Finite Group Databasebeta

← #18080308

Subgroups — #18080308

Order 4864.

578 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 135 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#14567952C211yesmaximal, characteristic
2#14563726C212yesmaximal, complemented
3#14563623C211yesmaximal, characteristic
4#14561503C212yesmaximal, complemented
5C19×#2972C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7C2×#10597291—21no—
8#11926483C412yescomplemented
9#11926480C412yescomplemented
10#11926442—21no—
11#11926424—21no—
12#11926416—21no—
13#11926404—21no—
14#11926404C2212yes—
15#11926404C2211yescharacteristic
16#11926311—21no—
17#11926307—24no—
18C2×C4×D4×C19C2211yescharacteristic
19C8×D4×C19—24no—
20C19×#431—21no—
21C2×C19×C22⋊C8—21no—
22C2×C19×C22⋊C8C2212yes—
23C22×D4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—21no—
27C22×C8×C19—22no—
28C22×C8×C19D414yes—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—22no—
37C2×C22⋊Dic19—22no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19—22no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—22no—
43C2×C4⋊Dic19C2×C412yes—
44C2×Dic19⋊C4—22no—
45C19×C4⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19×C22⋊C8—22no—
49C4×C8×C19—22no—
50#10597291—42no—
51C19⋊#95—22no—
52C19⋊#95—22no—
53C19⋊#95—22no—
54C19⋊#95C2×C412yes—
55C24×C19C22⋊C411yescharacteristic
56C24×C19C2×D411yescharacteristic
57C2×D4×C19—22no—
58C2×D4×C19—22no—
59C2×D4×C19SD1612yes—
60C2×D4×C19Q1612yes—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—42no—
64C22×C4×C19—42no—
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D412yes—
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19#4112yes—
72C22×Dic19—22no—
73C22×Dic19—22no—
74C22×Dic19—42no—
75C22×Dic19—42no—
76C22×Dic19—82no—
77C2×C8×C19—24no—
78C2×C8×C19—44no—
79C2×C8×C19—82no—
80C4⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C42×C19—21no—
84C42×C19—21no—
85C22⋊Dic19—42no—
86C22⋊Dic19—42no—
87C22⋊Dic19—42no—
88C22⋊Dic19—82no—
89C4⋊Dic19—24no—
90C4⋊Dic19—42no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—44no—
94Dic19⋊C4—82no—
95#9469—191nomaximal, Sylow
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19#10312yes—
103C23×C19C2×C22⋊C411yescharacteristic
104C23×C19#12112yes—
105C23×C19C2×SD1611yescharacteristic
106C23×C19C2×Q1611yescharacteristic
107C23×C19#13512yes—
108D4×C19—24no—
109D4×C19—24no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—24no—
113C2×C4×C19—22no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—41no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—81no—
122C2×C4×C19#10312yes—
123C2×C4×C19C4×D412yes—
124C2×C4×C19#12011yescharacteristic
125C2×C4×C19#12311yescharacteristic
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132C2×Dic19—84no—
133C2×Dic19—82no—
134C2×Dic19—82no—
135C2×Dic19—82no—
136C8×C19—44no—
137#2972D1911yescharacteristic
138#2487—191no—
139#1824—192no—
140#1799—191no—
141#1289—192no—
142C22×C19—21no—
143C22×C19—22no—
144C22×C19—21no—
145C22×C19—22no—
146C22×C19—22no—
147C22×C19—41no—
148C22×C19—41no—
149C22×C19—42no—
150C22×C19—42no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19—81no—
154C22×C19#38611yescharacteristic
155C22×C19C2×#10311yescharacteristic
156C22×C19#41611yescharacteristic
157C22×C19#46512yes—
158C22×C19#46712yes—
159C4×C19—21no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19#45812yes—
165Dic19—82no—
166Dic19—82no—
167Dic19—162no—
168C2×C4×D4C2×D1911yescharacteristic
169C22×C4⋊C4—191no—
170C8×D4—24no—
171#431—21no—
172C2×#99—381no—
173C2×C22⋊C8—21no—
174C2×C22⋊C8C2×D1912yes—
175#400—192no—
176#399—192no—
177#389—381no—
178#386—381no—
179#385—381no—
180#380—191no—
181#380—192no—
182#380—381no—
183#342—381no—
184#340—384no—
185C2×C19—21no—
186C2×C19—22no—
187C2×C19—21no—
188C2×C19—22no—
189C2×C19—42no—
190C2×C19#189011yescharacteristic
191C2×C19#189211yescharacteristic
192C2×C19#191011yescharacteristic
193C22×D4D7611yescharacteristic
194C23×C4—381no—
195C23×C4C22⋊D1911yescharacteristic
196C23×C4C22×D1911yescharacteristic
197C22×C8—22no—
198C22×C8C22⋊D1914yes—
199C4×D4—22no—
200C4×D4—22no—
201C2×C4⋊C4—192no—
202C2×C4⋊C4—382no—
203C2×C4⋊C4—382no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—382no—
207C2×C4⋊C4—382no—
208C2×C4⋊C4C4×D1911yescharacteristic
209C2×C22⋊C4—381no—
210C2×C22⋊C4—382no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4C4×D1911yescharacteristic
213C2×C22⋊C4D7611yescharacteristic
214C2×C42C22⋊D1911yescharacteristic
215C4⋊C8—22no—
216#99—762no—
217C22⋊C8—22no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C4×C8—22no—
221#95—192no—
222#95—382no—
223#95—382no—
224#95—382no—
225C19#946911yescharacteristic, complemented, Sylow
226C24(C2×D19)⋊C411yescharacteristic
227C24C2×D7611yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4#6451612yes—
231C2×D4Dic7612yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—382no—
237C22×C4—382no—
238C22×C4—762no—
239C22×C4—762no—
240C22×C4—1522no—
241C22×C4(C2×D19)⋊C411yescharacteristic
242C22×C4(C2×D19)⋊C411yescharacteristic
243C22×C4(C2×D19)⋊C411yescharacteristic
244C22×C4C2×C4×D1911yescharacteristic
245C22×C4#6454112yes—
246C22×C4C2×C22⋊D1912yes—
247C22×C4C2×C22⋊D1911yescharacteristic
248C2×C8—24no—
249C2×C8—44no—
250C2×C8—82no—
251C4⋊C4—22no—
252C4⋊C4—384no—
253C4⋊C4—762no—
254C4⋊C4—764no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C4⋊C4—1522no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—762no—
261C22⋊C4—762no—
262C22⋊C4—762no—
263C22⋊C4—1522no—
264C42—21no—
265C42—21no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23#1059727312yes—
273C23C2×#6451611yescharacteristic
274C23#1059735012yes—
275C23C2×Dic7611yescharacteristic
276C23C2×(C2×D19)⋊C411yescharacteristic
277C23#1059737612yes—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—762no—
293C2×C4—762no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4—762no—
298C2×C4—1522no—
299C2×C4—1522no—
300C2×C4—1522no—
301C2×C4—1524no—
302C2×C4#1059727312yes—
303C2×C4C4×C22⋊D1912yes—
304C2×C4#1059737511yescharacteristic
305C2×C4#1059739911yescharacteristic
306C8—44no—
307C22—21no—
308C22—22no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—41no—
313C22—42no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22#1192642311yescharacteristic
320C22C2×#1059727311yescharacteristic
321C22#1192654111yescharacteristic
322C22#1192677312yes—
323C22#1192678512yes—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—3042no—
330C4—1522no—
331C4—1522no—
332C4#1192673412yes—
333C2—22no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—42no—
338C2#1456404811yescharacteristic
339C2#1456405811yescharacteristic
340C2#1456416211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2972C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#2972D19
hypocenterC19#9469
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #14563726C2semidirect
4. #14561503C2semidirect
8. #11926483C4semidirect
9. #11926480C4semidirect
225. C19#9469semidirect

Maximal subgroups

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

subgroupindex
#145679522
#145637262
#145636232
#145615032
C19×#29722
#946919