Subgroups — C₃×C₄×#554 #10652774

Order 768.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₃×#2370	C₂	1	2	yes	maximal, complemented
3	C₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2368	C₂	1	4	yes	maximal, complemented
5	C₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2349	C₂	1	2	yes	maximal
8	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₃×#2345	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#125	C₂	1	2	yes	maximal, complemented
12	C₃×C₄×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
13	C₃×C₄×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₃×C₄²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄²×D₄	C₂	1	2	yes	maximal
16	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
17	C₂×C₃×C₄×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
18	C₄×#554	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#554	C₄	1	16	yes	direct product factor
20	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×#125	C₂²	1	2	yes	—
22	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₃×C₄²	C₂²	1	2	yes	—
36	C₂²×C₃×C₄²	C₂²	1	4	yes	—
37	C₃×#391	C₂²	1	2	yes	—
38	C₃×#391	C₂²	1	2	yes	—
39	C₃×#391	C₂²	1	4	yes	—
40	C₃×#389	C₂²	1	4	yes	—
41	C₃×#389	C₂²	1	2	yes	—
42	C₃×#389	C₂²	1	2	yes	—
43	C₃×#389	C₂²	1	2	yes	—
44	C₃×#389	C₂²	1	2	yes	—
45	C₃×#389	C₂²	1	2	yes	—
46	C₃×#387	C₂²	1	4	yes	—
47	C₃×#387	C₂²	1	4	yes	—
48	C₃×#387	C₂²	1	4	yes	—
49	C₃×#387	C₂²	1	4	yes	—
50	C₃×#387	C₂²	1	4	yes	—
51	C₃×#385	C₂²	1	4	yes	—
52	C₃×#385	C₂²	1	4	yes	—
53	C₃×#385	C₂²	1	4	yes	—
54	C₃×#384	C₂²	1	1	yes	characteristic
55	C₃×#382	C₂²	1	2	yes	—
56	C₃×#380	C₂²	1	2	yes	—
57	C₃×#380	C₂²	1	4	yes	—
58	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
59	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
60	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
61	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
62	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
66	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
67	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
69	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
70	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
71	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
73	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
76	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
77	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₂×C₃×#95	C₂²	1	4	yes	—
83	C₃×C₄³	C₂²	1	2	yes	—
84	C₃×C₄³	C₂²	1	1	yes	characteristic
85	C₂×#554	C₂×C₃	1	1	yes	characteristic
86	#2370	C₂×C₃	1	2	yes	complemented
87	#2369	C₂×C₃	1	1	yes	characteristic, complemented
88	#2368	C₂×C₃	1	4	yes	complemented
89	#2360	C₂×C₃	1	2	yes	complemented
90	#2355	C₂×C₃	1	1	yes	characteristic, complemented
91	#2349	C₂×C₃	1	2	yes	—
92	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
93	#2345	C₂×C₃	1	2	yes	complemented
94	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×#125	C₂×C₃	1	2	yes	complemented
96	C₄×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
97	C₄×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
98	C₄²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
99	C₄²×D₄	C₂×C₃	1	2	yes	—
100	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
101	C₂×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
102	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Q₈	C₂³	1	2	yes	—
104	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂³	1	2	yes	—
106	C₂³×C₃×C₄	C₂³	1	4	yes	—
107	C₂³×C₃×C₄	C₂³	1	2	yes	—
108	C₂³×C₃×C₄	C₂³	1	2	yes	—
109	C₂³×C₃×C₄	C₂³	1	4	yes	—
110	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
111	C₃×#125	C₂×C₄	1	16	yes	complemented
112	C₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
113	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
114	C₃×C₄×Q₈	—	2	4	no	—
115	C₃×C₄×Q₈	—	2	4	no	—
116	C₃×C₄×Q₈	—	4	4	no	—
117	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
118	C₃×C₄×D₄	—	2	8	no	—
119	C₃×C₄×D₄	—	2	4	no	—
120	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
121	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
122	C₃×C₄×D₄	Q₈	1	8	yes	complemented
123	C₂×C₃×C₄⋊C₄	—	2	8	no	—
124	C₂×C₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
125	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄²	—	2	8	no	—
150	C₂×C₃×C₄²	—	4	8	no	—
151	C₂×C₃×C₄²	C₂³	1	2	yes	—
152	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄²	C₂³	1	2	yes	—
154	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄²	C₂³	1	2	yes	—
156	C₂×C₃×C₄²	C₂³	1	2	yes	—
157	C₂×C₃×C₄²	C₂³	1	2	yes	—
158	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂³	1	2	yes	—
160	C₂×C₃×C₄²	C₂³	1	2	yes	—
161	C₂×C₃×C₄²	C₂³	1	4	yes	—
162	C₂×C₃×C₄²	C₂³	1	2	yes	—
163	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄²	C₂³	1	4	yes	—
165	C₂×C₃×C₄²	C₂³	1	4	yes	—
166	C₂×C₃×C₄²	C₂³	1	2	yes	—
167	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
170	C₃×#95	C₂³	1	2	yes	—
171	C₃×#95	C₂³	1	4	yes	—
172	C₃×#95	C₂³	1	4	yes	—
173	C₃×#95	C₂³	1	4	yes	—
174	C₃×#95	C₂³	1	2	yes	—
175	C₃×#95	C₂³	1	2	yes	—
176	C₃×#95	C₂³	1	4	yes	—
177	C₃×#95	C₂³	1	4	yes	—
178	C₃×#95	C₂³	1	4	yes	—
179	C₃×#95	C₂³	1	2	yes	—
180	C₃×#95	C₂³	1	2	yes	—
181	C₃×#95	C₂³	1	2	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	4	yes	—
184	#554	C₃×C₄	1	16	yes	direct product factor
185	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
186	C₂×#125	C₂²×C₃	1	2	yes	—
187	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
188	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
189	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
192	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
193	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
194	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
196	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
197	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
198	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
200	C₂²×C₄²	C₂²×C₃	1	2	yes	—
201	C₂²×C₄²	C₂²×C₃	1	4	yes	—
202	#391	C₂²×C₃	1	2	yes	—
203	#391	C₂²×C₃	1	2	yes	—
204	#391	C₂²×C₃	1	4	yes	—
205	#389	C₂²×C₃	1	2	yes	—
206	#389	C₂²×C₃	1	2	yes	—
207	#389	C₂²×C₃	1	2	yes	—
208	#389	C₂²×C₃	1	2	yes	—
209	#389	C₂²×C₃	1	2	yes	—
210	#389	C₂²×C₃	1	4	yes	—
211	#387	C₂²×C₃	1	4	yes	—
212	#387	C₂²×C₃	1	4	yes	—
213	#387	C₂²×C₃	1	4	yes	—
214	#387	C₂²×C₃	1	4	yes	—
215	#387	C₂²×C₃	1	4	yes	—
216	#385	C₂²×C₃	1	4	yes	—
217	#385	C₂²×C₃	1	4	yes	—
218	#385	C₂²×C₃	1	4	yes	—
219	#384	C₂²×C₃	1	1	yes	characteristic
220	#382	C₂²×C₃	1	2	yes	—
221	#380	C₂²×C₃	1	2	yes	—
222	#380	C₂²×C₃	1	4	yes	—
223	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
225	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
226	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
227	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
234	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
237	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
238	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
245	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
246	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
247	C₂×#95	C₂²×C₃	1	4	yes	—
248	C₄³	C₂²×C₃	1	2	yes	—
249	C₄³	C₂²×C₃	1	1	yes	characteristic
250	C₂⁴×C₃	C₂⁴	1	2	yes	—
251	C₂×C₃×Q₈	—	2	2	no	—
252	C₂×C₃×Q₈	—	2	2	no	—
253	C₂×C₃×Q₈	—	4	2	no	—
254	C₂×C₃×Q₈	—	4	2	no	—
255	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
256	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
257	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
258	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
259	C₂×C₃×D₄	#41	1	4	yes	—
260	C₂²×C₃×C₄	—	2	4	no	—
261	C₂²×C₃×C₄	—	2	4	no	—
262	C₂²×C₃×C₄	—	2	4	no	—
263	C₂²×C₃×C₄	—	2	4	no	—
264	C₂²×C₃×C₄	—	2	4	no	—
265	C₂²×C₃×C₄	—	2	8	no	—
266	C₂²×C₃×C₄	—	2	4	no	—
267	C₂²×C₃×C₄	—	2	8	no	—
268	C₂²×C₃×C₄	—	4	4	no	—
269	C₂²×C₃×C₄	—	4	4	no	—
270	C₂²×C₃×C₄	—	4	4	no	—
271	C₂²×C₃×C₄	—	4	2	no	—
272	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
273	C₂²×C₃×C₄	C₂²×C₄	1	16	yes	—
274	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
275	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
276	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
277	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
278	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
280	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
281	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
284	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
286	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
288	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
289	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
291	C₃×C₄⋊C₄	—	2	8	no	—
292	C₃×C₄⋊C₄	—	2	4	no	—
293	C₃×C₄⋊C₄	—	2	2	no	—
294	C₃×C₄⋊C₄	—	2	4	no	—
295	C₃×C₄⋊C₄	—	2	4	no	—
296	C₃×C₄⋊C₄	—	2	4	no	—
297	C₃×C₄⋊C₄	—	2	2	no	—
298	C₃×C₄⋊C₄	—	4	4	no	—
299	C₃×C₄⋊C₄	—	4	4	no	—
300	C₃×C₄⋊C₄	—	4	2	no	—
301	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
302	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
303	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
304	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
305	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
306	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
307	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
308	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
309	C₃×C₄⋊C₄	#41	1	4	yes	—
310	C₃×C₂²⋊C₄	—	2	8	no	—
311	C₃×C₂²⋊C₄	—	2	4	no	—
312	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
313	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
314	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
315	C₃×C₄²	—	2	4	no	—
316	C₃×C₄²	—	2	4	no	—
317	C₃×C₄²	—	2	4	no	—
318	C₃×C₄²	—	2	2	no	—
319	C₃×C₄²	—	2	4	no	—
320	C₃×C₄²	—	2	4	no	—
321	C₃×C₄²	—	2	2	no	—
322	C₃×C₄²	—	2	4	no	—
323	C₃×C₄²	—	2	4	no	—
324	C₃×C₄²	—	2	8	no	—
325	C₃×C₄²	—	2	2	no	—
326	C₃×C₄²	—	4	4	no	—
327	C₃×C₄²	—	4	4	no	—
328	C₃×C₄²	—	4	1	no	—
329	C₃×C₄²	—	4	2	no	—
330	C₃×C₄²	C₂²×C₄	1	8	yes	—
331	C₃×C₄²	C₂²×C₄	1	4	yes	—
332	C₃×C₄²	C₂×Q₈	1	4	yes	—
333	C₃×C₄²	#41	1	4	yes	—
334	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
335	C₂²×Q₈	C₂³×C₃	1	2	yes	—
336	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₃	1	4	yes	—
338	C₂³×C₄	C₂³×C₃	1	2	yes	—
339	C₂³×C₄	C₂³×C₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₃	1	2	yes	—
341	C₂³×C₄	C₂³×C₃	1	4	yes	—
342	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
343	#125	C₂×C₃×C₄	1	16	yes	complemented
344	C₂²⋊Q₈	C₂×C₃×C₄	1	32	yes	complemented
345	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	—	4	4	no	—
349	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
350	C₄×D₄	—	2	8	no	—
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
353	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
354	C₄×D₄	C₃×Q₈	1	8	yes	complemented
355	C₂×C₄⋊C₄	—	2	8	no	—
356	C₂×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
357	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
381	C₂×C₄²	—	2	8	no	—
382	C₂×C₄²	—	4	8	no	—
383	C₂×C₄²	C₂³×C₃	1	2	yes	—
384	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₃	1	2	yes	—
387	C₂×C₄²	C₂³×C₃	1	2	yes	—
388	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₃	1	4	yes	—
390	C₂×C₄²	C₂³×C₃	1	2	yes	—
391	C₂×C₄²	C₂³×C₃	1	2	yes	—
392	C₂×C₄²	C₂³×C₃	1	2	yes	—
393	C₂×C₄²	C₂³×C₃	1	2	yes	—
394	C₂×C₄²	C₂³×C₃	1	2	yes	—
395	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₃	1	4	yes	—
397	C₂×C₄²	C₂³×C₃	1	4	yes	—
398	C₂×C₄²	C₂³×C₃	1	2	yes	—
399	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
402	#95	C₂³×C₃	1	2	yes	—
403	#95	C₂³×C₃	1	4	yes	—
404	#95	C₂³×C₃	1	4	yes	—
405	#95	C₂³×C₃	1	4	yes	—
406	#95	C₂³×C₃	1	2	yes	—
407	#95	C₂³×C₃	1	2	yes	—
408	#95	C₂³×C₃	1	4	yes	—
409	#95	C₂³×C₃	1	4	yes	—
410	#95	C₂³×C₃	1	4	yes	—
411	#95	C₂³×C₃	1	2	yes	—
412	#95	C₂³×C₃	1	2	yes	—
413	#95	C₂³×C₃	1	2	yes	—
414	#95	C₂³×C₃	1	4	yes	—
415	#95	C₂³×C₃	1	4	yes	—
416	C₂³×C₃	—	2	2	no	—
417	C₂³×C₃	—	2	2	no	—
418	C₂³×C₃	—	2	2	no	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	C₂³×C₄	1	4	yes	—
421	C₂³×C₃	C₂²×Q₈	1	4	yes	—
422	C₂³×C₃	C₂×#41	1	4	yes	—
423	C₂³×C₃	C₂⁵	1	1	yes	characteristic
424	C₃×Q₈	—	2	8	no	—
425	C₃×Q₈	—	4	8	no	—
426	C₃×D₄	C₄×Q₈	1	16	yes	complemented
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	2	2	no	—
429	C₂×C₃×C₄	—	2	2	no	—
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	2	no	—
435	C₂×C₃×C₄	—	2	2	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	4	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	4	no	—
445	C₂×C₃×C₄	—	2	16	no	—
446	C₂×C₃×C₄	—	2	16	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	2	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	4	no	—
454	C₂×C₃×C₄	—	2	4	no	—
455	C₂×C₃×C₄	—	2	4	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	2	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	4	16	no	—
460	C₂×C₃×C₄	—	4	8	no	—
461	C₂×C₃×C₄	—	4	16	no	—
462	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
463	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
464	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
465	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
466	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
467	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
468	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
469	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
470	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
471	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
472	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
473	C₂×C₃×C₄	C₂×#41	1	2	yes	—
474	C₂×C₃×C₄	C₂×#41	1	4	yes	—
475	C₂×C₃×C₄	C₂×#41	1	2	yes	—
476	C₂×C₃×C₄	C₂×#41	1	2	yes	—
477	C₂×C₃×C₄	C₂×#41	1	2	yes	—
478	C₂×C₃×C₄	C₂×#41	1	2	yes	—
479	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
480	C₂⁴	C₂⁴×C₃	1	2	yes	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
486	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
487	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
488	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
489	C₂×D₄	C₃×#41	1	4	yes	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
503	C₂²×C₄	C₂²×C₃×C₄	1	16	yes	—
504	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
505	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
508	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	4	no	—
531	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
532	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
533	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
534	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
535	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
536	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
537	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
538	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
539	C₄⋊C₄	C₃×#41	1	4	yes	—
540	C₂²⋊C₄	—	2	8	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
543	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
544	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
545	C₄²	—	2	4	no	—
546	C₄²	—	2	4	no	—
547	C₄²	—	2	4	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	4	no	—
550	C₄²	—	2	4	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	2	8	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	4	4	no	—
557	C₄²	—	4	4	no	—
558	C₄²	—	4	1	no	—
559	C₄²	—	4	2	no	—
560	C₄²	C₂²×C₃×C₄	1	8	yes	—
561	C₄²	C₂²×C₃×C₄	1	4	yes	—
562	C₄²	C₂×C₃×Q₈	1	4	yes	—
563	C₄²	C₃×#41	1	4	yes	—
564	C₂²×C₃	—	2	4	no	—
565	C₂²×C₃	—	2	4	no	—
566	C₂²×C₃	—	2	4	no	—
567	C₂²×C₃	—	2	4	no	—
568	C₂²×C₃	—	2	4	no	—
569	C₂²×C₃	—	2	4	no	—
570	C₂²×C₃	C₂×C₄×Q₈	1	8	yes	—
571	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
572	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
573	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
574	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
575	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
576	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂²×C₃	#585	1	1	yes	characteristic
578	C₃×C₄	—	2	4	no	—
579	C₃×C₄	—	2	4	no	—
580	C₃×C₄	—	2	4	no	—
581	C₃×C₄	—	2	8	no	—
582	C₃×C₄	—	2	2	no	—
583	C₃×C₄	—	2	4	no	—
584	C₃×C₄	—	2	2	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	4	no	—
587	C₃×C₄	—	4	2	no	—
588	C₃×C₄	—	4	2	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	4	no	—
591	C₃×C₄	C₂×C₄×Q₈	1	4	yes	—
592	C₃×C₄	C₄×#41	1	4	yes	—
593	C₃×C₄	#554	1	4	yes	direct product factor
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	C₂³×C₃×C₄	1	4	yes	—
599	C₂³	C₂²×C₃×Q₈	1	4	yes	—
600	C₂³	C₂×C₃×#41	1	4	yes	—
601	C₂³	C₂⁵×C₃	1	1	yes	characteristic
602	Q₈	—	2	8	no	—
603	Q₈	—	4	8	no	—
604	D₄	C₃×C₄×Q₈	1	16	yes	complemented
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	16	no	—
624	C₂×C₄	—	2	16	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	4	16	no	—
638	C₂×C₄	—	4	8	no	—
639	C₂×C₄	—	4	16	no	—
640	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
641	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
642	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
643	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
644	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
645	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
646	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
647	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
648	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
649	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
650	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
651	C₂×C₄	C₂×C₃×#41	1	2	yes	—
652	C₂×C₄	C₂×C₃×#41	1	4	yes	—
653	C₂×C₄	C₂×C₃×#41	1	2	yes	—
654	C₂×C₄	C₂×C₃×#41	1	2	yes	—
655	C₂×C₄	C₂×C₃×#41	1	2	yes	—
656	C₂×C₄	C₂×C₃×#41	1	2	yes	—
657	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
658	C₂×C₃	—	2	8	no	—
659	C₂×C₃	C₂²×C₄×Q₈	1	1	yes	characteristic
660	C₂×C₃	C₂×C₄×#41	1	1	yes	characteristic
661	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂×C₃	C₂×#554	1	1	yes	characteristic
663	C₂×C₃	#3475	1	1	yes	characteristic
664	C₂×C₃	Q₈×#41	1	1	yes	characteristic
665	C₂×C₃	#3481	1	1	yes	characteristic
666	C₂²	—	2	4	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	C₂×C₃×C₄×Q₈	1	8	yes	—
673	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
674	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
675	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
676	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
677	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
678	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²	C₃×#585	1	1	yes	characteristic
680	C₄	—	2	4	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	8	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	4	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	1	no	—
693	C₄	C₂×C₃×C₄×Q₈	1	4	yes	—
694	C₄	C₃×C₄×#41	1	4	yes	—
695	C₄	C₃×#554	1	4	yes	direct product factor
696	C₃	C₄×#554	1	1	yes	characteristic, direct product factor, Sylow
697	C₂	—	2	8	no	—
698	C₂	C₂²×C₃×C₄×Q₈	1	1	yes	characteristic
699	C₂	C₂×C₃×C₄×#41	1	1	yes	characteristic
700	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂	C₂×C₃×#554	1	1	yes	characteristic
702	C₂	C₃×#3475	1	1	yes	characteristic
703	C₂	C₃×Q₈×#41	1	1	yes	characteristic
704	C₂	C₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
socle	C₂³×C₃	C₂⁵
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2370	C₂	semidirect
3. C₃×#2369	C₂	semidirect
4. C₃×#2368	C₂	semidirect
5. C₃×#2360	C₂	semidirect
6. C₃×#2355	C₂	semidirect
9. C₃×#2345	C₂	semidirect
10. C₃×C₄×C₄⋊Q₈	C₂	semidirect
11. C₃×C₄×#125	C₂	semidirect
12. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
13. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
14. C₃×C₄²×Q₈	C₂	semidirect
17. C₂×C₃×C₄×C₄⋊C₄	C₂	semidirect
18. C₄×#554	C₃	direct (N × H)
19. C₃×#554	C₄	direct (N × H)
86. #2370	C₂×C₃	semidirect
87. #2369	C₂×C₃	semidirect
88. #2368	C₂×C₃	semidirect
89. #2360	C₂×C₃	semidirect
90. #2355	C₂×C₃	semidirect
93. #2345	C₂×C₃	semidirect
94. C₄×C₄⋊Q₈	C₂×C₃	semidirect
95. C₄×#125	C₂×C₃	semidirect
96. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
97. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
98. C₄²×Q₈	C₂×C₃	semidirect
101. C₂×C₄×C₄⋊C₄	C₂×C₃	semidirect
110. C₃×C₄⋊Q₈	C₂×C₄	semidirect
111. C₃×#125	C₂×C₄	semidirect
112. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
113. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
117. C₃×C₄×Q₈	C₂×C₄	semidirect
122. C₃×C₄×D₄	Q₈	semidirect
124. C₂×C₃×C₄⋊C₄	C₂×C₄	semidirect
184. #554	C₃×C₄	direct (N × H)
342. C₄⋊Q₈	C₂×C₃×C₄	semidirect
343. #125	C₂×C₃×C₄	semidirect
344. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
345. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
349. C₄×Q₈	C₂×C₃×C₄	semidirect
354. C₄×D₄	C₃×Q₈	semidirect
356. C₂×C₄⋊C₄	C₂×C₃×C₄	semidirect
426. C₃×D₄	C₄×Q₈	semidirect
593. C₃×C₄	#554	direct (N × H)
604. D₄	C₃×C₄×Q₈	semidirect
695. C₄	C₃×#554	direct (N × H)
696. C₃	C₄×#554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#554	2
C₃×#2370	2
C₃×#2369	2
C₃×#2368	2
C₃×#2360	2
C₃×#2355	2
C₃×#2349	2
C₃×D₄×C₄⋊C₄	2
C₃×#2345	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#125	2
C₃×C₄×C₂²⋊Q₈	2
C₃×C₄²×Q₈	2
C₃×C₄²×D₄	2
C₂×C₃×C₄×C₄⋊C₄	2
C₄×#554	3

Subgroups — C3×C4×#554 #10652774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#554 #10652774