Subgroups — #86609

Order 384.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
2	#5806	C₂	1	1	yes	maximal, characteristic, complemented
3	#5806	C₂	1	1	yes	maximal, characteristic, complemented
4	#5806	C₂	1	2	yes	maximal, complemented
5	#5798	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#935	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#5719	C₂	1	1	yes	maximal, characteristic, complemented
9	#5713	C₂	1	1	yes	maximal, characteristic, complemented
10	#5614	C₂	1	1	yes	maximal, characteristic, complemented
11	#5611	C₂	1	1	yes	maximal, characteristic, complemented
12	#5603	C₂	1	1	yes	maximal, characteristic, complemented
13	#5602	C₂	1	2	yes	maximal, complemented
14	#5601	C₂	1	2	yes	maximal, complemented
15	#5600	C₂	1	1	yes	maximal, characteristic, complemented
16	#5593	C₂	1	2	yes	maximal, complemented
17	#5587	C₂	1	2	yes	maximal, complemented
18	#5587	C₂	1	2	yes	maximal, complemented
19	#5586	C₂	1	2	yes	maximal, complemented
20	#5546	C₂	1	1	yes	maximal, characteristic, complemented
21	#5541	C₂	1	1	yes	maximal, characteristic, complemented
22	#5539	C₂	1	1	yes	maximal, characteristic, complemented
23	#5538	C₂	1	1	yes	maximal, characteristic, complemented
24	#3513	—	3	1	no	maximal, Sylow
25	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₂²×C₃×D₄	C₂²	1	2	yes	—
28	C₂³×Dic₃	C₂²	1	2	yes	complemented
29	C₂×#237	C₂²	1	1	yes	characteristic
30	C₂×#237	C₂²	1	2	yes	complemented
31	C₃×#127	C₂²	1	1	yes	characteristic
32	C₃×#121	C₂²	1	1	yes	characteristic
33	C₃×#121	C₂²	1	2	yes	—
34	C₃×#121	C₂²	1	1	yes	characteristic
35	C₃×#120	C₂²	1	2	yes	—
36	C₃×#120	C₂²	1	2	yes	—
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	#953	C₂²	1	2	yes	complemented
40	#953	C₂²	1	2	yes	complemented
41	C₂×#217	C₂²	1	2	yes	complemented
42	C₂×#217	C₂²	1	2	yes	complemented
43	C₂×#217	C₂²	1	2	yes	complemented
44	C₂×#217	C₂²	1	2	yes	complemented
45	C₂×#217	C₂²	1	2	yes	complemented
46	#939	C₂²	1	1	yes	characteristic
47	#939	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	complemented
49	#939	C₂²	1	2	yes	complemented
50	#939	C₂²	1	2	yes	complemented
51	#938	C₂²	1	1	yes	characteristic, complemented
52	#938	C₂²	1	1	yes	characteristic, complemented
53	#938	C₂²	1	2	yes	complemented
54	#936	C₂²	1	1	yes	characteristic, complemented
55	#936	C₂²	1	1	yes	characteristic, complemented
56	#936	C₂²	1	2	yes	complemented
57	#936	C₂²	1	2	yes	complemented
58	#935	C₂²	1	1	yes	characteristic
59	#935	C₂²	1	2	yes	—
60	#935	C₂²	1	2	yes	complemented
61	#935	C₂²	1	2	yes	complemented
62	#935	C₂²	1	2	yes	complemented
63	#935	C₂²	1	2	yes	complemented
64	#935	C₂²	1	2	yes	complemented
65	#935	C₂²	1	2	yes	complemented
66	#935	C₂²	1	2	yes	complemented
67	#935	C₂²	1	2	yes	complemented
68	#935	C₂²	1	2	yes	complemented
69	#935	C₂²	1	2	yes	complemented
70	D₄×Dic₃	C₂²	1	1	yes	characteristic
71	D₄×Dic₃	C₂²	1	1	yes	characteristic
72	D₄×Dic₃	C₂²	1	1	yes	characteristic
73	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₃	C₂²	1	2	yes	complemented
76	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₃	C₂²	1	2	yes	complemented
79	D₄×Dic₃	C₂²	1	2	yes	complemented
80	D₄×Dic₃	C₂²	1	2	yes	complemented
81	D₄×Dic₃	C₂²	1	2	yes	complemented
82	D₄×Dic₃	C₂²	1	2	yes	complemented
83	C₄×#67	C₂²	1	1	yes	characteristic, complemented
84	C₄×#67	C₂²	1	1	yes	characteristic, complemented
85	C₄×#67	C₂²	1	2	yes	complemented
86	#926	C₂²	1	1	yes	characteristic, complemented
87	#926	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
89	#924	C₂²	1	2	yes	complemented
90	#924	C₂²	1	1	yes	characteristic, complemented
91	#924	C₂²	1	1	yes	characteristic, complemented
92	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
93	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
95	#898	C₂²	1	1	yes	characteristic, complemented
96	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	#890	C₂²	1	1	yes	characteristic, complemented
98	#889	C₂²	1	1	yes	characteristic, complemented
99	#889	C₂²	1	2	yes	complemented
100	#888	C₂²	1	1	yes	characteristic, complemented
101	#887	C₂²	1	1	yes	characteristic, complemented
102	#886	C₂²	1	1	yes	characteristic, complemented
103	#885	C₂²	1	1	yes	characteristic, complemented
104	#883	C₂²	1	2	yes	complemented
105	#67⋊C₄	C₂²	1	2	yes	complemented
106	#67⋊C₄	C₂²	1	2	yes	complemented
107	#879	C₂²	1	1	yes	characteristic, complemented
108	#879	C₂²	1	2	yes	complemented
109	#879	C₂²	1	2	yes	complemented
110	#879	C₂²	1	2	yes	complemented
111	#879	C₂²	1	2	yes	complemented
112	#878	C₂²	1	1	yes	characteristic, complemented
113	#878	C₂²	1	2	yes	complemented
114	#878	C₂²	1	2	yes	complemented
115	#878	C₂²	1	2	yes	complemented
116	#878	C₂²	1	2	yes	complemented
117	#877	C₂²	1	2	yes	complemented
118	#877	C₂²	1	2	yes	complemented
119	#877	C₂²	1	2	yes	complemented
120	#872	C₂²	1	1	yes	characteristic, complemented
121	#870	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#559	—	3	1	no	—
125	#554	—	3	1	no	—
126	#553	—	3	2	no	—
127	#553	—	3	1	no	—
128	#552	—	3	1	no	—
129	#551	—	3	2	no	—
130	#551	—	3	2	no	—
131	#547	—	3	1	no	—
132	#546	—	3	2	no	—
133	#546	—	3	1	no	—
134	#546	—	3	1	no	—
135	D₄²	D₃	1	1	yes	characteristic, complemented
136	#542	—	3	1	no	—
137	#540	—	3	1	no	—
138	#539	—	3	2	no	—
139	#538	—	3	2	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×#123	—	3	2	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂⁴×C₃	C₂³	1	2	yes	—
149	C₂×C₃×D₄	—	2	4	no	—
150	C₂×C₃×D₄	—	2	4	no	—
151	C₂×C₃×D₄	—	4	4	no	—
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂×C₃×D₄	C₂³	1	2	yes	—
154	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×D₄	C₂³	1	2	yes	—
157	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×D₄	C₂³	1	2	yes	—
159	C₂×C₃×D₄	C₂³	1	2	yes	—
160	C₂×C₃×D₄	C₂³	1	2	yes	—
161	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	2	yes	—
166	C₂×#67	C₂³	1	1	yes	characteristic
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	2	yes	—
169	C₂×#67	C₂³	1	1	yes	characteristic
170	C₂²×Dic₃	—	4	4	no	—
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	1	yes	characteristic
174	C₂²×Dic₃	C₂³	1	2	yes	—
175	C₂²×Dic₃	C₂³	1	1	yes	characteristic
176	C₂²×Dic₃	C₂³	1	2	yes	—
177	C₂²×Dic₃	C₂³	1	2	yes	—
178	C₂²×Dic₃	C₂³	1	2	yes	—
179	C₂²×Dic₃	C₂³	1	2	yes	—
180	C₂²×Dic₃	C₂³	1	2	yes	—
181	C₂²×Dic₃	C₂³	1	2	yes	—
182	#237	—	2	4	no	—
183	#237	—	4	4	no	—
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×Dic₆	C₂³	1	1	yes	characteristic
187	C₂×Dic₆	C₂³	1	1	yes	characteristic
188	C₂×Dic₆	C₂³	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄²	C₂³	1	1	yes	characteristic
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	#217	C₂³	1	2	yes	—
202	#217	C₂³	1	1	yes	characteristic
203	#217	C₂³	1	2	yes	—
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	1	yes	characteristic
208	#217	C₂³	1	1	yes	characteristic
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	2	yes	—
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	2	yes	—
215	#217	C₂³	1	2	yes	—
216	#217	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₃	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	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	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	2	yes	—
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	2	no	—
254	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
255	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
256	C₂²×D₄	C₂×D₃	1	2	yes	—
257	C₂³×C₄	—	3	2	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	#127	C₂×D₃	1	1	yes	characteristic
260	#126	—	3	1	no	—
261	#126	—	3	2	no	—
262	#126	—	3	1	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#125	—	3	1	no	—
267	#125	—	3	1	no	—
268	#125	—	3	2	no	—
269	#125	—	3	1	no	—
270	#124	—	3	1	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	3	1	no	—
274	#124	—	3	1	no	—
275	#123	—	3	1	no	—
276	#123	—	3	2	no	—
277	#123	—	3	2	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	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	1	no	—
288	#123	—	3	2	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	—	3	1	no	—
300	#121	—	3	2	no	—
301	#121	—	3	2	no	—
302	#121	—	3	1	no	—
303	#121	—	3	1	no	—
304	#121	—	3	2	no	—
305	#121	C₂×D₃	1	1	yes	characteristic
306	#121	C₂×D₃	1	2	yes	—
307	#121	C₂×D₃	1	1	yes	characteristic
308	#120	—	3	2	no	—
309	#120	—	3	2	no	—
310	#120	C₂×D₃	1	2	yes	—
311	#120	C₂×D₃	1	2	yes	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	2	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	C₂×D₃	1	1	yes	characteristic
334	C₄×D₄	C₂×D₃	1	1	yes	characteristic
335	#117	—	3	1	no	—
336	#117	—	3	1	no	—
337	#117	—	3	2	no	—
338	#117	—	3	2	no	—
339	#117	—	3	2	no	—
340	#117	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
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	—	2	4	no	—
352	C₂³×C₃	—	2	4	no	—
353	C₂³×C₃	—	2	4	no	—
354	C₂³×C₃	—	4	2	no	—
355	C₂³×C₃	—	4	2	no	—
356	C₂³×C₃	—	4	2	no	—
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₃	C₂⁴	1	2	yes	—
359	C₂³×C₃	C₂⁴	1	2	yes	—
360	C₂³×C₃	C₂⁴	1	2	yes	—
361	C₂³×C₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₃×D₄	—	2	4	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	4	2	no	—
370	C₃×D₄	—	4	2	no	—
371	C₃×D₄	—	4	2	no	—
372	C₃×D₄	#41	1	4	yes	complemented
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	#67	—	2	4	no	—
383	#67	—	2	2	no	—
384	#67	—	4	2	no	—
385	#67	—	4	1	no	—
386	#67	—	4	2	no	—
387	C₂×Dic₃	—	2	4	no	—
388	C₂×Dic₃	—	2	4	no	—
389	C₂×Dic₃	—	2	2	no	—
390	C₂×Dic₃	—	4	2	no	—
391	C₂×Dic₃	—	4	2	no	—
392	C₂×Dic₃	—	4	2	no	—
393	C₂×Dic₃	—	4	2	no	—
394	C₂×Dic₃	—	4	2	no	—
395	C₂×Dic₃	—	4	2	no	—
396	C₂×Dic₃	—	4	1	no	—
397	C₂×Dic₃	—	4	2	no	—
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	2	yes	—
400	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₃	C₂⁴	1	2	yes	—
404	C₂×Dic₃	C₂⁴	1	2	yes	—
405	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₃	C₂⁴	1	2	yes	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	4	2	no	—
411	Dic₆	—	2	2	no	—
412	Dic₆	—	4	1	no	—
413	Dic₆	—	4	2	no	—
414	C₂⁴	C₂²×D₃	1	2	yes	—
415	C₂⁴	C₂²×D₃	1	2	yes	—
416	#41	—	6	4	no	—
417	#41	—	12	4	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	3	1	no	—
420	C₂×Q₈	—	3	2	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	3	1	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	C₂²×D₃	1	2	yes	—
430	C₂×D₄	C₂²×D₃	1	2	yes	—
431	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
432	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
433	C₂×D₄	C₂²×D₃	1	2	yes	—
434	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₃	1	2	yes	—
436	C₂×D₄	C₂²×D₃	1	2	yes	—
437	C₂×D₄	C₂²×D₃	1	2	yes	—
438	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	12	4	no	—
453	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₃	1	2	yes	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	1	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	1	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	1	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	1	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	1	no	—
486	C₂²⋊C₄	—	3	1	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	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	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	1	no	—
502	C₂²⋊C₄	—	3	1	no	—
503	C₂²⋊C₄	—	3	1	no	—
504	C₂²⋊C₄	—	3	1	no	—
505	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	1	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	2	no	—
515	C₄²	—	3	2	no	—
516	C₄²	—	3	2	no	—
517	C₄²	—	3	1	no	—
518	C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	2	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	4	8	no	—
533	C₂²×C₃	—	8	4	no	—
534	C₂²×C₃	C₂×#41	1	4	yes	—
535	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
536	C₂²×C₃	C₂⁵	1	1	yes	characteristic
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	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	1	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	2	no	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	1	no	—
554	Dic₃	—	2	1	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	2	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	C₂³×D₃	1	1	yes	characteristic
565	C₂³	C₂³×D₃	1	2	yes	—
566	C₂³	C₂³×D₃	1	2	yes	—
567	C₂³	C₂³×D₃	1	2	yes	—
568	C₂³	C₂³×D₃	1	1	yes	characteristic
569	Q₈	—	6	2	no	—
570	Q₈	—	12	2	no	—
571	Q₈	—	12	1	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	4	no	—
576	D₄	—	2	2	no	—
577	D₄	—	2	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	6	4	no	—
582	D₄	—	6	2	no	—
583	D₄	—	12	2	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	1	no	—
586	D₄	#237	1	4	yes	complemented
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	3	1	no	—
590	C₂×C₄	—	3	2	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	2	no	—
597	C₂×C₄	—	3	1	no	—
598	C₂×C₄	—	3	1	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	6	4	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	6	4	no	—
604	C₂×C₄	—	6	2	no	—
605	C₂×C₄	—	12	2	no	—
606	C₂×C₄	—	12	2	no	—
607	C₂×C₄	—	12	2	no	—
608	C₂×C₄	—	12	2	no	—
609	C₂×C₄	—	12	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	—	12	2	no	—
612	C₂×C₄	—	12	1	no	—
613	C₂×C₄	—	12	2	no	—
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₃	1	2	yes	—
618	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₃	—	2	2	no	—
621	C₂×C₃	—	2	4	no	—
622	C₂×C₃	—	4	2	no	—
623	C₂×C₃	—	4	2	no	—
624	C₂×C₃	—	4	1	no	—
625	C₂×C₃	C₂²×#41	1	1	yes	characteristic
626	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×C₃	#585	1	1	yes	characteristic
628	D₃	—	4	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	6	1	no	—
644	C₂²	—	6	1	no	—
645	C₂²	—	6	1	no	—
646	C₂²	—	8	4	no	—
647	C₂²	C₂×#237	1	4	yes	—
648	C₂²	#1004	1	2	yes	—
649	C₂²	C₂⁴×D₃	1	1	yes	characteristic
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	6	1	no	—
656	C₄	—	6	2	no	—
657	C₄	—	6	1	no	—
658	C₄	—	6	1	no	—
659	C₄	—	6	2	no	—
660	C₄	—	6	2	no	—
661	C₄	—	6	1	no	—
662	C₄	—	6	1	no	—
663	C₄	—	6	2	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	C₂×#237	1	2	yes	—
667	C₃	#3513	1	1	yes	characteristic, complemented, Sylow
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	12	1	no	—
674	C₂	C₂²×#237	1	1	yes	characteristic
675	C₂	C₂×#1004	1	1	yes	characteristic
676	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×D₄²	C₂
hypercenter	D₄²	D₃
hypocenter	C₃	#3513
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₃×D₄²	C₂	semidirect
2. #5806	C₂	semidirect
3. #5806	C₂	semidirect
4. #5806	C₂	semidirect
5. #5798	C₂	semidirect
6. C₂×#935	C₂	semidirect
7. C₂×D₄×Dic₃	C₂	semidirect
8. #5719	C₂	semidirect
9. #5713	C₂	semidirect
10. #5614	C₂	semidirect
11. #5611	C₂	semidirect
12. #5603	C₂	semidirect
13. #5602	C₂	semidirect
14. #5601	C₂	semidirect
15. #5600	C₂	semidirect
16. #5593	C₂	semidirect
17. #5587	C₂	semidirect
18. #5587	C₂	semidirect
19. #5586	C₂	semidirect
20. #5546	C₂	semidirect
21. #5541	C₂	semidirect
22. #5539	C₂	semidirect
23. #5538	C₂	semidirect
28. C₂³×Dic₃	C₂²	semidirect
30. C₂×#237	C₂²	semidirect
39. #953	C₂²	semidirect
40. #953	C₂²	semidirect
41. C₂×#217	C₂²	semidirect
42. C₂×#217	C₂²	semidirect
43. C₂×#217	C₂²	semidirect
44. C₂×#217	C₂²	semidirect
45. C₂×#217	C₂²	semidirect
47. #939	C₂²	semidirect
48. #939	C₂²	semidirect
49. #939	C₂²	semidirect
50. #939	C₂²	semidirect
51. #938	C₂²	semidirect
52. #938	C₂²	semidirect
53. #938	C₂²	semidirect
54. #936	C₂²	semidirect
55. #936	C₂²	semidirect
56. #936	C₂²	semidirect
57. #936	C₂²	semidirect
60. #935	C₂²	semidirect
61. #935	C₂²	semidirect
62. #935	C₂²	semidirect
63. #935	C₂²	semidirect
64. #935	C₂²	semidirect
65. #935	C₂²	semidirect
66. #935	C₂²	semidirect
67. #935	C₂²	semidirect
68. #935	C₂²	semidirect
69. #935	C₂²	semidirect
73. D₄×Dic₃	C₂²	semidirect
74. D₄×Dic₃	C₂²	semidirect
75. D₄×Dic₃	C₂²	semidirect
76. D₄×Dic₃	C₂²	semidirect
77. D₄×Dic₃	C₂²	semidirect
78. D₄×Dic₃	C₂²	semidirect
79. D₄×Dic₃	C₂²	semidirect
80. D₄×Dic₃	C₂²	semidirect
81. D₄×Dic₃	C₂²	semidirect
82. D₄×Dic₃	C₂²	semidirect
83. C₄×#67	C₂²	semidirect
84. C₄×#67	C₂²	semidirect
85. C₄×#67	C₂²	semidirect
86. #926	C₂²	semidirect
87. #926	C₂²	semidirect
88. C₂×C₄⋊Dic₃	C₂²	semidirect
89. #924	C₂²	semidirect
90. #924	C₂²	semidirect
91. #924	C₂²	semidirect
92. C₂×Dic₃⋊C₄	C₂²	semidirect
93. C₂×Dic₃⋊C₄	C₂²	semidirect
94. C₂×C₄×Dic₃	C₂²	semidirect
95. #898	C₂²	semidirect
96. D₃×C₄⋊C₄	C₂²	semidirect
97. #890	C₂²	semidirect
98. #889	C₂²	semidirect
99. #889	C₂²	semidirect
100. #888	C₂²	semidirect
101. #887	C₂²	semidirect
102. #886	C₂²	semidirect
103. #885	C₂²	semidirect
104. #883	C₂²	semidirect
105. #67⋊C₄	C₂²	semidirect
106. #67⋊C₄	C₂²	semidirect
107. #879	C₂²	semidirect
108. #879	C₂²	semidirect
109. #879	C₂²	semidirect
110. #879	C₂²	semidirect
111. #879	C₂²	semidirect
112. #878	C₂²	semidirect
113. #878	C₂²	semidirect
114. #878	C₂²	semidirect
115. #878	C₂²	semidirect
116. #878	C₂²	semidirect
117. #877	C₂²	semidirect
118. #877	C₂²	semidirect
119. #877	C₂²	semidirect
120. #872	C₂²	semidirect
121. #870	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. D₄²	D₃	semidirect
372. C₃×D₄	#41	semidirect
586. D₄	#237	semidirect
667. C₃	#3513	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₄²	2
#5806	2
#5798	2
C₂×#935	2
C₂×D₄×Dic₃	2
#5719	2
#5713	2
#5614	2
#5611	2
#5603	2
#5602	2
#5601	2
#5600	2
#5593	2
#5587	2
#5586	2
#5546	2
#5541	2
#5539	2
#5538	2
#3513	3