Finite Group Databasebeta

← #18078136

Subgroups — #18078136

Order 4864.

684 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926496C211yesmaximal, characteristic, complemented
2#14571931C211yesmaximal, characteristic
3#14563398C211yesmaximal, characteristic, complemented
4C2×#11926284C211yesmaximal, characteristic, complemented
5#14561517C211yesmaximal, characteristic, complemented
6#14561517C211yesmaximal, characteristic, complemented
7C2×C19×#329C211yesmaximal, characteristic, complemented
8C22×#64515—21no—
9C2×#10597392C411yescharacteristic
10C2×#10597384C411yescharacteristic
11C2×C42×D19C2211yescharacteristic
12C2×(C2×D19)⋊C8—21no—
13#11926496—22no—
14#11926496—22no—
15C2×#10597260C2211yescharacteristic
16C2×#10597260C2211yescharacteristic
17C2×C8×Dic19—21no—
18#11926451C411yescharacteristic
19#11926447C411yescharacteristic
20#11926432—21no—
21#11926432—21no—
22#11926420—21no—
23#11926420—21no—
24#11926410C2211yescharacteristic
25#11926298—21no—
26#11926284—22no—
27C2×C19×#124C2211yescharacteristic
28C2×C19×#97C2211yescharacteristic
29C2×C19×#97C2211yescharacteristic
30C19×#329—22no—
31C22×Q8×C19C2×C411yescharacteristic
32C22×D4×C19C2×C411yescharacteristic
33C22×C22⋊D19—21no—
34C22×C4×D19C2×C411yescharacteristic
35C22×C4×D19D411yescharacteristic
36C22×C4×D19D411yescharacteristic
37C22×C8×C19—21no—
38C22×C8×C19—21no—
39C19×#124—21no—
40C19×#124—21no—
41C19×#124—21no—
42C19×#124—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C42×C19C2311yescharacteristic
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49#10597392—42no—
50#10597384—42no—
51C2×(C2×D19)⋊C4—21no—
52C2×C4⋊Dic19C2×C411yescharacteristic
53C2×C4⋊Dic19C2×C411yescharacteristic
54C2×Dic19⋊C4—21no—
55C2×C4×Dic19C2×C411yescharacteristic
56C2×C4×Dic19D411yescharacteristic
57C2×C4×Dic19D411yescharacteristic
58C22×C19⋊C8—21no—
59C22×C19⋊C8—21no—
60C2×#64515—24no—
61C2×#64515—24no—
62C2×#64515—24no—
63C42×D19—21no—
64C42×D19—21no—
65C42×D19—21no—
66C42×D19—21no—
67C19×#97—21no—
68C19×#97—21no—
69C19×#97—21no—
70C19×#97D412yescomplemented
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75(C2×D19)⋊C8—24no—
76C8×Dic19—24no—
77#10597260—21no—
78#10597260—21no—
79#10597260—21no—
80#10597260D412yescomplemented
81C24×C19—21no—
82C23×D19C22⋊C411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—41no—
86C2×Q8×C19—41no—
87C2×D4×C19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C22×C4×C19—21no—
92C22×C4×C19C22×C411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C2×C22⋊D19—42no—
96C2×C22⋊D19—42no—
97C2×C22⋊D19—42no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19C22⋊C411yescharacteristic
101C22×Dic19C22⋊C411yescharacteristic
102C22×Dic19C22⋊C411yescharacteristic
103C2×C4×D19—22no—
104C2×C4×D19—21no—
105C2×C4×D19—21no—
106C2×C4×D19—22no—
107C2×C4×D19—21no—
108C2×C4×D19—21no—
109C2×C4×D19—21no—
110C2×C4×D19—21no—
111C2×C4×D19—22no—
112C2×C4×D19—22no—
113C2×C4×D19—41no—
114C2×C4×D19—41no—
115C2×C8×C19—22no—
116C2×C8×C19—22no—
117C2×C8×C19—22no—
118C2×C8×C19—22no—
119C2×C8×C19—41no—
120C2×C8×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19—41no—
124C22⋊C4×C19—41no—
125C42×C19C2×D411yescharacteristic
126C42×C19C2×D411yescharacteristic
127C42×C19#4111yescharacteristic
128C42×C19#4111yescharacteristic
129C22⋊Dic19—42no—
130C22⋊Dic19—42no—
131C22⋊Dic19—42no—
132(C2×D19)⋊C4—42no—
133C4⋊Dic19—41no—
134C4⋊Dic19—41no—
135Dic19⋊C4—42no—
136C4×Dic19—21no—
137C4×Dic19—21no—
138C4×Dic19—21no—
139C4×Dic19—21no—
140C4×Dic19—21no—
141C4×Dic19—21no—
142C2×C19⋊C8—22no—
143C2×C19⋊C8—22no—
144C2×C19⋊C8—22no—
145C2×C19⋊C8—22no—
146C2×C19⋊C8—41no—
147C2×C19⋊C8—41no—
148#64515—216no—
149#9120—191nomaximal, Sylow
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19C2×C22⋊C411yescharacteristic
158C22×D19—21no—
159C22×D19—21no—
160C22×D19—21no—
161C22×D19—21no—
162C22×D19—21no—
163C22×D19—21no—
164C22×D19#10412yes—
165Q8×C19—81no—
166Q8×C19—81no—
167D4×C19—81no—
168D4×C19—81no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—21no—
172C2×C4×C19—21no—
173C2×C4×C19—21no—
174C2×C4×C19—21no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19C4×D411yescharacteristic
179C2×C4×C19C4×D411yescharacteristic
180C2×C4×C19#12011yescharacteristic
181C2×C4×C19#12111yescharacteristic
182C2×C4×C19#12111yescharacteristic
183C2×C4×C19#12311yescharacteristic
184C22⋊D19—84no—
185C2×Dic19—21no—
186C2×Dic19—21no—
187C2×Dic19—21no—
188C2×Dic19—21no—
189C2×Dic19—21no—
190C2×Dic19—21no—
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—41no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19#10012yes—
198C2×Dic19#10412yes—
199C2×Dic19#10412yes—
200C4×D19—24no—
201C4×D19—24no—
202C4×D19—42no—
203C4×D19—42no—
204C4×D19—42no—
205C4×D19—42no—
206C8×C19—24no—
207C8×C19—42no—
208C19⋊C8—24no—
209C19⋊C8—42no—
210C2×C4×M16—191no—
211#2850—191no—
212#1749—191no—
213C2×#329—191no—
214C2×#329D1911yescharacteristic, complemented
215#1295—191no—
216#1295—191no—
217C22×C19—81no—
218C22×C19—81no—
219C22×C19—81no—
220C22×C19—81no—
221C22×C19—81no—
222C22×C19—81no—
223C22×C19—81no—
224C22×C19#38611yescharacteristic
225C22×C19C2×#10011yescharacteristic
226C22×C19#41311yescharacteristic
227C22×C19C2×#10411yescharacteristic
228C22×C19C2×#10411yescharacteristic
229C22×C19C2×#10411yescharacteristic
230C22×C19#42111yescharacteristic
231C2×D19—22no—
232C2×D19—22no—
233C2×D19—22no—
234C2×D19—41no—
235C2×D19—41no—
236C2×D19—41no—
237C2×D19—41no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—21no—
243C4×C19—21no—
244C4×C19—81no—
245Dic19—22no—
246Dic19—22no—
247Dic19—22no—
248Dic19—81no—
249Dic19—81no—
250C22×M16—381no—
251C2×#124C2×D1911yescharacteristic
252C2×C22⋊Q8—191no—
253C2×#121—191no—
254C22×C42—191no—
255C2×C22⋊C8—381no—
256C4×M16—382no—
257C4×M16—382no—
258C2×#97—191no—
259C2×#97—191no—
260C2×#97C2×D1911yescharacteristic
261C2×#97C2×D1911yescharacteristic
262C2×C4×C8—381no—
263#391—191no—
264#390—191no—
265#388—381no—
266#388—381no—
267#386—381no—
268#386—381no—
269#382—191no—
270#336—381no—
271#329—22no—
272#329—382no—
273C2×C19—161no—
274C2×C19#152411yescharacteristic
275C2×C19#152511yescharacteristic
276C2×C19#152711yescharacteristic
277C2×C19#152911yescharacteristic
278C2×C19#187111yescharacteristic
279C2×C19#189611yescharacteristic
280C2×C19#190011yescharacteristic
281D19—42no—
282C22×Q8C4×D1911yescharacteristic
283C22×D4—381no—
284C22×D4C4×D1911yescharacteristic
285C23×C4—191no—
286C23×C4—191no—
287C23×C4—191no—
288C2×M16—384no—
289C2×M16—384no—
290C2×M16—384no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—381no—
294C22×C8—381no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124—21no—
299C22⋊Q8—762no—
300#121—762no—
301C2×C4⋊C4—191no—
302C2×C4⋊C4—191no—
303C2×C4⋊C4—381no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C42—191no—
311C2×C42—191no—
312C2×C42—191no—
313C2×C42—381no—
314C2×C42—381no—
315C2×C42—381no—
316C2×C42—381no—
317C2×C42C22×D1911yescharacteristic
318C22⋊C8—384no—
319#97—21no—
320#97—21no—
321#97—21no—
322#97—192no—
323#97—381no—
324#97—381no—
325#97—381no—
326#97C22⋊D1912yescomplemented
327C4×C8—384no—
328#95—381no—
329#95—381no—
330#95—381no—
331#95—381no—
332C19#912011yescharacteristic, complemented, Sylow
333C24—21no—
334C24—191no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—762no—
344C2×D4—762no—
345C2×D4—762no—
346C22×C4—21no—
347C22×C4—191no—
348C22×C4—191no—
349C22×C4—191no—
350C22×C4—382no—
351C22×C4—382no—
352C22×C4—382no—
353C22×C4—382no—
354C22×C4—381no—
355C22×C4—381no—
356C22×C4—381no—
357C22×C4—381no—
358C22×C4—381no—
359C22×C4—381no—
360C22×C4—381no—
361C22×C4—381no—
362C22×C4—761no—
363C22×C4—761no—
364C22×C4C2×C4×D1911yescharacteristic
365C22×C4D4×D1911yescharacteristic
366C22×C4D4×D1911yescharacteristic
367M16—3816no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—382no—
375C2×C8—382no—
376C2×C8—382no—
377C2×C8—382no—
378C2×C8—761no—
379C2×C8—761no—
380C4⋊C4—761no—
381C4⋊C4—761no—
382C4⋊C4—762no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—762no—
388C22⋊C4—762no—
389C22⋊C4—762no—
390C22⋊C4—762no—
391C42—381no—
392C42—381no—
393C42—381no—
394C42—381no—
395C42—381no—
396C42—381no—
397C42#6454111yescharacteristic
398C42D4×D1911yescharacteristic
399C42#6454311yescharacteristic
400C42C2×C22⋊D1911yescharacteristic
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—192no—
409C23—381no—
410C23—381no—
411C23—381no—
412C23—381no—
413C23—381no—
414C23—381no—
415C23C22⋊C4×D1911yescharacteristic
416Q8—81no—
417Q8—81no—
418D4—81no—
419D4—81no—
420D4—1524no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—192no—
431C2×C4—192no—
432C2×C4—192no—
433C2×C4—384no—
434C2×C4—384no—
435C2×C4—381no—
436C2×C4—381no—
437C2×C4—381no—
438C2×C4—381no—
439C2×C4—381no—
440C2×C4—381no—
441C2×C4—762no—
442C2×C4—762no—
443C2×C4—762no—
444C2×C4—762no—
445C2×C4—761no—
446C2×C4—761no—
447C2×C4—761no—
448C2×C4—761no—
449C2×C4—761no—
450C2×C4—761no—
451C2×C4(C22⋊D19)⋊C411yescharacteristic
452C2×C4#1059732911yescharacteristic
453C2×C4#1059733011yescharacteristic
454C2×C4C4×C22⋊D1911yescharacteristic
455C2×C4#1059738311yescharacteristic
456C2×C4#1059738411yescharacteristic
457C8—24no—
458C8—42no—
459C8—384no—
460C8—762no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—382no—
469C22—382no—
470C22—382no—
471C22—761no—
472C22—761no—
473C22—761no—
474C22—761no—
475C22#1192642011yescharacteristic
476C22#100×D1911yescharacteristic
477C22#1192652511yescharacteristic
478C22#104×D1911yescharacteristic
479C22#104×D1911yescharacteristic
480C22#104×D1911yescharacteristic
481C22#1192655911yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—81no—
489C4—382no—
490C4—382no—
491C4—382no—
492C4—1521no—
493C4—1521no—
494C2—161no—
495C2—762no—
496C2#1456222011yescharacteristic
497C2#1456222511yescharacteristic
498C2#1456223111yescharacteristic
499C2#1456223911yescharacteristic
500C2#1456393411yescharacteristic
501C2#1456407511yescharacteristic
502C2#1456409511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#329C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597384C4
cosocleC2×C42×C19C23
hypercenterC2×#329D19
hypocenterC19#9120
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
1. C2×#11926496C2semidirect
3. #14563398C2semidirect
4. C2×#11926284C2semidirect
5. #14561517C2semidirect
6. #14561517C2semidirect
7. C2×C19×#329C2semidirect
70. C19×#97D4semidirect
80. #10597260D4semidirect
214. C2×#329D19semidirect
326. #97C22⋊D19semidirect
332. C19#9120semidirect

Maximal subgroups

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

subgroupindex
C2×#119264962
#145719312
#145633982
C2×#119262842
#145615172
C2×C19×#3292
#912019