Finite Group Databasebeta

← #18079988

Subgroups — #18079988

Order 4864.

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

normal subgroups only

This group has 644 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#14569110C211yesmaximal, characteristic
2#14565990C211yesmaximal, characteristic, complemented
3#14562152C211yesmaximal, characteristic
4#14562150C211yesmaximal, characteristic
5#14561964C211yesmaximal, characteristic, complemented
6#14561521C211yesmaximal, characteristic, complemented
7C19×#1297C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597323—21no—
10C22×Dic19⋊C4C2211yescharacteristic
11#11926508C2211yescharacteristic
12#11926484C412yescomplemented
13#11926462C412yescomplemented
14#11926435—22no—
15#11926421—21no—
16#11926421—21no—
17C4×Dic19⋊C4—22no—
18#11926395—22no—
19C22⋊C4×Dic19—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926279—22no—
22#11926277—22no—
23#11926269—22no—
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C22×C22⋊D19—21no—
29C23×Dic19D411yescharacteristic
30C23×Dic19D411yescharacteristic
31C22×D76C2×C411yescharacteristic
32C2×M16×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19—21no—
37C2×C22⋊Dic19—21no—
38#10597376—21no—
39#10597376—21no—
40#10597376—21no—
41#10597376—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×C4⋊Dic19C2×C411yescharacteristic
46C2×Dic19⋊C4—22no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4C2×C412yes—
52C2×Dic19⋊C4D412yes—
53C2×C4×Dic19—22no—
54C2×C4×Dic19—22no—
55C2×C4×Dic19—21no—
56C2×#64520—21no—
57#10597323—28no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95C2×C412yes—
61C19×#95D412yes—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95D412yes—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68C24×C19C2×D411yescharacteristic
69C23×D19—21no—
70C22×C4×C19—22no—
71C22×C4×C19—22no—
72C22×C4×C19—81no—
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C2×C22⋊D19—44no—
80C2×C22⋊D19—41no—
81C2×C22⋊D19—41no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—24no—
85C22×Dic19—22no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—81no—
90C22×Dic19C22⋊C412yes—
91C22×Dic19C22⋊C412yes—
92C2×D76—21no—
93C2×D76—21no—
94C2×D76—81no—
95M16×C19—81no—
96C2×C8×C19—41no—
97C22⋊C4×C19—24no—
98C22⋊C4×C19—42no—
99C42×C19—81no—
100C42×C19—81no—
101C22⋊Dic19—24no—
102(C2×D19)⋊C4—41no—
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—44no—
105(C2×D19)⋊C4—82no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108Dic19⋊C4—28no—
109Dic19⋊C4—22no—
110Dic19⋊C4—22no—
111Dic19⋊C4—22no—
112Dic19⋊C4—22no—
113C4×Dic19—28no—
114C4×Dic19—81no—
115C4×Dic19—82no—
116#64520—81no—
117C2×C19⋊C8—41no—
118#9410—191nomaximal, Sylow
119C23×C19—22no—
120C23×C19—22no—
121C23×C19—41no—
122C23×C19C2×C22⋊C411yescharacteristic
123C23×C19#12011yescharacteristic
124C23×C19#12311yescharacteristic
125C22×D19—42no—
126C22×D19—42no—
127C22×D19—41no—
128C22×D19—42no—
129C2×C4×C19—24no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19C4×D411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19#12111yescharacteristic
144C2×C4×C19#12111yescharacteristic
145C22⋊D19—82no—
146C22⋊D19—82no—
147C2×Dic19—22no—
148C2×Dic19—22no—
149C2×Dic19—24no—
150C2×Dic19—22no—
151C2×Dic19—22no—
152C2×Dic19—24no—
153C2×Dic19—22no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—41no—
160C2×Dic19—81no—
161C2×Dic19#10414yes—
162D76—81no—
163D76—81no—
164C8×C19—81no—
165C19⋊C8—81no—
166#2591—191no—
167#2274—191no—
168#1507—191no—
169#1507—191no—
170#1463—191no—
171#1297—191no—
172#1297D1911yescharacteristic, complemented
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—44no—
181C22×C19#38611yescharacteristic
182C22×C19C2×#10412yes—
183C22×C19#45412yes—
184C2×D19—84no—
185C2×D19—81no—
186C2×D19—81no—
187C2×D19—81no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—44no—
193C4×C19—82no—
194Dic19—24no—
195Dic19—44no—
196Dic19—42no—
197Dic19—81no—
198C2×#121—191no—
199C2×#117—381no—
200C22×C4⋊C4—191no—
201#407—191no—
202#407C2×D1911yescharacteristic
203#400—192no—
204#394—192no—
205#388—382no—
206#386—381no—
207#386—381no—
208C4×C4⋊C4—382no—
209C4×C4⋊C4—382no—
210C4×C22⋊C4—191no—
211C4×C22⋊C4—381no—
212C4×C22⋊C4C2×D1911yescharacteristic
213C4×C22⋊C4C2×D1911yescharacteristic
214#327—382no—
215#327—382no—
216#324—382no—
217C2×C19—22no—
218C2×C19—22no—
219C2×C19—41no—
220C2×C19#188811yescharacteristic
221C2×C19#189611yescharacteristic
222C2×C19#191311yescharacteristic
223D19—161no—
224C22×D4—191no—
225C22×D4—381no—
226C23×C4—191no—
227C23×C4—191no—
228C23×C4C22×D1911yescharacteristic
229C2×M16—21no—
230C2×M16—381no—
231#121—381no—
232#121—381no—
233#121—381no—
234#121—381no—
235#117—388no—
236C2×C4⋊C4—192no—
237C2×C4⋊C4—192no—
238C2×C4⋊C4—191no—
239C2×C4⋊C4—382no—
240C2×C4⋊C4—381no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—381no—
247C2×C22⋊C4—382no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—382no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—382no—
253C2×C42—382no—
254C2×C42—381no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—381no—
258C22⋊C8—381no—
259#95—192no—
260#95—382no—
261#95—382no—
262#95—382no—
263#95C4×D1912yes—
264#95D7612yes—
265C19#941011yescharacteristic, complemented, Sylow
266C24—381no—
267C24D4×D1911yescharacteristic
268C2×D4—381no—
269C2×D4—381no—
270C2×D4—764no—
271C2×D4—761no—
272C2×D4—761no—
273C2×D4—1521no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—81no—
277C22×C4—192no—
278C22×C4—192no—
279C22×C4—384no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—382no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—1521no—
287C22×C4C2×C4×D1911yescharacteristic
288C22×C4C2×D7611yescharacteristic
289C22×C4#6454111yescharacteristic
290C22×C4D4×D1911yescharacteristic
291C22×C4D4×D1911yescharacteristic
292C22×C4#6454511yescharacteristic
293M16—81no—
294M16—1521no—
295C2×C8—41no—
296C2×C8—761no—
297C4⋊C4—388no—
298C4⋊C4—382no—
299C4⋊C4—382no—
300C4⋊C4—382no—
301C4⋊C4—382no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C22⋊C4—24no—
305C22⋊C4—42no—
306C22⋊C4—384no—
307C22⋊C4—764no—
308C22⋊C4—761no—
309C22⋊C4—761no—
310C22⋊C4—1522no—
311C42—81no—
312C42—81no—
313C42—388no—
314C42—1521no—
315C42—1522no—
316C23—22no—
317C23—22no—
318C23—41no—
319C23—762no—
320C23—762no—
321C23—762no—
322C23—761no—
323C23C22⋊C4×D1911yescharacteristic
324C23#1059732811yescharacteristic
325C23#1059734011yescharacteristic
326D4—1521no—
327D4—1521no—
328D4—1522no—
329D4—1522no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—194no—
343C2×C4—382no—
344C2×C4—382no—
345C2×C4—384no—
346C2×C4—382no—
347C2×C4—382no—
348C2×C4—384no—
349C2×C4—382no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—761no—
356C2×C4—1521no—
357C2×C4C4×D7611yescharacteristic
358C2×C4#1059733011yescharacteristic
359C2×C4#1059733911yescharacteristic
360C2×C4#1059734111yescharacteristic
361C8—81no—
362C8—1521no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—1524no—
372C22—1521no—
373C22—1521no—
374C22—1521no—
375C22#1192642211yescharacteristic
376C22#104×D1912yes—
377C22#1192671812yes—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—82no—
384C4—384no—
385C4—764no—
386C4—762no—
387C4—1521no—
388C2—22no—
389C2—22no—
390C2—41no—
391C2—3041no—
392C2#1456403711yescharacteristic
393C2#1456407711yescharacteristic
394C2#1456417611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1297D19
hypocenterC19#9410
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #14565990C2semidirect
5. #14561964C2semidirect
6. #14561521C2semidirect
7. C19×#1297C2semidirect
12. #11926484C4semidirect
13. #11926462C4semidirect
172. #1297D19semidirect
265. C19#9410semidirect

Maximal subgroups

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

subgroupindex
#145691102
#145659902
#145621522
#145621502
#145619642
#145615212
C19×#12972
#941019