Finite Group Databasebeta

← #18080248

Subgroups — #18080248

Order 4864.

690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 107 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#14568581C211yesmaximal, characteristic
2#14562348C212yesmaximal, complemented
3#14561976C211yesmaximal, characteristic, complemented
4#14561492C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic, complemented
6C2×#10597320C2211yescharacteristic
7C2×#10597386C412yes—
8C2×#10597376—21no—
9C2×#10597376—21no—
10#11926601C2212yes—
11#11926453—21no—
12#11926453—21no—
13#11926445C412yes—
14C4×C4⋊Dic19C2211yescharacteristic
15#11926287—24no—
16#11926268—21no—
17#11926268—21no—
18C2×C4×D4×C19C2211yescharacteristic
19C19×#435—24no—
20C19×#432C2212yes—
21C19×#407—21no—
22C2×C19×C22⋊C8—21no—
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—22no—
27C22×C22⋊D19—22no—
28C22×D76—21no—
29C22×D76—21no—
30C22×D76C2×C412yes—
31C2×M16×C19—22no—
32C22×C8×C19—22no—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C22⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C42×C19C2311yescharacteristic
39#10597386—44no—
40#10597376—44no—
41#10597376—44no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—22no—
44C2×C4⋊Dic19—21no—
45C2×C4×Dic19C2×C412yes—
46#10597320—22no—
47#10597320—22no—
48C19×C4⋊C8D414yescomplemented
49C19×C22⋊C8—22no—
50C19×C22⋊C8—22no—
51C19×C22⋊C8—22no—
52C19×#97—22no—
53C19⋊#95—21no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—22no—
56#10597260—22no—
57C24×C19C22⋊C411yescharacteristic
58C24×C19C22⋊C411yescharacteristic
59C23×D19—22no—
60C2×D4×C19—22no—
61C2×D4×C19—22no—
62C2×D4×C19—41no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C2×C22⋊D19—44no—
75C2×C22⋊D19—44no—
76C2×C22⋊D19—44no—
77C2×C22⋊D19—44no—
78C2×C22⋊D19—82no—
79C2×C22⋊D19—82no—
80C22×Dic19—22no—
81C2×D76—24no—
82C2×D76—42no—
83C2×D76—42no—
84C2×D76—42no—
85C2×D76—42no—
86C2×D76—41no—
87C2×D76—42no—
88C2×D76—41no—
89C2×D76—82no—
90M16×C19—82no—
91C2×C8×C19—24no—
92C2×C8×C19—82no—
93C4⋊C4×C19—22no—
94C22⋊C4×C19—22no—
95C22⋊C4×C19—22no—
96C42×C19C2×D412yes—
97C42×C19#4112yes—
98(C2×D19)⋊C4—44no—
99(C2×D19)⋊C4—44no—
100C4⋊Dic19—24no—
101C4×Dic19—42no—
102C2×C19⋊C8—42no—
103#9457—191nomaximal, Sylow
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19—41no—
113C23×C19#10012yes—
114C23×C19C2×C22⋊C411yescharacteristic
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122D4×C19—44no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—81no—
134C2×C4×C19—81no—
135C2×C4×C19C4×D412yes—
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12112yes—
138C2×C4×C19#12311yescharacteristic
139C22⋊D19—88no—
140C22⋊D19—88no—
141C2×Dic19—24no—
142C2×Dic19—42no—
143C2×Dic19—42no—
144D76—84no—
145D76—82no—
146D76—84no—
147D76—82no—
148C8×C19—44no—
149C19⋊C8—82no—
150#2973D1911yescharacteristic, complemented
151#2541—191no—
152#1555—192no—
153#1466—191no—
154#1285—192no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—22no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—81no—
166C22×C19—81no—
167C22×C19#38611yescharacteristic
168C22×C19C2×#10011yescharacteristic
169C22×C19#41311yescharacteristic
170C2×D19—82no—
171C2×D19—82no—
172C2×D19—82no—
173C2×D19—82no—
174C2×D19—82no—
175C2×D19—82no—
176C2×D19—82no—
177C4×C19—21no—
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—41no—
181C4×C19—41no—
182C4×C19#45312yes—
183Dic19—44no—
184C2×#127—192no—
185C2×#127—191no—
186C2×#121—381no—
187C2×#121—381no—
188C2×C4×D4C2×D1911yescharacteristic
189#435—24no—
190#432—192no—
191#432C2×D1912yes—
192#407—21no—
193C2×C22⋊C8—21no—
194#392—381no—
195#392—381no—
196#390—192no—
197C4×C4⋊C4—191no—
198#331—384no—
199#323—381no—
200#323—381no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19—42no—
204C2×C19—81no—
205C2×C19#188711yescharacteristic
206C2×C19#190011yescharacteristic
207C2×C19#191011yescharacteristic
208D19—162no—
209C22×D4—192no—
210C22×D4—382no—
211C22×D4—382no—
212C22×D4—381no—
213C22×D4—381no—
214C22×D4C4×D1911yescharacteristic
215C23×C4C22⋊D1911yescharacteristic
216C23×C4C22⋊D1911yescharacteristic
217C2×M16—22no—
218C22×C8—22no—
219#127—382no—
220#127—382no—
221#127—764no—
222#121—764no—
223#121—764no—
224C4×D4—22no—
225C4×D4—22no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4C4×D1911yescharacteristic
228C2×C22⋊C4—382no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4D7611yescharacteristic
231C2×C22⋊C4D7611yescharacteristic
232C2×C42—192no—
233C2×C42C22×D1911yescharacteristic
234C4⋊C8—382no—
235C4⋊C8C22⋊D1914yescomplemented
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239C22⋊C8—382no—
240#97—22no—
241#97—382no—
242#95—381no—
243C19#945711yescharacteristic, complemented, Sylow
244C24—382no—
245C24(C2×D19)⋊C411yescharacteristic
246C24(C2×D19)⋊C411yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—384no—
251C2×D4—762no—
252C2×D4—762no—
253C2×D4—762no—
254C2×D4—762no—
255C2×D4—764no—
256C2×D4—764no—
257C2×D4—764no—
258C2×D4—764no—
259C2×D4—762no—
260C2×D4—761no—
261C2×D4—761no—
262C2×D4—1522no—
263C2×D4—1522no—
264C2×D4—1522no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—382no—
272C22×C4(C2×D19)⋊C411yescharacteristic
273C22×C4(C2×D19)⋊C411yescharacteristic
274C22×C4C2×C4×D1911yescharacteristic
275C22×C4C2×D7611yescharacteristic
276C22×C4C2×C22⋊D1911yescharacteristic
277M16—82no—
278C2×C8—24no—
279C2×C8—82no—
280C2×C8—762no—
281C4⋊C4—22no—
282C4⋊C4—384no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—764no—
286C22⋊C4—764no—
287C42—762no—
288C42#6454112yes—
289C42C2×C22⋊D1912yes—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—762no—
300C23—762no—
301C23—762no—
302C23—762no—
303C23—762no—
304C23—762no—
305C23—762no—
306C23#1059728012yes—
307C23C2×(C2×D19)⋊C411yescharacteristic
308D4—44no—
309D4—1524no—
310D4—1522no—
311D4—1524no—
312D4—1528no—
313D4—1528no—
314D4—1522no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—384no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4C4×C22⋊D1912yes—
331C2×C4#1059737511yescharacteristic
332C2×C4#1059737612yes—
333C2×C4#1059739911yescharacteristic
334C8—44no—
335C8—1522no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22—1522no—
349C22—1522no—
350C22—1522no—
351C22—1522no—
352C22—1522no—
353C22—1522no—
354C22—1522no—
355C22#1192642311yescharacteristic
356C22C2×#1059728011yescharacteristic
357C22#1192652611yescharacteristic
358C4—22no—
359C4—22no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—764no—
364C4#1192671212yes—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—81no—
369C2—3042no—
370C2#1456403311yescharacteristic
371C2#1456409811yescharacteristic
372C2#1456416211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2973C2
socleC22×C19#386
prime radical#14568581C2
cosocleC2×C42×C19C23
hypercenter#2973D19
hypocenterC19#9457
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14562348C2semidirect
3. #14561976C2semidirect
4. #14561492C2semidirect
5. C19×#2973C2semidirect
48. C19×C4⋊C8D4semidirect
150. #2973D19semidirect
235. C4⋊C8C22⋊D19semidirect
243. C19#9457semidirect

Maximal subgroups

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

subgroupindex
#145685812
#145623482
#145619762
#145614922
C19×#29732
#945719