Subgroups — #11861191

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 441 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×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	#10592896	C₂	1	1	yes	maximal, characteristic, complemented
5	#10592843	C₂	1	2	yes	maximal, complemented
6	#10592593	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃⋊D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592523	C₂	1	2	yes	maximal, complemented
9	#10592520	C₂	1	2	yes	maximal, complemented
10	#10592416	C₂	1	1	yes	maximal, characteristic, complemented
11	#10592407	C₂	1	1	yes	maximal, characteristic, complemented
12	#79899	—	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×#97	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	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	D₃×#135	—	3	4	no	—
47	#5750	—	3	8	no	—
48	C₃×#444	D₃	1	4	yes	complemented
49	#5197	—	3	4	no	—
50	#5144	—	3	8	no	—
51	#4894	—	3	4	no	—
52	D₃×#108	—	3	4	no	—
53	#4824	—	3	8	no	—
54	#4821	—	3	8	no	—
55	#4717	—	3	4	no	—
56	#4708	—	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	2	yes	—
96	#3743	D₄	1	2	yes	—
97	C₈×C₃⋊D₃	—	2	2	no	—
98	C₈×C₃⋊D₃	—	2	2	no	—
99	C₈×C₃⋊D₃	—	2	2	no	—
100	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
101	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
102	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
103	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
104	#2957	—	9	1	no	Sylow
105	D₃×#41	—	3	8	no	—
106	C₃×#135	C₂×D₃	1	4	yes	—
107	C₃×#131	C₂×D₃	1	8	yes	complemented
108	#950	—	3	8	no	—
109	#948	—	3	8	no	—
110	#919	—	3	4	no	—
111	D₃×Q₁₆	—	3	4	no	—
112	#916	—	3	8	no	—
113	D₃×SD₁₆	—	3	8	no	—
114	#912	—	3	4	no	—
115	D₃×D₈	—	3	4	no	—
116	#907	—	3	8	no	—
117	#907	—	6	8	no	—
118	D₃×M₁₆	—	3	8	no	—
119	D₃×M₁₆	—	6	8	no	—
120	#904	—	3	4	no	—
121	#901	—	3	8	no	—
122	#901	—	6	8	no	—
123	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
124	C₂×ΓL(1,𝔽₂₅)	—	6	8	no	—
125	C₂×D₃×C₈	—	3	4	no	—
126	#872	—	3	4	no	—
127	C₃×#108	C₂×D₃	1	4	yes	complemented
128	C₃×#104	C₂×D₃	1	8	yes	complemented
129	C₃×#97	C₂×D₃	1	4	yes	complemented
130	#837	—	3	8	no	—
131	#825	—	3	8	no	—
132	#822	—	3	8	no	—
133	#819	—	3	4	no	—
134	#815	—	3	4	no	—
135	C₈×Dic₃	—	3	4	no	—
136	#805	—	3	8	no	—
137	C₄×C₃⋊C₈	—	3	4	no	—
138	C₂²×C₃⋊D₃	—	2	2	no	—
139	C₂²×C₃⋊D₃	#41	1	1	yes	characteristic
140	C₃²×Q₈	C₂²×C₄	1	2	yes	—
141	C₃²×D₄	—	2	2	no	—
142	C₃²×D₄	C₂²×C₄	1	2	yes	—
143	C₂×C₃²×C₄	—	2	2	no	—
144	C₂×C₃²×C₄	—	2	1	no	—
145	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
146	#638	—	2	2	no	—
147	#638	—	2	2	no	—
148	#638	—	2	2	no	—
149	C₂×C₃⋊Dic₃	—	2	2	no	—
150	C₂×C₃⋊Dic₃	—	2	1	no	—
151	C₂×C₃⋊Dic₃	#41	1	1	yes	characteristic
152	C₄⋊(C₃⋊D₃)	—	2	2	no	—
153	C₄⋊(C₃⋊D₃)	C₂²×C₄	1	2	yes	—
154	C₄×C₃⋊D₃	—	2	2	no	—
155	C₄×C₃⋊D₃	—	2	2	no	—
156	C₄×C₃⋊D₃	—	2	2	no	—
157	C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
159	C₄×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
160	C₄×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
161	#634	—	2	2	no	—
162	#634	C₂²×C₄	1	2	yes	—
163	C₃²×C₈	—	2	2	no	—
164	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
165	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
166	C₃²×C₈	C₂×D₄	1	2	yes	—
167	C₃⋊(C₃⋊C₈)	—	2	2	no	—
168	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
169	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
170	C₃⋊(C₃⋊C₈)	C₂×D₄	1	2	yes	—
171	C₂×#135	—	9	1	no	—
172	#568	—	9	2	no	—
173	#444	—	9	1	no	—
174	#444	—	9	1	no	—
175	#444	—	9	1	no	—
176	#444	C₃⋊D₃	1	1	yes	characteristic, complemented
177	#443	—	9	2	no	—
178	#443	—	9	2	no	—
179	C₂×#108	—	9	1	no	—
180	#421	—	9	2	no	—
181	#405	—	9	1	no	—
182	C₃×#41	C₂²×D₃	1	8	yes	—
183	#239	—	3	8	no	—
184	D₃×Q₈	—	3	8	no	—
185	#237	—	3	8	no	—
186	#237	—	6	8	no	—
187	D₃×D₄	—	3	8	no	—
188	D₃×D₄	—	6	8	no	—
189	#235	—	3	8	no	—
190	#235	—	6	8	no	—
191	C₂×C₄×D₃	—	3	4	no	—
192	C₂×C₄×D₃	—	6	8	no	—
193	C₃×Q₁₆	C₄×D₃	1	4	yes	—
194	C₃×SD₁₆	C₄×D₃	1	8	yes	—
195	C₃×D₈	C₄×D₃	1	4	yes	—
196	C₃×M₁₆	—	2	8	no	—
197	C₃×M₁₆	C₂²×D₃	1	8	yes	—
198	C₂×C₃×C₈	—	2	8	no	—
199	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
200	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
201	C₃×C₄²	C₂²×D₃	1	4	yes	—
202	#216	—	3	8	no	—
203	#215	—	3	8	no	—
204	#214	—	3	8	no	—
205	#213	—	3	8	no	—
206	(C₂×D₃)⋊C₄	—	6	4	no	—
207	Dic₃⋊C₄	—	6	4	no	—
208	C₄×Dic₃	—	3	4	no	—
209	#208	—	3	8	no	—
210	#208	—	6	8	no	—
211	C₂×C₃⋊C₈	—	3	4	no	—
212	C₂×C₃⋊C₈	—	3	4	no	—
213	C₂×C₃⋊C₈	—	6	8	no	—
214	Dic₁₂	—	3	4	no	—
215	D₂₄	—	3	4	no	—
216	#204	—	3	8	no	—
217	ΓL(1,𝔽₂₅)	—	3	8	no	—
218	ΓL(1,𝔽₂₅)	—	3	8	no	—
219	ΓL(1,𝔽₂₅)	—	6	8	no	—
220	ΓL(1,𝔽₂₅)	—	6	8	no	—
221	ΓL(1,𝔽₂₅)	—	6	8	no	—
222	D₃×C₈	—	3	4	no	—
223	D₃×C₈	—	3	4	no	—
224	D₃×C₈	—	3	4	no	—
225	D₃×C₈	—	3	4	no	—
226	D₃×C₈	—	6	8	no	—
227	D₃×C₈	—	6	8	no	—
228	D₃×C₈	—	6	8	no	—
229	C₂²×C₃²	—	2	2	no	—
230	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
231	C₂×C₃⋊D₃	—	2	2	no	—
232	C₂×C₃⋊D₃	—	4	1	no	—
233	C₂×C₃⋊D₃	—	8	2	no	—
234	C₂×C₃⋊D₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₃⋊D₃	C₄×D₄	1	1	yes	characteristic
236	C₃²×C₄	—	2	2	no	—
237	C₃²×C₄	—	4	1	no	—
238	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
239	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₃⋊Dic₃	—	2	2	no	—
241	C₃⋊Dic₃	—	4	1	no	—
242	C₃⋊Dic₃	C₄×D₄	1	1	yes	characteristic
243	C₃⋊Dic₃	C₄×D₄	1	1	yes	characteristic
244	C₂×#41	—	9	2	no	—
245	#135	—	9	2	no	—
246	#135	—	9	1	no	—
247	#135	—	9	2	no	—
248	#135	—	9	1	no	—
249	#135	—	9	1	no	—
250	#135	C₂×C₃⋊D₃	1	1	yes	characteristic
251	C₂×Q₁₆	—	9	1	no	—
252	C₂×SD₁₆	—	9	2	no	—
253	C₂×D₈	—	9	1	no	—
254	#131	—	9	2	no	—
255	#131	—	9	2	no	—
256	#131	—	9	2	no	—
257	#131	—	18	2	no	—
258	#131	—	18	2	no	—
259	#131	C₂×C₃⋊D₃	1	2	yes	complemented
260	C₂×M₁₆	—	9	1	no	—
261	C₂×M₁₆	—	9	2	no	—
262	C₂×M₁₆	—	18	2	no	—
263	C₂×M₁₆	—	18	2	no	—
264	C₂²×C₈	—	9	1	no	—
265	#117	—	9	1	no	—
266	#108	—	9	2	no	—
267	#108	—	9	1	no	—
268	#108	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
269	#104	—	9	2	no	—
270	#104	—	9	2	no	—
271	#104	—	9	2	no	—
272	#104	C₂×C₃⋊D₃	1	2	yes	complemented
273	#97	—	9	1	no	—
274	#97	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
275	C₄×C₈	—	9	1	no	—
276	C₄×C₈	—	9	1	no	—
277	C₂²×D₃	—	3	4	no	—
278	C₂²×D₃	—	6	8	no	—
279	C₃×Q₈	C₂×C₄×D₃	1	8	yes	—
280	C₃×D₄	—	2	8	no	—
281	C₃×D₄	C₂×C₄×D₃	1	8	yes	—
282	C₂×C₃×C₄	—	2	8	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
285	#67	—	6	8	no	—
286	#67	—	6	8	no	—
287	#67	—	6	8	no	—
288	C₂×Dic₃	—	3	4	no	—
289	C₂×Dic₃	—	6	8	no	—
290	C₂×Dic₃	—	6	4	no	—
291	D₁₂	—	3	8	no	—
292	D₁₂	—	6	8	no	—
293	C₄×D₃	—	3	4	no	—
294	C₄×D₃	—	3	4	no	—
295	C₄×D₃	—	3	4	no	—
296	C₄×D₃	—	3	4	no	—
297	C₄×D₃	—	6	8	no	—
298	C₄×D₃	—	6	8	no	—
299	C₄×D₃	—	6	8	no	—
300	Dic₆	—	3	8	no	—
301	Dic₆	—	6	8	no	—
302	C₃×C₈	—	2	8	no	—
303	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
304	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
305	C₃×C₈	D₃×D₄	1	8	yes	—
306	C₃⋊C₈	—	3	4	no	—
307	C₃⋊C₈	—	3	4	no	—
308	C₃⋊C₈	—	3	8	no	—
309	C₃⋊C₈	—	6	8	no	—
310	C₂×C₃²	—	2	1	no	—
311	C₂×C₃²	—	4	2	no	—
312	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
313	C₃⋊D₃	—	2	1	no	—
314	C₃⋊D₃	—	2	1	no	—
315	C₃⋊D₃	—	4	2	no	—
316	#41	—	9	2	no	—
317	#41	—	9	2	no	—
318	#41	—	9	2	no	—
319	#41	—	18	2	no	—
320	#41	—	18	2	no	—
321	#41	C₂²×C₃⋊D₃	1	2	yes	—
322	C₂×Q₈	—	9	2	no	—
323	C₂×D₄	—	9	2	no	—
324	C₂×D₄	—	18	2	no	—
325	C₂²×C₄	—	9	1	no	—
326	C₂²×C₄	—	18	2	no	—
327	Q₁₆	—	9	2	no	—
328	Q₁₆	—	9	1	no	—
329	Q₁₆	C₄×C₃⋊D₃	1	1	yes	characteristic
330	SD₁₆	—	9	2	no	—
331	SD₁₆	—	9	2	no	—
332	SD₁₆	—	9	2	no	—
333	SD₁₆	C₄×C₃⋊D₃	1	2	yes	—
334	D₈	—	9	2	no	—
335	D₈	—	9	1	no	—
336	D₈	C₄×C₃⋊D₃	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	9	2	no	—
339	M₁₆	—	9	2	no	—
340	M₁₆	—	9	2	no	—
341	M₁₆	—	18	2	no	—
342	M₁₆	—	18	2	no	—
343	M₁₆	—	18	2	no	—
344	M₁₆	—	18	2	no	—
345	M₁₆	C₂²×C₃⋊D₃	1	2	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	9	1	no	—
348	C₂×C₈	—	9	1	no	—
349	C₂×C₈	—	9	1	no	—
350	C₂×C₈	—	9	1	no	—
351	C₂×C₈	—	9	1	no	—
352	C₂×C₈	—	9	1	no	—
353	C₂×C₈	—	18	2	no	—
354	C₂×C₈	—	18	2	no	—
355	C₂×C₈	—	18	2	no	—
356	C₂×C₈	—	18	2	no	—
357	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
358	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
359	C₄⋊C₄	—	18	1	no	—
360	C₂²⋊C₄	—	18	1	no	—
361	C₄²	—	9	1	no	—
362	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
363	C₂²×C₃	—	2	8	no	—
364	C₂²×C₃	D₃×#41	1	4	yes	—
365	C₂×D₃	—	3	4	no	—
366	C₂×D₃	—	3	4	no	—
367	C₂×D₃	—	6	8	no	—
368	C₂×D₃	—	12	4	no	—
369	C₂×D₃	—	24	8	no	—
370	C₃×C₄	—	2	8	no	—
371	C₃×C₄	—	4	4	no	—
372	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
373	C₃×C₄	C₂×D₃×D₄	1	4	yes	—
374	Dic₃	—	3	4	no	—
375	Dic₃	—	3	4	no	—
376	Dic₃	—	6	8	no	—
377	Dic₃	—	12	4	no	—
378	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
379	C₂³	—	9	1	no	—
380	C₂³	—	18	2	no	—
381	Q₈	—	9	2	no	—
382	Q₈	—	18	2	no	—
383	Q₈	C₂×C₄×C₃⋊D₃	1	2	yes	—
384	D₄	—	2	2	no	—
385	D₄	—	9	2	no	—
386	D₄	—	18	2	no	—
387	D₄	—	18	2	no	—
388	D₄	—	18	2	no	—
389	D₄	—	18	2	no	—
390	D₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	9	1	no	—
394	C₂×C₄	—	9	1	no	—
395	C₂×C₄	—	9	1	no	—
396	C₂×C₄	—	9	1	no	—
397	C₂×C₄	—	9	1	no	—
398	C₂×C₄	—	18	2	no	—
399	C₂×C₄	—	18	2	no	—
400	C₂×C₄	—	18	2	no	—
401	C₂×C₄	—	18	2	no	—
402	C₂×C₄	—	18	1	no	—
403	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	9	1	no	—
406	C₈	—	9	1	no	—
407	C₈	—	9	2	no	—
408	C₈	—	18	2	no	—
409	C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
410	C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
411	C₈	D₄×C₃⋊D₃	1	2	yes	—
412	C₂×C₃	—	2	4	no	—
413	C₂×C₃	—	4	8	no	—
414	C₂×C₃	C₄×D₃×D₄	1	4	yes	—
415	D₃	—	6	4	no	—
416	D₃	—	6	4	no	—
417	D₃	—	12	8	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	9	1	no	—
420	C₂²	—	9	1	no	—
421	C₂²	—	18	2	no	—
422	C₂²	—	36	1	no	—
423	C₂²	—	72	2	no	—
424	C₂²	#41×C₃⋊D₃	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	9	1	no	—
428	C₄	—	9	1	no	—
429	C₄	—	18	2	no	—
430	C₄	—	36	1	no	—
431	C₄	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
432	C₄	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
433	C₃	#79899	1	4	yes	complemented
434	C₂	—	2	1	no	—
435	C₂	—	4	2	no	—
436	C₂	—	18	1	no	—
437	C₂	—	18	1	no	—
438	C₂	—	36	2	no	—
439	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×#444	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₃⋊D₃×#135	C₂
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#444	C₃⋊D₃
hypocenter	C₃²	#2957
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
2. #10596221	C₂	semidirect
3. C₃²×#444	C₂	semidirect
4. #10592896	C₂	semidirect
5. #10592843	C₂	semidirect
6. #10592593	C₂	semidirect
7. C₃⋊D₃×#108	C₂	semidirect
8. #10592523	C₂	semidirect
9. #10592520	C₂	semidirect
10. #10592416	C₂	semidirect
11. #10592407	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×#97	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. C₄×C₃⋊(C₃⋊C₈)	C₂²	semidirect
48. C₃×#444	D₃	semidirect
107. C₃×#131	C₂×D₃	semidirect
127. C₃×#108	C₂×D₃	semidirect
128. C₃×#104	C₂×D₃	semidirect
129. C₃×#97	C₂×D₃	semidirect
176. #444	C₃⋊D₃	semidirect
259. #131	C₂×C₃⋊D₃	semidirect
268. #108	C₂×C₃⋊D₃	semidirect
272. #104	C₂×C₃⋊D₃	semidirect
274. #97	C₂×C₃⋊D₃	semidirect
378. C₃²	#2957	semidirect
433. C₃	#79899	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×#444	2
#10592896	2
#10592843	2
#10592593	2
C₃⋊D₃×#108	2
#10592523	2
#10592520	2
#10592416	2
#10592407	2
#79899	3