Finite Group Databasebeta

← #18078325

Subgroups — #18078325

Order 4864.

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

normal subgroups only

This group has 648 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
1C2×#11926412C211yesmaximal, characteristic, complemented
2#14563703C211yesmaximal, characteristic, complemented
3C2×#11926278C212yesmaximal
4#14561513C212yesmaximal, complemented
5C19×#2854C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926412—24no—
8C2×C19⋊#95—21no—
9C2×C19⋊#95—21no—
10C2×C19⋊#95C2212yes—
11#11926299—22no—
12#11926278—24no—
13C2×C19×#123—21no—
14C2×C19×#121C2211yescharacteristic
15C22×C42×C19C2211yescharacteristic
16C19×#390C412yescomplemented
17C19×#389C412yescomplemented
18C19×#388—22no—
19C19×#386—21no—
20C19×#380C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—22no—
27C19×#123—44no—
28C19×#121—22no—
29C19×#121—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19C2×C412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19—22no—
38C2×C42×C19—22no—
39C2×C42×C19C2×C412yes—
40C2×C42×C19D412yes—
41C22×C19⋊C8—22no—
42C19×#95—22no—
43C19×#95—21no—
44C19⋊#95—24no—
45C19⋊#95—24no—
46C19⋊#95—22no—
47C19⋊#95D414yes—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19—21no—
51C24×C19C2×D411yescharacteristic
52C2×D4×C19—22no—
53C2×D4×C19—42no—
54C2×D4×C19—41no—
55C2×D4×C19—41no—
56C2×D4×C19—42no—
57C2×D4×C19—42no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—22no—
65C22×C4×C19—21no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C22⋊C412yes—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D412yes—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4112yes—
74C22×Dic19—24no—
75C22×Dic19—44no—
76C22×Dic19—44no—
77C22×Dic19—42no—
78C22×Dic19—42no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—42no—
81C4⋊C4×C19—44no—
82C22⋊C4×C19—44no—
83C22⋊C4×C19—44no—
84C22⋊C4×C19—42no—
85C22⋊C4×C19—42no—
86C42×C19—24no—
87C42×C19—24no—
88C2×C19⋊C8—44no—
89C2×C19⋊C8—42no—
90#9157—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—41no—
94C23×C19—42no—
95C23×C19—41no—
96C23×C19—41no—
97C23×C19—42no—
98C23×C19C2×C22⋊C411yescharacteristic
99C23×C19#12011yescharacteristic
100C23×C19#12311yescharacteristic
101C23×C19#13512yes—
102C23×C19AGL(1,ℤ/8)12yes—
103D4×C19—82no—
104D4×C19—82no—
105D4×C19—82no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19C4×D412yes—
127C2×C4×C19#12112yes—
128C2×Dic19—44no—
129C2×Dic19—44no—
130C2×Dic19—44no—
131C2×Dic19—84no—
132C2×Dic19—84no—
133C19⋊C8—82no—
134#2854D1911yescharacteristic
135C2×#383—191no—
136#1817—191no—
137C2×#327—192no—
138#1294—192no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—24no—
144C22×C19—24no—
145C22×C19—81no—
146C22×C19—81no—
147C22×C19—81no—
148C22×C19—82no—
149C22×C19—82no—
150C22×C19#38611yescharacteristic
151C22×C19#41012yes—
152C22×C19#41611yescharacteristic
153C22×C19#41811yescharacteristic
154C22×C19#42112yes—
155C22×C19#44912yes—
156C22×C19#48212yes—
157C4×C19—22no—
158C4×C19—22no—
159C4×C19—42no—
160C4×C19—42no—
161C4×C19—81no—
162C4×C19—82no—
163Dic19—84no—
164C2×#123—21no—
165C2×#121C2×D1911yescharacteristic
166C22×C42C2×D1911yescharacteristic
167C2×C22⋊C8—192no—
168#390Dic1912yescomplemented
169#389Dic1912yescomplemented
170#388—22no—
171#386—21no—
172#383—384no—
173#380C2×D1911yescharacteristic
174C2×#95—192no—
175C2×#95—381no—
176C2×#95—381no—
177#336—382no—
178#327—384no—
179C2×C19—22no—
180C2×C19—22no—
181C2×C19—161no—
182C2×C19#151412yes—
183C2×C19#152112yes—
184C2×C19#187511yescharacteristic
185C2×C19#189711yescharacteristic
186C2×C19#189911yescharacteristic
187C22×D4—21no—
188C22×D4C2×Dic1911yescharacteristic
189C23×C4—382no—
190C23×C4C22⋊D1911yescharacteristic
191C23×C4C22⋊D1911yescharacteristic
192C23×C4C22×D1911yescharacteristic
193C22×C8—382no—
194#123—44no—
195#121—22no—
196#121—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4C2×Dic1911yescharacteristic
199C2×C4⋊C4C2×Dic1912yes—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—21no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C2×Dic1912yes—
207C2×C42C22⋊D1912yes—
208C22⋊C8—382no—
209C22⋊C8—382no—
210#95—22no—
211#95—21no—
212#95—194no—
213#95—384no—
214#95—384no—
215#95—382no—
216C19#915711yescharacteristic, complemented, Sylow
217C24—21no—
218C24C2×C22⋊D1911yescharacteristic
219C2×D4—22no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—42no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—384no—
236C22×C4—764no—
237C22×C4—764no—
238C22×C4—762no—
239C22×C4—762no—
240C22×C4C22⋊Dic1912yes—
241C22×C4C22⋊Dic1912yes—
242C22×C4D4×D1912yes—
243C22×C4#6454312yes—
244C22×C4C22×Dic1911yescharacteristic
245C22×C4C2×C22⋊D1911yescharacteristic
246C2×C8—764no—
247C2×C8—762no—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—44no—
251C22⋊C4—44no—
252C22⋊C4—44no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C42—24no—
256C42—24no—
257C23—22no—
258C23—22no—
259C23—41no—
260C23—41no—
261C23—42no—
262C23—41no—
263C23—42no—
264C23#1059737812yes—
265C23#1059738111yescharacteristic
266C23#1059738311yescharacteristic
267C23#1059739612yes—
268C23C2×C22⋊Dic1911yescharacteristic
269D4—82no—
270D4—82no—
271D4—82no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—764no—
293C2×C4—764no—
294C2×C4—764no—
295C2×C4—1524no—
296C2×C4—1524no—
297C2×C4D4×Dic1912yes—
298C2×C4#1059738512yes—
299C8—1522no—
300C22—24no—
301C22—24no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—82no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22#1192642411yescharacteristic
312C22#1192651812yes—
313C22#1192654011yescharacteristic
314C22#1192654911yescharacteristic
315C22#1192656112yes—
316C22#1192668712yes—
317C22#1192686512yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—81no—
323C4—82no—
324C4—1524no—
325C2—22no—
326C2—22no—
327C2—161no—
328C2#1456218212yes—
329C2#1456221212yes—
330C2#1456395811yescharacteristic
331C2#1456408411yescharacteristic
332C2#1456409411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2854C2
socleC23×C19C2×C22⋊C4
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2854D19
hypocenterC19#9157
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#11926412C2semidirect
2. #14563703C2semidirect
4. #14561513C2semidirect
16. C19×#390C4semidirect
17. C19×#389C4semidirect
168. #390Dic19semidirect
169. #389Dic19semidirect
216. C19#9157semidirect

Maximal subgroups

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

subgroupindex
C2×#119264122
#145637032
C2×#119262782
#145615132
C19×#28542
#915719