Finite Group Databasebeta

← #18082830

Subgroups — #18082830

Order 4864.

778 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569442C211yesmaximal, characteristic
2C2×#11926479C211yesmaximal, characteristic
3#14563725C211yesmaximal, characteristic, complemented
4C2×#11926281C211yesmaximal, characteristic, complemented
5C2×#11926267C211yesmaximal, characteristic
6#14561515C211yesmaximal, characteristic, complemented
7C2×C19×#484C211yesmaximal, characteristic, complemented
8C22×Dic19⋊C4—21no—
9C22×(C2×D19)⋊C4—21no—
10C22×(C2×D19)⋊C4C2211yescharacteristic
11C2×C22⋊(C19⋊C8)C2211yescharacteristic
12#11926479—22no—
13#11926479—22no—
14#11926479—21no—
15#11926466—22no—
16#11926455—21no—
17#11926416—21no—
18#11926404C2211yescharacteristic
19#11926399—21no—
20C2×C19⋊#95C2211yescharacteristic
21#11926306—22no—
22#11926281—22no—
23#11926267—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#484—22no—
27C19×#484—22no—
28C2×C19×#107—21no—
29C2×C19×#103—21no—
30C2×C19×C22⋊C8C2211yescharacteristic
31C24×D19D411yescharacteristic
32C22×Q8×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19C2311yescharacteristic
35C23×Dic19—21no—
36C23×Dic19D411yescharacteristic
37C22×C8×C19—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—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×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D412yes—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊Dic19—21no—
52C2×(C2×D19)⋊C4—24no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4—22no—
60C2×(C2×D19)⋊C4—22no—
61C2×(C2×D19)⋊C4—44no—
62C2×C4⋊Dic19D412yes—
63C2×Dic19⋊C4—24no—
64C2×Dic19⋊C4—22no—
65C2×Dic19⋊C4—44no—
66C22×C19⋊C8—21no—
67C19×#107—24no—
68C19×#103—24no—
69C19×C22⋊C8—21no—
70C19×C22⋊C8D412yes—
71C19⋊#95—22no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95D412yes—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C23×D19—21no—
80C23×D19—21no—
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—21no—
84C23×D19—42no—
85C23×D19—42no—
86C23×D19Q1612yes—
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—42no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—22no—
93C22×C4×C19—42no—
94C22×C4×C19—42no—
95C22×C4×C19—42no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C22×Dic19—24no—
105C22×Dic19—22no—
106C22×Dic19—22no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—42no—
111C22×Dic19—41no—
112C22×Dic19—41no—
113C22×Dic19—42no—
114C2×C8×C19—22no—
115C2×C8×C19—42no—
116C4⋊C4×C19—22no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19—22no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—41no—
121C4⋊C4×C19—41no—
122C4⋊C4×C19—41no—
123C4⋊C4×C19—41no—
124C22⋊C4×C19—41no—
125C22⋊C4×C19—41no—
126C22⋊Dic19—41no—
127C22⋊Dic19—41no—
128(C2×D19)⋊C4—48no—
129(C2×D19)⋊C4—41no—
130(C2×D19)⋊C4—41no—
131(C2×D19)⋊C4—41no—
132(C2×D19)⋊C4—41no—
133(C2×D19)⋊C4—82no—
134(C2×D19)⋊C4—82no—
135C4⋊Dic19—42no—
136Dic19⋊C4—48no—
137Dic19⋊C4—82no—
138C2×C19⋊C8—42no—
139C2×C19⋊C8—41no—
140#9928—191nomaximal, Sylow
141C23×C19—22no—
142C23×C19—22no—
143C23×C19#12011yescharacteristic
144C23×C19#12011yescharacteristic
145C23×C19#12111yescharacteristic
146C23×C19C2×Q1611yescharacteristic
147C23×C19#13511yescharacteristic
148C23×C19#13711yescharacteristic
149C23×C19#13711yescharacteristic
150C22×D19—22no—
151C22×D19—22no—
152C22×D19—22no—
153C22×D19—44no—
154C22×D19—42no—
155C22×D19—44no—
156C22×D19—42no—
157C22×D19—41no—
158C22×D19—41no—
159C22×D19—41no—
160C22×D19—42no—
161C22×D19—42no—
162C22×D19—41no—
163C22×D19—82no—
164C22×D19—82no—
165C22×D19—81no—
166C22×D19—81no—
167Q8×C19—42no—
168Q8×C19—81no—
169C2×C4×C19—22no—
170C2×C4×C19—22no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—42no—
176C2×C4×C19—42no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—82no—
183C2×C4×C19—82no—
184C2×C4×C19#12011yescharacteristic
185C2×C4×C19#12111yescharacteristic
186C2×C4×C19#12111yescharacteristic
187C2×C4×C19#12711yescharacteristic
188C2×Dic19—24no—
189C2×Dic19—44no—
190C2×Dic19—44no—
191C2×Dic19—42no—
192C2×Dic19—42no—
193C2×Dic19—42no—
194C2×Dic19—41no—
195C2×Dic19—42no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—81no—
200C8×C19—42no—
201C19⋊C8—81no—
202C2×#484D1911yescharacteristic, complemented
203#2626—191no—
204C2×#399—191no—
205#1824—191no—
206C2×#328—191no—
207C2×#323—191no—
208#1294—191no—
209C22×C19—22no—
210C22×C19—22no—
211C22×C19—22no—
212C22×C19—22no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19#39211yescharacteristic
218C22×C19#45111yescharacteristic
219C22×C19#45111yescharacteristic
220C22×C19#45211yescharacteristic
221C22×C19#45211yescharacteristic
222C22×C19#45312yes—
223C22×C19#45812yes—
224C22×C19#46711yescharacteristic
225C22×C19#47011yescharacteristic
226C2×D19—44no—
227C2×D19—44no—
228C2×D19—42no—
229C2×D19—82no—
230C2×D19—82no—
231C2×D19—82no—
232C2×D19—81no—
233C2×D19—81no—
234C2×D19—82no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—81no—
240C4×C19—82no—
241C4×C19—81no—
242Dic19—44no—
243Dic19—82no—
244Dic19—81no—
245C2×C22⋊Q8C2×D1911yescharacteristic
246C22×C4⋊C4—381no—
247C22×C4⋊C4C2×D1911yescharacteristic
248C22×C22⋊C4—191no—
249C22×C22⋊C4—381no—
250#484—22no—
251#484—22no—
252C2×#107—21no—
253C2×#103—21no—
254C2×C22⋊C8—191no—
255C2×C22⋊C8C2×D1911yescharacteristic
256#399—382no—
257#399—381no—
258#399—382no—
259#396—382no—
260#393—381no—
261#385—381no—
262#380—191no—
263#379—381no—
264C2×#95—191no—
265#340—382no—
266#328—382no—
267#323—382no—
268C2×C19—21no—
269C2×C19—21no—
270C2×C19—21no—
271C2×C19—21no—
272C2×C19#161412yes—
273C2×C19#161812yes—
274C2×C19#200111yescharacteristic
275C2×C19#200211yescharacteristic
276C2×C19#202211yescharacteristic
277D19—82no—
278C25—191no—
279C22×Q8C22⋊D1911yescharacteristic
280C23×C4—21no—
281C23×C4—191no—
282C23×C4—381no—
283C23×C4C22×D1911yescharacteristic
284C22×C8—21no—
285C22×C8—381no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—192no—
297C2×C4⋊C4—384no—
298C2×C4⋊C4—382no—
299C2×C4⋊C4—764no—
300C2×C4⋊C4C22⋊D1912yes—
301C2×C4⋊C4C22⋊D1911yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—384no—
304C2×C22⋊C4—381no—
305C2×C22⋊C4—381no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C22⋊C4—381no—
311C2×C22⋊C4—382no—
312C2×C22⋊C4—382no—
313C2×C22⋊C4—764no—
314#107—24no—
315#103—24no—
316C22⋊C8—21no—
317C22⋊C8—381no—
318C22⋊C8—381no—
319C22⋊C8C22⋊D1912yes—
320#95—192no—
321#95—382no—
322#95—381no—
323#95—381no—
324C19#992811yescharacteristic, complemented, Sylow
325C24—192no—
326C24—381no—
327C24—381no—
328C24—381no—
329C24—381no—
330C24—381no—
331C24—381no—
332C24—762no—
333C24—762no—
334C24D4×D1911yescharacteristic
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—42no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—384no—
347C22×C4—382no—
348C22×C4—381no—
349C22×C4—382no—
350C22×C4—381no—
351C22×C4—381no—
352C22×C4—762no—
353C22×C4—761no—
354C22×C4—761no—
355C22×C4—762no—
356C22×C4D4×D1911yescharacteristic
357C22×C4D4×D1911yescharacteristic
358C22×C4#6454311yescharacteristic
359C22×C4C2×C22⋊D1911yescharacteristic
360C22×C4C2×C22⋊D1911yescharacteristic
361C22×C4C2×C22⋊D1911yescharacteristic
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—762no—
365C2×C8—761no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—762no—
375C4⋊C4—768no—
376C4⋊C4—1522no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—768no—
380C22⋊C4—761no—
381C22⋊C4—761no—
382C22⋊C4—761no—
383C22⋊C4—761no—
384C22⋊C4—761no—
385C22⋊C4—761no—
386C22⋊C4—1522no—
387C22⋊C4—1522no—
388C23—22no—
389C23—22no—
390C23—382no—
391C23—382no—
392C23—382no—
393C23—764no—
394C23—762no—
395C23—764no—
396C23—762no—
397C23—761no—
398C23—761no—
399C23—761no—
400C23—761no—
401C23—762no—
402C23—762no—
403C23—1522no—
404C23—1521no—
405C23—1522no—
406C23—1521no—
407C23Q16×D1911yescharacteristic
408C23#1059736411yescharacteristic
409C23#1059736411yescharacteristic
410C23#1059736511yescharacteristic
411C23#1059738311yescharacteristic
412C23#1059738311yescharacteristic
413C23#1059738411yescharacteristic
414Q8—42no—
415Q8—81no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—384no—
432C2×C4—764no—
433C2×C4—764no—
434C2×C4—762no—
435C2×C4—762no—
436C2×C4—762no—
437C2×C4—762no—
438C2×C4—761no—
439C2×C4—762no—
440C2×C4—762no—
441C2×C4—762no—
442C2×C4—1521no—
443C2×C4#1059738511yescharacteristic
444C2×C4#1059738511yescharacteristic
445C2×C4#1059738611yescharacteristic
446C2×C4#1059739911yescharacteristic
447C8—42no—
448C8—1521no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—21no—
456C22—21no—
457C22—764no—
458C22—762no—
459C22—764no—
460C22—1522no—
461C22—1522no—
462C22—1522no—
463C22—1521no—
464C22—1522no—
465C22—1521no—
466C22#1192645211yescharacteristic
467C22#1192669811yescharacteristic
468C22#1192669811yescharacteristic
469C22#1192670511yescharacteristic
470C22#1192670511yescharacteristic
471C22#1192671012yes—
472C22#1192673312yes—
473C22#1192678211yescharacteristic
474C22#1192679911yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—82no—
480C4—81no—
481C4—81no—
482C4—764no—
483C4—1521no—
484C4—1522no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—1522no—
490C2#1456265812yes—
491C2#1456268212yes—
492C2#1456464211yescharacteristic
493C2#1456464711yescharacteristic
494C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#484C2
socleC23×C19#120
prime radicalC24×D19D4
hypercenterC2×#484D19
hypocenterC19#9928
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #14563725C2semidirect
4. C2×#11926281C2semidirect
6. #14561515C2semidirect
7. C2×C19×#484C2semidirect
202. C2×#484D19semidirect
324. C19#9928semidirect

Maximal subgroups

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

subgroupindex
#145694422
C2×#119264792
#145637252
C2×#119262812
C2×#119262672
#145615152
C2×C19×#4842
#992819