Finite Group Databasebeta

← #18079877

Subgroups — #18079877

Order 4864.

532 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 103 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#14572054C211yesmaximal, characteristic
2#14569333C211yesmaximal, characteristic
3#14562238C212yesmaximal, complemented
4#14561527C212yesmaximal, complemented
5C19×#1464C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597316C2211yescharacteristic
8#11926500—24no—
9C4×#64520—21no—
10C4×#64520C2212yes—
11#11926483C411yescharacteristic
12#11926480C411yescharacteristic
13#11926474C411yescharacteristic
14#11926469C411yescharacteristic
15#11926439—21no—
16#11926438—21no—
17#11926428—21no—
18#11926417—21no—
19#11926390C2211yescharacteristic
20#11926285—24no—
21C2×C19×#117C2211yescharacteristic
22C19×#432C2212yes—
23C19×#324—21no—
24C19×#323—21no—
25C23×C4×C19D411yescharacteristic
26C19×#117—22no—
27C19×#117—22no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—21no—
35C2×C22⋊Dic19—21no—
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×Dic19⋊C4—21no—
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C2×C4×Dic19—21no—
43C2×#64520—24no—
44C2×#64520—24no—
45C2×#64520—22no—
46C2×#64520—22no—
47C22×C19⋊C8—22no—
48#10597316—22no—
49#10597316—22no—
50C19×C4⋊C8—22no—
51C19×C22⋊C8—22no—
52C19×#97—22no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95C2×C411yescharacteristic
59C19⋊#95C2×C411yescharacteristic
60#10597260—22no—
61#10597260D414yes—
62C4×C19⋊C8—22no—
63C4×C19⋊C8—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—
79C2×C8×C19—42no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C42×C19—21no—
85C42×C19—21no—
86C42×C19C2×D412yes—
87C42×C19#4112yes—
88C22⋊Dic19—42no—
89C22⋊Dic19—42no—
90C4⋊Dic19—22no—
91C4⋊Dic19—22no—
92Dic19⋊C4—42no—
93Dic19⋊C4—42no—
94Dic19⋊C4—41no—
95Dic19⋊C4—42no—
96Dic19⋊C4—41no—
97C4×Dic19—42no—
98#64520—28no—
99#64520—24no—
100#64520—24no—
101C2×C19⋊C8—28no—
102C2×C19⋊C8—24no—
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—82no—
141C19⋊C8—28no—
142#2873—191no—
143#2611—191no—
144#1528—192no—
145#1464D1911yescharacteristic
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—381no—
169C2×#125—191no—
170C2×#117C2×D1911yescharacteristic
171#432C2×D1912yes—
172#405—384no—
173C4×M16—192no—
174C4×M16—381no—
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—21no—
186#323—21no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19—42no—
190C2×C19#188411yescharacteristic
191C2×C19#189611yescharacteristic
192C2×C19#191511yescharacteristic
193C23×C4D7611yescharacteristic
194C2×M16—382no—
195C2×M16—384no—
196C2×M16—384no—
197C2×M16—382no—
198C22×C8—382no—
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⋊C4C22⋊D1911yescharacteristic
211C2×C22⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4C4×D1911yescharacteristic
214C2×C22⋊C4C22⋊D1911yescharacteristic
215C2×C42—381no—
216C2×C42D7611yescharacteristic
217C2×C42C22×D1911yescharacteristic
218C4⋊C8—22no—
219C22⋊C8—22no—
220#97—22no—
221#97—194no—
222#97—382no—
223C4×C8—382no—
224C4×C8—382no—
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—22no—
236C22×C4—21no—
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—388no—
249M16—384no—
250M16—384no—
251C2×C8—42no—
252C2×C8—388no—
253C2×C8—384no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—382no—
257C4⋊C4—382no—
258C4⋊C4—762no—
259C4⋊C4—762no—
260C4⋊C4—762no—
261C4⋊C4—761no—
262C4⋊C4—761no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—762no—
266C22⋊C4—762no—
267C42—21no—
268C42—21no—
269C42—762no—
270C42D4×D1912yes—
271C42#6454312yes—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#1059728212yes—
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#1059728212yes—
304C2×C4(C22⋊D19)⋊C412yes—
305C2×C4#1059732811yescharacteristic
306C2×C4#1059733211yescharacteristic
307C2×C4#1059738512yes—
308C8—82no—
309C8—388no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22#1192642111yescharacteristic
318C22C2×#1059728211yescharacteristic
319C22C2×#1059728211yescharacteristic
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#1456401611yescharacteristic
335C2#1456407611yescharacteristic
336C2#1456418511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1464C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1464D19
hypocenterC19#9388
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #14562238C2semidirect
4. #14561527C2semidirect
232. C19#9388semidirect

Maximal subgroups

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

subgroupindex
#145720542
#145693332
#145622382
#145615272
C19×#14642
#938819