Finite Group Databasebeta

← #18076510

Subgroups — #18076510

Order 4864.

532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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#14563928C211yesmaximal, characteristic
2#14563812C212yesmaximal, complemented
3C4×#10597291C211yesmaximal, characteristic
4#14561482C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic
6C23×C19⋊C8C2211yescharacteristic
7C2×Dic19⋊C8—22no—
8C2×#10597291C412yes—
9C2×C22⋊(C19⋊C8)—21no—
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11C4×C22⋊Dic19C2212yes—
12#11926311C411yescharacteristic
13#11926311C411yescharacteristic
14#11926299—21no—
15#11926298—22no—
16C2×C4×D4×C19C2211yescharacteristic
17C19×#435—22no—
18C19×#435—22no—
19C19×#432—21no—
20C19×#407—21no—
21C2×C19×C22⋊C8C2212yes—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C2×M16×C19—21no—
26C2×M16×C19—21no—
27C22×C8×C19D412yes—
28C22×C8×C19D412yes—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19Q811yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19Q811yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C22⋊Dic19C2×C412yes—
36C2×C22⋊Dic19C2×C412yes—
37C2×C4×Dic19—22no—
38C22×C19⋊C8—22no—
39C22×C19⋊C8—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—42no—
42C19×C4⋊C8—21no—
43C19×C4⋊C8—21no—
44C19×C22⋊C8—22no—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×#97—22no—
48#10597291—24no—
49C19⋊#95—22no—
50C22⋊(C19⋊C8)—22no—
51C22⋊(C19⋊C8)—42no—
52Dic19⋊C8—44no—
53C24×C19C4⋊C411yescharacteristic
54C24×C19C22×C411yescharacteristic
55C2×D4×C19—22no—
56C2×D4×C19—22no—
57C2×D4×C19—21no—
58C2×D4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19C4⋊C411yescharacteristic
66C22×C4×C19C4⋊C411yescharacteristic
67C22×C4×C19C4⋊C411yescharacteristic
68C22×C4×C19C2×D412yes—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×Q811yescharacteristic
71C22×C4×C19#4112yes—
72C22×Dic19—22no—
73C22×Dic19—22no—
74M16×C19—81no—
75M16×C19—81no—
76C2×C8×C19—22no—
77C2×C8×C19—22no—
78C2×C8×C19—42no—
79C2×C8×C19—42no—
80C4⋊C4×C19—22no—
81C22⋊C4×C19—22no—
82C22⋊C4×C19—22no—
83C42×C19—21no—
84C42×C19—21no—
85C22⋊Dic19—22no—
86C22⋊Dic19—22no—
87C22⋊Dic19—22no—
88C22⋊Dic19M1614yescomplemented
89C4×Dic19—42no—
90C4×Dic19—42no—
91C2×C19⋊C8—24no—
92C2×C19⋊C8—22no—
93C2×C19⋊C8—41no—
94C2×C19⋊C8—42no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99#8852—191nomaximal, Sylow
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—41no—
104C23×C19—41no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19C2×C4⋊C411yescharacteristic
108C23×C19C4×D412yes—
109C23×C19C2×M1612yes—
110C23×C19#13111yescharacteristic
111C23×C19#13111yescharacteristic
112D4×C19—42no—
113D4×C19—42no—
114C2×C4×C19—21no—
115C2×C4×C19—22no—
116C2×C4×C19—21no—
117C2×C4×C19—22no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—81no—
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19C22⋊Q812yes—
132C2×C4×C19#12311yescharacteristic
133C2×Dic19—24no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C8×C19—42no—
140C8×C19—42no—
141C19⋊C8—42no—
142C19⋊C8—81no—
143#2973D1911yescharacteristic
144#1869—191no—
145#1850—192no—
146C4×#99—191no—
147#1282—192no—
148C22×C19—22no—
149C22×C19—21no—
150C22×C19—22no—
151C22×C19—21no—
152C22×C19—42no—
153C22×C19—41no—
154C22×C19—41no—
155C22×C19—42no—
156C22×C19—41no—
157C22×C19—41no—
158C22×C19—41no—
159C22×C19—81no—
160C22×C19#38511yescharacteristic
161C22×C19#42311yescharacteristic
162C22×C19#42411yescharacteristic
163C22×C19#43512yes—
164C22×C19#43612yes—
165C4×C19—21no—
166C4×C19—22no—
167C4×C19—41no—
168C4×C19—41no—
169C4×C19—41no—
170C4×C19B(4,𝔽2)11yescharacteristic
171C4×C19#45811yescharacteristic
172Dic19—44no—
173Dic19—82no—
174C23×C8—191no—
175C2×C4×D4C2×D1911yescharacteristic
176#435—22no—
177#435—22no—
178#432—21no—
179C2×C4⋊C8—382no—
180C2×#99—192no—
181#407—21no—
182C2×C22⋊C8—191no—
183C2×C22⋊C8—381no—
184C2×C22⋊C8C2×D1912yes—
185C4×C22⋊C4—192no—
186#342—191no—
187#342—191no—
188#336—382no—
189#336—381no—
190C2×C19—22no—
191C2×C19—22no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19—81no—
195C2×C19#185111yescharacteristic
196C2×C19#186711yescharacteristic
197C2×C19#186811yescharacteristic
198C22×D4C4×D1911yescharacteristic
199C23×C4C22⋊D1911yescharacteristic
200C23×C4C22×D1911yescharacteristic
201C2×M16—21no—
202C2×M16—21no—
203C22×C8—381no—
204C22×C8—382no—
205C22×C8—381no—
206C22×C8—762no—
207C22×C8C22⋊D1912yes—
208C22×C8C22⋊D1912yes—
209C4×D4—22no—
210C4×D4—22no—
211C2×C4⋊C4Dic3811yescharacteristic
212C2×C22⋊C4—192no—
213C2×C22⋊C4—192no—
214C2×C22⋊C4Dic3811yescharacteristic
215C2×C22⋊C4C4×D1911yescharacteristic
216C2×C42—382no—
217C2×C42C22⋊D1911yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—764no—
221#99—384no—
222C22⋊C8—22no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225C22⋊C8—382no—
226C22⋊C8—762no—
227#97—22no—
228#95—382no—
229C19#885211yescharacteristic, complemented, Sylow
230C24Dic19⋊C411yescharacteristic
231C24C2×C4×D1911yescharacteristic
232C2×D4—22no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—382no—
243C22×C4—382no—
244C22×C4Dic19⋊C411yescharacteristic
245C22×C4Dic19⋊C411yescharacteristic
246C22×C4Dic19⋊C411yescharacteristic
247C22×C4C2×Dic3811yescharacteristic
248C22×C4#6454112yes—
249C22×C4C2×C22⋊D1912yes—
250C22×C4C2×C22⋊D1911yescharacteristic
251M16—81no—
252M16—81no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—382no—
258C2×C8—384no—
259C2×C8—762no—
260C2×C8—761no—
261C2×C8—761no—
262C2×C8—761no—
263C2×C8—761no—
264C2×C8—761no—
265C4⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—194no—
269C22⋊C4—382no—
270C22⋊C4—382no—
271C22⋊C4—382no—
272C42—21no—
273C42—21no—
274C42—762no—
275C42—762no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23M16×D1912yes—
284C23#1059735311yescharacteristic
285C23#1059735311yescharacteristic
286C23C2×Dic19⋊C411yescharacteristic
287C23C4×C22⋊D1912yes—
288D4—42no—
289D4—42no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—384no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—762no—
310C2×C4—762no—
311C2×C4—762no—
312C2×C4#1059737012yes—
313C2×C4#1059737511yescharacteristic
314C2×C4#1059739911yescharacteristic
315C8—42no—
316C8—42no—
317C8—762no—
318C8—1521no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1192641711yescharacteristic
332C22#1192656711yescharacteristic
333C22#1192657211yescharacteristic
334C22#1192661312yes—
335C22#1192662012yes—
336C4—21no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—764no—
342C4—1522no—
343C4#1192673111yescharacteristic
344C4#1192673411yescharacteristic
345C2—22no—
346C2—22no—
347C2—21no—
348C2—21no—
349C2—81no—
350C2#1456381811yescharacteristic
351C2#1456391611yescharacteristic
352C2#1456392111yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2973C2
socleC22×C19#385
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#2973D19
hypocenterC19#8852
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14563812C2semidirect
4. #14561482C2semidirect
88. C22⋊Dic19M16semidirect
229. C19#8852semidirect

Maximal subgroups

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

subgroupindex
#145639282
#145638122
C4×#105972912
#145614822
C19×#29732
#885219