Finite Group Databasebeta

← #18080339

Subgroups — #18080339

Order 4864.

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

normal subgroups only

This group has 958 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#14565988C211yesmaximal, characteristic, complemented
2#14563579C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561487C212yesmaximal, complemented
5C19×#2404C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×#10597294—24no—
8#11926508C2212yes—
9C22⋊C4×Dic19—24no—
10C4×C22⋊Dic19—21no—
11C4×C22⋊Dic19C2212yes—
12#11926268—22no—
13C22×#41×C19C2211yescharacteristic
14C2×C19×#120—21no—
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#393C412yescomplemented
17C19×#392C412yescomplemented
18C19×#386—21no—
19C19×#386—22no—
20C19×#381C2211yescharacteristic
21C25×C19D411yescharacteristic
22C2×#41×C19—22no—
23C2×#41×C19—22no—
24C2×#41×C19—44no—
25C22×Q8×C19C2×C411yescharacteristic, complemented
26C22×D4×C19—21no—
27C22×D4×C19—22no—
28C22×D4×C19C2×C411yescharacteristic, complemented
29C23×C4×C19—21no—
30C23×C4×C19D411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C23×Dic19—22no—
33C19×#120—44no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19C2×C412yes—
40C2×C22⋊C4×C19D412yes—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—28no—
43C2×C22⋊Dic19—22no—
44C2×C4×Dic19—22no—
45C2×C4×Dic19D414yescomplemented
46C2×#64520—22no—
47C19×#95—22no—
48C19×#95—21no—
49C19×#95C2×C412yescomplemented
50#10597294—48no—
51C19⋊#95—22no—
52C19⋊#95—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19—21no—
56C24×C19—24no—
57C24×C19—21no—
58C24×C19—21no—
59C24×C19—42no—
60C24×C19—81no—
61C24×C19C22⋊C412yes—
62C24×C19C2×D411yescharacteristic
63#41×C19—28no—
64#41×C19—44no—
65#41×C19—44no—
66#41×C19—44no—
67C2×Q8×C19—22no—
68C2×Q8×C19—42no—
69C2×D4×C19—24no—
70C2×D4×C19—22no—
71C2×D4×C19—42no—
72C2×D4×C19—42no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—44no—
76C2×D4×C19—44no—
77C2×D4×C19—82no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—22no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19—81no—
87C22×C4×C19C22⋊C412yes—
88C22×C4×C19C22×C411yescharacteristic
89C22×C4×C19C2×D412yes—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4112yes—
92C22×Dic19—24no—
93C22×Dic19—28no—
94C22×Dic19—82no—
95C22×Dic19—82no—
96C22⋊C4×C19—24no—
97C22⋊C4×C19—24no—
98C22⋊C4×C19—44no—
99C22⋊C4×C19—42no—
100C22⋊C4×C19—82no—
101C22⋊Dic19—28no—
102C22⋊Dic19—28no—
103C4×Dic19—44no—
104C4×Dic19—82no—
105#64520—44no—
106C2×C19⋊C8—42no—
107#9475—191nomaximal, Sylow
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—24no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—41no—
117C23×C19—42no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—41no—
122C23×C19—42no—
123C23×C19—41no—
124C23×C19—42no—
125C23×C19—81no—
126C23×C19—81no—
127C23×C19—88no—
128C23×C19#10414yescomplemented
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19#12011yescharacteristic
131C23×C19#12311yescharacteristic
132Q8×C19—24no—
133Q8×C19—42no—
134D4×C19—24no—
135D4×C19—42no—
136D4×C19—44no—
137D4×C19—44no—
138D4×C19—88no—
139C2×C4×C19—24no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—42no—
145C2×C4×C19—48no—
146C2×C4×C19—42no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—81no—
154C2×C4×C19C4×D412yes—
155C2×C4×C19#12112yes—
156C2×Dic19—28no—
157C2×Dic19—44no—
158C2×Dic19—44no—
159C2×Dic19—88no—
160C19⋊C8—82no—
161#2404D1911yescharacteristic
162#2273—191no—
163#1789—192no—
164#1462—191no—
165#1284—192no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—24no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—44no—
175C22×C19—44no—
176C22×C19—44no—
177C22×C19—44no—
178C22×C19—44no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—82no—
183C22×C19—82no—
184C22×C19—84no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19#38611yescharacteristic
188C22×C19C2×#10412yes—
189C22×C19B(4,𝔽2)12yes—
190C4×C19—22no—
191C4×C19—22no—
192C4×C19—42no—
193C4×C19—42no—
194C4×C19—82no—
195Dic19—48no—
196C22×#41C2×D1911yescharacteristic
197C2×#120—21no—
198C22×C22⋊C4—381no—
199C22×C22⋊C4C2×D1911yescharacteristic
200C2×#104—384no—
201#407—192no—
202#393Dic1912yescomplemented
203#392Dic1912yescomplemented
204#386—21no—
205#386—22no—
206#381C2×D1911yescharacteristic
207C4×C22⋊C4—192no—
208C4×C22⋊C4—384no—
209C4×C22⋊C4—381no—
210#323—382no—
211C2×C19—22no—
212C2×C19—22no—
213C2×C19—41no—
214C2×C19—44no—
215C2×C19—82no—
216C2×C19#188911yescharacteristic
217C2×C19#189611yescharacteristic
218C2×C19#191111yescharacteristic
219C25C22⋊D1911yescharacteristic
220C2×#41—22no—
221C2×#41—22no—
222C2×#41—44no—
223C22×Q8C2×Dic1911yescharacteristic, complemented
224C22×D4—21no—
225C22×D4—22no—
226C22×D4C2×Dic1911yescharacteristic, complemented
227C23×C4—21no—
228C23×C4—382no—
229C23×C4C22⋊D1911yescharacteristic
230C23×C4C22×D1911yescharacteristic
231C2×M16—382no—
232#120—44no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—388no—
239C2×C22⋊C4—382no—
240C2×C22⋊C4—382no—
241C2×C22⋊C4C2×Dic1912yes—
242C2×C22⋊C4C22⋊D1912yes—
243C2×C42—194no—
244C2×C42—382no—
245#104—768no—
246C22⋊C8—382no—
247C22⋊C8—382no—
248#95—22no—
249#95—21no—
250#95—382no—
251#95—382no—
252#95C2×Dic1912yescomplemented
253C19#947511yescharacteristic, complemented, Sylow
254C24—21no—
255C24—21no—
256C24—24no—
257C24—21no—
258C24—42no—
259C24—81no—
260C24C22⋊Dic1912yes—
261C24C2×C22⋊D1911yescharacteristic
262#41—28no—
263#41—44no—
264#41—44no—
265#41—44no—
266C2×Q8—22no—
267C2×Q8—42no—
268C2×D4—24no—
269C2×D4—22no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—44no—
275C2×D4—44no—
276C2×D4—82no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—81no—
286C22×C4—384no—
287C22×C4—388no—
288C22×C4—1522no—
289C22×C4—1522no—
290C22×C4C22⋊Dic1912yes—
291C22×C4D4×D1912yes—
292C22×C4#6454312yes—
293C22×C4C22×Dic1911yescharacteristic
294C22×C4C2×C22⋊D1911yescharacteristic
295M16—764no—
296C2×C8—762no—
297C22⋊C4—24no—
298C22⋊C4—24no—
299C22⋊C4—44no—
300C22⋊C4—42no—
301C22⋊C4—82no—
302C22⋊C4—388no—
303C22⋊C4—388no—
304C42—764no—
305C42—1522no—
306C23—22no—
307C23—22no—
308C23—24no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—41no—
320C23—42no—
321C23—42no—
322C23—41no—
323C23—81no—
324C23—81no—
325C23—88no—
326C23#1059729414yescomplemented
327C23#1059738111yescharacteristic
328C23#1059738311yescharacteristic
329C23C2×C22⋊Dic1911yescharacteristic
330Q8—24no—
331Q8—42no—
332D4—24no—
333D4—42no—
334D4—44no—
335D4—44no—
336D4—88no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—48no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—388no—
353C2×C4—764no—
354C2×C4—764no—
355C2×C4—1528no—
356C2×C4D4×Dic1912yes—
357C2×C4#1059738512yes—
358C8—1522no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—24no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—82no—
376C22—82no—
377C22—84no—
378C22—81no—
379C22—81no—
380C22#1192642411yescharacteristic
381C22C2×#1059729412yes—
382C22#1192673012yes—
383C4—22no—
384C4—22no—
385C4—42no—
386C4—42no—
387C4—82no—
388C4—768no—
389C2—22no—
390C2—22no—
391C2—41no—
392C2—44no—
393C2—82no—
394C2#1456404411yescharacteristic
395C2#1456407911yescharacteristic
396C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2404C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2404D19
hypocenterC19#9475
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. #14565988C2semidirect
2. #14563579C2semidirect
3. #14561962C2semidirect
4. #14561487C2semidirect
16. C19×#393C4semidirect
17. C19×#392C4semidirect
25. C22×Q8×C19C2×C4semidirect
28. C22×D4×C19C2×C4semidirect
45. C2×C4×Dic19D4semidirect
49. C19×#95C2×C4semidirect
128. C23×C19#104semidirect
202. #393Dic19semidirect
203. #392Dic19semidirect
223. C22×Q8C2×Dic19semidirect
226. C22×D4C2×Dic19semidirect
252. #95C2×Dic19semidirect
253. C19#9475semidirect
326. C23#10597294semidirect

Maximal subgroups

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

subgroupindex
#145659882
#145635792
#145619622
#145614872
C19×#24042
#947519