Finite Group Databasebeta

← #18071471

Subgroups — #18071471

Order 4864.

422 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 79 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#14571617C211yesmaximal, characteristic
2#14564878C211yesmaximal, characteristic, complemented
3#14564768C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic, complemented
5#14561457C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2024C211yesmaximal, characteristic, complemented
8C2×#10597292—21no—
9C2×#10597292—21no—
10C2×#10597266—21no—
11#11926471—21no—
12#11926462—21no—
13#11926455—21no—
14#11926446C2211yescharacteristic
15#11926442C2211yescharacteristic
16#11926436—21no—
17#11926434—21no—
18#11926431—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#103—21no—
24C19×#391C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19D411yescharacteristic
29C22×D76D411yescharacteristic
30C22×C8×C19—21no—
31C19×C4⋊Q8—42no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×(C2×D19)⋊C4—21no—
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×C4⋊Dic19D411yescharacteristic
43C2×C4⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×C4×Dic19—21no—
47C22×C19⋊C8—21no—
48C22×C19⋊C8—21no—
49C19×#103—42no—
50C19×#95—21no—
51C19×#95—21no—
52#10597292—42no—
53#10597292—42no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58#10597266—42no—
59C23×D19—21no—
60C2×Q8×C19—22no—
61C2×Q8×C19—21no—
62C2×Q8×C19—21no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—41no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79C2×D76—21no—
80C2×D76—21no—
81C2×D76—41no—
82C2×D76—41no—
83C2×C8×C19—41no—
84C2×C8×C19—41no—
85C2×C8×C19—41no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C42×C19—41no—
92(C2×D19)⋊C4—41no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—41no—
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—81no—
97(C2×D19)⋊C4—81no—
98(C2×D19)⋊C4—81no—
99(C2×D19)⋊C4—81no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—41no—
103C4⋊Dic19—41no—
104Dic19⋊C4—41no—
105Dic19⋊C4—41no—
106C4×Dic19—81no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113#7773—191nomaximal, Sylow
114C23×C19#12011yescharacteristic
115C22×D19—41no—
116C22×D19—41no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122Q8×C19—42no—
123Q8×C19—42no—
124Q8×C19—42no—
125Q8×C19—81no—
126Q8×C19—81no—
127Q8×C19—81no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—81no—
142C2×C4×C19—81no—
143C2×C4×C19#13511yescharacteristic
144C2×C4×C19#13511yescharacteristic
145C2×C4×C19#13511yescharacteristic
146C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C19#13711yescharacteristic
148C2×C4×C19#13711yescharacteristic
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158D76—42no—
159D76—81no—
160C8×C19—81no—
161C19⋊C8—81no—
162C19⋊C8—81no—
163#2808—191no—
164#2043—191no—
165#2024D1911yescharacteristic, complemented
166#2023—191no—
167#1272—191no—
168#1271—191no—
169#1270—191no—
170C22×C19#44911yescharacteristic
171C22×C19#45211yescharacteristic
172C22×C19#45211yescharacteristic
173C22×C19#45411yescharacteristic
174C22×C19#45511yescharacteristic
175C22×C19#45511yescharacteristic
176C22×C19B(4,𝔽2)11yescharacteristic
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—82no—
191C4×C19—81no—
192C4×C19—81no—
193Dic19—81no—
194Dic19—81no—
195Dic19—81no—
196C2×C4⋊Q8C2×D1911yescharacteristic
197C2×#103—21no—
198C2×#103—381no—
199C2×#103—381no—
200C2×#102—381no—
201#397—381no—
202#394—381no—
203#393—381no—
204#391C2×D1911yescharacteristic
205#390—191no—
206#389—191no—
207#388—381no—
208#388—381no—
209#387—381no—
210#340—21no—
211#340—381no—
212#336—191no—
213#336—191no—
214#336C2×D1911yescharacteristic
215C2×C19#159711yescharacteristic
216C2×C19#160611yescharacteristic
217C2×C19#160611yescharacteristic
218C2×C19#163811yescharacteristic
219C2×C19#164011yescharacteristic
220C2×C19#164611yescharacteristic
221C2×C19#166211yescharacteristic
222D19—161no—
223C22×Q8—21no—
224C22×Q8C22⋊D1911yescharacteristic
225C22×D4—191no—
226C22×C8—21no—
227C22×C8—381no—
228C22×C8—381no—
229C4⋊Q8—42no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—191no—
235C2×C4⋊C4—381no—
236C2×C4⋊C4C22⋊D1911yescharacteristic
237C2×C22⋊C4—381no—
238C2×C22⋊C4—381no—
239C2×C22⋊C4—381no—
240C2×C22⋊C4—381no—
241C2×C22⋊C4—381no—
242C2×C22⋊C4—381no—
243C2×C42—381no—
244C2×C42C22×D1911yescharacteristic
245#103—42no—
246#103—762no—
247#103—762no—
248#102—762no—
249#95—21no—
250#95—21no—
251#95—381no—
252#95—381no—
253#95—381no—
254#95—381no—
255C19#777311yescharacteristic, complemented, Sylow
256C24—381no—
257C2×Q8—22no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
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—41no—
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—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—381no—
295C4⋊C4—381no—
296C4⋊C4—761no—
297C4⋊C4—761no—
298C4⋊C4—761no—
299C4⋊C4—761no—
300C22⋊C4—761no—
301C22⋊C4—761no—
302C22⋊C4—761no—
303C22⋊C4—761no—
304C22⋊C4—1521no—
305C22⋊C4—1521no—
306C22⋊C4—1521no—
307C22⋊C4—1521no—
308C42—41no—
309C42—1521no—
310C23—761no—
311C23—761no—
312C23—761no—
313C23—761no—
314C23—761no—
315C23—761no—
316C23—761no—
317C23#1059738311yescharacteristic
318Q8—42no—
319Q8—42no—
320Q8—42no—
321Q8—81no—
322Q8—81no—
323Q8—81no—
324D4—762no—
325D4—1521no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4#1059736011yescharacteristic
351C2×C4#1059736211yescharacteristic
352C2×C4#1059736411yescharacteristic
353C2×C4#1059736511yescharacteristic
354C2×C4#1059738811yescharacteristic
355C2×C4#1059739611yescharacteristic
356C8—81no—
357C8—1521no—
358C8—1521no—
359C22—1521no—
360C22—1521no—
361C22—1521no—
362C22—1521no—
363C22—1521no—
364C22—1521no—
365C22—1521no—
366C22#1192668811yescharacteristic
367C22#1192670411yescharacteristic
368C22#1192670511yescharacteristic
369C22#1192671511yescharacteristic
370C22#1192672011yescharacteristic
371C22#1192672111yescharacteristic
372C22#1192673011yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—81no—
381C4—81no—
382C4—1521no—
383C4—1521no—
384C4—1521no—
385C2—3041no—
386C2#1456256311yescharacteristic
387C2#1456261311yescharacteristic
388C2#1456261411yescharacteristic
389C2#1456280611yescharacteristic
390C2#1456282011yescharacteristic
391C2#1456286011yescharacteristic
392C2#1456295711yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2024C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2024D19
hypocenterC19#7773
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. #14564878C2semidirect
4. #14561461C2semidirect
5. #14561457C2semidirect
7. C19×#2024C2semidirect
165. #2024D19semidirect
255. C19#7773semidirect

Maximal subgroups

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

subgroupindex
#145716172
#145648782
#145647682
#145614612
#145614572
#145614552
C19×#20242
#777319