Finite Group Databasebeta

← #18004286

Subgroups — #18004286

Order 4736.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924568C211yesmaximal, characteristic, complemented
2C2×#11924542C211yesmaximal, characteristic, complemented
3#14558113C211yesmaximal, characteristic
4#14558106C211yesmaximal, characteristic, complemented
5#14557789C211yesmaximal, characteristic, complemented
6#14557788C211yesmaximal, characteristic, complemented
7#14557781C211yesmaximal, characteristic, complemented
8#14557780C211yesmaximal, characteristic, complemented
9#14557773C211yesmaximal, characteristic, complemented
10#14557765C211yesmaximal, characteristic, complemented
11#14557762C211yesmaximal, characteristic, complemented
12#14557574C211yesmaximal, characteristic, complemented
13#14557528C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#467C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic
19#11924568—24no—
20C2×#10596942C2211yescharacteristic
21C2×#10596930C2211yescharacteristic
22C2×#10596941C2211yescharacteristic
23#11924542—24no—
24C2×#10596934C2211yescharacteristic
25C2×#10596929C2211yescharacteristic
26C2×#10596929C2211yescharacteristic
27C2×C8×D37C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic
29#11924535—21no—
30#11924522—21no—
31#11924521—21no—
32#11924518—21no—
33#11924516C2211yescharacteristic
34#11924515C2211yescharacteristic
35#11924514—21no—
36#11924512C2211yescharacteristic
37#11924512C2211yescharacteristic
38#11924511—21no—
39#11924511C2211yescharacteristic
40#11924510C2211yescharacteristic
41#11924509—21no—
42#11924509—21no—
43#11924494C2211yescharacteristic
44C4⋊C4×D37C2211yescharacteristic
45#11924469C2211yescharacteristic
46#11924468C2211yescharacteristic
47#11924467C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924460C2211yescharacteristic
50#11924460C2211yescharacteristic
51#11924459C2211yescharacteristic
52#11924458C2211yescharacteristic
53#11924456C2211yescharacteristic
54C2×Q16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic
56C22⋊Q8×C37C2211yescharacteristic
57C22⋊Q8×C37C2211yescharacteristic
58#107×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#103×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×Q8×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37D411yescharacteristic
66C2×C22⋊D37D411yescharacteristic
67#10596966—22no—
68#10596966—22no—
69Q8×D37—22no—
70Q8×D37—22no—
71#10596962—22no—
72#10596962—22no—
73C2×D148—21no—
74C2×D148—21no—
75C2×D148D411yescharacteristic
76C2×D148C2311yescharacteristic
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37C2311yescharacteristic
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—21no—
83C2×Dic74D411yescharacteristic
84C2×Dic74C2311yescharacteristic
85Q16×C37—22no—
86C2×C8×C37—22no—
87C2×C8×C37C2311yescharacteristic
88C2×C8×C37C2311yescharacteristic
89C4⋊C4×C37—21no—
90C4⋊C4×C37—21no—
91C4⋊C4×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊Dic37—21no—
96#10596942—22no—
97#10596941—22no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104C4⋊Dic37—21no—
105C4⋊Dic37C2311yescharacteristic
106C4⋊Dic37C2311yescharacteristic
107#10596936—21no—
108#10596936—21no—
109#10596936—21no—
110#10596936—21no—
111C4×Dic37—21no—
112#10596934—22no—
113C2×#64436C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115#10596930—22no—
116#10596929—22no—
117#10596929D414yescomplemented
118C8×D37—22no—
119C8×D37—22no—
120C23×C37C2×D411yescharacteristic
121C22×D37—21no—
122C22×D37C2×D411yescharacteristic
123C22×D37C2×D411yescharacteristic
124Q8×C37—21no—
125Q8×C37—21no—
126Q8×C37—21no—
127Q8×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2411yescharacteristic
136C22⋊D37—22no—
137C22⋊D37—22no—
138C22⋊D37—81no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144D148—22no—
145D148—21no—
146D148—21no—
147D148—42no—
148D148—81no—
149C4×D37—21no—
150C4×D37—21no—
151C4×D37—42no—
152C4×D37—42no—
153C4×D37—81no—
154C4×D37C2×D412yes—
155C4×D37#4112yes—
156Dic74—22no—
157Dic74—21no—
158Dic74—21no—
159Dic74—42no—
160C8×C37—21no—
161C8×C37C2×D412yes—
162#64436—21no—
163#64436C2×D412yes—
164C22×C37—21no—
165C22×C37—21no—
166C22×C37—21no—
167C22×C37C22×D411yescharacteristic
168C2×D37—21no—
169C2×D37—21no—
170C2×D37—21no—
171C2×D37—21no—
172C2×D37—21no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—41no—
176C2×D37#12112yes—
177C4×C37—21no—
178C4×C37—41no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37C22×D411yescharacteristic
183C4×C37C2×#4111yescharacteristic
184Dic37—21no—
185Dic37—41no—
186Dic37—41no—
187Dic37—41no—
188Dic37#12112yes—
189#3063—371nomaximal, Sylow
190C2×C37—41no—
191C2×C37C2×#12111yescharacteristic
192C2×C37#57711yescharacteristic
193C2×C37#57811yescharacteristic
194D37—22no—
195D37—41no—
196D37—81no—
197C2×#137—371no—
198C2×#131—371no—
199#537—371no—
200#536—371no—
201#470—371no—
202#470—371no—
203#468—371no—
204#468—371no—
205#467—371no—
206#467D3711yescharacteristic, complemented
207#465—371no—
208#465—371no—
209#428—371no—
210#416—371no—
211C2×#103—371no—
212C37#306311yescharacteristic, complemented, Sylow
213C2×#41—371no—
214C2×#41—371no—
215C22×Q8—371no—
216#137—744no—
217C2×Q16—371no—
218C2×Q16C2×D3711yescharacteristic
219C2×SD16—371no—
220C2×SD16—371no—
221#131—744no—
222C2×M16—371no—
223C2×M16—371no—
224C2×M16—371no—
225C22×C8—371no—
226C22×C8—371no—
227C22×C8C2×D3711yescharacteristic
228C4⋊Q8—741no—
229#124—741no—
230#123—741no—
231#123—741no—
232C22⋊Q8—371no—
233C22⋊Q8—371no—
234C22⋊Q8—371no—
235C22⋊Q8—371no—
236C22⋊Q8—741no—
237C22⋊Q8C2×D3711yescharacteristic
238C22⋊Q8C2×D3711yescharacteristic
239#121—371no—
240#121—371no—
241#121—741no—
242#121—741no—
243#121—741no—
244#117—371no—
245C2×C4⋊C4—371no—
246#107—371no—
247#107C2×D3711yescharacteristic
248#106—371no—
249#106—371no—
250#103—371no—
251#103—371no—
252#103—371no—
253#103—371no—
254#103C2×D3711yescharacteristic
255#103C2×D3711yescharacteristic
256#102—371no—
257#102—371no—
258#41—742no—
259#41—742no—
260#41—742no—
261#41—742no—
262C2×Q8—371no—
263C2×Q8—371no—
264C2×Q8—741no—
265C2×Q8—742no—
266C2×Q8—742no—
267C2×Q8C22×D3711yescharacteristic
268C2×Q8C22×D3711yescharacteristic
269C2×D4—371no—
270C2×D4—371no—
271C2×D4—371no—
272C2×D4—371no—
273C2×D4—741no—
274C2×D4—741no—
275C2×D4—741no—
276C22×C4—371no—
277C22×C4—371no—
278C22×C4—741no—
279C22×C4—741no—
280C22×C4—741no—
281C22×C4C22×D3711yescharacteristic
282Q16—22no—
283Q16—742no—
284SD16—742no—
285SD16—742no—
286M16—374no—
287M16—742no—
288M16—742no—
289C2×C8—22no—
290C2×C8—371no—
291C2×C8—371no—
292C2×C8—742no—
293C2×C8—742no—
294C2×C8C22×D3711yescharacteristic
295C2×C8C22×D3711yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—371no—
299C4⋊C4—371no—
300C4⋊C4—741no—
301C4⋊C4—741no—
302C4⋊C4—741no—
303C4⋊C4—741no—
304C4⋊C4—741no—
305C4⋊C4C22×D3711yescharacteristic
306C4⋊C4C22×D3711yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—741no—
310C22⋊C4—741no—
311C22⋊C4—741no—
312C22⋊C4—741no—
313C22⋊C4—741no—
314C22⋊C4—741no—
315C22⋊C4—741no—
316C42—741no—
317C23—371no—
318C23—371no—
319C23—741no—
320C23D4×D3711yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—742no—
326Q8—741no—
327Q8—741no—
328Q8—1482no—
329D4—2961no—
330D4—2961no—
331D4—742no—
332D4—742no—
333D4—742no—
334D4—741no—
335D4—741no—
336D4—1482no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—371no—
344C2×C4—372no—
345C2×C4—372no—
346C2×C4—371no—
347C2×C4—2961no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—741no—
352C2×C4—741no—
353C2×C4—1482no—
354C2×C4—1482no—
355C2×C4D4×D3711yescharacteristic
356C2×C4C23×D3711yescharacteristic
357C8—21no—
358C8—372no—
359C8—741no—
360C8D4×D3712yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—372no—
365C22—741no—
366C22—741no—
367C22—741no—
368C22—741no—
369C22—741no—
370C22—1481no—
371C22—1481no—
372C22—1481no—
373C22C2×D4×D3711yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—372no—
380C4—741no—
381C4—1481no—
382C4—1481no—
383C4—1481no—
384C4C2×D4×D3711yescharacteristic
385C4#41×D3711yescharacteristic
386C2—41no—
387C2—2961no—
388C2—742no—
389C2—1481no—
390C2#121×D3711yescharacteristic
391C2#1455834011yescharacteristic
392C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#467C2
socleC22×C37C22×D4
prime radical#14558113C2
hypercenter#467D37
hypocenterC37#3063
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#11924568C2semidirect
2. C2×#11924542C2semidirect
4. #14558106C2semidirect
5. #14557789C2semidirect
6. #14557788C2semidirect
7. #14557781C2semidirect
8. #14557780C2semidirect
9. #14557773C2semidirect
10. #14557765C2semidirect
11. #14557762C2semidirect
12. #14557574C2semidirect
13. #14557528C2semidirect
14. #103×D37C2semidirect
15. C37×#467C2semidirect
117. #10596929D4semidirect
206. #467D37semidirect
212. C37#3063semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
C2×#119245422
#145581132
#145581062
#145577892
#145577882
#145577812
#145577802
#145577732
#145577652
#145577622
#145575742
#145575282
#103×D372
C37×#4672
#306337