Finite Group Databasebeta

← #18071504

Subgroups — #18071504

Order 4864.

574 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 83 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#14569998C211yesmaximal, characteristic
2#14564965C211yesmaximal, characteristic, complemented
3#14564768C211yesmaximal, characteristic, complemented
4#14561457C211yesmaximal, characteristic, complemented
5#14561456C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic, complemented
7C19×#2013C211yesmaximal, characteristic, complemented
8C2×#10597329—21no—
9C2×#10597330—21no—
10C2×#10597265—21no—
11C2×#10597266—21no—
12#11926467—21no—
13#11926460—21no—
14#11926452—21no—
15#11926446C2211yescharacteristic
16#11926442C2211yescharacteristic
17#11926415—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C22×SD16×C19—21no—
23C2×C19×C4⋊Q8C2211yescharacteristic
24C2×C19×#103—21no—
25C19×#390C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D4×C19D411yescharacteristic
29C22×C22⋊D19—21no—
30C22×C22⋊D19—21no—
31C22×D76D411yescharacteristic
32C22×C4×D19—21no—
33C2×SD16×C19—42no—
34C2×SD16×C19—42no—
35C2×SD16×C19—42no—
36C22×C8×C19—21no—
37C19×C4⋊Q8—42no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19D411yescharacteristic
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×C4⋊Dic19D411yescharacteristic
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4⋊Dic19D411yescharacteristic
52C2×Dic19⋊C4—21no—
53C2×Dic19⋊C4—21no—
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56#10597330—42no—
57#10597330—42no—
58#10597329—42no—
59#10597329—42no—
60C19×#103—42no—
61C19⋊#95—21no—
62C19⋊#95—21no—
63#10597266—42no—
64#10597265—42no—
65C24×C19—21no—
66C23×D19—21no—
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C2×Q8×C19—41no—
73C2×D4×C19—21no—
74C2×D4×C19—21no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C22×C4×C19—21no—
78C22×C4×C19—41no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C2×C22⋊D19—42no—
83C2×C22⋊D19—42no—
84C2×C22⋊D19—42no—
85C2×C22⋊D19—81no—
86C2×C22⋊D19—81no—
87C2×C22⋊D19—81no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C2×D76—21no—
92C2×D76—41no—
93C2×D76—41no—
94C2×D76SD1612yescomplemented
95C2×C4×D19—42no—
96C2×C4×D19—42no—
97C2×C4×D19—81no—
98SD16×C19—48no—
99C2×C8×C19—22no—
100C2×C8×C19—41no—
101C2×C8×C19—41no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C42×C19—41no—
112C22⋊Dic19—42no—
113C22⋊Dic19—81no—
114(C2×D19)⋊C4—42no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—41no—
119C4⋊Dic19—21no—
120C4⋊Dic19—41no—
121C4⋊Dic19—41no—
122C4⋊Dic19SD1612yescomplemented
123Dic19⋊C4—42no—
124Dic19⋊C4—41no—
125Dic19⋊C4—41no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132#7778—191nomaximal, Sylow
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19#12011yescharacteristic
141C22×D19—22no—
142C22×D19—41no—
143C22×D19—41no—
144C22×D19—41no—
145C22×D19—41no—
146C22×D19—41no—
147C22×D19—41no—
148Q8×C19—42no—
149Q8×C19—42no—
150Q8×C19—81no—
151Q8×C19—81no—
152D4×C19—42no—
153D4×C19—81no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—42no—
164C2×C4×C19—81no—
165C2×C4×C19—81no—
166C2×C4×C19C2×SD1611yescharacteristic
167C2×C4×C19C2×SD1611yescharacteristic
168C2×C4×C19#13511yescharacteristic
169C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
172C22⋊D19—84no—
173C22⋊D19—84no—
174C2×Dic19—22no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183D76—42no—
184D76—81no—
185C4×D19—84no—
186C8×C19—42no—
187C19⋊C8—42no—
188C19⋊C8—81no—
189#2682—191no—
190#2058—191no—
191#2023—191no—
192#2013D1911yescharacteristic, complemented
193#1271—191no—
194#1270—191no—
195#1270—191no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19—81no—
200C22×C19—81no—
201C22×C19—81no—
202C22×C19—81no—
203C22×C19#44911yescharacteristic
204C22×C19#45011yescharacteristic
205C22×C19#45011yescharacteristic
206C22×C19#45311yescharacteristic
207C22×C19#45511yescharacteristic
208C22×C19#45611yescharacteristic
209C22×C19B(4,𝔽2)11yescharacteristic
210C2×D19—42no—
211C2×D19—42no—
212C2×D19—42no—
213C2×D19—81no—
214C2×D19—81no—
215C2×D19—81no—
216C2×D19—81no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—82no—
224C4×C19—81no—
225Dic19—42no—
226Dic19—81no—
227Dic19—81no—
228C22×SD16—21no—
229C2×C4⋊Q8C2×D1911yescharacteristic
230C2×#123—381no—
231C2×#121—381no—
232C2×#106—381no—
233C2×#103—21no—
234C2×#102—381no—
235#396—381no—
236#394—381no—
237#392—381no—
238#390—191no—
239#390C2×D1911yescharacteristic
240#389—191no—
241#385—381no—
242#340—381no—
243#340—381no—
244#336—191no—
245#336—191no—
246#336C2×D1911yescharacteristic
247C2×C19—161no—
248C2×C19#160011yescharacteristic
249C2×C19#160111yescharacteristic
250C2×C19#160411yescharacteristic
251C2×C19#162911yescharacteristic
252C2×C19#164211yescharacteristic
253C2×C19#165411yescharacteristic
254C2×C19#166111yescharacteristic
255D19—82no—
256C22×Q8—21no—
257C22×D4—191no—
258C22×D4—381no—
259C22×D4—381no—
260C22×D4C22⋊D1911yescharacteristic
261C23×C4—381no—
262C2×SD16—42no—
263C2×SD16—42no—
264C2×SD16—42no—
265C22×C8—21no—
266C22×C8—381no—
267C22×C8—381no—
268C4⋊Q8—42no—
269#123—762no—
270#123—762no—
271#121—762no—
272#121—762no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—191no—
276C2×C4⋊C4—191no—
277C2×C4⋊C4—191no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4—381no—
280C2×C4⋊C4C22⋊D1911yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4—381no—
288C2×C42C22×D1911yescharacteristic
289#106—762no—
290#103—42no—
291#102—762no—
292#95—381no—
293#95—381no—
294C19#777811yescharacteristic, complemented, Sylow
295C24—21no—
296C24—381no—
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—192no—
308C2×D4—381no—
309C2×D4—761no—
310C2×D4—761no—
311C2×D4—762no—
312C2×D4—762no—
313C2×D4—762no—
314C2×D4—1521no—
315C2×D4—1521no—
316C2×D4—1521no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—381no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—762no—
323C22×C4—762no—
324C22×C4—1521no—
325C22×C4D4×D1911yescharacteristic
326C22×C4D4×D1911yescharacteristic
327C22×C4C2×C22⋊D1911yescharacteristic
328SD16—48no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—382no—
333C2×C8—761no—
334C2×C8—761no—
335C2×C8—761no—
336C2×C8—761no—
337C2×C8—761no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—192no—
344C4⋊C4—381no—
345C4⋊C4—761no—
346C4⋊C4—761no—
347C4⋊C4—762no—
348C4⋊C4—761no—
349C4⋊C4—761no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—762no—
355C22⋊C4—762no—
356C22⋊C4—761no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C22⋊C4—1521no—
361C42—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—382no—
370C23—761no—
371C23—761no—
372C23—761no—
373C23—761no—
374C23—761no—
375C23—761no—
376C23#1059738311yescharacteristic
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—81no—
381D4—42no—
382D4—81no—
383D4—762no—
384D4—1521no—
385D4—1524no—
386D4—1524no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—382no—
400C2×C4—761no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—1524no—
409C2×C4SD16×D1911yescharacteristic
410C2×C4SD16×D1911yescharacteristic
411C2×C4#1059736011yescharacteristic
412C2×C4#1059736011yescharacteristic
413C2×C4#1059737811yescharacteristic
414C2×C4#1059739611yescharacteristic
415C8—42no—
416C8—762no—
417C8—1521no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—762no—
426C22—762no—
427C22—762no—
428C22—1521no—
429C22—1521no—
430C22—1521no—
431C22—1521no—
432C22#1192668711yescharacteristic
433C22#1192669311yescharacteristic
434C22#1192669311yescharacteristic
435C22#1192671111yescharacteristic
436C22#1192672011yescharacteristic
437C22#1192672511yescharacteristic
438C22#1192673011yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—81no—
447C4—762no—
448C4—1521no—
449C4—1521no—
450C2—161no—
451C2—1522no—
452C2#1456257911yescharacteristic
453C2#1456258511yescharacteristic
454C2#1456260211yescharacteristic
455C2#1456274911yescharacteristic
456C2#1456283311yescharacteristic
457C2#1456291711yescharacteristic
458C2#1456294911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2013C2
socleC23×C19#120
prime radical#14569998C2
hypercenter#2013D19
hypocenterC19#7778
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #14564965C2semidirect
3. #14564768C2semidirect
4. #14561457C2semidirect
5. #14561456C2semidirect
6. #14561455C2semidirect
7. C19×#2013C2semidirect
94. C2×D76SD16semidirect
122. C4⋊Dic19SD16semidirect
192. #2013D19semidirect
294. C19#7778semidirect

Maximal subgroups

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

subgroupindex
#145699982
#145649652
#145647682
#145614572
#145614562
#145614552
C19×#20132
#777819