Finite Group Databasebeta

← #18081699

Subgroups — #18081699

Order 4864.

506 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574210C211yesmaximal, characteristic
2#14564554C211yesmaximal, characteristic, complemented
3C4×#10597264C211yesmaximal, characteristic, complemented
4#14562130C211yesmaximal, characteristic, complemented
5#14562129C211yesmaximal, characteristic, complemented
6M16×C19⋊C8C211yesmaximal, characteristic, complemented
7C19×#1980C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926947C411yescharacteristic, complemented
10#11926920C411yescharacteristic, complemented
11#11926892C411yescharacteristic, complemented
12#11926890C411yescharacteristic, complemented
13#11926778—21no—
14#11926778—21no—
15C4×#64525—21no—
16C4×#64525—21no—
17#11926597C2211yescharacteristic
18C2×#10597264—21no—
19C2×#10597282—22no—
20C2×C4×C19⋊C8C2211yescharacteristic
21C4×C4⋊Dic19C2211yescharacteristic
22#11926306—21no—
23#11926278—22no—
24#11926277—22no—
25#11926265—21no—
26C8×C19⋊C8—21no—
27C19×#532C2211yescharacteristic
28C2×C19×#104—22no—
29C4×M16×C19C2211yescharacteristic
30C4×C4⋊C4×C19C2211yescharacteristic
31C2×#41×C19—21no—
32C2×#64541—21no—
33C2×M16×C19D412yes—
34C19×C4⋊Q8C2×C411yescharacteristic
35C19×#127C2×C411yescharacteristic
36C19×#124—21no—
37C19×#121—21no—
38C19×#121—21no—
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C42×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×#64525—21no—
45C2×#64525—21no—
46#10597376—21no—
47#10597376—21no—
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19—21no—
50C22×C19⋊C8D411yescharacteristic
51C22×C19⋊C8D411yescharacteristic
52#10597321—21no—
53#10597320C2×C411yescharacteristic
54C4×D76—21no—
55C4×D76—21no—
56#10597315C2×C411yescharacteristic
57C19×#104—44no—
58C19×#97—21no—
59C4×C8×C19—21no—
60C19×#95—21no—
61#10597289—21no—
62#10597289—21no—
63C19⋊#95—21no—
64C22⋊(C19⋊C8)D412yes—
65#10597282—44no—
66#10597266—21no—
67#10597266—21no—
68#10597264—24no—
69#10597264—21no—
70#10597264—21no—
71C4⋊(C19⋊C8)—21no—
72C4×C19⋊C8—21no—
73C4×C19⋊C8C2×C411yescharacteristic
74C4×C19⋊C8C2×C411yescharacteristic
75C4×C19⋊C8D411yescharacteristic
76C4×C19⋊C8D411yescharacteristic
77#41×C19—42no—
78#41×C19—42no—
79C2×Q8×C19—21no—
80C2×D4×C19—21no—
81C2×D4×C19—21no—
82C2×D4×C19—21no—
83C2×D4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C2×C22⋊D19—41no—
90C22×Dic19—41no—
91#64541—42no—
92#64541—42no—
93C2×D76—21no—
94C2×D76—21no—
95C2×D76—21no—
96C2×C4×D19—41no—
97C2×Dic38—21no—
98M16×C19—22no—
99M16×C19D814yescomplemented
100C2×C8×C19—22no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C42×C19—42no—
108C42×C19C22×C411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C42×C19#4111yescharacteristic
111C42×C19#4111yescharacteristic
112#64525—42no—
113#64525—42no—
114(C2×D19)⋊C4—41no—
115(C2×D19)⋊C4—41no—
116C4⋊Dic19—22no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—41no—
120C4×Dic19—42no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8C22⋊C411yescharacteristic
125C2×C19⋊C8C22⋊C411yescharacteristic
126C2×C19⋊C8C22⋊C411yescharacteristic
127C2×C19⋊C8C22⋊C411yescharacteristic
128#9719—191nomaximal, Sylow
129C23×C19—41no—
130C23×C19#12711yescharacteristic
131C22×D19—41no—
132Q8×C19—42no—
133D4×C19—41no—
134D4×C19—41no—
135D4×C19—42no—
136D4×C19—81no—
137D4×C19—81no—
138D4×C19—81no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—41no—
144C2×C4×C19—81no—
145C2×C4×C19—81no—
146C2×C4×C19—82no—
147C2×C4×C19C2×C22⋊C411yescharacteristic
148C2×C4×C19C4×D411yescharacteristic
149C2×C4×C19C4×D411yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12411yescharacteristic
153C2×C4×C19C2×D812yes—
154C2×C4×C19#13512yes—
155C22⋊D19—81no—
156C22⋊D19—81no—
157C2×Dic19—42no—
158C2×Dic19—41no—
159C2×Dic19—81no—
160C2×Dic19—81no—
161D76—41no—
162D76—41no—
163D76—42no—
164D76—81no—
165C4×D19—82no—
166Dic38—42no—
167C8×C19—24no—
168C19⋊C8—21no—
169C19⋊C8—21no—
170C19⋊C8—21no—
171C19⋊C8—42no—
172C19⋊C8#10412yescomplemented
173#3169—191no—
174#1980—191no—
175#1980D1911yescharacteristic, complemented
176C4×#107—191no—
177#1502—191no—
178#1502—191no—
179C8×M16—191no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19#39011yescharacteristic
186C22×C19#49311yescharacteristic
187C22×C19#49511yescharacteristic
188C2×D19—81no—
189C2×D19—81no—
190C2×D19—81no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—82no—
195C4×C19—81no—
196C4×C19C2×#10411yescharacteristic
197C4×C19#42111yescharacteristic
198C4×C19C4×D812yes—
199C4×C19#46612yes—
200Dic19—82no—
201Dic19—81no—
202#532—191no—
203#532C2×D1911yescharacteristic
204#500—191no—
205#493—191no—
206#486—191no—
207#486—191no—
208#466—381no—
209#466—381no—
210C4×D8—381no—
211C4×D8—381no—
212#431—191no—
213C2×#107—381no—
214C2×#104—22no—
215C2×#104—382no—
216C4×M16C2×D1911yescharacteristic
217C2×C4×C8—191no—
218C4×C4⋊C4—191no—
219C4×C4⋊C4C2×D1911yescharacteristic
220#340—381no—
221#327—382no—
222#327—382no—
223#322—381no—
224C82—381no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19—161no—
228C2×C19#197011yescharacteristic
229C2×C19#197611yescharacteristic
230C2×C19#198011yescharacteristic
231D19—161no—
232C2×#41—21no—
233C2×#41—381no—
234C2×D8—381no—
235C2×D8—381no—
236C2×M16C22⋊D1912yes—
237C22×C8—191no—
238C22×C8—191no—
239C4⋊Q8—191no—
240C4⋊Q8C4×D1911yescharacteristic
241#127—191no—
242#127C4×D1911yescharacteristic
243#124—21no—
244#124—381no—
245#121—21no—
246#121—21no—
247#121—381no—
248#121—381no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—381no—
252C4×D4—381no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—381no—
255C2×C42—21no—
256C2×C42—381no—
257C2×C42C22×D1911yescharacteristic
258#107—381no—
259#107—381no—
260#107—384no—
261C4⋊C8—381no—
262#104—44no—
263#104—764no—
264#102—381no—
265#102—381no—
266#102—381no—
267#102—381no—
268C22⋊C8—192no—
269#97—21no—
270C4×C8—21no—
271C4×C8—191no—
272C4×C8—191no—
273C4×C8—191no—
274C4×C8—191no—
275C4×C8—381no—
276#95—21no—
277#95—381no—
278C19#971911yescharacteristic, complemented, Sylow
279#41—42no—
280#41—42no—
281#41—762no—
282#41—762no—
283C2×Q8—21no—
284C2×Q8—381no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—381no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—761no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—761no—
296C22×C4—761no—
297C22×C4D4×D1911yescharacteristic
298C22×C4D4×D1911yescharacteristic
299C22×C4C2×C22⋊D1911yescharacteristic
300D8—762no—
301D8—762no—
302M16—22no—
303M16#6452514yescomplemented
304C2×C8—22no—
305C2×C8—191no—
306C2×C8—191no—
307C2×C8—191no—
308C2×C8—191no—
309C2×C8—382no—
310C2×C8—382no—
311C2×C8—761no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—382no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—761no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—761no—
323C22⋊C4—761no—
324C42—42no—
325C42—762no—
326C42C2×C4×D1911yescharacteristic
327C42#6454111yescharacteristic
328C42D4×D1911yescharacteristic
329C42#6454311yescharacteristic
330C23—41no—
331C23—761no—
332C23#1059738611yescharacteristic
333Q8—42no—
334Q8—762no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—761no—
342D4—761no—
343D4—762no—
344D4—1521no—
345D4—1521no—
346D4—1521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—82no—
355C2×C4—762no—
356C2×C4—761no—
357C2×C4—1521no—
358C2×C4—1521no—
359C2×C4—1522no—
360C2×C4C22⋊C4×D1911yescharacteristic
361C2×C4(C22⋊D19)⋊C411yescharacteristic
362C2×C4#1059733011yescharacteristic
363C2×C4#1059733111yescharacteristic
364C2×C4C4×C22⋊D1911yescharacteristic
365C2×C4C2×#6452512yes—
366C2×C4#1059738511yescharacteristic
367C2×C4#1059739612yes—
368C8—24no—
369C8—192no—
370C8—381no—
371C8—381no—
372C8—381no—
373C8—762no—
374C22—21no—
375C22—21no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—1521no—
380C22—1521no—
381C22—1521no—
382C22#1192644411yescharacteristic
383C22#1192692011yescharacteristic
384C22#1192692611yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—82no—
389C4—81no—
390C4—1522no—
391C4—1521no—
392C4#104×D1911yescharacteristic
393C4#1192655911yescharacteristic
394C4C4×#6452512yes—
395C4#1192677812yes—
396C2—21no—
397C2—21no—
398C2—161no—
399C2—3041no—
400C2#1456450011yescharacteristic
401C2#1456453211yescharacteristic
402C2#1456455211yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1980C2
socleC22×C19#390
prime radical#14574210C2
cosocleC2×C42×C19C23
hypercenter#1980D19
hypocenterC19#9719
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #14564554C2semidirect
3. C4×#10597264C2semidirect
4. #14562130C2semidirect
5. #14562129C2semidirect
6. M16×C19⋊C8C2semidirect
7. C19×#1980C2semidirect
9. #11926947C4semidirect
10. #11926920C4semidirect
11. #11926892C4semidirect
12. #11926890C4semidirect
99. M16×C19D8semidirect
172. C19⋊C8#104semidirect
175. #1980D19semidirect
278. C19#9719semidirect
303. M16#64525semidirect

Maximal subgroups

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

subgroupindex
#145742102
#145645542
C4×#105972642
#145621302
#145621292
M16×C19⋊C82
C19×#19802
#971919