂	semidirect
10. #5659	C₂	semidirect
11. #5650	C₂	semidirect
12. #5639	C₂	semidirect
13. #5636	C₂	semidirect
14. D₃×C₂²⋊Q₈	C₂	semidirect
15. #5625	C₂	semidirect
17. #5603	C₂	semidirect
18. #5578	C₂	semidirect
19. #5572	C₂	semidirect
20. #5557	C₂	semidirect
21. #5546	C₂	semidirect
22. D₃×#117	C₂	semidirect
23. #5518	C₂	semidirect
28. C₃×C₄⋊Q₈	C₂²	semidirect
29. C₃×#126	C₂²	semidirect
31. C₃×#124	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×Q₈	C₂²	semidirect
37. C₃×C₄×D₄	C₂²	semidirect
42. Q₈×Dic₃	C₂²	semidirect
43. Q₈×Dic₃	C₂²	semidirect
44. #944	C₂²	semidirect
45. #944	C₂²	semidirect
49. #936	C₂²	semidirect
52. D₄×Dic₃	C₂²	semidirect
56. #926	C₂²	semidirect
59. C₂×Dic₃⋊C₄	C₂²	semidirect
74. #890	C₂²	semidirect
75. #890	C₂²	semidirect
76. #890	C₂²	semidirect
77. #889	C₂²	semidirect
78. #889	C₂²	semidirect
79. #889	C₂²	semidirect
80. #889	C₂²	semidirect
81. #889	C₂²	semidirect
82. #888	C₂²	semidirect
83. #887	C₂²	semidirect
84. #887	C₂²	semidirect
85. #887	C₂²	semidirect
101. #879	C₂²	semidirect
102. #879	C₂²	semidirect
103. #879	C₂²	semidirect
105. #878	C₂²	semidirect
106. #878	C₂²	semidirect
107. #878	C₂²	semidirect
110. #877	C₂²	semidirect
111. #877	C₂²	semidirect
118. #870	C₂²	semidirect
119. #869	C₂²	semidirect
120. C₄×Dic₆	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
134. #542	D₃	semidirect
256. C₄⋊Q₈	C₂×D₃	semidirect
264. #126	C₂×D₃	semidirect
277. #124	C₂×D₃	semidirect
300. C₂²⋊Q₈	C₂×D₃	semidirect
313. C₄×Q₈	C₂×D₃	semidirect
321. C₄×D₄	C₂×D₃	semidirect
625. C₃	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₃×#542	2
#5729	2
#5728	2
#5708	2
#5680	2
#5679	2
#5675	2
#5671	2
#5659	2
#5650	2
#5639	2
#5636	2
D₃×C₂²⋊Q₈	2
#5625	2
#5606	2
#5603	2
#5578	2
#5572	2
#5557	2
#5546	2
D₃×#117	2
#5518	2
#3495	3