Finite Group Databasebeta

← #18077618

Subgroups — #18077618

Order 4864.

670 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566914C211yesmaximal, characteristic
2C4×#10597290C211yesmaximal, characteristic, complemented
3#14562077C212yesmaximal, complemented
4#14561527C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic, complemented
6C2×C4×D76C2211yescharacteristic
7C2×C4×C22⋊D19—21no—
8C2×C4×C22⋊D19—21no—
9C2×#10597290—21no—
10C4×#64520C2212yes—
11#11926480C411yescharacteristic
12#11926480C411yescharacteristic
13#11926479—21no—
14#11926453C411yescharacteristic
15#11926453C411yescharacteristic
16#11926452—21no—
17#11926390C2211yescharacteristic
18#11926313—21no—
19#11926271—24no—
20C2×C4×D4×C19C2211yescharacteristic
21C19×#435—24no—
22C19×#432C2212yes—
23C19×#407—21no—
24C2×C19×C22⋊C8—21no—
25C22×D4×C19D411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C22×C22⋊D19—21no—
29C22×C22⋊D19—21no—
30C22×D76C2×C411yescharacteristic
31C22×C4×D19—21no—
32C2×M16×C19—22no—
33C22×C8×C19—22no—
34C4×D4×C19—22no—
35C4×D4×C19—22no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19C2×C411yescharacteristic
39C2×C42×C19C2311yescharacteristic
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C4×C22⋊D19—44no—
43C4×C22⋊D19—44no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×C4⋊Dic19C2×C411yescharacteristic
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×C4×Dic19—21no—
51C2×#64520—22no—
52C4×D76—22no—
53C4×D76—22no—
54C19×C4⋊C8D414yescomplemented
55C19×C22⋊C8—22no—
56C19×C22⋊C8—22no—
57C19×C22⋊C8—22no—
58C19×#97—22no—
59#10597290—24no—
60C19⋊#95—21no—
61C19⋊#95C2×C411yescharacteristic
62C19⋊#95C2×C411yescharacteristic
63#10597260—22no—
64C4×C19⋊C8—22no—
65C24×C19C22⋊C411yescharacteristic
66C24×C19C22⋊C411yescharacteristic
67C23×D19—21no—
68C2×D4×C19—22no—
69C2×D4×C19—22no—
70C2×D4×C19—41no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—42no—
76C22×C4×C19—42no—
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C2×C22⋊D19—42no—
83C2×C22⋊D19—42no—
84C2×C22⋊D19—42no—
85C2×C22⋊D19—42no—
86C2×C22⋊D19—42no—
87C2×C22⋊D19—42no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C2×D76—22no—
92C2×D76—42no—
93C2×C4×D19—42no—
94C2×C4×D19—42no—
95C2×C4×D19—41no—
96C2×C4×D19—41no—
97M16×C19—82no—
98C2×C8×C19—24no—
99C2×C8×C19—82no—
100C4⋊C4×C19—22no—
101C22⋊C4×C19—22no—
102C22⋊C4×C19—22no—
103C42×C19C2×D412yes—
104C42×C19#4112yes—
105C22⋊Dic19—42no—
106C22⋊Dic19—42no—
107(C2×D19)⋊C4—42no—
108(C2×D19)⋊C4—42no—
109(C2×D19)⋊C4—42no—
110C4⋊Dic19—22no—
111Dic19⋊C4—42no—
112Dic19⋊C4—42no—
113C4×Dic19—24no—
114#64520—24no—
115#64520—42no—
116C2×C19⋊C8—42no—
117#9031—191nomaximal, Sylow
118C23×C19—21no—
119C23×C19—21no—
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—21no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19#10412yes—
128C23×C19C2×C22⋊C411yescharacteristic
129C22×D19—22no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135C22×D19—41no—
136D4×C19—44no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—22no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—81no—
148C2×C4×C19—81no—
149C2×C4×C19C4×D412yes—
150C2×C4×C19#12011yescharacteristic
151C2×C4×C19#12112yes—
152C2×C4×C19#12311yescharacteristic
153C22⋊D19—48no—
154C22⋊D19—48no—
155C2×Dic19—22no—
156C2×Dic19—22no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164D76—24no—
165D76—42no—
166C4×D19—82no—
167C4×D19—82no—
168C8×C19—44no—
169C19⋊C8—44no—
170#2973D1911yescharacteristic, complemented
171#2397—191no—
172C4×#100—191no—
173#1490—192no—
174#1300—192no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—22no—
178C22×C19—42no—
179C22×C19—42no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19#38611yescharacteristic
188C22×C19C2×#10411yescharacteristic
189C22×C19#42111yescharacteristic
190C2×D19—42no—
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—81no—
194C2×D19—81no—
195C2×D19—81no—
196C2×D19—81no—
197C4×C19—22no—
198C4×C19—21no—
199C4×C19—22no—
200C4×C19—41no—
201C4×C19—41no—
202C4×C19#45312yes—
203Dic19—42no—
204Dic19—42no—
205Dic19—81no—
206C2×C4×D4—191no—
207C2×C4×D4—381no—
208C2×C4×D4—381no—
209C2×C4×D4C2×D1911yescharacteristic
210#435—24no—
211#432C2×D1912yes—
212C2×#100—381no—
213#407—21no—
214C2×C22⋊C8—21no—
215C4×M16—192no—
216#399—191no—
217#399—191no—
218#399—381no—
219#392—191no—
220#392—191no—
221#392—381no—
222#376—191no—
223#343—381no—
224D4⋊C8—384no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19—42no—
228C2×C19—81no—
229C2×C19#187111yescharacteristic
230C2×C19#188711yescharacteristic
231C2×C19#189111yescharacteristic
232D19—82no—
233C22×D4—191no—
234C22×D4—381no—
235C22×D4—381no—
236C22×D4D7611yescharacteristic
237C23×C4—381no—
238C23×C4C22⋊D1911yescharacteristic
239C23×C4C22⋊D1911yescharacteristic
240C2×M16—22no—
241C2×M16—382no—
242C22×C8—22no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—382no—
246C4×D4—382no—
247C4×D4—764no—
248C4×D4—764no—
249C2×C4⋊C4—191no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4D7611yescharacteristic
253C2×C22⋊C4—381no—
254C2×C22⋊C4—381no—
255C2×C22⋊C4—381no—
256C2×C22⋊C4—381no—
257C2×C22⋊C4—381no—
258C2×C22⋊C4C4×D1911yescharacteristic
259C2×C22⋊C4C4×D1911yescharacteristic
260C2×C42—381no—
261C2×C42C22×D1911yescharacteristic
262C4⋊C8C22⋊D1914yescomplemented
263#100—384no—
264C22⋊C8—22no—
265C22⋊C8—22no—
266C22⋊C8—22no—
267#97—22no—
268#97—382no—
269C4×C8—382no—
270#95—191no—
271#95—191no—
272#95—381no—
273C19#903111yescharacteristic, complemented, Sylow
274C24—381no—
275C24(C2×D19)⋊C411yescharacteristic
276C24(C2×D19)⋊C411yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—382no—
281C2×D4—762no—
282C2×D4—762no—
283C2×D4—762no—
284C2×D4—762no—
285C2×D4—762no—
286C2×D4—762no—
287C2×D4—762no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—762no—
298C22×C4—762no—
299C22×C4—761no—
300C22×C4—761no—
301C22×C4(C2×D19)⋊C411yescharacteristic
302C22×C4(C2×D19)⋊C411yescharacteristic
303C22×C4C2×C4×D1911yescharacteristic
304C22×C4C2×D7611yescharacteristic
305C22×C4C2×C22⋊D1911yescharacteristic
306M16—82no—
307M16—384no—
308M16—762no—
309C2×C8—24no—
310C2×C8—82no—
311C2×C8—762no—
312C4⋊C4—22no—
313C4⋊C4—382no—
314C4⋊C4—762no—
315C4⋊C4—762no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—762no—
319C22⋊C4—762no—
320C22⋊C4—762no—
321C22⋊C4—762no—
322C22⋊C4—762no—
323C42—384no—
324C42#6454112yes—
325C42C2×C22⋊D1912yes—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—382no—
336C23—761no—
337C23—761no—
338C23—761no—
339C23—761no—
340C23—761no—
341C23—761no—
342C23#1059728212yes—
343C23C2×(C2×D19)⋊C411yescharacteristic
344D4—44no—
345D4—384no—
346D4—762no—
347D4—768no—
348D4—768no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—382no—
362C2×C4—382no—
363C2×C4—761no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—1522no—
371C2×C4—1522no—
372C2×C4C4×C22⋊D1912yes—
373C2×C4#1059737511yescharacteristic
374C2×C4#1059737612yes—
375C2×C4#1059739911yescharacteristic
376C8—44no—
377C8—764no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—762no—
391C22—762no—
392C22—762no—
393C22—1521no—
394C22—1521no—
395C22—1521no—
396C22—1521no—
397C22#1192642311yescharacteristic
398C22C2×#1059728211yescharacteristic
399C22#1192656011yescharacteristic
400C4—22no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—762no—
406C4—762no—
407C4—1521no—
408C4#1192671212yes—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—81no—
413C2—1522no—
414C2#1456393711yescharacteristic
415C2#1456403311yescharacteristic
416C2#1456405311yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radical#14566914C2
cosocleC2×C42×C19C23
hypercenter#2973D19
hypocenterC19#9031
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. C4×#10597290C2semidirect
3. #14562077C2semidirect
4. #14561527C2semidirect
5. C19×#2973C2semidirect
54. C19×C4⋊C8D4semidirect
170. #2973D19semidirect
262. C4⋊C8C22⋊D19semidirect
273. C19#9031semidirect

Maximal subgroups

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

subgroupindex
#145669142
C4×#105972902
#145620772
#145615272
C19×#29732
#903119