Subgroups — #86717

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	#5829	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#947	C₂	1	1	yes	maximal, characteristic, complemented
6	#5681	C₂	1	1	yes	maximal, characteristic, complemented
7	#5678	C₂	1	2	yes	maximal, complemented
8	D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	#5670	C₂	1	2	yes	maximal, complemented
10	#5640	C₂	1	2	yes	maximal, complemented
11	#5637	C₂	1	2	yes	maximal, complemented
12	#5633	C₂	1	1	yes	maximal, characteristic, complemented
13	#5624	C₂	1	1	yes	maximal, characteristic, complemented
14	#5617	C₂	1	2	yes	maximal, complemented
15	#5610	C₂	1	2	yes	maximal, complemented
16	#5609	C₂	1	1	yes	maximal, characteristic, complemented
17	#5600	C₂	1	1	yes	maximal, characteristic, complemented
18	#5580	C₂	1	1	yes	maximal, characteristic, complemented
19	#5568	C₂	1	1	yes	maximal, characteristic, complemented
20	#5556	C₂	1	2	yes	maximal, complemented
21	#5550	C₂	1	1	yes	maximal, characteristic, complemented
22	#5545	C₂	1	2	yes	maximal, complemented
23	C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
24	#3514	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×#237	C₂²	1	1	yes	characteristic
29	C₂×D₃×D₄	C₂²	1	2	yes	—
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₂×#235	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₁₂	C₂²	1	1	yes	characteristic
33	C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×#121	C₂²	1	1	yes	characteristic
38	C₃×#121	C₂²	1	2	yes	complemented
39	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×D₄	C₂²	1	2	yes	complemented
42	#947	C₂²	1	1	yes	characteristic
43	#947	C₂²	1	1	yes	characteristic
44	#947	C₂²	1	1	yes	characteristic, complemented
45	#947	C₂²	1	2	yes	complemented
46	#947	C₂²	1	2	yes	complemented
47	#947	C₂²	1	1	yes	characteristic, complemented
48	#946	C₂²	1	2	yes	complemented
49	#946	C₂²	1	1	yes	characteristic, complemented
50	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
51	#944	C₂²	1	2	yes	complemented
52	#944	C₂²	1	1	yes	characteristic, complemented
53	#940	C₂²	1	1	yes	characteristic
54	#939	C₂²	1	2	yes	complemented
55	#939	C₂²	1	2	yes	complemented
56	#939	C₂²	1	2	yes	complemented
57	#937	C₂²	1	2	yes	—
58	#937	C₂²	1	2	yes	complemented
59	#937	C₂²	1	2	yes	complemented
60	#936	C₂²	1	1	yes	characteristic, complemented
61	#935	C₂²	1	2	yes	complemented
62	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
64	D₄×Dic₃	C₂²	1	2	yes	complemented
65	#930	C₂²	1	1	yes	characteristic
66	#929	C₂²	1	2	yes	complemented
67	C₄×#67	C₂²	1	1	yes	characteristic
68	C₄×#67	C₂²	1	2	yes	—
69	C₄×#67	C₂²	1	1	yes	characteristic, complemented
70	C₄×#67	C₂²	1	2	yes	complemented
71	C₄×#67	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
74	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
75	#924	C₂²	1	1	yes	characteristic, complemented
76	#924	C₂²	1	2	yes	complemented
77	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
79	#898	C₂²	1	2	yes	complemented
80	#898	C₂²	1	2	yes	complemented
81	#898	C₂²	1	2	yes	complemented
82	#896	C₂²	1	2	yes	complemented
83	#896	C₂²	1	2	yes	complemented
84	#895	C₂²	1	1	yes	characteristic
85	#894	C₂²	1	2	yes	complemented
86	#894	C₂²	1	2	yes	complemented
87	#893	C₂²	1	1	yes	characteristic
88	#893	C₂²	1	2	yes	complemented
89	#892	C₂²	1	1	yes	characteristic, complemented
90	#892	C₂²	1	2	yes	complemented
91	#890	C₂²	1	1	yes	characteristic, complemented
92	#887	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	complemented
95	#886	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	complemented
97	#885	C₂²	1	2	yes	complemented
98	#885	C₂²	1	2	yes	complemented
99	#885	C₂²	1	2	yes	complemented
100	#884	C₂²	1	2	yes	—
101	#884	C₂²	1	2	yes	complemented
102	#884	C₂²	1	2	yes	complemented
103	#883	C₂²	1	2	yes	complemented
104	#882	C₂²	1	2	yes	—
105	#67⋊C₄	C₂²	1	1	yes	characteristic
106	#67⋊C₄	C₂²	1	2	yes	complemented
107	#67⋊C₄	C₂²	1	2	yes	complemented
108	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
110	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
111	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	#879	C₂²	1	2	yes	complemented
113	#877	C₂²	1	2	yes	complemented
114	#877	C₂²	1	1	yes	characteristic, complemented
115	#877	C₂²	1	1	yes	characteristic, complemented
116	#876	C₂²	1	2	yes	complemented
117	#875	C₂²	1	1	yes	characteristic
118	C₄×D₁₂	C₂²	1	2	yes	complemented
119	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
120	#872	C₂²	1	2	yes	complemented
121	#872	C₂²	1	2	yes	complemented
122	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#559	—	3	1	no	—
125	#556	—	3	1	no	—
126	#555	—	3	2	no	—
127	#551	—	3	2	no	—
128	#551	—	3	2	no	—
129	D₄×Q₈	—	3	1	no	—
130	#548	—	3	1	no	—
131	#548	D₃	1	1	yes	characteristic, complemented
132	#546	—	3	1	no	—
133	#546	—	3	2	no	—
134	#546	—	3	1	no	—
135	D₄²	—	3	1	no	—
136	#542	—	3	2	no	—
137	#538	—	3	2	no	—
138	#538	—	3	2	no	—
139	#532	—	3	1	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#529	—	3	1	no	—
143	C₂×#124	—	3	1	no	—
144	C₂×#124	—	3	1	no	—
145	#518	—	3	2	no	—
146	C₄×#41	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₃×#41	—	4	2	no	—
150	C₂×C₃×Q₈	—	4	2	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	C₂³	1	2	yes	—
155	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×D₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
161	C₂²×C₃×C₄	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	2	yes	—
166	C₂×#67	C₂³	1	2	yes	—
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	1	yes	characteristic
169	C₂²×Dic₃	C₂³	1	1	yes	characteristic
170	C₂²×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	1	yes	characteristic
173	C₂²×Dic₃	C₂³	1	1	yes	characteristic
174	D₃×Q₈	—	4	2	no	—
175	#237	—	2	4	no	—
176	D₃×D₄	—	2	8	no	—
177	D₃×D₄	—	4	2	no	—
178	#235	—	4	2	no	—
179	C₂×D₁₂	—	4	2	no	—
180	C₂×D₁₂	C₂³	1	2	yes	—
181	C₂×D₁₂	C₂³	1	1	yes	characteristic
182	C₂×D₁₂	C₂³	1	1	yes	characteristic
183	C₂×D₁₂	C₂³	1	2	yes	—
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₄×D₃	C₂³	1	2	yes	—
190	C₂×C₄×D₃	C₂³	1	2	yes	—
191	C₂×Dic₆	C₂³	1	1	yes	characteristic
192	C₂×Dic₆	C₂³	1	1	yes	characteristic
193	C₂×Dic₆	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×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₃×C₄²	C₂³	1	2	yes	—
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	1	yes	characteristic
208	#217	C₂³	1	1	yes	characteristic
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
227	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₃⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₄×Dic₃	C₂³	1	1	yes	characteristic
253	C₄×Dic₃	C₂³	1	2	yes	—
254	C₂×#41	—	3	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂×#41	C₂×D₃	1	1	yes	characteristic, complemented
257	C₂²×Q₈	—	3	1	no	—
258	C₂²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
259	C₂²×D₄	—	3	2	no	—
260	C₂²×D₄	—	3	1	no	—
261	C₂²×D₄	—	3	1	no	—
262	C₄⋊Q₈	—	3	1	no	—
263	C₄⋊Q₈	—	3	2	no	—
264	#127	—	3	1	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#126	—	3	2	no	—
269	#126	—	3	2	no	—
270	#125	—	3	1	no	—
271	#124	—	3	1	no	—
272	#124	—	3	1	no	—
273	#124	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	2	no	—
277	#124	—	3	1	no	—
278	#124	—	3	2	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	—	3	2	no	—
282	#124	—	3	1	no	—
283	#124	C₂×D₃	1	1	yes	characteristic, complemented
284	#124	C₂×D₃	1	2	yes	complemented
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	—	3	2	no	—
289	#123	—	3	2	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
299	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
300	#121	—	3	2	no	—
301	#121	—	3	2	no	—
302	#121	—	3	2	no	—
303	#121	—	3	1	no	—
304	#121	—	3	1	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	2	no	—
308	#121	C₂×D₃	1	1	yes	characteristic
309	#121	C₂×D₃	1	2	yes	complemented
310	#120	—	3	2	no	—
311	#120	—	3	2	no	—
312	#120	—	3	2	no	—
313	#120	—	3	2	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×Q₈	—	3	1	no	—
318	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	2	no	—
326	C₄×D₄	—	3	2	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	1	no	—
329	C₄×D₄	—	3	1	no	—
330	C₄×D₄	—	3	1	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
336	C₄×D₄	C₂×D₃	1	2	yes	complemented
337	#117	—	3	1	no	—
338	#117	—	3	2	no	—
339	#117	—	3	1	no	—
340	#117	—	3	1	no	—
341	#117	—	3	2	no	—
342	#117	—	3	2	no	—
343	#117	—	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×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	—	3	1	no	—
352	C₂×C₄²	—	3	1	no	—
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	2	4	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	—	4	2	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	C₂⁴	1	2	yes	—
363	C₂²×D₃	C₂⁴	1	2	yes	—
364	C₂²×D₃	C₂⁴	1	1	yes	characteristic
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	4	2	no	—
368	C₃×D₄	—	2	4	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	4	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	4	2	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	#67	—	2	2	no	—
385	#67	—	2	4	no	—
386	#67	—	4	2	no	—
387	#67	—	4	2	no	—
388	#67	—	4	2	no	—
389	#67	—	4	2	no	—
390	#67	#41	1	4	yes	complemented
391	C₂×Dic₃	—	2	2	no	—
392	C₂×Dic₃	—	2	2	no	—
393	C₂×Dic₃	—	4	1	no	—
394	C₂×Dic₃	—	4	1	no	—
395	C₂×Dic₃	—	4	2	no	—
396	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃	C₂⁴	1	2	yes	—
403	C₂×Dic₃	C₂⁴	1	2	yes	—
404	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
405	D₁₂	—	2	4	no	—
406	D₁₂	—	2	2	no	—
407	D₁₂	—	2	2	no	—
408	D₁₂	—	4	2	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	2	4	no	—
412	C₄×D₃	—	4	1	no	—
413	C₄×D₃	—	4	2	no	—
414	C₄×D₃	—	4	2	no	—
415	C₄×D₃	—	4	2	no	—
416	Dic₆	—	2	2	no	—
417	Dic₆	—	2	2	no	—
418	Dic₆	—	4	2	no	—
419	C₂⁴	—	3	2	no	—
420	C₂⁴	—	3	2	no	—
421	#41	—	4	2	no	—
422	#41	—	6	4	no	—
423	#41	—	12	2	no	—
424	C₂×Q₈	—	3	1	no	—
425	C₂×Q₈	—	3	1	no	—
426	C₂×Q₈	—	3	2	no	—
427	C₂×Q₈	—	4	2	no	—
428	C₂×Q₈	—	12	2	no	—
429	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
430	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
431	C₂×Q₈	C₂²×D₃	1	2	yes	—
432	C₂×D₄	—	3	1	no	—
433	C₂×D₄	—	3	1	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	3	1	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	6	8	no	—
444	C₂×D₄	—	12	2	no	—
445	C₂×D₄	—	12	2	no	—
446	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
447	C₂×D₄	C₂²×D₃	1	2	yes	—
448	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
449	C₂×D₄	C₂²×D₃	1	2	yes	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	2	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	2	no	—
462	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₃	1	2	yes	—
465	C₂²×C₄	C₂²×D₃	1	2	yes	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	1	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	2	no	—
479	C₄⋊C₄	—	3	2	no	—
480	C₄⋊C₄	C₂²×D₃	1	2	yes	—
481	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₃	1	2	yes	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	1	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	1	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	—	3	1	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	1	no	—
515	C₄²	—	3	1	no	—
516	C₄²	—	3	1	no	—
517	C₄²	—	3	1	no	—
518	C₄²	—	3	1	no	—
519	C₄²	—	3	1	no	—
520	C₄²	—	3	1	no	—
521	C₄²	—	3	1	no	—
522	C₄²	—	3	2	no	—
523	C₄²	—	3	2	no	—
524	C₄²	C₂²×D₃	1	1	yes	characteristic
525	C₄²	C₂²×D₃	1	2	yes	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	1	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	C₂×#41	1	2	yes	—
535	C₂²×C₃	C₂⁵	1	1	yes	characteristic
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	2	no	—
539	C₂×D₃	—	2	2	no	—
540	C₂×D₃	—	2	2	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	2	no	—
543	C₂×D₃	—	2	2	no	—
544	C₂×D₃	—	8	4	no	—
545	C₂×D₃	—	8	4	no	—
546	C₂×D₃	C₂×#41	1	2	yes	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	2	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	H(5,𝔽₂)	1	2	yes	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	2	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	1	no	—
560	Dic₃	—	2	2	no	—
561	Dic₃	—	2	1	no	—
562	Dic₃	—	2	1	no	—
563	Dic₃	C₂×#41	1	2	yes	—
564	C₂³	—	3	1	no	—
565	C₂³	—	3	2	no	—
566	C₂³	—	3	2	no	—
567	C₂³	—	6	4	no	—
568	C₂³	—	6	4	no	—
569	C₂³	—	12	2	no	—
570	C₂³	—	12	2	no	—
571	C₂³	—	12	2	no	—
572	C₂³	—	12	2	no	—
573	C₂³	C₂³×D₃	1	2	yes	—
574	C₂³	C₂³×D₃	1	1	yes	characteristic
575	C₂³	C₂³×D₃	1	1	yes	characteristic
576	Q₈	—	2	2	no	—
577	Q₈	—	2	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	6	2	no	—
580	Q₈	—	6	2	no	—
581	Q₈	—	12	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	3	4	no	—
586	D₄	—	4	2	no	—
587	D₄	—	6	4	no	—
588	D₄	—	6	4	no	—
589	D₄	—	6	2	no	—
590	D₄	—	6	2	no	—
591	D₄	—	6	2	no	—
592	D₄	—	12	2	no	—
593	D₄	—	12	2	no	—
594	D₄	—	12	2	no	—
595	D₄	—	12	2	no	—
596	D₄	—	12	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	3	1	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	1	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	3	1	no	—
605	C₂×C₄	—	3	1	no	—
606	C₂×C₄	—	3	2	no	—
607	C₂×C₄	—	3	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	6	4	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	—	6	2	no	—
613	C₂×C₄	—	6	2	no	—
614	C₂×C₄	—	6	2	no	—
615	C₂×C₄	—	12	2	no	—
616	C₂×C₄	—	12	2	no	—
617	C₂×C₄	—	12	1	no	—
618	C₂×C₄	—	12	2	no	—
619	C₂×C₄	—	12	1	no	—
620	C₂×C₄	—	12	2	no	—
621	C₂×C₄	—	12	1	no	—
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₃	1	2	yes	—
627	C₂×C₄	C₂³×D₃	1	2	yes	—
628	C₂×C₄	C₂³×D₃	1	2	yes	—
629	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
630	C₂×C₃	—	2	2	no	—
631	C₂×C₃	—	4	2	no	—
632	C₂×C₃	—	4	1	no	—
633	C₂×C₃	C₂²×#41	1	1	yes	characteristic
634	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂×C₃	#585	1	1	yes	characteristic
636	D₃	—	2	2	no	—
637	D₃	—	4	2	no	—
638	D₃	—	4	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	3	2	no	—
648	C₂²	—	6	1	no	—
649	C₂²	—	6	1	no	—
650	C₂²	—	6	2	no	—
651	C₂²	—	6	2	no	—
652	C₂²	—	6	2	no	—
653	C₂²	—	6	2	no	—
654	C₂²	—	6	2	no	—
655	C₂²	—	6	2	no	—
656	C₂²	—	24	4	no	—
657	C₂²	—	24	4	no	—
658	C₂²	D₃×#41	1	2	yes	—
659	C₂²	C₂⁴×D₃	1	1	yes	characteristic
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	3	2	no	—
668	C₄	—	6	1	no	—
669	C₄	—	6	2	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	2	no	—
675	C₄	—	6	1	no	—
676	C₄	#1004	1	2	yes	—
677	C₃	#3514	1	1	yes	characteristic, complemented, Sylow
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	6	2	no	—
682	C₂	—	12	2	no	—
683	C₂	—	12	2	no	—
684	C₂	C₂×#1004	1	1	yes	characteristic
685	C₂	C₂×D₃×#41	1	1	yes	characteristic
686	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#548	C₂
hypercenter	#548	D₃
hypocenter	C₃	#3514
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₃×#548	C₂	semidirect
2. #5832	C₂	semidirect
3. #5829	C₂	semidirect
4. Q₈×#67	C₂	semidirect
5. C₂×#947	C₂	semidirect
6. #5681	C₂	semidirect
7. #5678	C₂	semidirect
8. D₃×#124	C₂	semidirect
9. #5670	C₂	semidirect
10. #5640	C₂	semidirect
11. #5637	C₂	semidirect
12. #5633	C₂	semidirect
13. #5624	C₂	semidirect
14. #5617	C₂	semidirect
15. #5610	C₂	semidirect
16. #5609	C₂	semidirect
17. #5600	C₂	semidirect
18. #5580	C₂	semidirect
19. #5568	C₂	semidirect
20. #5556	C₂	semidirect
21. #5550	C₂	semidirect
22. #5545	C₂	semidirect
23. C₄×#237	C₂	semidirect
25. C₂×C₃×#41	C₂²	semidirect
26. C₂²×C₃×Q₈	C₂²	semidirect
27. C₂×D₃×Q₈	C₂²	semidirect
31. C₂×#235	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
39. C₃×C₄×Q₈	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
44. #947	C₂²	semidirect
45. #947	C₂²	semidirect
46. #947	C₂²	semidirect
47. #947	C₂²	semidirect
48. #946	C₂²	semidirect
49. #946	C₂²	semidirect
50. Q₈×Dic₃	C₂²	semidirect
51. #944	C₂²	semidirect
52. #944	C₂²	semidirect
54. #939	C₂²	semidirect
55. #939	C₂²	semidirect
56. #939	C₂²	semidirect
58. #937	C₂²	semidirect
59. #937	C₂²	semidirect
60. #936	C₂²	semidirect
61. #935	C₂²	semidirect
62. D₄×Dic₃	C₂²	semidirect
63. D₄×Dic₃	C₂²	semidirect
64. D₄×Dic₃	C₂²	semidirect
66. #929	C₂²	semidirect
69. C₄×#67	C₂²	semidirect
70. C₄×#67	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
72. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
73. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
74. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
75. #924	C₂²	semidirect
76. #924	C₂²	semidirect
77. C₂×C₄×Dic₃	C₂²	semidirect
78. C₂×C₄×Dic₃	C₂²	semidirect
79. #898	C₂²	semidirect
80. #898	C₂²	semidirect
81. #898	C₂²	semidirect
82. #896	C₂²	semidirect
83. #896	C₂²	semidirect
85. #894	C₂²	semidirect
86. #894	C₂²	semidirect
88. #893	C₂²	semidirect
89. #892	C₂²	semidirect
90. #892	C₂²	semidirect
91. #890	C₂²	semidirect
92. #887	C₂²	semidirect
93. #887	C₂²	semidirect
94. #886	C₂²	semidirect
95. #886	C₂²	semidirect
96. #885	C₂²	semidirect
97. #885	C₂²	semidirect
98. #885	C₂²	semidirect
99. #885	C₂²	semidirect
101. #884	C₂²	semidirect
102. #884	C₂²	semidirect
103. #883	C₂²	semidirect
106. #67⋊C₄	C₂²	semidirect
107. #67⋊C₄	C₂²	semidirect
108. #67⋊C₄	C₂²	semidirect
109. D₃×C₂²⋊C₄	C₂²	semidirect
110. D₃×C₂²⋊C₄	C₂²	semidirect
111. D₃×C₂²⋊C₄	C₂²	semidirect
112. #879	C₂²	semidirect
113. #877	C₂²	semidirect
114. #877	C₂²	semidirect
115. #877	C₂²	semidirect
116. #876	C₂²	semidirect
118. C₄×D₁₂	C₂²	semidirect
119. C₄×D₁₂	C₂²	semidirect
120. #872	C₂²	semidirect
121. #872	C₂²	semidirect
122. C₄²×D₃	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
131. #548	D₃	semidirect
256. C₂×#41	C₂×D₃	semidirect
258. C₂²×Q₈	C₂×D₃	semidirect
283. #124	C₂×D₃	semidirect
284. #124	C₂×D₃	semidirect
298. C₂²⋊Q₈	C₂×D₃	semidirect
299. C₂²⋊Q₈	C₂×D₃	semidirect
309. #121	C₂×D₃	semidirect
318. C₄×Q₈	C₂×D₃	semidirect
335. C₄×D₄	C₂×D₃	semidirect
336. C₄×D₄	C₂×D₃	semidirect
390. #67	#41	semidirect
677. C₃	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₃×#548	2
#5832	2
#5829	2
Q₈×#67	2
C₂×#947	2
#5681	2
#5678	2
D₃×#124	2
#5670	2
#5640	2
#5637	2
#5633	2
#5624	2
#5617	2
#5610	2
#5609	2
#5600	2
#5580	2
#5568	2
#5556	2
#5550	2
#5545	2
C₄×#237	2
#3514	3