Subgroups — #13179902

Order 1728.

3668 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#89080	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723990	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723983	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723960	C₂	1	2	yes	maximal, complemented
7	#11723959	C₂	1	2	yes	maximal, complemented
8	#11723957	C₂	1	2	yes	maximal, complemented
9	#11723955	C₂	1	2	yes	maximal, complemented
10	#11723949	C₂	1	1	yes	maximal, characteristic, complemented
11	M₁₆×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596248	—	3	13	no	maximal
13	C₃³×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
15	#89080	—	2	1	no	—
16	#89080	—	2	1	no	—
17	#89080	C₂²	1	2	yes	—
18	#89080	C₂²	1	2	yes	complemented
19	#89080	C₂²	1	1	yes	characteristic, complemented
20	Q₈×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
21	#89078	—	2	1	no	—
22	#89078	C₂²	1	1	yes	characteristic, complemented
23	D₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
24	D₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
25	#89076	—	2	1	no	—
26	#89076	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	—	2	1	no	—
28	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
30	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
31	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
32	C₃³×Q₁₆	C₂²	1	2	yes	complemented
33	C₃³×SD₁₆	C₂²	1	2	yes	complemented
34	C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	#88863	C₂²	1	2	yes	complemented
36	#88862	C₂²	1	2	yes	complemented
37	#88862	C₂²	1	2	yes	complemented
38	#88860	C₂²	1	2	yes	complemented
39	#88855	C₂²	1	1	yes	characteristic, complemented
40	#88852	C₂²	1	2	yes	complemented
41	#88851	C₂²	1	2	yes	complemented
42	#88850	C₂²	1	2	yes	complemented
43	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
44	#41×C₃⋊D₃	—	3	13	no	—
45	C₂×#3832	—	3	13	no	—
46	C₃²×#137	D₃	1	13	yes	complemented
47	#64158	—	3	13	no	—
48	#64151	—	3	13	no	—
49	#64128	—	3	26	no	—
50	#64127	—	3	26	no	—
51	#64125	—	3	26	no	—
52	#64123	—	3	26	no	—
53	#64117	—	3	13	no	—
54	M₁₆×C₃⋊D₃	—	3	13	no	—
55	C₂²×C₃⋊(C₃⋊D₃)	—	2	1	no	—
56	C₂²×C₃⋊(C₃⋊D₃)	—	2	1	no	—
57	C₂²×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
58	C₃³×Q₈	—	2	1	no	—
59	C₃³×Q₈	C₂³	1	1	yes	characteristic
60	C₃³×Q₈	C₂³	1	2	yes	—
61	C₃³×D₄	—	2	1	no	—
62	C₃³×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃³×C₄	—	2	1	no	—
64	C₂×C₃³×C₄	—	2	1	no	—
65	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
66	#6312	—	2	1	no	—
67	#6312	—	2	1	no	—
68	#6312	—	2	1	no	—
69	C₂×C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
70	C₂×C₃⋊(C₃⋊Dic₃)	D₄	1	1	yes	characteristic
71	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
72	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
73	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	1	no	—
74	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	1	no	—
75	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	2	yes	—
76	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	1	yes	characteristic
77	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
78	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
79	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
80	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
81	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
82	C₄×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
83	C₄×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
84	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
85	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
86	#6308	—	2	1	no	—
87	#6308	C₂³	1	1	yes	characteristic
88	C₃³×C₈	C₂³	1	2	yes	—
89	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	2	yes	—
90	#5777	—	9	13	no	—
91	C₃²×#41	C₂×D₃	1	13	yes	—
92	C₂×C₃²×Q₈	C₂×D₃	1	13	yes	complemented
93	#3832	—	3	26	no	—
94	#3832	—	3	26	no	—
95	#3832	—	3	13	no	—
96	#3832	—	6	13	no	—
97	#3832	—	6	13	no	—
98	Q₈×C₃⋊D₃	—	3	13	no	—
99	#3830	—	3	13	no	—
100	#3830	—	6	13	no	—
101	D₄×C₃⋊D₃	—	3	13	no	—
102	D₄×C₃⋊D₃	—	6	13	no	—
103	#3828	—	3	13	no	—
104	#3828	—	6	13	no	—
105	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
106	C₂×C₄⋊(C₃⋊D₃)	—	6	13	no	—
107	C₂×C₄×C₃⋊D₃	—	3	13	no	—
108	C₂×C₄×C₃⋊D₃	—	6	13	no	—
109	C₂×C₄×C₃⋊D₃	—	6	13	no	—
110	C₃²×Q₁₆	C₂×D₃	1	26	yes	complemented
111	C₃²×SD₁₆	C₂×D₃	1	26	yes	complemented
112	C₃²×M₁₆	C₂×D₃	1	13	yes	complemented
113	#3756	—	3	26	no	—
114	#3755	—	3	26	no	—
115	#3755	—	3	26	no	—
116	#3753	—	3	26	no	—
117	#3748	—	3	13	no	—
118	#3745	—	3	26	no	—
119	#3744	—	3	26	no	—
120	#3743	—	3	26	no	—
121	C₈×C₃⋊D₃	—	3	26	no	—
122	C₂²×C₃³	—	2	1	no	—
123	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
125	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
126	C₂×C₃⋊(C₃⋊D₃)	—	4	1	no	—
127	C₂×C₃⋊(C₃⋊D₃)	—	4	2	no	—
128	C₂×C₃⋊(C₃⋊D₃)	—	4	2	no	—
129	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	1	yes	characteristic
131	C₃³×C₄	—	2	1	no	—
132	C₃³×C₄	—	2	2	no	—
133	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
134	C₃³×C₄	C₂⁴	1	1	yes	characteristic
135	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
136	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	1	yes	characteristic
137	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	1	yes	characteristic
138	D₃×#41	—	9	13	no	—
139	C₂×#239	—	9	13	no	—
140	C₃×#137	C₃⋊D₃	1	13	yes	complemented
141	#949	—	9	13	no	—
142	#942	—	9	13	no	—
143	#919	—	9	26	no	—
144	#918	—	9	26	no	—
145	#916	—	9	26	no	—
146	#914	—	9	26	no	—
147	#908	—	9	13	no	—
148	D₃×M₁₆	—	9	13	no	—
149	C₂²×C₃⋊D₃	—	3	13	no	—
150	C₂²×C₃⋊D₃	—	6	13	no	—
151	C₂²×C₃⋊D₃	—	6	13	no	—
152	C₃²×Q₈	—	2	13	no	—
153	C₃²×Q₈	C₂²×D₃	1	13	yes	—
154	C₃²×Q₈	C₂²×D₃	1	26	yes	—
155	C₃²×D₄	—	2	13	no	—
156	C₃²×D₄	C₂²×D₃	1	13	yes	—
157	C₂×C₃²×C₄	—	2	13	no	—
158	C₂×C₃²×C₄	—	2	13	no	—
159	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
160	#638	—	6	13	no	—
161	#638	—	6	13	no	—
162	#638	—	6	13	no	—
163	C₂×C₃⋊Dic₃	—	3	13	no	—
164	C₂×C₃⋊Dic₃	—	6	13	no	—
165	C₄⋊(C₃⋊D₃)	—	3	26	no	—
166	C₄⋊(C₃⋊D₃)	—	3	13	no	—
167	C₄⋊(C₃⋊D₃)	—	6	26	no	—
168	C₄⋊(C₃⋊D₃)	—	6	26	no	—
169	C₄⋊(C₃⋊D₃)	—	6	13	no	—
170	C₄⋊(C₃⋊D₃)	—	6	13	no	—
171	C₄×C₃⋊D₃	—	3	13	no	—
172	C₄×C₃⋊D₃	—	3	13	no	—
173	C₄×C₃⋊D₃	—	3	13	no	—
174	C₄×C₃⋊D₃	—	3	13	no	—
175	C₄×C₃⋊D₃	—	6	13	no	—
176	C₄×C₃⋊D₃	—	6	26	no	—
177	C₄×C₃⋊D₃	—	6	26	no	—
178	C₄×C₃⋊D₃	—	6	13	no	—
179	C₄×C₃⋊D₃	—	6	13	no	—
180	#634	—	3	13	no	—
181	#634	—	6	13	no	—
182	C₃²×C₈	C₂²×D₃	1	26	yes	—
183	C₃⋊(C₃⋊C₈)	—	3	26	no	—
184	#575	—	27	1	no	Sylow
185	C₂×C₃³	—	2	1	no	—
186	C₂×C₃³	—	4	1	no	—
187	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
188	C₃⋊(C₃⋊D₃)	—	2	1	no	—
189	C₃⋊(C₃⋊D₃)	—	2	1	no	—
190	C₃⋊(C₃⋊D₃)	—	4	2	no	—
191	C₃⋊(C₃⋊D₃)	—	4	1	no	—
192	C₃×#41	C₂×C₃⋊D₃	1	13	yes	—
193	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	13	yes	complemented
194	#239	—	9	26	no	—
195	#239	—	9	26	no	—
196	#239	—	9	13	no	—
197	#239	—	18	13	no	—
198	#239	—	18	13	no	—
199	D₃×Q₈	—	9	13	no	—
200	#237	—	9	13	no	—
201	#237	—	18	13	no	—
202	D₃×D₄	—	9	13	no	—
203	D₃×D₄	—	18	13	no	—
204	#235	—	9	13	no	—
205	#235	—	18	13	no	—
206	C₂×D₁₂	—	9	13	no	—
207	C₂×D₁₂	—	18	13	no	—
208	C₂×C₄×D₃	—	9	13	no	—
209	C₂×C₄×D₃	—	18	13	no	—
210	C₂×C₄×D₃	—	18	13	no	—
211	C₃×Q₁₆	C₂×C₃⋊D₃	1	26	yes	complemented
212	C₃×SD₁₆	C₂×C₃⋊D₃	1	26	yes	complemented
213	C₃×M₁₆	C₂×C₃⋊D₃	1	13	yes	complemented
214	#216	—	9	26	no	—
215	#215	—	9	26	no	—
216	#215	—	9	26	no	—
217	#213	—	9	26	no	—
218	#208	—	9	13	no	—
219	D₂₄	—	9	26	no	—
220	#204	—	9	26	no	—
221	ΓL(1,𝔽₂₅)	—	9	26	no	—
222	D₃×C₈	—	9	26	no	—
223	C₂²×C₃²	—	2	13	no	—
224	C₂²×C₃²	D₃×D₄	1	13	yes	—
225	C₂×C₃⋊D₃	—	3	13	no	—
226	C₂×C₃⋊D₃	—	3	13	no	—
227	C₂×C₃⋊D₃	—	6	26	no	—
228	C₂×C₃⋊D₃	—	6	13	no	—
229	C₂×C₃⋊D₃	—	12	13	no	—
230	C₂×C₃⋊D₃	—	12	26	no	—
231	C₂×C₃⋊D₃	—	12	26	no	—
232	C₃²×C₄	—	2	13	no	—
233	C₃²×C₄	—	2	26	no	—
234	C₃²×C₄	D₃×D₄	1	13	yes	—
235	C₃²×C₄	C₂³×D₃	1	13	yes	—
236	C₃⋊Dic₃	—	3	13	no	—
237	C₃⋊Dic₃	—	3	13	no	—
238	C₃⋊Dic₃	—	6	13	no	—
239	C₂×#41	—	27	1	no	—
240	C₂×#41	—	27	1	no	—
241	#137	—	27	1	no	—
242	#137	—	27	2	no	—
243	#137	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
244	AGL(1,ℤ/8)	—	27	1	no	—
245	AGL(1,ℤ/8)	—	27	2	no	—
246	AGL(1,ℤ/8)	—	27	1	no	—
247	#135	—	27	2	no	—
248	#135	—	27	2	no	—
249	C₂×M₁₆	—	27	1	no	—
250	C₃³	#575	1	1	yes	characteristic, complemented, Sylow
251	C₂²×D₃	—	9	13	no	—
252	C₂²×D₃	—	18	13	no	—
253	C₂²×D₃	—	18	13	no	—
254	C₃×Q₈	—	2	13	no	—
255	C₃×Q₈	C₂²×C₃⋊D₃	1	13	yes	—
256	C₃×Q₈	C₂²×C₃⋊D₃	1	26	yes	—
257	C₃×D₄	—	2	13	no	—
258	C₃×D₄	C₂²×C₃⋊D₃	1	13	yes	—
259	C₂×C₃×C₄	—	2	13	no	—
260	C₂×C₃×C₄	—	2	13	no	—
261	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
262	#67	—	18	13	no	—
263	#67	—	18	13	no	—
264	#67	—	18	13	no	—
265	C₂×Dic₃	—	9	13	no	—
266	C₂×Dic₃	—	18	13	no	—
267	D₁₂	—	9	26	no	—
268	D₁₂	—	9	13	no	—
269	D₁₂	—	18	26	no	—
270	D₁₂	—	18	26	no	—
271	D₁₂	—	18	13	no	—
272	D₁₂	—	18	13	no	—
273	C₄×D₃	—	9	13	no	—
274	C₄×D₃	—	9	13	no	—
275	C₄×D₃	—	9	13	no	—
276	C₄×D₃	—	9	13	no	—
277	C₄×D₃	—	18	13	no	—
278	C₄×D₃	—	18	26	no	—
279	C₄×D₃	—	18	26	no	—
280	C₄×D₃	—	18	13	no	—
281	C₄×D₃	—	18	13	no	—
282	Dic₆	—	9	13	no	—
283	Dic₆	—	18	13	no	—
284	C₃×C₈	C₂²×C₃⋊D₃	1	26	yes	—
285	C₃⋊C₈	—	9	26	no	—
286	C₂×C₃²	—	2	13	no	—
287	C₂×C₃²	—	4	13	no	—
288	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
289	C₃⋊D₃	—	6	13	no	—
290	C₃⋊D₃	—	6	13	no	—
291	C₃⋊D₃	—	12	26	no	—
292	C₃⋊D₃	—	12	13	no	—
293	#41	—	27	1	no	—
294	#41	—	27	2	no	—
295	#41	—	27	2	no	—
296	#41	—	27	1	no	—
297	#41	—	27	1	no	—
298	#41	—	54	1	no	—
299	#41	—	54	1	no	—
300	#41	—	54	1	no	—
301	#41	—	54	1	no	—
302	#41	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
303	C₂×Q₈	—	27	1	no	—
304	C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
305	C₂×D₄	—	27	1	no	—
306	C₂×D₄	—	27	1	no	—
307	C₂×D₄	—	54	1	no	—
308	C₂×D₄	—	54	1	no	—
309	C₂²×C₄	—	27	1	no	—
310	C₂²×C₄	—	54	1	no	—
311	C₂²×C₄	—	54	1	no	—
312	Q₁₆	—	27	2	no	—
313	Q₁₆	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
314	SD₁₆	—	27	2	no	—
315	SD₁₆	—	27	2	no	—
316	SD₁₆	—	27	2	no	—
317	SD₁₆	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
318	D₈	—	27	2	no	—
319	D₈	—	27	2	no	—
320	M₁₆	—	27	1	no	—
321	M₁₆	—	27	2	no	—
322	M₁₆	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
323	C₂×C₈	—	27	2	no	—
324	C₂²×C₃	—	2	13	no	—
325	C₂²×C₃	D₄×C₃⋊D₃	1	13	yes	—
326	C₂×D₃	—	9	13	no	—
327	C₂×D₃	—	9	13	no	—
328	C₂×D₃	—	18	26	no	—
329	C₂×D₃	—	18	13	no	—
330	C₂×D₃	—	36	13	no	—
331	C₂×D₃	—	36	26	no	—
332	C₂×D₃	—	36	26	no	—
333	C₃×C₄	—	2	13	no	—
334	C₃×C₄	—	2	26	no	—
335	C₃×C₄	D₄×C₃⋊D₃	1	13	yes	—
336	C₃×C₄	C₂³×C₃⋊D₃	1	13	yes	—
337	Dic₃	—	9	13	no	—
338	Dic₃	—	9	13	no	—
339	Dic₃	—	18	13	no	—
340	C₃²	#5777	1	13	yes	complemented
341	C₂³	—	27	1	no	—
342	C₂³	—	54	1	no	—
343	C₂³	—	54	1	no	—
344	Q₈	—	2	1	no	—
345	Q₈	—	27	1	no	—
346	Q₈	—	54	1	no	—
347	Q₈	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
348	Q₈	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
349	D₄	—	2	1	no	—
350	D₄	—	27	2	no	—
351	D₄	—	27	1	no	—
352	D₄	—	54	1	no	—
353	D₄	—	54	2	no	—
354	D₄	—	54	2	no	—
355	D₄	—	54	1	no	—
356	D₄	—	54	1	no	—
357	D₄	—	54	1	no	—
358	D₄	—	54	1	no	—
359	D₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	27	1	no	—
363	C₂×C₄	—	27	1	no	—
364	C₂×C₄	—	27	1	no	—
365	C₂×C₄	—	27	1	no	—
366	C₂×C₄	—	27	1	no	—
367	C₂×C₄	—	54	1	no	—
368	C₂×C₄	—	54	2	no	—
369	C₂×C₄	—	54	2	no	—
370	C₂×C₄	—	54	1	no	—
371	C₂×C₄	—	54	1	no	—
372	C₂×C₄	—	54	1	no	—
373	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
374	C₈	—	27	2	no	—
375	C₈	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
376	C₂×C₃	—	2	13	no	—
377	C₂×C₃	—	4	13	no	—
378	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
379	D₃	—	18	13	no	—
380	D₃	—	18	13	no	—
381	D₃	—	36	26	no	—
382	D₃	—	36	13	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	27	1	no	—
385	C₂²	—	27	1	no	—
386	C₂²	—	54	2	no	—
387	C₂²	—	54	1	no	—
388	C₂²	—	108	1	no	—
389	C₂²	—	108	2	no	—
390	C₂²	—	108	2	no	—
391	C₂²	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	27	1	no	—
395	C₄	—	27	1	no	—
396	C₄	—	54	1	no	—
397	C₄	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
398	C₄	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
399	C₃	#10596248	1	13	yes	complemented
400	C₂	—	2	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	54	1	no	—
403	C₂	—	54	1	no	—
404	C₂	—	108	2	no	—
405	C₂	—	108	1	no	—
406	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)
commutator, cosocle	C₃³×C₄	C₂⁴
Frattini	C₄	C₂³×C₃⋊(C₃⋊D₃)
Fitting	C₃³×#137	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	#137	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#575
LCS	G ▷ C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #137

Complements

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

N	H ≅ G/N	type
1. #41×C₃⋊(C₃⋊D₃)	C₂	semidirect
2. C₂×#89080	C₂	semidirect
3. C₃³×#137	C₂	semidirect
4. #11723990	C₂	semidirect
5. #11723983	C₂	semidirect
6. #11723960	C₂	semidirect
7. #11723959	C₂	semidirect
8. #11723957	C₂	semidirect
9. #11723955	C₂	semidirect
10. #11723949	C₂	semidirect
11. M₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
14. C₂×C₃³×Q₈	C₂²	semidirect
18. #89080	C₂²	semidirect
19. #89080	C₂²	semidirect
20. Q₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
22. #89078	C₂²	semidirect
24. D₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
28. C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	semidirect
32. C₃³×Q₁₆	C₂²	semidirect
33. C₃³×SD₁₆	C₂²	semidirect
34. C₃³×M₁₆	C₂²	semidirect
35. #88863	C₂²	semidirect
36. #88862	C₂²	semidirect
37. #88862	C₂²	semidirect
38. #88860	C₂²	semidirect
39. #88855	C₂²	semidirect
40. #88852	C₂²	semidirect
41. #88851	C₂²	semidirect
42. #88850	C₂²	semidirect
43. C₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
46. C₃²×#137	D₃	semidirect
92. C₂×C₃²×Q₈	C₂×D₃	semidirect
110. C₃²×Q₁₆	C₂×D₃	semidirect
111. C₃²×SD₁₆	C₂×D₃	semidirect
112. C₃²×M₁₆	C₂×D₃	semidirect
140. C₃×#137	C₃⋊D₃	semidirect
193. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
211. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
212. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
213. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
243. #137	C₃⋊(C₃⋊D₃)	semidirect
250. C₃³	#575	semidirect
304. C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
313. Q₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
317. SD₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
322. M₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
340. C₃²	#5777	semidirect
399. C₃	#10596248	semidirect

Maximal subgroups

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

subgroup	index
#41×C₃⋊(C₃⋊D₃)	2
C₂×#89080	2
C₃³×#137	2
#11723990	2
#11723983	2
#11723960	2
#11723959	2
#11723957	2
#11723955	2
#11723949	2
M₁₆×C₃⋊(C₃⋊D₃)	2
#10596248	3