Finite Group Databasebeta

← #18082075

Subgroups — #18082075

Order 4864.

552 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926773C211yesmaximal, characteristic
2#14564620C211yesmaximal, characteristic, complemented
3#14564471C211yesmaximal, characteristic
4#14563664C211yesmaximal, characteristic, complemented
5#14562208C211yesmaximal, characteristic, complemented
6#14562204C211yesmaximal, characteristic
7C19×#1752C211yesmaximal, characteristic, complemented
8C22×#64516C411yescharacteristic, complemented
9C2×#10597370C2211yescharacteristic
10C2×#10597376C2211yescharacteristic
11#11926773—21no—
12#11926773—21no—
13#11926773—21no—
14#11926773—21no—
15C2×#10597275—21no—
16C2×#10597274C411yescharacteristic, complemented
17C2×#10597273C411yescharacteristic, complemented
18C2×#10597278C411yescharacteristic, complemented
19C2×#10597263—22no—
20#11926404C2211yescharacteristic
21#11926404C2211yescharacteristic
22#11926310—22no—
23#11926307—21no—
24#11926282—22no—
25#11926279—22no—
26C23×C8×C19C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C2×C19×#97—21no—
29C4×C22⋊C4×C19C2211yescharacteristic
30C19×#336—21no—
31C23×C4×C19C2311yescharacteristic
32C22×C22⋊D19—21no—
33C22×D76C2×C411yescharacteristic
34C22×Dic38C2×C411yescharacteristic
35C22×C8×C19—21no—
36C22×C8×C19—42no—
37C22×C8×C19C2×C411yescharacteristic
38C22×C8×C19C2×C411yescharacteristic
39C22×C8×C19D411yescharacteristic
40C22×C8×C19D411yescharacteristic
41C22×C8×C19D411yescharacteristic
42C22×C8×C19D411yescharacteristic
43C2×C22⋊C4×C19D412yes—
44C2×C42×C19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19—21no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52C2×(C2×D19)⋊C4—21no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19C2×C411yescharacteristic
56C2×C4⋊Dic19C2×C411yescharacteristic
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60#10597370—21no—
61C2×Dic19⋊C4—21no—
62C2×#64516—21no—
63C2×#64516—21no—
64C2×#64516—42no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8D412yes—
67C19×#97—42no—
68C19×#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71#10597278—21no—
72#10597278—21no—
73#10597275—42no—
74#10597274—21no—
75#10597274—21no—
76#10597273—21no—
77#10597273—21no—
78#10597263—44no—
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C22×C4×C19—22no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C2×C22⋊D19—41no—
91C2×C22⋊D19—41no—
92C2×C22⋊D19—42no—
93C2×C22⋊D19—42no—
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—41no—
98C22×Dic19—41no—
99C2×D76—21no—
100C2×D76—21no—
101C2×D76—41no—
102C2×D76—41no—
103C2×Dic38—21no—
104C2×Dic38—21no—
105C2×Dic38—41no—
106C2×Dic38—41no—
107C2×C8×C19—22no—
108C2×C8×C19—22no—
109C2×C8×C19—22no—
110C2×C8×C19—22no—
111C2×C8×C19—41no—
112C2×C8×C19—41no—
113C2×C8×C19—41no—
114C2×C8×C19—41no—
115C2×C8×C19—41no—
116C2×C8×C19C22⋊C411yescharacteristic
117C2×C8×C19C22⋊C411yescharacteristic
118C2×C8×C19C22⋊C411yescharacteristic
119C2×C8×C19C22⋊C411yescharacteristic
120C22⋊C4×C19—22no—
121C22⋊C4×C19—22no—
122C42×C19—41no—
123C42×C19—41no—
124C22⋊Dic19—41no—
125C22⋊Dic19—41no—
126C22⋊Dic19—42no—
127C22⋊Dic19—42no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132C4⋊Dic19—21no—
133C4⋊Dic19—21no—
134C4⋊Dic19—41no—
135C4⋊Dic19—41no—
136C4⋊Dic19—41no—
137C4⋊Dic19—41no—
138Dic19⋊C4—41no—
139Dic19⋊C4—41no—
140#64516—42no—
141#64516—42no—
142#9786—191nomaximal, Sylow
143C23×C19—41no—
144C23×C19—41no—
145C23×C19C4×D411yescharacteristic
146C23×C19#12111yescharacteristic
147C23×C19#12711yescharacteristic
148C23×C19AGL(1,ℤ/8)12yes—
149C23×C19#13712yes—
150C22×D19—41no—
151C22×D19—42no—
152C22×D19—81no—
153C22×D19—81no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19C2×C22⋊C411yescharacteristic
167C2×C4×C19C4×D411yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12411yescharacteristic
170C22⋊D19—82no—
171C22⋊D19—81no—
172C22⋊D19—81no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—42no—
177C2×Dic19—81no—
178C2×Dic19—81no—
179C2×Dic19—81no—
180C2×Dic19—81no—
181C2×Dic19—81no—
182C2×Dic19—81no—
183C2×Dic19—81no—
184C2×Dic19—81no—
185D76—41no—
186D76—41no—
187D76—81no—
188Dic38—41no—
189Dic38—41no—
190Dic38—81no—
191C8×C19—21no—
192C8×C19—21no—
193C8×C19—21no—
194C8×C19—42no—
195C8×C19#9912yescomplemented
196C2×#465—191no—
197#1996—191no—
198#1964—191no—
199#1808—191no—
200#1752D1911yescharacteristic, complemented
201#1520—191no—
202#1519—191no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—42no—
210C22×C19—42no—
211C22×C19#39011yescharacteristic
212C22×C19#44012yes—
213C22×C19#46812yes—
214C22×C19#49611yescharacteristic
215C22×C19#49711yescharacteristic
216C2×D19—81no—
217C2×D19—81no—
218C2×D19—81no—
219C2×D19—162no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—82no—
224C4×C19C2×#9911yescharacteristic
225C4×C19#41011yescharacteristic
226Dic19—81no—
227Dic19—81no—
228Dic19—81no—
229Dic19—161no—
230Dic19—161no—
231C22×SD16—191no—
232C23×C8C2×D1911yescharacteristic
233C2×C22⋊Q8—191no—
234C2×#121—191no—
235#465—381no—
236#465—381no—
237#465—381no—
238#465—381no—
239C2×#107—381no—
240C2×#106—191no—
241C2×#103—191no—
242C2×#102—191no—
243C2×#99—382no—
244C2×C22⋊C8C2×D1911yescharacteristic
245C2×#97—21no—
246#380—191no—
247#380—191no—
248C4×C22⋊C4C2×D1911yescharacteristic
249#342—382no—
250#340—381no—
251#336—21no—
252#328—382no—
253#327—382no—
254C2×C19—21no—
255C2×C19—22no—
256C2×C19—22no—
257C2×C19—21no—
258C2×C19#196411yescharacteristic
259C2×C19#197311yescharacteristic
260C2×C19#197611yescharacteristic
261D19—161no—
262C22×Q8—191no—
263C22×D4—191no—
264C22×D4—381no—
265C23×C4C22×D1911yescharacteristic
266C2×SD16—381no—
267C2×SD16—381no—
268C2×SD16—762no—
269C22×C8—21no—
270C22×C8—42no—
271C22×C8C4×D1911yescharacteristic
272C22×C8C4×D1911yescharacteristic
273C22×C8D7611yescharacteristic
274C22×C8D7611yescharacteristic
275C22×C8C22⋊D1911yescharacteristic
276C22×C8C22⋊D1911yescharacteristic
277C22⋊Q8—381no—
278C22⋊Q8—381no—
279C22⋊Q8—381no—
280C22⋊Q8—381no—
281#121—381no—
282#121—381no—
283#121—381no—
284#121—381no—
285C2×C4⋊C4—191no—
286C2×C4⋊C4—191no—
287C2×C4⋊C4—381no—
288C2×C4⋊C4—381no—
289C2×C4⋊C4—381no—
290C2×C22⋊C4—381no—
291C2×C22⋊C4—381no—
292C2×C22⋊C4—381no—
293C2×C22⋊C4—381no—
294C2×C22⋊C4D7612yes—
295C2×C42—21no—
296#107—762no—
297#106—381no—
298#106—381no—
299#103—381no—
300#103—381no—
301#102—381no—
302#102—381no—
303#99—764no—
304C22⋊C8—21no—
305C22⋊C8D7612yes—
306#97—42no—
307#95—21no—
308#95—381no—
309#95—381no—
310C19#978611yescharacteristic, complemented, Sylow
311C24—381no—
312C24C2×D7611yescharacteristic
313C2×Q8—381no—
314C2×Q8—381no—
315C2×Q8—761no—
316C2×Q8—761no—
317C2×D4—381no—
318C2×D4—381no—
319C2×D4—761no—
320C2×D4—761no—
321C2×D4—761no—
322C2×D4—761no—
323C2×D4—762no—
324C2×D4—762no—
325C22×C4—22no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—381no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—761no—
332C22×C4—761no—
333C22×C4C2×C4×D1911yescharacteristic
334C22×C4C2×D7611yescharacteristic
335C22×C4C2×D7611yescharacteristic
336C22×C4#6454111yescharacteristic
337C22×C4#6454111yescharacteristic
338C22×C4C2×C22⋊D1911yescharacteristic
339SD16—762no—
340SD16—762no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8(C2×D19)⋊C411yescharacteristic
351C2×C8(C2×D19)⋊C411yescharacteristic
352C2×C8(C2×D19)⋊C411yescharacteristic
353C2×C8(C2×D19)⋊C411yescharacteristic
354C4⋊C4—381no—
355C4⋊C4—381no—
356C4⋊C4—381no—
357C4⋊C4—381no—
358C4⋊C4—761no—
359C4⋊C4—761no—
360C4⋊C4—761no—
361C4⋊C4—761no—
362C4⋊C4—761no—
363C4⋊C4—761no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—761no—
367C22⋊C4—761no—
368C22⋊C4—761no—
369C22⋊C4—761no—
370C22⋊C4—762no—
371C22⋊C4—762no—
372C42—41no—
373C42—41no—
374C23—41no—
375C23—41no—
376C23—762no—
377C23—761no—
378C23—1521no—
379C23—1521no—
380C23C4×D7611yescharacteristic
381C23#1059732011yescharacteristic
382C23#1059735412yes—
383C23#1059735512yes—
384C23#1059737611yescharacteristic
385Q8—761no—
386Q8—761no—
387Q8—1521no—
388D4—761no—
389D4—761no—
390D4—1521no—
391D4—1522no—
392D4—1521no—
393D4—1521no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—762no—
407C2×C4—761no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4—1521no—
411C2×C4—1521no—
412C2×C4—1521no—
413C2×C4—1521no—
414C2×C4—1521no—
415C2×C4—1521no—
416C2×C4—1521no—
417C2×C4—1521no—
418C2×C4C4×D7611yescharacteristic
419C2×C4#1059732111yescharacteristic
420C2×C4C2×(C2×D19)⋊C411yescharacteristic
421C2×C4#1059737611yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—42no—
426C8#1059726312yescomplemented
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22—3042no—
436C22—1521no—
437C22—1521no—
438C22—1521no—
439C22#1192644611yescharacteristic
440C22#1192664612yes—
441C22#1192679012yes—
442C22#1192693311yescharacteristic
443C22#1192693811yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—82no—
448C4—3041no—
449C4—3041no—
450C4—1521no—
451C4—1521no—
452C4—1521no—
453C4C2×#1059726311yescharacteristic
454C4#1192651711yescharacteristic
455C2—22no—
456C2—21no—
457C2—22no—
458C2—21no—
459C2—3041no—
460C2#1456447111yescharacteristic
461C2#1456451611yescharacteristic
462C2#1456453311yescharacteristic
subgroupG/H
centerC22#11926446
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1752C2
socleC22×C19#390
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1752D19
hypocenterC19#9786
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. #14564620C2semidirect
4. #14563664C2semidirect
5. #14562208C2semidirect
7. C19×#1752C2semidirect
8. C22×#64516C4semidirect
16. C2×#10597274C4semidirect
17. C2×#10597273C4semidirect
18. C2×#10597278C4semidirect
195. C8×C19#99semidirect
200. #1752D19semidirect
310. C19#9786semidirect
426. C8#10597263semidirect

Maximal subgroups

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

subgroupindex
C2×#119267732
#145646202
#145644712
#145636642
#145622082
#145622042
C19×#17522
#978619