Finite Group Databasebeta

← #18078592

Subgroups — #18078592

Order 4864.

612 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 115 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#14569440C211yesmaximal, characteristic
2#14562206C212yesmaximal, complemented
3C2×#11926268C211yesmaximal, characteristic
4#14561502C212yesmaximal, complemented
5C19×#2312C211yesmaximal, characteristic
6C2×#10597370C2211yescharacteristic
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926480C412yescomplemented
9#11926467—22no—
10#11926456C412yescomplemented
11#11926417—21no—
12#11926404C2211yescharacteristic
13#11926400—21no—
14#11926280—24no—
15#11926268—22no—
16C22×C22⋊C4×C19C2211yescharacteristic
17C19×#388—24no—
18C19×#380C2212yes—
19C19×#379—21no—
20C4×C22⋊C4×C19—21no—
21C25×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×Dic38C2×C411yescharacteristic
25C2×C4⋊C4×C19—22no—
26C2×C22⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19C2×C412yes—
32C2×C22⋊C4×C19D412yes—
33C2×C42×C19—22no—
34C2×C22⋊Dic19—21no—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—22no—
37C2×C22⋊Dic19—22no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40#10597370—22no—
41#10597370—22no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—22no—
44C22×C19⋊C8—22no—
45C19×#95—22no—
46C19×#95D414yes—
47C19⋊#95—22no—
48C19⋊#95C2×C412yes—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19—21no—
52C24×C19—21no—
53C24×C19—22no—
54C24×C19—22no—
55C24×C19—81no—
56C24×C19—81no—
57C24×C19C22⋊C412yes—
58C24×C19C2×D411yescharacteristic
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—24no—
62C22×C4×C19—81no—
63C22×C4×C19—81no—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19#4112yes—
69C22×Dic19—21no—
70C22×Dic19—22no—
71C22×Dic19—21no—
72C2×Dic38—22no—
73C2×Dic38—81no—
74C4⋊C4×C19—82no—
75C22⋊C4×C19—24no—
76C22⋊C4×C19—24no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C22⋊C4×C19—82no—
80C22⋊C4×C19—82no—
81C42×C19—82no—
82C22⋊Dic19—41no—
83C22⋊Dic19—41no—
84C22⋊Dic19—42no—
85C22⋊Dic19—82no—
86C22⋊Dic19—82no—
87C4⋊Dic19—22no—
88C4⋊Dic19—81no—
89Dic19⋊C4—42no—
90Dic19⋊C4—82no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—82no—
93#9201—191nomaximal, Sylow
94C23×C19—22no—
95C23×C19—22no—
96C23×C19—22no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—42no—
100C23×C19—42no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19—42no—
104C23×C19—42no—
105C23×C19—81no—
106C23×C19—81no—
107C23×C19—84no—
108C23×C19—84no—
109C23×C19C2×C22⋊C411yescharacteristic
110C23×C19#12011yescharacteristic
111C23×C19#12311yescharacteristic
112C23×C19#13512yes—
113C23×C19#13712yes—
114C2×C4×C19—22no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—42no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—44no—
122C2×C4×C19—44no—
123C2×C4×C19—44no—
124C2×C4×C19—81no—
125C2×C4×C19C4×D412yes—
126C2×C4×C19#12112yes—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—42no—
134Dic38—82no—
135C19⋊C8—82no—
136#2626—191no—
137#2312D1911yescharacteristic
138#1520—192no—
139C2×#323—191no—
140#1289—192no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19—42no—
148C22×C19—42no—
149C22×C19—44no—
150C22×C19—42no—
151C22×C19—42no—
152C22×C19—42no—
153C22×C19—82no—
154C22×C19—84no—
155C22×C19—84no—
156C22×C19#38611yescharacteristic
157C22×C19#41611yescharacteristic
158C22×C19#41911yescharacteristic
159C22×C19#45212yes—
160C22×C19#48512yes—
161C4×C19—22no—
162C4×C19—22no—
163C4×C19—42no—
164C4×C19—84no—
165Dic19—82no—
166Dic19—81no—
167Dic19—81no—
168C2×C22⋊Q8—191no—
169C22×C22⋊C4C2×D1911yescharacteristic
170C2×C22⋊C8—192no—
171#399—192no—
172#396—382no—
173#393—192no—
174#388—24no—
175#385—381no—
176#380—191no—
177#380C2×D1912yes—
178#379—21no—
179#379—381no—
180C4×C22⋊C4—21no—
181#328—384no—
182#323—382no—
183C2×C19—21no—
184C2×C19—22no—
185C2×C19—21no—
186C2×C19—22no—
187C2×C19—82no—
188C2×C19#187311yescharacteristic
189C2×C19#191111yescharacteristic
190C2×C19#191311yescharacteristic
191C25C22⋊D1911yescharacteristic
192C22×Q8—191no—
193C23×C4C22⋊D1911yescharacteristic
194C23×C4C22×D1911yescharacteristic
195C22×C8—382no—
196C22⋊Q8—382no—
197C22⋊Q8—382no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—191no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4—382no—
202C2×C4⋊C4—381no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—381no—
209C2×C22⋊C4—381no—
210C2×C22⋊C4—382no—
211C2×C22⋊C4—382no—
212C2×C22⋊C4C4×D1912yes—
213C2×C22⋊C4D7612yes—
214C2×C42—22no—
215C22⋊C8—382no—
216C22⋊C8—382no—
217#95—22no—
218#95—192no—
219#95—382no—
220#95C22⋊D1914yes—
221C19#920111yescharacteristic, complemented, Sylow
222C24—21no—
223C24—22no—
224C24—22no—
225C24—21no—
226C24—81no—
227C24—81no—
228C24(C2×D19)⋊C412yes—
229C24C2×C22⋊D1911yescharacteristic
230C2×Q8—382no—
231C2×Q8—1521no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—24no—
235C22×C4—81no—
236C22×C4—81no—
237C22×C4—382no—
238C22×C4—381no—
239C22×C4—381no—
240C22×C4(C2×D19)⋊C412yes—
241C22×C4C2×C4×D1911yescharacteristic
242C22×C4C2×D7611yescharacteristic
243C22×C4#6454112yes—
244C22×C4C2×C22⋊D1912yes—
245C2×C8—762no—
246C2×C8—1522no—
247C4⋊C4—82no—
248C4⋊C4—382no—
249C4⋊C4—762no—
250C4⋊C4—1522no—
251C4⋊C4—1521no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—82no—
257C22⋊C4—82no—
258C22⋊C4—762no—
259C22⋊C4—761no—
260C22⋊C4—761no—
261C22⋊C4—1522no—
262C22⋊C4—1522no—
263C42—82no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—84no—
278C23—84no—
279C23C2×(C2×D19)⋊C411yescharacteristic
280C23#1059737511yescharacteristic
281C23#1059739612yes—
282C23#1059739712yes—
283C23#1059739911yescharacteristic
284Q8—1522no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—81no—
296C2×C4—762no—
297C2×C4—762no—
298C2×C4—762no—
299C2×C4—762no—
300C2×C4—762no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4C4×C22⋊D1912yes—
304C2×C4#1059737612yes—
305C8—1522no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22—84no—
320C22—84no—
321C22#1192642311yescharacteristic
322C22#1192653811yescharacteristic
323C22#1192655211yescharacteristic
324C22#1192670612yes—
325C22#1192688512yes—
326C4—22no—
327C4—22no—
328C4—42no—
329C4—84no—
330C4—1522no—
331C4—1521no—
332C4—1521no—
333C2—22no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—82no—
338C2#1456394711yescharacteristic
339C2#1456416711yescharacteristic
340C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2312C2
socleC22×C19#386
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#2312D19
hypocenterC19#9201
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #14562206C2semidirect
4. #14561502C2semidirect
8. #11926480C4semidirect
10. #11926456C4semidirect
221. C19#9201semidirect

Maximal subgroups

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

subgroupindex
#145694402
#145622062
C2×#119262682
#145615022
C19×#23122
#920119