Subgroups — #86982

Order 384.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#5730	C₂	1	1	yes	maximal, characteristic, complemented
3	#5729	C₂	1	1	yes	maximal, characteristic, complemented
4	#5708	C₂	1	2	yes	maximal, complemented
5	#5706	C₂	1	2	yes	maximal, complemented
6	#5705	C₂	1	2	yes	maximal, complemented
7	#5701	C₂	1	2	yes	maximal, complemented
8	#5679	C₂	1	2	yes	maximal, complemented
9	#5669	C₂	1	2	yes	maximal, complemented
10	#5639	C₂	1	1	yes	maximal, characteristic, complemented
11	#5635	C₂	1	1	yes	maximal, characteristic, complemented
12	#5628	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#5581	C₂	1	2	yes	maximal, complemented
15	#5581	C₂	1	1	yes	maximal, characteristic, complemented
16	#5578	C₂	1	2	yes	maximal, complemented
17	#5572	C₂	1	1	yes	maximal, characteristic, complemented
18	#5547	C₂	1	1	yes	maximal, characteristic
19	#5541	C₂	1	1	yes	maximal, characteristic, complemented
20	#5533	C₂	1	1	yes	maximal, characteristic, complemented
21	#5529	C₂	1	1	yes	maximal, characteristic, complemented
22	#5523	C₂	1	1	yes	maximal, characteristic, complemented
23	D₃×#117	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×#235	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	—
30	C₃×#126	C₂²	1	2	yes	complemented
31	C₃×#124	C₂²	1	2	yes	—
32	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
36	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₃×#117	C₂²	1	1	yes	characteristic
38	C₃×#117	C₂²	1	1	yes	characteristic, complemented
39	#946	C₂²	1	1	yes	characteristic
40	#946	C₂²	1	2	yes	—
41	#946	C₂²	1	2	yes	—
42	#946	C₂²	1	1	yes	characteristic, complemented
43	#946	C₂²	1	2	yes	complemented
44	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	#944	C₂²	1	2	yes	complemented
46	#939	C₂²	1	1	yes	characteristic
47	#937	C₂²	1	1	yes	characteristic
48	#935	C₂²	1	2	yes	—
49	C₄×#67	C₂²	1	1	yes	characteristic
50	C₄×#67	C₂²	1	1	yes	characteristic
51	#926	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
53	#924	C₂²	1	1	yes	characteristic
54	#924	C₂²	1	1	yes	characteristic, complemented
55	#897	C₂²	1	2	yes	—
56	#897	C₂²	1	1	yes	characteristic
57	#897	C₂²	1	1	yes	characteristic, complemented
58	#896	C₂²	1	2	yes	—
59	#896	C₂²	1	2	yes	—
60	#896	C₂²	1	1	yes	characteristic
61	#894	C₂²	1	2	yes	—
62	#894	C₂²	1	2	yes	—
63	#894	C₂²	1	1	yes	characteristic
64	#893	C₂²	1	2	yes	—
65	#892	C₂²	1	2	yes	—
66	#892	C₂²	1	1	yes	characteristic
67	#892	C₂²	1	1	yes	characteristic
68	#892	C₂²	1	2	yes	complemented
69	#892	C₂²	1	1	yes	characteristic, complemented
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	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	#890	C₂²	1	1	yes	characteristic, complemented
76	#890	C₂²	1	2	yes	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	#888	C₂²	1	2	yes	complemented
84	#887	C₂²	1	2	yes	complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#885	C₂²	1	2	yes	—
87	#885	C₂²	1	2	yes	complemented
88	#884	C₂²	1	1	yes	characteristic
89	#883	C₂²	1	2	yes	—
90	#883	C₂²	1	2	yes	—
91	#883	C₂²	1	2	yes	—
92	#883	C₂²	1	1	yes	characteristic
93	#882	C₂²	1	1	yes	characteristic
94	#67⋊C₄	C₂²	1	2	yes	—
95	#67⋊C₄	C₂²	1	2	yes	—
96	#67⋊C₄	C₂²	1	2	yes	complemented
97	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	#879	C₂²	1	2	yes	—
100	#879	C₂²	1	2	yes	—
101	#879	C₂²	1	2	yes	—
102	#879	C₂²	1	2	yes	complemented
103	#878	C₂²	1	2	yes	—
104	#878	C₂²	1	1	yes	characteristic
105	#878	C₂²	1	2	yes	complemented
106	#877	C₂²	1	2	yes	—
107	#877	C₂²	1	2	yes	complemented
108	#876	C₂²	1	2	yes	complemented
109	#876	C₂²	1	2	yes	complemented
110	C₄×D₁₂	C₂²	1	2	yes	—
111	C₄×D₁₂	C₂²	1	1	yes	characteristic
112	#872	C₂²	1	2	yes	—
113	#872	C₂²	1	2	yes	—
114	#872	C₂²	1	2	yes	—
115	#872	C₂²	1	2	yes	—
116	#872	C₂²	1	1	yes	characteristic
117	C₄²×D₃	C₂²	1	2	yes	—
118	#870	C₂²	1	2	yes	complemented
119	#870	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	2	yes	complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#556	—	3	1	no	—
125	#556	D₃	1	1	yes	characteristic, complemented
126	#554	—	3	1	no	—
127	#554	—	3	1	no	—
128	#552	—	3	2	no	—
129	#552	—	3	1	no	—
130	#552	—	3	1	no	—
131	#552	—	3	2	no	—
132	#552	—	3	1	no	—
133	#552	—	3	1	no	—
134	#551	—	3	2	no	—
135	#551	—	3	2	no	—
136	#544	—	3	1	no	—
137	#542	—	3	2	no	—
138	#541	—	3	2	no	—
139	#536	—	3	1	no	—
140	#533	—	3	2	no	—
141	#529	—	3	2	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	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂×#67	C₂³	1	1	yes	characteristic
154	C₂×#67	C₂³	1	1	yes	characteristic
155	C₂×#67	C₂³	1	1	yes	characteristic
156	C₂×#67	C₂³	1	1	yes	characteristic
157	C₂²×Dic₃	C₂³	1	1	yes	characteristic
158	C₂²×Dic₃	C₂³	1	2	yes	—
159	D₃×Q₈	—	2	4	no	—
160	#235	—	2	4	no	—
161	C₂×D₁₂	C₂³	1	1	yes	characteristic
162	C₂×D₁₂	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₃	—	2	4	no	—
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	2	yes	—
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	2	yes	—
172	C₂×C₄×D₃	C₂³	1	2	yes	—
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×Dic₆	C₂³	1	1	yes	characteristic
175	C₂×Dic₆	C₂³	1	2	yes	—
176	C₂×Dic₆	C₂³	1	1	yes	characteristic
177	C₂×Dic₆	C₂³	1	2	yes	—
178	C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄²	C₂³	1	2	yes	—
193	C₃×C₄²	C₂³	1	1	yes	characteristic
194	C₃×C₄²	C₂³	1	2	yes	—
195	C₃×C₄²	C₂³	1	2	yes	—
196	#217	C₂³	1	2	yes	—
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	1	yes	characteristic
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	1	yes	characteristic
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	2	yes	—
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₄⋊Dic₃	C₂³	1	2	yes	—
215	C₄⋊Dic₃	C₂³	1	2	yes	—
216	C₄⋊Dic₃	C₂³	1	2	yes	—
217	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₄⋊Dic₃	C₂³	1	2	yes	—
220	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	Dic₃⋊C₄	C₂³	1	2	yes	—
224	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₃⋊C₄	C₂³	1	2	yes	—
227	Dic₃⋊C₄	C₂³	1	2	yes	—
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
241	C₄×Dic₃	C₂³	1	2	yes	—
242	C₄×Dic₃	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
249	C₂×#41	—	3	1	no	—
250	C₂²×Q₈	—	3	1	no	—
251	C₂³×C₄	—	3	1	no	—
252	C₄⋊Q₈	—	3	2	no	—
253	C₄⋊Q₈	—	3	2	no	—
254	C₄⋊Q₈	—	3	1	no	—
255	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
256	#126	—	3	2	no	—
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	C₂×D₃	1	2	yes	—
263	#126	C₂×D₃	1	2	yes	complemented
264	#125	—	3	2	no	—
265	#125	—	3	2	no	—
266	#125	—	3	2	no	—
267	#125	—	3	2	no	—
268	#125	—	3	2	no	—
269	#125	—	3	2	no	—
270	#125	—	3	1	no	—
271	#125	—	3	2	no	—
272	#125	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	2	no	—
275	#124	C₂×D₃	1	2	yes	—
276	#123	—	3	2	no	—
277	#123	—	3	1	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	1	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	C₂²⋊Q₈	—	3	1	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	1	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	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	1	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	1	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
301	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
302	#121	—	3	1	no	—
303	#121	—	3	1	no	—
304	#120	—	3	1	no	—
305	#120	—	3	1	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	2	no	—
308	C₄×Q₈	—	3	1	no	—
309	C₄×Q₈	—	3	2	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	—	3	2	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
314	C₄×Q₈	C₂×D₃	1	2	yes	complemented
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	1	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	1	no	—
323	C₄×D₄	C₂×D₃	1	1	yes	characteristic
324	#117	—	3	1	no	—
325	#117	—	3	1	no	—
326	#117	—	3	1	no	—
327	#117	—	3	2	no	—
328	#117	—	3	1	no	—
329	#117	—	3	2	no	—
330	#117	—	3	2	no	—
331	#117	—	3	2	no	—
332	#117	—	3	2	no	—
333	#117	—	3	1	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	C₂×D₃	1	1	yes	characteristic
338	#117	C₂×D₃	1	1	yes	characteristic, complemented
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	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₄²	—	3	2	no	—
348	C₂³×C₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₃	C₂⁴	1	1	yes	characteristic
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	C₂²×D₃	C₂⁴	1	1	yes	characteristic
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	4	2	no	—
358	C₃×D₄	—	4	1	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	C₂⁴	1	2	yes	—
362	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂⁴	1	2	yes	—
365	C₂×C₃×C₄	C₂⁴	1	2	yes	—
366	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	#67	—	2	2	no	—
371	#67	—	2	2	no	—
372	#67	—	2	2	no	—
373	#67	—	4	1	no	—
374	C₂×Dic₃	—	2	2	no	—
375	C₂×Dic₃	—	4	2	no	—
376	C₂×Dic₃	C₂⁴	1	2	yes	—
377	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₃	C₂⁴	1	2	yes	—
380	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₃	C₂⁴	1	2	yes	—
382	C₂×Dic₃	C₂⁴	1	2	yes	—
383	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
385	D₁₂	—	2	2	no	—
386	D₁₂	—	2	2	no	—
387	C₄×D₃	—	2	2	no	—
388	C₄×D₃	—	2	4	no	—
389	C₄×D₃	—	2	4	no	—
390	C₄×D₃	—	2	2	no	—
391	C₄×D₃	—	2	2	no	—
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	4	2	no	—
394	C₄×D₃	—	4	2	no	—
395	C₄×D₃	—	4	2	no	—
396	C₄×D₃	#41	1	4	yes	—
397	Dic₆	—	2	2	no	—
398	Dic₆	—	2	2	no	—
399	Dic₆	—	2	4	no	—
400	Dic₆	—	4	2	no	—
401	C₂⁴	—	3	1	no	—
402	#41	—	6	4	no	—
403	C₂×Q₈	—	3	1	no	—
404	C₂×Q₈	—	3	2	no	—
405	C₂×Q₈	—	3	1	no	—
406	C₂×Q₈	—	3	2	no	—
407	C₂×Q₈	—	6	4	no	—
408	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
409	C₂×Q₈	C₂²×D₃	1	2	yes	—
410	C₂×D₄	—	3	1	no	—
411	C₂×D₄	—	3	1	no	—
412	C₂×D₄	—	3	1	no	—
413	C₂×D₄	—	3	1	no	—
414	C₂×D₄	—	3	1	no	—
415	C₂×D₄	—	3	1	no	—
416	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	2	no	—
422	C₂²×C₄	—	3	2	no	—
423	C₂²×C₄	—	3	1	no	—
424	C₂²×C₄	—	3	1	no	—
425	C₂²×C₄	—	3	1	no	—
426	C₂²×C₄	—	3	2	no	—
427	C₂²×C₄	—	3	2	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	6	4	no	—
430	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
432	C₄⋊C₄	—	3	1	no	—
433	C₄⋊C₄	—	3	1	no	—
434	C₄⋊C₄	—	3	2	no	—
435	C₄⋊C₄	—	3	1	no	—
436	C₄⋊C₄	—	3	2	no	—
437	C₄⋊C₄	—	3	2	no	—
438	C₄⋊C₄	—	3	2	no	—
439	C₄⋊C₄	—	3	2	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	2	no	—
442	C₄⋊C₄	—	3	2	no	—
443	C₄⋊C₄	—	3	1	no	—
444	C₄⋊C₄	—	3	1	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	1	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
462	C₄⋊C₄	C₂²×D₃	1	2	yes	—
463	C₄⋊C₄	C₂²×D₃	1	2	yes	—
464	C₄⋊C₄	C₂²×D₃	1	2	yes	—
465	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
466	C₄⋊C₄	C₂²×D₃	1	2	yes	—
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	1	no	—
471	C₂²⋊C₄	—	3	1	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₂²⋊C₄	—	3	2	no	—
476	C₂²⋊C₄	—	3	1	no	—
477	C₂²⋊C₄	—	3	1	no	—
478	C₂²⋊C₄	—	3	1	no	—
479	C₂²⋊C₄	—	3	1	no	—
480	C₂²⋊C₄	—	3	1	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
488	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
491	C₄²	—	3	2	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	—	3	1	no	—
499	C₄²	C₂²×D₃	1	2	yes	—
500	C₄²	C₂²×D₃	1	2	yes	—
501	C₄²	C₂²×D₃	1	2	yes	—
502	C₄²	C₂²×D₃	1	1	yes	characteristic
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	C₂⁵	1	1	yes	characteristic
510	C₂×D₃	—	2	1	no	—
511	C₂×D₃	—	2	1	no	—
512	C₂×D₃	—	2	1	no	—
513	C₂×D₃	—	2	1	no	—
514	C₂×D₃	—	2	1	no	—
515	C₂×D₃	—	2	1	no	—
516	C₂×D₃	—	2	1	no	—
517	C₂×D₃	—	4	4	no	—
518	C₂×D₃	C₂×#41	1	2	yes	—
519	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
520	C₃×C₄	—	2	2	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	2	no	—
526	C₃×C₄	—	2	2	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	C₂×#41	1	2	yes	—
529	Dic₃	—	2	2	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	1	no	—
532	Dic₃	—	2	2	no	—
533	Dic₃	—	2	1	no	—
534	Dic₃	—	2	1	no	—
535	Dic₃	—	2	2	no	—
536	Dic₃	—	2	2	no	—
537	Dic₃	C₂×#41	1	2	yes	—
538	C₂³	—	3	1	no	—
539	C₂³	—	3	1	no	—
540	C₂³	—	3	1	no	—
541	C₂³	—	6	2	no	—
542	C₂³	—	6	2	no	—
543	C₂³	—	12	1	no	—
544	C₂³	C₂³×D₃	1	1	yes	characteristic
545	C₂³	C₂³×D₃	1	1	yes	characteristic
546	Q₈	—	2	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	6	4	no	—
549	Q₈	—	6	2	no	—
550	Q₈	—	6	2	no	—
551	Q₈	—	12	2	no	—
552	D₄	—	4	1	no	—
553	D₄	—	6	2	no	—
554	D₄	—	6	2	no	—
555	D₄	—	6	2	no	—
556	D₄	—	6	2	no	—
557	D₄	—	6	2	no	—
558	D₄	—	12	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	3	1	no	—
562	C₂×C₄	—	3	4	no	—
563	C₂×C₄	—	3	2	no	—
564	C₂×C₄	—	3	1	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	2	no	—
567	C₂×C₄	—	3	2	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	2	no	—
570	C₂×C₄	—	3	1	no	—
571	C₂×C₄	—	6	2	no	—
572	C₂×C₄	—	6	2	no	—
573	C₂×C₄	—	6	4	no	—
574	C₂×C₄	—	6	4	no	—
575	C₂×C₄	—	6	2	no	—
576	C₂×C₄	—	6	2	no	—
577	C₂×C₄	—	6	2	no	—
578	C₂×C₄	—	12	2	no	—
579	C₂×C₄	—	12	2	no	—
580	C₂×C₄	—	12	2	no	—
581	C₂×C₄	—	12	2	no	—
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×C₄	C₂³×D₃	1	2	yes	—
586	C₂×C₄	C₂³×D₃	1	2	yes	—
587	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₃	1	2	yes	—
590	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
591	C₂×C₃	—	4	1	no	—
592	C₂×C₃	—	4	1	no	—
593	C₂×C₃	C₂²×#41	1	1	yes	characteristic
594	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
595	C₂×C₃	#585	1	1	yes	characteristic
596	D₃	—	2	2	no	—
597	D₃	—	2	2	no	—
598	D₃	—	4	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	3	2	no	—
606	C₂²	—	3	2	no	—
607	C₂²	—	6	1	no	—
608	C₂²	—	6	1	no	—
609	C₂²	—	6	1	no	—
610	C₂²	—	6	1	no	—
611	C₂²	—	6	1	no	—
612	C₂²	—	6	1	no	—
613	C₂²	—	6	1	no	—
614	C₂²	—	12	4	no	—
615	C₂²	C₂⁴×D₃	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	3	2	no	—
625	C₄	—	6	1	no	—
626	C₄	—	6	1	no	—
627	C₄	—	6	2	no	—
628	C₄	—	6	2	no	—
629	C₄	—	6	2	no	—
630	C₄	—	6	1	no	—
631	C₄	—	6	2	no	—
632	C₄	—	6	1	no	—
633	C₄	D₃×#41	1	2	yes	—
634	C₃	#3495	1	1	yes	characteristic, complemented, Sylow
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	6	2	no	—
638	C₂	—	6	2	no	—
639	C₂	—	12	1	no	—
640	C₂	C₂×D₃×#41	1	1	yes	characteristic
641	C₂	#5964	1	1	yes	characteristic
642	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×#556	C₂
prime radical	#5547	C₂
hypercenter	#556	D₃
hypocenter	C₃	#3495
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₃×#556	C₂	semidirect
2. #5730	C₂	semidirect
3. #5729	C₂	semidirect
4. #5708	C₂	semidirect
5. #5706	C₂	semidirect
6. #5705	C₂	semidirect
7. #5701	C₂	semidirect
8. #5679	C₂	semidirect
9. #5669	C₂	semidirect
10. #5639	C₂	semidirect
11. #5635	C₂	semidirect
12. #5628	C₂	semidirect
13. D₃×C₂²⋊Q₈	C₂	semidirect
14. #5581	C₂	semidirect
15. #5581	C₂	semidirect
16. #5578	C₂	semidirect
17. #5572	C₂	semidirect
19. #5541	C₂	semidirect
20. #5533	C₂	semidirect
21. #5529	C₂	semidirect
22. #5523	C₂	semidirect
23. D₃×#117	C₂	semidirect
28. C₃×C₄⋊Q₈	C₂²	semidirect
30. C₃×#126	C₂²	semidirect
33. C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₃×C₄×Q₈	C₂²	semidirect
35. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×#117	C₂²	semidirect
42. #946	C₂²	semidirect
43. #946	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. #944	C₂²	semidirect
52. C₂×C₄⋊Dic₃	C₂²	semidirect
54. #924	C₂²	semidirect
57. #897	C₂²	semidirect
68. #892	C₂²	semidirect
69. #892	C₂²	semidirect
74. D₃×C₄⋊C₄	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. #888	C₂²	semidirect
84. #887	C₂²	semidirect
85. #887	C₂²	semidirect
87. #885	C₂²	semidirect
96. #67⋊C₄	C₂²	semidirect
102. #879	C₂²	semidirect
105. #878	C₂²	semidirect
107. #877	C₂²	semidirect
108. #876	C₂²	semidirect
109. #876	C₂²	semidirect
118. #870	C₂²	semidirect
119. #870	C₂²	semidirect
120. C₄×Dic₆	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
125. #556	D₃	semidirect
255. C₄⋊Q₈	C₂×D₃	semidirect
263. #126	C₂×D₃	semidirect
301. C₂²⋊Q₈	C₂×D₃	semidirect
313. C₄×Q₈	C₂×D₃	semidirect
314. C₄×Q₈	C₂×D₃	semidirect
338. #117	C₂×D₃	semidirect
634. 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×#556	2
#5730	2
#5729	2
#5708	2
#5706	2
#5705	2
#5701	2
#5679	2
#5669	2
#5639	2
#5635	2
#5628	2
D₃×C₂²⋊Q₈	2
#5581	2
#5578	2
#5572	2
#5547	2
#5541	2
#5533	2
#5529	2
#5523	2
D₃×#117	2
#3495	3