Subgroups — #86878

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#5706	C₂	1	2	yes	maximal, complemented
3	#5705	C₂	1	2	yes	maximal, complemented
4	#5695	C₂	1	1	yes	maximal, characteristic, complemented
5	#5689	C₂	1	1	yes	maximal, characteristic, complemented
6	#5662	C₂	1	2	yes	maximal, complemented
7	#5654	C₂	1	2	yes	maximal, complemented
8	#5616	C₂	1	1	yes	maximal, characteristic, complemented
9	#5615	C₂	1	2	yes	maximal, complemented
10	#5614	C₂	1	1	yes	maximal, characteristic, complemented
11	#5612	C₂	1	2	yes	maximal, complemented
12	#5607	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	#5563	C₂	1	1	yes	maximal, characteristic, complemented
15	#5556	C₂	1	2	yes	maximal, complemented
16	#5551	C₂	1	1	yes	maximal, characteristic, complemented
17	#5548	C₂	1	2	yes	maximal, complemented
18	#5547	C₂	1	1	yes	maximal, characteristic, complemented
19	#5545	C₂	1	1	yes	maximal, characteristic, complemented
20	#5530	C₂	1	1	yes	maximal, characteristic, complemented
21	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
22	#5507	C₂	1	1	yes	maximal, characteristic, complemented
23	#5504	C₂	1	1	yes	maximal, characteristic, complemented
24	#3494	—	3	1	no	maximal, Sylow
25	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
26	C₂×D₃×D₄	C₂²	1	2	yes	—
27	C₂×#235	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	2	yes	complemented
29	C₂×#235	C₂²	1	2	yes	complemented
30	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₃×#126	C₂²	1	2	yes	complemented
32	C₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₃×#123	C₂²	1	2	yes	complemented
34	C₃×#121	C₂²	1	1	yes	characteristic
35	C₃×#121	C₂²	1	1	yes	characteristic, complemented
36	C₃×#121	C₂²	1	2	yes	complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×D₄	C₂²	1	2	yes	complemented
40	C₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	#940	C₂²	1	2	yes	complemented
43	#939	C₂²	1	2	yes	—
44	#939	C₂²	1	2	yes	complemented
45	#939	C₂²	1	1	yes	characteristic, complemented
46	#938	C₂²	1	1	yes	characteristic
47	#938	C₂²	1	2	yes	complemented
48	#938	C₂²	1	1	yes	characteristic, complemented
49	#938	C₂²	1	2	yes	complemented
50	#937	C₂²	1	1	yes	characteristic
51	#937	C₂²	1	2	yes	—
52	#936	C₂²	1	2	yes	complemented
53	#935	C₂²	1	2	yes	complemented
54	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
55	#930	C₂²	1	1	yes	characteristic
56	#930	C₂²	1	1	yes	characteristic, complemented
57	#929	C₂²	1	2	yes	complemented
58	C₄×#67	C₂²	1	2	yes	—
59	C₄×#67	C₂²	1	2	yes	complemented
60	C₄×#67	C₂²	1	2	yes	complemented
61	C₄×#67	C₂²	1	1	yes	characteristic, complemented
62	C₄×#67	C₂²	1	1	yes	characteristic, complemented
63	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
64	#926	C₂²	1	1	yes	characteristic, complemented
65	#926	C₂²	1	1	yes	characteristic, complemented
66	#924	C₂²	1	2	yes	complemented
67	#898	C₂²	1	2	yes	complemented
68	#897	C₂²	1	2	yes	—
69	#896	C₂²	1	2	yes	—
70	#896	C₂²	1	2	yes	complemented
71	#896	C₂²	1	1	yes	characteristic, complemented
72	#895	C₂²	1	1	yes	characteristic
73	#895	C₂²	1	2	yes	complemented
74	#895	C₂²	1	1	yes	characteristic, complemented
75	#894	C₂²	1	1	yes	characteristic
76	#894	C₂²	1	2	yes	complemented
77	#894	C₂²	1	2	yes	complemented
78	#893	C₂²	1	2	yes	—
79	#893	C₂²	1	2	yes	complemented
80	#893	C₂²	1	1	yes	characteristic, complemented
81	#892	C₂²	1	1	yes	characteristic
82	#892	C₂²	1	1	yes	characteristic
83	#892	C₂²	1	1	yes	characteristic, complemented
84	#892	C₂²	1	2	yes	complemented
85	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	#890	C₂²	1	1	yes	characteristic, complemented
90	#889	C₂²	1	2	yes	complemented
91	#888	C₂²	1	2	yes	complemented
92	#888	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	2	yes	complemented
94	#885	C₂²	1	2	yes	complemented
95	#885	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	complemented
97	#885	C₂²	1	2	yes	complemented
98	#884	C₂²	1	2	yes	—
99	#884	C₂²	1	2	yes	complemented
100	#884	C₂²	1	1	yes	characteristic, complemented
101	#883	C₂²	1	1	yes	characteristic
102	#883	C₂²	1	2	yes	complemented
103	#883	C₂²	1	2	yes	complemented
104	#883	C₂²	1	2	yes	complemented
105	#882	C₂²	1	1	yes	characteristic
106	#882	C₂²	1	2	yes	—
107	#67⋊C₄	C₂²	1	2	yes	complemented
108	#67⋊C₄	C₂²	1	2	yes	complemented
109	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
110	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
111	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	#879	C₂²	1	2	yes	complemented
113	#878	C₂²	1	1	yes	characteristic, complemented
114	#877	C₂²	1	2	yes	complemented
115	#877	C₂²	1	2	yes	complemented
116	#876	C₂²	1	2	yes	complemented
117	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₁₂	C₂²	1	2	yes	complemented
120	#872	C₂²	1	1	yes	characteristic
121	#872	C₂²	1	2	yes	—
122	C₄²×D₃	C₂²	1	2	yes	complemented
123	#869	C₂²	1	1	yes	characteristic, complemented
124	#555	—	3	1	no	—
125	#555	—	3	1	no	—
126	#553	—	3	1	no	—
127	#553	—	3	1	no	—
128	#553	—	3	1	no	—
129	#553	D₃	1	1	yes	characteristic, complemented
130	#551	—	3	2	no	—
131	#551	—	3	2	no	—
132	#547	—	3	1	no	—
133	#547	—	3	1	no	—
134	#546	—	3	2	no	—
135	#546	—	3	2	no	—
136	#544	—	3	1	no	—
137	#542	—	3	2	no	—
138	#540	—	3	2	no	—
139	#535	—	3	1	no	—
140	#532	—	3	2	no	—
141	#529	—	3	2	no	—
142	#525	—	3	1	no	—
143	C₂×#121	—	3	1	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	2	yes	—
156	C₂²×C₃×C₄	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	1	yes	characteristic
160	C₂×#67	C₂³	1	1	yes	characteristic
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	2	yes	—
166	C₂²×Dic₃	C₂³	1	1	yes	characteristic
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	D₃×D₄	—	2	4	no	—
169	D₃×D₄	—	4	4	no	—
170	#235	—	2	4	no	—
171	#235	—	4	4	no	—
172	#235	—	4	4	no	—
173	C₂×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×D₁₂	C₂³	1	1	yes	characteristic
175	C₂×D₁₂	C₂³	1	1	yes	characteristic
176	C₂×D₁₂	C₂³	1	2	yes	—
177	C₂×D₁₂	C₂³	1	2	yes	—
178	C₂×C₄×D₃	—	2	4	no	—
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	2	yes	—
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×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
190	C₂×Dic₆	C₂³	1	1	yes	characteristic
191	C₂×Dic₆	C₂³	1	2	yes	—
192	C₂×Dic₆	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
206	C₃×C₄²	C₂³	1	1	yes	characteristic
207	C₃×C₄²	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	1	yes	characteristic
211	#217	C₂³	1	2	yes	—
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	1	yes	characteristic
214	#217	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
222	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₃	C₂³	1	2	yes	—
235	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₃⋊C₄	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	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	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	2	yes	—
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	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	2	no	—
254	C₂×#41	—	3	2	no	—
255	C₂²×D₄	—	3	1	no	—
256	C₂²×D₄	—	3	2	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	2	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	#127	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	C₂×D₃	1	2	yes	complemented
266	#125	—	3	2	no	—
267	#125	—	3	1	no	—
268	#125	C₂×D₃	1	1	yes	characteristic, complemented
269	#124	—	3	2	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#123	—	3	2	no	—
275	#123	—	3	2	no	—
276	#123	—	3	1	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	1	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	C₂×D₃	1	2	yes	complemented
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	1	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	#121	—	3	2	no	—
291	#121	—	3	1	no	—
292	#121	—	3	1	no	—
293	#121	—	3	2	no	—
294	#121	—	3	1	no	—
295	#121	—	3	2	no	—
296	#121	—	3	2	no	—
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	2	no	—
303	#121	—	3	1	no	—
304	#121	—	3	2	no	—
305	#121	C₂×D₃	1	1	yes	characteristic
306	#121	C₂×D₃	1	1	yes	characteristic, complemented
307	#121	C₂×D₃	1	2	yes	complemented
308	#120	—	3	1	no	—
309	#120	—	3	2	no	—
310	#120	—	3	1	no	—
311	#120	—	3	2	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	2	no	—
322	C₄×D₄	—	3	2	no	—
323	C₄×D₄	—	3	2	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
328	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
329	C₄×D₄	C₂×D₃	1	2	yes	complemented
330	#117	—	3	1	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	1	no	—
334	#117	—	3	1	no	—
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	—	3	2	no	—
338	#117	—	3	2	no	—
339	#117	—	3	1	no	—
340	#117	C₂×D₃	1	1	yes	characteristic, complemented
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	1	no	—
345	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	2	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	2	yes	—
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	4	1	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	C₂⁴	1	2	yes	—
361	C₂²×D₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₃	C₂⁴	1	1	yes	characteristic
364	C₃×D₄	—	2	2	no	—
365	C₃×D₄	—	4	2	no	—
366	C₃×D₄	—	4	1	no	—
367	C₃×D₄	—	4	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	4	2	no	—
371	C₂×C₃×C₄	—	4	2	no	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	#67	—	2	2	no	—
381	#67	—	2	2	no	—
382	#67	—	2	4	no	—
383	#67	—	2	2	no	—
384	#67	—	2	4	no	—
385	#67	—	4	2	no	—
386	#67	—	4	2	no	—
387	#67	—	4	2	no	—
388	#67	—	4	1	no	—
389	C₂×Dic₃	—	2	2	no	—
390	C₂×Dic₃	—	4	2	no	—
391	C₂×Dic₃	C₂⁴	1	2	yes	—
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃	C₂⁴	1	2	yes	—
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	D₁₂	—	2	2	no	—
400	D₁₂	—	2	2	no	—
401	D₁₂	—	2	4	no	—
402	D₁₂	—	2	2	no	—
403	D₁₂	—	4	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	4	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	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	C₄×D₃	—	4	2	no	—
414	C₄×D₃	#41	1	4	yes	complemented
415	Dic₆	—	2	2	no	—
416	Dic₆	—	4	2	no	—
417	Dic₆	—	4	2	no	—
418	C₂⁴	—	3	1	no	—
419	C₂⁴	—	3	2	no	—
420	#41	—	6	4	no	—
421	#41	—	12	4	no	—
422	#41	—	12	4	no	—
423	C₂×Q₈	—	3	1	no	—
424	C₂×Q₈	—	3	2	no	—
425	C₂×Q₈	—	3	2	no	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	1	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	3	1	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	6	4	no	—
441	C₂×D₄	—	12	4	no	—
442	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
443	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
444	C₂×D₄	C₂²×D₃	1	2	yes	—
445	C₂×D₄	C₂²×D₃	1	2	yes	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	2	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	2	no	—
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	2	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	2	no	—
459	C₂²×C₄	—	6	4	no	—
460	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₃	1	2	yes	—
463	C₂²×C₄	C₂²×D₃	1	2	yes	—
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	2	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	2	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	1	no	—
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	C₄⋊C₄	C₂²×D₃	1	2	yes	—
484	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₃	1	2	yes	—
486	C₄⋊C₄	C₂²×D₃	1	2	yes	—
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	2	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	1	no	—
505	C₂²⋊C₄	—	3	1	no	—
506	C₂²⋊C₄	—	3	1	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	1	no	—
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	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
515	C₄²	—	3	2	no	—
516	C₄²	—	3	2	no	—
517	C₄²	—	3	2	no	—
518	C₄²	—	3	2	no	—
519	C₄²	—	3	2	no	—
520	C₄²	—	3	1	no	—
521	C₄²	C₂²×D₃	1	2	yes	—
522	C₄²	C₂²×D₃	1	1	yes	characteristic
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	C₂⁵	1	1	yes	characteristic
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	2	1	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	2	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	2	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	4	4	no	—
544	C₂×D₃	—	8	4	no	—
545	C₂×D₃	C₂×#41	1	2	yes	—
546	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	—	2	2	no	—
554	C₃×C₄	C₂×#41	1	2	yes	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	2	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	2	no	—
560	Dic₃	—	2	2	no	—
561	Dic₃	—	2	1	no	—
562	Dic₃	C₂×#41	1	2	yes	—
563	C₂³	—	3	1	no	—
564	C₂³	—	3	1	no	—
565	C₂³	—	3	2	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	6	2	no	—
568	C₂³	—	6	2	no	—
569	C₂³	—	6	4	no	—
570	C₂³	—	12	1	no	—
571	C₂³	—	12	2	no	—
572	C₂³	—	12	2	no	—
573	C₂³	C₂³×D₃	1	1	yes	characteristic
574	C₂³	C₂³×D₃	1	2	yes	—
575	C₂³	C₂³×D₃	1	1	yes	characteristic
576	Q₈	—	6	2	no	—
577	Q₈	—	12	2	no	—
578	Q₈	—	12	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	2	no	—
583	D₄	—	6	4	no	—
584	D₄	—	6	2	no	—
585	D₄	—	6	2	no	—
586	D₄	—	6	4	no	—
587	D₄	—	6	2	no	—
588	D₄	—	6	4	no	—
589	D₄	—	6	2	no	—
590	D₄	—	6	2	no	—
591	D₄	—	6	2	no	—
592	D₄	—	12	2	no	—
593	D₄	—	12	2	no	—
594	D₄	—	12	2	no	—
595	D₄	—	12	2	no	—
596	D₄	—	12	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	3	1	no	—
600	C₂×C₄	—	3	4	no	—
601	C₂×C₄	—	3	2	no	—
602	C₂×C₄	—	3	1	no	—
603	C₂×C₄	—	3	2	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	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	—	6	4	no	—
613	C₂×C₄	—	6	2	no	—
614	C₂×C₄	—	6	2	no	—
615	C₂×C₄	—	6	2	no	—
616	C₂×C₄	—	12	2	no	—
617	C₂×C₄	—	12	2	no	—
618	C₂×C₄	—	12	2	no	—
619	C₂×C₄	—	12	2	no	—
620	C₂×C₄	—	12	2	no	—
621	C₂×C₄	—	12	2	no	—
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₃	1	2	yes	—
625	C₂×C₄	C₂³×D₃	1	2	yes	—
626	C₂×C₄	C₂³×D₃	1	2	yes	—
627	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
630	C₂×C₃	—	4	1	no	—
631	C₂×C₃	—	4	2	no	—
632	C₂×C₃	—	4	1	no	—
633	C₂×C₃	C₂²×#41	1	1	yes	characteristic
634	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂×C₃	#585	1	1	yes	characteristic
636	D₃	—	2	2	no	—
637	D₃	—	2	2	no	—
638	D₃	—	4	1	no	—
639	D₃	—	4	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	3	2	no	—
650	C₂²	—	3	2	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	1	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	6	1	no	—
655	C₂²	—	6	1	no	—
656	C₂²	—	6	2	no	—
657	C₂²	—	6	2	no	—
658	C₂²	—	6	1	no	—
659	C₂²	—	6	1	no	—
660	C₂²	—	6	2	no	—
661	C₂²	—	12	4	no	—
662	C₂²	—	24	4	no	—
663	C₂²	C₂⁴×D₃	1	1	yes	characteristic
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	2	no	—
671	C₄	—	3	2	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	2	no	—
675	C₄	—	6	1	no	—
676	C₄	—	6	2	no	—
677	C₄	—	6	2	no	—
678	C₄	—	6	1	no	—
679	C₄	D₃×#41	1	2	yes	—
680	C₃	#3494	1	1	yes	characteristic, complemented, Sylow
681	C₂	—	4	1	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	6	2	no	—
685	C₂	—	6	2	no	—
686	C₂	—	12	2	no	—
687	C₂	—	12	1	no	—
688	C₂	C₂×D₃×#41	1	1	yes	characteristic
689	C₂	#5964	1	1	yes	characteristic
690	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×#553	C₂
hypercenter	#553	D₃
hypocenter	C₃	#3494
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₃×#553	C₂	semidirect
2. #5706	C₂	semidirect
3. #5705	C₂	semidirect
4. #5695	C₂	semidirect
5. #5689	C₂	semidirect
6. #5662	C₂	semidirect
7. #5654	C₂	semidirect
8. #5616	C₂	semidirect
9. #5615	C₂	semidirect
10. #5614	C₂	semidirect
11. #5612	C₂	semidirect
12. #5607	C₂	semidirect
13. D₃×#121	C₂	semidirect
14. #5563	C₂	semidirect
15. #5556	C₂	semidirect
16. #5551	C₂	semidirect
17. #5548	C₂	semidirect
18. #5547	C₂	semidirect
19. #5545	C₂	semidirect
20. #5530	C₂	semidirect
21. D₃×#117	C₂	semidirect
22. #5507	C₂	semidirect
23. #5504	C₂	semidirect
28. C₂×#235	C₂²	semidirect
29. C₂×#235	C₂²	semidirect
31. C₃×#126	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
35. C₃×#121	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
37. C₃×C₄×D₄	C₂²	semidirect
38. C₃×C₄×D₄	C₂²	semidirect
39. C₃×C₄×D₄	C₂²	semidirect
40. C₃×#117	C₂²	semidirect
41. C₂×C₃×C₄⋊C₄	C₂²	semidirect
42. #940	C₂²	semidirect
44. #939	C₂²	semidirect
45. #939	C₂²	semidirect
47. #938	C₂²	semidirect
48. #938	C₂²	semidirect
49. #938	C₂²	semidirect
52. #936	C₂²	semidirect
53. #935	C₂²	semidirect
54. D₄×Dic₃	C₂²	semidirect
56. #930	C₂²	semidirect
57. #929	C₂²	semidirect
59. C₄×#67	C₂²	semidirect
60. C₄×#67	C₂²	semidirect
61. C₄×#67	C₂²	semidirect
62. C₄×#67	C₂²	semidirect
64. #926	C₂²	semidirect
65. #926	C₂²	semidirect
66. #924	C₂²	semidirect
67. #898	C₂²	semidirect
70. #896	C₂²	semidirect
71. #896	C₂²	semidirect
73. #895	C₂²	semidirect
74. #895	C₂²	semidirect
76. #894	C₂²	semidirect
77. #894	C₂²	semidirect
79. #893	C₂²	semidirect
80. #893	C₂²	semidirect
83. #892	C₂²	semidirect
84. #892	C₂²	semidirect
86. D₃×C₄⋊C₄	C₂²	semidirect
87. D₃×C₄⋊C₄	C₂²	semidirect
88. D₃×C₄⋊C₄	C₂²	semidirect
89. #890	C₂²	semidirect
90. #889	C₂²	semidirect
91. #888	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
94. #885	C₂²	semidirect
95. #885	C₂²	semidirect
96. #885	C₂²	semidirect
97. #885	C₂²	semidirect
99. #884	C₂²	semidirect
100. #884	C₂²	semidirect
102. #883	C₂²	semidirect
103. #883	C₂²	semidirect
104. #883	C₂²	semidirect
107. #67⋊C₄	C₂²	semidirect
108. #67⋊C₄	C₂²	semidirect
112. #879	C₂²	semidirect
113. #878	C₂²	semidirect
114. #877	C₂²	semidirect
115. #877	C₂²	semidirect
116. #876	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
118. C₄×D₁₂	C₂²	semidirect
119. C₄×D₁₂	C₂²	semidirect
122. C₄²×D₃	C₂²	semidirect
123. #869	C₂²	semidirect
129. #553	D₃	semidirect
265. #126	C₂×D₃	semidirect
268. #125	C₂×D₃	semidirect
283. #123	C₂×D₃	semidirect
306. #121	C₂×D₃	semidirect
307. #121	C₂×D₃	semidirect
327. C₄×D₄	C₂×D₃	semidirect
328. C₄×D₄	C₂×D₃	semidirect
329. C₄×D₄	C₂×D₃	semidirect
340. #117	C₂×D₃	semidirect
345. C₂×C₄⋊C₄	C₂×D₃	semidirect
414. C₄×D₃	#41	semidirect
680. C₃	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₃×#553	2
#5706	2
#5705	2
#5695	2
#5689	2
#5662	2
#5654	2
#5616	2
#5615	2
#5614	2
#5612	2
#5607	2
D₃×#121	2
#5563	2
#5556	2
#5551	2
#5548	2
#5547	2
#5545	2
#5530	2
D₃×#117	2
#5507	2
#5504	2
#3494	3