Finite Group Databasebeta

← #18085461

Subgroups — #18085461

Order 4864.

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

normal subgroups only

This group has 672 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#14574437C211yesmaximal, characteristic
2#14568114C211yesmaximal, characteristic, complemented
3#14568106C211yesmaximal, characteristic
4#14563713C211yesmaximal, characteristic, complemented
5#14562152C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic, complemented
7C19×#1508C211yesmaximal, characteristic, complemented
8C2×#10597332—22no—
9C2×#10597376C2211yescharacteristic
10C22×C4⋊Dic19C2211yescharacteristic
11#11926877—21no—
12#11926857—21no—
13#11926792—22no—
14#11926694—21no—
15#11926683—21no—
16#11926508C2211yescharacteristic
17#11926481—22no—
18#11926474—22no—
19#11926451—21no—
20#11926446—21no—
21#11926416—22no—
22#11926414—21no—
23#11926413—21no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926312—22no—
26#11926279—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C19×#407C2211yescharacteristic
29C4×C22⋊C4×C19C2211yescharacteristic
30C19×#328—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C23×Dic19D412yes—
35C22×D76D411yescharacteristic
36C2×M16×C19—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C42×C19—21no—
46C2×C22⋊Dic19—21no—
47C2×#64527—22no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52C2×(C2×D19)⋊C4—24no—
53C2×(C2×D19)⋊C4—21no—
54C2×C4⋊Dic19—24no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19—21no—
61C2×C4⋊Dic19D411yescharacteristic
62C2×Dic19⋊C4—24no—
63C2×C4×Dic19—21no—
64C2×#64520D412yes—
65#10597332—48no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×#95D412yes—
69#10597292—22no—
70C19⋊#95—24no—
71C19⋊#95D412yes—
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—42no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C2×C22⋊D19—44no—
92C2×C22⋊D19—41no—
93C2×C22⋊D19—41no—
94C22×Dic19—22no—
95C22×Dic19—22no—
96C22×Dic19—22no—
97C22×Dic19—21no—
98C22×Dic19—22no—
99C22×Dic19—44no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—42no—
103M16×C19—42no—
104C2×C8×C19—41no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C22⋊C4×C19—24no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C42×C19—42no—
113C22⋊Dic19—24no—
114#64527—82no—
115(C2×D19)⋊C4—48no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—48no—
121C4⋊Dic19—41no—
122C4⋊Dic19—41no—
123C4⋊Dic19—41no—
124C4⋊Dic19—41no—
125Dic19⋊C4—84no—
126C4×Dic19—42no—
127#64520—42no—
128C2×C19⋊C8—22no—
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—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—42no—
155C2×C4×C19#12011yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C2×C4×C19#12111yescharacteristic
158C2×C4×C19#12711yescharacteristic
159C22⋊D19—82no—
160C22⋊D19—82no—
161C2×Dic19—24no—
162C2×Dic19—42no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19—44no—
166C2×Dic19—41no—
167C2×Dic19—42no—
168C2×Dic19—44no—
169C2×Dic19—82no—
170D76—42no—
171D76—81no—
172C8×C19—81no—
173C19⋊C8—42no—
174#3193—191no—
175#2502—191no—
176#2501—191no—
177#1821—191no—
178#1508D1911yescharacteristic, complemented
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—81no—
202C4×C19#45812yes—
203Dic19—44no—
204Dic19—82no—
205Dic19—81no—
206C2×#123—382no—
207C2×C22⋊Q8C2×D1911yescharacteristic
208C2×#121—191no—
209C22×C4⋊C4—191no—
210#484—381no—
211#480—381no—
212#468—382no—
213#450—381no—
214#448—381no—
215#407—191no—
216#407C2×D1911yescharacteristic
217#399—382no—
218#398—382no—
219#391—381no—
220#390—381no—
221#385—382no—
222#384—381no—
223#384—381no—
224C4×C22⋊C4—191no—
225C4×C22⋊C4C2×D1911yescharacteristic
226#343—382no—
227#328—22no—
228#327—382no—
229C2×C19—22no—
230C2×C19—22no—
231C2×C19—41no—
232C2×C19#200211yescharacteristic
233C2×C19#200511yescharacteristic
234C2×C19#202211yescharacteristic
235D19—161no—
236C22×Q8D7611yescharacteristic
237C22×D4—191no—
238C22×D4—381no—
239C23×C4—192no—
240C23×C4C22×D1911yescharacteristic
241C2×SD16—382no—
242C2×M16—21no—
243C2×M16—192no—
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—191no—
255C2×C4⋊C4—384no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4—381no—
258C2×C4⋊C4—381no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4—381no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4—384no—
263C2×C4⋊C4D7611yescharacteristic
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—21no—
275C22⋊C8—21no—
276C22⋊C8—381no—
277C22⋊C8—381no—
278#95—192no—
279#95—384no—
280#95C22⋊D1912yes—
281C19#1033111yescharacteristic, complemented, Sylow
282C24—381no—
283C24D4×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—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—382no—
298C22×C4—382no—
299C22×C4—381no—
300C22×C4—382no—
301C22×C4—382no—
302C22×C4—764no—
303C22×C4C2×D7611yescharacteristic
304C22×C4#6454111yescharacteristic
305C22×C4D4×D1911yescharacteristic
306C22×C4D4×D1911yescharacteristic
307C22×C4D4×D1911yescharacteristic
308C22×C4C2×C22⋊D1911yescharacteristic
309SD16—1522no—
310M16—42no—
311M16—762no—
312C2×C8—41no—
313C2×C8—382no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—381no—
319C4⋊C4—381no—
320C4⋊C4—768no—
321C4⋊C4—761no—
322C4⋊C4—761no—
323C4⋊C4—761no—
324C4⋊C4—761no—
325C4⋊C4—1524no—
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#1059732811yescharacteristic
343C23#1059733011yescharacteristic
344C23#1059738311yescharacteristic
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—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—384no—
365C2×C4—762no—
366C2×C4—762no—
367C2×C4—764no—
368C2×C4—762no—
369C2×C4—761no—
370C2×C4—762no—
371C2×C4—764no—
372C2×C4—1522no—
373C2×C4#1059732811yescharacteristic
374C2×C4#1059733011yescharacteristic
375C2×C4#1059737611yescharacteristic
376C2×C4#1059738611yescharacteristic
377C8—81no—
378C8—762no—
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#1192645311yescharacteristic
392C22#1192671312yes—
393C22#1192672512yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—44no—
398C4—81no—
399C4—81no—
400C4—764no—
401C4—1522no—
402C4—1521no—
403C4#1192673512yes—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—3041no—
408C2#1456464911yescharacteristic
409C2#1456467211yescharacteristic
410C2#1456476511yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1508C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#1508D19
hypocenterC19#10331
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
2. #14568114C2semidirect
4. #14563713C2semidirect
6. #14561521C2semidirect
7. C19×#1508C2semidirect
178. #1508D19semidirect
281. C19#10331semidirect

Maximal subgroups

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

subgroupindex
#145744372
#145681142
#145681062
#145637132
#145621522
#145615212
C19×#15082
#1033119