Finite Group Databasebeta

← #18080238

Subgroups — #18080238

Order 4864.

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

normal subgroups only

This group has 554 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#14568588C211yesmaximal, characteristic
2#14562353C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic
4#14561492C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7C2×#10597370—21no—
8C2×#10597370—21no—
9#11926601C2212yes—
10#11926480—21no—
11#11926480—21no—
12#11926447C412yes—
13#11926413C412yes—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926291—24no—
16#11926268—21no—
17#11926268—21no—
18C2×C4×D4×C19C2211yescharacteristic
19C19×#435—24no—
20C19×#432C2212yes—
21C19×#407—21no—
22C2×C19×C22⋊C8—21no—
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×Dic38—21no—
27C2×M16×C19—22no—
28C22×C8×C19—22no—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19D411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19—22no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19C2×C412yes—
40#10597370—44no—
41#10597370—44no—
42C2×Dic19⋊C4—22no—
43C2×Dic19⋊C4—22no—
44C2×C4×Dic19C2×C412yes—
45#10597315—22no—
46#10597315—22no—
47C19×C4⋊C8D414yes—
48C19×C22⋊C8—22no—
49C19×C22⋊C8—22no—
50C19×C22⋊C8—22no—
51C19×#97—22no—
52C19⋊#95—21no—
53C22⋊(C19⋊C8)—22no—
54C4⋊(C19⋊C8)—22no—
55#10597260—22no—
56C24×C19C22⋊C411yescharacteristic
57C24×C19C22⋊C411yescharacteristic
58C2×D4×C19—22no—
59C2×D4×C19—22no—
60C2×D4×C19—41no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22×C411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×Dic19—22no—
73C22×Dic19—22no—
74C2×Dic38—42no—
75C2×Dic38—42no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78M16×C19—82no—
79C2×C8×C19—24no—
80C2×C8×C19—82no—
81C4⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C42×C19C2×D412yes—
85C42×C19#4112yes—
86C22⋊Dic19—44no—
87C22⋊Dic19—44no—
88C4⋊Dic19—24no—
89C4⋊Dic19—24no—
90C4⋊Dic19—42no—
91Dic19⋊C4—44no—
92Dic19⋊C4—44no—
93C4×Dic19—42no—
94C2×C19⋊C8—42no—
95#9455—191nomaximal, Sylow
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—41no—
105C23×C19#10112yes—
106C23×C19C2×C22⋊C411yescharacteristic
107D4×C19—44no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—22no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—81no—
119C2×C4×C19—81no—
120C2×C4×C19C4×D412yes—
121C2×C4×C19#12011yescharacteristic
122C2×C4×C19#12112yes—
123C2×C4×C19#12311yescharacteristic
124C2×Dic19—24no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130Dic38—82no—
131Dic38—82no—
132C8×C19—44no—
133C19⋊C8—82no—
134#2973D1911yescharacteristic
135#2542—191no—
136#1556—192no—
137#1466—191no—
138#1285—192no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—22no—
142C22×C19—42no—
143C22×C19—42no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19—41no—
147C22×C19—41no—
148C22×C19—41no—
149C22×C19—81no—
150C22×C19—81no—
151C22×C19#38611yescharacteristic
152C22×C19C2×#10111yescharacteristic
153C22×C19#41311yescharacteristic
154C4×C19—21no—
155C4×C19—22no—
156C4×C19—22no—
157C4×C19—41no—
158C4×C19—41no—
159C4×C19#45312yes—
160Dic19—44no—
161Dic19—82no—
162C2×C4⋊Q8—191no—
163C2×C22⋊Q8—381no—
164C2×C22⋊Q8—381no—
165C2×C4×D4C2×D1911yescharacteristic
166#435—24no—
167#432—192no—
168#432C2×D1912yes—
169#407—21no—
170C2×C22⋊C8—21no—
171#399—381no—
172#399—381no—
173#390—192no—
174#384—192no—
175C4×C4⋊C4—191no—
176#332—384no—
177#323—381no—
178#323—381no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19—42no—
182C2×C19—81no—
183C2×C19#188711yescharacteristic
184C2×C19#190111yescharacteristic
185C2×C19#190911yescharacteristic
186C22×Q8—381no—
187C22×D4C4×D1911yescharacteristic
188C23×C4C22⋊D1911yescharacteristic
189C23×C4C22⋊D1911yescharacteristic
190C2×M16—22no—
191C22×C8—22no—
192C4⋊Q8—382no—
193C4⋊Q8—382no—
194C22⋊Q8—764no—
195C22⋊Q8—764no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—192no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4—382no—
201C2×C4⋊C4—382no—
202C2×C4⋊C4—381no—
203C2×C4⋊C4C4×D1911yescharacteristic
204C2×C22⋊C4—382no—
205C2×C22⋊C4—382no—
206C2×C22⋊C4D7611yescharacteristic
207C2×C22⋊C4D7611yescharacteristic
208C2×C42—192no—
209C2×C42C22×D1911yescharacteristic
210C4⋊C8—382no—
211C4⋊C8C22⋊D1914yes—
212C22⋊C8—22no—
213C22⋊C8—22no—
214C22⋊C8—22no—
215C22⋊C8—382no—
216#97—22no—
217#97—382no—
218#95—381no—
219C19#945511yescharacteristic, complemented, Sylow
220C24(C2×D19)⋊C411yescharacteristic
221C24(C2×D19)⋊C411yescharacteristic
222C2×Q8—762no—
223C2×Q8—762no—
224C2×Q8—761no—
225C2×Q8—761no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—382no—
236C22×C4—382no—
237C22×C4(C2×D19)⋊C411yescharacteristic
238C22×C4(C2×D19)⋊C411yescharacteristic
239C22×C4C2×C4×D1911yescharacteristic
240C22×C4C2×D7611yescharacteristic
241C22×C4C2×C22⋊D1911yescharacteristic
242M16—82no—
243C2×C8—24no—
244C2×C8—82no—
245C2×C8—762no—
246C4⋊C4—22no—
247C4⋊C4—384no—
248C4⋊C4—384no—
249C4⋊C4—764no—
250C4⋊C4—764no—
251C4⋊C4—762no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—764no—
255C22⋊C4—764no—
256C42—762no—
257C42#6454112yes—
258C42C2×C22⋊D1912yes—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23#1059728112yes—
269C23C2×(C2×D19)⋊C411yescharacteristic
270Q8—1522no—
271Q8—1522no—
272D4—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—384no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4—762no—
290C2×C4—762no—
291C2×C4C4×C22⋊D1912yes—
292C2×C4#1059737511yescharacteristic
293C2×C4#1059737612yes—
294C2×C4#1059739911yescharacteristic
295C8—44no—
296C8—1522no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#1192642311yescharacteristic
310C22C2×#1059728111yescharacteristic
311C22#1192652611yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—764no—
318C4—1522no—
319C4#1192671212yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—81no—
324C2#1456403311yescharacteristic
325C2#1456410311yescharacteristic
326C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2973D19
hypocenterC19#9455
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14562353C2semidirect
4. #14561492C2semidirect
219. C19#9455semidirect

Maximal subgroups

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

subgroupindex
#145685882
#145623532
#145619762
#145614922
C19×#29732
#945519