Finite Group Databasebeta

← #18079853

Subgroups — #18079853

Order 4864.

570 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572657C211yesmaximal, characteristic
2#14568815C211yesmaximal, characteristic
3#14563620C211yesmaximal, characteristic
4#14562208C211yesmaximal, characteristic, complemented
5#14562206C211yesmaximal, characteristic, complemented
6#14561514C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C2×#10597370C2211yescharacteristic
9C2×C4×C22⋊D19C2211yescharacteristic
10C8×C22⋊D19—22no—
11(C22⋊D19)⋊C8—22no—
12#11926594—21no—
13C2×#10597263—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C22⋊C8×D19—21no—
16#11926484C411yescharacteristic, complemented
17#11926481C411yescharacteristic, complemented
18#11926465C411yescharacteristic, complemented
19#11926457C411yescharacteristic, complemented
20#11926429—21no—
21#11926423—21no—
22#11926418—21no—
23#11926404—21no—
24#11926404C2211yescharacteristic
25#11926310—21no—
26#11926282—22no—
27#11926280—22no—
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C2×C19×#95C2211yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19D411yescharacteristic
34C22×C4×D19D411yescharacteristic
35C22×Dic38C2×C411yescharacteristic
36C22×C8×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19D411yescharacteristic
42C4×C22⋊D19—21no—
43C4×C22⋊D19—21no—
44C4×C22⋊D19—21no—
45C4×C22⋊D19—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4C2×C411yescharacteristic
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19C2×C411yescharacteristic
53#10597370—21no—
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4C2×C411yescharacteristic
59C2×C4×Dic19D411yescharacteristic
60C22×C19⋊C8—21no—
61C2×C8×D19—22no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8D412yes—
64C19×#95—21no—
65C19×#95—21no—
66C19×#95C2×C411yescharacteristic
67C19×#95C2×C411yescharacteristic
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D412yes—
75(C2×D19)⋊C8—22no—
76Dic19⋊C8—22no—
77C8×Dic19—22no—
78#10597263—42no—
79C24×C19C2×D411yescharacteristic
80C23×D19C22⋊C411yescharacteristic
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—42no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—81no—
88C22×C4×C19—81no—
89C22×C4×C19C22×C411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C2×C22⋊D19—21no—
96C2×C22⋊D19—21no—
97C2×C22⋊D19—21no—
98C2×C22⋊D19—21no—
99C2×C22⋊D19SD1612yes—
100C2×C22⋊D19Q1612yes—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—41no—
104C22×Dic19C22⋊C411yescharacteristic
105C22×Dic19C22⋊C411yescharacteristic
106C22×Dic19C22⋊C411yescharacteristic
107C2×C4×D19—21no—
108C2×C4×D19—21no—
109C2×C4×D19—81no—
110C2×Dic38—21no—
111C2×Dic38—21no—
112C2×Dic38—81no—
113C2×C8×C19—22no—
114C2×C8×C19—81no—
115C4⋊C4×C19—81no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊Dic19—21no—
119C22⋊Dic19—21no—
120C22⋊Dic19—41no—
121C22⋊Dic19—41no—
122C22⋊Dic19—41no—
123C22⋊Dic19—41no—
124(C2×D19)⋊C4—21no—
125(C2×D19)⋊C4—21no—
126(C2×D19)⋊C4—42no—
127(C2×D19)⋊C4—81no—
128C4⋊Dic19—21no—
129C4⋊Dic19—21no—
130C4⋊Dic19—42no—
131C4⋊Dic19—81no—
132C4⋊Dic19—81no—
133Dic19⋊C4—21no—
134Dic19⋊C4—21no—
135Dic19⋊C4—41no—
136Dic19⋊C4—41no—
137C4×Dic19—21no—
138C4×Dic19—21no—
139C2×C19⋊C8—22no—
140C2×C19⋊C8—81no—
141C8×D19—82no—
142#9383—191nomaximal, Sylow
143C23×C19—41no—
144C23×C19—41no—
145C23×C19C2×C22⋊C411yescharacteristic
146C23×C19#12111yescharacteristic
147C23×C19#12111yescharacteristic
148C23×C19C2×SD1611yescharacteristic
149C23×C19C2×Q1611yescharacteristic
150C23×C19#13511yescharacteristic
151C23×C19#13511yescharacteristic
152C22×D19—21no—
153C22×D19—21no—
154C22×D19—41no—
155C22×D19—41no—
156C22×D19#10312yes—
157C2×C4×C19—22no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—82no—
170C2×C4×C19—82no—
171C2×C4×C19—81no—
172C2×C4×C19—81no—
173C2×C4×C19—81no—
174C2×C4×C19C4×D411yescharacteristic
175C2×C4×C19C4×D411yescharacteristic
176C2×C4×C19#12011yescharacteristic
177C2×C4×C19#12311yescharacteristic
178C22⋊D19—22no—
179C22⋊D19—22no—
180C22⋊D19—22no—
181C22⋊D19—22no—
182C2×Dic19—21no—
183C2×Dic19—21no—
184C2×Dic19—21no—
185C2×Dic19—21no—
186C2×Dic19—41no—
187C2×Dic19—41no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190C2×Dic19—41no—
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—41no—
194C2×Dic19—81no—
195C2×Dic19—81no—
196C2×Dic19—81no—
197C2×Dic19#10312yes—
198C4×D19—42no—
199C4×D19—81no—
200Dic38—81no—
201Dic38—81no—
202C8×C19—42no—
203C19⋊C8—42no—
204#2972—191no—
205#2564—191no—
206#1799—191no—
207#1520—191no—
208#1520—191no—
209#1294—191no—
210#1294D1911yescharacteristic, complemented
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—41no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—41no—
221C22×C19#38611yescharacteristic
222C22×C19C2×#10311yescharacteristic
223C22×C19#41611yescharacteristic
224C22×C19#46511yescharacteristic
225C22×C19#46511yescharacteristic
226C22×C19#46711yescharacteristic
227C22×C19#46711yescharacteristic
228C2×D19—22no—
229C2×D19—41no—
230C2×D19—41no—
231C2×D19—42no—
232C2×D19—81no—
233C4×C19—21no—
234C4×C19—21no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—42no—
238C4×C19—81no—
239C4×C19—161no—
240Dic19—22no—
241Dic19—41no—
242Dic19—41no—
243Dic19—81no—
244Dic19—81no—
245Dic19—161no—
246C2×C22⋊Q8—191no—
247C2×C4×D4—191no—
248C8×D4—382no—
249C8×D4—382no—
250#431—381no—
251C2×#99—381no—
252C2×C22⋊C8—191no—
253C2×C22⋊C8—381no—
254C2×C22⋊C8C2×D1911yescharacteristic
255#400—191no—
256#399—191no—
257#395—191no—
258#393—191no—
259#387—381no—
260#386—381no—
261#385—381no—
262#380—191no—
263#380—381no—
264#380C2×D1911yescharacteristic
265C2×#95C2×D1911yescharacteristic
266#342—381no—
267#328—382no—
268#328—382no—
269C2×C19—21no—
270C2×C19—21no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19#188411yescharacteristic
276C2×C19#189211yescharacteristic
277C2×C19#191311yescharacteristic
278D19—42no—
279C22×Q8—191no—
280C22×D4—191no—
281C23×C4—21no—
282C23×C4—191no—
283C23×C4C22×D1911yescharacteristic
284C22×C8—21no—
285C22×C8—382no—
286C22×C8—381no—
287C22⋊Q8—381no—
288C22⋊Q8—381no—
289C22⋊Q8—381no—
290C22⋊Q8—381no—
291C4×D4—381no—
292C4×D4—381no—
293C4×D4—381no—
294C4×D4—381no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—191no—
297C2×C4⋊C4—191no—
298C2×C4⋊C4—381no—
299C2×C4⋊C4—381no—
300C2×C4⋊C4—381no—
301C2×C4⋊C4—381no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—191no—
304C2×C22⋊C4—191no—
305C2×C22⋊C4—381no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—381no—
309C2×C42—191no—
310C4⋊C8—382no—
311#99—762no—
312C22⋊C8—21no—
313C22⋊C8—192no—
314C22⋊C8—382no—
315C22⋊C8—381no—
316C22⋊C8D7612yes—
317C4×C8—382no—
318#95—21no—
319#95—21no—
320#95—381no—
321#95—381no—
322#95—381no—
323#95—381no—
324#95—381no—
325#95C4×D1911yescharacteristic
326#95C4×D1911yescharacteristic
327C19#938311yescharacteristic, complemented, Sylow
328C24—191no—
329C24D4×D1911yescharacteristic
330C2×Q8—381no—
331C2×Q8—381no—
332C2×Q8—1521no—
333C2×D4—192no—
334C2×D4—192no—
335C2×D4—381no—
336C2×D4—381no—
337C2×D4—381no—
338C2×D4—381no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—81no—
346C22×C4—81no—
347C22×C4—191no—
348C22×C4—191no—
349C22×C4—191no—
350C22×C4—381no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—381no—
354C22×C4—761no—
355C22×C4—1521no—
356C22×C4C2×C4×D1911yescharacteristic
357C22×C4C2×D7611yescharacteristic
358C22×C4#6454111yescharacteristic
359C22×C4D4×D1911yescharacteristic
360C22×C4D4×D1911yescharacteristic
361C22×C4#6454511yescharacteristic
362C2×C8—22no—
363C2×C8—81no—
364C2×C8—382no—
365C2×C8—1522no—
366C2×C8—1521no—
367C4⋊C4—81no—
368C4⋊C4—381no—
369C4⋊C4—381no—
370C4⋊C4—381no—
371C4⋊C4—381no—
372C4⋊C4—762no—
373C4⋊C4—761no—
374C4⋊C4—761no—
375C4⋊C4—1521no—
376C4⋊C4—1521no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—381no—
380C22⋊C4—381no—
381C22⋊C4—381no—
382C22⋊C4—381no—
383C22⋊C4—762no—
384C22⋊C4—761no—
385C22⋊C4—761no—
386C22⋊C4—761no—
387C22⋊C4—761no—
388C22⋊C4—1521no—
389C42—381no—
390C42—381no—
391C23—41no—
392C23—41no—
393C23—192no—
394C23—381no—
395C23—381no—
396C23—761no—
397C23—761no—
398C23C22⋊C4×D1911yescharacteristic
399C23#1059733011yescharacteristic
400C23#1059734111yescharacteristic
401C23#1059735811yescharacteristic
402C23SD16×D1911yescharacteristic
403C23#1059736211yescharacteristic
404C23Q16×D1911yescharacteristic
405Q8—1521no—
406Q8—1521no—
407D4—382no—
408D4—382no—
409D4—382no—
410D4—382no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—192no—
429C2×C4—381no—
430C2×C4—381no—
431C2×C4—381no—
432C2×C4—381no—
433C2×C4—762no—
434C2×C4—761no—
435C2×C4—761no—
436C2×C4—761no—
437C2×C4—761no—
438C2×C4—761no—
439C2×C4—761no—
440C2×C4—761no—
441C2×C4—761no—
442C2×C4—1521no—
443C2×C4—1521no—
444C2×C4—1521no—
445C2×C4—1521no—
446C2×C4C4×D7611yescharacteristic
447C2×C4#1059732811yescharacteristic
448C2×C4#1059733911yescharacteristic
449C2×C4#1059734011yescharacteristic
450C8—42no—
451C8—762no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—382no—
463C22—762no—
464C22—761no—
465C22—761no—
466C22—1521no—
467C22#1192642211yescharacteristic
468C22#103×D1911yescharacteristic
469C22#1192653711yescharacteristic
470C22#1192677211yescharacteristic
471C22#1192677411yescharacteristic
472C22#1192678411yescharacteristic
473C22#1192678611yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—81no—
480C4—161no—
481C4—382no—
482C4—3041no—
483C4—761no—
484C4—761no—
485C4—1521no—
486C4—1521no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—762no—
494C2#1456401711yescharacteristic
495C2#1456405711yescharacteristic
496C2#1456417611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC22×C19#386
prime radicalC22×C22⋊D19D4
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#9383
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #14562208C2semidirect
5. #14562206C2semidirect
6. #14561514C2semidirect
7. C19×#1294C2semidirect
16. #11926484C4semidirect
17. #11926481C4semidirect
18. #11926465C4semidirect
19. #11926457C4semidirect
210. #1294D19semidirect
327. C19#9383semidirect

Maximal subgroups

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

subgroupindex
#145726572
#145688152
#145636202
#145622082
#145622062
#145615142
C19×#12942
#938319