Subgroups — #72244366

Order 3456.

485 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10588588⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#10588397⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588392⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×#347	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588194⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#10588193⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#10588190⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#69091	—	3	1	no	maximal
9	#11797958	C₃	1	1	yes	maximal, characteristic, complemented
10	#63467⋊C₃	C₂²	1	1	yes	characteristic
11	C₂×D₇₂⋊C₃	C₂²	1	1	yes	characteristic
12	#63464⋊C₃	—	2	1	no	—
13	C₄×C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
14	3₋¹⁺²×M₃₂	C₂²	1	1	yes	characteristic
15	3₋¹⁺²×M₃₂	C₂²	1	1	yes	characteristic
16	3₋¹⁺²×#97	C₂²	1	1	yes	characteristic
17	#63380⋊C₃	—	2	1	no	—
18	#63377⋊C₃	C₂²	1	1	yes	characteristic
19	#63372⋊C₃	C₂²	1	1	yes	characteristic
20	#63364⋊C₃	—	2	1	no	—
21	#63359⋊C₃	C₄	1	2	yes	complemented
22	D₁₄₄⋊C₃	C₄	1	2	yes	complemented
23	C₃×#4908	—	3	1	no	—
24	C₃×#4717	—	3	1	no	—
25	C₃×#4711	—	3	1	no	—
26	C₃²×#347	D₃	1	1	yes	characteristic
27	C₃×#4518	—	3	1	no	—
28	C₃×#4516	—	3	1	no	—
29	C₃×#4513	—	3	1	no	—
30	#10588588	C₂×C₃	1	1	yes	characteristic
31	#10588397	C₂×C₃	1	1	yes	characteristic, complemented
32	#10588392	C₂×C₃	1	1	yes	characteristic, complemented
33	C₉×#347	—	2	1	no	—
34	C₉×#347	C₂×C₃	1	1	yes	characteristic, complemented
35	#10588194	C₂×C₃	1	1	yes	characteristic, complemented
36	#10588193	C₂×C₃	1	1	yes	characteristic, complemented
37	#10588190	C₂×C₃	1	1	yes	characteristic, complemented
38	#3697⋊C₃	—	2	1	no	—
39	C₂×C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
40	C₂×C₄×AGL(1,ℤ/9)	—	4	1	no	—
41	C₂×C₈×3₋¹⁺²	D₄	1	1	yes	characteristic
42	C₂×C₈×3₋¹⁺²	C₂³	1	1	yes	characteristic
43	C₄²×3₋¹⁺²	D₄	1	1	yes	characteristic
44	(C₂×AGL(1,ℤ/9))⋊C₄	—	4	1	no	—
45	C₄⋊(3₋¹⁺²⋊C₄)	—	2	1	no	—
46	#3667⋊C₃	—	2	1	no	—
47	D₇₂⋊C₃	—	2	1	no	—
48	D₇₂⋊C₃	C₂×C₄	1	2	yes	—
49	D₇₂⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented
50	#3664⋊C₃	—	2	1	no	—
51	#3663⋊C₃	—	4	1	no	—
52	C₈×AGL(1,ℤ/9)	—	4	1	no	—
53	Dic₃₆⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented
54	C₁₆×3₋¹⁺²	—	2	1	no	—
55	C₁₆×3₋¹⁺²	C₂×C₄	1	2	yes	complemented
56	C₃×AGL(1,ℤ/16)	—	9	1	no	—
57	#69091	—	3	1	no	—
58	C₃×#904	—	3	1	no	—
59	C₂×C₃×D₂₄	—	3	1	no	—
60	C₃×#901	—	6	1	no	—
61	C₃×C₄×D₁₂	—	6	1	no	—
62	C₃²×M₃₂	C₂×D₃	1	1	yes	characteristic
63	C₃²×M₃₂	C₂×D₃	1	1	yes	characteristic
64	C₃²×#97	C₂×D₃	1	1	yes	characteristic
65	C₃×#821	—	6	1	no	—
66	C₃×#819	—	3	1	no	—
67	C₃×#817	—	3	1	no	—
68	C₃×#805	—	6	1	no	—
69	C₃×#800	—	3	2	no	—
70	C₃×D₄₈	—	3	2	no	—
71	#63467	C₂²×C₃	1	1	yes	characteristic
72	C₂×D₇₂	C₂²×C₃	1	1	yes	characteristic
73	#63464	—	2	1	no	—
74	C₄×D₃₆	—	2	1	no	—
75	C₉×M₃₂	—	2	1	no	—
76	C₉×M₃₂	—	2	1	no	—
77	C₉×M₃₂	C₂²×C₃	1	1	yes	characteristic
78	C₉×M₃₂	C₂²×C₃	1	1	yes	characteristic
79	C₉×#97	—	2	1	no	—
80	C₉×#97	C₂²×C₃	1	1	yes	characteristic
81	#63380	—	2	1	no	—
82	#63377	C₂²×C₃	1	1	yes	characteristic
83	#63372	C₂²×C₃	1	1	yes	characteristic
84	#63364	—	2	1	no	—
85	#63359	C₃×C₄	1	2	yes	complemented
86	D₁₄₄	C₃×C₄	1	2	yes	complemented
87	C₂²×AGL(1,ℤ/9)	—	4	1	no	—
88	C₂×C₄×3₋¹⁺²	—	2	1	no	—
89	C₂×C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
90	#611⋊C₃	—	4	1	no	—
91	C₂×3₋¹⁺²⋊C₄	—	4	1	no	—
92	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
93	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
94	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
95	C₄×AGL(1,ℤ/9)	—	4	1	no	—
96	C₄×AGL(1,ℤ/9)	—	8	2	no	—
97	3₋¹⁺²⋊Q₈	—	2	1	no	—
98	C₈×3₋¹⁺²	—	2	1	no	—
99	C₈×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
100	C₈×3₋¹⁺²	#41	1	1	yes	characteristic
101	3₋¹⁺²⋊C₈	—	4	1	no	—
102	C₃×#509	—	9	1	no	—
103	C₃×#444	—	9	1	no	—
104	C₃×#442	—	9	1	no	—
105	#4908	—	3	1	no	—
106	#4717	—	3	1	no	—
107	#4711	—	3	1	no	—
108	C₃×#365	—	9	1	no	—
109	C₃×#361	—	9	1	no	—
110	C₃×#360	—	9	1	no	—
111	C₃×#347	—	6	1	no	—
112	C₃×#347	C₃×D₃	1	1	yes	characteristic
113	#4518	—	3	1	no	—
114	#4516	—	3	1	no	—
115	#4513	—	3	1	no	—
116	C₃×#235	—	6	1	no	—
117	C₂×C₃×D₁₂	—	6	1	no	—
118	C₂×C₃×C₄×D₃	—	12	1	no	—
119	C₂×C₃²×C₈	D₁₂	1	1	yes	characteristic
120	C₂×C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
121	C₃²×C₄²	D₁₂	1	1	yes	characteristic
122	C₃×(C₂×D₃)⋊C₄	—	12	1	no	—
123	C₃×C₄⋊Dic₃	—	6	1	no	—
124	C₃×#208	—	6	1	no	—
125	C₃×Dic₁₂	—	3	1	no	—
126	C₃×D₂₄	—	3	2	no	—
127	C₃×D₂₄	—	3	1	no	—
128	C₃×D₂₄	—	6	1	no	—
129	C₃×#204	—	6	1	no	—
130	C₃×ΓL(1,𝔽₂₅)	—	12	1	no	—
131	C₃×D₃×C₈	—	12	1	no	—
132	#3697	—	2	1	no	—
133	C₂×D₃₆	—	2	1	no	—
134	C₂×C₄×D₉	—	4	1	no	—
135	C₃²×C₁₆	—	2	1	no	—
136	C₃²×C₁₆	C₄×D₃	1	2	yes	—
137	C₂×C₈×C₉	—	2	1	no	—
138	C₂×C₈×C₉	—	2	1	no	—
139	C₂×C₈×C₉	C₃×D₄	1	1	yes	characteristic
140	C₂×C₈×C₉	C₂³×C₃	1	1	yes	characteristic
141	C₄²×C₉	—	2	1	no	—
142	C₄²×C₉	C₃×D₄	1	1	yes	characteristic
143	(C₂×D₉)⋊C₄	—	4	1	no	—
144	C₄⋊Dic₉	—	2	1	no	—
145	#3667	—	2	1	no	—
146	D₇₂	—	2	1	no	—
147	D₇₂	C₂×C₃×C₄	1	2	yes	—
148	D₇₂	C₂×C₃×C₄	1	1	yes	characteristic, complemented
149	#3664	—	2	1	no	—
150	#3663	—	4	1	no	—
151	C₈×D₉	—	4	1	no	—
152	Dic₃₆	C₂×C₃×C₄	1	1	yes	characteristic, complemented
153	C₉×C₁₆	—	2	1	no	—
154	C₉×C₁₆	—	2	1	no	—
155	C₉×C₁₆	—	2	2	no	—
156	C₉×C₁₆	—	2	1	no	—
157	C₉×C₁₆	C₂×C₃×C₄	1	2	yes	complemented
158	AGL(1,ℤ/16)	—	9	1	no	Sylow
159	C₂²×3₋¹⁺²	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×AGL(1,ℤ/9)	—	4	1	no	—
161	C₂×AGL(1,ℤ/9)	—	4	2	no	—
162	C₂×AGL(1,ℤ/9)	—	8	1	no	—
163	C₂×AGL(1,ℤ/9)	—	8	1	no	—
164	C₄×3₋¹⁺²	—	4	1	no	—
165	C₄×3₋¹⁺²	C₄×D₄	1	1	yes	characteristic
166	C₄×3₋¹⁺²	AGL(1,ℤ/8)	1	1	yes	characteristic
167	3₋¹⁺²⋊C₄	—	4	1	no	—
168	3₋¹⁺²⋊C₄	—	8	1	no	—
169	C₃×#135	—	9	1	no	—
170	C₂×C₃×D₈	—	9	1	no	—
171	C₃×#131	—	18	1	no	—
172	C₃×C₄×D₄	—	18	1	no	—
173	#904	—	3	1	no	—
174	C₂×D₂₄	—	3	1	no	—
175	#901	—	6	1	no	—
176	C₄×D₁₂	—	6	1	no	—
177	C₃×SD₃₂	—	9	2	no	—
178	C₃×D₁₆	—	9	2	no	—
179	C₃×M₃₂	—	6	1	no	—
180	C₃×M₃₂	—	6	1	no	—
181	C₃×M₃₂	C₂×C₃×D₃	1	1	yes	characteristic
182	C₃×M₃₂	C₂×C₃×D₃	1	1	yes	characteristic
183	C₃×#108	—	9	1	no	—
184	C₃×#106	—	9	1	no	—
185	C₃×#104	—	18	1	no	—
186	C₃×#102	—	18	1	no	—
187	C₃×#97	—	6	1	no	—
188	C₃×#97	C₂×C₃×D₃	1	1	yes	characteristic
189	#821	—	6	1	no	—
190	#819	—	3	1	no	—
191	#817	—	3	1	no	—
192	#805	—	6	1	no	—
193	#800	—	3	2	no	—
194	D₄₈	—	3	2	no	—
195	C₂²×C₃×D₃	—	12	1	no	—
196	C₂×C₃²×C₄	—	2	1	no	—
197	C₂×C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
198	C₃×#67	—	12	1	no	—
199	C₂×C₃×Dic₃	—	12	1	no	—
200	C₃×D₁₂	—	6	1	no	—
201	C₃×D₁₂	—	6	2	no	—
202	C₃×D₁₂	—	12	1	no	—
203	C₃×C₄×D₃	—	12	1	no	—
204	C₃×C₄×D₃	—	24	2	no	—
205	C₃×Dic₆	—	6	1	no	—
206	C₂²×D₉	—	4	1	no	—
207	C₃²×C₈	—	2	1	no	—
208	C₃²×C₈	C₂×C₄×D₃	1	1	yes	characteristic
209	C₃²×C₈	#235	1	1	yes	characteristic
210	C₃×C₃⋊C₈	—	12	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	4	1	no	—
214	C₂×C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
215	#611	—	4	1	no	—
216	C₂×Dic₉	—	4	1	no	—
217	D₃₆	—	2	1	no	—
218	D₃₆	—	2	2	no	—
219	D₃₆	—	4	1	no	—
220	C₄×D₉	—	4	1	no	—
221	C₄×D₉	—	8	2	no	—
222	Dic₁₈	—	2	1	no	—
223	C₈×C₉	—	2	1	no	—
224	C₈×C₉	—	2	1	no	—
225	C₈×C₉	—	2	1	no	—
226	C₈×C₉	—	4	1	no	—
227	C₈×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
228	C₈×C₉	C₃×#41	1	1	yes	characteristic
229	C₉⋊C₈	—	4	1	no	—
230	#509	—	9	1	no	—
231	#444	—	9	1	no	—
232	#442	—	9	1	no	—
233	#365	—	9	1	no	—
234	#361	—	9	1	no	—
235	#360	—	9	1	no	—
236	#347	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
237	C₂×3₋¹⁺²	—	2	1	no	—
238	C₂×3₋¹⁺²	#442	1	1	yes	characteristic
239	AGL(1,ℤ/9)	—	8	1	no	—
240	AGL(1,ℤ/9)	—	8	2	no	—
241	C₃×#41	—	18	1	no	—
242	C₂×C₃×D₄	—	18	1	no	—
243	C₂²×C₃×C₄	—	36	1	no	—
244	#235	—	6	1	no	—
245	C₂×D₁₂	—	6	1	no	—
246	C₂×C₄×D₃	—	12	1	no	—
247	C₃×Q₁₆	—	9	1	no	—
248	C₃×SD₁₆	—	18	1	no	—
249	C₃×D₈	—	9	1	no	—
250	C₃×D₈	—	9	2	no	—
251	C₃×D₈	—	18	1	no	—
252	C₃×M₁₆	—	18	1	no	—
253	C₃×M₁₆	—	36	1	no	—
254	C₂×C₃×C₈	—	6	1	no	—
255	C₂×C₃×C₈	—	6	1	no	—
256	C₂×C₃×C₈	—	36	1	no	—
257	C₂×C₃×C₈	C₃×D₁₂	1	1	yes	characteristic
258	C₂×C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
259	C₃×C₄⋊C₄	—	18	1	no	—
260	C₃×C₂²⋊C₄	—	36	1	no	—
261	C₃×C₄²	—	6	1	no	—
262	C₃×C₄²	C₃×D₁₂	1	1	yes	characteristic
263	(C₂×D₃)⋊C₄	—	12	1	no	—
264	C₄⋊Dic₃	—	6	1	no	—
265	#208	—	6	1	no	—
266	Dic₁₂	—	3	1	no	—
267	D₂₄	—	3	1	no	—
268	D₂₄	—	3	2	no	—
269	D₂₄	—	6	1	no	—
270	#204	—	6	1	no	—
271	ΓL(1,𝔽₂₅)	—	12	1	no	—
272	D₃×C₈	—	12	1	no	—
273	C₃×C₁₆	—	2	1	no	—
274	C₃×C₁₆	—	6	1	no	—
275	C₃×C₁₆	—	6	2	no	—
276	C₃×C₁₆	C₃×C₄×D₃	1	2	yes	—
277	C₂²×C₃²	#908	1	1	yes	characteristic
278	C₂×C₃×D₃	—	12	1	no	—
279	C₂×C₃×D₃	—	12	2	no	—
280	C₂×C₃×D₃	—	24	1	no	—
281	C₂×C₃×D₃	—	24	1	no	—
282	C₃²×C₄	—	4	1	no	—
283	C₃²×C₄	C₄×D₁₂	1	1	yes	characteristic
284	C₃²×C₄	#908	1	1	yes	characteristic
285	C₃×Dic₃	—	12	1	no	—
286	C₃×Dic₃	—	24	1	no	—
287	C₂²×C₉	—	2	1	no	—
288	C₂²×C₉	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₂×D₉	—	4	1	no	—
290	C₂×D₉	—	4	2	no	—
291	C₂×D₉	—	8	1	no	—
292	C₂×D₉	—	8	1	no	—
293	C₄×C₉	—	2	1	no	—
294	C₄×C₉	—	2	1	no	—
295	C₄×C₉	—	4	1	no	—
296	C₄×C₉	—	8	1	no	—
297	C₄×C₉	C₃×C₄×D₄	1	1	yes	characteristic
298	C₄×C₉	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
299	Dic₉	—	4	1	no	—
300	Dic₉	—	8	1	no	—
301	#135	—	9	1	no	—
302	C₂×D₈	—	9	1	no	—
303	#131	—	18	1	no	—
304	C₄×D₄	—	18	1	no	—
305	SD₃₂	—	9	2	no	—
306	D₁₆	—	9	2	no	—
307	M₃₂	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
308	M₃₂	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
309	#108	—	9	1	no	—
310	#106	—	9	1	no	—
311	#104	—	18	1	no	—
312	#102	—	18	1	no	—
313	#97	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
314	3₋¹⁺²	AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
315	C₂³×C₃	—	36	1	no	—
316	C₂²×D₃	—	12	1	no	—
317	C₃×Q₈	—	18	1	no	—
318	C₃×D₄	—	18	2	no	—
319	C₃×D₄	—	18	1	no	—
320	C₃×D₄	—	36	1	no	—
321	C₃×D₄	—	36	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	6	1	no	—
324	C₂×C₃×C₄	—	12	1	no	—
325	C₂×C₃×C₄	—	36	1	no	—
326	C₂×C₃×C₄	—	36	1	no	—
327	C₂×C₃×C₄	—	72	2	no	—
328	C₂×C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
329	#67	—	12	1	no	—
330	C₂×Dic₃	—	12	1	no	—
331	D₁₂	—	6	1	no	—
332	D₁₂	—	6	2	no	—
333	D₁₂	—	12	1	no	—
334	C₄×D₃	—	12	1	no	—
335	C₄×D₃	—	24	2	no	—
336	Dic₆	—	6	1	no	—
337	C₃×C₈	—	2	1	no	—
338	C₃×C₈	—	6	1	no	—
339	C₃×C₈	—	6	1	no	—
340	C₃×C₈	—	12	1	no	—
341	C₃×C₈	—	36	1	no	—
342	C₃×C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
343	C₃×C₈	C₃×#235	1	1	yes	characteristic
344	C₃⋊C₈	—	12	1	no	—
345	C₂×C₃²	—	2	1	no	—
346	C₂×C₃²	#4711	1	1	yes	characteristic
347	C₃×D₃	—	24	1	no	—
348	C₃×D₃	—	24	2	no	—
349	C₂×C₉	—	2	1	no	—
350	C₂×C₉	—	2	1	no	—
351	C₂×C₉	—	4	1	no	—
352	C₂×C₉	C₃×#442	1	1	yes	characteristic
353	D₉	—	8	1	no	—
354	D₉	—	8	2	no	—
355	#41	—	18	1	no	—
356	C₂×D₄	—	18	1	no	—
357	C₂²×C₄	—	36	1	no	—
358	Q₁₆	—	9	1	no	—
359	SD₁₆	—	18	1	no	—
360	D₈	—	9	1	no	—
361	D₈	—	9	2	no	—
362	D₈	—	18	1	no	—
363	M₁₆	—	18	1	no	—
364	M₁₆	—	36	1	no	—
365	C₂×C₈	—	36	1	no	—
366	C₂×C₈	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
367	C₂×C₈	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
368	C₄⋊C₄	—	18	1	no	—
369	C₂²⋊C₄	—	36	1	no	—
370	C₄²	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
371	C₁₆	—	2	1	no	—
372	C₁₆	C₄×AGL(1,ℤ/9)	1	2	yes	complemented
373	C₂²×C₃	—	6	1	no	—
374	C₂²×C₃	—	36	1	no	—
375	C₂²×C₃	—	36	2	no	—
376	C₂²×C₃	—	72	1	no	—
377	C₂²×C₃	—	72	1	no	—
378	C₂²×C₃	C₃×#908	1	1	yes	characteristic
379	C₂×D₃	—	12	1	no	—
380	C₂×D₃	—	12	2	no	—
381	C₂×D₃	—	24	1	no	—
382	C₂×D₃	—	24	1	no	—
383	C₃×C₄	—	4	1	no	—
384	C₃×C₄	—	6	1	no	—
385	C₃×C₄	—	6	1	no	—
386	C₃×C₄	—	24	1	no	—
387	C₃×C₄	—	36	1	no	—
388	C₃×C₄	—	72	1	no	—
389	C₃×C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
390	C₃×C₄	C₃×#908	1	1	yes	characteristic
391	Dic₃	—	12	1	no	—
392	Dic₃	—	24	1	no	—
393	C₃²	#69091	1	1	yes	characteristic
394	C₉	—	2	1	no	—
395	C₉	C₃×AGL(1,ℤ/16)	1	1	yes	characteristic, complemented
396	C₂³	—	36	1	no	—
397	Q₈	—	18	1	no	—
398	D₄	—	18	2	no	—
399	D₄	—	18	1	no	—
400	D₄	—	36	1	no	—
401	D₄	—	36	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	36	1	no	—
404	C₂×C₄	—	36	1	no	—
405	C₂×C₄	—	72	2	no	—
406	C₂×C₄	C₂×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
407	C₈	—	2	1	no	—
408	C₈	—	36	1	no	—
409	C₈	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
410	C₈	#3697⋊C₃	1	1	yes	characteristic
411	C₂×C₃	—	2	1	no	—
412	C₂×C₃	—	6	1	no	—
413	C₂×C₃	—	12	1	no	—
414	C₂×C₃	—	72	2	no	—
415	C₂×C₃	—	72	1	no	—
416	C₂×C₃	C₃×#4711	1	1	yes	characteristic
417	D₃	—	24	2	no	—
418	D₃	—	24	1	no	—
419	C₂²	—	36	1	no	—
420	C₂²	—	36	2	no	—
421	C₂²	—	72	1	no	—
422	C₂²	—	72	1	no	—
423	C₂²	#63470⋊C₃	1	1	yes	characteristic
424	C₄	—	4	1	no	—
425	C₄	—	36	1	no	—
426	C₄	—	72	1	no	—
427	C₄	C₄×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
428	C₄	#63470⋊C₃	1	1	yes	characteristic
429	C₃	—	6	1	no	—
430	C₃	C₃×#69091	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	72	2	no	—
433	C₂	—	72	1	no	—
434	C₂	#10588392⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10588392⋊C₃
commutator	C₈×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₈	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#347	C₂
socle	C₂×C₃	C₃×#4711
prime radical	#10588588⋊C₃	C₂
cosocle	C₂×C₈×C₉	C₂³×C₃
hypercenter	#347	AGL(1,ℤ/9)
hypocenter	C₉	C₃×AGL(1,ℤ/16)
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
2. #10588397⋊C₃	C₂	semidirect
3. #10588392⋊C₃	C₂	semidirect
4. 3₋¹⁺²×#347	C₂	semidirect
5. #10588194⋊C₃	C₂	semidirect
6. #10588193⋊C₃	C₂	semidirect
7. #10588190⋊C₃	C₂	semidirect
9. #11797958	C₃	semidirect
21. #63359⋊C₃	C₄	semidirect
22. D₁₄₄⋊C₃	C₄	semidirect
31. #10588397	C₂×C₃	semidirect
32. #10588392	C₂×C₃	semidirect
34. C₉×#347	C₂×C₃	semidirect
35. #10588194	C₂×C₃	semidirect
36. #10588193	C₂×C₃	semidirect
37. #10588190	C₂×C₃	semidirect
49. D₇₂⋊C₃	C₂×C₄	semidirect
53. Dic₃₆⋊C₃	C₂×C₄	semidirect
55. C₁₆×3₋¹⁺²	C₂×C₄	semidirect
85. #63359	C₃×C₄	semidirect
86. D₁₄₄	C₃×C₄	semidirect
148. D₇₂	C₂×C₃×C₄	semidirect
152. Dic₃₆	C₂×C₃×C₄	semidirect
157. C₉×C₁₆	C₂×C₃×C₄	semidirect
236. #347	AGL(1,ℤ/9)	semidirect
314. 3₋¹⁺²	AGL(1,ℤ/16)	semidirect
372. C₁₆	C₄×AGL(1,ℤ/9)	semidirect
395. C₉	C₃×AGL(1,ℤ/16)	semidirect

Maximal subgroups

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

subgroup	index
#10588588⋊C₃	2
#10588397⋊C₃	2
#10588392⋊C₃	2
3₋¹⁺²×#347	2
#10588194⋊C₃	2
#10588193⋊C₃	2
#10588190⋊C₃	2
C₃×#69091	3
#11797958	3