Finite Group Databasebeta

← #18080347

Subgroups — #18080347

Order 4864.

734 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 97 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#14567911C211yesmaximal, characteristic
2#14565987C211yesmaximal, characteristic
3#14563735C211yesmaximal, characteristic, complemented
4#14563732C211yesmaximal, characteristic, complemented
5#14561961C211yesmaximal, characteristic
6#14561487C211yesmaximal, characteristic, complemented
7C19×#1284C211yesmaximal, characteristic, complemented
8C2×#10597372C2211yescharacteristic
9C22×(C2×D19)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D19—21no—
11#11926508C2211yescharacteristic
12#11926481C412yescomplemented
13#11926471C412yescomplemented
14#11926436—22no—
15#11926419—21no—
16#11926399—21no—
17C22⋊C4×Dic19—21no—
18C4×(C2×D19)⋊C4—22no—
19C4×C22⋊Dic19C2211yescharacteristic
20#11926391—22no—
21#11926305—22no—
22#11926304—22no—
23#11926267—22no—
24C19×#407C2211yescharacteristic
25C19×#381C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C24×D19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C23×Dic19D411yescharacteristic
30C22×C4×D19—22no—
31C2×M16×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C42×C19D412yes—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4C2×C412yes—
45C2×(C2×D19)⋊C4D412yes—
46#10597372—21no—
47#10597372—21no—
48#10597372—21no—
49#10597372—21no—
50C2×C4⋊Dic19—22no—
51C2×C4⋊Dic19C2×C411yescharacteristic, complemented
52C2×C4⋊Dic19C2×C411yescharacteristic, complemented
53C2×C4×Dic19—21no—
54C2×C4×Dic19—22no—
55C2×C4×Dic19D412yes—
56C2×#64520—21no—
57C22⋊C4×D19—28no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95—21no—
61C19×#95—21no—
62C19×#95C2×C412yescomplemented
63C19⋊#95—22no—
64C19⋊#95—21no—
65C19⋊#95—22no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68C24×C19C2×D411yescharacteristic
69C23×D19—21no—
70C23×D19—21no—
71C23×D19—24no—
72C23×D19—42no—
73C23×D19—81no—
74C23×D19C22⋊C412yes—
75C22×C4×C19—22no—
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—22no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—81no—
90C22×Dic19C22⋊C412yes—
91C2×C4×D19—28no—
92C2×C4×D19—82no—
93C2×C4×D19—82no—
94M16×C19—42no—
95C2×C8×C19—41no—
96C22⋊C4×C19—24no—
97C22⋊C4×C19—42no—
98C42×C19—42no—
99C22⋊Dic19—24no—
100C22⋊Dic19—41no—
101C22⋊Dic19—41no—
102(C2×D19)⋊C4—28no—
103(C2×D19)⋊C4—22no—
104(C2×D19)⋊C4—22no—
105(C2×D19)⋊C4—22no—
106(C2×D19)⋊C4—22no—
107(C2×D19)⋊C4—44no—
108(C2×D19)⋊C4—82no—
109C4⋊Dic19—21no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—82no—
114C4×Dic19—41no—
115C4×Dic19—41no—
116C4×Dic19—42no—
117C4×Dic19—82no—
118#64520—42no—
119C2×C19⋊C8—41no—
120#9477—191nomaximal, Sylow
121C23×C19—22no—
122C23×C19—22no—
123C23×C19—41no—
124C23×C19C2×C22⋊C411yescharacteristic
125C23×C19#12011yescharacteristic
126C23×C19#12311yescharacteristic
127C22×D19—22no—
128C22×D19—22no—
129C22×D19—22no—
130C22×D19—24no—
131C22×D19—22no—
132C22×D19—42no—
133C22×D19—42no—
134C22×D19—42no—
135C22×D19—42no—
136C22×D19—88no—
137C22×D19—81no—
138C22×D19—81no—
139C22×D19#10414yes—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—24no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19C4×D411yescharacteristic
153C2×C4×C19C4×D411yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×Dic19—24no—
157C2×Dic19—22no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—42no—
166C2×Dic19—81no—
167C4×D19—88no—
168C8×C19—81no—
169C19⋊C8—81no—
170#2482—191no—
171#2273—191no—
172#1826—191no—
173#1826—191no—
174#1462—191no—
175#1284—191no—
176#1284D1911yescharacteristic, complemented
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—44no—
185C22×C19#38611yescharacteristic
186C22×C19C2×#10412yes—
187C22×C19#45812yes—
188C2×D19—24no—
189C2×D19—44no—
190C2×D19—44no—
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—44no—
194C2×D19—82no—
195C2×D19—84no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—44no—
201C4×C19—82no—
202Dic19—44no—
203Dic19—42no—
204Dic19—81no—
205Dic19—81no—
206C2×#117—191no—
207C22×C22⋊C4—191no—
208C22×C22⋊C4—381no—
209#407—191no—
210#407C2×D1911yescharacteristic
211#399—192no—
212#397—192no—
213#388—382no—
214#385—381no—
215#381C2×D1911yescharacteristic
216#379—381no—
217C4×C22⋊C4—191no—
218C4×C22⋊C4—382no—
219C4×C22⋊C4—381no—
220C4×C22⋊C4—382no—
221C4×C22⋊C4C2×D1911yescharacteristic
222#339—382no—
223#339—382no—
224#323—382no—
225C2×C19—22no—
226C2×C19—22no—
227C2×C19—41no—
228C2×C19#189011yescharacteristic
229C2×C19#189611yescharacteristic
230C2×C19#191111yescharacteristic
231D19—44no—
232C25—191no—
233C23×C4—191no—
234C23×C4—382no—
235C23×C4C22×D1911yescharacteristic
236C2×M16—21no—
237C2×M16—381no—
238#117—381no—
239#117—381no—
240#117—381no—
241#117—381no—
242C2×C4⋊C4—191no—
243C2×C4⋊C4—191no—
244C2×C4⋊C4—382no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—192no—
248C2×C22⋊C4—192no—
249C2×C22⋊C4—388no—
250C2×C22⋊C4—382no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C22⋊C4—381no—
255C2×C22⋊C4—381no—
256C2×C22⋊C4—382no—
257C2×C22⋊C4—381no—
258C2×C22⋊C4—382no—
259C2×C42—192no—
260C2×C42—381no—
261C2×C42—382no—
262C2×C42D7612yes—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—381no—
266C22⋊C8—381no—
267#95—21no—
268#95—21no—
269#95—382no—
270#95—382no—
271#95—381no—
272#95C4×D1912yescomplemented
273C19#947711yescharacteristic, complemented, Sylow
274C24—192no—
275C24—384no—
276C24—381no—
277C24—381no—
278C24—762no—
279C24—1521no—
280C24D4×D1911yescharacteristic
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—192no—
285C22×C4—388no—
286C22×C4—382no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—1522no—
292C22×C4—1522no—
293C22×C4—1521no—
294C22×C4C2×C4×D1911yescharacteristic
295C22×C4C2×D7611yescharacteristic
296C22×C4#6454111yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4D4×D1911yescharacteristic
299C22×C4#6454511yescharacteristic
300M16—42no—
301M16—762no—
302C2×C8—41no—
303C2×C8—761no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C4⋊C4—381no—
308C4⋊C4—1522no—
309C22⋊C4—24no—
310C22⋊C4—42no—
311C22⋊C4—388no—
312C22⋊C4—384no—
313C22⋊C4—382no—
314C22⋊C4—382no—
315C22⋊C4—382no—
316C22⋊C4—382no—
317C22⋊C4—764no—
318C22⋊C4—761no—
319C22⋊C4—761no—
320C22⋊C4—1522no—
321C42—42no—
322C42—762no—
323C42—761no—
324C42—761no—
325C42—1522no—
326C23—22no—
327C23—22no—
328C23—41no—
329C23—194no—
330C23—382no—
331C23—382no—
332C23—384no—
333C23—382no—
334C23—382no—
335C23—762no—
336C23—762no—
337C23—762no—
338C23—762no—
339C23—1521no—
340C23—1521no—
341C23—1528no—
342C23C22⋊C4×D1911yescharacteristic
343C23#1059732811yescharacteristic
344C23#1059734011yescharacteristic
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—384no—
358C2×C4—382no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—762no—
362C2×C4—762no—
363C2×C4—762no—
364C2×C4—762no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—1528no—
368C2×C4—1521no—
369C2×C4C4×D7611yescharacteristic
370C2×C4#1059733011yescharacteristic
371C2×C4#1059733911yescharacteristic
372C2×C4#1059734111yescharacteristic
373C8—81no—
374C8—1521no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—44no—
383C22—384no—
384C22—764no—
385C22—764no—
386C22—764no—
387C22—762no—
388C22—762no—
389C22—1522no—
390C22—1524no—
391C22#1192642211yescharacteristic
392C22#104×D1912yes—
393C22#1192673512yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—82no—
400C4—764no—
401C4—762no—
402C4—1521no—
403C4—1521no—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—764no—
408C2#1456404711yescharacteristic
409C2#1456407711yescharacteristic
410C2#1456416611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1284C2
socleC22×C19#386
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1284D19
hypocenterC19#9477
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
3. #14563735C2semidirect
4. #14563732C2semidirect
6. #14561487C2semidirect
7. C19×#1284C2semidirect
12. #11926481C4semidirect
13. #11926471C4semidirect
51. C2×C4⋊Dic19C2×C4semidirect
52. C2×C4⋊Dic19C2×C4semidirect
62. C19×#95C2×C4semidirect
176. #1284D19semidirect
272. #95C4×D19semidirect
273. C19#9477semidirect

Maximal subgroups

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

subgroupindex
#145679112
#145659872
#145637352
#145637322
#145619612
#145614872
C19×#12842
#947719