Finite Group Databasebeta

← #18079865

Subgroups — #18079865

Order 4864.

548 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 119 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#14572664C211yesmaximal, characteristic
2#14563623C211yesmaximal, characteristic
3#14562207C212yesmaximal, complemented
4#14561514C212yesmaximal, complemented
5C19×#2564C211yesmaximal, characteristic
6#11926616—24no—
7#11926601—21no—
8C2×#10597291—21no—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)C2212yes—
11#11926404C2212yes—
12#11926311—21no—
13#11926281—24no—
14C2×C19×C22⋊Q8C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#400C411yescharacteristic, complemented
17C19×#399C411yescharacteristic, complemented
18C19×#395C411yescharacteristic, complemented
19C19×#393C411yescharacteristic, complemented
20C19×#387—21no—
21C19×#386—21no—
22C19×#385—21no—
23C19×#380—21no—
24C2×C19×#95C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×D4×C19D411yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19D411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C19×C22⋊Q8—22no—
31C19×C22⋊Q8—22no—
32C4×D4×C19—22no—
33C4×D4×C19—22no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19C2×C411yescharacteristic
43C2×C22⋊C4×C19D411yescharacteristic
44C2×C42×C19D411yescharacteristic
45C2×C22⋊Dic19—22no—
46C2×C4⋊Dic19—22no—
47C2×#64520—22no—
48C22×C19⋊C8—22no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95C2×C411yescharacteristic
55C19×#95C2×C411yescharacteristic
56#10597291—42no—
57C19⋊#95—22no—
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)D414yes—
61C4⋊(C19⋊C8)—22no—
62#10597260—22no—
63C24×C19C22⋊C411yescharacteristic
64C24×C19C2×D411yescharacteristic
65C2×Q8×C19—22no—
66C2×Q8×C19—81no—
67C2×D4×C19—22no—
68C2×D4×C19—21no—
69C2×D4×C19—22no—
70C2×D4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—42no—
78C22×C4×C19—41no—
79C22×C4×C19—41no—
80C22×C4×C19—81no—
81C22×C4×C19—81no—
82C22×C4×C19—81no—
83C22×C4×C19C22⋊C411yescharacteristic
84C22×C4×C19C22⋊C411yescharacteristic
85C22×C4×C19C22⋊C411yescharacteristic
86C22×C4×C19C22×C411yescharacteristic
87C22×C4×C19C2×D412yes—
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4112yes—
90C22×Dic19—42no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—42no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—81no—
97C22⋊C4×C19—22no—
98C22⋊C4×C19—22no—
99C22⋊C4×C19—42no—
100C22⋊C4×C19—42no—
101C22⋊C4×C19—81no—
102C42×C19—21no—
103C42×C19—21no—
104C22⋊Dic19—42no—
105C22⋊Dic19—42no—
106C4⋊Dic19—82no—
107#64520—82no—
108C2×C19⋊C8—24no—
109C2×C19⋊C8—82no—
110#9385—191nomaximal, Sylow
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19#12112yes—
120C23×C19AGL(1,ℤ/8)11yescharacteristic
121C23×C19#13712yes—
122C23×C19#13711yescharacteristic
123Q8×C19—82no—
124D4×C19—42no—
125D4×C19—42no—
126C2×C4×C19—22no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—42no—
133C2×C4×C19—42no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—81no—
151C2×C4×C19—82no—
152C2×C4×C19—82no—
153C2×C4×C19C4×D412yes—
154C2×C4×C19#12011yescharacteristic
155C2×C4×C19#12311yescharacteristic
156C2×Dic19—82no—
157C2×Dic19—82no—
158C2×Dic19—82no—
159C19⋊C8—44no—
160#2973—191no—
161#2564D1911yescharacteristic
162#1799—191no—
163#1520—192no—
164#1294—192no—
165C22×C19—22no—
166C22×C19—21no—
167C22×C19—22no—
168C22×C19—21no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—81no—
177C22×C19#38611yescharacteristic
178C22×C19#41711yescharacteristic
179C22×C19#41911yescharacteristic
180C22×C19#46812yes—
181C22×C19#47012yes—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—22no—
185C4×C19—42no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19—41no—
189C4×C19—81no—
190C4×C19—81no—
191C4×C19—81no—
192Dic19—162no—
193C2×C22⋊Q8C2×D1911yescharacteristic
194C2×C4×D4C2×D1911yescharacteristic
195#435—384no—
196#432—381no—
197C2×#99—381no—
198#407—381no—
199C2×C22⋊C8—192no—
200#400Dic1911yescharacteristic, complemented
201#399Dic1911yescharacteristic, complemented
202#395Dic1911yescharacteristic, complemented
203#393Dic1911yescharacteristic, complemented
204#387—21no—
205#386—21no—
206#385—21no—
207#380—21no—
208#380—192no—
209C2×#95C2×D1911yescharacteristic
210#342—381no—
211#328—384no—
212C2×C19—22no—
213C2×C19—21no—
214C2×C19—21no—
215C2×C19—22no—
216C2×C19—81no—
217C2×C19#188411yescharacteristic
218C2×C19#189411yescharacteristic
219C2×C19#191311yescharacteristic
220C22×Q8C2×Dic1911yescharacteristic
221C22×D4C22⋊D1911yescharacteristic
222C23×C4—21no—
223C23×C4C22⋊D1911yescharacteristic
224C23×C4C22×D1911yescharacteristic
225C2×M16—382no—
226C22×C8—382no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C4×D4—22no—
230C4×D4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—382no—
235C2×C4⋊C4C2×Dic1911yescharacteristic
236C2×C4⋊C4C2×Dic1911yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—382no—
241C2×C22⋊C4C2×Dic1911yescharacteristic
242C2×C22⋊C4C22⋊D1911yescharacteristic
243C2×C42C22⋊D1911yescharacteristic
244C4⋊C8—382no—
245#99—762no—
246C22⋊C8—194no—
247C22⋊C8—382no—
248C22⋊C8—382no—
249#97—382no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—382no—
256#95C2×Dic1911yescharacteristic
257#95C2×Dic1911yescharacteristic
258C19#938511yescharacteristic, complemented, Sylow
259C24C22⋊Dic1911yescharacteristic
260C24C2×C22⋊D1911yescharacteristic
261C2×Q8—22no—
262C2×Q8—81no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—81no—
279C22×C4—762no—
280C22×C4C22⋊Dic1911yescharacteristic
281C22×C4C22⋊Dic1911yescharacteristic
282C22×C4C22⋊Dic1911yescharacteristic
283C22×C4D4×D1912yes—
284C22×C4#6454312yes—
285C22×C4C22×Dic1911yescharacteristic
286C22×C4C2×C22⋊D1911yescharacteristic
287M16—1522no—
288C2×C8—384no—
289C2×C8—1522no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—1522no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—81no—
302C22⋊C4—762no—
303C22⋊C4—762no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#1059738512yes—
314C23#1059738812yes—
315C23#1059739511yescharacteristic
316C23#1059739711yescharacteristic
317C23C2×C22⋊Dic1911yescharacteristic
318Q8—82no—
319D4—42no—
320D4—42no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—1522no—
349C2×C4—1522no—
350C2×C4—1522no—
351C2×C4D4×Dic1912yes—
352C2×C4#1059738111yescharacteristic
353C2×C4#1059738311yescharacteristic
354C8—764no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22#1192642411yescharacteristic
368C22#1192654511yescharacteristic
369C22#1192655311yescharacteristic
370C22#1192679212yes—
371C22#1192680012yes—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—42no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—3042no—
383C2—21no—
384C2—22no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#1456401911yescharacteristic
389C2#1456406911yescharacteristic
390C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2564C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#2564D19
hypocenterC19#9385
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #14562207C2semidirect
4. #14561514C2semidirect
16. C19×#400C4semidirect
17. C19×#399C4semidirect
18. C19×#395C4semidirect
19. C19×#393C4semidirect
200. #400Dic19semidirect
201. #399Dic19semidirect
202. #395Dic19semidirect
203. #393Dic19semidirect
258. C19#9385semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145636232
#145622072
#145615142
C19×#25642
#938519