Finite Group Databasebeta

← #18078148

Subgroups — #18078148

Order 4864.

614 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926496C211yesmaximal, characteristic
2#14571946C211yesmaximal, characteristic
3#14563398C211yesmaximal, characteristic
4C2×#11926285C211yesmaximal, characteristic, complemented
5C2×#11926285C211yesmaximal, characteristic, complemented
6#14561516C211yesmaximal, characteristic, complemented
7C19×#1295C211yesmaximal, characteristic, complemented
8C22×#64515—21no—
9C2×#10597316C2211yescharacteristic
10C2×C42×D19C2211yescharacteristic
11C2×(C2×D19)⋊C8—21no—
12#11926496—22no—
13#11926496—22no—
14C2×#10597260C2211yescharacteristic
15C2×#10597260C2211yescharacteristic
16C2×C8×Dic19—21no—
17#11926443C411yescharacteristic
18#11926443C411yescharacteristic
19#11926429—21no—
20#11926429—21no—
21#11926418—21no—
22#11926418—21no—
23#11926401C411yescharacteristic
24#11926401C411yescharacteristic
25#11926298—21no—
26#11926285—22no—
27#11926285—22no—
28C2×C19×#97C2211yescharacteristic
29C2×C19×#97C2211yescharacteristic
30C19×#382C2211yescharacteristic
31C22×C4×D19C2×C411yescharacteristic
32C22×C4×D19D411yescharacteristic
33C22×C4×D19D411yescharacteristic
34C22×C8×C19—21no—
35C22×C8×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C42×C19C2311yescharacteristic
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×C4×Dic19C2×C411yescharacteristic
48C2×C4×Dic19D411yescharacteristic
49C2×C4×Dic19D411yescharacteristic
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52C2×#64515—24no—
53C2×#64515—24no—
54C2×#64515—24no—
55C42×D19—21no—
56C42×D19—21no—
57C42×D19—21no—
58C42×D19—21no—
59#10597316—21no—
60#10597316—21no—
61#10597316—21no—
62#10597316—21no—
63C19×#97—21no—
64C19×#97—21no—
65C19×#97—21no—
66C19×#97D412yes—
67C19×#95—21no—
68C19×#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73(C2×D19)⋊C8—24no—
74C8×Dic19—24no—
75#10597260—21no—
76#10597260—21no—
77#10597260—21no—
78#10597260D412yes—
79C23×D19C22⋊C411yescharacteristic
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19C22×C411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19C22⋊C411yescharacteristic
88C22×Dic19C22⋊C411yescharacteristic
89C22×Dic19C22⋊C411yescharacteristic
90C2×C4×D19—22no—
91C2×C4×D19—21no—
92C2×C4×D19—21no—
93C2×C4×D19—22no—
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×C4×D19—21no—
97C2×C4×D19—21no—
98C2×C4×D19—22no—
99C2×C4×D19—22no—
100C2×C4×D19—41no—
101C2×C4×D19—41no—
102C2×C8×C19—22no—
103C2×C8×C19—22no—
104C2×C8×C19—22no—
105C2×C8×C19—22no—
106C2×C8×C19—41no—
107C2×C8×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19#4111yescharacteristic
113C42×C19#4111yescharacteristic
114(C2×D19)⋊C4—42no—
115(C2×D19)⋊C4—42no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—42no—
121C4⋊Dic19—42no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124Dic19⋊C4—41no—
125Dic19⋊C4—41no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128C4×Dic19—21no—
129C4×Dic19—21no—
130C4×Dic19—21no—
131C4×Dic19—21no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8—22no—
134C2×C19⋊C8—22no—
135C2×C19⋊C8—22no—
136C2×C19⋊C8—41no—
137C2×C19⋊C8—41no—
138#64515—216no—
139#9122—191nomaximal, Sylow
140C23×C19C2×C22⋊C411yescharacteristic
141C22×D19—21no—
142C22×D19—21no—
143C22×D19—21no—
144C22×D19—21no—
145C22×D19—21no—
146C22×D19—21no—
147C22×D19#10412yes—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19C4×D411yescharacteristic
161C2×C4×C19C4×D411yescharacteristic
162C2×C4×C19#12011yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12311yescharacteristic
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—21no—
171C2×Dic19—21no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19#10112yes—
179C2×Dic19#10412yes—
180C2×Dic19#10412yes—
181C4×D19—24no—
182C4×D19—24no—
183C4×D19—42no—
184C4×D19—42no—
185C4×D19—42no—
186C4×D19—42no—
187C8×C19—24no—
188C8×C19—42no—
189C19⋊C8—24no—
190C19⋊C8—42no—
191C2×C4×M16—191no—
192#2851—191no—
193#1749—191no—
194C2×#330—191no—
195C2×#330—191no—
196#1295—191no—
197#1295D1911yescharacteristic, complemented
198C22×C19#38611yescharacteristic
199C22×C19C2×#10111yescharacteristic
200C22×C19#41311yescharacteristic
201C22×C19C2×#10411yescharacteristic
202C22×C19C2×#10411yescharacteristic
203C22×C19C2×#10411yescharacteristic
204C22×C19#42111yescharacteristic
205C2×D19—22no—
206C2×D19—22no—
207C2×D19—22no—
208C2×D19—41no—
209C2×D19—41no—
210C2×D19—41no—
211C2×D19—41no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—81no—
219C4×C19—81no—
220Dic19—22no—
221Dic19—22no—
222Dic19—22no—
223Dic19—81no—
224Dic19—81no—
225C22×M16—381no—
226C2×#125—191no—
227C22×C42—191no—
228C2×C22⋊C8—381no—
229C4×M16—382no—
230C4×M16—382no—
231C2×#97—191no—
232C2×#97—191no—
233C2×#97C2×D1911yescharacteristic
234C2×#97C2×D1911yescharacteristic
235C2×C4×C8—381no—
236#389—191no—
237#389—191no—
238#387—381no—
239#387—381no—
240#385—381no—
241#385—381no—
242#382C2×D1911yescharacteristic
243#380—191no—
244#380—191no—
245#336—381no—
246#330—382no—
247#330—382no—
248C2×C19#152411yescharacteristic
249C2×C19#152611yescharacteristic
250C2×C19#152811yescharacteristic
251C2×C19#152911yescharacteristic
252C2×C19#187111yescharacteristic
253C2×C19#189611yescharacteristic
254C2×C19#190111yescharacteristic
255D19—42no—
256C23×C4—191no—
257C23×C4—191no—
258C23×C4—191no—
259C2×M16—384no—
260C2×M16—384no—
261C2×M16—384no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—381no—
265C22×C8—381no—
266#125—381no—
267#125—381no—
268#125—381no—
269#125—381no—
270C2×C4⋊C4—191no—
271C2×C4⋊C4—191no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—381no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4C4×D1911yescharacteristic
277C2×C4⋊C4C4×D1911yescharacteristic
278C2×C22⋊C4—381no—
279C2×C22⋊C4—381no—
280C2×C42—191no—
281C2×C42—191no—
282C2×C42—191no—
283C2×C42—381no—
284C2×C42—381no—
285C2×C42—381no—
286C2×C42—381no—
287C2×C42C22×D1911yescharacteristic
288C22⋊C8—384no—
289#97—21no—
290#97—21no—
291#97—21no—
292#97—192no—
293#97—381no—
294#97—381no—
295#97—381no—
296#97D7612yes—
297C4×C8—384no—
298#95—21no—
299#95—21no—
300#95—381no—
301#95—381no—
302#95—381no—
303#95—381no—
304C19#912211yescharacteristic, complemented, Sylow
305C24—191no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—191no—
309C22×C4—191no—
310C22×C4—191no—
311C22×C4—382no—
312C22×C4—382no—
313C22×C4—382no—
314C22×C4—382no—
315C22×C4—381no—
316C22×C4—381no—
317C22×C4—381no—
318C22×C4—381no—
319C22×C4—381no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—381no—
323C22×C4—761no—
324C22×C4—761no—
325C22×C4C2×C4×D1911yescharacteristic
326C22×C4D4×D1911yescharacteristic
327C22×C4D4×D1911yescharacteristic
328M16—3816no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—382no—
336C2×C8—382no—
337C2×C8—382no—
338C2×C8—382no—
339C2×C8—761no—
340C2×C8—761no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—381no—
344C4⋊C4—381no—
345C4⋊C4—381no—
346C4⋊C4—381no—
347C4⋊C4—762no—
348C4⋊C4—762no—
349C4⋊C4—761no—
350C4⋊C4—761no—
351C4⋊C4—761no—
352C4⋊C4—761no—
353C22⋊C4—762no—
354C22⋊C4—762no—
355C42—381no—
356C42—381no—
357C42—381no—
358C42—381no—
359C42—381no—
360C42—381no—
361C42C2×D7611yescharacteristic
362C42#6454111yescharacteristic
363C42D4×D1911yescharacteristic
364C42#6454511yescharacteristic
365C23—192no—
366C23—381no—
367C23—381no—
368C23—381no—
369C23—381no—
370C23—381no—
371C23—381no—
372C23C22⋊C4×D1911yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—192no—
386C2×C4—192no—
387C2×C4—192no—
388C2×C4—384no—
389C2×C4—384no—
390C2×C4—381no—
391C2×C4—381no—
392C2×C4—381no—
393C2×C4—381no—
394C2×C4—381no—
395C2×C4—381no—
396C2×C4—762no—
397C2×C4—762no—
398C2×C4—762no—
399C2×C4—762no—
400C2×C4—761no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4C4×D7611yescharacteristic
407C2×C4#1059732811yescharacteristic
408C2×C4#1059733011yescharacteristic
409C2×C4#1059733911yescharacteristic
410C2×C4#1059734011yescharacteristic
411C2×C4#1059734111yescharacteristic
412C8—24no—
413C8—42no—
414C8—384no—
415C8—762no—
416C22—382no—
417C22—382no—
418C22—382no—
419C22—761no—
420C22—761no—
421C22—761no—
422C22—761no—
423C22#1192642211yescharacteristic
424C22#101×D1911yescharacteristic
425C22#1192652511yescharacteristic
426C22#104×D1911yescharacteristic
427C22#104×D1911yescharacteristic
428C22#104×D1911yescharacteristic
429C22#1192655911yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—382no—
439C4—382no—
440C4—382no—
441C4—1521no—
442C4—1521no—
443C2—762no—
444C2#1456222011yescharacteristic
445C2#1456222811yescharacteristic
446C2#1456223511yescharacteristic
447C2#1456223911yescharacteristic
448C2#1456393611yescharacteristic
449C2#1456407711yescharacteristic
450C2#1456410211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1295D19
hypocenterC19#9122
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. C2×#11926285C2semidirect
5. C2×#11926285C2semidirect
6. #14561516C2semidirect
7. C19×#1295C2semidirect
197. #1295D19semidirect
304. C19#9122semidirect

Maximal subgroups

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

subgroupindex
C2×#119264962
#145719462
#145633982
C2×#119262852
#145615162
C19×#12952
#912219