Finite Group Databasebeta

← #18078583

Subgroups — #18078583

Order 4864.

684 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 135 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#14566249C211yesmaximal, characteristic
2#14562207C212yesmaximal, complemented
3C2×#11926268C211yesmaximal, characteristic
4#14561502C212yesmaximal, complemented
5C19×#2626C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926419—24no—
9#11926404—21no—
10#11926404C2212yes—
11#11926281—24no—
12#11926268—22no—
13C2×C19×C22⋊Q8C2211yescharacteristic
14C22×C22⋊C4×C19C2211yescharacteristic
15C19×#399C412yescomplemented
16C19×#396—22no—
17C19×#393C412yescomplemented
18C19×#385—21no—
19C19×#380C2211yescharacteristic
20C19×#379—21no—
21C25×C19D411yescharacteristic
22C22×Q8×C19C2×C411yescharacteristic, complemented
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C23×Dic19—22no—
26C19×C22⋊Q8—22no—
27C19×C22⋊Q8—22no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
32C2×C22⋊C4×C19—22no—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19D412yes—
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19—22no—
42C2×C22⋊Dic19—42no—
43C2×C22⋊Dic19—42no—
44C2×C4⋊Dic19—22no—
45C2×C4⋊Dic19—22no—
46C22×C19⋊C8—22no—
47C19×#95—22no—
48C19×#95C2×C412yescomplemented
49C19⋊#95—22no—
50C19⋊#95D414yes—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C24×C19—21no—
54C24×C19—21no—
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—81no—
58C24×C19—81no—
59C24×C19C22⋊C412yes—
60C24×C19SD1612yes—
61C24×C19Q1612yes—
62C24×C19C2×D411yescharacteristic
63C2×Q8×C19—22no—
64C2×Q8×C19—81no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—22no—
69C22×C4×C19—21no—
70C22×C4×C19—81no—
71C22×C4×C19—81no—
72C22×C4×C19C22⋊C412yes—
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D412yes—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19#4112yes—
77C22×Dic19—24no—
78C22×Dic19—44no—
79C22×Dic19—82no—
80C22×Dic19—82no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—42no—
83C4⋊C4×C19—81no—
84C4⋊C4×C19—82no—
85C22⋊C4×C19—24no—
86C22⋊C4×C19—24no—
87C22⋊C4×C19—41no—
88C22⋊C4×C19—41no—
89C22⋊C4×C19—41no—
90C22⋊C4×C19—41no—
91C22⋊C4×C19—82no—
92C22⋊C4×C19—82no—
93C22⋊Dic19—44no—
94C22⋊Dic19—42no—
95C22⋊Dic19—42no—
96C4⋊Dic19—82no—
97C4⋊Dic19—82no—
98C2×C19⋊C8—42no—
99C2×C19⋊C8—82no—
100#9199—191nomaximal, Sylow
101C23×C19—22no—
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—22no—
105C23×C19—22no—
106C23×C19—22no—
107C23×C19—41no—
108C23×C19—41no—
109C23×C19—42no—
110C23×C19—42no—
111C23×C19—42no—
112C23×C19—42no—
113C23×C19—81no—
114C23×C19—81no—
115C23×C19—82no—
116C23×C19—82no—
117C23×C19—82no—
118C23×C19—82no—
119C23×C19#10314yes—
120C23×C19C2×C22⋊C411yescharacteristic
121C23×C19#12011yescharacteristic
122C23×C19#12311yescharacteristic
123C23×C19C2×SD1611yescharacteristic
124C23×C19C2×Q1611yescharacteristic
125C23×C19AGL(1,ℤ/8)11yescharacteristic
126C23×C19#13711yescharacteristic
127Q8×C19—82no—
128C2×C4×C19—22no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—42no—
142C2×C4×C19—81no—
143C2×C4×C19C4×D412yes—
144C2×C4×C19#12112yes—
145C2×Dic19—44no—
146C2×Dic19—44no—
147C2×Dic19—44no—
148C2×Dic19—88no—
149C19⋊C8—82no—
150#2626D1911yescharacteristic
151#2315—191no—
152#1520—192no—
153C2×#323—191no—
154#1289—192no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—24no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—44no—
167C22×C19—44no—
168C22×C19—44no—
169C22×C19—42no—
170C22×C19—42no—
171C22×C19—82no—
172C22×C19—82no—
173C22×C19—82no—
174C22×C19#38611yescharacteristic
175C22×C19C2×#10311yescharacteristic
176C22×C19#41711yescharacteristic
177C22×C19#45011yescharacteristic
178C22×C19#45111yescharacteristic
179C22×C19#48311yescharacteristic
180C22×C19#48411yescharacteristic
181C4×C19—22no—
182C4×C19—22no—
183C4×C19—42no—
184C4×C19—82no—
185C4×C19—81no—
186C4×C19—81no—
187Dic19—84no—
188C2×C22⋊Q8C2×D1911yescharacteristic
189C22×C22⋊C4—381no—
190C22×C22⋊C4C2×D1911yescharacteristic
191C2×C22⋊C8—192no—
192#399Dic1912yescomplemented
193#396—22no—
194#393Dic1912yescomplemented
195#385—21no—
196#385—384no—
197#380—192no—
198#380—381no—
199#380C2×D1911yescharacteristic
200#379—21no—
201#328—384no—
202#323—382no—
203C2×C19—21no—
204C2×C19—21no—
205C2×C19—21no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—21no—
209C2×C19—44no—
210C2×C19#187211yescharacteristic
211C2×C19#191111yescharacteristic
212C2×C19#191311yescharacteristic
213C25C22⋊D1911yescharacteristic
214C22×Q8C2×Dic1911yescharacteristic, complemented
215C23×C4—382no—
216C23×C4C22⋊D1911yescharacteristic
217C23×C4C22×D1911yescharacteristic
218C22×C8—382no—
219C22⋊Q8—22no—
220C22⋊Q8—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—382no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4C2×Dic1911yescharacteristic, complemented
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—382no—
234C2×C22⋊C4—382no—
235C2×C22⋊C4—762no—
236C2×C22⋊C4—762no—
237C2×C22⋊C4C2×Dic1912yes—
238C2×C22⋊C4C22⋊D1912yes—
239C22⋊C8—382no—
240C22⋊C8—382no—
241#95—22no—
242#95—194no—
243#95—382no—
244#95C2×Dic1912yescomplemented
245C19#919911yescharacteristic, complemented, Sylow
246C24—21no—
247C24—21no—
248C24—21no—
249C24—21no—
250C24—81no—
251C24—81no—
252C24#6452712yes—
253C24#6452812yes—
254C24C22⋊Dic1912yes—
255C24C2×C22⋊D1911yescharacteristic
256C2×Q8—22no—
257C2×Q8—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4—384no—
266C22×C4—764no—
267C22×C4—1522no—
268C22×C4—1522no—
269C22×C4C22⋊Dic1912yes—
270C22×C4D4×D1912yes—
271C22×C4#6454312yes—
272C22×C4C22×Dic1911yescharacteristic
273C22×C4C2×C22⋊D1911yescharacteristic
274C2×C8—762no—
275C2×C8—1522no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—81no—
279C4⋊C4—82no—
280C4⋊C4—1522no—
281C4⋊C4—1522no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—82no—
289C22⋊C4—82no—
290C22⋊C4—764no—
291C22⋊C4—762no—
292C22⋊C4—762no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23#1059729214yes—
312C23#1059738111yescharacteristic
313C23#1059738311yescharacteristic
314C23C2×#6452711yescharacteristic
315C23C2×#6452811yescharacteristic
316C23#1059739511yescharacteristic
317C23#1059739711yescharacteristic
318C23C2×C22⋊Dic1911yescharacteristic
319Q8—82no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—764no—
336C2×C4—764no—
337C2×C4—764no—
338C2×C4—1528no—
339C2×C4D4×Dic1912yes—
340C2×C4#1059738512yes—
341C8—1522no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22#1192642411yescharacteristic
362C22C2×#1059729211yescharacteristic
363C22#1192654511yescharacteristic
364C22#1192669411yescharacteristic
365C22#1192669911yescharacteristic
366C22#1192687211yescharacteristic
367C22#1192687711yescharacteristic
368C4—22no—
369C4—22no—
370C4—42no—
371C4—82no—
372C4—81no—
373C4—81no—
374C4—1524no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2#1456394311yescharacteristic
383C2#1456416811yescharacteristic
384C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2626C2
socleC22×C19#386
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#2626D19
hypocenterC19#9199
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
2. #14562207C2semidirect
4. #14561502C2semidirect
15. C19×#399C4semidirect
17. C19×#393C4semidirect
22. C22×Q8×C19C2×C4semidirect
31. C2×C4⋊C4×C19C2×C4semidirect
48. C19×#95C2×C4semidirect
192. #399Dic19semidirect
194. #393Dic19semidirect
214. C22×Q8C2×Dic19semidirect
226. C2×C4⋊C4C2×Dic19semidirect
244. #95C2×Dic19semidirect
245. C19#9199semidirect

Maximal subgroups

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

subgroupindex
#145662492
#145622072
C2×#119262682
#145615022
C19×#26262
#919919