Finite Group Databasebeta

← #18080338

Subgroups — #18080338

Order 4864.

958 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 111 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#14566954C211yesmaximal, characteristic
2#14563580C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561488C212yesmaximal, complemented
5C19×#2273C211yesmaximal, characteristic, complemented
6C22×#64541C2211yescharacteristic
7C2×#10597399—21no—
8C2×#10597262—24no—
9#11926508C2212yes—
10#11926456C412yescomplemented
11#11926453C412yescomplemented
12#11926423—21no—
13#11926420—22no—
14#11926407C2211yescharacteristic
15#11926268—22no—
16C22×C22⋊C4×C19—21no—
17C22×C22⋊C4×C19C2211yescharacteristic
18C4×C22⋊C4×C19—21no—
19C4×C22⋊C4×C19—24no—
20C4×C22⋊C4×C19C2212yes—
21C25×C19D411yescharacteristic
22C23×C4×C19—22no—
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C22×C22⋊D19—21no—
26C22×C22⋊D19—22no—
27C2×#64541—22no—
28C2×#64541—22no—
29C2×#64541—44no—
30C22×D76C2×C411yescharacteristic, complemented
31C22×C4×D19—21no—
32C22×Dic38C2×C411yescharacteristic, complemented
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—28no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19D412yes—
40C2×C42×C19—22no—
41C2×C42×C19D414yescomplemented
42#10597399—44no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—21no—
45C2×(C2×D19)⋊C4—22no—
46C2×#64520—22no—
47C19×#95—22no—
48C19×#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C19⋊#95C2×C412yescomplemented
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54#10597262—48no—
55C24×C19—21no—
56C24×C19—24no—
57C24×C19—21no—
58C24×C19—42no—
59C24×C19—81no—
60C24×C19C22⋊C412yes—
61C24×C19C2×D411yescharacteristic
62C23×D19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—24no—
65C22×C4×C19—28no—
66C22×C4×C19—21no—
67C22×C4×C19—42no—
68C22×C4×C19—81no—
69C22×C4×C19—82no—
70C22×C4×C19—82no—
71C22×C4×C19C22⋊C412yes—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D412yes—
75C22×C4×C19#4112yes—
76C2×C22⋊D19—24no—
77C2×C22⋊D19—42no—
78C2×C22⋊D19—41no—
79C2×C22⋊D19—41no—
80C2×C22⋊D19—44no—
81C2×C22⋊D19—44no—
82C2×C22⋊D19—82no—
83C22×Dic19—21no—
84C22×Dic19—22no—
85#64541—28no—
86#64541—44no—
87#64541—44no—
88#64541—44no—
89C2×D76—22no—
90C2×D76—42no—
91C2×C4×D19—42no—
92C2×C4×D19—42no—
93C2×C4×D19—42no—
94C2×Dic38—22no—
95C2×Dic38—42no—
96C22⋊C4×C19—28no—
97C22⋊C4×C19—28no—
98C22⋊C4×C19—24no—
99C22⋊C4×C19—24no—
100C42×C19—44no—
101C42×C19—82no—
102C22⋊Dic19—44no—
103C22⋊Dic19—42no—
104(C2×D19)⋊C4—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—41no—
116C23×C19—42no—
117C23×C19—42no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—81no—
121C23×C19—81no—
122C23×C19—88no—
123C23×C19#10414yescomplemented
124C23×C19C2×C22⋊C411yescharacteristic
125C23×C19#12011yescharacteristic
126C23×C19#12311yescharacteristic
127C22×D19—22no—
128C22×D19—42no—
129C22×D19—41no—
130C22×D19—41no—
131C22×D19—42no—
132C2×C4×C19—24no—
133C2×C4×C19—28no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—42no—
138C2×C4×C19—44no—
139C2×C4×C19—42no—
140C2×C4×C19—44no—
141C2×C4×C19—42no—
142C2×C4×C19—81no—
143C2×C4×C19—88no—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12112yes—
146C22⋊D19—44no—
147C22⋊D19—44no—
148C22⋊D19—88no—
149C2×Dic19—22no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155D76—24no—
156D76—42no—
157C4×D19—48no—
158Dic38—24no—
159Dic38—42no—
160C19⋊C8—82no—
161#2404—191no—
162#2273D1911yescharacteristic, complemented
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—42no—
179C22×C19—42no—
180C22×C19—82no—
181C22×C19—84no—
182C22×C19#38611yescharacteristic
183C22×C19C2×#10412yes—
184C22×C19B(4,𝔽2)12yes—
185C2×D19—44no—
186C2×D19—42no—
187C2×D19—82no—
188C2×D19—81no—
189C2×D19—81no—
190C4×C19—22no—
191C4×C19—22no—
192C4×C19—48no—
193C4×C19—42no—
194Dic19—42no—
195Dic19—82no—
196C22×#41—191no—
197C2×#120—381no—
198C22×C22⋊C4—21no—
199C22×C22⋊C4C2×D1911yescharacteristic
200C2×#104—384no—
201#407—192no—
202#393—192no—
203#392—192no—
204#386—381no—
205#386—382no—
206#381—191no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4—24no—
209C4×C22⋊C4C2×D1912yes—
210#323—382no—
211C2×C19—22no—
212C2×C19—22no—
213C2×C19—41no—
214C2×C19—44no—
215C2×C19#188911yescharacteristic
216C2×C19#189611yescharacteristic
217C2×C19#191111yescharacteristic
218D19—82no—
219C25C22⋊D1911yescharacteristic
220C2×#41—382no—
221C2×#41—382no—
222C2×#41—764no—
223C22×Q8—191no—
224C22×D4—191no—
225C22×D4—381no—
226C22×D4—382no—
227C23×C4—22no—
228C23×C4—381no—
229C23×C4C22⋊D1911yescharacteristic
230C23×C4C22×D1911yescharacteristic
231C2×M16—382no—
232#120—764no—
233C2×C22⋊C4—28no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—382no—
239C2×C22⋊C4—381no—
240C2×C22⋊C4—382no—
241C2×C22⋊C4C4×D1912yes—
242C2×C22⋊C4D7612yes—
243C2×C42—22no—
244C2×C42C22⋊D1914yescomplemented
245#104—768no—
246C22⋊C8—382no—
247C22⋊C8—382no—
248#95—22no—
249#95—22no—
250#95—192no—
251#95—382no—
252#95—381no—
253C19#947511yescharacteristic, complemented, Sylow
254C24—21no—
255C24—24no—
256C24—21no—
257C24—42no—
258C24—81no—
259C24—381no—
260C24(C2×D19)⋊C412yes—
261C24C2×C22⋊D1911yescharacteristic
262#41—388no—
263#41—764no—
264#41—764no—
265#41—764no—
266C2×Q8—382no—
267C2×Q8—762no—
268C2×D4—384no—
269C2×D4—382no—
270C2×D4—762no—
271C2×D4—762no—
272C2×D4—761no—
273C2×D4—761no—
274C2×D4—764no—
275C2×D4—764no—
276C2×D4—1522no—
277C22×C4—21no—
278C22×C4—24no—
279C22×C4—28no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—81no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4—381no—
286C22×C4—382no—
287C22×C4—762no—
288C22×C4—762no—
289C22×C4—762no—
290C22×C4(C2×D19)⋊C412yes—
291C22×C4C2×C4×D1911yescharacteristic
292C22×C4C2×D7611yescharacteristic
293C22×C4#6454112yes—
294C22×C4C2×C22⋊D1912yes—
295M16—764no—
296C2×C8—762no—
297C22⋊C4—28no—
298C22⋊C4—28no—
299C22⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—764no—
302C22⋊C4—762no—
303C22⋊C4—1522no—
304C42—44no—
305C42—82no—
306C23—22no—
307C23—22no—
308C23—24no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—41no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—81no—
320C23—88no—
321C23—382no—
322C23—762no—
323C23—761no—
324C23—762no—
325C23—761no—
326C23#1059726214yescomplemented
327C23C2×(C2×D19)⋊C411yescharacteristic
328C23#1059737511yescharacteristic
329C23#1059739911yescharacteristic
330Q8—384no—
331Q8—762no—
332D4—384no—
333D4—762no—
334D4—764no—
335D4—764no—
336D4—1528no—
337C2×C4—24no—
338C2×C4—28no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—88no—
349C2×C4—382no—
350C2×C4—768no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4C4×C22⋊D1912yes—
357C2×C4#1059737612yes—
358C8—1522no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—24no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—42no—
372C22—42no—
373C22—82no—
374C22—84no—
375C22—764no—
376C22—762no—
377C22—1522no—
378C22—1521no—
379C22—1521no—
380C22#1192642311yescharacteristic
381C22C2×#1059726212yes—
382C22#1192673112yes—
383C4—22no—
384C4—22no—
385C4—48no—
386C4—42no—
387C4—762no—
388C4—1522no—
389C2—22no—
390C2—22no—
391C2—41no—
392C2—44no—
393C2—1522no—
394C2#1456404311yescharacteristic
395C2#1456407811yescharacteristic
396C2#1456416711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2273C2
socleC22×C19#386
prime radical#14566954C2
cosocleC23×C4×C19C23
hypercenter#2273D19
hypocenterC19#9475
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #14563580C2semidirect
3. #14561962C2semidirect
4. #14561488C2semidirect
5. C19×#2273C2semidirect
10. #11926456C4semidirect
11. #11926453C4semidirect
30. C22×D76C2×C4semidirect
32. C22×Dic38C2×C4semidirect
41. C2×C42×C19D4semidirect
51. C19⋊#95C2×C4semidirect
123. C23×C19#104semidirect
162. #2273D19semidirect
244. C2×C42C22⋊D19semidirect
253. C19#9475semidirect
326. C23#10597262semidirect

Maximal subgroups

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

subgroupindex
#145669542
#145635802
#145619622
#145614882
C19×#22732
#947519