Finite Group Databasebeta

← #18080365

Subgroups — #18080365

Order 4864.

614 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 93 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#14567905C211yesmaximal, characteristic
2#14566230C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic, complemented
4#14561961C211yesmaximal, characteristic
5#14561489C211yesmaximal, characteristic, complemented
6#14561488C211yesmaximal, characteristic, complemented
7C19×#1826C211yesmaximal, characteristic, complemented
8C22×(C2×D19)⋊C4C2211yescharacteristic
9#11926508C2211yescharacteristic
10#11926479C412yescomplemented
11#11926470C412yescomplemented
12#11926435—22no—
13#11926435—22no—
14#11926433—22no—
15#11926416—21no—
16#11926407C2211yescharacteristic
17#11926402—21no—
18#11926399—21no—
19#11926399—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926303—22no—
22#11926267—22no—
23C2×C19×#117C2211yescharacteristic
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C19×#339—22no—
27C24×D19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C23×Dic19D411yescharacteristic
30C2×M16×C19—21no—
31C19×#117—21no—
32C19×#117—21no—
33C19×#117—21no—
34C19×#117—21no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C42×C19—21no—
40C2×C42×C19D412yes—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4—22no—
51C2×(C2×D19)⋊C4C2×C412yes—
52C2×(C2×D19)⋊C4D412yes—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—22no—
55C2×C4×Dic19D412yes—
56C2×#64520—21no—
57C19×C22⋊C8—21no—
58C19×C22⋊C8—21no—
59C19×#95—21no—
60C19⋊#95—22no—
61C19⋊#95—21no—
62C19⋊#95—21no—
63C19⋊#95—22no—
64C19⋊#95C2×C412yes—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C24×C19C2×D411yescharacteristic
68C23×D19—21no—
69C23×D19—21no—
70C23×D19—42no—
71C23×D19—42no—
72C23×D19—81no—
73C23×D19C22⋊C412yes—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—22no—
77C22×C4×C19—42no—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—22no—
87C22×Dic19—22no—
88C22×Dic19—81no—
89C22×Dic19C22⋊C412yes—
90M16×C19—42no—
91C2×C8×C19—41no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C22⋊C4×C19—42no—
97C22⋊C4×C19—41no—
98C22⋊C4×C19—41no—
99C42×C19—42no—
100C42×C19—41no—
101C42×C19—41no—
102C22⋊Dic19—42no—
103C22⋊Dic19—42no—
104(C2×D19)⋊C4—22no—
105(C2×D19)⋊C4—22no—
106(C2×D19)⋊C4—22no—
107(C2×D19)⋊C4—22no—
108(C2×D19)⋊C4—44no—
109(C2×D19)⋊C4—82no—
110(C2×D19)⋊C4—82no—
111(C2×D19)⋊C4—82no—
112Dic19⋊C4—82no—
113Dic19⋊C4—82no—
114C4×Dic19—42no—
115#64520—42no—
116C2×C19⋊C8—41no—
117#9481—191nomaximal, Sylow
118C23×C19—22no—
119C23×C19—22no—
120C23×C19—41no—
121C23×C19C2×C22⋊C411yescharacteristic
122C23×C19#12011yescharacteristic
123C23×C19#12311yescharacteristic
124C22×D19—22no—
125C22×D19—22no—
126C22×D19—22no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—42no—
131C22×D19—42no—
132C22×D19—42no—
133C22×D19—81no—
134C22×D19—81no—
135C22×D19—88no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19C4×D411yescharacteristic
150C2×C4×C19C4×D411yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12111yescharacteristic
153C2×Dic19—22no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—81no—
163C8×C19—81no—
164C19⋊C8—81no—
165#2482—191no—
166#2312—191no—
167#1826—191no—
168#1826D1911yescharacteristic, complemented
169#1462—191no—
170#1284—191no—
171#1284—191no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—44no—
180C22×C19#38611yescharacteristic
181C22×C19#42112yes—
182C22×C19#45812yes—
183C2×D19—44no—
184C2×D19—42no—
185C2×D19—42no—
186C2×D19—42no—
187C2×D19—84no—
188C2×D19—84no—
189C2×D19—82no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—82no—
195C4×C19—81no—
196C4×C19—81no—
197Dic19—42no—
198Dic19—82no—
199Dic19—82no—
200C2×#117C2×D1911yescharacteristic
201C22×C22⋊C4—191no—
202#407—191no—
203#407C2×D1911yescharacteristic
204#399—192no—
205#397—192no—
206#388—382no—
207#388—382no—
208#388—382no—
209#385—381no—
210#381—191no—
211#380—381no—
212#379—381no—
213#379—381no—
214C4×C22⋊C4—191no—
215C4×C22⋊C4C2×D1911yescharacteristic
216#339—22no—
217#339—382no—
218#323—382no—
219C2×C19—22no—
220C2×C19—22no—
221C2×C19—41no—
222C2×C19#189011yescharacteristic
223C2×C19#189711yescharacteristic
224C2×C19#191111yescharacteristic
225D19—82no—
226C25—191no—
227C23×C4—191no—
228C23×C4C22×D1911yescharacteristic
229C2×M16—21no—
230C2×M16—381no—
231#117—21no—
232#117—21no—
233#117—21no—
234#117—21no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4—382no—
237C2×C4⋊C4C4×D1911yescharacteristic
238C2×C4⋊C4C4×D1911yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—192no—
242C2×C22⋊C4—192no—
243C2×C22⋊C4—381no—
244C2×C22⋊C4—381no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4—381no—
247C2×C22⋊C4—382no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—382no—
251C2×C22⋊C4—382no—
252C2×C22⋊C4—382no—
253C2×C42—21no—
254C2×C42—192no—
255C2×C42C22⋊D1912yes—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—381no—
259C22⋊C8—381no—
260#95—21no—
261#95—192no—
262#95—382no—
263#95—382no—
264#95—381no—
265#95—381no—
266C19#948111yescharacteristic, complemented, Sylow
267C24—192no—
268C24—381no—
269C24—381no—
270C24—762no—
271C24—762no—
272C24—1521no—
273C24D4×D1911yescharacteristic
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—192no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—382no—
282C22×C4—382no—
283C22×C4—1521no—
284C22×C4C2×C4×D1911yescharacteristic
285C22×C4#6454111yescharacteristic
286C22×C4D4×D1911yescharacteristic
287C22×C4D4×D1911yescharacteristic
288C22×C4#6454311yescharacteristic
289C22×C4C2×C22⋊D1911yescharacteristic
290M16—42no—
291M16—762no—
292C2×C8—41no—
293C2×C8—761no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—1522no—
299C4⋊C4—1522no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—382no—
304C22⋊C4—382no—
305C22⋊C4—382no—
306C22⋊C4—382no—
307C22⋊C4—764no—
308C22⋊C4—762no—
309C22⋊C4—762no—
310C22⋊C4—1522no—
311C22⋊C4—1522no—
312C22⋊C4—1522no—
313C42—42no—
314C42—41no—
315C42—41no—
316C42—762no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23—382no—
321C23—382no—
322C23—382no—
323C23—762no—
324C23—762no—
325C23—762no—
326C23—762no—
327C23—762no—
328C23—762no—
329C23—1521no—
330C23—1521no—
331C23—1528no—
332C23C22⋊C4×D1911yescharacteristic
333C23#1059732911yescharacteristic
334C23#1059738311yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—382no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—1521no—
358C2×C4(C22⋊D19)⋊C411yescharacteristic
359C2×C4#1059733011yescharacteristic
360C2×C4C4×C22⋊D1911yescharacteristic
361C2×C4#1059738411yescharacteristic
362C8—81no—
363C8—1521no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22—764no—
373C22—762no—
374C22—762no—
375C22—762no—
376C22—1522no—
377C22—1524no—
378C22—1524no—
379C22#1192642011yescharacteristic
380C22#1192655912yes—
381C22#1192673312yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—81no—
389C4—762no—
390C4—1522no—
391C4—1522no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—1522no—
396C2#1456404511yescharacteristic
397C2#1456408011yescharacteristic
398C2#1456416411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1826C2
socleC22×C19#386
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1826D19
hypocenterC19#9481
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #14563734C2semidirect
5. #14561489C2semidirect
6. #14561488C2semidirect
7. C19×#1826C2semidirect
10. #11926479C4semidirect
11. #11926470C4semidirect
168. #1826D19semidirect
266. C19#9481semidirect

Maximal subgroups

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

subgroupindex
#145679052
#145662302
#145637342
#145619612
#145614892
#145614882
C19×#18262
#948119