Finite Group Databasebeta

← #18082994

Subgroups — #18082994

Order 4864.

610 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 109 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#14574388C211yesmaximal, characteristic
2C2×#11926862C211yesmaximal, characteristic
3#14564471C211yesmaximal, characteristic
4#14563725C211yesmaximal, characteristic, complemented
5#14562207C211yesmaximal, characteristic, complemented
6#14561483C211yesmaximal, characteristic, complemented
7C19×#2502C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9#11926872—21no—
10#11926862—22no—
11#11926862—21no—
12#11926862—22no—
13#11926775—22no—
14#11926694—21no—
15#11926683—21no—
16C2×#10597265—21no—
17C2×#10597266—21no—
18C2×#10597263—22no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926404C2211yescharacteristic
22#11926306—22no—
23#11926281—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×C19—21no—
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—24no—
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C4⋊C4×C19D412yes—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19D412yes—
51C2×C42×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×#64527—22no—
54#10597376—21no—
55#10597376—21no—
56#10597376—21no—
57#10597376—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19D411yescharacteristic
61C22×C19⋊C8—21no—
62C22×C19⋊C8D412yes—
63C19×#95—24no—
64C19×#95—21no—
65#10597292—22no—
66C19⋊#95—21no—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)D412yes—
71#10597266—24no—
72#10597266—22no—
73#10597265—24no—
74#10597265—22no—
75#10597263—44no—
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—42no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—82no—
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—41no—
96C2×C22⋊D19—41no—
97C2×C22⋊D19—42no—
98C2×C22⋊D19—42no—
99C22×Dic19—21no—
100C22×Dic19—41no—
101C2×D76—21no—
102C2×D76—21no—
103C2×D76—42no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—84no—
113C22⋊C4×C19—22no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19SD1614yescomplemented
117C42×C19—42no—
118C22⋊Dic19—42no—
119#64527—82no—
120(C2×D19)⋊C4—41no—
121(C2×D19)⋊C4—41no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19—42no—
125C2×C19⋊C8—22no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—42no—
128C2×C19⋊C8—42no—
129#9951—191nomaximal, Sylow
130C23×C19—41no—
131C23×C19—41no—
132C23×C19#12011yescharacteristic
133C23×C19#12111yescharacteristic
134C23×C19#12711yescharacteristic
135C23×C19C2×SD1612yes—
136C23×C19#13712yes—
137C22×D19—41no—
138C22×D19—42no—
139C22×D19—81no—
140C22×D19—81no—
141Q8×C19—42no—
142Q8×C19—81no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—24no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—44no—
154C2×C4×C19—42no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—42no—
158C2×C4×C19—82no—
159C2×C4×C19—82no—
160C2×C4×C19#12011yescharacteristic
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12111yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C22⋊D19—82no—
165C22⋊D19—81no—
166C22⋊D19—81no—
167C2×Dic19—41no—
168C2×Dic19—42no—
169C2×Dic19—81no—
170C2×Dic19—81no—
171C2×Dic19—81no—
172D76—42no—
173D76—42no—
174C19⋊C8—42no—
175C19⋊C8—42no—
176#3187—191no—
177C2×#481—191no—
178#2502D1911yescharacteristic, complemented
179#1964—191no—
180#1824—191no—
181#1520—191no—
182#1282—191no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—42no—
190C22×C19—42no—
191C22×C19#39211yescharacteristic
192C22×C19#44812yes—
193C22×C19#46112yes—
194C22×C19#49211yescharacteristic
195C22×C19#49711yescharacteristic
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C2×D19—162no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—44no—
204C4×C19—81no—
205C4×C19—82no—
206C4×C19—81no—
207C4×C19#45812yes—
208Dic19—81no—
209Dic19—161no—
210C2×C22⋊Q8C2×D1911yescharacteristic
211C2×#121—191no—
212C22×C4⋊C4C2×D1911yescharacteristic
213#483—381no—
214#481—382no—
215#481—382no—
216#481—381no—
217#465—382no—
218#450—381no—
219#448—381no—
220C2×#106—381no—
221C2×#102—381no—
222C2×#99—382no—
223C2×C22⋊C8—191no—
224C2×C22⋊C8—191no—
225#398—22no—
226#391—21no—
227#385—22no—
228#384—21no—
229#380—191no—
230C4×C22⋊C4C2×D1911yescharacteristic
231#340—382no—
232#328—382no—
233C2×C19—21no—
234C2×C19—22no—
235C2×C19—22no—
236C2×C19—21no—
237C2×C19#200811yescharacteristic
238C2×C19#201311yescharacteristic
239C2×C19#202211yescharacteristic
240D19—161no—
241C22×Q8C22⋊D1911yescharacteristic
242C22×D4—191no—
243C22×D4—381no—
244C23×C4—21no—
245C23×C4C22×D1911yescharacteristic
246C2×SD16—382no—
247C22×C8—192no—
248C22×C8—381no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#121—381no—
254#121—381no—
255#121—381no—
256#121—381no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—191no—
265C2×C4⋊C4—381no—
266C2×C4⋊C4C22⋊D1912yes—
267C2×C4⋊C4C22⋊D1911yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—381no—
270C2×C22⋊C4—381no—
271C2×C22⋊C4C22⋊D1912yes—
272C2×C42—21no—
273#106—384no—
274#106—382no—
275#103—382no—
276#102—384no—
277#102—382no—
278#99—764no—
279C22⋊C8—192no—
280C22⋊C8—381no—
281C22⋊C8—381no—
282C22⋊C8—381no—
283#95—24no—
284#95—21no—
285#95—381no—
286C19#995111yescharacteristic, complemented, Sylow
287C24—381no—
288C24C2×C22⋊D1911yescharacteristic
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—42no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—762no—
295C2×D4—761no—
296C2×D4—762no—
297C2×D4—762no—
298C2×D4—761no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—82no—
307C22×C4—381no—
308C22×C4—761no—
309C22×C4D4×D1911yescharacteristic
310C22×C4D4×D1911yescharacteristic
311C22×C4D4×D1911yescharacteristic
312C22×C4#6454311yescharacteristic
313C22×C4C2×C22⋊D1911yescharacteristic
314C22×C4C2×C22⋊D1911yescharacteristic
315SD16—1522no—
316C2×C8—382no—
317C2×C8—382no—
318C2×C8—762no—
319C2×C8—762no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—84no—
329C4⋊C4—381no—
330C4⋊C4—381no—
331C4⋊C4—762no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—761no—
336C22⋊C4—761no—
337C22⋊C4—762no—
338C22⋊C4#6452714yescomplemented
339C42—42no—
340C23—41no—
341C23—41no—
342C23—762no—
343C23—761no—
344C23—1521no—
345C23—1521no—
346C23#1059738411yescharacteristic
347C23#1059738611yescharacteristic
348C23C2×#6452712yes—
349C23#1059738812yes—
350C23#1059739911yescharacteristic
351Q8—42no—
352Q8—81no—
353D4—762no—
354D4—762no—
355D4—1521no—
356D4—1521no—
357D4—1522no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—761no—
376C2×C4—762no—
377C2×C4—1521no—
378C2×C4—1521no—
379C2×C4—1521no—
380C2×C4#1059738311yescharacteristic
381C2×C4#1059738311yescharacteristic
382C2×C4#1059738511yescharacteristic
383C2×C4#1059738511yescharacteristic
384C8—762no—
385C8—762no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—3042no—
395C22—1521no—
396C22—1521no—
397C22—1521no—
398C22#1192645211yescharacteristic
399C22#1192668312yes—
400C22#1192674612yes—
401C22#1192691811yescharacteristic
402C22#1192693611yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—44no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—3041no—
411C4—1521no—
412C4#1192673312yes—
413C2—22no—
414C2—21no—
415C2—22no—
416C2—21no—
417C2—3041no—
418C2#1456468811yescharacteristic
419C2#1456471811yescharacteristic
420C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2502C2
socleC22×C19#392
prime radicalC2×#10597376C22
hypercenter#2502D19
hypocenterC19#9951
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
4. #14563725C2semidirect
5. #14562207C2semidirect
6. #14561483C2semidirect
7. C19×#2502C2semidirect
116. C22⋊C4×C19SD16semidirect
178. #2502D19semidirect
286. C19#9951semidirect
338. C22⋊C4#64527semidirect

Maximal subgroups

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

subgroupindex
#145743882
C2×#119268622
#145644712
#145637252
#145622072
#145614832
C19×#25022
#995119