Finite Group Databasebeta

← #18078588

Subgroups — #18078588

Order 4864.

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

normal subgroups only

This group has 560 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#14566253C211yesmaximal, characteristic
2#14562207C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic
4#14561502C212yesmaximal
5C19×#2627C211yesmaximal, characteristic
6C2×#10597372—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926443—24no—
9#11926404—21no—
10#11926404C2212yes—
11#11926281—24no—
12#11926270—22no—
13C2×C19×C22⋊Q8C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400C412yescomplemented
16C19×#398—22no—
17C19×#395C412yescomplemented
18C19×#385—21no—
19C19×#381—21no—
20C19×#380C2211yescharacteristic
21C22×Q8×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C19×C22⋊Q8—22no—
26C19×C22⋊Q8—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19D412yes—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊Dic19—22no—
38#10597372—42no—
39#10597372—42no—
40C2×C4⋊Dic19—22no—
41C2×C4⋊Dic19—22no—
42C2×C4⋊Dic19—22no—
43C2×C4×Dic19—22no—
44C22×C19⋊C8—22no—
45C19×#95—22no—
46C19×#95—22no—
47C19×#95—22no—
48C19×#95C2×C412yes—
49C19⋊#95—22no—
50C19⋊#95D414yes—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C24×C19C2×D411yescharacteristic
54C2×Q8×C19—22no—
55C2×Q8×C19—81no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—81no—
66C22×C4×C19—81no—
67C22×C4×C19C22⋊C412yes—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19SD1612yes—
70C22×C4×C19Q1612yes—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4112yes—
75C22×Dic19—24no—
76C4⋊C4×C19—24no—
77C4⋊C4×C19—24no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—42no—
80C4⋊C4×C19—81no—
81C4⋊C4×C19—82no—
82C22⋊C4×C19—41no—
83C22⋊C4×C19—41no—
84C22⋊C4×C19—41no—
85C22⋊C4×C19—41no—
86C22⋊Dic19—42no—
87C22⋊Dic19—42no—
88C4⋊Dic19—44no—
89C4⋊Dic19—82no—
90C4⋊Dic19—82no—
91C4×Dic19—44no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—82no—
94#9200—191nomaximal, Sylow
95C23×C19—41no—
96C23×C19—41no—
97C23×C19C2×C22⋊C411yescharacteristic
98C23×C19#12011yescharacteristic
99C23×C19#12311yescharacteristic
100C23×C19C2×SD1611yescharacteristic
101C23×C19C2×Q1611yescharacteristic
102C23×C19AGL(1,ℤ/8)11yescharacteristic
103C23×C19#13711yescharacteristic
104Q8×C19—82no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—81no—
126C2×C4×C19#10314yes—
127C2×C4×C19C4×D412yes—
128C2×C4×C19#12112yes—
129C2×Dic19—44no—
130C2×Dic19—44no—
131C2×Dic19—44no—
132C19⋊C8—82no—
133#2627D1911yescharacteristic
134#2316—191no—
135#1520—192no—
136C2×#324—191no—
137#1289—192no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—21no—
144C22×C19—41no—
145C22×C19—41no—
146C22×C19—41no—
147C22×C19—41no—
148C22×C19#38611yescharacteristic
149C22×C19C2×#10311yescharacteristic
150C22×C19#41711yescharacteristic
151C22×C19#45011yescharacteristic
152C22×C19#45111yescharacteristic
153C22×C19#48311yescharacteristic
154C22×C19#48411yescharacteristic
155C4×C19—24no—
156C4×C19—22no—
157C4×C19—22no—
158C4×C19—42no—
159C4×C19—82no—
160C4×C19—81no—
161C4×C19—81no—
162Dic19—84no—
163C2×C22⋊Q8C2×D1911yescharacteristic
164C2×#117—381no—
165C22×C4⋊C4C2×D1911yescharacteristic
166C2×C22⋊C8—192no—
167#400Dic1912yescomplemented
168#398—22no—
169#395Dic1912yescomplemented
170#389—384no—
171#385—21no—
172#381—21no—
173#380—192no—
174#380—381no—
175#380C2×D1911yescharacteristic
176#328—384no—
177#324—382no—
178C2×C19—21no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19—21no—
182C2×C19—21no—
183C2×C19—21no—
184C2×C19#187211yescharacteristic
185C2×C19#191211yescharacteristic
186C2×C19#191311yescharacteristic
187C22×Q8C2×Dic1911yescharacteristic
188C23×C4C22⋊D1911yescharacteristic
189C23×C4C22⋊D1911yescharacteristic
190C23×C4C22×D1911yescharacteristic
191C22×C8—382no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194#117—762no—
195#117—762no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—382no—
202C2×C4⋊C4—382no—
203C2×C4⋊C4—382no—
204C2×C4⋊C4C2×Dic1911yescharacteristic
205C2×C4⋊C4C2×Dic1912yes—
206C2×C4⋊C4C22⋊D1912yes—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—382no—
210C2×C42—382no—
211C22⋊C8—382no—
212C22⋊C8—382no—
213#95—22no—
214#95—22no—
215#95—22no—
216#95—194no—
217#95—382no—
218#95C2×Dic1912yes—
219C19#920011yescharacteristic, complemented, Sylow
220C24C2×C22⋊D1911yescharacteristic
221C2×Q8—22no—
222C2×Q8—81no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—384no—
235C22×C4#6452712yes—
236C22×C4#6452812yes—
237C22×C4C22⋊Dic1912yes—
238C22×C4C22⋊Dic1912yes—
239C22×C4D4×D1912yes—
240C22×C4#6454312yes—
241C22×C4C22×Dic1911yescharacteristic
242C22×C4C2×C22⋊D1911yescharacteristic
243C2×C8—762no—
244C2×C8—1522no—
245C4⋊C4—24no—
246C4⋊C4—24no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—81no—
250C4⋊C4—82no—
251C4⋊C4—764no—
252C4⋊C4—1522no—
253C4⋊C4—1522no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—762no—
259C22⋊C4—762no—
260C42—764no—
261C23—41no—
262C23—41no—
263C23#1059738111yescharacteristic
264C23#1059738311yescharacteristic
265C23C2×#6452711yescharacteristic
266C23C2×#6452811yescharacteristic
267C23#1059739511yescharacteristic
268C23#1059739711yescharacteristic
269C23C2×C22⋊Dic1911yescharacteristic
270Q8—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—764no—
293C2×C4—764no—
294C2×C4—764no—
295C2×C4#1059729214yes—
296C2×C4D4×Dic1912yes—
297C2×C4#1059738512yes—
298C8—1522no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1192642411yescharacteristic
310C22C2×#1059729211yescharacteristic
311C22#1192654511yescharacteristic
312C22#1192669411yescharacteristic
313C22#1192669911yescharacteristic
314C22#1192687211yescharacteristic
315C22#1192687711yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—82no—
321C4—81no—
322C4—81no—
323C4—1524no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1456394311yescharacteristic
331C2#1456417311yescharacteristic
332C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2627C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2627D19
hypocenterC19#9200
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
15. C19×#400C4semidirect
17. C19×#395C4semidirect
167. #400Dic19semidirect
169. #395Dic19semidirect
219. C19#9200semidirect

Maximal subgroups

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

subgroupindex
#145662532
#145622072
C2×#119262702
#145615022
C19×#26272
#920019