Subgroups — C₂×C₃×#5189 #11866994

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#946	C₂	1	2	yes	maximal
3	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#835	C₂	1	2	yes	maximal, complemented
5	C₃×#5189	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#470	—	3	1	no	maximal
8	C₂×#5189	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃²×Q₁₆	—	2	4	no	—
12	C₂×C₃²×Q₁₆	C₂²	1	4	yes	complemented
13	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
14	C₃×#946	—	2	4	no	—
15	C₃×#946	C₂²	1	8	yes	—
16	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
17	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×Dic₃⋊C₄	—	2	2	no	—
19	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
21	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
22	C₃×#835	C₂²	1	8	yes	complemented
23	C₃×#817	C₂²	1	4	yes	complemented
24	C₂²×C₃×Q₁₆	—	2	1	no	—
25	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂²×C₃×M₁₆	—	3	1	no	—
28	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
29	C₂×#946	C₂×C₃	1	2	yes	—
30	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
31	C₃×#470	—	3	8	no	—
32	C₂×C₃×#106	—	3	1	no	—
33	C₂×C₃×#103	—	3	2	no	—
34	C₂×#835	C₂×C₃	1	2	yes	complemented
35	#5189	C₂×C₃	1	8	yes	direct product factor
36	C₂×#817	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
38	C₂×C₃²×Q₈	—	2	2	no	—
39	C₂×C₃²×Q₈	—	2	4	no	—
40	C₂×C₃²×Q₈	—	2	4	no	—
41	C₂×C₃²×Q₈	C₂³	1	4	yes	—
42	C₂²×C₃²×C₄	—	2	2	no	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₃	—	2	2	no	—
45	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	—	2	2	no	—
47	C₂×C₃×C₄×D₃	—	2	2	no	—
48	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
50	C₃²×Q₁₆	—	2	8	no	—
51	C₂×C₃²×C₈	D₄	1	4	yes	—
52	C₂×C₃²×C₈	C₂³	1	2	yes	—
53	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
54	C₃×C₄⋊Dic₃	—	2	2	no	—
55	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
56	C₃×Dic₃⋊C₄	—	2	8	no	—
57	C₂×C₃×C₃⋊C₈	—	2	2	no	—
58	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
59	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
60	C₂×#470	—	3	1	no	Sylow
61	C₂²×C₃×Q₈	—	2	2	no	—
62	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
63	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
64	C₂³×C₃×C₄	—	3	1	no	—
65	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×Q₁₆	—	2	8	no	—
67	C₂×C₃×Q₁₆	—	2	4	no	—
68	C₂×C₃×Q₁₆	—	2	4	no	—
69	C₂×C₃×Q₁₆	—	2	4	no	—
70	C₂×C₃×Q₁₆	C₂×D₃	1	4	yes	complemented
71	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
72	C₂×C₃×M₁₆	—	3	4	no	—
73	C₂×C₃×M₁₆	—	6	4	no	—
74	C₂²×C₃×C₈	—	2	1	no	—
75	C₂²×C₃×C₈	—	3	1	no	—
76	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
78	C₃×C₂²⋊Q₈	—	3	8	no	—
79	C₃×C₂²⋊Q₈	—	6	4	no	—
80	C₂×C₃×C₄⋊C₄	—	3	2	no	—
81	C₂×C₃×C₄⋊C₄	—	6	2	no	—
82	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
83	#946	—	2	4	no	—
84	#946	C₂²×C₃	1	8	yes	—
85	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
87	C₂×Dic₃⋊C₄	—	2	2	no	—
88	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
90	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
91	C₃×#106	—	3	4	no	—
92	C₃×#103	—	3	8	no	—
93	#835	C₂²×C₃	1	8	yes	complemented
94	#817	C₂²×C₃	1	4	yes	complemented
95	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	2	no	—
97	C₂²×C₃×D₃	—	2	4	no	—
98	C₂²×C₃×D₃	C₂×D₄	1	2	yes	—
99	C₃²×Q₈	—	2	4	no	—
100	C₃²×Q₈	—	2	4	no	—
101	C₃²×Q₈	—	4	4	no	—
102	C₂×C₃²×C₄	—	2	4	no	—
103	C₂×C₃²×C₄	—	4	4	no	—
104	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
106	C₂×C₃²×C₄	#41	1	2	yes	—
107	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
108	C₂×C₃×Dic₃	—	2	2	no	—
109	C₂×C₃×Dic₃	—	2	4	no	—
110	C₂×C₃×Dic₃	—	4	4	no	—
111	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
112	C₃×C₄×D₃	—	2	4	no	—
113	C₃×C₄×D₃	—	2	2	no	—
114	C₃×C₄×D₃	—	2	2	no	—
115	C₃²×C₈	C₂×D₄	1	4	yes	—
116	C₃×C₃⋊C₈	—	2	2	no	—
117	C₂²×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
118	C₂²×M₁₆	—	3	1	no	—
119	C₂×C₂²⋊Q₈	—	3	2	no	—
120	#470	—	3	8	no	—
121	C₂×#106	—	3	1	no	—
122	C₂×#103	—	3	2	no	—
123	C₂⁴×C₃	—	3	1	no	—
124	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
125	C₂×C₃×Q₈	—	2	2	no	—
126	C₂×C₃×Q₈	—	2	2	no	—
127	C₂×C₃×Q₈	—	2	8	no	—
128	C₂×C₃×Q₈	—	2	4	no	—
129	C₂×C₃×Q₈	—	2	4	no	—
130	C₂×C₃×Q₈	—	2	4	no	—
131	C₂×C₃×Q₈	—	2	4	no	—
132	C₂×C₃×Q₈	—	2	4	no	—
133	C₂×C₃×Q₈	—	4	2	no	—
134	C₂×C₃×Q₈	—	4	4	no	—
135	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
136	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
137	C₂²×C₃×C₄	—	2	2	no	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	3	1	no	—
141	C₂²×C₃×C₄	—	3	2	no	—
142	C₂²×C₃×C₄	—	3	2	no	—
143	C₂²×C₃×C₄	—	4	2	no	—
144	C₂²×C₃×C₄	—	6	2	no	—
145	C₂²×C₃×C₄	—	6	2	no	—
146	C₂²×C₃×C₄	—	6	2	no	—
147	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂²×Dic₃	—	2	2	no	—
150	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
151	C₂×C₄×D₃	—	2	2	no	—
152	C₂×C₄×D₃	—	2	2	no	—
153	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
154	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
155	C₃×Q₁₆	—	2	16	no	—
156	C₃×Q₁₆	—	2	8	no	—
157	C₃×Q₁₆	—	2	8	no	—
158	C₃×M₁₆	—	6	8	no	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	3	2	no	—
162	C₂×C₃×C₈	—	6	2	no	—
163	C₂×C₃×C₈	#67	1	4	yes	—
164	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
165	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
166	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
167	C₃×C₄⋊C₄	—	3	4	no	—
168	C₃×C₄⋊C₄	—	6	8	no	—
169	C₃×C₄⋊C₄	—	6	2	no	—
170	C₃×C₂²⋊C₄	—	6	8	no	—
171	(C₂×D₃)⋊C₄	—	2	8	no	—
172	C₄⋊Dic₃	—	2	2	no	—
173	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
174	Dic₃⋊C₄	—	2	8	no	—
175	C₂×C₃⋊C₈	—	2	2	no	—
176	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
177	ΓL(1,𝔽₂₅)	—	2	8	no	—
178	C₂²×C₃²	#121	1	2	yes	—
179	C₂²×C₃²	#137	1	4	yes	—
180	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₃×D₃	—	2	2	no	—
182	C₂×C₃×D₃	—	2	4	no	—
183	C₂×C₃×D₃	—	4	4	no	—
184	C₃²×C₄	—	4	4	no	—
185	C₃²×C₄	#121	1	2	yes	—
186	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
187	C₃²×C₄	C₂×#41	1	1	yes	characteristic
188	C₃×Dic₃	—	2	2	no	—
189	C₃×Dic₃	—	4	4	no	—
190	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	—
191	C₂³×C₄	—	3	1	no	—
192	C₂×Q₁₆	—	2	4	no	—
193	C₂×Q₁₆	C₂×C₃×D₃	1	4	yes	complemented
194	C₂×M₁₆	—	3	4	no	—
195	C₂×M₁₆	—	6	4	no	—
196	C₂²×C₈	—	3	1	no	—
197	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
198	C₂²⋊Q₈	—	3	8	no	—
199	C₂²⋊Q₈	—	6	4	no	—
200	C₂×C₄⋊C₄	—	3	2	no	—
201	C₂×C₄⋊C₄	—	6	2	no	—
202	C₂×C₂²⋊C₄	—	6	2	no	—
203	#106	—	3	4	no	—
204	#103	—	3	8	no	—
205	C₂³×C₃	—	2	1	no	—
206	C₂³×C₃	—	3	2	no	—
207	C₂³×C₃	—	6	4	no	—
208	C₂³×C₃	—	6	2	no	—
209	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
210	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂²×D₃	—	2	2	no	—
212	C₂²×D₃	—	2	4	no	—
213	C₂²×D₃	C₂×C₃×D₄	1	2	yes	—
214	C₃×Q₈	—	2	8	no	—
215	C₃×Q₈	—	2	4	no	—
216	C₃×Q₈	—	2	4	no	—
217	C₃×Q₈	—	2	4	no	—
218	C₃×Q₈	—	2	4	no	—
219	C₃×Q₈	—	4	4	no	—
220	C₃×Q₈	—	4	8	no	—
221	C₃×Q₈	—	4	4	no	—
222	C₃×Q₈	—	4	4	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	3	2	no	—
230	C₂×C₃×C₄	—	4	4	no	—
231	C₂×C₃×C₄	—	4	8	no	—
232	C₂×C₃×C₄	—	4	4	no	—
233	C₂×C₃×C₄	—	4	4	no	—
234	C₂×C₃×C₄	—	6	2	no	—
235	C₂×C₃×C₄	—	6	4	no	—
236	C₂×C₃×C₄	—	6	2	no	—
237	C₂×C₃×C₄	—	6	2	no	—
238	C₂×C₃×C₄	—	6	4	no	—
239	C₂×C₃×C₄	—	12	4	no	—
240	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄	#237	1	2	yes	—
242	C₂×C₃×C₄	C₂×#67	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
245	C₂×C₃×C₄	C₃×#41	1	2	yes	—
246	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
248	C₂×Dic₃	—	2	2	no	—
249	C₂×Dic₃	—	2	4	no	—
250	C₂×Dic₃	—	4	4	no	—
251	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
252	C₄×D₃	—	2	4	no	—
253	C₄×D₃	—	2	2	no	—
254	C₄×D₃	—	2	2	no	—
255	C₃×C₈	—	2	4	no	—
256	C₃×C₈	—	6	2	no	—
257	C₃×C₈	C₂×#67	1	4	yes	—
258	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
259	C₃⋊C₈	—	2	2	no	—
260	C₂×C₃²	#470	1	4	yes	complemented
261	C₂×C₃²	C₂×#121	1	1	yes	characteristic
262	C₂×C₃²	C₂×#137	1	2	yes	—
263	C₃×D₃	—	4	2	no	—
264	C₂⁴	—	3	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	3	1	no	—
271	C₂²×C₄	—	3	2	no	—
272	C₂²×C₄	—	3	2	no	—
273	C₂²×C₄	—	6	2	no	—
274	C₂²×C₄	—	6	2	no	—
275	C₂²×C₄	—	6	2	no	—
276	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	Q₁₆	—	2	8	no	—
278	M₁₆	—	6	8	no	—
279	C₂×C₈	—	3	2	no	—
280	C₂×C₈	—	6	2	no	—
281	C₂×C₈	C₃×#67	1	4	yes	—
282	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
283	C₄⋊C₄	—	3	4	no	—
284	C₄⋊C₄	—	6	8	no	—
285	C₄⋊C₄	—	6	2	no	—
286	C₂²⋊C₄	—	6	8	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	6	4	no	—
291	C₂²×C₃	—	6	2	no	—
292	C₂²×C₃	—	12	4	no	—
293	C₂²×C₃	#918	1	4	yes	—
294	C₂²×C₃	#938	1	2	yes	—
295	C₂²×C₃	C₃×#121	1	2	yes	—
296	C₂²×C₃	C₃×#137	1	4	yes	—
297	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
298	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
299	C₂×D₃	—	2	4	no	—
300	C₂×D₃	—	2	2	no	—
301	C₂×D₃	—	4	4	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	4	8	no	—
306	C₃×C₄	—	4	4	no	—
307	C₃×C₄	—	4	4	no	—
308	C₃×C₄	—	6	2	no	—
309	C₃×C₄	—	12	4	no	—
310	C₃×C₄	#938	1	2	yes	—
311	C₃×C₄	C₃×#121	1	2	yes	—
312	C₃×C₄	C₂×#237	1	1	yes	characteristic
313	C₃×C₄	C₂²×#67	1	1	yes	characteristic
314	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
316	Dic₃	—	2	2	no	—
317	Dic₃	—	4	4	no	—
318	C₃²	C₂×#470	1	1	yes	characteristic, complemented, Sylow
319	C₂³	—	3	2	no	—
320	C₂³	—	6	4	no	—
321	C₂³	—	6	2	no	—
322	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
323	Q₈	—	2	4	no	—
324	Q₈	—	2	4	no	—
325	Q₈	—	4	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	6	2	no	—
330	C₂×C₄	—	6	4	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	6	2	no	—
333	C₂×C₄	—	6	4	no	—
334	C₂×C₄	—	12	4	no	—
335	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
336	C₂×C₄	C₃×#237	1	2	yes	—
337	C₂×C₄	C₂×C₃×#67	1	2	yes	—
338	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
339	C₈	—	6	2	no	—
340	C₈	C₂×C₃×#67	1	4	yes	—
341	C₂×C₃	—	2	2	no	—
342	C₂×C₃	—	2	4	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	12	2	no	—
345	C₂×C₃	#5189	1	4	yes	direct product factor
346	C₂×C₃	C₃×#470	1	4	yes	complemented
347	C₂×C₃	C₂×#918	1	2	yes	—
348	C₂×C₃	C₂×#938	1	1	yes	characteristic
349	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
350	C₂×C₃	C₂×C₃×#137	1	2	yes	—
351	D₃	—	4	2	no	—
352	C₂²	—	6	4	no	—
353	C₂²	—	6	2	no	—
354	C₂²	—	12	4	no	—
355	C₂²	C₃×#918	1	4	yes	—
356	C₂²	C₃×#938	1	2	yes	—
357	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
358	C₄	—	4	4	no	—
359	C₄	—	6	2	no	—
360	C₄	—	12	4	no	—
361	C₄	C₃×#938	1	2	yes	—
362	C₄	C₂×C₃×#237	1	1	yes	characteristic
363	C₄	C₂²×C₃×#67	1	1	yes	characteristic
364	C₃	—	2	1	no	—
365	C₃	C₂×#5189	1	1	yes	characteristic, direct product factor
366	C₃	C₂×C₃×#470	1	1	yes	characteristic, complemented
367	C₂	—	12	2	no	—
368	C₂	C₃×#5189	1	4	yes	direct product factor
369	C₂	C₂×C₃×#918	1	2	yes	—
370	C₂	C₂×C₃×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×Q₁₆	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂³×C₃×D₃	D₄
hypercenter	C₂²×C₃×Q₁₆	D₃
hypocenter	C₃	C₂×C₃×#470
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×Q₁₆	C₂	semidirect
4. C₂×C₃×#835	C₂	semidirect
5. C₃×#5189	C₂	direct (N × H)
6. C₂×C₃×#817	C₂	semidirect
8. C₂×#5189	C₃	direct (N × H)
12. C₂×C₃²×Q₁₆	C₂²	semidirect
22. C₃×#835	C₂²	semidirect
23. C₃×#817	C₂²	semidirect
25. C₂²×C₃×Q₁₆	D₃	semidirect
26. C₂²×C₃×Q₁₆	C₂×C₃	semidirect
34. C₂×#835	C₂×C₃	semidirect
35. #5189	C₂×C₃	direct (N × H)
36. C₂×#817	C₂×C₃	semidirect
70. C₂×C₃×Q₁₆	C₂×D₃	semidirect
71. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
93. #835	C₂²×C₃	semidirect
94. #817	C₂²×C₃	semidirect
117. C₂²×Q₁₆	C₃×D₃	semidirect
193. C₂×Q₁₆	C₂×C₃×D₃	semidirect
260. C₂×C₃²	#470	semidirect
318. C₃²	C₂×#470	semidirect
345. C₂×C₃	#5189	direct (N × H)
346. C₂×C₃	C₃×#470	semidirect
365. C₃	C₂×#5189	direct (N × H)
366. C₃	C₂×C₃×#470	semidirect
368. C₂	C₃×#5189	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×Q₁₆	2
C₂×C₃×#946	2
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂×C₃×#835	2
C₃×#5189	2
C₂×C₃×#817	2
C₂×C₃×#470	3
C₂×#5189	3

Subgroups — C2×C3×#5189 #11866994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5189 #11866994