Subgroups — C₃×#61788 #10680395

Order 768.

1846 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₃×#3354	C₂	1	2	yes	maximal, complemented
5	C₃×#3341	C₂	1	2	yes	maximal, complemented
6	C₃×#3340	C₂	1	2	yes	maximal, complemented
7	C₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₃×#3324	C₂	1	2	yes	maximal, complemented
9	C₃×#3295	C₂	1	2	yes	maximal, complemented
10	C₃×#3294	C₂	1	2	yes	maximal, complemented
11	C₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3198	C₂	1	4	yes	maximal, complemented
14	C₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3096	C₂	1	4	yes	maximal, complemented
17	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	#61788	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×H(3,𝔽₄)	—	2	2	no	—
20	C₃×#556	C₂²	1	2	yes	complemented
21	C₃×#555	—	2	1	no	—
22	C₃×#555	C₂²	1	2	yes	—
23	C₃×#555	C₂²	1	2	yes	—
24	C₃×#555	C₂²	1	2	yes	complemented
25	C₃×#554	C₂²	1	2	yes	complemented
26	C₃×#553	—	2	2	no	—
27	C₃×#548	—	2	2	no	—
28	C₃×#547	C₂²	1	2	yes	complemented
29	C₃×D₄²	—	2	1	no	—
30	C₃×D₄²	C₂²	1	2	yes	—
31	C₃×D₄²	C₂²	1	2	yes	—
32	C₃×#542	—	2	2	no	—
33	C₃×#537	C₂²	1	2	yes	complemented
34	C₃×#535	—	2	2	no	—
35	C₃×#535	—	2	2	no	—
36	C₃×#535	C₂²	1	4	yes	—
37	C₃×#533	—	2	1	no	—
38	C₃×#532	—	2	1	no	—
39	C₃×#532	C₂²	1	1	yes	characteristic
40	C₃×#532	C₂²	1	1	yes	characteristic
41	C₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₃×#520	C₂²	1	2	yes	complemented
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic, complemented
45	C₃×#500	C₂²	1	2	yes	complemented
46	C₃×#498	C₂²	1	2	yes	complemented
47	C₃×#486	C₂²	1	2	yes	—
48	C₃×#486	C₂²	1	2	yes	—
49	C₃×#485	C₂²	1	4	yes	complemented
50	C₃×#482	C₂²	1	4	yes	complemented
51	C₃×#482	C₂²	1	4	yes	complemented
52	C₃×#482	C₂²	1	4	yes	complemented
53	C₃×#482	C₂²	1	2	yes	complemented
54	C₃×#482	C₂²	1	2	yes	complemented
55	C₃×#481	C₂²	1	4	yes	complemented
56	C₃×#481	C₂²	1	4	yes	complemented
57	C₃×#480	C₂²	1	4	yes	complemented
58	C₃×#480	C₂²	1	4	yes	complemented
59	C₃×#477	C₂²	1	1	yes	characteristic, complemented
60	C₃×#477	C₂²	1	1	yes	characteristic, complemented
61	C₃×#476	C₂²	1	2	yes	complemented
62	C₃×#476	C₂²	1	2	yes	complemented
63	C₃×#476	C₂²	1	1	yes	characteristic, complemented
64	C₃×#476	C₂²	1	1	yes	characteristic, complemented
65	C₃×#474	C₂²	1	2	yes	complemented
66	C₃×#474	C₂²	1	2	yes	complemented
67	C₃×#469	C₂²	1	4	yes	complemented
68	C₃×#468	C₂²	1	4	yes	complemented
69	C₃×#466	C₂²	1	4	yes	complemented
70	C₃×#465	C₂²	1	4	yes	complemented
71	C₃×#460	C₂²	1	1	yes	characteristic
72	C₃×#460	C₂²	1	1	yes	characteristic
73	C₃×#459	C₂²	1	1	yes	characteristic
74	C₃×#459	C₂²	1	1	yes	characteristic
75	C₃×#450	C₂²	1	4	yes	complemented
76	C₃×#449	C₂²	1	2	yes	complemented
77	C₃×#449	C₂²	1	2	yes	complemented
78	C₃×#447	C₂²	1	4	yes	complemented
79	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
80	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
81	C₃×C₄×D₈	C₂²	1	2	yes	complemented
82	C₃×C₄×D₈	C₂²	1	2	yes	complemented
83	C₃×#436	C₂²	1	2	yes	complemented
84	C₃×#436	C₂²	1	2	yes	complemented
85	C₃×C₈×D₄	C₂²	1	2	yes	complemented
86	C₃×C₈×D₄	C₂²	1	2	yes	complemented
87	C₃×#431	C₂²	1	1	yes	characteristic, complemented
88	C₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₃×#428	C₂²	1	4	yes	complemented
90	C₃×#427	C₂²	1	4	yes	complemented
91	C₃×#418	C₂²	1	4	yes	complemented
92	C₂×C₃×#102	C₂²	1	4	yes	complemented
93	C₃×#408	C₂²	1	4	yes	complemented
94	#3549	C₂×C₃	1	1	yes	characteristic, complemented
95	#3511	C₂×C₃	1	1	yes	characteristic, complemented
96	#3357	C₂×C₃	1	2	yes	complemented
97	#3354	C₂×C₃	1	2	yes	complemented
98	#3341	C₂×C₃	1	2	yes	complemented
99	#3340	C₂×C₃	1	2	yes	complemented
100	#3325	C₂×C₃	1	2	yes	complemented
101	#3324	C₂×C₃	1	2	yes	complemented
102	#3295	C₂×C₃	1	2	yes	complemented
103	#3294	C₂×C₃	1	2	yes	complemented
104	#3227	C₂×C₃	1	1	yes	characteristic, complemented
105	#3226	C₂×C₃	1	1	yes	characteristic, complemented
106	#3198	C₂×C₃	1	4	yes	complemented
107	#3106	C₂×C₃	1	1	yes	characteristic, complemented
108	#3106	C₂×C₃	1	1	yes	characteristic, complemented
109	#3096	C₂×C₃	1	4	yes	complemented
110	#2979	C₂×C₃	1	1	yes	characteristic, complemented
111	C₂×C₃×#41	—	2	2	no	—
112	C₂×C₃×#41	—	2	1	no	—
113	C₂×C₃×#41	—	2	1	no	—
114	C₂×C₃×#41	C₂³	1	1	yes	characteristic
115	C₂×C₃×#41	C₂³	1	2	yes	—
116	C₂²×C₃×Q₈	—	2	1	no	—
117	C₂²×C₃×D₄	—	2	2	no	—
118	C₂²×C₃×D₄	—	2	2	no	—
119	C₂²×C₃×D₄	C₂³	1	4	yes	—
120	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
121	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
122	C₂×C₃×D₈	C₂³	1	2	yes	—
123	C₂×C₃×D₈	C₂³	1	2	yes	—
124	C₂×C₃×M₁₆	C₂³	1	4	yes	—
125	C₂²×C₃×C₈	C₂³	1	4	yes	—
126	C₃×C₄⋊Q₈	—	2	1	no	—
127	C₃×C₄⋊Q₈	—	2	1	no	—
128	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
129	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₃×#127	—	2	4	no	—
134	C₃×#127	D₄	1	1	yes	characteristic
135	C₃×#127	C₂³	1	1	yes	characteristic
136	C₃×#127	C₂³	1	1	yes	characteristic
137	C₃×#126	—	2	4	no	—
138	C₃×#125	—	2	2	no	—
139	C₃×#124	—	2	4	no	—
140	C₃×#124	—	2	2	no	—
141	C₃×#124	—	2	4	no	—
142	C₃×#124	—	2	4	no	—
143	C₃×#124	—	2	4	no	—
144	C₃×#124	—	2	1	no	—
145	C₃×#124	—	2	1	no	—
146	C₃×#124	D₄	1	2	yes	—
147	C₃×#123	—	2	4	no	—
148	C₃×C₂²⋊Q₈	—	2	2	no	—
149	C₃×C₂²⋊Q₈	—	2	2	no	—
150	C₃×C₂²⋊Q₈	—	2	4	no	—
151	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₃×#121	—	2	2	no	—
153	C₃×#121	—	2	2	no	—
154	C₃×#121	—	2	2	no	—
155	C₃×#121	—	2	2	no	—
156	C₃×#121	—	2	4	no	—
157	C₃×#121	—	2	1	no	—
158	C₃×#121	—	2	1	no	—
159	C₃×#121	—	2	2	no	—
160	C₃×#121	—	2	2	no	—
161	C₃×#121	D₄	1	2	yes	—
162	C₃×#121	D₄	1	2	yes	—
163	C₃×#121	C₂³	1	4	yes	—
164	C₃×#121	C₂³	1	2	yes	—
165	C₃×#121	C₂³	1	2	yes	—
166	C₃×#121	C₂³	1	4	yes	—
167	C₃×#121	C₂³	1	4	yes	—
168	C₃×#120	—	2	4	no	—
169	C₃×#120	—	2	4	no	—
170	C₃×#120	—	2	4	no	—
171	C₃×#120	—	2	4	no	—
172	C₃×C₄×Q₈	—	2	2	no	—
173	C₃×C₄×Q₈	—	2	2	no	—
174	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
175	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
176	C₃×C₄×D₄	—	2	2	no	—
177	C₃×C₄×D₄	—	2	4	no	—
178	C₃×C₄×D₄	—	2	2	no	—
179	C₃×C₄×D₄	—	2	1	no	—
180	C₃×C₄×D₄	—	2	1	no	—
181	C₃×C₄×D₄	—	2	1	no	—
182	C₃×C₄×D₄	—	2	1	no	—
183	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
184	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
185	C₃×C₄×D₄	C₂³	1	2	yes	—
186	C₃×C₄×D₄	C₂³	1	2	yes	—
187	C₃×C₄×D₄	C₂³	1	2	yes	—
188	C₃×C₄×D₄	C₂³	1	2	yes	—
189	C₃×#117	—	2	2	no	—
190	C₃×#117	—	2	2	no	—
191	C₃×#117	—	2	2	no	—
192	C₃×#117	—	2	1	no	—
193	C₃×#117	C₂³	1	4	yes	—
194	C₃×#117	C₂³	1	4	yes	—
195	C₃×#117	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	—	2	1	no	—
200	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×#107	C₂³	1	2	yes	—
202	C₃×#107	C₂³	1	4	yes	—
203	C₃×#107	C₂³	1	2	yes	—
204	C₃×#107	C₂³	1	4	yes	—
205	C₃×#106	C₂³	1	2	yes	—
206	C₃×#106	C₂³	1	4	yes	—
207	C₃×#106	C₂³	1	2	yes	—
208	C₃×#106	C₂³	1	4	yes	—
209	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃×#103	C₂³	1	2	yes	—
214	C₃×#103	C₂³	1	2	yes	—
215	C₃×#102	C₂³	1	2	yes	—
216	C₃×#102	C₂³	1	2	yes	—
217	C₃×#102	C₂³	1	4	yes	—
218	C₃×#102	C₂³	1	4	yes	—
219	C₃×#102	C₂³	1	2	yes	—
220	C₃×#102	C₂³	1	2	yes	—
221	C₃×#102	C₂³	1	4	yes	—
222	C₃×#102	C₂³	1	4	yes	—
223	C₃×#102	C₂³	1	2	yes	—
224	C₃×#102	C₂³	1	2	yes	—
225	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃×C₄×C₈	C₂³	1	2	yes	—
230	C₃×C₄×C₈	C₂³	1	2	yes	—
231	H(3,𝔽₄)	—	2	2	no	—
232	#556	C₂²×C₃	1	2	yes	complemented
233	#555	—	2	1	no	—
234	#555	C₂²×C₃	1	2	yes	—
235	#555	C₂²×C₃	1	2	yes	—
236	#555	C₂²×C₃	1	2	yes	complemented
237	#554	C₂²×C₃	1	2	yes	complemented
238	#553	—	2	2	no	—
239	#548	—	2	2	no	—
240	#547	C₂²×C₃	1	2	yes	complemented
241	D₄²	—	2	1	no	—
242	D₄²	C₂²×C₃	1	2	yes	—
243	D₄²	C₂²×C₃	1	2	yes	—
244	#542	—	2	2	no	—
245	#537	C₂²×C₃	1	2	yes	complemented
246	#535	—	2	2	no	—
247	#535	—	2	2	no	—
248	#535	C₂²×C₃	1	4	yes	—
249	#533	—	2	1	no	—
250	#532	—	2	1	no	—
251	#532	C₂²×C₃	1	1	yes	characteristic
252	#532	C₂²×C₃	1	1	yes	characteristic
253	#532	C₂²×C₃	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
255	#520	C₂²×C₃	1	2	yes	complemented
256	C₄×#41	C₂²×C₃	1	1	yes	characteristic, complemented
257	#500	C₂²×C₃	1	2	yes	complemented
258	#498	C₂²×C₃	1	2	yes	complemented
259	#486	C₂²×C₃	1	2	yes	—
260	#486	C₂²×C₃	1	2	yes	—
261	#485	C₂²×C₃	1	4	yes	complemented
262	#482	C₂²×C₃	1	4	yes	complemented
263	#482	C₂²×C₃	1	4	yes	complemented
264	#482	C₂²×C₃	1	4	yes	complemented
265	#482	C₂²×C₃	1	2	yes	complemented
266	#482	C₂²×C₃	1	2	yes	complemented
267	#481	C₂²×C₃	1	4	yes	complemented
268	#481	C₂²×C₃	1	4	yes	complemented
269	#480	C₂²×C₃	1	4	yes	complemented
270	#480	C₂²×C₃	1	4	yes	complemented
271	#477	C₂²×C₃	1	1	yes	characteristic, complemented
272	#477	C₂²×C₃	1	1	yes	characteristic, complemented
273	#476	C₂²×C₃	1	1	yes	characteristic, complemented
274	#476	C₂²×C₃	1	2	yes	complemented
275	#476	C₂²×C₃	1	1	yes	characteristic, complemented
276	#476	C₂²×C₃	1	2	yes	complemented
277	#474	C₂²×C₃	1	2	yes	complemented
278	#474	C₂²×C₃	1	2	yes	complemented
279	#469	C₂²×C₃	1	4	yes	complemented
280	#468	C₂²×C₃	1	4	yes	complemented
281	#466	C₂²×C₃	1	4	yes	complemented
282	#465	C₂²×C₃	1	4	yes	complemented
283	#460	C₂²×C₃	1	1	yes	characteristic
284	#460	C₂²×C₃	1	1	yes	characteristic
285	#459	C₂²×C₃	1	1	yes	characteristic
286	#459	C₂²×C₃	1	1	yes	characteristic
287	#450	C₂²×C₃	1	4	yes	complemented
288	#449	C₂²×C₃	1	2	yes	complemented
289	#449	C₂²×C₃	1	2	yes	complemented
290	#447	C₂²×C₃	1	4	yes	complemented
291	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
292	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
293	C₄×D₈	C₂²×C₃	1	2	yes	complemented
294	C₄×D₈	C₂²×C₃	1	2	yes	complemented
295	#436	C₂²×C₃	1	2	yes	complemented
296	#436	C₂²×C₃	1	2	yes	complemented
297	C₈×D₄	C₂²×C₃	1	2	yes	complemented
298	C₈×D₄	C₂²×C₃	1	2	yes	complemented
299	#431	C₂²×C₃	1	1	yes	characteristic, complemented
300	#431	C₂²×C₃	1	1	yes	characteristic, complemented
301	#428	C₂²×C₃	1	4	yes	complemented
302	#427	C₂²×C₃	1	4	yes	complemented
303	#418	C₂²×C₃	1	4	yes	complemented
304	C₂×#102	C₂²×C₃	1	4	yes	complemented
305	#408	C₂²×C₃	1	4	yes	complemented
306	C₂⁴×C₃	—	2	4	no	—
307	C₃×#41	—	4	2	no	—
308	C₃×#41	—	4	2	no	—
309	C₃×#41	—	4	1	no	—
310	C₃×#41	—	4	1	no	—
311	C₃×#41	—	8	2	no	—
312	C₃×#41	—	8	2	no	—
313	C₃×#41	—	8	4	no	—
314	C₂×C₃×Q₈	—	2	2	no	—
315	C₂×C₃×Q₈	—	2	2	no	—
316	C₂×C₃×Q₈	—	2	1	no	—
317	C₂×C₃×Q₈	—	2	1	no	—
318	C₂×C₃×Q₈	—	8	2	no	—
319	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
320	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
321	C₂×C₃×D₄	—	2	1	no	—
322	C₂×C₃×D₄	—	2	4	no	—
323	C₂×C₃×D₄	—	2	4	no	—
324	C₂×C₃×D₄	—	2	2	no	—
325	C₂×C₃×D₄	—	2	2	no	—
326	C₂×C₃×D₄	—	2	4	no	—
327	C₂×C₃×D₄	—	2	1	no	—
328	C₂×C₃×D₄	—	2	1	no	—
329	C₂×C₃×D₄	—	2	1	no	—
330	C₂×C₃×D₄	—	2	1	no	—
331	C₂×C₃×D₄	—	2	4	no	—
332	C₂×C₃×D₄	—	4	4	no	—
333	C₂×C₃×D₄	—	4	4	no	—
334	C₂×C₃×D₄	—	8	4	no	—
335	C₂×C₃×D₄	—	8	4	no	—
336	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
337	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
338	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
339	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
340	C₂×C₃×D₄	C₂⁴	1	2	yes	—
341	C₂×C₃×D₄	C₂⁴	1	2	yes	—
342	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₃×C₄	—	2	2	no	—
344	C₂²×C₃×C₄	—	2	4	no	—
345	C₂²×C₃×C₄	—	2	1	no	—
346	C₂²×C₃×C₄	—	2	1	no	—
347	C₂²×C₃×C₄	—	2	1	no	—
348	C₂²×C₃×C₄	—	2	2	no	—
349	C₂²×C₃×C₄	—	2	2	no	—
350	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
354	C₃×SD₁₆	—	4	2	no	—
355	C₃×SD₁₆	—	4	2	no	—
356	C₃×D₈	—	4	2	no	—
357	C₃×D₈	—	4	2	no	—
358	C₃×M₁₆	—	4	4	no	—
359	C₂×C₃×C₈	—	4	4	no	—
360	C₂×C₃×C₈	C₂⁴	1	2	yes	—
361	C₂×C₃×C₈	C₂⁴	1	2	yes	—
362	C₂×C₃×C₈	C₂⁴	1	2	yes	—
363	C₂×C₃×C₈	C₂⁴	1	2	yes	—
364	C₃×C₄⋊C₄	—	2	2	no	—
365	C₃×C₄⋊C₄	—	2	2	no	—
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	—	2	4	no	—
368	C₃×C₄⋊C₄	—	2	1	no	—
369	C₃×C₄⋊C₄	—	2	1	no	—
370	C₃×C₄⋊C₄	—	2	1	no	—
371	C₃×C₄⋊C₄	—	2	1	no	—
372	C₃×C₄⋊C₄	—	2	4	no	—
373	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
374	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
375	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
376	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
377	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
379	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
380	C₃×C₂²⋊C₄	—	2	1	no	—
381	C₃×C₂²⋊C₄	—	2	4	no	—
382	C₃×C₂²⋊C₄	—	2	4	no	—
383	C₃×C₂²⋊C₄	—	2	4	no	—
384	C₃×C₂²⋊C₄	—	2	1	no	—
385	C₃×C₂²⋊C₄	—	2	1	no	—
386	C₃×C₂²⋊C₄	—	2	4	no	—
387	C₃×C₂²⋊C₄	—	2	4	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	2	2	no	—
390	C₃×C₂²⋊C₄	—	2	2	no	—
391	C₃×C₂²⋊C₄	—	2	2	no	—
392	C₃×C₂²⋊C₄	—	2	2	no	—
393	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
394	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
395	C₃×C₄²	—	2	1	no	—
396	C₃×C₄²	—	2	1	no	—
397	C₃×C₄²	—	2	1	no	—
398	C₃×C₄²	—	2	4	no	—
399	C₃×C₄²	—	2	4	no	—
400	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
401	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
402	C₃×C₄²	C₂⁴	1	1	yes	characteristic
403	C₃×C₄²	C₂⁴	1	1	yes	characteristic
404	C₂×#41	—	2	2	no	—
405	C₂×#41	—	2	1	no	—
406	C₂×#41	—	2	1	no	—
407	C₂×#41	C₂³×C₃	1	1	yes	characteristic
408	C₂×#41	C₂³×C₃	1	2	yes	—
409	C₂²×Q₈	—	2	1	no	—
410	C₂²×D₄	—	2	2	no	—
411	C₂²×D₄	—	2	2	no	—
412	C₂²×D₄	C₂³×C₃	1	4	yes	—
413	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
414	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
415	C₂×D₈	C₂³×C₃	1	2	yes	—
416	C₂×D₈	C₂³×C₃	1	2	yes	—
417	C₂×M₁₆	C₂³×C₃	1	4	yes	—
418	C₂²×C₈	C₂³×C₃	1	4	yes	—
419	C₄⋊Q₈	—	2	1	no	—
420	C₄⋊Q₈	—	2	1	no	—
421	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
422	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
423	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
424	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
425	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
426	#127	—	2	4	no	—
427	#127	C₃×D₄	1	1	yes	characteristic
428	#127	C₂³×C₃	1	1	yes	characteristic
429	#127	C₂³×C₃	1	1	yes	characteristic
430	#126	—	2	4	no	—
431	#125	—	2	2	no	—
432	#124	—	2	4	no	—
433	#124	—	2	2	no	—
434	#124	—	2	4	no	—
435	#124	—	2	4	no	—
436	#124	—	2	4	no	—
437	#124	—	2	1	no	—
438	#124	—	2	1	no	—
439	#124	C₃×D₄	1	2	yes	—
440	#123	—	2	4	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	4	no	—
444	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
445	#121	—	2	2	no	—
446	#121	—	2	2	no	—
447	#121	—	2	2	no	—
448	#121	—	2	2	no	—
449	#121	—	2	4	no	—
450	#121	—	2	1	no	—
451	#121	—	2	1	no	—
452	#121	—	2	2	no	—
453	#121	—	2	2	no	—
454	#121	C₃×D₄	1	2	yes	—
455	#121	C₃×D₄	1	2	yes	—
456	#121	C₂³×C₃	1	2	yes	—
457	#121	C₂³×C₃	1	2	yes	—
458	#121	C₂³×C₃	1	4	yes	—
459	#121	C₂³×C₃	1	4	yes	—
460	#121	C₂³×C₃	1	4	yes	—
461	#120	—	2	4	no	—
462	#120	—	2	4	no	—
463	#120	—	2	4	no	—
464	#120	—	2	4	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
468	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	4	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	1	no	—
473	C₄×D₄	—	2	1	no	—
474	C₄×D₄	—	2	1	no	—
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
477	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
478	C₄×D₄	C₂³×C₃	1	2	yes	—
479	C₄×D₄	C₂³×C₃	1	2	yes	—
480	C₄×D₄	C₂³×C₃	1	2	yes	—
481	C₄×D₄	C₂³×C₃	1	2	yes	—
482	#117	—	2	2	no	—
483	#117	—	2	2	no	—
484	#117	—	2	2	no	—
485	#117	—	2	1	no	—
486	#117	C₂³×C₃	1	1	yes	characteristic
487	#117	C₂³×C₃	1	4	yes	—
488	#117	C₂³×C₃	1	4	yes	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
492	C₂×C₄²	—	2	1	no	—
493	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
494	#107	C₂³×C₃	1	2	yes	—
495	#107	C₂³×C₃	1	4	yes	—
496	#107	C₂³×C₃	1	2	yes	—
497	#107	C₂³×C₃	1	4	yes	—
498	#106	C₂³×C₃	1	2	yes	—
499	#106	C₂³×C₃	1	4	yes	—
500	#106	C₂³×C₃	1	2	yes	—
501	#106	C₂³×C₃	1	4	yes	—
502	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
503	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
504	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
505	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
506	#103	C₂³×C₃	1	2	yes	—
507	#103	C₂³×C₃	1	2	yes	—
508	#102	C₂³×C₃	1	2	yes	—
509	#102	C₂³×C₃	1	2	yes	—
510	#102	C₂³×C₃	1	4	yes	—
511	#102	C₂³×C₃	1	4	yes	—
512	#102	C₂³×C₃	1	2	yes	—
513	#102	C₂³×C₃	1	2	yes	—
514	#102	C₂³×C₃	1	4	yes	—
515	#102	C₂³×C₃	1	4	yes	—
516	#102	C₂³×C₃	1	2	yes	—
517	#102	C₂³×C₃	1	2	yes	—
518	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
519	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
520	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
521	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
522	C₄×C₈	C₂³×C₃	1	2	yes	—
523	C₄×C₈	C₂³×C₃	1	2	yes	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	2	no	—
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	8	4	no	—
528	C₂³×C₃	—	8	4	no	—
529	C₂³×C₃	—	8	4	no	—
530	C₂³×C₃	C₂²×D₄	1	4	yes	—
531	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
532	C₃×Q₈	—	2	1	no	—
533	C₃×Q₈	—	2	1	no	—
534	C₃×Q₈	—	4	2	no	—
535	C₃×Q₈	—	4	4	no	—
536	C₃×Q₈	—	8	2	no	—
537	C₃×Q₈	—	8	1	no	—
538	C₃×Q₈	—	8	1	no	—
539	C₃×D₄	—	2	4	no	—
540	C₃×D₄	—	2	4	no	—
541	C₃×D₄	—	2	1	no	—
542	C₃×D₄	—	2	1	no	—
543	C₃×D₄	—	2	2	no	—
544	C₃×D₄	—	2	2	no	—
545	C₃×D₄	—	2	2	no	—
546	C₃×D₄	—	2	2	no	—
547	C₃×D₄	—	4	2	no	—
548	C₃×D₄	—	4	4	no	—
549	C₃×D₄	—	4	2	no	—
550	C₃×D₄	—	4	2	no	—
551	C₃×D₄	—	4	2	no	—
552	C₃×D₄	—	8	4	no	—
553	C₃×D₄	—	8	1	no	—
554	C₃×D₄	—	8	1	no	—
555	C₃×D₄	—	8	4	no	—
556	C₃×D₄	—	8	4	no	—
557	C₃×D₄	—	8	2	no	—
558	C₃×D₄	—	8	4	no	—
559	C₃×D₄	—	8	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	4	no	—
563	C₂×C₃×C₄	—	2	4	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	4	no	—
572	C₂×C₃×C₄	—	4	2	no	—
573	C₂×C₃×C₄	—	4	4	no	—
574	C₂×C₃×C₄	—	4	2	no	—
575	C₂×C₃×C₄	—	4	2	no	—
576	C₂×C₃×C₄	—	4	4	no	—
577	C₂×C₃×C₄	—	8	2	no	—
578	C₂×C₃×C₄	—	8	4	no	—
579	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
580	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
586	C₃×C₈	—	2	2	no	—
587	C₃×C₈	—	2	2	no	—
588	C₃×C₈	—	2	2	no	—
589	C₃×C₈	—	2	2	no	—
590	C₂⁴	—	2	4	no	—
591	#41	—	4	2	no	—
592	#41	—	4	2	no	—
593	#41	—	4	1	no	—
594	#41	—	4	1	no	—
595	#41	—	8	2	no	—
596	#41	—	8	2	no	—
597	#41	—	8	4	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	8	2	no	—
603	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
604	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	8	4	no	—
619	C₂×D₄	—	8	4	no	—
620	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
621	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
622	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
623	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
624	C₂×D₄	C₂⁴×C₃	1	2	yes	—
625	C₂×D₄	C₂⁴×C₃	1	2	yes	—
626	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
635	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
638	SD₁₆	—	4	2	no	—
639	SD₁₆	—	4	2	no	—
640	D₈	—	4	2	no	—
641	D₈	—	4	2	no	—
642	M₁₆	—	4	4	no	—
643	C₂×C₈	—	4	4	no	—
644	C₂×C₈	C₂⁴×C₃	1	2	yes	—
645	C₂×C₈	C₂⁴×C₃	1	2	yes	—
646	C₂×C₈	C₂⁴×C₃	1	2	yes	—
647	C₂×C₈	C₂⁴×C₃	1	2	yes	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
658	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
659	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
660	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
661	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
662	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
678	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	4	no	—
684	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
685	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
686	C₄²	C₂⁴×C₃	1	1	yes	characteristic
687	C₄²	C₂⁴×C₃	1	1	yes	characteristic
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	4	no	—
690	C₂²×C₃	—	2	1	no	—
691	C₂²×C₃	—	2	4	no	—
692	C₂²×C₃	—	2	1	no	—
693	C₂²×C₃	—	2	4	no	—
694	C₂²×C₃	—	4	1	no	—
695	C₂²×C₃	—	4	2	no	—
696	C₂²×C₃	—	4	2	no	—
697	C₂²×C₃	—	4	1	no	—
698	C₂²×C₃	—	4	2	no	—
699	C₂²×C₃	—	4	2	no	—
700	C₂²×C₃	—	4	2	no	—
701	C₂²×C₃	—	4	1	no	—
702	C₂²×C₃	—	4	2	no	—
703	C₂²×C₃	—	16	8	no	—
704	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
705	C₃×C₄	—	2	1	no	—
706	C₃×C₄	—	2	4	no	—
707	C₃×C₄	—	2	1	no	—
708	C₃×C₄	—	2	1	no	—
709	C₃×C₄	—	4	1	no	—
710	C₃×C₄	—	4	1	no	—
711	C₃×C₄	—	4	2	no	—
712	C₃×C₄	—	4	4	no	—
713	C₃×C₄	—	4	1	no	—
714	C₃×C₄	—	4	2	no	—
715	C₃×C₄	#576	1	2	yes	—
716	C₃×C₄	#577	1	2	yes	—
717	C₃×C₄	#585	1	1	yes	characteristic
718	C₃×C₄	#585	1	1	yes	characteristic
719	C₂³	—	2	1	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	8	4	no	—
723	C₂³	—	8	4	no	—
724	C₂³	—	8	4	no	—
725	C₂³	C₂²×C₃×D₄	1	4	yes	—
726	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	4	4	no	—
731	Q₈	—	8	2	no	—
732	Q₈	—	8	1	no	—
733	Q₈	—	8	1	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	4	no	—
736	D₄	—	2	1	no	—
737	D₄	—	2	1	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	D₄	—	4	2	no	—
746	D₄	—	4	2	no	—
747	D₄	—	8	4	no	—
748	D₄	—	8	1	no	—
749	D₄	—	8	1	no	—
750	D₄	—	8	4	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	2	no	—
753	D₄	—	8	4	no	—
754	D₄	—	8	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	—	8	4	no	—
774	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
775	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
776	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
777	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
778	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
779	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
780	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
781	C₈	—	2	2	no	—
782	C₈	—	2	2	no	—
783	C₈	—	2	2	no	—
784	C₈	—	2	2	no	—
785	C₂×C₃	—	4	1	no	—
786	C₂×C₃	—	4	4	no	—
787	C₂×C₃	—	8	1	no	—
788	C₂×C₃	—	8	2	no	—
789	C₂×C₃	—	8	2	no	—
790	C₂×C₃	#3485	1	1	yes	characteristic
791	C₂×C₃	C₂×#576	1	1	yes	characteristic
792	C₂×C₃	C₂×#577	1	1	yes	characteristic
793	C₂²	—	2	1	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	16	8	no	—
809	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
810	C₄	—	2	1	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	4	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	1	no	—
820	C₄	C₃×#576	1	2	yes	—
821	C₄	C₃×#577	1	2	yes	—
822	C₄	C₃×#585	1	1	yes	characteristic
823	C₄	C₃×#585	1	1	yes	characteristic
824	C₃	#61788	1	1	yes	characteristic, direct product factor, Sylow
825	C₂	—	4	4	no	—
826	C₂	—	4	1	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	1	no	—
830	C₂	C₃×#3485	1	1	yes	characteristic
831	C₂	C₂×C₃×#576	1	1	yes	characteristic
832	C₂	C₂×C₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3549	C₂	semidirect
2. C₃×#3511	C₂	semidirect
3. C₃×#3357	C₂	semidirect
4. C₃×#3354	C₂	semidirect
5. C₃×#3341	C₂	semidirect
6. C₃×#3340	C₂	semidirect
7. C₃×#3325	C₂	semidirect
8. C₃×#3324	C₂	semidirect
9. C₃×#3295	C₂	semidirect
10. C₃×#3294	C₂	semidirect
11. C₃×#3227	C₂	semidirect
12. C₃×#3226	C₂	semidirect
13. C₃×#3198	C₂	semidirect
14. C₃×#3106	C₂	semidirect
15. C₃×#3106	C₂	semidirect
16. C₃×#3096	C₂	semidirect
17. C₃×#2979	C₂	semidirect
18. #61788	C₃	direct (N × H)
20. C₃×#556	C₂²	semidirect
24. C₃×#555	C₂²	semidirect
25. C₃×#554	C₂²	semidirect
28. C₃×#547	C₂²	semidirect
33. C₃×#537	C₂²	semidirect
42. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
43. C₃×#520	C₂²	semidirect
44. C₃×C₄×#41	C₂²	semidirect
45. C₃×#500	C₂²	semidirect
46. C₃×#498	C₂²	semidirect
49. C₃×#485	C₂²	semidirect
50. C₃×#482	C₂²	semidirect
51. C₃×#482	C₂²	semidirect
52. C₃×#482	C₂²	semidirect
53. C₃×#482	C₂²	semidirect
54. C₃×#482	C₂²	semidirect
55. C₃×#481	C₂²	semidirect
56. C₃×#481	C₂²	semidirect
57. C₃×#480	C₂²	semidirect
58. C₃×#480	C₂²	semidirect
59. C₃×#477	C₂²	semidirect
60. C₃×#477	C₂²	semidirect
61. C₃×#476	C₂²	semidirect
62. C₃×#476	C₂²	semidirect
63. C₃×#476	C₂²	semidirect
64. C₃×#476	C₂²	semidirect
65. C₃×#474	C₂²	semidirect
66. C₃×#474	C₂²	semidirect
67. C₃×#469	C₂²	semidirect
68. C₃×#468	C₂²	semidirect
69. C₃×#466	C₂²	semidirect
70. C₃×#465	C₂²	semidirect
75. C₃×#450	C₂²	semidirect
76. C₃×#449	C₂²	semidirect
77. C₃×#449	C₂²	semidirect
78. C₃×#447	C₂²	semidirect
79. C₃×C₄×SD₁₆	C₂²	semidirect
80. C₃×C₄×SD₁₆	C₂²	semidirect
81. C₃×C₄×D₈	C₂²	semidirect
82. C₃×C₄×D₈	C₂²	semidirect
83. C₃×#436	C₂²	semidirect
84. C₃×#436	C₂²	semidirect
85. C₃×C₈×D₄	C₂²	semidirect
86. C₃×C₈×D₄	C₂²	semidirect
87. C₃×#431	C₂²	semidirect
88. C₃×#431	C₂²	semidirect
89. C₃×#428	C₂²	semidirect
90. C₃×#427	C₂²	semidirect
91. C₃×#418	C₂²	semidirect
92. C₂×C₃×#102	C₂²	semidirect
93. C₃×#408	C₂²	semidirect
94. #3549	C₂×C₃	semidirect
95. #3511	C₂×C₃	semidirect
96. #3357	C₂×C₃	semidirect
97. #3354	C₂×C₃	semidirect
98. #3341	C₂×C₃	semidirect
99. #3340	C₂×C₃	semidirect
100. #3325	C₂×C₃	semidirect
101. #3324	C₂×C₃	semidirect
102. #3295	C₂×C₃	semidirect
103. #3294	C₂×C₃	semidirect
104. #3227	C₂×C₃	semidirect
105. #3226	C₂×C₃	semidirect
106. #3198	C₂×C₃	semidirect
107. #3106	C₂×C₃	semidirect
108. #3106	C₂×C₃	semidirect
109. #3096	C₂×C₃	semidirect
110. #2979	C₂×C₃	semidirect
232. #556	C₂²×C₃	semidirect
236. #555	C₂²×C₃	semidirect
237. #554	C₂²×C₃	semidirect
240. #547	C₂²×C₃	semidirect
245. #537	C₂²×C₃	semidirect
254. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
255. #520	C₂²×C₃	semidirect
256. C₄×#41	C₂²×C₃	semidirect
257. #500	C₂²×C₃	semidirect
258. #498	C₂²×C₃	semidirect
261. #485	C₂²×C₃	semidirect
262. #482	C₂²×C₃	semidirect
263. #482	C₂²×C₃	semidirect
264. #482	C₂²×C₃	semidirect
265. #482	C₂²×C₃	semidirect
266. #482	C₂²×C₃	semidirect
267. #481	C₂²×C₃	semidirect
268. #481	C₂²×C₃	semidirect
269. #480	C₂²×C₃	semidirect
270. #480	C₂²×C₃	semidirect
271. #477	C₂²×C₃	semidirect
272. #477	C₂²×C₃	semidirect
273. #476	C₂²×C₃	semidirect
274. #476	C₂²×C₃	semidirect
275. #476	C₂²×C₃	semidirect
276. #476	C₂²×C₃	semidirect
277. #474	C₂²×C₃	semidirect
278. #474	C₂²×C₃	semidirect
279. #469	C₂²×C₃	semidirect
280. #468	C₂²×C₃	semidirect
281. #466	C₂²×C₃	semidirect
282. #465	C₂²×C₃	semidirect
287. #450	C₂²×C₃	semidirect
288. #449	C₂²×C₃	semidirect
289. #449	C₂²×C₃	semidirect
290. #447	C₂²×C₃	semidirect
291. C₄×SD₁₆	C₂²×C₃	semidirect
292. C₄×SD₁₆	C₂²×C₃	semidirect
293. C₄×D₈	C₂²×C₃	semidirect
294. C₄×D₈	C₂²×C₃	semidirect
295. #436	C₂²×C₃	semidirect
296. #436	C₂²×C₃	semidirect
297. C₈×D₄	C₂²×C₃	semidirect
298. C₈×D₄	C₂²×C₃	semidirect
299. #431	C₂²×C₃	semidirect
300. #431	C₂²×C₃	semidirect
301. #428	C₂²×C₃	semidirect
302. #427	C₂²×C₃	semidirect
303. #418	C₂²×C₃	semidirect
304. C₂×#102	C₂²×C₃	semidirect
305. #408	C₂²×C₃	semidirect
824. C₃	#61788	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×#3549	2
C₃×#3511	2
C₃×#3357	2
C₃×#3354	2
C₃×#3341	2
C₃×#3340	2
C₃×#3325	2
C₃×#3324	2
C₃×#3295	2
C₃×#3294	2
C₃×#3227	2
C₃×#3226	2
C₃×#3198	2
C₃×#3106	2
C₃×#3096	2
C₃×#2979	2
#61788	3

Subgroups — C3×#61788 #10680395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61788 #10680395