Subgroups — C₃²×#3079 #11770128

Order 1152.

1248 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₃²×#477	C₂	1	2	yes	maximal, complemented
4	C₃²×#476	C₂	1	2	yes	maximal, complemented
5	C₃²×#475	C₂	1	2	yes	maximal, complemented
6	C₃²×#474	C₂	1	2	yes	maximal, complemented
7	C₃²×#428	C₂	1	2	yes	maximal, complemented
8	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#417	C₂	1	2	yes	maximal
10	C₃×#3079	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×Q₈	—	2	1	no	—
13	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
14	C₃²×C₄⋊Q₈	—	2	1	no	—
15	C₃²×C₄⋊Q₈	—	2	1	no	—
16	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
19	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
20	C₃²×C₄×D₄	—	2	1	no	—
21	C₃²×C₄×D₄	—	2	1	no	—
22	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
24	C₃²×#117	—	2	1	no	—
25	C₃²×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
27	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃²×C₄²	—	2	1	no	—
29	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
30	C₃²×#107	C₂²	1	4	yes	—
31	C₃²×#106	C₂²	1	4	yes	—
32	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
33	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
34	C₃²×#103	C₂²	1	4	yes	—
35	C₃²×#102	C₂²	1	4	yes	—
36	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	4	yes	complemented
37	C₃×C₄×#41	C₂×C₃	1	4	yes	—
38	C₃×#477	C₂×C₃	1	8	yes	complemented
39	C₃×#476	C₂×C₃	1	8	yes	complemented
40	C₃×#475	C₂×C₃	1	8	yes	complemented
41	C₃×#474	C₂×C₃	1	8	yes	complemented
42	C₃×#428	C₂×C₃	1	8	yes	complemented
43	C₃×#423	C₂×C₃	1	4	yes	complemented
44	C₃×#417	C₂×C₃	1	8	yes	—
45	C₃²×#41	—	2	2	no	—
46	C₃²×#41	Q₈	1	4	yes	complemented
47	C₂×C₃²×Q₈	—	2	2	no	—
48	C₂×C₃²×Q₈	—	2	2	no	—
49	C₂×C₃²×Q₈	—	4	4	no	—
50	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
51	C₂×C₃²×D₄	—	2	1	no	—
52	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
53	C₂²×C₃²×C₄	—	2	1	no	—
54	C₂²×C₃²×C₄	—	2	2	no	—
55	C₂²×C₃²×C₄	—	2	1	no	—
56	C₂²×C₃²×C₄	—	2	1	no	—
57	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
58	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
59	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
60	C₃²×M₁₆	—	2	4	no	—
61	C₂×C₃²×C₈	C₂³	1	4	yes	—
62	C₃²×C₄⋊C₄	—	2	2	no	—
63	C₃²×C₄⋊C₄	—	2	2	no	—
64	C₃²×C₄⋊C₄	—	2	2	no	—
65	C₃²×C₄⋊C₄	—	2	1	no	—
66	C₃²×C₄⋊C₄	—	2	1	no	—
67	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
68	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₃²×C₂²⋊C₄	—	2	1	no	—
71	C₃²×C₂²⋊C₄	—	2	1	no	—
72	C₃²×C₂²⋊C₄	—	2	1	no	—
73	C₃²×C₄²	—	2	1	no	—
74	C₃²×C₄²	—	2	1	no	—
75	C₃²×C₄²	—	2	1	no	—
76	C₃²×C₄²	D₄	1	1	yes	characteristic
77	C₃²×C₄²	D₄	1	1	yes	characteristic
78	C₃²×C₄²	C₂³	1	1	yes	characteristic
79	C₃²×C₄²	C₂³	1	1	yes	characteristic
80	#3079	C₃²	1	1	yes	characteristic, direct product factor, Sylow
81	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
82	C₂²×C₃×Q₈	—	2	4	no	—
83	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	—
84	C₃×C₄⋊Q₈	—	2	4	no	—
85	C₃×C₄⋊Q₈	—	2	4	no	—
86	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
87	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	—
88	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
89	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
90	C₃×C₄×D₄	—	2	4	no	—
91	C₃×C₄×D₄	—	2	4	no	—
92	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
93	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
94	C₃×#117	—	2	4	no	—
95	C₃×#117	C₂²×C₃	1	4	yes	—
96	C₂×C₃×C₄⋊C₄	—	2	4	no	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
98	C₂×C₃×C₄²	—	2	4	no	—
99	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
100	C₃×#107	C₂²×C₃	1	16	yes	—
101	C₃×#106	C₂²×C₃	1	16	yes	—
102	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
103	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
104	C₃×#103	C₂²×C₃	1	16	yes	—
105	C₃×#102	C₂²×C₃	1	16	yes	—
106	C₂³×C₃²	—	2	1	no	—
107	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
108	C₃²×Q₈	—	2	1	no	—
109	C₃²×Q₈	—	4	4	no	—
110	C₃²×Q₈	—	4	4	no	—
111	C₃²×Q₈	C₂×Q₈	1	2	yes	complemented
112	C₃²×D₄	—	2	4	no	—
113	C₃²×D₄	—	2	1	no	—
114	C₃²×D₄	C₂×Q₈	1	2	yes	complemented
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	4	no	—
117	C₂×C₃²×C₄	—	2	2	no	—
118	C₂×C₃²×C₄	—	2	2	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	—	4	4	no	—
123	C₂×C₃²×C₄	—	4	2	no	—
124	C₂×C₃²×C₄	—	4	2	no	—
125	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
131	C₂×C₃²×C₄	#41	1	2	yes	—
132	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
133	C₃²×C₈	—	2	4	no	—
134	C₂×C₄⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
135	C₄×#41	C₂×C₃²	1	1	yes	characteristic
136	#477	C₂×C₃²	1	2	yes	complemented
137	#476	C₂×C₃²	1	2	yes	complemented
138	#475	C₂×C₃²	1	2	yes	complemented
139	#474	C₂×C₃²	1	2	yes	complemented
140	#428	C₂×C₃²	1	2	yes	complemented
141	#423	C₂×C₃²	1	1	yes	characteristic, complemented
142	#417	C₂×C₃²	1	2	yes	—
143	C₃×#41	—	2	8	no	—
144	C₃×#41	C₃×Q₈	1	16	yes	complemented
145	C₂×C₃×Q₈	—	2	8	no	—
146	C₂×C₃×Q₈	—	2	8	no	—
147	C₂×C₃×Q₈	—	4	16	no	—
148	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
149	C₂×C₃×D₄	—	2	4	no	—
150	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	8	no	—
153	C₂²×C₃×C₄	—	2	4	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
156	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
158	C₃×M₁₆	—	2	16	no	—
159	C₂×C₃×C₈	C₂³×C₃	1	16	yes	—
160	C₃×C₄⋊C₄	—	2	8	no	—
161	C₃×C₄⋊C₄	—	2	8	no	—
162	C₃×C₄⋊C₄	—	2	8	no	—
163	C₃×C₄⋊C₄	—	2	4	no	—
164	C₃×C₄⋊C₄	—	2	4	no	—
165	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
166	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
167	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
168	C₃×C₂²⋊C₄	—	2	4	no	—
169	C₃×C₂²⋊C₄	—	2	4	no	—
170	C₃×C₂²⋊C₄	—	2	4	no	—
171	C₃×C₄²	—	2	4	no	—
172	C₃×C₄²	—	2	4	no	—
173	C₃×C₄²	—	2	4	no	—
174	C₃×C₄²	C₃×D₄	1	4	yes	—
175	C₃×C₄²	C₃×D₄	1	4	yes	—
176	C₃×C₄²	C₂³×C₃	1	4	yes	—
177	C₃×C₄²	C₂³×C₃	1	4	yes	—
178	C₂²×C₃²	—	2	1	no	—
179	C₂²×C₃²	—	2	1	no	—
180	C₂²×C₃²	—	2	2	no	—
181	C₂²×C₃²	—	4	1	no	—
182	C₂²×C₃²	—	4	1	no	—
183	C₂²×C₃²	C₂²⋊Q₈	1	2	yes	—
184	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
185	C₃²×C₄	—	2	2	no	—
186	C₃²×C₄	—	2	1	no	—
187	C₃²×C₄	—	2	1	no	—
188	C₃²×C₄	—	4	1	no	—
189	C₃²×C₄	—	4	4	no	—
190	C₃²×C₄	—	4	1	no	—
191	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
192	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
193	C₃²×C₄	#137	1	2	yes	—
194	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
195	C₃²×C₄	C₂×#41	1	1	yes	characteristic
196	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
197	C₂²×Q₈	—	2	1	no	—
198	C₂×M₁₆	C₂²×C₃²	1	2	yes	—
199	C₄⋊Q₈	—	2	1	no	—
200	C₄⋊Q₈	—	2	1	no	—
201	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
202	C₄⋊Q₈	C₂²×C₃²	1	2	yes	—
203	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
204	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic
205	C₄×D₄	—	2	1	no	—
206	C₄×D₄	—	2	1	no	—
207	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
208	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
209	#117	—	2	1	no	—
210	#117	C₂²×C₃²	1	1	yes	characteristic
211	C₂×C₄⋊C₄	—	2	1	no	—
212	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
215	#107	C₂²×C₃²	1	4	yes	—
216	#106	C₂²×C₃²	1	4	yes	—
217	C₄⋊C₈	C₂²×C₃²	1	2	yes	—
218	C₄⋊C₈	C₂²×C₃²	1	2	yes	—
219	#103	C₂²×C₃²	1	4	yes	—
220	#102	C₂²×C₃²	1	4	yes	—
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
223	C₃×Q₈	—	2	4	no	—
224	C₃×Q₈	—	4	16	no	—
225	C₃×Q₈	—	4	16	no	—
226	C₃×Q₈	C₂×C₃×Q₈	1	8	yes	complemented
227	C₃×D₄	—	2	16	no	—
228	C₃×D₄	—	2	4	no	—
229	C₃×D₄	C₂×C₃×Q₈	1	8	yes	complemented
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	16	no	—
232	C₂×C₃×C₄	—	2	8	no	—
233	C₂×C₃×C₄	—	2	8	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	16	no	—
237	C₂×C₃×C₄	—	4	16	no	—
238	C₂×C₃×C₄	—	4	8	no	—
239	C₂×C₃×C₄	—	4	8	no	—
240	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
241	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
242	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
243	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
244	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
245	C₂×C₃×C₄	C₂×C₃×Q₈	1	8	yes	—
246	C₂×C₃×C₄	C₃×#41	1	8	yes	—
247	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
248	C₃×C₈	—	2	16	no	—
249	C₂×C₃²	—	2	2	no	—
250	C₂×C₃²	—	4	2	no	—
251	C₂×C₃²	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂×C₃²	C₂×#137	1	1	yes	characteristic
254	#41	—	2	2	no	—
255	#41	C₃²×Q₈	1	4	yes	complemented
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	4	4	no	—
259	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
267	C₂²×C₄	C₃²×D₄	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
269	M₁₆	—	2	4	no	—
270	C₂×C₈	C₂³×C₃²	1	4	yes	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
277	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
278	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	1	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	C₃²×D₄	1	1	yes	characteristic
286	C₄²	C₃²×D₄	1	1	yes	characteristic
287	C₄²	C₂³×C₃²	1	1	yes	characteristic
288	C₄²	C₂³×C₃²	1	1	yes	characteristic
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	4	no	—
291	C₂²×C₃	—	2	8	no	—
292	C₂²×C₃	—	4	4	no	—
293	C₂²×C₃	—	4	4	no	—
294	C₂²×C₃	C₃×C₂²⋊Q₈	1	8	yes	—
295	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	2	8	no	—
299	C₃×C₄	—	4	16	no	—
300	C₃×C₄	—	4	4	no	—
301	C₃×C₄	—	4	4	no	—
302	C₃×C₄	C₃×C₂²⋊Q₈	1	8	yes	—
303	C₃×C₄	C₃×AGL(1,ℤ/8)	1	8	yes	—
304	C₃×C₄	C₃×#137	1	8	yes	—
305	C₃×C₄	C₂²×C₃×Q₈	1	4	yes	—
306	C₃×C₄	C₂×C₃×#41	1	4	yes	—
307	C₃²	#3079	1	1	yes	characteristic, direct product factor, Sylow
308	C₂³	—	2	1	no	—
309	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
310	Q₈	—	2	1	no	—
311	Q₈	—	4	4	no	—
312	Q₈	—	4	4	no	—
313	Q₈	C₂×C₃²×Q₈	1	2	yes	complemented
314	D₄	—	2	4	no	—
315	D₄	—	2	1	no	—
316	D₄	C₂×C₃²×Q₈	1	2	yes	complemented
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
328	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₃²×Q₈	1	2	yes	—
333	C₂×C₄	C₃²×#41	1	2	yes	—
334	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
335	C₈	—	2	4	no	—
336	C₂×C₃	—	2	8	no	—
337	C₂×C₃	—	4	8	no	—
338	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	4	yes	—
339	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	—
340	C₂×C₃	C₂×C₃×#137	1	4	yes	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	C₃²×C₂²⋊Q₈	1	2	yes	—
347	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	1	no	—
353	C₄	—	4	1	no	—
354	C₄	C₃²×C₂²⋊Q₈	1	2	yes	—
355	C₄	C₃²×AGL(1,ℤ/8)	1	2	yes	—
356	C₄	C₃²×#137	1	2	yes	—
357	C₄	C₂²×C₃²×Q₈	1	1	yes	characteristic
358	C₄	C₂×C₃²×#41	1	1	yes	characteristic
359	C₃	C₃×#3079	1	4	yes	direct product factor
360	C₂	—	2	2	no	—
361	C₂	—	4	2	no	—
362	C₂	C₂×C₃²×C₂²⋊Q₈	1	1	yes	characteristic
363	C₂	C₂×C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂	C₂×C₃²×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₂×C₃²×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄⋊Q₈	C₂	semidirect
3. C₃²×#477	C₂	semidirect
4. C₃²×#476	C₂	semidirect
5. C₃²×#475	C₂	semidirect
6. C₃²×#474	C₂	semidirect
7. C₃²×#428	C₂	semidirect
8. C₃²×#423	C₂	semidirect
10. C₃×#3079	C₃	direct (N × H)
36. C₂×C₃×C₄⋊Q₈	C₂×C₃	semidirect
38. C₃×#477	C₂×C₃	semidirect
39. C₃×#476	C₂×C₃	semidirect
40. C₃×#475	C₂×C₃	semidirect
41. C₃×#474	C₂×C₃	semidirect
42. C₃×#428	C₂×C₃	semidirect
43. C₃×#423	C₂×C₃	semidirect
46. C₃²×#41	Q₈	semidirect
80. #3079	C₃²	direct (N × H)
111. C₃²×Q₈	C₂×Q₈	semidirect
114. C₃²×D₄	C₂×Q₈	semidirect
134. C₂×C₄⋊Q₈	C₂×C₃²	semidirect
136. #477	C₂×C₃²	semidirect
137. #476	C₂×C₃²	semidirect
138. #475	C₂×C₃²	semidirect
139. #474	C₂×C₃²	semidirect
140. #428	C₂×C₃²	semidirect
141. #423	C₂×C₃²	semidirect
144. C₃×#41	C₃×Q₈	semidirect
226. C₃×Q₈	C₂×C₃×Q₈	semidirect
229. C₃×D₄	C₂×C₃×Q₈	semidirect
255. #41	C₃²×Q₈	semidirect
307. C₃²	#3079	direct (N × H)
313. Q₈	C₂×C₃²×Q₈	semidirect
316. D₄	C₂×C₃²×Q₈	semidirect
359. C₃	C₃×#3079	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄⋊Q₈	2
C₃²×C₄×#41	2
C₃²×#477	2
C₃²×#476	2
C₃²×#475	2
C₃²×#474	2
C₃²×#428	2
C₃²×#423	2
C₃²×#417	2
C₃×#3079	3

Subgroups — C32×#3079 #11770128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3079 #11770128