Finite Group Databasebeta

← #18078603

Subgroups — #18078603

Order 4864.

762 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 135 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#14566249C211yesmaximal, characteristic, complemented
2#14562203C212yesmaximal, complemented
3C2×#11926268C211yesmaximal, characteristic, complemented
4#14561502C212yesmaximal, complemented
5C19×#2617C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926419—24no—
9#11926404—21no—
10#11926404C2212yes—
11#11926278—24no—
12#11926268—22no—
13C2×C19×#121C2211yescharacteristic
14C2×C19×#120—21no—
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#397C412yescomplemented
17C19×#394—22no—
18C19×#392C412yescomplemented
19C19×#386—21no—
20C19×#380C2211yescharacteristic
21C25×C19D411yescharacteristic
22C22×D4×C19—21no—
23C22×D4×C19—22no—
24C22×D4×C19C2×C411yescharacteristic, complemented
25C23×C4×C19D411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19—22no—
28C19×#121—22no—
29C19×#121—22no—
30C19×#120—42no—
31C19×#120—42no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19C2×C412yes—
41C2×C22⋊C4×C19D412yes—
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—42no—
45C2×C22⋊Dic19—42no—
46C2×C4⋊Dic19—22no—
47C2×C4⋊Dic19—22no—
48C22×C19⋊C8—22no—
49C19×#95—22no—
50C19×#95C2×C412yescomplemented
51C19⋊#95—22no—
52C19⋊#95D414yescomplemented
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—21no—
58C24×C19—21no—
59C24×C19—21no—
60C24×C19—81no—
61C24×C19—81no—
62C24×C19C22⋊C412yes—
63C24×C19D812yes—
64C24×C19SD1612yes—
65C24×C19C2×D411yescharacteristic
66C2×D4×C19—22no—
67C2×D4×C19—44no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19—41no—
71C2×D4×C19—41no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C2×D4×C19—82no—
75C2×D4×C19—82no—
76C2×D4×C19—81no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—81no—
82C22×C4×C19—81no—
83C22×C4×C19C22⋊C412yes—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D412yes—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19#4112yes—
88C22×Dic19—24no—
89C22×Dic19—44no—
90C22×Dic19—82no—
91C22×Dic19—82no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—81no—
94C22⋊C4×C19—24no—
95C22⋊C4×C19—24no—
96C22⋊C4×C19—44no—
97C22⋊C4×C19—41no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—42no—
100C22⋊C4×C19—82no—
101C22⋊Dic19—44no—
102C22⋊Dic19—42no—
103C22⋊Dic19—42no—
104C4⋊Dic19—82no—
105C4⋊Dic19—82no—
106C2×C19⋊C8—42no—
107C2×C19⋊C8—82no—
108#9203—191nomaximal, Sylow
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—42no—
118C23×C19—42no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—42no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—81no—
127C23×C19—81no—
128C23×C19—82no—
129C23×C19—82no—
130C23×C19—82no—
131C23×C19—82no—
132C23×C19#10214yes—
133C23×C19C2×C22⋊C411yescharacteristic
134C23×C19#12011yescharacteristic
135C23×C19#12311yescharacteristic
136C23×C19C2×D811yescharacteristic
137C23×C19C2×SD1611yescharacteristic
138C23×C19AGL(1,ℤ/8)11yescharacteristic
139C23×C19#13711yescharacteristic
140D4×C19—82no—
141D4×C19—88no—
142D4×C19—81no—
143D4×C19—81no—
144D4×C19—81no—
145D4×C19—81no—
146C2×C4×C19—22no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—81no—
160C2×C4×C19C4×D412yes—
161C2×C4×C19#12112yes—
162C2×Dic19—44no—
163C2×Dic19—44no—
164C2×Dic19—44no—
165C2×Dic19—88no—
166C19⋊C8—82no—
167#2617D1911yescharacteristic
168#2315—191no—
169#1519—192no—
170C2×#323—191no—
171#1289—192no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—24no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—44no—
184C22×C19—44no—
185C22×C19—44no—
186C22×C19—42no—
187C22×C19—42no—
188C22×C19—82no—
189C22×C19—82no—
190C22×C19—82no—
191C22×C19—82no—
192C22×C19—82no—
193C22×C19—81no—
194C22×C19—81no—
195C22×C19—81no—
196C22×C19#38611yescharacteristic
197C22×C19C2×#10211yescharacteristic
198C22×C19#41711yescharacteristic
199C22×C19#44711yescharacteristic
200C22×C19#44811yescharacteristic
201C22×C19#48011yescharacteristic
202C22×C19#48111yescharacteristic
203C4×C19—22no—
204C4×C19—22no—
205C4×C19—42no—
206C4×C19—82no—
207C4×C19—81no—
208Dic19—84no—
209C2×#121C2×D1911yescharacteristic
210C2×#120—21no—
211C22×C22⋊C4—381no—
212C22×C22⋊C4C2×D1911yescharacteristic
213C2×C22⋊C8—192no—
214#397Dic1912yescomplemented
215#394—22no—
216#392Dic1912yescomplemented
217#386—21no—
218#385—384no—
219#380—192no—
220#380—381no—
221#380C2×D1911yescharacteristic
222#327—384no—
223#323—382no—
224C2×C19—21no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19—21no—
228C2×C19—21no—
229C2×C19—21no—
230C2×C19—44no—
231C2×C19—161no—
232C2×C19#187411yescharacteristic
233C2×C19#191111yescharacteristic
234C2×C19#191311yescharacteristic
235C25C22⋊D1911yescharacteristic
236C22×D4—21no—
237C22×D4—22no—
238C22×D4C2×Dic1911yescharacteristic, complemented
239C23×C4—382no—
240C23×C4C22⋊D1911yescharacteristic
241C23×C4C22×D1911yescharacteristic
242C22×C8—382no—
243#121—22no—
244#121—22no—
245#120—42no—
246#120—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—382no—
249C2×C4⋊C4—382no—
250C2×C4⋊C4C2×Dic1911yescharacteristic, complemented
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—382no—
258C2×C22⋊C4—382no—
259C2×C22⋊C4—762no—
260C2×C22⋊C4—762no—
261C2×C22⋊C4C2×Dic1912yes—
262C2×C22⋊C4C22⋊D1912yes—
263C22⋊C8—382no—
264C22⋊C8—382no—
265#95—22no—
266#95—194no—
267#95—382no—
268#95C2×Dic1912yescomplemented
269C19#920311yescharacteristic, complemented, Sylow
270C24—21no—
271C24—21no—
272C24—21no—
273C24—21no—
274C24—21no—
275C24—81no—
276C24—81no—
277C24#6452512yes—
278C24#6452612yes—
279C24C22⋊Dic1912yes—
280C24C2×C22⋊D1911yescharacteristic
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—44no—
289C2×D4—82no—
290C2×D4—82no—
291C2×D4—81no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—81no—
297C22×C4—81no—
298C22×C4—384no—
299C22×C4—764no—
300C22×C4—1522no—
301C22×C4—1522no—
302C22×C4C22⋊Dic1912yes—
303C22×C4D4×D1912yes—
304C22×C4#6454312yes—
305C22×C4C22×Dic1911yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307C2×C8—762no—
308C2×C8—1522no—
309C4⋊C4—22no—
310C4⋊C4—81no—
311C4⋊C4—1522no—
312C4⋊C4—1522no—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—44no—
318C22⋊C4—42no—
319C22⋊C4—82no—
320C22⋊C4—764no—
321C22⋊C4—762no—
322C22⋊C4—762no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23#1059728914yes—
347C23C2×#6452511yescharacteristic
348C23C2×#6452611yescharacteristic
349C23#1059738111yescharacteristic
350C23#1059738311yescharacteristic
351C23#1059739511yescharacteristic
352C23#1059739711yescharacteristic
353C23C2×C22⋊Dic1911yescharacteristic
354D4—82no—
355D4—88no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—764no—
375C2×C4—764no—
376C2×C4—764no—
377C2×C4—1528no—
378C2×C4D4×Dic1912yes—
379C2×C4#1059738512yes—
380C8—1522no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—42no—
396C22—42no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#1192642411yescharacteristic
406C22C2×#1059728911yescharacteristic
407C22#1192654511yescharacteristic
408C22#1192667711yescharacteristic
409C22#1192668211yescharacteristic
410C22#1192685511yescharacteristic
411C22#1192686011yescharacteristic
412C4—22no—
413C4—22no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4—1524no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2—44no—
425C2—161no—
426C2#1456395311yescharacteristic
427C2#1456416811yescharacteristic
428C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2617C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2617D19
hypocenterC19#9203
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. #14566249C2semidirect
2. #14562203C2semidirect
3. C2×#11926268C2semidirect
4. #14561502C2semidirect
16. C19×#397C4semidirect
18. C19×#392C4semidirect
24. C22×D4×C19C2×C4semidirect
33. C2×C4⋊C4×C19C2×C4semidirect
50. C19×#95C2×C4semidirect
52. C19⋊#95D4semidirect
214. #397Dic19semidirect
216. #392Dic19semidirect
238. C22×D4C2×Dic19semidirect
250. C2×C4⋊C4C2×Dic19semidirect
268. #95C2×Dic19semidirect
269. C19#9203semidirect

Maximal subgroups

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

subgroupindex
#145662492
#145622032
C2×#119262682
#145615022
C19×#26172
#920319