Subgroups — C₃×#61842 #10680449

Order 768.

1668 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3523	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3390	C₂	1	4	yes	maximal, complemented
4	C₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₃×#3383	C₂	1	2	yes	maximal, complemented
6	C₃×#3377	C₂	1	4	yes	maximal, complemented
7	C₃×#3374	C₂	1	2	yes	maximal, complemented
8	C₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₃×#3239	C₂	1	1	yes	maximal, characteristic
10	C₃×#3236	C₂	1	2	yes	maximal, complemented
11	C₃×#3232	C₂	1	2	yes	maximal
12	C₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3117	C₂	1	2	yes	maximal
14	C₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3108	C₂	1	1	yes	maximal, characteristic
16	C₃×#3104	C₂	1	2	yes	maximal, complemented
17	C₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	#61842	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#557	—	2	1	no	—
20	C₃×#557	—	2	1	no	—
21	C₃×#557	—	2	2	no	—
22	C₃×#557	C₂²	1	1	yes	characteristic
23	C₃×#557	C₂²	1	2	yes	—
24	C₃×#557	C₂²	1	2	yes	—
25	C₃×#557	C₂²	1	4	yes	—
26	C₃×#557	C₂²	1	2	yes	—
27	C₃×#557	C₂²	1	1	yes	characteristic
28	C₃×#556	C₂²	1	1	yes	characteristic
29	C₃×#556	C₂²	1	2	yes	—
30	C₃×#552	—	2	1	no	—
31	C₃×#552	—	2	2	no	—
32	C₃×D₄×Q₈	—	2	1	no	—
33	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
34	C₃×#541	—	2	2	no	—
35	C₃×#541	—	2	1	no	—
36	C₃×#533	C₂²	1	1	yes	characteristic
37	C₃×#533	C₂²	1	2	yes	—
38	C₂×C₃×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₃×#529	C₂²	1	2	yes	—
41	C₃×#529	C₂²	1	1	yes	characteristic
42	C₂×C₃×#125	—	2	2	no	—
43	C₂×C₃×#125	C₂²	1	2	yes	—
44	C₃×#519	—	2	1	no	—
45	C₂×C₃×C₄×Q₈	—	2	1	no	—
46	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
47	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₃×#501	C₂²	1	4	yes	—
50	C₃×#501	C₂²	1	2	yes	—
51	C₃×#500	C₂²	1	2	yes	—
52	C₃×#499	C₂²	1	4	yes	—
53	C₃×#491	C₂²	1	4	yes	—
54	C₃×#489	C₂²	1	2	yes	—
55	C₃×#488	C₂²	1	4	yes	—
56	C₃×#487	C₂²	1	2	yes	—
57	C₃×#484	C₂²	1	2	yes	—
58	C₃×#484	C₂²	1	2	yes	—
59	C₃×#484	C₂²	1	2	yes	—
60	C₃×#483	C₂²	1	2	yes	—
61	C₃×#483	C₂²	1	1	yes	characteristic
62	C₃×#481	C₂²	1	2	yes	—
63	C₃×#480	C₂²	1	1	yes	characteristic
64	C₃×#479	C₂²	1	2	yes	—
65	C₃×#479	C₂²	1	4	yes	—
66	C₃×#479	C₂²	1	4	yes	—
67	C₃×#479	C₂²	1	4	yes	—
68	C₃×#479	C₂²	1	4	yes	—
69	C₃×#478	C₂²	1	4	yes	—
70	C₃×#477	C₂²	1	4	yes	—
71	C₃×#477	C₂²	1	4	yes	—
72	C₃×#475	C₂²	1	2	yes	—
73	C₃×#475	C₂²	1	2	yes	—
74	C₃×#474	C₂²	1	2	yes	—
75	C₃×#464	C₂²	1	2	yes	—
76	C₃×#464	C₂²	1	4	yes	—
77	C₃×#462	C₂²	1	4	yes	—
78	C₃×#462	C₂²	1	2	yes	—
79	C₃×#451	C₂²	1	1	yes	characteristic
80	C₃×#451	C₂²	1	2	yes	—
81	C₃×#448	C₂²	1	1	yes	characteristic
82	C₃×#446	C₂²	1	2	yes	—
83	C₃×#446	C₂²	1	4	yes	—
84	C₃×C₈×Q₈	C₂²	1	2	yes	—
85	C₃×#441	C₂²	1	4	yes	—
86	C₃×#441	C₂²	1	4	yes	—
87	C₃×#440	C₂²	1	4	yes	—
88	C₃×C₄×Q₁₆	C₂²	1	4	yes	—
89	C₃×C₄×Q₁₆	C₂²	1	4	yes	—
90	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
91	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
92	C₃×#432	C₂²	1	2	yes	—
93	C₃×#432	C₂²	1	1	yes	characteristic
94	C₃×#431	C₂²	1	1	yes	characteristic
95	C₃×#431	C₂²	1	2	yes	—
96	#3523	C₂×C₃	1	1	yes	characteristic
97	C₂×#557	C₂×C₃	1	1	yes	characteristic, complemented
98	#3390	C₂×C₃	1	4	yes	complemented
99	#3386	C₂×C₃	1	2	yes	complemented
100	#3383	C₂×C₃	1	2	yes	complemented
101	#3377	C₂×C₃	1	4	yes	complemented
102	#3374	C₂×C₃	1	2	yes	complemented
103	#3364	C₂×C₃	1	2	yes	complemented
104	#3239	C₂×C₃	1	1	yes	characteristic
105	#3236	C₂×C₃	1	2	yes	complemented
106	#3232	C₂×C₃	1	2	yes	—
107	#3230	C₂×C₃	1	1	yes	characteristic, complemented
108	#3117	C₂×C₃	1	2	yes	—
109	#3113	C₂×C₃	1	1	yes	characteristic, complemented
110	#3108	C₂×C₃	1	1	yes	characteristic
111	#3104	C₂×C₃	1	2	yes	complemented
112	#2984	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂²×C₃×Q₈	—	2	1	no	—
114	C₂²×C₃×Q₈	—	2	1	no	—
115	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
116	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
117	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
118	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
119	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
120	C₃×C₄⋊Q₈	—	2	2	no	—
121	C₃×C₄⋊Q₈	—	2	2	no	—
122	C₃×C₄⋊Q₈	—	2	4	no	—
123	C₃×C₄⋊Q₈	—	2	1	no	—
124	C₃×C₄⋊Q₈	—	2	2	no	—
125	C₃×C₄⋊Q₈	—	2	1	no	—
126	C₃×C₄⋊Q₈	—	2	1	no	—
127	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₃×#126	—	2	2	no	—
134	C₃×#126	—	2	2	no	—
135	C₃×#126	—	2	2	no	—
136	C₃×#126	—	2	2	no	—
137	C₃×#126	—	2	1	no	—
138	C₃×#125	—	2	4	no	—
139	C₃×#125	—	2	4	no	—
140	C₃×#125	—	2	4	no	—
141	C₃×#125	—	2	4	no	—
142	C₃×#125	—	2	2	no	—
143	C₃×#125	—	2	2	no	—
144	C₃×#125	—	2	2	no	—
145	C₃×#125	—	2	1	no	—
146	C₃×#125	—	2	2	no	—
147	C₃×#125	—	2	2	no	—
148	C₃×#125	—	2	2	no	—
149	C₃×#125	—	2	2	no	—
150	C₃×#125	—	2	1	no	—
151	C₃×#125	C₂³	1	4	yes	—
152	C₃×#125	C₂³	1	4	yes	—
153	C₃×#125	C₂³	1	2	yes	—
154	C₃×#125	C₂³	1	1	yes	characteristic
155	C₃×#124	C₂³	1	2	yes	—
156	C₃×#124	C₂³	1	1	yes	characteristic
157	C₃×#123	—	2	2	no	—
158	C₃×#123	—	2	1	no	—
159	C₃×C₂²⋊Q₈	—	2	1	no	—
160	C₃×C₂²⋊Q₈	—	2	2	no	—
161	C₃×C₂²⋊Q₈	—	2	1	no	—
162	C₃×C₂²⋊Q₈	—	2	2	no	—
163	C₃×C₂²⋊Q₈	—	2	1	no	—
164	C₃×C₂²⋊Q₈	—	2	2	no	—
165	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₃×#121	C₂³	1	1	yes	characteristic
168	C₃×C₄×Q₈	—	2	1	no	—
169	C₃×C₄×Q₈	—	2	2	no	—
170	C₃×C₄×Q₈	—	2	2	no	—
171	C₃×C₄×Q₈	—	2	4	no	—
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	2	2	no	—
174	C₃×C₄×Q₈	—	2	2	no	—
175	C₃×C₄×Q₈	—	2	2	no	—
176	C₃×C₄×Q₈	—	2	1	no	—
177	C₃×C₄×Q₈	—	2	1	no	—
178	C₃×C₄×Q₈	—	2	2	no	—
179	C₃×C₄×Q₈	—	2	1	no	—
180	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
181	C₃×C₄×Q₈	D₄	1	2	yes	—
182	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
183	C₃×C₄×Q₈	C₂³	1	2	yes	—
184	C₃×C₄×Q₈	C₂³	1	4	yes	—
185	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
186	C₃×C₄×Q₈	C₂³	1	2	yes	—
187	C₃×C₄×Q₈	C₂³	1	2	yes	—
188	C₃×C₄×Q₈	C₂³	1	4	yes	—
189	C₃×C₄×Q₈	C₂³	1	2	yes	—
190	C₃×C₄×Q₈	C₂³	1	2	yes	—
191	C₃×C₄×Q₈	C₂³	1	2	yes	—
192	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
193	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
194	C₃×C₄×Q₈	C₂³	1	2	yes	—
195	C₃×C₄×D₄	—	2	1	no	—
196	C₃×C₄×D₄	—	2	2	no	—
197	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
198	C₃×C₄×D₄	C₂³	1	2	yes	—
199	C₃×#117	—	2	2	no	—
200	C₃×#117	—	2	1	no	—
201	C₃×#117	—	2	1	no	—
202	C₃×#117	—	2	2	no	—
203	C₃×#117	—	2	2	no	—
204	C₃×#117	—	2	1	no	—
205	C₂×C₃×C₄⋊C₄	—	2	2	no	—
206	C₂×C₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₃×C₄⋊C₄	—	2	2	no	—
208	C₂×C₃×C₄⋊C₄	—	2	1	no	—
209	C₂×C₃×C₄⋊C₄	—	2	2	no	—
210	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄²	—	2	2	no	—
215	C₂×C₃×C₄²	—	2	1	no	—
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₃×#107	C₂³	1	4	yes	—
219	C₃×#107	C₂³	1	4	yes	—
220	C₃×#107	C₂³	1	2	yes	—
221	C₃×#107	C₂³	1	4	yes	—
222	C₃×#106	C₂³	1	2	yes	—
223	C₃×#106	C₂³	1	4	yes	—
224	C₃×#106	C₂³	1	4	yes	—
225	C₃×C₄⋊C₈	C₂³	1	4	yes	—
226	C₃×C₄⋊C₈	C₂³	1	2	yes	—
227	C₃×C₄⋊C₈	C₂³	1	2	yes	—
228	C₃×C₄⋊C₈	C₂³	1	4	yes	—
229	C₃×#103	C₂³	1	2	yes	—
230	C₃×#103	C₂³	1	4	yes	—
231	C₃×#103	C₂³	1	2	yes	—
232	C₃×#103	C₂³	1	4	yes	—
233	C₃×#103	C₂³	1	4	yes	—
234	C₃×#103	C₂³	1	2	yes	—
235	C₃×#103	C₂³	1	4	yes	—
236	C₃×#103	C₂³	1	4	yes	—
237	C₃×#102	C₂³	1	2	yes	—
238	C₃×#102	C₂³	1	4	yes	—
239	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
240	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
241	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₃×#97	C₂³	1	4	yes	—
243	C₃×#97	C₂³	1	2	yes	—
244	C₃×C₄×C₈	C₂³	1	2	yes	—
245	C₃×C₄×C₈	C₂³	1	4	yes	—
246	#557	—	2	1	no	—
247	#557	—	2	1	no	—
248	#557	—	2	2	no	—
249	#557	C₂²×C₃	1	1	yes	characteristic
250	#557	C₂²×C₃	1	2	yes	—
251	#557	C₂²×C₃	1	2	yes	—
252	#557	C₂²×C₃	1	4	yes	—
253	#557	C₂²×C₃	1	1	yes	characteristic
254	#557	C₂²×C₃	1	2	yes	—
255	#556	C₂²×C₃	1	1	yes	characteristic
256	#556	C₂²×C₃	1	2	yes	—
257	#552	—	2	1	no	—
258	#552	—	2	2	no	—
259	D₄×Q₈	—	2	1	no	—
260	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
261	#541	—	2	2	no	—
262	#541	—	2	1	no	—
263	#533	C₂²×C₃	1	2	yes	—
264	#533	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	—	2	1	no	—
266	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
267	#529	C₂²×C₃	1	1	yes	characteristic
268	#529	C₂²×C₃	1	2	yes	—
269	C₂×#125	—	2	2	no	—
270	C₂×#125	C₂²×C₃	1	2	yes	—
271	#519	—	2	1	no	—
272	C₂×C₄×Q₈	—	2	1	no	—
273	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
274	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
276	#501	C₂²×C₃	1	4	yes	—
277	#501	C₂²×C₃	1	2	yes	—
278	#500	C₂²×C₃	1	2	yes	—
279	#499	C₂²×C₃	1	4	yes	—
280	#491	C₂²×C₃	1	4	yes	—
281	#489	C₂²×C₃	1	2	yes	—
282	#488	C₂²×C₃	1	4	yes	—
283	#487	C₂²×C₃	1	2	yes	—
284	#484	C₂²×C₃	1	2	yes	—
285	#484	C₂²×C₃	1	2	yes	—
286	#484	C₂²×C₃	1	2	yes	—
287	#483	C₂²×C₃	1	1	yes	characteristic
288	#483	C₂²×C₃	1	2	yes	—
289	#481	C₂²×C₃	1	2	yes	—
290	#480	C₂²×C₃	1	1	yes	characteristic
291	#479	C₂²×C₃	1	2	yes	—
292	#479	C₂²×C₃	1	4	yes	—
293	#479	C₂²×C₃	1	4	yes	—
294	#479	C₂²×C₃	1	4	yes	—
295	#479	C₂²×C₃	1	4	yes	—
296	#478	C₂²×C₃	1	4	yes	—
297	#477	C₂²×C₃	1	4	yes	—
298	#477	C₂²×C₃	1	4	yes	—
299	#475	C₂²×C₃	1	2	yes	—
300	#475	C₂²×C₃	1	2	yes	—
301	#474	C₂²×C₃	1	2	yes	—
302	#464	C₂²×C₃	1	2	yes	—
303	#464	C₂²×C₃	1	4	yes	—
304	#462	C₂²×C₃	1	4	yes	—
305	#462	C₂²×C₃	1	2	yes	—
306	#451	C₂²×C₃	1	1	yes	characteristic
307	#451	C₂²×C₃	1	2	yes	—
308	#448	C₂²×C₃	1	1	yes	characteristic
309	#446	C₂²×C₃	1	2	yes	—
310	#446	C₂²×C₃	1	4	yes	—
311	C₈×Q₈	C₂²×C₃	1	2	yes	—
312	#441	C₂²×C₃	1	4	yes	—
313	#441	C₂²×C₃	1	4	yes	—
314	#440	C₂²×C₃	1	4	yes	—
315	C₄×Q₁₆	C₂²×C₃	1	4	yes	—
316	C₄×Q₁₆	C₂²×C₃	1	4	yes	—
317	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
318	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
319	#432	C₂²×C₃	1	1	yes	characteristic
320	#432	C₂²×C₃	1	2	yes	—
321	#431	C₂²×C₃	1	2	yes	—
322	#431	C₂²×C₃	1	1	yes	characteristic
323	C₂×C₃×Q₈	—	2	4	no	—
324	C₂×C₃×Q₈	—	2	1	no	—
325	C₂×C₃×Q₈	—	2	2	no	—
326	C₂×C₃×Q₈	—	2	1	no	—
327	C₂×C₃×Q₈	—	2	2	no	—
328	C₂×C₃×Q₈	—	2	2	no	—
329	C₂×C₃×Q₈	—	4	2	no	—
330	C₂×C₃×Q₈	—	4	4	no	—
331	C₂×C₃×Q₈	—	4	4	no	—
332	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
333	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
334	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
335	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
336	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
337	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
338	C₂×C₃×D₄	—	2	1	no	—
339	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₃×C₄	—	2	1	no	—
341	C₂²×C₃×C₄	—	2	1	no	—
342	C₂²×C₃×C₄	—	2	2	no	—
343	C₂²×C₃×C₄	—	2	2	no	—
344	C₂²×C₃×C₄	—	2	1	no	—
345	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
346	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
349	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
350	C₃×Q₁₆	—	2	4	no	—
351	C₃×Q₁₆	—	2	8	no	—
352	C₃×SD₁₆	—	2	4	no	—
353	C₂×C₃×C₈	C₂⁴	1	2	yes	—
354	C₂×C₃×C₈	C₂⁴	1	4	yes	—
355	C₂×C₃×C₈	C₂⁴	1	2	yes	—
356	C₃×C₄⋊C₄	—	2	4	no	—
357	C₃×C₄⋊C₄	—	2	4	no	—
358	C₃×C₄⋊C₄	—	2	2	no	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	—	2	4	no	—
361	C₃×C₄⋊C₄	—	2	4	no	—
362	C₃×C₄⋊C₄	—	2	2	no	—
363	C₃×C₄⋊C₄	—	2	2	no	—
364	C₃×C₄⋊C₄	—	2	4	no	—
365	C₃×C₄⋊C₄	—	2	4	no	—
366	C₃×C₄⋊C₄	—	2	1	no	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	2	2	no	—
369	C₃×C₄⋊C₄	—	2	1	no	—
370	C₃×C₄⋊C₄	—	2	2	no	—
371	C₃×C₄⋊C₄	—	2	1	no	—
372	C₃×C₄⋊C₄	—	2	2	no	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	2	2	no	—
375	C₃×C₄⋊C₄	—	2	1	no	—
376	C₃×C₄⋊C₄	—	2	2	no	—
377	C₃×C₄⋊C₄	—	2	1	no	—
378	C₃×C₄⋊C₄	—	2	1	no	—
379	C₃×C₄⋊C₄	—	2	2	no	—
380	C₃×C₄⋊C₄	—	2	2	no	—
381	C₃×C₄⋊C₄	—	2	2	no	—
382	C₃×C₄⋊C₄	—	2	2	no	—
383	C₃×C₄⋊C₄	—	2	2	no	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
387	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
389	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
390	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
391	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
393	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
394	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
395	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
397	C₃×C₂²⋊C₄	—	2	1	no	—
398	C₃×C₂²⋊C₄	—	2	2	no	—
399	C₃×C₂²⋊C₄	—	2	1	no	—
400	C₃×C₂²⋊C₄	—	2	2	no	—
401	C₃×C₂²⋊C₄	—	2	1	no	—
402	C₃×C₂²⋊C₄	—	2	1	no	—
403	C₃×C₂²⋊C₄	—	2	2	no	—
404	C₃×C₂²⋊C₄	—	2	2	no	—
405	C₃×C₂²⋊C₄	—	2	1	no	—
406	C₃×C₄²	—	2	4	no	—
407	C₃×C₄²	—	2	4	no	—
408	C₃×C₄²	—	2	2	no	—
409	C₃×C₄²	—	2	2	no	—
410	C₃×C₄²	—	2	2	no	—
411	C₃×C₄²	—	2	2	no	—
412	C₃×C₄²	—	2	2	no	—
413	C₃×C₄²	—	2	2	no	—
414	C₃×C₄²	—	2	1	no	—
415	C₃×C₄²	C₂×D₄	1	2	yes	—
416	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
417	C₃×C₄²	C₂×D₄	1	2	yes	—
418	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
419	C₃×C₄²	C₂⁴	1	1	yes	characteristic
420	C₃×C₄²	C₂⁴	1	2	yes	—
421	C₃×C₄²	C₂⁴	1	2	yes	—
422	C₃×C₄²	C₂⁴	1	1	yes	characteristic
423	C₂²×Q₈	—	2	1	no	—
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
427	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
428	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
429	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
430	C₄⋊Q₈	—	2	2	no	—
431	C₄⋊Q₈	—	2	2	no	—
432	C₄⋊Q₈	—	2	4	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	C₄⋊Q₈	—	2	2	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
438	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
439	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
440	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
441	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
442	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
443	#126	—	2	2	no	—
444	#126	—	2	2	no	—
445	#126	—	2	2	no	—
446	#126	—	2	2	no	—
447	#126	—	2	1	no	—
448	#125	—	2	4	no	—
449	#125	—	2	4	no	—
450	#125	—	2	4	no	—
451	#125	—	2	4	no	—
452	#125	—	2	2	no	—
453	#125	—	2	2	no	—
454	#125	—	2	2	no	—
455	#125	—	2	1	no	—
456	#125	—	2	2	no	—
457	#125	—	2	2	no	—
458	#125	—	2	2	no	—
459	#125	—	2	2	no	—
460	#125	—	2	1	no	—
461	#125	C₂³×C₃	1	4	yes	—
462	#125	C₂³×C₃	1	4	yes	—
463	#125	C₂³×C₃	1	2	yes	—
464	#125	C₂³×C₃	1	1	yes	characteristic
465	#124	C₂³×C₃	1	2	yes	—
466	#124	C₂³×C₃	1	1	yes	characteristic
467	#123	—	2	2	no	—
468	#123	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
476	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
477	#121	C₂³×C₃	1	1	yes	characteristic
478	C₄×Q₈	—	2	1	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	—	2	4	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
491	C₄×Q₈	C₃×D₄	1	2	yes	—
492	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
493	C₄×Q₈	C₂³×C₃	1	2	yes	—
494	C₄×Q₈	C₂³×C₃	1	4	yes	—
495	C₄×Q₈	C₂³×C₃	1	4	yes	—
496	C₄×Q₈	C₂³×C₃	1	2	yes	—
497	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
498	C₄×Q₈	C₂³×C₃	1	2	yes	—
499	C₄×Q₈	C₂³×C₃	1	2	yes	—
500	C₄×Q₈	C₂³×C₃	1	2	yes	—
501	C₄×Q₈	C₂³×C₃	1	2	yes	—
502	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
503	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
504	C₄×Q₈	C₂³×C₃	1	2	yes	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
508	C₄×D₄	C₂³×C₃	1	2	yes	—
509	#117	—	2	2	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	—	2	2	no	—
513	#117	—	2	2	no	—
514	#117	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	2	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₄²	—	2	2	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	C₂³×C₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
528	#107	C₂³×C₃	1	4	yes	—
529	#107	C₂³×C₃	1	4	yes	—
530	#107	C₂³×C₃	1	2	yes	—
531	#107	C₂³×C₃	1	4	yes	—
532	#106	C₂³×C₃	1	2	yes	—
533	#106	C₂³×C₃	1	4	yes	—
534	#106	C₂³×C₃	1	4	yes	—
535	C₄⋊C₈	C₂³×C₃	1	4	yes	—
536	C₄⋊C₈	C₂³×C₃	1	2	yes	—
537	C₄⋊C₈	C₂³×C₃	1	2	yes	—
538	C₄⋊C₈	C₂³×C₃	1	4	yes	—
539	#103	C₂³×C₃	1	2	yes	—
540	#103	C₂³×C₃	1	4	yes	—
541	#103	C₂³×C₃	1	2	yes	—
542	#103	C₂³×C₃	1	4	yes	—
543	#103	C₂³×C₃	1	4	yes	—
544	#103	C₂³×C₃	1	2	yes	—
545	#103	C₂³×C₃	1	4	yes	—
546	#103	C₂³×C₃	1	4	yes	—
547	#102	C₂³×C₃	1	2	yes	—
548	#102	C₂³×C₃	1	4	yes	—
549	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
550	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
551	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
552	#97	C₂³×C₃	1	4	yes	—
553	#97	C₂³×C₃	1	2	yes	—
554	C₄×C₈	C₂³×C₃	1	2	yes	—
555	C₄×C₈	C₂³×C₃	1	4	yes	—
556	C₂³×C₃	—	2	1	no	—
557	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
558	C₃×Q₈	—	2	4	no	—
559	C₃×Q₈	—	2	2	no	—
560	C₃×Q₈	—	2	2	no	—
561	C₃×Q₈	—	2	2	no	—
562	C₃×Q₈	—	2	2	no	—
563	C₃×Q₈	—	2	4	no	—
564	C₃×Q₈	—	4	2	no	—
565	C₃×Q₈	—	4	4	no	—
566	C₃×Q₈	—	4	4	no	—
567	C₃×Q₈	—	4	2	no	—
568	C₃×Q₈	—	4	4	no	—
569	C₃×Q₈	2₋¹⁺⁴	1	4	yes	—
570	C₃×D₄	—	2	2	no	—
571	C₃×D₄	—	4	2	no	—
572	C₂×C₃×C₄	—	2	4	no	—
573	C₂×C₃×C₄	—	2	4	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	4	no	—
585	C₂×C₃×C₄	—	4	2	no	—
586	C₂×C₃×C₄	—	4	4	no	—
587	C₂×C₃×C₄	—	4	4	no	—
588	C₂×C₃×C₄	—	4	2	no	—
589	C₂×C₃×C₄	—	4	2	no	—
590	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
591	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
592	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
595	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
598	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
600	C₃×C₈	—	2	2	no	—
601	C₃×C₈	—	2	2	no	—
602	C₃×C₈	—	2	4	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×Q₈	—	4	4	no	—
611	C₂×Q₈	—	4	4	no	—
612	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
613	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
614	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
616	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
626	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
627	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
628	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
630	Q₁₆	—	2	4	no	—
631	Q₁₆	—	2	8	no	—
632	SD₁₆	—	2	4	no	—
633	C₂×C₈	C₂⁴×C₃	1	2	yes	—
634	C₂×C₈	C₂⁴×C₃	1	4	yes	—
635	C₂×C₈	C₂⁴×C₃	1	2	yes	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
666	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
667	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
668	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
669	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
670	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
671	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
674	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
675	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
676	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	1	no	—
695	C₄²	C₂×C₃×D₄	1	2	yes	—
696	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
697	C₄²	C₂×C₃×D₄	1	2	yes	—
698	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
699	C₄²	C₂⁴×C₃	1	1	yes	characteristic
700	C₄²	C₂⁴×C₃	1	2	yes	—
701	C₄²	C₂⁴×C₃	1	2	yes	—
702	C₄²	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₃	—	2	1	no	—
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	4	1	no	—
706	C₂²×C₃	—	4	1	no	—
707	C₂²×C₃	—	4	1	no	—
708	C₂²×C₃	#578	1	2	yes	—
709	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
710	C₃×C₄	—	2	4	no	—
711	C₃×C₄	—	2	1	no	—
712	C₃×C₄	—	2	1	no	—
713	C₃×C₄	—	2	2	no	—
714	C₃×C₄	—	2	2	no	—
715	C₃×C₄	—	2	2	no	—
716	C₃×C₄	—	2	2	no	—
717	C₃×C₄	—	2	1	no	—
718	C₃×C₄	—	2	1	no	—
719	C₃×C₄	—	4	1	no	—
720	C₃×C₄	—	4	2	no	—
721	C₃×C₄	—	4	2	no	—
722	C₃×C₄	—	4	1	no	—
723	C₃×C₄	—	4	4	no	—
724	C₃×C₄	—	4	2	no	—
725	C₃×C₄	—	4	1	no	—
726	C₃×C₄	#575	1	2	yes	—
727	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
728	C₂³	—	2	1	no	—
729	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
730	Q₈	—	2	4	no	—
731	Q₈	—	2	2	no	—
732	Q₈	—	2	2	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	2	no	—
735	Q₈	—	2	4	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	4	4	no	—
738	Q₈	—	4	4	no	—
739	Q₈	—	4	2	no	—
740	Q₈	—	4	4	no	—
741	Q₈	C₃×2₋¹⁺⁴	1	4	yes	—
742	D₄	—	2	2	no	—
743	D₄	—	4	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
763	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
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	2	yes	—
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	2	yes	—
770	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
771	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₈	—	2	4	no	—
775	C₂×C₃	—	2	2	no	—
776	C₂×C₃	—	8	1	no	—
777	C₂×C₃	#3486	1	1	yes	characteristic
778	C₂×C₃	C₂×#575	1	1	yes	characteristic
779	C₂×C₃	C₂×#578	1	1	yes	characteristic
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	C₃×#578	1	2	yes	—
786	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
787	C₄	—	2	4	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	4	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	C₃×#575	1	2	yes	—
804	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
805	C₃	#61842	1	1	yes	characteristic, direct product factor, Sylow
806	C₂	—	2	2	no	—
807	C₂	—	8	1	no	—
808	C₂	C₃×#3486	1	1	yes	characteristic
809	C₂	C₂×C₃×#575	1	1	yes	characteristic
810	C₂	C₂×C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#557	C₂	semidirect
3. C₃×#3390	C₂	semidirect
4. C₃×#3386	C₂	semidirect
5. C₃×#3383	C₂	semidirect
6. C₃×#3377	C₂	semidirect
7. C₃×#3374	C₂	semidirect
8. C₃×#3364	C₂	semidirect
10. C₃×#3236	C₂	semidirect
12. C₃×#3230	C₂	semidirect
14. C₃×#3113	C₂	semidirect
16. C₃×#3104	C₂	semidirect
17. C₃×#2984	C₂	semidirect
18. #61842	C₃	direct (N × H)
97. C₂×#557	C₂×C₃	semidirect
98. #3390	C₂×C₃	semidirect
99. #3386	C₂×C₃	semidirect
100. #3383	C₂×C₃	semidirect
101. #3377	C₂×C₃	semidirect
102. #3374	C₂×C₃	semidirect
103. #3364	C₂×C₃	semidirect
105. #3236	C₂×C₃	semidirect
107. #3230	C₂×C₃	semidirect
109. #3113	C₂×C₃	semidirect
111. #3104	C₂×C₃	semidirect
112. #2984	C₂×C₃	semidirect
805. C₃	#61842	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×#3523	2
C₂×C₃×#557	2
C₃×#3390	2
C₃×#3386	2
C₃×#3383	2
C₃×#3377	2
C₃×#3374	2
C₃×#3364	2
C₃×#3239	2
C₃×#3236	2
C₃×#3232	2
C₃×#3230	2
C₃×#3117	2
C₃×#3113	2
C₃×#3108	2
C₃×#3104	2
C₃×#2984	2
#61842	3

Subgroups — C3×#61842 #10680449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61842 #10680449