Finite Group Databasebeta

← #18080375

Subgroups — #18080375

Order 4864.

542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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#14572658C211yesmaximal, characteristic
2#14568993C211yesmaximal, characteristic
3#14563624C211yesmaximal, characteristic
4#14562064C211yesmaximal, characteristic, complemented
5#14561495C211yesmaximal, characteristic, complemented
6#14561494C211yesmaximal, characteristic, complemented
7C19×#1487C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9C8×D76—22no—
10#11926609—22no—
11#11926597C2211yescharacteristic
12#11926568C2211yescharacteristic
13C2×#10597280—21no—
14C22⋊C8×D19—22no—
15#11926479C412yes—
16#11926455C412yes—
17#11926446—21no—
18#11926442—21no—
19#11926415—22no—
20#11926410C2211yescharacteristic
21#11926312—21no—
22Q8⋊(C19⋊C8)—22no—
23C2×C4×Q8×C19C2211yescharacteristic
24C19×#431C2211yescharacteristic
25C19×#423C2211yescharacteristic
26C19×Q8⋊C8—22no—
27C22×Q8×C19C2×C411yescharacteristic
28C22×D76D411yescharacteristic
29C22×C4×D19D412yes—
30C2×M16×C19—21no—
31C4×Q8×C19—21no—
32C4×Q8×C19—21no—
33C4×Q8×C19—21no—
34C4×Q8×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C42×C19—21no—
38C2×C42×C19C2311yescharacteristic
39C2×(C2×D19)⋊C4—22no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4C2×C412yes—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19D411yescharacteristic
44C2×Dic19⋊C4—22no—
45C2×#64520—21no—
46C2×C8×D19—24no—
47C4×D76—21no—
48C4×D76—21no—
49C4×D76—21no—
50C4×D76—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C4×C8×C19D412yes—
56C19⋊#95—21no—
57C19⋊#95—22no—
58C19⋊#95C2×C412yes—
59C22⋊(C19⋊C8)—21no—
60#10597280—42no—
61(C2×D19)⋊C8—24no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4×C19⋊C8D412yes—
66C23×D19C22⋊C412yes—
67C2×Q8×C19—21no—
68C2×Q8×C19—21no—
69C2×Q8×C19—42no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—22no—
76C22×Dic19C22⋊C412yes—
77C2×D76—21no—
78C2×D76—21no—
79C2×D76—21no—
80C2×D76—21no—
81C2×D76SD1612yes—
82C2×D76Q1612yes—
83C2×C4×D19—22no—
84C2×C4×D19—22no—
85C2×C4×D19—82no—
86M16×C19—41no—
87M16×C19—41no—
88C2×C8×C19—22no—
89C2×C8×C19—41no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C42×C19—41no—
95C42×C19—41no—
96C42×C19C2×D411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19#4111yescharacteristic
99C42×C19#4111yescharacteristic
100(C2×D19)⋊C4—22no—
101(C2×D19)⋊C4—22no—
102(C2×D19)⋊C4—44no—
103(C2×D19)⋊C4—82no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19—41no—
107C4⋊Dic19—41no—
108Dic19⋊C4—82no—
109#64520—41no—
110#64520—41no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113C8×D19—84no—
114#9483—191nomaximal, Sylow
115C23×C19C2×C22⋊C411yescharacteristic
116C22×D19—22no—
117C22×D19—22no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19#10314yes—
121Q8×C19—22no—
122Q8×C19—22no—
123Q8×C19—41no—
124Q8×C19—41no—
125C2×C4×C19—22no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19C4×D411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12311yescharacteristic
139C2×C4×C19C2×SD1611yescharacteristic
140C2×C4×C19C2×Q1611yescharacteristic
141C2×C4×C19#13511yescharacteristic
142C2×C4×C19#13511yescharacteristic
143C2×Dic19—22no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148D76—22no—
149D76—22no—
150D76—22no—
151D76—22no—
152C4×D19—44no—
153C4×D19—82no—
154C8×C19—42no—
155C8×C19—81no—
156C19⋊C8—42no—
157C19⋊C8—81no—
158#2972—191no—
159#2580—191no—
160#1800—191no—
161#1487—191no—
162#1487D1911yescharacteristic, complemented
163#1286—191no—
164#1286—191no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19#38611yescharacteristic
168C22×C19C2×#10311yescharacteristic
169C22×C19#41611yescharacteristic
170C2×D19—24no—
171C2×D19—42no—
172C2×D19—42no—
173C2×D19—44no—
174C2×D19—82no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—42no—
180C4×C19—81no—
181C4×C19#46511yescharacteristic
182C4×C19#46511yescharacteristic
183C4×C19#46711yescharacteristic
184C4×C19#46711yescharacteristic
185Dic19—42no—
186Dic19—82no—
187C2×C4×Q8C2×D1911yescharacteristic
188C2×C4×D4—191no—
189C8×D4—382no—
190C8×D4—382no—
191#431—191no—
192#431C2×D1911yescharacteristic
193#423—191no—
194#423C2×D1911yescharacteristic
195C2×#100—381no—
196C2×C22⋊C8—382no—
197#399—192no—
198#393—192no—
199#390—381no—
200#389—381no—
201#385—382no—
202#382—191no—
203#343—381no—
204Q8⋊C8—22no—
205Q8⋊C8—382no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19#189111yescharacteristic
209C2×C19#189211yescharacteristic
210C2×C19#191111yescharacteristic
211D19—44no—
212C22×Q8C4×D1911yescharacteristic
213C22×D4—191no—
214C23×C4—192no—
215C2×M16—21no—
216C2×M16—381no—
217C22×C8—384no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×D4—381no—
223C4×D4—381no—
224C4×D4—381no—
225C4×D4—381no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—191no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—382no—
230C2×C4⋊C4C4×D1911yescharacteristic
231C2×C22⋊C4—192no—
232C2×C22⋊C4—382no—
233C2×C22⋊C4—382no—
234C2×C42—21no—
235C2×C42C22×D1911yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—381no—
240C4⋊C8—381no—
241C4⋊C8—381no—
242#100—762no—
243C22⋊C8—21no—
244C22⋊C8—384no—
245C22⋊C8—381no—
246C4×C8—192no—
247C4×C8C22⋊D1912yes—
248#95—192no—
249#95—382no—
250#95—381no—
251C19#948311yescharacteristic, complemented, Sylow
252C24—192no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—42no—
256C2×D4—192no—
257C2×D4—192no—
258C2×D4—381no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—192no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—382no—
268C22×C4—1522no—
269C22×C4C2×C4×D1911yescharacteristic
270C22×C4D4×D1911yescharacteristic
271C22×C4D4×D1911yescharacteristic
272M16—41no—
273M16—41no—
274M16—761no—
275M16—761no—
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—382no—
279C2×C8—761no—
280C2×C8—1524no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—1522no—
290C22⋊C4—382no—
291C22⋊C4—382no—
292C22⋊C4—764no—
293C22⋊C4—1522no—
294C42—41no—
295C42—41no—
296C42#6454111yescharacteristic
297C42D4×D1911yescharacteristic
298C42#6454311yescharacteristic
299C42C2×C22⋊D1911yescharacteristic
300C23—194no—
301C23—382no—
302C23—382no—
303C23—762no—
304C23—762no—
305C23C22⋊C4×D1911yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310D4—382no—
311D4—382no—
312D4—382no—
313D4—382no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—382no—
323C2×C4—764no—
324C2×C4—762no—
325C2×C4—762no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—1522no—
329C2×C4(C22⋊D19)⋊C411yescharacteristic
330C2×C4#1059732911yescharacteristic
331C2×C4#1059733011yescharacteristic
332C2×C4SD16×D1911yescharacteristic
333C2×C4#1059736211yescharacteristic
334C2×C4Q16×D1911yescharacteristic
335C2×C4#1059736511yescharacteristic
336C2×C4C4×C22⋊D1911yescharacteristic
337C2×C4#1059738311yescharacteristic
338C2×C4#1059738411yescharacteristic
339C8—42no—
340C8—81no—
341C8—762no—
342C8—1521no—
343C22—21no—
344C22—21no—
345C22—384no—
346C22—764no—
347C22—762no—
348C22—762no—
349C22—1522no—
350C22#1192642011yescharacteristic
351C22#103×D1911yescharacteristic
352C22#1192653911yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—81no—
359C4—762no—
360C4—1522no—
361C4#1192677011yescharacteristic
362C4#1192677611yescharacteristic
363C4#1192678211yescharacteristic
364C4#1192678411yescharacteristic
365C2—21no—
366C2—21no—
367C2—764no—
368C2#1456405011yescharacteristic
369C2#1456405511yescharacteristic
370C2#1456416411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1487C2
socleC22×C19#386
prime radicalC22×D76D4
cosocleC2×C42×C19C23
hypercenter#1487D19
hypocenterC19#9483
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #14562064C2semidirect
5. #14561495C2semidirect
6. #14561494C2semidirect
7. C19×#1487C2semidirect
162. #1487D19semidirect
251. C19#9483semidirect

Maximal subgroups

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

subgroupindex
#145726582
#145689932
#145636242
#145620642
#145614952
#145614942
C19×#14872
#948319