Subgroups — #13179756

Order 1728.

4620 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#89080	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723987	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723971	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723936	C₂	1	1	yes	maximal, characteristic, complemented
7	#11723935	C₂	1	2	yes	maximal, complemented
8	#11723934	C₂	1	2	yes	maximal, complemented
9	#11723933	C₂	1	1	yes	maximal, characteristic, complemented
10	#11723923	C₂	1	2	yes	maximal, complemented
11	#11723922	C₂	1	2	yes	maximal, complemented
12	#10596098	—	3	13	no	maximal
13	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂×#6312	C₂²	1	2	yes	—
17	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
18	#89080	—	2	4	no	—
19	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
23	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
28	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃³×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
31	#88859	C₂²	1	2	yes	—
32	#88859	C₂²	1	2	yes	—
33	#88859	C₂²	1	2	yes	complemented
34	#88859	C₂²	1	2	yes	complemented
35	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
36	#88857	C₂²	1	2	yes	complemented
37	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
38	C₂×#3832	—	3	13	no	—
39	C₂²×C₄×C₃⋊D₃	—	3	13	no	—
40	C₃²×C₂²⋊Q₈	D₃	1	13	yes	complemented
41	#64155	—	3	13	no	—
42	#64139	—	3	13	no	—
43	#64104	—	3	13	no	—
44	#64103	—	3	26	no	—
45	#64102	—	3	26	no	—
46	#64101	—	3	13	no	—
47	#64091	—	3	26	no	—
48	#64090	—	3	26	no	—
49	C₂³×C₃³	C₂³	1	1	yes	characteristic
50	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
51	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
52	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
53	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
54	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
55	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
56	C₃³×Q₈	—	2	2	no	—
57	C₂×C₃³×C₄	—	2	2	no	—
58	C₂×C₃³×C₄	C₂³	1	2	yes	—
59	C₂×C₃³×C₄	C₂³	1	2	yes	—
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
62	#6312	—	2	4	no	—
63	C₂×C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
64	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
65	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
66	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	4	no	—
68	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	4	no	—
69	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
70	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
71	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
72	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
73	C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
74	C₄×C₃⋊(C₃⋊D₃)	D₄	1	4	yes	complemented
75	#5627	—	9	13	no	—
76	C₂³×C₃⋊D₃	—	3	13	no	—
77	C₂×C₃²×Q₈	C₂×D₃	1	13	yes	complemented
78	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	—
79	C₂×#638	—	3	26	no	—
80	C₂²×C₃⋊Dic₃	—	3	13	no	—
81	#3832	—	6	52	no	—
82	C₂×C₄⋊(C₃⋊D₃)	—	3	26	no	—
83	C₂×C₄⋊(C₃⋊D₃)	—	3	26	no	—
84	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
85	C₂×C₄×C₃⋊D₃	—	3	13	no	—
86	C₂×C₄×C₃⋊D₃	—	3	26	no	—
87	C₂×C₄×C₃⋊D₃	—	3	13	no	—
88	C₂×C₄×C₃⋊D₃	—	3	13	no	—
89	C₂×C₄×C₃⋊D₃	—	3	13	no	—
90	C₂×C₄×C₃⋊D₃	—	6	52	no	—
91	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
92	C₃²×C₄⋊C₄	C₂×D₃	1	26	yes	complemented
93	C₃²×C₂²⋊C₄	C₂×D₃	1	26	yes	—
94	#3752	—	3	26	no	—
95	#3752	—	3	26	no	—
96	#3752	—	3	26	no	—
97	#3752	—	3	26	no	—
98	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
99	#3750	—	3	26	no	—
100	C₄×C₃⋊Dic₃	—	3	26	no	—
101	C₂²×C₃³	—	2	1	no	—
102	C₂²×C₃³	—	2	1	no	—
103	C₂²×C₃³	#41	1	2	yes	complemented
104	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
105	C₂×C₃⋊(C₃⋊D₃)	—	2	8	no	—
106	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
107	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
108	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
109	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
110	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
111	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
112	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
113	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	2	yes	—
114	C₂×C₃⋊(C₃⋊D₃)	#41	1	2	yes	complemented
115	C₃³×C₄	—	2	1	no	—
116	C₃³×C₄	—	2	2	no	—
117	C₃³×C₄	—	2	2	no	—
118	C₃³×C₄	C₂×D₄	1	2	yes	—
119	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
120	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
121	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	2	yes	—
122	C₂×#239	—	9	13	no	—
123	C₂²×C₄×D₃	—	9	13	no	—
124	C₃×C₂²⋊Q₈	C₃⋊D₃	1	13	yes	complemented
125	#946	—	9	13	no	—
126	#930	—	9	13	no	—
127	#895	—	9	13	no	—
128	#894	—	9	26	no	—
129	#893	—	9	26	no	—
130	#892	—	9	13	no	—
131	#882	—	9	26	no	—
132	#67⋊C₄	—	9	26	no	—
133	C₂³×C₃²	C₂²×D₃	1	13	yes	—
134	C₂²×C₃⋊D₃	—	3	13	no	—
135	C₂²×C₃⋊D₃	—	3	13	no	—
136	C₂²×C₃⋊D₃	—	3	26	no	—
137	C₂²×C₃⋊D₃	—	6	26	no	—
138	C₂²×C₃⋊D₃	—	6	26	no	—
139	C₂²×C₃⋊D₃	—	6	26	no	—
140	C₃²×Q₈	—	2	26	no	—
141	C₂×C₃²×C₄	—	2	26	no	—
142	C₂×C₃²×C₄	C₂²×D₃	1	26	yes	—
143	C₂×C₃²×C₄	C₂²×D₃	1	26	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
145	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
146	#638	—	6	52	no	—
147	C₂×C₃⋊Dic₃	—	3	13	no	—
148	C₂×C₃⋊Dic₃	—	3	26	no	—
149	C₂×C₃⋊Dic₃	—	3	13	no	—
150	C₂×C₃⋊Dic₃	—	6	26	no	—
151	C₄⋊(C₃⋊D₃)	—	6	52	no	—
152	C₄⋊(C₃⋊D₃)	—	6	52	no	—
153	C₄⋊(C₃⋊D₃)	—	6	26	no	—
154	C₄×C₃⋊D₃	—	3	52	no	—
155	C₄×C₃⋊D₃	—	6	26	no	—
156	C₄×C₃⋊D₃	—	6	52	no	—
157	C₄×C₃⋊D₃	—	6	26	no	—
158	C₄×C₃⋊D₃	—	6	26	no	—
159	#525	—	27	1	no	Sylow
160	C₂×C₃³	—	2	2	no	—
161	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃³	C₂×#41	1	1	yes	characteristic
163	C₂×C₃³	C₂×#41	1	1	yes	characteristic
164	C₃⋊(C₃⋊D₃)	—	2	2	no	—
165	C₃⋊(C₃⋊D₃)	—	2	2	no	—
166	C₃⋊(C₃⋊D₃)	—	4	2	no	—
167	C₂³×D₃	—	9	13	no	—
168	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	13	yes	complemented
169	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
170	C₂×#67	—	9	26	no	—
171	C₂²×Dic₃	—	9	13	no	—
172	#239	—	18	52	no	—
173	C₂×D₁₂	—	9	26	no	—
174	C₂×D₁₂	—	9	26	no	—
175	C₂×D₁₂	—	9	13	no	—
176	C₂×C₄×D₃	—	9	13	no	—
177	C₂×C₄×D₃	—	9	26	no	—
178	C₂×C₄×D₃	—	9	13	no	—
179	C₂×C₄×D₃	—	9	13	no	—
180	C₂×C₄×D₃	—	9	13	no	—
181	C₂×C₄×D₃	—	18	52	no	—
182	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
183	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	26	yes	complemented
184	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	26	yes	—
185	(C₂×D₃)⋊C₄	—	9	26	no	—
186	(C₂×D₃)⋊C₄	—	9	26	no	—
187	(C₂×D₃)⋊C₄	—	9	26	no	—
188	(C₂×D₃)⋊C₄	—	9	26	no	—
189	C₄⋊Dic₃	—	9	13	no	—
190	Dic₃⋊C₄	—	9	26	no	—
191	C₄×Dic₃	—	9	26	no	—
192	C₂²×C₃²	—	2	13	no	—
193	C₂²×C₃²	—	2	13	no	—
194	C₂²×C₃²	#239	1	26	yes	complemented
195	C₂²×C₃²	C₂³×D₃	1	13	yes	—
196	C₂×C₃⋊D₃	—	3	26	no	—
197	C₂×C₃⋊D₃	—	3	26	no	—
198	C₂×C₃⋊D₃	—	6	104	no	—
199	C₂×C₃⋊D₃	—	6	13	no	—
200	C₂×C₃⋊D₃	—	6	13	no	—
201	C₂×C₃⋊D₃	—	6	13	no	—
202	C₂×C₃⋊D₃	—	6	13	no	—
203	C₂×C₃⋊D₃	—	6	26	no	—
204	C₂×C₃⋊D₃	—	6	26	no	—
205	C₂×C₃⋊D₃	—	6	26	no	—
206	C₃²×C₄	—	2	13	no	—
207	C₃²×C₄	—	2	26	no	—
208	C₃²×C₄	—	2	26	no	—
209	C₃²×C₄	D₃×D₄	1	26	yes	—
210	C₃⋊Dic₃	—	3	26	no	—
211	C₃⋊Dic₃	—	6	13	no	—
212	C₃⋊Dic₃	—	6	26	no	—
213	C₂×#41	—	27	1	no	—
214	C₂³×C₄	—	27	1	no	—
215	#123	—	27	2	no	—
216	C₂²⋊Q₈	—	27	1	no	—
217	C₂²⋊Q₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
218	#121	—	27	1	no	—
219	#121	—	27	1	no	—
220	#120	—	27	2	no	—
221	C₄×D₄	—	27	2	no	—
222	C₄×D₄	—	27	2	no	—
223	#117	—	27	1	no	—
224	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
226	C₂²×D₃	—	9	13	no	—
227	C₂²×D₃	—	9	13	no	—
228	C₂²×D₃	—	9	26	no	—
229	C₂²×D₃	—	18	26	no	—
230	C₂²×D₃	—	18	26	no	—
231	C₂²×D₃	—	18	26	no	—
232	C₃×Q₈	—	2	26	no	—
233	C₂×C₃×C₄	—	2	26	no	—
234	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	26	yes	—
235	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	26	yes	—
236	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
237	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
238	#67	—	18	52	no	—
239	C₂×Dic₃	—	9	13	no	—
240	C₂×Dic₃	—	9	26	no	—
241	C₂×Dic₃	—	9	13	no	—
242	C₂×Dic₃	—	18	26	no	—
243	D₁₂	—	18	52	no	—
244	D₁₂	—	18	52	no	—
245	D₁₂	—	18	26	no	—
246	C₄×D₃	—	9	52	no	—
247	C₄×D₃	—	18	26	no	—
248	C₄×D₃	—	18	52	no	—
249	C₄×D₃	—	18	26	no	—
250	C₄×D₃	—	18	26	no	—
251	C₂×C₃²	—	2	26	no	—
252	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
253	C₂×C₃²	C₂×#239	1	13	yes	—
254	C₂×C₃²	D₃×#41	1	13	yes	—
255	C₃⋊D₃	—	6	26	no	—
256	C₃⋊D₃	—	6	26	no	—
257	C₃⋊D₃	—	12	26	no	—
258	C₂⁴	—	27	1	no	—
259	#41	—	54	4	no	—
260	C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
261	C₂×D₄	—	27	2	no	—
262	C₂×D₄	—	27	2	no	—
263	C₂×D₄	—	27	2	no	—
264	C₂×D₄	—	27	1	no	—
265	C₂²×C₄	—	27	1	no	—
266	C₂²×C₄	—	27	1	no	—
267	C₂²×C₄	—	27	1	no	—
268	C₂²×C₄	—	27	2	no	—
269	C₂²×C₄	—	27	1	no	—
270	C₂²×C₄	—	27	1	no	—
271	C₂²×C₄	—	54	4	no	—
272	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
273	C₄⋊C₄	—	27	1	no	—
274	C₄⋊C₄	—	27	2	no	—
275	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
276	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
277	C₂²⋊C₄	—	27	2	no	—
278	C₂²⋊C₄	—	27	2	no	—
279	C₂²⋊C₄	—	27	2	no	—
280	C₂²⋊C₄	—	27	2	no	—
281	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	—
282	C₄²	—	27	2	no	—
283	C₂²×C₃	—	2	13	no	—
284	C₂²×C₃	—	2	13	no	—
285	C₂²×C₃	#3832	1	26	yes	complemented
286	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
287	C₂×D₃	—	9	26	no	—
288	C₂×D₃	—	9	26	no	—
289	C₂×D₃	—	18	104	no	—
290	C₂×D₃	—	18	13	no	—
291	C₂×D₃	—	18	13	no	—
292	C₂×D₃	—	18	13	no	—
293	C₂×D₃	—	18	13	no	—
294	C₂×D₃	—	18	26	no	—
295	C₂×D₃	—	18	26	no	—
296	C₂×D₃	—	18	26	no	—
297	C₃×C₄	—	2	13	no	—
298	C₃×C₄	—	2	26	no	—
299	C₃×C₄	—	2	26	no	—
300	C₃×C₄	D₄×C₃⋊D₃	1	26	yes	—
301	Dic₃	—	9	26	no	—
302	Dic₃	—	18	13	no	—
303	Dic₃	—	18	26	no	—
304	C₃²	#5627	1	13	yes	complemented
305	C₂³	—	27	1	no	—
306	C₂³	—	27	1	no	—
307	C₂³	—	27	2	no	—
308	C₂³	—	54	2	no	—
309	C₂³	—	54	2	no	—
310	C₂³	—	54	2	no	—
311	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	D₄	—	54	4	no	—
314	D₄	—	54	4	no	—
315	D₄	—	54	4	no	—
316	D₄	—	54	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	27	1	no	—
319	C₂×C₄	—	27	4	no	—
320	C₂×C₄	—	27	2	no	—
321	C₂×C₄	—	27	1	no	—
322	C₂×C₄	—	54	2	no	—
323	C₂×C₄	—	54	4	no	—
324	C₂×C₄	—	54	2	no	—
325	C₂×C₄	—	54	2	no	—
326	C₂×C₄	—	54	2	no	—
327	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
328	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
330	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
331	C₂×C₃	—	2	26	no	—
332	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
333	C₂×C₃	C₂×#3832	1	13	yes	—
334	C₂×C₃	#41×C₃⋊D₃	1	13	yes	—
335	D₃	—	18	26	no	—
336	D₃	—	18	26	no	—
337	D₃	—	36	26	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	27	2	no	—
341	C₂²	—	27	2	no	—
342	C₂²	—	54	8	no	—
343	C₂²	—	54	1	no	—
344	C₂²	—	54	1	no	—
345	C₂²	—	54	1	no	—
346	C₂²	—	54	1	no	—
347	C₂²	—	54	2	no	—
348	C₂²	—	54	2	no	—
349	C₂²	—	54	2	no	—
350	C₂²	#89080	1	2	yes	complemented
351	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	27	2	no	—
356	C₄	—	54	1	no	—
357	C₄	—	54	2	no	—
358	C₄	D₄×C₃⋊(C₃⋊D₃)	1	2	yes	—
359	C₃	#10596098	1	13	yes	complemented
360	C₂	—	2	2	no	—
361	C₂	—	54	2	no	—
362	C₂	—	54	2	no	—
363	C₂	—	108	2	no	—
364	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
365	C₂	C₂×#89080	1	1	yes	characteristic
366	C₂	#41×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×C₂²⋊Q₈	C₂
hypercenter	C₂²⋊Q₈	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#525
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#89080	C₂	semidirect
2. C₂²×C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₃³×C₂²⋊Q₈	C₂	semidirect
4. #11723987	C₂	semidirect
5. #11723971	C₂	semidirect
6. #11723936	C₂	semidirect
7. #11723935	C₂	semidirect
8. #11723934	C₂	semidirect
9. #11723933	C₂	semidirect
10. #11723923	C₂	semidirect
11. #11723922	C₂	semidirect
14. C₂×C₃³×Q₈	C₂²	semidirect
21. C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	semidirect
27. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
28. C₃³×C₄⋊C₄	C₂²	semidirect
29. C₃³×C₄⋊C₄	C₂²	semidirect
33. #88859	C₂²	semidirect
34. #88859	C₂²	semidirect
35. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
36. #88857	C₂²	semidirect
37. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
40. C₃²×C₂²⋊Q₈	D₃	semidirect
74. C₄×C₃⋊(C₃⋊D₃)	D₄	semidirect
77. C₂×C₃²×Q₈	C₂×D₃	semidirect
91. C₃²×C₄⋊C₄	C₂×D₃	semidirect
92. C₃²×C₄⋊C₄	C₂×D₃	semidirect
103. C₂²×C₃³	#41	semidirect
114. C₂×C₃⋊(C₃⋊D₃)	#41	semidirect
124. C₃×C₂²⋊Q₈	C₃⋊D₃	semidirect
168. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
182. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
183. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
194. C₂²×C₃²	#239	semidirect
217. C₂²⋊Q₈	C₃⋊(C₃⋊D₃)	semidirect
224. C₃³	#525	semidirect
260. C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
275. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
276. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
285. C₂²×C₃	#3832	semidirect
304. C₃²	#5627	semidirect
350. C₂²	#89080	semidirect
359. C₃	#10596098	semidirect

Maximal subgroups

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

subgroup	index
C₂×#89080	2
C₂²×C₄×C₃⋊(C₃⋊D₃)	2
C₃³×C₂²⋊Q₈	2
#11723987	2
#11723971	2
#11723936	2
#11723935	2
#11723934	2
#11723933	2
#11723923	2
#11723922	2
#10596098	3