Subgroups — #11861374

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10596049	C₂	1	1	yes	maximal, characteristic
2	C₃²×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	#10592723	C₂	1	1	yes	maximal, characteristic, complemented
4	#10592538	C₂	1	1	yes	maximal, characteristic
5	#10592538	C₂	1	1	yes	maximal, characteristic
6	#10592536	C₂	1	1	yes	maximal, characteristic
7	#10592530	C₂	1	1	yes	maximal, characteristic, complemented
8	#10592527	C₂	1	1	yes	maximal, characteristic, complemented
9	#10592527	C₂	1	1	yes	maximal, characteristic, complemented
10	#10592407	C₂	1	1	yes	maximal, characteristic
11	C₃⋊D₃×#97	C₂	1	1	yes	maximal, characteristic
12	#10592400	C₂	1	1	yes	maximal, characteristic, complemented
13	#10592400	C₂	1	1	yes	maximal, characteristic, complemented
14	#10592388	C₂	1	1	yes	maximal, characteristic
15	#10592378	C₂	1	1	yes	maximal, characteristic, complemented
16	#79959	—	3	4	no	maximal
17	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
18	#64155	C₄	1	1	yes	characteristic
19	#64153	C₄	1	1	yes	characteristic
20	C₂×#3743	C₂²	1	1	yes	characteristic
21	C₂×#3743	C₂²	1	1	yes	characteristic
22	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
23	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
24	#64106	C₄	1	1	yes	characteristic
25	#64105	C₄	1	1	yes	characteristic
26	#64105	C₄	1	1	yes	characteristic
27	#64098	C₄	1	1	yes	characteristic
28	#64098	C₄	1	1	yes	characteristic
29	#64097	C₄	1	1	yes	characteristic
30	#64081	C₂²	1	1	yes	characteristic
31	#64081	C₂²	1	1	yes	characteristic
32	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
33	C₄×#634	C₂²	1	1	yes	characteristic
34	C₄×#634	C₂²	1	1	yes	characteristic
35	C₄×#634	C₂²	1	1	yes	characteristic
36	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃²×#97	C₂²	1	1	yes	characteristic
40	C₃²×#97	C₂²	1	1	yes	characteristic
41	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
42	#63642	C₂²	1	1	yes	characteristic
43	#63642	C₂²	1	1	yes	characteristic
44	#63642	C₂²	1	1	yes	characteristic
45	#63642	C₂²	1	1	yes	characteristic
46	#63641	C₂²	1	1	yes	characteristic
47	#63641	C₂²	1	1	yes	characteristic
48	#63641	C₂²	1	1	yes	characteristic
49	#63641	C₂²	1	1	yes	characteristic
50	#63641	C₂²	1	1	yes	characteristic
51	#63641	C₂²	1	1	yes	characteristic
52	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
53	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
54	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
55	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
56	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
57	#63630	C₂²	1	1	yes	characteristic
58	#63630	C₂²	1	1	yes	characteristic
59	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	#5578	—	3	4	no	—
61	C₃×#446	D₃	1	4	yes	complemented
62	#5024	—	3	4	no	—
63	#4839	—	3	4	no	—
64	#4839	—	3	4	no	—
65	#4837	—	3	4	no	—
66	#4831	—	3	4	no	—
67	#4828	—	3	4	no	—
68	#4828	—	3	4	no	—
69	#4708	—	3	4	no	—
70	D₃×#97	—	3	4	no	—
71	#4701	—	3	4	no	—
72	#4701	—	3	4	no	—
73	#4689	—	3	4	no	—
74	#4679	—	3	4	no	—
75	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
79	C₂×#634	C₂×C₄	1	1	yes	characteristic
80	C₂×#634	C₂×C₄	1	1	yes	characteristic
81	C₂×#634	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₃²×C₄²	C₂³	1	1	yes	characteristic
90	C₃²×C₄²	C₂³	1	1	yes	characteristic
91	C₃²×C₄²	C₂³	1	1	yes	characteristic
92	#3752	C₂×C₄	1	1	yes	characteristic
93	#3752	C₂×C₄	1	1	yes	characteristic
94	#3752	C₂×C₄	1	1	yes	characteristic
95	#3752	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
97	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
99	#3750	C₂×C₄	1	1	yes	characteristic
100	#3750	C₂×C₄	1	1	yes	characteristic
101	#3750	C₂×C₄	1	1	yes	characteristic
102	#3750	C₂×C₄	1	1	yes	characteristic
103	#3750	C₂×C₄	1	1	yes	characteristic
104	#3750	C₂×C₄	1	1	yes	characteristic
105	#3750	C₂×C₄	1	1	yes	characteristic
106	#3750	C₂×C₄	1	1	yes	characteristic
107	#3750	C₂×C₄	1	1	yes	characteristic
108	#3750	C₂×C₄	1	1	yes	characteristic
109	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
110	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
111	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
112	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
113	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
114	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
115	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
116	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
117	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
118	#3743	—	2	2	no	—
119	#3743	—	2	2	no	—
120	C₈×C₃⋊D₃	—	2	2	no	—
121	C₈×C₃⋊D₃	Q₈	1	4	yes	complemented
122	#2961	—	9	1	no	Sylow
123	C₃×C₄×Q₈	C₂×D₃	1	4	yes	—
124	#946	—	3	4	no	—
125	#944	—	3	4	no	—
126	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
127	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
128	C₂×D₃×C₈	—	3	4	no	—
129	C₂×D₃×C₈	—	3	4	no	—
130	#897	—	3	4	no	—
131	#896	—	3	4	no	—
132	#896	—	3	4	no	—
133	#889	—	3	4	no	—
134	#889	—	3	4	no	—
135	#888	—	3	4	no	—
136	#872	—	3	4	no	—
137	#872	—	3	4	no	—
138	C₄²×D₃	—	3	4	no	—
139	C₄×Dic₆	—	3	4	no	—
140	C₄×Dic₆	—	3	4	no	—
141	C₄×Dic₆	—	3	4	no	—
142	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	—
143	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	—
144	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	—
145	C₃×#97	C₂×D₃	1	4	yes	—
146	C₃×#97	C₂×D₃	1	4	yes	—
147	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
148	#815	—	3	4	no	—
149	#815	—	3	4	no	—
150	#815	—	3	4	no	—
151	#815	—	3	4	no	—
152	Dic₃⋊C₈	—	3	4	no	—
153	Dic₃⋊C₈	—	3	4	no	—
154	Dic₃⋊C₈	—	3	4	no	—
155	Dic₃⋊C₈	—	3	4	no	—
156	Dic₃⋊C₈	—	3	4	no	—
157	Dic₃⋊C₈	—	3	4	no	—
158	C₈×Dic₃	—	3	4	no	—
159	C₈×Dic₃	—	3	4	no	—
160	C₄⋊(C₃⋊C₈)	—	3	4	no	—
161	C₄⋊(C₃⋊C₈)	—	3	4	no	—
162	C₄⋊(C₃⋊C₈)	—	3	4	no	—
163	#803	—	3	4	no	—
164	#803	—	3	4	no	—
165	C₄×C₃⋊C₈	—	3	4	no	—
166	C₂²×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
167	C₃²×Q₈	—	4	1	no	—
168	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
175	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
182	C₄×C₃⋊D₃	—	4	1	no	—
183	C₄×C₃⋊D₃	—	4	1	no	—
184	C₄×C₃⋊D₃	C₂×Q₈	1	2	yes	—
185	C₄×C₃⋊D₃	#41	1	2	yes	—
186	#634	—	4	1	no	—
187	#634	—	4	1	no	—
188	#634	—	4	1	no	—
189	C₃²×C₈	—	2	1	no	—
190	C₃²×C₈	—	2	1	no	—
191	C₃²×C₈	—	2	1	no	—
192	C₃²×C₈	C₂×Q₈	1	2	yes	—
193	C₃⋊(C₃⋊C₈)	—	2	1	no	—
194	C₃⋊(C₃⋊C₈)	—	2	1	no	—
195	C₃⋊(C₃⋊C₈)	—	2	1	no	—
196	C₃⋊(C₃⋊C₈)	C₂×Q₈	1	2	yes	—
197	#533	—	9	1	no	—
198	#446	—	9	1	no	—
199	#446	—	9	1	no	—
200	#446	—	9	1	no	—
201	#446	—	9	1	no	—
202	#446	—	9	1	no	—
203	#446	—	9	1	no	—
204	#446	—	9	1	no	—
205	#446	C₃⋊D₃	1	1	yes	characteristic, complemented
206	#424	—	9	1	no	—
207	#424	—	9	1	no	—
208	#423	—	9	1	no	—
209	#405	—	9	1	no	—
210	#405	—	9	1	no	—
211	C₂×#97	—	9	1	no	—
212	C₂×C₃×Q₈	C₄×D₃	1	4	yes	—
213	C₂×C₄×D₃	—	3	4	no	—
214	C₂×C₄×D₃	—	3	4	no	—
215	C₂×C₄×D₃	—	3	4	no	—
216	C₂×Dic₆	—	3	4	no	—
217	C₂×Dic₆	—	3	4	no	—
218	C₂×Dic₆	—	3	4	no	—
219	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
220	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
221	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
222	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
223	C₃×C₄⋊C₄	C₄×D₃	1	4	yes	—
224	C₃×C₄⋊C₄	C₄×D₃	1	4	yes	—
225	C₃×C₄⋊C₄	C₄×D₃	1	4	yes	—
226	C₃×C₄²	C₂²×D₃	1	4	yes	—
227	C₃×C₄²	C₂²×D₃	1	4	yes	—
228	C₃×C₄²	C₂²×D₃	1	4	yes	—
229	(C₂×D₃)⋊C₄	—	3	4	no	—
230	(C₂×D₃)⋊C₄	—	3	4	no	—
231	(C₂×D₃)⋊C₄	—	3	4	no	—
232	(C₂×D₃)⋊C₄	—	3	4	no	—
233	C₄⋊Dic₃	—	3	4	no	—
234	C₄⋊Dic₃	—	3	4	no	—
235	C₄⋊Dic₃	—	3	4	no	—
236	Dic₃⋊C₄	—	3	4	no	—
237	Dic₃⋊C₄	—	3	4	no	—
238	Dic₃⋊C₄	—	3	4	no	—
239	Dic₃⋊C₄	—	3	4	no	—
240	Dic₃⋊C₄	—	3	4	no	—
241	Dic₃⋊C₄	—	3	4	no	—
242	Dic₃⋊C₄	—	3	4	no	—
243	Dic₃⋊C₄	—	3	4	no	—
244	Dic₃⋊C₄	—	3	4	no	—
245	Dic₃⋊C₄	—	3	4	no	—
246	C₄×Dic₃	—	3	4	no	—
247	C₄×Dic₃	—	3	4	no	—
248	C₄×Dic₃	—	3	4	no	—
249	C₄×Dic₃	—	3	4	no	—
250	C₄×Dic₃	—	3	4	no	—
251	C₂×C₃⋊C₈	—	3	4	no	—
252	C₂×C₃⋊C₈	—	3	4	no	—
253	C₂×C₃⋊C₈	—	3	4	no	—
254	C₂×C₃⋊C₈	—	3	4	no	—
255	ΓL(1,𝔽₂₅)	—	6	8	no	—
256	ΓL(1,𝔽₂₅)	—	6	8	no	—
257	D₃×C₈	—	3	16	no	—
258	D₃×C₈	—	6	8	no	—
259	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₃⋊D₃	—	2	1	no	—
261	C₂×C₃⋊D₃	—	2	1	no	—
262	C₂×C₃⋊D₃	C₄×Q₈	1	2	yes	—
263	C₃²×C₄	—	2	1	no	—
264	C₃²×C₄	—	2	1	no	—
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	1	no	—
268	C₃²×C₄	—	2	1	no	—
269	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
270	C₃²×C₄	C₂×#41	1	1	yes	characteristic
271	C₃⋊Dic₃	—	2	1	no	—
272	C₃⋊Dic₃	—	2	1	no	—
273	C₃⋊Dic₃	—	2	1	no	—
274	C₃⋊Dic₃	—	2	1	no	—
275	C₃⋊Dic₃	—	2	1	no	—
276	C₃⋊Dic₃	—	2	1	no	—
277	C₃⋊Dic₃	C₄×Q₈	1	2	yes	—
278	C₂×M₁₆	—	9	1	no	—
279	C₂×M₁₆	—	9	1	no	—
280	C₂²×C₈	—	9	1	no	—
281	C₂²×C₈	—	9	1	no	—
282	C₄⋊Q₈	—	9	1	no	—
283	C₄⋊Q₈	—	9	1	no	—
284	#125	—	9	1	no	—
285	#125	—	9	1	no	—
286	C₂²⋊Q₈	—	9	1	no	—
287	C₂²⋊Q₈	—	9	1	no	—
288	C₂²⋊Q₈	—	9	1	no	—
289	C₂²⋊Q₈	—	9	1	no	—
290	C₄×Q₈	—	9	1	no	—
291	C₄×Q₈	—	9	1	no	—
292	C₄×Q₈	—	9	1	no	—
293	C₄×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
294	#117	—	9	1	no	—
295	#117	—	9	1	no	—
296	C₂×C₄²	—	9	1	no	—
297	C₄⋊C₈	—	9	1	no	—
298	C₄⋊C₈	—	9	1	no	—
299	C₄⋊C₈	—	9	1	no	—
300	C₄⋊C₈	—	9	1	no	—
301	C₄⋊C₈	—	9	1	no	—
302	C₄⋊C₈	—	9	1	no	—
303	C₄⋊C₈	—	9	1	no	—
304	C₄⋊C₈	—	9	1	no	—
305	C₄⋊C₈	—	9	1	no	—
306	C₄⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
307	C₄⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
309	#97	—	9	1	no	—
310	#97	—	9	1	no	—
311	#97	—	9	1	no	—
312	#97	—	9	1	no	—
313	#97	—	9	1	no	—
314	#97	—	9	1	no	—
315	#97	C₂×C₃⋊D₃	1	1	yes	characteristic
316	#97	C₂×C₃⋊D₃	1	1	yes	characteristic
317	C₄×C₈	—	9	1	no	—
318	C₄×C₈	—	9	1	no	—
319	C₄×C₈	—	9	1	no	—
320	C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
321	C₂²×D₃	—	3	4	no	—
322	C₃×Q₈	—	4	4	no	—
323	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
324	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
325	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
326	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
327	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
328	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
329	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
330	C₂×Dic₃	—	3	4	no	—
331	C₂×Dic₃	—	3	4	no	—
332	C₂×Dic₃	—	3	4	no	—
333	C₂×Dic₃	—	3	4	no	—
334	C₂×Dic₃	—	3	4	no	—
335	C₂×Dic₃	—	3	4	no	—
336	C₂×Dic₃	—	3	4	no	—
337	C₄×D₃	—	3	8	no	—
338	C₄×D₃	—	3	8	no	—
339	C₄×D₃	—	12	4	no	—
340	C₄×D₃	—	12	4	no	—
341	Dic₆	—	12	4	no	—
342	Dic₆	—	12	4	no	—
343	Dic₆	—	12	4	no	—
344	C₃×C₈	—	2	4	no	—
345	C₃×C₈	—	2	4	no	—
346	C₃×C₈	—	2	4	no	—
347	C₃×C₈	D₃×Q₈	1	8	yes	—
348	C₃⋊C₈	—	3	8	no	—
349	C₃⋊C₈	—	6	4	no	—
350	C₃⋊C₈	—	6	4	no	—
351	C₃⋊C₈	—	6	4	no	—
352	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
353	C₂×C₃²	#568	1	1	yes	characteristic
354	C₂×C₃²	#568	1	1	yes	characteristic
355	C₃⋊D₃	—	2	2	no	—
356	C₂×Q₈	—	9	1	no	—
357	C₂×Q₈	—	9	1	no	—
358	C₂×Q₈	—	9	1	no	—
359	C₂×Q₈	C₄×C₃⋊D₃	1	1	yes	characteristic
360	C₂²×C₄	—	9	1	no	—
361	C₂²×C₄	—	9	1	no	—
362	C₂²×C₄	—	9	1	no	—
363	M₁₆	—	18	2	no	—
364	M₁₆	—	18	2	no	—
365	C₂×C₈	—	9	1	no	—
366	C₂×C₈	—	9	4	no	—
367	C₂×C₈	—	9	1	no	—
368	C₂×C₈	—	9	1	no	—
369	C₂×C₈	—	9	1	no	—
370	C₂×C₈	—	18	2	no	—
371	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
372	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
373	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
374	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
375	C₄⋊C₄	—	9	1	no	—
376	C₄⋊C₄	—	9	1	no	—
377	C₄⋊C₄	—	9	1	no	—
378	C₄⋊C₄	—	9	1	no	—
379	C₄⋊C₄	—	9	1	no	—
380	C₄⋊C₄	—	9	1	no	—
381	C₄⋊C₄	—	9	1	no	—
382	C₄⋊C₄	—	9	1	no	—
383	C₄⋊C₄	—	9	1	no	—
384	C₄⋊C₄	—	9	1	no	—
385	C₄⋊C₄	—	9	1	no	—
386	C₄⋊C₄	—	9	1	no	—
387	C₄⋊C₄	—	9	1	no	—
388	C₄⋊C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
389	C₄⋊C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
390	C₄⋊C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
391	C₂²⋊C₄	—	9	1	no	—
392	C₂²⋊C₄	—	9	1	no	—
393	C₂²⋊C₄	—	9	1	no	—
394	C₂²⋊C₄	—	9	1	no	—
395	C₄²	—	9	1	no	—
396	C₄²	—	9	1	no	—
397	C₄²	—	9	1	no	—
398	C₄²	—	9	1	no	—
399	C₄²	—	9	1	no	—
400	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
401	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
402	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
403	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
404	C₂×D₃	—	3	8	no	—
405	C₂×D₃	—	6	4	no	—
406	C₂×D₃	—	6	4	no	—
407	C₃×C₄	—	2	4	no	—
408	C₃×C₄	—	2	4	no	—
409	C₃×C₄	—	2	4	no	—
410	C₃×C₄	—	2	4	no	—
411	C₃×C₄	—	2	4	no	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	C₂×D₃×Q₈	1	4	yes	—
414	C₃×C₄	D₃×#41	1	4	yes	—
415	Dic₃	—	3	8	no	—
416	Dic₃	—	6	4	no	—
417	Dic₃	—	6	4	no	—
418	Dic₃	—	6	4	no	—
419	Dic₃	—	6	4	no	—
420	Dic₃	—	6	4	no	—
421	Dic₃	—	6	4	no	—
422	C₃²	#2961	1	1	yes	characteristic, complemented, Sylow
423	C₂³	—	9	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	36	1	no	—
426	Q₈	—	36	1	no	—
427	Q₈	—	36	1	no	—
428	C₂×C₄	—	9	1	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	9	2	no	—
431	C₂×C₄	—	9	1	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	9	1	no	—
434	C₂×C₄	—	9	1	no	—
435	C₂×C₄	—	9	1	no	—
436	C₂×C₄	—	9	1	no	—
437	C₂×C₄	—	36	1	no	—
438	C₂×C₄	—	36	1	no	—
439	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
440	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
441	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
442	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
444	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
445	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	9	2	no	—
450	C₈	—	18	1	no	—
451	C₈	—	18	1	no	—
452	C₈	—	18	1	no	—
453	C₈	Q₈×C₃⋊D₃	1	2	yes	—
454	C₂×C₃	C₄×D₃×Q₈	1	4	yes	—
455	C₂×C₃	#5745	1	4	yes	—
456	C₂×C₃	#5750	1	4	yes	—
457	D₃	—	6	8	no	—
458	C₂²	—	9	2	no	—
459	C₂²	—	18	1	no	—
460	C₂²	—	18	1	no	—
461	C₂²	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	9	2	no	—
469	C₄	—	18	1	no	—
470	C₄	—	18	1	no	—
471	C₄	—	18	1	no	—
472	C₄	—	18	1	no	—
473	C₄	—	18	1	no	—
474	C₄	—	18	1	no	—
475	C₄	C₂×Q₈×C₃⋊D₃	1	1	yes	characteristic
476	C₄	#41×C₃⋊D₃	1	1	yes	characteristic
477	C₃	#79959	1	4	yes	complemented
478	C₂	—	18	2	no	—
479	C₂	C₄×Q₈×C₃⋊D₃	1	1	yes	characteristic
480	C₂	#10596216	1	1	yes	characteristic
481	C₂	#10596221	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×C₃⋊D₃
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₃²×#446	C₂
prime radical	C₂²×C₃⋊D₃	C₂²×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	#446	C₃⋊D₃
hypocenter	C₃²	#2961
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. C₃²×#446	C₂	semidirect
3. #10592723	C₂	semidirect
7. #10592530	C₂	semidirect
8. #10592527	C₂	semidirect
9. #10592527	C₂	semidirect
12. #10592400	C₂	semidirect
13. #10592400	C₂	semidirect
15. #10592378	C₂	semidirect
61. C₃×#446	D₃	semidirect
121. C₈×C₃⋊D₃	Q₈	semidirect
205. #446	C₃⋊D₃	semidirect
422. C₃²	#2961	semidirect
477. C₃	#79959	semidirect

Maximal subgroups

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

subgroup	index
#10596049	2
C₃²×#446	2
#10592723	2
#10592538	2
#10592536	2
#10592530	2
#10592527	2
#10592407	2
C₃⋊D₃×#97	2
#10592400	2
#10592388	2
#10592378	2
#79959	3