Subgroups — #13179678

Order 1728.

4676 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#89076	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723978	C₂	1	2	yes	maximal, complemented
5	#11723971	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723965	C₂	1	1	yes	maximal, characteristic, complemented
7	#11723935	C₂	1	2	yes	maximal, complemented
8	#11723925	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
10	#11723916	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596021	—	3	13	no	maximal
13	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
17	C₂×#6312	C₂²	1	2	yes	complemented
18	C₂×#6312	C₂²	1	2	yes	complemented
19	#89076	—	2	4	no	—
20	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	—	2	4	no	—
21	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
25	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
26	C₂×#6308	C₂²	1	1	yes	characteristic, complemented
27	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
31	#88864	C₂²	1	2	yes	—
32	#88859	C₂²	1	2	yes	complemented
33	#88859	C₂²	1	2	yes	complemented
34	#88859	C₂²	1	2	yes	complemented
35	#88859	C₂²	1	2	yes	complemented
36	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
37	#88857	C₂²	1	2	yes	complemented
38	C₂×#3828	—	3	13	no	—
39	C₂²×C₄⋊(C₃⋊D₃)	—	3	13	no	—
40	C₃²×C₄×D₄	D₃	1	13	yes	complemented
41	#64146	—	3	26	no	—
42	#64139	—	3	13	no	—
43	#64133	—	3	13	no	—
44	#64103	—	3	26	no	—
45	#64093	—	3	26	no	—
46	C₂²⋊C₄×C₃⋊D₃	—	3	26	no	—
47	#64084	—	3	13	no	—
48	C₄×C₄⋊(C₃⋊D₃)	—	3	13	no	—
49	C₂³×C₃³	C₂³	1	1	yes	characteristic
50	C₂³×C₃³	C₂³	1	1	yes	characteristic
51	C₂²×C₃⋊(C₃⋊D₃)	—	2	4	no	—
52	C₂²×C₃⋊(C₃⋊D₃)	—	2	4	no	—
53	C₂²×C₃⋊(C₃⋊D₃)	—	4	2	no	—
54	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
55	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
56	C₃³×D₄	—	2	2	no	—
57	C₂×C₃³×C₄	—	2	2	no	—
58	C₂×C₃³×C₄	—	2	2	no	—
59	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	#6312	—	2	4	no	—
65	#6312	—	4	2	no	—
66	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
67	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
68	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	4	no	—
69	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
70	C₄⋊(C₃⋊(C₃⋊D₃))	D₄	1	4	yes	complemented
71	C₄×C₃⋊(C₃⋊D₃)	—	2	4	no	—
72	C₄×C₃⋊(C₃⋊D₃)	—	4	2	no	—
73	#6308	—	2	2	no	—
74	#5550	—	9	13	no	—
75	C₂³×C₃⋊D₃	—	3	26	no	—
76	C₂×C₃²×D₄	C₂×D₃	1	13	yes	—
77	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	—
78	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	complemented
79	C₂×#638	—	3	26	no	—
80	C₂×#638	—	3	26	no	—
81	#3828	—	6	52	no	—
82	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
83	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
84	C₂×C₄⋊(C₃⋊D₃)	—	3	26	no	—
85	C₂×C₄⋊(C₃⋊D₃)	—	6	52	no	—
86	C₂×C₄×C₃⋊D₃	—	3	26	no	—
87	C₂×C₄×C₃⋊D₃	—	3	26	no	—
88	C₂×#634	—	3	13	no	—
89	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
90	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
91	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	complemented
92	C₃²×C₄²	C₂×D₃	1	13	yes	complemented
93	#3757	—	3	26	no	—
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	C₂²×C₃³	—	2	1	no	—
101	C₂²×C₃³	—	2	1	no	—
102	C₂²×C₃³	—	2	1	no	—
103	C₂²×C₃³	—	2	1	no	—
104	C₂²×C₃³	—	2	1	no	—
105	C₂²×C₃³	#41	1	2	yes	complemented
106	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
107	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
108	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
109	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
110	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
111	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
112	C₂×C₃⋊(C₃⋊D₃)	—	4	8	no	—
113	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	4	yes	—
114	C₃³×C₄	—	2	1	no	—
115	C₃³×C₄	—	2	1	no	—
116	C₃³×C₄	—	2	1	no	—
117	C₃³×C₄	—	2	1	no	—
118	C₃³×C₄	C₂×D₄	1	2	yes	—
119	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
120	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
121	C₂×#235	—	9	13	no	—
122	C₂²×D₁₂	—	9	13	no	—
123	C₃×C₄×D₄	C₃⋊D₃	1	13	yes	complemented
124	#937	—	9	26	no	—
125	#930	—	9	13	no	—
126	#924	—	9	13	no	—
127	#894	—	9	26	no	—
128	#884	—	9	26	no	—
129	D₃×C₂²⋊C₄	—	9	26	no	—
130	#875	—	9	13	no	—
131	C₄×D₁₂	—	9	13	no	—
132	C₂³×C₃²	C₂²×D₃	1	13	yes	—
133	C₂³×C₃²	C₂²×D₃	1	13	yes	—
134	C₂²×C₃⋊D₃	—	3	26	no	—
135	C₂²×C₃⋊D₃	—	3	26	no	—
136	C₂²×C₃⋊D₃	—	6	52	no	—
137	C₂²×C₃⋊D₃	—	6	52	no	—
138	C₂²×C₃⋊D₃	—	12	26	no	—
139	C₃²×D₄	—	2	26	no	—
140	C₂×C₃²×C₄	—	2	26	no	—
141	C₂×C₃²×C₄	—	2	26	no	—
142	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
143	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
145	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
146	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
147	#638	—	6	52	no	—
148	#638	—	12	26	no	—
149	C₂×C₃⋊Dic₃	—	3	26	no	—
150	C₂×C₃⋊Dic₃	—	3	26	no	—
151	C₄⋊(C₃⋊D₃)	—	3	52	no	—
152	C₄⋊(C₃⋊D₃)	—	6	52	no	—
153	C₄⋊(C₃⋊D₃)	—	6	26	no	—
154	C₄×C₃⋊D₃	—	6	52	no	—
155	C₄×C₃⋊D₃	—	12	26	no	—
156	#634	—	6	26	no	—
157	#546	—	27	1	no	Sylow
158	C₂×C₃³	—	2	2	no	—
159	C₂×C₃³	—	4	1	no	—
160	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₃³	C₂×#41	1	1	yes	characteristic
162	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
163	C₃⋊(C₃⋊D₃)	—	2	4	no	—
164	C₃⋊(C₃⋊D₃)	—	4	2	no	—
165	C₂³×D₃	—	9	26	no	—
166	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	—
167	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
168	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	complemented
169	C₂×#67	—	9	26	no	—
170	C₂×#67	—	9	26	no	—
171	#235	—	18	52	no	—
172	C₂×D₁₂	—	9	13	no	—
173	C₂×D₁₂	—	9	13	no	—
174	C₂×D₁₂	—	9	26	no	—
175	C₂×D₁₂	—	18	52	no	—
176	C₂×C₄×D₃	—	9	26	no	—
177	C₂×C₄×D₃	—	9	26	no	—
178	C₂×Dic₆	—	9	13	no	—
179	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
180	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
181	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
182	C₃×C₄²	C₂×C₃⋊D₃	1	13	yes	complemented
183	#217	—	9	26	no	—
184	(C₂×D₃)⋊C₄	—	9	26	no	—
185	(C₂×D₃)⋊C₄	—	9	26	no	—
186	(C₂×D₃)⋊C₄	—	9	26	no	—
187	(C₂×D₃)⋊C₄	—	9	26	no	—
188	C₄⋊Dic₃	—	9	13	no	—
189	Dic₃⋊C₄	—	9	26	no	—
190	C₂²×C₃²	—	2	13	no	—
191	C₂²×C₃²	—	2	13	no	—
192	C₂²×C₃²	—	2	13	no	—
193	C₂²×C₃²	—	2	13	no	—
194	C₂²×C₃²	—	2	13	no	—
195	C₂²×C₃²	#235	1	26	yes	complemented
196	C₂²×C₃²	C₂³×D₃	1	13	yes	—
197	C₂×C₃⋊D₃	—	3	52	no	—
198	C₂×C₃⋊D₃	—	6	26	no	—
199	C₂×C₃⋊D₃	—	6	26	no	—
200	C₂×C₃⋊D₃	—	6	26	no	—
201	C₂×C₃⋊D₃	—	6	26	no	—
202	C₂×C₃⋊D₃	—	6	26	no	—
203	C₂×C₃⋊D₃	—	12	104	no	—
204	C₃²×C₄	—	2	13	no	—
205	C₃²×C₄	—	2	13	no	—
206	C₃²×C₄	—	2	13	no	—
207	C₃²×C₄	—	2	13	no	—
208	C₃²×C₄	D₃×D₄	1	26	yes	—
209	C₃⋊Dic₃	—	6	26	no	—
210	C₃⋊Dic₃	—	6	26	no	—
211	C₂×#41	—	27	1	no	—
212	C₂²×D₄	—	27	1	no	—
213	#124	—	27	1	no	—
214	#123	—	27	2	no	—
215	C₂²⋊Q₈	—	27	1	no	—
216	#121	—	27	1	no	—
217	#121	—	27	2	no	—
218	#120	—	27	2	no	—
219	C₄×D₄	—	27	1	no	—
220	C₄×D₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
221	C₂×C₂²⋊C₄	—	27	2	no	—
222	C₃³	#546	1	1	yes	characteristic, complemented, Sylow
223	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
224	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
225	C₂²×D₃	—	9	26	no	—
226	C₂²×D₃	—	9	26	no	—
227	C₂²×D₃	—	18	52	no	—
228	C₂²×D₃	—	18	52	no	—
229	C₂²×D₃	—	36	26	no	—
230	C₃×D₄	—	2	26	no	—
231	C₂×C₃×C₄	—	2	26	no	—
232	C₂×C₃×C₄	—	2	26	no	—
233	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
234	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
235	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	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	#67	—	36	26	no	—
240	C₂×Dic₃	—	9	26	no	—
241	C₂×Dic₃	—	9	26	no	—
242	D₁₂	—	9	52	no	—
243	D₁₂	—	18	52	no	—
244	D₁₂	—	18	26	no	—
245	C₄×D₃	—	18	52	no	—
246	C₄×D₃	—	36	26	no	—
247	Dic₆	—	18	26	no	—
248	C₂×C₃²	—	2	26	no	—
249	C₂×C₃²	—	4	13	no	—
250	C₂×C₃²	C₂×#235	1	13	yes	—
251	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
252	C₂×C₃²	#1009	1	13	yes	—
253	C₃⋊D₃	—	6	52	no	—
254	C₃⋊D₃	—	12	26	no	—
255	C₂⁴	—	27	2	no	—
256	#41	—	54	4	no	—
257	C₂×Q₈	—	27	1	no	—
258	C₂×D₄	—	27	2	no	—
259	C₂×D₄	—	27	2	no	—
260	C₂×D₄	—	27	1	no	—
261	C₂×D₄	—	27	2	no	—
262	C₂×D₄	—	27	1	no	—
263	C₂×D₄	—	54	4	no	—
264	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
265	C₂²×C₄	—	27	2	no	—
266	C₂²×C₄	—	27	2	no	—
267	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
269	C₄⋊C₄	—	27	1	no	—
270	C₄⋊C₄	—	27	2	no	—
271	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
272	C₂²⋊C₄	—	27	2	no	—
273	C₂²⋊C₄	—	27	2	no	—
274	C₂²⋊C₄	—	27	2	no	—
275	C₂²⋊C₄	—	27	2	no	—
276	C₂²⋊C₄	—	27	2	no	—
277	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
278	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
279	C₄²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
280	C₂²×C₃	—	2	13	no	—
281	C₂²×C₃	—	2	13	no	—
282	C₂²×C₃	—	2	13	no	—
283	C₂²×C₃	—	2	13	no	—
284	C₂²×C₃	—	2	13	no	—
285	C₂²×C₃	#3828	1	26	yes	complemented
286	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
287	C₂×D₃	—	9	52	no	—
288	C₂×D₃	—	18	26	no	—
289	C₂×D₃	—	18	26	no	—
290	C₂×D₃	—	18	26	no	—
291	C₂×D₃	—	18	26	no	—
292	C₂×D₃	—	18	26	no	—
293	C₂×D₃	—	36	104	no	—
294	C₃×C₄	—	2	13	no	—
295	C₃×C₄	—	2	13	no	—
296	C₃×C₄	—	2	13	no	—
297	C₃×C₄	—	2	13	no	—
298	C₃×C₄	D₄×C₃⋊D₃	1	26	yes	—
299	Dic₃	—	18	26	no	—
300	Dic₃	—	18	26	no	—
301	C₃²	#5550	1	13	yes	complemented
302	C₂³	—	27	2	no	—
303	C₂³	—	27	2	no	—
304	C₂³	—	54	4	no	—
305	C₂³	—	54	4	no	—
306	C₂³	—	108	2	no	—
307	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
308	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
309	Q₈	—	54	2	no	—
310	D₄	—	2	2	no	—
311	D₄	—	27	4	no	—
312	D₄	—	54	4	no	—
313	D₄	—	54	4	no	—
314	D₄	—	54	2	no	—
315	D₄	—	108	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	27	2	no	—
319	C₂×C₄	—	27	2	no	—
320	C₂×C₄	—	54	4	no	—
321	C₂×C₄	—	108	2	no	—
322	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
323	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
327	C₂×C₃	—	2	26	no	—
328	C₂×C₃	—	4	13	no	—
329	C₂×C₃	C₂×#3828	1	13	yes	—
330	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
331	C₂×C₃	#64366	1	13	yes	—
332	D₃	—	18	52	no	—
333	D₃	—	36	26	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	27	4	no	—
340	C₂²	—	54	2	no	—
341	C₂²	—	54	2	no	—
342	C₂²	—	54	2	no	—
343	C₂²	—	54	2	no	—
344	C₂²	—	54	2	no	—
345	C₂²	—	108	8	no	—
346	C₂²	#89076	1	2	yes	complemented
347	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	54	2	no	—
353	C₄	—	54	2	no	—
354	C₄	D₄×C₃⋊(C₃⋊D₃)	1	2	yes	—
355	C₃	#10596021	1	13	yes	complemented
356	C₂	—	2	2	no	—
357	C₂	—	4	1	no	—
358	C₂	—	54	4	no	—
359	C₂	—	108	2	no	—
360	C₂	C₂×#89076	1	1	yes	characteristic
361	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
362	C₂	#11724684	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×C₄×D₄	C₂
hypercenter	C₄×D₄	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#546
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#89076	C₂	semidirect
2. C₂²×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	semidirect
3. C₃³×C₄×D₄	C₂	semidirect
4. #11723978	C₂	semidirect
5. #11723971	C₂	semidirect
6. #11723965	C₂	semidirect
7. #11723935	C₂	semidirect
8. #11723925	C₂	semidirect
9. C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
10. #11723916	C₂	semidirect
11. C₄×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	semidirect
16. C₂²×C₃³×C₄	C₂²	semidirect
17. C₂×#6312	C₂²	semidirect
18. C₂×#6312	C₂²	semidirect
24. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
25. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
26. C₂×#6308	C₂²	semidirect
27. C₃³×C₄⋊C₄	C₂²	semidirect
29. C₃³×C₂²⋊C₄	C₂²	semidirect
30. C₃³×C₄²	C₂²	semidirect
32. #88859	C₂²	semidirect
33. #88859	C₂²	semidirect
34. #88859	C₂²	semidirect
35. #88859	C₂²	semidirect
36. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
37. #88857	C₂²	semidirect
40. C₃²×C₄×D₄	D₃	semidirect
70. C₄⋊(C₃⋊(C₃⋊D₃))	D₄	semidirect
78. C₂²×C₃²×C₄	C₂×D₃	semidirect
89. C₃²×C₄⋊C₄	C₂×D₃	semidirect
91. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
92. C₃²×C₄²	C₂×D₃	semidirect
105. C₂²×C₃³	#41	semidirect
123. C₃×C₄×D₄	C₃⋊D₃	semidirect
168. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
179. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
181. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
182. C₃×C₄²	C₂×C₃⋊D₃	semidirect
195. C₂²×C₃²	#235	semidirect
220. C₄×D₄	C₃⋊(C₃⋊D₃)	semidirect
222. C₃³	#546	semidirect
268. C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
271. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
278. C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
279. C₄²	C₂×C₃⋊(C₃⋊D₃)	semidirect
285. C₂²×C₃	#3828	semidirect
301. C₃²	#5550	semidirect
346. C₂²	#89076	semidirect
355. C₃	#10596021	semidirect

Maximal subgroups

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

subgroup	index
C₂×#89076	2
C₂²×C₄⋊(C₃⋊(C₃⋊D₃))	2
C₃³×C₄×D₄	2
#11723978	2
#11723971	2
#11723965	2
#11723935	2
#11723925	2
C₂²⋊C₄×C₃⋊(C₃⋊D₃)	2
#11723916	2
C₄×C₄⋊(C₃⋊(C₃⋊D₃))	2
#10596021	3