Finite Group Databasebeta

← #18083093

Subgroups — #18083093

Order 4864.

1020 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#11926694C212yesmaximal
2C2×#11926281C212yesmaximal, complemented
3#14561875C211yesmaximal, characteristic
4#14561478C211yesmaximal, characteristic, complemented
5C19×#2659C211yesmaximal, characteristic, complemented
6C23×D76C2211yescharacteristic
7C22×#64527—22no—
8C22×(C2×D19)⋊C4—22no—
9#11926694—24no—
10#11926694—24no—
11C2×#10597266—22no—
12C2×C22⋊(C19⋊C8)C2212yes—
13C2×C19⋊#95C2211yescharacteristic
14#11926281—24no—
15C2×C19×C22⋊Q8C2212yes—
16C19×#398—22no—
17C19×#395—22no—
18C19×#380—22no—
19C2×C19×#95C2211yescharacteristic
20C24×D19—21no—
21C22×Q8×C19D412yes—
22C23×C4×C19D412yes—
23C23×C4×C19C2311yescharacteristic
24C23×Dic19—21no—
25C22×D76—22no—
26C22×D76—22no—
27C22×D76—21no—
28C22×D76—44no—
29C22×D76D412yes—
30C19×C22⋊Q8—22no—
31C19×C22⋊Q8—22no—
32C19×C22⋊Q8—22no—
33C19×C22⋊Q8—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19—22no—
37C2×C4⋊C4×C19D412yes—
38C2×C22⋊C4×C19—22no—
39C2×#64527—28no—
40C2×#64527—48no—
41C2×(C2×D19)⋊C4—44no—
42C2×(C2×D19)⋊C4—44no—
43C2×(C2×D19)⋊C4—44no—
44C22×C19⋊C8—22no—
45C19×#95—24no—
46C19×#95—22no—
47C19⋊#95—22no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)D414yes—
50#10597266—28no—
51C24×C19C2×D411yescharacteristic
52C23×D19—24no—
53C23×D19—22no—
54C23×D19—42no—
55C23×D19—42no—
56C23×D19—42no—
57C23×D19—41no—
58C23×D19—41no—
59C23×D19—42no—
60C23×D19—42no—
61C2×Q8×C19—22no—
62C2×Q8×C19—22no—
63C2×Q8×C19—44no—
64C22×C4×C19—22no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—22no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19SD1614yescomplemented
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D412yes—
74C22×C4×C19C2×D412yes—
75C22×C4×C19#4111yescharacteristic
76C22×Dic19—22no—
77C22×Dic19—41no—
78C22×Dic19—42no—
79C22×Dic19—41no—
80C22×Dic19—42no—
81C2×D76—28no—
82C2×D76—24no—
83C2×D76—44no—
84C2×D76—48no—
85C2×D76—44no—
86C2×D76—44no—
87C2×D76—42no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—42no—
91C4⋊C4×C19—42no—
92C4⋊C4×C19—82no—
93C4⋊C4×C19—82no—
94C22⋊C4×C19—42no—
95C22⋊C4×C19—42no—
96#64527—416no—
97(C2×D19)⋊C4—416no—
98C2×C19⋊C8—24no—
99C2×C19⋊C8—44no—
100#9966—191nomaximal, Sylow
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—22no—
104C23×C19#12011yescharacteristic
105C23×C19#12111yescharacteristic
106C23×C19#12711yescharacteristic
107C23×C19C2×SD1612yes—
108C23×C19#13712yes—
109C22×D19—24no—
110C22×D19—44no—
111C22×D19—44no—
112C22×D19—42no—
113C22×D19—44no—
114C22×D19—44no—
115C22×D19—44no—
116C22×D19—44no—
117C22×D19—42no—
118C22×D19—44no—
119C22×D19—44no—
120C22×D19—82no—
121C22×D19—82no—
122C22×D19—82no—
123C22×D19—82no—
124C22×D19—82no—
125C22×D19—82no—
126C22×D19—81no—
127C22×D19—81no—
128C22×D19—81no—
129C22×D19—81no—
130Q8×C19—44no—
131Q8×C19—82no—
132C2×C4×C19—24no—
133C2×C4×C19—24no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—41no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—44no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—44no—
145C2×C4×C19—82no—
146C2×C4×C19#12012yes—
147C2×C4×C19#12112yes—
148C2×Dic19—44no—
149C2×Dic19—42no—
150C2×Dic19—82no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153D76—28no—
154D76—44no—
155D76—48no—
156C19⋊C8—44no—
157C2×#450—192no—
158#2659D1911yescharacteristic, complemented
159C2×#328—192no—
160#1438—191no—
161#1280—191no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19—22no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19#39211yescharacteristic
171C22×C19#44812yes—
172C22×C19#45311yescharacteristic
173C22×C19#45411yescharacteristic
174C22×C19B(4,𝔽2)12yes—
175C22×C19#46112yes—
176C22×C19#49211yescharacteristic
177C22×C19#49711yescharacteristic
178C2×D19—48no—
179C2×D19—44no—
180C2×D19—84no—
181C2×D19—84no—
182C2×D19—84no—
183C2×D19—84no—
184C2×D19—84no—
185C2×D19—82no—
186C2×D19—82no—
187C4×C19—22no—
188C4×C19—22no—
189C4×C19—44no—
190C4×C19—82no—
191C4×C19—82no—
192Dic19—82no—
193C23×D4—191no—
194C22×SD16—382no—
195C2×C22⋊Q8C2×D1912yes—
196C22×C22⋊C4—382no—
197#450—384no—
198#450—384no—
199C2×#102—382no—
200C2×C22⋊C8—192no—
201#398—22no—
202#395—22no—
203#380—22no—
204C2×#95—191no—
205C2×#95C2×D1911yescharacteristic
206#328—384no—
207C2×C19—21no—
208C2×C19—22no—
209C2×C19—21no—
210C2×C19#159612yes—
211C2×C19#159912yes—
212C2×C19#200611yescharacteristic
213C2×C19#201311yescharacteristic
214C2×C19#202111yescharacteristic
215D19—84no—
216C25—381no—
217C22×Q8C22⋊D1912yes—
218C22×D4—192no—
219C22×D4—382no—
220C22×D4—381no—
221C22×D4—382no—
222C22×D4—764no—
223C23×C4—381no—
224C23×C4C22⋊D1912yes—
225C23×C4C22×D1911yescharacteristic
226C2×SD16—388no—
227C2×SD16—768no—
228C22×C8—382no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4C22⋊D1912yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—764no—
239C2×C22⋊C4—764no—
240C2×C22⋊C4—764no—
241#102—388no—
242C22⋊C8—194no—
243C22⋊C8—382no—
244#95—24no—
245#95—22no—
246#95—382no—
247C19#996611yescharacteristic, complemented, Sylow
248C24—384no—
249C24—382no—
250C24—762no—
251C24—762no—
252C24—762no—
253C24—761no—
254C24—762no—
255C24—762no—
256C24—761no—
257C24C2×C22⋊D1911yescharacteristic
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—44no—
261C2×D4—388no—
262C2×D4—384no—
263C2×D4—764no—
264C2×D4—764no—
265C2×D4—768no—
266C2×D4—764no—
267C2×D4—762no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—382no—
276C22×C4—762no—
277C22×C4—761no—
278C22×C4—761no—
279C22×C4—762no—
280C22×C4#6452714yescomplemented
281C22×C4D4×D1911yescharacteristic
282C22×C4D4×D1912yes—
283C22×C4#6454311yescharacteristic
284C22×C4C2×C22⋊D1912yes—
285SD16—7616no—
286C2×C8—384no—
287C2×C8—764no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—82no—
293C4⋊C4—82no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—7616no—
297C23—21no—
298C23—21no—
299C23—22no—
300C23—384no—
301C23—764no—
302C23—764no—
303C23—762no—
304C23—764no—
305C23—764no—
306C23—764no—
307C23—764no—
308C23—762no—
309C23—764no—
310C23—764no—
311C23—1522no—
312C23—1522no—
313C23—1522no—
314C23—1522no—
315C23—1522no—
316C23—1521no—
317C23—1521no—
318C23—1522no—
319C23—1521no—
320C23—1521no—
321C23#1059738411yescharacteristic
322C23#1059738611yescharacteristic
323C23C2×#6452712yes—
324C23#1059738812yes—
325C23#1059739911yescharacteristic
326Q8—44no—
327Q8—82no—
328D4—388no—
329D4—764no—
330D4—768no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—82no—
345C2×C4—764no—
346C2×C4—762no—
347C2×C4—1522no—
348C2×C4—1521no—
349C2×C4—1521no—
350C2×C4#1059738312yes—
351C2×C4#1059738512yes—
352C8—764no—
353C22—22no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—768no—
362C22—764no—
363C22—1524no—
364C22—1524no—
365C22—1524no—
366C22—1524no—
367C22—1522no—
368C22—1522no—
369C22—1524no—
370C22#1192645211yescharacteristic
371C22#1192668312yes—
372C22#1192671211yescharacteristic
373C22#1192671711yescharacteristic
374C22#1192673112yes—
375C22#1192674612yes—
376C22#1192691811yescharacteristic
377C22#1192693611yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—82no—
382C4—82no—
383C4—1522no—
384C2—21no—
385C2—22no—
386C2—21no—
387C2—1524no—
388C2#1456255812yes—
389C2#1456257512yes—
390C2#1456467711yescharacteristic
391C2#1456471811yescharacteristic
392C2#1456475911yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2659C2
socleC23×C19#120
prime radicalC23×D76C22
hypercenter#2659D19
hypocenterC19#9966
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
2. C2×#11926281C2semidirect
4. #14561478C2semidirect
5. C19×#2659C2semidirect
71. C22×C4×C19SD16semidirect
158. #2659D19semidirect
247. C19#9966semidirect
280. C22×C4#64527semidirect

Maximal subgroups

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

subgroupindex
C2×#119266942
C2×#119262812
#145618752
#145614782
C19×#26592
#996619