Finite Group Databasebeta

← #18085769

Subgroups — #18085769

Order 4864.

602 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 75 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#14569296C211yesmaximal, characteristic, complemented
2#14563579C211yesmaximal, characteristic
3#14563553C211yesmaximal, characteristic
4#14561544C211yesmaximal, characteristic, complemented
5#14561489C211yesmaximal, characteristic, complemented
6#14561488C211yesmaximal, characteristic, complemented
7C19×#1789C211yesmaximal, characteristic
8C2×#10597294—21no—
9C2×#10597294—21no—
10C2×#10597291—21no—
11C2×#10597291—21no—
12#11926508C2211yescharacteristic
13#11926480—21no—
14#11926456—21no—
15#11926450—21no—
16#11926448—21no—
17#11926428—21no—
18#11926427—21no—
19#11926407C2211yescharacteristic
20#11926407C2211yescharacteristic
21C4×C22⋊Dic19C2211yescharacteristic
22C22×#41×C19C2211yescharacteristic
23C2×C19×#104—21no—
24C2×C19×#104—21no—
25C19×#407C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C2×#41×C19—21no—
28C2×#41×C19—21no—
29C2×#41×C19—21no—
30C2×#41×C19—21no—
31C2×#41×C19—42no—
32C2×#41×C19—42no—
33C22×Q8×C19Q811yescharacteristic, complemented
34C22×D4×C19—21no—
35C22×D4×C19Q811yescharacteristic, complemented
36C23×C4×C19—21no—
37C23×C4×C19C2311yescharacteristic
38C22×Dic38—21no—
39C2×M16×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19D411yescharacteristic
46C2×C22⋊Dic19D411yescharacteristic
47C2×C4⋊Dic19—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×C4×Dic19D411yescharacteristic
51C2×C4×Dic19D411yescharacteristic
52C2×#64520—21no—
53C19×#104—42no—
54C19×#104—42no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×#95—21no—
58#10597294—42no—
59#10597294—42no—
60#10597291—42no—
61#10597291—42no—
62C19⋊#95—21no—
63C19⋊#95—21no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C24×C19—21no—
74C24×C19C2×D411yescharacteristic
75#41×C19—22no—
76#41×C19—22no—
77#41×C19—22no—
78#41×C19—22no—
79#41×C19—41no—
80#41×C19—41no—
81#41×C19—41no—
82#41×C19—41no—
83#41×C19—42no—
84#41×C19—42no—
85#41×C19—42no—
86#41×C19—42no—
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—42no—
90C2×D4×C19—22no—
91C2×D4×C19—22no—
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—42no—
95C2×D4×C19—41no—
96C2×D4×C19—41no—
97C2×D4×C19—41no—
98C2×D4×C19—41no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19—42no—
105C22×C4×C19—42no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×Q811yescharacteristic
111C22×C4×C19#4111yescharacteristic
112C22×C4×C19#4111yescharacteristic
113C22×C4×C19#4111yescharacteristic
114C22×Dic19—21no—
115C22×Dic19—21no—
116C22×Dic19—21no—
117C22×Dic19—21no—
118C22×Dic19—41no—
119C2×Dic38—42no—
120C2×Dic38—42no—
121C2×Dic38—81no—
122M16×C19—41no—
123M16×C19—41no—
124C2×C8×C19—41no—
125C22⋊C4×C19—42no—
126C42×C19—41no—
127C42×C19—41no—
128C22⋊Dic19—42no—
129C22⋊Dic19—41no—
130C22⋊Dic19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—41no—
133C4⋊Dic19—42no—
134Dic19⋊C4—42no—
135Dic19⋊C4—81no—
136C4×Dic19—41no—
137C4×Dic19—41no—
138#64520—41no—
139#64520—41no—
140C2×C19⋊C8—41no—
141#10386—191nomaximal, Sylow
142C23×C19—21no—
143C23×C19—21no—
144C23×C19—22no—
145C23×C19—41no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—81no—
150C23×C19—81no—
151C23×C19#12011yescharacteristic
152C23×C19C22⋊Q811yescharacteristic
153C23×C19#12411yescharacteristic
154Q8×C19—22no—
155Q8×C19—22no—
156Q8×C19—41no—
157Q8×C19—41no—
158D4×C19—22no—
159D4×C19—22no—
160D4×C19—41no—
161D4×C19—41no—
162D4×C19—42no—
163D4×C19—42no—
164D4×C19—42no—
165D4×C19—42no—
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—22no—
171C2×C4×C19—22no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19C22⋊Q811yescharacteristic
188C2×C4×C19C22⋊Q811yescharacteristic
189C2×C4×C19#12411yescharacteristic
190C2×C4×C19#12411yescharacteristic
191C2×Dic19—22no—
192C2×Dic19—41no—
193C2×Dic19—41no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19—41no—
198C2×Dic19—41no—
199C2×Dic19—41no—
200C2×Dic19—41no—
201C2×Dic19—41no—
202C2×Dic19—41no—
203C2×Dic19—81no—
204C2×Dic19—81no—
205C2×Dic19—81no—
206Dic38—84no—
207C8×C19—81no—
208C19⋊C8—81no—
209#2607—191no—
210#1789—191no—
211#1789D1911yescharacteristic
212#1782—191no—
213#1306—191no—
214#1284—191no—
215#1284—191no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—21no—
222C22×C19—21no—
223C22×C19—21no—
224C22×C19—42no—
225C22×C19—81no—
226C22×C19—81no—
227C22×C19—82no—
228C22×C19—82no—
229C22×C19—81no—
230C22×C19—81no—
231C22×C19#39311yescharacteristic
232C22×C19B(4,𝔽2)11yescharacteristic
233C22×C19B(4,𝔽2)11yescharacteristic
234C4×C19—21no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—42no—
239C4×C19—42no—
240C4×C19—81no—
241Dic19—42no—
242Dic19—81no—
243Dic19—81no—
244Dic19—81no—
245Dic19—161no—
246C22×#41C2×D1911yescharacteristic
247C2×#104—21no—
248C2×#104—21no—
249C2×#104—381no—
250C2×#104—381no—
251C2×#99—381no—
252C2×#99—381no—
253#407—191no—
254#407C2×D1911yescharacteristic
255#399—381no—
256#393—381no—
257#391—381no—
258#391—381no—
259#387—381no—
260#387—381no—
261#381—191no—
262#381—191no—
263C4×C22⋊C4—191no—
264C4×C22⋊C4C2×D1911yescharacteristic
265C2×C19—21no—
266C2×C19—21no—
267C2×C19—41no—
268C2×C19—41no—
269C2×C19—82no—
270C2×C19#202911yescharacteristic
271C2×C19#203111yescharacteristic
272C2×C19#203111yescharacteristic
273C2×#41—21no—
274C2×#41—21no—
275C2×#41—21no—
276C2×#41—21no—
277C2×#41—42no—
278C2×#41—42no—
279C22×Q8—381no—
280C22×Q8Dic3811yescharacteristic, complemented
281C22×D4—21no—
282C22×D4Dic3811yescharacteristic, complemented
283C23×C4—21no—
284C23×C4C22×D1911yescharacteristic
285C2×M16—21no—
286C2×M16—381no—
287C2×C4⋊C4—381no—
288C2×C4⋊C4—381no—
289C2×C4⋊C4—381no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—191no—
292C2×C22⋊C4—191no—
293C2×C22⋊C4—381no—
294C2×C22⋊C4—381no—
295C2×C42—191no—
296C2×C42—191no—
297C2×C42C22⋊D1911yescharacteristic
298C2×C42C22⋊D1911yescharacteristic
299#104—42no—
300#104—42no—
301#104—762no—
302#104—762no—
303#99—762no—
304#99—762no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—381no—
308C22⋊C8—381no—
309#95—21no—
310#95—381no—
311#95—381no—
312#95—381no—
313#95—381no—
314#95—381no—
315#95—381no—
316#95—381no—
317#95—381no—
318#95—381no—
319C19#1038611yescharacteristic, complemented, Sylow
320C24—21no—
321C24D4×D1911yescharacteristic
322#41—22no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—42no—
337C2×Q8—762no—
338C2×Q8—762no—
339C2×Q8—1521no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—381no—
359C22×C4—381no—
360C22×C4—381no—
361C22×C4—381no—
362C22×C4—761no—
363C22×C4C2×Dic3811yescharacteristic
364C22×C4#6454111yescharacteristic
365C22×C4D4×D1911yescharacteristic
366C22×C4#6454311yescharacteristic
367C22×C4#6454311yescharacteristic
368C22×C4C2×C22⋊D1911yescharacteristic
369M16—41no—
370M16—41no—
371M16—761no—
372M16—761no—
373C2×C8—41no—
374C2×C8—761no—
375C4⋊C4—762no—
376C4⋊C4—762no—
377C4⋊C4—1521no—
378C22⋊C4—42no—
379C22⋊C4—762no—
380C22⋊C4—761no—
381C22⋊C4—761no—
382C22⋊C4—761no—
383C22⋊C4—761no—
384C42—41no—
385C42—41no—
386C42—761no—
387C42—761no—
388C23—21no—
389C23—21no—
390C23—22no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—81no—
396C23—81no—
397C23#1059732411yescharacteristic
398C23#1059733111yescharacteristic
399C23#1059738311yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—1524no—
405D4—22no—
406D4—22no—
407D4—41no—
408D4—41no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—382no—
435C2×C4—761no—
436C2×C4—761no—
437C2×C4—761no—
438C2×C4—761no—
439C2×C4—761no—
440C2×C4—761no—
441C2×C4—761no—
442C2×C4—761no—
443C2×C4—761no—
444C2×C4—761no—
445C2×C4—761no—
446C2×C4—1521no—
447C2×C4—1521no—
448C2×C4—1521no—
449C2×C4#1059732411yescharacteristic
450C2×C4#1059733111yescharacteristic
451C2×C4#1059737011yescharacteristic
452C2×C4#1059738211yescharacteristic
453C8—81no—
454C8—1521no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—42no—
464C22—81no—
465C22—81no—
466C22—82no—
467C22—82no—
468C22—81no—
469C22—81no—
470C22#1192645611yescharacteristic
471C22#1192673011yescharacteristic
472C22#1192673011yescharacteristic
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—3041no—
481C4—762no—
482C4—1521no—
483C4—1521no—
484C4—1521no—
485C2—21no—
486C2—21no—
487C2—41no—
488C2—41no—
489C2—82no—
490C2#1456479911yescharacteristic
491C2#1456480511yescharacteristic
492C2#1456480711yescharacteristic
subgroupG/H
centerC22#11926456
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1789C2
socleC22×C19#393
prime radicalC22×#41×C19C22
hypercenter#1789D19
hypocenterC19#10386
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #14569296C2semidirect
4. #14561544C2semidirect
5. #14561489C2semidirect
6. #14561488C2semidirect
33. C22×Q8×C19Q8semidirect
35. C22×D4×C19Q8semidirect
280. C22×Q8Dic38semidirect
282. C22×D4Dic38semidirect
319. C19#10386semidirect

Maximal subgroups

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

subgroupindex
#145692962
#145635792
#145635532
#145615442
#145614892
#145614882
C19×#17892
#1038619