Subgroups — #86739

Order 384.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 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	#5833	C₂	1	1	yes	maximal, characteristic, complemented
3	#5829	C₂	1	1	yes	maximal, characteristic, complemented
4	#5817	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#946	C₂	1	1	yes	maximal, characteristic, complemented
6	#5684	C₂	1	2	yes	maximal, complemented
7	#5682	C₂	1	1	yes	maximal, characteristic, complemented
8	#5678	C₂	1	2	yes	maximal, complemented
9	#5676	C₂	1	1	yes	maximal, characteristic, complemented
10	#5647	C₂	1	2	yes	maximal, complemented
11	#5635	C₂	1	1	yes	maximal, characteristic, complemented
12	#5634	C₂	1	2	yes	maximal, complemented
13	#5629	C₂	1	1	yes	maximal, characteristic, complemented
14	#5611	C₂	1	1	yes	maximal, characteristic, complemented
15	#5610	C₂	1	2	yes	maximal, complemented
16	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	#5597	C₂	1	2	yes	maximal, complemented
18	#5582	C₂	1	1	yes	maximal, characteristic, complemented
19	#5579	C₂	1	1	yes	maximal, characteristic, complemented
20	#5564	C₂	1	2	yes	maximal, complemented
21	#5555	C₂	1	1	yes	maximal, characteristic, complemented
22	#5554	C₂	1	2	yes	maximal, complemented
23	#5547	C₂	1	1	yes	maximal, characteristic, complemented
24	#3536	—	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×#239	C₂²	1	1	yes	characteristic, complemented
28	C₂×#237	C₂²	1	2	yes	complemented
29	C₂×#237	C₂²	1	2	yes	complemented
30	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
31	C₂×D₃×D₄	C₂²	1	2	yes	—
32	C₂×#235	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
34	C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×#124	C₂²	1	2	yes	complemented
36	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#121	C₂²	1	1	yes	characteristic
39	C₃×#121	C₂²	1	2	yes	complemented
40	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄×D₄	C₂²	1	2	yes	complemented
43	#947	C₂²	1	2	yes	complemented
44	#947	C₂²	1	1	yes	characteristic, complemented
45	#946	C₂²	1	2	yes	—
46	#946	C₂²	1	1	yes	characteristic
47	#946	C₂²	1	1	yes	characteristic
48	#946	C₂²	1	2	yes	complemented
49	#946	C₂²	1	2	yes	complemented
50	#946	C₂²	1	1	yes	characteristic, complemented
51	#946	C₂²	1	1	yes	characteristic, complemented
52	#946	C₂²	1	1	yes	characteristic, complemented
53	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	#939	C₂²	1	2	yes	—
55	#939	C₂²	1	2	yes	complemented
56	#939	C₂²	1	2	yes	complemented
57	#939	C₂²	1	2	yes	complemented
58	#939	C₂²	1	1	yes	characteristic, complemented
59	#938	C₂²	1	1	yes	characteristic
60	#938	C₂²	1	1	yes	characteristic, complemented
61	#937	C₂²	1	2	yes	—
62	#937	C₂²	1	1	yes	characteristic
63	#935	C₂²	1	2	yes	complemented
64	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
65	#930	C₂²	1	1	yes	characteristic
66	#930	C₂²	1	2	yes	complemented
67	#930	C₂²	1	2	yes	complemented
68	#930	C₂²	1	1	yes	characteristic, complemented
69	#929	C₂²	1	2	yes	complemented
70	C₄×#67	C₂²	1	1	yes	characteristic
71	C₄×#67	C₂²	1	1	yes	characteristic, complemented
72	C₄×#67	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
74	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
75	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
77	#924	C₂²	1	2	yes	complemented
78	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
79	#897	C₂²	1	2	yes	—
80	#897	C₂²	1	2	yes	complemented
81	#896	C₂²	1	1	yes	characteristic
82	#896	C₂²	1	2	yes	—
83	#896	C₂²	1	2	yes	complemented
84	#896	C₂²	1	2	yes	complemented
85	#896	C₂²	1	2	yes	complemented
86	#895	C₂²	1	1	yes	characteristic
87	#895	C₂²	1	2	yes	complemented
88	#894	C₂²	1	1	yes	characteristic, complemented
89	#894	C₂²	1	2	yes	complemented
90	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
92	#889	C₂²	1	2	yes	complemented
93	#888	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	complemented
95	#886	C₂²	1	2	yes	complemented
96	#886	C₂²	1	2	yes	complemented
97	#885	C₂²	1	2	yes	complemented
98	#884	C₂²	1	2	yes	—
99	#884	C₂²	1	1	yes	characteristic
100	#884	C₂²	1	2	yes	complemented
101	#884	C₂²	1	2	yes	complemented
102	#884	C₂²	1	2	yes	complemented
103	#883	C₂²	1	2	yes	complemented
104	#883	C₂²	1	2	yes	complemented
105	#883	C₂²	1	1	yes	characteristic, complemented
106	#882	C₂²	1	2	yes	—
107	#882	C₂²	1	1	yes	characteristic
108	#67⋊C₄	C₂²	1	2	yes	—
109	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
110	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
111	#879	C₂²	1	2	yes	complemented
112	#878	C₂²	1	2	yes	complemented
113	#878	C₂²	1	2	yes	complemented
114	#878	C₂²	1	2	yes	complemented
115	#878	C₂²	1	1	yes	characteristic, complemented
116	#876	C₂²	1	2	yes	complemented
117	#875	C₂²	1	2	yes	complemented
118	C₄×D₁₂	C₂²	1	1	yes	characteristic
119	C₄×D₁₂	C₂²	1	2	yes	—
120	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
121	#872	C₂²	1	1	yes	characteristic, complemented
122	#870	C₂²	1	2	yes	complemented
123	#869	C₂²	1	1	yes	characteristic, complemented
124	#562	—	3	2	no	—
125	#562	—	3	2	no	—
126	#554	—	3	1	no	—
127	#554	—	3	1	no	—
128	#548	—	3	1	no	—
129	#548	D₃	1	1	yes	characteristic, complemented
130	#547	—	3	1	no	—
131	#547	—	3	1	no	—
132	#546	—	3	1	no	—
133	#546	—	3	1	no	—
134	#546	—	3	2	no	—
135	#546	—	3	2	no	—
136	#543	—	3	2	no	—
137	#542	—	3	1	no	—
138	#542	—	3	1	no	—
139	#539	—	3	2	no	—
140	#538	—	3	2	no	—
141	#537	—	3	1	no	—
142	#537	—	3	1	no	—
143	#537	—	3	2	no	—
144	#525	—	3	1	no	—
145	C₂×C₂²⋊Q₈	—	3	1	no	—
146	C₂×#121	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₃×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
168	C₂×#67	C₂³	1	1	yes	characteristic
169	C₂×#67	C₂³	1	2	yes	—
170	C₂×#67	C₂³	1	2	yes	—
171	C₂²×Dic₃	C₂³	1	2	yes	—
172	C₂²×Dic₃	C₂³	1	2	yes	—
173	C₂²×Dic₃	C₂³	1	2	yes	—
174	C₂²×Dic₃	C₂³	1	1	yes	characteristic
175	#239	—	4	2	no	—
176	#237	—	4	4	no	—
177	#237	—	4	4	no	—
178	D₃×D₄	—	4	2	no	—
179	D₃×D₄	—	4	4	no	—
180	#235	—	4	2	no	—
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×D₁₂	C₂³	1	2	yes	—
185	C₂×D₁₂	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₃	—	4	2	no	—
187	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₃	C₂³	1	2	yes	—
191	C₂×C₄×D₃	C₂³	1	2	yes	—
192	C₂×C₄×D₃	C₂³	1	2	yes	—
193	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
194	C₂×C₄×D₃	C₂³	1	2	yes	—
195	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
196	C₂×Dic₆	C₂³	1	2	yes	—
197	C₂×Dic₆	C₂³	1	2	yes	—
198	C₂×Dic₆	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₃×C₄²	C₂³	1	2	yes	—
211	#217	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	1	yes	characteristic
215	#217	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	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	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
230	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
231	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
233	C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₃	C₂³	1	2	yes	—
239	C₄⋊Dic₃	C₂³	1	2	yes	—
240	C₄⋊Dic₃	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₃⋊C₄	C₂³	1	2	yes	—
248	Dic₃⋊C₄	C₂³	1	2	yes	—
249	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₃⋊C₄	C₂³	1	2	yes	—
251	Dic₃⋊C₄	C₂³	1	2	yes	—
252	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
253	C₄×Dic₃	C₂³	1	1	yes	characteristic
254	C₄×Dic₃	C₂³	1	2	yes	—
255	C₂×#41	—	3	1	no	—
256	C₂×#41	—	3	2	no	—
257	C₂×#41	—	3	2	no	—
258	C₂×#41	—	3	1	no	—
259	C₂×#41	C₂×D₃	1	1	yes	characteristic, complemented
260	C₂²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
261	C₂²×D₄	—	3	1	no	—
262	C₂²×D₄	—	3	2	no	—
263	C₂³×C₄	—	3	1	no	—
264	C₄⋊Q₈	—	3	1	no	—
265	C₄⋊Q₈	—	3	1	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#125	—	3	2	no	—
269	#125	—	3	2	no	—
270	#124	—	3	2	no	—
271	#124	—	3	1	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	C₂×D₃	1	2	yes	complemented
275	#124	C₂×D₃	1	1	yes	characteristic, complemented
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
278	#123	—	3	1	no	—
279	#123	—	3	2	no	—
280	#123	—	3	1	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	C₂²⋊Q₈	—	3	1	no	—
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	1	no	—
290	C₂²⋊Q₈	—	3	1	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	1	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	1	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
307	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
308	#121	—	3	2	no	—
309	#121	—	3	1	no	—
310	#121	—	3	1	no	—
311	#121	—	3	2	no	—
312	#121	—	3	1	no	—
313	#121	—	3	2	no	—
314	#121	—	3	2	no	—
315	#121	—	3	1	no	—
316	#121	—	3	1	no	—
317	#121	—	3	2	no	—
318	#121	—	3	2	no	—
319	#121	—	3	1	no	—
320	#121	—	3	2	no	—
321	#121	—	3	2	no	—
322	#121	—	3	1	no	—
323	#121	—	3	2	no	—
324	#121	—	3	2	no	—
325	#121	—	3	2	no	—
326	#121	C₂×D₃	1	1	yes	characteristic
327	#121	C₂×D₃	1	2	yes	complemented
328	#120	—	3	1	no	—
329	#120	—	3	2	no	—
330	#120	—	3	1	no	—
331	#120	—	3	2	no	—
332	C₄×Q₈	—	3	1	no	—
333	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	1	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	2	no	—
339	C₄×D₄	—	3	1	no	—
340	C₄×D₄	—	3	2	no	—
341	C₄×D₄	—	3	1	no	—
342	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
343	C₄×D₄	C₂×D₃	1	2	yes	complemented
344	#117	—	3	1	no	—
345	C₂×C₄⋊C₄	—	3	2	no	—
346	C₂×C₄⋊C₄	—	3	1	no	—
347	C₂×C₄⋊C₄	—	3	1	no	—
348	C₂×C₄⋊C₄	—	3	1	no	—
349	C₂×C₄⋊C₄	—	3	1	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₂²⋊C₄	—	3	2	no	—
354	C₂³×C₃	C₂⁴	1	2	yes	—
355	C₂³×C₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	—	2	2	no	—
358	C₂²×D₃	—	2	2	no	—
359	C₂²×D₃	—	2	4	no	—
360	C₂²×D₃	—	4	1	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	—	4	2	no	—
363	C₂²×D₃	C₂⁴	1	1	yes	characteristic
364	C₂²×D₃	C₂⁴	1	2	yes	—
365	C₂²×D₃	C₂⁴	1	1	yes	characteristic
366	C₂²×D₃	C₂⁴	1	1	yes	characteristic
367	C₃×Q₈	—	2	2	no	—
368	C₃×Q₈	—	2	2	no	—
369	C₃×Q₈	—	4	2	no	—
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	4	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	4	2	no	—
377	C₂×C₃×C₄	—	4	2	no	—
378	C₂×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	#67	—	2	4	no	—
387	#67	—	2	2	no	—
388	#67	—	2	2	no	—
389	#67	—	4	1	no	—
390	#67	—	4	1	no	—
391	#67	—	4	2	no	—
392	#67	—	4	2	no	—
393	#67	—	4	2	no	—
394	#67	—	4	2	no	—
395	C₂×Dic₃	—	2	4	no	—
396	C₂×Dic₃	—	4	1	no	—
397	C₂×Dic₃	—	4	2	no	—
398	C₂×Dic₃	—	4	2	no	—
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	2	yes	—
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₃	C₂⁴	1	2	yes	—
406	C₂×Dic₃	C₂⁴	1	2	yes	—
407	D₁₂	—	2	2	no	—
408	D₁₂	—	2	2	no	—
409	D₁₂	—	4	1	no	—
410	D₁₂	—	4	2	no	—
411	D₁₂	—	4	2	no	—
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	2	2	no	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	4	1	no	—
416	C₄×D₃	—	4	1	no	—
417	C₄×D₃	—	4	2	no	—
418	C₄×D₃	—	4	2	no	—
419	C₄×D₃	—	4	2	no	—
420	C₄×D₃	—	4	2	no	—
421	Dic₆	—	4	1	no	—
422	Dic₆	—	4	2	no	—
423	Dic₆	—	4	2	no	—
424	C₂⁴	—	3	1	no	—
425	C₂⁴	—	3	2	no	—
426	#41	—	4	2	no	—
427	#41	—	12	2	no	—
428	#41	—	12	4	no	—
429	#41	—	12	4	no	—
430	#41	—	12	2	no	—
431	C₂×Q₈	—	3	1	no	—
432	C₂×Q₈	—	3	2	no	—
433	C₂×Q₈	—	3	2	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
436	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
437	C₂×Q₈	C₂²×D₃	1	2	yes	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	3	1	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	1	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	1	no	—
448	C₂×D₄	—	3	1	no	—
449	C₂×D₄	—	3	1	no	—
450	C₂×D₄	—	3	2	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	12	2	no	—
453	C₂×D₄	—	12	4	no	—
454	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
456	C₂×D₄	C₂²×D₃	1	2	yes	—
457	C₂×D₄	C₂²×D₃	1	2	yes	—
458	C₂²×C₄	—	3	2	no	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	1	no	—
461	C₂²×C₄	—	3	2	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	3	2	no	—
467	C₂²×C₄	—	3	2	no	—
468	C₂²×C₄	—	3	2	no	—
469	C₂²×C₄	—	3	2	no	—
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	12	2	no	—
472	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₃	1	2	yes	—
475	C₂²×C₄	C₂²×D₃	1	2	yes	—
476	C₄⋊C₄	—	3	1	no	—
477	C₄⋊C₄	—	3	1	no	—
478	C₄⋊C₄	—	3	1	no	—
479	C₄⋊C₄	—	3	2	no	—
480	C₄⋊C₄	—	3	2	no	—
481	C₄⋊C₄	—	3	2	no	—
482	C₄⋊C₄	—	3	2	no	—
483	C₄⋊C₄	—	3	2	no	—
484	C₄⋊C₄	—	3	2	no	—
485	C₄⋊C₄	—	3	2	no	—
486	C₄⋊C₄	—	3	2	no	—
487	C₄⋊C₄	—	3	1	no	—
488	C₄⋊C₄	—	3	1	no	—
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	—	3	1	no	—
492	C₄⋊C₄	—	3	1	no	—
493	C₄⋊C₄	—	3	2	no	—
494	C₄⋊C₄	—	3	2	no	—
495	C₄⋊C₄	—	3	2	no	—
496	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₃	1	2	yes	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	1	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	1	no	—
505	C₂²⋊C₄	—	3	1	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	1	no	—
509	C₂²⋊C₄	—	3	2	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	3	2	no	—
512	C₂²⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	2	no	—
514	C₂²⋊C₄	—	3	2	no	—
515	C₂²⋊C₄	—	3	1	no	—
516	C₂²⋊C₄	—	3	1	no	—
517	C₂²⋊C₄	—	3	2	no	—
518	C₂²⋊C₄	—	3	2	no	—
519	C₂²⋊C₄	—	3	1	no	—
520	C₂²⋊C₄	—	3	2	no	—
521	C₂²⋊C₄	—	3	1	no	—
522	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
526	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
528	C₄²	—	3	1	no	—
529	C₄²	—	3	2	no	—
530	C₄²	C₂²×D₃	1	1	yes	characteristic
531	C₄²	C₂²×D₃	1	2	yes	—
532	C₂²×C₃	—	2	1	no	—
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	2	1	no	—
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	1	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
541	C₂²×C₃	C₂⁵	1	1	yes	characteristic
542	C₂×D₃	—	2	1	no	—
543	C₂×D₃	—	2	1	no	—
544	C₂×D₃	—	2	1	no	—
545	C₂×D₃	—	2	1	no	—
546	C₂×D₃	—	2	1	no	—
547	C₂×D₃	—	2	2	no	—
548	C₂×D₃	—	2	2	no	—
549	C₂×D₃	—	2	1	no	—
550	C₂×D₃	—	2	1	no	—
551	C₂×D₃	—	2	1	no	—
552	C₂×D₃	—	2	2	no	—
553	C₂×D₃	—	4	4	no	—
554	C₂×D₃	—	8	4	no	—
555	C₂×D₃	2₋¹⁺⁴	1	2	yes	—
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	2	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	2	no	—
561	C₃×C₄	—	2	2	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
564	Dic₃	—	2	1	no	—
565	Dic₃	—	2	1	no	—
566	Dic₃	—	2	1	no	—
567	Dic₃	—	2	2	no	—
568	Dic₃	—	2	2	no	—
569	Dic₃	—	2	2	no	—
570	Dic₃	—	2	1	no	—
571	Dic₃	—	2	1	no	—
572	C₂³	—	3	1	no	—
573	C₂³	—	3	1	no	—
574	C₂³	—	3	2	no	—
575	C₂³	—	3	1	no	—
576	C₂³	—	6	2	no	—
577	C₂³	—	6	4	no	—
578	C₂³	—	6	2	no	—
579	C₂³	—	12	1	no	—
580	C₂³	—	12	2	no	—
581	C₂³	—	12	2	no	—
582	C₂³	C₂³×D₃	1	2	yes	—
583	C₂³	C₂³×D₃	1	1	yes	characteristic
584	C₂³	C₂³×D₃	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	12	1	no	—
589	Q₈	—	12	2	no	—
590	Q₈	—	12	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	6	2	no	—
596	D₄	—	6	2	no	—
597	D₄	—	6	4	no	—
598	D₄	—	6	2	no	—
599	D₄	—	6	2	no	—
600	D₄	—	12	2	no	—
601	D₄	—	12	1	no	—
602	D₄	—	12	2	no	—
603	D₄	—	12	2	no	—
604	D₄	—	12	2	no	—
605	D₄	—	12	1	no	—
606	D₄	—	12	1	no	—
607	D₄	—	12	2	no	—
608	D₄	—	12	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	3	1	no	—
612	C₂×C₄	—	3	1	no	—
613	C₂×C₄	—	3	2	no	—
614	C₂×C₄	—	3	1	no	—
615	C₂×C₄	—	3	1	no	—
616	C₂×C₄	—	3	2	no	—
617	C₂×C₄	—	3	2	no	—
618	C₂×C₄	—	3	1	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	6	4	no	—
622	C₂×C₄	—	6	2	no	—
623	C₂×C₄	—	6	2	no	—
624	C₂×C₄	—	6	2	no	—
625	C₂×C₄	—	12	1	no	—
626	C₂×C₄	—	12	1	no	—
627	C₂×C₄	—	12	2	no	—
628	C₂×C₄	—	12	2	no	—
629	C₂×C₄	—	12	2	no	—
630	C₂×C₄	—	12	2	no	—
631	C₂×C₄	—	12	1	no	—
632	C₂×C₄	—	12	2	no	—
633	C₂×C₄	—	12	2	no	—
634	C₂×C₄	C₂³×D₃	1	2	yes	—
635	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₃	1	2	yes	—
637	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₃	1	2	yes	—
639	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
641	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
642	C₂×C₃	—	2	2	no	—
643	C₂×C₃	—	4	2	no	—
644	C₂×C₃	—	4	1	no	—
645	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
646	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
648	D₃	—	2	2	no	—
649	D₃	—	4	1	no	—
650	D₃	—	4	1	no	—
651	D₃	—	4	2	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	3	2	no	—
661	C₂²	—	6	1	no	—
662	C₂²	—	6	1	no	—
663	C₂²	—	6	1	no	—
664	C₂²	—	6	1	no	—
665	C₂²	—	6	2	no	—
666	C₂²	—	6	1	no	—
667	C₂²	—	6	2	no	—
668	C₂²	—	6	1	no	—
669	C₂²	—	6	1	no	—
670	C₂²	—	6	1	no	—
671	C₂²	—	6	2	no	—
672	C₂²	—	12	4	no	—
673	C₂²	—	24	4	no	—
674	C₂²	#1009	1	2	yes	—
675	C₂²	C₂⁴×D₃	1	1	yes	characteristic
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	6	1	no	—
684	C₄	—	6	1	no	—
685	C₄	—	6	1	no	—
686	C₄	—	6	2	no	—
687	C₄	—	6	2	no	—
688	C₄	—	6	2	no	—
689	C₄	—	6	1	no	—
690	C₄	—	6	1	no	—
691	C₄	#1004	1	2	yes	—
692	C₃	#3536	1	1	yes	characteristic, complemented, Sylow
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	6	2	no	—
697	C₂	—	12	1	no	—
698	C₂	—	12	2	no	—
699	C₂	—	12	1	no	—
700	C₂	C₂×#1004	1	1	yes	characteristic
701	C₂	C₂×#1009	1	1	yes	characteristic
702	C₂	D₃×2₋¹⁺⁴	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	#3536
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. #5833	C₂	semidirect
3. #5829	C₂	semidirect
4. #5817	C₂	semidirect
5. C₂×#946	C₂	semidirect
6. #5684	C₂	semidirect
7. #5682	C₂	semidirect
8. #5678	C₂	semidirect
9. #5676	C₂	semidirect
10. #5647	C₂	semidirect
11. #5635	C₂	semidirect
12. #5634	C₂	semidirect
13. #5629	C₂	semidirect
14. #5611	C₂	semidirect
15. #5610	C₂	semidirect
16. D₃×#121	C₂	semidirect
17. #5597	C₂	semidirect
18. #5582	C₂	semidirect
19. #5579	C₂	semidirect
20. #5564	C₂	semidirect
21. #5555	C₂	semidirect
22. #5554	C₂	semidirect
23. #5547	C₂	semidirect
25. C₂×C₃×#41	C₂²	semidirect
26. C₂²×C₃×Q₈	C₂²	semidirect
27. C₂×#239	C₂²	semidirect
28. C₂×#237	C₂²	semidirect
29. C₂×#237	C₂²	semidirect
32. C₂×#235	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₃×#121	C₂²	semidirect
40. C₃×C₄×Q₈	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
42. C₃×C₄×D₄	C₂²	semidirect
43. #947	C₂²	semidirect
44. #947	C₂²	semidirect
48. #946	C₂²	semidirect
49. #946	C₂²	semidirect
50. #946	C₂²	semidirect
51. #946	C₂²	semidirect
52. #946	C₂²	semidirect
53. Q₈×Dic₃	C₂²	semidirect
55. #939	C₂²	semidirect
56. #939	C₂²	semidirect
57. #939	C₂²	semidirect
58. #939	C₂²	semidirect
60. #938	C₂²	semidirect
63. #935	C₂²	semidirect
64. D₄×Dic₃	C₂²	semidirect
66. #930	C₂²	semidirect
67. #930	C₂²	semidirect
68. #930	C₂²	semidirect
69. #929	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
72. C₄×#67	C₂²	semidirect
75. C₂×C₄⋊Dic₃	C₂²	semidirect
76. C₂×C₄⋊Dic₃	C₂²	semidirect
77. #924	C₂²	semidirect
78. C₂×Dic₃⋊C₄	C₂²	semidirect
80. #897	C₂²	semidirect
83. #896	C₂²	semidirect
84. #896	C₂²	semidirect
85. #896	C₂²	semidirect
87. #895	C₂²	semidirect
88. #894	C₂²	semidirect
89. #894	C₂²	semidirect
91. D₃×C₄⋊C₄	C₂²	semidirect
92. #889	C₂²	semidirect
93. #888	C₂²	semidirect
94. #886	C₂²	semidirect
95. #886	C₂²	semidirect
96. #886	C₂²	semidirect
97. #885	C₂²	semidirect
100. #884	C₂²	semidirect
101. #884	C₂²	semidirect
102. #884	C₂²	semidirect
103. #883	C₂²	semidirect
104. #883	C₂²	semidirect
105. #883	C₂²	semidirect
111. #879	C₂²	semidirect
112. #878	C₂²	semidirect
113. #878	C₂²	semidirect
114. #878	C₂²	semidirect
115. #878	C₂²	semidirect
116. #876	C₂²	semidirect
117. #875	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. #872	C₂²	semidirect
122. #870	C₂²	semidirect
123. #869	C₂²	semidirect
129. #548	D₃	semidirect
259. C₂×#41	C₂×D₃	semidirect
260. C₂²×Q₈	C₂×D₃	semidirect
274. #124	C₂×D₃	semidirect
275. #124	C₂×D₃	semidirect
306. C₂²⋊Q₈	C₂×D₃	semidirect
307. C₂²⋊Q₈	C₂×D₃	semidirect
327. #121	C₂×D₃	semidirect
333. C₄×Q₈	C₂×D₃	semidirect
342. C₄×D₄	C₂×D₃	semidirect
343. C₄×D₄	C₂×D₃	semidirect
692. C₃	#3536	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
#5833	2
#5829	2
#5817	2
C₂×#946	2
#5684	2
#5682	2
#5678	2
#5676	2
#5647	2
#5635	2
#5634	2
#5629	2
#5611	2
#5610	2
D₃×#121	2
#5597	2
#5582	2
#5579	2
#5564	2
#5555	2
#5554	2
#5547	2
#3536	3