Subgroups — #13179764

Order 1728.

3472 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11723988	C₂	1	1	yes	maximal, characteristic, complemented
3	#11723987	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#6312	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88859	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723939	C₂	1	1	yes	maximal, characteristic, complemented
7	#11723939	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723935	C₂	1	1	yes	maximal, characteristic, complemented
9	#11723935	C₂	1	1	yes	maximal, characteristic, complemented
10	#11723934	C₂	1	1	yes	maximal, characteristic, complemented
11	#11723933	C₂	1	1	yes	maximal, characteristic, complemented
12	#11723927	C₂	1	1	yes	maximal, characteristic, complemented
13	#11723923	C₂	1	1	yes	maximal, characteristic
14	C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
15	#11723918	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596108	—	3	13	no	maximal
17	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
18	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
20	C₂×#6312	C₂²	1	1	yes	characteristic
21	C₂²×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
27	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	#88864	C₂²	1	1	yes	characteristic
33	#88859	C₂²	1	1	yes	characteristic
34	#88859	C₂²	1	1	yes	characteristic
35	#88859	C₂²	1	1	yes	characteristic
36	#88859	C₂²	1	1	yes	characteristic
37	#88859	C₂²	1	1	yes	characteristic
38	#88859	C₂²	1	1	yes	characteristic
39	#88859	C₂²	1	1	yes	characteristic
40	#88859	C₂²	1	1	yes	characteristic
41	#88859	C₂²	1	1	yes	characteristic, complemented
42	#88859	C₂²	1	1	yes	characteristic, complemented
43	#88859	C₂²	1	1	yes	characteristic, complemented
44	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	1	1	yes	characteristic, complemented
46	#88857	C₂²	1	1	yes	characteristic, complemented
47	#88857	C₂²	1	1	yes	characteristic, complemented
48	#88857	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
52	C₃²×C₂²⋊Q₈	D₃	1	13	yes	complemented
53	#64156	—	3	13	no	—
54	#64155	—	3	13	no	—
55	C₄×#638	—	3	13	no	—
56	C₂×#3752	—	3	13	no	—
57	#64107	—	3	13	no	—
58	#64107	—	3	13	no	—
59	#64103	—	3	13	no	—
60	#64103	—	3	13	no	—
61	#64102	—	3	13	no	—
62	#64101	—	3	13	no	—
63	#64095	—	3	13	no	—
64	#64091	—	3	13	no	—
65	C₂²⋊C₄×C₃⋊D₃	—	3	13	no	—
66	#64086	—	3	13	no	—
67	C₂³×C₃³	C₂³	1	1	yes	characteristic
68	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
69	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
70	C₂²×C₃⋊(C₃⋊D₃)	—	4	1	no	—
71	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
72	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
73	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
74	C₃³×Q₈	—	4	1	no	—
75	C₂×C₃³×C₄	—	4	1	no	—
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
78	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
79	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
80	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
81	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
82	#6312	—	2	2	no	—
83	C₂×C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
84	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
85	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
86	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
87	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
88	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	1	yes	characteristic
89	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
90	C₄⋊(C₃⋊(C₃⋊D₃))	—	4	1	no	—
91	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
92	C₄×C₃⋊(C₃⋊D₃)	—	4	1	no	—
93	C₄×C₃⋊(C₃⋊D₃)	—	4	1	no	—
94	#5637	—	9	13	no	—
95	C₂³×C₃⋊D₃	—	3	13	no	—
96	C₂×C₃²×Q₈	C₂×D₃	1	13	yes	complemented
97	C₂²×C₃²×C₄	C₂×D₃	1	13	yes	—
98	C₂×#638	—	3	13	no	—
99	C₂²×C₃⋊Dic₃	—	3	13	no	—
100	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
101	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
102	C₂×C₄×C₃⋊D₃	—	3	13	no	—
103	C₂×C₄×C₃⋊D₃	—	3	13	no	—
104	C₂×C₄×C₃⋊D₃	—	3	13	no	—
105	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
106	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
107	C₃²×C₄⋊C₄	C₂×D₃	1	13	yes	complemented
108	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
109	C₃²×C₂²⋊C₄	C₂×D₃	1	13	yes	—
110	#3757	—	3	13	no	—
111	#3752	—	3	13	no	—
112	#3752	—	3	13	no	—
113	#3752	—	3	13	no	—
114	#3752	—	3	13	no	—
115	#3752	—	3	13	no	—
116	#3752	—	3	13	no	—
117	#3752	—	3	13	no	—
118	#3752	—	3	13	no	—
119	#3752	—	3	13	no	—
120	#3752	—	3	13	no	—
121	#3752	—	3	13	no	—
122	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
123	C₄⋊(C₃⋊Dic₃)	—	3	13	no	—
124	#3750	—	3	13	no	—
125	#3750	—	3	13	no	—
126	#3750	—	3	13	no	—
127	C₄×C₃⋊Dic₃	—	3	13	no	—
128	C₄×C₃⋊Dic₃	—	3	13	no	—
129	C₄×C₃⋊Dic₃	—	3	13	no	—
130	C₂²×C₃³	—	2	1	no	—
131	C₂²×C₃³	—	2	1	no	—
132	C₂²×C₃³	#41	1	2	yes	—
133	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
134	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
135	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
136	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
137	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
138	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
139	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
140	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
141	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
142	C₂×C₃⋊(C₃⋊D₃)	—	4	4	no	—
143	C₂×C₃⋊(C₃⋊D₃)	#41	1	2	yes	—
144	C₃³×C₄	—	2	1	no	—
145	C₃³×C₄	—	2	1	no	—
146	C₃³×C₄	—	2	1	no	—
147	C₃³×C₄	—	2	1	no	—
148	C₃³×C₄	—	2	1	no	—
149	C₃³×C₄	—	2	1	no	—
150	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
151	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
152	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
153	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
154	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
155	C₃×C₂²⋊Q₈	C₃⋊D₃	1	13	yes	complemented
156	#947	—	9	13	no	—
157	#946	—	9	13	no	—
158	C₄×#67	—	9	13	no	—
159	C₂×(C₂×D₃)⋊C₄	—	9	13	no	—
160	#898	—	9	13	no	—
161	#898	—	9	13	no	—
162	#894	—	9	13	no	—
163	#894	—	9	13	no	—
164	#893	—	9	13	no	—
165	#892	—	9	13	no	—
166	#886	—	9	13	no	—
167	#882	—	9	13	no	—
168	D₃×C₂²⋊C₄	—	9	13	no	—
169	#877	—	9	13	no	—
170	C₂³×C₃²	C₂²×D₃	1	13	yes	—
171	C₂²×C₃⋊D₃	—	3	13	no	—
172	C₂²×C₃⋊D₃	—	3	13	no	—
173	C₂²×C₃⋊D₃	—	3	13	no	—
174	C₂²×C₃⋊D₃	—	6	26	no	—
175	C₂²×C₃⋊D₃	—	6	26	no	—
176	C₂²×C₃⋊D₃	—	12	13	no	—
177	C₃²×Q₈	—	4	13	no	—
178	C₂×C₃²×C₄	—	4	13	no	—
179	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
180	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
181	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
182	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
183	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
184	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
185	#638	—	6	26	no	—
186	C₂×C₃⋊Dic₃	—	3	13	no	—
187	C₂×C₃⋊Dic₃	—	3	13	no	—
188	C₂×C₃⋊Dic₃	—	3	13	no	—
189	C₂×C₃⋊Dic₃	—	3	13	no	—
190	C₂×C₃⋊Dic₃	—	3	13	no	—
191	C₂×C₃⋊Dic₃	—	6	26	no	—
192	C₄⋊(C₃⋊D₃)	—	6	26	no	—
193	C₄⋊(C₃⋊D₃)	—	12	13	no	—
194	C₄×C₃⋊D₃	—	6	26	no	—
195	C₄×C₃⋊D₃	—	12	13	no	—
196	C₄×C₃⋊D₃	—	12	13	no	—
197	#551	—	27	1	no	Sylow
198	C₂×C₃³	—	2	2	no	—
199	C₂×C₃³	C₂×#41	1	1	yes	characteristic
200	C₂×C₃³	C₂×#41	1	1	yes	characteristic
201	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
202	C₃⋊(C₃⋊D₃)	—	2	2	no	—
203	C₃⋊(C₃⋊D₃)	—	4	1	no	—
204	C₃⋊(C₃⋊D₃)	—	4	1	no	—
205	C₂³×D₃	—	9	13	no	—
206	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	13	yes	complemented
207	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
208	C₂×#67	—	9	13	no	—
209	C₂²×Dic₃	—	9	13	no	—
210	C₂×D₁₂	—	9	13	no	—
211	C₂×D₁₂	—	9	13	no	—
212	C₂×C₄×D₃	—	9	13	no	—
213	C₂×C₄×D₃	—	9	13	no	—
214	C₂×C₄×D₃	—	9	13	no	—
215	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
216	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
217	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	13	yes	complemented
218	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
219	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	13	yes	—
220	#217	—	9	13	no	—
221	(C₂×D₃)⋊C₄	—	9	13	no	—
222	(C₂×D₃)⋊C₄	—	9	13	no	—
223	(C₂×D₃)⋊C₄	—	9	13	no	—
224	(C₂×D₃)⋊C₄	—	9	13	no	—
225	(C₂×D₃)⋊C₄	—	9	13	no	—
226	(C₂×D₃)⋊C₄	—	9	13	no	—
227	(C₂×D₃)⋊C₄	—	9	13	no	—
228	(C₂×D₃)⋊C₄	—	9	13	no	—
229	(C₂×D₃)⋊C₄	—	9	13	no	—
230	(C₂×D₃)⋊C₄	—	9	13	no	—
231	(C₂×D₃)⋊C₄	—	9	13	no	—
232	C₄⋊Dic₃	—	9	13	no	—
233	C₄⋊Dic₃	—	9	13	no	—
234	Dic₃⋊C₄	—	9	13	no	—
235	Dic₃⋊C₄	—	9	13	no	—
236	Dic₃⋊C₄	—	9	13	no	—
237	C₄×Dic₃	—	9	13	no	—
238	C₄×Dic₃	—	9	13	no	—
239	C₄×Dic₃	—	9	13	no	—
240	C₂²×C₃²	—	2	13	no	—
241	C₂²×C₃²	—	2	13	no	—
242	C₂²×C₃²	#239	1	26	yes	—
243	C₂²×C₃²	C₂³×D₃	1	13	yes	—
244	C₂×C₃⋊D₃	—	3	26	no	—
245	C₂×C₃⋊D₃	—	6	13	no	—
246	C₂×C₃⋊D₃	—	6	13	no	—
247	C₂×C₃⋊D₃	—	6	13	no	—
248	C₂×C₃⋊D₃	—	6	13	no	—
249	C₂×C₃⋊D₃	—	6	13	no	—
250	C₂×C₃⋊D₃	—	6	13	no	—
251	C₂×C₃⋊D₃	—	6	13	no	—
252	C₂×C₃⋊D₃	—	6	13	no	—
253	C₂×C₃⋊D₃	—	12	52	no	—
254	C₃²×C₄	—	2	13	no	—
255	C₃²×C₄	—	2	13	no	—
256	C₃²×C₄	—	2	13	no	—
257	C₃²×C₄	—	2	13	no	—
258	C₃²×C₄	—	2	13	no	—
259	C₃²×C₄	—	2	13	no	—
260	C₃⋊Dic₃	—	6	13	no	—
261	C₃⋊Dic₃	—	6	13	no	—
262	C₃⋊Dic₃	—	6	13	no	—
263	C₃⋊Dic₃	—	6	13	no	—
264	C₃⋊Dic₃	—	6	13	no	—
265	#126	—	27	1	no	—
266	#126	—	27	1	no	—
267	#124	—	27	1	no	—
268	#123	—	27	1	no	—
269	#123	—	27	1	no	—
270	#123	—	27	1	no	—
271	C₂²⋊Q₈	—	27	1	no	—
272	C₂²⋊Q₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
273	#120	—	27	1	no	—
274	C₄×D₄	—	27	1	no	—
275	C₄×D₄	—	27	1	no	—
276	#117	—	27	1	no	—
277	#117	—	27	1	no	—
278	C₂×C₂²⋊C₄	—	27	1	no	—
279	C₂×C₂²⋊C₄	—	27	1	no	—
280	C₃³	#551	1	1	yes	characteristic, complemented, Sylow
281	C₂³×C₃	C₂²×C₃⋊D₃	1	13	yes	—
282	C₂²×D₃	—	9	13	no	—
283	C₂²×D₃	—	9	13	no	—
284	C₂²×D₃	—	9	13	no	—
285	C₂²×D₃	—	18	26	no	—
286	C₂²×D₃	—	18	26	no	—
287	C₂²×D₃	—	36	13	no	—
288	C₃×Q₈	—	4	13	no	—
289	C₂×C₃×C₄	—	4	13	no	—
290	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
291	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
292	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
293	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
294	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
295	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
296	#67	—	18	26	no	—
297	C₂×Dic₃	—	9	13	no	—
298	C₂×Dic₃	—	9	13	no	—
299	C₂×Dic₃	—	9	13	no	—
300	C₂×Dic₃	—	9	13	no	—
301	C₂×Dic₃	—	9	13	no	—
302	C₂×Dic₃	—	18	26	no	—
303	D₁₂	—	18	26	no	—
304	D₁₂	—	36	13	no	—
305	C₄×D₃	—	18	26	no	—
306	C₄×D₃	—	36	13	no	—
307	C₄×D₃	—	36	13	no	—
308	C₂×C₃²	—	2	26	no	—
309	C₂×C₃²	#1004	1	13	yes	—
310	C₂×C₃²	C₂×#239	1	13	yes	—
311	C₂×C₃²	D₃×#41	1	13	yes	—
312	C₃⋊D₃	—	6	26	no	—
313	C₃⋊D₃	—	12	13	no	—
314	C₃⋊D₃	—	12	13	no	—
315	C₂⁴	—	27	1	no	—
316	C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
317	C₂×D₄	—	27	1	no	—
318	C₂×D₄	—	27	1	no	—
319	C₂×D₄	—	27	1	no	—
320	C₂²×C₄	—	27	1	no	—
321	C₂²×C₄	—	27	1	no	—
322	C₂²×C₄	—	27	1	no	—
323	C₂²×C₄	—	27	1	no	—
324	C₂²×C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
325	C₄⋊C₄	—	27	1	no	—
326	C₄⋊C₄	—	27	1	no	—
327	C₄⋊C₄	—	27	1	no	—
328	C₄⋊C₄	—	27	1	no	—
329	C₄⋊C₄	—	27	1	no	—
330	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
331	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
332	C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
333	C₂²⋊C₄	—	27	1	no	—
334	C₂²⋊C₄	—	27	1	no	—
335	C₂²⋊C₄	—	27	1	no	—
336	C₂²⋊C₄	—	27	1	no	—
337	C₂²⋊C₄	—	27	1	no	—
338	C₂²⋊C₄	—	27	1	no	—
339	C₂²⋊C₄	—	27	1	no	—
340	C₂²⋊C₄	—	27	1	no	—
341	C₂²⋊C₄	—	27	1	no	—
342	C₂²⋊C₄	—	27	1	no	—
343	C₂²⋊C₄	—	27	1	no	—
344	C₂²⋊C₄	—	27	1	no	—
345	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
346	C₂²⋊C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
347	C₄²	—	27	1	no	—
348	C₄²	—	27	1	no	—
349	C₄²	—	27	1	no	—
350	C₂²×C₃	—	2	13	no	—
351	C₂²×C₃	—	2	13	no	—
352	C₂²×C₃	#3832	1	26	yes	—
353	C₂²×C₃	C₂³×C₃⋊D₃	1	13	yes	—
354	C₂×D₃	—	9	26	no	—
355	C₂×D₃	—	18	13	no	—
356	C₂×D₃	—	18	13	no	—
357	C₂×D₃	—	18	13	no	—
358	C₂×D₃	—	18	13	no	—
359	C₂×D₃	—	18	13	no	—
360	C₂×D₃	—	18	13	no	—
361	C₂×D₃	—	18	13	no	—
362	C₂×D₃	—	18	13	no	—
363	C₂×D₃	—	36	52	no	—
364	C₃×C₄	—	2	13	no	—
365	C₃×C₄	—	2	13	no	—
366	C₃×C₄	—	2	13	no	—
367	C₃×C₄	—	2	13	no	—
368	C₃×C₄	—	2	13	no	—
369	C₃×C₄	—	2	13	no	—
370	Dic₃	—	18	13	no	—
371	Dic₃	—	18	13	no	—
372	Dic₃	—	18	13	no	—
373	Dic₃	—	18	13	no	—
374	Dic₃	—	18	13	no	—
375	C₃²	#5637	1	13	yes	complemented
376	C₂³	—	27	1	no	—
377	C₂³	—	27	1	no	—
378	C₂³	—	27	1	no	—
379	C₂³	—	54	2	no	—
380	C₂³	—	54	2	no	—
381	C₂³	—	108	1	no	—
382	C₂³	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
383	Q₈	—	4	1	no	—
384	D₄	—	54	2	no	—
385	D₄	—	54	2	no	—
386	D₄	—	108	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	27	1	no	—
389	C₂×C₄	—	27	1	no	—
390	C₂×C₄	—	27	1	no	—
391	C₂×C₄	—	27	1	no	—
392	C₂×C₄	—	27	1	no	—
393	C₂×C₄	—	54	2	no	—
394	C₂×C₄	—	54	2	no	—
395	C₂×C₄	—	108	1	no	—
396	C₂×C₄	—	108	1	no	—
397	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
403	C₂×C₃	—	2	26	no	—
404	C₂×C₃	#64361	1	13	yes	—
405	C₂×C₃	C₂×#3832	1	13	yes	—
406	C₂×C₃	#41×C₃⋊D₃	1	13	yes	—
407	D₃	—	18	26	no	—
408	D₃	—	36	13	no	—
409	D₃	—	36	13	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	27	2	no	—
413	C₂²	—	54	1	no	—
414	C₂²	—	54	1	no	—
415	C₂²	—	54	1	no	—
416	C₂²	—	54	1	no	—
417	C₂²	—	54	1	no	—
418	C₂²	—	54	1	no	—
419	C₂²	—	54	1	no	—
420	C₂²	—	54	1	no	—
421	C₂²	—	108	4	no	—
422	C₂²	#89080	1	2	yes	—
423	C₂²	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	54	1	no	—
431	C₄	—	54	1	no	—
432	C₄	—	54	1	no	—
433	C₄	—	54	1	no	—
434	C₄	—	54	1	no	—
435	C₃	#10596108	1	13	yes	complemented
436	C₂	—	2	2	no	—
437	C₂	—	54	2	no	—
438	C₂	—	108	1	no	—
439	C₂	—	108	1	no	—
440	C₂	#11724679	1	1	yes	characteristic
441	C₂	C₂×#89080	1	1	yes	characteristic
442	C₂	#41×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×C₃⋊(C₃⋊D₃)
commutator, socle, cosocle	C₂²×C₃³	C₂⁴
Fitting	C₃³×C₂²⋊Q₈	C₂
prime radical	#11723923	C₂
hypercenter	C₂²⋊Q₈	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#551
LCS	G ▷ C₂²×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊Q₈	C₂	semidirect
2. #11723988	C₂	semidirect
3. #11723987	C₂	semidirect
4. C₄×#6312	C₂	semidirect
5. C₂×#88859	C₂	semidirect
6. #11723939	C₂	semidirect
7. #11723939	C₂	semidirect
8. #11723935	C₂	semidirect
9. #11723935	C₂	semidirect
10. #11723934	C₂	semidirect
11. #11723933	C₂	semidirect
12. #11723927	C₂	semidirect
14. C₂²⋊C₄×C₃⋊(C₃⋊D₃)	C₂	semidirect
15. #11723918	C₂	semidirect
18. C₂×C₃³×Q₈	C₂²	semidirect
26. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
27. C₃³×C₄⋊C₄	C₂²	semidirect
28. C₃³×C₄⋊C₄	C₂²	semidirect
29. C₃³×C₄⋊C₄	C₂²	semidirect
41. #88859	C₂²	semidirect
42. #88859	C₂²	semidirect
43. #88859	C₂²	semidirect
44. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
45. C₄⋊(C₃⋊(C₃⋊Dic₃))	C₂²	semidirect
46. #88857	C₂²	semidirect
47. #88857	C₂²	semidirect
48. #88857	C₂²	semidirect
49. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
50. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
51. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
52. C₃²×C₂²⋊Q₈	D₃	semidirect
96. C₂×C₃²×Q₈	C₂×D₃	semidirect
105. C₃²×C₄⋊C₄	C₂×D₃	semidirect
106. C₃²×C₄⋊C₄	C₂×D₃	semidirect
107. C₃²×C₄⋊C₄	C₂×D₃	semidirect
155. C₃×C₂²⋊Q₈	C₃⋊D₃	semidirect
206. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
215. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
216. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
217. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
272. C₂²⋊Q₈	C₃⋊(C₃⋊D₃)	semidirect
280. C₃³	#551	semidirect
316. C₂×Q₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
330. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
331. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
332. C₄⋊C₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
375. C₃²	#5637	semidirect
435. C₃	#10596108	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊Q₈	2
#11723988	2
#11723987	2
C₄×#6312	2
C₂×#88859	2
#11723939	2
#11723935	2
#11723934	2
#11723933	2
#11723927	2
#11723923	2
C₂²⋊C₄×C₃⋊(C₃⋊D₃)	2
#11723918	2
#10596108	3