Subgroups — C₃×#3542 #87426

Order 384.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#562	C₂	1	2	yes	maximal, complemented
2	C₃×#560	C₂	1	2	yes	maximal, complemented
3	C₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#551	C₂	1	2	yes	maximal, complemented
7	C₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#546	C₂	1	2	yes	maximal, complemented
10	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#540	C₂	1	2	yes	maximal, complemented
16	C₃×#538	C₂	1	2	yes	maximal, complemented
17	C₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#535	C₂	1	2	yes	maximal, complemented
19	C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#534	C₂	1	2	yes	maximal, complemented
21	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
24	#3542	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#41	C₂²	1	2	yes	complemented
28	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
30	C₂²×C₃×D₄	C₂²	1	2	yes	—
31	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
32	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×#127	C₂²	1	2	yes	complemented
36	C₃×#127	C₂²	1	2	yes	complemented
37	C₃×#127	C₂²	1	1	yes	characteristic, complemented
38	C₃×#126	C₂²	1	2	yes	complemented
39	C₃×#126	C₂²	1	2	yes	complemented
40	C₃×#126	C₂²	1	2	yes	complemented
41	C₃×#125	C₂²	1	2	yes	complemented
42	C₃×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃×#124	C₂²	1	2	yes	complemented
44	C₃×#124	C₂²	1	2	yes	complemented
45	C₃×#124	C₂²	1	2	yes	complemented
46	C₃×#124	C₂²	1	2	yes	complemented
47	C₃×#124	C₂²	1	1	yes	characteristic, complemented
48	C₃×#123	C₂²	1	2	yes	—
49	C₃×#123	C₂²	1	2	yes	complemented
50	C₃×#123	C₂²	1	2	yes	complemented
51	C₃×#123	C₂²	1	2	yes	complemented
52	C₃×#123	C₂²	1	2	yes	complemented
53	C₃×#123	C₂²	1	2	yes	complemented
54	C₃×#123	C₂²	1	2	yes	complemented
55	C₃×#123	C₂²	1	1	yes	characteristic, complemented
56	C₃×#123	C₂²	1	1	yes	characteristic, complemented
57	C₃×#123	C₂²	1	2	yes	complemented
58	C₃×#123	C₂²	1	2	yes	complemented
59	C₃×#123	C₂²	1	2	yes	complemented
60	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
67	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
68	C₃×#121	C₂²	1	1	yes	characteristic
69	C₃×#121	C₂²	1	1	yes	characteristic
70	C₃×#121	C₂²	1	1	yes	characteristic
71	C₃×#121	C₂²	1	1	yes	characteristic
72	C₃×#121	C₂²	1	1	yes	characteristic, complemented
73	C₃×#121	C₂²	1	2	yes	complemented
74	C₃×#121	C₂²	1	2	yes	complemented
75	C₃×#121	C₂²	1	2	yes	complemented
76	C₃×#121	C₂²	1	2	yes	complemented
77	C₃×#121	C₂²	1	2	yes	complemented
78	C₃×#121	C₂²	1	2	yes	complemented
79	C₃×#121	C₂²	1	2	yes	complemented
80	C₃×#121	C₂²	1	2	yes	complemented
81	C₃×#121	C₂²	1	1	yes	characteristic, complemented
82	C₃×#121	C₂²	1	2	yes	complemented
83	C₃×#121	C₂²	1	1	yes	characteristic, complemented
84	C₃×#121	C₂²	1	1	yes	characteristic, complemented
85	C₃×#121	C₂²	1	2	yes	complemented
86	C₃×#121	C₂²	1	2	yes	complemented
87	C₃×#121	C₂²	1	2	yes	complemented
88	C₃×#121	C₂²	1	2	yes	complemented
89	C₃×#121	C₂²	1	1	yes	characteristic, complemented
90	C₃×#121	C₂²	1	1	yes	characteristic, complemented
91	C₃×#121	C₂²	1	1	yes	characteristic, complemented
92	C₃×#121	C₂²	1	2	yes	complemented
93	C₃×#120	C₂²	1	1	yes	characteristic
94	C₃×#120	C₂²	1	2	yes	—
95	C₃×#120	C₂²	1	2	yes	complemented
96	C₃×#120	C₂²	1	2	yes	complemented
97	C₃×#120	C₂²	1	2	yes	complemented
98	C₃×#120	C₂²	1	2	yes	complemented
99	C₃×#120	C₂²	1	1	yes	characteristic, complemented
100	C₃×#120	C₂²	1	2	yes	complemented
101	C₃×#120	C₂²	1	2	yes	complemented
102	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×D₄	C₂²	1	2	yes	complemented
105	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
106	C₃×C₄×D₄	C₂²	1	2	yes	complemented
107	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
108	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
109	C₃×C₄×D₄	C₂²	1	2	yes	complemented
110	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
111	C₃×C₄×D₄	C₂²	1	2	yes	complemented
112	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
113	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
114	C₃×#117	C₂²	1	1	yes	characteristic, complemented
115	C₃×#117	C₂²	1	1	yes	characteristic, complemented
116	C₃×#117	C₂²	1	2	yes	complemented
117	C₃×#117	C₂²	1	1	yes	characteristic, complemented
118	C₃×#117	C₂²	1	2	yes	complemented
119	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	#562	C₂×C₃	1	2	yes	complemented
125	#560	C₂×C₃	1	2	yes	complemented
126	#555	C₂×C₃	1	1	yes	characteristic, complemented
127	#553	C₂×C₃	1	1	yes	characteristic, complemented
128	#552	C₂×C₃	1	1	yes	characteristic, complemented
129	#551	C₂×C₃	1	2	yes	complemented
130	#550	C₂×C₃	1	1	yes	characteristic, complemented
131	#547	C₂×C₃	1	1	yes	characteristic, complemented
132	#546	C₂×C₃	1	2	yes	complemented
133	#546	C₂×C₃	1	1	yes	characteristic, complemented
134	#546	C₂×C₃	1	1	yes	characteristic, complemented
135	D₄²	C₂×C₃	1	1	yes	characteristic, complemented
136	#542	C₂×C₃	1	1	yes	characteristic, complemented
137	#540	C₂×C₃	1	1	yes	characteristic, complemented
138	#540	C₂×C₃	1	2	yes	complemented
139	#538	C₂×C₃	1	2	yes	complemented
140	#537	C₂×C₃	1	1	yes	characteristic, complemented
141	#535	C₂×C₃	1	2	yes	complemented
142	#535	C₂×C₃	1	1	yes	characteristic, complemented
143	#534	C₂×C₃	1	2	yes	complemented
144	#525	C₂×C₃	1	1	yes	characteristic, complemented
145	#525	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×#121	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂⁴×C₃	C₂³	1	1	yes	characteristic
149	C₂⁴×C₃	C₂³	1	2	yes	—
150	C₃×#41	—	4	2	no	—
151	C₃×#41	—	4	4	no	—
152	C₃×#41	—	4	2	no	—
153	C₃×#41	—	4	2	no	—
154	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
155	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
156	C₂×C₃×Q₈	C₂³	1	2	yes	—
157	C₂×C₃×D₄	—	4	2	no	—
158	C₂×C₃×D₄	—	4	2	no	—
159	C₂×C₃×D₄	—	4	4	no	—
160	C₂×C₃×D₄	—	4	4	no	—
161	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×D₄	C₂³	1	2	yes	—
163	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×D₄	C₂³	1	2	yes	—
169	C₂×C₃×D₄	C₂³	1	2	yes	—
170	C₂×C₃×D₄	C₂³	1	2	yes	—
171	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×D₄	C₂³	1	2	yes	—
174	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×D₄	C₂³	1	2	yes	—
176	C₂×C₃×D₄	C₂³	1	2	yes	—
177	C₂×C₃×D₄	C₂³	1	2	yes	—
178	C₂×C₃×D₄	C₂³	1	2	yes	—
179	C₂×C₃×D₄	C₂³	1	2	yes	—
180	C₂×C₃×D₄	C₂³	1	2	yes	—
181	C₂×C₃×D₄	C₂³	1	2	yes	—
182	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×D₄	C₂³	1	2	yes	—
184	C₂×C₃×D₄	C₂³	1	2	yes	—
185	C₂×C₃×D₄	C₂³	1	2	yes	—
186	C₂²×C₃×C₄	—	4	2	no	—
187	C₂²×C₃×C₄	C₂³	1	2	yes	—
188	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³	1	2	yes	—
195	C₂²×C₃×C₄	C₂³	1	2	yes	—
196	C₂²×C₃×C₄	C₂³	1	2	yes	—
197	C₂²×C₃×C₄	C₂³	1	2	yes	—
198	C₂²×C₃×C₄	C₂³	1	2	yes	—
199	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³	1	2	yes	—
201	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₃×C₄²	C₂³	1	2	yes	—
251	C₃×C₄²	C₂³	1	2	yes	—
252	C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₃×C₄²	C₂³	1	2	yes	—
255	C₂×#41	C₂²×C₃	1	1	yes	characteristic, complemented
256	C₂×#41	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₂×#41	C₂²×C₃	1	2	yes	complemented
258	C₂×#41	C₂²×C₃	1	1	yes	characteristic, complemented
259	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
260	C₂²×D₄	C₂²×C₃	1	2	yes	—
261	C₂²×D₄	C₂²×C₃	1	2	yes	complemented
262	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
263	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
265	#127	C₂²×C₃	1	2	yes	complemented
266	#127	C₂²×C₃	1	2	yes	complemented
267	#127	C₂²×C₃	1	1	yes	characteristic, complemented
268	#126	C₂²×C₃	1	2	yes	complemented
269	#126	C₂²×C₃	1	2	yes	complemented
270	#126	C₂²×C₃	1	2	yes	complemented
271	#125	C₂²×C₃	1	1	yes	characteristic, complemented
272	#125	C₂²×C₃	1	2	yes	complemented
273	#124	C₂²×C₃	1	2	yes	complemented
274	#124	C₂²×C₃	1	2	yes	complemented
275	#124	C₂²×C₃	1	2	yes	complemented
276	#124	C₂²×C₃	1	2	yes	complemented
277	#124	C₂²×C₃	1	1	yes	characteristic, complemented
278	#123	C₂²×C₃	1	2	yes	—
279	#123	C₂²×C₃	1	1	yes	characteristic, complemented
280	#123	C₂²×C₃	1	1	yes	characteristic, complemented
281	#123	C₂²×C₃	1	2	yes	complemented
282	#123	C₂²×C₃	1	2	yes	complemented
283	#123	C₂²×C₃	1	2	yes	complemented
284	#123	C₂²×C₃	1	2	yes	complemented
285	#123	C₂²×C₃	1	2	yes	complemented
286	#123	C₂²×C₃	1	2	yes	complemented
287	#123	C₂²×C₃	1	2	yes	complemented
288	#123	C₂²×C₃	1	2	yes	complemented
289	#123	C₂²×C₃	1	2	yes	complemented
290	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
293	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
294	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
296	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
297	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
298	#121	C₂²×C₃	1	1	yes	characteristic
299	#121	C₂²×C₃	1	1	yes	characteristic
300	#121	C₂²×C₃	1	1	yes	characteristic
301	#121	C₂²×C₃	1	1	yes	characteristic
302	#121	C₂²×C₃	1	1	yes	characteristic, complemented
303	#121	C₂²×C₃	1	2	yes	complemented
304	#121	C₂²×C₃	1	1	yes	characteristic, complemented
305	#121	C₂²×C₃	1	2	yes	complemented
306	#121	C₂²×C₃	1	1	yes	characteristic, complemented
307	#121	C₂²×C₃	1	1	yes	characteristic, complemented
308	#121	C₂²×C₃	1	2	yes	complemented
309	#121	C₂²×C₃	1	2	yes	complemented
310	#121	C₂²×C₃	1	2	yes	complemented
311	#121	C₂²×C₃	1	2	yes	complemented
312	#121	C₂²×C₃	1	2	yes	complemented
313	#121	C₂²×C₃	1	2	yes	complemented
314	#121	C₂²×C₃	1	1	yes	characteristic, complemented
315	#121	C₂²×C₃	1	2	yes	complemented
316	#121	C₂²×C₃	1	1	yes	characteristic, complemented
317	#121	C₂²×C₃	1	2	yes	complemented
318	#121	C₂²×C₃	1	1	yes	characteristic, complemented
319	#121	C₂²×C₃	1	2	yes	complemented
320	#121	C₂²×C₃	1	2	yes	complemented
321	#121	C₂²×C₃	1	2	yes	complemented
322	#121	C₂²×C₃	1	2	yes	complemented
323	#120	C₂²×C₃	1	1	yes	characteristic
324	#120	C₂²×C₃	1	2	yes	—
325	#120	C₂²×C₃	1	2	yes	complemented
326	#120	C₂²×C₃	1	1	yes	characteristic, complemented
327	#120	C₂²×C₃	1	2	yes	complemented
328	#120	C₂²×C₃	1	2	yes	complemented
329	#120	C₂²×C₃	1	2	yes	complemented
330	#120	C₂²×C₃	1	2	yes	complemented
331	#120	C₂²×C₃	1	2	yes	complemented
332	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
333	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
334	C₄×D₄	C₂²×C₃	1	2	yes	complemented
335	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
336	C₄×D₄	C₂²×C₃	1	2	yes	complemented
337	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
338	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
339	C₄×D₄	C₂²×C₃	1	2	yes	complemented
340	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
341	C₄×D₄	C₂²×C₃	1	2	yes	complemented
342	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
343	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
344	#117	C₂²×C₃	1	1	yes	characteristic, complemented
345	#117	C₂²×C₃	1	1	yes	characteristic, complemented
346	#117	C₂²×C₃	1	2	yes	complemented
347	#117	C₂²×C₃	1	1	yes	characteristic, complemented
348	#117	C₂²×C₃	1	2	yes	complemented
349	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
350	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
351	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
352	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
353	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	2	4	no	—
356	C₂³×C₃	—	4	1	no	—
357	C₂³×C₃	—	4	1	no	—
358	C₂³×C₃	—	4	2	no	—
359	C₂³×C₃	—	4	2	no	—
360	C₂³×C₃	—	4	2	no	—
361	C₂³×C₃	—	4	2	no	—
362	C₂³×C₃	—	4	2	no	—
363	C₂³×C₃	C₂⁴	1	1	yes	characteristic
364	C₂³×C₃	C₂⁴	1	2	yes	—
365	C₂³×C₃	C₂⁴	1	1	yes	characteristic
366	C₂³×C₃	C₂⁴	1	1	yes	characteristic
367	C₂³×C₃	C₂⁴	1	2	yes	—
368	C₂³×C₃	C₂⁴	1	2	yes	—
369	C₂³×C₃	C₂⁴	1	1	yes	characteristic
370	C₂³×C₃	C₂⁴	1	1	yes	characteristic
371	C₃×Q₈	—	2	2	no	—
372	C₃×Q₈	—	4	1	no	—
373	C₃×Q₈	—	4	2	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	2	4	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	2	2	no	—
380	C₃×D₄	—	4	2	no	—
381	C₃×D₄	—	4	2	no	—
382	C₃×D₄	—	4	2	no	—
383	C₃×D₄	—	4	2	no	—
384	C₃×D₄	—	4	2	no	—
385	C₃×D₄	—	4	2	no	—
386	C₃×D₄	—	4	2	no	—
387	C₃×D₄	—	4	2	no	—
388	C₃×D₄	—	4	1	no	—
389	C₃×D₄	—	4	2	no	—
390	C₃×D₄	—	4	2	no	—
391	C₃×D₄	—	4	2	no	—
392	C₃×D₄	—	4	1	no	—
393	C₃×D₄	—	4	1	no	—
394	C₃×D₄	—	4	1	no	—
395	C₃×D₄	—	4	1	no	—
396	C₃×D₄	—	4	2	no	—
397	C₃×D₄	—	4	2	no	—
398	C₃×D₄	—	4	2	no	—
399	C₂×C₃×C₄	—	2	4	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	4	1	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	4	2	no	—
409	C₂×C₃×C₄	—	4	2	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	4	2	no	—
412	C₂×C₃×C₄	—	4	2	no	—
413	C₂×C₃×C₄	—	4	2	no	—
414	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂⁴	1	2	yes	—
422	C₂×C₃×C₄	C₂⁴	1	2	yes	—
423	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂⁴	1	2	yes	—
427	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂⁴	C₂³×C₃	1	2	yes	—
430	C₂⁴	C₂³×C₃	1	1	yes	characteristic
431	C₂⁴	C₂³×C₃	1	2	yes	—
432	#41	—	4	2	no	—
433	#41	—	4	4	no	—
434	#41	—	4	2	no	—
435	#41	—	4	2	no	—
436	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
437	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
438	C₂×Q₈	C₂³×C₃	1	2	yes	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
444	C₂×D₄	C₂³×C₃	1	2	yes	—
445	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
446	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
447	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
448	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
449	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
450	C₂×D₄	C₂³×C₃	1	2	yes	—
451	C₂×D₄	C₂³×C₃	1	2	yes	—
452	C₂×D₄	C₂³×C₃	1	2	yes	—
453	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
454	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
455	C₂×D₄	C₂³×C₃	1	2	yes	—
456	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
457	C₂×D₄	C₂³×C₃	1	2	yes	—
458	C₂×D₄	C₂³×C₃	1	2	yes	—
459	C₂×D₄	C₂³×C₃	1	2	yes	—
460	C₂×D₄	C₂³×C₃	1	2	yes	—
461	C₂×D₄	C₂³×C₃	1	2	yes	—
462	C₂×D₄	C₂³×C₃	1	2	yes	—
463	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
464	C₂×D₄	C₂³×C₃	1	2	yes	—
465	C₂×D₄	C₂³×C₃	1	2	yes	—
466	C₂×D₄	C₂³×C₃	1	2	yes	—
467	C₂×D₄	C₂³×C₃	1	2	yes	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	C₂³×C₃	1	2	yes	—
470	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
476	C₂²×C₄	C₂³×C₃	1	2	yes	—
477	C₂²×C₄	C₂³×C₃	1	2	yes	—
478	C₂²×C₄	C₂³×C₃	1	2	yes	—
479	C₂²×C₄	C₂³×C₃	1	2	yes	—
480	C₂²×C₄	C₂³×C₃	1	2	yes	—
481	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
482	C₂²×C₄	C₂³×C₃	1	2	yes	—
483	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₄⋊C₄	C₂³×C₃	1	2	yes	—
500	C₄⋊C₄	C₂³×C₃	1	2	yes	—
501	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
504	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
520	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₄²	C₂³×C₃	1	2	yes	—
533	C₄²	C₂³×C₃	1	2	yes	—
534	C₄²	C₂³×C₃	1	1	yes	characteristic
535	C₄²	C₂³×C₃	1	1	yes	characteristic
536	C₄²	C₂³×C₃	1	2	yes	—
537	C₂²×C₃	—	2	1	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	1	no	—
540	C₂²×C₃	—	2	1	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	1	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	2	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	1	no	—
549	C₂²×C₃	—	2	2	no	—
550	C₂²×C₃	—	2	1	no	—
551	C₂²×C₃	—	2	1	no	—
552	C₂²×C₃	—	2	2	no	—
553	C₂²×C₃	—	2	2	no	—
554	C₂²×C₃	—	2	1	no	—
555	C₂²×C₃	—	2	1	no	—
556	C₂²×C₃	—	2	1	no	—
557	C₂²×C₃	—	2	2	no	—
558	C₂²×C₃	—	2	1	no	—
559	C₂²×C₃	—	2	2	no	—
560	C₂²×C₃	—	4	4	no	—
561	C₂²×C₃	—	8	4	no	—
562	C₂²×C₃	—	8	4	no	—
563	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
564	C₂²×C₃	C₂⁵	1	1	yes	characteristic
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	2	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	2	1	no	—
569	C₃×C₄	—	2	1	no	—
570	C₃×C₄	—	2	2	no	—
571	C₃×C₄	—	2	1	no	—
572	C₃×C₄	—	2	1	no	—
573	C₃×C₄	—	2	2	no	—
574	C₃×C₄	—	2	1	no	—
575	C₃×C₄	—	2	2	no	—
576	C₃×C₄	—	2	1	no	—
577	C₃×C₄	—	2	2	no	—
578	C₃×C₄	—	2	1	no	—
579	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	C₂⁴×C₃	1	1	yes	characteristic
590	C₂³	C₂⁴×C₃	1	2	yes	—
591	C₂³	C₂⁴×C₃	1	1	yes	characteristic
592	C₂³	C₂⁴×C₃	1	1	yes	characteristic
593	C₂³	C₂⁴×C₃	1	2	yes	—
594	C₂³	C₂⁴×C₃	1	2	yes	—
595	C₂³	C₂⁴×C₃	1	1	yes	characteristic
596	C₂³	C₂⁴×C₃	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	4	2	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	1	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₂×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
643	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
644	C₂×C₄	C₂⁴×C₃	1	2	yes	—
645	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
646	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
647	C₂×C₄	C₂⁴×C₃	1	2	yes	—
648	C₂×C₄	C₂⁴×C₃	1	2	yes	—
649	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
650	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
651	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
652	C₂×C₄	C₂⁴×C₃	1	2	yes	—
653	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
654	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
655	C₂×C₃	—	2	2	no	—
656	C₂×C₃	—	4	1	no	—
657	C₂×C₃	—	4	1	no	—
658	C₂×C₃	—	4	1	no	—
659	C₂×C₃	—	4	2	no	—
660	C₂×C₃	—	4	2	no	—
661	C₂×C₃	—	4	1	no	—
662	C₂×C₃	—	4	2	no	—
663	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂×C₃	#585	1	1	yes	characteristic
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	8	4	no	—
691	C₂²	—	8	4	no	—
692	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
693	C₂²	C₂⁵×C₃	1	1	yes	characteristic
694	C₄	—	2	1	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	1	no	—
708	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
709	C₃	#3542	1	1	yes	characteristic, direct product factor, Sylow
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	1	no	—
714	C₂	—	4	2	no	—
715	C₂	—	4	2	no	—
716	C₂	—	4	2	no	—
717	C₂	—	4	1	no	—
718	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×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×#562	C₂	semidirect
2. C₃×#560	C₂	semidirect
3. C₃×#555	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#552	C₂	semidirect
6. C₃×#551	C₂	semidirect
7. C₃×#550	C₂	semidirect
8. C₃×#547	C₂	semidirect
9. C₃×#546	C₂	semidirect
10. C₃×#546	C₂	semidirect
11. C₃×#546	C₂	semidirect
12. C₃×D₄²	C₂	semidirect
13. C₃×#542	C₂	semidirect
14. C₃×#540	C₂	semidirect
15. C₃×#540	C₂	semidirect
16. C₃×#538	C₂	semidirect
17. C₃×#537	C₂	semidirect
18. C₃×#535	C₂	semidirect
19. C₃×#535	C₂	semidirect
20. C₃×#534	C₂	semidirect
21. C₃×#525	C₂	semidirect
22. C₃×#525	C₂	semidirect
23. C₂×C₃×#121	C₂	semidirect
24. #3542	C₃	direct (N × H)
25. C₂×C₃×#41	C₂²	semidirect
26. C₂×C₃×#41	C₂²	semidirect
27. C₂×C₃×#41	C₂²	semidirect
28. C₂×C₃×#41	C₂²	semidirect
31. C₂²×C₃×D₄	C₂²	semidirect
32. C₂²×C₃×D₄	C₂²	semidirect
33. C₂³×C₃×C₄	C₂²	semidirect
34. C₃×C₄⋊Q₈	C₂²	semidirect
35. C₃×#127	C₂²	semidirect
36. C₃×#127	C₂²	semidirect
37. C₃×#127	C₂²	semidirect
38. C₃×#126	C₂²	semidirect
39. C₃×#126	C₂²	semidirect
40. C₃×#126	C₂²	semidirect
41. C₃×#125	C₂²	semidirect
42. C₃×#125	C₂²	semidirect
43. C₃×#124	C₂²	semidirect
44. C₃×#124	C₂²	semidirect
45. C₃×#124	C₂²	semidirect
46. C₃×#124	C₂²	semidirect
47. C₃×#124	C₂²	semidirect
49. C₃×#123	C₂²	semidirect
50. C₃×#123	C₂²	semidirect
51. C₃×#123	C₂²	semidirect
52. C₃×#123	C₂²	semidirect
53. C₃×#123	C₂²	semidirect
54. C₃×#123	C₂²	semidirect
55. C₃×#123	C₂²	semidirect
56. C₃×#123	C₂²	semidirect
57. C₃×#123	C₂²	semidirect
58. C₃×#123	C₂²	semidirect
59. C₃×#123	C₂²	semidirect
60. C₃×C₂²⋊Q₈	C₂²	semidirect
61. C₃×C₂²⋊Q₈	C₂²	semidirect
62. C₃×C₂²⋊Q₈	C₂²	semidirect
63. C₃×C₂²⋊Q₈	C₂²	semidirect
64. C₃×C₂²⋊Q₈	C₂²	semidirect
65. C₃×C₂²⋊Q₈	C₂²	semidirect
66. C₃×C₂²⋊Q₈	C₂²	semidirect
67. C₃×C₂²⋊Q₈	C₂²	semidirect
72. C₃×#121	C₂²	semidirect
73. C₃×#121	C₂²	semidirect
74. C₃×#121	C₂²	semidirect
75. C₃×#121	C₂²	semidirect
76. C₃×#121	C₂²	semidirect
77. C₃×#121	C₂²	semidirect
78. C₃×#121	C₂²	semidirect
79. C₃×#121	C₂²	semidirect
80. C₃×#121	C₂²	semidirect
81. C₃×#121	C₂²	semidirect
82. C₃×#121	C₂²	semidirect
83. C₃×#121	C₂²	semidirect
84. C₃×#121	C₂²	semidirect
85. C₃×#121	C₂²	semidirect
86. C₃×#121	C₂²	semidirect
87. C₃×#121	C₂²	semidirect
88. C₃×#121	C₂²	semidirect
89. C₃×#121	C₂²	semidirect
90. C₃×#121	C₂²	semidirect
91. C₃×#121	C₂²	semidirect
92. C₃×#121	C₂²	semidirect
95. C₃×#120	C₂²	semidirect
96. C₃×#120	C₂²	semidirect
97. C₃×#120	C₂²	semidirect
98. C₃×#120	C₂²	semidirect
99. C₃×#120	C₂²	semidirect
100. C₃×#120	C₂²	semidirect
101. C₃×#120	C₂²	semidirect
102. C₃×C₄×Q₈	C₂²	semidirect
104. C₃×C₄×D₄	C₂²	semidirect
105. C₃×C₄×D₄	C₂²	semidirect
106. C₃×C₄×D₄	C₂²	semidirect
107. C₃×C₄×D₄	C₂²	semidirect
108. C₃×C₄×D₄	C₂²	semidirect
109. C₃×C₄×D₄	C₂²	semidirect
110. C₃×C₄×D₄	C₂²	semidirect
111. C₃×C₄×D₄	C₂²	semidirect
112. C₃×C₄×D₄	C₂²	semidirect
113. C₃×C₄×D₄	C₂²	semidirect
114. C₃×#117	C₂²	semidirect
115. C₃×#117	C₂²	semidirect
116. C₃×#117	C₂²	semidirect
117. C₃×#117	C₂²	semidirect
118. C₃×#117	C₂²	semidirect
119. C₂×C₃×C₄⋊C₄	C₂²	semidirect
120. C₂×C₃×C₄⋊C₄	C₂²	semidirect
121. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
123. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
124. #562	C₂×C₃	semidirect
125. #560	C₂×C₃	semidirect
126. #555	C₂×C₃	semidirect
127. #553	C₂×C₃	semidirect
128. #552	C₂×C₃	semidirect
129. #551	C₂×C₃	semidirect
130. #550	C₂×C₃	semidirect
131. #547	C₂×C₃	semidirect
132. #546	C₂×C₃	semidirect
133. #546	C₂×C₃	semidirect
134. #546	C₂×C₃	semidirect
135. D₄²	C₂×C₃	semidirect
136. #542	C₂×C₃	semidirect
137. #540	C₂×C₃	semidirect
138. #540	C₂×C₃	semidirect
139. #538	C₂×C₃	semidirect
140. #537	C₂×C₃	semidirect
141. #535	C₂×C₃	semidirect
142. #535	C₂×C₃	semidirect
143. #534	C₂×C₃	semidirect
144. #525	C₂×C₃	semidirect
145. #525	C₂×C₃	semidirect
146. C₂×#121	C₂×C₃	semidirect
255. C₂×#41	C₂²×C₃	semidirect
256. C₂×#41	C₂²×C₃	semidirect
257. C₂×#41	C₂²×C₃	semidirect
258. C₂×#41	C₂²×C₃	semidirect
261. C₂²×D₄	C₂²×C₃	semidirect
262. C₂²×D₄	C₂²×C₃	semidirect
263. C₂³×C₄	C₂²×C₃	semidirect
264. C₄⋊Q₈	C₂²×C₃	semidirect
265. #127	C₂²×C₃	semidirect
266. #127	C₂²×C₃	semidirect
267. #127	C₂²×C₃	semidirect
268. #126	C₂²×C₃	semidirect
269. #126	C₂²×C₃	semidirect
270. #126	C₂²×C₃	semidirect
271. #125	C₂²×C₃	semidirect
272. #125	C₂²×C₃	semidirect
273. #124	C₂²×C₃	semidirect
274. #124	C₂²×C₃	semidirect
275. #124	C₂²×C₃	semidirect
276. #124	C₂²×C₃	semidirect
277. #124	C₂²×C₃	semidirect
279. #123	C₂²×C₃	semidirect
280. #123	C₂²×C₃	semidirect
281. #123	C₂²×C₃	semidirect
282. #123	C₂²×C₃	semidirect
283. #123	C₂²×C₃	semidirect
284. #123	C₂²×C₃	semidirect
285. #123	C₂²×C₃	semidirect
286. #123	C₂²×C₃	semidirect
287. #123	C₂²×C₃	semidirect
288. #123	C₂²×C₃	semidirect
289. #123	C₂²×C₃	semidirect
290. C₂²⋊Q₈	C₂²×C₃	semidirect
291. C₂²⋊Q₈	C₂²×C₃	semidirect
292. C₂²⋊Q₈	C₂²×C₃	semidirect
293. C₂²⋊Q₈	C₂²×C₃	semidirect
294. C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₂²⋊Q₈	C₂²×C₃	semidirect
296. C₂²⋊Q₈	C₂²×C₃	semidirect
297. C₂²⋊Q₈	C₂²×C₃	semidirect
302. #121	C₂²×C₃	semidirect
303. #121	C₂²×C₃	semidirect
304. #121	C₂²×C₃	semidirect
305. #121	C₂²×C₃	semidirect
306. #121	C₂²×C₃	semidirect
307. #121	C₂²×C₃	semidirect
308. #121	C₂²×C₃	semidirect
309. #121	C₂²×C₃	semidirect
310. #121	C₂²×C₃	semidirect
311. #121	C₂²×C₃	semidirect
312. #121	C₂²×C₃	semidirect
313. #121	C₂²×C₃	semidirect
314. #121	C₂²×C₃	semidirect
315. #121	C₂²×C₃	semidirect
316. #121	C₂²×C₃	semidirect
317. #121	C₂²×C₃	semidirect
318. #121	C₂²×C₃	semidirect
319. #121	C₂²×C₃	semidirect
320. #121	C₂²×C₃	semidirect
321. #121	C₂²×C₃	semidirect
322. #121	C₂²×C₃	semidirect
325. #120	C₂²×C₃	semidirect
326. #120	C₂²×C₃	semidirect
327. #120	C₂²×C₃	semidirect
328. #120	C₂²×C₃	semidirect
329. #120	C₂²×C₃	semidirect
330. #120	C₂²×C₃	semidirect
331. #120	C₂²×C₃	semidirect
332. C₄×Q₈	C₂²×C₃	semidirect
334. C₄×D₄	C₂²×C₃	semidirect
335. C₄×D₄	C₂²×C₃	semidirect
336. C₄×D₄	C₂²×C₃	semidirect
337. C₄×D₄	C₂²×C₃	semidirect
338. C₄×D₄	C₂²×C₃	semidirect
339. C₄×D₄	C₂²×C₃	semidirect
340. C₄×D₄	C₂²×C₃	semidirect
341. C₄×D₄	C₂²×C₃	semidirect
342. C₄×D₄	C₂²×C₃	semidirect
343. C₄×D₄	C₂²×C₃	semidirect
344. #117	C₂²×C₃	semidirect
345. #117	C₂²×C₃	semidirect
346. #117	C₂²×C₃	semidirect
347. #117	C₂²×C₃	semidirect
348. #117	C₂²×C₃	semidirect
349. C₂×C₄⋊C₄	C₂²×C₃	semidirect
350. C₂×C₄⋊C₄	C₂²×C₃	semidirect
351. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
352. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
353. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
709. C₃	#3542	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×#562	2
C₃×#560	2
C₃×#555	2
C₃×#553	2
C₃×#552	2
C₃×#551	2
C₃×#550	2
C₃×#547	2
C₃×#546	2
C₃×D₄²	2
C₃×#542	2
C₃×#540	2
C₃×#538	2
C₃×#537	2
C₃×#535	2
C₃×#534	2
C₃×#525	2
C₂×C₃×#121	2
#3542	3

Subgroups — C3×#3542 #87426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3542 #87426