Finite Group Databasebeta

← #18085399

Subgroups — #18085399

Order 4864.

726 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 103 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#14571961C212yesmaximal, complemented
2#14563701C211yesmaximal, characteristic, complemented
3#14562203C212yesmaximal, complemented
4#14561503C211yesmaximal, characteristic, complemented
5C19×#3186C211yesmaximal, characteristic
6C2×#10597381—22no—
7C22×C4×Dic19C2211yescharacteristic
8C2×C22⋊(C19⋊C8)C2211yescharacteristic
9#11926447—22no—
10#11926440—22no—
11#11926432—24no—
12#11926424—22no—
13#11926404C2212yes—
14#11926298—22no—
15#11926278—24no—
16C2×C19×#121C2212yes—
17C19×#480—22no—
18C19×#466—22no—
19C19×#447—22no—
20C2×C19×C22⋊C8C2211yescharacteristic
21C22×D4×C19—22no—
22C22×D4×C19D412yes—
23C23×C4×C19C2311yescharacteristic
24C23×Dic19D411yescharacteristic
25C23×Dic19D411yescharacteristic
26C2×D8×C19—22no—
27C22×C8×C19D412yes—
28C19×#121—22no—
29C19×#121—22no—
30C19×#121—22no—
31C19×#121—22no—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊Dic19—24no—
35C2×C22⋊Dic19—24no—
36C2×C22⋊Dic19—22no—
37#10597381—44no—
38#10597381—44no—
39C2×C4⋊Dic19—22no—
40C2×Dic19⋊C4—24no—
41C2×C4×Dic19—21no—
42C2×C4×Dic19—22no—
43C2×C4×Dic19—22no—
44C2×C4×Dic19—21no—
45C22×C19⋊C8—21no—
46C19×#107—22no—
47C19×#102—24no—
48C19×C22⋊C8—22no—
49C19⋊#95—24no—
50C19⋊#95D414yes—
51C22⋊(C19⋊C8)—22no—
52C24×C19—22no—
53C24×C19C2×D411yescharacteristic
54C2×D4×C19—22no—
55C2×D4×C19—22no—
56C2×D4×C19—44no—
57C2×D4×C19—42no—
58C2×D4×C19—42no—
59C2×D4×C19—42no—
60C2×D4×C19—42no—
61C2×D4×C19—42no—
62C2×D4×C19—42no—
63C22×C4×C19—22no—
64C22×C4×C19—42no—
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D412yes—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19#4111yescharacteristic
69C22×Dic19—22no—
70C22×Dic19—22no—
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—22no—
75C22×Dic19—24no—
76C22×Dic19—42no—
77C22×Dic19D812yescomplemented
78D8×C19—82no—
79C2×C8×C19—22no—
80C2×C8×C19—42no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—42no—
85C22⋊Dic19—48no—
86C22⋊Dic19—48no—
87C22⋊Dic19—42no—
88C22⋊Dic19—42no—
89C4⋊Dic19—44no—
90Dic19⋊C4—48no—
91C4×Dic19—41no—
92C4×Dic19—42no—
93C4×Dic19—41no—
94C2×C19⋊C8—42no—
95C2×C19⋊C8—41no—
96#10321—191nomaximal, Sylow
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—44no—
100C23×C19—44no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19—42no—
104C23×C19#12012yes—
105C23×C19#12111yescharacteristic
106C23×C19C2×D811yescharacteristic
107C23×C19#13511yescharacteristic
108C23×C19AGL(1,ℤ/8)12yes—
109D4×C19—44no—
110D4×C19—82no—
111D4×C19—82no—
112D4×C19—82no—
113D4×C19—82no—
114D4×C19—82no—
115C2×C4×C19—22no—
116C2×C4×C19—24no—
117C2×C4×C19—42no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19#12011yescharacteristic
123C2×C4×C19#12112yes—
124C2×C4×C19#12711yescharacteristic
125C2×Dic19—24no—
126C2×Dic19—22no—
127C2×Dic19—24no—
128C2×Dic19—22no—
129C2×Dic19—42no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—42no—
134C2×Dic19—41no—
135C2×Dic19—44no—
136C2×Dic19—44no—
137C2×Dic19—44no—
138C8×C19—42no—
139C19⋊C8—81no—
140#3186D1911yescharacteristic
141#2854—192no—
142#1817—191no—
143#1519—192no—
144#1289—191no—
145C22×C19—22no—
146C22×C19—21no—
147C22×C19—22no—
148C22×C19—21no—
149C22×C19—41no—
150C22×C19—41no—
151C22×C19—42no—
152C22×C19—84no—
153C22×C19—84no—
154C22×C19—82no—
155C22×C19—82no—
156C22×C19—82no—
157C22×C19#39211yescharacteristic
158C22×C19#44712yes—
159C22×C19#44912yes—
160C22×C19#46611yescharacteristic
161C22×C19#46911yescharacteristic
162C4×C19—21no—
163C4×C19—22no—
164C4×C19—82no—
165C4×C19#45812yes—
166Dic19—42no—
167Dic19—42no—
168Dic19—84no—
169C2×#123—382no—
170C2×#121C2×D1912yes—
171C22×C42—191no—
172#480—22no—
173#466—22no—
174#447—22no—
175C2×C22⋊C8—191no—
176C2×C22⋊C8C2×D1911yescharacteristic
177#390—382no—
178#389—382no—
179#388—384no—
180#386—382no—
181#380—192no—
182#336—382no—
183#327—384no—
184C2×C19—22no—
185C2×C19—22no—
186C2×C19—21no—
187C2×C19—21no—
188C2×C19—162no—
189C2×C19#199911yescharacteristic
190C2×C19#201011yescharacteristic
191C2×C19#202211yescharacteristic
192C22×D4—22no—
193C22×D4C22⋊D1912yes—
194C23×C4—191no—
195C23×C4—191no—
196C23×C4C22×D1911yescharacteristic
197C2×D8—22no—
198C22×C8—381no—
199C22×C8C22⋊D1912yes—
200#123—764no—
201#123—764no—
202#121—22no—
203#121—22no—
204#121—22no—
205#121—22no—
206C2×C4⋊C4—384no—
207C2×C4⋊C4—382no—
208C2×C4⋊C4C22⋊D1912yes—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—384no—
211C2×C22⋊C4—384no—
212C2×C22⋊C4—382no—
213C2×C42—382no—
214C2×C42—381no—
215C2×C42—381no—
216C2×C42—382no—
217#107—22no—
218#102—24no—
219C22⋊C8—22no—
220C22⋊C8—382no—
221#95—194no—
222#95—384no—
223C19#1032111yescharacteristic, complemented, Sylow
224C24—22no—
225C24D4×D1911yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—44no—
229C2×D4—42no—
230C2×D4—42no—
231C2×D4—42no—
232C2×D4—42no—
233C2×D4—42no—
234C2×D4—42no—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4—192no—
238C22×C4—382no—
239C22×C4—382no—
240C22×C4—381no—
241C22×C4—381no—
242C22×C4—382no—
243C22×C4—381no—
244C22×C4—384no—
245C22×C4—762no—
246C22×C4D4×D1912yes—
247C22×C4#6454311yescharacteristic
248C22×C4C2×C22⋊D1912yes—
249C22×C4C2×C22⋊D1911yescharacteristic
250D8—82no—
251C2×C8—22no—
252C2×C8—42no—
253C2×C8—762no—
254C2×C8—761no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—764no—
258C4⋊C4—768no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—768no—
262C22⋊C4—768no—
263C22⋊C4—762no—
264C22⋊C4—762no—
265C42—762no—
266C42—761no—
267C42—761no—
268C23—41no—
269C23—41no—
270C23—44no—
271C23—44no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23D8×D1911yescharacteristic
276C23#1059735712yes—
277C23#1059735811yescharacteristic
278C23#1059738312yes—
279C23#1059738411yescharacteristic
280D4—44no—
281D4—82no—
282D4—82no—
283D4—82no—
284D4—82no—
285D4—82no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—384no—
294C2×C4—382no—
295C2×C4—384no—
296C2×C4—382no—
297C2×C4—762no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—762no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—764no—
304C2×C4—764no—
305C2×C4—764no—
306C2×C4#1059738512yes—
307C2×C4#1059738611yescharacteristic
308C2×C4#1059739911yescharacteristic
309C8—42no—
310C8—1521no—
311C22—22no—
312C22—21no—
313C22—22no—
314C22—21no—
315C22—41no—
316C22—42no—
317C22—41no—
318C22—84no—
319C22—84no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22#1192645211yescharacteristic
324C22#1192667612yes—
325C22#1192668612yes—
326C22#1192677711yescharacteristic
327C22#1192679411yescharacteristic
328C4—21no—
329C4—22no—
330C4—82no—
331C4—762no—
332C4—762no—
333C4—1524no—
334C4#1192673412yes—
335C2—22no—
336C2—22no—
337C2—21no—
338C2—21no—
339C2—162no—
340C2#1456463011yescharacteristic
341C2#1456469911yescharacteristic
342C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3186C2
socleC22×C19#392
hypercenter#3186D19
hypocenterC19#10321
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #14571961C2semidirect
2. #14563701C2semidirect
3. #14562203C2semidirect
4. #14561503C2semidirect
77. C22×Dic19D8semidirect
223. C19#10321semidirect

Maximal subgroups

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

subgroupindex
#145719612
#145637012
#145622032
#145615032
C19×#31862
#1032119