Finite Group Databasebeta

← #18085462

Subgroups — #18085462

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#14574441C211yesmaximal, characteristic
2#14568109C211yesmaximal, characteristic, complemented
3#14563715C211yesmaximal, characteristic, complemented
4#14562154C211yesmaximal, characteristic, complemented
5#14562151C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic, complemented
7C19×#2501C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926879—21no—
10#11926855—21no—
11#11926788—22no—
12#11926695—21no—
13#11926682—21no—
14#11926508C2211yescharacteristic
15#11926508C2211yescharacteristic
16#11926475—22no—
17#11926449—21no—
18#11926417—22no—
19#11926413—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926313—22no—
22#11926280—22no—
23#11926278—22no—
24C2×C19×#123—22no—
25C2×C19×#121C2211yescharacteristic
26C22×C4⋊C4×C19C2211yescharacteristic
27C19×#399—22no—
28C19×#390—21no—
29C19×#384—21no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19D412yes—
34C23×C4×C19C2311yescharacteristic
35C22×Dic38D411yescharacteristic
36C19×#123—48no—
37C19×#121—21no—
38C19×#121—21no—
39C19×#121—21no—
40C19×#121—21no—
41C2×C4⋊C4×C19—24no—
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—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—24no—
51C2×C22⋊C4×C19—21no—
52C2×C42×C19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55C2×#64526—22no—
56C2×C4⋊Dic19D411yescharacteristic
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60#10597370—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4—24no—
63C2×C4×Dic19—21no—
64C2×#64520—21no—
65C2×#64520D412yes—
66C19×#95D412yes—
67#10597289—22no—
68C19⋊#95—24no—
69C19⋊#95D412yes—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74#10597267—22no—
75#10597264—22no—
76C24×C19—21no—
77C24×C19C2×D411yescharacteristic
78C2×D4×C19—21no—
79C2×D4×C19—21no—
80C2×D4×C19—42no—
81C2×D4×C19—44no—
82C2×D4×C19—41no—
83C2×D4×C19—41no—
84C22×C4×C19—22no—
85C22×C4×C19—22no—
86C22×C4×C19—21no—
87C22×C4×C19—22no—
88C22×C4×C19—22no—
89C22×C4×C19—42no—
90C22×C4×C19—44no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—22no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C2×Dic38—21no—
101C2×Dic38—21no—
102C2×Dic38—42no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—48no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—24no—
111C22⋊C4×C19—48no—
112C22⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C42×C19—42no—
115C22⋊Dic19—24no—
116C22⋊Dic19—41no—
117C22⋊Dic19—41no—
118#64526—82no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121Dic19⋊C4—41no—
122Dic19⋊C4—41no—
123Dic19⋊C4—84no—
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—42no—
134C23×C19—42no—
135C23×C19—41no—
136C23×C19—42no—
137C23×C19#12011yescharacteristic
138C23×C19#12011yescharacteristic
139C23×C19#12111yescharacteristic
140D4×C19—42no—
141D4×C19—81no—
142D4×C19—82no—
143D4×C19—82no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
147C2×C4×C19—24no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—44no—
154C2×C4×C19—42no—
155C2×C4×C19—41no—
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
163C2×Dic19—24no—
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—42no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169C2×Dic19—42no—
170Dic38—42no—
171Dic38—81no—
172C19⋊C8—42no—
173C19⋊C8—81no—
174#3193—191no—
175#2502—191no—
176#2501D1911yescharacteristic
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—84no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19—81no—
193C22×C19#39211yescharacteristic
194C22×C19#45312yes—
195C22×C19#45612yes—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—44no—
200C4×C19—82no—
201C4×C19—81no—
202C4×C19#45812yes—
203Dic19—44no—
204Dic19—81no—
205Dic19—81no—
206C2×#123—22no—
207C2×C22⋊Q8—191no—
208C2×#121C2×D1911yescharacteristic
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—22no—
218#398—382no—
219#391—381no—
220#390—21no—
221#385—382no—
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—161no—
233C2×C19#200211yescharacteristic
234C2×C19#200511yescharacteristic
235C2×C19#202211yescharacteristic
236C22×Q8—191no—
237C22×D4—21no—
238C22×D4C22⋊D1911yescharacteristic
239C23×C4C22⋊D1912yes—
240C23×C4C22×D1911yescharacteristic
241C2×SD16—382no—
242C2×M16—192no—
243C2×M16—381no—
244#123—48no—
245C22⋊Q8—381no—
246C22⋊Q8—381no—
247C22⋊Q8—381no—
248C22⋊Q8—381no—
249#121—21no—
250#121—21no—
251#121—21no—
252#121—21no—
253C2×C4⋊C4—24no—
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—191no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4—384no—
263C2×C4⋊C4C22⋊D1911yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—381no—
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—192no—
279#95—384no—
280#95C22⋊D1912yes—
281C19#1033111yescharacteristic, complemented, Sylow
282C24—21no—
283C24C2×C22⋊D1911yescharacteristic
284C2×Q8—381no—
285C2×Q8—381no—
286C2×Q8—762no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—42no—
290C2×D4—44no—
291C2×D4—41no—
292C2×D4—41no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—42no—
299C22×C4—44no—
300C22×C4—382no—
301C22×C4—381no—
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—48no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—381no—
322C4⋊C4—381no—
323C4⋊C4—761no—
324C4⋊C4—761no—
325C4⋊C4—1524no—
326C22⋊C4—24no—
327C22⋊C4—48no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—384no—
331C22⋊C4—761no—
332C22⋊C4—761no—
333C42—42no—
334C42—762no—
335C23—22no—
336C23—22no—
337C23—41no—
338C23—42no—
339C23—42no—
340C23—41no—
341C23—42no—
342C23#1059738311yescharacteristic
343C23#1059738511yescharacteristic
344C23#1059739911yescharacteristic
345Q8—762no—
346Q8—1521no—
347D4—42no—
348D4—81no—
349D4—82no—
350D4—82no—
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—42no—
364C2×C4—44no—
365C2×C4—82no—
366C2×C4—384no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4—762no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4—762no—
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—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#1192645211yescharacteristic
392C22#1192671112yes—
393C22#1192672712yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—44no—
398C4—82no—
399C4—81no—
400C4—764no—
401C4—1521no—
402C4—1521no—
403C4#1192673312yes—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—161no—
408C2#1456465011yescharacteristic
409C2#1456466911yescharacteristic
410C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2501C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#2501D19
hypocenterC19#10331
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
2. #14568109C2semidirect
3. #14563715C2semidirect
4. #14562154C2semidirect
6. #14561521C2semidirect
281. C19#10331semidirect

Maximal subgroups

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

subgroupindex
#145744412
#145681092
#145637152
#145621542
#145621512
#145615212
C19×#25012
#1033119