Finite Group Databasebeta

← #18079879

Subgroups — #18079879

Order 4864.

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

normal subgroups only

This group has 532 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#14569333C211yesmaximal, characteristic
2#14562236C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561529C212yesmaximal, complemented
5C19×#2873C211yesmaximal, characteristic
6C2×#10597316C2211yescharacteristic
7#11926601C2212yes—
8#11926483C411yescharacteristic
9#11926480C411yescharacteristic
10#11926474C411yescharacteristic
11#11926469C411yescharacteristic
12#11926439—21no—
13#11926438—21no—
14#11926428—21no—
15#11926417—21no—
16#11926390C2211yescharacteristic
17#11926285—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
26C2×M16×C19—22no—
27C2×M16×C19—24no—
28C2×M16×C19—24no—
29C2×M16×C19—22no—
30C22×C8×C19—22no—
31C19×#117—22no—
32C19×#117—22no—
33C2×C4⋊C4×C19C2×C411yescharacteristic
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C22⋊C4×C19C2×C411yescharacteristic
36C2×C22⋊C4×C19D411yescharacteristic
37C2×C42×C19D411yescharacteristic
38C2×C42×C19C2311yescharacteristic
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×C4×Dic19—21no—
48#10597316—22no—
49#10597316—22no—
50C19×#97—22no—
51C19×#97D414yes—
52C4×C8×C19—22no—
53C4×C8×C19—22no—
54C19⋊#95—21no—
55C19⋊#95—21no—
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
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—21no—
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79M16×C19—28no—
80M16×C19—24no—
81M16×C19—24no—
82C2×C8×C19—28no—
83C2×C8×C19—24no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C22⋊C4×C19—22no—
87C22⋊C4×C19—22no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19C2×D412yes—
91C42×C19#4112yes—
92C22⋊Dic19—42no—
93C22⋊Dic19—42no—
94C4⋊Dic19—22no—
95C4⋊Dic19—22no—
96Dic19⋊C4—42no—
97Dic19⋊C4—42no—
98Dic19⋊C4—41no—
99Dic19⋊C4—42no—
100Dic19⋊C4—41no—
101C4×Dic19—42no—
102C2×C19⋊C8—42no—
103#9388—191nomaximal, Sylow
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—41no—
107C23×C19—41no—
108C23×C19#10412yes—
109C23×C19C2×C22⋊C411yescharacteristic
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—24no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19#10412yes—
124C2×C4×C19C4×D412yes—
125C2×C4×C19#12011yescharacteristic
126C2×C4×C19#12112yes—
127C2×C4×C19#12311yescharacteristic
128C2×Dic19—22no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C8×C19—28no—
141C19⋊C8—82no—
142#2873D1911yescharacteristic
143#2611—191no—
144#1528—192no—
145#1464—191no—
146#1300—192no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—42no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19—81no—
154C22×C19#38611yescharacteristic
155C22×C19C2×#10411yescharacteristic
156C22×C19C2×#10411yescharacteristic
157C4×C19—22no—
158C4×C19—21no—
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—22no—
162C4×C19—41no—
163C4×C19—41no—
164Dic19—42no—
165Dic19—81no—
166Dic19—81no—
167Dic19—81no—
168C22×M16—21no—
169C2×#125—191no—
170C2×#117C2×D1911yescharacteristic
171#432—192no—
172#405—24no—
173C4×M16—21no—
174C4×M16C2×D1912yes—
175#400—191no—
176#399—191no—
177#398—191no—
178#397—191no—
179#389—381no—
180#388—381no—
181#387—381no—
182#385—381no—
183#376—191no—
184#330—384no—
185#324—381no—
186#323—381no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19—42no—
190C2×C19#188411yescharacteristic
191C2×C19#189611yescharacteristic
192C2×C19#191511yescharacteristic
193C23×C4C22⋊D1911yescharacteristic
194C2×M16—24no—
195C2×M16—24no—
196C2×M16—22no—
197C2×M16—22no—
198C22×C8—22no—
199#125—382no—
200#125—382no—
201#117—22no—
202#117—22no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—191no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4C4×D1911yescharacteristic
210C2×C4⋊C4D7611yescharacteristic
211C2×C22⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4C4×D1911yescharacteristic
214C2×C22⋊C4D7611yescharacteristic
215C2×C42—381no—
216C2×C42C22⋊D1911yescharacteristic
217C2×C42C22×D1911yescharacteristic
218C4⋊C8—382no—
219C22⋊C8—382no—
220#97—22no—
221#97—382no—
222#97C22⋊D1914yes—
223C4×C8—22no—
224C4×C8—22no—
225#95—191no—
226#95—191no—
227#95—381no—
228#95—381no—
229#95—381no—
230#95—381no—
231#95—381no—
232C19#938811yescharacteristic, complemented, Sylow
233C24(C2×D19)⋊C411yescharacteristic
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—381no—
239C22×C4—381no—
240C22×C4—381no—
241C22×C4—381no—
242C22×C4(C2×D19)⋊C411yescharacteristic
243C22×C4(C2×D19)⋊C411yescharacteristic
244C22×C4(C2×D19)⋊C411yescharacteristic
245C22×C4C2×C4×D1911yescharacteristic
246C22×C4C2×D7611yescharacteristic
247C22×C4C2×C22⋊D1911yescharacteristic
248M16—28no—
249M16—24no—
250M16—24no—
251C2×C8—28no—
252C2×C8—24no—
253C2×C8—762no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—382no—
257C4⋊C4—382no—
258C4⋊C4—762no—
259C4⋊C4—762no—
260C4⋊C4—761no—
261C4⋊C4—762no—
262C4⋊C4—761no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—762no—
266C22⋊C4—762no—
267C42—21no—
268C42—21no—
269C42—762no—
270C42#6454112yes—
271C42C2×C22⋊D1912yes—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#1059726212yes—
277C23C2×(C2×D19)⋊C411yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—382no—
292C2×C4—761no—
293C2×C4—761no—
294C2×C4—761no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4#1059726212yes—
304C2×C4C4×C22⋊D1912yes—
305C2×C4#1059737511yescharacteristic
306C2×C4#1059737612yes—
307C2×C4#1059739911yescharacteristic
308C8—28no—
309C8—1522no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22#1192642311yescharacteristic
318C22C2×#1059726211yescharacteristic
319C22C2×#1059726211yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—762no—
328C4—1521no—
329C4—1521no—
330C4—1521no—
331C2—21no—
332C2—21no—
333C2—42no—
334C2#1456401811yescharacteristic
335C2#1456407811yescharacteristic
336C2#1456418711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2873C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2873D19
hypocenterC19#9388
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. #14562236C2semidirect
4. #14561529C2semidirect
232. C19#9388semidirect

Maximal subgroups

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

subgroupindex
#145693332
#145622362
#145619692
#145615292
C19×#28732
#938819