Finite Group Databasebeta

← #18071415

Subgroups — #18071415

Order 4864.

446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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#14570595C211yesmaximal, characteristic
2#14564878C211yesmaximal, characteristic, complemented
3#14564768C211yesmaximal, characteristic
4#14561458C211yesmaximal, characteristic, complemented
5#14561457C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2057C211yesmaximal, characteristic, complemented
8C2×#10597344—21no—
9C2×#10597292—21no—
10C2×#10597292—21no—
11C2×#10597266—21no—
12#11926479—21no—
13#11926466—21no—
14#11926462—21no—
15#11926446C2211yescharacteristic
16#11926442C2211yescharacteristic
17#11926441—21no—
18#11926434—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#107—21no—
24C19×#389C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D76D411yescharacteristic
29C22×C8×C19—21no—
30C19×C4⋊Q8—42no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×C4⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45C2×C4⋊Dic19D411yescharacteristic
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×C4×Dic19—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52#10597344—42no—
53#10597344—42no—
54C19×#107—42no—
55C19×#95—21no—
56#10597292—42no—
57#10597292—42no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60#10597266—42no—
61C23×D19—21no—
62C2×Q8×C19—22no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—41no—
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77C2×D76—21no—
78C2×D76—21no—
79C2×D76—41no—
80C2×D76—41no—
81C2×C8×C19—22no—
82C2×C8×C19—41no—
83C2×C8×C19—41no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C42×C19—41no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—41no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—41no—
100(C2×D19)⋊C4—81no—
101(C2×D19)⋊C4—81no—
102C4⋊Dic19—21no—
103C4⋊Dic19—41no—
104C4⋊Dic19—41no—
105C4⋊Dic19D812yes—
106Dic19⋊C4—42no—
107Dic19⋊C4—41no—
108Dic19⋊C4—41no—
109Dic19⋊C4—81no—
110C4×Dic19—42no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117#7765—191nomaximal, Sylow
118C23×C19#12011yescharacteristic
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126Q8×C19—42no—
127Q8×C19—42no—
128Q8×C19—81no—
129Q8×C19—81no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×C4×C19C2×D811yescharacteristic
146C2×C4×C19#13511yescharacteristic
147C2×C4×C19#13511yescharacteristic
148C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C19#13711yescharacteristic
150C2×C4×C19#13711yescharacteristic
151C2×Dic19—22no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160D76—42no—
161D76—81no—
162C8×C19—42no—
163C19⋊C8—81no—
164C19⋊C8—81no—
165#2727—191no—
166#2057D1911yescharacteristic, complemented
167#2043—191no—
168#2023—191no—
169#1271—191no—
170#1271—191no—
171#1270—191no—
172C22×C19#44711yescharacteristic
173C22×C19#45211yescharacteristic
174C22×C19#45211yescharacteristic
175C22×C19#45411yescharacteristic
176C22×C19#45511yescharacteristic
177C22×C19#45611yescharacteristic
178C22×C19B(4,𝔽2)11yescharacteristic
179C2×D19—81no—
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C2×D19—81no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—81no—
193C4×C19—82no—
194C4×C19—81no—
195Dic19—42no—
196Dic19—81no—
197Dic19—81no—
198C2×C4⋊Q8C2×D1911yescharacteristic
199C2×#126—381no—
200C2×#107—21no—
201C2×#103—381no—
202C2×#103—381no—
203C2×#102—381no—
204#399—381no—
205#396—381no—
206#394—381no—
207#390—191no—
208#389—191no—
209#389—381no—
210#389C2×D1911yescharacteristic
211#388—381no—
212#340—21no—
213#340—381no—
214#336—191no—
215#336—191no—
216#336C2×D1911yescharacteristic
217C2×C19#159811yescharacteristic
218C2×C19#160311yescharacteristic
219C2×C19#160611yescharacteristic
220C2×C19#163811yescharacteristic
221C2×C19#164111yescharacteristic
222C2×C19#164711yescharacteristic
223C2×C19#166411yescharacteristic
224D19—161no—
225C22×Q8—21no—
226C22×D4—191no—
227C22×C8—21no—
228C22×C8—381no—
229C22×C8—381no—
230C4⋊Q8—42no—
231#126—762no—
232#126—762no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—191no—
237C2×C4⋊C4—191no—
238C2×C4⋊C4—191no—
239C2×C4⋊C4—381no—
240C2×C4⋊C4—381no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4C22⋊D1911yescharacteristic
243C2×C4⋊C4C22⋊D1911yescharacteristic
244C2×C22⋊C4—381no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4—381no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C42—381no—
251C2×C42C22×D1911yescharacteristic
252#107—42no—
253#103—762no—
254#103—762no—
255#102—762no—
256#95—21no—
257#95—381no—
258#95—381no—
259C19#776511yescharacteristic, complemented, Sylow
260C24—381no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—381no—
268C2×D4—381no—
269C2×D4—761no—
270C2×D4—761no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4D4×D1911yescharacteristic
278C22×C4D4×D1911yescharacteristic
279C22×C4C2×C22⋊D1911yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—761no—
284C2×C8—761no—
285C2×C8—761no—
286C2×C8—761no—
287C2×C8—761no—
288C2×C8—761no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—192no—
299C4⋊C4—381no—
300C4⋊C4—761no—
301C4⋊C4—761no—
302C4⋊C4—762no—
303C4⋊C4—761no—
304C4⋊C4—761no—
305C4⋊C4—1521no—
306C22⋊C4—762no—
307C22⋊C4—762no—
308C22⋊C4—761no—
309C22⋊C4—761no—
310C22⋊C4—761no—
311C22⋊C4—761no—
312C22⋊C4—1521no—
313C22⋊C4—1521no—
314C42—41no—
315C42—762no—
316C23—761no—
317C23—761no—
318C23—761no—
319C23—761no—
320C23—761no—
321C23—761no—
322C23—761no—
323C23#1059738311yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—81no—
327Q8—81no—
328D4—762no—
329D4—1521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—382no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4D8×D1911yescharacteristic
355C2×C4#1059735711yescharacteristic
356C2×C4#1059736411yescharacteristic
357C2×C4#1059736511yescharacteristic
358C2×C4#1059738811yescharacteristic
359C2×C4#1059739611yescharacteristic
360C8—42no—
361C8—1521no—
362C8—1521no—
363C22—1521no—
364C22—1521no—
365C22—1521no—
366C22—1521no—
367C22—1521no—
368C22—1521no—
369C22—1521no—
370C22#1192667611yescharacteristic
371C22#1192670411yescharacteristic
372C22#1192670511yescharacteristic
373C22#1192671511yescharacteristic
374C22#1192672011yescharacteristic
375C22#1192672611yescharacteristic
376C22#1192673011yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—81no—
384C4—82no—
385C4—81no—
386C4—762no—
387C4—1521no—
388C4—1521no—
389C2—3041no—
390C2#1456256811yescharacteristic
391C2#1456259611yescharacteristic
392C2#1456261411yescharacteristic
393C2#1456280611yescharacteristic
394C2#1456282711yescharacteristic
395C2#1456286711yescharacteristic
396C2#1456296711yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2057C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2057D19
hypocenterC19#7765
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
2. #14564878C2semidirect
4. #14561458C2semidirect
5. #14561457C2semidirect
7. C19×#2057C2semidirect
166. #2057D19semidirect
259. C19#7765semidirect

Maximal subgroups

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

subgroupindex
#145705952
#145648782
#145647682
#145614582
#145614572
#145614552
C19×#20572
#776519