Subgroups — #87008

Order 384.

1058 conjugacy classes of subgroups.

The subgroup lattice has 690 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	#5734	C₂	1	1	yes	maximal, characteristic, complemented
3	#5733	C₂	1	1	yes	maximal, characteristic, complemented
4	#5711	C₂	1	2	yes	maximal, complemented
5	#5710	C₂	1	2	yes	maximal, complemented
6	#5705	C₂	1	2	yes	maximal, complemented
7	#5704	C₂	1	2	yes	maximal, complemented
8	#5683	C₂	1	2	yes	maximal, complemented
9	#5678	C₂	1	2	yes	maximal, complemented
10	#5633	C₂	1	1	yes	maximal, characteristic, complemented
11	#5630	C₂	1	1	yes	maximal, characteristic, complemented
12	#5628	C₂	1	1	yes	maximal, characteristic, complemented
13	#5627	C₂	1	1	yes	maximal, characteristic, complemented
14	#5585	C₂	1	2	yes	maximal, complemented
15	#5582	C₂	1	2	yes	maximal, complemented
16	#5582	C₂	1	1	yes	maximal, characteristic, complemented
17	#5576	C₂	1	1	yes	maximal, characteristic, complemented
18	#5550	C₂	1	1	yes	maximal, characteristic, complemented
19	#5547	C₂	1	1	yes	maximal, characteristic, complemented
20	#5533	C₂	1	1	yes	maximal, characteristic, complemented
21	#5532	C₂	1	1	yes	maximal, characteristic, complemented
22	#5525	C₂	1	1	yes	maximal, characteristic, complemented
23	#5524	C₂	1	1	yes	maximal, characteristic, complemented
24	#3540	—	3	1	no	maximal, Sylow
25	C₂×#239	C₂²	1	1	yes	characteristic
26	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂²×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#126	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	2	yes	—
35	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#947	C₂²	1	1	yes	characteristic, complemented
43	#947	C₂²	1	2	yes	complemented
44	#947	C₂²	1	2	yes	complemented
45	#947	C₂²	1	2	yes	complemented
46	#946	C₂²	1	2	yes	complemented
47	#946	C₂²	1	1	yes	characteristic, complemented
48	#939	C₂²	1	1	yes	characteristic
49	#937	C₂²	1	2	yes	—
50	#937	C₂²	1	1	yes	characteristic
51	#930	C₂²	1	1	yes	characteristic
52	C₄×#67	C₂²	1	1	yes	characteristic
53	C₄×#67	C₂²	1	1	yes	characteristic, complemented
54	#924	C₂²	1	1	yes	characteristic, complemented
55	#898	C₂²	1	2	yes	complemented
56	#897	C₂²	1	2	yes	complemented
57	#897	C₂²	1	1	yes	characteristic, complemented
58	#897	C₂²	1	1	yes	characteristic, complemented
59	#896	C₂²	1	2	yes	complemented
60	#896	C₂²	1	2	yes	complemented
61	#896	C₂²	1	1	yes	characteristic, complemented
62	#895	C₂²	1	2	yes	—
63	#895	C₂²	1	1	yes	characteristic
64	#895	C₂²	1	1	yes	characteristic
65	#895	C₂²	1	1	yes	characteristic
66	#895	C₂²	1	1	yes	characteristic, complemented
67	#895	C₂²	1	2	yes	complemented
68	#895	C₂²	1	2	yes	complemented
69	#895	C₂²	1	1	yes	characteristic, complemented
70	#894	C₂²	1	2	yes	complemented
71	#894	C₂²	1	2	yes	complemented
72	#894	C₂²	1	2	yes	complemented
73	#894	C₂²	1	2	yes	complemented
74	#894	C₂²	1	2	yes	complemented
75	#894	C₂²	1	1	yes	characteristic, complemented
76	#894	C₂²	1	2	yes	complemented
77	#893	C₂²	1	2	yes	complemented
78	#893	C₂²	1	2	yes	complemented
79	#893	C₂²	1	1	yes	characteristic, complemented
80	#892	C₂²	1	2	yes	complemented
81	#892	C₂²	1	1	yes	characteristic, complemented
82	#892	C₂²	1	1	yes	characteristic, complemented
83	#888	C₂²	1	2	yes	complemented
84	#888	C₂²	1	1	yes	characteristic, complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#886	C₂²	1	2	yes	complemented
87	#885	C₂²	1	2	yes	—
88	#885	C₂²	1	2	yes	—
89	#885	C₂²	1	2	yes	complemented
90	#885	C₂²	1	2	yes	complemented
91	#884	C₂²	1	1	yes	characteristic
92	#884	C₂²	1	2	yes	—
93	#884	C₂²	1	2	yes	complemented
94	#884	C₂²	1	2	yes	complemented
95	#883	C₂²	1	1	yes	characteristic
96	#883	C₂²	1	2	yes	complemented
97	#882	C₂²	1	2	yes	—
98	#882	C₂²	1	2	yes	—
99	#882	C₂²	1	2	yes	complemented
100	#882	C₂²	1	2	yes	complemented
101	#882	C₂²	1	2	yes	complemented
102	#882	C₂²	1	1	yes	characteristic, complemented
103	#67⋊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	1	yes	characteristic, complemented
108	#876	C₂²	1	2	yes	complemented
109	#876	C₂²	1	2	yes	complemented
110	#875	C₂²	1	2	yes	complemented
111	#875	C₂²	1	2	yes	complemented
112	#875	C₂²	1	2	yes	complemented
113	#875	C₂²	1	2	yes	complemented
114	#875	C₂²	1	1	yes	characteristic, complemented
115	#874	C₂²	1	2	yes	—
116	C₄×D₁₂	C₂²	1	2	yes	complemented
117	C₄×D₁₂	C₂²	1	2	yes	complemented
118	C₄×D₁₂	C₂²	1	2	yes	complemented
119	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
121	#872	C₂²	1	2	yes	complemented
122	#872	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	2	yes	complemented
124	H(3,𝔽₄)	—	3	2	no	—
125	#560	—	3	2	no	—
126	#559	—	3	2	no	—
127	#556	—	3	1	no	—
128	#556	D₃	1	1	yes	characteristic, complemented
129	#555	—	3	1	no	—
130	#555	—	3	1	no	—
131	#551	—	3	2	no	—
132	#548	—	3	1	no	—
133	#548	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#542	—	3	1	no	—
137	#542	—	3	2	no	—
138	#542	—	3	1	no	—
139	#542	—	3	2	no	—
140	#538	—	3	2	no	—
141	#538	—	3	2	no	—
142	#536	—	3	1	no	—
143	#535	—	3	1	no	—
144	#525	—	3	1	no	—
145	#525	—	3	1	no	—
146	#525	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂×#67	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	1	yes	characteristic
156	C₂×#67	C₂³	1	1	yes	characteristic
157	C₂×#67	C₂³	1	1	yes	characteristic
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	1	yes	characteristic
160	C₂²×Dic₃	C₂³	1	1	yes	characteristic
161	#239	—	4	2	no	—
162	D₃×Q₈	—	4	2	no	—
163	#235	—	4	2	no	—
164	#235	—	4	2	no	—
165	C₂×D₁₂	—	4	2	no	—
166	C₂×D₁₂	C₂³	1	1	yes	characteristic
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	2	yes	—
171	C₂×D₁₂	C₂³	1	1	yes	characteristic
172	C₂×D₁₂	C₂³	1	1	yes	characteristic
173	C₂×D₁₂	C₂³	1	2	yes	—
174	C₂×D₁₂	C₂³	1	2	yes	—
175	C₂×D₁₂	C₂³	1	2	yes	—
176	C₂×D₁₂	C₂³	1	2	yes	—
177	C₂×C₄×D₃	—	4	2	no	—
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	2	yes	—
182	C₂×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	2	yes	—
188	C₂×Dic₆	C₂³	1	1	yes	characteristic
189	C₂×Dic₆	C₂³	1	2	yes	—
190	C₂×Dic₆	C₂³	1	1	yes	characteristic
191	C₂×Dic₆	C₂³	1	2	yes	—
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	2	yes	—
207	C₃×C₄²	C₂³	1	2	yes	—
208	C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₃×C₄²	C₂³	1	2	yes	—
210	#217	C₂³	1	1	yes	characteristic
211	#217	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
234	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
235	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
236	C₄⋊Dic₃	C₂³	1	2	yes	—
237	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₃	C₂³	1	2	yes	—
239	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₃⋊C₄	C₂³	1	2	yes	—
247	Dic₃⋊C₄	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	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂×#41	—	3	1	no	—
255	C₂²×Q₈	—	3	1	no	—
256	C₂²×D₄	—	3	1	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	2	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
261	#127	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	C₂×D₃	1	2	yes	complemented
267	#126	C₂×D₃	1	2	yes	complemented
268	#124	—	3	2	no	—
269	#124	—	3	1	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	—	3	2	no	—
275	#124	—	3	2	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	1	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	C₂×D₃	1	2	yes	—
282	#123	—	3	2	no	—
283	#123	—	3	1	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	—	3	2	no	—
289	#123	—	3	2	no	—
290	#123	—	3	1	no	—
291	#123	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₂²⋊Q₈	—	3	1	no	—
297	C₂²⋊Q₈	—	3	1	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	1	no	—
302	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
303	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
304	#121	—	3	1	no	—
305	#121	—	3	1	no	—
306	#121	—	3	1	no	—
307	#121	—	3	1	no	—
308	#121	—	3	1	no	—
309	#121	—	3	1	no	—
310	#121	—	3	1	no	—
311	#121	—	3	2	no	—
312	#121	—	3	2	no	—
313	#121	—	3	2	no	—
314	#121	—	3	1	no	—
315	#121	—	3	2	no	—
316	#121	—	3	2	no	—
317	#121	—	3	2	no	—
318	#120	—	3	1	no	—
319	#120	—	3	2	no	—
320	#120	—	3	1	no	—
321	#120	—	3	2	no	—
322	#120	—	3	2	no	—
323	#120	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	C₄×Q₈	—	3	1	no	—
327	C₄×Q₈	—	3	2	no	—
328	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
329	C₄×Q₈	C₂×D₃	1	2	yes	complemented
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	1	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	2	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	—	3	1	no	—
338	C₄×D₄	—	3	2	no	—
339	C₄×D₄	—	3	2	no	—
340	C₄×D₄	—	3	1	no	—
341	C₄×D₄	C₂×D₃	1	1	yes	characteristic
342	#117	—	3	1	no	—
343	#117	—	3	1	no	—
344	#117	—	3	2	no	—
345	#117	—	3	1	no	—
346	#117	—	3	2	no	—
347	#117	C₂×D₃	1	1	yes	characteristic, complemented
348	#117	C₂×D₃	1	1	yes	characteristic, complemented
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂²×D₃	—	4	1	no	—
354	C₂²×D₃	—	4	1	no	—
355	C₂²×D₃	—	4	1	no	—
356	C₂²×D₃	—	4	2	no	—
357	C₂²×D₃	—	4	2	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	C₂⁴	1	1	yes	characteristic
360	C₂²×D₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₃	C₂⁴	1	2	yes	—
362	C₂²×D₃	C₂⁴	1	2	yes	—
363	C₂²×D₃	C₂⁴	1	1	yes	characteristic
364	C₃×Q₈	—	2	2	no	—
365	C₃×Q₈	—	4	2	no	—
366	C₃×D₄	—	4	1	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
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	2	yes	—
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	#67	—	4	2	no	—
379	#67	—	4	1	no	—
380	#67	—	4	1	no	—
381	#67	—	4	1	no	—
382	#67	—	4	2	no	—
383	#67	—	4	1	no	—
384	C₂×Dic₃	—	4	1	no	—
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	C₂×Dic₃	C₂⁴	1	2	yes	—
391	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
392	D₁₂	—	2	2	no	—
393	D₁₂	—	2	2	no	—
394	D₁₂	—	4	2	no	—
395	D₁₂	—	4	2	no	—
396	D₁₂	—	4	2	no	—
397	D₁₂	—	4	1	no	—
398	D₁₂	—	4	2	no	—
399	D₁₂	—	4	2	no	—
400	D₁₂	—	4	2	no	—
401	D₁₂	—	4	1	no	—
402	D₁₂	—	4	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	4	1	no	—
407	C₄×D₃	—	4	1	no	—
408	C₄×D₃	—	4	2	no	—
409	C₄×D₃	—	4	2	no	—
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	C₄×D₃	—	4	2	no	—
413	Dic₆	—	2	2	no	—
414	Dic₆	—	4	2	no	—
415	Dic₆	—	4	1	no	—
416	Dic₆	—	4	2	no	—
417	C₂⁴	—	3	2	no	—
418	C₂⁴	—	3	1	no	—
419	#41	—	12	2	no	—
420	#41	—	12	2	no	—
421	#41	—	12	2	no	—
422	C₂×Q₈	—	3	1	no	—
423	C₂×Q₈	—	3	2	no	—
424	C₂×Q₈	—	3	2	no	—
425	C₂×Q₈	—	3	1	no	—
426	C₂×Q₈	—	12	2	no	—
427	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₃	1	2	yes	—
429	C₂×D₄	—	3	1	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	1	no	—
433	C₂×D₄	—	3	1	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	3	1	no	—
441	C₂×D₄	—	3	2	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	1	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	12	2	no	—
447	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	—	3	2	no	—
454	C₂²×C₄	—	3	2	no	—
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	12	2	no	—
460	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	1	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₃	1	2	yes	—
477	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₃	1	2	yes	—
481	C₄⋊C₄	C₂²×D₃	1	2	yes	—
482	C₂²⋊C₄	—	3	1	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	1	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	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	1	no	—
497	C₂²⋊C₄	—	3	1	no	—
498	C₂²⋊C₄	—	3	2	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	1	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
509	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
514	C₄²	—	3	2	no	—
515	C₄²	—	3	2	no	—
516	C₄²	—	3	1	no	—
517	C₄²	—	3	2	no	—
518	C₄²	C₂²×D₃	1	2	yes	—
519	C₄²	C₂²×D₃	1	1	yes	characteristic
520	C₄²	C₂²×D₃	1	2	yes	—
521	C₄²	C₂²×D₃	1	2	yes	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	C₂⁵	1	1	yes	characteristic
529	C₂×D₃	—	2	1	no	—
530	C₂×D₃	—	2	1	no	—
531	C₂×D₃	—	2	1	no	—
532	C₂×D₃	—	2	2	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	2	no	—
541	C₂×D₃	—	2	1	no	—
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	2	2	no	—
544	C₂×D₃	—	4	4	no	—
545	C₂×D₃	—	8	4	no	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	1	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
555	Dic₃	—	2	2	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	1	no	—
560	Dic₃	—	2	2	no	—
561	Dic₃	—	2	1	no	—
562	C₂³	—	3	1	no	—
563	C₂³	—	3	1	no	—
564	C₂³	—	3	2	no	—
565	C₂³	—	3	2	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	12	1	no	—
568	C₂³	—	12	1	no	—
569	C₂³	—	12	1	no	—
570	C₂³	—	12	2	no	—
571	C₂³	—	12	2	no	—
572	C₂³	—	12	2	no	—
573	C₂³	C₂³×D₃	1	1	yes	characteristic
574	C₂³	C₂³×D₃	1	1	yes	characteristic
575	Q₈	—	2	2	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	6	2	no	—
578	Q₈	—	12	2	no	—
579	Q₈	—	12	1	no	—
580	Q₈	—	12	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	6	2	no	—
583	D₄	—	6	2	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	1	no	—
586	D₄	—	12	2	no	—
587	D₄	—	12	2	no	—
588	D₄	—	12	2	no	—
589	D₄	—	12	2	no	—
590	D₄	—	12	1	no	—
591	D₄	—	12	2	no	—
592	D₄	—	12	2	no	—
593	D₄	—	12	1	no	—
594	D₄	—	12	1	no	—
595	D₄	—	12	2	no	—
596	D₄	—	12	1	no	—
597	D₄	—	12	2	no	—
598	D₄	—	12	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	2	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	3	1	no	—
605	C₂×C₄	—	3	1	no	—
606	C₂×C₄	—	3	2	no	—
607	C₂×C₄	—	3	1	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	6	2	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	12	1	no	—
612	C₂×C₄	—	12	1	no	—
613	C₂×C₄	—	12	2	no	—
614	C₂×C₄	—	12	2	no	—
615	C₂×C₄	—	12	2	no	—
616	C₂×C₄	—	12	2	no	—
617	C₂×C₄	—	12	2	no	—
618	C₂×C₄	—	12	1	no	—
619	C₂×C₄	C₂³×D₃	1	2	yes	—
620	C₂×C₄	C₂³×D₃	1	2	yes	—
621	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₃	1	2	yes	—
623	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₃	1	2	yes	—
627	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
628	C₂×C₃	—	4	1	no	—
629	C₂×C₃	—	4	1	no	—
630	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂×C₃	#585	1	1	yes	characteristic
632	C₂×C₃	#585	1	1	yes	characteristic
633	D₃	—	4	1	no	—
634	D₃	—	4	1	no	—
635	D₃	—	4	1	no	—
636	D₃	—	4	2	no	—
637	D₃	—	4	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	6	1	no	—
645	C₂²	—	6	1	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	6	2	no	—
648	C₂²	—	6	2	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	6	1	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	1	no	—
653	C₂²	—	6	2	no	—
654	C₂²	—	6	2	no	—
655	C₂²	—	6	1	no	—
656	C₂²	—	6	1	no	—
657	C₂²	—	6	1	no	—
658	C₂²	—	6	2	no	—
659	C₂²	—	12	4	no	—
660	C₂²	—	24	4	no	—
661	C₂²	C₂⁴×D₃	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	2	no	—
674	C₄	—	6	1	no	—
675	C₄	—	6	2	no	—
676	C₄	—	6	1	no	—
677	C₄	#1009	1	2	yes	—
678	C₃	#3540	1	1	yes	characteristic, complemented, Sylow
679	C₂	—	4	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	12	1	no	—
682	C₂	—	12	1	no	—
683	C₂	—	12	2	no	—
684	C₂	—	12	2	no	—
685	C₂	—	12	1	no	—
686	C₂	C₂×#1009	1	1	yes	characteristic
687	C₂	#5964	1	1	yes	characteristic
688	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#556	C₂
hypercenter	#556	D₃
hypocenter	C₃	#3540
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. #5734	C₂	semidirect
3. #5733	C₂	semidirect
4. #5711	C₂	semidirect
5. #5710	C₂	semidirect
6. #5705	C₂	semidirect
7. #5704	C₂	semidirect
8. #5683	C₂	semidirect
9. #5678	C₂	semidirect
10. #5633	C₂	semidirect
11. #5630	C₂	semidirect
12. #5628	C₂	semidirect
13. #5627	C₂	semidirect
14. #5585	C₂	semidirect
15. #5582	C₂	semidirect
16. #5582	C₂	semidirect
17. #5576	C₂	semidirect
18. #5550	C₂	semidirect
19. #5547	C₂	semidirect
20. #5533	C₂	semidirect
21. #5532	C₂	semidirect
22. #5525	C₂	semidirect
23. #5524	C₂	semidirect
26. C₂×D₃×Q₈	C₂²	semidirect
29. C₂²×D₁₂	C₂²	semidirect
30. C₂²×C₄×D₃	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#126	C₂²	semidirect
33. C₃×#126	C₂²	semidirect
35. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₄×Q₈	C₂²	semidirect
38. C₃×C₄×Q₈	C₂²	semidirect
40. C₃×#117	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
42. #947	C₂²	semidirect
43. #947	C₂²	semidirect
44. #947	C₂²	semidirect
45. #947	C₂²	semidirect
46. #946	C₂²	semidirect
47. #946	C₂²	semidirect
53. C₄×#67	C₂²	semidirect
54. #924	C₂²	semidirect
55. #898	C₂²	semidirect
56. #897	C₂²	semidirect
57. #897	C₂²	semidirect
58. #897	C₂²	semidirect
59. #896	C₂²	semidirect
60. #896	C₂²	semidirect
61. #896	C₂²	semidirect
66. #895	C₂²	semidirect
67. #895	C₂²	semidirect
68. #895	C₂²	semidirect
69. #895	C₂²	semidirect
70. #894	C₂²	semidirect
71. #894	C₂²	semidirect
72. #894	C₂²	semidirect
73. #894	C₂²	semidirect
74. #894	C₂²	semidirect
75. #894	C₂²	semidirect
76. #894	C₂²	semidirect
77. #893	C₂²	semidirect
78. #893	C₂²	semidirect
79. #893	C₂²	semidirect
80. #892	C₂²	semidirect
81. #892	C₂²	semidirect
82. #892	C₂²	semidirect
83. #888	C₂²	semidirect
84. #888	C₂²	semidirect
85. #887	C₂²	semidirect
86. #886	C₂²	semidirect
89. #885	C₂²	semidirect
90. #885	C₂²	semidirect
93. #884	C₂²	semidirect
94. #884	C₂²	semidirect
96. #883	C₂²	semidirect
99. #882	C₂²	semidirect
100. #882	C₂²	semidirect
101. #882	C₂²	semidirect
102. #882	C₂²	semidirect
103. #67⋊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. #876	C₂²	semidirect
110. #875	C₂²	semidirect
111. #875	C₂²	semidirect
112. #875	C₂²	semidirect
113. #875	C₂²	semidirect
114. #875	C₂²	semidirect
116. C₄×D₁₂	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
118. C₄×D₁₂	C₂²	semidirect
119. C₄×D₁₂	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. #872	C₂²	semidirect
122. #872	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
128. #556	D₃	semidirect
260. C₄⋊Q₈	C₂×D₃	semidirect
266. #126	C₂×D₃	semidirect
267. #126	C₂×D₃	semidirect
302. C₂²⋊Q₈	C₂×D₃	semidirect
303. C₂²⋊Q₈	C₂×D₃	semidirect
328. C₄×Q₈	C₂×D₃	semidirect
329. C₄×Q₈	C₂×D₃	semidirect
347. #117	C₂×D₃	semidirect
348. #117	C₂×D₃	semidirect
678. C₃	#3540	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
#5734	2
#5733	2
#5711	2
#5710	2
#5705	2
#5704	2
#5683	2
#5678	2
#5633	2
#5630	2
#5628	2
#5627	2
#5585	2
#5582	2
#5576	2
#5550	2
#5547	2
#5533	2
#5532	2
#5525	2
#5524	2
#3540	3