Finite Group Databasebeta

← #18075249

Subgroups — #18075249

Order 4864.

548 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566099C211yesmaximal, characteristic
2C4×C4⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
3C2×#11926271C212yesmaximal
4#14561474C212yesmaximal, complemented
5C19×#1831C211yesmaximal, characteristic, complemented
6C2×C4×D76C2211yescharacteristic
7C2×#10597318—21no—
8C2×C4⋊(C19⋊C8)—21no—
9C2×C4×C19⋊C8C2212yes—
10#11926446C411yescharacteristic
11#11926446C411yescharacteristic
12#11926442C411yescharacteristic
13#11926442C411yescharacteristic
14#11926435—21no—
15#11926435—21no—
16C4×C4⋊Dic19C2211yescharacteristic
17C4×(C2×D19)⋊C4—21no—
18#11926299—21no—
19#11926271—24no—
20C2×C19×C4⋊C8C2212yes—
21C43×C19C2211yescharacteristic
22C19×#336—21no—
23C19×#336—21no—
24C22×D76C2×C411yescharacteristic
25C22×C4×D19—21no—
26C22×C8×C19—22no—
27C2×C42×C19C2×C411yescharacteristic
28C2×C42×C19C2×C411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×(C2×D19)⋊C4—21no—
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×C4×Dic19—21no—
45C22×C19⋊C8—22no—
46C4×D76—21no—
47C4×D76—21no—
48C4×D76D412yes—
49C4×D76Q812yes—
50#10597318—44no—
51C19×C4⋊C8—22no—
52C19×C4⋊C8—22no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C4⋊(C19⋊C8)—24no—
57C4×C19⋊C8—22no—
58C4×C19⋊C8—22no—
59C23×D19—21no—
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22×C411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×Dic19—21no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70C2×D76—22no—
71C2×D76—22no—
72C2×D76—21no—
73C2×D76C4⋊C412yes—
74C2×C4×D19—22no—
75C2×C4×D19—22no—
76C2×C4×D19—42no—
77C2×C4×D19—42no—
78C2×C8×C19—42no—
79C2×C8×C19—42no—
80C2×C8×C19—42no—
81C42×C19—22no—
82C42×C19—22no—
83C42×C19—22no—
84C42×C19—22no—
85C42×C19—22no—
86C42×C19—41no—
87C42×C19C2×D411yescharacteristic
88C42×C19C2×Q811yescharacteristic
89C42×C19#4111yescharacteristic
90C42×C19#4111yescharacteristic
91(C2×D19)⋊C4—22no—
92(C2×D19)⋊C4—22no—
93(C2×D19)⋊C4—42no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—42no—
97C4⋊Dic19—21no—
98C4⋊Dic19—22no—
99C4⋊Dic19—22no—
100C4⋊Dic19C4⋊C412yes—
101Dic19⋊C4—42no—
102Dic19⋊C4—42no—
103C4×Dic19—42no—
104C2×C19⋊C8—24no—
105C2×C19⋊C8—42no—
106C2×C19⋊C8—42no—
107#8569—191nomaximal, Sylow
108C23×C19C2×C22⋊C411yescharacteristic
109C22×D19—22no—
110C22×D19—41no—
111C22×D19—41no—
112C22×D19—41no—
113C22×D19—41no—
114C22×D19—41no—
115C22×D19—41no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19#10412yes—
130C2×C4×C19C2×C4⋊C411yescharacteristic
131C2×C4×C19#11711yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19C22⋊Q811yescharacteristic
135C2×C4×C19C22⋊Q811yescharacteristic
136C2×C4×C19#13112yes—
137C2×C4×C19#13112yes—
138C2×C4×C19#13512yes—
139C2×C4×C19AGL(1,ℤ/8)12yes—
140C2×Dic19—22no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149D76—24no—
150D76—42no—
151C4×D19—44no—
152C4×D19—44no—
153C8×C19—82no—
154C19⋊C8—44no—
155#2293—191no—
156#1831D1911yescharacteristic, complemented
157C4×C4⋊C8—191no—
158C2×D4⋊C8—192no—
159#1279—192no—
160C22×C19#38011yescharacteristic
161C22×C19#40811yescharacteristic
162C22×C19#40811yescharacteristic
163C22×C19#41611yescharacteristic
164C22×C19#41811yescharacteristic
165C22×C19C2×#10411yescharacteristic
166C22×C19#42111yescharacteristic
167C2×D19—42no—
168C2×D19—42no—
169C2×D19—42no—
170C2×D19—81no—
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—22no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19—41no—
180C4×C19#42412yes—
181C4×C19#43312yes—
182C4×C19#46312yes—
183C4×C19#47812yes—
184Dic19—42no—
185Dic19—81no—
186Dic19—81no—
187C2×C4×D4—191no—
188C2×#117—381no—
189C2×C4⋊C8—381no—
190C2×C4⋊C8C2×D1912yes—
191C2×C4×C8—192no—
192#390—191no—
193#390—191no—
194#389—191no—
195#389—191no—
196#388—381no—
197#388—381no—
198C4×C4⋊C4—191no—
199C4×C22⋊C4—381no—
200C43C2×D1911yescharacteristic
201#336—21no—
202#336—21no—
203#336—381no—
204D4⋊C8—384no—
205C2×C19#148211yescharacteristic
206C2×C19#148411yescharacteristic
207C2×C19#149411yescharacteristic
208C2×C19#149611yescharacteristic
209C2×C19#179811yescharacteristic
210C2×C19#180411yescharacteristic
211C2×C19#180611yescharacteristic
212D19—82no—
213C22×D4—191no—
214C23×C4—381no—
215C22×C8—22no—
216C22×C8—382no—
217C4×D4—192no—
218C4×D4—192no—
219C4×D4—381no—
220C4×D4—381no—
221#117—764no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4—381no—
227C2×C22⋊C4—381no—
228C2×C22⋊C4—381no—
229C2×C22⋊C4—381no—
230C2×C22⋊C4—381no—
231C2×C22⋊C4—381no—
232C2×C42—381no—
233C2×C42C4×D1911yescharacteristic
234C2×C42C4×D1911yescharacteristic
235C2×C42D7611yescharacteristic
236C2×C42D7611yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22⋊D1911yescharacteristic
239C2×C42C22×D1911yescharacteristic
240C4⋊C8—22no—
241C4⋊C8—22no—
242C4⋊C8—384no—
243C4×C8—382no—
244C4×C8—382no—
245#95—381no—
246#95—381no—
247#95—381no—
248C19#856911yescharacteristic, complemented, Sylow
249C24—381no—
250C2×D4—192no—
251C2×D4—381no—
252C2×D4—382no—
253C2×D4—382no—
254C22×C4—381no—
255C22×C4—382no—
256C22×C4—382no—
257C22×C4—381no—
258C22×C4—381no—
259C22×C4—762no—
260C22×C4—762no—
261C22×C4(C2×D19)⋊C411yescharacteristic
262C22×C4(C2×D19)⋊C411yescharacteristic
263C22×C4(C2×D19)⋊C411yescharacteristic
264C22×C4(C2×D19)⋊C411yescharacteristic
265C22×C4C2×C4×D1911yescharacteristic
266C22×C4C2×D7611yescharacteristic
267C22×C4C2×C22⋊D1911yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—384no—
272C2×C8—762no—
273C2×C8—762no—
274C4⋊C4—192no—
275C4⋊C4—381no—
276C4⋊C4—382no—
277C4⋊C4—382no—
278C4⋊C4—762no—
279C4⋊C4—762no—
280C22⋊C4—382no—
281C22⋊C4—382no—
282C22⋊C4—762no—
283C22⋊C4—762no—
284C22⋊C4—762no—
285C22⋊C4—762no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—762no—
293C42D4×D1911yescharacteristic
294C42#6454311yescharacteristic
295C42Q8×D1911yescharacteristic
296C42#6454511yescharacteristic
297C23—382no—
298C23—761no—
299C23—761no—
300C23—761no—
301C23—761no—
302C23—761no—
303C23—761no—
304C23C2×(C2×D19)⋊C411yescharacteristic
305D4—384no—
306D4—762no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—382no—
321C2×C4—761no—
322C2×C4—761no—
323C2×C4—764no—
324C2×C4—764no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4#1059728212yes—
332C2×C4C4⋊C4×D1911yescharacteristic
333C2×C4#1059733811yescharacteristic
334C2×C4#1059734111yescharacteristic
335C2×C4#1059734311yescharacteristic
336C2×C4#1059734712yes—
337C2×C4#1059735312yes—
338C2×C4#1059738411yescharacteristic
339C2×C4#1059739211yescharacteristic
340C2×C4#1059739512yes—
341C2×C4#1059739612yes—
342C8—82no—
343C8—764no—
344C22—762no—
345C22—762no—
346C22—762no—
347C22—1521no—
348C22—1521no—
349C22—1521no—
350C22—1521no—
351C22#1192640111yescharacteristic
352C22#1192651011yescharacteristic
353C22#1192651211yescharacteristic
354C22#1192653811yescharacteristic
355C22#1192654811yescharacteristic
356C22C2×#1059728211yescharacteristic
357C22#1192656011yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—762no—
365C4—1521no—
366C4—1521no—
367C4#1192656912yes—
368C4#1192660412yes—
369C4#1192675612yes—
370C4#1192684112yes—
371C2—1522no—
372C2#1456204111yescharacteristic
373C2#1456205111yescharacteristic
374C2#1456209311yescharacteristic
375C2#1456210311yescharacteristic
376C2#1456361611yescharacteristic
377C2#1456364211yescharacteristic
378C2#1456365211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1831C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1831D19
hypocenterC19#8569
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C19⋊C8)C2semidirect
4. #14561474C2semidirect
5. C19×#1831C2semidirect
156. #1831D19semidirect
248. C19#8569semidirect

Maximal subgroups

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

subgroupindex
#145660992
C4×C4⋊(C19⋊C8)2
C2×#119262712
#145614742
C19×#18312
#856919