Subgroups — C₃×Q₈×#217 #11804879

Order 1152.

2065 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Q₈×Dic₃	C₂	1	2	yes	maximal, complemented
3	C₃×#5229	C₂	1	6	yes	maximal, complemented
4	C₃×#5212	C₂	1	3	yes	maximal
5	C₃×C₄×#217	C₂	1	3	yes	maximal
6	C₃×Q₈×C₂²⋊C₄	—	3	1	no	maximal
7	Q₈×#217	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×Q₈	—	2	8	no	—
9	C₂²×C₃²×Q₈	C₄	1	8	yes	complemented
10	C₂²×C₃²×Q₈	C₂²	1	3	yes	—
11	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃²×C₄	C₂²	1	3	yes	—
13	C₂×C₃×#217	C₂²	1	3	yes	—
14	C₂×C₃×#217	C₂²	1	1	yes	characteristic
15	C₃×Q₈×Dic₃	—	2	8	no	—
16	C₂×C₃×C₄⋊Dic₃	C₂²	1	6	yes	—
17	C₂×C₃×C₄×Dic₃	C₂²	1	6	yes	—
18	C₃×C₃⋊#95	C₂²	1	6	yes	—
19	C₃×C₃⋊#95	C₂²	1	6	yes	—
20	C₂³×C₃×Q₈	—	2	1	no	—
21	C₂³×C₃×Q₈	D₃	1	1	yes	characteristic
22	C₂³×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×C₄×Q₈	—	3	2	no	—
24	C₂×Q₈×Dic₃	C₂×C₃	1	2	yes	complemented
25	C₃×#391	—	3	6	no	—
26	C₃×#380	—	3	3	no	—
27	C₃×C₄×C₂²⋊C₄	—	3	3	no	—
28	#5229	C₂×C₃	1	6	yes	complemented
29	#5212	C₂×C₃	1	3	yes	—
30	C₄×#217	C₂×C₃	1	3	yes	—
31	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
32	C₂×C₃²×Q₈	—	2	32	no	—
33	C₂×C₃²×Q₈	—	2	12	no	—
34	C₂×C₃²×Q₈	C₂×C₄	1	12	yes	—
35	C₂×C₃²×Q₈	C₂×C₄	1	4	yes	—
36	C₂×C₃²×Q₈	D₄	1	8	yes	—
37	C₂²×C₃²×C₄	—	2	12	no	—
38	C₂²×C₃²×C₄	C₂×C₄	1	12	yes	—
39	C₂²×C₃²×C₄	C₂³	1	3	yes	—
40	C₂²×C₃²×C₄	C₂³	1	3	yes	—
41	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
42	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
43	C₃×#217	—	2	6	no	—
44	C₃×#217	Q₈	1	4	yes	direct product factor
45	C₃×C₄⋊Dic₃	—	2	12	no	—
46	C₃×C₄×Dic₃	—	2	12	no	—
47	Q₈×C₂²⋊C₄	—	3	1	no	Sylow
48	C₂²×C₃×Q₈	—	2	16	no	—
49	C₂²×C₃×Q₈	—	2	8	no	—
50	C₂²×C₃×Q₈	—	2	8	no	—
51	C₂²×C₃×Q₈	—	2	8	no	—
52	C₂²×C₃×Q₈	—	2	3	no	—
53	C₂²×C₃×Q₈	—	2	1	no	—
54	C₂²×C₃×Q₈	Dic₃	1	8	yes	complemented
55	C₂²×C₃×Q₈	C₃×C₄	1	8	yes	complemented
56	C₂²×C₃×Q₈	C₂×D₃	1	3	yes	—
57	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
58	C₂²×C₃×Q₈	C₂²×C₃	1	3	yes	—
59	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₃×C₄	—	2	3	no	—
61	C₂³×C₃×C₄	C₂×D₃	1	3	yes	—
62	C₂³×C₃×C₄	C₂²×C₃	1	3	yes	—
63	C₃×C₄×Q₈	—	6	8	no	—
64	C₂×C₃×C₄⋊C₄	—	3	6	no	—
65	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
66	C₂×C₃×C₂²⋊C₄	—	3	3	no	—
67	C₂×C₃×C₄²	—	3	6	no	—
68	C₂×#217	C₂²×C₃	1	3	yes	—
69	C₂×#217	C₂²×C₃	1	1	yes	characteristic
70	Q₈×Dic₃	—	2	8	no	—
71	C₂×C₄⋊Dic₃	C₂²×C₃	1	6	yes	—
72	C₂×C₄×Dic₃	C₂²×C₃	1	6	yes	—
73	C₃×#95	—	3	6	no	—
74	C₃×#95	—	3	6	no	—
75	C₃⋊#95	C₂²×C₃	1	6	yes	—
76	C₃⋊#95	C₂²×C₃	1	6	yes	—
77	C₂³×C₃²	—	2	2	no	—
78	C₂³×C₃²	—	2	2	no	—
79	C₂³×C₃²	C₂²×C₄	1	2	yes	—
80	C₂³×C₃²	C₂×Q₈	1	2	yes	—
81	C₂³×C₃²	#41	1	2	yes	—
82	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
83	C₃²×Q₈	—	2	24	no	—
84	C₃²×Q₈	C₂²⋊C₄	1	16	yes	complemented
85	C₂×C₃²×C₄	—	2	6	no	—
86	C₂×C₃²×C₄	—	2	24	no	—
87	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
88	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
89	C₂×C₃²×C₄	C₂×D₄	1	12	yes	—
90	C₂×C₃×Dic₃	—	2	2	no	—
91	C₂×C₃×Dic₃	—	2	2	no	—
92	C₂×C₃×Dic₃	—	2	6	no	—
93	C₂×C₃×Dic₃	—	2	6	no	—
94	C₂×C₃×Dic₃	—	2	6	no	—
95	C₂×C₃×Dic₃	C₂×Q₈	1	4	yes	complemented
96	C₂³×Q₈	C₃×D₃	1	1	yes	characteristic
97	C₂×C₄×Q₈	—	3	2	no	—
98	#391	—	3	6	no	—
99	#380	—	3	3	no	—
100	C₄×C₂²⋊C₄	—	3	3	no	—
101	C₂⁴×C₃	—	2	1	no	—
102	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
103	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
104	C₂×C₃×Q₈	—	2	64	no	—
105	C₂×C₃×Q₈	—	2	24	no	—
106	C₂×C₃×Q₈	—	2	32	no	—
107	C₂×C₃×Q₈	—	2	32	no	—
108	C₂×C₃×Q₈	—	2	12	no	—
109	C₂×C₃×Q₈	—	2	12	no	—
110	C₂×C₃×Q₈	—	2	12	no	—
111	C₂×C₃×Q₈	—	2	4	no	—
112	C₂×C₃×Q₈	—	2	8	no	—
113	C₂×C₃×Q₈	C₂×Dic₃	1	12	yes	—
114	C₂×C₃×Q₈	C₂×Dic₃	1	4	yes	—
115	C₂×C₃×Q₈	#67	1	8	yes	—
116	C₂×C₃×Q₈	C₂×C₃×C₄	1	12	yes	—
117	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
118	C₂×C₃×Q₈	C₃×D₄	1	8	yes	—
119	C₂²×C₃×C₄	—	2	24	no	—
120	C₂²×C₃×C₄	—	2	12	no	—
121	C₂²×C₃×C₄	—	2	12	no	—
122	C₂²×C₃×C₄	—	2	12	no	—
123	C₂²×C₃×C₄	—	2	3	no	—
124	C₂²×C₃×C₄	—	2	3	no	—
125	C₂²×C₃×C₄	—	3	2	no	—
126	C₂²×C₃×C₄	—	3	6	no	—
127	C₂²×C₃×C₄	C₂×Dic₃	1	12	yes	—
128	C₂²×C₃×C₄	C₂×C₃×C₄	1	12	yes	—
129	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
130	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
131	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
132	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
133	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
134	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
135	C₃×C₄⋊C₄	—	6	12	no	—
136	C₃×C₂²⋊C₄	—	3	4	no	—
137	C₃×C₂²⋊C₄	—	6	6	no	—
138	C₃×C₄²	—	6	12	no	—
139	#217	—	2	6	no	—
140	#217	C₃×Q₈	1	4	yes	direct product factor
141	C₄⋊Dic₃	—	2	12	no	—
142	C₄×Dic₃	—	2	12	no	—
143	C₂²×C₃²	—	2	2	no	—
144	C₂²×C₃²	—	2	2	no	—
145	C₂²×C₃²	—	2	4	no	—
146	C₂²×C₃²	—	2	4	no	—
147	C₂²×C₃²	C₄×Q₈	1	4	yes	complemented
148	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
149	C₂²×C₃²	C₂²×D₄	1	2	yes	—
150	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
151	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
152	C₂²×C₃²	2₋¹⁺⁴	1	2	yes	—
153	C₃²×C₄	—	2	6	no	—
154	C₃²×C₄	C₂×C₂²⋊C₄	1	12	yes	—
155	C₃×Dic₃	—	2	4	no	—
156	C₃×Dic₃	—	4	6	no	—
157	C₂²×Q₈	—	2	8	no	—
158	C₂²×Q₈	C₃×Dic₃	1	8	yes	complemented
159	C₂²×Q₈	C₂×C₃×D₃	1	3	yes	—
160	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
161	C₂³×C₄	C₂×C₃×D₃	1	3	yes	—
162	C₄×Q₈	—	6	8	no	—
163	C₂×C₄⋊C₄	—	3	6	no	—
164	C₂×C₂²⋊C₄	—	3	1	no	—
165	C₂×C₂²⋊C₄	—	3	3	no	—
166	C₂×C₄²	—	3	6	no	—
167	#95	—	3	6	no	—
168	#95	—	3	6	no	—
169	C₂³×C₃	—	2	4	no	—
170	C₂³×C₃	—	2	4	no	—
171	C₂³×C₃	—	2	2	no	—
172	C₂³×C₃	—	2	2	no	—
173	C₂³×C₃	—	2	2	no	—
174	C₂³×C₃	—	2	2	no	—
175	C₂³×C₃	—	2	1	no	—
176	C₂³×C₃	—	2	2	no	—
177	C₂³×C₃	—	2	2	no	—
178	C₂³×C₃	—	2	2	no	—
179	C₂³×C₃	D₃×Q₈	1	2	yes	—
180	C₂³×C₃	#239	1	2	yes	—
181	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
182	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
183	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
184	C₂³×C₃	C₃×#41	1	2	yes	—
185	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
186	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
187	C₃×Q₈	—	2	48	no	—
188	C₃×Q₈	—	2	24	no	—
189	C₃×Q₈	—	2	24	no	—
190	C₃×Q₈	—	2	16	no	—
191	C₃×Q₈	#217	1	16	yes	direct product factor
192	C₃×Q₈	C₃×C₂²⋊C₄	1	16	yes	complemented
193	C₂×C₃×C₄	—	2	12	no	—
194	C₂×C₃×C₄	—	2	48	no	—
195	C₂×C₃×C₄	—	2	6	no	—
196	C₂×C₃×C₄	—	2	6	no	—
197	C₂×C₃×C₄	—	2	24	no	—
198	C₂×C₃×C₄	—	2	24	no	—
199	C₂×C₃×C₄	—	2	6	no	—
200	C₂×C₃×C₄	—	2	6	no	—
201	C₂×C₃×C₄	—	2	12	no	—
202	C₂×C₃×C₄	—	3	4	no	—
203	C₂×C₃×C₄	—	6	2	no	—
204	C₂×C₃×C₄	—	6	2	no	—
205	C₂×C₃×C₄	—	6	6	no	—
206	C₂×C₃×C₄	—	6	6	no	—
207	C₂×C₃×C₄	—	6	6	no	—
208	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
209	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
210	C₂×C₃×C₄	C₂×#67	1	12	yes	—
211	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
212	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
213	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
214	C₂×Dic₃	—	2	2	no	—
215	C₂×Dic₃	—	2	2	no	—
216	C₂×Dic₃	—	2	6	no	—
217	C₂×Dic₃	—	2	6	no	—
218	C₂×Dic₃	—	2	6	no	—
219	C₂×Dic₃	C₂×C₃×Q₈	1	4	yes	complemented
220	C₂×C₃²	—	2	4	no	—
221	C₂×C₃²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
223	C₂×C₃²	#519	1	1	yes	characteristic
224	C₂×C₃²	#548	1	2	yes	—
225	C₂×C₃²	D₄×Q₈	1	2	yes	—
226	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
227	C₂×Q₈	—	2	32	no	—
228	C₂×Q₈	—	2	12	no	—
229	C₂×Q₈	C₂×C₃×Dic₃	1	12	yes	—
230	C₂×Q₈	C₂×C₃×Dic₃	1	4	yes	—
231	C₂×Q₈	C₃×#67	1	8	yes	—
232	C₂²×C₄	—	2	12	no	—
233	C₂²×C₄	—	3	2	no	—
234	C₂²×C₄	—	3	6	no	—
235	C₂²×C₄	C₂×C₃×Dic₃	1	12	yes	—
236	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
237	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
238	C₄⋊C₄	—	6	12	no	—
239	C₂²⋊C₄	—	3	4	no	—
240	C₂²⋊C₄	—	6	6	no	—
241	C₄²	—	6	12	no	—
242	C₂²×C₃	—	2	4	no	—
243	C₂²×C₃	—	2	4	no	—
244	C₂²×C₃	—	2	8	no	—
245	C₂²×C₃	—	2	8	no	—
246	C₂²×C₃	—	2	2	no	—
247	C₂²×C₃	—	2	4	no	—
248	C₂²×C₃	—	2	4	no	—
249	C₂²×C₃	—	2	2	no	—
250	C₂²×C₃	—	2	2	no	—
251	C₂²×C₃	—	2	2	no	—
252	C₂²×C₃	—	2	4	no	—
253	C₂²×C₃	—	2	4	no	—
254	C₂²×C₃	—	2	4	no	—
255	C₂²×C₃	—	2	1	no	—
256	C₂²×C₃	—	2	1	no	—
257	C₂²×C₃	—	2	2	no	—
258	C₂²×C₃	—	2	1	no	—
259	C₂²×C₃	—	2	2	no	—
260	C₂²×C₃	Q₈×Dic₃	1	4	yes	complemented
261	C₂²×C₃	C₃×C₄×Q₈	1	4	yes	complemented
262	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
263	C₂²×C₃	C₂×#239	1	1	yes	characteristic
264	C₂²×C₃	#1007	1	2	yes	—
265	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
266	C₂²×C₃	C₂²×#67	1	2	yes	—
267	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
268	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
269	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
270	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
271	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
272	C₃×C₄	—	2	12	no	—
273	C₃×C₄	—	2	6	no	—
274	C₃×C₄	—	2	6	no	—
275	C₃×C₄	—	2	12	no	—
276	C₃×C₄	—	6	4	no	—
277	C₃×C₄	—	12	6	no	—
278	C₃×C₄	C₂×#217	1	12	yes	—
279	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	12	yes	—
280	Dic₃	—	2	4	no	—
281	Dic₃	—	4	6	no	—
282	C₃²	Q₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₃×D₃×Q₈	1	2	yes	—
286	C₂³	C₃×#239	1	2	yes	—
287	C₂³	C₂²×C₃×Dic₃	1	2	yes	—
288	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
289	Q₈	—	2	24	no	—
290	Q₈	C₃×#217	1	16	yes	direct product factor
291	C₂×C₄	—	2	6	no	—
292	C₂×C₄	—	2	24	no	—
293	C₂×C₄	—	3	4	no	—
294	C₂×C₄	—	6	2	no	—
295	C₂×C₄	—	6	2	no	—
296	C₂×C₄	—	6	6	no	—
297	C₂×C₄	—	6	6	no	—
298	C₂×C₄	—	6	6	no	—
299	C₂×C₄	C₂²×C₃×Dic₃	1	6	yes	—
300	C₂×C₄	C₂²×C₃×Dic₃	1	6	yes	—
301	C₂×C₄	C₂×C₃×#67	1	12	yes	—
302	C₂×C₃	—	2	8	no	—
303	C₂×C₃	—	2	4	no	—
304	C₂×C₃	—	2	4	no	—
305	C₂×C₃	—	2	1	no	—
306	C₂×C₃	—	2	1	no	—
307	C₂×C₃	—	2	2	no	—
308	C₂×C₃	—	2	2	no	—
309	C₂×C₃	—	2	1	no	—
310	C₂×C₃	C₂×Q₈×Dic₃	1	1	yes	characteristic
311	C₂×C₃	#5812	1	1	yes	characteristic
312	C₂×C₃	Q₈×#67	1	2	yes	—
313	C₂×C₃	#5817	1	2	yes	—
314	C₂×C₃	C₂²×#217	1	1	yes	characteristic
315	C₂×C₃	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
317	C₂×C₃	C₃×#519	1	1	yes	characteristic
318	C₂×C₃	C₃×#548	1	2	yes	—
319	C₂×C₃	C₃×D₄×Q₈	1	2	yes	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	2	no	—
324	C₂²	C₃×Q₈×Dic₃	1	4	yes	complemented
325	C₂²	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
326	C₂²	C₂×C₃×#239	1	1	yes	characteristic
327	C₂²	C₃×#1007	1	2	yes	—
328	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
329	C₂²	C₂²×C₃×#67	1	2	yes	—
330	C₄	—	2	6	no	—
331	C₄	—	6	4	no	—
332	C₄	—	12	6	no	—
333	C₄	C₂×C₃×#217	1	12	yes	—
334	C₃	—	2	1	no	—
335	C₃	Q₈×#217	1	1	yes	characteristic, direct product factor
336	C₃	C₃×Q₈×C₂²⋊C₄	1	1	yes	characteristic, complemented
337	C₂	—	2	4	no	—
338	C₂	C₂×C₃×Q₈×Dic₃	1	1	yes	characteristic
339	C₂	C₃×#5812	1	1	yes	characteristic
340	C₂	C₃×Q₈×#67	1	2	yes	—
341	C₂	C₃×#5817	1	2	yes	—
342	C₂	C₂²×C₃×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₃
Fitting	C₂³×C₃²×Q₈	C₂
socle	C₂³×C₃²	C₂⁴
prime radical	C₂⁴×C₃²	C₂³
cosocle	C₂³×C₃	C₂⁴×C₃
hypercenter	C₂³×C₃×Q₈	D₃
hypocenter	C₃	C₃×Q₈×C₂²⋊C₄
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₈×Dic₃	C₂	semidirect
3. C₃×#5229	C₂	semidirect
7. Q₈×#217	C₃	direct (N × H)
9. C₂²×C₃²×Q₈	C₄	semidirect
24. C₂×Q₈×Dic₃	C₂×C₃	semidirect
28. #5229	C₂×C₃	semidirect
44. C₃×#217	Q₈	direct (N × H)
54. C₂²×C₃×Q₈	Dic₃	semidirect
55. C₂²×C₃×Q₈	C₃×C₄	semidirect
84. C₃²×Q₈	C₂²⋊C₄	semidirect
95. C₂×C₃×Dic₃	C₂×Q₈	semidirect
140. #217	C₃×Q₈	direct (N × H)
147. C₂²×C₃²	C₄×Q₈	semidirect
158. C₂²×Q₈	C₃×Dic₃	semidirect
191. C₃×Q₈	#217	direct (N × H)
192. C₃×Q₈	C₃×C₂²⋊C₄	semidirect
219. C₂×Dic₃	C₂×C₃×Q₈	semidirect
260. C₂²×C₃	Q₈×Dic₃	semidirect
261. C₂²×C₃	C₃×C₄×Q₈	semidirect
282. C₃²	Q₈×C₂²⋊C₄	semidirect
290. Q₈	C₃×#217	direct (N × H)
324. C₂²	C₃×Q₈×Dic₃	semidirect
335. C₃	Q₈×#217	direct (N × H)
336. C₃	C₃×Q₈×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃²×Q₈	2
C₂×C₃×Q₈×Dic₃	2
C₃×#5229	2
C₃×#5212	2
C₃×C₄×#217	2
C₃×Q₈×C₂²⋊C₄	3
Q₈×#217	3

Subgroups — C3×Q8×#217 #11804879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×#217 #11804879