Subgroups — #85871

Order 384.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	#5562	C₂	1	1	yes	maximal, characteristic, complemented
5	#5560	C₂	1	2	yes	maximal, complemented
6	#5558	C₂	1	1	yes	maximal, characteristic, complemented
7	#5553	C₂	1	1	yes	maximal, characteristic, complemented
8	#5550	C₂	1	2	yes	maximal, complemented
9	D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#5548	C₂	1	1	yes	maximal, characteristic, complemented
11	#5547	C₂	1	2	yes	maximal, complemented
12	#5545	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
14	#5540	C₂	1	2	yes	maximal, complemented
15	#5539	C₂	1	1	yes	maximal, characteristic, complemented
16	#5535	C₂	1	1	yes	maximal, characteristic, complemented
17	#5532	C₂	1	1	yes	maximal, characteristic, complemented
18	#5530	C₂	1	1	yes	maximal, characteristic, complemented
19	#5528	C₂	1	1	yes	maximal, characteristic, complemented
20	#5494	C₂	1	2	yes	maximal, complemented
21	#5490	C₂	1	2	yes	maximal, complemented
22	#5490	C₂	1	2	yes	maximal, complemented
23	C₂×#884	C₂	1	2	yes	maximal, complemented
24	#3519	—	3	1	no	maximal, Sylow
25	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂²×#67	C₂²	1	2	yes	complemented
27	C₂²×#67	C₂²	1	2	yes	complemented
28	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
30	C₂×#235	C₂²	1	2	yes	complemented
31	C₂×#235	C₂²	1	2	yes	complemented
32	C₂²×D₁₂	C₂²	1	2	yes	complemented
33	C₂²×C₄×D₃	C₂²	1	2	yes	complemented
34	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₃×C₄×D₄	C₂²	1	2	yes	complemented
37	C₃×C₄×D₄	C₂²	1	2	yes	complemented
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
43	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
44	#953	C₂²	1	2	yes	complemented
45	#953	C₂²	1	2	yes	complemented
46	#940	C₂²	1	1	yes	characteristic, complemented
47	#940	C₂²	1	1	yes	characteristic, complemented
48	#939	C₂²	1	2	yes	complemented
49	#939	C₂²	1	2	yes	complemented
50	#938	C₂²	1	1	yes	characteristic, complemented
51	#938	C₂²	1	1	yes	characteristic, complemented
52	#937	C₂²	1	2	yes	complemented
53	#937	C₂²	1	2	yes	complemented
54	D₄×Dic₃	C₂²	1	1	yes	characteristic
55	D₄×Dic₃	C₂²	1	1	yes	characteristic
56	#930	C₂²	1	2	yes	complemented
57	#930	C₂²	1	2	yes	complemented
58	#930	C₂²	1	2	yes	complemented
59	#930	C₂²	1	1	yes	characteristic, complemented
60	#930	C₂²	1	1	yes	characteristic, complemented
61	#929	C₂²	1	2	yes	complemented
62	#929	C₂²	1	2	yes	complemented
63	C₄×#67	C₂²	1	2	yes	complemented
64	C₄×#67	C₂²	1	2	yes	complemented
65	C₄×#67	C₂²	1	2	yes	complemented
66	C₄×#67	C₂²	1	2	yes	complemented
67	C₄×#67	C₂²	1	1	yes	characteristic, complemented
68	C₄×#67	C₂²	1	1	yes	characteristic, complemented
69	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
70	#924	C₂²	1	2	yes	complemented
71	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
72	#898	C₂²	1	1	yes	characteristic, complemented
73	#896	C₂²	1	1	yes	characteristic, complemented
74	#895	C₂²	1	1	yes	characteristic, complemented
75	#895	C₂²	1	1	yes	characteristic, complemented
76	#894	C₂²	1	1	yes	characteristic, complemented
77	#894	C₂²	1	2	yes	complemented
78	#894	C₂²	1	2	yes	complemented
79	#893	C₂²	1	1	yes	characteristic, complemented
80	#893	C₂²	1	1	yes	characteristic, complemented
81	#892	C₂²	1	1	yes	characteristic, complemented
82	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	#890	C₂²	1	1	yes	characteristic, complemented
84	#889	C₂²	1	1	yes	characteristic, complemented
85	#888	C₂²	1	1	yes	characteristic, complemented
86	#885	C₂²	1	1	yes	characteristic, complemented
87	#885	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	complemented
89	#884	C₂²	1	1	yes	characteristic
90	#884	C₂²	1	2	yes	complemented
91	#884	C₂²	1	2	yes	complemented
92	#884	C₂²	1	2	yes	complemented
93	#884	C₂²	1	2	yes	complemented
94	#884	C₂²	1	2	yes	complemented
95	#884	C₂²	1	2	yes	complemented
96	#884	C₂²	1	2	yes	complemented
97	#884	C₂²	1	2	yes	complemented
98	#884	C₂²	1	2	yes	complemented
99	#883	C₂²	1	1	yes	characteristic, complemented
100	#883	C₂²	1	2	yes	complemented
101	#883	C₂²	1	2	yes	complemented
102	#882	C₂²	1	2	yes	complemented
103	#882	C₂²	1	2	yes	complemented
104	#67⋊C₄	C₂²	1	2	yes	complemented
105	#67⋊C₄	C₂²	1	2	yes	complemented
106	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	#879	C₂²	1	1	yes	characteristic, complemented
109	#879	C₂²	1	2	yes	complemented
110	#878	C₂²	1	2	yes	complemented
111	#878	C₂²	1	2	yes	complemented
112	#876	C₂²	1	2	yes	complemented
113	#875	C₂²	1	2	yes	complemented
114	#874	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₁₂	C₂²	1	2	yes	complemented
117	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
119	#872	C₂²	1	1	yes	characteristic, complemented
120	#872	C₂²	1	2	yes	complemented
121	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
122	#870	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#555	—	3	1	no	—
125	#554	—	3	1	no	—
126	#553	—	3	2	no	—
127	#553	—	3	1	no	—
128	#553	—	3	1	no	—
129	#550	—	3	1	no	—
130	#546	—	3	2	no	—
131	#546	—	3	2	no	—
132	#546	—	3	2	no	—
133	D₄²	—	3	1	no	—
134	D₄²	—	3	1	no	—
135	D₄²	—	3	1	no	—
136	#540	—	3	1	no	—
137	#540	—	3	1	no	—
138	#538	—	3	2	no	—
139	#538	—	3	2	no	—
140	#532	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	2	no	—
143	C₂×#121	—	3	2	no	—
144	#518	—	3	1	no	—
145	#518	D₃	1	1	yes	characteristic, complemented
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂³×D₃	C₂³	1	2	yes	—
150	C₂×C₃×D₄	—	2	4	no	—
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	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	C₂²×C₃×C₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	2	yes	—
159	C₂×#67	—	4	4	no	—
160	C₂×#67	—	4	4	no	—
161	C₂×#67	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
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	2	yes	—
172	C₂×#67	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	2	yes	—
174	C₂²×Dic₃	C₂³	1	2	yes	—
175	D₃×D₄	—	2	4	no	—
176	D₃×D₄	—	2	4	no	—
177	#235	—	4	4	no	—
178	#235	—	4	4	no	—
179	C₂×D₁₂	—	4	4	no	—
180	C₂×D₁₂	C₂³	1	1	yes	characteristic
181	C₂×D₁₂	C₂³	1	1	yes	characteristic
182	C₂×D₁₂	C₂³	1	2	yes	—
183	C₂×D₁₂	C₂³	1	1	yes	characteristic
184	C₂×D₁₂	C₂³	1	2	yes	—
185	C₂×D₁₂	C₂³	1	2	yes	—
186	C₂×D₁₂	C₂³	1	2	yes	—
187	C₂×C₄×D₃	—	4	4	no	—
188	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
191	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₃	C₂³	1	2	yes	—
193	C₂×C₄×D₃	C₂³	1	2	yes	—
194	C₂×C₄×D₃	C₂³	1	2	yes	—
195	C₂×C₄×D₃	C₂³	1	2	yes	—
196	C₂×C₄×D₃	C₂³	1	2	yes	—
197	C₂×Dic₆	C₂³	1	1	yes	characteristic
198	C₂×Dic₆	C₂³	1	2	yes	—
199	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃×C₄²	C₂³	1	1	yes	characteristic
211	C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₃×C₄²	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	2	yes	—
215	#217	C₂³	1	1	yes	characteristic
216	#217	C₂³	1	1	yes	characteristic
217	#217	C₂³	1	2	yes	—
218	#217	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
227	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
234	C₄⋊Dic₃	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	2	yes	—
238	C₄⋊Dic₃	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	1	yes	characteristic
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₃⋊C₄	C₂³	1	2	yes	—
249	Dic₃⋊C₄	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₄×Dic₃	C₂³	1	1	yes	characteristic
253	C₄×Dic₃	C₂³	1	1	yes	characteristic
254	C₄×Dic₃	C₂³	1	2	yes	—
255	C₂×#41	—	3	2	no	—
256	C₂×#41	—	3	2	no	—
257	C₂²×D₄	—	3	2	no	—
258	C₂²×D₄	—	3	2	no	—
259	C₂²×D₄	—	3	1	no	—
260	C₂²×D₄	—	3	1	no	—
261	C₂²×D₄	—	3	2	no	—
262	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
263	C₂³×C₄	—	3	2	no	—
264	C₄⋊Q₈	—	3	1	no	—
265	#127	—	3	1	no	—
266	#127	—	3	1	no	—
267	#127	—	3	1	no	—
268	#126	—	3	1	no	—
269	#126	—	3	1	no	—
270	#126	—	3	2	no	—
271	#126	—	3	2	no	—
272	#125	—	3	1	no	—
273	#125	—	3	1	no	—
274	#125	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	1	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	1	no	—
286	#123	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	#121	—	3	2	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	2	no	—
300	#121	—	3	1	no	—
301	#121	—	3	1	no	—
302	#121	—	3	1	no	—
303	#121	—	3	2	no	—
304	#121	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	2	no	—
311	#121	—	3	2	no	—
312	#120	—	3	2	no	—
313	#120	—	3	2	no	—
314	#120	—	3	2	no	—
315	#120	—	3	2	no	—
316	#120	—	3	2	no	—
317	#120	—	3	2	no	—
318	C₄×Q₈	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	1	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	—	3	1	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	1	no	—
332	C₄×D₄	—	3	1	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	C₂×D₃	1	1	yes	characteristic
336	C₄×D₄	C₂×D₃	1	1	yes	characteristic
337	C₄×D₄	C₂×D₃	1	2	yes	complemented
338	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
339	C₄×D₄	C₂×D₃	1	2	yes	complemented
340	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
341	#117	—	3	1	no	—
342	#117	—	3	1	no	—
343	#117	—	3	2	no	—
344	#117	C₂×D₃	1	1	yes	characteristic, complemented
345	#117	C₂×D₃	1	1	yes	characteristic, complemented
346	C₂×C₄⋊C₄	—	3	2	no	—
347	C₂×C₄⋊C₄	—	3	1	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
352	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
353	C₂×C₄²	—	3	1	no	—
354	C₂³×C₃	—	2	4	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	C₂²×D₃	—	2	4	no	—
361	C₂²×D₃	—	2	4	no	—
362	C₂²×D₃	—	2	4	no	—
363	C₂²×D₃	—	4	2	no	—
364	C₂²×D₃	—	4	2	no	—
365	C₂²×D₃	—	4	2	no	—
366	C₂²×D₃	C₂⁴	1	1	yes	characteristic
367	C₂²×D₃	C₂⁴	1	2	yes	—
368	C₂²×D₃	C₂⁴	1	2	yes	—
369	C₂²×D₃	C₂⁴	1	1	yes	characteristic
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	#41	1	4	yes	complemented
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	4	2	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	—	4	2	no	—
377	C₂×C₃×C₄	—	4	2	no	—
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	4	no	—
388	#67	—	2	4	no	—
389	#67	—	2	2	no	—
390	#67	—	2	4	no	—
391	#67	—	2	2	no	—
392	#67	—	4	2	no	—
393	#67	—	4	2	no	—
394	#67	—	4	2	no	—
395	#67	—	4	2	no	—
396	#67	—	4	2	no	—
397	#67	—	4	2	no	—
398	C₂×Dic₃	—	2	4	no	—
399	C₂×Dic₃	—	4	2	no	—
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	1	yes	characteristic
404	C₂×Dic₃	C₂⁴	1	2	yes	—
405	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₃	C₂⁴	1	2	yes	—
407	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
408	D₁₂	—	2	2	no	—
409	D₁₂	—	2	4	no	—
410	D₁₂	—	2	2	no	—
411	D₁₂	—	2	2	no	—
412	D₁₂	—	4	2	no	—
413	D₁₂	—	4	2	no	—
414	D₁₂	—	4	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	2	2	no	—
418	C₄×D₃	—	2	2	no	—
419	C₄×D₃	—	2	4	no	—
420	C₄×D₃	—	4	2	no	—
421	C₄×D₃	—	4	2	no	—
422	C₄×D₃	—	4	2	no	—
423	C₄×D₃	—	4	2	no	—
424	Dic₆	—	2	2	no	—
425	Dic₆	—	4	2	no	—
426	C₂⁴	—	3	2	no	—
427	C₂⁴	—	3	2	no	—
428	C₂⁴	C₂²×D₃	1	2	yes	—
429	#41	—	12	4	no	—
430	#41	—	12	4	no	—
431	C₂×Q₈	—	3	1	no	—
432	C₂×Q₈	—	3	2	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	3	1	no	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	3	2	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	1	no	—
447	C₂×D₄	—	3	1	no	—
448	C₂×D₄	—	3	2	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	2	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	6	4	no	—
454	C₂×D₄	—	6	4	no	—
455	C₂×D₄	—	12	4	no	—
456	C₂×D₄	—	12	4	no	—
457	C₂×D₄	—	12	4	no	—
458	C₂×D₄	C₂²×D₃	1	2	yes	—
459	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
460	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₄	—	3	2	no	—
462	C₂²×C₄	—	3	2	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	3	1	no	—
467	C₂²×C₄	—	3	2	no	—
468	C₂²×C₄	—	3	2	no	—
469	C₂²×C₄	—	3	2	no	—
470	C₂²×C₄	—	3	2	no	—
471	C₂²×C₄	—	3	2	no	—
472	C₂²×C₄	—	12	4	no	—
473	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₃	1	2	yes	—
475	C₂²×C₄	C₂²×D₃	1	2	yes	—
476	C₂²×C₄	C₂²×D₃	1	2	yes	—
477	C₂²×C₄	C₂²×D₃	1	2	yes	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	2	no	—
480	C₄⋊C₄	—	3	1	no	—
481	C₄⋊C₄	—	3	2	no	—
482	C₄⋊C₄	—	3	2	no	—
483	C₄⋊C₄	—	3	2	no	—
484	C₄⋊C₄	—	3	1	no	—
485	C₄⋊C₄	—	3	1	no	—
486	C₄⋊C₄	—	3	1	no	—
487	C₄⋊C₄	—	3	1	no	—
488	C₄⋊C₄	—	3	1	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₄⋊C₄	—	3	2	no	—
491	C₄⋊C₄	—	3	2	no	—
492	C₄⋊C₄	—	3	1	no	—
493	C₄⋊C₄	—	3	1	no	—
494	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	1	no	—
501	C₂²⋊C₄	—	3	1	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	1	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	2	no	—
512	C₂²⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	1	no	—
514	C₂²⋊C₄	—	3	1	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	C₂²×D₃	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
526	C₄²	—	3	1	no	—
527	C₄²	—	3	1	no	—
528	C₄²	—	3	1	no	—
529	C₄²	—	3	2	no	—
530	C₄²	—	3	1	no	—
531	C₄²	C₂²×D₃	1	1	yes	characteristic
532	C₄²	C₂²×D₃	1	2	yes	—
533	C₄²	C₂²×D₃	1	1	yes	characteristic
534	C₂²×C₃	—	2	2	no	—
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	1	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	—	2	1	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	8	4	no	—
543	C₂²×C₃	C₂×#41	1	4	yes	—
544	C₂²×C₃	C₂⁵	1	1	yes	characteristic
545	C₂×D₃	—	2	1	no	—
546	C₂×D₃	—	2	1	no	—
547	C₂×D₃	—	2	1	no	—
548	C₂×D₃	—	2	2	no	—
549	C₂×D₃	—	2	2	no	—
550	C₂×D₃	—	2	2	no	—
551	C₂×D₃	—	2	2	no	—
552	C₂×D₃	—	2	2	no	—
553	C₂×D₃	—	2	1	no	—
554	C₂×D₃	—	2	2	no	—
555	C₂×D₃	—	2	1	no	—
556	C₂×D₃	—	4	8	no	—
557	C₂×D₃	—	8	4	no	—
558	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	2	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	2	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	C₂×#41	1	2	yes	—
567	Dic₃	—	2	1	no	—
568	Dic₃	—	2	1	no	—
569	Dic₃	—	2	1	no	—
570	Dic₃	—	2	1	no	—
571	Dic₃	—	2	2	no	—
572	Dic₃	—	2	2	no	—
573	Dic₃	—	2	1	no	—
574	Dic₃	H(5,𝔽₂)	1	2	yes	—
575	C₂³	—	2	4	no	—
576	C₂³	—	3	1	no	—
577	C₂³	—	3	1	no	—
578	C₂³	—	3	2	no	—
579	C₂³	—	3	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	2	no	—
582	C₂³	—	6	4	no	—
583	C₂³	—	6	4	no	—
584	C₂³	—	6	4	no	—
585	C₂³	—	12	2	no	—
586	C₂³	—	12	2	no	—
587	C₂³	—	12	2	no	—
588	C₂³	C₂³×D₃	1	1	yes	characteristic
589	C₂³	C₂³×D₃	1	2	yes	—
590	C₂³	C₂³×D₃	1	2	yes	—
591	Q₈	—	6	2	no	—
592	Q₈	—	12	2	no	—
593	D₄	—	2	4	no	—
594	D₄	—	2	2	no	—
595	D₄	—	6	2	no	—
596	D₄	—	6	4	no	—
597	D₄	—	6	2	no	—
598	D₄	—	6	4	no	—
599	D₄	—	6	2	no	—
600	D₄	—	6	4	no	—
601	D₄	—	6	4	no	—
602	D₄	—	6	4	no	—
603	D₄	—	6	2	no	—
604	D₄	—	6	2	no	—
605	D₄	—	12	2	no	—
606	D₄	—	12	2	no	—
607	D₄	—	12	2	no	—
608	D₄	—	12	2	no	—
609	D₄	—	12	2	no	—
610	D₄	—	12	2	no	—
611	D₄	—	12	2	no	—
612	D₄	—	12	2	no	—
613	D₄	—	12	2	no	—
614	D₄	#235	1	4	yes	complemented
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	3	1	no	—
617	C₂×C₄	—	3	1	no	—
618	C₂×C₄	—	3	1	no	—
619	C₂×C₄	—	3	1	no	—
620	C₂×C₄	—	3	2	no	—
621	C₂×C₄	—	3	1	no	—
622	C₂×C₄	—	3	1	no	—
623	C₂×C₄	—	3	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	6	2	no	—
629	C₂×C₄	—	6	4	no	—
630	C₂×C₄	—	6	2	no	—
631	C₂×C₄	—	6	4	no	—
632	C₂×C₄	—	6	2	no	—
633	C₂×C₄	—	6	2	no	—
634	C₂×C₄	—	12	2	no	—
635	C₂×C₄	—	12	2	no	—
636	C₂×C₄	—	12	2	no	—
637	C₂×C₄	—	12	2	no	—
638	C₂×C₄	—	12	2	no	—
639	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
641	C₂×C₄	C₂³×D₃	1	2	yes	—
642	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
643	C₂×C₄	C₂³×D₃	1	2	yes	—
644	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
645	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
647	C₂×C₃	—	2	4	no	—
648	C₂×C₃	—	4	2	no	—
649	C₂×C₃	—	4	1	no	—
650	C₂×C₃	C₂²×#41	1	1	yes	characteristic
651	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
653	D₃	—	2	2	no	—
654	D₃	—	4	2	no	—
655	D₃	—	4	2	no	—
656	D₃	—	4	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	3	2	no	—
666	C₂²	—	6	1	no	—
667	C₂²	—	6	1	no	—
668	C₂²	—	6	1	no	—
669	C₂²	—	6	2	no	—
670	C₂²	—	6	2	no	—
671	C₂²	—	6	2	no	—
672	C₂²	—	6	2	no	—
673	C₂²	—	6	2	no	—
674	C₂²	—	6	1	no	—
675	C₂²	—	6	1	no	—
676	C₂²	—	6	2	no	—
677	C₂²	—	8	4	no	—
678	C₂²	—	12	8	no	—
679	C₂²	—	24	4	no	—
680	C₂²	C₂×#235	1	4	yes	—
681	C₂²	C₂⁴×D₃	1	1	yes	characteristic
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	1	no	—
689	C₄	—	3	2	no	—
690	C₄	—	6	1	no	—
691	C₄	—	6	1	no	—
692	C₄	—	6	2	no	—
693	C₄	—	6	1	no	—
694	C₄	—	6	1	no	—
695	C₄	—	6	2	no	—
696	C₄	—	6	1	no	—
697	C₄	C₂×#235	1	2	yes	—
698	C₃	#3519	1	1	yes	characteristic, complemented, Sylow
699	C₂	—	2	4	no	—
700	C₂	—	4	1	no	—
701	C₂	—	4	2	no	—
702	C₂	—	6	2	no	—
703	C₂	—	12	2	no	—
704	C₂	—	12	1	no	—
705	C₂	—	12	2	no	—
706	C₂	C₂²×#235	1	1	yes	characteristic
707	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
708	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×#518	C₂
hypercenter	#518	D₃
hypocenter	C₃	#3519
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. C₃×#518	C₂	semidirect
2. D₄×#67	C₂	semidirect
3. D₄×#67	C₂	semidirect
4. #5562	C₂	semidirect
5. #5560	C₂	semidirect
6. #5558	C₂	semidirect
7. #5553	C₂	semidirect
8. #5550	C₂	semidirect
9. D₄×D₁₂	C₂	semidirect
10. #5548	C₂	semidirect
11. #5547	C₂	semidirect
12. #5545	C₂	semidirect
13. C₄×D₃×D₄	C₂	semidirect
14. #5540	C₂	semidirect
15. #5539	C₂	semidirect
16. #5535	C₂	semidirect
17. #5532	C₂	semidirect
18. #5530	C₂	semidirect
19. #5528	C₂	semidirect
20. #5494	C₂	semidirect
21. #5490	C₂	semidirect
22. #5490	C₂	semidirect
23. C₂×#884	C₂	semidirect
26. C₂²×#67	C₂²	semidirect
27. C₂²×#67	C₂²	semidirect
30. C₂×#235	C₂²	semidirect
31. C₂×#235	C₂²	semidirect
32. C₂²×D₁₂	C₂²	semidirect
33. C₂²×C₄×D₃	C₂²	semidirect
36. C₃×C₄×D₄	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. C₃×#117	C₂²	semidirect
42. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
43. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
44. #953	C₂²	semidirect
45. #953	C₂²	semidirect
46. #940	C₂²	semidirect
47. #940	C₂²	semidirect
48. #939	C₂²	semidirect
49. #939	C₂²	semidirect
50. #938	C₂²	semidirect
51. #938	C₂²	semidirect
52. #937	C₂²	semidirect
53. #937	C₂²	semidirect
56. #930	C₂²	semidirect
57. #930	C₂²	semidirect
58. #930	C₂²	semidirect
59. #930	C₂²	semidirect
60. #930	C₂²	semidirect
61. #929	C₂²	semidirect
62. #929	C₂²	semidirect
63. C₄×#67	C₂²	semidirect
64. C₄×#67	C₂²	semidirect
65. C₄×#67	C₂²	semidirect
66. C₄×#67	C₂²	semidirect
67. C₄×#67	C₂²	semidirect
68. C₄×#67	C₂²	semidirect
69. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
70. #924	C₂²	semidirect
71. C₂×Dic₃⋊C₄	C₂²	semidirect
72. #898	C₂²	semidirect
73. #896	C₂²	semidirect
74. #895	C₂²	semidirect
75. #895	C₂²	semidirect
76. #894	C₂²	semidirect
77. #894	C₂²	semidirect
78. #894	C₂²	semidirect
79. #893	C₂²	semidirect
80. #893	C₂²	semidirect
81. #892	C₂²	semidirect
82. D₃×C₄⋊C₄	C₂²	semidirect
83. #890	C₂²	semidirect
84. #889	C₂²	semidirect
85. #888	C₂²	semidirect
86. #885	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
90. #884	C₂²	semidirect
91. #884	C₂²	semidirect
92. #884	C₂²	semidirect
93. #884	C₂²	semidirect
94. #884	C₂²	semidirect
95. #884	C₂²	semidirect
96. #884	C₂²	semidirect
97. #884	C₂²	semidirect
98. #884	C₂²	semidirect
99. #883	C₂²	semidirect
100. #883	C₂²	semidirect
101. #883	C₂²	semidirect
102. #882	C₂²	semidirect
103. #882	C₂²	semidirect
104. #67⋊C₄	C₂²	semidirect
105. #67⋊C₄	C₂²	semidirect
106. D₃×C₂²⋊C₄	C₂²	semidirect
107. D₃×C₂²⋊C₄	C₂²	semidirect
108. #879	C₂²	semidirect
109. #879	C₂²	semidirect
110. #878	C₂²	semidirect
111. #878	C₂²	semidirect
112. #876	C₂²	semidirect
113. #875	C₂²	semidirect
114. #874	C₂²	semidirect
115. C₄×D₁₂	C₂²	semidirect
116. C₄×D₁₂	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
118. C₄×D₁₂	C₂²	semidirect
119. #872	C₂²	semidirect
120. #872	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. #870	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
145. #518	D₃	semidirect
337. C₄×D₄	C₂×D₃	semidirect
338. C₄×D₄	C₂×D₃	semidirect
339. C₄×D₄	C₂×D₃	semidirect
340. C₄×D₄	C₂×D₃	semidirect
344. #117	C₂×D₃	semidirect
345. #117	C₂×D₃	semidirect
351. C₂×C₂²⋊C₄	C₂×D₃	semidirect
352. C₂×C₂²⋊C₄	C₂×D₃	semidirect
372. C₃×D₄	#41	semidirect
614. D₄	#235	semidirect
698. C₃	#3519	semidirect

Maximal subgroups

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

subgroup	index
C₃×#518	2
D₄×#67	2
#5562	2
#5560	2
#5558	2
#5553	2
#5550	2
D₄×D₁₂	2
#5548	2
#5547	2
#5545	2
C₄×D₃×D₄	2
#5540	2
#5539	2
#5535	2
#5532	2
#5530	2
#5528	2
#5494	2
#5490	2
C₂×#884	2
#3519	3