Finite Group Databasebeta

← #18078156

Subgroups — #18078156

Order 4864.

600 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
1C2×#11926599C211yesmaximal, 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
8C2×#10597392C411yescharacteristic
9C2×#10597384C411yescharacteristic
10C2×C42×D19C2211yescharacteristic
11#11926599—22no—
12#11926599—22no—
13C2×Dic19⋊C8—21no—
14C2×(C2×D19)⋊C8—21no—
15C2×(C2×D19)⋊C8—21no—
16C2×#10597260C2211yescharacteristic
17C2×#10597260C2211yescharacteristic
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—
60C42×D19—21no—
61C42×D19—21no—
62C42×D19—21no—
63C42×D19—21no—
64C19×#97—21no—
65C19×#97—21no—
66C19×#97—21no—
67C19×#97D412yescomplemented
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72(C2×D19)⋊C8—24no—
73(C2×D19)⋊C8—24no—
74Dic19⋊C8—24no—
75#10597260—21no—
76#10597260—21no—
77#10597260—21no—
78#10597260D412yescomplemented
79C24×C19—21no—
80C23×D19C22⋊C411yescharacteristic
81C2×Q8×C19—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—41no—
84C2×Q8×C19—41no—
85C2×D4×C19—21no—
86C2×D4×C19—21no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C22×C4×C19—21no—
90C22×C4×C19C22×C411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C2×C22⋊D19—42no—
94C2×C22⋊D19—42no—
95C2×C22⋊D19—42no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19C22⋊C411yescharacteristic
99C22×Dic19C22⋊C411yescharacteristic
100C22×Dic19C22⋊C411yescharacteristic
101C2×C4×D19—22no—
102C2×C4×D19—21no—
103C2×C4×D19—21no—
104C2×C4×D19—21no—
105C2×C4×D19—21no—
106C2×C4×D19—21no—
107C2×C4×D19—21no—
108C2×C4×D19—22no—
109C2×C4×D19—41no—
110C2×C4×D19—41no—
111C2×C4×D19—41no—
112C2×C4×D19—41no—
113C2×C8×C19—22no—
114C2×C8×C19—22no—
115C2×C8×C19—41no—
116C2×C8×C19—41no—
117C2×C8×C19—41no—
118C2×C8×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C42×C19C2×D411yescharacteristic
124C42×C19C2×D411yescharacteristic
125C42×C19#4111yescharacteristic
126C42×C19#4111yescharacteristic
127C22⋊Dic19—42no—
128C22⋊Dic19—42no—
129C22⋊Dic19—42no—
130(C2×D19)⋊C4—42no—
131C4⋊Dic19—41no—
132C4⋊Dic19—41no—
133Dic19⋊C4—42no—
134C4×Dic19—21no—
135C4×Dic19—21no—
136C4×Dic19—21no—
137C4×Dic19—21no—
138C4×Dic19—21no—
139C4×Dic19—21no—
140C2×C19⋊C8—22no—
141C2×C19⋊C8—22no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145C2×C19⋊C8—41no—
146#9124—191nomaximal, Sylow
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—41no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19C2×C22⋊C411yescharacteristic
155C22×D19—21no—
156C22×D19—21no—
157C22×D19—21no—
158C22×D19—21no—
159C22×D19—21no—
160C22×D19—21no—
161C22×D19#10012yes—
162Q8×C19—81no—
163Q8×C19—81no—
164D4×C19—81no—
165D4×C19—81no—
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—21no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19C4×D411yescharacteristic
176C2×C4×C19C4×D411yescharacteristic
177C2×C4×C19#12011yescharacteristic
178C2×C4×C19#12111yescharacteristic
179C2×C4×C19#12111yescharacteristic
180C2×C4×C19#12311yescharacteristic
181C22⋊D19—84no—
182C2×Dic19—21no—
183C2×Dic19—21no—
184C2×Dic19—21no—
185C2×Dic19—21no—
186C2×Dic19—21no—
187C2×Dic19—21no—
188C2×Dic19—21no—
189C2×Dic19—21no—
190C2×Dic19—41no—
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—41no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19#10412yes—
197C4×D19—42no—
198C4×D19—42no—
199C4×D19—42no—
200C4×D19—42no—
201C4×D19—42no—
202C4×D19—42no—
203C8×C19—42no—
204C8×C19—42no—
205C19⋊C8—42no—
206C19⋊C8—42no—
207C2×#432—191no—
208#2850—191no—
209#1749—191no—
210C2×#329—191no—
211C2×#329D1911yescharacteristic, complemented
212#1295—191no—
213#1295—191no—
214C22×C19—81no—
215C22×C19—81no—
216C22×C19—81no—
217C22×C19—81no—
218C22×C19—81no—
219C22×C19—81no—
220C22×C19—81no—
221C22×C19#38611yescharacteristic
222C22×C19C2×#10011yescharacteristic
223C22×C19#41311yescharacteristic
224C22×C19C2×#10411yescharacteristic
225C22×C19#42111yescharacteristic
226C22×C19#42111yescharacteristic
227C22×C19#42111yescharacteristic
228C2×D19—22no—
229C2×D19—22no—
230C2×D19—22no—
231C2×D19—41no—
232C2×D19—41no—
233C2×D19—41no—
234C2×D19—41no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—81no—
242Dic19—22no—
243Dic19—41no—
244Dic19—41no—
245Dic19—81no—
246Dic19—81no—
247C2×#124C2×D1911yescharacteristic
248C2×C22⋊Q8—191no—
249C2×#121—191no—
250C22×C42—191no—
251#432—382no—
252#432—382no—
253C2×C4⋊C8—381no—
254C2×C22⋊C8—381no—
255C2×C22⋊C8—381no—
256C2×#97—191no—
257C2×#97—191no—
258C2×#97C2×D1911yescharacteristic
259C2×#97C2×D1911yescharacteristic
260#391—191no—
261#390—191no—
262#388—381no—
263#388—381no—
264#386—381no—
265#386—381no—
266#382—191no—
267#336—381no—
268#329—22no—
269#329—382no—
270C2×C19—161no—
271C2×C19#152911yescharacteristic
272C2×C19#153011yescharacteristic
273C2×C19#153311yescharacteristic
274C2×C19#153511yescharacteristic
275C2×C19#187111yescharacteristic
276C2×C19#189711yescharacteristic
277C2×C19#190011yescharacteristic
278D19—42no—
279C22×Q8C4×D1911yescharacteristic
280C22×D4—381no—
281C22×D4C4×D1911yescharacteristic
282C23×C4—191no—
283C23×C4—191no—
284C23×C4—191no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—381no—
288C22×C8—381no—
289#124—21no—
290#124—21no—
291#124—21no—
292#124—21no—
293C22⋊Q8—762no—
294#121—762no—
295C2×C4⋊C4—191no—
296C2×C4⋊C4—191no—
297C2×C4⋊C4—381no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—381no—
301C2×C22⋊C4—381no—
302C2×C22⋊C4—381no—
303C2×C22⋊C4—381no—
304C2×C42—191no—
305C2×C42—191no—
306C2×C42—191no—
307C2×C42—381no—
308C2×C42—381no—
309C2×C42—381no—
310C2×C42—381no—
311C2×C42C22×D1911yescharacteristic
312C4⋊C8—384no—
313C22⋊C8—384no—
314C22⋊C8—384no—
315#97—21no—
316#97—21no—
317#97—21no—
318#97—192no—
319#97—381no—
320#97—381no—
321#97—381no—
322#97C22⋊D1912yescomplemented
323#95—381no—
324#95—381no—
325#95—381no—
326#95—381no—
327C19#912411yescharacteristic, complemented, Sylow
328C24—21no—
329C24—191no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—762no—
339C2×D4—762no—
340C2×D4—762no—
341C22×C4—21no—
342C22×C4—191no—
343C22×C4—191no—
344C22×C4—191no—
345C22×C4—382no—
346C22×C4—382no—
347C22×C4—381no—
348C22×C4—381no—
349C22×C4—381no—
350C22×C4—381no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—381no—
354C22×C4—381no—
355C22×C4—761no—
356C22×C4—761no—
357C22×C4—761no—
358C22×C4—761no—
359C22×C4C2×C4×D1911yescharacteristic
360C22×C4D4×D1911yescharacteristic
361C22×C4D4×D1911yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—382no—
369C2×C8—382no—
370C2×C8—761no—
371C2×C8—761no—
372C2×C8—761no—
373C2×C8—761no—
374C4⋊C4—761no—
375C4⋊C4—761no—
376C4⋊C4—762no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—762no—
382C22⋊C4—762no—
383C22⋊C4—762no—
384C22⋊C4—762no—
385C42—381no—
386C42—381no—
387C42—381no—
388C42—381no—
389C42—381no—
390C42—381no—
391C42#6454111yescharacteristic
392C42D4×D1911yescharacteristic
393C42#6454311yescharacteristic
394C42C2×C22⋊D1911yescharacteristic
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—192no—
403C23—381no—
404C23—381no—
405C23—381no—
406C23—381no—
407C23—381no—
408C23—381no—
409C23C22⋊C4×D1911yescharacteristic
410Q8—81no—
411Q8—81no—
412D4—81no—
413D4—81no—
414D4—1524no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—192no—
425C2×C4—381no—
426C2×C4—381no—
427C2×C4—381no—
428C2×C4—381no—
429C2×C4—381no—
430C2×C4—381no—
431C2×C4—381no—
432C2×C4—381no—
433C2×C4—762no—
434C2×C4—762no—
435C2×C4—762no—
436C2×C4—762no—
437C2×C4—762no—
438C2×C4—762no—
439C2×C4—761no—
440C2×C4—761no—
441C2×C4—761no—
442C2×C4—761no—
443C2×C4—761no—
444C2×C4—761no—
445C2×C4(C22⋊D19)⋊C411yescharacteristic
446C2×C4#1059732911yescharacteristic
447C2×C4#1059733011yescharacteristic
448C2×C4C4×C22⋊D1911yescharacteristic
449C2×C4#1059738311yescharacteristic
450C2×C4#1059738411yescharacteristic
451C8—42no—
452C8—42no—
453C8—762no—
454C8—762no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—382no—
463C22—382no—
464C22—382no—
465C22—761no—
466C22—761no—
467C22—761no—
468C22—761no—
469C22#1192642011yescharacteristic
470C22#100×D1911yescharacteristic
471C22#1192652511yescharacteristic
472C22#104×D1911yescharacteristic
473C22#1192655911yescharacteristic
474C22#1192655911yescharacteristic
475C22#1192655911yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—382no—
484C4—761no—
485C4—761no—
486C4—1521no—
487C4—1521no—
488C2—161no—
489C2—762no—
490C2#1456223911yescharacteristic
491C2#1456224411yescharacteristic
492C2#1456225711yescharacteristic
493C2#1456226311yescharacteristic
494C2#1456393411yescharacteristic
495C2#1456408011yescharacteristic
496C2#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#9124
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×#11926599C2semidirect
3. #14563398C2semidirect
4. C2×#11926284C2semidirect
5. #14561517C2semidirect
6. #14561517C2semidirect
7. C2×C19×#329C2semidirect
67. C19×#97D4semidirect
78. #10597260D4semidirect
211. C2×#329D19semidirect
322. #97C22⋊D19semidirect
327. C19#9124semidirect

Maximal subgroups

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

subgroupindex
C2×#119265992
#145719312
#145633982
C2×#119262842
#145615172
C2×C19×#3292
#912419