Subgroups — C₃×#3541 #87425

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	2	yes	maximal, complemented
2	C₃×#562	C₂	1	2	yes	maximal, complemented
3	C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#554	C₂	1	2	yes	maximal, complemented
6	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#553	C₂	1	2	yes	maximal, complemented
8	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#542	C₂	1	2	yes	maximal, complemented
15	C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#539	C₂	1	2	yes	maximal, complemented
17	C₃×#538	C₂	1	2	yes	maximal, complemented
18	C₃×#538	C₂	1	2	yes	maximal, complemented
19	C₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	#3541	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×#41	C₂²	1	1	yes	characteristic
27	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic
29	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×#126	C₂²	1	2	yes	—
36	C₃×#126	C₂²	1	2	yes	—
37	C₃×#126	C₂²	1	2	yes	—
38	C₃×#126	C₂²	1	2	yes	—
39	C₃×#126	C₂²	1	2	yes	complemented
40	C₃×#126	C₂²	1	2	yes	complemented
41	C₃×#126	C₂²	1	2	yes	complemented
42	C₃×#125	C₂²	1	2	yes	complemented
43	C₃×#125	C₂²	1	2	yes	complemented
44	C₃×#125	C₂²	1	2	yes	complemented
45	C₃×#125	C₂²	1	2	yes	complemented
46	C₃×#125	C₂²	1	1	yes	characteristic, complemented
47	C₃×#124	C₂²	1	2	yes	—
48	C₃×#124	C₂²	1	2	yes	—
49	C₃×#124	C₂²	1	2	yes	—
50	C₃×#124	C₂²	1	2	yes	—
51	C₃×#124	C₂²	1	2	yes	complemented
52	C₃×#124	C₂²	1	1	yes	characteristic, complemented
53	C₃×#123	C₂²	1	2	yes	—
54	C₃×#123	C₂²	1	2	yes	—
55	C₃×#123	C₂²	1	2	yes	—
56	C₃×#123	C₂²	1	1	yes	characteristic
57	C₃×#123	C₂²	1	1	yes	characteristic
58	C₃×#123	C₂²	1	2	yes	—
59	C₃×#123	C₂²	1	2	yes	—
60	C₃×#123	C₂²	1	2	yes	complemented
61	C₃×#123	C₂²	1	2	yes	complemented
62	C₃×#123	C₂²	1	2	yes	complemented
63	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
64	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
65	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
66	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
67	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
68	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
69	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
72	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
73	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
74	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
75	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
79	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
80	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
81	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
82	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
84	C₃×#121	C₂²	1	1	yes	characteristic
85	C₃×#121	C₂²	1	2	yes	—
86	C₃×#121	C₂²	1	2	yes	—
87	C₃×#121	C₂²	1	1	yes	characteristic
88	C₃×#121	C₂²	1	1	yes	characteristic
89	C₃×#121	C₂²	1	1	yes	characteristic
90	C₃×#121	C₂²	1	2	yes	—
91	C₃×#121	C₂²	1	2	yes	—
92	C₃×#121	C₂²	1	2	yes	—
93	C₃×#121	C₂²	1	2	yes	—
94	C₃×#121	C₂²	1	2	yes	complemented
95	C₃×#121	C₂²	1	1	yes	characteristic, complemented
96	C₃×#120	C₂²	1	1	yes	characteristic
97	C₃×#120	C₂²	1	2	yes	—
98	C₃×#120	C₂²	1	1	yes	characteristic
99	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
100	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
101	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
102	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
103	C₃×C₄×D₄	C₂²	1	2	yes	—
104	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×D₄	C₂²	1	2	yes	—
109	C₃×C₄×D₄	C₂²	1	2	yes	—
110	C₃×C₄×D₄	C₂²	1	2	yes	—
111	C₃×C₄×D₄	C₂²	1	2	yes	—
112	C₃×C₄×D₄	C₂²	1	2	yes	—
113	C₃×C₄×D₄	C₂²	1	2	yes	complemented
114	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×#117	C₂²	1	1	yes	characteristic
116	C₃×#117	C₂²	1	1	yes	characteristic
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
120	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
123	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
124	#563	C₂×C₃	1	2	yes	complemented
125	#562	C₂×C₃	1	2	yes	complemented
126	#556	C₂×C₃	1	1	yes	characteristic, complemented
127	#554	C₂×C₃	1	1	yes	characteristic, complemented
128	#554	C₂×C₃	1	2	yes	complemented
129	#553	C₂×C₃	1	1	yes	characteristic, complemented
130	#553	C₂×C₃	1	2	yes	complemented
131	#552	C₂×C₃	1	1	yes	characteristic, complemented
132	D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
133	#548	C₂×C₃	1	1	yes	characteristic, complemented
134	#548	C₂×C₃	1	1	yes	characteristic, complemented
135	#547	C₂×C₃	1	1	yes	characteristic, complemented
136	#542	C₂×C₃	1	1	yes	characteristic, complemented
137	#542	C₂×C₃	1	2	yes	complemented
138	#541	C₂×C₃	1	1	yes	characteristic, complemented
139	#539	C₂×C₃	1	2	yes	complemented
140	#538	C₂×C₃	1	2	yes	complemented
141	#538	C₂×C₃	1	2	yes	complemented
142	#537	C₂×C₃	1	1	yes	characteristic, complemented
143	#536	C₂×C₃	1	1	yes	characteristic, complemented
144	#525	C₂×C₃	1	1	yes	characteristic, complemented
145	#525	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂⁴×C₃	C₂³	1	1	yes	characteristic
148	C₃×#41	—	4	2	no	—
149	C₃×#41	—	4	2	no	—
150	C₃×#41	—	4	2	no	—
151	C₂×C₃×Q₈	—	4	2	no	—
152	C₂×C₃×Q₈	—	4	2	no	—
153	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
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×Q₈	C₂³	1	2	yes	—
158	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
159	C₂×C₃×Q₈	C₂³	1	2	yes	—
160	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×D₄	C₂³	1	2	yes	—
168	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×D₄	C₂³	1	2	yes	—
170	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×D₄	C₂³	1	2	yes	—
172	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×C₄	—	4	2	no	—
174	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³	1	2	yes	—
180	C₂²×C₃×C₄	C₂³	1	2	yes	—
181	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³	1	2	yes	—
183	C₂²×C₃×C₄	C₂³	1	2	yes	—
184	C₂²×C₃×C₄	C₂³	1	2	yes	—
185	C₂²×C₃×C₄	C₂³	1	2	yes	—
186	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³	1	2	yes	—
188	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₄⋊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	2	yes	—
205	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
213	C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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×C₄²	C₂³	1	2	yes	—
246	C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₃×C₄²	C₂³	1	2	yes	—
249	C₃×C₄²	C₂³	1	2	yes	—
250	C₃×C₄²	C₂³	1	2	yes	—
251	C₃×C₄²	C₂³	1	2	yes	—
252	C₂×#41	C₂²×C₃	1	1	yes	characteristic
253	C₂×#41	C₂²×C₃	1	1	yes	characteristic
254	C₂×#41	C₂²×C₃	1	1	yes	characteristic, complemented
255	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic
256	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic
258	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
259	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
260	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
261	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
262	#126	C₂²×C₃	1	2	yes	—
263	#126	C₂²×C₃	1	2	yes	—
264	#126	C₂²×C₃	1	2	yes	—
265	#126	C₂²×C₃	1	2	yes	—
266	#126	C₂²×C₃	1	2	yes	complemented
267	#126	C₂²×C₃	1	2	yes	complemented
268	#126	C₂²×C₃	1	2	yes	complemented
269	#125	C₂²×C₃	1	2	yes	complemented
270	#125	C₂²×C₃	1	2	yes	complemented
271	#125	C₂²×C₃	1	1	yes	characteristic, complemented
272	#125	C₂²×C₃	1	2	yes	complemented
273	#125	C₂²×C₃	1	2	yes	complemented
274	#124	C₂²×C₃	1	2	yes	—
275	#124	C₂²×C₃	1	2	yes	—
276	#124	C₂²×C₃	1	2	yes	—
277	#124	C₂²×C₃	1	2	yes	—
278	#124	C₂²×C₃	1	1	yes	characteristic, complemented
279	#124	C₂²×C₃	1	2	yes	complemented
280	#123	C₂²×C₃	1	1	yes	characteristic
281	#123	C₂²×C₃	1	1	yes	characteristic
282	#123	C₂²×C₃	1	2	yes	—
283	#123	C₂²×C₃	1	2	yes	—
284	#123	C₂²×C₃	1	2	yes	—
285	#123	C₂²×C₃	1	2	yes	—
286	#123	C₂²×C₃	1	2	yes	—
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
291	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
292	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
293	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
294	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
295	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
296	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
297	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
298	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
299	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
300	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
301	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
302	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
306	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
307	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
308	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
309	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
310	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
311	#121	C₂²×C₃	1	1	yes	characteristic
312	#121	C₂²×C₃	1	1	yes	characteristic
313	#121	C₂²×C₃	1	1	yes	characteristic
314	#121	C₂²×C₃	1	1	yes	characteristic
315	#121	C₂²×C₃	1	2	yes	—
316	#121	C₂²×C₃	1	2	yes	—
317	#121	C₂²×C₃	1	2	yes	—
318	#121	C₂²×C₃	1	2	yes	—
319	#121	C₂²×C₃	1	2	yes	—
320	#121	C₂²×C₃	1	2	yes	—
321	#121	C₂²×C₃	1	1	yes	characteristic, 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	1	yes	characteristic
326	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
329	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
330	C₄×D₄	C₂²×C₃	1	2	yes	—
331	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
332	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
333	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
334	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
335	C₄×D₄	C₂²×C₃	1	2	yes	—
336	C₄×D₄	C₂²×C₃	1	2	yes	—
337	C₄×D₄	C₂²×C₃	1	2	yes	—
338	C₄×D₄	C₂²×C₃	1	2	yes	—
339	C₄×D₄	C₂²×C₃	1	2	yes	—
340	C₄×D₄	C₂²×C₃	1	2	yes	complemented
341	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
342	#117	C₂²×C₃	1	1	yes	characteristic
343	#117	C₂²×C₃	1	1	yes	characteristic
344	#117	C₂²×C₃	1	1	yes	characteristic, complemented
345	#117	C₂²×C₃	1	2	yes	complemented
346	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
349	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
350	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	4	1	no	—
353	C₂³×C₃	—	4	1	no	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₃	C₂⁴	1	2	yes	—
359	C₂³×C₃	C₂⁴	1	1	yes	characteristic
360	C₃×Q₈	—	2	2	no	—
361	C₃×Q₈	—	2	2	no	—
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	4	2	no	—
364	C₃×Q₈	—	4	2	no	—
365	C₃×Q₈	—	4	2	no	—
366	C₃×Q₈	—	4	1	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	4	no	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	4	1	no	—
372	C₃×D₄	—	4	2	no	—
373	C₃×D₄	—	4	2	no	—
374	C₃×D₄	—	4	1	no	—
375	C₃×D₄	—	4	1	no	—
376	C₃×D₄	—	4	1	no	—
377	C₃×D₄	—	4	1	no	—
378	C₃×D₄	—	4	2	no	—
379	C₃×D₄	—	4	2	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	4	1	no	—
386	C₂×C₃×C₄	—	4	1	no	—
387	C₂×C₃×C₄	—	4	1	no	—
388	C₂×C₃×C₄	—	4	2	no	—
389	C₂×C₃×C₄	—	4	2	no	—
390	C₂×C₃×C₄	—	4	2	no	—
391	C₂×C₃×C₄	—	4	2	no	—
392	C₂×C₃×C₄	—	4	2	no	—
393	C₂×C₃×C₄	—	4	2	no	—
394	C₂×C₃×C₄	—	4	2	no	—
395	C₂×C₃×C₄	C₂⁴	1	2	yes	—
396	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂⁴	1	2	yes	—
400	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂×C₃×C₄	C₂⁴	1	2	yes	—
404	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂×C₃×C₄	C₂⁴	1	2	yes	—
407	C₂×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂⁴	C₂³×C₃	1	1	yes	characteristic
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	#41	—	4	2	no	—
416	C₂×Q₈	—	4	2	no	—
417	C₂×Q₈	—	4	2	no	—
418	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
419	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
420	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
421	C₂×Q₈	C₂³×C₃	1	2	yes	—
422	C₂×Q₈	C₂³×C₃	1	2	yes	—
423	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
424	C₂×Q₈	C₂³×C₃	1	2	yes	—
425	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
426	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×D₄	C₂³×C₃	1	2	yes	—
428	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
429	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
430	C₂×D₄	C₂³×C₃	1	2	yes	—
431	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
432	C₂×D₄	C₂³×C₃	1	2	yes	—
433	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
434	C₂×D₄	C₂³×C₃	1	2	yes	—
435	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
436	C₂×D₄	C₂³×C₃	1	2	yes	—
437	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
440	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
444	C₂²×C₄	C₂³×C₃	1	2	yes	—
445	C₂²×C₄	C₂³×C₃	1	2	yes	—
446	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
447	C₂²×C₄	C₂³×C₃	1	2	yes	—
448	C₂²×C₄	C₂³×C₃	1	2	yes	—
449	C₂²×C₄	C₂³×C₃	1	2	yes	—
450	C₂²×C₄	C₂³×C₃	1	2	yes	—
451	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
452	C₂²×C₄	C₂³×C₃	1	2	yes	—
453	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂³×C₃	1	2	yes	—
456	C₄⋊C₄	C₂³×C₃	1	2	yes	—
457	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
458	C₄⋊C₄	C₂³×C₃	1	2	yes	—
459	C₄⋊C₄	C₂³×C₃	1	2	yes	—
460	C₄⋊C₄	C₂³×C₃	1	2	yes	—
461	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
463	C₄⋊C₄	C₂³×C₃	1	2	yes	—
464	C₄⋊C₄	C₂³×C₃	1	2	yes	—
465	C₄⋊C₄	C₂³×C₃	1	2	yes	—
466	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
467	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
468	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂³×C₃	1	2	yes	—
470	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂³×C₃	1	2	yes	—
473	C₄⋊C₄	C₂³×C₃	1	2	yes	—
474	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
492	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
504	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	C₄²	C₂³×C₃	1	2	yes	—
511	C₄²	C₂³×C₃	1	1	yes	characteristic
512	C₄²	C₂³×C₃	1	1	yes	characteristic
513	C₄²	C₂³×C₃	1	2	yes	—
514	C₄²	C₂³×C₃	1	2	yes	—
515	C₄²	C₂³×C₃	1	2	yes	—
516	C₄²	C₂³×C₃	1	2	yes	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	1	no	—
530	C₂²×C₃	—	2	2	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	2	1	no	—
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	4	4	no	—
535	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
536	C₂²×C₃	C₂⁵	1	1	yes	characteristic
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	C₂⁴×C₃	1	1	yes	characteristic
558	C₂³	C₂⁴×C₃	1	1	yes	characteristic
559	C₂³	C₂⁴×C₃	1	1	yes	characteristic
560	C₂³	C₂⁴×C₃	1	1	yes	characteristic
561	C₂³	C₂⁴×C₃	1	2	yes	—
562	C₂³	C₂⁴×C₃	1	1	yes	characteristic
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	2	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
600	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
602	C₂×C₄	C₂⁴×C₃	1	2	yes	—
603	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
604	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
605	C₂×C₄	C₂⁴×C₃	1	2	yes	—
606	C₂×C₄	C₂⁴×C₃	1	2	yes	—
607	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
608	C₂×C₄	C₂⁴×C₃	1	2	yes	—
609	C₂×C₄	C₂⁴×C₃	1	2	yes	—
610	C₂×C₄	C₂⁴×C₃	1	2	yes	—
611	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
612	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
613	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
615	C₂×C₃	—	2	2	no	—
616	C₂×C₃	—	4	1	no	—
617	C₂×C₃	—	4	1	no	—
618	C₂×C₃	—	4	2	no	—
619	C₂×C₃	—	4	1	no	—
620	C₂×C₃	—	4	1	no	—
621	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
623	C₂×C₃	#585	1	1	yes	characteristic
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	4	4	no	—
642	C₂²	C₃×2₋¹⁺⁴	1	2	yes	—
643	C₂²	C₂⁵×C₃	1	1	yes	characteristic
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
661	C₃	#3541	1	1	yes	characteristic, direct product factor, Sylow
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
670	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×#563	C₂	semidirect
2. C₃×#562	C₂	semidirect
3. C₃×#556	C₂	semidirect
4. C₃×#554	C₂	semidirect
5. C₃×#554	C₂	semidirect
6. C₃×#553	C₂	semidirect
7. C₃×#553	C₂	semidirect
8. C₃×#552	C₂	semidirect
9. C₃×D₄×Q₈	C₂	semidirect
10. C₃×#548	C₂	semidirect
11. C₃×#548	C₂	semidirect
12. C₃×#547	C₂	semidirect
13. C₃×#542	C₂	semidirect
14. C₃×#542	C₂	semidirect
15. C₃×#541	C₂	semidirect
16. C₃×#539	C₂	semidirect
17. C₃×#538	C₂	semidirect
18. C₃×#538	C₂	semidirect
19. C₃×#537	C₂	semidirect
20. C₃×#536	C₂	semidirect
21. C₃×#525	C₂	semidirect
22. C₃×#525	C₂	semidirect
23. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
24. #3541	C₃	direct (N × H)
27. C₂×C₃×#41	C₂²	semidirect
29. C₂²×C₃×Q₈	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×C₄⋊Q₈	C₂²	semidirect
33. C₃×C₄⋊Q₈	C₂²	semidirect
34. C₃×C₄⋊Q₈	C₂²	semidirect
39. C₃×#126	C₂²	semidirect
40. C₃×#126	C₂²	semidirect
41. C₃×#126	C₂²	semidirect
42. C₃×#125	C₂²	semidirect
43. C₃×#125	C₂²	semidirect
44. C₃×#125	C₂²	semidirect
45. C₃×#125	C₂²	semidirect
46. C₃×#125	C₂²	semidirect
51. C₃×#124	C₂²	semidirect
52. C₃×#124	C₂²	semidirect
60. C₃×#123	C₂²	semidirect
61. C₃×#123	C₂²	semidirect
62. C₃×#123	C₂²	semidirect
75. C₃×C₂²⋊Q₈	C₂²	semidirect
76. C₃×C₂²⋊Q₈	C₂²	semidirect
77. C₃×C₂²⋊Q₈	C₂²	semidirect
78. C₃×C₂²⋊Q₈	C₂²	semidirect
79. C₃×C₂²⋊Q₈	C₂²	semidirect
80. C₃×C₂²⋊Q₈	C₂²	semidirect
81. C₃×C₂²⋊Q₈	C₂²	semidirect
82. C₃×C₂²⋊Q₈	C₂²	semidirect
83. C₃×C₂²⋊Q₈	C₂²	semidirect
94. C₃×#121	C₂²	semidirect
95. C₃×#121	C₂²	semidirect
99. C₃×C₄×Q₈	C₂²	semidirect
100. C₃×C₄×Q₈	C₂²	semidirect
101. C₃×C₄×Q₈	C₂²	semidirect
102. C₃×C₄×Q₈	C₂²	semidirect
113. C₃×C₄×D₄	C₂²	semidirect
114. C₃×C₄×D₄	C₂²	semidirect
117. C₃×#117	C₂²	semidirect
118. C₃×#117	C₂²	semidirect
121. C₂×C₃×C₄⋊C₄	C₂²	semidirect
122. C₂×C₃×C₄⋊C₄	C₂²	semidirect
124. #563	C₂×C₃	semidirect
125. #562	C₂×C₃	semidirect
126. #556	C₂×C₃	semidirect
127. #554	C₂×C₃	semidirect
128. #554	C₂×C₃	semidirect
129. #553	C₂×C₃	semidirect
130. #553	C₂×C₃	semidirect
131. #552	C₂×C₃	semidirect
132. D₄×Q₈	C₂×C₃	semidirect
133. #548	C₂×C₃	semidirect
134. #548	C₂×C₃	semidirect
135. #547	C₂×C₃	semidirect
136. #542	C₂×C₃	semidirect
137. #542	C₂×C₃	semidirect
138. #541	C₂×C₃	semidirect
139. #539	C₂×C₃	semidirect
140. #538	C₂×C₃	semidirect
141. #538	C₂×C₃	semidirect
142. #537	C₂×C₃	semidirect
143. #536	C₂×C₃	semidirect
144. #525	C₂×C₃	semidirect
145. #525	C₂×C₃	semidirect
146. C₂×C₂²⋊Q₈	C₂×C₃	semidirect
254. C₂×#41	C₂²×C₃	semidirect
256. C₂²×Q₈	C₂²×C₃	semidirect
258. C₄⋊Q₈	C₂²×C₃	semidirect
259. C₄⋊Q₈	C₂²×C₃	semidirect
260. C₄⋊Q₈	C₂²×C₃	semidirect
261. C₄⋊Q₈	C₂²×C₃	semidirect
266. #126	C₂²×C₃	semidirect
267. #126	C₂²×C₃	semidirect
268. #126	C₂²×C₃	semidirect
269. #125	C₂²×C₃	semidirect
270. #125	C₂²×C₃	semidirect
271. #125	C₂²×C₃	semidirect
272. #125	C₂²×C₃	semidirect
273. #125	C₂²×C₃	semidirect
278. #124	C₂²×C₃	semidirect
279. #124	C₂²×C₃	semidirect
287. #123	C₂²×C₃	semidirect
288. #123	C₂²×C₃	semidirect
289. #123	C₂²×C₃	semidirect
302. C₂²⋊Q₈	C₂²×C₃	semidirect
303. C₂²⋊Q₈	C₂²×C₃	semidirect
304. C₂²⋊Q₈	C₂²×C₃	semidirect
305. C₂²⋊Q₈	C₂²×C₃	semidirect
306. C₂²⋊Q₈	C₂²×C₃	semidirect
307. C₂²⋊Q₈	C₂²×C₃	semidirect
308. C₂²⋊Q₈	C₂²×C₃	semidirect
309. C₂²⋊Q₈	C₂²×C₃	semidirect
310. C₂²⋊Q₈	C₂²×C₃	semidirect
321. #121	C₂²×C₃	semidirect
322. #121	C₂²×C₃	semidirect
326. C₄×Q₈	C₂²×C₃	semidirect
327. C₄×Q₈	C₂²×C₃	semidirect
328. C₄×Q₈	C₂²×C₃	semidirect
329. C₄×Q₈	C₂²×C₃	semidirect
340. C₄×D₄	C₂²×C₃	semidirect
341. C₄×D₄	C₂²×C₃	semidirect
344. #117	C₂²×C₃	semidirect
345. #117	C₂²×C₃	semidirect
348. C₂×C₄⋊C₄	C₂²×C₃	semidirect
349. C₂×C₄⋊C₄	C₂²×C₃	semidirect
661. C₃	#3541	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×#563	2
C₃×#562	2
C₃×#556	2
C₃×#554	2
C₃×#553	2
C₃×#552	2
C₃×D₄×Q₈	2
C₃×#548	2
C₃×#547	2
C₃×#542	2
C₃×#541	2
C₃×#539	2
C₃×#538	2
C₃×#537	2
C₃×#536	2
C₃×#525	2
C₂×C₃×C₂²⋊Q₈	2
#3541	3

Subgroups — C3×#3541 #87425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3541 #87425