Finite Group Databasebeta

← #18082943

Subgroups — #18082943

Order 4864.

654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573579C211yesmaximal, characteristic, complemented
2#14567909C211yesmaximal, characteristic
3#14563735C211yesmaximal, characteristic, complemented
4#14562168C211yesmaximal, characteristic, complemented
5#14561962C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic, complemented
7C19×#2561C211yesmaximal, characteristic
8C2×#10597372C2211yescharacteristic
9#11926882—22no—
10#11926877—21no—
11#11926872—21no—
12#11926584—21no—
13#11926553—21no—
14#11926508C2211yescharacteristic
15#11926508C2211yescharacteristic
16#11926480—21no—
17#11926469—21no—
18#11926432—22no—
19#11926417—21no—
20#11926407C2211yescharacteristic
21#11926400—21no—
22#11926304—22no—
23#11926281—22no—
24#11926268—22no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C22×C22⋊C4×C19C2211yescharacteristic
27C19×#397—21no—
28C19×#393—21no—
29C19×#388—22no—
30C19×#381—21no—
31C19×#379—21no—
32C4×C22⋊C4×C19C2211yescharacteristic
33C25×C19D411yescharacteristic
34C22×Q8×C19D411yescharacteristic
35C23×C4×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C22⋊C4×C19—22no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—22no—
53C2×C42×C19D412yes—
54C2×C22⋊Dic19—22no—
55C2×C22⋊Dic19—21no—
56C2×C22⋊Dic19—21no—
57C2×C22⋊Dic19—22no—
58#10597372—21no—
59#10597372—21no—
60#10597372—21no—
61#10597372—21no—
62C2×C4⋊Dic19D411yescharacteristic
63C2×C4⋊Dic19D411yescharacteristic
64C2×Dic19⋊C4—22no—
65C2×C4×Dic19—21no—
66C2×#64520—21no—
67C2×#64520—21no—
68C19×#95—22no—
69C19×#95—22no—
70C19×#95—21no—
71#10597292—22no—
72#10597292—22no—
73C19⋊#95—22no—
74C19⋊#95—21no—
75C19⋊#95D412yes—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)D412yes—
80#10597265—22no—
81#10597264—22no—
82C24×C19—21no—
83C24×C19—21no—
84C24×C19—21no—
85C24×C19—42no—
86C24×C19—42no—
87C24×C19—42no—
88C24×C19C2×D411yescharacteristic
89C2×Q8×C19—21no—
90C2×Q8×C19—21no—
91C2×Q8×C19—42no—
92C22×C4×C19—22no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—42no—
99C22×C4×C19—42no—
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×Dic19—22no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—42no—
114C22⋊C4×C19—44no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—82no—
122C42×C19—42no—
123C22⋊Dic19—42no—
124C22⋊Dic19—44no—
125C22⋊Dic19—41no—
126C22⋊Dic19—41no—
127C22⋊Dic19—82no—
128C4⋊Dic19—21no—
129C4⋊Dic19—21no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132Dic19⋊C4—82no—
133C4×Dic19—41no—
134C4×Dic19—41no—
135#64520—42no—
136#64520—42no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—41no—
139#9944—191nomaximal, Sylow
140C23×C19—22no—
141C23×C19—22no—
142C23×C19—22no—
143C23×C19—22no—
144C23×C19—22no—
145C23×C19—41no—
146C23×C19—42no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—42no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—42no—
153C23×C19—42no—
154C23×C19—81no—
155C23×C19—81no—
156C23×C19—88no—
157C23×C19#12011yescharacteristic
158C23×C19#12011yescharacteristic
159C23×C19#12111yescharacteristic
160Q8×C19—42no—
161Q8×C19—81no—
162C2×C4×C19—22no—
163C2×C4×C19—22no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—42no—
169C2×C4×C19—42no—
170C2×C4×C19—42no—
171C2×C4×C19—42no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—42no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—81no—
179C2×C4×C19#12011yescharacteristic
180C2×C4×C19#12111yescharacteristic
181C2×C4×C19#12111yescharacteristic
182C2×C4×C19#12711yescharacteristic
183C2×Dic19—42no—
184C2×Dic19—42no—
185C2×Dic19—42no—
186C2×Dic19—41no—
187C2×Dic19—41no—
188C2×Dic19—42no—
189C2×Dic19—42no—
190C19⋊C8—42no—
191C19⋊C8—81no—
192#3095—191no—
193#2561D1911yescharacteristic
194#2482—191no—
195#1826—191no—
196#1511—191no—
197#1462—191no—
198#1284—191no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—44no—
207C22×C19—44no—
208C22×C19—44no—
209C22×C19—42no—
210C22×C19—82no—
211C22×C19—82no—
212C22×C19—82no—
213C22×C19—82no—
214C22×C19—81no—
215C22×C19—81no—
216C22×C19#39211yescharacteristic
217C22×C19#45512yes—
218C22×C19#45812yes—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—82no—
224C4×C19—81no—
225C4×C19—81no—
226C4×C19—81no—
227Dic19—82no—
228Dic19—81no—
229Dic19—81no—
230C2×C22⋊Q8C2×D1911yescharacteristic
231C2×#117—191no—
232C22×C22⋊C4C2×D1911yescharacteristic
233#485—382no—
234#484—381no—
235#483—381no—
236#428—381no—
237#419—381no—
238#407—191no—
239#407—191no—
240#399—381no—
241#397—21no—
242#397—381no—
243#393—21no—
244#388—22no—
245#388—382no—
246#385—381no—
247#381—21no—
248#381—191no—
249#379—21no—
250#379—381no—
251C4×C22⋊C4C2×D1911yescharacteristic
252#339—382no—
253#328—382no—
254#323—382no—
255C2×C19—22no—
256C2×C19—22no—
257C2×C19—41no—
258C2×C19—82no—
259C2×C19#200411yescharacteristic
260C2×C19#201011yescharacteristic
261C2×C19#202211yescharacteristic
262C25C22⋊D1911yescharacteristic
263C22×Q8C22⋊D1911yescharacteristic
264C23×C4C22⋊D1911yescharacteristic
265C23×C4C22×D1911yescharacteristic
266C2×M16—381no—
267C2×M16—381no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#117—381no—
273#117—381no—
274#117—381no—
275#117—381no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—191no—
278C2×C4⋊C4—191no—
279C2×C4⋊C4—382no—
280C2×C4⋊C4C22⋊D1911yescharacteristic
281C2×C22⋊C4—22no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—382no—
292C2×C22⋊C4—381no—
293C2×C22⋊C4—381no—
294C2×C22⋊C4—382no—
295C2×C42—381no—
296C2×C42C22⋊D1912yes—
297#107—382no—
298#106—382no—
299#103—382no—
300#103—382no—
301C22⋊C8—192no—
302C22⋊C8—381no—
303C22⋊C8—381no—
304C22⋊C8—381no—
305#95—22no—
306#95—22no—
307#95—21no—
308#95—192no—
309#95—382no—
310#95—381no—
311C19#994411yescharacteristic, complemented, Sylow
312C24—21no—
313C24—21no—
314C24—21no—
315C24—42no—
316C24—42no—
317C24—42no—
318C24C2×C22⋊D1911yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—42no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—382no—
331C22×C4—381no—
332C22×C4—381no—
333C22×C4D4×D1911yescharacteristic
334C22×C4D4×D1911yescharacteristic
335C22×C4D4×D1911yescharacteristic
336C22×C4#6454311yescharacteristic
337C22×C4C2×C22⋊D1911yescharacteristic
338C22×C4C2×C22⋊D1911yescharacteristic
339M16—762no—
340M16—762no—
341C2×C8—382no—
342C2×C8—761no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—381no—
348C4⋊C4—381no—
349C4⋊C4—381no—
350C4⋊C4—381no—
351C4⋊C4—1522no—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—82no—
361C22⋊C4—762no—
362C22⋊C4—764no—
363C22⋊C4—761no—
364C22⋊C4—761no—
365C22⋊C4—1522no—
366C42—42no—
367C42—761no—
368C42—761no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—88no—
386C23#1059738311yescharacteristic
387C23#1059738511yescharacteristic
388C23#1059739911yescharacteristic
389Q8—42no—
390Q8—81no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—762no—
409C2×C4—762no—
410C2×C4—762no—
411C2×C4—761no—
412C2×C4—761no—
413C2×C4—762no—
414C2×C4—762no—
415C2×C4#1059738311yescharacteristic
416C2×C4#1059738411yescharacteristic
417C2×C4#1059738511yescharacteristic
418C2×C4#1059738611yescharacteristic
419C8—762no—
420C8—1521no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22#1192645211yescharacteristic
439C22#1192672112yes—
440C22#1192673412yes—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—1522no—
450C4—1521no—
451C4—1521no—
452C2—22no—
453C2—22no—
454C2—41no—
455C2—82no—
456C2#1456466411yescharacteristic
457C2#1456470011yescharacteristic
458C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2561C2
socleC22×C19#392
prime radicalC25×C19D4
hypercenter#2561D19
hypocenterC19#9944
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2561

Complements

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

NH ≅ G/Ntype
1. #14573579C2semidirect
3. #14563735C2semidirect
4. #14562168C2semidirect
6. #14561488C2semidirect
311. C19#9944semidirect

Maximal subgroups

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

subgroupindex
#145735792
#145679092
#145637352
#145621682
#145619622
#145614882
C19×#25612
#994419