Finite Group Databasebeta

← #18079014

Subgroups — #18079014

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574412C211yesmaximal, characteristic
2#14562139C211yesmaximal, characteristic
3C2×#11926282C211yesmaximal, characteristic, complemented
4#14561998C211yesmaximal, characteristic, complemented
5#14561523C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#2977C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926885—21no—
10#11926872C411yescharacteristic, complemented
11#11926855C411yescharacteristic, complemented
12#11926783—21no—
13#11926771—21no—
14#11926706—21no—
15#11926699C411yescharacteristic, complemented
16#11926682C411yescharacteristic, complemented
17#11926508C2211yescharacteristic
18C2×C22⋊(C19⋊C8)C2211yescharacteristic
19C2×C19⋊#95C2211yescharacteristic
20#11926282—21no—
21#11926282—21no—
22#11926281—21no—
23#11926278—21no—
24#11926269—21no—
25#11926269—21no—
26C19×#525C2211yescharacteristic
27C19×#435—21no—
28C19×#435—21no—
29C8×D4×C19—21no—
30C8×D4×C19—21no—
31C19×#433—21no—
32C19×#408—21no—
33C2×C19×C22⋊C8C2211yescharacteristic
34C2×C19×C22⋊C8C2211yescharacteristic
35C2×#41×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C23×Dic19—21no—
38C22×Dic38C2×C411yescharacteristic
39C2×M16×C19—21no—
40C22×C8×C19—21no—
41C22×C8×C19—21no—
42C22×C8×C19—21no—
43C19×#123—21no—
44C19×C22⋊Q8C2×C411yescharacteristic
45C19×C22⋊Q8D411yescharacteristic
46C19×#121C2×C411yescharacteristic
47C19×#121D411yescharacteristic
48C19×#120—21no—
49C4×D4×C19—21no—
50C4×D4×C19—21no—
51C19×#117D411yescharacteristic
52C2×C22⋊Dic19—21no—
53C2×#64528—21no—
54C2×#64526—21no—
55C2×C4⋊Dic19C2×C411yescharacteristic
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60C2×Dic19⋊C4—21no—
61C2×#64520—21no—
62C22×C19⋊C8—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8D411yescharacteristic
70C19×C22⋊C8D411yescharacteristic
71C19×C22⋊C8D411yescharacteristic
72C19×C22⋊C8D411yescharacteristic
73C19×#97—21no—
74C4×C8×C19—21no—
75#10597292—21no—
76#10597289—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)C2×C411yescharacteristic
83C22⋊(C19⋊C8)C2×C411yescharacteristic
84#10597267—21no—
85#10597267—21no—
86#10597265—21no—
87#10597264—21no—
88C24×C19#4111yescharacteristic
89#41×C19—81no—
90C2×Q8×C19C22⋊C411yescharacteristic
91C2×D4×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19C22⋊C411yescharacteristic
95C22×C4×C19—21no—
96C22×C4×C19—81no—
97C22×C4×C19C22×C411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×Dic19—21no—
104C22×Dic19—22no—
105C22×Dic19—21no—
106C22×Dic19—41no—
107C22×Dic19—41no—
108C22×Dic19—81no—
109C22×Dic19—81no—
110C2×Dic38—21no—
111C2×Dic38—21no—
112C2×Dic38—81no—
113M16×C19—81no—
114C2×C8×C19—21no—
115C2×C8×C19—21no—
116C2×C8×C19—21no—
117C2×C8×C19—21no—
118C2×C8×C19—81no—
119C2×C8×C19—81no—
120C2×C8×C19—81no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19C22⋊C411yescharacteristic
124C4⋊C4×C19C22⋊C411yescharacteristic
125C22⋊C4×C19—21no—
126C22⋊C4×C19—21no—
127C22⋊C4×C19—21no—
128C22⋊C4×C19—21no—
129C22⋊C4×C19—21no—
130C42×C19—21no—
131C22⋊Dic19—41no—
132C22⋊Dic19—41no—
133#64528—81no—
134#64526—81no—
135C4⋊Dic19—21no—
136C4⋊Dic19—21no—
137Dic19⋊C4—41no—
138Dic19⋊C4—41no—
139#64520—81no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—81no—
144#9263—191nomaximal, Sylow
145C23×C19—21no—
146C23×C19—21no—
147C23×C19—21no—
148C23×C19—21no—
149C23×C19—21no—
150C23×C19—41no—
151C23×C19C4×D411yescharacteristic
152C23×C19#12111yescharacteristic
153C23×C19#12311yescharacteristic
154Q8×C19—41no—
155D4×C19—41no—
156D4×C19—41no—
157D4×C19—41no—
158D4×C19—41no—
159D4×C19—41no—
160D4×C19—81no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19C2×C22⋊C411yescharacteristic
173C2×C4×C19C4×D411yescharacteristic
174C2×C4×C19#12011yescharacteristic
175C2×C4×C19#12111yescharacteristic
176C2×Dic19—42no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—81no—
182C2×Dic19—82no—
183C2×Dic19—81no—
184C2×Dic19—81no—
185C2×Dic19—82no—
186Dic38—41no—
187Dic38—41no—
188Dic38—81no—
189C8×C19—41no—
190C8×C19—41no—
191C8×C19—41no—
192C8×C19—41no—
193C19⋊C8—41no—
194C19⋊C8—41no—
195C19⋊C8—81no—
196#3190—191no—
197#2977D1911yescharacteristic
198#1504—191no—
199C2×#328—191no—
200#1472—191no—
201#1298—191no—
202#1280—191no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—41no—
211C22×C19—41no—
212C22×C19—41no—
213C22×C19—41no—
214C22×C19—41no—
215C22×C19—41no—
216C22×C19—41no—
217C22×C19#38611yescharacteristic
218C22×C19#44311yescharacteristic
219C22×C19#44411yescharacteristic
220C22×C19#47111yescharacteristic
221C22×C19#47311yescharacteristic
222C4×C19—21no—
223C4×C19—21no—
224C4×C19—21no—
225C4×C19—21no—
226C4×C19—41no—
227C4×C19—41no—
228C4×C19—41no—
229Dic19—82no—
230Dic19—81no—
231Dic19—81no—
232#525C2×D1911yescharacteristic
233C2×C22⋊Q8—191no—
234#485—381no—
235#483—191no—
236#480—191no—
237#467—381no—
238#465—381no—
239#452—381no—
240#451—191no—
241#448—191no—
242#435—21no—
243#435—21no—
244C8×D4—21no—
245C8×D4—21no—
246#433—21no—
247#408—21no—
248#407—191no—
249C2×C22⋊C8—191no—
250C2×C22⋊C8C2×D1911yescharacteristic
251C2×C22⋊C8C2×D1911yescharacteristic
252C2×#95—191no—
253#328—381no—
254#328—381no—
255#328—381no—
256#327—381no—
257#324—381no—
258#324—381no—
259C2×C19—21no—
260C2×C19—21no—
261C2×C19—21no—
262C2×C19—21no—
263C2×C19—41no—
264C2×C19—81no—
265C2×C19#187611yescharacteristic
266C2×C19#190811yescharacteristic
267C2×C19#191311yescharacteristic
268C2×#41C22⋊D1911yescharacteristic
269C22×Q8—191no—
270C23×C4—381no—
271C23×C4C22×D1911yescharacteristic
272C2×Q16—381no—
273C2×SD16—381no—
274C2×M16—21no—
275C2×M16—381no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—381no—
280#123—21no—
281C22⋊Q8—381no—
282C22⋊Q8—381no—
283C22⋊Q8—381no—
284C22⋊Q8—381no—
285C22⋊Q8C4×D1911yescharacteristic
286C22⋊Q8D7611yescharacteristic
287#121C4×D1911yescharacteristic
288#121D7611yescharacteristic
289#120—21no—
290C4×D4—21no—
291C4×D4—21no—
292#117C22⋊D1911yescharacteristic
293C2×C4⋊C4—191no—
294C2×C4⋊C4—381no—
295C2×C22⋊C4—381no—
296#107—381no—
297#106—381no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300#103—381no—
301#103—381no—
302#103—381no—
303#102—381no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—191no—
309C22⋊C8—191no—
310C22⋊C8—381no—
311C22⋊C8—381no—
312C22⋊C8—381no—
313C22⋊C8C22⋊D1911yescharacteristic
314C22⋊C8C22⋊D1911yescharacteristic
315C22⋊C8C22⋊D1911yescharacteristic
316C22⋊C8C22⋊D1911yescharacteristic
317#97—21no—
318C4×C8—21no—
319#95—381no—
320#95—381no—
321C19#926311yescharacteristic, complemented, Sylow
322C24#6454111yescharacteristic
323#41—81no—
324C2×Q8—381no—
325C2×Q8—381no—
326C2×Q8—1521no—
327C2×Q8(C2×D19)⋊C411yescharacteristic
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4(C2×D19)⋊C411yescharacteristic
332C22×C4—21no—
333C22×C4—81no—
334C22×C4—381no—
335C22×C4—382no—
336C22×C4—381no—
337C22×C4—761no—
338C22×C4—761no—
339C22×C4—1521no—
340C22×C4—1521no—
341C22×C4C2×C4×D1911yescharacteristic
342C22×C4C2×D7611yescharacteristic
343C22×C4#6454111yescharacteristic
344C22×C4C2×C22⋊D1911yescharacteristic
345C22×C4C2×C22⋊D1911yescharacteristic
346C22×C4C2×C22⋊D1911yescharacteristic
347Q16—1521no—
348SD16—1521no—
349M16—81no—
350M16—1521no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—81no—
356C2×C8—81no—
357C2×C8—81no—
358C2×C8—381no—
359C2×C8—381no—
360C2×C8—761no—
361C2×C8—1521no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—381no—
365C4⋊C4—381no—
366C4⋊C4—761no—
367C4⋊C4—761no—
368C4⋊C4(C2×D19)⋊C411yescharacteristic
369C4⋊C4(C2×D19)⋊C411yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—761no—
376C22⋊C4—761no—
377C42—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23C4×C22⋊D1911yescharacteristic
385C23#1059737511yescharacteristic
386C23#1059737611yescharacteristic
387Q8—41no—
388Q8—761no—
389Q8—761no—
390Q8—1521no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—81no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—762no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4—761no—
412C2×C4—761no—
413C2×C4—1521no—
414C2×C4—1522no—
415C2×C4—1521no—
416C2×C4—1521no—
417C2×C4—1522no—
418C2×C4C2×(C2×D19)⋊C411yescharacteristic
419C2×C4C4×C22⋊D1911yescharacteristic
420C2×C4#1059737611yescharacteristic
421C2×C4#1059739911yescharacteristic
422C8—41no—
423C8—41no—
424C8—41no—
425C8—41no—
426C8—761no—
427C8—761no—
428C8—1521no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22#1192642311yescharacteristic
444C22#1192665911yescharacteristic
445C22#1192666411yescharacteristic
446C22#1192680711yescharacteristic
447C22#1192681911yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—1522no—
456C4—1521no—
457C4—1521no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—81no—
464C2#1456396211yescharacteristic
465C2#1456415011yescharacteristic
466C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2977C2
socleC22×C19#386
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#2977D19
hypocenterC19#9263
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
3. C2×#11926282C2semidirect
4. #14561998C2semidirect
5. #14561523C2semidirect
6. #14561477C2semidirect
10. #11926872C4semidirect
11. #11926855C4semidirect
15. #11926699C4semidirect
16. #11926682C4semidirect
321. C19#9263semidirect

Maximal subgroups

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

subgroupindex
#145744122
#145621392
C2×#119262822
#145619982
#145615232
#145614772
C19×#29772
#926319