Finite Group Databasebeta

← #18006100

Subgroups — #18006100

Order 4736.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D37C211yesmaximal, characteristic, complemented
2Q8×C22⋊D37C211yesmaximal, characteristic, complemented
3#14558171C211yesmaximal, characteristic
4#14557926C211yesmaximal, characteristic, complemented
5#14557779C211yesmaximal, characteristic, complemented
6#14557771C211yesmaximal, characteristic, complemented
7#14557757C211yesmaximal, characteristic, complemented
8#14557736C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557687C211yesmaximal, characteristic, complemented
11#14557682C211yesmaximal, characteristic, complemented
12#14557672C211yesmaximal, characteristic, complemented
13#14557634C211yesmaximal, characteristic, complemented
14#14557602C211yesmaximal, characteristic, complemented
15C2×#137×C37C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596942C2211yescharacteristic, complemented
19C2×#10596930C2211yescharacteristic
20C2×#10596940C2211yescharacteristic
21C2×#10596941C2211yescharacteristic
22C2×#10596941C2211yescharacteristic
23SD16×D37—24no—
24C2×C8×D37C2211yescharacteristic
25#11924534—21no—
26#11924534C2211yescharacteristic, complemented
27#11924525C2211yescharacteristic
28#11924519—21no—
29#11924515—21no—
30#11924515C2211yescharacteristic, complemented
31#11924512—21no—
32#11924512C2211yescharacteristic
33#11924512C2211yescharacteristic
34#11924510C2211yescharacteristic
35#11924508—21no—
36#11924504—21no—
37Q8×Dic37C2211yescharacteristic, complemented
38D4×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37C2211yescharacteristic
41C2×#10596938—21no—
42#11924470C2211yescharacteristic, complemented
43#11924465C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924460C2211yescharacteristic, complemented
46#11924460C2211yescharacteristic, complemented
47#11924460C2211yescharacteristic, complemented
48#11924458C2211yescharacteristic
49#11924457C2211yescharacteristic
50C22⋊#64436C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic
52#11924446C2211yescharacteristic, complemented
53C2×#41×C37C2211yescharacteristic
54C22×Q8×C37C2211yescharacteristic, complemented
55#137×C37—24no—
56C2×Q16×C37C2211yescharacteristic, complemented
57C2×Q16×C37C2211yescharacteristic, complemented
58C2×SD16×C37C2211yescharacteristic
59C2×SD16×C37C2211yescharacteristic
60C2×M16×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62#41×C37—22no—
63#41×C37—41no—
64C2×Q8×C37—21no—
65C2×Q8×C37—22no—
66C2×Q8×C37—41no—
67C2×Q8×C37C2311yescharacteristic
68C2×Q8×C37C2311yescharacteristic
69C2×Q8×C37C2311yescharacteristic
70C2×D4×C37—21no—
71C2×D4×C37C2311yescharacteristic
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37C2311yescharacteristic
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C2×C22⋊D37D411yescharacteristic
78C22×Dic37—21no—
79Q8×D37—22no—
80Q8×D37—41no—
81D4×D37—22no—
82D4×D37—41no—
83C2×D148C2311yescharacteristic
84C2×C4×D37—21no—
85C2×C4×D37C2311yescharacteristic
86C2×Dic74—21no—
87C2×Dic74C2311yescharacteristic
88Q16×C37—22no—
89Q16×C37—22no—
90SD16×C37—22no—
91SD16×C37D414yescomplemented
92M16×C37—22no—
93C2×C8×C37C2311yescharacteristic
94C2×C8×C37C2311yescharacteristic
95C22⋊Dic37—21no—
96C22⋊Dic37—21no—
97C22⋊Dic37D411yescharacteristic
98#10596942—41no—
99#10596941—22no—
100#10596941—41no—
101#10596940—22no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938D411yescharacteristic
108C4⋊Dic37—21no—
109C4⋊Dic37C2311yescharacteristic
110C4⋊Dic37C2311yescharacteristic
111#10596936—21no—
112#10596936—21no—
113#10596936—21no—
114#10596936—21no—
115#10596936—21no—
116#10596936D411yescharacteristic
117C4×Dic37—21no—
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121#10596930—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—42no—
127C22×D37—42no—
128C22×D37—81no—
129C22×D37C2×D411yescharacteristic
130Q8×C37—21no—
131Q8×C37—21no—
132Q8×C37—21no—
133Q8×C37—21no—
134Q8×C37—21no—
135Q8×C37—42no—
136Q8×C37C2×D412yes—
137D4×C37—21no—
138D4×C37—42no—
139D4×C37C2×D412yes—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—42no—
146C2×C4×C37—42no—
147C2×C4×C37C2×D411yescharacteristic
148C2×C4×C37C2411yescharacteristic
149C22⋊D37—22no—
150C22⋊D37—42no—
151C22⋊D37—81no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—81no—
156C2×Dic37C2×D411yescharacteristic
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159D148—21no—
160D148—21no—
161C4×D37—21no—
162C4×D37—21no—
163C4×D37—42no—
164Dic74—21no—
165Dic74—21no—
166Dic74—42no—
167C8×C37—21no—
168C8×C37C2×D412yes—
169#64436—21no—
170#64436—21no—
171C22×C37—22no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37C22×D411yescharacteristic
178C2×D37—21no—
179C2×D37—21no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—84no—
184C2×D37#13712yescomplemented
185C4×C37—22no—
186C4×C37—21no—
187C4×C37—41no—
188C4×C37—41no—
189C4×C37C22×D411yescharacteristic
190C4×C37H(5,𝔽2)11yescharacteristic
191Dic37—21no—
192Dic37—21no—
193Dic37—21no—
194Dic37—41no—
195Dic37—41no—
196Dic37—41no—
197#3266—371nomaximal, Sylow
198C2×C37—42no—
199C2×C37—41no—
200C2×C37D4211yescharacteristic
201C2×C37C2×#13711yescharacteristic
202C2×C37#57711yescharacteristic
203D37—22no—
204D37—81no—
205C2×#137D3711yescharacteristic, complemented
206C22×SD16—371no—
207D4×Q8—371no—
208#546—371no—
209#497—371no—
210#468—371no—
211#467—371no—
212#464—371no—
213#461—371no—
214#452—371no—
215#451—371no—
216#450—371no—
217#448—371no—
218#440—371no—
219#435—371no—
220C37#326611yescharacteristic, complemented, Sylow
221C2×#41C2×D3711yescharacteristic
222C22×Q8—371no—
223C22×Q8C2×D3711yescharacteristic, complemented
224C22×D4—371no—
225#137—24no—
226C2×Q16—371no—
227C2×Q16C2×D3711yescharacteristic, complemented
228C2×Q16C2×D3711yescharacteristic, complemented
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—371no—
233C2×SD16—744no—
234C2×SD16C2×D3711yescharacteristic
235C2×SD16C2×D3711yescharacteristic
236C2×M16C2×D3711yescharacteristic, complemented
237C22×C8—371no—
238C4⋊Q8—371no—
239C4⋊Q8—741no—
240#124—371no—
241#123—741no—
242C22⋊Q8—371no—
243C22⋊Q8—371no—
244C22⋊Q8—371no—
245C22⋊Q8—741no—
246C22⋊Q8—741no—
247#121—371no—
248#121—741no—
249#120—741no—
250C4×Q8—371no—
251C4×D4—371no—
252C4×D4—371no—
253C4×D4—741no—
254C2×C22⋊C4—741no—
255#107—371no—
256C4⋊C8—371no—
257#103—371no—
258#103—371no—
259#103—371no—
260#103—371no—
261#102—371no—
262#102—371no—
263C22⋊C8—371no—
264C22⋊C8—371no—
265#97—371no—
266C24—741no—
267#41—22no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—371no—
273C2×Q8—741no—
274C2×Q8—742no—
275C2×Q8—1481no—
276C2×Q8C22×D3711yescharacteristic
277C2×Q8C22×D3711yescharacteristic
278C2×Q8C22×D3711yescharacteristic
279C2×D4—21no—
280C2×D4—371no—
281C2×D4—371no—
282C2×D4—741no—
283C2×D4—741no—
284C2×D4—742no—
285C2×D4—1481no—
286C2×D4C22×D3711yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—371no—
290C22×C4—741no—
291C22×C4—741no—
292C22×C4C22×D3711yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—1481no—
296SD16—22no—
297SD16—742no—
298SD16—742no—
299SD16—742no—
300SD16—1481no—
301SD16C22⋊D3714yescomplemented
302M16—22no—
303C2×C8—371no—
304C2×C8—371no—
305C2×C8—742no—
306C2×C8C22×D3711yescharacteristic
307C2×C8C22×D3711yescharacteristic
308C4⋊C4—371no—
309C4⋊C4—371no—
310C4⋊C4—371no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4—741no—
314C4⋊C4—741no—
315C4⋊C4—741no—
316C4⋊C4—741no—
317C22⋊C4—371no—
318C22⋊C4—371no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C42—371no—
327C42—741no—
328C23—21no—
329C23—371no—
330C23—2961no—
331C23—741no—
332C23—1482no—
333C23—1482no—
334C23D4×D3711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—741no—
342Q8—741no—
343Q8—1482no—
344Q8C2×C22⋊D3712yes—
345D4—21no—
346D4—42no—
347D4—2961no—
348D4—742no—
349D4—741no—
350D4—741no—
351D4—1482no—
352D4C2×C22⋊D3712yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—371no—
361C2×C4—371no—
362C2×C4—371no—
363C2×C4—2961no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—1482no—
370C2×C4D4×D3711yescharacteristic
371C2×C4C23×D3711yescharacteristic
372C8—21no—
373C8—741no—
374C8—741no—
375C8C2×C22⋊D3712yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—372no—
383C22—2964no—
384C22—741no—
385C22—741no—
386C22—1481no—
387C22—1481no—
388C22—1481no—
389C22C2×D4×D3711yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—741no—
395C4—741no—
396C4—741no—
397C4—1481no—
398C4—1481no—
399C4—1481no—
400C4C22×C22⋊D3711yescharacteristic
401C4#1192458111yescharacteristic
402C2—41no—
403C2—42no—
404C2—2961no—
405C2—742no—
406C2D4×C22⋊D3711yescharacteristic
407C2#137×D3711yescharacteristic
408C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#137×C37C2
socleC22×C37C22×D4
prime radical#14558171C2
hypercenterC2×#137D37
hypocenterC37#3266
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D37C2semidirect
2. Q8×C22⋊D37C2semidirect
4. #14557926C2semidirect
5. #14557779C2semidirect
6. #14557771C2semidirect
7. #14557757C2semidirect
8. #14557736C2semidirect
9. #14557695C2semidirect
10. #14557687C2semidirect
11. #14557682C2semidirect
12. #14557672C2semidirect
13. #14557634C2semidirect
14. #14557602C2semidirect
15. C2×#137×C37C2semidirect
18. C2×#10596942C22semidirect
26. #11924534C22semidirect
30. #11924515C22semidirect
37. Q8×Dic37C22semidirect
42. #11924470C22semidirect
43. #11924465C22semidirect
44. #11924461C22semidirect
45. #11924460C22semidirect
46. #11924460C22semidirect
47. #11924460C22semidirect
50. C22⋊#64436C22semidirect
52. #11924446C22semidirect
54. C22×Q8×C37C22semidirect
56. C2×Q16×C37C22semidirect
57. C2×Q16×C37C22semidirect
60. C2×M16×C37C22semidirect
91. SD16×C37D4semidirect
184. C2×D37#137semidirect
205. C2×#137D37semidirect
220. C37#3266semidirect
223. C22×Q8C2×D37semidirect
227. C2×Q16C2×D37semidirect
228. C2×Q16C2×D37semidirect
236. C2×M16C2×D37semidirect
301. SD16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D372
Q8×C22⋊D372
#145581712
#145579262
#145577792
#145577712
#145577572
#145577362
#145576952
#145576872
#145576822
#145576722
#145576342
#145576022
C2×#137×C372
#326637