Finite Group Databasebeta

← #18077522

Subgroups — #18077522

Order 4864.

558 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 95 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#14572674C211yesmaximal, characteristic
2#14566895C211yesmaximal, characteristic
3#14563735C211yesmaximal, characteristic, complemented
4#14563732C211yesmaximal, characteristic, complemented
5C4×#10597263C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic, complemented
7C19×#1297C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D19C2211yescharacteristic
9C2×#10597372C2211yescharacteristic
10#11926620—22no—
11#11926619—22no—
12#11926594—21no—
13C2×#10597263—21no—
14#11926508C2211yescharacteristic
15#11926506—21no—
16#11926484C411yescharacteristic, complemented
17#11926481C411yescharacteristic, complemented
18#11926476C411yescharacteristic, complemented
19#11926471C411yescharacteristic, complemented
20#11926469—21no—
21#11926460—21no—
22C4×C4⋊Dic19—21no—
23C4×(C2×D19)⋊C4—21no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926310—21no—
26#11926305—22no—
27#11926304—22no—
28C19×#407C2211yescharacteristic
29C4×C22⋊C4×C19C2211yescharacteristic
30C4×C22⋊C4×C19C2211yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C22×C22⋊D19D411yescharacteristic
33C22×C4×D19D411yescharacteristic
34C2×M16×C19D412yes—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19—21no—
38C2×C42×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19D411yescharacteristic
42C4×C22⋊D19—21no—
43C4×C22⋊D19—21no—
44C4×C22⋊D19—21no—
45C4×C22⋊D19—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4C2×C411yescharacteristic
49#10597372—21no—
50#10597372—21no—
51#10597372—21no—
52#10597372—21no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19C2×C411yescharacteristic
56C2×C4⋊Dic19C2×C411yescharacteristic
57C2×Dic19⋊C4C2×C411yescharacteristic
58C2×C4×Dic19—21no—
59C2×C4×Dic19—21no—
60C2×C4×Dic19D411yescharacteristic
61C2×#64520D412yes—
62C2×#64515—22no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×#95—21no—
66C19×#95C2×C411yescharacteristic
67C19×#95C2×C411yescharacteristic
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75(C2×D19)⋊C8—22no—
76Dic19⋊C8—22no—
77C8×Dic19—22no—
78#10597263—24no—
79C24×C19C2×D411yescharacteristic
80C23×D19C22⋊C411yescharacteristic
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—42no—
84C22×C4×C19—41no—
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C2×C22⋊D19—21no—
92C2×C22⋊D19—21no—
93C2×C22⋊D19—22no—
94C2×C22⋊D19—41no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—41no—
98C22×Dic19C22⋊C411yescharacteristic
99C22×Dic19C22⋊C411yescharacteristic
100C22×Dic19C22⋊C411yescharacteristic
101C2×C4×D19—21no—
102C2×C4×D19—21no—
103C2×C4×D19—42no—
104M16×C19—42no—
105C2×C8×C19—22no—
106C22⋊C4×C19—22no—
107C22⋊C4×C19—42no—
108C22⋊C4×C19—41no—
109C42×C19—42no—
110C42×C19—42no—
111C22⋊Dic19—21no—
112C22⋊Dic19—21no—
113C22⋊Dic19—22no—
114C22⋊Dic19—41no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117(C2×D19)⋊C4—21no—
118(C2×D19)⋊C4—21no—
119(C2×D19)⋊C4—42no—
120(C2×D19)⋊C4—42no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125C4⋊Dic19—42no—
126C4⋊Dic19—42no—
127Dic19⋊C4—21no—
128Dic19⋊C4—21no—
129C4×Dic19—21no—
130C4×Dic19—21no—
131C4×Dic19—41no—
132C4×Dic19—41no—
133C4×Dic19—42no—
134#64520—42no—
135C2×C19⋊C8—22no—
136#64515—82no—
137#9012—191nomaximal, Sylow
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19C2×C22⋊C411yescharacteristic
143C23×C19#12111yescharacteristic
144C23×C19#12111yescharacteristic
145C22×D19—21no—
146C22×D19—21no—
147C22×D19—21no—
148C22×D19—41no—
149C22×D19—41no—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
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—42no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—81no—
164C2×C4×C19—81no—
165C2×C4×C19C4×D411yescharacteristic
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12311yescharacteristic
169C22⋊D19—42no—
170C22⋊D19—42no—
171C2×Dic19—21no—
172C2×Dic19—21no—
173C2×Dic19—21no—
174C2×Dic19—21no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—42no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—41no—
184C2×Dic19—81no—
185C2×Dic19—81no—
186C2×Dic19#10412yes—
187C4×D19—42no—
188C4×D19—81no—
189C8×C19—42no—
190C19⋊C8—42no—
191#2975—191no—
192#2395—191no—
193#1826—191no—
194#1826—191no—
195C4×#99—191no—
196#1297—191no—
197#1297D1911yescharacteristic, complemented
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—81no—
207C22×C19—81no—
208C22×C19#38611yescharacteristic
209C22×C19C2×#10411yescharacteristic
210C22×C19#42111yescharacteristic
211C2×D19—42no—
212C2×D19—41no—
213C2×D19—41no—
214C2×D19—41no—
215C2×D19—81no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—42no—
220C4×C19—81no—
221C4×C19—82no—
222C4×C19#45812yes—
223Dic19—22no—
224Dic19—41no—
225Dic19—41no—
226Dic19—82no—
227Dic19—81no—
228Dic19—81no—
229C2×C4×D4—191no—
230C2×#117—191no—
231#436—382no—
232#436—382no—
233#431—381no—
234C2×#99—381no—
235#407—191no—
236#407—381no—
237#407C2×D1911yescharacteristic
238#400—191no—
239#399—191no—
240#398—191no—
241#397—191no—
242#397—381no—
243#394—381no—
244C4×C4⋊C4—381no—
245C4×C22⋊C4—191no—
246C4×C22⋊C4—381no—
247C4×C22⋊C4C2×D1911yescharacteristic
248C4×C22⋊C4C2×D1911yescharacteristic
249#342—381no—
250#339—382no—
251#339—382no—
252C2×C19—21no—
253C2×C19—21no—
254C2×C19—41no—
255C2×C19—41no—
256C2×C19#187111yescharacteristic
257C2×C19#188411yescharacteristic
258C2×C19#189011yescharacteristic
259D19—81no—
260C22×D4—191no—
261C23×C4—191no—
262C23×C4C22×D1911yescharacteristic
263C2×M16—192no—
264C2×M16—382no—
265C2×M16D7612yes—
266C4×D4—381no—
267C4×D4—381no—
268C4×D4—381no—
269C4×D4—381no—
270#117—381no—
271#117—381no—
272#117—381no—
273#117—381no—
274C2×C4⋊C4—191no—
275C2×C4⋊C4—191no—
276C2×C4⋊C4—191no—
277C2×C4⋊C4—381no—
278C2×C4⋊C4—381no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—191no—
282C2×C22⋊C4—191no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—381no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—191no—
290C2×C42—381no—
291C2×C42—381no—
292C4⋊C8—382no—
293#99—384no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—382no—
297C22⋊C8—381no—
298C22⋊C8—381no—
299C4×C8—382no—
300#95—21no—
301#95—381no—
302#95—381no—
303#95—381no—
304#95—381no—
305#95—381no—
306#95C4×D1911yescharacteristic
307#95C4×D1911yescharacteristic
308C19#901211yescharacteristic, complemented, Sylow
309C24—191no—
310C24D4×D1911yescharacteristic
311C2×D4—382no—
312C2×D4—381no—
313C2×D4—381no—
314C2×D4—761no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—191no—
320C22×C4—191no—
321C22×C4—191no—
322C22×C4—381no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—762no—
327C22×C4—761no—
328C22×C4C2×C4×D1911yescharacteristic
329C22×C4C2×D7611yescharacteristic
330C22×C4#6454111yescharacteristic
331C22×C4D4×D1911yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4#6454511yescharacteristic
334M16—42no—
335M16—762no—
336M16—1522no—
337C2×C8—22no—
338C2×C8—382no—
339C4⋊C4—381no—
340C4⋊C4—381no—
341C4⋊C4—381no—
342C4⋊C4—381no—
343C4⋊C4—381no—
344C4⋊C4—381no—
345C4⋊C4—762no—
346C4⋊C4—762no—
347C22⋊C4—22no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C22⋊C4—381no—
351C22⋊C4—381no—
352C22⋊C4—381no—
353C22⋊C4—381no—
354C22⋊C4—382no—
355C22⋊C4—762no—
356C22⋊C4—762no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C42—42no—
361C42—42no—
362C42—381no—
363C42—381no—
364C42—762no—
365C42—761no—
366C42—761no—
367C23—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—381no—
372C23—381no—
373C23—381no—
374C23—761no—
375C23—761no—
376C23C22⋊C4×D1911yescharacteristic
377C23#1059733011yescharacteristic
378C23#1059734111yescharacteristic
379D4—762no—
380D4—762no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—192no—
397C2×C4—381no—
398C2×C4—381no—
399C2×C4—381no—
400C2×C4—381no—
401C2×C4—762no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—762no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4—1521no—
412C2×C4—1521no—
413C2×C4—1521no—
414C2×C4C4×D7611yescharacteristic
415C2×C4#1059732811yescharacteristic
416C2×C4#1059733911yescharacteristic
417C2×C4#1059734011yescharacteristic
418C8—42no—
419C8—762no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—81no—
429C22—81no—
430C22—762no—
431C22—761no—
432C22—761no—
433C22—761no—
434C22—1521no—
435C22#1192642211yescharacteristic
436C22#104×D1911yescharacteristic
437C22#1192655911yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—81no—
443C4—82no—
444C4—382no—
445C4—761no—
446C4—761no—
447C4—1522no—
448C4—1521no—
449C4—1521no—
450C4#1192673512yes—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—1521no—
456C2#1456393611yescharacteristic
457C2#1456401711yescharacteristic
458C2#1456404711yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1297C2
socleC22×C19#386
prime radicalC22×C22⋊D19D4
cosocleC23×C4×C19C23
hypercenter#1297D19
hypocenterC19#9012
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
3. #14563735C2semidirect
4. #14563732C2semidirect
6. #14561521C2semidirect
7. C19×#1297C2semidirect
16. #11926484C4semidirect
17. #11926481C4semidirect
18. #11926476C4semidirect
19. #11926471C4semidirect
197. #1297D19semidirect
308. C19#9012semidirect

Maximal subgroups

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

subgroupindex
#145726742
#145668952
#145637352
#145637322
C4×#105972632
#145615212
C19×#12972
#901219