Subgroups — #86672

Order 384.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#5834	C₂	1	1	yes	maximal, characteristic, complemented
3	#5833	C₂	1	1	yes	maximal, characteristic, complemented
4	#5805	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	#5680	C₂	1	1	yes	maximal, characteristic, complemented
7	#5676	C₂	1	1	yes	maximal, characteristic, complemented
8	#5666	C₂	1	2	yes	maximal, complemented
9	#5662	C₂	1	2	yes	maximal, complemented
10	#5641	C₂	1	1	yes	maximal, characteristic, complemented
11	#5629	C₂	1	1	yes	maximal, characteristic, complemented
12	#5613	C₂	1	2	yes	maximal, complemented
13	#5611	C₂	1	1	yes	maximal, characteristic, complemented
14	#5607	C₂	1	1	yes	maximal, characteristic, complemented
15	#5599	C₂	1	2	yes	maximal, complemented
16	#5595	C₂	1	2	yes	maximal, complemented
17	#5592	C₂	1	2	yes	maximal, complemented
18	#5565	C₂	1	1	yes	maximal, characteristic, complemented
19	#5558	C₂	1	1	yes	maximal, characteristic, complemented
20	#5548	C₂	1	1	yes	maximal, characteristic, complemented
21	#5548	C₂	1	1	yes	maximal, characteristic, complemented
22	#5494	C₂	1	2	yes	maximal, complemented
23	#5490	C₂	1	2	yes	maximal, complemented
24	#3546	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₂²×#67	C₂²	1	2	yes	—
28	C₂×#239	C₂²	1	1	yes	characteristic, complemented
29	C₂×#237	C₂²	1	2	yes	complemented
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₂×#235	C₂²	1	2	yes	complemented
32	C₂×#235	C₂²	1	1	yes	characteristic, complemented
33	C₂×#235	C₂²	1	1	yes	characteristic, complemented
34	C₃×#124	C₂²	1	1	yes	characteristic
35	C₃×#123	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×#121	C₂²	1	1	yes	characteristic
38	C₃×#121	C₂²	1	2	yes	complemented
39	C₃×#120	C₂²	1	2	yes	complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
43	#953	C₂²	1	2	yes	—
44	#953	C₂²	1	2	yes	complemented
45	#953	C₂²	1	2	yes	complemented
46	#946	C₂²	1	1	yes	characteristic, complemented
47	#946	C₂²	1	1	yes	characteristic, complemented
48	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
49	#940	C₂²	1	1	yes	characteristic
50	#940	C₂²	1	1	yes	characteristic
51	#940	C₂²	1	2	yes	complemented
52	#940	C₂²	1	2	yes	complemented
53	#940	C₂²	1	2	yes	complemented
54	#939	C₂²	1	2	yes	—
55	#939	C₂²	1	2	yes	complemented
56	#939	C₂²	1	2	yes	complemented
57	#939	C₂²	1	2	yes	complemented
58	#938	C₂²	1	1	yes	characteristic
59	#938	C₂²	1	1	yes	characteristic
60	#938	C₂²	1	1	yes	characteristic
61	#938	C₂²	1	1	yes	characteristic, complemented
62	#938	C₂²	1	1	yes	characteristic, complemented
63	#938	C₂²	1	1	yes	characteristic, complemented
64	#938	C₂²	1	2	yes	complemented
65	#937	C₂²	1	2	yes	—
66	#937	C₂²	1	2	yes	complemented
67	#936	C₂²	1	2	yes	complemented
68	#935	C₂²	1	2	yes	complemented
69	D₄×Dic₃	C₂²	1	1	yes	characteristic
70	#930	C₂²	1	1	yes	characteristic
71	#930	C₂²	1	2	yes	complemented
72	#930	C₂²	1	2	yes	complemented
73	#930	C₂²	1	1	yes	characteristic, complemented
74	#929	C₂²	1	2	yes	complemented
75	C₄×#67	C₂²	1	1	yes	characteristic
76	C₄×#67	C₂²	1	2	yes	complemented
77	C₄×#67	C₂²	1	2	yes	complemented
78	C₄×#67	C₂²	1	2	yes	complemented
79	C₄×#67	C₂²	1	1	yes	characteristic, complemented
80	#926	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
82	#924	C₂²	1	2	yes	complemented
83	#898	C₂²	1	2	yes	complemented
84	#898	C₂²	1	2	yes	complemented
85	#896	C₂²	1	2	yes	complemented
86	#895	C₂²	1	1	yes	characteristic, complemented
87	#895	C₂²	1	2	yes	complemented
88	#895	C₂²	1	1	yes	characteristic, complemented
89	#892	C₂²	1	1	yes	characteristic, complemented
90	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	#888	C₂²	1	1	yes	characteristic, complemented
92	#888	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	2	yes	complemented
94	#885	C₂²	1	2	yes	—
95	#885	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	complemented
97	#885	C₂²	1	1	yes	characteristic, complemented
98	#885	C₂²	1	1	yes	characteristic, complemented
99	#884	C₂²	1	1	yes	characteristic
100	#884	C₂²	1	2	yes	complemented
101	#884	C₂²	1	2	yes	complemented
102	#884	C₂²	1	2	yes	complemented
103	#884	C₂²	1	2	yes	complemented
104	#884	C₂²	1	2	yes	complemented
105	#884	C₂²	1	1	yes	characteristic, complemented
106	#883	C₂²	1	2	yes	complemented
107	#883	C₂²	1	2	yes	complemented
108	#883	C₂²	1	2	yes	complemented
109	#883	C₂²	1	2	yes	complemented
110	#882	C₂²	1	2	yes	complemented
111	#882	C₂²	1	2	yes	complemented
112	#67⋊C₄	C₂²	1	2	yes	complemented
113	#67⋊C₄	C₂²	1	2	yes	complemented
114	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	#879	C₂²	1	2	yes	complemented
116	#879	C₂²	1	2	yes	complemented
117	#879	C₂²	1	2	yes	complemented
118	#878	C₂²	1	2	yes	complemented
119	#877	C₂²	1	2	yes	complemented
120	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
122	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
123	#870	C₂²	1	1	yes	characteristic, complemented
124	#560	—	3	2	no	—
125	#560	—	3	2	no	—
126	#556	—	3	1	no	—
127	#553	—	3	1	no	—
128	#553	—	3	1	no	—
129	#550	—	3	1	no	—
130	#550	—	3	2	no	—
131	#547	—	3	1	no	—
132	#546	—	3	1	no	—
133	#546	—	3	2	no	—
134	#546	D₃	1	1	yes	characteristic, complemented
135	D₄²	—	3	1	no	—
136	#542	—	3	2	no	—
137	#538	—	3	2	no	—
138	#538	—	3	2	no	—
139	#537	—	3	1	no	—
140	#537	—	3	1	no	—
141	#535	—	3	1	no	—
142	#535	—	3	1	no	—
143	#535	—	3	2	no	—
144	#532	—	3	1	no	—
145	#532	—	3	1	no	—
146	#529	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₃×#41	—	4	2	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×D₄	—	4	2	no	—
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂³	1	2	yes	—
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×D₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
161	C₂²×C₃×C₄	C₂³	1	2	yes	—
162	C₂×#67	—	4	4	no	—
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	1	yes	characteristic
165	C₂×#67	C₂³	1	2	yes	—
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	C₂×#67	C₂³	1	1	yes	characteristic
172	C₂×#67	C₂³	1	1	yes	characteristic
173	C₂×#67	C₂³	1	2	yes	—
174	C₂×#67	C₂³	1	2	yes	—
175	C₂×#67	C₂³	1	2	yes	—
176	C₂×#67	C₂³	1	2	yes	—
177	C₂×#67	C₂³	1	1	yes	characteristic
178	C₂×#67	C₂³	1	1	yes	characteristic
179	C₂²×Dic₃	C₂³	1	2	yes	—
180	C₂²×Dic₃	C₂³	1	2	yes	—
181	#239	—	4	2	no	—
182	#237	—	4	4	no	—
183	D₃×D₄	—	4	2	no	—
184	#235	—	4	4	no	—
185	#235	—	4	2	no	—
186	#235	—	4	2	no	—
187	C₂×D₁₂	C₂³	1	1	yes	characteristic
188	C₂×D₁₂	C₂³	1	1	yes	characteristic
189	C₂×D₁₂	C₂³	1	1	yes	characteristic
190	C₂×D₁₂	C₂³	1	2	yes	—
191	C₂×D₁₂	C₂³	1	2	yes	—
192	C₂×D₁₂	C₂³	1	1	yes	characteristic
193	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
194	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
195	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
196	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
197	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
198	C₂×C₄×D₃	C₂³	1	2	yes	—
199	C₂×C₄×D₃	C₂³	1	2	yes	—
200	C₂×C₄×D₃	C₂³	1	2	yes	—
201	C₂×Dic₆	C₂³	1	2	yes	—
202	C₂×Dic₆	C₂³	1	1	yes	characteristic
203	C₂×Dic₆	C₂³	1	1	yes	characteristic
204	C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃×C₄²	C₂³	1	1	yes	characteristic
215	#217	C₂³	1	2	yes	—
216	#217	C₂³	1	2	yes	—
217	#217	C₂³	1	1	yes	characteristic
218	#217	C₂³	1	2	yes	—
219	#217	C₂³	1	2	yes	—
220	#217	C₂³	1	2	yes	—
221	#217	C₂³	1	2	yes	—
222	#217	C₂³	1	2	yes	—
223	#217	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
233	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₃	C₂³	1	2	yes	—
240	C₄⋊Dic₃	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	1	yes	characteristic
245	Dic₃⋊C₄	C₂³	1	2	yes	—
246	Dic₃⋊C₄	C₂³	1	2	yes	—
247	Dic₃⋊C₄	C₂³	1	2	yes	—
248	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₄×Dic₃	C₂³	1	2	yes	—
253	C₄×Dic₃	C₂³	1	2	yes	—
254	C₄×Dic₃	C₂³	1	2	yes	—
255	C₂×#41	—	3	1	no	—
256	C₂×#41	—	3	2	no	—
257	C₂×#41	—	3	1	no	—
258	C₂×#41	—	3	1	no	—
259	C₂×#41	—	3	2	no	—
260	C₂×#41	C₂×D₃	1	1	yes	characteristic, complemented
261	C₂²×D₄	—	3	2	no	—
262	C₂²×D₄	—	3	1	no	—
263	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
264	C₄⋊Q₈	—	3	1	no	—
265	C₄⋊Q₈	—	3	1	no	—
266	#127	—	3	1	no	—
267	#127	—	3	1	no	—
268	#127	—	3	2	no	—
269	#127	—	3	2	no	—
270	#127	—	3	2	no	—
271	#126	—	3	2	no	—
272	#126	—	3	2	no	—
273	#126	—	3	2	no	—
274	#126	—	3	2	no	—
275	#126	—	3	2	no	—
276	#125	—	3	1	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	1	no	—
280	#124	—	3	1	no	—
281	#124	—	3	2	no	—
282	#124	—	3	2	no	—
283	#124	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	2	yes	complemented
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	#121	—	3	1	no	—
298	#121	—	3	1	no	—
299	#121	—	3	1	no	—
300	#121	—	3	2	no	—
301	#121	—	3	1	no	—
302	#121	—	3	1	no	—
303	#121	—	3	2	no	—
304	#121	—	3	1	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	2	no	—
308	#121	—	3	1	no	—
309	#121	—	3	1	no	—
310	#121	—	3	2	no	—
311	#121	—	3	2	no	—
312	#121	—	3	1	no	—
313	#121	—	3	1	no	—
314	#121	—	3	2	no	—
315	#121	—	3	1	no	—
316	#121	—	3	1	no	—
317	#121	—	3	2	no	—
318	#121	—	3	2	no	—
319	#121	—	3	2	no	—
320	#121	—	3	2	no	—
321	#121	—	3	2	no	—
322	#121	C₂×D₃	1	1	yes	characteristic
323	#121	C₂×D₃	1	2	yes	complemented
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	#120	—	3	2	no	—
327	#120	—	3	2	no	—
328	#120	—	3	2	no	—
329	#120	—	3	2	no	—
330	#120	—	3	2	no	—
331	#120	C₂×D₃	1	2	yes	complemented
332	C₄×Q₈	—	3	1	no	—
333	C₄×Q₈	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	2	no	—
336	C₄×D₄	—	3	1	no	—
337	C₄×D₄	—	3	1	no	—
338	C₄×D₄	—	3	2	no	—
339	C₄×D₄	—	3	2	no	—
340	C₄×D₄	—	3	2	no	—
341	C₄×D₄	—	3	2	no	—
342	C₄×D₄	—	3	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
345	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
346	#117	—	3	1	no	—
347	#117	—	3	1	no	—
348	#117	—	3	2	no	—
349	C₂×C₄⋊C₄	—	3	1	no	—
350	C₂×C₄⋊C₄	—	3	1	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
353	C₂×C₄²	—	3	1	no	—
354	C₂³×C₃	—	4	2	no	—
355	C₂³×C₃	—	4	2	no	—
356	C₂³×C₃	—	4	2	no	—
357	C₂³×C₃	C₂⁴	1	2	yes	—
358	C₂³×C₃	C₂⁴	1	1	yes	characteristic
359	C₂³×C₃	C₂⁴	1	2	yes	—
360	C₂³×C₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	—	4	2	no	—
363	C₂²×D₃	—	4	2	no	—
364	C₂²×D₃	C₂⁴	1	1	yes	characteristic
365	C₂²×D₃	C₂⁴	1	2	yes	—
366	C₂²×D₃	C₂⁴	1	1	yes	characteristic
367	C₂²×D₃	C₂⁴	1	1	yes	characteristic
368	C₃×Q₈	—	2	2	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	4	2	no	—
372	C₃×D₄	—	4	2	no	—
373	C₃×D₄	—	4	1	no	—
374	C₃×D₄	—	4	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	4	2	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	—	2	2	no	—
388	#67	—	2	2	no	—
389	#67	—	4	2	no	—
390	#67	—	4	1	no	—
391	#67	—	4	1	no	—
392	#67	—	4	1	no	—
393	#67	—	4	1	no	—
394	#67	—	4	2	no	—
395	#67	—	4	2	no	—
396	#67	—	4	2	no	—
397	#67	—	4	2	no	—
398	#67	—	4	2	no	—
399	#67	—	4	2	no	—
400	#67	—	4	2	no	—
401	#67	—	4	2	no	—
402	C₂×Dic₃	—	2	4	no	—
403	C₂×Dic₃	—	4	2	no	—
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	C₂×Dic₃	C₂⁴	1	2	yes	—
410	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
412	D₁₂	—	2	2	no	—
413	D₁₂	—	4	1	no	—
414	D₁₂	—	4	2	no	—
415	D₁₂	—	4	1	no	—
416	D₁₂	—	4	1	no	—
417	D₁₂	—	4	2	no	—
418	C₄×D₃	—	2	2	no	—
419	C₄×D₃	—	2	2	no	—
420	C₄×D₃	—	2	2	no	—
421	C₄×D₃	—	2	2	no	—
422	C₄×D₃	—	4	1	no	—
423	C₄×D₃	—	4	2	no	—
424	C₄×D₃	—	4	2	no	—
425	C₄×D₃	—	4	2	no	—
426	Dic₆	—	2	4	no	—
427	Dic₆	—	4	1	no	—
428	Dic₆	—	4	1	no	—
429	C₂⁴	—	3	2	no	—
430	C₂⁴	C₂²×D₃	1	2	yes	—
431	#41	—	4	2	no	—
432	#41	—	12	2	no	—
433	#41	—	12	2	no	—
434	#41	—	12	4	no	—
435	#41	—	12	4	no	—
436	#41	—	12	2	no	—
437	C₂×Q₈	—	3	2	no	—
438	C₂×Q₈	—	3	1	no	—
439	C₂×Q₈	—	3	1	no	—
440	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	1	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	2	no	—
448	C₂×D₄	—	3	1	no	—
449	C₂×D₄	—	3	2	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	3	2	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂×D₄	—	3	1	no	—
458	C₂×D₄	—	3	1	no	—
459	C₂×D₄	—	3	1	no	—
460	C₂×D₄	—	3	2	no	—
461	C₂×D₄	—	3	2	no	—
462	C₂×D₄	—	3	1	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	12	2	no	—
465	C₂×D₄	—	12	4	no	—
466	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
467	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
468	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₃	1	2	yes	—
470	C₂×D₄	C₂²×D₃	1	2	yes	—
471	C₂×D₄	C₂²×D₃	1	2	yes	—
472	C₂²×C₄	—	3	2	no	—
473	C₂²×C₄	—	3	2	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₂²×C₄	—	3	1	no	—
476	C₂²×C₄	—	3	1	no	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	3	2	no	—
480	C₂²×C₄	—	3	2	no	—
481	C₂²×C₄	—	3	2	no	—
482	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
484	C₂²×C₄	C₂²×D₃	1	2	yes	—
485	C₂²×C₄	C₂²×D₃	1	2	yes	—
486	C₄⋊C₄	—	3	1	no	—
487	C₄⋊C₄	—	3	1	no	—
488	C₄⋊C₄	—	3	2	no	—
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	—	3	2	no	—
492	C₄⋊C₄	—	3	2	no	—
493	C₄⋊C₄	—	3	1	no	—
494	C₄⋊C₄	—	3	2	no	—
495	C₄⋊C₄	—	3	1	no	—
496	C₄⋊C₄	—	3	2	no	—
497	C₄⋊C₄	—	3	1	no	—
498	C₄⋊C₄	—	3	2	no	—
499	C₄⋊C₄	—	3	2	no	—
500	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₃	1	2	yes	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	1	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	2	no	—
509	C₂²⋊C₄	—	3	2	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	3	1	no	—
512	C₂²⋊C₄	—	3	1	no	—
513	C₂²⋊C₄	—	3	2	no	—
514	C₂²⋊C₄	—	3	2	no	—
515	C₂²⋊C₄	—	3	1	no	—
516	C₂²⋊C₄	—	3	1	no	—
517	C₂²⋊C₄	—	3	2	no	—
518	C₂²⋊C₄	—	3	2	no	—
519	C₂²⋊C₄	—	3	2	no	—
520	C₂²⋊C₄	—	3	2	no	—
521	C₂²⋊C₄	—	3	2	no	—
522	C₂²⋊C₄	—	3	1	no	—
523	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
529	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
530	C₄²	—	3	1	no	—
531	C₄²	—	3	1	no	—
532	C₄²	—	3	1	no	—
533	C₄²	—	3	2	no	—
534	C₄²	—	3	2	no	—
535	C₄²	—	3	2	no	—
536	C₄²	C₂²×D₃	1	1	yes	characteristic
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	—	2	1	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	1	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	1	no	—
549	C₂²×C₃	—	8	4	no	—
550	C₂²×C₃	C₂⁵	1	1	yes	characteristic
551	C₂×D₃	—	2	1	no	—
552	C₂×D₃	—	2	1	no	—
553	C₂×D₃	—	2	1	no	—
554	C₂×D₃	—	2	1	no	—
555	C₂×D₃	—	2	1	no	—
556	C₂×D₃	—	2	2	no	—
557	C₂×D₃	—	2	2	no	—
558	C₂×D₃	—	2	1	no	—
559	C₂×D₃	—	2	1	no	—
560	C₂×D₃	—	2	1	no	—
561	C₂×D₃	—	2	1	no	—
562	C₂×D₃	—	2	2	no	—
563	C₂×D₃	—	8	4	no	—
564	C₃×C₄	—	2	2	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	2	2	no	—
569	C₃×C₄	—	2	1	no	—
570	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
571	Dic₃	—	2	2	no	—
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	Dic₃	—	2	1	no	—
575	Dic₃	—	2	2	no	—
576	Dic₃	—	2	1	no	—
577	Dic₃	—	2	2	no	—
578	Dic₃	H(5,𝔽₂)	1	2	yes	—
579	C₂³	—	3	1	no	—
580	C₂³	—	3	2	no	—
581	C₂³	—	3	1	no	—
582	C₂³	—	3	1	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	12	2	no	—
587	C₂³	—	12	2	no	—
588	C₂³	—	12	2	no	—
589	C₂³	C₂³×D₃	1	2	yes	—
590	C₂³	C₂³×D₃	1	1	yes	characteristic
591	C₂³	C₂³×D₃	1	2	yes	—
592	C₂³	C₂³×D₃	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	6	4	no	—
595	Q₈	—	12	1	no	—
596	Q₈	—	12	1	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	4	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	1	no	—
603	D₄	—	6	2	no	—
604	D₄	—	6	4	no	—
605	D₄	—	6	2	no	—
606	D₄	—	6	2	no	—
607	D₄	—	12	1	no	—
608	D₄	—	12	1	no	—
609	D₄	—	12	2	no	—
610	D₄	—	12	2	no	—
611	D₄	—	12	1	no	—
612	D₄	—	12	2	no	—
613	D₄	—	12	2	no	—
614	D₄	—	12	2	no	—
615	D₄	—	12	1	no	—
616	D₄	—	12	1	no	—
617	D₄	—	12	1	no	—
618	D₄	—	12	1	no	—
619	D₄	—	12	2	no	—
620	D₄	—	12	2	no	—
621	D₄	—	12	2	no	—
622	D₄	—	12	2	no	—
623	D₄	—	12	2	no	—
624	D₄	—	12	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	2	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	3	2	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	3	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	6	2	no	—
638	C₂×C₄	—	6	4	no	—
639	C₂×C₄	—	6	2	no	—
640	C₂×C₄	—	6	2	no	—
641	C₂×C₄	—	6	2	no	—
642	C₂×C₄	—	12	2	no	—
643	C₂×C₄	—	12	2	no	—
644	C₂×C₄	—	12	2	no	—
645	C₂×C₄	—	12	1	no	—
646	C₂×C₄	—	12	2	no	—
647	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₃	1	2	yes	—
651	C₂×C₄	C₂³×D₃	1	2	yes	—
652	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
654	C₂×C₃	—	4	2	no	—
655	C₂×C₃	—	4	1	no	—
656	C₂×C₃	—	4	2	no	—
657	C₂×C₃	—	4	1	no	—
658	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂×C₃	#585	1	1	yes	characteristic
661	D₃	—	4	1	no	—
662	D₃	—	4	1	no	—
663	D₃	—	4	2	no	—
664	D₃	—	4	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	6	1	no	—
678	C₂²	—	6	1	no	—
679	C₂²	—	6	1	no	—
680	C₂²	—	6	2	no	—
681	C₂²	—	6	1	no	—
682	C₂²	—	6	1	no	—
683	C₂²	—	6	2	no	—
684	C₂²	—	6	1	no	—
685	C₂²	—	6	1	no	—
686	C₂²	—	6	1	no	—
687	C₂²	—	6	2	no	—
688	C₂²	—	6	1	no	—
689	C₂²	—	8	4	no	—
690	C₂²	—	24	4	no	—
691	C₂²	C₂⁴×D₃	1	1	yes	characteristic
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	3	2	no	—
699	C₄	—	6	1	no	—
700	C₄	—	6	1	no	—
701	C₄	—	6	1	no	—
702	C₄	—	6	1	no	—
703	C₄	—	6	2	no	—
704	C₄	—	6	2	no	—
705	C₄	—	6	2	no	—
706	C₄	#1004	1	2	yes	—
707	C₃	#3546	1	1	yes	characteristic, complemented, Sylow
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	12	1	no	—
713	C₂	—	12	2	no	—
714	C₂	—	12	1	no	—
715	C₂	—	12	1	no	—
716	C₂	C₂×#1004	1	1	yes	characteristic
717	C₂	#5964	1	1	yes	characteristic
718	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×#546	C₂
hypercenter	#546	D₃
hypocenter	C₃	#3546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₃×#546	C₂	semidirect
2. #5834	C₂	semidirect
3. #5833	C₂	semidirect
4. #5805	C₂	semidirect
5. D₄×#67	C₂	semidirect
6. #5680	C₂	semidirect
7. #5676	C₂	semidirect
8. #5666	C₂	semidirect
9. #5662	C₂	semidirect
10. #5641	C₂	semidirect
11. #5629	C₂	semidirect
12. #5613	C₂	semidirect
13. #5611	C₂	semidirect
14. #5607	C₂	semidirect
15. #5599	C₂	semidirect
16. #5595	C₂	semidirect
17. #5592	C₂	semidirect
18. #5565	C₂	semidirect
19. #5558	C₂	semidirect
20. #5548	C₂	semidirect
21. #5548	C₂	semidirect
22. #5494	C₂	semidirect
23. #5490	C₂	semidirect
25. C₂×C₃×#41	C₂²	semidirect
28. C₂×#239	C₂²	semidirect
29. C₂×#237	C₂²	semidirect
31. C₂×#235	C₂²	semidirect
32. C₂×#235	C₂²	semidirect
33. C₂×#235	C₂²	semidirect
35. C₃×#123	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
39. C₃×#120	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
42. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
44. #953	C₂²	semidirect
45. #953	C₂²	semidirect
46. #946	C₂²	semidirect
47. #946	C₂²	semidirect
48. Q₈×Dic₃	C₂²	semidirect
51. #940	C₂²	semidirect
52. #940	C₂²	semidirect
53. #940	C₂²	semidirect
55. #939	C₂²	semidirect
56. #939	C₂²	semidirect
57. #939	C₂²	semidirect
61. #938	C₂²	semidirect
62. #938	C₂²	semidirect
63. #938	C₂²	semidirect
64. #938	C₂²	semidirect
66. #937	C₂²	semidirect
67. #936	C₂²	semidirect
68. #935	C₂²	semidirect
71. #930	C₂²	semidirect
72. #930	C₂²	semidirect
73. #930	C₂²	semidirect
74. #929	C₂²	semidirect
76. C₄×#67	C₂²	semidirect
77. C₄×#67	C₂²	semidirect
78. C₄×#67	C₂²	semidirect
79. C₄×#67	C₂²	semidirect
80. #926	C₂²	semidirect
81. C₂×C₄⋊Dic₃	C₂²	semidirect
82. #924	C₂²	semidirect
83. #898	C₂²	semidirect
84. #898	C₂²	semidirect
85. #896	C₂²	semidirect
86. #895	C₂²	semidirect
87. #895	C₂²	semidirect
88. #895	C₂²	semidirect
89. #892	C₂²	semidirect
90. D₃×C₄⋊C₄	C₂²	semidirect
91. #888	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
95. #885	C₂²	semidirect
96. #885	C₂²	semidirect
97. #885	C₂²	semidirect
98. #885	C₂²	semidirect
100. #884	C₂²	semidirect
101. #884	C₂²	semidirect
102. #884	C₂²	semidirect
103. #884	C₂²	semidirect
104. #884	C₂²	semidirect
105. #884	C₂²	semidirect
106. #883	C₂²	semidirect
107. #883	C₂²	semidirect
108. #883	C₂²	semidirect
109. #883	C₂²	semidirect
110. #882	C₂²	semidirect
111. #882	C₂²	semidirect
112. #67⋊C₄	C₂²	semidirect
113. #67⋊C₄	C₂²	semidirect
114. D₃×C₂²⋊C₄	C₂²	semidirect
115. #879	C₂²	semidirect
116. #879	C₂²	semidirect
117. #879	C₂²	semidirect
118. #878	C₂²	semidirect
119. #877	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. C₄×D₁₂	C₂²	semidirect
122. C₄²×D₃	C₂²	semidirect
123. #870	C₂²	semidirect
134. #546	D₃	semidirect
260. C₂×#41	C₂×D₃	semidirect
290. #123	C₂×D₃	semidirect
296. C₂²⋊Q₈	C₂×D₃	semidirect
323. #121	C₂×D₃	semidirect
331. #120	C₂×D₃	semidirect
344. C₄×D₄	C₂×D₃	semidirect
345. C₄×D₄	C₂×D₃	semidirect
352. C₂×C₂²⋊C₄	C₂×D₃	semidirect
707. C₃	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₃×#546	2
#5834	2
#5833	2
#5805	2
D₄×#67	2
#5680	2
#5676	2
#5666	2
#5662	2
#5641	2
#5629	2
#5613	2
#5611	2
#5607	2
#5599	2
#5595	2
#5592	2
#5565	2
#5558	2
#5548	2
#5494	2
#5490	2
#3546	3