Subgroups — C₄×#63512 #11860257

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#63512	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588916	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588709	C₂	1	2	yes	maximal, complemented
6	C₄×#3675	C₂	1	2	yes	maximal, complemented
7	#10588697	C₂	1	2	yes	maximal, complemented
8	C₄×#3673	C₂	1	2	yes	maximal, complemented
9	#10588682	C₂	1	1	yes	maximal, characteristic, complemented
10	#10588679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#3667	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#949	—	3	1	no	maximal
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×D₃₆	C₂²	1	1	yes	characteristic
15	C₂²×C₄×D₉	—	2	1	no	—
16	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₄×D₄×C₉	—	2	1	no	—
19	C₄×D₄×C₉	—	2	1	no	—
20	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₉×#117	—	2	1	no	—
23	C₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₉	—	2	1	no	—
25	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
26	#63512	C₄	1	8	yes	direct product factor
27	C₂×#3675	C₂²	1	2	yes	—
28	C₂×#3673	C₂²	1	2	yes	—
29	C₂×(C₂×D₉)⋊C₄	—	2	1	no	—
30	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
31	C₂×#3667	C₂²	1	1	yes	characteristic
32	C₂×#3667	C₂²	1	1	yes	characteristic
33	C₄×D₃₆	—	2	1	no	—
34	C₄×D₃₆	—	2	1	no	—
35	C₄×D₃₆	C₂²	1	2	yes	—
36	C₄×D₃₆	C₂²	1	2	yes	—
37	#63395	C₂²	1	2	yes	complemented
38	#63392	C₂²	1	2	yes	complemented
39	#63369	C₂²	1	2	yes	—
40	#63369	C₂²	1	2	yes	—
41	#63367	C₂²	1	2	yes	complemented
42	#63366	C₂²	1	2	yes	complemented
43	#63362	C₂²	1	2	yes	complemented
44	C₄×C₉⋊C₈	C₂²	1	2	yes	complemented
45	C₃×C₄×#41	D₃	1	1	yes	characteristic
46	C₂×#949	—	3	1	no	—
47	C₂×C₄×D₁₂	—	3	1	no	—
48	#5232	—	3	1	no	—
49	#5026	—	3	2	no	—
50	C₄×#215	—	3	2	no	—
51	#5014	—	3	2	no	—
52	C₄×#213	—	3	2	no	—
53	#5001	—	3	1	no	—
54	#4995	—	3	1	no	—
55	C₄×#208	—	3	1	no	—
56	C₂³×D₉	—	2	1	no	—
57	C₉×#41	—	2	2	no	—
58	C₉×#41	C₂×C₄	1	4	yes	complemented
59	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	—	2	1	no	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
66	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₉	—	2	1	no	—
69	C₂×D₃₆	—	2	1	no	—
70	C₂×D₃₆	—	2	2	no	—
71	C₂×D₃₆	C₂×C₄	1	4	yes	complemented
72	C₂×D₃₆	C₂³	1	2	yes	—
73	C₂×C₄×D₉	—	2	2	no	—
74	C₂×C₄×D₉	—	2	2	no	—
75	C₂×C₄×D₉	—	4	4	no	—
76	C₉×C₄⋊C₄	—	2	1	no	—
77	C₉×C₄⋊C₄	—	2	1	no	—
78	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₉×C₂²⋊C₄	—	2	1	no	—
81	C₉×C₂²⋊C₄	—	2	1	no	—
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₄²×C₉	—	2	1	no	—
84	C₄²×C₉	—	2	1	no	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	D₄	1	1	yes	characteristic
87	C₄²×C₉	D₄	1	1	yes	characteristic
88	C₄²×C₉	C₂³	1	1	yes	characteristic
89	C₄²×C₉	C₂³	1	1	yes	characteristic
90	#3675	C₂×C₄	1	8	yes	complemented
91	#3673	C₂×C₄	1	8	yes	complemented
92	(C₂×D₉)⋊C₄	—	2	2	no	—
93	(C₂×D₉)⋊C₄	—	2	2	no	—
94	C₄⋊Dic₉	—	2	1	no	—
95	C₄⋊Dic₉	C₂³	1	2	yes	—
96	#3667	—	2	2	no	—
97	#3667	C₂×C₄	1	4	yes	complemented
98	C₂×C₉⋊C₈	C₂³	1	2	yes	—
99	C₂×C₉⋊C₈	C₂³	1	2	yes	—
100	C₄×AGL(1,ℤ/8)	—	9	1	no	Sylow
101	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
102	C₂²×D₁₂	—	3	1	no	—
103	C₂²×C₄×D₃	—	6	1	no	—
104	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
105	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
106	C₃×C₄×D₄	—	2	1	no	—
107	C₃×C₄×D₄	—	2	1	no	—
108	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
109	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
110	C₃×#117	—	2	1	no	—
111	C₃×#117	C₂×D₃	1	1	yes	characteristic
112	C₂×C₃×C₄²	—	2	1	no	—
113	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
114	#949	—	3	8	no	—
115	C₂×#215	—	3	2	no	—
116	C₂×#213	—	3	2	no	—
117	C₂×(C₂×D₃)⋊C₄	—	6	1	no	—
118	C₂×C₄⋊Dic₃	—	3	1	no	—
119	C₂×#208	—	3	1	no	—
120	C₂×#208	—	3	1	no	—
121	C₄×D₁₂	—	3	2	no	—
122	C₄×D₁₂	—	3	2	no	—
123	C₄×D₁₂	—	6	1	no	—
124	C₄×D₁₂	—	6	1	no	—
125	#835	—	3	2	no	—
126	#832	—	3	2	no	—
127	#809	—	3	2	no	—
128	#809	—	3	2	no	—
129	#808	—	3	2	no	—
130	#807	—	3	2	no	—
131	#803	—	3	2	no	—
132	C₄×C₃⋊C₈	—	3	2	no	—
133	C₂³×C₉	—	2	1	no	—
134	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×D₉	—	2	4	no	—
136	C₂²×D₉	—	2	2	no	—
137	C₂²×D₉	—	4	2	no	—
138	C₂²×D₉	—	4	2	no	—
139	Q₈×C₉	—	2	1	no	—
140	Q₈×C₉	C₂²×C₄	1	2	yes	complemented
141	D₄×C₉	—	2	4	no	—
142	D₄×C₉	—	2	1	no	—
143	D₄×C₉	C₂²×C₄	1	2	yes	complemented
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	4	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	4	1	no	—
150	C₂×C₄×C₉	—	4	2	no	—
151	C₂×C₄×C₉	—	4	2	no	—
152	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₉	#41	1	2	yes	—
159	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₉	—	2	2	no	—
161	C₂×Dic₉	—	4	2	no	—
162	D₃₆	—	2	4	no	—
163	D₃₆	—	2	2	no	—
164	D₃₆	C₂²×C₄	1	4	yes	—
165	C₄×D₉	—	4	4	no	—
166	C₄×D₉	—	4	4	no	—
167	C₉⋊C₈	—	2	2	no	—
168	C₉⋊C₈	C₂²×C₄	1	4	yes	complemented
169	C₂×AGL(1,ℤ/8)	—	9	1	no	—
170	C₄×#41	D₉	1	1	yes	characteristic, complemented
171	C₂×C₄×D₄	—	9	1	no	—
172	#442	—	9	2	no	—
173	#440	—	9	2	no	—
174	C₄×SD₁₆	—	9	2	no	—
175	C₄×D₈	—	9	2	no	—
176	#428	—	9	1	no	—
177	#418	—	9	1	no	—
178	#417	—	9	1	no	—
179	C₄×M₁₆	—	9	1	no	—
180	C₂³×D₃	—	6	1	no	—
181	C₃×#41	—	2	2	no	—
182	C₃×#41	C₄×D₃	1	4	yes	—
183	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
186	C₂²×C₃×C₄	—	2	1	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	#67	1	1	yes	characteristic
190	C₂²×C₃×C₄	#67	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
192	C₂²×Dic₃	—	6	1	no	—
193	C₂×D₁₂	—	3	4	no	—
194	C₂×D₁₂	—	3	2	no	—
195	C₂×D₁₂	—	6	2	no	—
196	C₂×D₁₂	—	6	1	no	—
197	C₂×C₄×D₃	—	6	2	no	—
198	C₂×C₄×D₃	—	6	2	no	—
199	C₂×C₄×D₃	—	12	4	no	—
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	—	2	1	no	—
202	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
203	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
204	C₃×C₂²⋊C₄	—	2	1	no	—
205	C₃×C₂²⋊C₄	—	2	1	no	—
206	C₃×C₂²⋊C₄	—	2	1	no	—
207	C₃×C₄²	—	2	1	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	—	2	1	no	—
210	C₃×C₄²	#67	1	1	yes	characteristic
211	C₃×C₄²	#67	1	1	yes	characteristic
212	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
213	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
214	#215	—	3	8	no	—
215	#213	—	3	8	no	—
216	(C₂×D₃)⋊C₄	—	6	2	no	—
217	(C₂×D₃)⋊C₄	—	6	2	no	—
218	C₄⋊Dic₃	—	3	2	no	—
219	C₄⋊Dic₃	—	6	1	no	—
220	#208	—	3	4	no	—
221	#208	—	6	2	no	—
222	C₂×C₃⋊C₈	—	3	2	no	—
223	C₂×C₃⋊C₈	—	3	2	no	—
224	C₂²×C₉	—	2	1	no	—
225	C₂²×C₉	—	2	1	no	—
226	C₂²×C₉	—	2	2	no	—
227	C₂²×C₉	—	4	1	no	—
228	C₂²×C₉	—	4	1	no	—
229	C₂²×C₉	C₄×D₄	1	2	yes	—
230	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×D₉	—	2	4	no	—
232	C₂×D₉	—	4	8	no	—
233	C₂×D₉	—	4	2	no	—
234	C₂×D₉	—	4	2	no	—
235	C₄×C₉	—	2	2	no	—
236	C₄×C₉	—	2	1	no	—
237	C₄×C₉	—	2	1	no	—
238	C₄×C₉	—	2	1	no	—
239	C₄×C₉	—	4	1	no	—
240	C₄×C₉	—	4	1	no	—
241	C₄×C₉	C₄×D₄	1	2	yes	—
242	C₄×C₉	AGL(1,ℤ/8)	1	2	yes	complemented
243	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
244	C₄×C₉	C₂×#41	1	1	yes	characteristic
245	Dic₉	—	4	2	no	—
246	C₂×#41	C₂×D₉	1	1	yes	characteristic
247	C₂²×D₄	—	9	1	no	—
248	C₂³×C₄	—	18	1	no	—
249	AGL(1,ℤ/8)	—	9	8	no	—
250	C₂×SD₁₆	—	9	2	no	—
251	C₂×D₈	—	9	2	no	—
252	C₂×M₁₆	—	9	1	no	—
253	C₂×M₁₆	—	9	1	no	—
254	C₄×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
255	C₄×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	9	2	no	—
259	C₄×D₄	—	9	2	no	—
260	C₄×D₄	—	18	1	no	—
261	C₄×D₄	—	18	1	no	—
262	C₄×D₄	C₂×D₉	1	1	yes	characteristic, complemented
263	C₄×D₄	C₂×D₉	1	1	yes	characteristic, complemented
264	#117	—	2	1	no	—
265	#117	C₂×D₉	1	1	yes	characteristic
266	C₂×C₄⋊C₄	—	9	1	no	—
267	C₂×C₂²⋊C₄	—	18	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
270	#107	—	9	2	no	—
271	#106	—	9	2	no	—
272	#103	—	9	2	no	—
273	#102	—	9	2	no	—
274	#102	—	9	2	no	—
275	#102	—	9	2	no	—
276	#97	—	9	2	no	—
277	C₄×C₈	—	9	2	no	—
278	C₂³×C₃	—	2	1	no	—
279	C₂³×C₃	C₂×#67	1	1	yes	characteristic
280	C₂²×D₃	—	6	4	no	—
281	C₂²×D₃	—	6	2	no	—
282	C₂²×D₃	—	12	2	no	—
283	C₂²×D₃	—	12	2	no	—
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
286	C₃×D₄	—	2	4	no	—
287	C₃×D₄	—	2	1	no	—
288	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	—	4	2	no	—
296	C₂×C₃×C₄	—	4	2	no	—
297	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
298	C₂×C₃×C₄	#235	1	2	yes	—
299	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
305	C₂×Dic₃	—	6	2	no	—
306	C₂×Dic₃	—	12	2	no	—
307	D₁₂	—	3	4	no	—
308	D₁₂	—	6	4	no	—
309	D₁₂	—	6	2	no	—
310	C₄×D₃	—	12	4	no	—
311	C₄×D₃	—	12	4	no	—
312	C₃⋊C₈	—	3	4	no	—
313	C₃⋊C₈	—	6	2	no	—
314	C₂×C₉	—	2	2	no	—
315	C₂×C₉	—	4	2	no	—
316	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
317	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂×C₉	#575	1	1	yes	characteristic
319	D₉	—	4	4	no	—
320	C₂⁴	—	18	1	no	—
321	#41	—	2	2	no	—
322	#41	C₄×D₉	1	4	yes	complemented
323	C₂×Q₈	C₂²×D₉	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	9	4	no	—
326	C₂×D₄	—	9	2	no	—
327	C₂×D₄	—	18	2	no	—
328	C₂×D₄	—	18	1	no	—
329	C₂×D₄	C₂²×D₉	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	18	1	no	—
334	C₂²×C₄	—	18	2	no	—
335	C₂²×C₄	—	18	2	no	—
336	C₂²×C₄	—	36	4	no	—
337	C₂²×C₄	#611	1	1	yes	characteristic
338	C₂²×C₄	#611	1	1	yes	characteristic
339	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
340	SD₁₆	—	9	8	no	—
341	D₈	—	9	8	no	—
342	M₁₆	—	9	4	no	—
343	M₁₆	—	18	2	no	—
344	C₂×C₈	—	9	2	no	—
345	C₂×C₈	—	9	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	9	2	no	—
349	C₄⋊C₄	—	18	1	no	—
350	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	18	2	no	—
356	C₂²⋊C₄	—	18	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	#611	1	1	yes	characteristic
361	C₄²	#611	1	1	yes	characteristic
362	C₄²	C₂²×D₉	1	1	yes	characteristic
363	C₄²	C₂²×D₉	1	1	yes	characteristic
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	4	1	no	—
368	C₂²×C₃	—	4	1	no	—
369	C₂²×C₃	C₄×#67	1	2	yes	—
370	C₂²×C₃	C₂²×#67	1	1	yes	characteristic
371	C₂×D₃	—	6	4	no	—
372	C₂×D₃	—	12	8	no	—
373	C₂×D₃	—	12	2	no	—
374	C₂×D₃	—	12	2	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	4	1	no	—
380	C₃×C₄	—	4	1	no	—
381	C₃×C₄	C₄×#67	1	2	yes	—
382	C₃×C₄	#949	1	2	yes	—
383	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
384	C₃×C₄	C₂×#235	1	1	yes	characteristic
385	Dic₃	—	12	2	no	—
386	C₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
387	C₂³	—	2	1	no	—
388	C₂³	—	18	4	no	—
389	C₂³	—	18	2	no	—
390	C₂³	—	36	2	no	—
391	C₂³	—	36	2	no	—
392	C₂³	C₂×#611	1	1	yes	characteristic
393	Q₈	—	2	1	no	—
394	Q₈	C₂×C₄×D₉	1	2	yes	complemented
395	D₄	—	2	4	no	—
396	D₄	—	2	1	no	—
397	D₄	—	9	4	no	—
398	D₄	—	18	4	no	—
399	D₄	—	18	2	no	—
400	D₄	C₂×C₄×D₉	1	2	yes	complemented
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	18	2	no	—
410	C₂×C₄	—	36	4	no	—
411	C₂×C₄	—	36	2	no	—
412	C₂×C₄	—	36	4	no	—
413	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
414	C₂×C₄	#3697	1	2	yes	—
415	C₂×C₄	C₂×#611	1	1	yes	characteristic
416	C₂×C₄	C₂×#611	1	1	yes	characteristic
417	C₂×C₄	C₂×#611	1	1	yes	characteristic
418	C₂×C₄	C₂×#611	1	1	yes	characteristic
419	C₂×C₄	C₂×#611	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
421	C₈	—	9	4	no	—
422	C₈	—	18	2	no	—
423	C₂×C₃	—	2	2	no	—
424	C₂×C₃	—	4	2	no	—
425	C₂×C₃	C₂×C₄×#67	1	1	yes	characteristic
426	C₂×C₃	C₂×#949	1	1	yes	characteristic
427	C₂×C₃	#5822	1	1	yes	characteristic
428	D₃	—	12	4	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	18	4	no	—
435	C₂²	—	36	8	no	—
436	C₂²	—	36	2	no	—
437	C₂²	—	36	2	no	—
438	C₂²	C₄×#611	1	2	yes	—
439	C₂²	C₂²×#611	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	36	2	no	—
447	C₄	C₄×#611	1	2	yes	—
448	C₄	#63512	1	2	yes	direct product factor
449	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
450	C₄	C₂×#3697	1	1	yes	characteristic
451	C₃	C₄×#949	1	1	yes	characteristic
452	C₂	—	2	2	no	—
453	C₂	—	4	2	no	—
454	C₂	—	36	4	no	—
455	C₂	C₂×C₄×#611	1	1	yes	characteristic
456	C₂	C₂×#63512	1	1	yes	characteristic
457	C₂	#10589925	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#611
commutator	C₄×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₄×C₉×#41	C₂
socle	C₂²×C₃	C₂²×#67
prime radical	C₂×#63512	C₂
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₄×#41	D₉
hypocenter	C₉	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₄×C₉×#41	C₂	semidirect
3. C₂×C₄×D₃₆	C₂	semidirect
4. #10588916	C₂	semidirect
5. #10588709	C₂	semidirect
6. C₄×#3675	C₂	semidirect
7. #10588697	C₂	semidirect
8. C₄×#3673	C₂	semidirect
9. #10588682	C₂	semidirect
10. #10588679	C₂	semidirect
11. C₄×#3667	C₂	semidirect
16. C₄×Q₈×C₉	C₂²	semidirect
17. C₄×Q₈×C₉	C₂²	semidirect
20. C₄×D₄×C₉	C₂²	semidirect
21. C₄×D₄×C₉	C₂²	semidirect
26. #63512	C₄	direct (N × H)
37. #63395	C₂²	semidirect
38. #63392	C₂²	semidirect
41. #63367	C₂²	semidirect
42. #63366	C₂²	semidirect
43. #63362	C₂²	semidirect
44. C₄×C₉⋊C₈	C₂²	semidirect
58. C₉×#41	C₂×C₄	semidirect
71. C₂×D₃₆	C₂×C₄	semidirect
90. #3675	C₂×C₄	semidirect
91. #3673	C₂×C₄	semidirect
97. #3667	C₂×C₄	semidirect
140. Q₈×C₉	C₂²×C₄	semidirect
143. D₄×C₉	C₂²×C₄	semidirect
168. C₉⋊C₈	C₂²×C₄	semidirect
170. C₄×#41	D₉	semidirect
242. C₄×C₉	AGL(1,ℤ/8)	semidirect
254. C₄×Q₈	C₂×D₉	semidirect
255. C₄×Q₈	C₂×D₉	semidirect
262. C₄×D₄	C₂×D₉	semidirect
263. C₄×D₄	C₂×D₉	semidirect
322. #41	C₄×D₉	semidirect
386. C₉	C₄×AGL(1,ℤ/8)	semidirect
394. Q₈	C₂×C₄×D₉	semidirect
400. D₄	C₂×C₄×D₉	semidirect
448. C₄	#63512	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₉×#41	2
C₂×#63512	2
C₂×C₄×D₃₆	2
#10588916	2
#10588709	2
C₄×#3675	2
#10588697	2
C₄×#3673	2
#10588682	2
#10588679	2
C₄×#3667	2
C₄×#949	3

Subgroups — C4×#63512 #11860257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63512 #11860257