Subgroups — C₂×C₃×#63505 #13153633

Order 1728.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic
3	C₃×#63505	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3675	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3674	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3667	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#942	—	3	1	no	maximal
8	C₂×#63505	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×Q₈×C₉	—	2	1	no	—
10	C₂×C₃×Q₈×C₉	—	2	2	no	—
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₂×C₃×Q₈×C₉	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₄×C₉	—	2	1	no	—
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×#611	—	2	1	no	—
16	C₃×#3697	—	2	2	no	—
17	C₃×#3697	C₂²	1	4	yes	—
18	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₉	—	2	1	no	—
20	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
21	C₃×#3675	C₂²	1	8	yes	complemented
22	C₃×#3674	C₂²	1	8	yes	complemented
23	C₃×#3667	C₂²	1	4	yes	complemented
24	C₂×C₃×C₉⋊C₈	C₂²	1	2	yes	—
25	C₂²×C₃²×Q₈	D₃	1	1	yes	characteristic
26	C₂×C₃×#235	—	3	1	no	—
27	C₂×C₃×#216	—	3	2	no	—
28	C₃×#942	—	3	8	no	—
29	C₂×C₃×#215	—	3	2	no	—
30	C₂×C₃×#208	—	3	1	no	—
31	C₂²×Q₈×C₉	—	2	1	no	—
32	C₂²×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#3697	C₂×C₃	1	1	yes	characteristic
34	#63505	C₂×C₃	1	8	yes	direct product factor
35	C₂×#3675	C₂×C₃	1	2	yes	complemented
36	C₂×#3674	C₂×C₃	1	2	yes	complemented
37	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
39	C₂²×C₃×D₉	—	2	1	no	—
40	C₃×Q₈×C₉	—	2	2	no	—
41	C₃×Q₈×C₉	—	2	4	no	—
42	C₃×Q₈×C₉	C₂³	1	4	yes	—
43	C₂×C₃×C₄×C₉	—	2	2	no	—
44	C₂×C₃×C₄×C₉	—	2	4	no	—
45	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
49	C₃×#611	—	2	4	no	—
50	C₂×C₃×Dic₉	—	2	1	no	—
51	C₃×D₃₆	—	2	1	no	—
52	C₃×D₃₆	C₂³	1	2	yes	—
53	C₃×C₄×D₉	—	2	4	no	—
54	C₃×Dic₁₈	—	2	1	no	—
55	C₃×Dic₁₈	C₂³	1	2	yes	—
56	C₃×C₉⋊C₈	C₂³	1	4	yes	—
57	C₂×C₃×#137	—	9	1	no	—
58	C₂×#942	—	3	1	no	—
59	C₂×C₃²×Q₈	—	2	1	no	—
60	C₂×C₃²×Q₈	—	2	2	no	—
61	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
62	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
63	C₂²×C₃²×C₄	—	2	1	no	—
64	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
65	C₂×C₃×#67	—	6	1	no	—
66	C₃×#235	—	3	4	no	—
67	C₃×#235	—	6	2	no	—
68	C₂×C₃×D₁₂	—	3	1	no	—
69	C₂×C₃×C₄×D₃	—	6	1	no	—
70	C₂×C₃×Dic₆	—	3	1	no	—
71	C₃×#216	—	3	8	no	—
72	C₃×#215	—	3	8	no	—
73	C₃×#208	—	3	4	no	—
74	C₂×C₃×C₃⋊C₈	—	3	2	no	—
75	C₂×Q₈×C₉	—	2	2	no	—
76	C₂×Q₈×C₉	—	2	4	no	—
77	C₂×Q₈×C₉	—	2	2	no	—
78	C₂×Q₈×C₉	—	2	4	no	—
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	—	2	2	no	—
81	C₂×Q₈×C₉	C₂²×C₃	1	2	yes	—
82	C₂×Q₈×C₉	C₂²×C₃	1	4	yes	complemented
83	C₂²×C₄×C₉	—	2	2	no	—
84	C₂²×C₄×C₉	—	2	1	no	—
85	C₂²×C₄×C₉	—	2	1	no	—
86	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
87	C₂×#611	—	2	1	no	—
88	#3697	—	2	2	no	—
89	#3697	C₂²×C₃	1	4	yes	—
90	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₄×D₉	—	2	1	no	—
92	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
93	#3675	C₂²×C₃	1	8	yes	complemented
94	#3674	C₂²×C₃	1	8	yes	complemented
95	#3667	C₂²×C₃	1	4	yes	complemented
96	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	—
97	C₂²×C₃×C₉	—	2	2	no	—
98	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
99	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×D₉	—	2	2	no	—
101	C₂×C₃×D₉	—	4	2	no	—
102	C₃×C₄×C₉	—	2	4	no	—
103	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
104	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
105	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
106	C₃×Dic₉	—	2	2	no	—
107	C₂×C₃×#41	—	9	1	no	—
108	C₂²×C₃×Q₈	—	2	1	no	—
109	C₂²×C₃×Q₈	D₉	1	1	yes	characteristic, complemented
110	C₂²×C₃×Q₈	C₃×D₃	1	1	yes	characteristic
111	C₂×#235	—	3	1	no	—
112	C₃×#137	—	9	8	no	—
113	C₂×C₃×Q₁₆	—	9	2	no	—
114	C₂×C₃×SD₁₆	—	9	2	no	—
115	C₂×C₃×M₁₆	—	9	1	no	—
116	C₂×#216	—	3	2	no	—
117	#942	—	3	8	no	—
118	C₂×#215	—	3	2	no	—
119	C₂×#208	—	3	1	no	—
120	C₂³×C₃²	#67	1	1	yes	characteristic
121	C₂²×C₃×D₃	—	6	1	no	—
122	C₃²×Q₈	—	2	2	no	—
123	C₃²×Q₈	—	2	4	no	—
124	C₃²×Q₈	C₂²×D₃	1	4	yes	—
125	C₂×C₃²×C₄	—	2	4	no	—
126	C₂×C₃²×C₄	—	2	2	no	—
127	C₂×C₃²×C₄	#67	1	1	yes	characteristic
128	C₂×C₃²×C₄	#67	1	2	yes	—
129	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
131	C₃×#67	—	6	4	no	—
132	C₂×C₃×Dic₃	—	6	1	no	—
133	C₃×D₁₂	—	3	2	no	—
134	C₃×D₁₂	—	6	1	no	—
135	C₃×C₄×D₃	—	6	4	no	—
136	C₃×Dic₆	—	3	2	no	—
137	C₃×Dic₆	—	6	1	no	—
138	C₂³×C₉	—	2	1	no	—
139	C₂³×C₉	C₃×D₄	1	1	yes	characteristic
140	C₂²×D₉	—	2	1	no	—
141	C₃×C₃⋊C₈	—	3	4	no	—
142	Q₈×C₉	—	2	4	no	—
143	Q₈×C₉	—	2	8	no	—
144	Q₈×C₉	—	2	2	no	—
145	Q₈×C₉	—	2	4	no	—
146	Q₈×C₉	—	2	4	no	—
147	Q₈×C₉	C₂³×C₃	1	4	yes	—
148	C₂×C₄×C₉	—	2	4	no	—
149	C₂×C₄×C₉	—	2	8	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	2	4	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
158	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
159	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
160	#611	—	2	4	no	—
161	C₂×Dic₉	—	2	1	no	—
162	D₃₆	—	2	1	no	—
163	D₃₆	C₂³×C₃	1	2	yes	—
164	C₄×D₉	—	2	4	no	—
165	Dic₁₈	—	2	1	no	—
166	Dic₁₈	C₂³×C₃	1	2	yes	—
167	C₉⋊C₈	C₂³×C₃	1	4	yes	—
168	C₂×#137	—	9	1	no	Sylow
169	C₂×C₃×C₉	—	2	2	no	—
170	C₂×C₃×C₉	#137	1	2	yes	complemented
171	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
172	C₃×D₉	—	4	2	no	—
173	C₃×#41	—	9	4	no	—
174	C₃×#41	—	18	2	no	—
175	C₂×C₃×Q₈	—	2	2	no	—
176	C₂×C₃×Q₈	—	2	4	no	—
177	C₂×C₃×Q₈	—	2	2	no	—
178	C₂×C₃×Q₈	—	2	1	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	2	2	no	—
181	C₂×C₃×Q₈	—	2	2	no	—
182	C₂×C₃×Q₈	—	2	4	no	—
183	C₂×C₃×Q₈	—	9	1	no	—
184	C₂×C₃×Q₈	C₂×D₉	1	2	yes	—
185	C₂×C₃×Q₈	C₂×D₉	1	4	yes	complemented
186	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
187	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
188	C₂×C₃×D₄	—	9	1	no	—
189	C₂×C₃×D₄	—	18	1	no	—
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	18	1	no	—
195	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
197	C₂×#67	—	6	1	no	—
198	#235	—	3	4	no	—
199	#235	—	6	2	no	—
200	C₂×D₁₂	—	3	1	no	—
201	C₂×C₄×D₃	—	6	1	no	—
202	C₂×Dic₆	—	3	1	no	—
203	C₃×Q₁₆	—	9	8	no	—
204	C₃×SD₁₆	—	9	8	no	—
205	C₃×M₁₆	—	9	4	no	—
206	C₂×C₃×C₈	—	9	2	no	—
207	#216	—	3	8	no	—
208	#215	—	3	8	no	—
209	#208	—	3	4	no	—
210	C₂×C₃⋊C₈	—	3	2	no	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	C₂×#67	1	2	yes	—
213	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
214	C₂×C₃×D₃	—	6	2	no	—
215	C₂×C₃×D₃	—	12	2	no	—
216	C₃²×C₄	—	2	4	no	—
217	C₃²×C₄	C₂×#67	1	1	yes	characteristic
218	C₃²×C₄	C₂×#67	1	2	yes	—
219	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
220	C₃×Dic₃	—	6	2	no	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	2	1	no	—
225	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
226	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
227	C₂×D₉	—	2	2	no	—
228	C₂×D₉	—	4	2	no	—
229	C₄×C₉	—	2	8	no	—
230	C₄×C₉	—	2	4	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	2	1	no	—
233	C₄×C₉	—	2	2	no	—
234	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
235	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
236	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
237	Dic₉	—	2	2	no	—
238	C₂×#41	—	9	1	no	—
239	C₂²×Q₈	C₃×D₉	1	1	yes	characteristic, complemented
240	#137	—	9	8	no	—
241	C₂×Q₁₆	—	9	2	no	—
242	C₂×SD₁₆	—	9	2	no	—
243	C₂×M₁₆	—	9	1	no	—
244	C₃×C₉	C₂×#137	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	—	18	1	no	—
247	C₂³×C₃	#611	1	1	yes	characteristic
248	C₂³×C₃	C₃×#67	1	1	yes	characteristic
249	C₂²×D₃	—	6	1	no	—
250	C₃×Q₈	—	2	4	no	—
251	C₃×Q₈	—	2	8	no	—
252	C₃×Q₈	—	2	2	no	—
253	C₃×Q₈	—	2	4	no	—
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×Q₈	—	2	4	no	—
257	C₃×Q₈	—	9	2	no	—
258	C₃×Q₈	—	18	1	no	—
259	C₃×Q₈	C₂²×D₉	1	4	yes	—
260	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
261	C₃×D₄	—	9	2	no	—
262	C₃×D₄	—	18	4	no	—
263	C₃×D₄	—	18	1	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	8	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	18	1	no	—
275	C₂×C₃×C₄	—	18	4	no	—
276	C₂×C₃×C₄	#611	1	2	yes	—
277	C₂×C₃×C₄	#611	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
279	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
280	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
281	C₂×C₃×C₄	C₃×#67	1	2	yes	—
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
284	#67	—	6	4	no	—
285	C₂×Dic₃	—	6	1	no	—
286	D₁₂	—	3	2	no	—
287	D₁₂	—	6	1	no	—
288	C₄×D₃	—	6	4	no	—
289	Dic₆	—	3	2	no	—
290	Dic₆	—	6	1	no	—
291	C₃×C₈	—	9	4	no	—
292	C₃⋊C₈	—	3	4	no	—
293	C₂×C₃²	—	2	2	no	—
294	C₂×C₃²	#942	1	2	yes	—
295	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
296	C₃×D₃	—	12	2	no	—
297	C₂×C₉	—	2	4	no	—
298	C₂×C₉	—	2	2	no	—
299	C₂×C₉	—	2	2	no	—
300	C₂×C₉	—	2	1	no	—
301	C₂×C₉	C₃×#137	1	2	yes	complemented
302	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
303	D₉	—	4	2	no	—
304	#41	—	9	4	no	—
305	#41	—	18	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	9	1	no	—
309	C₂×Q₈	C₂×C₃×D₉	1	2	yes	—
310	C₂×Q₈	C₂×C₃×D₉	1	4	yes	complemented
311	C₂×D₄	—	9	1	no	—
312	C₂×D₄	—	18	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	18	1	no	—
315	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
316	Q₁₆	—	9	8	no	—
317	SD₁₆	—	9	8	no	—
318	M₁₆	—	9	4	no	—
319	C₂×C₈	—	9	2	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	18	2	no	—
326	C₂²×C₃	—	36	2	no	—
327	C₂²×C₃	C₂×#611	1	2	yes	—
328	C₂²×C₃	C₂×#611	1	1	yes	characteristic
329	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
330	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
331	C₂×D₃	—	6	2	no	—
332	C₂×D₃	—	12	2	no	—
333	C₃×C₄	—	2	8	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	18	2	no	—
340	C₃×C₄	C₂×#611	1	2	yes	—
341	C₃×C₄	C₂×#611	1	1	yes	characteristic
342	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
343	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃×#67	1	2	yes	—
345	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
346	Dic₃	—	6	2	no	—
347	C₃²	C₂×#942	1	1	yes	characteristic
348	C₉	—	2	1	no	—
349	C₉	C₂×C₃×#137	1	1	yes	characteristic, complemented
350	C₂³	—	18	1	no	—
351	C₂³	C₃×#611	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	9	2	no	—
355	Q₈	—	18	1	no	—
356	Q₈	C₂²×C₃×D₉	1	4	yes	—
357	D₄	—	9	2	no	—
358	D₄	—	18	4	no	—
359	D₄	—	18	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	18	1	no	—
363	C₂×C₄	—	18	4	no	—
364	C₂×C₄	C₃×#611	1	1	yes	characteristic
365	C₂×C₄	C₃×#611	1	2	yes	—
366	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
368	C₈	—	9	4	no	—
369	C₂×C₃	—	2	4	no	—
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	36	2	no	—
375	C₂×C₃	#63505	1	2	yes	direct product factor
376	C₂×C₃	C₂²×#611	1	1	yes	characteristic
377	C₂×C₃	C₃×#942	1	2	yes	—
378	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
379	D₃	—	12	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	—	36	2	no	—
383	C₂²	C₂×C₃×#611	1	2	yes	—
384	C₂²	C₂×C₃×#611	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	18	2	no	—
387	C₄	C₂×C₃×#611	1	2	yes	—
388	C₄	C₂×C₃×#611	1	1	yes	characteristic
389	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
390	C₃	—	2	1	no	—
391	C₃	C₂×#63505	1	1	yes	characteristic, direct product factor
392	C₃	C₂×C₃×#942	1	1	yes	characteristic
393	C₂	—	2	2	no	—
394	C₂	—	36	2	no	—
395	C₂	C₃×#63505	1	2	yes	direct product factor
396	C₂	C₂²×C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#611
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃×Q₈×C₉	C₂
socle	C₂²×C₃²	C₂×#67
prime radical	C₂×C₃×#3697	C₂
hypercenter	C₂²×C₃×Q₈	D₉
hypocenter	C₉	C₂×C₃×#137
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×C₉	C₂	semidirect
3. C₃×#63505	C₂	direct (N × H)
4. C₂×C₃×#3675	C₂	semidirect
5. C₂×C₃×#3674	C₂	semidirect
6. C₂×C₃×#3667	C₂	semidirect
8. C₂×#63505	C₃	direct (N × H)
12. C₂×C₃×Q₈×C₉	C₂²	semidirect
21. C₃×#3675	C₂²	semidirect
22. C₃×#3674	C₂²	semidirect
23. C₃×#3667	C₂²	semidirect
32. C₂²×Q₈×C₉	C₂×C₃	semidirect
34. #63505	C₂×C₃	direct (N × H)
35. C₂×#3675	C₂×C₃	semidirect
36. C₂×#3674	C₂×C₃	semidirect
37. C₂×#3667	C₂×C₃	semidirect
82. C₂×Q₈×C₉	C₂²×C₃	semidirect
93. #3675	C₂²×C₃	semidirect
94. #3674	C₂²×C₃	semidirect
95. #3667	C₂²×C₃	semidirect
109. C₂²×C₃×Q₈	D₉	semidirect
170. C₂×C₃×C₉	#137	semidirect
185. C₂×C₃×Q₈	C₂×D₉	semidirect
239. C₂²×Q₈	C₃×D₉	semidirect
244. C₃×C₉	C₂×#137	semidirect
301. C₂×C₉	C₃×#137	semidirect
310. C₂×Q₈	C₂×C₃×D₉	semidirect
349. C₉	C₂×C₃×#137	semidirect
375. C₂×C₃	#63505	direct (N × H)
391. C₃	C₂×#63505	direct (N × H)
395. C₂	C₃×#63505	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×C₃×Q₈×C₉	2
C₂×C₃×#3697	2
C₃×#63505	2
C₂×C₃×#3675	2
C₂×C₃×#3674	2
C₂×C₃×#3667	2
C₂×C₃×#942	3
C₂×#63505	3

Subgroups — C2×C3×#63505 #13153633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63505 #13153633