Subgroups — #11790345

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic
2	C₃×#4935	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×#63573	C₂	1	2	yes	maximal
5	#10589164	C₂	1	2	yes	maximal
6	#70454	—	3	1	no	maximal
7	#69568	—	3	1	no	maximal
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₃⋊Dic₃	—	2	1	no	—
12	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
13	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
14	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
15	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
16	#63658	—	2	1	no	—
17	C₃×C₄⋊(C₃⋊C₈)	C₄	1	4	yes	complemented
18	#63573	—	2	4	no	—
19	C₂×C₃×C₄⋊C₈	—	3	1	no	—
20	C₃×#384	—	3	1	no	—
21	C₂×#817	—	3	2	no	—
22	C₂×#808	—	3	2	no	—
23	#4935	D₃	1	1	yes	characteristic
24	C₄×C₄⋊Dic₃	—	3	1	no	—
25	C₄×C₄⋊Dic₃	—	3	1	no	—
26	C₄×C₄⋊Dic₃	—	6	1	no	—
27	C₂×C₄⋊(C₃⋊C₈)	D₃	1	1	yes	characteristic
28	#4551	—	3	2	no	—
29	#4529	—	3	2	no	—
30	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
33	C₂²×C₃⋊Dic₃	—	2	1	no	—
34	C₂²×C₃⋊Dic₃	—	2	1	no	—
35	C₂²×C₃×Dic₃	—	2	2	no	—
36	C₃²×C₄²	C₂×C₄	1	2	yes	—
37	C₃²×C₄²	Q₈	1	2	yes	—
38	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
39	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
40	C₄⋊(C₃⋊Dic₃)	D₄	1	2	yes	—
41	C₄⋊(C₃⋊Dic₃)	Q₈	1	2	yes	—
42	C₄×C₃⋊Dic₃	—	4	2	no	—
43	C₃×C₄⋊Dic₃	—	2	2	no	—
44	C₃×C₄⋊Dic₃	—	2	2	no	—
45	C₃×C₄⋊Dic₃	—	4	2	no	—
46	C₃×C₄⋊Dic₃	—	4	2	no	—
47	C₂×C₃×C₃⋊C₈	—	2	2	no	—
48	C₂×C₃×C₃⋊C₈	—	2	2	no	—
49	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
50	#1948	—	9	1	no	Sylow
51	C₂²×C₃×C₈	—	3	2	no	—
52	C₂×C₃×C₄⋊C₄	—	3	2	no	—
53	C₂×C₃×C₄⋊C₄	—	6	1	no	—
54	C₂×C₃×C₄⋊C₄	—	6	1	no	—
55	C₂×C₃×C₄²	—	2	1	no	—
56	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
58	C₂×C₄⋊Dic₃	—	2	1	no	—
59	C₂×C₄⋊Dic₃	—	2	1	no	—
60	C₂×C₄⋊Dic₃	—	3	1	no	—
61	C₂×C₄⋊Dic₃	—	3	1	no	—
62	C₂×C₄⋊Dic₃	—	3	1	no	—
63	C₂×C₄⋊Dic₃	—	3	1	no	—
64	C₂×C₄⋊Dic₃	—	6	1	no	—
65	C₂×C₄⋊Dic₃	—	6	1	no	—
66	C₂×C₄⋊Dic₃	C₂×D₃	1	2	yes	—
67	C₂×C₄×Dic₃	—	6	2	no	—
68	C₂×C₄×Dic₃	—	6	1	no	—
69	C₂×C₄×Dic₃	—	6	1	no	—
70	C₂²×C₃⋊C₈	C₂×D₃	1	2	yes	—
71	C₃×C₄⋊C₈	—	3	4	no	—
72	C₃⋊#95	—	6	2	no	—
73	C₃⋊#95	—	6	1	no	—
74	C₃⋊#95	—	6	1	no	—
75	#817	—	6	4	no	—
76	#808	—	6	4	no	—
77	C₄⋊(C₃⋊C₈)	Dic₃	1	4	yes	complemented
78	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃²×C₄	—	2	1	no	—
80	C₂×C₃²×C₄	—	2	1	no	—
81	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
82	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
83	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
84	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
85	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₃²×C₄	#41	1	1	yes	characteristic
90	C₂×C₃²×C₄	#41	1	1	yes	characteristic
91	C₂×C₃⋊Dic₃	—	2	2	no	—
92	C₂×C₃⋊Dic₃	—	2	2	no	—
93	C₂×C₃⋊Dic₃	—	4	1	no	—
94	C₂×C₃⋊Dic₃	—	4	1	no	—
95	C₂×C₃⋊Dic₃	—	4	1	no	—
96	C₂×C₃⋊Dic₃	—	4	1	no	—
97	C₂×C₃×Dic₃	—	4	2	no	—
98	C₂×C₃×Dic₃	—	4	2	no	—
99	C₂×C₃×Dic₃	—	4	2	no	—
100	C₃×C₃⋊C₈	—	2	4	no	—
101	C₂×#106	—	9	2	no	—
102	C₂×C₄⋊C₈	—	3	1	no	—
103	#384	—	3	1	no	—
104	C₄×C₄⋊C₄	—	9	1	no	—
105	#340	—	9	2	no	—
106	C₂²×C₃×C₄	—	2	1	no	—
107	C₂²×C₃×C₄	—	2	1	no	—
108	C₂²×C₃×C₄	—	2	1	no	—
109	C₂²×C₃×C₄	—	6	2	no	—
110	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
111	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
112	C₂²×C₃×C₄	#67	1	1	yes	characteristic
113	C₂²×C₃×C₄	#67	1	1	yes	characteristic
114	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
115	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
116	C₂²×Dic₃	—	2	2	no	—
117	C₂²×Dic₃	—	6	2	no	—
118	C₂²×Dic₃	—	6	2	no	—
119	C₂²×Dic₃	—	6	1	no	—
120	C₂²×Dic₃	—	6	1	no	—
121	C₂²×Dic₃	—	6	1	no	—
122	C₂²×Dic₃	—	6	1	no	—
123	C₂×C₃×C₈	—	3	4	no	—
124	C₂×C₃×C₈	—	6	2	no	—
125	C₂×C₃×C₈	—	6	2	no	—
126	C₃×C₄⋊C₄	—	6	2	no	—
127	C₃×C₄⋊C₄	—	6	2	no	—
128	C₃×C₄⋊C₄	—	12	2	no	—
129	C₃×C₄⋊C₄	—	12	2	no	—
130	C₃×C₄²	—	2	2	no	—
131	C₃×C₄²	—	2	2	no	—
132	C₃×C₄²	Dic₆	1	2	yes	—
133	C₃×C₄²	Dic₆	1	2	yes	—
134	C₃×C₄²	C₄×D₃	1	2	yes	—
135	C₃×C₄²	C₂×Dic₃	1	2	yes	—
136	C₄⋊Dic₃	—	2	2	no	—
137	C₄⋊Dic₃	—	2	2	no	—
138	C₄⋊Dic₃	—	3	2	no	—
139	C₄⋊Dic₃	—	3	2	no	—
140	C₄⋊Dic₃	—	3	2	no	—
141	C₄⋊Dic₃	—	3	2	no	—
142	C₄⋊Dic₃	—	4	2	no	—
143	C₄⋊Dic₃	—	4	2	no	—
144	C₄⋊Dic₃	—	6	2	no	—
145	C₄⋊Dic₃	—	6	2	no	—
146	C₄⋊Dic₃	—	6	2	no	—
147	C₄⋊Dic₃	—	6	2	no	—
148	C₄⋊Dic₃	—	6	1	no	—
149	C₄⋊Dic₃	—	6	1	no	—
150	C₄⋊Dic₃	—	6	1	no	—
151	C₄⋊Dic₃	—	6	1	no	—
152	C₄×Dic₃	—	12	4	no	—
153	C₄×Dic₃	—	12	2	no	—
154	C₄×Dic₃	—	12	2	no	—
155	C₂×C₃⋊C₈	—	2	2	no	—
156	C₂×C₃⋊C₈	—	2	2	no	—
157	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	—
158	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₃²	#121	1	1	yes	characteristic
160	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
162	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
163	C₂²×C₃²	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂²×C₃²	#137	1	1	yes	characteristic
165	C₃²×C₄	—	2	2	no	—
166	C₃²×C₄	#106	1	4	yes	complemented
167	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
168	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
169	C₃²×C₄	#125	1	1	yes	characteristic
170	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
171	C₃⋊Dic₃	—	4	2	no	—
172	C₃⋊Dic₃	—	4	2	no	—
173	C₃×Dic₃	—	8	2	no	—
174	C₂²×C₈	—	3	2	no	—
175	C₂×C₄⋊C₄	—	3	2	no	—
176	C₂×C₄⋊C₄	—	6	1	no	—
177	C₂×C₄⋊C₄	—	6	1	no	—
178	C₂×C₄⋊C₄	—	9	1	no	—
179	C₂×C₄⋊C₄	—	9	1	no	—
180	C₂×C₄²	—	18	1	no	—
181	C₂×C₄²	D₃²	1	1	yes	characteristic
182	#106	—	18	4	no	—
183	C₄⋊C₈	—	3	4	no	—
184	#95	—	18	1	no	—
185	C₂³×C₃	—	2	1	no	—
186	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
187	C₂³×C₃	C₂×#67	1	1	yes	characteristic
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	2	1	no	—
190	C₂×C₃×C₄	—	2	1	no	—
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	2	no	—
193	C₂×C₃×C₄	—	2	2	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	2	1	no	—
199	C₂×C₃×C₄	—	2	1	no	—
200	C₂×C₃×C₄	—	2	1	no	—
201	C₂×C₃×C₄	—	2	1	no	—
202	C₂×C₃×C₄	—	4	1	no	—
203	C₂×C₃×C₄	—	4	1	no	—
204	C₂×C₃×C₄	—	12	2	no	—
205	C₂×C₃×C₄	—	12	2	no	—
206	C₂×C₃×C₄	—	12	2	no	—
207	C₂×C₃×C₄	#204	1	2	yes	—
208	C₂×C₃×C₄	#204	1	2	yes	—
209	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
210	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
211	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
212	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
213	C₂×C₃×C₄	#214	1	2	yes	—
214	C₂×C₃×C₄	#215	1	2	yes	—
215	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
218	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄	#237	1	1	yes	characteristic
221	C₂×C₃×C₄	#237	1	1	yes	characteristic
222	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
223	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
224	C₂×C₃×C₄	#239	1	1	yes	characteristic
225	C₂×C₃×C₄	#239	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
227	C₂×Dic₃	—	4	2	no	—
228	C₂×Dic₃	—	4	2	no	—
229	C₂×Dic₃	—	4	2	no	—
230	C₂×Dic₃	—	6	4	no	—
231	C₂×Dic₃	—	6	4	no	—
232	C₂×Dic₃	—	6	2	no	—
233	C₂×Dic₃	—	6	2	no	—
234	C₂×Dic₃	—	6	2	no	—
235	C₂×Dic₃	—	6	2	no	—
236	C₂×Dic₃	—	12	2	no	—
237	C₂×Dic₃	—	12	2	no	—
238	C₂×Dic₃	—	12	2	no	—
239	C₂×Dic₃	—	12	2	no	—
240	C₂×Dic₃	—	12	1	no	—
241	C₂×Dic₃	—	12	1	no	—
242	C₂×Dic₃	—	12	1	no	—
243	C₂×Dic₃	—	12	1	no	—
244	C₂×Dic₃	—	12	1	no	—
245	C₂×Dic₃	—	12	1	no	—
246	C₂×Dic₃	—	12	1	no	—
247	C₂×Dic₃	—	12	1	no	—
248	C₃×C₈	—	6	4	no	—
249	C₃⋊C₈	—	2	4	no	—
250	C₂×C₃²	#389	1	1	yes	characteristic
251	C₂×C₃²	C₂×#106	1	1	yes	characteristic
252	C₂×C₃²	#428	1	1	yes	characteristic
253	C₂×C₃²	#460	1	1	yes	characteristic
254	C₂×C₃²	#461	1	1	yes	characteristic
255	C₂×C₃²	#475	1	1	yes	characteristic
256	C₂×C₃²	#476	1	1	yes	characteristic
257	C₂²×C₄	—	6	2	no	—
258	C₂²×C₄	—	18	1	no	—
259	C₂²×C₄	—	18	1	no	—
260	C₂²×C₄	#626	1	1	yes	characteristic
261	C₂²×C₄	#626	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
263	C₂×C₈	—	3	4	no	—
264	C₂×C₈	—	6	2	no	—
265	C₂×C₈	—	6	2	no	—
266	C₄⋊C₄	—	6	2	no	—
267	C₄⋊C₄	—	6	2	no	—
268	C₄⋊C₄	—	9	2	no	—
269	C₄⋊C₄	—	9	2	no	—
270	C₄⋊C₄	—	12	2	no	—
271	C₄⋊C₄	—	12	2	no	—
272	C₄⋊C₄	—	18	1	no	—
273	C₄⋊C₄	—	18	1	no	—
274	C₄²	—	36	2	no	—
275	C₄²	D₃×Dic₃	1	2	yes	—
276	C₄²	#627	1	2	yes	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	#895	1	1	yes	characteristic
285	C₂²×C₃	#897	1	1	yes	characteristic
286	C₂²×C₃	C₂×#204	1	1	yes	characteristic
287	C₂²×C₃	C₂×#204	1	1	yes	characteristic
288	C₂²×C₃	#908	1	1	yes	characteristic
289	C₂²×C₃	#909	1	1	yes	characteristic
290	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
291	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
292	C₂²×C₃	#932	1	1	yes	characteristic
293	C₂²×C₃	C₂×#214	1	1	yes	characteristic
294	C₂²×C₃	#938	1	1	yes	characteristic
295	C₂²×C₃	C₂×#215	1	1	yes	characteristic
296	C₂²×C₃	#942	1	1	yes	characteristic
297	C₂²×C₃	#946	1	1	yes	characteristic
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	—	2	4	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	4	2	no	—
306	C₃×C₄	—	24	2	no	—
307	C₃×C₄	#808	1	4	yes	complemented
308	C₃×C₄	#817	1	4	yes	complemented
309	C₃×C₄	#887	1	1	yes	characteristic
310	C₃×C₄	#888	1	1	yes	characteristic
311	C₃×C₄	#888	1	1	yes	characteristic
312	C₃×C₄	#890	1	1	yes	characteristic
313	C₃×C₄	#890	1	1	yes	characteristic
314	C₃×C₄	#893	1	1	yes	characteristic
315	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
316	C₃×C₄	Q₈×Dic₃	1	1	yes	characteristic
317	Dic₃	—	8	2	no	—
318	Dic₃	—	12	4	no	—
319	Dic₃	—	12	4	no	—
320	Dic₃	—	12	2	no	—
321	Dic₃	—	12	2	no	—
322	Dic₃	—	12	2	no	—
323	Dic₃	—	12	2	no	—
324	C₃²	#1948	1	1	yes	characteristic, complemented, Sylow
325	C₂³	C₂×#626	1	1	yes	characteristic
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	12	2	no	—
329	C₂×C₄	—	12	2	no	—
330	C₂×C₄	—	12	2	no	—
331	C₂×C₄	—	18	2	no	—
332	C₂×C₄	—	18	2	no	—
333	C₂×C₄	—	36	1	no	—
334	C₂×C₄	—	36	1	no	—
335	C₂×C₄	—	36	1	no	—
336	C₂×C₄	—	36	1	no	—
337	C₂×C₄	#3716	1	2	yes	—
338	C₂×C₄	#3717	1	2	yes	—
339	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
340	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
341	C₂×C₄	#3796	1	1	yes	characteristic
342	C₂×C₄	#3796	1	1	yes	characteristic
343	C₂×C₄	#3797	1	1	yes	characteristic
344	C₂×C₄	#3802	1	1	yes	characteristic
345	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
346	C₂×C₄	C₂×#627	1	1	yes	characteristic
347	C₈	—	6	4	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	#4841	1	1	yes	characteristic
356	C₂×C₃	#4842	1	1	yes	characteristic
357	C₂×C₃	#4848	1	1	yes	characteristic
358	C₂×C₃	#4851	1	1	yes	characteristic
359	C₂×C₃	C₂×#808	1	1	yes	characteristic
360	C₂×C₃	#4964	1	1	yes	characteristic
361	C₂×C₃	#4972	1	1	yes	characteristic
362	C₂×C₃	#4984	1	1	yes	characteristic
363	C₂×C₃	#5075	1	1	yes	characteristic
364	C₂×C₃	#5083	1	1	yes	characteristic
365	C₂×C₃	#5084	1	1	yes	characteristic
366	C₂×C₃	#5094	1	1	yes	characteristic
367	C₂×C₃	C₂×#817	1	1	yes	characteristic
368	C₂×C₃	#5121	1	1	yes	characteristic
369	C₂²	C₂×#3716	1	1	yes	characteristic
370	C₂²	#63830	1	1	yes	characteristic
371	C₂²	C₂×#3717	1	1	yes	characteristic
372	C₂²	#63833	1	1	yes	characteristic
373	C₂²	#63871	1	1	yes	characteristic
374	C₂²	#63916	1	1	yes	characteristic
375	C₂²	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	24	2	no	—
378	C₄	—	36	2	no	—
379	C₄	—	36	2	no	—
380	C₄	#63573	1	4	yes	complemented
381	C₄	#63843	1	1	yes	characteristic
382	C₄	#63872	1	1	yes	characteristic
383	C₄	#63898	1	1	yes	characteristic
384	C₄	#63919	1	1	yes	characteristic
385	C₃	—	2	1	no	—
386	C₃	#69568	1	1	yes	characteristic, complemented
387	C₃	#70454	1	1	yes	characteristic, complemented
388	C₂	#10590300	1	1	yes	characteristic
389	C₂	#10590307	1	1	yes	characteristic
390	C₂	#10590377	1	1	yes	characteristic
391	C₂	#10590379	1	1	yes	characteristic
392	C₂	C₂×#63573	1	1	yes	characteristic
393	C₂	#10591130	1	1	yes	characteristic
394	C₂	#10591357	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#626
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#1948
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
17. C₃×C₄⋊(C₃⋊C₈)	C₄	semidirect
77. C₄⋊(C₃⋊C₈)	Dic₃	semidirect
166. C₃²×C₄	#106	semidirect
307. C₃×C₄	#808	semidirect
308. C₃×C₄	#817	semidirect
324. C₃²	#1948	semidirect
380. C₄	#63573	semidirect
386. C₃	#69568	semidirect
387. C₃	#70454	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊(C₃⋊Dic₃)	2
C₃×#4935	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×#63573	2
#10589164	2
#70454	3
#69568	3