Subgroups — #11861185

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×#135	C₂	1	1	yes	maximal, characteristic
2	#10596221	C₂	1	2	yes	maximal, complemented
3	C₃²×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	#10592895	C₂	1	1	yes	maximal, characteristic, complemented
5	#10592844	C₂	1	2	yes	maximal, complemented
6	#10592594	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃⋊D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592522	C₂	1	2	yes	maximal, complemented
9	#10592520	C₂	1	2	yes	maximal, complemented
10	#10592399	C₂	1	1	yes	maximal, characteristic, complemented
11	#10592388	C₂	1	1	yes	maximal, characteristic, complemented
12	#79890	—	3	4	no	maximal
13	#41×C₃⋊D₃	C₂²	1	2	yes	—
14	C₃²×#135	C₂²	1	1	yes	characteristic
15	C₃²×#131	C₂²	1	2	yes	complemented
16	#64159	C₂²	1	2	yes	—
17	#64157	C₂²	1	2	yes	complemented
18	#64128	C₄	1	1	yes	characteristic, complemented
19	Q₁₆×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
20	#64125	C₄	1	2	yes	complemented
21	SD₁₆×C₃⋊D₃	C₄	1	2	yes	complemented
22	#64121	C₄	1	1	yes	characteristic, complemented
23	D₈×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
24	#64116	—	2	2	no	—
25	#64116	C₂²	1	2	yes	complemented
26	M₁₆×C₃⋊D₃	—	2	2	no	—
27	M₁₆×C₃⋊D₃	C₂²	1	2	yes	—
28	#64113	C₂²	1	1	yes	characteristic
29	#64110	—	2	2	no	—
30	#64110	C₂²	1	2	yes	complemented
31	C₂×#3743	—	2	2	no	—
32	C₂×#3743	C₂²	1	1	yes	characteristic
33	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
34	#64081	C₂²	1	1	yes	characteristic
35	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#104	C₂²	1	2	yes	complemented
37	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
38	#63664	C₂²	1	2	yes	complemented
39	#63652	C₂²	1	2	yes	complemented
40	#63649	C₂²	1	2	yes	complemented
41	#63646	C₂²	1	1	yes	characteristic, complemented
42	#63642	C₂²	1	1	yes	characteristic, complemented
43	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
44	#63632	C₂²	1	2	yes	complemented
45	#63630	C₂²	1	1	yes	characteristic, complemented
46	D₃×#135	—	3	4	no	—
47	#5750	—	3	8	no	—
48	C₃×#443	D₃	1	4	yes	complemented
49	#5196	—	3	4	no	—
50	#5145	—	3	8	no	—
51	#4895	—	3	4	no	—
52	D₃×#108	—	3	4	no	—
53	#4823	—	3	8	no	—
54	#4821	—	3	8	no	—
55	#4700	—	3	4	no	—
56	#4689	—	3	4	no	—
57	C₃²×#41	C₂³	1	2	yes	—
58	#3832	C₂×C₄	1	2	yes	—
59	Q₈×C₃⋊D₃	C₂×C₄	1	2	yes	—
60	#3830	—	2	2	no	—
61	#3830	C₂×C₄	1	2	yes	—
62	D₄×C₃⋊D₃	—	2	2	no	—
63	D₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
64	#3828	—	2	2	no	—
65	#3828	C₂³	1	2	yes	—
66	C₂×C₄×C₃⋊D₃	—	2	2	no	—
67	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
68	C₃²×Q₁₆	C₂×C₄	1	1	yes	characteristic
69	C₃²×SD₁₆	C₂×C₄	1	2	yes	—
70	C₃²×D₈	C₂×C₄	1	1	yes	characteristic
71	C₃²×M₁₆	—	2	2	no	—
72	C₃²×M₁₆	C₂³	1	2	yes	—
73	C₂×C₃²×C₈	—	2	2	no	—
74	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
76	C₃²×C₄²	C₂³	1	1	yes	characteristic
77	#3756	C₂×C₄	1	2	yes	—
78	#3755	C₂×C₄	1	2	yes	—
79	#3754	C₂×C₄	1	2	yes	—
80	#3753	C₂×C₄	1	2	yes	—
81	#3752	—	2	1	no	—
82	#3750	—	2	1	no	—
83	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
84	#3748	—	2	2	no	—
85	#3748	C₂³	1	2	yes	—
86	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
87	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
88	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
89	#3746	C₂×C₄	1	1	yes	characteristic
90	#3745	C₂×C₄	1	1	yes	characteristic
91	#3744	C₂×C₄	1	2	yes	—
92	#3743	—	2	2	no	—
93	#3743	—	2	2	no	—
94	#3743	—	2	2	no	—
95	#3743	D₄	1	1	yes	characteristic
96	#3743	D₄	1	1	yes	characteristic
97	#3743	D₄	1	1	yes	characteristic
98	#3743	D₄	1	1	yes	characteristic
99	C₈×C₃⋊D₃	—	2	2	no	—
100	C₈×C₃⋊D₃	—	2	2	no	—
101	C₈×C₃⋊D₃	—	2	2	no	—
102	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
103	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
104	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
105	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
106	#2957	—	9	1	no	Sylow
107	D₃×#41	—	3	8	no	—
108	C₃×#135	C₂×D₃	1	4	yes	—
109	C₃×#131	C₂×D₃	1	8	yes	complemented
110	#950	—	3	8	no	—
111	#948	—	3	8	no	—
112	#919	—	3	4	no	—
113	D₃×Q₁₆	—	3	4	no	—
114	#916	—	3	8	no	—
115	D₃×SD₁₆	—	3	8	no	—
116	#912	—	3	4	no	—
117	D₃×D₈	—	3	4	no	—
118	#907	—	3	8	no	—
119	#907	—	6	8	no	—
120	D₃×M₁₆	—	3	8	no	—
121	D₃×M₁₆	—	6	8	no	—
122	#904	—	3	4	no	—
123	#901	—	3	8	no	—
124	#901	—	6	8	no	—
125	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
126	C₂×ΓL(1,𝔽₂₅)	—	6	8	no	—
127	C₂×D₃×C₈	—	3	4	no	—
128	#872	—	3	4	no	—
129	C₃×#108	C₂×D₃	1	4	yes	complemented
130	C₃×#104	C₂×D₃	1	8	yes	complemented
131	C₃×C₄×C₈	C₂×D₃	1	4	yes	complemented
132	#837	—	3	8	no	—
133	#825	—	3	8	no	—
134	#822	—	3	8	no	—
135	#819	—	3	4	no	—
136	#815	—	3	4	no	—
137	C₈×Dic₃	—	3	4	no	—
138	#805	—	3	8	no	—
139	#803	—	3	4	no	—
140	C₂²×C₃⋊D₃	—	2	2	no	—
141	C₂²×C₃⋊D₃	#41	1	1	yes	characteristic
142	C₃²×Q₈	C₂²×C₄	1	2	yes	—
143	C₃²×D₄	—	2	2	no	—
144	C₃²×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃²×C₄	—	2	2	no	—
146	C₂×C₃²×C₄	—	2	1	no	—
147	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
148	#638	—	2	2	no	—
149	#638	—	2	2	no	—
150	#638	—	2	2	no	—
151	C₂×C₃⋊Dic₃	—	2	2	no	—
152	C₂×C₃⋊Dic₃	—	2	1	no	—
153	C₂×C₃⋊Dic₃	#41	1	1	yes	characteristic
154	C₄⋊(C₃⋊D₃)	—	2	2	no	—
155	C₄⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
156	C₄×C₃⋊D₃	—	2	2	no	—
157	C₄×C₃⋊D₃	—	2	2	no	—
158	C₄×C₃⋊D₃	—	2	2	no	—
159	C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
160	C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
161	C₄×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
162	C₄×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
163	#634	—	2	2	no	—
164	#634	C₂²×C₄	1	2	yes	—
165	C₃²×C₈	—	2	2	no	—
166	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
169	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
170	C₃⋊(C₃⋊C₈)	—	2	2	no	—
171	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
172	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
173	C₃⋊(C₃⋊C₈)	C₂×D₄	1	1	yes	characteristic
174	C₃⋊(C₃⋊C₈)	C₂×D₄	1	1	yes	characteristic
175	C₂×#135	—	9	1	no	—
176	#568	—	9	2	no	—
177	#444	—	9	2	no	—
178	#444	—	9	2	no	—
179	#443	—	9	1	no	—
180	#443	—	9	1	no	—
181	#443	—	9	1	no	—
182	#443	C₃⋊D₃	1	1	yes	characteristic, complemented
183	C₂×#108	—	9	1	no	—
184	#421	—	9	2	no	—
185	#405	—	9	1	no	—
186	C₃×#41	C₂²×D₃	1	8	yes	—
187	#239	—	3	8	no	—
188	D₃×Q₈	—	3	8	no	—
189	#237	—	3	8	no	—
190	#237	—	6	8	no	—
191	D₃×D₄	—	3	8	no	—
192	D₃×D₄	—	6	8	no	—
193	#235	—	3	8	no	—
194	#235	—	6	8	no	—
195	C₂×C₄×D₃	—	3	4	no	—
196	C₂×C₄×D₃	—	6	8	no	—
197	C₃×Q₁₆	C₄×D₃	1	4	yes	—
198	C₃×SD₁₆	C₄×D₃	1	8	yes	—
199	C₃×D₈	C₄×D₃	1	4	yes	—
200	C₃×M₁₆	—	2	8	no	—
201	C₃×M₁₆	C₂²×D₃	1	8	yes	—
202	C₂×C₃×C₈	—	2	8	no	—
203	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
204	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
205	C₃×C₄²	C₂²×D₃	1	4	yes	—
206	#216	—	3	8	no	—
207	#215	—	3	8	no	—
208	#214	—	3	8	no	—
209	#213	—	3	8	no	—
210	(C₂×D₃)⋊C₄	—	6	4	no	—
211	Dic₃⋊C₄	—	6	4	no	—
212	C₄×Dic₃	—	3	4	no	—
213	#208	—	3	8	no	—
214	#208	—	6	8	no	—
215	C₂×C₃⋊C₈	—	3	4	no	—
216	C₂×C₃⋊C₈	—	3	4	no	—
217	C₂×C₃⋊C₈	—	6	8	no	—
218	Dic₁₂	—	3	4	no	—
219	D₂₄	—	3	4	no	—
220	#204	—	3	8	no	—
221	ΓL(1,𝔽₂₅)	—	3	4	no	—
222	ΓL(1,𝔽₂₅)	—	3	4	no	—
223	ΓL(1,𝔽₂₅)	—	3	4	no	—
224	ΓL(1,𝔽₂₅)	—	3	4	no	—
225	ΓL(1,𝔽₂₅)	—	6	8	no	—
226	ΓL(1,𝔽₂₅)	—	6	8	no	—
227	ΓL(1,𝔽₂₅)	—	6	8	no	—
228	D₃×C₈	—	3	4	no	—
229	D₃×C₈	—	3	4	no	—
230	D₃×C₈	—	3	4	no	—
231	D₃×C₈	—	3	4	no	—
232	D₃×C₈	—	6	8	no	—
233	D₃×C₈	—	6	8	no	—
234	D₃×C₈	—	6	8	no	—
235	C₂²×C₃²	—	2	2	no	—
236	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
237	C₂×C₃⋊D₃	—	2	2	no	—
238	C₂×C₃⋊D₃	—	4	1	no	—
239	C₂×C₃⋊D₃	—	8	2	no	—
240	C₂×C₃⋊D₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₃⋊D₃	C₄×D₄	1	1	yes	characteristic
242	C₃²×C₄	—	2	2	no	—
243	C₃²×C₄	—	4	1	no	—
244	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
245	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
246	C₃⋊Dic₃	—	2	2	no	—
247	C₃⋊Dic₃	—	4	1	no	—
248	C₃⋊Dic₃	C₄×D₄	1	1	yes	characteristic
249	C₃⋊Dic₃	C₄×D₄	1	1	yes	characteristic
250	C₂×#41	—	9	2	no	—
251	#135	—	9	2	no	—
252	#135	—	9	1	no	—
253	#135	—	9	2	no	—
254	#135	—	9	1	no	—
255	#135	—	9	1	no	—
256	#135	C₂×C₃⋊D₃	1	1	yes	characteristic
257	C₂×Q₁₆	—	9	1	no	—
258	C₂×SD₁₆	—	9	2	no	—
259	C₂×D₈	—	9	1	no	—
260	#131	—	9	2	no	—
261	#131	—	9	2	no	—
262	#131	—	9	2	no	—
263	#131	—	18	2	no	—
264	#131	—	18	2	no	—
265	#131	C₂×C₃⋊D₃	1	2	yes	complemented
266	C₂×M₁₆	—	9	1	no	—
267	C₂×M₁₆	—	9	2	no	—
268	C₂×M₁₆	—	18	2	no	—
269	C₂×M₁₆	—	18	2	no	—
270	C₂²×C₈	—	9	1	no	—
271	#117	—	9	1	no	—
272	#108	—	9	2	no	—
273	#108	—	9	1	no	—
274	#108	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
275	#104	—	9	2	no	—
276	#104	—	9	2	no	—
277	#104	—	9	2	no	—
278	#104	C₂×C₃⋊D₃	1	2	yes	complemented
279	#97	—	9	1	no	—
280	#97	—	9	1	no	—
281	C₄×C₈	—	9	1	no	—
282	C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
283	C₂²×D₃	—	3	4	no	—
284	C₂²×D₃	—	6	8	no	—
285	C₃×Q₈	C₂×C₄×D₃	1	8	yes	—
286	C₃×D₄	—	2	8	no	—
287	C₃×D₄	C₂×C₄×D₃	1	8	yes	—
288	C₂×C₃×C₄	—	2	8	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
291	#67	—	6	8	no	—
292	#67	—	6	8	no	—
293	#67	—	6	8	no	—
294	C₂×Dic₃	—	3	4	no	—
295	C₂×Dic₃	—	6	8	no	—
296	C₂×Dic₃	—	6	4	no	—
297	D₁₂	—	3	8	no	—
298	D₁₂	—	6	8	no	—
299	C₄×D₃	—	3	4	no	—
300	C₄×D₃	—	3	4	no	—
301	C₄×D₃	—	3	4	no	—
302	C₄×D₃	—	3	4	no	—
303	C₄×D₃	—	6	8	no	—
304	C₄×D₃	—	6	8	no	—
305	C₄×D₃	—	6	8	no	—
306	Dic₆	—	3	8	no	—
307	Dic₆	—	6	8	no	—
308	C₃×C₈	—	2	8	no	—
309	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
310	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
311	C₃×C₈	D₃×D₄	1	4	yes	—
312	C₃×C₈	D₃×D₄	1	4	yes	—
313	C₃⋊C₈	—	3	4	no	—
314	C₃⋊C₈	—	3	4	no	—
315	C₃⋊C₈	—	3	4	no	—
316	C₃⋊C₈	—	3	4	no	—
317	C₃⋊C₈	—	6	8	no	—
318	C₂×C₃²	—	2	1	no	—
319	C₂×C₃²	—	4	2	no	—
320	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
321	C₃⋊D₃	—	2	1	no	—
322	C₃⋊D₃	—	2	1	no	—
323	C₃⋊D₃	—	4	2	no	—
324	#41	—	9	2	no	—
325	#41	—	9	2	no	—
326	#41	—	9	2	no	—
327	#41	—	18	2	no	—
328	#41	—	18	2	no	—
329	#41	C₂²×C₃⋊D₃	1	2	yes	—
330	C₂×Q₈	—	9	2	no	—
331	C₂×D₄	—	9	2	no	—
332	C₂×D₄	—	18	2	no	—
333	C₂²×C₄	—	9	1	no	—
334	C₂²×C₄	—	18	2	no	—
335	Q₁₆	—	9	2	no	—
336	Q₁₆	—	9	1	no	—
337	Q₁₆	C₄×C₃⋊D₃	1	1	yes	characteristic
338	SD₁₆	—	9	2	no	—
339	SD₁₆	—	9	2	no	—
340	SD₁₆	—	9	2	no	—
341	SD₁₆	C₄×C₃⋊D₃	1	2	yes	—
342	D₈	—	9	2	no	—
343	D₈	—	9	1	no	—
344	D₈	C₄×C₃⋊D₃	1	1	yes	characteristic
345	M₁₆	—	2	2	no	—
346	M₁₆	—	9	1	no	—
347	M₁₆	—	9	1	no	—
348	M₁₆	—	9	1	no	—
349	M₁₆	—	9	1	no	—
350	M₁₆	—	9	2	no	—
351	M₁₆	—	18	2	no	—
352	M₁₆	—	18	2	no	—
353	M₁₆	—	18	2	no	—
354	M₁₆	—	18	2	no	—
355	M₁₆	C₂²×C₃⋊D₃	1	2	yes	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	9	1	no	—
358	C₂×C₈	—	9	1	no	—
359	C₂×C₈	—	9	1	no	—
360	C₂×C₈	—	9	1	no	—
361	C₂×C₈	—	9	1	no	—
362	C₂×C₈	—	9	1	no	—
363	C₂×C₈	—	18	2	no	—
364	C₂×C₈	—	18	2	no	—
365	C₂×C₈	—	18	2	no	—
366	C₂×C₈	—	18	2	no	—
367	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
368	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
369	C₄⋊C₄	—	18	1	no	—
370	C₂²⋊C₄	—	18	1	no	—
371	C₄²	—	9	1	no	—
372	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
373	C₂²×C₃	—	2	8	no	—
374	C₂²×C₃	D₃×#41	1	4	yes	—
375	C₂×D₃	—	3	4	no	—
376	C₂×D₃	—	3	4	no	—
377	C₂×D₃	—	6	8	no	—
378	C₂×D₃	—	12	4	no	—
379	C₂×D₃	—	24	8	no	—
380	C₃×C₄	—	2	8	no	—
381	C₃×C₄	—	4	4	no	—
382	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
383	C₃×C₄	C₂×D₃×D₄	1	4	yes	—
384	Dic₃	—	3	4	no	—
385	Dic₃	—	3	4	no	—
386	Dic₃	—	6	8	no	—
387	Dic₃	—	12	4	no	—
388	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
389	C₂³	—	9	1	no	—
390	C₂³	—	18	2	no	—
391	Q₈	—	9	2	no	—
392	Q₈	—	18	2	no	—
393	Q₈	C₂×C₄×C₃⋊D₃	1	2	yes	—
394	D₄	—	2	2	no	—
395	D₄	—	9	2	no	—
396	D₄	—	18	2	no	—
397	D₄	—	18	2	no	—
398	D₄	—	18	2	no	—
399	D₄	—	18	2	no	—
400	D₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	9	1	no	—
404	C₂×C₄	—	9	1	no	—
405	C₂×C₄	—	9	1	no	—
406	C₂×C₄	—	9	1	no	—
407	C₂×C₄	—	9	1	no	—
408	C₂×C₄	—	18	2	no	—
409	C₂×C₄	—	18	2	no	—
410	C₂×C₄	—	18	2	no	—
411	C₂×C₄	—	18	2	no	—
412	C₂×C₄	—	18	1	no	—
413	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	9	1	no	—
416	C₈	—	9	1	no	—
417	C₈	—	9	1	no	—
418	C₈	—	9	1	no	—
419	C₈	—	18	2	no	—
420	C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
421	C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
422	C₈	D₄×C₃⋊D₃	1	1	yes	characteristic
423	C₈	D₄×C₃⋊D₃	1	1	yes	characteristic
424	C₂×C₃	—	2	4	no	—
425	C₂×C₃	—	4	8	no	—
426	C₂×C₃	C₄×D₃×D₄	1	4	yes	—
427	D₃	—	6	4	no	—
428	D₃	—	6	4	no	—
429	D₃	—	12	8	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	9	1	no	—
432	C₂²	—	9	1	no	—
433	C₂²	—	18	2	no	—
434	C₂²	—	36	1	no	—
435	C₂²	—	72	2	no	—
436	C₂²	#41×C₃⋊D₃	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	4	1	no	—
439	C₄	—	9	1	no	—
440	C₄	—	9	1	no	—
441	C₄	—	18	2	no	—
442	C₄	—	36	1	no	—
443	C₄	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
444	C₄	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
445	C₃	#79890	1	4	yes	complemented
446	C₂	—	2	1	no	—
447	C₂	—	4	2	no	—
448	C₂	—	18	1	no	—
449	C₂	—	18	1	no	—
450	C₂	—	36	2	no	—
451	C₂	C₄×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×C₃⋊D₃
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₃²×#443	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₃⋊D₃×#135	C₂
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#443	C₃⋊D₃
hypocenter	C₃²	#2957
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
2. #10596221	C₂	semidirect
3. C₃²×#443	C₂	semidirect
4. #10592895	C₂	semidirect
5. #10592844	C₂	semidirect
6. #10592594	C₂	semidirect
7. C₃⋊D₃×#108	C₂	semidirect
8. #10592522	C₂	semidirect
9. #10592520	C₂	semidirect
10. #10592399	C₂	semidirect
11. #10592388	C₂	semidirect
15. C₃²×#131	C₂²	semidirect
17. #64157	C₂²	semidirect
18. #64128	C₄	semidirect
19. Q₁₆×C₃⋊D₃	C₄	semidirect
20. #64125	C₄	semidirect
21. SD₁₆×C₃⋊D₃	C₄	semidirect
22. #64121	C₄	semidirect
23. D₈×C₃⋊D₃	C₄	semidirect
25. #64116	C₂²	semidirect
30. #64110	C₂²	semidirect
35. C₃²×#108	C₂²	semidirect
36. C₃²×#104	C₂²	semidirect
37. C₃²×C₄×C₈	C₂²	semidirect
38. #63664	C₂²	semidirect
39. #63652	C₂²	semidirect
40. #63649	C₂²	semidirect
41. #63646	C₂²	semidirect
42. #63642	C₂²	semidirect
43. C₈×C₃⋊Dic₃	C₂²	semidirect
44. #63632	C₂²	semidirect
45. #63630	C₂²	semidirect
48. C₃×#443	D₃	semidirect
109. C₃×#131	C₂×D₃	semidirect
129. C₃×#108	C₂×D₃	semidirect
130. C₃×#104	C₂×D₃	semidirect
131. C₃×C₄×C₈	C₂×D₃	semidirect
182. #443	C₃⋊D₃	semidirect
265. #131	C₂×C₃⋊D₃	semidirect
274. #108	C₂×C₃⋊D₃	semidirect
278. #104	C₂×C₃⋊D₃	semidirect
282. C₄×C₈	C₂×C₃⋊D₃	semidirect
388. C₃²	#2957	semidirect
445. C₃	#79890	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×#135	2
#10596221	2
C₃²×#443	2
#10592895	2
#10592844	2
#10592594	2
C₃⋊D₃×#108	2
#10592522	2
#10592520	2
#10592399	2
#10592388	2
#79890	3