Finite Group Databasebeta

← #18078992

Subgroups — #18078992

Order 4864.

594 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926858C211yesmaximal, characteristic
2#14566502C211yesmaximal, characteristic, complemented
3#14564471C211yesmaximal, characteristic
4#14563722C211yesmaximal, characteristic, complemented
5#14562204C211yesmaximal, characteristic
6#14561503C211yesmaximal, characteristic, complemented
7C19×#1282C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597323—21no—
10C22×C4⋊Dic19C2211yescharacteristic
11#11926858—22no—
12#11926858—21no—
13#11926858—21no—
14C2×#10597275C412yescomplemented
15C2×#10597278C412yescomplemented
16C2×#10597263—21no—
17C2×#10597263—21no—
18#11926442—21no—
19#11926429—22no—
20#11926405—21no—
21#11926404C2211yescharacteristic
22#11926404C2211yescharacteristic
23C4×C4⋊Dic19—21no—
24#11926307—22no—
25#11926279—22no—
26C2×C19×C22⋊C8C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C4×C22⋊C4×C19C2211yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×C22⋊D19—21no—
31C23×Dic19—21no—
32C22×D76C2×C411yescharacteristic
33C22×C8×C19—21no—
34C22×C8×C19C2×C412yes—
35C2×C22⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19D411yescharacteristic
37C2×C42×C19—21no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376—21no—
43#10597376—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19C2×C411yescharacteristic
51C2×C4⋊Dic19C2×C412yes—
52C2×C4⋊Dic19D412yes—
53C2×C4⋊Dic19D411yescharacteristic
54C2×C4⋊Dic19D411yescharacteristic
55C2×Dic19⋊C4—22no—
56C2×C4×Dic19—22no—
57#10597323—42no—
58#10597323—42no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64C19⋊#95—22no—
65C19⋊#95—22no—
66C19⋊#95—21no—
67C19⋊#95D412yes—
68#10597278—22no—
69#10597278—22no—
70#10597275—22no—
71#10597275—22no—
72#10597263—42no—
73#10597263—42no—
74C24×C19C2×D411yescharacteristic
75C23×D19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—42no—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C2×C22⋊D19—41no—
86C2×C22⋊D19—41no—
87C2×C22⋊D19—41no—
88C2×C22⋊D19—41no—
89C2×C22⋊D19—41no—
90C2×C22⋊D19—41no—
91C22×Dic19—22no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—22no—
95C22×Dic19—21no—
96C22×Dic19—22no—
97C22×Dic19—41no—
98C22×Dic19—41no—
99C22×Dic19—41no—
100C22×Dic19—41no—
101C22×Dic19—41no—
102C2×D76—21no—
103C2×D76—21no—
104C2×D76—42no—
105C2×C8×C19—22no—
106C2×C8×C19—42no—
107C2×C8×C19—42no—
108C2×C8×C19—41no—
109C22⋊C4×C19—21no—
110C22⋊C4×C19—21no—
111C22⋊C4×C19—21no—
112C22⋊C4×C19D812yes—
113C42×C19—42no—
114C22⋊Dic19—41no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117C22⋊Dic19—41no—
118(C2×D19)⋊C4—41no—
119(C2×D19)⋊C4—41no—
120C4⋊Dic19—22no—
121C4⋊Dic19—22no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125C4⋊Dic19—21no—
126C4⋊Dic19—42no—
127C4⋊Dic19—42no—
128C4⋊Dic19C22⋊C412yes—
129C4⋊Dic19C22⋊C412yes—
130Dic19⋊C4—44no—
131C4×Dic19—44no—
132#9260—191nomaximal, Sylow
133C23×C19—41no—
134C23×C19—41no—
135C23×C19C4×D411yescharacteristic
136C23×C19#12011yescharacteristic
137C23×C19#12111yescharacteristic
138C23×C19C2×D811yescharacteristic
139C23×C19#13511yescharacteristic
140C23×C19AGL(1,ℤ/8)11yescharacteristic
141C23×C19AGL(1,ℤ/8)11yescharacteristic
142C22×D19—41no—
143C22×D19—41no—
144C22×D19—41no—
145C22×D19—81no—
146C22×D19—81no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—22no—
151C2×C4×C19—41no—
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×C19C2×C22⋊C411yescharacteristic
160C2×C4×C19C4×D411yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×C4×C19#12311yescharacteristic
163C22⋊D19—81no—
164C22⋊D19—81no—
165C22⋊D19—81no—
166C22⋊D19—81no—
167C2×Dic19—22no—
168C2×Dic19—22no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—42no—
183C2×Dic19—81no—
184C2×Dic19—81no—
185C2×Dic19—81no—
186D76—42no—
187D76—81no—
188C8×C19—42no—
189C8×C19—81no—
190C2×#480—191no—
191#2344—191no—
192#1964—191no—
193#1823—191no—
194#1519—191no—
195#1289—191no—
196#1282D1911yescharacteristic, complemented
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19—41no—
206C22×C19—41no—
207C22×C19#38611yescharacteristic
208C22×C19C4×D811yescharacteristic
209C22×C19#44211yescharacteristic
210C22×C19#44711yescharacteristic
211C22×C19#44911yescharacteristic
212C22×C19#45911yescharacteristic
213C22×C19#46311yescharacteristic
214C2×D19—81no—
215C2×D19—81no—
216C2×D19—81no—
217C2×D19—161no—
218C2×D19—161no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—42no—
223C4×C19—81no—
224C4×C19#41012yes—
225Dic19—42no—
226Dic19—42no—
227Dic19—82no—
228Dic19—81no—
229Dic19—161no—
230C2×#121—191no—
231C2×#117—381no—
232C22×C4⋊C4—191no—
233#480—382no—
234#480—381no—
235#480—381no—
236C2×#107—192no—
237C2×#102—192no—
238C2×#99—381no—
239C2×#99—381no—
240C2×C22⋊C8C2×D1911yescharacteristic
241C2×C22⋊C8C2×D1911yescharacteristic
242#389—381no—
243#387—382no—
244#381—381no—
245#380—191no—
246#380—191no—
247C4×C4⋊C4—381no—
248C4×C22⋊C4C2×D1911yescharacteristic
249#340—382no—
250#327—382no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—21no—
254C2×C19—21no—
255C2×C19—21no—
256C2×C19—21no—
257C2×C19#187911yescharacteristic
258C2×C19#189911yescharacteristic
259C2×C19#190511yescharacteristic
260D19—161no—
261C22×D4—191no—
262C22×D4—381no—
263C23×C4—381no—
264C23×C4C22×D1911yescharacteristic
265C22×C8—21no—
266C22×C8C4×D1912yes—
267#121—381no—
268#121—381no—
269#121—381no—
270#121—381no—
271#117—762no—
272#117—762no—
273C2×C4⋊C4—192no—
274C2×C4⋊C4—192no—
275C2×C4⋊C4—191no—
276C2×C4⋊C4—191no—
277C2×C4⋊C4—191no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4—381no—
280C2×C4⋊C4—381no—
281C2×C4⋊C4—382no—
282C2×C4⋊C4—381no—
283C2×C4⋊C4—381no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4D7611yescharacteristic
288C2×C22⋊C4D7611yescharacteristic
289C2×C42—21no—
290C2×C42—382no—
291#107—382no—
292#107—382no—
293#102—382no—
294#102—382no—
295#99—762no—
296#99—762no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301#95—21no—
302#95—192no—
303#95—382no—
304#95—382no—
305#95—381no—
306C19#926011yescharacteristic, complemented, Sylow
307C24—381no—
308C24C2×D7611yescharacteristic
309C2×D4—381no—
310C2×D4—381no—
311C2×D4—762no—
312C2×D4—761no—
313C2×D4—761no—
314C2×D4—761no—
315C2×D4—761no—
316C2×D4—761no—
317C2×D4—761no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—382no—
322C22×C4—381no—
323C22×C4—381no—
324C22×C4—382no—
325C22×C4—381no—
326C22×C4—382no—
327C22×C4—761no—
328C22×C4—761no—
329C22×C4—761no—
330C22×C4—761no—
331C22×C4—761no—
332C22×C4C2×C4×D1911yescharacteristic
333C22×C4#6454111yescharacteristic
334C22×C4D4×D1911yescharacteristic
335C22×C4D4×D1911yescharacteristic
336C22×C4D4×D1911yescharacteristic
337C22×C4#6454511yescharacteristic
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—41no—
342C4⋊C4—192no—
343C4⋊C4—192no—
344C4⋊C4—382no—
345C4⋊C4—382no—
346C4⋊C4—381no—
347C4⋊C4—381no—
348C4⋊C4—381no—
349C4⋊C4—381no—
350C4⋊C4—764no—
351C4⋊C4—762no—
352C4⋊C4—762no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—761no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C22⋊C4—761no—
361C22⋊C4—761no—
362C22⋊C4D15212yes—
363C42—42no—
364C42—764no—
365C23—41no—
366C23—41no—
367C23—761no—
368C23—761no—
369C23—761no—
370C23—1521no—
371C23—1521no—
372C23C4×D7611yescharacteristic
373C23#1059732811yescharacteristic
374C23#1059734111yescharacteristic
375C23C2×D15211yescharacteristic
376C23#1059735011yescharacteristic
377C23#1059735411yescharacteristic
378C23#1059735411yescharacteristic
379D4—762no—
380D4—1521no—
381D4—1521no—
382D4—1521no—
383D4—1521no—
384D4—1521no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—382no—
398C2×C4—382no—
399C2×C4—762no—
400C2×C4—762no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—762no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4—761no—
412C2×C4—762no—
413C2×C4—1521no—
414C2×C4—1521no—
415C2×C4—1521no—
416C2×C4C22⋊C4×D1911yescharacteristic
417C2×C4#1059733011yescharacteristic
418C2×C4#1059733911yescharacteristic
419C2×C4#1059734011yescharacteristic
420C8—42no—
421C8—81no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—3041no—
433C22—3041no—
434C22—1521no—
435C22—1521no—
436C22—1521no—
437C22#1192642211yescharacteristic
438C22C4×D15211yescharacteristic
439C22#1192665711yescharacteristic
440C22#1192668011yescharacteristic
441C22#1192669111yescharacteristic
442C22#1192674011yescharacteristic
443C22#1192676011yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—81no—
449C4—3041no—
450C4—762no—
451C4—762no—
452C4—1522no—
453C4—1521no—
454C4#1192651612yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—3041no—
462C2#1456398211yescharacteristic
463C2#1456409211yescharacteristic
464C2#1456412811yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1282C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1282D19
hypocenterC19#9260
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
2. #14566502C2semidirect
4. #14563722C2semidirect
6. #14561503C2semidirect
7. C19×#1282C2semidirect
14. C2×#10597275C4semidirect
15. C2×#10597278C4semidirect
196. #1282D19semidirect
306. C19#9260semidirect

Maximal subgroups

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

subgroupindex
C2×#119268582
#145665022
#145644712
#145637222
#145622042
#145615032
C19×#12822
#926019