Subgroups — #86678

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	#5832	C₂	1	2	yes	maximal, complemented
3	#5829	C₂	1	2	yes	maximal, complemented
4	#5734	C₂	1	1	yes	maximal, characteristic, complemented
5	#5729	C₂	1	1	yes	maximal, characteristic, complemented
6	#5663	C₂	1	2	yes	maximal, complemented
7	#5659	C₂	1	2	yes	maximal, complemented
8	#5654	C₂	1	2	yes	maximal, complemented
9	#5649	C₂	1	2	yes	maximal, complemented
10	#5640	C₂	1	2	yes	maximal, complemented
11	#5637	C₂	1	2	yes	maximal, complemented
12	#5618	C₂	1	1	yes	maximal, characteristic, complemented
13	#5616	C₂	1	1	yes	maximal, characteristic, complemented
14	#5607	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#5565	C₂	1	1	yes	maximal, characteristic, complemented
17	#5558	C₂	1	1	yes	maximal, characteristic, complemented
18	#5547	C₂	1	1	yes	maximal, characteristic, complemented
19	#5545	C₂	1	1	yes	maximal, characteristic, complemented
20	#5514	C₂	1	1	yes	maximal, characteristic, complemented
21	#5507	C₂	1	1	yes	maximal, characteristic, complemented
22	#5504	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#892	C₂	1	1	yes	maximal, characteristic, complemented
24	#3494	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	2	yes	complemented
26	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×D₃×D₄	C₂²	1	2	yes	—
28	C₂×#235	C₂²	1	1	yes	characteristic
29	C₂×#235	C₂²	1	2	yes	complemented
30	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×#123	C₂²	1	2	yes	complemented
33	C₃×#123	C₂²	1	2	yes	complemented
34	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#947	C₂²	1	2	yes	complemented
42	#947	C₂²	1	2	yes	complemented
43	#946	C₂²	1	2	yes	—
44	#944	C₂²	1	2	yes	complemented
45	#940	C₂²	1	2	yes	complemented
46	#939	C₂²	1	2	yes	—
47	#939	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	complemented
49	#939	C₂²	1	1	yes	characteristic, complemented
50	#939	C₂²	1	2	yes	complemented
51	#938	C₂²	1	1	yes	characteristic
52	#938	C₂²	1	1	yes	characteristic, complemented
53	#937	C₂²	1	2	yes	—
54	#937	C₂²	1	1	yes	characteristic
55	#936	C₂²	1	2	yes	complemented
56	D₄×Dic₃	C₂²	1	2	yes	complemented
57	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	#930	C₂²	1	1	yes	characteristic
59	#930	C₂²	1	2	yes	complemented
60	#930	C₂²	1	1	yes	characteristic, complemented
61	#929	C₂²	1	2	yes	complemented
62	#929	C₂²	1	2	yes	complemented
63	C₄×#67	C₂²	1	2	yes	—
64	C₄×#67	C₂²	1	2	yes	complemented
65	C₄×#67	C₂²	1	2	yes	complemented
66	C₄×#67	C₂²	1	2	yes	complemented
67	C₄×#67	C₂²	1	2	yes	complemented
68	C₄×#67	C₂²	1	1	yes	characteristic, complemented
69	C₄×#67	C₂²	1	1	yes	characteristic, complemented
70	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
71	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
72	#926	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄×Dic₃	C₂²	1	2	yes	complemented
75	#898	C₂²	1	2	yes	complemented
76	#898	C₂²	1	2	yes	complemented
77	#896	C₂²	1	2	yes	—
78	#896	C₂²	1	1	yes	characteristic, complemented
79	#896	C₂²	1	2	yes	complemented
80	#895	C₂²	1	1	yes	characteristic
81	#895	C₂²	1	2	yes	complemented
82	#895	C₂²	1	1	yes	characteristic, complemented
83	#894	C₂²	1	1	yes	characteristic
84	#894	C₂²	1	2	yes	complemented
85	#894	C₂²	1	2	yes	complemented
86	#893	C₂²	1	2	yes	—
87	#893	C₂²	1	1	yes	characteristic, complemented
88	#892	C₂²	1	2	yes	—
89	#892	C₂²	1	1	yes	characteristic
90	#892	C₂²	1	1	yes	characteristic
91	#892	C₂²	1	2	yes	complemented
92	#892	C₂²	1	2	yes	complemented
93	#892	C₂²	1	1	yes	characteristic, complemented
94	#892	C₂²	1	1	yes	characteristic, complemented
95	#892	C₂²	1	1	yes	characteristic, complemented
96	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	#890	C₂²	1	1	yes	characteristic, complemented
99	#889	C₂²	1	2	yes	complemented
100	#888	C₂²	1	1	yes	characteristic, complemented
101	#887	C₂²	1	2	yes	complemented
102	#886	C₂²	1	2	yes	complemented
103	#885	C₂²	1	2	yes	complemented
104	#885	C₂²	1	2	yes	complemented
105	#884	C₂²	1	2	yes	—
106	#884	C₂²	1	2	yes	complemented
107	#884	C₂²	1	1	yes	characteristic, complemented
108	#883	C₂²	1	1	yes	characteristic
109	#883	C₂²	1	2	yes	complemented
110	#882	C₂²	1	2	yes	—
111	#882	C₂²	1	1	yes	characteristic
112	#67⋊C₄	C₂²	1	2	yes	complemented
113	#67⋊C₄	C₂²	1	2	yes	complemented
114	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
115	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	#879	C₂²	1	2	yes	complemented
117	#879	C₂²	1	2	yes	complemented
118	#878	C₂²	1	1	yes	characteristic, complemented
119	#877	C₂²	1	2	yes	complemented
120	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
122	#872	C₂²	1	1	yes	characteristic
123	#870	C₂²	1	1	yes	characteristic, complemented
124	#555	—	3	1	no	—
125	#555	—	3	1	no	—
126	#553	—	3	1	no	—
127	#553	—	3	1	no	—
128	#553	—	3	1	no	—
129	#553	—	3	1	no	—
130	#551	—	3	2	no	—
131	#551	—	3	2	no	—
132	#547	—	3	1	no	—
133	#547	D₃	1	1	yes	characteristic, complemented
134	#546	—	3	2	no	—
135	#546	—	3	2	no	—
136	#544	—	3	1	no	—
137	#542	—	3	2	no	—
138	#540	—	3	2	no	—
139	#535	—	3	1	no	—
140	#532	—	3	2	no	—
141	#529	—	3	2	no	—
142	#525	—	3	1	no	—
143	C₂×#121	—	3	1	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₃×#41	—	4	4	no	—
150	C₂×C₃×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×C₄	C₂³	1	2	yes	—
156	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³	1	2	yes	—
159	C₂²×C₃×C₄	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	1	yes	characteristic
163	C₂×#67	C₂³	1	1	yes	characteristic
164	C₂×#67	C₂³	1	1	yes	characteristic
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	2	yes	—
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	D₃×D₄	—	2	4	no	—
173	D₃×D₄	—	4	4	no	—
174	#235	—	2	4	no	—
175	#235	—	4	4	no	—
176	C₂×D₁₂	C₂³	1	1	yes	characteristic
177	C₂×D₁₂	C₂³	1	1	yes	characteristic
178	C₂×D₁₂	C₂³	1	1	yes	characteristic
179	C₂×D₁₂	C₂³	1	2	yes	—
180	C₂×D₁₂	C₂³	1	2	yes	—
181	C₂×C₄×D₃	—	2	4	no	—
182	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
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	2	yes	—
188	C₂×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₄×D₃	C₂³	1	2	yes	—
190	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
191	C₂×Dic₆	C₂³	1	1	yes	characteristic
192	C₂×Dic₆	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₄²	C₂³	1	1	yes	characteristic
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	1	yes	characteristic
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	1	yes	characteristic
211	#217	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
231	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₄⋊Dic₃	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	2	no	—
254	C₂×#41	C₂×D₃	1	2	yes	complemented
255	C₂²×D₄	—	3	1	no	—
256	C₂²×D₄	—	3	2	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	2	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
261	#127	—	3	2	no	—
262	#126	—	3	2	no	—
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#125	—	3	2	no	—
267	#125	—	3	1	no	—
268	#125	—	3	1	no	—
269	#124	—	3	2	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#123	—	3	2	no	—
275	#123	—	3	2	no	—
276	#123	—	3	1	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	1	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	C₂×D₃	1	2	yes	complemented
283	#123	C₂×D₃	1	2	yes	complemented
284	C₂²⋊Q₈	—	3	2	no	—
285	C₂²⋊Q₈	—	3	1	no	—
286	C₂²⋊Q₈	—	3	2	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
290	#121	—	3	2	no	—
291	#121	—	3	1	no	—
292	#121	—	3	1	no	—
293	#121	—	3	2	no	—
294	#121	—	3	2	no	—
295	#121	—	3	1	no	—
296	#121	—	3	2	no	—
297	#121	—	3	1	no	—
298	#121	—	3	1	no	—
299	#121	—	3	2	no	—
300	#121	—	3	1	no	—
301	#121	—	3	1	no	—
302	#121	—	3	2	no	—
303	#121	—	3	2	no	—
304	#121	—	3	1	no	—
305	#121	—	3	2	no	—
306	#121	C₂×D₃	1	1	yes	characteristic
307	#121	C₂×D₃	1	1	yes	characteristic, complemented
308	#120	—	3	1	no	—
309	#120	—	3	2	no	—
310	#120	—	3	1	no	—
311	#120	—	3	2	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	2	no	—
321	C₄×D₄	—	3	2	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	C₂×D₃	1	1	yes	characteristic, complemented
329	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
330	#117	—	3	1	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	2	no	—
334	#117	—	3	2	no	—
335	#117	—	3	1	no	—
336	#117	—	3	1	no	—
337	#117	—	3	1	no	—
338	#117	—	3	2	no	—
339	#117	—	3	2	no	—
340	#117	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
345	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	2	no	—
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₃	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	4	1	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₃	C₂⁴	1	2	yes	—
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₃	C₂⁴	1	1	yes	characteristic
364	C₃×Q₈	—	4	2	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	4	2	no	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	4	2	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	#67	—	2	2	no	—
383	#67	—	2	4	no	—
384	#67	—	2	2	no	—
385	#67	—	2	2	no	—
386	#67	—	2	4	no	—
387	#67	—	4	2	no	—
388	#67	—	4	1	no	—
389	#67	—	4	2	no	—
390	#67	—	4	2	no	—
391	C₂×Dic₃	—	2	2	no	—
392	C₂×Dic₃	—	4	2	no	—
393	C₂×Dic₃	—	4	2	no	—
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃	C₂⁴	1	2	yes	—
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	D₁₂	—	2	2	no	—
403	D₁₂	—	2	2	no	—
404	D₁₂	—	4	1	no	—
405	D₁₂	—	4	2	no	—
406	D₁₂	—	4	2	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	2	no	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	4	2	no	—
412	C₄×D₃	—	4	2	no	—
413	C₄×D₃	—	4	2	no	—
414	C₄×D₃	—	4	2	no	—
415	C₄×D₃	#41	1	4	yes	complemented
416	Dic₆	—	2	2	no	—
417	Dic₆	—	4	2	no	—
418	C₂⁴	—	3	1	no	—
419	C₂⁴	—	3	2	no	—
420	#41	—	4	4	no	—
421	#41	—	6	4	no	—
422	#41	—	12	4	no	—
423	C₂×Q₈	—	3	1	no	—
424	C₂×Q₈	—	3	2	no	—
425	C₂×Q₈	C₂²×D₃	1	2	yes	—
426	C₂×D₄	—	3	1	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	1	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	3	1	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	2	no	—
440	C₂×D₄	—	6	4	no	—
441	C₂×D₄	—	12	4	no	—
442	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
443	C₂×D₄	C₂²×D₃	1	2	yes	—
444	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
445	C₂×D₄	C₂²×D₃	1	2	yes	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	2	no	—
449	C₂²×C₄	—	3	2	no	—
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	2	no	—
456	C₂²×C₄	—	3	2	no	—
457	C₂²×C₄	—	3	2	no	—
458	C₂²×C₄	—	6	4	no	—
459	C₂²×C₄	C₂²×D₃	1	2	yes	—
460	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₃	1	2	yes	—
463	C₂²×C₄	C₂²×D₃	1	2	yes	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
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	2	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	2	no	—
479	C₄⋊C₄	—	3	1	no	—
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×D₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₃	1	2	yes	—
486	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	1	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	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	2	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	1	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	1	no	—
508	C₂²⋊C₄	—	3	1	no	—
509	C₂²⋊C₄	—	3	1	no	—
510	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
515	C₄²	—	3	2	no	—
516	C₄²	—	3	2	no	—
517	C₄²	—	3	2	no	—
518	C₄²	—	3	2	no	—
519	C₄²	—	3	2	no	—
520	C₄²	—	3	2	no	—
521	C₄²	—	3	1	no	—
522	C₄²	C₂²×D₃	1	1	yes	characteristic
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
532	C₂²×C₃	C₂⁵	1	1	yes	characteristic
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	2	1	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	2	1	no	—
539	C₂×D₃	—	2	2	no	—
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	2	1	no	—
544	C₂×D₃	—	4	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	1	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	C₂×#41	1	2	yes	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	2	no	—
559	Dic₃	—	2	2	no	—
560	Dic₃	—	2	1	no	—
561	Dic₃	—	2	2	no	—
562	Dic₃	C₂×#41	1	2	yes	—
563	C₂³	—	3	1	no	—
564	C₂³	—	3	2	no	—
565	C₂³	—	3	1	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	6	2	no	—
568	C₂³	—	6	4	no	—
569	C₂³	—	6	2	no	—
570	C₂³	—	12	1	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	—	4	2	no	—
577	Q₈	—	6	2	no	—
578	Q₈	—	12	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	6	2	no	—
584	D₄	—	6	4	no	—
585	D₄	—	6	2	no	—
586	D₄	—	6	2	no	—
587	D₄	—	6	4	no	—
588	D₄	—	6	2	no	—
589	D₄	—	6	2	no	—
590	D₄	—	12	2	no	—
591	D₄	—	12	2	no	—
592	D₄	—	12	1	no	—
593	D₄	—	12	2	no	—
594	D₄	—	12	1	no	—
595	D₄	—	12	2	no	—
596	D₄	—	12	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	3	4	no	—
602	C₂×C₄	—	3	1	no	—
603	C₂×C₄	—	3	2	no	—
604	C₂×C₄	—	3	1	no	—
605	C₂×C₄	—	3	2	no	—
606	C₂×C₄	—	3	1	no	—
607	C₂×C₄	—	3	1	no	—
608	C₂×C₄	—	3	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	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	—	6	2	no	—
616	C₂×C₄	—	12	2	no	—
617	C₂×C₄	—	12	2	no	—
618	C₂×C₄	—	12	2	no	—
619	C₂×C₄	—	12	2	no	—
620	C₂×C₄	—	12	2	no	—
621	C₂×C₄	—	12	2	no	—
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	2	yes	—
624	C₂×C₄	C₂³×D₃	1	2	yes	—
625	C₂×C₄	C₂³×D₃	1	2	yes	—
626	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
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	1	no	—
638	D₃	—	4	1	no	—
639	D₃	—	4	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	3	2	no	—
649	C₂²	—	6	1	no	—
650	C₂²	—	6	1	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	2	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	6	1	no	—
655	C₂²	—	6	1	no	—
656	C₂²	—	6	2	no	—
657	C₂²	—	6	2	no	—
658	C₂²	—	6	1	no	—
659	C₂²	—	6	1	no	—
660	C₂²	—	12	4	no	—
661	C₂²	—	24	4	no	—
662	C₂²	#1004	1	2	yes	—
663	C₂²	C₂⁴×D₃	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	3	2	no	—
672	C₄	—	6	2	no	—
673	C₄	—	6	1	no	—
674	C₄	—	6	1	no	—
675	C₄	—	6	1	no	—
676	C₄	—	6	2	no	—
677	C₄	—	6	1	no	—
678	C₄	—	6	2	no	—
679	C₄	D₃×#41	1	2	yes	—
680	C₃	#3494	1	1	yes	characteristic, complemented, Sylow
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	6	2	no	—
685	C₂	—	12	1	no	—
686	C₂	—	12	2	no	—
687	C₂	—	12	1	no	—
688	C₂	C₂×#1004	1	1	yes	characteristic
689	C₂	C₂×D₃×#41	1	1	yes	characteristic
690	C₂	#5968	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#547	C₂
hypercenter	#547	D₃
hypocenter	C₃	#3494
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₃×#547	C₂	semidirect
2. #5832	C₂	semidirect
3. #5829	C₂	semidirect
4. #5734	C₂	semidirect
5. #5729	C₂	semidirect
6. #5663	C₂	semidirect
7. #5659	C₂	semidirect
8. #5654	C₂	semidirect
9. #5649	C₂	semidirect
10. #5640	C₂	semidirect
11. #5637	C₂	semidirect
12. #5618	C₂	semidirect
13. #5616	C₂	semidirect
14. #5607	C₂	semidirect
15. D₃×#121	C₂	semidirect
16. #5565	C₂	semidirect
17. #5558	C₂	semidirect
18. #5547	C₂	semidirect
19. #5545	C₂	semidirect
20. #5514	C₂	semidirect
21. #5507	C₂	semidirect
22. #5504	C₂	semidirect
23. C₂×#892	C₂	semidirect
25. C₂×C₃×#41	C₂²	semidirect
29. C₂×#235	C₂²	semidirect
31. C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#123	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
34. C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
37. C₃×C₄×D₄	C₂²	semidirect
38. C₃×C₄×D₄	C₂²	semidirect
39. C₂×C₃×C₄⋊C₄	C₂²	semidirect
40. C₂×C₃×C₄⋊C₄	C₂²	semidirect
41. #947	C₂²	semidirect
42. #947	C₂²	semidirect
44. #944	C₂²	semidirect
45. #940	C₂²	semidirect
47. #939	C₂²	semidirect
48. #939	C₂²	semidirect
49. #939	C₂²	semidirect
50. #939	C₂²	semidirect
52. #938	C₂²	semidirect
55. #936	C₂²	semidirect
56. D₄×Dic₃	C₂²	semidirect
57. D₄×Dic₃	C₂²	semidirect
59. #930	C₂²	semidirect
60. #930	C₂²	semidirect
61. #929	C₂²	semidirect
62. #929	C₂²	semidirect
64. C₄×#67	C₂²	semidirect
65. C₄×#67	C₂²	semidirect
66. C₄×#67	C₂²	semidirect
67. C₄×#67	C₂²	semidirect
68. C₄×#67	C₂²	semidirect
69. C₄×#67	C₂²	semidirect
72. #926	C₂²	semidirect
73. C₂×C₄⋊Dic₃	C₂²	semidirect
74. C₂×C₄×Dic₃	C₂²	semidirect
75. #898	C₂²	semidirect
76. #898	C₂²	semidirect
78. #896	C₂²	semidirect
79. #896	C₂²	semidirect
81. #895	C₂²	semidirect
82. #895	C₂²	semidirect
84. #894	C₂²	semidirect
85. #894	C₂²	semidirect
87. #893	C₂²	semidirect
91. #892	C₂²	semidirect
92. #892	C₂²	semidirect
93. #892	C₂²	semidirect
94. #892	C₂²	semidirect
95. #892	C₂²	semidirect
97. D₃×C₄⋊C₄	C₂²	semidirect
98. #890	C₂²	semidirect
99. #889	C₂²	semidirect
100. #888	C₂²	semidirect
101. #887	C₂²	semidirect
102. #886	C₂²	semidirect
103. #885	C₂²	semidirect
104. #885	C₂²	semidirect
106. #884	C₂²	semidirect
107. #884	C₂²	semidirect
109. #883	C₂²	semidirect
112. #67⋊C₄	C₂²	semidirect
113. #67⋊C₄	C₂²	semidirect
116. #879	C₂²	semidirect
117. #879	C₂²	semidirect
118. #878	C₂²	semidirect
119. #877	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. C₄×D₁₂	C₂²	semidirect
123. #870	C₂²	semidirect
133. #547	D₃	semidirect
254. C₂×#41	C₂×D₃	semidirect
260. C₄⋊Q₈	C₂×D₃	semidirect
282. #123	C₂×D₃	semidirect
283. #123	C₂×D₃	semidirect
289. C₂²⋊Q₈	C₂×D₃	semidirect
307. #121	C₂×D₃	semidirect
328. C₄×D₄	C₂×D₃	semidirect
329. C₄×D₄	C₂×D₃	semidirect
344. C₂×C₄⋊C₄	C₂×D₃	semidirect
345. C₂×C₄⋊C₄	C₂×D₃	semidirect
415. C₄×D₃	#41	semidirect
680. C₃	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₃×#547	2
#5832	2
#5829	2
#5734	2
#5729	2
#5663	2
#5659	2
#5654	2
#5649	2
#5640	2
#5637	2
#5618	2
#5616	2
#5607	2
D₃×#121	2
#5565	2
#5558	2
#5547	2
#5545	2
#5514	2
#5507	2
#5504	2
C₂×#892	2
#3494	3