Finite Group Databasebeta

← #18080313

Subgroups — #18080313

Order 4864.

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

normal subgroups only

This group has 598 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
1#14567943C211yesmaximal, characteristic
2#14563722C212yesmaximal, complemented
3#14563623C211yesmaximal, characteristic
4#14561503C212yesmaximal, complemented
5C19×#2972C211yesmaximal, characteristic
6C2×#10597381—21no—
7C22×C4⋊Dic19C2211yescharacteristic
8C2×#10597291—21no—
9#11926474C412yescomplemented
10#11926469C412yescomplemented
11#11926442—21no—
12#11926405—21no—
13#11926404—21no—
14#11926404C2212yes—
15#11926404C2211yescharacteristic
16#11926311—21no—
17#11926307—24no—
18C2×C4×D4×C19C2211yescharacteristic
19C8×D4×C19—24no—
20C19×#431—21no—
21C2×C19×C22⋊C8—21no—
22C2×C19×C22⋊C8C2212yes—
23C22×D4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—21no—
27C22×C8×C19—22no—
28C22×C8×C19D414yes—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—22no—
38#10597381—42no—
39#10597381—42no—
40C2×C4⋊Dic19—22no—
41C2×C4⋊Dic19—22no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—22no—
45C2×C4⋊Dic19C2×C412yes—
46C2×Dic19⋊C4—22no—
47C19×C4⋊C8—22no—
48C19×C22⋊C8—22no—
49C19×C22⋊C8—22no—
50C19×C22⋊C8—22no—
51C4×C8×C19—22no—
52#10597291—42no—
53C19⋊#95—22no—
54C19⋊#95—22no—
55C19⋊#95—22no—
56C19⋊#95C2×C412yes—
57C24×C19C22⋊C411yescharacteristic
58C24×C19C2×D411yescharacteristic
59C2×D4×C19—22no—
60C2×D4×C19—22no—
61C2×D4×C19D812yes—
62C2×D4×C19SD1612yes—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D412yes—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19#4112yes—
74C22×Dic19—22no—
75C22×Dic19—22no—
76C22×Dic19—42no—
77C22×Dic19—41no—
78C22×Dic19—41no—
79C22×Dic19—42no—
80C22×Dic19—42no—
81C2×C8×C19—24no—
82C2×C8×C19—44no—
83C2×C8×C19—82no—
84C4⋊C4×C19—22no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—22no—
87C42×C19—21no—
88C42×C19—21no—
89C22⋊Dic19—44no—
90C22⋊Dic19—41no—
91C22⋊Dic19—41no—
92C22⋊Dic19—42no—
93C22⋊Dic19—42no—
94C4⋊Dic19—24no—
95C4⋊Dic19—42no—
96C4⋊Dic19—41no—
97C4⋊Dic19—41no—
98C4⋊Dic19—44no—
99Dic19⋊C4—44no—
100#9470—191nomaximal, Sylow
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—41no—
104C23×C19—41no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19#10212yes—
108C23×C19C2×C22⋊C411yescharacteristic
109C23×C19#12112yes—
110C23×C19C2×D811yescharacteristic
111C23×C19C2×SD1611yescharacteristic
112C23×C19#13512yes—
113D4×C19—24no—
114D4×C19—24no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—24no—
118C2×C4×C19—22no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—41no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—81no—
127C2×C4×C19#10212yes—
128C2×C4×C19C4×D412yes—
129C2×C4×C19#12011yescharacteristic
130C2×C4×C19#12311yescharacteristic
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—82no—
138C2×Dic19—82no—
139C2×Dic19—82no—
140C2×Dic19—82no—
141C2×Dic19—82no—
142C8×C19—44no—
143#2972D1911yescharacteristic
144#2486—191no—
145#1823—192no—
146#1799—191no—
147#1289—192no—
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—21no—
151C22×C19—22no—
152C22×C19—22no—
153C22×C19—41no—
154C22×C19—41no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19—41no—
158C22×C19—41no—
159C22×C19—81no—
160C22×C19#38611yescharacteristic
161C22×C19C2×#10211yescharacteristic
162C22×C19#41611yescharacteristic
163C22×C19#46512yes—
164C22×C19#46612yes—
165C4×C19—21no—
166C4×C19—22no—
167C4×C19—22no—
168C4×C19—41no—
169C4×C19—41no—
170C4×C19#45812yes—
171Dic19—82no—
172Dic19—82no—
173Dic19—162no—
174C2×#123—381no—
175C2×C4×D4C2×D1911yescharacteristic
176C22×C4⋊C4—191no—
177C8×D4—24no—
178#431—21no—
179C2×#99—381no—
180C2×C22⋊C8—21no—
181C2×C22⋊C8C2×D1912yes—
182#398—192no—
183#397—192no—
184#389—381no—
185#381—381no—
186#380—191no—
187#380—192no—
188#380—381no—
189#342—381no—
190#340—384no—
191C2×C19—21no—
192C2×C19—22no—
193C2×C19—21no—
194C2×C19—22no—
195C2×C19—42no—
196C2×C19#189011yescharacteristic
197C2×C19#189311yescharacteristic
198C2×C19#190911yescharacteristic
199C22×D4D7611yescharacteristic
200C23×C4—381no—
201C23×C4C22⋊D1911yescharacteristic
202C23×C4C22×D1911yescharacteristic
203C22×C8—22no—
204C22×C8C22⋊D1914yes—
205#123—762no—
206#123—762no—
207C4×D4—22no—
208C4×D4—22no—
209C2×C4⋊C4—192no—
210C2×C4⋊C4—382no—
211C2×C4⋊C4—382no—
212C2×C4⋊C4—382no—
213C2×C4⋊C4—381no—
214C2×C4⋊C4—381no—
215C2×C4⋊C4—382no—
216C2×C4⋊C4C4×D1911yescharacteristic
217C2×C22⋊C4—382no—
218C2×C22⋊C4—381no—
219C2×C22⋊C4—382no—
220C2×C22⋊C4C4×D1911yescharacteristic
221C2×C22⋊C4D7611yescharacteristic
222C2×C42C22⋊D1911yescharacteristic
223C4⋊C8—22no—
224#99—762no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C4×C8—22no—
229#95—192no—
230#95—382no—
231#95—382no—
232#95—382no—
233C19#947011yescharacteristic, complemented, Sylow
234C24(C2×D19)⋊C411yescharacteristic
235C24C2×D7611yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4#6451612yes—
239C2×D4D15212yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—382no—
245C22×C4—382no—
246C22×C4—762no—
247C22×C4—761no—
248C22×C4—761no—
249C22×C4—762no—
250C22×C4—762no—
251C22×C4(C2×D19)⋊C411yescharacteristic
252C22×C4(C2×D19)⋊C411yescharacteristic
253C22×C4(C2×D19)⋊C411yescharacteristic
254C22×C4C2×C4×D1911yescharacteristic
255C22×C4#6454112yes—
256C22×C4C2×C22⋊D1912yes—
257C22×C4C2×C22⋊D1911yescharacteristic
258C2×C8—24no—
259C2×C8—44no—
260C2×C8—82no—
261C4⋊C4—22no—
262C4⋊C4—384no—
263C4⋊C4—762no—
264C4⋊C4—764no—
265C4⋊C4—761no—
266C4⋊C4—764no—
267C4⋊C4—761no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—764no—
271C22⋊C4—761no—
272C22⋊C4—761no—
273C22⋊C4—762no—
274C22⋊C4—762no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#1059727812yes—
284C23C2×#6451611yescharacteristic
285C23C2×D15211yescharacteristic
286C23#1059735012yes—
287C23C2×(C2×D19)⋊C411yescharacteristic
288C23#1059737612yes—
289D4—24no—
290D4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—762no—
304C2×C4—762no—
305C2×C4—762no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—1522no—
310C2×C4—1522no—
311C2×C4—1522no—
312C2×C4—1522no—
313C2×C4—1522no—
314C2×C4#1059727812yes—
315C2×C4C4×C22⋊D1912yes—
316C2×C4#1059737511yescharacteristic
317C2×C4#1059739911yescharacteristic
318C8—44no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1192642311yescharacteristic
332C22C2×#1059727811yescharacteristic
333C22#1192654111yescharacteristic
334C22#1192677312yes—
335C22#1192678012yes—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—3042no—
342C4—1522no—
343C4—1522no—
344C4#1192673412yes—
345C2—22no—
346C2—21no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2#1456404811yescharacteristic
351C2#1456406311yescharacteristic
352C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2972C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#2972D19
hypocenterC19#9470
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #14563722C2semidirect
4. #14561503C2semidirect
9. #11926474C4semidirect
10. #11926469C4semidirect
233. C19#9470semidirect

Maximal subgroups

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

subgroupindex
#145679432
#145637222
#145636232
#145615032
C19×#29722
#947019