Subgroups — #86949

Order 384.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#5729	C₂	1	1	yes	maximal, characteristic, complemented
3	#5727	C₂	1	1	yes	maximal, characteristic, complemented
4	#5690	C₂	1	1	yes	maximal, characteristic, complemented
5	#5690	C₂	1	1	yes	maximal, characteristic, complemented
6	#5689	C₂	1	1	yes	maximal, characteristic, complemented
7	#5688	C₂	1	1	yes	maximal, characteristic, complemented
8	#5636	C₂	1	2	yes	maximal, complemented
9	#5636	C₂	1	2	yes	maximal, complemented
10	#5634	C₂	1	2	yes	maximal, complemented
11	#5634	C₂	1	2	yes	maximal, complemented
12	#5632	C₂	1	2	yes	maximal, complemented
13	D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	#5579	C₂	1	1	yes	maximal, characteristic, complemented
15	#5578	C₂	1	1	yes	maximal, characteristic, complemented
16	#5545	C₂	1	1	yes	maximal, characteristic
17	#5545	C₂	1	1	yes	maximal, characteristic
18	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
19	#5539	C₂	1	1	yes	maximal, characteristic, complemented
20	#5539	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
22	#5511	C₂	1	2	yes	maximal, complemented
23	C₂×#896	C₂	1	2	yes	maximal, complemented
24	#3501	—	3	1	no	maximal, Sylow
25	C₂×D₃×Q₈	C₂²	1	2	yes	complemented
26	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₃	C₂²	1	2	yes	—
28	C₂²×Dic₆	C₂²	1	2	yes	complemented
29	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
40	#946	C₂²	1	1	yes	characteristic
41	#946	C₂²	1	2	yes	—
42	#946	C₂²	1	2	yes	complemented
43	#946	C₂²	1	2	yes	complemented
44	#944	C₂²	1	2	yes	complemented
45	#944	C₂²	1	1	yes	characteristic, complemented
46	D₄×Dic₃	C₂²	1	1	yes	characteristic
47	D₄×Dic₃	C₂²	1	1	yes	characteristic
48	D₄×Dic₃	C₂²	1	1	yes	characteristic
49	C₄×#67	C₂²	1	2	yes	—
50	C₄×#67	C₂²	1	2	yes	—
51	C₄×#67	C₂²	1	2	yes	—
52	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
53	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
54	#924	C₂²	1	2	yes	complemented
55	#924	C₂²	1	2	yes	complemented
56	#924	C₂²	1	2	yes	complemented
57	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
58	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
59	#897	C₂²	1	1	yes	characteristic
60	#897	C₂²	1	2	yes	—
61	#897	C₂²	1	2	yes	complemented
62	#897	C₂²	1	2	yes	complemented
63	#896	C₂²	1	2	yes	—
64	#896	C₂²	1	2	yes	—
65	#896	C₂²	1	2	yes	—
66	#896	C₂²	1	2	yes	—
67	#896	C₂²	1	1	yes	characteristic
68	#896	C₂²	1	1	yes	characteristic
69	#896	C₂²	1	2	yes	complemented
70	#896	C₂²	1	2	yes	complemented
71	#896	C₂²	1	2	yes	complemented
72	#896	C₂²	1	2	yes	complemented
73	#896	C₂²	1	2	yes	complemented
74	#896	C₂²	1	2	yes	complemented
75	#896	C₂²	1	2	yes	complemented
76	#896	C₂²	1	2	yes	complemented
77	#893	C₂²	1	1	yes	characteristic
78	#893	C₂²	1	1	yes	characteristic
79	#893	C₂²	1	1	yes	characteristic
80	#892	C₂²	1	1	yes	characteristic
81	#892	C₂²	1	1	yes	characteristic
82	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
84	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
85	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
86	#890	C₂²	1	1	yes	characteristic, complemented
87	#890	C₂²	1	1	yes	characteristic, complemented
88	#889	C₂²	1	2	yes	complemented
89	#889	C₂²	1	1	yes	characteristic, complemented
90	#889	C₂²	1	2	yes	complemented
91	#889	C₂²	1	1	yes	characteristic, complemented
92	#888	C₂²	1	1	yes	characteristic, complemented
93	#888	C₂²	1	2	yes	complemented
94	#888	C₂²	1	1	yes	characteristic, complemented
95	#888	C₂²	1	1	yes	characteristic, complemented
96	#888	C₂²	1	1	yes	characteristic, complemented
97	#888	C₂²	1	1	yes	characteristic, complemented
98	#887	C₂²	1	2	yes	complemented
99	#887	C₂²	1	2	yes	complemented
100	#67⋊C₄	C₂²	1	2	yes	—
101	#67⋊C₄	C₂²	1	2	yes	—
102	#67⋊C₄	C₂²	1	2	yes	—
103	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	#878	C₂²	1	2	yes	complemented
107	#878	C₂²	1	2	yes	complemented
108	#878	C₂²	1	2	yes	complemented
109	#878	C₂²	1	2	yes	complemented
110	#878	C₂²	1	2	yes	complemented
111	#878	C₂²	1	2	yes	complemented
112	C₄×D₁₂	C₂²	1	1	yes	characteristic
113	C₄×D₁₂	C₂²	1	1	yes	characteristic
114	C₄×D₁₂	C₂²	1	1	yes	characteristic
115	#872	C₂²	1	1	yes	characteristic
116	#872	C₂²	1	1	yes	characteristic
117	C₄²×D₃	C₂²	1	1	yes	characteristic
118	#870	C₂²	1	1	yes	characteristic, complemented
119	#870	C₂²	1	1	yes	characteristic, complemented
120	#869	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#554	—	3	1	no	—
125	#554	—	3	1	no	—
126	#554	—	3	2	no	—
127	#554	—	3	2	no	—
128	#554	—	3	1	no	—
129	#554	—	3	1	no	—
130	#554	—	3	1	no	—
131	#554	—	3	2	no	—
132	#554	D₃	1	1	yes	characteristic, complemented
133	D₄×Q₈	—	3	1	no	—
134	D₄×Q₈	—	3	2	no	—
135	D₄×Q₈	—	3	1	no	—
136	#544	—	3	1	no	—
137	#544	—	3	1	no	—
138	#543	—	3	2	no	—
139	#543	—	3	2	no	—
140	#533	—	3	1	no	—
141	#533	—	3	1	no	—
142	C₂×C₂²⋊Q₈	—	3	2	no	—
143	C₂×C₂²⋊Q₈	—	3	2	no	—
144	#518	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	C₂³	1	2	yes	—
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂³	1	2	yes	—
152	C₂²×C₃×C₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	C₂³	1	2	yes	—
154	C₂×#67	C₂³	1	2	yes	—
155	C₂²×Dic₃	C₂³	1	2	yes	—
156	C₂²×Dic₃	C₂³	1	2	yes	—
157	C₂²×Dic₃	C₂³	1	2	yes	—
158	D₃×Q₈	—	4	4	no	—
159	D₃×D₄	Q₈	1	8	yes	complemented
160	C₂×D₁₂	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₃	—	4	4	no	—
162	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₃	C₂³	1	2	yes	—
164	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂³	1	2	yes	—
166	C₂×C₄×D₃	C₂³	1	2	yes	—
167	C₂×C₄×D₃	C₂³	1	2	yes	—
168	C₂×C₄×D₃	C₂³	1	2	yes	—
169	C₂×C₄×D₃	C₂³	1	2	yes	—
170	C₂×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
172	C₂×Dic₆	—	4	4	no	—
173	C₂×Dic₆	C₂³	1	1	yes	characteristic
174	C₂×Dic₆	C₂³	1	1	yes	characteristic
175	C₂×Dic₆	C₂³	1	2	yes	—
176	C₂×Dic₆	C₂³	1	1	yes	characteristic
177	C₂×Dic₆	C₂³	1	2	yes	—
178	C₂×Dic₆	C₂³	1	2	yes	—
179	C₂×Dic₆	C₂³	1	2	yes	—
180	C₂×Dic₆	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄²	C₂³	1	1	yes	characteristic
196	C₃×C₄²	C₂³	1	1	yes	characteristic
197	C₃×C₄²	C₂³	1	1	yes	characteristic
198	#217	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₃	C₂³	1	2	yes	—
221	C₄⋊Dic₃	C₂³	1	2	yes	—
222	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₂²×Q₈	—	3	2	no	—
251	C₂²×Q₈	—	3	2	no	—
252	C₂²×D₄	—	3	1	no	—
253	C₂³×C₄	—	3	2	no	—
254	C₄⋊Q₈	—	3	1	no	—
255	C₄⋊Q₈	—	3	2	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	C₄⋊Q₈	—	3	1	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	2	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	—	3	1	no	—
262	C₄⋊Q₈	—	3	1	no	—
263	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
264	#125	—	3	1	no	—
265	#125	—	3	1	no	—
266	#125	—	3	2	no	—
267	#125	—	3	2	no	—
268	#125	—	3	1	no	—
269	#125	—	3	1	no	—
270	#125	—	3	1	no	—
271	#125	—	3	1	no	—
272	#125	C₂×D₃	1	1	yes	characteristic, complemented
273	#125	C₂×D₃	1	1	yes	characteristic, complemented
274	C₂²⋊Q₈	—	3	2	no	—
275	C₂²⋊Q₈	—	3	1	no	—
276	C₂²⋊Q₈	—	3	2	no	—
277	C₂²⋊Q₈	—	3	2	no	—
278	C₂²⋊Q₈	—	3	2	no	—
279	C₂²⋊Q₈	—	3	2	no	—
280	C₂²⋊Q₈	—	3	2	no	—
281	C₂²⋊Q₈	—	3	1	no	—
282	C₂²⋊Q₈	—	3	2	no	—
283	C₂²⋊Q₈	—	3	1	no	—
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	2	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
306	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
307	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
308	C₄×Q₈	—	3	2	no	—
309	C₄×Q₈	—	3	2	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×Q₈	—	3	1	no	—
313	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	1	no	—
316	C₄×D₄	—	3	1	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	2	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	C₂×D₃	1	1	yes	characteristic
330	C₄×D₄	C₂×D₃	1	1	yes	characteristic
331	C₄×D₄	C₂×D₃	1	1	yes	characteristic
332	#117	—	3	1	no	—
333	#117	—	3	1	no	—
334	#117	—	3	1	no	—
335	#117	—	3	1	no	—
336	C₂×C₄⋊C₄	—	3	2	no	—
337	C₂×C₄⋊C₄	—	3	2	no	—
338	C₂×C₄⋊C₄	—	3	1	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	2	no	—
342	C₂×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂³×C₃	C₂⁴	1	2	yes	—
350	C₂²×D₃	—	4	2	no	—
351	C₂²×D₃	—	4	2	no	—
352	C₂²×D₃	C₂×Q₈	1	8	yes	complemented
353	C₂²×D₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	C₂⁴	1	2	yes	—
355	C₃×Q₈	—	4	2	no	—
356	C₃×Q₈	—	4	1	no	—
357	C₃×D₄	C₂×Q₈	1	4	yes	complemented
358	C₂×C₃×C₄	—	4	2	no	—
359	C₂×C₃×C₄	—	4	2	no	—
360	C₂×C₃×C₄	—	4	2	no	—
361	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂⁴	1	2	yes	—
364	C₂×C₃×C₄	C₂⁴	1	2	yes	—
365	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴	1	2	yes	—
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	#67	C₂×Q₈	1	8	yes	complemented
372	C₂×Dic₃	—	2	4	no	—
373	C₂×Dic₃	—	4	2	no	—
374	C₂×Dic₃	—	4	2	no	—
375	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₃	C₂⁴	1	2	yes	—
378	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₃	C₂⁴	1	2	yes	—
381	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₃	C₂⁴	1	2	yes	—
383	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
385	D₁₂	C₂×Q₈	1	4	yes	complemented
386	C₄×D₃	—	2	2	no	—
387	C₄×D₃	—	2	4	no	—
388	C₄×D₃	—	4	2	no	—
389	C₄×D₃	—	4	2	no	—
390	C₄×D₃	—	4	1	no	—
391	C₄×D₃	—	4	2	no	—
392	C₄×D₃	—	4	2	no	—
393	C₄×D₃	—	4	2	no	—
394	C₄×D₃	—	4	2	no	—
395	C₄×D₃	C₂×Q₈	1	4	yes	complemented
396	Dic₆	—	2	2	no	—
397	Dic₆	—	2	4	no	—
398	Dic₆	—	2	2	no	—
399	Dic₆	—	4	2	no	—
400	Dic₆	—	4	2	no	—
401	Dic₆	—	4	2	no	—
402	Dic₆	—	4	1	no	—
403	Dic₆	—	4	2	no	—
404	C₂⁴	—	3	2	no	—
405	C₂×Q₈	—	3	2	no	—
406	C₂×Q₈	—	3	1	no	—
407	C₂×Q₈	—	3	1	no	—
408	C₂×Q₈	—	3	2	no	—
409	C₂×Q₈	—	3	1	no	—
410	C₂×Q₈	—	3	2	no	—
411	C₂×Q₈	—	3	2	no	—
412	C₂×Q₈	—	3	2	no	—
413	C₂×Q₈	—	12	4	no	—
414	C₂×Q₈	—	12	4	no	—
415	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
416	C₂×Q₈	C₂²×D₃	1	2	yes	—
417	C₂×D₄	—	3	2	no	—
418	C₂×D₄	—	3	8	no	—
419	C₂×D₄	—	3	1	no	—
420	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
421	C₂²×C₄	—	3	1	no	—
422	C₂²×C₄	—	3	2	no	—
423	C₂²×C₄	—	3	2	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	3	1	no	—
426	C₂²×C₄	—	3	2	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	2	no	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	12	4	no	—
435	C₂²×C₄	C₂²×D₃	1	2	yes	—
436	C₂²×C₄	C₂²×D₃	1	2	yes	—
437	C₂²×C₄	C₂²×D₃	1	2	yes	—
438	C₄⋊C₄	—	3	1	no	—
439	C₄⋊C₄	—	3	2	no	—
440	C₄⋊C₄	—	3	1	no	—
441	C₄⋊C₄	—	3	2	no	—
442	C₄⋊C₄	—	3	1	no	—
443	C₄⋊C₄	—	3	1	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	3	1	no	—
446	C₄⋊C₄	—	3	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	2	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	1	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₃	1	2	yes	—
470	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×D₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×D₃	1	2	yes	—
474	C₄⋊C₄	C₂²×D₃	1	2	yes	—
475	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	1	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
496	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
497	C₄²	—	3	1	no	—
498	C₄²	—	3	1	no	—
499	C₄²	—	3	1	no	—
500	C₄²	—	3	2	no	—
501	C₄²	—	3	2	no	—
502	C₄²	—	3	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	C₂²×D₃	1	1	yes	characteristic
505	C₄²	C₂²×D₃	1	1	yes	characteristic
506	C₄²	C₂²×D₃	1	1	yes	characteristic
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	2	no	—
509	C₂²×C₃	C₂²×Q₈	1	4	yes	—
510	C₂²×C₃	C₂⁵	1	1	yes	characteristic
511	C₂×D₃	—	2	2	no	—
512	C₂×D₃	—	2	1	no	—
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	2	1	no	—
515	C₂×D₃	—	4	8	no	—
516	C₂×D₃	C₂²×Q₈	1	2	yes	—
517	C₂×D₃	C₂²×Q₈	1	4	yes	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	C₂²×Q₈	1	2	yes	—
528	Dic₃	—	2	1	no	—
529	Dic₃	—	2	2	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	2	no	—
532	Dic₃	—	2	1	no	—
533	Dic₃	—	2	1	no	—
534	Dic₃	—	2	2	no	—
535	Dic₃	—	2	1	no	—
536	Dic₃	C₂²×Q₈	1	2	yes	—
537	Dic₃	H(5,𝔽₂)	1	2	yes	—
538	C₂³	—	3	1	no	—
539	C₂³	—	3	2	no	—
540	C₂³	—	3	8	no	—
541	C₂³	—	12	2	no	—
542	C₂³	—	12	2	no	—
543	C₂³	C₂³×D₃	1	2	yes	—
544	Q₈	—	4	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	6	2	no	—
547	Q₈	—	6	4	no	—
548	Q₈	—	6	2	no	—
549	Q₈	—	12	2	no	—
550	Q₈	—	12	2	no	—
551	Q₈	—	12	2	no	—
552	Q₈	—	12	2	no	—
553	Q₈	—	12	1	no	—
554	D₄	—	3	8	no	—
555	D₄	—	3	4	no	—
556	D₄	D₃×Q₈	1	4	yes	complemented
557	C₂×C₄	—	3	1	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	3	4	no	—
560	C₂×C₄	—	3	1	no	—
561	C₂×C₄	—	3	1	no	—
562	C₂×C₄	—	3	2	no	—
563	C₂×C₄	—	3	1	no	—
564	C₂×C₄	—	3	1	no	—
565	C₂×C₄	—	3	2	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	3	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	6	2	no	—
572	C₂×C₄	—	6	4	no	—
573	C₂×C₄	—	6	4	no	—
574	C₂×C₄	—	12	2	no	—
575	C₂×C₄	—	12	2	no	—
576	C₂×C₄	—	12	2	no	—
577	C₂×C₄	—	12	2	no	—
578	C₂×C₄	—	12	2	no	—
579	C₂×C₄	—	12	2	no	—
580	C₂×C₄	—	12	1	no	—
581	C₂×C₄	—	12	2	no	—
582	C₂×C₄	—	12	2	no	—
583	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₃	1	2	yes	—
586	C₂×C₄	C₂³×D₃	1	2	yes	—
587	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₃	1	2	yes	—
592	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
593	C₂×C₃	—	2	4	no	—
594	C₂×C₃	C₂³×Q₈	1	1	yes	characteristic
595	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂×C₃	#585	1	1	yes	characteristic
597	D₃	—	2	2	no	—
598	D₃	—	2	4	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	3	2	no	—
602	C₂²	—	3	4	no	—
603	C₂²	—	6	2	no	—
604	C₂²	—	6	1	no	—
605	C₂²	—	6	2	no	—
606	C₂²	—	6	1	no	—
607	C₂²	—	12	8	no	—
608	C₂²	C₂×D₃×Q₈	1	4	yes	—
609	C₂²	C₂⁴×D₃	1	1	yes	characteristic
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	3	2	no	—
620	C₄	—	3	2	no	—
621	C₄	—	6	1	no	—
622	C₄	—	6	2	no	—
623	C₄	—	6	1	no	—
624	C₄	—	6	1	no	—
625	C₄	—	6	2	no	—
626	C₄	—	6	1	no	—
627	C₄	—	6	2	no	—
628	C₄	—	6	1	no	—
629	C₄	C₂×D₃×Q₈	1	2	yes	—
630	C₃	#3501	1	1	yes	characteristic, complemented, Sylow
631	C₂	—	2	4	no	—
632	C₂	—	6	2	no	—
633	C₂	—	6	4	no	—
634	C₂	C₂²×D₃×Q₈	1	1	yes	characteristic
635	C₂	#5964	1	1	yes	characteristic
636	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#554	C₂
prime radical	C₂×D₃×D₄	C₂²
hypercenter	#554	D₃
hypocenter	C₃	#3501
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₃×#554	C₂	semidirect
2. #5729	C₂	semidirect
3. #5727	C₂	semidirect
4. #5690	C₂	semidirect
5. #5690	C₂	semidirect
6. #5689	C₂	semidirect
7. #5688	C₂	semidirect
8. #5636	C₂	semidirect
9. #5636	C₂	semidirect
10. #5634	C₂	semidirect
11. #5634	C₂	semidirect
12. #5632	C₂	semidirect
13. D₃×C₂²⋊Q₈	C₂	semidirect
14. #5579	C₂	semidirect
15. #5578	C₂	semidirect
19. #5539	C₂	semidirect
20. #5539	C₂	semidirect
21. D₄×Dic₆	C₂	semidirect
22. #5511	C₂	semidirect
23. C₂×#896	C₂	semidirect
25. C₂×D₃×Q₈	C₂²	semidirect
28. C₂²×Dic₆	C₂²	semidirect
29. C₃×C₄⋊Q₈	C₂²	semidirect
30. C₃×#125	C₂²	semidirect
31. C₃×#125	C₂²	semidirect
32. C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₃×C₂²⋊Q₈	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
35. C₃×C₄×Q₈	C₂²	semidirect
39. C₂×C₃×C₄⋊C₄	C₂²	semidirect
42. #946	C₂²	semidirect
43. #946	C₂²	semidirect
44. #944	C₂²	semidirect
45. #944	C₂²	semidirect
54. #924	C₂²	semidirect
55. #924	C₂²	semidirect
56. #924	C₂²	semidirect
57. C₂×Dic₃⋊C₄	C₂²	semidirect
58. C₂×Dic₃⋊C₄	C₂²	semidirect
61. #897	C₂²	semidirect
62. #897	C₂²	semidirect
69. #896	C₂²	semidirect
70. #896	C₂²	semidirect
71. #896	C₂²	semidirect
72. #896	C₂²	semidirect
73. #896	C₂²	semidirect
74. #896	C₂²	semidirect
75. #896	C₂²	semidirect
76. #896	C₂²	semidirect
83. D₃×C₄⋊C₄	C₂²	semidirect
84. D₃×C₄⋊C₄	C₂²	semidirect
85. D₃×C₄⋊C₄	C₂²	semidirect
86. #890	C₂²	semidirect
87. #890	C₂²	semidirect
88. #889	C₂²	semidirect
89. #889	C₂²	semidirect
90. #889	C₂²	semidirect
91. #889	C₂²	semidirect
92. #888	C₂²	semidirect
93. #888	C₂²	semidirect
94. #888	C₂²	semidirect
95. #888	C₂²	semidirect
96. #888	C₂²	semidirect
97. #888	C₂²	semidirect
98. #887	C₂²	semidirect
99. #887	C₂²	semidirect
106. #878	C₂²	semidirect
107. #878	C₂²	semidirect
108. #878	C₂²	semidirect
109. #878	C₂²	semidirect
110. #878	C₂²	semidirect
111. #878	C₂²	semidirect
118. #870	C₂²	semidirect
119. #870	C₂²	semidirect
120. #869	C₂²	semidirect
121. C₄×Dic₆	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
132. #554	D₃	semidirect
159. D₃×D₄	Q₈	semidirect
263. C₄⋊Q₈	C₂×D₃	semidirect
272. #125	C₂×D₃	semidirect
273. #125	C₂×D₃	semidirect
305. C₂²⋊Q₈	C₂×D₃	semidirect
306. C₂²⋊Q₈	C₂×D₃	semidirect
307. C₂²⋊Q₈	C₂×D₃	semidirect
313. C₄×Q₈	C₂×D₃	semidirect
342. C₂×C₄⋊C₄	C₂×D₃	semidirect
352. C₂²×D₃	C₂×Q₈	semidirect
357. C₃×D₄	C₂×Q₈	semidirect
371. #67	C₂×Q₈	semidirect
385. D₁₂	C₂×Q₈	semidirect
395. C₄×D₃	C₂×Q₈	semidirect
556. D₄	D₃×Q₈	semidirect
630. C₃	#3501	semidirect

Maximal subgroups

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

subgroup	index
C₃×#554	2
#5729	2
#5727	2
#5690	2
#5689	2
#5688	2
#5636	2
#5634	2
#5632	2
D₃×C₂²⋊Q₈	2
#5579	2
#5578	2
#5545	2
C₄×D₃×D₄	2
#5539	2
D₄×Dic₆	2
#5511	2
C₂×#896	2
#3501	3