Finite Group Databasebeta

← #18075114

Subgroups — #18075114

Order 4864.

1062 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 139 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#14564089C214yesmaximal, complemented
2#14563709C211yesmaximal, characteristic, complemented
3#14561884C211yesmaximal, characteristic, complemented
4C19×#3490C211yesmaximal, characteristic
5C22×C22⋊Dic19C2212yes—
6C2×#10597291—24no—
7#11926400C2212yes—
8C2×C19⋊#95—22no—
9#11926311—22no—
10#11926311—24no—
11C19×#551—24no—
12C19×#546—24no—
13C19×#543C411yescharacteristic, complemented
14C19×#538—22no—
15C19×#534C411yescharacteristic, complemented
16C19×#525—22no—
17C2×C19×#120C2212yes—
18C19×#518C412yescomplemented
19C22×C22⋊C4×C19C2211yescharacteristic
20C25×C19C2311yescharacteristic
21C2×#41×C19—22no—
22C22×D4×C19C2×C412yes—
23C22×D4×C19D414yes—
24C23×C4×C19D412yes—
25C23×Dic19—22no—
26C19×#126—24no—
27C19×#124—24no—
28C19×#123—24no—
29C19×#123—24no—
30C19×#123—22no—
31C19×C22⋊Q8—22no—
32C19×C22⋊Q8—22no—
33C19×C22⋊Q8—24no—
34C19×#121—22no—
35C19×#121—24no—
36C19×#121—22no—
37C19×#120—22no—
38C19×#120—22no—
39C19×#120—22no—
40C19×#120—24no—
41C4×D4×C19—24no—
42C4×D4×C19—24no—
43C4×D4×C19—24no—
44C19×#117—22no—
45C19×#117—22no—
46C2×C22⋊C4×C19—22no—
47C2×C22⋊C4×C19—24no—
48C2×C22⋊C4×C19C2×C411yescharacteristic
49C2×C22⋊C4×C19C2×C411yescharacteristic
50C2×C22⋊C4×C19C2×C412yes—
51C2×C22⋊C4×C19D412yes—
52C2×C22⋊C4×C19D414yes—
53C2×C22⋊Dic19—24no—
54C2×C22⋊Dic19—22no—
55C2×C22⋊Dic19—24no—
56C2×C22⋊Dic19—44no—
57#10597291—48no—
58C19⋊#95—44no—
59C24×C19—42no—
60C24×C19—42no—
61C24×C19—42no—
62C24×C19C22⋊C412yes—
63C24×C19C22×C411yescharacteristic
64C24×C19C2×D411yescharacteristic
65C24×C19C2×D414yes—
66C24×C19C2×D411yescharacteristic
67#41×C19—82no—
68#41×C19—82no—
69C2×Q8×C19—22no—
70C2×D4×C19—22no—
71C2×D4×C19—22no—
72C2×D4×C19—24no—
73C2×D4×C19—22no—
74C2×D4×C19—24no—
75C2×D4×C19—44no—
76C2×D4×C19—44no—
77C2×D4×C19—44no—
78C22×C4×C19—22no—
79C22×C4×C19—24no—
80C22×C4×C19—22no—
81C22×C4×C19—42no—
82C22×C4×C19—42no—
83C22×C4×C19C22⋊C412yes—
84C22×C4×C19C22⋊C414yes—
85C22×C4×C19C22⋊C412yes—
86C22×C4×C19C22⋊C412yes—
87C22×Dic19—24no—
88C22×Dic19—42no—
89C22×Dic19—42no—
90C22×Dic19—42no—
91C22×Dic19—42no—
92C22×Dic19—42no—
93C22×Dic19—42no—
94C22×Dic19—42no—
95C4⋊C4×C19—24no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—24no—
99C22⋊C4×C19—24no—
100C22⋊C4×C19—24no—
101C22⋊C4×C19—22no—
102C22⋊C4×C19—22no—
103C22⋊C4×C19—22no—
104C22⋊C4×C19—22no—
105C22⋊C4×C19—24no—
106C22⋊C4×C19—24no—
107C22⋊C4×C19—24no—
108C42×C19—24no—
109C22⋊Dic19—28no—
110C22⋊Dic19—44no—
111C22⋊Dic19—44no—
112C22⋊Dic19—44no—
113C22⋊Dic19—44no—
114#8535—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—22no—
118C23×C19—22no—
119C23×C19—22no—
120C23×C19—24no—
121C23×C19—24no—
122C23×C19—22no—
123C23×C19—42no—
124C23×C19—44no—
125C23×C19—44no—
126C23×C19—42no—
127C23×C19—42no—
128C23×C19—44no—
129C23×C19—82no—
130C23×C19—82no—
131C23×C19—82no—
132C23×C19—82no—
133C23×C19C2×C22⋊C412yes—
134C23×C19C2×C22⋊C411yescharacteristic
135C23×C19#12012yes—
136C23×C19#12012yes—
137Q8×C19—82no—
138D4×C19—44no—
139D4×C19—44no—
140D4×C19—44no—
141D4×C19—44no—
142D4×C19—84no—
143D4×C19—82no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—24no—
147C2×C4×C19—22no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—44no—
154C2×C4×C19—82no—
155C2×C4×C19—84no—
156C2×Dic19—44no—
157C2×Dic19—44no—
158C2×Dic19—44no—
159C2×Dic19—82no—
160C2×Dic19—82no—
161C2×Dic19—82no—
162C2×Dic19—82no—
163C2×Dic19—82no—
164C2×Dic19—84no—
165#3490D1911yescharacteristic
166#1898—194no—
167#1819—191no—
168#1440—191no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19—22no—
172C22×C19—22no—
173C22×C19—22no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19—24no—
179C22×C19—24no—
180C22×C19—42no—
181C22×C19—44no—
182C22×C19—84no—
183C22×C19—82no—
184C22×C19—82no—
185C22×C19—84no—
186C22×C19—162no—
187C22×C19#37911yescharacteristic
188C22×C19#41012yes—
189C22×C19B(4,𝔽2)12yes—
190C22×C19#45812yes—
191C4×C19—42no—
192C4×C19—42no—
193C4×C19—42no—
194C4×C19—44no—
195Dic19—84no—
196Dic19—162no—
197#551—24no—
198#546—24no—
199#543Dic1911yescharacteristic, complemented
200#538—22no—
201#534Dic1911yescharacteristic, complemented
202#525—22no—
203C2×#120C2×D1912yes—
204#518Dic1912yescomplemented
205C22×C22⋊C4—192no—
206C22×C22⋊C4C2×D1911yescharacteristic
207C2×#99—384no—
208#379—192no—
209C2×#95—382no—
210#342—382no—
211#342—384no—
212C2×C19—22no—
213C2×C19—22no—
214C2×C19—22no—
215C2×C19—42no—
216C2×C19—42no—
217C2×C19—82no—
218C2×C19#178211yescharacteristic
219C2×C19#179012yes—
220C25C22×D1911yescharacteristic
221C2×#41—22no—
222C22×D4C2×Dic1912yes—
223C22×D4C22⋊D1914yes—
224C23×C4—382no—
225C23×C4C22⋊D1912yes—
226#126—24no—
227#124—24no—
228#123—24no—
229#123—24no—
230#123—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C22⋊Q8—24no—
234#121—22no—
235#121—24no—
236#121—22no—
237#120—22no—
238#120—22no—
239#120—22no—
240#120—24no—
241C4×D4—24no—
242C4×D4—24no—
243C4×D4—24no—
244#117—22no—
245#117—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—24no—
248C2×C22⋊C4—384no—
249C2×C22⋊C4—382no—
250C2×C22⋊C4—384no—
251C2×C22⋊C4—764no—
252C2×C22⋊C4C2×Dic1911yescharacteristic
253C2×C22⋊C4C2×Dic1911yescharacteristic
254C2×C22⋊C4C2×Dic1912yes—
255C2×C22⋊C4C22⋊D1912yes—
256C2×C22⋊C4C22⋊D1914yes—
257#99—768no—
258#95—764no—
259C19#853511yescharacteristic, complemented, Sylow
260C24—42no—
261C24—42no—
262C24—42no—
263C24C22⋊Dic1912yes—
264C24C22×Dic1911yescharacteristic
265C24C2×C22⋊D1911yescharacteristic
266C24C2×C22⋊D1914yes—
267C24C2×C22⋊D1911yescharacteristic
268#41—82no—
269#41—82no—
270C2×Q8—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—24no—
274C2×D4—22no—
275C2×D4—24no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—44no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—384no—
285C22×C4—762no—
286C22×C4—762no—
287C22×C4—762no—
288C22×C4—762no—
289C22×C4—762no—
290C22×C4—762no—
291C22×C4—762no—
292C22×C4C22⋊Dic1912yes—
293C22×C4C22⋊Dic1914yes—
294C22×C4C22⋊Dic1912yes—
295C22×C4C22⋊Dic1912yes—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—24no—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—388no—
310C22⋊C4—764no—
311C22⋊C4—764no—
312C22⋊C4—764no—
313C22⋊C4—764no—
314C42—24no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—24no—
319C23—24no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—42no—
324C23—44no—
325C23—42no—
326C23—44no—
327C23—42no—
328C23—44no—
329C23—82no—
330C23—82no—
331C23—82no—
332C23—82no—
333C23C2×C22⋊Dic1912yes—
334C23C2×C22⋊Dic1911yescharacteristic
335C23#1059739912yes—
336C23#1059739912yes—
337Q8—82no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—44no—
342D4—84no—
343D4—82no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—82no—
355C2×C4—84no—
356C2×C4—764no—
357C2×C4—764no—
358C2×C4—764no—
359C2×C4—1522no—
360C2×C4—1524no—
361C2×C4—1522no—
362C2×C4—1522no—
363C2×C4—1522no—
364C2×C4—1522no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—24no—
375C22—24no—
376C22—42no—
377C22—44no—
378C22—84no—
379C22—84no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22#1192640011yescharacteristic
384C22#1192651812yes—
385C22#1192673112yes—
386C22#1192673412yes—
387C4—42no—
388C4—42no—
389C4—42no—
390C4—44no—
391C4—3042no—
392C4—1524no—
393C2—22no—
394C2—22no—
395C2—22no—
396C2—42no—
397C2—42no—
398C2—82no—
399C2#1456355311yescharacteristic
400C2#1456358312yes—
subgroupG/H
centerC22#11926400
commutatorC24×C19C22×C4
FrattiniC25C22×D19
Fitting, prime radicalC19×#3490C2
socleC22×C19#379
cosocleC25×C19C23
hypercenter#3490D19
hypocenterC19#8535
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #3490

Complements

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

NH ≅ G/Ntype
1. #14564089C2semidirect
2. #14563709C2semidirect
3. #14561884C2semidirect
13. C19×#543C4semidirect
15. C19×#534C4semidirect
18. C19×#518C4semidirect
199. #543Dic19semidirect
201. #534Dic19semidirect
204. #518Dic19semidirect
259. C19#8535semidirect

Maximal subgroups

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

subgroupindex
#145640892
#145637092
#145618842
C19×#34902
#853519