Subgroups — C₃×#62913 #10681520

Order 768.

6974 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3554	C₂	1	6	yes	maximal, complemented
2	C₃×#3552	C₂	1	6	yes	maximal, complemented
3	C₃×#3550	C₂	1	6	yes	maximal, complemented
4	C₃×#3547	C₂	1	6	yes	maximal, complemented
5	C₃×#3541	C₂	1	12	yes	maximal, complemented
6	C₃×#3523	C₂	1	2	yes	maximal, complemented
7	C₃×#3518	C₂	1	2	yes	maximal, complemented
8	C₃×#3511	C₂	1	3	yes	maximal, complemented
9	C₃×#3506	C₂	1	3	yes	maximal, complemented
10	C₃×#3503	C₂	1	3	yes	maximal, complemented
11	C₃×#3499	C₂	1	2	yes	maximal, complemented
12	C₃×#3497	C₂	1	2	yes	maximal, complemented
13	C₃×#3486	C₂	1	4	yes	maximal, complemented
14	C₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3460	C₂	1	3	yes	maximal, complemented
18	#62913	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
20	C₂³×C₃×Q₈	C₂²	1	2	yes	—
21	C₃×#563	C₂²	1	24	yes	complemented
22	C₃×#562	C₂²	1	24	yes	complemented
23	C₃×#559	C₂²	1	12	yes	—
24	C₃×#559	C₂²	1	3	yes	complemented
25	C₃×Q₈²	C₂²	1	1	yes	characteristic, complemented
26	C₃×Q₈²	C₂²	1	6	yes	complemented
27	C₃×#557	C₂²	1	3	yes	complemented
28	C₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃×#557	C₂²	1	6	yes	complemented
30	C₃×#556	C₂²	1	6	yes	—
31	C₃×#556	C₂²	1	3	yes	complemented
32	C₃×#556	C₂²	1	6	yes	complemented
33	C₃×#556	C₂²	1	12	yes	complemented
34	C₃×#555	C₂²	1	6	yes	—
35	C₃×#555	C₂²	1	6	yes	complemented
36	C₃×#554	C₂²	1	6	yes	—
37	C₃×#554	C₂²	1	12	yes	—
38	C₃×#554	C₂²	1	3	yes	complemented
39	C₃×#554	C₂²	1	6	yes	complemented
40	C₃×#554	C₂²	1	6	yes	complemented
41	C₃×#553	C₂²	1	6	yes	—
42	C₃×#553	C₂²	1	12	yes	—
43	C₃×#553	C₂²	1	12	yes	—
44	C₃×#552	C₂²	1	12	yes	complemented
45	C₃×#550	C₂²	1	6	yes	—
46	C₃×#550	C₂²	1	1	yes	characteristic, complemented
47	C₃×D₄×Q₈	C₂²	1	2	yes	—
48	C₃×D₄×Q₈	C₂²	1	2	yes	—
49	C₃×D₄×Q₈	C₂²	1	6	yes	—
50	C₃×D₄×Q₈	C₂²	1	6	yes	—
51	C₃×D₄×Q₈	C₂²	1	2	yes	—
52	C₃×D₄×Q₈	C₂²	1	12	yes	—
53	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃×D₄×Q₈	C₂²	1	4	yes	complemented
55	C₃×D₄×Q₈	C₂²	1	12	yes	complemented
56	C₃×D₄×Q₈	C₂²	1	6	yes	complemented
57	C₃×#548	C₂²	1	2	yes	—
58	C₃×#548	C₂²	1	12	yes	—
59	C₃×#548	C₂²	1	4	yes	complemented
60	C₃×#548	C₂²	1	12	yes	complemented
61	C₃×#548	C₂²	1	12	yes	complemented
62	C₃×#547	C₂²	1	6	yes	—
63	C₃×#547	C₂²	1	6	yes	complemented
64	C₃×#547	C₂²	1	12	yes	complemented
65	C₃×#544	C₂²	1	3	yes	—
66	C₃×#544	C₂²	1	12	yes	complemented
67	C₃×#542	C₂²	1	6	yes	—
68	C₃×#542	C₂²	1	6	yes	—
69	C₃×#542	C₂²	1	12	yes	complemented
70	C₃×#542	C₂²	1	12	yes	complemented
71	C₃×#542	C₂²	1	24	yes	complemented
72	C₃×#541	C₂²	1	12	yes	complemented
73	C₃×#540	C₂²	1	6	yes	—
74	C₃×#540	C₂²	1	6	yes	—
75	C₃×#539	C₂²	1	24	yes	complemented
76	C₃×#538	C₂²	1	12	yes	—
77	C₃×#538	C₂²	1	12	yes	—
78	C₃×#537	C₂²	1	3	yes	—
79	C₃×#537	C₂²	1	12	yes	complemented
80	C₃×#536	C₂²	1	12	yes	complemented
81	C₃×#536	C₂²	1	12	yes	complemented
82	C₃×#536	C₂²	1	12	yes	complemented
83	C₃×#535	C₂²	1	1	yes	characteristic
84	C₃×#535	C₂²	1	3	yes	—
85	C₃×#533	C₂²	1	3	yes	—
86	C₃×#533	C₂²	1	6	yes	complemented
87	C₃×#533	C₂²	1	6	yes	complemented
88	C₃×#533	C₂²	1	6	yes	complemented
89	C₃×#532	C₂²	1	6	yes	—
90	C₃×#532	C₂²	1	6	yes	—
91	C₃×#532	C₂²	1	3	yes	—
92	C₃×#532	C₂²	1	6	yes	complemented
93	C₂×C₃×C₄⋊Q₈	C₂²	1	3	yes	—
94	C₂×C₃×C₄⋊Q₈	C₂²	1	6	yes	complemented
95	C₃×#529	C₂²	1	6	yes	—
96	C₃×#529	C₂²	1	6	yes	—
97	C₃×#529	C₂²	1	6	yes	complemented
98	C₃×#525	C₂²	1	12	yes	—
99	C₃×#525	C₂²	1	12	yes	—
100	C₂×C₃×C₂²⋊Q₈	C₂²	1	6	yes	—
101	C₃×#520	C₂²	1	6	yes	—
102	C₃×#519	C₂²	1	4	yes	complemented
103	C₃×C₄×#41	C₂²	1	3	yes	—
104	C₃×C₄×#41	C₂²	1	3	yes	—
105	C₃×C₄×#41	C₂²	1	2	yes	complemented
106	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
107	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
108	C₂×C₃×C₄×D₄	C₂²	1	3	yes	—
109	#3554	C₂×C₃	1	6	yes	complemented
110	#3552	C₂×C₃	1	6	yes	complemented
111	#3550	C₂×C₃	1	6	yes	complemented
112	#3547	C₂×C₃	1	6	yes	complemented
113	#3541	C₂×C₃	1	12	yes	complemented
114	#3523	C₂×C₃	1	2	yes	complemented
115	#3518	C₂×C₃	1	2	yes	complemented
116	#3511	C₂×C₃	1	3	yes	complemented
117	#3506	C₂×C₃	1	3	yes	complemented
118	#3503	C₂×C₃	1	3	yes	complemented
119	#3499	C₂×C₃	1	2	yes	complemented
120	#3497	C₂×C₃	1	2	yes	complemented
121	#3486	C₂×C₃	1	4	yes	complemented
122	#3480	C₂×C₃	1	1	yes	characteristic, complemented
123	Q₈×#41	C₂×C₃	1	1	yes	characteristic, complemented
124	C₂×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
125	#3460	C₂×C₃	1	3	yes	complemented
126	C₃×2₋¹⁺⁴	—	4	16	no	—
127	C₂×C₃×#41	C₂³	1	2	yes	—
128	C₂×C₃×#41	C₂³	1	1	yes	characteristic
129	C₂×C₃×#41	C₂³	1	3	yes	—
130	C₂×C₃×#41	C₂³	1	12	yes	—
131	C₂×C₃×#41	C₂³	1	12	yes	—
132	C₂×C₃×#41	C₂³	1	12	yes	—
133	C₂²×C₃×Q₈	—	4	8	no	—
134	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
135	C₂²×C₃×Q₈	C₂³	1	4	yes	—
136	C₂²×C₃×Q₈	C₂³	1	2	yes	—
137	C₂²×C₃×Q₈	C₂³	1	6	yes	—
138	C₂²×C₃×Q₈	C₂³	1	12	yes	—
139	C₂²×C₃×Q₈	C₂³	1	12	yes	—
140	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂³	1	6	yes	—
142	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
143	C₃×C₄⋊Q₈	C₂³	1	12	yes	—
144	C₃×C₄⋊Q₈	C₂³	1	24	yes	—
145	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
146	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
147	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
148	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
149	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
150	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
151	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
152	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
153	C₃×C₄⋊Q₈	C₂³	1	12	yes	—
154	C₃×C₄⋊Q₈	C₂³	1	3	yes	—
155	C₃×C₄⋊Q₈	C₂³	1	6	yes	—
156	C₃×#127	C₂³	1	6	yes	—
157	C₃×#127	C₂³	1	3	yes	—
158	C₃×#127	C₂³	1	2	yes	—
159	C₃×#126	C₂³	1	12	yes	—
160	C₃×#126	C₂³	1	12	yes	—
161	C₃×#126	C₂³	1	24	yes	—
162	C₃×#126	C₂³	1	24	yes	—
163	C₃×#126	C₂³	1	12	yes	—
164	C₃×#125	C₂³	1	24	yes	—
165	C₃×#125	C₂³	1	12	yes	—
166	C₃×#125	C₂³	1	12	yes	—
167	C₃×#125	C₂³	1	6	yes	—
168	C₃×#125	C₂³	1	6	yes	—
169	C₃×#125	C₂³	1	6	yes	—
170	C₃×#125	C₂³	1	6	yes	—
171	C₃×#124	C₂³	1	6	yes	—
172	C₃×#124	C₂³	1	6	yes	—
173	C₃×#124	C₂³	1	24	yes	—
174	C₃×#124	C₂³	1	6	yes	—
175	C₃×#124	C₂³	1	24	yes	—
176	C₃×#124	C₂³	1	12	yes	—
177	C₃×#124	C₂³	1	2	yes	—
178	C₃×#124	C₂³	1	12	yes	—
179	C₃×#124	C₂³	1	12	yes	—
180	C₃×#123	C₂³	1	24	yes	—
181	C₃×#123	C₂³	1	24	yes	—
182	C₃×#123	C₂³	1	12	yes	—
183	C₃×#123	C₂³	1	12	yes	—
184	C₃×#123	C₂³	1	24	yes	—
185	C₃×#123	C₂³	1	12	yes	—
186	C₃×#123	C₂³	1	12	yes	—
187	C₃×#123	C₂³	1	12	yes	—
188	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
189	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
190	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
191	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
192	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
193	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
194	C₃×C₂²⋊Q₈	C₂³	1	24	yes	—
195	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
196	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
197	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
198	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
199	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
200	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
201	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
202	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
203	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
204	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
205	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
206	C₃×C₂²⋊Q₈	C₂³	1	6	yes	—
207	C₃×C₂²⋊Q₈	C₂³	1	12	yes	—
208	C₃×#121	C₂³	1	12	yes	—
209	C₃×#121	C₂³	1	12	yes	—
210	C₃×#121	C₂³	1	12	yes	—
211	C₃×#121	C₂³	1	24	yes	—
212	C₃×#121	C₂³	1	6	yes	—
213	C₃×#121	C₂³	1	12	yes	—
214	C₃×#121	C₂³	1	12	yes	—
215	C₃×#121	C₂³	1	2	yes	—
216	C₃×#121	C₂³	1	6	yes	—
217	C₃×#121	C₂³	1	6	yes	—
218	C₃×#121	C₂³	1	2	yes	—
219	C₃×#121	C₂³	1	6	yes	—
220	C₃×#121	C₂³	1	6	yes	—
221	C₃×#121	C₂³	1	6	yes	—
222	C₃×#121	C₂³	1	12	yes	—
223	C₃×#121	C₂³	1	6	yes	—
224	C₃×#120	C₂³	1	4	yes	—
225	C₃×#120	C₂³	1	12	yes	—
226	C₃×C₄×Q₈	C₂³	1	3	yes	—
227	C₃×C₄×Q₈	C₂³	1	6	yes	—
228	C₃×C₄×Q₈	C₂³	1	12	yes	—
229	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₃×C₄×Q₈	C₂³	1	2	yes	—
231	C₃×C₄×Q₈	C₂³	1	3	yes	—
232	C₃×C₄×Q₈	C₂³	1	12	yes	—
233	C₃×C₄×Q₈	C₂³	1	3	yes	—
234	C₃×C₄×Q₈	C₂³	1	3	yes	—
235	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₃×C₄×Q₈	C₂³	1	3	yes	—
237	C₃×C₄×Q₈	C₂³	1	6	yes	—
238	C₃×C₄×Q₈	C₂³	1	6	yes	—
239	C₃×C₄×Q₈	C₂³	1	3	yes	—
240	C₃×C₄×Q₈	C₂³	1	2	yes	—
241	C₃×C₄×Q₈	C₂³	1	12	yes	—
242	C₃×C₄×Q₈	C₂³	1	12	yes	—
243	C₃×C₄×D₄	C₂³	1	6	yes	—
244	C₃×C₄×D₄	C₂³	1	12	yes	—
245	C₃×C₄×D₄	C₂³	1	24	yes	—
246	C₃×C₄×D₄	C₂³	1	3	yes	—
247	C₃×C₄×D₄	C₂³	1	6	yes	—
248	C₃×C₄×D₄	C₂³	1	6	yes	—
249	C₃×C₄×D₄	C₂³	1	6	yes	—
250	C₃×C₄×D₄	C₂³	1	6	yes	—
251	C₃×C₄×D₄	C₂³	1	6	yes	—
252	C₃×C₄×D₄	C₂³	1	6	yes	—
253	C₃×C₄×D₄	C₂³	1	3	yes	—
254	C₃×C₄×D₄	C₂³	1	3	yes	—
255	C₃×C₄×D₄	C₂³	1	6	yes	—
256	C₃×C₄×D₄	C₂³	1	6	yes	—
257	C₃×C₄×D₄	C₂³	1	3	yes	—
258	C₃×C₄×D₄	C₂³	1	6	yes	—
259	C₃×C₄×D₄	C₂³	1	24	yes	—
260	C₃×C₄×D₄	C₂³	1	12	yes	—
261	C₃×C₄×D₄	C₂³	1	12	yes	—
262	C₃×C₄×D₄	C₂³	1	6	yes	—
263	C₃×C₄×D₄	C₂³	1	12	yes	—
264	C₃×#117	C₂³	1	1	yes	characteristic
265	C₃×#117	C₂³	1	3	yes	—
266	C₃×#117	C₂³	1	6	yes	—
267	C₃×#117	C₂³	1	6	yes	—
268	C₃×#117	C₂³	1	6	yes	—
269	C₃×#117	C₂³	1	12	yes	—
270	C₃×#117	C₂³	1	12	yes	—
271	C₃×#117	C₂³	1	12	yes	—
272	C₃×#117	C₂³	1	12	yes	—
273	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
274	C₂×C₃×C₄⋊C₄	C₂³	1	3	yes	—
275	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
276	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
277	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
278	C₂×C₃×C₄⋊C₄	C₂³	1	12	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	6	yes	—
280	C₂×C₃×C₄²	C₂³	1	3	yes	—
281	C₂×C₃×C₄²	C₂³	1	6	yes	—
282	C₂×C₃×C₄²	C₂³	1	6	yes	—
283	C₂×2₋¹⁺⁴	C₂²×C₃	1	4	yes	complemented
284	C₂³×Q₈	C₂²×C₃	1	2	yes	—
285	#563	C₂²×C₃	1	24	yes	complemented
286	#562	C₂²×C₃	1	24	yes	complemented
287	#559	C₂²×C₃	1	12	yes	—
288	#559	C₂²×C₃	1	3	yes	complemented
289	Q₈²	C₂²×C₃	1	1	yes	characteristic, complemented
290	Q₈²	C₂²×C₃	1	6	yes	complemented
291	#557	C₂²×C₃	1	3	yes	complemented
292	#557	C₂²×C₃	1	1	yes	characteristic, complemented
293	#557	C₂²×C₃	1	6	yes	complemented
294	#556	C₂²×C₃	1	6	yes	—
295	#556	C₂²×C₃	1	3	yes	complemented
296	#556	C₂²×C₃	1	6	yes	complemented
297	#556	C₂²×C₃	1	12	yes	complemented
298	#555	C₂²×C₃	1	6	yes	—
299	#555	C₂²×C₃	1	6	yes	complemented
300	#554	C₂²×C₃	1	6	yes	—
301	#554	C₂²×C₃	1	12	yes	—
302	#554	C₂²×C₃	1	3	yes	complemented
303	#554	C₂²×C₃	1	6	yes	complemented
304	#554	C₂²×C₃	1	6	yes	complemented
305	#553	C₂²×C₃	1	6	yes	—
306	#553	C₂²×C₃	1	12	yes	—
307	#553	C₂²×C₃	1	12	yes	—
308	#552	C₂²×C₃	1	12	yes	complemented
309	#550	C₂²×C₃	1	6	yes	—
310	#550	C₂²×C₃	1	1	yes	characteristic, complemented
311	D₄×Q₈	C₂²×C₃	1	2	yes	—
312	D₄×Q₈	C₂²×C₃	1	2	yes	—
313	D₄×Q₈	C₂²×C₃	1	6	yes	—
314	D₄×Q₈	C₂²×C₃	1	6	yes	—
315	D₄×Q₈	C₂²×C₃	1	2	yes	—
316	D₄×Q₈	C₂²×C₃	1	12	yes	—
317	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
318	D₄×Q₈	C₂²×C₃	1	4	yes	complemented
319	D₄×Q₈	C₂²×C₃	1	12	yes	complemented
320	D₄×Q₈	C₂²×C₃	1	6	yes	complemented
321	#548	C₂²×C₃	1	2	yes	—
322	#548	C₂²×C₃	1	12	yes	—
323	#548	C₂²×C₃	1	4	yes	complemented
324	#548	C₂²×C₃	1	12	yes	complemented
325	#548	C₂²×C₃	1	12	yes	complemented
326	#547	C₂²×C₃	1	6	yes	—
327	#547	C₂²×C₃	1	6	yes	complemented
328	#547	C₂²×C₃	1	12	yes	complemented
329	#544	C₂²×C₃	1	3	yes	—
330	#544	C₂²×C₃	1	12	yes	complemented
331	#542	C₂²×C₃	1	6	yes	—
332	#542	C₂²×C₃	1	6	yes	—
333	#542	C₂²×C₃	1	12	yes	complemented
334	#542	C₂²×C₃	1	12	yes	complemented
335	#542	C₂²×C₃	1	24	yes	complemented
336	#541	C₂²×C₃	1	12	yes	complemented
337	#540	C₂²×C₃	1	6	yes	—
338	#540	C₂²×C₃	1	6	yes	—
339	#539	C₂²×C₃	1	24	yes	complemented
340	#538	C₂²×C₃	1	12	yes	—
341	#538	C₂²×C₃	1	12	yes	—
342	#537	C₂²×C₃	1	3	yes	—
343	#537	C₂²×C₃	1	12	yes	complemented
344	#536	C₂²×C₃	1	12	yes	complemented
345	#536	C₂²×C₃	1	12	yes	complemented
346	#536	C₂²×C₃	1	12	yes	complemented
347	#535	C₂²×C₃	1	1	yes	characteristic
348	#535	C₂²×C₃	1	3	yes	—
349	#533	C₂²×C₃	1	3	yes	—
350	#533	C₂²×C₃	1	6	yes	complemented
351	#533	C₂²×C₃	1	6	yes	complemented
352	#533	C₂²×C₃	1	6	yes	complemented
353	#532	C₂²×C₃	1	6	yes	—
354	#532	C₂²×C₃	1	6	yes	—
355	#532	C₂²×C₃	1	3	yes	—
356	#532	C₂²×C₃	1	6	yes	complemented
357	C₂×C₄⋊Q₈	C₂²×C₃	1	3	yes	—
358	C₂×C₄⋊Q₈	C₂²×C₃	1	6	yes	complemented
359	#529	C₂²×C₃	1	6	yes	—
360	#529	C₂²×C₃	1	6	yes	—
361	#529	C₂²×C₃	1	6	yes	complemented
362	#525	C₂²×C₃	1	12	yes	—
363	#525	C₂²×C₃	1	12	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
365	#520	C₂²×C₃	1	6	yes	—
366	#519	C₂²×C₃	1	4	yes	complemented
367	C₄×#41	C₂²×C₃	1	3	yes	—
368	C₄×#41	C₂²×C₃	1	3	yes	—
369	C₄×#41	C₂²×C₃	1	2	yes	complemented
370	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
372	C₂×C₄×D₄	C₂²×C₃	1	3	yes	—
373	C₂⁴×C₃	C₂⁴	1	2	yes	—
374	C₃×#41	—	2	8	no	—
375	C₃×#41	—	2	4	no	—
376	C₃×#41	—	2	12	no	—
377	C₃×#41	—	4	24	no	—
378	C₃×#41	—	4	24	no	—
379	C₃×#41	—	4	24	no	—
380	C₂×C₃×Q₈	—	2	4	no	—
381	C₂×C₃×Q₈	—	2	16	no	—
382	C₂×C₃×Q₈	—	2	8	no	—
383	C₂×C₃×Q₈	—	4	12	no	—
384	C₂×C₃×Q₈	—	4	24	no	—
385	C₂×C₃×Q₈	—	4	24	no	—
386	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
388	C₂×C₃×Q₈	C₂⁴	1	3	yes	—
389	C₂×C₃×Q₈	C₂⁴	1	12	yes	—
390	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
391	C₂×C₃×Q₈	C₂⁴	1	6	yes	—
392	C₂×C₃×Q₈	C₂⁴	1	12	yes	—
393	C₂×C₃×Q₈	C₂⁴	1	12	yes	—
394	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₃×D₄	—	2	4	no	—
396	C₂×C₃×D₄	C₂⁴	1	2	yes	—
397	C₂×C₃×D₄	C₂⁴	1	6	yes	—
398	C₂×C₃×D₄	C₂⁴	1	2	yes	—
399	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
400	C₂×C₃×D₄	C₂⁴	1	2	yes	—
401	C₂×C₃×D₄	C₂⁴	1	3	yes	—
402	C₂×C₃×D₄	C₂⁴	1	6	yes	—
403	C₂×C₃×D₄	C₂⁴	1	4	yes	—
404	C₂×C₃×D₄	C₂⁴	1	12	yes	—
405	C₂×C₃×D₄	C₂⁴	1	6	yes	—
406	C₂×C₃×D₄	C₂⁴	1	12	yes	—
407	C₂×C₃×D₄	C₂⁴	1	4	yes	—
408	C₂×C₃×D₄	C₂⁴	1	12	yes	—
409	C₂²×C₃×C₄	—	4	12	no	—
410	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
418	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	6	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	24	yes	—
421	C₂²×C₃×C₄	C₂⁴	1	12	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
423	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
424	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
425	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
426	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
427	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
428	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
429	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
430	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
431	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
432	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
433	C₃×C₄⋊C₄	C₂⁴	1	24	yes	—
434	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
435	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
436	C₃×C₄⋊C₄	C₂⁴	1	3	yes	—
437	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
438	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
439	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
442	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
443	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
444	C₃×C₄⋊C₄	C₂⁴	1	6	yes	—
445	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
446	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
447	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
448	C₃×C₄⋊C₄	C₂⁴	1	12	yes	—
449	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
450	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
451	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
452	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
453	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
454	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
455	C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
456	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
457	C₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
458	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
459	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
460	C₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
461	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
462	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
463	C₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
464	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
465	C₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
466	C₃×C₄²	C₂⁴	1	2	yes	—
467	C₃×C₄²	C₂⁴	1	3	yes	—
468	C₃×C₄²	C₂⁴	1	3	yes	—
469	C₃×C₄²	C₂⁴	1	3	yes	—
470	C₃×C₄²	C₂⁴	1	6	yes	—
471	C₃×C₄²	C₂⁴	1	6	yes	—
472	C₃×C₄²	C₂⁴	1	3	yes	—
473	C₃×C₄²	C₂⁴	1	6	yes	—
474	C₃×C₄²	C₂⁴	1	6	yes	—
475	C₃×C₄²	C₂⁴	1	6	yes	—
476	C₃×C₄²	C₂⁴	1	24	yes	—
477	2₋¹⁺⁴	—	4	16	no	—
478	C₂×#41	C₂³×C₃	1	1	yes	characteristic
479	C₂×#41	C₂³×C₃	1	3	yes	—
480	C₂×#41	C₂³×C₃	1	2	yes	—
481	C₂×#41	C₂³×C₃	1	12	yes	—
482	C₂×#41	C₂³×C₃	1	12	yes	—
483	C₂×#41	C₂³×C₃	1	12	yes	—
484	C₂²×Q₈	—	4	8	no	—
485	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₃	1	2	yes	—
487	C₂²×Q₈	C₂³×C₃	1	4	yes	—
488	C₂²×Q₈	C₂³×C₃	1	6	yes	—
489	C₂²×Q₈	C₂³×C₃	1	12	yes	—
490	C₂²×Q₈	C₂³×C₃	1	12	yes	—
491	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₃	1	6	yes	—
493	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
494	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
495	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
496	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
497	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
498	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
499	C₄⋊Q₈	C₂³×C₃	1	12	yes	—
500	C₄⋊Q₈	C₂³×C₃	1	12	yes	—
501	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
502	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
503	C₄⋊Q₈	C₂³×C₃	1	3	yes	—
504	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
505	C₄⋊Q₈	C₂³×C₃	1	6	yes	—
506	C₄⋊Q₈	C₂³×C₃	1	24	yes	—
507	#127	C₂³×C₃	1	2	yes	—
508	#127	C₂³×C₃	1	3	yes	—
509	#127	C₂³×C₃	1	6	yes	—
510	#126	C₂³×C₃	1	12	yes	—
511	#126	C₂³×C₃	1	12	yes	—
512	#126	C₂³×C₃	1	12	yes	—
513	#126	C₂³×C₃	1	24	yes	—
514	#126	C₂³×C₃	1	24	yes	—
515	#125	C₂³×C₃	1	6	yes	—
516	#125	C₂³×C₃	1	6	yes	—
517	#125	C₂³×C₃	1	6	yes	—
518	#125	C₂³×C₃	1	6	yes	—
519	#125	C₂³×C₃	1	12	yes	—
520	#125	C₂³×C₃	1	12	yes	—
521	#125	C₂³×C₃	1	24	yes	—
522	#124	C₂³×C₃	1	2	yes	—
523	#124	C₂³×C₃	1	6	yes	—
524	#124	C₂³×C₃	1	6	yes	—
525	#124	C₂³×C₃	1	12	yes	—
526	#124	C₂³×C₃	1	12	yes	—
527	#124	C₂³×C₃	1	6	yes	—
528	#124	C₂³×C₃	1	12	yes	—
529	#124	C₂³×C₃	1	24	yes	—
530	#124	C₂³×C₃	1	24	yes	—
531	#123	C₂³×C₃	1	12	yes	—
532	#123	C₂³×C₃	1	12	yes	—
533	#123	C₂³×C₃	1	24	yes	—
534	#123	C₂³×C₃	1	12	yes	—
535	#123	C₂³×C₃	1	12	yes	—
536	#123	C₂³×C₃	1	12	yes	—
537	#123	C₂³×C₃	1	24	yes	—
538	#123	C₂³×C₃	1	24	yes	—
539	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
540	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
541	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
542	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
543	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
544	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
545	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
546	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
547	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
548	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
549	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
550	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
551	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
552	C₂²⋊Q₈	C₂³×C₃	1	6	yes	—
553	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
554	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
555	C₂²⋊Q₈	C₂³×C₃	1	12	yes	—
556	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
557	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
558	C₂²⋊Q₈	C₂³×C₃	1	24	yes	—
559	#121	C₂³×C₃	1	6	yes	—
560	#121	C₂³×C₃	1	12	yes	—
561	#121	C₂³×C₃	1	12	yes	—
562	#121	C₂³×C₃	1	12	yes	—
563	#121	C₂³×C₃	1	2	yes	—
564	#121	C₂³×C₃	1	6	yes	—
565	#121	C₂³×C₃	1	6	yes	—
566	#121	C₂³×C₃	1	2	yes	—
567	#121	C₂³×C₃	1	6	yes	—
568	#121	C₂³×C₃	1	6	yes	—
569	#121	C₂³×C₃	1	6	yes	—
570	#121	C₂³×C₃	1	12	yes	—
571	#121	C₂³×C₃	1	6	yes	—
572	#121	C₂³×C₃	1	12	yes	—
573	#121	C₂³×C₃	1	12	yes	—
574	#121	C₂³×C₃	1	24	yes	—
575	#120	C₂³×C₃	1	4	yes	—
576	#120	C₂³×C₃	1	12	yes	—
577	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
578	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
579	C₄×Q₈	C₂³×C₃	1	3	yes	—
580	C₄×Q₈	C₂³×C₃	1	3	yes	—
581	C₄×Q₈	C₂³×C₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₃	1	6	yes	—
583	C₄×Q₈	C₂³×C₃	1	6	yes	—
584	C₄×Q₈	C₂³×C₃	1	3	yes	—
585	C₄×Q₈	C₂³×C₃	1	3	yes	—
586	C₄×Q₈	C₂³×C₃	1	3	yes	—
587	C₄×Q₈	C₂³×C₃	1	3	yes	—
588	C₄×Q₈	C₂³×C₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₃	1	12	yes	—
590	C₄×Q₈	C₂³×C₃	1	12	yes	—
591	C₄×Q₈	C₂³×C₃	1	12	yes	—
592	C₄×Q₈	C₂³×C₃	1	6	yes	—
593	C₄×Q₈	C₂³×C₃	1	12	yes	—
594	C₄×D₄	C₂³×C₃	1	6	yes	—
595	C₄×D₄	C₂³×C₃	1	6	yes	—
596	C₄×D₄	C₂³×C₃	1	6	yes	—
597	C₄×D₄	C₂³×C₃	1	6	yes	—
598	C₄×D₄	C₂³×C₃	1	6	yes	—
599	C₄×D₄	C₂³×C₃	1	6	yes	—
600	C₄×D₄	C₂³×C₃	1	3	yes	—
601	C₄×D₄	C₂³×C₃	1	3	yes	—
602	C₄×D₄	C₂³×C₃	1	6	yes	—
603	C₄×D₄	C₂³×C₃	1	6	yes	—
604	C₄×D₄	C₂³×C₃	1	3	yes	—
605	C₄×D₄	C₂³×C₃	1	3	yes	—
606	C₄×D₄	C₂³×C₃	1	6	yes	—
607	C₄×D₄	C₂³×C₃	1	6	yes	—
608	C₄×D₄	C₂³×C₃	1	24	yes	—
609	C₄×D₄	C₂³×C₃	1	12	yes	—
610	C₄×D₄	C₂³×C₃	1	12	yes	—
611	C₄×D₄	C₂³×C₃	1	12	yes	—
612	C₄×D₄	C₂³×C₃	1	24	yes	—
613	C₄×D₄	C₂³×C₃	1	6	yes	—
614	C₄×D₄	C₂³×C₃	1	12	yes	—
615	#117	C₂³×C₃	1	1	yes	characteristic
616	#117	C₂³×C₃	1	3	yes	—
617	#117	C₂³×C₃	1	6	yes	—
618	#117	C₂³×C₃	1	6	yes	—
619	#117	C₂³×C₃	1	6	yes	—
620	#117	C₂³×C₃	1	12	yes	—
621	#117	C₂³×C₃	1	12	yes	—
622	#117	C₂³×C₃	1	12	yes	—
623	#117	C₂³×C₃	1	12	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
625	C₂×C₄⋊C₄	C₂³×C₃	1	3	yes	—
626	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
627	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
628	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
629	C₂×C₄⋊C₄	C₂³×C₃	1	12	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
631	C₂×C₄²	C₂³×C₃	1	3	yes	—
632	C₂×C₄²	C₂³×C₃	1	6	yes	—
633	C₂×C₄²	C₂³×C₃	1	6	yes	—
634	C₂³×C₃	—	2	4	no	—
635	C₂³×C₃	—	4	2	no	—
636	C₂³×C₃	—	4	2	no	—
637	C₂³×C₃	C₂⁵	1	4	yes	—
638	C₂³×C₃	C₂⁵	1	2	yes	—
639	C₂³×C₃	C₂⁵	1	6	yes	—
640	C₂³×C₃	C₂⁵	1	1	yes	characteristic
641	C₃×Q₈	—	2	6	no	—
642	C₃×Q₈	—	2	24	no	—
643	C₃×Q₈	—	2	12	no	—
644	C₃×Q₈	—	2	2	no	—
645	C₃×Q₈	—	2	6	no	—
646	C₃×Q₈	—	4	12	no	—
647	C₃×Q₈	—	4	12	no	—
648	C₃×Q₈	—	4	6	no	—
649	C₃×Q₈	H(5,𝔽₂)	1	4	yes	—
650	C₃×D₄	—	2	4	no	—
651	C₃×D₄	—	2	12	no	—
652	C₃×D₄	—	2	12	no	—
653	C₃×D₄	—	2	4	no	—
654	C₃×D₄	—	2	4	no	—
655	C₃×D₄	—	2	2	no	—
656	C₃×D₄	—	2	6	no	—
657	C₃×D₄	—	4	4	no	—
658	C₃×D₄	—	4	6	no	—
659	C₃×D₄	—	4	12	no	—
660	C₃×D₄	—	4	4	no	—
661	C₃×D₄	—	4	12	no	—
662	C₃×D₄	—	4	12	no	—
663	C₂×C₃×C₄	—	2	6	no	—
664	C₂×C₃×C₄	—	2	24	no	—
665	C₂×C₃×C₄	—	2	12	no	—
666	C₂×C₃×C₄	—	2	12	no	—
667	C₂×C₃×C₄	—	2	12	no	—
668	C₂×C₃×C₄	—	2	4	no	—
669	C₂×C₃×C₄	—	4	6	no	—
670	C₂×C₃×C₄	—	4	12	no	—
671	C₂×C₃×C₄	—	4	3	no	—
672	C₂×C₃×C₄	—	4	6	no	—
673	C₂×C₃×C₄	—	4	6	no	—
674	C₂×C₃×C₄	—	4	24	no	—
675	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	complemented
676	C₂×C₃×C₄	C₂⁵	1	6	yes	—
677	C₂×C₃×C₄	C₂⁵	1	2	yes	—
678	C₂×C₃×C₄	C₂⁵	1	6	yes	—
679	C₂×C₃×C₄	C₂⁵	1	3	yes	—
680	C₂×C₃×C₄	C₂⁵	1	2	yes	—
681	C₂×C₃×C₄	C₂⁵	1	3	yes	—
682	C₂×C₃×C₄	C₂⁵	1	2	yes	—
683	C₂×C₃×C₄	C₂⁵	1	3	yes	—
684	C₂×C₃×C₄	C₂⁵	1	12	yes	—
685	C₂×C₃×C₄	C₂⁵	1	6	yes	—
686	C₂×C₃×C₄	C₂⁵	1	3	yes	—
687	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
688	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
689	C₂⁴	C₂⁴×C₃	1	2	yes	—
690	#41	—	2	8	no	—
691	#41	—	2	4	no	—
692	#41	—	2	12	no	—
693	#41	—	4	24	no	—
694	#41	—	4	24	no	—
695	#41	—	4	24	no	—
696	C₂×Q₈	—	2	4	no	—
697	C₂×Q₈	—	2	16	no	—
698	C₂×Q₈	—	2	8	no	—
699	C₂×Q₈	—	4	12	no	—
700	C₂×Q₈	—	4	24	no	—
701	C₂×Q₈	—	4	24	no	—
702	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
703	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
704	C₂×Q₈	C₂⁴×C₃	1	3	yes	—
705	C₂×Q₈	C₂⁴×C₃	1	12	yes	—
706	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
707	C₂×Q₈	C₂⁴×C₃	1	6	yes	—
708	C₂×Q₈	C₂⁴×C₃	1	12	yes	—
709	C₂×Q₈	C₂⁴×C₃	1	12	yes	—
710	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	C₂⁴×C₃	1	2	yes	—
713	C₂×D₄	C₂⁴×C₃	1	6	yes	—
714	C₂×D₄	C₂⁴×C₃	1	2	yes	—
715	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₂×D₄	C₂⁴×C₃	1	2	yes	—
717	C₂×D₄	C₂⁴×C₃	1	3	yes	—
718	C₂×D₄	C₂⁴×C₃	1	6	yes	—
719	C₂×D₄	C₂⁴×C₃	1	4	yes	—
720	C₂×D₄	C₂⁴×C₃	1	12	yes	—
721	C₂×D₄	C₂⁴×C₃	1	6	yes	—
722	C₂×D₄	C₂⁴×C₃	1	12	yes	—
723	C₂×D₄	C₂⁴×C₃	1	4	yes	—
724	C₂×D₄	C₂⁴×C₃	1	12	yes	—
725	C₂²×C₄	—	4	12	no	—
726	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
728	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
729	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
730	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
731	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
732	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
733	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
734	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
735	C₂²×C₄	C₂⁴×C₃	1	6	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	24	yes	—
737	C₂²×C₄	C₂⁴×C₃	1	12	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
740	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
741	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
742	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
743	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
744	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
745	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
746	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
747	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
748	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
749	C₄⋊C₄	C₂⁴×C₃	1	24	yes	—
750	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
751	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
752	C₄⋊C₄	C₂⁴×C₃	1	3	yes	—
753	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
754	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
755	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
758	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
759	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
760	C₄⋊C₄	C₂⁴×C₃	1	6	yes	—
761	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
762	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
763	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
764	C₄⋊C₄	C₂⁴×C₃	1	12	yes	—
765	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
766	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
767	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
768	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
769	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
770	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
771	C₂²⋊C₄	C₂⁴×C₃	1	2	yes	—
772	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
773	C₂²⋊C₄	C₂⁴×C₃	1	24	yes	—
774	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
775	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
776	C₂²⋊C₄	C₂⁴×C₃	1	6	yes	—
777	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
778	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
779	C₂²⋊C₄	C₂⁴×C₃	1	4	yes	—
780	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
781	C₂²⋊C₄	C₂⁴×C₃	1	12	yes	—
782	C₄²	C₂⁴×C₃	1	2	yes	—
783	C₄²	C₂⁴×C₃	1	3	yes	—
784	C₄²	C₂⁴×C₃	1	3	yes	—
785	C₄²	C₂⁴×C₃	1	3	yes	—
786	C₄²	C₂⁴×C₃	1	6	yes	—
787	C₄²	C₂⁴×C₃	1	6	yes	—
788	C₄²	C₂⁴×C₃	1	3	yes	—
789	C₄²	C₂⁴×C₃	1	6	yes	—
790	C₄²	C₂⁴×C₃	1	6	yes	—
791	C₄²	C₂⁴×C₃	1	6	yes	—
792	C₄²	C₂⁴×C₃	1	24	yes	—
793	C₂²×C₃	—	2	1	no	—
794	C₂²×C₃	—	2	1	no	—
795	C₂²×C₃	—	2	4	no	—
796	C₂²×C₃	—	2	2	no	—
797	C₂²×C₃	—	2	6	no	—
798	C₂²×C₃	—	2	2	no	—
799	C₂²×C₃	—	2	6	no	—
800	C₂²×C₃	—	2	4	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	6	no	—
803	C₂²×C₃	—	2	4	no	—
804	C₂²×C₃	—	4	8	no	—
805	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
806	C₂²×C₃	C₂⁶	1	1	yes	characteristic
807	C₃×C₄	—	2	2	no	—
808	C₃×C₄	—	2	6	no	—
809	C₃×C₄	—	2	12	no	—
810	C₃×C₄	—	2	3	no	—
811	C₃×C₄	—	2	6	no	—
812	C₃×C₄	—	2	2	no	—
813	C₃×C₄	—	2	3	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	3	no	—
816	C₃×C₄	—	2	6	no	—
817	C₃×C₄	C₂×H(5,𝔽₂)	1	6	yes	—
818	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
819	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
820	C₂³	—	2	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	4	2	no	—
823	C₂³	C₂⁵×C₃	1	4	yes	—
824	C₂³	C₂⁵×C₃	1	2	yes	—
825	C₂³	C₂⁵×C₃	1	6	yes	—
826	C₂³	C₂⁵×C₃	1	1	yes	characteristic
827	Q₈	—	2	6	no	—
828	Q₈	—	2	24	no	—
829	Q₈	—	2	12	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	2	6	no	—
832	Q₈	—	4	12	no	—
833	Q₈	—	4	12	no	—
834	Q₈	—	4	6	no	—
835	Q₈	C₃×H(5,𝔽₂)	1	4	yes	—
836	D₄	—	2	4	no	—
837	D₄	—	2	12	no	—
838	D₄	—	2	12	no	—
839	D₄	—	2	4	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	6	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	12	no	—
845	D₄	—	4	12	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	6	no	—
848	D₄	—	4	12	no	—
849	C₂×C₄	—	2	6	no	—
850	C₂×C₄	—	2	24	no	—
851	C₂×C₄	—	2	12	no	—
852	C₂×C₄	—	2	12	no	—
853	C₂×C₄	—	2	12	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	4	6	no	—
856	C₂×C₄	—	4	12	no	—
857	C₂×C₄	—	4	24	no	—
858	C₂×C₄	—	4	3	no	—
859	C₂×C₄	—	4	6	no	—
860	C₂×C₄	—	4	6	no	—
861	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	complemented
862	C₂×C₄	C₂⁵×C₃	1	6	yes	—
863	C₂×C₄	C₂⁵×C₃	1	2	yes	—
864	C₂×C₄	C₂⁵×C₃	1	6	yes	—
865	C₂×C₄	C₂⁵×C₃	1	3	yes	—
866	C₂×C₄	C₂⁵×C₃	1	2	yes	—
867	C₂×C₄	C₂⁵×C₃	1	3	yes	—
868	C₂×C₄	C₂⁵×C₃	1	2	yes	—
869	C₂×C₄	C₂⁵×C₃	1	3	yes	—
870	C₂×C₄	C₂⁵×C₃	1	12	yes	—
871	C₂×C₄	C₂⁵×C₃	1	6	yes	—
872	C₂×C₄	C₂⁵×C₃	1	3	yes	—
873	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
874	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
875	C₂×C₃	—	2	2	no	—
876	C₂×C₃	—	4	2	no	—
877	C₂×C₃	—	4	6	no	—
878	C₂×C₃	—	4	4	no	—
879	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
880	C₂×C₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
881	C₂×C₃	2₋¹⁺⁶	1	1	yes	characteristic
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	6	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	6	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	6	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	4	8	no	—
894	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
895	C₂²	C₂⁶×C₃	1	1	yes	characteristic
896	C₄	—	2	2	no	—
897	C₄	—	2	6	no	—
898	C₄	—	2	12	no	—
899	C₄	—	2	3	no	—
900	C₄	—	2	6	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	3	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	3	no	—
905	C₄	—	2	6	no	—
906	C₄	C₂×C₃×H(5,𝔽₂)	1	6	yes	—
907	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
908	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
909	C₃	#62913	1	1	yes	characteristic, direct product factor, Sylow
910	C₂	—	2	2	no	—
911	C₂	—	4	4	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	6	no	—
914	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
915	C₂	C₂²×C₃×2₋¹⁺⁴	1	1	yes	characteristic
916	C₂	C₃×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3554	C₂	semidirect
2. C₃×#3552	C₂	semidirect
3. C₃×#3550	C₂	semidirect
4. C₃×#3547	C₂	semidirect
5. C₃×#3541	C₂	semidirect
6. C₃×#3523	C₂	semidirect
7. C₃×#3518	C₂	semidirect
8. C₃×#3511	C₂	semidirect
9. C₃×#3506	C₂	semidirect
10. C₃×#3503	C₂	semidirect
11. C₃×#3499	C₂	semidirect
12. C₃×#3497	C₂	semidirect
13. C₃×#3486	C₂	semidirect
14. C₃×#3480	C₂	semidirect
15. C₃×Q₈×#41	C₂	semidirect
16. C₂×C₃×D₄×Q₈	C₂	semidirect
17. C₃×#3460	C₂	semidirect
18. #62913	C₃	direct (N × H)
19. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
21. C₃×#563	C₂²	semidirect
22. C₃×#562	C₂²	semidirect
24. C₃×#559	C₂²	semidirect
25. C₃×Q₈²	C₂²	semidirect
26. C₃×Q₈²	C₂²	semidirect
27. C₃×#557	C₂²	semidirect
28. C₃×#557	C₂²	semidirect
29. C₃×#557	C₂²	semidirect
31. C₃×#556	C₂²	semidirect
32. C₃×#556	C₂²	semidirect
33. C₃×#556	C₂²	semidirect
35. C₃×#555	C₂²	semidirect
38. C₃×#554	C₂²	semidirect
39. C₃×#554	C₂²	semidirect
40. C₃×#554	C₂²	semidirect
44. C₃×#552	C₂²	semidirect
46. C₃×#550	C₂²	semidirect
53. C₃×D₄×Q₈	C₂²	semidirect
54. C₃×D₄×Q₈	C₂²	semidirect
55. C₃×D₄×Q₈	C₂²	semidirect
56. C₃×D₄×Q₈	C₂²	semidirect
59. C₃×#548	C₂²	semidirect
60. C₃×#548	C₂²	semidirect
61. C₃×#548	C₂²	semidirect
63. C₃×#547	C₂²	semidirect
64. C₃×#547	C₂²	semidirect
66. C₃×#544	C₂²	semidirect
69. C₃×#542	C₂²	semidirect
70. C₃×#542	C₂²	semidirect
71. C₃×#542	C₂²	semidirect
72. C₃×#541	C₂²	semidirect
75. C₃×#539	C₂²	semidirect
79. C₃×#537	C₂²	semidirect
80. C₃×#536	C₂²	semidirect
81. C₃×#536	C₂²	semidirect
82. C₃×#536	C₂²	semidirect
86. C₃×#533	C₂²	semidirect
87. C₃×#533	C₂²	semidirect
88. C₃×#533	C₂²	semidirect
92. C₃×#532	C₂²	semidirect
94. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
97. C₃×#529	C₂²	semidirect
102. C₃×#519	C₂²	semidirect
105. C₃×C₄×#41	C₂²	semidirect
107. C₂×C₃×C₄×Q₈	C₂²	semidirect
109. #3554	C₂×C₃	semidirect
110. #3552	C₂×C₃	semidirect
111. #3550	C₂×C₃	semidirect
112. #3547	C₂×C₃	semidirect
113. #3541	C₂×C₃	semidirect
114. #3523	C₂×C₃	semidirect
115. #3518	C₂×C₃	semidirect
116. #3511	C₂×C₃	semidirect
117. #3506	C₂×C₃	semidirect
118. #3503	C₂×C₃	semidirect
119. #3499	C₂×C₃	semidirect
120. #3497	C₂×C₃	semidirect
121. #3486	C₂×C₃	semidirect
122. #3480	C₂×C₃	semidirect
123. Q₈×#41	C₂×C₃	semidirect
124. C₂×D₄×Q₈	C₂×C₃	semidirect
125. #3460	C₂×C₃	semidirect
283. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
285. #563	C₂²×C₃	semidirect
286. #562	C₂²×C₃	semidirect
288. #559	C₂²×C₃	semidirect
289. Q₈²	C₂²×C₃	semidirect
290. Q₈²	C₂²×C₃	semidirect
291. #557	C₂²×C₃	semidirect
292. #557	C₂²×C₃	semidirect
293. #557	C₂²×C₃	semidirect
295. #556	C₂²×C₃	semidirect
296. #556	C₂²×C₃	semidirect
297. #556	C₂²×C₃	semidirect
299. #555	C₂²×C₃	semidirect
302. #554	C₂²×C₃	semidirect
303. #554	C₂²×C₃	semidirect
304. #554	C₂²×C₃	semidirect
308. #552	C₂²×C₃	semidirect
310. #550	C₂²×C₃	semidirect
317. D₄×Q₈	C₂²×C₃	semidirect
318. D₄×Q₈	C₂²×C₃	semidirect
319. D₄×Q₈	C₂²×C₃	semidirect
320. D₄×Q₈	C₂²×C₃	semidirect
323. #548	C₂²×C₃	semidirect
324. #548	C₂²×C₃	semidirect
325. #548	C₂²×C₃	semidirect
327. #547	C₂²×C₃	semidirect
328. #547	C₂²×C₃	semidirect
330. #544	C₂²×C₃	semidirect
333. #542	C₂²×C₃	semidirect
334. #542	C₂²×C₃	semidirect
335. #542	C₂²×C₃	semidirect
336. #541	C₂²×C₃	semidirect
339. #539	C₂²×C₃	semidirect
343. #537	C₂²×C₃	semidirect
344. #536	C₂²×C₃	semidirect
345. #536	C₂²×C₃	semidirect
346. #536	C₂²×C₃	semidirect
350. #533	C₂²×C₃	semidirect
351. #533	C₂²×C₃	semidirect
352. #533	C₂²×C₃	semidirect
356. #532	C₂²×C₃	semidirect
358. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
361. #529	C₂²×C₃	semidirect
366. #519	C₂²×C₃	semidirect
369. C₄×#41	C₂²×C₃	semidirect
371. C₂×C₄×Q₈	C₂²×C₃	semidirect
675. C₂×C₃×C₄	2₋¹⁺⁴	semidirect
861. C₂×C₄	C₃×2₋¹⁺⁴	semidirect
909. C₃	#62913	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×#3554	2
C₃×#3552	2
C₃×#3550	2
C₃×#3547	2
C₃×#3541	2
C₃×#3523	2
C₃×#3518	2
C₃×#3511	2
C₃×#3506	2
C₃×#3503	2
C₃×#3499	2
C₃×#3497	2
C₃×#3486	2
C₃×#3480	2
C₃×Q₈×#41	2
C₂×C₃×D₄×Q₈	2
C₃×#3460	2
#62913	3

Subgroups — C3×#62913 #10681520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62913 #10681520