Finite Group Databasebeta

← #18069284

Subgroups — #18069284

Order 4864.

692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14561875C211yesmaximal, characteristic
2#14561478C211yesmaximal, characteristic, complemented
3C19×#1280C211yesmaximal, characteristic, complemented
4C23×D76C411yescharacteristic
5C22×(C2×D19)⋊C4—21no—
6C22×(C2×D19)⋊C4—21no—
7C2×C22⋊(C19⋊C8)—21no—
8C2×C19⋊#95C411yescharacteristic
9C2×C19×C22⋊C8—21no—
10C2×C19×#95C2211yescharacteristic
11C24×D19—21no—
12C23×C4×C19C2×C411yescharacteristic
13C23×C4×C19D411yescharacteristic
14C23×C4×C19D411yescharacteristic
15C23×Dic19—21no—
16C22×D76—21no—
17C22×D76—41no—
18C22×D76—41no—
19C22×D76—42no—
20C22×D76—42no—
21C22×D76C812yescomplemented
22C22×C8×C19—41no—
23C2×(C2×D19)⋊C4—42no—
24C2×(C2×D19)⋊C4—42no—
25C2×(C2×D19)⋊C4—42no—
26C2×(C2×D19)⋊C4—42no—
27C2×(C2×D19)⋊C4—41no—
28C2×(C2×D19)⋊C4—41no—
29C2×(C2×D19)⋊C4—41no—
30C2×(C2×D19)⋊C4—41no—
31C22×C19⋊C8—41no—
32C19×C22⋊C8—22no—
33C19×C22⋊C8—41no—
34C19×#95—41no—
35C19⋊#95—41no—
36C22⋊(C19⋊C8)—22no—
37C22⋊(C19⋊C8)—41no—
38C24×C19C22⋊C411yescharacteristic
39C23×D19—22no—
40C23×D19—22no—
41C23×D19—22no—
42C23×D19—41no—
43C23×D19—41no—
44C23×D19—41no—
45C23×D19—41no—
46C23×D19—41no—
47C23×D19—41no—
48C23×D19—41no—
49C23×D19—41no—
50C23×D19—41no—
51C23×D19—41no—
52C23×D19—41no—
53C23×D19—41no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19—41no—
66C22×C4×C19C2×C811yescharacteristic
67C22×C4×C19M1611yescharacteristic
68C22×C4×C19D811yescharacteristic
69C22×C4×C19D811yescharacteristic
70C22×C4×C19SD1611yescharacteristic
71C22×C4×C19SD1611yescharacteristic
72C22×Dic19—22no—
73C22×Dic19—41no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C22×Dic19—41no—
77C22×Dic19—41no—
78C22×Dic19—41no—
79C2×D76—42no—
80C2×D76—42no—
81C2×D76—44no—
82C2×D76—42no—
83C2×D76—42no—
84C2×D76—48no—
85C2×D76—42no—
86C2×D76—42no—
87C2×D76—44no—
88C2×C8×C19—42no—
89C2×C8×C19—81no—
90C2×C8×C19—81no—
91(C2×D19)⋊C4—44no—
92(C2×D19)⋊C4—44no—
93(C2×D19)⋊C4—44no—
94(C2×D19)⋊C4—44no—
95C2×C19⋊C8—42no—
96C2×C19⋊C8—81no—
97C2×C19⋊C8—81no—
98#7103—191nomaximal, Sylow
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19C22⋊C811yescharacteristic
104C23×C19#9911yescharacteristic
105C23×C19#10011yescharacteristic
106C23×C19#10211yescharacteristic
107C23×C19#10211yescharacteristic
108C23×C19#10411yescharacteristic
109C23×C19#10411yescharacteristic
110C22×D19—24no—
111C22×D19—42no—
112C22×D19—42no—
113C22×D19—42no—
114C22×D19—42no—
115C22×D19—42no—
116C22×D19—42no—
117C22×D19—42no—
118C22×D19—42no—
119C22×D19—42no—
120C22×D19—42no—
121C22×D19—42no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19—42no—
126C22×D19—42no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19—81no—
131C22×D19—81no—
132C22×D19—81no—
133C22×D19—81no—
134C22×D19—81no—
135C22×D19—81no—
136C22×D19—81no—
137C22×D19—81no—
138C22×D19—81no—
139C22×D19—81no—
140C22×D19—81no—
141C22×D19—81no—
142C22×D19—81no—
143C22×D19—81no—
144C22×D19—81no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
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×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—81no—
165C2×C4×C19—81no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—81no—
170C2×Dic19—81no—
171C2×Dic19—81no—
172C2×Dic19—81no—
173D76—44no—
174D76—44no—
175D76—44no—
176D76—44no—
177C8×C19—82no—
178C19⋊C8—82no—
179#1438—191no—
180#1280—191no—
181#1280D1911yescharacteristic, complemented
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19#32311yescharacteristic
195C22×C19D4⋊C811yescharacteristic
196C22×C19D4⋊C811yescharacteristic
197C22×C19#32711yescharacteristic
198C22×C19#32711yescharacteristic
199C22×C19#32911yescharacteristic
200C22×C19#33111yescharacteristic
201C22×C19AΣL(1,𝔽16)11yescharacteristic
202C22×C19AΣL(1,𝔽16)11yescharacteristic
203C22×C19#35311yescharacteristic
204C22×C19#35511yescharacteristic
205C2×D19—44no—
206C2×D19—44no—
207C2×D19—44no—
208C2×D19—82no—
209C2×D19—82no—
210C2×D19—82no—
211C2×D19—82no—
212C2×D19—82no—
213C2×D19—82no—
214C2×D19—82no—
215C2×D19—82no—
216C2×D19—82no—
217C2×D19—82no—
218C2×D19—82no—
219C2×D19—82no—
220C4×C19—41no—
221C4×C19—41no—
222C4×C19—41no—
223C4×C19—41no—
224C4×C19—41no—
225C4×C19—41no—
226Dic19—82no—
227C23×D4—191no—
228C22×C22⋊C4—381no—
229C22×C22⋊C4—381no—
230C2×C22⋊C8—21no—
231C2×C22⋊C8—381no—
232C2×#95—191no—
233C2×#95C2×D1911yescharacteristic
234C2×C19—21no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19—21no—
238C2×C19#127011yescharacteristic
239C2×C19#131611yescharacteristic
240C2×C19#131811yescharacteristic
241C2×C19#134311yescharacteristic
242C2×C19#134311yescharacteristic
243C2×C19#134511yescharacteristic
244C2×C19#134511yescharacteristic
245D19—84no—
246C25—381no—
247C22×D4—192no—
248C22×D4—381no—
249C22×D4—761no—
250C22×D4—761no—
251C22×D4—762no—
252C22×D4—762no—
253C23×C4—381no—
254C23×C4C4×D1911yescharacteristic
255C23×C4D7611yescharacteristic
256C23×C4C22⋊D1911yescharacteristic
257C22×C8—41no—
258C22×C8—761no—
259C2×C22⋊C4—762no—
260C2×C22⋊C4—762no—
261C2×C22⋊C4—762no—
262C2×C22⋊C4—762no—
263C2×C22⋊C4—761no—
264C2×C22⋊C4—761no—
265C2×C22⋊C4—761no—
266C2×C22⋊C4—761no—
267C22⋊C8—22no—
268C22⋊C8—41no—
269C22⋊C8—382no—
270C22⋊C8—761no—
271#95—41no—
272#95—761no—
273C19#710311yescharacteristic, complemented, Sylow
274C24—382no—
275C24—382no—
276C24—382no—
277C24—761no—
278C24—761no—
279C24—761no—
280C24—761no—
281C24—761no—
282C24—761no—
283C24—761no—
284C24—761no—
285C24—761no—
286C24—761no—
287C24—761no—
288C24—761no—
289C24(C2×D19)⋊C411yescharacteristic
290C2×D4—762no—
291C2×D4—762no—
292C2×D4—764no—
293C2×D4—762no—
294C2×D4—762no—
295C2×D4—768no—
296C2×D4—762no—
297C2×D4—762no—
298C2×D4—764no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—382no—
312C22×C4—761no—
313C22×C4—761no—
314C22×C4—761no—
315C22×C4—761no—
316C22×C4—761no—
317C22×C4—761no—
318C22×C4C8×D1911yescharacteristic
319C22×C4#6451511yescharacteristic
320C22×C4#6451611yescharacteristic
321C22×C4D15211yescharacteristic
322C22×C4#6452511yescharacteristic
323C22×C4#6452711yescharacteristic
324C2×C8—42no—
325C2×C8—81no—
326C2×C8—81no—
327C2×C8—762no—
328C2×C8—1521no—
329C2×C8—1521no—
330C22⋊C4—764no—
331C22⋊C4—764no—
332C22⋊C4—764no—
333C22⋊C4—764no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—384no—
339C23—762no—
340C23—762no—
341C23—762no—
342C23—762no—
343C23—762no—
344C23—762no—
345C23—762no—
346C23—762no—
347C23—762no—
348C23—762no—
349C23—762no—
350C23—762no—
351C23—762no—
352C23—762no—
353C23—762no—
354C23—762no—
355C23—762no—
356C23—762no—
357C23—1521no—
358C23—1521no—
359C23—1521no—
360C23—1521no—
361C23—1521no—
362C23—1521no—
363C23—1521no—
364C23—1521no—
365C23—1521no—
366C23—1521no—
367C23—1521no—
368C23—1521no—
369C23—1521no—
370C23—1521no—
371C23—1521no—
372C23—1521no—
373C23#1059726211yescharacteristic
374C23#1059726311yescharacteristic
375C23#1059726611yescharacteristic
376C23(C2×D19)⋊C811yescharacteristic
377C23#1059727811yescharacteristic
378C23#1059728011yescharacteristic
379C23#1059728211yescharacteristic
380D4—764no—
381D4—764no—
382D4—764no—
383D4—764no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—1521no—
409C2×C4—1521no—
410C2×C4—1521no—
411C2×C4—1521no—
412C8—82no—
413C8—1522no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—764no—
427C22—764no—
428C22—764no—
429C22—1522no—
430C22—1522no—
431C22—1522no—
432C22—1522no—
433C22—1522no—
434C22—1522no—
435C22—1522no—
436C22—1522no—
437C22—1522no—
438C22—1522no—
439C22—1522no—
440C22—1522no—
441C22#1192626711yescharacteristic
442C22#1192627111yescharacteristic
443C22#1192627311yescharacteristic
444C22#1192627711yescharacteristic
445C22#1192627911yescharacteristic
446C22#1192628311yescharacteristic
447C22#1192628711yescharacteristic
448C22#1192633011yescharacteristic
449C22#1192633211yescharacteristic
450C22#1192633611yescharacteristic
451C22#1192634011yescharacteristic
452C4—41no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—1522no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—1524no—
464C2#1456145511yescharacteristic
465C2#1456156211yescharacteristic
466C2#1456156611yescharacteristic
467C2#1456163111yescharacteristic
468C2#1456163311yescharacteristic
469C2#1456163711yescharacteristic
470C2#1456163911yescharacteristic
subgroupG/H
centerC23#10597263
commutatorC22×C4×C19C2×C8
FrattiniC2×#95C2×D19
FittingC19×#1280C2
socleC23×C19#99
prime radicalC23×D76C4
cosocleC2×C19×#95C22
hypercenter#1280D19
hypocenterC19#7103
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24 ◁ C2×#95 ◁ #1280

Complements

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

NH ≅ G/Ntype
2. #14561478C2semidirect
3. C19×#1280C2semidirect
21. C22×D76C8semidirect
181. #1280D19semidirect
273. C19#7103semidirect

Maximal subgroups

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

subgroupindex
#145618752
#145614782
C19×#12802
#710319