Finite Group Databasebeta

← #18071807

Subgroups — #18071807

Order 4864.

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

normal subgroups only

This group has 418 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#14570564C211yesmaximal, characteristic
2#14565197C211yesmaximal, characteristic, complemented
3#14565169C211yesmaximal, characteristic
4#14561458C211yesmaximal, characteristic, complemented
5#14561457C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2100C211yesmaximal, characteristic, complemented
8C2×#10597340—21no—
9C2×#10597265—21no—
10C2×#10597266—21no—
11#11926477—21no—
12#11926471—21no—
13#11926470—21no—
14#11926446C2211yescharacteristic
15#11926442C2211yescharacteristic
16#11926418—21no—
17#11926415—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C19×#389C2211yescharacteristic
23C19×#384C2211yescharacteristic
24C19×#340—21no—
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×D76D411yescharacteristic
28C22×C4×D19—21no—
29C22×C8×C19—21no—
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×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×C4⋊Dic19D411yescharacteristic
43C2×C4⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C22×C19⋊C8—21no—
48C22×C19⋊C8—21no—
49#10597340—42no—
50#10597340—42no—
51C19×#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56#10597266—42no—
57#10597265—42no—
58C23×D19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—41no—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—21no—
68C2×D76—21no—
69C2×D76—41no—
70C2×D76—41no—
71C2×D76SD1612yes—
72C2×C4×D19—42no—
73C2×C4×D19—81no—
74C2×C4×D19—81no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C4⋊C4×C19—21no—
79C4⋊C4×C19—21no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—42no—
82C4⋊C4×C19—42no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C42×C19—41no—
88(C2×D19)⋊C4—42no—
89(C2×D19)⋊C4—42no—
90(C2×D19)⋊C4—42no—
91(C2×D19)⋊C4—41no—
92(C2×D19)⋊C4—41no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—41no—
95C4⋊Dic19—21no—
96C4⋊Dic19—21no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99Dic19⋊C4—41no—
100Dic19⋊C4—41no—
101Dic19⋊C4—81no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108#7824—191nomaximal, Sylow
109C23×C19#12011yescharacteristic
110C22×D19—22no—
111C22×D19—41no—
112C22×D19—41no—
113C22×D19—41no—
114C22×D19—41no—
115C22×D19—41no—
116C22×D19—41no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—81no—
130C2×C4×C19—81no—
131C2×C4×C19—81no—
132C2×C4×C19C2×SD1611yescharacteristic
133C2×C4×C19#13511yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147D76—42no—
148D76—81no—
149C4×D19—84no—
150C8×C19—81no—
151C19⋊C8—42no—
152C19⋊C8—81no—
153#2724—191no—
154#2100—191no—
155#2100D1911yescharacteristic, complemented
156#2094—191no—
157#1271—191no—
158#1271—191no—
159#1270—191no—
160C22×C19#45011yescharacteristic
161C22×C19#45211yescharacteristic
162C22×C19#45211yescharacteristic
163C22×C19#45311yescharacteristic
164C22×C19#45411yescharacteristic
165C22×C19#45411yescharacteristic
166C22×C19#45811yescharacteristic
167C2×D19—42no—
168C2×D19—42no—
169C2×D19—42no—
170C2×D19—81no—
171C2×D19—81no—
172C2×D19—81no—
173C2×D19—81no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—81no—
181C4×C19—81no—
182C4×C19—161no—
183Dic19—81no—
184Dic19—81no—
185Dic19—81no—
186C2×#123—381no—
187C2×#106—381no—
188C2×#102—381no—
189#398—381no—
190#397—381no—
191#397—381no—
192#390—191no—
193#389—191no—
194#389C2×D1911yescharacteristic
195#385—381no—
196#385—381no—
197#384C2×D1911yescharacteristic
198#340—21no—
199#340—21no—
200#340—381no—
201#340—381no—
202#336—191no—
203#336—191no—
204#336C2×D1911yescharacteristic
205C2×C19#161311yescharacteristic
206C2×C19#161511yescharacteristic
207C2×C19#161511yescharacteristic
208C2×C19#163011yescharacteristic
209C2×C19#163511yescharacteristic
210C2×C19#163511yescharacteristic
211C2×C19#165711yescharacteristic
212D19—82no—
213C22×D4—191no—
214C23×C4—381no—
215C22×C8—21no—
216C22×C8—381no—
217C22×C8—381no—
218#123—762no—
219#123—762no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—191no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4C22⋊D1911yescharacteristic
230C2×C4⋊C4C22⋊D1911yescharacteristic
231C2×C22⋊C4—381no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C22⋊C4—381no—
235C2×C22⋊C4—381no—
236C2×C42C22×D1911yescharacteristic
237#106—762no—
238#102—762no—
239#95—21no—
240#95—381no—
241#95—381no—
242#95—381no—
243#95—381no—
244C19#782411yescharacteristic, complemented, Sylow
245C24—381no—
246C2×D4—192no—
247C2×D4—381no—
248C2×D4—761no—
249C2×D4—761no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—381no—
254C22×C4—381no—
255C22×C4—381no—
256C22×C4—762no—
257C22×C4—1521no—
258C22×C4—1521no—
259C22×C4D4×D1911yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—382no—
266C2×C8—761no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—761no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4—761no—
283C4⋊C4—761no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—1521no—
287C22⋊C4—762no—
288C22⋊C4—762no—
289C22⋊C4—762no—
290C22⋊C4—761no—
291C22⋊C4—761no—
292C22⋊C4—761no—
293C22⋊C4—761no—
294C42—41no—
295C23—382no—
296C23—761no—
297C23—761no—
298C23—761no—
299C23—761no—
300C23—761no—
301C23—761no—
302C23#1059738311yescharacteristic
303D4—762no—
304D4—1521no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—761no—
321C2×C4—761no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—1524no—
330C2×C4SD16×D1911yescharacteristic
331C2×C4#1059736011yescharacteristic
332C2×C4#1059736411yescharacteristic
333C2×C4#1059736511yescharacteristic
334C2×C4#1059738811yescharacteristic
335C2×C4#1059739611yescharacteristic
336C8—81no—
337C8—762no—
338C8—1521no—
339C22—762no—
340C22—762no—
341C22—762no—
342C22—1521no—
343C22—1521no—
344C22—1521no—
345C22—1521no—
346C22#1192669311yescharacteristic
347C22#1192670411yescharacteristic
348C22#1192670511yescharacteristic
349C22#1192671011yescharacteristic
350C22#1192671511yescharacteristic
351C22#1192671611yescharacteristic
352C22#1192673311yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—81no—
361C4—161no—
362C4—1521no—
363C4—1521no—
364C4—1521no—
365C2—1522no—
366C2#1456265311yescharacteristic
367C2#1456266411yescharacteristic
368C2#1456266511yescharacteristic
369C2#1456275511yescharacteristic
370C2#1456278311yescharacteristic
371C2#1456278511yescharacteristic
372C2#1456293211yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2100C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2100D19
hypocenterC19#7824
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
2. #14565197C2semidirect
4. #14561458C2semidirect
5. #14561457C2semidirect
7. C19×#2100C2semidirect
155. #2100D19semidirect
244. C19#7824semidirect

Maximal subgroups

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

subgroupindex
#145705642
#145651972
#145651692
#145614582
#145614572
#145614552
C19×#21002
#782419