Finite Group Databasebeta

← #18080282

Subgroups — #18080282

Order 4864.

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

normal subgroups only

This group has 610 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#14568106C211yesmaximal, characteristic
2#14566236C211yesmaximal, characteristic, complemented
3#14563713C211yesmaximal, characteristic, complemented
4#14562165C211yesmaximal, characteristic
5#14562163C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic, complemented
7C19×#1284C211yesmaximal, characteristic, complemented
8C2×#10597332—21no—
9C2×#10597332—21no—
10C2×#10597376C2211yescharacteristic
11C22×C4⋊Dic19C2211yescharacteristic
12#11926508C2211yescharacteristic
13#11926481—22no—
14#11926446C412yescomplemented
15#11926429—22no—
16#11926427—22no—
17#11926414C412yescomplemented
18#11926407C2211yescharacteristic
19#11926402—21no—
20C22⋊C4×Dic19—21no—
21#11926312—22no—
22#11926279—22no—
23#11926277—22no—
24C19×#407C2211yescharacteristic
25C19×#381C2211yescharacteristic
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×C19C2×C412yes—
36C2×C22⋊Dic19—21no—
37#10597376—21no—
38#10597376—21no—
39#10597376—21no—
40#10597376—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—22no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—22no—
49C2×C4⋊Dic19—22no—
50C2×C4⋊Dic19C2×C411yescharacteristic
51C2×C4⋊Dic19C2×C412yes—
52C2×C4⋊Dic19D412yes—
53C2×Dic19⋊C4—22no—
54C2×C4×Dic19—22no—
55C2×#64520—21no—
56#10597332—44no—
57#10597332—44no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95—21no—
61C19×#95—21no—
62C19×#95D412yes—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95—21no—
66C19⋊#95D412yes—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69C24×C19C2×D411yescharacteristic
70C23×D19—21no—
71C22×C4×C19—22no—
72C22×C4×C19—22no—
73C22×C4×C19—42no—
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C2×C22⋊D19—42no—
81C2×C22⋊D19—42no—
82C2×C22⋊D19—41no—
83C2×C22⋊D19—41no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—22no—
90C22×Dic19—42no—
91C22×Dic19—42no—
92C22×Dic19C22⋊C412yes—
93C22×Dic19C22⋊C412yes—
94C2×D76—21no—
95C2×D76—21no—
96C2×D76—42no—
97M16×C19—42no—
98C2×C8×C19—41no—
99C22⋊C4×C19—24no—
100C22⋊C4×C19—42no—
101C42×C19—42no—
102C22⋊Dic19—42no—
103(C2×D19)⋊C4—44no—
104(C2×D19)⋊C4—44no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—41no—
107C4⋊Dic19—22no—
108C4⋊Dic19—22no—
109C4⋊Dic19—22no—
110C4⋊Dic19—22no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—44no—
114C4⋊Dic19—44no—
115Dic19⋊C4—82no—
116C4×Dic19—82no—
117#64520—42no—
118C2×C19⋊C8—41no—
119#9464—191nomaximal, Sylow
120C23×C19—22no—
121C23×C19—22no—
122C23×C19—41no—
123C23×C19C2×C22⋊C411yescharacteristic
124C23×C19#12011yescharacteristic
125C23×C19#12311yescharacteristic
126C22×D19—41no—
127C22×D19—41no—
128C22×D19—42no—
129C22×D19—41no—
130C22×D19—42no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—24no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19C4×D411yescharacteristic
144C2×C4×C19C4×D411yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C22⋊D19—82no—
148C22⋊D19—82no—
149C2×Dic19—22no—
150C2×Dic19—22no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—41no—
160C2×Dic19—42no—
161C2×Dic19—81no—
162C2×Dic19—81no—
163D76—81no—
164D76—81no—
165C8×C19—81no—
166C19⋊C8—81no—
167#2501—191no—
168#2313—191no—
169#1821—191no—
170#1510—191no—
171#1510—191no—
172#1284—191no—
173#1284D1911yescharacteristic, complemented
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—44no—
182C22×C19#38611yescharacteristic
183C22×C19#41012yes—
184C22×C19#45312yes—
185C2×D19—82no—
186C2×D19—82no—
187C2×D19—81no—
188C2×D19—81no—
189C2×D19—81no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—44no—
195C4×C19—82no—
196Dic19—42no—
197Dic19—42no—
198Dic19—82no—
199Dic19—81no—
200C2×#123—381no—
201C2×#123—381no—
202C2×#121—191no—
203C22×C4⋊C4—191no—
204#407—191no—
205#407C2×D1911yescharacteristic
206#399—382no—
207#390—192no—
208#387—382no—
209#387—382no—
210#384—192no—
211#381—191no—
212#381C2×D1911yescharacteristic
213#380—381no—
214C4×C22⋊C4—381no—
215C4×C22⋊C4C2×D1911yescharacteristic
216#343—382no—
217#327—382no—
218#327—382no—
219C2×C19—22no—
220C2×C19—22no—
221C2×C19—41no—
222C2×C19#188711yescharacteristic
223C2×C19#189911yescharacteristic
224C2×C19#191211yescharacteristic
225D19—161no—
226C22×D4—191no—
227C22×D4—381no—
228C23×C4—191no—
229C23×C4—191no—
230C23×C4C22×D1911yescharacteristic
231C2×M16—21no—
232C2×M16—381no—
233#123—764no—
234#123—764no—
235#121—381no—
236#121—381no—
237#121—381no—
238#121—381no—
239C2×C4⋊C4—192no—
240C2×C4⋊C4—192no—
241C2×C4⋊C4—191no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—382no—
247C2×C4⋊C4—382no—
248C2×C4⋊C4—382no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—382no—
252C2×C22⋊C4—382no—
253C2×C22⋊C4—381no—
254C2×C22⋊C4—381no—
255C2×C42—382no—
256C2×C42C4×D1912yes—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—381no—
260C22⋊C8—381no—
261#95—21no—
262#95—21no—
263#95—192no—
264#95—382no—
265#95—382no—
266#95—381no—
267#95D7612yes—
268C19#946411yescharacteristic, complemented, Sylow
269C24—381no—
270C24D4×D1911yescharacteristic
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—762no—
274C2×D4—762no—
275C2×D4—762no—
276C2×D4—761no—
277C2×D4—761no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—192no—
282C22×C4—192no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—382no—
289C22×C4—762no—
290C22×C4—762no—
291C22×C4C2×C4×D1911yescharacteristic
292C22×C4C2×D7611yescharacteristic
293C22×C4#6454111yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4#6454511yescharacteristic
297M16—42no—
298M16—762no—
299C2×C8—41no—
300C2×C8—761no—
301C4⋊C4—382no—
302C4⋊C4—382no—
303C4⋊C4—382no—
304C4⋊C4—382no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C4⋊C4—764no—
308C4⋊C4—764no—
309C4⋊C4—1522no—
310C22⋊C4—24no—
311C22⋊C4—42no—
312C22⋊C4—764no—
313C22⋊C4—764no—
314C22⋊C4—762no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C42—42no—
318C42—1522no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23—761no—
323C23—761no—
324C23—762no—
325C23—761no—
326C23—762no—
327C23C22⋊C4×D1911yescharacteristic
328C23#1059732811yescharacteristic
329C23#1059734011yescharacteristic
330D4—1521no—
331D4—1521no—
332D4—1522no—
333D4—1522no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
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—42no—
346C2×C4—382no—
347C2×C4—382no—
348C2×C4—762no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—762no—
356C2×C4—761no—
357C2×C4—762no—
358C2×C4—1521no—
359C2×C4—1521no—
360C2×C4C4×D7611yescharacteristic
361C2×C4#1059733011yescharacteristic
362C2×C4#1059733911yescharacteristic
363C2×C4#1059734111yescharacteristic
364C8—81no—
365C8—1521no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—44no—
374C22—1522no—
375C22—1522no—
376C22—1521no—
377C22—1521no—
378C22—1521no—
379C22#1192642211yescharacteristic
380C22#1192651612yes—
381C22#1192671312yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—44no—
387C4—82no—
388C4—762no—
389C4—762no—
390C4—1522no—
391C4—1521no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—3041no—
396C2#1456403211yescharacteristic
397C2#1456409211yescharacteristic
398C2#1456417111yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1284C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1284D19
hypocenterC19#9464
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
2. #14566236C2semidirect
3. #14563713C2semidirect
6. #14561488C2semidirect
7. C19×#1284C2semidirect
14. #11926446C4semidirect
17. #11926414C4semidirect
173. #1284D19semidirect
268. C19#9464semidirect

Maximal subgroups

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

subgroupindex
#145681062
#145662362
#145637132
#145621652
#145621632
#145614882
C19×#12842
#946419