Finite Group Databasebeta

← #18071613

Subgroups — #18071613

Order 4864.

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

normal subgroups only

This group has 420 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#14570594C211yesmaximal, characteristic
2#14565163C211yesmaximal, characteristic
3#14565113C211yesmaximal, characteristic, complemented
4#14565108C211yesmaximal, characteristic, complemented
5#14561459C211yesmaximal, characteristic, complemented
6#14561457C211yesmaximal, characteristic, complemented
7C19×#1270C211yesmaximal, characteristic
8C2×#10597325—21no—
9C2×#10597275—21no—
10C2×#10597264—21no—
11C2×#10597274—21no—
12C2×#10597289—21no—
13#11926480—21no—
14#11926467—21no—
15#11926458—21no—
16#11926442C2211yescharacteristic
17#11926442C2211yescharacteristic
18#11926439—21no—
19#11926437—21no—
20#11926414C2211yescharacteristic
21#11926307—21no—
22#11926307—21no—
23#11926299C2211yescharacteristic
24C19×#390C2211yescharacteristic
25C19×#336C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×D4×C19D411yescharacteristic
28C22×C8×C19—21no—
29C22×C8×C19—21no—
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C22⋊C4×C19—21no—
32C2×C22⋊C4×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—21no—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19D411yescharacteristic
42C2×C4⋊Dic19D411yescharacteristic
43C2×C4⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×C4×Dic19—21no—
50C22×C19⋊C8—21no—
51#10597325—42no—
52#10597325—42no—
53#10597289—42no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57#10597275—42no—
58#10597274—42no—
59#10597264—42no—
60C24×C19—21no—
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—41no—
64C2×D4×C19—41no—
65C22×C4×C19—21no—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×Dic19—21no—
70C22×Dic19—21no—
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—41no—
74C2×C8×C19—22no—
75C2×C8×C19—22no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C4⋊C4×C19—41no—
81C22⋊C4×C19—41no—
82C22⋊C4×C19—41no—
83C22⋊C4×C19—41no—
84C22⋊C4×C19—41no—
85C42×C19—41no—
86C22⋊Dic19—42no—
87C22⋊Dic19—42no—
88C22⋊Dic19—81no—
89C22⋊Dic19—81no—
90C4⋊Dic19—21no—
91C4⋊Dic19—21no—
92C4⋊Dic19—21no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99C4⋊Dic19—41no—
100C4⋊Dic19—41no—
101C4⋊Dic19D812yes—
102Dic19⋊C4—42no—
103Dic19⋊C4—41no—
104Dic19⋊C4—41no—
105Dic19⋊C4—41no—
106Dic19⋊C4—41no—
107Dic19⋊C4—81no—
108C4×Dic19—42no—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112#7793—191nomaximal, Sylow
113C23×C19—41no—
114C23×C19—41no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19#12011yescharacteristic
121D4×C19—42no—
122D4×C19—81no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19C2×D811yescharacteristic
133C2×C4×C19#13511yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C2×Dic19—22no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—81no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153C8×C19—42no—
154C8×C19—42no—
155C19⋊C8—42no—
156#2727—191no—
157#2093—191no—
158#2084—191no—
159#2083—191no—
160#1271—191no—
161#1271—191no—
162#1270D1911yescharacteristic
163C22×C19—81no—
164C22×C19—81no—
165C22×C19—81no—
166C22×C19—81no—
167C22×C19—81no—
168C22×C19—81no—
169C22×C19—81no—
170C22×C19#44711yescharacteristic
171C22×C19#44911yescharacteristic
172C22×C19#45211yescharacteristic
173C22×C19#45311yescharacteristic
174C22×C19#45611yescharacteristic
175C22×C19#45611yescharacteristic
176C22×C19#45811yescharacteristic
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—81no—
184Dic19—42no—
185Dic19—81no—
186Dic19—81no—
187Dic19—81no—
188Dic19—161no—
189C2×#126—381no—
190C2×#107—381no—
191C2×#107—381no—
192C2×#106—381no—
193C2×#102—381no—
194#399—381no—
195#396—381no—
196#394—381no—
197#390C2×D1911yescharacteristic
198#389—191no—
199#389—191no—
200#389—381no—
201#388—381no—
202#384—191no—
203#340—381no—
204#340—381no—
205#336—191no—
206#336C2×D1911yescharacteristic
207#336C2×D1911yescharacteristic
208C2×C19—161no—
209C2×C19#160911yescharacteristic
210C2×C19#161011yescharacteristic
211C2×C19#161811yescharacteristic
212C2×C19#162111yescharacteristic
213C2×C19#164711yescharacteristic
214C2×C19#165211yescharacteristic
215C2×C19#166011yescharacteristic
216C22×D4D7611yescharacteristic
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—381no—
220#126—762no—
221#126—762no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—381no—
231C2×C4⋊C4—381no—
232C2×C4⋊C4—381no—
233C2×C4⋊C4D7611yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—381no—
238C2×C22⋊C4—381no—
239C2×C22⋊C4—381no—
240C2×C42—381no—
241C2×C42C22×D1911yescharacteristic
242#107—762no—
243#107—762no—
244#106—762no—
245#102—762no—
246#95—381no—
247#95—381no—
248#95—381no—
249C19#779311yescharacteristic, complemented, Sylow
250C24—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—381no—
257C22×C4—381no—
258C22×C4—381no—
259C22×C4—381no—
260C22×C4—761no—
261C22×C4C2×D7611yescharacteristic
262C22×C4D4×D1911yescharacteristic
263C22×C4D4×D1911yescharacteristic
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—382no—
271C2×C8—761no—
272C2×C8—761no—
273C4⋊C4—41no—
274C4⋊C4—192no—
275C4⋊C4—381no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C4⋊C4—761no—
281C4⋊C4—761no—
282C4⋊C4—762no—
283C4⋊C4—761no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C4⋊C4—761no—
291C4⋊C4—1521no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—762no—
297C22⋊C4—762no—
298C22⋊C4—1521no—
299C22⋊C4—1521no—
300C42—41no—
301C42—762no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#1059732811yescharacteristic
310D4—42no—
311D4—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—382no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—1521no—
334C2×C4—1521no—
335C2×C4—1521no—
336C2×C4#1059735011yescharacteristic
337C2×C4#1059735511yescharacteristic
338C2×C4D8×D1911yescharacteristic
339C2×C4#1059735711yescharacteristic
340C2×C4#1059736011yescharacteristic
341C2×C4#1059736211yescharacteristic
342C8—42no—
343C8—42no—
344C8—762no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#1192667911yescharacteristic
353C22#1192669011yescharacteristic
354C22#1192670811yescharacteristic
355C22#1192671411yescharacteristic
356C22#1192672811yescharacteristic
357C22#1192672811yescharacteristic
358C22#1192673511yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—3041no—
367C4—762no—
368C4—1521no—
369C4—1521no—
370C4—1521no—
371C2—161no—
372C2#1456263311yescharacteristic
373C2#1456263911yescharacteristic
374C2#1456268511yescharacteristic
375C2#1456270111yescharacteristic
376C2#1456287311yescharacteristic
377C2#1456290811yescharacteristic
378C2#1456294711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7793
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
3. #14565113C2semidirect
4. #14565108C2semidirect
5. #14561459C2semidirect
6. #14561457C2semidirect
249. C19#7793semidirect

Maximal subgroups

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

subgroupindex
#145705942
#145651632
#145651132
#145651082
#145614592
#145614572
C19×#12702
#779319