Subgroups — #86056

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#5833	C₂	1	1	yes	maximal, characteristic, complemented
3	#5825	C₂	1	1	yes	maximal, characteristic, complemented
4	#5791	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	#5662	C₂	1	2	yes	maximal, complemented
7	#5660	C₂	1	2	yes	maximal, complemented
8	#5646	C₂	1	2	yes	maximal, complemented
9	#5636	C₂	1	2	yes	maximal, complemented
10	#5621	C₂	1	2	yes	maximal, complemented
11	#5601	C₂	1	2	yes	maximal, complemented
12	#5593	C₂	1	2	yes	maximal, complemented
13	#5593	C₂	1	2	yes	maximal, complemented
14	#5565	C₂	1	1	yes	maximal, characteristic, complemented
15	#5552	C₂	1	1	yes	maximal, characteristic, complemented
16	#5552	C₂	1	1	yes	maximal, characteristic, complemented
17	#5551	C₂	1	1	yes	maximal, characteristic, complemented
18	#5543	C₂	1	1	yes	maximal, characteristic, complemented
19	#5542	C₂	1	1	yes	maximal, characteristic, complemented
20	#5541	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
22	#5534	C₂	1	1	yes	maximal, characteristic, complemented
23	#5518	C₂	1	1	yes	maximal, characteristic, complemented
24	#3541	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic, complemented
29	C₂²×Dic₆	C₂²	1	1	yes	characteristic
30	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#123	C₂²	1	1	yes	characteristic
32	C₃×#123	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#121	C₂²	1	1	yes	characteristic
37	C₃×#120	C₂²	1	1	yes	characteristic
38	C₃×#120	C₂²	1	1	yes	characteristic
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₃×#117	C₂²	1	1	yes	characteristic
44	#953	C₂²	1	2	yes	—
45	C₂×#217	C₂²	1	2	yes	—
46	#946	C₂²	1	2	yes	complemented
47	#944	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	—
49	#939	C₂²	1	2	yes	—
50	#939	C₂²	1	2	yes	—
51	#939	C₂²	1	2	yes	—
52	#939	C₂²	1	2	yes	complemented
53	#938	C₂²	1	2	yes	—
54	#938	C₂²	1	2	yes	—
55	#936	C₂²	1	2	yes	—
56	#936	C₂²	1	2	yes	—
57	#935	C₂²	1	2	yes	—
58	#935	C₂²	1	2	yes	—
59	#935	C₂²	1	2	yes	complemented
60	D₄×Dic₃	C₂²	1	2	yes	—
61	D₄×Dic₃	C₂²	1	2	yes	—
62	#930	C₂²	1	1	yes	characteristic
63	#930	C₂²	1	1	yes	characteristic
64	#930	C₂²	1	1	yes	characteristic, complemented
65	#929	C₂²	1	2	yes	—
66	C₄×#67	C₂²	1	2	yes	—
67	C₄×#67	C₂²	1	2	yes	—
68	#926	C₂²	1	1	yes	characteristic
69	#926	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
71	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
72	#924	C₂²	1	2	yes	—
73	#924	C₂²	1	2	yes	—
74	#924	C₂²	1	1	yes	characteristic
75	#924	C₂²	1	1	yes	characteristic
76	#924	C₂²	1	1	yes	characteristic
77	#924	C₂²	1	1	yes	characteristic
78	#924	C₂²	1	1	yes	characteristic
79	#924	C₂²	1	1	yes	characteristic
80	#924	C₂²	1	1	yes	characteristic, complemented
81	#924	C₂²	1	1	yes	characteristic, complemented
82	#924	C₂²	1	1	yes	characteristic, complemented
83	C₂×Dic₃⋊C₄	C₂²	1	2	yes	—
84	#898	C₂²	1	2	yes	complemented
85	#898	C₂²	1	2	yes	complemented
86	#896	C₂²	1	2	yes	complemented
87	#896	C₂²	1	2	yes	complemented
88	#896	C₂²	1	2	yes	complemented
89	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
90	#890	C₂²	1	2	yes	complemented
91	#889	C₂²	1	2	yes	complemented
92	#889	C₂²	1	2	yes	complemented
93	#889	C₂²	1	2	yes	complemented
94	#888	C₂²	1	2	yes	complemented
95	#887	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	—
97	#885	C₂²	1	2	yes	—
98	#885	C₂²	1	2	yes	complemented
99	#883	C₂²	1	2	yes	—
100	#883	C₂²	1	2	yes	—
101	#883	C₂²	1	2	yes	complemented
102	#883	C₂²	1	2	yes	complemented
103	#67⋊C₄	C₂²	1	2	yes	—
104	#67⋊C₄	C₂²	1	2	yes	—
105	#67⋊C₄	C₂²	1	2	yes	complemented
106	#879	C₂²	1	2	yes	—
107	#879	C₂²	1	2	yes	—
108	#879	C₂²	1	2	yes	—
109	#879	C₂²	1	2	yes	—
110	#879	C₂²	1	2	yes	complemented
111	#878	C₂²	1	2	yes	—
112	#878	C₂²	1	2	yes	—
113	#878	C₂²	1	2	yes	complemented
114	#878	C₂²	1	2	yes	complemented
115	#877	C₂²	1	2	yes	complemented
116	#875	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
118	#870	C₂²	1	1	yes	characteristic, complemented
119	#869	C₂²	1	1	yes	characteristic, complemented
120	#869	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆	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	#563	—	3	2	no	—
125	#562	—	3	2	no	—
126	#556	—	3	1	no	—
127	#554	—	3	2	no	—
128	#554	—	3	1	no	—
129	#553	—	3	2	no	—
130	#553	—	3	1	no	—
131	#552	—	3	1	no	—
132	D₄×Q₈	—	3	1	no	—
133	#548	—	3	1	no	—
134	#548	—	3	1	no	—
135	#547	—	3	1	no	—
136	#542	—	3	2	no	—
137	#542	—	3	1	no	—
138	#541	—	3	1	no	—
139	#539	—	3	2	no	—
140	#538	—	3	2	no	—
141	#538	—	3	2	no	—
142	#537	—	3	1	no	—
143	#536	—	3	1	no	—
144	#525	—	3	1	no	—
145	#525	D₃	1	1	yes	characteristic, complemented
146	C₂×C₂²⋊Q₈	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	1	yes	characteristic
148	C₃×#41	—	4	2	no	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄	—	4	2	no	—
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×C₄	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	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
166	C₂×#67	C₂³	1	2	yes	—
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	2	yes	—
169	C₂×#67	C₂³	1	2	yes	—
170	C₂×#67	C₂³	1	2	yes	—
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	2	yes	—
174	C₂²×Dic₃	C₂³	1	2	yes	—
175	#235	—	4	2	no	—
176	#235	—	4	2	no	—
177	C₂×D₁₂	C₂³	1	1	yes	characteristic
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×Dic₆	—	4	2	no	—
182	C₂×Dic₆	—	4	2	no	—
183	C₂×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×Dic₆	C₂³	1	1	yes	characteristic
185	C₂×Dic₆	C₂³	1	1	yes	characteristic
186	C₂×Dic₆	C₂³	1	2	yes	—
187	C₂×Dic₆	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₃×C₄²	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
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	2	yes	—
217	#217	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	2	yes	—
223	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	2	yes	—
232	C₄⋊Dic₃	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	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	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	2	yes	—
246	Dic₃⋊C₄	C₂³	1	2	yes	—
247	C₄×Dic₃	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	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂×#41	C₂×D₃	1	1	yes	characteristic
255	C₂²×Q₈	—	3	1	no	—
256	C₂²×Q₈	—	3	1	no	—
257	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
258	C₄⋊Q₈	—	3	2	no	—
259	C₄⋊Q₈	—	3	2	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	—	3	1	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#126	—	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	2	no	—
275	#124	—	3	2	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	1	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	2	no	—
288	#123	C₂×D₃	1	1	yes	characteristic
289	#123	C₂×D₃	1	1	yes	characteristic
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	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	2	no	—
297	C₂²⋊Q₈	—	3	1	no	—
298	C₂²⋊Q₈	—	3	1	no	—
299	C₂²⋊Q₈	—	3	1	no	—
300	C₂²⋊Q₈	—	3	1	no	—
301	C₂²⋊Q₈	—	3	1	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	C₂²⋊Q₈	—	3	2	no	—
307	C₂²⋊Q₈	—	3	2	no	—
308	C₂²⋊Q₈	—	3	2	no	—
309	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
310	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
311	#121	—	3	2	no	—
312	#121	—	3	2	no	—
313	#121	—	3	2	no	—
314	#121	—	3	2	no	—
315	#121	—	3	2	no	—
316	#121	—	3	2	no	—
317	#121	—	3	2	no	—
318	#121	—	3	1	no	—
319	#121	—	3	1	no	—
320	#121	—	3	1	no	—
321	#121	C₂×D₃	1	1	yes	characteristic
322	#121	C₂×D₃	1	1	yes	characteristic
323	#120	—	3	2	no	—
324	#120	C₂×D₃	1	1	yes	characteristic
325	#120	C₂×D₃	1	1	yes	characteristic
326	C₄×Q₈	—	3	2	no	—
327	C₄×Q₈	—	3	1	no	—
328	C₄×Q₈	—	3	1	no	—
329	C₄×Q₈	—	3	1	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	2	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	—	3	1	no	—
338	C₄×D₄	C₂×D₃	1	1	yes	characteristic
339	C₄×D₄	C₂×D₃	1	1	yes	characteristic
340	C₄×D₄	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	3	2	no	—
347	C₂×C₄⋊C₄	—	3	1	no	—
348	C₂×C₄⋊C₄	—	3	1	no	—
349	C₂×C₄⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	4	1	no	—
353	C₂³×C₃	—	4	1	no	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₃	C₂⁴	1	2	yes	—
360	C₃×Q₈	—	4	1	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	4	1	no	—
364	C₃×D₄	—	4	1	no	—
365	C₃×D₄	—	4	1	no	—
366	C₃×D₄	—	4	1	no	—
367	C₃×D₄	—	4	1	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	4	1	no	—
374	C₂×C₃×C₄	—	4	1	no	—
375	C₂×C₃×C₄	—	4	1	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	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	#67	—	2	4	no	—
387	#67	—	4	2	no	—
388	#67	—	4	2	no	—
389	#67	—	4	2	no	—
390	#67	—	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	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	2	yes	—
398	C₂×Dic₃	C₂⁴	1	2	yes	—
399	C₂×Dic₃	C₂⁴	1	2	yes	—
400	C₂×Dic₃	C₂⁴	1	2	yes	—
401	C₂×Dic₃	C₂⁴	1	2	yes	—
402	D₁₂	—	2	2	no	—
403	C₄×D₃	—	4	2	no	—
404	C₄×D₃	—	4	2	no	—
405	C₄×D₃	—	4	2	no	—
406	Dic₆	—	2	2	no	—
407	Dic₆	—	2	2	no	—
408	Dic₆	—	2	2	no	—
409	Dic₆	—	4	2	no	—
410	Dic₆	—	4	2	no	—
411	Dic₆	—	4	2	no	—
412	C₂⁴	C₂²×D₃	1	1	yes	characteristic
413	#41	—	4	2	no	—
414	#41	—	12	2	no	—
415	#41	—	12	2	no	—
416	C₂×Q₈	—	3	1	no	—
417	C₂×Q₈	—	3	1	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	3	2	no	—
420	C₂×Q₈	—	3	2	no	—
421	C₂×Q₈	—	3	2	no	—
422	C₂×Q₈	—	12	2	no	—
423	C₂×Q₈	—	12	2	no	—
424	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	1	no	—
431	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
432	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
433	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
436	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
437	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
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	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	3	2	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	2	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	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	—	3	2	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	2	no	—
477	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	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	C₂²×D₃	1	1	yes	characteristic
501	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
502	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
503	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
504	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
505	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
507	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
509	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
510	C₄²	—	3	2	no	—
511	C₄²	—	3	2	no	—
512	C₄²	—	3	2	no	—
513	C₄²	—	3	2	no	—
514	C₄²	—	3	2	no	—
515	C₄²	C₂²×D₃	1	1	yes	characteristic
516	C₄²	C₂²×D₃	1	1	yes	characteristic
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
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	—	2	1	no	—
529	C₂²×C₃	—	2	1	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	4	4	no	—
532	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
533	C₂²×C₃	C₂⁵	1	1	yes	characteristic
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	2	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
547	Dic₃	—	2	2	no	—
548	Dic₃	—	2	2	no	—
549	Dic₃	—	2	2	no	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	2	no	—
552	Dic₃	—	2	2	no	—
553	Dic₃	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	3	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	C₂³×D₃	1	1	yes	characteristic
559	C₂³	C₂³×D₃	1	1	yes	characteristic
560	C₂³	C₂³×D₃	1	1	yes	characteristic
561	C₂³	C₂³×D₃	1	1	yes	characteristic
562	C₂³	C₂³×D₃	1	1	yes	characteristic
563	Q₈	—	4	1	no	—
564	Q₈	—	6	2	no	—
565	Q₈	—	6	2	no	—
566	Q₈	—	6	2	no	—
567	Q₈	—	12	2	no	—
568	Q₈	—	12	2	no	—
569	Q₈	—	12	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	6	4	no	—
578	D₄	—	6	2	no	—
579	D₄	—	12	2	no	—
580	D₄	—	12	2	no	—
581	D₄	—	12	2	no	—
582	D₄	—	12	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	3	2	no	—
591	C₂×C₄	—	3	2	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	3	2	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	12	2	no	—
599	C₂×C₄	—	12	2	no	—
600	C₂×C₄	—	12	2	no	—
601	C₂×C₄	—	12	2	no	—
602	C₂×C₄	—	12	2	no	—
603	C₂×C₄	—	12	2	no	—
604	C₂×C₄	—	12	2	no	—
605	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₃	—	2	2	no	—
616	C₂×C₃	—	4	1	no	—
617	C₂×C₃	—	4	1	no	—
618	C₂×C₃	—	4	1	no	—
619	C₂×C₃	—	4	1	no	—
620	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
622	C₂×C₃	#585	1	1	yes	characteristic
623	D₃	—	4	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	6	2	no	—
640	C₂²	—	6	2	no	—
641	C₂²	—	6	2	no	—
642	C₂²	#1010	1	2	yes	—
643	C₂²	C₂⁴×D₃	1	1	yes	characteristic
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	6	2	no	—
654	C₄	—	6	2	no	—
655	C₄	—	6	2	no	—
656	C₄	—	6	2	no	—
657	C₄	—	6	2	no	—
658	C₄	—	6	2	no	—
659	C₄	—	6	2	no	—
660	C₄	#1004	1	2	yes	—
661	C₃	#3541	1	1	yes	characteristic, complemented, Sylow
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	12	2	no	—
668	C₂	C₂×#1004	1	1	yes	characteristic
669	C₂	C₂×#1010	1	1	yes	characteristic
670	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#525	C₂
hypercenter	#525	D₃
hypocenter	C₃	#3541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₃×#525	C₂	semidirect
2. #5833	C₂	semidirect
3. #5825	C₂	semidirect
4. #5791	C₂	semidirect
5. C₂×#924	C₂	semidirect
6. #5662	C₂	semidirect
7. #5660	C₂	semidirect
8. #5646	C₂	semidirect
9. #5636	C₂	semidirect
10. #5621	C₂	semidirect
11. #5601	C₂	semidirect
12. #5593	C₂	semidirect
13. #5593	C₂	semidirect
14. #5565	C₂	semidirect
15. #5552	C₂	semidirect
16. #5552	C₂	semidirect
17. #5551	C₂	semidirect
18. #5543	C₂	semidirect
19. #5542	C₂	semidirect
20. #5541	C₂	semidirect
21. D₄×Dic₆	C₂	semidirect
22. #5534	C₂	semidirect
23. #5518	C₂	semidirect
28. C₂×#235	C₂²	semidirect
30. C₂²×Dic₆	C₂²	semidirect
46. #946	C₂²	semidirect
47. #944	C₂²	semidirect
52. #939	C₂²	semidirect
59. #935	C₂²	semidirect
64. #930	C₂²	semidirect
69. #926	C₂²	semidirect
71. C₂×C₄⋊Dic₃	C₂²	semidirect
80. #924	C₂²	semidirect
81. #924	C₂²	semidirect
82. #924	C₂²	semidirect
84. #898	C₂²	semidirect
85. #898	C₂²	semidirect
86. #896	C₂²	semidirect
87. #896	C₂²	semidirect
88. #896	C₂²	semidirect
89. D₃×C₄⋊C₄	C₂²	semidirect
90. #890	C₂²	semidirect
91. #889	C₂²	semidirect
92. #889	C₂²	semidirect
93. #889	C₂²	semidirect
94. #888	C₂²	semidirect
95. #887	C₂²	semidirect
98. #885	C₂²	semidirect
101. #883	C₂²	semidirect
102. #883	C₂²	semidirect
105. #67⋊C₄	C₂²	semidirect
110. #879	C₂²	semidirect
113. #878	C₂²	semidirect
114. #878	C₂²	semidirect
115. #877	C₂²	semidirect
116. #875	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
118. #870	C₂²	semidirect
119. #869	C₂²	semidirect
120. #869	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
145. #525	D₃	semidirect
661. C₃	#3541	semidirect

Maximal subgroups

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

subgroup	index
C₃×#525	2
#5833	2
#5825	2
#5791	2
C₂×#924	2
#5662	2
#5660	2
#5646	2
#5636	2
#5621	2
#5601	2
#5593	2
#5565	2
#5552	2
#5551	2
#5543	2
#5542	2
#5541	2
D₄×Dic₆	2
#5534	2
#5518	2
#3541	3