Subgroups — C₂²×#64330 #11919224

Order 1152.

13801 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#638	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	2	yes	maximal, complemented
3	C₂×#64330	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#3811	C₂	1	2	yes	maximal, complemented
5	C₂²×D₃×#67	C₂	1	4	yes	maximal, complemented
6	C₂²×#3805	C₂	1	2	yes	maximal, complemented
7	C₂²×#3804	C₂	1	4	yes	maximal, complemented
8	C₂²×#1004	—	3	2	no	maximal
9	C₂⁵×C₃²	C₂²	1	1	yes	characteristic, complemented
10	C₂⁴×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
11	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
12	C₂³×D₃²	C₂²	1	2	yes	complemented
13	C₂²×#638	C₂²	1	4	yes	complemented
14	C₂²×#638	C₂²	1	24	yes	complemented
15	C₂³×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×#67	C₂²	1	4	yes	complemented
17	C₂²×C₃×#67	C₂²	1	4	yes	complemented
18	C₂²×C₃×#67	C₂²	1	48	yes	complemented
19	C₂³×C₃×Dic₃	C₂²	1	2	yes	complemented
20	#64330	C₂²	1	256	yes	direct product factor
21	C₂×#3811	C₂²	1	48	yes	complemented
22	C₂×D₃×#67	C₂²	1	96	yes	complemented
23	C₂²×#627	C₂²	1	2	yes	complemented
24	C₂²×#626	C₂²	1	4	yes	complemented
25	C₂²×#625	C₂²	1	2	yes	complemented
26	C₂²×#624	C₂²	1	2	yes	complemented
27	C₂×#3805	C₂²	1	48	yes	complemented
28	C₂×#3804	C₂²	1	96	yes	complemented
29	C₂²×D₃×Dic₃	C₂²	1	4	yes	complemented
30	C₂³×C₃×D₄	—	3	2	no	—
31	C₂³×#67	—	3	4	no	—
32	C₂³×#67	—	3	2	no	—
33	C₂³×#67	—	6	1	no	—
34	C₂³×#67	D₃	1	2	yes	complemented
35	C₂×#1004	—	3	96	no	—
36	C₂²×#237	—	3	4	no	—
37	C₂²×#237	—	3	4	no	—
38	C₂²×D₃×D₄	—	3	4	no	—
39	C₂²×D₃×D₄	—	3	4	no	—
40	C₂²×#235	—	3	4	no	—
41	C₂⁴×C₃²	—	4	4	no	—
42	C₂⁴×C₃²	C₂³	1	2	yes	—
43	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
44	C₂⁴×C₃²	C₂³	1	12	yes	complemented
45	C₂³×C₃⋊D₃	—	4	4	no	—
46	C₂³×C₃⋊D₃	C₂³	1	2	yes	—
47	C₂³×C₃⋊D₃	C₂³	1	12	yes	complemented
48	C₂³×C₃×D₃	—	4	8	no	—
49	C₂³×C₃×D₃	C₂³	1	4	yes	—
50	C₂³×C₃×D₃	C₂³	1	24	yes	complemented
51	C₂²×D₃²	—	4	8	no	—
52	C₂²×D₃²	C₂³	1	24	yes	complemented
53	C₂×#638	C₂³	1	48	yes	complemented
54	C₂×#638	C₂³	1	64	yes	complemented
55	C₂²×C₃⋊Dic₃	C₂³	1	2	yes	—
56	C₂²×C₃⋊Dic₃	C₂³	1	12	yes	complemented
57	C₂×C₃×#67	C₂³	1	48	yes	complemented
58	C₂×C₃×#67	C₂³	1	48	yes	complemented
59	C₂×C₃×#67	C₂³	1	128	yes	complemented
60	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
61	C₂²×C₃×Dic₃	C₂³	1	24	yes	complemented
62	#3811	C₂³	1	128	yes	complemented
63	D₃×#67	C₂³	1	256	yes	complemented
64	C₂×#627	C₂³	1	24	yes	complemented
65	C₂×#626	C₂³	1	48	yes	complemented
66	C₂×#625	C₂³	1	24	yes	complemented
67	C₂×#624	C₂³	1	24	yes	complemented
68	#3805	C₂³	1	128	yes	complemented
69	#3804	C₂³	1	256	yes	complemented
70	C₂×D₃×Dic₃	C₂³	1	48	yes	complemented
71	C₂²×H(5,𝔽₂)	—	9	1	no	Sylow
72	C₂⁵×C₃	—	2	1	no	—
73	C₂⁵×C₃	—	3	2	no	—
74	C₂⁵×C₃	C₂×D₃	1	2	yes	complemented
75	C₂⁴×D₃	—	3	2	no	—
76	C₂⁴×D₃	—	3	4	no	—
77	C₂⁴×D₃	—	6	1	no	—
78	C₂⁴×D₃	C₂×D₃	1	2	yes	complemented
79	C₂²×C₃×D₄	—	3	4	no	—
80	C₂²×C₃×D₄	—	3	4	no	—
81	C₂²×C₃×D₄	—	3	48	no	—
82	C₂³×C₃×C₄	—	3	2	no	—
83	C₂²×#67	—	3	4	no	—
84	C₂²×#67	—	3	4	no	—
85	C₂²×#67	—	3	48	no	—
86	C₂²×#67	—	3	4	no	—
87	C₂²×#67	—	3	96	no	—
88	C₂²×#67	—	3	4	no	—
89	C₂²×#67	—	6	4	no	—
90	C₂²×#67	—	6	24	no	—
91	C₂²×#67	C₂×D₃	1	4	yes	complemented
92	C₂²×#67	C₂×D₃	1	4	yes	complemented
93	C₂²×#67	C₂×D₃	1	48	yes	complemented
94	C₂³×Dic₃	—	3	2	no	—
95	C₂³×Dic₃	—	3	4	no	—
96	C₂³×Dic₃	—	6	1	no	—
97	C₂³×Dic₃	C₂×D₃	1	2	yes	complemented
98	#1004	—	3	512	no	—
99	C₂×#237	—	3	96	no	—
100	C₂×#237	—	3	96	no	—
101	C₂×D₃×D₄	—	3	96	no	—
102	C₂×D₃×D₄	—	3	96	no	—
103	C₂×#235	—	3	96	no	—
104	C₂²×D₁₂	—	3	4	no	—
105	C₂²×C₄×D₃	—	3	4	no	—
106	C₂²×C₄×D₃	—	3	4	no	—
107	C₂²×Dic₆	—	3	4	no	—
108	C₂³×C₃²	—	2	4	no	—
109	C₂³×C₃²	—	2	8	no	—
110	C₂³×C₃²	—	4	24	no	—
111	C₂³×C₃²	C₂⁴	1	12	yes	—
112	C₂³×C₃²	C₂⁴	1	6	yes	—
113	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
114	C₂³×C₃²	C₂⁴	1	16	yes	complemented
115	C₂²×C₃⋊D₃	—	2	8	no	—
116	C₂²×C₃⋊D₃	—	4	24	no	—
117	C₂²×C₃⋊D₃	C₂⁴	1	12	yes	—
118	C₂²×C₃⋊D₃	C₂⁴	1	16	yes	complemented
119	C₂²×C₃×D₃	—	2	16	no	—
120	C₂²×C₃×D₃	—	4	48	no	—
121	C₂²×C₃×D₃	C₂⁴	1	24	yes	—
122	C₂²×C₃×D₃	C₂⁴	1	32	yes	complemented
123	C₂×D₃²	—	4	48	no	—
124	C₂×D₃²	C₂⁴	1	32	yes	complemented
125	#638	C₂⁴	1	64	yes	complemented
126	C₂×C₃⋊Dic₃	C₂⁴	1	12	yes	—
127	C₂×C₃⋊Dic₃	C₂⁴	1	16	yes	complemented
128	C₃×#67	C₂⁴	1	64	yes	complemented
129	C₃×#67	C₂⁴	1	64	yes	complemented
130	C₂×C₃×Dic₃	C₂⁴	1	24	yes	—
131	C₂×C₃×Dic₃	C₂⁴	1	32	yes	complemented
132	#627	C₂⁴	1	32	yes	complemented
133	#626	C₂⁴	1	64	yes	complemented
134	#625	C₂⁴	1	32	yes	complemented
135	#624	C₂⁴	1	32	yes	complemented
136	D₃×Dic₃	C₂⁴	1	64	yes	complemented
137	C₂×H(5,𝔽₂)	—	9	48	no	—
138	C₂²×#41	—	9	4	no	—
139	C₂²×#41	—	9	2	no	—
140	C₂³×D₄	—	3	2	no	—
141	C₂³×D₄	—	9	2	no	—
142	C₂³×D₄	—	9	4	no	—
143	C₂³×D₄	—	9	1	no	—
144	C₂⁴×C₃	—	2	1	no	—
145	C₂⁴×C₃	—	2	2	no	—
146	C₂⁴×C₃	—	2	12	no	—
147	C₂⁴×C₃	—	3	4	no	—
148	C₂⁴×C₃	—	3	24	no	—
149	C₂⁴×C₃	—	4	8	no	—
150	C₂⁴×C₃	—	4	8	no	—
151	C₂⁴×C₃	—	12	8	no	—
152	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
153	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
154	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
155	C₂⁴×C₃	C₂²×D₃	1	24	yes	complemented
156	C₂³×D₃	—	3	4	no	—
157	C₂³×D₃	—	3	24	no	—
158	C₂³×D₃	—	3	48	no	—
159	C₂³×D₃	—	4	8	no	—
160	C₂³×D₃	—	6	2	no	—
161	C₂³×D₃	—	6	12	no	—
162	C₂³×D₃	—	12	16	no	—
163	C₂³×D₃	—	12	8	no	—
164	C₂³×D₃	—	12	8	no	—
165	C₂³×D₃	C₂²×D₃	1	4	yes	—
166	C₂³×D₃	C₂²×D₃	1	24	yes	complemented
167	C₂×C₃×D₄	—	3	48	no	—
168	C₂×C₃×D₄	—	3	48	no	—
169	C₂×C₃×D₄	—	3	128	no	—
170	C₂²×C₃×C₄	—	3	4	no	—
171	C₂²×C₃×C₄	—	3	24	no	—
172	C₂×#67	—	3	48	no	—
173	C₂×#67	—	3	48	no	—
174	C₂×#67	—	3	128	no	—
175	C₂×#67	—	3	48	no	—
176	C₂×#67	—	3	256	no	—
177	C₂×#67	—	3	48	no	—
178	C₂×#67	—	6	48	no	—
179	C₂×#67	—	6	64	no	—
180	C₂×#67	C₂²×D₃	1	48	yes	complemented
181	C₂×#67	C₂²×D₃	1	48	yes	complemented
182	C₂×#67	C₂²×D₃	1	128	yes	complemented
183	C₂²×Dic₃	—	3	4	no	—
184	C₂²×Dic₃	—	3	24	no	—
185	C₂²×Dic₃	—	3	48	no	—
186	C₂²×Dic₃	—	6	2	no	—
187	C₂²×Dic₃	—	6	12	no	—
188	C₂²×Dic₃	C₂²×D₃	1	4	yes	—
189	C₂²×Dic₃	C₂²×D₃	1	24	yes	complemented
190	#237	—	3	256	no	—
191	#237	—	3	256	no	—
192	D₃×D₄	—	3	256	no	—
193	D₃×D₄	—	3	256	no	—
194	#235	—	3	256	no	—
195	C₂×D₁₂	—	3	48	no	—
196	C₂×C₄×D₃	—	3	48	no	—
197	C₂×C₄×D₃	—	3	48	no	—
198	C₂×Dic₆	—	3	48	no	—
199	C₂²×C₃²	—	2	12	no	—
200	C₂²×C₃²	—	2	24	no	—
201	C₂²×C₃²	—	4	16	no	—
202	C₂²×C₃²	H(5,𝔽₂)	1	4	yes	complemented
203	C₂²×C₃²	C₂⁵	1	8	yes	—
204	C₂²×C₃²	C₂⁵	1	4	yes	—
205	C₂²×C₃²	C₂⁵	1	3	yes	—
206	C₂×C₃⋊D₃	—	2	24	no	—
207	C₂×C₃⋊D₃	—	4	16	no	—
208	C₂×C₃⋊D₃	C₂⁵	1	8	yes	—
209	C₂×C₃×D₃	—	2	48	no	—
210	C₂×C₃×D₃	—	4	32	no	—
211	C₂×C₃×D₃	C₂⁵	1	16	yes	—
212	D₃²	—	4	32	no	—
213	C₃⋊Dic₃	C₂⁵	1	8	yes	—
214	C₃×Dic₃	C₂⁵	1	16	yes	—
215	C₂⁵	—	3	2	no	—
216	C₂⁵	—	9	2	no	—
217	C₂⁵	—	9	1	no	—
218	C₂⁵	D₃²	1	1	yes	characteristic, complemented
219	H(5,𝔽₂)	—	9	256	no	—
220	C₂×#41	—	9	96	no	—
221	C₂×#41	—	9	48	no	—
222	C₂²×Q₈	—	9	2	no	—
223	C₂²×D₄	—	3	4	no	—
224	C₂²×D₄	—	3	4	no	—
225	C₂²×D₄	—	3	48	no	—
226	C₂²×D₄	—	9	4	no	—
227	C₂²×D₄	—	9	48	no	—
228	C₂²×D₄	—	9	96	no	—
229	C₂²×D₄	—	9	2	no	—
230	C₂²×D₄	—	9	4	no	—
231	C₂²×D₄	—	9	24	no	—
232	C₂³×C₄	—	3	2	no	—
233	C₂³×C₄	—	9	2	no	—
234	C₂³×C₄	—	9	4	no	—
235	C₂³×C₄	—	9	1	no	—
236	C₂³×C₃	—	2	8	no	—
237	C₂³×C₃	—	2	8	no	—
238	C₂³×C₃	—	2	8	no	—
239	C₂³×C₃	—	2	8	no	—
240	C₂³×C₃	—	2	6	no	—
241	C₂³×C₃	—	2	12	no	—
242	C₂³×C₃	—	2	1	no	—
243	C₂³×C₃	—	2	16	no	—
244	C₂³×C₃	—	3	24	no	—
245	C₂³×C₃	—	3	32	no	—
246	C₂³×C₃	—	4	8	no	—
247	C₂³×C₃	—	4	48	no	—
248	C₂³×C₃	—	4	48	no	—
249	C₂³×C₃	—	6	16	no	—
250	C₂³×C₃	—	12	48	no	—
251	C₂³×C₃	C₂³×D₃	1	12	yes	—
252	C₂³×C₃	C₂³×D₃	1	12	yes	—
253	C₂³×C₃	C₂³×D₃	1	12	yes	—
254	C₂³×C₃	C₂³×D₃	1	2	yes	—
255	C₂³×C₃	C₂³×D₃	1	32	yes	complemented
256	C₂²×D₃	—	2	16	no	—
257	C₂²×D₃	—	3	24	no	—
258	C₂²×D₃	—	3	32	no	—
259	C₂²×D₃	—	3	64	no	—
260	C₂²×D₃	—	4	48	no	—
261	C₂²×D₃	—	6	12	no	—
262	C₂²×D₃	—	6	16	no	—
263	C₂²×D₃	—	6	16	no	—
264	C₂²×D₃	—	12	8	no	—
265	C₂²×D₃	—	12	96	no	—
266	C₂²×D₃	—	12	48	no	—
267	C₂²×D₃	—	12	48	no	—
268	C₂²×D₃	C₂³×D₃	1	24	yes	—
269	C₂²×D₃	C₂³×D₃	1	32	yes	complemented
270	C₃×D₄	—	3	64	no	—
271	C₃×D₄	—	3	64	no	—
272	C₂×C₃×C₄	—	3	24	no	—
273	C₂×C₃×C₄	—	3	32	no	—
274	#67	—	3	64	no	—
275	#67	—	3	64	no	—
276	#67	—	3	64	no	—
277	#67	—	3	64	no	—
278	#67	—	6	64	no	—
279	#67	C₂³×D₃	1	64	yes	complemented
280	#67	C₂³×D₃	1	64	yes	complemented
281	C₂×Dic₃	—	3	24	no	—
282	C₂×Dic₃	—	3	32	no	—
283	C₂×Dic₃	—	3	64	no	—
284	C₂×Dic₃	—	6	12	no	—
285	C₂×Dic₃	—	6	16	no	—
286	C₂×Dic₃	C₂³×D₃	1	24	yes	—
287	C₂×Dic₃	C₂³×D₃	1	32	yes	complemented
288	D₁₂	—	3	64	no	—
289	C₄×D₃	—	3	64	no	—
290	C₄×D₃	—	3	64	no	—
291	Dic₆	—	3	64	no	—
292	C₂×C₃²	—	2	4	no	—
293	C₂×C₃²	—	2	8	no	—
294	C₂×C₃²	C₂×H(5,𝔽₂)	1	6	yes	complemented
295	C₂×C₃²	C₂⁶	1	1	yes	characteristic
296	C₃⋊D₃	—	2	8	no	—
297	C₃×D₃	—	2	16	no	—
298	C₂⁴	—	3	4	no	—
299	C₂⁴	—	3	24	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	9	24	no	—
302	C₂⁴	—	9	2	no	—
303	C₂⁴	—	9	12	no	—
304	C₂⁴	—	12	8	no	—
305	C₂⁴	—	36	4	no	—
306	C₂⁴	—	36	8	no	—
307	C₂⁴	C₂×D₃²	1	2	yes	—
308	C₂⁴	C₂×D₃²	1	1	yes	characteristic
309	C₂⁴	C₂×D₃²	1	12	yes	complemented
310	#41	—	9	256	no	—
311	#41	—	9	128	no	—
312	C₂×Q₈	—	9	24	no	—
313	C₂×D₄	—	3	48	no	—
314	C₂×D₄	—	3	48	no	—
315	C₂×D₄	—	3	128	no	—
316	C₂×D₄	—	9	48	no	—
317	C₂×D₄	—	9	128	no	—
318	C₂×D₄	—	9	256	no	—
319	C₂×D₄	—	9	24	no	—
320	C₂×D₄	—	9	48	no	—
321	C₂×D₄	—	9	64	no	—
322	C₂²×C₄	—	3	24	no	—
323	C₂²×C₄	—	3	4	no	—
324	C₂²×C₄	—	9	24	no	—
325	C₂²×C₄	—	9	48	no	—
326	C₂²×C₄	—	9	12	no	—
327	C₂²×C₄	—	9	2	no	—
328	C₂²×C₃	—	2	24	no	—
329	C₂²×C₃	—	2	24	no	—
330	C₂²×C₃	—	2	24	no	—
331	C₂²×C₃	—	2	24	no	—
332	C₂²×C₃	—	2	4	no	—
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	2	3	no	—
335	C₂²×C₃	—	2	8	no	—
336	C₂²×C₃	—	3	16	no	—
337	C₂²×C₃	—	4	24	no	—
338	C₂²×C₃	—	4	32	no	—
339	C₂²×C₃	—	4	32	no	—
340	C₂²×C₃	—	6	48	no	—
341	C₂²×C₃	—	12	32	no	—
342	C₂²×C₃	#1004	1	8	yes	complemented
343	C₂²×C₃	C₂⁴×D₃	1	8	yes	—
344	C₂²×C₃	C₂⁴×D₃	1	8	yes	—
345	C₂²×C₃	C₂⁴×D₃	1	8	yes	—
346	C₂²×C₃	C₂⁴×D₃	1	6	yes	—
347	C₂×D₃	—	2	48	no	—
348	C₂×D₃	—	3	16	no	—
349	C₂×D₃	—	4	32	no	—
350	C₂×D₃	—	6	8	no	—
351	C₂×D₃	—	6	48	no	—
352	C₂×D₃	—	12	24	no	—
353	C₂×D₃	—	12	64	no	—
354	C₂×D₃	—	12	32	no	—
355	C₂×D₃	—	12	32	no	—
356	C₂×D₃	C₂⁴×D₃	1	16	yes	—
357	C₃×C₄	—	3	16	no	—
358	Dic₃	—	3	16	no	—
359	Dic₃	—	6	8	no	—
360	Dic₃	C₂⁴×D₃	1	16	yes	—
361	C₃²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
362	C₂³	—	2	8	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	3	24	no	—
365	C₂³	—	3	32	no	—
366	C₂³	—	4	24	no	—
367	C₂³	—	6	16	no	—
368	C₂³	—	9	32	no	—
369	C₂³	—	9	12	no	—
370	C₂³	—	9	16	no	—
371	C₂³	—	12	48	no	—
372	C₂³	—	18	8	no	—
373	C₂³	—	36	24	no	—
374	C₂³	—	36	48	no	—
375	C₂³	C₂²×D₃²	1	12	yes	—
376	C₂³	C₂²×D₃²	1	6	yes	—
377	C₂³	C₂²×D₃²	1	1	yes	characteristic
378	C₂³	C₂²×D₃²	1	16	yes	complemented
379	Q₈	—	9	32	no	—
380	D₄	—	3	64	no	—
381	D₄	—	3	64	no	—
382	D₄	—	9	64	no	—
383	D₄	—	9	32	no	—
384	D₄	—	9	64	no	—
385	C₂×C₄	—	3	24	no	—
386	C₂×C₄	—	3	32	no	—
387	C₂×C₄	—	9	32	no	—
388	C₂×C₄	—	9	64	no	—
389	C₂×C₄	—	9	12	no	—
390	C₂×C₄	—	9	16	no	—
391	C₂×C₃	—	2	8	no	—
392	C₂×C₃	—	2	8	no	—
393	C₂×C₃	—	2	8	no	—
394	C₂×C₃	—	2	8	no	—
395	C₂×C₃	—	2	6	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	4	8	no	—
398	C₂×C₃	—	6	16	no	—
399	C₂×C₃	C₂×#1004	1	12	yes	complemented
400	C₂×C₃	C₂⁵×D₃	1	2	yes	—
401	D₃	—	2	16	no	—
402	D₃	—	6	16	no	—
403	D₃	—	12	8	no	—
404	C₂²	—	2	24	no	—
405	C₂²	—	2	12	no	—
406	C₂²	—	3	16	no	—
407	C₂²	—	4	16	no	—
408	C₂²	—	6	48	no	—
409	C₂²	—	9	8	no	—
410	C₂²	—	12	32	no	—
411	C₂²	—	18	24	no	—
412	C₂²	—	36	16	no	—
413	C₂²	—	36	32	no	—
414	C₂²	#64330	1	4	yes	direct product factor
415	C₂²	C₂³×D₃²	1	8	yes	—
416	C₂²	C₂³×D₃²	1	4	yes	—
417	C₂²	C₂³×D₃²	1	3	yes	—
418	C₄	—	3	16	no	—
419	C₄	—	9	8	no	—
420	C₃	—	2	1	no	—
421	C₃	C₂²×#1004	1	2	yes	complemented
422	C₂	—	2	8	no	—
423	C₂	—	2	4	no	—
424	C₂	—	6	16	no	—
425	C₂	—	18	8	no	—
426	C₂	C₂×#64330	1	6	yes	direct product factor
427	C₂	C₂⁴×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃²
commutator, cosocle	C₂×C₃²	C₂⁶
Frattini	C₂	C₂⁴×D₃²
Fitting	C₂⁵×C₃²	C₂²
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂⁵	D₃²
hypocenter	C₃²	C₂²×H(5,𝔽₂)
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂³×#638	C₂	semidirect
2. C₂³×C₃×#67	C₂	semidirect
3. C₂×#64330	C₂	direct (N × H)
4. C₂²×#3811	C₂	semidirect
5. C₂²×D₃×#67	C₂	semidirect
6. C₂²×#3805	C₂	semidirect
7. C₂²×#3804	C₂	semidirect
9. C₂⁵×C₃²	C₂²	semidirect
10. C₂⁴×C₃⋊D₃	C₂²	semidirect
11. C₂⁴×C₃×D₃	C₂²	semidirect
12. C₂³×D₃²	C₂²	semidirect
13. C₂²×#638	C₂²	semidirect
14. C₂²×#638	C₂²	semidirect
15. C₂³×C₃⋊Dic₃	C₂²	semidirect
16. C₂²×C₃×#67	C₂²	semidirect
17. C₂²×C₃×#67	C₂²	semidirect
18. C₂²×C₃×#67	C₂²	semidirect
19. C₂³×C₃×Dic₃	C₂²	semidirect
20. #64330	C₂²	direct (N × H)
21. C₂×#3811	C₂²	semidirect
22. C₂×D₃×#67	C₂²	semidirect
23. C₂²×#627	C₂²	semidirect
24. C₂²×#626	C₂²	semidirect
25. C₂²×#625	C₂²	semidirect
26. C₂²×#624	C₂²	semidirect
27. C₂×#3805	C₂²	semidirect
28. C₂×#3804	C₂²	semidirect
29. C₂²×D₃×Dic₃	C₂²	semidirect
34. C₂³×#67	D₃	semidirect
44. C₂⁴×C₃²	C₂³	semidirect
47. C₂³×C₃⋊D₃	C₂³	semidirect
50. C₂³×C₃×D₃	C₂³	semidirect
52. C₂²×D₃²	C₂³	semidirect
53. C₂×#638	C₂³	semidirect
54. C₂×#638	C₂³	semidirect
56. C₂²×C₃⋊Dic₃	C₂³	semidirect
57. C₂×C₃×#67	C₂³	semidirect
58. C₂×C₃×#67	C₂³	semidirect
59. C₂×C₃×#67	C₂³	semidirect
61. C₂²×C₃×Dic₃	C₂³	semidirect
62. #3811	C₂³	semidirect
63. D₃×#67	C₂³	semidirect
64. C₂×#627	C₂³	semidirect
65. C₂×#626	C₂³	semidirect
66. C₂×#625	C₂³	semidirect
67. C₂×#624	C₂³	semidirect
68. #3805	C₂³	semidirect
69. #3804	C₂³	semidirect
70. C₂×D₃×Dic₃	C₂³	semidirect
74. C₂⁵×C₃	C₂×D₃	semidirect
78. C₂⁴×D₃	C₂×D₃	semidirect
91. C₂²×#67	C₂×D₃	semidirect
92. C₂²×#67	C₂×D₃	semidirect
93. C₂²×#67	C₂×D₃	semidirect
97. C₂³×Dic₃	C₂×D₃	semidirect
114. C₂³×C₃²	C₂⁴	semidirect
118. C₂²×C₃⋊D₃	C₂⁴	semidirect
122. C₂²×C₃×D₃	C₂⁴	semidirect
124. C₂×D₃²	C₂⁴	semidirect
125. #638	C₂⁴	semidirect
127. C₂×C₃⋊Dic₃	C₂⁴	semidirect
128. C₃×#67	C₂⁴	semidirect
129. C₃×#67	C₂⁴	semidirect
131. C₂×C₃×Dic₃	C₂⁴	semidirect
132. #627	C₂⁴	semidirect
133. #626	C₂⁴	semidirect
134. #625	C₂⁴	semidirect
135. #624	C₂⁴	semidirect
136. D₃×Dic₃	C₂⁴	semidirect
155. C₂⁴×C₃	C₂²×D₃	semidirect
166. C₂³×D₃	C₂²×D₃	semidirect
180. C₂×#67	C₂²×D₃	semidirect
181. C₂×#67	C₂²×D₃	semidirect
182. C₂×#67	C₂²×D₃	semidirect
189. C₂²×Dic₃	C₂²×D₃	semidirect
202. C₂²×C₃²	H(5,𝔽₂)	semidirect
218. C₂⁵	D₃²	semidirect
255. C₂³×C₃	C₂³×D₃	semidirect
269. C₂²×D₃	C₂³×D₃	semidirect
279. #67	C₂³×D₃	semidirect
280. #67	C₂³×D₃	semidirect
287. C₂×Dic₃	C₂³×D₃	semidirect
294. C₂×C₃²	C₂×H(5,𝔽₂)	semidirect
309. C₂⁴	C₂×D₃²	semidirect
342. C₂²×C₃	#1004	semidirect
361. C₃²	C₂²×H(5,𝔽₂)	semidirect
378. C₂³	C₂²×D₃²	semidirect
399. C₂×C₃	C₂×#1004	semidirect
414. C₂²	#64330	direct (N × H)
421. C₃	C₂²×#1004	semidirect
426. C₂	C₂×#64330	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#638	2
C₂³×C₃×#67	2
C₂×#64330	2
C₂²×#3811	2
C₂²×D₃×#67	2
C₂²×#3805	2
C₂²×#3804	2
C₂²×#1004	3

Subgroups — C22×#64330 #11919224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64330 #11919224