Finite Group Databasebeta

← #18078608

Subgroups — #18078608

Order 4864.

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

normal subgroups only

This group has 622 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#14566253C211yesmaximal, characteristic, complemented
2#14562203C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic, complemented
4#14561502C212yesmaximal, complemented
5C19×#2618C211yesmaximal, characteristic
6C2×#10597372—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926443—24no—
9#11926404—21no—
10#11926404C2212yes—
11#11926278—24no—
12#11926270—22no—
13C2×C19×#123—21no—
14C2×C19×#121C2211yescharacteristic
15C22×C4⋊C4×C19C2211yescharacteristic
16C19×#398C412yescomplemented
17C19×#396—22no—
18C19×#394C412yescomplemented
19C19×#386—21no—
20C19×#380C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C19×#123—42no—
27C19×#123—42no—
28C19×#121—22no—
29C19×#121—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C412yes—
36C2×C4⋊C4×C19D412yes—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊Dic19—22no—
42#10597372—42no—
43#10597372—42no—
44C2×C4⋊Dic19—22no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—22no—
47C2×C4×Dic19—22no—
48C22×C19⋊C8—22no—
49C19×#95—22no—
50C19×#95C2×C412yes—
51C19⋊#95—22no—
52C19⋊#95D414yes—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19—21no—
56C24×C19C2×D411yescharacteristic
57C2×D4×C19—22no—
58C2×D4×C19—41no—
59C2×D4×C19—41no—
60C2×D4×C19—41no—
61C2×D4×C19—41no—
62C2×D4×C19—41no—
63C2×D4×C19—41no—
64C2×D4×C19—81no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—22no—
72C22×C4×C19—21no—
73C22×C4×C19—81no—
74C22×C4×C19—81no—
75C22×C4×C19C22⋊C412yes—
76C22×C4×C19C22⋊C412yes—
77C22×C4×C19D812yes—
78C22×C4×C19SD1612yes—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D412yes—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4112yes—
83C22×Dic19—24no—
84C4⋊C4×C19—24no—
85C4⋊C4×C19—24no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—44no—
88C4⋊C4×C19—81no—
89C22⋊C4×C19—41no—
90C22⋊C4×C19—41no—
91C22⋊C4×C19—44no—
92C22⋊C4×C19—42no—
93C22⋊C4×C19—82no—
94C22⋊Dic19—42no—
95C22⋊Dic19—42no—
96C4⋊Dic19—44no—
97C4⋊Dic19—82no—
98C4⋊Dic19—82no—
99C4×Dic19—44no—
100C2×C19⋊C8—42no—
101C2×C19⋊C8—82no—
102#9204—191nomaximal, Sylow
103C23×C19—41no—
104C23×C19—41no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—41no—
108C23×C19—41no—
109C23×C19—41no—
110C23×C19C2×C22⋊C411yescharacteristic
111C23×C19#12011yescharacteristic
112C23×C19#12311yescharacteristic
113C23×C19C2×D811yescharacteristic
114C23×C19C2×SD1611yescharacteristic
115C23×C19AGL(1,ℤ/8)11yescharacteristic
116C23×C19#13711yescharacteristic
117D4×C19—82no—
118D4×C19—81no—
119D4×C19—81no—
120D4×C19—81no—
121D4×C19—81no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—41no—
138C2×C4×C19—42no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—81no—
142C2×C4×C19#10214yes—
143C2×C4×C19C4×D412yes—
144C2×C4×C19#12112yes—
145C2×Dic19—44no—
146C2×Dic19—44no—
147C2×Dic19—44no—
148C19⋊C8—82no—
149#2618D1911yescharacteristic
150#2316—191no—
151#1519—192no—
152C2×#324—191no—
153#1289—192no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—82no—
165C22×C19—82no—
166C22×C19—81no—
167C22×C19—81no—
168C22×C19—81no—
169C22×C19#38611yescharacteristic
170C22×C19C2×#10211yescharacteristic
171C22×C19#41711yescharacteristic
172C22×C19#44711yescharacteristic
173C22×C19#44811yescharacteristic
174C22×C19#48011yescharacteristic
175C22×C19#48111yescharacteristic
176C4×C19—24no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—42no—
180C4×C19—82no—
181C4×C19—81no—
182Dic19—84no—
183C2×#123—21no—
184C2×#121C2×D1911yescharacteristic
185C2×#117—381no—
186C22×C4⋊C4C2×D1911yescharacteristic
187C2×C22⋊C8—192no—
188#398Dic1912yescomplemented
189#396—22no—
190#394Dic1912yescomplemented
191#389—384no—
192#386—21no—
193#380—192no—
194#380—381no—
195#380C2×D1911yescharacteristic
196#327—384no—
197#324—382no—
198C2×C19—21no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19—161no—
205C2×C19#187411yescharacteristic
206C2×C19#191211yescharacteristic
207C2×C19#191311yescharacteristic
208C22×D4—21no—
209C22×D4C2×Dic1911yescharacteristic
210C23×C4C22⋊D1911yescharacteristic
211C23×C4C22⋊D1911yescharacteristic
212C23×C4C22×D1911yescharacteristic
213C22×C8—382no—
214#123—42no—
215#123—42no—
216#121—22no—
217#121—22no—
218#117—762no—
219#117—762no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—382no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4—382no—
227C2×C4⋊C4C2×Dic1911yescharacteristic
228C2×C4⋊C4C2×Dic1912yes—
229C2×C4⋊C4C22⋊D1912yes—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—382no—
235C2×C42—382no—
236C22⋊C8—382no—
237C22⋊C8—382no—
238#95—22no—
239#95—194no—
240#95—382no—
241#95C2×Dic1912yes—
242C19#920411yescharacteristic, complemented, Sylow
243C24—21no—
244C24C2×C22⋊D1911yescharacteristic
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—384no—
264C22×C4#6452512yes—
265C22×C4#6452612yes—
266C22×C4C22⋊Dic1912yes—
267C22×C4C22⋊Dic1912yes—
268C22×C4D4×D1912yes—
269C22×C4#6454312yes—
270C22×C4C22×Dic1911yescharacteristic
271C22×C4C2×C22⋊D1911yescharacteristic
272C2×C8—762no—
273C2×C8—1522no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—44no—
278C4⋊C4—81no—
279C4⋊C4—764no—
280C4⋊C4—1522no—
281C4⋊C4—1522no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—44no—
286C22⋊C4—82no—
287C22⋊C4—762no—
288C22⋊C4—762no—
289C42—764no—
290C23—41no—
291C23—41no—
292C23—42no—
293C23—42no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×#6452511yescharacteristic
298C23C2×#6452611yescharacteristic
299C23#1059738111yescharacteristic
300C23#1059738311yescharacteristic
301C23#1059739511yescharacteristic
302C23#1059739711yescharacteristic
303C23C2×C22⋊Dic1911yescharacteristic
304D4—82no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—764no—
330C2×C4—764no—
331C2×C4—764no—
332C2×C4#1059728914yes—
333C2×C4D4×Dic1912yes—
334C2×C4#1059738512yes—
335C8—1522no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—82no—
347C22—82no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22#1192642411yescharacteristic
352C22C2×#1059728911yescharacteristic
353C22#1192654511yescharacteristic
354C22#1192667711yescharacteristic
355C22#1192668211yescharacteristic
356C22#1192685511yescharacteristic
357C22#1192686011yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—82no—
363C4—81no—
364C4—1524no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—161no—
372C2#1456395311yescharacteristic
373C2#1456417311yescharacteristic
374C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2618C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2618D19
hypocenterC19#9204
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. #14566253C2semidirect
3. C2×#11926270C2semidirect
4. #14561502C2semidirect
16. C19×#398C4semidirect
18. C19×#394C4semidirect
188. #398Dic19semidirect
190. #394Dic19semidirect
242. C19#9204semidirect

Maximal subgroups

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

subgroupindex
#145662532
#145622032
C2×#119262702
#145615022
C19×#26182
#920419