Finite Group Databasebeta

← #18071392

Subgroups — #18071392

Order 4864.

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

normal subgroups only

This group has 542 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#14569997C211yesmaximal, characteristic
2#14564768C211yesmaximal, characteristic, complemented
3#14564768C211yesmaximal, characteristic, complemented
4#14561458C211yesmaximal, characteristic, complemented
5#14561455C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic, complemented
7C19×#2043C211yesmaximal, characteristic, complemented
8C2×#10597340—21no—
9C2×#10597341—21no—
10C2×#10597266—21no—
11C2×#10597266—21no—
12#11926466—21no—
13#11926461—21no—
14#11926454—21no—
15#11926446C2211yescharacteristic
16#11926446C2211yescharacteristic
17#11926418—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#103—21no—
24C2×C19×#103—21no—
25C19×#389C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D76—21no—
29C22×D76—21no—
30C22×D76D411yescharacteristic
31C22×D76D411yescharacteristic
32C22×C4×D19—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8—42no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C42×C19C2311yescharacteristic
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×C4⋊Dic19D411yescharacteristic
49C2×C4⋊Dic19D411yescharacteristic
50C2×Dic19⋊C4—21no—
51C22×C19⋊C8—21no—
52C22×C19⋊C8—21no—
53#10597341—42no—
54#10597341—42no—
55#10597340—42no—
56#10597340—42no—
57C19×#103—42no—
58C19×#103—42no—
59C19×#95—21no—
60C19⋊#95—21no—
61#10597266—42no—
62#10597266—42no—
63C23×D19—21no—
64C23×D19—21no—
65C2×Q8×C19—22no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—41no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79C2×D76—21no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—41no—
83C2×D76—41no—
84C2×D76—41no—
85C2×D76—41no—
86C2×D76—42no—
87C2×D76—42no—
88C2×D76—42no—
89C2×D76—81no—
90C2×D76—81no—
91C2×D76—81no—
92C2×D76SD1612yes—
93C2×C4×D19—42no—
94C2×C4×D19—42no—
95C2×C4×D19—81no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19D812yes—
108C42×C19—41no—
109(C2×D19)⋊C4—42no—
110(C2×D19)⋊C4—42no—
111(C2×D19)⋊C4—41no—
112(C2×D19)⋊C4—41no—
113(C2×D19)⋊C4—41no—
114(C2×D19)⋊C4—41no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—41no—
119(C2×D19)⋊C4—81no—
120C4⋊Dic19—41no—
121C4⋊Dic19—41no—
122Dic19⋊C4—42no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129#7762—191nomaximal, Sylow
130C23×C19#12011yescharacteristic
131C22×D19—22no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135C22×D19—41no—
136C22×D19—41no—
137C22×D19—41no—
138C22×D19—41no—
139C22×D19—41no—
140C22×D19—41no—
141C22×D19—41no—
142C22×D19—41no—
143C22×D19—41no—
144C22×D19—41no—
145Q8×C19—42no—
146Q8×C19—42no—
147Q8×C19—81no—
148Q8×C19—81no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—22no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—42no—
161C2×C4×C19—41no—
162C2×C4×C19—81no—
163C2×C4×C19—81no—
164C2×C4×C19C2×D811yescharacteristic
165C2×C4×C19C2×SD1611yescharacteristic
166C2×C4×C19#13511yescharacteristic
167C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C19#13711yescharacteristic
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176D76—42no—
177D76—42no—
178D76—81no—
179D76—81no—
180D76—84no—
181D76—84no—
182C4×D19—84no—
183C8×C19—81no—
184C19⋊C8—81no—
185C19⋊C8—81no—
186#2682—191no—
187#2043D1911yescharacteristic, complemented
188#2023—191no—
189#2023—191no—
190#1271—191no—
191#1270—191no—
192#1270—191no—
193C22×C19#44711yescharacteristic
194C22×C19#45011yescharacteristic
195C22×C19#45211yescharacteristic
196C22×C19#45411yescharacteristic
197C22×C19#45511yescharacteristic
198C22×C19#45511yescharacteristic
199C22×C19B(4,𝔽2)11yescharacteristic
200C2×D19—42no—
201C2×D19—42no—
202C2×D19—42no—
203C2×D19—81no—
204C2×D19—81no—
205C2×D19—81no—
206C2×D19—81no—
207C2×D19—81no—
208C2×D19—81no—
209C2×D19—81no—
210C2×D19—81no—
211C2×D19—81no—
212C2×D19—81no—
213C2×D19—81no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—42no—
221C4×C19—82no—
222C4×C19—81no—
223Dic19—81no—
224Dic19—81no—
225C2×C4⋊Q8C2×D1911yescharacteristic
226C2×#123—381no—
227C2×#121—381no—
228C2×#103—21no—
229C2×#103—21no—
230C2×#102—381no—
231C2×#102—381no—
232#396—381no—
233#394—381no—
234#392—381no—
235#390—191no—
236#390—191no—
237#389C2×D1911yescharacteristic
238#385—381no—
239#340—381no—
240#340—381no—
241#336—191no—
242#336—191no—
243#336C2×D1911yescharacteristic
244C2×C19#159811yescharacteristic
245C2×C19#160111yescharacteristic
246C2×C19#160611yescharacteristic
247C2×C19#163511yescharacteristic
248C2×C19#163911yescharacteristic
249C2×C19#164111yescharacteristic
250C2×C19#166211yescharacteristic
251D19—82no—
252D19—161no—
253C22×Q8—21no—
254C22×D4—191no—
255C22×D4—191no—
256C22×D4—381no—
257C22×D4—381no—
258C23×C4—381no—
259C22×C8—21no—
260C22×C8—381no—
261C22×C8—381no—
262C4⋊Q8—42no—
263#123—762no—
264#123—762no—
265#121—762no—
266#121—762no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—191no—
271C2×C4⋊C4—191no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4C22⋊D1911yescharacteristic
274C2×C4⋊C4C22⋊D1911yescharacteristic
275C2×C22⋊C4—381no—
276C2×C22⋊C4—381no—
277C2×C22⋊C4—381no—
278C2×C22⋊C4—381no—
279C2×C22⋊C4—381no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—381no—
282C2×C42C22×D1911yescharacteristic
283#103—42no—
284#103—42no—
285#102—762no—
286#102—762no—
287#95—21no—
288#95—381no—
289C19#776211yescharacteristic, complemented, Sylow
290C24—381no—
291C24—381no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×D4—192no—
299C2×D4—381no—
300C2×D4—381no—
301C2×D4—381no—
302C2×D4—761no—
303C2×D4—761no—
304C2×D4—761no—
305C2×D4—761no—
306C2×D4—762no—
307C2×D4—762no—
308C2×D4—762no—
309C2×D4—1521no—
310C2×D4—1521no—
311C2×D4—1521no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—381no—
316C22×C4—381no—
317C22×C4—762no—
318C22×C4—762no—
319C22×C4—1521no—
320C22×C4D4×D1911yescharacteristic
321C22×C4D4×D1911yescharacteristic
322C22×C4C2×C22⋊D1911yescharacteristic
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—761no—
327C2×C8—761no—
328C2×C8—761no—
329C2×C8—761no—
330C2×C8—761no—
331C2×C8—761no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—761no—
341C4⋊C4—761no—
342C4⋊C4—762no—
343C4⋊C4#6452512yes—
344C22⋊C4—762no—
345C22⋊C4—762no—
346C22⋊C4—761no—
347C22⋊C4—761no—
348C22⋊C4—761no—
349C22⋊C4—761no—
350C22⋊C4—761no—
351C22⋊C4—761no—
352C22⋊C4—761no—
353C22⋊C4—761no—
354C22⋊C4—1521no—
355C42—41no—
356C23—382no—
357C23—761no—
358C23—761no—
359C23—761no—
360C23—761no—
361C23—761no—
362C23—761no—
363C23—761no—
364C23—761no—
365C23—761no—
366C23—761no—
367C23—761no—
368C23—761no—
369C23—761no—
370C23#1059738311yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—762no—
376D4—762no—
377D4—1521no—
378D4—1521no—
379D4—1524no—
380D4—1524no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—761no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—761no—
401C2×C4—761no—
402C2×C4—1524no—
403C2×C4SD16×D1911yescharacteristic
404C2×C4#1059736011yescharacteristic
405C2×C4#1059736411yescharacteristic
406C2×C4#1059736511yescharacteristic
407C2×C4C2×#6452511yescharacteristic
408C2×C4#1059739511yescharacteristic
409C8—81no—
410C8—1521no—
411C8—1521no—
412C22—762no—
413C22—762no—
414C22—762no—
415C22—1521no—
416C22—1521no—
417C22—1521no—
418C22—1521no—
419C22—1521no—
420C22—1521no—
421C22—1521no—
422C22—1521no—
423C22—1521no—
424C22—1521no—
425C22—1521no—
426C22#1192667711yescharacteristic
427C22#1192669311yescharacteristic
428C22#1192670511yescharacteristic
429C22#1192671611yescharacteristic
430C22#1192672011yescharacteristic
431C22#1192672011yescharacteristic
432C22#1192673011yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—82no—
441C4—81no—
442C4—1521no—
443C4—1521no—
444C2—3041no—
445C2—1522no—
446C2#1456256911yescharacteristic
447C2#1456258511yescharacteristic
448C2#1456261411yescharacteristic
449C2#1456278311yescharacteristic
450C2#1456281211yescharacteristic
451C2#1456282611yescharacteristic
452C2#1456295611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2043C2
socleC23×C19#120
prime radical#14569997C2
hypercenter#2043D19
hypocenterC19#7762
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. #14564768C2semidirect
3. #14564768C2semidirect
4. #14561458C2semidirect
5. #14561455C2semidirect
6. #14561455C2semidirect
7. C19×#2043C2semidirect
187. #2043D19semidirect
289. C19#7762semidirect

Maximal subgroups

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

subgroupindex
#145699972
#145647682
#145614582
#145614552
C19×#20432
#776219