Subgroups — #85841

Order 384.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	#5824	C₂	1	1	yes	maximal, characteristic, complemented
4	#5581	C₂	1	1	yes	maximal, characteristic, complemented
5	#5580	C₂	1	1	yes	maximal, characteristic, complemented
6	#5578	C₂	1	1	yes	maximal, characteristic, complemented
7	#5568	C₂	1	1	yes	maximal, characteristic, complemented
8	#5556	C₂	1	2	yes	maximal, complemented
9	#5554	C₂	1	1	yes	maximal, characteristic, complemented
10	#5547	C₂	1	2	yes	maximal, complemented
11	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#5540	C₂	1	2	yes	maximal, complemented
13	#5539	C₂	1	1	yes	maximal, characteristic, complemented
14	#5538	C₂	1	2	yes	maximal, complemented
15	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
16	#5532	C₂	1	1	yes	maximal, characteristic, complemented
17	#5531	C₂	1	2	yes	maximal, complemented
18	#5529	C₂	1	1	yes	maximal, characteristic, complemented
19	#5527	C₂	1	2	yes	maximal, complemented
20	#5479	C₂	1	1	yes	maximal, characteristic, complemented
21	#5479	C₂	1	2	yes	maximal, complemented
22	C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#872	C₂	1	2	yes	maximal, complemented
24	#3475	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×#237	C₂²	1	1	yes	characteristic
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃	C₂²	1	2	yes	—
30	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×D₄	C₂²	1	2	yes	complemented
35	C₃×C₄×D₄	C₂²	1	2	yes	complemented
36	C₃×#117	C₂²	1	2	yes	complemented
37	C₃×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄²	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
40	#947	C₂²	1	1	yes	characteristic
41	#946	C₂²	1	1	yes	characteristic
42	#946	C₂²	1	1	yes	characteristic, complemented
43	#944	C₂²	1	1	yes	characteristic, complemented
44	#939	C₂²	1	2	yes	—
45	#939	C₂²	1	2	yes	complemented
46	#937	C₂²	1	2	yes	—
47	#935	C₂²	1	2	yes	complemented
48	D₄×Dic₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₃	C₂²	1	1	yes	characteristic
50	#930	C₂²	1	1	yes	characteristic
51	#930	C₂²	1	2	yes	—
52	#929	C₂²	1	2	yes	—
53	#929	C₂²	1	2	yes	complemented
54	#929	C₂²	1	2	yes	complemented
55	C₄×#67	C₂²	1	1	yes	characteristic
56	C₄×#67	C₂²	1	1	yes	characteristic
57	C₄×#67	C₂²	1	2	yes	—
58	C₄×#67	C₂²	1	1	yes	characteristic, complemented
59	C₄×#67	C₂²	1	1	yes	characteristic, complemented
60	C₄×#67	C₂²	1	2	yes	complemented
61	C₄×#67	C₂²	1	2	yes	complemented
62	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
63	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
64	#926	C₂²	1	1	yes	characteristic, complemented
65	#924	C₂²	1	1	yes	characteristic, complemented
66	#924	C₂²	1	2	yes	complemented
67	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
68	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
70	#898	C₂²	1	2	yes	complemented
71	#898	C₂²	1	2	yes	complemented
72	#897	C₂²	1	1	yes	characteristic
73	#896	C₂²	1	2	yes	—
74	#896	C₂²	1	2	yes	complemented
75	#895	C₂²	1	1	yes	characteristic
76	#894	C₂²	1	2	yes	—
77	#894	C₂²	1	2	yes	complemented
78	#893	C₂²	1	1	yes	characteristic
79	#892	C₂²	1	1	yes	characteristic, complemented
80	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#890	C₂²	1	1	yes	characteristic, complemented
82	#889	C₂²	1	2	yes	complemented
83	#889	C₂²	1	2	yes	complemented
84	#888	C₂²	1	1	yes	characteristic, complemented
85	#887	C₂²	1	1	yes	characteristic, complemented
86	#886	C₂²	1	2	yes	—
87	#885	C₂²	1	2	yes	complemented
88	#884	C₂²	1	2	yes	complemented
89	#883	C₂²	1	2	yes	—
90	#882	C₂²	1	2	yes	—
91	#67⋊C₄	C₂²	1	2	yes	—
92	#67⋊C₄	C₂²	1	2	yes	complemented
93	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
94	#879	C₂²	1	2	yes	complemented
95	#878	C₂²	1	2	yes	complemented
96	#878	C₂²	1	2	yes	complemented
97	#877	C₂²	1	2	yes	complemented
98	#876	C₂²	1	2	yes	complemented
99	#876	C₂²	1	2	yes	complemented
100	#876	C₂²	1	2	yes	complemented
101	#875	C₂²	1	1	yes	characteristic
102	#875	C₂²	1	2	yes	complemented
103	C₄×D₁₂	C₂²	1	1	yes	characteristic
104	C₄×D₁₂	C₂²	1	1	yes	characteristic
105	C₄×D₁₂	C₂²	1	1	yes	characteristic
106	C₄×D₁₂	C₂²	1	2	yes	complemented
107	#872	C₂²	1	1	yes	characteristic
108	#872	C₂²	1	2	yes	—
109	#872	C₂²	1	2	yes	—
110	#872	C₂²	1	2	yes	—
111	#872	C₂²	1	2	yes	complemented
112	#872	C₂²	1	2	yes	complemented
113	#872	C₂²	1	2	yes	complemented
114	#872	C₂²	1	2	yes	complemented
115	#872	C₂²	1	1	yes	characteristic, complemented
116	C₄²×D₃	C₂²	1	1	yes	characteristic
117	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
118	#870	C₂²	1	2	yes	complemented
119	#870	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₆	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	2	yes	complemented
124	#556	—	3	1	no	—
125	#555	—	3	1	no	—
126	#554	—	3	1	no	—
127	#553	—	3	2	no	—
128	#552	—	3	1	no	—
129	#552	—	3	1	no	—
130	#552	—	3	2	no	—
131	#551	—	3	2	no	—
132	#551	—	3	2	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#533	—	3	1	no	—
137	#529	—	3	1	no	—
138	#529	—	3	2	no	—
139	#529	—	3	2	no	—
140	#529	—	3	1	no	—
141	#525	—	3	2	no	—
142	C₄×#41	—	3	1	no	—
143	C₄×#41	—	3	1	no	—
144	C₄×#41	D₃	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄	—	3	1	no	—
146	C₂×#117	—	3	2	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₃×#41	—	2	4	no	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	C₂³	1	2	yes	—
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³	1	2	yes	—
157	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	1	yes	characteristic
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂×#67	C₂³	1	2	yes	—
163	C₂²×Dic₃	C₂³	1	2	yes	—
164	C₂²×Dic₃	C₂³	1	2	yes	—
165	C₂²×Dic₃	C₂³	1	2	yes	—
166	#237	—	2	4	no	—
167	D₃×D₄	—	2	4	no	—
168	#235	—	2	4	no	—
169	C₂×D₁₂	C₂³	1	1	yes	characteristic
170	C₂×D₁₂	C₂³	1	1	yes	characteristic
171	C₂×D₁₂	C₂³	1	2	yes	—
172	C₂×C₄×D₃	—	2	8	no	—
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₃	C₂³	1	2	yes	—
177	C₂×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×Dic₆	C₂³	1	1	yes	characteristic
183	C₂×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄²	C₂³	1	1	yes	characteristic
193	C₃×C₄²	C₂³	1	1	yes	characteristic
194	C₃×C₄²	C₂³	1	2	yes	—
195	C₃×C₄²	C₂³	1	1	yes	characteristic
196	C₃×C₄²	C₂³	1	2	yes	—
197	C₃×C₄²	C₂³	1	1	yes	characteristic
198	C₃×C₄²	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	#217	C₂³	1	1	yes	characteristic
202	#217	C₂³	1	2	yes	—
203	#217	C₂³	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₄⋊Dic₃	C₂³	1	2	yes	—
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	2	yes	—
226	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
229	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	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	C₄×Dic₃	C₂³	1	1	yes	characteristic
243	C₄×Dic₃	C₂³	1	2	yes	—
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₂×#41	—	3	1	no	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	C₂×D₃	1	1	yes	characteristic
254	C₂²×D₄	—	3	1	no	—
255	C₂³×C₄	—	3	2	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	C₄⋊Q₈	—	3	1	no	—
258	#126	—	3	2	no	—
259	#126	—	3	2	no	—
260	#126	—	3	2	no	—
261	#126	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#125	—	3	2	no	—
265	#125	—	3	1	no	—
266	#125	—	3	2	no	—
267	#125	—	3	2	no	—
268	#125	—	3	1	no	—
269	#124	—	3	1	no	—
270	#124	—	3	2	no	—
271	#124	—	3	1	no	—
272	#124	—	3	2	no	—
273	#123	—	3	2	no	—
274	#123	—	3	2	no	—
275	#123	—	3	2	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	C₂²⋊Q₈	—	3	1	no	—
282	C₂²⋊Q₈	—	3	1	no	—
283	C₂²⋊Q₈	—	3	1	no	—
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	1	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	#121	—	3	2	no	—
291	#121	—	3	2	no	—
292	#121	—	3	2	no	—
293	#121	—	3	1	no	—
294	#121	—	3	1	no	—
295	#121	—	3	2	no	—
296	#120	—	3	2	no	—
297	#120	—	3	2	no	—
298	C₄×Q₈	—	3	1	no	—
299	C₄×Q₈	—	3	1	no	—
300	C₄×Q₈	—	3	1	no	—
301	C₄×Q₈	—	3	1	no	—
302	C₄×Q₈	—	3	2	no	—
303	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
304	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
305	C₄×D₄	—	3	1	no	—
306	C₄×D₄	—	3	1	no	—
307	C₄×D₄	—	3	2	no	—
308	C₄×D₄	—	3	2	no	—
309	C₄×D₄	—	3	1	no	—
310	C₄×D₄	—	3	1	no	—
311	C₄×D₄	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	2	no	—
314	C₄×D₄	—	3	1	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	C₂×D₃	1	1	yes	characteristic
322	C₄×D₄	C₂×D₃	1	1	yes	characteristic
323	C₄×D₄	C₂×D₃	1	2	yes	complemented
324	C₄×D₄	C₂×D₃	1	2	yes	complemented
325	#117	—	3	1	no	—
326	#117	—	3	1	no	—
327	#117	—	3	2	no	—
328	#117	—	3	1	no	—
329	#117	—	3	2	no	—
330	#117	—	3	2	no	—
331	#117	—	3	2	no	—
332	#117	—	3	2	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	—	3	2	no	—
336	#117	—	3	1	no	—
337	#117	C₂×D₃	1	2	yes	complemented
338	#117	C₂×D₃	1	1	yes	characteristic, complemented
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₄²	—	3	2	no	—
346	C₂×C₄²	—	3	1	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	C₂×D₃	1	2	yes	complemented
349	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
350	C₂³×C₃	C₂⁴	1	1	yes	characteristic
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂²×D₃	—	2	4	no	—
353	C₂²×D₃	—	2	4	no	—
354	C₂²×D₃	—	4	2	no	—
355	C₂²×D₃	C₂⁴	1	2	yes	—
356	C₂²×D₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	C₂⁴	1	1	yes	characteristic
358	C₃×Q₈	—	2	2	no	—
359	C₃×D₄	—	2	4	no	—
360	C₃×D₄	#41	1	4	yes	complemented
361	C₂×C₃×C₄	—	2	4	no	—
362	C₂×C₃×C₄	—	2	4	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	4	2	no	—
366	C₂×C₃×C₄	—	4	1	no	—
367	C₂×C₃×C₄	C₂⁴	1	2	yes	—
368	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	#67	—	2	4	no	—
377	#67	—	2	4	no	—
378	#67	—	2	2	no	—
379	#67	—	2	2	no	—
380	#67	—	4	2	no	—
381	C₂×Dic₃	—	2	4	no	—
382	C₂×Dic₃	—	2	4	no	—
383	C₂×Dic₃	—	4	2	no	—
384	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₃	C₂⁴	1	2	yes	—
388	C₂×Dic₃	C₂⁴	1	2	yes	—
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₃	C₂⁴	1	2	yes	—
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	D₁₂	—	2	2	no	—
394	D₁₂	—	2	2	no	—
395	D₁₂	—	4	2	no	—
396	C₄×D₃	—	2	4	no	—
397	C₄×D₃	—	2	4	no	—
398	C₄×D₃	—	2	2	no	—
399	C₄×D₃	—	2	2	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	4	no	—
402	C₄×D₃	—	4	1	no	—
403	C₄×D₃	—	4	1	no	—
404	C₄×D₃	#41	1	4	yes	complemented
405	Dic₆	—	2	2	no	—
406	Dic₆	—	2	2	no	—
407	Dic₆	—	4	2	no	—
408	C₂⁴	—	3	2	no	—
409	#41	—	2	4	no	—
410	#41	—	6	4	no	—
411	#41	—	6	4	no	—
412	C₂×Q₈	—	3	1	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
416	C₂×D₄	—	3	1	no	—
417	C₂×D₄	—	3	2	no	—
418	C₂×D₄	—	3	1	no	—
419	C₂×D₄	—	3	2	no	—
420	C₂×D₄	—	3	2	no	—
421	C₂×D₄	—	3	1	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	6	4	no	—
425	C₂×D₄	C₂²×D₃	1	2	yes	—
426	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	6	8	no	—
440	C₂²×C₄	C₂²×D₃	1	2	yes	—
441	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
442	C₂²×C₄	C₂²×D₃	1	2	yes	—
443	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²×D₃	1	2	yes	—
445	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	—	3	1	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	1	no	—
462	C₄⋊C₄	—	3	1	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	2	no	—
468	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂²×D₃	1	2	yes	—
471	C₄⋊C₄	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	2	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	—	3	2	no	—
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	1	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
496	C₄²	—	3	2	no	—
497	C₄²	—	3	2	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	1	no	—
500	C₄²	—	3	1	no	—
501	C₄²	—	3	1	no	—
502	C₄²	—	3	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	2	no	—
505	C₄²	C₂²×D₃	1	2	yes	—
506	C₄²	C₂²×D₃	1	2	yes	—
507	C₄²	C₂²×D₃	1	1	yes	characteristic
508	C₄²	C₂²×D₃	1	1	yes	characteristic
509	C₄²	C₂²×D₃	1	1	yes	characteristic
510	C₄²	C₂²×D₃	1	1	yes	characteristic
511	C₄²	C₂²×D₃	1	2	yes	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	2	1	no	—
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	C₂×#41	1	4	yes	—
518	C₂²×C₃	C₂⁵	1	1	yes	characteristic
519	C₂×D₃	—	2	1	no	—
520	C₂×D₃	—	2	1	no	—
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	2	1	no	—
523	C₂×D₃	—	2	1	no	—
524	C₂×D₃	—	2	2	no	—
525	C₂×D₃	—	2	1	no	—
526	C₂×D₃	—	2	2	no	—
527	C₂×D₃	—	4	8	no	—
528	C₂×D₃	C₂×#41	1	2	yes	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	C₂×#41	1	2	yes	—
537	C₃×C₄	C₂×#41	1	2	yes	—
538	Dic₃	—	2	1	no	—
539	Dic₃	—	2	2	no	—
540	Dic₃	—	2	2	no	—
541	Dic₃	—	2	1	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	—	2	2	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	C₂×#41	1	2	yes	—
547	C₂³	—	3	1	no	—
548	C₂³	—	3	2	no	—
549	C₂³	—	3	1	no	—
550	C₂³	—	6	4	no	—
551	C₂³	—	6	4	no	—
552	C₂³	—	12	2	no	—
553	C₂³	C₂³×D₃	1	1	yes	characteristic
554	C₂³	C₂³×D₃	1	2	yes	—
555	Q₈	—	2	2	no	—
556	Q₈	—	6	2	no	—
557	Q₈	—	6	2	no	—
558	Q₈	—	12	2	no	—
559	D₄	—	2	4	no	—
560	D₄	—	6	2	no	—
561	D₄	—	6	2	no	—
562	D₄	—	6	2	no	—
563	D₄	—	6	4	no	—
564	D₄	—	6	4	no	—
565	D₄	—	6	2	no	—
566	D₄	—	12	2	no	—
567	D₄	—	12	2	no	—
568	D₄	#235	1	4	yes	complemented
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	3	1	no	—
574	C₂×C₄	—	3	4	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	1	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	2	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	6	4	no	—
586	C₂×C₄	—	6	4	no	—
587	C₂×C₄	—	6	4	no	—
588	C₂×C₄	—	6	4	no	—
589	C₂×C₄	—	6	2	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	4	no	—
592	C₂×C₄	—	6	2	no	—
593	C₂×C₄	—	12	1	no	—
594	C₂×C₄	—	12	1	no	—
595	C₂×C₄	—	12	2	no	—
596	C₂×C₄	C₂³×D₃	1	2	yes	—
597	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
602	C₂×C₄	C₂³×D₃	1	2	yes	—
603	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₃	—	2	4	no	—
606	C₂×C₃	—	4	1	no	—
607	C₂×C₃	C₂²×#41	1	1	yes	characteristic
608	C₂×C₃	C₂²×#41	1	1	yes	characteristic
609	C₂×C₃	#585	1	1	yes	characteristic
610	D₃	—	2	2	no	—
611	D₃	—	4	1	no	—
612	D₃	—	4	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	3	2	no	—
619	C₂²	—	6	1	no	—
620	C₂²	—	6	1	no	—
621	C₂²	—	6	1	no	—
622	C₂²	—	6	2	no	—
623	C₂²	—	6	2	no	—
624	C₂²	—	6	1	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	2	no	—
627	C₂²	—	12	8	no	—
628	C₂²	C₂×#235	1	4	yes	—
629	C₂²	C₂⁴×D₃	1	1	yes	characteristic
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	3	2	no	—
638	C₄	—	6	1	no	—
639	C₄	—	6	1	no	—
640	C₄	—	6	2	no	—
641	C₄	—	6	2	no	—
642	C₄	—	6	1	no	—
643	C₄	—	6	1	no	—
644	C₄	—	6	2	no	—
645	C₄	—	6	1	no	—
646	C₄	C₂×#235	1	2	yes	—
647	C₄	D₃×#41	1	2	yes	—
648	C₃	#3475	1	1	yes	characteristic, complemented, Sylow
649	C₂	—	2	4	no	—
650	C₂	—	4	1	no	—
651	C₂	—	6	2	no	—
652	C₂	—	12	2	no	—
653	C₂	—	12	1	no	—
654	C₂	C₂²×#235	1	1	yes	characteristic
655	C₂	C₂×D₃×#41	1	1	yes	characteristic
656	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Frattini	C₂²	C₂⁴×D₃
Fitting	C₃×C₄×#41	C₂
hypercenter	C₄×#41	D₃
hypocenter	C₃	#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×#41	C₂	semidirect
2. #5829	C₂	semidirect
3. #5824	C₂	semidirect
4. #5581	C₂	semidirect
5. #5580	C₂	semidirect
6. #5578	C₂	semidirect
7. #5568	C₂	semidirect
8. #5556	C₂	semidirect
9. #5554	C₂	semidirect
10. #5547	C₂	semidirect
11. C₄×D₃×D₄	C₂	semidirect
12. #5540	C₂	semidirect
13. #5539	C₂	semidirect
14. #5538	C₂	semidirect
15. C₄×#237	C₂	semidirect
16. #5532	C₂	semidirect
17. #5531	C₂	semidirect
18. #5529	C₂	semidirect
19. #5527	C₂	semidirect
20. #5479	C₂	semidirect
21. #5479	C₂	semidirect
22. C₄×#235	C₂	semidirect
23. C₂×#872	C₂	semidirect
30. C₃×C₄×Q₈	C₂²	semidirect
31. C₃×C₄×Q₈	C₂²	semidirect
34. C₃×C₄×D₄	C₂²	semidirect
35. C₃×C₄×D₄	C₂²	semidirect
36. C₃×#117	C₂²	semidirect
37. C₃×#117	C₂²	semidirect
38. C₂×C₃×C₄²	C₂²	semidirect
39. C₂×C₃×C₄²	C₂²	semidirect
42. #946	C₂²	semidirect
43. #944	C₂²	semidirect
45. #939	C₂²	semidirect
47. #935	C₂²	semidirect
53. #929	C₂²	semidirect
54. #929	C₂²	semidirect
58. C₄×#67	C₂²	semidirect
59. C₄×#67	C₂²	semidirect
60. C₄×#67	C₂²	semidirect
61. C₄×#67	C₂²	semidirect
64. #926	C₂²	semidirect
65. #924	C₂²	semidirect
66. #924	C₂²	semidirect
67. C₂×Dic₃⋊C₄	C₂²	semidirect
68. C₂×Dic₃⋊C₄	C₂²	semidirect
69. C₂×C₄×Dic₃	C₂²	semidirect
70. #898	C₂²	semidirect
71. #898	C₂²	semidirect
74. #896	C₂²	semidirect
77. #894	C₂²	semidirect
79. #892	C₂²	semidirect
81. #890	C₂²	semidirect
82. #889	C₂²	semidirect
83. #889	C₂²	semidirect
84. #888	C₂²	semidirect
85. #887	C₂²	semidirect
87. #885	C₂²	semidirect
88. #884	C₂²	semidirect
92. #67⋊C₄	C₂²	semidirect
94. #879	C₂²	semidirect
95. #878	C₂²	semidirect
96. #878	C₂²	semidirect
97. #877	C₂²	semidirect
98. #876	C₂²	semidirect
99. #876	C₂²	semidirect
100. #876	C₂²	semidirect
102. #875	C₂²	semidirect
106. C₄×D₁₂	C₂²	semidirect
111. #872	C₂²	semidirect
112. #872	C₂²	semidirect
113. #872	C₂²	semidirect
114. #872	C₂²	semidirect
115. #872	C₂²	semidirect
117. C₄²×D₃	C₂²	semidirect
118. #870	C₂²	semidirect
119. #870	C₂²	semidirect
120. C₄×Dic₆	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
144. C₄×#41	D₃	semidirect
303. C₄×Q₈	C₂×D₃	semidirect
304. C₄×Q₈	C₂×D₃	semidirect
323. C₄×D₄	C₂×D₃	semidirect
324. C₄×D₄	C₂×D₃	semidirect
337. #117	C₂×D₃	semidirect
338. #117	C₂×D₃	semidirect
348. C₂×C₄²	C₂×D₃	semidirect
349. C₂×C₄²	C₂×D₃	semidirect
360. C₃×D₄	#41	semidirect
404. C₄×D₃	#41	semidirect
568. D₄	#235	semidirect
648. C₃	#3475	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#41	2
#5829	2
#5824	2
#5581	2
#5580	2
#5578	2
#5568	2
#5556	2
#5554	2
#5547	2
C₄×D₃×D₄	2
#5540	2
#5539	2
#5538	2
C₄×#237	2
#5532	2
#5531	2
#5529	2
#5527	2
#5479	2
C₄×#235	2
C₂×#872	2
#3475	3