Finite Group Databasebeta

← #18080218

Subgroups — #18080218

Order 4864.

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

normal subgroups only

This group has 518 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#14568627C211yesmaximal, characteristic
2#14562360C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic
4#14561492C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7C2×#10597382C412yes—
8#11926601C2212yes—
9#11926469—21no—
10#11926469—21no—
11#11926449C412yes—
12#11926404—21no—
13#11926404—21no—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926292—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×Dic38C2×C412yes—
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—
37#10597382—44no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4×Dic19C2×C412yes—
42#10597315—22no—
43#10597315—22no—
44C19×C4⋊C8D414yes—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19×#97—22no—
49C19⋊#95—22no—
50C19⋊#95—22no—
51C19⋊#95—21no—
52C22⋊(C19⋊C8)—22no—
53C4⋊(C19⋊C8)—22no—
54#10597260—22no—
55C24×C19C22⋊C411yescharacteristic
56C24×C19C22⋊C411yescharacteristic
57C2×D4×C19—22no—
58C2×D4×C19—22no—
59C2×D4×C19—41no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—42no—
65C22×C4×C19—42no—
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—22no—
72C22×Dic19—22no—
73C2×Dic38—24no—
74C2×Dic38—42no—
75C2×Dic38—42no—
76M16×C19—82no—
77C2×C8×C19—24no—
78C2×C8×C19—82no—
79C4⋊C4×C19—22no—
80C22⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C42×C19C2×D412yes—
83C42×C19#4112yes—
84C22⋊Dic19—44no—
85C22⋊Dic19—44no—
86C4⋊Dic19—42no—
87C4⋊Dic19—41no—
88C4⋊Dic19—42no—
89C4⋊Dic19—41no—
90C4×Dic19—42no—
91C2×C19⋊C8—42no—
92#9451—191nomaximal, Sylow
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—21no—
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19#10012yes—
103C23×C19C2×C22⋊C411yescharacteristic
104D4×C19—44no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—41no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19C4×D412yes—
118C2×C4×C19#12011yescharacteristic
119C2×C4×C19#12112yes—
120C2×C4×C19#12311yescharacteristic
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127Dic38—84no—
128C8×C19—44no—
129C19⋊C8—82no—
130#2973D1911yescharacteristic
131#2547—191no—
132#1558—192no—
133#1466—191no—
134#1285—192no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—22no—
138C22×C19—42no—
139C22×C19—42no—
140C22×C19—41no—
141C22×C19—41no—
142C22×C19—41no—
143C22×C19—41no—
144C22×C19—41no—
145C22×C19—81no—
146C22×C19—81no—
147C22×C19#38611yescharacteristic
148C22×C19C2×#10011yescharacteristic
149C22×C19#41311yescharacteristic
150C4×C19—21no—
151C4×C19—22no—
152C4×C19—22no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19#45512yes—
156Dic19—82no—
157Dic19—82no—
158C2×C4⋊Q8—191no—
159C2×#124—192no—
160C2×C4×D4C2×D1911yescharacteristic
161#435—24no—
162#432—192no—
163#432C2×D1912yes—
164#407—21no—
165C2×C22⋊C8—21no—
166#397—381no—
167#397—381no—
168#391—192no—
169#380—381no—
170#380—381no—
171C4×C4⋊C4—191no—
172#333—384no—
173#323—381no—
174#323—381no—
175C2×C19—21no—
176C2×C19—21no—
177C2×C19—42no—
178C2×C19—81no—
179C2×C19#188511yescharacteristic
180C2×C19#190011yescharacteristic
181C2×C19#190911yescharacteristic
182C22×Q8—192no—
183C22×D4C4×D1911yescharacteristic
184C23×C4C22⋊D1911yescharacteristic
185C23×C4C22⋊D1911yescharacteristic
186C2×M16—22no—
187C22×C8—22no—
188C4⋊Q8—382no—
189C4⋊Q8—382no—
190#124—764no—
191C4×D4—22no—
192C4×D4—22no—
193C2×C4⋊C4—381no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4—381no—
196C2×C4⋊C4C4×D1911yescharacteristic
197C2×C22⋊C4—382no—
198C2×C22⋊C4—382no—
199C2×C22⋊C4D7611yescharacteristic
200C2×C22⋊C4D7611yescharacteristic
201C2×C42—192no—
202C2×C42C22×D1911yescharacteristic
203C4⋊C8—382no—
204C4⋊C8C22⋊D1914yes—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—382no—
209#97—22no—
210#97—382no—
211#95—382no—
212#95—382no—
213#95—381no—
214C19#945111yescharacteristic, complemented, Sylow
215C24(C2×D19)⋊C411yescharacteristic
216C24(C2×D19)⋊C411yescharacteristic
217C2×Q8—384no—
218C2×Q8—762no—
219C2×Q8—762no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—382no—
230C22×C4—382no—
231C22×C4(C2×D19)⋊C411yescharacteristic
232C22×C4(C2×D19)⋊C411yescharacteristic
233C22×C4C2×C4×D1911yescharacteristic
234C22×C4C2×D7611yescharacteristic
235C22×C4C2×C22⋊D1911yescharacteristic
236M16—82no—
237C2×C8—24no—
238C2×C8—82no—
239C2×C8—762no—
240C4⋊C4—22no—
241C4⋊C4—762no—
242C4⋊C4—762no—
243C4⋊C4—761no—
244C4⋊C4—761no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—764no—
248C22⋊C4—764no—
249C42—762no—
250C42#6454112yes—
251C42C2×C22⋊D1912yes—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#1059728012yes—
262C23C2×(C2×D19)⋊C411yescharacteristic
263Q8—1524no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4C4×C22⋊D1912yes—
284C2×C4#1059737511yescharacteristic
285C2×C4#1059737612yes—
286C2×C4#1059739911yescharacteristic
287C8—44no—
288C8—1522no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22#1192642311yescharacteristic
302C22C2×#1059728011yescharacteristic
303C22#1192652611yescharacteristic
304C4—22no—
305C4—22no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—1522no—
310C4—1522no—
311C4#1192672212yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#1456402311yescharacteristic
317C2#1456409811yescharacteristic
318C2#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#9451
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. #14562360C2semidirect
4. #14561492C2semidirect
214. C19#9451semidirect

Maximal subgroups

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

subgroupindex
#145686272
#145623602
#145619762
#145614922
C19×#29732
#945119