Finite Group Databasebeta

← #18085421

Subgroups — #18085421

Order 4864.

910 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 103 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#14574410C211yesmaximal, characteristic, complemented
2#14571922C212yesmaximal
3#14562208C212yesmaximal, complemented
4#14561503C211yesmaximal, characteristic, complemented
5C19×#1779C211yesmaximal, characteristic
6C2×#10597370—22no—
7C2×#10597370C2212yes—
8#11926880—22no—
9#11926785—22no—
10#11926702—22no—
11#11926417—24no—
12#11926417—22no—
13#11926404—22no—
14#11926404C2212yes—
15#11926400—22no—
16#11926282—24no—
17C24×C4×C19C2211yescharacteristic
18C2×C19×C22⋊C8—22no—
19C2×C19×C22⋊C8C2211yescharacteristic
20C2×C19×C22⋊C8C2211yescharacteristic
21C25×C19D411yescharacteristic
22C23×C4×C19—22no—
23C23×C4×C19—21no—
24C23×C4×C19—22no—
25C23×C4×C19—21no—
26C23×C4×C19—44no—
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C22×Dic38D412yes—
30C22×C8×C19—21no—
31C22×C8×C19D412yes—
32C2×C22⋊Dic19—24no—
33C2×C22⋊Dic19—24no—
34C2×C22⋊Dic19—22no—
35C2×C22⋊Dic19—22no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19D412yes—
38#10597370—22no—
39#10597370—22no—
40#10597370—22no—
41#10597370—22no—
42#10597370—48no—
43C2×Dic19⋊C4—24no—
44C2×Dic19⋊C4—22no—
45C2×Dic76—22no—
46C19×C22⋊C8—22no—
47C19×C22⋊C8—22no—
48C19×C22⋊C8—44no—
49C19⋊#95—24no—
50C19⋊#95D414yes—
51#10597275—22no—
52#10597273—24no—
53C24×C19—22no—
54C24×C19—21no—
55C24×C19—21no—
56C24×C19—22no—
57C24×C19—42no—
58C24×C19—42no—
59C24×C19Q1612yescomplemented
60C24×C19C2×D411yescharacteristic
61C22×C4×C19—24no—
62C22×C4×C19—28no—
63C22×C4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19—44no—
68C22×C4×C19—42no—
69C22×C4×C19—44no—
70C22×C4×C19—42no—
71C22×C4×C19—44no—
72C22×C4×C19—42no—
73C22×C4×C19—41no—
74C22×C4×C19—42no—
75C22×C4×C19—41no—
76C22×C4×C19C2×D412yes—
77C22×C4×C19C2×D412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C22×Dic19—22no—
81C22×Dic19—22no—
82C22×Dic19—24no—
83C2×Dic38—22no—
84C2×Dic38—22no—
85C2×Dic38—44no—
86C2×C8×C19—22no—
87C2×C8×C19—42no—
88C2×C8×C19—42no—
89C2×C8×C19—41no—
90C22⋊Dic19—48no—
91C22⋊Dic19—48no—
92C22⋊Dic19—42no—
93C22⋊Dic19—42no—
94C22⋊Dic19—42no—
95C22⋊Dic19—42no—
96C4⋊Dic19—22no—
97C4⋊Dic19—22no—
98C4⋊Dic19—44no—
99Dic19⋊C4—48no—
100Dic19⋊C4—42no—
101Dic19⋊C4—42no—
102Dic76—82no—
103#10324—191nomaximal, Sylow
104C23×C19—24no—
105C23×C19—24no—
106C23×C19—22no—
107C23×C19—22no—
108C23×C19—24no—
109C23×C19—22no—
110C23×C19—41no—
111C23×C19—44no—
112C23×C19—41no—
113C23×C19—42no—
114C23×C19—41no—
115C23×C19—42no—
116C23×C19—41no—
117C23×C19—44no—
118C23×C19—48no—
119C23×C19—41no—
120C23×C19—42no—
121C23×C19—41no—
122C23×C19#12012yes—
123C23×C19#12111yescharacteristic
124C23×C19C2×Q1611yescharacteristic
125C23×C19#13511yescharacteristic
126C23×C19#13712yes—
127C2×C4×C19—24no—
128C2×C4×C19—22no—
129C2×C4×C19—24no—
130C2×C4×C19—22no—
131C2×C4×C19—42no—
132C2×C4×C19—41no—
133C2×C4×C19—44no—
134C2×C4×C19—48no—
135C2×C4×C19—42no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—44no—
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12112yes—
141C2×C4×C19#12711yescharacteristic
142C2×Dic19—44no—
143C2×Dic19—44no—
144C2×Dic19—44no—
145C2×Dic19—44no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—44no—
149Dic38—44no—
150Dic38—82no—
151C8×C19—42no—
152C8×C19—81no—
153#3189—191no—
154#2848—192no—
155#1779D1911yescharacteristic
156#1520—192no—
157#1289—191no—
158C22×C19—22no—
159C22×C19—21no—
160C22×C19—22no—
161C22×C19—21no—
162C22×C19—28no—
163C22×C19—24no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—42no—
167C22×C19—44no—
168C22×C19—44no—
169C22×C19—44no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—42no—
174C22×C19—42no—
175C22×C19—42no—
176C22×C19#39211yescharacteristic
177C22×C19#45112yes—
178C22×C19#45212yes—
179C22×C19#46711yescharacteristic
180C22×C19#47011yescharacteristic
181C4×C19—21no—
182C4×C19—22no—
183C4×C19—42no—
184C4×C19B(4,𝔽2)12yes—
185Dic19—84no—
186Dic19—82no—
187Dic19—82no—
188C24×C4C2×D1911yescharacteristic
189C2×C22⋊Q8—192no—
190C2×C22⋊Q8—382no—
191#484—382no—
192#467—382no—
193#451—382no—
194C2×C22⋊C8—22no—
195C2×C22⋊C8C2×D1911yescharacteristic
196C2×C22⋊C8C2×D1911yescharacteristic
197#385—384no—
198#385—382no—
199#380—192no—
200#380—382no—
201#379—382no—
202#328—384no—
203C2×C19—22no—
204C2×C19—22no—
205C2×C19—21no—
206C2×C19—21no—
207C2×C19—44no—
208C2×C19#200111yescharacteristic
209C2×C19#201011yescharacteristic
210C2×C19#202111yescharacteristic
211C25D7611yescharacteristic
212C22×Q8—192no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—22no—
217C23×C4—44no—
218C23×C4D7611yescharacteristic
219C23×C4C22×D1911yescharacteristic
220C2×Q16—382no—
221C22×C8—21no—
222C22×C8C22⋊D1912yes—
223C22⋊Q8—382no—
224C22⋊Q8—382no—
225C22⋊Q8—382no—
226C22⋊Q8—382no—
227C22⋊Q8—768no—
228C2×C4⋊C4—192no—
229C2×C4⋊C4—384no—
230C2×C4⋊C4—382no—
231C2×C4⋊C4—382no—
232C2×C22⋊C4—384no—
233C2×C22⋊C4—384no—
234C2×C22⋊C4—382no—
235C2×C22⋊C4—382no—
236#107—382no—
237#103—384no—
238C22⋊C8—22no—
239C22⋊C8—22no—
240C22⋊C8—44no—
241#95—194no—
242#95—384no—
243C19#1032411yescharacteristic, complemented, Sylow
244C24—21no—
245C24—22no—
246C24—21no—
247C24—22no—
248C24—42no—
249C24—42no—
250C24Dic7612yescomplemented
251C24C2×D7611yescharacteristic
252C2×Q8—382no—
253C2×Q8—382no—
254C2×Q8—764no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—44no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—44no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—384no—
271C22×C4—382no—
272C22×C4—382no—
273C22×C4#6454111yescharacteristic
274C22×C4D4×D1912yes—
275C22×C4D4×D1912yes—
276C22×C4C2×C22⋊D1911yescharacteristic
277Q16—1522no—
278C2×C8—22no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—41no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—768no—
285C4⋊C4—764no—
286C4⋊C4—762no—
287C4⋊C4—762no—
288C22⋊C4—768no—
289C22⋊C4—768no—
290C22⋊C4—762no—
291C22⋊C4—762no—
292C22⋊C4—762no—
293C22⋊C4—762no—
294C23—24no—
295C23—24no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—24no—
300C23—41no—
301C23—44no—
302C23—41no—
303C23—42no—
304C23—41no—
305C23—42no—
306C23—41no—
307C23—44no—
308C23—48no—
309C23—41no—
310C23—42no—
311C23—41no—
312C23#1059732812yes—
313C23#1059735011yescharacteristic
314C23C2×Dic7611yescharacteristic
315C23#1059735512yes—
316C23#1059737611yescharacteristic
317Q8—764no—
318Q8—1522no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—764no—
332C2×C4—764no—
333C2×C4—764no—
334C2×C4—764no—
335C2×C4—764no—
336C2×C4—762no—
337C2×C4—762no—
338C2×C4#1059733012yes—
339C2×C4#1059738311yescharacteristic
340C2×C4#1059738611yescharacteristic
341C8—42no—
342C8—81no—
343C22—22no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—24no—
348C22—28no—
349C22—41no—
350C22—41no—
351C22—42no—
352C22—44no—
353C22—44no—
354C22—42no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22#1192645311yescharacteristic
362C22#1192670212yes—
363C22#1192670812yes—
364C22#1192678511yescharacteristic
365C22#1192680211yescharacteristic
366C4—21no—
367C4—22no—
368C4—42no—
369C4—1524no—
370C4—1522no—
371C4—1522no—
372C4#1192673012yes—
373C2—22no—
374C2—21no—
375C2—22no—
376C2—21no—
377C2—44no—
378C2#1456464511yescharacteristic
379C2#1456470211yescharacteristic
380C2#1456476111yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC22×C19#392
prime radicalC25×C19D4
hypercenter#1779D19
hypocenterC19#10324
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. #14574410C2semidirect
3. #14562208C2semidirect
4. #14561503C2semidirect
59. C24×C19Q16semidirect
243. C19#10324semidirect
250. C24Dic76semidirect

Maximal subgroups

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

subgroupindex
#145744102
#145719222
#145622082
#145615032
C19×#17792
#1032419