Finite Group Databasebeta

← #18070760

Subgroups — #18070760

Order 4864.

874 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 109 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
1D19×#390C211yesmaximal, characteristic
2#14563396C212yesmaximal, complemented
3#14561456C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic, complemented
6C22×D4×D19C411yescharacteristic
7C2×C4⋊C4×D19C411yescharacteristic
8C2×C22⋊C4×D19—22no—
9C2×C42×D19C2211yescharacteristic
10C2×(C2×D19)⋊C8—22no—
11C2×#10597272—22no—
12#11926447C411yescharacteristic
13#11926446C2211yescharacteristic
14#11926445C411yescharacteristic
15#11926444—22no—
16#11926299C2212yescomplemented
17C19×#390C2211yescharacteristic
18C19×#336C2212yescomplemented
19C24×D19—21no—
20C22×D4×C19C2×C411yescharacteristic
21C22×C22⋊D19—21no—
22C2×D4×D19—22no—
23C2×D4×D19—22no—
24C2×D4×D19—42no—
25C2×D4×D19—42no—
26C22×D76C2×C411yescharacteristic
27C22×C4×D19—21no—
28C22×C4×D19C2×C411yescharacteristic
29C22×C4×D19D412yes—
30C22×C8×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19—22no—
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×Dic19⋊C4—21no—
39C2×C4×Dic19C2×C411yescharacteristic
40C2×C4×Dic19D412yes—
41C22×C19⋊C8—22no—
42C4⋊C4×D19—42no—
43C22⋊C4×D19—44no—
44C22⋊C4×D19—44no—
45C42×D19—42no—
46(C2×D19)⋊C8—28no—
47#10597272—44no—
48C24×C19—21no—
49C23×D19—24no—
50C23×D19—21no—
51C23×D19—42no—
52C23×D19—44no—
53C23×D19—42no—
54C23×D19—44no—
55C23×D19C22⋊C411yescharacteristic
56C2×D4×C19—21no—
57C2×D4×C19—41no—
58C2×D4×C19—41no—
59C2×D4×C19M1612yes—
60C22×C4×C19—21no—
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D412yes—
63C2×C22⋊D19—24no—
64C2×C22⋊D19—42no—
65C2×C22⋊D19—42no—
66C22×Dic19—21no—
67C22×Dic19C22⋊C412yes—
68C22×Dic19C22⋊C411yescharacteristic
69D4×D19—48no—
70D4×D19—48no—
71C2×D76—21no—
72C2×D76—41no—
73C2×D76—41no—
74C2×D76M1612yes—
75C2×C4×D19—22no—
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19—22no—
79C2×C4×D19—24no—
80C2×C4×D19—22no—
81C2×C4×D19—22no—
82C2×C4×D19—42no—
83C2×C4×D19—44no—
84C2×C4×D19—42no—
85C2×C8×C19—24no—
86C2×C8×C19—42no—
87C2×C8×C19—42no—
88C4⋊C4×C19—41no—
89C22⋊C4×C19—42no—
90C22⋊C4×C19—42no—
91C42×C19—41no—
92C22⋊Dic19—44no—
93(C2×D19)⋊C4—44no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96C4⋊Dic19—41no—
97Dic19⋊C4—42no—
98C4×Dic19—24no—
99C4×Dic19—41no—
100C2×C19⋊C8—24no—
101C2×C19⋊C8—42no—
102C2×C19⋊C8—42no—
103#7626—191nomaximal, Sylow
104C23×C19—22no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19C2×C22⋊C411yescharacteristic
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—22no—
113C22×D19—22no—
114C22×D19—48no—
115C22×D19—416no—
116C22×D19—41no—
117C22×D19—41no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19—84no—
121C22×D19—88no—
122C22×D19—84no—
123C22×D19#10012yes—
124C22×D19#10414yes—
125D4×C19—42no—
126D4×C19—42no—
127C2×C4×C19—22no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—22no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19C2×M1611yescharacteristic
134C2×C4×C19C2×M1611yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)12yes—
136C2×C4×C19AGL(1,ℤ/8)12yes—
137C22⋊D19—48no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—22no—
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19—42no—
145C2×Dic19#9912yes—
146D76—42no—
147D76—42no—
148C4×D19—24no—
149C4×D19—24no—
150C4×D19—44no—
151C4×D19—44no—
152C4×D19—84no—
153C8×C19—44no—
154C19⋊C8—44no—
155C2×#390—191no—
156#1749—192no—
157#1270—191no—
158#1270—192no—
159#1270D1911yescharacteristic, complemented
160C22×C19—42no—
161C22×C19—44no—
162C22×C19—81no—
163C22×C19—82no—
164C22×C19—81no—
165C22×C19#40711yescharacteristic
166C22×C19C2×#9911yescharacteristic
167C22×C19C2×#10011yescharacteristic
168C22×C19#41812yes—
169C22×C19C2×#10412yes—
170C2×D19—22no—
171C2×D19—22no—
172C2×D19—24no—
173C2×D19—24no—
174C2×D19—42no—
175C2×D19—44no—
176C2×D19—816no—
177C2×D19—81no—
178C2×D19—82no—
179C2×D19—81no—
180C2×D19#32914yes—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—22no—
184C4×C19—22no—
185C4×C19—81no—
186Dic19—22no—
187Dic19—42no—
188Dic19—81no—
189C23×D4—191no—
190C22×C4⋊C4—191no—
191C22×C22⋊C4—382no—
192C22×C42—191no—
193C2×C22⋊C8—382no—
194C2×#97—382no—
195#390—191no—
196#390—191no—
197#390—191no—
198#390—382no—
199#390C2×D1911yescharacteristic
200#336—192no—
201#336C2×D1912yescomplemented
202C2×C19—82no—
203C2×C19#146211yescharacteristic
204C2×C19#149012yes—
205C2×C19#150712yes—
206C2×C19C2×#32911yescharacteristic
207C2×C19#155511yescharacteristic
208D19—24no—
209D19—82no—
210C25—381no—
211C22×D4—191no—
212C22×D4—381no—
213C22×D4—382no—
214C22×D4—382no—
215C22×D4—762no—
216C22×D4—762no—
217C22×D4C4×D1911yescharacteristic
218C23×C4—191no—
219C23×C4—192no—
220C23×C4—381no—
221C22×C8—22no—
222C22×C8—382no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—762no—
226C2×C4⋊C4C4×D1911yescharacteristic
227C2×C22⋊C4—22no—
228C2×C22⋊C4—382no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4—382no—
231C2×C22⋊C4—764no—
232C2×C22⋊C4—764no—
233C2×C42—192no—
234C2×C42—191no—
235C2×C42—762no—
236C2×C42C22×D1911yescharacteristic
237C22⋊C8—388no—
238#97—764no—
239C19#762611yescharacteristic, complemented, Sylow
240C24—21no—
241C24—191no—
242C24—384no—
243C24—381no—
244C24—762no—
245C24—764no—
246C24—764no—
247C24—762no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—192no—
252C2×D4—384no—
253C2×D4—381no—
254C2×D4—761no—
255C2×D4—761no—
256C2×D4—762no—
257C2×D4—768no—
258C2×D4—768no—
259C2×D4—762no—
260C2×D4#6451512yes—
261C22×C4—21no—
262C22×C4—191no—
263C22×C4—192no—
264C22×C4—382no—
265C22×C4—382no—
266C22×C4—384no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—382no—
270C22×C4—382no—
271C22×C4—381no—
272C22×C4—762no—
273C22×C4—762no—
274C22×C4—764no—
275C22×C4C2×C4×D1911yescharacteristic
276C22×C4D4×D1912yes—
277C2×C8—24no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—384no—
281C2×C8—762no—
282C2×C8—762no—
283C4⋊C4—41no—
284C4⋊C4—761no—
285C4⋊C4—762no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—764no—
289C22⋊C4—764no—
290C22⋊C4—762no—
291C22⋊C4—762no—
292C42—41no—
293C42—384no—
294C42—761no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23—41no—
299C23—41no—
300C23—194no—
301C23—192no—
302C23—382no—
303C23—381no—
304C23—381no—
305C23—382no—
306C23—768no—
307C23—7616no—
308C23—762no—
309C23—762no—
310C23—761no—
311C23—761no—
312C23—1524no—
313C23—1524no—
314C23—1528no—
315C23C22⋊C4×D1911yescharacteristic
316D4—42no—
317D4—42no—
318D4—762no—
319D4—762no—
320D4—768no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—192no—
328C2×C4—384no—
329C2×C4—384no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—382no—
335C2×C4—764no—
336C2×C4—764no—
337C2×C4—762no—
338C2×C4—761no—
339C2×C4—1524no—
340C2×C4C2×#6451511yescharacteristic
341C2×C4M16×D1911yescharacteristic
342C2×C4#1059735712yes—
343C2×C4#1059736012yes—
344C8—44no—
345C8—764no—
346C22—44no—
347C22—42no—
348C22—81no—
349C22—82no—
350C22—81no—
351C22—194no—
352C22—384no—
353C22—382no—
354C22—384no—
355C22—382no—
356C22—764no—
357C22—762no—
358C22—15216no—
359C22—1521no—
360C22—1522no—
361C22—1521no—
362C22#1192650611yescharacteristic
363C22#99×D1911yescharacteristic
364C22#100×D1911yescharacteristic
365C22#1192654712yes—
366C22#104×D1912yes—
367C4—22no—
368C4—22no—
369C4—21no—
370C4—21no—
371C4—81no—
372C4—382no—
373C4—762no—
374C4—1521no—
375C2—82no—
376C2—384no—
377C2—1522no—
378C2#1456196011yescharacteristic
379C2#1456207612yes—
380C2#1456214912yes—
381C2D19×#32911yescharacteristic
382C2#1456234711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D4×D19C4
cosocleC2×C42×C19C23
hypercenter#1270D19
hypocenterC19#7626
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14563396C2semidirect
3. #14561456C2semidirect
4. #14561455C2semidirect
5. C19×#1270C2semidirect
16. #11926299C22semidirect
18. C19×#336C22semidirect
159. #1270D19semidirect
201. #336C2×D19semidirect
239. C19#7626semidirect

Maximal subgroups

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

subgroupindex
D19×#3902
#145633962
#145614562
#145614552
C19×#12702
#762619