Finite Group Databasebeta

← #18082938

Subgroups — #18082938

Order 4864.

798 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 85 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#14572895C211yesmaximal, characteristic
2#14569015C211yesmaximal, characteristic, complemented
3#14563579C211yesmaximal, characteristic
4#14562167C211yesmaximal, characteristic, complemented
5#14561965C211yesmaximal, characteristic, complemented
6#14561487C211yesmaximal, characteristic, complemented
7C19×#2406C211yesmaximal, characteristic
8C2×#10597397—21no—
9C2×#10597370C2211yescharacteristic
10#11926706—22no—
11#11926700—21no—
12#11926695—21no—
13C2×#10597294—22no—
14#11926545—21no—
15#11926508C2211yescharacteristic
16#11926508C2211yescharacteristic
17#11926474—21no—
18#11926464—21no—
19#11926439—22no—
20#11926417—21no—
21#11926417—21no—
22C4×C22⋊Dic19C2211yescharacteristic
23#11926280—22no—
24#11926270—22no—
25C22×#41×C19C2211yescharacteristic
26C2×C19×#123—21no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C19×#395—21no—
29C19×#394—21no—
30C19×#386—21no—
31C19×#385—22no—
32C19×#381C2211yescharacteristic
33C2×#41×C19—21no—
34C2×#41×C19—21no—
35C2×#41×C19—21no—
36C2×#41×C19—21no—
37C2×#41×C19—44no—
38C22×Q8×C19D411yescharacteristic
39C22×D4×C19—21no—
40C22×D4×C19D411yescharacteristic
41C23×C4×C19—21no—
42C23×C4×C19D411yescharacteristic
43C23×C4×C19D411yescharacteristic
44C23×C4×C19C2311yescharacteristic
45C22×Dic38D411yescharacteristic
46C19×#123—44no—
47C2×C4⋊C4×C19—22no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19—21no—
54C2×C22⋊C4×C19—22no—
55C2×C22⋊C4×C19—22no—
56C2×C22⋊C4×C19—21no—
57C2×C22⋊Dic19—21no—
58C2×C22⋊Dic19—21no—
59#10597397—44no—
60C2×#64528—22no—
61C2×#64526—22no—
62C2×C4⋊Dic19D411yescharacteristic
63#10597370—21no—
64#10597370—21no—
65#10597370—21no—
66#10597370—21no—
67C2×Dic19⋊C4—22no—
68C2×Dic19⋊C4—21no—
69C2×Dic19⋊C4—22no—
70C2×C4×Dic19D412yes—
71C2×#64520—21no—
72C2×#64520—21no—
73C19×#95—22no—
74C19×#95—21no—
75C19×#95D412yes—
76#10597294—44no—
77#10597292—22no—
78#10597289—22no—
79C19⋊#95—22no—
80C19⋊#95—22no—
81C19⋊#95—21no—
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84C22⋊(C19⋊C8)—21no—
85C22⋊(C19⋊C8)D412yes—
86C24×C19—21no—
87C24×C19C2×D411yescharacteristic
88#41×C19—24no—
89#41×C19—24no—
90#41×C19—42no—
91#41×C19—42no—
92#41×C19—42no—
93#41×C19—42no—
94#41×C19—42no—
95#41×C19—42no—
96C2×Q8×C19—21no—
97C2×Q8×C19—21no—
98C2×Q8×C19—42no—
99C2×D4×C19—24no—
100C2×D4×C19—21no—
101C2×D4×C19—21no—
102C2×D4×C19—42no—
103C2×D4×C19—42no—
104C2×D4×C19—41no—
105C2×D4×C19—41no—
106C22×C4×C19—21no—
107C22×C4×C19—21no—
108C22×C4×C19—21no—
109C22×C4×C19—21no—
110C22×C4×C19—22no—
111C22×C4×C19—21no—
112C22×C4×C19—21no—
113C22×C4×C19—21no—
114C22×C4×C19—42no—
115C22×C4×C19—42no—
116C22×C4×C19—42no—
117C22×C4×C19—42no—
118C22×C4×C19—41no—
119C22×C4×C19—41no—
120C22×C4×C19—42no—
121C22×C4×C19C2×D411yescharacteristic
122C22×C4×C19C2×D411yescharacteristic
123C22×C4×C19C2×D411yescharacteristic
124C22×C4×C19C2×D411yescharacteristic
125C22×C4×C19C2×D411yescharacteristic
126C22×C4×C19#4111yescharacteristic
127C22×Dic19—22no—
128C22×Dic19—21no—
129C22×Dic19—21no—
130C2×Dic38—21no—
131C2×Dic38—21no—
132C2×Dic38—42no—
133C4⋊C4×C19—44no—
134C4⋊C4×C19—41no—
135C4⋊C4×C19—41no—
136C4⋊C4×C19—41no—
137C4⋊C4×C19—41no—
138C22⋊C4×C19—44no—
139C22⋊C4×C19—42no—
140C22⋊C4×C19—44no—
141C22⋊Dic19—24no—
142C22⋊Dic19—41no—
143C22⋊Dic19—41no—
144#64528—44no—
145#64526—44no—
146C4⋊Dic19—21no—
147C4⋊Dic19—21no—
148Dic19⋊C4—44no—
149Dic19⋊C4—41no—
150Dic19⋊C4—41no—
151Dic19⋊C4—82no—
152C4×Dic19—42no—
153#64520—42no—
154#64520—42no—
155C2×C19⋊C8—22no—
156C2×C19⋊C8—41no—
157#9943—191nomaximal, Sylow
158C23×C19—22no—
159C23×C19—22no—
160C23×C19—22no—
161C23×C19—41no—
162C23×C19—42no—
163C23×C19—41no—
164C23×C19—41no—
165C23×C19—42no—
166C23×C19#12011yescharacteristic
167C23×C19#12011yescharacteristic
168C23×C19#12111yescharacteristic
169Q8×C19—22no—
170Q8×C19—22no—
171Q8×C19—41no—
172Q8×C19—41no—
173D4×C19—22no—
174D4×C19—22no—
175D4×C19—41no—
176D4×C19—41no—
177D4×C19—44no—
178D4×C19—44no—
179C2×C4×C19—22no—
180C2×C4×C19—22no—
181C2×C4×C19—22no—
182C2×C4×C19—22no—
183C2×C4×C19—22no—
184C2×C4×C19—22no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—44no—
190C2×C4×C19—44no—
191C2×C4×C19—41no—
192C2×C4×C19—41no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—42no—
198C2×C4×C19—42no—
199C2×C4×C19—42no—
200C2×C4×C19—41no—
201C2×C4×C19—42no—
202C2×C4×C19—42no—
203C2×C4×C19—81no—
204C2×C4×C19#12011yescharacteristic
205C2×C4×C19#12111yescharacteristic
206C2×C4×C19#12111yescharacteristic
207C2×C4×C19#12711yescharacteristic
208C2×Dic19—24no—
209C2×Dic19—42no—
210C2×Dic19—42no—
211C2×Dic19—42no—
212C2×Dic19—41no—
213C2×Dic19—41no—
214C2×Dic19—42no—
215Dic38—42no—
216Dic38—81no—
217C19⋊C8—42no—
218C19⋊C8—81no—
219#3007—191no—
220#2583—191no—
221#2406D1911yescharacteristic
222#1789—191no—
223#1511—191no—
224#1463—191no—
225#1284—191no—
226C22×C19—21no—
227C22×C19—21no—
228C22×C19—21no—
229C22×C19—21no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—44no—
234C22×C19—44no—
235C22×C19—42no—
236C22×C19—82no—
237C22×C19—81no—
238C22×C19—81no—
239C22×C19#39211yescharacteristic
240C22×C19#45612yes—
241C22×C19B(4,𝔽2)12yes—
242C4×C19—21no—
243C4×C19—21no—
244C4×C19—21no—
245C4×C19—21no—
246C4×C19—42no—
247C4×C19—42no—
248C4×C19—82no—
249C4×C19—81no—
250Dic19—44no—
251Dic19—81no—
252Dic19—81no—
253C22×#41C2×D1911yescharacteristic
254C2×#137—381no—
255C2×#123—21no—
256C2×C22⋊Q8—191no—
257C22×C4⋊C4C2×D1911yescharacteristic
258#452—382no—
259#451—381no—
260#450—381no—
261C2×#104—382no—
262#417—381no—
263#407—191no—
264#407—191no—
265#398—381no—
266#395—21no—
267#395—381no—
268#394—21no—
269#389—382no—
270#386—21no—
271#385—22no—
272#385—381no—
273#385—381no—
274#381C2×D1911yescharacteristic
275C4×C22⋊C4—191no—
276#328—382no—
277#324—382no—
278C2×C19—22no—
279C2×C19—22no—
280C2×C19—41no—
281C2×C19—82no—
282C2×C19#200511yescharacteristic
283C2×C19#201011yescharacteristic
284C2×C19#202111yescharacteristic
285C2×#41—21no—
286C2×#41—21no—
287C2×#41—21no—
288C2×#41—21no—
289C2×#41—44no—
290C22×Q8—191no—
291C22×Q8C22⋊D1911yescharacteristic
292C22×D4—21no—
293C22×D4C22⋊D1911yescharacteristic
294C23×C4—21no—
295C23×C4C22⋊D1911yescharacteristic
296C23×C4C22⋊D1911yescharacteristic
297C23×C4C22×D1911yescharacteristic
298#137—764no—
299C2×Q16—382no—
300C2×SD16—382no—
301C2×M16—381no—
302C2×M16—381no—
303#123—44no—
304C22⋊Q8—381no—
305C22⋊Q8—381no—
306C22⋊Q8—381no—
307C22⋊Q8—381no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—191no—
316C2×C4⋊C4—382no—
317C2×C4⋊C4—381no—
318C2×C4⋊C4—382no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—381no—
323C2×C22⋊C4—381no—
324C2×C42—192no—
325#104—764no—
326#103—382no—
327#102—382no—
328C22⋊C8—192no—
329C22⋊C8—381no—
330C22⋊C8—381no—
331C22⋊C8—381no—
332#95—22no—
333#95—21no—
334#95—382no—
335#95—382no—
336#95—381no—
337#95C22⋊D1912yes—
338C19#994311yescharacteristic, complemented, Sylow
339C24—21no—
340C24C2×C22⋊D1911yescharacteristic
341#41—24no—
342#41—24no—
343#41—42no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—42no—
352C2×Q8—381no—
353C2×Q8—381no—
354C2×Q8—762no—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4—41no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—42no—
377C22×C4—382no—
378C22×C4—381no—
379C22×C4—381no—
380C22×C4D4×D1911yescharacteristic
381C22×C4D4×D1911yescharacteristic
382C22×C4D4×D1911yescharacteristic
383C22×C4#6454311yescharacteristic
384C22×C4C2×C22⋊D1911yescharacteristic
385C22×C4C2×C22⋊D1911yescharacteristic
386Q16—764no—
387SD16—764no—
388M16—762no—
389M16—762no—
390C2×C8—382no—
391C2×C8—761no—
392C4⋊C4—44no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—381no—
398C4⋊C4—381no—
399C4⋊C4—764no—
400C4⋊C4—761no—
401C4⋊C4—761no—
402C4⋊C4—1522no—
403C22⋊C4—44no—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—384no—
407C22⋊C4—761no—
408C22⋊C4—761no—
409C42—762no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23#1059738311yescharacteristic
419C23#1059738511yescharacteristic
420C23#1059739911yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—762no—
426Q8—1521no—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—384no—
459C2×C4—762no—
460C2×C4—762no—
461C2×C4—762no—
462C2×C4—761no—
463C2×C4—761no—
464C2×C4—762no—
465C2×C4#1059738311yescharacteristic
466C2×C4#1059738411yescharacteristic
467C2×C4#1059738511yescharacteristic
468C2×C4#1059738611yescharacteristic
469C8—762no—
470C8—1521no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—44no—
479C22—44no—
480C22—42no—
481C22—82no—
482C22—81no—
483C22—81no—
484C22#1192645211yescharacteristic
485C22#1192672712yes—
486C22#1192673012yes—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—764no—
496C4—1521no—
497C4—1521no—
498C2—22no—
499C2—22no—
500C2—41no—
501C2—82no—
502C2#1456466911yescharacteristic
503C2#1456470011yescharacteristic
504C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2406C2
socleC22×C19#392
prime radicalC22×#41×C19C22
hypercenter#2406D19
hypocenterC19#9943
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
2. #14569015C2semidirect
4. #14562167C2semidirect
5. #14561965C2semidirect
6. #14561487C2semidirect
338. C19#9943semidirect

Maximal subgroups

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

subgroupindex
#145728952
#145690152
#145635792
#145621672
#145619652
#145614872
C19×#24062
#994319