Subgroups — C₃²×#3285 #11770334

Order 1152.

1446 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#548	C₂	1	2	yes	maximal, complemented
4	C₃²×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#464	C₂	1	2	yes	maximal, complemented
8	C₃²×#452	C₂	1	2	yes	maximal, complemented
9	C₃²×#448	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3285	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	2	yes	—
14	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
15	C₃²×#135	—	2	4	no	—
16	C₂×C₃²×Q₁₆	—	2	4	no	—
17	C₂×C₃²×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
21	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
22	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
25	C₃²×#124	—	2	2	no	—
26	C₃²×#124	C₂²	1	2	yes	—
27	C₃²×C₂²⋊Q₈	—	2	2	no	—
28	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₃²×#121	—	2	2	no	—
30	C₃²×#121	C₂²	1	2	yes	—
31	C₃²×C₄×Q₈	C₂²	1	2	yes	—
32	C₃²×C₄×D₄	—	2	2	no	—
33	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₃²×#107	C₂²	1	1	yes	characteristic
35	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₃²×#103	C₂²	1	2	yes	—
37	C₃²×#103	C₂²	1	2	yes	—
38	C₃²×#102	C₂²	1	2	yes	—
39	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×#135	C₂×C₃	1	4	yes	complemented
43	C₂²×C₃×Q₁₆	C₂×C₃	1	4	yes	complemented
44	C₃×#548	C₂×C₃	1	8	yes	complemented
45	C₃×#495	C₂×C₃	1	4	yes	complemented
46	C₃×#467	C₂×C₃	1	4	yes	complemented
47	C₃×#466	C₂×C₃	1	4	yes	complemented
48	C₃×#464	C₂×C₃	1	8	yes	complemented
49	C₃×#452	C₂×C₃	1	8	yes	complemented
50	C₃×#448	C₂×C₃	1	8	yes	complemented
51	C₃×C₄×Q₁₆	C₂×C₃	1	4	yes	complemented
52	C₃×C₈×D₄	C₂×C₃	1	4	yes	complemented
53	C₃²×#41	—	2	4	no	—
54	C₃²×#41	—	4	2	no	—
55	C₂×C₃²×Q₈	—	2	2	no	—
56	C₂×C₃²×Q₈	—	2	4	no	—
57	C₂×C₃²×Q₈	—	4	2	no	—
58	C₂×C₃²×Q₈	C₂³	1	2	yes	—
59	C₂×C₃²×Q₈	C₂³	1	2	yes	—
60	C₂×C₃²×D₄	—	2	2	no	—
61	C₂×C₃²×D₄	—	2	2	no	—
62	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
63	C₂×C₃²×D₄	C₂³	1	2	yes	—
64	C₂²×C₃²×C₄	—	2	2	no	—
65	C₂²×C₃²×C₄	—	2	2	no	—
66	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
68	C₃²×Q₁₆	—	2	4	no	—
69	C₃²×Q₁₆	—	2	2	no	—
70	C₃²×Q₁₆	D₄	1	4	yes	complemented
71	C₃²×SD₁₆	—	2	4	no	—
72	C₃²×SD₁₆	—	4	2	no	—
73	C₃²×D₈	—	2	2	no	—
74	C₂×C₃²×C₈	—	2	2	no	—
75	C₂×C₃²×C₈	—	2	2	no	—
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	—	2	2	no	—
81	C₃²×C₄⋊C₄	—	2	2	no	—
82	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
84	C₃²×C₂²⋊C₄	—	2	2	no	—
85	C₃²×C₂²⋊C₄	—	2	2	no	—
86	C₃²×C₂²⋊C₄	—	2	2	no	—
87	C₃²×C₂²⋊C₄	—	2	2	no	—
88	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
89	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
90	C₃²×C₄²	—	2	2	no	—
91	C₃²×C₄²	C₂³	1	1	yes	characteristic
92	#3285	C₃²	1	1	yes	characteristic, direct product factor, Sylow
93	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
94	C₂²×C₃×Q₈	C₂²×C₃	1	8	yes	—
95	C₃×#135	—	2	16	no	—
96	C₂×C₃×Q₁₆	—	2	16	no	—
97	C₂×C₃×Q₁₆	C₂²×C₃	1	8	yes	—
98	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
99	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
100	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
102	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
103	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
104	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
105	C₃×#124	—	2	8	no	—
106	C₃×#124	C₂²×C₃	1	8	yes	—
107	C₃×C₂²⋊Q₈	—	2	8	no	—
108	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
109	C₃×#121	—	2	8	no	—
110	C₃×#121	C₂²×C₃	1	8	yes	—
111	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	—
112	C₃×C₄×D₄	—	2	8	no	—
113	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
114	C₃×#107	C₂²×C₃	1	4	yes	—
115	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
116	C₃×#103	C₂²×C₃	1	8	yes	—
117	C₃×#103	C₂²×C₃	1	8	yes	—
118	C₃×#102	C₂²×C₃	1	8	yes	—
119	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
120	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
121	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
122	C₂³×C₃²	—	2	2	no	—
123	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
125	C₃²×Q₈	—	2	2	no	—
126	C₃²×Q₈	—	2	2	no	—
127	C₃²×Q₈	—	2	2	no	—
128	C₃²×Q₈	—	4	4	no	—
129	C₃²×Q₈	C₂×D₄	1	4	yes	—
130	C₃²×D₄	—	2	2	no	—
131	C₃²×D₄	—	2	2	no	—
132	C₃²×D₄	—	2	2	no	—
133	C₃²×D₄	—	4	4	no	—
134	C₃²×D₄	—	4	4	no	—
135	C₂×C₃²×C₄	—	2	2	no	—
136	C₂×C₃²×C₄	—	2	1	no	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	—	2	2	no	—
141	C₂×C₃²×C₄	—	2	2	no	—
142	C₂×C₃²×C₄	—	4	4	no	—
143	C₂×C₃²×C₄	—	4	4	no	—
144	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
149	C₃²×C₈	—	2	1	no	—
150	C₃²×C₈	—	2	1	no	—
151	C₃²×C₈	—	2	1	no	—
152	C₃²×C₈	C₂×D₄	1	2	yes	—
153	C₂×#135	C₂×C₃²	1	1	yes	characteristic, complemented
154	C₂²×Q₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
155	#548	C₂×C₃²	1	2	yes	complemented
156	#495	C₂×C₃²	1	1	yes	characteristic, complemented
157	#467	C₂×C₃²	1	1	yes	characteristic, complemented
158	#466	C₂×C₃²	1	1	yes	characteristic, complemented
159	#464	C₂×C₃²	1	2	yes	complemented
160	#452	C₂×C₃²	1	2	yes	complemented
161	#448	C₂×C₃²	1	2	yes	complemented
162	C₄×Q₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
163	C₈×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
164	C₃×#41	—	2	16	no	—
165	C₃×#41	—	4	8	no	—
166	C₂×C₃×Q₈	—	2	8	no	—
167	C₂×C₃×Q₈	—	2	16	no	—
168	C₂×C₃×Q₈	—	4	8	no	—
169	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
170	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
171	C₂×C₃×D₄	—	2	8	no	—
172	C₂×C₃×D₄	—	2	8	no	—
173	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
174	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
175	C₂²×C₃×C₄	—	2	8	no	—
176	C₂²×C₃×C₄	—	2	8	no	—
177	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
178	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
179	C₃×Q₁₆	—	2	16	no	—
180	C₃×Q₁₆	—	2	8	no	—
181	C₃×Q₁₆	C₃×D₄	1	16	yes	complemented
182	C₃×SD₁₆	—	2	16	no	—
183	C₃×SD₁₆	—	4	8	no	—
184	C₃×D₈	—	2	8	no	—
185	C₂×C₃×C₈	—	2	8	no	—
186	C₂×C₃×C₈	—	2	8	no	—
187	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
188	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
189	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
190	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
191	C₃×C₄⋊C₄	—	2	8	no	—
192	C₃×C₄⋊C₄	—	2	8	no	—
193	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
194	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
195	C₃×C₂²⋊C₄	—	2	8	no	—
196	C₃×C₂²⋊C₄	—	2	8	no	—
197	C₃×C₂²⋊C₄	—	2	8	no	—
198	C₃×C₂²⋊C₄	—	2	8	no	—
199	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
200	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
201	C₃×C₄²	—	2	8	no	—
202	C₃×C₄²	C₂³×C₃	1	4	yes	—
203	C₂²×C₃²	—	2	1	no	—
204	C₂²×C₃²	—	2	1	no	—
205	C₂²×C₃²	—	2	1	no	—
206	C₂²×C₃²	—	2	1	no	—
207	C₂²×C₃²	—	2	1	no	—
208	C₂²×C₃²	—	4	2	no	—
209	C₂²×C₃²	—	4	2	no	—
210	C₂²×C₃²	—	4	2	no	—
211	C₂²×C₃²	#135	1	2	yes	complemented
212	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
213	C₃²×C₄	—	2	1	no	—
214	C₃²×C₄	—	2	1	no	—
215	C₃²×C₄	—	2	4	no	—
216	C₃²×C₄	—	2	1	no	—
217	C₃²×C₄	—	2	1	no	—
218	C₃²×C₄	—	4	2	no	—
219	C₃²×C₄	—	4	2	no	—
220	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
221	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×#41	C₂²×C₃²	1	2	yes	—
223	C₂²×Q₈	C₂²×C₃²	1	2	yes	—
224	#135	—	2	4	no	—
225	C₂×Q₁₆	—	2	4	no	—
226	C₂×Q₁₆	C₂²×C₃²	1	2	yes	—
227	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic
228	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic
229	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
230	C₂×SD₁₆	C₂²×C₃²	1	2	yes	—
231	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic
232	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
233	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
234	#124	—	2	2	no	—
235	#124	C₂²×C₃²	1	2	yes	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
238	#121	—	2	2	no	—
239	#121	C₂²×C₃²	1	2	yes	—
240	C₄×Q₈	C₂²×C₃²	1	2	yes	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
243	#107	C₂²×C₃²	1	1	yes	characteristic
244	C₄⋊C₈	C₂²×C₃²	1	1	yes	characteristic
245	#103	C₂²×C₃²	1	2	yes	—
246	#103	C₂²×C₃²	1	2	yes	—
247	#102	C₂²×C₃²	1	2	yes	—
248	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
249	C₂²⋊C₈	C₂²×C₃²	1	1	yes	characteristic
250	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
251	C₂³×C₃	—	2	8	no	—
252	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
253	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
254	C₃×Q₈	—	2	8	no	—
255	C₃×Q₈	—	2	8	no	—
256	C₃×Q₈	—	2	8	no	—
257	C₃×Q₈	—	4	16	no	—
258	C₃×Q₈	C₂×C₃×D₄	1	16	yes	—
259	C₃×D₄	—	2	8	no	—
260	C₃×D₄	—	2	8	no	—
261	C₃×D₄	—	2	8	no	—
262	C₃×D₄	—	4	16	no	—
263	C₃×D₄	—	4	16	no	—
264	C₂×C₃×C₄	—	2	8	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	2	8	no	—
270	C₂×C₃×C₄	—	2	8	no	—
271	C₂×C₃×C₄	—	4	16	no	—
272	C₂×C₃×C₄	—	4	16	no	—
273	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
274	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
275	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
276	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
277	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
278	C₃×C₈	—	2	4	no	—
279	C₃×C₈	—	2	4	no	—
280	C₃×C₈	—	2	4	no	—
281	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
282	C₂×C₃²	—	2	2	no	—
283	C₂×C₃²	—	4	1	no	—
284	C₂×C₃²	—	8	2	no	—
285	C₂×C₃²	D₄²	1	1	yes	characteristic
286	C₂×C₃²	C₂×#135	1	1	yes	characteristic
287	C₂×C₃²	#578	1	1	yes	characteristic
288	#41	—	2	4	no	—
289	#41	—	4	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	C₂³×C₃²	1	2	yes	—
294	C₂×Q₈	C₂³×C₃²	1	2	yes	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
298	C₂×D₄	C₂³×C₃²	1	2	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
303	Q₁₆	—	2	4	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	C₃²×D₄	1	4	yes	complemented
306	SD₁₆	—	2	4	no	—
307	SD₁₆	—	4	2	no	—
308	D₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
312	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
313	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
314	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	C₃²×D₄	1	1	yes	characteristic
318	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	C₃²×D₄	1	1	yes	characteristic
324	C₂²⋊C₄	C₃²×D₄	1	1	yes	characteristic
325	C₄²	—	2	2	no	—
326	C₄²	C₂³×C₃²	1	1	yes	characteristic
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	2	4	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	4	8	no	—
333	C₂²×C₃	—	4	8	no	—
334	C₂²×C₃	—	4	8	no	—
335	C₂²×C₃	C₃×#135	1	8	yes	complemented
336	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	2	4	no	—
340	C₃×C₄	—	2	4	no	—
341	C₃×C₄	—	2	16	no	—
342	C₃×C₄	—	4	8	no	—
343	C₃×C₄	—	4	8	no	—
344	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
345	C₃×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
346	C₃²	#3285	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
349	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	4	no	—
354	Q₈	C₂×C₃²×D₄	1	4	yes	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
373	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	C₂×C₃²×D₄	1	2	yes	—
378	C₂×C₃	—	2	8	no	—
379	C₂×C₃	—	4	4	no	—
380	C₂×C₃	—	8	8	no	—
381	C₂×C₃	C₃×D₄²	1	4	yes	—
382	C₂×C₃	C₂×C₃×#135	1	4	yes	—
383	C₂×C₃	C₃×#578	1	4	yes	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₃²×#135	1	2	yes	complemented
393	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
402	C₄	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
403	C₃	C₃×#3285	1	4	yes	direct product factor
404	C₂	—	2	2	no	—
405	C₂	—	4	1	no	—
406	C₂	—	8	2	no	—
407	C₂	C₃²×D₄²	1	1	yes	characteristic
408	C₂	C₂×C₃²×#135	1	1	yes	characteristic
409	C₂	C₃²×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#135	C₂	semidirect
2. C₂²×C₃²×Q₁₆	C₂	semidirect
3. C₃²×#548	C₂	semidirect
4. C₃²×#495	C₂	semidirect
5. C₃²×#467	C₂	semidirect
6. C₃²×#466	C₂	semidirect
7. C₃²×#464	C₂	semidirect
8. C₃²×#452	C₂	semidirect
9. C₃²×#448	C₂	semidirect
10. C₃²×C₄×Q₁₆	C₂	semidirect
11. C₃²×C₈×D₄	C₂	semidirect
12. C₃×#3285	C₃	direct (N × H)
42. C₂×C₃×#135	C₂×C₃	semidirect
43. C₂²×C₃×Q₁₆	C₂×C₃	semidirect
44. C₃×#548	C₂×C₃	semidirect
45. C₃×#495	C₂×C₃	semidirect
46. C₃×#467	C₂×C₃	semidirect
47. C₃×#466	C₂×C₃	semidirect
48. C₃×#464	C₂×C₃	semidirect
49. C₃×#452	C₂×C₃	semidirect
50. C₃×#448	C₂×C₃	semidirect
51. C₃×C₄×Q₁₆	C₂×C₃	semidirect
52. C₃×C₈×D₄	C₂×C₃	semidirect
70. C₃²×Q₁₆	D₄	semidirect
92. #3285	C₃²	direct (N × H)
153. C₂×#135	C₂×C₃²	semidirect
154. C₂²×Q₁₆	C₂×C₃²	semidirect
155. #548	C₂×C₃²	semidirect
156. #495	C₂×C₃²	semidirect
157. #467	C₂×C₃²	semidirect
158. #466	C₂×C₃²	semidirect
159. #464	C₂×C₃²	semidirect
160. #452	C₂×C₃²	semidirect
161. #448	C₂×C₃²	semidirect
162. C₄×Q₁₆	C₂×C₃²	semidirect
163. C₈×D₄	C₂×C₃²	semidirect
181. C₃×Q₁₆	C₃×D₄	semidirect
211. C₂²×C₃²	#135	semidirect
305. Q₁₆	C₃²×D₄	semidirect
335. C₂²×C₃	C₃×#135	semidirect
346. C₃²	#3285	direct (N × H)
392. C₂²	C₃²×#135	semidirect
403. C₃	C₃×#3285	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×#135	2
C₂²×C₃²×Q₁₆	2
C₃²×#548	2
C₃²×#495	2
C₃²×#467	2
C₃²×#466	2
C₃²×#464	2
C₃²×#452	2
C₃²×#448	2
C₃²×C₄×Q₁₆	2
C₃²×C₈×D₄	2
C₃×#3285	3

Subgroups — C32×#3285 #11770334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3285 #11770334