Finite Group Databasebeta

← #18005281

Subgroups — #18005281

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#14557943C211yesmaximal, characteristic, complemented
3#14557920C211yesmaximal, characteristic, complemented
4#14557890C211yesmaximal, characteristic, complemented
5#14557879C211yesmaximal, characteristic, complemented
6#14557784C211yesmaximal, characteristic, complemented
7#14557777C211yesmaximal, characteristic, complemented
8#14557767C211yesmaximal, characteristic, complemented
9#14557760C211yesmaximal, characteristic, complemented
10#14557643C211yesmaximal, characteristic, complemented
11#14557633C211yesmaximal, characteristic, complemented
12C4×#10596940C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557489C211yesmaximal, characteristic, complemented
15C37×#540C211yesmaximal, characteristic, complemented
16C2×#10596940C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596934C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22#11924536C2211yescharacteristic
23#11924531—21no—
24#11924524C2211yescharacteristic
25#11924522—21no—
26#11924518—21no—
27#11924515C2211yescharacteristic
28#11924514—21no—
29#11924510C2211yescharacteristic
30C4×Dic74C2211yescharacteristic
31C4×D148C2211yescharacteristic
32#11924469C2211yescharacteristic
33#11924469C2211yescharacteristic
34#11924467C2211yescharacteristic
35#11924467C2211yescharacteristic
36#11924459C2211yescharacteristic
37#11924459C2211yescharacteristic
38#11924457C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44#11924447C2211yescharacteristic
45#11924447C2211yescharacteristic
46C4×#64436C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#127×C37C2211yescharacteristic
49#125×C37C2211yescharacteristic
50#123×C37—21no—
51#123×C37—21no—
52#121×C37—21no—
53#121×C37—21no—
54#121×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58#117×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×Dic74—21no—
72C2×Dic74C2311yescharacteristic
73C4⋊C4×C37—21no—
74C4⋊C4×C37—21no—
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37D411yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C22⋊C4×C37D411yescharacteristic
84C22⋊C4×C37D411yescharacteristic
85C42×C37C2311yescharacteristic
86C42×C37C2311yescharacteristic
87C22⋊Dic37—21no—
88#10596940—22no—
89#10596940—22no—
90#10596939—22no—
91#10596939—22no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102#10596934—22no—
103C2×#64436—22no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37—21no—
110C23×C37C2×D411yescharacteristic
111C22×D37—21no—
112D4×C37—21no—
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—81no—
117D4×C37—81no—
118D4×C37—81no—
119D4×C37—81no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—81no—
125C2×C4×C37—81no—
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2411yescharacteristic
132C22⋊D37—81no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136D148—21no—
137D148—21no—
138C4×D37—81no—
139Dic74—21no—
140Dic74—21no—
141Dic74—81no—
142#64436—21no—
143#64436—21no—
144#64436#4112yes—
145#64436#4112yes—
146C22×C37—21no—
147C22×C37—21no—
148C22×C37—21no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
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×C37—41no—
165C4×C37—41no—
166C4×C37C2×#4111yescharacteristic
167C4×C37C2×#4111yescharacteristic
168Dic37—41no—
169Dic37—41no—
170Dic37—41no—
171#3179—371nomaximal, Sylow
172C2×C37—41no—
173C2×C37—81no—
174C2×C37—81no—
175C2×C37#53211yescharacteristic
176C2×C37#57611yescharacteristic
177C2×C37#57711yescharacteristic
178D37—81no—
179#542—371no—
180#540D3711yescharacteristic, complemented
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#405—371no—
194C37#317911yescharacteristic, complemented, Sylow
195C2×SD16—371no—
196C2×SD16—371no—
197C2×D8—371no—
198C2×D8—371no—
199C2×M16—371no—
200C22×C8—371no—
201C4⋊Q8—371no—
202#127C2×D3711yescharacteristic
203#126—741no—
204#125C2×D3711yescharacteristic
205#124—371no—
206#124—741no—
207#123—21no—
208#123—21no—
209#123—741no—
210C22⋊Q8—371no—
211C22⋊Q8—741no—
212#121—21no—
213#121—21no—
214#121—371no—
215#121C2×D3711yescharacteristic
216#121C2×D3711yescharacteristic
217C4×Q8—371no—
218C4×D4—371no—
219C4×D4C2×D3711yescharacteristic
220C4×D4C2×D3711yescharacteristic
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#97—371no—
235#97—371no—
236C4×C8—371no—
237C4×C8—371no—
238C2×Q8—371no—
239C2×Q8—741no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—371no—
245C2×D4—741no—
246C2×D4C22×D3711yescharacteristic
247C2×D4C22×D3711yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—741no—
251C22×C4C22×D3711yescharacteristic
252SD16—742no—
253SD16—742no—
254D8—742no—
255D8—742no—
256M16—742no—
257C2×C8—371no—
258C2×C8—371no—
259C2×C8—371no—
260C2×C8—371no—
261C2×C8—742no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—371no—
265C4⋊C4—371no—
266C4⋊C4—741no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4C22⋊D3711yescharacteristic
270C4⋊C4C22⋊D3711yescharacteristic
271C4⋊C4C22×D3711yescharacteristic
272C4⋊C4C22×D3711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4C22⋊D3711yescharacteristic
283C22⋊C4C22⋊D3711yescharacteristic
284C42—741no—
285C42C22×D3711yescharacteristic
286C42C22×D3711yescharacteristic
287C23—21no—
288C23—21no—
289C23—741no—
290C23C2×C22⋊D3711yescharacteristic
291Q8—2961no—
292Q8—741no—
293Q8—741no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—2961no—
303D4—741no—
304D4—741no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—2961no—
312C2×C4—741no—
313C2×C4—741no—
314C2×C4—741no—
315C2×C4C2×C22⋊D3711yescharacteristic
316C2×C4C2×C22⋊D3711yescharacteristic
317C2×C4C2×C22⋊D3711yescharacteristic
318C2×C4C2×C22⋊D3711yescharacteristic
319C2×C4C2×C22⋊D3711yescharacteristic
320C2×C4C23×D3711yescharacteristic
321C8—372no—
322C8—372no—
323C8—741no—
324C8—741no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22C22×C22⋊D3711yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1481no—
346C4—1481no—
347C4—1481no—
348C4#41×D3711yescharacteristic
349C4#41×D3711yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—2961no—
354C2#1455807911yescharacteristic
355C2#1455833611yescharacteristic
356C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#540C2
socleC22×C37C22×D4
hypercenter#540D37
hypocenterC37#3179
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14557943C2semidirect
3. #14557920C2semidirect
4. #14557890C2semidirect
5. #14557879C2semidirect
6. #14557784C2semidirect
7. #14557777C2semidirect
8. #14557767C2semidirect
9. #14557760C2semidirect
10. #14557643C2semidirect
11. #14557633C2semidirect
12. C4×#10596940C2semidirect
13. C4×#10596939C2semidirect
14. #14557489C2semidirect
15. C37×#540C2semidirect
180. #540D37semidirect
194. C37#3179semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145579432
#145579202
#145578902
#145578792
#145577842
#145577772
#145577672
#145577602
#145576432
#145576332
C4×#105969402
C4×#105969392
#145574892
C37×#5402
#317937