Finite Group Databasebeta

← #18077623

Subgroups — #18077623

Order 4864.

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

normal subgroups only

This group has 516 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#14566918C211yesmaximal, characteristic
2C4×#10597293C211yesmaximal, characteristic, complemented
3#14562077C212yesmaximal
4#14561527C212yesmaximal, complemented
5C19×#2983C211yesmaximal, characteristic, complemented
6C2×C4×D76C2211yescharacteristic
7C2×#10597293—21no—
8C4×#64520C2212yes—
9#11926483C411yescharacteristic
10#11926483C411yescharacteristic
11#11926470—21no—
12#11926461C411yescharacteristic
13#11926461C411yescharacteristic
14#11926455—21no—
15C4×(C2×D19)⋊C4—21no—
16C4×(C2×D19)⋊C4—21no—
17#11926390C2211yescharacteristic
18#11926313—21no—
19#11926271—24no—
20C2×C4×Q8×C19C2211yescharacteristic
21C19×#446—24no—
22C19×#432—21no—
23C19×#432C2212yes—
24C19×#431—21no—
25C22×Q8×C19D411yescharacteristic
26C22×D76C2×C411yescharacteristic
27C22×C4×D19—21no—
28C4×Q8×C19—22no—
29C4×Q8×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×C4×Dic19—21no—
43C2×#64520—22no—
44C4×D76—22no—
45C4×D76—22no—
46C19×C4⋊C8—22no—
47C19×C4⋊C8—22no—
48C19×C4⋊C8D414yes—
49C19×C22⋊C8—22no—
50C19×#97—22no—
51C19×#97—22no—
52C4×C8×C19—22no—
53#10597293—24no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95C2×C411yescharacteristic
60C19⋊#95C2×C411yescharacteristic
61#10597260—22no—
62C4×C19⋊C8—22no—
63C23×D19—21no—
64C2×Q8×C19—22no—
65C2×Q8×C19—22no—
66C2×Q8×C19—41no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77C2×D76—22no—
78C2×D76—42no—
79C2×C4×D19—42no—
80C2×C4×D19—42no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83C2×C8×C19—24no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C42×C19—21no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19C2×D412yes—
92C42×C19#4112yes—
93(C2×D19)⋊C4—42no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—42no—
97(C2×D19)⋊C4—42no—
98C4⋊Dic19—22no—
99C4×Dic19—42no—
100#64520—24no—
101#64520—42no—
102C2×C19⋊C8—42no—
103#9032—191nomaximal, Sylow
104C23×C19C2×C22⋊C411yescharacteristic
105C22×D19—22no—
106C22×D19—41no—
107C22×D19—41no—
108C22×D19—41no—
109C22×D19—41no—
110C22×D19—41no—
111C22×D19—41no—
112Q8×C19—44no—
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—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19#10412yes—
127C2×C4×C19C4×D412yes—
128C2×C4×C19#12011yescharacteristic
129C2×C4×C19#12112yes—
130C2×C4×C19#12311yescharacteristic
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—
140D76—24no—
141D76—42no—
142C4×D19—82no—
143C4×D19—82no—
144C8×C19—44no—
145C19⋊C8—44no—
146#2983D1911yescharacteristic, complemented
147#2398—191no—
148C4×#101—191no—
149#1490—192no—
150#1300—192no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19#38611yescharacteristic
154C22×C19C2×#10411yescharacteristic
155C22×C19#42111yescharacteristic
156C2×D19—42no—
157C2×D19—42no—
158C2×D19—42no—
159C2×D19—81no—
160C2×D19—81no—
161C2×D19—81no—
162C2×D19—81no—
163C4×C19—22no—
164C4×C19—22no—
165C4×C19—21no—
166C4×C19—22no—
167C4×C19—41no—
168C4×C19—41no—
169C4×C19—41no—
170C4×C19#45412yes—
171Dic19—81no—
172Dic19—81no—
173Dic19—81no—
174C2×C4×Q8C2×D1911yescharacteristic
175C2×C4×D4—191no—
176#446—24no—
177#432—21no—
178#432C2×D1912yes—
179#431—21no—
180C2×#101—381no—
181C4×M16—192no—
182#400—191no—
183#400—191no—
184#397—381no—
185#394—191no—
186#394—191no—
187#393—381no—
188C4×C22⋊C4—381no—
189C4×C22⋊C4—381no—
190#376—191no—
191#343—381no—
192D4⋊C8—384no—
193C2×C19—21no—
194C2×C19—21no—
195C2×C19#187111yescharacteristic
196C2×C19#188811yescharacteristic
197C2×C19#189111yescharacteristic
198D19—82no—
199C22×Q8D7611yescharacteristic
200C22×D4—191no—
201C23×C4—381no—
202C2×M16—382no—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×D4—382no—
206C4×D4—382no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4C4×D1911yescharacteristic
209C2×C4⋊C4C4×D1911yescharacteristic
210C2×C4⋊C4D7611yescharacteristic
211C2×C22⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C22⋊C4—381no—
214C2×C22⋊C4—381no—
215C2×C22⋊C4—381no—
216C2×C42—381no—
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22⋊D1911yescharacteristic
219C2×C42C22×D1911yescharacteristic
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8C22⋊D1914yes—
223#101—384no—
224C22⋊C8—22no—
225#97—22no—
226#97—22no—
227#97—382no—
228C4×C8—22no—
229C4×C8—382no—
230#95—191no—
231#95—191no—
232#95—381no—
233#95—381no—
234#95—381no—
235#95—381no—
236#95—381no—
237C19#903211yescharacteristic, complemented, Sylow
238C24—381no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—382no—
243C2×D4—762no—
244C22×C4—381no—
245C22×C4—381no—
246C22×C4—381no—
247C22×C4—762no—
248C22×C4—762no—
249C22×C4—761no—
250C22×C4—761no—
251C22×C4(C2×D19)⋊C411yescharacteristic
252C22×C4(C2×D19)⋊C411yescharacteristic
253C22×C4(C2×D19)⋊C411yescharacteristic
254C22×C4(C2×D19)⋊C411yescharacteristic
255C22×C4C2×C4×D1911yescharacteristic
256C22×C4C2×D7611yescharacteristic
257C22×C4C2×C22⋊D1911yescharacteristic
258M16—384no—
259M16—762no—
260C2×C8—24no—
261C2×C8—762no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—382no—
266C22⋊C4—762no—
267C22⋊C4—762no—
268C22⋊C4—762no—
269C22⋊C4—762no—
270C22⋊C4—762no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—762no—
276C42#6454112yes—
277C42C2×C22⋊D1912yes—
278C23—382no—
279C23—761no—
280C23—761no—
281C23—761no—
282C23—761no—
283C23—761no—
284C23—761no—
285C23C2×(C2×D19)⋊C411yescharacteristic
286Q8—44no—
287D4—384no—
288D4—762no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—1522no—
312C2×C4—1522no—
313C2×C4#1059728212yes—
314C2×C4C4×C22⋊D1912yes—
315C2×C4#1059737511yescharacteristic
316C2×C4#1059737612yes—
317C2×C4#1059739911yescharacteristic
318C8—44no—
319C8—764no—
320C22—21no—
321C22—21no—
322C22—762no—
323C22—762no—
324C22—762no—
325C22—1521no—
326C22—1521no—
327C22—1521no—
328C22—1521no—
329C22#1192642311yescharacteristic
330C22C2×#1059728211yescharacteristic
331C22#1192656011yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1521no—
340C4—1521no—
341C4—1521no—
342C4#1192671712yes—
343C2—21no—
344C2—21no—
345C2—1522no—
346C2#1456393711yescharacteristic
347C2#1456403811yescharacteristic
348C2#1456405311yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2983C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#2983D19
hypocenterC19#9032
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. C4×#10597293C2semidirect
4. #14561527C2semidirect
5. C19×#2983C2semidirect
146. #2983D19semidirect
237. C19#9032semidirect

Maximal subgroups

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

subgroupindex
#145669182
C4×#105972932
#145620772
#145615272
C19×#29832
#903219