Finite Group Databasebeta

← #18079874

Subgroups — #18079874

Order 4864.

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

normal subgroups only

This group has 582 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#14569322C211yesmaximal, characteristic
2#14562232C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic, complemented
4#14561529C212yesmaximal, complemented
5C19×#2873C211yesmaximal, characteristic, complemented
6C2×#10597321C2211yescharacteristic
7#11926601C2212yes—
8#11926464C411yescharacteristic
9#11926461C411yescharacteristic
10#11926456C411yescharacteristic
11#11926453C411yescharacteristic
12#11926444—21no—
13#11926435—21no—
14#11926434—21no—
15#11926423—21no—
16#11926390C2211yescharacteristic
17#11926283—24no—
18#11926270—21no—
19#11926268—21no—
20C22×M16×C19—21no—
21C2×C19×#117C2211yescharacteristic
22C19×#405—24no—
23C4×M16×C19—21no—
24C4×M16×C19C2212yes—
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—21no—
27C22×D76C2×C411yescharacteristic
28C22×Dic38C2×C411yescharacteristic
29C2×M16×C19—22no—
30C2×M16×C19—24no—
31C2×M16×C19—24no—
32C2×M16×C19—22no—
33C22×C8×C19—22no—
34C19×#117—22no—
35C19×#117—22no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19C2311yescharacteristic
42C2×C22⋊Dic19—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×C4×Dic19—21no—
50#10597321—22no—
51#10597321—22no—
52C19×#97—22no—
53C19×#97D414yescomplemented
54C4×C8×C19—22no—
55C4×C8×C19—22no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95C2×C411yescharacteristic
60C19⋊#95C2×C411yescharacteristic
61C22⋊(C19⋊C8)—22no—
62C4⋊(C19⋊C8)—22no—
63#10597260—22no—
64C24×C19C22⋊C411yescharacteristic
65C23×D19—21no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C2×C22⋊D19—42no—
77C2×C22⋊D19—42no—
78C2×C22⋊D19—81no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C2×D76—22no—
83C2×D76—81no—
84C2×Dic38—22no—
85C2×Dic38—81no—
86M16×C19—28no—
87M16×C19—24no—
88M16×C19—24no—
89C2×C8×C19—28no—
90C2×C8×C19—24no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—22no—
93C22⋊C4×C19—22no—
94C22⋊C4×C19—22no—
95C42×C19—21no—
96C42×C19—21no—
97C42×C19C2×D412yes—
98C42×C19#4112yes—
99C22⋊Dic19—81no—
100(C2×D19)⋊C4—42no—
101(C2×D19)⋊C4—42no—
102(C2×D19)⋊C4—41no—
103(C2×D19)⋊C4—42no—
104(C2×D19)⋊C4—41no—
105(C2×D19)⋊C4—81no—
106Dic19⋊C4—81no—
107C4×Dic19—42no—
108C2×C19⋊C8—42no—
109#9387—191nomaximal, Sylow
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—41no—
113C23×C19—41no—
114C23×C19#10412yes—
115C23×C19C2×C22⋊C411yescharacteristic
116C22×D19—41no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—41no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—24no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19#10412yes—
137C2×C4×C19C4×D412yes—
138C2×C4×C19#12011yescharacteristic
139C2×C4×C19#12112yes—
140C2×C4×C19#12311yescharacteristic
141C22⋊D19—84no—
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151D76—82no—
152Dic38—82no—
153C8×C19—28no—
154C19⋊C8—82no—
155#2873D1911yescharacteristic, complemented
156#2610—191no—
157#1527—192no—
158#1464—191no—
159#1300—192no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—22no—
163C22×C19—42no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—81no—
167C22×C19#38611yescharacteristic
168C22×C19C2×#10411yescharacteristic
169C22×C19C2×#10411yescharacteristic
170C2×D19—81no—
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C2×D19—81no—
175C2×D19—81no—
176C2×D19—81no—
177C4×C19—22no—
178C4×C19—21no—
179C4×C19—22no—
180C4×C19—21no—
181C4×C19—22no—
182C4×C19—41no—
183C4×C19—41no—
184Dic19—42no—
185Dic19—81no—
186Dic19—81no—
187C22×M16—21no—
188C2×#124—191no—
189C2×#117C2×D1911yescharacteristic
190#432—192no—
191#405—24no—
192C4×M16—21no—
193C4×M16C2×D1912yes—
194#395—191no—
195#394—191no—
196#393—191no—
197#392—191no—
198#390—381no—
199#388—381no—
200#388—381no—
201#386—381no—
202#376—191no—
203#329—384no—
204#324—381no—
205#323—381no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—42no—
209C2×C19#188411yescharacteristic
210C2×C19#189611yescharacteristic
211C2×C19#191411yescharacteristic
212D19—161no—
213C22×Q8—191no—
214C22×D4—191no—
215C22×D4—381no—
216C23×C4C22⋊D1911yescharacteristic
217C2×M16—24no—
218C2×M16—24no—
219C2×M16—22no—
220C2×M16—22no—
221C22×C8—22no—
222#124—382no—
223#124—382no—
224#117—22no—
225#117—22no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4C4×D1911yescharacteristic
228C2×C4⋊C4D7611yescharacteristic
229C2×C22⋊C4—381no—
230C2×C22⋊C4—381no—
231C2×C22⋊C4—381no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C22⋊C4—381no—
235C2×C22⋊C4C4×D1911yescharacteristic
236C2×C22⋊C4D7611yescharacteristic
237C2×C42—381no—
238C2×C42C22⋊D1911yescharacteristic
239C2×C42C22×D1911yescharacteristic
240C4⋊C8—382no—
241C22⋊C8—382no—
242#97—22no—
243#97—382no—
244#97C22⋊D1914yescomplemented
245C4×C8—22no—
246C4×C8—22no—
247#95—191no—
248#95—191no—
249#95—381no—
250#95—381no—
251#95—381no—
252C19#938711yescharacteristic, complemented, Sylow
253C24—381no—
254C24(C2×D19)⋊C411yescharacteristic
255C2×Q8—382no—
256C2×Q8—1521no—
257C2×D4—382no—
258C2×D4—762no—
259C2×D4—762no—
260C2×D4—1521no—
261C2×D4—1521no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4(C2×D19)⋊C411yescharacteristic
270C22×C4(C2×D19)⋊C411yescharacteristic
271C22×C4(C2×D19)⋊C411yescharacteristic
272C22×C4C2×C4×D1911yescharacteristic
273C22×C4C2×D7611yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275M16—28no—
276M16—24no—
277M16—24no—
278C2×C8—28no—
279C2×C8—24no—
280C2×C8—762no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—1521no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—762no—
287C22⋊C4—762no—
288C22⋊C4—761no—
289C22⋊C4—762no—
290C22⋊C4—761no—
291C22⋊C4—1521no—
292C22⋊C4—1521no—
293C42—21no—
294C42—21no—
295C42—762no—
296C42#6454112yes—
297C42C2×C22⋊D1912yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—761no—
303C23—761no—
304C23—761no—
305C23—761no—
306C23—761no—
307C23—761no—
308C23—761no—
309C23#1059726212yes—
310C23C2×(C2×D19)⋊C411yescharacteristic
311Q8—1522no—
312D4—1522no—
313D4—1524no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—382no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4#1059726212yes—
337C2×C4C4×C22⋊D1912yes—
338C2×C4#1059737511yescharacteristic
339C2×C4#1059737612yes—
340C2×C4#1059739911yescharacteristic
341C8—28no—
342C8—1522no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—1521no—
351C22—1521no—
352C22—1521no—
353C22—1521no—
354C22—1521no—
355C22—1521no—
356C22—1521no—
357C22#1192642311yescharacteristic
358C22C2×#1059726211yescharacteristic
359C22C2×#1059726211yescharacteristic
360C4—22no—
361C4—22no—
362C4—21no—
363C4—22no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—762no—
368C4—1521no—
369C4—1521no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—3041no—
374C2#1456401811yescharacteristic
375C2#1456407811yescharacteristic
376C2#1456418211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2873C2
socleC22×C19#386
prime radical#11926453C4
cosocleC2×C42×C19C23
hypercenter#2873D19
hypocenterC19#9387
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #14562232C2semidirect
3. #14561969C2semidirect
4. #14561529C2semidirect
5. C19×#2873C2semidirect
53. C19×#97D4semidirect
155. #2873D19semidirect
244. #97C22⋊D19semidirect
252. C19#9387semidirect

Maximal subgroups

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

subgroupindex
#145693222
#145622322
#145619692
#145615292
C19×#28732
#938719