Finite Group Databasebeta

← #18080350

Subgroups — #18080350

Order 4864.

610 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 97 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#14567918C211yesmaximal, characteristic
2#14565990C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic
4#14561964C211yesmaximal, characteristic
5#14561489C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#1826C211yesmaximal, characteristic
8C2×#10597323—21no—
9C22×Dic19⋊C4C2211yescharacteristic
10#11926508C2211yescharacteristic
11#11926482C412yescomplemented
12#11926475C412yescomplemented
13#11926428—22no—
14#11926416—21no—
15#11926407C2211yescharacteristic
16#11926405—21no—
17C4×Dic19⋊C4—22no—
18#11926395—22no—
19C22⋊C4×Dic19—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926303—22no—
22#11926269—22no—
23C2×C19×#117C2211yescharacteristic
24C19×#407C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C19×#339—22no—
27C23×C4×C19C2311yescharacteristic
28C23×Dic19D411yescharacteristic
29C23×Dic19D411yescharacteristic
30C2×M16×C19—21no—
31C19×#117—21no—
32C19×#117—21no—
33C19×#117—21no—
34C19×#117—21no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C42×C19—21no—
40C2×C42×C19D412yes—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×Dic19⋊C4—22no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—22no—
49C2×Dic19⋊C4C2×C412yes—
50C2×Dic19⋊C4D412yes—
51C2×C4×Dic19—22no—
52C2×C4×Dic19—22no—
53C2×C4×Dic19D412yes—
54C2×#64520—21no—
55#10597323—28no—
56C19×C22⋊C8—21no—
57C19×C22⋊C8—21no—
58C19×#95—21no—
59C19⋊#95—22no—
60C19⋊#95—21no—
61C19⋊#95—21no—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95C2×C412yes—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68C24×C19C2×D411yescharacteristic
69C22×C4×C19—22no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—42no—
73C22×C4×C19C22×C411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—24no—
82C22×Dic19—22no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—22no—
86C22×Dic19—42no—
87C22×Dic19C22⋊C412yes—
88C22×Dic19C22⋊C412yes—
89M16×C19—42no—
90C2×C8×C19—41no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C22⋊C4×C19—24no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—41no—
98C42×C19—42no—
99C42×C19—41no—
100C42×C19—41no—
101C22⋊Dic19—24no—
102C22⋊Dic19—42no—
103Dic19⋊C4—28no—
104Dic19⋊C4—22no—
105Dic19⋊C4—22no—
106Dic19⋊C4—22no—
107Dic19⋊C4—22no—
108Dic19⋊C4—44no—
109C4×Dic19—28no—
110C4×Dic19—42no—
111C4×Dic19—82no—
112#64520—42no—
113C2×C19⋊C8—41no—
114#9478—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—41no—
118C23×C19C2×C22⋊C411yescharacteristic
119C23×C19#12011yescharacteristic
120C23×C19#12311yescharacteristic
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—24no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19C4×D411yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×Dic19—22no—
139C2×Dic19—22no—
140C2×Dic19—24no—
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—24no—
144C2×Dic19—22no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19—42no—
151C2×Dic19—42no—
152C2×Dic19—81no—
153C2×Dic19#10414yes—
154C8×C19—81no—
155C19⋊C8—81no—
156#2484—191no—
157#2274—191no—
158#1826—191no—
159#1826D1911yescharacteristic
160#1463—191no—
161#1284—191no—
162#1284—191no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—44no—
171C22×C19#38611yescharacteristic
172C22×C19C2×#10412yes—
173C22×C19#45812yes—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—44no—
179C4×C19—81no—
180C4×C19—81no—
181Dic19—24no—
182Dic19—44no—
183Dic19—42no—
184Dic19—82no—
185C2×#117—381no—
186C2×#117C2×D1911yescharacteristic
187C22×C4⋊C4—191no—
188#407—191no—
189#407C2×D1911yescharacteristic
190#400—192no—
191#398—192no—
192#387—382no—
193#385—381no—
194#381—191no—
195#381—381no—
196C4×C4⋊C4—382no—
197C4×C4⋊C4—382no—
198C4×C22⋊C4—191no—
199C4×C22⋊C4—381no—
200C4×C22⋊C4C2×D1911yescharacteristic
201#339—22no—
202#339—382no—
203#324—382no—
204C2×C19—22no—
205C2×C19—22no—
206C2×C19—41no—
207C2×C19#189011yescharacteristic
208C2×C19#189611yescharacteristic
209C2×C19#191211yescharacteristic
210C23×C4—191no—
211C23×C4—191no—
212C23×C4C22×D1911yescharacteristic
213C2×M16—21no—
214C2×M16—381no—
215#117—21no—
216#117—21no—
217#117—21no—
218#117—21no—
219#117—388no—
220C2×C4⋊C4—192no—
221C2×C4⋊C4—192no—
222C2×C4⋊C4—382no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—382no—
228C2×C4⋊C4C4×D1911yescharacteristic
229C2×C4⋊C4C4×D1911yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C42—21no—
235C2×C42—192no—
236C2×C42—382no—
237C2×C42—382no—
238C2×C42C22⋊D1912yes—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8—381no—
242C22⋊C8—381no—
243#95—21no—
244#95—192no—
245#95—382no—
246#95—382no—
247#95—382no—
248#95—382no—
249#95—381no—
250#95—381no—
251C19#947811yescharacteristic, complemented, Sylow
252C24D4×D1911yescharacteristic
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—192no—
258C22×C4—192no—
259C22×C4—384no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4—382no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—382no—
266C22×C4—762no—
267C22×C4C2×C4×D1911yescharacteristic
268C22×C4#6454111yescharacteristic
269C22×C4D4×D1911yescharacteristic
270C22×C4D4×D1911yescharacteristic
271C22×C4#6454311yescharacteristic
272C22×C4C2×C22⋊D1911yescharacteristic
273M16—42no—
274M16—762no—
275C2×C8—41no—
276C2×C8—761no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—388no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—382no—
285C4⋊C4—382no—
286C4⋊C4—764no—
287C22⋊C4—24no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—384no—
291C22⋊C4—762no—
292C42—42no—
293C42—41no—
294C42—41no—
295C42—388no—
296C42—762no—
297C42—1522no—
298C23—22no—
299C23—22no—
300C23—41no—
301C23C22⋊C4×D1911yescharacteristic
302C23#1059732911yescharacteristic
303C23#1059738311yescharacteristic
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—194no—
318C2×C4—382no—
319C2×C4—382no—
320C2×C4—384no—
321C2×C4—382no—
322C2×C4—382no—
323C2×C4—384no—
324C2×C4—382no—
325C2×C4—762no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—762no—
332C2×C4—1521no—
333C2×C4(C22⋊D19)⋊C411yescharacteristic
334C2×C4#1059733011yescharacteristic
335C2×C4C4×C22⋊D1911yescharacteristic
336C2×C4#1059738411yescharacteristic
337C8—81no—
338C8—1521no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#1192642011yescharacteristic
348C22#104×D1912yes—
349C22#1192673312yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—44no—
355C4—81no—
356C4—81no—
357C4—384no—
358C4—764no—
359C4—762no—
360C4—1522no—
361C2—22no—
362C2—22no—
363C2—41no—
364C2#1456404511yescharacteristic
365C2#1456407511yescharacteristic
366C2#1456416911yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1826C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1826D19
hypocenterC19#9478
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
11. #11926482C4semidirect
12. #11926475C4semidirect
251. C19#9478semidirect

Maximal subgroups

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

subgroupindex
#145679182
#145659902
#145637342
#145619642
#145614892
#145614882
C19×#18262
#947819