Subgroups — C₃×#29287 #10647894

Order 768.

756 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#2088	C₂	1	4	yes	maximal
4	C₃×#1988	C₂	1	2	yes	maximal
5	C₃×#1987	C₂	1	2	yes	maximal
6	C₃×#1948	C₂	1	2	yes	maximal
7	C₃×#1948	C₂	1	2	yes	maximal
8	C₃×#1842	C₂	1	1	yes	maximal, characteristic
9	#29287	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Q₈	—	2	1	no	—
13	C₂×C₃×C₄×Q₈	—	2	1	no	—
14	C₂×C₃×#106	C₂²	1	4	yes	—
15	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₃×#391	—	2	1	no	—
19	C₃×#391	—	2	1	no	—
20	C₃×#389	—	2	1	no	—
21	C₃×#389	—	2	1	no	—
22	C₃×#389	C₂²	1	2	yes	—
23	C₃×#389	C₂²	1	2	yes	—
24	C₃×#384	C₂²	1	1	yes	characteristic
25	C₃×#384	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₄⋊C₄	—	2	1	no	—
27	C₃×C₄×C₄⋊C₄	—	2	1	no	—
28	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
29	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
30	C₃×C₄³	C₂²	1	1	yes	characteristic
31	C₃×#340	C₂²	1	4	yes	—
32	C₃×#340	C₂²	1	4	yes	—
33	C₃×#340	C₂²	1	4	yes	—
34	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
35	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
36	#2088	C₂×C₃	1	4	yes	—
37	#1988	C₂×C₃	1	2	yes	—
38	#1987	C₂×C₃	1	2	yes	—
39	#1948	C₂×C₃	1	2	yes	—
40	#1948	C₂×C₃	1	2	yes	—
41	#1842	C₂×C₃	1	1	yes	characteristic
42	C₂²×C₃×Q₈	—	2	1	no	—
43	C₂²×C₃×Q₈	—	2	1	no	—
44	C₂²×C₃×C₈	C₂³	1	4	yes	—
45	C₃×C₄⋊Q₈	—	2	2	no	—
46	C₃×C₄⋊Q₈	—	2	2	no	—
47	C₃×C₄⋊Q₈	Q₈	1	4	yes	complemented
48	C₃×C₄⋊Q₈	Q₈	1	4	yes	complemented
49	C₃×C₄×Q₈	—	4	4	no	—
50	C₃×C₄×Q₈	—	4	4	no	—
51	C₂×C₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₃×C₄²	—	2	2	no	—
64	C₂×C₃×C₄²	—	2	2	no	—
65	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
66	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
67	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
68	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
69	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
72	C₃×#106	—	4	4	no	—
73	C₃×C₄⋊C₈	—	2	4	no	—
74	C₃×C₄⋊C₈	—	2	4	no	—
75	C₃×C₄⋊C₈	—	4	2	no	—
76	C₃×#95	—	2	2	no	—
77	C₃×#95	—	2	2	no	—
78	C₃×#95	—	2	2	no	—
79	C₃×#95	—	2	2	no	—
80	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×Q₈	—	2	1	no	—
83	C₂×C₄×Q₈	—	2	1	no	—
84	C₂×#106	C₂²×C₃	1	4	yes	—
85	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
86	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
87	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
88	#391	—	2	1	no	—
89	#391	—	2	1	no	—
90	#389	—	2	1	no	—
91	#389	—	2	1	no	—
92	#389	C₂²×C₃	1	2	yes	—
93	#389	C₂²×C₃	1	2	yes	—
94	#384	C₂²×C₃	1	1	yes	characteristic
95	#384	C₂²×C₃	1	1	yes	characteristic
96	C₄×C₄⋊C₄	—	2	1	no	—
97	C₄×C₄⋊C₄	—	2	1	no	—
98	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₄³	C₂²×C₃	1	1	yes	characteristic
101	#340	C₂²×C₃	1	4	yes	—
102	#340	C₂²×C₃	1	4	yes	—
103	#340	C₂²×C₃	1	4	yes	—
104	C₂×C₃×Q₈	—	2	4	no	—
105	C₂×C₃×Q₈	—	2	4	no	—
106	C₂×C₃×Q₈	—	4	2	no	—
107	C₂×C₃×Q₈	—	4	2	no	—
108	C₂×C₃×Q₈	—	4	2	no	—
109	C₂×C₃×Q₈	—	4	2	no	—
110	C₂²×C₃×C₄	—	2	2	no	—
111	C₂²×C₃×C₄	—	2	2	no	—
112	C₂²×C₃×C₄	—	2	2	no	—
113	C₂²×C₃×C₄	—	2	2	no	—
114	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×C₈	—	2	4	no	—
122	C₂×C₃×C₈	—	2	4	no	—
123	C₂×C₃×C₈	—	2	4	no	—
124	C₃×C₄⋊C₄	—	2	4	no	—
125	C₃×C₄⋊C₄	—	2	4	no	—
126	C₃×C₄⋊C₄	—	2	2	no	—
127	C₃×C₄⋊C₄	—	2	2	no	—
128	C₃×C₄⋊C₄	—	2	2	no	—
129	C₃×C₄⋊C₄	—	2	2	no	—
130	C₃×C₄⋊C₄	—	2	2	no	—
131	C₃×C₄⋊C₄	—	2	2	no	—
132	C₃×C₄⋊C₄	—	4	2	no	—
133	C₃×C₄⋊C₄	—	4	2	no	—
134	C₃×C₄⋊C₄	—	4	4	no	—
135	C₃×C₄⋊C₄	—	4	4	no	—
136	C₃×C₄⋊C₄	—	4	2	no	—
137	C₃×C₄⋊C₄	—	4	2	no	—
138	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
139	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
140	C₃×C₄²	—	2	2	no	—
141	C₃×C₄²	—	2	2	no	—
142	C₃×C₄²	—	2	1	no	—
143	C₃×C₄²	—	2	1	no	—
144	C₃×C₄²	—	4	1	no	—
145	C₃×C₄²	—	4	4	no	—
146	C₃×C₄²	—	4	4	no	—
147	C₃×C₄²	SD₁₆	1	4	yes	—
148	C₃×C₄²	C₂×Q₈	1	2	yes	—
149	C₃×C₄²	C₂×Q₈	1	2	yes	—
150	C₃×C₄²	#41	1	2	yes	—
151	C₃×C₄²	#41	1	2	yes	—
152	C₂²×Q₈	—	2	1	no	—
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×C₈	C₂³×C₃	1	4	yes	—
155	C₄⋊Q₈	—	2	2	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	C₃×Q₈	1	4	yes	complemented
158	C₄⋊Q₈	C₃×Q₈	1	4	yes	complemented
159	C₄×Q₈	—	4	4	no	—
160	C₄×Q₈	—	4	4	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
170	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
171	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
172	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
173	C₂×C₄²	—	2	2	no	—
174	C₂×C₄²	—	2	2	no	—
175	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
176	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
177	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
178	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
179	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
182	#106	—	4	4	no	—
183	C₄⋊C₈	—	2	4	no	—
184	C₄⋊C₈	—	2	4	no	—
185	C₄⋊C₈	—	4	2	no	—
186	#95	—	2	2	no	—
187	#95	—	2	2	no	—
188	#95	—	2	2	no	—
189	#95	—	2	2	no	—
190	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
191	C₃×Q₈	—	4	8	no	—
192	C₃×Q₈	—	4	8	no	—
193	C₂×C₃×C₄	—	2	1	no	—
194	C₂×C₃×C₄	—	2	1	no	—
195	C₂×C₃×C₄	—	2	1	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	2	1	no	—
199	C₂×C₃×C₄	—	2	4	no	—
200	C₂×C₃×C₄	—	2	4	no	—
201	C₂×C₃×C₄	—	2	1	no	—
202	C₂×C₃×C₄	—	2	1	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	4	2	no	—
205	C₂×C₃×C₄	—	4	2	no	—
206	C₂×C₃×C₄	—	4	2	no	—
207	C₂×C₃×C₄	—	4	2	no	—
208	C₂×C₃×C₄	—	4	2	no	—
209	C₂×C₃×C₄	—	4	2	no	—
210	C₂×C₃×C₄	—	4	2	no	—
211	C₂×C₃×C₄	—	4	2	no	—
212	C₂×C₃×C₄	—	4	2	no	—
213	C₂×C₃×C₄	—	4	2	no	—
214	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
215	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
216	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
217	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
218	C₂×C₃×C₄	C₂×SD₁₆	1	2	yes	—
219	C₂×C₃×C₄	C₂×SD₁₆	1	2	yes	—
220	C₂×C₃×C₄	C₂×SD₁₆	1	2	yes	—
221	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
222	C₂×C₃×C₄	#137	1	2	yes	—
223	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
227	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
229	C₃×C₈	—	4	4	no	—
230	C₂×Q₈	—	2	4	no	—
231	C₂×Q₈	—	2	4	no	—
232	C₂×Q₈	—	4	2	no	—
233	C₂×Q₈	—	4	2	no	—
234	C₂×Q₈	—	4	2	no	—
235	C₂×Q₈	—	4	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	4	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	2	4	no	—
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	2	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄⋊C₄	—	4	4	no	—
260	C₄⋊C₄	—	4	2	no	—
261	C₄⋊C₄	—	4	4	no	—
262	C₄⋊C₄	—	4	2	no	—
263	C₄⋊C₄	—	4	2	no	—
264	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
265	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
266	C₄²	—	2	2	no	—
267	C₄²	—	2	2	no	—
268	C₄²	—	2	1	no	—
269	C₄²	—	2	1	no	—
270	C₄²	—	4	1	no	—
271	C₄²	—	4	4	no	—
272	C₄²	—	4	4	no	—
273	C₄²	C₃×SD₁₆	1	4	yes	—
274	C₄²	C₂×C₃×Q₈	1	2	yes	—
275	C₄²	C₂×C₃×Q₈	1	2	yes	—
276	C₄²	C₃×#41	1	2	yes	—
277	C₄²	C₃×#41	1	2	yes	—
278	C₂²×C₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
279	C₂²×C₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
280	C₂²×C₃	#537	1	1	yes	characteristic
281	C₂²×C₃	C₂²×SD₁₆	1	1	yes	characteristic
282	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₃	C₂×#137	1	1	yes	characteristic
284	C₂²×C₃	#575	1	1	yes	characteristic
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	2	2	no	—
287	C₃×C₄	—	2	2	no	—
288	C₃×C₄	—	4	4	no	—
289	C₃×C₄	—	4	1	no	—
290	C₃×C₄	—	4	4	no	—
291	C₃×C₄	—	8	2	no	—
292	C₃×C₄	—	8	2	no	—
293	C₃×C₄	#475	1	4	yes	—
294	C₃×C₄	#476	1	4	yes	—
295	C₃×C₄	#557	1	1	yes	characteristic
296	C₃×C₄	#557	1	1	yes	characteristic
297	C₃×C₄	Q₈²	1	1	yes	characteristic
298	C₃×C₄	#559	1	1	yes	characteristic
299	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
300	Q₈	—	4	8	no	—
301	Q₈	—	4	8	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
324	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
325	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
326	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
327	C₂×C₄	C₂×C₃×SD₁₆	1	2	yes	—
328	C₂×C₄	C₂×C₃×SD₁₆	1	2	yes	—
329	C₂×C₄	C₂×C₃×SD₁₆	1	2	yes	—
330	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
331	C₂×C₄	C₃×#137	1	2	yes	—
332	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
333	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
334	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
335	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
336	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
338	C₈	—	4	4	no	—
339	C₂×C₃	#2582	1	1	yes	characteristic
340	C₂×C₃	C₂×#476	1	1	yes	characteristic
341	C₂×C₃	C₂×#475	1	1	yes	characteristic
342	C₂×C₃	#3077	1	1	yes	characteristic
343	C₂×C₃	#3078	1	1	yes	characteristic
344	C₂×C₃	#3246	1	1	yes	characteristic
345	C₂×C₃	#3254	1	1	yes	characteristic
346	C₂²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
347	C₂²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
348	C₂²	C₃×#537	1	1	yes	characteristic
349	C₂²	C₂²×C₃×SD₁₆	1	1	yes	characteristic
350	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂²	C₂×C₃×#137	1	1	yes	characteristic
352	C₂²	C₃×#575	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	4	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	C₃×#475	1	4	yes	—
362	C₄	C₃×#476	1	4	yes	—
363	C₄	C₃×#557	1	1	yes	characteristic
364	C₄	C₃×#557	1	1	yes	characteristic
365	C₄	C₃×Q₈²	1	1	yes	characteristic
366	C₄	C₃×#559	1	1	yes	characteristic
367	C₃	#29287	1	1	yes	characteristic, direct product factor, Sylow
368	C₂	C₃×#2582	1	1	yes	characteristic
369	C₂	C₂×C₃×#476	1	1	yes	characteristic
370	C₂	C₂×C₃×#475	1	1	yes	characteristic
371	C₂	C₃×#3077	1	1	yes	characteristic
372	C₂	C₃×#3078	1	1	yes	characteristic
373	C₂	C₃×#3246	1	1	yes	characteristic
374	C₂	C₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄³ ◁ G

Complements

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

N	H ≅ G/N	type
9. #29287	C₃	direct (N × H)
47. C₃×C₄⋊Q₈	Q₈	semidirect
48. C₃×C₄⋊Q₈	Q₈	semidirect
157. C₄⋊Q₈	C₃×Q₈	semidirect
158. C₄⋊Q₈	C₃×Q₈	semidirect
367. C₃	#29287	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₄⋊Q₈	2
C₃×#2088	2
C₃×#1988	2
C₃×#1987	2
C₃×#1948	2
C₃×#1842	2
#29287	3

Subgroups — C3×#29287 #10647894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#29287 #10647894