Finite Group Databasebeta

← #18071393

Subgroups — #18071393

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#14569999C211yesmaximal, characteristic
2#14564878C211yesmaximal, characteristic, complemented
3#14564768C211yesmaximal, characteristic, complemented
4#14561459C211yesmaximal, characteristic, complemented
5#14561456C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic, complemented
7C19×#2023C211yesmaximal, characteristic, complemented
8C2×#10597332—21no—
9C2×#10597385—21no—
10C2×#10597292—21no—
11C2×#10597292—21no—
12C2×#10597266—21no—
13#11926466—21no—
14#11926460—21no—
15#11926453—21no—
16#11926446C2211yescharacteristic
17#11926442C2211yescharacteristic
18#11926419—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#102—21no—
24C19×#390C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D4×C19D411yescharacteristic
29C22×C22⋊D19—21no—
30C22×C22⋊D19—21no—
31C23×Dic19—21no—
32C22×D76D411yescharacteristic
33C22×C8×C19—21no—
34C19×C4⋊Q8—42no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C42×C19C2311yescharacteristic
41C2×C22⋊Dic19—21no—
42#10597385—42no—
43#10597385—42no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19D411yescharacteristic
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4⋊Dic19D411yescharacteristic
52C2×Dic19⋊C4—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55#10597332—42no—
56#10597332—42no—
57C19×#102—42no—
58#10597292—42no—
59#10597292—42no—
60C19⋊#95—21no—
61C19⋊#95—21no—
62#10597266—42no—
63C24×C19—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—
71C2×D4×C19—21no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C2×D4×C19SD1612yes—
75C22×C4×C19—21no—
76C22×C4×C19—41no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C2×C22⋊D19—42no—
81C2×C22⋊D19—42no—
82C2×C22⋊D19—42no—
83C2×C22⋊D19—81no—
84C2×C22⋊D19—81no—
85C2×C22⋊D19—81no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—42no—
90C22×Dic19—42no—
91C22×Dic19—81no—
92C2×D76—21no—
93C2×D76—21no—
94C2×D76—41no—
95C2×D76—41no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C42×C19—41no—
109C22⋊Dic19—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—81no—
116C4⋊Dic19—21no—
117C4⋊Dic19—42no—
118C4⋊Dic19—41no—
119C4⋊Dic19—41no—
120C4⋊Dic19D812yes—
121Dic19⋊C4—41no—
122Dic19⋊C4—41no—
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—22no—
131C23×C19—41no—
132C23×C19—41no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19#12011yescharacteristic
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—
149D4×C19—42no—
150D4×C19—81no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—42no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19C2×D811yescharacteristic
164C2×C4×C19C2×SD1611yescharacteristic
165C2×C4×C19#13511yescharacteristic
166C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C19#13711yescharacteristic
169C22⋊D19—84no—
170C22⋊D19—84no—
171C2×Dic19—22no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—84no—
181D76—42no—
182D76—81no—
183C8×C19—81no—
184C19⋊C8—81no—
185C19⋊C8—81no—
186#2682—191no—
187#2043—191no—
188#2023—191no—
189#2023D1911yescharacteristic, complemented
190#1271—191no—
191#1270—191no—
192#1270—191no—
193C22×C19—42no—
194C22×C19—42no—
195C22×C19—42no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19—81no—
200C22×C19#44711yescharacteristic
201C22×C19#45011yescharacteristic
202C22×C19#45211yescharacteristic
203C22×C19#45411yescharacteristic
204C22×C19#45511yescharacteristic
205C22×C19#45511yescharacteristic
206C22×C19B(4,𝔽2)11yescharacteristic
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—82no—
221C4×C19—81no—
222Dic19—42no—
223Dic19—81no—
224Dic19—81no—
225C2×C4⋊Q8C2×D1911yescharacteristic
226C2×#123—381no—
227C2×#121—381no—
228C2×#103—381no—
229C2×#103—381no—
230C2×#102—21no—
231C2×#102—381no—
232#396—381no—
233#394—381no—
234#392—381no—
235#390—191no—
236#390C2×D1911yescharacteristic
237#389—191no—
238#385—381no—
239#340—21no—
240#340—381no—
241#336—191no—
242#336—191no—
243#336C2×D1911yescharacteristic
244C2×C19—82no—
245C2×C19#159811yescharacteristic
246C2×C19#160111yescharacteristic
247C2×C19#160611yescharacteristic
248C2×C19#163511yescharacteristic
249C2×C19#163911yescharacteristic
250C2×C19#164111yescharacteristic
251C2×C19#166211yescharacteristic
252D19—161no—
253C22×Q8—21no—
254C22×D4—191no—
255C22×D4—381no—
256C22×D4—381no—
257C22×D4C22⋊D1911yescharacteristic
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—191no—
270C2×C4⋊C4—191no—
271C2×C4⋊C4—191no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4C22⋊D1911yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
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—762no—
284#103—762no—
285#102—42no—
286#102—762no—
287#95—381no—
288#95—381no—
289C19#776211yescharacteristic, complemented, Sylow
290C24—21no—
291C24—381no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—381no—
302C2×D4—381no—
303C2×D4—761no—
304C2×D4—761no—
305C2×D4—762no—
306C2×D4—762no—
307C2×D4—762no—
308C2×D4—1521no—
309C2×D4—1521no—
310C2×D4—1521no—
311C2×D4#6452712yes—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—381no—
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—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—192no—
338C4⋊C4—381no—
339C4⋊C4—761no—
340C4⋊C4—761no—
341C4⋊C4—762no—
342C4⋊C4—761no—
343C4⋊C4—761no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—762no—
349C22⋊C4—762no—
350C22⋊C4—761no—
351C22⋊C4—761no—
352C22⋊C4—761no—
353C22⋊C4—761no—
354C22⋊C4—1521no—
355C42—41no—
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
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—42no—
376D4—81no—
377D4—762no—
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—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—382no—
394C2×C4—761no—
395C2×C4—761no—
396C2×C4—761no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—761no—
401C2×C4—761no—
402C2×C4—1524no—
403C2×C4D8×D1911yescharacteristic
404C2×C4#1059735711yescharacteristic
405C2×C4#1059736111yescharacteristic
406C2×C4#1059736211yescharacteristic
407C2×C4C2×#6452711yescharacteristic
408C2×C4#1059739511yescharacteristic
409C8—81no—
410C8—1521no—
411C8—1521no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—1521no—
420C22—1521no—
421C22—1521no—
422C22—1521no—
423C22—1521no—
424C22—1521no—
425C22—1521no—
426C22#1192667611yescharacteristic
427C22#1192669411yescharacteristic
428C22#1192670311yescharacteristic
429C22#1192671511yescharacteristic
430C22#1192672011yescharacteristic
431C22#1192672111yescharacteristic
432C22#1192673011yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—82no—
440C4—81no—
441C4—762no—
442C4—1521no—
443C4—1521no—
444C2—82no—
445C2—3041no—
446C2#1456256811yescharacteristic
447C2#1456258611yescharacteristic
448C2#1456261211yescharacteristic
449C2#1456278411yescharacteristic
450C2#1456281311yescharacteristic
451C2#1456282511yescharacteristic
452C2#1456295711yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2023C2
socleC23×C19#120
prime radical#14569999C2
hypercenter#2023D19
hypocenterC19#7762
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
2. #14564878C2semidirect
3. #14564768C2semidirect
4. #14561459C2semidirect
5. #14561456C2semidirect
6. #14561455C2semidirect
7. C19×#2023C2semidirect
189. #2023D19semidirect
289. C19#7762semidirect

Maximal subgroups

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

subgroupindex
#145699992
#145648782
#145647682
#145614592
#145614562
#145614552
C19×#20232
#776219