Finite Group Databasebeta

← #18085460

Subgroups — #18085460

Order 4864.

672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 89 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#14574437C211yesmaximal, characteristic
2#14568102C211yesmaximal, characteristic
3#14563715C211yesmaximal, characteristic, complemented
4#14562155C211yesmaximal, characteristic, complemented
5#14562150C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic, complemented
7C19×#2502C211yesmaximal, characteristic, complemented
8C2×#10597375—22no—
9C2×#10597376C2211yescharacteristic
10#11926877—21no—
11#11926857—21no—
12#11926792—22no—
13#11926694—21no—
14#11926683—21no—
15#11926508C2211yescharacteristic
16#11926508C2211yescharacteristic
17#11926479—22no—
18#11926445—21no—
19#11926413—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926313—22no—
22#11926281—22no—
23#11926277—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#398—22no—
27C19×#391—21no—
28C19×#385—22no—
29C19×#384—21no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19D412yes—
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C22×D76D411yescharacteristic
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—24no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C42×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×#64527—22no—
54#10597376—21no—
55#10597376—21no—
56#10597376—21no—
57#10597376—21no—
58#10597375—48no—
59C2×(C2×D19)⋊C4—24no—
60C2×(C2×D19)⋊C4—21no—
61C2×C4⋊Dic19D411yescharacteristic
62C2×Dic19⋊C4—24no—
63C2×C4×Dic19—21no—
64C2×#64520—21no—
65C2×#64520D412yes—
66C19×#95—24no—
67C19×#95D412yes—
68#10597292—22no—
69C19⋊#95D412yes—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74#10597266—22no—
75#10597264—22no—
76C24×C19C2×D411yescharacteristic
77C23×D19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—42no—
81C22×C4×C19—22no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—22no—
85C22×C4×C19—22no—
86C22×C4×C19—22no—
87C22×C4×C19—42no—
88C22×C4×C19—44no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C2×C22⋊D19—44no—
96C2×C22⋊D19—41no—
97C2×C22⋊D19—41no—
98C22×Dic19—22no—
99C22×Dic19—21no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—42no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—84no—
112C22⋊C4×C19—24no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C42×C19—42no—
116C22⋊Dic19—24no—
117#64527—82no—
118(C2×D19)⋊C4—48no—
119(C2×D19)⋊C4—41no—
120(C2×D19)⋊C4—41no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123Dic19⋊C4—48no—
124C4×Dic19—42no—
125#64520—42no—
126#64520—42no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—41no—
129#10331—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19—22no—
132C23×C19—41no—
133C23×C19#12011yescharacteristic
134C23×C19#12011yescharacteristic
135C23×C19#12111yescharacteristic
136C22×D19—42no—
137C22×D19—42no—
138C22×D19—41no—
139C22×D19—42no—
140Q8×C19—42no—
141Q8×C19—81no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—24no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—44no—
152C2×C4×C19—42no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—44no—
158C2×C4×C19—82no—
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×C4×C19#12711yescharacteristic
163C22⋊D19—82no—
164C22⋊D19—82no—
165C2×Dic19—24no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—41no—
170D76—42no—
171D76—81no—
172C19⋊C8—42no—
173C19⋊C8—81no—
174#3193—191no—
175#2502D1911yescharacteristic, complemented
176#2501—191no—
177#1821—191no—
178#1508—191no—
179#1507—191no—
180#1297—191no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—44no—
189C22×C19#39211yescharacteristic
190C22×C19#45312yes—
191C22×C19#45612yes—
192C2×D19—84no—
193C2×D19—81no—
194C2×D19—81no—
195C2×D19—81no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—44no—
200C4×C19—81no—
201C4×C19—82no—
202C4×C19—81no—
203C4×C19#45812yes—
204Dic19—44no—
205Dic19—81no—
206C2×#123—382no—
207C2×C22⋊Q8C2×D1911yescharacteristic
208C2×#121—191no—
209C22×C4⋊C4C2×D1911yescharacteristic
210#484—381no—
211#480—381no—
212#468—382no—
213#450—381no—
214#448—381no—
215#407—191no—
216#407—191no—
217#399—382no—
218#398—22no—
219#391—21no—
220#390—381no—
221#385—22no—
222#384—21no—
223#384—381no—
224C4×C22⋊C4—191no—
225C4×C22⋊C4C2×D1911yescharacteristic
226#343—382no—
227#328—382no—
228#327—382no—
229C2×C19—22no—
230C2×C19—22no—
231C2×C19—41no—
232C2×C19#200211yescharacteristic
233C2×C19#200511yescharacteristic
234C2×C19#202211yescharacteristic
235D19—161no—
236C22×Q8C22⋊D1911yescharacteristic
237C22×D4—191no—
238C22×D4—381no—
239C23×C4C22⋊D1912yes—
240C23×C4C22×D1911yescharacteristic
241C2×SD16—382no—
242C2×M16—192no—
243C2×M16—381no—
244#123—768no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249#121—381no—
250#121—381no—
251#121—381no—
252#121—381no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—191no—
262C2×C4⋊C4—384no—
263C2×C4⋊C4C22⋊D1911yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—381no—
267C2×C22⋊C4—384no—
268C2×C22⋊C4—381no—
269C2×C42—21no—
270C2×C42—381no—
271#107—382no—
272#103—382no—
273#102—382no—
274C22⋊C8—381no—
275C22⋊C8—381no—
276C22⋊C8—381no—
277C22⋊C8—381no—
278#95—24no—
279#95—192no—
280#95C22⋊D1912yes—
281C19#1033111yescharacteristic, complemented, Sylow
282C24—381no—
283C24C2×C22⋊D1911yescharacteristic
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—762no—
290C2×D4—764no—
291C2×D4—761no—
292C2×D4—761no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—382no—
302C22×C4—381no—
303C22×C4D4×D1911yescharacteristic
304C22×C4D4×D1911yescharacteristic
305C22×C4D4×D1911yescharacteristic
306C22×C4#6454311yescharacteristic
307C22×C4C2×C22⋊D1911yescharacteristic
308C22×C4C2×C22⋊D1911yescharacteristic
309SD16—1522no—
310M16—762no—
311M16—762no—
312C2×C8—382no—
313C2×C8—761no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—84no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4—768no—
326C22⋊C4—24no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—384no—
330C22⋊C4—768no—
331C22⋊C4—761no—
332C22⋊C4—761no—
333C42—42no—
334C42—762no—
335C23—22no—
336C23—22no—
337C23—41no—
338C23—762no—
339C23—762no—
340C23—761no—
341C23—762no—
342C23#1059738311yescharacteristic
343C23#1059738511yescharacteristic
344C23#1059739911yescharacteristic
345Q8—42no—
346Q8—81no—
347D4—762no—
348D4—1521no—
349D4—1522no—
350D4—1522no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—82no—
368C2×C4—384no—
369C2×C4—762no—
370C2×C4—762no—
371C2×C4—762no—
372C2×C4—761no—
373C2×C4#1059738311yescharacteristic
374C2×C4#1059738411yescharacteristic
375C2×C4#1059738511yescharacteristic
376C2×C4#1059738611yescharacteristic
377C8—762no—
378C8—1521no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—44no—
387C22—1524no—
388C22—1521no—
389C22—1521no—
390C22—1521no—
391C22#1192645211yescharacteristic
392C22#1192671212yes—
393C22#1192672612yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—44no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—764no—
402C4—1521no—
403C4#1192673312yes—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—3041no—
408C2#1456464811yescharacteristic
409C2#1456467111yescharacteristic
410C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2502C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#2502D19
hypocenterC19#10331
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
3. #14563715C2semidirect
4. #14562155C2semidirect
6. #14561521C2semidirect
7. C19×#2502C2semidirect
175. #2502D19semidirect
281. C19#10331semidirect

Maximal subgroups

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

subgroupindex
#145744372
#145681022
#145637152
#145621552
#145621502
#145615212
C19×#25022
#1033119