Finite Group Databasebeta

← #18079016

Subgroups — #18079016

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#14572691C211yesmaximal, characteristic
2#14562139C211yesmaximal, characteristic
3C2×#11926281C211yesmaximal, characteristic, complemented
4#14561999C211yesmaximal, characteristic, complemented
5#14561523C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#3190C211yesmaximal, characteristic
8#11926616—21no—
9#11926616—21no—
10D4×C19⋊C8—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926511—21no—
14#11926508C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C19⋊#95C2211yescharacteristic
18#11926281—21no—
19#11926281—21no—
20#11926281—21no—
21#11926278—21no—
22#11926270—21no—
23#11926270—21no—
24C19×#525C2211yescharacteristic
25C2×C19×C22⋊Q8C2211yescharacteristic
26C19×#485—21no—
27C19×#483C411yescharacteristic, complemented
28C19×#480C411yescharacteristic, complemented
29C19×#467—21no—
30C19×#465—21no—
31C19×#452—21no—
32C19×#451C411yescharacteristic, complemented
33C19×#448C411yescharacteristic, complemented
34C2×C19×C22⋊C8C2211yescharacteristic
35C2×#41×C19D411yescharacteristic
36C22×Q8×C19C2×C411yescharacteristic
37C23×C4×C19C2311yescharacteristic
38C23×Dic19—21no—
39C2×Q16×C19—21no—
40C2×SD16×C19—21no—
41C22×C8×C19—21no—
42C19×#123—21no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8C2×C411yescharacteristic
48C19×C22⋊Q8D411yescharacteristic
49C19×#121C2×C411yescharacteristic
50C19×#121D411yescharacteristic
51C19×#120—21no—
52C4×D4×C19—21no—
53C4×D4×C19—21no—
54C19×#117D411yescharacteristic
55C2×C4⋊C4×C19—21no—
56C2×C4⋊C4×C19C2×C411yescharacteristic
57C2×C22⋊C4×C19—21no—
58C2×#64520—21no—
59C2×#64520—21no—
60C22×C19⋊C8—21no—
61C22×C19⋊C8—21no—
62C22×C19⋊C8—21no—
63C19×#107—21no—
64C19×#106—21no—
65C19×#103—21no—
66C19×#103—21no—
67C19×#103—21no—
68C19×#102—21no—
69C19×C22⋊C8—21no—
70C19×C22⋊C8C2×C411yescharacteristic
71C19×C22⋊C8C2×C411yescharacteristic
72C19⋊#95—21no—
73C19⋊#95—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)D411yescharacteristic
81C22⋊(C19⋊C8)D411yescharacteristic
82C22⋊(C19⋊C8)D411yescharacteristic
83C22⋊(C19⋊C8)D411yescharacteristic
84C4⋊(C19⋊C8)—21no—
85C4⋊(C19⋊C8)—21no—
86#10597260—21no—
87C4×C19⋊C8—21no—
88C24×C19#4111yescharacteristic
89#41×C19—81no—
90C2×Q8×C19—21no—
91C2×Q8×C19—21no—
92C2×Q8×C19—81no—
93C2×Q8×C19C22⋊C411yescharacteristic
94C2×D4×C19—21no—
95C2×D4×C19—21no—
96C2×D4×C19—21no—
97C2×D4×C19C22⋊C411yescharacteristic
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—81no—
102C22×C4×C19C22×C411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19#4111yescharacteristic
108C22×Dic19—22no—
109C22×Dic19—41no—
110C22×Dic19—41no—
111C22×Dic19—81no—
112C22×Dic19—81no—
113Q16×C19—81no—
114SD16×C19—81no—
115C2×C8×C19—21no—
116C2×C8×C19—21no—
117C2×C8×C19—81no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—41no—
123C4⋊C4×C19—41no—
124C4⋊C4×C19C22⋊C411yescharacteristic
125C4⋊C4×C19C22⋊C411yescharacteristic
126C22⋊C4×C19—21no—
127C22⋊C4×C19—21no—
128C22⋊C4×C19—21no—
129C22⋊C4×C19—21no—
130C22⋊C4×C19—21no—
131C22⋊C4×C19—41no—
132C22⋊C4×C19—41no—
133C42×C19—21no—
134#64520—81no—
135#64520—81no—
136C2×C19⋊C8—21no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—41no—
141C2×C19⋊C8—81no—
142C2×C19⋊C8—81no—
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—
155Q8×C19—41no—
156Q8×C19—41no—
157Q8×C19—81no—
158D4×C19—41no—
159D4×C19—41no—
160D4×C19—41no—
161D4×C19—41no—
162D4×C19—41no—
163D4×C19—81no—
164C2×C4×C19—21no—
165C2×C4×C19—21no—
166C2×C4×C19—21no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—81no—
180C2×C4×C19C2×C22⋊C411yescharacteristic
181C2×C4×C19C4×D411yescharacteristic
182C2×C4×C19#12011yescharacteristic
183C2×C4×C19#12111yescharacteristic
184C2×Dic19—42no—
185C2×Dic19—81no—
186C2×Dic19—82no—
187C2×Dic19—81no—
188C2×Dic19—82no—
189C8×C19—41no—
190C8×C19—41no—
191C19⋊C8—41no—
192C19⋊C8—41no—
193C19⋊C8—41no—
194C19⋊C8—41no—
195C19⋊C8—81no—
196#3190D1911yescharacteristic
197#2977—191no—
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—
229C4×C19—81no—
230C4×C19—81no—
231Dic19—82no—
232#525C2×D1911yescharacteristic
233C2×C22⋊Q8C2×D1911yescharacteristic
234#485—21no—
235#483Dic1911yescharacteristic, complemented
236#480Dic1911yescharacteristic, complemented
237#467—21no—
238#465—21no—
239#452—21no—
240#451Dic1911yescharacteristic, complemented
241#448Dic1911yescharacteristic, complemented
242#435—381no—
243#435—381no—
244C8×D4—381no—
245C8×D4—381no—
246#433—381no—
247#408—381no—
248#407—191no—
249C2×C22⋊C8—191no—
250C2×C22⋊C8—191no—
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×Q8C2×Dic1911yescharacteristic
270C23×C4—381no—
271C23×C4C22×D1911yescharacteristic
272C2×Q16—21no—
273C2×SD16—21no—
274C2×M16—381no—
275C2×M16—381no—
276C22×C8—21no—
277C22×C8—381no—
278C22×C8—381no—
279C22×C8—381no—
280#123—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8C2×Dic1911yescharacteristic
286C22⋊Q8C22⋊D1911yescharacteristic
287#121C2×Dic1911yescharacteristic
288#121C22⋊D1911yescharacteristic
289#120—21no—
290C4×D4—21no—
291C4×D4—21no—
292#117C22⋊D1911yescharacteristic
293C2×C4⋊C4—21no—
294C2×C4⋊C4C2×Dic1911yescharacteristic
295C2×C22⋊C4—21no—
296#107—21no—
297#106—21no—
298C4⋊C8—381no—
299C4⋊C8—381no—
300#103—21no—
301#103—21no—
302#103—21no—
303#102—21no—
304C22⋊C8—21no—
305C22⋊C8—191no—
306C22⋊C8—191no—
307C22⋊C8—191no—
308C22⋊C8—191no—
309C22⋊C8—381no—
310C22⋊C8—381no—
311C22⋊C8—381no—
312C22⋊C8—381no—
313C22⋊C8—381no—
314C22⋊C8—381no—
315C22⋊C8C2×Dic1911yescharacteristic
316C22⋊C8C2×Dic1911yescharacteristic
317#97—381no—
318C4×C8—381no—
319#95—381no—
320#95—381no—
321C19#926311yescharacteristic, complemented, Sylow
322C24#6454311yescharacteristic
323#41—81no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8C22⋊Dic1911yescharacteristic
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4C22⋊Dic1911yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—81no—
336C22×C4—382no—
337C22×C4—761no—
338C22×C4—761no—
339C22×C4—1521no—
340C22×C4—1521no—
341C22×C4D4×D1911yescharacteristic
342C22×C4D4×D1911yescharacteristic
343C22×C4#6454311yescharacteristic
344C22×C4C22×Dic1911yescharacteristic
345C22×C4C2×C22⋊D1911yescharacteristic
346C22×C4C2×C22⋊D1911yescharacteristic
347Q16—81no—
348SD16—81no—
349M16—1521no—
350M16—1521no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—81no—
354C2×C8—381no—
355C2×C8—381no—
356C2×C8—381no—
357C2×C8—381no—
358C2×C8—761no—
359C2×C8—1521no—
360C2×C8—1521no—
361C2×C8—1521no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4C22⋊Dic1911yescharacteristic
369C4⋊C4C22⋊Dic1911yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C42—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23D4×Dic1911yescharacteristic
385C23#1059738111yescharacteristic
386C23#1059738511yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—81no—
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—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—81no—
413C2×C4—762no—
414C2×C4—1521no—
415C2×C4—1522no—
416C2×C4—1521no—
417C2×C4—1522no—
418C2×C4D4×Dic1911yescharacteristic
419C2×C4#1059738311yescharacteristic
420C2×C4#1059738511yescharacteristic
421C2×C4C2×C22⋊Dic1911yescharacteristic
422C8—41no—
423C8—41no—
424C8—761no—
425C8—761no—
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#1192642411yescharacteristic
444C22#1192666111yescharacteristic
445C22#1192666611yescharacteristic
446C22#1192680911yescharacteristic
447C22#1192681711yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—81no—
456C4—81no—
457C4—1522no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—81no—
464C2#1456396411yescharacteristic
465C2#1456415211yescharacteristic
466C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3190C2
socleC22×C19#386
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#3190D19
hypocenterC19#9263
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3190

Complements

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

NH ≅ G/Ntype
3. C2×#11926281C2semidirect
4. #14561999C2semidirect
5. #14561523C2semidirect
6. #14561477C2semidirect
27. C19×#483C4semidirect
28. C19×#480C4semidirect
32. C19×#451C4semidirect
33. C19×#448C4semidirect
235. #483Dic19semidirect
236. #480Dic19semidirect
240. #451Dic19semidirect
241. #448Dic19semidirect
321. C19#9263semidirect

Maximal subgroups

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

subgroupindex
#145726912
#145621392
C2×#119262812
#145619992
#145615232
#145614772
C19×#31902
#926319