Finite Group Databasebeta

← #18085784

Subgroups — #18085784

Order 4864.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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#14569302C211yesmaximal, characteristic
2#14563734C211yesmaximal, characteristic
3#14563712C211yesmaximal, characteristic
4#14561544C211yesmaximal, characteristic
5#14561489C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#1826C211yesmaximal, characteristic
8#11926508C2211yescharacteristic
9#11926467—21no—
10#11926467—21no—
11#11926442—21no—
12#11926441—21no—
13#11926431—21no—
14#11926428—21no—
15#11926407C2211yescharacteristic
16#11926407C2211yescharacteristic
17C4×C22⋊Dic19C2211yescharacteristic
18#11926311—21no—
19#11926311—21no—
20#11926303—21no—
21#11926303—21no—
22C2×C19×#117C2211yescharacteristic
23C19×#407C2211yescharacteristic
24C4×C22⋊C4×C19C2211yescharacteristic
25C19×#339—21no—
26C19×#339—21no—
27C23×C4×C19C2311yescharacteristic
28C2×M16×C19—21no—
29C19×#117—21no—
30C19×#117—21no—
31C19×#117—21no—
32C19×#117—21no—
33C2×C4⋊C4×C19Q811yescharacteristic
34C2×C4⋊C4×C19Q811yescharacteristic
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19—21no—
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19D411yescharacteristic
43C2×C22⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×C4×Dic19D411yescharacteristic
51C2×C4×Dic19D411yescharacteristic
52C2×#64520—21no—
53C19×C22⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61C19⋊#95—21no—
62C19⋊#95—21no—
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65C24×C19C2×D411yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×Q811yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—41no—
83M16×C19—41no—
84M16×C19—41no—
85C2×C8×C19—41no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—41no—
92C22⋊C4×C19—41no—
93C42×C19—41no—
94C42×C19—41no—
95C42×C19—41no—
96C42×C19—41no—
97C22⋊Dic19—42no—
98C22⋊Dic19—41no—
99C22⋊Dic19—41no—
100C22⋊Dic19—41no—
101C22⋊Dic19—41no—
102C4⋊Dic19—42no—
103C4⋊Dic19—81no—
104Dic19⋊C4—42no—
105Dic19⋊C4—42no—
106Dic19⋊C4—42no—
107Dic19⋊C4—81no—
108C4×Dic19—41no—
109C4×Dic19—41no—
110#64520—41no—
111#64520—41no—
112C2×C19⋊C8—41no—
113#10389—191nomaximal, Sylow
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19#12011yescharacteristic
119C23×C19C22⋊Q811yescharacteristic
120C23×C19#12411yescharacteristic
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
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×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—81no—
138C2×C4×C19—81no—
139C2×C4×C19C22⋊Q811yescharacteristic
140C2×C4×C19C22⋊Q811yescharacteristic
141C2×C4×C19#12411yescharacteristic
142C2×C4×C19#12411yescharacteristic
143C2×Dic19—22no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—81no—
156C2×Dic19—81no—
157C2×Dic19—81no—
158C8×C19—81no—
159C19⋊C8—81no—
160#2608—191no—
161#1826—191no—
162#1826D1911yescharacteristic
163#1820—191no—
164#1306—191no—
165#1284—191no—
166#1284—191no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—81no—
176C22×C19—81no—
177C22×C19#39311yescharacteristic
178C22×C19#45811yescharacteristic
179C22×C19#45811yescharacteristic
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—42no—
185C4×C19—81no—
186C4×C19—81no—
187C4×C19—81no—
188Dic19—42no—
189Dic19—81no—
190Dic19—81no—
191Dic19—81no—
192Dic19—161no—
193C2×#117C2×D1911yescharacteristic
194#407—191no—
195#407C2×D1911yescharacteristic
196#396—381no—
197#396—381no—
198#389—381no—
199#389—381no—
200#387—381no—
201#387—381no—
202#381—191no—
203#381—191no—
204C4×C22⋊C4—191no—
205C4×C22⋊C4C2×D1911yescharacteristic
206#342—381no—
207#342—381no—
208#339—21no—
209#339—21no—
210#339—381no—
211#339—381no—
212C2×C19—21no—
213C2×C19—21no—
214C2×C19—41no—
215C2×C19—41no—
216C2×C19#203011yescharacteristic
217C2×C19#203111yescharacteristic
218C2×C19#203111yescharacteristic
219C23×C4C22×D1911yescharacteristic
220C2×M16—21no—
221C2×M16—381no—
222#117—21no—
223#117—21no—
224#117—21no—
225#117—21no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—381no—
231C2×C4⋊C4—381no—
232C2×C4⋊C4Dic3811yescharacteristic
233C2×C4⋊C4Dic3811yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—191no—
237C2×C22⋊C4—191no—
238C2×C22⋊C4—381no—
239C2×C22⋊C4—381no—
240C2×C42—21no—
241C2×C42—191no—
242C2×C42—191no—
243C2×C42C22⋊D1911yescharacteristic
244C2×C42C22⋊D1911yescharacteristic
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—381no—
248C22⋊C8—381no—
249#95—21no—
250#95—381no—
251#95—381no—
252#95—381no—
253#95—381no—
254#95—381no—
255#95—381no—
256#95—381no—
257C19#1038911yescharacteristic, complemented, Sylow
258C24D4×D1911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4—761no—
270C22×C4C2×Dic3811yescharacteristic
271C22×C4#6454111yescharacteristic
272C22×C4D4×D1911yescharacteristic
273C22×C4#6454311yescharacteristic
274C22×C4#6454311yescharacteristic
275C22×C4C2×C22⋊D1911yescharacteristic
276M16—41no—
277M16—41no—
278M16—761no—
279M16—761no—
280C2×C8—41no—
281C2×C8—761no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—762no—
287C4⋊C4—762no—
288C4⋊C4—762no—
289C4⋊C4—762no—
290C4⋊C4—1521no—
291C4⋊C4—1521no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—762no—
296C22⋊C4—761no—
297C22⋊C4—761no—
298C22⋊C4—761no—
299C22⋊C4—761no—
300C42—41no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—761no—
305C42—761no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23#1059732411yescharacteristic
311C23#1059733111yescharacteristic
312C23#1059738311yescharacteristic
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—382no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4—761no—
336C2×C4—761no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—1521no—
344C2×C4—1521no—
345C2×C4—1521no—
346C2×C4#1059732411yescharacteristic
347C2×C4#1059733111yescharacteristic
348C2×C4#1059737011yescharacteristic
349C2×C4#1059738211yescharacteristic
350C8—81no—
351C8—1521no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22#1192645611yescharacteristic
363C22#1192673311yescharacteristic
364C22#1192673311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—3041no—
374C4—762no—
375C4—1521no—
376C4—1521no—
377C4—1521no—
378C2—21no—
379C2—21no—
380C2—41no—
381C2—41no—
382C2#1456480211yescharacteristic
383C2#1456480511yescharacteristic
384C2#1456480711yescharacteristic
subgroupG/H
centerC22#11926456
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1826C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#1826D19
hypocenterC19#10389
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
257. C19#10389semidirect

Maximal subgroups

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

subgroupindex
#145693022
#145637342
#145637122
#145615442
#145614892
#145614882
C19×#18262
#1038919