Finite Group Databasebeta

← #18081924

Subgroups — #18081924

Order 4864.

408 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573960C211yesmaximal, characteristic
2#14563797C211yesmaximal, characteristic, complemented
3#14562199C211yesmaximal, characteristic, complemented
4#14562196C211yesmaximal, characteristic
5#14562194C211yesmaximal, characteristic
6#14561928C211yesmaximal, characteristic, complemented
7C19×#1518C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926901—21no—
10#11926901—21no—
11#11926896C411yescharacteristic, complemented
12#11926896C411yescharacteristic, complemented
13#11926892C411yescharacteristic, complemented
14#11926892C411yescharacteristic, complemented
15#11926597C2211yescharacteristic
16C2×#10597264—21no—
17C2×#10597265—21no—
18#11926538—21no—
19#11926538—21no—
20C2×C4×C19⋊C8C2211yescharacteristic
21#11926410C2211yescharacteristic
22#11926281—22no—
23#11926279—22no—
24#11926277—22no—
25#11926266—21no—
26#11926265—21no—
27C19×#533C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#382C2211yescharacteristic
30C19×#328—22no—
31C2×#64541—21no—
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×#125—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C19×#117—21no—
40C2×C4⋊C4×C19—21no—
41C2×C42×C19C2311yescharacteristic
42#10597376—21no—
43#10597376—21no—
44C2×C4⋊Dic19—21no—
45C22×C19⋊C8D411yescharacteristic
46C22×C19⋊C8D411yescharacteristic
47#10597321—21no—
48#10597320C2×C411yescharacteristic
49C4×D76—21no—
50C4×D76—21no—
51#10597315C2×C411yescharacteristic
52C19×C4⋊C8—21no—
53C19×C22⋊C8D412yes—
54C4×C8×C19—21no—
55C19×#95—21no—
56C19×#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C22⋊(C19⋊C8)D412yes—
60#10597267—21no—
61#10597267—21no—
62#10597267—21no—
63#10597267—21no—
64#10597266—21no—
65#10597266—21no—
66#10597266—21no—
67#10597266—21no—
68#10597265—42no—
69#10597264—42no—
70C4⋊(C19⋊C8)—21no—
71C4×C19⋊C8—21no—
72C4×C19⋊C8C2×C411yescharacteristic
73C4×C19⋊C8C2×C411yescharacteristic
74C4×C19⋊C8D411yescharacteristic
75C4×C19⋊C8D411yescharacteristic
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C22×C4×C19—41no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C2×C22⋊D19—41no—
83C22×Dic19—41no—
84#64541—41no—
85#64541—41no—
86#64541—41no—
87#64541—41no—
88C2×D76—21no—
89C2×D76—21no—
90C2×D76—21no—
91C2×C4×D19—41no—
92C2×Dic38—21no—
93C2×C8×C19—22no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C22⋊C4×C19—41no—
103C42×C19—41no—
104C42×C19C22×C411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107C42×C19#4111yescharacteristic
108(C2×D19)⋊C4—41no—
109(C2×D19)⋊C4—41no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—41no—
113C4⋊Dic19—41no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8—21no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8C22⋊C411yescharacteristic
120C2×C19⋊C8C22⋊C411yescharacteristic
121C2×C19⋊C8C22⋊C411yescharacteristic
122C2×C19⋊C8C22⋊C411yescharacteristic
123#9758—191nomaximal, Sylow
124C23×C19#12711yescharacteristic
125C22×D19—41no—
126Q8×C19—81no—
127Q8×C19—81no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—81no—
133C2×C4×C19—81no—
134C2×C4×C19—81no—
135C2×C4×C19C2×C22⋊C411yescharacteristic
136C2×C4×C19C4×D411yescharacteristic
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12411yescharacteristic
141C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C19#13711yescharacteristic
144C2×C4×C19#13711yescharacteristic
145C22⋊D19—81no—
146C22⋊D19—81no—
147C2×Dic19—41no—
148C2×Dic19—81no—
149C2×Dic19—81no—
150C2×Dic19—81no—
151D76—41no—
152D76—41no—
153D76—81no—
154D76—81no—
155C4×D19—81no—
156C4×D19—81no—
157Dic38—41no—
158Dic38—41no—
159C8×C19—42no—
160C19⋊C8—21no—
161C19⋊C8—21no—
162C19⋊C8—21no—
163C19⋊C8—21no—
164C19⋊C8—42no—
165#3131—191no—
166#1846—191no—
167#1518—191no—
168#1518D1911yescharacteristic, complemented
169#1517—191no—
170#1517—191no—
171#1452—191no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19#39011yescharacteristic
175C22×C19#49611yescharacteristic
176C22×C19#49711yescharacteristic
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—81no—
185C4×C19—81no—
186C4×C19—161no—
187C4×C19#41711yescharacteristic
188C4×C19#41711yescharacteristic
189C4×C19#48911yescharacteristic
190C4×C19#48911yescharacteristic
191Dic19—81no—
192Dic19—161no—
193#533C2×D1911yescharacteristic
194#532—191no—
195#488—381no—
196#488—381no—
197#487—191no—
198#487—191no—
199#486—191no—
200#486—191no—
201#431—191no—
202#431C2×D1911yescharacteristic
203C2×#107—381no—
204C2×#106—381no—
205#416—381no—
206#416—381no—
207C2×C4×C8—191no—
208#382—191no—
209#382C2×D1911yescharacteristic
210#328—22no—
211#328—382no—
212#327—382no—
213#327—382no—
214#322—381no—
215#322—381no—
216C2×C19—21no—
217C2×C19—21no—
218C2×C19#195911yescharacteristic
219C2×C19#197611yescharacteristic
220C2×C19#197611yescharacteristic
221D19—161no—
222C2×#41—381no—
223C22×C8—191no—
224C22×C8—191no—
225C4⋊Q8—191no—
226C4⋊Q8C4×D1911yescharacteristic
227C4⋊Q8C4×D1911yescharacteristic
228#127—191no—
229#125—21no—
230#124—381no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233#121—381no—
234#121—381no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—381no—
238C4×D4—381no—
239#117—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—381no—
242C2×C42C22×D1911yescharacteristic
243#107—762no—
244#106—762no—
245C4⋊C8—21no—
246C4⋊C8—381no—
247#103—381no—
248#103—381no—
249#103—381no—
250#103—381no—
251#102—381no—
252#102—381no—
253#102—381no—
254#102—381no—
255C22⋊C8—192no—
256C22⋊C8C22⋊D1912yes—
257C4×C8—21no—
258C4×C8—191no—
259C4×C8—191no—
260C4×C8—191no—
261C4×C8—191no—
262C4×C8—381no—
263#95—21no—
264#95—21no—
265#95—381no—
266#95—381no—
267C19#975811yescharacteristic, complemented, Sylow
268#41—761no—
269#41—761no—
270#41—761no—
271#41—761no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—761no—
279C22×C4—41no—
280C22×C4—761no—
281C22×C4—761no—
282C22×C4D4×D1911yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C22×C4C2×C22⋊D1911yescharacteristic
285C2×C8—22no—
286C2×C8—191no—
287C2×C8—191no—
288C2×C8—191no—
289C2×C8—191no—
290C2×C8—381no—
291C2×C8—381no—
292C2×C8—381no—
293C2×C8—381no—
294C2×C8—382no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—381no—
304C4⋊C4—381no—
305C4⋊C4—761no—
306C4⋊C4—761no—
307C22⋊C4—41no—
308C22⋊C4—761no—
309C22⋊C4—761no—
310C42—41no—
311C42C2×C4×D1911yescharacteristic
312C42#6454111yescharacteristic
313C42D4×D1911yescharacteristic
314C42#6454311yescharacteristic
315C23—761no—
316C23#1059738611yescharacteristic
317Q8—81no—
318Q8—81no—
319Q8—761no—
320Q8—761no—
321D4—761no—
322D4—761no—
323D4—1521no—
324D4—1521no—
325D4—1521no—
326D4—1521no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—761no—
335C2×C4—1521no—
336C2×C4—1521no—
337C2×C4—1521no—
338C2×C4—1521no—
339C2×C4—1521no—
340C2×C4C22⋊C4×D1911yescharacteristic
341C2×C4(C22⋊D19)⋊C411yescharacteristic
342C2×C4#1059733011yescharacteristic
343C2×C4#1059733111yescharacteristic
344C2×C4#1059736011yescharacteristic
345C2×C4#1059736011yescharacteristic
346C2×C4#1059736411yescharacteristic
347C2×C4#1059736411yescharacteristic
348C2×C4C4×C22⋊D1911yescharacteristic
349C2×C4#1059738511yescharacteristic
350C8—42no—
351C8—381no—
352C8—381no—
353C8—381no—
354C8—381no—
355C8—762no—
356C22—21no—
357C22—21no—
358C22—1521no—
359C22—1521no—
360C22—1521no—
361C22#1192644411yescharacteristic
362C22#1192693011yescharacteristic
363C22#1192693711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—161no—
371C4—3041no—
372C4—1521no—
373C4#1192654411yescharacteristic
374C4#1192654411yescharacteristic
375C4#1192690511yescharacteristic
376C4#1192690511yescharacteristic
377C2—21no—
378C2—21no—
379C2—3041no—
380C2#1456444811yescharacteristic
381C2#1456453011yescharacteristic
382C2#1456453211yescharacteristic
subgroupG/H
centerC22#11926444
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1518C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1518D19
hypocenterC19#9758
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #14563797C2semidirect
3. #14562199C2semidirect
6. #14561928C2semidirect
7. C19×#1518C2semidirect
11. #11926896C4semidirect
12. #11926896C4semidirect
13. #11926892C4semidirect
14. #11926892C4semidirect
168. #1518D19semidirect
267. C19#9758semidirect

Maximal subgroups

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

subgroupindex
#145739602
#145637972
#145621992
#145621962
#145621942
#145619282
C19×#15182
#975819