Subgroups — C₃×#3513 #87397

Order 384.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#553	C₂	1	2	yes	maximal, complemented
5	C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#551	C₂	1	2	yes	maximal, complemented
7	C₃×#551	C₂	1	2	yes	maximal, complemented
8	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#546	C₂	1	2	yes	maximal, 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×#539	C₂	1	2	yes	maximal, complemented
16	C₃×#538	C₂	1	2	yes	maximal, complemented
17	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#525	C₂	1	2	yes	maximal, complemented
20	C₂×C₃×#123	C₂	1	2	yes	maximal, complemented
21	C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	#3513	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	2	yes	complemented
27	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
29	C₂²×C₃×D₄	C₂²	1	2	yes	—
30	C₂³×C₃×C₄	C₂²	1	2	yes	complemented
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#127	C₂²	1	1	yes	characteristic
33	C₃×#126	C₂²	1	2	yes	complemented
34	C₃×#126	C₂²	1	1	yes	characteristic, complemented
35	C₃×#126	C₂²	1	1	yes	characteristic, complemented
36	C₃×#126	C₂²	1	2	yes	complemented
37	C₃×#126	C₂²	1	2	yes	complemented
38	C₃×#126	C₂²	1	2	yes	complemented
39	C₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₃×#125	C₂²	1	1	yes	characteristic, complemented
41	C₃×#125	C₂²	1	2	yes	complemented
42	C₃×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃×#124	C₂²	1	1	yes	characteristic, complemented
44	C₃×#124	C₂²	1	2	yes	complemented
45	C₃×#124	C₂²	1	1	yes	characteristic, complemented
46	C₃×#124	C₂²	1	1	yes	characteristic, complemented
47	C₃×#124	C₂²	1	2	yes	complemented
48	C₃×#123	C₂²	1	1	yes	characteristic
49	C₃×#123	C₂²	1	2	yes	—
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	2	yes	complemented
56	C₃×#123	C₂²	1	2	yes	complemented
57	C₃×#123	C₂²	1	1	yes	characteristic, complemented
58	C₃×#123	C₂²	1	2	yes	complemented
59	C₃×#123	C₂²	1	2	yes	complemented
60	C₃×#123	C₂²	1	2	yes	complemented
61	C₃×#123	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	2	yes	complemented
67	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
70	C₃×#121	C₂²	1	1	yes	characteristic
71	C₃×#121	C₂²	1	1	yes	characteristic
72	C₃×#121	C₂²	1	2	yes	—
73	C₃×#121	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
79	C₃×#121	C₂²	1	2	yes	complemented
80	C₃×#121	C₂²	1	1	yes	characteristic, complemented
81	C₃×#120	C₂²	1	2	yes	—
82	C₃×#120	C₂²	1	2	yes	—
83	C₃×#120	C₂²	1	2	yes	complemented
84	C₃×#120	C₂²	1	2	yes	complemented
85	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
87	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
88	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
89	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
90	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
91	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
92	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
93	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
94	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
95	C₃×C₄×D₄	C₂²	1	2	yes	complemented
96	C₃×C₄×D₄	C₂²	1	2	yes	complemented
97	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
98	C₃×C₄×D₄	C₂²	1	2	yes	complemented
99	C₃×C₄×D₄	C₂²	1	2	yes	complemented
100	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
101	C₃×C₄×D₄	C₂²	1	2	yes	complemented
102	C₃×C₄×D₄	C₂²	1	2	yes	complemented
103	C₃×C₄×D₄	C₂²	1	2	yes	complemented
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×#117	C₂²	1	1	yes	characteristic, complemented
109	C₃×#117	C₂²	1	1	yes	characteristic, complemented
110	C₃×#117	C₂²	1	1	yes	characteristic, complemented
111	C₃×#117	C₂²	1	2	yes	complemented
112	C₃×#117	C₂²	1	2	yes	complemented
113	C₃×#117	C₂²	1	2	yes	complemented
114	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
116	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
124	#559	C₂×C₃	1	1	yes	characteristic, complemented
125	#554	C₂×C₃	1	1	yes	characteristic, complemented
126	#553	C₂×C₃	1	1	yes	characteristic, complemented
127	#553	C₂×C₃	1	2	yes	complemented
128	#552	C₂×C₃	1	1	yes	characteristic, complemented
129	#551	C₂×C₃	1	2	yes	complemented
130	#551	C₂×C₃	1	2	yes	complemented
131	#547	C₂×C₃	1	1	yes	characteristic, complemented
132	#546	C₂×C₃	1	1	yes	characteristic, complemented
133	#546	C₂×C₃	1	1	yes	characteristic, complemented
134	#546	C₂×C₃	1	2	yes	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	#539	C₂×C₃	1	2	yes	complemented
139	#538	C₂×C₃	1	2	yes	complemented
140	#529	C₂×C₃	1	1	yes	characteristic, complemented
141	#529	C₂×C₃	1	1	yes	characteristic, complemented
142	#525	C₂×C₃	1	2	yes	complemented
143	C₂×#123	C₂×C₃	1	2	yes	complemented
144	#520	C₂×C₃	1	1	yes	characteristic, complemented
145	#518	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂⁴×C₃	C₂³	1	2	yes	—
149	C₃×#41	—	2	4	no	—
150	C₃×#41	—	4	4	no	—
151	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃×Q₈	C₂³	1	2	yes	—
154	C₂×C₃×D₄	—	2	4	no	—
155	C₂×C₃×D₄	—	2	4	no	—
156	C₂×C₃×D₄	—	4	4	no	—
157	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×D₄	C₂³	1	2	yes	—
159	C₂×C₃×D₄	C₂³	1	2	yes	—
160	C₂×C₃×D₄	C₂³	1	2	yes	—
161	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×D₄	C₂³	1	2	yes	—
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	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	C₂²×C₃×C₄	—	4	4	no	—
173	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³	1	2	yes	—
176	C₂²×C₃×C₄	C₂³	1	2	yes	—
177	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³	1	2	yes	—
181	C₂²×C₃×C₄	C₂³	1	2	yes	—
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	2	yes	—
187	C₂²×C₃×C₄	C₂³	1	2	yes	—
188	C₂²×C₃×C₄	C₂³	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
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	1	yes	characteristic
212	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
240	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₃×C₄²	C₂³	1	1	yes	characteristic
244	C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₃×C₄²	C₂³	1	2	yes	—
248	C₃×C₄²	C₂³	1	2	yes	—
249	C₃×C₄²	C₂³	1	2	yes	—
250	C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×#41	C₂²×C₃	1	1	yes	characteristic
253	C₂×#41	C₂²×C₃	1	2	yes	complemented
254	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
255	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
256	C₂²×D₄	C₂²×C₃	1	2	yes	—
257	C₂³×C₄	C₂²×C₃	1	2	yes	complemented
258	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
259	#127	C₂²×C₃	1	1	yes	characteristic
260	#126	C₂²×C₃	1	2	yes	complemented
261	#126	C₂²×C₃	1	1	yes	characteristic, complemented
262	#126	C₂²×C₃	1	1	yes	characteristic, complemented
263	#126	C₂²×C₃	1	2	yes	complemented
264	#126	C₂²×C₃	1	2	yes	complemented
265	#126	C₂²×C₃	1	2	yes	complemented
266	#125	C₂²×C₃	1	1	yes	characteristic, complemented
267	#125	C₂²×C₃	1	1	yes	characteristic, complemented
268	#125	C₂²×C₃	1	2	yes	complemented
269	#125	C₂²×C₃	1	1	yes	characteristic, complemented
270	#124	C₂²×C₃	1	1	yes	characteristic, complemented
271	#124	C₂²×C₃	1	1	yes	characteristic, complemented
272	#124	C₂²×C₃	1	2	yes	complemented
273	#124	C₂²×C₃	1	2	yes	complemented
274	#124	C₂²×C₃	1	1	yes	characteristic, complemented
275	#123	C₂²×C₃	1	1	yes	characteristic
276	#123	C₂²×C₃	1	2	yes	—
277	#123	C₂²×C₃	1	2	yes	complemented
278	#123	C₂²×C₃	1	2	yes	complemented
279	#123	C₂²×C₃	1	2	yes	complemented
280	#123	C₂²×C₃	1	2	yes	complemented
281	#123	C₂²×C₃	1	2	yes	complemented
282	#123	C₂²×C₃	1	2	yes	complemented
283	#123	C₂²×C₃	1	1	yes	characteristic, 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	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
290	C₂²⋊Q₈	C₂²×C₃	1	2	yes	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	2	yes	complemented
294	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
295	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
296	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
297	#121	C₂²×C₃	1	1	yes	characteristic
298	#121	C₂²×C₃	1	1	yes	characteristic
299	#121	C₂²×C₃	1	2	yes	—
300	#121	C₂²×C₃	1	1	yes	characteristic
301	#121	C₂²×C₃	1	2	yes	complemented
302	#121	C₂²×C₃	1	2	yes	complemented
303	#121	C₂²×C₃	1	2	yes	complemented
304	#121	C₂²×C₃	1	2	yes	complemented
305	#121	C₂²×C₃	1	1	yes	characteristic, complemented
306	#121	C₂²×C₃	1	2	yes	complemented
307	#121	C₂²×C₃	1	1	yes	characteristic, complemented
308	#120	C₂²×C₃	1	2	yes	—
309	#120	C₂²×C₃	1	2	yes	—
310	#120	C₂²×C₃	1	2	yes	complemented
311	#120	C₂²×C₃	1	2	yes	complemented
312	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
316	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
317	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
318	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
319	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
320	C₄×D₄	C₂²×C₃	1	2	yes	complemented
321	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₄×D₄	C₂²×C₃	1	2	yes	complemented
323	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
324	C₄×D₄	C₂²×C₃	1	2	yes	complemented
325	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
326	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×D₄	C₂²×C₃	1	2	yes	complemented
328	C₄×D₄	C₂²×C₃	1	2	yes	complemented
329	C₄×D₄	C₂²×C₃	1	2	yes	complemented
330	C₄×D₄	C₂²×C₃	1	2	yes	complemented
331	C₄×D₄	C₂²×C₃	1	2	yes	complemented
332	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
333	C₄×D₄	C₂²×C₃	1	2	yes	complemented
334	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
335	#117	C₂²×C₃	1	1	yes	characteristic, complemented
336	#117	C₂²×C₃	1	1	yes	characteristic, complemented
337	#117	C₂²×C₃	1	1	yes	characteristic, complemented
338	#117	C₂²×C₃	1	2	yes	complemented
339	#117	C₂²×C₃	1	2	yes	complemented
340	#117	C₂²×C₃	1	2	yes	complemented
341	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
342	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
343	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
344	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
345	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
346	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
347	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
348	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
349	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
350	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
351	C₂³×C₃	—	2	4	no	—
352	C₂³×C₃	—	2	4	no	—
353	C₂³×C₃	—	2	4	no	—
354	C₂³×C₃	—	4	2	no	—
355	C₂³×C₃	—	4	2	no	—
356	C₂³×C₃	—	4	2	no	—
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₃	C₂⁴	1	2	yes	—
359	C₂³×C₃	C₂⁴	1	2	yes	—
360	C₂³×C₃	C₂⁴	1	1	yes	characteristic
361	C₂³×C₃	C₂⁴	1	2	yes	—
362	C₂³×C₃	C₂⁴	1	1	yes	characteristic
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	4	1	no	—
365	C₃×Q₈	—	4	2	no	—
366	C₃×D₄	—	2	4	no	—
367	C₃×D₄	—	2	4	no	—
368	C₃×D₄	—	2	4	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	4	2	no	—
375	C₃×D₄	—	4	2	no	—
376	C₃×D₄	—	4	2	no	—
377	C₃×D₄	—	4	1	no	—
378	C₃×D₄	—	4	2	no	—
379	C₃×D₄	—	4	2	no	—
380	C₃×D₄	#41	1	4	yes	complemented
381	C₂×C₃×C₄	—	2	4	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	4	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	4	2	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	1	no	—
393	C₂×C₃×C₄	—	4	2	no	—
394	C₂×C₃×C₄	—	4	2	no	—
395	C₂×C₃×C₄	—	4	2	no	—
396	C₂×C₃×C₄	—	4	2	no	—
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	1	yes	characteristic
403	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂⁴	1	2	yes	—
410	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂⁴	1	2	yes	—
413	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂⁴	C₂³×C₃	1	2	yes	—
415	C₂⁴	C₂³×C₃	1	2	yes	—
416	#41	—	2	4	no	—
417	#41	—	4	4	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	2	yes	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×D₄	C₂³×C₃	1	2	yes	—
426	C₂×D₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
436	C₂×D₄	C₂³×C₃	1	2	yes	—
437	C₂×D₄	C₂³×C₃	1	2	yes	—
438	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂²×C₄	C₂³×C₃	1	2	yes	—
443	C₂²×C₄	C₂³×C₃	1	2	yes	—
444	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
445	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
452	C₂²×C₄	C₂³×C₃	1	2	yes	—
453	C₂²×C₄	C₂³×C₃	1	2	yes	—
454	C₂²×C₄	C₂³×C₃	1	2	yes	—
455	C₂²×C₄	C₂³×C₃	1	2	yes	—
456	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
457	C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
467	C₄⋊C₄	C₂³×C₃	1	2	yes	—
468	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
475	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
486	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
487	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
492	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
502	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
510	C₄²	C₂³×C₃	1	1	yes	characteristic
511	C₄²	C₂³×C₃	1	1	yes	characteristic
512	C₄²	C₂³×C₃	1	1	yes	characteristic
513	C₄²	C₂³×C₃	1	1	yes	characteristic
514	C₄²	C₂³×C₃	1	2	yes	—
515	C₄²	C₂³×C₃	1	2	yes	—
516	C₄²	C₂³×C₃	1	2	yes	—
517	C₄²	C₂³×C₃	1	1	yes	characteristic
518	C₄²	C₂³×C₃	1	1	yes	characteristic
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	2	2	no	—
532	C₂²×C₃	—	2	1	no	—
533	C₂²×C₃	—	2	2	no	—
534	C₂²×C₃	—	2	1	no	—
535	C₂²×C₃	—	4	8	no	—
536	C₂²×C₃	—	8	4	no	—
537	C₂²×C₃	C₂×#41	1	4	yes	—
538	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
539	C₂²×C₃	C₂⁵	1	1	yes	characteristic
540	C₃×C₄	—	2	1	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	1	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	2	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	1	no	—
551	C₃×C₄	—	2	1	no	—
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	—	2	1	no	—
555	C₃×C₄	—	2	1	no	—
556	C₃×C₄	C₂×#41	1	2	yes	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	C₂⁴×C₃	1	1	yes	characteristic
564	C₂³	C₂⁴×C₃	1	2	yes	—
565	C₂³	C₂⁴×C₃	1	2	yes	—
566	C₂³	C₂⁴×C₃	1	1	yes	characteristic
567	C₂³	C₂⁴×C₃	1	2	yes	—
568	C₂³	C₂⁴×C₃	1	1	yes	characteristic
569	Q₈	—	2	2	no	—
570	Q₈	—	4	2	no	—
571	Q₈	—	4	1	no	—
572	D₄	—	2	4	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	2	no	—
586	D₄	C₃×#41	1	4	yes	complemented
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	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	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
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	1	yes	characteristic
607	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
608	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
609	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
610	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
611	C₂×C₄	C₂⁴×C₃	1	2	yes	—
612	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
613	C₂×C₄	C₂⁴×C₃	1	2	yes	—
614	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₃	1	2	yes	—
616	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₃	1	2	yes	—
619	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
620	C₂×C₃	—	2	2	no	—
621	C₂×C₃	—	2	4	no	—
622	C₂×C₃	—	4	1	no	—
623	C₂×C₃	—	4	2	no	—
624	C₂×C₃	—	4	2	no	—
625	C₂×C₃	—	4	1	no	—
626	C₂×C₃	C₂²×#41	1	1	yes	characteristic
627	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₃	#585	1	1	yes	characteristic
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	4	8	no	—
646	C₂²	—	8	4	no	—
647	C₂²	C₂×C₃×#41	1	4	yes	—
648	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
649	C₂²	C₂⁵×C₃	1	1	yes	characteristic
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	C₂×C₃×#41	1	2	yes	—
667	C₃	#3513	1	1	yes	characteristic, direct product factor, Sylow
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	4	1	no	—
674	C₂	C₂²×C₃×#41	1	1	yes	characteristic
675	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
676	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×#559	C₂	semidirect
2. C₃×#554	C₂	semidirect
3. C₃×#553	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#552	C₂	semidirect
6. C₃×#551	C₂	semidirect
7. C₃×#551	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×#539	C₂	semidirect
16. C₃×#538	C₂	semidirect
17. C₃×#529	C₂	semidirect
18. C₃×#529	C₂	semidirect
19. C₃×#525	C₂	semidirect
20. C₂×C₃×#123	C₂	semidirect
21. C₃×#520	C₂	semidirect
22. C₃×#518	C₂	semidirect
23. C₂×C₃×C₄×D₄	C₂	semidirect
24. #3513	C₃	direct (N × H)
26. C₂×C₃×#41	C₂²	semidirect
30. C₂³×C₃×C₄	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
33. C₃×#126	C₂²	semidirect
34. C₃×#126	C₂²	semidirect
35. C₃×#126	C₂²	semidirect
36. C₃×#126	C₂²	semidirect
37. C₃×#126	C₂²	semidirect
38. C₃×#126	C₂²	semidirect
39. C₃×#125	C₂²	semidirect
40. C₃×#125	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
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×#123	C₂²	semidirect
61. C₃×#123	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
68. C₃×C₂²⋊Q₈	C₂²	semidirect
69. C₃×C₂²⋊Q₈	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
83. C₃×#120	C₂²	semidirect
84. C₃×#120	C₂²	semidirect
85. C₃×C₄×Q₈	C₂²	semidirect
86. C₃×C₄×Q₈	C₂²	semidirect
87. C₃×C₄×Q₈	C₂²	semidirect
93. C₃×C₄×D₄	C₂²	semidirect
94. C₃×C₄×D₄	C₂²	semidirect
95. C₃×C₄×D₄	C₂²	semidirect
96. C₃×C₄×D₄	C₂²	semidirect
97. C₃×C₄×D₄	C₂²	semidirect
98. C₃×C₄×D₄	C₂²	semidirect
99. C₃×C₄×D₄	C₂²	semidirect
100. C₃×C₄×D₄	C₂²	semidirect
101. C₃×C₄×D₄	C₂²	semidirect
102. C₃×C₄×D₄	C₂²	semidirect
103. C₃×C₄×D₄	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×#117	C₂²	semidirect
109. C₃×#117	C₂²	semidirect
110. C₃×#117	C₂²	semidirect
111. C₃×#117	C₂²	semidirect
112. C₃×#117	C₂²	semidirect
113. C₃×#117	C₂²	semidirect
114. C₂×C₃×C₄⋊C₄	C₂²	semidirect
115. C₂×C₃×C₄⋊C₄	C₂²	semidirect
116. C₂×C₃×C₄⋊C₄	C₂²	semidirect
117. C₂×C₃×C₄⋊C₄	C₂²	semidirect
118. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
119. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
120. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
121. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
123. C₂×C₃×C₄²	C₂²	semidirect
124. #559	C₂×C₃	semidirect
125. #554	C₂×C₃	semidirect
126. #553	C₂×C₃	semidirect
127. #553	C₂×C₃	semidirect
128. #552	C₂×C₃	semidirect
129. #551	C₂×C₃	semidirect
130. #551	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. #539	C₂×C₃	semidirect
139. #538	C₂×C₃	semidirect
140. #529	C₂×C₃	semidirect
141. #529	C₂×C₃	semidirect
142. #525	C₂×C₃	semidirect
143. C₂×#123	C₂×C₃	semidirect
144. #520	C₂×C₃	semidirect
145. #518	C₂×C₃	semidirect
146. C₂×C₄×D₄	C₂×C₃	semidirect
253. C₂×#41	C₂²×C₃	semidirect
257. C₂³×C₄	C₂²×C₃	semidirect
258. C₄⋊Q₈	C₂²×C₃	semidirect
260. #126	C₂²×C₃	semidirect
261. #126	C₂²×C₃	semidirect
262. #126	C₂²×C₃	semidirect
263. #126	C₂²×C₃	semidirect
264. #126	C₂²×C₃	semidirect
265. #126	C₂²×C₃	semidirect
266. #125	C₂²×C₃	semidirect
267. #125	C₂²×C₃	semidirect
268. #125	C₂²×C₃	semidirect
269. #125	C₂²×C₃	semidirect
270. #124	C₂²×C₃	semidirect
271. #124	C₂²×C₃	semidirect
272. #124	C₂²×C₃	semidirect
273. #124	C₂²×C₃	semidirect
274. #124	C₂²×C₃	semidirect
277. #123	C₂²×C₃	semidirect
278. #123	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. C₂²⋊Q₈	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
301. #121	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
310. #120	C₂²×C₃	semidirect
311. #120	C₂²×C₃	semidirect
312. C₄×Q₈	C₂²×C₃	semidirect
313. C₄×Q₈	C₂²×C₃	semidirect
314. C₄×Q₈	C₂²×C₃	semidirect
320. C₄×D₄	C₂²×C₃	semidirect
321. C₄×D₄	C₂²×C₃	semidirect
322. C₄×D₄	C₂²×C₃	semidirect
323. C₄×D₄	C₂²×C₃	semidirect
324. C₄×D₄	C₂²×C₃	semidirect
325. C₄×D₄	C₂²×C₃	semidirect
326. C₄×D₄	C₂²×C₃	semidirect
327. C₄×D₄	C₂²×C₃	semidirect
328. C₄×D₄	C₂²×C₃	semidirect
329. C₄×D₄	C₂²×C₃	semidirect
330. C₄×D₄	C₂²×C₃	semidirect
331. C₄×D₄	C₂²×C₃	semidirect
332. C₄×D₄	C₂²×C₃	semidirect
333. C₄×D₄	C₂²×C₃	semidirect
334. C₄×D₄	C₂²×C₃	semidirect
335. #117	C₂²×C₃	semidirect
336. #117	C₂²×C₃	semidirect
337. #117	C₂²×C₃	semidirect
338. #117	C₂²×C₃	semidirect
339. #117	C₂²×C₃	semidirect
340. #117	C₂²×C₃	semidirect
341. C₂×C₄⋊C₄	C₂²×C₃	semidirect
342. C₂×C₄⋊C₄	C₂²×C₃	semidirect
343. C₂×C₄⋊C₄	C₂²×C₃	semidirect
344. C₂×C₄⋊C₄	C₂²×C₃	semidirect
345. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
346. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
347. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
348. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
349. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
350. C₂×C₄²	C₂²×C₃	semidirect
380. C₃×D₄	#41	semidirect
586. D₄	C₃×#41	semidirect
667. C₃	#3513	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×#559	2
C₃×#554	2
C₃×#553	2
C₃×#552	2
C₃×#551	2
C₃×#547	2
C₃×#546	2
C₃×D₄²	2
C₃×#542	2
C₃×#540	2
C₃×#539	2
C₃×#538	2
C₃×#529	2
C₃×#525	2
C₂×C₃×#123	2
C₃×#520	2
C₃×#518	2
C₂×C₃×C₄×D₄	2
#3513	3

Subgroups — C3×#3513 #87397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3513 #87397