Finite Group Databasebeta

← #18079880

Subgroups — #18079880

Order 4864.

532 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 111 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#14562237C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561528C212yesmaximal, complemented
5C19×#2611C211yesmaximal, characteristic
6C22×#64520—21no—
7#11926601C2212yes—
8#11926500—24no—
9C4×#64520—21no—
10C4×#64520C2212yes—
11#11926286—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C19×#125C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#400C411yescharacteristic
17C19×#399C411yescharacteristic
18C19×#398C411yescharacteristic
19C19×#397C411yescharacteristic
20C19×#389—21no—
21C19×#388—21no—
22C19×#387—21no—
23C19×#385—21no—
24C19×#376C2211yescharacteristic
25C23×C4×C19D411yescharacteristic
26C19×#125—22no—
27C19×#125—22no—
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19D411yescharacteristic
42C2×C42×C19—21no—
43C2×C42×C19D411yescharacteristic
44C2×C42×C19C2311yescharacteristic
45C2×#64520—24no—
46C2×#64520—24no—
47C2×#64520—22no—
48C2×#64520—22no—
49C22×C19⋊C8—22no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95C2×C411yescharacteristic
56C19×#95C2×C411yescharacteristic
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59#10597260—22no—
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×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22×C411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C4⋊C4×C19—22no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—42no—
84C4⋊C4×C19—42no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—42no—
87C4⋊C4×C19—41no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—42no—
92C42×C19—21no—
93C42×C19—21no—
94C42×C19—42no—
95C42×C19C2×D412yes—
96C42×C19#4112yes—
97#64520—28no—
98#64520—24no—
99#64520—24no—
100C2×C19⋊C8—28no—
101C2×C19⋊C8—24no—
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—22no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19#10412yes—
136C2×C4×C19C4×D412yes—
137C2×C4×C19#12011yescharacteristic
138C2×C4×C19#12112yes—
139C2×C4×C19#12311yescharacteristic
140C19⋊C8—28no—
141C19⋊C8—82no—
142#2873—191no—
143#2611D1911yescharacteristic
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—42no—
163C4×C19—41no—
164C4×C19—41no—
165C4×C19—81no—
166C4×C19—81no—
167C4×C19—81no—
168C22×M16—381no—
169C2×#125C2×D1911yescharacteristic
170C2×#117C2×D1911yescharacteristic
171#432—192no—
172#405—384no—
173C4×M16—192no—
174C4×M16—381no—
175#400Dic1911yescharacteristic
176#399Dic1911yescharacteristic
177#398Dic1911yescharacteristic
178#397Dic1911yescharacteristic
179#389—21no—
180#388—21no—
181#387—21no—
182#385—21no—
183#376C2×D1911yescharacteristic
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—382no—
195C2×M16—384no—
196C2×M16—384no—
197C2×M16—382no—
198C22×C8—382no—
199#125—22no—
200#125—22no—
201#117—22no—
202#117—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic1911yescharacteristic
208C2×C4⋊C4C2×Dic1911yescharacteristic
209C2×C4⋊C4C2×Dic1911yescharacteristic
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4C2×Dic1911yescharacteristic
214C2×C22⋊C4C22⋊D1911yescharacteristic
215C2×C42—21no—
216C2×C42C22⋊D1911yescharacteristic
217C2×C42C22×D1911yescharacteristic
218C4⋊C8—382no—
219C22⋊C8—382no—
220#97—194no—
221#97—382no—
222#97—382no—
223C4×C8—382no—
224C4×C8—382no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95C2×Dic1911yescharacteristic
231#95C2×Dic1911yescharacteristic
232C19#938811yescharacteristic, complemented, Sylow
233C24C22⋊Dic1911yescharacteristic
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C22⋊Dic1911yescharacteristic
243C22×C4C22⋊Dic1911yescharacteristic
244C22×C4C22⋊Dic1911yescharacteristic
245C22×C4C22×Dic1911yescharacteristic
246C22×C4C2×C22⋊D1911yescharacteristic
247C22×C4C2×C22⋊D1911yescharacteristic
248M16—388no—
249M16—384no—
250M16—384no—
251C2×C8—388no—
252C2×C8—384no—
253C2×C8—762no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C42—21no—
268C42—21no—
269C42—42no—
270C42D4×D1912yes—
271C42#6454312yes—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#1059729412yes—
277C23C2×C22⋊Dic1911yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4#1059729412yes—
304C2×C4D4×Dic1912yes—
305C2×C4#1059738111yescharacteristic
306C2×C4#1059738311yescharacteristic
307C2×C4#1059738512yes—
308C8—388no—
309C8—1522no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22#1192642411yescharacteristic
318C22C2×#1059729411yescharacteristic
319C22C2×#1059729411yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—22no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—21no—
332C2—21no—
333C2—42no—
334C2#1456401911yescharacteristic
335C2#1456407911yescharacteristic
336C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2611C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2611D19
hypocenterC19#9388
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2611

Complements

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

NH ≅ G/Ntype
2. #14562237C2semidirect
4. #14561528C2semidirect
232. C19#9388semidirect

Maximal subgroups

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

subgroupindex
#145720542
#145622372
#145619692
#145615282
C19×#26112
#938819