Subgroups — C₃×#60854 #10679461

Order 768.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3240	C₂	1	4	yes	maximal, complemented
4	C₃×#3239	C₂	1	2	yes	maximal, complemented
5	C₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₃×#3237	C₂	1	2	yes	maximal, complemented
7	C₃×#3236	C₂	1	2	yes	maximal, complemented
8	C₃×#3235	C₂	1	2	yes	maximal, complemented
9	C₃×#3234	C₂	1	2	yes	maximal, complemented
10	C₃×#3162	C₂	1	2	yes	maximal, complemented
11	C₃×#3135	C₂	1	2	yes	maximal, complemented
12	C₃×#3091	C₂	1	4	yes	maximal, complemented
13	C₃×#3076	C₂	1	4	yes	maximal, complemented
14	C₂×C₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
15	#60854	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃×#533	—	2	1	no	—
17	C₃×#533	—	2	1	no	—
18	C₃×#533	—	2	1	no	—
19	C₃×#533	—	2	1	no	—
20	C₃×#533	C₂²	1	1	yes	characteristic
21	C₃×#533	C₂²	1	1	yes	characteristic
22	C₃×#533	C₂²	1	2	yes	—
23	C₃×#533	C₂²	1	2	yes	—
24	C₃×#533	C₂²	1	2	yes	—
25	C₃×#533	C₂²	1	2	yes	—
26	C₃×#533	C₂²	1	1	yes	characteristic
27	C₃×#532	C₂²	1	1	yes	characteristic
28	C₃×#532	C₂²	1	1	yes	characteristic
29	C₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×#529	—	2	1	no	—
33	C₃×#529	—	2	1	no	—
34	C₃×#529	—	2	1	no	—
35	C₃×#529	—	2	1	no	—
36	C₃×#529	C₂²	1	2	yes	—
37	C₃×#529	C₂²	1	2	yes	—
38	C₂×C₃×#125	C₂²	1	2	yes	—
39	C₃×#525	—	2	1	no	—
40	C₃×#525	—	2	1	no	—
41	C₃×#525	C₂²	1	2	yes	—
42	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
44	C₃×C₄×#41	—	2	1	no	—
45	C₃×C₄×#41	—	2	1	no	—
46	C₃×C₄×#41	C₂²	1	2	yes	—
47	C₂×C₃×C₄×Q₈	—	2	1	no	—
48	C₂×C₃×C₄×Q₈	—	2	1	no	—
49	C₂×C₃×#117	C₂²	1	2	yes	—
50	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
51	C₃×#501	C₂²	1	4	yes	complemented
52	C₃×#501	C₂²	1	4	yes	complemented
53	C₃×#501	C₂²	1	4	yes	complemented
54	C₃×#501	C₂²	1	4	yes	complemented
55	C₃×#491	C₂²	1	4	yes	complemented
56	C₃×#490	C₂²	1	4	yes	complemented
57	C₃×#489	C₂²	1	4	yes	complemented
58	C₃×#489	C₂²	1	4	yes	complemented
59	C₃×#485	C₂²	1	8	yes	—
60	C₃×#484	C₂²	1	4	yes	—
61	C₃×#483	C₂²	1	4	yes	—
62	C₃×#482	C₂²	1	8	yes	—
63	C₃×#481	C₂²	1	4	yes	—
64	C₃×#480	C₂²	1	4	yes	—
65	C₃×#479	C₂²	1	8	yes	complemented
66	C₃×#478	C₂²	1	8	yes	complemented
67	C₃×#477	C₂²	1	4	yes	complemented
68	C₃×#476	C₂²	1	4	yes	complemented
69	C₃×#475	C₂²	1	4	yes	complemented
70	C₃×#474	C₂²	1	4	yes	complemented
71	C₃×#432	C₂²	1	2	yes	—
72	C₃×#432	C₂²	1	2	yes	—
73	C₃×#432	C₂²	1	2	yes	—
74	C₃×#432	C₂²	1	2	yes	—
75	C₃×#427	C₂²	1	8	yes	—
76	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
77	C₃×#416	C₂²	1	8	yes	—
78	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
79	C₂×C₃×#97	C₂²	1	2	yes	—
80	#3444	C₂×C₃	1	1	yes	characteristic
81	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
82	#3240	C₂×C₃	1	4	yes	complemented
83	#3239	C₂×C₃	1	2	yes	complemented
84	#3238	C₂×C₃	1	2	yes	complemented
85	#3237	C₂×C₃	1	2	yes	complemented
86	#3236	C₂×C₃	1	2	yes	complemented
87	#3235	C₂×C₃	1	2	yes	complemented
88	#3234	C₂×C₃	1	2	yes	complemented
89	#3162	C₂×C₃	1	2	yes	complemented
90	#3135	C₂×C₃	1	2	yes	complemented
91	#3091	C₂×C₃	1	4	yes	complemented
92	#3076	C₂×C₃	1	4	yes	complemented
93	C₂×#432	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃×#41	—	2	1	no	—
95	C₂×C₃×#41	—	2	1	no	—
96	C₂×C₃×#41	C₂³	1	2	yes	—
97	C₂²×C₃×Q₈	—	2	1	no	—
98	C₂²×C₃×Q₈	—	2	1	no	—
99	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
100	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
101	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₈	C₂³	1	4	yes	—
103	C₃×C₄⋊Q₈	—	2	1	no	—
104	C₃×C₄⋊Q₈	—	2	1	no	—
105	C₃×C₄⋊Q₈	—	2	1	no	—
106	C₃×C₄⋊Q₈	—	2	1	no	—
107	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃×#127	C₂³	1	1	yes	characteristic
115	C₃×#126	—	2	2	no	—
116	C₃×#126	—	2	2	no	—
117	C₃×#125	—	2	2	no	—
118	C₃×#125	—	2	2	no	—
119	C₃×#125	—	2	1	no	—
120	C₃×#125	—	2	1	no	—
121	C₃×#125	C₂³	1	4	yes	—
122	C₃×#125	C₂³	1	4	yes	—
123	C₃×#125	C₂³	1	2	yes	—
124	C₃×#124	—	2	1	no	—
125	C₃×#124	—	2	1	no	—
126	C₃×#124	C₂³	1	2	yes	—
127	C₃×#123	—	2	2	no	—
128	C₃×#123	—	2	2	no	—
129	C₃×#123	—	2	2	no	—
130	C₃×C₂²⋊Q₈	—	2	2	no	—
131	C₃×C₂²⋊Q₈	—	2	2	no	—
132	C₃×C₂²⋊Q₈	—	2	2	no	—
133	C₃×C₂²⋊Q₈	—	2	2	no	—
134	C₃×C₂²⋊Q₈	—	2	2	no	—
135	C₃×C₂²⋊Q₈	—	2	2	no	—
136	C₃×C₂²⋊Q₈	—	2	2	no	—
137	C₃×C₂²⋊Q₈	—	2	2	no	—
138	C₃×C₂²⋊Q₈	—	2	1	no	—
139	C₃×C₂²⋊Q₈	—	2	1	no	—
140	C₃×C₂²⋊Q₈	—	2	1	no	—
141	C₃×C₂²⋊Q₈	—	2	1	no	—
142	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₃×#121	—	2	1	no	—
145	C₃×#121	—	2	1	no	—
146	C₃×#121	—	2	1	no	—
147	C₃×#121	—	2	1	no	—
148	C₃×#121	C₂³	1	2	yes	—
149	C₃×#121	C₂³	1	2	yes	—
150	C₃×#120	—	2	2	no	—
151	C₃×C₄×Q₈	—	2	2	no	—
152	C₃×C₄×Q₈	—	2	2	no	—
153	C₃×C₄×Q₈	—	2	2	no	—
154	C₃×C₄×Q₈	—	2	2	no	—
155	C₃×C₄×Q₈	—	2	2	no	—
156	C₃×C₄×Q₈	—	2	2	no	—
157	C₃×C₄×Q₈	—	2	2	no	—
158	C₃×C₄×Q₈	—	2	2	no	—
159	C₃×C₄×Q₈	—	2	1	no	—
160	C₃×C₄×Q₈	—	2	1	no	—
161	C₃×C₄×Q₈	—	2	1	no	—
162	C₃×C₄×Q₈	—	2	1	no	—
163	C₃×C₄×Q₈	C₂³	1	2	yes	—
164	C₃×C₄×Q₈	C₂³	1	2	yes	—
165	C₃×C₄×D₄	—	2	2	no	—
166	C₃×C₄×D₄	—	2	2	no	—
167	C₃×C₄×D₄	—	2	2	no	—
168	C₃×C₄×D₄	—	2	2	no	—
169	C₃×C₄×D₄	—	2	2	no	—
170	C₃×C₄×D₄	—	2	2	no	—
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	—	2	1	no	—
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	C₂³	1	2	yes	—
176	C₃×C₄×D₄	C₂³	1	2	yes	—
177	C₃×#117	—	2	2	no	—
178	C₃×#117	—	2	2	no	—
179	C₃×#117	—	2	1	no	—
180	C₃×#117	—	2	1	no	—
181	C₃×#117	—	2	2	no	—
182	C₃×#117	—	2	2	no	—
183	C₃×#117	—	2	2	no	—
184	C₃×#117	C₂³	1	4	yes	—
185	C₃×#117	C₂³	1	2	yes	—
186	C₃×#117	C₂³	1	4	yes	—
187	C₂×C₃×C₄⋊C₄	—	2	2	no	—
188	C₂×C₃×C₄⋊C₄	—	2	2	no	—
189	C₂×C₃×C₄⋊C₄	—	2	1	no	—
190	C₂×C₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
194	C₂×C₃×C₄²	—	2	2	no	—
195	C₂×C₃×C₄²	—	2	2	no	—
196	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
197	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
198	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
199	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
200	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
201	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₃×#107	C₂³	1	8	yes	—
209	C₃×#107	C₂³	1	8	yes	—
210	C₃×#106	C₂³	1	8	yes	—
211	C₃×#106	C₂³	1	8	yes	—
212	C₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₃×#103	C₂³	1	8	yes	—
215	C₃×#103	C₂³	1	8	yes	—
216	C₃×#102	C₂³	1	8	yes	—
217	C₃×#102	C₂³	1	8	yes	—
218	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
219	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
220	C₃×#97	C₂³	1	4	yes	—
221	C₃×#97	C₂³	1	4	yes	—
222	#533	—	2	1	no	—
223	#533	—	2	1	no	—
224	#533	—	2	1	no	—
225	#533	—	2	1	no	—
226	#533	C₂²×C₃	1	1	yes	characteristic
227	#533	C₂²×C₃	1	1	yes	characteristic
228	#533	C₂²×C₃	1	2	yes	—
229	#533	C₂²×C₃	1	2	yes	—
230	#533	C₂²×C₃	1	1	yes	characteristic
231	#533	C₂²×C₃	1	2	yes	—
232	#533	C₂²×C₃	1	2	yes	—
233	#532	C₂²×C₃	1	1	yes	characteristic
234	#532	C₂²×C₃	1	1	yes	characteristic
235	#532	C₂²×C₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
238	#529	—	2	1	no	—
239	#529	—	2	1	no	—
240	#529	—	2	1	no	—
241	#529	—	2	1	no	—
242	#529	C₂²×C₃	1	2	yes	—
243	#529	C₂²×C₃	1	2	yes	—
244	C₂×#125	C₂²×C₃	1	2	yes	—
245	#525	—	2	1	no	—
246	#525	—	2	1	no	—
247	#525	C₂²×C₃	1	2	yes	—
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₄×#41	—	2	1	no	—
251	C₄×#41	—	2	1	no	—
252	C₄×#41	C₂²×C₃	1	2	yes	—
253	C₂×C₄×Q₈	—	2	1	no	—
254	C₂×C₄×Q₈	—	2	1	no	—
255	C₂×#117	C₂²×C₃	1	2	yes	—
256	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
257	#501	C₂²×C₃	1	4	yes	complemented
258	#501	C₂²×C₃	1	4	yes	complemented
259	#501	C₂²×C₃	1	4	yes	complemented
260	#501	C₂²×C₃	1	4	yes	complemented
261	#491	C₂²×C₃	1	4	yes	complemented
262	#490	C₂²×C₃	1	4	yes	complemented
263	#489	C₂²×C₃	1	4	yes	complemented
264	#489	C₂²×C₃	1	4	yes	complemented
265	#485	C₂²×C₃	1	8	yes	—
266	#484	C₂²×C₃	1	4	yes	—
267	#483	C₂²×C₃	1	4	yes	—
268	#482	C₂²×C₃	1	8	yes	—
269	#481	C₂²×C₃	1	4	yes	—
270	#480	C₂²×C₃	1	4	yes	—
271	#479	C₂²×C₃	1	8	yes	complemented
272	#478	C₂²×C₃	1	8	yes	complemented
273	#477	C₂²×C₃	1	4	yes	complemented
274	#476	C₂²×C₃	1	4	yes	complemented
275	#475	C₂²×C₃	1	4	yes	complemented
276	#474	C₂²×C₃	1	4	yes	complemented
277	#432	C₂²×C₃	1	2	yes	—
278	#432	C₂²×C₃	1	2	yes	—
279	#432	C₂²×C₃	1	2	yes	—
280	#432	C₂²×C₃	1	2	yes	—
281	#427	C₂²×C₃	1	8	yes	—
282	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
283	#416	C₂²×C₃	1	8	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
285	C₂×#97	C₂²×C₃	1	2	yes	—
286	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
287	C₃×#41	—	2	8	no	—
288	C₃×#41	—	4	4	no	—
289	C₃×#41	—	4	4	no	—
290	C₂×C₃×Q₈	—	2	1	no	—
291	C₂×C₃×Q₈	—	2	1	no	—
292	C₂×C₃×Q₈	—	2	2	no	—
293	C₂×C₃×Q₈	—	2	2	no	—
294	C₂×C₃×Q₈	—	2	2	no	—
295	C₂×C₃×Q₈	—	2	2	no	—
296	C₂×C₃×Q₈	—	4	4	no	—
297	C₂×C₃×Q₈	—	4	4	no	—
298	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	2	2	no	—
302	C₂×C₃×D₄	—	2	1	no	—
303	C₂×C₃×D₄	—	2	1	no	—
304	C₂×C₃×D₄	C₂⁴	1	2	yes	—
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	2	no	—
307	C₂²×C₃×C₄	—	2	2	no	—
308	C₂²×C₃×C₄	—	2	2	no	—
309	C₂²×C₃×C₄	—	2	2	no	—
310	C₂²×C₃×C₄	—	2	2	no	—
311	C₂²×C₃×C₄	—	4	2	no	—
312	C₂²×C₃×C₄	—	4	2	no	—
313	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
331	C₂×C₃×C₈	—	2	8	no	—
332	C₂×C₃×C₈	C₂⁴	1	8	yes	—
333	C₃×C₄⋊C₄	—	2	4	no	—
334	C₃×C₄⋊C₄	—	2	4	no	—
335	C₃×C₄⋊C₄	—	2	4	no	—
336	C₃×C₄⋊C₄	—	2	4	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	2	no	—
341	C₃×C₄⋊C₄	—	2	2	no	—
342	C₃×C₄⋊C₄	—	2	2	no	—
343	C₃×C₄⋊C₄	—	2	1	no	—
344	C₃×C₄⋊C₄	—	2	1	no	—
345	C₃×C₄⋊C₄	—	2	1	no	—
346	C₃×C₄⋊C₄	—	2	1	no	—
347	C₃×C₄⋊C₄	—	2	2	no	—
348	C₃×C₄⋊C₄	—	2	2	no	—
349	C₃×C₄⋊C₄	—	2	2	no	—
350	C₃×C₄⋊C₄	—	2	2	no	—
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
354	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
355	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
356	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₂²⋊C₄	—	2	2	no	—
360	C₃×C₂²⋊C₄	—	2	2	no	—
361	C₃×C₂²⋊C₄	—	2	2	no	—
362	C₃×C₂²⋊C₄	—	2	2	no	—
363	C₃×C₂²⋊C₄	—	2	2	no	—
364	C₃×C₂²⋊C₄	—	2	2	no	—
365	C₃×C₂²⋊C₄	—	2	2	no	—
366	C₃×C₂²⋊C₄	—	2	2	no	—
367	C₃×C₂²⋊C₄	—	2	2	no	—
368	C₃×C₄²	—	2	2	no	—
369	C₃×C₄²	—	2	2	no	—
370	C₃×C₄²	—	2	4	no	—
371	C₃×C₄²	—	2	2	no	—
372	C₃×C₄²	—	2	4	no	—
373	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
374	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
375	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
376	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
377	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
378	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
379	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
380	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
381	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
382	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
383	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
384	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
385	C₃×C₄²	C₂⁴	1	1	yes	characteristic
386	C₃×C₄²	C₂⁴	1	1	yes	characteristic
387	C₃×C₄²	C₂⁴	1	1	yes	characteristic
388	C₃×C₄²	C₂⁴	1	1	yes	characteristic
389	C₂×#41	—	2	1	no	—
390	C₂×#41	—	2	1	no	—
391	C₂×#41	C₂³×C₃	1	2	yes	—
392	C₂²×Q₈	—	2	1	no	—
393	C₂²×Q₈	—	2	1	no	—
394	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
395	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₃	1	4	yes	—
398	C₄⋊Q₈	—	2	1	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	—	2	1	no	—
401	C₄⋊Q₈	—	2	1	no	—
402	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
403	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
404	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
405	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
406	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
407	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
408	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
409	#127	C₂³×C₃	1	1	yes	characteristic
410	#126	—	2	2	no	—
411	#126	—	2	2	no	—
412	#125	—	2	2	no	—
413	#125	—	2	2	no	—
414	#125	—	2	1	no	—
415	#125	—	2	1	no	—
416	#125	C₂³×C₃	1	4	yes	—
417	#125	C₂³×C₃	1	4	yes	—
418	#125	C₂³×C₃	1	2	yes	—
419	#124	—	2	1	no	—
420	#124	—	2	1	no	—
421	#124	C₂³×C₃	1	2	yes	—
422	#123	—	2	2	no	—
423	#123	—	2	2	no	—
424	#123	—	2	2	no	—
425	C₂²⋊Q₈	—	2	2	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	1	no	—
434	C₂²⋊Q₈	—	2	1	no	—
435	C₂²⋊Q₈	—	2	1	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
438	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
439	#121	—	2	1	no	—
440	#121	—	2	1	no	—
441	#121	—	2	1	no	—
442	#121	—	2	1	no	—
443	#121	C₂³×C₃	1	2	yes	—
444	#121	C₂³×C₃	1	2	yes	—
445	#120	—	2	2	no	—
446	C₄×Q₈	—	2	2	no	—
447	C₄×Q₈	—	2	2	no	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	—	2	2	no	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	—	2	1	no	—
457	C₄×Q₈	—	2	1	no	—
458	C₄×Q₈	C₂³×C₃	1	2	yes	—
459	C₄×Q₈	C₂³×C₃	1	2	yes	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	2	1	no	—
467	C₄×D₄	—	2	1	no	—
468	C₄×D₄	—	2	1	no	—
469	C₄×D₄	—	2	1	no	—
470	C₄×D₄	C₂³×C₃	1	2	yes	—
471	C₄×D₄	C₂³×C₃	1	2	yes	—
472	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	#117	—	2	1	no	—
475	#117	—	2	1	no	—
476	#117	—	2	2	no	—
477	#117	—	2	2	no	—
478	#117	—	2	2	no	—
479	#117	C₂³×C₃	1	4	yes	—
480	#117	C₂³×C₃	1	4	yes	—
481	#117	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	—	2	2	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₂²⋊C₄	—	2	2	no	—
489	C₂×C₄²	—	2	2	no	—
490	C₂×C₄²	—	2	2	no	—
491	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
492	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
493	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
494	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
495	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
496	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
503	#107	C₂³×C₃	1	8	yes	—
504	#107	C₂³×C₃	1	8	yes	—
505	#106	C₂³×C₃	1	8	yes	—
506	#106	C₂³×C₃	1	8	yes	—
507	C₄⋊C₈	C₂³×C₃	1	4	yes	—
508	C₄⋊C₈	C₂³×C₃	1	4	yes	—
509	#103	C₂³×C₃	1	8	yes	—
510	#103	C₂³×C₃	1	8	yes	—
511	#102	C₂³×C₃	1	8	yes	—
512	#102	C₂³×C₃	1	8	yes	—
513	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
514	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
515	#97	C₂³×C₃	1	4	yes	—
516	#97	C₂³×C₃	1	4	yes	—
517	C₂³×C₃	—	2	2	no	—
518	C₂³×C₃	—	2	2	no	—
519	C₂³×C₃	—	2	2	no	—
520	C₂³×C₃	—	4	1	no	—
521	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
523	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
524	C₃×Q₈	—	2	4	no	—
525	C₃×Q₈	—	4	4	no	—
526	C₃×Q₈	—	4	4	no	—
527	C₃×Q₈	—	4	4	no	—
528	C₃×Q₈	—	4	2	no	—
529	C₃×Q₈	—	4	2	no	—
530	C₃×Q₈	—	4	4	no	—
531	C₃×D₄	—	2	4	no	—
532	C₃×D₄	—	4	2	no	—
533	C₃×D₄	—	4	2	no	—
534	C₃×D₄	—	4	4	no	—
535	C₃×D₄	—	4	4	no	—
536	C₃×D₄	—	4	4	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	4	no	—
551	C₂×C₃×C₄	—	2	4	no	—
552	C₂×C₃×C₄	—	4	1	no	—
553	C₂×C₃×C₄	—	4	1	no	—
554	C₂×C₃×C₄	—	4	1	no	—
555	C₂×C₃×C₄	—	4	1	no	—
556	C₂×C₃×C₄	—	4	1	no	—
557	C₂×C₃×C₄	—	4	1	no	—
558	C₂×C₃×C₄	—	4	1	no	—
559	C₂×C₃×C₄	—	4	4	no	—
560	C₂×C₃×C₄	—	4	4	no	—
561	C₂×C₃×C₄	—	4	4	no	—
562	C₂×C₃×C₄	—	4	4	no	—
563	C₂×C₃×C₄	—	4	4	no	—
564	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
576	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
577	C₃×C₈	—	2	8	no	—
578	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
579	#41	—	2	8	no	—
580	#41	—	4	4	no	—
581	#41	—	4	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	4	4	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	C₂⁴×C₃	1	2	yes	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
606	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
607	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
608	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
609	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
610	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
612	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
615	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
617	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
619	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
623	C₂×C₈	—	2	8	no	—
624	C₂×C₈	C₂⁴×C₃	1	8	yes	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
646	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
647	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
666	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
667	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
668	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
669	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
670	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
671	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
672	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
673	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
674	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
675	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
676	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
677	C₄²	C₂⁴×C₃	1	1	yes	characteristic
678	C₄²	C₂⁴×C₃	1	1	yes	characteristic
679	C₄²	C₂⁴×C₃	1	1	yes	characteristic
680	C₄²	C₂⁴×C₃	1	1	yes	characteristic
681	C₂²×C₃	—	2	1	no	—
682	C₂²×C₃	—	2	1	no	—
683	C₂²×C₃	—	2	1	no	—
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	2	1	no	—
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	4	4	no	—
689	C₂²×C₃	—	4	2	no	—
690	C₂²×C₃	—	4	2	no	—
691	C₂²×C₃	—	4	2	no	—
692	C₂²×C₃	#536	1	2	yes	—
693	C₂²×C₃	#575	1	2	yes	—
694	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
695	C₃×C₄	—	2	1	no	—
696	C₃×C₄	—	2	1	no	—
697	C₃×C₄	—	2	1	no	—
698	C₃×C₄	—	2	1	no	—
699	C₃×C₄	—	2	1	no	—
700	C₃×C₄	—	2	1	no	—
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	4	2	no	—
705	C₃×C₄	—	4	2	no	—
706	C₃×C₄	—	4	2	no	—
707	C₃×C₄	—	4	4	no	—
708	C₃×C₄	—	4	4	no	—
709	C₃×C₄	#536	1	2	yes	—
710	C₃×C₄	#575	1	2	yes	—
711	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	4	1	no	—
716	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
717	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
718	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
719	Q₈	—	2	4	no	—
720	Q₈	—	4	4	no	—
721	Q₈	—	4	4	no	—
722	Q₈	—	4	4	no	—
723	Q₈	—	4	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	4	no	—
726	D₄	—	2	4	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
760	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
762	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
763	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
764	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
765	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
766	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
768	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
769	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
770	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
771	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
772	C₈	—	2	8	no	—
773	C₂×C₃	—	2	2	no	—
774	C₂×C₃	—	2	2	no	—
775	C₂×C₃	—	4	1	no	—
776	C₂×C₃	—	8	2	no	—
777	C₂×C₃	C₂×#536	1	1	yes	characteristic
778	C₂×C₃	C₂×#575	1	1	yes	characteristic
779	C₂×C₃	C₂×#575	1	1	yes	characteristic
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	C₃×#536	1	2	yes	—
792	C₂²	C₃×#575	1	2	yes	—
793	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	4	no	—
807	C₄	—	4	4	no	—
808	C₄	C₃×#536	1	2	yes	—
809	C₄	C₃×#575	1	2	yes	—
810	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
811	C₃	#60854	1	1	yes	characteristic, direct product factor, Sylow
812	C₂	—	2	2	no	—
813	C₂	—	2	2	no	—
814	C₂	—	4	1	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×C₃×#536	1	1	yes	characteristic
817	C₂	C₂×C₃×#575	1	1	yes	characteristic
818	C₂	C₂×C₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
prime radical	C₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#533	C₂	semidirect
3. C₃×#3240	C₂	semidirect
4. C₃×#3239	C₂	semidirect
5. C₃×#3238	C₂	semidirect
6. C₃×#3237	C₂	semidirect
7. C₃×#3236	C₂	semidirect
8. C₃×#3235	C₂	semidirect
9. C₃×#3234	C₂	semidirect
10. C₃×#3162	C₂	semidirect
11. C₃×#3135	C₂	semidirect
12. C₃×#3091	C₂	semidirect
13. C₃×#3076	C₂	semidirect
14. C₂×C₃×#432	C₂	semidirect
15. #60854	C₃	direct (N × H)
51. C₃×#501	C₂²	semidirect
52. C₃×#501	C₂²	semidirect
53. C₃×#501	C₂²	semidirect
54. C₃×#501	C₂²	semidirect
55. C₃×#491	C₂²	semidirect
56. C₃×#490	C₂²	semidirect
57. C₃×#489	C₂²	semidirect
58. C₃×#489	C₂²	semidirect
65. C₃×#479	C₂²	semidirect
66. C₃×#478	C₂²	semidirect
67. C₃×#477	C₂²	semidirect
68. C₃×#476	C₂²	semidirect
69. C₃×#475	C₂²	semidirect
70. C₃×#474	C₂²	semidirect
81. C₂×#533	C₂×C₃	semidirect
82. #3240	C₂×C₃	semidirect
83. #3239	C₂×C₃	semidirect
84. #3238	C₂×C₃	semidirect
85. #3237	C₂×C₃	semidirect
86. #3236	C₂×C₃	semidirect
87. #3235	C₂×C₃	semidirect
88. #3234	C₂×C₃	semidirect
89. #3162	C₂×C₃	semidirect
90. #3135	C₂×C₃	semidirect
91. #3091	C₂×C₃	semidirect
92. #3076	C₂×C₃	semidirect
93. C₂×#432	C₂×C₃	semidirect
257. #501	C₂²×C₃	semidirect
258. #501	C₂²×C₃	semidirect
259. #501	C₂²×C₃	semidirect
260. #501	C₂²×C₃	semidirect
261. #491	C₂²×C₃	semidirect
262. #490	C₂²×C₃	semidirect
263. #489	C₂²×C₃	semidirect
264. #489	C₂²×C₃	semidirect
271. #479	C₂²×C₃	semidirect
272. #478	C₂²×C₃	semidirect
273. #477	C₂²×C₃	semidirect
274. #476	C₂²×C₃	semidirect
275. #475	C₂²×C₃	semidirect
276. #474	C₂²×C₃	semidirect
811. C₃	#60854	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3444	2
C₂×C₃×#533	2
C₃×#3240	2
C₃×#3239	2
C₃×#3238	2
C₃×#3237	2
C₃×#3236	2
C₃×#3235	2
C₃×#3234	2
C₃×#3162	2
C₃×#3135	2
C₃×#3091	2
C₃×#3076	2
C₂×C₃×#432	2
#60854	3

Subgroups — C3×#60854 #10679461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60854 #10679461