Subgroups — C₃²×#3505 #11770554

Order 1152.

3456 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#553	C₂	1	4	yes	maximal, complemented
2	C₃²×#553	C₂	1	2	yes	maximal, complemented
3	C₃²×#552	C₂	1	2	yes	maximal, complemented
4	C₃²×#551	C₂	1	4	yes	maximal, complemented
5	C₃²×#548	C₂	1	2	yes	maximal, complemented
6	C₃²×#546	C₂	1	2	yes	maximal, complemented
7	C₃²×#539	C₂	1	2	yes	maximal, complemented
8	C₃²×#538	C₂	1	2	yes	maximal, complemented
9	C₃²×#534	C₂	1	2	yes	maximal, complemented
10	C₃²×#529	C₂	1	2	yes	maximal, complemented
11	C₃²×#525	C₂	1	2	yes	maximal, complemented
12	C₂×C₃²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃²×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#518	C₂	1	2	yes	maximal, complemented
15	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3505	C₃	1	4	yes	maximal, direct product factor
17	C₂×C₃²×#41	C₂²	1	2	yes	complemented
18	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃²×D₄	C₂²	1	2	yes	—
21	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃²×#126	C₂²	1	4	yes	complemented
25	C₃²×#126	C₂²	1	4	yes	complemented
26	C₃²×#126	C₂²	1	4	yes	complemented
27	C₃²×#125	C₂²	1	2	yes	complemented
28	C₃²×#125	C₂²	1	4	yes	complemented
29	C₃²×#124	C₂²	1	4	yes	complemented
30	C₃²×#124	C₂²	1	2	yes	complemented
31	C₃²×#123	C₂²	1	4	yes	—
32	C₃²×#123	C₂²	1	4	yes	complemented
33	C₃²×#123	C₂²	1	4	yes	complemented
34	C₃²×#123	C₂²	1	4	yes	complemented
35	C₃²×#123	C₂²	1	4	yes	complemented
36	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
38	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
42	C₃²×#121	C₂²	1	2	yes	—
43	C₃²×#121	C₂²	1	2	yes	—
44	C₃²×#121	C₂²	1	2	yes	complemented
45	C₃²×#121	C₂²	1	4	yes	complemented
46	C₃²×#121	C₂²	1	2	yes	complemented
47	C₃²×#121	C₂²	1	2	yes	complemented
48	C₃²×#121	C₂²	1	4	yes	complemented
49	C₃²×#121	C₂²	1	4	yes	complemented
50	C₃²×#120	C₂²	1	4	yes	—
51	C₃²×#120	C₂²	1	4	yes	complemented
52	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
53	C₃²×C₄×D₄	C₂²	1	2	yes	—
54	C₃²×C₄×D₄	C₂²	1	2	yes	—
55	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
56	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
57	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
58	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
59	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
60	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
61	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
62	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
63	C₃²×#117	C₂²	1	4	yes	complemented
64	C₃²×#117	C₂²	1	4	yes	complemented
65	C₃²×#117	C₂²	1	2	yes	complemented
66	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
73	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	complemented
74	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
76	C₃×#553	C₂×C₃	1	8	yes	complemented
77	C₃×#553	C₂×C₃	1	16	yes	complemented
78	C₃×#552	C₂×C₃	1	8	yes	complemented
79	C₃×#551	C₂×C₃	1	16	yes	complemented
80	C₃×#548	C₂×C₃	1	8	yes	complemented
81	C₃×#546	C₂×C₃	1	8	yes	complemented
82	C₃×#539	C₂×C₃	1	8	yes	complemented
83	C₃×#538	C₂×C₃	1	8	yes	complemented
84	C₃×#534	C₂×C₃	1	8	yes	complemented
85	C₃×#529	C₂×C₃	1	8	yes	complemented
86	C₃×#525	C₂×C₃	1	8	yes	complemented
87	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
88	C₂×C₃×#121	C₂×C₃	1	4	yes	complemented
89	C₃×#518	C₂×C₃	1	8	yes	complemented
90	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	complemented
91	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
92	C₂⁴×C₃²	C₂³	1	2	yes	—
93	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
94	C₃²×#41	—	4	4	no	—
95	C₂×C₃²×Q₈	—	4	2	no	—
96	C₂×C₃²×Q₈	C₂³	1	2	yes	—
97	C₂×C₃²×Q₈	C₂³	1	2	yes	—
98	C₂×C₃²×D₄	—	2	4	no	—
99	C₂×C₃²×D₄	—	2	8	no	—
100	C₂×C₃²×D₄	—	4	2	no	—
101	C₂×C₃²×D₄	C₂³	1	2	yes	—
102	C₂×C₃²×D₄	C₂³	1	4	yes	—
103	C₂×C₃²×D₄	C₂³	1	2	yes	—
104	C₂×C₃²×D₄	C₂³	1	4	yes	—
105	C₂×C₃²×D₄	C₂³	1	2	yes	—
106	C₂×C₃²×D₄	C₂³	1	2	yes	—
107	C₂×C₃²×D₄	C₂³	1	4	yes	—
108	C₂×C₃²×D₄	C₂³	1	4	yes	—
109	C₂²×C₃²×C₄	—	4	2	no	—
110	C₂²×C₃²×C₄	—	4	2	no	—
111	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
112	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
113	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
114	C₂²×C₃²×C₄	C₂³	1	2	yes	—
115	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃²×C₄	C₂³	1	2	yes	—
117	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
121	C₂²×C₃²×C₄	C₂³	1	2	yes	—
122	C₂²×C₃²×C₄	C₂³	1	2	yes	—
123	C₂²×C₃²×C₄	C₂³	1	4	yes	—
124	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃²×C₄	C₂³	1	2	yes	—
126	C₂²×C₃²×C₄	C₂³	1	4	yes	—
127	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
130	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
136	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₃²×C₄²	C₂³	1	2	yes	—
154	C₃²×C₄²	C₂³	1	2	yes	—
155	C₃²×C₄²	C₂³	1	4	yes	—
156	C₃²×C₄²	C₂³	1	4	yes	—
157	#3505	C₃²	1	1	yes	characteristic, direct product factor, Sylow
158	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
159	C₂²×C₃×Q₈	C₂²×C₃	1	4	yes	complemented
160	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
161	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
162	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	complemented
163	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
164	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	complemented
165	C₃×#126	C₂²×C₃	1	16	yes	complemented
166	C₃×#126	C₂²×C₃	1	16	yes	complemented
167	C₃×#126	C₂²×C₃	1	16	yes	complemented
168	C₃×#125	C₂²×C₃	1	8	yes	complemented
169	C₃×#125	C₂²×C₃	1	16	yes	complemented
170	C₃×#124	C₂²×C₃	1	8	yes	complemented
171	C₃×#124	C₂²×C₃	1	16	yes	complemented
172	C₃×#123	C₂²×C₃	1	16	yes	—
173	C₃×#123	C₂²×C₃	1	16	yes	complemented
174	C₃×#123	C₂²×C₃	1	16	yes	complemented
175	C₃×#123	C₂²×C₃	1	16	yes	complemented
176	C₃×#123	C₂²×C₃	1	16	yes	complemented
177	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
178	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
179	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
180	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
181	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
182	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
183	C₃×#121	C₂²×C₃	1	8	yes	—
184	C₃×#121	C₂²×C₃	1	8	yes	—
185	C₃×#121	C₂²×C₃	1	8	yes	complemented
186	C₃×#121	C₂²×C₃	1	8	yes	complemented
187	C₃×#121	C₂²×C₃	1	8	yes	complemented
188	C₃×#121	C₂²×C₃	1	16	yes	complemented
189	C₃×#121	C₂²×C₃	1	16	yes	complemented
190	C₃×#121	C₂²×C₃	1	16	yes	complemented
191	C₃×#120	C₂²×C₃	1	16	yes	—
192	C₃×#120	C₂²×C₃	1	16	yes	complemented
193	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
194	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
195	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
196	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
197	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
198	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
199	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
200	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
201	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
202	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
203	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
204	C₃×#117	C₂²×C₃	1	16	yes	complemented
205	C₃×#117	C₂²×C₃	1	8	yes	complemented
206	C₃×#117	C₂²×C₃	1	16	yes	complemented
207	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
208	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
209	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
210	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
211	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
214	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
215	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
216	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	complemented
217	C₂³×C₃²	—	2	2	no	—
218	C₂³×C₃²	—	2	4	no	—
219	C₂³×C₃²	—	4	1	no	—
220	C₂³×C₃²	—	4	1	no	—
221	C₂³×C₃²	—	4	1	no	—
222	C₂³×C₃²	—	4	1	no	—
223	C₂³×C₃²	—	4	2	no	—
224	C₂³×C₃²	—	4	2	no	—
225	C₂³×C₃²	#41	1	4	yes	complemented
226	C₂³×C₃²	C₂⁴	1	2	yes	—
227	C₂³×C₃²	C₂⁴	1	4	yes	—
228	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
229	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
230	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
231	C₃²×Q₈	—	2	4	no	—
232	C₃²×Q₈	—	4	2	no	—
233	C₃²×D₄	—	2	4	no	—
234	C₃²×D₄	—	2	8	no	—
235	C₃²×D₄	—	2	4	no	—
236	C₃²×D₄	—	2	8	no	—
237	C₃²×D₄	—	2	4	no	—
238	C₃²×D₄	—	4	2	no	—
239	C₃²×D₄	—	4	4	no	—
240	C₃²×D₄	—	4	4	no	—
241	C₂×C₃²×C₄	—	2	4	no	—
242	C₂×C₃²×C₄	—	2	2	no	—
243	C₂×C₃²×C₄	—	2	2	no	—
244	C₂×C₃²×C₄	—	2	2	no	—
245	C₂×C₃²×C₄	—	2	2	no	—
246	C₂×C₃²×C₄	—	2	4	no	—
247	C₂×C₃²×C₄	—	4	1	no	—
248	C₂×C₃²×C₄	—	4	2	no	—
249	C₂×C₃²×C₄	—	4	1	no	—
250	C₂×C₃²×C₄	—	4	1	no	—
251	C₂×C₃²×C₄	—	4	1	no	—
252	C₂×C₃²×C₄	—	4	1	no	—
253	C₂×C₃²×C₄	—	4	4	no	—
254	C₂×C₃²×C₄	—	4	2	no	—
255	C₂×C₃²×C₄	—	4	2	no	—
256	C₂×C₃²×C₄	—	4	4	no	—
257	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
258	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
259	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
260	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
261	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
262	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
263	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
264	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
266	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
267	#553	C₂×C₃²	1	2	yes	complemented
268	#553	C₂×C₃²	1	4	yes	complemented
269	#552	C₂×C₃²	1	2	yes	complemented
270	#551	C₂×C₃²	1	4	yes	complemented
271	#548	C₂×C₃²	1	2	yes	complemented
272	#546	C₂×C₃²	1	2	yes	complemented
273	#539	C₂×C₃²	1	2	yes	complemented
274	#538	C₂×C₃²	1	2	yes	complemented
275	#534	C₂×C₃²	1	2	yes	complemented
276	#529	C₂×C₃²	1	2	yes	complemented
277	#525	C₂×C₃²	1	2	yes	complemented
278	C₂×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
279	C₂×#121	C₂×C₃²	1	1	yes	characteristic, complemented
280	#518	C₂×C₃²	1	2	yes	complemented
281	C₂×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
282	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
283	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
284	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
285	C₃×#41	—	4	16	no	—
286	C₂×C₃×Q₈	—	4	8	no	—
287	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
288	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
289	C₂×C₃×D₄	—	2	16	no	—
290	C₂×C₃×D₄	—	2	32	no	—
291	C₂×C₃×D₄	—	4	8	no	—
292	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
293	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
294	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
295	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
296	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
297	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
298	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
299	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
300	C₂²×C₃×C₄	—	4	8	no	—
301	C₂²×C₃×C₄	—	4	8	no	—
302	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
303	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
304	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
305	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
306	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
307	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
308	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
309	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
310	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
311	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
312	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
313	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
314	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
315	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
316	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
317	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
318	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
319	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
320	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
321	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
322	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
323	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
324	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
325	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
326	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
327	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
328	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
329	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
330	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
331	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
332	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
333	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
334	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
335	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
336	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
337	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
338	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
339	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
340	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
341	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
342	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
343	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
344	C₃×C₄²	C₂³×C₃	1	8	yes	—
345	C₃×C₄²	C₂³×C₃	1	8	yes	—
346	C₃×C₄²	C₂³×C₃	1	16	yes	—
347	C₃×C₄²	C₂³×C₃	1	16	yes	—
348	C₂²×C₃²	—	2	1	no	—
349	C₂²×C₃²	—	2	1	no	—
350	C₂²×C₃²	—	2	1	no	—
351	C₂²×C₃²	—	2	1	no	—
352	C₂²×C₃²	—	2	1	no	—
353	C₂²×C₃²	—	2	1	no	—
354	C₂²×C₃²	—	2	2	no	—
355	C₂²×C₃²	—	2	4	no	—
356	C₂²×C₃²	—	2	2	no	—
357	C₂²×C₃²	—	2	4	no	—
358	C₂²×C₃²	—	2	4	no	—
359	C₂²×C₃²	—	2	2	no	—
360	C₂²×C₃²	—	4	4	no	—
361	C₂²×C₃²	—	4	4	no	—
362	C₂²×C₃²	—	8	4	no	—
363	C₂²×C₃²	C₂×#41	1	2	yes	—
364	C₂²×C₃²	C₂×#41	1	2	yes	—
365	C₂²×C₃²	C₂×#41	1	2	yes	—
366	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
367	C₃²×C₄	—	2	4	no	—
368	C₃²×C₄	—	2	2	no	—
369	C₃²×C₄	—	2	1	no	—
370	C₃²×C₄	—	2	2	no	—
371	C₃²×C₄	—	2	1	no	—
372	C₃²×C₄	—	2	1	no	—
373	C₃²×C₄	—	2	4	no	—
374	C₃²×C₄	—	2	2	no	—
375	C₃²×C₄	—	2	4	no	—
376	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
377	C₂×#41	C₂²×C₃²	1	2	yes	complemented
378	C₂²×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
379	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
380	C₂²×D₄	C₂²×C₃²	1	2	yes	—
381	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
382	C₂³×C₄	C₂²×C₃²	1	1	yes	characteristic
383	C₂³×C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
384	#126	C₂²×C₃²	1	4	yes	complemented
385	#126	C₂²×C₃²	1	4	yes	complemented
386	#126	C₂²×C₃²	1	4	yes	complemented
387	#125	C₂²×C₃²	1	2	yes	complemented
388	#125	C₂²×C₃²	1	4	yes	complemented
389	#124	C₂²×C₃²	1	2	yes	complemented
390	#124	C₂²×C₃²	1	4	yes	complemented
391	#123	C₂²×C₃²	1	4	yes	—
392	#123	C₂²×C₃²	1	4	yes	complemented
393	#123	C₂²×C₃²	1	4	yes	complemented
394	#123	C₂²×C₃²	1	4	yes	complemented
395	#123	C₂²×C₃²	1	4	yes	complemented
396	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
397	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
398	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
399	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
400	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
401	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
402	#121	C₂²×C₃²	1	2	yes	—
403	#121	C₂²×C₃²	1	2	yes	—
404	#121	C₂²×C₃²	1	2	yes	complemented
405	#121	C₂²×C₃²	1	2	yes	complemented
406	#121	C₂²×C₃²	1	2	yes	complemented
407	#121	C₂²×C₃²	1	4	yes	complemented
408	#121	C₂²×C₃²	1	4	yes	complemented
409	#121	C₂²×C₃²	1	4	yes	complemented
410	#120	C₂²×C₃²	1	4	yes	—
411	#120	C₂²×C₃²	1	4	yes	complemented
412	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
413	C₄×D₄	C₂²×C₃²	1	2	yes	—
414	C₄×D₄	C₂²×C₃²	1	2	yes	—
415	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
416	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
417	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
418	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
419	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
420	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
421	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
422	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
423	#117	C₂²×C₃²	1	4	yes	complemented
424	#117	C₂²×C₃²	1	2	yes	complemented
425	#117	C₂²×C₃²	1	4	yes	complemented
426	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
427	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
428	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
429	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
430	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
433	C₂×C₂²⋊C₄	C₂²×C₃²	1	4	yes	complemented
434	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
435	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
436	C₂³×C₃	—	2	8	no	—
437	C₂³×C₃	—	2	16	no	—
438	C₂³×C₃	—	4	4	no	—
439	C₂³×C₃	—	4	4	no	—
440	C₂³×C₃	—	4	4	no	—
441	C₂³×C₃	—	4	4	no	—
442	C₂³×C₃	—	4	8	no	—
443	C₂³×C₃	—	4	8	no	—
444	C₂³×C₃	C₃×#41	1	16	yes	complemented
445	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
446	C₂³×C₃	C₂⁴×C₃	1	16	yes	—
447	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
448	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
449	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
450	C₃×Q₈	—	2	16	no	—
451	C₃×Q₈	—	4	8	no	—
452	C₃×D₄	—	2	16	no	—
453	C₃×D₄	—	2	32	no	—
454	C₃×D₄	—	2	16	no	—
455	C₃×D₄	—	2	32	no	—
456	C₃×D₄	—	2	16	no	—
457	C₃×D₄	—	4	8	no	—
458	C₃×D₄	—	4	16	no	—
459	C₃×D₄	—	4	16	no	—
460	C₂×C₃×C₄	—	2	16	no	—
461	C₂×C₃×C₄	—	2	8	no	—
462	C₂×C₃×C₄	—	2	8	no	—
463	C₂×C₃×C₄	—	2	8	no	—
464	C₂×C₃×C₄	—	2	8	no	—
465	C₂×C₃×C₄	—	2	16	no	—
466	C₂×C₃×C₄	—	4	4	no	—
467	C₂×C₃×C₄	—	4	8	no	—
468	C₂×C₃×C₄	—	4	4	no	—
469	C₂×C₃×C₄	—	4	4	no	—
470	C₂×C₃×C₄	—	4	4	no	—
471	C₂×C₃×C₄	—	4	4	no	—
472	C₂×C₃×C₄	—	4	16	no	—
473	C₂×C₃×C₄	—	4	8	no	—
474	C₂×C₃×C₄	—	4	8	no	—
475	C₂×C₃×C₄	—	4	16	no	—
476	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
477	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
478	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
479	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
480	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
481	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
482	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
483	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
484	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
485	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
486	C₂×C₃²	—	2	2	no	—
487	C₂×C₃²	—	2	2	no	—
488	C₂×C₃²	—	2	2	no	—
489	C₂×C₃²	—	4	2	no	—
490	C₂×C₃²	—	4	4	no	—
491	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
492	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₃²	#585	1	1	yes	characteristic
494	C₂⁴	C₂³×C₃²	1	2	yes	—
495	C₂⁴	C₂³×C₃²	1	1	yes	characteristic
496	C₂⁴	C₂³×C₃²	1	1	yes	characteristic
497	#41	—	4	4	no	—
498	C₂×Q₈	—	4	2	no	—
499	C₂×Q₈	C₂³×C₃²	1	2	yes	—
500	C₂×Q₈	C₂³×C₃²	1	2	yes	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	8	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	C₂³×C₃²	1	2	yes	—
505	C₂×D₄	C₂³×C₃²	1	4	yes	—
506	C₂×D₄	C₂³×C₃²	1	2	yes	—
507	C₂×D₄	C₂³×C₃²	1	4	yes	—
508	C₂×D₄	C₂³×C₃²	1	2	yes	—
509	C₂×D₄	C₂³×C₃²	1	4	yes	—
510	C₂×D₄	C₂³×C₃²	1	4	yes	—
511	C₂×D₄	C₂³×C₃²	1	2	yes	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
515	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
516	C₂²×C₄	C₂³×C₃²	1	2	yes	—
517	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
518	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
519	C₂²×C₄	C₂³×C₃²	1	2	yes	—
520	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
521	C₂²×C₄	C₂³×C₃²	1	2	yes	—
522	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
523	C₂²×C₄	C₂³×C₃²	1	2	yes	—
524	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
525	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
526	C₂²×C₄	C₂³×C₃²	1	4	yes	—
527	C₂²×C₄	C₂³×C₃²	1	4	yes	—
528	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
529	C₂²×C₄	C₂³×C₃²	1	2	yes	—
530	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
531	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
532	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
533	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
534	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
535	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
536	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
537	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
538	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
539	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
540	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
541	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
542	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
544	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
545	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
546	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
547	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
548	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
550	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
551	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
552	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
553	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
554	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
555	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
556	C₄²	C₂³×C₃²	1	2	yes	—
557	C₄²	C₂³×C₃²	1	2	yes	—
558	C₄²	C₂³×C₃²	1	4	yes	—
559	C₄²	C₂³×C₃²	1	4	yes	—
560	C₂²×C₃	—	2	4	no	—
561	C₂²×C₃	—	2	4	no	—
562	C₂²×C₃	—	2	4	no	—
563	C₂²×C₃	—	2	4	no	—
564	C₂²×C₃	—	2	4	no	—
565	C₂²×C₃	—	2	4	no	—
566	C₂²×C₃	—	2	8	no	—
567	C₂²×C₃	—	2	16	no	—
568	C₂²×C₃	—	2	8	no	—
569	C₂²×C₃	—	2	16	no	—
570	C₂²×C₃	—	2	16	no	—
571	C₂²×C₃	—	2	8	no	—
572	C₂²×C₃	—	4	16	no	—
573	C₂²×C₃	—	4	16	no	—
574	C₂²×C₃	—	8	16	no	—
575	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
576	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
577	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
578	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
579	C₃×C₄	—	2	16	no	—
580	C₃×C₄	—	2	8	no	—
581	C₃×C₄	—	2	4	no	—
582	C₃×C₄	—	2	8	no	—
583	C₃×C₄	—	2	4	no	—
584	C₃×C₄	—	2	4	no	—
585	C₃×C₄	—	2	16	no	—
586	C₃×C₄	—	2	8	no	—
587	C₃×C₄	—	2	16	no	—
588	C₃×C₄	C₃×H(5,𝔽₂)	1	8	yes	—
589	C₃²	#3505	1	1	yes	characteristic, direct product factor, Sylow
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	2	no	—
598	C₂³	C₃²×#41	1	4	yes	complemented
599	C₂³	C₂⁴×C₃²	1	2	yes	—
600	C₂³	C₂⁴×C₃²	1	4	yes	—
601	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
602	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
603	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
604	Q₈	—	2	4	no	—
605	Q₈	—	4	2	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	8	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	8	no	—
610	D₄	—	2	4	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
631	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
632	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
633	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
634	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
635	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
636	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
637	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
638	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
639	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
640	C₂×C₃	—	2	8	no	—
641	C₂×C₃	—	2	8	no	—
642	C₂×C₃	—	2	8	no	—
643	C₂×C₃	—	4	8	no	—
644	C₂×C₃	—	4	16	no	—
645	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
646	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
647	C₂×C₃	C₃×#585	1	4	yes	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	4	no	—
662	C₂²	—	8	4	no	—
663	C₂²	C₂×C₃²×#41	1	2	yes	—
664	C₂²	C₂×C₃²×#41	1	2	yes	—
665	C₂²	C₂×C₃²×#41	1	2	yes	—
666	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
667	C₄	—	2	4	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	4	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	C₃²×H(5,𝔽₂)	1	2	yes	—
677	C₃	C₃×#3505	1	4	yes	direct product factor
678	C₂	—	2	2	no	—
679	C₂	—	2	2	no	—
680	C₂	—	2	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	4	4	no	—
683	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
684	C₂	C₂×C₃²×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂	C₃²×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#553	C₂	semidirect
2. C₃²×#553	C₂	semidirect
3. C₃²×#552	C₂	semidirect
4. C₃²×#551	C₂	semidirect
5. C₃²×#548	C₂	semidirect
6. C₃²×#546	C₂	semidirect
7. C₃²×#539	C₂	semidirect
8. C₃²×#538	C₂	semidirect
9. C₃²×#534	C₂	semidirect
10. C₃²×#529	C₂	semidirect
11. C₃²×#525	C₂	semidirect
12. C₂×C₃²×C₂²⋊Q₈	C₂	semidirect
13. C₂×C₃²×#121	C₂	semidirect
14. C₃²×#518	C₂	semidirect
15. C₂×C₃²×C₄×D₄	C₂	semidirect
16. C₃×#3505	C₃	direct (N × H)
17. C₂×C₃²×#41	C₂²	semidirect
18. C₂²×C₃²×Q₈	C₂²	semidirect
21. C₂²×C₃²×D₄	C₂²	semidirect
23. C₂³×C₃²×C₄	C₂²	semidirect
24. C₃²×#126	C₂²	semidirect
25. C₃²×#126	C₂²	semidirect
26. C₃²×#126	C₂²	semidirect
27. C₃²×#125	C₂²	semidirect
28. C₃²×#125	C₂²	semidirect
29. C₃²×#124	C₂²	semidirect
30. C₃²×#124	C₂²	semidirect
32. C₃²×#123	C₂²	semidirect
33. C₃²×#123	C₂²	semidirect
34. C₃²×#123	C₂²	semidirect
35. C₃²×#123	C₂²	semidirect
36. C₃²×C₂²⋊Q₈	C₂²	semidirect
37. C₃²×C₂²⋊Q₈	C₂²	semidirect
38. C₃²×C₂²⋊Q₈	C₂²	semidirect
39. C₃²×C₂²⋊Q₈	C₂²	semidirect
40. C₃²×C₂²⋊Q₈	C₂²	semidirect
41. C₃²×C₂²⋊Q₈	C₂²	semidirect
44. C₃²×#121	C₂²	semidirect
45. C₃²×#121	C₂²	semidirect
46. C₃²×#121	C₂²	semidirect
47. C₃²×#121	C₂²	semidirect
48. C₃²×#121	C₂²	semidirect
49. C₃²×#121	C₂²	semidirect
51. C₃²×#120	C₂²	semidirect
52. C₃²×C₄×Q₈	C₂²	semidirect
55. C₃²×C₄×D₄	C₂²	semidirect
56. C₃²×C₄×D₄	C₂²	semidirect
57. C₃²×C₄×D₄	C₂²	semidirect
58. C₃²×C₄×D₄	C₂²	semidirect
59. C₃²×C₄×D₄	C₂²	semidirect
60. C₃²×C₄×D₄	C₂²	semidirect
61. C₃²×C₄×D₄	C₂²	semidirect
62. C₃²×C₄×D₄	C₂²	semidirect
63. C₃²×#117	C₂²	semidirect
64. C₃²×#117	C₂²	semidirect
65. C₃²×#117	C₂²	semidirect
66. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
67. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
68. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
69. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
72. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
73. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
74. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
75. C₂×C₃²×C₄²	C₂²	semidirect
76. C₃×#553	C₂×C₃	semidirect
77. C₃×#553	C₂×C₃	semidirect
78. C₃×#552	C₂×C₃	semidirect
79. C₃×#551	C₂×C₃	semidirect
80. C₃×#548	C₂×C₃	semidirect
81. C₃×#546	C₂×C₃	semidirect
82. C₃×#539	C₂×C₃	semidirect
83. C₃×#538	C₂×C₃	semidirect
84. C₃×#534	C₂×C₃	semidirect
85. C₃×#529	C₂×C₃	semidirect
86. C₃×#525	C₂×C₃	semidirect
87. C₂×C₃×C₂²⋊Q₈	C₂×C₃	semidirect
88. C₂×C₃×#121	C₂×C₃	semidirect
89. C₃×#518	C₂×C₃	semidirect
90. C₂×C₃×C₄×D₄	C₂×C₃	semidirect
157. #3505	C₃²	direct (N × H)
158. C₂×C₃×#41	C₂²×C₃	semidirect
159. C₂²×C₃×Q₈	C₂²×C₃	semidirect
162. C₂²×C₃×D₄	C₂²×C₃	semidirect
164. C₂³×C₃×C₄	C₂²×C₃	semidirect
165. C₃×#126	C₂²×C₃	semidirect
166. C₃×#126	C₂²×C₃	semidirect
167. C₃×#126	C₂²×C₃	semidirect
168. C₃×#125	C₂²×C₃	semidirect
169. C₃×#125	C₂²×C₃	semidirect
170. C₃×#124	C₂²×C₃	semidirect
171. C₃×#124	C₂²×C₃	semidirect
173. C₃×#123	C₂²×C₃	semidirect
174. C₃×#123	C₂²×C₃	semidirect
175. C₃×#123	C₂²×C₃	semidirect
176. C₃×#123	C₂²×C₃	semidirect
177. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
178. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
179. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
180. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
181. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
182. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
185. C₃×#121	C₂²×C₃	semidirect
186. C₃×#121	C₂²×C₃	semidirect
187. C₃×#121	C₂²×C₃	semidirect
188. C₃×#121	C₂²×C₃	semidirect
189. C₃×#121	C₂²×C₃	semidirect
190. C₃×#121	C₂²×C₃	semidirect
192. C₃×#120	C₂²×C₃	semidirect
193. C₃×C₄×Q₈	C₂²×C₃	semidirect
196. C₃×C₄×D₄	C₂²×C₃	semidirect
197. C₃×C₄×D₄	C₂²×C₃	semidirect
198. C₃×C₄×D₄	C₂²×C₃	semidirect
199. C₃×C₄×D₄	C₂²×C₃	semidirect
200. C₃×C₄×D₄	C₂²×C₃	semidirect
201. C₃×C₄×D₄	C₂²×C₃	semidirect
202. C₃×C₄×D₄	C₂²×C₃	semidirect
203. C₃×C₄×D₄	C₂²×C₃	semidirect
204. C₃×#117	C₂²×C₃	semidirect
205. C₃×#117	C₂²×C₃	semidirect
206. C₃×#117	C₂²×C₃	semidirect
207. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
208. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
209. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
210. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
213. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
214. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
215. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
216. C₂×C₃×C₄²	C₂²×C₃	semidirect
225. C₂³×C₃²	#41	semidirect
267. #553	C₂×C₃²	semidirect
268. #553	C₂×C₃²	semidirect
269. #552	C₂×C₃²	semidirect
270. #551	C₂×C₃²	semidirect
271. #548	C₂×C₃²	semidirect
272. #546	C₂×C₃²	semidirect
273. #539	C₂×C₃²	semidirect
274. #538	C₂×C₃²	semidirect
275. #534	C₂×C₃²	semidirect
276. #529	C₂×C₃²	semidirect
277. #525	C₂×C₃²	semidirect
278. C₂×C₂²⋊Q₈	C₂×C₃²	semidirect
279. C₂×#121	C₂×C₃²	semidirect
280. #518	C₂×C₃²	semidirect
281. C₂×C₄×D₄	C₂×C₃²	semidirect
377. C₂×#41	C₂²×C₃²	semidirect
378. C₂²×Q₈	C₂²×C₃²	semidirect
381. C₂²×D₄	C₂²×C₃²	semidirect
383. C₂³×C₄	C₂²×C₃²	semidirect
384. #126	C₂²×C₃²	semidirect
385. #126	C₂²×C₃²	semidirect
386. #126	C₂²×C₃²	semidirect
387. #125	C₂²×C₃²	semidirect
388. #125	C₂²×C₃²	semidirect
389. #124	C₂²×C₃²	semidirect
390. #124	C₂²×C₃²	semidirect
392. #123	C₂²×C₃²	semidirect
393. #123	C₂²×C₃²	semidirect
394. #123	C₂²×C₃²	semidirect
395. #123	C₂²×C₃²	semidirect
396. C₂²⋊Q₈	C₂²×C₃²	semidirect
397. C₂²⋊Q₈	C₂²×C₃²	semidirect
398. C₂²⋊Q₈	C₂²×C₃²	semidirect
399. C₂²⋊Q₈	C₂²×C₃²	semidirect
400. C₂²⋊Q₈	C₂²×C₃²	semidirect
401. C₂²⋊Q₈	C₂²×C₃²	semidirect
404. #121	C₂²×C₃²	semidirect
405. #121	C₂²×C₃²	semidirect
406. #121	C₂²×C₃²	semidirect
407. #121	C₂²×C₃²	semidirect
408. #121	C₂²×C₃²	semidirect
409. #121	C₂²×C₃²	semidirect
411. #120	C₂²×C₃²	semidirect
412. C₄×Q₈	C₂²×C₃²	semidirect
415. C₄×D₄	C₂²×C₃²	semidirect
416. C₄×D₄	C₂²×C₃²	semidirect
417. C₄×D₄	C₂²×C₃²	semidirect
418. C₄×D₄	C₂²×C₃²	semidirect
419. C₄×D₄	C₂²×C₃²	semidirect
420. C₄×D₄	C₂²×C₃²	semidirect
421. C₄×D₄	C₂²×C₃²	semidirect
422. C₄×D₄	C₂²×C₃²	semidirect
423. #117	C₂²×C₃²	semidirect
424. #117	C₂²×C₃²	semidirect
425. #117	C₂²×C₃²	semidirect
426. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
427. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
428. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
429. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
432. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
433. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
434. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
435. C₂×C₄²	C₂²×C₃²	semidirect
444. C₂³×C₃	C₃×#41	semidirect
589. C₃²	#3505	direct (N × H)
598. C₂³	C₃²×#41	semidirect
677. C₃	C₃×#3505	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#553	2
C₃²×#552	2
C₃²×#551	2
C₃²×#548	2
C₃²×#546	2
C₃²×#539	2
C₃²×#538	2
C₃²×#534	2
C₃²×#529	2
C₃²×#525	2
C₂×C₃²×C₂²⋊Q₈	2
C₂×C₃²×#121	2
C₃²×#518	2
C₂×C₃²×C₄×D₄	2
C₃×#3505	3

Subgroups — C32×#3505 #11770554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3505 #11770554