Finite Group Databasebeta

← #18085467

Subgroups — #18085467

Order 4864.

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

normal subgroups only

This group has 600 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#14568123C211yesmaximal, characteristic
3#14563715C211yesmaximal, characteristic, complemented
4#14562155C211yesmaximal, characteristic, complemented
5#14562150C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic, complemented
7C19×#2503C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9#11926877—21no—
10#11926857—21no—
11#11926792—22no—
12#11926694—21no—
13#11926683—21no—
14#11926508C2211yescharacteristic
15#11926508C2211yescharacteristic
16#11926470—22no—
17#11926445—21no—
18#11926423—22no—
19#11926409—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926313—22no—
22#11926281—22no—
23#11926277—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#400—22no—
27C19×#391—21no—
28C19×#382—21no—
29C19×#381—22no—
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×C19D411yescharacteristic
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C42×C19—21no—
51C2×C22⋊Dic19—21no—
52C2×#64527—22no—
53#10597376—21no—
54#10597376—21no—
55#10597376—21no—
56#10597376—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—24no—
59C2×C4⋊Dic19D411yescharacteristic
60C2×C4×Dic19—21no—
61C2×#64520—21no—
62C2×#64520D412yes—
63C19×#95—24no—
64C19×#95—24no—
65C19×#95D412yes—
66#10597292—22no—
67C19⋊#95—24no—
68C19⋊#95D412yes—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73#10597266—22no—
74#10597264—22no—
75C24×C19C2×D411yescharacteristic
76C23×D19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—42no—
80C22×C4×C19—22no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—22no—
84C22×C4×C19—22no—
85C22×C4×C19—22no—
86C22×C4×C19—42no—
87C22×C4×C19—44no—
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×C22⋊D19—44no—
95C2×C22⋊D19—41no—
96C2×C22⋊D19—41no—
97C22×Dic19—22no—
98C22×Dic19—21no—
99C2×D76—21no—
100C2×D76—21no—
101C2×D76—42no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—42no—
111C22⋊C4×C19—41no—
112C22⋊C4×C19—41no—
113C42×C19—42no—
114C22⋊Dic19—42no—
115#64527—82no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—84no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4×Dic19—42no—
122#64520—42no—
123#64520—42no—
124C2×C19⋊C8—22no—
125C2×C19⋊C8—41no—
126#10332—191nomaximal, Sylow
127C23×C19—22no—
128C23×C19—22no—
129C23×C19—41no—
130C23×C19#12011yescharacteristic
131C23×C19#12011yescharacteristic
132C23×C19#12111yescharacteristic
133C22×D19—42no—
134C22×D19—42no—
135C22×D19—41no—
136C22×D19—42no—
137Q8×C19—42no—
138Q8×C19—81no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—44no—
148C2×C4×C19—42no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—44no—
155C2×C4×C19—82no—
156C2×C4×C19#12011yescharacteristic
157C2×C4×C19#12111yescharacteristic
158C2×C4×C19#12111yescharacteristic
159C2×C4×C19#12711yescharacteristic
160C22⋊D19—82no—
161C22⋊D19—82no—
162C2×Dic19—42no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19—41no—
166C2×Dic19—42no—
167D76—42no—
168D76—81no—
169C19⋊C8—42no—
170C19⋊C8—81no—
171#3193—191no—
172#2504—191no—
173#2503D1911yescharacteristic, complemented
174#1821—191no—
175#1508—191no—
176#1507—191no—
177#1297—191no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—44no—
186C22×C19#39211yescharacteristic
187C22×C19#45412yes—
188C22×C19#45512yes—
189C2×D19—84no—
190C2×D19—81no—
191C2×D19—81no—
192C2×D19—81no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—82no—
197C4×C19—81no—
198C4×C19—82no—
199C4×C19—81no—
200C4×C19#45812yes—
201Dic19—82no—
202Dic19—81no—
203C2×C22⋊Q8C2×D1911yescharacteristic
204C2×#121—191no—
205C22×C4⋊C4C2×D1911yescharacteristic
206#484—381no—
207#480—381no—
208#468—382no—
209#450—381no—
210#448—381no—
211#407—191no—
212#407—191no—
213#400—22no—
214#397—382no—
215#391—21no—
216#390—381no—
217#386—382no—
218#382—21no—
219#382—381no—
220#381—22no—
221C4×C22⋊C4—191no—
222C4×C22⋊C4C2×D1911yescharacteristic
223#343—382no—
224#328—382no—
225#327—382no—
226C2×C19—22no—
227C2×C19—22no—
228C2×C19—41no—
229C2×C19#200311yescharacteristic
230C2×C19#200411yescharacteristic
231C2×C19#202211yescharacteristic
232D19—161no—
233C22×Q8C22⋊D1911yescharacteristic
234C22×D4—191no—
235C22×D4—381no—
236C23×C4C22⋊D1912yes—
237C23×C4C22×D1911yescharacteristic
238C2×SD16—382no—
239C2×M16—192no—
240C2×M16—381no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245#121—381no—
246#121—381no—
247#121—381no—
248#121—381no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—191no—
257C2×C4⋊C4C22⋊D1911yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C22⋊C4—384no—
263C2×C42—21no—
264C2×C42—381no—
265#107—382no—
266#103—382no—
267#102—382no—
268C22⋊C8—381no—
269C22⋊C8—381no—
270C22⋊C8—381no—
271C22⋊C8—381no—
272#95—24no—
273#95—24no—
274#95—192no—
275#95—384no—
276#95C22⋊D1912yes—
277C19#1033211yescharacteristic, complemented, Sylow
278C24—381no—
279C24C2×C22⋊D1911yescharacteristic
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—42no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4—762no—
286C2×D4—764no—
287C2×D4—761no—
288C2×D4—761no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—42no—
296C22×C4—44no—
297C22×C4—382no—
298C22×C4—381no—
299C22×C4D4×D1911yescharacteristic
300C22×C4D4×D1911yescharacteristic
301C22×C4D4×D1911yescharacteristic
302C22×C4#6454311yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305SD16—1522no—
306M16—762no—
307M16—762no—
308C2×C8—382no—
309C2×C8—761no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—381no—
319C4⋊C4—381no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—762no—
324C22⋊C4—761no—
325C22⋊C4—761no—
326C22⋊C4—1524no—
327C42—42no—
328C42—762no—
329C23—22no—
330C23—22no—
331C23—41no—
332C23—762no—
333C23—762no—
334C23—761no—
335C23—762no—
336C23#1059738311yescharacteristic
337C23#1059738511yescharacteristic
338C23#1059739911yescharacteristic
339Q8—42no—
340Q8—81no—
341D4—762no—
342D4—1521no—
343D4—1522no—
344D4—1522no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—82no—
362C2×C4—762no—
363C2×C4—762no—
364C2×C4—762no—
365C2×C4—761no—
366C2×C4—762no—
367C2×C4#1059738311yescharacteristic
368C2×C4#1059738411yescharacteristic
369C2×C4#1059738511yescharacteristic
370C2×C4#1059738611yescharacteristic
371C8—762no—
372C8—1521no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22—1524no—
382C22—1521no—
383C22—1521no—
384C22—1521no—
385C22#1192645211yescharacteristic
386C22#1192671712yes—
387C22#1192672112yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—81no—
393C4—82no—
394C4—81no—
395C4—1522no—
396C4—1521no—
397C4#1192673312yes—
398C2—22no—
399C2—22no—
400C2—41no—
401C2—3041no—
402C2#1456465511yescharacteristic
403C2#1456466411yescharacteristic
404C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2503C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#2503D19
hypocenterC19#10332
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
3. #14563715C2semidirect
4. #14562155C2semidirect
6. #14561521C2semidirect
7. C19×#2503C2semidirect
173. #2503D19semidirect
277. C19#10332semidirect

Maximal subgroups

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

subgroupindex
#145744372
#145681232
#145637152
#145621552
#145621502
#145615212
C19×#25032
#1033219