Finite Group Databasebeta

← #18071610

Subgroups — #18071610

Order 4864.

420 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 87 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#14565163C211yesmaximal, characteristic
2#14565111C211yesmaximal, characteristic, complemented
3#14565106C211yesmaximal, characteristic, complemented
4#14561458C211yesmaximal, characteristic, complemented
5#14561458C211yesmaximal, characteristic, complemented
6#14561456C211yesmaximal, characteristic
7C19×#2727C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597264—21no—
10C2×#10597265—21no—
11C2×#10597289—21no—
12#11926414C2211yescharacteristic
13#11926306—21no—
14#11926306—21no—
15#11926299C2211yescharacteristic
16#11926299C2211yescharacteristic
17#11926299C2211yescharacteristic
18C2×C19×#126—21no—
19C19×#399—21no—
20C19×#396—21no—
21C19×#394—21no—
22C19×#390C2211yescharacteristic
23C19×#389—21no—
24C19×#389C2211yescharacteristic
25C19×#389C2211yescharacteristic
26C19×#388—21no—
27C22×D4×C19D411yescharacteristic
28C19×#126—42no—
29C19×#126—42no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52C22×C19⋊C8—21no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95—21no—
56#10597289—42no—
57#10597265—42no—
58#10597264—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×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×Dic19—41no—
74C4⋊C4×C19—21no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19—21no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—42no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—81no—
86C4⋊C4×C19D812yes—
87C22⋊C4×C19—42no—
88C22⋊C4×C19—42no—
89C22⋊C4×C19—41no—
90C22⋊C4×C19—41no—
91C22⋊C4×C19—41no—
92C22⋊C4×C19—41no—
93C22⋊C4×C19—81no—
94C22⋊C4×C19—81no—
95C42×C19—41no—
96C42×C19—42no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99C4⋊Dic19—41no—
100C4⋊Dic19—41no—
101C4⋊Dic19—41no—
102C4⋊Dic19—41no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
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—22no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
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—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19C2×D811yescharacteristic
145C2×C4×C19#13511yescharacteristic
146C2×C4×C19#13511yescharacteristic
147C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C19#13711yescharacteristic
150C2×Dic19—81no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153C19⋊C8—42no—
154C19⋊C8—42no—
155C19⋊C8—42no—
156#2727D1911yescharacteristic
157#2093—191no—
158#2084—191no—
159#2083—191no—
160#1271—191no—
161#1271—191no—
162#1270—191no—
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—42no—
184C4×C19—81no—
185C4×C19—81no—
186C4×C19—81no—
187C4×C19—81no—
188Dic19—161no—
189C2×#126—21no—
190C2×#107—381no—
191C2×#107—381no—
192C2×#106—381no—
193C2×#102—381no—
194#399—21no—
195#396—21no—
196#394—21no—
197#390C2×D1911yescharacteristic
198#389—21no—
199#389C2×D1911yescharacteristic
200#389C2×D1911yescharacteristic
201#388—21no—
202#384—191no—
203#340—381no—
204#340—381no—
205#336—191no—
206#336—191no—
207#336—191no—
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×D4C22⋊D1911yescharacteristic
217C22×C8—381no—
218C22×C8—381no—
219C22×C8—381no—
220#126—42no—
221#126—42no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4C22⋊D1911yescharacteristic
230C2×C4⋊C4C22⋊D1911yescharacteristic
231C2×C4⋊C4C22⋊D1911yescharacteristic
232C2×C4⋊C4C22⋊D1911yescharacteristic
233C2×C4⋊C4C22⋊D1911yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D1911yescharacteristic
242#107—762no—
243#107—762no—
244#106—762no—
245#102—762no—
246#95—21no—
247#95—21no—
248#95—21no—
249C19#779311yescharacteristic, complemented, Sylow
250C24—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—761no—
261C22×C4C2×C22⋊D1911yescharacteristic
262C22×C4C2×C22⋊D1911yescharacteristic
263C22×C4C2×C22⋊D1911yescharacteristic
264C2×C8—382no—
265C2×C8—382no—
266C2×C8—382no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—761no—
271C2×C8—761no—
272C2×C8—761no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C4⋊C4—761no—
291C4⋊C4#6452512yes—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C42—41no—
301C42—42no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#1059739911yescharacteristic
310D4—42no—
311D4—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—1521no—
334C2×C4—1521no—
335C2×C4—1521no—
336C2×C4C2×#6452511yescharacteristic
337C2×C4#1059737811yescharacteristic
338C2×C4#1059739511yescharacteristic
339C2×C4#1059739611yescharacteristic
340C2×C4#1059739611yescharacteristic
341C2×C4#1059739711yescharacteristic
342C8—762no—
343C8—762no—
344C8—762no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#1192667811yescharacteristic
353C22#1192668911yescharacteristic
354C22#1192670611yescharacteristic
355C22#1192671211yescharacteristic
356C22#1192672711yescharacteristic
357C22#1192672711yescharacteristic
358C22#1192673411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—3041no—
371C2—161no—
372C2#1456263211yescharacteristic
373C2#1456263811yescharacteristic
374C2#1456268311yescharacteristic
375C2#1456270011yescharacteristic
376C2#1456287011yescharacteristic
377C2#1456290511yescharacteristic
378C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2727C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2727D19
hypocenterC19#7793
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2727

Complements

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

NH ≅ G/Ntype
2. #14565111C2semidirect
3. #14565106C2semidirect
4. #14561458C2semidirect
5. #14561458C2semidirect
249. C19#7793semidirect

Maximal subgroups

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

subgroupindex
#145651632
#145651112
#145651062
#145614582
#145614562
C19×#27272
#779319