Finite Group Databasebeta

← #18081940

Subgroups — #18081940

Order 4864.

440 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#14574194C211yesmaximal, characteristic
2#14562398C211yesmaximal, characteristic, complemented
3#14562249C211yesmaximal, characteristic, complemented
4#14562245C211yesmaximal, characteristic
5#14562146C211yesmaximal, characteristic, complemented
6#14562142C211yesmaximal, characteristic
7C19×#1726C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9#11927094C2211yescharacteristic
10#11926942C411yescharacteristic, complemented
11#11926917C411yescharacteristic, complemented
12#11926895C411yescharacteristic, complemented
13#11926891C411yescharacteristic, complemented
14#11926773—21no—
15#11926773—21no—
16C4×#64516—21no—
17C4×#64516—21no—
18#11926601C2211yescharacteristic
19#11926601C2211yescharacteristic
20#11926297—21no—
21#11926295—21no—
22#11926285—22no—
23#11926283—22no—
24#11926280—22no—
25#11926277—22no—
26C2×C19×#97—21no—
27C2×C19×#97C2211yescharacteristic
28C2×C4×C8×C19—21no—
29C2×C4×C8×C19C2211yescharacteristic
30C19×#376C2211yescharacteristic
31C2×#64541—21no—
32C22×C8×C19—21no—
33C22×C8×C19D411yescharacteristic
34C22×C8×C19D411yescharacteristic
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37#10597376—21no—
38#10597376—21no—
39#10597372—21no—
40#10597370—21no—
41#10597370—21no—
42C2×#64516—21no—
43C2×#64516—21no—
44#10597321—21no—
45#10597320C2×C411yescharacteristic
46C4×D76—21no—
47C4×D76—21no—
48#10597316—21no—
49#10597315C2×C411yescharacteristic
50#10597315C2×C411yescharacteristic
51#10597315C2×C411yescharacteristic
52C4×Dic38—21no—
53C4×Dic38—21no—
54C19×#97—24no—
55C19×#97—21no—
56C19×#97D412yes—
57C4×C8×C19—24no—
58C4×C8×C19C2×C411yescharacteristic
59C4×C8×C19C2×C411yescharacteristic
60C4×C8×C19D411yescharacteristic
61C4×C8×C19D411yescharacteristic
62C19×#95—21no—
63C19×#95D412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66#10597278—21no—
67#10597278—21no—
68#10597274—21no—
69#10597274—21no—
70#10597273—21no—
71#10597273—21no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74#10597260—21no—
75#10597260—21no—
76C22×C4×C19—22no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C2×C22⋊D19—41no—
81#64541—82no—
82C2×D76—21no—
83C2×D76—21no—
84C2×D76—21no—
85C2×C4×D19—41no—
86C2×Dic38—21no—
87C2×Dic38—21no—
88C2×Dic38—21no—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19C22⋊C411yescharacteristic
95C2×C8×C19C22⋊C411yescharacteristic
96C2×C8×C19C22⋊C411yescharacteristic
97C2×C8×C19C22⋊C411yescharacteristic
98C42×C19—22no—
99C42×C19—22no—
100C42×C19C22×C411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19#4111yescharacteristic
104C22⋊Dic19—41no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—41no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113Dic19⋊C4—41no—
114Dic19⋊C4—41no—
115C4×Dic19—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118#64516—42no—
119#64516—42no—
120#9761—191nomaximal, Sylow
121C23×C19#12111yescharacteristic
122C22×D19—41no—
123C2×C4×C19—22no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—24no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12411yescharacteristic
135C2×C4×C19#12711yescharacteristic
136C22⋊D19—82no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140D76—41no—
141D76—41no—
142D76—81no—
143D76—81no—
144C4×D19—82no—
145Dic38—41no—
146Dic38—41no—
147Dic38—81no—
148Dic38—81no—
149C8×C19—24no—
150C8×C19—21no—
151C8×C19—21no—
152C8×C19#10412yes—
153C8×C19#10412yes—
154C19⋊C8—81no—
155C19⋊C8—81no—
156#3167—191no—
157#1726D1911yescharacteristic, complemented
158#1568—191no—
159#1531—191no—
160#1530—191no—
161#1506—191no—
162#1505—191no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19#39011yescharacteristic
166C22×C19#47112yes—
167C2×D19—81no—
168C2×D19—81no—
169C2×D19—81no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—44no—
176C4×C19C2×#10411yescharacteristic
177C4×C19C2×#10411yescharacteristic
178Dic19—81no—
179Dic19—81no—
180Dic19—81no—
181#533—191no—
182#532—191no—
183#498—191no—
184#492—191no—
185#487—191no—
186#486—191no—
187#465—381no—
188#465—381no—
189C4×SD16—381no—
190C4×SD16—381no—
191#432—191no—
192#432—191no—
193C2×#97—21no—
194C2×#97C2×D1911yescharacteristic
195C2×C4×C8—21no—
196C2×C4×C8C2×D1911yescharacteristic
197#376C2×D1911yescharacteristic
198#335—381no—
199#334—381no—
200#330—382no—
201#329—382no—
202#328—382no—
203#327—382no—
204C2×C19—22no—
205C2×C19#196211yescharacteristic
206C2×C19#197611yescharacteristic
207C2×C19#197711yescharacteristic
208D19—161no—
209C2×#41—381no—
210C2×SD16—381no—
211C2×SD16—381no—
212C22×C8—21no—
213C22×C8C22⋊D1911yescharacteristic
214C22×C8C22⋊D1911yescharacteristic
215C4⋊Q8—191no—
216C4⋊Q8—191no—
217C4⋊Q8—191no—
218#127—191no—
219#125—381no—
220#124—381no—
221C22⋊Q8—381no—
222C22⋊Q8—381no—
223#121—381no—
224#121—381no—
225C4×Q8—381no—
226C4×Q8—381no—
227C4×D4—381no—
228C4×D4—381no—
229#117—381no—
230C2×C42—21no—
231C2×C42C22×D1911yescharacteristic
232#106—381no—
233#106—381no—
234C4⋊C8—381no—
235C4⋊C8—381no—
236#103—381no—
237#103—381no—
238#102—381no—
239#102—381no—
240C22⋊C8—381no—
241C22⋊C8—381no—
242#97—24no—
243#97—21no—
244#97—381no—
245#97—381no—
246#97D7612yes—
247C4×C8—24no—
248C4×C8C4×D1911yescharacteristic
249C4×C8C4×D1911yescharacteristic
250C4×C8D7611yescharacteristic
251C4×C8D7611yescharacteristic
252#95—21no—
253#95D7612yes—
254C19#976111yescharacteristic, complemented, Sylow
255#41—1522no—
256C2×Q8—381no—
257C2×Q8—381no—
258C2×Q8—381no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—761no—
263C22×C4—22no—
264C22×C4—761no—
265C22×C4C2×D7611yescharacteristic
266C22×C4#6454111yescharacteristic
267C22×C4C2×C22⋊D1911yescharacteristic
268SD16—762no—
269SD16—762no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—761no—
276C2×C8—761no—
277C2×C8(C2×D19)⋊C411yescharacteristic
278C2×C8(C2×D19)⋊C411yescharacteristic
279C2×C8(C2×D19)⋊C411yescharacteristic
280C2×C8(C2×D19)⋊C411yescharacteristic
281C4⋊C4—381no—
282C4⋊C4—381no—
283C4⋊C4—381no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C22⋊C4—761no—
290C22⋊C4—761no—
291C22⋊C4—761no—
292C42—22no—
293C42—22no—
294C42—761no—
295C42C2×C4×D1911yescharacteristic
296C42C2×D7611yescharacteristic
297C42C2×D7611yescharacteristic
298C42#6454111yescharacteristic
299C23—761no—
300C23#1059737611yescharacteristic
301Q8—761no—
302Q8—761no—
303Q8—1521no—
304Q8—1521no—
305D4—761no—
306D4—761no—
307D4—1521no—
308D4—1521no—
309D4—1522no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—761no—
318C2×C4—761no—
319C2×C4—761no—
320C2×C4—1522no—
321C2×C4C4×D7611yescharacteristic
322C2×C4C4×D7611yescharacteristic
323C2×C4#1059732011yescharacteristic
324C2×C4#1059732111yescharacteristic
325C2×C4C2×(C2×D19)⋊C411yescharacteristic
326C2×C4#1059737611yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—1521no—
331C8—1521no—
332C8#1059726212yes—
333C8#1059726212yes—
334C22—21no—
335C22—21no—
336C22—1521no—
337C22—1521no—
338C22—1521no—
339C22#1192644611yescharacteristic
340C22#1192680712yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—1521no—
348C4—1521no—
349C4—1521no—
350C4C2×#1059726211yescharacteristic
351C4C2×#1059726211yescharacteristic
352C2—22no—
353C2—3041no—
354C2#1456446311yescharacteristic
355C2#1456453311yescharacteristic
356C2#1456453811yescharacteristic
subgroupG/H
centerC22#11926446
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1726C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1726D19
hypocenterC19#9761
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #14562398C2semidirect
3. #14562249C2semidirect
5. #14562146C2semidirect
7. C19×#1726C2semidirect
10. #11926942C4semidirect
11. #11926917C4semidirect
12. #11926895C4semidirect
13. #11926891C4semidirect
157. #1726D19semidirect
254. C19#9761semidirect

Maximal subgroups

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

subgroupindex
#145741942
#145623982
#145622492
#145622452
#145621462
#145621422
C19×#17262
#976119