Subgroups — #86618

Order 384.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
2	#5806	C₂	1	1	yes	maximal, characteristic, complemented
3	#5806	C₂	1	2	yes	maximal, complemented
4	#5805	C₂	1	1	yes	maximal, characteristic, complemented
5	#5804	C₂	1	2	yes	maximal, complemented
6	D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#936	C₂	1	1	yes	maximal, characteristic, complemented
8	#5715	C₂	1	1	yes	maximal, characteristic, complemented
9	#5713	C₂	1	1	yes	maximal, characteristic, complemented
10	#5621	C₂	1	2	yes	maximal, complemented
11	#5613	C₂	1	2	yes	maximal, complemented
12	#5612	C₂	1	1	yes	maximal, characteristic, complemented
13	#5603	C₂	1	1	yes	maximal, characteristic, complemented
14	#5598	C₂	1	1	yes	maximal, characteristic, complemented
15	#5596	C₂	1	1	yes	maximal, characteristic, complemented
16	#5594	C₂	1	2	yes	maximal, complemented
17	#5593	C₂	1	2	yes	maximal, complemented
18	#5593	C₂	1	2	yes	maximal, complemented
19	#5591	C₂	1	2	yes	maximal, complemented
20	#5561	C₂	1	1	yes	maximal, characteristic, complemented
21	#5559	C₂	1	1	yes	maximal, characteristic, complemented
22	#5552	C₂	1	1	yes	maximal, characteristic, complemented
23	#5538	C₂	1	1	yes	maximal, characteristic, complemented
24	#3558	—	3	1	no	maximal, Sylow
25	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
27	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#67	C₂²	1	2	yes	complemented
29	C₂×#237	C₂²	1	1	yes	characteristic, complemented
30	C₂×#237	C₂²	1	2	yes	complemented
31	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×#235	C₂²	1	1	yes	characteristic, complemented
33	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
34	C₃×#127	C₂²	1	1	yes	characteristic
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₃×#121	C₂²	1	2	yes	complemented
38	C₃×#120	C₂²	1	2	yes	complemented
39	C₃×#120	C₂²	1	2	yes	complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	#953	C₂²	1	2	yes	complemented
43	#953	C₂²	1	2	yes	complemented
44	#953	C₂²	1	2	yes	complemented
45	#953	C₂²	1	2	yes	complemented
46	C₂×#217	C₂²	1	2	yes	complemented
47	C₂×#217	C₂²	1	2	yes	complemented
48	C₂×#217	C₂²	1	2	yes	complemented
49	#940	C₂²	1	1	yes	characteristic
50	#940	C₂²	1	1	yes	characteristic, complemented
51	#939	C₂²	1	1	yes	characteristic
52	#939	C₂²	1	2	yes	complemented
53	#939	C₂²	1	2	yes	complemented
54	#939	C₂²	1	2	yes	complemented
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	2	yes	complemented
59	#938	C₂²	1	1	yes	characteristic
60	#938	C₂²	1	2	yes	complemented
61	#938	C₂²	1	2	yes	complemented
62	#938	C₂²	1	2	yes	complemented
63	#937	C₂²	1	2	yes	complemented
64	#937	C₂²	1	2	yes	complemented
65	#937	C₂²	1	2	yes	complemented
66	#937	C₂²	1	2	yes	complemented
67	#936	C₂²	1	1	yes	characteristic, complemented
68	#936	C₂²	1	1	yes	characteristic, complemented
69	#936	C₂²	1	2	yes	complemented
70	#936	C₂²	1	1	yes	characteristic, complemented
71	#936	C₂²	1	1	yes	characteristic, complemented
72	#936	C₂²	1	1	yes	characteristic, complemented
73	#936	C₂²	1	2	yes	complemented
74	#936	C₂²	1	2	yes	complemented
75	#936	C₂²	1	2	yes	complemented
76	#935	C₂²	1	2	yes	complemented
77	#935	C₂²	1	2	yes	complemented
78	#935	C₂²	1	1	yes	characteristic, complemented
79	#935	C₂²	1	2	yes	complemented
80	#935	C₂²	1	2	yes	complemented
81	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₃	C₂²	1	2	yes	complemented
84	D₄×Dic₃	C₂²	1	2	yes	complemented
85	#930	C₂²	1	1	yes	characteristic, complemented
86	#929	C₂²	1	2	yes	complemented
87	#929	C₂²	1	2	yes	complemented
88	C₄×#67	C₂²	1	1	yes	characteristic, complemented
89	C₄×#67	C₂²	1	1	yes	characteristic, complemented
90	C₄×#67	C₂²	1	2	yes	complemented
91	#926	C₂²	1	1	yes	characteristic, complemented
92	#924	C₂²	1	1	yes	characteristic, complemented
93	#924	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
95	#898	C₂²	1	1	yes	characteristic, complemented
96	#897	C₂²	1	1	yes	characteristic, complemented
97	#896	C₂²	1	2	yes	complemented
98	#893	C₂²	1	1	yes	characteristic, complemented
99	#889	C₂²	1	1	yes	characteristic, complemented
100	#888	C₂²	1	1	yes	characteristic, complemented
101	#887	C₂²	1	1	yes	characteristic, complemented
102	#886	C₂²	1	1	yes	characteristic, complemented
103	#885	C₂²	1	1	yes	characteristic, complemented
104	#885	C₂²	1	2	yes	complemented
105	#885	C₂²	1	2	yes	complemented
106	#885	C₂²	1	2	yes	complemented
107	#885	C₂²	1	2	yes	complemented
108	#885	C₂²	1	2	yes	complemented
109	#883	C₂²	1	2	yes	complemented
110	#883	C₂²	1	2	yes	complemented
111	#67⋊C₄	C₂²	1	2	yes	complemented
112	#67⋊C₄	C₂²	1	2	yes	complemented
113	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	#879	C₂²	1	1	yes	characteristic, complemented
115	#879	C₂²	1	2	yes	complemented
116	#879	C₂²	1	2	yes	complemented
117	#878	C₂²	1	1	yes	characteristic, complemented
118	#878	C₂²	1	2	yes	complemented
119	#878	C₂²	1	2	yes	complemented
120	#875	C₂²	1	1	yes	characteristic, complemented
121	#872	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	#562	—	3	2	no	—
125	H(3,𝔽₄)	—	3	2	no	—
126	#559	—	3	1	no	—
127	#559	—	3	1	no	—
128	#548	—	3	1	no	—
129	#548	—	3	1	no	—
130	#546	—	3	2	no	—
131	#546	—	3	1	no	—
132	#546	—	3	1	no	—
133	#546	—	3	2	no	—
134	D₄²	—	3	1	no	—
135	D₄²	D₃	1	1	yes	characteristic, complemented
136	#542	—	3	1	no	—
137	#542	—	3	1	no	—
138	#538	—	3	2	no	—
139	#538	—	3	2	no	—
140	#538	—	3	2	no	—
141	#535	—	3	1	no	—
142	#535	—	3	1	no	—
143	#534	—	3	2	no	—
144	#532	—	3	1	no	—
145	#529	—	3	1	no	—
146	C₂×#124	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₂⁴×C₃	C₂³	1	2	yes	—
149	C₂³×D₃	C₂³	1	2	yes	—
150	C₂×C₃×D₄	—	4	2	no	—
151	C₂×C₃×D₄	—	4	2	no	—
152	C₂×C₃×D₄	—	4	4	no	—
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
158	C₂×C₃×D₄	C₂³	1	2	yes	—
159	C₂×C₃×D₄	C₂³	1	2	yes	—
160	C₂×C₃×D₄	C₂³	1	2	yes	—
161	C₂×C₃×D₄	C₂³	1	2	yes	—
162	C₂×C₃×D₄	C₂³	1	2	yes	—
163	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³	1	2	yes	—
166	C₂×#67	—	4	4	no	—
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	1	yes	characteristic
169	C₂×#67	C₂³	1	2	yes	—
170	C₂×#67	C₂³	1	2	yes	—
171	C₂×#67	C₂³	1	2	yes	—
172	C₂×#67	C₂³	1	1	yes	characteristic
173	C₂×#67	C₂³	1	2	yes	—
174	C₂×#67	C₂³	1	2	yes	—
175	C₂×#67	C₂³	1	2	yes	—
176	C₂×#67	C₂³	1	2	yes	—
177	C₂×#67	C₂³	1	2	yes	—
178	C₂²×Dic₃	C₂³	1	1	yes	characteristic
179	C₂²×Dic₃	C₂³	1	1	yes	characteristic
180	C₂²×Dic₃	C₂³	1	2	yes	—
181	C₂²×Dic₃	C₂³	1	2	yes	—
182	C₂²×Dic₃	C₂³	1	2	yes	—
183	C₂²×Dic₃	C₂³	1	2	yes	—
184	#237	—	4	2	no	—
185	#237	—	4	4	no	—
186	D₃×D₄	—	4	2	no	—
187	#235	—	4	2	no	—
188	C₂×D₁₂	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×Dic₆	—	4	2	no	—
193	C₂×Dic₆	C₂³	1	1	yes	characteristic
194	C₂×Dic₆	C₂³	1	1	yes	characteristic
195	C₂×Dic₆	C₂³	1	1	yes	characteristic
196	C₂×Dic₆	C₂³	1	2	yes	—
197	C₂×Dic₆	C₂³	1	2	yes	—
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	1	yes	characteristic
211	#217	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	#217	C₂³	1	2	yes	—
215	#217	C₂³	1	2	yes	—
216	#217	C₂³	1	2	yes	—
217	#217	C₂³	1	2	yes	—
218	#217	C₂³	1	2	yes	—
219	#217	C₂³	1	2	yes	—
220	#217	C₂³	1	1	yes	characteristic
221	#217	C₂³	1	2	yes	—
222	#217	C₂³	1	2	yes	—
223	#217	C₂³	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
229	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
231	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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	2	yes	—
238	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	Dic₃⋊C₄	C₂³	1	2	yes	—
246	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₃⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₃	C₂³	1	1	yes	characteristic
255	C₂×#41	—	3	2	no	—
256	C₂×#41	—	3	1	no	—
257	C₂×#41	—	3	1	no	—
258	C₂²×Q₈	—	3	1	no	—
259	C₂²×D₄	—	3	2	no	—
260	C₂²×D₄	—	3	1	no	—
261	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
262	C₂²×D₄	C₂×D₃	1	2	yes	complemented
263	C₂²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
264	C₄⋊Q₈	—	3	1	no	—
265	#127	—	3	1	no	—
266	#127	—	3	1	no	—
267	#127	C₂×D₃	1	1	yes	characteristic
268	#126	—	3	1	no	—
269	#126	—	3	1	no	—
270	#126	—	3	2	no	—
271	#126	—	3	2	no	—
272	#125	—	3	1	no	—
273	#124	—	3	1	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	—	3	1	no	—
277	#124	—	3	1	no	—
278	#124	—	3	2	no	—
279	#124	—	3	1	no	—
280	#124	—	3	2	no	—
281	#124	—	3	2	no	—
282	#124	—	3	1	no	—
283	#124	—	3	2	no	—
284	#124	—	3	2	no	—
285	#124	—	3	2	no	—
286	#124	—	3	2	no	—
287	#124	—	3	2	no	—
288	#124	—	3	1	no	—
289	#123	—	3	1	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	#123	—	3	2	no	—
293	#123	—	3	2	no	—
294	#123	—	3	2	no	—
295	#123	—	3	2	no	—
296	#123	—	3	1	no	—
297	#123	—	3	2	no	—
298	#123	—	3	2	no	—
299	C₂²⋊Q₈	—	3	1	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	1	no	—
303	C₂²⋊Q₈	—	3	1	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	#121	—	3	1	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	2	no	—
311	#121	—	3	2	no	—
312	#121	—	3	2	no	—
313	#121	—	3	2	no	—
314	#121	—	3	2	no	—
315	#121	—	3	2	no	—
316	#121	—	3	2	no	—
317	#121	—	3	1	no	—
318	#121	—	3	1	no	—
319	#121	C₂×D₃	1	1	yes	characteristic
320	#121	C₂×D₃	1	1	yes	characteristic, complemented
321	#121	C₂×D₃	1	2	yes	complemented
322	#120	—	3	2	no	—
323	#120	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	#120	—	3	2	no	—
327	#120	—	3	2	no	—
328	#120	—	3	2	no	—
329	#120	—	3	2	no	—
330	#120	C₂×D₃	1	2	yes	complemented
331	#120	C₂×D₃	1	2	yes	complemented
332	C₄×Q₈	—	3	1	no	—
333	C₄×Q₈	—	3	1	no	—
334	C₄×Q₈	—	3	1	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	—	3	1	no	—
340	C₄×D₄	—	3	1	no	—
341	C₄×D₄	—	3	2	no	—
342	C₄×D₄	—	3	1	no	—
343	C₄×D₄	—	3	2	no	—
344	C₄×D₄	—	3	2	no	—
345	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
346	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
347	#117	—	3	1	no	—
348	#117	—	3	1	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₄²	—	3	1	no	—
354	C₂³×C₃	—	2	4	no	—
355	C₂³×C₃	—	4	2	no	—
356	C₂³×C₃	—	4	2	no	—
357	C₂³×C₃	—	4	2	no	—
358	C₂³×C₃	—	4	2	no	—
359	C₂³×C₃	—	4	2	no	—
360	C₂³×C₃	C₂⁴	1	2	yes	—
361	C₂³×C₃	C₂⁴	1	1	yes	characteristic
362	C₂³×C₃	C₂⁴	1	2	yes	—
363	C₂³×C₃	C₂⁴	1	2	yes	—
364	C₂³×C₃	C₂⁴	1	1	yes	characteristic
365	C₂²×D₃	—	4	2	no	—
366	C₂²×D₃	—	4	2	no	—
367	C₂²×D₃	—	4	2	no	—
368	C₂²×D₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₃	C₂⁴	1	2	yes	—
370	C₃×D₄	—	2	4	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	4	2	no	—
376	C₃×D₄	—	4	2	no	—
377	C₃×D₄	—	4	2	no	—
378	C₃×D₄	—	4	2	no	—
379	C₃×D₄	—	4	2	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	#67	—	2	4	no	—
390	#67	—	2	2	no	—
391	#67	—	4	2	no	—
392	#67	—	4	2	no	—
393	#67	—	4	2	no	—
394	#67	—	4	2	no	—
395	#67	—	4	2	no	—
396	#67	—	4	2	no	—
397	#67	—	4	1	no	—
398	#67	—	4	2	no	—
399	#67	—	4	2	no	—
400	C₂×Dic₃	—	2	2	no	—
401	C₂×Dic₃	—	4	2	no	—
402	C₂×Dic₃	—	4	2	no	—
403	C₂×Dic₃	—	4	2	no	—
404	C₂×Dic₃	—	4	1	no	—
405	C₂×Dic₃	—	4	2	no	—
406	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₃	C₂⁴	1	2	yes	—
413	C₂×Dic₃	C₂⁴	1	2	yes	—
414	C₂×Dic₃	C₂⁴	1	2	yes	—
415	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
416	D₁₂	—	2	2	no	—
417	C₄×D₃	—	2	2	no	—
418	C₄×D₃	—	4	2	no	—
419	C₄×D₃	—	4	2	no	—
420	Dic₆	—	2	2	no	—
421	Dic₆	—	2	2	no	—
422	Dic₆	—	4	2	no	—
423	Dic₆	—	4	1	no	—
424	Dic₆	—	4	2	no	—
425	C₂⁴	—	3	2	no	—
426	C₂⁴	C₂²×D₃	1	2	yes	—
427	C₂⁴	C₂²×D₃	1	2	yes	—
428	#41	—	12	2	no	—
429	#41	—	12	4	no	—
430	#41	—	12	2	no	—
431	C₂×Q₈	—	3	1	no	—
432	C₂×Q₈	—	3	1	no	—
433	C₂×Q₈	—	3	1	no	—
434	C₂×Q₈	—	3	2	no	—
435	C₂×Q₈	—	3	2	no	—
436	C₂×Q₈	—	12	2	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	3	1	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	3	2	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	2	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	2	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	2	no	—
448	C₂×D₄	—	3	1	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	12	2	no	—
453	C₂×D₄	—	12	4	no	—
454	C₂×D₄	C₂²×D₃	1	2	yes	—
455	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
456	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
457	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
458	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
459	C₂×D₄	C₂²×D₃	1	2	yes	—
460	C₂×D₄	C₂²×D₃	1	2	yes	—
461	C₂×D₄	C₂²×D₃	1	2	yes	—
462	C₂×D₄	C₂²×D₃	1	2	yes	—
463	C₂×D₄	C₂²×D₃	1	2	yes	—
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	—	3	2	no	—
472	C₂²×C₄	—	3	2	no	—
473	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
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	1	no	—
480	C₄⋊C₄	—	3	1	no	—
481	C₄⋊C₄	—	3	1	no	—
482	C₄⋊C₄	—	3	1	no	—
483	C₄⋊C₄	—	3	1	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	2	no	—
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
493	C₂²⋊C₄	—	3	1	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	2	no	—
504	C₂²⋊C₄	—	3	1	no	—
505	C₂²⋊C₄	—	3	1	no	—
506	C₂²⋊C₄	—	3	1	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	2	no	—
509	C₂²⋊C₄	—	3	2	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	3	1	no	—
512	C₂²⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	1	no	—
514	C₂²⋊C₄	—	3	1	no	—
515	C₂²⋊C₄	—	3	1	no	—
516	C₂²⋊C₄	—	3	2	no	—
517	C₂²⋊C₄	—	3	2	no	—
518	C₂²⋊C₄	—	3	2	no	—
519	C₂²⋊C₄	—	3	2	no	—
520	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
522	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
525	C₄²	—	3	1	no	—
526	C₄²	—	3	1	no	—
527	C₄²	—	3	1	no	—
528	C₄²	—	3	1	no	—
529	C₄²	—	3	1	no	—
530	C₄²	—	3	2	no	—
531	C₄²	—	3	2	no	—
532	C₄²	C₂²×D₃	1	1	yes	characteristic
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	2	1	no	—
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	—	2	2	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	2	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	2	2	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	8	4	no	—
548	C₂²×C₃	—	8	4	no	—
549	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
550	C₂²×C₃	C₂⁵	1	1	yes	characteristic
551	C₂×D₃	—	2	1	no	—
552	C₂×D₃	—	2	2	no	—
553	C₂×D₃	—	2	2	no	—
554	C₂×D₃	—	2	1	no	—
555	C₂×D₃	—	2	2	no	—
556	C₂×D₃	—	2	1	no	—
557	C₂×D₃	—	8	4	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	2	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
564	Dic₃	—	2	2	no	—
565	Dic₃	—	2	2	no	—
566	Dic₃	—	2	1	no	—
567	Dic₃	—	2	2	no	—
568	Dic₃	—	2	1	no	—
569	Dic₃	—	2	1	no	—
570	Dic₃	—	2	1	no	—
571	Dic₃	—	2	1	no	—
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	3	1	no	—
576	C₂³	—	3	2	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	4	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	2	no	—
582	C₂³	—	12	2	no	—
583	C₂³	—	12	2	no	—
584	C₂³	—	12	2	no	—
585	C₂³	C₂³×D₃	1	2	yes	—
586	C₂³	C₂³×D₃	1	1	yes	characteristic
587	C₂³	C₂³×D₃	1	2	yes	—
588	C₂³	C₂³×D₃	1	2	yes	—
589	C₂³	C₂³×D₃	1	1	yes	characteristic
590	Q₈	—	6	2	no	—
591	Q₈	—	6	2	no	—
592	Q₈	—	12	2	no	—
593	Q₈	—	12	2	no	—
594	Q₈	—	12	1	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	6	2	no	—
606	D₄	—	6	4	no	—
607	D₄	—	6	2	no	—
608	D₄	—	12	2	no	—
609	D₄	—	12	2	no	—
610	D₄	—	12	2	no	—
611	D₄	—	12	2	no	—
612	D₄	—	12	2	no	—
613	D₄	—	12	2	no	—
614	D₄	—	12	2	no	—
615	D₄	—	12	1	no	—
616	D₄	—	12	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	3	1	no	—
620	C₂×C₄	—	3	1	no	—
621	C₂×C₄	—	3	1	no	—
622	C₂×C₄	—	3	1	no	—
623	C₂×C₄	—	3	1	no	—
624	C₂×C₄	—	3	2	no	—
625	C₂×C₄	—	3	2	no	—
626	C₂×C₄	—	3	2	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	6	2	no	—
631	C₂×C₄	—	6	2	no	—
632	C₂×C₄	—	12	2	no	—
633	C₂×C₄	—	12	2	no	—
634	C₂×C₄	—	12	2	no	—
635	C₂×C₄	—	12	2	no	—
636	C₂×C₄	—	12	2	no	—
637	C₂×C₄	—	12	2	no	—
638	C₂×C₄	—	12	1	no	—
639	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
641	C₂×C₄	C₂³×D₃	1	2	yes	—
642	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
643	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
644	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
645	C₂×C₃	—	2	2	no	—
646	C₂×C₃	—	4	2	no	—
647	C₂×C₃	—	4	2	no	—
648	C₂×C₃	—	4	1	no	—
649	C₂×C₃	—	4	2	no	—
650	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂×C₃	#585	1	1	yes	characteristic
653	D₃	—	4	2	no	—
654	D₃	—	4	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	6	1	no	—
670	C₂²	—	6	2	no	—
671	C₂²	—	6	2	no	—
672	C₂²	—	6	1	no	—
673	C₂²	—	6	2	no	—
674	C₂²	—	6	1	no	—
675	C₂²	—	8	4	no	—
676	C₂²	—	8	4	no	—
677	C₂²	—	24	4	no	—
678	C₂²	#1004	1	2	yes	—
679	C₂²	C₂⁴×D₃	1	1	yes	characteristic
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	6	1	no	—
686	C₄	—	6	1	no	—
687	C₄	—	6	1	no	—
688	C₄	—	6	1	no	—
689	C₄	—	6	2	no	—
690	C₄	—	6	2	no	—
691	C₄	—	6	2	no	—
692	C₄	—	6	1	no	—
693	C₄	—	6	1	no	—
694	C₄	—	6	1	no	—
695	C₄	#1004	1	2	yes	—
696	C₃	#3558	1	1	yes	characteristic, complemented, Sylow
697	C₂	—	2	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	2	no	—
700	C₂	—	4	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	12	1	no	—
703	C₂	—	12	2	no	—
704	C₂	C₂×#1004	1	1	yes	characteristic
705	C₂	C₂×#1004	1	1	yes	characteristic
706	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×D₄²	C₂
hypercenter	D₄²	D₃
hypocenter	C₃	#3558
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₃×D₄²	C₂	semidirect
2. #5806	C₂	semidirect
3. #5806	C₂	semidirect
4. #5805	C₂	semidirect
5. #5804	C₂	semidirect
6. D₄×#67	C₂	semidirect
7. C₂×#936	C₂	semidirect
8. #5715	C₂	semidirect
9. #5713	C₂	semidirect
10. #5621	C₂	semidirect
11. #5613	C₂	semidirect
12. #5612	C₂	semidirect
13. #5603	C₂	semidirect
14. #5598	C₂	semidirect
15. #5596	C₂	semidirect
16. #5594	C₂	semidirect
17. #5593	C₂	semidirect
18. #5593	C₂	semidirect
19. #5591	C₂	semidirect
20. #5561	C₂	semidirect
21. #5559	C₂	semidirect
22. #5552	C₂	semidirect
23. #5538	C₂	semidirect
26. C₂²×C₃×D₄	C₂²	semidirect
27. C₂²×C₃×D₄	C₂²	semidirect
28. C₂²×#67	C₂²	semidirect
29. C₂×#237	C₂²	semidirect
30. C₂×#237	C₂²	semidirect
31. C₂×D₃×D₄	C₂²	semidirect
32. C₂×#235	C₂²	semidirect
33. C₂²×Dic₆	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
37. C₃×#121	C₂²	semidirect
38. C₃×#120	C₂²	semidirect
39. C₃×#120	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
42. #953	C₂²	semidirect
43. #953	C₂²	semidirect
44. #953	C₂²	semidirect
45. #953	C₂²	semidirect
46. C₂×#217	C₂²	semidirect
47. C₂×#217	C₂²	semidirect
48. C₂×#217	C₂²	semidirect
50. #940	C₂²	semidirect
52. #939	C₂²	semidirect
53. #939	C₂²	semidirect
54. #939	C₂²	semidirect
55. #939	C₂²	semidirect
56. #939	C₂²	semidirect
57. #939	C₂²	semidirect
58. #939	C₂²	semidirect
60. #938	C₂²	semidirect
61. #938	C₂²	semidirect
62. #938	C₂²	semidirect
63. #937	C₂²	semidirect
64. #937	C₂²	semidirect
65. #937	C₂²	semidirect
66. #937	C₂²	semidirect
67. #936	C₂²	semidirect
68. #936	C₂²	semidirect
69. #936	C₂²	semidirect
70. #936	C₂²	semidirect
71. #936	C₂²	semidirect
72. #936	C₂²	semidirect
73. #936	C₂²	semidirect
74. #936	C₂²	semidirect
75. #936	C₂²	semidirect
76. #935	C₂²	semidirect
77. #935	C₂²	semidirect
78. #935	C₂²	semidirect
79. #935	C₂²	semidirect
80. #935	C₂²	semidirect
81. D₄×Dic₃	C₂²	semidirect
82. D₄×Dic₃	C₂²	semidirect
83. D₄×Dic₃	C₂²	semidirect
84. D₄×Dic₃	C₂²	semidirect
85. #930	C₂²	semidirect
86. #929	C₂²	semidirect
87. #929	C₂²	semidirect
88. C₄×#67	C₂²	semidirect
89. C₄×#67	C₂²	semidirect
90. C₄×#67	C₂²	semidirect
91. #926	C₂²	semidirect
92. #924	C₂²	semidirect
93. #924	C₂²	semidirect
94. C₂×C₄×Dic₃	C₂²	semidirect
95. #898	C₂²	semidirect
96. #897	C₂²	semidirect
97. #896	C₂²	semidirect
98. #893	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
105. #885	C₂²	semidirect
106. #885	C₂²	semidirect
107. #885	C₂²	semidirect
108. #885	C₂²	semidirect
109. #883	C₂²	semidirect
110. #883	C₂²	semidirect
111. #67⋊C₄	C₂²	semidirect
112. #67⋊C₄	C₂²	semidirect
113. D₃×C₂²⋊C₄	C₂²	semidirect
114. #879	C₂²	semidirect
115. #879	C₂²	semidirect
116. #879	C₂²	semidirect
117. #878	C₂²	semidirect
118. #878	C₂²	semidirect
119. #878	C₂²	semidirect
120. #875	C₂²	semidirect
121. #872	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. D₄²	D₃	semidirect
262. C₂²×D₄	C₂×D₃	semidirect
263. C₂²×D₄	C₂×D₃	semidirect
320. #121	C₂×D₃	semidirect
321. #121	C₂×D₃	semidirect
330. #120	C₂×D₃	semidirect
331. #120	C₂×D₃	semidirect
345. C₄×D₄	C₂×D₃	semidirect
346. C₄×D₄	C₂×D₃	semidirect
696. C₃	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₄²	2
#5806	2
#5805	2
#5804	2
D₄×#67	2
C₂×#936	2
#5715	2
#5713	2
#5621	2
#5613	2
#5612	2
#5603	2
#5598	2
#5596	2
#5594	2
#5593	2
#5591	2
#5561	2
#5559	2
#5552	2
#5538	2
#3558	3