Finite Group Databasebeta

← #18071326

Subgroups — #18071326

Order 4864.

740 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 95 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#14564771C212yesmaximal, complemented
2#14564717C211yesmaximal, characteristic, complemented
3#14561456C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic, complemented
5C19×#2679C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic, complemented
8C2×#10597267—21no—
9C2×#10597289—22no—
10#11926306—22no—
11#11926299C2211yescharacteristic, complemented
12#11926299C2212yescomplemented
13C2×C19×#120—21no—
14C2×C19×#120—22no—
15C19×#394—21no—
16C19×#394—22no—
17C19×#390C2211yescharacteristic
18C19×#390C2212yes—
19C25×C19—21no—
20C22×D4×C19—22no—
21C22×D4×C19—21no—
22C22×D4×C19D411yescharacteristic
23C22×D4×C19D412yes—
24C22×Dic38—21no—
25C19×#120—42no—
26C19×#120—44no—
27C19×#120—42no—
28C19×#120—44no—
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C4⋊C4×C19D412yes—
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—22no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36C2×C42×C19C2311yescharacteristic
37C2×#64526—42no—
38C2×#64526—42no—
39C2×#64526—42no—
40C2×C4⋊Dic19—22no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8—22no—
43#10597315—42no—
44C19×#95—21no—
45#10597289—44no—
46#10597267—42no—
47C24×C19—21no—
48C24×C19—22no—
49C24×C19—42no—
50C24×C19—44no—
51C24×C19—81no—
52C24×C19—82no—
53C24×C19—81no—
54C2×D4×C19—21no—
55C2×D4×C19—22no—
56C2×D4×C19—41no—
57C2×D4×C19—41no—
58C2×D4×C19—42no—
59C2×D4×C19—42no—
60C2×D4×C19—44no—
61C2×D4×C19—44no—
62C2×D4×C19—44no—
63C2×D4×C19—81no—
64C2×D4×C19—82no—
65C2×D4×C19D812yes—
66C2×D4×C19SD1614yescomplemented
67C22×C4×C19—22no—
68C22×C4×C19—21no—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D412yes—
71C22×Dic19—41no—
72C2×Dic38—22no—
73C2×Dic38—41no—
74C2×Dic38—41no—
75C2×Dic38—41no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C4⋊C4×C19—42no—
79C4⋊C4×C19—41no—
80C22⋊C4×C19—42no—
81C22⋊C4×C19—44no—
82C22⋊C4×C19—42no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—42no—
85C22⋊C4×C19—42no—
86C22⋊C4×C19—42no—
87C22⋊C4×C19—42no—
88C42×C19—41no—
89#64526—48no—
90C4⋊Dic19—24no—
91C4⋊Dic19—42no—
92C2×C19⋊C8—22no—
93C2×C19⋊C8—41no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—42no—
96C2×C19⋊C8—42no—
97C2×C19⋊C8—42no—
98#7750—191nomaximal, Sylow
99C23×C19—22no—
100C23×C19—24no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19—42no—
104C23×C19—41no—
105C23×C19—42no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19—41no—
110C23×C19—42no—
111C23×C19—84no—
112C23×C19—88no—
113C23×C19—84no—
114C23×C19—88no—
115C23×C19—84no—
116C23×C19#12011yescharacteristic
117D4×C19—42no—
118D4×C19—44no—
119D4×C19—81no—
120D4×C19—82no—
121D4×C19—84no—
122D4×C19—88no—
123C2×C4×C19—21no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—41no—
131C2×C4×C19—42no—
132C2×C4×C19C2×D811yescharacteristic
133C2×C4×C19C2×SD1612yes—
134C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)12yes—
136C2×Dic19—42no—
137C2×Dic19—81no—
138C2×Dic19—81no—
139Dic38—42no—
140Dic38—42no—
141Dic38—81no—
142Dic38—81no—
143C19⋊C8—42no—
144C19⋊C8—82no—
145#2679D1911yescharacteristic
146#2023—192no—
147#2013—191no—
148#1270—192no—
149#1270—191no—
150C22×C19—42no—
151C22×C19—44no—
152C22×C19—44no—
153C22×C19—44no—
154C22×C19—44no—
155C22×C19—816no—
156C22×C19—82no—
157C22×C19—82no—
158C22×C19—82no—
159C22×C19—81no—
160C22×C19—82no—
161C22×C19—81no—
162C22×C19—82no—
163C22×C19#44711yescharacteristic
164C22×C19#45012yes—
165C22×C19#45311yescharacteristic
166C22×C19#45512yes—
167C22×C19B(4,𝔽2)11yescharacteristic
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—22no—
171C4×C19—22no—
172C4×C19—81no—
173C4×C19—82no—
174Dic19—82no—
175C22×SD16—381no—
176C2×C4⋊Q8—191no—
177C2×#120—21no—
178C2×#120—22no—
179C2×#103—381no—
180C2×#102—382no—
181#394—22no—
182#394—21no—
183#390C2×D1911yescharacteristic
184#390C2×D1912yes—
185#340—382no—
186#336—191no—
187#336—192no—
188C2×C19—82no—
189C2×C19—84no—
190C2×C19#159511yescharacteristic
191C2×C19#160112yes—
192C2×C19#162911yescharacteristic
193C2×C19#163912yes—
194C2×C19#165911yescharacteristic
195C25—21no—
196C22×Q8—381no—
197C22×D4—22no—
198C22×D4—21no—
199C22×D4C22⋊D1911yescharacteristic
200C22×D4C22⋊D1912yes—
201C2×SD16—762no—
202C2×SD16—762no—
203C2×SD16—762no—
204C22×C8—381no—
205C22×C8—382no—
206C4⋊Q8—762no—
207#120—42no—
208#120—44no—
209#120—42no—
210#120—44no—
211C2×C4⋊C4—382no—
212C2×C4⋊C4C22⋊D1912yes—
213C2×C4⋊C4C22⋊D1911yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C42C22×D1911yescharacteristic
220#103—762no—
221#102—764no—
222#95—21no—
223C19#775011yescharacteristic, complemented, Sylow
224C24—21no—
225C24—22no—
226C24—42no—
227C24—44no—
228C24—81no—
229C24—82no—
230C24—81no—
231C2×Q8—382no—
232C2×Q8—761no—
233C2×Q8—761no—
234C2×Q8—761no—
235C2×Q8—761no—
236C2×Q8—761no—
237C2×D4—21no—
238C2×D4—22no—
239C2×D4—42no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—81no—
247C2×D4—82no—
248C2×D4#6452512yes—
249C2×D4#6452614yescomplemented
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—761no—
253C22×C4C2×C22⋊D1911yescharacteristic
254C22×C4C2×C22⋊D1912yes—
255SD16—768no—
256C2×C8—382no—
257C2×C8—761no—
258C2×C8—761no—
259C2×C8—762no—
260C2×C8—762no—
261C2×C8—762no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—384no—
265C4⋊C4—762no—
266C22⋊C4—42no—
267C22⋊C4—44no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C42—41no—
275C23—22no—
276C23—24no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—41no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23—42no—
285C23—42no—
286C23—41no—
287C23—84no—
288C23—88no—
289C23—88no—
290C23—84no—
291C23—84no—
292C23#1059739911yescharacteristic
293Q8—762no—
294Q8—762no—
295Q8—1521no—
296Q8—1521no—
297D4—42no—
298D4—44no—
299D4—82no—
300D4—81no—
301D4—84no—
302D4—88no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—762no—
313C2×C4—1521no—
314C2×C4—1521no—
315C2×C4C2×#6452511yescharacteristic
316C2×C4#1059737811yescharacteristic
317C2×C4#1059737812yes—
318C2×C4C2×#6452612yes—
319C8—762no—
320C8—1522no—
321C22—44no—
322C22—44no—
323C22—42no—
324C22—44no—
325C22—44no—
326C22—816no—
327C22—82no—
328C22—82no—
329C22—81no—
330C22—82no—
331C22—81no—
332C22—82no—
333C22—82no—
334C22#1192667811yescharacteristic
335C22#1192669512yes—
336C22#1192671211yescharacteristic
337C22#1192672212yes—
338C22#1192673111yescharacteristic
339C4—22no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—81no—
344C4—82no—
345C4—1522no—
346C2—84no—
347C2—82no—
348C2#1456255311yescharacteristic
349C2#1456258712yes—
350C2#1456275111yescharacteristic
351C2#1456281412yes—
352C2#1456294111yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2679C2
socleC23×C19#120
hypercenter#2679D19
hypocenterC19#7750
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. #14564771C2semidirect
2. #14564717C2semidirect
3. #14561456C2semidirect
4. #14561456C2semidirect
7. C2×#10597315C22semidirect
11. #11926299C22semidirect
12. #11926299C22semidirect
66. C2×D4×C19SD16semidirect
223. C19#7750semidirect
249. C2×D4#64526semidirect

Maximal subgroups

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

subgroupindex
#145647712
#145647172
#145614562
C19×#26792
#775019