Subgroups — C₂×C₃×D₃×#108 #11858607

Order 1152.

1013 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#822	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₃×#108	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₃×#108	—	3	1	no	maximal
8	C₂×D₃×#108	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₃×D₃×M₁₆	—	2	4	no	—
15	C₃×D₃×M₁₆	C₂²	1	8	yes	—
16	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
17	C₂×C₃×D₃×C₈	—	2	2	no	—
18	C₂×C₃×D₃×C₈	C₄	1	2	yes	—
19	C₂×C₃×D₃×C₈	C₄	1	4	yes	—
20	C₂×C₃×D₃×C₈	C₄	1	2	yes	—
21	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
22	C₃²×#108	C₂²	1	4	yes	complemented
23	C₃×#822	C₂²	1	8	yes	complemented
24	C₃×#819	C₂²	1	4	yes	complemented
25	C₂²×C₃×M₁₆	—	3	2	no	—
26	C₂³×C₃×C₈	—	3	1	no	—
27	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
28	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#108	—	2	1	no	—
30	C₂×C₃×#108	—	3	2	no	—
31	C₂×C₃×#108	—	3	1	no	—
32	C₂×C₃×#108	—	3	8	no	—
33	C₂×C₃×#108	D₃	1	1	yes	characteristic, direct product factor
34	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#822	C₂×C₃	1	2	yes	complemented
36	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
37	D₃×#108	C₂×C₃	1	8	yes	direct product factor
38	C₂³×C₃×D₃	Q₈	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₃	Q₈	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
47	C₂×C₃×C₄×D₃	Q₈	1	2	yes	—
48	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
49	C₃²×M₁₆	—	2	2	no	—
50	C₃²×M₁₆	C₂³	1	4	yes	—
51	C₂×C₃²×C₈	—	2	2	no	—
52	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
53	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
54	C₂×C₃²×C₈	C₂³	1	2	yes	—
55	C₃×#208	—	2	2	no	—
56	C₃×#208	C₂³	1	4	yes	—
57	C₂×C₃×C₃⋊C₈	—	2	2	no	—
58	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
61	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
62	C₃×D₃×C₈	—	2	8	no	—
63	C₃×D₃×C₈	C₂×C₄	1	8	yes	—
64	C₃×D₃×C₈	C₂×C₄	1	8	yes	—
65	C₂²×#108	—	3	1	no	Sylow
66	C₂³×C₃×C₄	—	3	1	no	—
67	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×M₁₆	—	2	2	no	—
69	C₂×C₃×M₁₆	—	3	2	no	—
70	C₂×C₃×M₁₆	—	3	8	no	—
71	C₂×C₃×M₁₆	—	6	2	no	—
72	C₂×C₃×M₁₆	—	6	4	no	—
73	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
74	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
75	C₂²×C₃×C₈	—	2	1	no	—
76	C₂²×C₃×C₈	—	3	1	no	—
77	C₂²×C₃×C₈	—	3	2	no	—
78	C₂²×C₃×C₈	—	3	2	no	—
79	C₂²×C₃×C₈	—	3	4	no	—
80	C₂²×C₃×C₈	—	3	4	no	—
81	C₂²×C₃×C₈	—	6	2	no	—
82	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×#208	C₂²×C₃	1	2	yes	—
85	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
86	D₃×M₁₆	—	2	4	no	—
87	D₃×M₁₆	C₂²×C₃	1	8	yes	—
88	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
89	C₂×D₃×C₈	—	2	2	no	—
90	C₂×D₃×C₈	C₃×C₄	1	2	yes	—
91	C₂×D₃×C₈	C₃×C₄	1	4	yes	—
92	C₂×D₃×C₈	C₃×C₄	1	2	yes	—
93	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
94	C₃×#108	—	2	4	no	—
95	C₃×#108	—	3	8	no	—
96	C₃×#108	—	3	4	no	—
97	C₃×#108	C₂×D₃	1	4	yes	direct product factor
98	C₃×#108	C₂²×C₃	1	4	yes	complemented
99	#822	C₂²×C₃	1	8	yes	complemented
100	#819	C₂²×C₃	1	4	yes	complemented
101	C₂³×C₃²	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₃×D₃	—	2	4	no	—
103	C₂²×C₃×D₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
105	C₂²×C₃×D₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×D₃	C₂×Q₈	1	2	yes	—
107	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
113	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
114	C₂×C₃×Dic₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₃×Dic₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₃×Dic₃	C₂×Q₈	1	2	yes	—
117	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
118	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
119	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
120	C₃×C₄×D₃	C₄⋊C₄	1	2	yes	—
121	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
122	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
123	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
124	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
125	C₃²×C₈	—	2	4	no	—
126	C₃²×C₈	C₂²×C₄	1	4	yes	—
127	C₃×C₃⋊C₈	—	2	4	no	—
128	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
129	C₂²×M₁₆	—	3	2	no	—
130	C₂³×C₈	—	3	1	no	—
131	C₂×#108	—	3	2	no	—
132	C₂×#108	—	3	1	no	—
133	C₂×#108	—	3	8	no	—
134	C₂×#108	C₃×D₃	1	1	yes	characteristic, direct product factor
135	C₂⁴×C₃	—	3	1	no	—
136	C₂³×D₃	C₃×Q₈	1	1	yes	characteristic
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	3	1	no	—
139	C₂²×C₃×C₄	—	3	1	no	—
140	C₂²×C₃×C₄	—	3	2	no	—
141	C₂²×C₃×C₄	—	3	1	no	—
142	C₂²×C₃×C₄	—	3	2	no	—
143	C₂²×C₃×C₄	—	3	1	no	—
144	C₂²×C₃×C₄	—	3	1	no	—
145	C₂²×C₃×C₄	—	3	2	no	—
146	C₂²×C₃×C₄	—	3	2	no	—
147	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂²×Dic₃	C₃×Q₈	1	1	yes	characteristic
150	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
151	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
154	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
155	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
156	C₂×C₄×D₃	C₃×Q₈	1	2	yes	—
157	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
158	C₃×M₁₆	—	2	2	no	—
159	C₃×M₁₆	—	2	2	no	—
160	C₃×M₁₆	—	2	4	no	—
161	C₃×M₁₆	—	3	4	no	—
162	C₃×M₁₆	—	4	2	no	—
163	C₃×M₁₆	—	6	8	no	—
164	C₃×M₁₆	—	6	2	no	—
165	C₃×M₁₆	C₂²×D₃	1	4	yes	—
166	C₃×M₁₆	C₂³×C₃	1	4	yes	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	3	2	no	—
173	C₂×C₃×C₈	—	3	2	no	—
174	C₂×C₃×C₈	—	3	2	no	—
175	C₂×C₃×C₈	—	3	8	no	—
176	C₂×C₃×C₈	—	3	8	no	—
177	C₂×C₃×C₈	—	4	2	no	—
178	C₂×C₃×C₈	—	6	8	no	—
179	C₂×C₃×C₈	—	6	2	no	—
180	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
181	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
182	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
183	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
184	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
185	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
186	#208	—	2	2	no	—
187	#208	C₂³×C₃	1	4	yes	—
188	C₂×C₃⋊C₈	—	2	2	no	—
189	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
190	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
191	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
192	ΓL(1,𝔽₂₅)	—	2	8	no	—
193	D₃×C₈	—	2	8	no	—
194	D₃×C₈	C₂×C₃×C₄	1	8	yes	—
195	D₃×C₈	C₂×C₃×C₄	1	8	yes	—
196	C₂²×C₃²	—	2	2	no	—
197	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₃×D₃	—	2	2	no	—
201	C₂×C₃×D₃	—	2	4	no	—
202	C₂×C₃×D₃	—	2	4	no	—
203	C₂×C₃×D₃	#108	1	4	yes	direct product factor
204	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
206	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
209	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
210	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
211	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
212	C₂³×C₄	—	3	1	no	—
213	C₂×M₁₆	—	3	2	no	—
214	C₂×M₁₆	—	3	8	no	—
215	C₂×M₁₆	—	6	2	no	—
216	C₂×M₁₆	—	6	4	no	—
217	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
218	C₂²×C₈	—	3	1	no	—
219	C₂²×C₈	—	3	2	no	—
220	C₂²×C₈	—	3	4	no	—
221	C₂²×C₈	—	3	2	no	—
222	C₂²×C₈	—	3	4	no	—
223	C₂²×C₈	—	6	2	no	—
224	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
225	#108	—	3	8	no	—
226	#108	—	3	4	no	—
227	#108	C₂×C₃×D₃	1	4	yes	direct product factor
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	3	1	no	—
230	C₂³×C₃	—	3	2	no	—
231	C₂³×C₃	—	3	1	no	—
232	C₂³×C₃	—	3	2	no	—
233	C₂³×C₃	—	6	4	no	—
234	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
235	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
236	C₂²×D₃	—	2	4	no	—
237	C₂²×D₃	C₃×C₄⋊C₄	1	1	yes	characteristic
238	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
239	C₂²×D₃	C₃×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×D₃	C₂×C₃×Q₈	1	2	yes	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	3	1	no	—
249	C₂×C₃×C₄	—	3	1	no	—
250	C₂×C₃×C₄	—	3	2	no	—
251	C₂×C₃×C₄	—	3	2	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	2	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	3	2	no	—
256	C₂×C₃×C₄	—	3	2	no	—
257	C₂×C₃×C₄	—	3	2	no	—
258	C₂×C₃×C₄	—	3	2	no	—
259	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
271	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
272	C₂×Dic₃	C₃×C₄⋊C₄	1	1	yes	characteristic
273	C₂×Dic₃	C₃×C₄⋊C₄	1	1	yes	characteristic
274	C₂×Dic₃	C₂×C₃×Q₈	1	2	yes	—
275	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
276	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
277	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
278	C₄×D₃	C₃×C₄⋊C₄	1	2	yes	—
279	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
280	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
281	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
282	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
283	C₃×C₈	—	2	4	no	—
284	C₃×C₈	—	2	4	no	—
285	C₃×C₈	—	2	4	no	—
286	C₃×C₈	—	3	4	no	—
287	C₃×C₈	—	4	4	no	—
288	C₃×C₈	—	6	4	no	—
289	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
290	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
291	C₃⋊C₈	—	2	4	no	—
292	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
293	C₂×C₃²	—	2	1	no	—
294	C₂×C₃²	—	2	1	no	—
295	C₂×C₃²	C₂×#108	1	2	yes	complemented
296	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
297	C₃×D₃	—	2	2	no	—
298	C₃×D₃	C₂×#108	1	4	yes	direct product factor
299	C₂⁴	—	3	1	no	—
300	C₂²×C₄	—	3	1	no	—
301	C₂²×C₄	—	3	2	no	—
302	C₂²×C₄	—	3	1	no	—
303	C₂²×C₄	—	3	2	no	—
304	C₂²×C₄	—	3	1	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	—	3	2	no	—
307	C₂²×C₄	—	3	1	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
310	M₁₆	—	2	2	no	—
311	M₁₆	—	3	4	no	—
312	M₁₆	—	6	8	no	—
313	M₁₆	—	6	2	no	—
314	M₁₆	C₂²×C₃×D₃	1	4	yes	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	3	2	no	—
317	C₂×C₈	—	3	2	no	—
318	C₂×C₈	—	3	2	no	—
319	C₂×C₈	—	3	8	no	—
320	C₂×C₈	—	3	8	no	—
321	C₂×C₈	—	6	8	no	—
322	C₂×C₈	—	6	2	no	—
323	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
324	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
325	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	3	4	no	—
332	C₂²×C₃	—	3	2	no	—
333	C₂²×C₃	—	3	2	no	—
334	C₂²×C₃	—	4	2	no	—
335	C₂²×C₃	—	6	4	no	—
336	C₂²×C₃	—	6	4	no	—
337	C₂²×C₃	—	6	2	no	—
338	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
339	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
340	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
341	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
342	C₂²×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
343	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
344	C₂×D₃	—	2	2	no	—
345	C₂×D₃	—	2	4	no	—
346	C₂×D₃	—	2	4	no	—
347	C₂×D₃	C₃×#108	1	4	yes	direct product factor
348	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
349	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	3	2	no	—
355	C₃×C₄	—	3	2	no	—
356	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
357	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
358	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
359	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
360	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
361	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
362	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
363	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
364	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
365	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
366	C₃²	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
367	C₂³	—	3	1	no	—
368	C₂³	—	3	2	no	—
369	C₂³	—	3	1	no	—
370	C₂³	—	3	2	no	—
371	C₂³	—	6	4	no	—
372	C₂³	C₃×D₃×Q₈	1	1	yes	characteristic
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	3	1	no	—
375	C₂×C₄	—	3	1	no	—
376	C₂×C₄	—	3	2	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	3	2	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	3	2	no	—
382	C₂×C₄	—	3	2	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
387	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
388	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
389	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
390	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	3	4	no	—
393	C₈	—	6	4	no	—
394	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	3	4	no	—
402	C₂×C₃	—	4	1	no	—
403	C₂×C₃	—	4	1	no	—
404	C₂×C₃	—	6	2	no	—
405	C₂×C₃	D₃×#108	1	2	yes	direct product factor
406	C₂×C₃	C₂×C₃×#108	1	2	yes	complemented
407	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
408	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
409	D₃	—	2	2	no	—
410	D₃	C₂×C₃×#108	1	4	yes	direct product factor
411	C₂²	—	2	2	no	—
412	C₂²	—	3	2	no	—
413	C₂²	—	3	4	no	—
414	C₂²	—	3	2	no	—
415	C₂²	—	6	4	no	—
416	C₂²	—	6	4	no	—
417	C₂²	—	6	2	no	—
418	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
419	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
420	C₂²	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
421	C₄	—	3	2	no	—
422	C₄	—	3	2	no	—
423	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
424	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
425	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
426	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
427	C₃	—	2	1	no	—
428	C₃	C₂×D₃×#108	1	1	yes	characteristic, direct product factor
429	C₃	C₂²×C₃×#108	1	1	yes	characteristic, complemented
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	3	4	no	—
433	C₂	—	6	2	no	—
434	C₂	C₃×D₃×#108	1	2	yes	direct product factor
435	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₃	Q₈
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₂²×C₃×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
3. C₂×C₃²×#108	C₂	semidirect
4. C₂×C₃×#822	C₂	semidirect
5. C₂×C₃×#819	C₂	semidirect
6. C₃×D₃×#108	C₂	direct (N × H)
8. C₂×D₃×#108	C₃	direct (N × H)
22. C₃²×#108	C₂²	semidirect
23. C₃×#822	C₂²	semidirect
24. C₃×#819	C₂²	semidirect
33. C₂×C₃×#108	D₃	direct (N × H)
34. C₂×C₃×#108	C₂×C₃	semidirect
35. C₂×#822	C₂×C₃	semidirect
36. C₂×#819	C₂×C₃	semidirect
37. D₃×#108	C₂×C₃	direct (N × H)
97. C₃×#108	C₂×D₃	direct (N × H)
98. C₃×#108	C₂²×C₃	semidirect
99. #822	C₂²×C₃	semidirect
100. #819	C₂²×C₃	semidirect
134. C₂×#108	C₃×D₃	direct (N × H)
203. C₂×C₃×D₃	#108	direct (N × H)
227. #108	C₂×C₃×D₃	direct (N × H)
295. C₂×C₃²	C₂×#108	semidirect
298. C₃×D₃	C₂×#108	direct (N × H)
347. C₂×D₃	C₃×#108	direct (N × H)
366. C₃²	C₂²×#108	semidirect
405. C₂×C₃	D₃×#108	direct (N × H)
406. C₂×C₃	C₂×C₃×#108	semidirect
410. D₃	C₂×C₃×#108	direct (N × H)
428. C₃	C₂×D₃×#108	direct (N × H)
429. C₃	C₂²×C₃×#108	semidirect
434. C₂	C₃×D₃×#108	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×C₃×D₃×M₁₆	2
C₂²×C₃×D₃×C₈	2
C₂×C₃²×#108	2
C₂×C₃×#822	2
C₂×C₃×#819	2
C₃×D₃×#108	2
C₂²×C₃×#108	3
C₂×D₃×#108	3

Subgroups — C2×C3×D3×#108 #11858607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×#108 #11858607