Subgroups — #86934

Order 384.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#5733	C₂	1	1	yes	maximal, characteristic, complemented
3	#5727	C₂	1	1	yes	maximal, characteristic, complemented
4	#5693	C₂	1	2	yes	maximal, complemented
5	#5692	C₂	1	2	yes	maximal, complemented
6	#5643	C₂	1	1	yes	maximal, characteristic, complemented
7	#5638	C₂	1	2	yes	maximal, complemented
8	#5637	C₂	1	2	yes	maximal, complemented
9	#5633	C₂	1	2	yes	maximal, complemented
10	#5631	C₂	1	1	yes	maximal, characteristic, complemented
11	#5630	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
13	#5622	C₂	1	1	yes	maximal, characteristic, complemented
14	#5574	C₂	1	1	yes	maximal, characteristic, complemented
15	#5568	C₂	1	1	yes	maximal, characteristic, complemented
16	#5556	C₂	1	2	yes	maximal, complemented
17	#5550	C₂	1	1	yes	maximal, characteristic, complemented
18	#5547	C₂	1	2	yes	maximal, complemented
19	#5538	C₂	1	1	yes	maximal, characteristic, complemented
20	#5511	C₂	1	1	yes	maximal, characteristic, complemented
21	#5507	C₂	1	1	yes	maximal, characteristic, complemented
22	#5504	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#893	C₂	1	1	yes	maximal, characteristic, complemented
24	#3520	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×Q₈	C₂²	1	2	yes	complemented
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	2	yes	complemented
29	C₂²×D₁₂	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃	C₂²	1	2	yes	—
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#125	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×D₄	C₂²	1	2	yes	—
40	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	#947	C₂²	1	1	yes	characteristic
43	#947	C₂²	1	2	yes	complemented
44	#946	C₂²	1	2	yes	complemented
45	#946	C₂²	1	2	yes	complemented
46	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	#944	C₂²	1	1	yes	characteristic, complemented
48	#939	C₂²	1	1	yes	characteristic
49	#937	C₂²	1	2	yes	—
50	#935	C₂²	1	1	yes	characteristic
51	#930	C₂²	1	1	yes	characteristic
52	#929	C₂²	1	2	yes	complemented
53	C₄×#67	C₂²	1	2	yes	—
54	C₄×#67	C₂²	1	1	yes	characteristic
55	C₄×#67	C₂²	1	2	yes	complemented
56	C₄×#67	C₂²	1	2	yes	complemented
57	C₄×#67	C₂²	1	1	yes	characteristic, complemented
58	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
59	#926	C₂²	1	1	yes	characteristic, complemented
60	#924	C₂²	1	1	yes	characteristic
61	#924	C₂²	1	2	yes	—
62	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
63	#898	C₂²	1	2	yes	complemented
64	#898	C₂²	1	2	yes	complemented
65	#898	C₂²	1	1	yes	characteristic, complemented
66	#898	C₂²	1	2	yes	complemented
67	#897	C₂²	1	2	yes	complemented
68	#897	C₂²	1	1	yes	characteristic, complemented
69	#896	C₂²	1	2	yes	complemented
70	#896	C₂²	1	2	yes	complemented
71	#896	C₂²	1	2	yes	complemented
72	#896	C₂²	1	2	yes	complemented
73	#896	C₂²	1	2	yes	complemented
74	#895	C₂²	1	2	yes	—
75	#895	C₂²	1	1	yes	characteristic
76	#894	C₂²	1	2	yes	—
77	#894	C₂²	1	2	yes	—
78	#894	C₂²	1	2	yes	complemented
79	#894	C₂²	1	2	yes	complemented
80	#894	C₂²	1	2	yes	complemented
81	#893	C₂²	1	2	yes	—
82	#893	C₂²	1	2	yes	—
83	#893	C₂²	1	1	yes	characteristic
84	#893	C₂²	1	1	yes	characteristic
85	#893	C₂²	1	1	yes	characteristic
86	#893	C₂²	1	1	yes	characteristic
87	#893	C₂²	1	1	yes	characteristic
88	#893	C₂²	1	2	yes	complemented
89	#892	C₂²	1	2	yes	complemented
90	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
91	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
92	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
93	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	#889	C₂²	1	2	yes	complemented
95	#889	C₂²	1	2	yes	complemented
96	#889	C₂²	1	1	yes	characteristic, complemented
97	#888	C₂²	1	1	yes	characteristic, complemented
98	#888	C₂²	1	1	yes	characteristic, complemented
99	#887	C₂²	1	2	yes	complemented
100	#887	C₂²	1	1	yes	characteristic, complemented
101	#887	C₂²	1	1	yes	characteristic, complemented
102	#886	C₂²	1	1	yes	characteristic
103	#885	C₂²	1	1	yes	characteristic, complemented
104	#885	C₂²	1	2	yes	complemented
105	#884	C₂²	1	2	yes	—
106	#884	C₂²	1	2	yes	complemented
107	#883	C₂²	1	2	yes	complemented
108	#883	C₂²	1	2	yes	complemented
109	#882	C₂²	1	2	yes	—
110	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
111	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	#879	C₂²	1	1	yes	characteristic, complemented
113	#878	C₂²	1	1	yes	characteristic
114	#878	C₂²	1	2	yes	—
115	#877	C₂²	1	2	yes	—
116	#876	C₂²	1	2	yes	complemented
117	#875	C₂²	1	1	yes	characteristic
118	C₄×D₁₂	C₂²	1	1	yes	characteristic
119	C₄×D₁₂	C₂²	1	2	yes	complemented
120	#872	C₂²	1	2	yes	complemented
121	#872	C₂²	1	2	yes	complemented
122	#872	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#556	—	3	1	no	—
125	#554	—	3	1	no	—
126	#554	D₃	1	1	yes	characteristic, complemented
127	#552	—	3	2	no	—
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	D₄×Q₈	—	3	1	no	—
131	#548	—	3	2	no	—
132	#547	—	3	1	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#542	—	3	1	no	—
137	#542	—	3	1	no	—
138	#539	—	3	2	no	—
139	#539	—	3	2	no	—
140	#533	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×C₂²⋊Q₈	—	3	2	no	—
144	#520	—	3	1	no	—
145	#520	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
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	C₂²×C₃×C₄	C₂³	1	2	yes	—
154	C₂²×C₃×C₄	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	1	yes	characteristic
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	1	yes	characteristic
158	C₂×#67	C₂³	1	2	yes	—
159	C₂²×Dic₃	C₂³	1	1	yes	characteristic
160	C₂²×Dic₃	C₂³	1	1	yes	characteristic
161	#239	—	2	4	no	—
162	D₃×Q₈	—	4	4	no	—
163	#235	—	2	4	no	—
164	#235	—	4	4	no	—
165	C₂×D₁₂	—	2	4	no	—
166	C₂×D₁₂	C₂³	1	2	yes	—
167	C₂×D₁₂	C₂³	1	1	yes	characteristic
168	C₂×D₁₂	C₂³	1	2	yes	—
169	C₂×D₁₂	C₂³	1	2	yes	—
170	C₂×D₁₂	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₃	—	4	4	no	—
172	C₂×C₄×D₃	C₂³	1	2	yes	—
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	C₂³	1	2	yes	—
175	C₂×C₄×D₃	C₂³	1	2	yes	—
176	C₂×C₄×D₃	C₂³	1	2	yes	—
177	C₂×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₄×D₃	C₂³	1	2	yes	—
180	C₂×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₄×D₃	C₂³	1	2	yes	—
182	C₂×Dic₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₂×Dic₆	C₂³	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×C₄²	C₂³	1	2	yes	—
202	#217	C₂³	1	2	yes	—
203	#217	C₂³	1	1	yes	characteristic
204	#217	C₂³	1	1	yes	characteristic
205	#217	C₂³	1	1	yes	characteristic
206	#217	C₂³	1	1	yes	characteristic
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	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
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	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	2	yes	—
248	C₄×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂×#41	—	3	2	no	—
255	C₂²×Q₈	—	3	2	no	—
256	C₂²×D₄	—	3	1	no	—
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
262	#126	—	3	1	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	1	no	—
267	#126	—	3	2	no	—
268	#125	—	3	1	no	—
269	#125	—	3	2	no	—
270	#125	—	3	2	no	—
271	#125	C₂×D₃	1	2	yes	complemented
272	#124	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	—	3	1	no	—
277	#123	—	3	1	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	—	3	1	no	—
286	#123	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	2	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	1	no	—
298	C₂²⋊Q₈	—	3	1	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	C₂×D₃	1	2	yes	—
301	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
302	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
303	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
304	#121	—	3	1	no	—
305	#121	—	3	1	no	—
306	#121	—	3	2	no	—
307	#121	—	3	1	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#120	—	3	2	no	—
311	#120	—	3	2	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	2	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	C₂×D₃	1	2	yes	—
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic
335	#117	—	3	1	no	—
336	#117	—	3	2	no	—
337	#117	—	3	2	no	—
338	#117	—	3	1	no	—
339	#117	—	3	2	no	—
340	#117	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	2	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂²×D₃	—	2	4	no	—
354	C₂²×D₃	—	2	4	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	C₂⁴	1	2	yes	—
357	C₂²×D₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃	C₂⁴	1	2	yes	—
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	—	4	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	4	2	no	—
365	C₂×C₃×C₄	—	4	2	no	—
366	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴	1	2	yes	—
368	C₂×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	#67	—	2	2	no	—
376	#67	—	2	4	no	—
377	#67	—	2	2	no	—
378	#67	—	4	2	no	—
379	C₂×Dic₃	—	2	2	no	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₃	C₂⁴	1	2	yes	—
385	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
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	D₁₂	—	2	4	no	—
391	D₁₂	—	2	4	no	—
392	D₁₂	—	2	2	no	—
393	D₁₂	—	4	2	no	—
394	D₁₂	#41	1	4	yes	complemented
395	C₄×D₃	—	2	4	no	—
396	C₄×D₃	—	2	4	no	—
397	C₄×D₃	—	2	2	no	—
398	C₄×D₃	—	2	4	no	—
399	C₄×D₃	—	2	4	no	—
400	C₄×D₃	—	4	2	no	—
401	C₄×D₃	—	4	2	no	—
402	C₄×D₃	—	4	2	no	—
403	C₄×D₃	—	4	2	no	—
404	C₄×D₃	—	4	2	no	—
405	Dic₆	—	2	2	no	—
406	Dic₆	—	2	4	no	—
407	Dic₆	—	2	2	no	—
408	Dic₆	—	4	2	no	—
409	C₂⁴	—	3	2	no	—
410	#41	—	6	4	no	—
411	#41	—	6	4	no	—
412	#41	—	12	4	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	1	no	—
415	C₂×Q₈	—	3	2	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	12	4	no	—
418	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
419	C₂×Q₈	C₂²×D₃	1	2	yes	—
420	C₂×D₄	—	3	1	no	—
421	C₂×D₄	—	3	2	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	1	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	1	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	6	4	no	—
430	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	12	4	no	—
444	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
446	C₂²×C₄	C₂²×D₃	1	2	yes	—
447	C₂²×C₄	C₂²×D₃	1	2	yes	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	1	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	1	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	1	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	1	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₃	1	2	yes	—
470	C₄⋊C₄	C₂²×D₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₃	1	2	yes	—
473	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₃	1	2	yes	—
476	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₂²⋊C₄	—	3	1	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	1	no	—
481	C₂²⋊C₄	—	3	1	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	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	1	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	1	no	—
500	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
501	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
503	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	1	no	—
508	C₄²	—	3	2	no	—
509	C₄²	—	3	2	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	1	no	—
512	C₄²	C₂²×D₃	1	2	yes	—
513	C₄²	C₂²×D₃	1	1	yes	characteristic
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	2	1	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
520	C₂²×C₃	C₂⁵	1	1	yes	characteristic
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	2	2	no	—
523	C₂×D₃	—	2	1	no	—
524	C₂×D₃	—	2	2	no	—
525	C₂×D₃	—	2	2	no	—
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	2	no	—
529	C₂×D₃	—	4	8	no	—
530	C₂×D₃	C₂×#41	1	4	yes	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	2	no	—
536	C₃×C₄	—	2	2	no	—
537	C₃×C₄	—	2	2	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	C₂×#41	1	2	yes	—
540	Dic₃	—	2	2	no	—
541	Dic₃	—	2	1	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	2	no	—
544	Dic₃	—	2	1	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	1	no	—
547	Dic₃	—	2	1	no	—
548	Dic₃	H(5,𝔽₂)	1	2	yes	—
549	C₂³	—	3	2	no	—
550	C₂³	—	3	2	no	—
551	C₂³	—	3	1	no	—
552	C₂³	—	6	4	no	—
553	C₂³	—	6	4	no	—
554	C₂³	—	12	2	no	—
555	C₂³	C₂³×D₃	1	1	yes	characteristic
556	C₂³	C₂³×D₃	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	6	2	no	—
560	Q₈	—	6	4	no	—
561	Q₈	—	6	2	no	—
562	Q₈	—	12	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	3	4	no	—
565	D₄	—	6	4	no	—
566	D₄	—	6	4	no	—
567	D₄	—	6	2	no	—
568	D₄	—	6	4	no	—
569	D₄	—	6	2	no	—
570	D₄	—	6	2	no	—
571	D₄	—	12	2	no	—
572	D₄	—	12	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	1	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	2	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	2	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	6	4	no	—
587	C₂×C₄	—	6	4	no	—
588	C₂×C₄	—	6	4	no	—
589	C₂×C₄	—	6	4	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	6	2	no	—
593	C₂×C₄	—	12	2	no	—
594	C₂×C₄	—	12	2	no	—
595	C₂×C₄	—	12	2	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	2	no	—
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	2	yes	—
600	C₂×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₄	C₂³×D₃	1	2	yes	—
602	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₃	1	2	yes	—
606	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
607	C₂×C₃	—	2	2	no	—
608	C₂×C₃	—	4	1	no	—
609	C₂×C₃	C₂²×#41	1	1	yes	characteristic
610	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
612	D₃	—	2	4	no	—
613	D₃	—	4	1	no	—
614	D₃	—	4	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	3	4	no	—
621	C₂²	—	6	2	no	—
622	C₂²	—	6	2	no	—
623	C₂²	—	6	1	no	—
624	C₂²	—	6	2	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	2	no	—
627	C₂²	—	6	2	no	—
628	C₂²	—	6	1	no	—
629	C₂²	—	12	8	no	—
630	C₂²	#1007	1	2	yes	—
631	C₂²	C₂⁴×D₃	1	1	yes	characteristic
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	3	2	no	—
641	C₄	—	6	1	no	—
642	C₄	—	6	1	no	—
643	C₄	—	6	1	no	—
644	C₄	—	6	1	no	—
645	C₄	—	6	2	no	—
646	C₄	—	6	1	no	—
647	C₄	—	6	2	no	—
648	C₄	—	6	1	no	—
649	C₄	D₃×#41	1	2	yes	—
650	C₃	#3520	1	1	yes	characteristic, complemented, Sylow
651	C₂	—	2	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	6	4	no	—
654	C₂	—	12	2	no	—
655	C₂	—	12	1	no	—
656	C₂	C₂×#1007	1	1	yes	characteristic
657	C₂	C₂×D₃×#41	1	1	yes	characteristic
658	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×#554	C₂
hypercenter	#554	D₃
hypocenter	C₃	#3520
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₃×#554	C₂	semidirect
2. #5733	C₂	semidirect
3. #5727	C₂	semidirect
4. #5693	C₂	semidirect
5. #5692	C₂	semidirect
6. #5643	C₂	semidirect
7. #5638	C₂	semidirect
8. #5637	C₂	semidirect
9. #5633	C₂	semidirect
10. #5631	C₂	semidirect
11. #5630	C₂	semidirect
12. D₃×C₂²⋊Q₈	C₂	semidirect
13. #5622	C₂	semidirect
14. #5574	C₂	semidirect
15. #5568	C₂	semidirect
16. #5556	C₂	semidirect
17. #5550	C₂	semidirect
18. #5547	C₂	semidirect
19. #5538	C₂	semidirect
20. #5511	C₂	semidirect
21. #5507	C₂	semidirect
22. #5504	C₂	semidirect
23. C₂×#893	C₂	semidirect
26. C₂×D₃×Q₈	C₂²	semidirect
28. C₂×#235	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
35. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₄×Q₈	C₂²	semidirect
41. C₂×C₃×C₄⋊C₄	C₂²	semidirect
43. #947	C₂²	semidirect
44. #946	C₂²	semidirect
45. #946	C₂²	semidirect
46. Q₈×Dic₃	C₂²	semidirect
47. #944	C₂²	semidirect
52. #929	C₂²	semidirect
55. C₄×#67	C₂²	semidirect
56. C₄×#67	C₂²	semidirect
57. C₄×#67	C₂²	semidirect
59. #926	C₂²	semidirect
63. #898	C₂²	semidirect
64. #898	C₂²	semidirect
65. #898	C₂²	semidirect
66. #898	C₂²	semidirect
67. #897	C₂²	semidirect
68. #897	C₂²	semidirect
69. #896	C₂²	semidirect
70. #896	C₂²	semidirect
71. #896	C₂²	semidirect
72. #896	C₂²	semidirect
73. #896	C₂²	semidirect
78. #894	C₂²	semidirect
79. #894	C₂²	semidirect
80. #894	C₂²	semidirect
88. #893	C₂²	semidirect
89. #892	C₂²	semidirect
90. D₃×C₄⋊C₄	C₂²	semidirect
91. D₃×C₄⋊C₄	C₂²	semidirect
92. D₃×C₄⋊C₄	C₂²	semidirect
93. D₃×C₄⋊C₄	C₂²	semidirect
94. #889	C₂²	semidirect
95. #889	C₂²	semidirect
96. #889	C₂²	semidirect
97. #888	C₂²	semidirect
98. #888	C₂²	semidirect
99. #887	C₂²	semidirect
100. #887	C₂²	semidirect
101. #887	C₂²	semidirect
103. #885	C₂²	semidirect
104. #885	C₂²	semidirect
106. #884	C₂²	semidirect
107. #883	C₂²	semidirect
108. #883	C₂²	semidirect
112. #879	C₂²	semidirect
116. #876	C₂²	semidirect
119. C₄×D₁₂	C₂²	semidirect
120. #872	C₂²	semidirect
121. #872	C₂²	semidirect
122. #872	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
126. #554	D₃	semidirect
261. C₄⋊Q₈	C₂×D₃	semidirect
271. #125	C₂×D₃	semidirect
302. C₂²⋊Q₈	C₂×D₃	semidirect
303. C₂²⋊Q₈	C₂×D₃	semidirect
317. C₄×Q₈	C₂×D₃	semidirect
346. C₂×C₄⋊C₄	C₂×D₃	semidirect
394. D₁₂	#41	semidirect
650. C₃	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₃×#554	2
#5733	2
#5727	2
#5693	2
#5692	2
#5643	2
#5638	2
#5637	2
#5633	2
#5631	2
#5630	2
D₃×C₂²⋊Q₈	2
#5622	2
#5574	2
#5568	2
#5556	2
#5550	2
#5547	2
#5538	2
#5511	2
#5507	2
#5504	2
C₂×#893	2
#3520	3