Finite Group Databasebeta

← #18005279

Subgroups — #18005279

Order 4736.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic, complemented
2#14558138C211yesmaximal, characteristic, complemented
3#14557942C211yesmaximal, characteristic, complemented
4#14557922C211yesmaximal, characteristic, complemented
5#14557888C211yesmaximal, characteristic, complemented
6#14557880C211yesmaximal, characteristic, complemented
7#14557786C211yesmaximal, characteristic, complemented
8#14557779C211yesmaximal, characteristic, complemented
9#14557769C211yesmaximal, characteristic, complemented
10#14557762C211yesmaximal, characteristic, complemented
11#14557646C211yesmaximal, characteristic, complemented
12#14557635C211yesmaximal, characteristic, complemented
13C4×#10596930C211yesmaximal, characteristic, complemented
14C4×D296C211yesmaximal, characteristic, complemented
15C37×#405C211yesmaximal, characteristic, complemented
16C2×#10596930C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×D296C2211yescharacteristic
19C2×D296C2211yescharacteristic
20#11924536C2211yescharacteristic
21#11924533C2211yescharacteristic
22#11924531—21no—
23#11924528C2211yescharacteristic
24#11924524C2211yescharacteristic
25#11924522—21no—
26#11924521—21no—
27#11924521—21no—
28#11924518—21no—
29#11924515C2211yescharacteristic
30#11924514—21no—
31#11924510C2211yescharacteristic
32#11924510C2211yescharacteristic
33#11924510C2211yescharacteristic
34#11924509—21no—
35#11924509—21no—
36C4×Dic74C2211yescharacteristic
37C4×D148C2211yescharacteristic
38C4×D148C2211yescharacteristic
39C4×D148C2211yescharacteristic
40#11924470C2211yescharacteristic
41#11924470C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924468C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52C2×M16×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54#117×C37C2211yescharacteristic
55#97×C37C2211yescharacteristic
56#97×C37C2211yescharacteristic
57C4×C8×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C2×C22⋊D37—21no—
61C2×C22⋊D37—21no—
62C2×C22⋊D37—21no—
63C2×D148—21no—
64C2×D148—21no—
65C2×D148C2311yescharacteristic
66C2×D148C2311yescharacteristic
67C2×D148C2311yescharacteristic
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37—21no—
71C2×Dic74—21no—
72C2×Dic74C2311yescharacteristic
73M16×C37—22no—
74C2×C8×C37—22no—
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37D411yescharacteristic
80C4⋊C4×C37D411yescharacteristic
81C22⋊C4×C37D411yescharacteristic
82C22⋊C4×C37D411yescharacteristic
83C42×C37C2311yescharacteristic
84C42×C37C2311yescharacteristic
85C22⋊Dic37—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103C4×Dic37—21no—
104D296—22no—
105D296—22no—
106#10596930—22no—
107#10596930—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37C2×D411yescharacteristic
115C2×C4×C37C2×D411yescharacteristic
116C2×C4×C37C2×D411yescharacteristic
117C2×C4×C37C2×D411yescharacteristic
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C22⋊D37—81no—
121C22⋊D37—81no—
122C22⋊D37—81no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128D148—21no—
129D148—21no—
130D148—21no—
131D148—21no—
132D148—21no—
133D148—21no—
134D148—81no—
135D148—81no—
136C4×D37—81no—
137C4×D37—81no—
138C4×D37—81no—
139Dic74—21no—
140Dic74—21no—
141Dic74—81no—
142C8×C37—21no—
143C8×C37—21no—
144C8×C37#4112yes—
145C8×C37#4112yes—
146C22×C37—21no—
147C22×C37—21no—
148C22×C37—21no—
149C22×C37C22×D411yescharacteristic
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C2×D37—41no—
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C4×C37—21no—
160C4×C37—21no—
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37C2×#4111yescharacteristic
165C4×C37C2×#4111yescharacteristic
166Dic37—41no—
167Dic37—41no—
168Dic37—41no—
169Dic37—41no—
170Dic37—41no—
171#3179—371nomaximal, Sylow
172C2×C37—41no—
173C2×C37#53211yescharacteristic
174C2×C37#57611yescharacteristic
175C2×C37#57711yescharacteristic
176D37—81no—
177D37—81no—
178D37—81no—
179#542—371no—
180#540—371no—
181#501—371no—
182#496—371no—
183#488—371no—
184#486—371no—
185#469—371no—
186#468—371no—
187#466—371no—
188#465—371no—
189#442—371no—
190#440—371no—
191C4×SD16—371no—
192C4×D8—371no—
193#405D3711yescharacteristic, complemented
194C37#317911yescharacteristic, complemented, Sylow
195C2×SD16—371no—
196C2×SD16—371no—
197C2×D8—371no—
198C2×D8—371no—
199C2×M16C2×D3711yescharacteristic
200C22×C8C2×D3711yescharacteristic
201C4⋊Q8—371no—
202#127—371no—
203#126—741no—
204#125—371no—
205#124—371no—
206#124—741no—
207#123—741no—
208#123—741no—
209#123—741no—
210C22⋊Q8—371no—
211C22⋊Q8—741no—
212#121—371no—
213#121—371no—
214#121—371no—
215#121—741no—
216#121—741no—
217C4×Q8—371no—
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—371no—
221#117C2×D3711yescharacteristic
222#107—371no—
223#107—371no—
224#106—371no—
225#106—371no—
226#103—371no—
227#103—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#97C2×D3711yescharacteristic
235#97C2×D3711yescharacteristic
236C4×C8C2×D3711yescharacteristic
237C4×C8C2×D3711yescharacteristic
238C2×Q8—371no—
239C2×Q8—741no—
240C2×D4—371no—
241C2×D4—371no—
242C2×D4—371no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4—741no—
248C22×C4—741no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4C22×D3711yescharacteristic
252SD16—742no—
253SD16—742no—
254D8—742no—
255D8—742no—
256M16—22no—
257C2×C8—22no—
258C2×C8C22×D3711yescharacteristic
259C2×C8C22×D3711yescharacteristic
260C2×C8C22×D3711yescharacteristic
261C2×C8C22×D3711yescharacteristic
262C4⋊C4—371no—
263C4⋊C4—371no—
264C4⋊C4—371no—
265C4⋊C4—371no—
266C4⋊C4—741no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4D14811yescharacteristic
272C4⋊C4D14811yescharacteristic
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4D14811yescharacteristic
283C22⋊C4D14811yescharacteristic
284C42—741no—
285C42C22×D3711yescharacteristic
286C42C22×D3711yescharacteristic
287C23—741no—
288C23—741no—
289C23—741no—
290C23C2×D14811yescharacteristic
291Q8—2961no—
292Q8—741no—
293Q8—741no—
294D4—2961no—
295D4—2961no—
296D4—2961no—
297D4—2961no—
298D4—2961no—
299D4—741no—
300D4—741no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—741no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2961no—
308C2×C4—2961no—
309C2×C4—2961no—
310C2×C4—741no—
311C2×C4—741no—
312C2×C4—741no—
313C2×C4—741no—
314C2×C4—741no—
315C2×C4C2×D14811yescharacteristic
316C2×C4C2×D14811yescharacteristic
317C2×C4C2×D14811yescharacteristic
318C2×C4C2×D14811yescharacteristic
319C2×C4C2×D14811yescharacteristic
320C2×C4C23×D3711yescharacteristic
321C8—21no—
322C8—21no—
323C8#1059696212yes—
324C8#1059696212yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1481no—
329C22—1481no—
330C22—1481no—
331C22—1481no—
332C22—1481no—
333C22—1481no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22C22×D14811yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—1481no—
344C4—1481no—
345C4—1481no—
346C4—1481no—
347C4—1481no—
348C4C2×#1059696211yescharacteristic
349C4C2×#1059696211yescharacteristic
350C2—41no—
351C2—2961no—
352C2—2961no—
353C2—2961no—
354C2#1455808311yescharacteristic
355C2#1455833811yescharacteristic
356C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#405C2
socleC22×C37C22×D4
hypercenter#405D37
hypocenterC37#3179
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14558138C2semidirect
3. #14557942C2semidirect
4. #14557922C2semidirect
5. #14557888C2semidirect
6. #14557880C2semidirect
7. #14557786C2semidirect
8. #14557779C2semidirect
9. #14557769C2semidirect
10. #14557762C2semidirect
11. #14557646C2semidirect
12. #14557635C2semidirect
13. C4×#10596930C2semidirect
14. C4×D296C2semidirect
15. C37×#405C2semidirect
193. #405D37semidirect
194. C37#3179semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145581382
#145579422
#145579222
#145578882
#145578802
#145577862
#145577792
#145577692
#145577622
#145576462
#145576352
C4×#105969302
C4×D2962
C37×#4052
#317937