Finite Group Databasebeta

← #18079911

Subgroups — #18079911

Order 4864.

594 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 117 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#14568589C211yesmaximal, characteristic
3#14563624C211yesmaximal, characteristic
4#14562320C211yesmaximal, characteristic, complemented
5#14561537C211yesmaximal, characteristic, complemented
6#14561536C211yesmaximal, characteristic, complemented
7C19×#1549C211yesmaximal, characteristic, complemented
8C2×#10597392—22no—
9C2×C4×D76C2211yescharacteristic
10C8×D76—22no—
11#11926609—22no—
12#11926597C2211yescharacteristic
13#11926568C2211yescharacteristic
14C2×#10597280—21no—
15C22⋊C8×D19—22no—
16#11926479C414yes—
17#11926445—21no—
18#11926413—21no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926312—21no—
21#11926290—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C19×#431C2211yescharacteristic
24C19×#423C2211yescharacteristic
25C19×#332—22no—
26C22×Q8×C19—21no—
27C22×D76D411yescharacteristic
28C22×C4×D19D412yes—
29C2×M16×C19—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19C2×C412yes—
36C2×C42×C19C2311yescharacteristic
37#10597392—48no—
38C2×(C2×D19)⋊C4—24no—
39C2×(C2×D19)⋊C4C2×C412yes—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19D411yescharacteristic
42C2×Dic19⋊C4—24no—
43C2×C4×Dic19—21no—
44C2×#64520—21no—
45C2×C8×D19—24no—
46C4×D76—21no—
47C4×D76—21no—
48C4×D76—21no—
49C4×D76—21no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8D412yes—
53C19×C22⋊C8—21no—
54C4×C8×C19—21no—
55C19⋊#95C2×C412yes—
56C22⋊(C19⋊C8)—21no—
57#10597280—42no—
58(C2×D19)⋊C8—24no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)D412yes—
62C4×C19⋊C8—21no—
63C23×D19C22⋊C412yes—
64C2×Q8×C19—44no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C22×C4×C19—22no—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—22no—
72C22×Dic19C22⋊C412yes—
73C2×D76—21no—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76SD1612yes—
78C2×D76Q1612yes—
79C2×C4×D19—22no—
80C2×C4×D19—22no—
81C2×C4×D19—44no—
82M16×C19—41no—
83M16×C19—41no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C42×C19C2×D411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19#4111yescharacteristic
93C42×C19#4111yescharacteristic
94(C2×D19)⋊C4—22no—
95(C2×D19)⋊C4—22no—
96(C2×D19)⋊C4—48no—
97C4⋊Dic19—24no—
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100Dic19⋊C4—48no—
101C4×Dic19—41no—
102C4×Dic19—41no—
103#64520—41no—
104#64520—41no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—41no—
107C8×D19—84no—
108#9395—191nomaximal, Sylow
109C23×C19C2×C22⋊C411yescharacteristic
110C22×D19—22no—
111C22×D19—22no—
112C22×D19—42no—
113C22×D19—42no—
114C22×D19#10314yes—
115Q8×C19—82no—
116Q8×C19—82no—
117C2×C4×C19—22no—
118C2×C4×C19—41no—
119C2×C4×C19—44no—
120C2×C4×C19—42no—
121C2×C4×C19C4×D411yescharacteristic
122C2×C4×C19C4×D411yescharacteristic
123C2×C4×C19#12011yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12111yescharacteristic
126C2×C4×C19#12311yescharacteristic
127C2×C4×C19C2×SD1611yescharacteristic
128C2×C4×C19C2×Q1611yescharacteristic
129C2×C4×C19#13511yescharacteristic
130C2×C4×C19#13511yescharacteristic
131C2×Dic19—24no—
132C2×Dic19—22no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136D76—22no—
137D76—22no—
138D76—22no—
139D76—22no—
140C4×D19—44no—
141C4×D19—82no—
142C8×C19—42no—
143C8×C19—81no—
144C19⋊C8—42no—
145C19⋊C8—81no—
146#2972—191no—
147#2542—191no—
148#1800—191no—
149#1549—191no—
150#1549D1911yescharacteristic, complemented
151#1303—191no—
152#1303—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19#38611yescharacteristic
156C22×C19C2×#10311yescharacteristic
157C22×C19#41611yescharacteristic
158C2×D19—24no—
159C2×D19—42no—
160C2×D19—42no—
161C2×D19—44no—
162C2×D19—82no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—82no—
167C4×C19#45312yes—
168C4×C19#46511yescharacteristic
169C4×C19#46511yescharacteristic
170C4×C19#46711yescharacteristic
171C4×C19#46711yescharacteristic
172Dic19—44no—
173Dic19—42no—
174C2×C4⋊Q8C2×D1911yescharacteristic
175C2×C22⋊Q8—382no—
176C2×C4×D4—191no—
177C8×D4—382no—
178C8×D4—382no—
179#431—191no—
180#431C2×D1911yescharacteristic
181#423—191no—
182#423C2×D1911yescharacteristic
183C2×#100—381no—
184C2×C22⋊C8—382no—
185#399—194no—
186#390—381no—
187#384—381no—
188C4×C4⋊C4—191no—
189#343—381no—
190#332—22no—
191#332—382no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19#188711yescharacteristic
195C2×C19#189211yescharacteristic
196C2×C19#191511yescharacteristic
197D19—44no—
198C22×Q8—21no—
199C22×D4—191no—
200C23×C4—192no—
201C2×M16—21no—
202C2×M16—381no—
203C22×C8—384no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C22⋊Q8—768no—
209C4×D4—381no—
210C4×D4—381no—
211C4×D4—381no—
212C4×D4—381no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—381no—
216C2×C4⋊C4—384no—
217C2×C4⋊C4C4×D1912yes—
218C2×C22⋊C4—192no—
219C2×C22⋊C4—384no—
220C2×C42—381no—
221C2×C42C22×D1911yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—192no—
225C4⋊C8—381no—
226C4⋊C8—381no—
227C4⋊C8C22⋊D1912yes—
228#100—762no—
229C22⋊C8—21no—
230C22⋊C8—384no—
231C22⋊C8—381no—
232C4×C8—21no—
233C4×C8—381no—
234#95—192no—
235C19#939511yescharacteristic, complemented, Sylow
236C24—192no—
237C2×Q8—44no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×D4—192no—
241C2×D4—192no—
242C2×D4—381no—
243C2×D4—381no—
244C2×D4—381no—
245C2×D4—381no—
246C22×C4—22no—
247C22×C4—192no—
248C22×C4—382no—
249C22×C4—382no—
250C22×C4—382no—
251C22×C4—764no—
252C22×C4C2×C4×D1911yescharacteristic
253C22×C4D4×D1911yescharacteristic
254C22×C4D4×D1911yescharacteristic
255M16—41no—
256M16—41no—
257M16—761no—
258M16—761no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—382no—
262C2×C8—761no—
263C2×C8—1524no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—384no—
269C4⋊C4—381no—
270C4⋊C4—381no—
271C4⋊C4—768no—
272C22⋊C4—382no—
273C22⋊C4—382no—
274C22⋊C4—768no—
275C42—761no—
276C42—761no—
277C42#6454111yescharacteristic
278C42D4×D1911yescharacteristic
279C42#6454311yescharacteristic
280C42C2×C22⋊D1911yescharacteristic
281C23—194no—
282C23—382no—
283C23—382no—
284C23—762no—
285C23—762no—
286C23C22⋊C4×D1911yescharacteristic
287Q8—82no—
288Q8—82no—
289D4—382no—
290D4—382no—
291D4—382no—
292D4—382no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—384no—
298C2×C4—382no—
299C2×C4—762no—
300C2×C4—762no—
301C2×C4—764no—
302C2×C4—762no—
303C2×C4—1522no—
304C2×C4(C22⋊D19)⋊C411yescharacteristic
305C2×C4#1059732911yescharacteristic
306C2×C4#1059733011yescharacteristic
307C2×C4SD16×D1911yescharacteristic
308C2×C4#1059736211yescharacteristic
309C2×C4Q16×D1911yescharacteristic
310C2×C4#1059736511yescharacteristic
311C2×C4C4×C22⋊D1911yescharacteristic
312C2×C4#1059738311yescharacteristic
313C2×C4#1059738411yescharacteristic
314C8—42no—
315C8—81no—
316C8—762no—
317C8—1521no—
318C22—21no—
319C22—21no—
320C22—384no—
321C22—764no—
322C22—762no—
323C22—762no—
324C22—1522no—
325C22#1192642011yescharacteristic
326C22#103×D1911yescharacteristic
327C22#1192653911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—764no—
333C4—762no—
334C4#1192671012yes—
335C4#1192677011yescharacteristic
336C4#1192677611yescharacteristic
337C4#1192678211yescharacteristic
338C4#1192678411yescharacteristic
339C2—21no—
340C2—21no—
341C2—764no—
342C2#1456403011yescharacteristic
343C2#1456405511yescharacteristic
344C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1549C2
socleC22×C19#386
prime radicalC22×D76D4
cosocleC2×C42×C19C23
hypercenter#1549D19
hypocenterC19#9395
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #14562320C2semidirect
5. #14561537C2semidirect
6. #14561536C2semidirect
7. C19×#1549C2semidirect
150. #1549D19semidirect
235. C19#9395semidirect

Maximal subgroups

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

subgroupindex
#145726582
#145685892
#145636242
#145623202
#145615372
#145615362
C19×#15492
#939519